question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
sequencelengths 1.02k
1.02k
|
|---|---|---|
<p>A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a
harmonic spring, so that its energy as a function of the separation between the atoms $\mathbf{r}=\mathbf{r}_1-\mathbf{r}_2$
is $$U(r) = (akTr^2)/2$$</p>
<p>Assuming that the molecule lives in one dimensions, what will be the overdamped <a href="http://en.wikipedia.org/wiki/Langevin_equation" rel="nofollow">Langevin equation</a>(s) for the motion of the molecule?</p> | 4,551 | [
-0.01747177541255951,
-0.03352348878979683,
0.01755121350288391,
-0.05510514974594116,
0.024738391861319542,
0.008962073363363743,
-0.038985464721918106,
-0.0061523569747805595,
-0.001939025823958218,
-0.05355053022503853,
0.03858999162912369,
0.04557191953063011,
0.054988961666822433,
0.04715859889984131,
0.034900862723588943,
-0.021787047386169434,
-0.003925783094018698,
-0.016224468126893044,
-0.019367292523384094,
-0.05413006618618965,
0.01733274571597576,
-0.03041945770382881,
0.028566142544150352,
-0.011484374292194843,
-0.023883609101176262,
0.03114239312708378,
0.04154116287827492,
-0.008340215310454369,
0.021762007847428322,
0.03336603567004204,
-0.01425747200846672,
-0.003027571365237236,
0.025216488167643547,
0.017027439549565315,
0.049524854868650436,
0.008761614561080933,
-0.07061462849378586,
-0.012781195342540741,
-0.01740415021777153,
0.03651656582951546,
-0.042999017983675,
-0.003994071390479803,
0.009477310813963413,
0.02978435531258583,
-0.018641110509634018,
0.0094338059425354,
0.058667659759521484,
-0.006769219413399696,
0.04518058896064758,
-0.03557527810335159,
0.04027527570724487,
-0.008850924670696259,
0.0171735268086195,
0.0052202846854925156,
-0.007188546936959028,
-0.013799063861370087,
0.047499947249889374,
0.09117832034826279,
-0.014185984618961811,
-0.057365719228982925,
-0.010360267013311386,
-0.0038775268476456404,
-0.01379138883203268,
0.01130108255892992,
-0.018494779244065285,
0.041402507573366165,
-0.012352713383734226,
-0.020008275285363197,
0.0551617257297039,
0.024954088032245636,
-0.008911612443625927,
0.005217876750975847,
0.05043228715658188,
-0.016843073070049286,
0.03416120260953903,
-0.025722157210111618,
0.010759343393146992,
0.03530331701040268,
0.02448050118982792,
0.053750015795230865,
-0.026904543861746788,
-0.00140952633228153,
0.056577637791633606,
0.045707568526268005,
-0.0031277535017579794,
-0.03720001131296158,
0.06596335023641586,
0.01059383898973465,
-0.00019418552983552217,
0.028973925858736038,
-0.0056578610092401505,
0.03547115623950958,
0.02083064243197441,
0.03151498734951019,
-0.013520347885787487,
0.03214479982852936,
0.000027660020350595005,
0.07552903145551682,
-0.011660558171570301,
-0.015796219930052757,
-0.015923412516713142,
-0.032507579773664474,
0.007438188418745995,
0.0593104362487793,
-0.013616788201034069,
-0.05359337478876114,
0.0099308080971241,
-0.033990029245615005,
-0.02829681523144245,
-0.03482339158654213,
-0.05028083175420761,
0.032397303730249405,
0.005281784571707249,
-0.027721047401428223,
0.013192540965974331,
-0.029237277805805206,
-0.009645913727581501,
-0.011100792326033115,
0.0007935903850011528,
0.051283787935972214,
0.029910525307059288,
-0.02110191062092781,
0.017884952947497368,
-0.01901964284479618,
-0.03366829454898834,
0.016355043277144432,
0.01767086796462536,
-0.011955805122852325,
-0.028480710461735725,
0.027219265699386597,
-0.008002513088285923,
0.0028835313860327005,
0.006976437289267778,
-0.017434824258089066,
0.06371654570102692,
-0.008720176294445992,
-0.11097914725542068,
-0.05319258198142052,
0.0709533765912056,
0.008361594751477242,
0.0031690599862486124,
-0.07368309050798416,
-0.005157249979674816,
0.005110958591103554,
0.06516063958406448,
0.005484662484377623,
0.004495615139603615,
0.036076921969652176,
0.02336934581398964,
-0.011408316902816296,
0.0040055387653410435,
-0.013181213289499283,
-0.008525584824383259,
-0.02791108563542366,
-0.003508201101794839,
-0.05345585569739342,
0.039103928953409195,
0.011759169399738312,
0.0020006231497973204,
-0.00020637904526665807,
0.04876330494880676,
0.006851336918771267,
-0.01432671956717968,
-0.006815215107053518,
0.003733506193384528,
-0.04902036488056183,
0.09269287437200546,
0.036267224699258804,
-0.003826936474069953,
0.012409229762852192,
0.002131206216290593,
0.013633353635668755,
-0.024118339642882347,
0.019015273079276085,
0.059819094836711884,
-0.015200585126876831,
-0.01714637503027916,
-0.02535034343600273,
0.010970449075102806,
-0.005744544323533773,
-0.05520421266555786,
-0.0231289304792881,
-0.006316614802926779,
-0.021937930956482887,
-0.014672277495265007,
0.0003815600066445768,
0.01216906774789095,
0.030016131699085236,
-0.013782409019768238,
-0.03687640652060509,
-0.002383868908509612,
-0.035408277064561844,
0.027216864749789238,
-0.02027001976966858,
-0.02503848448395729,
0.06023796647787094,
0.028694812208414078,
0.0009063708712346852,
-0.01932060904800892,
-0.024685315787792206,
-0.046019475907087326,
0.026496652513742447,
0.007239039521664381,
0.004249704070389271,
0.02137586660683155,
0.07596307247877121,
0.0448550283908844,
0.013836517930030823,
0.018403740599751472,
-0.011986417695879936,
-0.011225678957998753,
-0.01699776202440262,
-0.026562171056866646,
0.02191617526113987,
0.00417435634881258,
-0.026219546794891357,
0.015500434674322605,
-0.03670995682477951,
0.008672148920595646,
0.008316702209413052,
-0.018148602917790413,
0.0416845977306366,
0.050936561077833176,
-0.0021745439153164625,
0.007347580511122942,
0.02432713657617569,
-0.005645608529448509,
0.016811469569802284,
-0.004908768925815821,
0.013550186529755592,
-0.039941202849149704,
0.003116230247542262,
0.07037200778722763,
0.03536159172654152,
-0.027182456105947495,
-0.0053552198223769665,
0.048085033893585205,
0.0044258213602006435,
0.021509598940610886,
-0.0014598321868106723,
-0.00926875974982977,
-0.04853346571326256,
0.025104917585849762,
0.00815032608807087,
0.009774133563041687,
-0.007504861336201429,
-0.0002822401584126055,
0.01084112748503685,
0.04310324788093567,
-0.018143849447369576,
-0.019105274230241776,
0.037934646010398865,
0.010172584094107151,
0.012101114727556705,
0.023379718884825706,
-0.011970359832048416,
0.04717785865068436,
0.010487938299775124,
0.035316117107868195,
0.005053047090768814,
-0.014092790894210339,
-0.003501456929370761,
0.020434565842151642,
-0.006344649009406567,
-0.003430292708799243,
0.015177268534898758,
-0.015870152041316032,
-0.038242537528276443,
0.02897750400006771,
-0.04824244603514671,
-0.004880559630692005,
0.004735743161290884,
0.0019832674879580736,
0.023262638598680496,
0.0024087252095341682,
0.053694430738687515,
0.02024289406836033,
0.036040548235177994,
-0.02301422692835331,
-0.010983808897435665,
-0.0038690539076924324,
-0.05575312674045563,
0.004485112149268389,
0.002215588465332985,
-0.001929841353558004,
0.04385271295905113,
-0.010615725070238113,
0.007257996127009392,
0.022269967943429947,
0.0009072296088561416,
-0.005508516449481249,
-0.0023704979103058577,
0.0018669863929972053,
-0.07575055956840515,
-0.039612624794244766,
-0.027495263144373894,
0.012755496427416801,
-0.05020774155855179,
-0.010774261318147182,
0.03711042180657387,
-0.03248067572712898,
-0.004882410634309053,
0.031872835010290146,
-0.032404299825429916,
-0.03246685117483139,
-0.020081298425793648,
-0.00402587465941906,
0.02387026697397232,
0.00921238586306572,
0.04162182658910751,
0.014875402674078941,
-0.05819200351834297,
-0.04653878137469292,
-0.07111554592847824,
-0.016899310052394867,
0.02856294810771942,
-0.03132812678813934,
0.06008028984069824,
0.009153862483799458,
0.011545302346348763,
0.07382857799530029,
0.0009863286977633834,
-0.04271968454122543,
0.0018858868861570954,
-0.0217069610953331,
-0.009735523723065853,
-0.008731089532375336,
0.0385221503674984,
0.045669540762901306,
0.0028552706353366375,
0.025690000504255295,
0.03169487789273262,
0.008462770842015743,
0.0399048887193203,
-0.028175780549645424,
0.0034883562475442886,
-0.0024580885656177998,
-0.001811839989386499,
-0.00456593744456768,
0.03656291961669922,
0.006618404295295477,
-0.003692593425512314,
0.03666392341256142,
-0.02233189344406128,
0.058159008622169495,
0.06373656541109085,
-0.07995602488517761,
0.059946585446596146,
-0.006890726741403341,
0.009678083471953869,
-0.03418385609984398,
0.016122670844197273,
0.024508891627192497,
-0.02367958426475525,
-0.01131212804466486,
0.029253071174025536,
0.0667191669344902,
0.01148760225623846,
0.016952691599726677,
0.028301579877734184,
0.045544568449258804,
0.02970510721206665,
-0.028934579342603683,
0.004429871682077646,
0.02780214697122574,
0.0034743028227239847,
-0.04375278577208519,
-0.03935575485229492,
0.009285969659686089,
0.030454888939857483,
0.00021942140301689506,
0.01685212180018425,
-0.0546342097222805,
-0.01398136280477047,
-0.05534297972917557,
-0.033315688371658325,
-0.03306678682565689,
0.05076014623045921,
0.011832158081233501,
0.05117974057793617,
-0.02402408793568611,
0.015317949466407299,
0.015452463179826736,
0.020999323576688766,
-0.09768315404653549,
0.00978048238903284,
-0.014438671991229057,
-0.033715810626745224,
-0.0022084261290729046,
0.001849965425208211,
0.016344068571925163,
-0.04131067544221878,
0.004661176819354296,
0.008396580815315247,
-0.015855012461543083,
-0.05671083927154541,
-0.012346670031547546,
-0.04552715644240379,
-0.00904291495680809,
-0.005552839022129774,
0.0718652755022049,
0.05230944976210594,
-0.03916257619857788,
0.028788810595870018,
0.05707505717873573,
-0.01188941951841116,
0.006026609800755978,
-0.027196070179343224,
-0.012643818743526936,
0.014798573218286037,
0.010714128613471985,
-0.004336562938988209,
-0.00337996706366539,
0.0310075506567955,
0.0013617095537483692,
0.022856447845697403,
0.030469365417957306,
0.006415238603949547,
0.011907077394425869,
-0.013073761016130447,
-0.045895617455244064,
0.014415440149605274,
-0.010404898785054684,
0.03773723915219307,
-0.0022344498429447412,
0.006018198560923338,
-0.00636047450825572,
0.014492489397525787,
-0.01326905656605959,
0.049027252942323685,
0.04700957611203194,
0.028712129220366478,
-0.0033805640414357185,
-0.046372268348932266,
-0.020778272300958633,
0.00007536478369729593,
0.012104690074920654,
0.02607565186917782,
-0.022064920514822006,
-0.03659161552786827,
0.04603668674826622,
-0.03930192440748215,
0.06856435537338257,
0.016094215214252472,
-0.02265772596001625,
-0.050020817667245865,
0.04519139975309372,
-0.01868380792438984,
-0.040483489632606506,
-0.016682865098118782,
-0.013287578709423542,
0.063069187104702,
0.019405610859394073,
0.03473302349448204,
-0.10249265283346176,
-0.003416197607293725,
-0.0016561727970838547,
0.01704947091639042,
-0.009908383712172508,
0.015583079308271408,
-0.02243424393236637,
-0.005420546513050795,
0.05306360125541687,
-0.04663386940956116,
0.019268127158284187,
0.01889635995030403,
0.029226670041680336,
-0.04831836745142937,
-0.03583035618066788,
-0.031414423137903214,
-0.029010551050305367,
-0.005453120451420546,
0.0022985057439655066,
0.010109051130712032,
0.004551495425403118,
-0.009600779041647911,
-0.020783687010407448,
0.02017681673169136,
0.08257261663675308,
-0.005434041377156973,
-0.024592509493231773,
0.01997997611761093,
0.007046164479106665,
-0.004444725811481476,
-0.059475112706422806,
-0.005040689837187529,
0.015624363906681538,
-0.02292763441801071,
0.026756618171930313,
-0.07254200428724289,
-0.05642808973789215,
0.06386009603738785,
0.003228043904528022,
0.009540469385683537,
0.0036131718661636114,
-0.007519843056797981,
0.044243086129426956,
0.04588443040847778,
-0.0312495119869709,
0.0494336299598217,
0.03319501131772995,
-0.0005600337171927094,
0.018652787432074547,
-0.005822919309139252,
0.014184762723743916,
-0.03076193295419216,
0.016374852508306503,
-0.055908121168613434,
0.009182428941130638,
-0.04979877546429634,
0.02645736001431942,
-0.03495253995060921,
0.024474849924445152,
-0.017641769722104073,
-0.024238726124167442,
0.001715114340186119,
0.05238491669297218,
-0.017985541373491287,
-0.004877501633018255,
-0.007862097583711147,
0.020358454436063766,
-0.017765235155820847,
0.007493668235838413,
0.016365259885787964,
-0.021777138113975525,
0.01657671481370926,
0.040954042226076126,
-0.02461322769522667,
0.034577857702970505,
-0.026776250451803207,
-0.02413102239370346,
-0.003018986666575074,
-0.053846947848796844,
0.02806069515645504,
-0.007294568233191967,
0.03238103538751602,
0.01408316008746624,
-0.022286398336291313,
-0.03357730433344841,
0.04578618332743645,
-0.03297983109951019,
0.03022284433245659,
-0.004504702519625425,
-0.0001849774707807228,
0.0027324550319463015,
-0.0025545256212353706,
-0.04355840012431145,
-0.03825053200125694,
0.04404010623693466,
0.024380123242735863,
0.013173907995223999,
-0.032191984355449677,
0.01690475083887577,
-0.022037610411643982,
-0.008644243702292442,
-0.005016497801989317,
0.03808652237057686,
0.01789444126188755,
-0.0005187063943594694,
0.01841060258448124,
0.02569068968296051,
0.048742424696683884,
-0.016432488337159157,
0.002974304836243391,
0.009570237249135971,
-0.02539948560297489,
-0.017451876774430275,
0.004155327100306749,
0.06077391281723976,
-0.03236254304647446,
-0.017989935353398323,
-0.001629389706067741,
-0.021718524396419525,
0.01802356354892254,
-0.025643080472946167,
-0.008588142693042755,
0.014874950982630253,
0.013132207095623016,
-0.01163632795214653,
-0.04249459132552147,
0.0156415943056345,
-0.0081851901486516,
0.025277409702539444,
0.008295961655676365,
-0.012517261318862438,
-0.001256995485164225,
-0.06229342520236969,
-0.025621086359024048,
0.02253604307770729,
0.010616348125040531,
-0.010217086412012577,
0.0848245620727539,
-0.008703443221747875,
-0.0005857112701050937,
0.03398837149143219,
-0.027950195595622063,
0.06308245658874512,
-0.038908906280994415,
-0.010963874869048595,
-0.011230021715164185,
0.0226669330149889,
-0.007435180246829987,
-0.05978716164827347,
-0.01905978098511696,
0.005763764958828688,
0.025740299373865128,
-0.017859088256955147,
-0.005777908489108086,
-0.006223526317626238,
0.006001524161547422,
-0.018733659759163857,
-0.01681671477854252,
-0.018921460956335068,
-0.004450742155313492,
-0.00252154259942472,
0.03577108308672905,
-0.03939130902290344,
0.018606487661600113,
0.015476993285119534,
0.02205532044172287,
-0.005368441343307495,
0.022604787722229958,
0.01851646788418293,
0.0300068948417902,
0.0024455529637634754,
-0.030967142432928085,
-0.00940853450447321,
0.040345869958400726,
-0.013169290497899055,
0.06146218627691269,
-0.00263660354539752,
-0.025678392499685287,
0.04210672527551651,
0.008562887087464333,
0.03573499247431755,
-0.07260290533304214,
0.028678186237812042,
-0.04402313753962517,
0.020987296476960182,
-0.01370756234973669,
0.04301502928137779,
0.022592205554246902,
0.013352296315133572,
0.006918349303305149,
0.02827516570687294,
0.027755040675401688,
-0.0009570232941769063,
-0.05140407755970955,
0.0012048210483044386,
0.007011012639850378,
-0.08354943245649338,
0.013682985678315163,
-0.001420237822458148,
-0.06254447251558304,
0.07440796494483948,
-0.03547702357172966,
0.03460528701543808,
0.009737672284245491,
0.0333336777985096,
0.009269819594919682,
0.09636834263801575,
-0.0027541257441043854,
0.043679237365722656,
-0.03706591948866844,
0.01720781996846199,
0.09967859089374542,
0.050781264901161194,
0.050204820930957794,
-0.030805679038167,
-0.02238437905907631,
0.003623390570282936,
0.007312193047255278,
-0.05614836513996124,
0.005042853765189648,
-0.0009293371113017201,
0.005586876068264246,
0.013102691620588303,
0.06924664229154587,
-0.011732393875718117,
-0.03391846641898155,
0.02171747013926506,
-0.007803625427186489,
-0.007834543474018574,
-0.01584904082119465,
-0.034055184572935104,
-0.019421199336647987,
-0.025674380362033844,
-0.03960028290748596,
0.02222018875181675,
-0.03719542175531387,
-0.015632890164852142,
-0.05370897799730301,
-0.05966545641422272,
0.021003609523177147,
0.022881675511598587,
-0.015720536932349205,
0.007288632448762655,
-0.0159720778465271,
-0.0012825019657611847,
-0.02265581116080284,
0.03869543969631195,
0.018491238355636597,
-0.04378227889537811,
0.03959590196609497,
0.056955356150865555,
0.006509515922516584,
0.020937006920576096,
0.008766821585595608,
0.006411293055862188,
-0.028506191447377205,
-0.026805907487869263,
-0.051315709948539734,
0.02128426544368267,
-0.016650712117552757,
-0.02277672104537487,
0.0029422694351524115,
0.020447365939617157,
0.010430820286273956,
-0.02779318392276764,
-0.029938964173197746,
-0.00901183020323515,
0.05791635811328888,
-0.029680222272872925,
0.021314570680260658,
-0.023406237363815308,
0.00868901051580906,
0.029186254367232323,
0.005166690330952406,
-0.06272444128990173,
-0.030651727691292763,
0.0039094896055758,
0.023346062749624252,
0.054713793098926544,
-0.02604721114039421,
-0.015132817439734936,
-0.035487446933984756,
-0.004959718324244022,
-0.06555093824863434,
-0.001048861537128687,
0.022553149610757828,
0.014616361819207668,
0.04595792293548584,
-0.015302709303796291,
-0.0015192589489743114,
-0.06294336915016174,
-0.072215735912323,
0.03489330783486366,
-0.023086704313755035,
-0.028474515303969383,
0.010998747311532497,
-0.029712039977312088,
0.025600692257285118,
0.0009377245442010462,
-0.0166188795119524,
0.037016380578279495,
-0.01266666129231453,
0.029520371928811073,
0.033647533506155014,
-0.0003266373823862523,
0.022314559668302536,
-0.012829025276005268,
-0.021725939586758614,
0.025052903220057487,
0.007997604086995125,
0.051042817533016205,
0.008235796354711056,
-0.0031526824459433556,
0.002739040879532695,
0.031187402084469795,
-0.029294265434145927,
-0.007207239978015423,
0.033729080110788345,
-0.037398479878902435,
-0.023198094218969345,
0.015260539948940277,
0.009608033113181591,
-0.04821194335818291,
-0.02249828167259693,
-0.02149159647524357,
-0.015278599224984646,
0.006429214496165514,
0.04734070226550102,
-0.03201467916369438,
0.00002123550439137034,
-0.01712385006248951,
0.006688212044537067,
-0.014411750249564648,
0.014760271646082401,
-0.027038872241973877,
-0.002697983291000128,
0.024226143956184387,
0.019231587648391724,
0.002551858313381672,
0.03590570017695427,
-0.02010616660118103,
0.004055922385305166,
0.004642651882022619,
0.05926767736673355,
0.011314066126942635,
-0.00332399969920516,
0.010736444033682346,
-0.01635168120265007,
0.03373073786497116,
0.013546413742005825,
-0.012216095812618732,
0.033104266971349716,
-0.04837159812450409,
-0.05174747109413147,
0.022357800975441933,
-0.016741052269935608,
-0.00952241662889719,
-0.013272857293486595,
0.01854458637535572,
-0.024513760581612587,
0.035545334219932556,
-0.023078270256519318,
-0.004800167866051197,
0.006921508349478245,
-0.06545888632535934,
-0.04167710617184639,
-0.017755676060914993,
-0.014203619211912155,
-0.010078503750264645,
0.003891432425007224,
0.028348466381430626,
0.046741701662540436,
-0.014177941717207432,
0.019565248861908913,
0.013956280425190926,
-0.023008447140455246,
0.004012853838503361,
-0.016492148861289024,
0.011426654644310474,
0.0013484380906447768,
0.07233922928571701,
-0.04498574137687683,
0.025977814570069313,
0.01666881889104843,
0.00537524838000536,
-0.1081765666604042,
-0.025144442915916443,
-0.01501415390521288,
-0.04525982216000557,
-0.005471522454172373,
-0.05315177142620087,
0.01311681792140007,
0.03566490486264229,
-0.09524326026439667,
0.014105981215834618,
-0.014724984765052795,
0.012339279986917973,
-0.021278757601976395,
-0.032303936779499054,
-0.03800022974610329,
0.026176486164331436,
-0.014224124141037464,
0.04023725166916847,
-0.014762481674551964,
0.02034180611371994,
-0.0020988518372178078,
0.002088314387947321,
0.010598480701446533,
0.06033997982740402,
-0.03912157937884331,
-0.016341879963874817,
0.07528449594974518,
-0.018060894683003426,
-0.009474938735365868,
0.015547258779406548,
-0.048519548028707504,
0.035486556589603424,
-0.018147021532058716,
0.007049789186567068,
-0.024384871125221252,
0.009976954199373722,
-0.006161324679851532,
-0.028645740821957588,
-0.007733411621302366,
0.04630838707089424,
-0.018763912841677666,
0.00461855623871088,
-0.020677560940384865,
0.011197878047823906,
0.002052130876109004,
-0.04998423531651497,
-0.033743083477020264,
0.050054796040058136,
0.01769089698791504,
0.011444921605288982,
-0.01035078801214695,
-0.003958199173212051,
0.012322369031608105,
0.003657647641375661,
-0.03031223639845848,
-0.005772920325398445,
0.010579707100987434,
0.007940301671624184,
0.013967596925795078,
-0.0020187629852443933,
0.02824404463171959,
-0.023542508482933044,
-0.04205804318189621,
-0.017080260440707207,
-0.018010461702942848,
-0.0515374019742012,
-0.08948509395122528,
-0.03644760325551033,
-0.020457839593291283,
0.016112972050905228,
-0.01604137383401394,
-0.04636174440383911,
-0.009498190134763718,
0.043049708008766174,
0.02304881438612938,
0.020024949684739113,
-0.022838328033685684,
-0.05267210677266121,
-0.02719101682305336,
-0.10236120969057083,
0.028759606182575226,
-0.01158808171749115,
-0.028456244617700577,
-0.0232621468603611,
-0.01804039441049099,
0.02061491087079048,
0.0026324186474084854,
0.07729847729206085,
0.03218034654855728,
-0.016901787370443344,
0.0020566347520798445,
-0.028106356039643288,
0.013710577972233295,
-0.0403265655040741,
-0.01490139402449131,
0.0035415668971836567,
0.0050066434778273106,
-0.020514192059636116,
0.003668839344754815,
-0.015125788748264313,
0.02100214920938015,
0.03531436249613762,
-0.020557641983032227,
0.030396223068237305,
0.003961719572544098,
-0.022660329937934875,
0.036026131361722946,
-0.03113515116274357,
0.015100235119462013,
0.06787122786045074,
0.011393635533750057,
0.013940799050033092,
0.007027396932244301,
-0.05391867458820343,
-0.06288588792085648,
0.033767908811569214,
-0.027270909398794174,
-0.005376840941607952,
-0.028743697330355644,
-0.01807275228202343,
0.019135158509016037,
-0.053971193730831146,
-0.01079558115452528,
0.0246773399412632,
-0.025905007496476173,
-0.0032295554410666227,
-0.005180942825973034,
-0.003167853457853198,
0.05865613743662834,
-0.008184732869267464,
0.05662671476602554,
0.004609252326190472,
0.003744505811482668,
-0.0067572337575256824,
0.02873406745493412,
0.010783053003251553,
0.014709494076669216,
0.024463867768645287,
-0.0093569066375494,
-0.02068331651389599,
0.03029775246977806,
0.018989257514476776,
0.006035820581018925,
-0.03093656338751316,
-0.022877998650074005,
0.01714060828089714,
-0.0252308938652277,
0.026957949623465538,
0.03988420590758324,
-0.02276858501136303,
0.07618454098701477,
0.006118268705904484,
-0.0003062761388719082,
-0.024130577221512794,
-0.028638668358325958,
-0.007246080785989761,
0.013401702977716923,
0.004335123114287853,
0.019108783453702927,
-0.03754256293177605,
-0.005400051828473806,
-0.007154135964810848,
0.025842422619462013,
0.002459924668073654,
-0.007266951724886894,
0.0074674393981695175,
0.010773002170026302,
-0.017160164192318916,
-0.018633905798196793,
0.005554542411118746,
-0.0023106776643544436,
-0.015534112229943275,
0.05850699543952942,
0.05127204209566116,
-0.004842375870794058,
0.028134295716881752,
0.008405320346355438,
0.021683156490325928,
0.08237798511981964,
-0.030704345554113388,
0.0014365263050422072,
-0.001605187077075243,
0.04511900246143341,
-0.045048099011182785,
-0.006274178624153137
] |
<p>I'm having some trouble with successfully working out a rotation about the $z$-axis on the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a>.
Now, I know how this is performed, in principle.
A rotation of the Bloch-sphere around an axis $\boldsymbol n$ by an angle $\theta$ is given by
$$ R_{\boldsymbol n}(\theta)=e^{-i\theta \boldsymbol \sigma\cdot \boldsymbol n/2} $$
where $\boldsymbol \sigma$ is the vector of Pauli-matrices.</p>
<p>So for example if I start in \begin{pmatrix}
1 \\
0 \\
\end{pmatrix}</p>
<p>And I want to rotate by pi/2 around the x-axis, I simply compute the product with </p>
<p>\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{-i}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>And I end up with
\begin{pmatrix}
\frac{1}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, now I want to rotate this around the z-axis, by an angle theta. Now from what I can tell this simply corresponds to the matrix multiplication with
\begin{pmatrix}
e^{\frac{-i\theta}{2}} & 0 \\
0 & e^{\frac{i\theta}{2}} \\
\end{pmatrix}</p>
<p>so that I end up with the vector</p>
<p>\begin{pmatrix}
\frac{e^{\frac{-i\theta}{2}}}{\sqrt{2}} \\
\frac{-ie^{\frac{i\theta}{2}}}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, here things go wrong. For example, I know that if I rotate by $2\pi$, I should end up back at the same spot, but instead I end up at
\begin{pmatrix}
\frac{-1}{\sqrt{2}} \\
\frac{i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>which is not correct. Could someone point out the obvious error?</p> | 4,552 | [
0.0011045645223930478,
-0.0007368138176389039,
-0.02374294400215149,
-0.050233613699674606,
0.022493917495012283,
-0.013630329631268978,
-0.05506360903382301,
-0.03700616955757141,
-0.007893725298345089,
-0.06598349660634995,
0.04709918424487114,
0.034183770418167114,
0.08791861683130264,
0.05574698746204376,
0.030801940709352493,
0.019466524943709373,
-0.00902758352458477,
-0.027248719707131386,
-0.0003541538608260453,
-0.008528434671461582,
0.03626728430390358,
0.03858122229576111,
-0.0019967034459114075,
-0.006250547245144844,
-0.004693135153502226,
0.051177944988012314,
0.009919838979840279,
0.003365817479789257,
-0.015452477149665356,
0.0412876158952713,
-0.008949249982833862,
-0.03548432141542435,
0.0644473060965538,
0.00895621906965971,
-0.0020452486351132393,
-0.01585112325847149,
-0.017697030678391457,
-0.013363205827772617,
0.0017523705027997494,
0.021109919995069504,
-0.022944534197449684,
-0.004241356626152992,
-0.0507742241024971,
0.049498915672302246,
0.008802538737654686,
0.0049886275082826614,
-0.03362003713846207,
0.012635811232030392,
0.05246967077255249,
-0.05324530228972435,
0.08546459674835205,
0.017923252657055855,
-0.005827777087688446,
-0.005142544861882925,
0.003862170735374093,
-0.015386620536446571,
0.06808948516845703,
0.051422689110040665,
0.0059680757112801075,
-0.04423598572611809,
-0.026378868147730827,
-0.028804751113057137,
-0.017981192097067833,
-0.047974955290555954,
-0.01942220702767372,
-0.04077606648206711,
0.008424624800682068,
-0.027560018002986908,
0.047001104801893234,
-0.012783846817910671,
0.016506778076291084,
0.0022042240016162395,
0.006563008762896061,
-0.07059106230735779,
0.001791626214981079,
-0.03401259332895279,
-0.010083962231874466,
-0.0031364168971776962,
-0.0062118712812662125,
0.02624964527785778,
-0.0186332818120718,
0.027473347261548042,
0.016425155103206635,
0.010046287439763546,
0.00011329540575388819,
0.021179823204874992,
0.047472257167100906,
0.004435516893863678,
0.021413518115878105,
0.027909182012081146,
-0.0015668642008677125,
0.01181447971612215,
0.03788284957408905,
-0.026195401325821877,
0.0018029653001576662,
0.03271842747926712,
-0.017067361623048782,
0.039248816668987274,
-0.011174730025231838,
-0.04978512227535248,
0.00036365314736030996,
-0.0032989231403917074,
-0.02846512384712696,
0.060747820883989334,
-0.016483210027217865,
0.04092736914753914,
-0.013034507632255554,
-0.0010752981761470437,
-0.039856769144535065,
-0.0476071871817112,
-0.024080876260995865,
0.04628261551260948,
-0.0417470820248127,
0.02263510413467884,
-0.02154325693845749,
-0.05792738124728203,
-0.04935641959309578,
0.002793559804558754,
0.02619672566652298,
0.0707709863781929,
-0.0018594455905258656,
-0.02136004902422428,
-0.0008502917480655015,
-0.057857442647218704,
-0.0572773739695549,
0.03159891068935394,
0.028648246079683304,
-0.003922706935554743,
-0.05792713537812233,
0.0022028873208910227,
0.03110640123486519,
-0.010104119777679443,
0.023571927100419998,
0.027563180774450302,
0.04289078339934349,
-0.010554886423051357,
-0.12620460987091064,
-0.05341428890824318,
0.05764491483569145,
-0.038856104016304016,
0.013695744797587395,
-0.08601906150579453,
0.010272112675011158,
0.02914392203092575,
0.11201851069927216,
0.02987310290336609,
0.022715585306286812,
-0.002714532660320401,
0.0375828817486763,
0.027597185224294662,
-0.010721934959292412,
-0.009482435882091522,
-0.010398034006357193,
-0.03617800399661064,
0.01609063148498535,
0.024051325395703316,
0.030955813825130463,
0.011507852002978325,
-0.011825035326182842,
-0.0002400248049525544,
0.06878982484340668,
0.02010052651166916,
0.0187899898737669,
0.029076633974909782,
-0.017846278846263885,
-0.03223530948162079,
0.0672546997666359,
0.01821787655353546,
0.02167302370071411,
0.044210080057382584,
-0.04485221207141876,
0.02278919145464897,
-0.031420350074768066,
0.024806831032037735,
0.04607567563652992,
-0.02431965060532093,
0.006545445881783962,
-0.02497219480574131,
0.035437632352113724,
0.0035635889507830143,
-0.016255496069788933,
-0.03628319501876831,
-0.006015532184392214,
-0.004797342699021101,
-0.004553560167551041,
0.04722438380122185,
0.02559247985482216,
0.0041358582675457,
-0.0026452085003256798,
-0.028129369020462036,
-0.01374391932040453,
-0.02377532422542572,
0.030488358810544014,
0.018023552373051643,
-0.06294067203998566,
0.03334740921854973,
0.002213363768532872,
0.027970237657427788,
0.02942473441362381,
-0.07006032019853592,
-0.01615322194993496,
0.038045283406972885,
-0.005422176327556372,
-0.013161567971110344,
0.03141287714242935,
0.08886808902025223,
0.02721310965716839,
0.008406034670770168,
0.014022421091794968,
-0.024042123928666115,
0.0021285221446305513,
-0.027990609407424927,
-0.0030122296884655952,
0.0063955411314964294,
0.033548809587955475,
-0.013910176232457161,
0.012124775908887386,
0.003994452301412821,
-0.02955637313425541,
-0.02300470881164074,
-0.018924858421087265,
0.07437620311975479,
0.03603792190551758,
0.011132998391985893,
0.020902518182992935,
0.030605394393205643,
0.04043257236480713,
0.014483731240034103,
0.02500699833035469,
-0.0223969928920269,
-0.04375792667269707,
0.005244914907962084,
0.05247635394334793,
0.03916078060865402,
-0.07585358619689941,
-0.0050536938942968845,
0.02553395926952362,
0.04330714792013168,
0.01902586780488491,
0.025993749499320984,
-0.039184071123600006,
-0.05291581153869629,
0.002947061089798808,
-0.004173497669398785,
-0.005783646833151579,
0.019715318456292152,
0.03096693381667137,
-0.006463512312620878,
0.027091851457953453,
0.025609232485294342,
-0.06753935664892197,
0.03960553556680679,
-0.04405369237065315,
-0.02336832508444786,
0.04682029411196709,
0.005655286367982626,
0.005538472905755043,
0.027205605059862137,
-0.010014745406806469,
0.01397145539522171,
-0.004174781031906605,
0.002357097342610359,
-0.024027204141020775,
-0.023221906274557114,
0.005991104058921337,
0.0078238220885396,
-0.005145032424479723,
0.0006981492042541504,
0.029433876276016235,
-0.01598154939711094,
-0.018058093264698982,
0.00040712396730668843,
0.005908732768148184,
0.03170573338866234,
0.0015640204073861241,
0.009896541014313698,
0.030903276056051254,
-0.0030232095159590244,
0.0051575289107859135,
-0.01741352491080761,
0.0588640533387661,
-0.0007874162402004004,
0.022014174610376358,
0.04117932170629501,
-0.0408705435693264,
-0.0006710390443913639,
-0.04877226799726486,
-0.01955212838947773,
-0.00593646289780736,
0.022359048947691917,
-0.007021460682153702,
0.006589127238839865,
0.02967623993754387,
-0.05075608193874359,
0.0020194523967802525,
-0.0028491809498518705,
-0.03209424763917923,
-0.043670617043972015,
-0.017151642590761185,
0.021834051236510277,
0.009400743991136551,
-0.035615067929029465,
-0.024685952812433243,
-0.040516193956136703,
-0.04882452264428139,
-0.04746113717556,
0.01305302046239376,
0.05082930624485016,
-0.04313475266098976,
0.016596734523773193,
-0.006634019315242767,
-0.006920210085809231,
0.015494707971811295,
-0.0400884635746479,
0.010395600460469723,
-0.025574104860424995,
0.004167507402598858,
-0.018527774140238762,
0.018315814435482025,
-0.0324534997344017,
0.07378636300563812,
-0.010559058748185635,
-0.02935434877872467,
-0.021875031292438507,
-0.003975606989115477,
0.019465375691652298,
-0.07417609542608261,
-0.0036674707662314177,
0.027258332818746567,
-0.024854185059666634,
0.015992989763617516,
-0.02137528918683529,
0.014236067421734333,
0.060282014310359955,
-0.002069139154627919,
-0.017017649486660957,
0.02912052720785141,
-0.010762574151158333,
-0.014165974222123623,
0.032783471047878265,
-0.016123589128255844,
0.0305620189756155,
0.028892522677779198,
0.031878512352705,
0.00870337150990963,
0.0036860015243291855,
-0.07312293350696564,
0.016968313604593277,
-0.01667848974466324,
0.022825824096798897,
-0.005128303077071905,
0.052474841475486755,
0.00544756930321455,
-0.01216733269393444,
-0.004358779173344374,
0.028681127354502678,
0.046909675002098083,
-0.014899571426212788,
-0.004431746434420347,
0.044694919139146805,
-0.003228783840313554,
0.011285975575447083,
-0.014173945412039757,
-0.010852969251573086,
-0.03071187622845173,
0.04708012193441391,
-0.0506136491894722,
-0.03911985829472542,
0.008741147816181183,
0.0769144669175148,
-0.0014159136917442083,
-0.025838671252131462,
-0.03373781219124794,
0.0007109604775905609,
-0.009413177147507668,
0.010913033038377762,
-0.034604303538799286,
0.04175669327378273,
-0.0045873490162193775,
0.05219695344567299,
0.017660748213529587,
0.017939258366823196,
-0.009288324974477291,
-0.017643943428993225,
-0.06793897598981857,
0.015267794020473957,
-0.015929842367768288,
-0.0173876341432333,
0.013169304467737675,
-0.0005274932482279837,
0.0175001360476017,
0.005872989539057016,
-0.01563125103712082,
-0.02266729436814785,
-0.022503571584820747,
-0.030500002205371857,
0.0444391705095768,
-0.034488603472709656,
-0.014690321870148182,
-0.034009501338005066,
0.06000419333577156,
0.03959723189473152,
-0.04009906202554703,
0.010734151117503643,
0.026328260079026222,
-0.03537127375602722,
0.03654288873076439,
0.0034544835798442364,
0.02520606853067875,
0.01130007766187191,
0.012414936907589436,
0.01968834176659584,
0.00865932460874319,
0.012833231128752232,
-0.015329118818044662,
-0.03349556401371956,
0.035641107708215714,
0.02313271537423134,
-0.0193328857421875,
0.013805416412651539,
-0.034248072654008865,
0.015643255785107613,
-0.04348006471991539,
0.08972098678350449,
-0.027137422934174538,
0.044362571090459824,
0.047296397387981415,
-0.02466713637113571,
0.013052713125944138,
0.010876040905714035,
0.0394241064786911,
-0.007639346644282341,
-0.011130167171359062,
-0.029443293809890747,
-0.0412142276763916,
-0.008768807165324688,
0.0016255584778264165,
0.01587662845849991,
-0.021330973133444786,
-0.03331788256764412,
-0.011971010826528072,
0.024090450257062912,
0.005182330030947924,
-0.007799453567713499,
0.019038863480091095,
0.01341943722218275,
0.045344918966293335,
0.05192123353481293,
-0.01379062607884407,
0.0013856010045856237,
0.016800619661808014,
0.045531727373600006,
-0.008562281727790833,
0.021802375093102455,
-0.06554140895605087,
-0.006888442672789097,
0.02967297099530697,
0.03422921150922775,
0.014962044544517994,
0.0009380923002026975,
-0.04706919938325882,
-0.050786979496479034,
0.04314763844013214,
-0.042038388550281525,
0.06585556268692017,
-0.026452094316482544,
0.008753195405006409,
-0.03919503837823868,
-0.0420587919652462,
-0.06659287214279175,
-0.011048938147723675,
-0.03172304853796959,
0.02434132620692253,
-0.018095772713422775,
-0.015349110588431358,
-0.03868703916668892,
-0.0013820671010762453,
0.011336015537381172,
0.003835744922980666,
-0.003055325010791421,
0.01957130618393421,
0.022020161151885986,
0.057020820677280426,
-0.014300099574029446,
-0.0807848572731018,
-0.010286225937306881,
0.020206715911626816,
-0.011754099279642105,
0.037851639091968536,
-0.042298559099435806,
-0.047542836517095566,
0.018202610313892365,
-0.0017309269169345498,
0.008955291472375393,
0.014506153762340546,
-0.0049217939376831055,
0.011936797760426998,
0.04215305671095848,
-0.0332811065018177,
0.05685816705226898,
0.042385805398225784,
0.006097520235925913,
0.001640745555050671,
-0.06889400631189346,
0.008010095916688442,
-0.006876968778669834,
-0.005714771803468466,
-0.020106114447116852,
0.0010045923991128802,
0.005665933713316917,
0.043566543608903885,
-0.03151695430278778,
0.036167580634355545,
-0.012655554339289665,
-0.018836552277207375,
-0.01801946945488453,
0.02006705291569233,
-0.04682125523686409,
-0.002500177128240466,
-0.005202925764024258,
-0.0013051904970780015,
-0.006148858927190304,
-0.013697654940187931,
0.009855709038674831,
0.008227037265896797,
-0.004807307850569487,
0.017861368134617805,
-0.046718530356884,
0.0036485744640231133,
-0.007026671897619963,
-0.017545420676469803,
-0.037532951682806015,
-0.07739122956991196,
0.04895738512277603,
-0.022961139678955078,
-0.027201257646083832,
0.015310891903936863,
-0.05861644819378853,
-0.046837110072374344,
0.01573878899216652,
-0.002917436184361577,
-0.024181796237826347,
-0.01490514911711216,
-0.028186319395899773,
0.05678519606590271,
-0.006917907390743494,
-0.046334158629179,
-0.0292489193379879,
0.0018132374389097095,
-0.033588383346796036,
0.01125508826225996,
-0.01880219765007496,
-0.024964766576886177,
0.04022547975182533,
-0.05840921774506569,
0.011248435825109482,
0.03016265667974949,
-0.010222087614238262,
0.03215262293815613,
0.02585688605904579,
0.030674219131469727,
0.04306959733366966,
-0.0609503835439682,
-0.038473669439554214,
0.01523047685623169,
-0.014129966497421265,
-0.012577167712152004,
0.025481441989541054,
0.01680442877113819,
-0.03153245151042938,
-0.038445938378572464,
-0.0011795643949881196,
0.016087651252746582,
0.01165679469704628,
0.001497976598329842,
-0.03243926540017128,
0.015920620411634445,
0.03229038044810295,
0.051373980939388275,
-0.040710899978876114,
-0.029847245663404465,
0.015879664570093155,
0.027389859780669212,
-0.017772825434803963,
-0.0007245115120895207,
-0.018425125628709793,
-0.020305773243308067,
0.0334886871278286,
-0.01891430839896202,
0.02651764638721943,
0.013795851729810238,
0.0654999315738678,
-0.011994325555860996,
0.010097404941916466,
0.006547881755977869,
0.0188785120844841,
-0.004857836291193962,
0.025606200098991394,
0.013759808614850044,
0.03348224237561226,
-0.025862935930490494,
-0.029589638113975525,
-0.04024626314640045,
-0.05461347848176956,
0.004873054102063179,
0.07380220293998718,
0.021244600415229797,
0.05234665796160698,
0.0004384426574688405,
0.012736514210700989,
-0.035737983882427216,
-0.029862888157367706,
-0.016563642770051956,
-0.007251853588968515,
0.014707637019455433,
0.028238575905561447,
-0.04915093630552292,
-0.005501020234078169,
0.00908643752336502,
0.0449991449713707,
-0.05003293603658676,
0.009269185364246368,
0.018894298002123833,
0.014579841867089272,
-0.005151978228241205,
0.0016094706952571869,
-0.020613111555576324,
0.05273396894335747,
-0.05745930224657059,
0.05857236310839653,
-0.020344777032732964,
-0.007805742789059877,
0.027611661702394485,
0.019710397347807884,
0.03075997345149517,
-0.02270882949233055,
-0.005664833355695009,
-0.04453627020120621,
0.01158418320119381,
0.01968051865696907,
-0.035647567361593246,
-0.0011318966280668974,
-0.005114362575113773,
0.029079794883728027,
-0.0026770017575472593,
0.0029912947211414576,
-0.038829412311315536,
-0.022933630272746086,
0.01969211734831333,
-0.0465591698884964,
-0.048204563558101654,
0.07553517818450928,
0.005962589289993048,
0.018008289858698845,
0.01870826631784439,
0.0035301053430885077,
0.0329030342400074,
0.009889953769743443,
0.03202065825462341,
-0.018547553569078445,
0.058725472539663315,
-0.009847895242273808,
0.025722181424498558,
0.042063552886247635,
-0.011528288014233112,
0.12327032536268234,
0.0308199692517519,
-0.013558738864958286,
-0.053797636181116104,
0.01676691509783268,
-0.011494415812194347,
0.03437117487192154,
-0.021975407376885414,
0.006038443651050329,
-0.02352496236562729,
-0.017618047073483467,
0.009852854534983635,
0.06140068918466568,
0.015677832067012787,
-0.00986693799495697,
0.04357647895812988,
-0.001337350346148014,
-0.053473178297281265,
-0.019994068890810013,
0.020499372854828835,
-0.019062353298068047,
0.013847672380506992,
-0.012694730423390865,
0.05410529673099518,
-0.08319258689880371,
-0.01210118643939495,
-0.04301907494664192,
-0.034380849450826645,
0.010878433473408222,
-0.015197999775409698,
-0.028120193630456924,
0.02873716689646244,
-0.007098915055394173,
0.004906029440462589,
0.007739251013845205,
0.003798317164182663,
0.01666851155459881,
0.020865710452198982,
0.0205629151314497,
-0.001866542617790401,
0.007524177432060242,
0.016969705000519753,
0.008136719465255737,
-0.029452858492732048,
-0.06895380467176437,
0.011318004690110683,
-0.04938979819417,
0.06401177495718002,
-0.02227514609694481,
-0.007618976291269064,
-0.031419169157743454,
-0.004869232885539532,
0.0016893506981432438,
-0.06190550699830055,
0.0219678096473217,
-0.015088129788637161,
0.024648822844028473,
-0.022645343095064163,
0.004173001274466515,
0.017462117597460747,
0.028062352910637856,
0.040239010006189346,
0.0496249757707119,
-0.026357974857091904,
-0.023826289921998978,
-0.003201909828931093,
0.0075134593062102795,
0.0370798259973526,
-0.0209922157227993,
-0.020320400595664978,
-0.006243648007512093,
-0.0009321400430053473,
-0.03830241784453392,
-0.03893087059259415,
0.031905945390462875,
-0.0015451518120244145,
0.045112866908311844,
-0.00928174052387476,
-0.020894624292850494,
-0.01455522421747446,
-0.042068224400281906,
0.011440151371061802,
-0.015915140509605408,
-0.019846728071570396,
-0.0036351752933114767,
0.014120573177933693,
0.0463792160153389,
0.03793909028172493,
-0.06452139467000961,
-0.010902485810220242,
0.02521238476037979,
0.03076266124844551,
0.044102806597948074,
0.009498769417405128,
-0.05069815739989281,
0.010077954269945621,
-0.006664198357611895,
0.020007723942399025,
-0.025565631687641144,
-0.004784352146089077,
0.05817781016230583,
-0.004167374689131975,
-0.0032042234670370817,
0.049429211765527725,
-0.011691966094076633,
-0.020794188603758812,
0.0031716853845864534,
-0.011299218982458115,
0.0166627187281847,
0.05775751173496246,
-0.010800808668136597,
-0.04787188395857811,
0.0076628681272268295,
0.0018995815189555287,
-0.01219230517745018,
-0.0004180755349807441,
0.019677873700857162,
-0.036845579743385315,
-0.015156175941228867,
-0.03236938640475273,
-0.005286156199872494,
-0.005136733874678612,
-0.011182501912117004,
-0.027685262262821198,
0.04858686402440071,
0.0011997572146356106,
0.03126803785562515,
-0.035102397203445435,
0.03867200016975403,
0.029611213132739067,
0.00205268245190382,
0.04429435729980469,
0.04925307258963585,
-0.013340595178306103,
-0.013479961082339287,
0.024291926994919777,
-0.012075555510818958,
0.02021833509206772,
-0.0015550402458757162,
0.0014743999345228076,
0.01042598020285368,
-0.015229150652885437,
-0.03652900084853172,
0.06181009113788605,
0.008121994324028492,
0.02384217083454132,
0.036329735070466995,
-0.020221194252371788,
-0.02686215192079544,
0.025088516995310783,
-0.03884686157107353,
-0.03317506983876228,
-0.04548068717122078,
-0.014029189944267273,
-0.021464167162775993,
-0.03799775242805481,
0.022708887234330177,
-0.036845576018095016,
0.0019158963114023209,
0.05962485074996948,
0.013504757545888424,
-0.05075899139046669,
0.014360026456415653,
-0.021640710532665253,
-0.01429987233132124,
0.043071452528238297,
0.04140348359942436,
-0.007388829719275236,
0.04692519083619118,
0.030328357592225075,
-0.02361295185983181,
0.018928974866867065,
0.0020396574400365353,
-0.005411791615188122,
-0.06735356897115707,
-0.0419875867664814,
0.0036292599979788065,
0.014158184640109539,
0.08444822579622269,
-0.04676654189825058,
0.009480191394686699,
0.04540066048502922,
-0.06993789970874786,
0.015306118875741959,
-0.03201793134212494,
-0.061365820467472076,
0.020321452990174294,
-0.01244291476905346,
-0.016517844051122665,
0.004854131955653429,
0.03572883829474449,
0.034731779247522354,
0.022762460634112358,
0.0038339176680892706,
-0.03569680452346802,
-0.03970374912023544,
0.020879920572042465,
0.03601553663611412,
0.01252946350723505,
-0.026734108105301857,
0.04485255852341652,
-0.011377501301467419,
-0.001595566514879465,
0.018044816330075264,
0.010252818465232849,
0.02641921490430832,
-0.018989812582731247,
0.035396747291088104,
-0.012001285329461098,
0.051813457161188126,
-0.01257428340613842,
0.018159201368689537,
-0.02259650081396103,
-0.030154502019286156,
0.05740785598754883,
0.006615483667701483,
0.005786508321762085,
-0.00010409245442133397,
0.0252092108130455,
0.004107663407921791,
-0.0063832951709628105,
0.027592426165938377,
-0.014817830175161362,
-0.011390863917768002,
0.003083057003095746,
-0.004113055299967527,
0.0054663014598190784,
-0.049039777368307114,
0.04814572632312775,
-0.03639521822333336,
-0.004019401967525482,
0.017297497019171715,
-0.01059004571288824,
0.0007244216394610703,
-0.012003271840512753,
-0.018283607438206673,
-0.055967070162296295,
0.03228061646223068,
-0.0009282331448048353,
-0.02910119853913784,
-0.04134612902998924,
-0.022498393431305885,
0.03375498950481415,
-0.018889229744672775,
0.03444834053516388,
-0.012433163821697235,
-0.008956396020948887,
0.044659145176410675,
0.00859622098505497,
0.03239230066537857,
-0.023653173819184303,
-0.027282871305942535,
-0.020608169957995415,
-0.06737874448299408,
0.008821099996566772,
-0.0042511215433478355,
-0.014490209519863129,
-0.02213224768638611,
0.0046293484047055244,
0.012335614301264286,
0.016773076727986336,
0.048287518322467804,
0.004252653568983078,
0.02217763289809227,
0.0159414391964674,
0.023259710520505905,
0.03424125909805298,
-0.05420660227537155,
0.032166168093681335,
-0.025620153173804283,
-0.018845733255147934,
0.011107396334409714,
0.005257586482912302,
-0.04062969610095024,
0.03162301704287529,
0.0026920130476355553,
-0.004719912074506283,
0.009310307912528515,
-0.002540805609896779,
-0.05106661096215248,
0.034285880625247955,
0.005310031585395336,
-0.026195909827947617,
0.0346309095621109,
-0.00984108354896307,
0.004702935926616192,
0.0615512952208519,
-0.03393233194947243,
-0.02766985259950161,
0.0012122908374294639,
-0.008991576731204987,
-0.03954765573143959,
-0.01142677292227745,
-0.024422071874141693,
0.05743091553449631,
-0.027962425723671913,
0.0009666259866207838,
0.02417524717748165,
-0.0679350420832634,
0.008995292708277702,
0.03250499442219734,
-0.000527987431269139,
0.026999376714229584,
0.008723516948521137,
0.032866571098566055,
0.015574927441775799,
0.006538094952702522,
0.04374465346336365,
0.03641502559185028,
0.011711697094142437,
-0.013091926462948322,
0.01918327435851097,
0.03354901075363159,
-0.016988296061754227,
0.011963567696511745,
-0.0031708902679383755,
-0.002677920740097761,
-0.017136042937636375,
0.005906876642256975,
0.02929122932255268,
-0.04218931868672371,
-0.020662330090999603,
0.044150978326797485,
-0.022290149703621864,
0.08795591443777084,
-0.0317058339715004,
0.04634111747145653,
-0.01992793381214142,
0.002700258046388626,
0.004089549649506807,
0.0053497301414608955,
0.007991396822035313,
0.04132573679089546,
-0.022112883627414703,
-0.016861923038959503,
-0.018440989777445793,
-0.030685972422361374,
-0.012514470145106316,
-0.017703812569379807,
0.016624657437205315,
0.053977105766534805,
0.014679739251732826,
-0.01282606739550829,
-0.050209201872348785,
-0.038135431706905365,
-0.046559493988752365,
0.023000765591859818,
0.008458000607788563,
0.007178557105362415,
0.012032878585159779,
-0.035157717764377594,
-0.03342821076512337,
0.023190289735794067,
-0.02137637697160244,
-0.012607533484697342,
0.009260272607207298,
-0.00580628914758563,
-0.0006820429698564112,
0.04123498126864433
] |
<p>I am considering the cathode ray tube of the set up, when the cathode rays were discovered</p>
<p>Voltage = Very High<br />
Gas = any<br />
Atmospheric Pressure = We change</p>
<p>(In the following example i am just changing the atmospheric pressure everything else is kept same)</p>
<p>At <br />
1 atmospheric pressure (atm) -> Tube Does not glow<br />
0.1 atm -> The whole tube lightens<br />
0.01 atm -> The tube glows at the anode end (Glowing is shown as there is a detector coating of ZnS)</p>
<p>[Note: I don't have this set-up this is just taken by me from theory]</p>
<p>My Question: why when i am just reducing the atm from 1 to 0.01 first it is not glowing then it glows completely and after that it glow just at one end. Why so?</p>
<p>[I am asking this question here because on chemistry forum i was suggested by someone to post it here too as it was related to plasma and people over here could help me better. <a href="http://chemistry.stackexchange.com/questions/8632/cathode-ray-tube">Link</a> to my question on chemistry forum]</p> | 4,553 | [
-0.0014988378388807178,
-0.011326729319989681,
0.022920990362763405,
-0.004154447000473738,
0.033670615404844284,
-0.014433617703616619,
-0.00997783150523901,
-0.022236773744225502,
-0.019364483654499054,
-0.024238014593720436,
0.036079712212085724,
0.05773187056183815,
0.055186714977025986,
0.05492483451962471,
0.005859855562448502,
-0.0014692058321088552,
0.00960717536509037,
-0.047915857285261154,
0.0048834518529474735,
-0.029908213764429092,
-0.027833204716444016,
-0.006703411694616079,
-0.006283598951995373,
0.030818015336990356,
-0.02356712706387043,
0.03621327131986618,
0.03946138173341751,
0.02192564122378826,
0.02724020555615425,
0.014652791433036327,
-0.045069094747304916,
0.0007185836439020932,
0.011230699717998505,
-0.0275656096637249,
0.03225789591670036,
0.018219856545329094,
-0.024562444537878036,
-0.03301618993282318,
-0.02147761359810829,
0.043919455260038376,
0.034213803708553314,
0.025873247534036636,
0.009133713319897652,
0.034062910825014114,
-0.02116176299750805,
0.005308637395501137,
-0.029177311807870865,
0.04734376072883606,
0.045202743262052536,
-0.0694718062877655,
-0.0028507960960268974,
-0.019555682316422462,
0.02630164846777916,
0.05071643367409706,
0.013449565507471561,
0.004670390859246254,
0.045403216034173965,
0.040005795657634735,
0.02978816069662571,
-0.034697018563747406,
0.02889215759932995,
-0.012819867581129074,
-0.01026830729097128,
0.013670681044459343,
-0.0024783287663012743,
-0.005037811119109392,
-0.019778264686465263,
-0.033247001469135284,
0.03601672500371933,
0.007353134453296661,
0.030493857339024544,
0.013595267198979855,
-0.03516989201307297,
0.0031986157409846783,
-0.015359150245785713,
0.022959135472774506,
0.013604044914245605,
0.03422540798783302,
0.07246017456054688,
0.053911637514829636,
-0.033340226858854294,
-0.011602622456848621,
0.03753802552819252,
0.03418292477726936,
0.010019823908805847,
-0.007029494270682335,
0.11005929112434387,
-0.024092132225632668,
-0.0013741619186475873,
0.02314399741590023,
0.014139433391392231,
0.014797145500779152,
0.022430159151554108,
0.02211560495197773,
-0.004655171185731888,
0.02192354016005993,
-0.03004218451678753,
0.07393960654735565,
-0.03856346011161804,
-0.00033424835419282317,
0.01692436821758747,
0.023853331804275513,
0.0421011820435524,
0.021424390375614166,
-0.024588990956544876,
-0.030311819165945053,
-0.022247523069381714,
-0.014973676763474941,
0.018173430114984512,
-0.017058253288269043,
-0.03487369790673256,
0.017939314246177673,
-0.0004859000910073519,
0.010918655432760715,
-0.04706990718841553,
-0.030328428372740746,
0.02689814567565918,
-0.007359676528722048,
0.07010788470506668,
0.04503336921334267,
0.019823405891656876,
-0.0061845965683460236,
-0.0061064050532877445,
-0.025853438302874565,
-0.07524044811725616,
-0.011659434996545315,
-0.016350548714399338,
0.004392147064208984,
0.04005613178014755,
0.03907601907849312,
-0.011030474677681923,
-0.02816939540207386,
0.026131849735975266,
0.00035176804522052407,
0.06466047465801239,
0.01347260270267725,
-0.0712902769446373,
-0.06765887141227722,
0.019822973757982254,
0.007980582304298878,
0.006991121452301741,
-0.06419555842876434,
0.014323222450911999,
0.01846536621451378,
0.051488764584064484,
-0.0032321270555257797,
-0.030006151646375656,
-0.016439935192465782,
0.04994455724954605,
0.021862823516130447,
-0.013156229630112648,
-0.006787641439586878,
0.03010532446205616,
-0.03287235647439957,
-0.010654773563146591,
-0.056405507028102875,
0.03245547041296959,
0.023191047832369804,
0.00737563893198967,
-0.016302673146128654,
0.048263635486364365,
-0.015707973390817642,
0.0042675938457250595,
-0.022074131295084953,
0.026175018399953842,
-0.033074550330638885,
0.08081631362438202,
0.024317242205142975,
-0.003623287659138441,
0.025549598038196564,
-0.016286199912428856,
0.02328048273921013,
-0.03456118702888489,
-0.00977796409279108,
0.03961198404431343,
-0.024217408150434494,
-0.0341375395655632,
-0.046657171100378036,
0.016358161345124245,
0.020594332367181778,
-0.03700961172580719,
0.005000434350222349,
-0.020642273128032684,
0.005176701582968235,
0.04621097072958946,
0.08122386038303375,
0.002621518913656473,
-0.0023795180022716522,
0.020352544263005257,
-0.061175812035799026,
-0.0013567934511229396,
-0.02614118903875351,
0.023475835099816322,
-0.04003669321537018,
-0.019231829792261124,
-0.011547558009624481,
-0.007220746949315071,
0.01412442047148943,
-0.003510128241032362,
-0.013961907476186752,
-0.02593199536204338,
0.036080826073884964,
0.002102527068927884,
-0.006361302454024553,
0.020500553771853447,
0.0456576831638813,
0.021493539214134216,
0.004076801240444183,
0.002431335160508752,
-0.03006194904446602,
-0.0007249744958244264,
0.013832087628543377,
-0.020108047872781754,
-0.0008329404518008232,
0.018012721091508865,
0.007211746647953987,
-0.01221899501979351,
0.01813136786222458,
0.015310225076973438,
0.04104309156537056,
-0.036609236150979996,
0.08266828209161758,
0.06331241130828857,
-0.002411307767033577,
0.02500893734395504,
0.050507087260484695,
0.02665119245648384,
0.01834975555539131,
0.023057209327816963,
-0.02188405767083168,
-0.03905126452445984,
-0.003986883908510208,
0.04180997237563133,
-0.0018973862752318382,
-0.04425147548317909,
0.02433660440146923,
0.012591147795319557,
-0.01982673816382885,
0.03586265817284584,
0.02295248582959175,
-0.016676580533385277,
-0.03196524828672409,
0.007682410534471273,
0.014289936982095242,
0.009950931183993816,
-0.010708780027925968,
0.019290093332529068,
0.017787249758839607,
0.03020922653377056,
-0.012094362638890743,
0.024739408865571022,
0.015016770921647549,
-0.004350140690803528,
0.002092474838718772,
-0.010621976107358932,
0.039864297956228256,
0.05417349934577942,
-0.015712488442659378,
0.011296330951154232,
0.03284212946891785,
0.0004106664564460516,
0.03788125142455101,
-0.025668440386652946,
-0.011454136110842228,
-0.006836974993348122,
0.0088713513687253,
-0.032879188656806946,
0.0024860233534127474,
0.006719663739204407,
-0.07604439556598663,
0.023519735783338547,
-0.05479303374886513,
-0.0027412271592766047,
-0.05135786160826683,
0.024534761905670166,
0.015662813559174538,
0.02741369977593422,
0.02807963453233242,
-0.06953448057174683,
-0.0611407496035099,
-0.027197575196623802,
-0.034188855439424515,
0.007131983991712332,
0.03823568671941757,
0.0037985723465681076,
-0.02731073647737503,
-0.027343789115548134,
-0.035353753715753555,
0.05239209532737732,
-0.005029014777392149,
0.02072354406118393,
0.013536147773265839,
-0.01003599539399147,
-0.035236816853284836,
-0.019407806918025017,
-0.038038983941078186,
-0.023020338267087936,
0.0072648790664970875,
-0.021416381001472473,
0.04661273583769798,
0.02247973345220089,
-0.013805233873426914,
0.03767924755811691,
-0.038297832012176514,
-0.008347502909600735,
-0.014071203768253326,
-0.00468968553468585,
-0.006499145179986954,
-0.03730260580778122,
0.031763263046741486,
0.014475574716925621,
-0.042071349918842316,
-0.025026878342032433,
-0.023105787113308907,
-0.03988407179713249,
-0.007739814464002848,
0.040769390761852264,
0.031370870769023895,
-0.004275941755622625,
-0.016938427463173866,
0.06250698864459991,
0.009372342377901077,
-0.02755952626466751,
-0.04317496716976166,
-0.025678403675556183,
-0.020902713760733604,
-0.0528128556907177,
-0.015140258707106113,
0.04890691488981247,
-0.03577147051692009,
0.015180409885942936,
-0.02126217447221279,
0.0674009919166565,
0.051000166684389114,
0.05914561450481415,
0.01748095080256462,
-0.021161509677767754,
0.013485410250723362,
-0.003035186091437936,
0.05369648337364197,
0.010918200947344303,
0.0004091499140486121,
-0.009839488193392754,
-0.009950428269803524,
0.04020668566226959,
0.04430147260427475,
-0.06327538937330246,
0.0469675213098526,
0.021143298596143723,
0.04382745921611786,
0.005970943719148636,
-0.005598173942416906,
0.014643987640738487,
-0.008830012753605843,
-0.0036896306555718184,
0.043774206191301346,
0.025942927226424217,
-0.01565348170697689,
-0.01861082762479782,
0.04053809493780136,
0.05320844426751137,
-0.03313535451889038,
-0.06895957887172699,
0.02391648292541504,
-0.02525622956454754,
0.006418921053409576,
0.002669717650860548,
-0.012077532708644867,
0.07671114802360535,
0.008544775657355785,
0.039401210844516754,
0.007323499768972397,
-0.04072562977671623,
-0.02384185791015625,
-0.047225456684827805,
-0.0015269835712388158,
-0.01748622953891754,
0.05690942704677582,
0.009387307800352573,
0.07242775708436966,
0.04212971404194832,
0.046718813478946686,
-0.0009143069037236273,
0.019289366900920868,
-0.10317104309797287,
0.015466665849089622,
0.010782361961901188,
0.011159585788846016,
-0.030334625393152237,
0.00864165648818016,
-0.02845304273068905,
-0.01723932847380638,
0.0034760478883981705,
-0.0030255825258791447,
0.00008417932986048982,
-0.032508354634046555,
0.06134885177016258,
-0.003602155949920416,
-0.008034429512917995,
-0.08745221048593521,
0.04179495573043823,
0.032333165407180786,
0.007150583900511265,
0.01107077207416296,
-0.002326223999261856,
-0.028215298429131508,
0.011628380045294762,
-0.03477295860648155,
0.041473858058452606,
0.04237916320562363,
0.06532656401395798,
0.05165885388851166,
0.009595534764230251,
-0.00016588678408879787,
0.024201178923249245,
0.03751429542899132,
0.024410244077444077,
-0.049632325768470764,
0.004112902097404003,
-0.005812367424368858,
-0.023108800873160362,
-0.03280739486217499,
-0.02382100559771061,
0.030308963730931282,
-0.031210079789161682,
0.012268335558474064,
-0.01081920601427555,
-0.046223558485507965,
-0.019950302317738533,
0.03456583246588707,
0.039183758199214935,
-0.01819188892841339,
-0.014889699406921864,
-0.020078714936971664,
0.010798681527376175,
-0.04710203781723976,
0.004429725464433432,
0.007883778773248196,
0.037177424877882004,
-0.029338976368308067,
-0.016269361600279808,
0.02616521157324314,
0.03006187453866005,
0.001826272695325315,
-0.026120267808437347,
-0.01819593459367752,
0.01846230775117874,
-0.00928065087646246,
0.012057062238454819,
0.005818817764520645,
-0.01786254532635212,
0.021932236850261688,
-0.006372503470629454,
-0.011318511329591274,
-0.08239584416151047,
-0.034663163125514984,
0.02951299026608467,
0.07935699075460434,
-0.022102216258645058,
-0.033232223242521286,
-0.07152234017848969,
-0.025199634954333305,
0.02445009909570217,
-0.018020115792751312,
0.03806553781032562,
-0.04412474483251572,
0.026987584307789803,
-0.0025213751941919327,
-0.03389895707368851,
-0.015623891726136208,
-0.007253932300955057,
0.0001057829795172438,
0.00007398442539852113,
-0.000929790548980236,
-0.01617623306810856,
-0.015387202613055706,
-0.007301187142729759,
0.03372775390744209,
0.06597906351089478,
0.001569522195495665,
0.013596371747553349,
0.005532356910407543,
-0.007310353219509125,
-0.006053380202502012,
-0.05971703305840492,
-0.0223498847335577,
-0.01584448106586933,
0.03733993321657181,
0.018917953595519066,
-0.03141576796770096,
-0.07410359382629395,
0.039837948977947235,
0.021050598472356796,
-0.010446736589074135,
0.00045026393490843475,
-0.005237485747784376,
0.050610512495040894,
0.052671778947114944,
-0.03624366223812103,
0.049123309552669525,
0.07337319105863571,
-0.0576452873647213,
0.011825554072856903,
-0.02665168233215809,
-0.013797969557344913,
-0.009095685556530952,
-0.026977403089404106,
0.0036983881145715714,
0.036967553198337555,
-0.02526952512562275,
0.050806306302547455,
-0.014933194033801556,
0.004357498604804277,
0.009364364668726921,
-0.02132977731525898,
0.06223376840353012,
0.017166242003440857,
-0.025262730196118355,
-0.005932599771767855,
-0.01810269057750702,
0.024331556633114815,
-0.011213232763111591,
-0.02927790954709053,
0.01226708386093378,
-0.015875302255153656,
0.008121686987578869,
0.007913807407021523,
-0.024107810109853745,
0.01886444352567196,
-0.03956760838627815,
0.03121323511004448,
0.017464177682995796,
-0.05055614188313484,
0.058582644909620285,
-0.006246079690754414,
0.008263679221272469,
-0.000025693954739836045,
-0.02815869264304638,
-0.03968432545661926,
0.00395042821764946,
-0.01918848045170307,
0.02187398634850979,
-0.05002454295754433,
0.08000835031270981,
-0.02769658900797367,
0.0011632057139649987,
-0.06134030222892761,
-0.028814489021897316,
0.03209347650408745,
0.037733934819698334,
-0.04777118191123009,
0.018150338903069496,
-0.007091464474797249,
-0.022295787930488586,
-0.006755354814231396,
-0.0013995141489431262,
-0.0037928002420812845,
-0.04793084040284157,
-0.04042743518948555,
0.055385295301675797,
0.011997108347713947,
0.022685673087835312,
0.021757947281003,
-0.03952572122216225,
-0.0258674044162035,
-0.026311829686164856,
-0.011080569587647915,
-0.004308628384023905,
0.01743476092815399,
0.00597534142434597,
-0.05995812639594078,
0.0014611795777454972,
0.0004963328246958554,
0.013306984677910805,
-0.03818681091070175,
0.0013968918938189745,
0.03755876049399376,
-0.00015508530486840755,
0.025211213156580925,
-0.0027585821226239204,
0.03971080482006073,
-0.032457660883665085,
0.020399006083607674,
0.027226217091083527,
0.03645056486129761,
-0.05817228555679321,
-0.039638619869947433,
-0.0379461906850338,
-0.01689162291586399,
0.007573604583740234,
-0.012307736091315746,
0.05273115634918213,
0.007159084547311068,
-0.01354664284735918,
0.029015405103564262,
-0.044108014553785324,
-0.009877089411020279,
0.008487096056342125,
-0.0032185225281864405,
0.056016791611909866,
0.01280023343861103,
-0.0017928960733115673,
-0.03666047379374504,
-0.028157072141766548,
-0.016467547044157982,
0.04860411211848259,
-0.0039068046025931835,
0.04582485929131508,
-0.039017945528030396,
0.010676524601876736,
0.00791847798973322,
-0.01694825291633606,
-0.002872475888580084,
-0.015032107941806316,
0.009003040380775928,
0.014878214336931705,
-0.010967990383505821,
0.018184656277298927,
0.0083883386105299,
0.036528054624795914,
0.033662404865026474,
0.0157882459461689,
0.046518828719854355,
-0.004535522777587175,
0.06089876964688301,
-0.023457584902644157,
-0.013844289816915989,
0.05493989214301109,
-0.016549909487366676,
0.02103903517127037,
0.022122856229543686,
-0.0017726244404911995,
0.027543796226382256,
-0.04182485118508339,
0.013767857104539871,
-0.08815605938434601,
-0.012527992017567158,
-0.04325752332806587,
0.00974440947175026,
-0.010428234934806824,
-0.018030444160103798,
0.014094752259552479,
0.019668882712721825,
0.011666018515825272,
-0.006313769146800041,
0.036792486906051636,
-0.04287920147180557,
-0.014185357838869095,
-0.01286996342241764,
-0.018097322434186935,
-0.060150645673274994,
0.03695405274629593,
-0.020104078575968742,
-0.046893078833818436,
-0.0042252629064023495,
-0.06046095862984657,
0.042325813323259354,
0.00846147257834673,
0.025016119703650475,
0.016911711543798447,
0.06694475561380386,
-0.014247409068048,
0.047241877764463425,
0.03680320084095001,
0.033059198409318924,
0.11640677601099014,
0.01447569951415062,
0.017450524494051933,
-0.05859895795583725,
0.002178153023123741,
-0.012087032198905945,
0.04831303283572197,
-0.000034703934943536296,
0.016123555600643158,
-0.05198908597230911,
-0.0023919222876429558,
0.017050771042704582,
0.03354889899492264,
0.00015993710258044302,
0.052919305860996246,
0.016317207366228104,
-0.05071549490094185,
-0.013503397814929485,
-0.00897916592657566,
0.017437707632780075,
-0.02685830555856228,
0.029213909059762955,
-0.029303375631570816,
0.02916584350168705,
-0.06659162789583206,
0.000014812635527050588,
-0.023689402267336845,
-0.02444160170853138,
0.02062082104384899,
-0.02266174927353859,
-0.041017480194568634,
0.01297713816165924,
-0.002897791098803282,
-0.014765724539756775,
-0.05959940329194069,
0.01356362085789442,
0.055509041994810104,
0.00015285758126992732,
0.00011727213131962344,
0.019329188391566277,
0.00588533841073513,
-0.001740367617458105,
0.00196053646504879,
0.010946261696517467,
-0.05544454604387283,
-0.021300261840224266,
0.002366527682170272,
0.036753568798303604,
-0.029266146942973137,
-0.006262697745114565,
-0.010845139622688293,
-0.006915530189871788,
0.017233742401003838,
-0.05005728080868721,
-0.0543263740837574,
-0.0038910345174372196,
0.026342129334807396,
-0.010580543428659439,
-0.04600371792912483,
-0.020566552877426147,
0.01857331208884716,
-0.015835624188184738,
0.03231150284409523,
0.008835995569825172,
0.008619307540357113,
-0.014435597695410252,
-0.016142049804329872,
0.03828994184732437,
-0.0016389694064855576,
-0.01126293558627367,
-0.007350211497396231,
0.013951531611382961,
-0.03109857253730297,
-0.039045240730047226,
-0.0073002539575099945,
0.0122414855286479,
0.04143993556499481,
0.004364411346614361,
0.002879647770896554,
-0.016132168471813202,
-0.08153718709945679,
0.03863435238599777,
0.013554860837757587,
0.006078755017369986,
-0.031125538051128387,
0.0031006832141429186,
0.0007499654311686754,
0.03931901231408119,
-0.03462817519903183,
-0.018651718273758888,
0.04095984250307083,
0.04481198266148567,
0.015920013189315796,
-0.07245688140392303,
-0.03373262286186218,
0.029127582907676697,
-0.034239135682582855,
0.014853563159704208,
-0.022703837603330612,
0.06668519228696823,
-0.005257909186184406,
-0.0051781185902655125,
0.01298060268163681,
0.007040716707706451,
-0.04177049547433853,
-0.0063668242655694485,
-0.013445070944726467,
-0.020990651100873947,
0.04138842225074768,
-0.003888743929564953,
-0.011041545309126377,
-0.01923094131052494,
-0.014711168594658375,
-0.02001367136836052,
-0.014276683330535889,
-0.015847234055399895,
-0.003604424186050892,
0.03726983442902565,
0.03753029182553291,
-0.03249018266797066,
-0.019293630495667458,
-0.011123680509626865,
-0.008706673048436642,
-0.028654133901000023,
-0.00878967810422182,
-0.01834867149591446,
-0.0027353730984032154,
-0.02402520179748535,
0.05680377408862114,
-0.017728574573993683,
-0.030188975855708122,
-0.0019441423937678337,
0.054011549800634384,
-0.01637652888894081,
-0.0014236865099519491,
-0.018945882096886635,
0.011655266396701336,
0.030244914814829826,
-0.024711571633815765,
-0.023502172902226448,
0.031183922663331032,
-0.03356272354722023,
-0.02925656922161579,
0.0438147597014904,
-0.007680670358240604,
0.019253874197602272,
0.01590185984969139,
-0.024123137816786766,
0.007043395657092333,
0.07847572863101959,
0.00797673873603344,
0.0036973573733121157,
-0.006389945279806852,
-0.06294327974319458,
0.04024316370487213,
0.021906577050685883,
-0.027095025405287743,
-0.0064445482566952705,
-0.0022716086823493242,
0.019313804805278778,
0.024217605590820312,
-0.013008070178329945,
0.013574774377048016,
-0.02553817816078663,
0.004777512978762388,
0.0203572865575552,
0.03662298247218132,
0.005834660027176142,
0.018191896378993988,
0.045071180909872055,
-0.04096917062997818,
0.0253567174077034,
-0.019831553101539612,
0.003803097642958164,
-0.0795120894908905,
-0.008684925734996796,
-0.018967697396874428,
0.00008940538828028366,
0.007992775179445744,
-0.026510929688811302,
0.014013871550559998,
0.01077936589717865,
-0.07902944833040237,
-0.024104567244648933,
0.0066171614453196526,
-0.024887003004550934,
-0.06255630403757095,
-0.01046767272055149,
-0.012690216302871704,
0.023125415667891502,
0.027181480079889297,
0.03623005747795105,
0.05323801934719086,
0.027909018099308014,
-0.009951779618859291,
-0.021665364503860474,
-0.006041090935468674,
0.03630856052041054,
-0.012985585257411003,
-0.00006248864519875497,
0.0600375235080719,
-0.04844176396727562,
0.00900452584028244,
0.021266547963023186,
-0.01024248730391264,
-0.006687814369797707,
-0.01887512393295765,
0.009516077116131783,
-0.0006944838096387684,
0.045319341123104095,
0.007370199542492628,
-0.0054296646267175674,
-0.0045584458857774734,
0.0072222501039505005,
0.0330495610833168,
-0.024708837270736694,
0.012030337005853653,
0.025185704231262207,
0.0241517536342144,
-0.01655009761452675,
-0.035039022564888,
0.006452813744544983,
0.011472033336758614,
-0.0024586848448961973,
-0.00872005894780159,
0.04655710235238075,
0.01148789282888174,
-0.0659605860710144,
-0.018883896991610527,
-0.043722964823246,
0.01926610991358757,
0.025501996278762817,
0.004793781787157059,
-0.007648187689483166,
-0.004467738792300224,
-0.03898138925433159,
-0.033538591116666794,
0.03717701509594917,
-0.0250373724848032,
-0.037397123873233795,
-0.0008433841867372394,
-0.02636195346713066,
-0.014301326125860214,
0.04633735492825508,
0.025741660967469215,
-0.04398591071367264,
-0.03306389972567558,
0.015269878320395947,
0.0070537906140089035,
0.04677138850092888,
-0.0008219284354709089,
-0.0569038949906826,
-0.025475358590483665,
-0.07596811652183533,
0.03482048213481903,
-0.009515552781522274,
-0.01795649155974388,
-0.057233620434999466,
-0.05296539515256882,
-0.04036426171660423,
0.04082342982292175,
0.07667583227157593,
-0.0070119621232151985,
-0.045992411673069,
-0.018307272344827652,
0.017888914793729782,
0.008683753199875355,
-0.0179654061794281,
0.008759536780416965,
0.0183118786662817,
-0.04475351423025131,
0.01923327147960663,
-0.0035301949828863144,
-0.028792589902877808,
0.03006441332399845,
0.03412993624806404,
-0.016304446384310722,
-0.021075615659356117,
-0.004815834108740091,
-0.010725941509008408,
0.013938331976532936,
0.006608275696635246,
-0.05716560408473015,
0.0861668586730957,
0.024513021111488342,
-0.019992433488368988,
0.0208032988011837,
0.006649994757026434,
-0.03503439947962761,
0.008640323765575886,
-0.0014729558024555445,
0.008857733570039272,
-0.028748521581292152,
-0.0458492785692215,
0.018007973209023476,
-0.0642990693449974,
-0.003793867537751794,
0.01678166165947914,
-0.04047060385346413,
-0.006104840897023678,
0.055577412247657776,
0.012994331307709217,
0.03466121479868889,
-0.010698945261538029,
0.007528018672019243,
-0.028914490714669228,
0.01909307949244976,
0.0003635701141320169,
0.05363840237259865,
0.010679482482373714,
0.0031802321318536997,
0.04015054926276207,
0.020251072943210602,
0.0411861352622509,
0.0034394757822155952,
0.011162110604345798,
0.020829271525144577,
-0.021537456661462784,
0.013797862455248833,
0.015501093119382858,
-0.019458986818790436,
-0.030330143868923187,
0.05340059846639633,
-0.014340979978442192,
0.06604619324207306,
-0.0325033999979496,
-0.0024949137587100267,
-0.0109643479809165,
0.02645247057080269,
0.010685655288398266,
0.03829076886177063,
0.0210610069334507,
0.022950781509280205,
-0.03468748554587364,
-0.014882064424455166,
0.0003326888254377991,
0.005109554622322321,
0.020782534033060074,
-0.027202259749174118,
0.02529514580965042,
-0.053379204124212265,
-0.028255809098482132,
-0.013890975154936314,
0.005268915556371212,
0.015352095477283001,
0.003135712118819356,
0.009837482124567032,
0.026711849495768547,
-0.0075669498182833195,
0.0024622268974781036,
0.0037036933936178684,
-0.030542973428964615,
0.02559801936149597,
-0.07295692712068558,
-0.03166418522596359,
-0.00463537173345685,
-0.0023547199089080095,
-0.013519753701984882,
-0.04416925087571144
] |
<p>On pp 103 - 105 of <em>The Character of Physical Law</em>, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum:</p>
<p><img src="http://i.stack.imgur.com/BrYgE.jpg" alt="enter image description here"></p>
<p>To paraphrase Feynman's argument (if I understand it correctly), a particle's trajectory is the path AB. Space is horizontal; time vertical. </p>
<p>Because of spatial translation symmetry, the path CD has the same action as AB. Because AB has stationary action, ACDB has the same action as well.</p>
<p>That means the action of AC and BD are the same. (Note that they are traversed in opposite directions on the path ACDB.) This is a conserved quantity, and it turns out to be the momentum.</p>
<p>My question is about the meaning of the action of AC and BD. These paths aren't physical trajectories; they represent infinite velocity. I tried thinking of the trajectory as if the velocity, as a function of time, has two delta functions in it. However, because the Lagrangian depends on $v^2$, I think this leads to infinite action for the horizontal segments.</p>
<p>Mathematically, I see that the symmetry here implies $\frac{\partial L}{\partial x} = 0$. Least action implies $\frac{\partial L}{\partial x} = \frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial \dot{x}}$. Combining these shows that the momentum $\frac{\partial L}{\partial \dot{x}}$ is constant, but I don't quite understand the connection to the picture.</p>
<p>Also, Feynman doesn't describe how he knows the conserved quantity is the momentum. Is there a way to get this from the picture? Finally, if momentum is being conserved, why isn't the trajectory a straight line?</p> | 4,554 | [
-0.012456719763576984,
-0.011880879290401936,
-0.015685370191931725,
0.014879806898534298,
0.02618151530623436,
-0.013755212537944317,
-0.032546401023864746,
0.009239579550921917,
-0.0016418640734627843,
-0.03490003943443298,
0.016586724668741226,
0.007344522513449192,
0.04794960096478462,
0.04770270362496376,
0.033430714160203934,
0.017474211752414703,
-0.009444870054721832,
-0.00691575463861227,
0.001389188109897077,
-0.036941904574632645,
-0.0010301839793100953,
-0.0015002316795289516,
0.004103182349354029,
0.004910529125481844,
-0.030078653246164322,
0.014127491042017937,
-0.006717727053910494,
0.00795286800712347,
-0.006609136238694191,
0.0596429742872715,
-0.019823968410491943,
0.005086563527584076,
-0.007204949855804443,
0.025193070992827415,
0.009255241602659225,
0.006655300501734018,
-0.013816334307193756,
-0.057261381298303604,
-0.000626038818154484,
0.016628840938210487,
-0.0307371374219656,
-0.0034656673669815063,
-0.04666496813297272,
0.08492311090230942,
-0.026160623878240585,
0.03098144754767418,
-0.008429354056715965,
0.03406216576695442,
0.10172421485185623,
-0.043128643184900284,
0.07935507595539093,
0.012836122885346413,
0.033287908881902695,
-0.004140940494835377,
-0.006458786781877279,
-0.05266295745968819,
0.047912709414958954,
0.04801197722554207,
0.024612070992588997,
-0.04759302735328674,
-0.028232160955667496,
-0.026655033230781555,
-0.00021765154087916017,
0.005947299767285585,
-0.006602714769542217,
-0.01531318947672844,
0.02815311588346958,
-0.016449080780148506,
-0.010990243405103683,
0.004220337141305208,
0.017050664871931076,
0.008112823590636253,
0.03517964482307434,
-0.01083565503358841,
-0.005338872317224741,
0.020541997626423836,
0.052311912178993225,
0.017813296988606453,
-0.0017443165415897965,
0.020017536357045174,
-0.006307330913841724,
0.018678583204746246,
0.014655699022114277,
0.03040221519768238,
0.002509241458028555,
0.005303420592099428,
0.06718359887599945,
0.013997628353536129,
0.003831206588074565,
0.02198474481701851,
0.029598215594887733,
0.014091444201767445,
0.02463499642908573,
0.0032965801656246185,
-0.034202151000499725,
0.04725365340709686,
0.0010383358458057046,
0.038742076605558395,
-0.0062596783973276615,
-0.007634979207068682,
-0.00515776639804244,
-0.01161268912255764,
0.0006255775224417448,
0.02220376394689083,
0.007465388625860214,
-0.0229233056306839,
-0.008999135345220566,
0.03684122487902641,
-0.016722189262509346,
-0.009768063202500343,
-0.08365640789270401,
0.012104376219213009,
-0.01577429100871086,
0.026223650202155113,
0.013495825231075287,
-0.03158077597618103,
0.008458958007395267,
-0.007625104393810034,
0.04278602823615074,
0.06292631477117538,
0.0274933110922575,
-0.043504539877176285,
0.03960629925131798,
-0.017891814932227135,
-0.08346854895353317,
0.0015590982511639595,
0.022762449458241463,
0.02399434521794319,
-0.02951977029442787,
0.031561896204948425,
0.019594181329011917,
0.03258997201919556,
-0.009202348068356514,
0.019079478457570076,
0.04161776974797249,
-0.028246017172932625,
-0.08638442307710648,
-0.042071763426065445,
0.03803030028939247,
0.044257067143917084,
-0.01577887125313282,
-0.0847463384270668,
-0.0126577727496624,
0.03038514405488968,
0.05585633963346481,
-0.05494200438261032,
0.02984142303466797,
-0.037453070282936096,
0.0316917784512043,
-0.008181186392903328,
-0.03616359457373619,
0.000013741400834987871,
0.008213349618017673,
-0.05051938444375992,
-0.014314492233097553,
-0.03656114637851715,
0.008082970976829529,
0.03796859458088875,
0.014854677021503448,
-0.02206261083483696,
0.09485365450382233,
-0.061557233333587646,
-0.0062234606593847275,
0.0026554313953965902,
0.0005915046203881502,
-0.007845072075724602,
0.04746858775615692,
0.02844356559216976,
-0.0032006045803427696,
0.005762925371527672,
0.024924274533987045,
0.041683994233608246,
-0.02492612600326538,
-0.009956534020602703,
0.0801214724779129,
-0.02243233658373356,
-0.03306032344698906,
0.002946177264675498,
-0.03807009384036064,
0.0015014053788036108,
-0.049003951251506805,
-0.04567474126815796,
-0.0429094098508358,
0.00635015033185482,
-0.016533901914954185,
0.04024958238005638,
-0.009860794991254807,
0.0044812834821641445,
-0.007238294929265976,
-0.07247224450111389,
-0.03739522024989128,
-0.08046001940965652,
0.017742276191711426,
-0.0029669939540326595,
-0.03029516711831093,
0.05899340659379959,
0.002342016203328967,
0.030896486714482307,
-0.03773382306098938,
-0.048639148473739624,
-0.008556955493986607,
0.030617721378803253,
0.016351258382201195,
0.0019079173216596246,
-0.010012364946305752,
0.0347229540348053,
0.035370588302612305,
0.011833533644676208,
0.004100890830159187,
-0.022595437243580818,
-0.011169282719492912,
0.014700224623084068,
-0.005130082368850708,
0.03241831436753273,
0.012962184846401215,
0.0006365794688463211,
0.0020910073071718216,
0.003212442621588707,
-0.006810361985117197,
0.045835915952920914,
-0.0344008170068264,
0.06628527492284775,
0.07352465391159058,
-0.04269109666347504,
-0.024527983739972115,
0.06237540766596794,
0.001254386967048049,
0.011944394558668137,
-0.001572617213241756,
-0.026813911274075508,
-0.014259863644838333,
-0.01378265954554081,
-0.021867183968424797,
0.011060807853937149,
-0.00990916695445776,
0.022382136434316635,
0.00999314896762371,
0.035960886627435684,
0.024608977138996124,
-0.00006445329927373677,
0.008240874856710434,
-0.03210178762674332,
0.015173563733696938,
-0.0055558159947395325,
0.011550365947186947,
-0.0006349364412017167,
0.013619553297758102,
-0.0026887415442615747,
0.02410547249019146,
0.013634479604661465,
-0.032279692590236664,
0.04920750483870506,
-0.008909737691283226,
0.007246839813888073,
0.015127082355320454,
-0.015117372386157513,
0.06125729903578758,
-0.014163208194077015,
0.036070484668016434,
0.04138486087322235,
-0.020051082596182823,
0.0025274569634348154,
-0.03857346251606941,
-0.033492036163806915,
-0.0135681526735425,
0.007153468206524849,
0.008619744330644608,
-0.021244294941425323,
0.02069774456322193,
-0.027556532993912697,
0.02657034993171692,
-0.02806883491575718,
-0.018224013969302177,
-0.003483742708340287,
-0.003493496449664235,
0.04294683411717415,
0.028435299172997475,
0.01974271982908249,
-0.02322460152208805,
-0.03780059143900871,
-0.0015188658144325018,
-0.0031541555654257536,
-0.007229374255985022,
0.03185293823480606,
-0.029210349544882774,
0.011158335022628307,
-0.05050665885210037,
-0.017653847113251686,
0.028938813135027885,
0.023102708160877228,
0.049057889729738235,
0.00981358252465725,
-0.02830173633992672,
-0.08902081102132797,
-0.009831777773797512,
-0.03426682949066162,
0.020228516310453415,
-0.026572687551379204,
-0.00158027617726475,
0.05841664597392082,
0.003935554530471563,
-0.01594206690788269,
0.01245114766061306,
-0.026539675891399384,
-0.052365485578775406,
-0.026873957365751266,
0.01675805263221264,
-0.008159358985722065,
-0.019416624680161476,
0.007322140969336033,
0.028662478551268578,
-0.008597036823630333,
-0.012950535863637924,
-0.0484570674598217,
-0.015840353444218636,
0.011436772532761097,
0.015400941483676434,
-0.007325359154492617,
-0.02868005447089672,
-0.037051666527986526,
0.08328453451395035,
0.08132276684045792,
-0.012459066696465015,
-0.02303689531981945,
-0.023868883028626442,
0.012559139169752598,
-0.03448190167546272,
-0.016833236441016197,
0.02617650106549263,
0.005076185800135136,
0.03894496336579323,
0.03266849368810654,
0.0502738431096077,
-0.014723855070769787,
-0.032538045197725296,
-0.0019817806314677,
0.011315125972032547,
0.006238133646547794,
0.012510961852967739,
0.024757318198680878,
0.011020323261618614,
-0.007806109730154276,
-0.002662840997800231,
-0.002166908234357834,
0.04141570255160332,
0.004778759088367224,
-0.061405524611473083,
0.05129840970039368,
0.015028503723442554,
-0.011202630586922169,
-0.027057664468884468,
0.017732009291648865,
-0.01254335604608059,
-0.0362749844789505,
0.004776379093527794,
0.0060835937038064,
0.024929789826273918,
-0.021191852167248726,
-0.009254354052245617,
0.017285164445638657,
0.044327471405267715,
-0.010760916396975517,
-0.04653429239988327,
0.006853763479739428,
0.03406107798218727,
0.027979103848338127,
0.0036101615987718105,
-0.038516443222761154,
0.02805197238922119,
0.020812200382351875,
-0.0017298292368650436,
0.020231829956173897,
-0.06268777698278427,
-0.018012462183833122,
-0.04437242075800896,
0.03583582490682602,
0.021199600771069527,
0.01978822983801365,
-0.012056284584105015,
0.0530993677675724,
0.01140216551721096,
0.002903480315580964,
-0.015346424654126167,
0.007610578555613756,
-0.11428968608379364,
0.02871951274573803,
-0.001556574017740786,
-0.00967536959797144,
0.002445848658680916,
-0.012933911755681038,
0.02186810038983822,
-0.03271796554327011,
-0.007953302003443241,
0.00781509280204773,
-0.0010243937140330672,
-0.044639963656663895,
-0.011770771816372871,
-0.06845998764038086,
-0.04639069736003876,
-0.02065291441977024,
0.02356472797691822,
0.05602559819817543,
-0.05848557502031326,
0.0022707893513143063,
0.06364640593528748,
-0.01547424215823412,
-0.004628768190741539,
-0.008504204452037811,
-0.008744936436414719,
0.040297895669937134,
-0.010853463783860207,
0.01257231179624796,
0.0005885402788408101,
0.032639436423778534,
0.018787557259202003,
0.039428867399692535,
0.047832928597927094,
-0.011252577416598797,
-0.00100784155074507,
-0.025093233212828636,
-0.03348339721560478,
-0.008538558147847652,
0.0027032445650547743,
0.02443922869861126,
0.05149400606751442,
0.008841617964208126,
0.0725235790014267,
0.04696135222911835,
0.002531707054004073,
0.06841674447059631,
0.03402717411518097,
0.037692759186029434,
-0.01020616851747036,
-0.04751146212220192,
0.02360685169696808,
-0.027879245579242706,
-0.012267225421965122,
0.03360217809677124,
-0.012366616167128086,
-0.015632737427949905,
-0.009602849371731281,
0.0063574044033885,
0.020772438496351242,
-0.022826537489891052,
-0.017813589423894882,
-0.03824245557188988,
0.018833419308066368,
0.00007763820030959323,
0.014443231746554375,
0.026877902448177338,
0.02414535917341709,
0.03356347978115082,
0.013863543048501015,
0.005265290383249521,
-0.06789810955524445,
-0.025045666843652725,
0.01866661012172699,
0.03200743347406387,
0.01189578790217638,
0.0075705284252762794,
-0.038217101246118546,
-0.03689449653029442,
0.034809596836566925,
-0.03598364442586899,
0.021833742037415504,
-0.02406766079366207,
-0.010118628852069378,
-0.019720666110515594,
-0.046460967510938644,
-0.020054686814546585,
-0.000016773796232882887,
-0.013395092450082302,
-0.006588729098439217,
-0.02793065644800663,
-0.014194880612194538,
-0.012495720759034157,
0.019083097577095032,
-0.02497377060353756,
0.011365693062543869,
0.01104935072362423,
0.017700785771012306,
-0.009413708001375198,
0.024984797462821007,
-0.032618600875139236,
-0.10131675750017166,
-0.027684880420565605,
0.03205939382314682,
0.02247472293674946,
0.06087407469749451,
-0.022060571238398552,
-0.05991009250283241,
0.05928158015012741,
-0.008960873819887638,
-0.02355131134390831,
0.0010040587512776256,
-0.03320275992155075,
0.015096109360456467,
0.030235476791858673,
-0.03561841696500778,
0.04072928801178932,
-0.002241259440779686,
-0.006606138311326504,
-0.03851928561925888,
0.025441788136959076,
0.07348286360502243,
-0.0011035053757950664,
0.018509309738874435,
-0.09985034167766571,
0.024711422622203827,
-0.04098908603191376,
0.03471216931939125,
-0.001237206277437508,
-0.01378864236176014,
-0.007279824931174517,
0.0015413322253152728,
-0.004845678340643644,
0.02463635802268982,
0.04259520769119263,
-0.014710663817822933,
-0.02362266555428505,
0.03018597885966301,
-0.009443031623959541,
-0.027657991275191307,
-0.001833981485106051,
-0.0006223020609468222,
-0.006852482445538044,
0.016389163210988045,
0.016933685168623924,
0.028994839638471603,
-0.008159313350915909,
-0.043187350034713745,
-0.002944147912785411,
-0.047549739480018616,
-0.005957243964076042,
0.01574145257472992,
-0.017279861494898796,
0.021705714985728264,
-0.042877811938524246,
-0.05158037692308426,
-0.005828028079122305,
-0.01640327461063862,
-0.009581634774804115,
-0.05532576143741608,
0.022398561239242554,
0.003817368997260928,
-0.004894341807812452,
-0.07412990927696228,
-0.05973147600889206,
-0.006647995673120022,
-0.006412238348275423,
-0.0396861769258976,
-0.031330373138189316,
-0.004173286259174347,
-0.016280362382531166,
-0.02245047129690647,
-0.0010154820047318935,
0.059600040316581726,
-0.017389224842190742,
-0.008043884299695492,
0.03569735586643219,
0.030796661972999573,
0.050731346011161804,
-0.03294578194618225,
0.011356006376445293,
-0.006375097203999758,
0.0041351960971951485,
-0.010828539729118347,
-0.0035460686776787043,
0.06431804597377777,
-0.01819518581032753,
-0.012404657900333405,
-0.003050415776669979,
0.01370062306523323,
0.032853830605745316,
-0.010575927793979645,
0.003959175664931536,
0.007233267650008202,
0.010454095900058746,
-0.043334536254405975,
-0.015148540958762169,
-0.03705282136797905,
-0.029464226216077805,
0.01594032160937786,
0.01023067906498909,
0.009566545486450195,
-0.011661688797175884,
-0.03253202512860298,
0.03506186604499817,
-0.023434177041053772,
-0.0009505365742370486,
0.02928239479660988,
0.037303175777196884,
-0.013012217357754707,
0.04379016533493996,
0.05614301934838295,
-0.0029368477407842875,
0.03040221519768238,
0.002058702288195491,
0.025588538497686386,
0.0015175632433965802,
-0.00612166291102767,
-0.0301461573690176,
-0.036697182804346085,
-0.03179316222667694,
0.062410660088062286,
0.02628421038389206,
-0.016668453812599182,
0.05894743651151657,
0.015152759850025177,
-0.015558266080915928,
0.025936847552657127,
-0.014457290060818195,
-0.022706065326929092,
-0.0434199795126915,
0.034101441502571106,
0.026332495734095573,
-0.030939627438783646,
-0.03678068146109581,
0.0671834722161293,
-0.0007897877949289978,
-0.02106349729001522,
-0.02724633179605007,
0.0627950057387352,
-0.023306554183363914,
0.010042623616755009,
0.004812973085790873,
-0.026784120127558708,
0.0280139222741127,
0.0036156161222606897,
0.04803048446774483,
0.010685797780752182,
-0.04778207838535309,
0.05630058795213699,
0.011653944849967957,
0.019179238006472588,
-0.00037875332054682076,
-0.014603765681385994,
-0.08160170167684555,
0.038756970316171646,
0.009116615168750286,
0.04627809673547745,
0.023017361760139465,
0.0008404286345466971,
0.0466480478644371,
-0.03486783057451248,
0.013775244355201721,
-0.024532446637749672,
-0.024779880419373512,
-0.035616591572761536,
-0.01900722086429596,
-0.010846010409295559,
0.07570840418338776,
-0.02958652749657631,
-0.011231880635023117,
-0.025792064145207405,
-0.038905512541532516,
0.009392896667122841,
0.0001858377072494477,
0.03477001190185547,
-0.01355546060949564,
0.07664400339126587,
0.011835506185889244,
0.03360538184642792,
-0.0341210700571537,
-0.008935431949794292,
0.12152794003486633,
0.03281598165631294,
-0.0020094753708690405,
-0.0415225476026535,
0.010282757692039013,
-0.02330692857503891,
0.006013127975165844,
-0.031941644847393036,
0.026488101109862328,
0.03168343007564545,
-0.007667550817131996,
-0.006696699187159538,
0.04750584065914154,
-0.018954254686832428,
-0.01393961813300848,
0.06667841970920563,
-0.038732223212718964,
-0.0332612544298172,
0.024413293227553368,
0.013604731298983097,
-0.014808116480708122,
0.005080395843833685,
-0.034043800085783005,
0.04206180199980736,
-0.0017529645701870322,
0.01521250419318676,
0.0028986933175474405,
-0.07662618160247803,
0.0012429461348801851,
0.0003534493444021791,
-0.016354793682694435,
-0.019091753289103508,
0.033383727073669434,
-0.024677345529198647,
-0.03162703663110733,
-0.019434688612818718,
-0.006524268537759781,
0.0024454460944980383,
0.0445684939622879,
0.06297735124826431,
0.0317307710647583,
0.029370255768299103,
0.0051652840338647366,
0.006775983143597841,
-0.02045775018632412,
-0.009322079829871655,
-0.019119350239634514,
0.0628693550825119,
-0.015122286975383759,
0.006418917793780565,
-0.012519275769591331,
0.01035100594162941,
-0.003969451412558556,
-0.08297409117221832,
0.009155148640275002,
0.002174374647438526,
0.04832954704761505,
-0.010086637921631336,
0.024878963828086853,
-0.027771051973104477,
-0.010079949162900448,
0.0032694507390260696,
-0.006521441042423248,
-0.0038947223220020533,
0.0015417691320180893,
0.003120444482192397,
-0.02886883169412613,
0.02879292145371437,
-0.02564312145113945,
-0.006427858956158161,
-0.0504026785492897,
0.0032158128451555967,
-0.028425153344869614,
0.017032768577337265,
0.05179813876748085,
0.02909531444311142,
0.011141708120703697,
-0.01051125954836607,
-0.019020749256014824,
-0.006983444560319185,
-0.08447265625,
0.03768786042928696,
-0.0241495743393898,
-0.01417959202080965,
0.03979669511318207,
0.023463431745767593,
0.011778180487453938,
0.06670920550823212,
-0.04659048095345497,
0.015643510967493057,
-0.0020096551161259413,
0.03566865995526314,
-0.018339520320296288,
-0.012980414554476738,
-0.037944115698337555,
0.009095207788050175,
-0.005299009848386049,
-0.02397158555686474,
0.018112247809767723,
-0.004156583454459906,
0.015147075057029724,
0.015713803470134735,
0.008246909826993942,
0.03816411271691322,
-0.01576785184442997,
0.006308186799287796,
0.027410700917243958,
-0.044794484972953796,
0.013154457323253155,
0.0599893182516098,
0.005680805537849665,
-0.04901328682899475,
-0.006467791274189949,
-0.028753481805324554,
0.020602967590093613,
-0.007032020948827267,
0.007107266690582037,
-0.03969551995396614,
0.013241351582109928,
-0.04585737735033035,
0.011342206038534641,
-0.04770001769065857,
-0.00658806087449193,
-0.05824664607644081,
0.029625296592712402,
-0.007702826522290707,
-0.014269459992647171,
-0.012555103749036789,
0.06291932612657547,
-0.009298196993768215,
-0.03160238638520241,
0.005692401435226202,
0.02230052277445793,
0.0018984383204951882,
0.0012089589145034552,
0.019233813509345055,
0.0296317208558321,
0.03861009702086449,
-0.015221916139125824,
-0.0419275127351284,
0.02023850381374359,
0.00397083442658186,
-0.07540412247180939,
0.05404869467020035,
-0.00525987334549427,
-0.014633575454354286,
0.005539404693990946,
-0.030604667961597443,
-0.001113210804760456,
0.04371693357825279,
-0.023312775418162346,
0.009106828831136227,
-0.02059289626777172,
-0.07636084407567978,
-0.026670068502426147,
-0.05981156975030899,
0.053722530603408813,
0.00024640365154482424,
0.005092756822705269,
0.017862586304545403,
0.01496901735663414,
-0.013018246740102768,
0.01864462159574032,
-0.01631787233054638,
-0.016459081321954727,
0.044114578515291214,
0.006842473521828651,
0.01657208800315857,
-0.012690839357674122,
0.06846918910741806,
-0.03578240051865578,
0.012394205667078495,
-0.015183258801698685,
0.006467635277658701,
-0.09607139974832535,
-0.002978723030537367,
-0.013080783188343048,
0.01228705607354641,
0.037296686321496964,
-0.08692960441112518,
-0.006932120304554701,
0.03984195739030838,
-0.05388190597295761,
0.026423735544085503,
-0.05200856178998947,
0.007776445243507624,
-0.012389390729367733,
-0.03053772635757923,
-0.008630931377410889,
0.11117476969957352,
0.03338316082954407,
0.042153503745794296,
0.03434937819838524,
0.015357505530118942,
0.02179845981299877,
-0.030142484232783318,
-0.00828605331480503,
0.03562198951840401,
0.001986261922866106,
0.019742237403988838,
0.07315917313098907,
-0.004700968042016029,
-0.060540974140167236,
0.0208160188049078,
-0.00968681275844574,
0.024073004722595215,
-0.031622160226106644,
0.007778687868267298,
0.012008446268737316,
0.03110687993466854,
-0.0058191437274217606,
0.01661832630634308,
-0.0062623657286167145,
0.005926134530454874,
0.03691113740205765,
-0.0022713460493832827,
0.01102797407656908,
0.016640303656458855,
0.009894154034554958,
-0.04056331142783165,
-0.020603232085704803,
0.032098278403282166,
-0.019323382526636124,
-0.02677968516945839,
0.008576680906116962,
-0.006023308262228966,
0.028742987662553787,
0.00014892566832713783,
0.00984350685030222,
-0.053255949169397354,
-0.009669428691267967,
0.021907402202486992,
-0.029054023325443268,
-0.007207144051790237,
-0.0007841390906833112,
0.008474908769130707,
-0.033277835696935654,
0.030040960758924484,
0.022507699206471443,
-0.02831832319498062,
-0.07080444693565369,
-0.01286787074059248,
-0.018308578059077263,
-0.013875624164938927,
-0.02238163724541664,
-0.007773356977850199,
-0.046868521720170975,
0.006310711614787579,
0.009323828853666782,
0.022820543497800827,
-0.0349750742316246,
-0.03653034567832947,
0.004495605360716581,
-0.03333040699362755,
0.0324646420776844,
0.02379305101931095,
-0.018066370859742165,
-0.039215926080942154,
-0.005803534295409918,
0.01685933768749237,
0.006735497619956732,
0.03032628633081913,
-0.012568586505949497,
-0.008568931370973587,
0.038538120687007904,
0.02636142261326313,
-0.008712192997336388,
-0.028460603207349777,
-0.00033700914354994893,
-0.037679173052310944,
0.00442953547462821,
-0.017636293545365334,
0.012421633116900921,
-0.02290414832532406,
0.016607575118541718,
0.006669664289802313,
-0.0018216765020042658,
0.014557291753590107,
-0.001021584146656096,
-0.054836809635162354,
0.03412020206451416,
0.00473829498514533,
-0.01105829793959856,
0.045267701148986816,
0.031519342213869095,
0.008339484222233295,
0.029095111414790154,
-0.01901012659072876,
-0.02726268209517002,
0.02165718376636505,
-0.047777242958545685,
-0.028483225032687187,
-0.008702293038368225,
-0.006592696066945791,
0.028725506737828255,
-0.04830232262611389,
0.006513306405395269,
0.06241871044039726,
-0.003245420753955841,
-0.02354082278907299,
0.05114253610372543,
0.014607847668230534,
0.02677847258746624,
0.03041183575987816,
0.0021947810892015696,
0.018095554783940315,
0.03913462162017822,
0.007757971528917551,
0.030691808089613914,
0.0316833034157753,
0.0005712299607694149,
0.014996699057519436,
0.010721184313297272,
-0.017671851441264153,
0.0437077172100544,
0.009749041870236397,
0.027157548815011978,
-0.03243805095553398,
0.00043999936315231025,
0.014820734038949013,
-0.021225901320576668,
0.015283689834177494,
-0.005691484548151493,
-0.010516775771975517,
0.05091594532132149,
-0.015306133776903152,
-0.006848209071904421,
-0.01082846149802208,
0.005850681569427252,
-0.01852390542626381,
0.020438427105545998,
0.011872150003910065,
0.04229959473013878,
-0.01651209220290184,
-0.012924561277031898,
-0.02098645456135273,
0.032609011977910995,
-0.0006332028424367309,
-0.019513845443725586,
-0.00739564374089241,
-0.00619497150182724,
-0.029689088463783264,
0.019401993602514267,
-0.019825661554932594,
-0.03429800271987915,
-0.028471829369664192,
0.02336522564291954,
0.05980546772480011,
0.03788989782333374,
0.013857921585440636,
0.01663823612034321,
-0.051973793655633926,
0.08929973840713501,
-0.04604225605726242,
-0.050443779677152634,
-0.0006171111599542201,
-0.01888699270784855,
0.010204232297837734,
-0.00702164089307189
] |
<p>Imagine a vertical pipe (both ends opened) in the water. Drop several ping-pong balls into pipe and cover them with a cylinder. When you have enough balls, the cylinder will float. Now start adding weight into the top of a cylinder, and simultaneously start adding ping-pong balls via the bottom of pipe, to compensate the increasing weight. </p>
<p><img src="http://i.stack.imgur.com/Y3ZOT.jpg" alt="enter image description here"></p>
<p>At the some weight (and balls columng height) the topmost row of balls start crunching due the buoyancy pressure. <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur">In this question</a> @mms <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur/8851#8851">answered</a> than one ping-pong ball can withstand 3 atmosphere pressure.</p>
<p>The question is: how to approximate the maximum heigh of ball column (or maximum weight is possible float) for the pipe radius "R" before the topmost row of balls start crunching?</p>
<p>Or, maybe will start crunching not the topmost row, but somewhere else because the sum of buoyancy pressure (from the balls bellow) and water pressure will be more the 3atm. How to determine?</p> | 4,555 | [
-0.035020362585783005,
-0.01759725622832775,
-0.023411830887198448,
0.01586858741939068,
0.013366637751460075,
-0.00035598318208940327,
-0.01639711484313011,
-0.041755229234695435,
0.04028695076704025,
-0.030327467247843742,
0.039870209991931915,
0.052291322499513626,
0.02058407850563526,
0.029959633946418762,
0.014784620143473148,
0.012359567917883396,
0.000769310281611979,
-0.026448480784893036,
0.0026833966840058565,
-0.01152336597442627,
-0.017956217750906944,
-0.017815016210079193,
-0.037608709186315536,
-0.003823074046522379,
-0.005954856518656015,
0.016468171030282974,
0.038606200367212296,
-0.016302168369293213,
0.003988484852015972,
0.03789505362510681,
0.009958415292203426,
0.004830832593142986,
0.01738530397415161,
0.012904481031000614,
0.06728255748748779,
0.036434683948755264,
-0.008908218704164028,
-0.02895483188331127,
-0.04384623467922211,
0.02022447995841503,
-0.013733104802668095,
0.0012517176801338792,
0.02079230546951294,
0.0034695002250373363,
-0.04264560341835022,
0.06804013252258301,
-0.019735876470804214,
-0.02120799757540226,
0.049446284770965576,
-0.06298311054706573,
0.04325634986162186,
0.0382763035595417,
0.0395372249186039,
0.03843826800584793,
-0.022266898304224014,
-0.027164388447999954,
0.05569599196314812,
0.06713694334030151,
-0.017336633056402206,
-0.03412257134914398,
0.0005581576260738075,
-0.012055969797074795,
-0.045188527554273605,
-0.03733242675662041,
-0.0034564598463475704,
0.05025773495435715,
-0.02097921445965767,
-0.010133398696780205,
0.022996744140982628,
-0.03257320076227188,
-0.010425414890050888,
-0.017426619306206703,
0.03927653282880783,
-0.02754131890833378,
0.03246188163757324,
-0.00016057235188782215,
0.011619778349995613,
0.028601456433534622,
-0.007575321942567825,
0.02901899442076683,
-0.03459534794092178,
0.009864145889878273,
0.05574297159910202,
0.036336857825517654,
0.042920082807540894,
-0.017628677189350128,
0.07019263505935669,
-0.01714252308011055,
0.01253420952707529,
0.019903991371393204,
-0.020466908812522888,
0.0026535342913120985,
-0.008456035517156124,
0.011151417158544064,
0.002684350125491619,
0.03090616874396801,
0.03281582519412041,
0.04820668324828148,
-0.02056208997964859,
-0.01883317343890667,
0.009585392661392689,
-0.0354137159883976,
0.028749069198966026,
0.06707900762557983,
0.019359933212399483,
0.007523948792368174,
-0.0693548321723938,
-0.0016572054009884596,
-0.024341003969311714,
-0.005210254807025194,
-0.015004743821918964,
-0.010304264724254608,
-0.018618144094944,
-0.0321931391954422,
-0.02818758599460125,
-0.027792802080512047,
0.026961181312799454,
-0.02066624164581299,
0.0313861183822155,
0.013375706970691681,
0.04466231167316437,
-0.024677373468875885,
0.034890007227659225,
-0.041060395538806915,
-0.08272083848714828,
0.02516842447221279,
0.03235705569386482,
-0.03182273730635643,
-0.06318266689777374,
0.04124091565608978,
-0.0013792839599773288,
0.004594522528350353,
0.010532290674746037,
0.010757804848253727,
0.0500279925763607,
-0.03693295642733574,
-0.10893849283456802,
-0.030766397714614868,
0.03503553569316864,
0.01623285561800003,
-0.046809859573841095,
-0.05638667196035385,
-0.0015127770602703094,
0.04532533511519432,
0.05983758717775345,
0.00901060737669468,
0.045592956244945526,
-0.012582984752953053,
0.017816228792071342,
0.005135080777108669,
0.000053970150474924594,
0.028734948486089706,
-0.008429245091974735,
-0.02855164185166359,
0.007413757964968681,
-0.04878082498908043,
-0.004829939920455217,
0.03721084073185921,
0.03465908765792847,
-0.005312097258865833,
0.033048201352357864,
-0.03412280231714249,
-0.014830152504146099,
-0.04545692726969719,
-0.0252052191644907,
-0.014661885797977448,
0.05248260125517845,
-0.01914975419640541,
-0.028705094009637833,
0.04582584649324417,
-0.026733804494142532,
-0.026489032432436943,
-0.04436381161212921,
0.006556984968483448,
0.07530413568019867,
-0.048223454505205154,
-0.007748776115477085,
-0.023149486631155014,
0.01287597045302391,
0.0028139217756688595,
-0.004797196015715599,
-0.018354561179876328,
0.011223251931369305,
0.031767453998327255,
0.04377201572060585,
0.02455473691225052,
0.030350472778081894,
-0.04117514565587044,
0.027083132416009903,
-0.05505261942744255,
0.01872945763170719,
-0.054570965468883514,
0.04082736372947693,
0.014290561899542809,
0.010079712606966496,
0.02554694004356861,
-0.024510536342859268,
-0.0031425885390490294,
-0.015272079966962337,
-0.0011157839326187968,
-0.011316328309476376,
0.010560703463852406,
0.026073353365063667,
0.013449824415147305,
-0.023048682138323784,
0.04372558742761612,
0.01566757634282112,
-0.03763597458600998,
-0.0020021460950374603,
-0.0378648042678833,
0.001987114315852523,
-0.00011477463704068214,
-0.02359960228204727,
-0.014000860042870045,
-0.013550848700106144,
0.019928712397813797,
0.06273751705884933,
-0.0030314698815345764,
-0.012491402216255665,
0.015519076026976109,
-0.027019353583455086,
0.0645856186747551,
0.06983007490634918,
0.015149369835853577,
0.01752513088285923,
-0.006871150806546211,
-0.0025672384072095156,
0.004216966684907675,
0.003195155179128051,
-0.020027056336402893,
-0.06837157160043716,
-0.014693468809127808,
-0.022149110212922096,
0.03689422830939293,
-0.00933047104626894,
0.0034834849648177624,
0.02530702017247677,
0.015478093177080154,
0.03436986729502678,
0.047986503690481186,
-0.029201410710811615,
0.02363317646086216,
-0.00023100216640159488,
0.06467075645923615,
-0.0016211004694923759,
0.00819555763155222,
0.0005557404947467148,
0.02443644218146801,
0.009843720123171806,
-0.01637449488043785,
-0.016721881926059723,
-0.0014081879053264856,
0.03216832876205444,
0.02952076680958271,
-0.0241060983389616,
-0.009358822368085384,
0.021533198654651642,
-0.017004068940877914,
0.003171144984662533,
0.02512720413506031,
0.0014101250562816858,
-0.004335628356784582,
-0.054490625858306885,
-0.03880452364683151,
0.008440847508609295,
0.06491100043058395,
0.004055241588503122,
-0.029953550547361374,
0.033941999077796936,
-0.010824992321431637,
-0.029489442706108093,
-0.011463524773716927,
0.006284820381551981,
-0.02702108584344387,
0.027875283733010292,
0.035832084715366364,
0.0006095258868299425,
0.04754086211323738,
-0.025270575657486916,
0.001876379712484777,
-0.026112468913197517,
-0.01352628879249096,
-0.014165984466671944,
-0.028390685096383095,
-0.04325634241104126,
0.004060198087245226,
0.01933414489030838,
-0.03843347355723381,
0.021000226959586143,
0.026951506733894348,
0.000871783762704581,
0.030470021069049835,
0.034777190536260605,
0.011755810119211674,
0.026888299733400345,
-0.016952212899923325,
0.010047498159110546,
-0.009627626277506351,
-0.01136926468461752,
0.05484139546751976,
0.01921212300658226,
-0.06306711584329605,
0.03619065135717392,
-0.05786818638443947,
-0.03832504525780678,
-0.012123532593250275,
-0.006849142722785473,
-0.00280633382499218,
-0.018130410462617874,
0.027372784912586212,
-0.012654922902584076,
0.015915583819150925,
-0.010103068314492702,
-0.09738446772098541,
-0.04755093902349472,
-0.0141008784994483,
-0.008090343326330185,
0.0343749113380909,
0.01343643106520176,
-0.022038409486413002,
0.08369032293558121,
-0.03792986273765564,
-0.04061572626233101,
-0.014299476519227028,
0.005178485531359911,
0.0235226321965456,
-0.021533435210585594,
0.021860428154468536,
0.018360335379838943,
-0.04095440357923508,
0.04625923931598663,
0.023980535566806793,
0.022859906777739525,
0.02405676804482937,
0.03541289269924164,
0.010615849867463112,
-0.004751994740217924,
0.0171308945864439,
-0.022790690883994102,
0.0545409731566906,
0.016773775219917297,
0.011425329372286797,
0.019832374528050423,
-0.012698770500719547,
0.0018659400520846248,
0.019352804869413376,
-0.036769334226846695,
0.027416786178946495,
0.037423230707645416,
-0.013578549958765507,
-0.0200001522898674,
0.038621481508016586,
0.010685451328754425,
-0.07009561359882355,
0.029259875416755676,
0.023290066048502922,
0.035670407116413116,
0.004328626673668623,
-0.02944330684840679,
0.06455741822719574,
0.08066835254430771,
-0.008987178094685078,
-0.036510296165943146,
-0.028346871957182884,
-0.0087504917755723,
0.021514736115932465,
-0.0031970147974789143,
-0.007885733619332314,
0.03671117126941681,
-0.008320199325680733,
0.022774284705519676,
-0.013495104387402534,
-0.015885449945926666,
-0.01993357390165329,
-0.07212904095649719,
-0.03902355954051018,
0.006690564565360546,
0.08197830617427826,
0.002474377630278468,
0.01784548908472061,
0.04266836866736412,
-0.004028834868222475,
0.05670976638793945,
0.03386200591921806,
-0.09943539649248123,
-0.006479782983660698,
-0.010385580360889435,
-0.019117282703518867,
0.008155525662004948,
-0.04986048489809036,
-0.005301287397742271,
-0.022153783589601517,
-0.0037035683635622263,
-0.028203444555401802,
-0.0056291306391358376,
-0.04903638735413551,
0.025820279493927956,
-0.02644091285765171,
0.02781754359602928,
0.03745798394083977,
0.02552233822643757,
0.026172786951065063,
-0.013416583649814129,
0.05496741458773613,
0.024774618446826935,
-0.03315155208110809,
0.013380531221628189,
0.008810644969344139,
0.032802775502204895,
-0.017247727140784264,
0.02310585230588913,
0.002649020403623581,
0.05165449529886246,
-0.007611296605318785,
-0.023276308551430702,
-0.011166512034833431,
0.005271687638014555,
-0.012190917506814003,
-0.02292771078646183,
-0.02573002688586712,
-0.01979064755141735,
-0.008007386699318886,
0.012264502234756947,
0.02604283206164837,
-0.006716337986290455,
0.007977624423801899,
-0.00967604573816061,
-0.025724217295646667,
0.029395705088973045,
0.055320270359516144,
0.07161653786897659,
-0.0056940168142318726,
-0.03231693059206009,
-0.029012897983193398,
-0.04027799516916275,
-0.028518447652459145,
0.015234556049108505,
0.0013381155440583825,
0.0519961342215538,
0.0009790033800527453,
0.021009081974625587,
0.05037060007452965,
0.026815542951226234,
-0.020849036052823067,
0.018720543012022972,
0.009408663026988506,
0.024954648688435555,
-0.04936657100915909,
0.012984201312065125,
-0.006141373421996832,
0.04482364282011986,
0.0616123229265213,
-0.011575022712349892,
-0.05767416954040527,
-0.058861684054136276,
-0.06356394290924072,
0.04337386041879654,
0.05358954519033432,
-0.0019235439831390977,
0.018082354217767715,
-0.016910355538129807,
-0.005177393089979887,
0.05217020958662033,
-0.05314132198691368,
0.0430612750351429,
-0.037713658064603806,
0.04163603484630585,
-0.003281638026237488,
-0.038762349635362625,
-0.02211308293044567,
0.034647759050130844,
-0.035113751888275146,
0.03908849507570267,
0.0006334593053907156,
0.026502428576350212,
0.0038947274442762136,
0.02280203066766262,
0.037810709327459335,
0.010611764155328274,
-0.022965164855122566,
-0.017941199243068695,
-0.051785681396722794,
-0.004267735872417688,
-0.04504747688770294,
-0.059485115110874176,
0.03713776171207428,
-0.000007312591151276138,
-0.02871161326766014,
0.04093604534864426,
-0.045784782618284225,
-0.03218875080347061,
0.0471988208591938,
0.014645908027887344,
-0.00474574975669384,
-0.0009436033433303237,
-0.03794568404555321,
0.057550352066755295,
0.07005592435598373,
0.01574336737394333,
0.009907225146889687,
0.041965700685977936,
-0.011210383847355843,
-0.01661296933889389,
-0.02561618573963642,
-0.013366155326366425,
-0.03840918838977814,
-0.014659451320767403,
-0.007978470996022224,
0.00031638689688406885,
-0.05474355071783066,
0.018302716314792633,
0.016261521726846695,
0.01587444730103016,
0.005470397882163525,
-0.030385036021471024,
0.018754709511995316,
0.012647231109440327,
0.04163050651550293,
0.03480859473347664,
-0.0062903449870646,
0.05210615694522858,
0.001847736886702478,
-0.02308257482945919,
0.011731516569852829,
-0.01053040474653244,
0.02908148430287838,
-0.0031751750502735376,
0.004061216954141855,
0.03961867839097977,
0.01468927413225174,
0.02420412003993988,
0.027249636128544807,
-0.05551338568329811,
0.08643010258674622,
-0.021061642095446587,
0.002325506880879402,
0.023942245170474052,
-0.026512963697314262,
0.017056327313184738,
-0.01550543587654829,
-0.03448367118835449,
0.0010457064490765333,
0.0005338524933904409,
0.027456875890493393,
0.016084622591733932,
0.007076709996908903,
-0.03075427934527397,
-0.05175333842635155,
0.04238549619913101,
0.02544552832841873,
-0.016974356025457382,
-0.034202661365270615,
-0.008541638031601906,
-0.03894886374473572,
-0.01981290802359581,
-0.03130212053656578,
0.013257676735520363,
-0.02157631702721119,
0.00021140412718523294,
0.052546001970767975,
0.02524271048605442,
0.05902661010622978,
0.0033154913689941168,
-0.004840333014726639,
0.015105349943041801,
-0.026293236762285233,
0.010891787707805634,
-0.005302701611071825,
0.003388036508113146,
-0.049298275262117386,
-0.023122597485780716,
0.010515430942177773,
-0.008233226835727692,
0.04365435615181923,
0.0001914139575092122,
0.01681651920080185,
-0.025084301829338074,
0.0075493319891393185,
-0.0004821917391382158,
-0.011576063930988312,
0.025596218183636665,
0.012117668054997921,
0.025241322815418243,
-0.014434841461479664,
-0.014031643979251385,
-0.027255045250058174,
-0.04041176289319992,
0.03761376067996025,
-0.007301828823983669,
-0.004273307975381613,
-0.01103465911000967,
0.051098842173814774,
-0.010711751878261566,
-0.02381865680217743,
-0.003025578334927559,
0.007511519826948643,
0.052613504230976105,
0.029798131436109543,
-0.018534397706389427,
0.020651407539844513,
0.021214762702584267,
-0.008577902801334858,
-0.016723735257983208,
-0.03262316808104515,
0.03872576728463173,
0.053767766803503036,
-0.0630054771900177,
0.07134942710399628,
0.03324519097805023,
0.0041732583194971085,
0.003248803550377488,
-0.012960470281541348,
0.0058116065338253975,
-0.0004446661623660475,
0.011578937992453575,
0.02884571999311447,
-0.05936900153756142,
0.0022998410277068615,
0.035684872418642044,
0.016733508557081223,
0.009795395657420158,
0.01901361346244812,
0.028970859944820404,
0.02202378585934639,
0.005512078758329153,
-0.06911437958478928,
-0.006373816169798374,
0.0340389721095562,
-0.04805431142449379,
0.013071354478597641,
0.01414759922772646,
0.0017565647140145302,
0.04113822802901268,
0.04758213460445404,
-0.026063844561576843,
-0.06295439600944519,
-0.026182886213064194,
-0.026712296530604362,
0.003121627727523446,
0.025360198691487312,
-0.003838922595605254,
-0.0043128435499966145,
0.013960640877485275,
0.012776781804859638,
-0.024574246257543564,
0.034216348081827164,
-0.061198484152555466,
-0.04865850880742073,
-0.007422633469104767,
-0.035792965441942215,
-0.0537094920873642,
0.028110118582844734,
0.04792458191514015,
-0.0210588239133358,
0.016345813870429993,
-0.02574336901307106,
0.016852540895342827,
0.024821242317557335,
0.017226701602339745,
-0.040356431156396866,
0.05845612660050392,
-0.019597001373767853,
0.015605066902935505,
-0.001575286965817213,
-0.017257358878850937,
0.1329185962677002,
0.04760592058300972,
0.028602994978427887,
-0.008584554307162762,
-0.022728540003299713,
0.04553244635462761,
-0.004943047184497118,
-0.02861670032143593,
-0.04446591064333916,
0.005187411792576313,
0.006182384677231312,
-0.00232857302762568,
0.0730028823018074,
-0.0270532313734293,
-0.009844410233199596,
0.02475808933377266,
-0.08051034808158875,
-0.00546877970919013,
-0.006966385990381241,
0.026947395876049995,
0.004789195489138365,
-0.003852674039080739,
-0.05272756889462471,
0.04681379720568657,
-0.0036223840434104204,
-0.0030036463867872953,
-0.029432449489831924,
-0.00893204566091299,
0.020693624392151833,
-0.03851296007633209,
-0.05356810614466667,
0.04008747637271881,
-0.002723781857639551,
-0.06370899081230164,
-0.03994787484407425,
0.02256515622138977,
0.026502331718802452,
-0.017679596319794655,
-0.002101625083014369,
0.02357921004295349,
0.039136432111263275,
0.01027101930230856,
0.0025168689899146557,
0.04895440861582756,
-0.06693868339061737,
0.008435027673840523,
-0.05434117093682289,
0.019204186275601387,
0.0011666998034343123,
-0.031182968989014626,
0.01253340020775795,
-0.03126796707510948,
0.00031489672255702317,
-0.04364161193370819,
-0.03383143991231918,
-0.0027993887197226286,
0.03390238434076309,
-0.003702451940625906,
-0.04949299991130829,
0.036189064383506775,
0.011276152916252613,
0.04941489174962044,
-0.010513442568480968,
-0.01931263692677021,
-0.01282145269215107,
-0.03146247938275337,
-0.03208160400390625,
0.03773912787437439,
-0.027819175273180008,
0.010744943283498287,
-0.037008754909038544,
0.021885624155402184,
-0.03873128816485405,
0.010684773325920105,
-0.008439375087618828,
0.011104018427431583,
0.0427670031785965,
0.016165556386113167,
0.024093857035040855,
-0.007849317975342274,
-0.03818877041339874,
0.02775050513446331,
-0.03865044564008713,
-0.011019062250852585,
-0.0741167962551117,
-0.04149460420012474,
0.006757253315299749,
0.04840521514415741,
0.013408523984253407,
-0.02244497463107109,
0.012158410623669624,
0.0790020152926445,
0.008469399996101856,
-0.010882804170250893,
-0.03701820969581604,
-0.00810791552066803,
-0.03906494006514549,
0.0437040738761425,
-0.014290032908320427,
0.04876861721277237,
0.03495509922504425,
-0.003574658650904894,
0.006777344737201929,
-0.0013758583227172494,
-0.02511727251112461,
-0.02040093019604683,
0.033002883195877075,
-0.012894346378743649,
-0.04134448245167732,
0.03231959789991379,
-0.011868469417095184,
-0.02868318185210228,
-0.003965109586715698,
-0.014233377762138844,
-0.04432693123817444,
-0.008682635612785816,
-0.012949848547577858,
-0.02478771097958088,
0.021024253219366074,
-0.035344596952199936,
-0.035835012793540955,
-0.004683570936322212,
-0.014291883446276188,
-0.056711722165346146,
-0.002677846234291792,
0.008639351464807987,
-0.016447441652417183,
-0.033767927438020706,
0.033366650342941284,
-0.04978405311703682,
-0.0363217294216156,
-0.022336745634675026,
0.01202026754617691,
-0.01293214038014412,
-0.004080763086676598,
0.0050695063546299934,
-0.014502986334264278,
0.009864404797554016,
0.016200874000787735,
-0.041081927716732025,
0.012844480574131012,
-0.04718944802880287,
-0.010343316942453384,
0.03642261028289795,
-0.013082706369459629,
0.03530184179544449,
0.028978807851672173,
-0.008122364059090614,
-0.022887708619236946,
0.07036365568637848,
-0.013614116236567497,
-0.018530728295445442,
-0.009406865574419498,
-0.04627029597759247,
-0.028578920289874077,
0.027845997363328934,
0.008006765507161617,
-0.025317035615444183,
-0.018234973773360252,
-0.0037937217857688665,
0.02842450886964798,
0.004025684669613838,
0.0028480300679802895,
-0.00859356950968504,
0.008012449368834496,
0.031351059675216675,
-0.020632416009902954,
-0.018814848735928535,
0.038184233009815216,
0.05360660329461098,
-0.02257300727069378,
0.03633490204811096,
-0.024055544286966324,
-0.012182879261672497,
-0.0877467691898346,
0.025146089494228363,
0.01426119077950716,
-0.005647285841405392,
0.030066512525081635,
-0.04541314020752907,
0.03528030961751938,
0.02799234725534916,
-0.06270160526037216,
-0.000426099548349157,
-0.04213196784257889,
0.026096027344465256,
-0.050949156284332275,
0.018850181251764297,
-0.011442956514656544,
0.04178193584084511,
0.00018511951202526689,
0.0040981099009513855,
0.017182955518364906,
0.03153514489531517,
0.00851582083851099,
-0.02685650996863842,
0.02006453648209572,
0.06307469308376312,
-0.016581105068325996,
-0.007618094328790903,
0.058171212673187256,
-0.017898429185152054,
-0.014471272937953472,
0.012464931234717369,
-0.06088775768876076,
0.001270775799639523,
-0.01949760690331459,
-0.010293694213032722,
-0.002770534949377179,
0.01628732495009899,
0.00062320422148332,
0.01054893247783184,
0.003988290671259165,
0.040400926023721695,
-0.01435343362390995,
0.002946524415165186,
-0.025402333587408066,
0.014646823517978191,
0.025506550446152687,
-0.017034098505973816,
-0.016436930745840073,
0.027738453820347786,
-0.02560686133801937,
0.03315402939915657,
0.028865378350019455,
-0.006079420913010836,
0.02794330008327961,
-0.00752077205106616,
-0.043097369372844696,
-0.028097210451960564,
0.04752293601632118,
0.012339536100625992,
0.026687510311603546,
-0.039633311331272125,
-0.004238751716911793,
-0.02579767256975174,
-0.011458703316748142,
-0.024389851838350296,
-0.027059493586421013,
-0.006860842928290367,
-0.0037856113631278276,
0.004755509085953236,
0.027386099100112915,
0.001025149947963655,
-0.0027721442747861147,
-0.042405206710100174,
-0.03376556932926178,
0.03285360336303711,
0.01593913324177265,
0.018781034275889397,
0.033090800046920776,
-0.008910093456506729,
0.0059939660131931305,
-0.1098768562078476,
0.022738516330718994,
-0.019260844215750694,
-0.02034418284893036,
-0.019289027899503708,
-0.03786209970712662,
0.0073836566880345345,
0.0318719819188118,
0.031935542821884155,
-0.03828476369380951,
-0.013651973567903042,
0.0009272663737647235,
-0.02643299102783203,
0.016582945361733437,
-0.01928001269698143,
-0.0025454892311245203,
-0.006616656202822924,
-0.016983162611722946,
0.031355876475572586,
0.02316136844456196,
0.032782722264528275,
-0.02447410486638546,
0.03673961013555527,
0.01830563321709633,
0.011907441541552544,
0.02869965136051178,
-0.03708915039896965,
-0.0017973619978874922,
0.014841115102171898,
0.03323621675372124,
0.06777774542570114,
-0.019671905785799026,
-0.012018870562314987,
-0.009041298180818558,
-0.013771618716418743,
-0.014152171090245247,
0.052213605493307114,
-0.043103184551000595,
-0.014266075566411018,
-0.011132384650409222,
-0.0312642939388752,
-0.0210547037422657,
-0.07123522460460663,
-0.019748447462916374,
-0.0038964184932410717,
-0.01746659353375435,
-0.025879548862576485,
0.02421257458627224,
0.02076668292284012,
0.012204231694340706,
-0.038153182715177536,
0.009274674579501152,
-0.004951100796461105,
-0.0396406427025795,
-0.011574179865419865,
0.024548325687646866,
0.05909755080938339,
-0.023945104330778122,
0.008194745518267155,
0.025946108624339104,
0.019767118617892265,
0.03894231468439102,
0.010413657873868942,
0.02659749612212181,
-0.009644283913075924,
-0.020727751776576042,
-0.002426720457151532,
0.002555475104600191,
-0.019741807132959366,
0.014486164785921574,
0.02412366308271885,
0.027528738602995872,
-0.008859502151608467,
0.0047769732773303986,
-0.01838962361216545,
-0.0008526527089998126,
0.003209012094885111,
0.021652230992913246,
-0.007297532167285681,
0.006827447563409805,
-0.003306654514744878,
0.011879968456923962,
-0.01957797445356846,
0.013309411704540253,
0.016434533521533012,
0.030841656029224396,
0.05458581820130348,
0.006735878996551037,
0.049208540469408035,
0.003723534755408764,
-0.04012124612927437,
-0.01620585098862648,
0.007307029794901609,
0.06828963756561279,
0.024845212697982788,
0.004893451929092407,
-0.03929319605231285,
-0.023293737322092056,
-0.027035066857933998,
0.06455139815807343,
-0.05406884104013443,
-0.06444968283176422,
-0.0409930944442749,
0.04498377814888954,
0.019531462341547012,
-0.012258858419954777
] |
<p>My 8yo son is in the Cub Scouts.</p>
<p>He has a pinewood derby coming up next month and I would like to take this project and turn it into a fun, physics lesson for him. </p>
<p>For those not familiar, a pinewood derby is where you shape a block of wood into a car (or truck, or where ever your imagination leads you) and race it on a track against other cars.</p>
<p>The track looks something like this (not to scale):
<img src="http://i.stack.imgur.com/mo6UI.jpg" alt="Pinewood Derby"></p>
<p>The black curve represents the track. The peculiar, red triangle with wheels is the car. (<a href="http://scouting.org/scoutsource/CubScouts/Cub%20Scouts/ThingsToDo/PineDesign.aspx" rel="nofollow">Click this link</a> to see the various options for the block of wood.)</p>
<p>So, a few talking points that come to mind are as follows:</p>
<ol>
<li><strong>Gravity.</strong> Obviously w/o this the car would go nowhere when released. </li>
<li><strong>Friction.</strong> All wheels come with metal axles. We are allowed to use powered graphite to reduce the friction and make the car move quicker.</li>
<li><strong>Weight.</strong> The heaver it is, the faster it will move. However, there is a 5oz max weight the car can reach. Should the weight of the car be evenly distributed to maximize speed?</li>
<li><strong>Design.</strong> I imagine the design of the car is important to reduce drag...are there any designs from the previous link you would pick regarding that?</li>
</ol>
<p>Any thoughts on how to elaborate on the items above?</p>
<p>Is there anything I haven't listed that would be helpful to talk about?</p> | 4,556 | [
-0.036827344447374344,
-0.05584690347313881,
-0.00016637858061585575,
0.009916489012539387,
0.04162828251719475,
0.009147446602582932,
-0.009323075413703918,
-0.0728917047381401,
0.01957891881465912,
-0.009578037075698376,
0.01305442675948143,
0.06404238194227219,
0.040139686316251755,
0.0687999352812767,
0.03277771174907684,
0.021525759249925613,
0.021721402183175087,
-0.03174635395407677,
0.014040755107998848,
-0.050894495099782944,
-0.010183745995163918,
-0.050813693553209305,
0.00012699446233455092,
0.006613819859921932,
0.013802249915897846,
0.02806723304092884,
0.017261050641536713,
-0.02176445536315441,
0.005720156244933605,
0.0641358271241188,
-0.010179645381867886,
-0.01966041699051857,
0.015638425946235657,
-0.009904187172651291,
0.038518115878105164,
0.0031216414645314217,
-0.06684184074401855,
0.03593973442912102,
-0.020335746929049492,
0.008948846720159054,
-0.010804526507854462,
-0.020917583256959915,
-0.014216570183634758,
0.023507706820964813,
-0.003055776469409466,
0.016850007697939873,
0.014780111610889435,
-0.06626825779676437,
0.05029609799385071,
-0.05484269931912422,
0.01846027746796608,
0.0036450130864977837,
-0.013037906028330326,
0.05981256812810898,
0.011375883594155312,
-0.03294435143470764,
0.04599691927433014,
0.07874508202075958,
-0.03350177779793739,
-0.033271074295043945,
-0.026542391628026962,
-0.035710860043764114,
-0.0069567556492984295,
-0.001678425120189786,
-0.012657476589083672,
-0.001570344204083085,
-0.028249280527234077,
-0.020172646269202232,
0.00622144527733326,
0.00040848596836440265,
-0.0054285707883536816,
0.04471563547849655,
0.0517735481262207,
0.032401833683252335,
0.007594696711748838,
-0.03787582367658615,
0.008073368109762669,
0.03770963102579117,
0.02588452212512493,
0.037433188408613205,
-0.07280269265174866,
0.036623407155275345,
0.017859896644949913,
0.08462239801883698,
0.00709941191598773,
-0.044495489448308945,
0.04718247056007385,
-0.005098498426377773,
0.01195148192346096,
-0.005401258356869221,
0.010964764282107353,
-0.023715388029813766,
0.07162821292877197,
-0.026805397123098373,
0.005741389002650976,
0.02328566275537014,
0.017389368265867233,
0.024823982268571854,
0.010248159989714622,
-0.010362605564296246,
0.04297041520476341,
-0.03777439519762993,
-0.001142750377766788,
0.07458268851041794,
0.016179203987121582,
-0.02685295045375824,
-0.013035912998020649,
0.027051076292991638,
-0.009061929769814014,
0.006595550570636988,
0.0048998030833899975,
0.0022222972474992275,
0.025141166523098946,
-0.020778901875019073,
0.014744918793439865,
-0.06678953766822815,
-0.01293468102812767,
0.036724209785461426,
0.020420843735337257,
-0.02844550460577011,
0.025933733209967613,
-0.038153667002916336,
0.008844503201544285,
-0.022328240796923637,
-0.03453507646918297,
0.033522624522447586,
0.02593562938272953,
-0.028835434466600418,
-0.0010897185420617461,
0.02815082110464573,
0.044833432883024216,
-0.007816250436007977,
0.027701033279299736,
-0.03137558326125145,
0.028067616745829582,
0.01827535592019558,
-0.04614803194999695,
-0.05735604837536812,
0.0510927177965641,
0.019664965569972992,
-0.01103975623846054,
-0.07618800550699234,
-0.002689923392608762,
0.021597271785140038,
0.05741046741604805,
-0.017106294631958008,
0.0030244579538702965,
-0.013358030468225479,
0.050934188067913055,
0.012930914759635925,
-0.00379478489048779,
-0.013907021842896938,
-0.0025997289922088385,
-0.04089387133717537,
-0.010721979662775993,
-0.05717542767524719,
0.03659588471055031,
0.03331662341952324,
-0.009322788566350937,
-0.03304494917392731,
0.02692992053925991,
-0.0288117453455925,
0.006696970202028751,
-0.008583802729845047,
0.02331833355128765,
-0.016538189724087715,
0.05190073698759079,
0.03560379520058632,
-0.009630607441067696,
0.03274022787809372,
0.013381369411945343,
0.05181434378027916,
0.036359503865242004,
0.0021755420602858067,
0.05367346107959747,
-0.03915250301361084,
-0.0178458821028471,
-0.007383527234196663,
-0.020020926371216774,
0.003497798927128315,
-0.050310682505369186,
-0.020938288420438766,
-0.003897320246323943,
0.019107060506939888,
-0.005318321753293276,
0.04588191583752632,
0.007709471974521875,
0.04059184715151787,
0.015560612082481384,
-0.02323143556714058,
-0.04330585524439812,
-0.0973866879940033,
0.01801551878452301,
-0.009611432440578938,
-0.009813318960368633,
0.023514913395047188,
-0.03220783919095993,
0.04179235175251961,
-0.038042567670345306,
0.006516969762742519,
0.006649547256529331,
0.051274374127388,
0.008883408270776272,
0.015376501716673374,
-0.0134695153683424,
0.05013571307063103,
0.032504599541425705,
-0.03408009558916092,
-0.016136012971401215,
-0.025806641206145287,
-0.01973029039800167,
-0.012097806669771671,
-0.014586512930691242,
-0.020381378009915352,
0.020702622830867767,
0.01706158183515072,
0.026824284344911575,
-0.010580580681562424,
0.01635034941136837,
0.022857189178466797,
0.004814325366169214,
0.08078943938016891,
0.02869485877454281,
-0.02303251065313816,
0.046923503279685974,
0.018256399780511856,
-0.009285771287977695,
0.006112522445619106,
-0.0033868795726448298,
-0.00731849018484354,
-0.07180170714855194,
-0.016058694571256638,
0.01932113617658615,
0.02247798629105091,
-0.0589907169342041,
0.024703174829483032,
0.05588488653302193,
0.026069266721606255,
0.037199970334768295,
0.01294288132339716,
-0.052953146398067474,
0.02712574228644371,
0.006837834138423204,
-0.0006940301391296089,
0.03801211342215538,
0.03513479232788086,
0.027707813307642937,
0.0574156679213047,
0.008678767830133438,
-0.01680208556354046,
-0.02976643666625023,
0.011082733981311321,
0.029649078845977783,
0.0014445421984419227,
-0.004341635387390852,
-0.030042478814721107,
0.04685566574335098,
-0.014116576872766018,
0.013661721721291542,
0.0499238558113575,
0.013356467708945274,
-0.007198887411504984,
-0.05439718812704086,
-0.02873116545379162,
0.0013688842300325632,
0.013929123058915138,
-0.024467259645462036,
0.004247714299708605,
0.03370830789208412,
-0.01600182242691517,
0.00316778221167624,
-0.012610777281224728,
0.02689792960882187,
-0.009713764302432537,
0.016863897442817688,
0.02714644931256771,
-0.0075760758481919765,
0.006520057562738657,
-0.012185400351881981,
-0.050957269966602325,
-0.017961502075195312,
-0.015820538625121117,
0.0016398889711126685,
-0.003087508026510477,
-0.1051136702299118,
-0.006053047254681587,
-0.03420752286911011,
-0.014772742055356503,
0.07568864524364471,
0.01681562326848507,
-0.028243253007531166,
0.0374203585088253,
-0.036287304013967514,
-0.027755174785852432,
-0.03258974850177765,
0.0049083177000284195,
0.008746345527470112,
-0.051334355026483536,
-0.020031381398439407,
0.071528360247612,
-0.011584287509322166,
-0.027167802676558495,
-0.01748543791472912,
-0.030065016821026802,
0.0018478274578228593,
-0.022253675386309624,
0.011275445111095905,
0.011728699319064617,
0.02794581837952137,
0.0077682798728346825,
-0.016364093869924545,
-0.03574695810675621,
0.028630640357732773,
-0.04247418791055679,
0.014989473856985569,
0.017944790422916412,
-0.006291361525654793,
0.07788330316543579,
-0.04445379227399826,
-0.008534383960068226,
0.0811360627412796,
0.0034856938291341066,
-0.03276209160685539,
-0.03840098902583122,
-0.014077971689403057,
-0.01798410527408123,
-0.043030645698308945,
-0.01552659459412098,
0.03735752031207085,
-0.020568836480379105,
-0.0019465599907562137,
0.02663063071668148,
0.016446154564619064,
0.01650751195847988,
-0.0040727839805185795,
-0.02648489736020565,
-0.010181047022342682,
-0.000049680435040500015,
-0.04149105027318001,
0.03810955584049225,
0.04624979570508003,
-0.036333050578832626,
0.018939092755317688,
-0.018379416316747665,
0.049292515963315964,
0.02226298116147518,
-0.08385257422924042,
0.037842851132154465,
0.010540573857724667,
0.01361900381743908,
0.030338669195771217,
0.000910895352717489,
-0.0020693005062639713,
-0.043574776500463486,
-0.027112381532788277,
0.009063946083188057,
0.052605040371418,
-0.0002486213343217969,
-0.004787799436599016,
0.02200859971344471,
0.024566112086176872,
-0.024565866217017174,
-0.027142401784658432,
-0.016066409647464752,
-0.008389784954488277,
0.007220583502203226,
-0.02378212660551071,
0.02932494319975376,
-0.018205540254712105,
-0.005774535238742828,
0.04487369582056999,
-0.00045156804844737053,
-0.028005536645650864,
0.01743936724960804,
-0.08945707231760025,
0.009858021512627602,
-0.017543643712997437,
0.044052403420209885,
-0.0088347801938653,
0.019115053117275238,
-0.010614092461764812,
0.006883401423692703,
0.0490584596991539,
-0.009645904414355755,
-0.1147317960858345,
0.0037422857712954283,
-0.03244980424642563,
-0.009089814499020576,
0.02051636204123497,
0.0009541676263324916,
-0.022380227223038673,
-0.015161187388002872,
-0.0030469985213130713,
0.038431111723184586,
0.008686600252985954,
-0.006608919706195593,
-0.016502534970641136,
-0.015301674604415894,
-0.06841540336608887,
0.022952580824494362,
0.0024489557836204767,
0.04860767349600792,
-0.006588194984942675,
0.010344683192670345,
-0.005831465590745211,
-0.0005054977373220026,
-0.003421628847718239,
-0.055966567248106,
0.001662241411395371,
0.013811229728162289,
0.04948360472917557,
-0.017328310757875443,
-0.01169041357934475,
0.004148942418396473,
-0.01886754110455513,
-0.0016745126340538263,
0.04438900575041771,
-0.005873895715922117,
0.060580071061849594,
-0.046752531081438065,
-0.028527405112981796,
-0.03653450310230255,
0.02510732039809227,
0.014331369660794735,
-0.035685475915670395,
0.05687518045306206,
-0.008915252983570099,
0.01381107047200203,
-0.02419099770486355,
0.03991130366921425,
0.04967289790511131,
0.012533372268080711,
-0.008332604542374611,
-0.014045554213225842,
-0.057784032076597214,
-0.02866237238049507,
-0.019572213292121887,
0.0024875961244106293,
0.029786469414830208,
-0.020415494218468666,
-0.04091830179095268,
-0.01502799428999424,
0.015876220539212227,
0.011015086434781551,
0.05768163874745369,
-0.06316306442022324,
0.04670136049389839,
-0.0356929711997509,
-0.0019846369978040457,
-0.006998453754931688,
0.012413416989147663,
0.005906987935304642,
-0.0177431832998991,
-0.013464011251926422,
-0.06957457959651947,
-0.01479252427816391,
0.06206579506397247,
0.03931249678134918,
-0.012568805366754532,
0.014688300900161266,
-0.02755015157163143,
-0.009801281616091728,
0.03521145507693291,
-0.042373280972242355,
0.040872447192668915,
-0.025447221472859383,
0.01660844124853611,
-0.029411528259515762,
0.003263938706368208,
-0.012135165743529797,
0.018502580001950264,
-0.01600610837340355,
0.028237590566277504,
-0.01858089119195938,
-0.008220283314585686,
0.002811374142765999,
0.0005293028661981225,
0.03310302272439003,
0.023632172495126724,
0.022693686187267303,
-0.026812702417373657,
0.014222326688468456,
-0.007688462268561125,
-0.029716558754444122,
-0.08625581115484238,
0.007358168251812458,
0.028491023927927017,
-0.03174278885126114,
-0.003471472067758441,
-0.048220444470644,
-0.051939014345407486,
0.013962685130536556,
-0.02547537349164486,
-0.021059373393654823,
-0.007505154237151146,
-0.07226520031690598,
0.022396039217710495,
0.034047093242406845,
-0.005203144159168005,
-0.04289616644382477,
0.06470879167318344,
-0.022188197821378708,
0.012007292360067368,
-0.0006188966799527407,
0.02183331735432148,
0.026645507663488388,
0.010990113951265812,
-0.0678010880947113,
0.03379363566637039,
-0.035430796444416046,
0.015696002170443535,
0.0011575043899938464,
0.026111185550689697,
-0.03480293229222298,
-0.037885863333940506,
-0.009547614492475986,
0.040510393679142,
0.006251123268157244,
-0.020336376503109932,
-0.01937994360923767,
-0.022462818771600723,
-0.026499178260564804,
-0.03880435228347778,
0.02790229395031929,
0.014027666300535202,
0.025626985356211662,
0.003296557115390897,
-0.0007955858600325882,
0.022285539656877518,
-0.029359491541981697,
-0.0020842133089900017,
0.010060308501124382,
-0.051085423678159714,
0.082218237221241,
0.001636186265386641,
0.016194067895412445,
0.03329731151461601,
-0.038591984659433365,
-0.014983728528022766,
0.022000808268785477,
-0.023445436730980873,
0.009529652073979378,
-0.051681436598300934,
0.04646909981966019,
-0.015452126041054726,
0.004374276846647263,
-0.014210107736289501,
-0.04530724883079529,
0.027605241164565086,
0.01901501789689064,
0.028974423184990883,
-0.01960347220301628,
-0.03277445212006569,
-0.020269744098186493,
-0.04373769462108612,
-0.023504633456468582,
0.036818165332078934,
-0.002049661474302411,
0.021203061565756798,
0.04074473679065704,
-0.0316535159945488,
0.11547470092773438,
0.021042563021183014,
-0.024431800469756126,
0.028815899044275284,
-0.0439603254199028,
-0.010833627544343472,
-0.0093254828825593,
0.0353500097990036,
-0.032017823308706284,
-0.023067407310009003,
0.01632608473300934,
0.04347691312432289,
0.04013312980532646,
-0.0032598336692899466,
0.04777880758047104,
0.03962772712111473,
0.03842407464981079,
-0.03330191224813461,
-0.009874539449810982,
0.0444747656583786,
-0.02450290322303772,
0.00145831354893744,
-0.014516105875372887,
0.032381221652030945,
-0.03881495073437691,
-0.05137837305665016,
0.018382500857114792,
-0.004414089024066925,
0.006412125192582607,
-0.022783534601330757,
0.04519559442996979,
-0.026479262858629227,
-0.042498525232076645,
0.03164585679769516,
-0.04412165284156799,
0.0684797540307045,
0.060174766927957535,
0.009806283749639988,
0.00840399693697691,
-0.006093128584325314,
0.02979312837123871,
-0.0321565717458725,
0.0006591707351617515,
-0.004379506688565016,
0.026760082691907883,
-0.046657513827085495,
0.03601246699690819,
0.02305697649717331,
-0.028764599934220314,
-0.0030011485796421766,
0.03893927484750748,
-0.009991158731281757,
-0.008101126179099083,
0.01864430494606495,
0.014574897475540638,
-0.012434206902980804,
-0.013799364678561687,
0.014705618843436241,
0.022067733108997345,
0.033068060874938965,
-0.02997584268450737,
0.04069430008530617,
0.010352162644267082,
0.017242558300495148,
-0.022221365943551064,
-0.02729816362261772,
-0.004840944893658161,
0.009043782949447632,
0.08131828159093857,
-0.012593609280884266,
0.033721283078193665,
0.07798066735267639,
0.00079378392547369,
0.004373686388134956,
-0.03509937971830368,
0.008636514656245708,
-0.057749565690755844,
0.004051797557622194,
0.027243437245488167,
-0.021143006160855293,
-0.008961819112300873,
0.007870301604270935,
0.0022471717093139887,
-0.015890011563897133,
0.017235949635505676,
-0.09618942439556122,
-0.07360118627548218,
-0.007462047040462494,
-0.015099944546818733,
-0.03334052115678787,
0.042568713426589966,
0.00825612060725689,
-0.02887178771197796,
0.02605128102004528,
-0.013218921609222889,
0.014799010939896107,
0.04256685450673103,
0.06600572913885117,
0.026281069964170456,
0.08608783781528473,
-0.03004978969693184,
-0.0046667978167533875,
-0.003577031195163727,
-0.00995905976742506,
0.1266395002603531,
0.0017608158523216844,
-0.0038645050954073668,
-0.004120745696127415,
0.00738590769469738,
-0.03546295315027237,
0.0020360436756163836,
-0.0038369728717952967,
-0.005357632879167795,
0.005741228815168142,
0.028651442378759384,
0.01663217321038246,
0.021549716591835022,
-0.04260096326470375,
-0.030284635722637177,
0.027414416894316673,
-0.023237720131874084,
-0.0029873521998524666,
-0.034235287457704544,
0.02228480949997902,
-0.00344346696510911,
0.011812837794423103,
-0.05105625092983246,
0.0025881691835820675,
0.008459838107228279,
0.011451168917119503,
0.0026864479295909405,
-0.047976892441511154,
0.03171231970191002,
0.010386585257947445,
0.0094981100410223,
0.0361093170940876,
0.013036846183240414,
-0.019909361377358437,
-0.0251846332103014,
0.012525178492069244,
0.0036775032058358192,
0.0017295993166044354,
0.0014012738829478621,
0.07107323408126831,
0.01750999689102173,
-0.007165160030126572,
0.025549164041876793,
0.030961330980062485,
-0.011738227680325508,
0.011493011377751827,
-0.031557388603687286,
0.023501478135585785,
-0.025521470233798027,
-0.014364974573254585,
0.007928215898573399,
0.03346507251262665,
-0.009394301101565361,
-0.05936715379357338,
-0.013511067256331444,
-0.006893910933285952,
0.04242577403783798,
-0.022764094173908234,
-0.021499378606677055,
0.014698725193738937,
-0.002584627363830805,
0.0023416271433234215,
-0.014160559512674809,
0.012204833328723907,
0.00795662309974432,
-0.028136879205703735,
-0.045156192034482956,
0.04644322022795677,
0.027236174792051315,
-0.04257119446992874,
-0.008701778016984463,
0.0033986251801252365,
-0.023714564740657806,
0.030263828113675117,
-0.020105252042412758,
0.01923786662518978,
-0.018577665090560913,
0.006936077028512955,
-0.021474305540323257,
0.010496936738491058,
0.007860375568270683,
0.04137231409549713,
0.004589845892041922,
0.003136818530037999,
-0.023270385339856148,
0.013440718874335289,
0.022652359679341316,
0.001841841614805162,
-0.03402065113186836,
0.018081946298480034,
-0.009260245598852634,
0.03508216142654419,
0.02075958251953125,
-0.03548378124833107,
-0.014643857255578041,
0.01641807146370411,
-0.03182099387049675,
0.03629988431930542,
0.029707500711083412,
0.07575024664402008,
-0.006831769831478596,
-0.03006185218691826,
-0.01385555136948824,
0.015274020843207836,
0.013162746094167233,
0.014758007600903511,
0.008816705085337162,
-0.03243312984704971,
-0.026052165776491165,
-0.006440160796046257,
0.0008246373618021607,
-0.03103419952094555,
-0.018582956865429878,
-0.05128391832113266,
-0.05327831581234932,
-0.028814448043704033,
0.022927233949303627,
0.010175234638154507,
0.026184145361185074,
-0.04187099635601044,
0.04626022279262543,
-0.032967403531074524,
0.03641895949840546,
-0.010570685379207134,
-0.009761380031704903,
0.035515688359737396,
0.0156352948397398,
-0.022853033617138863,
0.023210471495985985,
-0.004454347304999828,
-0.016963128000497818,
-0.00012252737360540777,
0.007151884958148003,
0.005991464480757713,
-0.02039908990263939,
0.00024437805404886603,
0.03960176557302475,
0.06232011318206787,
-0.024729788303375244,
-0.02705349400639534,
0.044198475778102875,
0.010200073942542076,
-0.022060556337237358,
-0.021137427538633347,
-0.065731942653656,
0.025149263441562653,
-0.02782183140516281,
-0.01766054891049862,
-0.013416558504104614,
0.08773691952228546,
-0.0455537773668766,
0.0025975352618843317,
0.005711851175874472,
-0.013381702825427055,
0.0035509252920746803,
-0.03144437447190285,
0.007557936944067478,
-0.036719709634780884,
-0.010854762978851795,
0.0069742146879434586,
0.050473861396312714,
-0.018691400066018105,
0.01370294764637947,
-0.011126170866191387,
-0.00014830967120360583,
-0.029855474829673767,
-0.00230566062964499,
0.0031940448097884655,
0.03360656648874283,
0.03086932748556137,
-0.0362342968583107,
0.017115412279963493,
-0.04218541458249092,
0.004685963504016399,
-0.07676582038402557,
-0.005139263812452555,
0.0016031158156692982,
-0.01382619421929121,
0.03690941631793976,
-0.0397157296538353,
0.02764110639691353,
-0.006348807364702225,
-0.023281747475266457,
0.026784440502524376,
-0.01784573681652546,
-0.046788427978754044,
-0.047903627157211304,
-0.054878804832696915,
-0.022906983271241188,
0.040269635617733,
-0.007960771210491657,
0.03751405328512192,
-0.01374019030481577,
0.04268161207437515,
-0.013261540792882442,
-0.024189883843064308,
0.04031428322196007,
0.025600489228963852,
0.0037240542005747557,
0.015102571807801723,
0.05711932107806206,
-0.033050745725631714,
0.012175105512142181,
0.019702915102243423,
-0.02949538826942444,
0.01911223493516445,
-0.013333008624613285,
-0.01584765315055847,
-0.05105722323060036,
0.014271833002567291,
0.011563325300812721,
-0.00331275537610054,
-0.00961930863559246,
0.04139016196131706,
-0.007428552955389023,
0.01733607053756714,
-0.012643903493881226,
0.023373709991574287,
0.02540854550898075,
-0.010259246453642845,
-0.043675098568201065,
0.03309442475438118,
-0.02340002730488777,
0.010581142269074917,
-0.0011797058396041393,
-0.02915564738214016,
0.02020861953496933,
-0.027437547221779823,
-0.08532700687646866,
-0.001017840811982751,
0.0162487905472517,
0.009716133587062359,
-0.01910213753581047,
-0.008750487118959427,
0.026811698451638222,
-0.012971012853085995,
0.00026001682272180915,
-0.052769992500543594,
-0.047192227095365524,
-0.040113650262355804,
-0.028731398284435272,
0.02333979122340679,
0.023599719628691673,
0.0069024330005049706,
0.0024352327454835176,
-0.021971743553876877,
-0.002676574280485511,
0.04743744432926178,
0.017826680094003677,
-0.025557853281497955,
0.008887692354619503,
0.025746755301952362,
0.025434458628296852,
-0.04740366339683533,
0.012145726010203362,
0.010637504048645496,
-0.027593890205025673,
-0.020229393616318703,
-0.035667888820171356,
0.03884106129407883,
0.02222573012113571,
0.03982783108949661,
-0.040830839425325394,
-0.03541979566216469,
0.01973084732890129,
0.01125134713947773,
-0.022240228950977325,
0.0012018937850371003,
0.024750899523496628,
0.012398173101246357,
-0.010200856253504753,
-0.009117649868130684,
0.014538523741066456,
-0.015180756337940693,
-0.014197283424437046,
0.05386519432067871,
0.03207162395119667,
0.002801822731271386,
-0.01058083213865757,
-0.02497337944805622,
-0.017142804339528084,
0.007068203762173653,
-0.009617656469345093,
0.04657101258635521,
0.008893840946257114,
0.00015961081953719258,
-0.005901535041630268,
-0.007796861696988344,
-0.03989487141370773,
0.05496399849653244,
-0.0269724540412426,
0.019941089674830437,
-0.00708348723128438,
-0.04072299972176552,
0.05167084559798241,
-0.041716355830430984,
0.018561959266662598,
0.0044948989525437355,
-0.016459036618471146,
-0.021870922297239304,
0.010440967977046967,
0.03494375944137573,
0.045148950070142746,
-0.028751032426953316,
-0.005373403895646334,
0.0009188817348331213,
-0.05356647074222565,
-0.012722414918243885,
0.002464765915647149,
0.022220823913812637,
0.02390744350850582,
-0.012778123840689659,
0.061756838113069534,
0.02915179170668125,
0.05410749465227127,
0.03325033560395241,
0.03606630116701126,
0.015271139331161976,
0.011080384254455566,
0.006138392258435488,
-0.023079650476574898,
0.0009886270854622126,
0.02027074806392193,
-0.006585765164345503,
0.0679965391755104,
0.006157275754958391,
-0.017790231853723526,
-0.02519717812538147,
0.011803604662418365,
-0.011580373160541058,
0.006680076010525227,
-0.0026048931758850813,
0.03671687841415405,
-0.0204056054353714,
-0.040615301579236984,
0.00820073951035738,
0.008731629699468613,
0.04485168680548668,
0.038969334214925766,
0.04514794424176216,
-0.06652066111564636,
0.0023147850297391415,
0.00939522311091423,
-0.011638187803328037,
-0.01261973287910223,
-0.011184440925717354,
0.04288104549050331,
0.04628315195441246,
0.0003438465064391494,
-0.04395296424627304,
-0.02529134787619114,
0.009043342433869839,
0.06834854930639267,
-0.019528139382600784,
-0.0009374426444992423,
-0.032074131071567535,
0.00381346233189106,
-0.01093896385282278,
0.010812213644385338
] |
<p>When <code>taxpayers</code> pay <code>money</code> for expensive research (irrespective of the <code>partition-function</code> wheither a few projects worth <code>megabucks</code> [<code>M$</code>] or many smaller cheaper experiments), should the <code>raw data</code>/<code>designs</code>/... that result from it be <code>gratis</code> (as in linux), <code>opensource</code> (as in the source of beer) or even licensefree?</p>
<p>(the question is not intended as a binary one: it is more ethics of modern physics funding, assume it is possible)</p>
<p>this would also more easily allow people with or without diplomes to try processing the scientific data...</p>
<p>(<code>upvotes</code> if you can present your argument <code>completely formalized</code> in <code>deontologic</code> <code>Kripke semantics</code>)</p> | 4,557 | [
-0.01777404546737671,
-0.026090655475854874,
-0.01637612096965313,
-0.009703632444143295,
0.021709369495511055,
0.006242191419005394,
-0.007428134325891733,
-0.020838910713791847,
-0.00016928129480220377,
-0.01726003736257553,
0.05978383123874664,
0.021612482145428658,
0.009490562602877617,
0.03274988755583763,
0.006817768793553114,
0.009130191057920456,
0.005818929523229599,
-0.004551904741674662,
0.004754472523927689,
-0.025648750364780426,
0.022865917533636093,
0.015538615174591541,
0.0037439726293087006,
0.009894641116261482,
-0.04508098587393761,
0.03288476541638374,
0.006823369767516851,
0.010249044746160507,
-0.0033355720806866884,
0.06746410578489304,
-0.02833796665072441,
-0.03945329040288925,
0.02863897942006588,
0.01050329115241766,
0.005405943375080824,
0.02227282151579857,
-0.042290639132261276,
0.0021073182579129934,
0.027278326451778412,
-0.029412509873509407,
-0.02052224799990654,
-0.0067420946434140205,
-0.013674234971404076,
-0.0019739381968975067,
0.00540607376024127,
0.018179329112172127,
0.008063212037086487,
0.018213069066405296,
-0.010189143940806389,
-0.023012448102235794,
0.039680663496255875,
0.00430785957723856,
0.03837209567427635,
-0.019609954208135605,
-0.014719575643539429,
-0.009250001050531864,
0.03912322223186493,
0.10952870547771454,
0.02977677248418331,
-0.037062615156173706,
0.0009270994924008846,
0.007668514735996723,
0.010116750374436378,
0.016235869377851486,
-0.029833728447556496,
0.023691654205322266,
-0.028362100943922997,
0.03979115188121796,
0.01844753883779049,
-0.013382382690906525,
0.02481718175113201,
0.006734033580869436,
0.011122038587927818,
-0.01659059338271618,
0.01914764568209648,
0.020095419138669968,
-0.021792609244585037,
-0.007273528724908829,
0.017236584797501564,
0.053323205560445786,
-0.010154049843549728,
-0.00699023250490427,
0.027652308344841003,
0.06611485034227371,
0.021841520443558693,
-0.024181466549634933,
0.06670448184013367,
-0.037639517337083817,
-0.003300544572994113,
0.007446723524481058,
0.0243658646941185,
-0.045323945581912994,
0.057721033692359924,
0.016968118026852608,
-0.04722033441066742,
0.024664292111992836,
0.020022833719849586,
0.04925645887851715,
-0.030225833877921104,
-0.03929990157485008,
-0.003564717248082161,
-0.003022767836228013,
-0.012501807883381844,
0.05578039959073067,
-0.008397536352276802,
-0.03666073456406593,
-0.008726797997951508,
0.018999235704541206,
-0.0016304460586979985,
-0.03175300732254982,
-0.02770659327507019,
0.021562254056334496,
-0.008364342153072357,
-0.005545928608626127,
0.022348014637827873,
-0.06438925117254257,
-0.0003965955402236432,
-0.02434041164815426,
0.06616522371768951,
0.055300645530223846,
0.06815047562122345,
0.004444838967174292,
0.032628383487463,
-0.027252594009041786,
-0.05933006852865219,
0.02062303200364113,
0.028280362486839294,
-0.03346864879131317,
-0.023487141355872154,
0.012972834520041943,
-0.010674976743757725,
-0.024428319185972214,
0.02729610726237297,
-0.004408346023410559,
0.03870120272040367,
-0.015498299151659012,
-0.09763304144144058,
-0.061998557299375534,
0.04463649541139603,
0.037005044519901276,
-0.04107080027461052,
-0.0669403225183487,
0.02719697915017605,
-0.02205556631088257,
0.05851392075419426,
0.013837910257279873,
0.007759463042020798,
0.0047908625565469265,
0.06070517748594284,
0.0193309523165226,
0.019180607050657272,
-0.001656492706388235,
-0.013149942271411419,
-0.03565295413136482,
-0.020891666412353516,
-0.03476715087890625,
-0.009722835384309292,
0.029839469119906425,
-0.024546857923269272,
-0.002419463824480772,
0.03168677166104317,
-0.001005851780064404,
-0.00988627690821886,
-0.034396976232528687,
-0.015286811627447605,
-0.030386433005332947,
0.05664520338177681,
0.022611089050769806,
0.07428243011236191,
0.01482758205384016,
-0.02644883282482624,
0.027706438675522804,
-0.03738122060894966,
0.001833246904425323,
0.01760854199528694,
-0.039640072733163834,
0.0031684685964137316,
-0.011281135492026806,
0.023861179128289223,
-0.02928709238767624,
-0.007225369103252888,
-0.016737954691052437,
-0.021123431622982025,
0.00820892583578825,
0.025840388610959053,
0.022856706753373146,
0.0312331672757864,
0.0010776256676763296,
0.03261570632457733,
-0.06774072349071503,
-0.02491411566734314,
-0.07416489720344543,
0.015384028665721416,
-0.021270575001835823,
-0.0027424306608736515,
0.0008344862726517022,
-0.02496960759162903,
-0.000620280101429671,
-0.009479111060500145,
-0.021010393276810646,
0.042999934405088425,
0.0463203564286232,
0.04376737400889397,
0.02028244361281395,
-0.007632466498762369,
0.05951826646924019,
0.009732317179441452,
-0.017746848985552788,
0.028378669172525406,
0.03238045051693916,
-0.06811247766017914,
0.0014268963132053614,
-0.04467849060893059,
0.004703081212937832,
0.0028534026350826025,
0.029261700809001923,
0.02808908000588417,
0.020071569830179214,
0.005851068999618292,
0.004084628075361252,
-0.05311587452888489,
0.1025567352771759,
0.04653818905353546,
0.020236600190401077,
0.0018476479453966022,
0.026665838435292244,
-0.017078546807169914,
0.024311423301696777,
-0.00858262088149786,
0.005985446274280548,
-0.05279713496565819,
0.017316997051239014,
0.046077385544776917,
0.036891791969537735,
-0.03962603956460953,
0.059613343328237534,
0.029608923941850662,
0.022981736809015274,
0.014743847772479057,
-0.0168379507958889,
-0.03660784289240837,
-0.022645726799964905,
0.06718966364860535,
-0.025991803035140038,
-0.00742766447365284,
0.022864332422614098,
0.002790976082906127,
-0.004864450544118881,
0.011765135452151299,
0.0034131251741200686,
0.038697440177202225,
0.016138989478349686,
0.013675154186785221,
-0.0057687717489898205,
0.00856079813092947,
-0.030473092570900917,
0.029190242290496826,
-0.006779700983315706,
0.02714945748448372,
0.019403813406825066,
-0.01173656340688467,
0.018051445484161377,
-0.006186216603964567,
-0.02532322332262993,
-0.01820630021393299,
0.016551584005355835,
-0.03193656727671623,
0.0018445305759087205,
0.044163621962070465,
-0.010071820579469204,
0.00042292129364795983,
-0.02368377335369587,
-0.015253462828695774,
-0.047127824276685715,
0.012229513376951218,
0.013538206927478313,
-0.009531127288937569,
0.0007679780246689916,
-0.02764892578125,
0.005895827431231737,
-0.008047877810895443,
-0.012253735214471817,
0.0023943930864334106,
0.018305644392967224,
-0.060693301260471344,
0.009765155613422394,
-0.013845527544617653,
-0.03784957155585289,
0.023527219891548157,
0.023548927158117294,
0.009583250619471073,
-0.009104869328439236,
0.0033931939397007227,
-0.027420775964856148,
-0.007282673846930265,
-0.019024383276700974,
-0.032863497734069824,
-0.03618820384144783,
0.00029020741931162775,
0.042928121984004974,
0.009436114691197872,
-0.04661773145198822,
0.0036144836340099573,
-0.017278997227549553,
-0.04724285751581192,
0.010543775744736195,
-0.016624175012111664,
0.013212247751653194,
-0.023808253929018974,
0.026463352143764496,
0.008222182281315327,
-0.05725465342402458,
-0.027914369478821754,
-0.08778145164251328,
-0.08633363991975784,
0.015271996147930622,
-0.009019712917506695,
0.027328643947839737,
0.045027393847703934,
-0.003068272490054369,
0.0526905432343483,
0.04714128375053406,
-0.03075222484767437,
-0.005716504994779825,
-0.03608439862728119,
0.0021976304706186056,
-0.019153300672769547,
0.012487747706472874,
-0.0025504163932055235,
-0.006199372000992298,
-0.011931954883038998,
0.03587864339351654,
0.04061422497034073,
0.00962359830737114,
-0.007563689257949591,
-0.024211496114730835,
0.003999543841928244,
0.017671937122941017,
-0.03657662868499756,
0.061492811888456345,
0.009362188167870045,
-0.03141840547323227,
0.006388675421476364,
-0.0100741321220994,
0.014258104376494884,
0.04381183907389641,
-0.06001335009932518,
0.03358488902449608,
0.01880541630089283,
0.00680127926170826,
-0.01878555864095688,
0.03867414593696594,
0.013059303164482117,
-0.04136800393462181,
0.02099706046283245,
0.03666257858276367,
0.003987263888120651,
0.004980410914868116,
0.022346628829836845,
0.018701976165175438,
0.08380116522312164,
-0.025002116337418556,
-0.03180551156401634,
0.0002945449377875775,
0.005441340617835522,
0.017609450966119766,
-0.020468618720769882,
-0.0021293219178915024,
0.024228624999523163,
0.0342179499566555,
0.013730020262300968,
-0.009007474407553673,
-0.036743007600307465,
-0.037551552057266235,
-0.09731754660606384,
-0.0019508107798174024,
-0.03135739266872406,
0.0833955705165863,
0.010298102162778378,
0.06086748093366623,
0.022314948961138725,
-0.01924005150794983,
-0.0636187493801117,
0.005544729996472597,
-0.07389577478170395,
0.00960389431566,
-0.0015998585149645805,
0.026847822591662407,
-0.006154149770736694,
-0.006198334041982889,
-0.013898301869630814,
-0.01589750498533249,
-0.00713669927790761,
0.001960426801815629,
0.011613065376877785,
-0.06564367562532425,
-0.011549854651093483,
-0.02644764445722103,
-0.015100459568202496,
0.023335866630077362,
0.006791183724999428,
0.0321761779487133,
0.0021600869949907064,
0.012956731021404266,
0.00926185492426157,
-0.020136652514338493,
-0.039858948439359665,
0.008844496682286263,
0.028072552755475044,
0.002238218206912279,
0.06250929832458496,
0.003678926033899188,
0.0009403826552443206,
-0.026099540293216705,
-0.00021052703959867358,
0.005623207427561283,
0.0359174944460392,
0.0021432433277368546,
-0.024617524817585945,
-0.002571792108938098,
-0.06225227564573288,
-0.03406773507595062,
0.00675643514841795,
0.016265660524368286,
0.0049912515096366405,
-0.00272046634927392,
0.02361288294196129,
0.011728418990969658,
-0.029097717255353928,
0.045396991074085236,
0.08713146299123764,
-0.01483583077788353,
-0.008137435652315617,
0.004986052867025137,
-0.053113874047994614,
-0.025640316307544708,
0.007997669279575348,
0.005461215507239103,
0.053921062499284744,
-0.004181578289717436,
0.013328070752322674,
-0.007355721667408943,
0.0035615882370620966,
-0.00953261461108923,
0.02744511142373085,
0.012350214645266533,
0.04594740644097328,
-0.009922260418534279,
0.0047728498466312885,
-0.005166931077837944,
0.062801793217659,
0.03480882570147514,
0.0436534658074379,
-0.014246651902794838,
-0.07880911231040955,
0.0009929274674504995,
0.05417437478899956,
0.04875265061855316,
-0.003075388725847006,
-0.022007834166288376,
-0.05943528190255165,
-0.0021569605451077223,
0.024931764230132103,
-0.028904790058732033,
0.014870891347527504,
-0.036239705979824066,
0.020547449588775635,
0.00040148920379579067,
-0.0021838010288774967,
-0.03187020123004913,
0.0014988766051828861,
-0.016821840777993202,
0.03786151483654976,
-0.033404380083084106,
-0.028366491198539734,
-0.035897936671972275,
0.04757101833820343,
0.01819767616689205,
0.02543570287525654,
-0.02987603284418583,
-0.02456693723797798,
-0.025596996769309044,
-0.00017154106171801686,
-0.06383451074361801,
-0.06426920741796494,
-0.015220106579363346,
-0.025803500786423683,
0.0233147069811821,
0.0382552333176136,
-0.011268815025687218,
-0.0511464960873127,
0.019329801201820374,
0.0018220430938526988,
-0.02269299142062664,
0.030722610652446747,
-0.01662469655275345,
0.049200545996427536,
0.029050851240754128,
0.044919926673173904,
0.04931970313191414,
0.08171668648719788,
-0.025216378271579742,
0.01665486954152584,
-0.03181999549269676,
-0.04406546801328659,
-0.03245733678340912,
0.003663880517706275,
-0.02907804772257805,
-0.020359685644507408,
-0.044281940907239914,
0.005707872565835714,
-0.014512909576296806,
0.006462999153882265,
-0.029086090624332428,
-0.02935440093278885,
-0.029367800801992416,
0.0187773946672678,
-0.027520503848791122,
-0.0420914851129055,
-0.01598248817026615,
0.02847016230225563,
-0.005512209143489599,
-0.004551324062049389,
0.025028031319379807,
-0.010980016551911831,
0.008530618622899055,
-0.020314984023571014,
-0.059372156858444214,
0.02864271216094494,
-0.019542066380381584,
0.00025434463168494403,
0.011134203523397446,
-0.013702873140573502,
0.03414073586463928,
-0.010937693528831005,
0.03999132290482521,
0.04418088123202324,
-0.07103840261697769,
-0.006225319113582373,
0.018676800653338432,
0.0006243048701435328,
-0.02512618713080883,
-0.03701335936784744,
0.030496696010231972,
-0.019616737961769104,
0.03320399671792984,
-0.07044218480587006,
-0.013122699223458767,
0.03417077288031578,
-0.021237393841147423,
-0.01369596179574728,
-0.03727283701300621,
-0.011343699879944324,
-0.02316383458673954,
-0.024191809818148613,
-0.00801320094615221,
0.0702933818101883,
-0.06407881528139114,
-0.006262024398893118,
-0.016225900501012802,
0.003818334313109517,
0.07467859983444214,
-0.03150945156812668,
0.022554030641913414,
-0.00019234807405155152,
0.0052434843964874744,
-0.005982150789350271,
0.01227700337767601,
-0.01586126908659935,
-0.0149461068212986,
-0.03824877366423607,
-0.022300323471426964,
-0.021103492006659508,
0.003126829396933317,
0.006811364553868771,
0.0006319002131931484,
0.016040004789829254,
-0.028273144736886024,
-0.008020805194973946,
-0.015972040593624115,
0.034949686378240585,
0.010734698735177517,
0.001605298137292266,
-0.019099051132798195,
-0.05122467502951622,
-0.011385321617126465,
-0.03351530060172081,
0.006166309118270874,
0.025191262364387512,
-0.0144226448610425,
0.02703762799501419,
0.059676311910152435,
-0.008919097483158112,
-0.01925557479262352,
0.027520345523953438,
-0.01877397857606411,
0.034176189452409744,
-0.02599022164940834,
-0.001920197275467217,
-0.0024142912589013577,
0.020547546446323395,
-0.017998870462179184,
-0.010716360993683338,
-0.044278524816036224,
-0.028967518359422684,
0.044618941843509674,
0.01984425075352192,
0.03570869192481041,
0.016569046303629875,
-0.025517066940665245,
0.00603569345548749,
-0.006298534106463194,
0.010019335895776749,
-0.015191762708127499,
0.025606907904148102,
0.018671391531825066,
-0.02496814914047718,
-0.03886103630065918,
0.023566653952002525,
-0.0017395967151969671,
-0.015066037885844707,
0.013451472856104374,
0.015548103488981724,
0.008997532539069653,
0.011942042969167233,
-0.08286165446043015,
-0.04591658338904381,
0.03160933405160904,
-0.09336497634649277,
0.028026506304740906,
0.013281404972076416,
-0.046779341995716095,
0.04078003019094467,
0.012992543168365955,
0.016492819413542747,
-0.03086966462433338,
0.019570449367165565,
-0.06572411209344864,
0.001340816612355411,
0.03560382127761841,
-0.01796719618141651,
0.005799992475658655,
-0.01601303368806839,
0.008833461441099644,
0.008047079667448997,
-0.0017960038967430592,
-0.01661980338394642,
-0.055924490094184875,
-0.045367296785116196,
-0.030028164386749268,
-0.06217348575592041,
0.08583682775497437,
0.039806969463825226,
-0.004346380475908518,
0.026265623047947884,
-0.031900808215141296,
0.054614171385765076,
0.0590226836502552,
0.043655361980199814,
-0.03752155601978302,
0.06742861121892929,
-0.0417901985347271,
0.01953868195414543,
-0.04325640946626663,
0.004423119127750397,
0.1385347694158554,
0.03989294543862343,
0.04931691661477089,
-0.030109843239188194,
0.052222803235054016,
0.024608584120869637,
0.04418221488595009,
0.027835970744490623,
-0.0019176403293386102,
0.013618607074022293,
0.00308015919290483,
0.06611134856939316,
0.023788083344697952,
0.007741427514702082,
0.05757846310734749,
0.05840422585606575,
-0.04360973834991455,
-0.02030019648373127,
0.025529097765684128,
0.04750971496105194,
0.023663979023694992,
0.0006987865781411529,
-0.051556218415498734,
-0.01011506374925375,
-0.000893979799002409,
-0.016609685495495796,
-0.004802334122359753,
-0.0436149537563324,
0.008639258332550526,
0.010932614095509052,
-0.026435814797878265,
-0.003563432488590479,
-0.0016565292607992887,
-0.0037977248430252075,
-0.03064052015542984,
-0.010010363534092903,
0.011681715026497841,
-0.02110334485769272,
0.013766761869192123,
0.055586010217666626,
0.0488705188035965,
-0.0020321719348430634,
-0.03569336235523224,
0.010269316844642162,
-0.043818630278110504,
0.01319718174636364,
-0.005246334243565798,
0.0324648879468441,
-0.06417495012283325,
-0.03598155453801155,
-0.005588221363723278,
0.006472025066614151,
-0.00752447172999382,
-0.03461497649550438,
-0.04493125155568123,
0.030252959579229355,
-0.00005339905328582972,
0.012284825555980206,
-0.02644798718392849,
0.019620144739747047,
0.03112439624965191,
-0.029761848971247673,
0.0064472416415810585,
-0.02201100066304207,
-0.005077152047306299,
-0.0192978847771883,
0.010416426695883274,
0.019053172320127487,
0.010623317211866379,
0.001417070860043168,
-0.03202797845005989,
-0.014767199754714966,
-0.037244901061058044,
-0.025759365409612656,
0.0012460729340091348,
0.010855578817427158,
-0.018193120136857033,
-0.017097920179367065,
0.01944780722260475,
-0.008725816383957863,
0.006551489699631929,
0.03490101173520088,
-0.028089841827750206,
-0.018450269475579262,
-0.043924588710069656,
-0.01717524603009224,
-0.0077472347766160965,
0.015606977045536041,
0.0066930977627635,
-0.019712038338184357,
0.060591284185647964,
0.03806239366531372,
-0.002306190552189946,
-0.03381045162677765,
-0.009976066648960114,
-0.019384171813726425,
-0.04281993955373764,
-0.006084331311285496,
0.009249878115952015,
0.03763166069984436,
0.009996362030506134,
0.01869029738008976,
-0.010959847830235958,
0.020594067871570587,
-0.000693619076628238,
0.02970779873430729,
0.02265642024576664,
-0.05658654868602753,
-0.04766540974378586,
0.01741359569132328,
0.030851639807224274,
-0.03425662964582443,
-0.02495919167995453,
-0.024460740387439728,
-0.017937788739800453,
0.013179758563637733,
-0.006008937489241362,
-0.03195777162909508,
0.01749582029879093,
-0.028665123507380486,
0.0126582570374012,
-0.018511593341827393,
0.02314302884042263,
-0.033915333449840546,
-0.04182527959346771,
-0.029654506593942642,
0.0011336279567331076,
0.04307582974433899,
0.030467381700873375,
-0.003807611297816038,
0.007684396114200354,
0.02124171331524849,
0.05081582069396973,
-0.029498497024178505,
0.01422165147960186,
0.03170212358236313,
0.026165449991822243,
-0.0031160551588982344,
-0.019423335790634155,
-0.024057677015662193,
0.010158170014619827,
-0.0510123111307621,
-0.029916688799858093,
-0.005822573788464069,
-0.031707409769296646,
0.04942408576607704,
-0.007437855005264282,
-0.02330782450735569,
-0.03838003799319267,
0.059056710451841354,
-0.024101635441184044,
-0.020689211785793304,
0.0477556474506855,
-0.009730415418744087,
0.03450654819607735,
0.007820678874850273,
0.019175611436367035,
-0.03959893807768822,
-0.0016100879292935133,
0.032183583825826645,
0.011542762629687786,
-0.0060080899856984615,
0.023214085027575493,
-0.00917617604136467,
0.025719113647937775,
-0.025915764272212982,
0.023682530969381332,
-0.01779494807124138,
-0.026539837941527367,
0.04123786836862564,
-0.06535430997610092,
0.024789869785308838,
-0.0005509428447112441,
0.019428454339504242,
-0.08453212678432465,
-0.006328926887363195,
0.010206455364823341,
0.0040405443869531155,
0.024685420095920563,
-0.02918819896876812,
0.0518372505903244,
0.02799200266599655,
-0.038479119539260864,
0.026642268523573875,
-0.035861674696207047,
-0.03646552935242653,
-0.05646287277340889,
0.03576222434639931,
-0.04267339035868645,
0.05799437686800957,
-0.0005573975504375994,
0.023984715342521667,
0.03493838012218475,
0.009116711094975471,
0.026968352496623993,
-0.011513461358845234,
-0.04373342916369438,
0.02069896273314953,
-0.027841808274388313,
-0.015337732620537281,
0.06629357486963272,
-0.02853420190513134,
-0.013257375918328762,
0.03591645136475563,
0.018806451931595802,
-0.0014659109292551875,
-0.017483951523900032,
0.007757578510791063,
0.012428279966115952,
0.03724862262606621,
0.03543639928102493,
0.009354798123240471,
0.0029731467366218567,
-0.001615342334844172,
0.03175124153494835,
0.03493636101484299,
0.0018163335043936968,
0.05184857174754143,
-0.00006212483276613057,
-0.00782883819192648,
0.0032331114634871483,
0.022996924817562103,
-0.0032131413463503122,
0.007874690927565098,
-0.017703287303447723,
0.0008121783612295985,
0.022873787209391594,
-0.057062819600105286,
0.0006132823182269931,
-0.051846347749233246,
0.03560164198279381,
0.0395188108086586,
-0.016058312729001045,
-0.0080792848020792,
0.007169704884290695,
-0.0038639178965240717,
-0.02318885736167431,
-0.018383339047431946,
0.02946677803993225,
0.00459060026332736,
-0.014007916674017906,
-0.006059042178094387,
0.005060994066298008,
0.028297720476984978,
-0.008171622641384602,
-0.040655605494976044,
-0.028326068073511124,
0.02475111559033394,
-0.013345629908144474,
0.016710180789232254,
-0.0066904546692967415,
-0.019152255728840828,
0.021275542676448822,
-0.08710075914859772,
0.021523235365748405,
0.018868910148739815,
0.016740363091230392,
-0.024580076336860657,
-0.022608589380979538,
-0.02462667226791382,
0.008535592816770077,
0.022929515689611435,
-0.015734553337097168,
-0.02385563589632511,
-0.02248937450349331,
-0.0426824688911438,
0.01317159365862608,
-0.019753962755203247,
0.02797260694205761,
-0.03452906012535095,
-0.0197316762059927,
-0.00770169124007225,
-0.020582448691129684,
-0.03693057596683502,
0.017395345494151115,
0.08069038391113281,
0.013095729984343052,
-0.006711997557431459,
0.012962603941559792,
-0.003848407417535782,
0.028383800759911537,
-0.03201279416680336,
0.0021040518768131733,
0.048604801297187805,
-0.013528511859476566,
0.03331689536571503,
0.0252128466963768,
-0.018179044127464294,
-0.04156186431646347,
0.03400026634335518,
-0.03535949066281319,
-0.04309254139661789,
-0.030709221959114075,
0.005922167561948299,
0.019962534308433533,
-0.05664656683802605,
0.010217724367976189,
0.036997150629758835,
-0.04515513405203819,
-0.016696905717253685,
0.03814225271344185,
0.02456166408956051,
0.035414308309555054,
0.026255110278725624,
0.05064545199275017,
-0.011960087344050407,
-0.02094890922307968,
-0.004723707213997841,
0.04929008334875107,
0.07999841123819351,
0.0003869853971991688,
0.04348677396774292,
0.04591257497668266,
0.015347461216151714,
0.028566719964146614,
0.012232670560479164,
0.08442103117704391,
-0.020619777962565422,
-0.010022610425949097,
0.041202861815690994,
-0.01040736585855484,
0.020535586401820183,
0.0007434028084389865,
0.008172613568603992,
0.07257768511772156,
0.01136456523090601,
-0.009618791751563549,
-0.047926463186740875,
-0.042474664747714996,
-0.0020335838198661804,
0.03403395414352417,
-0.002931129653006792,
0.057031434029340744,
-0.032315388321876526,
-0.019903844222426414,
-0.027002980932593346,
0.019828619435429573,
0.053920455276966095,
-0.02840683050453663,
0.03266877308487892,
0.018016647547483444,
-0.0015955354319885373,
0.02835717238485813,
-0.005163399502635002,
-0.002463187323883176,
-0.027764925733208656,
0.0498768649995327,
0.022412065416574478,
-0.007131113205105066,
-0.007304458878934383,
-0.014330952428281307,
-0.04158160835504532,
0.03767737001180649,
-0.03183772787451744,
-0.016230333596467972,
-0.0038609288167208433,
0.02463570050895214,
-0.024531390517950058,
0.02187967859208584
] |
<p>A <a href="http://en.wikipedia.org/wiki/Vortex_tube">Vortex Tube</a> takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. <a href="http://www.exair.com/Cultures/en-US/Primary+Navigation/Products/Vortex+Tubes+and+Spot+Cooling/Vortex+Tubes/A+Phenomenon+of+Physics">Apparently, it has been described as a Maxwell's Demon</a>.</p>
<p>Both linked sources are scarce with information about how and why this works. Now, I have two questions:</p>
<ul>
<li><p>Why does it work, specifically why should the situation in the vortex lead to a transfer of thermal energy from the inner stream to the outer one?</p></li>
<li><p>How efficient can it be? </p></li>
<li><p>How do you define the efficiency of a device that may be closer to Maxwell's Demon than to a heat pump? My feeling is that any analysis should not only take into account the sum of input energy (thermal and mechanical energy instream) and sum output (thermal energies and pressures of both gas streams), but also the Temperature differential that is created - since that contains an ability to create work.*</p></li>
<li><p>If course it's pointless to create heat from high grade 8mech.) energy to transform it back to mech. energy - but it gives an idea on the worth of the output.</p></li>
</ul> | 316 | [
-0.022903455421328545,
0.0030082538723945618,
-0.05531931668519974,
-0.048657383769750595,
0.048152584582567215,
0.014936111867427826,
-0.0370212160050869,
-0.005325406789779663,
-0.001510102767497301,
-0.005279889330267906,
0.014044567011296749,
0.01990460604429245,
0.03456606715917587,
-0.013786610215902328,
-0.007353013381361961,
0.02962273173034191,
0.013046333566308022,
-0.014518453739583492,
0.020993879064917564,
-0.035863786935806274,
-0.010883334092795849,
0.037481844425201416,
0.014278191141784191,
-0.000838528445456177,
-0.07737094908952713,
0.03220358118414879,
-0.004925900604575872,
-0.02380707859992981,
-0.010536395944654942,
0.013223552145063877,
-0.04110780358314514,
-0.022486083209514618,
0.024766065180301666,
0.005240833852440119,
0.01059645228087902,
-0.007084239274263382,
-0.07128853350877762,
-0.01196362730115652,
0.026984911412000656,
0.02740994282066822,
-0.015123878605663776,
0.0039057666435837746,
-0.015739144757390022,
0.027037344872951508,
-0.031748317182064056,
-0.005145966541022062,
-0.019812628626823425,
-0.02008303441107273,
0.039998508989810944,
-0.09683249890804291,
0.016440359875559807,
0.00999522302299738,
0.012642958201467991,
0.011125510558485985,
0.004729341249912977,
0.0015856147510930896,
0.05742955952882767,
0.06379180401563644,
-0.030013432726264,
-0.051021236926317215,
0.016505641862750053,
0.036144278943538666,
-0.03950967639684677,
0.011478384956717491,
-0.00947799626737833,
0.024004986509680748,
-0.004575955215841532,
-0.007096049841493368,
0.04684743657708168,
-0.011394315399229527,
0.04816906154155731,
0.02657594531774521,
-0.028742622584104538,
-0.0027947810012847185,
0.012532811611890793,
-0.014701670967042446,
-0.0021188275422900915,
0.0467999130487442,
0.03694833815097809,
0.042132388800382614,
-0.033244188874959946,
0.023188913241028786,
0.02326560579240322,
0.050174787640571594,
0.012916110455989838,
0.005229919217526913,
0.07958631962537766,
-0.04848127067089081,
0.00043394844396971166,
0.0383308082818985,
-0.0007431497797369957,
0.00256277434527874,
0.029528258368372917,
0.02124779112637043,
-0.011181884445250034,
-0.00003204708264092915,
-0.014940230175852776,
0.027609819546341896,
0.030291616916656494,
-0.05782121419906616,
0.01237407699227333,
0.005833748262375593,
0.009120884351432323,
0.08367100358009338,
0.0037052021361887455,
-0.011022058315575123,
-0.02989988401532173,
0.024626150727272034,
-0.030806340277194977,
0.02035968005657196,
-0.05872022360563278,
0.005264872685074806,
-0.012098191305994987,
-0.023719778284430504,
-0.018320942297577858,
0.005468863528221846,
0.013903415761888027,
-0.021161487326025963,
0.061904244124889374,
0.04064834117889404,
0.018532413989305496,
-0.008194666355848312,
0.04626527056097984,
-0.04025119170546532,
-0.05696869269013405,
0.021079301834106445,
0.033826202154159546,
-0.026405908167362213,
-0.027969157323241234,
0.013349493034183979,
0.001204316969960928,
-0.009149179793894291,
-0.020750710740685463,
0.0082078967243433,
-0.008122949860990047,
-0.0077036842703819275,
-0.06733336299657822,
-0.06017186492681503,
0.07374583929777145,
-0.01652096025645733,
-0.039345383644104004,
-0.058777760714292526,
-0.004304965026676655,
0.03399689868092537,
0.09484437853097916,
-0.0013330227229744196,
-0.025835538282990456,
-0.04334113746881485,
0.06107782572507858,
0.001146748079918325,
-0.02533271163702011,
0.004755272064357996,
-0.008982227183878422,
-0.04116426408290863,
0.0009638905758038163,
-0.05624580383300781,
0.04147925227880478,
0.029518816620111465,
-0.025796014815568924,
-0.0016400833847001195,
0.03377861902117729,
-0.0036645515356212854,
-0.004812904633581638,
0.0015894151292741299,
-0.009201337583363056,
-0.020178459584712982,
0.0897144079208374,
-0.010591619648039341,
0.045802246779203415,
0.021741574630141258,
-0.0050626834854483604,
0.030833493918180466,
-0.006797651760280132,
0.013977755792438984,
0.021472830325365067,
-0.019039319828152657,
0.01803586818277836,
-0.026097267866134644,
-0.00877929013222456,
0.014267075806856155,
-0.04001476243138313,
-0.037233103066682816,
-0.0033150939270853996,
-0.027862632647156715,
0.0375797338783741,
0.05946280434727669,
-0.01972140558063984,
0.007658513728529215,
-0.007025356404483318,
-0.0570840984582901,
-0.039526183158159256,
-0.06778748333454132,
0.028341859579086304,
-0.037275396287441254,
-0.0017278437735512853,
0.006229885388165712,
-0.004461797419935465,
0.0640198290348053,
-0.03884459286928177,
-0.039111461490392685,
0.016919462010264397,
0.02121654339134693,
-0.005164383444935083,
0.019307462498545647,
-0.02021324262022972,
0.05846574157476425,
0.01959334872663021,
-0.01649515889585018,
0.016320079565048218,
-0.019323663786053658,
-0.06096423789858818,
-0.020618537440896034,
-0.016654200851917267,
0.01222766749560833,
0.012979133985936642,
-0.003976699896156788,
0.03472837433218956,
0.02222028188407421,
-0.00016977559425868094,
0.028404315933585167,
-0.01793898642063141,
0.06956438720226288,
0.06219618767499924,
0.028430620208382607,
-0.013916777446866035,
0.03231639787554741,
0.019388161599636078,
0.0220935121178627,
0.005657721310853958,
-0.02520117163658142,
-0.04438740387558937,
0.008604082278907299,
0.01855379529297352,
0.051002923399209976,
-0.06083006411790848,
0.024404603987932205,
0.0709257423877716,
0.004570384509861469,
0.018601281568408012,
-0.005163742229342461,
-0.0049575380980968475,
0.010955387726426125,
0.03692653775215149,
0.02692265249788761,
0.02152146026492119,
0.004766554106026888,
0.05371088907122612,
0.01502575259655714,
-0.041267573833465576,
0.02965579181909561,
-0.009163659997284412,
0.07674112170934677,
0.008839188143610954,
-0.008841128088533878,
-0.002080345991998911,
0.01261904090642929,
0.02265249937772751,
-0.018154259771108627,
0.017621051520109177,
0.009107298217713833,
0.017439596354961395,
0.012727334164083004,
-0.040516067296266556,
-0.028534308075904846,
-0.0357000008225441,
0.010810396634042263,
0.049263846129179,
-0.012784582562744617,
0.04639410227537155,
-0.03356795758008957,
0.023690611124038696,
-0.031770411878824234,
0.033132873475551605,
-0.036221783608198166,
0.03552176430821419,
-0.01853911764919758,
-0.005459625739604235,
0.014006157405674458,
-0.030405940487980843,
-0.054876793175935745,
-0.0034034010022878647,
-0.033381376415491104,
-0.0036288988776504993,
0.018153652548789978,
-0.06466879695653915,
0.010041429661214352,
-0.02175343595445156,
-0.017167609184980392,
0.04775524511933327,
-0.006710786372423172,
-0.02202022448182106,
0.002116694115102291,
0.04702545702457428,
-0.059842780232429504,
0.01985093019902706,
-0.035704731941223145,
-0.0004893734003417194,
-0.007818271405994892,
0.0007258294499479234,
0.04158388078212738,
-0.04123423993587494,
-0.04789721593260765,
0.03958877548575401,
-0.022512272000312805,
-0.0058036744594573975,
0.014964264817535877,
-0.029296614229679108,
-0.004671668168157339,
-0.0058784098364412785,
0.026798037812113762,
0.011726237833499908,
-0.0500868484377861,
-0.0216511357575655,
-0.0444219708442688,
-0.059340495616197586,
0.015449823811650276,
-0.006478435825556517,
0.04872661456465721,
0.02136762998998165,
-0.0075460392981767654,
0.07104159891605377,
-0.006368259433656931,
-0.04519340395927429,
0.02714604325592518,
-0.015653016045689583,
0.00040850709774531424,
-0.024913961067795753,
0.011981275863945484,
0.05609392747282982,
-0.034625131636857986,
0.0054907347075641155,
-0.0010825875215232372,
0.034958548843860626,
0.016411781311035156,
0.0326354093849659,
-0.022365476936101913,
0.021008072420954704,
0.013717763125896454,
-0.007084425538778305,
0.03398238867521286,
0.009657146409153938,
-0.015080438926815987,
0.023454969748854637,
-0.02245030365884304,
0.017298560589551926,
0.029279066249728203,
-0.06459634006023407,
0.029539193958044052,
0.030780687928199768,
-0.026635736227035522,
-0.006415818817913532,
0.02331174910068512,
-0.04014698415994644,
-0.005928962957113981,
0.0001390830730088055,
0.01777035742998123,
0.048369742929935455,
-0.0061313011683523655,
-0.022874921560287476,
0.03288058936595917,
0.05782656371593475,
-0.006833783350884914,
-0.04167162999510765,
-0.02886975184082985,
-0.0020689922384917736,
-0.013670259155333042,
0.0019107017433270812,
-0.005969622638076544,
0.05100615322589874,
0.039264015853405,
0.042662397027015686,
0.03075014241039753,
-0.0007949971477501094,
0.023179752752184868,
-0.05387807637453079,
0.013519419357180595,
-0.02628377452492714,
0.07783070206642151,
-0.0128833819180727,
0.018216781318187714,
-0.021778058260679245,
0.037124354392290115,
0.03160101920366287,
-0.04074421897530556,
-0.07774617522954941,
0.037257544696331024,
0.0012392794014886022,
-0.04404359683394432,
0.008973592892289162,
-0.016499118879437447,
-0.006619032938033342,
-0.03340049088001251,
-0.03758842498064041,
0.023479675874114037,
0.036719683557748795,
-0.04212654009461403,
0.023962311446666718,
-0.024409333243966103,
-0.07989739626646042,
-0.016220200806856155,
0.012325449846684933,
0.038988664746284485,
-0.041742365807294846,
0.008610221557319164,
0.01658194325864315,
-0.029626240953803062,
0.00960934441536665,
-0.03534321114420891,
0.03625248372554779,
0.04898277670145035,
0.035108234733343124,
0.039498429745435715,
0.01317949965596199,
-0.025102192535996437,
0.03656713292002678,
0.011054297909140587,
0.012247275561094284,
-0.038662176579236984,
-0.010334085673093796,
-0.06486406177282333,
-0.008005489595234394,
-0.02732441946864128,
0.04974641650915146,
0.07308901846408844,
0.008977274410426617,
0.04704487323760986,
-0.035605933517217636,
0.006055885460227728,
-0.00008984761370811611,
0.0333038754761219,
0.013289710506796837,
-0.03115968592464924,
-0.005706374533474445,
-0.044856034219264984,
-0.03977073356509209,
-0.006154558155685663,
0.005408846773207188,
0.037738390266895294,
-0.003569653257727623,
-0.009831606410443783,
-0.015648696571588516,
-0.018915507942438126,
0.012393276207149029,
-0.018144438043236732,
-0.0002951567876152694,
-0.0002157835115212947,
0.01802019774913788,
0.00616218987852335,
-0.002795920241624117,
0.013835516758263111,
0.03140467777848244,
0.024626879021525383,
0.024697281420230865,
0.010406609624624252,
-0.08353576064109802,
-0.02075134962797165,
0.04049508646130562,
0.041577547788619995,
0.0017511688638478518,
-0.021120287477970123,
-0.03295153006911278,
0.018460508435964584,
0.031188348308205605,
-0.022777609527111053,
0.07492014020681381,
-0.01193976029753685,
0.0187571682035923,
-0.025226691737771034,
-0.05492805689573288,
0.006854687817394733,
0.01574881374835968,
-0.025411618873476982,
0.022564848884940147,
-0.000754126871470362,
-0.0877704843878746,
-0.0007181147811934352,
0.005853906739503145,
0.026166602969169617,
0.00900382548570633,
-0.003174635348841548,
-0.005537147168070078,
-0.02975105121731758,
0.03283579647541046,
0.0009158281027339399,
-0.06999026238918304,
-0.042760539799928665,
-0.012514383532106876,
-0.024564655497670174,
0.023515135049819946,
-0.04975711554288864,
-0.02004403993487358,
0.029969288036227226,
-0.00184105325024575,
-0.01729983277618885,
-0.01700105145573616,
-0.07129025459289551,
0.05831010267138481,
0.03333688899874687,
0.048239145427942276,
0.04636050760746002,
0.04822177439928055,
-0.030889200046658516,
0.019614893943071365,
-0.015041659586131573,
0.04223472997546196,
0.00273791397921741,
-0.01941143348813057,
-0.03883553296327591,
0.008410820737481117,
-0.04246658831834793,
0.059535589069128036,
0.012044291943311691,
0.016591591760516167,
-0.030912792310118675,
-0.00639369385316968,
-0.013598731718957424,
0.008147982880473137,
-0.03291093185544014,
-0.0019669830799102783,
0.009986670687794685,
0.012204884551465511,
0.012166829779744148,
0.003917884547263384,
0.03774238005280495,
0.006801654119044542,
0.027684608474373817,
0.0006869365461170673,
-0.025447433814406395,
0.026349999010562897,
-0.02988210693001747,
0.013110192492604256,
0.030144650489091873,
-0.017557645216584206,
0.06525486707687378,
-0.004384005442261696,
0.0074869729578495026,
0.01580018363893032,
-0.04634241759777069,
-0.0320136584341526,
0.02065468393266201,
0.060681622475385666,
-0.020515622571110725,
-0.04911663383245468,
0.01871114782989025,
-0.0020118895918130875,
0.005018983967602253,
-0.03989197313785553,
-0.027231214568018913,
-0.010918614454567432,
-0.004384519997984171,
0.010440746322274208,
-0.02750971168279648,
0.0020257842261344194,
-0.01590155065059662,
-0.05403394624590874,
-0.010886003263294697,
0.02843061089515686,
-0.03668700158596039,
0.015327461063861847,
0.010140280239284039,
0.02923784777522087,
0.04610000178217888,
0.02579309791326523,
-0.06175624951720238,
0.00301075610332191,
-0.009324145503342152,
0.0012139902682974935,
-0.00003777349047595635,
-0.0007181934779509902,
-0.02792753092944622,
-0.016372719779610634,
0.0324915274977684,
0.010033509694039822,
0.07392186671495438,
0.009570760652422905,
0.024386994540691376,
0.022891776636242867,
0.004508874379098415,
-0.02934342809021473,
-0.004262626636773348,
0.008841500617563725,
-0.02288593165576458,
0.04638144373893738,
0.008107835426926613,
-0.031130662187933922,
-0.024257266893982887,
-0.030147777870297432,
-0.010155783034861088,
-0.009240087121725082,
-0.021760404109954834,
-0.00484790513291955,
0.048667456954717636,
-0.027987362816929817,
0.01965138502418995,
0.0112757608294487,
-0.01911723054945469,
0.011484643444418907,
-0.011937319301068783,
0.026961440220475197,
-0.0099447350949049,
-0.010444837622344494,
-0.01005121972411871,
-0.06653774529695511,
-0.03757139667868614,
0.005109524354338646,
0.034444477409124374,
0.0003404586750548333,
0.05596357583999634,
0.026710204780101776,
-0.030816178768873215,
0.020882776007056236,
-0.01726681925356388,
-0.017296424135565758,
0.015931805595755577,
0.0049634105525910854,
0.03354116156697273,
0.022915715351700783,
-0.0035778400488197803,
0.03001265972852707,
0.03834448754787445,
-0.026571184396743774,
-0.02783382125198841,
0.031117726117372513,
0.001926760538481176,
-0.00411609560251236,
-0.011716870591044426,
-0.03799421340227127,
0.030803553760051727,
-0.07515494525432587,
0.04094541817903519,
-0.03210383281111717,
0.034831684082746506,
0.032296765595674515,
0.008295563980937004,
-0.0193198099732399,
-0.08551541715860367,
-0.011221466585993767,
-0.049360379576683044,
0.0025511665735393763,
-0.01397616881877184,
-0.020558135583996773,
0.0301689300686121,
0.01765633374452591,
0.024311719462275505,
-0.03429951146245003,
0.009276283904910088,
-0.0007778600556775928,
-0.02143253944814205,
-0.005950148217380047,
-0.008004236966371536,
-0.06212998554110527,
0.038183439522981644,
-0.012601939029991627,
-0.00007661306881345809,
0.029869074001908302,
-0.03771768510341644,
0.010925943031907082,
-0.015125107020139694,
0.011479032225906849,
0.0009025832987390459,
0.07031849771738052,
-0.0062303803861141205,
0.024546843022108078,
0.0008056668448261917,
0.03510583937168121,
0.1111389771103859,
0.016470303758978844,
0.023512260988354683,
-0.0629904493689537,
0.023004040122032166,
-0.04401223361492157,
0.0026170515920966864,
-0.04775146022439003,
0.052335549145936966,
-0.023986531421542168,
0.01185692846775055,
0.037936270236968994,
0.02886009030044079,
-0.003614681074395776,
0.017030857503414154,
0.022795675322413445,
-0.05467679351568222,
-0.018526848405599594,
0.025828534737229347,
0.014305966906249523,
-0.0015136394649744034,
0.013176367618143559,
-0.006000349763780832,
-0.014673063531517982,
0.006309467367827892,
-0.013918966054916382,
-0.013887605629861355,
-0.03471223637461662,
0.049938641488552094,
-0.014590924605727196,
-0.03871101886034012,
0.00391718465834856,
-0.0052381535060703754,
0.010537534952163696,
-0.013455170206725597,
-0.006481815129518509,
0.023603098466992378,
-0.010505042038857937,
0.04520833119750023,
0.047859299927949905,
0.048904161900281906,
-0.028496582061052322,
0.05079403519630432,
0.014768377877771854,
-0.047786496579647064,
-0.009896459989249706,
-0.036431748420000076,
0.03189103305339813,
-0.021406300365924835,
-0.0031858240254223347,
-0.016751104965806007,
0.023068059235811234,
0.04599832743406296,
-0.04280831664800644,
-0.03756311163306236,
-0.024449368938803673,
-0.00015411648200824857,
-0.014427227899432182,
-0.06279542297124863,
-0.011445436626672745,
0.001678299973718822,
0.01433559600263834,
0.008785718120634556,
-0.03315602242946625,
0.014683965593576431,
-0.01646754890680313,
0.031105156987905502,
0.05022822320461273,
-0.000647665117867291,
-0.027815915644168854,
-0.010322689078748226,
-0.006905767135322094,
-0.03032098524272442,
0.02320660650730133,
-0.033382631838321686,
0.0018397410167381167,
0.016683433204889297,
0.0299250278621912,
-0.031074687838554382,
0.0041615222580730915,
-0.07694169878959656,
0.006505691912025213,
-0.004549223463982344,
-0.00804102048277855,
-0.004060832783579826,
0.025114543735980988,
-0.0005666482029482722,
0.044281721115112305,
-0.0005730914999730885,
-0.038390789180994034,
0.014131021685898304,
0.03992445021867752,
0.012537195347249508,
-0.03280235081911087,
-0.049674056470394135,
0.014842762611806393,
-0.048114798963069916,
-0.011821841821074486,
0.009367410093545914,
0.029513949528336525,
0.00799164455384016,
-0.008868022821843624,
0.0018403618596494198,
-0.009690347127616405,
-0.013671387918293476,
0.020038826391100883,
0.04742493852972984,
-0.042580194771289825,
0.01442807074636221,
0.0007720671710558236,
-0.03291599079966545,
-0.01941118948161602,
-0.02792699635028839,
-0.01584608480334282,
0.0030449361074715853,
-0.020380275323987007,
-0.0020673221442848444,
0.015458683483302593,
0.022894788533449173,
-0.03533545508980751,
0.031933628022670746,
-0.06394048035144806,
0.01599159464240074,
-0.02553780935704708,
0.017650706693530083,
0.017028070986270905,
-0.0037343893200159073,
-0.004882985260337591,
0.049660854041576385,
-0.034846894443035126,
0.01980433240532875,
0.0013406348880380392,
0.040308352559804916,
-0.053342998027801514,
-0.029686417430639267,
0.0009180849301628768,
0.029272323474287987,
0.05434667319059372,
0.011889307759702206,
-0.016641009598970413,
0.026052266359329224,
-0.002503368305042386,
-0.034563302993774414,
0.03909875452518463,
0.0250867810100317,
0.006361566483974457,
0.02185310609638691,
-0.008534615859389305,
0.007887175306677818,
0.05780211463570595,
0.008472428657114506,
-0.027213558554649353,
-0.00725686876103282,
-0.04328950494527817,
0.009217465296387672,
-0.018810322508215904,
0.029305100440979004,
-0.03610331192612648,
0.00677449582144618,
0.033382851630449295,
0.04217168688774109,
0.0361037440598011,
-0.030293628573417664,
-0.009676720015704632,
0.0010235587833449244,
0.026626328006386757,
0.003713273676112294,
0.013211941346526146,
0.047799430787563324,
0.05828143283724785,
-0.021044451743364334,
-0.009596544317901134,
0.019692150875926018,
-0.01330943126231432,
-0.13483822345733643,
0.016232799738645554,
0.00471680099144578,
-0.010215540416538715,
0.010934477671980858,
-0.01778462901711464,
0.03973596915602684,
-0.0012786865700036287,
-0.033604029566049576,
-0.009419367648661137,
-0.0030335893388837576,
-0.02886056713759899,
-0.03397534042596817,
0.012341250665485859,
-0.02146773785352707,
0.02336171828210354,
0.019291913136839867,
-0.00249266205355525,
0.015020809136331081,
0.00478355260565877,
-0.0280170738697052,
-0.023248178884387016,
0.01806671731173992,
0.018587466329336166,
-0.0069419280625879765,
0.008071549236774445,
0.06134119629859924,
-0.020161066204309464,
-0.007899928838014603,
0.047894563525915146,
-0.028767844662070274,
0.013560334220528603,
-0.02289179526269436,
0.03323495388031006,
-0.030742036178708076,
0.03064204379916191,
0.024225452914834023,
0.004760781303048134,
-0.0014160817954689264,
-0.02036057785153389,
0.017856182530522346,
0.028718484565615654,
-0.012126598507165909,
-0.0023425244726240635,
0.03566533327102661,
0.025098050013184547,
-0.013238346204161644,
0.056485675275325775,
-0.03466189652681351,
-0.02451159618794918,
0.03525661304593086,
-0.021959956735372543,
0.04253300651907921,
-0.010156512260437012,
0.014099696651101112,
-0.055868033319711685,
-0.0250498466193676,
0.027423543855547905,
0.010074603371322155,
-0.013340291567146778,
-0.04072096571326256,
-0.008471602573990822,
-0.038673557341098785,
0.04405009374022484,
-0.0017706030048429966,
0.006617231760174036,
-0.05919913202524185,
0.009434949606657028,
-0.007794143632054329,
-0.0044840555638074875,
-0.024937450885772705,
-0.07466720044612885,
-0.015490269288420677,
0.05044828727841377,
0.03060632012784481,
0.03892230987548828,
0.004807931836694479,
-0.014518246054649353,
-0.001491199596785009,
-0.05038798972964287,
0.026017185300588608,
-0.019109288230538368,
0.01228018943220377,
-0.03784577548503876,
-0.056325022131204605,
0.03617648780345917,
0.045390527695417404,
0.0542776919901371,
0.00021751680469606072,
-0.018011856824159622,
0.029839584603905678,
-0.0003903294273186475,
0.022777102887630463,
-0.03734239935874939,
0.026534220203757286,
-0.0064859539270401,
-0.012510715052485466,
0.026873385533690453,
-0.02009102888405323,
-0.03150370717048645,
0.012914268299937248,
0.06781190633773804,
-0.007370627485215664,
0.009438279084861279,
-0.051336221396923065,
-0.03202752396464348,
0.01170369889587164,
0.025869159027934074,
-0.035062018781900406,
0.03671517223119736,
-0.0022848183289170265,
0.03397849202156067,
-0.0386776328086853,
-0.003404689719900489,
-0.03721547871828079,
0.016879744827747345,
-0.03739333897829056,
0.03739272803068161,
-0.019713759422302246,
-0.07118837535381317,
0.03390054404735565,
-0.05808928236365318,
0.006460892967879772,
0.02455933950841427,
-0.03671664372086525,
-0.0024999137967824936,
0.05167469009757042,
0.03412661328911781,
0.013399044051766396,
-0.047117237001657486,
0.01725262962281704,
-0.03053193911910057,
-0.0029473183676600456,
-0.03524738922715187,
0.04265442490577698,
0.05425724759697914,
0.02393338456749916,
-0.006059241946786642,
0.04489891603589058,
-0.03047700971364975,
0.017674777656793594,
0.006914667319506407,
-0.0016380505403503776,
-0.011181788519024849,
-0.05174105241894722,
0.041713520884513855,
0.0030942580197006464,
-0.017911434173583984,
0.05074348673224449,
-0.016573963686823845,
0.04923968017101288,
0.013137325644493103,
0.011062453500926495,
-0.05480831488966942,
0.013283603824675083,
-0.032809484750032425,
0.016438672319054604,
-0.00808694027364254,
0.06738235801458359,
0.019684864208102226,
0.011892283335328102,
0.004469965118914843,
0.012776484712958336,
0.02446744218468666,
-0.013746668584644794,
0.00746580958366394,
-0.02093156799674034,
0.0033667930401861668,
-0.02521147020161152,
-0.012882114388048649,
-0.0034025695640593767,
-0.06962822377681732,
0.013196173124015331,
0.0431240051984787,
0.006546382326632738,
0.03638061136007309,
-0.014956154860556126,
0.0002552151563577354,
0.05937759205698967,
-0.04483142867684364,
-0.007040183525532484,
-0.010637611150741577,
0.013573960401117802,
0.002850521355867386,
0.01253211498260498
] |
<p>Ive read a few courses on <strong>statistical mechanics</strong>, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading between the lines you can see some mathematical construct. Has statistical mechanics been formalized in the sense that say analysis has been formalized (<em>down to quantifiers, sets, functions,...</em>) more rigorously? Where can one find a <strong>formal axiomatic approach</strong> to statistical mechanics as opposed to an introductory descriptory approach?</p> | 4,558 | [
-0.020449712872505188,
-0.03840967267751694,
0.004684532526880503,
-0.03578926622867584,
0.026273349300026894,
0.031548429280519485,
0.040131717920303345,
0.0017138164257630706,
-0.001202513463795185,
-0.00953133124858141,
0.03371797874569893,
0.025820571929216385,
0.07146228104829788,
0.033704936504364014,
0.0390096977353096,
-0.045479949563741684,
0.01888749748468399,
-0.022817611694335938,
-0.009478861466050148,
0.0071127465926110744,
0.0018200644990429282,
0.020073177292943,
0.011440644972026348,
-0.021204302087426186,
0.00014551333151757717,
0.012447820045053959,
-0.007229148875921965,
0.007698871660977602,
0.03731783479452133,
0.05178213119506836,
-0.033754948526620865,
0.0013178250519558787,
-0.0057932003401219845,
0.020129403099417686,
0.033567797392606735,
-0.01589295268058777,
-0.019316842779517174,
-0.010198102332651615,
0.007524813991039991,
-0.012398255057632923,
-0.07515090703964233,
-0.02581901103258133,
-0.017897125333547592,
0.008589074946939945,
-0.03927101939916611,
0.021620195358991623,
-0.01685565710067749,
-0.007475051563233137,
0.019653016701340675,
-0.045703522861003876,
0.056948669254779816,
0.017370793968439102,
0.0633823350071907,
0.06191542372107506,
-0.01219102181494236,
-0.00459856353700161,
0.0467713326215744,
0.07102182507514954,
-0.004936066456139088,
-0.05231393873691559,
0.015451611950993538,
0.005131535232067108,
0.02691223844885826,
-0.04596593976020813,
-0.03734069690108299,
0.05867178738117218,
0.007761844899505377,
-0.035145364701747894,
0.05896706506609917,
0.0005175306578166783,
-0.025341037660837173,
0.03417418152093887,
0.0720139890909195,
-0.000042809675505850464,
0.008842877112329006,
0.011845529079437256,
0.01860879920423031,
-0.015416199341416359,
0.02290608361363411,
0.03768957778811455,
0.023950839415192604,
0.022105200216174126,
0.016591446474194527,
0.021649576723575592,
-0.004763432312756777,
-0.05386081710457802,
0.06428160518407822,
-0.042392365634441376,
-0.02567552775144577,
0.02266620472073555,
-0.005812700372189283,
0.005512025207281113,
0.024509523063898087,
-0.024336200207471848,
-0.05021333321928978,
0.019413884729146957,
-0.016991235315799713,
0.06829245388507843,
0.011651532724499702,
-0.01886049471795559,
0.014534855261445045,
-0.036375731229782104,
0.0072662606835365295,
0.058121610432863235,
-0.021077698096632957,
-0.0031641093082726,
-0.02634718455374241,
0.013353301212191582,
-0.00031642295653000474,
-0.006168347783386707,
-0.022292161360383034,
0.03160468488931656,
0.011091053485870361,
0.02339542657136917,
0.005438010208308697,
-0.005340877920389175,
0.008530642837285995,
-0.02169235795736313,
0.01827428676187992,
0.10449615865945816,
0.037894316017627716,
-0.040328893810510635,
0.03556336835026741,
-0.02554492838680744,
-0.06551497429609299,
0.013914099894464016,
0.028031378984451294,
-0.024236954748630524,
-0.022792430594563484,
0.0430496484041214,
-0.006025808397680521,
0.020915472880005836,
0.010211124084889889,
0.016612835228443146,
0.003120471490547061,
-0.039468515664339066,
-0.07641738653182983,
-0.04698173329234123,
0.057056643068790436,
0.008020663633942604,
-0.024661710485816002,
-0.056278619915246964,
0.030037138611078262,
0.047065723687410355,
0.04205278679728508,
0.020262975245714188,
0.03577826917171478,
-0.015113127417862415,
0.027092820033431053,
-0.003092522034421563,
-0.03748137876391411,
-0.013121464289724827,
0.011871987022459507,
0.02049548365175724,
0.005392766557633877,
-0.062244970351457596,
0.04658569395542145,
0.03941085934638977,
0.020546309649944305,
-0.02516097016632557,
0.06609832495450974,
-0.03775973990559578,
-0.014212481677532196,
0.014846019446849823,
-0.01751304790377617,
-0.017367536202073097,
0.05837181955575943,
0.01334850862622261,
0.04481346532702446,
0.026606831699609756,
0.0024895737878978252,
0.01752300374209881,
-0.001262300880625844,
0.02744261547923088,
0.03976474329829216,
-0.017745522782206535,
0.0004827130469493568,
0.021662745624780655,
-0.004246879834681749,
0.026471611112356186,
-0.03699374198913574,
0.0006118242163211107,
-0.01056746393442154,
0.03277343511581421,
-0.03370197117328644,
0.020729145035147667,
0.014514612033963203,
-0.04309467971324921,
0.012171312235295773,
-0.07197218388319016,
-0.04259951785206795,
-0.09191688895225525,
0.028812631964683533,
-0.03620951622724533,
-0.01649458520114422,
0.05391865596175194,
-0.006295404862612486,
0.012273075990378857,
-0.05061722174286842,
-0.0303744338452816,
-0.015524802729487419,
0.015538789331912994,
0.02635832689702511,
-0.014071398414671421,
0.01057436503469944,
0.047433506697416306,
0.02997376024723053,
-0.004842675291001797,
0.041920196264982224,
-0.04141811281442642,
-0.06016895920038223,
-0.00640882458537817,
-0.013477998785674572,
0.020483771339058876,
0.00911293737590313,
-0.01003449596464634,
0.008170299232006073,
-0.031198402866721153,
-0.031145986169576645,
0.031631067395210266,
-0.02551397494971752,
0.05201176553964615,
0.0233745239675045,
0.02188771776854992,
-0.009439862333238125,
0.053465791046619415,
0.0037903047632426023,
-0.0015967920189723372,
0.010699194855988026,
-0.021576469764113426,
-0.043642181903123856,
-0.0021387215238064528,
0.05527123808860779,
0.06728734821081161,
-0.043170955032110214,
0.0033873198553919792,
0.016688134521245956,
0.03172137588262558,
0.00919424369931221,
0.03207582235336304,
-0.04747982323169708,
-0.02759549394249916,
0.011018222197890282,
-0.008110800758004189,
0.03803452476859093,
0.003699397435411811,
-0.02210676297545433,
0.030642295256257057,
0.010926038026809692,
0.030891548842191696,
-0.03522207960486412,
0.0181096363812685,
-0.010098646394908428,
-0.011994734406471252,
-0.007561241742223501,
-0.030654918402433395,
0.0484074205160141,
0.0046655526384711266,
0.02913566119968891,
0.0030364785343408585,
0.0036426710430532694,
-0.003924477379769087,
-0.0410347580909729,
-0.004861690569669008,
-0.01580716110765934,
0.013928769156336784,
-0.013795370236039162,
0.0014540585689246655,
0.017143715173006058,
-0.030548956245183945,
0.020058104768395424,
-0.030901458114385605,
-0.016775794327259064,
-0.022087188437581062,
0.02059137262403965,
0.030438954010605812,
-0.0076562147587537766,
0.011215170845389366,
-0.03826117888092995,
-0.018030036240816116,
-0.025845810770988464,
-0.03008304536342621,
0.034909509122371674,
0.04830659553408623,
-0.04550427570939064,
0.013379031792283058,
-0.030932407826185226,
-0.0492221899330616,
0.0307211484760046,
-0.03911478817462921,
0.005096155218780041,
-0.012960539199411869,
-0.001477666781283915,
-0.053971413522958755,
0.0023040028754621744,
0.017664197832345963,
-0.0027846861630678177,
-0.0031889823731034994,
0.00971798226237297,
0.03061860054731369,
-0.04193734750151634,
-0.013814016245305538,
0.014893094077706337,
-0.03840075805783272,
-0.05860861390829086,
-0.05239935964345932,
0.008030024357140064,
0.019465042278170586,
-0.003879960160702467,
-0.008793486282229424,
0.08802387863397598,
-0.036419376730918884,
-0.019362974911928177,
-0.036855410784482956,
-0.03331339731812477,
0.03891737386584282,
-0.043197669088840485,
0.03634032607078552,
0.010134427808225155,
-0.00906432792544365,
0.04826728254556656,
0.02246432565152645,
-0.06674705445766449,
0.00040892206015996635,
0.021592382341623306,
-0.041795533150434494,
0.0058599901385605335,
0.032870881259441376,
-0.018473437055945396,
0.004771328065544367,
0.026456212624907494,
0.05524666979908943,
0.002397439908236265,
0.03114587999880314,
0.014211462810635567,
-0.016939964145421982,
0.027032431215047836,
0.000871952623128891,
-0.0007712808437645435,
0.033922433853149414,
0.021490316838026047,
-0.03982727974653244,
0.01000010222196579,
-0.0066519444808363914,
0.022917114198207855,
0.03385033458471298,
-0.04794182628393173,
0.05801307037472725,
0.03566452115774155,
0.002248866017907858,
-0.03314575180411339,
0.04682184010744095,
-0.01251143030822277,
-0.007264940999448299,
0.025204751640558243,
0.027160855010151863,
-0.006289517506957054,
-0.02189660631120205,
0.005464733112603426,
0.04710330814123154,
0.05869181454181671,
-0.05455278232693672,
0.020419573411345482,
0.0019414544804021716,
0.001958045642822981,
0.022345148026943207,
-0.015947876498103142,
-0.012993973679840565,
0.03661942109465599,
0.011877770535647869,
0.0124498987570405,
0.012416929006576538,
-0.02272207848727703,
-0.0012150920229032636,
-0.05716634541749954,
-0.0049503459595143795,
-0.00942438468337059,
0.0247030071914196,
0.001309607527218759,
0.07417620718479156,
-0.016790742054581642,
0.005470295436680317,
0.014631258323788643,
0.010175698436796665,
-0.09223077446222305,
0.017429018393158913,
-0.009944560006260872,
-0.014550653286278248,
-0.003231167094781995,
0.011069470085203648,
0.04111713916063309,
-0.04025206342339516,
-0.03542931377887726,
-0.0347929410636425,
0.008683480322360992,
-0.08454426378011703,
-0.028883256018161774,
-0.05065016448497772,
-0.038940075784921646,
0.005341390147805214,
0.029708240181207657,
0.04558858275413513,
-0.035176437348127365,
0.03076561540365219,
0.0401589572429657,
-0.07079482823610306,
0.02250286564230919,
-0.03133844584226608,
0.041713763028383255,
0.03910154476761818,
0.01998048834502697,
0.007966347970068455,
0.05120205879211426,
-0.02510901167988777,
0.007537780795246363,
0.03911122307181358,
0.0550176277756691,
0.008077380247414112,
-0.03771597519516945,
-0.011708959005773067,
-0.05942082405090332,
-0.02307583950459957,
-0.004358093719929457,
0.032469987869262695,
0.015631435438990593,
0.0033612146507948637,
0.043482840061187744,
0.01773611269891262,
-0.05473271757364273,
0.043420080095529556,
0.038188088685274124,
-0.015693701803684235,
-0.00893422681838274,
-0.036853138357400894,
-0.020594637840986252,
-0.04390621557831764,
0.01562904193997383,
0.05374336242675781,
0.0189069714397192,
-0.009062266908586025,
0.051396023482084274,
-0.01553573738783598,
-0.006590157747268677,
-0.05180439352989197,
-0.01700933277606964,
-0.0074146585538983345,
0.004455498419702053,
-0.003529751906171441,
-0.014305093325674534,
0.028663787990808487,
0.03600623458623886,
0.019603926688432693,
0.03066899999976158,
-0.0012442521983757615,
-0.034408364444971085,
0.004087080247700214,
0.05262359231710434,
-0.04366052523255348,
-0.01998649723827839,
0.032071106135845184,
-0.04686364158987999,
-0.03473508358001709,
0.07221125811338425,
0.002449525985866785,
0.01610543765127659,
-0.02882496267557144,
-0.037538785487413406,
-0.010540598072111607,
-0.010015220381319523,
-0.040354613214731216,
0.003614607034251094,
0.006105953361839056,
0.021884161978960037,
-0.009814872406423092,
0.00473485654219985,
-0.059281859546899796,
0.02654515579342842,
0.01687123253941536,
0.03492588922381401,
-0.006262483075261116,
-0.027529284358024597,
-0.023442696779966354,
-0.0034420080482959747,
-0.04277505353093147,
-0.05984727293252945,
-0.0070741246454417706,
0.020659107714891434,
-0.017045052722096443,
-0.0078094154596328735,
-0.012409242801368237,
-0.028560679405927658,
0.013822907581925392,
-0.017399543896317482,
0.006118915043771267,
0.028109319508075714,
-0.003924001939594746,
0.07003267109394073,
0.014296808280050755,
0.01921437308192253,
0.03271852433681488,
0.005463230423629284,
-0.0036911070346832275,
0.02158094383776188,
-0.03877124562859535,
0.03685511276125908,
-0.0142021169885993,
0.012775478884577751,
-0.05402977392077446,
-0.01920377090573311,
-0.03374309465289116,
0.0431780107319355,
0.027179181575775146,
-0.0004733883251901716,
-0.009721594862639904,
-0.03245096653699875,
0.012561379000544548,
0.011758726090192795,
0.013577520847320557,
-0.007299598306417465,
-0.01935509406030178,
0.028888743370771408,
0.0010471496498212218,
-0.011881797574460506,
0.02779805101454258,
-0.0005247535300441086,
0.005822519306093454,
-0.0036194634158164263,
-0.03460531681776047,
0.016132023185491562,
-0.05649491772055626,
-0.030617475509643555,
-0.00640465272590518,
-0.03714514151215553,
0.055970534682273865,
-0.00998780969530344,
0.028218625113368034,
0.010488025844097137,
-0.07284560799598694,
-0.04372234269976616,
-0.007846863940358162,
0.009844343177974224,
-0.003419105429202318,
-0.035034094005823135,
0.019303906708955765,
-0.003056134330108762,
-0.023939000442624092,
-0.05041199177503586,
-0.05822692811489105,
-0.004316451493650675,
0.022686365991830826,
-0.050417765974998474,
-0.043406568467617035,
0.041364338248968124,
0.006497128866612911,
-0.014649135991930962,
0.013768612407147884,
0.04027432203292847,
-0.0071305581368505955,
-0.03009994700551033,
0.023210890591144562,
0.014172965660691261,
0.04766952618956566,
-0.014612977392971516,
0.0030235089361667633,
-0.007337572984397411,
0.02009781263768673,
0.008428649976849556,
0.01689954474568367,
0.02014237456023693,
-0.010141641832888126,
-0.004221830051392317,
-0.018646832555532455,
0.010016934014856815,
0.008017114363610744,
-0.021595729514956474,
0.0029573298525065184,
0.006568114273250103,
-0.008425834588706493,
-0.01536764856427908,
-0.039388589560985565,
0.0046976422891020775,
-0.015644896775484085,
0.02043541707098484,
-0.0222632959485054,
0.0028910133987665176,
0.017677737399935722,
-0.029936382547020912,
0.020586969330906868,
-0.01109057106077671,
0.012745466083288193,
0.04313891753554344,
-0.007477710954844952,
0.007085041143000126,
0.016519660130143166,
0.029297461733222008,
-0.022985780611634254,
0.006724910344928503,
-0.04284670948982239,
0.01426499243825674,
0.010877864435315132,
0.008562030270695686,
-0.0032120223622769117,
-0.05967606231570244,
-0.03974130004644394,
0.015744997188448906,
0.03887849301099777,
0.012918409891426563,
0.043227147310972214,
0.0186937116086483,
-0.012467269785702229,
0.003271187422797084,
-0.028876546770334244,
-0.015614885836839676,
0.017338786274194717,
0.014479655772447586,
0.06916853785514832,
-0.04246336221694946,
0.006918501574546099,
0.03650594875216484,
0.0484778992831707,
-0.06633544713258743,
0.01492952462285757,
0.002861166372895241,
-0.006142100784927607,
0.03025897964835167,
-0.0038489121943712234,
-0.034689657390117645,
0.07238893955945969,
-0.04853464290499687,
0.04528912529349327,
-0.0077187735587358475,
-0.03285921737551689,
0.019813917577266693,
0.006973575334995985,
0.0018653370207175612,
-0.038413602858781815,
-0.03232245519757271,
-0.020150989294052124,
0.046046484261751175,
-0.0009102530311793089,
0.06088321655988693,
0.04297855496406555,
-0.022950559854507446,
0.01044543832540512,
-0.004672219976782799,
0.004505288787186146,
0.022890372201800346,
-0.06715214252471924,
0.0034840665757656097,
-0.043336354196071625,
-0.059946272522211075,
0.039919164031744,
0.014383358880877495,
-0.03352760523557663,
-0.008967566303908825,
-0.04662598669528961,
0.057585861533880234,
0.01980714499950409,
0.03155389428138733,
-0.008249873295426369,
0.06253927201032639,
-0.023131560534238815,
0.05164090916514397,
-0.029140012338757515,
0.007504780776798725,
0.10978065431118011,
0.041605256497859955,
0.02017352357506752,
-0.09261956065893173,
0.01356992032378912,
-0.01548541709780693,
-0.005245773587375879,
-0.034564025700092316,
0.016406122595071793,
-0.00041658850386738777,
0.006738274358212948,
-0.012986846268177032,
0.07873407006263733,
-0.005583570338785648,
-0.009751235134899616,
0.059931639581918716,
-0.07187363505363464,
-0.011176738888025284,
0.004399503115564585,
-0.004933640826493502,
-0.01826367899775505,
0.03282056003808975,
-0.07373730838298798,
-0.02682335115969181,
0.013970966450870037,
-0.02862640470266342,
-0.040605589747428894,
-0.017365561798214912,
0.041394252330064774,
0.014235236681997776,
-0.02039763517677784,
-0.017576459795236588,
0.01934082992374897,
-0.012467441149055958,
-0.04276901111006737,
-0.014670277014374733,
0.020228572189807892,
0.0009570110705681145,
0.02854975312948227,
0.01892889477312565,
0.03289693221449852,
0.01344758179038763,
0.02333398349583149,
0.008696496486663818,
0.0005386302946135402,
-0.011199326254427433,
-0.013812408782541752,
0.054365526884794235,
-0.0403716117143631,
-0.007470055017620325,
0.02223985828459263,
-0.03377710282802582,
-0.002869095653295517,
-0.024782659485936165,
-0.026185180991888046,
0.01104282308369875,
0.05875468999147415,
-0.03192504867911339,
-0.00563979335129261,
-0.032129764556884766,
0.025822838768363,
-0.053990256041288376,
0.015618156641721725,
-0.006235695444047451,
-0.02528110332787037,
-0.011141180992126465,
-0.00021190715779084712,
0.01533974427729845,
-0.03398008644580841,
-0.03488576412200928,
-0.044137340039014816,
0.00824478454887867,
-0.043113067746162415,
-0.0295370165258646,
-0.01764827035367489,
-0.013778717257082462,
0.03977585211396217,
0.024805596098303795,
-0.010557333938777447,
0.020821094512939453,
-0.022654416039586067,
0.019233621656894684,
-0.030674008652567863,
0.0042386590503156185,
0.01974383369088173,
-0.01847449690103531,
0.018789784982800484,
0.08252539485692978,
-0.016735214740037918,
-0.011170703917741776,
0.014697084203362465,
-0.018359869718551636,
0.03648582845926285,
-0.04996982961893082,
0.012685440480709076,
-0.00013644529099110514,
-0.030383529141545296,
-0.013689977116882801,
-0.009332144632935524,
0.020868027582764626,
0.03293662145733833,
0.03623763471841812,
-0.004860949702560902,
0.026727184653282166,
0.03205244615674019,
0.017553962767124176,
0.005470363888889551,
-0.01757058873772621,
0.007191262673586607,
0.014299238100647926,
-0.00700134364888072,
-0.061857670545578,
-0.065301313996315,
-0.03744747117161751,
0.011803532019257545,
-0.013208679854869843,
0.0037914193235337734,
-0.03268555924296379,
0.01248603593558073,
0.01458665356040001,
0.026329779997467995,
-0.026724448427557945,
-0.010257153771817684,
-0.03437839448451996,
-0.01445415522903204,
0.024577084928750992,
0.003921702969819307,
0.0029810452833771706,
0.0511288084089756,
-0.005110454745590687,
-0.047276899218559265,
0.04876062646508217,
0.02434212900698185,
0.00917070358991623,
-0.02156994119286537,
0.01230743620544672,
0.00002016574035224039,
0.048786554485559464,
-0.02299395389854908,
-0.030546247959136963,
0.009560441598296165,
-0.04352305084466934,
-0.04160400480031967,
0.007244465872645378,
-0.02755827084183693,
-0.007674987893551588,
0.04838813468813896,
0.00784621387720108,
-0.01256389170885086,
0.0225914865732193,
-0.0023688110522925854,
0.003792263800278306,
0.008536720648407936,
-0.029404718428850174,
-0.027456074953079224,
-0.02934870682656765,
0.021299807354807854,
0.02531454525887966,
-0.03782970458269119,
0.01377158984541893,
0.022429656237363815,
0.018603568896651268,
-0.03085939958691597,
0.024332085624337196,
-0.023281492292881012,
0.04839150607585907,
0.018089229241013527,
0.021034078672528267,
0.04545331001281738,
0.06143275275826454,
-0.03990940377116203,
0.05275651440024376,
0.0028199711814522743,
-0.007252811919897795,
-0.10405754297971725,
-0.003374694846570492,
0.024827033281326294,
-0.01071412768214941,
0.017434505745768547,
-0.06145240366458893,
0.02694515325129032,
-0.003920479211956263,
-0.067567378282547,
-0.0053840815089643,
-0.030889196321368217,
-0.005777221173048019,
-0.022063907235860825,
0.016720185056328773,
-0.02680012211203575,
0.038651976734399796,
-0.0061600892804563046,
0.03375111520290375,
0.017900312319397926,
0.02463371492922306,
0.010615920647978783,
0.015986420214176178,
-0.02732502855360508,
0.031231455504894257,
-0.012522425502538681,
-0.03148757293820381,
0.05253830552101135,
-0.017392287030816078,
-0.05921352282166481,
-0.0017498208908364177,
-0.010104886256158352,
0.0027975395787507296,
0.02171924151480198,
-0.019840069115161896,
-0.0019275274826213717,
0.02814633399248123,
0.04707833752036095,
-0.018860826268792152,
0.01871306076645851,
0.011384476907551289,
0.008418439887464046,
0.018200088292360306,
-0.007473282981663942,
-0.018241198733448982,
0.04262469708919525,
-0.02603548765182495,
-0.02436246909201145,
0.03196581080555916,
0.023149799555540085,
-0.019829874858260155,
-0.026438312605023384,
0.006029016803950071,
0.01335485652089119,
-0.00945676863193512,
0.05973492190241814,
-0.044878773391246796,
0.013394179753959179,
0.02962416224181652,
0.038850024342536926,
-0.01901276409626007,
-0.008903838694095612,
0.005537704098969698,
-0.02179219201207161,
-0.019084474071860313,
0.0031273714266717434,
-0.018041519448161125,
-0.05290806293487549,
-0.007494539488106966,
0.019048722460865974,
-0.009020944125950336,
0.0034123247023671865,
-0.057093679904937744,
-0.03622271865606308,
0.02772960439324379,
-0.012080428190529346,
0.04743288457393646,
0.0037964885123074055,
-0.04410663992166519,
0.010575917549431324,
-0.07460765540599823,
0.037085507065057755,
-0.000645086111035198,
0.026989763602614403,
-0.04268211871385574,
0.0313694104552269,
0.003807846689596772,
-0.0157774705439806,
0.049100615084171295,
0.024610010907053947,
0.0047328881919384,
-0.0007240211707539856,
0.018123304471373558,
0.03522593528032303,
-0.009073249064385891,
-0.007013682741671801,
-0.05112382024526596,
0.018803084269165993,
-0.008256074972450733,
-0.019585637375712395,
-0.002334710443392396,
0.037946052849292755,
0.030192404985427856,
-0.001446933252736926,
-0.000019654808056657203,
-0.01599019579589367,
-0.03427466005086899,
0.06642085313796997,
-0.013546084053814411,
-0.004985740873962641,
0.049095481634140015,
-0.043461721390485764,
0.034891050308942795,
0.02458459697663784,
-0.028208976611495018,
-0.005111768841743469,
0.005599798168987036,
-0.03576046600937843,
-0.04211036488413811,
-0.02890721894800663,
0.022845592349767685,
0.016812874004244804,
-0.06188365817070007,
0.003251227317377925,
-0.0034523264039307833,
-0.02747580036520958,
-0.02062797360122204,
0.00880770105868578,
0.01717711240053177,
0.0462585911154747,
0.003242670791223645,
-0.013014684431254864,
0.03610445186495781,
-0.006281659007072449,
-0.014597184956073761,
0.0628182515501976,
0.0780395120382309,
-0.013389225117862225,
0.02569061890244484,
0.019880592823028564,
-0.017684804275631905,
0.006607480347156525,
0.03392920270562172,
0.05067333206534386,
-0.024284228682518005,
-0.020871201530098915,
-0.00030152915860526264,
-0.011588728055357933,
0.033784862607717514,
0.008637586608529091,
-0.029038598760962486,
0.09860359877347946,
-0.013683798722922802,
0.00042635423596948385,
-0.02264080010354519,
0.014918159693479538,
-0.026349451392889023,
-0.0012848351616412401,
0.009849091991782188,
0.019739937037229538,
-0.010144046507775784,
0.03575449436903,
-0.014306051656603813,
0.02928883023560047,
0.015147330239415169,
-0.027951141819357872,
-0.00341039034537971,
0.007604725193232298,
-0.0404098778963089,
0.014518915675580502,
-0.0033019259572029114,
-0.010665728710591793,
-0.006907984148710966,
0.036114759743213654,
0.03708701953291893,
0.032447412610054016,
0.008454284630715847,
0.01137686800211668,
-0.049536604434251785,
0.061004944145679474,
-0.0730501115322113,
0.009957770816981792,
-0.05372525379061699,
0.012088378891348839,
-0.029756903648376465,
-0.02132871374487877
] |
<p>Please move this if it's not in the right location.</p>
<p>I'm looking for the name of a device that I frequently see in many scenarios, specifically that of an office/library which can be described as having multiple rings that rotate in various directions. I was thinking it was a gyroscope or perhaps a celestial globe, but something tells me that it's not quite what I'm looking for. I recall that there is a movie production company which uses this device as their symbolic figure of their logo.</p> | 4,559 | [
-0.08653197437524796,
-0.018616972491145134,
-0.012102590873837471,
0.03236602619290352,
0.05811778083443642,
-0.03191971033811569,
-0.031206782907247543,
-0.0018373283091932535,
-0.028051504865288734,
-0.01479970570653677,
0.04015481844544411,
0.06374766677618027,
0.07405782490968704,
0.023866821080446243,
-0.0008052440243773162,
-0.004981628153473139,
0.0016503621591255069,
0.009257561527192593,
0.009118900634348392,
-0.05025194212794304,
0.0026259052101522684,
0.001981067005544901,
-0.04123848304152489,
0.045130304992198944,
-0.013100212439894676,
0.03304610773921013,
0.03536026552319527,
-0.03129495680332184,
0.009831354022026062,
0.04124758392572403,
-0.08827155083417892,
-0.02429969795048237,
0.00015727932623121887,
0.0263481717556715,
0.03706315904855728,
-0.023665104061365128,
-0.003950479906052351,
-0.018261415883898735,
-0.023123351857066154,
0.039761096239089966,
-0.003573292400687933,
0.026828618720173836,
-0.026461193338036537,
0.050164755433797836,
-0.03368314728140831,
0.015926796942949295,
-0.07255958765745163,
0.0012068060459569097,
0.026182452216744423,
-0.04145968705415726,
0.08868880569934845,
-0.009927176870405674,
0.004670487716794014,
0.010691607370972633,
-0.016364844515919685,
0.033689286559820175,
0.03864661231637001,
0.023770779371261597,
-0.007749692536890507,
-0.06429825723171234,
-0.03887716308236122,
0.012328509241342545,
0.0014488841407001019,
-0.028649259358644485,
0.0020032741595059633,
-0.035807058215141296,
-0.00997239351272583,
0.02565624751150608,
0.045981235802173615,
0.005076352972537279,
0.004749048035591841,
0.05817966163158417,
0.039923422038555145,
-0.021170826628804207,
-0.01531124021857977,
-0.06262742727994919,
0.012020913884043694,
0.010233568958938122,
0.04869532585144043,
-0.00346752000041306,
0.013985644094645977,
-0.0056179906241595745,
-0.017016595229506493,
-0.022308778017759323,
0.041714850813150406,
-0.010984553024172783,
0.1050650104880333,
-0.03535878658294678,
0.01727808266878128,
0.008873880840837955,
0.010272014886140823,
-0.006829982157796621,
0.029272712767124176,
0.017959995195269585,
-0.05436709150671959,
0.027789391577243805,
-0.020871488377451897,
0.03991533815860748,
-0.014923691749572754,
-0.008664654567837715,
0.0010029466357082129,
0.01371409185230732,
-0.005788556300103664,
0.07967141270637512,
-0.0038161962293088436,
0.004621407948434353,
-0.015264595858752728,
0.0268953088670969,
0.005795548669993877,
-0.007183461915701628,
-0.034757278859615326,
-0.002784981159493327,
0.028960801661014557,
0.033680785447359085,
-0.007897715084254742,
-0.0003153627912979573,
-0.016082612797617912,
0.0468132346868515,
0.039636339992284775,
0.05389774963259697,
0.05887739732861519,
-0.019376365467905998,
0.011850058101117611,
-0.08047191053628922,
-0.05903972312808037,
0.020942891016602516,
0.0330410972237587,
-0.01634404994547367,
-0.011022163555026054,
0.06153063103556633,
0.051002923399209976,
0.014871789142489433,
0.034533534198999405,
-0.01884417049586773,
0.049562688916921616,
-0.016352582722902298,
-0.08384298533201218,
-0.05662672594189644,
0.05076739564538002,
0.017643654718995094,
-0.02304554358124733,
-0.03954330459237099,
0.021766291931271553,
0.011341121979057789,
0.0664418488740921,
0.01390934269875288,
-0.06847894936800003,
0.02379089966416359,
0.049950167536735535,
-0.0024394846986979246,
-0.054245397448539734,
0.020787447690963745,
-0.0021655037999153137,
-0.05749591439962387,
-0.0043308003805577755,
-0.06010708585381508,
-0.0009681726805865765,
0.02298635058104992,
0.03145889937877655,
-0.03410935401916504,
0.019029630348086357,
-0.0029455688782036304,
-0.005356193520128727,
0.015299005433917046,
0.006020413711667061,
-0.05442128702998161,
0.06842827051877975,
-0.006293767131865025,
-0.05288482829928398,
0.035443343222141266,
0.020317792892456055,
0.05701315775513649,
0.02141348272562027,
0.020272737368941307,
0.06325740367174149,
-0.027585690841078758,
0.03778964281082153,
0.004897311795502901,
0.019762717187404633,
-0.016922635957598686,
-0.012965742498636246,
-0.054530952125787735,
-0.006842643488198519,
-0.017068497836589813,
0.012650146149098873,
0.06334507465362549,
-0.06498821824789047,
-0.01023098360747099,
0.008691532537341118,
-0.049204494804143906,
0.028122853487730026,
-0.008780228905379772,
0.01926422491669655,
-0.04285408928990364,
0.002698298776522279,
0.034659989178180695,
0.02310454100370407,
0.059408023953437805,
-0.01798137091100216,
-0.037525475025177,
0.005670131649821997,
0.009211028926074505,
0.03835303708910942,
0.012779159471392632,
-0.036781150847673416,
0.04383007809519768,
-0.01527635008096695,
-0.017004676163196564,
-0.026122672483325005,
-0.04078831151127815,
0.01865626871585846,
-0.026203608140349388,
0.006807469762861729,
0.01632469706237316,
-0.028336521238088608,
-0.011274466291069984,
0.019478950649499893,
0.06718383729457855,
0.017296843230724335,
0.005305382888764143,
-0.021105686202645302,
0.021652700379490852,
0.07780088484287262,
-0.020475242286920547,
0.02151515893638134,
0.03930274397134781,
0.029398055747151375,
0.007655238267034292,
0.00573632400482893,
-0.0362483374774456,
-0.04694679006934166,
0.007813881151378155,
0.060564640909433365,
0.0025193970650434494,
-0.01088068075478077,
0.03795398026704788,
0.030917445197701454,
0.06270825117826462,
-0.00777086615562439,
0.009316537529230118,
-0.03214900195598602,
0.014606142416596413,
0.001152867334894836,
0.011823871172964573,
0.051791831851005554,
0.0023637977428734303,
0.037264369428157806,
0.009992588311433792,
0.014356587082147598,
-0.0075034950859844685,
-0.006884596776217222,
0.029862090945243835,
-0.010698898695409298,
0.04154474288225174,
0.028955696150660515,
-0.016704950481653214,
0.03094710223376751,
-0.015048559755086899,
0.00013842439511790872,
0.012080644257366657,
0.005532201379537582,
0.01574590429663658,
-0.012689944356679916,
-0.008490512147545815,
-0.02509097009897232,
0.016086790710687637,
-0.03363370895385742,
-0.029601074755191803,
0.03863444924354553,
-0.009899928234517574,
0.042113203555345535,
-0.008502122946083546,
0.016019530594348907,
0.028770392760634422,
-0.0015336311189457774,
-0.004442758392542601,
0.018084002658724785,
0.016270693391561508,
-0.006131978239864111,
-0.0295027457177639,
-0.04513530805706978,
-0.03235061466693878,
-0.007813945412635803,
0.0037767114117741585,
-0.05849640071392059,
0.00304107996635139,
0.02963428944349289,
-0.031358398497104645,
0.0045885792933404446,
0.006709311623126268,
-0.05312629044055939,
0.01322454959154129,
0.0449119471013546,
-0.053392957895994186,
-0.00009575762669555843,
-0.03316352516412735,
0.048463184386491776,
-0.0468563437461853,
-0.01723705604672432,
0.019084293395280838,
-0.030261823907494545,
-0.03005264513194561,
0.013787918724119663,
-0.047195516526699066,
-0.014310112223029137,
0.016055282205343246,
-0.010256965644657612,
0.026582444086670876,
-0.036385003477334976,
-0.03726889193058014,
-0.011373386718332767,
0.017051327973604202,
-0.02705424837768078,
-0.018321923911571503,
-0.06214320659637451,
-0.0077848960645496845,
0.009637909941375256,
0.049792297184467316,
0.017477845773100853,
0.005152108613401651,
0.07509145885705948,
0.01896323449909687,
-0.024659909307956696,
-0.04105007275938988,
-0.02842758223414421,
0.0033876157831400633,
-0.08959298580884933,
0.013796254992485046,
0.03612696751952171,
-0.026974545791745186,
0.02607416734099388,
0.014518686570227146,
-0.024859929457306862,
0.028623245656490326,
0.005307801999151707,
-0.003012098604813218,
0.029019737616181374,
-0.016091665253043175,
-0.0004554110346361995,
0.04430880770087242,
0.010987176559865475,
-0.005690735299140215,
-0.004678130615502596,
-0.013195907697081566,
0.008262606337666512,
0.007609491236507893,
-0.055873803794384,
0.006691339425742626,
-0.032809238880872726,
-0.039833202958106995,
0.028971727937459946,
0.009643823839724064,
0.006889382377266884,
-0.04032232612371445,
-0.028448931872844696,
0.027532245963811874,
0.07896406203508377,
-0.013234398327767849,
-0.030190156772732735,
0.05580935999751091,
0.02529803104698658,
-0.01076322328299284,
-0.016634304076433182,
-0.03308212757110596,
0.021201733499765396,
0.008198466151952744,
-0.021939031779766083,
-0.010580023750662804,
0.027547672390937805,
-0.0012105798814445734,
-0.009261851198971272,
0.011378426104784012,
-0.04467114433646202,
0.021645262837409973,
-0.04787156730890274,
0.014338718727231026,
-0.0001943531387951225,
0.00822286307811737,
-0.020731093361973763,
0.03346686810255051,
0.009392350912094116,
0.02266065962612629,
0.009864968247711658,
-0.022466564550995827,
-0.03444484993815422,
0.005799590609967709,
-0.02954104356467724,
0.047829821705818176,
0.006242568138986826,
0.02946656569838524,
-0.004768263082951307,
0.005467246752232313,
-0.008076123893260956,
-0.01771361380815506,
-0.012532188557088375,
-0.05873211845755577,
0.04687149450182915,
-0.0032748219091445208,
-0.011828972026705742,
-0.004545968491584063,
0.020806601271033287,
0.03199964389204979,
0.005706168711185455,
0.09089914709329605,
-0.014249001629650593,
0.0031612145248800516,
-0.01876196824014187,
-0.008467443287372589,
-0.022730687633156776,
-0.02421049401164055,
-0.002915365854278207,
0.019200827926397324,
0.005479827988892794,
-0.02390369027853012,
-0.015742355957627296,
-0.01227203756570816,
0.02167852409183979,
0.020486703142523766,
-0.022519003599882126,
-0.022528117522597313,
-0.013908354565501213,
-0.003691607853397727,
-0.01007961854338646,
0.04001608490943909,
0.012090455740690231,
0.01945185475051403,
0.05474402755498886,
0.016290776431560516,
-0.006187110673636198,
-0.0019287458853796124,
0.044274456799030304,
0.01570001058280468,
-0.027952736243605614,
0.01389089971780777,
-0.011075186543166637,
-0.01424476783722639,
-0.017811762169003487,
-0.0018816973315551877,
0.0028302171267569065,
-0.024348771199584007,
-0.011961782351136208,
-0.012108147144317627,
-0.025647036731243134,
-0.05036723613739014,
0.007222866639494896,
-0.030378757044672966,
0.036350544542074203,
-0.0063060009852051735,
0.026345590129494667,
0.03538653254508972,
0.015521829947829247,
0.016155285760760307,
0.045681990683078766,
-0.029271848499774933,
-0.09378734976053238,
-0.011075998656451702,
0.04172106087207794,
0.023495489731431007,
-0.004409343004226685,
-0.0023022908717393875,
-0.04404255747795105,
-0.0169274490326643,
0.006666970439255238,
-0.03796038404107094,
0.026479067280888557,
-0.018685312941670418,
-0.0004960353835485876,
0.001176689867861569,
-0.012861869297921658,
0.014091426506638527,
-0.0015495617408305407,
-0.054425109177827835,
-0.022990457713603973,
-0.004907841328531504,
0.007169628981500864,
0.005978976842015982,
0.00474936468526721,
0.03201431408524513,
-0.001213765237480402,
0.04201846942305565,
-0.020967407152056694,
0.028442060574889183,
0.06112382933497429,
-0.03295779973268509,
-0.0641479641199112,
-0.00011436209024395794,
0.030367450788617134,
-0.024867793545126915,
0.038321930915117264,
-0.027160266414284706,
-0.030604243278503418,
0.0032519157975912094,
-0.03027205727994442,
0.005288660991936922,
0.0008992028888314962,
-0.017306560650467873,
-0.022751593962311745,
0.08320760726928711,
0.03744727000594139,
0.05366841331124306,
0.03292655572295189,
-0.004484137520194054,
0.007953706197440624,
-0.019226161763072014,
0.015203527174890041,
-0.004858492407947779,
-0.00409415690228343,
-0.01860075816512108,
0.014564269222319126,
-0.049244917929172516,
0.017718739807605743,
-0.006076810881495476,
0.009928347542881966,
0.03763697296380997,
-0.00920412689447403,
-0.03133707493543625,
0.036829929798841476,
-0.010349966585636139,
-0.009578656405210495,
0.0323747843503952,
0.029261330142617226,
0.02265382558107376,
-0.015655547380447388,
-0.005277095828205347,
-0.03538445010781288,
0.007764509413391352,
0.04995761439204216,
-0.007546319626271725,
-0.010784627869725227,
-0.03332505002617836,
-0.014264484867453575,
0.009752398356795311,
-0.02804684080183506,
0.08793831616640091,
-0.021062927320599556,
0.011614298447966576,
0.05416669324040413,
-0.06730323284864426,
-0.05318779870867729,
0.013906355947256088,
0.00849048513919115,
-0.02189752645790577,
-0.04674479737877846,
-0.019801024347543716,
-0.030442558228969574,
0.016843479126691818,
-0.027630286291241646,
-0.01918473280966282,
0.04251370579004288,
0.01891608163714409,
-0.020477397367358208,
-0.01642422564327717,
0.012143396772444248,
0.014625057578086853,
-0.046744655817747116,
-0.010178572498261929,
0.00876972172409296,
-0.028216637670993805,
-0.0032929866574704647,
0.03527674823999405,
-0.002160457894206047,
0.0763467475771904,
0.012151329778134823,
-0.036252498626708984,
0.0016589828301221132,
0.02176242135465145,
0.00422805268317461,
-0.0030824674759060144,
0.05492519959807396,
-0.023258738219738007,
-0.05603604391217232,
-0.01169124711304903,
0.027898525819182396,
0.050642918795347214,
-0.04266707971692085,
0.03371372073888779,
0.03535231202840805,
-0.0028730144258588552,
-0.014537390321493149,
-0.0222514308989048,
0.006645528133958578,
-0.011358106508851051,
0.005960205569863319,
-0.030041348189115524,
0.003990300465375185,
-0.0205735731869936,
-0.03981487825512886,
0.005744584370404482,
0.03708433732390404,
-0.018065983429551125,
-0.0034802777227014303,
0.06469187140464783,
0.009118028916418552,
0.006208326667547226,
0.03974982351064682,
-0.015474407933652401,
0.022325478494167328,
-0.014100898057222366,
0.004486727062612772,
0.00565206166356802,
0.01904498040676117,
-0.024255279451608658,
-0.01835040934383869,
0.004100147169083357,
-0.01393147837370634,
0.05626021698117256,
-0.033533234149217606,
0.04484305530786514,
0.0635349303483963,
-0.009830235503613949,
-0.007703568786382675,
-0.009546633809804916,
-0.004791988525539637,
0.016948293894529343,
-0.0008127060136757791,
0.05809581279754639,
-0.029568230733275414,
0.037533994764089584,
0.016086895018815994,
0.05383088439702988,
0.0009384836885146797,
-0.007407220546156168,
0.039345767349004745,
0.016457363963127136,
-0.011789070442318916,
0.014240600168704987,
-0.051264699548482895,
0.02168886363506317,
-0.027127206325531006,
0.07331325858831406,
0.014749390073120594,
-0.012895825318992138,
0.03607102483510971,
0.011423691175878048,
0.008456303738057613,
-0.022062405943870544,
-0.0022326158359646797,
-0.029335608705878258,
-0.00707126734778285,
0.01320229098200798,
0.002053804462775588,
-0.06398168951272964,
-0.013200348243117332,
0.056218892335891724,
-0.0008280860492959619,
-0.0077365972101688385,
-0.034289635717868805,
-0.04104316234588623,
-0.03824946656823158,
-0.0048682778142392635,
-0.03987829387187958,
0.07138131558895111,
-0.014348885975778103,
0.011956451460719109,
0.007627740036696196,
-0.037659235298633575,
-0.038536496460437775,
0.034991856664419174,
0.047127172350883484,
0.011866842396557331,
0.07674645632505417,
-0.014788436703383923,
0.02259071171283722,
-0.029059475287795067,
0.0009094835841096938,
0.13040077686309814,
0.027509717270731926,
0.024740098044276237,
-0.054705239832401276,
-0.013749543577432632,
-0.02609890326857567,
0.00848784577101469,
-0.05918605253100395,
0.02467965893447399,
-0.05354373902082443,
0.058669500052928925,
0.03893359377980232,
0.05583999305963516,
-0.003665665164589882,
0.033648837357759476,
0.024859368801116943,
0.02017776295542717,
-0.02152007445693016,
0.01915816217660904,
-0.010449898429214954,
-0.016686752438545227,
0.0032863968517631292,
-0.06917351484298706,
0.05091480910778046,
-0.03485811501741409,
-0.014450540766119957,
-0.033347323536872864,
-0.03741836920380592,
0.040284376591444016,
0.02449614368379116,
-0.005249695852398872,
-0.002995268441736698,
-0.012467469088733196,
-0.01917419582605362,
-0.011748675256967545,
-0.0004763341275975108,
0.010927214287221432,
0.00014523642312269658,
0.004583613481372595,
0.039389435201883316,
0.00416575837880373,
0.0009495930280536413,
0.02995271235704422,
-0.01118239015340805,
-0.032085053622722626,
-0.007216479629278183,
0.00016606833378318697,
-0.03148141875863075,
-0.0185660682618618,
0.04601011425256729,
-0.052815992385149,
0.02106822095811367,
-0.0057942126877605915,
-0.044558946043252945,
-0.005422007758170366,
0.00409090006724,
0.005077457055449486,
0.011483095586299896,
-0.03502149507403374,
-0.00020270240202080458,
0.012187963351607323,
-0.0170894805341959,
0.01534283347427845,
-0.04634916037321091,
-0.0066304635256528854,
0.04500005766749382,
0.0035651850048452616,
0.03788863122463226,
-0.003371293656527996,
0.000447986793005839,
-0.005870372522622347,
0.02502782829105854,
-0.046583015471696854,
0.0360250249505043,
-0.020408086478710175,
0.00679168151691556,
0.010896716266870499,
0.0251101553440094,
-0.026406684890389442,
-0.012328516691923141,
-0.009536485187709332,
0.009185087867081165,
-0.03275233134627342,
-0.06197410449385643,
-0.01312705036252737,
-0.020904401317238808,
0.057800114154815674,
-0.009906389750540257,
0.009372932836413383,
0.0033045108430087566,
-0.000749384518712759,
0.021774712949991226,
0.018729500472545624,
-0.011615951545536518,
-0.018324242904782295,
0.028953280299901962,
-0.02631768211722374,
-0.008136496879160404,
-0.0528683103621006,
0.039570003747940063,
0.02646140195429325,
-0.012974269688129425,
0.032640766352415085,
0.022312447428703308,
-0.046928294003009796,
-0.004355122800916433,
0.014252572320401669,
-0.03450089693069458,
-0.0033393255434930325,
-0.006174566689878702,
-0.025798022747039795,
-0.04432147741317749,
-0.013192089274525642,
0.005561846774071455,
-0.02485790103673935,
-0.00014860973169561476,
0.04941554740071297,
-0.03339564800262451,
0.0232350155711174,
-0.03026692196726799,
0.024022217839956284,
-0.027127545326948166,
0.04824231564998627,
-0.04108082503080368,
-0.03041447512805462,
0.03653459623456001,
-0.0027778639923781157,
-0.03114917501807213,
0.04052487015724182,
-0.017333460971713066,
-0.0025782946031540632,
0.017481643706560135,
-0.017652789130806923,
-0.01593557372689247,
0.018858976662158966,
-0.0131716663017869,
-0.024494990706443787,
0.008532962761819363,
-0.016276327893137932,
0.014841437339782715,
0.04456595331430435,
0.004378035198897123,
-0.027842232957482338,
0.025524143129587173,
0.01976059563457966,
0.023542148992419243,
0.0229208804666996,
-0.0015846927417442203,
0.012119767256081104,
0.021258873865008354,
-0.0238664411008358,
-0.030327076092362404,
0.007396823260933161,
0.006948061753064394,
0.04562221094965935,
-0.021210037171840668,
0.014513335190713406,
-0.04600147157907486,
-0.041831597685813904,
0.010791417211294174,
0.05977996811270714,
-0.004489355720579624,
-0.013164609670639038,
-0.025863999500870705,
-0.03507372364401817,
-0.002738119103014469,
0.007172653451561928,
0.02310831844806671,
0.03807792812585831,
-0.014708149246871471,
-0.0721578374505043,
0.012268108315765858,
0.04232792183756828,
-0.007491367403417826,
-0.046019431203603745,
-0.038110338151454926,
-0.005921824369579554,
-0.006678537931293249,
0.03934602439403534,
-0.053600527346134186,
-0.023052873089909554,
0.04775593429803848,
-0.04509943723678589,
0.034293316304683685,
-0.013868428766727448,
-0.06400939077138901,
-0.022515293210744858,
-0.01898159645497799,
0.02645527943968773,
0.013536836951971054,
0.006029664073139429,
0.016305336728692055,
0.017834734171628952,
0.02999788336455822,
-0.04591258615255356,
-0.04085197672247887,
0.015927691012620926,
-0.0017384740058332682,
0.009642395190894604,
0.0030003131832927465,
0.04495115205645561,
-0.02611834555864334,
-0.03764143958687782,
0.07952482253313065,
-0.01102896872907877,
0.020197482779622078,
-0.011181708425283432,
-0.00805414654314518,
0.008598149754106998,
0.04062250629067421,
0.014717974700033665,
0.012717663310468197,
-0.11363624781370163,
0.0223676860332489,
0.022533591836690903,
0.04779771342873573,
-0.004864661023020744,
-0.009007067419588566,
0.001203635474666953,
-0.03618641570210457,
-0.020352764055132866,
0.015701891854405403,
-0.05071143060922623,
0.029102638363838196,
-0.02398773655295372,
0.0012229093117639422,
-0.009858731180429459,
-0.006431924179196358,
0.018224170431494713,
-0.04458892345428467,
0.00005200774467084557,
-0.005801146384328604,
-0.022971780970692635,
0.009346188977360725,
0.03140438720583916,
0.019402949139475822,
-0.05676698312163353,
0.024475131183862686,
-0.04202526435256004,
-0.03454063460230827,
-0.07297085225582123,
0.0031932578422129154,
0.015779893845319748,
-0.01852375455200672,
0.025340968742966652,
0.01224882435053587,
0.016373824328184128,
0.040474388748407364,
0.018878737464547157,
0.019049715250730515,
0.025685075670480728,
-0.043652985244989395,
-0.0076712435111403465,
-0.03214457258582115,
0.034110840409994125,
0.023798979818820953,
0.00024014049267861992,
-0.030576283112168312,
-0.06690677255392075,
-0.022799497470259666,
0.02651921473443508,
0.05125388503074646,
-0.015625059604644775,
0.01561531238257885,
0.00933228712528944,
-0.0012910111108794808,
0.012928917072713375,
-0.038965631276369095,
0.008916058577597141,
0.025382673367857933,
-0.05585647374391556,
0.02769174985587597,
-0.03257276862859726,
-0.03209587186574936,
-0.04322724789381027,
0.027763331308960915,
0.0014243503101170063,
0.005856858100742102,
-0.0426708422601223,
-0.0035429943818598986,
0.016963070258498192,
0.035930465906858444,
-0.020416254177689552,
0.05280281975865364,
-0.020430121570825577,
-0.03606234863400459,
0.015458332374691963,
-0.034026727080345154,
-0.027035659179091454,
0.038948528468608856,
-0.02771274372935295,
-0.022430049255490303,
-0.03832335025072098,
-0.004923062864691019,
0.054597146809101105,
-0.05570143833756447,
-0.007237753365188837,
0.00390617735683918,
-0.04200822860002518,
-0.019953565672039986,
0.08727457374334335,
-0.011333657428622246,
0.01270341593772173,
-0.007943263277411461,
0.007605695631355047,
0.02261766605079174,
-0.030527591705322266,
0.013279865495860577,
0.05678250640630722,
0.01662754826247692,
0.051016222685575485,
0.006544026080518961,
0.022840870544314384,
0.01951989345252514,
0.04152657836675644,
-0.011142211966216564,
0.03404984623193741,
-0.03542761877179146,
0.014868268743157387,
0.0171646848320961,
-0.019448615610599518,
-0.027709510177373886,
0.012402229011058807,
-0.012329122982919216,
0.05793371424078941,
-0.01423143781721592,
0.0019239488756284118,
-0.05251602455973625,
0.007422506809234619,
0.017124680802226067,
0.006873914506286383,
0.004596962593495846,
0.015019197948276997,
-0.03635125607252121,
0.031940482556819916,
-0.009243969805538654,
-0.023335669189691544,
0.0049160500057041645,
-0.011545704677700996,
0.0043753162026405334,
-0.04052186757326126,
0.01964607462286949,
0.004768499173223972,
-0.016812309622764587,
-0.02435447834432125,
-0.026381831616163254,
0.004156759474426508,
-0.004217888694256544,
0.01802784763276577,
0.0018261814257130027,
0.0020225171465426683,
-0.004929513204842806,
0.016802456229925156,
-0.07378513365983963,
0.013969216495752335,
-0.02102353423833847,
0.059564054012298584,
0.00948654767125845,
0.028331847861409187
] |
<p>Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that satisfy some differential equation. What mathematical result says that modeling fluids as continuous objects can accurately predict the discrete behavior of the particles? I don't know anything about fluid mechanics, so my initial assumption may in itself be wrong.</p> | 187 | [
-0.014553994871675968,
-0.033004049211740494,
0.001167152775451541,
-0.018027719110250473,
0.027426207438111305,
-0.013141743838787079,
-0.014942700043320656,
0.01039491593837738,
-0.009574736468493938,
0.01253190916031599,
0.06422237306833267,
0.01499229297041893,
0.041232381016016006,
0.00434560002759099,
0.018344901502132416,
0.008223094046115875,
-0.028616728261113167,
-0.014636264182627201,
0.0181743111461401,
0.004052018281072378,
-0.005713023245334625,
0.021828796714544296,
0.04561842978000641,
-0.03249923884868622,
-0.021680742502212524,
0.025613807141780853,
0.006029730662703514,
-0.023802652955055237,
0.019997041672468185,
0.016431264579296112,
-0.01165845524519682,
-0.03351925313472748,
0.018855953589081764,
0.06256652623414993,
-0.028668290004134178,
0.027919674292206764,
-0.055436573922634125,
-0.017132489010691643,
-0.029183510690927505,
0.009067774750292301,
-0.08773525059223175,
-0.04931911453604698,
0.013178727589547634,
0.03916526213288307,
-0.023982873186469078,
0.01766088418662548,
0.03813895210623741,
-0.04513582959771156,
0.04792199283838272,
-0.06353091448545456,
0.09529539197683334,
0.011543580330908298,
0.07548223435878754,
0.00660737557336688,
-0.00644089188426733,
0.003083043498918414,
0.0628155767917633,
0.06223471090197563,
-0.018731066957116127,
-0.036540910601615906,
-0.013234381563961506,
-0.0015451119979843497,
0.013803543522953987,
-0.026751894503831863,
-0.011198634281754494,
0.021361209452152252,
-0.017687495797872543,
-0.04376358538866043,
-0.010364644229412079,
0.006325933150947094,
-0.015872521325945854,
-0.010186073370277882,
0.0768229067325592,
0.033581413328647614,
0.03157694265246391,
0.04357170686125755,
-0.002456189366057515,
0.004671662580221891,
0.029218105599284172,
0.023876843973994255,
-0.052716419100761414,
-0.022596821188926697,
0.027464624494314194,
0.03337232396006584,
-0.01503756269812584,
-0.028742732480168343,
0.054118309170007706,
-0.005907203536480665,
0.04072760045528412,
0.014681367203593254,
-0.034712255001068115,
-0.0077650099992752075,
0.028755642473697662,
0.0053371586836874485,
-0.04264300689101219,
0.0033170508686453104,
0.017104333266615868,
0.01064316090196371,
0.0008569898782297969,
-0.049916163086891174,
-0.00608075363561511,
-0.028683241456747055,
0.01877325214445591,
0.07576778531074524,
-0.0360310934484005,
-0.01699361577630043,
-0.04804769158363342,
-0.024402232840657234,
-0.037859175354242325,
0.0047362265177071095,
-0.009252402931451797,
-0.009775565005838871,
0.00009439125278731808,
-0.01928456872701645,
0.036927998065948486,
0.010483097285032272,
0.023864692077040672,
-0.04322914779186249,
0.04658785089850426,
0.07823649793863297,
0.05195601284503937,
-0.04292837902903557,
0.033820990473032,
-0.0052619208581745625,
-0.04257713630795479,
0.0014852741733193398,
0.027429966256022453,
-0.025503192096948624,
-0.029509564861655235,
0.015918517485260963,
-0.0030755377374589443,
0.0025243188720196486,
-0.010385291650891304,
0.016708238050341606,
0.025399012491106987,
-0.04699106141924858,
-0.053509436547756195,
-0.0142213748767972,
0.031732697039842606,
-0.0011702030897140503,
-0.031224071979522705,
-0.07065389305353165,
0.004244655836373568,
0.05272158235311508,
0.05541706085205078,
-0.007431701757013798,
0.008871067315340042,
-0.020567307248711586,
0.06876825541257858,
-0.03910116106271744,
-0.05320106819272041,
0.012168310582637787,
0.003107136581093073,
-0.016167052090168,
-0.02004542201757431,
-0.02837379090487957,
0.028795184567570686,
0.015831513330340385,
0.029493296518921852,
-0.02081909030675888,
0.05256909132003784,
-0.03199660778045654,
-0.006289077457040548,
0.017764519900083542,
0.01975477673113346,
-0.03025011159479618,
0.035918042063713074,
-0.0016882600029930472,
0.04094308242201805,
0.01803654246032238,
0.04578125849366188,
0.008196390233933926,
0.04158417880535126,
0.04375984147191048,
0.03997022286057472,
-0.03635483980178833,
-0.0016432498814538121,
-0.004569368436932564,
0.0036948348861187696,
0.003916905727237463,
-0.00687124440446496,
-0.024776943027973175,
0.002666271524503827,
0.004847235046327114,
-0.011527123861014843,
0.008574375882744789,
0.008830650709569454,
-0.00040850197547115386,
0.0023147279862314463,
-0.050419751554727554,
-0.005949525628238916,
-0.08551570028066635,
0.042607858777046204,
-0.005607799626886845,
-0.0009148039971478283,
0.06306901574134827,
0.006251256447285414,
0.005376540590077639,
-0.04329264536499977,
-0.024202410131692886,
-0.05848926305770874,
-0.030099039897322655,
0.001190611277706921,
-0.026882071048021317,
0.005236449651420116,
0.038701482117176056,
0.038226135075092316,
0.010044139809906483,
-0.0005341393407434225,
0.02442280575633049,
-0.042885202914476395,
-0.02909930795431137,
-0.013157788664102554,
0.053365882486104965,
-0.053850769996643066,
-0.0235764030367136,
0.03655301406979561,
-0.029858572408556938,
0.0006025148322805762,
0.027434904128313065,
-0.040963269770145416,
0.0342264324426651,
0.047220148146152496,
0.014941687695682049,
0.0005374145694077015,
0.021441278979182243,
0.005777962040156126,
-0.03873085230588913,
0.013521447777748108,
-0.0377371720969677,
-0.03398815542459488,
0.0028001333121210337,
0.04871841147542,
0.07837200164794922,
-0.01780243031680584,
-0.017009779810905457,
0.025087673217058182,
0.04809315875172615,
0.031813472509384155,
0.009051202796399593,
-0.03224831447005272,
-0.00020948574820067734,
0.041615080088377,
0.012733984738588333,
0.029090339317917824,
0.0011702061165124178,
0.004877097439020872,
0.028667710721492767,
0.028131645172834396,
-0.0037058796733617783,
-0.030818143859505653,
0.020773563534021378,
0.010202622041106224,
-0.021107560023665428,
-0.041292790323495865,
-0.0109937135130167,
0.039470136165618896,
-0.0218958780169487,
-0.01572473719716072,
0.027057502418756485,
-0.007757402025163174,
-0.0005541466525755823,
-0.042005449533462524,
-0.002691948786377907,
0.042627543210983276,
0.004639414604753256,
-0.02099899761378765,
-0.025346778333187103,
0.031986918300390244,
-0.06290887296199799,
0.011308273300528526,
-0.009153875522315502,
-0.004626346752047539,
-0.014058689586818218,
0.04116019606590271,
0.0070572285912930965,
0.02982700988650322,
0.002950102323666215,
-0.01702849008142948,
-0.02185540646314621,
-0.0064038499258458614,
-0.0310056172311306,
0.009826641529798508,
0.03474343940615654,
-0.07720860838890076,
0.01004074141383171,
-0.017048461362719536,
-0.03317305073142052,
0.046077851206064224,
0.0032000108622014523,
0.0030442147981375456,
0.016414286568760872,
-0.03575308993458748,
-0.049063362181186676,
0.009427051991224289,
-0.025998365134000778,
-0.003013580571860075,
-0.0306672565639019,
0.007935306057333946,
0.01074153371155262,
-0.03357679396867752,
-0.026678627356886864,
-0.00783361867070198,
-0.02710186317563057,
-0.042834341526031494,
-0.021070878952741623,
-0.0032690120860934258,
0.022408807650208473,
-0.014373553916811943,
0.03175831213593483,
0.05661514401435852,
-0.03669163957238197,
0.0016377302818000317,
-0.06625702977180481,
-0.07257408648729324,
0.02810768224298954,
-0.0355856753885746,
0.04772545397281647,
0.008661797270178795,
-0.012893479317426682,
0.04576269909739494,
-0.016088318079710007,
-0.07876648008823395,
0.025670824572443962,
0.0023067903239279985,
-0.001706996001303196,
-0.02363482490181923,
0.015493398532271385,
0.030017241835594177,
-0.0021187427919358015,
-0.013486407697200775,
0.027827151119709015,
0.0051114922389388084,
0.016494331881403923,
-0.0026431602891534567,
-0.007815900258719921,
0.02107289619743824,
0.006284192204475403,
0.03228634223341942,
-0.007734695915132761,
0.028855351731181145,
-0.04252399504184723,
0.0585695281624794,
-0.03157270699739456,
0.02817993238568306,
0.03451774641871452,
-0.06094764173030853,
0.04138358309864998,
0.009221041575074196,
0.00821947306394577,
0.003515716176480055,
0.023850353434681892,
-0.03959910199046135,
-0.03972340375185013,
0.012234659865498543,
0.04952147603034973,
0.02338755503296852,
-0.0017545059090480208,
-0.007980597205460072,
0.046133432537317276,
0.046003442257642746,
-0.011719942092895508,
-0.02350747399032116,
-0.01043652929365635,
-0.03894522413611412,
0.03890259563922882,
-0.02868793159723282,
-0.00036003030254505575,
0.046995069831609726,
-0.007733452599495649,
0.008346318267285824,
-0.014586100354790688,
-0.03316766023635864,
-0.018476715311408043,
-0.04882711544632912,
-0.004727042745798826,
-0.016853058710694313,
0.037007447332143784,
-0.006885427515953779,
0.07232517749071121,
-0.01033055130392313,
0.01676253415644169,
-0.00911976583302021,
0.027309836819767952,
-0.09162985533475876,
0.0008437808719463646,
0.0018853673245757818,
0.009720404632389545,
0.00003449700307101011,
-0.011610799469053745,
0.04992571100592613,
-0.024331718683242798,
-0.01647902838885784,
-0.004403170198202133,
0.009977051056921482,
-0.038733791559934616,
-0.03308115527033806,
-0.047712910920381546,
-0.043664976954460144,
-0.011325237341225147,
-0.007951479405164719,
0.025078466162085533,
-0.032943207770586014,
0.061360716819763184,
0.0378476046025753,
-0.028979357331991196,
-0.008001305162906647,
-0.02084316872060299,
0.025923795998096466,
0.0380987673997879,
0.014518443495035172,
0.04178585857152939,
0.030689746141433716,
-0.012305159121751785,
0.020519115030765533,
-0.010531200096011162,
0.04879281669855118,
-0.015239579603075981,
0.002804761053994298,
-0.024565355852246284,
-0.06999135762453079,
-0.005035568494349718,
0.03666290268301964,
0.043936435133218765,
0.012414572760462761,
0.009639941155910492,
0.05275432765483856,
0.005231106653809547,
0.004635154269635677,
0.029208585619926453,
0.043011561036109924,
0.036641426384449005,
-0.04474227502942085,
-0.028661372140049934,
0.011396773159503937,
-0.00360465538688004,
0.029664963483810425,
0.020922524854540825,
0.005630696192383766,
0.0036943566519767046,
0.008940929546952248,
-0.0033427507150918245,
0.01209236029535532,
-0.024874113500118256,
-0.06642996519804001,
0.0008790476713329554,
0.04651889204978943,
-0.026737239211797714,
0.02080090157687664,
0.021591419354081154,
0.059762004762887955,
0.01421317458152771,
0.008660270832479,
-0.024991052225232124,
-0.1052650511264801,
0.006045463960617781,
0.02233383245766163,
0.005219066981226206,
-0.0012901582522317767,
0.0166939664632082,
-0.04127984866499901,
-0.01858162321150303,
0.05717477574944496,
0.0019246741430833936,
-0.027121176943182945,
0.012808400206267834,
-0.007273707073181868,
0.00817870069295168,
-0.0013410490937530994,
-0.016544057056307793,
0.018045606091618538,
0.008396981284022331,
-0.00112108641769737,
-0.031602539122104645,
0.00023755153233651072,
-0.05386856943368912,
0.020378315821290016,
0.03974739462137222,
0.027122147381305695,
0.022022463381290436,
-0.019083507359027863,
0.022543301805853844,
-0.006844073534011841,
-0.05496404692530632,
-0.04554476588964462,
0.010312141850590706,
0.004418717697262764,
0.009105476550757885,
0.030735019594430923,
-0.022124068811535835,
-0.044640835374593735,
0.014527034014463425,
-0.0046248240396380424,
-0.013294327072799206,
0.0193566232919693,
-0.02261429652571678,
0.05550359562039375,
-0.010719327256083488,
0.01364605501294136,
0.034265872091054916,
0.03642715513706207,
0.00930837169289589,
-0.04143165051937103,
-0.018711760640144348,
0.043279096484184265,
0.00813988409936428,
-0.01179475337266922,
-0.041870471090078354,
-0.006941383704543114,
-0.025650465860962868,
0.013671787455677986,
0.010505050420761108,
-0.0021728642750531435,
0.030600938946008682,
-0.03120666742324829,
0.018600542098283768,
0.03210610896348953,
0.025847485288977623,
-0.02234571985900402,
-0.022069914266467094,
0.026966042816638947,
0.035995081067085266,
-0.0034774041268974543,
0.04474861919879913,
-0.002906297566369176,
-0.0005307838437147439,
0.010727636516094208,
-0.0468672551214695,
-0.005119262728840113,
-0.0072508277371525764,
-0.012899958528578281,
0.019016820937395096,
0.0031891928520053625,
0.04750126227736473,
-0.02104855701327324,
0.006662525702267885,
0.014650901779532433,
-0.06945935636758804,
0.003919993527233601,
0.012794777750968933,
-0.004155145958065987,
0.04595638066530228,
-0.024880433455109596,
-0.01014652755111456,
0.003736874321475625,
0.011562601663172245,
-0.07287665456533432,
-0.06508412212133408,
0.04112106189131737,
0.02641284465789795,
-0.014734533615410328,
-0.06732058525085449,
0.017906391993165016,
-0.06278897076845169,
-0.028906235471367836,
0.02545084059238434,
0.06380365043878555,
-0.008379578590393066,
-0.0250865388661623,
0.04350660368800163,
0.03719327226281166,
0.03674958273768425,
0.007858160883188248,
-0.006734178401529789,
-0.006362604908645153,
0.003779957303777337,
-0.0006886511691845953,
-0.022777503356337547,
0.04557833820581436,
-0.031590819358825684,
0.03221353515982628,
-0.0057302359491586685,
-0.031431928277015686,
0.033649519085884094,
-0.04612018167972565,
0.02187325805425644,
0.018826773390173912,
-0.014509678818285465,
0.013796665705740452,
-0.009518851526081562,
-0.00823595654219389,
-0.015059247612953186,
0.024322520941495895,
-0.014152285642921925,
-0.0016525911632925272,
0.016687415540218353,
-0.025001147761940956,
0.05344127118587494,
0.008937312290072441,
-0.03430769592523575,
0.026012012735009193,
0.04548485577106476,
-0.019554786384105682,
-0.015237107872962952,
0.03684861958026886,
0.01593315601348877,
0.03452010452747345,
-0.014369270764291286,
-0.012925154529511929,
0.001158271566964686,
0.02352498471736908,
-0.04230693727731705,
-0.05294746160507202,
-0.04451757296919823,
0.011729962192475796,
0.02729475311934948,
-0.04817657545208931,
0.03476179391145706,
0.01457833219319582,
0.020053470507264137,
-0.03231915086507797,
-0.008239061571657658,
-0.005275678355246782,
0.04739407077431679,
-0.02055729553103447,
0.029176298528909683,
-0.036439962685108185,
-0.03562169894576073,
-0.00034088685060851276,
0.03068646229803562,
-0.039771031588315964,
0.008483808487653732,
0.0044429670087993145,
0.00210237642750144,
-0.0028245681896805763,
-0.0006743675330653787,
-0.011551612988114357,
0.04057374224066734,
-0.04735206067562103,
0.023456202819943428,
0.0007204698049463332,
0.011646929197013378,
0.02251674048602581,
0.008284552954137325,
0.015062428079545498,
-0.02333640493452549,
0.007062702439725399,
-0.01133725792169571,
0.04137936979532242,
0.024676773697137833,
0.022313978523015976,
0.011761413887143135,
0.020366759970784187,
0.0031792777590453625,
0.02910805121064186,
0.007939578033983707,
0.017050035297870636,
-0.04769100621342659,
-0.002098327036947012,
-0.034347690641880035,
-0.03665495663881302,
0.008984049782156944,
0.05319059640169144,
-0.05139434337615967,
-0.00911503005772829,
0.005689407233148813,
0.035158928483724594,
0.019589629024267197,
0.009943561628460884,
-0.011925320141017437,
0.05280293896794319,
-0.01380901224911213,
0.011294707655906677,
-0.04337527975440025,
0.02273445762693882,
0.09869562834501266,
0.0564526729285717,
0.03887170925736427,
-0.06821301579475403,
0.009630227461457253,
-0.0007237571990117431,
-0.009848455898463726,
-0.057537976652383804,
0.02985142171382904,
0.02874087542295456,
0.010154652409255505,
-0.015551730990409851,
0.049143530428409576,
0.0102101881057024,
0.022386476397514343,
0.04161643236875534,
-0.05398686230182648,
-0.03803924471139908,
-0.021539174020290375,
-0.02137668989598751,
-0.012563487514853477,
0.029275404289364815,
-0.05293211713433266,
0.023091347888112068,
-0.009788078255951405,
-0.019207367673516273,
-0.019599709659814835,
-0.003345229895785451,
0.012455726973712444,
0.009252050891518593,
-0.060977671295404434,
-0.005784221459180117,
0.004395224619656801,
-0.025113418698310852,
-0.043429069221019745,
0.00037269823951646686,
0.011191128753125668,
-0.0012850320199504495,
0.021829068660736084,
0.01613593101501465,
0.0033530823420733213,
0.04067125543951988,
-0.014260898344218731,
0.013141823001205921,
-0.022431857883930206,
-0.02115790732204914,
-0.08260833472013474,
0.026375068351626396,
-0.03330923244357109,
-0.0031585770193487406,
0.020599784329533577,
-0.023632323369383812,
-0.023184064775705338,
-0.04465219005942345,
-0.04425932094454765,
-0.007953120395541191,
0.031180983409285545,
0.00045278953621163964,
-0.008694288320839405,
-0.04198850691318512,
0.04815756902098656,
-0.04499495401978493,
-0.006481533870100975,
0.007356741465628147,
-0.04402971640229225,
0.007162168156355619,
0.03371957689523697,
0.040618136525154114,
-0.0010522652883082628,
-0.02738817408680916,
-0.036750297993421555,
-0.01606120727956295,
-0.0443127416074276,
-0.0005436959327198565,
0.006527324207127094,
0.017841611057519913,
0.026991214603185654,
-0.007027693558484316,
0.0215160995721817,
0.020204300060868263,
-0.06885404139757156,
0.031051000580191612,
0.004299935884773731,
-0.027231285348534584,
-0.04090390354394913,
0.005007444880902767,
-0.028766538947820663,
0.0407462902367115,
-0.03982989117503166,
0.001365805510431528,
-0.023810483515262604,
0.02287951670587063,
0.01786785013973713,
-0.026458298787474632,
-0.022246628999710083,
-0.00011165870819240808,
-0.04713030532002449,
0.009134015068411827,
0.010841215029358864,
0.0617201142013073,
0.017738591879606247,
0.021519973874092102,
0.008880866691470146,
0.03551315516233444,
-0.009211241267621517,
0.043530695140361786,
0.013365209102630615,
-0.004697167780250311,
-0.01960691623389721,
0.02433186024427414,
-0.006208238657563925,
-0.046732645481824875,
-0.06475073844194412,
-0.025172462686896324,
0.010476706549525261,
0.004130578599870205,
-0.012608411721885204,
-0.00798964872956276,
-0.012006710283458233,
-0.013571416959166527,
0.040450651198625565,
-0.040269553661346436,
-0.008719922974705696,
-0.06936785578727722,
0.0039821709506213665,
0.005836049560457468,
-0.04294411092996597,
0.009123513475060463,
-0.011410274542868137,
-0.0025624583940953016,
-0.012101455591619015,
0.041975926607847214,
0.003837119322270155,
0.04695095494389534,
-0.004072705749422312,
0.04656095802783966,
-0.011461344547569752,
0.05702505633234978,
-0.023116830736398697,
-0.0609552264213562,
0.04198799654841423,
-0.021751463413238525,
-0.0522596649825573,
0.0009741269750520587,
-0.045882899314165115,
0.00673076044768095,
0.002996940864250064,
0.008714293129742146,
0.0007339944713748991,
0.08052290976047516,
-0.017120106145739555,
0.02149191126227379,
-0.0037915261927992105,
-0.009139001369476318,
-0.028285110369324684,
-0.05998820438981056,
0.034758929163217545,
-0.00011738791363313794,
0.0011440836824476719,
0.0285001453012228,
0.042450617998838425,
0.01868956722319126,
-0.027405517175793648,
0.044245097786188126,
-0.02444574236869812,
0.017356254160404205,
0.05987919494509697,
0.059456922113895416,
0.01834232732653618,
0.07344046235084534,
-0.04075690358877182,
0.008679087273776531,
0.035404641181230545,
-0.0019280381966382265,
-0.10155583173036575,
-0.002846948802471161,
0.02246519923210144,
-0.007921497337520123,
0.012991823256015778,
-0.0511757992208004,
-0.013255343772470951,
0.032346319407224655,
-0.04573717340826988,
-0.02766469120979309,
-0.06235428526997566,
-0.0012761555844917893,
-0.029896920546889305,
-0.02863762155175209,
-0.03377606347203255,
0.04957479238510132,
0.037021394819021225,
0.022400571033358574,
0.0007156888605095446,
0.002800244139507413,
0.005304606631398201,
0.011640523560345173,
0.033765967935323715,
0.0395192950963974,
-0.013018729165196419,
-0.016422150656580925,
0.05255912244319916,
-0.003649976570159197,
-0.01901174895465374,
-0.007307234685868025,
0.00007511140574933961,
0.004211817402392626,
0.0016820685705170035,
0.0008760610944591463,
-0.005779738537967205,
0.04087386652827263,
0.009065086022019386,
-0.005402334034442902,
0.012120402418076992,
0.035803720355033875,
0.010663595981895924,
0.02933088317513466,
-0.03364282473921776,
0.007322909776121378,
0.025869207456707954,
-0.015668882057070732,
-0.05943233147263527,
0.048038266599178314,
0.004258155357092619,
-0.004745757207274437,
0.0013471647398546338,
-0.0022838308941572905,
0.012598404660820961,
-0.007057194598019123,
0.03228791430592537,
-0.02537509612739086,
-0.008453361690044403,
0.028469329699873924,
0.0528799444437027,
-0.008189009502530098,
0.013709377497434616,
0.007108462508767843,
-0.0313146710395813,
-0.0203847736120224,
0.009495257399976254,
-0.0037976468447595835,
-0.056310974061489105,
0.005224608350545168,
0.015869706869125366,
-0.010251305066049099,
-0.015332325361669064,
-0.07152102142572403,
-0.014654670841991901,
0.04947735741734505,
0.030509287491440773,
0.027243023738265038,
0.02735298126935959,
-0.06892994791269302,
-0.02525811642408371,
-0.06787002831697464,
0.04955737665295601,
-0.01917225494980812,
0.018451163545250893,
-0.007924254983663559,
0.024987969547510147,
0.0014691331889480352,
0.005856430158019066,
0.0445222444832325,
0.017262166365981102,
-0.015109018422663212,
0.00835397932678461,
0.015699714422225952,
0.021479995921254158,
-0.0016030102269724011,
-0.03762579336762428,
-0.04678404703736305,
-0.0009723989060148597,
0.003362787887454033,
-0.012429652735590935,
0.0023009120486676693,
-0.0012525948695838451,
0.018711941316723824,
-0.003468023147433996,
0.02739640884101391,
0.0031655968632549047,
-0.05563970282673836,
0.027648545801639557,
0.05891699343919754,
0.003139425767585635,
0.09656592458486557,
-0.03306107968091965,
0.000016925998352235183,
0.007715212646871805,
-0.021973179653286934,
-0.03544394671916962,
0.023129411041736603,
-0.02723545953631401,
-0.0018257932970300317,
-0.026137590408325195,
-0.004541581030935049,
-0.00861427467316389,
-0.024749241769313812,
0.03721193969249725,
0.043000224977731705,
-0.023862715810537338,
0.008438566699624062,
0.008074674755334854,
0.010674824938178062,
0.05190727114677429,
-0.02978760004043579,
-0.001639490365050733,
0.057891152799129486,
0.035275232046842575,
-0.012586619704961777,
0.06159673631191254,
0.08169422298669815,
-0.023834438994526863,
-0.006998940836638212,
-0.004301913548260927,
-0.04586775228381157,
0.024273307994008064,
0.010892448015511036,
-0.010848191566765308,
-0.01098391693085432,
-0.03832640126347542,
0.008721696212887764,
-0.02086174488067627,
-0.006011181510984898,
0.013344084843993187,
0.005222936160862446,
0.09795752167701721,
-0.035084068775177,
0.0010070980060845613,
-0.03343965485692024,
-0.004095525946468115,
-0.0005138160777278244,
0.013781670480966568,
0.03591090068221092,
0.02727547287940979,
0.014858725480735302,
0.014182397164404392,
-0.002542051486670971,
-0.012962846085429192,
0.005167915020138025,
-0.015029210597276688,
0.01457645557820797,
0.03152022510766983,
-0.0023149047046899796,
-0.011709848418831825,
-0.0232191514223814,
-0.01659942977130413,
-0.03912230208516121,
0.025270940735936165,
0.059754323214292526,
0.03720826283097267,
0.008877945132553577,
-0.010107506066560745,
-0.0394052155315876,
0.07157661765813828,
-0.08376463502645493,
-0.01781999133527279,
-0.023396030068397522,
0.03362186625599861,
-0.00006939627201063558,
-0.0027821639087051153
] |
<blockquote>
<p>If it takes work W to stretch a Hooke’s-law spring (F = kx) a distance d from its unstressed length, determine the extra work required to stretch it an additional distance d (Hint: draw a graph and give answer in terms of W!).</p>
</blockquote>
<p>I don't understand why the answer is not 2W since Force is proportional to x, or even how to begin using a graph to disprove why the answer is not 2W. Any help would be greatly appreciated.</p> | 4,560 | [
-0.016728617250919342,
0.016090145334601402,
0.009656842797994614,
-0.033798448741436005,
0.0207578893750906,
-0.050414588302373886,
-0.040498893707990646,
-0.010510748252272606,
-0.013625274412333965,
-0.01596706733107567,
0.02250000089406967,
0.018641190603375435,
0.05373307690024376,
0.040210988372564316,
-0.010374561883509159,
0.007257681339979172,
0.0022395970299839973,
-0.021729018539190292,
0.029360331594944,
0.008249920792877674,
-0.008969615213572979,
-0.04844716936349869,
-0.004532855469733477,
-0.012514958158135414,
-0.004369818605482578,
0.017139438539743423,
0.05786100775003433,
-0.020945359021425247,
0.007730814628303051,
0.03078751638531685,
0.009450002573430538,
-0.023108601570129395,
0.036956679075956345,
0.046588994562625885,
0.07053563743829727,
0.027533795684576035,
-0.024829614907503128,
-0.03330845758318901,
-0.008403994143009186,
0.03794220834970474,
0.007162627298384905,
0.023925410583615303,
-0.0005955160595476627,
0.007648615166544914,
-0.02634454518556595,
0.04488099738955498,
0.0034339663106948137,
-0.04693484306335449,
0.08206599205732346,
-0.0034625749103724957,
0.07802454382181168,
-0.0032804287038743496,
0.025555692613124847,
0.00645750155672431,
-0.03730868548154831,
-0.013234495185315609,
0.0893387645483017,
0.07637447863817215,
-0.0255117267370224,
-0.025072291493415833,
-0.028584063053131104,
-0.022736648097634315,
-0.027032503858208656,
-0.03321513533592224,
0.004795708227902651,
0.05166659504175186,
-0.007733324076980352,
0.0039036571979522705,
0.03563469275832176,
-0.0036067075561732054,
0.029478808864951134,
0.005490872543305159,
0.04709671810269356,
-0.019008256494998932,
-0.01882542110979557,
-0.0008805695688351989,
0.003960105124861002,
0.040820855647325516,
0.015594860538840294,
0.0649123266339302,
-0.014500153250992298,
0.03351716697216034,
0.09479773044586182,
0.08915646374225616,
-0.008099909871816635,
-0.040339767932891846,
0.05823715776205063,
0.025903288275003433,
0.012476351112127304,
0.007561010308563709,
0.029322225600481033,
-0.005786911118775606,
0.036015208810567856,
-0.024565495550632477,
0.04442198574542999,
0.015308371745049953,
-0.03832358494400978,
0.034823644906282425,
0.021901680156588554,
0.01415896974503994,
-0.021300800144672394,
-0.04248037189245224,
-0.010068871080875397,
0.056681495159864426,
0.023328302428126335,
0.0010627721203491092,
-0.009278322570025921,
0.017610881477594376,
-0.025472799316048622,
0.01443586964160204,
-0.056683365255594254,
0.03296447545289993,
-0.002262016525492072,
0.019987404346466064,
-0.016120735555887222,
-0.02098158933222294,
-0.020620713010430336,
-0.0040396288968622684,
0.07140368223190308,
0.01449836976826191,
0.004040546249598265,
-0.04837334156036377,
0.038874950259923935,
-0.009194348007440567,
-0.023566417396068573,
0.018031541258096695,
0.046147968620061874,
-0.05189981684088707,
-0.022240599617362022,
0.016159163787961006,
0.017161639407277107,
-0.007087835110723972,
-0.023337913677096367,
0.0311293788254261,
0.04214562475681305,
0.012898044660687447,
-0.10742493718862534,
-0.0807838886976242,
0.0333927646279335,
0.029199399054050446,
-0.006278698332607746,
-0.06379829347133636,
0.02904089353978634,
0.048336390405893326,
0.08696486800909042,
-0.0033665404189378023,
0.01927235536277294,
-0.02451234497129917,
-0.00999739021062851,
-0.02432621456682682,
0.01171606034040451,
-0.005860250908881426,
-0.002184920245781541,
-0.025954676792025566,
0.013425380922853947,
-0.04046722501516342,
-0.010096712037920952,
0.03570881485939026,
-0.013184988871216774,
-0.01781405322253704,
0.04475586861371994,
-0.012737279757857323,
-0.007152878679335117,
0.0062784468755126,
-0.03658532723784447,
-0.05738009512424469,
0.0722060352563858,
-0.02266155369579792,
0.0020409896969795227,
0.0016745389439165592,
-0.02935919165611267,
0.02131706476211548,
-0.017296036705374718,
0.010368983261287212,
0.02639293670654297,
-0.03993602842092514,
-0.040734753012657166,
-0.01907450146973133,
0.017456023022532463,
0.00634207297116518,
-0.016325190663337708,
-0.04125220701098442,
-0.020041557028889656,
0.012315153144299984,
0.0029584141448140144,
0.02097976952791214,
0.018212024122476578,
0.01725652627646923,
0.019047370180487633,
0.00357564864680171,
-0.030956391245126724,
-0.06077510118484497,
0.024792520329356194,
0.008041110821068287,
-0.01678878255188465,
0.0044765411876142025,
-0.0005287434905767441,
0.01917244680225849,
-0.027427267283201218,
-0.024748899042606354,
0.01842646487057209,
0.028712302446365356,
0.019488178193569183,
-0.008524426259100437,
0.018987605348229408,
0.0725812315940857,
0.05938470736145973,
0.05894261598587036,
0.032646916806697845,
-0.04733775556087494,
-0.009492002427577972,
0.038836538791656494,
-0.0656232088804245,
-0.006732332985848188,
-0.008889020420610905,
0.029521575197577477,
-0.0015777089865878224,
-0.005657395347952843,
-0.033712565898895264,
0.030781393870711327,
0.0002371116279391572,
0.07805786281824112,
0.08341028541326523,
-0.01753959059715271,
-0.01268046721816063,
0.009116782806813717,
-0.003907034173607826,
0.03203946724534035,
-0.032204825431108475,
-0.0075635481625795364,
-0.02582438848912716,
-0.011434489861130714,
0.029515963047742844,
0.017766380682587624,
0.007229350972920656,
-0.02021600492298603,
0.007959652692079544,
0.002142534125596285,
0.008488530293107033,
0.021411363035440445,
-0.006732662674039602,
-0.05158716067671776,
0.013096393086016178,
0.018856020644307137,
0.0017049035523086786,
0.022927524521946907,
0.0334022119641304,
0.04777322709560394,
-0.0023688729852437973,
0.0002599800645839423,
0.01827152818441391,
0.03668110445141792,
-0.01178422849625349,
0.03499510884284973,
0.040321510285139084,
-0.007904373109340668,
0.03934190422296524,
-0.00864876713603735,
0.01907239854335785,
0.0771450400352478,
-0.012975010089576244,
0.02984699234366417,
-0.008179334923624992,
-0.026161091402173042,
-0.004464833531528711,
-0.0403035543859005,
-0.029786646366119385,
-0.005282815545797348,
0.03452015295624733,
-0.06141974404454231,
-0.014981458894908428,
-0.024137848988175392,
-0.025313081219792366,
0.016307752579450607,
-0.03547602891921997,
0.035021521151065826,
0.03217653930187225,
0.02256436087191105,
-0.01218703668564558,
-0.0013253900688141584,
0.014922121539711952,
-0.03871964290738106,
-0.009332755580544472,
-0.0481269508600235,
-0.013602201826870441,
0.01533301081508398,
0.005685831420123577,
-0.027012255042791367,
0.036751482635736465,
-0.012376351282000542,
0.003637762041762471,
-0.0016681668348610401,
0.00928730983287096,
-0.012773819267749786,
0.006588375195860863,
-0.02559257298707962,
0.023619769141077995,
-0.020729901269078255,
-0.008041897788643837,
0.036783166229724884,
-0.008047985844314098,
-0.045658379793167114,
0.019643645733594894,
-0.04480467736721039,
-0.032351743429899216,
-0.030182702466845512,
-0.011844631284475327,
0.03506483882665634,
0.016295665875077248,
0.026384340599179268,
-0.014736617915332317,
-0.048120614141225815,
-0.005290871486067772,
-0.05810713768005371,
-0.03664654120802879,
-0.008255581371486187,
-0.0010163290426135063,
0.05254725366830826,
-0.0002969710039906204,
-0.052785154432058334,
0.07174710184335709,
0.03331206366419792,
-0.010015275329351425,
-0.019656952470541,
-0.0556352399289608,
0.008456043899059296,
-0.06006836146116257,
0.009362692944705486,
0.040130600333213806,
-0.006644443608820438,
0.019627844914793968,
0.007702968083322048,
0.022557847201824188,
0.032440438866615295,
-0.015171777456998825,
-0.011739014647901058,
-0.0010512779699638486,
0.01077205128967762,
-0.01721435785293579,
0.04778863862156868,
0.035565268248319626,
-0.013945289887487888,
0.007206951268017292,
0.007632526569068432,
0.026959728449583054,
0.0018203358631581068,
-0.07805728912353516,
0.020323002710938454,
0.009564338251948357,
0.03405078127980232,
-0.061949752271175385,
0.0700913816690445,
0.042571745812892914,
-0.034896429628133774,
0.0027183322235941887,
-0.008235082030296326,
0.03881823644042015,
-0.003685138188302517,
-0.0022224541753530502,
0.012765266932547092,
0.012832773849368095,
-0.009134986437857151,
-0.028216859325766563,
-0.036673810333013535,
0.0024967717472463846,
0.010511890053749084,
0.015123439021408558,
-0.02055811695754528,
0.020682474598288536,
0.02715943194925785,
0.029285546392202377,
0.007441950496286154,
-0.06143246218562126,
-0.01867627538740635,
-0.06768934428691864,
-0.047705553472042084,
-0.014793472364544868,
0.04089362919330597,
-0.020145149901509285,
0.015018007718026638,
0.029850760474801064,
0.05432106554508209,
0.024154381826519966,
-0.021813686937093735,
-0.0694969892501831,
0.05800192430615425,
-0.06449488550424576,
-0.0019908654503524303,
0.03312937170267105,
-0.022487951442599297,
-0.015277921222150326,
-0.05340009182691574,
-0.03606724739074707,
0.002608788665384054,
0.025629479438066483,
-0.04666262865066528,
0.03603387624025345,
0.007004679646342993,
-0.024936135858297348,
0.012728803791105747,
0.003567767795175314,
0.0262942835688591,
-0.044870808720588684,
0.022787470370531082,
0.04614317789673805,
-0.0049757095985114574,
-0.017198313027620316,
0.00040688642184250057,
-0.028298048302531242,
0.011546590365469456,
0.03358883038163185,
0.005561597645282745,
0.005255351308733225,
0.01194188091903925,
-0.00795960146933794,
0.016957633197307587,
0.013806515373289585,
0.012502924539148808,
-0.005210688803344965,
-0.03675021976232529,
-0.05145185813307762,
-0.01227361150085926,
-0.021562160924077034,
0.07366181164979935,
-0.027823900803923607,
0.02163107320666313,
-0.0057349130511283875,
0.0029626130126416683,
-0.005136269610375166,
0.02263445034623146,
0.05296798795461655,
0.01377318799495697,
-0.03580070659518242,
-0.030519407242536545,
-0.017115918919444084,
-0.04847508668899536,
-0.022798269987106323,
-0.01830604113638401,
-0.03399462252855301,
0.0002759677590802312,
0.010070513933897018,
0.006120010279119015,
0.012235745787620544,
0.008698773570358753,
0.02212117612361908,
-0.02428293041884899,
0.021335674449801445,
0.031378861516714096,
-0.014107645489275455,
0.049050431698560715,
-0.007404838688671589,
0.030509531497955322,
-0.002339569851756096,
-0.03209557756781578,
-0.09608619660139084,
-0.009962123818695545,
0.028741613030433655,
0.037830647081136703,
-0.02797396294772625,
0.007899440824985504,
-0.011134494096040726,
-0.0008273074054159224,
0.008580220863223076,
-0.036585330963134766,
0.03142581135034561,
-0.013438336551189423,
0.055251345038414,
-0.017102152109146118,
-0.055333204567432404,
-0.07240709662437439,
-0.0017088466556742787,
-0.001035044202581048,
0.017633287236094475,
0.021640760824084282,
0.017910810187458992,
0.009275984950363636,
-0.02577696368098259,
0.027724888175725937,
0.046872589737176895,
0.010357638821005821,
-0.021122414618730545,
-0.042587172240018845,
0.015104704536497593,
-0.033383239060640335,
-0.05871936306357384,
0.0028972646687179804,
0.014154331758618355,
-0.02238050289452076,
0.01394275575876236,
-0.04373340681195259,
-0.03863372653722763,
0.05029973015189171,
-0.011923136189579964,
-0.01861247606575489,
0.012818971648812294,
-0.012309729121625423,
0.03854931890964508,
0.07480175048112869,
0.01531889010220766,
0.05293063074350357,
0.06525230407714844,
-0.028381172567605972,
0.026831187307834625,
0.012777873314917088,
-0.0006774213979952037,
-0.04041875898838043,
0.015841109678149223,
-0.04336465895175934,
0.015683919191360474,
-0.021219732239842415,
0.002082084771245718,
-0.02311970852315426,
0.026356104761362076,
-0.05224838852882385,
-0.0312640443444252,
-0.01865329034626484,
-0.00532487453892827,
0.021076489239931107,
0.010683328844606876,
-0.001282769488170743,
0.028242619708180428,
-0.010651093907654285,
-0.016174225136637688,
0.013301079161465168,
0.017519043758511543,
-0.024261312559247017,
0.022990010678768158,
0.016756201162934303,
-0.005720445886254311,
-0.012904155999422073,
-0.011563354171812534,
0.023375779390335083,
-0.0333520732820034,
0.033330097794532776,
-0.020871996879577637,
0.007211711723357439,
-0.013478152453899384,
0.00035375833977013826,
-0.020884517580270767,
0.012874459847807884,
-0.0068575837649405,
0.012448901310563087,
-0.020339850336313248,
0.022013530135154724,
0.031323276460170746,
-0.015012966468930244,
-0.05829751864075661,
-0.031776685267686844,
0.009430479258298874,
-0.00891084037721157,
0.012391835451126099,
-0.012999221682548523,
0.0021763751283288,
-0.016991591081023216,
-0.018861524760723114,
0.009013814851641655,
0.041315771639347076,
-0.030811309814453125,
0.027542155236005783,
-0.01742623746395111,
-0.010268734768033028,
0.02727470174431801,
0.014449398033320904,
-0.011544788256287575,
-0.03591650351881981,
-0.008216430433094501,
-0.040859121829271317,
-0.01718900352716446,
0.007419961504638195,
-0.02851508930325508,
-0.02545771934092045,
0.02192121371626854,
-0.0020410900469869375,
0.02585623599588871,
-0.014302615076303482,
-0.04058884456753731,
0.035540126264095306,
0.032298047095537186,
-0.02271106094121933,
-0.028447823598980904,
0.016119565814733505,
0.013826151378452778,
0.04534721001982689,
0.004052113741636276,
0.018358342349529266,
-0.06730632483959198,
-0.01526044774800539,
-0.01533733494579792,
0.019726041704416275,
0.0013175117783248425,
-0.01738177053630352,
0.06246813014149666,
-0.06049227714538574,
0.001802529557608068,
0.03139089420437813,
-0.018166575580835342,
0.0025132661685347557,
0.00191831449046731,
0.004790999926626682,
-0.008429880253970623,
0.015406492166221142,
-0.05513370782136917,
0.0033952356316149235,
-0.01932709664106369,
0.019719671458005905,
0.057817257940769196,
-0.03226730599999428,
0.040055666118860245,
0.01355714164674282,
-0.023923877626657486,
0.03164098039269447,
-0.008705507963895798,
-0.017322426661849022,
-0.025330806151032448,
0.0046329740434885025,
0.025244951248168945,
-0.021298889070749283,
0.0066216252744197845,
0.05595256760716438,
-0.008690369315445423,
-0.02026762068271637,
-0.02711557224392891,
0.004829016514122486,
-0.006122657097876072,
-0.012786533683538437,
-0.005396044813096523,
-0.0539202019572258,
0.008719717152416706,
0.005264619365334511,
0.04774489253759384,
-0.0009978075977414846,
-0.04855750501155853,
0.060908690094947815,
-0.024385888129472733,
-0.01847163587808609,
-0.05113668367266655,
-0.020580342039465904,
-0.02864115498960018,
0.005414434242993593,
-0.026944901794195175,
0.02956364117562771,
0.019874589517712593,
-0.01370927132666111,
0.026644859462976456,
0.0037195845507085323,
0.047281086444854736,
-0.03328799456357956,
-0.050102751702070236,
-0.017645185813307762,
-0.02475062757730484,
-0.034596025943756104,
0.023079803213477135,
-0.021970266476273537,
-0.0741121843457222,
0.0431818887591362,
-0.03731915354728699,
0.032482340931892395,
-0.004433915484696627,
0.022467931732535362,
-0.01388134527951479,
0.06342736631631851,
-0.025227660313248634,
0.01976972632110119,
-0.03247791901230812,
0.0033341767266392708,
0.10513290017843246,
0.03967427462339401,
0.03944001346826553,
-0.021098753437399864,
0.022614846006035805,
-0.033960942178964615,
-0.00983242318034172,
-0.0283905491232872,
0.028731264173984528,
-0.01252079475671053,
-0.023027194663882256,
0.007167879492044449,
0.05756472796201706,
-0.033678486943244934,
-0.012262118048965931,
0.051752835512161255,
-0.023821108043193817,
-0.051589228212833405,
0.017585525289177895,
-0.012408295646309853,
0.023655209690332413,
0.012653190642595291,
-0.007534805219620466,
0.010861391201615334,
-0.051478710025548935,
0.007074151188135147,
-0.001493972260504961,
-0.03448963910341263,
0.026203034445643425,
-0.014651024714112282,
-0.05523600056767464,
0.024548858404159546,
0.03624102845788002,
-0.018487626686692238,
-0.02824587933719158,
-0.0017562644788995385,
0.0317368283867836,
-0.01300806924700737,
-0.0026170015335083008,
0.06751785427331924,
0.02555466629564762,
0.021755410358309746,
-0.020770173519849777,
0.038196489214897156,
-0.05806754156947136,
0.05867934972047806,
-0.02759983390569687,
0.008865649811923504,
0.005779027007520199,
0.04759522154927254,
0.04555797204375267,
0.0013705345336347818,
-0.015331925824284554,
-0.009435928426682949,
-0.002332122065126896,
-0.0008432248141616583,
0.021033911034464836,
-0.019856015220284462,
-0.04108375683426857,
-0.0011477823136374354,
0.006538990885019302,
0.006528448313474655,
0.0335286483168602,
0.00968172587454319,
0.0013178333174437284,
0.00033945648465305567,
0.018471471965312958,
0.041426729410886765,
-0.01773291826248169,
-0.030734296888113022,
-0.03782636672258377,
-0.0023244256153702736,
0.008864747360348701,
0.031232697889208794,
0.006334477569907904,
0.009755528531968594,
0.019974583759903908,
-0.0034866270143538713,
-0.025048259645700455,
-0.09312926232814789,
-0.015849560499191284,
0.026368793100118637,
0.015439406968653202,
0.008178271353244781,
-0.05670231580734253,
0.03943769633769989,
0.037360258400440216,
0.035689208656549454,
0.013284359127283096,
0.010296093299984932,
0.00837558601051569,
0.0003621914074756205,
0.026895368471741676,
-0.025851333513855934,
-0.01137462817132473,
-0.007897624745965004,
-0.0322473868727684,
-0.015792882069945335,
0.01676071062684059,
0.026939740404486656,
0.07819578051567078,
0.007378824520856142,
0.003662241855636239,
0.007852088660001755,
-0.016214432194828987,
0.007342026103287935,
0.04420526698231697,
-0.025398969650268555,
-0.01402321457862854,
0.053475234657526016,
-0.02320234477519989,
-0.05111527442932129,
-0.018960213288664818,
-0.03315085917711258,
-0.029037222266197205,
-0.012358537875115871,
0.024129439145326614,
0.010822546668350697,
0.00589310098439455,
0.0016029735561460257,
0.04594767466187477,
-0.05085791274905205,
-0.002787231933325529,
-0.0047980607487261295,
-0.04418075829744339,
-0.010461305268108845,
-0.0038483496755361557,
0.0008886990835890174,
0.029946357011795044,
-0.005970231723040342,
0.006074490956962109,
0.011959971860051155,
0.04519898444414139,
0.0063561261631548405,
0.008691017515957355,
0.012569909915328026,
-0.00006785712321288884,
0.029957376420497894,
-0.0019495192682370543,
-0.018126817420125008,
0.04805581644177437,
-0.03954503685235977,
-0.012389697134494781,
0.024808764457702637,
-0.02568761073052883,
0.03818411007523537,
-0.035864684730768204,
-0.006764980033040047,
-0.0030205983202904463,
0.028261177241802216,
-0.05094287171959877,
0.025989940389990807,
-0.013057122938334942,
-0.03215544670820236,
-0.005576919298619032,
-0.043287284672260284,
-0.027721766382455826,
-0.030789056792855263,
0.03225018456578255,
0.02143101766705513,
0.017261754721403122,
0.002156792674213648,
-0.044369176030159,
0.02026395872235298,
0.01719643920660019,
0.0009951995452865958,
0.016144348308444023,
0.021138271316885948,
0.03576011210680008,
0.02238759770989418,
-0.036015626043081284,
0.02170543372631073,
-0.04269852489233017,
-0.009412821382284164,
-0.14313457906246185,
0.006818373687565327,
-0.017384396865963936,
-0.0008450500899925828,
0.043030671775341034,
-0.029116295278072357,
0.008877945132553577,
0.007178426254540682,
-0.08212807029485703,
0.05323446914553642,
-0.017614198848605156,
-0.04073605686426163,
-0.006313504185527563,
-0.022259807214140892,
0.008921822533011436,
0.03846107795834541,
0.013517121784389019,
0.07478684186935425,
0.00806230679154396,
0.012757617980241776,
0.0035741699393838644,
-0.015997357666492462,
0.0006288246950134635,
0.015686562284827232,
-0.020787524059414864,
-0.0016858314629644156,
0.03208987042307854,
-0.01239144615828991,
0.02665720134973526,
0.03514483943581581,
-0.013389403000473976,
0.05409854277968407,
-0.014108597300946712,
-0.012269841507077217,
0.02248840592801571,
0.03568119928240776,
0.030072979629039764,
-0.016212696209549904,
-0.011015382595360279,
-0.013129997998476028,
-0.013727168552577496,
-0.009343564510345459,
-0.03158034384250641,
0.008793911896646023,
0.04401181638240814,
-0.04240598529577255,
-0.013524919748306274,
0.011708986945450306,
-0.014724469743669033,
0.0384342260658741,
0.02967512235045433,
0.01657310500741005,
0.00029882637318223715,
-0.012090744450688362,
-0.018591590225696564,
-0.02197938598692417,
-0.00418007280677557,
0.04055587202310562,
-0.009434004314243793,
-0.014205924235284328,
0.0015592988347634673,
0.0014862418174743652,
0.02701999619603157,
-0.0432082936167717,
-0.024780673906207085,
-0.016558874398469925,
-0.07594424486160278,
0.003871859982609749,
-0.005661786533892155,
0.02073415368795395,
0.015229160897433758,
0.002861695596948266,
-0.034922584891319275,
0.023867983371019363,
0.02833821251988411,
0.0055557130835950375,
0.010790546424686909,
0.005741072352975607,
-0.0318126305937767,
-0.06968757510185242,
0.03591379150748253,
0.04367931932210922,
-0.02462642453610897,
-0.024738477542996407,
-0.002921067178249359,
0.015061561018228531,
0.040505893528461456,
0.052471473813056946,
-0.0063261124305427074,
-0.022274896502494812,
0.00737150339409709,
-0.007641484960913658,
-0.002237917622551322,
-0.0718025416135788,
0.018994275480508804,
0.000987777253612876,
-0.0015269146533682942,
0.017523599788546562,
-0.014925849623978138,
-0.0037670640740543604,
0.02725723199546337,
-0.008269870653748512,
-0.0039056625682860613,
-0.016716251149773598,
0.029748791828751564,
-0.02321585640311241,
-0.009929426945745945,
-0.028431996703147888,
-0.007317631039768457,
0.06238006055355072,
0.002153923502191901,
0.03305684030056,
-0.01991078443825245,
-0.024808712303638458,
-0.07650617510080338,
0.04857025295495987,
-0.03451172634959221,
0.034457311034202576,
-0.06055815890431404,
-0.016637399792671204,
0.04622749611735344,
-0.053979966789484024,
-0.04712003469467163,
0.05773010849952698,
-0.038729239255189896,
-0.01150078047066927,
-0.015075917355716228,
0.0349782295525074,
0.0363193042576313,
-0.024788739159703255,
0.05124742537736893,
-0.01913990080356598,
-0.0168316550552845,
0.029483448714017868,
-0.004919758532196283,
0.06490722298622131,
-0.006774581503123045,
-0.0019432288827374578,
0.04839502274990082,
-0.03127351403236389,
0.04906754568219185,
0.006219771690666676,
0.00753960432484746,
-0.05357644334435463,
-0.0377969890832901,
0.013623642735183239,
-0.006791658233851194,
-0.015224012546241283,
0.01804508827626705,
-0.01589387282729149,
0.04375044256448746,
0.013303859159350395,
0.017572809010744095,
-0.012592927552759647,
-0.008348171599209309,
-0.012640225701034069,
-0.005305267870426178,
0.07315924018621445,
0.03230806440114975,
-0.03126934543251991,
-0.01637786626815796,
-0.0053480444476008415,
-0.012002076953649521,
0.029898010194301605,
0.03450332581996918,
-0.0011175073450431228,
-0.019741682335734367,
-0.03056613728404045,
-0.02264302782714367,
-0.0014264656929299235,
-0.0611531063914299,
0.009870223701000214,
0.08680123835802078,
0.058166008442640305,
-0.04876357316970825,
0.01208111084997654,
-0.017579268664121628,
0.012261987663805485,
0.04071183130145073,
-0.009238769300282001,
-0.017320076003670692,
-0.03633275628089905,
-0.010809751227498055,
0.021564284339547157,
-0.033865440636873245
] |
<p>Is it possible to reclaim nuclear waste from commercial reactors for useful purposes, if not necessarily energy production?</p> | 4,561 | [
0.0028909840621054173,
-0.02405196987092495,
-0.00884341076016426,
-0.009855112060904503,
0.01789255067706108,
-0.008636906743049622,
-0.044398531317710876,
-0.044356174767017365,
-0.005447076633572578,
-0.06950222700834274,
0.012683231383562088,
0.03453047573566437,
0.03276308253407478,
-0.03783903643488884,
-0.028453610837459564,
0.022190142422914505,
0.0012898739660158753,
-0.02794930525124073,
-0.006901800632476807,
-0.007313299458473921,
0.04022553935647011,
-0.015277097001671791,
-0.020892366766929626,
-0.0020301274489611387,
-0.0021178091410547495,
0.01127978041768074,
0.00005021799370297231,
0.009949812665581703,
0.03980405628681183,
0.05119720846414566,
0.03976605832576752,
-0.05977796018123627,
0.004729067906737328,
0.04176553338766098,
0.01805257983505726,
-0.007734533865004778,
-0.0028634665068238974,
-0.018566124141216278,
-0.018902232870459557,
0.013956238515675068,
-0.01595914177596569,
-0.057461246848106384,
0.021783841773867607,
0.05221628025174141,
0.022252533584833145,
0.013885067775845528,
-0.01752604730427265,
-0.02186911553144455,
0.02330499328672886,
-0.06120028346776962,
0.031755708158016205,
-0.007538164965808392,
0.03084438480436802,
0.017071513459086418,
0.012717070057988167,
0.006042844150215387,
0.05895747244358063,
0.051671065390110016,
0.008042817935347557,
0.002056810772046447,
0.0004814051790162921,
0.03615088015794754,
-0.0022241261322051287,
-0.011494763195514679,
-0.014962047338485718,
0.0011360831558704376,
-0.012318176217377186,
0.002946153748780489,
-0.021859386935830116,
-0.0033385457936674356,
0.034248244017362595,
0.029746973887085915,
0.010577654466032982,
0.021379828453063965,
0.010811004787683487,
-0.030770376324653625,
0.004312708508223295,
-0.01503648143261671,
0.0077677201479673386,
0.05125661566853523,
0.0012714863987639546,
0.020136455073952675,
0.0400884747505188,
0.008698111400008202,
0.023997317999601364,
-0.0016891085542738438,
0.06370566040277481,
-0.03522615134716034,
0.05144102871417999,
0.004753082059323788,
0.0476519837975502,
-0.033933207392692566,
0.08135586231946945,
0.011022543534636497,
-0.0384732224047184,
-0.009035090915858746,
-0.0013619117671623826,
0.07351718842983246,
0.029774239286780357,
-0.021419566124677658,
0.0684240534901619,
0.028975876048207283,
0.033759668469429016,
0.06345473974943161,
0.007117754314094782,
-0.02707492746412754,
-0.010698037222027779,
0.014484483748674393,
0.017162544652819633,
-0.01254591066390276,
-0.060984499752521515,
-0.0017233400139957666,
-0.005730516277253628,
-0.02062860317528248,
0.02811453863978386,
-0.023232752457261086,
-0.02224111557006836,
-0.04640817269682884,
0.04850037023425102,
0.047044605016708374,
0.03777458518743515,
0.0023944529239088297,
0.05124972388148308,
-0.020588716492056847,
-0.05833939462900162,
-0.0026136368978768587,
0.03756947070360184,
-0.015113621950149536,
-0.04397904872894287,
0.022518839687108994,
-0.0187884122133255,
0.0007340512820519507,
-0.008302642963826656,
0.02770194411277771,
0.010801046155393124,
0.0016304877353832126,
-0.10123690217733383,
-0.062492240220308304,
0.017275968566536903,
-0.030675474554300308,
-0.015983719378709793,
-0.0771578699350357,
0.031295761466026306,
0.041938845068216324,
0.042588166892528534,
0.0058875433169305325,
-0.04093916714191437,
0.01398935541510582,
0.016247641295194626,
-0.02267315983772278,
0.013687673956155777,
-0.02799922600388527,
0.023046493530273438,
-0.06133831664919853,
0.00022224515851121396,
-0.07194923609495163,
0.009494969621300697,
0.05691811442375183,
0.015442676842212677,
-0.03077898919582367,
0.02483282797038555,
0.01066287886351347,
0.01579575054347515,
-0.008434799499809742,
-0.014600861817598343,
-0.02305852808058262,
0.06262597441673279,
-0.012730616144835949,
0.0037961353082209826,
0.04753905534744263,
0.0390167310833931,
0.026154546067118645,
0.04742919281125069,
0.024580247700214386,
-0.015802903100848198,
-0.047142550349235535,
-0.0030068710912019014,
-0.01390371099114418,
0.005386525299400091,
0.006517510861158371,
-0.04133482277393341,
0.01136161107569933,
-0.008634595200419426,
-0.015317562967538834,
0.016099944710731506,
0.060204487293958664,
-0.002396979369223118,
-0.023104967549443245,
0.01677285134792328,
-0.03438231348991394,
0.0040289913304150105,
-0.05869992449879646,
0.008014404214918613,
-0.015388918109238148,
0.001116502215154469,
-0.03493012860417366,
0.0035097410436719656,
0.023743564262986183,
-0.04291147738695145,
-0.020044991746544838,
0.0026090601459145546,
0.04549030959606171,
0.026260610669851303,
0.014491663314402103,
-0.011193442158401012,
0.057314515113830566,
0.03461074456572533,
0.004513631574809551,
0.022467302158474922,
-0.006801195442676544,
-0.02798507921397686,
-0.04458920285105705,
-0.028176693245768547,
-0.02897537499666214,
-0.014996175654232502,
-0.015470229089260101,
0.016379723325371742,
0.002314443700015545,
-0.022824836894869804,
0.02563622035086155,
0.01067713275551796,
0.08753826469182968,
0.016254035755991936,
0.06826140731573105,
-0.010490125976502895,
0.016602274030447006,
0.027205854654312134,
0.018735239282250404,
-0.020815420895814896,
-0.03377606347203255,
-0.07463373988866806,
-0.020733030512928963,
0.02295483462512493,
0.052673663944005966,
-0.04438066855072975,
0.04720761626958847,
-0.013095954433083534,
0.029343707486987114,
0.032050006091594696,
0.012353772297501564,
-0.020498618483543396,
0.02099371701478958,
0.050846949219703674,
-0.011504787020385265,
-0.009702347218990326,
0.0011730551486834884,
-0.01633906178176403,
0.04591512307524681,
0.03201514109969139,
-0.03833848237991333,
0.03151010349392891,
-0.001807179767638445,
-0.022489650174975395,
-0.03461175411939621,
0.00530207110568881,
-0.07146777957677841,
0.04549337923526764,
-0.0493398979306221,
0.009812646545469761,
-0.00908499862998724,
-0.0080246077850461,
0.023898432031273842,
0.024800829589366913,
-0.019445184618234634,
0.014903328381478786,
-0.011114677414298058,
-0.00998079776763916,
-0.0031321474816650152,
0.04373132809996605,
-0.02693323791027069,
0.0102226035669446,
-0.03323318436741829,
0.03996662423014641,
0.0028982136864215136,
0.009934979490935802,
0.002055829158052802,
-0.03619794175028801,
0.030715446919202805,
-0.012185738421976566,
-0.022535158321261406,
-0.015710221603512764,
-0.04277956485748291,
-0.029729807749390602,
0.02728874981403351,
-0.03516477346420288,
0.031176945194602013,
0.010015774518251419,
-0.008633822202682495,
0.011955059133470058,
0.008089913986623287,
0.02934693917632103,
0.011353456415235996,
0.019877735525369644,
-0.08451322466135025,
-0.007864206098020077,
-0.004878224804997444,
-0.0138373002409935,
0.032958369702100754,
-0.0008515361114405096,
0.02012462541460991,
-0.010334578342735767,
-0.04196230322122574,
-0.0014372681034728885,
-0.0497891865670681,
-0.017456041648983955,
0.005805468186736107,
0.011774413287639618,
0.00794980302453041,
-0.03276906535029411,
0.020302170887589455,
0.012809970416128635,
-0.06469286978244781,
0.0035780970938503742,
-0.04940711334347725,
-0.061249442398548126,
0.040301647037267685,
-0.04056650772690773,
0.016503095626831055,
0.000464128126623109,
-0.005061656702309847,
0.07654330134391785,
0.020456349477171898,
-0.019192427396774292,
0.01748221553862095,
-0.030680019408464432,
-0.006176504772156477,
0.0030584288761019707,
-0.029799316078424454,
0.01232333667576313,
0.004870718810707331,
-0.003241533413529396,
-0.0070211743004620075,
0.009141345508396626,
0.026972103863954544,
0.03982558846473694,
-0.02613227441906929,
-0.005508549977093935,
0.028109664097428322,
0.026897383853793144,
0.015211770310997963,
-0.03881978988647461,
-0.04129822552204132,
0.006947580724954605,
-0.01126073393970728,
0.049174994230270386,
0.008891813457012177,
-0.052110496908426285,
0.03353583812713623,
0.03459172323346138,
0.022667452692985535,
-0.034642286598682404,
0.044817399233579636,
0.0013305960455909371,
0.009399903938174248,
0.010101904161274433,
0.01897495426237583,
0.07258350402116776,
0.012596547603607178,
0.010403471067547798,
0.016962043941020966,
0.05790039151906967,
-0.02127115987241268,
-0.03784719854593277,
-0.02108968049287796,
-0.010925771668553352,
0.000511635560542345,
0.037920139729976654,
0.027773261070251465,
0.03437167406082153,
-0.008870928548276424,
0.02649015188217163,
-0.009175059385597706,
-0.0016494632000103593,
0.020778954029083252,
-0.08767668902873993,
-0.01787063293159008,
-0.014874915592372417,
0.04928959161043167,
0.013528420589864254,
0.011996785178780556,
0.0013402234762907028,
-0.010631592012941837,
-0.011336106806993484,
-0.014323512092232704,
-0.03575820103287697,
0.030034109950065613,
-0.04400477930903435,
0.03752659261226654,
-0.007360135670751333,
-0.015707608312368393,
-0.024817446246743202,
0.017508938908576965,
-0.034803781658411026,
-0.043822210282087326,
0.024039341136813164,
-0.034663282334804535,
0.014241347089409828,
-0.0012164695654064417,
-0.039944350719451904,
0.017439648509025574,
-0.001619851915165782,
0.039498940110206604,
-0.028417978435754776,
0.02557569555938244,
-0.011292882263660431,
-0.030179688706994057,
0.016918031498789787,
-0.0008085151785053313,
0.011770127341151237,
-0.0296022929251194,
0.056924570351839066,
0.02737351693212986,
0.04762623459100723,
-0.008331037126481533,
0.007515983190387487,
-0.012748991139233112,
0.00640561617910862,
0.005461160093545914,
0.0009495202684774995,
-0.058579277247190475,
-0.07066234946250916,
0.0021683061495423317,
0.037720128893852234,
0.011271661147475243,
-0.024588124826550484,
0.010518749244511127,
0.0031961994245648384,
-0.017736423760652542,
-0.03090767376124859,
-0.0013614625204354525,
0.04127510264515877,
0.03230122849345207,
-0.00878205057233572,
-0.02920636534690857,
-0.026210932061076164,
-0.012874525040388107,
-0.002886186819523573,
0.018994705751538277,
-0.00804898887872696,
-0.0630711019039154,
-0.011616064235568047,
0.03004465438425541,
0.07023775577545166,
-0.04283089563250542,
0.02318175695836544,
0.027056563645601273,
0.018742691725492477,
-0.003275486873462796,
0.001144915004260838,
0.029415566474199295,
0.02630988135933876,
0.028484715148806572,
0.01922629214823246,
0.006033599842339754,
-0.10838200151920319,
-0.012868349440395832,
0.02961256355047226,
0.06348849087953568,
-0.02379816211760044,
-0.01029522530734539,
-0.06381276994943619,
-0.03677060827612877,
0.07009726762771606,
0.010568387806415558,
0.017818672582507133,
-0.07645530253648758,
-0.0003512022376526147,
0.009132778272032738,
-0.03111197240650654,
0.02078002318739891,
0.020306043326854706,
-0.025409575551748276,
-0.01642678678035736,
-0.01707194745540619,
-0.02683812938630581,
-0.0065336087718605995,
0.02028639055788517,
0.011293957941234112,
0.04254540801048279,
0.013379370793700218,
0.01866738498210907,
-0.02640111744403839,
0.044278863817453384,
-0.021069569513201714,
-0.03692992031574249,
-0.01773400977253914,
0.010222292505204678,
-0.0397484190762043,
0.02862728387117386,
-0.017246276140213013,
-0.06115076690912247,
0.027116000652313232,
0.020848814398050308,
-0.009541298262774944,
-0.04774584621191025,
-0.04254527390003204,
0.016799062490463257,
0.056830961257219315,
0.016673464328050613,
0.0553588792681694,
0.08392951637506485,
0.000854929443448782,
-0.01082102581858635,
-0.03999868407845497,
0.053814832121133804,
-0.024105798453092575,
-0.01977771893143654,
0.04788748174905777,
-0.005910607520490885,
0.02970367856323719,
0.004045781679451466,
-0.004601120483130217,
0.045215267688035965,
0.014609702862799168,
-0.033758074045181274,
0.022510746493935585,
-0.0015083183534443378,
0.003122026566416025,
-0.022052716463804245,
-0.0031916003208607435,
0.009407217614352703,
-0.013311367481946945,
-0.054775066673755646,
-0.03701908513903618,
0.004835260100662708,
0.021420126780867577,
0.02082718163728714,
-0.04199102520942688,
0.008181053213775158,
-0.04630368947982788,
-0.002636557212099433,
0.03135694935917854,
0.0024898136034607887,
0.06483354419469833,
0.00010942789231194183,
0.02552509307861328,
0.01525078248232603,
-0.06543966382741928,
0.01204102672636509,
0.010198259726166725,
0.015398521907627583,
-0.008655553683638573,
-0.05583692342042923,
0.05862712487578392,
0.01917523518204689,
0.021634327247738838,
-0.05796275660395622,
-0.051626257598400116,
0.012299474328756332,
0.01931392401456833,
-0.029710732400417328,
-0.057677365839481354,
-0.01881689578294754,
0.01446326170116663,
-0.01222153753042221,
-0.046737756580114365,
0.07975723594427109,
-0.035742197185754776,
0.009675989858806133,
0.01331941969692707,
0.016682298853993416,
0.09435076266527176,
-0.01150860171765089,
-0.02687743492424488,
-0.004437955562025309,
-0.0028412332758307457,
0.01839475706219673,
-0.028009893372654915,
0.009170797653496265,
-0.04051092267036438,
-0.024880241602659225,
-0.00759347528219223,
-0.04126480221748352,
0.047211576253175735,
0.005069454666227102,
-0.004831594415009022,
0.03516045957803726,
0.009288784116506577,
-0.03980713710188866,
0.0325421579182148,
0.02892574854195118,
0.024987222626805305,
0.034392278641462326,
-0.015107699669897556,
-0.017105530947446823,
-0.008253592997789383,
-0.010036468505859375,
0.033549774438142776,
0.011942722834646702,
-0.02459109015762806,
0.03951982781291008,
0.05976519361138344,
0.0059507787227630615,
-0.0274234339594841,
0.003248014487326145,
0.0005456369835883379,
0.014593256637454033,
-0.02843531221151352,
0.03459572046995163,
-0.017615370452404022,
-0.020185191184282303,
-0.03902197256684303,
-0.07057603448629379,
-0.021776683628559113,
-0.03859269246459007,
0.0023846649564802647,
-0.04806414246559143,
0.006773993838578463,
-0.002727891318500042,
-0.007700268179178238,
0.006926273927092552,
-0.026862038299441338,
-0.01262595970183611,
0.038307830691337585,
-0.011732394807040691,
0.02295866794884205,
0.024418553337454796,
-0.019456183537840843,
0.014560356736183167,
0.01959986612200737,
0.0094534857198596,
0.03579358011484146,
0.0024379671085625887,
0.022107267752289772,
-0.0035743105690926313,
-0.017120806500315666,
-0.062249310314655304,
-0.0013935086317360401,
-0.03718704357743263,
0.0075441268272697926,
0.0024757508654147387,
-0.05543024465441704,
0.025388803333044052,
-0.03751637786626816,
-0.018073517829179764,
-0.028057236224412918,
0.0011373916640877724,
-0.04356607422232628,
0.02703627198934555,
0.012802455574274063,
0.020750820636749268,
-0.01997736096382141,
-0.016089938580989838,
0.007854348979890347,
0.020134156569838524,
0.028057843446731567,
0.0228229109197855,
-0.07118470966815948,
-0.008809326216578484,
-0.014112318865954876,
-0.048764169216156006,
0.010820834897458553,
0.003907050006091595,
-0.022046701982617378,
0.012429016642272472,
-0.0197469349950552,
0.03690739721059799,
-0.00031028612283989787,
0.032394569367170334,
0.015559113584458828,
0.047172918915748596,
0.005434156395494938,
0.02569960430264473,
-0.02490393817424774,
0.01850077696144581,
0.12148379534482956,
0.04078488051891327,
0.008490309119224548,
-0.05339111387729645,
0.005471802782267332,
-0.03841179609298706,
0.021225227043032646,
-0.00826328620314598,
-0.013776186853647232,
0.01541162934154272,
-0.00400128960609436,
0.02138688415288925,
0.008999444544315338,
-0.007120803464204073,
0.027075843885540962,
0.06172388419508934,
-0.013776101171970367,
-0.0561099611222744,
0.012261969037353992,
0.0032572736963629723,
-0.05524539574980736,
-0.012165626510977745,
-0.029022112488746643,
-0.010440868325531483,
0.005883338861167431,
-0.059741418808698654,
-0.02451002039015293,
0.007164760027080774,
0.04864317923784256,
-0.006117713171988726,
-0.02004830725491047,
-0.005582922138273716,
-0.023505035787820816,
0.029424352571368217,
-0.0021957147400826216,
0.036083023995161057,
-0.0006898215506225824,
-0.013364073820412159,
-0.020413020625710487,
-0.007071573752909899,
0.05725743621587753,
0.000987884122878313,
-0.03686642274260521,
0.014918988570570946,
-0.05815502628684044,
0.026882758364081383,
-0.004104762338101864,
-0.015415722504258156,
-0.019504785537719727,
0.013329818844795227,
-0.031559739261865616,
-0.023986557498574257,
0.023551134392619133,
0.004628635477274656,
-0.02644173987209797,
0.039376866072416306,
-0.003502536565065384,
0.026863066479563713,
-0.010883745737373829,
-0.03180064260959625,
-0.0010953795863315463,
-0.04301571100950241,
0.01494914386421442,
0.0032050355803221464,
-0.007342653814703226,
0.025446664541959763,
-0.00936779286712408,
-0.0049269841983914375,
-0.01189297903329134,
-0.02296149544417858,
-0.0896947830915451,
0.00757109560072422,
-0.007895567454397678,
0.00010654245124896988,
0.005290634464472532,
0.003411310724914074,
0.03698994964361191,
0.024060893803834915,
-0.03173213079571724,
-0.007391041610389948,
-0.053283628076314926,
0.11895560473203659,
-0.030906029045581818,
-0.01409590058028698,
-0.05431448668241501,
0.0038892910815775394,
0.020717723295092583,
0.055674754083156586,
0.010158962570130825,
0.01637251488864422,
-0.01943403109908104,
0.01228930801153183,
0.009147264063358307,
-0.031761761754751205,
0.001650972873903811,
-0.026993537321686745,
-0.03448103368282318,
0.00010681513231247663,
-0.0192622859030962,
0.022412771359086037,
0.0432780496776104,
-0.019495058804750443,
-0.022031133994460106,
0.0022601427044719458,
-0.0154601214453578,
0.034531332552433014,
0.036671582609415054,
-0.011463448405265808,
-0.017893552780151367,
0.01498500443994999,
-0.006934038363397121,
-0.017136601731181145,
-0.029120640829205513,
-0.03625583276152611,
-0.03536098822951317,
0.03647594898939133,
0.047059446573257446,
0.0066511561162769794,
-0.011679545976221561,
-0.039727333933115005,
0.05844741687178612,
-0.01682717725634575,
-0.011375587433576584,
-0.0616091713309288,
-0.031365104019641876,
-0.03083518147468567,
-0.009962654672563076,
-0.027288340032100677,
0.011031029745936394,
0.027710482478141785,
0.038606155663728714,
0.055681176483631134,
-0.0019246296724304557,
-0.018108967691659927,
0.012591859325766563,
0.02216584049165249,
0.02382647432386875,
0.04582156613469124,
-0.04830674082040787,
-0.011091410182416439,
0.038711924105882645,
-0.030375629663467407,
-0.03400467708706856,
-0.027368273586034775,
-0.013161037117242813,
0.06772433966398239,
0.011592994444072247,
-0.02787158638238907,
-0.015333786606788635,
0.06082124635577202,
-0.03918761387467384,
0.004562098998576403,
-0.005656224675476551,
0.036870282143354416,
0.015150570310652256,
0.00766302365809679,
-0.004197065718472004,
-0.009889747947454453,
-0.017291925847530365,
0.0395447313785553,
0.02389095164835453,
-0.0028726959135383368,
0.01080978475511074,
-0.023108402267098427,
0.009339899756014347,
-0.011796006001532078,
0.02976401150226593,
0.00673375790938735,
0.023487241938710213,
0.01869853027164936,
-0.039805371314287186,
0.024573704227805138,
0.04383188858628273,
0.0060935476794838905,
-0.09134674817323685,
-0.036097582429647446,
-0.013685894198715687,
-0.014788025990128517,
0.02320350892841816,
-0.025431189686059952,
0.03149211406707764,
0.043747685849666595,
-0.0443916991353035,
0.008201275952160358,
-0.011354638263583183,
-0.10544204711914062,
-0.0009764792048372328,
0.019411081448197365,
-0.005403244402259588,
0.05573108047246933,
0.05085819214582443,
0.06782753765583038,
0.014090067707002163,
0.014125119894742966,
-0.0077663566917181015,
0.028096476569771767,
-0.011355577036738396,
-0.010341744869947433,
0.00006975560972932726,
-0.00759710930287838,
0.05479623004794121,
-0.03886320814490318,
-0.014413888566195965,
0.027225812897086143,
-0.003328871913254261,
0.02477198652923107,
0.006873785518109798,
0.024791933596134186,
0.0048970067873597145,
0.04914233461022377,
0.03999275341629982,
0.004958638455718756,
-0.04919116944074631,
0.03284188732504845,
0.008137916214764118,
0.017625344917178154,
-0.010951397009193897,
0.020938673987984657,
0.02760811150074005,
-0.010412819683551788,
0.023046981543302536,
0.04998580366373062,
-0.018801279366016388,
-0.05165968835353851,
-0.013129058293998241,
-0.012547525577247143,
0.027303768321871758,
0.008839428424835205,
-0.00436415895819664,
-0.05573287233710289,
-0.021287893876433372,
0.021300313994288445,
-0.04786128178238869,
-0.01814776100218296,
0.038591183722019196,
0.017337575554847717,
-0.034814462065696716,
0.014847073704004288,
-0.004608550108969212,
-0.042899489402770996,
-0.027335593476891518,
0.01886189915239811,
0.02390618808567524,
0.0076894923113286495,
-0.006927581038326025,
-0.035082459449768066,
-0.03794474899768829,
0.05829555168747902,
0.024182535707950592,
0.021219082176685333,
0.068051777780056,
-0.032306790351867676,
-0.03884578496217728,
-0.01591545343399048,
0.042668674141168594,
-0.0017521725967526436,
-0.007579992525279522,
-0.0046823881566524506,
-0.05520439147949219,
-0.012763388454914093,
-0.00941936019808054,
0.03343438729643822,
-0.011958430521190166,
0.01374890748411417,
-0.004091096110641956,
-0.016067922115325928,
0.038499653339385986,
-0.01846640557050705,
0.041795119643211365,
0.0058281500823795795,
-0.025403980165719986,
-0.012593298219144344,
0.011937547475099564,
-0.024969886988401413,
0.025655806064605713,
0.03998249024152756,
0.009333906695246696,
-0.036252330988645554,
-0.00748810637742281,
0.014108195900917053,
0.07772964984178543,
0.0028856603894382715,
-0.014430051669478416,
0.06235091760754585,
-0.0518144890666008,
0.047056786715984344,
0.004049409180879593,
-0.017582949250936508,
-0.029211025685071945,
0.025194982066750526,
-0.0338294692337513,
0.003076436696574092,
0.005440862383693457,
-0.026195989921689034,
0.01265502255409956,
-0.036937884986400604,
-0.0034239250235259533,
0.01725725829601288,
-0.029055632650852203,
0.037229448556900024,
0.04044625908136368,
0.011816492304205894,
0.0017939211102202535,
0.015390954911708832,
-0.0017391809960827231,
-0.002025146270170808,
-0.002251042751595378,
0.00951424241065979,
0.01929393596947193,
0.04286770522594452,
-0.01781858690083027,
0.00659728841856122,
0.013548615388572216,
-0.005217853467911482,
-0.0017060521058738232,
0.01732947677373886,
0.027534233406186104,
-0.05553359538316727,
-0.028800152242183685,
0.02611721120774746,
-0.022269122302532196,
-0.019075028598308563,
0.010169480927288532,
-0.03979400917887688,
0.06674834340810776,
0.00517853582277894,
0.02603914402425289,
-0.0292883962392807,
-0.021433493122458458,
0.0235553327947855,
-0.00860643945634365,
0.015667229890823364,
0.03601923584938049,
-0.020061375573277473,
-0.006845058407634497,
0.0007903162040747702,
0.04645153507590294,
0.030028926208615303,
-0.025532959029078484,
0.03015179932117462,
-0.030295006930828094,
0.015978800132870674,
-0.040429845452308655,
-0.05520128458738327,
-0.04986700415611267,
-0.04480224847793579,
0.012447508983314037,
0.052337467670440674,
0.03370828181505203,
0.02099781669676304,
-0.013815507292747498,
-0.01841830648481846,
0.05301308259367943,
-0.01700892485678196,
0.02529929392039776,
-0.000016146956113516353,
-0.022214241325855255,
0.0021179369650781155,
0.010846217162907124
] |
<p>Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. If they ever communicated in the future they would be the same age. Is this correct?</p>
<p>Case 2: one person wakes up in a room on earth, another on a spaceship accelerating 1g. Same measuring restrictions. Again neither could determine if they were on a spaceship or earth. However now if they communicated in the future they would find they are different ages. Is this correct?</p>
<p>I've heard acceleration from a rocket or gravity are the same (e.g. time slows down near a black hole). But case 2 above seems there is a difference?</p> | 4,562 | [
-0.014849155209958553,
-0.07586788386106491,
-0.05964139476418495,
-0.04026947170495987,
0.022537685930728912,
-0.01834072545170784,
-0.04209483787417412,
0.0015370945911854506,
0.02617894858121872,
-0.02109951712191105,
0.037641964852809906,
0.03868914023041725,
0.04455134645104408,
0.014901499263942242,
0.03953862190246582,
0.012124736793339252,
-0.007463362999260426,
0.0019829634111374617,
-0.01911391317844391,
0.004591054283082485,
0.03680500015616417,
0.011904704384505749,
0.006860274355858564,
-0.030068080872297287,
-0.030041584745049477,
0.017881514504551888,
0.000478248402941972,
-0.0361308827996254,
0.006085394416004419,
0.043968189507722855,
-0.0039338478818535805,
-0.009591570124030113,
-0.008762795478105545,
0.04123682901263237,
0.013169554993510246,
-0.005775740370154381,
-0.056312840431928635,
-0.029065463691949844,
-0.0008737295283935964,
0.013167137280106544,
-0.042720209807157516,
-0.02535201981663704,
0.024221815168857574,
0.07193740457296371,
-0.04250416159629822,
-0.00522476015612483,
-0.0032059194054454565,
-0.011212021112442017,
0.03537615388631821,
-0.04841999337077141,
0.033922675997018814,
-0.03345142677426338,
0.006480332929641008,
0.022385749965906143,
-0.0027433871291577816,
0.0026628472842276096,
0.0700240358710289,
0.0565958172082901,
0.023619284853339195,
-0.020895177498459816,
-0.038846682757139206,
-0.004265205468982458,
0.01209138985723257,
-0.013272502459585667,
0.0011208488140255213,
0.007031220011413097,
-0.058137256652116776,
-0.04145330190658569,
0.010522298514842987,
-0.041103433817625046,
0.027259428054094315,
0.030881915241479874,
0.010582011193037033,
0.0035703445319086313,
0.028075506910681725,
-0.03848116472363472,
0.016407599672675133,
-0.003329585073515773,
0.060593318194150925,
0.0637817233800888,
-0.04558023065328598,
-0.011863608844578266,
0.07590462267398834,
0.019371850416064262,
0.01674732193350792,
-0.0027266638353466988,
0.06756030023097992,
0.005707604344934225,
0.010019398294389248,
0.040740083903074265,
-0.01976868323981762,
0.02491002529859543,
-0.016879549250006676,
-0.017404329031705856,
-0.02277124859392643,
0.03431549295783043,
0.003148559480905533,
0.029811032116413116,
0.007325083017349243,
-0.0036148978397250175,
-0.011147519573569298,
-0.02472022920846939,
0.03513333573937416,
0.059727489948272705,
-0.005690693389624357,
-0.0308864563703537,
-0.02713976427912712,
0.0005886081489734352,
-0.032635338604450226,
-0.011175916530191898,
-0.02009386196732521,
0.0005464513669721782,
-0.000570046657230705,
0.021409817039966583,
0.036730580031871796,
-0.013950536027550697,
-0.010110747069120407,
-0.018083583563566208,
0.08723574876785278,
0.051788803189992905,
0.05235620588064194,
-0.012485118582844734,
-0.0027495124377310276,
0.006877870298922062,
-0.036993857473134995,
0.017631448805332184,
0.0015170910628512502,
-0.03275497630238533,
-0.021827585995197296,
0.06091998517513275,
-0.016743263229727745,
-0.008333506062626839,
0.026341356337070465,
-0.02372824400663376,
0.037747833877801895,
0.011860481463372707,
-0.1268375664949417,
-0.04873235896229744,
0.025014400482177734,
0.02224172279238701,
0.019317548722028732,
-0.07389616221189499,
0.027974965050816536,
0.015590258873999119,
0.07877550274133682,
0.019448241218924522,
-0.0004319773579481989,
0.012183383107185364,
0.035777781158685684,
0.02650635503232479,
-0.013662908226251602,
0.023148871958255768,
-0.029525592923164368,
-0.036659304052591324,
0.005716295447200537,
-0.05307107791304588,
-0.0032324024941772223,
0.04085887223482132,
0.0011564412852749228,
-0.043740831315517426,
0.07312246412038803,
-0.036610305309295654,
0.0020200524013489485,
0.03277502581477165,
0.04866015538573265,
-0.0034990219864994287,
0.07600749284029007,
0.028933392837643623,
-0.011726788245141506,
0.07606998085975647,
0.061447083950042725,
0.03495777025818825,
-0.003211068222299218,
-0.0026035055052489042,
0.027976416051387787,
-0.009472290053963661,
-0.015024704858660698,
-0.001349449041299522,
-0.00437574228271842,
-0.014695207588374615,
-0.037819791585206985,
-0.02635212615132332,
-0.04653789475560188,
-0.021717552095651627,
-0.000617689045611769,
0.002340589417144656,
0.0038807985838502645,
0.02097550965845585,
-0.006526143755763769,
0.009274519979953766,
-0.011702412739396095,
-0.08951158821582794,
0.032591890543699265,
0.02392023429274559,
0.02422819659113884,
0.014387357980012894,
-0.003087277291342616,
0.05335227772593498,
-0.060433048754930496,
-0.01989520899951458,
0.005677125416696072,
0.030385999009013176,
-0.01725086197257042,
-0.051200173795223236,
-0.005249563604593277,
0.05604839324951172,
0.019628573209047318,
-0.01210951991379261,
-0.024122973904013634,
-0.007423905190080404,
-0.016668954864144325,
0.02918330579996109,
-0.014771399088203907,
0.03554107993841171,
0.01042648870497942,
0.021172555163502693,
0.008948247879743576,
0.009058898314833641,
-0.010843547061085701,
0.04539310559630394,
-0.030686751008033752,
0.07466267049312592,
0.036704447120428085,
-0.022320207208395004,
-0.003296241629868746,
0.0005930318729951978,
0.03547198697924614,
0.011260566301643848,
-0.004060138948261738,
-0.03734593838453293,
-0.06402667611837387,
-0.0613669790327549,
0.020589131861925125,
0.003024699166417122,
0.010286524891853333,
0.02454523742198944,
0.0478060320019722,
0.04723954573273659,
0.017922991886734962,
0.00248938356526196,
0.007670222781598568,
-0.06543726474046707,
0.0069709885865449905,
0.02512926235795021,
-0.0007704052259214222,
0.03823209926486015,
0.04626459628343582,
0.0030263089574873447,
0.0056664589792490005,
-0.019909119233489037,
0.014033771120011806,
0.00781699363142252,
-0.006064217071980238,
0.030627036467194557,
-0.02176942490041256,
-0.021314837038517,
0.017594950273633003,
-0.032302603125572205,
0.016112705692648888,
0.010023720562458038,
-0.016088111326098442,
-0.031829141080379486,
-0.024942703545093536,
-0.004564080853015184,
-0.021931733936071396,
0.003857656382024288,
-0.03295806795358658,
-0.02591399848461151,
0.02994030900299549,
-0.049768805503845215,
0.02030533365905285,
-0.013543259352445602,
-0.02497233636677265,
-0.013658399693667889,
0.009969842620193958,
0.01946638897061348,
-0.017302194610238075,
0.02193942852318287,
-0.04563584178686142,
-0.02996404655277729,
-0.0010170756140723825,
-0.052927590906620026,
0.02468102052807808,
0.02529148757457733,
-0.05396347492933273,
0.0699891597032547,
-0.02047760970890522,
-0.03525625541806221,
0.04299173131585121,
0.014253010042011738,
0.01728801429271698,
0.0485934242606163,
0.013620586134493351,
-0.03789091110229492,
-0.006852693390101194,
-0.05230742320418358,
0.008939790539443493,
-0.014457711949944496,
-0.004819873720407486,
0.0585009902715683,
0.007295823656022549,
-0.022319622337818146,
0.014583081007003784,
-0.05335140973329544,
-0.03302277624607086,
0.005571895278990269,
0.016449671238660812,
-0.009420393966138363,
-0.010878807865083218,
-0.01571555994451046,
0.059296395629644394,
-0.023249642923474312,
-0.04509767144918442,
-0.04417383670806885,
-0.092030368745327,
0.06259606033563614,
-0.003731410251930356,
0.03345874696969986,
-0.04203256964683533,
0.004748642910271883,
0.04264794662594795,
0.032659489661455154,
0.023957984521985054,
-0.051909927278757095,
-0.001166067086160183,
0.0014326017117127776,
-0.008713542483747005,
0.0008628492360003293,
0.02065248414874077,
0.00957019068300724,
0.001562903868034482,
0.03459957614541054,
0.043524693697690964,
0.018624717369675636,
0.020490365102887154,
0.011360039003193378,
-0.010249948129057884,
0.026397844776511192,
0.011557517573237419,
0.07227567583322525,
0.03541255742311478,
-0.033786069601774216,
0.005117754451930523,
-0.008960198611021042,
0.024602115154266357,
0.01264935452491045,
-0.03989393264055252,
0.05257997661828995,
0.023549480363726616,
0.004978682845830917,
-0.026467178016901016,
0.006589273922145367,
-0.005949751939624548,
0.0357261560857296,
-0.027683746069669724,
0.008096049539744854,
0.03105085715651512,
-0.024622200056910515,
-0.008098162710666656,
0.03292957693338394,
0.028934143483638763,
-0.01666790246963501,
-0.04927997663617134,
0.035376712679862976,
0.012578247115015984,
0.0610913410782814,
-0.028104430064558983,
-0.038421981036663055,
0.03204901143908501,
0.03603735566139221,
0.005025627091526985,
0.02462228573858738,
-0.019547389820218086,
0.008528904989361763,
-0.08017388731241226,
0.029917320236563683,
-0.012258734554052353,
0.05773613229393959,
0.0077530997805297375,
0.042164575308561325,
0.02882140688598156,
0.007816741243004799,
0.021215250715613365,
-0.01202466245740652,
-0.08906949311494827,
0.0016623556148260832,
-0.037750132381916046,
-0.03789115324616432,
-0.00927108246833086,
0.00670077046379447,
-0.024516772478818893,
-0.036660462617874146,
-0.025125697255134583,
0.006948364432901144,
-0.004761989694088697,
-0.0675862655043602,
0.015245801769196987,
-0.05077412351965904,
-0.03645380958914757,
-0.02407449670135975,
0.005711539648473263,
0.0036781460512429476,
0.0017116996459662914,
0.0056896149180829525,
0.041424237191677094,
-0.00038486457196995616,
-0.006017542909830809,
-0.007122241426259279,
-0.011079531162977219,
0.016472365707159042,
0.050839316099882126,
0.05046543851494789,
0.004585299175232649,
-0.027827374637126923,
0.02384021319448948,
0.028016913682222366,
-0.013956215232610703,
-0.02184423804283142,
-0.023447668179869652,
-0.03542206436395645,
0.0011591102229431272,
-0.03375003859400749,
-0.002154199406504631,
0.02688414789736271,
-0.009885301813483238,
0.017778882756829262,
-0.0001656364620430395,
0.016718842089176178,
0.03820033743977547,
0.041218604892492294,
0.07829267531633377,
-0.05431203544139862,
-0.01115540973842144,
0.009030552580952644,
-0.04959748685359955,
-0.029414786025881767,
-0.03343801200389862,
0.024014882743358612,
0.03128965198993683,
-0.01874886453151703,
-0.01708393543958664,
0.0019569117575883865,
-0.009065180085599422,
-0.03665076941251755,
0.008279304951429367,
0.014840525574982166,
0.00952869188040495,
0.011774116195738316,
0.012696071527898312,
-0.017343996092677116,
0.01949309930205345,
0.028874743729829788,
0.0012694229371845722,
-0.022241096943616867,
-0.06398133188486099,
-0.0010576244676485658,
-0.00569525733590126,
0.018020419403910637,
-0.0009737185318954289,
-0.018213292583823204,
-0.044092271476984024,
-0.014380722306668758,
0.009406411089003086,
0.005275180097669363,
0.031494807451963425,
0.017972461879253387,
-0.008372006006538868,
-0.006796206813305616,
-0.012033306993544102,
0.0017594719538465142,
0.008892474696040154,
-0.012304926291108131,
0.01526816375553608,
-0.0007813602569513023,
0.006307752802968025,
0.011620698496699333,
0.0074146222323179245,
0.04357805475592613,
0.051056619733572006,
0.011385386809706688,
0.011393660679459572,
-0.0019626421853899956,
0.004645140375941992,
-0.019747229292988777,
-0.05949150025844574,
0.02568424865603447,
0.01587975025177002,
-0.04714512079954147,
0.05799182504415512,
-0.0439840629696846,
-0.05088347941637039,
0.03196786716580391,
-0.008967391215264797,
-0.012590521946549416,
-0.04581538215279579,
-0.018854979425668716,
0.047175951302051544,
0.02757437340915203,
-0.003465300891548395,
0.02770659513771534,
-0.0018484124448150396,
-0.00286469841375947,
0.035409580916166306,
-0.01717199943959713,
0.013921460136771202,
-0.06927423924207687,
0.028276721015572548,
-0.0006150690605863929,
0.0071249958127737045,
-0.025959160178899765,
0.05687696859240532,
0.008471336215734482,
0.0230228491127491,
0.0028139669448137283,
-0.045740220695734024,
0.0171310156583786,
0.03859850391745567,
0.012064590118825436,
0.015520432963967323,
-0.01934288814663887,
-0.02044171467423439,
-0.01746000535786152,
-0.021955953910946846,
0.007569777779281139,
-0.012913367711007595,
-0.000548698240891099,
0.03944836184382439,
-0.02022632770240307,
0.011867937631905079,
0.007365016732364893,
0.005903698969632387,
0.0361495316028595,
-0.04711483418941498,
0.020236456766724586,
-0.006530536338686943,
0.01487966813147068,
0.04014965519309044,
0.004938883241266012,
-0.017107954248785973,
-0.007586073130369186,
-0.006172113586217165,
0.031604792922735214,
-0.03274611011147499,
0.033185094594955444,
0.019762007519602776,
0.0053088185377418995,
-0.05642497539520264,
-0.016205089166760445,
0.012943755835294724,
0.027006013318896294,
-0.005313537083566189,
-0.014345980249345303,
0.010122060775756836,
-0.07198252528905869,
-0.006233436055481434,
-0.026852644979953766,
0.04764189198613167,
0.007715457119047642,
-0.05094565451145172,
-0.004529955331236124,
0.03406593203544617,
0.06681853532791138,
-0.011065282858908176,
-0.010019351728260517,
-0.01570352353155613,
0.005590321030467749,
0.01409370731562376,
-0.027976248413324356,
0.05518890172243118,
-0.032626923173666,
-0.024948444217443466,
-0.021451791748404503,
0.009492124430835247,
-0.004082477651536465,
-0.058234408497810364,
-0.005618504714220762,
0.06721248477697372,
-0.008771410211920738,
0.007034958805888891,
-0.00799766555428505,
0.03878059610724449,
-0.039879441261291504,
-0.023062890395522118,
-0.01624983549118042,
-0.002029180061072111,
-0.004438828676939011,
-0.031193461269140244,
0.020439215004444122,
0.012015108950436115,
-0.020654160529375076,
0.026278918609023094,
0.05953849107027054,
0.01880185306072235,
-0.02385564148426056,
0.012999792583286762,
-0.022174006327986717,
0.040133122354745865,
-0.0406925193965435,
-0.011002302169799805,
0.025543851777911186,
-0.01432671770453453,
-0.03624126315116882,
-0.02098531648516655,
-0.02904481068253517,
-0.009554605931043625,
0.08577149361371994,
0.01726733334362507,
0.10282628983259201,
-0.0021479178685694933,
0.02411498874425888,
0.0012359701795503497,
-0.044765178114175797,
0.002706908155232668,
0.007222374435514212,
-0.05446738749742508,
0.02007858082652092,
-0.05359279736876488,
-0.04848089814186096,
0.03389206528663635,
0.04334653913974762,
-0.007195464801043272,
0.012336782179772854,
0.04800755903124809,
0.024339741095900536,
0.03687681257724762,
-0.014646508730947971,
-0.0014101422857493162,
0.028298141434788704,
-0.020234238356351852,
0.0027343337424099445,
-0.020677274093031883,
0.04606837406754494,
0.04309085011482239,
0.025640176609158516,
0.0030784686096012592,
-0.04434706270694733,
-0.025331156328320503,
-0.06821694225072861,
-0.013149072416126728,
0.053391799330711365,
0.021931638941168785,
0.021338099613785744,
-0.02128683030605316,
0.023650415241718292,
0.02271878905594349,
-0.0020783934742212296,
-0.015152364037930965,
-0.0810512900352478,
-0.019355466589331627,
-0.04832014814019203,
-0.03900817036628723,
0.03582102432847023,
0.03031286783516407,
-0.03404437005519867,
0.018227960914373398,
-0.032332535833120346,
0.015206905081868172,
0.01964469999074936,
0.056447651237249374,
-0.024524172767996788,
0.07729711383581161,
-0.027678757905960083,
0.013509579002857208,
-0.016900140792131424,
0.047567158937454224,
0.08821050822734833,
0.06250931322574615,
-0.022397516295313835,
-0.026282912120223045,
0.012956309132277966,
0.0005516960518434644,
-0.0019101276993751526,
-0.013517756946384907,
0.025033216923475266,
-0.02163652516901493,
0.007482654415071011,
0.04073667898774147,
0.05176286771893501,
0.025521432980895042,
-0.04295571893453598,
0.033596161752939224,
-0.019172722473740578,
-0.01877077855169773,
-0.014672127552330494,
0.042207539081573486,
0.015285184606909752,
0.010711374692618847,
0.018458586186170578,
0.03365458548069,
-0.02957831509411335,
0.006820354610681534,
-0.028387010097503662,
-0.006870802491903305,
0.04029505327343941,
-0.005570902023464441,
-0.060305558145046234,
0.03732840344309807,
-0.0013583018444478512,
-0.029043108224868774,
-0.04700028896331787,
0.01116056740283966,
-0.013041633181273937,
-0.012793535366654396,
-0.008980327285826206,
0.035561397671699524,
0.011691158637404442,
-0.008936327882111073,
0.010163522325456142,
-0.01440230943262577,
-0.07915212959051132,
-0.035728201270103455,
-0.01688358373939991,
0.043474894016981125,
-0.02219926007091999,
-0.05942109227180481,
0.006150015629827976,
0.02101825922727585,
-0.006203250959515572,
-0.08318722993135452,
-0.026905091479420662,
0.020100856199860573,
0.026284195482730865,
0.007583485916256905,
0.01940252259373665,
-0.024803457781672478,
0.017369044944643974,
0.003944960422813892,
0.024307144805788994,
0.021705808117985725,
0.022420529276132584,
0.05522029101848602,
-0.02355908416211605,
0.03804296627640724,
-0.018534338101744652,
-0.026512309908866882,
-0.010860150679945946,
0.01259883213788271,
-0.05745896324515343,
0.004248395096510649,
0.00824666116386652,
0.05126849189400673,
0.037391260266304016,
0.02118084207177162,
0.017073044553399086,
-0.025324907153844833,
-0.014220978133380413,
0.021778631955385208,
-0.0016091257566586137,
-0.0085113774985075,
0.005079401191323996,
-0.013215437531471252,
0.015569032169878483,
-0.0012388556497171521,
-0.035304293036460876,
-0.03625857084989548,
-0.010659039951860905,
0.04592937231063843,
0.02682848647236824,
0.0011764650698751211,
0.006061514839529991,
-0.006186818704009056,
-0.04134075716137886,
-0.020734719932079315,
-0.04755747690796852,
0.03475939854979515,
0.037571582943201065,
-0.024901779368519783,
0.01871355250477791,
-0.004708731546998024,
-0.02740706130862236,
0.007372588384896517,
0.030137494206428528,
0.0011424091644585133,
0.01722361333668232,
-0.004551864694803953,
0.030016914010047913,
0.004691754002124071,
-0.040072109550237656,
-0.032288383692502975,
0.0019370234804227948,
0.000048820689698914066,
0.010665950365364552,
0.02709014341235161,
0.020796215161681175,
0.001098526525311172,
0.004385821055620909,
-0.03427839279174805,
0.00987448450177908,
-0.04356490820646286,
0.045797403901815414,
0.013434209860861301,
-0.04959392547607422,
0.011119391769170761,
0.056190069764852524,
-0.029824228957295418,
-0.03597486391663551,
0.014307442121207714,
0.0008588510099798441,
-0.03225300461053848,
-0.018519064411520958,
0.004412660840898752,
-0.04168802127242088,
0.02910969965159893,
-0.03040255606174469,
-0.056936223059892654,
-0.02584771253168583,
-0.021634064614772797,
-0.0406954251229763,
0.07419772446155548,
0.0050779106095433235,
0.03631815314292908,
0.00782747846096754,
-0.03605056554079056,
-0.00542263500392437,
0.0784870907664299,
-0.0024939400609582663,
0.0087584238499403,
0.003716724691912532,
-0.019315270707011223,
-0.0236460343003273,
-0.008843609131872654,
0.01903664320707321,
0.009390401653945446,
-0.015496479347348213,
0.024390164762735367,
0.01156675722450018,
-0.0013955614995211363,
0.03695687651634216,
-0.053061582148075104,
-0.010245565325021744,
-0.008776427246630192,
0.026454754173755646,
-0.004035154823213816,
0.03633155673742294,
0.07457228749990463,
-0.024310659617185593,
0.03528507798910141,
0.02472231723368168,
-0.0014731039991602302,
-0.05595134571194649,
-0.01750633306801319,
0.03402048349380493,
0.01659124530851841,
0.01815173588693142,
-0.0407533124089241,
0.0158158577978611,
0.0312142726033926,
-0.07849523425102234,
-0.00015208420518320054,
-0.02918008156120777,
-0.024700595065951347,
-0.01436733640730381,
0.00043110246770083904,
0.015972841531038284,
0.024099765345454216,
0.03341425210237503,
0.03681381419301033,
-0.020604416728019714,
0.018450209870934486,
-0.02970609813928604,
-0.04311243072152138,
-0.02128659561276436,
0.013689643703401089,
0.00022751057986170053,
-0.004347515292465687,
0.04813007265329361,
-0.04733344912528992,
-0.015069090761244297,
0.02281125821173191,
-0.0032421734649688005,
-0.004231030121445656,
0.005728496704250574,
0.007422735448926687,
0.03784448280930519,
-0.0011672812979668379,
0.0063618547283113,
-0.01132025383412838,
-0.03352535888552666,
0.02090786211192608,
-0.0075563713908195496,
0.024946199730038643,
-0.003344754921272397,
-0.03603016957640648,
-0.014343731105327606,
-0.010367892682552338,
-0.0018379205139353871,
0.01657394878566265,
-0.005855869501829147,
-0.013332687318325043,
0.01424709614366293,
0.00867623183876276,
-0.02091735228896141,
-0.02191299945116043,
-0.007331519387662411,
-0.03242393583059311,
-0.02624576725065708,
0.03755158931016922,
0.015161906369030476,
-0.026571614667773247,
-0.017531737685203552,
-0.05828718841075897,
0.001979717519134283,
0.006405551452189684,
0.0048293862491846085,
0.017474953085184097,
0.0008389571448788047,
-0.0261427890509367,
-0.022480053827166557,
0.025144726037979126,
0.0099445516243577,
-0.05855808034539223,
-0.026808690279722214,
0.046397287398576736,
0.005431835073977709,
0.016540328040719032,
-0.019015757367014885,
-0.01318307500332594,
-0.032929230481386185,
-0.058162279427051544,
-0.0015457100234925747,
0.018002886325120926,
-0.016822950914502144,
-0.05589502304792404,
-0.015880703926086426,
-0.03592138737440109,
0.013215702958405018,
0.0653868094086647,
0.026792101562023163,
-0.013678534887731075,
0.024361340329051018,
-0.021272087469697,
-0.011677799746394157,
-0.025310616940259933,
0.028408847749233246,
0.007311291992664337,
-0.03078358806669712,
-0.002540658228099346,
-0.0031775706447660923,
-0.0392688550055027,
-0.0010952288284897804,
0.030862243846058846,
-0.03851897642016411,
0.054319869726896286,
0.03736145794391632,
0.0068818554282188416,
0.05359473451972008,
0.03831334039568901,
-0.0034462707117199898,
0.041679251939058304,
-0.014098761603236198,
0.004629552364349365,
0.03793331980705261,
0.00881964061409235,
-0.05774980038404465,
0.06308613717556,
-0.019902480766177177,
0.01978149451315403,
0.023622669279575348,
-0.0038304238114506006,
-0.006239102687686682,
-0.02706887573003769,
-0.015700824558734894,
0.04014323651790619,
-0.01816358044743538,
-0.007840138860046864,
0.039209865033626556,
0.03804120793938637,
0.00023802749637980014,
-0.03365296497941017,
-0.01250354666262865,
0.02331566996872425,
-0.0012241157237440348,
-0.022312061861157417,
0.043945346027612686,
0.04121636599302292,
-0.01474850159138441,
0.050617702305316925,
0.055198196321725845,
0.0027114537078887224,
-0.010095552541315556,
0.011999622918665409,
0.038139645010232925,
-0.020190466195344925,
0.010935666970908642,
-0.02012326382100582,
0.013266013003885746,
0.0033257377799600363,
0.034798428416252136,
-0.028474994003772736,
0.05299874767661095,
-0.06255371868610382,
-0.005446502938866615,
0.0065667773596942425,
-0.010644887574017048,
-0.059882402420043945,
0.01206679455935955,
0.006543250754475594,
0.0244162417948246,
0.025610532611608505,
-0.015481626614928246,
-0.026817917823791504,
-0.041189953684806824,
0.02484511025249958,
-0.05635599419474602,
0.00018118137086275965,
-0.03030458092689514,
-0.004923560190945864,
-0.007650692947208881,
-0.04380946233868599,
-0.05304370075464249,
-0.013721111230552197,
0.03832510858774185,
0.006844710558652878,
0.038105372339487076,
-0.07426981627941132,
-0.007199387066066265,
-0.012079770676791668,
0.038972023874521255,
-0.06718041002750397,
-0.01897629350423813,
-0.0040197051130235195,
0.044868167489767075,
-0.007114178501069546,
-0.015133628621697426
] |
<p>I just want a book on classical mechanics that covers the same ground as Goldstein's book but is more on the line of DJ Griffiths's Classical Electrodynamics. I mean less formal and more conversational. </p> | 98 | [
-0.02966318465769291,
-0.024611443281173706,
0.024684010073542595,
-0.03304707258939743,
0.0086214579641819,
0.03564935922622681,
0.020639708265662193,
-0.023023568093776703,
-0.010388930328190327,
0.0035574110224843025,
0.010280006565153599,
0.03161734715104103,
0.07636875659227371,
0.020173462107777596,
0.015209836885333061,
-0.02740514650940895,
0.01904003508388996,
-0.033588651567697525,
-0.03549743443727493,
-0.03778167441487312,
-0.017418691888451576,
-0.018463492393493652,
-0.02437344379723072,
0.023886971175670624,
-0.005161549896001816,
0.004834805149585009,
0.032705023884773254,
-0.02681925892829895,
-0.01274184137582779,
0.0692397952079773,
-0.034161683171987534,
0.017655514180660248,
-0.041096799075603485,
0.0054504224099218845,
0.022812504321336746,
-0.000951850728597492,
-0.026084918528795242,
-0.032538384199142456,
-0.016887767240405083,
-0.03115527704358101,
-0.04567883536219597,
-0.018697280436754227,
-0.008005880750715733,
0.040871862322092056,
-0.0051793064922094345,
0.059367820620536804,
0.010519472882151604,
0.01737353205680847,
0.03592582046985626,
-0.06849140673875809,
0.08442894369363785,
0.00297033810056746,
0.014871385879814625,
0.01368031557649374,
0.001733417739160359,
-0.0037851925007998943,
0.07750988006591797,
0.05178316682577133,
0.015334777534008026,
-0.051773615181446075,
-0.025881819427013397,
0.007669113110750914,
0.010936006903648376,
-0.05795954167842865,
-0.03941246122121811,
0.06034574657678604,
0.004581018351018429,
-0.06465499103069305,
0.04156237468123436,
-0.01704106107354164,
-0.04765065386891365,
0.025165019556879997,
0.0706576257944107,
-0.02827434055507183,
0.004780749790370464,
-0.037583306431770325,
-0.005347733851522207,
0.006480234209448099,
0.003031538100913167,
-0.010014411062002182,
-0.027996473014354706,
-0.001075743930414319,
0.03760315105319023,
0.0346059612929821,
-0.01074210461229086,
-0.03523387759923935,
0.07679702341556549,
0.01254415325820446,
-0.015710270032286644,
0.039991345256567,
-0.026910845190286636,
0.01921326294541359,
0.010418974794447422,
0.007544470485299826,
-0.0442945696413517,
0.012928491458296776,
-0.009395130909979343,
0.07922521978616714,
-0.00217618839815259,
-0.022371893748641014,
0.033897291868925095,
-0.010987249203026295,
0.005100035108625889,
0.04146415367722511,
0.040446825325489044,
-0.03872506693005562,
-0.037859391421079636,
-0.00416467385366559,
-0.04320378601551056,
-0.012411922216415405,
-0.015329909510910511,
0.030714716762304306,
-0.02193734236061573,
-0.018955698236823082,
-0.012796186842024326,
-0.02987794019281864,
-0.008020218461751938,
-0.00843804795295,
0.09334123134613037,
0.07241445779800415,
0.060462746769189835,
-0.04396101087331772,
0.04215347766876221,
-0.049399446696043015,
-0.06663453578948975,
-0.0205573420971632,
0.0548589788377285,
-0.013500803150236607,
0.0038264268077909946,
-0.0003715382772497833,
-0.011750473640859127,
0.01700773648917675,
-0.03129750117659569,
0.022638564929366112,
-0.0017064792336896062,
-0.0477515272796154,
-0.06050614267587662,
-0.04977255314588547,
0.050700921565294266,
-0.022813299670815468,
-0.011847925372421741,
-0.06496524810791016,
0.020923607051372528,
0.024723423644900322,
0.04089963063597679,
0.04299002140760422,
0.0014145526802167296,
-0.013842452317476273,
0.07026247680187225,
-0.017013365402817726,
-0.02964737080037594,
-0.009092183783650398,
0.001010253094136715,
0.018183397129178047,
-0.0023356822784990072,
-0.08200070261955261,
-0.011110496707260609,
0.026992453262209892,
0.03479216992855072,
0.015018464997410774,
0.04786909371614456,
-0.029693927615880966,
-0.006314033642411232,
0.02429022639989853,
0.004754842258989811,
-0.0346418060362339,
0.04690783843398094,
0.028076056391000748,
0.006088270805776119,
0.0011594555107876658,
0.010386883281171322,
0.05881701409816742,
-0.028333909809589386,
0.017531931400299072,
0.03813514485955238,
-0.05579090118408203,
-0.020229237154126167,
0.06574516743421555,
0.01386099774390459,
0.01633867621421814,
0.023587509989738464,
-0.055196553468704224,
0.0019517126493155956,
0.01358299795538187,
-0.032161276787519455,
0.04667981341481209,
0.0023354422301054,
0.061206866055727005,
-0.00019399180018808693,
-0.002469391329213977,
0.0005543091101571918,
-0.028043262660503387,
0.05738763511180878,
-0.023307079449295998,
-0.010847599245607853,
0.060142796486616135,
0.017462395131587982,
0.040855295956134796,
-0.018351005390286446,
-0.06237417086958885,
0.004554243292659521,
0.014635585248470306,
-0.010747918859124184,
-0.004250814206898212,
0.007513331715017557,
0.044017862528562546,
0.06029846519231796,
-0.00983758457005024,
0.014079883694648743,
-0.0037320638075470924,
-0.031200936064124107,
0.022818375378847122,
-0.0021171767730265856,
0.04160762578248978,
0.017809364944696426,
0.04296773299574852,
0.03528287634253502,
-0.03580663725733757,
0.006921152584254742,
0.017100125551223755,
-0.05090624466538429,
0.026186855509877205,
0.022689364850521088,
0.03027079626917839,
0.018069786950945854,
0.07189151644706726,
-0.02254062332212925,
0.01925596036016941,
0.005137035623192787,
0.03393679857254028,
0.03434006869792938,
0.01164426188915968,
0.0517897829413414,
0.03310826048254967,
-0.024203890934586525,
0.03965446352958679,
0.029948027804493904,
0.032318685203790665,
0.0274200476706028,
0.03362322971224785,
-0.03026697039604187,
-0.06375375390052795,
0.03107514977455139,
0.01822640374302864,
-0.017645740881562233,
0.029273662716150284,
0.05100443214178085,
0.004639099817723036,
-0.00481837335973978,
0.002934311982244253,
-0.030159803107380867,
0.007397529203444719,
0.006097080651670694,
0.012899699620902538,
0.014543946832418442,
-0.02287108823657036,
0.05048393830657005,
-0.0005523744621314108,
0.02455645054578781,
-0.004193694330751896,
-0.04370233044028282,
0.012468220666050911,
-0.02314269356429577,
-0.011656586080789566,
-0.01671590283513069,
-0.006826444063335657,
-0.014125627465546131,
-0.028568832203745842,
0.03833170607686043,
-0.06665243208408356,
0.011348175816237926,
0.0014359393389895558,
-0.009702270850539207,
-0.026816261932253838,
-0.027376513928174973,
-0.011550640687346458,
0.009726038202643394,
0.025462748482823372,
-0.009344092570245266,
-0.014329975470900536,
0.0261867493391037,
-0.02363414503633976,
0.025851814076304436,
0.03348772972822189,
-0.028117142617702484,
0.0034217725042253733,
-0.04349646717309952,
-0.0326961874961853,
0.06366003304719925,
-0.016226056963205338,
0.03271428123116493,
0.018984198570251465,
-0.018954310566186905,
-0.03749306872487068,
-0.011498719453811646,
-0.020155303180217743,
-0.02971145510673523,
-0.03863861784338951,
-0.010131830349564552,
0.03969403728842735,
-0.03578421100974083,
-0.02431323379278183,
-0.024622397497296333,
-0.04355759918689728,
-0.06648475676774979,
-0.020615700632333755,
-0.013084887526929379,
0.01594940945506096,
-0.043587516993284225,
-0.03452974557876587,
0.03175002336502075,
-0.04593082517385483,
-0.003094368614256382,
-0.053435735404491425,
-0.04281872138381004,
0.03146738559007645,
-0.011813824065029621,
0.01801939122378826,
0.030658366158604622,
-0.010897845961153507,
0.06352382153272629,
-0.01495333481580019,
-0.03810699284076691,
-0.010171547532081604,
0.012839882634580135,
-0.03270815685391426,
-0.031627245247364044,
-0.00029915315099060535,
0.019589535892009735,
-0.0015874960226938128,
0.004737747833132744,
0.005654631182551384,
-0.004508985672146082,
0.018234802410006523,
0.012784741818904877,
0.020599279552698135,
0.023717641830444336,
-0.003965654876083136,
0.012699611485004425,
-0.006217620335519314,
0.03726553916931152,
-0.05499396473169327,
-0.0076451837085187435,
0.004080573096871376,
0.007353528868407011,
0.02038363367319107,
-0.03928396478295326,
0.04313157498836517,
0.017378907650709152,
0.00358698726631701,
0.011716291308403015,
-0.0077479868195950985,
-0.032012127339839935,
-0.034798383712768555,
0.008216585032641888,
0.04374762624502182,
0.0016686063027009368,
0.01499939989298582,
-0.015303031541407108,
0.05061831325292587,
0.02985600382089615,
-0.02032485418021679,
0.005031917709857225,
0.00980317685753107,
0.006679605692625046,
-0.00420722272247076,
-0.011174410581588745,
0.009116997942328453,
0.07016369700431824,
-0.015235413797199726,
0.0438217893242836,
0.016563715413212776,
-0.02777870185673237,
0.020295333117246628,
-0.05374163016676903,
0.011392639018595219,
-0.010691860690712929,
0.04176296666264534,
0.010339680127799511,
0.04337799549102783,
0.0113778505474329,
0.016157275065779686,
0.017643095925450325,
-0.0012981075560674071,
-0.10770412534475327,
0.053774766623973846,
-0.03858587145805359,
-0.0051360949873924255,
0.008234799839556217,
0.06020429730415344,
-0.012481248006224632,
0.0007940907380543649,
-0.05042951554059982,
-0.022509347647428513,
0.005166527349501848,
-0.07625070959329605,
0.0099659888073802,
-0.04893368482589722,
-0.05811043083667755,
0.006137908436357975,
0.020270133391022682,
0.04024241864681244,
-0.03925096243619919,
0.01944710686802864,
0.016688711941242218,
-0.045213647186756134,
-0.011049769818782806,
-0.0059068831615149975,
0.024420686066150665,
-0.00871395505964756,
-0.013580681756138802,
0.02623317763209343,
0.05706941708922386,
-0.018574019894003868,
0.012803482823073864,
0.003646544646471739,
0.012773344293236732,
0.0052314577624201775,
-0.007738979067653418,
-0.024822011590003967,
-0.04927678033709526,
-0.018251098692417145,
0.0004260566784068942,
0.03794223442673683,
0.02876328118145466,
-0.025595877319574356,
0.026625512167811394,
-0.03510148078203201,
-0.013595188967883587,
0.03801560029387474,
-0.01814785785973072,
0.01711488515138626,
-0.052313182502985,
-0.004909102339297533,
0.004757052753120661,
-0.023368490859866142,
0.014025110751390457,
0.010536945424973965,
0.007133359555155039,
0.008517549373209476,
-0.016204535961151123,
-0.006061394698917866,
0.014509415253996849,
-0.02916759066283703,
-0.02026238851249218,
0.0010469644330441952,
0.023335007950663567,
-0.002188565209507942,
0.00221887300722301,
0.026870913803577423,
0.03711667284369469,
0.05762390419840813,
0.012046409770846367,
-0.012960017658770084,
-0.06309244781732559,
-0.006024549249559641,
0.03370024263858795,
0.021004918962717056,
-0.03690824657678604,
0.0019820344168692827,
-0.030606670305132866,
-0.031657278537750244,
0.06007407233119011,
-0.009072034619748592,
0.008381370455026627,
-0.019973181188106537,
-0.026498354971408844,
-0.021320682018995285,
-0.01177486777305603,
-0.05620768293738365,
0.017009185627102852,
0.04126806929707527,
0.015208772383630276,
0.0010393181582912803,
0.02814297378063202,
-0.011678284965455532,
0.05553363263607025,
0.06697925180196762,
0.06121589615941048,
0.031176693737506866,
0.011724741198122501,
0.013865305110812187,
0.012477255426347256,
-0.01827920973300934,
-0.0732683539390564,
-0.002875345293432474,
-0.008931581862270832,
-0.02783534675836563,
-0.010013858787715435,
-0.0116085484623909,
-0.04654781147837639,
-0.000648751447442919,
-0.026026485487818718,
-0.0024173560086637735,
0.019662583246827126,
-0.02143549732863903,
0.004725838545709848,
-0.003606405109167099,
0.013067816384136677,
0.018341287970542908,
0.024288304150104523,
-0.034275613725185394,
-0.019002502784132957,
-0.022705532610416412,
0.046534471213817596,
-0.04587876424193382,
-0.014873193576931953,
-0.032406628131866455,
0.010840793140232563,
-0.04229854419827461,
0.06614330410957336,
-0.022528309375047684,
-0.003009294392541051,
-0.023341108113527298,
-0.02612673118710518,
0.005005097948014736,
0.004941086284816265,
-0.014888012781739235,
-0.028017127886414528,
-0.005069378297775984,
0.0253483634442091,
0.01707587018609047,
0.0014443835243582726,
0.0060861194506287575,
-0.01307323295623064,
-0.0015162251656875014,
0.028052765876054764,
-0.020215004682540894,
-0.001166538568213582,
-0.059022434055805206,
-0.027093486860394478,
-0.0023786076344549656,
-0.04613020643591881,
0.068109892308712,
-0.00874688196927309,
-0.005304865539073944,
0.050064027309417725,
-0.060828663408756256,
-0.03475511074066162,
0.008899361826479435,
-0.006381093990057707,
0.019843656569719315,
-0.051009226590394974,
-0.02835947461426258,
0.00740667013451457,
-0.011930890381336212,
-0.03813264146447182,
-0.03770110011100769,
0.042681269347667694,
-0.0045520830899477005,
-0.017049718648195267,
-0.04184392839670181,
0.037972524762153625,
-0.01955120451748371,
-0.0014481482794508338,
-0.003447795519605279,
0.039678677916526794,
-0.0016349551733583212,
0.004840103443711996,
0.01848866045475006,
0.027304725721478462,
-0.005001848563551903,
0.010503266006708145,
-0.02831663005053997,
0.011409107595682144,
0.023882687091827393,
-0.004441055003553629,
-0.022070351988077164,
0.07098615914583206,
0.006211569998413324,
-0.014200315810739994,
0.028296487405896187,
0.023969413712620735,
0.0407901406288147,
-0.04891057685017586,
0.017805591225624084,
0.019785365089774132,
-0.0036752696614712477,
-0.02772730588912964,
-0.03355298191308975,
-0.003479584353044629,
0.0020625542383641005,
0.022664228454232216,
-0.025765037164092064,
0.014395248144865036,
-0.00240132724866271,
-0.053728945553302765,
0.01916496455669403,
0.008779165334999561,
-0.0003766862500924617,
-0.012267854064702988,
0.02384910359978676,
0.02144601196050644,
-0.029370473697781563,
0.027242740616202354,
-0.0037584654055535793,
-0.019896307960152626,
-0.03117375448346138,
0.019671617075800896,
0.021732984110713005,
-0.015174739994108677,
-0.0051025343127548695,
-0.07689160853624344,
0.004714369773864746,
0.06657828390598297,
0.06526810675859451,
0.008973372168838978,
0.06591690331697464,
0.0125963119789958,
0.007925042882561684,
-0.014241541735827923,
0.014911300502717495,
-0.008057773113250732,
0.014645611867308617,
0.026064442470669746,
0.023912811651825905,
-0.028482815250754356,
0.03416890650987625,
0.039136309176683426,
0.05299413576722145,
0.008798651397228241,
0.011506644077599049,
0.0011040669633075595,
0.0415537990629673,
0.007536622229963541,
-0.0012335166102275252,
-0.041200753301382065,
0.06232161074876785,
-0.06077791005373001,
0.048203710466623306,
0.014654730446636677,
-0.04049226641654968,
0.028432803228497505,
0.03455764427781105,
0.011046172119677067,
0.02705758437514305,
-0.006660447455942631,
-0.06322790682315826,
0.05296711251139641,
0.020843565464019775,
0.0012272816384211183,
0.0019375985721126199,
0.05073043704032898,
0.01314746867865324,
-0.025257904082536697,
0.0010905071394518018,
0.039360083639621735,
-0.06679540872573853,
-0.034667227417230606,
-0.04708871990442276,
-0.05734657496213913,
0.04194142669439316,
0.03137718513607979,
0.011372375302016735,
0.020095108076930046,
-0.028699183836579323,
0.01937810145318508,
0.02408340759575367,
0.022287996485829353,
-0.01488685142248869,
0.05347786843776703,
-0.00015642725338693708,
-0.0006959384772926569,
-0.01585284247994423,
-0.026930779218673706,
0.13339082896709442,
0.006131527945399284,
0.018786294385790825,
-0.07501090317964554,
0.009609539993107319,
-0.04159592464566231,
0.012658114545047283,
-0.044863250106573105,
0.016047172248363495,
-0.026720786467194557,
-0.003987713251262903,
0.00516835181042552,
0.05720771849155426,
0.03352880850434303,
-0.0008232982945628464,
0.05023964121937752,
-0.011347807943820953,
-0.012070013210177422,
-0.005229402333498001,
0.01910647377371788,
0.009944782592356205,
0.001254789880476892,
-0.028646862134337425,
0.05037172511219978,
-0.044599954038858414,
-0.007564319763332605,
-0.026257239282131195,
-0.05562585964798927,
0.02530398592352867,
0.01278525311499834,
-0.0337967574596405,
-0.018489032983779907,
0.02249828912317753,
-0.039465926587581635,
-0.02626650035381317,
0.050731148570775986,
0.033491067588329315,
0.0064276112243533134,
0.02491259202361107,
0.008979919366538525,
0.030345957726240158,
0.016973940655589104,
0.011461257934570312,
0.02085789106786251,
-0.03150622546672821,
0.03144700080156326,
-0.033138006925582886,
0.039465244859457016,
-0.01758251152932644,
0.025505373254418373,
0.018710438162088394,
-0.013982902280986309,
-0.015319808386266232,
-0.042463261634111404,
-0.005569630768150091,
-0.0122767249122262,
0.01977298967540264,
-0.03611451014876366,
-0.028283823281526566,
-0.029533937573432922,
0.026935024186968803,
-0.025432797148823738,
0.012330969795584679,
-0.026322118937969208,
-0.03307328373193741,
-0.001863272162154317,
-0.004892773926258087,
0.019354423508048058,
-0.015701455995440483,
-0.04717360809445381,
-0.037267062813043594,
0.0009416317334398627,
-0.04489493742585182,
-0.03353128582239151,
-0.021268967539072037,
0.00965945515781641,
0.028472865000367165,
-0.007803180254995823,
-0.030436694622039795,
-0.021281270310282707,
-0.031177910044789314,
0.02371767722070217,
-0.00839297566562891,
0.020598890259861946,
0.004573256708681583,
-0.01031396072357893,
0.031006503850221634,
0.03427545353770256,
-0.024404184892773628,
-0.015311706811189651,
0.014018232002854347,
0.008686160668730736,
0.05079961195588112,
0.0035638308618217707,
0.009688355028629303,
0.004471594467759132,
-0.014007472433149815,
0.007221983280032873,
-0.02456965483725071,
0.012715714052319527,
0.03874046728014946,
-0.008660262450575829,
-0.006676841527223587,
0.01713768020272255,
-0.00024538501747883856,
0.010557289235293865,
0.016250664368271828,
-0.042031027376651764,
-0.0058508156798779964,
0.04889136925339699,
0.025906478986144066,
-0.0328349769115448,
-0.04389175400137901,
-0.03786626085639,
-0.0070287929847836494,
-0.020386453717947006,
0.048986222594976425,
-0.022178392857313156,
0.04635754972696304,
0.022377753630280495,
0.0025019077584147453,
-0.030255571007728577,
0.006580634042620659,
-0.041259340941905975,
0.014227274805307388,
-0.005252307280898094,
-0.010557021014392376,
-0.016482949256896973,
0.031234072521328926,
0.008636405691504478,
-0.02469511143863201,
0.0016858808230608702,
0.029231129214167595,
0.007933082059025764,
0.00406317412853241,
0.005336254369467497,
-0.010087968781590462,
0.047456830739974976,
0.007525233086198568,
-0.010059055872261524,
0.02946547418832779,
-0.04724005237221718,
-0.07068906724452972,
0.009807108901441097,
-0.01271158829331398,
-0.005683727562427521,
0.025576503947377205,
-0.03877623751759529,
-0.022181300446391106,
0.06642339378595352,
0.011977638117969036,
-0.04695812240242958,
-0.003162239445373416,
-0.030309220775961876,
-0.012318603694438934,
-0.05186165124177933,
0.00406985729932785,
-0.015420649200677872,
-0.030482210218906403,
0.023403432220220566,
0.052387163043022156,
0.004841656424105167,
-0.002120369113981724,
-0.008485826663672924,
0.003354845102876425,
-0.0065927389077842236,
0.01174883358180523,
-0.0027227133978158236,
0.012539421208202839,
0.03466816991567612,
-0.030012426897883415,
-0.012277096509933472,
0.012286409735679626,
-0.004088730085641146,
-0.07916436344385147,
0.00027218853938393295,
-0.030189603567123413,
0.023168103769421577,
0.04231895133852959,
-0.05724676325917244,
0.01074154768139124,
0.013241884298622608,
-0.10141624510288239,
0.011914928443729877,
-0.013747764751315117,
-0.029344314709305763,
-0.00543843163177371,
-0.04262114316225052,
-0.009618926793336868,
0.060776226222515106,
0.006739990320056677,
0.035339485853910446,
0.018862677738070488,
0.011287427507340908,
0.01498589850962162,
-0.014506051316857338,
-0.02171216532588005,
0.02286609821021557,
-0.025710469111800194,
-0.01474377978593111,
0.04564700648188591,
-0.0245074313133955,
-0.06845224648714066,
0.02627011388540268,
0.013656871393322945,
0.016207609325647354,
0.00624094670638442,
0.02447572350502014,
0.010376062244176865,
0.025860045105218887,
0.014175145886838436,
-0.006648323033004999,
-0.010989353060722351,
-0.02440590038895607,
0.030674610286951065,
-0.005055073648691177,
-0.05723193660378456,
0.030135637149214745,
0.01649853028357029,
-0.029269032180309296,
-0.05230056121945381,
0.016620023176074028,
-0.017793742939829826,
0.006397512275725603,
-0.010599742643535137,
0.028696805238723755,
-0.015107390470802784,
-0.00574238458648324,
0.02387421578168869,
-0.04434794932603836,
-0.0033040170092135668,
0.006473070941865444,
0.022513780742883682,
0.038647860288619995,
0.0312751941382885,
0.0006713349721394479,
-0.011137614026665688,
0.00366201251745224,
0.006698334123939276,
0.04193674027919769,
-0.04991401731967926,
-0.010768854059278965,
0.012492815963923931,
0.03489748015999794,
-0.005707527045160532,
-0.07648933678865433,
-0.05280828848481178,
-0.0201602503657341,
0.025599423795938492,
0.002089048270136118,
0.01931493543088436,
-0.008449646644294262,
0.021344583481550217,
-0.060228899121284485,
0.03674064576625824,
0.03196882829070091,
-0.005930901505053043,
0.020711716264486313,
-0.021246621385216713,
0.015206879004836082,
-0.02581014856696129,
0.0597887821495533,
-0.03862267732620239,
-0.021239833906292915,
0.005441498477011919,
-0.018013594672083855,
0.045086998492479324,
-0.04423733055591583,
0.013726823031902313,
-0.022480890154838562,
-0.024489833042025566,
0.027049800381064415,
-0.015392293222248554,
-0.014447532594203949,
-0.013456917367875576,
0.04081984609365463,
-0.005663161166012287,
0.030673332512378693,
-0.007291792891919613,
-0.06103773042559624,
0.056032732129096985,
0.020841330289840698,
0.00868944264948368,
0.0325486920773983,
-0.028612101450562477,
-0.003617235692217946,
0.010496914386749268,
-0.040775932371616364,
-0.03255665674805641,
0.050205957144498825,
-0.02627161145210266,
-0.03351428732275963,
-0.009738117456436157,
-0.024115657433867455,
-0.006721785292029381,
-0.02237047255039215,
0.02139866352081299,
0.03369026258587837,
-0.00982639566063881,
-0.0013938973424956203,
0.04200591519474983,
0.007549666333943605,
0.02547091618180275,
0.03922884538769722,
0.00006992729322519153,
0.06581433117389679,
-0.0192475076764822,
-0.016293002292513847,
0.018908880650997162,
0.055851273238658905,
0.02288210019469261,
0.010328784584999084,
0.03179294243454933,
-0.008750049397349358,
0.0386626273393631,
0.02092382311820984,
0.04822753742337227,
-0.01501557044684887,
-0.04158879816532135,
0.01592942886054516,
-0.004151132423430681,
0.0004304375033825636,
0.04821076616644859,
-0.019119301810860634,
0.0780368223786354,
-0.06064888462424278,
0.00036125705810263753,
-0.010129529051482677,
0.00401094276458025,
-0.02104949951171875,
-0.029006244614720345,
0.008556470274925232,
0.0511535182595253,
-0.009910870343446732,
0.016429273411631584,
-0.03261254355311394,
-0.015138952992856503,
0.024871375411748886,
-0.052916333079338074,
0.03528468310832977,
0.0194515660405159,
0.012238522060215473,
0.025376446545124054,
-0.012097367085516453,
-0.00797861348837614,
-0.02218789793550968,
0.03964198753237724,
0.01622430607676506,
0.04378574341535568,
-0.03382837399840355,
0.016184689477086067,
-0.061167147010564804,
0.0352507121860981,
-0.07441367208957672,
-0.0006347838207148015,
-0.04318290576338768,
-0.009541948325932026,
-0.00909329205751419,
0.025310223922133446
] |
<p>In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the fundamental representation of this Gauge group.</p>
<ol>
<li><p>What is the <a href="http://en.wikipedia.org/wiki/Fundamental_representation" rel="nofollow">fundamental representation</a>, and why do we require fermions to be in it?</p></li>
<li><p>What does it mean for a field to <em>belong to a certain <a href="http://en.wikipedia.org/wiki/Group_representation" rel="nofollow">representation</a></em>? Is this just a way of stating that the fields are the "targets" of the Gauge transformations we introduced, meaning that they belong to the vector space where the representation of these transformations act?</p></li>
<li><p>A Gauge transformation must by definition not change the physics. This means that given any field $\psi$ we have to identify as a single physical entity all the fields that can be obtained by $\psi$ by means of any element of the Gauge group. Is the formalization of this concept the reason we require fields to belong to <a href="http://en.wikipedia.org/wiki/Irreducible_representation" rel="nofollow">irreducible</a> representations? Is there any other justification for it?</p></li>
</ol> | 4,563 | [
0.0023245292250066996,
0.01954181306064129,
-0.008617651648819447,
-0.0205024853348732,
0.03658841550350189,
0.023730887100100517,
-0.04231523722410202,
-0.02307993918657303,
0.0006640690262429416,
-0.05429695174098015,
0.012826653197407722,
-0.017997074872255325,
0.04677584767341614,
0.0009164902730844915,
0.021978097036480904,
0.04677074775099754,
0.006758430972695351,
-0.009859982877969742,
-0.03926713019609451,
-0.02391931414604187,
-0.01806855946779251,
0.06410440057516098,
0.0015589501708745956,
0.02158653736114502,
-0.01092628575861454,
0.017225094139575958,
0.007676540873944759,
0.05830690264701843,
0.017027003690600395,
0.05721595883369446,
-0.012385731562972069,
-0.02993619628250599,
0.002348151756450534,
0.0028256841469556093,
-0.02211267128586769,
-0.016278501600027084,
-0.01650797761976719,
-0.026613758876919746,
-0.012283368967473507,
-0.012807013466954231,
-0.05093270167708397,
-0.00796224270015955,
-0.03298014774918556,
0.0655401274561882,
0.0022224457934498787,
0.02188514918088913,
-0.0028189700096845627,
0.01767519861459732,
0.0504152737557888,
-0.03712873533368111,
0.050540074706077576,
0.015204333700239658,
0.007037169765681028,
0.005749293603003025,
-0.005752519704401493,
-0.02339451014995575,
0.0635627806186676,
0.037181954830884933,
-0.034554701298475266,
-0.08631691336631775,
-0.03074430301785469,
-0.030135763809084892,
0.017128830775618553,
-0.0337979830801487,
-0.012066973373293877,
0.0176710095256567,
0.015503941103816032,
-0.00010372907854616642,
-0.00021362717961892486,
-0.005804625805467367,
-0.0007065762765705585,
0.008453608490526676,
0.014682631008327007,
-0.010179261676967144,
0.020121458917856216,
-0.013135816901922226,
0.0107140326872468,
0.024180307984352112,
0.02265203557908535,
0.030003651976585388,
-0.004561788868159056,
0.029807647690176964,
0.01333470456302166,
-0.011864340864121914,
0.014928543008863926,
-0.018005190417170525,
0.07615745067596436,
0.0061381845735013485,
0.010259629227221012,
0.024503717198967934,
-0.024083014577627182,
-0.005409150384366512,
0.03867875039577484,
-0.041554711759090424,
-0.044629260897636414,
0.04234875366091728,
0.02254108153283596,
0.029865417629480362,
-0.025185247883200645,
-0.029278459027409554,
0.013602189719676971,
-0.008059876970946789,
-0.002109264023602009,
0.07280589640140533,
-0.020742150023579597,
0.01829174906015396,
-0.046717554330825806,
-0.005273173563182354,
-0.014600255526602268,
-0.02715665102005005,
-0.036794718354940414,
0.014588960446417332,
-0.034116070717573166,
0.019061580300331116,
-0.025551101192831993,
-0.020730692893266678,
0.0010892869904637337,
-0.008324440568685532,
0.06082017719745636,
0.07072604447603226,
0.05755816772580147,
-0.05058831721544266,
-0.000895680976100266,
0.006827353499829769,
-0.07824677973985672,
0.028280947357416153,
0.032396819442510605,
0.00908974651247263,
-0.03337377309799194,
-0.0031098690815269947,
-0.00845849234610796,
-0.00021379195095505565,
-0.0015693169552832842,
0.013518651947379112,
0.03226204216480255,
-0.041813068091869354,
-0.10677864402532578,
-0.0490957610309124,
0.03789380192756653,
-0.014127378351986408,
-0.022098476067185402,
-0.054978515952825546,
0.018479088321328163,
0.0053404225036501884,
0.06507954746484756,
-0.030590396374464035,
0.01264094840735197,
0.001980049069970846,
0.013571757823228836,
0.01436686236411333,
-0.001498116529546678,
-0.01793024130165577,
-0.012227868661284447,
-0.04971188306808472,
-0.010050097480416298,
-0.028822772204875946,
0.040877290070056915,
0.01619725488126278,
-0.008923129178583622,
-0.0007127444259822369,
0.05612039566040039,
-0.006860502064228058,
-0.0012876489199697971,
0.04290132224559784,
-0.013749320060014725,
0.01794600859284401,
0.0615396723151207,
-0.007741839159280062,
0.04518958181142807,
0.06332744657993317,
-0.019437838345766068,
0.02309168502688408,
0.02417759597301483,
0.05413057282567024,
0.054285671561956406,
-0.02135990373790264,
-0.04673174396157265,
-0.038142334669828415,
-0.006255938671529293,
-0.02092484012246132,
-0.031552769243717194,
-0.031657036393880844,
-0.012028153985738754,
0.0069528003223240376,
0.0005620869342237711,
0.016501398757100105,
0.009407688863575459,
-0.026548800989985466,
0.0012166351079940796,
-0.04701679199934006,
-0.02626672200858593,
-0.0770370364189148,
0.029755856841802597,
-0.02552984654903412,
-0.016147511079907417,
0.033432673662900925,
0.01583646424114704,
0.010866356082260609,
-0.045523252338171005,
-0.09052741527557373,
-0.016549281775951385,
0.032471705228090286,
-0.005292889196425676,
0.015114041045308113,
0.021002041175961494,
0.048144448548555374,
0.03576522693037987,
-0.02209101989865303,
0.04947211220860481,
-0.019541217014193535,
-0.040340304374694824,
-0.003454804653301835,
-0.021042324602603912,
0.05233196169137955,
-0.013668104074895382,
0.012097416445612907,
-0.007160126697272062,
0.009575368836522102,
-0.05002572759985924,
0.03136876970529556,
-0.04325330629944801,
0.06693147122859955,
0.034190833568573,
-0.01789289526641369,
-0.011747777462005615,
0.03651191294193268,
-0.014194974675774574,
0.024375921115279198,
-0.010569080710411072,
-0.029305996373295784,
-0.06235295161604881,
-0.013932488858699799,
0.06044889986515045,
0.03464583307504654,
-0.005468260962516069,
0.025736719369888306,
-0.0048026470467448235,
0.044603295624256134,
0.017766227945685387,
0.009579980745911598,
-0.019225437194108963,
-0.0440799705684185,
0.0029762687627226114,
0.002955056494101882,
0.009104481898248196,
-0.016267672181129456,
0.008269884623587132,
-0.02233264409005642,
0.022316481918096542,
0.005202070809900761,
-0.015324175357818604,
0.06652889400720596,
-0.02611284889280796,
0.000769411853980273,
0.011725657619535923,
-0.025845907628536224,
0.03868706896901131,
-0.024883657693862915,
0.062309060245752335,
-0.0066628651693463326,
-0.03441234305500984,
0.000741173280403018,
-0.02354029007256031,
-0.0009861994767561555,
0.019135627895593643,
-0.007692818995565176,
-0.03113800846040249,
0.005991759710013866,
-0.0021157898008823395,
-0.03654402866959572,
0.011326552368700504,
-0.005410436075180769,
-0.020570702850818634,
-0.016294201835989952,
0.020915258675813675,
0.020065318793058395,
-0.00931608211249113,
0.029559899121522903,
-0.04986932501196861,
-0.01999531127512455,
0.03668786957859993,
-0.03059166669845581,
0.006237010005861521,
0.036392033100128174,
-0.014334483072161674,
0.032456450164318085,
-0.07120563089847565,
-0.021240346133708954,
0.026878666132688522,
-0.02947532944381237,
0.013826433569192886,
-0.022205183282494545,
-0.010347550734877586,
-0.04658474773168564,
0.006138224620372057,
-0.0366835817694664,
0.04002632200717926,
-0.0020647651981562376,
0.009222742170095444,
0.04812973737716675,
-0.007417169399559498,
-0.0387897826731205,
0.005577165633440018,
-0.003363906405866146,
-0.019960099831223488,
-0.010727723129093647,
-0.011347516439855099,
0.00794850755482912,
-0.03667646273970604,
0.05322650074958801,
0.03036888875067234,
-0.06292280554771423,
-0.010094000026583672,
-0.056353285908699036,
-0.03764168545603752,
-0.0014526968589052558,
0.007204713765531778,
0.027364790439605713,
0.00818212516605854,
-0.044528499245643616,
0.06007971614599228,
0.050715118646621704,
-0.06473959982395172,
-0.012118751183152199,
0.009308414533734322,
-0.008342107757925987,
-0.045516833662986755,
-0.0031137801706790924,
0.013003393076360226,
0.012530996464192867,
0.035851381719112396,
0.02535649761557579,
0.03721584379673004,
-0.0008717136224731803,
0.01098557561635971,
-0.03204236924648285,
0.022257540374994278,
0.027183659374713898,
0.0229034461081028,
0.045379478484392166,
0.014993924647569656,
0.0028288187459111214,
-0.014232737012207508,
0.007861905731260777,
0.02383180521428585,
0.016998441889882088,
-0.010748577304184437,
0.06449297815561295,
0.037041742354631424,
0.028029367327690125,
-0.04017576575279236,
0.03830607980489731,
-0.008413795381784439,
-0.04616347700357437,
0.01806178130209446,
0.01563485898077488,
-0.021600404754281044,
-0.0007606418803334236,
0.004764075390994549,
0.006835542619228363,
0.0409669354557991,
-0.07153373211622238,
-0.0070412843488156796,
-0.007971816696226597,
-0.017985204234719276,
0.046002067625522614,
-0.015322137624025345,
-0.0341155119240284,
0.023496633395552635,
0.05091406777501106,
0.03136591240763664,
0.0169979277998209,
-0.03833587467670441,
-0.021129796281456947,
-0.05214429274201393,
0.00803613755851984,
0.016731126233935356,
0.05451313033699989,
0.003934758249670267,
0.06033579632639885,
0.027084559202194214,
0.008774429559707642,
-0.024740023538470268,
0.020070554688572884,
-0.08370605856180191,
0.007462335284799337,
0.006827009376138449,
-0.0011566031025722623,
-0.03821548447012901,
-0.027904052287340164,
0.010767096653580666,
-0.012824776582419872,
-0.048407092690467834,
-0.02734883315861225,
-0.007335524540394545,
-0.030428560450673103,
0.007480120752006769,
-0.057928357273340225,
-0.034499697387218475,
-0.013709822669625282,
0.03590928763151169,
0.05773604288697243,
-0.039493318647146225,
0.03342857211828232,
0.02777130715548992,
-0.04253602772951126,
-0.00832146406173706,
0.012987758032977581,
0.012400715611875057,
0.04690485820174217,
0.006464052479714155,
0.057586319744586945,
0.02035192772746086,
-0.029132064431905746,
-0.005684285424649715,
0.04674020782113075,
0.06393694132566452,
-0.011042993515729904,
-0.025673914700746536,
-0.01554189808666706,
-0.07120388746261597,
-0.013824180699884892,
0.0036918597761541605,
0.055634163320064545,
0.029486844316124916,
-0.009567398577928543,
0.035419899970293045,
0.0020244538318365812,
-0.0361400805413723,
0.05233219638466835,
0.044793158769607544,
-0.004820845555514097,
-0.05178606137633324,
-0.012952955439686775,
0.01205960288643837,
0.02627580240368843,
-0.02445404976606369,
0.011886178515851498,
0.002503898460417986,
-0.00913313589990139,
0.004557397682219744,
0.019480613991618156,
0.02092696726322174,
-0.026846570894122124,
-0.0054546804167330265,
0.010796294547617435,
0.0026859049685299397,
0.018336888402700424,
0.014400232583284378,
0.007010484114289284,
0.05286740884184837,
0.04651036113500595,
0.011432974599301815,
-0.016794899478554726,
-0.06269197911024094,
0.019924696534872055,
0.03872806951403618,
0.03982530161738396,
0.025653086602687836,
-0.011178215965628624,
-0.015419588424265385,
-0.024941405281424522,
0.028137516230344772,
-0.008109250105917454,
0.02349032461643219,
-0.010797657072544098,
-0.025255413725972176,
-0.027629617601633072,
-0.05197063088417053,
-0.01230214349925518,
0.03438875451683998,
-0.008024785667657852,
0.014436084777116776,
-0.035484906286001205,
0.0007430592668242753,
-0.02120315097272396,
0.0022669704630970955,
-0.029159413650631905,
0.007754077669233084,
0.015475575812160969,
0.02796321175992489,
0.012301575392484665,
0.038841381669044495,
-0.010291295126080513,
-0.0825982615351677,
-0.006333519238978624,
0.025014769285917282,
0.019320379942655563,
0.030916383489966393,
-0.022606372833251953,
-0.060550909489393234,
-0.0029291175305843353,
0.01421089842915535,
-0.0061790249310433865,
0.009953800588846207,
-0.07094617933034897,
0.07754933834075928,
0.024639587849378586,
0.016833869740366936,
0.04697561636567116,
0.018274608999490738,
-0.04764128848910332,
-0.013731170445680618,
-0.017223620787262917,
0.0231618732213974,
-0.017842305824160576,
0.031491201370954514,
-0.01896250806748867,
0.012589511461555958,
-0.009670082479715347,
0.06296318769454956,
-0.03331463783979416,
-0.008838312700390816,
-0.0013509407872334123,
-0.020807629451155663,
-0.04077845439314842,
-0.022569973021745682,
-0.01613675057888031,
-0.03098541870713234,
-0.0159118864685297,
0.03552497178316116,
-0.02299853041768074,
-0.03975667059421539,
0.0005424869013950229,
0.02448350191116333,
0.0005352432490326464,
0.017965801060199738,
-0.014434480108320713,
0.02331751026213169,
-0.019894879311323166,
-0.016601666808128357,
-0.001286736223846674,
-0.044398434460163116,
0.05317997932434082,
0.012259213253855705,
-0.00863128062337637,
0.010896600782871246,
-0.04549035802483559,
-0.05743037909269333,
-0.0013083595549687743,
-0.009122517891228199,
0.022570060566067696,
-0.006853268947452307,
0.008791142143309116,
0.03671441972255707,
0.020739957690238953,
-0.06987538188695908,
-0.05451719090342522,
-0.007818302139639854,
0.02749963104724884,
-0.027920333668589592,
-0.028424536809325218,
0.013536054641008377,
-0.05227915942668915,
-0.019819116219878197,
0.015775807201862335,
0.05346962437033653,
-0.03455797955393791,
-0.02168336510658264,
0.0030007425229996443,
0.05720769986510277,
0.05565056949853897,
-0.0080369021743536,
-0.008177478797733784,
0.010357857681810856,
0.016276434063911438,
0.010138501413166523,
0.023814206942915916,
0.04725220799446106,
0.0002624626213219017,
-0.025243422016501427,
-0.003698904998600483,
-0.0243595689535141,
0.0008642085595056415,
0.008062400855123997,
0.011963214725255966,
0.03726811334490776,
0.01536315493285656,
-0.00785465445369482,
-0.024034105241298676,
-0.008301413618028164,
0.019611382856965065,
0.06376860290765762,
-0.025879744440317154,
0.011592540889978409,
-0.014820178039371967,
-0.05476698651909828,
0.07302891463041306,
-0.016955656930804253,
0.01070755161345005,
0.037477560341358185,
0.024756142869591713,
-0.025868240743875504,
0.021688299253582954,
0.031806569546461105,
-0.03371964767575264,
-0.006752172019332647,
-0.0537717267870903,
0.037125177681446075,
0.021712979301810265,
-0.0036630055401474237,
-0.02100769802927971,
-0.0023203666787594557,
-0.03177066519856453,
-0.009844210930168629,
0.0406186617910862,
-0.004879896063357592,
0.05545836687088013,
0.02355995401740074,
-0.018151359632611275,
-0.0117668267339468,
-0.015583083033561707,
0.0025781013537198305,
0.0053625148721039295,
-0.00390852615237236,
0.020166467875242233,
-0.017717598006129265,
-0.030467238277196884,
0.012525737285614014,
0.026126455515623093,
-0.04808284714818001,
0.0008037131046876311,
0.02784026600420475,
0.041752126067876816,
0.00889182835817337,
-0.014339924789965153,
-0.04147249087691307,
0.06578592956066132,
-0.050316233187913895,
0.03735103830695152,
0.015933256596326828,
-0.0072431438602507114,
0.03706550970673561,
0.03306017071008682,
0.012350276112556458,
0.016933683305978775,
-0.005789540708065033,
-0.056444425135850906,
0.025350278243422508,
-0.0009352285997010767,
0.011282350867986679,
0.003894114401191473,
-0.02359226532280445,
0.053455814719200134,
-0.009811398573219776,
-0.006134206894785166,
-0.00376800331287086,
-0.04165789484977722,
-0.02136545069515705,
-0.04533691704273224,
-0.012566477991640568,
0.04591446742415428,
-0.03424633666872978,
-0.021199407055974007,
-0.02708865888416767,
-0.02577306516468525,
0.01086066197603941,
-0.005595345050096512,
0.036002907902002335,
-0.06184591352939606,
0.05632028728723526,
0.0032660504803061485,
0.01954706385731697,
-0.005057079717516899,
-0.013398618437349796,
0.10244864225387573,
0.06245242804288864,
0.01745358668267727,
-0.0637768805027008,
0.01642586849629879,
-0.029573896899819374,
0.02090270444750786,
0.0025495991576462984,
0.03224511817097664,
-0.012785100378096104,
0.020474672317504883,
0.0035965575370937586,
0.07335841655731201,
-0.005152340512722731,
-0.003833200316876173,
0.045142434537410736,
-0.05252126604318619,
-0.04787777364253998,
0.0017631987575441599,
0.033374037593603134,
-0.030536936596035957,
0.04433882609009743,
-0.06996921449899673,
0.0015547128859907389,
-0.0024422064889222383,
0.029804877936840057,
-0.011029189452528954,
-0.02567989192903042,
0.03746303915977478,
0.024003762751817703,
-0.02933454141020775,
-0.022730305790901184,
-0.0257693063467741,
-0.005451171658933163,
-0.061038579791784286,
-0.0012907416094094515,
0.007379275746643543,
-0.005954783409833908,
0.04545177146792412,
0.04139949753880501,
-0.002455882029607892,
-0.018087118864059448,
-0.00615154393017292,
0.0034252686891704798,
-0.04580164700746536,
-0.03711073845624924,
-0.020765133202075958,
0.08178780227899551,
-0.030729442834854126,
-0.0026479451917111874,
0.00683028856292367,
-0.031185951083898544,
-0.003083849558606744,
-0.02095176838338375,
0.004421787336468697,
-0.012519787065684795,
0.03953678160905838,
-0.00977371260523796,
0.005612650886178017,
-0.020207300782203674,
0.05381719768047333,
-0.016741566359996796,
0.019469594582915306,
-0.02214001677930355,
-0.016801932826638222,
0.0015355594223365188,
-0.008185852319002151,
0.024720100685954094,
0.01967412233352661,
0.010389665141701698,
-0.022520754486322403,
-0.01696392521262169,
-0.019735220819711685,
-0.01993151381611824,
0.025536563247442245,
0.02053622528910637,
0.05778176337480545,
0.02009391225874424,
0.04214830696582794,
0.0012938653817400336,
-0.06114763021469116,
0.031640876084566116,
-0.014724287204444408,
-0.02739434875547886,
-0.006898844614624977,
0.006177780218422413,
0.031146513298153877,
0.07665658742189407,
-0.029866594821214676,
-0.02610595151782036,
-0.010435563512146473,
-0.006002764217555523,
0.03341568261384964,
-0.03122626431286335,
-0.022015294060111046,
0.010966415517032146,
-0.012148245237767696,
0.0022868223022669554,
-0.014774370938539505,
0.02433907426893711,
0.05672292038798332,
0.022195739671587944,
0.016535088419914246,
0.04333049803972244,
0.030804000794887543,
0.023472309112548828,
0.005033931229263544,
-0.007609413471072912,
0.02195090427994728,
0.034773100167512894,
0.003615507623180747,
-0.05480741336941719,
-0.052902378141880035,
-0.00411340594291687,
0.0060319919139146805,
0.0033410186879336834,
0.007651085499674082,
-0.03876744583249092,
-0.01732814684510231,
-0.03268836438655853,
0.03696148842573166,
-0.06394878774881363,
-0.0029664067551493645,
-0.061228666454553604,
0.011539218947291374,
-0.015605263411998749,
-0.019048122689127922,
0.003802709048613906,
0.03124956227838993,
-0.04101144149899483,
-0.03739004209637642,
0.027892794460058212,
0.011280291713774204,
-0.05198880657553673,
0.011720278300344944,
-0.02588587999343872,
-0.0031516021117568016,
0.009056179784238338,
-0.003626773599535227,
-0.03153476119041443,
0.03885567560791969,
-0.011299307458102703,
-0.03812672570347786,
0.03990568965673447,
0.005942622199654579,
0.03840886801481247,
0.05263494700193405,
0.006587449461221695,
-0.025569194927811623,
0.0007825136999599636,
-0.011800684966146946,
0.019067633897066116,
-0.039473824203014374,
-0.03713430091738701,
-0.02498159185051918,
-0.05041135847568512,
0.02892765961587429,
0.016036726534366608,
-0.01873229816555977,
0.007786663249135017,
0.014250113628804684,
-0.004266053903847933,
-0.006460912525653839,
-0.0028468722011893988,
0.007579461671411991,
0.01697768084704876,
0.0448555126786232,
0.030269714072346687,
0.006743535399436951,
0.026082834228873253,
-0.030475690960884094,
0.011088326573371887,
0.011486144736409187,
-0.015512256883084774,
-0.10457011312246323,
-0.03469270095229149,
0.039263974875211716,
0.0037868893705308437,
0.017079250887036324,
-0.057633381336927414,
0.0014935035724192858,
0.03483610227704048,
-0.0863758996129036,
0.024126507341861725,
-0.018385466188192368,
-0.01909123919904232,
-0.012408588081598282,
-0.0036486380267888308,
0.008949141949415207,
0.08225896954536438,
0.04148826375603676,
0.015881361439824104,
-0.013173936866223812,
-0.010152249597012997,
0.020507045090198517,
-0.013231474906206131,
-0.0431051030755043,
0.013081002049148083,
-0.008516743779182434,
-0.02852921187877655,
0.07761748135089874,
-0.028445009142160416,
0.012254511006176472,
0.0020284918136894703,
-0.005598241928964853,
-0.015077751129865646,
0.0009756445651873946,
-0.0035375182051211596,
0.036557070910930634,
0.014841615222394466,
0.023179316893219948,
0.015027816407382488,
-0.012098231352865696,
0.007697572465986013,
0.02850416488945484,
0.02168196253478527,
-0.000956789415795356,
-0.0027559641748666763,
0.00824015587568283,
-0.03256390988826752,
-0.0075264377519488335,
0.022805387154221535,
-0.04613562673330307,
-0.034956708550453186,
0.0086283590644598,
0.010973591357469559,
-0.018391676247119904,
-0.00828355923295021,
0.014050732366740704,
-0.041725289076566696,
-0.025680052116513252,
0.03284498304128647,
0.002906322944909334,
-0.007954852655529976,
0.0239859689027071,
0.011483745649456978,
-0.025799086317420006,
0.038135629147291183,
0.027398141101002693,
0.0062706368044018745,
-0.06604637950658798,
0.0051468657329678535,
0.03173300251364708,
-0.027860119938850403,
0.0294329971075058,
-0.024504512548446655,
-0.029063697904348373,
0.004907612688839436,
-0.004611193668097258,
0.03172505646944046,
-0.04886050149798393,
-0.026862019672989845,
0.0046465396881103516,
-0.054875969886779785,
0.051183946430683136,
0.007296002469956875,
-0.005271549336612225,
-0.03560865297913551,
-0.016711436212062836,
-0.0010936023900285363,
0.01635093241930008,
0.057120006531476974,
0.003223194507881999,
-0.02109375409781933,
0.03993051499128342,
0.016768375411629677,
0.03821356222033501,
-0.03967737779021263,
-0.017657266929745674,
-0.020905420184135437,
-0.009511817246675491,
-0.018966559320688248,
-0.01127588003873825,
-0.031130585819482803,
0.026683777570724487,
0.031695712357759476,
-0.011507065035402775,
-0.0029197174590080976,
0.007369374856352806,
-0.05824657529592514,
0.06843877583742142,
0.005572257097810507,
-0.0014736155280843377,
0.058049168437719345,
-0.005363669246435165,
0.02030985616147518,
0.03327200189232826,
-0.026778705418109894,
-0.023266831412911415,
0.011285712011158466,
-0.05792476236820221,
-0.012334886938333511,
-0.006412292364984751,
-0.01349269412457943,
0.05631045624613762,
-0.038604769855737686,
0.014032321982085705,
0.03153875842690468,
-0.027571434155106544,
-0.01990709826350212,
0.08579559624195099,
0.027286969125270844,
0.04062074050307274,
0.013168944045901299,
-0.025360317900776863,
0.002534699160605669,
0.004535843152552843,
0.0018484784523025155,
0.05118399113416672,
0.05515352264046669,
0.017794985324144363,
0.02073790319263935,
0.04657995328307152,
-0.011781078763306141,
-0.009945415891706944,
0.014090841636061668,
0.04601127281785011,
-0.048493508249521255,
0.009673664346337318,
0.031484946608543396,
-0.015206377021968365,
0.014212126843631268,
0.030217288061976433,
-0.027091754600405693,
0.07233615219593048,
-0.026869673281908035,
-0.0029432789888232946,
0.003779070684686303,
0.034171368926763535,
-0.02363160252571106,
0.05192948877811432,
0.04459253326058388,
0.0723627582192421,
0.00758822588250041,
-0.015264877118170261,
-0.03378412872552872,
0.008978978730738163,
0.013068744912743568,
-0.03607942909002304,
0.041007235646247864,
0.013659033924341202,
-0.04249483719468117,
0.003227054141461849,
-0.023084037005901337,
-0.028207095339894295,
-0.012844255194067955,
-0.0005764194065704942,
0.04107881337404251,
0.02020476944744587,
-0.017975319176912308,
-0.029379548504948616,
-0.041860971599817276,
0.04691920801997185,
-0.055473294109106064,
0.022587645798921585,
-0.03567356988787651,
0.007423675153404474,
0.00004142651232541539,
0.004693393595516682
] |
<p>How does one see it as obvious that</p>
<p>$$\int_S \frac{\partial A_i}{\partial x^j} dS^{ji} = \int_S\frac{1}{2}(\frac{\partial A_j}{\partial x^i} - \frac{\partial A_i}{\partial x^j})dS^{ij}$$</p>
<p>where $d S^{ij} = dx^i dx^{j*} - dx^j dx^{i*} $</p>
<p>From <a href="http://books.google.ie/books?id=X18PF4oKyrUC&lpg=PP1&pg=PA22#v=onepage&q&f=false" rel="nofollow">Landau's CToF</a>.</p> | 4,564 | [
0.0018447338370606303,
0.024181367829442024,
-0.002121457364410162,
-0.05583519488573074,
0.046982236206531525,
0.017977777868509293,
-0.014568342827260494,
-0.03494467958807945,
-0.0042450884357094765,
-0.039935797452926636,
0.06440342217683792,
-0.019821083173155785,
0.07256736606359482,
0.04550904780626297,
0.025886597111821175,
0.006704525090754032,
-0.0070436387322843075,
-0.012314156629145145,
0.03198453411459923,
-0.005758768878877163,
-0.0032080591190606356,
0.07080484926700592,
-0.021451720967888832,
-0.011200970970094204,
-0.027611905708909035,
0.006639915052801371,
-0.02336100861430168,
-0.02394919842481613,
0.005634902976453304,
0.08207917213439941,
-0.05153118446469307,
-0.006496452260762453,
0.03231514245271683,
-0.012932755053043365,
0.013712632469832897,
-0.013548392802476883,
-0.019168654456734657,
-0.03669445961713791,
-0.005483226850628853,
0.01841116137802601,
-0.02582431398332119,
-0.011732473969459534,
0.004033199045807123,
0.06338762491941452,
-0.014661643654108047,
0.01756640151143074,
-0.01458954531699419,
-0.01715303771197796,
0.012954315170645714,
-0.05803253874182701,
0.06592778861522675,
0.009171332232654095,
0.0015894740354269743,
0.03137803450226784,
-0.005205291323363781,
-0.024257497861981392,
0.017024975270032883,
0.038925617933273315,
0.0013598969671875238,
-0.06685621291399002,
-0.040517475455999374,
-0.001320246490649879,
0.0024186645168811083,
-0.028519833460450172,
-0.0032183497678488493,
0.021583672612905502,
0.016722874715924263,
-0.049569953233003616,
0.00002358629171794746,
-0.029318150132894516,
-0.010961145162582397,
0.01176111213862896,
0.00648706778883934,
-0.007135882042348385,
0.0024344604462385178,
0.014215605333447456,
0.0197808425873518,
0.03933315724134445,
0.04270665720105171,
0.018413154408335686,
0.03350869566202164,
0.001069205580279231,
0.030564621090888977,
0.01692238077521324,
0.032202865928411484,
0.020611731335520744,
0.08761236816644669,
-0.008615340106189251,
0.01695377565920353,
0.06993082910776138,
-0.02817884273827076,
0.01667408086359501,
0.049959130585193634,
-0.056928038597106934,
0.0025701834820210934,
-0.040566034615039825,
0.002373090945184231,
0.06451693922281265,
-0.008552680723369122,
-0.007161960005760193,
-0.036780595779418945,
-0.025067273527383804,
-0.004841430112719536,
0.04901287332177162,
0.0026128808967769146,
-0.01328478753566742,
-0.045249681919813156,
0.002176608657464385,
0.011254304088652134,
-0.028706969693303108,
-0.06007442995905876,
0.054018352180719376,
-0.008395892567932606,
-0.009856992401182652,
-0.03800661489367485,
0.033279724419116974,
-0.05338539183139801,
-0.014092152938246727,
0.025312675163149834,
0.032240696251392365,
0.05525163933634758,
0.005979051347821951,
-0.002428077394142747,
-0.03167757764458656,
-0.08993343263864517,
0.037960685789585114,
0.039914507418870926,
0.015453956089913845,
-0.04198025166988373,
-0.0012589343823492527,
-0.00046216550981625915,
0.011235011741518974,
-0.030709270387887955,
0.030287187546491623,
0.01009733323007822,
0.005492036230862141,
-0.09492270648479462,
-0.05834358185529709,
0.030322594568133354,
-0.039206210523843765,
-0.015264715999364853,
-0.07196427136659622,
0.002072579227387905,
0.04179207235574722,
0.07672352343797684,
-0.021919213235378265,
0.026541389524936676,
-0.01036137156188488,
0.0274884682148695,
0.02105538547039032,
-0.005952334962785244,
-0.038681987673044205,
-0.03139585629105568,
-0.03727932274341583,
-0.009949235245585442,
-0.06760422140359879,
0.03837257996201515,
0.04745782911777496,
-0.01490850280970335,
-0.022936079651117325,
0.08280669897794724,
0.016319667920470238,
0.015803273767232895,
0.01746501587331295,
-0.003399319015443325,
-0.04412955790758133,
0.08475145697593689,
0.0021651030983775854,
0.04984617978334427,
0.031950220465660095,
0.004828399047255516,
-0.009859607554972172,
-0.008287978358566761,
0.031163690611720085,
0.00986396986991167,
-0.03713550046086311,
-0.014064736664295197,
0.006696359720081091,
0.007317363750189543,
-0.001030651037581265,
-0.019043784588575363,
-0.03842189162969589,
-0.006417127326130867,
0.02178710326552391,
-0.0035262855235487223,
0.0538482591509819,
-0.005847708787769079,
0.009800545871257782,
-0.010205276310443878,
-0.0587477833032608,
-0.04068934917449951,
-0.0394635908305645,
0.046954911202192307,
-0.013290083035826683,
-0.01942918635904789,
0.05893610417842865,
-0.021070199087262154,
0.012357407249510288,
-0.012602239847183228,
-0.024935239925980568,
0.01754704676568508,
0.019783463329076767,
0.018957985565066338,
-0.016292037442326546,
0.03584712743759155,
0.0038039630744606256,
0.02449350617825985,
-0.0025872583501040936,
0.05222484841942787,
-0.03947993367910385,
-0.04705110192298889,
-0.000204382959054783,
-0.03482380881905556,
0.03627559170126915,
0.011909054592251778,
-0.02191275544464588,
0.01141528319567442,
0.03394191339612007,
-0.011155877262353897,
0.048377860337495804,
-0.052277643233537674,
0.059266798198223114,
0.0583835169672966,
0.04783688858151436,
0.00044659903505817056,
0.04956769943237305,
0.012789092026650906,
0.052404459565877914,
0.0017428265418857336,
-0.001572237815707922,
-0.03697171434760094,
-0.004849831108003855,
0.05948946252465248,
0.06810683757066727,
-0.029539117589592934,
-0.005760568659752607,
0.04984135553240776,
0.015739794820547104,
0.012407401576638222,
0.023926129564642906,
0.012273346073925495,
-0.04769428074359894,
-0.018483437597751617,
0.009536150842905045,
-0.011810468509793282,
0.03746939077973366,
-0.010729558765888214,
-0.03566065430641174,
0.012850172817707062,
0.009000434540212154,
-0.03100636415183544,
0.06777990609407425,
-0.011872687377035618,
-0.029200781136751175,
-0.007105369586497545,
0.016852470114827156,
0.01928854174911976,
-0.0172752495855093,
0.03284628689289093,
0.03548967465758324,
0.01263241097331047,
-0.03765909746289253,
-0.004906501155346632,
-0.03017163835465908,
0.03567488119006157,
-0.055451977998018265,
-0.003372981445863843,
-0.021562661975622177,
-0.0018741770181804895,
-0.04634678736329079,
-0.02624088153243065,
-0.012048943899571896,
0.034048475325107574,
-0.007521718740463257,
0.020135875791311264,
0.01022480707615614,
0.04106319695711136,
0.0005424272967502475,
-0.01698552630841732,
-0.033525578677654266,
0.022867735475301743,
-0.02947978489100933,
0.04053701460361481,
0.03632284328341484,
-0.015557818114757538,
-0.018182668834924698,
-0.04171771556138992,
-0.012855827808380127,
0.05473322048783302,
-0.014287736266851425,
0.02166557125747204,
0.01039935927838087,
-0.016004549339413643,
-0.0409424751996994,
-0.028357936069369316,
0.006437314674258232,
0.0063430070877075195,
-0.053227610886096954,
0.00005696711014024913,
0.022055570036172867,
-0.026104921475052834,
-0.0436418242752552,
-0.006093216594308615,
0.011676045134663582,
-0.04631904140114784,
0.020530248060822487,
0.001609703409485519,
0.02586858719587326,
-0.051583487540483475,
0.02075881138443947,
0.016113005578517914,
-0.025351352989673615,
-0.01148525346070528,
-0.070759117603302,
-0.02844764105975628,
0.010465480387210846,
0.011786351911723614,
0.009178217500448227,
-0.012103253044188023,
-0.05854238197207451,
0.08932991325855255,
-0.012308642268180847,
-0.03898194804787636,
-0.01186442282050848,
-0.017898013815283775,
-0.028460949659347534,
-0.0041602118872106075,
0.020459236577153206,
0.03764869645237923,
-0.033903565257787704,
0.043153051286935806,
-0.013908312655985355,
0.03286958858370781,
0.02611582539975643,
-0.0016556358896195889,
-0.007588537875562906,
0.01515891496092081,
-0.048162732273340225,
0.0022653723135590553,
0.06769881397485733,
-0.013996276073157787,
0.008419900201261044,
0.0019335737451910973,
0.0006109739770181477,
0.018691955134272575,
0.044018521904945374,
-0.03501306101679802,
0.06460385769605637,
-0.0022579014766961336,
-0.006445031613111496,
-0.007673312909901142,
0.029181823134422302,
0.009455892257392406,
-0.055579137057065964,
-0.015873024240136147,
0.03545387461781502,
0.030105983838438988,
-0.02499174326658249,
-0.00207905494607985,
0.011039615608751774,
0.015246009454131126,
-0.006732909474521875,
-0.030449751764535904,
-0.03432915732264519,
0.00012916485138703138,
0.014301800169050694,
-0.04857947677373886,
-0.02642042562365532,
0.01767648383975029,
0.03635530546307564,
0.03855983540415764,
-0.034960974007844925,
-0.03575700521469116,
-0.0021870769560337067,
-0.06541900336742401,
0.021306313574314117,
-0.024090996012091637,
0.0407966747879982,
0.023253683000802994,
0.03755202144384384,
0.026518622413277626,
0.03986547514796257,
-0.0036117136478424072,
-0.0012452559312805533,
-0.10148952901363373,
0.01685132272541523,
-0.015911951661109924,
-0.006130887661129236,
-0.015992920845746994,
-0.02529084123671055,
0.022041071206331253,
-0.040604911744594574,
0.007811948657035828,
-0.029144296422600746,
0.01466795802116394,
-0.06709200143814087,
0.02183045819401741,
-0.04874065890908241,
-0.04778468981385231,
-0.037374693900346756,
0.03026008978486061,
0.016358615830540657,
-0.03850233927369118,
0.003430509939789772,
0.017713826149702072,
-0.024094946682453156,
-0.03376663476228714,
-0.009687399491667747,
0.006738109048455954,
0.04909197986125946,
0.0033634149003773928,
0.03281313553452492,
-0.014342368580400944,
-0.04373187944293022,
0.013930153101682663,
0.004695089068263769,
0.018131213262677193,
0.02049289643764496,
-0.024452421814203262,
-0.015534934587776661,
-0.030197039246559143,
-0.027963787317276,
0.014855749905109406,
0.07784916460514069,
0.00763921020552516,
0.016271136701107025,
0.024320611730217934,
0.007423862814903259,
0.013908411376178265,
0.03412895277142525,
0.053240757435560226,
-0.013360260054469109,
0.00844388734549284,
-0.030329840257763863,
-0.006183418445289135,
-0.04406262934207916,
-0.01854548044502735,
0.013524537906050682,
-0.007481239270418882,
-0.021357547491788864,
-0.008496052585542202,
0.0006160537013784051,
0.002421818906441331,
-0.010155461728572845,
0.006821606773883104,
0.006607504561543465,
0.009047259576618671,
0.019420200958848,
-0.01757846027612686,
0.03607263043522835,
0.03480236977338791,
0.03121541067957878,
-0.0024340825621038675,
-0.034641996026039124,
-0.07869500666856766,
-0.014913009479641914,
0.023415958508849144,
0.05448656156659126,
-0.005184362176805735,
0.02242969535291195,
-0.03902166336774826,
-0.013164614327251911,
0.029110470786690712,
-0.0015094706322997808,
0.03691519796848297,
-0.0037706855218857527,
-0.00955014768987894,
-0.028773026540875435,
-0.03779827803373337,
-0.016545629128813744,
0.028968874365091324,
-0.001269546803086996,
0.023418225347995758,
-0.06572658568620682,
-0.005149271804839373,
-0.06971585750579834,
0.033713605254888535,
0.014914610423147678,
0.012540530413389206,
0.015292702242732048,
0.00951751321554184,
-0.02942483499646187,
0.0718914121389389,
-0.0677899718284607,
-0.06468308717012405,
0.016554493457078934,
-0.002553507685661316,
-0.038279786705970764,
0.034763336181640625,
-0.01753510721027851,
-0.06211422011256218,
0.041843611747026443,
0.02052208222448826,
-0.005912338383495808,
0.021541647613048553,
-0.017624735832214355,
0.07993634045124054,
0.04881157726049423,
0.023620251566171646,
0.04043668508529663,
0.010173690505325794,
-0.03413557633757591,
0.006112867034971714,
-0.013412549160420895,
0.01197453960776329,
-0.01133823487907648,
-0.02847636304795742,
-0.027714544907212257,
0.03633233904838562,
-0.04419881850481033,
0.025878239423036575,
-0.009307581931352615,
-0.00002116582436428871,
-0.016853120177984238,
-0.03965860605239868,
0.004096117801964283,
-0.003176853060722351,
0.027841562405228615,
0.002454263623803854,
0.032803844660520554,
0.037232160568237305,
0.04675275459885597,
-0.047424741089344025,
0.04099332541227341,
-0.025237098336219788,
0.009550390765070915,
0.044429630041122437,
0.013581729494035244,
0.008976059034466743,
-0.009646018035709858,
-0.016915395855903625,
0.007793162018060684,
-0.020044557750225067,
0.011804192326962948,
-0.004668387118726969,
0.009742521680891514,
0.0034624189138412476,
-0.012090724892914295,
-0.027778001502156258,
0.007225302048027515,
-0.008193244226276875,
0.014721049927175045,
-0.03875914216041565,
0.005334432236850262,
0.028402084484696388,
0.00037465555942617357,
-0.051035378128290176,
-0.006437352392822504,
0.000633138814009726,
0.014501724392175674,
-0.046801429241895676,
-0.007535648997873068,
-0.026382824406027794,
-0.012434810400009155,
-0.0044486867263913155,
-0.034159235656261444,
0.022920867428183556,
-0.032791540026664734,
-0.01984347403049469,
0.02463695779442787,
0.053207509219646454,
0.02559901587665081,
-0.0015102194156497717,
-0.028156140819191933,
-0.01729702763259411,
-0.033128585666418076,
-0.012286010198295116,
0.002022947883233428,
0.05338423699140549,
-0.010366931557655334,
-0.011281682178378105,
0.00378985982388258,
-0.01780916564166546,
0.048609524965286255,
-0.01651022396981716,
-0.039834145456552505,
-0.005449536722153425,
0.009415154345333576,
0.011840143240988255,
-0.0417991541326046,
-0.016611402854323387,
0.008701101876795292,
0.050166115164756775,
0.03949195146560669,
-0.003734826110303402,
0.0069988686591386795,
-0.023448748514056206,
-0.002459396841004491,
-0.02635696902871132,
0.0006198852206580341,
-0.005708959419280291,
0.0483507439494133,
-0.013849121518433094,
-0.016198286786675453,
0.027484402060508728,
0.00034263546695001423,
0.02174089103937149,
-0.005906995851546526,
0.034760262817144394,
0.021836860105395317,
-0.0025252399500459433,
-0.02204499952495098,
-0.034632112830877304,
-0.035193610936403275,
0.037110213190317154,
0.04956132173538208,
0.013926323503255844,
0.029741931706666946,
0.027331320568919182,
0.043933406472206116,
-0.0009860019199550152,
0.033782847225666046,
-0.01977376453578472,
-0.015273883007466793,
-0.0030133596155792475,
0.008658392354846,
-0.008974995464086533,
-0.008911531418561935,
0.0397288016974926,
0.029112109914422035,
-0.09757643193006516,
-0.003542852122336626,
0.021370133385062218,
0.039047133177518845,
0.021613942459225655,
0.007860416546463966,
-0.016654647886753082,
0.0598435215651989,
-0.011286893859505653,
-0.004059947561472654,
0.004754521418362856,
-0.01853465847671032,
0.05072403699159622,
0.016746072098612785,
0.024996956810355186,
-0.03757358342409134,
-0.024999171495437622,
0.021706491708755493,
0.022661034017801285,
0.023040955886244774,
0.008614645339548588,
0.030845165252685547,
-0.022331830114126205,
0.009943665936589241,
0.015388588421046734,
-0.006681987550109625,
-0.008554564788937569,
-0.03547035530209541,
0.000017047625078703277,
-0.008113325573503971,
-0.026965973898768425,
0.039797089993953705,
0.016129180788993835,
-0.024315623566508293,
-0.013599507510662079,
-0.03806962072849274,
0.01253166701644659,
0.009496971033513546,
0.015103939920663834,
0.018589144572615623,
0.06680954247713089,
0.0028513839934021235,
0.029326746240258217,
-0.011620479635894299,
-0.00371059263125062,
0.13454094529151917,
0.017484843730926514,
-0.006646054331213236,
-0.0853714644908905,
0.006668580695986748,
-0.019782958552241325,
0.04315798357129097,
-0.0006855797837488353,
0.030113456770777702,
-0.03135240077972412,
-0.0034143810626119375,
0.012627139687538147,
0.04311465471982956,
-0.02187512442469597,
0.004294279962778091,
0.004194155335426331,
-0.04869996756315231,
-0.02718149870634079,
0.020144347101449966,
0.02632644772529602,
-0.018560202792286873,
-0.029224220663309097,
-0.013593408279120922,
-0.006555164698511362,
-0.031180299818515778,
0.03813530132174492,
0.005987435579299927,
-0.06366240978240967,
-0.002383063081651926,
0.0023738108575344086,
-0.09611697494983673,
0.041590139269828796,
0.03622906282544136,
-0.02264944091439247,
-0.028300315141677856,
0.033112384378910065,
0.024240368977189064,
0.006097874604165554,
0.03899793699383736,
0.04155910387635231,
0.0390789769589901,
0.007583734579384327,
0.006820425391197205,
0.059074413031339645,
-0.017402978613972664,
-0.02351328544318676,
-0.02300948090851307,
0.04432225599884987,
0.008434219285845757,
0.024862680584192276,
-0.003438100451603532,
-0.03978588059544563,
0.011036260053515434,
-0.030175957828760147,
-0.03183755278587341,
-0.0027311970479786396,
0.032417669892311096,
-0.03269036114215851,
-0.011193723417818546,
-0.007756493985652924,
0.015437901020050049,
0.011781071312725544,
0.016331050544977188,
-0.011964378878474236,
-0.035957854241132736,
-0.003801434999331832,
0.03405296429991722,
0.028624504804611206,
-0.0022073870059102774,
0.01599358767271042,
-0.03539668396115303,
-0.010739118792116642,
-0.0490160770714283,
-0.014240729622542858,
-0.03259318321943283,
-0.0051942253485322,
0.06840498745441437,
-0.003436008468270302,
-0.028383499011397362,
0.001408794429153204,
-0.060645125806331635,
0.00707267364487052,
-0.0008633449324406683,
0.01893548294901848,
-0.031245430931448936,
-0.022132886573672295,
0.02738690748810768,
0.013600090518593788,
-0.02402178756892681,
0.0031132891308516264,
0.005338623188436031,
0.050463754683732986,
0.007779153063893318,
-0.020027441903948784,
-0.02782841958105564,
0.0102752186357975,
0.008290017955005169,
0.03086298704147339,
0.04503071308135986,
-0.0032465094700455666,
0.02431250363588333,
0.052684810012578964,
-0.031184637919068336,
0.054931383579969406,
-0.03638498857617378,
0.01062645111232996,
0.012829506769776344,
-0.01094082836061716,
-0.023150885477662086,
0.045737434178590775,
-0.0021685974206775427,
-0.02400851994752884,
-0.021840766072273254,
-0.018246466293931007,
0.026935869827866554,
-0.006265139207243919,
0.0005390753503888845,
-0.05234614759683609,
0.006520878989249468,
-0.022471489384770393,
0.028823386877775192,
-0.07170525193214417,
-0.003436332568526268,
-0.028254464268684387,
0.000191127706784755,
0.005902731791138649,
0.002740043681114912,
-0.015227843075990677,
0.026632333174347878,
-0.011391335166990757,
-0.016414644196629524,
0.026052867993712425,
0.03233857452869415,
-0.03548920154571533,
-0.026020416989922523,
-0.022519929334521294,
-0.01670033112168312,
0.02628963440656662,
0.0030357022769749165,
-0.036847200244665146,
0.026291951537132263,
-0.039686523377895355,
-0.05623054504394531,
0.013028941117227077,
0.012780840508639812,
-0.007371974643319845,
0.026544449850916862,
-0.019747335463762283,
-0.015478181652724743,
0.04816200211644173,
0.018561895936727524,
-0.016585366800427437,
-0.017587604001164436,
-0.019887924194335938,
0.0016201414400711656,
-0.043480295687913895,
-0.0023069686722010374,
0.008363408967852592,
0.019776811823248863,
-0.0020099258981645107,
0.014361142180860043,
-0.009149308316409588,
-0.0008659990271553397,
0.009246354922652245,
-0.0005466683069244027,
0.03005373850464821,
0.0013371846871450543,
0.021100608631968498,
0.01063760370016098,
0.040908586233854294,
-0.025797296315431595,
0.02707156166434288,
-0.028011856600642204,
0.014771150425076485,
-0.06525055319070816,
0.0236979853361845,
-0.01968827284872532,
0.02965397946536541,
0.029937220737338066,
-0.04895416647195816,
0.007613255642354488,
0.06754909455776215,
-0.062421709299087524,
0.036352116614580154,
-0.06400909274816513,
-0.01917538046836853,
-0.05091381445527077,
-0.02808515913784504,
-0.022182779386639595,
0.06953181326389313,
0.026924841105937958,
0.002844169270247221,
-0.017332516610622406,
0.006853348575532436,
0.0004978296346962452,
-0.005942768417298794,
-0.029354237020015717,
0.033501919358968735,
-0.008321083150804043,
-0.029391372576355934,
0.07179621607065201,
0.011017926968634129,
-0.023615699261426926,
0.005354246590286493,
-0.0006807001191191375,
-0.0023187673650681973,
-0.02373465523123741,
0.014559455215930939,
0.05902545899152756,
0.020549753680825233,
0.012137198820710182,
-0.011473065242171288,
0.010140974074602127,
-0.021585606038570404,
-0.017873354256153107,
0.004712535999715328,
-0.004796805791556835,
0.009298949502408504,
0.0287194661796093,
0.021166685968637466,
-0.03582444041967392,
0.04239159822463989,
-0.009785180911421776,
0.005338176153600216,
-0.022816501557826996,
0.03154072165489197,
0.021957701072096825,
-0.025348205119371414,
0.04213616997003555,
-0.07840875536203384,
-0.021828753873705864,
0.027980785816907883,
-0.0013036394957453012,
-0.017178483307361603,
0.021527200937271118,
-0.005665279924869537,
-0.05605415254831314,
0.05375603586435318,
0.03213723003864288,
-0.01762019842863083,
-0.03520302474498749,
-0.029884932562708855,
-0.02680208347737789,
0.027876073494553566,
0.017864735797047615,
-0.018602751195430756,
-0.05283680930733681,
0.004166940227150917,
0.023028606548905373,
0.030823642387986183,
-0.009938236325979233,
-0.04301399737596512,
0.005490571726113558,
-0.06866440922021866,
0.06783650070428848,
-0.0027163811028003693,
-0.021244866773486137,
-0.020416811108589172,
-0.031730830669403076,
0.010713218711316586,
0.025975173339247704,
0.04285632073879242,
0.040756940841674805,
-0.028067562729120255,
0.030867261812090874,
0.022501742467284203,
0.025842001661658287,
-0.03827254846692085,
-0.010469748638570309,
-0.016095321625471115,
0.026511652395129204,
0.06662893295288086,
0.017240118235349655,
-0.016031285747885704,
0.016584059223532677,
0.022313222289085388,
-0.01948782615363598,
0.034093134105205536,
-0.021421795710921288,
-0.06680604815483093,
0.02211015671491623,
-0.021734420210123062,
-0.0231507308781147,
0.05579646676778793,
-0.01146764401346445,
-0.007565609645098448,
0.004283495247364044,
-0.006620889529585838,
-0.037991397082805634,
0.028891917318105698,
-0.027562778443098068,
-0.017834894359111786,
-0.033374104648828506,
-0.03325151652097702,
0.0024701186921447515,
-0.002749746898189187,
0.007784114219248295,
0.05586933717131615,
-0.017142437398433685,
-0.031214643269777298,
0.04663670063018799,
0.0409717820584774,
-0.00845070369541645,
0.046399738639593124,
0.03795190528035164,
0.019102731719613075,
-0.002796389162540436,
-0.005209452472627163,
0.002915141638368368,
0.042392414063215256,
0.004705585073679686,
0.00014315100270323455,
0.027996990829706192,
-0.026652708649635315,
0.0013709344202652574,
0.01936616748571396,
0.0017071440815925598,
-0.03240914270281792,
-0.027038060128688812,
0.04157654196023941,
-0.022284090518951416,
0.016620488837361336,
-0.003286981489509344,
-0.02949797920882702,
0.08683944493532181,
-0.011979575268924236,
0.03202873840928078,
-0.022123945876955986,
-0.010149981826543808,
-0.024524493142962456,
-0.006619046442210674,
0.07172129303216934,
0.03810499235987663,
-0.0387086421251297,
0.0024684728123247623,
0.02074047550559044,
-0.03850231319665909,
0.013524062000215054,
-0.04443968087434769,
0.0007414667634293437,
0.02869550511240959,
-0.02163500152528286,
-0.010392657481133938,
-0.039405375719070435,
-0.02620071917772293,
-0.011061042547225952,
0.043732475489377975,
0.06081768125295639,
0.02014513686299324,
-0.00018389974138699472,
-0.003091624239459634,
-0.0309919323772192,
0.010883422568440437,
-0.06208473816514015,
0.012628929689526558,
-0.007697672583162785,
0.04334616661071777,
0.007877401076257229,
-0.017294470220804214
] |
<p>Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(x)$ in the quasistatic limit $\frac{d}{dt}=0$. </p>
<p>Hints:</p>
<p>$\frac{d^{2} \phi}{dx^{2}}=-\rho/ \varepsilon_{0}$ (Poisson equation)</p>
<p>$j=\rho v$</p>
<p>$\frac{d}{dx}(\rho v)=0$ (Continuity equation)</p>
<p>$\frac{1}{2} mv^{2}=q\phi$(Energy Conservation)</p>
<p>My attempt for solving it was:
From the energy conservation equation we get that
$$\frac{1}{v}=\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Continuity equation tells us that $j$ is constant, then
$$ \rho = \frac{j}{v}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Using Laplace equation
$$-\varepsilon_{0}\frac{d^{2} \phi}{dx^{2}}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Then
$$\frac{d^{2} \phi}{dx^{2}}+\frac{j}{\varepsilon_{0}}\sqrt{\frac{m}{2q}} \phi^{-1/2}=0$$
This is just an equation of the form
$$ f^{\prime\prime}+kf^{-1/2}=0$$
Multiplying by $f^{\prime}$ and integrating
$$ \int f^{\prime}f^{\prime\prime}dx+k\int f^{\prime}f^{-1/2}dx=0$$
$$ \frac{1}{2}(f^{\prime})^2+2k\sqrt{f}=0$$
$$ (f^{\prime})^2=-4k\sqrt{f}$$
$$ f^{\prime}=\sqrt{-4k} f^{1/4}$$
And here is my problem, i have the $\sqrt{-4k}$ term that in general is not real!
$$ \frac{df}{f^{1/4}}=\sqrt{-4k}dx $$
$$ \frac{4}{3} f^{3/4}=\sqrt{-4k}x +C $$
$$ f={\frac{3}{4}[\sqrt{-4k}x +C]}^{4/3} $$</p> | 4,565 | [
-0.0171359833329916,
0.013803491368889809,
0.04494389891624451,
-0.002825716743245721,
0.022730151191353798,
-0.030431674793362617,
-0.0005131417419761419,
0.00036350739537738264,
0.007913630455732346,
0.013089538551867008,
0.045561227947473526,
0.019865646958351135,
0.04521507769823074,
0.037170954048633575,
0.0020869465079158545,
-0.0049891346134245396,
-0.011662648990750313,
-0.02841661311686039,
-0.006060278974473476,
-0.03687110170722008,
-0.01924542523920536,
0.038305819034576416,
0.04775729402899742,
-0.004284212831407785,
-0.04322848096489906,
0.04295364022254944,
0.010389664210379124,
-0.028417877852916718,
-0.013176077045500278,
0.004868593532592058,
-0.030411990359425545,
0.01492287591099739,
0.005899691488593817,
-0.009726843796670437,
0.007186143659055233,
0.03816286846995354,
-0.033327557146549225,
-0.04503607749938965,
0.0035521117970347404,
0.029181620106101036,
-0.02314239740371704,
0.03544639050960541,
-0.015658045187592506,
0.031910594552755356,
-0.010720793157815933,
0.010373757220804691,
0.054798830300569534,
-0.011841905303299427,
0.07997745275497437,
-0.0736481100320816,
0.049328360706567764,
0.011573960073292255,
0.04956875741481781,
-0.005314625333994627,
-0.01408168114721775,
-0.025699293240904808,
0.032989468425512314,
0.09217230975627899,
-0.0038882819935679436,
-0.05320224538445473,
-0.03105391003191471,
-0.024201732128858566,
-0.03517734259366989,
-0.03158274665474892,
0.028731834143400192,
0.008445399813354015,
-0.02824084460735321,
-0.03328133374452591,
0.03350994735956192,
-0.01762552745640278,
0.026701489463448524,
0.015667064115405083,
0.011197579093277454,
-0.002335658762603998,
0.014024737291038036,
0.017305627465248108,
-0.0031703582499176264,
0.031278111040592194,
0.00018061010632663965,
0.027249736711382866,
-0.011507425457239151,
-0.009933867491781712,
0.008681870996952057,
0.03560640290379524,
0.015016910620033741,
-0.0300324447453022,
0.069071926176548,
0.011373951099812984,
0.0014785652747377753,
0.0356760248541832,
-0.005009911023080349,
0.014364936389029026,
0.006087855435907841,
0.013586039654910564,
0.0202626995742321,
0.044267814606428146,
-0.02147722989320755,
0.01740087755024433,
0.00868784636259079,
-0.0229218527674675,
-0.015130049549043179,
-0.0487077571451664,
0.021065406501293182,
0.06987324357032776,
-0.02890295535326004,
-0.03338790684938431,
-0.004289383068680763,
-0.03688398003578186,
-0.030177930369973183,
0.008578887209296227,
-0.05162576586008072,
0.015061536803841591,
0.02379264123737812,
0.010265382006764412,
-0.018984103575348854,
0.004658838734030724,
-0.004635510500520468,
-0.04897143691778183,
0.029999302700161934,
0.05892103910446167,
0.0306862723082304,
-0.01854887790977955,
0.007767279166728258,
-0.01828787475824356,
-0.05969436839222908,
0.019504375755786896,
0.03148890286684036,
0.02887572906911373,
-0.006021921057254076,
0.0004771907697431743,
-0.0067105283960700035,
0.014506462030112743,
-0.017916828393936157,
-0.016711268573999405,
0.0405641533434391,
-0.03069307841360569,
-0.08624357730150223,
-0.04322558268904686,
0.012917999178171158,
-0.00019456722657196224,
-0.0008981933351606131,
-0.06802906095981598,
-0.03402574360370636,
0.032673198729753494,
0.07772661745548248,
-0.013679479248821735,
-0.030395623296499252,
-0.007885260507464409,
0.01930050365626812,
-0.016913892701268196,
-0.009492131881415844,
-0.02524711564183235,
-0.008024083450436592,
-0.02183188684284687,
0.024136174470186234,
-0.025786960497498512,
0.021705003455281258,
0.015581675805151463,
-0.011041661724448204,
-0.006147632375359535,
0.01213147398084402,
0.005195658188313246,
-0.0011443053372204304,
-0.002448709448799491,
-0.0009476527920924127,
-0.004768195562064648,
0.08331075310707092,
0.03665042296051979,
0.005981722380965948,
0.001288632396608591,
0.021918650716543198,
0.003398637054488063,
-0.020357226952910423,
0.006337578874081373,
0.027517683804035187,
-0.04832688719034195,
-0.01912204921245575,
-0.05211986228823662,
-0.013005909509956837,
0.004626896232366562,
-0.01842258870601654,
-0.04201178625226021,
-0.026339029893279076,
-0.018665332347154617,
0.035973139107227325,
0.02632260136306286,
0.012220142409205437,
0.03731945902109146,
-0.018862739205360413,
-0.013964558951556683,
-0.02029029279947281,
-0.0313589833676815,
0.021866127848625183,
0.003429942764341831,
-0.021612869575619698,
0.020015183836221695,
-0.021644556894898415,
-0.0010768508072942495,
-0.04375489801168442,
-0.013161774724721909,
-0.001824837294407189,
0.00926376786082983,
-0.04373428598046303,
-0.01280110701918602,
0.03790822625160217,
0.013432024046778679,
0.03349946066737175,
0.022142956033349037,
0.0037761307321488857,
0.00829416885972023,
0.006684265099465847,
-0.03492683172225952,
-0.055631548166275024,
0.05801377817988396,
0.00030476992833428085,
0.016582386568188667,
-0.004884352441877127,
-0.02754569612443447,
-0.026973772794008255,
-0.02679941989481449,
-0.02630084939301014,
0.04780421778559685,
0.06159639731049538,
-0.015162535943090916,
-0.01789388433098793,
0.035810936242341995,
-0.02726362831890583,
0.01782827638089657,
-0.006853826809674501,
-0.06205599755048752,
-0.04110213741660118,
0.008047442883253098,
0.046868860721588135,
0.04086529463529587,
-0.013162409886717796,
-0.0074696228839457035,
0.05029815062880516,
-0.0000021256457785057137,
0.06964471191167831,
-0.03921925276517868,
-0.017899272963404655,
-0.036994434893131256,
0.059583939611911774,
-0.0003075568238273263,
-0.01652119681239128,
0.018286295235157013,
0.03798139467835426,
-0.009180363267660141,
-0.004056458827108145,
-0.02534385211765766,
-0.007686737924814224,
0.015273130498826504,
0.022067992016673088,
0.026288481429219246,
0.037528131157159805,
-0.008463467471301556,
0.052845750004053116,
0.0370897613465786,
0.0672428086400032,
0.07711156457662582,
-0.011204760521650314,
0.014131881296634674,
-0.0041162860579788685,
0.0037983206566423178,
0.014740518294274807,
0.015689823776483536,
-0.011872764676809311,
-0.023350752890110016,
0.01857190951704979,
-0.05552268400788307,
-0.015651673078536987,
0.0039257630705833435,
-0.012824567966163158,
0.019250107929110527,
-0.018596632406115532,
0.024785205721855164,
0.03033456765115261,
0.007659283000975847,
-0.04086348041892052,
0.01153363287448883,
0.04015715792775154,
-0.027654601261019707,
0.03204897418618202,
0.04144150763750076,
-0.007826672866940498,
-0.011257925070822239,
-0.03645436838269234,
-0.029237983748316765,
0.06901625543832779,
0.011531217955052853,
-0.025967972353100777,
0.04894145950675011,
-0.017222829163074493,
-0.05202672258019447,
-0.009378408081829548,
-0.029662180691957474,
0.009233503602445126,
-0.03663937374949455,
0.015112596563994884,
0.02747628092765808,
0.01772792637348175,
-0.038185007870197296,
0.026448074728250504,
-0.07371938228607178,
-0.05063482001423836,
-0.05807405710220337,
0.0032759257592260838,
0.028716981410980225,
-0.00978800468146801,
0.049220290035009384,
0.01761728897690773,
0.0036824599374085665,
0.012136208824813366,
-0.04212271422147751,
-0.03098663128912449,
0.020708397030830383,
0.011242284439504147,
0.05388270691037178,
-0.011675012297928333,
-0.04815838858485222,
0.06066548451781273,
0.03593186289072037,
0.0005997680709697306,
0.023149307817220688,
-0.0010904354276135564,
-0.009555886499583721,
-0.010413379408419132,
-0.005986482370644808,
0.03668321296572685,
-0.04104943200945854,
-0.0053612967021763325,
-0.00907543022185564,
0.07675699889659882,
0.03445781022310257,
-0.015933731570839882,
-0.022157303988933563,
0.018648866564035416,
0.021287744864821434,
0.028259489685297012,
0.040599215775728226,
-0.005350551102310419,
0.015151548199355602,
0.009259365499019623,
-0.015696750953793526,
0.002806825563311577,
0.01188412494957447,
-0.08305635303258896,
0.057704534381628036,
-0.00005001259341952391,
0.00964302197098732,
-0.02295011468231678,
0.02248191274702549,
0.01878909394145012,
-0.02748352475464344,
0.01576004922389984,
0.03634847328066826,
0.03975358605384827,
-0.013702909462153912,
0.010701608844101429,
0.03768901526927948,
0.04057801142334938,
-0.007702619768679142,
-0.03722906857728958,
0.00197198917157948,
0.005490720737725496,
0.019871341064572334,
-0.04887126013636589,
-0.016367107629776,
0.00020691251847893,
0.018852945417165756,
0.024537445977330208,
-0.01470083836466074,
0.011388001032173634,
-0.008635948412120342,
-0.04497399181127548,
-0.02391003631055355,
-0.028756199404597282,
0.061983995139598846,
0.0009208127739839256,
0.06561163067817688,
0.0019199576927348971,
0.04104716330766678,
0.010201203636825085,
0.0352327823638916,
-0.07794882357120514,
0.021601879969239235,
-0.0034983521327376366,
-0.019502533599734306,
-0.030349072068929672,
0.029652409255504608,
-0.008407673798501492,
-0.006264904513955116,
-0.01911652646958828,
-0.004514958709478378,
-0.008620047941803932,
-0.06038406118750572,
0.018424473702907562,
-0.02633599564433098,
-0.07207764685153961,
-0.040884051471948624,
0.030566958710551262,
0.04767107591032982,
-0.03549577668309212,
-0.013280789367854595,
0.04114735126495361,
-0.021209781989455223,
-0.011883429251611233,
-0.01648036763072014,
-0.024050960317254066,
0.03635934367775917,
0.016253117471933365,
-0.042710356414318085,
0.012339338660240173,
0.027286937460303307,
-0.012204953469336033,
-0.008769253268837929,
0.043386686593294144,
-0.011243964545428753,
-0.016536379233002663,
-0.016783753409981728,
-0.028416387736797333,
0.0033327792771160603,
-0.019061103463172913,
0.07862068712711334,
-0.0173732191324234,
0.002896609716117382,
0.013292369432747364,
0.005886193830519915,
0.025716105476021767,
0.03469455614686012,
0.04985374957323074,
0.013066611252725124,
-0.016415372490882874,
-0.04526631906628609,
0.02551804482936859,
-0.02006501331925392,
0.0019180047092959285,
0.024038303643465042,
-0.04815837740898132,
-0.00724992947652936,
-0.00623773830011487,
0.008404450491070747,
0.05867140740156174,
-0.0016398918814957142,
0.0006254851468838751,
0.01510663889348507,
0.010737522505223751,
0.01864873617887497,
0.011241876520216465,
0.03709295019507408,
-0.010342356748878956,
0.021228596568107605,
-0.007411222439259291,
0.01770198531448841,
-0.07185287773609161,
-0.03911900892853737,
0.003634659806266427,
0.006970060057938099,
0.005777876824140549,
0.013115696609020233,
-0.06786748766899109,
-0.039467960596084595,
0.04821368679404259,
-0.02669914811849594,
0.041651174426078796,
0.005073204170912504,
0.01257624477148056,
0.006026108283549547,
-0.04582802951335907,
-0.07915005087852478,
0.00828188844025135,
-0.006995254196226597,
-0.008486874401569366,
-0.006116135511547327,
0.02637329511344433,
-0.02040928788483143,
0.019060537219047546,
0.01736677996814251,
0.11145108938217163,
-0.010573743842542171,
-0.026355307549238205,
-0.008549344725906849,
-0.0351223461329937,
-0.018694447353482246,
-0.1003473550081253,
0.024550287052989006,
0.003036159323528409,
0.019169460982084274,
0.025323471054434776,
-0.03316923603415489,
-0.04644713178277016,
0.04100697487592697,
0.017149977385997772,
-0.029473252594470978,
0.02184259332716465,
-0.03217465803027153,
0.04449654743075371,
0.041568271815776825,
-0.00523448595777154,
0.03088652342557907,
0.020896119996905327,
-0.045365046709775925,
0.00997539609670639,
-0.028097879141569138,
0.012117946520447731,
-0.014868305996060371,
-0.02548254281282425,
-0.024747386574745178,
0.03371240198612213,
-0.0409557968378067,
0.03304555267095566,
-0.019446460530161858,
0.0018863814184442163,
-0.02547500655055046,
-0.01748162880539894,
0.04459753632545471,
0.029162928462028503,
-0.0061229439452290535,
0.0026483871042728424,
-0.00821670051664114,
0.00008386515401070938,
0.03877925127744675,
-0.013683038763701916,
0.023013636469841003,
0.005402851849794388,
-0.0068957870826125145,
0.04225456714630127,
-0.018228810280561447,
-0.0403946116566658,
-0.03577554598450661,
-0.008344689384102821,
-0.021799279376864433,
-0.06767280399799347,
0.044681616127491,
-0.026676373556256294,
0.01176278293132782,
0.04361544921994209,
-0.039737652987241745,
-0.06882490962743759,
0.04132911562919617,
0.01062320452183485,
-0.016613757237792015,
0.0019004507921636105,
0.02058003842830658,
0.0333617702126503,
0.02310321293771267,
-0.09042415022850037,
-0.010084404610097408,
0.015482067130506039,
-0.014023592695593834,
-0.02490702085196972,
-0.03797263279557228,
-0.02580888569355011,
0.007719544693827629,
-0.0257705170661211,
0.03447069600224495,
-0.009816944599151611,
-0.01555570401251316,
0.019178660586476326,
0.053251177072525024,
0.05516607686877251,
0.008835788816213608,
0.010223058983683586,
0.022519759833812714,
0.042931653559207916,
-0.014803440310060978,
-0.043942853808403015,
-0.011671721003949642,
0.04916020855307579,
-0.013016714714467525,
-0.0433194600045681,
-0.02124352566897869,
-0.0035975868813693523,
0.006833842024207115,
-0.034650105983018875,
-0.029564710333943367,
0.03031560592353344,
0.0316496342420578,
-0.0002658597659319639,
-0.018664417788386345,
-0.009686024859547615,
0.0021224413067102432,
-0.0027260957285761833,
0.0257263220846653,
0.004654459655284882,
-0.0769822895526886,
-0.019156308844685555,
0.01347484439611435,
-0.02369745634496212,
0.009565510787069798,
-0.0024233164731413126,
0.04678162932395935,
-0.029534408822655678,
-0.016150401905179024,
0.06954854726791382,
0.03795254975557327,
0.025185616686940193,
-0.004920504055917263,
-0.0239460077136755,
0.0029662754386663437,
0.01301572099328041,
-0.016797130927443504,
-0.007265110034495592,
-0.05150461569428444,
0.017748087644577026,
0.07272873818874359,
0.02732483111321926,
0.05416242778301239,
-0.019706755876541138,
0.014227979816496372,
0.005967714823782444,
-0.003962568938732147,
-0.007841339334845543,
-0.0023029004223644733,
0.0036229384131729603,
0.015944750979542732,
-0.049797285348176956,
-0.016510237008333206,
0.030664430931210518,
0.05928562209010124,
-0.0417792871594429,
0.021825086325407028,
-0.005612576846033335,
0.030607325956225395,
0.037010591477155685,
-0.0509677417576313,
-0.027698945254087448,
0.04643861576914787,
-0.02947511523962021,
0.06179210916161537,
-0.012140756472945213,
-0.021044226363301277,
0.06538902968168259,
0.0095673231408,
-0.007048842031508684,
-0.0403139665722847,
-0.0022494872100651264,
-0.019947556778788567,
0.044924985617399216,
0.014712553471326828,
0.022870942950248718,
-0.00466638570651412,
0.039815764874219894,
0.01494782604277134,
-0.009026148356497288,
0.041538942605257034,
-0.006369051989167929,
-0.008512591011822224,
0.0005190276424400508,
0.009360280819237232,
-0.041605062782764435,
0.016692550852894783,
-0.004028751514852047,
0.023057719692587852,
0.023823516443371773,
-0.020966365933418274,
0.026270803064107895,
0.044278793036937714,
-0.011795694939792156,
-0.021764714270830154,
0.04219268262386322,
-0.01681637018918991,
0.01793503202497959,
-0.06237853690981865,
0.02580239623785019,
0.15119385719299316,
0.04783400893211365,
0.03661363944411278,
-0.012099167332053185,
-0.01808227226138115,
-0.0323820523917675,
0.017895549535751343,
-0.03708484396338463,
0.015975942835211754,
-0.02715737745165825,
-0.006053187884390354,
0.0022265349980443716,
0.039108484983444214,
-0.011948488652706146,
0.003122638911008835,
0.02997521124780178,
-0.0025104000233113766,
-0.027120720595121384,
0.0020195317920297384,
-0.005124800838530064,
-0.03695737197995186,
0.044347550719976425,
0.017536794766783714,
0.0833275094628334,
-0.02541426196694374,
0.010517298243939877,
-0.05348845198750496,
-0.01974606141448021,
0.0036193844862282276,
0.009296481497585773,
-0.0613887719810009,
0.0101619902998209,
0.026066487655043602,
-0.025424746796488762,
0.017295775935053825,
0.0013613883638754487,
0.045631539076566696,
-0.008372042328119278,
0.008535072207450867,
0.03068883903324604,
-0.014815747737884521,
0.030256520956754684,
0.02415742725133896,
0.010695653967559338,
-0.025985505431890488,
0.012284905649721622,
-0.07217532396316528,
0.047100529074668884,
0.009343176148831844,
0.018500149250030518,
0.015525382943451405,
0.008943560533225536,
-0.03447460010647774,
-0.03153744712471962,
-0.02358967997133732,
-0.024674037471413612,
0.027096109464764595,
0.0070576597936451435,
0.03537687286734581,
-0.01499185524880886,
0.0016834625275805593,
0.03158191964030266,
-0.027468761429190636,
-0.026032378897070885,
-0.002133872825652361,
-0.014237227849662304,
0.0006288562435656786,
0.054868537932634354,
-0.023009346798062325,
-0.009123655967414379,
-0.03559287637472153,
-0.034270234405994415,
-0.023803509771823883,
-0.02632429264485836,
-0.028772085905075073,
0.027560964226722717,
0.0598863884806633,
0.007174451369792223,
-0.004639525432139635,
-0.006734590977430344,
-0.09935779124498367,
0.02449694089591503,
0.03650438040494919,
-0.005289184395223856,
-0.035188861191272736,
-0.024077575653791428,
-0.007985752075910568,
0.05885496735572815,
-0.03180505707859993,
-0.0030643136706203222,
0.00016663574206177145,
0.05365724116563797,
-0.004496230743825436,
0.016929108649492264,
-0.06368786096572876,
-0.013521477580070496,
-0.02287979982793331,
0.05416290834546089,
-0.03505147993564606,
-0.0213670302182436,
0.012677797116339207,
0.028650455176830292,
0.002483242889866233,
0.015997080132365227,
-0.0318322479724884,
0.02470991760492325,
0.017274806275963783,
-0.020143384113907814,
0.0021396104712039232,
0.0035133969504386187,
0.036290161311626434,
-0.005207729991525412,
-0.01695392280817032,
0.0008996024262160063,
0.011923241429030895,
-0.05166871100664139,
0.003729735966771841,
-0.01424109935760498,
-0.021954048424959183,
-0.03590007871389389,
0.01915626786649227,
-0.014192285016179085,
-0.009001703932881355,
0.009548294357955456,
0.03061036765575409,
-0.013481111265718937,
0.04406767338514328,
-0.022019093856215477,
0.0024398434907197952,
-0.041845209896564484,
0.01874191127717495,
0.006226675119251013,
0.01485062949359417,
-0.012498565018177032,
0.017966806888580322,
0.024719199165701866,
0.02746664173901081,
0.02435494214296341,
-0.028663745149970055,
0.008872290141880512,
0.032545946538448334,
-0.03189922869205475,
-0.027525871992111206,
0.0040579852648079395,
0.039545804262161255,
0.016279829666018486,
0.0015523009933531284,
-0.0024655908346176147,
-0.027747023850679398,
0.04020817577838898,
-0.016667980700731277,
-0.014892691746354103,
-0.010049493983387947,
-0.07022085785865784,
-0.00317575060762465,
-0.03131962567567825,
-0.019563525915145874,
-0.01337500475347042,
0.01094953902065754,
0.03557990863919258,
-0.01760273054242134,
-0.03028283081948757,
-0.008224579505622387,
0.0149444080889225,
-0.023859191685914993,
-0.011396871879696846,
0.03930048644542694,
0.02206740900874138,
0.01780574768781662,
0.04299566522240639,
0.0018312722677364945,
-0.013900783844292164,
0.0023745268117636442,
-0.02947271801531315,
-0.09993958473205566,
-0.05132143199443817,
-0.03189770504832268,
0.03441962972283363,
0.024485725909471512,
-0.07505550235509872,
-0.012237169779837132,
0.03131331875920296,
-0.08365961909294128,
0.022852230817079544,
-0.028147347271442413,
0.0036360921803861856,
-0.025985850021243095,
-0.024201814085245132,
-0.0317440889775753,
0.04685606062412262,
0.03424826264381409,
0.04168172553181648,
0.008917358703911304,
0.028604550287127495,
0.007268268149346113,
-0.0023582482244819403,
0.030363701283931732,
0.0279985461384058,
-0.015605797991156578,
-0.00035464594839140773,
0.04451499879360199,
-0.02618422545492649,
0.03677912428975105,
0.01413032691925764,
-0.019032470881938934,
-0.017676344141364098,
-0.008870854042470455,
0.02719297632575035,
-0.0005960527923889458,
0.04955087602138519,
-0.00577876390889287,
0.016869455575942993,
0.019607609137892723,
-0.03279697895050049,
0.023777276277542114,
0.013589754700660706,
-0.01780688390135765,
-0.004549739882349968,
0.05491454899311066,
-0.0414472259581089,
-0.06055331975221634,
0.06993622332811356,
-0.022496957331895828,
-0.013448009267449379,
0.047227464616298676,
0.03024800680577755,
0.014518811367452145,
0.010821039788424969,
-0.003585599362850189,
-0.039441656321287155,
0.0013714726082980633,
0.00989797618240118,
0.01634235866367817,
-0.013902947306632996,
0.03703068941831589,
0.008150416426360607,
-0.00964556448161602,
0.041475147008895874,
0.00258353422395885,
-0.018853861838579178,
-0.07473602145910263,
-0.00559155223891139,
-0.030259499326348305,
0.0464303195476532,
-0.016945982351899147,
-0.05222656950354576,
-0.02901921235024929,
0.0291628185659647,
0.02238762378692627,
0.03298557177186012,
-0.0201726071536541,
-0.017410067841410637,
-0.0155025664716959,
-0.08426796644926071,
-0.007548660505563021,
0.01785687729716301,
-0.08864444494247437,
-0.0036181509494781494,
-0.0388721227645874,
-0.009249524213373661,
0.020691080018877983,
0.06508003920316696,
0.009404301643371582,
-0.029288509860634804,
0.029005495831370354,
-0.00900695938616991,
0.02985333651304245,
-0.06036054342985153,
-0.010568455792963505,
0.012017838656902313,
0.012772918678820133,
0.008912133052945137,
0.04964105784893036,
-0.023604732006788254,
0.010791284032166004,
0.009493328630924225,
-0.005089303944259882,
0.008867687545716763,
-0.0018689701100811362,
-0.0463305227458477,
0.005599151365458965,
-0.009182319045066833,
0.00827073771506548,
0.0695071592926979,
-0.04697897285223007,
0.010614776983857155,
-0.0011057335650548339,
-0.046043530106544495,
-0.028640493750572205,
-0.020996008068323135,
-0.038530074059963226,
-0.015340527519583702,
-0.004689391236752272,
-0.02135930024087429,
0.05391351506114006,
-0.04236232861876488,
0.001867595361545682,
0.051665086299180984,
-0.03292301297187805,
-0.03552151098847389,
0.020780183374881744,
0.014755649492144585,
0.02727244608104229,
0.021145550534129143,
0.007799857761710882,
-0.007931324653327465,
0.004168161191046238,
-0.0063721793703734875,
0.014073757454752922,
0.009926022961735725,
-0.027185533195734024,
-0.003637312212958932,
0.04707777500152588,
-0.022030211985111237,
-0.0038112502079457045,
0.0049164630472660065,
-0.03276059031486511,
-0.02464183419942856,
0.004877494648098946,
0.05200081318616867,
-0.023404784500598907,
-0.026176486164331436,
0.017094073817133904,
-0.008928949013352394,
0.0633636936545372,
-0.011641363613307476,
0.027108747512102127,
0.012474194169044495,
-0.02217148058116436,
-0.01795143261551857,
0.031177913770079613,
-0.005202386062592268,
0.03897428140044212,
-0.02785555273294449,
-0.010703636333346367,
-0.022143840789794922,
-0.004056498873978853,
-0.0047690290957689285,
-0.0586431510746479,
0.014668276533484459,
0.056487929075956345,
-0.008335514925420284,
-0.00606147525832057,
0.011540260165929794,
0.026153912767767906,
0.008907840587198734,
0.010816539637744427,
0.0060670459643006325,
-0.00881390180438757,
0.005186786875128746,
0.021885572001338005,
-0.030694738030433655,
0.0485578253865242,
-0.05024515092372894,
-0.031638387590646744,
0.009631989523768425,
-0.01883157715201378,
0.006607284769415855,
0.019325675442814827
] |
<p>Photons have no charge. Light is a form of electromagnetic energy.</p>
<p>All spectroscopic effects (to my knowledge) are due to changes in electron state, induced either through an interior or exterior EM (Electro-Magnetic) field. EM forces may affect that state, which in turn affects the light emitted during the change of state, e.g. the Zeeman effect, etc. </p>
<p>However, if we <strong><em>exclude</strong> all such spectroscopic phenomena</em>, and consider EM fields purely energetically on the one side, and light energy on the other, are there any know <strong>direct</strong> effects of EM fields on light itself? </p>
<p>(I'd really like to hear from physicists with hands on knowledge - and please keep all the Tags as is because I have reasons for selecting them, thx.)</p> | 4,566 | [
-0.031091662123799324,
-0.04912423714995384,
-0.000942234939429909,
-0.020934240892529488,
0.03091798536479473,
0.04021789878606796,
-0.03239046037197113,
-0.0369403176009655,
0.006914752069860697,
-0.04137171059846878,
0.044831860810518265,
0.030944207683205605,
0.05090686306357384,
0.0133071169257164,
-0.0047615887597203255,
0.0073163993656635284,
0.016703512519598007,
-0.014878732152283192,
-0.011896202340722084,
-0.028887296095490456,
-0.011656572110950947,
0.027697330340743065,
-0.007187630515545607,
0.05339205265045166,
-0.041678816080093384,
0.035804279148578644,
0.044290948659181595,
0.016634874045848846,
0.02681734599173069,
0.033184487372636795,
-0.008415675722062588,
-0.021663274616003036,
-0.02496226690709591,
-0.002159458352252841,
0.019665854051709175,
-0.017457664012908936,
-0.04964154586195946,
-0.04461907967925072,
0.013570038601756096,
-0.007420661859214306,
-0.031028980389237404,
-0.011126167140901089,
-0.01637696474790573,
0.012119392864406109,
-0.058686863631010056,
0.005158764310181141,
-0.02113882638514042,
0.0088955108076334,
0.06173160672187805,
-0.052139293402433395,
0.06263992935419083,
-0.05006793513894081,
0.014233292080461979,
0.029844803735613823,
-0.012251323089003563,
0.006740010809153318,
0.06909924745559692,
0.053888287395238876,
0.0076213618740439415,
-0.04145083576440811,
0.022204793989658356,
0.004828513599932194,
-0.010000603273510933,
-0.025916703045368195,
-0.04296034201979637,
0.02395893633365631,
0.006411117035895586,
-0.019366897642612457,
0.07558700442314148,
0.04710332676768303,
0.0017338922480121255,
0.004090867005288601,
0.029025109484791756,
-0.006813522428274155,
-0.014068039134144783,
-0.027036158367991447,
0.03420772776007652,
0.014733856543898582,
0.052644867449998856,
0.03760954365134239,
-0.02697702683508396,
-0.008566095493733883,
0.0021256902255117893,
0.04795566573739052,
0.014990752562880516,
-0.02411767840385437,
0.06733940541744232,
-0.015108786523342133,
0.02157871052622795,
-0.005299767013639212,
-0.010075376369059086,
0.0071153766475617886,
0.01089620590209961,
-0.0005939971888437867,
-0.03396015986800194,
0.015490518882870674,
-0.008693083189427853,
0.052363473922014236,
0.012924710288643837,
-0.008720657788217068,
0.01572977751493454,
0.02944772318005562,
0.03590783104300499,
0.06752019375562668,
-0.004085208754986525,
-0.05038421228528023,
-0.01005734782665968,
0.01279392372816801,
-0.03224056959152222,
-0.0027756765484809875,
-0.003986935131251812,
0.0036853833589702845,
0.00614706939086318,
-0.013464882969856262,
0.0217600017786026,
-0.04920753836631775,
0.02159144915640354,
-0.012786917388439178,
0.07782220840454102,
0.08537033945322037,
0.037150848656892776,
-0.07497940957546234,
0.006985554937273264,
-0.040524329990148544,
-0.07690158486366272,
-0.00916757620871067,
0.024745728820562363,
0.013573854230344296,
-0.038652580231428146,
0.02571174129843712,
-0.00989872682839632,
-0.0033028526231646538,
0.00498034805059433,
-0.015220589004456997,
0.031427040696144104,
-0.01932307705283165,
-0.09256384521722794,
-0.06912171095609665,
0.0010454215807840228,
-0.008005702868103981,
-0.024157261475920677,
-0.048772793263196945,
-0.015110583044588566,
0.02092237025499344,
0.09215065091848373,
-0.0032114654313772917,
-0.02733530104160309,
-0.02536187693476677,
0.04949343949556351,
0.012816649861633778,
-0.01285322941839695,
0.009363983757793903,
-0.014100942760705948,
-0.02970227599143982,
0.015438519418239594,
-0.07916254550218582,
0.030454479157924652,
0.00906573049724102,
0.00928683765232563,
0.012905566953122616,
0.08217334747314453,
-0.039372336119413376,
0.022054241970181465,
0.010312259197235107,
-0.004515171051025391,
-0.025891263037919998,
0.09780849516391754,
0.039406731724739075,
0.01480990182608366,
0.021586041897535324,
0.016991954296827316,
0.0453852154314518,
-0.015252482146024704,
0.0037561513017863035,
0.028471795842051506,
-0.05971493571996689,
-0.04825190082192421,
-0.0201885849237442,
0.047103915363550186,
-0.01065873447805643,
-0.026228366419672966,
-0.026975028216838837,
-0.030995216220617294,
0.0021155052818357944,
0.011668628081679344,
0.060469333082437515,
-0.013269330374896526,
-0.034800563007593155,
-0.0006817273097112775,
-0.031648796051740646,
0.01076778769493103,
-0.032525356858968735,
0.0669328048825264,
-0.008140628226101398,
-0.031210128217935562,
0.031671762466430664,
-0.013248334638774395,
0.0038216356188058853,
-0.05077749118208885,
-0.052195604890584946,
0.018909454345703125,
0.032538220286369324,
-0.005336665082722902,
-0.027672022581100464,
0.010781307704746723,
0.02105054445564747,
0.033246055245399475,
-0.0036662588827311993,
0.02832266502082348,
-0.040372930467128754,
-0.05823662132024765,
0.0065075489692389965,
-0.04560881108045578,
0.03235103562474251,
0.02294028177857399,
0.0032052514143288136,
-0.005362253170460463,
0.004183642566204071,
-0.04353582486510277,
0.04655031859874725,
-0.034345004707574844,
0.08049555122852325,
0.0336025170981884,
-0.017564944922924042,
-0.004065967630594969,
0.04572740197181702,
0.004186699632555246,
0.009348303079605103,
-0.017968179658055305,
-0.04825896769762039,
-0.04962630569934845,
0.01675098016858101,
0.04938450828194618,
-0.026195475831627846,
-0.05726953595876694,
0.039731159806251526,
0.0001596375514054671,
0.06509910523891449,
0.02811596915125847,
0.029626289382576942,
-0.05529533699154854,
-0.052755679935216904,
0.03388310223817825,
0.03257008641958237,
0.025610128417611122,
0.016664791852235794,
0.00650048116222024,
0.00561043294146657,
0.037840187549591064,
0.026597879827022552,
-0.00036395940696820617,
0.022323191165924072,
-0.023312287405133247,
0.01946331188082695,
0.002665569307282567,
-0.0648282840847969,
0.007854674942791462,
-0.058290671557188034,
0.02660277672111988,
-0.006931139621883631,
-0.04681123048067093,
0.00010190458124270663,
-0.00579627463594079,
-0.029092563316226006,
-0.019465984776616096,
-0.021369200199842453,
-0.05656762421131134,
0.010543931275606155,
0.028177447617053986,
-0.03863675892353058,
0.013074408285319805,
0.030545596033334732,
-0.00464133033528924,
-0.021023238077759743,
-0.02308141440153122,
0.03466923162341118,
0.0034743209835141897,
0.03431188687682152,
-0.035847008228302,
-0.026060882955789566,
-0.018003784120082855,
-0.0737336203455925,
-0.00044960141531191766,
0.020219873636960983,
0.002372563350945711,
0.019911648705601692,
-0.0675133690237999,
-0.03111720271408558,
0.07249661535024643,
-0.01586921513080597,
-0.017583560198545456,
0.056339748203754425,
-0.004722604528069496,
-0.0719730332493782,
-0.0018870332278311253,
-0.013800275512039661,
0.0038864577654749155,
-0.023236257955431938,
-0.017566140741109848,
0.05395372956991196,
-0.0001475503231631592,
-0.030975334346294403,
-0.013728083111345768,
-0.02081212028861046,
-0.023455530405044556,
-0.02517089620232582,
-0.007426697760820389,
0.011869825422763824,
-0.019628453999757767,
0.01699467934668064,
0.016208261251449585,
-0.0752016082406044,
0.0026050989981740713,
-0.028633112087845802,
-0.03374908119440079,
0.01558193750679493,
0.0010953531600534916,
-0.0035759268794208765,
-0.017511451616883278,
-0.04569926857948303,
0.0272207111120224,
0.05270550772547722,
-0.03863145411014557,
-0.02100309170782566,
-0.04775368422269821,
-0.03658671677112579,
-0.029595855623483658,
-0.008597440086305141,
0.012763643637299538,
0.008840341120958328,
0.028459085151553154,
0.013671716675162315,
0.015170068480074406,
-0.03844592347741127,
0.01464804820716381,
-0.01228010281920433,
0.04218517616391182,
-0.014643942005932331,
0.007101820316165686,
0.03659417852759361,
0.046047136187553406,
-0.009394819848239422,
-0.013152604922652245,
0.008883373811841011,
0.009035209193825722,
0.0011877099750563502,
-0.018368523567914963,
0.0505017414689064,
0.03145964443683624,
0.01851997710764408,
-0.03375093638896942,
0.03164127469062805,
-0.007382174488157034,
-0.0048867398872971535,
0.0010148936416953802,
0.03537116199731827,
0.007020527496933937,
-0.02598307654261589,
0.017300361767411232,
0.007972600869834423,
0.0943400114774704,
-0.024602582678198814,
-0.031310711055994034,
0.022622734308242798,
0.002180697163566947,
0.022423164919018745,
-0.026289599016308784,
-0.007307454477995634,
0.05136200785636902,
0.03283564746379852,
0.03286852315068245,
-0.00013136668712832034,
-0.04731132462620735,
-0.015610916540026665,
-0.02507537417113781,
0.012235396541655064,
-0.016693703830242157,
0.051734596490859985,
0.02167799510061741,
0.060008563101291656,
0.004826814401894808,
0.007806010544300079,
0.01923280954360962,
0.02780124731361866,
-0.07036413252353668,
0.01375630497932434,
-0.008835050277411938,
-0.01690186932682991,
-0.011573664844036102,
0.017290489748120308,
-0.04078495502471924,
-0.029311509802937508,
-0.003808678826317191,
-0.044783059507608414,
-0.00032668988569639623,
-0.03923223912715912,
-0.020611198619008064,
-0.04994844272732735,
-0.045594289898872375,
-0.026763608679175377,
0.014305777847766876,
0.020827636122703552,
-0.029537877067923546,
-0.01132823433727026,
0.0016256055096164346,
-0.046717580407857895,
-0.0003536373842507601,
-0.027449950575828552,
0.04047367721796036,
0.019141316413879395,
0.04134460911154747,
0.04833722859621048,
-0.005859581287950277,
-0.009405781514942646,
0.03330050781369209,
0.0393112376332283,
0.06435380131006241,
0.010138344950973988,
-0.027376357465982437,
-0.0072254217229783535,
-0.001897825626656413,
-0.00906512700021267,
0.00931604579091072,
0.05981054902076721,
0.010271955281496048,
0.013263482600450516,
0.02550576813519001,
-0.004081843886524439,
-0.00554695213213563,
0.035424165427684784,
0.011040041223168373,
0.03417135402560234,
-0.006539070047438145,
-0.03373599052429199,
0.027047550305724144,
0.00017687943181954324,
0.010168724693357944,
0.006148048676550388,
0.0224893931299448,
0.02261347882449627,
0.0044863237999379635,
-0.009189383126795292,
0.012592866085469723,
-0.0027429384645074606,
-0.0001335534470854327,
0.010236645117402077,
-0.02545027993619442,
0.00236885785125196,
0.0054488228633999825,
-0.004955872893333435,
0.00949124712496996,
0.06426233798265457,
-0.0022119174245744944,
0.027061546221375465,
-0.0724000632762909,
0.04107113182544708,
0.0669214054942131,
0.05694282054901123,
-0.014355182647705078,
-0.03084142878651619,
-0.016241293400526047,
0.02786029316484928,
-0.00564216636121273,
-0.01639978401362896,
0.03696243837475777,
-0.0026949408929795027,
-0.0230695977807045,
-0.006348638329654932,
-0.04279366135597229,
-0.05652579665184021,
0.020687276497483253,
0.008376605808734894,
0.049341633915901184,
-0.026949690654873848,
-0.04768930748105049,
0.013136405497789383,
0.03109927661716938,
0.05703640729188919,
0.03902079164981842,
0.010255526751279831,
-0.03297026455402374,
-0.004124966915696859,
0.02485540509223938,
-0.021918656304478645,
-0.0784534364938736,
-0.012833875603973866,
0.03200925886631012,
-0.01801033318042755,
0.06571739912033081,
-0.008125574328005314,
-0.03975897654891014,
0.008247732184827328,
0.014159434475004673,
-0.011169347912073135,
-0.009169786237180233,
-0.006207279860973358,
-0.003156394697725773,
0.03324658423662186,
-0.009665981866419315,
0.05552692711353302,
0.05984451249241829,
-0.0561470091342926,
0.016033532097935677,
-0.00447458541020751,
0.051911842077970505,
-0.018172696232795715,
-0.018284939229488373,
-0.020552877336740494,
-0.01618075557053089,
-0.04415962100028992,
0.056321706622838974,
-0.035696398466825485,
-0.015734927728772163,
0.025863295421004295,
-0.032541338354349136,
-0.016299888491630554,
0.01363306026905775,
-0.04149327054619789,
0.009654324501752853,
-0.06082916259765625,
0.03373883664608002,
-0.019112635403871536,
0.0030438120011240244,
0.03082427568733692,
0.03560405969619751,
0.008560938760638237,
0.021727770566940308,
-0.02304241433739662,
0.014429313130676746,
-0.02616174891591072,
0.014180587604641914,
-0.012772014364600182,
-0.024100525304675102,
0.06177021563053131,
-0.004091235809028149,
0.002140444004908204,
0.011972653679549694,
-0.06684625148773193,
-0.04123971238732338,
0.034684013575315475,
-0.039864540100097656,
0.01537175104022026,
-0.0320848748087883,
0.02295657992362976,
0.0046489364467561245,
-0.001094314968213439,
-0.058356501162052155,
-0.0654853954911232,
0.004538821522146463,
0.05405417084693909,
0.008297543972730637,
-0.004189777188003063,
-0.006209447514265776,
-0.07133704423904419,
-0.028909415006637573,
0.0022613208275288343,
0.03760084882378578,
-0.03187190741300583,
0.03342987596988678,
0.044851697981357574,
-0.012712552212178707,
0.026596713811159134,
0.013035401701927185,
-0.02287714183330536,
0.022025838494300842,
-0.004039234481751919,
0.009605497121810913,
0.011680633760988712,
0.03418637439608574,
0.012596719898283482,
-0.05569809302687645,
-0.009089779108762741,
0.004338580183684826,
0.016861621290445328,
-0.026199104264378548,
-0.0017760992050170898,
0.06328147649765015,
0.01821388676762581,
-0.0057091792114079,
-0.014681252650916576,
0.04194208234548569,
-0.00046390853822231293,
0.04392080754041672,
0.012496515177190304,
-0.012345448136329651,
-0.022665586322546005,
-0.0669577494263649,
0.012234123423695564,
0.0031682117842137814,
0.022595679387450218,
-0.007212079130113125,
0.05964916571974754,
0.006652706302702427,
0.012890000827610493,
0.03469909355044365,
0.009147652424871922,
0.018348464742302895,
-0.05627187341451645,
0.02399151399731636,
0.02342825196683407,
0.015164007432758808,
-0.0065040974877774715,
-0.04593997821211815,
-0.02993098273873329,
-0.02481871470808983,
0.05274935066699982,
-0.008270933292806149,
0.04034570977091789,
0.009796437807381153,
-0.009016205556690693,
-0.010097749531269073,
-0.009860383346676826,
-0.014131053350865841,
0.028504660353064537,
-0.0023234218824654818,
0.016936169937253,
0.013921410776674747,
0.021084602922201157,
0.021053090691566467,
0.054692767560482025,
-0.0375496968626976,
0.00757264019921422,
0.04616696015000343,
0.052294518798589706,
0.03517190366983414,
-0.04050389304757118,
-0.04767770320177078,
0.02350570447742939,
-0.07721851766109467,
-0.006632143631577492,
0.040442705154418945,
0.0015445150202140212,
0.029970286414027214,
0.03543543070554733,
0.030266325920820236,
-0.0068338713608682156,
-0.028833825141191483,
-0.05372337996959686,
0.013846850953996181,
-0.029579145833849907,
-0.0077799479477107525,
-0.027908891439437866,
0.006008616182953119,
0.034385547041893005,
-0.012836840003728867,
-0.004645149689167738,
0.006930219475179911,
-0.06830641627311707,
-0.04098719358444214,
-0.03222249820828438,
-0.010288144461810589,
0.07531395554542542,
-0.016971420496702194,
-0.02847112901508808,
0.003037781920284033,
-0.02711138129234314,
0.04326087236404419,
0.03222782537341118,
0.042872264981269836,
0.001289402018301189,
-0.01713903807103634,
-0.04143261909484863,
-0.005678756628185511,
-0.022519689053297043,
-0.006454323884099722,
0.1065102219581604,
0.03764877840876579,
0.02794840559363365,
-0.03501496836543083,
-0.012460609897971153,
-0.05095306783914566,
0.017826365306973457,
-0.0034458492882549763,
0.0032330667600035667,
-0.04002099111676216,
0.023221638053655624,
0.002611241303384304,
0.04022848233580589,
0.031010784208774567,
-0.01124715618789196,
0.01505583431571722,
-0.05090669170022011,
-0.03680097311735153,
0.029323680326342583,
0.0198341254144907,
0.010965980589389801,
0.033661339432001114,
-0.0803285464644432,
-0.015565607696771622,
-0.06225502863526344,
0.013384228572249413,
-0.022072693333029747,
-0.04356454685330391,
0.01595831662416458,
0.012285829521715641,
-0.029041431844234467,
-0.03206432983279228,
0.0023488877341151237,
0.0028877651784569025,
-0.06666684150695801,
0.029718751087784767,
0.05462303385138512,
0.0065594809129834175,
-0.0028659584932029247,
0.02711903676390648,
0.033058471977710724,
0.004986737389117479,
0.02272462658584118,
0.004830827470868826,
-0.05466306954622269,
-0.005217834375798702,
-0.02873545140028,
0.037409014999866486,
0.002967637963593006,
0.02854345366358757,
-0.006731439381837845,
0.016628222540020943,
-0.007976814173161983,
-0.03572354093194008,
-0.012032882310450077,
-0.027435924857854843,
0.013757781125605106,
-0.023244595155119896,
0.0026026363484561443,
-0.017818333581089973,
0.051321037113666534,
0.018612146377563477,
0.008236238732933998,
-0.009673718363046646,
0.013032527640461922,
0.00828057061880827,
-0.009652332402765751,
0.034406878054142,
-0.010332662612199783,
-0.02660362422466278,
-0.007814381271600723,
-0.025958925485610962,
-0.02747303992509842,
-0.024982240051031113,
0.0375215969979763,
0.04001513868570328,
0.02825549617409706,
0.008871983736753464,
0.0011211944511160254,
-0.022237425670027733,
-0.06579302996397018,
0.03265756741166115,
-0.012479376047849655,
-0.0477592758834362,
-0.0015552527038380504,
0.018392812460660934,
0.013196627609431744,
0.015059256926178932,
0.014376156032085419,
-0.004810793325304985,
0.006790095008909702,
0.019804706797003746,
0.001296631875447929,
-0.0386849008500576,
-0.009799991734325886,
0.001509734196588397,
0.013814390636980534,
-0.020464837551116943,
0.006043476052582264,
0.02095205895602703,
-0.012806588783860207,
-0.009478568099439144,
0.0005133640952408314,
0.030700374394655228,
0.0007682076538912952,
-0.041836511343717575,
0.023690588772296906,
-0.002430647611618042,
-0.00011456949869170785,
0.03675183281302452,
0.010212562046945095,
-0.00755231361836195,
-0.02457507699728012,
-0.02629379741847515,
-0.0011758935870602727,
-0.011552219279110432,
-0.0014540315605700016,
-0.023336276412010193,
-0.003505847416818142,
-0.025544490665197372,
0.013749738223850727,
-0.035523492842912674,
-0.013011457398533821,
-0.06175502762198448,
0.017217392101883888,
0.024570517241954803,
-0.0015905824257060885,
0.01742524467408657,
0.013676046393811703,
-0.033125340938568115,
-0.018458371981978416,
0.04490215331315994,
0.04437020793557167,
-0.003267521969974041,
0.004510112106800079,
0.020134801045060158,
-0.008153180591762066,
0.05616265535354614,
0.007538780570030212,
-0.010815536603331566,
0.027484484016895294,
-0.03505667299032211,
-0.012173205614089966,
0.02638889104127884,
-0.04092041775584221,
0.021126847714185715,
0.053498607128858566,
0.016437938436865807,
-0.0224663857370615,
0.05824979767203331,
0.012758375145494938,
0.006075493525713682,
-0.009348800405859947,
-0.02729826048016548,
-0.014247342012822628,
0.0003684266994241625,
0.04614287242293358,
-0.01818830892443657,
-0.02216978929936886,
0.01684621535241604,
0.00698856171220541,
0.02363460510969162,
-0.02625868283212185,
-0.013600535690784454,
0.0029011506121605635,
0.002018322702497244,
0.025562649592757225,
0.0007320891600102186,
0.023768676444888115,
0.03908238187432289,
-0.03377850353717804,
0.03864303603768349,
0.026491153985261917,
0.004699213895946741,
-0.10125669836997986,
-0.00576432328671217,
-0.00419759564101696,
0.00463500153273344,
0.03571746125817299,
-0.04420451447367668,
0.026061315089464188,
0.015777191147208214,
-0.09551569819450378,
-0.009611527435481548,
0.01442958414554596,
0.0027270361315459013,
0.00964167807251215,
0.03667313978075981,
-0.025900930166244507,
0.035396113991737366,
-0.006080513820052147,
0.027157362550497055,
-0.022277172654867172,
0.02348397672176361,
-0.007193891331553459,
-0.0032185802701860666,
-0.06286508589982986,
0.03278927505016327,
-0.0013498772168532014,
0.005386686883866787,
0.07034779340028763,
-0.018561551347374916,
-0.008964905515313148,
-0.013011394068598747,
-0.017855996266007423,
0.022691361606121063,
-0.016505446285009384,
-0.0027866584714502096,
0.006214578170329332,
0.025787003338336945,
0.02437346801161766,
-0.024314813315868378,
-0.025984635576605797,
0.026892784982919693,
-0.005482671316713095,
0.03430533409118652,
0.011586114764213562,
0.0007999486406333745,
0.01211409829556942,
-0.050464510917663574,
-0.013477232307195663,
0.02887830324470997,
-0.008997646160423756,
-0.008301615715026855,
0.011367217637598515,
0.04405803605914116,
0.017366835847496986,
-0.002893387572839856,
0.011857402510941029,
-0.07929589599370956,
-0.010563483461737633,
-0.021010858938097954,
0.01943255588412285,
0.004824036732316017,
0.012025102972984314,
0.022321121767163277,
-0.05086497589945793,
-0.009139911271631718,
-0.009738963097333908,
0.0020494472701102495,
-0.022275039926171303,
0.028872501105070114,
0.03392212465405464,
0.007991799153387547,
-0.010015160776674747,
-0.026071671396493912,
-0.0637335330247879,
0.026188265532255173,
-0.006414185743778944,
0.01178896427154541,
0.005839969031512737,
-0.0455971397459507,
-0.008052397519350052,
-0.06558152288198471,
0.0279243141412735,
-0.020557597279548645,
0.018872667104005814,
-0.04023972153663635,
-0.0018530497327446938,
0.012128980830311775,
0.032947879284620285,
0.05200686305761337,
-0.019477669149637222,
-0.024174513295292854,
0.03343850374221802,
-0.026091009378433228,
0.000815159291960299,
-0.059507664293050766,
0.0001063533200067468,
-0.0062460945919156075,
-0.005636353045701981,
-0.012332669459283352,
0.0049118478782474995,
-0.04468262195587158,
-0.002757190726697445,
0.014401917345821857,
-0.0027652003336697817,
0.00035021037911064923,
-0.023907190188765526,
-0.010596253909170628,
0.07883717119693756,
-0.000002013879338846891,
0.021106775850057602,
0.05664222687482834,
0.012298991903662682,
0.03526577726006508,
0.0392095148563385,
-0.038359057158231735,
-0.011706381104886532,
0.017023714259266853,
-0.03992080315947533,
-0.00621320866048336,
-0.0004863041976932436,
-0.015732230618596077,
0.042067598551511765,
-0.0012376998784020543,
0.013214089907705784,
0.024214832112193108,
-0.049553994089365005,
0.0025909265968948603,
0.025453832000494003,
0.015225807204842567,
0.02936183474957943,
0.01586376503109932,
0.03218797594308853,
0.0035188014153391123,
0.0018081835005432367,
-0.022682281211018562,
0.0637301430106163,
0.025341030210256577,
0.03357761353254318,
0.02743750996887684,
0.02614615671336651,
-0.007371626328676939,
-0.0017990684136748314,
0.0069105783477425575,
-0.009069486521184444,
-0.024982715025544167,
0.006200249772518873,
0.0099504254758358,
0.050549548119306564,
-0.0029434794560074806,
-0.017389681190252304,
-0.0018942032475024462,
0.05929233878850937,
-0.05436033383011818,
0.022390829399228096,
-0.025936538353562355,
0.018019992858171463,
0.02692527510225773,
0.0411643423140049,
-0.012141238898038864,
0.0630917027592659,
0.021085349842905998,
-0.0032786824740469456,
-0.048723362386226654,
-0.014130859635770321,
-0.0015878159319981933,
-0.03784189000725746,
0.018766233697533607,
-0.015465686097741127,
-0.032393939793109894,
0.0030647502280771732,
-0.001037186710163951,
0.012825715355575085,
-0.02863311767578125,
-0.0035979715175926685,
0.01962444745004177,
0.014333253726363182,
-0.010393957607448101,
0.0036301829386502504,
-0.03435130789875984,
0.03657382354140282,
-0.05156886205077171,
-0.0014395472826436162,
-0.023184822872281075,
0.05616013705730438,
-0.012667132541537285,
-0.002609455259516835
] |
<p>For years I have been very fascinated by the "mystery" aspect of gravity. Functionally, we understand it perfectly for our all applications, but in my (limited to undergrad General Physics 3 quarters) understanding, we don't know WHY it exists or HOW the "pull" works. </p>
<p>I'm very sorry for what is surely trite pop-science term use, but, to provide an example of what I mean: there has to be SOME "measurable material" of gravity between say the earth and the moon -- some kind of 'graviton' (not that it needs to be a particle or anything, I have <em>zero</em> claims as to the nature of how gravity does what it does). The [butchered] saying of "pluck a flower and move the furthest moon," because gravity in theory, has an infinite range (?) and moving a flower on earth could maybe move an atom on jupiter ever so slightly (?)."</p>
<p>Anyway, similar to how we had "very good" hypotheses about the existence of higgs-boson that the LHC 99%+ confirmed, do we have any "very good" hypotheses in regards to the fundamental way how gravity does what we have long-known it to do?</p> | 4,567 | [
-0.01685478538274765,
-0.012923764996230602,
0.02235458977520466,
-0.043473195284605026,
0.006917527876794338,
0.034176308661699295,
0.004909921437501907,
-0.005365436431020498,
0.015733640640974045,
-0.04945511743426323,
-0.0012412312207743526,
0.04293830320239067,
0.031222669407725334,
0.009141121059656143,
0.008800219744443893,
0.005608388688415289,
-0.002713823923841119,
-0.027320045977830887,
-0.02742384932935238,
-0.03130283206701279,
-0.009179691784083843,
0.05324530974030495,
-0.03234057500958443,
0.0057885777205228806,
0.00340078747831285,
-0.022913863882422447,
0.009473624639213085,
0.011162110604345798,
0.0026040091179311275,
0.06700051575899124,
0.0029539475217461586,
0.012250988744199276,
-0.01798289455473423,
0.03854645788669586,
0.03724829852581024,
0.018566083163022995,
-0.00995610747486353,
-0.014669349417090416,
0.014144632034003735,
0.014078681357204914,
-0.0483848936855793,
-0.02770112082362175,
-0.028680525720119476,
0.033035364001989365,
-0.03071722388267517,
0.01368231512606144,
0.03151837736368179,
0.003323130775243044,
0.07536151260137558,
-0.08661400526762009,
0.03950842097401619,
0.031490277498960495,
0.033698976039886475,
0.025338971987366676,
-0.015013908967375755,
-0.02601039595901966,
0.06922738254070282,
0.04191560298204422,
-0.03419329598546028,
-0.07971814274787903,
-0.029532350599765778,
-0.005325400270521641,
-0.011616441421210766,
-0.025218691676855087,
-0.011232007294893265,
0.056751642376184464,
-0.023549677804112434,
-0.02866140380501747,
0.05036522075533867,
-0.006972034927457571,
0.024542905390262604,
0.02343505434691906,
0.026683490723371506,
0.037957511842250824,
0.011906695552170277,
-0.023162707686424255,
0.010786781087517738,
-0.019340502098202705,
0.008015510626137257,
0.03340690955519676,
-0.011307244189083576,
0.009560042060911655,
0.046911049634218216,
0.04814505577087402,
0.010421843267977238,
-0.0018220219062641263,
0.06668076664209366,
-0.03512369468808174,
-0.02038937248289585,
0.06798528879880905,
-0.03872264176607132,
-0.0020391226280480623,
0.015406105667352676,
0.003375898813828826,
-0.023546375334262848,
0.022386372089385986,
0.004247694741934538,
0.04336920008063316,
-0.0034726678859442472,
-0.01959572546184063,
-0.006825918331742287,
-0.020385507494211197,
-0.0040581864304840565,
0.08171870559453964,
-0.01680648885667324,
-0.013760555535554886,
-0.010998912155628204,
0.01695205643773079,
-0.012666602618992329,
0.019140012562274933,
-0.02421651966869831,
0.004666394554078579,
0.00843727681785822,
-0.037583403289318085,
0.021776456385850906,
-0.005063151475042105,
0.01862380839884281,
-0.043923862278461456,
0.05254150182008743,
0.053906120359897614,
0.039843060076236725,
-0.01793726533651352,
0.013214437291026115,
-0.04007299244403839,
-0.021406300365924835,
0.004577273968607187,
0.06718278676271439,
-0.030217867344617844,
-0.022050173953175545,
0.015711188316345215,
0.022075604647397995,
0.0304576326161623,
-0.023320773616433144,
-0.0005295979208312929,
0.05380582436919212,
-0.021795885637402534,
-0.07900390774011612,
-0.055401869118213654,
0.07122528553009033,
0.0344214141368866,
-0.029552653431892395,
-0.04382450506091118,
-0.023073453456163406,
0.020240621641278267,
0.0697946697473526,
0.0023165952879935503,
-0.0008834670879878104,
-0.019978223368525505,
0.030793599784374237,
0.02179836295545101,
-0.013823830522596836,
-0.019694646820425987,
0.03622746467590332,
-0.024932490661740303,
-0.010232674889266491,
-0.0994361862540245,
0.008970998227596283,
-0.005416302941739559,
-0.008223295211791992,
-0.02610459178686142,
0.08237775415182114,
0.014191492460668087,
0.015596195124089718,
-0.004730866756290197,
-0.01135085616260767,
-0.022129923105239868,
0.06789285689592361,
0.005595831666141748,
-0.00842027086764574,
0.05522065982222557,
0.014269180595874786,
0.03356712684035301,
0.012770346365869045,
0.022432059049606323,
0.00714838644489646,
-0.07936841994524002,
-0.030511775985360146,
-0.029800334945321083,
0.0036735006142407656,
-0.012780704535543919,
-0.0036940802820026875,
-0.025814538821578026,
0.00695156492292881,
-0.007421552203595638,
-0.016879351809620857,
0.01826629973948002,
-0.008427273482084274,
-0.03494212403893471,
0.03640902414917946,
-0.039164721965789795,
0.01378756482154131,
-0.06820615381002426,
-0.008474127389490604,
-0.01949615590274334,
-0.014957387931644917,
0.029039235785603523,
0.010054465383291245,
0.006814842112362385,
-0.05454776808619499,
-0.044517695903778076,
-0.004451168701052666,
0.030846845358610153,
-0.005903469864279032,
0.009654965251684189,
0.01744779571890831,
0.04859430342912674,
0.019999142736196518,
0.003473892342299223,
0.009588108398020267,
-0.021432410925626755,
-0.04574594646692276,
0.01864614151418209,
-0.006896733306348324,
0.02531670778989792,
0.0027040906716138124,
0.0561286062002182,
-0.004158013965934515,
-0.0066644735634326935,
-0.00990021601319313,
0.04138032719492912,
-0.05224484205245972,
0.07985346019268036,
0.04251556843519211,
0.02936515212059021,
-0.0008304240182042122,
0.06115477904677391,
0.0014074157224968076,
-0.008746016770601273,
-0.016780061647295952,
-0.014012816362082958,
-0.060710206627845764,
-0.03784087672829628,
0.027311161160469055,
0.037595417350530624,
0.01151643693447113,
0.006438372191041708,
0.01840054802596569,
0.054645176976919174,
-0.0008596600382588804,
0.016082629561424255,
-0.01316425483673811,
-0.01661241240799427,
0.023158088326454163,
0.020820071920752525,
0.007386243902146816,
0.041491203010082245,
0.06209952384233475,
0.028538940474390984,
-0.006152402143925428,
0.001110771088860929,
-0.031195316463708878,
0.021562686190009117,
0.03143714368343353,
0.01975676231086254,
0.007883691228926182,
-0.0009078283910639584,
0.0447445884346962,
-0.03238871321082115,
0.0025384093169122934,
0.021555989980697632,
-0.0019327271729707718,
-0.008989638648927212,
-0.054583583027124405,
-0.019268609583377838,
0.008711786940693855,
0.013742631301283836,
0.01206557173281908,
0.0051635513082146645,
0.02971712313592434,
-0.04535872861742973,
-0.01268740464001894,
-0.01501515693962574,
-0.0264588575810194,
-0.019325997680425644,
0.028329772874712944,
-0.01908298209309578,
0.028781689703464508,
0.048506494611501694,
-0.018490351736545563,
-0.02118539623916149,
0.03894779831171036,
-0.019393352791666985,
0.01027444377541542,
0.043782636523246765,
-0.04241633415222168,
0.02115965075790882,
-0.03700893744826317,
0.0020758924074470997,
0.059334687888622284,
-0.013359139673411846,
0.021066002547740936,
0.0027610203251242638,
-0.029926370829343796,
-0.013712395913898945,
-0.003665883094072342,
-0.05007581040263176,
0.01882488839328289,
-0.029944730922579765,
0.019147424027323723,
0.02273288182914257,
-0.019778147339820862,
-0.048122286796569824,
0.016625571995973587,
-0.04160380735993385,
-0.03797571733593941,
-0.002568978350609541,
0.00973370112478733,
-0.00854828953742981,
-0.030409356579184532,
0.0062746391631662846,
0.0036355897318571806,
-0.054598744958639145,
0.014725219458341599,
-0.05496557429432869,
-0.03910414129495621,
0.022665010765194893,
-0.00852216873317957,
0.018055396154522896,
-0.010577639564871788,
-0.0036928250920027494,
0.08519180119037628,
0.011445942334830761,
0.00845117773860693,
-0.02898586168885231,
0.0104089779779315,
0.0046716537326574326,
0.008808143436908722,
0.046680014580488205,
0.019973047077655792,
0.02733611688017845,
0.03209944814443588,
0.02383788302540779,
0.041082713752985,
-0.017626259475946426,
0.04463465139269829,
0.0023515510838478804,
0.029181737452745438,
0.004604588262736797,
0.004334256052970886,
0.030025223270058632,
0.03960181027650833,
-0.02320445328950882,
0.0021013119257986546,
-0.00580779230222106,
0.011717216111719608,
0.006491078995168209,
-0.035969797521829605,
0.06435311585664749,
0.033777087926864624,
0.008351931348443031,
0.006316178012639284,
-0.015746433287858963,
-0.0444054938852787,
-0.02364458702504635,
0.0169728584587574,
-0.007489120587706566,
0.03699032962322235,
0.03760319575667381,
-0.008226897567510605,
0.02269899658858776,
0.047941967844963074,
-0.036779362708330154,
-0.03356822952628136,
-0.035690147429704666,
-0.014764174818992615,
-0.008249708451330662,
0.010402325540781021,
0.03467453271150589,
0.02835937961935997,
0.05390268191695213,
0.02679367922246456,
-0.0032280373852699995,
-0.03615199401974678,
-0.030132105574011803,
-0.052820947021245956,
-0.019963417202234268,
-0.004020861815661192,
0.045619454234838486,
-0.018273230642080307,
0.030642567202448845,
0.033654600381851196,
0.04325994849205017,
0.0019442288903519511,
0.019035007804632187,
-0.13211111724376678,
0.02665111981332302,
-0.0746249184012413,
-0.02368926629424095,
-0.012116494588553905,
0.0023531292099505663,
0.010888587683439255,
-0.013450748287141323,
-0.036512553691864014,
-0.029987527057528496,
0.02124897949397564,
-0.07357019931077957,
0.02441665716469288,
-0.017382970079779625,
-0.05715569853782654,
-0.005903113633394241,
0.0035176845267415047,
0.030917992815375328,
-0.012181028723716736,
0.0021047519985586405,
0.006900606211274862,
-0.000918534817174077,
-0.006197978276759386,
-0.009254084900021553,
0.0071130418218672276,
0.013704461045563221,
0.011465062387287617,
0.007342535071074963,
0.029542429372668266,
-0.033981405198574066,
0.0011372460285201669,
0.010497055947780609,
0.052778396755456924,
0.0010509061394259334,
0.008198174647986889,
-0.008145790547132492,
-0.05416712537407875,
-0.027246003970503807,
0.014007906429469585,
0.05845024436712265,
-0.0003541421901900321,
-0.012538519687950611,
0.018687454983592033,
0.012445603497326374,
-0.003275931114330888,
0.03223234415054321,
0.04438917711377144,
0.004807610530406237,
-0.05257580056786537,
-0.01046158280223608,
-0.04211732745170593,
-0.034772761166095734,
0.0029072309844195843,
0.00843963585793972,
-0.023030688986182213,
-0.05243288725614548,
0.016285130754113197,
0.009020077995955944,
0.017546946182847023,
-0.024950340390205383,
-0.05106252431869507,
-0.005025725811719894,
0.06075546145439148,
-0.02980419248342514,
0.03417413309216499,
0.017031827941536903,
0.04313753545284271,
0.0311278086155653,
0.014076805673539639,
0.01426348090171814,
-0.08309489488601685,
-0.005650117993354797,
0.05043726786971092,
0.03120484948158264,
-0.025786537677049637,
-0.008756419643759727,
-0.027868008241057396,
-0.018813950940966606,
0.025886496528983116,
-0.013286089524626732,
0.002351384377107024,
-0.024747563526034355,
-0.0008397079072892666,
-0.01526319608092308,
-0.011046788655221462,
-0.0007955916807986796,
0.015832120552659035,
-0.035159677267074585,
-0.0012770614121109247,
-0.02486230805516243,
0.023647591471672058,
-0.02802249975502491,
0.07594160735607147,
0.013509250245988369,
0.017671486362814903,
0.027626771479845047,
0.010983659885823727,
-0.0046932813711464405,
-0.021486788988113403,
-0.038166385143995285,
-0.1164407730102539,
-0.024442994967103004,
0.008331147022545338,
-0.04162963852286339,
0.05594101548194885,
-0.012898057699203491,
-0.06314755231142044,
-0.0018619681941345334,
-0.003838845994323492,
0.005460564978420734,
0.017043787986040115,
-0.03760669007897377,
0.015745731070637703,
0.060719095170497894,
0.04321017861366272,
0.022485075518488884,
0.02027592435479164,
-0.029534338042140007,
0.009686692617833614,
-0.010033570230007172,
0.03945423290133476,
-0.02913057431578636,
0.006471082102507353,
-0.017112066969275475,
-0.009950421750545502,
-0.04698166996240616,
0.02944348007440567,
0.019656090065836906,
-0.002572419820353389,
0.0024980525486171246,
-0.06253354996442795,
-0.028530819341540337,
0.04198303446173668,
0.02769593894481659,
0.016732674092054367,
0.030075592920184135,
0.020188888534903526,
-0.0003273084294050932,
-0.020394867286086082,
-0.01429669838398695,
0.06130462884902954,
-0.018194740638136864,
0.017905376851558685,
0.021876726299524307,
0.0027282959781587124,
-0.014987228438258171,
-0.013360681012272835,
0.035001013427972794,
-0.029443642124533653,
0.07994667440652847,
-0.008864437229931355,
-0.006686506327241659,
0.027409875765442848,
-0.047324053943157196,
-0.039410848170518875,
0.0001388640230288729,
0.010867116041481495,
0.029225368052721024,
-0.01887558586895466,
-0.008581072092056274,
0.0019434469286352396,
0.009490658529102802,
-0.07271409034729004,
-0.03730490803718567,
0.014417861588299274,
0.022898206487298012,
-0.03493792563676834,
-0.027950890362262726,
0.022374887019395828,
-0.047242239117622375,
-0.01165483333170414,
-0.008647359907627106,
0.03158336132764816,
-0.04527760669589043,
0.00920360442250967,
0.02604108676314354,
0.015389669686555862,
0.047395702451467514,
-0.015309450216591358,
-0.03326703608036041,
0.02068008854985237,
0.027361279353499413,
0.01612251251935959,
0.017415111884474754,
0.04726187512278557,
-0.019269747659564018,
-0.022912461310625076,
-0.018510183319449425,
-0.007137583568692207,
-0.007945319637656212,
-0.04025738313794136,
0.011609452776610851,
0.06558683514595032,
0.021951111033558846,
0.004406406078487635,
-0.014925595372915268,
0.016001280397176743,
-0.010586416348814964,
0.012503387406468391,
-0.011734986677765846,
0.022139299660921097,
0.003599250689148903,
-0.0504678338766098,
0.07286211848258972,
-0.01275512296706438,
-0.016084231436252594,
-0.0003645638353191316,
0.005186700262129307,
0.0291188545525074,
-0.0332195982336998,
0.019850408658385277,
0.018609274178743362,
0.002267098054289818,
-0.00668202992528677,
0.04440075159072876,
-0.004716387018561363,
-0.010556028224527836,
-0.040257181972265244,
-0.04072419926524162,
-0.01864522509276867,
-0.013241240754723549,
0.05694336071610451,
-0.003979827277362347,
0.05737634375691414,
0.029437657445669174,
-0.03439400717616081,
-0.025066612288355827,
-0.029549088329076767,
-0.016146434471011162,
-0.016411803662776947,
0.010788116604089737,
-0.014948124065995216,
-0.011906314641237259,
0.007763113360852003,
0.01933717355132103,
0.03668425232172012,
-0.05381978675723076,
-0.01785569079220295,
0.02533547952771187,
0.02836632914841175,
0.05478297919034958,
-0.009425066411495209,
-0.05372314155101776,
0.04351257160305977,
-0.01806960627436638,
0.06058308482170105,
0.0161431934684515,
-0.012203609570860863,
0.025067932903766632,
0.029368409886956215,
0.02002342976629734,
-0.01608157902956009,
-0.04754327982664108,
-0.04521998018026352,
0.0032435895409435034,
0.04744630306959152,
0.012680304236710072,
-0.002966057974845171,
-0.014607004821300507,
-0.0017391876317560673,
0.004669984336942434,
0.0016776691190898418,
-0.018501486629247665,
-0.09483844041824341,
-0.019317662343382835,
-0.026676779612898827,
-0.039887312799692154,
0.04821523278951645,
-0.005948385689407587,
-0.028807569295167923,
0.014655361883342266,
-0.04317720606923103,
0.009960681200027466,
0.04530535265803337,
0.01120829675346613,
-0.02249547839164734,
0.08042003959417343,
-0.0356430746614933,
0.018416961655020714,
-0.017164867371320724,
-0.009727222844958305,
0.11959177255630493,
0.0467563271522522,
-0.020510723814368248,
-0.053965386003255844,
0.0018536640563979745,
-0.036962538957595825,
-0.006237308029085398,
-0.01065815519541502,
0.026330625638365746,
-0.028057193383574486,
0.024262171238660812,
-0.0176725871860981,
0.05759108439087868,
-0.024233078584074974,
-0.02000187523663044,
0.05583275854587555,
-0.019179031252861023,
-0.037409376353025436,
0.0017711898544803262,
0.02954695001244545,
-0.005339310970157385,
0.006002196576446295,
-0.03231663629412651,
0.01859072595834732,
-0.03751276805996895,
0.006674743723124266,
-0.017738856375217438,
-0.04294447600841522,
0.006275300867855549,
-0.009757633320987225,
-0.05674838647246361,
0.008719243109226227,
0.011377637274563313,
-0.027955148369073868,
-0.028981605544686317,
0.025915004312992096,
0.013669757172465324,
-0.007834916934370995,
0.017870938405394554,
0.02973215840756893,
-0.02313903346657753,
0.0005953158834017813,
0.006570558995008469,
0.0011779696214944124,
-0.042015574872493744,
-0.010409635491669178,
0.004658771678805351,
0.08378612250089645,
-0.05740528181195259,
-0.02538057044148445,
0.019686441868543625,
-0.05168081447482109,
-0.01219209935516119,
-0.024984942749142647,
-0.008762309327721596,
-0.02944081462919712,
0.036179520189762115,
-0.005886994302272797,
-0.02508322335779667,
0.028928430750966072,
0.052400145679712296,
-0.015677545219659805,
0.03583178669214249,
0.00006279395165620372,
0.016726497560739517,
0.018221816048026085,
-0.007043641526252031,
0.048146963119506836,
0.006545227020978928,
-0.03352037072181702,
-0.037030819803476334,
-0.015275911428034306,
-0.04160742834210396,
0.017857197672128677,
-0.0018300500232726336,
0.02395152859389782,
0.0281363632529974,
0.000970378634519875,
-0.015526849776506424,
-0.00034642487298697233,
0.011536638252437115,
0.03452836722135544,
-0.03117767907679081,
-0.010044851340353489,
-0.063405841588974,
0.0037841193843632936,
0.006513484753668308,
0.03580198436975479,
0.02453821524977684,
-0.005464376416057348,
-0.00805133581161499,
0.019840899854898453,
-0.0019196821376681328,
-0.026053214445710182,
-0.030814433470368385,
-0.002041529631242156,
-0.006351326126605272,
0.001330518047325313,
0.0014312283601611853,
-0.01583033800125122,
0.02316897176206112,
0.018103064969182014,
-0.0011607302585616708,
-0.005789784248918295,
-0.02889997698366642,
0.024376660585403442,
0.037691012024879456,
-0.005479497369378805,
-0.017295820638537407,
0.0004401812911964953,
-0.007536953780800104,
-0.052069440484046936,
-0.03935622423887253,
-0.0263492651283741,
-0.0016092093428596854,
-0.02081967517733574,
0.059265587478876114,
-0.034621793776750565,
0.030575906857848167,
0.009831986390054226,
0.018350111320614815,
-0.057014890015125275,
0.03737824782729149,
-0.05355365201830864,
0.0015266583068296313,
-0.0063273711130023,
-0.011448297649621964,
0.006256823893636465,
0.03509780764579773,
-0.028600307181477547,
-0.034983452409505844,
0.00401689950376749,
0.017363866791129112,
-0.033684540539979935,
0.028547193855047226,
0.010551385581493378,
-0.03141115605831146,
0.02686699666082859,
0.0009247523848898709,
-0.004836102947592735,
0.04232215881347656,
-0.03147841617465019,
-0.04550880566239357,
0.022060606628656387,
-0.012516481801867485,
0.017214912921190262,
0.030177932232618332,
-0.053549591451883316,
-0.028358537703752518,
0.026614291593432426,
0.010889431461691856,
0.023977648466825485,
-0.03876740112900734,
-0.007023490499705076,
-0.038762275129556656,
0.007687629200518131,
0.013418404385447502,
-0.053530674427747726,
-0.007736186496913433,
0.032153110951185226,
-0.009380546398460865,
-0.004319401923567057,
0.0171042550355196,
0.011856433935463428,
-0.03360963240265846,
-0.022038275375962257,
0.014654113911092281,
-0.011321022175252438,
0.02078974060714245,
0.06654778867959976,
-0.06655509769916534,
0.03804520145058632,
0.043276842683553696,
0.01970997080206871,
-0.07875052839517593,
-0.008046935312449932,
-0.0002613072283565998,
-0.023018764331936836,
0.039049871265888214,
-0.05582219734787941,
0.006218066904693842,
-0.00577542046085,
-0.05511292442679405,
0.04063619300723076,
-0.027181493118405342,
-0.015711426734924316,
-0.0033615869469940662,
-0.011398994363844395,
0.009527618996798992,
0.05125606060028076,
0.05407141149044037,
0.054860856384038925,
-0.02582986280322075,
0.0014824753161519766,
0.006271349266171455,
0.012770825065672398,
-0.002379719400778413,
0.03409719839692116,
-0.015683654695749283,
0.021143682301044464,
0.07647012174129486,
-0.013205436058342457,
-0.0023416182957589626,
0.01967542991042137,
0.014128726907074451,
-0.0013362858444452286,
-0.012185581028461456,
-0.004796667490154505,
-0.008175658993422985,
0.057969775050878525,
0.015747861936688423,
-0.008781719021499157,
-0.003309705527499318,
0.018497059121727943,
0.00047608991735614836,
0.07060828804969788,
-0.007665399461984634,
0.014914222061634064,
-0.010034201666712761,
-0.04424114525318146,
-0.0076807765290141106,
-0.0031328205950558186,
-0.02285459265112877,
0.02924974076449871,
0.030130188912153244,
0.012780655175447464,
-0.008214276283979416,
0.012765610590577126,
0.004585911054164171,
-0.06446002423763275,
-0.02441463991999626,
0.01847490854561329,
0.04476860538125038,
-0.014920634217560291,
0.022880053147673607,
-0.018718749284744263,
0.012445115484297276,
-0.020494740456342697,
-0.009028660133481026,
0.009111360646784306,
-0.044936537742614746,
-0.010241606272757053,
0.002515525324270129,
0.01851283758878708,
0.01586732640862465,
-0.05623289570212364,
-0.031845781952142715,
0.05044010281562805,
0.007976456545293331,
0.019281452521681786,
-0.009082820266485214,
-0.03310799226164818,
0.023571614176034927,
-0.07132994383573532,
0.05936386436223984,
0.033529967069625854,
0.03710850328207016,
-0.022020863369107246,
-0.0335211381316185,
0.008725563995540142,
-0.01631242036819458,
0.03200226277112961,
-0.04401172697544098,
-0.0023716927971690893,
0.016440795734524727,
-0.001348609570413828,
0.02173398993909359,
-0.004490689840167761,
0.01568545214831829,
-0.004431096836924553,
-0.02779954858124256,
-0.00017989556363318115,
-0.016442203894257545,
-0.004370527341961861,
0.0048142047598958015,
0.030764279887080193,
-0.025614868849515915,
0.03894760087132454,
-0.020347511395812035,
-0.031684309244155884,
0.08157925307750702,
0.015703607350587845,
-0.017695220187306404,
0.05838419497013092,
-0.021780140697956085,
0.012797466479241848,
0.029857531189918518,
-0.017989754676818848,
-0.036993082612752914,
0.045235712081193924,
-0.030384480953216553,
-0.027531027793884277,
-0.02954619936645031,
-0.013483145274221897,
0.004359549377113581,
-0.01355999056249857,
-0.003879895433783531,
0.04329879581928253,
-0.04034866765141487,
-0.008386163972318172,
0.039753157645463943,
0.0025723427534103394,
0.04448472335934639,
-0.012205919250845909,
-0.03255460038781166,
0.025393061339855194,
0.00984431616961956,
-0.004353773780167103,
0.033158302307128906,
0.048651859164237976,
0.02413587085902691,
0.002754013519734144,
0.033242616802453995,
-0.017880599945783615,
-0.004426357336342335,
0.011107065714895725,
0.020852195098996162,
-0.05905228853225708,
-0.0345933735370636,
-0.0009783314308151603,
-0.013340224511921406,
0.03815742954611778,
0.023395726457238197,
-0.0275273397564888,
0.09190596640110016,
-0.006525310687720776,
-0.016674378886818886,
0.016385722905397415,
-0.007638194132596254,
0.04139639809727669,
-0.007741143926978111,
-0.014613163657486439,
0.03617203235626221,
0.009030519053339958,
0.01503145694732666,
-0.034559473395347595,
0.01921635866165161,
0.021069787442684174,
-0.02215168997645378,
0.015856172889471054,
-0.01218068040907383,
-0.013538425788283348,
0.002579836407676339,
-0.03280516341328621,
-0.06910393387079239,
-0.035634759813547134,
0.04843287542462349,
0.009645633399486542,
0.012591786682605743,
-0.025247149169445038,
-0.003802601248025894,
-0.044480495154857635,
0.060835208743810654,
-0.0724463015794754,
0.0074602533131837845,
-0.04711421951651573,
0.014359070919454098,
-0.018752751871943474,
-0.017671624198555946
] |
<p>Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it while not getting absorbed to the inside ? It's simple to understand how earth orbits the sun, but the black hole is something more energetic and at most pulls everything to it's center.
By looking to this image for example:
<img src="http://i.stack.imgur.com/MXn7W.jpg" alt="enter image description here"></p>
<p>If we follow the bright lines it looks like everything is really going to the true center like a vortex.
If you have any simple ways to enlighten me or any references to read I will be thankful, because sometimes I don't know what topic should I search for to find answers without posting questions like this one.</p>
<p>And also, would our galaxy run out of stars since the black hole devours them fast while they take too long to reproduce ?</p> | 4,568 | [
-0.034750230610370636,
-0.04572729021310806,
-0.0036064572632312775,
-0.029723210260272026,
0.06324373185634613,
-0.00852157361805439,
-0.009161863476037979,
-0.05619204416871071,
-0.010925783775746822,
-0.05450792238116264,
0.0009701840463094413,
0.05865169316530228,
0.04441073164343834,
0.011500723659992218,
-0.005220838822424412,
0.007377071306109428,
-0.01882260851562023,
-0.028868023306131363,
-0.032348550856113434,
-0.015497017651796341,
-0.008943265303969383,
0.021082520484924316,
-0.00435783201828599,
0.02595534361898899,
-0.0480739027261734,
0.028560003265738487,
0.022088967263698578,
0.014074343256652355,
0.021576466038823128,
0.04708284139633179,
0.0011962439166381955,
-0.010676221922039986,
0.010063791647553444,
0.04604863002896309,
0.02326565608382225,
0.015750424936413765,
-0.006934128236025572,
-0.0123891057446599,
-0.01176542416214943,
0.01150040328502655,
-0.04305044561624527,
-0.03044486604630947,
-0.027214789763092995,
0.05383434519171715,
-0.03326955810189247,
-0.03661700710654259,
-0.017128953710198402,
0.0030035050585865974,
0.030544009059667587,
-0.04977572709321976,
0.05668943375349045,
0.00854465365409851,
0.021818120032548904,
0.021012792363762856,
0.03190186619758606,
-0.011941959150135517,
0.1014564037322998,
0.06861767917871475,
-0.02950403094291687,
-0.05306418612599373,
-0.007372774183750153,
0.021092092618346214,
-0.04595623165369034,
-0.035222023725509644,
-0.011323065496981144,
0.047572579234838486,
-0.024439804255962372,
-0.025743097066879272,
0.03670201078057289,
0.030393416061997414,
-0.010668848641216755,
0.010233480483293533,
-0.017492832615971565,
-0.018007824197411537,
-0.0208030603826046,
-0.06116018816828728,
0.037031687796115875,
-0.019596287980675697,
0.027174290269613266,
0.027769794687628746,
-0.03914361074566841,
-0.0021721988450735807,
0.03331231325864792,
0.036868561059236526,
0.012814497575163841,
0.04241078346967697,
0.09235085546970367,
-0.01563950441777706,
0.0322357676923275,
0.018112443387508392,
-0.012985499575734138,
0.019384140148758888,
0.018536994233727455,
-0.013073970563709736,
-0.027968212962150574,
0.018194247037172318,
0.011558376252651215,
0.06677921861410141,
0.005512021016329527,
-0.020406460389494896,
0.017438998445868492,
0.03129434585571289,
-0.0010887815151363611,
0.07825765758752823,
0.029547255486249924,
-0.008288886398077011,
-0.1050383597612381,
0.014053908176720142,
-0.02229963429272175,
-0.020015794783830643,
-0.06505212187767029,
0.007418443914502859,
-0.004193924367427826,
-0.02652716636657715,
0.03235609829425812,
-0.0382465198636055,
0.013928238302469254,
-0.01965925469994545,
0.058544643223285675,
0.06414558738470078,
0.030003473162651062,
-0.02660646103322506,
0.027911266312003136,
-0.04248253256082535,
-0.052466824650764465,
0.05307517573237419,
0.03925871476531029,
0.0014779340708628297,
-0.049431212246418,
0.021497175097465515,
0.007069752085953951,
0.0033124787732958794,
-0.005052477587014437,
-0.017238544300198555,
0.04569413885474205,
-0.017459848895668983,
-0.09855379164218903,
-0.06316055357456207,
0.04396170377731323,
-0.011128759942948818,
-0.01397990994155407,
-0.03155778720974922,
-0.005068221595138311,
0.021196484565734863,
0.0988311916589737,
-0.008315939456224442,
-0.04108971729874611,
0.026413744315505028,
0.018571333959698677,
0.004964854568243027,
-0.008372947573661804,
0.0054932329803705215,
-0.021600978448987007,
-0.03606279939413071,
0.02239084616303444,
-0.09803345054388046,
0.034886956214904785,
0.017106708139181137,
0.038480617105960846,
-0.06991041451692581,
0.06054936721920967,
-0.0047712670639157295,
-0.0011156585533171892,
0.008186304941773415,
-0.01942369155585766,
-0.012016897089779377,
0.09153193980455399,
0.00959651730954647,
-0.0006374001386575401,
0.049815986305475235,
0.011972635984420776,
0.04541387781500816,
0.027207281440496445,
0.037678103893995285,
0.02735874615609646,
-0.044490739703178406,
0.016696834936738014,
-0.016225425526499748,
-0.009787827730178833,
-0.015008142217993736,
-0.034098800271749496,
-0.01870119385421276,
0.012797467410564423,
-0.014894225634634495,
0.012899727560579777,
0.06798072159290314,
-0.008644687943160534,
-0.03813115134835243,
-0.02298477478325367,
-0.029048340395092964,
0.009852664545178413,
-0.03836008533835411,
0.0064100525341928005,
-0.020982902497053146,
0.0016833465779200196,
0.0010489795822650194,
0.016497280448675156,
0.03206447511911392,
-0.032057445496320724,
-0.0315474197268486,
0.012053378857672215,
0.049857452511787415,
0.004673514980822802,
-0.007353898603469133,
0.018020501360297203,
0.030232740566134453,
0.027297979220747948,
-0.04021913558244705,
0.003473208285868168,
-0.012003202922642231,
-0.006107907276600599,
-0.011286819353699684,
-0.003822972998023033,
0.0046358597464859486,
-0.01052111852914095,
0.015267152339220047,
0.024417517706751823,
0.046365633606910706,
0.05611547827720642,
0.02843681536614895,
-0.0392112173140049,
0.10059485584497452,
-0.005402849521487951,
0.017514299601316452,
0.014573929831385612,
0.025617588311433792,
-0.005047780927270651,
-0.0011439059162512422,
-0.0035721624735742807,
-0.00396792171522975,
-0.057935215532779694,
0.023360662162303925,
0.04335620626807213,
-0.023752793669700623,
-0.02524609863758087,
0.007436302490532398,
0.0437869168817997,
0.034256402403116226,
0.027086881920695305,
0.0014801332727074623,
-0.016248535364866257,
-0.003213371615856886,
-0.04439212381839752,
0.001851455308496952,
0.0072390115819871426,
0.04201268404722214,
0.04502787068486214,
0.016469456255435944,
0.009380497969686985,
0.015243438072502613,
-0.01908666267991066,
0.07594024389982224,
0.024791063740849495,
0.011878788471221924,
0.012972218915820122,
-0.01460188813507557,
0.04187852144241333,
-0.022638503462076187,
0.003510803682729602,
0.0060295220464468,
-0.011438010260462761,
0.0018937005661427975,
-0.0372544564306736,
0.012991788797080517,
-0.00998822320252657,
0.03149133548140526,
-0.008183496072888374,
0.010975658893585205,
0.018395401537418365,
-0.030849626287817955,
0.042851682752370834,
-0.022880854085087776,
-0.0019489619880914688,
-0.058617208153009415,
0.02423430234193802,
0.014196105301380157,
0.017039522528648376,
-0.018436266109347343,
-0.01978939026594162,
-0.04838400334119797,
0.0036617484875023365,
-0.035022299736738205,
-0.022731086239218712,
0.03409818559885025,
-0.06300172209739685,
0.011792910285294056,
-0.031731173396110535,
-0.028056897222995758,
0.0645882710814476,
0.023663965985178947,
0.01228758879005909,
0.0013960053911432624,
-0.025723904371261597,
-0.04743292182683945,
0.023330681025981903,
-0.0036252618301659822,
0.027260437607765198,
-0.051990967243909836,
0.0020177762489765882,
0.0437297560274601,
-0.024268530309200287,
-0.027086040005087852,
0.043280601501464844,
-0.034019600600004196,
-0.06429719924926758,
-0.007135296240448952,
0.01704872027039528,
0.0065390728414058685,
-0.011811032891273499,
0.029235033318400383,
0.008186006918549538,
-0.03170366585254669,
0.010942613705992699,
-0.028014957904815674,
-0.015080365352332592,
0.012554598972201347,
0.01055656373500824,
0.009719655849039555,
-0.018645724281668663,
-0.024846207350492477,
0.053947094827890396,
0.016469668596982956,
-0.0047135129570961,
-0.03025469183921814,
-0.006541849114000797,
-0.0531538724899292,
-0.00008097617683233693,
0.032626938074827194,
0.014894622378051281,
0.00008083156717475504,
-0.010997369885444641,
0.011927702464163303,
0.0059756068512797356,
0.006760910619050264,
0.015966860577464104,
-0.03828052803874016,
0.015442819334566593,
-0.023266859352588654,
0.0017238998552784324,
0.053611405193805695,
-0.02148977480828762,
-0.059824321419000626,
0.03216572850942612,
-0.00871644914150238,
0.05457780137658119,
0.016753725707530975,
-0.03405235707759857,
0.026536833494901657,
-0.015120884403586388,
0.018579954281449318,
-0.014788460917770863,
0.003124009817838669,
0.01243471261113882,
0.009949413128197193,
0.013855197466909885,
-0.00032885250402614474,
0.07860355079174042,
0.03318443521857262,
-0.01156435813754797,
-0.018741372972726822,
-0.0016122058732435107,
-0.03199582174420357,
0.002515299478545785,
-0.02347921021282673,
-0.024356888607144356,
0.0029304090421646833,
-0.015169231221079826,
-0.008572272956371307,
0.03687066584825516,
0.03832998126745224,
0.02083038166165352,
-0.0024690839927643538,
-0.05371234193444252,
0.011743772774934769,
-0.09112443774938583,
-0.0017105629667639732,
-0.008222686126828194,
0.015586219727993011,
0.008835726417601109,
0.04466515779495239,
0.042403753846883774,
0.02347571775317192,
0.011520592495799065,
-0.006448666099458933,
-0.07498295605182648,
0.019693715497851372,
-0.02229302003979683,
-0.024913271889090538,
-0.01034934539347887,
-0.024429136887192726,
0.002282401779666543,
-0.002450656145811081,
-0.004081584047526121,
-0.008626752533018589,
-0.019838104024529457,
-0.02676800824701786,
0.0019447259837761521,
-0.03067300096154213,
-0.014699356630444527,
-0.02056187391281128,
0.035578515380620956,
0.03895415738224983,
-0.005570061970502138,
0.01561395451426506,
0.0020318948663771152,
-0.007059741765260696,
-0.034152764827013016,
-0.010439104400575161,
0.006842911243438721,
0.03047098219394684,
0.017024395987391472,
0.03477476164698601,
0.0020805958192795515,
-0.03458646684885025,
-0.03124089166522026,
0.035483527928590775,
0.021131938323378563,
-0.002993734320625663,
-0.018726656213402748,
-0.00012407693429850042,
-0.056559279561042786,
-0.023849569261074066,
-0.013840940780937672,
0.07296323776245117,
-0.007184033282101154,
0.027822356671094894,
0.05034203827381134,
-0.01570657640695572,
-0.012195847928524017,
0.013658755458891392,
0.04499882459640503,
-0.005756901111453772,
-0.03501486778259277,
-0.07372142374515533,
-0.04380850866436958,
-0.01852446421980858,
0.011228937655687332,
0.01688120700418949,
-0.013758797198534012,
-0.035999275743961334,
-0.007994595915079117,
0.017259936779737473,
0.0015202701324597,
-0.0021622206550091505,
-0.0018169661052525043,
-0.005456550512462854,
0.04939550533890724,
-0.03938448429107666,
0.02427275851368904,
0.013823168352246284,
0.04476061463356018,
0.06993620842695236,
0.003008844330906868,
0.01615327224135399,
-0.041418761014938354,
-0.022921640425920486,
0.045826736837625504,
0.04487431421875954,
-0.010699374601244926,
0.0006197100155986845,
-0.07518231123685837,
-0.015342723578214645,
0.05350920557975769,
-0.013896712101995945,
0.044000472873449326,
-0.014558163471519947,
-0.03338242694735527,
0.031202251091599464,
-0.00885718036442995,
-0.004502543713897467,
0.013215365819633007,
-0.04069214686751366,
0.021479396149516106,
-0.01583622209727764,
0.018897447735071182,
-0.03333711996674538,
0.0216139554977417,
0.008509732782840729,
0.023225676268339157,
0.017102831974625587,
-0.012681074440479279,
0.01867278479039669,
0.026276612654328346,
-0.03129909560084343,
-0.06511399149894714,
-0.007242561783641577,
-0.012084109708666801,
-0.06420693546533585,
0.04584818705916405,
-0.013933541253209114,
-0.04979220777750015,
0.021820764988660812,
0.014655706472694874,
-0.015053765848279,
0.0024831921327859163,
-0.0519443079829216,
-0.017350994050502777,
0.03292471542954445,
0.007920447736978531,
0.04272391274571419,
0.012869905680418015,
-0.005308343097567558,
-0.025894949212670326,
-0.04037650302052498,
0.021660251542925835,
-0.059796303510665894,
-0.008859749883413315,
-0.004409393761307001,
-0.014305687509477139,
-0.027763502672314644,
0.043881043791770935,
0.027229567989706993,
-0.008586453273892403,
-0.00044230319326743484,
-0.02346731536090374,
0.014186730608344078,
0.025332165881991386,
-0.017290279269218445,
0.004000606946647167,
-0.008201860822737217,
0.022194070741534233,
0.010811381042003632,
-0.03342338651418686,
0.010734803043305874,
-0.0012080268934369087,
-0.021883158013224602,
0.020058095455169678,
0.026284530758857727,
0.010704679414629936,
-0.02782384119927883,
-0.03083658218383789,
0.018380051478743553,
-0.0654856339097023,
0.07439000904560089,
-0.03284691274166107,
0.01526126079261303,
0.02757074497640133,
-0.07745718955993652,
-0.03327959030866623,
-0.01620507426559925,
-0.030936386436223984,
0.01875755563378334,
-0.011616023257374763,
0.0633353441953659,
0.024649836122989655,
0.015407661907374859,
-0.09694575518369675,
-0.029910413548350334,
0.040878452360630035,
0.009115432389080524,
-0.020711185410618782,
-0.030428126454353333,
0.04148545116186142,
-0.05223909392952919,
-0.019790168851614,
-0.018651168793439865,
0.006156920455396175,
-0.03045729361474514,
-0.009432782419025898,
0.015849323943257332,
-0.019229819998145103,
0.047870129346847534,
-0.012907298281788826,
-0.010856556706130505,
0.005963570438325405,
0.004092865157872438,
0.008333302102982998,
-0.013977333903312683,
0.06159808114171028,
-0.027613885700702667,
-0.04039609432220459,
-0.012029833160340786,
-0.004115269519388676,
0.02653958648443222,
-0.008897901512682438,
0.0083398362621665,
0.03454362228512764,
0.04373336583375931,
0.006434208247810602,
0.01124478131532669,
0.03153485432267189,
-0.008767944760620594,
0.005612607579678297,
0.007303598336875439,
0.013098206371068954,
0.019074460491538048,
-0.05392734706401825,
0.06625685095787048,
-0.017278553918004036,
-0.006764725781977177,
0.006581793539226055,
0.06328915059566498,
0.018575729802250862,
-0.00988109689205885,
0.0073370980098843575,
-0.018702199682593346,
0.027265790849924088,
0.014750763773918152,
0.018216906115412712,
-0.0019044261425733566,
0.04268870875239372,
-0.02482239343225956,
-0.01574375107884407,
-0.030397901311516762,
0.004490615800023079,
0.047731801867485046,
-0.004950177390128374,
0.009414407424628735,
-0.01502048410475254,
0.004289507400244474,
-0.023139161989092827,
-0.03767381235957146,
0.013282245956361294,
0.013383210636675358,
0.008701538667082787,
-0.0027100061997771263,
0.0007136512431316078,
-0.0010327870259061456,
0.05100825056433678,
0.04651518166065216,
-0.013026685453951359,
0.061476994305849075,
0.017308099195361137,
-0.027272796258330345,
0.051442962139844894,
0.023196682333946228,
-0.03368772938847542,
0.02552693523466587,
-0.012755273841321468,
0.056400034576654434,
0.00566325057297945,
-0.016941919922828674,
0.03911300003528595,
0.0017741587944328785,
0.016688557341694832,
-0.03376487269997597,
-0.038744013756513596,
-0.031423162668943405,
0.0015822026180103421,
-0.006739579141139984,
-0.004661141894757748,
-0.02165878750383854,
0.025418201461434364,
-0.00259319762699306,
0.019578393548727036,
0.0028079913463443518,
-0.03186797723174095,
-0.07374793291091919,
-0.03682629019021988,
-0.01669592596590519,
-0.0468120276927948,
0.05083712562918663,
0.020078707486391068,
-0.03423469513654709,
0.002612808020785451,
0.00038369803223758936,
0.0012087674112990499,
0.014662538655102253,
0.028657184913754463,
-0.00020478834630921483,
0.07111278921365738,
0.016838811337947845,
-0.00968546699732542,
-0.017482172697782516,
0.017743969336152077,
0.09615115076303482,
0.04292845353484154,
-0.010779295116662979,
-0.05502907559275627,
0.0072210393846035,
-0.004871653858572245,
0.02173941768705845,
-0.04515228047966957,
0.03794650360941887,
0.0015282985987141728,
0.014669738709926605,
0.02743580937385559,
0.045769691467285156,
-0.007449536118656397,
-0.016386227682232857,
0.028107497841119766,
-0.011440680362284184,
-0.027044624090194702,
0.0010568439029157162,
0.03168525546789169,
-0.01361403800547123,
0.00007665353768970817,
-0.04108736664056778,
0.04236911982297897,
-0.01973770372569561,
-0.0027895134408026934,
-0.019817201420664787,
-0.03485111892223358,
0.0063505517318844795,
-0.014710246585309505,
-0.06013017147779465,
-0.017256848514080048,
-0.002912436379119754,
-0.04980453848838806,
-0.031027434393763542,
0.00852865632623434,
0.025415612384676933,
-0.04125938192009926,
0.02880099043250084,
0.03493567183613777,
-0.016800250858068466,
0.032405223697423935,
0.006089700851589441,
0.02172442153096199,
-0.032753318548202515,
0.009437286294996738,
-0.01937485672533512,
0.035574305802583694,
-0.04185175895690918,
-0.005989514756947756,
-0.010032318532466888,
0.0380263589322567,
0.04558706656098366,
-0.03726152703166008,
0.00893444661051035,
-0.0009270335431210697,
0.013547887094318867,
-0.010876284912228584,
-0.04126530513167381,
0.004930699244141579,
-0.00690421462059021,
0.012981812469661236,
0.030452918261289597,
-0.00440462538972497,
0.03346903249621391,
-0.0019202354596927762,
-0.03671783581376076,
0.06045771762728691,
-0.02728680893778801,
0.022581737488508224,
-0.006575864739716053,
0.005080136004835367,
-0.03822299465537071,
0.03475330397486687,
0.042664557695388794,
0.02594006061553955,
-0.033017516136169434,
0.02431478165090084,
0.007165172137320042,
-0.004253964405506849,
-0.022621627897024155,
0.026656650006771088,
0.010031694546341896,
-0.04013140872120857,
-0.015552233904600143,
0.006152006331831217,
0.044952526688575745,
0.021535033360123634,
-0.012032539583742619,
-0.0016355982515960932,
-0.002033810131251812,
0.034757692366838455,
-0.002257527085021138,
-0.0402996800839901,
-0.02417352795600891,
-0.002843263326212764,
-0.026390841230750084,
-0.02251356840133667,
-0.01042856927961111,
0.011006836779415607,
0.023439152166247368,
0.027554044499993324,
0.010098266415297985,
0.036644697189331055,
-0.029863247647881508,
0.008966908790171146,
0.015429293736815453,
-0.050282157957553864,
-0.01641484722495079,
-0.0013357832795009017,
0.024743013083934784,
-0.0223203394562006,
-0.053998127579689026,
-0.03820088505744934,
-0.013507477007806301,
-0.03883408010005951,
0.0372624471783638,
-0.029285607859492302,
0.060028091073036194,
-0.03125029802322388,
0.004505254328250885,
-0.05212315171957016,
0.033213093876838684,
-0.08700033277273178,
-0.002584761241450906,
0.008148188702762127,
-0.03679855912923813,
0.02106502465903759,
0.021662242710590363,
-0.0009051781962625682,
-0.031031539663672447,
0.02450239099562168,
0.0006202816148288548,
-0.033287350088357925,
0.016306636855006218,
0.023377997800707817,
-0.017631107941269875,
0.04050193727016449,
-0.0035202805884182453,
0.010470793582499027,
0.04841850697994232,
-0.03963430970907211,
-0.02081349305808544,
0.0017166826874017715,
-0.03491692245006561,
0.03249885514378548,
0.003015585709363222,
-0.016351040452718735,
-0.005019946489483118,
0.06089061498641968,
-0.008923009037971497,
-0.016173208132386208,
0.0059977928176522255,
-0.005667130928486586,
0.013699770905077457,
0.04159890487790108,
0.014320958405733109,
-0.04550996422767639,
-0.024784499779343605,
0.01837591454386711,
0.0030238612089306116,
-0.006429848726838827,
-0.006448197644203901,
-0.01932918094098568,
-0.04201465845108032,
0.02074093371629715,
-0.0029911028686910868,
-0.0033895678352564573,
0.013311662711203098,
0.04537014663219452,
-0.04723241552710533,
0.08090784400701523,
0.03582855314016342,
-0.0403774231672287,
-0.09604736417531967,
-0.0028343249578028917,
-0.003048382932320237,
-0.013766000047326088,
0.02419295720756054,
-0.033771321177482605,
0.025139255449175835,
0.019448235630989075,
-0.04678675904870033,
0.016427673399448395,
-0.04139309003949165,
0.0030741605442017317,
-0.009639278054237366,
-0.014814870432019234,
-0.005787782836705446,
0.030389806255698204,
0.04326692223548889,
0.01446326170116663,
-0.01289654802531004,
-0.006689454894512892,
-0.025612512603402138,
-0.013852523639798164,
0.014669825322926044,
0.026701973751187325,
-0.017647957429289818,
0.001055063446983695,
0.06762678921222687,
-0.02107354626059532,
-0.019206980243325233,
0.04152136668562889,
0.010779345408082008,
0.04143387824296951,
0.016843879595398903,
-0.025767862796783447,
-0.01584339328110218,
-0.00961899384856224,
0.02434103935956955,
-0.0008293495629914105,
-0.005089243408292532,
0.030564187094569206,
0.00922409538179636,
0.0434965156018734,
-0.014954162761569023,
0.01692773774266243,
0.013356037437915802,
-0.04578980803489685,
-0.010705564171075821,
0.028088821098208427,
-0.013806434348225594,
0.017572710290551186,
-0.011760649271309376,
0.011076264083385468,
0.038948286324739456,
-0.05161457881331444,
0.010357256978750229,
-0.04420961067080498,
0.00711757130920887,
0.005758099257946014,
0.018642310053110123,
0.00837915949523449,
0.011480324901640415,
0.027448538690805435,
-0.0037625781260430813,
0.0026569010224193335,
-0.006105321459472179,
0.007701593451201916,
-0.026517309248447418,
0.007815185002982616,
-0.011610894463956356,
0.0013688207836821675,
0.0015702907694503665,
-0.043380700051784515,
-0.033180005848407745,
0.07558096945285797,
0.024004487320780754,
0.026568282395601273,
0.017007295042276382,
-0.060126613825559616,
-0.018251722678542137,
-0.04913511872291565,
0.010034682229161263,
-0.03316514939069748,
0.006299527827650309,
-0.03366134315729141,
-0.06422866135835648,
-0.009175886400043964,
-0.018164843320846558,
0.04408254846930504,
-0.01118549332022667,
0.027444452047348022,
0.03094726987183094,
-0.024573706090450287,
0.010380353778600693,
-0.0741894319653511,
0.010144605301320553,
0.007011319510638714,
-0.07901322096586227,
-0.0028236606158316135,
0.006813238374888897,
-0.0337618812918663,
0.023958975449204445,
0.046331118792295456,
0.010721597820520401,
0.047646332532167435,
0.01041149441152811,
0.00242407969199121,
0.030616531148552895,
-0.015296835452318192,
0.021921031177043915,
0.06607529520988464,
0.003311819164082408,
0.0048820823431015015,
0.0679662823677063,
-0.011477908119559288,
-0.00921587459743023,
0.043027181178331375,
-0.05608578398823738,
0.0038563294801861048,
-0.01393660344183445,
-0.05479830875992775,
0.044541653245687485,
-0.05884752795100212,
0.01670626364648342,
0.02080896683037281,
-0.026142198592424393,
-0.019231341779232025,
0.021023085340857506,
0.0017095457296818495,
0.028603345155715942,
-0.013472385704517365,
-0.005396283697336912,
-0.01024202536791563,
-0.0028668008744716644,
-0.03248773515224457,
0.05419207364320755,
0.02942570298910141,
0.003001842414960265,
0.029432570561766624,
0.010577372275292873,
0.030527213588356972,
0.03429945558309555,
-0.04970625415444374,
0.05519882217049599,
-0.04569658637046814,
0.0008333211299031973,
0.00016337311535608023,
-0.03390040621161461,
0.009850983507931232,
0.005097793880850077,
-0.006324981339275837,
0.10182791203260422,
-0.003998638596385717,
0.008416163735091686,
0.011310099624097347,
-0.02946891449391842,
-0.033936966210603714,
0.04308035969734192,
-0.00972823891788721,
0.021627262234687805,
0.008388984017074108,
-0.024018801748752594,
0.003924920689314604,
0.020838258787989616,
0.040477339178323746,
-0.011430857703089714,
0.011653824709355831,
-0.013221054337918758,
-0.030592361465096474,
-0.023241735994815826,
0.00936796609312296,
-0.03487439081072807,
-0.04360959678888321,
0.02779255248606205,
0.05161014571785927,
0.006894392892718315,
0.035381149500608444,
0.016050394624471664,
-0.0022694584913551807,
0.050845418125391006,
-0.0558081679046154,
-0.02034880593419075,
-0.027142925187945366,
0.031603794544935226,
-0.023114748299121857,
-0.02986520156264305
] |
<p>Suppose I have plenty of food I want to heat (which will provide load) in the microwave, and one item I don't want to heat. What properties would make a material a a good shield, to reduce or prevent heating of that item? I know metal can work as a barrier in the form of a Faraday cage, but that there are also potential issues with arcing. Presumably some kind of smoothly flexible metal mesh would be a good candidate - what properties would it need to be effective? (For example, we might consider mesh spacing, wire diameter, and the choice of metal.)</p>
<p><sub>(Note: this is based on <a href="http://cooking.stackexchange.com/q/33871/1672">this question</a>, which was recently migrated over to Seasoned Advice (food and cooking), but I think that it could really use physics expertise, so this is a rephrased version, addressing the complaints I saw leading to that question's migration.)</sub></p> | 4,569 | [
-0.06635402888059616,
-0.024262186139822006,
0.017162777483463287,
-0.021208839491009712,
0.009970389306545258,
0.01464154664427042,
-0.009963544085621834,
-0.0028066483791917562,
0.0016343273455277085,
-0.005691335536539555,
0.0629827156662941,
0.047737590968608856,
0.04869958758354187,
0.031884126365184784,
-0.0015259854262694716,
-0.005246058572083712,
0.021320179104804993,
-0.048608675599098206,
-0.018370965495705605,
-0.03790822997689247,
0.03998864069581032,
-0.012770509347319603,
-0.005355971399694681,
0.005280471872538328,
-0.026797974482178688,
0.031509365886449814,
0.025532696396112442,
-0.02674657665193081,
0.029823705554008484,
0.013001584447920322,
-0.027480624616146088,
-0.023412613198161125,
0.00803652685135603,
-0.02828836999833584,
0.02353123016655445,
-0.013033119961619377,
-0.06160013750195503,
-0.018713267520070076,
0.00035413188743405044,
0.05252879858016968,
0.006122677121311426,
0.007715402636677027,
-0.01606106385588646,
0.03158868849277496,
-0.00961885042488575,
-0.012070508673787117,
-0.029703138396143913,
-0.002660631202161312,
0.04648461565375328,
-0.060745254158973694,
0.02112918347120285,
-0.03611571341753006,
0.01833193749189377,
0.05608309432864189,
0.00874981377273798,
-0.009150189347565174,
0.09874880313873291,
0.05662355199456215,
-0.019809985533356667,
-0.059178426861763,
-0.01753229834139347,
-0.028125517070293427,
-0.03983738273382187,
-0.023129353299736977,
-0.009004955179989338,
0.06306304782629013,
0.01000248920172453,
-0.026649348437786102,
0.018489113077521324,
0.01468033529818058,
0.004137181211262941,
0.005966618191450834,
0.005069740582257509,
0.003097434528172016,
0.022238893434405327,
-0.009273168630897999,
-0.010278888046741486,
0.028400355949997902,
0.04783200845122337,
0.05262625962495804,
0.007071063853800297,
-0.005530762020498514,
0.018630286678671837,
0.033254582434892654,
0.025535620748996735,
-0.028413336724042892,
0.09695751219987869,
0.006887043360620737,
-0.017808930948376656,
0.013650450855493546,
0.022335967049002647,
0.007552172057330608,
0.03685268387198448,
0.011378120630979538,
-0.003205894259735942,
0.004537720233201981,
0.004975604359060526,
0.04366472736001015,
-0.019620593637228012,
0.011619536206126213,
-0.02314353734254837,
0.017970936372876167,
0.04797463119029999,
0.08259285241365433,
0.03695667162537575,
-0.048252638429403305,
-0.02598944678902626,
-0.0152254868298769,
-0.0024891754146665335,
-0.027726110070943832,
-0.010543315671384335,
0.0256604366004467,
-0.008534368127584457,
-0.012360609136521816,
0.029659178107976913,
-0.05666518583893776,
0.00491460831835866,
-0.021717816591262817,
0.04042644426226616,
0.06654386967420578,
0.02396426536142826,
0.017148690298199654,
0.049172088503837585,
-0.04348563402891159,
-0.0978335440158844,
-0.009200792759656906,
-0.001700723310932517,
0.03283071145415306,
-0.017477883026003838,
0.017908014357089996,
-0.011854992248117924,
-0.024109473451972008,
0.04209597408771515,
-0.019306747242808342,
0.01970045268535614,
0.02033005654811859,
-0.08447373658418655,
-0.07772982865571976,
0.03883499652147293,
-0.015723178163170815,
-0.048246074467897415,
-0.06720087677240372,
-0.03479623794555664,
0.0189655814319849,
0.07897308468818665,
0.00498631177470088,
-0.04350048303604126,
-0.05633166432380676,
0.04759736731648445,
-0.014037354849278927,
-0.02854127436876297,
-0.00686455424875021,
0.0033901697024703026,
-0.0035948529839515686,
0.01909041963517666,
-0.028782283887267113,
0.019577110186219215,
0.02236429788172245,
-0.01223671343177557,
-0.019583402201533318,
0.058923155069351196,
-0.03327152878046036,
0.024092933163046837,
-0.02492659166455269,
-0.03145201876759529,
0.0013843717752024531,
0.07505011558532715,
0.002224520081654191,
-0.01538421306759119,
0.01933654211461544,
-0.008407351560890675,
0.0011939132818952203,
0.0010962040396407247,
-0.015092470683157444,
0.04581296071410179,
-0.025838015601038933,
0.013723297044634819,
0.0013835260178893805,
0.003902312833815813,
0.005026381928473711,
-0.013148310594260693,
-0.00229466101154685,
0.020363710820674896,
0.005409794859588146,
0.021805835887789726,
0.07134188711643219,
0.007345125544816256,
-0.024762265384197235,
0.01889626681804657,
-0.02923234924674034,
-0.03861236572265625,
-0.0345771424472332,
0.02011171542108059,
-0.029441433027386665,
0.003283425932750106,
-0.004498919006437063,
0.0011086728191003203,
-0.027952155098319054,
-0.02162541262805462,
-0.014514300972223282,
0.015569067560136318,
0.02711367979645729,
0.027235282585024834,
0.0046437401324510574,
0.003305145539343357,
0.04730357974767685,
0.028165169060230255,
-0.03811091184616089,
0.0051673781126737595,
-0.05056465417146683,
-0.04644957184791565,
-0.029308101162314415,
-0.040861427783966064,
0.025860454887151718,
0.03906309977173805,
-0.04333493858575821,
0.022500699386000633,
-0.012289756909012794,
-0.02294105850160122,
0.024642959237098694,
-0.0157395601272583,
0.06711672991514206,
0.030726753175258636,
0.01488653663545847,
0.02664015255868435,
0.020462406799197197,
0.008719315752387047,
0.01884814351797104,
0.04230552911758423,
-0.0044565824791789055,
-0.07580326497554779,
-0.015168501995503902,
0.05626515671610832,
0.0283596683293581,
-0.06480790674686432,
0.024968422949314117,
-0.02461804635822773,
0.019525980576872826,
0.022902216762304306,
-0.0075087095610797405,
-0.009013477712869644,
-0.008962816558778286,
0.05636926740407944,
-0.005233115516602993,
-0.000906654866412282,
-0.009127678349614143,
-0.04510955512523651,
0.026167459785938263,
-0.033022891730070114,
0.04547327384352684,
0.02205166220664978,
0.017854470759630203,
0.055795662105083466,
0.035420116037130356,
-0.009309266693890095,
-0.02340124547481537,
0.011366569437086582,
-0.031148618087172508,
0.011996431276202202,
0.013279438950121403,
0.04850556701421738,
0.013207725249230862,
-0.009393365122377872,
0.006816166918724775,
0.017251815646886826,
-0.011204631999135017,
0.000981688965111971,
0.038119375705718994,
0.03802626207470894,
-0.05066119134426117,
-0.02210908755660057,
0.0316828116774559,
0.014211748726665974,
0.006193434353917837,
-0.027901800349354744,
-0.009130993857979774,
0.015497513115406036,
0.055288564413785934,
-0.022693486884236336,
-0.016472266986966133,
0.019946476444602013,
-0.030644681304693222,
-0.019217759370803833,
-0.014847816899418831,
-0.04070192947983742,
-0.005003639031201601,
-0.02297426015138626,
-0.020447777584195137,
0.07833992689847946,
0.0071477764286100864,
-0.0322994627058506,
0.03516938537359238,
0.028521394357085228,
-0.05021531879901886,
-0.023693079128861427,
-0.01973971724510193,
0.03293800354003906,
-0.01848924160003662,
-0.028988569974899292,
0.0442730076611042,
0.0223038662225008,
-0.0362980030477047,
0.005003839731216431,
-0.04058065637946129,
-0.05568394437432289,
-0.005207151640206575,
-0.03421761468052864,
0.03057253733277321,
0.03198869898915291,
0.01001586951315403,
0.012538950890302658,
-0.04440091922879219,
0.04105398431420326,
-0.04816758260130882,
-0.05361125245690346,
-0.027186650782823563,
-0.005814762320369482,
0.024095768108963966,
0.019779449328780174,
-0.02199588157236576,
0.05966314673423767,
0.006859662476927042,
-0.04349967837333679,
0.0010751114459708333,
-0.027966046705842018,
-0.026129432022571564,
-0.051710955798625946,
0.010278155095875263,
0.050099290907382965,
-0.02439059130847454,
-0.008443716913461685,
0.02570999413728714,
0.007773299235850573,
0.04066081717610359,
0.027074679732322693,
-0.0012071470264345407,
0.017222095280885696,
0.006107841152697802,
-0.01406447496265173,
0.035909779369831085,
0.012376856058835983,
-0.010315951891243458,
0.000840282766148448,
0.0005675909924320877,
0.036345090717077255,
0.04794200137257576,
-0.05140471085906029,
0.032481178641319275,
-0.02079286240041256,
0.023698823526501656,
-0.025228241458535194,
0.05893997102975845,
-0.027362065389752388,
-0.017465824261307716,
0.01445014402270317,
0.042536068707704544,
0.04126530513167381,
-0.005066927522420883,
0.0026382191572338343,
0.045800574123859406,
0.08860591799020767,
-0.018980858847498894,
0.04260915517807007,
0.015934260562062263,
-0.007931573316454887,
-0.01656470261514187,
-0.002556724241003394,
0.02108004316687584,
0.03718344867229462,
0.020607823505997658,
0.025990040972828865,
0.027875991538167,
-0.01110256090760231,
-0.016678236424922943,
-0.08766276389360428,
-0.02674863301217556,
0.006727732252329588,
0.08312053233385086,
-0.014950647950172424,
0.011063709855079651,
0.04614461958408356,
-0.0031372448429465294,
-0.00726604787632823,
0.043054308742284775,
-0.07821911573410034,
0.03363293781876564,
-0.022177373990416527,
0.012356722727417946,
-0.00511949323117733,
-0.008444594219326973,
-0.07287096232175827,
-0.008369317278265953,
0.010678594000637531,
-0.011972354725003242,
0.016140786930918694,
-0.006394707597792149,
0.030024219304323196,
-0.006736172363162041,
-0.04567069932818413,
-0.008304057642817497,
0.020225143060088158,
0.0440019816160202,
-0.0165537241846323,
-0.0036432791966944933,
0.030341587960720062,
-0.026709256693720818,
-0.02817629650235176,
-0.03089512325823307,
0.02545102685689926,
-0.0248205978423357,
0.05189872533082962,
-0.01940866746008396,
0.013120133429765701,
-0.01840539090335369,
0.009046908468008041,
0.04749259352684021,
0.014220088720321655,
-0.03093579411506653,
-0.014694501645863056,
-0.029249470680952072,
-0.058220528066158295,
-0.05301408842206001,
0.007429943885654211,
0.07957201451063156,
-0.03657278046011925,
-0.0106267761439085,
0.016801420599222183,
-0.010851987637579441,
-0.006784692406654358,
0.0013955303002148867,
0.05604363977909088,
0.024219810962677002,
-0.01742960885167122,
-0.025685736909508705,
-0.013094641268253326,
-0.015573003329336643,
0.0005652711261063814,
0.0120954355224967,
0.004990575835108757,
0.02607898786664009,
0.014198936522006989,
0.002090511843562126,
0.0044991266913712025,
0.02602461911737919,
0.02328498288989067,
0.027017125859856606,
0.014002629555761814,
-0.01967008039355278,
-0.020895060151815414,
-0.0302247516810894,
0.022985273972153664,
0.06338568031787872,
-0.017657842487096786,
-0.0024065286852419376,
-0.09375391155481339,
-0.016233405098319054,
0.045860033482313156,
0.06353562325239182,
-0.021420057862997055,
-0.004803156480193138,
-0.07856482267379761,
-0.027086837217211723,
0.05125509947538376,
0.008865229785442352,
0.04423492029309273,
-0.06300382316112518,
-0.007569275330752134,
-0.030518120154738426,
-0.027592789381742477,
-0.012062893249094486,
-0.022273080423474312,
0.034655749797821045,
0.008157296106219292,
0.0029353308491408825,
0.0025173677131533623,
0.011563517153263092,
0.007162466645240784,
0.054887041449546814,
0.019694846123456955,
0.007126637268811464,
0.013557636179029942,
0.008607561700046062,
-0.0016676869709044695,
-0.015367158688604832,
-0.022720886394381523,
-0.0050822594203054905,
0.019976472482085228,
-0.019869035109877586,
0.01556292176246643,
-0.03064480796456337,
-0.002067714696750045,
0.03273391351103783,
-0.0033504909370094538,
-0.011257331818342209,
-0.0006413621595129371,
-0.002003686036914587,
0.07575514912605286,
0.03702252358198166,
0.019269227981567383,
0.04592512175440788,
0.08654654771089554,
-0.028411971405148506,
0.00045993091771379113,
-0.006651794537901878,
0.03106628730893135,
-0.040107935667037964,
0.010043509304523468,
-0.030841439962387085,
-0.009178496897220612,
-0.04761974886059761,
0.04095098376274109,
-0.002273222431540489,
0.0013116627233102918,
-0.005272909067571163,
-0.02448244020342827,
-0.002821587724611163,
0.017481697723269463,
-0.0037277627270668745,
-0.0459006205201149,
0.011652026325464249,
-0.004803156480193138,
-0.033832747489213943,
-0.02786102704703808,
0.044523756951093674,
-0.02170379087328911,
0.024740761145949364,
0.008846723474562168,
-0.03761935234069824,
0.023890355601906776,
-0.055743977427482605,
-0.019749987870454788,
-0.028755176812410355,
-0.05103826895356178,
0.05905814468860626,
0.002846977673470974,
0.029143281280994415,
0.049028798937797546,
-0.0842134952545166,
0.0032568792812526226,
0.021106544882059097,
0.02074805647134781,
-0.012800434604287148,
-0.05635347217321396,
0.015325317159295082,
-0.025042634457349777,
-0.0008657630532979965,
-0.017003877088427544,
-0.007566721644252539,
0.021884841844439507,
0.011960203759372234,
0.013562371022999287,
-0.05440838262438774,
-0.020091773942112923,
-0.042500775307416916,
-0.05564888194203377,
-0.015017113648355007,
0.04639103636145592,
-0.054048508405685425,
0.017556197941303253,
0.023142172023653984,
0.006898351013660431,
0.048841144889593124,
0.022356942296028137,
-0.022990435361862183,
0.004542057402431965,
-0.05948632210493088,
-0.005511899013072252,
-0.01808219589293003,
0.015512882731854916,
-0.03163914382457733,
-0.02495870552957058,
-0.0013745733303949237,
-0.0014049020828679204,
0.056715793907642365,
0.0005920863477513194,
-0.0187872052192688,
0.026389149948954582,
-0.02660955861210823,
-0.03727909177541733,
-0.025441737845540047,
0.050583429634571075,
0.010313646867871284,
0.03249960392713547,
-0.01821955107152462,
0.0431809164583683,
-0.028341514989733696,
-0.0370124988257885,
0.016825271770358086,
-0.028320960700511932,
-0.004478298127651215,
-0.02643277496099472,
0.06521845608949661,
-0.023790784180164337,
0.012629366479814053,
0.012537854723632336,
-0.017095204442739487,
0.04634657874703407,
-0.008546953089535236,
-0.0019669949542731047,
0.01323610357940197,
-0.000782179064117372,
-0.023940619081258774,
-0.046512726694345474,
-0.01578553579747677,
-0.03671734407544136,
0.026557855308055878,
-0.045393601059913635,
0.03551199659705162,
-0.0039746202528476715,
-0.04427826404571533,
-0.02502412721514702,
0.005761065986007452,
-0.01766536757349968,
0.01406015083193779,
-0.015060605481266975,
0.018246229737997055,
-0.0007216317462734878,
0.0075744143687188625,
0.021076535806059837,
0.015432778745889664,
0.012667332775890827,
0.003108878619968891,
0.04049654304981232,
0.04096231237053871,
0.045740097761154175,
-0.06616832315921783,
-0.052484627813100815,
0.03225017711520195,
-0.07118554413318634,
0.008744706399738789,
0.001007173559628427,
0.000031977873732103035,
0.022445814684033394,
0.021601136773824692,
0.0006612472934648395,
-0.034070100635290146,
-0.0026906784623861313,
-0.0007032757857814431,
0.016497472301125526,
0.015202985145151615,
-0.03008555807173252,
0.006262396462261677,
-0.010347213596105576,
0.04864852502942085,
-0.02193654328584671,
0.021335765719413757,
-0.00657103443518281,
-0.06243317574262619,
-0.009587607346475124,
-0.0390913225710392,
-0.008698883466422558,
0.060531340539455414,
0.010735687799751759,
-0.0073852273635566235,
-0.005186910275369883,
-0.034085072576999664,
0.016738178208470345,
0.007463056594133377,
0.006788145750761032,
-0.034965045750141144,
0.04283088073134422,
-0.048966437578201294,
0.0068582952953875065,
-0.002960694022476673,
0.0035804721992462873,
0.1445559412240982,
-0.0030677265021950006,
0.018529361113905907,
-0.02419654093682766,
-0.004374105017632246,
-0.006059350445866585,
0.0018003846053034067,
-0.03100494109094143,
-0.043242715299129486,
-0.04664180427789688,
0.05232697352766991,
-0.003266442334279418,
0.02040330320596695,
0.004972113762050867,
0.05482815206050873,
0.021995775401592255,
-0.03926641866564751,
0.03289569914340973,
-0.005056434776633978,
0.010236461646854877,
-0.0288520660251379,
0.005107967648655176,
-0.032717883586883545,
0.024124750867486,
-0.005252881441265345,
-0.005361754447221756,
-0.009680370800197124,
-0.004123025108128786,
0.02784348651766777,
-0.016080081462860107,
-0.017861369997262955,
0.00026292362599633634,
-0.008272646926343441,
-0.0021422437857836485,
-0.005453532095998526,
0.021358929574489594,
0.054105259478092194,
0.013846021145582199,
0.0012608435936272144,
0.013082139194011688,
0.056870874017477036,
-0.009061246179044247,
0.05015866830945015,
0.01957804150879383,
-0.053154319524765015,
-0.01111223641782999,
-0.04476461559534073,
-0.009171589277684689,
0.012218669056892395,
-0.036588914692401886,
0.026095693930983543,
0.004383472725749016,
0.019307594746351242,
-0.015916116535663605,
-0.01599952019751072,
-0.001694627571851015,
0.033618196845054626,
0.0017180396243929863,
-0.008934516459703445,
-0.006711533293128014,
0.05478620156645775,
0.010857703164219856,
-0.00789095088839531,
0.016989439725875854,
-0.02812379226088524,
-0.04018417373299599,
0.01096386183053255,
0.04516923055052757,
0.022100131958723068,
0.010506381280720234,
-0.0424266941845417,
-0.01296384260058403,
0.0055303690023720264,
-0.005057151895016432,
0.012805511243641376,
0.059100303798913956,
0.051238052546978,
-0.02855655923485756,
0.0033019063994288445,
0.012919568456709385,
-0.06597583740949631,
0.04119332507252693,
-0.03396354988217354,
-0.01294783316552639,
-0.04630694165825844,
-0.02952197939157486,
0.0003704038099385798,
0.009113436564803123,
-0.0021767786238342524,
-0.005838094279170036,
0.0007265991298481822,
0.010747646912932396,
0.005807572975754738,
0.017807666212320328,
-0.03757858648896217,
0.02102937363088131,
-0.037027906626462936,
0.022601451724767685,
0.027634913101792336,
0.08610094338655472,
0.018820546567440033,
-0.03176536783576012,
-0.013171466998755932,
0.006887014023959637,
-0.021614931523799896,
-0.008391033858060837,
0.018224138766527176,
-0.0230522733181715,
-0.029454994946718216,
-0.008054510690271854,
-0.01064103003591299,
0.02954544872045517,
-0.05888812243938446,
-0.017565174028277397,
-0.05897698551416397,
-0.030882608145475388,
0.042319756001234055,
0.009421108290553093,
0.056405846029520035,
-0.012417584657669067,
-0.0007823437335900962,
-0.035797975957393646,
0.005826384294778109,
-0.06554198265075684,
-0.028923241421580315,
0.023384282365441322,
-0.017830507829785347,
-0.007545691914856434,
0.03528791293501854,
-0.04585908725857735,
0.008793972432613373,
-0.010732844471931458,
0.004976486787199974,
-0.010515778325498104,
-0.004177432972937822,
-0.01026153564453125,
0.024876950308680534,
0.06743333488702774,
-0.041031960397958755,
-0.014583139680325985,
0.03785475343465805,
0.002863460686057806,
-0.008643705397844315,
0.007064859848469496,
-0.004390739370137453,
0.029514318332076073,
0.013166870921850204,
0.0037032528780400753,
0.0037923443596810102,
0.07065048068761826,
-0.00027650949778035283,
0.009372797794640064,
-0.0338677354156971,
-0.02265937253832817,
0.05386727303266525,
0.012109961360692978,
-0.03287762776017189,
-0.033931124955415726,
-0.0069797951728105545,
0.016293538734316826,
0.011523805558681488,
0.02630212903022766,
-0.052594948559999466,
-0.010809674859046936,
-0.03762888163328171,
-0.02652188576757908,
-0.031568218022584915,
0.037522315979003906,
0.0032163129653781652,
0.04406194016337395,
-0.04154136776924133,
0.002236683387309313,
-0.003820871002972126,
-0.027690885588526726,
-0.10144887119531631,
-0.008726146072149277,
0.017623085528612137,
0.01647670567035675,
0.027900241315364838,
-0.05588992312550545,
0.04759768769145012,
0.016294505447149277,
-0.08340921252965927,
0.012553824111819267,
-0.0015159249305725098,
-0.009259074926376343,
-0.04332607984542847,
0.002441355725750327,
-0.03847373276948929,
0.04420215263962746,
-0.018944891169667244,
0.04921547695994377,
0.037281665951013565,
0.037780266255140305,
-0.039271995425224304,
-0.03870373219251633,
0.016989815980196,
0.03897795081138611,
-0.008571028709411621,
-0.002327329246327281,
0.04450097680091858,
0.01585403084754944,
-0.029857179149985313,
0.01849081926047802,
0.010539374314248562,
0.01903247833251953,
-0.021875012665987015,
0.013217276893556118,
0.016361691057682037,
-0.005709751974791288,
-0.008380645886063576,
-0.016406353563070297,
0.0007430637488141656,
0.002720258664339781,
0.0012588573154062033,
0.007349216844886541,
-0.0052475412376224995,
0.0009741761605255306,
0.008307020179927349,
-0.004713783040642738,
-0.01442241296172142,
0.0068033491261303425,
-0.05242781713604927,
-0.02963799424469471,
0.0225053820759058,
0.010646133683621883,
0.04142159968614578,
-0.016505304723978043,
-0.04710926488041878,
-0.08453753590583801,
-0.017803773283958435,
0.04587383568286896,
-0.011187511496245861,
0.01555592380464077,
0.0016650264151394367,
0.0067057255655527115,
-0.019236844033002853,
-0.006667416542768478,
0.02190454863011837,
-0.05286586284637451,
-0.006319791078567505,
-0.00495073152706027,
-0.0041375854052603245,
0.047484055161476135,
-0.0032862063962966204,
0.02034691721200943,
-0.030498990789055824,
0.012251279316842556,
0.022249987348914146,
0.02055538073182106,
0.01401936262845993,
-0.025946184992790222,
0.003652216400951147,
-0.019264161586761475,
0.004866074305027723,
-0.012269409373402596,
-0.030140412971377373,
0.0018431436037644744,
-0.05416726693511009,
-0.02045373059809208,
0.02950451709330082,
0.06659407913684845,
-0.01790742203593254,
-0.0018035387620329857,
-0.031875550746917725,
-0.029495248571038246,
0.01811649277806282,
-0.06604496389627457,
0.06277178972959518,
0.024478640407323837,
-0.0184871144592762,
0.007193580269813538,
0.014015370048582554,
0.017205247655510902,
-0.003339551854878664,
0.02520250901579857,
-0.013267752714455128,
0.01336186844855547,
-0.01939770206809044,
-0.02115175873041153,
0.0015396579401567578,
0.0011680318275466561,
-0.004511093255132437,
0.01949678361415863,
-0.023539364337921143,
-0.022858409211039543,
-0.009117063134908676,
0.01217686478048563,
-0.008998877368867397,
0.02042216807603836,
-0.03553863614797592,
0.02104499377310276,
-0.02489224262535572,
0.019316133111715317,
0.04895847290754318,
-0.06587865203619003,
0.007967101410031319,
0.02842225506901741,
0.009719370864331722,
-0.03026132471859455,
0.03085092082619667,
0.03227955102920532,
0.036184098571538925,
0.019205110147595406,
-0.005995112005621195,
0.003460896434262395,
-0.04006681591272354,
-0.007251356728374958,
0.04214448109269142,
0.03495781868696213,
-0.00974974874407053,
0.025570055469870567,
0.033413637429475784,
-0.009141292423009872,
-0.025384526699781418,
-0.00009377241804031655,
0.02553475648164749,
-0.015209168195724487,
0.02981877513229847,
0.03071385994553566,
0.0013567566638812423,
-0.052250493317842484,
0.05826902389526367,
-0.022778086364269257,
0.03999263420701027,
0.025036020204424858,
0.007268022745847702,
-0.01887122541666031,
0.04358185827732086,
0.003428335301578045,
0.03523004800081253,
0.023488329723477364,
0.03158635273575783,
-0.017207441851496696,
0.02066134661436081,
0.013866817578673363,
-0.023401960730552673,
0.017014143988490105,
-0.023526951670646667,
0.023997312411665916,
-0.012905511073768139,
0.0008670228999108076,
-0.02946537919342518,
-0.033248066902160645,
0.015155471861362457,
0.010755926370620728,
0.045928556472063065,
0.03186511620879173,
0.0015162526397034526,
-0.04320700466632843,
0.010036634281277657,
0.0011186228366568685,
0.036406006664037704,
-0.044389866292476654,
0.010939396917819977,
-0.03116397000849247,
0.016766374930739403,
-0.021946262568235397,
0.022556938230991364
] |
<p>I'm trying to introduce myself to QFT following <a href="http://www.damtp.cam.ac.uk/user/tong/qft.html" rel="nofollow">these lectures</a> by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz transformation of the form</p>
<p>$$\tag{1.49} {\Lambda^\mu}_\nu={\delta^\mu}_\nu+{\omega^\mu}_\nu,$$</p>
<p>where $\omega$ is antisymmetric, the variation of the Lagrangian density $\mathcal{L}$ is</p>
<p>$$\tag{1.53} \delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L}).$$</p>
<p>Using $\mathcal{L}=\mathcal{L}(\phi,\partial_\mu\phi)$, I've tried computing $\delta\mathcal{L}$ directly using</p>
<p>$$\tag{1.52} \delta\phi=-{\omega^\mu}_\nu{x}^\nu\partial_\mu\phi$$</p>
<p>[which I obtained earlier computing explicitly $\phi(x)\to\phi(\Lambda^{-1}x)$], however, I get
$$\delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L})-\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}{\omega^\sigma}_\mu\partial_\sigma\phi$$
The extra term arises when I compute
$$\partial_\mu(\delta\phi)=-{\omega^\sigma}_\nu\left[{\delta^\nu}_\mu\partial_\sigma\phi+x^\nu\partial_{\mu\sigma}\phi\right]=-{\omega^\sigma}_\mu\partial_{\sigma}\phi-{\omega^\sigma}_\nu{x}^\nu\partial_{\mu\sigma}\phi$$</p>
<p>[because I'm assuming $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$]; I thought I'd get rid of it just replacing $\phi$ with $\partial_\sigma\phi$ in $(1.52)$, however $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$ should still hold, ain't it? I also tried using (the previous expression to) 1.27 in the lectures, namely that the derivatives of the field transform as</p>
<p>$$\tag{1.26b} \partial_\mu\phi(x)\to{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x),$$</p>
<p>but I still get (to the first order in $\omega$),</p>
<p>\begin{align}{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x)&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\partial_\nu\phi(x^\sigma-{\omega^\sigma}_\rho{x}^\rho)\\&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\left[\partial_\nu\phi(x)-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\nu}\phi(x)\right]\\&=\partial_\mu\phi-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\mu}\phi-{\omega^\nu}_\mu\partial_\nu\phi\end{align} </p>
<p>I'm resisting the idea that ${\omega^\nu}_\mu\partial_\nu\phi=0$, but I don't understand what I'm doing wrong.</p> | 4,570 | [
0.028701189905405045,
-0.012622836977243423,
0.018918393179774284,
-0.03312202915549278,
0.02635318413376808,
0.012659146450459957,
-0.05229535326361656,
-0.017729217186570168,
-0.011447751894593239,
-0.03900362178683281,
0.03292005509138107,
0.02759217843413353,
0.10088693350553513,
0.0150247598066926,
0.032669808715581894,
0.01789626106619835,
-0.015094449743628502,
-0.004789348691701889,
-0.008782695978879929,
-0.06919639557600021,
0.021402569487690926,
0.037632185965776443,
-0.018731551244854927,
0.006256412714719772,
-0.03690048307180405,
0.0348610058426857,
-0.0041421400383114815,
0.005734012927860022,
-0.024416476488113403,
0.08852771669626236,
-0.023269496858119965,
-0.032932769507169724,
0.0222285445779562,
0.016117090359330177,
0.017510486766695976,
0.07619715481996536,
-0.01734890043735504,
-0.02900703251361847,
-0.018169546499848366,
-0.007650676183402538,
-0.060504280030727386,
-0.010515570640563965,
-0.012302701361477375,
0.06989680230617523,
-0.02303151972591877,
0.001235652482137084,
0.016885099932551384,
-0.008490831591188908,
0.08342978358268738,
-0.030070053413510323,
0.08207523822784424,
0.03176924213767052,
0.0218057744204998,
0.033928681164979935,
-0.007125199306756258,
-0.05213940143585205,
0.046711698174476624,
0.06685715168714523,
0.022031517699360847,
-0.06465961784124374,
-0.0030695779714733362,
-0.039391402155160904,
0.014346549287438393,
-0.029394524171948433,
0.000544106587767601,
0.014503776095807552,
0.03315793722867966,
0.027363231405615807,
0.01716754026710987,
-0.006865052506327629,
0.0006942361360415816,
-0.021086830645799637,
0.022793244570493698,
-0.015027104876935482,
-0.016257641837000847,
0.002908869180828333,
-0.029701361432671547,
0.01492640282958746,
-0.0009649116545915604,
0.021320631727576256,
0.011957029812037945,
0.021393027156591415,
0.018153205513954163,
-0.004565651062875986,
0.0003448292554821819,
-0.019295813515782356,
0.06274969130754471,
0.03585217148065567,
-0.020745407789945602,
0.0399935208261013,
-0.016998106613755226,
0.011473913677036762,
-0.004519861191511154,
-0.05165579169988632,
-0.01696276292204857,
0.050070732831954956,
0.023397695273160934,
-0.007811674382537603,
0.015335648320615292,
0.002885345835238695,
-0.07461308687925339,
-0.021080411970615387,
0.03073161281645298,
0.040374014526605606,
0.0005353643209673464,
-0.035778168588876724,
-0.03953183814883232,
0.00781622901558876,
-0.021310774609446526,
-0.05298873037099838,
-0.03263724595308304,
0.03449069708585739,
-0.04343624785542488,
0.0001663388538872823,
-0.025171861052513123,
-0.03845258802175522,
-0.035315465182065964,
-0.020042315125465393,
0.028003482148051262,
0.06586548686027527,
0.05554576590657234,
0.01126131322234869,
0.019013594835996628,
-0.02270316518843174,
-0.06413176655769348,
0.010575000196695328,
0.05539146810770035,
-0.010264815762639046,
-0.0428445041179657,
-0.004771650768816471,
0.007521191146224737,
0.012812349013984203,
-0.014990362338721752,
0.00656992569565773,
0.03643041104078293,
-0.01268540509045124,
-0.11868645995855331,
-0.05125079303979874,
0.026160623878240585,
0.004964692052453756,
-0.011936244554817677,
-0.04798280447721481,
-0.003985739313066006,
0.05553167313337326,
0.05965223163366318,
-0.018723472952842712,
0.02535153366625309,
-0.009358217008411884,
-0.005345631390810013,
0.011233692057430744,
0.0023325972724705935,
-0.017115887254476547,
0.002907257527112961,
-0.035387072712183,
-0.0038219911511987448,
-0.03886737301945686,
-0.0037046887446194887,
0.021143656224012375,
-0.009298278018832207,
-0.009666248224675655,
0.08523476868867874,
-0.005577444098889828,
0.006659369915723801,
0.02387957274913788,
-0.009215100668370724,
-0.02873014472424984,
0.0756901279091835,
0.020914236083626747,
0.017115604132413864,
0.023948505520820618,
-0.02766161412000656,
-0.01598593033850193,
-0.051063746213912964,
0.014497029595077038,
0.058475129306316376,
-0.0468231700360775,
0.00002188649887102656,
-0.0430946908891201,
0.006663587410002947,
0.004907446447759867,
-0.0233467984944582,
-0.0056009674444794655,
-0.03669259697198868,
-0.0012081523891538382,
0.0005301450146362185,
0.02429959736764431,
-0.012058155611157417,
0.001021458418108523,
0.005029978696256876,
-0.06500916182994843,
-0.053279876708984375,
-0.056085363030433655,
0.003083889838308096,
0.0002915537334047258,
-0.04809294268488884,
0.04447171092033386,
0.004049791023135185,
0.021069860085844994,
-0.03362845256924629,
-0.03731618821620941,
-0.002613961696624756,
0.0201531071215868,
0.029397012665867805,
-0.009871468879282475,
0.0257492046803236,
0.04244716465473175,
0.01860366016626358,
-0.017263172194361687,
-0.0013578739017248154,
-0.032682254910469055,
0.010064717382192612,
0.020856332033872604,
-0.010641434229910374,
0.01598912850022316,
-0.03374559059739113,
-0.0035475031472742558,
0.0010468077380210161,
0.025445960462093353,
-0.018489722162485123,
0.022892020642757416,
-0.027856068685650826,
0.027655281126499176,
0.06678065657615662,
-0.009107298217713833,
-0.00006141451740404591,
0.03772682324051857,
-0.016163567081093788,
0.04024169594049454,
-0.013753713108599186,
-0.022090889513492584,
-0.016280224546790123,
-0.004050892777740955,
0.059607695788145065,
0.02882245182991028,
-0.010204783640801907,
-0.02452092431485653,
0.02545318379998207,
0.0018303646938875318,
0.05043531954288483,
0.06165250390768051,
-0.009174683131277561,
-0.09040218591690063,
0.038244567811489105,
0.0015021571889519691,
0.01764065958559513,
-0.0031464442145079374,
0.05807347968220711,
-0.009350034408271313,
0.007208424620330334,
0.0012820428237318993,
-0.028681762516498566,
0.0362936370074749,
-0.015558267943561077,
-0.01565825752913952,
-0.008134420029819012,
-0.01581941917538643,
0.044075869023799896,
-0.0007630025502294302,
0.037248700857162476,
0.02477806620299816,
-0.04245052486658096,
-0.006744599435478449,
-0.02173003926873207,
-0.011780555360019207,
-0.01084661204367876,
0.004898739047348499,
0.0038504137191921473,
0.020669473335146904,
0.00006855760148027912,
-0.03899543732404709,
-0.03802129998803139,
0.04169176146388054,
-0.027613922953605652,
0.004579287488013506,
0.003316024085506797,
0.003301429795101285,
0.029711974784731865,
0.005285677034407854,
-0.031447041779756546,
-0.02726723812520504,
0.05054756626486778,
0.04276338964700699,
0.03756440803408623,
0.0481884740293026,
-0.025983242318034172,
-0.01933879405260086,
-0.03601950779557228,
-0.03394933417439461,
0.0063192518427968025,
0.011190035380423069,
0.016247116029262543,
0.011399208568036556,
-0.01630513370037079,
-0.060074333101511,
-0.029687393456697464,
-0.030191708356142044,
-0.00795995257794857,
0.010149051435291767,
0.012467163614928722,
0.049541737884283066,
0.033061522990465164,
-0.05086953938007355,
0.007602188270539045,
-0.017670849338173866,
-0.049877606332302094,
-0.03198954090476036,
0.023791857063770294,
-0.0005684500210918486,
-0.022673584520816803,
0.02399349771440029,
0.009265863336622715,
0.021929001435637474,
0.029517440125346184,
-0.02419409714639187,
-0.009558302350342274,
0.015781085938215256,
0.032503269612789154,
0.005204043351113796,
0.007208769675344229,
-0.03386189043521881,
0.10293249785900116,
0.05525392293930054,
-0.015731487423181534,
-0.04141053184866905,
0.01969379186630249,
0.00696366373449564,
-0.05283892899751663,
0.0077996510080993176,
0.019967973232269287,
-0.07013212889432907,
0.044461749494075775,
0.0026362768840044737,
0.05326079577207565,
0.012866864912211895,
0.026102907955646515,
0.011691908352077007,
0.04364956170320511,
-0.03720208629965782,
0.02476324699819088,
0.04864375293254852,
-0.014645528979599476,
-0.015474392101168633,
-0.0363941565155983,
0.029879529029130936,
0.004981163889169693,
0.00027135899290442467,
-0.0024534109979867935,
0.08255518972873688,
0.045241065323352814,
-0.02273489721119404,
-0.0611475370824337,
0.034080106765031815,
0.0024443576112389565,
-0.07621576637029648,
-0.008159040473401546,
0.009295724332332611,
-0.008014888502657413,
0.002888405928388238,
-0.024552859365940094,
0.029174339026212692,
0.023429537191987038,
-0.037332773208618164,
-0.00736234663054347,
-0.04099772870540619,
0.005076918751001358,
0.042386479675769806,
-0.04237246885895729,
0.0005868044099770486,
0.02980496548116207,
0.06555283069610596,
-0.012719869613647461,
-0.027675163000822067,
-0.024903027340769768,
-0.013050888665020466,
-0.02256576530635357,
-0.010806906037032604,
0.004977617412805557,
0.05683163180947304,
0.0254451185464859,
0.07841642946004868,
0.015610826201736927,
0.01112695224583149,
-0.02983962930738926,
0.03186790645122528,
-0.06806573271751404,
0.02281847782433033,
-0.006408059038221836,
-0.0189360324293375,
0.0008407947025261819,
-0.004662003368139267,
0.03672216832637787,
-0.03376133367419243,
-0.018812816590070724,
-0.024680420756340027,
-0.04652079939842224,
-0.02843598462641239,
0.02794487029314041,
-0.02988254651427269,
-0.01658898964524269,
-0.03198765218257904,
0.0368645116686821,
0.04350609704852104,
-0.015867242589592934,
-0.013618802651762962,
0.019148919731378555,
-0.03424030914902687,
0.0049774497747421265,
-0.027441753074526787,
0.010825649835169315,
0.026915835216641426,
0.011729736812412739,
0.000362388847861439,
0.01711353473365307,
0.0003937011060770601,
0.0649106577038765,
0.029486844316124916,
0.03898878023028374,
0.03134789690375328,
-0.013838237151503563,
-0.010948178358376026,
-0.04239512234926224,
-0.012590250000357628,
0.03689301013946533,
0.06749346852302551,
0.005180848762392998,
-0.03341437876224518,
0.040916524827480316,
0.016202518716454506,
0.017281008884310722,
0.03496244549751282,
0.03519214689731598,
-0.00986442156136036,
-0.0031450095120817423,
-0.03216990455985069,
0.004068860784173012,
-0.04110036417841911,
0.014767737127840519,
0.02058529667556286,
0.017065200954675674,
-0.00028358615236356854,
0.006463117431849241,
0.012623382732272148,
0.02406427077949047,
-0.006974138785153627,
-0.0021289288997650146,
-0.006366128101944923,
0.0027290203142911196,
0.000552557350602001,
0.005005466751754284,
-0.014237605966627598,
0.036338601261377335,
0.059893056750297546,
0.0072296843864023685,
0.02172035537660122,
-0.053021036088466644,
-0.04336100444197655,
0.03200927749276161,
0.03851929306983948,
0.02144010365009308,
-0.0024230366107076406,
-0.08350537717342377,
-0.040488388389348984,
0.009248325601220131,
-0.007571862079203129,
0.038429830223321915,
0.01214415393769741,
0.01330103725194931,
0.013258347287774086,
-0.0653621032834053,
-0.02133132889866829,
0.03214797005057335,
-0.02678057923913002,
-0.005728560034185648,
-0.061944808810949326,
0.02997273951768875,
-0.01967303268611431,
0.03217065706849098,
-0.008349986746907234,
0.04319152981042862,
-0.007054710760712624,
-0.012189140543341637,
-0.04044623672962189,
0.02441130019724369,
0.002557101659476757,
-0.08265676349401474,
-0.013961417600512505,
0.017153998836874962,
-0.006519019138067961,
0.03024403564631939,
-0.01293635368347168,
-0.0349126011133194,
0.03636123612523079,
0.02648172900080681,
-0.046961911022663116,
0.008453605696558952,
-0.05995301902294159,
0.05804174393415451,
0.004736512433737516,
-0.015645187348127365,
0.06015947833657265,
0.014646350406110287,
-0.013268055394291878,
0.012316932901740074,
-0.038659095764160156,
0.013714834116399288,
-0.01552081573754549,
0.018872175365686417,
-0.0321679525077343,
-0.005777463782578707,
0.0020497480873018503,
0.05532568320631981,
-0.052919477224349976,
0.012909496203064919,
0.0033499286510050297,
-0.003416151273995638,
0.006716619245707989,
0.012031693942844868,
-0.0056030405685305595,
-0.0008437481010332704,
0.022830383852124214,
0.007528271060436964,
0.037421587854623795,
-0.006570648401975632,
-0.00019419471209403127,
0.0026423989329487085,
-0.0011708062374964356,
0.0408405177295208,
-0.02765757590532303,
0.03099753148853779,
-0.010318513959646225,
-0.04740968346595764,
0.001309043844230473,
-0.008166369050741196,
0.020576581358909607,
0.028500879183411598,
0.017536139115691185,
0.031248748302459717,
-0.016937116160988808,
-0.04531760513782501,
-0.004596992861479521,
-0.018118632957339287,
-0.019673999398946762,
-0.02288677729666233,
-0.0008219988667406142,
0.04845013841986656,
0.007629167288541794,
-0.07624559849500656,
-0.007623570971190929,
-0.013093380257487297,
-0.06012997031211853,
-0.036044035106897354,
-0.026552164927124977,
0.0030490527860820293,
-0.004592621698975563,
-0.016809454187750816,
0.004768239799886942,
0.021606622263789177,
-0.019667435437440872,
0.01174080278724432,
-0.0028395731933414936,
0.01566906087100506,
0.02174045704305172,
-0.02926972508430481,
-0.0157245434820652,
-0.017930418252944946,
0.01970822922885418,
-0.016147194430232048,
0.02065308950841427,
0.03625302389264107,
-0.006429275963455439,
-0.02605806104838848,
-0.0025365788023918867,
-0.016866112127900124,
0.005806739442050457,
-0.007188985589891672,
-0.017381146550178528,
0.028354967013001442,
0.0069376518949866295,
-0.005444754846394062,
-0.02244093082845211,
-0.022927479818463326,
-0.007705660071223974,
0.06275077909231186,
-0.012194263748824596,
-0.011784217320382595,
-0.020150454714894295,
-0.004859933163970709,
0.0420527309179306,
-0.009289231151342392,
-0.002177105052396655,
-0.0012859738199040294,
0.06904326379299164,
-0.031509775668382645,
-0.006937715224921703,
0.0455208420753479,
-0.021328307688236237,
0.0027406567241996527,
0.023845704272389412,
0.0365908145904541,
0.01230127178132534,
0.010834204033017159,
-0.025201790034770966,
-0.0216254573315382,
-0.023748932406306267,
0.013505247421562672,
0.06222537159919739,
0.024494033306837082,
0.02787531167268753,
0.03148006647825241,
-0.016349202021956444,
0.018128609284758568,
-0.0009153545834124088,
-0.03640429303050041,
0.0012733903713524342,
-0.02283354289829731,
0.04923209547996521,
-0.06492502987384796,
0.0015223093796521425,
0.0453287810087204,
0.0033474289812147617,
-0.030895810574293137,
0.036404579877853394,
0.004187779501080513,
-0.004708797205239534,
0.013257008045911789,
-0.021799897775053978,
-0.054034311324357986,
0.05129064619541168,
-0.030741704627871513,
0.05793611332774162,
-0.021830502897500992,
0.01659930869936943,
0.027539333328604698,
0.017818422988057137,
0.027452558279037476,
0.007422065362334251,
-0.007876099087297916,
-0.04936855658888817,
0.017108792439103127,
0.035832833498716354,
0.024518471211194992,
0.016344701871275902,
0.01195960771292448,
0.0444992370903492,
-0.003544710809364915,
0.007738575339317322,
0.015156472101807594,
-0.03133459389209747,
-0.009604156017303467,
-0.02764902077615261,
-0.04153340309858322,
0.07278121262788773,
-0.02278265729546547,
-0.03335907682776451,
0.03194548934698105,
-0.026594670489430428,
0.05248995125293732,
0.018718499690294266,
0.00422603078186512,
-0.03828485310077667,
0.09643878787755966,
-0.018510738387703896,
0.04109445586800575,
-0.04903887212276459,
0.0071786572225391865,
0.12873922288417816,
0.03083708882331848,
0.01344015821814537,
-0.0638519674539566,
0.014447666704654694,
-0.01084438432008028,
0.009383752942085266,
-0.05313935875892639,
0.02605678327381611,
-0.029736759141087532,
-0.025184493511915207,
-0.04809354990720749,
0.0695914700627327,
0.0018870319472625852,
-0.029367098584771156,
0.04371057078242302,
-0.047467079013586044,
-0.028721051290631294,
0.0009280939702875912,
0.0044776322320103645,
-0.009281537495553493,
0.0224135909229517,
-0.03191668912768364,
0.03362387791275978,
-0.04077555611729622,
0.034860607236623764,
-0.02996685728430748,
-0.05891747400164604,
-0.0036003252025693655,
-0.020068153738975525,
-0.04074521362781525,
-0.0011602689046412706,
0.017849426716566086,
0.0014211158268153667,
-0.015940450131893158,
-0.014022743329405785,
0.0456155389547348,
-0.02454029954969883,
0.04795422777533531,
0.05185543745756149,
0.005444595590233803,
0.02997501753270626,
0.011828898452222347,
0.03604380786418915,
-0.02770136296749115,
0.01857476495206356,
-0.023130197077989578,
0.06262408941984177,
-0.011235003359615803,
0.022141525521874428,
-0.005838874727487564,
0.007494188379496336,
0.007750230375677347,
-0.04113896191120148,
-0.028461424633860588,
-0.014226553030312061,
0.03904334828257561,
-0.0003598267794586718,
0.005498332437127829,
-0.014171930029988289,
0.008343636058270931,
0.010182224214076996,
0.027238184586167336,
-0.021132096648216248,
-0.014500722289085388,
0.0050082881934940815,
0.0033942610025405884,
-0.007419672794640064,
-0.035889361053705215,
0.005809613037854433,
-0.017920425161719322,
-0.009832603856921196,
-0.016448700800538063,
-0.01715768501162529,
-0.03022918663918972,
-0.007501940708607435,
0.06739573180675507,
-0.006028090603649616,
-0.005598702467978001,
-0.03413420170545578,
-0.08869398385286331,
-0.007749767508357763,
-0.01826699636876583,
-0.007013206370174885,
0.0053766337223351,
-0.013683290220797062,
0.006143772043287754,
0.028409264981746674,
-0.005611446686089039,
-0.0351874940097332,
0.05981345474720001,
0.03432692214846611,
0.03358559310436249,
-0.028748158365488052,
-0.033433567732572556,
-0.017006566748023033,
0.008110285736620426,
-0.002647694665938616,
-0.032959505915641785,
-0.0023762325290590525,
0.02412557043135166,
0.041210174560546875,
-0.00940751750022173,
0.03052649460732937,
-0.005223556887358427,
-0.032366011291742325,
0.03395857289433479,
0.004883664660155773,
0.003099162830039859,
0.058952417224645615,
0.029247041791677475,
-0.039346352219581604,
-0.042568501085042953,
0.022208092734217644,
-0.007015308830887079,
0.00408973777666688,
0.00015438548871316016,
-0.06294737011194229,
-0.02192734181880951,
0.001959002111107111,
-0.0231328085064888,
-0.02628380060195923,
-0.030531147494912148,
-0.01647963561117649,
0.01673477701842785,
-0.026465948671102524,
-0.0024295561015605927,
-0.0326436385512352,
0.027781115844845772,
-0.01765269972383976,
0.004713579546660185,
0.009803172200918198,
0.035743460059165955,
0.0015731018502265215,
-0.01727079041302204,
0.03564279153943062,
0.015491633675992489,
0.026425296440720558,
0.023493792861700058,
-0.023599132895469666,
0.01394362561404705,
-0.02558741718530655,
-0.03289216011762619,
0.04854535311460495,
0.03675225004553795,
0.026784978806972504,
0.0307594146579504,
-0.03801116347312927,
-0.05488809570670128,
0.026883265003561974,
-0.016330618411302567,
0.0100129758939147,
-0.031126083806157112,
-0.0301276296377182,
0.013252351433038712,
-0.032518237829208374,
-0.005291995592415333,
-0.02434537373483181,
0.006118283607065678,
0.001610028208233416,
0.008989756926894188,
-0.04034685716032982,
-0.012008024379611015,
0.005989522207528353,
-0.0053446656093001366,
-0.017877670004963875,
-0.027420630678534508,
0.013628615066409111,
0.006936637219041586,
0.04079052805900574,
-0.02805076353251934,
0.01530835684388876,
-0.008940709754824638,
0.0028868180233985186,
-0.07016454637050629,
-0.018862644210457802,
-0.009430755861103535,
0.04825466498732567,
0.04347267746925354,
-0.05936751514673233,
0.02352522686123848,
0.019326601177453995,
-0.024055128917098045,
0.01219126395881176,
-0.012918379157781601,
0.013040641322731972,
-0.030388494953513145,
-0.04489060863852501,
-0.01651734858751297,
0.04936615005135536,
0.03587326034903526,
0.029888495802879333,
0.010904267430305481,
0.01705550216138363,
0.003906372468918562,
0.025328435003757477,
-0.037216223776340485,
0.017589738592505455,
-0.014403913170099258,
-0.03588445484638214,
0.03999746963381767,
0.007675873581320047,
-0.07314002513885498,
0.019214387983083725,
0.014293039217591286,
-0.05416848137974739,
0.011106249876320362,
0.04120894894003868,
0.04890675097703934,
-0.00047494168393313885,
0.023635927587747574,
0.03237142041325569,
0.02214188314974308,
-0.005821378901600838,
0.06460878252983093,
0.023925350978970528,
-0.021048255264759064,
-0.028050048276782036,
-0.006050741765648127,
-0.024934764951467514,
-0.04683679714798927,
0.05068016052246094,
-0.018336769193410873,
-0.00023733933630865067,
-0.013637710362672806,
-0.011178924702107906,
0.0016938484041020274,
-0.004559638909995556,
0.015798069536685944,
-0.02535981871187687,
-0.007521677762269974,
0.044579531997442245,
-0.02082410641014576,
-0.01157458033412695,
0.00437914626672864,
0.01633906364440918,
-0.02569575048983097,
0.05023692920804024,
0.004454596899449825,
0.010039418935775757,
-0.03728798031806946,
-0.014596342109143734,
-0.021550612524151802,
0.024198077619075775,
0.03935088589787483,
-0.027714425697922707,
-0.05379843711853027,
-0.0065848748199641705,
-0.014889243990182877,
0.008832436986267567,
-0.04502056539058685,
-0.006969512905925512,
0.04051602631807327,
-0.08368363976478577,
0.003044427838176489,
0.02256164886057377,
-0.018527625128626823,
-0.007912675850093365,
-0.008370045572519302,
-0.02244887873530388,
0.01395709253847599,
0.041938379406929016,
-0.015038421377539635,
-0.024060336872935295,
0.02572963759303093,
-0.0030180085450410843,
0.018273891881108284,
-0.0054618739522993565,
-0.000997836235910654,
-0.022378306835889816,
-0.030055245384573936,
0.030242914333939552,
0.011091495864093304,
-0.01644800417125225,
0.07290944457054138,
0.006255004554986954,
0.0128505052998662,
0.022397657856345177,
-0.005862451624125242,
-0.018617859110236168,
0.041124168783426285,
-0.02669212408363819,
-0.005676289089024067,
0.03742222115397453,
0.018229452893137932,
0.015225203707814217,
0.028832022100687027,
-0.031720034778118134,
-0.06650660932064056,
0.006255312357097864,
-0.04057183489203453,
0.0026556041557341814,
-0.028263576328754425,
-0.00702582998201251,
0.03576306998729706,
-0.033021923154592514,
-0.004798225127160549,
0.059801749885082245,
-0.013756143860518932,
-0.04273121803998947,
0.041450630873441696,
-0.016796555370092392,
0.044058408588171005,
0.013245615176856518,
0.0029072463512420654,
-0.00865043792873621,
-0.004582407884299755,
0.048423055559396744,
-0.009344357065856457,
0.03271176293492317,
0.000530984892975539,
-0.003960009664297104,
0.021495195105671883,
-0.048588503152132034,
0.010000783018767834,
0.004017948638647795,
0.024686729535460472,
-0.027025073766708374,
0.012624005787074566,
0.007562318351119757,
-0.017901413142681122,
-0.006362550426274538,
0.00023338540631812066,
-0.025932282209396362,
0.05792511999607086,
-0.01725371927022934,
0.05178279057145119,
-0.01900777965784073,
0.008372027426958084,
-0.0018482994055375457,
0.040442317724227905,
0.021429892629384995,
0.09067215025424957,
-0.001760207931511104,
-0.004746768623590469,
-0.05406622588634491,
-0.04092758148908615,
0.005860312841832638,
-0.04996603727340698,
-0.038966692984104156,
0.026695018634200096,
-0.017017412930727005,
0.04918571189045906,
-0.020972223952412605,
-0.001515292446129024,
-0.03549835458397865,
0.01811223104596138,
0.008427035994827747,
0.02058795653283596,
-0.02776106633245945,
-0.022244201973080635,
-0.0027037677355110645,
0.06084727495908737,
-0.02848505973815918,
-0.004324380308389664,
0.00745754037052393,
-0.023104656487703323,
-0.0348568856716156,
-0.0022090545389801264
] |
<p>In proving that the action $$S\equiv \int^{t_2}_{t_1}L(x, x',t)dt$$ has a has a stationary point $x_0$ that satisfies the following:
$$\frac{d}{dt}(\frac{\partial L}{\partial x'_0})=\frac{\partial L}{\partial x_0}$$
My textbook finds the action of $$x_a(t)\equiv x_0(t)+a\beta (t)$$ differentiated with respect a to the first order to reach the expression:
$$\frac{\partial}{\partial a} S[x_a(t)]=\int^{t_2}_{t_1}(\frac{\partial L}{\partial x_a} - \frac{d}{dt}(\frac{\partial L}{\partial x'_a}))\beta dt$$
It then says that the only way this can be 0 for all $\beta$ is if the expression in the parentheses evaluated at $a=0$ is identically equal to zero. I don't understand why we can evaluate it at 0, please could someone explain? (I would understand if the thing in the parentheses had to be 0 for all $a$ but why does been it been 0 for $a=0$ imply it is 0 for all $a$?)</p> | 4,571 | [
0.012732386589050293,
0.014554891735315323,
-0.016183452680706978,
-0.0016040608752518892,
0.03880155086517334,
-0.0007952784653753042,
-0.0461343415081501,
-0.010438820347189903,
-0.00298290210776031,
-0.011102382093667984,
-0.0008171697263605893,
0.0018985558999702334,
0.03122042864561081,
-0.002921812003478408,
0.06749523431062698,
-0.0037789586931467056,
-0.01805097423493862,
-0.00981228705495596,
0.004090148955583572,
0.01747054234147072,
-0.030778106302022934,
0.016766712069511414,
0.005399479065090418,
-0.002830172423273325,
-0.008495460264384747,
-0.004733525216579437,
-0.056803155690431595,
0.02466684952378273,
-0.011893617920577526,
0.0871545821428299,
-0.046421464532613754,
-0.03103478252887726,
-0.030065467581152916,
0.02032405510544777,
0.0057356832548975945,
0.03643263503909111,
-0.07728475332260132,
-0.03335260599851608,
-0.009881634265184402,
0.02931821532547474,
-0.0011142910225316882,
-0.024581151083111763,
0.008221166208386421,
0.08040511608123779,
-0.0161576084792614,
0.022748470306396484,
0.04608408361673355,
-0.003278982127085328,
0.04596433416008949,
-0.02997906506061554,
0.041073430329561234,
-0.0027139189187437296,
0.060822341591119766,
0.05431542545557022,
0.018826929852366447,
-0.0015110013773664832,
0.029250584542751312,
0.034033529460430145,
-0.002856782404705882,
-0.03541389852762222,
-0.040403131395578384,
-0.01347209233790636,
0.001431148499250412,
-0.03505565971136093,
-0.006694970652461052,
-0.011788452044129372,
0.008440017700195312,
-0.0096691669896245,
0.027333704754710197,
-0.040010321885347366,
-0.011534473858773708,
-0.0007640559924766421,
-0.020319849252700806,
0.011129205115139484,
-0.01013251580297947,
-0.00839686207473278,
0.015889408066868782,
0.001378834480419755,
0.043334510177373886,
0.02011771872639656,
0.002639411250129342,
0.006497771013528109,
0.02217239886522293,
0.03683343157172203,
-0.029205169528722763,
-0.004796217195689678,
0.048792533576488495,
0.007949532009661198,
0.030340971425175667,
0.015844035893678665,
0.005705719813704491,
0.014927318319678307,
-0.0062902565114200115,
-0.0115806320682168,
0.011590643785893917,
0.04950565844774246,
0.007302945479750633,
0.01984945684671402,
-0.003490729723125696,
-0.040577664971351624,
-0.011644285172224045,
-0.06010016053915024,
0.015268421731889248,
0.03440452739596367,
0.014302008785307407,
-0.01593877375125885,
-0.02671443298459053,
0.03790275752544403,
-0.005832222755998373,
-0.01278544869273901,
-0.046180397272109985,
0.010346435941755772,
0.003270209301263094,
0.0038134418427944183,
-0.02318493463099003,
-0.013332968577742577,
0.0006255015032365918,
0.01351682934910059,
-0.015226460993289948,
0.011613680981099606,
0.033630795776844025,
-0.018812796100974083,
0.015133848413825035,
0.03193895146250725,
-0.0690235123038292,
0.030798662453889847,
0.011651485227048397,
-0.011168834753334522,
-0.02991761639714241,
0.017986217513680458,
0.009722347371280193,
-0.03381243720650673,
0.00485726073384285,
0.029384003952145576,
0.025264980271458626,
-0.030418818816542625,
-0.04570217430591583,
-0.03038177452981472,
0.029422134160995483,
-0.020235933363437653,
0.00407980615273118,
-0.05339448153972626,
-0.0321974977850914,
0.02533652074635029,
0.07316820323467255,
-0.04998881369829178,
0.022104596719145775,
0.023435264825820923,
0.018882473930716515,
-0.017777519300580025,
-0.007008022163063288,
-0.015362066216766834,
-0.02430512197315693,
-0.04825635626912117,
0.011707738973200321,
-0.0031527795363217592,
0.04323878884315491,
0.0323600210249424,
0.00234413705766201,
-0.04733942449092865,
0.08242935687303543,
-0.04648629575967789,
0.0036430908367037773,
0.011958559043705463,
-0.010040469467639923,
-0.010629231110215187,
0.07324153184890747,
0.01090796384960413,
0.007611740846186876,
0.009026454761624336,
0.040317367762327194,
0.026445966213941574,
-0.05995389446616173,
0.06518623232841492,
0.02329682931303978,
-0.03295285999774933,
-0.03404703363776207,
-0.020453713834285736,
-0.009476283565163612,
0.028183402493596077,
-0.038523945957422256,
0.008775926195085049,
-0.01518470048904419,
0.020052248612046242,
0.007732918485999107,
0.061753321439027786,
-0.01756093092262745,
0.033066876232624054,
-0.02384013682603836,
-0.03602597489953041,
-0.027905674651265144,
-0.08979390561580658,
0.03940150886774063,
-0.005639306269586086,
-0.007546830456703901,
0.02714942768216133,
0.0006948708323761821,
0.006184147205203772,
-0.023490410298109055,
0.0105896620079875,
-0.01415170170366764,
0.001270210719667375,
-0.005138726439327002,
-0.028164494782686234,
0.03916829451918602,
0.03778570517897606,
0.07075896114110947,
-0.0001619656104594469,
0.06230141595005989,
-0.025017453357577324,
-0.005173610523343086,
0.025284258648753166,
-0.0015728221042081714,
0.060385409742593765,
-0.006600667722523212,
0.000269033684162423,
-0.025311654433608055,
-0.025184018537402153,
-0.037404924631118774,
0.05446721240878105,
-0.052941594272851944,
0.04368085414171219,
0.09356498718261719,
-0.0028754500672221184,
-0.009649889543652534,
0.038529884070158005,
-0.0010754573158919811,
0.029851874336600304,
-0.00620612595230341,
-0.042017512023448944,
-0.030075157061219215,
0.0008539095288142562,
0.04156428202986717,
0.04530925303697586,
-0.02994939684867859,
0.009459459222853184,
0.040510427206754684,
0.011694824323058128,
-0.00012236199108883739,
0.027156593278050423,
0.007912831380963326,
-0.005460088141262531,
0.05489545688033104,
-0.007025528233498335,
-0.002593924291431904,
0.02049739472568035,
0.04464677348732948,
-0.004855784587562084,
0.06986473500728607,
0.045472338795661926,
-0.03353191912174225,
0.07071501016616821,
-0.008412540890276432,
0.004050008952617645,
-0.013209310360252857,
-0.007502408232539892,
0.04643315076828003,
0.01941927708685398,
0.06288348138332367,
0.02630847878754139,
0.042755406349897385,
0.0072807627730071545,
-0.02266409434378147,
0.0029506655409932137,
0.0401090644299984,
-0.03472648933529854,
-0.006638118531554937,
-0.03951210528612137,
0.02105306088924408,
-0.011248132213950157,
-0.004096595104783773,
-0.0018822163110598922,
-0.05475073680281639,
-0.02189326286315918,
-0.012520547956228256,
0.041944101452827454,
0.014423125423491001,
-0.003971362020820379,
-0.01665499247610569,
-0.02137327939271927,
-0.04001975804567337,
-0.009779943153262138,
0.06112808734178543,
0.034004051238298416,
-0.0663747563958168,
0.014573442749679089,
-0.005709382705390453,
-0.013716677203774452,
0.06825102865695953,
0.02519717440009117,
0.030639169737696648,
0.028125032782554626,
-0.04761607199907303,
-0.05732474476099014,
-0.040521010756492615,
-0.050845563411712646,
0.0028551046270877123,
-0.02348080836236477,
0.021183084696531296,
0.05255373939871788,
-0.006505281198769808,
-0.03384655341506004,
0.009899085387587547,
-0.03986572474241257,
-0.013976644724607468,
-0.021632835268974304,
-0.008344882167875767,
0.03396029397845268,
-0.032115694135427475,
0.054940614849328995,
0.010142730548977852,
-0.048003099858760834,
-0.03690577670931816,
-0.053088851273059845,
-0.010684638284146786,
-0.015844309702515602,
0.00594745809212327,
0.025771290063858032,
-0.03027692623436451,
-0.04724610596895218,
0.08369861543178558,
0.03419198840856552,
-0.005297691095620394,
0.007482059765607119,
-0.004924119915813208,
-0.03812907636165619,
-0.05865921452641487,
-0.004147226456552744,
-0.0023358885664492846,
-0.04161863774061203,
0.046133942902088165,
0.02871747687458992,
0.043374013155698776,
0.048377953469753265,
0.00938478298485279,
0.004866095259785652,
0.004889824893325567,
0.01715787872672081,
0.027058260515332222,
0.017280450090765953,
0.03958333283662796,
0.03294729068875313,
0.022941291332244873,
0.0017099357210099697,
0.03652450442314148,
0.03054760955274105,
-0.0347771979868412,
0.027211815118789673,
0.004755151458084583,
-0.006633276119828224,
-0.04995303601026535,
0.04172880947589874,
-0.000517416512593627,
-0.0020158325787633657,
-0.03376452997326851,
-0.01541964802891016,
0.024574553593993187,
-0.06637351959943771,
-0.015554206445813179,
-0.00172651675529778,
0.01456568855792284,
-0.011175356805324554,
-0.061370473355054855,
-0.0032232259400188923,
-0.028336547315120697,
0.01717005856335163,
-0.005446747411042452,
-0.024430496618151665,
0.015128545463085175,
0.013658178970217705,
-0.0011904534185305238,
-0.024170011281967163,
-0.05439648777246475,
-0.015907254070043564,
-0.04935045540332794,
0.0286836139857769,
0.014781104400753975,
0.05038372799754143,
0.009108593687415123,
0.012191773392260075,
0.008981551975011826,
0.03917694836854935,
-0.004078037571161985,
0.017659852281212807,
-0.06860709190368652,
0.03162965551018715,
-0.01380417961627245,
-0.04656253382563591,
0.003009533742442727,
0.02352692186832428,
0.031580690294504166,
-0.023977169767022133,
-0.007360854651778936,
-0.04805390536785126,
-0.007552543189376593,
-0.06684993952512741,
-0.023601040244102478,
-0.0554792582988739,
-0.025252103805541992,
-0.05491179972887039,
0.010291771031916142,
-0.009198511950671673,
-0.031248679384589195,
0.02776741422712803,
0.05502748861908913,
-0.041763726621866226,
0.011212271638214588,
-0.06693511456251144,
-0.01732652634382248,
0.04419815167784691,
0.023492613807320595,
0.05496171489357948,
0.011599955148994923,
0.005581050645560026,
0.008666475303471088,
0.000017975067748920992,
0.0685943067073822,
-0.005310075357556343,
-0.021052127704024315,
-0.033358387649059296,
-0.02375970035791397,
-0.023920796811580658,
0.008495374582707882,
0.03516846150159836,
0.01838172785937786,
0.0004160134994890541,
0.012400350533425808,
0.03383346274495125,
-0.013296041637659073,
0.03488287702202797,
0.048193883150815964,
-0.01255706511437893,
0.00021089703659527004,
-0.00981592945754528,
-0.0034578589256852865,
-0.052351370453834534,
0.00010535919136600569,
-0.004805827978998423,
-0.03491128236055374,
-0.007339228875935078,
-0.009087474085390568,
-0.008873921819031239,
0.013180682435631752,
0.009115250781178474,
-0.001302178017795086,
0.023733582347631454,
0.015183808282017708,
0.021120771765708923,
-0.027545563876628876,
0.04369031637907028,
0.016432086005806923,
0.015140638686716557,
0.0038636603858321905,
-0.0038381514605134726,
-0.04662642255425453,
-0.005152717232704163,
-0.00670491112396121,
0.04793991893529892,
-0.0049452041275799274,
-0.021320711821317673,
-0.03003344126045704,
-0.0033850164618343115,
0.018214767798781395,
-0.036053434014320374,
0.01219450868666172,
-0.008425799198448658,
0.0016006279038265347,
-0.005996029824018478,
-0.008665905334055424,
-0.01708250865340233,
0.005410331301391125,
0.0011426297714933753,
0.03813941031694412,
-0.0065470850095152855,
-0.009642482735216618,
-0.028829997405409813,
-0.01708275079727173,
-0.018670594319701195,
0.01912066899240017,
0.008490451611578465,
0.019067594781517982,
-0.000611807219684124,
0.07288993895053864,
-0.050840236246585846,
-0.07341846078634262,
0.009782085195183754,
-0.0026673292741179466,
-0.005756064783781767,
0.05034696310758591,
-0.026494234800338745,
-0.052132368087768555,
0.05825817584991455,
0.023528018966317177,
0.010144110769033432,
0.005580552853643894,
-0.008808921091258526,
0.015918465331196785,
0.04008683189749718,
0.01616613380610943,
0.06363432109355927,
0.03608084097504616,
0.0057686008512973785,
-0.0019719540141522884,
0.02028636448085308,
0.006348433904349804,
-0.014397067949175835,
0.003110162215307355,
-0.07570675015449524,
0.002918270416557789,
-0.020503094419836998,
0.032900579273700714,
-0.042418599128723145,
-0.02926698513329029,
0.020611898973584175,
-0.00745221134275198,
-0.0067070177756249905,
0.06033748388290405,
0.03563970699906349,
0.0012415529927238822,
-0.023736726492643356,
0.023247499018907547,
-0.0011804619571194053,
-0.007336848881095648,
0.04236777871847153,
-0.035602111369371414,
0.00940582063049078,
0.030940674245357513,
0.007397235371172428,
0.03383030742406845,
-0.007255563512444496,
-0.03276204690337181,
0.0033105260226875544,
-0.04011734947562218,
0.041259292513132095,
0.023722488433122635,
0.0029843407683074474,
-0.002541967900469899,
-0.028598923236131668,
-0.04050002992153168,
0.007959442213177681,
-0.004950844217091799,
0.010847959667444229,
-0.08431628346443176,
0.011920538730919361,
0.04409433528780937,
-0.014289508573710918,
-0.0759633257985115,
-0.06601645052433014,
0.01203180942684412,
0.029621178284287453,
-0.004847744945436716,
-0.007844075560569763,
0.0067732385359704494,
-0.013773997314274311,
-0.034690409898757935,
0.008613948710262775,
0.03510959818959236,
-0.006727180443704128,
-0.0021022558212280273,
0.027705363929271698,
0.05069269984960556,
0.05240509659051895,
0.03768407925963402,
-0.003970677498728037,
-0.0042932587675750256,
-0.05249103531241417,
-0.03922804445028305,
-0.015177832916378975,
0.05931132659316063,
-0.022404640913009644,
0.012200920842587948,
0.0003454336547292769,
0.0034498563036322594,
0.018471160903573036,
-0.009651439264416695,
-0.014429604634642601,
-0.021816808730363846,
0.02232186309993267,
0.02841849997639656,
-0.04927804321050644,
-0.008202368393540382,
0.012525656260550022,
0.031477611511945724,
0.02162500098347664,
-0.021713724359869957,
-0.006015529856085777,
-0.06148959696292877,
-0.016112299636006355,
-0.027603069320321083,
-0.008035775274038315,
-0.011243045330047607,
0.1006377562880516,
-0.0244964137673378,
0.017732974141836166,
0.016238899901509285,
0.006980904843658209,
0.02652464434504509,
-0.009160676971077919,
0.0012889161007478833,
-0.0027619656175374985,
-0.046255387365818024,
-0.046386703848838806,
0.008538808673620224,
-0.02989482693374157,
0.06573508679866791,
0.05211873725056648,
-0.003511159447953105,
0.029592925682663918,
0.04584662243723869,
-0.008749453350901604,
-0.0069574955850839615,
-0.022060493007302284,
-0.019194671884179115,
-0.004047504160553217,
-0.010944640263915062,
0.030008835718035698,
-0.0247278343886137,
-0.021695362403988838,
0.050992950797080994,
0.02087065763771534,
-0.002025204012170434,
-0.00796681921929121,
0.025744222104549408,
-0.026725877076387405,
0.002181165385991335,
0.028672125190496445,
-0.04368053749203682,
0.037238944321870804,
0.002724507125094533,
0.03308698534965515,
-0.017183255404233932,
-0.02875615283846855,
0.028790751472115517,
-0.013267156668007374,
0.0031491017434746027,
-0.03193095698952675,
-0.019740616902709007,
-0.04442201554775238,
0.03726213052868843,
-0.0014480209210887551,
0.012894564308226109,
0.06078796833753586,
0.011361556127667427,
0.02206534706056118,
-0.008989034220576286,
0.039062369614839554,
0.003354733344167471,
-0.0002955793170258403,
-0.018648061901330948,
-0.05884808301925659,
-0.011905506253242493,
0.04435427859425545,
-0.01725323125720024,
-0.016064554452896118,
-0.01712745428085327,
-0.05484548956155777,
0.035198356956243515,
0.037545494735240936,
-0.007215824443846941,
-0.005908292718231678,
0.10401908308267593,
0.020558271557092667,
0.04814263433218002,
-0.008488607592880726,
-0.005524021107703447,
0.10366013646125793,
0.06884502619504929,
0.0006165608065202832,
-0.08674569427967072,
-0.011283078230917454,
-0.013613390736281872,
0.022271890193223953,
-0.027806445956230164,
0.05832742527127266,
0.040548648685216904,
0.0038595558144152164,
0.014905312098562717,
0.044517986476421356,
-0.01782642863690853,
-0.011114644818007946,
0.030344316735863686,
-0.051501329988241196,
-0.05509499832987785,
-0.023730874061584473,
-0.003755201818421483,
-0.03301908075809479,
0.006784557364881039,
-0.05400747433304787,
0.010191874578595161,
-0.014120487496256828,
0.026850519701838493,
-0.013577497564256191,
-0.034454576671123505,
0.010498616844415665,
-0.015690350905060768,
-0.03246420621871948,
0.004574250895529985,
0.03404076769948006,
-0.00848077517002821,
-0.09983931481838226,
0.012876330874860287,
0.0074950773268938065,
0.026342596858739853,
0.04270242154598236,
0.054375533014535904,
-0.0010843551717698574,
0.02608577162027359,
0.03338906913995743,
0.041843563318252563,
-0.0058429366908967495,
-0.04348183795809746,
-0.022464469075202942,
0.06311885267496109,
-0.013390759937465191,
0.011193421669304371,
-0.010728960856795311,
-0.006644443143159151,
-0.015013850294053555,
-0.037551190704107285,
-0.01629953645169735,
0.0033352826721966267,
0.018008098006248474,
0.00723686721175909,
-0.007137985434383154,
-0.028507255017757416,
-0.0043905433267354965,
-0.008434253744781017,
-0.024468954652547836,
0.022536449134349823,
-0.016687199473381042,
0.0015415531815961003,
-0.026137711480259895,
0.013890134170651436,
-0.03323645144701004,
-0.010434717871248722,
0.0071832300163805485,
-0.014996698126196861,
-0.015484694391489029,
-0.019044021144509315,
0.00026541430270299315,
-0.024681907147169113,
0.035549283027648926,
0.00683398125693202,
-0.01097035314887762,
-0.005591246765106916,
-0.06684593111276627,
0.015366694889962673,
-0.03283742070198059,
-0.0023384143132716417,
-0.002340502105653286,
-0.017892872914671898,
-0.015743739902973175,
0.056809041649103165,
-0.026575548574328423,
-0.004226974677294493,
-0.0003583315701689571,
0.04005303233861923,
0.011142248287796974,
-0.042785145342350006,
-0.011444761417806149,
0.026629384607076645,
-0.03133273869752884,
0.009096263907849789,
0.03266337513923645,
0.02788158878684044,
0.02617487497627735,
0.0286245197057724,
-0.02329595945775509,
0.022083835676312447,
-0.011703201569616795,
-0.011509482748806477,
0.017920084297657013,
-0.023256825283169746,
0.04197518154978752,
0.06425448507070541,
0.01089529786258936,
-0.02819717861711979,
-0.029790710657835007,
-0.014349721372127533,
0.024929868057370186,
0.021973609924316406,
0.008290627039968967,
-0.024801146239042282,
0.010448435321450233,
-0.03269366919994354,
0.0043652174063026905,
-0.06426861137151718,
-0.013804112561047077,
-0.04395128786563873,
0.010081340558826923,
0.033556874841451645,
-0.009943920187652111,
-0.0071467687375843525,
0.03248293697834015,
0.011735409498214722,
-0.03978433832526207,
0.0014586523175239563,
0.015421642921864986,
-0.00914050918072462,
-0.02343554049730301,
0.04276064783334732,
-0.020230649039149284,
0.0076890201307833195,
-0.0020971233025193214,
-0.029283661395311356,
0.024878082796931267,
-0.03514759987592697,
-0.05391963943839073,
0.010001560673117638,
0.03833403438329697,
0.029563168063759804,
0.017277806997299194,
-0.008796660229563713,
-0.028500309213995934,
0.044487349689006805,
0.0018269593128934503,
-0.01752667874097824,
0.004185899160802364,
-0.04716913402080536,
-0.021819675341248512,
-0.026219327002763748,
0.024112621322274208,
0.03486949950456619,
-0.0014900320675224066,
0.003628632053732872,
0.032296840101480484,
-0.036231670528650284,
-0.03164758160710335,
0.024816343560814857,
-0.014723770320415497,
0.041235391050577164,
0.03496987372636795,
0.01727285236120224,
0.021747516468167305,
0.06929570436477661,
0.010089783929288387,
0.00020213118114043027,
-0.03094799630343914,
0.040539439767599106,
-0.07922286540269852,
0.028591301292181015,
-0.01683872751891613,
-0.005254336632788181,
0.044226355850696564,
-0.03163592144846916,
0.024296963587403297,
0.05830002948641777,
-0.020629076287150383,
-0.027458783239126205,
-0.035769205540418625,
-0.011164492927491665,
-0.00481313606724143,
-0.03826111927628517,
-0.012866683304309845,
0.0616350881755352,
0.06862597167491913,
0.04488814249634743,
0.03240935876965523,
0.006594215985387564,
0.0009681903757154942,
0.00162581040058285,
0.0029009156860411167,
0.025436153635382652,
-0.023200178518891335,
-0.00417568301782012,
0.06296586990356445,
-0.004087365232408047,
-0.023477068170905113,
0.022914672270417213,
-0.02892695926129818,
-0.02243945561349392,
-0.0055458093993365765,
0.05946211889386177,
0.01252890657633543,
0.02056284435093403,
0.03307388350367546,
0.023024138063192368,
-0.0042032343335449696,
0.019173666834831238,
0.02201419696211815,
-0.013768657110631466,
-0.031791672110557556,
-0.013954917900264263,
0.03658837080001831,
-0.03745455667376518,
-0.044671282172203064,
0.033301714807748795,
-0.03320248797535896,
-0.03653819113969803,
-0.01691526174545288,
-0.009601463563740253,
0.029056383296847343,
-0.03439032658934593,
0.004095485899597406,
0.00877375341951847,
-0.012672455981373787,
0.02294466830790043,
0.021408656612038612,
-0.015616674907505512,
-0.0017779000336304307,
-0.020593706518411636,
-0.04112817347049713,
0.042665693908929825,
0.017107630148530006,
-0.011489929631352425,
-0.08846079558134079,
-0.030136020854115486,
-0.01906987652182579,
-0.05137265473604202,
-0.048620883375406265,
0.007244236301630735,
-0.05904914066195488,
0.005332444328814745,
0.024521272629499435,
0.019343789666891098,
-0.005597521550953388,
-0.044724155217409134,
-0.009261738508939743,
-0.0806274265050888,
0.08064272999763489,
-0.016101088374853134,
-0.024731306359171867,
-0.042889829725027084,
0.010845300741493702,
-0.018943488597869873,
0.003348030149936676,
0.010570231825113297,
-0.0024704057723283768,
0.018465252593159676,
0.055787038058042526,
0.03008914180099964,
0.006659636739641428,
-0.0029259526636451483,
0.0053856451995670795,
-0.004276799038052559,
-0.013651831075549126,
-0.02860397845506668,
0.008579924702644348,
0.0031058017630130053,
0.0463823638856411,
-0.007669168058782816,
-0.0017040794482454658,
-0.006614945363253355,
0.00008241119212470949,
-0.03738319128751755,
0.032064441591501236,
0.02488950453698635,
-0.012649618089199066,
0.07961631566286087,
0.008884698152542114,
0.023962855339050293,
0.001160886138677597,
-0.03963693976402283,
-0.024898573756217957,
0.012811691500246525,
-0.03290465846657753,
-0.006034824997186661,
-0.01981077529489994,
-0.005887707229703665,
-0.024660857394337654,
0.0026154587976634502,
0.004680015612393618,
0.04622524231672287,
-0.003507840447127819,
-0.03897421434521675,
0.0124354287981987,
0.01081865280866623,
0.02101275324821472,
0.01872723363339901,
-0.016270676627755165,
0.028034774586558342,
0.04310792684555054,
0.047602854669094086,
0.045820094645023346,
0.017098447307944298,
-0.033428601920604706,
-0.02614603564143181,
0.0141120795160532,
-0.04104802757501602,
0.002699822885915637,
-0.008951093070209026,
0.04377881810069084,
-0.057960398495197296,
-0.04397157207131386,
-0.01166793704032898,
-0.016212385147809982,
0.0042837816290557384,
0.003109965706244111,
-0.02910684049129486,
0.05335330218076706,
-0.0190297681838274,
0.03586079552769661,
0.013307825662195683,
0.01395094022154808,
-0.0013563705142587423,
-0.02658962272107601,
0.04394422471523285,
0.025620831176638603,
-0.03521600365638733,
0.027873819693922997,
-0.01128785777837038,
-0.02524399757385254,
0.021531442180275917,
-0.03245069459080696,
-0.009716602973639965,
0.030896738171577454,
-0.015784358605742455,
-0.04645979404449463,
-0.028754880651831627,
-0.027250539511442184,
-0.024054216220974922,
0.038662828505039215,
0.03926309943199158,
-0.011998173780739307,
0.002660416066646576,
-0.03789733722805977,
-0.05947566032409668,
0.0527695007622242,
-0.06889180094003677,
-0.024677302688360214,
0.0020373472943902016,
-0.01818174310028553,
0.0024375729262828827,
0.012644106522202492
] |
<p>I am looking for a device to provide variable excitation voltage (30VDC to 200VDC) to a Transducer for a variable time (10 to 20 milliseconds).</p>
<p>Can someone please advise how I could achieve this using an off the shelf product? </p> | 4,572 | [
0.015432002022862434,
-0.017437368631362915,
0.015824180096387863,
-0.01426380593329668,
0.01605548895895481,
-0.01331054326146841,
-0.01735161803662777,
-0.0015981850447133183,
0.04863119497895241,
-0.036052267998456955,
0.010100211016833782,
0.07369432598352432,
0.02632061019539833,
0.012615629471838474,
0.0039361403323709965,
-0.011923865415155888,
0.010218130424618721,
-0.020441735163331032,
-0.02258080430328846,
-0.05023499205708504,
-0.013051427900791168,
-0.009145638905465603,
-0.022391611710190773,
0.014313851483166218,
-0.00474918819963932,
0.026966316625475883,
0.04179549217224121,
0.015353686176240444,
-0.019880685955286026,
0.039095439016819,
-0.052401285618543625,
-0.0620807483792305,
-0.0245132427662611,
0.02692381665110588,
0.03338339179754257,
-0.023641448467969894,
-0.0496382899582386,
-0.06977306306362152,
0.0046699619852006435,
0.020455140620470047,
-0.0066875615157186985,
0.014443942345678806,
0.02047455683350563,
0.06095665693283081,
0.010251190513372421,
0.015964670106768608,
-0.038585007190704346,
-0.029395965859293938,
0.014888830482959747,
-0.0637698769569397,
0.05285166576504707,
-0.03248045966029167,
0.05216185003519058,
0.007337002549320459,
-0.013783363625407219,
0.0110359201207757,
0.06023233011364937,
0.0742688924074173,
0.011566811241209507,
-0.05385668948292732,
0.010988036170601845,
-0.005220974329859018,
-0.017687352374196053,
-0.05276026204228401,
-0.06134248152375221,
-0.016974184662103653,
0.040016092360019684,
0.0013178868684917688,
0.00466798385605216,
-0.06532299518585205,
0.03120400756597519,
-0.01457075122743845,
0.01708250865340233,
0.03276417776942253,
-0.016584152355790138,
-0.054869767278432846,
-0.016290349885821342,
0.04502800479531288,
0.029021747410297394,
0.0582122765481472,
0.015138639137148857,
-0.015628615394234657,
-0.0029843926895409822,
0.03805287554860115,
-0.0064468239434063435,
-0.016803495585918427,
0.08525378257036209,
-0.03058747388422489,
0.035052549093961716,
0.04751903936266899,
-0.05326572805643082,
0.029294008389115334,
0.029638756066560745,
0.05718153342604637,
-0.023442041128873825,
-0.029973017051815987,
-0.020970534533262253,
0.04312124475836754,
0.016247039660811424,
-0.0301373228430748,
0.07465160638093948,
-0.01585150696337223,
0.0028439240995794535,
0.043039459735155106,
-0.001450850279070437,
0.017134707421064377,
0.027257060632109642,
-0.020531611517071724,
-0.003992465324699879,
-0.008182479999959469,
-0.03815979138016701,
-0.00650359969586134,
-0.0007870201952755451,
0.026930173859000206,
0.012853732332587242,
-0.026651522144675255,
-0.0350724533200264,
-0.019153563305735588,
0.0236370749771595,
0.019818739965558052,
0.03384338691830635,
-0.05046777427196503,
0.027609989047050476,
-0.06051606684923172,
-0.054178234189748764,
0.007394249085336924,
0.002321483101695776,
0.026846913620829582,
-0.013342482037842274,
0.020652679726481438,
0.030656438320875168,
-0.046144891530275345,
0.02314331941306591,
-0.035929325968027115,
0.06846598535776138,
-0.024273395538330078,
-0.07429824024438858,
-0.0688793808221817,
0.04469506815075874,
-0.002301169326528907,
-0.0008329578558914363,
-0.07233350723981857,
0.007540449965745211,
0.03422817587852478,
0.01701967790722847,
0.02120613493025303,
-0.007274152711033821,
0.025753086432814598,
-0.015756629407405853,
-0.005661145783960819,
-0.016154475510120392,
-0.01432214118540287,
-0.007485378999263048,
0.02118438109755516,
0.0028042993508279324,
-0.04910536855459213,
0.04019101336598396,
0.034204550087451935,
0.0029687692876905203,
0.012923446483910084,
0.006991909351199865,
-0.004243304952979088,
-0.026483237743377686,
0.015847155824303627,
0.026944564655423164,
-0.029782740399241447,
0.07789415121078491,
-0.0074248723685741425,
0.00013035260781180114,
-0.014603450894355774,
0.008797798305749893,
0.02300354465842247,
0.03124949336051941,
-0.0047850036062300205,
0.024295110255479813,
-0.020458495244383812,
0.005076086614280939,
0.003718295367434621,
0.004559777677059174,
0.04003174230456352,
-0.009060082957148552,
-0.038898494094610214,
0.008373173885047436,
0.022415872663259506,
-0.0029675692785531282,
-0.004375434014946222,
-0.0327814482152462,
0.05306825414299965,
0.007614768110215664,
-0.04194677993655205,
-0.036813195794820786,
-0.028557484969496727,
0.05296735465526581,
0.008757197298109531,
-0.03406166657805443,
0.017413752153515816,
-0.012645119801163673,
0.014304841868579388,
0.010404267348349094,
-0.04262089729309082,
-0.029796015471220016,
-0.011255527846515179,
0.02626749500632286,
0.00655664736405015,
-0.0009492277167737484,
0.025155747309327126,
0.036576032638549805,
-0.04088156297802925,
-0.002824964467436075,
-0.00917020719498396,
-0.03616616874933243,
-0.010158712044358253,
-0.020595651119947433,
0.059355854988098145,
-0.035662516951560974,
0.009646184742450714,
0.007562617771327496,
0.025619132444262505,
-0.011360710486769676,
0.035640545189380646,
-0.03041665628552437,
0.044596023857593536,
0.09115671366453171,
0.005036186892539263,
0.011438320390880108,
0.018343281000852585,
0.017969977110624313,
0.013247833587229252,
0.012863745912909508,
-0.04057524725794792,
-0.06927376240491867,
0.0017031233292073011,
0.02881021797657013,
-0.0025830711238086224,
0.01666298136115074,
0.04223779961466789,
0.06690163910388947,
-0.000450320600066334,
0.054456423968076706,
0.022342659533023834,
0.015515759587287903,
0.0030030293855816126,
-0.02221802994608879,
0.006192729342728853,
-0.004584493115544319,
0.009381174109876156,
0.03377371281385422,
-0.011635188944637775,
0.0464521162211895,
-0.019389603286981583,
0.0007216148660518229,
0.03692646697163582,
-0.01523219421505928,
0.016656165942549706,
0.0251885075122118,
-0.029538750648498535,
0.01848897896707058,
-0.02454613707959652,
0.047001369297504425,
0.018358055502176285,
0.009813455864787102,
0.04056160897016525,
0.017212392762303352,
-0.010592140257358551,
0.02722463384270668,
0.0015729282749816775,
0.02015059068799019,
-0.009647930972278118,
0.022339368239045143,
-0.04535349830985069,
0.012436865828931332,
-0.00964711420238018,
-0.008029768243432045,
-0.009631124325096607,
-0.01895587332546711,
0.04121378809213638,
0.03319134935736656,
0.041497278958559036,
-0.019001994282007217,
-0.04255906492471695,
0.030095448717474937,
-0.060528360307216644,
0.008728398941457272,
-0.008481139317154884,
-0.0028742996510118246,
0.004981594625860453,
0.013865094631910324,
-0.03697631508111954,
0.05707196146249771,
0.017697466537356377,
0.012579118832945824,
0.00044688559137284756,
0.004497370682656765,
-0.0632070004940033,
0.020169157534837723,
-0.02147599309682846,
0.021159028634428978,
-0.021905293688178062,
-0.011225596070289612,
0.0310500618070364,
0.03779706731438637,
-0.06885333359241486,
0.01890205778181553,
-0.0786449983716011,
0.03651734068989754,
0.010851265862584114,
0.00447538448497653,
0.033064525574445724,
-0.046619050204753876,
0.005454907193779945,
0.0635056272149086,
-0.022535091266036034,
-0.010426118969917297,
-0.006311782635748386,
-0.06440360099077225,
0.011369064450263977,
-0.0003083600022364408,
0.05302442982792854,
0.0007993255276232958,
-0.025488751009106636,
0.053303930908441544,
0.008277477696537971,
-0.0326228141784668,
-0.014712026342749596,
-0.057091739028692245,
0.018559539690613747,
-0.06147891655564308,
0.015544340945780277,
0.02535456046462059,
-0.047597646713256836,
0.0005484048160724342,
0.009819159284234047,
0.00045288196997717023,
0.07621166110038757,
0.01474468968808651,
-0.02161894552409649,
0.008983300998806953,
0.034112319350242615,
0.020795268937945366,
0.05776983126997948,
0.026792796328663826,
-0.06122473627328873,
-0.02135515958070755,
-0.021454107016324997,
0.01400318369269371,
-0.0036492592189460993,
-0.02177758887410164,
0.01880643703043461,
0.007403371389955282,
-0.00897199660539627,
-0.034951817244291306,
-0.0026814814191311598,
-0.0167009886354208,
-0.021162474527955055,
-0.0484725646674633,
0.06863728910684586,
0.042965367436409,
-0.01840624026954174,
0.0027654666919261217,
0.05201103165745735,
0.0278864074498415,
0.004848210606724024,
-0.02626223675906658,
0.020667674019932747,
0.004276819992810488,
0.04340599849820137,
-0.02391870878636837,
-0.019585395231842995,
0.035273075103759766,
0.005734584294259548,
0.05146649479866028,
0.014362986199557781,
-0.002222547773271799,
0.011054589413106441,
-0.05106755718588829,
0.01964820921421051,
-0.031230861321091652,
0.07555816322565079,
0.046045251190662384,
0.0596981942653656,
0.026560021564364433,
-0.018833372741937637,
0.041797198355197906,
-0.016312623396515846,
-0.09217362850904465,
0.05663805082440376,
-0.021635744720697403,
-0.010900743305683136,
0.013160096481442451,
-0.013268507085740566,
-0.03135514631867409,
0.013088837265968323,
-0.04334491863846779,
-0.01881394162774086,
0.026241200044751167,
-0.06606653332710266,
0.010685261338949203,
-0.015783805400133133,
0.010400338098406792,
-0.04916498810052872,
0.015770696103572845,
0.0020336287561804056,
-0.017668364569544792,
0.023989306762814522,
-0.017181366682052612,
0.016553882509469986,
0.024525806307792664,
0.017536381259560585,
-0.0045870342291891575,
-0.005662661045789719,
0.03427518531680107,
-0.0016539643984287977,
0.03377309441566467,
-0.047047194093465805,
-0.013677853159606457,
-0.019113115966320038,
0.05019455403089523,
0.01599375158548355,
-0.00015083719335962087,
-0.0707220584154129,
-0.03506416082382202,
0.008620355278253555,
0.024818113073706627,
0.0318547822535038,
0.05496946722269058,
-0.0073615191504359245,
0.021228820085525513,
-0.015851415693759918,
-0.06101440638303757,
0.019232483580708504,
0.03875495120882988,
0.011791541241109371,
-0.01831461675465107,
-0.027409810572862625,
0.010255985893309116,
-0.015379105694591999,
-0.04156011715531349,
0.0007983207469806075,
0.02334843948483467,
-0.014361968263983727,
-0.003716779174283147,
0.026950133964419365,
-0.0014646040508523583,
0.009399292059242725,
0.002173762768507004,
0.014763935469090939,
0.008018704131245613,
0.023236582055687904,
-0.002095225965604186,
0.012513992376625538,
0.012010029517114162,
0.049460817128419876,
0.02625635452568531,
-0.01465330459177494,
-0.1193816289305687,
-0.040329575538635254,
0.00876191072165966,
0.07439009845256805,
-0.023699920624494553,
-0.02545805461704731,
-0.02580387331545353,
-0.028155608102679253,
0.009774900041520596,
-0.05433829873800278,
-0.013858416117727757,
-0.01606260985136032,
-0.015658214688301086,
-0.041912294924259186,
-0.016403811052441597,
-0.016657905653119087,
0.021418724209070206,
-0.026179421693086624,
0.004181355703622103,
0.004192919470369816,
-0.004886203911155462,
0.03540267422795296,
-0.010203147307038307,
0.02190215140581131,
0.10041893273591995,
0.006276729982346296,
0.001974975224584341,
0.041624635457992554,
0.02887110598385334,
-0.0020878342911601067,
-0.05712155997753143,
0.008974386379122734,
0.0018742410466074944,
0.020137185230851173,
0.007912101224064827,
-0.01644214428961277,
-0.05954143777489662,
0.04998619854450226,
-0.007293309085071087,
-0.015010359697043896,
-0.007426248397678137,
-0.0002013103076023981,
0.020834218710660934,
0.031525954604148865,
0.01563994586467743,
0.02543133869767189,
0.05930755287408829,
-0.012796076014637947,
-0.006286559160798788,
0.02521633356809616,
0.007763876114040613,
-0.05627436563372612,
-0.006306238006800413,
-0.0059076654724776745,
0.0302928127348423,
-0.03993091359734535,
0.03288506716489792,
-0.019708406180143356,
0.009279576130211353,
-0.006535310298204422,
-0.0344037227332592,
-0.004474565852433443,
0.05111454054713249,
-0.0262489952147007,
-0.020972993224859238,
-0.01165973674505949,
0.0046250177547335625,
-0.009794317185878754,
0.0005729591939598322,
0.009637371636927128,
-0.020383959636092186,
0.006250912323594093,
0.022720808163285255,
-0.01692887209355831,
-0.024776048958301544,
-0.0324208065867424,
-0.013626008294522762,
0.015187950804829597,
-0.04698822647333145,
0.07839559018611908,
0.005176882725208998,
0.04681461676955223,
0.02468201518058777,
-0.02595551870763302,
-0.009159112349152565,
0.06796339899301529,
0.011509345844388008,
0.01180114783346653,
-0.05692689120769501,
0.026351824402809143,
-0.019327370449900627,
0.03270872309803963,
-0.019089000299572945,
-0.08303165435791016,
0.06405501812696457,
0.024743499234318733,
-0.011997154913842678,
-0.020039014518260956,
0.008634930476546288,
0.005007465835660696,
-0.004210222978144884,
0.03738563135266304,
0.015132871456444263,
0.021838413551449776,
-0.010930180549621582,
-0.007908730767667294,
0.015955312177538872,
0.03497155010700226,
0.0016770986840128899,
-0.00008802888623904437,
0.0007991120801307261,
-0.01937120035290718,
-0.03578414395451546,
-0.007036502938717604,
0.04014205560088158,
-0.02110697142779827,
-0.021174678578972816,
0.0038883001543581486,
0.012323562055826187,
0.05476738139986992,
-0.011614441871643066,
0.023573465645313263,
-0.002044428838416934,
0.03124401345849037,
-0.005488611292093992,
-0.07089643180370331,
0.05060200393199921,
0.010076126083731651,
0.029584994539618492,
-0.023845095187425613,
-0.018494760617613792,
-0.06293199211359024,
-0.033603984862565994,
-0.0007286142790690064,
0.04353950172662735,
-0.006620129104703665,
0.0002773913147393614,
0.036752473562955856,
-0.02819680981338024,
0.010025007650256157,
0.01703093759715557,
-0.038642898201942444,
0.039468925446271896,
-0.020704485476017,
-0.0038192598149180412,
-0.0024702963419258595,
-0.01194746419787407,
-0.0067656091414391994,
-0.04393729940056801,
-0.029841046780347824,
-0.0031796323601156473,
0.01872594840824604,
-0.022539786994457245,
0.042519278824329376,
0.043665237724781036,
-0.025881659239530563,
-0.027197523042559624,
-0.01864326000213623,
-0.040188878774642944,
-0.002848060103133321,
-0.03124936670064926,
0.010118013247847557,
0.0003849616623483598,
-0.002899901242926717,
-0.0033910097554326057,
0.06506193429231644,
-0.0017028285656124353,
0.009898314252495766,
0.03996849060058594,
0.062161799520254135,
0.002867500064894557,
-0.03699163720011711,
-0.03846365585923195,
0.005717257969081402,
-0.054711177945137024,
0.058852292597293854,
-0.011120563372969627,
0.0030647229868918657,
0.012740431353449821,
-0.005859758704900742,
0.015299954451620579,
-0.019097676500678062,
0.04432341083884239,
-0.02562202885746956,
0.022012844681739807,
0.002058484824374318,
-0.026595594361424446,
0.0390147902071476,
0.030360739678144455,
0.03033427707850933,
-0.007631807122379541,
-0.003215457545593381,
-0.031647950410842896,
-0.07157642394304276,
0.009617911651730537,
-0.009863522835075855,
-0.0518658272922039,
0.07861766964197159,
-0.025322718545794487,
-0.03784769028425217,
0.007900386117398739,
-0.00854066014289856,
0.027122056111693382,
0.009558971971273422,
0.016642514616250992,
-0.009143863804638386,
0.09305205196142197,
-0.016236456111073494,
-0.003323982935398817,
-0.024446452036499977,
0.0035818086471408606,
0.1445208638906479,
0.021128740161657333,
0.009514476172626019,
-0.06382739543914795,
0.01391826756298542,
-0.027351438999176025,
0.021607056260108948,
-0.010455937124788761,
0.026591328904032707,
0.02359287440776825,
-0.026729309931397438,
0.012477083131670952,
0.0026150790508836508,
-0.029995180666446686,
0.03295152634382248,
0.045860644429922104,
0.010212423279881477,
-0.01860213465988636,
0.04296299070119858,
-0.014427748508751392,
0.01345691829919815,
0.004561604466289282,
-0.05531739443540573,
0.03086763434112072,
-0.018969327211380005,
-0.04900209605693817,
-0.0414329469203949,
-0.053509797900915146,
0.05347246304154396,
0.005418755579739809,
-0.0031346012838184834,
-0.020555192604660988,
0.015868276357650757,
0.002278456697240472,
-0.04240831360220909,
0.01069109607487917,
-0.019265947863459587,
0.03480523079633713,
-0.00628015398979187,
0.0492003932595253,
0.036167990416288376,
-0.035864196717739105,
-0.001777460565790534,
0.0069785285741090775,
-0.0366370789706707,
0.0004152124165557325,
-0.05204065144062042,
0.0034608200658112764,
0.025023626163601875,
-0.02733389288187027,
-0.018313167616724968,
0.05440779775381088,
0.0360778346657753,
-0.06426449865102768,
-0.03191743791103363,
0.028964530676603317,
0.0044315168634057045,
-0.005368742160499096,
-0.018948394805192947,
-0.01405648048967123,
0.011474010534584522,
0.0044800410978496075,
-0.004652662668377161,
-0.033715274184942245,
-0.026801474392414093,
0.016223713755607605,
0.005702826660126448,
0.007233715616166592,
0.014064622111618519,
-0.03497221693396568,
0.019891371950507164,
0.007491337135434151,
-0.018637046217918396,
0.03699732571840286,
0.0027752884197980165,
-0.009681526571512222,
0.02024266868829727,
-0.02350390888750553,
-0.024667002260684967,
-0.00619238568469882,
-0.06013454869389534,
0.04515131190419197,
0.02238818071782589,
-0.0017250173259526491,
-0.0011194775579497218,
0.01636917144060135,
0.0029021799564361572,
0.04635104164481163,
-0.011936045251786709,
0.031834498047828674,
0.0005335210589691997,
-0.002671316498890519,
0.02422160655260086,
-0.026918480172753334,
-0.042634956538677216,
0.0332309864461422,
-0.031048253178596497,
0.009290087036788464,
0.000896441750228405,
0.052430689334869385,
0.006196670234203339,
-0.012876478023827076,
-0.02501683682203293,
0.019896337762475014,
-0.01435892004519701,
-0.009639413096010685,
0.009793886914849281,
-0.021444907411932945,
-0.007289770990610123,
-0.04876498878002167,
0.03334030136466026,
-0.02109871804714203,
-0.016954874619841576,
-0.018624451011419296,
0.0022724936716258526,
-0.009851700626313686,
-0.0014489023014903069,
0.000006857298558315961,
0.026138901710510254,
-0.07535311579704285,
-0.02931991033256054,
-0.018830738961696625,
0.033184830099344254,
-0.00240773381665349,
-0.020641755312681198,
0.015345494262874126,
0.049566611647605896,
-0.01643035188317299,
0.006007918156683445,
-0.03862965479493141,
-0.020824609324336052,
0.04088893160223961,
0.04142286628484726,
0.016466274857521057,
0.006592298857867718,
-0.0055914027616381645,
0.005472265183925629,
0.013137838803231716,
-0.05291704088449478,
-0.033982645720243454,
0.025694865733385086,
-0.02341792918741703,
-0.008880271576344967,
0.043929629027843475,
0.02528240904211998,
0.00846716295927763,
0.03488898277282715,
-0.003016728674992919,
0.016495542600750923,
0.04638056457042694,
0.027928829193115234,
-0.03044441156089306,
0.007973127998411655,
0.010850646533071995,
0.026676472276449203,
0.006877570878714323,
-0.007703754585236311,
-0.022383932024240494,
0.02513231337070465,
0.01957642287015915,
0.026518575847148895,
0.02446802705526352,
-0.034120846539735794,
-0.0034312629140913486,
0.04648706689476967,
0.03734120354056358,
0.017404841259121895,
-0.002651639748364687,
0.040028166025877,
0.0072028194554150105,
-0.025165032595396042,
-0.016652164980769157,
0.013678738847374916,
-0.0175840612500906,
-0.05752959102392197,
-0.0411207415163517,
-0.015900935977697372,
0.008456576615571976,
0.006826799362897873,
-0.029678825289011,
0.010433875024318695,
-0.000245793693466112,
-0.08274752646684647,
0.012373662553727627,
-0.004610522650182247,
-0.01765323430299759,
-0.017899584025144577,
0.010266294702887535,
0.013186165131628513,
0.033594902604818344,
0.015066532418131828,
0.01594032347202301,
0.03079923801124096,
0.014817777089774609,
-0.009312951005995274,
-0.03618726134300232,
-0.006611131597310305,
0.03820467367768288,
0.03580417484045029,
-0.05058082565665245,
0.03483595699071884,
-0.06156152859330177,
-0.033080313354730606,
0.04323510825634003,
-0.020310940220952034,
0.008398075588047504,
0.006065716966986656,
0.044878311455249786,
-0.003132237121462822,
0.031616512686014175,
0.04776288941502571,
-0.01020969357341528,
-0.02176041156053543,
0.002868868410587311,
0.010408801957964897,
-0.0009464589529670775,
-0.034217871725559235,
0.027646638453006744,
0.036157675087451935,
0.01608501933515072,
0.0008275498985312879,
0.02111542597413063,
-0.08405440300703049,
-0.05388248339295387,
0.01870308257639408,
0.007923809811472893,
0.009814897552132607,
-0.020129019394516945,
-0.04154939949512482,
-0.030000895261764526,
-0.03714318573474884,
0.01765158772468567,
-0.01314605213701725,
0.03671863302588463,
-0.01902654394507408,
-0.03879385069012642,
-0.038358259946107864,
0.02129601128399372,
0.03236434981226921,
-0.026995332911610603,
-0.06607773154973984,
-0.0013650523032993078,
-0.0020846975967288017,
-0.0035207553301006556,
0.0073994542472064495,
0.011133755557239056,
-0.006823370233178139,
0.0246835146099329,
0.012867990881204605,
0.03535838797688484,
-0.002453553257510066,
-0.011566504836082458,
0.03459650278091431,
-0.03814505413174629,
0.06301591545343399,
-0.0020349156111478806,
-0.043450914323329926,
-0.013096856884658337,
-0.05270562693476677,
0.000277555052889511,
0.014730523340404034,
0.06350825726985931,
-0.03550577536225319,
-0.008960122242569923,
0.00605998607352376,
0.028723999857902527,
0.006061967462301254,
-0.003097511362284422,
0.03336850926280022,
0.007484738249331713,
-0.04706590622663498,
0.0048295725136995316,
-0.0033028624020516872,
-0.03733782470226288,
0.01367943175137043,
0.01351862121373415,
-0.013178089633584023,
0.01201628614217043,
-0.04299711436033249,
-0.020333142951130867,
0.012661775574088097,
-0.018815109506249428,
-0.00590491620823741,
0.01839851588010788,
-0.04188581183552742,
0.006999925710260868,
-0.04206753522157669,
0.009446701966226101,
-0.06770604103803635,
-0.021434757858514786,
-0.06843774765729904,
0.023843150585889816,
-0.029659464955329895,
-0.01794895902276039,
-0.022974537685513496,
-0.05779551714658737,
0.013069935142993927,
-0.014961190521717072,
-0.025136061012744904,
0.011122624389827251,
0.07156387716531754,
0.012726443819701672,
0.03651456534862518,
0.013456904329359531,
0.028935443609952927,
-0.0304790660738945,
0.011509817093610764,
0.00107204623054713,
-0.006969512905925512,
0.03090057149529457,
-0.014565421268343925,
0.02312731184065342,
0.00821093562990427,
0.010962911881506443,
0.03949679061770439,
0.025941118597984314,
0.00983333308249712,
0.011488438583910465,
-0.052412841469049454,
0.01265657413750887,
-0.0265347920358181,
-0.046521175652742386,
0.009328325279057026,
-0.02122274599969387,
0.055720578879117966,
-0.005220021586865187,
-0.010053091682493687,
-0.04817498102784157,
0.011010359041392803,
0.009286642074584961,
-0.018018212169408798,
0.002608699956908822,
0.03677406162023544,
-0.042318545281887054,
0.02233000472187996,
0.005489656701683998,
-0.0025724205188453197,
0.03585990518331528,
-0.07260562479496002,
0.024923596531152725,
-0.01813279651105404,
0.004165820777416229,
0.01569662243127823,
-0.016376782208681107,
-0.045804496854543686,
-0.021929118782281876,
0.009873325005173683,
0.013352959416806698,
0.007929808460175991,
-0.011750654317438602,
-0.005433082580566406,
-0.024206694215536118,
0.0034268475137650967,
-0.050210438668727875,
0.01824149116873741,
-0.01055514719337225,
-0.013192949816584587,
0.013255557045340538,
0.05049363896250725
] |
<p>I know that if the Helmholtz free energy, $A$, is expressed as a function $A\sim A(N,V,T)$, then this function contains all thermodynamic information about the system. For instance, the pressure of the system is given by:</p>
<p>$$P(N,V,T) = -\frac{\partial A}{\partial V}\Bigg|_{n,T}$$</p>
<p>Indeed, if we imagine $N$ and $T$ are fixed, then this in effect gives us pressure as a function of volume:</p>
<p>$$P\sim f(V).$$</p>
<p>My question relates to the inverse of this equation. If we are given $P$ rather than $V$ (still with $T$ and $N$ fixed and known) then either numerically or analytically we can solve this to find $V$. But if the equation is complicated enough, <em>there maybe multiple values of $V$ for a given $P$, $T$ and $N$</em>.</p>
<p>This didn't seem too unreasonable to me (perhaps physically this represents a gas and a liquid co-existing at the same $T$, $P$ and $N$ at equilibrium), until I realised that, if we worked with the Gibbs free energy instead, and found values of $G(T,P,N)$, then in that case</p>
<p>$$V(T,P,N) = \frac{\partial G}{\partial P} \Bigg|_{N,T}$$</p>
<p>and this gives us an explicit, <em>single-valued</em> equation for $V$ as a function of $P$, $T$ and $N$ (though perhaps the inverse $P(V)$ is now multi-valued?).</p>
<p>What's going on here? One formulation of thermodynamics gives me an EOS in which there can exist multiple values of $V$ for a given $P$, and the other says I can have multiple values of $P$ for a given $V$! </p> | 4,573 | [
0.003042332362383604,
0.03082120604813099,
0.012525367550551891,
-0.045885395258665085,
0.015170677565038204,
-0.02150345779955387,
-0.02938828617334366,
0.013860590755939484,
-0.019934112206101418,
-0.015422257594764233,
0.037448450922966,
0.002100463258102536,
0.02636982500553131,
0.0059270430356264114,
0.006346721667796373,
0.006145271938294172,
-0.03300463408231735,
0.017102092504501343,
0.019329098984599113,
-0.007162569090723991,
0.0035479653161019087,
0.030921796336770058,
-0.023343192413449287,
-0.021709566935896873,
-0.027438828721642494,
0.03293900936841965,
-0.012313168495893478,
-0.01360103115439415,
0.01969541795551777,
0.0515010729432106,
-0.017522724345326424,
-0.040256425738334656,
0.0054408833384513855,
0.019602853804826736,
0.006572827231138945,
0.032297518104314804,
-0.030945491045713425,
0.011350354179739952,
-0.0038085076957941055,
0.06188824772834778,
-0.04360239952802658,
0.0060499282553792,
-0.007507931441068649,
0.006988705601543188,
0.0055282884277403355,
0.027064666152000427,
0.01677321083843708,
0.006354589480906725,
0.00879697035998106,
-0.04481102153658867,
0.03625011071562767,
0.01970299892127514,
0.054919227957725525,
0.075136698782444,
-0.025373052805662155,
0.009231473319232464,
0.04852063208818436,
0.06138021498918533,
0.042207468301057816,
-0.0725448802113533,
-0.006830953061580658,
0.017022594809532166,
-0.01821444369852543,
-0.03930523246526718,
-0.02123871259391308,
-0.013438883237540722,
0.024448048323392868,
-0.013585568405687809,
0.0045717377215623856,
-0.01220534648746252,
-0.00003588605613913387,
-0.018077589571475983,
0.0011406049598008394,
-0.0005218221922405064,
0.03490612655878067,
0.015387177467346191,
-0.00225438573397696,
-0.0008783341618254781,
0.010225397534668446,
-0.006333759520202875,
0.00010463338549016044,
0.029198206961154938,
0.020425662398338318,
0.039488714188337326,
0.0024429913610219955,
-0.0071883900091052055,
0.05885288864374161,
-0.02629808336496353,
0.041507210582494736,
-0.005534191615879536,
-0.005746206734329462,
0.016125014051795006,
0.03730803728103638,
-0.03377816453576088,
-0.010202350094914436,
-0.005905859172344208,
-0.012449356727302074,
-0.001728474861010909,
0.006684531457722187,
-0.04470326751470566,
0.0005372665473259985,
-0.028858020901679993,
-0.039388593286275864,
0.0874779149889946,
-0.024115759879350662,
-0.05067502334713936,
-0.047503940761089325,
-0.0010581074748188257,
0.027913633733987808,
-0.013111847452819347,
-0.02395743317902088,
-0.003252960741519928,
-0.021970372647047043,
0.014086124487221241,
-0.013417484238743782,
0.0011229015653952956,
0.030265595763921738,
-0.02989300899207592,
0.052642758935689926,
0.06540560722351074,
0.018940959125757217,
-0.02208937145769596,
0.007508545648306608,
-0.002544800518080592,
-0.11644206196069717,
-0.0077039580792188644,
0.01007238682359457,
0.004467241931706667,
-0.015468962490558624,
-0.007567938882857561,
0.0045075127854943275,
-0.00728287547826767,
0.05082559585571289,
0.018763795495033264,
0.017018169164657593,
-0.004037606995552778,
-0.062255483120679855,
-0.041367895901203156,
0.030659763142466545,
-0.04047173261642456,
-0.05019770935177803,
-0.07690665125846863,
-0.0178080927580595,
0.0496038980782032,
0.03964272886514664,
-0.016339831054210663,
0.01794291101396084,
-0.0016384631162509322,
0.05399904400110245,
-0.00181989383418113,
-0.04242408275604248,
0.011692266911268234,
-0.011578111909329891,
-0.017784159630537033,
0.0015144142089411616,
-0.04313937947154045,
0.0406651645898819,
0.030429106205701828,
-0.008552945218980312,
0.023803554475307465,
0.0445660762488842,
-0.019143037497997284,
-0.038554295897483826,
0.025141846388578415,
-0.03114369884133339,
-0.02805856056511402,
0.057661231607198715,
-0.012710782699286938,
0.05285048857331276,
0.021899301558732986,
0.006165753118693829,
0.00594307528808713,
-0.017452074214816093,
0.04614003747701645,
0.020389920100569725,
-0.018833419308066368,
-0.03693809360265732,
-0.017390545457601547,
0.0090660210698843,
0.02322392910718918,
-0.01452931109815836,
-0.020006710663437843,
0.021590260788798332,
0.018131187185645103,
0.026518087834119797,
0.0234268419444561,
-0.009377654641866684,
-0.0008862374234013259,
0.00040910221287049353,
-0.06221570074558258,
-0.026461102068424225,
-0.05633501708507538,
0.004031817428767681,
-0.040675338357686996,
-0.000997430644929409,
0.06882968544960022,
0.00948486290872097,
0.0014174024108797312,
-0.025231489911675453,
-0.027333015576004982,
0.0068618617951869965,
0.03630058839917183,
0.0369248166680336,
-0.029279891401529312,
0.04145805537700653,
0.018310341984033585,
0.051913950592279434,
-0.0010116474004462361,
0.03596619516611099,
-0.006703081540763378,
-0.01945575885474682,
0.007377795409411192,
-0.0390935055911541,
0.02258826605975628,
-0.01993159018456936,
-0.0512973889708519,
0.00944425631314516,
0.0017170977080240846,
0.038204483687877655,
0.00911496952176094,
-0.04098829627037048,
0.020399054512381554,
0.07911614328622818,
0.015010991133749485,
0.01063591055572033,
0.04824722558259964,
0.017944246530532837,
0.024924632161855698,
0.022223275154829025,
-0.020297035574913025,
-0.013766367919743061,
-0.004262255504727364,
0.05357896536588669,
0.09657135605812073,
-0.01470882073044777,
0.010369342751801014,
0.05389012396335602,
0.011383705772459507,
0.028829222545027733,
-0.007880466058850288,
-0.02204436995089054,
-0.048239998519420624,
0.06221539527177811,
0.027690505608916283,
0.022784151136875153,
0.02360324002802372,
0.015556511469185352,
0.032245103269815445,
0.04527848958969116,
-0.014609127305448055,
-0.021504564210772514,
0.0503937304019928,
0.015203199349343777,
-0.03391774743795395,
-0.023326944559812546,
0.015931271016597748,
0.0002986339677590877,
-0.027144961059093475,
0.0355536974966526,
-0.0018643366638571024,
0.019508929923176765,
-0.007778639905154705,
-0.04696899279952049,
-0.010568934492766857,
0.016486801207065582,
0.009902313351631165,
-0.002453823573887348,
-0.0032058267388492823,
0.005953936371952295,
-0.04920120909810066,
-0.00014301466580945998,
-0.027135265991091728,
0.019162869080901146,
0.003584809135645628,
-0.011241108179092407,
0.008500290103256702,
-0.015000191517174244,
-0.037894658744335175,
-0.036941688507795334,
-0.017098985612392426,
0.002402045764029026,
-0.006085370201617479,
0.006464344449341297,
0.04397844895720482,
-0.04123792424798012,
0.01644391566514969,
-0.014081140048801899,
-0.028157098218798637,
0.007881389930844307,
-0.007074050139635801,
0.0016719438135623932,
0.014840849675238132,
-0.04044249653816223,
-0.06359894573688507,
-0.0014281354378908873,
-0.053137894719839096,
-0.002855297178030014,
-0.027523377910256386,
0.022819271311163902,
0.037556033581495285,
0.007635342422872782,
-0.04865520820021629,
-0.007553812116384506,
-0.028525646775960922,
-0.06363646686077118,
-0.02018517442047596,
-0.0059947301633656025,
0.018414603546261787,
-0.004769264254719019,
0.056443870067596436,
0.04967169836163521,
-0.035964615643024445,
-0.022929295897483826,
-0.06336048990488052,
-0.0510437898337841,
0.013595900498330593,
-0.006723484955728054,
0.009253889322280884,
-0.0005171304219402373,
-0.04341981187462807,
0.06690006703138351,
-0.011726150289177895,
-0.02585323341190815,
0.021078646183013916,
0.016268473118543625,
-0.016721222549676895,
-0.04399961978197098,
0.028801362961530685,
0.039429549127817154,
-0.029259175062179565,
0.04578348249197006,
-0.02375384047627449,
0.04382266849279404,
0.0280876774340868,
0.010315127670764923,
0.007133530452847481,
0.05027392506599426,
0.03281521424651146,
0.007684652227908373,
0.05407386273145676,
0.0073091196827590466,
0.010755114257335663,
0.024668103083968163,
-0.005240515805780888,
0.029038552194833755,
0.05735906586050987,
-0.0665883868932724,
0.04487764462828636,
0.014925485476851463,
0.015380121767520905,
-0.0715329647064209,
0.019962312653660774,
0.0016874137800186872,
-0.0009322284022346139,
-0.002452924381941557,
0.018113242462277412,
0.058721549808979034,
-0.05595073476433754,
-0.02529875747859478,
0.06336948275566101,
0.030589651316404343,
-0.015633434057235718,
-0.03706057742238045,
-0.006114262156188488,
-0.011793993413448334,
0.024887068197131157,
-0.0012013070518150926,
0.009350255131721497,
0.04169677570462227,
0.02565629966557026,
0.031084338203072548,
-0.009112621657550335,
-0.027709169313311577,
0.004143261816352606,
-0.054864317178726196,
-0.025388360023498535,
-0.02051355689764023,
0.011207585223019123,
-0.00670763710513711,
0.07182588428258896,
-0.0028252273332327604,
0.02647337317466736,
-0.01556319184601307,
0.030015142634510994,
-0.0711662620306015,
0.00836748257279396,
0.0106496661901474,
-0.006816199515014887,
-0.017861943691968918,
-0.009004880674183369,
0.05835670605301857,
-0.04438161477446556,
-0.02042374387383461,
0.031435899436473846,
0.026004252955317497,
-0.08277063071727753,
0.02467314898967743,
-0.05564851313829422,
-0.011187181808054447,
-0.027275972068309784,
0.06094720959663391,
0.040061064064502716,
-0.034133683890104294,
0.002022482454776764,
0.05641396343708038,
-0.02444269508123398,
0.014519616030156612,
-0.0233868807554245,
0.004061469342559576,
0.03278445452451706,
0.027876567095518112,
0.018656769767403603,
0.012997576966881752,
0.01467042975127697,
-0.007211179938167334,
0.03064367175102234,
0.05952214077115059,
0.006805481854826212,
-0.0016977405175566673,
-0.017638664692640305,
-0.05318921431899071,
-0.018451515585184097,
0.00219311797991395,
0.05253113433718681,
0.007477691397070885,
0.022688420489430428,
0.008498843759298325,
0.005702556576579809,
-0.01734915003180504,
0.03656799718737602,
0.025208918377757072,
-0.027228927239775658,
-0.03310426324605942,
-0.02079295925796032,
-0.005244389176368713,
-0.026340914890170097,
0.020749136805534363,
0.014846475794911385,
0.006350388750433922,
-0.051018908619880676,
0.011998672969639301,
0.019033387303352356,
0.002266037743538618,
-0.01896669901907444,
-0.01314542070031166,
0.02610882744193077,
0.028461890295147896,
0.00011779181659221649,
0.002713111462071538,
0.02498198114335537,
0.04018783941864967,
-0.014986472204327583,
-0.0380144827067852,
-0.0011061998084187508,
-0.08027738332748413,
-0.015225723385810852,
0.028329109773039818,
0.03587827831506729,
-0.010277653113007545,
0.030686918646097183,
-0.025193732231855392,
-0.014709139242768288,
0.03846023976802826,
-0.04186774417757988,
-0.0015137643786147237,
0.021117037162184715,
0.012552670203149319,
0.022370439022779465,
-0.055670615285634995,
-0.016037624329328537,
-0.0060835229232907295,
-0.027628827840089798,
-0.002520902780815959,
-0.05379079654812813,
-0.00012782866542693228,
-0.00008312259160447866,
0.033003319054841995,
0.011099770665168762,
0.04743829742074013,
-0.019773246720433235,
-0.0433613546192646,
-0.009541532956063747,
0.016179369762539864,
-0.018723374232649803,
-0.0810822993516922,
0.01326957531273365,
-0.014529584906995296,
0.026291340589523315,
0.009509601630270481,
-0.023718252778053284,
-0.07603422552347183,
0.07816850394010544,
-0.01954861544072628,
-0.0044861165806651115,
0.014410031959414482,
-0.0012017895933240652,
0.07451266050338745,
0.01703377068042755,
-0.0027963717002421618,
0.05044419318437576,
-0.006672114599496126,
-0.009424815885722637,
-0.035800304263830185,
-0.04790627211332321,
0.019465256482362747,
-0.06840946525335312,
-0.00972356554120779,
-0.01770777441561222,
-0.008169028908014297,
0.012037578970193863,
0.03777932748198509,
0.011120764538645744,
0.006645753514021635,
0.015432548709213734,
-0.025839148089289665,
-0.0010414363350719213,
0.00785622838884592,
0.030629189684987068,
0.0019596924539655447,
0.014255502261221409,
-0.000280308275250718,
0.01841687224805355,
-0.029640836641192436,
0.01886942982673645,
0.00421425374224782,
0.005131254903972149,
0.028850382193922997,
-0.01101810485124588,
0.017805621027946472,
-0.014193433336913586,
-0.012332236394286156,
0.01280098408460617,
-0.012387972325086594,
0.03343260660767555,
0.005983135662972927,
0.047676052898168564,
0.012090573087334633,
-0.056956928223371506,
-0.04335949197411537,
0.017413517460227013,
-0.015814436599612236,
-0.005919736810028553,
-0.03296927362680435,
0.009176434949040413,
0.014810494147241116,
0.02489851973950863,
-0.0453801304101944,
0.035365182906389236,
0.03193627670407295,
-0.02836555801331997,
-0.04977484792470932,
-0.014276751317083836,
-0.014538672752678394,
0.00947005208581686,
-0.02288017049431801,
0.03772980347275734,
0.03408060967922211,
-0.018274229019880295,
-0.004950796719640493,
-0.02294272556900978,
0.046838775277137756,
0.021168598905205727,
-0.005811654031276703,
-0.013094857335090637,
-0.0014821882359683514,
-0.010753795504570007,
0.015306881628930569,
0.026887865737080574,
0.010931025259196758,
0.004067785106599331,
0.021939793601632118,
0.006027335301041603,
-0.01685037463903427,
0.020995698869228363,
-0.009160704910755157,
0.006902990862727165,
0.02349558100104332,
-0.00819743238389492,
-0.0368255153298378,
-0.0034007541835308075,
-0.021476663649082184,
-0.008369042538106441,
0.06048952415585518,
0.014654457569122314,
-0.005988636054098606,
0.005785028450191021,
-0.005245405249297619,
-0.019034935161471367,
-0.04521968960762024,
-0.024522852152585983,
-0.01154432911425829,
0.06888900697231293,
-0.002716063056141138,
-0.0020585062447935343,
0.0024484579917043447,
-0.017811423167586327,
0.06192125752568245,
0.03534523397684097,
-0.02573632448911667,
-0.019616559147834778,
-0.018830662593245506,
-0.07803700119256973,
-0.06275267153978348,
-0.08388585597276688,
0.01834832690656185,
0.05762185528874397,
0.011398756876587868,
0.066309854388237,
-0.01351404283195734,
-0.0038352562114596367,
-0.005088720005005598,
-0.033833928406238556,
-0.003935566172003746,
0.04460354894399643,
-0.0030662943609058857,
0.023192323744297028,
-0.0056014591827988625,
-0.07770180702209473,
0.03685497120022774,
-0.01608775556087494,
-0.050155241042375565,
0.00471836980432272,
-0.011691799387335777,
0.011108005419373512,
-0.018203748390078545,
-0.0467514730989933,
-0.06445642560720444,
0.06659410148859024,
-0.061494652181863785,
0.04302181303501129,
-0.0033023448195308447,
-0.004293164238333702,
0.0252627432346344,
0.0112997991964221,
0.017568999901413918,
-0.09405603259801865,
-0.029337573796510696,
-0.01815863884985447,
0.027228975668549538,
-0.011936638504266739,
-0.00458934111520648,
0.0055900621227920055,
-0.01037329901009798,
0.022025035694241524,
-0.023069798946380615,
0.017866583541035652,
0.015308143571019173,
-0.04412690922617912,
0.02413899451494217,
0.0038264538161456585,
-0.01471228338778019,
0.02318616583943367,
-0.003437107428908348,
-0.02225709892809391,
0.00466375844553113,
-0.050540726631879807,
0.01469388883560896,
0.003050710540264845,
0.0105739152058959,
-0.0020678204018622637,
0.08915980905294418,
0.012089603580534458,
0.042679786682128906,
-0.027288537472486496,
0.0191081240773201,
0.16760948300361633,
0.033735889941453934,
0.03523455932736397,
-0.0295439250767231,
-0.006799456663429737,
-0.016866011545062065,
-0.0075653837993741035,
-0.020845796912908554,
0.026815664023160934,
0.02800123207271099,
-0.006945925299078226,
-0.0008354265592060983,
0.020501021295785904,
-0.021105892956256866,
-0.00681617297232151,
0.012835782021284103,
-0.029106665402650833,
0.0024433608632534742,
0.007643959019333124,
0.031184250488877296,
-0.034348588436841965,
0.03545805811882019,
0.002813988132402301,
-0.023014795035123825,
0.0031059670727699995,
0.015146530233323574,
-0.008566420525312424,
-0.03914298117160797,
0.038642555475234985,
0.03388771042227745,
-0.04715469107031822,
0.012368490919470787,
-0.008551337756216526,
-0.014018918387591839,
-0.024907654151320457,
0.02474702149629593,
-0.006843453273177147,
0.012133564800024033,
-0.03203780949115753,
0.014953126199543476,
-0.01608894392848015,
0.004866452421993017,
0.0010548264253884554,
0.0020412569865584373,
-0.024017246440052986,
-0.005811142735183239,
-0.02679106779396534,
0.04382301867008209,
-0.009164237417280674,
0.023116890341043472,
0.016657816246151924,
0.0012395675294101238,
0.012146597728133202,
-0.017891284078359604,
-0.011951836757361889,
-0.015870723873376846,
0.04154882952570915,
-0.006088730879127979,
-0.01813599094748497,
-0.000564131245482713,
-0.014419954270124435,
-0.015619839541614056,
0.027418579906225204,
-0.0171827282756567,
-0.013450817205011845,
0.01177702285349369,
-0.01844724453985691,
0.049027618020772934,
-0.013633228838443756,
0.011036925949156284,
-0.015061664395034313,
-0.00379014341160655,
-0.055435385555028915,
-0.059244703501462936,
0.033610980957746506,
-0.014216279610991478,
0.01616460643708706,
0.03969791159033775,
0.0026642547454684973,
-0.02660791389644146,
-0.09333815425634384,
0.019969461485743523,
-0.025340259075164795,
0.0004744407196994871,
-0.029204627498984337,
0.00825527310371399,
-0.014498489908874035,
0.06824716180562973,
0.007949259132146835,
0.008037473075091839,
0.013735995627939701,
0.027988366782665253,
0.01635708473622799,
-0.05849233269691467,
-0.07353103905916214,
-0.004337084945291281,
-0.06323648244142532,
0.01928313635289669,
0.04780370369553566,
0.03889947757124901,
0.03975146263837814,
0.05363753065466881,
-0.025001270696520805,
0.040521059185266495,
-0.01109331101179123,
0.0008032076875679195,
0.013500234112143517,
-0.0026957709342241287,
0.03174803778529167,
0.02334725297987461,
0.005588352680206299,
0.0007087135454639792,
-0.024621473625302315,
0.005690793506801128,
0.010101167485117912,
0.015986433252692223,
-0.0057289088144898415,
-0.0056772916577756405,
0.014875249937176704,
-0.02631705440580845,
0.012985787354409695,
-0.04311056062579155,
0.004737630020827055,
-0.04446641355752945,
-0.005323473829776049,
0.004140900913625956,
0.026574159041047096,
-0.008076557889580727,
0.02722061797976494,
-0.03721030429005623,
-0.023638272657990456,
0.04705844074487686,
0.06114714592695236,
0.03373129293322563,
-0.05975600704550743,
0.05723530426621437,
0.007357262074947357,
0.030846809968352318,
0.0070318495854735374,
-0.06685840338468552,
0.01903432607650757,
-0.018744545057415962,
-0.03905651345849037,
-0.004468115977942944,
0.024011466652154922,
0.040915943682193756,
0.046987395733594894,
0.010781860910356045,
-0.04445471987128258,
0.08232603222131729,
-0.04384639859199524,
0.03416328504681587,
-0.0120388213545084,
-0.05650317296385765,
-0.01785985939204693,
-0.04121987894177437,
0.04125405102968216,
0.025456897914409637,
0.03343755379319191,
0.030002674087882042,
0.013537760823965073,
-0.004341131076216698,
-0.02593587152659893,
0.0624392144382,
-0.019192572683095932,
-0.00899512693285942,
0.028796732425689697,
0.003681016154587269,
0.012456477619707584,
0.03161919489502907,
0.007856922224164009,
0.02893744222819805,
0.056353334337472916,
0.024013254791498184,
-0.09896202385425568,
-0.007016976363956928,
0.050802115350961685,
0.01046187523752451,
0.04647514596581459,
-0.022202176973223686,
0.012691641226410866,
-0.015590586699545383,
-0.03668023645877838,
0.011712641455233097,
-0.03532465547323227,
-0.007566905580461025,
-0.03597787767648697,
0.010338464751839638,
-0.04815935716032982,
0.045195795595645905,
0.028499959036707878,
0.02285063825547695,
0.025407208129763603,
0.013796242885291576,
-0.016171108931303024,
-0.03399338573217392,
-0.00030559353763237596,
0.030849991366267204,
-0.014426294714212418,
-0.027202138677239418,
0.018615802749991417,
-0.038357555866241455,
-0.06151043251156807,
-0.003474373137578368,
-0.034058790653944016,
-0.012210545130074024,
-0.024602914229035378,
0.013183769769966602,
-0.007408290635794401,
0.05244343727827072,
0.0324898436665535,
0.005769708193838596,
-0.01670284941792488,
0.011737087741494179,
-0.027166888117790222,
0.0014401806984096766,
-0.00342907989397645,
-0.009029665030539036,
-0.02219155617058277,
-0.02570621483027935,
-0.01061378512531519,
0.008209978230297565,
-0.023063376545906067,
-0.0016680705593898892,
0.01287868618965149,
-0.015211083926260471,
-0.0011266194051131606,
-0.028624650090932846,
0.01677802950143814,
-0.0485408753156662,
-0.012791070155799389,
0.025176333263516426,
0.03584802523255348,
0.005303890444338322,
0.0005939695984125137,
-0.002620941260829568,
-0.023740272969007492,
0.034999195486307144,
-0.005885397549718618,
-0.02412550523877144,
-0.07027877122163773,
-0.021412555128335953,
0.010182052850723267,
-0.03238772228360176,
-0.0223837923258543,
-0.03427021950483322,
-0.027095625177025795,
0.011228250339627266,
0.033821165561676025,
0.025192398577928543,
-0.05283546447753906,
-0.061990972608327866,
0.008249102160334587,
-0.04455684497952461,
0.028201797977089882,
-0.015471584163606167,
-0.0012205372331663966,
-0.02859552577137947,
-0.017214130610227585,
0.022433653473854065,
-0.0038823618087917566,
0.04446936398744583,
0.0015197410248219967,
0.0026270512025803328,
-0.014187822118401527,
0.0251504797488451,
0.020211713388562202,
-0.028331059962511063,
-0.03978189826011658,
-0.03677595406770706,
-0.00963016226887703,
0.0476512685418129,
-0.005320382304489613,
0.002666918095201254,
0.03899029642343521,
0.0479704849421978,
-0.05306065082550049,
-0.011822231113910675,
0.02230243571102619,
-0.015608211047947407,
0.041607048362493515,
-0.01785973645746708,
-0.030549384653568268,
0.03948511555790901,
-0.021711159497499466,
0.0006601756904274225,
0.02302999421954155,
-0.0013588056899607182,
-0.028270872309803963,
-0.02150772139430046,
-0.0071929991245269775,
-0.04102475941181183,
0.0009431099169887602,
0.02169962227344513,
0.04166211932897568,
-0.024028075858950615,
0.005165387410670519,
0.03175818547606468,
-0.04777023568749428,
-0.006909457966685295,
0.03326926752924919,
0.011174648068845272,
0.021747831255197525,
-0.034493133425712585,
0.016341662034392357,
0.011091583408415318,
-0.012158950790762901,
0.00729752192273736,
0.03542036563158035,
0.05539396405220032,
0.004093288443982601,
-0.014762530103325844,
0.033009398728609085,
-0.026329459622502327,
-0.009097658097743988,
0.027048420161008835,
0.0037922393530607224,
-0.037416163831949234,
-0.03545644134283066,
0.036683838814496994,
-0.004181316588073969,
0.02841263823211193,
0.0018873546505346894,
0.007563469465821981,
0.1120196282863617,
0.016755860298871994,
-0.018108149990439415,
-0.03304021805524826,
0.049622584134340286,
-0.009249926544725895,
-0.02270088903605938,
-0.0014938918175175786,
0.009764955379068851,
-0.016199586912989616,
0.01889461651444435,
0.004275784827768803,
-0.025110341608524323,
0.0016388557851314545,
-0.0511043556034565,
0.002972432179376483,
0.019985457882285118,
-0.002435518428683281,
-0.05437237396836281,
0.008561898954212666,
-0.05185430496931076,
-0.025418721139431,
0.0331260971724987,
0.035367004573345184,
0.026747802272439003,
0.030963748693466187,
-0.011227273382246494,
-0.02931923419237137,
0.05575462058186531,
-0.013369977474212646,
-0.05043680965900421,
-0.0054335580207407475,
0.011993997730314732,
0.03393140435218811,
-0.009637683629989624
] |
<p>Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$:</p>
<p>$$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum \phi_i^*\phi'_i}$$</p>
<p>For the coherent (boson) states $|\phi\rangle=e^{\sum\phi_ia^\dagger_i}|0\rangle $. When I try to prove this I get a factor of 1/2 in the exponent. I'm going to take a simple example $A=a_i^\dagger a_i$ to try and find my mistake. First I define $\eta'=\sum \phi'_ia_i^\dagger$, and use the identity</p>
<p>$$a_i\eta'^n=n\phi'_i\eta'^{n-1}+\eta'^n a_i.$$</p>
<p>Then I can show</p>
<p>$$a_i|\phi'\rangle=(e^{\eta'}a_i+\phi'_ie^{\eta'})|0\rangle$$</p>
<p>One term of which kills the vacuum so I have shown</p>
<p>$$\langle \phi |a^\dagger_i a_i|\phi'\rangle=\langle 0| \phi^*_i\phi'_ie^{\eta^*}e^{\eta'}|0\rangle$$</p>
<p>Then I want to use the Baker-Campbell-Hausdorf formula. The commutator </p>
<p>\begin{equation}
[\eta^*,\eta']=[\sum\phi^*_ia_i,\sum\phi_ja^\dagger_j]=\sum[\phi^*_ia_i,\phi_i'a_i^\dagger]+\sum_{i\neq j}[\phi^*_ia_i,\phi_ja^\dagger_j]=\sum\phi_i^*\phi'_i,\qquad (1)
\end{equation}
and when you commute everything through the second term and kill the vacuum. Since this is a scalar, the BCH formula gives</p>
<p>$$\ln(e^{\eta^*}e^{\eta'})=\eta^*+\eta'+\frac{1}{2}\sum\phi_i^*\phi_i'$$</p>
<p>Rearrange the sum, exponentiate, kill some more vacuum and I get the right expression but with a factor of 1/2!</p>
<p>What am I doing wrong? My first guess is in equation (1), maybe there is some dobule-counting I don't see but you can write things like</p>
<p>$$[\sum,\sum]=[1,\sum]+[2,\sum]+...=[1,1]+[1,\sum_{\neq 1}]+[2,2]+[2,\sum_{\neq 2}]+...$$
$$=\sum[i,i]+\sum_{i\neq j}[i,j].$$</p> | 4,574 | [
0.022577792406082153,
-0.02406945824623108,
-0.005823694169521332,
-0.005551390815526247,
0.03309759497642517,
0.0045424713753163815,
-0.061747562140226364,
-0.025886770337820053,
-0.002843801397830248,
-0.04769595339894295,
0.07273651659488678,
-0.04161197319626808,
0.032919298857450485,
0.01656373217701912,
-0.007295117247849703,
0.01833724044263363,
-0.021430548280477524,
-0.0033390712924301624,
-0.006394624710083008,
-0.02227255329489708,
0.013121872209012508,
0.03239128738641739,
-0.01922677643597126,
-0.011222445406019688,
-0.013238158077001572,
0.04047994688153267,
-0.016644371673464775,
0.03808161988854408,
-0.027885617688298225,
0.07041376829147339,
-0.015617774799466133,
-0.043763354420661926,
-0.00833506416529417,
-0.0020933146588504314,
0.00852489285171032,
0.02288973517715931,
-0.00017084446153603494,
-0.005050226114690304,
-0.0026058668736368418,
-0.006073372904211283,
0.006662728730589151,
-0.01878395676612854,
0.009944780729711056,
0.020351463928818703,
0.002298531820997596,
0.002445158315822482,
-0.029160406440496445,
0.030917925760149956,
0.032934464514255524,
-0.04209528863430023,
0.06038057431578636,
0.023954471573233604,
0.013261780142784119,
0.008089962415397167,
0.002568386262282729,
-0.0249966811388731,
0.025036994367837906,
0.051234304904937744,
-0.022950533777475357,
-0.05659923702478409,
-0.0028338164556771517,
-0.007183819077908993,
-0.022960064932703972,
-0.030265074223279953,
-0.004707857500761747,
-0.030623510479927063,
0.041791126132011414,
-0.009485645219683647,
0.025590112432837486,
-0.023223096504807472,
0.014521313831210136,
-0.021160580217838287,
0.024323919788002968,
-0.0597224161028862,
0.0019342201994732022,
-0.0121950414031744,
-0.015085460618138313,
0.029949622228741646,
0.03974376246333122,
0.028008799999952316,
0.0062101962976157665,
0.02220245450735092,
0.007700664922595024,
0.008806886151432991,
0.001816418720409274,
0.006305423565208912,
0.09136633574962616,
-0.028788525611162186,
0.010503557510674,
0.04600454866886139,
-0.02938137762248516,
0.020975163206458092,
0.03829207271337509,
0.008592845872044563,
0.034479960799217224,
0.06955615431070328,
-0.016192644834518433,
0.029276888817548752,
-0.009181417524814606,
-0.019303882494568825,
-0.06257311999797821,
-0.03482050076127052,
0.0075437817722558975,
0.06869664788246155,
-0.001216859556734562,
-0.004938133992254734,
-0.03639351576566696,
0.02818814106285572,
-0.05785594508051872,
-0.06822406500577927,
-0.047506172209978104,
0.032233983278274536,
-0.05634075403213501,
0.04685471951961517,
-0.01800430379807949,
-0.0314348042011261,
0.002953976159915328,
-0.03850122168660164,
0.04103066027164459,
0.08286579698324203,
0.05288223922252655,
0.028631970286369324,
0.02196275256574154,
-0.04641777649521828,
-0.06168710067868233,
0.03403838723897934,
0.03853559121489525,
0.013863074593245983,
-0.03708227723836899,
-0.004740350414067507,
0.02135634794831276,
0.020521553233265877,
0.001587905571796,
0.00843009538948536,
0.005220050923526287,
-0.0062301428988575935,
-0.10720587521791458,
-0.023912737146019936,
0.03302725777029991,
-0.04953376576304436,
0.003183795837685466,
-0.0843876525759697,
0.021295763552188873,
0.011260048486292362,
0.07689513266086578,
-0.0007169616874307394,
0.008677694015204906,
0.010436441749334335,
0.03705013915896416,
0.04030792787671089,
-0.0027310659643262625,
-0.0501079261302948,
-0.0021801262628287077,
-0.0418582446873188,
-0.033995453268289566,
-0.028536617755889893,
0.058031272143125534,
0.02844949997961521,
0.007814433425664902,
0.010706867091357708,
0.08238714933395386,
-0.01716134510934353,
-0.004119241610169411,
-0.023490658029913902,
0.006813765969127417,
-0.05117734521627426,
0.06801290065050125,
0.016741225495934486,
0.024882039055228233,
0.022886784747242928,
-0.014750469475984573,
0.024493901059031487,
-0.031417667865753174,
0.008704137988388538,
0.043143995106220245,
-0.01574477180838585,
0.0064067416824400425,
-0.0782242864370346,
-0.002927956869825721,
0.003937918227165937,
-0.037402402609586716,
-0.030290981754660606,
-0.0363813154399395,
0.017032893374562263,
-0.012229488231241703,
-0.005431214813143015,
0.016346920281648636,
0.015766164287924767,
-0.007636077236384153,
-0.05817641690373421,
-0.030077574774622917,
-0.05906054750084877,
-0.0010829585371538997,
0.025542287155985832,
-0.03379112109541893,
0.05074319615960121,
-0.009804974310100079,
0.020085591822862625,
0.0067732492461800575,
-0.020747734233736992,
0.0005965602467767894,
0.013107532635331154,
0.007940509356558323,
-0.03391626104712486,
0.04508981108665466,
0.03084745444357395,
0.047876451164484024,
0.000952174246776849,
0.06778981536626816,
0.015404853969812393,
0.009386684745550156,
-0.0018208661349490285,
0.012227591127157211,
-0.008229156024754047,
0.014634293504059315,
0.008541766554117203,
0.0482492670416832,
-0.0002943745639640838,
-0.03609143942594528,
0.015386192128062248,
-0.03154633194208145,
0.029997870326042175,
0.04129525646567345,
-0.01308087445795536,
-0.034205421805381775,
0.0413639098405838,
0.0016401392640545964,
0.006636699195951223,
-0.02637982927262783,
-0.015480231493711472,
-0.016648873686790466,
-0.006650550756603479,
-0.0032202706206589937,
0.0432775616645813,
-0.05426320061087608,
0.03351008892059326,
-0.0045521799474954605,
0.036768388003110886,
0.04864615947008133,
0.02602025866508484,
0.0012254253961145878,
-0.029127776622772217,
0.044254615902900696,
-0.020343447104096413,
-0.01333522703498602,
0.0097874840721488,
-0.004108148161321878,
-0.04398637264966965,
0.03599375858902931,
-0.01265337411314249,
-0.02207588218152523,
0.010634031146764755,
-0.0461379736661911,
-0.017718255519866943,
0.0070471251383423805,
0.01876230165362358,
0.008661613799631596,
-0.005001450888812542,
0.044607099145650864,
0.04076350852847099,
-0.017071712762117386,
-0.016567258164286613,
-0.0344139002263546,
-0.0363541878759861,
0.022777242586016655,
-0.04566770792007446,
-0.012018777430057526,
0.0004806340439245105,
0.01878051459789276,
-0.014053993858397007,
0.001272979541681707,
0.0031753191724419594,
-0.010416482575237751,
-0.023507796227931976,
-0.015746258199214935,
0.03430458903312683,
0.04331598058342934,
-0.006001019850373268,
-0.04425685480237007,
-0.03672301769256592,
0.04748407378792763,
0.022013673558831215,
0.020472144708037376,
0.04125121608376503,
-0.049885258078575134,
0.011356300674378872,
-0.05058520287275314,
-0.022416159510612488,
0.02390984259545803,
-0.013518017716705799,
-0.0036767267156392336,
0.027092233300209045,
-0.02313774824142456,
-0.03304982930421829,
-0.011924912221729755,
-0.011976420879364014,
0.0029978740494698286,
-0.05551784858107567,
-0.023325471207499504,
0.010172958485782146,
-0.012010211125016212,
-0.05351094529032707,
0.0023584605660289526,
0.014207764528691769,
-0.04633743315935135,
-0.024825770407915115,
-0.013897595927119255,
-0.016959093511104584,
-0.04728394001722336,
0.02779538184404373,
0.0044860392808914185,
0.006411642301827669,
-0.026097768917679787,
-0.02659543976187706,
-0.04734215885400772,
0.004105753730982542,
0.005719955079257488,
0.008772030472755432,
0.020174486562609673,
-0.04905346781015396,
0.10605578124523163,
0.013818303123116493,
-0.030695829540491104,
-0.003080644877627492,
-0.0038603623397648335,
0.005068421829491854,
-0.015973100438714027,
-0.011014727875590324,
0.00471483776345849,
-0.035691723227500916,
0.058417387306690216,
0.03827742114663124,
0.037477366626262665,
0.043079033493995667,
0.008209074847400188,
-0.01868327707052231,
0.016889911144971848,
-0.001359474379569292,
-0.008455121889710426,
0.04666312783956528,
0.015454286709427834,
0.012747294269502163,
0.010996339842677116,
0.029349828138947487,
0.005859652534127235,
-0.01475282572209835,
-0.06245007738471031,
0.027219541370868683,
-0.016403021290898323,
0.01752094365656376,
0.005027548409998417,
0.06087523326277733,
-0.019926102831959724,
-0.015163102187216282,
-0.034092213958501816,
0.01920938305556774,
0.019348185509443283,
-0.05161122977733612,
0.020865947008132935,
0.03237837180495262,
0.05417453870177269,
0.005207984242588282,
-0.02198769338428974,
0.002586411079391837,
-0.024650361388921738,
0.055349674075841904,
-0.03477705270051956,
-0.04247356206178665,
0.002774139167740941,
0.01823391392827034,
-0.006990642286837101,
-0.017957046627998352,
-0.016865046694874763,
-0.012063182890415192,
-0.026486728340387344,
0.04397037625312805,
-0.03929007798433304,
0.06922917813062668,
0.002379307523369789,
0.07172495126724243,
0.021136891096830368,
-0.016701698303222656,
0.006752698216587305,
-0.018555400893092155,
-0.060215212404727936,
0.022276706993579865,
0.016317375004291534,
-0.013485954143106937,
0.01563052274286747,
-0.05176110193133354,
0.026946108788251877,
-0.0070191798731684685,
-0.020146911963820457,
-0.014163759537041187,
-0.013910055160522461,
-0.043632201850414276,
0.029869776219129562,
-0.06770765781402588,
-0.0708700641989708,
-0.03711068257689476,
-0.012282420881092548,
0.03254766762256622,
0.022072358056902885,
-0.0060388678684830666,
0.05065320432186127,
-0.00972141046077013,
-0.015263238921761513,
-0.013239058665931225,
0.03824055939912796,
0.01721305213868618,
0.008974168449640274,
0.034851931035518646,
0.011448116041719913,
-0.01849115639925003,
-0.006608098745346069,
-0.03565797209739685,
0.04675392806529999,
0.011189917102456093,
-0.04040651023387909,
0.023730065673589706,
-0.021937651559710503,
-0.0406506173312664,
0.017135735601186752,
0.07709241658449173,
0.03264971449971199,
-0.010532061569392681,
0.0287241879850626,
0.016611730679869652,
0.01218752283602953,
0.009852888062596321,
0.07183883339166641,
0.027713241055607796,
0.005237547680735588,
-0.00696503184735775,
0.01806490123271942,
-0.01608903519809246,
0.0003896704001817852,
-0.01209350861608982,
0.01303416583687067,
-0.012427160516381264,
0.014084127731621265,
-0.00128641608171165,
0.013491066172719002,
-0.0035716339480131865,
-0.0059218998067080975,
-0.004126541316509247,
-0.07321227341890335,
0.04151293635368347,
0.0007853746647015214,
-0.002632406773045659,
0.008981814607977867,
-0.0005142877926118672,
0.008105229586362839,
0.06336565315723419,
-0.05360613390803337,
-0.037082377821207047,
0.01430524606257677,
0.032404426485300064,
-0.004324066918343306,
0.01413190271705389,
-0.01970667578279972,
-0.05454060807824135,
0.019477101042866707,
-0.045283712446689606,
0.03900602087378502,
0.000412624649470672,
-0.017848990857601166,
0.01803410053253174,
-0.04058920592069626,
-0.044505875557661057,
0.042205918580293655,
-0.009929494000971317,
0.0007876206072978675,
-0.02159995771944523,
0.004048298113048077,
-0.04018596187233925,
-0.004523587413132191,
-0.014788014814257622,
0.01750350184738636,
0.008499709889292717,
0.0008998439298011363,
0.02362881228327751,
0.046349987387657166,
-0.031597111374139786,
-0.04567774385213852,
0.05073130130767822,
-0.0019320326391607523,
0.016414625570178032,
0.00774019118398428,
-0.00758766895160079,
-0.02266482263803482,
0.007183355279266834,
0.02735629677772522,
-0.01629050076007843,
0.05423578992486,
-0.02259599231183529,
0.05233404040336609,
0.0016222172416746616,
-0.00667553162202239,
0.04776079207658768,
0.05552536994218826,
-0.021564623340964317,
0.011354119516909122,
-0.05571854114532471,
0.04307417944073677,
-0.00360292661935091,
0.04063643515110016,
-0.018540620803833008,
0.007786075118929148,
-0.00032638985430821776,
0.038016702979803085,
-0.04481438919901848,
0.03406763821840286,
0.019263559952378273,
-0.014988012611865997,
0.033801544457674026,
0.007857000455260277,
-0.049884483218193054,
0.006275435909628868,
0.008360198698937893,
0.02296016924083233,
0.048387158662080765,
-0.0030671043787151575,
0.02875124290585518,
0.010598639957606792,
0.0059973555617034435,
-0.0012332169571891427,
-0.008149935863912106,
0.04420683532953262,
-0.02791905775666237,
-0.014785210601985455,
-0.010162307880818844,
-0.038110777735710144,
0.012471412308514118,
0.012973927892744541,
-0.006938821170479059,
-0.005233073607087135,
-0.015589263290166855,
-0.07326406240463257,
-0.010912884026765823,
-0.025077959522604942,
0.022338252514600754,
-0.0022164355032145977,
-0.01882232166826725,
0.03463900834321976,
0.005762612447142601,
-0.07685030996799469,
-0.01434516441076994,
-0.004285705741494894,
-0.03145202249288559,
-0.01732983998954296,
-0.030088379979133606,
0.01701667532324791,
0.003250847803428769,
-0.012710108421742916,
-0.02752305008471012,
0.03071402944624424,
-0.03523879870772362,
-0.006597419269382954,
0.009878968819975853,
0.022955244407057762,
0.006864308845251799,
0.018581418320536613,
-0.03505474701523781,
0.01059095747768879,
-0.030579948797822,
0.017885826528072357,
0.032174307852983475,
0.02516205608844757,
-0.02349104918539524,
-0.06520870327949524,
-0.0039709387347102165,
-0.028062956407666206,
0.017224261537194252,
0.009317747317254543,
-0.010668333619832993,
0.0008871719473972917,
0.01355938334017992,
0.013259303756058216,
-0.005694771651178598,
-0.05689649656414986,
0.016780396923422813,
0.04176236316561699,
-0.005040097516030073,
-0.009523389860987663,
-0.010955103673040867,
-0.05115154758095741,
-0.0062456801533699036,
-0.02959328517317772,
-0.026361573487520218,
-0.010244479402899742,
0.026015017181634903,
-0.017935967072844505,
0.014735760167241096,
0.041731223464012146,
-0.019028790295124054,
-0.007988532073795795,
-0.0038816805463284254,
0.015432028099894524,
0.029882969334721565,
-0.01602744124829769,
-0.009663938544690609,
-0.018839439377188683,
-0.0831366553902626,
0.023963946849107742,
0.03994282707571983,
0.002995287301018834,
0.022428875789046288,
-0.0046052346006035805,
0.0025767553597688675,
-0.03271079808473587,
0.0031085526570677757,
-0.027372408658266068,
0.01790742762386799,
-0.00000573271108805784,
-0.006785858888179064,
-0.06536588817834854,
-0.016898225992918015,
0.011728988960385323,
0.05027247592806816,
-0.05113153159618378,
0.016520831733942032,
-0.0007721111760474741,
0.030824629589915276,
-0.03757503256201744,
-0.037444282323122025,
-0.016444509848952293,
0.0790468379855156,
-0.036129023879766464,
0.03235038369894028,
0.008738534525036812,
-0.011773857288062572,
0.005313097033649683,
0.013733492232859135,
-0.00976207759231329,
-0.031084097921848297,
-0.04184243455529213,
-0.046168405562639236,
0.028677375987172127,
0.01655968278646469,
-0.004612605087459087,
0.04307232424616814,
-0.012958831153810024,
0.02113506942987442,
0.00661836750805378,
0.02883835695683956,
0.0006847676704637706,
-0.028451094403862953,
0.020581234246492386,
-0.020542720332741737,
-0.060495998710393906,
0.025442713871598244,
-0.04626494646072388,
0.005168060772120953,
-0.004008702468127012,
-0.014685380272567272,
0.04281254857778549,
0.028812222182750702,
0.007221572566777468,
0.009230626747012138,
0.05248301103711128,
0.006000780500471592,
0.03831863775849342,
0.009531350806355476,
0.0030831745825707912,
0.1456688791513443,
0.04604949429631233,
0.015836935490369797,
-0.03594989329576492,
-0.02107652835547924,
0.026925526559352875,
0.03638153150677681,
-0.019105829298496246,
0.012620346620678902,
-0.012874167412519455,
-0.013618774712085724,
-0.015527983196079731,
0.0694810301065445,
-0.03258488327264786,
0.002676215022802353,
0.03904416412115097,
-0.0322209894657135,
-0.05945366993546486,
0.012198538519442081,
0.049104269593954086,
-0.012792606838047504,
-0.012288881465792656,
0.0025164857506752014,
-0.0006056696292944252,
-0.03109150193631649,
0.007642686832696199,
-0.04575217887759209,
0.01970868743956089,
0.0025442263577133417,
0.008179758675396442,
-0.002282026456668973,
-0.02629675343632698,
0.013058163225650787,
-0.02388540282845497,
0.004033938050270081,
0.0021474172826856375,
0.025129709392786026,
-0.008046835660934448,
0.016367394477128983,
0.04391377791762352,
0.025387104600667953,
0.023190755397081375,
0.04539893940091133,
0.019226931035518646,
-0.01402559969574213,
-0.023457089439034462,
-0.005636700429022312,
0.06815702468156815,
-0.00996220950037241,
0.04732254520058632,
-0.004348990973085165,
-0.03721454739570618,
0.016183016821742058,
-0.0334654375910759,
-0.019785789772868156,
0.007418542634695768,
-0.014849754981696606,
-0.04602169618010521,
0.013424054719507694,
-0.02427857369184494,
0.01282412838190794,
0.02628047578036785,
0.04363192617893219,
-0.045231517404317856,
-0.009152717888355255,
-0.006254614796489477,
-0.005696390755474567,
0.025459783151745796,
0.027896074578166008,
-0.0026487228460609913,
-0.013533012941479683,
-0.02292686700820923,
-0.04675930365920067,
-0.057028986513614655,
-0.02266879193484783,
-0.006377244833856821,
0.050354763865470886,
0.01727667823433876,
-0.03088691458106041,
-0.03384629637002945,
-0.0657653883099556,
0.008525881916284561,
-0.022295692935585976,
-0.034446876496076584,
-0.019555898383259773,
-0.02149798534810543,
-0.013318397104740143,
0.050692785531282425,
-0.016085026785731316,
-0.03425705432891846,
0.040896009653806686,
0.04594241827726364,
0.07997684180736542,
0.02339749038219452,
-0.03008095733821392,
-0.0030806877184659243,
-0.06667055189609528,
0.007940706796944141,
-0.009649988263845444,
-0.030208390206098557,
0.020734794437885284,
0.0028005291242152452,
-0.0036512569058686495,
0.039259351789951324,
-0.038429297506809235,
-0.04220137745141983,
-0.010648696683347225,
-0.005629262421280146,
0.03464416041970253,
0.061049818992614746,
0.03297560662031174,
-0.03916030749678612,
-0.03605123609304428,
0.005793189629912376,
0.0021579614840447903,
0.00621334183961153,
-0.0065813446417450905,
-0.03500996530056,
-0.018566252663731575,
0.016920367255806923,
0.04074859619140625,
-0.03475906699895859,
0.0015002880245447159,
-0.006286043208092451,
0.024904990568757057,
0.0030658384785056114,
0.05217106640338898,
-0.01102790329605341,
0.01732471212744713,
0.03708254173398018,
-0.016330726444721222,
0.03882542997598648,
0.027106184512376785,
-0.0010848203673958778,
-0.041660331189632416,
0.009949392639100552,
0.023912208154797554,
0.024436334148049355,
0.04342413693666458,
-0.04976211488246918,
-0.009544056840240955,
-0.01750803552567959,
-0.03284576162695885,
0.03668929263949394,
0.01960092969238758,
-0.00005337180846254341,
0.06810027360916138,
-0.01742326281964779,
-0.061422668397426605,
0.016147926449775696,
-0.007922961376607418,
-0.015758132562041283,
-0.021614089608192444,
-0.03323536366224289,
0.011740075424313545,
0.002818209817633033,
-0.014942804351449013,
-0.0002675446739885956,
0.014439992606639862,
0.01568765565752983,
0.019535554572939873,
-0.01152632012963295,
0.010325719602406025,
0.015202104113996029,
0.02344771847128868,
0.042307235300540924,
0.02601431868970394,
-0.03182946518063545,
-0.022059371694922447,
0.04166821017861366,
-0.01883605122566223,
0.010862579569220543,
0.029352817684412003,
0.01544156763702631,
-0.06485067307949066,
-0.012205231934785843,
0.006277917884290218,
0.03311992809176445,
0.023384006693959236,
0.0018815303919836879,
0.023550691083073616,
0.02973262220621109,
-0.077999547123909,
0.018589071929454803,
-0.0047550927847623825,
-0.0016926659736782312,
-0.05489051714539528,
0.00685102678835392,
-0.041510093957185745,
0.03630203381180763,
0.03780059516429901,
0.03344191610813141,
0.009291446767747402,
-0.008467428386211395,
0.010899601504206657,
-0.022662872448563576,
-0.024828897789120674,
0.020116707310080528,
0.02949483133852482,
-0.027664529159665108,
0.050932858139276505,
0.019130758941173553,
-0.009228887967765331,
0.04278316721320152,
-0.00523706478998065,
-0.022817503660917282,
-0.0008745011873543262,
0.04418758302927017,
0.04142877832055092,
0.013256489299237728,
-0.006177979055792093,
0.008191915228962898,
-0.006068898364901543,
0.010014905594289303,
0.041519150137901306,
0.005338510498404503,
-0.02689269185066223,
-0.005063377320766449,
0.06099509820342064,
-0.02683483622968197,
-0.03724077343940735,
0.018723713234066963,
-0.04072897881269455,
-0.0011160459835082293,
0.012574290856719017,
-0.02923654206097126,
-0.0300836730748415,
0.01612960733473301,
0.040711864829063416,
-0.042837828397750854,
0.0019344775937497616,
0.021726476028561592,
0.025611605495214462,
-0.0004664589068852365,
0.030234625563025475,
-0.03373192250728607,
-0.03412184491753578,
0.0660569965839386,
0.05365704745054245,
-0.0045068212784826756,
-0.029035549610853195,
-0.006959585472941399,
-0.010103640146553516,
0.02598227746784687,
0.007958244532346725,
-0.022435834631323814,
-0.07021106779575348,
0.01994764432311058,
0.00037740563857369125,
0.022738216444849968,
-0.06921274960041046,
-0.02923319675028324,
0.032340385019779205,
-0.06671680510044098,
0.01209972333163023,
0.033852871507406235,
-0.025300513952970505,
-0.0261575598269701,
-0.003106623189523816,
0.024583999067544937,
0.05161115154623985,
0.05390939489006996,
-0.02159157022833824,
-0.015972210094332695,
0.018850166350603104,
-0.0022228017915040255,
0.04738716036081314,
0.006289777811616659,
0.011302443221211433,
0.004749678540974855,
0.005777725018560886,
-0.003505117492750287,
0.03306501358747482,
-0.038034588098526,
0.03291138634085655,
0.036890797317028046,
0.0035836189053952694,
-0.03279046341776848,
-0.005775026045739651,
-0.05257014185190201,
0.029713934287428856,
-0.01442031841725111,
0.010056896135210991,
0.08908553421497345,
-0.03401025012135506,
-0.0026427346747368574,
0.02153286710381508,
-0.036686453968286514,
-0.0588301345705986,
-0.00014530701446346939,
-0.03576742485165596,
0.004910184536129236,
0.024642514064908028,
0.031733039766550064,
0.008602738380432129,
-0.0353643074631691,
0.04034235700964928,
0.043065328150987625,
-0.021652827039361,
-0.019619593396782875,
0.02217857725918293,
-0.013462388888001442,
-0.0002445703139528632,
0.042844586074352264,
0.04457329958677292,
0.0010311041260138154,
0.026473423466086388,
0.07036884874105453,
0.0449141226708889,
0.022815890610218048,
0.00034758291440084577,
0.01597696915268898,
-0.007998498156666756,
-0.03225962445139885,
0.031556349247694016,
-0.04151397570967674,
0.019221799448132515,
-0.006057928316295147,
-0.016997840255498886,
0.025066528469324112,
-0.05730979144573212,
-0.013485792092978954,
0.04862292483448982,
-0.015531777404248714,
0.0669337585568428,
-0.025054218247532845,
0.032834459096193314,
-0.0014954794896766543,
0.01936652697622776,
-0.03482571244239807,
-0.01568462699651718,
0.013827109709382057,
0.02479497157037258,
-0.051965370774269104,
-0.02041182853281498,
-0.054440852254629135,
-0.01830921694636345,
0.005088976584374905,
-0.05968187376856804,
-0.05300973355770111,
0.08070108294487,
-0.02416965737938881,
0.017916955053806305,
-0.009252768941223621,
-0.016348060220479965,
-0.03528617322444916,
0.010238013230264187,
0.015435398556292057,
-0.01797015406191349,
0.024797916412353516,
-0.010545996949076653,
-0.0035981216933578253,
0.06377337872982025,
-0.024701068177819252,
-0.025146087631583214,
0.0013718854170292616,
-0.014266162179410458,
-0.008042238652706146,
-0.0036848075687885284
] |
<p>Can we generate a pulse , transmit it and after that can we record it's response time ?</p>
<p>I am curious because I want to know that is it possible to make a mapping device (like SLAM) which uses this technique.
I have done a little search but didn't get the satisfying result .
If any one has any idea about this or where I can get more knowledge about it please share it.</p> | 4,575 | [
-0.022481495514512062,
0.00009239376959158108,
0.005902996752411127,
-0.02935861423611641,
0.05841473862528801,
-0.007623771205544472,
-0.05223583057522774,
-0.022425174713134766,
0.052424509078264236,
-0.0018938304856419563,
0.013359073549509048,
0.021053561940789223,
0.01700473017990589,
0.0034589527640491724,
0.014927093870937824,
-0.009712128899991512,
0.008702371269464493,
-0.01856137625873089,
-0.04805047810077667,
-0.04994083195924759,
0.01904189959168434,
0.0022896069567650557,
0.017711710184812546,
-0.023269208148121834,
-0.02788137085735798,
0.0045406874269247055,
0.04287114366889,
-0.041443292051553726,
-0.00408113794401288,
0.06083545461297035,
-0.07911129295825958,
-0.013410031795501709,
-0.03625507280230522,
0.045917630195617676,
0.034866031259298325,
-0.019709952175617218,
-0.1265752613544464,
-0.05832807719707489,
0.02867841348052025,
0.017045006155967712,
-0.01853463426232338,
-0.011364622972905636,
-0.008808271959424019,
0.051544271409511566,
-0.008594125509262085,
0.011537188664078712,
0.0011043985141441226,
-0.02159285917878151,
0.0029340656474232674,
-0.04379282891750336,
0.06568998098373413,
-0.007500383537262678,
0.04641598090529442,
-0.008953114040195942,
0.009974490851163864,
0.02690098248422146,
0.09008102118968964,
0.05448358133435249,
-0.01647305302321911,
-0.029961014166474342,
0.01467184815555811,
-0.015387820079922676,
-0.007618114352226257,
-0.0659857764840126,
-0.04708770290017128,
-0.014673716388642788,
0.011472607031464577,
-0.016398129984736443,
0.03429904952645302,
-0.01177595742046833,
0.0035302038304507732,
-0.010204503312706947,
0.04987155273556709,
0.008331922814249992,
0.03718540444970131,
-0.05829954892396927,
0.03454491123557091,
0.009097270667552948,
0.01720336265861988,
0.039660096168518066,
0.006265430245548487,
-0.03057425282895565,
0.004766752943396568,
0.016519885510206223,
0.00931139662861824,
-0.02890053763985634,
0.034180574119091034,
-0.01464706938713789,
0.01274622417986393,
-0.01123769860714674,
-0.012599129229784012,
0.013109090737998486,
-0.023276207968592644,
0.023655936121940613,
-0.041271086782217026,
0.01457235123962164,
-0.0043317521922290325,
0.07158645987510681,
0.008540981449186802,
-0.03296690434217453,
0.004947279579937458,
-0.043898046016693115,
0.02057405561208725,
0.020105773583054543,
-0.013362321071326733,
0.02149915136396885,
0.029340293258428574,
0.02281305007636547,
-0.04535726085305214,
0.022069910541176796,
-0.047979552298784256,
-0.01977819949388504,
0.03722994774580002,
0.035046860575675964,
0.02320888638496399,
-0.030215783044695854,
-0.000156817797687836,
-0.03343450650572777,
0.04934339597821236,
0.08533108979463577,
0.005565913859754801,
-0.040922705084085464,
-0.005742260720580816,
-0.06381159275770187,
-0.06950986385345459,
0.00195887079462409,
-0.011187512427568436,
0.018329784274101257,
-0.04991918429732323,
0.03372190520167351,
-0.005558670964092016,
0.0017307723173871636,
0.03296560049057007,
-0.013609394431114197,
0.02068907767534256,
-0.024846283718943596,
-0.14429093897342682,
-0.04896943271160126,
0.022046364843845367,
0.0013979445211589336,
0.029907818883657455,
-0.0982227548956871,
0.08208025246858597,
0.023394064977765083,
0.020986855030059814,
-0.008237781934440136,
0.018113819882273674,
0.009625189006328583,
0.004238123539835215,
-0.021107200533151627,
-0.003512140130624175,
-0.05045772343873978,
0.04098326340317726,
-0.0472358800470829,
0.030056558549404144,
-0.04384002089500427,
0.004037002567201853,
0.021753409877419472,
-0.016451671719551086,
-0.02560797706246376,
0.010153957642614841,
0.012759252451360226,
0.01155086886137724,
0.02491041086614132,
0.005963355768471956,
-0.03584714233875275,
0.0923539251089096,
0.007033240981400013,
0.027080286294221878,
0.015169200487434864,
-0.010317152366042137,
0.014689680188894272,
0.027925314381718636,
0.0324648842215538,
0.036192309111356735,
-0.06066969409584999,
-0.04582587257027626,
0.03067655861377716,
-0.010369939729571342,
-0.013344362378120422,
0.003096896456554532,
-0.03914175182580948,
0.0037171710282564163,
0.04589517042040825,
0.013051548972725868,
-0.018115822225809097,
0.020762214437127113,
-0.007787300739437342,
0.023442966863512993,
-0.047435831278562546,
0.011461048386991024,
-0.021971527487039566,
0.0654565617442131,
0.03889637812972069,
-0.014438288286328316,
0.013897215016186237,
-0.029832279309630394,
-0.005574338138103485,
-0.0035426607355475426,
-0.06587355583906174,
-0.022181866690516472,
-0.01643153838813305,
0.018600238487124443,
-0.030574262142181396,
-0.0266884732991457,
0.09041070193052292,
0.009387443773448467,
-0.013947928324341774,
0.022242365404963493,
0.0021630795672535896,
-0.022895947098731995,
-0.03458475321531296,
-0.007784218527376652,
0.03161279857158661,
-0.01772679015994072,
0.009478503838181496,
0.02961360476911068,
0.03330507501959801,
-0.03315289318561554,
-0.007772788405418396,
-0.04155115410685539,
0.09088107198476791,
0.08358243852853775,
-0.015601872466504574,
0.013164214789867401,
0.008730749599635601,
0.017231155186891556,
-0.021777473390102386,
0.00564697477966547,
-0.029335828498005867,
-0.05404243990778923,
0.0004370494862087071,
0.01057360228151083,
0.015463079325854778,
-0.02291485294699669,
0.03362904116511345,
0.04432322084903717,
0.02499305084347725,
0.03597855567932129,
0.01673896610736847,
-0.010589949786663055,
0.002234748564660549,
0.008272089064121246,
0.02261062152683735,
0.006937494035810232,
0.005968132987618446,
-0.009589915163815022,
0.0028210505843162537,
0.013483038172125816,
0.012393956072628498,
0.010451963171362877,
0.019488992169499397,
-0.026860075071454048,
-0.008181195706129074,
0.02676883339881897,
-0.0037456899881362915,
0.020646030083298683,
-0.03010363131761551,
0.025793561711907387,
0.03247512876987457,
0.004168556537479162,
0.0035185846500098705,
0.0032061818055808544,
-0.04880129173398018,
-0.0030306626576930285,
0.04073528200387955,
-0.008748252876102924,
-0.042315125465393066,
0.020315127447247505,
-0.030521705746650696,
0.03555294871330261,
-0.019652191549539566,
-0.012263133190572262,
-0.058430831879377365,
-0.045055631548166275,
0.051946233958005905,
-0.017023300752043724,
0.031583964824676514,
-0.07276177406311035,
-0.006833641789853573,
0.0011120445560663939,
-0.004191634710878134,
0.005683176685124636,
0.015430864877998829,
-0.04696691408753395,
0.009865198284387589,
0.0054256496950984,
-0.01639755256474018,
0.025483980774879456,
-0.018050996586680412,
0.0006461400771513581,
-0.006068618036806583,
-0.0010681893909350038,
-0.06097019463777542,
-0.014635198749601841,
-0.03627687320113182,
0.030069943517446518,
0.0002827286662068218,
0.02695648744702339,
0.06784474104642868,
0.011171303689479828,
-0.06720459461212158,
-0.005804168526083231,
-0.030890146270394325,
0.013044031336903572,
-0.030313991010189056,
-0.02574385702610016,
0.02373635582625866,
-0.053698569536209106,
0.007038372103124857,
0.024373097345232964,
-0.039788149297237396,
0.0006173564470373094,
-0.044395942240953445,
-0.05734247341752052,
0.008287079632282257,
0.0043444642797112465,
0.04546867683529854,
0.006077974569052458,
-0.016836728900671005,
0.05227270349860191,
0.005024223122745752,
-0.04753623530268669,
-0.022095991298556328,
-0.015582943335175514,
0.030770251527428627,
-0.034290947020053864,
0.00292897573672235,
0.016636867076158524,
-0.05380968004465103,
-0.003333404893055558,
-0.01063016802072525,
-0.010004236362874508,
0.05526571348309517,
0.044891055673360825,
-0.02229657769203186,
0.0018557620933279395,
0.0101389829069376,
0.007238535210490227,
0.05420432984828949,
0.01894240453839302,
-0.07829935848712921,
-0.0012059853179380298,
-0.02228083461523056,
-0.01002452615648508,
0.019281381741166115,
-0.02349509485065937,
0.002583967987447977,
0.007155656814575195,
-0.020923025906085968,
-0.02296457812190056,
0.009033466689288616,
-0.006191513501107693,
-0.0026980896946042776,
-0.025344382971525192,
0.10600493103265762,
0.056638993322849274,
-0.0024287330452352762,
-0.0327148362994194,
0.06243058294057846,
0.015813535079360008,
-0.025611180812120438,
0.007989483885467052,
0.008095466531813145,
0.02087547816336155,
0.024973852559924126,
0.009129497222602367,
-0.029383229091763496,
0.059322431683540344,
0.012289829552173615,
0.04282355681061745,
0.035268157720565796,
0.017137685790657997,
-0.031859271228313446,
-0.017471374943852425,
0.01644466444849968,
0.03693552315235138,
0.061586540192365646,
0.007004838436841965,
0.06390752643346786,
0.05711079388856888,
0.029291756451129913,
-0.008758574724197388,
-0.003378369379788637,
-0.06210457906126976,
-0.045761093497276306,
-0.03313097730278969,
-0.05352349579334259,
-0.0016222012927755713,
-0.055624350905418396,
0.017401989549398422,
-0.033261436969041824,
-0.028574544936418533,
-0.007630031555891037,
-0.015516716986894608,
-0.06734559684991837,
-0.00878178421407938,
-0.0045698462054133415,
-0.04526416212320328,
-0.028447311371564865,
0.017706142738461494,
0.011222651228308678,
-0.004012405872344971,
0.005405129864811897,
0.01853877305984497,
0.01904226653277874,
-0.00010457049211254343,
0.02450663410127163,
-0.031298961490392685,
-0.023610850796103477,
0.03208662196993828,
-0.012041483074426651,
0.041325170546770096,
-0.0199753250926733,
0.009735522791743279,
0.012559697031974792,
0.04657400771975517,
0.034078821539878845,
-0.03255699947476387,
-0.035431548953056335,
-0.014581347815692425,
-0.004842670634388924,
0.03355761617422104,
0.06340476870536804,
-0.01397933904081583,
-0.017873821780085564,
0.0017682632897049189,
0.004725564271211624,
-0.015367656014859676,
0.032469283789396286,
0.039281561970710754,
-0.0024394963402301073,
0.010161449201405048,
-0.04902687296271324,
-0.023063451051712036,
0.026946380734443665,
0.0009441268630325794,
0.0035961056128144264,
0.0218101404607296,
-0.011435694992542267,
0.009822152554988861,
0.012023883871734142,
0.019615499302744865,
0.012410910800099373,
-0.005860411562025547,
0.0062551493756473064,
-0.017283108085393906,
-0.017190605401992798,
0.0291507076472044,
0.02252437360584736,
0.03367023542523384,
0.013933303765952587,
0.028966104611754417,
-0.05879781395196915,
-0.11724281311035156,
-0.03567223623394966,
-0.005218931939452887,
0.0022005781065672636,
0.0009391441126354039,
0.0031963076908141375,
-0.02652660943567753,
-0.013073239475488663,
0.009206055663526058,
-0.03764650225639343,
0.040147777646780014,
0.00305375037714839,
-0.038843974471092224,
-0.03361869975924492,
0.0014837398193776608,
0.020036999136209488,
0.027504976838827133,
0.0096574192866683,
0.02187599427998066,
0.0047623272985219955,
-0.018035264685750008,
0.02120339497923851,
0.027736002579331398,
0.03950474038720131,
0.07594311982393265,
-0.009049511514604092,
0.017578249797225,
-0.026544902473688126,
0.004748671315610409,
-0.03443683311343193,
-0.03566881641745567,
0.01685449108481407,
0.01670265384018421,
-0.010086368769407272,
0.07203786820173264,
0.010564385913312435,
-0.040667757391929626,
0.05982665717601776,
0.013856489211320877,
0.006563451606780291,
0.006447031162679195,
-0.04589999467134476,
0.019750846549868584,
0.043092284351587296,
-0.006651843897998333,
0.04420236870646477,
0.04437539726495743,
-0.007687519304454327,
0.02770930714905262,
0.016408005729317665,
0.017842696979641914,
-0.05112352594733238,
-0.00731344148516655,
0.01877783238887787,
0.0531618632376194,
-0.02928857132792473,
0.08011096715927124,
0.01129836868494749,
0.011159765534102917,
-0.016859883442521095,
-0.0396515391767025,
-0.025500161573290825,
0.050682052969932556,
0.027276987209916115,
0.03433244675397873,
-0.02117745950818062,
0.005666752811521292,
0.0069655501283705235,
-0.01145496591925621,
-0.006373823154717684,
-0.01181013509631157,
0.00972362607717514,
0.04367946833372116,
0.01018724124878645,
0.013455661945044994,
-0.06853976845741272,
0.0231106486171484,
0.06606321781873703,
-0.038359031081199646,
0.031389020383358,
-0.0018218415789306164,
0.022435883060097694,
0.01567612774670124,
-0.03836515173316002,
0.014383881352841854,
0.02950485423207283,
-0.017308762297034264,
0.009080160409212112,
-0.02654467336833477,
0.02117377519607544,
-0.014886205084621906,
0.026738878339529037,
-0.06439096480607986,
-0.05316181108355522,
0.013113057240843773,
-0.010637037456035614,
-0.00031526217935606837,
-0.0356203094124794,
0.009689037688076496,
-0.015468214638531208,
-0.028746962547302246,
0.01417783834040165,
0.017753448337316513,
-0.004999600816518068,
0.0009853403316810727,
-0.009313204325735569,
-0.017407841980457306,
0.004610555246472359,
0.014638609252870083,
-0.007142361719161272,
0.029709970578551292,
0.002690117573365569,
-0.002886109985411167,
-0.016620932146906853,
0.03545760735869408,
-0.03627936914563179,
-0.031106868758797646,
-0.0028868610970675945,
0.0202140174806118,
0.0692867711186409,
-0.001977479550987482,
-0.020778793841600418,
0.04508916661143303,
0.003911819774657488,
-0.03287109360098839,
-0.036581605672836304,
0.01748858019709587,
0.020664513111114502,
-0.028155015781521797,
-0.03506271541118622,
0.022401319816708565,
-0.037042196840047836,
-0.029835831373929977,
0.037847623229026794,
0.021015044301748276,
0.024144722148776054,
-0.023833604529500008,
0.04018380492925644,
-0.033488355576992035,
-0.006529783830046654,
0.0354953370988369,
-0.009972501546144485,
0.016790706664323807,
-0.033353958278894424,
0.007665416691452265,
0.012073633261024952,
0.015518015250563622,
-0.037857696413993835,
-0.02123076654970646,
-0.01796741411089897,
-0.022869950160384178,
0.061567239463329315,
-0.011728844605386257,
0.028708431869745255,
0.04117923229932785,
-0.0219377763569355,
0.006111600901931524,
-0.008958939462900162,
-0.0015640006167814136,
-0.0008123738807626069,
0.0022796583361923695,
0.06131083518266678,
0.037039030343294144,
-0.012073889374732971,
0.016336193308234215,
0.0461447574198246,
0.024006223306059837,
0.006952694617211819,
0.019064918160438538,
0.06113472208380699,
0.04177139699459076,
-0.0440521314740181,
-0.06807821989059448,
0.040646620094776154,
-0.048043690621852875,
0.026722192764282227,
0.024691319093108177,
-0.00253645284101367,
0.03720817714929581,
-0.00996608380228281,
0.006371044088155031,
-0.03980570286512375,
0.02264542691409588,
-0.0588037446141243,
0.01092082541435957,
-0.00705330353230238,
0.009959436021745205,
0.00733189145103097,
-0.0026820788625627756,
0.04207129403948784,
-0.028648007661104202,
0.00008896029612515122,
-0.01672249287366867,
-0.071063332259655,
-0.023162316530942917,
-0.022934336215257645,
-0.0587131567299366,
0.06657272577285767,
-0.026210932061076164,
0.019476616755127907,
0.03442580625414848,
-0.019081292673945427,
0.02536596730351448,
-0.0034097563475370407,
0.038886118680238724,
-0.04573950543999672,
0.10513214766979218,
0.011789323762059212,
0.008824928663671017,
-0.03839587792754173,
0.005024367477744818,
0.09910932183265686,
0.040070127695798874,
0.01229052897542715,
-0.0388975664973259,
0.02108999527990818,
-0.00894839409738779,
0.009351828135550022,
-0.02666458487510681,
0.011536865495145321,
0.03222956508398056,
-0.014929339289665222,
0.026965036988258362,
-0.0025488785468041897,
0.0030598219018429518,
-0.014823829755187035,
0.006805876735597849,
-0.0024084635078907013,
-0.016644176095724106,
0.03157777711749077,
0.019664255902171135,
-0.01374034583568573,
0.01926068402826786,
0.002639752347022295,
0.035859398543834686,
-0.002343340078368783,
-0.07275370508432388,
-0.01047880481928587,
-0.0023094601929187775,
0.02113703079521656,
0.01322170440107584,
-0.0333152674138546,
-0.009003213606774807,
0.027260413393378258,
-0.0033137870486825705,
-0.03449058160185814,
0.02397492155432701,
-0.02092021331191063,
0.029037613421678543,
-0.03437116742134094,
0.02220272272825241,
0.02991740219295025,
-0.01936102844774723,
-0.0232763160020113,
0.007720454595983028,
-0.06189253553748131,
0.0017377734184265137,
-0.024447081610560417,
0.0428665466606617,
-0.019978085532784462,
0.021358786150813103,
-0.007258065976202488,
0.027679141610860825,
0.04826406016945839,
-0.049759458750486374,
-0.030198415741324425,
0.023470934480428696,
0.026593409478664398,
-0.01061697956174612,
-0.00522269494831562,
-0.03410704806447029,
0.016972457990050316,
-0.00011616324627539143,
-0.016258301213383675,
0.0015503213508054614,
0.004423525184392929,
0.005751716438680887,
-0.012831656262278557,
0.030219757929444313,
0.0025787746999412775,
0.000314622709993273,
-0.00967233907431364,
0.0007237311801873147,
-0.009308965876698494,
-0.002322744345292449,
0.027311163023114204,
-0.017965728417038918,
-0.006343009881675243,
0.01054933201521635,
-0.029964081943035126,
-0.014992216601967812,
-0.06623481959104538,
0.03501763194799423,
-0.01711660623550415,
0.0021527037024497986,
-0.024676142260432243,
-0.010356257669627666,
0.065384641289711,
0.033136751502752304,
0.0032101674005389214,
0.0031049377284944057,
-0.044291794300079346,
0.01441493071615696,
0.0205482579767704,
-0.02808327041566372,
-0.008287574164569378,
0.012368659488856792,
-0.02852635830640793,
0.025914406403899193,
-0.03214902803301811,
0.03931119665503502,
0.03556056320667267,
0.017914751544594765,
-0.00581104401499033,
-0.0015583254862576723,
-0.008103463798761368,
-0.020745517686009407,
0.0010479468619450927,
-0.025262411683797836,
-0.015770481899380684,
-0.034817200154066086,
0.046585071831941605,
0.021662110462784767,
-0.00956733152270317,
-0.020245801657438278,
-0.002863147994503379,
-0.025127774104475975,
-0.026901347562670708,
-0.010429206304252148,
0.002529036020860076,
-0.014557530172169209,
0.012361763045191765,
-0.023012440651655197,
0.018887285143136978,
0.01200478058308363,
-0.03802458196878433,
-0.021181827411055565,
-0.020739303901791573,
0.0018482391024008393,
-0.015911594033241272,
-0.029571520164608955,
0.004703572951257229,
0.037708625197410583,
0.01817292720079422,
-0.013164606876671314,
0.020756425336003304,
0.019753163680434227,
0.016305288299918175,
0.02678619883954525,
-0.0015128692612051964,
-0.015876201912760735,
0.058246124535799026,
-0.05147867277264595,
-0.03027522750198841,
0.06336855888366699,
0.0000767258316045627,
0.03203274682164192,
0.015286215580999851,
-0.0004550845769699663,
0.01659262180328369,
0.04841979593038559,
0.007184500806033611,
-0.030849352478981018,
0.033364132046699524,
0.004443919751793146,
0.008756370283663273,
0.04098841920495033,
0.03988662362098694,
-0.03807052969932556,
0.013090589083731174,
0.009446695446968079,
-0.01123103965073824,
0.011608977802097797,
0.007321534678339958,
0.03535683453083038,
0.0004302826419007033,
0.026830753311514854,
0.009827258996665478,
-0.0604725144803524,
0.04785681515932083,
0.023419862613081932,
-0.0037278933450579643,
-0.012245960533618927,
-0.02194884419441223,
0.01538374274969101,
-0.07210900634527206,
-0.008769525215029716,
-0.020693045109510422,
0.010099370032548904,
0.03376194089651108,
-0.04361974447965622,
-0.019894830882549286,
0.022837437689304352,
-0.07768240571022034,
0.011890287511050701,
0.008654278703033924,
-0.01482404489070177,
-0.028488142415881157,
0.04969019815325737,
-0.010050080716609955,
0.010767796076834202,
0.03926260769367218,
0.026643026620149612,
0.021075492724776268,
0.0176156647503376,
0.024522172287106514,
-0.0008950986666604877,
-0.028514839708805084,
0.005905462428927422,
0.025333374738693237,
0.0017985139274969697,
0.05187766253948212,
-0.04941518232226372,
-0.023478157818317413,
0.001170673524029553,
-0.013793808408081532,
0.03171635791659355,
-0.0005431095487438142,
0.020927878096699715,
0.020197337493300438,
0.002575364662334323,
0.033847685903310776,
-0.029356634244322777,
0.013510734774172306,
-0.020336609333753586,
-0.030248943716287613,
0.0400296151638031,
-0.0021190783008933067,
0.009504863992333412,
0.015956932678818703,
-0.006122960243374109,
-0.0031997142359614372,
0.02792469598352909,
-0.04735138639807701,
-0.035434022545814514,
0.054853085428476334,
-0.0123488400131464,
0.015374877490103245,
-0.015530982054769993,
-0.025675121694803238,
-0.032079897820949554,
-0.004094632342457771,
0.003717687213793397,
-0.02329271286725998,
-0.020774034783244133,
0.00576502550393343,
-0.045419059693813324,
-0.014394445344805717,
0.0446326769888401,
-0.012362043373286724,
0.029631365090608597,
-0.06185666471719742,
-0.039283934980630875,
0.0036535325925797224,
0.03317892551422119,
-0.019172145053744316,
0.034915730357170105,
0.0004197983071208,
0.012596833519637585,
-0.010824249126017094,
0.04033617302775383,
0.03947572037577629,
-0.004729989916086197,
-0.025875695049762726,
-0.04559169337153435,
0.05081610381603241,
0.014053469523787498,
0.004963309969753027,
-0.05375320464372635,
-0.02763407863676548,
0.01037015113979578,
0.0361388623714447,
0.031983837485313416,
-0.028572143986821175,
-0.015702499076724052,
0.021412603557109833,
0.02171066775918007,
0.04281594604253769,
-0.009967613965272903,
0.015799647197127342,
-0.024576328694820404,
-0.01730126328766346,
0.00820477306842804,
-0.006722216494381428,
-0.0471954308450222,
-0.002957910066470504,
0.013060919009149075,
0.0404004231095314,
-0.012488235719501972,
-0.055828556418418884,
-0.05026940628886223,
0.0005381249357014894,
0.02346978895366192,
0.014531601220369339,
0.047652482986450195,
0.0003940374590456486,
-0.004149655811488628,
-0.006703574676066637,
-0.031643398106098175,
-0.05521078035235405,
0.009011968038976192,
-0.044890519231557846,
0.023652026429772377,
-0.014584864489734173,
-0.005260443780571222,
0.03143136948347092,
-0.06268047541379929,
-0.02927803061902523,
0.0007032333523966372,
-0.02589264139533043,
0.017380759119987488,
0.05151832103729248,
-0.002604471519589424,
0.01139925792813301,
-0.009356271475553513,
0.04847010225057602,
-0.018060926347970963,
-0.007577221840620041,
-0.026975130662322044,
0.024031102657318115,
-0.0007610650500282645,
-0.042189136147499084,
0.013427497819066048,
0.03240200877189636,
0.008713888935744762,
0.016654742881655693,
0.014990177005529404,
0.05252306908369064,
0.009787905029952526,
-0.0013598474906757474,
0.01929723285138607,
0.004185948055237532,
-0.005916151218116283,
0.03787589073181152,
-0.024341557174921036,
0.06558959186077118,
-0.02757873199880123,
-0.023215800523757935,
-0.07560139149427414,
0.010119974613189697,
-0.023096371442079544,
0.015129080973565578,
0.022808192297816277,
0.03847331181168556,
-0.0006945084896869957,
0.03637557849287987,
-0.03264109417796135,
-0.008853866718709469,
0.03571423888206482,
-0.0528811477124691,
-0.0008268402307294309,
-0.027553588151931763,
0.01823185570538044,
0.0035180561244487762,
-0.02063584513962269,
-0.030619490891695023,
0.0024619363248348236,
0.007879620417952538,
0.0012892112135887146,
0.0010767719941213727,
-0.006717927288264036,
-0.020958859473466873,
-0.013133415021002293,
0.03189952298998833,
-0.07310399413108826,
0.003672613063827157,
-0.03771451860666275,
0.027380352839827538,
-0.0019765791948884726,
0.030174704268574715
] |
<p>In the book "A Briefer History of Time" Stephen Hawking wrote:</p>
<blockquote>
<p>The unpredictable, random element comes in only when we try to
interpret the wave in terms of the positions and velocities of
particles. But maybe that is our mistake: maybe there are no particle
positions and velocities, but only waves. It is just that we try to
fit the waves to our preconceived ideas of positions and velocities.
The resulting mismatch is the cause of the apparent unpredictability.</p>
</blockquote>
<p>Are there evidences that disprove this hypothesis? </p>
<p>If true, would it eliminate most of the apparent quantum paradoxes, and necessity to <a href="http://en.wikipedia.org/wiki/Copenhagen_interpretation#Alternatives" rel="nofollow">"Shut up and calculate!"</a> for those who attempt to interpret quantum physics with common sense?</p>
<p><strong>Edit:</strong> I assume that S. Hawking is aware of Standard Model, and he considers this statement as a legitimate hypothesis. Are there evidences that prove that it's not? In other words, is it a philosophical or scientific question?</p> | 4,576 | [
-0.019142411649227142,
-0.02729845978319645,
0.01809762977063656,
-0.05712633207440376,
0.06192655861377716,
-0.007631110958755016,
-0.0036180729512125254,
-0.01869494467973709,
-0.017530865967273712,
-0.011805995367467403,
0.015963194891810417,
0.03269217908382416,
0.07156858593225479,
0.046387962996959686,
0.03454088419675827,
0.02479626052081585,
0.008660813793540001,
-0.037312597036361694,
-0.02829582802951336,
-0.04499231278896332,
0.015800965949892998,
0.02642057277262211,
-0.008475348353385925,
-0.00477959867566824,
-0.032901324331760406,
0.023023638874292374,
0.03760645166039467,
0.023466387763619423,
0.013731473125517368,
0.035150397568941116,
-0.022381434217095375,
-0.0036166321951895952,
0.026104213669896126,
0.036043379455804825,
0.02420821599662304,
-0.010557606816291809,
0.0125350933521986,
-0.011849184520542622,
-0.01162168849259615,
0.0030291914008557796,
0.012036120519042015,
0.002071014605462551,
-0.006948031019419432,
0.07548166811466217,
-0.022941885516047478,
0.03478197753429413,
0.011365599930286407,
-0.010555657558143139,
0.0712946355342865,
-0.04760961979627609,
0.07567098736763,
-0.014152484014630318,
-0.005043365992605686,
0.01066242903470993,
-0.025347057729959488,
-0.005626481957733631,
0.09841123968362808,
0.03157630190253258,
-0.04527530074119568,
-0.0686720684170723,
0.016890015453100204,
-0.013725116848945618,
-0.00815889984369278,
0.019528260454535484,
0.00010768981883302331,
0.04421078786253929,
-0.01635945774614811,
-0.03965636342763901,
0.0437886044383049,
-0.006485441699624062,
-0.0004817123990505934,
-0.03781145438551903,
0.03530396148562431,
0.03205352649092674,
0.04636793211102486,
-0.04606103524565697,
0.009431762620806694,
-0.002084634965285659,
0.002574747893959284,
0.07096055895090103,
-0.012733332812786102,
-0.0010698613477870822,
0.05066316947340965,
0.01585439220070839,
0.011197826825082302,
-0.02855621837079525,
0.02961866371333599,
-0.03284480795264244,
-0.014478359371423721,
0.06876850873231888,
-0.016061246395111084,
0.01995079033076763,
0.046710044145584106,
0.01705283485352993,
-0.03130040690302849,
0.034011416137218475,
0.024483125656843185,
0.03653610870242119,
0.025645514950156212,
-0.041112009435892105,
0.023819968104362488,
-0.02030501514673233,
0.049202676862478256,
0.07119675725698471,
-0.02000896818935871,
-0.004362065345048904,
-0.039412591606378555,
0.041832905262708664,
-0.009679965674877167,
-0.021516213193535805,
-0.027285339310765266,
0.03916560113430023,
0.011746052652597427,
0.027748459950089455,
0.01508138608187437,
-0.006542689632624388,
0.005951175466179848,
-0.013200769200921059,
0.08662824332714081,
0.058548472821712494,
0.006104883272200823,
-0.04345608875155449,
0.011405193246901035,
-0.01397809199988842,
-0.04198072850704193,
-0.0011390963336452842,
0.03785199299454689,
-0.011412166059017181,
0.0017282444750890136,
0.042979646474123,
0.00938461720943451,
0.007448166608810425,
0.01972787268459797,
0.030818674713373184,
0.03609415143728256,
-0.014112096279859543,
-0.12539894878864288,
-0.058169927448034286,
0.06075713410973549,
0.0035793862771242857,
-0.022774197161197662,
-0.07676991075277328,
0.0023717612493783236,
0.017329519614577293,
0.06685901433229446,
-0.028860105201601982,
0.02413269132375717,
-0.014047620818018913,
0.010899411514401436,
0.025838591158390045,
-0.03482108563184738,
0.002800595248118043,
0.019284186884760857,
-0.056858841329813004,
0.002695152536034584,
-0.05338754132390022,
0.009742925874888897,
0.04686112329363823,
0.01995350606739521,
0.006100160535424948,
0.016559096053242683,
-0.024593660607933998,
-0.02581094764173031,
0.007958026602864265,
0.00924335140734911,
-0.04124116152524948,
0.05895305052399635,
0.03916560113430023,
0.0024714607279747725,
0.03672795370221138,
0.0008041572873480618,
0.02120840549468994,
0.0045184846967458725,
0.026285314932465553,
0.02094152942299843,
-0.06377778947353363,
-0.007631165906786919,
0.00858014915138483,
-0.010559269227087498,
-0.039226263761520386,
-0.036977674812078476,
-0.0043700458481907845,
-0.01031340379267931,
0.0015896769473329186,
0.010184571146965027,
0.040854208171367645,
-0.011655649170279503,
0.030409112572669983,
-0.014991460368037224,
-0.03858577087521553,
-0.015994742512702942,
-0.06998968869447708,
-0.00035466719418764114,
-0.00785970687866211,
0.002367607317864895,
0.06190840154886246,
0.005507672671228647,
0.017656845971941948,
-0.05177220702171326,
-0.012875956483185291,
-0.006120739039033651,
0.02494088001549244,
0.02251608483493328,
0.01700969599187374,
0.013527587056159973,
0.0795697569847107,
0.022501813247799873,
-0.014102826826274395,
0.0023524248972535133,
-0.0010795006528496742,
-0.0327325239777565,
-0.01534135453402996,
-0.027984770014882088,
0.026334287598729134,
0.011087186634540558,
0.02358938939869404,
-0.0015274460893124342,
-0.014179682359099388,
-0.010086661204695702,
0.028131987899541855,
-0.025165965780615807,
0.030277162790298462,
0.0009229959105141461,
0.033734653145074844,
-0.027600154280662537,
0.06284893304109573,
0.014164367690682411,
-0.011696964502334595,
0.04313645139336586,
-0.01922452077269554,
-0.027926050126552582,
0.021677011623978615,
0.00022133697348181158,
0.032016169279813766,
-0.020916862413287163,
-0.018643159419298172,
0.02955174632370472,
0.04924101009964943,
0.02203156054019928,
0.018664127215743065,
-0.00041982458787970245,
-0.04243791475892067,
-0.01682431437075138,
-0.0179949551820755,
0.013168781995773315,
0.02031431905925274,
0.05390172824263573,
-0.0014206405030563474,
0.00024346844293177128,
-0.01901284232735634,
-0.01815180480480194,
0.01523115485906601,
-0.03595677390694618,
0.02797342836856842,
0.002921454841271043,
-0.046092964708805084,
0.013566485606133938,
0.005830374546349049,
0.027378860861063004,
0.00879152026027441,
0.007709996774792671,
-0.029874466359615326,
-0.04419557377696037,
-0.007018557284027338,
-0.01171189546585083,
0.00023253123799804598,
-0.016008669510483742,
-0.0028190775774419308,
0.03788980469107628,
-0.031206617131829262,
-0.007620811462402344,
-0.026302292943000793,
-0.014239231124520302,
-0.022509494796395302,
-0.012001348659396172,
0.03923387825489044,
0.0008684489876031876,
0.0314270444214344,
-0.02579464763402939,
-0.05461831018328667,
0.003669997677206993,
-0.015097398310899734,
-0.02569606527686119,
-0.001262689707800746,
-0.06251300871372223,
0.022456131875514984,
-0.03853907063603401,
-0.04561764746904373,
0.03095504269003868,
-0.03789941966533661,
0.03134072944521904,
0.01759769208729267,
-0.030862485989928246,
-0.04936777800321579,
0.012849219143390656,
-0.053792376071214676,
0.0014089192263782024,
-0.018094714730978012,
-0.02625039778649807,
0.031935203820466995,
0.006094359792768955,
-0.04024834558367729,
0.016623198986053467,
-0.003375731408596039,
-0.07287545502185822,
-0.008206315338611603,
-0.01796349510550499,
-0.006634917110204697,
-0.05423891544342041,
0.03125708922743797,
0.01839474029839039,
-0.022948339581489563,
0.01635797880589962,
-0.0102686183527112,
-0.08173808455467224,
0.004389223642647266,
-0.01664956845343113,
0.046870894730091095,
-0.011985617689788342,
0.01000932976603508,
0.03494591638445854,
0.02274407632648945,
-0.02779676578938961,
-0.0031591132283210754,
0.004555251449346542,
0.018976926803588867,
-0.013251258060336113,
-0.0026455193292349577,
0.04203201085329056,
0.0300437081605196,
0.06630444526672363,
-0.00238299579359591,
0.03647150471806526,
-0.007847131229937077,
0.009099166840314865,
-0.011936918832361698,
-0.01934914104640484,
-0.0053537460044026375,
-0.0058088465593755245,
0.06196427717804909,
0.004891727119684219,
-0.04592841491103172,
0.0017633155221119523,
-0.014768252149224281,
0.026796260848641396,
0.016168829053640366,
-0.029254935681819916,
0.05230364575982094,
0.01842946745455265,
0.02504855953156948,
-0.018990319222211838,
0.017233936116099358,
0.002038165694102645,
-0.02009117417037487,
0.0004932949086651206,
0.018033523112535477,
0.031679872423410416,
0.045455191284418106,
0.02728249877691269,
0.028334006667137146,
0.04403556138277054,
-0.024470534175634384,
-0.030764879658818245,
-0.018955685198307037,
-0.0036481006536632776,
0.02182452753186226,
-0.025093529373407364,
-0.05474371463060379,
0.0591040775179863,
0.0600314736366272,
0.03579910844564438,
0.010481880977749825,
-0.06450163573026657,
0.013597307726740837,
-0.03926921635866165,
-0.012029550969600677,
-0.004884425085037947,
0.02742847055196762,
0.010296013206243515,
0.03586800396442413,
0.03213312476873398,
-0.011446136049926281,
-0.01053471677005291,
-0.022656669840216637,
-0.08122486621141434,
0.002018027938902378,
-0.04427433758974075,
-0.02433071658015251,
-0.03803298994898796,
-0.06703785061836243,
0.011128130368888378,
-0.0367605946958065,
-0.022987088188529015,
0.0037849389482289553,
0.005214055068790913,
-0.07252741605043411,
0.0014427911955863237,
-0.02542784810066223,
-0.038393761962652206,
-0.011747727170586586,
0.03543448448181152,
0.04856107756495476,
-0.02245989814400673,
0.002029272262006998,
0.03818555176258087,
-0.028896907344460487,
-0.013387473300099373,
-0.0018939924193546176,
0.040627866983413696,
-0.00011072008783230558,
0.035023562610149384,
0.030954323709011078,
-0.013378787785768509,
-0.05816592276096344,
0.014977716840803623,
0.01522989571094513,
0.054068922996520996,
-0.0033148459624499083,
0.007134757470339537,
-0.02933758683502674,
-0.009959651157259941,
0.016465596854686737,
-0.002244061091914773,
0.051866475492715836,
0.019091427326202393,
0.03931402415037155,
0.03889437019824982,
0.006064672023057938,
-0.0382547602057457,
0.054210878908634186,
0.043663252145051956,
-0.03767902031540871,
0.0005078827380202711,
-0.03208249434828758,
-0.04357169568538666,
-0.005558169446885586,
-0.01370335929095745,
0.011963313445448875,
0.02178940922021866,
0.00172805052716285,
0.0002618377038743347,
0.010514448396861553,
0.005693032406270504,
-0.020933661609888077,
0.03624695539474487,
-0.04349137842655182,
0.0007097487687133253,
-0.00989071186631918,
0.0017832013545557857,
0.018628519028425217,
-0.003368355566635728,
0.02562548778951168,
0.0268019400537014,
-0.02963358350098133,
-0.04633224382996559,
-0.02886553481221199,
0.029759826138615608,
0.03777218237519264,
-0.02253854088485241,
0.005463366396725178,
-0.042226918041706085,
0.015149982646107674,
0.050095267593860626,
-0.008239922113716602,
0.004103609826415777,
-0.015610804781317711,
0.018870262429118156,
-0.026705769822001457,
-0.03512587770819664,
0.0076442803256213665,
0.010271990671753883,
-0.01964118704199791,
0.018478989601135254,
-0.002891580341383815,
-0.00501242745667696,
-0.04194871708750725,
-0.015451416373252869,
0.030309034511446953,
0.055657099932432175,
0.00463292608037591,
0.024036286398768425,
0.016595173627138138,
-0.009321596473455429,
-0.031732797622680664,
-0.09476354718208313,
0.016871722415089607,
-0.01791841723024845,
-0.015164063312113285,
0.04886101558804512,
-0.021752869710326195,
-0.05896550416946411,
0.019070548936724663,
-0.006649194285273552,
-0.0015881338622421026,
0.02016998827457428,
-0.048666223883628845,
0.03361938148736954,
0.001985698938369751,
0.04035966098308563,
-0.005183791741728783,
0.020064957439899445,
0.002973714377731085,
0.017357584089040756,
0.0028107487596571445,
0.020290352404117584,
-0.03929518163204193,
0.013205436989665031,
-0.016256853938102722,
0.0027432770002633333,
-0.0362900011241436,
0.04231271892786026,
0.04153747111558914,
0.01821560226380825,
0.02516832947731018,
-0.028108956292271614,
-0.06058795750141144,
-0.026654407382011414,
-0.004058496560901403,
0.019681783393025398,
-0.061298761516809464,
0.0018403586000204086,
-0.0018628246616572142,
-0.027973005548119545,
-0.009045040234923363,
0.006001055706292391,
0.02468366175889969,
0.03183664381504059,
0.022259369492530823,
0.023883156478405,
-0.04570521041750908,
-0.0022144094109535217,
0.02307928539812565,
-0.050967734307050705,
0.002667960710823536,
-0.00021466064208652824,
-0.000251280318479985,
0.01986858807504177,
-0.04558142274618149,
-0.07623148709535599,
-0.01723327301442623,
-0.0035985547583550215,
-0.0019964680541306734,
-0.03717207908630371,
0.021716922521591187,
0.009998389519751072,
0.05596541613340378,
-0.08025334775447845,
-0.03433505818247795,
0.020574046298861504,
0.024677732959389687,
-0.007683987729251385,
-0.017044218257069588,
0.06566382199525833,
-0.0627552941441536,
0.0024024969898164272,
-0.005340579431504011,
0.013550600036978722,
-0.021994533017277718,
-0.026530837640166283,
0.024928441271185875,
0.014780758880078793,
0.06011205166578293,
-0.02314927987754345,
-0.03320303559303284,
0.02865343727171421,
0.0023938464000821114,
-0.008322548121213913,
-0.00485624885186553,
0.03271333873271942,
-0.017935030162334442,
-0.051219746470451355,
-0.011416531167924404,
0.004879624582827091,
0.010320578701794147,
-0.02441774494946003,
0.0056144134141504765,
0.049569424241781235,
0.016477111726999283,
0.031671661883592606,
-0.01024941448122263,
-0.00017898391524795443,
-0.01910739205777645,
0.021608475595712662,
0.02507944218814373,
0.0028695641085505486,
0.021687660366296768,
-0.022534718737006187,
0.048664990812540054,
0.001230540918186307,
-0.02299167402088642,
0.02102457918226719,
-0.0024588860105723143,
0.025754425674676895,
-0.021531373262405396,
-0.014962870627641678,
-0.01861395128071308,
0.003550546243786812,
0.0005542588187381625,
0.012322775088250637,
-0.01791721023619175,
0.009576196782290936,
0.004062195774167776,
-0.048045285046100616,
-0.02237118035554886,
0.03221086040139198,
0.04942898079752922,
0.007546104025095701,
0.03400512412190437,
0.037026725709438324,
-0.013928014785051346,
-0.03359793871641159,
-0.02034459076821804,
0.007735121995210648,
-0.011939755640923977,
0.030287813395261765,
-0.0005837695207446814,
-0.0312882661819458,
0.0359492190182209,
0.011920414865016937,
0.04921037703752518,
-0.021678278222680092,
0.010992757976055145,
0.02665196731686592,
0.03680748865008354,
0.03606952354311943,
0.017192425206303596,
-0.03769391030073166,
0.01682460866868496,
-0.025709055364131927,
0.02788536623120308,
0.0009329449385404587,
0.030983291566371918,
-0.013430038467049599,
-0.01278400793671608,
-0.006964877247810364,
0.0004883578512817621,
0.0056866975501179695,
-0.05584585666656494,
-0.009801500476896763,
-0.0037909718230366707,
0.024867108091711998,
0.005666750017553568,
-0.010281587950885296,
0.019384728744626045,
0.010868406854569912,
0.007609746418893337,
-0.02522239275276661,
-0.1084185242652893,
-0.029718240723013878,
-0.03005557507276535,
-0.013979041017591953,
0.07400109618902206,
-0.01016420777887106,
-0.038579147309064865,
-0.01305457204580307,
-0.031026076525449753,
0.01191590167582035,
0.021598495543003082,
0.012445698492228985,
-0.04142231494188309,
0.0545048825442791,
0.003253263421356678,
-0.014744334854185581,
-0.05947336554527283,
0.04227520525455475,
0.13061551749706268,
0.0270711537450552,
0.022264353930950165,
-0.0411493293941021,
0.00036802073009312153,
0.0014373637968674302,
0.021700968965888023,
0.004532971885055304,
0.03562060371041298,
-0.02021108753979206,
0.011350697837769985,
-0.021246090531349182,
0.02908581681549549,
0.03341291844844818,
-0.02488246187567711,
0.030058978125452995,
-0.06523231416940689,
-0.03739424794912338,
0.013695328496396542,
-0.0006044941255822778,
0.023411646485328674,
0.008725407533347607,
-0.010647335089743137,
0.013924665749073029,
-0.05908522009849548,
-0.020312821492552757,
0.022307872772216797,
-0.0176435187458992,
-0.030983803793787956,
0.027781685814261436,
-0.045563481748104095,
0.013534476049244404,
0.043659426271915436,
-0.024139605462551117,
-0.02495025098323822,
0.030940547585487366,
0.030531059950590134,
-0.008294668048620224,
0.04408831521868706,
0.028159886598587036,
0.004664544947445393,
-0.012143000960350037,
0.009136281907558441,
0.03474126383662224,
-0.027934005483984947,
0.002668591681867838,
0.0023184865713119507,
0.045344028621912,
-0.009513755328953266,
-0.02247994765639305,
-0.006533606443554163,
-0.024541262537240982,
-0.01444998662918806,
-0.060417190194129944,
0.009868941269814968,
-0.015120535157620907,
0.039504747837781906,
-0.015222612768411636,
-0.039386216551065445,
0.007519144099205732,
0.008466892875730991,
-0.031001431867480278,
0.038236454129219055,
0.021368112415075302,
-0.010067429393529892,
-0.03460841625928879,
0.0011843505781143904,
0.028520267456769943,
-0.002629946917295456,
-0.012866407632827759,
-0.03954632580280304,
-0.006838392931967974,
-0.09471384435892105,
-0.031770527362823486,
0.04885091260075569,
0.04504616931080818,
0.04191270470619202,
0.0018027054611593485,
0.006563644390553236,
-0.007800951600074768,
-0.037328578531742096,
0.03622893989086151,
-0.03691664710640907,
-0.01025468111038208,
-0.0060539268888533115,
0.018760018050670624,
0.03145196661353111,
0.05344153195619583,
-0.05718647316098213,
-0.020600106567144394,
0.031286437064409256,
0.020453739911317825,
0.011258150450885296,
-0.029408713802695274,
-0.02642449177801609,
0.019646646454930305,
-0.04465223848819733,
0.01765812188386917,
-0.00035481565282680094,
0.014181653037667274,
0.031897835433483124,
-0.005635322071611881,
-0.018372971564531326,
0.06630878895521164,
0.007564377039670944,
-0.03326119855046272,
0.0321161113679409,
-0.028042960911989212,
0.003441743552684784,
0.04112095385789871,
0.026528730988502502,
-0.033522285521030426,
-0.027819406241178513,
-0.027751930058002472,
0.01982586830854416,
-0.024855349212884903,
0.00835014134645462,
-0.04045946151018143,
0.03817205876111984,
-0.0314662866294384,
0.026171019300818443,
-0.021072527393698692,
-0.0114408815279603,
-0.05160798877477646,
0.005261818412691355,
-0.034485552459955215,
-0.023183664306998253,
-0.03793596476316452,
0.03901180252432823,
0.0003353161155246198,
-0.040391236543655396,
0.013672643341124058,
0.0035931330639868975,
-0.02352321147918701,
0.02470802515745163,
-0.0122268320992589,
0.0021997566800564528,
0.01291315071284771,
-0.026264764368534088,
-0.03900924324989319,
0.0038371242117136717,
-0.044646646827459335,
-0.05954602733254433,
0.0375247560441494,
-0.049417026340961456,
0.010732610709965229,
0.04102063551545143,
0.0006041020387783647,
0.02535327337682247,
0.057028163224458694,
-0.048395559191703796,
0.0028689031023532152,
-0.0059900772757828236,
-0.021992960944771767,
0.005034786649048328,
-0.018615368753671646,
0.009380684234201908,
0.012011912651360035,
-0.028368068858981133,
0.059512097388505936,
0.016121821478009224,
0.01063395943492651,
0.011450771242380142,
0.0017618314595893025,
-0.01900843344628811,
0.001167265698313713,
0.03741079196333885,
-0.01618177257478237,
-0.01358335092663765,
0.03770533949136734,
-0.048143185675144196,
0.049868613481521606,
0.0013342027086764574,
0.0071067363023757935,
-0.10574499517679214,
-0.013820630498230457,
0.016320476308465004,
0.0008253182750195265,
0.022387804463505745,
-0.003226135391741991,
0.013850516639649868,
0.006411005277186632,
-0.09398537874221802,
-0.003806323977187276,
-0.008597765117883682,
-0.03664886951446533,
-0.01240118220448494,
0.009049735032022,
-0.05075439065694809,
0.055308885872364044,
0.028072481974959373,
0.023940037935972214,
-0.003381376387551427,
0.005720764864236116,
-0.0021993115078657866,
-0.03888583555817604,
0.003743377048522234,
0.02124078758060932,
0.0034074324648827314,
-0.02350320667028427,
0.05188525840640068,
-0.05561503767967224,
-0.001615711022168398,
0.05819914862513542,
0.025491666048765182,
0.051984239369630814,
-0.033625051379203796,
0.007738971617072821,
0.005087108351290226,
0.04608379676938057,
0.037113890051841736,
-0.00453468132764101,
0.0016410782700404525,
-0.00588505994528532,
0.02574899233877659,
0.03897915408015251,
0.03195637837052345,
-0.01720982789993286,
-0.01423976942896843,
-0.04625938832759857,
-0.046756405383348465,
-0.0208730585873127,
-0.005725370720028877,
-0.016432814300060272,
-0.01328288298100233,
0.025265496224164963,
-0.0020125824958086014,
0.002784794196486473,
0.005973435007035732,
-0.038852669298648834,
-0.017230957746505737,
0.017514415085315704,
0.01770874299108982,
-0.01620357297360897,
0.0012806134764105082,
-0.020341986790299416,
-0.026113560423254967,
0.01836908422410488,
-0.002591757569462061,
-0.013739938847720623,
-0.05541298910975456,
-0.022594209760427475,
0.004701727069914341,
0.03092896193265915,
0.022186769172549248,
-0.06176856905221939,
-0.03939587250351906,
0.011252732016146183,
-0.011550309136509895,
0.03181823343038559,
-0.02614496648311615,
-0.007542131002992392,
-0.006071394309401512,
-0.04803920164704323,
0.07115915417671204,
0.013502707704901695,
0.05093340575695038,
-0.05069094896316528,
-0.01799449510872364,
0.0015440385323017836,
0.03903542086482048,
0.05337508022785187,
-0.01665356382727623,
-0.0013525130925700068,
0.026682304218411446,
-0.017558272927999496,
0.027516817674040794,
-0.028294604271650314,
-0.013018235564231873,
0.003253896487876773,
-0.02751578390598297,
-0.009793710894882679,
-0.03174437955021858,
0.011823541484773159,
0.025799591094255447,
0.050424911081790924,
0.005176849197596312,
0.054469604045152664,
0.0007171339238993824,
-0.040797099471092224,
0.014413892291486263,
0.029463548213243484,
-0.007880297489464283,
0.043001819401979446,
0.01209264062345028,
0.05388438701629639,
0.03544194623827934,
0.005258465185761452,
-0.04647836089134216,
0.03898632153868675,
-0.025347374379634857,
-0.06281804293394089,
0.031303104013204575,
0.004517776425927877,
0.023254355415701866,
-0.054876845329999924,
-0.01176212728023529,
0.04271587356925011,
-0.058713410049676895,
-0.005186576396226883,
0.0318031907081604,
0.009091075509786606,
0.04113796725869179,
0.02157900482416153,
-0.0242791585624218,
0.014036672189831734,
-0.013592592440545559,
0.018934860825538635,
0.04445846378803253,
0.05861133337020874,
0.010100346989929676,
0.023167842999100685,
0.030372576788067818,
-0.007744820788502693,
0.021870195865631104,
0.010971360839903355,
0.0329960361123085,
-0.007765845861285925,
0.014266387559473515,
0.03008349798619747,
0.00339492573402822,
-0.005077370908111334,
0.05132368579506874,
-0.017049329355359077,
0.08134513348340988,
-0.003941378090530634,
-0.0010660543339326978,
-0.02425828017294407,
0.027994966134428978,
-0.016825350001454353,
0.0065516093745827675,
0.013211051933467388,
0.015738364309072495,
-0.02554834820330143,
-0.022140543907880783,
-0.0034128951374441385,
0.03444036468863487,
0.02645902894437313,
-0.05151952803134918,
-0.028561200946569443,
-0.018949197605252266,
-0.04101845994591713,
0.004788200370967388,
0.016572890803217888,
-0.030516935512423515,
-0.006202873773872852,
0.04665164276957512,
0.02252289652824402,
-0.027580374851822853,
-0.022549303248524666,
-0.006735693197697401,
-0.041048966348171234,
0.05413589999079704,
-0.03695888817310333,
0.005234715528786182,
-0.03527840971946716,
0.03005247749388218,
-0.05856030806899071,
-0.007384214550256729
] |
<p>What happens if I charged a capacitor then i touch the 2 poles in same time?</p> | 4,577 | [
-0.012511167675256729,
-0.04694800078868866,
0.003897919785231352,
-0.015156536363065243,
0.019906310364603996,
-0.014560095965862274,
-0.016921767964959145,
-0.005728967022150755,
0.030786553397774696,
-0.012615910731256008,
0.012409077025949955,
0.058756060898303986,
0.023369785398244858,
-0.017345638945698738,
-0.010772275738418102,
-0.020076707005500793,
-0.00567548256367445,
-0.010709370486438274,
0.008126575499773026,
0.00322851724922657,
-0.03191500902175903,
0.03380003571510315,
0.019582603126764297,
0.019162703305482864,
-0.015117018483579159,
0.026230480521917343,
0.023766985163092613,
0.007087872829288244,
0.002982770325616002,
0.044271837919950485,
-0.0475638248026371,
-0.05191870033740997,
0.011001489125192165,
0.01722068525850773,
0.048186298459768295,
-0.03667003661394119,
-0.04676982760429382,
-0.07444431632757187,
-0.009596653282642365,
0.00816053245216608,
0.00022337819973472506,
-0.005804314743727446,
-0.016756288707256317,
0.0005336125614121556,
-0.025370541960000992,
-0.002246477408334613,
-0.0015034814132377505,
-0.015179277397692204,
0.07985151559114456,
-0.04985474422574043,
0.0741887018084526,
-0.010445734485983849,
0.04281586781144142,
0.0299465823918581,
-0.0005295767332427204,
0.04572170227766037,
0.0715743750333786,
0.05656234547495842,
-0.023073645308613777,
-0.008296322077512741,
-0.032119978219270706,
0.0031845970079302788,
-0.01235872507095337,
-0.031387217342853546,
-0.05770274996757507,
0.06721008569002151,
-0.00942546222358942,
-0.01153381634503603,
-0.016259726136922836,
-0.003210362745448947,
0.01384799461811781,
0.020955916494131088,
0.03748326748609543,
-0.027344247326254845,
0.021445393562316895,
-0.024481382220983505,
0.030908238142728806,
0.022546550258994102,
0.019171718508005142,
0.049766283482313156,
-0.031224949285387993,
0.009526294656097889,
0.02991962991654873,
0.03274160251021385,
0.014931698329746723,
-0.041273459792137146,
0.017357666045427322,
0.012991557829082012,
0.02104649879038334,
0.0013078832998871803,
0.018099866807460785,
-0.0059499237686395645,
0.017565323039889336,
-0.010951848700642586,
-0.02565406635403633,
-0.01529649831354618,
-0.010482735000550747,
0.051406726241111755,
-0.023778337985277176,
-0.024588439613580704,
0.027092745527625084,
-0.018075555562973022,
0.006555306725203991,
0.03593062236905098,
0.0075050098821520805,
-0.03015710413455963,
0.006833790335804224,
0.00377779477275908,
-0.003035131376236677,
-0.004666920751333237,
-0.06548366695642471,
0.003377258311957121,
0.00802437774837017,
-0.018965844064950943,
0.029548069462180138,
-0.020828071981668472,
0.00384236266836524,
-0.01307608000934124,
0.03691894933581352,
0.0275553148239851,
0.01709589548408985,
-0.03872670605778694,
0.005621911026537418,
-0.03819331154227257,
-0.043909039348363876,
-0.0028073382563889027,
0.005148633383214474,
-0.009643075056374073,
-0.021064940840005875,
0.007290381472557783,
-0.022817987948656082,
-0.017623957246541977,
-0.016669124364852905,
-0.017299093306064606,
0.031376954168081284,
-0.03509960323572159,
-0.10674665123224258,
-0.02576969563961029,
0.011823851615190506,
-0.000493900733999908,
-0.008641230873763561,
-0.09118366241455078,
0.010623387061059475,
0.024250630289316177,
0.06988780945539474,
0.01909574307501316,
-0.03337067738175392,
-0.008802290074527264,
0.0407528281211853,
0.031475357711315155,
0.0071979728527367115,
-0.028047993779182434,
0.005020723212510347,
-0.009359091520309448,
0.01890925131738186,
-0.03628711402416229,
0.021237820386886597,
0.048929765820503235,
0.001992330653592944,
-0.0136127769947052,
0.03547926992177963,
0.012885858304798603,
0.007713388651609421,
0.015337183140218258,
-0.04774439334869385,
-0.019842104986310005,
0.08901502937078476,
0.016854532063007355,
-0.0030594621784985065,
0.047169849276542664,
0.024114051833748817,
0.06467761099338531,
-0.01717272400856018,
0.04627100005745888,
0.047219064086675644,
-0.049783412367105484,
-0.02722775749862194,
-0.019081436097621918,
0.04486214742064476,
-0.02437766268849373,
-0.05732345953583717,
-0.035558197647333145,
-0.014542934484779835,
0.030731385573744774,
0.005142109002918005,
0.03426581993699074,
-0.009526660665869713,
-0.023264842107892036,
-0.05246777832508087,
-0.024569882079958916,
-0.028914043679833412,
-0.07189299911260605,
0.06335467100143433,
0.00554148992523551,
-0.02434641309082508,
0.02919464185833931,
0.011068494990468025,
0.043768368661403656,
-0.06139430031180382,
-0.02317243628203869,
-0.01417892798781395,
0.036674484610557556,
-0.0032170037738978863,
0.0037283082492649555,
0.026048598811030388,
0.06601567566394806,
0.03670864552259445,
0.04602784663438797,
0.018891453742980957,
-0.03469349816441536,
0.0013946292456239462,
0.0026715463027358055,
-0.010460684075951576,
0.014801912941038609,
0.03439242020249367,
0.048946455121040344,
0.029889047145843506,
-0.0010796310380101204,
-0.006355474703013897,
0.043578971177339554,
0.009264113381505013,
0.07509059458971024,
0.049126192927360535,
-0.004216434899717569,
0.004271139856427908,
0.007870837114751339,
-0.016321906819939613,
-0.009219900704920292,
-0.02243836037814617,
-0.04619453102350235,
-0.019321244210004807,
0.017818473279476166,
0.04214903712272644,
0.01893528737127781,
-0.014506710693240166,
0.016429979354143143,
0.0313396193087101,
0.02885180525481701,
0.026516951620578766,
0.019299333915114403,
0.00987241417169571,
0.005165678448975086,
0.023552080616354942,
-0.016482288017868996,
0.0048592668026685715,
-0.0180638637393713,
0.0325092151761055,
0.012661497108638287,
0.03269064053893089,
0.021712321788072586,
-0.034444138407707214,
0.010614713653922081,
-0.01471099816262722,
0.06141849234700203,
0.04709654673933983,
-0.05556797608733177,
0.017135092988610268,
-0.01900288090109825,
-0.002168951788917184,
0.005594049114733934,
0.02353602834045887,
0.002083550440147519,
0.0018324335105717182,
0.02022789604961872,
0.014709497801959515,
0.005208930000662804,
-0.017746685072779655,
-0.06361901760101318,
0.03607431799173355,
-0.0415445901453495,
0.029116718098521233,
0.03535287082195282,
-0.03673360124230385,
-0.005774271208792925,
0.006281675770878792,
0.009888984262943268,
0.03928394615650177,
0.09838555753231049,
-0.047518540173769,
-0.04539100080728531,
-0.03357629105448723,
-0.01634524203836918,
0.02900543436408043,
-0.0006929523660801351,
-0.04337700828909874,
0.0010494106682017446,
-0.0459231473505497,
-0.017704375088214874,
0.03635252267122269,
0.021265637129545212,
0.0067390259355306625,
0.006613361183553934,
-0.017556646838784218,
-0.05541858449578285,
-0.007347500417381525,
-0.00406112102791667,
0.04156956076622009,
-0.041220773011446,
0.0018209367990493774,
0.06166350841522217,
-0.0032538948580622673,
-0.06695304811000824,
0.03582531213760376,
-0.015702024102211,
-0.027550790458917618,
0.0134782949462533,
-0.008266860619187355,
0.028236914426088333,
-0.07165571302175522,
0.006606068927794695,
-0.023575356230139732,
-0.04719706252217293,
-0.03619726747274399,
-0.03691406175494194,
-0.021670786663889885,
0.01592625118792057,
0.0053904736414551735,
0.03811025246977806,
-0.025455452501773834,
-0.04246680438518524,
0.0528518371284008,
-0.006471825297921896,
-0.004987169522792101,
0.023890424519777298,
-0.033595651388168335,
-0.0585002526640892,
-0.024994567036628723,
0.006334185134619474,
0.05820530280470848,
-0.025429176166653633,
-0.003898477414622903,
0.0368901826441288,
0.03916168957948685,
0.04963381215929985,
0.018871258944272995,
0.005794317461550236,
-0.009612875059247017,
0.02870572730898857,
-0.02024761773645878,
0.010293817147612572,
-0.002765373094007373,
0.004542618989944458,
0.014074066653847694,
0.02089145965874195,
0.033229708671569824,
0.046032778918743134,
0.019646070897579193,
0.057466328144073486,
-0.007566163316369057,
0.011848541907966137,
-0.03125254809856415,
0.05403073877096176,
0.03678104281425476,
-0.005579834338277578,
-0.035022906959056854,
0.04287552833557129,
0.09591780602931976,
-0.0361512117087841,
-0.010936060920357704,
0.01176908053457737,
0.043901875615119934,
-0.035587165504693985,
-0.04350418597459793,
-0.007038172334432602,
0.007352948654443026,
0.03769383952021599,
-0.017668476328253746,
-0.02689242549240589,
0.05838610604405403,
-0.0026692443061619997,
0.00958868209272623,
0.012877042405307293,
-0.013340889476239681,
-0.021718159317970276,
-0.05156327784061432,
-0.0008627655915915966,
0.0023673162795603275,
0.013063782826066017,
0.01674105040729046,
0.07540977746248245,
0.012428895570337772,
-0.0017197225242853165,
-0.005072006024420261,
0.006709609180688858,
-0.08959348499774933,
0.02976406365633011,
-0.019672522321343422,
-0.0069469730369746685,
0.0005029893945902586,
0.009947488084435463,
0.0061918217688798904,
0.0030553932301700115,
-0.006240513641387224,
-0.020517172291874886,
-0.04221387207508087,
-0.04955943673849106,
0.019621824845671654,
-0.012972837314009666,
-0.010393435135483742,
-0.01224428229033947,
0.012812571600079536,
0.022427955642342567,
-0.028495775535702705,
0.004684832412749529,
0.03253651037812233,
-0.023613963276147842,
0.010291495360434055,
0.006774810142815113,
-0.014451941475272179,
0.00611934345215559,
0.02109442465007305,
0.008090557530522346,
0.005842655431479216,
-0.0013247611932456493,
-0.009555544704198837,
-0.01913020946085453,
0.05764472857117653,
0.025797756388783455,
-0.013298861682415009,
-0.027925794944167137,
-0.07246958464384079,
-0.018019182607531548,
-0.012793171219527721,
0.06860143691301346,
-0.04328213632106781,
0.0011028771987184882,
-0.009766029193997383,
-0.0004977800417691469,
0.012025374919176102,
0.05280230566859245,
0.03903970122337341,
0.014715914614498615,
-0.022591421380639076,
-0.05248124897480011,
-0.010129393078386784,
-0.02898750826716423,
0.0023563301656395197,
0.007798637729138136,
-0.01827504299581051,
-0.03766248747706413,
-0.02470606192946434,
-0.013214047066867352,
0.021982664242386818,
-0.008207847364246845,
0.02409750036895275,
0.01872951164841652,
-0.014389216899871826,
-0.03110961988568306,
-0.009638221003115177,
0.0021676893811672926,
0.0036932588554918766,
0.03304343298077583,
-0.022760558873414993,
-0.03529708459973335,
-0.064815454185009,
0.0012243420351296663,
0.03477109968662262,
0.008689472451806068,
-0.017868446186184883,
-0.002331908093765378,
-0.040370553731918335,
-0.024826614186167717,
0.018642321228981018,
-0.04523768648505211,
0.02624666504561901,
-0.027865465730428696,
-0.002274100435897708,
-0.043700091540813446,
-0.005133139900863171,
-0.04193465784192085,
0.06237407401204109,
0.011350883170962334,
0.031238963827490807,
-0.0009735409985296428,
-0.019356604665517807,
0.006774331908673048,
0.009697449393570423,
0.06216393783688545,
0.07621955126523972,
-0.000015020855244074482,
0.018530618399381638,
-0.016657810658216476,
0.013608786277472973,
-0.03979092091321945,
-0.08952012658119202,
0.010956616140902042,
-0.0294396560639143,
-0.03363996371626854,
0.044064268469810486,
-0.022355126217007637,
-0.05391649901866913,
0.016552118584513664,
-0.0028974979650229216,
0.03577306121587753,
-0.016529986634850502,
-0.013897820375859737,
0.043987665325403214,
0.03500846028327942,
-0.005684240255504847,
0.04043228179216385,
0.004884321242570877,
-0.04070623219013214,
0.0015584592474624515,
0.016052566468715668,
0.06261616200208664,
0.009512283839285374,
0.013592642731964588,
-0.00409843772649765,
0.014613887295126915,
-0.06042089685797691,
0.056144606322050095,
-0.047998033463954926,
0.02525114268064499,
-0.02771979197859764,
-0.018536277115345,
-0.0161818228662014,
0.013689540326595306,
0.012111140415072441,
-0.014727383852005005,
-0.03821422904729843,
-0.001097507425583899,
-0.011685600504279137,
-0.023780493065714836,
0.034623127430677414,
-0.008796101436018944,
0.02500905469059944,
0.013580617494881153,
0.0033377804793417454,
0.0027886738535016775,
-0.03704633563756943,
0.008566870354115963,
0.003873073495924473,
-0.04105577990412712,
0.019907085224986076,
-0.02667265199124813,
-0.016382141038775444,
0.012613791972398758,
-0.03777465969324112,
-0.06648927181959152,
0.06350076198577881,
-0.027341203764081,
0.011045827530324459,
-0.08079306781291962,
0.029654795303940773,
0.033834122121334076,
-0.002102100756019354,
-0.022719208151102066,
-0.09836779534816742,
0.043757062405347824,
0.02980889566242695,
0.0454496406018734,
-0.0014341850765049458,
-0.030370932072401047,
-0.018606876954436302,
-0.02494799718260765,
-0.006010943558067083,
0.032403986901044846,
-0.03201742842793465,
0.00010173871123697609,
-0.006007195916026831,
-0.0045351022854447365,
0.052580807358026505,
0.027262192219495773,
-0.012210942804813385,
0.005101930350065231,
-0.0577293336391449,
-0.06114978715777397,
-0.036124423146247864,
0.031481143087148666,
-0.04794159531593323,
-0.03037375397980213,
-0.005750140640884638,
-0.02793203480541706,
0.03217301145195961,
-0.026630263775587082,
-0.015015914104878902,
0.03719149902462959,
0.023738784715533257,
0.0020279046148061752,
-0.004479534924030304,
0.028078414499759674,
0.024843797087669373,
0.0026673965621739626,
0.025474581867456436,
-0.04264512658119202,
-0.0353117398917675,
-0.04205384850502014,
-0.02926361747086048,
0.03899991884827614,
-0.015472883358597755,
-0.0039026495069265366,
0.052978646010160446,
-0.031075749546289444,
-0.0011549745686352253,
0.014951608143746853,
-0.012305617332458496,
0.0039268797263503075,
-0.018194744363427162,
-0.019157730042934418,
0.00671503646299243,
-0.009765143506228924,
-0.03955982252955437,
0.0032439802307635546,
-0.025300050154328346,
-0.02719905413687229,
0.05576426908373833,
0.006478909403085709,
0.052500441670417786,
0.008450472727417946,
-0.01371279638260603,
-0.006708456669002771,
0.014628872275352478,
-0.013544156216084957,
-0.008503288961946964,
-0.00757861090824008,
0.01666584424674511,
-0.006707449443638325,
0.0011929647298529744,
0.045003946870565414,
0.04707946255803108,
0.0030511198565363884,
-0.008993237279355526,
0.04618559777736664,
0.03494634851813316,
0.05095786601305008,
-0.013983407989144325,
-0.03371869772672653,
0.040935955941677094,
-0.062135662883520126,
0.003905161749571562,
0.015538699924945831,
-0.016636038199067116,
0.03573259338736534,
0.026092620566487312,
-0.04106192663311958,
-0.021832861006259918,
-0.026740513741970062,
-0.04092831164598465,
-0.009261728264391422,
-0.03192056715488434,
0.02255905419588089,
-0.0009855312528088689,
0.01176551915705204,
0.03963477537035942,
0.011382190510630608,
0.030066434293985367,
-0.010106461122632027,
-0.05264200270175934,
-0.04220552369952202,
-0.025452537462115288,
-0.02354556694626808,
0.0483146533370018,
0.00767049053683877,
-0.0030104760080575943,
0.016453061252832413,
-0.01812177151441574,
0.051007989794015884,
0.02866855449974537,
0.05189254879951477,
-0.025521283969283104,
0.0874202698469162,
-0.012170146219432354,
0.013509413227438927,
-0.032655782997608185,
0.007095754612237215,
0.1250169575214386,
0.025638161227107048,
-0.006682734005153179,
-0.08363567292690277,
0.036180898547172546,
-0.02992759272456169,
0.01871510036289692,
-0.03193465620279312,
-0.022301796823740005,
-0.02607257105410099,
-0.004595113918185234,
0.029327666386961937,
0.032263800501823425,
0.02513853833079338,
0.033945854753255844,
0.04665413498878479,
-0.012891795486211777,
-0.011052782647311687,
-0.016136059537529945,
0.02832985296845436,
-0.009895313531160355,
0.03105473890900612,
-0.0339069589972496,
0.02707025222480297,
-0.07398288697004318,
0.018425574526190758,
-0.01767790876328945,
-0.02623182162642479,
0.07410548627376556,
0.03627559170126915,
-0.03271826356649399,
0.014129086397588253,
0.02811732329428196,
-0.009467261843383312,
-0.03706331551074982,
0.050085943192243576,
0.01768849976360798,
0.04412797838449478,
0.003383111208677292,
0.013613687828183174,
0.020000005140900612,
0.012566335499286652,
0.0077501446940004826,
0.008092112839221954,
-0.05598893389105797,
0.02589140273630619,
-0.028874382376670837,
0.04148346930742264,
0.00901114009320736,
-0.030000347644090652,
-0.019274789839982986,
0.007056602742522955,
0.0057570249773561954,
-0.04035364091396332,
-0.04349946603178978,
0.012238123454153538,
0.007768584415316582,
0.002317215548828244,
0.014828642830252647,
-0.05773042142391205,
0.029601041227579117,
0.015322394669055939,
0.0036099767312407494,
-0.013989956118166447,
-0.03041556477546692,
0.023595687001943588,
0.011264065280556679,
0.01802236959338188,
0.013258440420031548,
-0.034064292907714844,
-0.005039336159825325,
-0.0182941947132349,
-0.031240390613675117,
-0.030477574095129967,
-0.003571516601368785,
0.05545102804899216,
0.02783917635679245,
-0.022306038066744804,
-0.030680246651172638,
-0.02006738819181919,
-0.04000622406601906,
0.06451727449893951,
0.04739172384142876,
0.0032575277145951986,
-0.01609780266880989,
-0.013725860975682735,
0.02286483906209469,
0.05098084360361099,
-0.027406075969338417,
0.010325619019567966,
-0.012070049531757832,
0.04660410061478615,
0.022319570183753967,
-0.033912863582372665,
-0.004293488804250956,
0.03328011929988861,
-0.06354822963476181,
0.00411075446754694,
-0.016059210523962975,
0.020377013832330704,
0.007609996944665909,
-0.0012181630590930581,
-0.000048021476686699316,
-0.003956437576562166,
-0.05623916536569595,
-0.0179813914000988,
0.0428975448012352,
0.00575110362842679,
-0.019288640469312668,
0.012422110885381699,
0.022963598370552063,
-0.0023081975523382425,
-0.02871379815042019,
-0.01709659770131111,
0.01836087927222252,
-0.005037906114012003,
0.02372429333627224,
-0.026924092322587967,
0.014077572152018547,
-0.02868441864848137,
0.04403889551758766,
-0.00412512244656682,
-0.041884779930114746,
-0.07487675547599792,
0.002765132812783122,
0.006155514158308506,
-0.0047875684686005116,
0.029990360140800476,
0.02200751006603241,
-0.02553938888013363,
0.023441914469003677,
0.021104948595166206,
0.022772997617721558,
-0.0038529576268047094,
0.0024854314979165792,
0.019318612292408943,
0.002797685330733657,
-0.0021971333771944046,
-0.03234953060746193,
-0.05964541435241699,
0.07548113167285919,
-0.031215602532029152,
-0.04454762861132622,
0.007660066708922386,
-0.016465196385979652,
0.056551046669483185,
0.0342465378344059,
-0.03474421426653862,
0.0036870604380965233,
0.06576164066791534,
-0.02956545725464821,
-0.015795521438121796,
0.0062799397855997086,
-0.004463196732103825,
-0.016904808580875397,
0.034462638199329376,
0.006584072019904852,
-0.027439847588539124,
-0.01839059218764305,
0.016006262972950935,
0.025103820487856865,
0.003245161846280098,
-0.019297540187835693,
0.020326973870396614,
0.017066307365894318,
0.002910712268203497,
0.027193281799554825,
-0.003469906747341156,
0.024953940883278847,
0.04334916174411774,
-0.0030418045353144407,
0.007936437614262104,
-0.009609567001461983,
-0.001220790552906692,
-0.06453746557235718,
-0.030363909900188446,
-0.022203190252184868,
-0.01722593791782856,
0.05726383626461029,
-0.010191273875534534,
-0.005891827866435051,
0.03204743564128876,
-0.058000754565000534,
-0.006328774616122246,
-0.002753844251856208,
-0.056948330253362656,
-0.00868933368474245,
0.00458500673994422,
-0.009108338505029678,
0.025359345600008965,
0.030679045245051384,
0.05028296634554863,
0.01797613687813282,
-0.009588806889951229,
0.013047797605395317,
-0.030343255028128624,
0.018547946587204933,
0.047841090708971024,
0.003570521716028452,
0.02231449820101261,
0.03807835653424263,
-0.04736658185720444,
0.0020303817000240088,
0.03237151354551315,
-0.02898479253053665,
-0.03291005641222,
-0.010840984992682934,
0.0379742830991745,
0.01472222339361906,
0.043862465769052505,
-0.002882034983485937,
-0.027700362727046013,
-0.03653145208954811,
0.00144970475230366,
0.04384917393326759,
0.009561107493937016,
0.006596277933567762,
0.019459787756204605,
0.0350458063185215,
-0.021333839744329453,
-0.012664936482906342,
0.014614732936024666,
-0.03127410262823105,
-0.01056672353297472,
0.014027435332536697,
0.025096280500292778,
0.028192441910505295,
-0.034505631774663925,
-0.013249751180410385,
-0.0013848210219293833,
0.004010781180113554,
0.020081939175724983,
-0.01031741127371788,
0.050486717373132706,
-0.0008119334233924747,
-0.015722844749689102,
-0.006764561869204044,
0.030294539406895638,
0.04042096808552742,
-0.007991607300937176,
-0.05343541130423546,
-0.02576507069170475,
0.021027766168117523,
0.014487603679299355,
0.026226680725812912,
-0.08472228795289993,
0.004168561659753323,
0.029117081314325333,
0.03370765224099159,
0.015144062228500843,
0.024020781740546227,
-0.057603854686021805,
-0.019130518659949303,
-0.059442151337862015,
0.051325492560863495,
-0.00844526942819357,
0.0008054716163314879,
-0.03454762324690819,
-0.03713523969054222,
-0.009833957068622112,
-0.0053279465064406395,
0.051469750702381134,
-0.017189163714647293,
-0.01649932935833931,
0.010577664710581303,
-0.018839634954929352,
0.028216097503900528,
-0.07342571765184402,
-0.022787977010011673,
0.04293489083647728,
-0.007744838483631611,
0.0047736577689647675,
-0.006390320602804422,
-0.00728396512567997,
-0.003865825943648815,
0.025971047580242157,
0.017819343134760857,
0.0021539132576435804,
-0.015774985775351524,
-0.01856953464448452,
0.048924192786216736,
0.032151997089385986,
-0.014252500608563423,
0.07149408012628555,
-0.0020583167206496,
0.017645632848143578,
-0.00983765535056591,
-0.04812566936016083,
-0.02187739685177803,
0.005149048753082752,
-0.0110324090346694,
0.017348680645227432,
-0.04604063555598259,
-0.00177553400862962,
0.0008847787394188344,
-0.027776317670941353,
-0.028190046548843384,
-0.007409852463752031,
-0.031089473515748978,
-0.011918400414288044,
0.0481354184448719,
-0.02012782357633114,
0.018070681020617485,
-0.01114595215767622,
0.015054607763886452,
0.014587358571588993,
0.004680052865296602,
-0.0032941573299467564,
0.00390775827690959,
-0.003957398235797882,
-0.013775370083749294,
-0.006038156803697348,
0.028656383976340294,
0.005936764646321535,
0.026553714647889137,
0.008038712665438652,
0.04664172604680061,
-0.009730575606226921,
-0.05621730163693428,
0.004713099449872971,
-0.028232185170054436,
0.02202414907515049,
-0.0037564383819699287,
0.004513496067374945,
0.06584332138299942,
-0.04087822139263153,
0.0007839136524125934,
0.008106468245387077,
0.026916567236185074,
0.020532654598355293,
-0.0192971620708704,
0.004958074074238539,
0.025763822719454765,
-0.011403701268136501,
-0.024873841553926468,
-0.03072270005941391,
-0.007076380308717489,
0.03450310230255127,
-0.058519069105386734,
0.03691764548420906,
0.011718517169356346,
0.017815962433815002,
-0.019034959375858307,
-0.03264620900154114,
-0.03412645682692528,
-0.055070895701646805,
0.03531317412853241,
0.019708052277565002,
0.018229078501462936,
-0.01693403534591198,
0.0157629307359457,
0.010757013224065304,
0.03963702544569969,
-0.0781165137887001,
-0.01719198189675808,
-0.008489423431456089,
0.05559977889060974,
0.021918676793575287,
0.02305418998003006
] |
<p>This question is a follow-up to <a href="http://physics.stackexchange.com/users/2190/david-bar-moshe">David Bar Moshe</a>'s answer to my earlier question on the <a href="http://physics.stackexchange.com/questions/34990/aharonov-bohm-effect-and-flux-quantization-in-superconductors">Aharonov-Bohm effect and flux-quantization</a>. What I forgot was that it is not the <em>wavefunction</em> that must be single-valued, but rather, the <em>probability density</em> (wavefunction-squared).</p>
<p>But if that is so, how do I justify the quantization condition $m=\{\ldots,-1,0,1\ldots\}$ based on the boundary condition on the azimuthal part of spherically symmetric wavefunctions $\psi(x,y,z)\sim R(r)\Theta(\theta)\Phi(\phi)$:</p>
<p>$$\Phi(\phi)\sim e^{im\phi}$$</p>
<p>whose square (probability density) is unity, independent of $m$?</p> | 4,578 | [
-0.014593576081097126,
-0.01895984821021557,
0.013415534049272537,
-0.05773008242249489,
0.02856113761663437,
-0.004939556587487459,
-0.05833926051855087,
-0.025986939668655396,
0.014393526129424572,
-0.02646675705909729,
0.06101640313863754,
0.009433910250663757,
0.10701600462198257,
0.06929256021976471,
-0.014617469161748886,
0.0036455898080021143,
-0.020073993131518364,
-0.023565828800201416,
-0.029120318591594696,
-0.019105102866888046,
-0.005740229971706867,
0.058445509523153305,
0.02985503152012825,
-0.014824405312538147,
-0.035467278212308884,
0.019161883741617203,
-0.01973375305533409,
0.01284654252231121,
0.02225813828408718,
0.07185797393321991,
-0.03238629922270775,
-0.02037617936730385,
0.03744759038090706,
-0.0010930098360404372,
-0.02098969928920269,
-0.016254587098956108,
-0.013898147270083427,
0.004981655161827803,
-0.029206112027168274,
0.01420457661151886,
-0.033782582730054855,
-0.015214407816529274,
-0.013339458033442497,
0.04174092039465904,
-0.037635721266269684,
-0.014197813346982002,
-0.013481995090842247,
-0.020401276648044586,
0.07175333797931671,
-0.05835411697626114,
0.05053560435771942,
-0.014080413617193699,
0.03479921445250511,
0.03636917844414711,
0.010353479534387589,
-0.0151875214651227,
0.06096397712826729,
0.0669059082865715,
0.0306539386510849,
-0.03253478184342384,
-0.03004688397049904,
-0.017654284834861755,
0.0021519367583096027,
-0.004855152685195208,
-0.014613102190196514,
0.007276206277310848,
0.023323915898799896,
-0.04391489550471306,
-0.0049318186938762665,
-0.005671198945492506,
-0.0002926505694631487,
0.037101566791534424,
-0.007886412553489208,
-0.03685132786631584,
0.026737716048955917,
-0.008862501010298729,
0.007516541052609682,
0.015397288836538792,
0.005224612541496754,
0.025656405836343765,
-0.011425510048866272,
-0.003707106690853834,
0.02474082075059414,
-0.0001288415223825723,
0.02261660248041153,
-0.018885819241404533,
0.05824298784136772,
0.003143847221508622,
-0.007623081561177969,
0.006985911633819342,
-0.0020768202375620604,
0.014606944285333157,
0.024719087406992912,
0.001163524342700839,
-0.0845070630311966,
-0.003015166614204645,
0.0005433110636658967,
0.050202831625938416,
-0.008544513955712318,
-0.037378259003162384,
-0.03266514465212822,
-0.045555148273706436,
0.03517249971628189,
0.08585404604673386,
-0.03602718561887741,
0.0252399779856205,
-0.016819600015878677,
0.007855094969272614,
-0.03760160505771637,
-0.04413820803165436,
-0.058740075677633286,
0.018477991223335266,
-0.013465751893818378,
0.002639303682371974,
0.00048627660726197064,
-0.009367372840642929,
-0.021264955401420593,
0.007784501649439335,
0.04679258167743683,
0.07639557123184204,
0.048560455441474915,
0.003487104782834649,
0.012260042130947113,
-0.00503523601219058,
-0.06448807567358017,
0.026667920872569084,
0.009366093203425407,
-0.03179839253425598,
-0.023633217439055443,
0.025111455470323563,
0.008635156787931919,
0.0106743723154068,
0.028012970462441444,
-0.02973940223455429,
0.027982575818896294,
0.0014875589404255152,
-0.08786515891551971,
-0.0725209042429924,
0.024561459198594093,
-0.02240513265132904,
-0.02051195502281189,
-0.02744373492896557,
-0.0031343477312475443,
0.015647849068045616,
0.10657794773578644,
-0.016886329278349876,
0.013429594226181507,
-0.013593408279120922,
0.07905293256044388,
0.017767054960131645,
-0.03420085087418556,
-0.02324320562183857,
-0.015393903478980064,
-0.04060477763414383,
-0.015149248763918877,
-0.03464166820049286,
0.061644572764635086,
0.027310922741889954,
0.02456127107143402,
-0.007916265167295933,
0.09761396795511246,
0.00728288758546114,
0.031781431287527084,
-0.03329110145568848,
-0.027706261724233627,
-0.03542202711105347,
0.06742621213197708,
-0.011184358038008213,
0.039581507444381714,
0.03389359638094902,
-0.01101045124232769,
-0.03622274100780487,
0.004433192778378725,
0.03959851339459419,
0.0070324367843568325,
-0.0467047356069088,
-0.009612511843442917,
-0.0516834557056427,
0.020894795656204224,
-0.007006107363849878,
-0.020093517377972603,
0.009797920472919941,
-0.022079316899180412,
-0.00897887721657753,
0.009827854111790657,
0.04484529420733452,
0.018368566408753395,
-0.04283832386136055,
-0.03668290376663208,
-0.03585164621472359,
-0.019497210159897804,
-0.03138701617717743,
0.0182633176445961,
0.017016800120472908,
-0.05131962150335312,
0.013675019145011902,
-0.006129964720457792,
-0.006589655764400959,
-0.006379800848662853,
-0.026391129940748215,
0.003555295756086707,
0.023860272020101547,
0.010242775082588196,
-0.0035255318507552147,
0.01414560992270708,
0.012076573446393013,
0.04159977287054062,
0.0035018473863601685,
0.02391878142952919,
-0.012200881727039814,
-0.011382641270756721,
-0.02971421554684639,
0.021682830527424812,
0.04966871440410614,
0.022643420845270157,
-0.000939417106565088,
-0.00024743317044340074,
0.02092178910970688,
-0.0108340410515666,
0.020077276974916458,
-0.03706604242324829,
0.022852381691336632,
0.016317086294293404,
0.010324440896511078,
0.02351747825741768,
0.055679164826869965,
0.010852361097931862,
-0.008260282687842846,
0.0009689090074971318,
-0.040024932473897934,
-0.03000519797205925,
0.04124698042869568,
0.030859636142849922,
0.0036657466553151608,
-0.04101011902093887,
0.024163370952010155,
-0.0032179600093513727,
0.02388503961265087,
0.03452567756175995,
-0.002866229973733425,
-0.03257343918085098,
-0.050001244992017746,
0.02471073344349861,
0.01775345765054226,
0.004244206938892603,
-0.005558833479881287,
0.026198484003543854,
0.012993776239454746,
0.03534500673413277,
-0.01858697645366192,
-0.021315230056643486,
-0.006413960829377174,
-0.03949498012661934,
-0.013645927421748638,
-0.02161352150142193,
-0.013335093855857849,
0.01335668284446001,
-0.022038165479898453,
0.006284418050199747,
0.031482256948947906,
0.0040032947435975075,
0.01530431117862463,
-0.018317051231861115,
-0.019763873890042305,
0.04216217249631882,
-0.0059627690352499485,
-0.012992922216653824,
-0.01606525108218193,
0.034757256507873535,
-0.0221414677798748,
-0.014392003417015076,
0.0070396969094872475,
-0.02781374379992485,
0.035574477165937424,
0.010473102331161499,
0.012439360842108727,
0.0243822131305933,
0.054233454167842865,
-0.033611368387937546,
-0.0076859514228999615,
0.017679031938314438,
-0.00005389232319430448,
0.017395103350281715,
0.039739709347486496,
-0.0448296032845974,
0.010356790386140347,
-0.046266745775938034,
-0.007264690939337015,
0.033371493220329285,
0.027805525809526443,
-0.03131556883454323,
-0.010346151888370514,
0.03272758424282074,
-0.049099527299404144,
-0.007615323178470135,
-0.03539533540606499,
0.013283507898449898,
-0.06186935678124428,
-0.013111048378050327,
0.03716863691806793,
-0.023055901750922203,
-0.019719267264008522,
0.005106129217892885,
-0.03995027020573616,
-0.029364027082920074,
-0.0007061107316985726,
0.01835055649280548,
0.04086243361234665,
-0.02902759611606598,
0.04378470778465271,
0.0385177843272686,
-0.03187105804681778,
-0.021731216460466385,
-0.027791526168584824,
-0.03885602205991745,
0.003955567255616188,
-0.0336780920624733,
0.027262259274721146,
0.006784182973206043,
-0.04195407032966614,
0.08274636417627335,
0.0161051657050848,
-0.015760866925120354,
-0.001493370276875794,
0.004244654905050993,
-0.02184681035578251,
-0.05960159748792648,
0.007504407316446304,
0.07573512196540833,
-0.02984541282057762,
0.04776926711201668,
0.011490857228636742,
0.030876444652676582,
-0.004146096762269735,
0.01078580692410469,
-0.0067391712218523026,
0.03382362052798271,
0.0027770870365202427,
-0.002281452063471079,
0.0701778307557106,
-0.005058572627604008,
0.0044134194031357765,
0.012152189388871193,
-0.02313101664185524,
-0.001823763712309301,
0.0548354871571064,
-0.039571695029735565,
0.05609893053770065,
-0.02360137738287449,
0.045567166060209274,
-0.012884779833257198,
0.04250165447592735,
0.02093491330742836,
-0.022446462884545326,
-0.01039230264723301,
-0.005612582433968782,
0.028802813962101936,
-0.02949579991400242,
-0.012635372579097748,
0.028978964313864708,
0.02028800919651985,
-0.020660122856497765,
-0.02854751981794834,
-0.03248421847820282,
0.008386613801121712,
0.0722666084766388,
-0.03790130093693733,
-0.03588348627090454,
-0.012043497525155544,
0.041264649480581284,
0.004279979970306158,
-0.0439927875995636,
-0.0094874557107687,
-0.013543948531150818,
-0.046782881021499634,
0.002801638562232256,
-0.055595774203538895,
0.03933519124984741,
0.02384651079773903,
0.03889273852109909,
0.026763183996081352,
-0.01730976812541485,
0.0023583481088280678,
0.024288900196552277,
-0.09078744053840637,
-0.011132066138088703,
0.009798798710107803,
-0.010745635256171227,
-0.01769031397998333,
-0.004972067661583424,
0.040439117699861526,
-0.0052127414382994175,
-0.008483937941491604,
-0.006897564046084881,
-0.016914358362555504,
-0.055374208837747574,
0.01424587145447731,
-0.028091812506318092,
-0.04218783974647522,
-0.015839720144867897,
0.05864566192030907,
-0.004823310766369104,
-0.03789600729942322,
-0.0037834662944078445,
0.018253298476338387,
-0.07218648493289948,
0.015568374656140804,
-0.008924887515604496,
0.04862597957253456,
-0.0057169245555996895,
0.016320789232850075,
0.0037851124070584774,
-0.006638206075876951,
-0.015371034853160381,
0.010012935847043991,
0.014151258394122124,
0.06528173387050629,
0.015923943370580673,
-0.00624763173982501,
-0.029279906302690506,
-0.022819451987743378,
-0.02102418802678585,
0.013709573075175285,
0.06291874498128891,
0.009191359393298626,
-0.022014649584889412,
0.0441419780254364,
0.0017301859334111214,
0.019315462559461594,
0.00876691471785307,
0.07135710120201111,
-0.01292501762509346,
0.007553195580840111,
-0.043487802147865295,
0.009616195224225521,
-0.0010423687053844333,
-0.005526273977011442,
-0.009392347186803818,
0.009558171033859253,
-0.03190116956830025,
-0.02685883454978466,
0.007974699139595032,
0.03148937597870827,
0.0299969669431448,
-0.018976332619786263,
0.009010683745145798,
0.036789100617170334,
-0.0030900989659130573,
0.019461914896965027,
0.017690882086753845,
0.03121824935078621,
0.05308745801448822,
-0.010968605987727642,
-0.020380191504955292,
-0.03339037671685219,
-0.019212201237678528,
0.02613123506307602,
0.013645488768815994,
0.028691299259662628,
0.027440208941698074,
-0.07369664311408997,
-0.014340471476316452,
0.0526251420378685,
0.0039022404234856367,
0.029723891988396645,
0.004664198495447636,
-0.019823642447590828,
-0.017720313742756844,
-0.01833566464483738,
-0.027463926002383232,
0.02629796229302883,
0.016267746686935425,
0.04014886915683746,
-0.02984529174864292,
-0.012790583074092865,
-0.04929294437170029,
-0.007300263270735741,
0.012242014519870281,
0.06706457585096359,
0.004440071992576122,
-0.019139735028147697,
-0.02974870055913925,
0.021140428259968758,
-0.01593884639441967,
-0.08924663811922073,
0.01955815777182579,
-0.024325143545866013,
0.012671547941863537,
0.016891710460186005,
-0.030764399096369743,
-0.04125488921999931,
0.03501676023006439,
-0.007348373997956514,
-0.018484774976968765,
0.06733842194080353,
0.004541001748293638,
0.07223721593618393,
0.01837075501680374,
0.01865444891154766,
0.025861941277980804,
0.02666507661342621,
-0.004031082149595022,
-0.013984950259327888,
-0.022114697843790054,
0.014449591748416424,
-0.02195335365831852,
0.014012569561600685,
-0.02966955117881298,
0.006420907098799944,
-0.07210193574428558,
0.035194944590330124,
-0.05980978533625603,
-0.02434665709733963,
-0.030024763196706772,
-0.02012498863041401,
0.01270938292145729,
-0.003569411113858223,
-0.044568952172994614,
-0.011362281627953053,
-0.003808782435953617,
0.0005774458404630423,
-0.0073041049763560295,
-0.002319520805031061,
-0.0013113270979374647,
0.0009610657580196857,
0.01633709855377674,
0.028229260817170143,
-0.025365209206938744,
0.02769686095416546,
-0.0276720579713583,
-0.009283756837248802,
0.008474491536617279,
-0.06183621659874916,
0.04195811599493027,
-0.004990357905626297,
-0.001879624673165381,
-0.007901212200522423,
-0.018493061885237694,
-0.005254783201962709,
0.027463587000966072,
-0.005803094711154699,
0.01470528170466423,
-0.02927137166261673,
-0.015351933427155018,
0.016462404280900955,
0.01656886376440525,
-0.07406973838806152,
-0.03674325346946716,
0.0022655613720417023,
0.028670458123087883,
0.008662564679980278,
-0.016749132424592972,
0.013241628184914589,
-0.04350929334759712,
-0.018794072791934013,
-0.014618724584579468,
0.020826105028390884,
-0.03131689131259918,
-0.024167750030755997,
0.007729204837232828,
0.054937366396188736,
0.03514261916279793,
-0.007721702568233013,
0.0060576582327485085,
0.043525006622076035,
-0.0482342503964901,
0.019087500870227814,
-0.0010107510024681687,
0.033613722771406174,
-0.04881933331489563,
-0.03907338157296181,
-0.020722223445773125,
-0.030164439231157303,
0.0352347157895565,
0.016127659007906914,
-0.017881937325000763,
-0.0002145774196833372,
-0.010713344439864159,
-0.0014527100138366222,
0.006485578138381243,
0.0003950886311940849,
0.00977306254208088,
0.034140005707740784,
-0.007649201434105635,
-0.030488556250929832,
-0.056322045624256134,
0.008903616108000278,
0.01574440859258175,
0.0011901555117219687,
0.0014794804155826569,
-0.0011313894065096974,
0.10271961987018585,
0.0303104966878891,
-0.01735120266675949,
0.01630929671227932,
0.028912866488099098,
-0.0026484604459255934,
0.002829630160704255,
-0.00949444156140089,
0.03185349702835083,
0.009528770111501217,
-0.024231936782598495,
-0.025486376136541367,
-0.03265099599957466,
-0.008192694745957851,
0.04069264605641365,
-0.015402935445308685,
0.046247441321611404,
-0.0025361550506204367,
-0.014961893670260906,
-0.02121201530098915,
-0.027363916859030724,
0.0042943283915519714,
-0.009287877939641476,
0.012892388738691807,
0.017532816156744957,
-0.04425233229994774,
0.004198377951979637,
0.027899371460080147,
0.017313893884420395,
-0.020095117390155792,
0.008431755006313324,
0.04091523587703705,
0.040047913789749146,
0.09137535840272903,
-0.015848543494939804,
-0.01883883588016033,
0.056912925094366074,
-0.05747540295124054,
0.018743038177490234,
-0.018310721963644028,
0.02042173407971859,
0.04190334305167198,
0.0419791080057621,
0.020802445709705353,
-0.03342680633068085,
0.0038748830556869507,
-0.03280754014849663,
-0.009892767295241356,
0.0291468296200037,
-0.0025481090415269136,
-0.008442400023341179,
-0.014731067232787609,
0.0046845050528645515,
0.013036338612437248,
-0.02736552432179451,
-0.007509368937462568,
-0.08284885436296463,
0.014178481884300709,
-0.023046700283885002,
-0.06745779514312744,
0.03398226201534271,
0.0016085164388641715,
-0.03031272254884243,
0.023167874664068222,
-0.019167805090546608,
0.0450747013092041,
0.014860005117952824,
-0.02019285410642624,
-0.008704382926225662,
0.04841792583465576,
0.0005232185940258205,
0.04132207855582237,
-0.01817801594734192,
0.0009506955975666642,
0.13149073719978333,
0.0655922070145607,
0.05403803661465645,
-0.05126142129302025,
0.02824953757226467,
-0.01580970361828804,
0.0093668969348073,
-0.05626078322529793,
-0.004990853369235992,
-0.004343085456639528,
0.007983656600117683,
0.00012794803478755057,
0.07838450372219086,
0.017845667898654938,
0.007234854623675346,
0.012672847136855125,
-0.057679351419210434,
-0.022901156917214394,
-0.03548244759440422,
0.04244618117809296,
-0.0017565065063536167,
0.008894325233995914,
-0.026567772030830383,
-0.011645222082734108,
-0.04812704026699066,
-0.01170353777706623,
-0.051261309534311295,
-0.03764794021844864,
0.030209770426154137,
0.014121277257800102,
-0.010879124514758587,
-0.002178381197154522,
0.0373338907957077,
0.02803349308669567,
-0.019907783716917038,
0.0023963870480656624,
0.03776903823018074,
-0.00042099953861907125,
0.03851430490612984,
0.03643864765763283,
-0.02370857633650303,
-0.01407257467508316,
0.036469969898462296,
-0.00007586227729916573,
-0.049188412725925446,
-0.009284214116632938,
-0.036674343049526215,
0.06713249534368515,
-0.02925143949687481,
-0.03737133368849754,
-0.02184576913714409,
-0.04040871560573578,
0.006943185348063707,
-0.02909114584326744,
-0.00988881103694439,
-0.0007057492621243,
0.034466952085494995,
-0.006729549262672663,
-0.002692132256925106,
0.000991574488580227,
0.03677390143275261,
0.03752085939049721,
-0.004954578820616007,
-0.0014256471768021584,
-0.02984529547393322,
-0.004988736007362604,
0.0385558195412159,
-0.0042437161318957806,
-0.01780073530972004,
-0.0019222889095544815,
-0.010251217521727085,
-0.0012067911447957158,
-0.05067221820354462,
0.0006860282155685127,
0.026807736605405807,
-0.02640327252447605,
0.03197846934199333,
-0.008473602123558521,
0.018529012799263,
0.00047809246461838484,
-0.0571582168340683,
-0.0218906719237566,
-0.001297929440625012,
0.007345613092184067,
0.00311314151622355,
-0.0017060352256521583,
-0.008723081089556217,
0.03143531456589699,
-0.02963900752365589,
-0.02286265790462494,
0.023134460672736168,
0.035844359546899796,
0.03529825806617737,
0.0028295363299548626,
-0.05169636383652687,
-0.001501348684541881,
-0.045128826051950455,
0.02224777452647686,
-0.0519256591796875,
-0.02944703958928585,
-0.03063265234231949,
0.04936916381120682,
0.006013025064021349,
0.05308494716882706,
0.006132061593234539,
-0.018944265320897102,
0.019316406920552254,
-0.07508435100317001,
-0.015086391940712929,
-0.0011338716140016913,
0.051749877631664276,
-0.011439509689807892,
-0.031805288046598434,
-0.009970574639737606,
-0.001983016263693571,
0.0063886577263474464,
0.01853243261575699,
-0.06132299080491066,
-0.03206690773367882,
-0.00018371877376921475,
0.010865886695683002,
0.006443492136895657,
0.002065155189484358,
0.0025011056568473577,
-0.007227823603898287,
0.029256805777549744,
0.02805948071181774,
0.02247815765440464,
0.002616723533719778,
-0.04871068894863129,
0.011108321137726307,
0.01813029870390892,
-0.034324824810028076,
-0.036629568785429,
0.028149215504527092,
0.01849658228456974,
0.0645749419927597,
0.03657832741737366,
-0.031029002740979195,
-0.0021671405993402004,
0.028374744579195976,
-0.03975003585219383,
-0.014030132442712784,
0.050786007195711136,
-0.02226058393716812,
0.05516144633293152,
0.047601208090782166,
-0.022906430065631866,
-0.026020102202892303,
0.03502688184380531,
-0.03140872344374657,
0.01957894116640091,
-0.0033121744636446238,
-0.011749882251024246,
0.01852533034980297,
-0.02182721346616745,
0.005818651523441076,
-0.009783731773495674,
0.024944059550762177,
0.022310271859169006,
0.06423881649971008,
0.010470107197761536,
-0.010680058971047401,
-0.015152658335864544,
0.025491861626505852,
-0.0008237271104007959,
0.014064328745007515,
0.030359862372279167,
0.020982030779123306,
0.03110405057668686,
-0.028896059840917587,
0.04264700040221214,
0.022570030763745308,
0.01121704000979662,
-0.08699333667755127,
-0.023482181131839752,
0.04011090472340584,
0.027255747467279434,
0.04138939827680588,
-0.04104151576757431,
0.02420108951628208,
0.008407989516854286,
-0.07109172642230988,
0.009849565103650093,
0.0050892592407763,
0.002272476442158222,
-0.044031623750925064,
-0.03657195717096329,
-0.0466897189617157,
0.05439386144280434,
0.01141583826392889,
0.041487812995910645,
0.025787685066461563,
0.03584066405892372,
-0.03757048025727272,
-0.03657769411802292,
-0.015591265633702278,
0.05218449980020523,
-0.0005464003188535571,
-0.02053755894303322,
0.06876762211322784,
-0.014119846746325493,
-0.028528448194265366,
0.016071606427431107,
-0.0090632950887084,
-0.001649637590162456,
0.02334844507277012,
0.05142664909362793,
0.008325846865773201,
0.027211522683501244,
-0.0064452216029167175,
0.009563007391989231,
-0.028516730293631554,
-0.022487150505185127,
0.039441291242837906,
0.019441181793808937,
-0.02348838932812214,
-0.020586660131812096,
0.020811084657907486,
-0.02471105568110943,
-0.041750792413949966,
0.029136599972844124,
-0.035550717264413834,
0.0013294582022354007,
0.022089319303631783,
-0.004440848249942064,
0.027670610696077347,
0.0009174052393063903,
0.0041933367028832436,
-0.040869586169719696,
-0.04336162656545639,
-0.00444889348000288,
0.020699787884950638,
0.011988435871899128,
-0.0026644247118383646,
-0.005251860711723566,
-0.06647258251905441,
0.017769617959856987,
0.014076357707381248,
-0.023911241441965103,
-0.04382738843560219,
-0.028032736852765083,
0.002452446846291423,
0.017465194687247276,
0.039307285100221634,
-0.044417086988687515,
-0.013682862743735313,
-0.0011302981292828918,
0.009686099365353584,
0.04313279315829277,
-0.04983215779066086,
-0.04266232252120972,
-0.018867127597332,
-0.08717641979455948,
0.03601357713341713,
0.0245383158326149,
-0.00635951105505228,
0.016261035576462746,
-0.03465019911527634,
0.016355277970433235,
-0.00281807454302907,
0.06420749425888062,
0.00978321023285389,
0.002890085568651557,
0.028404248878359795,
-0.03709061071276665,
0.025489604100584984,
-0.041048403829336166,
0.032469674944877625,
0.024703871458768845,
-0.009548641741275787,
0.019862854853272438,
-0.0019327059853821993,
0.02551119588315487,
0.007635017856955528,
0.03464056923985481,
0.01112541276961565,
-0.008595729246735573,
-0.014753724448382854,
-0.01520046591758728,
0.04304768145084381,
-0.008792450651526451,
-0.00115104834549129,
0.04591131955385208,
-0.024273594841361046,
0.022276030853390694,
0.002623857231810689,
-0.014109550975263119,
-0.026422608643770218,
0.014021648094058037,
-0.030267931520938873,
-0.04586994647979736,
-0.03541676327586174,
0.03191586583852768,
0.05470820888876915,
-0.052424732595682144,
-0.006467896047979593,
0.047824688255786896,
-0.02451929822564125,
-0.027876904234290123,
0.06979656964540482,
0.027224035933613777,
0.03543778508901596,
-0.008905792608857155,
-0.0396219864487648,
-0.011559820733964443,
-0.010875663720071316,
0.017253229394555092,
0.021886663511395454,
0.016655247658491135,
0.001231605070643127,
0.020447997376322746,
0.016952168196439743,
-0.0018873445224016905,
0.018681403249502182,
0.002403239719569683,
0.0018212345894426107,
-0.02592107094824314,
-0.015194320119917393,
0.023545080795884132,
-0.03671259433031082,
-0.006203284952789545,
-0.005575171671807766,
0.005546972155570984,
0.09016235917806625,
0.010728941299021244,
0.009118011221289635,
-0.03265386074781418,
0.014234802685678005,
-0.02075987495481968,
0.018770327791571617,
0.04039725288748741,
0.059053558856248856,
-0.016219308599829674,
-0.01651459001004696,
-0.03927203267812729,
-0.029178235679864883,
0.03436760604381561,
-0.07478606700897217,
-0.02204636111855507,
-0.011422869749367237,
-0.01876675710082054,
-0.0006621350767090917,
-0.013187795877456665,
-0.01425085961818695,
0.004803156945854425,
0.03147401288151741,
0.02493934892117977,
0.023196937516331673,
-0.0025313827209174633,
-0.0069943699054419994,
-0.03036455251276493,
0.07400741428136826,
-0.04367179423570633,
0.004614557139575481,
0.0032983743585646152,
0.04701372608542442,
-0.003237838391214609,
0.015616741962730885
] |
<p>I would like to point to the beautiful section 4.3 (page 42) of <a href="http://www.people.fas.harvard.edu/~xiyin/253b_Lectures.pdf">these lecture notes.</a> I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I love best about it is that it does it without using diagramatics (and its confusing combinatorics)(..though of course these are equivalent..but I find this language most comfortable..) </p>
<p>I have the following questions in relation to the above, </p>
<ul>
<li><p>In the above the author has picked out the terms quadratic in the fluctuations in equation 4.40 and evaluated the determinant and that gives the 1-loop effective action. </p>
<p>What would one do in this method if one had to go to 2-loops or higher?
What is the relationship between how many orders one keeps in the fluctuation field and how many loop result it translates into? (..if there a reference which shows going to higher loops in this method?..) </p></li>
<li><p>Can I use the method in these notes to evaluate the corrected gauge or the Fermion propagator? If someone could outline the steps.. </p>
<p>Here the author has chosen a constant and static background gauge (why?) and hence he has in 4.40 no term which is a derivative of the background gauge field left. I guess one would have to lift this restriction if one had to calculate the gauge field propagator correction. With this assumption about the background gauge field lifted I guess that one would have to then compute the $\Gamma^{1-loop}$ as defined in equation 4.41 and pick out the terms quadratic in the gauge field in it and invert that. </p></li>
<li><p>In the above the author has picked out from $\Gamma^{1-loop}$ only the terms quartic in the gauge field and and calculated the divergent contribution to it which is the shift in the gauge coupling constant. But the gauge coupling constant is also multiplying the term cubic in the gauge field and there is a 1-loop shift even there. What about that? Is there some theorem which guarantees that the beta-function derived by tacking the cubic term would have been the same? </p></li>
</ul>
<p>I guess that since even after choosing a constant and static gauge field one can track a change in the gauge coupling constant through a quartic term, it makes sense. But if one were in a theory (or in light-cone gauge!) where the gauge coupling constant were existing only in a term which has derivatives of the gauge field then I guess this choice of a background would not work. </p>
<p>I would like to know of a precise way of understanding the above. (...there is also the issue of whether the 1-loop effective action done this way can throw up terms that were removed by a gauge choice..and then what would one do..) </p> | 4,579 | [
0.006782369688153267,
0.013776816427707672,
0.05180001258850098,
0.0013645689468830824,
0.05161438137292862,
0.038927800953388214,
-0.031582947820425034,
-0.04219919815659523,
0.006865102332085371,
-0.08160953223705292,
0.026186814531683922,
0.0002878110099118203,
0.07303199917078018,
0.04405786469578743,
0.026566660031676292,
-0.002705199643969536,
0.022976063191890717,
-0.011929042637348175,
0.008609718643128872,
-0.02708645723760128,
-0.019908633083105087,
0.06086062639951706,
-0.018965696915984154,
-0.00309764058329165,
-0.00031138458871282637,
0.01505984365940094,
-0.004982032813131809,
0.017189407721161842,
-0.03253429755568504,
0.08113941550254822,
-0.020631739869713783,
-0.030172742903232574,
0.049928344786167145,
0.006978627759963274,
0.014752700924873352,
0.022884881123900414,
-0.0013866790104657412,
-0.044397272169589996,
0.01278696022927761,
0.02637467347085476,
-0.04221891611814499,
-0.018439114093780518,
-0.02714623138308525,
0.027620483189821243,
0.020713161677122116,
0.02151355892419815,
-0.034830231219530106,
0.0007764421752654016,
0.09664065390825272,
-0.0299389511346817,
0.051519881933927536,
0.011469111777842045,
0.04047992452979088,
0.02241465263068676,
-0.01549290306866169,
-0.02260304056107998,
0.04468000680208206,
0.05765346437692642,
-0.007644049823284149,
-0.050019461661577225,
0.004601551219820976,
-0.053836673498153687,
0.004052273463457823,
-0.014084290713071823,
0.05229386314749718,
0.005653228610754013,
-0.0036458626855164766,
0.01416040025651455,
0.018229220062494278,
-0.02963707037270069,
0.00888151116669178,
-0.019744493067264557,
0.03249024599790573,
-0.006642295978963375,
0.0020944189745932817,
0.012163135223090649,
-0.0036855211947113276,
-0.006905755028128624,
0.011255858466029167,
0.03606762737035751,
-0.003790105925872922,
0.0012039212742820382,
0.050330616533756256,
0.016371173784136772,
-0.025102533400058746,
-0.020870158448815346,
0.06407736241817474,
-0.030478263273835182,
-0.019230462610721588,
0.04417208954691887,
0.014869165606796741,
0.019779259338974953,
0.03626774996519089,
-0.023616153746843338,
-0.03957086056470871,
0.03384736180305481,
0.007873224094510078,
0.039780113846063614,
-0.020463405176997185,
0.0004378337471280247,
-0.02873227372765541,
-0.03225278854370117,
-0.01988091878592968,
0.07453671842813492,
0.007018544245511293,
0.021861635148525238,
-0.013202725909650326,
0.016206596046686172,
-0.0010792897082865238,
-0.043729472905397415,
-0.059803884476423264,
-0.003899691626429558,
-0.017567627131938934,
-0.03162649646401405,
-0.051914945244789124,
-0.025046007707715034,
-0.016843784600496292,
-0.014193041250109673,
0.054278288036584854,
0.03928793966770172,
0.003191637573763728,
-0.0491894893348217,
-0.004168522544205189,
-0.017846902832388878,
-0.04872593656182289,
0.013106231577694416,
0.03813573345541954,
-0.0031227078288793564,
-0.053738292306661606,
0.012813224457204342,
0.03035951778292656,
0.007868426851928234,
0.017203975468873978,
0.04621060937643051,
-0.013637855648994446,
-0.013166872784495354,
-0.0949672982096672,
-0.04174894466996193,
0.0882461741566658,
-0.006046806462109089,
0.015745552256703377,
-0.06434716284275055,
0.008180278353393078,
0.038458604365587234,
0.0822235494852066,
0.002669142559170723,
0.013338249176740646,
0.002966211875900626,
0.009117753244936466,
0.0065384600311517715,
-0.050660278648138046,
-0.0171543937176466,
-0.00541091850027442,
-0.044018108397722244,
-0.035245198756456375,
-0.014476217329502106,
0.046668827533721924,
0.04049883037805557,
-0.005040059797465801,
0.007174964528530836,
0.0720701590180397,
0.002840443281456828,
-0.0024579165037721395,
0.03849723935127258,
-0.006026600953191519,
-0.022922862321138382,
0.02952881157398224,
-0.026569994166493416,
0.02587888017296791,
0.019575437530875206,
-0.03171681985259056,
0.0007775651174597442,
-0.02005569450557232,
-0.0034617010969668627,
0.054893407970666885,
-0.03099104017019272,
-0.018792951479554176,
-0.023217063397169113,
-0.022831333801150322,
-0.0175809133797884,
-0.014969123527407646,
-0.043240588158369064,
-0.05051896348595619,
0.03629987686872482,
-0.017675328999757767,
-0.00725595885887742,
-0.009667249396443367,
0.023572180420160294,
0.02132595144212246,
-0.07246741652488708,
-0.03831624239683151,
-0.06666664034128189,
0.011792763136327267,
0.012215698137879372,
-0.009903335012495518,
0.02937551774084568,
-0.005331019870936871,
-0.001592024345882237,
-0.006554806604981422,
-0.03536265343427658,
-0.00912737101316452,
0.035086069256067276,
0.036386895924806595,
0.03334396705031395,
0.030256694182753563,
0.03009752929210663,
0.028652280569076538,
0.00827790703624487,
0.08446275442838669,
-0.018671996891498566,
-0.012447253800928593,
0.008623233065009117,
-0.04121292755007744,
0.03226354718208313,
-0.01500325184315443,
-0.005749506875872612,
-0.00035444923560135067,
-0.019196512177586555,
-0.013226917013525963,
0.024328865110874176,
-0.036958958953619,
0.07413603365421295,
0.04391894489526749,
0.015172011218965054,
-0.018277417868375778,
0.027248336002230644,
-0.013772698119282722,
0.038688402622938156,
-0.016443872824311256,
-0.00024164699425455183,
-0.03999679163098335,
-0.017773255705833435,
0.05002575367689133,
0.04184935241937637,
0.0019930812995880842,
0.023990564048290253,
0.023096315562725067,
-0.00031884119380265474,
0.0067601632326841354,
0.022056130692362785,
-0.015054530464112759,
-0.030992573127150536,
0.011278029531240463,
0.033463358879089355,
0.01143771130591631,
-0.003786509856581688,
0.019538313150405884,
-0.013250935822725296,
0.020793482661247253,
-0.020351624116301537,
-0.019028307870030403,
0.0054521718993783,
-0.022881338372826576,
-0.018165873363614082,
-0.022212650626897812,
0.006866083014756441,
0.05774333328008652,
0.0016524757957085967,
0.05173227936029434,
0.03116672858595848,
-0.029643390327692032,
0.043912459164857864,
0.01201658882200718,
-0.02799069695174694,
0.02649788185954094,
-0.016056427732110023,
-0.03769974410533905,
-0.0333029069006443,
-0.0021062614396214485,
-0.0284129548817873,
0.026012763381004333,
-0.033483557403087616,
-0.045044075697660446,
-0.028017312288284302,
-0.010023153387010098,
0.01781022548675537,
0.04461456462740898,
0.0027483252342790365,
-0.05456714332103729,
-0.026738960295915604,
0.035402052104473114,
-0.001504359534010291,
0.011994550004601479,
0.031960226595401764,
-0.012306845746934414,
-0.020438523963093758,
-0.06971652805805206,
0.00518503924831748,
0.020379502326250076,
0.03268367052078247,
-0.026542333886027336,
0.004667351488023996,
0.013141254894435406,
-0.045173898339271545,
-0.028652973473072052,
-0.004335862584412098,
-0.010182203724980354,
-0.023863261565566063,
-0.037139467895030975,
0.042058635503053665,
0.017958559095859528,
-0.02263655699789524,
-0.014222292229533195,
-0.005487662274390459,
-0.04007628932595253,
-0.002532248618081212,
-0.0033656135201454163,
0.0028699266258627176,
-0.02105129510164261,
0.04883864149451256,
-0.007051292806863785,
0.0003632588777691126,
0.008732129819691181,
-0.04459793493151665,
-0.002852948382496834,
-0.008778922259807587,
0.005017503630369902,
0.03780292347073555,
0.016316231340169907,
-0.059466663748025894,
0.1032632365822792,
0.04449208825826645,
-0.025866055861115456,
-0.030851591378450394,
0.026988349854946136,
-0.018420958891510963,
-0.0016278118127956986,
0.0025148510467261076,
0.022888250648975372,
-0.001961213070899248,
0.0024381140246987343,
-0.0028642138931900263,
0.056184977293014526,
0.053670644760131836,
0.01559367123991251,
0.015204756520688534,
0.04195866733789444,
-0.013545283116400242,
-0.012006794102489948,
0.05229753628373146,
-0.025820665061473846,
0.0046713394112885,
-0.014678680337965488,
0.034010134637355804,
0.019334131851792336,
0.021554745733737946,
-0.052366647869348526,
0.047043707221746445,
0.041945770382881165,
0.006784964818507433,
-0.02277197130024433,
0.03949524834752083,
0.023583654314279556,
-0.0723038837313652,
-0.0034486930817365646,
-0.005583514459431171,
0.0207833219319582,
-0.009259546175599098,
0.02158234640955925,
0.02449665777385235,
0.04195956140756607,
-0.03400964289903641,
-0.03149665892124176,
0.01801053062081337,
-0.016853485256433487,
0.02725685015320778,
-0.04131924360990524,
-0.01586875133216381,
0.04352441802620888,
0.054012030363082886,
-0.015266130678355694,
-0.023049693554639816,
-0.043011270463466644,
-0.012931077741086483,
-0.056041937321424484,
0.007537517696619034,
-0.0381171815097332,
0.048599135130643845,
0.027871396392583847,
-0.01918460801243782,
-0.030731378123164177,
-0.0038519951049238443,
0.01671423204243183,
-0.0011286232620477676,
-0.043596673756837845,
0.0039470503106713295,
-0.01820976473391056,
-0.03582364320755005,
0.008337102830410004,
-0.015592793934047222,
0.05423421040177345,
0.019518308341503143,
-0.050779879093170166,
-0.049006957560777664,
-0.03224118798971176,
-0.027873406186699867,
0.03811816871166229,
-0.03916708007454872,
-0.04970264434814453,
-0.02270922064781189,
0.02768295630812645,
0.045181553810834885,
-0.05041516572237015,
0.02262745425105095,
0.027064522728323936,
-0.01617388240993023,
0.00024450887576676905,
-0.023544006049633026,
0.016720805317163467,
0.028397731482982635,
0.01821373775601387,
0.0012654195306822658,
0.004559727851301432,
-0.04790796339511871,
-0.028764043003320694,
0.05576975643634796,
0.04300316795706749,
0.013790244236588478,
-0.02127852849662304,
0.01772686094045639,
-0.005890821106731892,
-0.02349242754280567,
0.0007749204523861408,
0.06076105684041977,
-0.002398331416770816,
0.021429572254419327,
0.06358078122138977,
0.02707544155418873,
-0.0459100678563118,
0.03483539819717407,
0.04549189656972885,
0.003987399861216545,
-0.026678502559661865,
-0.05979428440332413,
0.0035824920050799847,
0.017163412645459175,
0.018168112263083458,
-0.04116266220808029,
-0.004371051210910082,
-0.01567334681749344,
-0.023850714787840843,
0.025159697979688644,
0.015575865283608437,
-0.044321902096271515,
-0.008335585705935955,
0.02468152530491352,
-0.0033822290133684874,
0.006413297727704048,
-0.020033687353134155,
0.02432996593415737,
0.05823034048080444,
0.03429681435227394,
0.020845353603363037,
0.0036600357852876186,
-0.056255266070365906,
-0.03779285401105881,
0.024546468630433083,
0.03595416620373726,
-0.00046886500786058605,
0.000557578750886023,
-0.05384545028209686,
0.000904794258531183,
0.03861774131655693,
0.02366964891552925,
0.045782994478940964,
-0.011228079907596111,
-0.011052165180444717,
-0.024518005549907684,
-0.01999603398144245,
-0.059636857360601425,
0.026965636759996414,
-0.022704388946294785,
0.0066400496289134026,
-0.034951101988554,
-0.0008854492916725576,
-0.034936048090457916,
0.029491782188415527,
-0.02822146750986576,
0.06243857368826866,
0.04743779078125954,
0.010508965700864792,
0.010860336944460869,
0.005896064918488264,
-0.01837020181119442,
-0.08506444096565247,
0.05044062063097954,
-0.014025715179741383,
-0.037964146584272385,
0.03692403808236122,
0.0018956701969727874,
-0.04501241073012352,
-0.0072118728421628475,
0.008723217062652111,
-0.009242472238838673,
-0.037037063390016556,
-0.06920873373746872,
0.05482891574501991,
0.06486436724662781,
-0.011605399660766125,
0.04361213743686676,
0.05336519703269005,
-0.044814374297857285,
0.012253988534212112,
-0.02916405163705349,
0.004943246021866798,
-0.020498007535934448,
0.013348205015063286,
-0.039309874176979065,
0.00405078986659646,
-0.03172978386282921,
0.04020998626947403,
-0.03417041525244713,
0.03086225315928459,
-0.02004069648683071,
-0.036644384264945984,
0.011919509619474411,
0.007177046034485102,
-0.021142981946468353,
-0.030036376789212227,
0.012681353837251663,
0.018344154581427574,
0.00857086293399334,
-0.011226746253669262,
0.033367305994033813,
-0.012128788977861404,
0.019853662699460983,
0.027677372097969055,
0.0007217685924842954,
-0.0154145248234272,
-0.021801196038722992,
0.01171706523746252,
-0.010361017659306526,
-0.02482686936855316,
0.06131697818636894,
0.010954860597848892,
-0.0027638592291623354,
-0.012248287908732891,
-0.03132801875472069,
-0.06416969746351242,
-0.004221815150231123,
-0.022069308906793594,
0.02674906887114048,
-0.020289646461606026,
0.01461599301546812,
-0.0021152927074581385,
0.0048317438922822475,
-0.07890383899211884,
-0.016120435670018196,
-0.011235764250159264,
-0.012076440267264843,
-0.02826712839305401,
-0.01504664309322834,
0.004221931099891663,
-0.013873565942049026,
-0.044920664280653,
0.026406288146972656,
0.015730518847703934,
-0.04236200824379921,
-0.012478974647819996,
-0.003268234431743622,
0.06947868317365646,
0.06319095194339752,
0.00021704903338104486,
-0.03473985195159912,
0.017577411606907845,
-0.041745297610759735,
-0.01436292938888073,
0.014498565346002579,
0.008028443902730942,
-0.030834324657917023,
-0.014356451109051704,
0.006623006891459227,
0.02419319748878479,
0.013015792705118656,
-0.015001025050878525,
-0.007421592716127634,
0.011358206160366535,
0.021329935640096664,
-0.005102832801640034,
-0.046728964895009995,
-0.025028256699442863,
0.007756857667118311,
0.044870827347040176,
0.026555513963103294,
0.020358039066195488,
0.0006166070234030485,
-0.026984691619873047,
0.06192758306860924,
-0.007498899940401316,
-0.019244693219661713,
-0.007174978964030743,
0.060373205691576004,
-0.01505898404866457,
-0.01774122752249241,
0.030640579760074615,
-0.03804849460721016,
-0.025407126173377037,
0.010766753926873207,
0.046035848557949066,
0.04021453112363815,
-0.01297043263912201,
-0.021400336176156998,
-0.0395619161427021,
-0.03863378241658211,
-0.001571747357957065,
0.06882023066282272,
-0.0013152124593034387,
0.0007386979414150119,
0.00761397834867239,
-0.0005945155280642211,
0.009601209312677383,
0.0019632955081760883,
-0.023263536393642426,
-0.0057711731642484665,
0.0037290065083652735,
0.05303804948925972,
-0.06730001419782639,
-0.017527973279356956,
0.032890547066926956,
0.04307978227734566,
-0.05220315232872963,
0.0006549874669872224,
0.024684803560376167,
0.0041558025404810905,
0.006778734270483255,
0.00736025907099247,
-0.04525002837181091,
0.061341430991888046,
-0.008433312177658081,
0.021457888185977936,
-0.022933967411518097,
-0.013955061323940754,
0.06856635212898254,
0.058696527034044266,
-0.0027046529576182365,
0.002683744067326188,
-0.01015285961329937,
-0.04920469969511032,
-0.013204935006797314,
0.021106639876961708,
0.011905533261597157,
0.009306351654231548,
0.007480257656425238,
0.04688168689608574,
-0.006494701374322176,
0.033880192786455154,
-0.016788838431239128,
-0.020091462880373,
-0.0268606785684824,
-0.011078625917434692,
-0.04599529504776001,
0.07770141959190369,
-0.010910502634942532,
-0.07207304984331131,
-0.020868858322501183,
-0.015403450466692448,
0.024619432166218758,
0.011869956739246845,
0.03807259351015091,
0.004005282185971737,
0.043677035719156265,
-0.03222237899899483,
0.008364113047719002,
0.0035206966567784548,
-0.015514574944972992,
0.12802469730377197,
0.06726935505867004,
0.0013210654724389315,
-0.06892284005880356,
0.015395247377455235,
-0.00011353527224855497,
0.023719925433397293,
-0.02917763777077198,
0.013212109915912151,
-0.04162636771798134,
-0.005660798866301775,
0.013640210032463074,
0.05871380865573883,
0.004303363151848316,
-0.01783503033220768,
0.03367528319358826,
-0.031148988753557205,
-0.05982919782400131,
-0.011166530661284924,
0.022510619834065437,
-0.024680621922016144,
0.018783418461680412,
-0.05472194775938988,
0.004626166075468063,
0.01317819207906723,
0.041937701404094696,
-0.05108264461159706,
-0.04110454022884369,
0.008371882140636444,
-0.014107797294855118,
-0.02922750636935234,
-0.006884384900331497,
-0.03398369625210762,
0.0002818882931023836,
-0.018831463530659676,
-0.007461005821824074,
0.006350433453917503,
-0.021116020157933235,
0.053458910435438156,
0.04789861664175987,
-0.026710916310548782,
-0.012546157464385033,
0.03396260365843773,
0.020918983966112137,
-0.03417849913239479,
-0.003300533862784505,
-0.007303184363991022,
0.06213252618908882,
-0.005916151218116283,
-0.04722045361995697,
0.00025212272885255516,
-0.02163548208773136,
0.012489204294979572,
0.007272012997418642,
0.016596529632806778,
-0.006315595470368862,
0.026293285191059113,
-0.049145810306072235,
0.008043849840760231,
0.01878616213798523,
0.0552360825240612,
0.018429765477776527,
-0.01677774079144001,
-0.01413041539490223,
-0.04275297746062279,
-0.018169308081269264,
0.0027791308239102364,
0.030514515936374664,
0.0015547547955065966,
-0.026089847087860107,
-0.045609522610902786,
-0.01170498225837946,
-0.031129470095038414,
-0.021880382671952248,
-0.012496712617576122,
0.005396749824285507,
0.04930150508880615,
0.006794995162636042,
0.008429891429841518,
-0.027974039316177368,
-0.054486703127622604,
0.03497818857431412,
-0.0009105014614760876,
0.041239477694034576,
-0.010462382808327675,
-0.00846803281456232,
-0.016352051869034767,
0.03600235655903816,
0.038191404193639755,
0.000800033682025969,
0.011719650588929653,
0.03760213032364845,
0.010428536683321,
-0.006782349199056625,
-0.0009502476896159351,
0.02481137402355671,
-0.015851035714149475,
-0.013419563882052898,
-0.004585190210491419,
-0.006637488026171923,
0.052957985550165176,
-0.006522936746478081,
0.0059738061390817165,
0.04750077426433563,
0.004173106513917446,
-0.025946222245693207,
0.014728644862771034,
-0.04614037275314331,
0.004792405292391777,
0.03513675183057785,
0.03907835856080055,
-0.03521668538451195,
-0.03881056234240532,
-0.017449041828513145,
-0.01257182564586401,
-0.006869335193186998,
0.015123541466891766,
-0.04074219986796379,
-0.010647700168192387,
-0.020063653588294983,
-0.004954992327839136,
-0.04117835685610771,
-0.006368455942720175,
-0.0030555548146367073,
0.02781575545668602,
0.00120078946929425,
0.0010158589575439692,
0.01057335827499628,
0.03917238861322403,
0.009814473800361156,
0.013816879130899906,
0.014566044323146343,
0.029662171378731728,
-0.021273666992783546,
-0.00747927650809288,
-0.002442668890580535,
0.013299732469022274,
0.00780917564406991,
-0.01297845970839262,
-0.01750241592526436,
0.00372882978990674,
-0.015135399997234344,
-0.05385341867804527,
0.03971876949071884,
0.0011802167864516377,
0.018756931647658348,
0.004934121388942003,
-0.018953362479805946,
-0.031113047152757645,
0.016837960109114647,
-0.009296409785747528,
-0.020028850063681602,
-0.023126469925045967,
-0.025053735822439194,
0.01890670135617256,
-0.07822874933481216,
0.003359690075740218,
0.0017744619399309158,
0.008899657055735588,
0.002477032830938697,
-0.0017532124184072018,
-0.0070751202292740345,
-0.017112772911787033,
0.0029348868411034346,
-0.04334649443626404,
0.02496369555592537,
0.0017554484074935317,
0.013031245209276676,
-0.010899986140429974,
0.06612402945756912,
0.004827510099858046,
0.017572788521647453,
-0.025574123486876488,
0.037238746881484985,
-0.09229405969381332,
-0.007887352257966995,
0.013347115367650986,
0.04899127781391144,
0.0462200902402401,
-0.0677059218287468,
0.02902033179998398,
0.02838762290775776,
-0.0545857809484005,
0.00745625514537096,
-0.022525088861584663,
-0.03926604613661766,
-0.009281335398554802,
-0.008300479501485825,
-0.009213377721607685,
0.05132603645324707,
0.046818990260362625,
0.02514808438718319,
0.00033318516216240823,
-0.007367890793830156,
-0.02177850529551506,
-0.030365191400051117,
-0.01389743760228157,
0.008724466897547245,
0.008898340165615082,
-0.01864907518029213,
0.04356684535741806,
-0.011206738650798798,
-0.01697833091020584,
0.010970750823616982,
0.027353676036000252,
0.0015196457970887423,
-0.02604622021317482,
0.0032552280463278294,
0.0003595584712456912,
0.047056350857019424,
0.027799496427178383,
-0.004534839652478695,
0.024565832689404488,
-0.009666689671576023,
0.02489892952144146,
0.03441634029150009,
-0.010861887596547604,
0.009460004046559334,
0.013303360901772976,
-0.02038605324923992,
-0.05346396937966347,
0.05567034333944321,
-0.022167405113577843,
-0.05460489168763161,
0.012753171846270561,
0.005009960848838091,
-0.009997250512242317,
-0.015197652392089367,
0.03009773977100849,
-0.01707141473889351,
0.0004037654143758118,
0.049699947237968445,
0.03341574966907501,
0.012255278415977955,
0.028142066672444344,
-0.0010568555444478989,
-0.021930960938334465,
0.01772472821176052,
-0.0005055764922872186,
-0.0011577918194234371,
-0.03208647668361664,
-0.0037477940786629915,
0.0028626788407564163,
0.007962311618030071,
0.016111107543110847,
-0.008690301328897476,
-0.016157355159521103,
0.003660159884020686,
-0.0006387348985299468,
-0.005670282058417797,
-0.045289453119039536,
-0.029556123539805412,
0.008195667527616024,
-0.05298683047294617,
0.04219447076320648,
0.03602607175707817,
-0.024747667834162712,
-0.008796853944659233,
-0.010097324848175049,
-0.009933371096849442,
0.01269794162362814,
0.06980010867118835,
-0.007542629260569811,
-0.041197456419467926,
0.026046380400657654,
0.03519416227936745,
0.020827412605285645,
-0.025050543248653412,
-0.011262170039117336,
-0.014335250481963158,
0.03834375739097595,
-0.02451290935277939,
-0.0005449308082461357,
-0.04054911434650421,
0.04428433999419212,
0.010753548704087734,
0.03379302844405174,
0.0017119116382673383,
0.006369908340275288,
-0.0580378957092762,
0.048507895320653915,
-0.0012041274458169937,
-0.05223079398274422,
0.06453060358762741,
-0.012038689106702805,
0.018212277442216873,
0.04495653137564659,
-0.03249837085604668,
-0.08544828742742538,
0.014429540373384953,
-0.05297482758760452,
-0.005486099980771542,
-0.015849722549319267,
-0.02046213299036026,
0.009435749612748623,
-0.011490428820252419,
0.036627575755119324,
0.03250752389431,
-0.013015183620154858,
-0.02668236568570137,
0.052563562989234924,
0.023591093719005585,
0.04912934824824333,
0.025988880544900894,
-0.008918988518416882,
0.015455071814358234,
-0.0022810627706348896,
0.018235770985484123,
0.01879842020571232,
0.01682102121412754,
0.021573416888713837,
-0.021281631663441658,
0.015382543206214905,
-0.004088832996785641,
0.011271302588284016,
0.03147776797413826,
0.009987578727304935,
-0.02500010095536709,
0.008575895801186562,
0.043518077582120895,
-0.024853669106960297,
0.010158726014196873,
0.04829159379005432,
-0.04333037883043289,
0.0637139305472374,
-0.04669317603111267,
0.011542581021785736,
-0.02412162534892559,
0.0014400891959667206,
-0.030413663014769554,
0.029832595959305763,
-0.007418204564601183,
0.10214763134717941,
-0.013811915181577206,
-0.00687975762411952,
0.011465227231383324,
-0.02445586398243904,
-0.0048401495441794395,
-0.05772152170538902,
0.02095424011349678,
0.012683787383139133,
0.006522661540657282,
0.012074253521859646,
-0.04400702193379402,
-0.03185339272022247,
-0.020985065028071404,
0.04328636825084686,
0.017478827387094498,
0.01006106473505497,
0.01446374598890543,
-0.020333457738161087,
-0.04370291903614998,
0.09052131325006485,
-0.013804941438138485,
-0.0351395308971405,
-0.034896593540906906,
0.0018049424979835749,
-0.004707732237875462,
-0.026750212535262108
] |
<p>I've looked in and out the forum, and found no precise definition of the meaning of <a href="http://en.wikipedia.org/wiki/Fine-tuning" rel="nofollow">fine-tuning</a> in physics.</p>
<p><strong>QUESTION</strong></p>
<p>Is it possible to give a precise definition of fine-tuning?</p>
<p>Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the reason behind my question.</p> | 4,580 | [
0.0022532930597662926,
0.01815001107752323,
-0.007099386304616928,
-0.02849525213241577,
0.03575842082500458,
0.051251981407403946,
0.007176991086453199,
-0.02157682552933693,
-0.006413441151380539,
-0.02518463134765625,
0.016136692836880684,
0.04977741092443466,
0.03440500423312187,
0.019967393949627876,
0.02388441190123558,
0.026576844975352287,
0.009556164033710957,
0.02672778256237507,
-0.020992612466216087,
-0.0428033322095871,
-0.008120809681713581,
-0.005195247009396553,
-0.01439450029283762,
0.030585721135139465,
-0.009631806053221226,
-0.012325792573392391,
0.02782175876200199,
0.014872095547616482,
0.033983390778303146,
0.0010458813048899174,
-0.021658439189195633,
-0.011794954538345337,
0.025718024000525475,
0.005518416408449411,
0.02325899340212345,
-0.0042395200580358505,
0.009985690005123615,
0.020954523235559464,
-0.00504595460370183,
-0.00014118445687927306,
-0.043944451957941055,
0.003026508027687669,
-0.02877061255276203,
0.011896331794559956,
-0.032237373292446136,
-0.005492079071700573,
0.0017948177410289645,
-0.048942260444164276,
0.06592433899641037,
-0.05939610302448273,
0.07139959186315536,
-0.01715909130871296,
0.0023167056497186422,
0.031074509024620056,
-0.012060001492500305,
0.0070478105917572975,
0.08207282423973083,
0.060686249285936356,
-0.0418616384267807,
-0.07429924607276917,
-0.0011200692970305681,
-0.055568426847457886,
0.0005848014261573553,
0.01264697965234518,
-0.004018329083919525,
0.039943281561136246,
-0.02355998009443283,
-0.02855062298476696,
0.025780098512768745,
0.019832229241728783,
-0.03297242894768715,
0.009115523658692837,
0.045959848910570145,
-0.012810895219445229,
0.023313669487833977,
-0.05619564652442932,
0.005116225685924292,
0.018671110272407532,
0.011298833414912224,
0.041669782251119614,
-0.01834084279835224,
0.01310995314270258,
0.001317873247899115,
0.02327132225036621,
-0.018917910754680634,
0.002142239362001419,
0.06032393127679825,
-0.07946029305458069,
0.04149053990840912,
0.029778754338622093,
-0.03494637832045555,
0.012898752465844154,
0.013595057651400566,
0.015829168260097504,
-0.04429691284894943,
0.035334739834070206,
0.008925090543925762,
0.03298146277666092,
-0.0036344260443001986,
-0.05850984528660774,
0.020135514438152313,
-0.01644560508430004,
-0.01044475194066763,
0.06295730918645859,
-0.01669694110751152,
0.0217273086309433,
-0.027651872485876083,
-0.008981085382401943,
-0.027251090854406357,
0.001450316864065826,
-0.005666079465299845,
0.006410493515431881,
-0.010118803940713406,
0.024440476670861244,
-0.010431388393044472,
0.0011616694973781705,
-0.00865332130342722,
0.006129004526883364,
0.08491557836532593,
0.013386487029492855,
0.057503487914800644,
-0.052175283432006836,
0.02036011777818203,
0.025863872841000557,
-0.06097211688756943,
0.053985174745321274,
0.03755628690123558,
-0.02256302535533905,
-0.02297721989452839,
0.013625143095850945,
0.009637325070798397,
0.0060785626992583275,
-0.015507468953728676,
0.03166072443127632,
0.011764365248382092,
-0.009058752097189426,
-0.10388337820768356,
-0.05837563797831535,
0.06275869905948639,
0.02983085997402668,
-0.008536453358829021,
-0.09443643689155579,
0.027256900444626808,
0.01085881981998682,
0.08696530014276505,
0.04087260365486145,
0.006655474659055471,
-0.025882262736558914,
-0.023332474753260612,
0.03666196018457413,
-0.032370589673519135,
-0.013380707241594791,
0.005974731408059597,
-0.04027080535888672,
-0.021394792944192886,
-0.07157538086175919,
0.025367040187120438,
0.0312369242310524,
-0.023848066106438637,
0.012379460036754608,
0.03849362954497337,
-0.017339879646897316,
-0.01773194596171379,
0.01722903735935688,
-0.02039279416203499,
-0.024918628856539726,
0.07797539234161377,
0.016878463327884674,
-0.013188136741518974,
0.06393610686063766,
-0.004508706741034985,
0.043633900582790375,
0.009660420008003712,
0.021539831534028053,
0.02852027863264084,
0.00959687028080225,
0.0071854908019304276,
-0.03816349431872368,
0.006103966850787401,
-0.03921827673912048,
-0.03561534732580185,
-0.029925741255283356,
-0.0014757526805624366,
0.044796016067266464,
-0.03243795782327652,
0.022238830104470253,
-0.018394682556390762,
-0.01870817132294178,
0.004420839250087738,
-0.0757807195186615,
-0.002398068318143487,
-0.08570493757724762,
-0.009345450438559055,
-0.022015368565917015,
-0.031163359060883522,
0.0309457890689373,
-0.02508952096104622,
0.006824016571044922,
-0.026258300989866257,
-0.009150161407887936,
0.0008039423264563084,
0.02527043968439102,
0.036079347133636475,
-0.026259344071149826,
0.04461407661437988,
0.07974687963724136,
0.0029584302101284266,
0.01885172352194786,
0.05108655244112015,
-0.014357147738337517,
-0.05424211919307709,
-0.0014771752757951617,
-0.027053656056523323,
0.02611071616411209,
0.02558412030339241,
-0.015629485249519348,
0.005973252933472395,
-0.039139274507761,
-0.01671746000647545,
0.03165027126669884,
-0.038127798587083817,
0.05474800243973732,
0.012879237532615662,
0.018368221819400787,
-0.009310592897236347,
0.07284894585609436,
-0.018047234043478966,
0.02214144356548786,
-0.023708168417215347,
-0.020416440442204475,
-0.04783259704709053,
-0.0014748923713341355,
0.04369611293077469,
0.03882889077067375,
-0.017191806808114052,
-0.018659302964806557,
0.018631333485245705,
0.031390901654958725,
0.04030824452638626,
0.028862545266747475,
-0.04874324053525925,
-0.002195066073909402,
0.00562983937561512,
0.0358923077583313,
0.0137340622022748,
0.050688665360212326,
0.01893756352365017,
0.031305454671382904,
0.018629921600222588,
-0.004011681769043207,
0.008223118260502815,
0.0671856701374054,
-0.029881712049245834,
0.0014640380395576358,
0.03079378418624401,
-0.004734273999929428,
-0.010605587624013424,
-0.019044365733861923,
0.045284368097782135,
0.013140080496668816,
-0.026353439316153526,
0.006029218900948763,
-0.019567018374800682,
0.007083453703671694,
0.004632278345525265,
-0.0002508386387489736,
-0.03638741746544838,
-0.010078604333102703,
0.02869361639022827,
0.009615583345293999,
0.010664775036275387,
-0.026243014261126518,
0.014494759030640125,
-0.032975997775793076,
-0.027955522760748863,
-0.02294551581144333,
0.026854757219552994,
0.029639048501849174,
0.003963184542953968,
-0.04126141220331192,
-0.011027852073311806,
-0.04732823371887207,
0.009308048523962498,
-0.010205131024122238,
-0.0038038359489291906,
0.0031080213375389576,
-0.003943817224353552,
-0.03993481770157814,
0.038277868181467056,
-0.06849060207605362,
0.038883011788129807,
-0.0035939752124249935,
-0.016724690794944763,
-0.03364130109548569,
0.010212413035333157,
-0.013397950679063797,
0.006836981978267431,
-0.0023031241726130247,
-0.011194447986781597,
0.03795876353979111,
0.010625017806887627,
-0.03785787895321846,
0.00013745680917054415,
-0.014684179797768593,
-0.028133327141404152,
-0.025458035990595818,
-0.005458635278046131,
0.03708992525935173,
-0.02511342242360115,
0.03142383694648743,
0.03486232832074165,
-0.04993128404021263,
-0.005176708567887545,
-0.029781758785247803,
-0.057194869965314865,
0.0315648689866066,
-0.029907172545790672,
0.047853365540504456,
0.0033301033545285463,
-0.042715128511190414,
0.07586866617202759,
0.007162621710449457,
-0.035125985741615295,
-0.019099704921245575,
0.016161244362592697,
0.023316722363233566,
-0.03407783433794975,
0.03215623274445534,
0.04065880551934242,
0.01333923451602459,
0.020384736359119415,
0.034747928380966187,
0.032406702637672424,
0.005696000996977091,
0.0016501619247719646,
-0.03368176892399788,
-0.006821317132562399,
0.004572889767587185,
-0.01611475460231304,
-0.010527780279517174,
0.026156896725296974,
-0.03136691823601723,
0.003211656119674444,
-0.023403888568282127,
0.022357763722538948,
0.013004336506128311,
-0.018846701830625534,
0.07105105370283127,
0.017069753259420395,
-0.0004079628852196038,
0.01567700505256653,
0.01049857959151268,
-0.0031623856630176306,
-0.01735634170472622,
-0.029214268550276756,
0.025664187967777252,
-0.021529661491513252,
0.005115731619298458,
0.009945251047611237,
0.026535047218203545,
0.06417641043663025,
-0.012812205590307713,
-0.003995520528405905,
0.007262254599481821,
-0.005417524836957455,
-0.001355801592580974,
-0.03566671162843704,
-0.06455641984939575,
0.05235936865210533,
0.020580723881721497,
0.02386046200990677,
0.014263161458075047,
-0.029555918648838997,
0.010660168714821339,
-0.08764281868934631,
0.002711565000936389,
-0.015490958467125893,
0.03239671513438225,
-0.030431685969233513,
0.04753013327717781,
0.025852330029010773,
0.03504890576004982,
0.016913939267396927,
-0.015866858884692192,
-0.12203562259674072,
0.05245635658502579,
-0.02545095793902874,
-0.024884816259145737,
-0.008368037641048431,
-0.006054030265659094,
0.009493282996118069,
-0.048425666987895966,
-0.01292551588267088,
-0.028299013152718544,
0.013613243587315083,
-0.03091627173125744,
-0.00012512723333202302,
0.014481219463050365,
-0.021436799317598343,
-0.0278595183044672,
0.012899721972644329,
0.03741487115621567,
-0.01565532572567463,
0.019593199715018272,
0.0201412383466959,
-0.00987351592630148,
-0.010883818380534649,
-0.0008702389313839376,
-0.018514586612582207,
0.009276255965232849,
0.04122448340058327,
0.030062193050980568,
0.045574892312288284,
-0.053675055503845215,
0.0686413124203682,
0.011577868834137917,
0.06902307271957397,
0.017415227368474007,
-0.04415436461567879,
-0.03689961135387421,
-0.05449245125055313,
0.00709080696105957,
0.007784151006489992,
0.05975582078099251,
0.01690078340470791,
-0.020599709823727608,
0.05296509712934494,
0.0015392532804980874,
-0.035297196358442307,
0.03857490420341492,
0.02714419737458229,
0.0005310398992151022,
-0.03893328085541725,
-0.03850318118929863,
0.004469371400773525,
0.002705906517803669,
0.018173187971115112,
0.02413204312324524,
0.0041045499965548515,
-0.003444081638008356,
0.02229311130940914,
-0.009301298297941685,
0.023010501638054848,
-0.013343335129320621,
0.015911493450403214,
-0.004182541277259588,
0.009731353260576725,
0.005148093681782484,
-0.0025408228393644094,
-0.016644231975078583,
0.05734556168317795,
0.03338529169559479,
0.009998416528105736,
-0.007283053360879421,
-0.09188267588615417,
0.00814079400151968,
0.05383630841970444,
0.022083071991801262,
-0.05823681503534317,
0.007351667620241642,
-0.02854200080037117,
-0.004038912709802389,
0.03371015563607216,
-0.038816291838884354,
0.05805543065071106,
-0.04377251863479614,
0.004419464617967606,
-0.0400221049785614,
0.010523460805416107,
-0.005861513316631317,
0.025035513564944267,
0.020381614565849304,
0.003437088569626212,
-0.025426028296351433,
0.0005977904656901956,
-0.023321347311139107,
0.0008052907069213688,
-0.005785160232335329,
0.059155263006687164,
0.008646456524729729,
-0.012594477273523808,
0.0071832225657999516,
0.0029490443412214518,
0.0010505171958357096,
-0.0950060486793518,
0.010057304985821247,
0.021519329398870468,
-0.018077414482831955,
-0.016915954649448395,
-0.014190527610480785,
-0.04098137095570564,
0.037796009331941605,
0.002470781095325947,
-0.016612518578767776,
0.018277503550052643,
-0.02684600092470646,
0.03537347912788391,
0.019113726913928986,
0.017445145174860954,
0.04536949843168259,
0.029765095561742783,
-0.07602410018444061,
-0.009714400395751,
-0.00518160592764616,
0.021021854132413864,
-0.02582644857466221,
0.019725417718291283,
-0.002868711482733488,
-0.012965535745024681,
-0.04299110546708107,
0.028624488040804863,
0.017249077558517456,
0.0319751538336277,
-0.008553331717848778,
-0.03523200750350952,
-0.057236574590206146,
0.04199548810720444,
-0.013653844594955444,
-0.025366144254803658,
0.009556987322866917,
0.043361030519008636,
0.017246779054403305,
-0.009287911467254162,
-0.026162631809711456,
0.016000162810087204,
0.013235109858214855,
0.06483481824398041,
-0.033321477472782135,
0.019329480826854706,
-0.03500085324048996,
-0.03827844560146332,
0.017181064933538437,
-0.032663993537425995,
0.03513406589627266,
-0.03053729049861431,
-0.005247557070106268,
-0.008360574953258038,
-0.07550574094057083,
-0.04178667813539505,
-0.020461002364754677,
-0.029863402247428894,
0.024479474872350693,
-0.016168801113963127,
0.03947105631232262,
-0.0054621146991848946,
-0.001617808942683041,
-0.0415312685072422,
-0.027429478242993355,
0.03678169474005699,
0.017375122755765915,
-0.03540001064538956,
-0.004494903143495321,
-0.010401946492493153,
-0.024736884981393814,
-0.04242232069373131,
-0.014866550453007221,
0.04971185326576233,
-0.022327426820993423,
-0.03163135051727295,
0.011740046553313732,
0.028369130566716194,
0.03827611729502678,
0.0009391834028065205,
-0.013354523107409477,
0.00020663527538999915,
-0.01069747842848301,
-0.02166440151631832,
0.02112128958106041,
0.03299202024936676,
-0.030447090044617653,
-0.02027699537575245,
-0.02172488160431385,
0.0006484221667051315,
0.010602656751871109,
0.001868253923021257,
0.003602587850764394,
0.013840900734066963,
0.007220754865556955,
0.04262297973036766,
-0.021519815549254417,
-0.013593092560768127,
-0.013939895667135715,
0.021994860842823982,
0.040327318012714386,
0.001818923745304346,
0.01125443633645773,
-0.03635217249393463,
0.037681493908166885,
0.012121590785682201,
-0.006756818387657404,
0.007253771647810936,
0.07064184546470642,
0.012464931234717369,
-0.0009549621026962996,
-0.002406518906354904,
-0.02143065445125103,
0.010065308772027493,
-0.009141768328845501,
0.03540422022342682,
0.027031369507312775,
0.01051604188978672,
-0.01434511411935091,
-0.020522963255643845,
-0.020567093044519424,
-0.047265153378248215,
0.059867676347494125,
-0.03151461109519005,
0.04950302094221115,
0.01923268847167492,
-0.042692095041275024,
-0.033970244228839874,
-0.009184243157505989,
-0.017490128055214882,
-0.006228328216820955,
0.013288416899740696,
0.017764007672667503,
-0.04414468631148338,
-0.02473665401339531,
0.02410481870174408,
0.023652607575058937,
-0.038729529827833176,
0.025727348402142525,
0.028383640572428703,
0.09590968489646912,
-0.029711302369832993,
-0.03090406395494938,
-0.03406701609492302,
0.09134828299283981,
-0.04042195901274681,
0.0439160019159317,
0.03693637624382973,
-0.012794245034456253,
0.009789888747036457,
0.029214106500148773,
0.01530467439442873,
-0.01912347786128521,
-0.004431466106325388,
-0.05724520608782768,
0.011399946175515652,
0.002384212799370289,
-0.014625280164182186,
0.00021463115990627557,
-0.025478709489107132,
-0.0012718576472252607,
0.034789975732564926,
0.007511398755013943,
-0.0066094291396439075,
-0.035820022225379944,
-0.011823556385934353,
-0.04192913696169853,
-0.009485021233558655,
0.014322691597044468,
-0.012860803864896297,
-0.05188799649477005,
0.025139160454273224,
-0.008863681927323341,
0.029967064037919044,
0.04859119653701782,
0.053032804280519485,
-0.0413229875266552,
0.04565699025988579,
-0.01429497916251421,
0.03731389343738556,
0.03199347108602524,
-0.005191359203308821,
0.10911329835653305,
0.07363633066415787,
-0.019050506874918938,
-0.07292202860116959,
-0.015318180434405804,
-0.05726352706551552,
0.010045616887509823,
-0.01646631956100464,
-0.0315505713224411,
0.01042273361235857,
0.021864300593733788,
0.019197799265384674,
0.02667294628918171,
0.026000171899795532,
-0.012956345453858376,
0.06922454386949539,
-0.03253907710313797,
-0.0422431156039238,
0.02117004804313183,
0.00929253175854683,
-0.0005654121632687747,
-0.02123790606856346,
-0.06988757848739624,
-0.007718739099800587,
0.005914417561143637,
0.0022315664682537317,
-0.004104139748960733,
-0.008902209810912609,
0.01042823027819395,
0.00812370516359806,
-0.03490860387682915,
0.005042628385126591,
-0.02936200052499771,
-0.0009713639155961573,
-0.03947237879037857,
0.01138108130544424,
-0.013306335546076298,
-0.019158778712153435,
0.007309298031032085,
0.04843723028898239,
0.025158466771245003,
0.0033326081465929747,
-0.007445317693054676,
0.011652763932943344,
-0.0184953436255455,
-0.012969018891453743,
-0.012847530655562878,
0.012180386111140251,
-0.022256840020418167,
-0.021941784769296646,
-0.039595216512680054,
0.008876947686076164,
-0.009001513011753559,
-0.028145939111709595,
0.006267353426665068,
0.006758437026292086,
0.02691737748682499,
-0.009156265296041965,
-0.030195480212569237,
0.018059581518173218,
0.009677513502538204,
-0.038795147091150284,
0.03342755511403084,
-0.010456131771206856,
0.005842883605509996,
0.006463504396378994,
0.027232907712459564,
0.04624154791235924,
-0.001910896971821785,
-0.03100581094622612,
-0.022137803956866264,
-0.010520964860916138,
-0.05827144905924797,
-0.003111341269686818,
0.04181462898850441,
0.007956203073263168,
0.04433465003967285,
0.0002337749465368688,
-0.0018684347160160542,
-0.02487524412572384,
-0.003923514857888222,
0.033968716859817505,
-0.010002882219851017,
0.00026431449805386364,
-0.027896812185645103,
0.013415670953691006,
0.03539600595831871,
0.04451766237616539,
0.00007818379526725039,
0.020698372274637222,
0.02072116918861866,
-0.008260894566774368,
0.03724992647767067,
-0.022092510014772415,
-0.043567121028900146,
0.028009530156850815,
-0.01773316040635109,
0.008837923407554626,
0.025987491011619568,
0.05584559589624405,
0.013658684678375721,
-0.017246494069695473,
-0.0011581451399251819,
0.02687673084437847,
-0.024088675156235695,
-0.002854750258848071,
0.028666354715824127,
-0.00002442338882246986,
0.0038768756203353405,
0.007811784744262695,
0.009236124344170094,
-0.048421017825603485,
-0.012904020957648754,
-0.034472644329071045,
-0.011674151755869389,
0.0012353977654129267,
0.04689311236143112,
0.003985981922596693,
0.04180297255516052,
0.012882709503173828,
0.0010261170100420713,
-0.04264304041862488,
0.002098140772432089,
-0.057798292487859726,
0.007276781834661961,
-0.022744109854102135,
0.007426714524626732,
0.01045676413923502,
0.030758291482925415,
-0.0448022298514843,
-0.038615632802248,
0.021521635353565216,
0.012735380791127682,
0.0012460629222914577,
-0.0031130709685385227,
-0.020107274875044823,
-0.02112852968275547,
0.03347902372479439,
-0.04678567498922348,
-0.02427465096116066,
0.042148418724536896,
-0.053719814866781235,
-0.0496637187898159,
0.02074507065117359,
-0.020880600437521935,
-0.0035721389576792717,
0.043023448437452316,
-0.049815598875284195,
-0.01226703729480505,
0.038588251918554306,
0.001873557223007083,
0.02530168928205967,
0.005578052718192339,
0.009048298932611942,
-0.036919210106134415,
-0.017574617639183998,
0.009707340970635414,
-0.04343705624341965,
-0.015773160383105278,
0.0376494899392128,
0.04498707875609398,
0.006509086582809687,
-0.007922014221549034,
0.02694997563958168,
0.015683190897107124,
-0.00007521577208535746,
-0.007034345529973507,
0.029843991622328758,
0.01618202216923237,
0.03102092258632183,
-0.010743900202214718,
0.039790038019418716,
0.0010467040119692683,
-0.006775213871151209,
-0.09797203540802002,
-0.014029962942004204,
-0.015239035710692406,
0.002682481426745653,
0.019572492688894272,
-0.04181447625160217,
0.08032812923192978,
-0.022797975689172745,
-0.04866692051291466,
-0.0045251669362187386,
-0.03477904945611954,
-0.03349517285823822,
-0.02669457346200943,
0.005749201867729425,
-0.015156110748648643,
0.04436172544956207,
0.051998432725667953,
-0.01736212521791458,
-0.0023068718146532774,
-0.0030097083654254675,
-0.01752059906721115,
-0.01735719107091427,
-0.010195924900472164,
0.03225809708237648,
0.013333454728126526,
-0.018766844645142555,
0.0562078133225441,
0.0011951349442824721,
-0.03732822835445404,
0.03134899586439133,
0.01827954687178135,
0.027684874832630157,
0.003120294539257884,
0.04148511216044426,
0.042517099529504776,
0.028305262327194214,
-0.002895141253247857,
-0.03301610052585602,
-0.035505510866642,
0.01889355666935444,
0.031997304409742355,
0.05387500301003456,
-0.005268110893666744,
-0.0056120408698916435,
-0.005244252737611532,
-0.031935665756464005,
-0.04058418050408363,
0.014041807502508163,
-0.011968874372541904,
0.0019810593221336603,
0.030887050554156303,
-0.012858157977461815,
0.033771414309740067,
-0.03602500259876251,
0.018974704667925835,
-0.022746337577700615,
-0.02447979338467121,
0.04030623286962509,
0.028129976242780685,
-0.028911013156175613,
0.00041938284994103014,
-0.025313839316368103,
-0.030141815543174744,
0.028779929503798485,
0.011123454198241234,
-0.02583886869251728,
-0.041670482605695724,
-0.046650081872940063,
-0.002005754504352808,
-0.009979014284908772,
-0.008233060128986835,
-0.003372420324012637,
-0.04347966983914375,
0.031196806579828262,
0.0068466635420918465,
0.0026716997381299734,
-0.01087141502648592,
-0.05144147574901581,
-0.022845732048153877,
-0.062396835535764694,
0.06837938725948334,
0.0022888423409312963,
0.014638956636190414,
-0.041642770171165466,
-0.00986266229301691,
-0.003141415072605014,
0.029392650350928307,
0.040803685784339905,
-0.001905742334201932,
-0.0367407463490963,
0.014695338904857635,
0.02695702202618122,
0.039793845266103745,
-0.04614311829209328,
0.0366872139275074,
-0.01369176059961319,
-0.03282563388347626,
-0.03638966381549835,
-0.03367350250482559,
-0.03187653422355652,
0.020355865359306335,
0.03258278965950012,
0.025994842872023582,
0.05458598583936691,
-0.008473402820527554,
-0.06526145339012146,
0.058122292160987854,
0.020868245512247086,
0.028391703963279724,
0.05531889200210571,
-0.022320609539747238,
0.028824031352996826,
0.029225105419754982,
-0.0013982044765725732,
-0.021859215572476387,
-0.004447498824447393,
-0.027030400931835175,
-0.0008161913137882948,
0.004178926348686218,
-0.017697717994451523,
0.01633281633257866,
-0.02225581556558609,
-0.02615910768508911,
0.04115574061870575,
-0.038741376250982285,
-0.011782665736973286,
0.06010894104838371,
0.024965418502688408,
0.03800800442695618,
-0.0002018801897065714,
-0.02364269830286503,
-0.008579461835324764,
-0.0396265871822834,
-0.029671238735318184,
0.054546158760786057,
0.02575896494090557,
0.023973938077688217,
0.05414775013923645,
0.0333581417798996,
-0.00005573900853050873,
0.02807721309363842,
0.014958502724766731,
0.045677997171878815,
-0.025646522641181946,
-0.010507731698453426,
0.022837655618786812,
-0.011654426343739033,
0.011147048324346542,
0.0230583306401968,
-0.011868035420775414,
0.07943996042013168,
-0.038457270711660385,
-0.023235943168401718,
0.0047696842812001705,
0.04243003576993942,
-0.0011444080155342817,
0.0016126802656799555,
0.0060314759612083435,
0.04712056741118431,
-0.024537600576877594,
0.0011608300264924765,
-0.007487716153264046,
0.01753779873251915,
0.018793487921357155,
-0.04308519884943962,
0.020053988322615623,
-0.006606845185160637,
0.01090224552899599,
-0.0006604965892620385,
0.016378669068217278,
-0.05063849315047264,
-0.02994406223297119,
0.000818809901829809,
0.044844284653663635,
0.023761752992868423,
0.011753788217902184,
-0.011635249480605125,
-0.03605073317885399,
0.03496432676911354,
-0.0920320600271225,
-0.007624433841556311,
-0.03176778554916382,
0.011053056456148624,
-0.039367660880088806,
-0.028335759416222572
] |
<p>I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$)</p>
<p>$$ Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 \;d^3x $$ </p>
<p>But, I presume that the formula is different for a frequency-dependent electric field. I've searched Griffiths and Jackson but can't quite find what I'm looking for...</p>
<p>I've also tried to Fourier transform my expression for the electric field back to space/time, but my electric field is a fairly gruesome expression - I couldn't FT it easily. I was hoping to compute the energy from $E(\mathbf{x},\omega)$ via computational integral, once I find an expression for the energy.</p> | 4,581 | [
0.00009609979315428063,
-0.040627364069223404,
0.014626814983785152,
-0.03398223966360092,
0.04561065509915352,
-0.005379944574087858,
-0.027849212288856506,
-0.03132274001836777,
0.016949215903878212,
-0.03965627774596214,
0.009232358075678349,
0.04678522050380707,
0.06948594003915787,
0.0017925527645274997,
0.019690055400133133,
-0.010628433898091316,
0.0038186409510672092,
0.01997324638068676,
-0.010500662960112095,
-0.06688062101602554,
0.0042967298068106174,
0.03184733912348747,
-0.010026405565440655,
-0.005744620691984892,
0.0002949541958514601,
0.024199366569519043,
0.04755515977740288,
-0.024247897788882256,
0.005070883315056562,
0.05563248693943024,
-0.028446875512599945,
-0.04168997332453728,
0.014531643129885197,
0.023864315822720528,
0.015878040343523026,
0.03799112141132355,
-0.06877735257148743,
-0.05084853246808052,
0.0002065400331048295,
0.03609909117221832,
-0.02015058510005474,
0.005021541845053434,
-0.002935277996584773,
0.05227482691407204,
-0.0016814868431538343,
0.02414654567837715,
0.004171677865087986,
-0.014811468310654163,
0.025793656706809998,
-0.047461386770009995,
0.09566830843687057,
-0.03190407529473305,
0.07172438502311707,
0.018640149384737015,
-0.04911193996667862,
0.009281930513679981,
0.07358161360025406,
0.054742272943258286,
0.01462259329855442,
-0.03528843820095062,
-0.042810093611478806,
-0.029386155307292938,
0.0004933922318741679,
-0.025153441354632378,
-0.006656083278357983,
0.0014367663534358144,
0.0014991095522418618,
-0.013836723752319813,
0.019376125186681747,
-0.015490074642002583,
0.018130971118807793,
0.03910503908991814,
0.04854698106646538,
-0.016989000141620636,
-0.004328458569943905,
0.02084195986390114,
0.025912735611200333,
0.000033111627999460325,
0.04741472005844116,
0.01785069704055786,
-0.03218047320842743,
-0.00037291055195964873,
0.029376070946455002,
0.03194351866841316,
0.0034359062556177378,
0.01975451409816742,
0.023853424936532974,
-0.003149326890707016,
-0.02040720358490944,
0.024180056527256966,
-0.02804846316576004,
0.03709380701184273,
0.008795622736215591,
-0.0203495305031538,
-0.027930108830332756,
0.031198464334011078,
-0.004801296629011631,
0.04763637110590935,
-0.00019757228437811136,
-0.044330570846796036,
0.008120935410261154,
-0.03131716698408127,
0.012462874874472618,
0.0687512531876564,
-0.000659031153190881,
-0.027821235358715057,
-0.03968152403831482,
0.0056455922313034534,
-0.003596264636144042,
-0.008783054538071156,
-0.04247969761490822,
0.013094539754092693,
0.012868456542491913,
-0.01633244939148426,
0.0023222933523356915,
-0.01656993478536606,
0.007383071351796389,
0.0007012765854597092,
0.044991035014390945,
0.06937588006258011,
0.02864951640367508,
-0.018878471106290817,
0.05556415021419525,
-0.020100710913538933,
-0.07391173392534256,
0.010873605497181416,
0.03570236265659332,
-0.0034142406657338142,
-0.030574986711144447,
0.02118726260960102,
-0.02218804694712162,
-0.043629951775074005,
0.0057129524648189545,
-0.004204676952213049,
0.00836588442325592,
-0.020698508247733116,
-0.07397928088903427,
-0.02708323672413826,
-0.011012238450348377,
-0.03932412713766098,
-0.01397146936506033,
-0.08199218660593033,
-0.007533641532063484,
0.018253644928336143,
0.0681188553571701,
0.029384111985564232,
-0.012116494588553905,
-0.014803112484514713,
0.05440899729728699,
0.022472670301795006,
-0.033063579350709915,
-0.04089201241731644,
-0.029893290251493454,
0.00630167406052351,
0.003448483534157276,
-0.02390235848724842,
0.005810628645122051,
0.012093321420252323,
-0.03571454808115959,
-0.009988882578909397,
0.0827251598238945,
-0.008218021132051945,
-0.019926730543375015,
0.007573628332465887,
0.014841032214462757,
-0.042248569428920746,
0.07055018842220306,
0.0013982801465317607,
0.024557512253522873,
0.017640719190239906,
0.00362551212310791,
0.005762157030403614,
-0.0064286133274436,
0.017716029658913612,
0.05636276304721832,
-0.06733790040016174,
0.010153529234230518,
-0.015466190874576569,
0.022322125732898712,
0.007594557013362646,
-0.0034535748418420553,
-0.06047998368740082,
0.021402396261692047,
-0.02949046902358532,
0.004564439877867699,
0.05301065370440483,
-0.007082585711032152,
-0.00378790101967752,
-0.00012566741497721523,
-0.012676483020186424,
0.024539189413189888,
-0.039748892188072205,
0.05910472199320793,
0.025121644139289856,
-0.0023538018576800823,
0.01890600472688675,
-0.020145505666732788,
0.029896419495344162,
-0.04065289348363876,
-0.048543110489845276,
0.0036425527650862932,
0.032343681901693344,
0.011971570551395416,
-0.034831661731004715,
0.03515343740582466,
0.02607899159193039,
0.043150126934051514,
0.00013702496653422713,
0.0004490623832680285,
0.007682591211050749,
-0.03698160871863365,
0.002067006193101406,
-0.06867397576570511,
0.0543547086417675,
0.013610472902655602,
0.0010920754866674542,
0.037529878318309784,
-0.005209438502788544,
-0.02164948545396328,
0.003968123346567154,
-0.0009905423503369093,
0.04781671613454819,
0.05350075662136078,
0.00577775901183486,
0.016048315912485123,
0.06951058655977249,
-0.0035535376518964767,
0.03492026403546333,
-0.02503436990082264,
-0.0348140150308609,
-0.038228653371334076,
0.01550245564430952,
0.07973376661539078,
0.03601305931806564,
-0.0329977311193943,
-0.014631872065365314,
0.06330863386392593,
0.009611680172383785,
0.061663612723350525,
0.016051016747951508,
-0.003856707364320755,
-0.03387913480401039,
0.027886969968676567,
0.0050604878924787045,
-0.004035010002553463,
0.012593108229339123,
0.01880493573844433,
-0.0012883442686870694,
0.011580643244087696,
-0.004025105852633715,
-0.0010916461469605565,
0.04789864271879196,
-0.008883709087967873,
0.02512545883655548,
0.010212980210781097,
-0.010347273200750351,
0.015631558373570442,
-0.050455089658498764,
0.03617100790143013,
0.03113687038421631,
-0.04960469529032707,
0.016620026901364326,
0.005070973187685013,
-0.011698979884386063,
0.03621828183531761,
0.0069138421677052975,
-0.018218284472823143,
-0.010714908130466938,
0.014677675440907478,
-0.01873430237174034,
0.006164988968521357,
0.03989371284842491,
0.015502781607210636,
-0.0005079364054836333,
-0.023102913051843643,
0.0076211560517549515,
-0.014574236236512661,
-0.0009682753589004278,
-0.03201860561966896,
0.01856265217065811,
0.0036039697006344795,
-0.03344150260090828,
0.0023092946503311396,
0.004660794977098703,
-0.037865471094846725,
-0.02866338938474655,
-0.025600336492061615,
-0.02353328838944435,
0.0436163991689682,
-0.02463536523282528,
-0.015845589339733124,
0.030791087076067924,
-0.02332274429500103,
-0.08552706241607666,
0.004140579141676426,
-0.00471094436943531,
0.009655472822487354,
-0.0089412247762084,
0.009749425575137138,
0.054391950368881226,
-0.04300093278288841,
-0.05412764847278595,
0.028955653309822083,
-0.0023178730625659227,
-0.03956549987196922,
-0.02096438594162464,
-0.002128272783011198,
0.02704872563481331,
-0.04015430435538292,
0.05877170339226723,
-0.005601181648671627,
-0.06183828040957451,
-0.005085933022201061,
-0.0652116984128952,
-0.027941204607486725,
0.01166277565062046,
0.016667300835251808,
0.03162837401032448,
-0.006343460641801357,
-0.05192171409726143,
0.05723804980516434,
0.02630087360739708,
-0.03684251755475998,
-0.002813704777508974,
-0.035339828580617905,
0.0006309011369012296,
-0.02435322105884552,
0.012004124000668526,
0.006434573791921139,
-0.03608959913253784,
0.007513101678341627,
-0.045581985265016556,
0.014905675314366817,
0.0518396720290184,
0.04369691014289856,
-0.02769862674176693,
0.032610006630420685,
-0.045609958469867706,
0.03291992098093033,
0.03720321133732796,
-0.008183721452951431,
-0.012025018222630024,
-0.0006868408527225256,
0.014623817056417465,
0.002249816432595253,
0.025399893522262573,
-0.045193396508693695,
0.013278273865580559,
-0.004303643014281988,
-0.0068921372294425964,
-0.028418703004717827,
0.04177695885300636,
-0.015333760529756546,
-0.012526758946478367,
0.00850352831184864,
0.05273672193288803,
0.04824169725179672,
0.009763720445334911,
0.014695321209728718,
0.01370028406381607,
0.037445053458213806,
0.008089879527688026,
-0.040292851626873016,
-0.020826855674386024,
0.02982981875538826,
0.026647647842764854,
-0.030077649280428886,
-0.03825850784778595,
0.03263960778713226,
0.04590114951133728,
0.048356492072343826,
0.018609724938869476,
0.008491791784763336,
-0.023641612380743027,
-0.04579426720738411,
-0.027944514527916908,
-0.010512217879295349,
0.06572966277599335,
0.037365589290857315,
0.051825717091560364,
0.008011830039322376,
0.007918753661215305,
0.03133973106741905,
-0.006515554618090391,
-0.06664269417524338,
0.035884205251932144,
-0.0009624575031921268,
0.0035883993841707706,
-0.021988846361637115,
0.026181660592556,
0.008094221353530884,
-0.0013693871442228556,
-0.012785890139639378,
-0.018917793408036232,
0.02033875696361065,
-0.06552797555923462,
-0.005489025730639696,
0.002145889215171337,
-0.004730761982500553,
-0.02747173234820366,
0.08266740292310715,
0.02456081099808216,
-0.05660620704293251,
-0.013283113949000835,
0.04029969871044159,
-0.06544700264930725,
0.003996734973043203,
0.021550048142671585,
-0.016524873673915863,
0.008632997050881386,
-0.000975785544142127,
0.02218635194003582,
0.024010181427001953,
0.020227620378136635,
0.005112455226480961,
0.0029766177758574486,
0.027111535891890526,
0.008232352323830128,
-0.006029738113284111,
-0.03140037879347801,
-0.021341558545827866,
0.017829718068242073,
0.0007440754561685026,
0.0824340209364891,
-0.04208039492368698,
0.01876988634467125,
0.021071571856737137,
0.018830474466085434,
-0.01410711370408535,
0.050963304936885834,
0.04064398258924484,
-0.0193778183311224,
-0.010276665911078453,
-0.050434693694114685,
0.048190947622060776,
-0.04076811298727989,
-0.03137102350592613,
0.0017222441965714097,
-0.012165907770395279,
-0.013974307104945183,
-0.006155757699161768,
-0.000436204019933939,
0.005439344793558121,
0.02040468156337738,
-0.00742673221975565,
0.03681252524256706,
-0.027860961854457855,
0.01061189640313387,
-0.026669280603528023,
0.0034564172383397818,
-0.00594406109303236,
0.061964962631464005,
0.014437364414334297,
0.017206508666276932,
-0.09641296416521072,
-0.027382759377360344,
0.028167378157377243,
0.03156336396932602,
0.04011549428105354,
-0.02641015499830246,
-0.04351939260959625,
0.006712886039167643,
0.024317044764757156,
-0.04099864512681961,
0.019305909052491188,
0.014963176101446152,
0.000058660829381551594,
-0.018929418176412582,
-0.061199117451906204,
-0.03461431711912155,
0.013670778833329678,
-0.015427281148731709,
0.04084758833050728,
-0.033510226756334305,
-0.008783220313489437,
0.015004142187535763,
0.053174618631601334,
0.023884037509560585,
0.03475340083241463,
-0.0005060131079517305,
-0.02531045861542225,
-0.011038480326533318,
0.035764180123806,
-0.04014432802796364,
-0.07387302070856094,
-0.023344090208411217,
0.009235261008143425,
0.013878533616662025,
0.037311770021915436,
-0.05520527809858322,
-0.04671328887343407,
0.031752828508615494,
0.011726468801498413,
0.023277344182133675,
0.006861527916043997,
-0.011817893013358116,
0.06958550214767456,
0.023434195667505264,
0.031149638816714287,
0.06942835450172424,
0.06796140968799591,
-0.020544905215501785,
-0.002972311107441783,
-0.013996131718158722,
0.04767776280641556,
-0.044468704611063004,
0.009249485097825527,
-0.0017285445937886834,
0.00992577988654375,
-0.028977861627936363,
0.05934673175215721,
-0.03031201846897602,
0.014886852353811264,
-0.014575526118278503,
-0.022796520963311195,
0.014007164165377617,
0.010988320223987103,
0.015790624544024467,
-0.0007699443376623094,
-0.0018035229295492172,
0.0016042746137827635,
0.003404374234378338,
-0.019868958741426468,
-0.004622281063348055,
-0.0052674091421067715,
-0.011114307679235935,
0.037744659930467606,
0.004038369748741388,
0.021682102233171463,
-0.020254014059901237,
-0.025093117728829384,
-0.013030226342380047,
-0.03122473694384098,
-0.007470266427844763,
-0.023764969781041145,
0.043340668082237244,
0.007875635288655758,
-0.05968856438994408,
-0.037789762020111084,
-0.004930450581014156,
0.014133041724562645,
0.036320678889751434,
-0.028814662247896194,
-0.02116924524307251,
0.021470986306667328,
0.014639911241829395,
-0.055672962218523026,
-0.06851694732904434,
0.03203236684203148,
0.03170112147927284,
-0.012978221289813519,
-0.072272390127182,
0.007928701117634773,
-0.043887365609407425,
0.007336679846048355,
0.028757406398653984,
0.022511962801218033,
-0.011127709411084652,
0.015205007046461105,
-0.003227310488000512,
0.02902567945420742,
0.020801739767193794,
-0.006427566520869732,
-0.005027626175433397,
0.0276953037828207,
0.006509609520435333,
-0.029013657942414284,
-0.03009651042521,
0.04341668263077736,
-0.029776515439152718,
-0.007199572399258614,
-0.0054062120616436005,
0.016436150297522545,
0.041544172912836075,
-0.025588829070329666,
-0.029085082933306694,
0.06121981889009476,
0.007661113515496254,
0.004896948579698801,
-0.030574044212698936,
0.006989576388150454,
0.001003405312076211,
0.016458818688988686,
-0.010134085081517696,
-0.008842174895107746,
-0.08016274124383926,
0.012886024080216885,
-0.019894180819392204,
-0.004921238869428635,
0.0051213777624070644,
-0.021698927506804466,
0.04472004622220993,
-0.023305391892790794,
0.006142188794910908,
0.014694670215249062,
-0.0078063528053462505,
0.006671539507806301,
-0.01910116709768772,
-0.004370226990431547,
0.016337502747774124,
0.02691621705889702,
-0.039259057492017746,
-0.03619709610939026,
-0.044194772839546204,
0.006337362341582775,
0.05825478211045265,
-0.023059066385030746,
0.06593812257051468,
0.030514277517795563,
0.01794702373445034,
-0.0024617407470941544,
0.002526405965909362,
-0.031224144622683525,
0.031744252890348434,
-0.03840535506606102,
0.011008566245436668,
-0.0022513195872306824,
-0.007770134601742029,
0.03531505912542343,
0.02402094565331936,
-0.04186522215604782,
0.023158477619290352,
0.0008787778206169605,
0.05514213442802429,
0.04089640825986862,
-0.031897179782390594,
-0.05196814611554146,
0.025403035804629326,
-0.028137363493442535,
0.025849785655736923,
0.003202765015885234,
-0.01883673667907715,
0.06464064121246338,
0.0473942831158638,
-0.008506431244313717,
-0.006807432044297457,
0.017571093514561653,
-0.016722023487091064,
-0.0034759005066007376,
0.022440800443291664,
-0.0028449962846934795,
0.03567606210708618,
0.04748784750699997,
0.03232141584157944,
0.006251661106944084,
-0.00440550921484828,
0.0444817990064621,
-0.049173932522535324,
-0.002754425397142768,
-0.03087950311601162,
-0.03685193881392479,
0.026366442441940308,
0.007401136681437492,
-0.0034089491236954927,
0.016583649441599846,
-0.010238721035420895,
0.028398199006915092,
0.018679065629839897,
0.0005783938686363399,
-0.026961645111441612,
0.09676588326692581,
-0.0028230163734406233,
0.03341852128505707,
-0.02466537058353424,
0.0072898161597549915,
0.09007657319307327,
0.06727807968854904,
0.041380103677511215,
-0.053789183497428894,
0.012504450976848602,
-0.06786522269248962,
0.01141232531517744,
-0.06011338531970978,
-0.0012690969742834568,
-0.040739212185144424,
-0.025012696161866188,
0.015049192123115063,
0.06078526750206947,
0.025998717173933983,
-0.05249805003404617,
0.0196673646569252,
-0.01967255212366581,
0.011575142852962017,
0.058194879442453384,
0.008088015019893646,
-0.016258802264928818,
-0.018055882304906845,
-0.04038619250059128,
0.03777112439274788,
-0.050087276846170425,
-0.0005897172377444804,
-0.043769702315330505,
-0.06820081174373627,
0.03483553230762482,
-0.03277428448200226,
-0.04514121264219284,
-0.009106622077524662,
-0.01163217332214117,
0.00943352747708559,
-0.01379087008535862,
0.0066873859614133835,
0.03585698455572128,
0.018067926168441772,
0.03327597677707672,
0.04386904463171959,
0.03174798563122749,
0.037023816257715225,
-0.011754925362765789,
0.008759358897805214,
-0.030430741608142853,
-0.048747021704912186,
-0.055420927703380585,
0.0790773332118988,
0.006450041197240353,
-0.013339526951313019,
0.022047435864806175,
0.0048230173997581005,
-0.0027510938234627247,
-0.06265491992235184,
-0.018747501075267792,
-0.029486805200576782,
0.019565477967262268,
-0.02085920050740242,
0.004952409770339727,
-0.038386017084121704,
0.02230081893503666,
0.011648252606391907,
0.006241144612431526,
-0.020448477938771248,
-0.004561031702905893,
0.021850677207112312,
0.013944663107395172,
0.05342395231127739,
-0.005308032035827637,
-0.043446134775877,
0.008221269585192204,
-0.03645111247897148,
-0.008575857616961002,
-0.02150113694369793,
-0.0070170569233596325,
0.022880150005221367,
0.01469491608440876,
-0.007772400509566069,
-0.028957687318325043,
-0.03635242581367493,
-0.1173042431473732,
0.02585657685995102,
-0.0016841518227010965,
-0.01971047930419445,
0.003395789535716176,
0.0008530821069143713,
0.02442013844847679,
0.03356911987066269,
-0.0004283322487026453,
0.022420108318328857,
0.014685538597404957,
0.014727957546710968,
0.02277965471148491,
-0.029360221698880196,
-0.033636342734098434,
-0.0009798890678212047,
0.00781545415520668,
0.013486862182617188,
-0.028972579166293144,
0.004221623297780752,
-0.019733674824237823,
0.011351739056408405,
0.014332001097500324,
0.04881883040070534,
-0.019745908677577972,
-0.0009839064441621304,
-0.026236386969685555,
-0.01765093393623829,
-0.007433577440679073,
-0.0007907436811365187,
-0.010598639957606792,
-0.03790866211056709,
-0.008890599943697453,
-0.003109790850430727,
0.03416754677891731,
-0.026245592162013054,
0.00745994271710515,
-0.015085681341588497,
-0.018048705533146858,
-0.03460092842578888,
0.010575849562883377,
-0.01630503498017788,
-0.0006176914903335273,
-0.005969593301415443,
0.011885291896760464,
-0.031010104343295097,
-0.005058459006249905,
-0.025870641693472862,
0.039338983595371246,
-0.043151240795850754,
-0.0227828286588192,
0.024148570373654366,
0.02568415366113186,
-0.01837901584804058,
-0.0011678128503262997,
0.002178919268772006,
-0.005003250669687986,
0.06106320023536682,
-0.006845836527645588,
-0.016758689656853676,
0.028953343629837036,
-0.04532172903418541,
-0.05818013474345207,
0.052200812846422195,
0.013702724128961563,
0.007391124032437801,
0.05062935873866081,
-0.0017415779875591397,
-0.03305160626769066,
0.041945528239011765,
-0.007666612509638071,
0.012097925879061222,
0.020980874076485634,
-0.04540807381272316,
-0.012908084318041801,
-0.012129893526434898,
-0.00345537974499166,
-0.0055389972403645515,
-0.0015850741183385253,
0.03148878738284111,
0.0061604296788573265,
-0.029951928183436394,
0.010378667153418064,
0.03904044255614281,
0.018477102741599083,
-0.011334951035678387,
0.047480639070272446,
0.007535441312938929,
0.03397105261683464,
0.07026569545269012,
0.012972209602594376,
0.008030813187360764,
-0.002225459087640047,
-0.0054457648657262325,
-0.11288707703351974,
-0.010763970203697681,
-0.03817681223154068,
0.03283463791012764,
0.06403928250074387,
-0.06578812748193741,
0.0076300580985844135,
0.013971245847642422,
-0.06735138595104218,
0.012424902059137821,
-0.004782965872436762,
-0.0009226977126672864,
-0.007551757153123617,
-0.01063130609691143,
-0.02498481422662735,
0.014883173629641533,
0.021599112078547478,
0.021545592695474625,
0.02498205564916134,
0.027656560763716698,
-0.0023740227334201336,
-0.05115187168121338,
-0.022812895476818085,
0.05336156487464905,
0.005807384382933378,
0.005723654758185148,
0.0387914776802063,
-0.023035436868667603,
-0.02136700041592121,
0.005599739030003548,
0.004394595045596361,
-0.02094237506389618,
-0.02420303225517273,
0.014356176368892193,
-0.008105347864329815,
0.05686626210808754,
0.0009684932301752269,
-0.004934897180646658,
0.010314167477190495,
-0.008695363067090511,
0.01992684230208397,
-0.026212645694613457,
-0.020899837836623192,
-0.0013722314033657312,
0.013345703482627869,
-0.012595660984516144,
-0.03969154506921768,
0.04988512769341469,
0.010581635870039463,
-0.007134706247597933,
0.01631859503686428,
-0.008981229737401009,
0.005800467915832996,
-0.0341506265103817,
0.0059542786329984665,
-0.0756300613284111,
-0.026018114760518074,
0.035650648176670074,
-0.022086089476943016,
0.004648726899176836,
-0.0012199663324281573,
-0.005683028604835272,
-0.050924573093652725,
0.050487734377384186,
0.019267158582806587,
-0.029878081753849983,
-0.052383702248334885,
-0.02431408502161503,
0.03203427419066429,
-0.007017672061920166,
0.007306427229195833,
-0.029107391834259033,
-0.051228977739810944,
0.01127570029348135,
0.0029284642077982426,
-0.011284570209681988,
-0.0010201099794358015,
-0.01316903904080391,
-0.017509151250123978,
-0.0501185841858387,
0.0070874341763556,
0.019724130630493164,
-0.07177270203828812,
-0.020754899829626083,
-0.02980402670800686,
-0.00860209297388792,
0.009824837557971478,
0.030637593939900398,
-0.01426005270332098,
-0.04355348274111748,
-0.005535925272852182,
-0.020016323775053024,
0.04277251660823822,
-0.06907468289136887,
0.01568957045674324,
0.00803831871598959,
-0.0022534134332090616,
0.017552973702549934,
0.007823687046766281,
-0.006256989669054747,
0.011141232214868069,
0.00966060720384121,
-0.012559227645397186,
0.0039969198405742645,
-0.0017586905742064118,
-0.0057099987752735615,
0.023171840235590935,
-0.018577929586172104,
-0.0033088410273194313,
0.041060108691453934,
-0.035776615142822266,
0.0050826845690608025,
0.006806318648159504,
-0.016945913434028625,
-0.017062176018953323,
-0.005711853038519621,
-0.04798777773976326,
-0.006319325417280197,
-0.019031371921300888,
0.009610013104975224,
0.050460100173950195,
-0.04149637743830681,
-0.05055869743227959,
0.03633275628089905,
-0.026172850281000137,
-0.0005149391945451498,
0.07734561711549759,
-0.001601366326212883,
0.014641130343079567,
0.029994674026966095,
0.04039369896054268,
0.014007402583956718,
0.028467506170272827,
-0.0016593232285231352,
0.0003016167029272765,
0.03712121769785881,
-0.03189900517463684,
0.04726637899875641,
0.02301863767206669,
-0.019798897206783295,
-0.01578054390847683,
0.018659930676221848,
-0.0027551068924367428,
-0.0528767928481102,
-0.02973821759223938,
0.008402124047279358,
0.013325260952115059,
-0.0062721786089241505,
0.008459864184260368,
-0.036479320377111435,
0.07426320761442184,
-0.004306083545088768,
0.007164412643760443,
0.0032992714550346136,
-0.030835885554552078,
-0.02415999211370945,
0.036186061799526215,
0.038698527961969376,
0.05082351341843605,
-0.034918561577796936,
0.020570123568177223,
-0.002789122052490711,
0.010569466277956963,
-0.003384961746633053,
-0.058437250554561615,
0.003755448153242469,
0.004395090974867344,
-0.013632583431899548,
-0.032421670854091644,
0.00865834392607212,
-0.01314090471714735,
-0.03913067281246185,
-0.0075358739122748375,
0.0306593906134367,
0.0545228086411953,
-0.0035374935250729322,
0.015412554144859314,
-0.01357576809823513,
0.05713203549385071,
-0.05780628323554993,
0.007123582996428013,
0.0009322017431259155,
0.036919593811035156,
0.015153542160987854,
0.04096805304288864
] |
<p>I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, while he said that they are different, and he said he supplied a proof showing otherwise.</p>
<p>He didn't say whether or not the cars are the same mass, but I assumed they were. To state it more clearly, in the first instance each car is traveling at 50mph in the opposite direction and they collide with each other. In the second scenario, a car travels at 100 mph and crashes into a brick wall. Which one is "worse"?</p>
<p>When I first heard it, I thought, "of course they're the same!" But then I took a step back and thought about it again. It seems like in the first scenario the total energy of the system is the KE of the two cars, or $\frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. In the second scenario, it's the KE of the car plus wall, which is $\frac{1}{2}m(2v)^2 + 0 = 2mv^2$. So the car crashing into the wall has to absorb (and dissipate via heat) twice as much energy, so crashing into the wall is in fact worse.</p>
<p>Is this correct?</p>
<p>To clarify, I'm not concerned with the difference between a wall and a car, and I don't think that's what the question is getting at. Imagine instead that in the second scenario, a car is crashing at 100mph into the same car sitting there at 0mph (with it's brakes on of course). First scenario is the same, two of the same cars going 50mph in opposite directions collide. Are those two situations identical?</p> | 58 | [
-0.04299153760075569,
-0.012026566080749035,
-0.023677058517932892,
0.0005112664075568318,
0.01660134270787239,
-0.012323609553277493,
-0.0018770333845168352,
-0.03240969032049179,
0.0074528297409415245,
0.01990087889134884,
0.0065885488875210285,
0.045607440173625946,
0.04775315523147583,
0.024775182828307152,
0.03297116234898567,
0.035151246935129166,
-0.012817701324820518,
-0.029499288648366928,
0.011996163986623287,
-0.0119323106482625,
-0.027687223628163338,
0.002030613599345088,
0.03532755374908447,
0.0015100898453965783,
-0.051484253257513046,
0.0300920270383358,
0.023777520284056664,
-0.015111254528164864,
-0.002957927528768778,
0.013600015081465244,
0.022336088120937347,
-0.017270836979150772,
0.006319127976894379,
0.03418741002678871,
0.010884386487305164,
0.02485942654311657,
-0.01740972325205803,
-0.009512913413345814,
-0.05329044908285141,
0.023167701438069344,
-0.02208103984594345,
-0.04478764906525612,
0.009362159296870232,
0.060915421694517136,
-0.03957543149590492,
-0.00672311382368207,
0.028269905596971512,
-0.05422360077500343,
-0.0036195507273077965,
-0.0604628250002861,
0.08515439182519913,
0.0015933412360027432,
0.032149139791727066,
0.026234159246087074,
-0.011898833326995373,
-0.017847521230578423,
0.0252709798514843,
0.07007922232151031,
-0.019262729212641716,
-0.03959651291370392,
-0.020088965073227882,
0.011703775264322758,
-0.028800738975405693,
0.00866058561950922,
-0.013661525212228298,
0.03390517458319664,
-0.025999028235673904,
-0.03848432004451752,
0.046899616718292236,
0.010230325162410736,
0.009320961311459541,
-0.009760363958775997,
0.04101772606372833,
-0.0005458644591271877,
0.031965699046850204,
-0.008029207587242126,
0.022406991571187973,
0.029798069968819618,
0.07342316955327988,
0.022218801081180573,
-0.015903590247035027,
-0.005730634089559317,
0.0766075849533081,
0.10488686710596085,
0.025819329544901848,
-0.022663628682494164,
0.05854923278093338,
0.0015644796658307314,
0.026126835495233536,
0.03127799555659294,
0.021217232570052147,
0.011648798361420631,
0.01676734909415245,
-0.017526809126138687,
0.021986771374940872,
0.03645700961351395,
0.024750636890530586,
0.05751868337392807,
0.030010109767317772,
0.015475590713322163,
-0.019038226455450058,
0.012759107165038586,
0.009069640189409256,
0.04075424373149872,
0.05476134642958641,
-0.011042519472539425,
-0.0185691025108099,
0.006931661628186703,
-0.01994706504046917,
0.006105121225118637,
-0.025454552844166756,
0.031708672642707825,
-0.005726470611989498,
0.014009900391101837,
-0.0022188317961990833,
-0.00584001699462533,
0.011372181586921215,
-0.017061816528439522,
0.03509168699383736,
0.004817462991923094,
0.04366106539964676,
-0.03116009011864662,
0.02259327657520771,
-0.0504479855298996,
-0.06441059708595276,
0.02335122972726822,
0.025268111377954483,
-0.001616062130779028,
-0.05654069408774376,
0.031107207760214806,
0.023694878444075584,
0.008757101371884346,
-0.02268972434103489,
-0.03284476324915886,
0.03334280475974083,
-0.029454724863171577,
-0.06257360428571701,
-0.05975445732474327,
0.02993694692850113,
0.043516140431165695,
-0.043083593249320984,
-0.07241977006196976,
-0.030438965186476707,
0.004791774787008762,
0.07397635281085968,
0.019115304574370384,
0.034151945263147354,
0.03599962219595909,
0.02951357513666153,
0.007632283493876457,
0.00931606162339449,
-0.027623038738965988,
-0.02661152184009552,
-0.03313459828495979,
0.028309544548392296,
-0.055840373039245605,
0.005013859365135431,
0.037502773106098175,
-0.019377775490283966,
0.013569435104727745,
0.05650784447789192,
-0.012063894420862198,
-0.03658077120780945,
0.02723175473511219,
-0.01198351290076971,
0.002399176126345992,
0.05172538012266159,
0.010960225015878677,
0.0116188395768404,
0.018417147919535637,
0.06490539759397507,
0.014264741912484169,
-0.023810233920812607,
0.010627144016325474,
0.05231175944209099,
-0.0355168953537941,
-0.0070587266236543655,
-0.05326651781797409,
0.01932164840400219,
-0.0021118526346981525,
-0.04679993540048599,
-0.03853680193424225,
0.01716044545173645,
-0.012971434742212296,
-0.0070571741089224815,
0.025326892733573914,
0.0003011581429746002,
0.0003024755569640547,
0.02158309891819954,
0.0015763933770358562,
-0.054162971675395966,
-0.07103276252746582,
0.026128139346837997,
0.006261983886361122,
-0.004763544537127018,
0.012608882039785385,
-0.016341784968972206,
0.021475888788700104,
-0.04199974238872528,
-0.021344589069485664,
0.022772323340177536,
0.020544221624732018,
-0.010831122286617756,
-0.017174813896417618,
-0.0006010898505337536,
0.04425942897796631,
0.02765624038875103,
-0.011539386585354805,
-0.00620891060680151,
-0.04551060125231743,
-0.025474466383457184,
0.02310270071029663,
-0.03181931748986244,
0.014901326037943363,
0.0020363295916467905,
-0.0216820165514946,
0.046568796038627625,
-0.033416472375392914,
0.012234780006110668,
0.0348396860063076,
-0.06363570690155029,
0.080780990421772,
0.037327393889427185,
0.024701585993170738,
-0.009985582903027534,
0.035615116357803345,
-0.004072218202054501,
0.009463242255151272,
-0.035608142614364624,
-0.026458118110895157,
-0.024917729198932648,
0.0258713960647583,
0.023362480103969574,
0.006884891539812088,
-0.04141376167535782,
0.0008134415838867426,
0.04568206146359444,
0.033790819346904755,
0.02260151132941246,
-0.007747085765004158,
0.02074064128100872,
-0.03195936977863312,
0.03619002550840378,
0.013790824450552464,
-0.007030046544969082,
0.0013457894092425704,
0.03213824704289436,
-0.011386575177311897,
-0.012382686138153076,
-0.0021504550240933895,
-0.02203258126974106,
0.03681115061044693,
0.005221082828938961,
0.03429584577679634,
0.023588670417666435,
-0.00791155081242323,
0.005123376380652189,
-0.05162963643670082,
0.016126105561852455,
0.038665395230054855,
-0.011463268660008907,
-0.026085475459694862,
-0.031137894839048386,
0.009510727599263191,
-0.015408575534820557,
0.011708341538906097,
-0.013262040913105011,
0.011649603955447674,
0.03365158662199974,
-0.016556553542613983,
0.003986085299402475,
0.039210014045238495,
-0.01967676542699337,
-0.005908909719437361,
-0.007902728393673897,
0.024420127272605896,
-0.03915715962648392,
0.012183806858956814,
-0.06509917229413986,
0.0010216445662081242,
-0.018253490328788757,
-0.039945073425769806,
-0.002585239475592971,
0.014598512090742588,
-0.04380073398351669,
0.05470858886837959,
-0.06203179061412811,
-0.04065300151705742,
0.04992227628827095,
-0.004500593524426222,
-0.009710106998682022,
0.052414994686841965,
0.004446426406502724,
-0.033265188336372375,
-0.02060205116868019,
-0.014622046612203121,
-0.009907854720950127,
-0.042516376823186874,
-0.01625099405646324,
0.04802802577614784,
-0.008558684028685093,
-0.07228650897741318,
-0.0019492564024403691,
-0.05224126949906349,
-0.04402640834450722,
-0.02011221833527088,
-0.04909200593829155,
0.0331866554915905,
-0.013307529501616955,
-0.013258906081318855,
0.042620692402124405,
-0.021786825731396675,
-0.02129223756492138,
-0.03423000127077103,
-0.050362780690193176,
-0.001200157799758017,
-0.01921708695590496,
0.04063338413834572,
-0.012240375392138958,
-0.0018974512349814177,
0.05894671380519867,
0.026325859129428864,
-0.011730145663022995,
-0.028968866914510727,
-0.0051285880617797375,
-0.006661023013293743,
-0.013947688043117523,
-0.03295835480093956,
0.05275280401110649,
-0.02407442405819893,
0.019172415137290955,
0.011068884283304214,
0.04883074387907982,
0.03790108487010002,
0.0027866242453455925,
-0.019033463671803474,
-0.01459062471985817,
0.004948848392814398,
0.003812901210039854,
0.05489499866962433,
0.013445178978145123,
-0.038508426398038864,
0.062485963106155396,
0.0035801040939986706,
0.040206510573625565,
0.004053039941936731,
-0.041814934462308884,
0.07507485896348953,
-0.003816476557403803,
0.009827723726630211,
-0.07654671370983124,
0.02824433147907257,
-0.007662740536034107,
0.03248264268040657,
-0.009803739376366138,
0.010313840582966805,
0.02748360112309456,
-0.03780745342373848,
0.04039264842867851,
0.016864528879523277,
0.041344184428453445,
-0.011516692116856575,
-0.0540044791996479,
-0.015616318210959435,
0.004431779496371746,
0.007861357182264328,
-0.00754626514390111,
-0.026922695338726044,
0.04220045357942581,
0.037364132702350616,
0.04044955596327782,
0.008802867494523525,
-0.022265348583459854,
-0.0006237429333850741,
-0.05625174194574356,
-0.05727967247366905,
0.008007144555449486,
0.04846253618597984,
-0.001465711509808898,
0.015027863904833794,
-0.021923094987869263,
-0.005144620314240456,
0.013838464394211769,
-0.023544035851955414,
-0.07251247763633728,
0.025641564279794693,
-0.01881667971611023,
-0.030083002522587776,
0.029783528298139572,
-0.036642592400312424,
0.030671516433358192,
-0.039370983839035034,
0.018656160682439804,
0.007122677750885487,
0.010274436324834824,
-0.05140599608421326,
-0.0002841668901965022,
-0.04818743094801903,
-0.0593048557639122,
0.017910435795783997,
0.023220257833600044,
0.029510628432035446,
-0.02274034358561039,
0.012357188388705254,
0.04848785698413849,
-0.017494389787316322,
0.010471462272107601,
-0.0048080142587423325,
0.012875301763415337,
0.027205154299736023,
0.023717353120446205,
-0.0088527025654912,
0.005541363265365362,
0.0168386809527874,
0.015158434398472309,
0.02755669504404068,
0.016816643998026848,
-0.014045785181224346,
-0.030060376971960068,
-0.02432846464216709,
-0.03565847501158714,
-0.020914487540721893,
-0.05661119893193245,
0.03339012339711189,
-0.011180671863257885,
-0.008010162971913815,
-0.00421622721478343,
0.06546521186828613,
0.021503904834389687,
0.05199875682592392,
0.036927804350852966,
0.008526487275958061,
0.006354139652103186,
-0.0625804215669632,
-0.04115574434399605,
-0.032115332782268524,
-0.011167451739311218,
0.013521667569875717,
-0.03545062988996506,
-0.011217651888728142,
-0.0023870051372796297,
0.03367597982287407,
0.014589868485927582,
-0.014912884682416916,
0.009670578874647617,
-0.022395767271518707,
-0.011775359511375427,
0.006567324511706829,
-0.014432069845497608,
-0.027265435084700584,
0.026734385639429092,
0.009535636752843857,
0.021035587415099144,
-0.02102750353515148,
-0.06776855140924454,
-0.00009644487727200612,
0.0031675207428634167,
0.043525371700525284,
-0.026912473142147064,
-0.007142931222915649,
-0.003057316644117236,
-0.0009170087869279087,
0.038298100233078,
-0.018183749169111252,
0.03382306545972824,
0.008997196331620216,
0.038880232721567154,
-0.017223963513970375,
-0.02797786332666874,
0.00934460386633873,
-0.014460026286542416,
-0.009734648279845715,
0.03785177320241928,
0.022960804402828217,
-0.015003505162894726,
-0.013876122422516346,
0.0016915820306167006,
0.0284561887383461,
0.011955219320952892,
-0.020689718425273895,
-0.008347286842763424,
-0.03164980188012123,
0.02090352028608322,
-0.04125871881842613,
-0.0895034670829773,
-0.024709058925509453,
-0.005721277091652155,
-0.03448956087231636,
0.019644038751721382,
-0.0410408079624176,
0.004192824941128492,
0.03879915550351143,
-0.023644816130399704,
-0.005020649638026953,
0.016892435029149055,
-0.012577859684824944,
0.04557625949382782,
0.027191320434212685,
0.03260955214500427,
0.05449294298887253,
0.017926037311553955,
0.014161174185574055,
0.015709780156612396,
-0.011314627714455128,
0.024146584793925285,
-0.058705564588308334,
-0.017624275758862495,
-0.03041381575167179,
-0.010087755508720875,
-0.019757429137825966,
0.02083422616124153,
0.022456131875514984,
0.07929467409849167,
-0.04531810060143471,
-0.0682755559682846,
0.002582055516541004,
0.009627949446439743,
-0.006129122339189053,
-0.0048037138767540455,
-0.02183874137699604,
0.013003897853195667,
-0.0007358082220889628,
-0.042848873883485794,
0.01113789901137352,
0.01602424494922161,
-0.026038724929094315,
0.025097321718931198,
-0.03693987429141998,
0.0365724042057991,
-0.03974808007478714,
-0.022442039102315903,
0.02279786765575409,
-0.021345429122447968,
0.04822072386741638,
-0.02621801756322384,
-0.007360341027379036,
0.008111018687486649,
-0.031019385904073715,
-0.007512861862778664,
0.0026471619494259357,
-0.011159014888107777,
0.021423786878585815,
-0.017071999609470367,
0.023295413702726364,
0.027936793863773346,
-0.005293229129165411,
-0.06488196551799774,
-0.015367185696959496,
0.015682850033044815,
-0.021163588389754295,
-0.013691218569874763,
-0.0025656449142843485,
-0.021632300689816475,
-0.027876611799001694,
-0.04812813922762871,
0.0035399282351136208,
0.047072622925043106,
0.0009378786780871451,
-0.0018026325851678848,
-0.011645945720374584,
0.01540807168930769,
0.02286396361887455,
-0.000010200604265264701,
-0.02225540205836296,
-0.01325528509914875,
-0.038557060062885284,
-0.03203177452087402,
-0.009603523649275303,
0.0662902221083641,
-0.02493002638220787,
0.031491927802562714,
0.008306341245770454,
-0.03245148807764053,
0.05365325137972832,
0.02031955122947693,
0.024918068200349808,
0.07280264049768448,
0.015233886428177357,
-0.011512374505400658,
-0.011117052286863327,
0.0564873106777668,
0.0014698628801852465,
0.019516129046678543,
0.004931091796606779,
-0.006421899888664484,
-0.026572642847895622,
-0.03436228632926941,
0.0200563482940197,
0.011467467062175274,
0.013743753544986248,
0.014198245480656624,
0.08024270832538605,
-0.0026940691750496626,
0.001272596069611609,
-0.006330747622996569,
-0.029655249789357185,
0.041640520095825195,
-0.025447996333241463,
0.018099861219525337,
0.016413073986768723,
0.008113057352602482,
-0.01968401111662388,
-0.024810515344142914,
-0.04844796657562256,
0.028893308714032173,
0.027184046804904938,
-0.035790927708148956,
0.05541288107633591,
0.002707980340346694,
-0.0021637273021042347,
0.03001023642718792,
-0.051924705505371094,
0.00101481971796602,
0.018430473282933235,
0.007676522713154554,
0.033798448741436005,
-0.04214882478117943,
-0.010198337025940418,
0.06213026121258736,
0.0419069305062294,
-0.007329256739467382,
-0.004751336295157671,
0.01724110171198845,
0.030880706384778023,
0.02973005920648575,
-0.027018552646040916,
0.00405379431322217,
0.03372134268283844,
-0.027311505749821663,
0.011480897665023804,
-0.05361759662628174,
-0.03064817003905773,
0.061468273401260376,
0.0163169726729393,
-0.012999244034290314,
-0.06812935322523117,
0.0019007312366738915,
-0.05567535385489464,
0.04675862565636635,
-0.001124854665249586,
0.00012869400961790234,
0.019132137298583984,
-0.00008898178930394351,
0.02169671840965748,
0.03920683264732361,
0.004428209736943245,
-0.011166165582835674,
-0.03825129568576813,
-0.009766935370862484,
-0.019141774624586105,
-0.026507668197155,
0.005710619501769543,
0.019563809037208557,
0.015419693663716316,
0.05081680789589882,
-0.07162050902843475,
-0.002724157180637121,
-0.004309401381760836,
0.004644552245736122,
0.019756857305765152,
0.06592843681573868,
0.0015408910112455487,
0.04552517831325531,
-0.0354396253824234,
0.0036545898765325546,
0.10117281973361969,
0.03302163630723953,
0.024822872132062912,
0.00831031147390604,
0.025560127571225166,
0.008068905211985111,
0.013453909195959568,
-0.037748660892248154,
0.033333342522382736,
-0.004373140167444944,
0.013309543952345848,
0.03599168360233307,
0.09538639336824417,
-0.003443019697442651,
-0.01955193467438221,
0.01830754615366459,
-0.009565160609781742,
-0.014040679670870304,
-0.018039776012301445,
0.03431721404194832,
0.022402334958314896,
0.000599313119892031,
0.0036676593590527773,
0.02022186852991581,
-0.01188745815306902,
0.042915403842926025,
-0.0011404334800317883,
-0.04631160572171211,
0.013358783908188343,
-0.001547789666801691,
-0.040448401123285294,
0.03140636160969734,
0.010160286910831928,
-0.02677234448492527,
-0.04196939244866371,
0.021562965586781502,
0.0441662035882473,
-0.0008977739489637315,
0.010995176620781422,
0.02075684815645218,
0.03543975204229355,
0.02065012976527214,
-0.008827063255012035,
0.01341888215392828,
-0.05883816257119179,
0.021329693496227264,
-0.05523841455578804,
0.03489138185977936,
-0.005330472718924284,
0.016713537275791168,
0.00393128814175725,
-0.01014732662588358,
0.0018161397892981768,
-0.018277563154697418,
-0.029025064781308174,
-0.008848615922033787,
0.049744851887226105,
0.006751498207449913,
0.0027417554520070553,
-0.03854828327894211,
0.05311200022697449,
0.0013294025557115674,
0.0025058258324861526,
0.04622712358832359,
-0.014166200533509254,
-0.03171490132808685,
0.010763305239379406,
0.08847305923700333,
-0.021970201283693314,
-0.0027142807375639677,
-0.023071106523275375,
-0.035547807812690735,
-0.04591849073767662,
-0.04556969553232193,
-0.01177151221781969,
0.03689003735780716,
0.07144381105899811,
-0.006685274187475443,
0.0044156634248793125,
-0.04191267862915993,
-0.03741598129272461,
0.020408323034644127,
0.007291861809790134,
0.0008228219812735915,
-0.03423226252198219,
-0.012301157228648663,
0.0012429055059328675,
0.018938256427645683,
-0.05253974720835686,
-0.004835464060306549,
0.025512635707855225,
0.030079690739512444,
-0.01484064944088459,
-0.029278365895152092,
-0.023272110149264336,
-0.0037330943159759045,
-0.04660408943891525,
0.03509242460131645,
-0.033085718750953674,
-0.0037300216499716043,
-0.02394404262304306,
-0.014472832903265953,
0.024483438581228256,
0.045185696333646774,
0.002759245689958334,
-0.00680262828245759,
0.021210838109254837,
-0.06280699372291565,
-0.023002255707979202,
0.027141284197568893,
0.03269081562757492,
-0.01040093693882227,
-0.017831280827522278,
-0.012984160333871841,
-0.01048960629850626,
-0.03528441861271858,
0.02967849373817444,
0.008791552856564522,
0.014382297173142433,
-0.04522762820124626,
0.04365800321102142,
-0.04426012933254242,
-0.008455149829387665,
-0.0608600452542305,
0.03418807312846184,
0.024192389100790024,
-0.05608036741614342,
-0.04872967675328255,
0.02477286383509636,
-0.011735021136701107,
0.016610534861683846,
0.02133154682815075,
0.03518873080611229,
-0.07274940609931946,
-0.018441110849380493,
0.012774497270584106,
-0.020957492291927338,
0.06920527666807175,
-0.044749900698661804,
-0.025609398260712624,
0.05561332777142525,
-0.029339248314499855,
-0.024478666484355927,
0.009829136542975903,
0.011683871038258076,
0.00935231614857912,
-0.017687732353806496,
-0.005658320616930723,
-0.0303421001881361,
0.11021880805492401,
-0.0458257757127285,
-0.010129920206964016,
0.011192716658115387,
-0.03967048227787018,
-0.04051772877573967,
0.009732705540955067,
0.032735712826251984,
-0.032851628959178925,
0.00888410396873951,
0.026649313047528267,
0.04862527549266815,
-0.04800251126289368,
0.03197040781378746,
-0.04174228385090828,
-0.03519955277442932,
0.018011124804615974,
0.00708024250343442,
0.042161036282777786,
0.039114344865083694,
0.05008222907781601,
-0.034016914665699005,
0.015818847343325615,
0.004572098609060049,
0.007554265204817057,
-0.07312493771314621,
0.005559229291975498,
0.026513097807765007,
-0.017401689663529396,
0.0351766012609005,
-0.02659543603658676,
0.032183688133955,
0.03672879934310913,
-0.07937571406364441,
-0.02053053304553032,
-0.03755670413374901,
0.004295919090509415,
-0.07572172582149506,
-0.004096794407814741,
-0.026012269780039787,
0.01580490544438362,
0.007650330197066069,
0.04807373508810997,
0.019044622778892517,
0.006599548272788525,
-0.010120495222508907,
0.00872194953262806,
0.00772127928212285,
0.01930406130850315,
-0.031971435993909836,
0.03478998690843582,
0.06794682890176773,
-0.01766355335712433,
-0.0019438693998381495,
0.0030412760097533464,
-0.01266063004732132,
-0.001114135724492371,
-0.02979975938796997,
0.010039476677775383,
0.004695998504757881,
0.02352641522884369,
-0.002906020963564515,
-0.009256132878363132,
0.009390882216393948,
0.009448777884244919,
0.015379423275589943,
0.0006519610178656876,
0.003164938185364008,
0.005337939597666264,
0.02380192093551159,
-0.027112796902656555,
-0.038422856479883194,
0.016344888135790825,
-0.00009614678856451064,
-0.011037076823413372,
-0.01153994258493185,
0.028062276542186737,
0.037437450140714645,
-0.006610477808862925,
-0.001990793738514185,
-0.03057917207479477,
-0.03618048503994942,
0.06177376210689545,
-0.022153524681925774,
0.025121882557868958,
0.02943868562579155,
-0.009574192576110363,
0.02409820258617401,
-0.012853546068072319,
0.012602238915860653,
-0.03581365942955017,
-0.05908969044685364,
-0.029823478311300278,
0.012174462899565697,
-0.00906274002045393,
-0.05503188073635101,
-0.07981212437152863,
-0.04192157834768295,
0.054568346589803696,
0.018014706671237946,
0.04622361809015274,
0.02926107868552208,
-0.04345037415623665,
-0.022092599421739578,
-0.06781147420406342,
0.015089543536305428,
-0.029407929629087448,
-0.013574576005339622,
-0.04045712947845459,
-0.03566954284906387,
0.015087599866092205,
-0.007939551025629044,
0.06360169500112534,
0.0016964247915893793,
-0.0077650598250329494,
0.013879133388400078,
-0.02819453738629818,
0.03169596940279007,
-0.018659286201000214,
-0.01091004628688097,
-0.03060627542436123,
-0.0036143786273896694,
0.02155129797756672,
0.03309084475040436,
0.009002145379781723,
-0.01794631965458393,
0.06865635514259338,
-0.04702899605035782,
0.017151180654764175,
-0.019850751385092735,
0.023714585229754448,
0.032001908868551254,
0.005059029906988144,
-0.018246065825223923,
0.07935918122529984,
-0.004712552763521671,
0.04974294453859329,
0.016242047771811485,
-0.023763461038470268,
-0.051113441586494446,
0.010855828411877155,
-0.009953200817108154,
0.008740122430026531,
-0.024960817769169807,
-0.0356435589492321,
0.03249343857169151,
-0.010205845348536968,
0.0015060059959068894,
0.02967439591884613,
-0.03526054322719574,
-0.02608984336256981,
0.00851532258093357,
0.05947286635637283,
0.03277583047747612,
-0.0028111108113080263,
0.043782055377960205,
-0.010680630803108215,
-0.005376500077545643,
-0.010785497725009918,
0.04057301580905914,
0.04645277559757233,
0.004703709855675697,
-0.024591118097305298,
0.06115514785051346,
-0.0315961055457592,
0.011611314490437508,
0.02623317390680313,
0.025560954585671425,
-0.006777588743716478,
-0.057366274297237396,
-0.02365364320576191,
-0.0018920229049399495,
-0.01282731257379055,
-0.009297213517129421,
-0.002237828681245446,
0.03474901616573334,
-0.002671909285709262,
-0.004106907639652491,
-0.012718499638140202,
-0.0034643509425222874,
-0.01598091796040535,
0.021656909957528114,
0.0002436055801808834,
0.03273741528391838,
-0.0006708273431286216,
-0.033825330436229706,
-0.02375066839158535,
-0.007552767638117075,
-0.007842911407351494,
-0.01619144342839718,
0.017793266102671623,
-0.01271184254437685,
-0.016159290447831154,
-0.05170302838087082,
-0.026844684034585953,
-0.004594721365720034,
-0.02772579900920391,
0.02106318809092045,
0.055375974625349045,
0.016234681010246277,
-0.0024098139256238937,
-0.018057888373732567,
-0.0045319898054003716,
0.0547892302274704,
-0.0482650101184845,
-0.023171531036496162,
-0.014421987347304821,
0.0383312925696373,
0.011031546629965305,
-0.011941014789044857
] |
<p>Are all <a href="http://en.wikipedia.org/wiki/Wave" rel="nofollow">waves</a> in the universe the same as <a href="http://en.wikipedia.org/wiki/Electromagnetic_waves" rel="nofollow">electromagnetic waves</a>?</p>
<p>Basically, my question arises from an equation I found in my chemistry textbook:</p>
<p>$$\lambda \nu ~=~ c.$$</p>
<p>This states that the wavelength (distance from crest to crest) times the frequency (amount of times the wave passes the center point) equals the speed of light. Now, I know this applies in a vacuum and that the speed of light changes based on density. However, does this apply to all waves? If so, does this apply to a wave in water?</p>
<p>It seems as though it should. You have a high frequency of light that is incredibly high compared to water, but you have a incredibly small wavelength which causes that value to be lower. In the case of water, if you considered only the wavelength, the value would be too high, but if you also consider that the frequency is going to be orders of magnitude lower than light, you can see where I might arrive at this conclusion.</p>
<p>If we measure the crest of a <a href="http://en.wikipedia.org/wiki/Surface_wave" rel="nofollow">wave</a> of water and the frequency of that wave (I assume from the surface of the body of water) and consider the density of the water in our calculation (as some other variable that is normally used when calculating this), would the result also be the speed of light? In addition, if water was within a vacuum and we were to create a wave, how would this react? If we could create a wave in water in this vacuum, would our values reflect $c$ or a variation of $c$ based on the density of the water?</p>
<p>If $\lambda \nu ~=~ c$ is valid for all waves, what other attributes must be supplied within the equation to make the math work out to give the correct answer of $c$?</p> | 4,582 | [
-0.0031336587853729725,
-0.015366977080702782,
0.01539729442447424,
-0.0312841571867466,
0.053575754165649414,
0.0019504554802551866,
-0.07000917941331863,
-0.04510367661714554,
0.02282620593905449,
-0.038878705352544785,
0.03718246519565582,
0.049696020781993866,
0.061367254704236984,
0.0366644561290741,
0.04053546488285065,
0.021568456664681435,
0.010580128990113735,
0.01863495633006096,
-0.02878032997250557,
-0.03946232050657272,
0.033663101494312286,
0.024197334423661232,
-0.009480718523263931,
0.014608197845518589,
-0.035947535187006,
0.03873591497540474,
0.0143422931432724,
0.007812513038516045,
0.01717899926006794,
0.02104947157204151,
0.0027713675517588854,
-0.044993095099925995,
-0.008587601594626904,
0.035972386598587036,
0.015932083129882812,
0.019799020141363144,
-0.016731377691030502,
-0.014864902012050152,
-0.00255792448297143,
0.01469152420759201,
0.016810180619359016,
-0.009150750935077667,
-0.005944748874753714,
0.04093020409345627,
-0.01680142804980278,
0.004644274245947599,
0.021216584369540215,
-0.039966799318790436,
0.028374886140227318,
-0.04290551692247391,
0.04504545032978058,
0.010067812167108059,
0.025924181565642357,
-0.0003184504166711122,
0.0011007437715306878,
-0.011511815711855888,
0.09392022341489792,
0.04051108658313751,
-0.013746976852416992,
-0.052596624940633774,
0.004779612645506859,
0.004570639692246914,
-0.038005340844392776,
-0.0007445618975907564,
0.0022998142521828413,
0.026512419804930687,
-0.016671404242515564,
0.027359971776604652,
0.016133161261677742,
-0.005321933887898922,
-0.0028761078137904406,
-0.01566050760447979,
0.01664569228887558,
-0.005918326787650585,
0.02940429002046585,
-0.05436278134584427,
0.0027772332541644573,
0.04067281261086464,
0.007379328832030296,
0.07127559185028076,
-0.005270622670650482,
0.008464856073260307,
-0.0020255628041923046,
0.015155154280364513,
0.029050467535853386,
-0.008571992628276348,
0.04832086339592934,
-0.002389056608080864,
0.004092262126505375,
0.0201594028621912,
-0.02052062377333641,
-0.01696901209652424,
-0.002222835784777999,
-0.0033610647078603506,
0.015423865057528019,
0.004765388090163469,
-0.0031348001211881638,
0.03340775892138481,
0.03341095894575119,
-0.06231443211436272,
-0.00978211872279644,
-0.006792482919991016,
0.0065608094446361065,
0.08878140151500702,
0.01296283770352602,
-0.038933299481868744,
-0.031139152124524117,
0.023982826620340347,
-0.05298587679862976,
-0.044241927564144135,
-0.040267281234264374,
0.005662485025823116,
-0.011725669726729393,
-0.00917019136250019,
-0.03284236788749695,
-0.018623551353812218,
0.06082318350672722,
-0.03638703376054764,
0.10670463740825653,
0.07352017611265182,
0.03468411788344383,
-0.04366119205951691,
-0.017232783138751984,
-0.020649438723921776,
-0.03185097128152847,
0.022198595106601715,
-0.006000216584652662,
0.007431562524288893,
-0.021804329007864,
0.0046938033774495125,
-0.028140036389231682,
0.004201054107397795,
0.03256683051586151,
-0.024038413539528847,
0.013045743107795715,
-0.01313383225351572,
-0.12153824418783188,
-0.07891368120908737,
0.02219691313803196,
0.00901568029075861,
-0.0358491949737072,
-0.08217541873455048,
0.024242185056209564,
-0.0006733191548846662,
0.06279534101486206,
0.003902602707967162,
0.010790337808430195,
-0.014566107653081417,
0.04086219519376755,
-0.0021072071976959705,
-0.0021752864122390747,
-0.002169620478525758,
0.01700780913233757,
-0.05691509693861008,
-0.011543115600943565,
-0.040249280631542206,
-0.01452844962477684,
0.008123780600726604,
0.00851885974407196,
0.02530566044151783,
0.07371782511472702,
-0.04228915646672249,
0.004190064501017332,
0.020746048539876938,
0.008744165301322937,
-0.0503804087638855,
0.07147706300020218,
0.030925335362553596,
0.018393151462078094,
0.020346777513623238,
-0.00974699854850769,
0.0026045702397823334,
-0.02782188542187214,
-0.008039339445531368,
0.04754839465022087,
-0.034548450261354446,
0.0052969856187701225,
-0.04323325306177139,
-0.002878815634176135,
-0.005500627215951681,
-0.010612180456519127,
-0.03489885479211807,
-0.01522514782845974,
0.031631119549274445,
0.020743926987051964,
0.05023462697863579,
-0.020865388214588165,
-0.007941216230392456,
-0.015781395137310028,
-0.04496185854077339,
0.015271964482963085,
-0.0009535420103929937,
0.02075446955859661,
0.008094324730336666,
0.023477934300899506,
0.02111857198178768,
0.012786772102117538,
-0.00764123909175396,
-0.04367530718445778,
-0.02844059281051159,
0.03426607698202133,
0.06670249998569489,
0.027057308703660965,
-0.003609897568821907,
0.013268859125673771,
0.05501450225710869,
0.03486624360084534,
-0.004033302888274193,
-0.0017637943383306265,
-0.015316719189286232,
-0.01686190441250801,
0.009598251432180405,
-0.035578224807977676,
0.028375228866934776,
-0.02293994277715683,
0.0002616208221297711,
0.03757993504405022,
-0.009768798016011715,
-0.0058833640068769455,
0.009195567108690739,
-0.00994701124727726,
0.05894836038351059,
0.020640160888433456,
-0.003261108649894595,
0.04929881542921066,
0.029613396152853966,
0.001487944507971406,
0.0170612670481205,
0.004626465030014515,
-0.024399062618613243,
-0.05603296682238579,
-0.006848090328276157,
0.032707661390304565,
-0.004485211800783873,
-0.01490272581577301,
0.0065919095650315285,
0.005291281268000603,
0.04514743760228157,
0.07131512463092804,
-0.009998232126235962,
-0.013341926969587803,
-0.04259627312421799,
0.01195599976927042,
0.031517066061496735,
0.015992620959877968,
0.03200318664312363,
0.01663966290652752,
-0.0034466737415641546,
0.03736122325062752,
-0.0684157982468605,
0.00291246734559536,
0.010322775691747665,
0.009430678561329842,
0.029396558180451393,
-0.007488060276955366,
-0.006624300964176655,
0.011140285059809685,
-0.038326557725667953,
0.018047185614705086,
0.014326846227049828,
-0.012410953640937805,
0.0012947347713634372,
-0.05564604327082634,
0.01641957461833954,
-0.01768445037305355,
0.015592589974403381,
-0.04407375305891037,
0.01141559612005949,
0.024538379162549973,
-0.053367871791124344,
0.0034079905599355698,
-0.018496299162507057,
-0.017801553010940552,
-0.017843646928668022,
-0.03668326511979103,
0.040292903780937195,
0.030988052487373352,
0.050068195909261703,
-0.06634068489074707,
-0.037706512957811356,
0.019594665616750717,
-0.04205019399523735,
-0.04100799933075905,
-0.005289840511977673,
-0.019341694191098213,
0.022257627919316292,
-0.040956541895866394,
-0.04720127582550049,
0.02608477510511875,
-0.002973846858367324,
-0.006253852508962154,
0.01776774227619171,
0.003727091010659933,
-0.07099392265081406,
-0.012593413703143597,
-0.054066356271505356,
-0.0027538109570741653,
-0.03374112397432327,
-0.0018376901280134916,
0.04966013506054878,
-0.027277935296297073,
-0.03465013951063156,
0.02656201645731926,
-0.002353205345571041,
-0.056882068514823914,
-0.017031917348504066,
-0.009154165163636208,
0.017262758687138557,
-0.04116681590676308,
0.028038833290338516,
0.014372974634170532,
-0.05145764723420143,
0.020643269643187523,
-0.0511886402964592,
-0.07856780290603638,
0.06740429252386093,
-0.03079262189567089,
0.09924905002117157,
0.0022231757175177336,
-0.03169532120227814,
0.042724404484033585,
0.05437881126999855,
-0.041887301951646805,
-0.021228177472949028,
0.011745583266019821,
0.023244930431246758,
-0.01820128969848156,
-0.00916212983429432,
0.05133271589875221,
-0.041724298149347305,
-0.00776247214525938,
-0.017500242218375206,
0.03604002296924591,
0.027793368324637413,
0.018893776461482048,
0.005640520714223385,
0.02711566910147667,
0.01669144630432129,
0.04003085568547249,
0.06039129197597504,
0.005867137107998133,
0.006793393287807703,
0.023455023765563965,
-0.02694963477551937,
0.015101728960871696,
0.030918801203370094,
-0.028941545635461807,
0.047065649181604385,
0.0366348959505558,
-0.004127466585487127,
-0.040056563913822174,
0.03138251230120659,
-0.004184084944427013,
-0.0006799460970796645,
0.01592303439974785,
0.01766636222600937,
0.04418528825044632,
0.0030361537355929613,
0.008939188905060291,
0.0366300493478775,
0.07483406364917755,
0.0036594762932509184,
-0.031069237738847733,
-0.0071144383400678635,
-0.012382099404931068,
0.022887669503688812,
-0.04041554778814316,
-0.007340996526181698,
0.07050151377916336,
0.03776712715625763,
0.0023153899237513542,
-0.02125369943678379,
-0.031224770471453667,
-0.018942948430776596,
-0.01399504765868187,
-0.024724747985601425,
0.0010499845957383513,
0.03993944451212883,
0.010392064228653908,
0.09579000622034073,
0.0461856946349144,
0.012859757989645004,
-0.0033902761060744524,
0.008142957463860512,
-0.08275655657052994,
-0.02189386449754238,
-0.041240859776735306,
-0.014928516000509262,
-0.03556995466351509,
-0.05577683076262474,
-0.03361963480710983,
-0.005220654886215925,
-0.03352833911776543,
-0.03512878343462944,
-0.007476000115275383,
-0.044932153075933456,
0.04376273602247238,
-0.02351369522511959,
-0.04869665578007698,
-0.002476678928360343,
0.04644415155053139,
0.023258041590452194,
0.00385196297429502,
0.004078067373484373,
0.03264712914824486,
-0.037213753908872604,
0.011922159232199192,
-0.0007044068770483136,
-0.021220114082098007,
0.03440999984741211,
0.027524176985025406,
0.04026186466217041,
0.010767482221126556,
-0.04305596277117729,
0.005120301619172096,
0.025791103020310402,
0.03988042101264,
0.0017267484217882156,
-0.026309575885534286,
-0.044709742069244385,
-0.010800151154398918,
-0.00725782522931695,
-0.004538084380328655,
0.05699696019291878,
-0.01453622616827488,
-0.03493396192789078,
0.01091805286705494,
-0.04663827270269394,
0.011497900821268559,
0.08133913576602936,
0.016145780682563782,
0.006942679639905691,
0.011422548443078995,
-0.04552803561091423,
-0.004399953410029411,
-0.02180693857371807,
-0.013643617741763592,
-0.010949129238724709,
0.024049725383520126,
0.005015851929783821,
-0.03853708878159523,
0.016387375071644783,
0.0021866229362785816,
-0.014233115129172802,
-0.004084059968590736,
-0.013351470232009888,
-0.02659814991056919,
-0.04581098258495331,
-0.02068675309419632,
-0.0144349941983819,
0.029427025467157364,
0.0404740571975708,
-0.027366533875465393,
0.008399998769164085,
-0.0759083703160286,
-0.07556532323360443,
-0.0018507421482354403,
0.03518866002559662,
0.020979423075914383,
-0.008098242804408073,
-0.06798343360424042,
-0.04418868571519852,
0.0052119470201432705,
-0.03707684203982353,
0.03307726979255676,
0.01954301819205284,
0.012536370195448399,
-0.014010432176291943,
-0.014257211238145828,
-0.002374538453295827,
0.016860516741871834,
-0.008653045631945133,
-0.00892504770308733,
-0.045200005173683167,
0.02038465440273285,
-0.011904563754796982,
0.0077977292239665985,
0.020176613703370094,
0.01700180023908615,
-0.01804634928703308,
-0.010824319906532764,
0.026091577485203743,
-0.027687784284353256,
-0.012476502917706966,
-0.07003933936357498,
0.03360297530889511,
0.009508897550404072,
0.059160422533750534,
0.029591282829642296,
0.005646678153425455,
-0.031452350318431854,
0.03788150101900101,
0.04566190019249916,
-0.005800005979835987,
0.03422444686293602,
-0.031445689499378204,
0.05566637963056564,
0.003390406956896186,
0.00290962983854115,
0.050064489245414734,
0.04275764152407646,
-0.03206031024456024,
-0.015300850383937359,
-0.0433608703315258,
0.04242092743515968,
-0.032319456338882446,
-0.018956445157527924,
-0.004708663560450077,
-0.03309967741370201,
-0.025592651218175888,
0.03658616542816162,
-0.015465721487998962,
-0.021174924448132515,
0.001499472069554031,
-0.026477765291929245,
-0.009971034713089466,
-0.025152573361992836,
-0.010663594119250774,
0.006135953590273857,
-0.013256790116429329,
0.014545743353664875,
0.03057987429201603,
0.010689117014408112,
0.03712299093604088,
0.00018289046420250088,
-0.004332114476710558,
0.0026737458538264036,
-0.009143814444541931,
0.0034261883702129126,
-0.015378509648144245,
0.007594527211040258,
0.023690447211265564,
-0.03435150906443596,
0.06735595315694809,
-0.025118719786405563,
0.01872439682483673,
0.011916293762624264,
-0.021784156560897827,
-0.04149327054619789,
0.026611000299453735,
-0.017596695572137833,
0.034018512815237045,
-0.02491307258605957,
0.007621570024639368,
0.030250966548919678,
0.03285069391131401,
-0.02582979016005993,
-0.018169768154621124,
0.0197676382958889,
0.01738736405968666,
0.0025319992564618587,
-0.024415936321020126,
0.025139976292848587,
-0.03823012486100197,
-0.03319622948765755,
-0.001134200836531818,
0.013299101032316685,
-0.04361205920577049,
-0.01813129335641861,
0.003886251710355282,
0.014740685932338238,
0.07064393162727356,
-0.0056066978722810745,
-0.028652764856815338,
0.008895560167729855,
-0.020894577726721764,
0.012120217084884644,
-0.0009084520861506462,
0.06100699305534363,
-0.029544657096266747,
-0.027372997254133224,
-0.001994671765714884,
-0.02040601707994938,
0.016050949692726135,
-0.02405436895787716,
-0.035653386265039444,
0.015157284215092659,
0.03079064190387726,
-0.01811745949089527,
-0.020592594519257545,
0.017405841499567032,
-0.004548768978565931,
0.020530041307210922,
-0.015612302348017693,
-0.013064357452094555,
-0.04653548449277878,
-0.02928920090198517,
0.0047835479490458965,
-0.010739555582404137,
0.02503305859863758,
-0.04010162129998207,
0.0650673359632492,
-0.027110669761896133,
-0.022209955379366875,
-0.012098409235477448,
-0.016571013256907463,
-0.003693815553560853,
0.009188851341605186,
-0.02164967730641365,
0.023861393332481384,
0.0037469968665391207,
-0.001249220804311335,
-0.014938903972506523,
-0.060309384018182755,
0.008375131525099277,
0.06176590919494629,
0.004515146836638451,
0.03472524136304855,
0.0070971339009702206,
-0.02518899366259575,
0.0015010328497737646,
-0.029971502721309662,
-0.025582440197467804,
0.03315964713692665,
-0.010005149058997631,
0.025109775364398956,
-0.023859350010752678,
-0.016057396307587624,
0.04879876226186752,
0.037906017154455185,
-0.004355584736913443,
0.015790587291121483,
0.04291890189051628,
0.04823353514075279,
-0.0045950463972985744,
-0.027096018195152283,
-0.05904079228639603,
0.028249690309166908,
-0.026402750983834267,
0.03226368501782417,
0.020540175959467888,
0.001316011999733746,
0.030987536534667015,
0.01550923753529787,
0.004734714049845934,
-0.05586886405944824,
0.014943940564990044,
-0.029685726389288902,
-0.011417267844080925,
0.008726213127374649,
0.014441361650824547,
-0.004923197440803051,
-0.00016350913210771978,
0.0415184311568737,
-0.018728142604231834,
0.015335419215261936,
-0.005648862104862928,
-0.06311672925949097,
0.018665391951799393,
-0.05172711983323097,
-0.05553577467799187,
0.0626956969499588,
0.010071461088955402,
-0.07732350379228592,
0.03887449949979782,
-0.059930749237537384,
0.041941262781620026,
0.04910349100828171,
-0.007312533911317587,
-0.02953939326107502,
0.027012111619114876,
-0.003009264590218663,
0.011502968147397041,
-0.016060004010796547,
-0.0040543717332184315,
0.12163467705249786,
0.05590219795703888,
0.022908201441168785,
-0.006608553230762482,
0.02419770136475563,
-0.014459405094385147,
0.035041455179452896,
-0.02188565954566002,
-0.02580968104302883,
-0.02566213347017765,
0.018379265442490578,
0.014170055277645588,
0.046988602727651596,
0.0011078562820330262,
-0.004769948776811361,
0.03101561963558197,
-0.04155169799923897,
0.0027019488625228405,
0.007318970747292042,
0.01606755517423153,
0.014960942789912224,
0.05122299864888191,
-0.0035752386320382357,
0.017089730128645897,
-0.0300308708101511,
-0.03116687200963497,
-0.043606728315353394,
0.01652676984667778,
0.021895449608564377,
-0.0003713812038768083,
-0.08027293533086777,
-0.012983661144971848,
0.004437219817191362,
-0.04477720707654953,
-0.04374680668115616,
0.05411692336201668,
0.06514018774032593,
-0.024776825681328773,
-0.014567449688911438,
0.02193472348153591,
0.014543499797582626,
0.01386907696723938,
0.017365548759698868,
0.0478600338101387,
-0.050844911485910416,
0.0274350568652153,
-0.048303332179784775,
0.03610258176922798,
-0.0013611334143206477,
0.00524906674399972,
-0.012041113339364529,
0.03518940508365631,
0.0019734539091587067,
-0.05245489999651909,
0.036120422184467316,
-0.010163473896682262,
0.056223563849925995,
0.021676210686564445,
-0.0033001720439642668,
-0.00792961847037077,
0.02223563753068447,
-0.02065708301961422,
0.01603967323899269,
0.017789993435144424,
-0.01890123263001442,
-0.07559098303318024,
0.004308321513235569,
0.018570058047771454,
-0.013775485567748547,
-0.02290300279855728,
-0.02435128204524517,
-0.004617467988282442,
-0.04495389759540558,
-0.009660841897130013,
-0.0056973956525325775,
0.029838737100362778,
0.029208356514573097,
0.015516678802669048,
-0.004351465962827206,
-0.035916782915592194,
-0.08179076015949249,
0.03652007505297661,
-0.025052707642316818,
-0.02878670021891594,
-0.025385431945323944,
-0.022002266719937325,
-0.0012126457877457142,
0.034036729484796524,
-0.012532480992376804,
0.021098962053656578,
0.012145468965172768,
0.033200427889823914,
0.051878493279218674,
-0.012574497610330582,
-0.03581203892827034,
0.005907313898205757,
0.018648505210876465,
-0.0069989534094929695,
-0.00624430924654007,
0.01857697032392025,
0.03851677104830742,
0.000012350460565357935,
0.029252339154481888,
0.01874925196170807,
-0.03284411132335663,
-0.026593968272209167,
-0.0039774770848453045,
-0.016368268057703972,
0.025147221982479095,
-0.005009746178984642,
0.04791978374123573,
0.00004663312574848533,
-0.030414601787924767,
0.0045003220438957214,
-0.0007182635017670691,
0.00609391275793314,
0.014158466830849648,
-0.0040318164974451065,
0.007440146524459124,
-0.007658341899514198,
0.004042802844196558,
-0.03903887793421745,
-0.05713776871562004,
-0.03184981644153595,
0.022892920300364494,
0.0026327036321163177,
-0.01660771481692791,
-0.032328180968761444,
0.04244007170200348,
-0.036797910928726196,
-0.030572686344385147,
0.01616651564836502,
-0.005859576165676117,
0.010185464285314083,
-0.009478668682277203,
0.02762412838637829,
0.03321211040019989,
0.025911133736371994,
0.009515977464616299,
-0.04121939092874527,
0.03992201015353203,
-0.029826954007148743,
-0.03200334683060646,
0.04827989265322685,
-0.018755396828055382,
0.020642247051000595,
0.03626597672700882,
0.03485067933797836,
0.018673481419682503,
0.04606391489505768,
-0.005501784849911928,
0.03703394532203674,
-0.027997242286801338,
-0.040430013090372086,
0.02761690691113472,
-0.016581391915678978,
0.03418336063623428,
0.012665562331676483,
0.012544538825750351,
0.05376172810792923,
0.009335476905107498,
-0.01893126778304577,
0.02256220206618309,
-0.008082914166152477,
-0.060360137373209,
-0.029016096144914627,
0.01303135883063078,
0.001062592607922852,
-0.017272407189011574,
0.03303283452987671,
-0.022161634638905525,
0.05553651228547096,
0.022115876898169518,
-0.010063990950584412,
-0.11025985330343246,
-0.0003958414599765092,
0.0137406587600708,
0.0404178649187088,
0.03656967356801033,
-0.021028749644756317,
0.014177112840116024,
0.005834128707647324,
-0.08347810059785843,
0.023580277338624,
-0.001486802939325571,
0.0033116252161562443,
-0.042759474366903305,
-0.004186645150184631,
-0.03787919133901596,
0.02514556795358658,
0.011968804523348808,
0.04797661677002907,
0.03542747721076012,
0.027934325858950615,
-0.009503424167633057,
-0.029982127249240875,
-0.0009101089672185481,
0.030621450394392014,
0.024228127673268318,
0.0006969417445361614,
0.049260061234235764,
-0.017359081655740738,
-0.0005114719970151782,
0.005813906900584698,
-0.005705086514353752,
0.05609404668211937,
-0.015962958335876465,
0.003012825967743993,
0.03092164546251297,
0.024347122758626938,
0.01036115549504757,
-0.021782536059617996,
-0.026042649522423744,
0.06605502218008041,
0.022680066525936127,
0.006492843385785818,
0.011299626901745796,
-0.009251687675714493,
0.03650471568107605,
-0.07762155681848526,
-0.02249026671051979,
0.011552197858691216,
-0.0389263890683651,
0.01629563234746456,
0.039686672389507294,
-0.0409436859190464,
0.02019006758928299,
-0.004687469452619553,
0.00160343071911484,
-0.044325314462184906,
-0.013367622159421444,
0.03236529231071472,
0.01446510385721922,
-0.04269946366548538,
0.010958691127598286,
0.014696202240884304,
-0.015607609413564205,
-0.0007908916450105608,
-0.008884415961802006,
0.007366663310676813,
-0.037038080394268036,
-0.010186263360083103,
0.000733251916244626,
-0.006416013464331627,
0.011652616783976555,
0.010516763664782047,
-0.04042784124612808,
0.014612516388297081,
0.026162169873714447,
0.008056593127548695,
-0.025583332404494286,
-0.013205468654632568,
-0.039144303649663925,
-0.06534797698259354,
0.002200760180130601,
0.02194572240114212,
0.009976762346923351,
-0.045806534588336945,
0.004926058929413557,
-0.009995648637413979,
0.03321770578622818,
0.05297631770372391,
0.022844873368740082,
-0.02485879883170128,
0.0036159981973469257,
-0.01569569855928421,
0.02029220014810562,
-0.053170982748270035,
-0.019439809024333954,
0.006656982470303774,
-0.02192404493689537,
-0.0009733382030390203,
0.007184891030192375,
-0.0022138734348118305,
-0.0034889515955001116,
0.03894234821200371,
-0.003398473607376218,
0.02164277993142605,
0.013273379765450954,
-0.0273673664778471,
0.04061269387602806,
-0.011795752681791782,
-0.027182267978787422,
0.07690773904323578,
-0.0024001102428883314,
0.02017761394381523,
0.03285776451230049,
-0.050221677869558334,
-0.06885083019733429,
0.013919008895754814,
-0.0007096794433891773,
0.003433978883549571,
0.02872859686613083,
0.0063095698133111,
0.014454903081059456,
-0.011360635049641132,
0.015329103916883469,
0.05172320082783699,
-0.017834722995758057,
-0.033367156982421875,
0.05354239419102669,
-0.025632601231336594,
0.007126685231924057,
-0.005010827444493771,
0.0185464546084404,
0.006868661381304264,
-0.02590990997850895,
-0.017970029264688492,
0.021128790453076363,
0.050601858645677567,
-0.01353486068546772,
0.03144020587205887,
0.059425268322229385,
-0.008540979586541653,
-0.006199591793119907,
0.01885795034468174,
0.007697324268519878,
-0.018153397366404533,
-0.02999396249651909,
0.040632154792547226,
-0.02132667601108551,
-0.02287425473332405,
0.03406355530023575,
-0.008184155449271202,
0.08937645703554153,
-0.003913229331374168,
0.016049060970544815,
-0.013628321699798107,
-0.014513186179101467,
-0.011951911263167858,
0.024603094905614853,
-0.018221339210867882,
0.020050743594765663,
-0.0200823787599802,
-0.00011233306577196345,
-0.029648523777723312,
-0.0034618829376995564,
0.010444503277540207,
-0.05019748955965042,
0.021011343225836754,
0.03097967989742756,
-0.021073341369628906,
0.01763061061501503,
-0.002714024158194661,
0.000943637453019619,
-0.03215837851166725,
0.03011205419898033,
-0.011608540080487728,
-0.03849191591143608,
0.026539521291851997,
-0.01374796312302351,
0.007830574177205563,
0.05635971203446388,
-0.03269176930189133,
-0.022833963856101036,
-0.0007000964833423495,
0.020166048780083656,
-0.010415084660053253,
-0.051240984350442886
] |
<p>I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean plane, that have properties such as position, velocity, mass, radius and the resultant force.</p>
<p>I want to update the universe in small time steps, usually a few milliseconds, but I'm not sure how to correctly calculate the changes in position.</p>
<p>The force is simple: <code>fr = sum(G * body.m * bodyi.m / dist(body, bodyi)^2)</code>.</p>
<p>But how do I go on from there?</p>
<p>I could do this:</p>
<pre><code>a = Fr/body.m
v += a*dt
position += v*dt
</code></pre>
<p>But that would, of course, be false. Maybe if I added <code>0.5</code> as a factor in position calculation?</p> | 4,583 | [
0.02455749176442623,
-0.01765194907784462,
-0.027411092072725296,
-0.03044547513127327,
0.020166490226984024,
-0.0009203073568642139,
-0.014793089590966702,
-0.0324447862803936,
0.018767552450299263,
-0.0183701291680336,
0.00506348954513669,
0.0708862692117691,
0.058943502604961395,
0.01166286040097475,
0.022676512598991394,
-0.03408976271748543,
-0.0006118422606959939,
-0.032034844160079956,
0.003301043761894107,
-0.04944663122296333,
0.01503931637853384,
-0.003366408171132207,
0.04475032538175583,
-0.033826958388090134,
0.009752247482538223,
0.05533560365438461,
0.008521252311766148,
-0.048540148884058,
-0.025227665901184082,
0.057984206825494766,
-0.0331784226000309,
-0.04230969399213791,
0.008724525570869446,
0.033858686685562134,
0.03719852864742279,
0.02784569002687931,
-0.061263687908649445,
-0.034065280109643936,
0.010829676873981953,
0.002284726593643427,
-0.030807949602603912,
0.01270480640232563,
-0.006290819961577654,
0.052485574036836624,
-0.007655533030629158,
0.03414856642484665,
-0.0006306593422777951,
0.009011366404592991,
0.126607283949852,
-0.014711610041558743,
0.06095275655388832,
-0.00016550194413866848,
0.04159950464963913,
0.03479950875043869,
-0.043678585439920425,
-0.003346399636939168,
0.07814186066389084,
0.0405743345618248,
-0.01920638419687748,
-0.02331353910267353,
-0.03193660452961922,
-0.04759766906499863,
-0.012226536870002747,
-0.048832204192876816,
0.005844569765031338,
0.019232161343097687,
-0.05247178673744202,
-0.0064878459088504314,
0.024053411558270454,
-0.00048686660011298954,
0.024679111316800117,
-0.012412722222507,
0.011230935342609882,
-0.0223428662866354,
-0.022710096091032028,
-0.004522138740867376,
0.027371542528271675,
0.007328726816922426,
0.035029783844947815,
0.04422707483172417,
-0.04730543494224548,
0.0012141800252720714,
0.044495657086372375,
0.06573325395584106,
0.028386041522026062,
0.0033042198047041893,
-0.003343393560498953,
-0.0051214308477938175,
0.0056856004521250725,
0.012536492198705673,
-0.025639528408646584,
0.00479432288557291,
0.0521981306374073,
-0.004403281956911087,
-0.013587689958512783,
0.019599013030529022,
-0.010953143239021301,
0.015290009789168835,
0.03352031484246254,
-0.0033819666132330894,
-0.02059945836663246,
-0.025842439383268356,
-0.0014961331617087126,
0.03296350687742233,
-0.019655847921967506,
-0.035885266959667206,
-0.02334713004529476,
-0.03095988556742668,
-0.022547626867890358,
-0.0014311099657788873,
-0.02706381492316723,
-0.03303445130586624,
-0.009343414567410946,
0.008349401876330376,
0.039400190114974976,
-0.027096569538116455,
-0.041880976408720016,
-0.001746703521348536,
0.053994301706552505,
0.007926622405648232,
0.06564906984567642,
-0.02143694832921028,
0.04274211823940277,
-0.03654490411281586,
-0.017156554386019707,
-0.013854341581463814,
-0.0017488724552094936,
-0.028625983744859695,
-0.02055821567773819,
-0.0007550311274826527,
-0.0016777702840045094,
-0.017454933375120163,
0.01601869985461235,
-0.004374031908810139,
0.06190265715122223,
0.014027820900082588,
-0.06966061890125275,
-0.07612725347280502,
0.017044201493263245,
0.0063489750027656555,
0.017724445089697838,
-0.05771436542272568,
0.00449394341558218,
0.023675229400396347,
0.06577856838703156,
0.053385261446237564,
-0.021593520417809486,
0.0032876194454729557,
0.047771502286195755,
-0.005937119480222464,
-0.030009713023900986,
-0.027480464428663254,
-0.02986656129360199,
-0.029005393385887146,
-0.0030011264607310295,
-0.07293006777763367,
0.012948081828653812,
0.05280832201242447,
-0.02188791148364544,
-0.008630632422864437,
0.06555147469043732,
-0.029604164883494377,
0.030189765617251396,
0.007922088727355003,
-0.002682150574401021,
-0.020190060138702393,
0.0818125531077385,
0.026477718725800514,
0.005520601756870747,
0.00874567311257124,
0.01551621314138174,
0.011128869839012623,
0.0008134193485602736,
0.006208890583366156,
0.08164630830287933,
-0.02991986647248268,
-0.002631079638376832,
0.00426030857488513,
0.014671788550913334,
0.005197606049478054,
-0.03295455127954483,
-0.048187505453825,
0.009669979102909565,
-0.019834592938423157,
0.032046325504779816,
0.037054914981126785,
0.005814808886498213,
0.02499322034418583,
0.007637354079633951,
-0.04550313949584961,
-0.000019212729966966435,
-0.08943548798561096,
0.01751050166785717,
-0.002153900219127536,
0.0010973882162943482,
-0.049478527158498764,
0.034795284271240234,
0.029368562623858452,
-0.01615948975086212,
-0.025599604472517967,
-0.045730359852313995,
0.010591667145490646,
0.050321485847234726,
-0.014729921706020832,
-0.021712729707360268,
0.07381252944469452,
0.037617433816194534,
-0.007026902865618467,
-0.011152321472764015,
0.0165878776460886,
0.005494789220392704,
-0.024363556876778603,
-0.04028451442718506,
0.01673070341348648,
0.005263646598905325,
-0.017806977033615112,
0.025453444570302963,
0.007156865671277046,
-0.00015029418864287436,
0.008007139898836613,
-0.030790379270911217,
0.08083994686603546,
0.06193164363503456,
0.01728021167218685,
0.03588093817234039,
0.022202249616384506,
0.007992418482899666,
0.02514989674091339,
0.028467880561947823,
-0.06527958810329437,
-0.057016611099243164,
-0.0177280493080616,
0.019142886623740196,
0.004561226814985275,
-0.008261313661932945,
0.0008450579480268061,
0.10143445432186127,
0.01596962846815586,
0.04650374501943588,
0.041011661291122437,
-0.01703198254108429,
0.017846478149294853,
0.024640828371047974,
0.010942777618765831,
0.039908040314912796,
-0.0004959132056683302,
0.05511334910988808,
0.05870790034532547,
0.01271447166800499,
-0.023603487759828568,
0.03510276973247528,
-0.01817365549504757,
0.03204132989048958,
0.0014830034924671054,
-0.0031756588723510504,
-0.01942397467792034,
0.016523586586117744,
0.01592072658240795,
0.004397394601255655,
0.03555595502257347,
0.010627253912389278,
-0.04977458342909813,
-0.05577431991696358,
-0.04323793575167656,
0.0027587260119616985,
0.008189692161977291,
-0.05327288806438446,
-0.010183150880038738,
0.03347725793719292,
-0.00879746861755848,
0.030548295006155968,
0.012868549674749374,
-0.016088122501969337,
-0.06747350841760635,
0.019657699391245842,
-0.00036159137380309403,
0.05976765602827072,
0.03996765613555908,
-0.003073554951697588,
-0.02238612435758114,
-0.040615513920784,
-0.02134157158434391,
-0.01937042362987995,
0.023524925112724304,
-0.03802834451198578,
0.04289618507027626,
0.026414478197693825,
-0.029569877311587334,
0.048985738307237625,
0.008463006466627121,
-0.042138583958148956,
0.02526094764471054,
0.00548997987061739,
-0.02191215567290783,
-0.006536119617521763,
-0.037901896983385086,
-0.018053455278277397,
0.005456533282995224,
0.017125939950346947,
0.005396638996899128,
-0.022669104859232903,
-0.052149951457977295,
0.03701582923531532,
-0.06945212185382843,
-0.0007091499282978475,
-0.04994498938322067,
0.0065394057892262936,
0.0116958012804389,
-0.028271472081542015,
-0.011189454235136509,
0.014710424467921257,
-0.028848756104707718,
-0.0043197572231292725,
-0.043554555624723434,
-0.054615288972854614,
-0.010504317469894886,
0.011482153087854385,
0.051601964980363846,
-0.009226709604263306,
-0.0323907844722271,
0.08827177435159683,
0.016957825049757957,
-0.036692846566438675,
-0.03503279760479927,
0.005203703884035349,
0.01933516375720501,
-0.004091126844286919,
0.007010661065578461,
0.0017882128013297915,
0.0026687097270041704,
-0.010700100101530552,
0.0110123036429286,
-0.002995328512042761,
0.05209120735526085,
0.0060170479118824005,
-0.013201226480305195,
-0.021371757611632347,
0.040798746049404144,
0.0007381511968560517,
0.04511900991201401,
0.0473591648042202,
-0.014177137985825539,
0.028959253802895546,
-0.015646347776055336,
-0.0015932671958580613,
-0.0011195436818525195,
-0.047034893184900284,
0.0034418259747326374,
0.019311469048261642,
-0.005080566741526127,
0.011758233420550823,
0.01911795884370804,
-0.02902330830693245,
-0.02539055049419403,
0.0015414434019476175,
0.028537610545754433,
0.043957460671663284,
0.017151562497019768,
-0.006720204371958971,
0.018666962161660194,
0.014726194553077221,
-0.010280035436153412,
0.013556614518165588,
-0.018053371459245682,
0.013921931385993958,
0.021756676957011223,
-0.04842903092503548,
-0.0012372906785458326,
0.06935156881809235,
0.037511974573135376,
0.026117373257875443,
0.030293988063931465,
-0.04348614066839218,
-0.014079351909458637,
-0.043567411601543427,
-0.0333869494497776,
-0.006117803510278463,
0.053588323295116425,
0.011344772763550282,
0.0310414619743824,
0.00234194821678102,
0.0022713348735123873,
0.013761792331933975,
-0.029488418251276016,
-0.060113705694675446,
0.050800103694200516,
-0.01219918206334114,
-0.048314135521650314,
0.013636400923132896,
-0.0013260445557534695,
-0.013618413358926773,
-0.03244156390428543,
0.027239246293902397,
-0.038039688020944595,
-0.021267281845211983,
-0.03491489589214325,
0.0201670303940773,
-0.027626343071460724,
-0.0062955282628536224,
-0.03775087371468544,
0.024637805297970772,
0.06724267452955246,
-0.011333492584526539,
0.025103172287344933,
0.03411952778697014,
-0.035069938749074936,
-0.019528424367308617,
-0.009027784690260887,
-0.02580328658223152,
0.02846655622124672,
0.013836817815899849,
0.048501696437597275,
0.0544404499232769,
-0.05304523929953575,
0.035716619342565536,
0.010552853345870972,
0.0225345641374588,
0.05135961249470711,
-0.010242418386042118,
-0.004998574033379555,
-0.04979955032467842,
-0.027463611215353012,
0.009614580310881138,
0.03578103706240654,
0.0012636667815968394,
0.018916497007012367,
-0.009817351587116718,
0.022684140130877495,
-0.008770100772380829,
0.014373870566487312,
0.10571469366550446,
-0.03260815143585205,
-0.024105776101350784,
-0.05151407793164253,
-0.019122062250971794,
-0.009365865029394627,
0.0070028421469032764,
0.01329753641039133,
0.024544550105929375,
-0.015093384310603142,
-0.001834788592532277,
-0.0018819862743839622,
0.0060789380222558975,
-0.021921468898653984,
0.005616278853267431,
-0.017400160431861877,
0.05183796212077141,
-0.004813812673091888,
0.013122189790010452,
0.0016136253252625465,
0.01345056388527155,
0.012980062514543533,
0.019898230209946632,
-0.012798277661204338,
-0.10405317693948746,
-0.019777923822402954,
0.02269938588142395,
0.023980412632226944,
0.009412041865289211,
-0.0039334986358881,
-0.03598526865243912,
-0.06077360734343529,
0.04213530197739601,
-0.07038960605859756,
0.04544425383210182,
-0.0008159119170159101,
0.009727392345666885,
0.004757986869663,
-0.028569355607032776,
-0.04325949028134346,
0.059351176023483276,
-0.06275677680969238,
0.04540501534938812,
-0.04091838374733925,
-0.017048954963684082,
-0.01904841884970665,
0.016094647347927094,
0.001085804309695959,
0.04915093630552292,
-0.009715050458908081,
-0.029854344204068184,
-0.01972750574350357,
-0.010408248752355576,
-0.01938890852034092,
-0.0358116514980793,
0.013719971291720867,
0.0260159969329834,
-0.019938666373491287,
0.027514394372701645,
-0.011621345765888691,
-0.010105731897056103,
0.03507096692919731,
-0.00519805820658803,
0.0016261115670204163,
-0.02151607535779476,
-0.013447029516100883,
0.022462932392954826,
0.046695832163095474,
0.015629902482032776,
0.01773778349161148,
0.013111842796206474,
-0.031440868973731995,
0.035396404564380646,
-0.015619694255292416,
-0.006180949509143829,
0.017628775909543037,
0.01555222924798727,
-0.030119962990283966,
0.01238520909100771,
-0.026440342888236046,
0.012619758024811745,
0.031132465228438377,
0.018539978191256523,
0.004799704998731613,
-0.005619784351438284,
-0.01885811612010002,
0.06646396219730377,
0.004728213883936405,
0.011494182981550694,
0.027169249951839447,
-0.02459246665239334,
0.013863232918083668,
-0.0005634156404994428,
0.01740722730755806,
0.021513741463422775,
-0.01663191430270672,
0.008561832830309868,
0.004292426630854607,
-0.010634851641952991,
0.0129510797560215,
-0.013222661800682545,
-0.006032364908605814,
-0.053680773824453354,
0.013054070062935352,
-0.01107881125062704,
0.025437233969569206,
0.04087475687265396,
-0.049028363078832626,
-0.0050697242841124535,
0.013447895646095276,
-0.005758569110184908,
-0.023464791476726532,
-0.0410979799926281,
-0.010203314945101738,
0.003311180742457509,
0.022756468504667282,
-0.00446321489289403,
-0.045505017042160034,
0.031559962779283524,
-0.014428522437810898,
-0.018346058204770088,
-0.04150989651679993,
-0.005743993446230888,
-0.053975582122802734,
0.03314279392361641,
-0.009109457023441792,
0.04071006923913956,
-0.046666041016578674,
0.00559320067986846,
0.032654520124197006,
-0.015673495829105377,
0.05380333214998245,
-0.028007954359054565,
0.02973104640841484,
0.02889845333993435,
0.025919221341609955,
0.0007089953287504613,
0.024812836199998856,
0.04045076668262482,
-0.058070674538612366,
-0.009822743944823742,
-0.03305504843592644,
0.012243280187249184,
0.015647852793335915,
0.0304383784532547,
0.01059164572507143,
0.036228518933057785,
-0.00950157642364502,
0.02539951168000698,
-0.0434083566069603,
0.030095255002379417,
-0.017759649083018303,
0.01284890528768301,
-0.008625778369605541,
0.021473247557878494,
0.010464387014508247,
0.009594751521945,
0.014689476229250431,
0.026785805821418762,
0.007711022160947323,
-0.013413389213383198,
0.06848292797803879,
-0.0053556556813418865,
0.004966360051184893,
0.05778833478689194,
0.007842889055609703,
0.03366556018590927,
-0.002634995384141803,
-0.034664154052734375,
0.01841733045876026,
0.024406835436820984,
-0.04478161782026291,
-0.015814367681741714,
-0.03680030256509781,
-0.005931543186306953,
0.07553005963563919,
-0.02709300071001053,
0.06665638089179993,
0.03171385079622269,
0.03711218386888504,
-0.05177205801010132,
0.006311280187219381,
-0.055975548923015594,
0.004046320449560881,
-0.03326939791440964,
0.03496377542614937,
-0.024402590468525887,
-0.007807125337421894,
0.0005228510708548129,
0.04139222949743271,
0.005986719857901335,
-0.007189049851149321,
0.014553309418261051,
-0.004619410261511803,
0.014638172462582588,
-0.027070892974734306,
0.008710351772606373,
0.029875202104449272,
-0.053414102643728256,
0.07042808085680008,
-0.00730331614613533,
-0.02702884003520012,
0.029604410752654076,
0.028003700077533722,
-0.011308377608656883,
-0.07475890219211578,
0.010319466702640057,
-0.04299147427082062,
-0.021428182721138,
0.014744061045348644,
-0.02837495692074299,
0.0014676123391836882,
-0.015636203810572624,
0.021584974601864815,
-0.0030770895536988974,
0.022295501083135605,
-0.03844381496310234,
-0.05157240852713585,
-0.03953605890274048,
-0.06309861689805984,
-0.02881615050137043,
0.05400286987423897,
0.025314990431070328,
-0.042456842958927155,
0.033621180802583694,
-0.02970486506819725,
0.05676110461354256,
0.0075791627168655396,
0.030309690162539482,
-0.006088712252676487,
0.08270815014839172,
-0.012236730195581913,
-0.01610654592514038,
-0.02196941152215004,
0.013424495235085487,
0.1390077918767929,
0.019483299925923347,
-0.01479184627532959,
-0.006593137979507446,
0.01462186872959137,
0.008264103904366493,
0.015845293179154396,
-0.02703600749373436,
-0.0034313946962356567,
0.02498878538608551,
-0.0070610856637358665,
0.012852274812757969,
0.003648048033937812,
0.018764294683933258,
0.0044343192130327225,
0.030566686764359474,
-0.03729952126741409,
-0.03804846480488777,
0.0004997417563572526,
-0.004770162049680948,
0.027715327218174934,
0.02341424860060215,
-0.09549716860055923,
-0.002262345515191555,
-0.018040306866168976,
0.012459768913686275,
-0.007067263126373291,
-0.022732697427272797,
-0.005162282846868038,
0.04184279218316078,
-0.08649040758609772,
0.045604314655065536,
-0.0079745939001441,
-0.023589543998241425,
-0.017675630748271942,
0.032095201313495636,
0.02593567781150341,
0.010300117544829845,
0.015520024113357067,
0.028293192386627197,
0.009627348743379116,
0.013221222907304764,
-0.028584783896803856,
-0.01495020929723978,
-0.05148454010486603,
0.0003637300105765462,
-0.06792254000902176,
0.053563300520181656,
-0.013518350198864937,
0.010002103634178638,
0.006436062045395374,
0.0028059000615030527,
-0.005176848731935024,
-0.05064256861805916,
0.005817836150527,
0.022507203742861748,
0.026102717965841293,
-0.007125711999833584,
0.009182273410260677,
0.0022281291894614697,
0.021918337792158127,
0.003078947076573968,
-0.013089676387608051,
0.015747185796499252,
0.012726373970508575,
-0.012310994789004326,
-0.005365950055420399,
0.0473962128162384,
-0.05263184756040573,
-0.024669740349054337,
0.025796137750148773,
-0.02195112407207489,
-0.021749038249254227,
0.004053333308547735,
-0.01611451804637909,
0.02972271479666233,
-0.02234766073524952,
-0.039159372448921204,
-0.004379493650048971,
-0.014215710572898388,
-0.039110250771045685,
0.01796170137822628,
-0.011527121998369694,
-0.014313905499875546,
-0.03614671900868416,
-0.02442142739892006,
0.04761240631341934,
0.016537988558411598,
0.0002484974393155426,
-0.0003018830029759556,
-0.06159760802984238,
0.016253761947155,
0.01754947192966938,
-0.005709426943212748,
-0.035844430327415466,
0.03944351151585579,
-0.015436246991157532,
0.014841033145785332,
-0.0368649959564209,
0.06783845275640488,
0.03138027712702751,
-0.02956014685332775,
-0.009319028817117214,
0.0393901988863945,
-0.02096794731914997,
0.03321434184908867,
0.007453295402228832,
-0.02768816612660885,
-0.035110633820295334,
-0.0027830207254737616,
-0.03419066593050957,
-0.0229200329631567,
0.030812352895736694,
-0.047633808106184006,
-0.028778422623872757,
-0.04173789173364639,
0.0043131583370268345,
-0.015788841992616653,
0.04919306933879852,
-0.015649190172553062,
-0.001361242146231234,
-0.012739724479615688,
0.04926628619432449,
-0.0330917052924633,
-0.015542840585112572,
-0.013898875564336777,
0.0038424846716225147,
-0.03815241530537605,
0.023724181577563286,
-0.05393292009830475,
-0.0020792351569980383,
0.013160423375666142,
0.00242297793738544,
0.021609708666801453,
-0.004424359183758497,
0.02626829221844673,
-0.000405662547564134,
0.03775981813669205,
-0.022147327661514282,
-0.022758375853300095,
-0.013853570446372032,
-0.04883556067943573,
-0.04704960808157921,
0.07157794386148453,
-0.014821946620941162,
0.06515217572450638,
0.005864648148417473,
-0.02534118853509426,
0.012950092554092407,
0.0829472690820694,
-0.037216272205114365,
-0.01832122914493084,
0.02355339191854,
-0.02875616028904915,
0.006796484347432852,
-0.0065129464492201805,
0.016108866780996323,
-0.04613519832491875,
0.012547031044960022,
-0.016196997836232185,
0.02308463864028454,
0.0026697060093283653,
0.007944690994918346,
0.015471987426280975,
0.019429896026849747,
-0.059157487004995346,
0.027287591248750687,
-0.0023547157179564238,
0.04136836528778076,
0.0667777955532074,
-0.05507732182741165,
0.02520318701863289,
-0.0018007031176239252,
0.013273097574710846,
-0.06250545382499695,
0.012749229557812214,
-0.015827666968107224,
-0.003723025554791093,
0.04667249321937561,
-0.06732749938964844,
0.002185945864766836,
0.012926202267408371,
-0.06846165657043457,
0.0233526099473238,
-0.06276310235261917,
-0.012655931524932384,
-0.00871774647384882,
0.008974060416221619,
0.00206571351736784,
0.005047991406172514,
0.05394236743450165,
0.008104989305138588,
0.028394440189003944,
-0.017318647354841232,
-0.0013045951491221786,
-0.03311808407306671,
0.00901033729314804,
0.04692511260509491,
-0.015640156343579292,
-0.008844511583447456,
0.003056854475289583,
-0.001459520310163498,
-0.026133449748158455,
0.030407225713133812,
-0.04969782754778862,
0.004599371459335089,
-0.021004365757107735,
0.032983578741550446,
0.012559134513139725,
0.06622766703367233,
-0.012493097223341465,
0.012524870224297047,
-0.034532707184553146,
0.007925866171717644,
-0.01883430778980255,
0.007345764432102442,
-0.02935652621090412,
0.015831490978598595,
0.026537632569670677,
-0.005910967011004686,
-0.005643660668283701,
0.009419689886271954,
0.013180485926568508,
0.03523525595664978,
0.0007319712312892079,
0.03992926701903343,
-0.005046109668910503,
-0.03467470407485962,
-0.06750375032424927,
-0.02226215973496437,
0.05572698265314102,
0.029342759400606155,
-0.0255790576338768,
-0.005054302979260683,
-0.0268702432513237,
-0.010528967715799809,
0.006687655579298735,
-0.00875141192227602,
0.008983816020190716,
-0.01914108917117119,
-0.01944143883883953,
-0.03879428282380104,
0.019875280559062958,
-0.024591565132141113,
-0.0018766445573419333,
-0.016285788267850876,
-0.006205473095178604,
0.03587295114994049,
0.05196305364370346,
-0.025082899257540703,
-0.027811335399746895,
0.012443325482308865,
0.003652897896245122,
-0.07547079026699066,
0.01916099712252617,
0.039328571408987045,
-0.01104719378054142,
-0.05828259140253067,
-0.014935154467821121,
-0.003774793818593025,
0.009058857336640358,
0.021137159317731857,
-0.014964664354920387,
0.016591118648648262,
-0.0012787394225597382,
-0.01548372395336628,
0.015399948693811893,
-0.043349720537662506,
0.0019174987683072686,
-0.02743389829993248,
-0.027611466124653816,
0.00044178401003591716,
-0.011786039918661118,
-0.020185081288218498,
-0.01904832199215889,
0.026055432856082916,
0.0013197115622460842,
0.034438177943229675,
0.0020948913879692554,
-0.030272087082266808,
0.013545803725719452,
0.018218064680695534,
0.005856628529727459,
0.025827055796980858,
0.031499091535806656,
0.0011483667185530066,
0.0323178730905056,
-0.018420208245515823,
-0.02093956619501114,
0.036639682948589325,
-0.052348680794239044,
-0.035983748733997345,
-0.048676736652851105,
-0.021521933376789093,
-0.007556816563010216,
-0.07344307750463486,
-0.005346201825886965,
0.013682541437447071,
-0.026080626994371414,
0.012822655960917473,
0.02042734995484352,
-0.006306915078312159,
0.0389287956058979,
0.01158592477440834,
0.023154685273766518,
0.039053775370121,
0.0011787883704528213,
-0.016899792477488518,
0.012183760292828083,
0.009605645202100277,
0.024366317316889763,
0.032509591430425644,
0.028520526364445686,
-0.004680005367845297,
0.027516532689332962,
-0.02396482415497303,
0.0401344895362854,
0.005536472890526056,
0.019198914989829063,
0.010405594483017921,
0.004069906659424305,
-0.007003610488027334,
0.028195450082421303,
0.022471023723483086,
0.04287067800760269,
-0.0617794506251812,
0.020793858915567398,
-0.028201088309288025,
-0.015619739890098572,
-0.01849621720612049,
0.015755128115415573,
-0.03521018847823143,
0.02815205045044422,
-0.02023099549114704,
0.011375977657735348,
-0.014203607104718685,
-0.013567337766289711,
0.04503824561834335,
-0.010900264605879784,
0.016117535531520844,
0.023556478321552277,
0.01506088487803936,
0.04203934222459793,
0.015093408524990082,
-0.025645578280091286,
-0.019235407933592796,
0.03782954439520836,
0.0241104643791914,
0.031267937272787094,
-0.04808304086327553,
-0.006502818316221237,
-0.010570075362920761,
0.002409079112112522,
-0.039940182119607925,
-0.015858905389904976,
-0.022986575961112976,
0.02683894708752632,
0.0005472825723700225,
-0.018785158172249794
] |
<p>We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two parameters $t_1$ and $t_2$ or else in Lorentz matrix
$$\eta_{00} = \eta_{11} = -1$$ and, $$\eta_{22} = \eta_{33} = 1.$$</p>
<p>Is there any physical reason for not taking this, like the norms become negative or something else? </p> | 4,584 | [
0.011325533501803875,
0.006698705721646547,
-0.013757959008216858,
-0.038441002368927,
0.04471421241760254,
0.004316073842346668,
-0.04820866137742996,
-0.011937430128455162,
-0.006170482374727726,
-0.003949359524995089,
0.0009727721917442977,
0.00146258354652673,
0.020999645814299583,
0.03955089673399925,
0.023096591234207153,
0.04740828275680542,
-0.010338623076677322,
-0.021999113261699677,
-0.03636930510401726,
-0.023577935993671417,
0.005235936958342791,
0.01440503727644682,
0.021403798833489418,
0.03345886990427971,
-0.04777791351079941,
0.04387016221880913,
0.052010275423526764,
-0.03898114338517189,
0.0033917941618710756,
0.0527917854487896,
-0.021522223949432373,
-0.03708739951252937,
0.02051786705851555,
0.05424591526389122,
0.014639140106737614,
-0.016577111557126045,
-0.0403541661798954,
-0.030258214101195335,
-0.006560293957591057,
0.03327805548906326,
-0.0377238392829895,
-0.020367588847875595,
-0.03464511036872864,
0.01011069118976593,
-0.022162815555930138,
0.05460399389266968,
0.012825541198253632,
-0.025331690907478333,
0.053288351744413376,
-0.04892120882868767,
0.06013110652565956,
0.010380584746599197,
0.008621335960924625,
0.001131419907324016,
-0.013119456358253956,
-0.01383855938911438,
0.09648196399211884,
0.022112078964710236,
0.03847825899720192,
-0.0642310380935669,
-0.027991149574518204,
-0.007518364582210779,
-0.0054969023913145065,
-0.004156633745878935,
-0.0000017112744217229192,
0.021823450922966003,
0.012226687744259834,
-0.02129572257399559,
-0.011761407367885113,
-0.022348478436470032,
-0.0011861597886309028,
-0.008387578651309013,
0.04903551936149597,
-0.0020931356120854616,
0.010548668913543224,
0.010909473523497581,
0.04993464797735214,
0.02821515128016472,
0.04508630931377411,
0.0352836549282074,
-0.0006629455019719899,
0.006458489689975977,
0.06310471892356873,
0.032643772661685944,
-0.010745526291429996,
-0.02414410002529621,
0.06747917085886002,
-0.00524508161470294,
-0.008897504769265652,
0.007117243483662605,
0.003483114531263709,
0.0034331539645791054,
0.06137588247656822,
-0.025171922519803047,
-0.011664241552352905,
0.021152867004275322,
0.020532311871647835,
0.02564035914838314,
0.000017936630683834665,
0.009985028766095638,
-0.03632114827632904,
0.0050956024788320065,
0.0017752953572198749,
0.028482802212238312,
-0.0006074292468838394,
0.03320353478193283,
-0.00716182217001915,
0.005512177478522062,
-0.018838029354810715,
-0.0030757489148527384,
-0.0516572929918766,
-0.017426904290914536,
-0.023169701918959618,
0.017348840832710266,
0.012282844632863998,
-0.02299770712852478,
0.01281469315290451,
-0.02760239876806736,
0.02474621869623661,
0.11649923026561737,
0.04573185369372368,
-0.013355624862015247,
0.003154072444885969,
-0.00376146100461483,
-0.08285576105117798,
0.038441963493824005,
0.03902101144194603,
0.01440337486565113,
-0.02998453378677368,
0.04622335359454155,
-0.0006003802991472185,
0.005451880395412445,
0.04614672437310219,
-0.004219315480440855,
0.05554928630590439,
0.00024438861873932183,
-0.07781361043453217,
-0.05855521187186241,
0.044756267219781876,
-0.008974136784672737,
-0.05197572335600853,
-0.07887612283229828,
0.013354616239666939,
0.015338489785790443,
0.1068771556019783,
0.016941238194704056,
0.04720725119113922,
0.012217890471220016,
0.012601426802575588,
0.0030623110942542553,
-0.053339920938014984,
0.010015162639319897,
-0.0025011361576616764,
0.0008390644798055291,
0.00473152007907629,
-0.052248015999794006,
-0.004243320785462856,
0.029558366164565086,
0.013278200291097164,
0.007656559348106384,
0.04404332488775253,
0.004723559133708477,
-0.0025016714353114367,
0.04138123244047165,
-0.02104494906961918,
-0.039422620087862015,
0.03481638804078102,
0.005457484163343906,
-0.01650496944785118,
0.015726929530501366,
-0.015922911465168,
0.025426065549254417,
0.012213096022605896,
0.0742739886045456,
0.02796773612499237,
-0.0007583833648823202,
-0.02960381843149662,
0.034345563501119614,
0.005056764930486679,
-0.015911919996142387,
-0.04742922633886337,
-0.03447902202606201,
-0.03915025666356087,
0.011926145292818546,
0.006002219393849373,
0.018917812034487724,
-0.02216375060379505,
-0.002210780279710889,
0.01995353028178215,
-0.02532932534813881,
0.01238725520670414,
-0.07405243813991547,
-0.016357392072677612,
0.05976448953151703,
-0.02704675868153572,
0.05433576926589012,
0.010844234377145767,
0.026469841599464417,
-0.03763170912861824,
-0.007790287956595421,
-0.0544811487197876,
0.03476535901427269,
-0.007309459615498781,
0.0003350863989908248,
0.03466970473527908,
0.06033501401543617,
0.033583201467990875,
0.007602740079164505,
-0.001752179698087275,
-0.01286901906132698,
-0.04745825007557869,
-0.005636174697428942,
-0.026812270283699036,
0.06805465370416641,
0.016300104558467865,
-0.02474316768348217,
-0.008666768670082092,
-0.0028091215062886477,
-0.03070385754108429,
0.03536323085427284,
-0.0325234979391098,
0.0725417360663414,
0.05744191259145737,
-0.01484590768814087,
-0.013764015398919582,
0.029031116515398026,
0.00643030134961009,
0.004937612917274237,
-0.0008323265938088298,
-0.014095121994614601,
-0.015533904545009136,
0.003366324817761779,
0.02302020601928234,
0.0750577300786972,
-0.018675900995731354,
0.004713594447821379,
0.022685296833515167,
0.03643606975674629,
-0.04000477120280266,
0.027501963078975677,
-0.007748181466013193,
-0.05141383036971092,
-0.018349850550293922,
-0.026364309713244438,
0.006998193915933371,
-0.0017340992344543338,
0.03490995988249779,
0.00686353025957942,
-0.016741733998060226,
0.0008345775422640145,
-0.018910806626081467,
0.039971597492694855,
-0.03198191896080971,
0.0038214793894439936,
0.01769673079252243,
-0.009345723316073418,
0.03831883519887924,
-0.006441364996135235,
0.0353504903614521,
0.06315203756093979,
0.02995661459863186,
-0.030268317088484764,
-0.004177139140665531,
-0.009151843376457691,
-0.023563381284475327,
0.041541337966918945,
0.008598771877586842,
-0.035931553691625595,
0.04817148670554161,
-0.050417590886354446,
0.003819658188149333,
0.01964576356112957,
-0.035081420093774796,
-0.02332066185772419,
-0.04232381284236908,
0.05560488998889923,
0.008576138876378536,
0.03282179683446884,
-0.012417731806635857,
-0.03242979571223259,
0.014146815985441208,
0.005223817657679319,
0.005479726940393448,
0.027356639504432678,
-0.022574257105588913,
0.035918138921260834,
-0.03535871207714081,
0.010711589828133583,
0.020179694518446922,
-0.012842955067753792,
0.05006815865635872,
0.01004027109593153,
-0.025124194100499153,
-0.05714526027441025,
-0.05038227513432503,
-0.017939912155270576,
0.009447251446545124,
-0.016001928597688675,
-0.028052017092704773,
0.06282858550548553,
0.012005455791950226,
-0.06249883770942688,
-0.02413337305188179,
-0.0546577088534832,
-0.0656476616859436,
-0.036127861589193344,
-0.000843566027469933,
-0.011476577259600163,
-0.032789796590805054,
0.0021865235175937414,
0.05030230060219765,
-0.02844216860830784,
-0.0008328540716320276,
-0.06462564319372177,
-0.01920691691339016,
0.04267630726099014,
-0.023806095123291016,
0.050711099058389664,
-0.011609591543674469,
-0.027566229924559593,
0.0752171128988266,
0.010397708974778652,
0.003962044604122639,
-0.032707732170820236,
0.0017210033256560564,
-0.02384524792432785,
-0.04772794246673584,
0.03566831722855568,
0.04647571220993996,
0.020081467926502228,
0.04587828367948532,
0.014922620728611946,
0.056286029517650604,
0.03348119929432869,
0.014733352698385715,
-0.04429222643375397,
-0.00005405311821959913,
0.003852822119370103,
0.01239938847720623,
0.024561243131756783,
0.006179823540151119,
-0.024826856330037117,
0.013388488441705704,
-0.010995055548846722,
0.06019992381334305,
0.007356628309935331,
-0.019712764769792557,
0.03534180670976639,
0.005404092837125063,
0.027499908581376076,
-0.027419602498412132,
0.01900610700249672,
-0.006865364965051413,
0.002282538218423724,
-0.03212660923600197,
0.025324620306491852,
0.008837452158331871,
-0.05633307248353958,
0.015399729833006859,
0.001680782181210816,
0.026259003207087517,
-0.02442554198205471,
0.0007861409685574472,
0.02052890881896019,
0.025611329823732376,
0.04146793857216835,
-0.025207696482539177,
0.0016079163178801537,
0.042447492480278015,
0.0450211800634861,
0.004361235070973635,
0.016352882608771324,
-0.03429708629846573,
-0.030729476362466812,
-0.06489837914705276,
-0.011532149277627468,
-0.007040343247354031,
0.04467184841632843,
0.014947130344808102,
0.009220928885042667,
0.0002869171148631722,
0.010038568638265133,
0.017385335639119148,
-0.028142638504505157,
-0.06878717988729477,
-0.025803767144680023,
-0.03662201762199402,
-0.0028238832019269466,
-0.0031553558073937893,
0.010970846749842167,
0.013948677107691765,
-0.06933609396219254,
-0.028251316398382187,
0.01836918480694294,
-0.01946994848549366,
-0.06982646137475967,
-0.013614876195788383,
-0.026817994192242622,
-0.023347148671746254,
-0.04209529608488083,
0.02375248819589615,
0.05885068699717522,
-0.016035640612244606,
0.014486080966889858,
0.009679431095719337,
-0.04104134067893028,
-0.01016645971685648,
0.014858166687190533,
0.025107644498348236,
0.03842032328248024,
0.03693576157093048,
-0.016322126612067223,
0.013614780269563198,
-0.019788099452853203,
0.01180746778845787,
0.007553716190159321,
0.035797666758298874,
0.0010202545672655106,
0.00465224077925086,
-0.02820172905921936,
-0.024509962648153305,
-0.0324387364089489,
-0.004536578431725502,
0.056969620287418365,
-0.0005867248401045799,
0.003401420312002301,
0.02532472275197506,
0.024786770343780518,
-0.00820337887853384,
-0.0024463902227580547,
0.06828684359788895,
-0.030372947454452515,
0.0005374442553147674,
-0.02837527170777321,
-0.055564191192388535,
-0.02064407616853714,
-0.027915386483073235,
-0.009027685038745403,
-0.02687450498342514,
-0.030511077493429184,
0.024644503369927406,
0.00880705751478672,
0.016999030485749245,
-0.025075245648622513,
0.007714633364230394,
0.022141046822071075,
-0.005803703796118498,
0.012251167558133602,
-0.004808209836483002,
-0.02166905626654625,
0.04690387472510338,
0.02804090641438961,
0.004348846152424812,
0.0002900333784054965,
-0.0706988275051117,
-0.02126369997859001,
-0.002555042039602995,
0.032521579414606094,
0.02486775629222393,
-0.02400926873087883,
-0.042861729860305786,
-0.04236796870827675,
0.04590322822332382,
-0.005998949985951185,
0.008273121900856495,
0.02100509963929653,
-0.039545003324747086,
-0.04593854397535324,
-0.019894849509000778,
-0.000042851690523093566,
0.01810556836426258,
0.031467851251363754,
0.014836031012237072,
0.014102679677307606,
0.00985557958483696,
-0.020696429535746574,
0.04646691679954529,
-0.0029097890947014093,
0.04251895844936371,
-0.001022107433527708,
0.01022036001086235,
-0.003462764900177717,
0.0038323483895510435,
-0.013717691414058208,
-0.0737968161702156,
0.0017860203515738249,
0.05669521167874336,
-0.007735689170658588,
0.0364333838224411,
-0.02771230787038803,
-0.022137578576803207,
-0.00948735699057579,
-0.021463846787810326,
0.0028682469855993986,
0.04884081333875656,
-0.02627849206328392,
0.026363177224993706,
0.003627002937719226,
0.0016878161113709211,
0.03496063873171806,
0.018756136298179626,
-0.00942070223391056,
0.003212893847376108,
-0.022993145510554314,
0.034299951046705246,
-0.0360652320086956,
0.02540859580039978,
-0.02108064480125904,
-0.02064773067831993,
-0.02787678688764572,
0.04181777313351631,
-0.0007701963186264038,
0.02885724976658821,
0.030756177380681038,
-0.006651559844613075,
-0.005095068830996752,
0.06959784775972366,
0.027357565239071846,
0.0016032196581363678,
-0.006194221321493387,
0.008600951172411442,
-0.016406893730163574,
-0.05185719206929207,
0.027876123785972595,
-0.038927119225263596,
-0.012705953791737556,
0.02668163739144802,
-0.009331578388810158,
0.02122405357658863,
0.012746026739478111,
0.005183480679988861,
-0.0072080520913004875,
-0.05133787542581558,
0.025282997637987137,
-0.008771836757659912,
-0.021836865693330765,
-0.01810464635491371,
-0.005597382318228483,
-0.020662453025579453,
-0.015206838957965374,
-0.04729485884308815,
0.02577267773449421,
-0.04747987166047096,
0.04193393141031265,
0.01750253513455391,
0.014098582789301872,
-0.0949045866727829,
-0.02693045325577259,
0.01695081777870655,
-0.0143362358212471,
0.007408240810036659,
-0.0009123592171818018,
0.010737731121480465,
-0.06783648580312729,
-0.033890217542648315,
0.009827313013374805,
0.07743430137634277,
0.006182957906275988,
-0.04571001976728439,
0.011504624970257282,
0.03061637096107006,
0.03560185804963112,
0.003042523982003331,
-0.008390548638999462,
0.027146127074956894,
-0.013436999171972275,
-0.02038499526679516,
-0.023922041058540344,
0.018866755068302155,
-0.033627815544605255,
-0.003427790477871895,
-0.0036821868270635605,
-0.004738028161227703,
0.0038453172892332077,
-0.028427384793758392,
-0.003849871689453721,
0.028543032705783844,
-0.0006557794404216111,
0.02530508302152157,
-0.05577179044485092,
0.035994816571474075,
0.001866684528067708,
-0.006889405660331249,
-0.006218322552740574,
-0.021375443786382675,
-0.022306112572550774,
-0.041340719908475876,
0.03923213854432106,
0.013090971857309341,
-0.03201624006032944,
-0.0013049037661403418,
-0.023964958265423775,
0.010961562395095825,
-0.022072074934840202,
0.030092578381299973,
-0.014945202507078648,
0.006043767090886831,
-0.017634471878409386,
0.0020419040229171515,
0.05168579891324043,
0.011953914538025856,
-0.035855140537023544,
-0.05050267279148102,
-0.024520421400666237,
0.035403817892074585,
0.053562264889478683,
-0.042661625891923904,
0.05763448029756546,
0.026178324595093727,
-0.029684016481041908,
-0.0046483660116791725,
-0.013956733047962189,
0.014616228640079498,
0.023747242987155914,
-0.017747092992067337,
0.010141468606889248,
-0.025423740968108177,
0.009489532560110092,
0.02480616234242916,
0.03160162270069122,
-0.03768191859126091,
0.02395826391875744,
0.012489422224462032,
-0.012895865365862846,
0.013634969480335712,
-0.025812752544879913,
-0.029671764001250267,
0.04383087530732155,
-0.03484061732888222,
-0.02549612708389759,
0.02601848542690277,
-0.005100446753203869,
0.03184547647833824,
-0.006905676331371069,
-0.004791926126927137,
-0.020914016291499138,
-0.014141712337732315,
-0.06480959057807922,
-0.012532197870314121,
0.03899697586894035,
0.036288484930992126,
0.011829386465251446,
-0.03265481814742088,
0.053407616913318634,
0.019096825271844864,
-0.004891606047749519,
0.0041852472350001335,
-0.0694655105471611,
-0.00894892681390047,
-0.034624338150024414,
-0.029361318796873093,
0.05359672009944916,
-0.004132351838052273,
-0.004836489912122488,
-0.00810993742197752,
-0.041650719940662384,
-0.005809531081467867,
0.02595078945159912,
0.07198696583509445,
-0.06041768193244934,
0.05376206710934639,
-0.009798312559723854,
0.011184324510395527,
-0.052745867520570755,
0.012787727639079094,
0.09116958826780319,
0.05452824756503105,
0.01953912153840065,
-0.056418731808662415,
0.010823770426213741,
-0.016632573679089546,
-0.02479543909430504,
-0.025262536481022835,
0.0297661405056715,
-0.021980874240398407,
0.023339463397860527,
0.0008729029796086252,
0.07056071609258652,
0.006376889534294605,
-0.06984985619783401,
0.00966027844697237,
-0.022128216922283173,
-0.018763437867164612,
-0.014487885870039463,
0.036759063601493835,
-0.010623853653669357,
0.0032090472523123026,
-0.014401255175471306,
0.06903299689292908,
-0.009464495815336704,
0.03046363592147827,
-0.007331504952162504,
0.004986430052667856,
-0.0057923439890146255,
-0.0263291597366333,
-0.07603269070386887,
-0.0006525776698254049,
0.05400344356894493,
0.01491666492074728,
-0.04902969300746918,
-0.002911387011408806,
-0.010173620656132698,
-0.03907620906829834,
-0.0020697908475995064,
0.035928476601839066,
-0.009260025806725025,
0.010165909305214882,
0.008824636228382587,
-0.0063460879027843475,
-0.026118310168385506,
-0.008753495290875435,
-0.0213748961687088,
0.060317132622003555,
-0.03492584824562073,
-0.018717031925916672,
0.017239514738321304,
0.009373536333441734,
0.015534899197518826,
-0.04972200468182564,
-0.03215905278921127,
-0.011363203637301922,
0.04851161316037178,
0.0018186880042776465,
0.01685757003724575,
-0.012448371388018131,
0.01935095153748989,
0.025740623474121094,
0.016464903950691223,
0.018587026745080948,
-0.010837146081030369,
0.012159108184278011,
0.012129513546824455,
0.072198785841465,
0.05245284363627434,
0.007834963500499725,
-0.023437757045030594,
0.002209836384281516,
-0.07110968977212906,
-0.0036643717903643847,
0.020258737727999687,
0.04117744415998459,
0.03397320210933685,
0.00329409702681005,
-0.02507096529006958,
-0.022123539820313454,
-0.017664166167378426,
0.01656149886548519,
-0.030982445925474167,
0.0032278383150696754,
-0.003022083779796958,
-0.01401591207832098,
-0.021974481642246246,
0.003456518752500415,
-0.051927272230386734,
-0.006036063656210899,
0.0157800130546093,
0.029315399006009102,
0.0224774107336998,
-0.044126689434051514,
0.007827642373740673,
-0.004973725415766239,
-0.06024933606386185,
-0.0016372461104765534,
-0.032898224890232086,
0.014180557802319527,
-0.00926471222192049,
-0.0066256653517484665,
0.024613790214061737,
0.03702521324157715,
-0.006941742729395628,
-0.03380155563354492,
0.038183555006980896,
-0.023056576028466225,
0.010076399892568588,
0.024437084794044495,
0.011930971406400204,
-0.029377153143286705,
-0.012220821343362331,
-0.02178572304546833,
-0.01816551946103573,
-0.01077622827142477,
0.026822352781891823,
-0.01029319316148758,
0.005670441780239344,
-0.028628423810005188,
0.013485681265592575,
-0.022572722285985947,
0.004386229440569878,
-0.018186304718255997,
0.01424528006464243,
-0.027933957055211067,
-0.03993513435125351,
0.00012664380483329296,
0.0073607065714895725,
-0.028885729610919952,
-0.006985407322645187,
0.029532676562666893,
0.011928732506930828,
-0.01802782155573368,
0.0019208540907129645,
0.010294566862285137,
0.01630598120391369,
0.034024596214294434,
0.0004798056907020509,
-0.06384618580341339,
0.03379148244857788,
-0.019967246800661087,
-0.007439193781465292,
0.03200948238372803,
-0.017977893352508545,
0.02116018906235695,
0.026638388633728027,
-0.03455619886517525,
-0.05233542248606682,
0.06202230229973793,
-0.025723213329911232,
-0.020879829302430153,
0.03125922754406929,
-0.015611601062119007,
0.004316623322665691,
-0.009125364944338799,
0.013266394846141338,
-0.0063168322667479515,
-0.03264086693525314,
-0.004560297355055809,
0.02307645045220852,
-0.0036528778728097677,
-0.025386536493897438,
0.005284673534333706,
-0.022352058440446854,
0.04353857412934303,
0.012494668364524841,
-0.014698942191898823,
-0.028936272487044334,
0.05660064518451691,
-0.05470694974064827,
-0.0066687879152596,
0.03728379309177399,
-0.02340707927942276,
-0.12320255488157272,
-0.027509331703186035,
0.05217841640114784,
0.006659131497144699,
0.03198003023862839,
-0.055617764592170715,
-0.010801075026392937,
0.030551889911293983,
-0.06154755875468254,
0.023148642852902412,
0.0019541888032108545,
-0.04907146841287613,
-0.004154144320636988,
-0.04072479158639908,
-0.012536780908703804,
0.057019248604774475,
0.02530727908015251,
0.05734219029545784,
-0.016236718744039536,
0.003445960348471999,
-0.05511707067489624,
-0.06681499630212784,
-0.005360674578696489,
0.032939374446868896,
-0.02830476313829422,
0.0294811949133873,
0.06583020091056824,
-0.008427963592112064,
-0.032274626195430756,
0.045695818960666656,
0.04052760824561119,
0.009957102127373219,
-0.005024085287004709,
-0.0007583440165035427,
0.01946847327053547,
0.037078965455293655,
0.03702745959162712,
0.0004137708165217191,
0.025686005130410194,
0.014872800558805466,
-0.005631227511912584,
-0.023614943027496338,
0.004017360974103212,
0.0197607334703207,
0.01548074372112751,
-0.037938863039016724,
-0.005651760846376419,
0.04184824228286743,
-0.00943769235163927,
-0.008140163496136665,
0.007638861425220966,
0.02199741080403328,
-0.0068936096504330635,
0.016834422945976257,
-0.005880017764866352,
-0.03763240948319435,
-0.019986184313893318,
0.006059492472559214,
0.007295546587556601,
-0.033738549798727036,
0.01997300423681736,
-0.008649340830743313,
-0.027619319036602974,
0.024453718215227127,
0.019323790445923805,
0.005365096032619476,
-0.07394187897443771,
-0.023738525807857513,
0.006056312005966902,
0.018029265105724335,
-0.011412274092435837,
-0.02160726860165596,
-0.05445796623826027,
0.028783194720745087,
0.03506937623023987,
0.07837654650211334,
0.01345152873545885,
-0.06449778378009796,
-0.009717044420540333,
-0.08089059591293335,
0.00993799977004528,
0.017162254080176353,
0.029361899942159653,
0.001561869983561337,
-0.022548222914338112,
-0.04508260637521744,
0.0418512299656868,
0.08804455399513245,
0.030162835493683815,
-0.006939341314136982,
-0.0008490050677210093,
0.01706598326563835,
0.02626834437251091,
-0.014843259938061237,
-0.013624747283756733,
0.007084791548550129,
-0.026288049295544624,
-0.005931566469371319,
0.0010609400924295187,
0.017690224573016167,
0.00035588108585216105,
0.021956956014037132,
-0.015124926343560219,
0.0343598946928978,
0.01873781718313694,
-0.0504971407353878,
0.05378191918134689,
-0.02043951489031315,
0.004174582660198212,
0.07230890542268753,
0.008523162454366684,
0.03364073857665062,
-0.028885425999760628,
-0.032145850360393524,
-0.03289121016860008,
0.0009602844947949052,
-0.0075561474077403545,
-0.004123665392398834,
-0.03565974533557892,
0.008438991382718086,
0.014971275813877583,
-0.011701446957886219,
0.020177295431494713,
0.08120036125183105,
-0.010950868017971516,
0.00870037917047739,
0.03234350308775902,
0.02379322238266468,
0.03003752790391445,
-0.030794460326433182,
0.0163215771317482,
0.04760082811117172,
0.0037480988539755344,
0.03179242089390755,
0.026247462257742882,
0.025269443169236183,
-0.025176184251904488,
0.008748991414904594,
0.023869866505265236,
-0.049935419112443924,
0.00620593037456274,
0.010759314522147179,
0.025676684454083443,
-0.02667650207877159,
0.026327187195420265,
0.03449975326657295,
0.02271847054362297,
0.007403196766972542,
0.0028342383448034525,
-0.014308142475783825,
0.0774310827255249,
-0.0036873039789497852,
0.0033897683024406433,
-0.04057048261165619,
0.006674714852124453,
-0.02422928996384144,
0.013784805312752724,
0.009076159447431564,
0.04707689583301544,
-0.008918005041778088,
0.009548266418278217,
-0.03142165392637253,
0.004317693877965212,
-0.01255084853619337,
-0.05284291133284569,
-0.008029405027627945,
0.031182365491986275,
-0.006012137979269028,
-0.024790102615952492,
0.0006538235465995967,
-0.029328925535082817,
-0.06166909262537956,
0.02601885050535202,
0.013735294342041016,
0.02464083954691887,
0.0007651528576388955,
0.023028099909424782,
-0.007535392884165049,
0.01852419786155224,
-0.045989029109478,
-0.038068246096372604,
-0.03677535057067871,
0.05282169207930565,
-0.03917941451072693,
0.0005259578465484083
] |
<p>Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ or $0$.</p>
<p>Now If we consider </p>
<p>$$\begin{align}
S=1,L=2 &\to 2S+1=3; J=3,2,1\\
S=0,L=2 &\to 2S+1=1; J=2\\
S=1,L=1 &\to 2S+1=3; J=2,1,0\\
S=0,L=1 &\to 2S+1=1; J=1\\
S=1,L=0 &\to 2S+1=3; J=1\end{align}$$</p>
<p>But the last one does not show that $2S+1$ is multiplicity as it has only one $J$ value. Where am I making a mistake?</p> | 4,585 | [
-0.014194190502166748,
0.016642045229673386,
-0.005467154085636139,
0.0021420856937766075,
0.01684911735355854,
-0.031223777681589127,
-0.018557045608758926,
-0.06123606115579605,
0.004513045772910118,
-0.03194677084684372,
0.09511261433362961,
0.007917207665741444,
0.020274478942155838,
0.06288036704063416,
0.037346210330724716,
0.018187562003731728,
-0.008364928886294365,
-0.013209749013185501,
0.009518878534436226,
0.024799438193440437,
-0.02335210144519806,
-0.003924389835447073,
0.00832490622997284,
-0.02693760022521019,
-0.01723591238260269,
0.03279821202158928,
0.0060287280939519405,
-0.0028240408282727003,
0.058900799602270126,
0.04699943587183952,
0.009574921801686287,
-0.05352318659424782,
0.05238042399287224,
0.033826299011707306,
0.009690799750387669,
0.025039738044142723,
-0.01570899784564972,
-0.039174359291791916,
0.015135782770812511,
0.03604064881801605,
-0.036344993859529495,
-0.019150536507368088,
-0.02030775137245655,
0.01076577603816986,
0.005536416079849005,
-0.0032012390438467264,
0.011434164829552174,
-0.004136069677770138,
0.05825462564826012,
-0.04921484366059303,
0.066217802464962,
0.021489324048161507,
0.01645607128739357,
-0.013358972035348415,
-0.01307582389563322,
0.007062009070068598,
0.06278925389051437,
0.060823578387498856,
0.007555388379842043,
-0.04856626316905022,
-0.017102109268307686,
-0.04429003596305847,
0.029117196798324585,
0.011125481687486172,
-0.034976594150066376,
0.01767585426568985,
0.0028501348569989204,
-0.06967364996671677,
0.020410966128110886,
-0.0010128297144547105,
-0.022923802956938744,
0.017427774146199226,
0.007264371961355209,
-0.053528305143117905,
0.01997540518641472,
-0.01994231715798378,
0.055048391222953796,
0.024317817762494087,
0.004253613296896219,
0.04042569920420647,
0.008488043211400509,
0.013318615965545177,
0.020251614972949028,
0.03293566033244133,
0.0016081079374998808,
-0.03230651095509529,
0.06152891740202904,
0.035720448940992355,
-0.009913605637848377,
0.010030871257185936,
0.0014495818177238107,
0.030201831832528114,
0.016413679346442223,
-0.004379838705062866,
-0.015932250767946243,
0.03112587332725525,
-0.01481932308524847,
0.03302885219454765,
0.012959393672645092,
-0.01625288650393486,
0.0008151307119987905,
-0.054563432931900024,
0.04318265989422798,
0.043387748301029205,
-0.007622252684086561,
0.004034603480249643,
-0.05053747072815895,
-0.008274145424365997,
0.009489252232015133,
0.0009973206324502826,
-0.003618535352870822,
0.0330948643386364,
0.02285008132457733,
-0.006655274424701929,
-0.017527727410197258,
-0.008991620503365993,
-0.022598452866077423,
-0.005898552481085062,
0.016307108104228973,
0.05528606101870537,
0.007057315204292536,
-0.04941009357571602,
0.024475960060954094,
-0.003964578732848167,
-0.08041298389434814,
0.01845802366733551,
0.020734116435050964,
-0.010421129874885082,
-0.04899553582072258,
0.009305397048592567,
-0.0008921140688471496,
-0.0014728077221661806,
0.03180518001317978,
0.0015460256254300475,
0.032294176518917084,
-0.020311612635850906,
-0.09011216461658478,
-0.0357225202023983,
0.004182110074907541,
-0.011271746829152107,
-0.0025705297011882067,
-0.0662384182214737,
0.009763925336301327,
0.01722533255815506,
0.07584396004676819,
0.004977785050868988,
-0.01085530687123537,
0.004255244974046946,
0.030090445652604103,
0.054522134363651276,
0.007477607578039169,
-0.00009028098429553211,
0.0101493364199996,
-0.04184620827436447,
0.010131518356502056,
-0.029464703053236008,
0.04109058529138565,
0.02428695186972618,
0.026874560862779617,
-0.041724108159542084,
0.056780170649290085,
-0.033587440848350525,
0.010586217977106571,
0.016391735523939133,
-0.012782702222466469,
-0.02314477227628231,
0.06667311489582062,
0.015216482803225517,
0.014088612049818039,
0.04067453742027283,
0.025721117854118347,
0.007288138382136822,
-0.026350244879722595,
0.03623971343040466,
0.021720649674534798,
-0.056024882942438126,
-0.03867829218506813,
-0.04966229572892189,
0.032149504870176315,
0.001291819498874247,
-0.07123297452926636,
-0.010074835270643234,
0.009346607141196728,
0.0447070486843586,
0.012350499629974365,
0.042029350996017456,
0.00020979596592951566,
0.00269009149633348,
-0.008795437403023243,
-0.03250737860798836,
0.017411664128303528,
-0.061054691672325134,
0.018520496785640717,
-0.01263035461306572,
-0.048485565930604935,
0.06497528403997421,
-0.021811192855238914,
0.01579076237976551,
0.01622961089015007,
0.005533475428819656,
-0.010427677072584629,
0.03820525482296944,
0.005029850173741579,
-0.04735080525279045,
0.027620894834399223,
0.07076828181743622,
0.037111178040504456,
0.03506462648510933,
0.0243462435901165,
-0.029024895280599594,
0.010970275849103928,
0.021986795589327812,
0.004962954670190811,
0.026700899004936218,
0.0036853384226560593,
-0.030877605080604553,
-0.007541934493929148,
-0.0034276535734534264,
0.00007532611925853416,
0.07104223221540451,
-0.02590346895158291,
0.04928198829293251,
0.06546851247549057,
0.010702510364353657,
0.0018915337277576327,
-0.027089368551969528,
0.003611996304243803,
0.047322746366262436,
0.008991946466267109,
-0.029296698048710823,
-0.034070294350385666,
0.041104745119810104,
0.02853439375758171,
0.03165764734148979,
-0.032976482063531876,
0.017423925921320915,
0.0070190695114433765,
0.019613036885857582,
-0.0010572464670985937,
0.006338959559798241,
-0.05718974769115448,
-0.01760530285537243,
0.0220637246966362,
0.00841789972037077,
0.023370470851659775,
0.02381526678800583,
0.010686993598937988,
0.012129705399274826,
0.014316537417471409,
0.007077639456838369,
-0.02445940300822258,
0.0454762727022171,
-0.04035408794879913,
-0.0005324696539901197,
0.021562835201621056,
-0.0035555236972868443,
0.002667173044756055,
-0.007351370994001627,
0.03675569221377373,
0.04327443242073059,
-0.015896499156951904,
-0.021461475640535355,
0.0020350825507193804,
-0.009285279549658298,
0.006599397398531437,
-0.004412540700286627,
-0.034818802028894424,
-0.024872912093997,
0.0037019592709839344,
-0.05548571050167084,
0.011575675569474697,
-0.018244879320263863,
0.017710808664560318,
-0.013175713829696178,
0.008679796941578388,
0.045597124844789505,
-0.008203170262277126,
0.012917676940560341,
-0.05697289854288101,
-0.019934698939323425,
-0.01632070727646351,
-0.03663741052150726,
0.06155839189887047,
-0.006035794969648123,
-0.02779787965118885,
-0.012070373632013798,
-0.027419866994023323,
-0.03913728892803192,
0.06169473007321358,
0.00859000999480486,
0.0012792610796168447,
-0.026318304240703583,
-0.013097134418785572,
-0.020898638293147087,
-0.034728966653347015,
-0.04150873050093651,
0.055422358214855194,
-0.03619121015071869,
-0.005739931017160416,
0.0392923578619957,
-0.004171804524958134,
-0.037479106336832047,
0.00009446583135286346,
-0.021166834980249405,
-0.028806960210204124,
-0.014384453184902668,
-0.0410250686109066,
0.018173985183238983,
-0.01435801200568676,
-0.008296306245028973,
0.020077798515558243,
-0.046181365847587585,
-0.03690014407038689,
-0.07280700653791428,
-0.04069177433848381,
0.005051499232649803,
-0.0008875317289493978,
0.026709849014878273,
-0.014937467873096466,
-0.02401016838848591,
0.06355927884578705,
0.007183744106441736,
0.0020420432556420565,
0.00021963373001199216,
0.013956841081380844,
-0.04287383705377579,
-0.004173762630671263,
-0.0021511514205485582,
0.039070114493370056,
0.02320164442062378,
0.045951250940561295,
-0.01200798712670803,
0.07631877809762955,
0.07911152392625809,
-0.01679079979658127,
-0.00814607460051775,
0.02612612210214138,
-0.03397725895047188,
0.012323946692049503,
0.06012894585728645,
0.0009138829773291945,
-0.011952253058552742,
0.02312595397233963,
0.010679243132472038,
0.019139578565955162,
0.006472019013017416,
-0.05228320136666298,
0.04232696443796158,
-0.0008066980517469347,
0.036952391266822815,
-0.031402576714754105,
0.02826831117272377,
0.061761658638715744,
-0.011784970760345459,
-0.010019299574196339,
0.02118917927145958,
0.044977206736803055,
-0.03726678341627121,
0.000881092855706811,
0.03310318663716316,
-0.007514783646911383,
-0.04240693151950836,
-0.040143709629774094,
0.04705357179045677,
-0.012193282134830952,
0.02706226333975792,
-0.02815915457904339,
-0.06283141672611237,
0.03212868422269821,
0.031794700771570206,
0.023552343249320984,
-0.01543356105685234,
-0.029241757467389107,
0.02384057082235813,
-0.07454278320074081,
-0.031147271394729614,
-0.019256215542554855,
0.05286015570163727,
-0.000041949562728405,
0.054122328758239746,
0.04671357199549675,
0.0010193701600655913,
-0.03171245753765106,
0.003430459415540099,
-0.051500990986824036,
0.01055561751127243,
-0.00011706045916071162,
0.01510649174451828,
0.005340498872101307,
-0.04170924052596092,
-0.0019843841437250376,
-0.08171281963586807,
-0.005310812499374151,
-0.016255563125014305,
-0.019267616793513298,
-0.035474855452775955,
-0.0004443534999154508,
-0.06804212182760239,
-0.005344040226191282,
-0.02226749248802662,
0.06633765250444412,
0.011119825765490532,
-0.04245666414499283,
-0.007378081791102886,
0.04306381568312645,
-0.05591515079140663,
0.0032759085297584534,
-0.02872287854552269,
0.021994272246956825,
0.03865582123398781,
0.013736710883677006,
0.037312302738428116,
0.0076364497654139996,
-0.012344139628112316,
-0.027164801955223083,
-0.0069967880845069885,
0.05440879985690117,
0.020559115335345268,
-0.010921703651547432,
-0.00012718461221084,
0.004582234192639589,
-0.0313565656542778,
-0.0010926363756880164,
0.047008123248815536,
-0.008871017955243587,
0.029565704986453056,
0.03293956443667412,
0.029594022780656815,
-0.031089870259165764,
0.03525668382644653,
0.05088670179247856,
-0.026155591011047363,
-0.032427120953798294,
-0.05051707476377487,
-0.01345175039023161,
-0.043545790016651154,
-0.007972308434545994,
0.026866473257541656,
0.0022245668806135654,
-0.01395595446228981,
-0.03265250474214554,
0.01648605801165104,
0.017939992249011993,
-0.029173467308282852,
0.015400066040456295,
-0.014621211215853691,
0.03922635689377785,
0.01588599942624569,
0.002451432403177023,
0.0031493392307311296,
-0.009586378931999207,
-0.02314627729356289,
-0.006711679045110941,
-0.010300622321665287,
-0.06402691453695297,
0.018088174983859062,
0.007582452613860369,
0.06789838522672653,
-0.031696617603302,
0.04645485803484917,
-0.026149235665798187,
-0.0017214349936693907,
0.0037610079161822796,
-0.03501090034842491,
0.05847751721739769,
-0.015301679261028767,
-0.0028826615307480097,
0.005848854314535856,
-0.04879156872630119,
-0.016473108902573586,
0.04847945272922516,
0.007747230585664511,
0.01794997788965702,
-0.03374230116605759,
0.030061636120080948,
-0.028954163193702698,
0.002842534799128771,
0.035503167659044266,
0.06246808171272278,
-0.015750957652926445,
-0.008972741663455963,
-0.01757289096713066,
0.03099542111158371,
-0.018211213871836662,
-0.06405967473983765,
0.02672971785068512,
-0.026983963325619698,
-0.017683150246739388,
0.03325933963060379,
-0.05453120917081833,
-0.0661790668964386,
0.07090414315462112,
0.00918605923652649,
-0.009798238053917885,
-0.008954980410635471,
-0.011715502478182316,
0.0542999804019928,
0.036805905401706696,
0.010185453109443188,
0.010448501445353031,
0.03332046791911125,
-0.035655174404382706,
0.03762277960777283,
-0.03630832955241203,
0.0017842919332906604,
-0.0315718948841095,
0.012744651176035404,
-0.03656059131026268,
0.012711339630186558,
-0.03577197343111038,
0.059394605457782745,
0.016920845955610275,
-0.007505844347178936,
-0.026595624163746834,
-0.026211874559521675,
0.009643026627600193,
0.011702428571879864,
0.004848466720432043,
0.04139834642410278,
-0.019746776670217514,
0.023030728101730347,
0.02834138460457325,
-0.0338931605219841,
0.014971221797168255,
-0.03789177164435387,
-0.01274376455694437,
0.03652137890458107,
-0.007629967760294676,
0.05233857408165932,
-0.034253619611263275,
-0.015146128833293915,
-0.02960875630378723,
-0.04953132942318916,
0.03198598697781563,
-0.008164585568010807,
-0.019059041514992714,
-0.03126285597681999,
-0.022697556763887405,
-0.034147195518016815,
0.014579457230865955,
-0.005246423184871674,
0.00484568253159523,
-0.042399369180202484,
0.018039118498563766,
0.02252076007425785,
-0.010756956413388252,
-0.08492449671030045,
-0.02964213117957115,
0.016752418130636215,
0.022172298282384872,
-0.030384037643671036,
0.011621242389082909,
-0.012691862881183624,
-0.007142717484384775,
-0.019522594287991524,
-0.005275794770568609,
0.030238192528486252,
-0.06890388578176498,
-0.05088598653674126,
0.015978408977389336,
0.032891109585762024,
0.03106987290084362,
-0.0053363097831606865,
-0.003809842513874173,
-0.0036560148000717163,
-0.04020465910434723,
-0.0003471940290182829,
-0.015085780993103981,
0.015385515056550503,
-0.03444304317235947,
-0.060693759471178055,
-0.008615219965577126,
-0.023967379704117775,
0.04678693041205406,
-0.04291602224111557,
-0.041584406048059464,
-0.016607897356152534,
-0.009415287524461746,
0.016501832753419876,
-0.0058827633038163185,
0.016983913257718086,
-0.0028036872390657663,
0.02397260256111622,
0.0357513464987278,
0.010235815308988094,
-0.02492344193160534,
-0.009596328251063824,
-0.025211896747350693,
0.023045875132083893,
-0.017330100759863853,
0.004589460324496031,
0.07755254954099655,
-0.000752194260712713,
0.010683717206120491,
0.052213288843631744,
-0.03125673905014992,
0.02563893049955368,
-0.018709447234869003,
0.024342672899365425,
0.00437259441241622,
0.028391169384121895,
-0.021964220330119133,
-0.016642751172184944,
-0.018075479194521904,
0.05761304125189781,
0.040986549109220505,
-0.0021022071596235037,
-0.02455751597881317,
0.009023180231451988,
0.028471698984503746,
0.028960099443793297,
-0.0008072920609265566,
-0.044862180948257446,
0.011424179188907146,
-0.00841022189706564,
0.031300947070121765,
-0.035508450120687485,
-0.0025975455064326525,
0.05097318813204765,
0.0496838353574276,
-0.01899677701294422,
-0.006985119543969631,
0.03611243888735771,
-0.019021812826395035,
-0.005693456158041954,
-0.0022488837130367756,
-0.02092815190553665,
0.059601686894893646,
0.0052406396716833115,
0.027958067134022713,
-0.012168940156698227,
-0.03513414412736893,
0.06194331869482994,
-0.028311317786574364,
0.023415645584464073,
-0.04729987680912018,
-0.043549858033657074,
-0.00814101193100214,
0.03007357381284237,
0.010932192206382751,
-0.007346917409449816,
0.02037041075527668,
0.007227546535432339,
0.036222636699676514,
0.025038158521056175,
0.01768570952117443,
0.001254161586984992,
-0.04972106218338013,
0.011557092890143394,
-0.01770205795764923,
-0.022887086495757103,
0.008893108926713467,
-0.012103639543056488,
-0.006863982416689396,
0.014493530616164207,
0.0160920899361372,
0.05153829976916313,
0.027272025123238564,
0.055785708129405975,
-0.011336005292832851,
0.06285586953163147,
-0.009637787006795406,
0.029226195067167282,
0.028256455436348915,
-0.01993335224688053,
0.13322608172893524,
0.040051043033599854,
0.004249596036970615,
-0.05064978823065758,
0.0027592212427407503,
-0.0005565499886870384,
0.03342290595173836,
0.018634473904967308,
0.032052237540483475,
-0.04656204208731651,
0.03041350096464157,
-0.043385475873947144,
0.05666188895702362,
-0.01834217458963394,
0.04792795330286026,
0.0245711337774992,
-0.014202728867530823,
-0.027606800198554993,
-0.03397282212972641,
0.023595493286848068,
0.016145439818501472,
-0.02408554218709469,
-0.049052752554416656,
0.007959415204823017,
-0.02504509501159191,
0.018745772540569305,
-0.03962922841310501,
-0.0074403779581189156,
0.038408033549785614,
0.017559317871928215,
-0.02366645820438862,
0.009811270982027054,
0.03570486232638359,
-0.018221426755189896,
-0.030364250764250755,
-0.00782682653516531,
0.04193207249045372,
-0.006304808892309666,
0.010333718731999397,
0.06424039602279663,
0.026210101321339607,
0.016177864745259285,
0.034777428954839706,
0.007899175398051739,
-0.057225845754146576,
-0.008107204921543598,
-0.017845341935753822,
0.03983825072646141,
-0.021165505051612854,
-0.036758121103048325,
-0.007682753261178732,
-0.024013789370656013,
-0.015329249203205109,
-0.038578685373067856,
-0.05313391238451004,
0.013054370880126953,
0.009215354919433594,
-0.007665563374757767,
0.013585750013589859,
-0.025162136182188988,
0.011781306937336922,
0.006293745711445808,
-0.009232952259480953,
0.016300037503242493,
0.0030278314370661974,
0.012484624050557613,
0.025835277512669563,
0.03278251737356186,
0.0407632514834404,
0.028013771399855614,
-0.04803834483027458,
-0.01039116270840168,
-0.005486046429723501,
-0.051374390721321106,
0.02808477357029915,
0.04894087091088295,
0.07803219556808472,
0.02453169971704483,
-0.013950696215033531,
-0.000149848114233464,
-0.09836044907569885,
0.0060466499999165535,
0.023930924013257027,
-0.020359473302960396,
-0.005359701346606016,
-0.011698185466229916,
0.019531991332769394,
-0.004343218170106411,
-0.046979792416095734,
0.024859726428985596,
0.017132660374045372,
0.040481626987457275,
-0.0003173905424773693,
-0.0675763189792633,
0.004014862701296806,
-0.010730779729783535,
-0.011678571812808514,
0.04043104872107506,
-0.010308715514838696,
0.0015689331339672208,
0.008322583511471748,
0.04822596162557602,
0.00425622146576643,
0.045193370431661606,
-0.0437164232134819,
-0.009098835289478302,
0.003518927376717329,
0.0015322411200031638,
-0.005936420988291502,
0.03798593580722809,
0.034524306654930115,
0.006051072385162115,
-0.039254751056432724,
-0.0014397013001143932,
0.014917314052581787,
0.023333361372351646,
0.013680742122232914,
-0.04131273925304413,
-0.017505768686532974,
0.0010984701802954078,
-0.0034783855080604553,
-0.022809812799096107,
-0.004464003723114729,
-0.02978089451789856,
0.0019661206752061844,
0.004998750519007444,
-0.012465845793485641,
-0.032260797917842865,
-0.0029499130323529243,
0.012331518344581127,
0.017400173470377922,
0.06283196061849594,
0.04092671722173691,
-0.019417863339185715,
-0.03576147183775902,
0.01805245317518711,
-0.020065918564796448,
0.026249565184116364,
-0.06137586012482643,
-0.01402695570141077,
0.0004486584512051195,
-0.012269394472241402,
-0.004077773075550795,
-0.006663901265710592,
-0.010058706626296043,
0.03202222287654877,
0.024692969396710396,
0.012818826362490654,
-0.02839674986898899,
0.05550601705908775,
-0.026439949870109558,
0.004557327833026648,
0.029835369437932968,
0.017930859699845314,
0.005415427498519421,
-0.01959400810301304,
-0.0539589524269104,
0.00026945609715767205,
0.026869162917137146,
0.029454948380589485,
0.021014707162976265,
-0.004008505959063768,
-0.0037303930148482323,
-0.019342729821801186,
0.001266024075448513,
0.057313237339258194,
0.02607504092156887,
-0.0027469152119010687,
0.007055589463561773,
0.009174324572086334,
0.0067284926772117615,
0.05339082330465317,
0.004204775206744671,
0.004209091886878014,
-0.03135649114847183,
-0.013876539655029774,
-0.009517469443380833,
0.0011638421565294266,
0.0016182921826839447,
-0.007203001528978348,
0.013253052718937397,
0.04828744754195213,
-0.06824923306703568,
-0.007543534971773624,
-0.027989190071821213,
-0.0564035065472126,
-0.034894756972789764,
-0.0431879386305809,
-0.08287975192070007,
0.026717515662312508,
0.00630005169659853,
0.06627918034791946,
0.02373766340315342,
0.015953615307807922,
0.0062560513615608215,
-0.0377722792327404,
-0.03154588118195534,
0.028288451954722404,
-0.014969872310757637,
-0.0279229748994112,
0.03954501450061798,
-0.00832408294081688,
-0.03052530437707901,
0.0018892529187723994,
0.01138041727244854,
-0.01754148304462433,
-0.008816001936793327,
0.037070516496896744,
-0.02044835314154625,
0.04835895821452141,
-0.010347167029976845,
0.023247310891747475,
-0.0054558259434998035,
-0.005424426402896643,
0.006861662492156029,
0.02286129631102085,
-0.03582775592803955,
-0.010095898993313313,
0.03446482494473457,
-0.029252730309963226,
-0.07762312889099121,
0.02996932342648506,
-0.011812503449618816,
0.025573451071977615,
-0.010967760346829891,
0.02913236990571022,
0.02081550657749176,
-0.07425039261579514,
-0.006773952394723892,
-0.029084591194987297,
-0.02291983552277088,
0.047179147601127625,
0.022537121549248695,
0.01643228530883789,
-0.011714055202901363,
-0.022351350635290146,
-0.02922947145998478,
0.02853049896657467,
0.019078342244029045,
-0.015864450484514236,
-0.05886787176132202,
0.004788856953382492,
0.021676702424883842,
0.015176229178905487,
-0.026911169290542603,
-0.028478456661105156,
-0.04729348421096802,
0.03247161954641342,
-0.008746965788304806,
0.035398129373788834,
-0.007762557826936245,
-0.010942374356091022,
-0.005342528223991394,
-0.08852872252464294,
0.0475267730653286,
0.04608893766999245,
-0.01695605367422104,
-0.04098588228225708,
-0.017187124118208885,
-0.022508539259433746,
0.028648559004068375,
0.06447490304708481,
0.02018698863685131,
0.00021780469978693873,
-0.006719393655657768,
-0.0027022240683436394,
0.03555666655302048,
-0.014642429538071156,
-0.027780551463365555,
-0.017052071169018745,
-0.004745872691273689,
-0.018965842202305794,
-0.018196316435933113,
-0.03730571269989014,
0.01902378909289837,
0.0185431856662035,
-0.006792525760829449,
0.000246436771703884,
-0.021809503436088562,
-0.038359347730875015,
-0.0023865890689194202,
-0.0256631039083004,
-0.016683191061019897,
0.06948480010032654,
0.021366164088249207,
0.009286932647228241,
0.010180915705859661,
-0.02276994287967682,
-0.07938749343156815,
0.016201088204979897,
-0.03500891849398613,
0.008055534213781357,
-0.05199607461690903,
-0.019572287797927856,
0.03339175507426262,
-0.03664573282003403,
0.02297493815422058,
0.02706170082092285,
-0.003964697476476431,
-0.04545016586780548,
0.03080054186284542,
0.0260759387165308,
0.031162887811660767,
0.046568311750888824,
0.03806884586811066,
0.04281747341156006,
-0.02679417096078396,
0.05235441029071808,
0.031935159116983414,
0.0031854885164648294,
0.000401124736526981,
0.021405654028058052,
0.03420231491327286,
0.007429779041558504,
-0.020509356632828712,
0.01830924116075039,
0.0040086377412080765,
-0.008644425310194492,
0.02464897371828556,
0.04162317141890526,
-0.020231585949659348,
0.016716035082936287,
-0.020600896328687668,
-0.018497973680496216,
0.05523629114031792,
-0.01899995468556881,
0.022928591817617416,
-0.033827971667051315,
-0.015496605075895786,
-0.012715641409158707,
-0.013202406466007233,
0.0010508798295632005,
0.027440181002020836,
-0.03075985610485077,
-0.03282555565237999,
-0.021954433992505074,
-0.008123585022985935,
0.047600939869880676,
-0.050320934504270554,
0.036269813776016235,
-0.02137460745871067,
-0.03383958339691162,
-0.02550172060728073,
-0.025828177109360695,
-0.010268762707710266,
-0.03136873245239258,
-0.001602786360308528,
0.028344782069325447,
0.006612658500671387,
-0.043228693306446075,
-0.009632370434701443,
-0.0230411347001791,
0.03447464480996132,
-0.031201591715216637,
-0.05709564685821533,
-0.035851191729307175,
0.02105615846812725,
-0.03086956776678562,
-0.04944169148802757
] |
<p>The question I have in mind is: <strong>If we place a conductor (arbitrary shape) of total charge zero in a uniform external electric field $\textbf{E}_0$, does it experience any net force? Why (not)?</strong></p>
<p>Now I will discuss the context of the question. I am working on Griffiths <em>Introduction to Electrodynamics, Fourth Edition</em>, p.112 Problem 2.59 (<strong>not homework problem</strong>, though). it says,</p>
<blockquote>
<p>Prove or disprove (with a counterexample) the following</p>
<p>Theorem: Suppose a conductor carrying a net charge $Q$, when placed in
an external electric field $\textbf{E}_e$, experiences a force
$\textbf{F}$; if the external field is now reversed ($\textbf{E}_e \to
- \textbf{E}_e$), the force also reverses ($\textbf{F} \to -\textbf{F}$).</p>
<p>What if we stipulate that the external field is <em>uniform</em>?</p>
</blockquote>
<p>In general this is obviously not true. I will first <strong>limit myself to the case of $Q=0$</strong>.</p>
<p>One approach: when $\textbf{E}$ is reversed, the surface charged distribution $\sigma$ is also reversed (to cancel $\textbf{E}$), so the electrostatic pressure at every point, $\frac{1}{2\epsilon_0} \sigma^2\, \hat{\textbf{n}}$ stays the same. Consequently, $\textbf{F}$ stays the same rather than flips sign.</p>
<p>Another approach: there is an intuitive counterexample. A conductor is generally attracted to a point charge nearby; if the sign of the point charge is flipped, the conductor is still attracted rather than repulsed.</p>
<p>So the first question is easy, and the interesting one is "<strong>What if we stipulate that the external field is <em>uniform</em>?</strong>" I suspect that in a uniform external field the net force is zero, so that $\textbf{F} = 0 = -\textbf{F}$, but I can't think of a way to prove or disprove it.</p> | 4,586 | [
-0.022756004706025124,
-0.0031479722820222378,
0.027492867782711983,
-0.012786212377250195,
-0.011271515861153603,
-0.00501291174441576,
0.02286582812666893,
0.028589002788066864,
-0.01610560715198517,
-0.030954815447330475,
0.021412741392850876,
0.003379277652129531,
0.06982431560754776,
0.00786107312887907,
0.0023941919207572937,
0.020375316962599754,
-0.022267069667577744,
-0.023279275745153427,
-0.00987960398197174,
-0.04992373660206795,
0.0012301801471039653,
0.05936655402183533,
0.020376164466142654,
0.015013333410024643,
-0.049167703837156296,
0.013216568157076836,
-0.016745731234550476,
-0.04432699456810951,
-0.010372973047196865,
0.05750900134444237,
-0.018141137436032295,
-0.03557024151086807,
0.019459523260593414,
-0.014341630041599274,
0.012961129657924175,
0.000183054682565853,
0.004638832062482834,
-0.04479542747139931,
-0.022801615297794342,
0.008933980017900467,
0.006479410454630852,
0.00854992400854826,
0.017773490399122238,
0.02415875345468521,
0.029422542080283165,
-0.00095124333165586,
-0.027478942647576332,
0.015820009633898735,
0.043452247977256775,
-0.0627945140004158,
0.02686017006635666,
-0.01565811038017273,
0.03860662505030632,
0.028497915714979172,
0.005541637539863586,
-0.05529383569955826,
0.0630786269903183,
0.013362840749323368,
0.0072960820980370045,
-0.045603059232234955,
0.000891687348484993,
-0.028352363035082817,
-0.03703263774514198,
-0.028526265174150467,
-0.020382538437843323,
0.030297571793198586,
0.005791838746517897,
0.009619084186851978,
0.010504298843443394,
-0.010641132481396198,
-0.002461038762703538,
0.04544910788536072,
-0.018198922276496887,
0.0037904204800724983,
0.025943724438548088,
0.011679784394800663,
0.020466763526201248,
-0.0005280663608573377,
0.023678401485085487,
0.03704240545630455,
-0.05214022472500801,
0.016613328829407692,
0.01385052315890789,
0.04379630833864212,
0.021930428221821785,
-0.026229431852698326,
0.050994377583265305,
-0.021343894302845,
0.026737332344055176,
0.050088826566934586,
-0.008572757244110107,
0.008430986665189266,
0.007473877165466547,
-0.03959096968173981,
-0.008455202914774418,
-0.00044060731306672096,
0.018691251054406166,
0.02740144170820713,
-0.0034298698883503675,
-0.022791096940636635,
-0.04237573966383934,
-0.03836643695831299,
-0.002110847970470786,
0.07377501577138901,
0.006361984647810459,
-0.0350397452712059,
-0.011102714575827122,
-0.01000138372182846,
-0.016411416232585907,
-0.014794220216572285,
-0.015371314249932766,
0.011205639690160751,
-0.0025030372198671103,
-0.010774017311632633,
0.004266185220330954,
-0.00921300146728754,
-0.008281550370156765,
-0.022017167881131172,
0.02997526153922081,
0.05860915407538414,
0.021588122472167015,
-0.024307074025273323,
0.0022594125475734472,
-0.023455582559108734,
-0.023953013122081757,
0.00792720913887024,
0.05103302001953125,
-0.0021351452451199293,
0.007797816768288612,
-0.012654311023652554,
0.016578147187829018,
0.011653093621134758,
0.026467548683285713,
0.014115381054580212,
0.03428545966744423,
0.005699066910892725,
-0.07992781698703766,
-0.04881608486175537,
0.04741020128130913,
-0.003965208772569895,
0.013911682181060314,
-0.06575698405504227,
-0.03537781536579132,
0.04182391241192818,
0.03904690220952034,
-0.008207582868635654,
0.01026165671646595,
0.000033579552109586075,
0.040000151842832565,
0.020414741709828377,
0.011683547869324684,
0.011202559806406498,
-0.014702430926263332,
-0.019021272659301758,
-0.05946432054042816,
-0.02542966790497303,
0.06920578330755234,
0.0028084355872124434,
0.026066236197948456,
-0.009827075526118279,
0.07118427008390427,
-0.05545251443982124,
0.021854884922504425,
-0.00741589767858386,
-0.05680720508098602,
-0.009928878396749496,
0.09080750495195389,
0.024656416848301888,
-0.007230828050523996,
0.02791149914264679,
0.000052304989367257804,
0.005245962180197239,
-0.005839554127305746,
0.014902240596711636,
0.03029639832675457,
-0.09059978276491165,
-0.00079276820179075,
-0.06082960590720177,
0.010668384842574596,
0.00004535355037660338,
-0.051266860216856,
-0.0002318947808817029,
-0.00947817973792553,
-0.0075391787104308605,
0.008138986304402351,
0.028933841735124588,
-0.007002296391874552,
-0.01047517079859972,
0.005305927712470293,
-0.03629622980952263,
-0.03222208097577095,
-0.0703643187880516,
0.05260740593075752,
0.040221597999334335,
-0.02289694920182228,
0.0321832112967968,
-0.026410004124045372,
0.0138721177354455,
-0.027815524488687515,
0.0015634609153494239,
0.010356278158724308,
0.023039301857352257,
-0.013276706449687481,
-0.04466940835118294,
0.025100359693169594,
0.039742857217788696,
0.06242933124303818,
0.01844809204339981,
0.015481132082641125,
-0.04009039327502251,
-0.00831185095012188,
-0.009322846308350563,
-0.04365906864404678,
0.025349445641040802,
0.043975718319416046,
0.000040913946577347815,
0.04043072834610939,
0.0019189134472981095,
-0.013692033477127552,
0.010084202513098717,
-0.025204377248883247,
0.017384294420480728,
0.04563678801059723,
0.012401686981320381,
0.009040376171469688,
0.030405666679143906,
0.008298425935208797,
0.009847814217209816,
-0.02082306519150734,
-0.0217953622341156,
-0.046574536710977554,
0.013835522346198559,
0.025157585740089417,
0.05208564177155495,
-0.033602871000766754,
0.03233252465724945,
0.014476343058049679,
0.014024624601006508,
0.015105759724974632,
-0.02681228145956993,
-0.007562580984085798,
-0.033821288496255875,
0.026623979210853577,
-0.0035139743704348803,
0.005548432469367981,
-0.0006289641023613513,
0.03000243566930294,
-0.00350766209885478,
0.018479760736227036,
0.00917095597833395,
-0.014493211172521114,
0.00046790906344540417,
0.0014572055079042912,
0.05500245839357376,
0.01105045061558485,
-0.03265629708766937,
0.04096607863903046,
-0.005514063872396946,
0.025631776079535484,
0.018820464611053467,
-0.012360013090074062,
0.0162985660135746,
-0.04294087365269661,
0.022929318249225616,
0.04017324000597,
-0.029625143855810165,
0.030384758487343788,
-0.011532814241945744,
0.01968442276120186,
-0.042880114167928696,
0.007708535995334387,
0.01092773862183094,
-0.008477509953081608,
-0.0008100104751065373,
-0.023927848786115646,
0.04478653147816658,
0.02160736918449402,
-0.005919872783124447,
-0.021630320698022842,
0.0028830706141889095,
0.017097342759370804,
-0.0001970836310647428,
0.030031360685825348,
0.04203014820814133,
-0.05171000957489014,
-0.01693098247051239,
-0.053210724145174026,
-0.019828427582979202,
0.05888143181800842,
0.029043221846222878,
-0.013644058257341385,
0.04220199957489967,
0.013360859826207161,
-0.044189389795064926,
0.011163664981722832,
-0.04255882278084755,
-0.019369235262274742,
-0.02494196407496929,
-0.028010016307234764,
0.09672389179468155,
-0.017784949392080307,
-0.04496430233120918,
0.01396111398935318,
-0.054303813725709915,
-0.051380593329668045,
0.011042830534279346,
-0.03138960525393486,
0.00359670864418149,
-0.028914084658026695,
0.035777486860752106,
0.02576732449233532,
-0.023103822022676468,
-0.012819834984838963,
-0.06753435730934143,
-0.016930554062128067,
0.0004652265924960375,
-0.021162260323762894,
0.03936801105737686,
-0.024330755695700645,
-0.03742106631398201,
0.06588408350944519,
0.027212999761104584,
0.0064415945671498775,
0.02501150406897068,
-0.03135385736823082,
-0.022743312641978264,
-0.03184749558568001,
-0.024965116754174232,
0.028079332783818245,
-0.034197501838207245,
0.008688834495842457,
-0.0014594497624784708,
0.051038045436143875,
-0.03232746943831444,
0.006724787410348654,
-0.023369962349534035,
-0.004174579866230488,
0.019339745864272118,
0.02119620330631733,
0.05107444152235985,
-0.014414903707802296,
0.0012307921424508095,
0.01944020949304104,
0.00865976046770811,
0.03249013051390648,
0.04259246587753296,
-0.03105190582573414,
0.04539946839213371,
-0.016189124435186386,
0.03285171091556549,
-0.03916645795106888,
0.06832282245159149,
0.012002711184322834,
-0.03800828754901886,
-0.027981432154774666,
0.00545625202357769,
0.040689412504434586,
-0.05748964101076126,
0.009450938552618027,
0.04032638296484947,
0.08325201272964478,
-0.021334074437618256,
-0.07413468509912491,
0.017086457461118698,
-0.003448314731940627,
0.029582194983959198,
-0.0496848002076149,
0.004617798607796431,
0.024834534153342247,
0.07483197748661041,
0.043438464403152466,
0.03256315365433693,
0.015209984965622425,
-0.01712178811430931,
-0.01433606818318367,
-0.016004567965865135,
0.015934912487864494,
0.04450560361146927,
0.012943931855261326,
0.03465548902750015,
0.020305465906858444,
0.0238103736191988,
-0.018017180263996124,
0.05295886844396591,
-0.09214755147695541,
0.015031973831355572,
-0.001257320516742766,
-0.008315250277519226,
-0.03194860368967056,
-0.028036292642354965,
0.024457724764943123,
0.01319893728941679,
-0.009046793915331364,
-0.017192477360367775,
0.03221689537167549,
-0.04471439868211746,
-0.014138746075332165,
-0.028279529884457588,
-0.05731656029820442,
-0.010454652830958366,
0.06557700037956238,
0.027762696146965027,
-0.07292333245277405,
0.007918091490864754,
0.004960692021995783,
-0.059994593262672424,
-0.004839146975427866,
-0.0030221769120544195,
0.027987515553832054,
0.002978730481117964,
0.014736181125044823,
0.021910879760980606,
-0.01573147252202034,
-0.032096195966005325,
0.0031736150849610567,
0.04080270975828171,
0.04154219850897789,
0.021307962015271187,
-0.005276906304061413,
-0.010014377534389496,
-0.03844751790165901,
-0.05240766704082489,
-0.022343559190630913,
0.06410446763038635,
0.007973907515406609,
-0.017933765426278114,
0.027866020798683167,
-0.023074937984347343,
0.02565728686749935,
0.03894803300499916,
0.013227122835814953,
0.05078676715493202,
-0.012464478611946106,
-0.039726901799440384,
0.004193039610981941,
-0.037930190563201904,
0.023198945447802544,
0.050405774265527725,
-0.012718519195914268,
-0.015920965000987053,
-0.015597889199852943,
0.027383342385292053,
0.04150555655360222,
0.0074000912718474865,
0.01375852432101965,
-0.00024042690347414464,
0.016464654356241226,
-0.0003197725454811007,
0.026590773835778236,
0.013136784546077251,
0.014649244956672192,
0.03906100615859032,
0.029572943225502968,
-0.0400630384683609,
-0.05999414622783661,
-0.030776597559452057,
0.027837518602609634,
0.015086532570421696,
-0.0019056197488680482,
0.019779987633228302,
-0.055053386837244034,
-0.0073443748988211155,
0.00878996029496193,
-0.025696083903312683,
-0.007686525583267212,
-0.00961401779204607,
0.008009199984371662,
-0.012348047457635403,
-0.036440782248973846,
-0.03432765603065491,
0.013407033868134022,
-0.024537278339266777,
0.02432745136320591,
-0.027961986139416695,
0.005807015113532543,
0.0035270103253424168,
-0.0133544085547328,
0.022074274718761444,
0.06620384752750397,
-0.0026427775155752897,
-0.0007114996551536024,
-0.0007064404198899865,
-0.04364680498838425,
-0.04066059738397598,
-0.11796494573354721,
0.012650164775550365,
-0.0049172635190188885,
0.04858597368001938,
0.016302814707159996,
-0.04857194423675537,
-0.028172267600893974,
0.011921425350010395,
-0.007864794693887234,
-0.011528526432812214,
0.013826877810060978,
-0.04504254460334778,
0.05210771784186363,
0.016906647011637688,
0.01521061547100544,
0.060673218220472336,
0.027239693328738213,
0.006818246562033892,
-0.021630818024277687,
-0.01092615257948637,
0.006568593438714743,
-0.022931696847081184,
0.002351155038923025,
-0.042335543781518936,
0.01067604310810566,
-0.038875412195920944,
0.049711912870407104,
-0.01535473670810461,
0.05266261845827103,
0.014949571341276169,
-0.036259595304727554,
0.0007915089372545481,
0.008181365206837654,
-0.018422085791826248,
0.02804393507540226,
-0.0319627970457077,
0.029854925349354744,
0.010515798814594746,
-0.034475602209568024,
-0.009123596362769604,
-0.002103468170389533,
0.033044107258319855,
0.042344480752944946,
-0.009224606677889824,
0.00777472835034132,
-0.002030964707955718,
-0.023906705901026726,
-0.05017881095409393,
-0.03940806910395622,
0.031187623739242554,
0.002171010710299015,
-0.0009160665795207024,
0.025935975834727287,
-0.04972546547651291,
-0.002215446438640356,
0.05188491940498352,
-0.00537317618727684,
-0.0004747379571199417,
-0.029418393969535828,
-0.009105272591114044,
0.0881810188293457,
0.028334256261587143,
-0.05917542800307274,
-0.05286092311143875,
-0.01583082601428032,
-0.007959467358887196,
-0.0233935434371233,
-0.0020664124749600887,
-0.04418858885765076,
0.0037773619405925274,
-0.03547500818967819,
0.01804661750793457,
0.03441872447729111,
-0.037599045783281326,
0.009288179688155651,
0.061223238706588745,
0.022045854479074478,
0.06324192881584167,
-0.022974131628870964,
-0.010061493143439293,
-0.0017724232748150826,
-0.04773035645484924,
0.008509472943842411,
0.002040448132902384,
0.023011401295661926,
-0.0023284635972231627,
-0.011854606680572033,
-0.03443814069032669,
-0.005747831892222166,
0.025099866092205048,
0.008906973525881767,
-0.008669678121805191,
0.016318101435899734,
0.012340692803263664,
-0.02578156255185604,
-0.004883605521172285,
-0.029100876301527023,
-0.010561153292655945,
0.04389706254005432,
-0.0017951070331037045,
-0.0002478969981893897,
-0.03042704612016678,
-0.05110468342900276,
-0.006604946218430996,
0.017538422718644142,
-0.0003071301325690001,
0.010822339914739132,
0.04730060696601868,
-0.025817085057497025,
-0.04157903417944908,
-0.005054021254181862,
-0.019786043092608452,
0.04253630340099335,
0.01860111579298973,
-0.002107254695147276,
-0.01938515342772007,
-0.020288698375225067,
0.0018414296209812164,
-0.023966947570443153,
-0.020555701106786728,
0.01729683205485344,
0.05388437584042549,
0.0339890792965889,
0.05705602467060089,
0.013882058672606945,
0.010133101604878902,
-0.03266235440969467,
-0.026661090552806854,
0.01972448080778122,
-0.029920736327767372,
0.024644501507282257,
0.004458888433873653,
-0.02211826667189598,
0.030658286064863205,
0.053230736404657364,
0.052993182092905045,
-0.05586981400847435,
-0.03290560469031334,
0.0206551942974329,
0.016431381925940514,
0.04911797121167183,
-0.056625042110681534,
-0.01295211911201477,
0.05405530706048012,
-0.05635857209563255,
0.013792874291539192,
0.016710015013813972,
-0.03150185942649841,
0.038140226155519485,
0.018741458654403687,
0.017614278942346573,
-0.02913621813058853,
-0.04370947927236557,
-0.014179667457938194,
0.0038337185978889465,
-0.01690870337188244,
0.049024756997823715,
-0.010296273045241833,
-0.011965848505496979,
0.033253345638513565,
-0.020042233169078827,
0.012693057768046856,
-0.004338283557444811,
-0.07759604603052139,
-0.00840198714286089,
-0.013856368139386177,
-0.023974895477294922,
0.03116661123931408,
-0.014453302137553692,
-0.016573704779148102,
0.01732681132853031,
-0.042426880449056625,
0.05654152110219002,
0.074372798204422,
-0.029046032577753067,
-0.015036076307296753,
0.04008718580007553,
-0.014557779766619205,
0.02679206058382988,
-0.04888733848929405,
-0.01970381662249565,
0.14922687411308289,
0.02831992693245411,
0.051935017108917236,
-0.07295502722263336,
-0.021064812317490578,
-0.0066528222523629665,
0.01685754954814911,
-0.02602255344390869,
0.01832806132733822,
-0.052336763590574265,
0.021961459890007973,
0.015425994992256165,
0.041510481387376785,
0.001940047601237893,
-0.041070606559515,
0.04569520056247711,
-0.028867211192846298,
-0.010777907446026802,
-0.026842813938856125,
0.018870845437049866,
-0.014716234058141708,
0.03206585347652435,
-0.07242784649133682,
0.015380715020000935,
-0.04827353358268738,
0.0009147402597591281,
-0.03106909617781639,
0.00937656406313181,
0.016180505976080894,
-0.005278563592582941,
-0.04014301300048828,
-0.012755034491419792,
0.03506368398666382,
-0.05139105021953583,
-0.034598540514707565,
0.04327290877699852,
0.017740070819854736,
-0.010445969179272652,
0.021087950095534325,
0.03326699137687683,
-0.004643486812710762,
0.03639339655637741,
0.07115998864173889,
0.012521284632384777,
-0.04225052148103714,
0.010676019825041294,
-0.058121517300605774,
0.057695478200912476,
-0.0005153880920261145,
0.012695854529738426,
0.016716210171580315,
0.007381935138255358,
0.02403196319937706,
-0.03395705670118332,
-0.027101971209049225,
-0.0337824784219265,
0.030659252777695656,
0.016762545332312584,
-0.024857891723513603,
0.0038859720807522535,
0.07912908494472504,
0.0019434804562479258,
-0.02837180718779564,
0.019347574561834335,
-0.025291552767157555,
-0.007898688316345215,
0.03288920223712921,
0.04655664786696434,
0.033661119639873505,
-0.015235565602779388,
-0.01949474774301052,
-0.00966004841029644,
-0.03226274624466896,
-0.018966224044561386,
-0.013705075718462467,
0.043862029910087585,
0.03736267238855362,
0.010164109990000725,
0.012687244452536106,
-0.038690220564603806,
-0.06954480707645416,
0.028516439720988274,
-0.02978447824716568,
0.005255721043795347,
0.005855470430105925,
-0.030585158616304398,
-0.01083410531282425,
0.023548275232315063,
-0.0010044658556580544,
-0.016761615872383118,
0.06254346668720245,
0.09098266810178757,
0.010618079453706741,
-0.02822326309978962,
-0.0625777617096901,
-0.003613603999838233,
-0.03559443727135658,
0.0432567372918129,
0.014751166105270386,
-0.007863987237215042,
0.0028215462807565928,
0.0029266285710036755,
0.008013435639441013,
0.02683039754629135,
-0.027667026966810226,
-0.029939182102680206,
0.030705338343977928,
0.009296385571360588,
0.020942039787769318,
0.029906680807471275,
-0.007902409881353378,
-0.06125245243310928,
-0.036080896854400635,
0.03915320336818695,
0.01531937625259161,
-0.01577187329530716,
0.036972776055336,
-0.03687238320708275,
-0.01621590182185173,
-0.02636856585741043,
0.017378434538841248,
-0.02985396236181259,
-0.03213634714484215,
-0.04306033253669739,
-0.03698175027966499,
0.020217010751366615,
0.008481159806251526,
-0.000711715838406235,
0.015119839459657669,
-0.0314674898982048,
0.006700093857944012,
0.029859958216547966,
-0.00226775836199522,
-0.010366898961365223,
0.0029080433305352926,
-0.00990730244666338,
0.006481320597231388,
-0.014339901506900787,
-0.013338369317352772,
0.0011189192300662398,
0.033494818955659866,
-0.04268638417124748,
-0.0432901456952095,
-0.005051757209002972,
0.00323946843855083,
0.007499374449253082,
-0.0038260985165834427,
0.005483181681483984,
-0.017730114981532097,
0.02199418656527996,
-0.0008160759462043643,
0.0056432089768350124,
-0.039325639605522156,
-0.031064508482813835,
-0.010797129012644291,
-0.05273408815264702,
-0.003652023384347558,
-0.005650558974593878,
0.050104446709156036,
0.0047975461930036545,
0.02648402750492096,
-0.0370568223297596,
-0.008104349486529827,
0.020954275503754616,
-0.023546753451228142,
-0.005016691517084837,
0.04428025707602501,
0.031856510788202286,
-0.03524334356188774,
0.029745057225227356,
-0.02245655283331871,
0.007734678220003843,
-0.0069753690622746944,
0.0032609475310891867,
-0.11735092848539352,
-0.02919727936387062,
0.06235601752996445,
0.013836747966706753,
0.03594463691115379,
-0.03558545932173729,
-0.017856059595942497,
0.004351892042905092,
-0.063622385263443,
0.039308033883571625,
0.015428372658789158,
-0.011443189345300198,
-0.022588582709431648,
0.0007129653240554035,
-0.012303215451538563,
0.0072940802201628685,
0.0006690016016364098,
0.05081481859087944,
-0.002846329240128398,
0.01899508386850357,
0.0047149877063930035,
-0.019218193367123604,
-0.026144912466406822,
0.020420830696821213,
0.016175514087080956,
-0.0055959527380764484,
0.047443922609090805,
0.014842266216874123,
0.003060983493924141,
0.028255930170416832,
0.004962801933288574,
-0.029229536652565002,
-0.008092726580798626,
0.023845911026000977,
-0.006965637672692537,
0.027711084112524986,
-0.03811964392662048,
0.000887604255694896,
-0.01848495379090309,
0.013634566217660904,
0.01456979475915432,
0.0034194786567240953,
-0.006289547309279442,
0.012337211519479752,
0.01606420800089836,
-0.029918314889073372,
-0.013158402405679226,
0.031853094696998596,
-0.03632187098264694,
-0.010153960436582565,
0.004109915345907211,
0.029338622465729713,
-0.003895222907885909,
0.0016706817550584674,
-0.01793098822236061,
-0.05331508442759514,
-0.01428396999835968,
0.013522949069738388,
0.027273405343294144,
0.04299383610486984,
0.04234904795885086,
0.008865407668054104,
-0.022601502016186714,
0.030514657497406006,
-0.007791853975504637,
-0.008070002309978008,
-0.08200407028198242,
0.012367242015898228,
-0.008950995281338692,
0.011169287376105785,
0.019954614341259003,
-0.042288441210985184,
-0.018281927332282066,
0.007576754316687584,
0.021104123443365097,
0.0205053873360157,
-0.02820952981710434,
-0.0505121573805809,
0.012348618358373642,
-0.05017279461026192,
-0.001396902953274548,
-0.014402695000171661,
-0.028164705261588097,
0.009809300303459167,
-0.036000028252601624,
-0.004829002544283867,
0.03334873914718628,
0.05428043380379677,
0.00391404889523983,
-0.02288993075489998,
0.02451283484697342,
0.002528891898691654,
0.0288434699177742,
-0.06411129236221313,
-0.009484726004302502,
0.014899440109729767,
0.010937012732028961,
0.025960613042116165,
0.005274883937090635,
-0.003715789644047618,
0.015390733256936073,
0.007013496942818165,
0.016047297045588493,
0.02010323666036129,
-0.023756779730319977,
-0.038093116134405136,
0.03860253468155861,
0.012795647606253624,
0.014219962991774082,
0.08036594837903976,
-0.029322549700737,
0.012717802077531815,
-0.057698678225278854,
-0.06407982110977173,
-0.02794848382472992,
0.028805669397115707,
0.0030460571870207787,
-0.0038896172773092985,
-0.03847554326057434,
0.037115756422281265,
0.03291138634085655,
-0.020306823775172234,
-0.02522391453385353,
0.021144697442650795,
-0.04755406826734543,
-0.026004580780863762,
0.048768553882837296,
0.016000518575310707,
0.025990048423409462,
-0.014042722061276436,
-0.011588661931455135,
0.0013807821087539196,
-0.007961994037032127,
0.027012648060917854,
-0.009035959839820862,
0.03550158441066742,
-0.016029778867959976,
0.009527355432510376,
0.0824296623468399,
-0.0004286632756702602,
0.005593357142060995,
-0.0015906976768746972,
-0.0025010069366544485,
-0.01153433509171009,
-0.00439252657815814,
0.07043321430683136,
0.02194402739405632,
0.0031636685598641634,
0.0016773338429629803,
-0.010622193105518818,
0.0727408304810524,
-0.029751919209957123,
0.04446013271808624,
0.005855983588844538,
0.002105501713231206,
0.01230133417993784,
0.03503457456827164,
-0.01764250546693802,
0.05333694443106651,
-0.04288659244775772,
-0.03144211322069168,
-0.005604452453553677,
0.0010860302718356252,
0.001311102882027626,
-0.008072220720350742,
0.010177099145948887,
0.022711200639605522,
0.0026853785384446383,
-0.03939226269721985,
0.0004984469269402325,
0.004232937004417181,
-0.05325297266244888,
-0.0012036986881867051,
0.00782587006688118,
0.03271269425749779,
0.02511456049978733,
0.0063104513101279736,
-0.012748010456562042,
0.04311841353774071,
-0.02122867852449417,
-0.041046977043151855,
-0.01208953745663166,
0.06093985214829445,
0.0046168058179318905,
0.023455973714590073
] |
<p><a href="http://physics.stackexchange.com/q/27939/2451">Here</a> and <a href="http://physics.stackexchange.com/q/28181/2451">here</a> it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an <a href="http://en.wikipedia.org/wiki/Ordinary_differential_equation" rel="nofollow">ODE</a> class in the math department. I have a student that heard the above stated in a physics course. She is wondering whether this is an appropriate project for my class. So, does this fact come from some differential equations? </p> | 4,587 | [
-0.023772763088345528,
-0.009502822533249855,
0.015270699746906757,
0.01952389068901539,
0.015704963356256485,
0.013122374191880226,
-0.03020024113357067,
-0.031146205961704254,
0.001082252711057663,
-0.005198218394070864,
0.05650438740849495,
0.05163579434156418,
0.04528588429093361,
0.028350332751870155,
0.036357246339321136,
0.015059271827340126,
-0.017490657046437263,
-0.008794108405709267,
0.024739403277635574,
-0.0053258733823895454,
0.008608980104327202,
0.023249013349413872,
-0.012875925749540329,
-0.009474392980337143,
-0.012062445282936096,
0.012359856627881527,
-0.017382970079779625,
0.006949212402105331,
0.0008464045240543783,
0.04285160452127457,
0.004412992857396603,
-0.0218939371407032,
0.044015198945999146,
0.04772711917757988,
0.045670006424188614,
0.050051234662532806,
-0.029333507642149925,
0.003601046046242118,
-0.004441438242793083,
0.044665075838565826,
-0.04353449493646622,
-0.0721229836344719,
0.014979667030274868,
0.009840102866292,
0.007289815228432417,
0.024311795830726624,
0.027217891067266464,
-0.04934392869472504,
0.056841891258955,
-0.0547926165163517,
0.038487449288368225,
0.028593771159648895,
0.04023820534348488,
0.02196960151195526,
0.022971205413341522,
0.026082973927259445,
0.0640602558851242,
0.045265235006809235,
0.002116832649335265,
-0.03941290080547333,
-0.014734848402440548,
-0.01413890440016985,
-0.03843330219388008,
0.012782738544046879,
-0.016619088128209114,
0.03452293202280998,
-0.016771143302321434,
-0.023315925151109695,
-0.0020831318106502295,
-0.01822482794523239,
-0.02624933421611786,
0.010201885364949703,
0.038979627192020416,
0.01233405526727438,
0.03455907478928566,
-0.008646229282021523,
-0.007121471222490072,
0.0077704377472400665,
-0.00893431156873703,
0.029356084764003754,
-0.04986918345093727,
0.02378571592271328,
-0.01775369979441166,
0.01968504674732685,
-0.0012831633212044835,
-0.0003549539251253009,
0.024887103587388992,
-0.002638906706124544,
0.04351801797747612,
0.057046741247177124,
-0.024478740990161896,
-0.02894406206905842,
-0.007967548444867134,
0.007101899944245815,
0.020308030769228935,
-0.015076057985424995,
0.004826751537621021,
0.05783787742257118,
0.026151614263653755,
-0.0466451458632946,
0.0019861741457134485,
-0.029954154044389725,
-0.00010561386443441734,
0.08103591948747635,
0.015033112838864326,
-0.031655777245759964,
-0.015097862109541893,
0.0018267333507537842,
-0.033025771379470825,
0.0032785118091851473,
-0.054934147745370865,
-0.006806845311075449,
-0.014200040139257908,
-0.03375371918082237,
0.010212300345301628,
-0.009540685452520847,
0.013698686845600605,
0.0018593468703329563,
0.022323474287986755,
0.02532116509974003,
0.05571562796831131,
-0.0141518609598279,
0.018868761137127876,
-0.04791657254099846,
-0.04514573514461517,
0.029750561341643333,
0.015209967270493507,
-0.015662621706724167,
-0.025047896429896355,
0.03855214640498161,
-0.0024329633451998234,
0.05213572084903717,
0.006966376211494207,
-0.00286398665048182,
0.014392444863915443,
-0.006645151413977146,
-0.06489196419715881,
-0.06856518983840942,
0.07723524421453476,
0.004586437251418829,
-0.03596901521086693,
-0.09870245307683945,
0.0001603242417331785,
0.014419850893318653,
0.03880035877227783,
-0.014869539998471737,
0.0442349873483181,
-0.016032535582780838,
0.05173484981060028,
0.013775207102298737,
0.01729779876768589,
-0.011359003372490406,
0.005322060082107782,
-0.03393060341477394,
-0.009398778900504112,
-0.046821363270282745,
-0.016737157478928566,
0.011513718403875828,
0.005136217921972275,
-0.008451058529317379,
0.05293847993016243,
-0.025635669007897377,
0.007096034474670887,
0.04053245484828949,
0.016315951943397522,
-0.005848148372024298,
0.0784376785159111,
0.017676882445812225,
0.010807981714606285,
0.013111656531691551,
0.01851409301161766,
0.050582148134708405,
0.007995863445103168,
0.012398197315633297,
0.027521871030330658,
-0.03141031786799431,
-0.0023104785941541195,
-0.059292953461408615,
0.038260772824287415,
0.04202105477452278,
0.029632190242409706,
-0.011718050576746464,
0.008068937808275223,
0.00032722821924835443,
-0.02009652927517891,
0.048924412578344345,
-0.012780144810676575,
-0.012316059321165085,
-0.007192566525191069,
-0.05432387441396713,
-0.02673530764877796,
-0.023313233628869057,
0.015034385956823826,
-0.02708752267062664,
0.00015534597332589328,
0.009548993781208992,
-0.004606709815561771,
0.04324107989668846,
-0.04112992808222771,
-0.01302043441683054,
-0.014585884287953377,
0.0190589502453804,
0.030637674033641815,
0.02887909859418869,
0.0422908216714859,
0.038699761033058167,
0.025382280349731445,
-0.04008454456925392,
-0.009039461612701416,
-0.052516400814056396,
-0.026104317978024483,
-0.03352803736925125,
-0.005147723481059074,
0.02873118780553341,
0.012697986327111721,
-0.022271599620580673,
0.013902682811021805,
0.0013083461672067642,
0.005409560166299343,
0.039743050932884216,
0.008491529151797295,
0.07494618743658066,
0.03441426530480385,
0.039961375296115875,
0.022899460047483444,
0.025333574041724205,
0.018947962671518326,
0.022365853190422058,
0.016911331564188004,
-0.017064161598682404,
-0.036801181733608246,
-0.012888230383396149,
0.008009269833564758,
0.03667591139674187,
-0.07922076433897018,
0.026405178010463715,
0.01457829587161541,
0.026138443499803543,
0.07435711473226547,
0.016788186505436897,
-0.01924397051334381,
-0.028678657487034798,
0.028234316036105156,
0.03546813130378723,
0.017285192385315895,
0.06719861179590225,
0.03345194458961487,
0.03528115525841713,
0.032831475138664246,
-0.03685479983687401,
-0.0037423756439238787,
0.0064150081016123295,
-0.03550407290458679,
0.011998141184449196,
-0.019385352730751038,
-0.02686394937336445,
0.011127087287604809,
-0.08414282649755478,
0.022067857906222343,
0.040122419595718384,
-0.01774688996374607,
0.03243955969810486,
-0.038814716041088104,
-0.029334910213947296,
-0.004684600047767162,
-0.005250214133411646,
-0.03858327120542526,
-0.013852096162736416,
0.03185759484767914,
-0.05916101485490799,
0.007425082381814718,
-0.003866675077006221,
-0.027413109317421913,
-0.025233833119273186,
0.03477155417203903,
0.04197518527507782,
-0.010953438468277454,
0.001818182528950274,
-0.01666230708360672,
-0.03266002610325813,
-0.007407912518829107,
-0.004749617539346218,
-0.040292833000421524,
0.01335818786174059,
-0.05676248297095299,
0.018764816224575043,
0.014126049354672432,
-0.03289182484149933,
0.07088448852300644,
0.014882702380418777,
-0.017453962936997414,
0.023060305044054985,
0.005056323949247599,
-0.015640035271644592,
-0.029002787545323372,
-0.028652694076299667,
0.022592592984437943,
-0.011436307802796364,
-0.016980934888124466,
0.06331364810466766,
-0.0558212585747242,
-0.02086292766034603,
-0.009790100157260895,
-0.06122661754488945,
-0.04833628609776497,
-0.0033953096717596054,
-0.011151283979415894,
-0.0009867629269137979,
0.012962577864527702,
0.018988827243447304,
0.027369694784283638,
-0.039202332496643066,
-0.03487617149949074,
-0.06374777108430862,
-0.07799643278121948,
0.049825269728899,
0.009275777265429497,
0.07942160218954086,
0.00725468760356307,
-0.03995322808623314,
0.052381906658411026,
0.009100861847400665,
-0.06847575306892395,
-0.03687361255288124,
-0.028838103637099266,
-0.007111261133104563,
-0.004612267017364502,
-0.00414346344769001,
0.058629360049963,
-0.03064379096031189,
-0.024550633504986763,
0.030880633741617203,
0.0178779698908329,
0.014299553819000721,
-0.0014758198522031307,
-0.002344846725463867,
0.015403499826788902,
-0.006604882888495922,
-0.013650713488459587,
0.06390302628278732,
0.02984263189136982,
-0.03797372058033943,
0.004326597321778536,
-0.03449898958206177,
0.026976682245731354,
0.03311273828148842,
-0.03065125271677971,
0.0492442324757576,
0.020855043083429337,
-0.005137136206030846,
-0.02981695346534252,
0.010560889728367329,
-0.012004781514406204,
-0.01623772643506527,
0.0019230819307267666,
0.022293997928500175,
0.01886480115354061,
-0.00437625776976347,
0.000924449588637799,
0.028938448056578636,
0.04489286243915558,
-0.03485637158155441,
-0.009645730257034302,
0.018882719799876213,
-0.023962652310729027,
0.03830089047551155,
-0.02807641588151455,
0.00003020428448508028,
0.03907269984483719,
-0.022344978526234627,
0.0066863661631941795,
-0.03895273804664612,
-0.02971484512090683,
0.01627611182630062,
-0.08806385844945908,
-0.025304175913333893,
-0.019485939294099808,
0.04562455788254738,
0.0074997516348958015,
0.023964280262589455,
0.010653492994606495,
0.035610172897577286,
0.03721547871828079,
0.04296338930726051,
-0.04191524162888527,
0.01813734695315361,
-0.03378875553607941,
0.0242390725761652,
-0.0041150422766804695,
-0.03575638309121132,
0.007642095908522606,
-0.02052648738026619,
-0.020781314000487328,
-0.009429161436855793,
-0.01693691313266754,
-0.040034230798482895,
-0.009551789611577988,
-0.03474588692188263,
-0.027728835120797157,
-0.02999160625040531,
0.01666063442826271,
0.048950254917144775,
-0.024994703009724617,
0.05956962704658508,
0.04907894879579544,
-0.031142864376306534,
-0.015121874399483204,
-0.0388401560485363,
0.029335765168070793,
0.024168049916625023,
0.03265319764614105,
0.005213520489633083,
0.017297787591814995,
-0.06276721507310867,
-0.004651590716093779,
-0.012582125142216682,
0.0360480397939682,
-0.018206357955932617,
-0.0032410614658147097,
-0.029309730976819992,
0.004827199969440699,
0.0026331404224038124,
0.006128466688096523,
0.029291342943906784,
-0.0031324008014053106,
0.026044894009828568,
-0.0017953504575416446,
-0.0247743371874094,
0.012602526694536209,
0.062459781765937805,
0.06291235238313675,
-0.030839357525110245,
-0.0012817166280001402,
-0.027538588270545006,
-0.01752251572906971,
-0.033731646835803986,
0.01748526655137539,
0.018934981897473335,
0.02161058969795704,
-0.004385349340736866,
-0.009910195134580135,
-0.019927721470594406,
0.01773979887366295,
-0.01769089326262474,
0.028060326352715492,
-0.0027622554916888475,
0.012900660745799541,
-0.02918444201350212,
-0.019727075472474098,
-0.005449295975267887,
0.03666889667510986,
0.036000996828079224,
-0.02404218725860119,
-0.01430324837565422,
-0.08803130686283112,
-0.017857268452644348,
0.0023890940938144922,
0.07247143983840942,
0.01581990346312523,
0.038774412125349045,
-0.04217272996902466,
-0.010157805867493153,
0.06284048408269882,
-0.017783790826797485,
0.029711183160543442,
-0.017149286344647408,
-0.006208048202097416,
-0.0237381923943758,
-0.006773022003471851,
-0.009004758670926094,
-0.009656885638833046,
-0.0021943554747849703,
-0.010866472497582436,
-0.01092961709946394,
-0.0060211289674043655,
-0.008324375376105309,
0.047304220497608185,
0.02038336545228958,
0.041307199746370316,
0.018362820148468018,
-0.02385096624493599,
0.028006814420223236,
-0.007828665897250175,
-0.054275672882795334,
-0.052368126809597015,
-0.02120610885322094,
-0.02816029079258442,
0.013546532019972801,
0.010309719480574131,
-0.03914973512291908,
-0.03482925891876221,
0.03246382623910904,
-0.0034331507049500942,
-0.029860805720090866,
0.00840836763381958,
-0.017491186037659645,
0.0321710929274559,
0.030405351892113686,
-0.0013502422953024507,
0.008664676919579506,
0.0732160285115242,
0.024271458387374878,
-0.025147071108222008,
-0.054774750024080276,
0.03577706590294838,
-0.027317944914102554,
-0.02236161381006241,
-0.04112539067864418,
0.01727866940200329,
-0.0625058189034462,
0.03993545100092888,
-0.029460836201906204,
0.02948443591594696,
-0.020393436774611473,
-0.020251810550689697,
0.038647186011075974,
-0.013628877699375153,
0.0015847909962758422,
-0.025502705946564674,
-0.01935577392578125,
-0.020569246262311935,
-0.00114763667806983,
-0.017677705734968185,
0.012904047966003418,
-0.006809906102716923,
0.027117453515529633,
0.02782283164560795,
-0.03520386666059494,
0.024928783997893333,
-0.04198324680328369,
-0.02564256452023983,
0.04071910306811333,
-0.06366955488920212,
0.043403878808021545,
-0.00874248892068863,
0.008346225135028362,
0.0385308563709259,
-0.0434713177382946,
0.0017884772969409823,
0.010089785791933537,
0.027340851724147797,
0.04190005362033844,
-0.025954771786928177,
0.009534260258078575,
-0.015597228892147541,
0.03886427730321884,
-0.025241713970899582,
-0.07361103594303131,
0.04409180209040642,
0.003501935862004757,
-0.03585665673017502,
-0.04027586802840233,
0.0037667544092983007,
-0.03151485323905945,
-0.001824923325330019,
0.014963521622121334,
0.028222277760505676,
0.002425570972263813,
-0.009553221054375172,
-0.019042091444134712,
0.029571056365966797,
0.08720643818378448,
0.006455680355429649,
0.006041146814823151,
-0.031376682221889496,
0.00449023162946105,
-0.01414545439183712,
-0.019281886518001556,
0.023644277825951576,
-0.04184338077902794,
-0.005161058157682419,
-0.01403229683637619,
-0.0020825855899602175,
0.05008453130722046,
-0.0347549244761467,
-0.012573488056659698,
0.04842915013432503,
0.051750075072050095,
-0.0030033260118216276,
-0.05873900279402733,
0.024781357496976852,
-0.04914865642786026,
-0.012458225712180138,
0.005623887293040752,
0.01806611381471157,
-0.023569386452436447,
-0.03913116455078125,
-0.004175436682999134,
-0.00811189878731966,
-0.010165774263441563,
-0.00324408826418221,
0.07943292707204819,
0.005891676060855389,
-0.03822473809123039,
0.006266214419156313,
0.0006296554929576814,
-0.00003640822251327336,
0.033311955630779266,
-0.01811494678258896,
-0.00043383194133639336,
0.004293359350413084,
-0.05110801383852959,
-0.032836075872182846,
-0.02065988816320896,
0.05784308537840843,
0.064457006752491,
-0.01710975170135498,
0.058063436299562454,
0.030172210186719894,
0.002186752622947097,
0.03096962720155716,
0.0048653483390808105,
-0.013443805277347565,
0.047152530401945114,
-0.008220902644097805,
0.02936786785721779,
-0.03531191498041153,
-0.011274515651166439,
-0.006893048994243145,
0.01729632541537285,
-0.006289354991167784,
0.0060573057271540165,
0.0280240960419178,
0.0025935948360711336,
-0.038947153836488724,
-0.02370740845799446,
-0.03700059652328491,
0.05318659171462059,
-0.04393967241048813,
0.018514536321163177,
-0.022737612947821617,
-0.012834320776164532,
0.035880301147699356,
-0.009574907831847668,
0.007991586811840534,
-0.0367141030728817,
-0.020209496840834618,
-0.005047831684350967,
-0.01417025737464428,
0.03871013596653938,
0.006482531316578388,
-0.01638343557715416,
0.010321004316210747,
0.03959161788225174,
0.018769921734929085,
0.050968848168849945,
-0.029975526034832,
-0.05023925006389618,
-0.0026285273488610983,
-0.017476877197623253,
-0.04543337598443031,
0.008159545250236988,
0.014305402524769306,
-0.07407644391059875,
0.014935057610273361,
-0.030847841873764992,
0.024042990058660507,
0.05837409943342209,
0.050847478210926056,
0.005577768664807081,
0.02850140817463398,
-0.008714931085705757,
-0.006893475074321032,
0.011710179969668388,
0.016110897064208984,
0.11827770620584488,
0.09761852771043777,
0.041487134993076324,
-0.0298453439027071,
0.0015252716839313507,
0.005385052412748337,
0.00793312955647707,
-0.0332924984395504,
0.007991687394678593,
-0.015574987977743149,
-0.0013494538143277168,
0.013669612817466259,
0.05253884568810463,
0.020183870568871498,
0.03604103624820709,
0.03813416138291359,
-0.010150290094316006,
-0.010684624314308167,
0.04487812891602516,
0.0037791135255247355,
0.0007973640458658338,
0.025879409164190292,
-0.03872153162956238,
-0.0033075676765292883,
-0.017459189519286156,
-0.013213100843131542,
-0.02436280995607376,
0.003840852063149214,
0.039122942835092545,
-0.01547111477702856,
-0.035714853554964066,
0.01559059601277113,
0.013102582655847073,
0.019350344315171242,
-0.046969179064035416,
-0.00403184350579977,
-0.012594354338943958,
-0.01627844199538231,
0.015081096440553665,
0.037663381546735764,
0.026900775730609894,
0.00993569940328598,
0.016203036531805992,
0.06083879619836807,
-0.01630169339478016,
-0.0019793598912656307,
-0.02334361895918846,
0.008117674849927425,
-0.023256152868270874,
-0.00023891375167295337,
0.014464134350419044,
-0.011364257894456387,
-0.014655307866632938,
-0.043575648218393326,
-0.03939599543809891,
-0.0006003195885568857,
0.03699840232729912,
-0.009821505285799503,
-0.007544177584350109,
-0.039275042712688446,
0.0038894275203347206,
-0.037788521498441696,
-0.009404271841049194,
-0.01515351701527834,
0.0006211416330188513,
-0.005304619204252958,
-0.001546035404317081,
0.03407697379589081,
-0.04936018958687782,
-0.019252492114901543,
-0.04459176957607269,
0.004698433913290501,
-0.030875269323587418,
-0.03078170120716095,
-0.023166446015238762,
-0.0024959438014775515,
0.02194504626095295,
0.03579054772853851,
-0.020639002323150635,
-0.0025465821381658316,
-0.015759635716676712,
-0.014741184189915657,
0.01694389060139656,
-0.02329125814139843,
-0.045818306505680084,
-0.015569673851132393,
0.0036599067971110344,
0.030694058164954185,
0.0002432668989058584,
0.00043218329665251076,
0.020241763442754745,
0.00793838407844305,
0.011193117126822472,
-0.04391089826822281,
0.0030561829917132854,
-0.0009415817330591381,
-0.06618862599134445,
0.0036313992459326982,
-0.005441067740321159,
0.04944126307964325,
0.017147768288850784,
0.019897371530532837,
-0.006301037967205048,
0.010582998394966125,
-0.020637961104512215,
0.014967834576964378,
0.007562799379229546,
-0.03415641933679581,
-0.01798558235168457,
-0.03394823893904686,
0.018359068781137466,
-0.006563409231603146,
-0.024654971435666084,
-0.023225847631692886,
0.002198138739913702,
-0.03361301124095917,
0.030436230823397636,
-0.015498184598982334,
-0.004292220342904329,
-0.027325130999088287,
-0.011716777458786964,
-0.051126834005117416,
-0.011274035088717937,
-0.07060191035270691,
0.009622684679925442,
0.05426967889070511,
0.012760939076542854,
-0.034649938344955444,
0.03764043375849724,
-0.021076086908578873,
-0.004193821456283331,
0.021880637854337692,
-0.007521464955061674,
-0.01435302197933197,
-0.025804758071899414,
0.02108411118388176,
0.021623168140649796,
0.0576164573431015,
-0.017639482393860817,
-0.06505230814218521,
0.050512246787548065,
-0.04833751544356346,
-0.02606680430471897,
-0.0027759328950196505,
-0.02953897975385189,
0.002165410667657852,
0.044065918773412704,
0.030027011409401894,
0.017597895115613937,
0.06187979504466057,
-0.0014403591630980372,
0.043061044067144394,
0.02034386619925499,
-0.0420260950922966,
0.017305228859186172,
0.027922527864575386,
0.014672070741653442,
0.021286703646183014,
0.007708427961915731,
-0.005314617417752743,
0.011164695955812931,
0.019236862659454346,
0.003027095226570964,
0.015666045248508453,
-0.01336521003395319,
-0.025063879787921906,
0.009299003519117832,
0.016675874590873718,
-0.005693096201866865,
0.06858699768781662,
-0.03291395679116249,
0.020060215145349503,
0.02706710249185562,
0.023319000378251076,
-0.08902871608734131,
0.011236618272960186,
0.033217038959264755,
-0.021515395492315292,
0.016031166538596153,
-0.04076996073126793,
0.043931744992733,
0.03173695504665375,
-0.07623104751110077,
0.003333820728585124,
-0.06377749145030975,
-0.003404162358492613,
-0.06712052971124649,
-0.006492887623608112,
-0.006395788863301277,
0.055781055241823196,
0.027810029685497284,
0.02346564084291458,
-0.005852153990417719,
0.02852669544517994,
-0.0028075245209038258,
0.018755335360765457,
0.03649749234318733,
0.05125582963228226,
0.022143978625535965,
0.0011354162124916911,
0.04387317970395088,
0.03428537771105766,
-0.056471437215805054,
0.03450256586074829,
-0.03241177648305893,
0.003040531650185585,
-0.0013813457917422056,
-0.018253065645694733,
-0.02639833465218544,
0.026045601814985275,
0.04658753052353859,
-0.014186191372573376,
-0.01763208955526352,
-0.0002619732404127717,
0.018806368112564087,
0.020329279825091362,
-0.00626222463324666,
-0.005885728634893894,
0.033241916447877884,
-0.02026907540857792,
-0.04198891669511795,
0.06939686834812164,
-0.005274104420095682,
0.011571074835956097,
-0.005098525434732437,
-0.051095958799123764,
0.029428966343402863,
-0.03131654113531113,
-0.012052824720740318,
-0.02508597820997238,
-0.016492750495672226,
0.01570938155055046,
0.011355512775480747,
0.012160954996943474,
0.017199378460645676,
0.049447931349277496,
-0.02376863732933998,
-0.001493912423029542,
-0.013880378566682339,
-0.03894060477614403,
-0.026296941563487053,
0.03345377743244171,
-0.02596973441541195,
-0.015729939565062523,
-0.02617676556110382,
-0.039789531379938126,
-0.05802130699157715,
0.0726921558380127,
0.017618922516703606,
0.002185197314247489,
0.02191334217786789,
-0.02730257250368595,
-0.02363547682762146,
-0.07629946619272232,
0.030931787565350533,
-0.02128877304494381,
0.028468165546655655,
-0.0019136788323521614,
0.025878336280584335,
-0.0019680147524923086,
0.03306671977043152,
0.052856530994176865,
0.015624875202775002,
0.008204427547752857,
0.05373845621943474,
0.01782127656042576,
-0.02024509571492672,
-0.07230837643146515,
-0.02772962860763073,
0.008858704008162022,
0.003110582008957863,
0.01943575218319893,
0.009576668962836266,
0.008730684407055378,
-0.01540474221110344,
0.008541757240891457,
0.00652310298755765,
0.04187595471739769,
0.010715540498495102,
-0.024433379992842674,
0.034078359603881836,
0.010368992574512959,
-0.011904880404472351,
0.08894633501768112,
-0.025217924267053604,
-0.004902339540421963,
-0.0285349078476429,
-0.014344104565680027,
-0.035857804119586945,
0.06121891364455223,
-0.016765085980296135,
-0.025143828243017197,
0.008092442527413368,
-0.03771728649735451,
0.003714868100360036,
-0.050449587404727936,
-0.01083534024655819,
0.06593966484069824,
-0.05443009361624718,
-0.026367351412773132,
0.02602996863424778,
0.026320479810237885,
0.03294919803738594,
-0.04823945090174675,
-0.005308957304805517,
0.0133676677942276,
-0.04470205679535866,
-0.05599350854754448,
0.05809672176837921,
0.035583700984716415,
-0.028903381898999214,
-0.01162109524011612,
0.03427251800894737,
0.0023105801083147526,
-0.007714149076491594,
0.03228604421019554,
-0.014147866517305374,
-0.03359045088291168,
-0.04623947665095329,
0.01912045106291771,
-0.005860796198248863,
-0.002979293232783675,
0.005804819520562887,
-0.014279586263000965,
0.05395940691232681,
-0.017974602058529854,
-0.0027601527981460094,
-0.03810567408800125,
-0.012720261700451374,
-0.044378262013196945,
0.00949044805020094,
-0.010953146032989025,
0.010535556823015213,
-0.028022509068250656,
-0.011798668652772903,
-0.012674562633037567,
0.002190208761021495,
0.007186709437519312,
-0.021428871899843216,
0.01904149539768696,
-0.012217782437801361,
0.016962608322501183,
0.03569260239601135,
0.009791492484509945,
-0.03325171396136284,
-0.01793012209236622,
0.058740388602018356,
0.007558452431112528,
-0.011074120178818703,
0.0002995482354890555,
-0.04853644222021103,
0.01663479395210743,
0.08768582344055176,
-0.017146585509181023,
-0.03453819453716278,
-0.003543172962963581,
0.02938985824584961,
0.001679537002928555,
-0.053584836423397064
] |
<blockquote>
<p>I have a pot with water of mass $m$ and it is heated by a stove
element of temperature $T_E$ and with a surface area of $A$. The
water starts at temperature $T_W > 0^\circ\, C$.</p>
<p>How long would it take to heat up this water to a final temperature of
$T_F$ ($T_W<T_F < 100^\circ \, C$)? Metal of the pot is negligible.</p>
</blockquote>
<p>The heat travels with convection in the water, presumably. I was trying to figure out a solution to this problem, but I am unsure as to what formula to use. </p>
<p>Would the answer change if someone is constantly stirring?</p> | 4,588 | [
0.01374049298465252,
-0.033737462013959885,
-0.004596624057739973,
-0.027203118428587914,
0.05467528477311134,
-0.04231799766421318,
-0.045364197343587875,
0.004495042376220226,
0.01059048343449831,
-0.012874463573098183,
0.06819701939821243,
0.05426762253046036,
0.05208124965429306,
-0.018027998507022858,
0.03360915556550026,
0.005720268469303846,
0.0052042994648218155,
-0.009640044532716274,
0.022016478702425957,
-0.018777672201395035,
0.016859473660588264,
-0.022973332554101944,
-0.00789456907659769,
0.0011160260764881968,
-0.03852181136608124,
0.02296333760023117,
0.0018349629826843739,
0.006962612736970186,
-0.013690597377717495,
0.041664231568574905,
-0.000740066752769053,
-0.06301447004079819,
0.025383424013853073,
0.0034454804845154285,
0.04158773645758629,
0.006029398646205664,
-0.038551557809114456,
-0.03709293156862259,
-0.026284554973244667,
0.003495258279144764,
-0.008392917923629284,
-0.0426550917327404,
0.013145100325345993,
0.013711011968553066,
0.011764594353735447,
0.013427255675196648,
-0.0034094159491360188,
-0.04126541316509247,
0.031144438311457634,
-0.04458710551261902,
0.014861559495329857,
0.026888910681009293,
0.06100967898964882,
-0.017107220366597176,
0.026407960802316666,
0.005973257590085268,
0.06268719583749771,
0.02837350033223629,
-0.012564346194267273,
-0.02482740581035614,
-0.02573433890938759,
-0.009792882017791271,
-0.026804998517036438,
-0.03075915388762951,
-0.017171744257211685,
0.0017375139286741614,
-0.008946388959884644,
0.0022612004540860653,
-0.017620576545596123,
-0.019249659031629562,
0.03771866112947464,
-0.02924753539264202,
0.05857449024915695,
-0.001859040348790586,
-0.013424352742731571,
-0.021935494616627693,
0.006228868383914232,
0.044071048498153687,
0.005088109523057938,
0.0668153315782547,
-0.009795726276934147,
-0.0037865317426621914,
0.029862545430660248,
0.01564977318048477,
0.007888231426477432,
0.010837498120963573,
0.029728688299655914,
0.038154829293489456,
0.03865384683012962,
0.031877994537353516,
-0.022074857726693153,
0.019758077338337898,
0.020387614145874977,
-0.005207200534641743,
0.040630754083395004,
-0.003720682580024004,
-0.002652211580425501,
0.04055820778012276,
0.0034407118801027536,
-0.035696521401405334,
0.01041786652058363,
-0.010604489594697952,
0.00471713300794363,
0.06303101778030396,
0.008841830305755138,
-0.01947838068008423,
-0.021634889766573906,
-0.012182941660284996,
-0.008077490143477917,
0.0006438617710955441,
-0.01901402324438095,
-0.009798446670174599,
-0.01629769802093506,
-0.010497449897229671,
0.007171190343797207,
-0.0011821786174550653,
0.007326655555516481,
-0.05230255052447319,
0.06477027386426926,
0.023241296410560608,
0.03505479544401169,
-0.034685999155044556,
0.04022775590419769,
-0.025674870237708092,
-0.057538148015737534,
0.03650910407304764,
0.0008254930726252496,
-0.003802067833021283,
-0.028350796550512314,
0.025631112977862358,
0.008609635755419731,
-0.019661979749798775,
0.018582578748464584,
-0.026193533092737198,
-0.008845235221087933,
-0.008349141106009483,
-0.07048966735601425,
-0.0664832815527916,
0.0495927631855011,
-0.03476676717400551,
-0.028214991092681885,
-0.06776072084903717,
0.008861836977303028,
0.017283745110034943,
0.05028245970606804,
-0.008911974728107452,
0.010176143608987331,
-0.03422359377145767,
0.054761726409196854,
-0.023430781438946724,
-0.06413141638040543,
-0.04590781033039093,
0.020551254972815514,
-0.024084027856588364,
0.038331255316734314,
-0.02296203188598156,
0.023718180134892464,
0.041526973247528076,
0.02376426011323929,
-0.01471626851707697,
0.049405548721551895,
-0.005129076074808836,
-0.012386796995997429,
0.027298564091324806,
0.008319898508489132,
-0.043659888207912445,
0.09922119230031967,
-0.0032158251851797104,
0.043131012469530106,
0.01409168541431427,
0.004227321594953537,
-0.001450594631023705,
-0.014508523046970367,
-0.006761627271771431,
0.037509530782699585,
-0.03660088777542114,
0.015816522762179375,
0.0068034278228878975,
0.02066371962428093,
0.06399844586849213,
-0.003284565405920148,
-0.003927641082555056,
0.019149914383888245,
-0.006367785390466452,
0.03573155403137207,
0.0625239759683609,
-0.00419021537527442,
0.016648216173052788,
-0.020002011209726334,
-0.03453821688890457,
-0.018518732860684395,
-0.06055542454123497,
-0.003846989246085286,
0.01763618364930153,
0.03159981593489647,
0.028309687972068787,
-0.05691973865032196,
0.05044149234890938,
-0.017220107838511467,
-0.05161205679178238,
0.018576759845018387,
0.03002760373055935,
0.014819699339568615,
-0.017931224778294563,
0.021748049184679985,
0.06520088762044907,
0.04136994853615761,
0.00591758219525218,
0.04022396355867386,
-0.014768901281058788,
-0.0024221441708505154,
-0.02175954356789589,
-0.01915949024260044,
0.031589169055223465,
0.006640356499701738,
-0.026301702484488487,
0.009890646673738956,
-0.017888344824314117,
0.016114478930830956,
0.022722788155078888,
-0.031127870082855225,
0.059208210557699203,
0.04147135466337204,
0.015222836285829544,
-0.0014373642625287175,
0.04713096469640732,
0.007347464095801115,
-0.020639818161725998,
-0.002119330922141671,
-0.05989987030625343,
-0.036503829061985016,
-0.042173270136117935,
0.0399542860686779,
0.008331692777574062,
-0.04400506243109703,
0.02045069821178913,
0.02711562253534794,
0.04376621171832085,
0.04713914543390274,
0.029889460653066635,
-0.028303993865847588,
-0.013388344086706638,
0.04668641835451126,
0.008068768307566643,
-0.039138488471508026,
0.04185668006539345,
-0.01709499955177307,
0.03259057551622391,
0.00209442968480289,
0.03635019436478615,
-0.020115774124860764,
0.0020687838550657034,
0.0023639879655092955,
0.0060142106376588345,
-0.01614551432430744,
-0.0010310676880180836,
0.007207568269222975,
-0.06191343069076538,
-0.011196204461157322,
-0.00608923239633441,
0.00800926424562931,
0.016420897096395493,
-0.042438771575689316,
-0.02841000072658062,
0.012240631505846977,
0.003829529043287039,
-0.013358993455767632,
-0.03315180540084839,
0.021364562213420868,
-0.019294168800115585,
-0.0029036090709269047,
0.005988414399325848,
0.02403929829597473,
0.008658239617943764,
0.003400563495233655,
0.030369294807314873,
0.025591745972633362,
0.019666440784931183,
-0.04102575406432152,
-0.028811350464820862,
0.042126771062612534,
-0.024243159219622612,
-0.0058480603620409966,
-0.005986515898257494,
-0.043390486389398575,
-0.005267567932605743,
0.014255674555897713,
-0.03644558787345886,
0.04996992275118828,
0.018006037920713425,
0.011601448990404606,
0.001973975682631135,
-0.0019372067181393504,
-0.06375177949666977,
0.00626013707369566,
0.005016997456550598,
0.05001116171479225,
-0.04677150771021843,
-0.0051186406053602695,
0.045679859817028046,
-0.01597328670322895,
-0.030451597645878792,
0.01099882461130619,
-0.06112895533442497,
-0.04616423323750496,
-0.020387915894389153,
-0.008572448045015335,
0.035808123648166656,
-0.021265743300318718,
0.028327444568276405,
0.003909411374479532,
-0.042296797037124634,
0.010489263571798801,
-0.07570154219865799,
-0.06258631497621536,
0.002878438448533416,
-0.025167440995573997,
0.05865941196680069,
0.03849847987294197,
-0.05855267494916916,
0.06498414278030396,
0.031472742557525635,
-0.055310219526290894,
-0.0071724154986441135,
-0.02096921019256115,
0.02037695050239563,
-0.043155357241630554,
-0.007578640710562468,
0.03223748132586479,
-0.055108051747083664,
-0.0031607456039637327,
-0.005597027018666267,
0.03245456889271736,
0.0682472288608551,
0.0026317716110497713,
0.015762178227305412,
0.025725554674863815,
-0.0038604862056672573,
0.030978461727499962,
0.024368135258555412,
-0.017822040244936943,
-0.008320572786033154,
0.026465153321623802,
-0.06707808375358582,
0.03219202160835266,
0.05633676424622536,
-0.04778668284416199,
0.028766965493559837,
-0.022677427157759666,
0.012497774325311184,
-0.08157705515623093,
0.07751048356294632,
-0.02506016008555889,
0.0034535403829067945,
0.020929554477334023,
0.04558916017413139,
0.05789904296398163,
-0.02011515386402607,
0.02570122852921486,
0.020914461463689804,
0.05375850573182106,
0.011544904671609402,
-0.0333896167576313,
0.0024037284310907125,
0.00953611359000206,
0.0020812654402107,
-0.01776849292218685,
0.0036804191768169403,
0.029581550508737564,
0.008456463925540447,
0.039338309317827225,
0.00017312511045020074,
-0.029190365225076675,
-0.003541443031281233,
-0.06629587709903717,
-0.05261490121483803,
0.046518199145793915,
0.07210041582584381,
-0.0061913360841572285,
0.031154613941907883,
0.023685846477746964,
0.007122180424630642,
0.006467238999903202,
-0.010387416929006577,
-0.06344926357269287,
0.02370535396039486,
-0.04493149369955063,
0.01410432904958725,
-0.011506188660860062,
-0.002225541742518544,
-0.016002213582396507,
-0.001410177443176508,
-0.00658461544662714,
0.020386196672916412,
0.028783904388546944,
-0.013197659514844418,
0.0358535535633564,
-0.028154566884040833,
-0.02534670941531658,
-0.0014498784439638257,
-0.008175292983651161,
0.019762113690376282,
-0.03893560916185379,
0.046237606555223465,
0.04299420863389969,
0.002087293192744255,
0.004509422928094864,
-0.02900325320661068,
-0.023173080757260323,
0.020560434088110924,
0.009538203477859497,
0.029409470036625862,
0.03631880506873131,
-0.05447474122047424,
0.029231438413262367,
0.006581141613423824,
0.006005220115184784,
-0.024236710742115974,
0.005809074267745018,
-0.04507817327976227,
-0.04188097268342972,
-0.013135397806763649,
0.04898897558450699,
0.0052708107978105545,
-0.026360705494880676,
0.023810777813196182,
0.022746846079826355,
-0.008521097712218761,
-0.018111590296030045,
0.06415731459856033,
0.02534586191177368,
0.011003184132277966,
-0.03259921073913574,
-0.028475446626544,
0.03384872525930405,
-0.012076801620423794,
0.0100391935557127,
-0.011456094682216644,
0.016081783920526505,
0.024203646928071976,
-0.012247069738805294,
0.023249998688697815,
-0.010260858573019505,
0.020606456324458122,
0.04597500339150429,
0.030499646440148354,
0.041994836181402206,
0.0004630698240362108,
-0.02551158517599106,
-0.03507625684142113,
0.05200308933854103,
-0.003918779548257589,
-0.06665237247943878,
-0.019354958087205887,
-0.050173576921224594,
-0.015236073173582554,
0.036758847534656525,
0.06647294014692307,
-0.02753586880862713,
0.05572475492954254,
-0.07718808948993683,
-0.03932608291506767,
0.03334960713982582,
-0.028757505118846893,
0.006032000761479139,
-0.02731943316757679,
0.009611590765416622,
0.04282069951295853,
-0.043764159083366394,
-0.017061058431863785,
-0.0124507499858737,
0.006272434256970882,
0.006197104696184397,
-0.024127380922436714,
-0.030882516875863075,
0.03312964737415314,
-0.0015935449628159404,
0.027908626943826675,
-0.043923430144786835,
-0.01150523591786623,
-0.004337215796113014,
0.018702391535043716,
-0.014226861298084259,
0.019141066819429398,
-0.07017319649457932,
0.0028371086809784174,
-0.013597337529063225,
0.008972338400781155,
0.0007649468025192618,
-0.03221893310546875,
-0.064391128718853,
0.025965508073568344,
0.06311634182929993,
-0.004185380879789591,
-0.03471272066235542,
0.0038928776048123837,
0.07001490145921707,
0.00938378181308508,
-0.008764202706515789,
0.04723843187093735,
0.04161086678504944,
-0.002837248146533966,
-0.023064550012350082,
-0.027250315994024277,
0.03650211542844772,
-0.008752048015594482,
0.00919845886528492,
-0.03640462085604668,
-0.0125901373103261,
-0.025457153096795082,
0.05231665074825287,
-0.014044229872524738,
-0.0070221200585365295,
-0.03607044368982315,
-0.026617752388119698,
0.011465921066701412,
-0.010408295318484306,
0.039207663387060165,
-0.01455232035368681,
0.01976788602769375,
0.005566239822655916,
0.053566206246614456,
-0.03832487761974335,
0.03849833831191063,
-0.028967835009098053,
0.043105389922857285,
0.008093706332147121,
-0.01784384995698929,
0.010408619418740273,
-0.06616003811359406,
-0.02411666512489319,
0.00820546131581068,
-0.043688125908374786,
0.04088052734732628,
-0.02224651351571083,
0.017557384446263313,
0.014476657845079899,
-0.05449443310499191,
-0.0045066457241773605,
0.016056403517723083,
0.02951064147055149,
0.016381341964006424,
-0.05081811174750328,
0.0014596054097637534,
0.019550926983356476,
0.0068858303129673,
-0.07165317982435226,
-0.040990374982357025,
0.00780298700556159,
0.0027349458541721106,
0.0021948744542896748,
-0.05522504448890686,
-0.002251921221613884,
-0.0630565732717514,
-0.025735270231962204,
0.01270390022546053,
0.043492503464221954,
0.019598588347434998,
0.00407959520816803,
0.001802662736736238,
0.03883836418390274,
0.051674239337444305,
0.027260692790150642,
0.000517348584253341,
0.004091375507414341,
-0.033566318452358246,
-0.036054424941539764,
0.019915662705898285,
0.04350447654724121,
-0.051777713000774384,
0.00012443267041817307,
0.00800471380352974,
-0.01322312280535698,
0.030398162081837654,
0.01042239461094141,
-0.01152478251606226,
0.01662575826048851,
0.03269180282950401,
0.004861205816268921,
-0.043121036142110825,
0.048383068293333054,
0.038537587970495224,
0.02744481898844242,
-0.0185580812394619,
0.002284671412780881,
-0.01268744096159935,
-0.01930885575711727,
0.005044464021921158,
-0.035632289946079254,
-0.007629679515957832,
-0.024075835943222046,
0.0427442342042923,
-0.011621310375630856,
-0.030585456639528275,
0.01920977421104908,
0.0034714830107986927,
0.03867674618959427,
0.0055953687988221645,
-0.011746051721274853,
0.004991434048861265,
-0.04249200224876404,
-0.013262280263006687,
-0.006708825472742319,
-0.0355103425681591,
-0.0066316560842096806,
0.05094000697135925,
-0.01755267195403576,
0.049727652221918106,
0.014159994199872017,
0.0025456759613007307,
0.01993483118712902,
0.02719184011220932,
-0.0181813295930624,
0.033344246447086334,
0.0008707881206646562,
0.037004854530096054,
0.003480413230136037,
0.006628004834055901,
0.044746048748493195,
0.027222217991948128,
-0.018746018409729004,
0.04526424780488014,
-0.008801322430372238,
-0.011812631972134113,
0.013055393472313881,
-0.0186894740909338,
-0.038644082844257355,
0.024038584902882576,
-0.020228002220392227,
0.01650875061750412,
-0.03816794604063034,
-0.04972631111741066,
0.02925143949687481,
0.019808867946267128,
-0.002417606534436345,
-0.038343753665685654,
0.0036838625092059374,
-0.044132571667432785,
-0.04359995573759079,
0.013409814797341824,
-0.01580967754125595,
0.0015438144328072667,
0.019454525783658028,
0.010668709874153137,
-0.012706056237220764,
0.012842501513659954,
-0.001958270324394107,
-0.010824320837855339,
-0.020906895399093628,
-0.013836939819157124,
-0.0444217175245285,
0.011307548731565475,
-0.017123425379395485,
-0.043416086584329605,
-0.015151798725128174,
-0.03955462947487831,
0.004681746941059828,
0.004316342994570732,
0.007351127453148365,
-0.04305046424269676,
0.0861658900976181,
0.011287271976470947,
0.02494852803647518,
0.00937704648822546,
0.017204731702804565,
0.09837605059146881,
0.03753452003002167,
0.02475566789507866,
-0.06407172232866287,
0.0007565133855678141,
-0.012490796856582165,
-0.011744382791221142,
-0.04072410240769386,
-0.007143404334783554,
-0.004085617605596781,
0.009255900047719479,
0.04129723086953163,
0.08113691210746765,
-0.01106580626219511,
0.05048925802111626,
0.006540798116475344,
-0.014748827554285526,
-0.02385850064456463,
0.025154966861009598,
-0.0044190771877765656,
0.013401047326624393,
0.004574028309434652,
-0.039589278399944305,
0.014009262435138226,
-0.05160072073340416,
0.0012324800482019782,
0.016671227291226387,
-0.02383204735815525,
0.02678215689957142,
0.018238993361592293,
-0.08300482481718063,
0.023001577705144882,
-0.00046479597222059965,
-0.010639244690537453,
-0.010630526579916477,
0.008128532208502293,
0.04875867813825607,
-0.006974446587264538,
0.03159211575984955,
0.049694567918777466,
0.023039037361741066,
0.02109367772936821,
0.02952353097498417,
0.03841317817568779,
-0.03742961212992668,
-0.02251024916768074,
-0.05131548270583153,
-0.02003711462020874,
-0.016497023403644562,
0.004852363374084234,
0.01492447592318058,
-0.00340921338647604,
-0.00728203821927309,
-0.04263385757803917,
0.0026489300653338432,
0.021159037947654724,
0.041469939053058624,
-0.005408543162047863,
-0.03163169324398041,
-0.025702569633722305,
0.02707732655107975,
-0.031844280660152435,
-0.014368816278874874,
0.049938447773456573,
-0.009555350989103317,
-0.02223462238907814,
0.03768283873796463,
0.039720553904771805,
0.03642420098185539,
-0.02449316717684269,
-0.03227568790316582,
-0.03690126910805702,
0.008141407743096352,
-0.00015821885608602315,
0.016397401690483093,
0.017791636288166046,
0.02798689529299736,
0.0011379232164472342,
-0.01892557367682457,
-0.01230031531304121,
-0.07568510621786118,
0.023002807050943375,
0.01820213533937931,
-0.018220463767647743,
-0.0395868681371212,
-0.0052350671030581,
0.0032111727632582188,
0.042742494493722916,
-0.0319250263273716,
-0.01683410443365574,
0.010010202415287495,
0.018205109983682632,
0.035252880305051804,
-0.04456011578440666,
-0.0059596579521894455,
0.005299996118992567,
-0.030239854007959366,
-0.018354840576648712,
0.0007061736541800201,
0.05807824805378914,
0.05462883040308952,
-0.01727849431335926,
0.006632436066865921,
-0.0016255113296210766,
-0.005519646219909191,
0.02214977890253067,
0.017447540536522865,
-0.022809283807873726,
-0.017003681510686874,
-0.006887197960168123,
-0.032810863107442856,
-0.0033866637386381626,
-0.05475550517439842,
-0.02562492899596691,
0.011483103968203068,
-0.00378120387904346,
0.03174540400505066,
-0.031127454712986946,
0.017461074516177177,
-0.020371371880173683,
0.015305506065487862,
-0.03042851760983467,
-0.007217073813080788,
-0.04189185053110123,
-0.01086638867855072,
0.04403328150510788,
0.014784778468310833,
-0.021913759410381317,
0.03741202503442764,
-0.020783696323633194,
0.008936584927141666,
0.013029966503381729,
0.020044436678290367,
0.026107287034392357,
-0.04984923452138901,
0.005323273129761219,
-0.032036516815423965,
0.05887880548834801,
-0.0226834025233984,
-0.04324708133935928,
0.058448225259780884,
-0.03989849612116814,
-0.04598112031817436,
0.04530742019414902,
-0.02370014600455761,
0.041308410465717316,
0.04172857850790024,
-0.03262461721897125,
0.046940747648477554,
0.045353733003139496,
-0.03780640289187431,
-0.00004804182390216738,
-0.010249964892864227,
-0.00921773724257946,
0.016820864751935005,
-0.02645038813352585,
0.02238265611231327,
0.013104734942317009,
-0.003497766563668847,
-0.00721390638500452,
0.06584089249372482,
-0.014620296657085419,
0.015539497137069702,
-0.024653885513544083,
-0.03269762545824051,
0.0032625035382807255,
0.029740840196609497,
0.001506326487287879,
-0.011084267869591713,
0.0712306872010231,
-0.028716769069433212,
-0.01504448987543583,
-0.03180436044931412,
-0.002849123440682888,
-0.10841625928878784,
0.012461161240935326,
-0.000015135124158405233,
0.01847582682967186,
0.038332387804985046,
-0.04320608451962471,
0.0004727207706309855,
0.06583808362483978,
-0.06500828266143799,
0.03464003652334213,
-0.03146616742014885,
0.01715673878788948,
-0.04244615510106087,
-0.008605914190411568,
-0.005301676224917173,
0.02855561301112175,
0.04202181473374367,
0.017283199355006218,
0.030436506494879723,
0.04831966012716293,
-0.02172333374619484,
-0.012960797175765038,
0.06112930178642273,
0.04484421759843826,
0.005165952257812023,
-0.02859681472182274,
0.03061489202082157,
-0.0010118219070136547,
-0.04390991851687431,
0.0007436228333972394,
-0.02758018486201763,
0.028392313048243523,
-0.037191975861787796,
0.0462924987077713,
0.004219085443764925,
0.03547683358192444,
-0.013827112503349781,
-0.034190960228443146,
0.005183348432183266,
0.07688655704259872,
0.012716452591121197,
0.01909460686147213,
-0.00786169059574604,
0.0059976656921207905,
0.009814287535846233,
-0.012678427621722221,
-0.060516469180583954,
0.061831239610910416,
-0.03677744045853615,
-0.04623870179057121,
0.02945568971335888,
-0.02127966098487377,
0.04812316969037056,
-0.015083862468600273,
-0.014263312332332134,
-0.031245291233062744,
0.017583515495061874,
0.044050611555576324,
-0.011827003210783005,
-0.0240187831223011,
-0.041975926607847214,
0.008448725566267967,
-0.015340025536715984,
0.029512695968151093,
-0.024288980290293694,
-0.05115923658013344,
-0.037401676177978516,
-0.01952272653579712,
0.0056886328384280205,
0.020583350211381912,
-0.025327622890472412,
-0.018482210114598274,
-0.005484464578330517,
0.033281728625297546,
0.010222051292657852,
0.026708852499723434,
0.023352600634098053,
0.01157835591584444,
-0.03853475674986839,
-0.03514886647462845,
0.003873312845826149,
-0.013764317147433758,
0.00005008336665923707,
-0.029193338006734848,
-0.008051182143390179,
0.002529931953176856,
0.011398231610655785,
0.05143474042415619,
0.03279862925410271,
-0.020282190293073654,
0.021756842732429504,
0.0053728604689240456,
0.028008757159113884,
-0.06992703676223755,
0.031094077974557877,
-0.024191029369831085,
-0.006496910471469164,
0.008667844347655773,
-0.0023887711577117443,
0.010576865635812283,
-0.0072257025167346,
0.017672669142484665,
-0.03946986421942711,
-0.013494787737727165,
0.010875001549720764,
-0.008506913669407368,
0.028534667566418648,
0.014718767255544662,
-0.0051640598103404045,
0.06232590600848198,
0.020938372239470482,
-0.022925037890672684,
0.03592219576239586,
-0.02305629663169384,
-0.0396287702023983,
0.006272290367633104,
0.0030945478938519955,
0.027470776811242104,
0.01612458936870098,
-0.029390186071395874,
-0.0054476093500852585,
-0.04394335299730301,
-0.002175843110308051,
0.02478201687335968,
-0.026295235380530357,
-0.021096954122185707,
-0.0027233310975134373,
0.02667146921157837,
0.04173653945326805,
-0.013261944055557251,
-0.006718647666275501,
-0.001091702259145677,
0.036494091153144836,
-0.0056337169371545315,
0.04321104288101196,
0.034893348813056946,
-0.02458775043487549,
0.05857597291469574,
0.009302224032580853,
-0.020875750109553337,
0.03393107280135155,
0.013959563337266445,
-0.013028846122324467,
0.011592374183237553,
-0.019475974142551422,
0.035811398178339005,
-0.031394924968481064,
-0.021740248426795006,
0.008892057463526726,
-0.029698196798563004,
0.08611182868480682,
-0.013499577529728413,
-0.00943685881793499,
-0.03780592232942581,
0.010831059888005257,
-0.04420829564332962,
0.02157396264374256,
0.02279234118759632,
0.031529173254966736,
-0.05811480060219765,
-0.006776320282369852,
0.014568835496902466,
-0.002660212805494666,
0.0031618892680853605,
-0.023369869217276573,
0.014768469147384167,
-0.013691864907741547,
0.00304079195484519,
-0.050296735018491745,
-0.03545260801911354,
-0.021380409598350525,
-0.05774916335940361,
0.03057745471596718,
0.044176314026117325,
0.037963055074214935,
-0.009182391688227654,
-0.04314010962843895,
0.006036818493157625,
0.06313461065292358,
-0.08367892354726791,
-0.019539397209882736,
-0.029289832338690758,
0.007252476643770933,
-0.004367569461464882,
-0.05357854440808296
] |
<p>$$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$</p>
<p>I can't understand this formula, what is the magnetostatic stored potential energy?! What does it show?
Does it explain anything relative to magnetization?</p> | 4,589 | [
-0.03227641060948372,
-0.02136951871216297,
-0.009315615519881248,
-0.06567154079675674,
0.05014917999505997,
0.016032012179493904,
-0.05655401945114136,
-0.03281820937991142,
0.00914110615849495,
-0.023852208629250526,
0.00604394543915987,
0.014608834870159626,
0.03758585825562477,
-0.01111466996371746,
0.04269564896821976,
-0.003777772653847933,
0.007303794380277395,
0.002163766883313656,
0.010287250392138958,
-0.05508672446012497,
0.004088494926691055,
-0.015316300094127655,
0.013833372853696346,
0.0055363173596560955,
-0.032371025532484055,
0.03332220017910004,
0.027604147791862488,
-0.02115488424897194,
0.017116650938987732,
0.06435195356607437,
-0.01686582714319229,
-0.03374822065234184,
0.03387073427438736,
-0.019264034926891327,
-0.007298070006072521,
-0.013169636949896812,
-0.02440609410405159,
-0.05134616419672966,
-0.03036733716726303,
0.04778217896819115,
-0.029932796955108643,
-0.019678540527820587,
-0.0025769146159291267,
0.04898728430271149,
-0.021503876894712448,
-0.011807392351329327,
-0.022902298718690872,
0.0025575419422239065,
0.024097828194499016,
-0.058198995888233185,
0.04512586444616318,
-0.01738674007356167,
0.062192901968955994,
-0.014797336421906948,
-0.02426011860370636,
0.0017830595606938004,
0.051939789205789566,
0.051206570118665695,
0.009881201200187206,
-0.05051352456212044,
-0.03212858736515045,
-0.02847827412188053,
0.0099466098472476,
-0.0423133485019207,
-0.018334655091166496,
0.03438922017812729,
0.032360054552555084,
0.0004955744370818138,
0.050020359456539154,
0.02890213020145893,
0.009048867039382458,
0.024484742432832718,
0.018952365964651108,
-0.02197103388607502,
0.05901689454913139,
-0.03679065778851509,
0.027239378541707993,
-0.001995653612539172,
0.018061937764286995,
0.020589174702763557,
0.00027251895517110825,
0.013353098183870316,
0.04646935313940048,
0.06948742270469666,
-0.0030441845301538706,
-0.012689851224422455,
0.0720352753996849,
0.02773188427090645,
0.057050373405218124,
0.012902605347335339,
-0.0034461936447769403,
0.039339154958724976,
0.015632184222340584,
-0.023380078375339508,
-0.03457349166274071,
0.032985616475343704,
0.010168159380555153,
0.03969937190413475,
-0.014968750067055225,
-0.01856711320579052,
0.018077941611409187,
-0.0012672956800088286,
0.009249110706150532,
0.04165058583021164,
0.022211873903870583,
-0.06655513495206833,
-0.004905375652015209,
0.012712745927274227,
-0.022246479988098145,
-0.02304931730031967,
-0.051464881747961044,
0.03346286341547966,
0.004247086122632027,
-0.010798433795571327,
0.0037942384369671345,
-0.011350208893418312,
0.0009000953286886215,
-0.0017434771871194243,
0.013562067411839962,
0.05754132196307182,
-0.013913209550082684,
-0.02928549237549305,
-0.0009199189371429384,
-0.03561466932296753,
-0.09028859436511993,
0.024037985131144524,
0.01306896936148405,
0.002406403888016939,
-0.0481831319630146,
0.02070048078894615,
-0.030468611046671867,
-0.019447647035121918,
-0.01000858936458826,
0.0030454404186457396,
0.014670315198600292,
-0.018258526921272278,
-0.07941371947526932,
-0.00318539934232831,
0.049626149237155914,
-0.06210808455944061,
-0.005065375939011574,
-0.061453185975551605,
-0.0064713540486991405,
0.019584516063332558,
0.08040586113929749,
0.02751648798584938,
0.0009929209481924772,
-0.01218742411583662,
0.03346798196434975,
0.01819620281457901,
-0.03902577608823776,
-0.053546130657196045,
-0.031561579555273056,
-0.008669077418744564,
-0.01584327220916748,
-0.06524228304624557,
0.0019440010655671358,
0.027855616062879562,
-0.025667928159236908,
-0.012197292409837246,
0.06166306883096695,
-0.006197485141456127,
-0.008311151526868343,
-0.005156252067536116,
-0.03906683623790741,
-0.04943600296974182,
0.06417382508516312,
-0.024636339396238327,
0.029155243188142776,
0.023386232554912567,
-0.00703619047999382,
0.01970764622092247,
-0.02973461151123047,
0.058138925582170486,
0.0427984893321991,
-0.03452881798148155,
-0.015546105802059174,
-0.029827849939465523,
0.0025791004300117493,
0.02390156500041485,
-0.04193316772580147,
-0.03625237196683884,
0.006654815748333931,
-0.016062790527939796,
-0.00009285795385949314,
0.033566828817129135,
-0.021666718646883965,
0.0019442214397713542,
-0.033824190497398376,
-0.04282916337251663,
0.0017641916638240218,
-0.0526466965675354,
0.048335228115320206,
-0.03471256420016289,
-0.01693533919751644,
0.05006833001971245,
-0.01160375028848648,
0.01700722612440586,
-0.022222336381673813,
-0.030298011377453804,
0.02211594022810459,
0.01725035347044468,
-0.014951870776712894,
-0.0024336494971066713,
-0.0035989878233522177,
0.02878042683005333,
0.02053854987025261,
-0.010276982560753822,
0.0160993505269289,
-0.018688419833779335,
-0.03460608050227165,
-0.006608854979276657,
-0.02865472249686718,
0.03319021314382553,
0.014537215232849121,
-0.025892404839396477,
0.002951171947643161,
-0.009083911776542664,
-0.008683348074555397,
0.020857155323028564,
-0.033522650599479675,
0.04214920848608017,
0.03904946148395538,
0.0033859116956591606,
0.020133914425969124,
0.051086705178022385,
-0.01640217937529087,
0.022233350202441216,
-0.03814622759819031,
-0.003466125577688217,
-0.011456523090600967,
-0.0055692968890070915,
0.04137556999921799,
0.054192040115594864,
-0.046786271035671234,
-0.007753815036267042,
0.025429222732782364,
0.029143495485186577,
0.036466751247644424,
-0.0013759515713900328,
-0.03118264116346836,
-0.02731149271130562,
0.028279514983296394,
0.006695766933262348,
-0.03698994964361191,
0.01795177534222603,
0.022209307178854942,
0.03021058440208435,
0.025787990540266037,
0.014863427728414536,
-0.0007204666617326438,
0.06539544463157654,
-0.015608809888362885,
0.012829204089939594,
0.006022221874445677,
-0.027426820248365402,
0.02150861732661724,
-0.030242854729294777,
0.04606369510293007,
0.0024737960193306208,
-0.019242798909544945,
0.022421931847929955,
-0.042511455714702606,
-0.013325247913599014,
0.006027244497090578,
-0.02309684455394745,
0.03944278135895729,
-0.023213081061840057,
0.008719523437321186,
-0.014925439842045307,
0.007958232425153255,
0.0029125914443284273,
0.018080411478877068,
-0.0131598562002182,
-0.016824871301651,
0.014142543077468872,
-0.017015375196933746,
0.016867242753505707,
-0.03544114902615547,
-0.020394548773765564,
0.0007866732776165009,
-0.022157205268740654,
0.02593313530087471,
0.014449668116867542,
-0.0559515580534935,
-0.02460470236837864,
-0.018204020336270332,
0.004157823510468006,
0.0579032227396965,
0.017968885600566864,
-0.013690325431525707,
0.018041497096419334,
0.000381355726858601,
-0.07039687037467957,
-0.024034658446907997,
0.0252226609736681,
0.015201789326965809,
-0.027213165536522865,
-0.0052930498495697975,
0.05405228212475777,
-0.026892345398664474,
-0.01906951703131199,
-0.01822286657989025,
-0.024801336228847504,
-0.016267623752355576,
-0.004633309319615364,
-0.010750269517302513,
0.012639120221138,
-0.031171003356575966,
0.08131591230630875,
0.049548517912626266,
-0.0626060888171196,
-0.021412037312984467,
-0.07416851818561554,
-0.001593681168742478,
0.009885178878903389,
-0.03994391858577728,
-0.005997287109494209,
-0.01816193386912346,
-0.028286051005125046,
0.08647030591964722,
0.025200774893164635,
-0.03530183807015419,
-0.000973154790699482,
-0.044204022735357285,
0.0061364974826574326,
-0.060559045523405075,
0.027113327756524086,
0.06210010126233101,
-0.0170070081949234,
0.008183292113244534,
-0.001806180109269917,
0.04380660504102707,
0.02718038111925125,
-0.011760647408664227,
0.0018263976089656353,
0.01576569490134716,
-0.024348542094230652,
0.010383659973740578,
0.06129717454314232,
-0.020021237432956696,
-0.029525941237807274,
0.01713031716644764,
0.025221440941095352,
0.05811957269906998,
0.04022837430238724,
-0.03936287388205528,
0.08064541220664978,
-0.02976270020008087,
0.0054445150308310986,
-0.04440675303339958,
0.0489361472427845,
0.004061363637447357,
-0.026318922638893127,
-0.012259149923920631,
0.03932233899831772,
0.037195298820734024,
-0.01742127165198326,
-0.0040353829972445965,
-0.0011432793689891696,
0.0058542657643556595,
0.004821470007300377,
-0.033637452870607376,
-0.04773847013711929,
-0.017551716417074203,
-0.004628689959645271,
-0.019426831975579262,
-0.019346503540873528,
0.02657306380569935,
0.0310270544141531,
0.014948791824281216,
0.0011817384511232376,
-0.013871331699192524,
-0.04939120635390282,
-0.06497500091791153,
-0.014232032932341099,
0.005607164930552244,
0.022055691108107567,
0.012857906520366669,
0.02161039598286152,
0.005675730761140585,
-0.013875322416424751,
0.03531069681048393,
-0.02251398004591465,
-0.07704334706068039,
0.035743337124586105,
-0.00009625755046727136,
0.007832759991288185,
0.0022561263758689165,
-0.0024181189946830273,
0.00020867072453256696,
-0.04600219801068306,
-0.017382724210619926,
0.00023061160754878074,
0.009156626649200916,
-0.06601759791374207,
-0.01048115361481905,
-0.00893531646579504,
0.041857607662677765,
-0.0636153444647789,
0.027178961783647537,
0.04198095574975014,
-0.026219045743346214,
-0.01715116761624813,
0.01947527937591076,
-0.04882696270942688,
0.0037633192259818316,
-0.0009713949402794242,
0.0035780700854957104,
0.015269557014107704,
0.015912141650915146,
0.03551838546991348,
-0.017415402457118034,
0.019070768728852272,
0.006546924822032452,
0.03415235877037048,
0.029781030490994453,
0.055346012115478516,
0.003972316160798073,
-0.01290588453412056,
-0.048698559403419495,
-0.015334956347942352,
-0.003451320808380842,
0.04364725947380066,
0.0006976922159083188,
0.03695247694849968,
0.001058751717209816,
0.014488632790744305,
-0.020925717428326607,
0.05443767458200455,
0.06748572736978531,
0.0297741387039423,
-0.015926385298371315,
-0.07576555013656616,
0.02916298247873783,
-0.05193948373198509,
-0.003365027718245983,
-0.004145050421357155,
-0.033754389733076096,
-0.044154997915029526,
-0.009716792963445187,
-0.009623990394175053,
0.009902836754918098,
0.004385245498269796,
-0.020495904609560966,
0.015637094154953957,
0.02642415277659893,
0.01893014647066593,
-0.0023529878817498684,
0.008973436430096626,
0.011945459991693497,
0.0480433814227581,
-0.020218243822455406,
-0.011513987556099892,
-0.09768591076135635,
0.011044854298233986,
0.014423051849007607,
0.013149154372513294,
0.017177268862724304,
-0.00991949625313282,
-0.044843558222055435,
0.0231842752546072,
0.013354228809475899,
-0.05201445892453194,
0.02666180208325386,
0.00803501158952713,
0.013239435851573944,
-0.06487086415290833,
-0.022731399163603783,
-0.0037926866207271814,
0.02308674529194832,
0.0020799904596060514,
0.0639796331524849,
-0.0248784888535738,
0.024654269218444824,
-0.01460939645767212,
0.010101772844791412,
0.022571327164769173,
0.047847848385572433,
-0.016540227457880974,
0.02961474098265171,
0.04428987577557564,
0.05231243744492531,
-0.013321825303137302,
-0.09684684872627258,
-0.009462053887546062,
-0.004568593576550484,
-0.007686672732234001,
0.02019031159579754,
-0.031085554510354996,
-0.04039224982261658,
0.047293294221162796,
0.02672644890844822,
0.03630170226097107,
-0.0022458028979599476,
-0.031230201944708824,
0.04878263175487518,
0.0340353362262249,
-0.021295882761478424,
0.04937167093157768,
0.013822671957314014,
-0.014296714216470718,
0.004636384546756744,
-0.024954786524176598,
0.03063751943409443,
-0.035456087440252304,
-0.01590033806860447,
-0.047716282308101654,
0.048915307968854904,
-0.05048471689224243,
0.05979296192526817,
-0.022124813869595528,
0.003911039792001247,
-0.032907769083976746,
-0.015279766172170639,
-0.03887006640434265,
0.0070356749929487705,
0.01268300972878933,
-0.05514691025018692,
0.02996118739247322,
-0.013900255784392357,
0.02598685212433338,
-0.01149373222142458,
0.011138200759887695,
-0.01932818815112114,
-0.00399429677054286,
0.04758220165967941,
-0.005987731274217367,
0.002166327089071274,
-0.007101933006197214,
-0.0331585593521595,
0.022589772939682007,
-0.03317366912961006,
0.013675282709300518,
-0.023190895095467567,
0.016058236360549927,
0.01061675138771534,
-0.029608294367790222,
-0.02632654830813408,
0.009773149155080318,
-0.009266509674489498,
-0.0032778067979961634,
-0.009861975908279419,
0.009578528814017773,
0.03667781502008438,
0.014210590161383152,
-0.023956334218382835,
-0.036959629505872726,
0.03414309769868851,
-0.008419140242040157,
-0.02786139026284218,
-0.0003595645830500871,
-0.01790553145110607,
-0.02307329699397087,
-0.02085275575518608,
0.04598972946405411,
0.009298944845795631,
-0.015695517882704735,
0.009500551968812943,
0.006464795675128698,
-0.0009168572723865509,
0.055894531309604645,
0.030129067599773407,
-0.02638252265751362,
0.01815648376941681,
-0.012857729569077492,
-0.02530571259558201,
-0.011579860933125019,
0.03162936866283417,
-0.005259010475128889,
-0.018221065402030945,
0.007136879023164511,
-0.000034293992939637974,
0.04714827612042427,
-0.02130996808409691,
-0.021503711119294167,
0.041960086673498154,
0.01820555329322815,
-0.016115980222821236,
-0.047700434923172,
0.0036981950979679823,
0.011267377063632011,
0.041431453078985214,
0.02857944741845131,
-0.005829327739775181,
-0.04118189215660095,
0.008620103821158409,
0.011130728758871555,
0.022320140153169632,
0.015409339219331741,
-0.006438759621232748,
0.06129636615514755,
0.004603751935064793,
-0.005531363654881716,
0.02372370846569538,
-0.00536787835881114,
-0.004906781017780304,
-0.004682342056185007,
0.012158866971731186,
-0.0030690173152834177,
0.029616596177220345,
-0.04459311068058014,
-0.028080882504582405,
-0.03445339575409889,
0.04292838275432587,
0.04302173852920532,
-0.024750277400016785,
0.036779701709747314,
-0.009534431621432304,
-0.03498930484056473,
-0.031012585386633873,
-0.035624705255031586,
-0.026399167254567146,
0.015524175949394703,
-0.02174503169953823,
0.03451192378997803,
0.0012715058401226997,
0.010245870798826218,
0.018037643283605576,
0.05478200316429138,
-0.05179506167769432,
-0.013409830629825592,
0.05981604382395744,
0.05996202304959297,
0.01211000606417656,
-0.013283214531838894,
-0.05098637565970421,
0.066472128033638,
-0.007130875717848539,
0.020366400480270386,
0.011139443144202232,
-0.003349496051669121,
0.04584916681051254,
0.028225135058164597,
0.011355726048350334,
-0.03331049159169197,
0.0011198469437658787,
-0.03013431467115879,
0.002066831337288022,
0.03575630858540535,
-0.04874137416481972,
0.01217053271830082,
0.047293294221162796,
0.024236518889665604,
0.015238345600664616,
0.0015173194697126746,
0.026448026299476624,
-0.0702948048710823,
0.0011303182691335678,
0.002903655171394348,
-0.06955806165933609,
0.012347899377346039,
-0.03892681375145912,
-0.023003756999969482,
-0.008810221217572689,
-0.01648060791194439,
0.03981007635593414,
0.004799524787813425,
-0.00860885065048933,
-0.021924197673797607,
0.09888175874948502,
-0.0074341814033687115,
0.023670244961977005,
-0.012413048185408115,
-0.01829424500465393,
0.12987108528614044,
0.04104231670498848,
0.018041348084807396,
-0.06463520973920822,
0.01543460600078106,
-0.04089484363794327,
0.0025328537449240685,
-0.025992678478360176,
0.029807358980178833,
-0.017231807112693787,
0.00504562072455883,
0.007027970161288977,
0.052407342940568924,
-0.005449507851153612,
0.014101598411798477,
-0.004522661678493023,
-0.013720490038394928,
-0.01170090027153492,
0.01049038115888834,
0.04417392984032631,
-0.05271616578102112,
-0.012739213183522224,
-0.03020169958472252,
0.024285312741994858,
-0.051579657942056656,
0.0027437685057520866,
-0.002528858371078968,
-0.05039548501372337,
0.022328626364469528,
0.00558658828958869,
-0.0036983841564506292,
0.011812251061201096,
-0.029607921838760376,
0.0243072509765625,
-0.006696034222841263,
0.010099473409354687,
0.02751980349421501,
0.038126274943351746,
0.031268272548913956,
0.016903027892112732,
0.02326010912656784,
0.013781646266579628,
0.005227439571171999,
0.033579252660274506,
-0.040119338780641556,
-0.017479807138442993,
-0.03275609388947487,
0.06780553609132767,
-0.01967107504606247,
0.0017238715663552284,
0.013208556920289993,
0.02257685177028179,
0.00628460431471467,
-0.022395364940166473,
-0.054357580840587616,
-0.01771172136068344,
0.005002513527870178,
-0.03649495169520378,
-0.010295907966792583,
-0.05778546258807182,
0.005083695985376835,
0.014301749877631664,
0.02664378099143505,
-0.06276028603315353,
0.007246387656778097,
0.02991926111280918,
-0.003147781128063798,
0.03401913493871689,
-0.00684600044041872,
-0.015510265715420246,
-0.004508106503635645,
-0.045893389731645584,
-0.017755456268787384,
-0.026011841371655464,
0.00396727817133069,
-0.031726788729429245,
-0.003117993474006653,
-0.01608656533062458,
-0.014592582359910011,
-0.004718235693871975,
-0.0774812400341034,
0.06291273236274719,
-0.0071175782941281796,
0.0059479279443621635,
-0.019235825166106224,
0.011569660156965256,
0.03093879297375679,
0.05825212225317955,
-0.012467541731894016,
0.012510525994002819,
0.014965776354074478,
0.004044312052428722,
-0.03060028702020645,
-0.0006332640186883509,
-0.018608814105391502,
0.011368234641849995,
-0.057704899460077286,
0.024729054421186447,
-0.007117887493222952,
0.007440703921020031,
0.0011194953694939613,
0.03927619382739067,
0.010353523306548595,
0.050565991550683975,
0.005942896939814091,
0.0005933872307650745,
-0.0008818882633931935,
-0.01809309981763363,
0.00033720562350936234,
-0.019077837467193604,
-0.005161147098988295,
-0.007023336365818977,
-0.017148561775684357,
-0.01569308154284954,
-0.011626237072050571,
0.012674497440457344,
0.026187706738710403,
-0.056590571999549866,
0.012021716684103012,
-0.026694906875491142,
0.06279942393302917,
-0.03499884903430939,
0.000399052572902292,
-0.002853263868018985,
0.03479917719960213,
0.004725896753370762,
-0.013517303392291069,
-0.007253873627632856,
0.0033260758500546217,
-0.025075463578104973,
0.006765068508684635,
0.022194979712367058,
0.00825649593025446,
-0.006439135409891605,
-0.007223727181553841,
0.023063907399773598,
-0.004516491200774908,
0.030191561207175255,
-0.007595482282340527,
-0.002977795898914337,
0.05478347837924957,
-0.03319379314780235,
-0.05179798603057861,
0.022249598056077957,
0.042660798877477646,
0.01882825791835785,
0.0436115525662899,
-0.013831843622028828,
-0.013972287066280842,
0.03689302131533623,
-0.022195255383849144,
-0.0016831447137519717,
0.030282659456133842,
-0.04336047172546387,
0.0012539444724097848,
0.00033608084777370095,
0.01658167876303196,
0.004316246602684259,
0.006767835933715105,
0.030267538502812386,
0.013246788643300533,
-0.008862258866429329,
-0.02385398931801319,
0.01564096286892891,
0.019530951976776123,
-0.05141998454928398,
0.036859478801488876,
-0.027687272056937218,
0.03504384681582451,
0.04701412469148636,
0.00008785984391579404,
-0.006306390278041363,
0.0053140828385949135,
0.0027095370460301638,
-0.07737477123737335,
-0.0025743963196873665,
-0.007122310809791088,
-0.022763215005397797,
0.05487750098109245,
-0.037878502160310745,
0.004019553307443857,
0.042418353259563446,
-0.06443524360656738,
-0.030359718948602676,
-0.030885927379131317,
0.008648970164358616,
0.0015270640142261982,
-0.011890755034983158,
0.019231900572776794,
0.07939594984054565,
0.005876648239791393,
0.03057139553129673,
0.044220875948667526,
0.011714971624314785,
0.00039394976920448244,
-0.03881467506289482,
-0.04024580493569374,
0.05071471258997917,
-0.0010571853490546346,
-0.017905524000525475,
0.08796247839927673,
-0.04004950448870659,
-0.0340721569955349,
0.0138383274897933,
-0.016486622393131256,
-0.002885715337470174,
0.0131920101121068,
0.03540544584393501,
-0.011513796634972095,
0.05553823336958885,
0.00022894839639775455,
-0.01476231962442398,
0.010075758211314678,
0.008972454816102982,
0.029702838510274887,
0.040392205119132996,
0.01017089281231165,
0.002540344139561057,
0.0013915878953412175,
-0.03256421536207199,
-0.0022476469166576862,
0.05711618810892105,
-0.04131953790783882,
-0.041211169213056564,
0.03528913855552673,
-0.011916806921362877,
0.01060829684138298,
-0.03649347648024559,
0.028987927362322807,
-0.02765563875436783,
0.001632142928428948,
0.02030283585190773,
-0.013096793554723263,
0.01985643059015274,
0.025504019111394882,
0.022560184821486473,
-0.03547857701778412,
0.03931714594364166,
0.02399114891886711,
-0.012713155709207058,
-0.04744326323270798,
0.0021894341334700584,
0.03295862674713135,
-0.0030931225046515465,
-0.03089691884815693,
-0.018132416531443596,
-0.059464771300554276,
0.035829901695251465,
0.03560713306069374,
0.001040355651639402,
0.023522483184933662,
-0.041569460183382034,
-0.01685112714767456,
-0.037349868565797806,
0.004848787561058998,
-0.01750991679728031,
-0.043701156973838806,
-0.022960461676120758,
-0.021355200558900833,
0.0023025725968182087,
-0.013453680090606213,
0.08022048324346542,
-0.01512401644140482,
-0.03835763409733772,
0.018669195473194122,
-0.001436077058315277,
0.03810920566320419,
-0.05526489019393921,
-0.009874875657260418,
0.03433195501565933,
-0.004306737799197435,
0.05476868897676468,
0.00745565677061677,
0.023456120863556862,
-0.002443373668938875,
-0.012273325584828854,
0.0003057345165871084,
-0.007780113723129034,
-0.0137929143384099,
0.013806289993226528,
0.020099110901355743,
-0.006835567764937878,
-0.05995809659361839,
0.07212776690721512,
-0.03227410465478897,
-0.021146703511476517,
-0.0013590670423582196,
-0.009164387360215187,
-0.021026164293289185,
-0.008085215464234352,
-0.032043613493442535,
0.022936632856726646,
-0.017708715051412582,
-0.02896219491958618,
0.061968881636857986,
-0.02065386064350605,
-0.0232970230281353,
0.037688449025154114,
-0.030487922951579094,
-0.000622317660599947,
0.0649309828877449,
0.0034229883458465338,
0.0429077111184597,
0.0021613859571516514,
0.0580342635512352,
0.0015211389400064945,
0.00398964062333107,
0.008069559000432491,
0.06858176738023758,
0.005317541770637035,
-0.01540741603821516,
0.007107841782271862,
0.020991574972867966,
-0.013041495345532894,
0.0035970378667116165,
0.04353952407836914,
0.05034980922937393,
-0.01483012642711401,
-0.022549308836460114,
-0.0000441794290964026,
-0.023092787712812424,
0.038561705499887466,
0.028429552912712097,
0.0009761525434441864,
0.10399888455867767,
-0.04314517229795456,
-0.05050880089402199,
0.0006067838403396308,
0.02575754001736641,
-0.008527941070497036,
0.006833786144852638,
0.012593929655849934,
0.046026136726140976,
-0.0097770681604743,
0.007453173864632845,
0.0022055048029869795,
0.051066942512989044,
0.03962075337767601,
-0.04234369099140167,
0.05254115164279938,
0.024960221722722054,
0.017994271591305733,
-0.054711829870939255,
-0.02798175998032093,
-0.029533827677369118,
-0.010874687694013119,
-0.008328287862241268,
0.013322167098522186,
0.030854590237140656,
-0.0056136054918169975,
-0.0061871870420873165,
-0.03663840889930725,
0.051947303116321564,
-0.09189947694540024,
0.006979044061154127,
-0.05670367181301117,
0.02497139573097229,
-0.006466574501246214,
0.00804518535733223
] |
<p>I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint:</p>
<p>$$S=-m\int d\tau \sqrt{\dot x_{\nu}\dot x^{\nu}}$$</p>
<p>$\phi=p_{\mu}p^{\mu}-m^2=0$ $-$ <a href="http://en.wikipedia.org/wiki/First_class_constraint" rel="nofollow">first class constraint</a>.</p>
<p>Then $$H=H_{0}+\lambda \phi=\lambda \phi.$$ </p>
<p><strong>So, I want to show that I can obtain from this Hamiltonian the same equation of motion, as obtained from Lagrangian.</strong></p>
<p>But the problem is that I'm not sure what to do with $\lambda=\lambda(q,p)$. I tried the following thing:</p>
<p>$\dot x_{\mu}=\{x_{\mu},\lambda \phi\}=\{x_{\mu},\lambda p^2\}-m^2\{x_{\mu},\lambda\}=\lambda\{x_{\mu},p^2\}+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\frac{\partial \lambda}{\partial p^{\mu}}-m^2\frac{\partial \lambda}{\partial p^{\mu}}$</p>
<p>$\dot \lambda=\{\lambda, \lambda \phi \}=\{\lambda,\lambda p^2\}-m^2\{\lambda,\lambda\}=\lambda\{\lambda,p^2\}+p^2\{\lambda,p^2\}=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>$\dot p_{\mu}=\{p_{\mu},\lambda p^{2}-m^2\lambda \}=p^{2}\{p_{\mu},\lambda\}-m^2\{p_{\mu},\lambda\}=-p^{2}\frac{\partial \lambda}{\partial x^{\mu}}+m^2\frac{\partial \lambda}{\partial x^{\mu}}$</p>
<p>If we recall that $p^2-m^2=0$, then we get from the third equation: $\dot p=0$, and from the first: $\dot x_{\mu}=2\lambda\eta_{ak}p^{a}$.</p>
<p>So we have </p>
<p>1) $\dot x_{\mu}=2\lambda\eta_{\mu b}p^{b}$</p>
<p>2) $\dot \lambda=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>3) $\dot p=0$</p>
<p><em>But I dont know what to do next.</em> Can you help me?</p> | 4,590 | [
0.011816169135272503,
0.010533125139772892,
0.050109487026929855,
-0.020494084805250168,
0.00044266623444855213,
0.033221952617168427,
-0.014023171737790108,
-0.04706663265824318,
0.00569801963865757,
-0.056781671941280365,
0.04544035717844963,
0.018638111650943756,
0.04129883646965027,
-0.002152232686057687,
0.03230588883161545,
0.009912923909723759,
-0.015068186447024345,
-0.03474489226937294,
-0.0056993551552295685,
0.0038067528512328863,
-0.01860666461288929,
0.014858846552670002,
-0.014280661940574646,
0.004164290148764849,
-0.004187814891338348,
0.015478786081075668,
0.02060714364051819,
-0.0013021633494645357,
-0.014435826800763607,
0.08293591439723969,
-0.007033539470285177,
0.0004994849441573024,
-0.011438966728746891,
0.0007266685133799911,
0.025118336081504822,
0.029538773000240326,
-0.02615489438176155,
-0.03267741948366165,
-0.0011242072796449065,
-0.0010073096491396427,
-0.042019348591566086,
-0.00876583345234394,
0.009950253181159496,
0.04609537124633789,
0.013949979096651077,
0.04590865969657898,
0.03918524831533432,
-0.019038524478673935,
0.0627700537443161,
-0.00661288620904088,
0.07698953151702881,
0.04839937016367912,
0.01688910834491253,
0.009900267235934734,
-0.015744788572192192,
-0.05151908099651337,
0.06708124279975891,
0.06894750893115997,
-0.015427849255502224,
-0.054568734019994736,
-0.019448181614279747,
-0.030130477622151375,
-0.004833494313061237,
-0.027039196342229843,
-0.017307035624980927,
0.007290039211511612,
0.00006333072087727487,
0.008222515694797039,
0.0018191675189882517,
-0.03089984506368637,
0.009261741302907467,
-0.02606174722313881,
0.03115689754486084,
-0.025007858872413635,
0.011657279916107655,
-0.020087704062461853,
0.00028636158094741404,
0.0076688602566719055,
-0.0027231865096837282,
0.012908779084682465,
0.02691873162984848,
0.009855851531028748,
0.024065867066383362,
0.03454970940947533,
-0.01741674542427063,
-0.03211633116006851,
0.04494592174887657,
0.020305927842855453,
0.0034182420931756496,
0.02137446030974388,
-0.025878863409161568,
0.01979391649365425,
0.031329814344644547,
-0.002673628507182002,
-0.00804046355187893,
0.04118925333023071,
0.004429487511515617,
0.037718210369348526,
0.0038918405771255493,
-0.03711077570915222,
-0.03293860703706741,
-0.030515462160110474,
-0.008103668689727783,
0.07199171930551529,
0.011886893771588802,
-0.028083331882953644,
-0.007020709104835987,
0.023363294079899788,
-0.0345379114151001,
-0.017996452748775482,
-0.023254290223121643,
0.021647728979587555,
0.0022553871385753155,
-0.018313759937882423,
-0.010963096283376217,
-0.05536332726478577,
0.021133214235305786,
-0.009736818261444569,
0.03415282443165779,
0.05849849060177803,
0.040686964988708496,
0.000369569897884503,
0.06388818472623825,
-0.024234790354967117,
-0.04998779296875,
-0.004491905681788921,
0.03284086659550667,
-0.0014982828870415688,
-0.02985839918255806,
-0.024798981845378876,
0.02765546552836895,
-0.008703609928488731,
-0.03437364473938942,
0.03757694736123085,
0.0323721207678318,
-0.03414415568113327,
-0.09931837022304535,
-0.046845290809869766,
0.017855104058980942,
-0.011774720624089241,
-0.02742713689804077,
-0.04093591496348381,
-0.002609352581202984,
0.05587499961256981,
0.11850233376026154,
-0.007740160450339317,
-0.01251316163688898,
0.02378659136593342,
0.048192478716373444,
-0.0011458788067102432,
-0.00102599011734128,
0.012386360205709934,
-0.015621033497154713,
-0.0246892087161541,
0.0035085033159703016,
-0.0753876119852066,
-0.0201868899166584,
-0.004055270459502935,
0.024468954652547836,
0.022083939984440804,
0.08888637274503708,
-0.025577625259757042,
0.007101755123585463,
-0.002121768891811371,
-0.009209527634084225,
-0.000810461409855634,
0.05097690224647522,
0.03388912230730057,
-0.0192059688270092,
0.02390480414032936,
0.018297085538506508,
0.02153044193983078,
-0.037159472703933716,
0.03309012949466705,
0.03196469694375992,
-0.036453958600759506,
-0.054178427904844284,
0.00026412084116600454,
-0.007699000649154186,
-0.007581320125609636,
-0.013612283393740654,
-0.02589460276067257,
-0.00785369798541069,
-0.008489459753036499,
-0.012816916219890118,
0.024907080456614494,
0.009649539366364479,
0.02904132939875126,
-0.025181911885738373,
-0.02694534882903099,
-0.009296965785324574,
-0.05518617853522301,
0.022752758115530014,
0.016619093716144562,
-0.04203084111213684,
0.059295654296875,
-0.015048973262310028,
-0.0011355740716680884,
-0.00001772584073478356,
-0.03494545444846153,
-0.03262460231781006,
0.029612665995955467,
-0.01592463068664074,
0.014123598113656044,
0.02250874973833561,
0.038823191076517105,
0.04728257656097412,
0.01335364393889904,
0.04156672954559326,
0.013931311666965485,
-0.004477755166590214,
0.0024044017773121595,
0.011177348904311657,
0.0174874234944582,
-0.02757638692855835,
0.038198694586753845,
0.021802647039294243,
-0.04540273919701576,
-0.016692589968442917,
0.0032003535889089108,
-0.06647765636444092,
0.031207140535116196,
0.011804644949734211,
0.004753754008561373,
0.03437987342476845,
0.024470673874020576,
-0.012569828890264034,
0.03874889761209488,
-0.008561485446989536,
0.004425108432769775,
-0.018894528970122337,
-0.01399277150630951,
0.005975952837616205,
0.0519159734249115,
-0.06121131777763367,
0.014385810121893883,
0.0052646454423666,
0.03131501004099846,
0.038100164383649826,
0.04305945336818695,
-0.017391525208950043,
-0.05964616686105728,
0.07729513943195343,
0.011151677928864956,
-0.00029275784618221223,
0.02227802202105522,
0.010867545381188393,
-0.018525490537285805,
0.014726124703884125,
-0.01432920154184103,
-0.03420957550406456,
0.04275383800268173,
-0.026822568848729134,
-0.03869911655783653,
0.03665711358189583,
-0.051519252359867096,
0.041225895285606384,
0.0019066516542807221,
0.07415514439344406,
0.04113669693470001,
-0.0036167569924145937,
-0.00965652335435152,
-0.09252873063087463,
0.0025266199372708797,
0.002747700549662113,
-0.012704318389296532,
-0.0004565092094708234,
-0.0025127080734819174,
-0.003311005188152194,
-0.04192810133099556,
-0.02243652381002903,
0.007335183210670948,
-0.04705129563808441,
-0.029924975708127022,
0.010377337224781513,
0.015803702175617218,
0.037717025727033615,
-0.0018004800658673048,
-0.029863787814974785,
-0.024139100685715675,
0.02726428583264351,
0.026338592171669006,
0.0264444462954998,
0.01097817625850439,
-0.02695523016154766,
-0.009669626131653786,
-0.04869954288005829,
-0.02181595005095005,
0.06487227231264114,
0.013185400515794754,
0.03324466571211815,
0.026545856148004532,
-0.008925963193178177,
-0.05337271839380264,
-0.008561075665056705,
-0.031307823956012726,
-0.06083991378545761,
-0.02662285603582859,
0.019773056730628014,
0.04197567701339722,
0.027572868391871452,
-0.0563693605363369,
-0.021626560017466545,
-0.02745751477777958,
-0.03254059702157974,
-0.022739777341485023,
0.0152676897123456,
0.040445584803819656,
-0.015726720914244652,
0.03966904804110527,
0.05874035134911537,
0.027929004281759262,
0.03395035117864609,
-0.06760597229003906,
-0.03313387557864189,
0.025415876880288124,
-0.02301211468875408,
0.02448686584830284,
-0.01187962293624878,
-0.03295709937810898,
0.09654605388641357,
0.03380503132939339,
-0.012996400706470013,
-0.041601307690143585,
0.0261232927441597,
0.03743070363998413,
-0.06776774674654007,
-0.007318168878555298,
0.02212025225162506,
-0.06159304827451706,
0.05313552916049957,
0.0015867423499003053,
0.013171249069273472,
-0.00038247444899752736,
-0.01002686470746994,
0.012494576163589954,
0.02720709890127182,
-0.0008025279967114329,
0.007341805845499039,
0.04815240576863289,
0.01117748487740755,
0.008261765353381634,
0.019602669402956963,
-0.020232930779457092,
0.013720882125198841,
-0.026756754145026207,
-0.05453096702694893,
0.059313446283340454,
0.01985740102827549,
-0.027138812467455864,
-0.016728464514017105,
0.02870660461485386,
-0.036292120814323425,
-0.03073316439986229,
0.007871213369071484,
-0.008409776724874973,
0.005211865995079279,
-0.0020155843812972307,
-0.007926465943455696,
0.0635034590959549,
0.023238159716129303,
0.001328329904936254,
-0.013047018088400364,
-0.003957591485232115,
-0.002399444580078125,
0.02317238226532936,
-0.02059120312333107,
-0.0007700896239839494,
0.0038917153142392635,
0.0047214520163834095,
0.03824904188513756,
0.0046485066413879395,
-0.024522200226783752,
0.0002595609985291958,
-0.04705892130732536,
-0.01341788936406374,
-0.009051376022398472,
0.04876662790775299,
-0.011911751702427864,
0.07430970668792725,
0.013037508353590965,
0.011370647698640823,
-0.005727480165660381,
0.024050302803516388,
-0.08625015616416931,
0.06930463761091232,
-0.019510434940457344,
-0.02395232766866684,
0.0026574258226901293,
-0.02722932957112789,
-0.004490002524107695,
-0.04178532212972641,
-0.007679515052586794,
-0.017998570576310158,
0.009058583527803421,
-0.05477599799633026,
0.028373876586556435,
-0.057295992970466614,
-0.034336939454078674,
-0.005594354588538408,
0.031683359295129776,
0.03133442625403404,
-0.0013857599114999175,
0.007051775231957436,
0.0484471470117569,
-0.04174633324146271,
0.033724237233400345,
-0.026122601702809334,
-0.006540464702993631,
0.001713195932097733,
-0.0010918995831161737,
0.021927520632743835,
0.03474478796124458,
0.023670857772231102,
-0.015562346205115318,
0.02864571288228035,
0.04030642658472061,
0.04099016264081001,
-0.007680263835936785,
0.014974987134337425,
-0.043765172362327576,
-0.016185764223337173,
0.003947195131331682,
0.07047194242477417,
0.01791074126958847,
-0.012965296395123005,
0.029700368642807007,
-0.026369623839855194,
0.021958528086543083,
0.006736081093549728,
0.028550488874316216,
-0.0017229089280590415,
-0.010267551988363266,
-0.06261327862739563,
-0.014033331535756588,
-0.04665694758296013,
0.01033752877265215,
0.0014769232366234064,
-0.017687177285552025,
-0.024115195497870445,
-0.00311132799834013,
0.018389232456684113,
0.009490382857620716,
-0.024443477392196655,
-0.009506968781352043,
-0.02326994575560093,
0.01820092834532261,
0.015934236347675323,
0.015053262934088707,
0.023883018642663956,
0.06150909513235092,
0.018161332234740257,
-0.005320223979651928,
0.03018917515873909,
-0.07524679601192474,
-0.042297735810279846,
-0.019307920709252357,
0.035940021276474,
0.02053787373006344,
0.0054019745439291,
-0.05830180272459984,
-0.01065229345113039,
0.03105981834232807,
-0.03946472704410553,
0.051015567034482956,
0.044685449451208115,
0.026291657239198685,
-0.011044374667108059,
-0.036483034491539,
-0.046422310173511505,
0.03257342427968979,
-0.02765684947371483,
0.02332068420946598,
-0.05825328454375267,
0.0013544625835493207,
-0.011239847168326378,
0.02301507443189621,
0.017558148130774498,
0.03459657356142998,
0.0015562045155093074,
-0.02085733413696289,
0.016289575025439262,
0.030578555539250374,
-0.03792598843574524,
-0.08683247864246368,
-0.00952459778636694,
0.014357463456690311,
-0.007137232925742865,
0.022984914481639862,
-0.030548887327313423,
-0.0210329107940197,
0.02122769132256508,
0.007724155206233263,
-0.0003504300839267671,
0.04113618656992912,
-0.03491106629371643,
0.0344097837805748,
-0.002581546548753977,
-0.023511037230491638,
0.017081674188375473,
0.01952790841460228,
-0.003410670207813382,
-0.03355884552001953,
-0.03625420108437538,
0.01858334429562092,
-0.031119784340262413,
-0.010777692310512066,
-0.07182370126247406,
-0.012179023586213589,
-0.007258124649524689,
0.03206793963909149,
-0.01708165742456913,
-0.01343518402427435,
-0.004493075422942638,
-0.018227091059088707,
-0.011107250116765499,
0.033752068877220154,
-0.006122218910604715,
0.0046518356539309025,
-0.004109171684831381,
0.002553221071138978,
0.04184076562523842,
-0.012135814875364304,
-0.008373355492949486,
-0.0028288550674915314,
-0.005587659310549498,
0.033621031790971756,
-0.031526997685432434,
0.02154514752328396,
0.012169081717729568,
-0.025882896035909653,
-0.01977905072271824,
-0.04477160796523094,
0.040980514138936996,
0.01610747165977955,
0.006012340076267719,
0.03256937116384506,
-0.04340001568198204,
-0.04970419034361839,
0.01721656136214733,
-0.01598212495446205,
-0.007904279045760632,
-0.03754248470067978,
-0.01581844501197338,
0.0506313219666481,
0.023058529943227768,
-0.07023262232542038,
-0.010034400038421154,
-0.002875079633668065,
-0.06648866832256317,
-0.03498678281903267,
-0.012080454267561436,
0.0006679314537905157,
-0.02097364142537117,
-0.04898063465952873,
0.015345421619713306,
0.05728590488433838,
-0.03587024658918381,
-0.007994174025952816,
-0.013236775994300842,
0.026449568569660187,
-0.010984744876623154,
-0.024179862812161446,
-0.0232407134026289,
0.006734361406415701,
-0.032829467207193375,
0.022542232647538185,
0.017751313745975494,
0.020271791145205498,
0.010446751490235329,
-0.028502967208623886,
-0.043145161122083664,
0.008168872445821762,
0.012089553289115429,
-0.0002209304366260767,
-0.008966173976659775,
0.04579168185591698,
0.043807074427604675,
-0.026647822931408882,
-0.018607771024107933,
-0.040584489703178406,
0.015532508492469788,
0.034945324063301086,
0.02746722474694252,
-0.0007728475029580295,
-0.04604645073413849,
-0.0439811646938324,
0.059541791677474976,
-0.04206616431474686,
-0.019476857036352158,
-0.02400991879403591,
0.06886717677116394,
-0.015206757001578808,
0.005340007599443197,
0.011699960567057133,
-0.0020156563259661198,
0.0044255065731704235,
0.0023317181039601564,
0.00031011077226139605,
0.029069917276501656,
-0.010627730749547482,
-0.022439008578658104,
0.010935512371361256,
-0.06037848815321922,
0.03119213506579399,
0.06455961614847183,
-0.0007097268826328218,
0.07352791726589203,
0.0076112342067062855,
0.025424165651202202,
-0.01892741210758686,
-0.009192417375743389,
-0.024560103192925453,
-0.010592127218842506,
0.0024928590282797813,
0.039048124104738235,
-0.02924000285565853,
-0.008230424486100674,
0.05608266219496727,
0.02925693430006504,
-0.034063972532749176,
-0.024060407653450966,
0.014355108141899109,
0.039944931864738464,
-0.023368392139673233,
-0.02172686532139778,
-0.06313364952802658,
0.03390154242515564,
-0.03147207945585251,
0.057739902287721634,
-0.008314285427331924,
-0.004462309647351503,
0.008237787522375584,
-0.004376153461635113,
0.004693282768130302,
-0.018474744632840157,
0.002996519673615694,
-0.02580508030951023,
0.049383483827114105,
0.02597028762102127,
-0.014567776583135128,
0.02204132452607155,
0.01014798879623413,
0.06990589946508408,
-0.01816703751683235,
0.02857198379933834,
-0.002116505056619644,
-0.03503459692001343,
-0.005909434985369444,
-0.04526766389608383,
-0.053747888654470444,
0.08259136974811554,
-0.0029383255168795586,
-0.0010192544432356954,
0.0023573811631649733,
-0.0021563752088695765,
0.012431136332452297,
0.02789081446826458,
0.013022039085626602,
-0.0188008900731802,
0.061647191643714905,
-0.019749391824007034,
-0.019090766087174416,
-0.0204489603638649,
0.0062038651667535305,
0.12734201550483704,
0.031302981078624725,
0.006475695408880711,
-0.04175444692373276,
-0.002406561514362693,
-0.01131540909409523,
0.017153466120362282,
-0.022177763283252716,
0.06501540541648865,
0.01586276851594448,
-0.04018726572394371,
-0.012354235164821148,
0.04858727380633354,
0.00014173952513374388,
-0.01567099243402481,
0.07621502131223679,
-0.040521569550037384,
-0.03813480958342552,
-0.006120684091001749,
0.005553565453737974,
-0.006663678213953972,
0.019678035750985146,
-0.0074667190201580524,
0.00345720537006855,
-0.03342293202877045,
0.02101779170334339,
-0.03875207528471947,
-0.04595281928777695,
0.005875784903764725,
-0.018208323046565056,
-0.038315579295158386,
-0.0040033427067101,
0.010128178633749485,
-0.02336886152625084,
-0.009065047837793827,
0.00030160770984366536,
0.00413944898173213,
-0.004683233797550201,
0.029426658526062965,
0.013729888945817947,
0.011695603840053082,
0.0009061108576133847,
0.028125640004873276,
0.027873337268829346,
-0.034221138805150986,
0.011209252290427685,
-0.044421736150979996,
0.09839099645614624,
-0.009100780822336674,
0.01709621585905552,
0.014384440146386623,
-0.011762880720198154,
-0.013925948180258274,
-0.024200890213251114,
0.019340625032782555,
-0.01102637778967619,
0.01982681080698967,
0.021497448906302452,
0.00673068268224597,
-0.03461871296167374,
0.03359200060367584,
-0.0015285672852769494,
-0.012654563412070274,
-0.018989890813827515,
0.0003371000348124653,
0.012579970061779022,
-0.007498317863792181,
0.00046510875108651817,
-0.03810356929898262,
-0.0020833779126405716,
-0.017695600166916847,
-0.01893533393740654,
-0.04991694167256355,
-0.008608823642134666,
0.0025160498917102814,
0.0021505176555365324,
0.019089248031377792,
0.004017413593828678,
-0.012779325246810913,
-0.041306402534246445,
-0.07660828530788422,
0.008871191181242466,
-0.012440833263099194,
-0.033392537385225296,
0.010543993674218655,
0.007701505441218615,
0.005581006407737732,
0.07585524022579193,
-0.01465898472815752,
0.02191571518778801,
0.04877760633826256,
0.02401924878358841,
0.010318557731807232,
-0.0013464419171214104,
-0.042705584317445755,
0.025935865938663483,
-0.00555668119341135,
0.00792029220610857,
-0.0032099816016852856,
-0.021369224414229393,
0.01757679507136345,
0.01722448132932186,
-0.000008062382221396547,
0.03792702034115791,
0.012621190398931503,
0.0007558568613603711,
0.05059593543410301,
-0.01915714517235756,
0.008654325269162655,
0.032727669924497604,
0.049616098403930664,
-0.05410948768258095,
0.008052345365285873,
0.006465734448283911,
-0.022670261561870575,
0.005659285932779312,
-0.011061474680900574,
-0.04715438187122345,
-0.008268064819276333,
-0.01034393347799778,
-0.0030402124393731356,
-0.02268979512155056,
-0.00235218764282763,
-0.05659950152039528,
0.04763306677341461,
-0.03620846942067146,
-0.009613435715436935,
-0.03624189645051956,
0.05195344239473343,
-0.005381173919886351,
-0.011940374039113522,
0.029891151934862137,
0.03592284768819809,
-0.04111273214221001,
0.016208481043577194,
0.004715987015515566,
0.01782233454287052,
0.03551751747727394,
0.039880409836769104,
0.004824360366910696,
-0.022011619061231613,
-0.04128259792923927,
-0.005093793384730816,
0.026998721063137054,
0.029981518164277077,
0.02072538249194622,
0.04393232986330986,
-0.04513481631875038,
0.0043898276053369045,
0.0638171136379242,
-0.02388405241072178,
-0.016609448939561844,
0.010443330742418766,
-0.0682302936911583,
-0.047419775277376175,
-0.038162656128406525,
0.024713365361094475,
-0.018989156931638718,
0.007083385717123747,
0.008367720991373062,
0.024302467703819275,
-0.03213750943541527,
-0.0021668400149792433,
0.01819491572678089,
-0.011801009066402912,
0.038312461227178574,
0.011086142621934414,
0.004908643662929535,
0.01532528642565012,
0.04600107669830322,
-0.04439138248562813,
0.021053042262792587,
0.014026294462382793,
0.011424212716519833,
-0.09621668606996536,
-0.0007789520896039903,
0.010518036782741547,
0.02205318957567215,
0.077415332198143,
-0.027409076690673828,
0.024358177557587624,
0.019627753645181656,
-0.034067943692207336,
0.003549448912963271,
-0.012116163037717342,
0.03964441269636154,
0.014825946651399136,
-0.02314090169966221,
-0.04486912488937378,
0.1122567281126976,
0.043036650866270065,
0.0287892185151577,
0.04432402923703194,
0.01459469087421894,
-0.008031737990677357,
-0.0058602080680429935,
-0.01370718702673912,
0.016776947304606438,
0.02122775837779045,
-0.029176834970712662,
0.06127560883760452,
-0.0012812967179343104,
-0.02720496989786625,
0.012952694669365883,
-0.018574479967355728,
0.008219800889492035,
-0.02188497968018055,
0.05068862810730934,
0.015022161416709423,
0.007859266363084316,
0.02704443596303463,
0.004642510320991278,
0.01399760041385889,
-0.01956566423177719,
0.030551068484783173,
0.023006929084658623,
-0.03731193020939827,
-0.0034101952333003283,
0.031013578176498413,
-0.054262254387140274,
-0.05107088387012482,
0.042595505714416504,
-0.026231033727526665,
0.00040485081262886524,
0.004778384231030941,
-0.01976722478866577,
0.0045402818359434605,
-0.005052892491221428,
0.015391613356769085,
-0.024726051837205887,
-0.0014381594955921173,
0.02758348546922207,
0.019520601257681847,
-0.01571783982217312,
0.02331998571753502,
-0.012617041356861591,
-0.031079845502972603,
0.023847520351409912,
-0.002833874896168709,
-0.013019458390772343,
-0.07161659747362137,
-0.016194770112633705,
-0.014733381569385529,
-0.004950148519128561,
-0.024600639939308167,
-0.023868970572948456,
-0.02484833262860775,
0.034764401614665985,
-0.00039294545422308147,
0.0076509988866746426,
-0.058790553361177444,
-0.010939745232462883,
0.01585039123892784,
-0.06786298751831055,
0.0038901471998542547,
0.02421565353870392,
0.009675950743258,
0.012088684365153313,
-0.041924480348825455,
0.015783702954649925,
0.027133483439683914,
0.01650962233543396,
0.0021833598148077726,
0.0006086747162044048,
0.03228529542684555,
-0.00047970222658477724,
0.0376141183078289,
-0.003742888104170561,
-0.006842384114861488,
0.006762985605746508,
0.0038832640275359154,
0.02422841638326645,
0.007247631438076496,
-0.020648397505283356,
0.01838197000324726,
0.018390903249382973,
-0.001050580758601427,
0.030886592343449593,
0.02732141502201557,
-0.03837555646896362,
0.031633052974939346,
-0.012035996653139591,
-0.0116722472012043,
0.052711572498083115,
-0.0004463373916223645,
0.00776961212977767,
0.07110206037759781,
-0.063831627368927,
-0.0382615327835083,
-0.028142767027020454,
-0.04775937646627426,
-0.031730473041534424,
0.022598620504140854,
-0.030160684138536453,
-0.01835387386381626,
-0.05403886362910271,
0.0008228991646319628,
0.01667546108365059,
-0.01003213133662939,
-0.042886797338724136,
0.05620911717414856,
0.0032297654543071985,
-0.0009697830537334085,
0.009805114939808846,
0.030781587585806847,
-0.015506764873862267,
-0.01120599266141653,
0.03541843593120575,
0.010557960718870163,
0.02448667772114277,
-0.020956046879291534,
0.020403681322932243,
0.05738639459013939,
-0.03857795521616936,
-0.007605208083987236,
0.013102875091135502,
0.010624649934470654,
-0.020751982927322388,
-0.024721059948205948,
0.02798665128648281,
-0.008552133105695248,
0.014269714243710041,
0.0005695816944353282,
-0.008676647208631039,
0.04215973988175392,
-0.046293675899505615,
-0.002769684651866555,
0.0070214965380728245,
0.010330150835216045,
-0.0068429759703576565,
0.016496999189257622,
-0.028987323865294456,
0.06982692331075668,
0.016830381006002426,
-0.011746760457754135,
-0.022503308951854706,
-0.01989077217876911,
-0.00944521650671959,
0.0020862461533397436,
-0.012413902208209038,
0.051943883299827576,
-0.021143974736332893,
-0.01790052466094494,
-0.0267619825899601,
0.03822825103998184,
-0.028796404600143433,
0.03297360986471176,
0.07908353209495544,
-0.022415854036808014,
-0.03460023179650307,
-0.008421446196734905,
-0.06264261901378632,
0.04433372616767883,
-0.055591460317373276,
-0.03494944050908089,
-0.010241922922432423,
-0.04401079937815666,
-0.0036599584855139256,
-0.0020419657230377197
] |
<p>Let's have potential
$$
U(r) = -U_{0}e^{-\frac{r}{a}}.
$$
I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly solvable, so I need some method which can help to find approximate energy levels.</p>
<p>What to do?</p>
<p>I reduced the Schrodinger equation to the form (with normalized $r \to \frac{r}{a}$ and $\Psi (r, \varphi , \theta ) = \kappa e^{-\beta r}r^{l}\kappa (r) Y_{lm}(\theta , \varphi )$)
$$
r\kappa '' + \kappa {'}(2l + 2 - 2\beta r) + \kappa (\alpha^{2}r e^{-r} - 2\beta (l + 1)) = 0,
$$
where
$$
\alpha^{2} = \frac{2mU_{0}a^{2}}{\hbar^{2}}, \quad \beta^{2} = \frac{2m |E|a^{2}}{\hbar^{2}}.
$$
It would be tempting to use the approximation
$$
r \approx \frac{1 - e^{-r}}{e^{-r}},
$$
but $r e^{-r}$ didn't reduce to the normal form.</p>
<p>The exact solution for $l = 0$ is existed.</p> | 4,591 | [
0.004133729264140129,
0.013121242634952068,
-0.016442973166704178,
0.006946768146008253,
0.028226716443896294,
-0.03948744386434555,
-0.028577160090208054,
-0.06785169988870621,
0.038162149488925934,
-0.03747417777776718,
0.04075371474027634,
-0.0021801036782562733,
0.04244629293680191,
0.016381870955228806,
0.02650253288447857,
-0.0005899413372389972,
-0.041238345205783844,
-0.022606568410992622,
-0.0174656230956316,
0.004718592390418053,
0.019038701429963112,
0.030256815254688263,
0.02346133254468441,
-0.01903427764773369,
-0.03012092225253582,
0.03678645193576813,
0.023618880659341812,
-0.017061395570635796,
-0.017057990655303,
0.04357820376753807,
-0.001888472237624228,
-0.02708214521408081,
0.03677597641944885,
0.00834084115922451,
0.027622250840067863,
0.00888025015592575,
-0.06870706379413605,
-0.013676567934453487,
-0.006951494608074427,
0.047244854271411896,
-0.05285695940256119,
-0.04517752677202225,
0.00016111519653350115,
0.045266956090927124,
0.02859344892203808,
-0.04725690931081772,
0.016188975423574448,
-0.02458222582936287,
0.05016956105828285,
-0.04353241249918938,
0.07477952539920807,
0.020888477563858032,
0.0015600192127749324,
0.017261113971471786,
-0.011969581246376038,
-0.03150885924696922,
0.03261057659983635,
0.08079980313777924,
0.016130076721310616,
-0.023596417158842087,
-0.032113343477249146,
-0.03140005096793175,
-0.025539183989167213,
-0.000246862240601331,
-0.027819642797112465,
0.011933057568967342,
-0.0041944971308112144,
-0.023287363350391388,
0.004354418255388737,
-0.002246191492304206,
0.02698628604412079,
0.029110562056303024,
0.015080275014042854,
-0.023765163496136665,
0.028511490672826767,
-0.042326342314481735,
-0.0324261300265789,
0.03540202975273132,
0.009838342666625977,
0.028811683878302574,
-0.006630634889006615,
0.028240999206900597,
0.03811057657003403,
0.04973414167761803,
-0.03422774747014046,
-0.008255465887486935,
0.08225332200527191,
-0.01013384573161602,
-0.029745440930128098,
0.03797848895192146,
-0.006848858203738928,
0.03783935680985451,
0.027705764397978783,
0.007591866422444582,
-0.049640119075775146,
0.018057337030768394,
-0.0018905493197962642,
0.06439612060785294,
0.008589823730289936,
-0.035130683332681656,
-0.004245827440172434,
-0.05032156780362129,
0.01943092979490757,
0.0903351902961731,
-0.0064153773710131645,
-0.03480003774166107,
-0.025904089212417603,
-0.014034420251846313,
0.010738326236605644,
-0.02672049216926098,
-0.02160673215985298,
-0.000781149254180491,
0.0017721662297844887,
-0.0025193700566887856,
0.002054086420685053,
-0.0014774359297007322,
-0.021791087463498116,
-0.029520252719521523,
0.023154279217123985,
0.044179823249578476,
0.03505462408065796,
-0.015391758643090725,
0.025912726297974586,
-0.01781964860856533,
-0.04538622125983238,
0.023326043039560318,
0.021009737625718117,
-0.015486018732190132,
-0.05684275925159454,
-0.007959243841469288,
-0.011050999164581299,
0.008251529186964035,
0.004518235567957163,
-0.014351950958371162,
0.03541060909628868,
-0.003321921918541193,
-0.100748211145401,
-0.04627500846982002,
-0.006972527131438255,
-0.018612641841173172,
0.02385878935456276,
-0.04998987540602684,
-0.004465432837605476,
0.02901049144566059,
0.08350249379873276,
0.01587657816708088,
0.003321269992738962,
0.011692374013364315,
0.015779314562678337,
-0.00856809876859188,
0.0017467476427555084,
-0.017520437017083168,
-0.028470413759350777,
-0.04524243250489235,
-0.00591910257935524,
-0.05390654131770134,
0.005963320843875408,
-0.006772555876523256,
0.02460244484245777,
0.010208419524133205,
0.10809388756752014,
-0.06217431649565697,
0.006149820983409882,
0.0014395327307283878,
-0.0007836584700271487,
-0.01711020991206169,
0.08831135183572769,
0.02050727792084217,
0.005179906729608774,
0.05767882242798805,
-0.028326325118541718,
0.03837313503026962,
-0.008706916123628616,
-0.0019642875995486975,
0.0635235607624054,
-0.037691451609134674,
-0.029844123870134354,
-0.04812004789710045,
0.03035813756287098,
0.02526238188147545,
-0.04157112538814545,
-0.011962982825934887,
-0.0021688775159418583,
0.007270411588251591,
0.03961898013949394,
0.028158964589238167,
0.003005622187629342,
-0.011652149260044098,
-0.03639113903045654,
-0.06551264226436615,
-0.00296470383182168,
-0.025055229663848877,
0.024140257388353348,
-0.008975556120276451,
0.007182546425610781,
0.07149835675954819,
0.0074260057881474495,
0.007678504567593336,
0.006156347692012787,
-0.04310796037316322,
-0.020540177822113037,
0.002908280584961176,
0.018912378698587418,
0.009102492593228817,
0.05042046308517456,
0.04145020619034767,
0.03316854313015938,
-0.0123135419562459,
0.05364052951335907,
-0.04756121337413788,
-0.020435521379113197,
-0.03911896422505379,
0.010354462079703808,
0.0509745255112648,
0.03100254200398922,
0.029536467045545578,
-0.021879665553569794,
-0.03663275018334389,
0.009612996131181717,
0.008987913839519024,
-0.07819207012653351,
0.06424014270305634,
0.05567673593759537,
0.0313442200422287,
0.009819257073104382,
0.05674133449792862,
0.009831012226641178,
0.025543879717588425,
0.023340201005339622,
-0.04217584431171417,
-0.018172336742281914,
0.002288831863552332,
0.040356408804655075,
0.010616890154778957,
-0.07327723503112793,
0.0011391466250643134,
0.04018470272421837,
0.03500142693519592,
0.033522315323352814,
0.0006778987590223551,
-0.05305534973740578,
-0.015143336728215218,
0.0397217832505703,
0.03265012428164482,
-0.023269735276699066,
-0.00458034360781312,
0.037405021488666534,
0.031546611338853836,
0.007040902506560087,
-0.03025820106267929,
-0.01986955665051937,
0.03591660037636757,
-0.03248372673988342,
-0.013000080361962318,
-0.005557718686759472,
-0.0418744832277298,
0.053032923489809036,
-0.03839654475450516,
0.06089057773351669,
0.04717003181576729,
-0.04802287369966507,
-0.0007834779098629951,
-0.002650511683896184,
-0.002726322039961815,
0.054298121482133865,
0.0007294919341802597,
-0.01633666642010212,
0.002977783093228936,
0.020202739164233208,
-0.0326930433511734,
-0.001440778374671936,
-0.03661012277007103,
-0.02902751788496971,
-0.011988617479801178,
0.012553983367979527,
0.02431638166308403,
0.025411859154701233,
-0.014263327233493328,
-0.025143608450889587,
-0.002866753377020359,
-0.000665130908600986,
-0.01147282961755991,
0.012315534055233002,
0.033906083554029465,
-0.05038619413971901,
0.007309455890208483,
-0.022410830482840538,
0.03863031417131424,
0.026503950357437134,
0.019534124061465263,
-0.01798771508038044,
-0.002537540625780821,
0.0027084513567388058,
-0.049548521637916565,
-0.017329750582575798,
-0.006159044336527586,
0.004112302325665951,
-0.03211362287402153,
0.009301241487264633,
0.03551042824983597,
-0.0031692679040133953,
0.001603524899110198,
0.004099932033568621,
-0.021380728110671043,
-0.02880200557410717,
-0.01573709025979042,
0.01424930989742279,
0.019697921350598335,
-0.017306577414274216,
0.038373854011297226,
0.017449090257287025,
-0.03611079230904579,
-0.008585046045482159,
-0.0669887438416481,
-0.020909951999783516,
-0.0005270044202916324,
0.015369340777397156,
-0.01216920092701912,
0.01150083914399147,
-0.0241082850843668,
0.1166381761431694,
-0.007474514655768871,
-0.04298429191112518,
-0.04418153688311577,
0.0068796295672655106,
-0.004267307464033365,
0.00009871543443296105,
-0.01390885841101408,
0.042267244309186935,
-0.00312766432762146,
0.015197213739156723,
-0.009359147399663925,
0.03490965813398361,
0.042845141142606735,
0.01674937643110752,
-0.00044132769107818604,
0.042958490550518036,
0.01935952715575695,
0.01122461911290884,
0.08180918544530869,
-0.04057895764708519,
0.007714003324508667,
0.03065422922372818,
0.014468014240264893,
0.02512265183031559,
0.03225665166974068,
-0.07065272331237793,
0.016229761764407158,
-0.0036296371836215258,
0.025179821997880936,
0.0188578050583601,
0.020811134949326515,
0.002379658864811063,
-0.0052235121838748455,
-0.024359822273254395,
0.02306528575718403,
0.051975052803754807,
-0.008627698756754398,
0.011007413268089294,
0.03492986410856247,
0.024899287149310112,
0.00019457860616967082,
-0.030265579000115395,
0.0022282805293798447,
-0.03119480237364769,
0.04979406297206879,
-0.06210961937904358,
-0.04171314463019371,
0.044672682881355286,
0.04875123128294945,
0.003770691342651844,
-0.0453675352036953,
-0.024700427427887917,
-0.01455752830952406,
-0.054628342390060425,
-0.018950676545500755,
-0.06195339187979698,
0.05502292886376381,
0.012330559082329273,
0.049731504172086716,
0.027779430150985718,
-0.010601025074720383,
0.032046396285295486,
0.03406120091676712,
-0.06664199382066727,
0.00019066753156948835,
0.0018917340785264969,
0.0060067735612392426,
-0.013611447997391224,
0.018163427710533142,
0.0019054324366152287,
-0.014654605649411678,
-0.03511238843202591,
-0.025491194799542427,
-0.0334659107029438,
-0.018352963030338287,
-0.00476654851809144,
-0.040904611349105835,
-0.03320463001728058,
-0.054678402841091156,
0.03687277436256409,
0.0035538701340556145,
0.008577639237046242,
-0.0246669240295887,
0.06011350080370903,
-0.05551783740520477,
0.0060510654002428055,
-0.05549905449151993,
0.02043430134654045,
-0.003174584126099944,
0.04651230201125145,
0.01542583853006363,
0.019234780222177505,
-0.0012104118941351771,
-0.022305991500616074,
0.006363761145621538,
0.034312859177589417,
0.021842140704393387,
0.015253907069563866,
-0.007979558780789375,
-0.023712612688541412,
0.02338295988738537,
0.003865442704409361,
0.025113346055150032,
-0.01805860362946987,
0.0300784632563591,
0.01776137948036194,
0.01589309796690941,
-0.008855660445988178,
0.021962398663163185,
0.055643774569034576,
-0.005477072671055794,
0.012354708276689053,
-0.03601505607366562,
-0.006748285610228777,
-0.0191668588668108,
-0.008508107624948025,
-0.014646035619080067,
-0.04105038940906525,
-0.017530597746372223,
-0.01469278335571289,
0.023407313972711563,
0.009321065619587898,
-0.005074181593954563,
-0.046972308307886124,
0.0004874833975918591,
0.00037763972068205476,
-0.003917353227734566,
-0.01013996172696352,
0.012311020866036415,
0.037560101598501205,
0.042719196528196335,
-0.023941079154610634,
0.030971655622124672,
-0.049871835857629776,
-0.01756363734602928,
0.030104396864771843,
0.04510720074176788,
0.030671067535877228,
-0.02277747541666031,
-0.011083252727985382,
-0.017834486439824104,
0.060351062566041946,
-0.01957317441701889,
0.03536832705140114,
0.014459333382546902,
-0.011145642027258873,
-0.005918132606893778,
-0.05380626022815704,
-0.056289192289114,
0.0285574309527874,
0.028265684843063354,
0.0189556535333395,
-0.028474444523453712,
0.006698299665004015,
-0.051824476569890976,
0.0038817226886749268,
-0.0010516253532841802,
0.06382900476455688,
0.04892042279243469,
-0.017710691317915916,
0.008862320333719254,
-0.02010846696794033,
-0.044535938650369644,
-0.05652741715312004,
0.003817145712673664,
-0.0005134285311214626,
-0.007335658650845289,
0.009648477658629417,
-0.0478312186896801,
-0.05284891277551651,
0.04832291230559349,
0.006311413366347551,
0.021355530247092247,
0.000636862765531987,
-0.03240956366062164,
0.07519934326410294,
0.06063322350382805,
0.040955401957035065,
0.08089146763086319,
0.045376967638731,
-0.028524156659841537,
-0.008469256572425365,
-0.0482015386223793,
-0.03697547689080238,
0.004806391429156065,
-0.0008447553846053779,
-0.016427407041192055,
-0.020937958732247353,
-0.01578863337635994,
0.05778475105762482,
-0.03325524181127548,
0.015134194865822792,
-0.02623029425740242,
-0.013688771985471249,
-0.010735759511590004,
0.03622571378946304,
-0.0480954647064209,
-0.01932123489677906,
0.006234049331396818,
0.0035020862706005573,
0.025641068816184998,
0.001376854139380157,
0.017761632800102234,
-0.025490080937743187,
-0.0058759539388120174,
0.031972695142030716,
-0.0376775786280632,
0.03700588271021843,
-0.025801850482821465,
0.0026951467152684927,
0.0022243838757276535,
-0.09818948805332184,
0.04769933223724365,
-0.02662855200469494,
-0.041896164417266846,
0.008828544989228249,
-0.04060634598135948,
-0.012125407345592976,
0.023070670664310455,
-0.010435504838824272,
-0.005512032192200422,
-0.0028354504611343145,
-0.012690695933997631,
0.031229913234710693,
0.005122481845319271,
-0.07744211703538895,
-0.016651641577482224,
0.035457298159599304,
0.01433610450476408,
0.013216405175626278,
-0.031958553940057755,
0.00825136061757803,
-0.02041756361722946,
0.0176237765699625,
0.02801762893795967,
0.00942128524184227,
-0.024469571188092232,
-0.004416905343532562,
0.002394329058006406,
0.011607971973717213,
0.03916731849312782,
-0.000399413809645921,
-0.011655000038444996,
0.016992032527923584,
-0.010939125902950764,
0.01745319552719593,
0.006284439470618963,
0.07512719184160233,
-0.021331019699573517,
-0.022802766412496567,
-0.01691325195133686,
-0.022365085780620575,
0.05146828666329384,
-0.028814775869250298,
-0.021068118512630463,
0.031753912568092346,
0.031745437532663345,
0.013954538851976395,
-0.005658636335283518,
-0.011681177653372288,
0.00611395388841629,
0.01702127419412136,
0.00016346146003343165,
-0.01925227791070938,
-0.031124362722039223,
-0.006741160526871681,
0.028997329995036125,
-0.013556567952036858,
-0.02604001760482788,
-0.006869664881378412,
0.10742639005184174,
-0.028181780129671097,
0.0018534495029598475,
0.016125809401273727,
0.004639202728867531,
-0.03344176337122917,
-0.02138981595635414,
0.019167641177773476,
0.01687730848789215,
0.025055747479200363,
-0.023737261071801186,
-0.057010069489479065,
-0.04131970927119255,
0.001931249164044857,
0.045042041689157486,
0.004741462413221598,
0.01883704587817192,
0.010105150751769543,
0.027572082355618477,
-0.02527274377644062,
-0.0314592607319355,
-0.04926140233874321,
-0.01014571264386177,
0.016062751412391663,
0.04400017485022545,
-0.0373983234167099,
0.016707520931959152,
-0.006327356677502394,
0.049337103962898254,
-0.024044394493103027,
0.0013941713841632009,
0.03697569668292999,
0.05630816891789436,
0.028131751343607903,
-0.019039660692214966,
-0.013871760107576847,
0.03576790168881416,
0.004495791159570217,
0.04297596961259842,
0.029791943728923798,
-0.02805917151272297,
0.04090430215001106,
0.011778493411839008,
0.026502232998609543,
-0.025509968400001526,
-0.005505790468305349,
-0.015532705001533031,
0.03977743163704872,
0.0009735281346365809,
-0.024751221761107445,
0.022811321541666985,
0.030763762071728706,
0.036859359592199326,
0.0198440533131361,
0.019232653081417084,
-0.010558727197349072,
-0.03924174606800079,
-0.010825084522366524,
-0.05139763280749321,
-0.0664694607257843,
0.026042882353067398,
0.0052492436952888966,
-0.014410958625376225,
0.010435390286147594,
0.01902114227414131,
0.01038974430412054,
0.0007360800518654287,
-0.00683090602979064,
-0.022761888802051544,
0.03866130858659744,
-0.008267130702733994,
0.015634195879101753,
-0.0009185872040688992,
-0.008590953424572945,
0.11660487949848175,
0.07000699639320374,
0.03143264725804329,
-0.06962887942790985,
-0.006075856741517782,
-0.012833083979785442,
0.0038070916198194027,
-0.019493425264954567,
-0.014156261458992958,
-0.009872648864984512,
-0.049233127385377884,
-0.031590886414051056,
0.07122699916362762,
-0.02962815947830677,
0.046198323369026184,
0.038520365953445435,
-0.025902124121785164,
-0.036181364208459854,
-0.0027520370204001665,
-0.01346348226070404,
-0.007277104537934065,
0.007956487126648426,
-0.01940254494547844,
0.0276950653642416,
-0.05329332500696182,
-0.019197164103388786,
-0.04732877016067505,
-0.04296831786632538,
0.052470751106739044,
-0.046433206647634506,
-0.035584934055805206,
0.021351251751184464,
-0.0008150650537572801,
-0.01835271716117859,
0.013186871074140072,
0.02688267081975937,
0.04422144219279289,
-0.016631580889225006,
0.05719815567135811,
0.03587671369314194,
0.0006768397288396955,
0.006731119472533464,
0.022491952404379845,
0.019849497824907303,
-0.005706010852009058,
-0.025491133332252502,
-0.017729561775922775,
0.08940453827381134,
-0.04933594912290573,
-0.03928970918059349,
-0.0027878659311681986,
-0.03521771356463432,
-0.006943104788661003,
-0.004721927922219038,
0.003751895623281598,
0.01298469677567482,
0.03461367264389992,
-0.02522028051316738,
0.007122693583369255,
-0.01015798095613718,
0.0003290252643637359,
0.05314641445875168,
0.009203796274960041,
-0.0050208852626383305,
0.010729710571467876,
0.013021565042436123,
-0.03666004166007042,
0.03885074704885483,
0.002238967688754201,
-0.00656995689496398,
-0.004293994512408972,
-0.021614396944642067,
-0.02758670784533024,
-0.024821095168590546,
0.010705375112593174,
0.0034937604796141386,
0.040350209921598434,
-0.005262970458716154,
-0.009386001154780388,
-0.020663805305957794,
-0.08565273880958557,
-0.0066170478239655495,
0.008052102290093899,
-0.014075561426579952,
-0.007567658554762602,
-0.020602557808160782,
0.00003939212183468044,
0.02184014767408371,
-0.013412642292678356,
0.0041784122586250305,
0.008265702985227108,
0.03350907191634178,
0.022695550695061684,
-0.01719783805310726,
-0.05154974013566971,
-0.029431501403450966,
-0.03744672238826752,
0.034611620008945465,
-0.007120090536773205,
-0.011295177042484283,
-0.025707794353365898,
0.015263278037309647,
0.009501566179096699,
0.03513079881668091,
-0.050939541310071945,
-0.01049698144197464,
-0.006922245491296053,
-0.029224295169115067,
0.009017609059810638,
-0.011200066655874252,
0.020269829779863358,
0.005498206242918968,
0.009253447875380516,
-0.036727726459503174,
-0.028897134587168694,
0.007929862476885319,
-0.005288473330438137,
-0.01115651149302721,
0.018028441816568375,
-0.012086356990039349,
-0.026096593588590622,
-0.04285242781043053,
0.04640175774693489,
-0.002490149112418294,
0.046397361904382706,
-0.005932650528848171,
-0.01738642528653145,
-0.0267825685441494,
0.03205680102109909,
0.02234049141407013,
-0.004941295832395554,
0.036288995295763016,
0.031153451651334763,
0.006650986149907112,
-0.0005227699293754995,
0.01600003056228161,
0.002280572662129998,
0.03481508046388626,
-0.006900567561388016,
-0.025187183171510696,
-0.01789817586541176,
-0.04457418620586395,
-0.02380635030567646,
0.03179391846060753,
-0.003957138862460852,
0.04001693055033684,
0.04797875136137009,
-0.047128744423389435,
-0.006494729779660702,
0.04567532241344452,
-0.003464099019765854,
-0.030447397381067276,
0.0062786550261080265,
-0.014292609877884388,
0.013998775742948055,
-0.010139805264770985,
0.0019541613291949034,
-0.0009165643714368343,
0.0044025941751897335,
0.011742976494133472,
0.0247932318598032,
-0.008667029440402985,
0.0012752765323966742,
0.012146336026489735,
0.03379860147833824,
0.02771722711622715,
0.008967460133135319,
-0.0013232751516625285,
0.03851983696222305,
0.03082101233303547,
-0.026719843968749046,
0.04513583704829216,
0.03259744495153427,
0.013079371303319931,
-0.08230923861265182,
-0.014831922017037868,
0.0019075474701821804,
-0.009012588299810886,
0.06966859847307205,
-0.05202469974756241,
0.05290806293487549,
0.0433918721973896,
-0.04735584557056427,
-0.0064357672818005085,
-0.05494990572333336,
0.008257501758635044,
0.0130454171448946,
-0.004205826669931412,
-0.0638485699892044,
0.014289714395999908,
0.011836274527013302,
0.06111971661448479,
0.020435385406017303,
-0.013222560286521912,
0.009043491445481777,
-0.03146994113922119,
0.02547507733106613,
0.04851934313774109,
0.007796776480972767,
-0.014661970548331738,
0.0779438391327858,
-0.013774115592241287,
-0.013734824024140835,
0.002923819702118635,
-0.03692394495010376,
0.013783940114080906,
-0.010834651067852974,
0.034470416605472565,
-0.04599558562040329,
0.045873552560806274,
0.021161045879125595,
-0.002989677246659994,
-0.03997373580932617,
-0.03206415846943855,
0.025596050545573235,
0.00990567822009325,
-0.04439388960599899,
0.0023577697575092316,
0.020227108150720596,
-0.005672602914273739,
-0.06412972509860992,
0.07026512920856476,
-0.016782213002443314,
0.014079323969781399,
-0.009837258607149124,
-0.00041050821891985834,
-0.010599053464829922,
-0.040606144815683365,
0.004478722810745239,
-0.01855214685201645,
0.010486816987395287,
-0.007786068134009838,
0.015155278146266937,
0.011706817895174026,
0.014114554971456528,
-0.027881313115358353,
-0.05854425206780434,
0.002986832521855831,
0.005439638625830412,
-0.010823187418282032,
-0.06452327966690063,
0.031738266348838806,
-0.0170245673507452,
0.013174042105674744,
-0.02074846625328064,
-0.023547515273094177,
-0.04172135889530182,
0.015050254762172699,
0.002057770499959588,
0.002171875210478902,
-0.025628255680203438,
-0.003536808770149946,
-0.0012813359498977661,
-0.044418249279260635,
0.033246129751205444,
0.018654275685548782,
-0.025410091504454613,
0.009293035604059696,
-0.0032674463000148535,
0.006513725966215134,
0.034058522433042526,
0.08005742728710175,
-0.022085243836045265,
-0.0034078448079526424,
0.007380505092442036,
-0.01406798418611288,
-0.0004862551868427545,
-0.03555462509393692,
-0.02286108210682869,
0.009685898199677467,
-0.012785193510353565,
0.0036249386612325907,
0.010223939083516598,
-0.01788962446153164,
0.02047652192413807,
0.005956029053777456,
0.011797203682363033,
-0.02259085327386856,
0.012951014563441277,
-0.03357306495308876,
0.03082221746444702,
-0.019307374954223633,
-0.013439234346151352,
0.05389905720949173,
0.015396992675960064,
0.03322377800941467,
0.021164076402783394,
-0.033018141984939575,
-0.01990298368036747,
0.046971503645181656,
-0.05439437925815582,
-0.03799840807914734,
0.004037271253764629,
-0.03325900062918663,
0.01999361626803875,
-0.061793725937604904,
-0.004472994711250067,
0.045552317053079605,
-0.03441791236400604,
-0.014906518161296844,
0.03516010940074921,
-0.011459393426775932,
0.0412786528468132,
0.05574385076761246,
0.032597217708826065,
0.038464583456516266,
0.012938819825649261,
0.019474061205983162,
0.019534558057785034,
0.016501687467098236,
0.020287632942199707,
0.02390509657561779,
0.03493557870388031,
-0.025308430194854736,
0.0016584510449320078,
0.008687134832143784,
0.0027501042932271957,
-0.012559661641716957,
0.003774696495383978,
0.03535688668489456,
-0.00788984727114439,
-0.019035151228308678,
-0.0028108907863497734,
-0.04602951556444168,
0.07119264453649521,
-0.053999077528715134,
0.004746591206640005,
-0.02850627712905407,
-0.0007349400548264384,
0.011151397600769997,
0.019530877470970154,
-0.017096076160669327,
-0.0017862371169030666,
0.007669248152524233,
-0.004454236011952162,
-0.05335818603634834,
0.019171636551618576,
0.012191908434033394,
-0.012452921830117702,
-0.031863465905189514,
-0.0027263881638646126,
-0.010000242851674557,
-0.007075164467096329,
-0.036129072308540344,
-0.018096711486577988,
-0.03744521364569664,
0.000610155810136348,
0.020336996763944626,
0.03430191054940224,
-0.005312440451234579,
-0.013692082837224007,
-0.04844390228390694,
0.06633983552455902,
-0.037877440452575684,
-0.010938732884824276,
0.0032005084212869406,
-0.007314571179449558,
-0.036744993180036545,
-0.014195377938449383
] |
<p>With relativistic aberration, a sky full of stars gets concentrated in the direction of motion. As a rough measure of the degree of concentration, one could use the radius of a small circle, centered on the direction of motion, which contains the objects which, when you are at rest, are in half the sky (if you take my meaning).</p>
<p>Using the formula for relativistic aberration:</p>
<p>beta=0: half-sky radius=90 deg</p>
<p>beta=0.8: half-sky radius= 36.87 deg (this is just arcos(beta))</p>
<p>When I compare this calculation with diagrams created both by others and myself, there seems to be a difference of a few degrees, and I can't figure out why. I seem to be missing something.</p>
<p>For the case of beta=0.80, I measure the half-sky radius as 39 degrees. The difference is small, but it's large enough that I'm pretty sure it's not a measurement error.</p>
<p>You can measure this for yourself, using this diagram (created by someone else), with the 90 deg lines:
<a href="http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html" rel="nofollow">http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html</a></p> | 4,592 | [
-0.0031169105786830187,
-0.017603304237127304,
0.04011275991797447,
-0.021148718893527985,
0.06585892289876938,
0.012597063556313515,
-0.03797755017876625,
-0.01936621591448784,
0.0012479675933718681,
-0.026074785739183426,
0.037902768701314926,
0.03117958828806877,
0.09055660665035248,
0.03177780285477638,
-0.006112908013164997,
-0.023410972207784653,
0.00041769069503061473,
0.0003223647072445601,
-0.013568642549216747,
-0.043165288865566254,
-0.00013848418893758208,
0.016752835363149643,
-0.000037441757740452886,
-0.030291998758912086,
-0.049040064215660095,
0.010065566748380661,
0.026855219155550003,
0.0015918643912300467,
0.009652726352214813,
0.032932672649621964,
-0.006897442974150181,
-0.001211873721331358,
0.0046167923137545586,
-0.010630101896822453,
0.03849540650844574,
0.006074071861803532,
0.007711697369813919,
-0.010305991396307945,
-0.0064624096266925335,
0.036272551864385605,
0.004773079417645931,
-0.006920784246176481,
-0.041533078998327255,
0.03442974016070366,
-0.03707446902990341,
-0.0011994841042906046,
0.01914449967443943,
0.003138254163786769,
0.08824417740106583,
-0.030452987179160118,
0.05524029582738876,
0.010206443257629871,
0.04567475989460945,
0.032995015382766724,
0.008801240473985672,
-0.005974907428026199,
0.02533547952771187,
0.06798884272575378,
-0.03734903037548065,
-0.04216437041759491,
-0.03949350863695145,
-0.03525421768426895,
-0.011502668261528015,
0.003187525551766157,
0.012060039676725864,
0.01268036663532257,
-0.015221618115901947,
-0.0021331605967134237,
0.029111240059137344,
0.009221495129168034,
0.0018238433403894305,
0.00789022259414196,
0.0014812573790550232,
-0.0029580150730907917,
-0.0241080429404974,
-0.021967200562357903,
0.03990980237722397,
0.023014092817902565,
0.03028644062578678,
-0.003201892366632819,
-0.005253349430859089,
0.010080545209348202,
0.024637378752231598,
0.019936582073569298,
0.01284417137503624,
-0.005497153382748365,
0.0773736909031868,
-0.024342598393559456,
0.0030681320931762457,
0.03433346003293991,
0.0036639024037867785,
0.04625731706619263,
0.04608242213726044,
0.02800917811691761,
-0.060566291213035583,
0.06632836908102036,
-0.022084975615143776,
0.04464590921998024,
-0.02246769890189171,
-0.011291082948446274,
-0.023776661604642868,
0.01272043026983738,
-0.003939976915717125,
0.0704747810959816,
0.008837777189910412,
-0.04255076125264168,
-0.0421399362385273,
0.016933688893914223,
-0.02847970649600029,
-0.03334930166602135,
-0.0488443598151207,
0.027833808213472366,
-0.01003964152187109,
0.04351180046796799,
0.04706103354692459,
-0.009966758079826832,
0.007538424804806709,
0.021388594061136246,
0.06951718777418137,
0.06695510447025299,
0.027279185131192207,
-0.007722408045083284,
-0.010215985588729382,
-0.01616818457841873,
-0.05354311689734459,
0.04977281019091606,
0.03911987692117691,
-0.0219808928668499,
-0.07613148540258408,
-0.005645595025271177,
0.0016609688755124807,
-0.013920744881033897,
0.03171572461724281,
0.023169511929154396,
-0.015958867967128754,
0.01859878934919834,
-0.0754808709025383,
-0.04907318577170372,
0.034647513180971146,
0.05876309797167778,
0.007035024464130402,
-0.061294686049222946,
0.0013666590675711632,
0.0491371750831604,
0.12827438116073608,
-0.007755361031740904,
0.030538592487573624,
-0.005368954036384821,
0.06234142184257507,
0.00867422018200159,
-0.06323730200529099,
0.007232606410980225,
-0.014464547857642174,
-0.05176418274641037,
-0.02664368413388729,
-0.06858702003955841,
-0.011730528436601162,
0.04350312426686287,
0.010217664763331413,
-0.020103013142943382,
0.029253121465444565,
-0.009601826779544353,
-0.0012502634199336171,
-0.022013317793607712,
-0.0018112020334228873,
-0.03660815581679344,
0.06217922642827034,
0.03895153850317001,
-0.04316725954413414,
0.04559941589832306,
-0.020365288481116295,
0.07411777973175049,
0.01452146377414465,
-0.016029493883252144,
0.05735199153423309,
-0.02443697676062584,
-0.011124451644718647,
-0.029332637786865234,
-0.008758238516747952,
0.015192636288702488,
-0.05700661987066269,
-0.009949436411261559,
-0.038890037685632706,
0.05015840753912926,
0.014658610336482525,
0.06193980202078819,
-0.027152221649885178,
-0.0012979432940483093,
0.010623805224895477,
-0.04466727375984192,
-0.004309401381760836,
-0.053824346512556076,
-0.019253268837928772,
-0.015826920047402382,
-0.02553902007639408,
-0.01875508576631546,
0.0017495228676125407,
0.005298111122101545,
-0.0040430836379528046,
-0.012206354178488255,
-0.0009390190243721008,
0.0571792796254158,
0.013675134629011154,
-0.009355769492685795,
0.028904186561703682,
0.06280235201120377,
0.03424862399697304,
-0.011473234742879868,
0.00500912731513381,
-0.023833947256207466,
-0.012365736067295074,
-0.016404664143919945,
0.0005603395402431488,
-0.001964204479008913,
-0.0030892372597008944,
-0.0011642193421721458,
-0.014923314563930035,
0.020683882758021355,
0.005477869883179665,
0.027880296111106873,
-0.013395760208368301,
0.05402681976556778,
0.029456885531544685,
0.013349305838346481,
0.041605718433856964,
0.02619311399757862,
0.034698572009801865,
0.011584319174289703,
0.00602302048355341,
-0.01906035840511322,
-0.039938561618328094,
0.005413625854998827,
0.049278564751148224,
-0.027937402948737144,
-0.03197057172656059,
0.002462835283949971,
0.034427862614393234,
0.040706586092710495,
-0.01444401778280735,
0.01881524734199047,
-0.011542056687176228,
-0.04608910158276558,
-0.044280584901571274,
0.0039999340660870075,
0.007922111079096794,
-0.003440745873376727,
0.017951617017388344,
-0.0031713470816612244,
0.004717014729976654,
-0.03471185639500618,
0.004127476830035448,
0.008916974999010563,
-0.002704181708395481,
-0.028297696262598038,
0.012954073026776314,
0.015270267613232136,
0.06393013894557953,
-0.005723204929381609,
0.016612842679023743,
0.05697455257177353,
-0.007367526181042194,
0.026299122720956802,
-0.013539401814341545,
-0.022621361538767815,
0.04381123185157776,
0.011977387592196465,
-0.037392254918813705,
-0.0061615873128175735,
0.01584872417151928,
-0.0370904877781868,
-0.00020769094408024102,
-0.03060031309723854,
0.014972633682191372,
-0.01613534241914749,
0.02716701291501522,
0.023290790617465973,
0.05508933961391449,
0.001316123059950769,
-0.04537389799952507,
-0.01676866039633751,
-0.002609850838780403,
0.025330564007163048,
0.0020445529371500015,
0.02526412345468998,
-0.06582402437925339,
0.02212904766201973,
-0.01094128843396902,
-0.030249610543251038,
-0.017305387184023857,
0.01352899894118309,
-0.018228160217404366,
-0.004035519901663065,
0.014145820401608944,
-0.04362627863883972,
-0.018578944727778435,
-0.026141133159399033,
-0.02363528311252594,
-0.056671421974897385,
0.005442899186164141,
0.00783548690378666,
0.017319465056061745,
-0.0257573164999485,
0.037145741283893585,
-0.008575639687478542,
-0.039430905133485794,
-0.0296736191958189,
0.021065834909677505,
0.018317781388759613,
-0.012552428059279919,
0.009451291523873806,
0.0008647416834719479,
0.029787760227918625,
-0.0397854782640934,
-0.03799692168831825,
-0.06436680257320404,
-0.0008741516503505409,
-0.00610264390707016,
0.031150422990322113,
-0.0005610880325548351,
-0.013097154907882214,
0.051133692264556885,
0.034517187625169754,
-0.02888985350728035,
-0.04954766482114792,
0.05331577733159065,
-0.029982341453433037,
-0.015656352043151855,
-0.03144463896751404,
0.019637683406472206,
-0.004080567508935928,
-0.0009475191473029554,
-0.03891778737306595,
0.012317687273025513,
0.0238163024187088,
0.016078181564807892,
0.005833350121974945,
-0.017213445156812668,
-0.035360440611839294,
-0.00012357046944089234,
0.030451713129878044,
0.0471842885017395,
0.002929331036284566,
-0.002318072132766247,
-0.01568652130663395,
0.06965204328298569,
0.013508155010640621,
-0.09677066653966904,
0.00021393595670815557,
-0.009691010229289532,
0.01572357304394245,
0.011795096099376678,
0.012453999370336533,
0.004385985899716616,
0.03004796802997589,
-0.020355133339762688,
-0.0014477780787274241,
0.07233152538537979,
-0.0031213026959449053,
-0.007730602286756039,
0.01918930560350418,
0.05524597689509392,
0.016511788591742516,
-0.04363264515995979,
-0.0464458167552948,
-8.62915612742654e-7,
0.01127368863672018,
-0.03159037604928017,
-0.034671999514102936,
0.04831114038825035,
0.04694969207048416,
-0.003838934237137437,
-0.01716141402721405,
-0.04564531892538071,
-0.004888725932687521,
-0.09100499749183655,
-0.023091161623597145,
-0.03643941506743431,
0.0019072126597166061,
0.008413503877818584,
0.004775707144290209,
0.006100079510360956,
-0.02245434932410717,
-0.01770775020122528,
-0.0017039322992786765,
-0.07410552352666855,
0.0071256947703659534,
-0.02843073569238186,
-0.030034884810447693,
-0.02145918644964695,
0.017376722767949104,
-0.016683749854564667,
-0.03687658905982971,
0.019480906426906586,
-0.03333009406924248,
-0.0091407997533679,
-0.03687555715441704,
0.017119593918323517,
-0.04202727973461151,
-0.0387159138917923,
-0.03332921862602234,
0.07415406405925751,
0.010855400934815407,
-0.012253408320248127,
0.04793921485543251,
0.009992153383791447,
-0.031372152268886566,
-0.0034658985678106546,
-0.055289044976234436,
0.022203044965863228,
-0.016449496150016785,
0.02455301769077778,
0.03314332664012909,
0.013052912428975105,
-0.01914871856570244,
-0.01907104067504406,
0.04023025557398796,
-0.011738518252968788,
0.005026912782341242,
-0.018873389810323715,
0.024325361475348473,
-0.0331224724650383,
-0.030476467683911324,
-0.023404385894536972,
0.022790901362895966,
-0.016074802726507187,
0.04271584376692772,
0.050872888416051865,
0.0038978687953203917,
-0.01620287075638771,
0.016302410513162613,
-0.012271256186068058,
-0.02938692271709442,
0.0038743377663195133,
-0.050116945058107376,
-0.005109257530421019,
0.006209040991961956,
0.004275635816156864,
0.02850564382970333,
0.013150887563824654,
-0.014384843409061432,
-0.0057079726830124855,
0.035688068717718124,
-0.05607374384999275,
-0.02133246511220932,
0.0437859483063221,
-0.06198623776435852,
-0.02512914501130581,
-0.024887392297387123,
-0.001064287731423974,
-0.0006836848333477974,
0.0364840142428875,
0.041966039687395096,
0.023930970579385757,
0.012977123260498047,
-0.05422656238079071,
-0.026573097333312035,
0.0038276754785329103,
0.014829287305474281,
0.02801496908068657,
-0.021841567009687424,
-0.05882653594017029,
-0.02996477670967579,
0.03081587702035904,
-0.03208187222480774,
0.018169932067394257,
-0.029156209900975227,
0.022203950211405754,
-0.0021437883842736483,
-0.03810184448957443,
-0.048985496163368225,
-0.002987373387441039,
-0.02691466361284256,
0.023576177656650543,
-0.02002333663403988,
-0.000023847976990509778,
0.0180869959294796,
0.001485524931922555,
0.02181551419198513,
0.03710425645112991,
0.025363342836499214,
-0.04103837162256241,
0.006016996223479509,
0.02109587751328945,
-0.02327273227274418,
-0.06839942187070847,
0.004868875257670879,
0.007458346430212259,
-0.023777179419994354,
0.038854725658893585,
-0.012678907252848148,
-0.01807303912937641,
0.029708003625273705,
0.04097214713692665,
-0.030927905812859535,
0.008550975471735,
-0.031039565801620483,
0.03300975635647774,
0.05390205606818199,
0.026858391240239143,
0.08509461581707001,
0.03525327891111374,
0.0134811382740736,
-0.007246583700180054,
-0.007322173099964857,
0.03937651589512825,
-0.012101588770747185,
0.0012902780435979366,
-0.006690394598990679,
-0.026086868718266487,
-0.04858974367380142,
0.04128512740135193,
-0.009830511175096035,
0.028994884341955185,
0.07303933054208755,
-0.01818614825606346,
0.007407055702060461,
0.003956908360123634,
-0.0022579568903893232,
0.02749135158956051,
0.032919757068157196,
-0.018267998471856117,
0.03301747888326645,
0.007846497930586338,
0.03826550021767616,
-0.02964668907225132,
0.016446150839328766,
0.04006357491016388,
-0.027626095339655876,
0.026177413761615753,
-0.037912752479314804,
-0.008381259627640247,
-0.028886618092656136,
-0.05436364561319351,
0.02912100777029991,
-0.00840124860405922,
0.007317027077078819,
0.012925432994961739,
-0.03446083888411522,
-0.05051768571138382,
-0.013293045572936535,
-0.05385015159845352,
0.01887478306889534,
-0.02002754621207714,
-0.002853177720680833,
0.0178235974162817,
0.02331223525106907,
-0.05325309559702873,
-0.019806643947958946,
0.029968081042170525,
0.019779914990067482,
-0.023916853591799736,
-0.0037597641348838806,
-0.016350802034139633,
-0.005097809713333845,
-0.02277868613600731,
-0.007748621050268412,
0.03655756264925003,
-0.0365639254450798,
-0.03563973680138588,
-0.01660660281777382,
-0.010740047320723534,
0.06622271984815598,
-0.03383868187665939,
-0.03783128783106804,
-0.0025763176381587982,
0.012005058117210865,
-0.0024677410256117582,
0.0370967835187912,
0.06139647960662842,
-0.022188203409314156,
-0.0627119168639183,
-0.03180832415819168,
0.01716560870409012,
0.030080053955316544,
-0.01910855434834957,
-0.021220294758677483,
0.02546359971165657,
0.0011021144455298781,
0.006689287722110748,
0.006226350553333759,
-0.010502451099455357,
0.029713379219174385,
-0.01987539604306221,
0.005045862402766943,
-0.006469997111707926,
-0.01683501899242401,
-0.04226074740290642,
0.040734488517045975,
0.0207318514585495,
0.031176015734672546,
-0.026629723608493805,
0.07476800680160522,
-0.009875278919935226,
-0.011936815455555916,
0.004567066673189402,
-0.001458673388697207,
0.026319069787859917,
-0.0033348677679896355,
0.029178231954574585,
0.04477108269929886,
0.016152404248714447,
-0.02322317846119404,
-0.011850638315081596,
-0.0350031815469265,
0.01306183822453022,
0.07339605689048767,
0.0001742816821206361,
0.03699151799082756,
0.01233386155217886,
0.016040390357375145,
-0.008728565648198128,
-0.021246694028377533,
-0.016563013195991516,
-0.03685004264116287,
-0.004435632843524218,
0.033872783184051514,
-0.044150594621896744,
-0.03562697395682335,
0.020716870203614235,
0.07279322296380997,
-0.008803841657936573,
-0.008574068546295166,
0.026614023372530937,
0.0628303736448288,
0.013450573198497295,
-0.02337823249399662,
-0.01697223074734211,
0.022949084639549255,
-0.013735913671553135,
0.027145182713866234,
0.014108183793723583,
-0.0017528737662360072,
0.058161769062280655,
-0.023853063583374023,
0.03838920220732689,
-0.07844625413417816,
-0.014237970113754272,
-0.004361662548035383,
-0.022758785635232925,
0.032740868628025055,
-0.02576661854982376,
-0.030626315623521805,
-0.016511820256710052,
0.04247640445828438,
0.017177939414978027,
0.017143364995718002,
0.004055861383676529,
-0.06301622092723846,
-0.034653641283512115,
-0.03691330924630165,
-0.06472554802894592,
0.05846066027879715,
-0.01862720213830471,
-0.05088701471686363,
-0.01040966622531414,
0.0010222668061032891,
-0.0034176590852439404,
0.04448147863149643,
-0.0000047250559873646125,
-0.003927705343812704,
0.008824546821415424,
-0.002108749933540821,
0.035591647028923035,
-0.008364617824554443,
-0.008153353817760944,
0.1339254230260849,
0.02330225519835949,
0.01370376255363226,
-0.005225511267781258,
-0.0035075144842267036,
-0.017194364219903946,
0.031096039339900017,
-0.045535970479249954,
0.019101493060588837,
-0.027514969930052757,
-0.008640807121992111,
0.028433043509721756,
0.0566590242087841,
0.02325431816279888,
-0.03963286429643631,
0.024993352591991425,
-0.01794786937534809,
-0.019800398498773575,
0.05774471536278725,
0.051012974232435226,
0.025419091805815697,
0.007559650111943483,
-0.03331666812300682,
0.01929277367889881,
-0.004856030456721783,
0.02357793040573597,
-0.031385790556669235,
-0.014065493829548359,
-0.010248377919197083,
0.006091334391385317,
-0.02853606455028057,
0.008446598425507545,
0.016145067289471626,
-0.050086382776498795,
-0.014335068874061108,
0.0017742076888680458,
0.04589399695396423,
-0.03492061048746109,
-0.004949512891471386,
0.0034995267633348703,
-0.028426803648471832,
0.02804569900035858,
0.002367937471717596,
0.04519692435860634,
-0.05550014227628708,
-0.03657245635986328,
-0.034387342631816864,
0.031914122402668,
-0.03549513220787048,
-0.008691733703017235,
-0.02329232729971409,
-0.026801539584994316,
0.005425532814115286,
-0.06936950236558914,
-0.00801717396825552,
0.0012359373504295945,
-0.03442045673727989,
0.014472004026174545,
-0.01908578723669052,
0.003817533142864704,
0.041644856333732605,
0.025636445730924606,
-0.001212697010487318,
-0.016027377918362617,
0.004787541460245848,
-0.014111626893281937,
0.006247852463275194,
0.06968104094266891,
0.019879015162587166,
-0.02688203565776348,
-0.02346736378967762,
0.016180315986275673,
-0.024281930178403854,
0.03585449606180191,
0.014278328977525234,
0.008461615070700645,
0.017798198387026787,
0.007619828917086124,
-0.020499715581536293,
-0.01008073054254055,
-0.03314105048775673,
-0.00542892049998045,
-0.04169951751828194,
-0.05709085240960121,
-0.030748704448342323,
0.014298462308943272,
0.026769131422042847,
0.029374226927757263,
-0.0303818192332983,
-0.0018247786210849881,
0.016188839450478554,
0.03740618750452995,
-0.029850732535123825,
-0.018967512995004654,
-0.020753266289830208,
0.025463931262493134,
0.014042630791664124,
0.017451580613851547,
-0.04532049968838692,
0.03492961451411247,
0.034188412129879,
0.020711643621325493,
0.029759405180811882,
0.039097581058740616,
-0.025251604616642,
0.008925419300794601,
-0.021058036014437675,
-0.03908061608672142,
-0.01220308244228363,
-0.004873939324170351,
-0.00041864681406877935,
-0.08492525666952133,
0.012112559750676155,
-0.04919610545039177,
-0.02500826120376587,
0.012135706841945648,
0.01867266371846199,
-0.018232345581054688,
0.029409710317850113,
0.0005039879470132291,
-0.01924310252070427,
-0.029522167518734932,
0.0288845244795084,
-0.008124861866235733,
0.035914644598960876,
-0.02424653246998787,
0.04421631619334221,
-0.021330546587705612,
0.006357475183904171,
0.014317070133984089,
-0.01579074002802372,
0.0055726622231304646,
0.01828082650899887,
0.007963933981955051,
0.014357517473399639,
0.00788312591612339,
0.02281348407268524,
0.03258059546351433,
-0.023122519254684448,
-0.025922296568751335,
0.03617074340581894,
-0.009233261458575726,
-0.06761484593153,
0.054899297654628754,
0.0018147834343835711,
0.01140870712697506,
-0.007439831271767616,
-0.006201065145432949,
0.0000815321909612976,
0.07888691127300262,
0.018445085734128952,
-0.040981095284223557,
0.014183982275426388,
-0.01367684081196785,
0.05750486999750137,
-0.028164785355329514,
0.01898965798318386,
-0.01622754894196987,
0.009050911292433739,
0.03173786774277687,
0.0015283691463992,
-0.030967209488153458,
0.019761977717280388,
-0.006593251600861549,
-0.042945101857185364,
-0.028071675449609756,
0.010695026256144047,
0.038670700043439865,
0.031131941825151443,
-0.0017232048558071256,
-0.05651382356882095,
0.06023753806948662,
0.0375659205019474,
0.020988209173083305,
-0.10312415659427643,
0.012654265388846397,
-0.0384351871907711,
0.0566905178129673,
0.03305574506521225,
-0.04461274668574333,
0.03218090906739235,
0.055095694959163666,
-0.04676507040858269,
-0.000532416976056993,
-0.044678568840026855,
-0.012551560997962952,
-0.06298226118087769,
0.0021606935188174248,
-0.019635338336229324,
0.04247516766190529,
0.049575623124837875,
0.05859176442027092,
0.03428773581981659,
0.017110299319028854,
-0.024340542033314705,
-0.04956328868865967,
0.0032398609910160303,
0.01795181818306446,
0.0022716044913977385,
0.00901723187416792,
0.05646238476037979,
-0.007080282084643841,
-0.030527470633387566,
0.02673467807471752,
0.009790479205548763,
0.025426460430026054,
-0.0018365702126175165,
-0.004186638630926609,
-0.0008708463283255696,
0.02497144415974617,
0.03324699029326439,
-0.008617916144430637,
-0.012589504942297935,
-0.01935446634888649,
0.012262364849448204,
0.011085927486419678,
-0.037003353238105774,
-0.016948828473687172,
0.02785697765648365,
-0.0232858769595623,
-0.030894476920366287,
0.04952220246195793,
-0.00008253342093667015,
-0.017112672328948975,
-0.0037666927091777325,
0.0034524311777204275,
-0.01513835322111845,
-0.046271912753582,
0.04356933385133743,
-0.05384059622883797,
0.02353491447865963,
0.03085840679705143,
-0.019252797588706017,
-0.02908204309642315,
0.023711053654551506,
-0.019432200118899345,
-0.03607453405857086,
-0.021985989063978195,
-0.0017069029854610562,
-0.0050725475884974,
-0.019014950841665268,
0.018792584538459778,
0.0047255465760827065,
0.005926721729338169,
0.04112859070301056,
0.009977612644433975,
-0.026069624349474907,
0.04658594727516174,
0.04450865834951401,
-0.023656746372580528,
-0.026373527944087982,
-0.0016813714755699039,
-0.004297530744224787,
-0.07947356253862381,
0.014464367181062698,
0.00889546051621437,
-0.018516315147280693,
-0.017159301787614822,
-0.013354266062378883,
-0.017573833465576172,
0.02843109890818596,
0.03327733650803566,
0.016814574599266052,
-0.006156463176012039,
0.021021416410803795,
-0.038926418870687485,
-0.0042767953127622604,
-0.051489148288965225,
-0.019131164997816086,
0.01342441700398922,
-0.025362322106957436,
-0.007620304822921753,
-0.026564210653305054,
-0.03213832154870033,
0.003260772442445159,
0.02708032727241516,
0.01832868717610836,
0.0605643168091774,
0.007353596854954958,
-0.00040656389319337904,
0.041582170873880386,
0.011404436081647873,
-0.028402069583535194,
0.04246646538376808,
0.046746816486120224,
-0.00905434601008892,
0.06772048026323318,
-0.026818986982107162,
-0.026650942862033844,
0.015972204506397247,
0.006725971587002277,
-0.019767019897699356,
-0.007173134945333004,
-0.03304430842399597,
0.00925632007420063,
-0.017772134393453598,
0.010742824524641037,
0.03593601658940315,
-0.03312480077147484,
-0.03348298370838165,
0.029333163052797318,
-0.008442847058176994,
0.04742834344506264,
-0.001762013416737318,
0.023717783391475677,
0.04468761011958122,
-0.0427723303437233,
0.0041761500760912895,
0.055051546543836594,
0.008547167293727398,
0.0403091199696064,
0.00783842895179987,
0.057474639266729355,
0.04021412879228592,
0.014248967170715332,
-0.008835581131279469,
0.018129553645849228,
-0.011186167597770691,
0.00688926363363862,
0.0011340540368109941,
-0.03513192757964134,
-0.005165428854525089,
-0.015952235087752342,
-0.010273780673742294,
0.06282564997673035,
-0.0251933541148901,
0.009201855398714542,
0.029863648116588593,
-0.03517649322748184,
-0.03667756915092468,
0.04726440832018852,
-0.010912611149251461,
0.028129108250141144,
0.020902611315250397,
-0.03611980751156807,
-0.019865255802869797,
-0.0035087524447590113,
-0.006677558645606041,
-0.027251258492469788,
0.0008764525991864502,
-0.019329283386468887,
0.003313236404210329,
-0.0008193416288122535,
0.012528065592050552,
0.01721803843975067,
-0.0312691256403923,
0.02210780791938305,
0.04840659350156784,
0.018105125054717064,
-0.0013878499157726765,
-0.03946797549724579,
-0.014406357891857624,
0.039172545075416565,
-0.05722679942846298,
-0.04420709237456322,
-0.0036551104858517647,
0.03616933152079582,
-0.013587631285190582,
-0.0164636243134737
] |
<p>I would like to buy a good book on Variational Calculus. Most of the books that I find seem to be rather formal in a mathematical sense, which is not necessarily bad, but makes the studying a bit cumbersome.</p>
<p>Could you provide me with advice on a good variational calculus books which focuses on physics problems and has plenty of examples, preferably in the field of mechanics.</p> | 150 | [
-0.004527419339865446,
-0.00949010718613863,
0.030512439087033272,
0.0012139795580878854,
0.026600589975714684,
0.06004814803600311,
0.00735050905495882,
-0.01463253889232874,
0.005941176321357489,
-0.010302846319973469,
0.008670669049024582,
0.040346890687942505,
0.048649609088897705,
0.0112234428524971,
0.011806180700659752,
-0.0008286169613711536,
-0.019847707822918892,
-0.05655142664909363,
-0.05303137004375458,
-0.01773899607360363,
-0.006442035548388958,
-0.005401401314884424,
-0.01252696942538023,
0.016971750184893608,
-0.018394533544778824,
-0.004936313256621361,
-0.003082229057326913,
-0.019261276349425316,
0.006356905214488506,
0.06376919895410538,
-0.06703683733940125,
-0.010625287890434265,
-0.04959766939282417,
0.012163788080215454,
0.01732610911130905,
0.017356889322400093,
-0.04429101571440697,
-0.03199661895632744,
-0.022203147411346436,
-0.0040914807468652725,
-0.033144254237413406,
-0.0364239327609539,
0.0019496229942888021,
0.05690447986125946,
-0.035084068775177,
0.04441685602068901,
-0.004780496470630169,
-0.02874964289367199,
0.049091704189777374,
-0.052526962012052536,
0.10001622140407562,
0.03441018983721733,
0.04551076516509056,
0.010650279931724072,
0.008863725699484348,
-0.010620350949466228,
0.05609245225787163,
0.07329163700342178,
-0.013771609403192997,
-0.06352090835571289,
0.008307424373924732,
-0.05198239907622337,
-0.005867780186235905,
-0.03441987186670303,
-0.05160674825310707,
0.07152540981769562,
-0.004496281500905752,
-0.03697098046541214,
0.028874186798930168,
-0.020219020545482635,
0.014155495911836624,
0.009704623371362686,
0.03725569322705269,
-0.01630682311952114,
-0.013828165829181671,
-0.014388634823262691,
0.002491856226697564,
0.014317670837044716,
0.03846786171197891,
0.02759358286857605,
0.005234607961028814,
0.014072183519601822,
0.017939409241080284,
0.04234235733747482,
-0.03400890901684761,
-0.052449505776166916,
0.09449416399002075,
0.009035803377628326,
-0.017435666173696518,
0.024972345679998398,
-0.019787661731243134,
-0.0051024314016103745,
0.0032178948167711496,
0.0030237033497542143,
-0.03235224261879921,
0.031855225563049316,
-0.008045848459005356,
0.04705124720931053,
0.025230614468455315,
-0.022450877353549004,
0.02010093815624714,
-0.03845421224832535,
-0.0060025607235729694,
0.0401054210960865,
0.013830955140292645,
-0.015196457505226135,
-0.038995739072561264,
0.02312161587178707,
-0.006718484219163656,
0.015194796025753021,
-0.015687305480241776,
0.015858355909585953,
-0.015091893263161182,
0.02728395164012909,
0.0035613940563052893,
-0.016407370567321777,
-0.01860087737441063,
-0.018844829872250557,
0.004838352557271719,
0.06581229716539383,
0.08177514374256134,
-0.05657195672392845,
0.07516216486692429,
-0.03843066841363907,
-0.0646568089723587,
-0.020144306123256683,
0.039965029805898666,
-0.012530929408967495,
-0.029776163399219513,
0.018702927976846695,
0.0058272844180464745,
0.010447590611875057,
0.008941304869949818,
0.0053959921933710575,
0.02068685181438923,
-0.030346158891916275,
-0.0566440224647522,
-0.06318197399377823,
0.04891882464289665,
-0.029583925381302834,
-0.023506321012973785,
-0.06176392734050751,
0.011165889911353588,
0.04793088883161545,
0.06414323300123215,
-0.0163811556994915,
0.001119658350944519,
0.006012022495269775,
0.039195965975522995,
-0.060193415731191635,
-0.019538162276148796,
-0.028566665947437286,
0.014110679738223553,
-0.021921059116721153,
0.02719920687377453,
-0.0751226544380188,
0.02058025449514389,
0.03676751255989075,
0.03905206918716431,
-0.03335915878415108,
0.0630623996257782,
-0.017941810190677643,
0.007119952235370874,
0.0007390624959953129,
0.00007989020377863199,
0.00986569095402956,
0.03908045217394829,
0.006693318020552397,
0.007429743651300669,
0.02005082368850708,
0.027094850316643715,
0.016085058450698853,
-0.0058429851196706295,
0.016927866265177727,
0.027261575683951378,
-0.04689980670809746,
-0.006215042434632778,
0.028122257441282272,
0.004932775627821684,
0.01911299116909504,
-0.0018332900945097208,
-0.03119676560163498,
-0.026494363322854042,
0.019968463107943535,
-0.03197241201996803,
0.034423116594552994,
0.02814731001853943,
0.015254931524395943,
0.016650740057229996,
-0.03249930962920189,
-0.04585123062133789,
-0.06831566244363785,
0.05505490303039551,
-0.021610168740153313,
-0.01153585221618414,
0.06356216222047806,
0.014722885563969612,
-0.008312118239700794,
-0.03719682991504669,
-0.049386557191610336,
-0.013702007941901684,
0.03334539756178856,
-0.025274060666561127,
-0.011312520131468773,
0.000575255835428834,
0.06349501758813858,
0.031835149973630905,
0.011769244447350502,
0.01488279178738594,
-0.026814835146069527,
-0.04801458120346069,
0.012577014043927193,
-0.002363105770200491,
0.02559616230428219,
-0.011892716400325298,
0.02494375966489315,
0.0004260429705027491,
-0.012382903136312962,
-0.004392651375383139,
-0.001760201877914369,
-0.07641620188951492,
0.059767384082078934,
0.07025626301765442,
0.013952940702438354,
0.005782158114016056,
0.05000199377536774,
-0.009955759160220623,
0.012492651119828224,
0.013677835464477539,
-0.0004707361222244799,
-0.017012519761919975,
0.01518493052572012,
0.05218915641307831,
0.049702491611242294,
-0.024812495335936546,
0.005769290961325169,
0.05595402792096138,
0.02154269441962242,
0.0129824448376894,
0.036905672401189804,
-0.028182776644825935,
-0.06895720958709717,
0.047411877661943436,
0.0034991006832569838,
-0.007909726351499557,
0.037019018083810806,
-0.014619785360991955,
0.027440117672085762,
-0.005990295205265284,
-0.013519244268536568,
-0.035385437309741974,
0.01381363533437252,
-0.003946106415241957,
0.03668706491589546,
0.03248950466513634,
-0.028425952419638634,
0.04865025356411934,
-0.019876981154084206,
0.01530359499156475,
0.007604209240525961,
-0.028823653236031532,
0.011341871693730354,
-0.01835320144891739,
-0.02512475661933422,
0.018889248371124268,
-0.012202542275190353,
-0.02118777297437191,
-0.02505362406373024,
0.03324369341135025,
-0.05071543902158737,
-0.014560436829924583,
-0.008011111989617348,
-0.0043716407380998135,
-0.0221843384206295,
-0.0122639499604702,
0.015205992385745049,
0.018880082294344902,
0.03511970862746239,
0.003220214042812586,
-0.024290671572089195,
0.02942836284637451,
-0.02695413865149021,
0.01487562246620655,
0.016520431265234947,
-0.049362391233444214,
0.02118380181491375,
-0.04460196942090988,
-0.03700074180960655,
0.06949971616268158,
-0.015279911458492279,
0.018015319481492043,
0.02129710093140602,
0.015331349335610867,
-0.034817107021808624,
-0.009273300878703594,
-0.018441326916217804,
0.0024618615861982107,
0.01614978350698948,
0.018182463943958282,
0.037442561239004135,
-0.00985055509954691,
-0.022099167108535767,
-0.005988700781017542,
-0.05856883525848389,
-0.04321113973855972,
-0.037139564752578735,
0.019650649279356003,
0.010498659685254097,
-0.00762077746912837,
-0.029474599286913872,
0.0387912392616272,
-0.03065168671309948,
-0.0034552051220089197,
-0.06372010707855225,
-0.04414331912994385,
0.011682789772748947,
-0.023239290341734886,
0.0309447068721056,
0.011376935057342052,
-0.026425963267683983,
0.07694492489099503,
0.016078824177384377,
-0.04785357043147087,
-0.0012751505710184574,
-0.0008364693494513631,
-0.003604263998568058,
-0.017324043437838554,
0.03675583377480507,
0.020602012053132057,
-0.035487134009599686,
0.015052772127091885,
0.01881786808371544,
0.022728921845555305,
0.035693589597940445,
0.02079606242477894,
0.010480057448148727,
0.016252780333161354,
0.017806094139814377,
0.002524032024666667,
0.007683411240577698,
0.04711461067199707,
-0.032430343329906464,
-0.009261875413358212,
0.0007424086215905845,
-0.005380034446716309,
0.005623215809464455,
-0.02838217280805111,
0.031481605023145676,
0.018473267555236816,
-0.02428162842988968,
-0.037254974246025085,
0.031103389337658882,
-0.016891013830900192,
-0.02341434545814991,
0.013567101210355759,
0.020477842539548874,
0.007345456629991531,
-0.009814891032874584,
0.015347166918218136,
0.045852575451135635,
0.05798355117440224,
-0.035280145704746246,
-0.028408100828528404,
0.004584501031786203,
0.016299182549118996,
0.04297343268990517,
-0.016870005056262016,
0.00938393920660019,
0.05853414162993431,
0.01523054949939251,
0.025062840431928635,
-0.0028186046984046698,
-0.06473110616207123,
0.02124088630080223,
-0.05568890646100044,
0.0003371035272721201,
0.007793115917593241,
0.05919422581791878,
-0.00725273322314024,
0.06684383004903793,
0.021917134523391724,
0.031559061259031296,
0.04192044585943222,
-0.009915589354932308,
-0.11861022561788559,
0.042411353439092636,
-0.01909056305885315,
0.0050697955302894115,
0.0022099155467003584,
0.03763687610626221,
0.0009501641616225243,
-0.005396701395511627,
-0.03748379647731781,
-0.03382105380296707,
-0.009583466686308384,
-0.05948885530233383,
-0.007158465217798948,
-0.04138685017824173,
-0.07697918266057968,
-0.022228986024856567,
-0.022480780258774757,
0.040944069623947144,
-0.029350774362683296,
0.019411049783229828,
0.02861267328262329,
-0.04431871697306633,
-0.018704162910580635,
0.0056850542314350605,
0.015979954972863197,
0.009468726813793182,
0.021396910771727562,
-0.009735946543514729,
0.03521425276994705,
0.0249448474496603,
0.041487693786621094,
-0.001976143103092909,
0.06255300343036652,
0.0022357674315571785,
-0.020084019750356674,
-0.018236856907606125,
-0.08493522554636002,
-0.008978374302387238,
-0.008127568289637566,
0.056816477328538895,
0.015936775133013725,
-0.012815102003514767,
0.03219427168369293,
0.015537593513727188,
-0.048251595348119736,
0.016239838674664497,
0.032182104885578156,
0.006275340914726257,
-0.033097051084041595,
-0.013350837863981724,
0.014186392538249493,
-0.042979542165994644,
-0.007571455556899309,
0.017165429890155792,
-0.01435382105410099,
-0.04953168332576752,
-0.005234015639871359,
0.028770029544830322,
0.02429395169019699,
-0.03729201480746269,
-0.008653628639876842,
-0.0005098091787658632,
0.012943902984261513,
-0.007926915772259235,
-0.04241976514458656,
0.011865963228046894,
0.036195073276758194,
0.06440891325473785,
0.006671925541013479,
-0.019521621987223625,
-0.05154361203312874,
-0.006951289251446724,
0.061441078782081604,
0.03204553201794624,
-0.024892697110772133,
0.012374082580208778,
-0.040731657296419144,
-0.04671310633420944,
0.07106099277734756,
0.0014824303798377514,
-0.0013563004322350025,
-0.0005989262717776,
-0.014744764193892479,
-0.03247225657105446,
-0.03152856230735779,
-0.0030315653420984745,
0.006269899196922779,
0.019307995215058327,
0.021571695804595947,
-0.02131780982017517,
0.013877332210540771,
-0.021336833015084267,
0.01561486255377531,
0.036444928497076035,
0.06751465052366257,
0.02781573496758938,
-0.012914640828967094,
0.0031614857725799084,
0.012908273376524448,
-0.032271094620227814,
-0.05057211220264435,
-0.01425571832805872,
-0.005864277482032776,
-0.010018626227974892,
-0.01008068397641182,
-0.018354328349232674,
-0.04586106538772583,
0.013184815645217896,
-0.022615564987063408,
-0.013228967785835266,
-0.006413083523511887,
-0.0200610663741827,
0.02314824052155018,
0.0324556790292263,
0.0160084068775177,
0.03123081848025322,
0.026285162195563316,
-0.01868000254034996,
-0.00602309824898839,
0.023163992911577225,
0.03717965632677078,
-0.011121239513158798,
-0.025851430371403694,
-0.04142048582434654,
-0.04070982336997986,
-0.03160503879189491,
0.02031339332461357,
-0.029721153900027275,
0.014092761091887951,
-0.034913886338472366,
-0.014986646361649036,
-0.01586296781897545,
0.01669762283563614,
0.009338440373539925,
-0.02646864578127861,
0.024301595985889435,
0.013108532875776291,
0.041838955134153366,
-0.003437160747125745,
0.015383308753371239,
0.020934224128723145,
-0.004339015576988459,
0.043229881674051285,
-0.0005622873432002962,
0.019969819113612175,
-0.07034502923488617,
-0.032773442566394806,
0.0017820362700149417,
-0.05802111327648163,
0.054454658180475235,
0.022892169654369354,
0.023599831387400627,
0.04277992248535156,
-0.029518943279981613,
-0.05027231574058533,
-0.003030249150469899,
-0.0010611409088596702,
0.010261953808367252,
-0.06769360601902008,
0.0072082956321537495,
-0.015323677100241184,
0.021206004545092583,
-0.07281281799077988,
-0.04110238328576088,
0.03117530792951584,
-0.010467195883393288,
-0.05363092198967934,
-0.02325277216732502,
0.05020110681653023,
-0.023714447394013405,
-0.02003798820078373,
0.00671596871688962,
0.042731091380119324,
-0.01755913905799389,
0.02006262168288231,
0.01348169706761837,
-0.011708502657711506,
0.03565056249499321,
0.016489356756210327,
-0.022861821576952934,
0.03943681716918945,
0.014871058985590935,
-0.035054150968790054,
-0.020681126043200493,
0.06191140413284302,
-0.022669395431876183,
0.0037147807888686657,
-0.009050874039530754,
0.02271382510662079,
0.03280007839202881,
-0.04028509557247162,
0.03410489112138748,
0.04824666306376457,
0.013801558874547482,
-0.028895333409309387,
-0.0008561771828681231,
0.0013535571051761508,
-0.0028534389566630125,
0.005223134998232126,
0.010381286963820457,
-0.007629763800650835,
0.013176552020013332,
-0.04480539262294769,
0.0021693133749067783,
-0.008910346776247025,
0.020962513983249664,
-0.007097880821675062,
0.0518803671002388,
-0.015905991196632385,
-0.01687246561050415,
0.018323468044400215,
0.005232997238636017,
0.0032793479040265083,
-0.025400575250387192,
0.004248457960784435,
0.0037150513380765915,
0.0027849802281707525,
-0.03605566918849945,
-0.04402054101228714,
-0.03091503120958805,
0.025163494050502777,
0.04923190176486969,
-0.008884738199412823,
0.06241351366043091,
0.06806331127882004,
0.010177520103752613,
0.005059356335550547,
0.011045650579035282,
-0.03749673441052437,
-0.009127296507358551,
0.029073335230350494,
0.023467998951673508,
-0.03489334508776665,
0.003276305040344596,
0.02767792157828808,
0.010549033991992474,
-0.03446965292096138,
0.011831398122012615,
-0.02024417743086815,
0.04363108053803444,
0.03789272904396057,
-0.036900024861097336,
-0.07756523787975311,
0.023139070719480515,
-0.04311535507440567,
0.08071977645158768,
-0.02181532233953476,
-0.04198755696415901,
0.0012082390021532774,
0.02211943082511425,
0.010706513188779354,
0.012351649813354015,
-0.01284770667552948,
-0.03187717869877815,
0.018412042409181595,
0.02435155026614666,
0.002645361004397273,
-0.01279552560299635,
0.03954844921827316,
0.03444889560341835,
-0.0013793190009891987,
0.029188092797994614,
-0.010955657809972763,
-0.06754135340452194,
-0.022851618006825447,
-0.01646151766180992,
-0.040191393345594406,
0.039468493312597275,
0.006377253215759993,
-0.015520470216870308,
-0.0018942957976832986,
-0.004097343422472477,
0.016440704464912415,
0.018380798399448395,
0.011656590737402439,
0.010080987587571144,
0.06739598512649536,
-0.03704285994172096,
0.020422250032424927,
-0.01176871731877327,
-0.002639862010255456,
0.11930935829877853,
0.030822617933154106,
0.01882801204919815,
-0.07156239449977875,
0.05739135667681694,
-0.03130466863512993,
0.0035005793906748295,
-0.03606250882148743,
0.03188066929578781,
0.01685386523604393,
0.008332641795277596,
-0.00867031142115593,
0.024288928136229515,
-0.01782669685781002,
-0.014271806925535202,
0.0842304453253746,
-0.0698406770825386,
-0.055264558643102646,
-0.0016288376646116376,
-0.0037690119352191687,
-0.01963578537106514,
0.027139630168676376,
-0.02311742678284645,
0.0058088540099561214,
-0.04325750842690468,
-0.025214295834302902,
-0.03807065635919571,
-0.07045670598745346,
0.0462067611515522,
0.02064242586493492,
-0.01303921826183796,
-0.011584495194256306,
0.005977180786430836,
-0.018015392124652863,
-0.02153484709560871,
0.01608036458492279,
0.008702981285750866,
0.017027411609888077,
0.01614566706120968,
0.026258882135152817,
0.033577144145965576,
-0.0006065942579880357,
-0.0006646869005635381,
0.024436920881271362,
-0.037765901535749435,
0.015718813985586166,
-0.047911278903484344,
0.037404127418994904,
-0.026710961014032364,
0.03668751195073128,
-0.009009826928377151,
0.013652434572577477,
0.006848785560578108,
-0.0431281141936779,
-0.006844864692538977,
-0.007208348251879215,
0.04026437923312187,
-0.015519944950938225,
0.006528194528073072,
-0.02540898695588112,
0.036331240087747574,
-0.03225540742278099,
0.0021029224153608084,
-0.0018450211500748992,
-0.05404626578092575,
-0.007881361991167068,
-0.008701955899596214,
0.006286613643169403,
-0.06569260358810425,
-0.01515424344688654,
-0.01006575208157301,
0.01426417101174593,
-0.02166559174656868,
-0.009225882589817047,
0.0102941719815135,
0.009290437214076519,
0.03364576771855354,
-0.013685083016753197,
-0.022638589143753052,
0.0018340013921260834,
-0.03824567049741745,
0.023608418181538582,
-0.02067774161696434,
0.012116245925426483,
-0.031416915357112885,
0.0054676728323102,
0.03171997144818306,
0.015730401501059532,
0.004954604431986809,
-0.0018048301571980119,
-0.019247528165578842,
-0.010588190518319607,
0.06320522725582123,
-0.012792825698852539,
-0.02623676508665085,
-0.02035081945359707,
-0.01868600770831108,
0.014963669702410698,
-0.007447234354913235,
0.036247026175260544,
0.04211781173944473,
-0.00687529519200325,
0.019419986754655838,
-0.00048350924043916166,
-0.014757596887648106,
0.024280428886413574,
0.012445809319615364,
-0.04564732313156128,
-0.012620434165000916,
0.03039131686091423,
0.02378942258656025,
-0.04923815652728081,
-0.00922017265111208,
-0.0044134072959423065,
0.03312677517533302,
-0.004468593746423721,
0.04881422594189644,
-0.021256649866700172,
0.05699681118130684,
-0.0014910786412656307,
0.034472037106752396,
-0.04142282158136368,
0.021739143878221512,
-0.04443984851241112,
0.01579849235713482,
0.002740918193012476,
0.01030188798904419,
-0.029414555057883263,
0.033342670649290085,
-0.0035027984995394945,
-0.033170778304338455,
0.013907774351537228,
0.016300249844789505,
0.012826887890696526,
-0.0013380973832681775,
0.049365103244781494,
-0.029195552691817284,
0.05752968788146973,
-0.023400766775012016,
-0.009229565039277077,
0.041795361787080765,
-0.046590905636548996,
-0.059140417724847794,
0.006828733719885349,
0.0036553724203258753,
0.011597450822591782,
-0.006947463843971491,
-0.032645367085933685,
-0.04077380895614624,
0.056977301836013794,
0.023740490898489952,
-0.012038655579090118,
-0.008030693046748638,
-0.0041427286341786385,
-0.004827046766877174,
-0.037906087934970856,
0.01611708477139473,
-0.03345854580402374,
-0.0055958908051252365,
-0.00129087851382792,
0.04735125973820686,
-0.014471950940787792,
-0.014746703207492828,
0.010356166400015354,
-0.01075887493789196,
0.018102135509252548,
0.013083870522677898,
-0.00248739798553288,
0.0700623095035553,
0.02703651785850525,
-0.012377940118312836,
0.01590241678059101,
0.0063806870020926,
-0.0051152827218174934,
-0.08142711222171783,
-0.020661871880292892,
-0.02482977695763111,
0.010320167988538742,
0.030629850924015045,
-0.06239182502031326,
0.012611979618668556,
-0.0007627145387232304,
-0.03927968069911003,
0.02352147363126278,
-0.018080364912748337,
-0.01314535178244114,
0.01179332472383976,
-0.05277211219072342,
-0.0055934106931090355,
0.07314629852771759,
0.008289854973554611,
0.05422935262322426,
0.025066636502742767,
0.022754864767193794,
0.005741367116570473,
-0.022260455414652824,
-0.0070580230094492435,
0.029832132160663605,
-0.01683039404451847,
-0.03233190253376961,
0.04079023003578186,
-0.0007091887528076768,
-0.05089375004172325,
0.008808769285678864,
-0.00007363110489677638,
0.009245718829333782,
-0.012545458972454071,
0.02234584651887417,
0.005458120722323656,
0.024169592186808586,
0.012603648006916046,
-0.0017768936231732368,
-0.0016341486480087042,
-0.020153464749455452,
0.012497331947088242,
0.010304841212928295,
-0.016133179888129234,
0.041718412190675735,
0.030898643657565117,
-0.037733715027570724,
-0.05137452110648155,
0.031724508851766586,
0.014722082763910294,
-0.03437920659780502,
-0.022775214165449142,
-0.018942920491099358,
0.028096141293644905,
-0.01347151305526495,
0.011947553604841232,
-0.02464289590716362,
0.002549646655097604,
0.0034646347630769014,
-0.004691524896770716,
0.03640357032418251,
0.025167107582092285,
-0.0004228711186442524,
-0.03123760037124157,
0.008491446264088154,
0.020860763266682625,
0.002314372919499874,
-0.055362991988658905,
0.008608690463006496,
0.04209272563457489,
-0.0272543765604496,
-0.01681024394929409,
-0.056121837347745895,
-0.009600890800356865,
-0.02793578803539276,
0.00949032511562109,
0.004572752397507429,
0.005917754024267197,
-0.0030778946820646524,
0.0099616264924407,
-0.06572999805212021,
0.03921571001410484,
0.0025465150829404593,
-0.022786712273955345,
0.006662706844508648,
-0.015590472146868706,
0.0006062596803531051,
0.02166132815182209,
0.03263172507286072,
-0.05984992906451225,
-0.04466615617275238,
0.011520005762577057,
-0.0007653830689378083,
0.02608412690460682,
-0.03261183574795723,
0.0045235371217131615,
-0.004298830404877663,
-0.03392432630062103,
0.001762427855283022,
0.004594998899847269,
0.02276425063610077,
-0.01417115144431591,
-0.019281510263681412,
0.01409919559955597,
0.01734110154211521,
-0.009336777031421661,
-0.021328410133719444,
0.06849098950624466,
0.027307529002428055,
-0.0009366211015731096,
0.07234426587820053,
-0.01711294800043106,
0.02016664855182171,
0.025414206087589264,
-0.02778766304254532,
-0.03662698343396187,
0.014856529422104359,
-0.05767850577831268,
-0.028338799253106117,
-0.02321680448949337,
-0.024819526821374893,
0.003963875118643045,
-0.06687279045581818,
0.01576485112309456,
0.04729738458991051,
-0.023389078676700592,
0.00368284503929317,
0.06870230287313461,
0.038645189255476,
0.04697612300515175,
0.013386672362685204,
-0.013034948147833347,
0.04094665125012398,
-0.006556564010679722,
-0.022976558655500412,
0.007150793448090553,
0.06011117994785309,
0.014360125176608562,
0.01226845383644104,
0.03911757841706276,
-0.032307229936122894,
0.03410223498940468,
0.00981490220874548,
0.017531469464302063,
-0.040230803191661835,
-0.021280420944094658,
0.005235593765974045,
0.00550718791782856,
0.0006352768978103995,
0.016139116138219833,
-0.03307194262742996,
0.07565795630216599,
-0.029996586963534355,
0.015729190781712532,
-0.024644870311021805,
0.039914898574352264,
-0.017062310129404068,
-0.030292976647615433,
0.03992868959903717,
0.050758372992277145,
0.004576735198497772,
0.031240301206707954,
-0.03010687790811062,
-0.018374701961874962,
0.0219656303524971,
-0.038070160895586014,
0.02093987539410591,
-0.009772212244570255,
0.00009992051491281018,
-0.0023562400601804256,
-0.007166748400777578,
-0.013892830349504948,
-0.012636675499379635,
0.0148387486115098,
0.05836409330368042,
0.03133999556303024,
-0.019559217616915703,
0.021715741604566574,
-0.0565708763897419,
0.06122095137834549,
-0.053665485233068466,
0.01987159624695778,
-0.02821928821504116,
-0.018081938847899437,
-0.0072878277860581875,
0.03291616588830948
] |
<p>The equation of motion for the harmonic oscillator (mass on spring model)</p>
<p>$$\frac{d^2x}{dt^2} + \omega_0^2 x = 0$$</p>
<p>with $\omega_0^2 = D/m$, $D$ and $m$ being the force constant of the spring and the mass, has the solution</p>
<p>$$x=ce^{\lambda t}$$</p>
<p>where $c$ and $\lambda$ are a constant and a parameter.
Inserting $x$ leads to</p>
<p>$$\lambda_1 = +i\omega_0$$</p>
<p>and</p>
<p>$$\lambda_2 = -i\omega_0$$</p>
<p>and so the solutions are</p>
<p>$$x_1(t) = c_1 e^{i \omega_0 t}$$</p>
<p>and</p>
<p>$$x_2(t) = c_2 e^{-i \omega_0 t}.$$</p>
<p>In my book, I now read "...these solutions are linearly independent for $\omega_0 \neq 0$."</p>
<p>What does this mean (i.e. how can I see this) and why is it important?</p> | 4,593 | [
-0.004640732891857624,
-0.0027035665698349476,
-0.009063216857612133,
-0.026427580043673515,
0.025346532464027405,
-0.011195994913578033,
-0.038750749081373215,
-0.013907374814152718,
0.010122540406882763,
-0.03838518634438515,
0.011089934036135674,
0.01651827245950699,
0.05805926397442818,
0.01642572320997715,
0.058365728706121445,
0.004313956946134567,
-0.03510590270161629,
-0.00690452940762043,
0.002451670356094837,
-0.045273151248693466,
-0.009854755364358425,
-0.012307053431868553,
0.0038702755700796843,
-0.022157929837703705,
-0.016875913366675377,
0.022677050903439522,
0.02242983691394329,
0.003233549417927861,
0.0034911553375422955,
0.039536502212285995,
-0.021693119779229164,
-0.02678992785513401,
-0.01694091409444809,
0.023918887600302696,
0.01071461383253336,
0.01892978884279728,
-0.033316586166620255,
-0.024357261136174202,
0.01858488842844963,
0.026334542781114578,
-0.034591030329465866,
-0.017310135066509247,
0.024011515080928802,
0.04637452960014343,
-0.01340540312230587,
0.011754482053220272,
0.06165115907788277,
-0.05068312585353851,
0.0799136757850647,
0.002699613105505705,
0.07401226460933685,
-0.026211824268102646,
0.03765420615673065,
0.004503974225372076,
0.0019545441027730703,
-0.020514456555247307,
0.04093227908015251,
0.022729918360710144,
-0.021400336176156998,
-0.062094636261463165,
-0.009355425834655762,
0.006460521370172501,
-0.0021311689633876085,
-0.03260868415236473,
-0.00778165040537715,
0.04423019662499428,
0.021769559010863304,
-0.013028566725552082,
0.03142848238348961,
-0.009340500459074974,
0.016014156863093376,
0.013719392940402031,
0.05579688400030136,
-0.029042353853583336,
0.007473875302821398,
-0.0461835116147995,
0.014561384916305542,
0.007632373832166195,
0.005256797187030315,
0.007420200388878584,
0.011371905915439129,
-0.010059906169772148,
0.0014740752521902323,
0.025689955800771713,
-0.03285427764058113,
-0.012534186244010925,
0.03577454760670662,
0.04364648833870888,
0.019882868975400925,
0.018151728436350822,
0.04135594144463539,
0.030264129862189293,
0.049836739897727966,
-0.041985828429460526,
0.006065026391297579,
0.057755324989557266,
0.02478824555873871,
0.04132291302084923,
0.007199359126389027,
-0.0019007030641660094,
-0.018774058669805527,
-0.04935923218727112,
0.009940213523805141,
0.07446009665727615,
0.025104699656367302,
-0.012119028717279434,
-0.030679384246468544,
0.050590578466653824,
-0.023615475744009018,
-0.02220323495566845,
-0.04079679399728775,
-0.01565340906381607,
0.018623724579811096,
-0.01550060324370861,
-0.009039116092026234,
-0.006425743922591209,
0.010362536646425724,
-0.004553919658064842,
0.0301385335624218,
0.04686610400676727,
0.03036779724061489,
-0.029911698773503304,
0.04080549255013466,
0.00570234889164567,
-0.053423330187797546,
-0.019286375492811203,
0.031769540160894394,
-0.008282160386443138,
-0.015573632903397083,
0.025099532678723335,
0.008576350286602974,
-0.005984915420413017,
-0.01784994639456272,
0.034580912441015244,
0.008431678637862206,
-0.00973344687372446,
-0.07984350621700287,
-0.07689087837934494,
0.016504429280757904,
-0.017125895246863365,
-0.014546716585755348,
-0.08103705942630768,
-0.025356270372867584,
0.06046929955482483,
0.09316779673099518,
-0.018424248322844505,
-0.02445831149816513,
0.013713117688894272,
0.03222384303808212,
-0.012653118930757046,
-0.01731676422059536,
-0.03374019265174866,
-0.03650819510221481,
-0.05385544151067734,
0.008648856543004513,
-0.05330028012394905,
0.008442097343504429,
0.027401527389883995,
-0.011804618872702122,
-0.003526838030666113,
0.07238494604825974,
-0.006397515069693327,
-0.0000708116713212803,
0.02857237681746483,
-0.0158707145601511,
-0.03908941149711609,
0.07700745761394501,
-0.010350038297474384,
-0.0022779463324695826,
0.03621642664074898,
0.01895870640873909,
0.045595452189445496,
-0.00830982718616724,
0.01608205959200859,
-0.014025913551449776,
-0.0167332012206316,
-0.04627731814980507,
-0.032831549644470215,
0.004246761556714773,
0.005801856517791748,
-0.044209882616996765,
-0.043400414288043976,
-0.00455554760992527,
0.034865133464336395,
-0.016720155254006386,
0.0714484453201294,
-0.012323502451181412,
0.036032434552907944,
0.0061408234760165215,
-0.02058614045381546,
0.003936620894819498,
-0.042883455753326416,
0.04999242722988129,
-0.03009810671210289,
-0.021069081500172615,
0.057087142020463943,
0.017829442396759987,
-0.0007337765418924391,
0.005817957688122988,
-0.023797571659088135,
-0.020133549347519875,
0.01568685844540596,
0.029588669538497925,
-0.016524964943528175,
0.0388985238969326,
0.04728099703788757,
0.01739967241883278,
0.010463939048349857,
0.02738839201629162,
-0.030768457800149918,
0.007546189706772566,
0.014204413630068302,
-0.017086423933506012,
0.008266816847026348,
-0.0033623725175857544,
-0.0023672394454479218,
-0.010622256435453892,
-0.040827929973602295,
-0.016904478892683983,
0.03977219760417938,
-0.056935206055641174,
0.06401724368333817,
0.0767708420753479,
0.016750283539295197,
0.00357946683652699,
0.04667706415057182,
0.024480508640408516,
0.04551095515489578,
-0.01875077374279499,
0.010941041633486748,
-0.056231822818517685,
-0.019483426585793495,
0.021853379905223846,
0.0443878099322319,
-0.030608640983700752,
-0.00585136329755187,
0.06775505095720291,
0.04094240069389343,
-0.0018514454131945968,
0.0016121302032843232,
0.0002841661626007408,
-0.018321050330996513,
0.0373118631541729,
-0.019358117133378983,
0.003689769422635436,
0.027745798230171204,
0.038046207278966904,
0.01945602335035801,
0.021452192217111588,
-0.03195657581090927,
0.01527221780270338,
0.09615261852741241,
0.00895344465970993,
-0.001939247245900333,
0.021032078191637993,
0.008331215009093285,
0.03616000711917877,
0.004814950283616781,
0.05042723938822746,
0.04378274828195572,
-0.00835717748850584,
0.008153989911079407,
0.0014715787256136537,
0.01599879562854767,
-0.009328148327767849,
-0.024372173473238945,
-0.04977688193321228,
-0.043537043035030365,
0.017740825191140175,
-0.07474197447299957,
-0.021784624084830284,
-0.005101635120809078,
-0.048077695071697235,
-0.025522446259856224,
-0.01775064691901207,
0.05719216540455818,
0.04774034768342972,
0.022006597369909286,
-0.008046495728194714,
-0.04912372678518295,
-0.007178909610956907,
-0.04570707306265831,
-0.0068932692520320415,
0.017566343769431114,
-0.04091498628258705,
0.011189050041139126,
-0.043441034853458405,
-0.03108428604900837,
0.049248576164245605,
0.017267396673560143,
-0.004664163570851088,
0.012981712818145752,
0.0009855397511273623,
-0.05739181488752365,
-0.07971637696027756,
-0.02846321277320385,
0.011814330704510212,
-0.04918826371431351,
-0.010672521777451038,
0.061939481645822525,
-0.027485370635986328,
0.010292749851942062,
0.031107615679502487,
-0.06467774510383606,
-0.012492610141634941,
-0.028428761288523674,
-0.0237403754144907,
0.06082206591963768,
-0.013649770058691502,
0.003653568448498845,
0.0010616586077958345,
-0.024403367191553116,
-0.003984652925282717,
-0.06949301064014435,
-0.053130388259887695,
-0.005652759224176407,
0.01464859303086996,
0.060171179473400116,
-0.0107039799913764,
-0.03272474929690361,
0.11967285722494125,
0.05269254371523857,
-0.016333255916833878,
-0.017947286367416382,
0.004054467659443617,
-0.02174397185444832,
-0.054956089705228806,
-0.003739603329449892,
0.04887224733829498,
-0.03122132457792759,
0.027717581018805504,
0.009735858999192715,
0.01925087347626686,
0.022027861326932907,
-0.02117001637816429,
-0.013079825788736343,
0.00817679613828659,
0.024743786081671715,
0.0001771351380739361,
0.06681696325540543,
0.030934719368815422,
0.009762801229953766,
0.0369449257850647,
0.010116205550730228,
0.027044551447033882,
0.007896696217358112,
-0.06296983361244202,
0.04227913171052933,
0.009838847443461418,
-0.04431561380624771,
-0.007714422885328531,
0.03770633414387703,
0.008492733351886272,
0.002635278506204486,
-0.011191347613930702,
-0.015908943489193916,
0.053759124130010605,
-0.030587423592805862,
-0.016367612406611443,
0.020361794158816338,
0.01702757179737091,
-0.0059180608950555325,
-0.012172632850706577,
-0.020930945873260498,
0.00887866597622633,
0.012189450673758984,
-0.009630220010876656,
0.0059683192521333694,
0.03535205125808716,
0.006236754357814789,
0.04276370257139206,
-0.019258921965956688,
-0.04134996235370636,
-0.008911505341529846,
-0.09018642455339432,
-0.017388850450515747,
-0.013779912143945694,
0.04568888247013092,
0.000763915479183197,
0.06979367136955261,
0.009364224970340729,
0.023983892053365707,
0.05533672869205475,
-0.005333421751856804,
-0.05522289127111435,
0.044400639832019806,
-0.039452433586120605,
-0.006254898849874735,
0.0013683297438547015,
0.009331551380455494,
0.018452974036335945,
-0.01695910096168518,
-0.02890692837536335,
-0.0020130211487412453,
0.0018865854945033789,
-0.07549910247325897,
0.014841960743069649,
-0.012360820546746254,
-0.0399617962539196,
-0.011617489159107208,
0.02956129051744938,
-0.008075429126620293,
0.0027548805810511112,
-0.029987609013915062,
0.08262819051742554,
-0.028104402124881744,
0.014107093214988708,
-0.04655870050191879,
-0.03947922959923744,
0.007944174110889435,
0.006704804953187704,
0.022995710372924805,
0.03485412523150444,
0.005805341061204672,
0.011931031942367554,
0.04221603646874428,
0.05485120043158531,
0.01790190488100052,
0.012184174731373787,
-0.0012410260969772935,
-0.04813288897275925,
0.007544524036347866,
-0.0348096638917923,
0.05318087339401245,
-0.0019485633820295334,
-0.015161649323999882,
0.041786354035139084,
-0.008403382264077663,
0.02815685234963894,
0.05122692510485649,
0.02601807564496994,
0.011828875169157982,
0.0017066334839910269,
-0.03174996003508568,
-0.02322545275092125,
-0.049910228699445724,
-0.002885000081732869,
-0.041531868278980255,
-0.019167380407452583,
0.006181773263961077,
0.010851583443582058,
0.021730324253439903,
0.03497960790991783,
0.025377759709954262,
-0.014784904196858406,
-0.012387103401124477,
0.035271644592285156,
-0.027304910123348236,
-0.04107769951224327,
0.01673538237810135,
0.014662454836070538,
0.04776905104517937,
0.006664298940449953,
0.011272654868662357,
-0.07650446146726608,
-0.033306363970041275,
0.004347729962319136,
0.013987050391733646,
0.002824378665536642,
0.006690347567200661,
-0.04824719578027725,
-0.04335339367389679,
0.03868994116783142,
-0.014876490458846092,
0.06097271293401718,
0.04602114483714104,
-0.007319184951484203,
-0.021895846351981163,
-0.01634439080953598,
-0.048651084303855896,
0.0014610197395086288,
-0.002521352842450142,
0.005415013525635004,
-0.06404376029968262,
-0.0003676552150864154,
0.003121822141110897,
0.030631009489297867,
-0.014963090419769287,
0.057840991765260696,
-0.019725613296031952,
-0.021112317219376564,
0.0038622168358415365,
0.026495758444070816,
-0.018942726776003838,
-0.0832614079117775,
-0.007219007704406977,
0.024066759273409843,
-0.0165285374969244,
0.018367934972047806,
-0.05937616899609566,
-0.043226610869169235,
-0.014407600276172161,
0.039370667189359665,
-0.021007532253861427,
0.008744960650801659,
-0.02244427241384983,
0.020637797191739082,
0.011223535984754562,
0.014533317647874355,
0.04086141288280487,
0.053351763635873795,
-0.03059144876897335,
-0.03972671926021576,
0.01730160228908062,
0.025276193395256996,
-0.027222955599427223,
0.03592272102832794,
-0.06112842634320259,
0.020330894738435745,
-0.04499572142958641,
0.037402547895908356,
-0.004862932488322258,
0.024764029309153557,
-0.017982646822929382,
-0.02798432856798172,
0.020415831357240677,
0.07159055769443512,
0.017168888822197914,
0.006513774394989014,
0.015495434403419495,
0.01767134852707386,
-0.015280706807971,
-0.018444007262587547,
0.011950786225497723,
-0.018655456602573395,
0.009164223447442055,
0.06846742331981659,
-0.010233921930193901,
0.013006750494241714,
-0.01968734711408615,
-0.03537924960255623,
0.02261418104171753,
-0.050766721367836,
0.0077862972393631935,
0.010762767866253853,
0.015618639066815376,
0.045486584305763245,
-0.04407833144068718,
-0.05307171121239662,
-0.0019298186525702477,
-0.0023912207689136267,
0.014186030253767967,
-0.03649403899908066,
-0.004337541293352842,
0.01834733784198761,
0.000874255842063576,
-0.05007445812225342,
-0.06923573464155197,
0.006308999843895435,
-0.034272126853466034,
-0.014645163901150227,
-0.002013463294133544,
-0.006416164338588715,
-0.002579671796411276,
-0.03287392109632492,
0.009237061254680157,
0.053011100739240646,
0.0013690331252291799,
-0.02531050704419613,
0.0178018007427454,
0.06894613057374954,
0.02345789037644863,
0.020349709317088127,
-0.021015221253037453,
0.012116845697164536,
0.022105667740106583,
-0.030268413946032524,
-0.008662392385303974,
0.08527073264122009,
-0.022433463484048843,
-0.022838041186332703,
-0.016547512263059616,
0.0016508951084688306,
0.02620585635304451,
-0.003024323610588908,
-0.06117317080497742,
0.04308399558067322,
0.03633923456072807,
-0.00313367648050189,
-0.03207731246948242,
-0.02272430807352066,
-0.002065545879304409,
0.020889919251203537,
0.03622833266854286,
0.002510109217837453,
-0.04007004573941231,
-0.06736720353364944,
0.014787506312131882,
-0.028925245627760887,
0.010863755829632282,
0.009393168613314629,
0.08123219758272171,
-0.0024372872430831194,
0.04274726286530495,
0.025409091264009476,
0.021846823394298553,
0.03268013894557953,
0.014993259683251381,
0.0011186257470399141,
-0.00018669523706194013,
0.012588013894855976,
-0.038926418870687485,
-0.03855345770716667,
-0.03536257892847061,
0.043783970177173615,
0.0691131055355072,
-0.039573147892951965,
0.035935595631599426,
0.029011907055974007,
0.0007280549616552889,
-0.007140113972127438,
-0.011424563825130463,
-0.02892673760652542,
-0.023054059594869614,
-0.002313335193321109,
0.03910515084862709,
-0.03480689600110054,
-0.040269069373607635,
0.052112117409706116,
0.02751445583999157,
-0.006298857741057873,
-0.02813013084232807,
0.01956908218562603,
-0.008452695794403553,
-0.016048915684223175,
0.00725483987480402,
-0.039037104696035385,
0.032507479190826416,
0.0034078522585332394,
0.05369861051440239,
-0.012380742467939854,
-0.026802321895956993,
0.037021901458501816,
0.02987791784107685,
-0.017843768000602722,
-0.02731672115623951,
-0.0049869283102452755,
-0.040239427238702774,
0.032884631305933,
0.03466920927166939,
-0.0032246247865259647,
0.02329208329319954,
-0.0011713610729202628,
0.030320988968014717,
0.017955977469682693,
0.03310433775186539,
0.007540777791291475,
-0.03255540132522583,
-0.023954885080456734,
-0.03154623135924339,
-0.033843740820884705,
0.059502966701984406,
-0.030412960797548294,
-0.003689858829602599,
-0.005643191747367382,
-0.03833381459116936,
0.02722376212477684,
0.03417772054672241,
0.014143663458526134,
-0.026920054107904434,
0.08582485467195511,
-0.014227183535695076,
-0.0019599180668592453,
-0.020536521449685097,
0.015842273831367493,
0.09859577566385269,
0.04238063097000122,
-0.0036999734584242105,
-0.03342589735984802,
-0.01692739687860012,
0.0043580494821071625,
0.028521018102765083,
-0.01294630952179432,
0.03375104069709778,
-0.007820080034434795,
-0.0001779770536813885,
0.004672375041991472,
0.008630525320768356,
-0.012253878638148308,
-0.01008701790124178,
0.041372451931238174,
-0.02211814559996128,
-0.05015750601887703,
-0.01048772968351841,
-0.008219229057431221,
-0.03557584434747696,
-0.034464478492736816,
0.010908041149377823,
0.02110852673649788,
-0.024155881255865097,
-0.012480705045163631,
-0.037707217037677765,
-0.04702802002429962,
0.017978312447667122,
0.028895171359181404,
-0.040479980409145355,
0.018836596980690956,
0.008437336422502995,
-0.003571739885956049,
-0.02731458842754364,
0.029233459383249283,
0.022924339398741722,
-0.002780841663479805,
0.03331715986132622,
0.04925496503710747,
0.007609754800796509,
-0.004810929764062166,
0.0007541727391071618,
0.014464124105870724,
-0.028195589780807495,
0.003427555551752448,
-0.03731412813067436,
0.053044818341732025,
-0.006606550887227058,
0.0012467060005292296,
-0.006100117228925228,
0.006871665827929974,
-0.015543775632977486,
-0.04570898041129112,
0.0046873269602656364,
-0.0006059784791432321,
0.03165314719080925,
-0.0224467683583498,
-0.0022061862982809544,
-0.01957327127456665,
0.00010760733130155131,
0.01587136834859848,
0.00862130243331194,
-0.003686791518703103,
-0.026364799588918686,
0.0036181022878736258,
-0.013211180455982685,
0.05642601102590561,
-0.004924322944134474,
-0.0013481752248480916,
-0.02529101073741913,
-0.026951491832733154,
-0.01773170195519924,
0.01274712011218071,
-0.0004812745610252023,
0.023767126724123955,
0.04232155531644821,
0.031086958944797516,
-0.030903279781341553,
-0.020411333069205284,
-0.027368908748030663,
0.005145098082721233,
0.03379443660378456,
-0.0014215994160622358,
-0.013734734617173672,
0.004778798669576645,
0.007236998528242111,
0.033621855080127716,
-0.0013936712639406323,
0.004491657484322786,
0.020129017531871796,
0.015248404815793037,
0.004435578361153603,
-0.018015453591942787,
-0.029655300080776215,
0.05660288408398628,
-0.013941890560090542,
0.0239899642765522,
-0.015361558645963669,
0.03158104419708252,
0.01802484318614006,
0.024406902492046356,
0.008516502566635609,
0.04190252721309662,
-0.004076840355992317,
-0.017192507162690163,
0.011955203488469124,
-0.01658431813120842,
-0.019627468660473824,
0.026623837649822235,
0.010995029471814632,
-0.029614774510264397,
-0.022475572302937508,
-0.042630620300769806,
-0.023968439549207687,
-0.011340825818479061,
0.040619704872369766,
-0.04900667071342468,
0.027805203571915627,
-0.04291689768433571,
0.015657318755984306,
-0.05657193437218666,
-0.015386316925287247,
-0.025960572063922882,
0.012787338346242905,
0.01900331676006317,
0.0022461223416030407,
-0.00091543112648651,
0.03238343447446823,
-0.02345823496580124,
-0.02842092514038086,
-0.007656869012862444,
0.05069432780146599,
-0.003506622975692153,
0.003080714261159301,
0.024344030767679214,
-0.023919470608234406,
0.02640690840780735,
-0.003141612047329545,
-0.005680061411112547,
0.03917766362428665,
-0.02643522620201111,
-0.020702863112092018,
0.004971549846231937,
0.02715086191892624,
0.03758560121059418,
-0.0011394480243325233,
-0.02575359120965004,
-0.019471697509288788,
0.013428804464638233,
-0.03841051459312439,
0.004341230262070894,
-0.007796686142683029,
-0.05534188449382782,
-0.029034826904535294,
-0.016391174867749214,
-0.02710602805018425,
-0.03667246550321579,
0.013619096018373966,
-0.0038833587896078825,
0.03242427483201027,
-0.01918812468647957,
-0.030900858342647552,
0.01389092393219471,
0.007255987264215946,
-0.002926864428445697,
0.006850287318229675,
0.05107387900352478,
0.01678343117237091,
0.041970741003751755,
0.008638368919491768,
0.03549126535654068,
0.0161978080868721,
0.009639536961913109,
-0.11327508091926575,
0.005218380130827427,
-0.02726367488503456,
0.020006319507956505,
0.04362056404352188,
0.005899440497159958,
-0.04073699563741684,
0.037792060524225235,
-0.04191580414772034,
0.003132666926831007,
-0.058993712067604065,
0.006418199278414249,
0.0021248573902994394,
-0.019530583173036575,
-0.014750479720532894,
0.06538381427526474,
0.07255970686674118,
0.028474990278482437,
0.03635188937187195,
0.03342599421739578,
0.004353870637714863,
-0.017431072890758514,
-0.0022120641078799963,
0.021014582365751266,
-0.005891533102840185,
-0.02109862118959427,
0.04297182336449623,
-0.02415803074836731,
-0.031206006184220314,
0.03294502943754196,
-0.023649677634239197,
-0.035143643617630005,
-0.011891205795109272,
0.021854253485798836,
-0.0014747970271855593,
0.04116504266858101,
0.027142925187945366,
0.000704638718161732,
-0.02095099538564682,
0.01419876515865326,
0.014239417389035225,
0.003741568187251687,
-0.012437758035957813,
-0.02321401983499527,
-0.002752492669969797,
-0.04350687935948372,
-0.0541301891207695,
0.029808219522237778,
-0.02597655914723873,
0.010937592945992947,
0.030934002250432968,
-0.021184056997299194,
-0.005755867343395948,
-0.02143239974975586,
0.0068279290571808815,
-0.012196420691907406,
-0.033484168350696564,
0.027891162782907486,
-0.007192287128418684,
-0.008692927658557892,
0.0401783250272274,
-0.00616086320951581,
-0.045808177441358566,
0.03638698533177376,
0.015471668913960457,
-0.00873411912471056,
-0.0781545415520668,
-0.022630469873547554,
-0.023498954251408577,
-0.011063547804951668,
-0.024703439325094223,
-0.008465209044516087,
-0.04858684912323952,
0.02904917486011982,
0.012321846559643745,
-0.0005114222876727581,
-0.038012780249118805,
-0.03495955839753151,
-0.017410267144441605,
-0.05713395029306412,
0.05548018217086792,
0.03982143849134445,
-0.029550572857260704,
-0.02927153743803501,
-0.017833318561315536,
-0.02845122665166855,
0.03366933763027191,
0.025608330965042114,
-0.012133548967540264,
-0.003440104890614748,
0.028695935383439064,
-0.035007067024707794,
0.009543861262500286,
-0.0150871891528368,
0.025571564212441444,
0.007194403558969498,
-0.007941672578454018,
0.0206719022244215,
0.014856611378490925,
-0.011518270708620548,
0.02178426831960678,
0.03828498721122742,
-0.002221785020083189,
0.06330208480358124,
-0.004188213497400284,
-0.04378413036465645,
0.018169764429330826,
0.009942061267793179,
-0.02387174963951111,
0.08999253809452057,
-0.00007327406638069078,
0.021026091650128365,
0.015560785308480263,
-0.05176108703017235,
-0.06754131615161896,
0.02052292414009571,
-0.047887567430734634,
-0.03364423289895058,
-0.018800631165504456,
-0.005570322275161743,
-0.00024554491392336786,
-0.020044760778546333,
0.0032222820445895195,
0.04936973378062248,
-0.023929709568619728,
-0.04209914430975914,
0.008355028927326202,
0.021815011277794838,
0.04056774824857712,
0.03132232278585434,
0.016996363177895546,
0.02610626071691513,
-0.013629228807985783,
0.006624598056077957,
0.007500537671148777,
0.02387678064405918,
0.016799913719296455,
-0.036828167736530304,
0.03905697166919708,
-0.006024774629622698,
0.025390679016709328,
0.0076283058151602745,
0.01678810641169548,
-0.06910402327775955,
-0.035787519067525864,
0.016410063952207565,
-0.016094965860247612,
-0.011254409328103065,
0.026468636468052864,
-0.020151011645793915,
0.051218822598457336,
-0.03884787857532501,
0.01748647727072239,
-0.023569220677018166,
0.037215568125247955,
-0.007946204394102097,
-0.015009932219982147,
-0.028999781236052513,
0.03195639327168465,
-0.021016446873545647,
0.012923797592520714,
-0.01802174560725689,
-0.01622282899916172,
0.01726524531841278,
-0.04522969201207161,
-0.004760527517646551,
0.01232483796775341,
-0.01806880347430706,
0.02493968792259693,
-0.027080168947577477,
-0.004896926693618298,
-0.02500523068010807,
0.07958751916885376,
0.02954139932990074,
-0.00564088998362422,
-0.013050860725343227,
-0.02105451188981533,
-0.006234918721020222,
0.029105914756655693,
-0.061209194362163544,
-0.011450083926320076,
-0.01938585937023163,
0.004765620920807123,
0.018342845141887665,
-0.021294452250003815
] |
<p>We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant?
But how can I deduce this from the postulate of equal probability? </p> | 4,594 | [
-0.025554073974490166,
0.013854105025529861,
0.03893224522471428,
-0.012693203054368496,
0.023248285055160522,
-0.013488546013832092,
-0.021192926913499832,
-0.009409149177372456,
0.005939583294093609,
-0.03501901403069496,
0.03318477421998978,
0.02941909246146679,
0.03287167847156525,
0.04059750214219093,
0.01566649228334427,
0.007751028053462505,
0.001082958304323256,
-0.011178812943398952,
-0.021237477660179138,
-0.023711128160357475,
0.004080011043697596,
0.04085564240813255,
0.04627623409032822,
-0.016598530113697052,
-0.03500307351350784,
0.04819716140627861,
-0.00888833962380886,
0.001963287591934204,
0.04238986596465111,
0.0866062343120575,
-0.025274183601140976,
-0.057662323117256165,
0.03917854279279709,
0.03381829708814621,
0.044638097286224365,
0.004583468660712242,
-0.017527956515550613,
-0.01818201318383217,
0.02931860275566578,
0.008683043532073498,
-0.047452691942453384,
0.010316595435142517,
-0.005630658008158207,
0.039310503751039505,
-0.04590929299592972,
0.02674539014697075,
0.04028495028614998,
-0.044958729296922684,
0.024927591904997826,
-0.04727868363261223,
0.07698468118906021,
-0.00503182178363204,
0.08013097196817398,
0.04124505817890167,
0.006758968811482191,
0.010236730799078941,
0.04173990711569786,
0.06710659712553024,
-0.012404128909111023,
-0.03971287980675697,
-0.03468681871891022,
-0.036604586988687515,
-0.0019795801490545273,
-0.032390423119068146,
0.0073551456443965435,
0.006120497826486826,
0.01405420619994402,
-0.023057477548718452,
0.014293573796749115,
-0.026556072756648064,
-0.0248391292989254,
0.032891254872083664,
0.05290500447154045,
-0.0269230455160141,
0.017971092835068703,
-0.03081372007727623,
0.029781782999634743,
0.0031049984972923994,
0.017178278416395187,
0.018126467242836952,
0.032930999994277954,
-0.010041240602731705,
0.01644038036465645,
0.023426998406648636,
0.010587864555418491,
-0.020923595875501633,
0.033670783042907715,
-0.024434030055999756,
0.018276557326316833,
0.0074544339440763,
-0.004565348383039236,
0.025132080540060997,
0.0410374291241169,
0.000184452481335029,
-0.05092944949865341,
0.06345851719379425,
-0.0052003576420247555,
0.014787955209612846,
-0.035572536289691925,
-0.018672479316592216,
-0.008507397957146168,
-0.013004317879676819,
0.042320914566516876,
0.041764043271541595,
0.02592860534787178,
0.008681870065629482,
-0.06417343020439148,
0.022628648206591606,
0.004115444608032703,
0.0011208897922188044,
-0.021549927070736885,
0.08043593913316727,
0.044149238616228104,
0.013837099075317383,
0.004421683959662914,
-0.02560131996870041,
0.00869537703692913,
-0.014497337862849236,
0.0455603264272213,
0.06938465684652328,
0.008753148838877678,
-0.0007126556592993438,
0.030736370012164116,
-0.020225150510668755,
-0.04349738359451294,
0.04603785276412964,
0.013189930468797684,
0.007704666815698147,
-0.06523888558149338,
0.030518867075443268,
-0.005562032572925091,
-0.008191687986254692,
0.0006791793275624514,
0.03636721894145012,
0.046824514865875244,
-0.007257297169417143,
-0.11286257207393646,
-0.02071448788046837,
0.013726228848099709,
-0.015534119680523872,
-0.04027322307229042,
-0.06162285432219505,
0.0500209741294384,
0.036251235753297806,
0.058186616748571396,
0.0036868485622107983,
-0.005052777472883463,
-0.025866370648145676,
0.01848251186311245,
0.01266818679869175,
-0.020724697038531303,
-0.06377290934324265,
-0.009152744896709919,
-0.055665671825408936,
0.0013352774549275637,
-0.09850413352251053,
0.0050754789263010025,
0.027307013049721718,
-0.002462842036038637,
0.00831400416791439,
0.05502113327383995,
-0.005734306760132313,
-0.04622754827141762,
-0.008767198771238327,
-0.0001518619537819177,
-0.03880499675869942,
0.08349739760160446,
-0.010047377087175846,
0.019135957583785057,
0.017246650531888008,
-0.019306214526295662,
0.029678883031010628,
-0.00697733648121357,
0.0431368388235569,
0.032033003866672516,
-0.046984411776065826,
-0.04284825548529625,
0.011079193092882633,
0.03567907586693764,
0.0005004097474738955,
-0.04283865541219711,
0.02191891521215439,
0.0018284464022144675,
0.01906292513012886,
0.0006199299823492765,
0.012868661433458328,
-0.019395358860492706,
0.0027336524799466133,
-0.020902259275317192,
-0.03314833343029022,
-0.02156796306371689,
-0.07659146934747696,
0.012303132563829422,
0.03336641192436218,
-0.014887859113514423,
0.05946923792362213,
0.03019469790160656,
-0.005939316935837269,
-0.009861554019153118,
-0.01720288023352623,
-0.0284240934997797,
0.0021879884880036116,
0.007945279590785503,
-0.036388617008924484,
0.055465519428253174,
0.020182814449071884,
0.043918631970882416,
-0.007430277764797211,
0.047671038657426834,
-0.012653622776269913,
-0.02976762317121029,
0.008447395637631416,
-0.06275907158851624,
0.023772824555635452,
0.007972683757543564,
0.023988716304302216,
0.00507341930642724,
-0.029988737776875496,
0.00508917449042201,
0.04220746457576752,
-0.04413888603448868,
0.0405581034719944,
0.032924115657806396,
-0.00991089642047882,
-0.007708998862653971,
0.04613453149795532,
0.004278901033103466,
0.021309802308678627,
0.0006343260174617171,
-0.05573754385113716,
-0.051730845123529434,
-0.00037819365388713777,
0.02951747551560402,
0.042048487812280655,
-0.020862022414803505,
0.006782694719731808,
0.03606555610895157,
0.03480783477425575,
0.007288048509508371,
0.0374482087790966,
-0.02446100115776062,
-0.023654989898204803,
0.006314877886325121,
0.010320781730115414,
0.0048553068190813065,
0.0012680522631853819,
0.010584721341729164,
0.016105690971016884,
0.0032569209579378366,
-0.008525772020220757,
-0.017594603821635246,
0.009968235157430172,
-0.01911495253443718,
0.043786365538835526,
0.00224444386549294,
-0.04558901488780975,
-0.0012388936011120677,
0.014275679364800453,
0.05296070873737335,
0.02292914129793644,
-0.030586108565330505,
0.004798293579369783,
-0.021549589931964874,
-0.04565233364701271,
0.005838567391037941,
-0.0036872313357889652,
-0.08144879341125488,
-0.02569328248500824,
0.027011267840862274,
-0.006369010545313358,
0.026901228353381157,
0.003991384524852037,
-0.03442331403493881,
0.030240807682275772,
-0.0076514980755746365,
0.04338705539703369,
0.01452962588518858,
0.024976927787065506,
-0.03991791605949402,
-0.0032830636482685804,
0.01924375630915165,
-0.006778207141906023,
0.005395272746682167,
0.02475591003894806,
-0.04382912069559097,
0.003317110938951373,
-0.028767190873622894,
-0.04415936395525932,
0.02736595645546913,
-0.015469239093363285,
0.03830450400710106,
0.020929548889398575,
0.006295268889516592,
-0.033405158668756485,
-0.006916866172105074,
0.013402209617197514,
-0.01838875748217106,
-0.05445416644215584,
-0.0073899682611227036,
0.046839065849781036,
0.015545975416898727,
-0.03731517493724823,
-0.009630026295781136,
-0.02187405526638031,
-0.02594301849603653,
0.005620279349386692,
-0.028915846720337868,
0.04065758362412453,
-0.008849789388477802,
0.042610447853803635,
0.05470740795135498,
-0.03289903327822685,
-0.03478618711233139,
-0.06522274762392044,
-0.06112191453576088,
0.031222200021147728,
0.02210588939487934,
0.05788702890276909,
0.012682851403951645,
-0.04134974256157875,
0.0731998160481453,
0.02756510302424431,
-0.0337994322180748,
0.00925604160875082,
-0.023466376587748528,
-0.021521471440792084,
-0.031131047755479813,
-0.003204646985977888,
0.016076456755399704,
0.0006541910115629435,
0.0353974811732769,
0.047755103558301926,
0.032768093049526215,
0.04592893272638321,
-0.01740121841430664,
0.012100249528884888,
0.013676379807293415,
0.0009951191022992134,
-0.0013607089640572667,
0.05821980535984039,
-0.03382780775427818,
-0.03138250485062599,
-0.003775185439735651,
0.034121282398700714,
0.02225019596517086,
-0.0045942883007228374,
-0.047465041279792786,
0.05174689367413521,
-0.009388732723891735,
0.03149792551994324,
-0.03283402696251869,
0.0421379916369915,
0.012181182391941547,
-0.003085382515564561,
0.05514548718929291,
0.042971279472112656,
0.02721298113465309,
-0.02782030589878559,
0.009065789170563221,
0.04841475188732147,
0.02158840373158455,
-0.02459052763879299,
-0.024300504475831985,
0.014640501700341702,
-0.016072619706392288,
0.00313522107899189,
-0.021436728537082672,
-0.04900307580828667,
0.0397171676158905,
0.0053595248609781265,
0.02174261212348938,
-0.02193579263985157,
-0.03728025034070015,
-0.005966049153357744,
-0.06048450991511345,
-0.001769868191331625,
0.01792162097990513,
0.0102340467274189,
-0.0007243959698826075,
0.04835144057869911,
0.0027992494869977236,
-0.02403511479496956,
-0.008674700744450092,
-0.01071945670992136,
-0.0562698058784008,
-0.00410143006592989,
-0.011088830418884754,
-0.012165944091975689,
-0.008060517720878124,
-0.005942427087575197,
0.003740948159247637,
-0.02390238270163536,
-0.05365942046046257,
-0.0009339178213849664,
-0.02349512092769146,
-0.06848304718732834,
0.009871593676507473,
-0.06375867128372192,
-0.07924254238605499,
-0.04164043068885803,
0.03774072229862213,
0.03217263147234917,
-0.005541845224797726,
0.007323525846004486,
0.022586584091186523,
-0.049906160682439804,
0.005713955964893103,
0.019677424803376198,
0.002198769012466073,
0.022079093381762505,
0.022725572809576988,
0.03285876661539078,
0.028089987114071846,
-0.005644199904054403,
-0.0019598028156906366,
-0.01997276023030281,
0.055372510105371475,
0.032021209597587585,
-0.018637295812368393,
-0.008298484608530998,
-0.029255244880914688,
-0.00972590409219265,
-0.01509113796055317,
0.02613581344485283,
-0.005019970238208771,
-0.0025779036805033684,
0.044616006314754486,
0.04780041426420212,
-0.04542416334152222,
0.029351774603128433,
0.06801821291446686,
0.019795209169387817,
-0.02578437328338623,
-0.036371853202581406,
0.006826250813901424,
-0.04931393638253212,
0.023794641718268394,
-0.004613847006112337,
-0.030692262575030327,
-0.021087633445858955,
0.024721432477235794,
-0.013154054060578346,
0.01261579804122448,
0.02982417866587639,
-0.048827268183231354,
-0.029148776084184647,
0.031126974150538445,
-0.0032658064737915993,
-0.05369868129491806,
0.014744147658348083,
0.028773827478289604,
-0.007789898198097944,
0.034424662590026855,
0.019110701978206635,
-0.04144718497991562,
0.00008487054583383724,
0.029104994609951973,
0.023908313363790512,
0.005589598789811134,
0.0010537157068029046,
-0.04705704748630524,
-0.01696895807981491,
0.047366540879011154,
0.005640226881951094,
0.04569961875677109,
0.009975059889256954,
-0.0038090618327260017,
-0.016759544610977173,
0.004287120420485735,
-0.008222630247473717,
0.02448737621307373,
0.012898813933134079,
0.013767273165285587,
-0.018020547926425934,
-0.02884313277900219,
-0.039971522986888885,
0.001301588723435998,
0.025545114651322365,
0.07167748361825943,
-0.013788745738565922,
-0.00489191384986043,
-0.00011691116378642619,
0.008402697741985321,
-0.02794000133872032,
-0.08139955252408981,
0.017776263877749443,
-0.026064766570925713,
-0.010788900777697563,
0.02292163483798504,
-0.02252862975001335,
-0.02140646241605282,
-0.0213953647762537,
-0.018397511914372444,
-0.016712719574570656,
0.030618106946349144,
-0.014183949679136276,
0.0365709513425827,
-0.01184607669711113,
-0.012452008202672005,
0.01803555339574814,
0.015898926183581352,
-0.0172259621322155,
0.010444891639053822,
-0.03980885446071625,
0.037734150886535645,
-0.038477662950754166,
0.02002258040010929,
-0.050626736134290695,
0.010911097750067711,
-0.029130304232239723,
0.008677946403622627,
-0.020826900377869606,
0.03627390414476395,
0.038750577718019485,
-0.018422558903694153,
-0.021923229098320007,
0.027733488008379936,
-0.03135516121983528,
0.006297895219177008,
-0.015897182747721672,
0.024855153635144234,
-0.012236413545906544,
-0.019213376566767693,
0.019657481461763382,
0.027884317561984062,
0.022223709151148796,
-0.003343199146911502,
0.024713585153222084,
0.054714277386665344,
-0.06291307508945465,
-0.04160954803228378,
0.018756892532110214,
-0.050022196024656296,
0.025156542658805847,
-0.01789548061788082,
0.052080851048231125,
0.014640983194112778,
-0.03782673552632332,
-0.032512836158275604,
0.005537907127290964,
-0.015801429748535156,
0.023627329617738724,
-0.02854272909462452,
0.03437477722764015,
-0.0011975883971899748,
0.005532204173505306,
-0.12830457091331482,
-0.02550409734249115,
0.015085810795426369,
0.025686044245958328,
-0.021181844174861908,
-0.06538092344999313,
-0.0029903145041316748,
0.0065264515578746796,
0.006883758585900068,
0.012043744325637817,
0.031117035076022148,
0.03308634087443352,
-0.035145070403814316,
-0.020389577373862267,
0.035519715398550034,
0.05764085799455643,
-0.011082055978477001,
-0.005248856730759144,
0.021091632544994354,
-0.022810107097029686,
0.01365120243281126,
-0.0084416838362813,
0.016740428283810616,
-0.007915453054010868,
-0.007528646383434534,
0.002528238343074918,
-0.0017597750993445516,
0.012325025163590908,
-0.06884059309959412,
0.006517353933304548,
0.006383928004652262,
0.004416171461343765,
0.0005687354132533073,
-0.01460291538387537,
0.010042889043688774,
-0.02709938958287239,
0.02717553824186325,
0.04258915036916733,
-0.027936216443777084,
-0.026338431984186172,
-0.01683252677321434,
0.012578990310430527,
0.003844041610136628,
-0.004535579588264227,
-0.007753587327897549,
0.08691859990358353,
0.022399408742785454,
-0.019729191437363625,
0.03315700590610504,
-0.009496535174548626,
-0.020458174869418144,
-0.01019350253045559,
-0.016158679500222206,
0.0035430346615612507,
-0.0077670905739068985,
-0.022189315408468246,
-0.026175161823630333,
-0.0789695680141449,
0.03661486878991127,
0.005349527578800917,
0.0034163473173975945,
0.032600656151771545,
0.023852895945310593,
0.015642710030078888,
-0.013564548455178738,
0.00724173104390502,
-0.0015656015602871776,
-0.013011683709919453,
-0.029278863221406937,
0.030190736055374146,
-0.013903934508562088,
-0.01090310886502266,
0.06073459982872009,
0.10136108100414276,
-0.039190296083688736,
0.029854467138648033,
0.033983271569013596,
0.011563888750970364,
0.032278578728437424,
0.01563168875873089,
-0.005454651545733213,
0.05815555900335312,
-0.040505729615688324,
0.030924823135137558,
-0.012108270078897476,
-0.00913503672927618,
0.020999690517783165,
0.02759939804673195,
-0.014882258139550686,
-0.014676946215331554,
-0.01701265759766102,
-0.021592507138848305,
0.06351274251937866,
0.00953415222465992,
0.044690102338790894,
0.007593581452965736,
0.021648725494742393,
0.01990697905421257,
0.005499396473169327,
-0.004561979789286852,
0.004608183167874813,
-0.046803414821624756,
-0.037158675491809845,
-0.04391825944185257,
-0.04222872853279114,
-0.0042348881252110004,
-0.019163578748703003,
-0.05916568264365196,
-0.001632053405046463,
-0.004306471440941095,
-0.013773106969892979,
0.002780927810817957,
0.04683046042919159,
0.025465015321969986,
0.0717802345752716,
0.020194854587316513,
0.02871527709066868,
-0.00036059730337001383,
0.027558429166674614,
0.1277555376291275,
0.05175270885229111,
0.008297622203826904,
-0.036139409989118576,
0.012877979315817356,
-0.016108207404613495,
0.008843488991260529,
-0.02991294674575329,
0.024606997147202492,
0.001312574022449553,
0.00047819357132539153,
-0.0009243316017091274,
0.031215284019708633,
0.004343001637607813,
-0.000013619653145724442,
0.0435122549533844,
-0.02146654948592186,
0.003738110652193427,
-0.00263602240011096,
0.041658639907836914,
-0.025124242529273033,
-0.02641696110367775,
-0.020813433453440666,
0.011489574797451496,
0.011132941581308842,
0.0288042314350605,
-0.020226309075951576,
-0.04956178739666939,
0.009498631581664085,
0.006141184363514185,
-0.007950407452881336,
-0.000010079732419399079,
0.037974096834659576,
0.01293562725186348,
-0.029654763638973236,
-0.003909359686076641,
0.025078967213630676,
0.034263961017131805,
-0.009780227206647396,
0.025242917239665985,
0.0026765489019453526,
0.014563091099262238,
0.017085332423448563,
0.0007393694249913096,
-0.009016790427267551,
-0.020586904138326645,
-0.030476892367005348,
0.027562448754906654,
-0.006784056778997183,
-0.007625488098710775,
-0.004493352957069874,
-0.03096863254904747,
-0.0435248501598835,
-0.038694996386766434,
-0.01188606582581997,
0.008798032999038696,
0.0029631981160491705,
-0.030210591852664948,
-0.019993560388684273,
-0.0319446362555027,
-0.013375821523368359,
0.005587035324424505,
0.0017702679615467787,
-0.024811876937747,
0.022991415113210678,
-0.004815090913325548,
0.012672948651015759,
0.02995452657341957,
-0.01691565103828907,
-0.024731555953621864,
-0.015832962468266487,
-0.06748185306787491,
-0.057984404265880585,
-0.07395245134830475,
0.008557931520044804,
-0.020396655425429344,
0.03721193969249725,
0.02606823667883873,
0.0037057928275316954,
0.015119137242436409,
-0.03748125210404396,
-0.03021545149385929,
0.004953046794980764,
-0.025405604392290115,
0.00041541640530340374,
0.02271968685090542,
-0.022129546850919724,
0.03930439427495003,
0.004139449913054705,
0.0007383346674032509,
0.008137170225381851,
0.010702792555093765,
0.0021433846559375525,
-0.01892346702516079,
-0.008074698969721794,
-0.02646155096590519,
-0.02150803431868553,
0.045398738235235214,
-0.021451683714985847,
0.0033311934676021338,
0.006940782535821199,
0.007393375970423222,
-0.012528338469564915,
0.03717123344540596,
-0.0119189927354455,
0.03672498092055321,
-0.0012288244906812906,
-0.024984067305922508,
0.004902082961052656,
0.027536839246749878,
0.003510632086545229,
-0.014485345222055912,
-0.04131220281124115,
-0.043442077934741974,
0.004956034477800131,
-0.005506963934749365,
0.015764500945806503,
-0.02650819905102253,
-0.022847024723887444,
-0.028101416304707527,
0.01234562136232853,
-0.03529810532927513,
-0.04678565263748169,
-0.009658822789788246,
0.008658100850880146,
0.023773182183504105,
0.02198903076350689,
-0.013038670644164085,
0.025570658966898918,
0.006895639933645725,
-0.024851258844137192,
0.026350539177656174,
0.013884944841265678,
-0.03589223697781563,
-0.024523800238966942,
0.058131568133831024,
-0.007641234900802374,
0.05801286920905113,
-0.04402746260166168,
-0.019554680213332176,
0.015383086167275906,
-0.03380850329995155,
-0.016877315938472748,
-0.003357785288244486,
-0.005620604380965233,
0.05365950986742973,
0.05094398185610771,
-0.028669847175478935,
0.009151042439043522,
0.04173058643937111,
-0.04397958144545555,
-0.007502024061977863,
-0.017209473997354507,
-0.002474307781085372,
-0.020247580483555794,
0.002637733006849885,
0.0022940963972359896,
-0.008603054098784924,
0.004812835715711117,
0.034325696527957916,
0.03749532252550125,
-0.005600412841886282,
-0.014138320460915565,
0.011065016500651836,
0.029683424159884453,
-0.009869097732007504,
0.0687934011220932,
0.018116990104317665,
0.016790296882390976,
0.04831905663013458,
-0.016001081094145775,
0.0282581839710474,
0.008756590075790882,
0.02059970237314701,
-0.09772055596113205,
-0.011028952896595001,
-0.0007513315649703145,
-0.02120271511375904,
0.03458007797598839,
-0.0035114872734993696,
0.008163636550307274,
0.030220624059438705,
-0.11732405424118042,
-0.0005882668774574995,
-0.014271642081439495,
0.0011452562175691128,
-0.011724247597157955,
0.033389508724212646,
-0.046669233590364456,
0.059441275894641876,
0.03548829257488251,
0.033903781324625015,
0.04422278702259064,
0.01467273198068142,
-0.001413022051565349,
-0.015032690018415451,
-0.017910245805978775,
0.04316089674830437,
0.002421808196231723,
-0.01709960214793682,
0.0665382593870163,
0.003622609656304121,
-0.023902853950858116,
0.013614936731755733,
0.000380398501874879,
-0.020253868773579597,
-0.0002601112355478108,
0.04128125309944153,
-0.011354660615324974,
0.03270985558629036,
0.021212199702858925,
-0.013646217063069344,
-0.02132909931242466,
-0.007074564695358276,
0.015770303085446358,
0.019816944375634193,
-0.012230027467012405,
-0.02498803474009037,
0.023100517690181732,
-0.03383927047252655,
-0.07973098754882812,
0.049471382051706314,
0.012962562963366508,
-0.0038003281224519014,
0.007637087721377611,
0.01856229640543461,
0.0011730724945664406,
-0.02688741497695446,
0.021466504782438278,
-0.05176646634936333,
0.006072185002267361,
-0.0047552878968417645,
0.03508741781115532,
0.024865493178367615,
-0.024610046297311783,
-0.014268644154071808,
-0.05209093168377876,
0.05341212823987007,
0.028162293136119843,
-0.04429241269826889,
-0.09309370070695877,
-0.02010715752840042,
0.00008988376066554338,
0.025123419240117073,
-0.005808732472360134,
-0.07964572310447693,
-0.06745942682027817,
0.01706601120531559,
0.024232346564531326,
-0.015045901760458946,
-0.036535944789648056,
-0.04049035161733627,
-0.010385158471763134,
-0.05093361437320709,
0.03138810023665428,
-0.03872475028038025,
-0.006239625625312328,
-0.05469253286719322,
0.010173359885811806,
-0.010052447207272053,
-0.0030168171506375074,
0.0355612076818943,
0.05261729657649994,
0.0053377836011350155,
-0.02072579599916935,
-0.01984316110610962,
0.019397836178541183,
-0.045931968837976456,
0.023586630821228027,
-0.001361908740364015,
-0.034478385001420975,
-0.0032162785064429045,
-0.007864085957407951,
-0.002136153168976307,
0.040870439261198044,
0.013622657395899296,
-0.006992370821535587,
0.009900841861963272,
0.033995769917964935,
-0.03131033480167389,
0.036526329815387726,
0.0026381686329841614,
-0.0024088560603559017,
0.06366976350545883,
-0.033821992576122284,
0.038835570216178894,
0.02035885863006115,
-0.012116221711039543,
-0.05954444035887718,
0.03231218457221985,
-0.06608846783638,
-0.016402166336774826,
0.002216614782810211,
0.019174395129084587,
0.026536302641034126,
-0.03654005005955696,
-0.02619168907403946,
0.04366997256875038,
-0.027139678597450256,
-0.020819569006562233,
0.020051807165145874,
0.0017606290057301521,
0.06656104326248169,
0.01962909661233425,
0.033928822726011276,
-0.017587129026651382,
0.017165876924991608,
-0.013273300603032112,
0.04263288527727127,
0.036579180508852005,
-0.014215998351573944,
0.01598513498902321,
0.03716222569346428,
-0.038089070469141006,
0.04226885363459587,
0.021983429789543152,
-0.017211565747857094,
-0.017229147255420685,
-0.003856083145365119,
0.002109870780259371,
-0.016637219116091728,
-0.00043065642239525914,
0.025407282635569572,
0.0027782500255852938,
0.05526448041200638,
-0.0068397363647818565,
-0.01072591170668602,
-0.0551009327173233,
-0.008051449432969093,
-0.0499529130756855,
0.0009818610269576311,
0.0514150932431221,
0.012680793181061745,
-0.00975006353110075,
0.0221242792904377,
-0.02340017445385456,
0.021403443068265915,
0.016615400090813637,
-0.04038188233971596,
0.027977442368865013,
0.02783442661166191,
-0.010950839146971703,
-0.02433980442583561,
0.001409774413332343,
-0.02917880192399025,
0.005123572424054146,
0.002280980348587036,
0.025112180039286613,
0.021562647074460983,
0.002466056030243635,
-0.05087379738688469,
-0.03922754526138306,
0.07105419784784317,
-0.05083499848842621,
-0.02686253935098648,
-0.02191433683037758,
0.03138190507888794,
-0.02184922806918621,
0.026713777333498
] |
<p>I am trying to the calculate the link budget for link between a ground station on Earth (with a particular latitude and longitude) and a rover at a particular location on the surface of Mars, either directly or through a satellite on Mars. Now, if I need to determine the link availability between the rover and the ground station, the first step is to determine weather I have a line of sight between the ground station and the rover.</p>
<p>For this, the first step is to determine whether Mars is above our horizon or not and if so, for how long. This can be easily done using packages such as PyEphem or Novas.</p>
<p>The next step would be to determine if the rover is actually facing Earth or is on the other side of Mars. It is this second step that I need to determine with reasonable accuracy, but have not been able to figure out how to so far.</p>
<p>Later on I would need to include the satellites in the link path as well, but for now, I need to determine if I can get a straight line of sight communication between the rover on Mars and ground station on Earth.</p>
<p>Any sort of help will be appreciated.</p> | 4,595 | [
-0.0015719430521130562,
-0.013279150240123272,
-0.037423912435770035,
0.03204543516039848,
0.04443700239062309,
0.0336313359439373,
-0.0066522289998829365,
0.011498368345201015,
0.042838290333747864,
-0.03580429032444954,
0.011028798297047615,
0.07628810405731201,
0.021230898797512054,
0.014238597825169563,
0.03279537707567215,
-0.017457328736782074,
-0.0261624027043581,
-0.02943478338420391,
0.018397683277726173,
-0.027608854696154594,
0.022938942536711693,
0.006365063600242138,
0.015298077836632729,
-0.011764244176447392,
-0.04011940211057663,
0.04870528355240822,
0.02245761826634407,
-0.03204386308789253,
-0.003601247910410166,
0.05399411916732788,
-0.03236055374145508,
-0.019771698862314224,
0.03017335571348667,
0.04991213232278824,
0.02277073822915554,
0.032098494470119476,
-0.0419987253844738,
-0.023545732721686363,
-0.009471602737903595,
0.03432625159621239,
-0.021802684292197227,
0.012756172567605972,
0.0033094827085733414,
0.03788204491138458,
-0.0409730039536953,
0.00669431546702981,
-0.0028271793853491545,
0.0015897747362032533,
0.04623102396726608,
-0.058044906705617905,
0.06742946058511734,
-0.01055832952260971,
0.023319009691476822,
-0.014316420070827007,
-0.01210317574441433,
-0.015707693994045258,
0.05253703147172928,
0.07718941569328308,
0.03422265499830246,
-0.03897620737552643,
-0.030566945672035217,
-0.030257688835263252,
-0.02771228924393654,
-0.04645867273211479,
0.0013992630410939455,
-0.017930006608366966,
-0.01999353989958763,
-0.028734887018799782,
0.01530076377093792,
0.019726326689124107,
0.003473543329164386,
-0.028639841824769974,
-0.006591010373085737,
0.002108911983668804,
0.006517497356981039,
-0.05307973921298981,
-0.018126007169485092,
0.05232728272676468,
0.021351613104343414,
0.03199682757258415,
-0.01710897870361805,
-0.006736787501722574,
0.004268541932106018,
0.013169686309993267,
0.03644517436623573,
-0.011259461753070354,
0.04062221944332123,
-0.02528056688606739,
-0.004758686292916536,
-0.020503202453255653,
0.04077661409974098,
0.025999680161476135,
0.008535444736480713,
0.013812889344990253,
-0.013915699906647205,
0.02853044867515564,
-0.023836512118577957,
0.01201023068279028,
-0.036146603524684906,
-0.031137041747570038,
0.00757480226457119,
-0.026451120153069496,
0.013843403197824955,
0.06975748389959335,
0.02274571731686592,
-0.02192096598446369,
0.007975433953106403,
-0.017653072252869606,
-0.015933429822325706,
0.008399266749620438,
-0.05841289088129997,
-0.0011003861436620355,
0.0026664012111723423,
0.019426848739385605,
0.013365467078983784,
-0.03633395954966545,
0.00040720473043620586,
-0.01730949804186821,
0.0379924401640892,
0.07527443021535873,
0.07440726459026337,
0.008010832592844963,
0.03165210410952568,
-0.0544314906001091,
-0.061879172921180725,
0.0539688803255558,
-0.0021970216184854507,
-0.02573394402861595,
-0.014110716059803963,
0.008081900887191296,
0.020493758842349052,
-0.02159060351550579,
0.00927135068923235,
-0.032026052474975586,
0.017242973670363426,
-0.014915134757757187,
-0.06270230561494827,
-0.04330167919397354,
0.009592113085091114,
-0.0069072796031832695,
0.032165609300136566,
-0.05338739976286888,
0.06395154446363449,
0.0319305881857872,
0.04744500666856766,
-0.00042606735951267183,
0.04701822251081467,
0.0055803838185966015,
0.011792799457907677,
-0.0371280200779438,
-0.0728796049952507,
-0.020551500841975212,
-0.02334929257631302,
-0.04506335407495499,
-0.0012162039056420326,
-0.0525175966322422,
0.06455710530281067,
0.014653082937002182,
0.03232676908373833,
-0.003799180267378688,
0.044459979981184006,
0.0382419191300869,
0.001614628010429442,
0.015076505951583385,
-0.007124020718038082,
-0.010974470525979996,
0.08025175333023071,
0.0022416734136641026,
0.006860767491161823,
0.018759435042738914,
0.01866818219423294,
0.011282983236014843,
0.009167101234197617,
-0.008247021585702896,
0.07937736064195633,
-0.04497077688574791,
0.0014555847737938166,
0.0014716451987624168,
-0.013197703287005424,
0.010814869776368141,
-0.023210078477859497,
-0.04389752075076103,
0.023195680230855942,
0.005448764655739069,
0.04990946501493454,
0.05453379452228546,
0.008272814564406872,
0.004373430740088224,
0.06748874485492706,
-0.0267777256667614,
-0.011092521250247955,
-0.004430538509041071,
-0.009790717624127865,
-0.009168562479317188,
-0.007182770408689976,
-0.020776305347681046,
0.024398406967520714,
0.00807751901447773,
0.0018951547099277377,
-0.03292618691921234,
0.022484315559267998,
0.017017589882016182,
0.06681058555841446,
-0.0030325630214065313,
-0.01016128621995449,
0.06805191189050674,
0.0584220290184021,
-0.03330748528242111,
0.018609680235385895,
-0.021227700635790825,
-0.054568514227867126,
-0.05146116390824318,
-0.040355272591114044,
0.02102101966738701,
0.036573104560375214,
-0.021429255604743958,
-0.00017904229753185064,
0.035583607852458954,
-0.01712421327829361,
-0.008916706778109074,
-0.013223299756646156,
0.02781340666115284,
0.06351254135370255,
0.008794202469289303,
0.0454200841486454,
-0.006741171702742577,
0.030972640961408615,
0.02565990760922432,
-0.005340357776731253,
0.006539502646774054,
-0.05672449246048927,
-0.0435628741979599,
0.021311871707439423,
-0.0006719082011841238,
-0.018172457814216614,
-0.00551139609888196,
0.08349692076444626,
-0.011627226136624813,
0.03620366379618645,
0.04063275083899498,
-0.010781788267195225,
-0.004056466277688742,
0.023153573274612427,
0.036132629960775375,
0.036671966314315796,
-0.012490859255194664,
-0.029543759301304817,
0.008391273207962513,
-0.013177812099456787,
-0.01190621592104435,
-0.022416844964027405,
0.03054477833211422,
-0.009316597133874893,
0.004403435159474611,
0.008228227496147156,
-0.029173502698540688,
0.06568494439125061,
-0.031709376722574234,
-0.005637124180793762,
0.03799227252602577,
0.009896868839859962,
-0.021844668313860893,
0.00927905272692442,
-0.026287173852324486,
0.009176429361104965,
0.020646361634135246,
-0.024982145056128502,
0.010695887729525566,
0.03435772284865379,
-0.04719178006052971,
0.023707814514636993,
-0.04273471608757973,
-0.03869691118597984,
-0.0038188558537513018,
-0.01070146169513464,
0.04035076126456261,
-0.01499573141336441,
0.03577635437250137,
-0.02214035578072071,
-0.018579039722681046,
-0.007946006022393703,
0.0001234652881976217,
-0.017968205735087395,
0.022401606664061546,
-0.01294033881276846,
0.009108230471611023,
0.030705133453011513,
-0.012734202668070793,
0.030971363186836243,
0.022723203524947166,
-0.03298027068376541,
0.0070006162859499454,
0.02050194703042507,
-0.026224717497825623,
-0.028693756088614464,
-0.06785213202238083,
0.0072796884924173355,
-0.03503342345356941,
0.0003333810600452125,
0.014340411871671677,
0.017510708421468735,
-0.040311723947525024,
0.04713832214474678,
-0.08267465978860855,
-0.016552459448575974,
0.00014839025971014053,
-0.013202519156038761,
-0.03831959888339043,
-0.044892359524965286,
0.002483182121068239,
0.014222034253180027,
-0.013066468760371208,
0.0007410685648210347,
-0.06327295303344727,
-0.09766078740358353,
0.026089759543538094,
0.028948599472641945,
0.03778049349784851,
-0.004137091804295778,
-0.013733972795307636,
0.06813656538724899,
0.00590878538787365,
-0.017895586788654327,
-0.02187560498714447,
0.005682982038706541,
0.026662955060601234,
0.0003273899492342025,
0.020327936857938766,
-0.006493262015283108,
-0.018032316118478775,
0.01963355951011181,
0.0043131448328495026,
-0.007575241848826408,
0.07588005065917969,
0.010613705962896347,
0.002055836608633399,
-0.03757304698228836,
0.0055056060664355755,
-0.012862364761531353,
0.05093090236186981,
0.04523114114999771,
-0.020205242559313774,
0.021052196621894836,
-0.013249620795249939,
0.02838665246963501,
0.01799241453409195,
-0.08895973861217499,
-0.023821434006094933,
-0.005479832179844379,
0.0067467885091900826,
0.018797922879457474,
0.023537861183285713,
-0.005309786647558212,
-0.014199833385646343,
0.0019424951169639826,
0.020139236003160477,
0.0930284932255745,
-0.025124525651335716,
-0.0368775874376297,
0.08194026350975037,
0.05507476627826691,
-0.03727133572101593,
-0.05720697343349457,
-0.02187020145356655,
-0.016123374924063683,
-0.005300776567310095,
-0.03729458153247833,
-0.02818620577454567,
0.03538203239440918,
0.028857309371232986,
-0.0006787444581277668,
0.04728015512228012,
-0.027546780183911324,
-0.014177593402564526,
-0.05900213494896889,
-0.006384809967130423,
-0.03731535002589226,
0.03707628697156906,
0.0009242303785867989,
0.017476843670010567,
0.014148488640785217,
0.03252311423420906,
0.05224032700061798,
0.0047191171906888485,
-0.07028196007013321,
0.025744600221514702,
-0.004482181277126074,
-0.06054174154996872,
0.0077031636610627174,
-0.0006784055149182677,
-0.014352361671626568,
-0.040265947580337524,
0.010771147906780243,
-0.0023013835307210684,
0.016541577875614166,
-0.011698204092681408,
0.017587833106517792,
0.00285275187343359,
-0.02001011371612549,
-0.0599529929459095,
0.023503996431827545,
0.059646833688020706,
-0.010495402850210667,
0.010294097475707531,
0.03311493620276451,
-0.01083650253713131,
-0.05011807009577751,
-0.023070992901921272,
0.020131444558501244,
-0.0327189639210701,
0.007347350008785725,
0.01321641355752945,
0.027762942016124725,
-0.0010714851086959243,
0.009468489326536655,
0.0003417624393478036,
0.03660758584737778,
0.0008891415782272816,
0.028768418356776237,
0.015260948799550533,
-0.040933579206466675,
-0.020858027040958405,
0.037496667355298996,
-0.00011274010466877371,
-0.03894238919019699,
-0.03736712783575058,
0.07056684792041779,
0.007022203411906958,
-0.0004918155609630048,
0.030729644000530243,
0.05309348553419113,
-0.01221216656267643,
0.015444406308233738,
-0.01808028109371662,
-0.012802878394722939,
-0.026360543444752693,
0.003768172115087509,
0.02060268260538578,
0.042496100068092346,
-0.00044415713637135923,
-0.01921304315328598,
0.023759225383400917,
-0.023275963962078094,
-0.02094806358218193,
0.024497106671333313,
-0.027653230354189873,
0.03427913412451744,
-0.003044281853362918,
-0.00782670546323061,
0.016335682943463326,
0.02692975476384163,
-0.00494840182363987,
0.01015105377882719,
-0.019015759229660034,
-0.11288018524646759,
-0.01443483866751194,
0.03654805198311806,
0.05649520456790924,
-0.010474719107151031,
-0.0768778845667839,
-0.06733516603708267,
0.010730993933975697,
0.013688401319086552,
-0.02051416225731373,
0.04309888184070587,
-0.0073078772984445095,
0.035174474120140076,
-0.04297839477658272,
-0.04221336543560028,
-0.0394267663359642,
0.002110778819769621,
0.008517875336110592,
0.0024111794773489237,
-0.02370869368314743,
-0.039522185921669006,
-0.034008707851171494,
0.027499215677380562,
0.04256859049201012,
0.05002281442284584,
0.05383045971393585,
-0.008228362537920475,
0.007308759726583958,
0.01258742157369852,
-0.027852440252900124,
-0.06409081071615219,
-0.015370526351034641,
0.016692858189344406,
-0.013591999188065529,
0.056322820484638214,
-0.013675043359398842,
-0.00035148943425156176,
0.07048209756612778,
0.022454556077718735,
-0.00961300078779459,
-0.02238018997013569,
-0.03568992391228676,
0.0013415605062618852,
0.0348232164978981,
0.012550516985356808,
0.07134617865085602,
-0.0072630648501217365,
-0.0022663387935608625,
0.020170578733086586,
-0.01464516669511795,
0.03002544492483139,
-0.030121060088276863,
-0.02350904606282711,
-0.014116482809185982,
-0.0032431399449706078,
-0.02935630828142166,
-0.0006626950344070792,
-0.012776212766766548,
0.03257235512137413,
-0.013572905212640762,
-0.0034248533193022013,
-0.03764430433511734,
0.02443658746778965,
0.0028579062782227993,
0.039147377014160156,
0.03636832535266876,
0.03521003574132919,
-0.03247036784887314,
0.015526600182056427,
0.0053871613927185535,
-0.01556132361292839,
-0.0077188764698803425,
-0.05221875384449959,
-0.017421171069145203,
-0.006985087413340807,
-0.022406578063964844,
0.010743769817054272,
0.002297273138538003,
-0.028422154486179352,
0.05284437909722328,
0.011989804916083813,
-0.015381560660898685,
0.0383211188018322,
-0.030373085290193558,
-0.004697037860751152,
0.06370826065540314,
0.01586359366774559,
-0.012193876318633556,
-0.007235293742269278,
-0.011549585498869419,
-0.002447328995913267,
0.023198353126645088,
-0.028369296342134476,
-0.008379284292459488,
0.01664557121694088,
0.03350961208343506,
-0.037908535450696945,
-0.03335869684815407,
-0.014557555317878723,
0.00548751512542367,
-0.040641721338033676,
0.008366035297513008,
0.05517592653632164,
-0.03966926410794258,
0.002427667146548629,
-0.025495851412415504,
0.022227831184864044,
0.04066598042845726,
-0.027555309236049652,
0.035073861479759216,
0.005665849428623915,
0.0010628573363646865,
0.028313301503658295,
-0.03217126801609993,
0.02333766780793667,
-0.021465519443154335,
-0.0791190043091774,
-0.029584750533103943,
0.010878566652536392,
0.033503495156764984,
-0.022427326068282127,
-0.03740500658750534,
0.00017430089064873755,
0.019033163785934448,
-0.04464390128850937,
0.011573621071875095,
0.001810687594115734,
-0.009174559265375137,
-0.0026089749298989773,
-0.05255858972668648,
-0.002451554872095585,
-0.0034415870904922485,
-0.011966971680521965,
-0.016454152762889862,
-0.0060613094829022884,
-0.0001391552505083382,
0.030967604368925095,
0.08843924850225449,
-0.003360940143465996,
0.04058985039591789,
0.028899207711219788,
-0.0027603022754192352,
0.0005823791143484414,
-0.008762801997363567,
0.003855542978271842,
0.016302868723869324,
0.00410222914069891,
-0.008177129551768303,
-0.0310067068785429,
-0.04001828283071518,
-0.036256950348615646,
0.07078038901090622,
-0.02137625403702259,
0.025441758334636688,
0.04546365514397621,
0.01696554385125637,
-0.01565318927168846,
0.022902807220816612,
-0.021957946941256523,
-0.002922086277976632,
0.0405961312353611,
0.053275216370821,
-0.019277120009064674,
-0.017595410346984863,
0.02861841581761837,
0.004541176836937666,
0.03090921975672245,
-0.0179095808416605,
0.01527999248355627,
0.009004190564155579,
0.021049577742815018,
-0.04597947746515274,
-0.040386006236076355,
-0.0026682803872972727,
-0.03243933245539665,
-0.014442342333495617,
0.016624819487333298,
-0.024465514346957207,
0.04970591515302658,
0.00255658314563334,
0.000027960471925325692,
-0.02117462083697319,
-0.013140970841050148,
-0.03942643851041794,
0.01643769070506096,
0.055230189114809036,
-0.004862792789936066,
0.017823919653892517,
0.031663648784160614,
0.039304014295339584,
-0.02517608366906643,
0.03633740916848183,
-0.014164838008582592,
-0.03195001929998398,
-0.009750320576131344,
-0.01599419303238392,
-0.053768083453178406,
0.07363935559988022,
-0.01703602261841297,
-0.009527934715151787,
0.013052284717559814,
-0.008727293461561203,
0.02440893091261387,
0.022205829620361328,
0.057839784771203995,
-0.04180242866277695,
0.043360836803913116,
-0.02078237012028694,
-0.005549531430006027,
0.0006972377886995673,
-0.012580959126353264,
0.11588269472122192,
0.06117817759513855,
0.013744617812335491,
-0.013992073945701122,
-0.0069132279604673386,
-0.001565422397106886,
-0.0211123526096344,
-0.06196589767932892,
0.02690870314836502,
-0.0027725864201784134,
0.0046759555116295815,
0.05751869082450867,
0.004506013356149197,
-0.029815368354320526,
-0.011473659425973892,
0.04517892003059387,
-0.016961771994829178,
-0.006124135106801987,
0.045645032078027725,
-0.018995342776179314,
-0.02241339348256588,
0.010462062433362007,
0.006623024120926857,
0.05447004362940788,
-0.030608605593442917,
-0.023811757564544678,
-0.04948195442557335,
-0.0031853346154093742,
0.030239295214414597,
-0.02365577593445778,
-0.02407046966254711,
0.03409601375460625,
-0.007386539131402969,
0.006638494785875082,
0.04346563294529915,
0.057403814047575,
0.01636539399623871,
-0.032724782824516296,
-0.002035535406321287,
0.006652966607362032,
0.0282448660582304,
-0.024135150015354156,
0.0037561203353106976,
0.030061988160014153,
-0.0313308946788311,
-0.016494937241077423,
-0.014443127438426018,
0.05407588928937912,
0.0005355453467927873,
-0.0003385363088455051,
-0.0116501459851861,
0.04642739146947861,
0.002696637762710452,
-0.0700301080942154,
0.04964594915509224,
0.02558913081884384,
0.008968845941126347,
-0.034889936447143555,
-0.008861103095114231,
0.011667381040751934,
0.011847937479615211,
0.03432578966021538,
-0.014525292441248894,
0.03505547344684601,
0.004736811853945255,
-0.020143771544098854,
-0.014174694195389748,
0.03996770456433296,
-0.009434511885046959,
-0.030626796185970306,
-0.04008759185671806,
-0.011189738288521767,
-0.02650696225464344,
-0.026101352646946907,
0.042965784668922424,
-0.0017319376347586513,
0.007766077294945717,
0.007891793735325336,
-0.048790138214826584,
-0.01804373599588871,
-0.06080098822712898,
-0.007722590118646622,
-0.038306038826704025,
-0.037773434072732925,
-0.028707189485430717,
-0.0029994025826454163,
0.044047486037015915,
-0.016978895291686058,
0.029296599328517914,
0.002869263757020235,
-0.028234604746103287,
-0.0008820798830129206,
0.007185439113527536,
-0.027030350640416145,
-0.026178689673542976,
0.01174912042915821,
-0.04085889086127281,
-0.018406985327601433,
0.01614641398191452,
0.049073874950408936,
0.015739070251584053,
0.019473720341920853,
-0.013238947838544846,
0.012694695964455605,
-0.05825541540980339,
-0.013312231749296188,
0.04132094979286194,
-0.009207609109580517,
-0.008264017291367054,
-0.016175895929336548,
0.006326647941023111,
-0.03889695554971695,
0.015439503826200962,
-0.02420630492269993,
-0.0222425926476717,
0.03633296862244606,
-0.02085384912788868,
-0.03117075189948082,
0.04294795170426369,
-0.007348332554101944,
0.0057615721598267555,
-0.005318186711519957,
0.03451583907008171,
-0.01617722027003765,
-0.019609563052654266,
-0.037643950432538986,
-0.01817931793630123,
-0.0049538034945726395,
0.00772849190980196,
-0.04215071722865105,
-0.021298769861459732,
0.02302921563386917,
0.016621548682451248,
-0.006435781251639128,
0.004908840637654066,
0.027267614379525185,
0.012019641697406769,
0.07325518876314163,
-0.047372300177812576,
-0.015086045488715172,
0.016995955258607864,
-0.016017837449908257,
-0.027600061148405075,
0.03114479035139084,
0.024821940809488297,
0.04898080602288246,
0.02832195535302162,
-0.06379149109125137,
-0.025667734444141388,
0.04748532921075821,
-0.0016686858143657446,
-0.01754339411854744,
0.02898746356368065,
0.0038490069564431906,
0.03511916100978851,
0.0181641336530447,
0.01277125719934702,
-0.03342995047569275,
0.013297460041940212,
0.010791906155645847,
0.017294637858867645,
-0.006923974025994539,
0.049379169940948486,
0.01888727955520153,
-0.018563978374004364,
-0.030213696882128716,
-0.014267916791141033,
-0.024181343615055084,
0.036841537803411484,
0.032312385737895966,
-0.026514900848269463,
0.03764539584517479,
0.025499368086457253,
0.0397045873105526,
-0.03265906497836113,
0.004073568619787693,
0.004500371403992176,
0.040715284645557404,
0.01825244538486004,
-0.10345549136400223,
0.021022019907832146,
0.0857190415263176,
-0.039653338491916656,
-0.014885290525853634,
0.001424526795744896,
0.0014366466784849763,
-0.048638250678777695,
0.013564448803663254,
-0.025800317525863647,
0.009428117424249649,
-0.001985207898542285,
-0.002975338837131858,
0.011121382005512714,
-0.007596365176141262,
-0.0347442626953125,
-0.032248757779598236,
-0.001441783388145268,
0.01864386908710003,
-0.026644891127943993,
0.00429441686719656,
0.05781936272978783,
-0.021922625601291656,
-0.02113048918545246,
0.03166145458817482,
-0.0076135024428367615,
0.017804129049181938,
-0.00037277035880833864,
0.04988458380103111,
0.023120196536183357,
0.02758864313364029,
0.017696073278784752,
-0.02766359969973564,
-0.006793449632823467,
-0.03695906698703766,
-0.005589142441749573,
0.038444455713033676,
0.022982904687523842,
0.024202080443501472,
-0.003962724935263395,
-0.036430779844522476,
-0.030438881367444992,
0.016397999599575996,
-0.014883765019476414,
-0.003966513089835644,
0.009396162815392017,
-0.014671631157398224,
-0.018899571150541306,
-0.07308679819107056,
-0.013888162560760975,
-0.07567080855369568,
0.0050852736458182335,
0.03719059377908707,
-0.01848462224006653,
-0.012395546771585941,
-0.019851824268698692,
-0.02815297432243824,
-0.04013160243630409,
0.06562638282775879,
-0.019139032810926437,
-0.007845590822398663,
-0.056326624006032944,
0.008404631167650223,
-0.03662949427962303,
0.01232606265693903,
0.007977442815899849,
0.02584882639348507,
-0.014098508283495903,
0.030141115188598633,
-0.03661736845970154,
0.00461866520345211,
0.004614351782947779,
0.002288813004270196,
0.030441150069236755,
-0.04845722019672394,
0.02830568514764309,
0.013359332457184792,
0.01091213058680296,
-0.039404891431331635,
-0.036910898983478546,
-0.03745593503117561,
0.022486617788672447,
0.03000578284263611,
-0.015191157348453999,
-0.012933103367686272,
-0.0208418145775795,
0.02660958096385002,
-0.0050722393207252026,
-0.04698112607002258,
0.027202660217881203,
-0.002761672716587782,
-0.03907802700996399,
-0.00036602086038328707,
-0.047552693635225296,
-0.011784709990024567,
0.01931474544107914,
0.043711159378290176,
0.0142051437869668,
0.01956784538924694,
-0.000628035340923816,
-0.03137888386845589,
0.0015738719375804067,
0.035832393914461136,
-0.022788189351558685,
0.0732589066028595,
0.025311289355158806,
0.0035005772951990366,
0.024391237646341324,
0.0003298234660178423,
-0.02903267927467823,
0.06250078231096268,
-0.030904941260814667,
0.0025789765641093254,
-0.0029078919906169176,
-0.031234923750162125,
0.05076056346297264,
-0.09496032446622849,
-0.0033137518912553787,
0.02791714482009411,
-0.03575466573238373,
0.012304168194532394,
0.04721132665872574,
-0.02823823131620884,
-0.009315740317106247,
-0.02436750754714012,
0.06294264644384384,
0.021529164165258408,
-0.05167940631508827,
-0.021067040041089058,
0.015509071759879589,
0.01317656971514225,
0.009167712181806564,
0.03895990177989006,
0.04875282198190689,
0.014870010316371918,
0.01718536764383316,
-0.002684495411813259,
0.04212147742509842,
-0.02108391746878624,
-0.022279879078269005,
0.04132595658302307,
0.013775303028523922,
-0.010880399495363235,
0.0025571424048393965,
-0.012795563787221909,
0.021380119025707245,
-0.043879006057977676,
0.005363949574530125,
-0.05449169501662254,
-0.00819928664714098,
-0.03871578723192215,
0.02957225777208805,
-0.046730611473321915,
-0.00037768392940051854,
0.0057921805419027805,
0.01349637657403946,
0.03212091699242592,
-0.0031105498783290386,
0.03183816000819206,
-0.037279125303030014,
0.006742571946233511,
-0.01886669360101223,
0.03405988961458206,
-0.00509431678801775,
-0.024052150547504425,
-0.036045365035533905,
0.01889774017035961,
0.022939147427678108,
0.019238244742155075,
0.0018497082637622952,
-0.028781628236174583,
-0.007196089252829552,
-0.009235243313014507,
0.03859345614910126,
-0.06253237277269363,
-0.010550870560109615,
-0.02803892455995083,
0.0009531992836855352,
0.001090523204766214,
-0.0012365445727482438
] |
<p>When working with Bose-Einstein condensates trapped in potentials, how can one tell what the density of state of a system of identical bosons given the Hamiltonian, $H$? (I have been told that it is possible.)</p>
<p>Suppose the Hamiltonian is some 2D harmonic oscillator -- so $$H=p^2/2m+(1/2)(a^2x^2+b^2y^2) \quad ?$$</p>
<p>I think there is some general formula, something like $$\rho(E)=[gV_dS_dp^{d-1}/(2\pi\hbar)^{d}] (dp/dE) \quad ,$$ where $d$ is the dimension of the space we are working in, $g=2s+1$ where $s$ is the spin of the particles and $V_d$ is the $d-$dimensional "volume", so for a fixed volume box, this is the volume of the box.</p>
<p>But what is $V_d$ in this case? And is $p$ simply $$p^2=2m[E-(1/2)(a^2x^2+b^2y^2)] \quad ?$$</p> | 4,596 | [
-0.030801746994256973,
-0.03295012190937996,
0.026768382638692856,
-0.06174841895699501,
0.05330125242471695,
0.002545590279623866,
-0.037851087749004364,
-0.0487828329205513,
0.03958328440785408,
-0.03534173220396042,
0.060073379427194595,
0.018012015148997307,
0.05601164326071739,
0.024119539186358452,
0.0005176948616281152,
-0.004522161092609167,
-0.0027097915299236774,
-0.01641492359340191,
0.012752460315823555,
-0.04515789821743965,
0.014008359052240849,
0.042394332587718964,
0.00941106304526329,
-0.00992219615727663,
-0.008937740698456764,
0.06199359893798828,
-0.0006445616018027067,
-0.03442035987973213,
0.023954356089234352,
0.060573842376470566,
-0.02034478820860386,
-0.028133030980825424,
0.049590032547712326,
0.044553451240062714,
0.05955088883638382,
-0.02106638438999653,
-0.05280305817723274,
-0.05347571521997452,
-0.022412195801734924,
0.025932515040040016,
-0.07488568127155304,
-0.0325436033308506,
0.003569840220734477,
0.02064353972673416,
-0.017020603641867638,
-0.01687418855726719,
0.037649016827344894,
-0.058934107422828674,
0.02716987393796444,
-0.08215082436800003,
0.06446212530136108,
0.019026290625333786,
0.02677644044160843,
0.04001548886299133,
0.01637423411011696,
-0.02757398784160614,
0.031850554049015045,
0.06427868455648422,
0.018881430849432945,
-0.04908832907676697,
-0.031356003135442734,
0.00010593805927783251,
-0.01613183505833149,
-0.020193858072161674,
-0.029072530567646027,
0.023560259491205215,
0.009641528129577637,
-0.033750806003808975,
-0.002316512865945697,
-0.007826547138392925,
0.030025329440832138,
0.006110566668212414,
0.015265917405486107,
-0.060080636292696,
0.04654472693800926,
0.0032924776896834373,
0.014334006235003471,
0.032820701599121094,
-0.006417389493435621,
0.019039848819375038,
-0.02728738635778427,
0.019627287983894348,
0.023749034851789474,
0.021833233535289764,
0.01648721657693386,
-0.024762673303484917,
0.05262758210301399,
-0.03386257588863373,
0.0047767492942512035,
0.05981091782450676,
-0.002861068584024906,
0.03182731568813324,
0.05209805443882942,
-0.01883563958108425,
-0.03549792245030403,
-0.002438151277601719,
0.0035157911479473114,
0.09446901828050613,
-0.017097607254981995,
-0.036733478307724,
-0.002069666516035795,
-0.018061663955450058,
-0.00358474045060575,
0.07028800994157791,
-0.05380333960056305,
-0.020330537110567093,
-0.034399520605802536,
0.024146631360054016,
0.020082911476492882,
0.002873889170587063,
-0.048114534467458725,
0.0016602526884526014,
-0.014553459361195564,
-0.01707269623875618,
0.010441971942782402,
0.0019741214346140623,
-0.016820760443806648,
0.004994432907551527,
0.05586787685751915,
0.05830534175038338,
0.013457736931741238,
-0.007872740738093853,
0.0012101795291528106,
-0.07389930635690689,
-0.08751582354307175,
-0.03664899244904518,
0.05790894106030464,
0.02494816668331623,
-0.061256665736436844,
0.027976300567388535,
0.028078878298401833,
-0.011774331331253052,
0.00839556660503149,
-0.0036718801129609346,
0.023401346057653427,
-0.028199784457683563,
-0.08109062910079956,
-0.04523313418030739,
0.014725273475050926,
-0.011620106175541878,
-0.03931772708892822,
-0.06386226415634155,
0.0025212420150637627,
0.024062814190983772,
0.056782376021146774,
-0.026876909658312798,
0.019045691937208176,
0.007060354575514793,
0.034865155816078186,
0.02009158954024315,
-0.015435666777193546,
-0.01909482665359974,
-0.009295345284044743,
-0.03722875565290451,
0.02379000373184681,
-0.058627236634492874,
0.018877282738685608,
0.0344732291996479,
0.007602674420922995,
-0.008884643204510212,
0.05380909889936447,
-0.006670746952295303,
-0.013116619549691677,
0.012225984595716,
-0.016754360869526863,
-0.031695302575826645,
0.07909534126520157,
-0.0021593065466731787,
-0.007947520352900028,
0.03865118324756622,
-0.023655887693166733,
0.0003077451838180423,
-0.0014061296824365854,
-0.0004292485537007451,
0.038181792944669724,
-0.0016555440379306674,
-0.03951816260814667,
-0.025724725797772408,
0.031925853341817856,
0.022499091923236847,
-0.02324194274842739,
-0.014717151410877705,
-0.0032839870546013117,
-0.0018210988491773605,
-0.007080980110913515,
0.009225033223628998,
0.004893115721642971,
0.008231489919126034,
-0.027204828336834908,
-0.07073678076267242,
-0.010094737634062767,
-0.08670586347579956,
0.010260534472763538,
-0.013446076773107052,
0.007637075614184141,
0.061835337430238724,
0.052374809980392456,
0.002467646263539791,
-0.02955431304872036,
-0.037077050656080246,
-0.0030288465786725283,
0.03939489647746086,
0.015656379982829094,
-0.015176521614193916,
0.0056472946889698505,
0.005843365099281073,
0.01651018112897873,
-0.009640348143875599,
0.034911178052425385,
-0.02580874413251877,
-0.04002454876899719,
-0.03758818656206131,
-0.00950610637664795,
0.014161004684865475,
-0.02530178427696228,
0.014832046814262867,
-0.001938534784130752,
0.012436578050255775,
-0.008308837190270424,
0.012619824148714542,
-0.024288872256875038,
0.04480275511741638,
0.06931253522634506,
0.014758669771254063,
0.011048096232116222,
0.01803046092391014,
-0.0013753141975030303,
0.024880150333046913,
0.0027556426357477903,
-0.008395375683903694,
-0.04778233915567398,
-0.013860560022294521,
0.008985425345599651,
0.054570842534303665,
-0.005420227535068989,
0.012708930298686028,
0.028964953497052193,
0.030287163332104683,
0.023114193230867386,
-0.014255872927606106,
-0.044036056846380234,
-0.02093142457306385,
0.042177215218544006,
-0.001258630072697997,
-0.003304888727143407,
0.019636530429124832,
-0.002629995346069336,
0.024960817769169807,
0.023679742589592934,
-0.006438040174543858,
-0.033596158027648926,
0.03851214796304703,
-0.041105691343545914,
-0.009765570983290672,
-0.011979025788605213,
-0.0337962880730629,
0.023537371307611465,
-0.02086346596479416,
0.028187548741698265,
0.024977069348096848,
-0.022931264713406563,
-0.010514730587601662,
-0.03890331834554672,
-0.05682625249028206,
0.01771603897213936,
0.01855594664812088,
-0.03227870538830757,
-0.010887937620282173,
0.018911661580204964,
-0.03921248018741608,
-0.00990553479641676,
0.023383179679512978,
0.007794054225087166,
-0.005326027516275644,
0.05836385115981102,
0.021066132932901382,
0.01833319664001465,
0.026010554283857346,
-0.012543239630758762,
-0.01651228591799736,
0.010940013453364372,
-0.021301133558154106,
0.030609501525759697,
0.0028359945863485336,
-0.05540008470416069,
-0.000382870202884078,
-0.053900063037872314,
-0.013505707494914532,
0.0139540396630764,
0.003291751490905881,
-0.014195873402059078,
0.02833821251988411,
-0.003127239178866148,
-0.047055840492248535,
-0.02114512398838997,
0.003330460051074624,
0.002615580800920725,
-0.03897690773010254,
0.044836562126874924,
0.004441722296178341,
-0.0022204674314707518,
-0.014152641408145428,
-0.000044259882997721434,
-0.018339836969971657,
-0.032802317291498184,
-0.021142907440662384,
-0.008541352115571499,
0.028491348028182983,
-0.039786722511053085,
0.049038857221603394,
0.038524750620126724,
-0.012764167971909046,
-0.034408558160066605,
-0.05797537788748741,
-0.037969786673784256,
0.016320906579494476,
-0.0012830477207899094,
0.040172986686229706,
-0.010966801084578037,
-0.04446127265691757,
0.1146363690495491,
0.004010004922747612,
-0.03159405291080475,
-0.004993122071027756,
-0.005651027429848909,
0.0249217189848423,
0.019873911514878273,
-0.023825962096452713,
0.047115497291088104,
-0.0211187656968832,
0.0361834391951561,
0.026350537315011024,
0.05012424662709236,
0.021644003689289093,
-0.002137943869456649,
-0.028636565431952477,
0.04345424100756645,
0.014974788762629032,
-0.0021341033279895782,
0.08708363026380539,
-0.006579582113772631,
0.02076270431280136,
0.0046132099814713,
-0.020358510315418243,
-0.004606704693287611,
0.030132710933685303,
-0.05871635302901268,
0.04391864687204361,
-0.007445195224136114,
0.014875967055559158,
0.002003241330385208,
0.01956419087946415,
-0.004726088140159845,
-0.031327925622463226,
0.006692887749522924,
0.0075588347390294075,
0.024459129199385643,
0.02508382499217987,
-0.035001035779714584,
0.04509986564517021,
0.016002794727683067,
0.003425698261708021,
-0.025559138506650925,
0.021203698590397835,
0.01638968102633953,
0.013588730245828629,
-0.023584242910146713,
-0.0310116708278656,
0.019196484237909317,
0.018236802890896797,
0.03731890022754669,
-0.06065422296524048,
-0.03052876889705658,
-0.012004617601633072,
-0.05430031567811966,
-0.03078443929553032,
-0.021245591342449188,
0.05103740096092224,
0.015681669116020203,
0.024445265531539917,
0.023641863837838173,
0.016310259699821472,
0.04679349437355995,
-0.03339870646595955,
-0.06289412826299667,
-0.013316468335688114,
-0.011758794076740742,
0.04663620516657829,
-0.016521994024515152,
-0.02414560317993164,
0.053216755390167236,
-0.0562654584646225,
-0.03307933360338211,
0.007720073219388723,
0.02716483734548092,
-0.04114799201488495,
0.004787532612681389,
-0.058092694729566574,
-0.018712524324655533,
-0.03756962716579437,
0.05954807996749878,
0.005732931196689606,
-0.014809230342507362,
0.032337747514247894,
0.055144596844911575,
-0.013251733966171741,
-0.0008217111462727189,
-0.0005985677125863731,
0.00020563890575431287,
0.01373350527137518,
0.035789187997579575,
0.02443530037999153,
0.03184940293431282,
-0.034037504345178604,
-0.021581990644335747,
0.01886606588959694,
0.04013096168637276,
0.011030465364456177,
0.015653114765882492,
0.019827017560601234,
-0.0075826034881174564,
-0.017229726538062096,
-0.017814287915825844,
0.052002307027578354,
-0.0011778513435274363,
0.019269656389951706,
0.025571489706635475,
0.011358862742781639,
-0.01484044548124075,
0.03648186847567558,
0.06793168187141418,
-0.009656347334384918,
-0.007958578877151012,
-0.03693738952279091,
0.002205442637205124,
-0.04369569942355156,
0.0013972342712804675,
-0.02354859933257103,
-0.011326098814606667,
-0.03597603738307953,
0.03277847170829773,
0.011628469452261925,
0.03735550865530968,
-0.023108651861548424,
0.00019640183018054813,
-0.014830213040113449,
0.004538070876151323,
-0.007437711115926504,
0.01124389749020338,
-0.016988765448331833,
0.03176090866327286,
0.011394894681870937,
-0.0015797262312844396,
0.011751681566238403,
-0.058557964861392975,
-0.033205244690179825,
0.01618068292737007,
0.034180983901023865,
0.025019416585564613,
-0.002988847903907299,
-0.026794856414198875,
-0.009167705662548542,
0.08005436509847641,
-0.02954699471592903,
0.004128295928239822,
0.014678418636322021,
-0.020862696692347527,
0.01572944037616253,
-0.02871858701109886,
-0.013770326972007751,
0.032518159598112106,
-0.0011564682936295867,
-0.0015037722187116742,
-0.03510235249996185,
0.020023943856358528,
-0.008957663550972939,
0.02007317915558815,
-0.010570270009338856,
0.06572885811328888,
-0.00478554330766201,
0.016448242589831352,
0.01589301973581314,
-0.00011426494893385097,
-0.045557811856269836,
-0.06582289189100266,
0.004948194604367018,
-0.006583617068827152,
0.004674064461141825,
0.03735807165503502,
-0.028683753684163094,
-0.08567480742931366,
0.027449171990156174,
-0.00787233654409647,
-0.021198820322752,
0.03967316076159477,
-0.016937972977757454,
0.0763571634888649,
0.031699035316705704,
-0.004718707408756018,
0.04851425811648369,
0.000039446440496249124,
-0.01565120741724968,
-0.006558435503393412,
-0.03134220838546753,
0.05610449239611626,
-0.01868051290512085,
-0.013090659864246845,
-0.05209273099899292,
0.04289712756872177,
-0.027128521353006363,
0.02333400957286358,
-0.01754610799252987,
0.01787102222442627,
0.02897615358233452,
-0.04885479435324669,
0.008077338337898254,
0.03783522546291351,
0.007820291444659233,
-0.023218629881739616,
0.031081218272447586,
0.024396082386374474,
0.028331242501735687,
-0.03998956084251404,
0.002801859751343727,
0.009433087892830372,
0.03735034167766571,
0.026348819956183434,
-0.0008958145626820624,
0.04820512235164642,
-0.037832941859960556,
0.00966890063136816,
0.034105151891708374,
-0.04922683909535408,
0.043036140501499176,
-0.012833517976105213,
0.0011498489184305072,
0.004116622265428305,
-0.03216095641255379,
-0.025354010984301567,
-0.011052493005990982,
0.012457670643925667,
-0.0005860657547600567,
-0.04666927084326744,
0.0005282083293423057,
-0.0032738978043198586,
0.028487365692853928,
-0.0681501030921936,
-0.009946172125637531,
0.007726005744189024,
-0.0010690925410017371,
-0.004161552060395479,
-0.03432247042655945,
0.010110395029187202,
0.013664623722434044,
-0.01621348224580288,
-0.02414225973188877,
0.03170759230852127,
0.004511227365583181,
0.004392777569591999,
0.023307612165808678,
0.05125979334115982,
0.02091420255601406,
0.004538620822131634,
-0.015611008740961552,
-0.021410707384347916,
0.010325944982469082,
0.026584044098854065,
0.03873467072844505,
0.025888672098517418,
-0.051627710461616516,
-0.06362783908843994,
-0.013015258125960827,
-0.02016514353454113,
0.03519367054104805,
-0.024131154641509056,
-0.004154471214860678,
0.03690868616104126,
0.01995856687426567,
-0.010554836131632328,
-0.02267754264175892,
-0.02502134069800377,
-0.01829073205590248,
0.022766143083572388,
-0.030897419899702072,
-0.038001418113708496,
-0.030777670443058014,
-0.021626576781272888,
0.0036562734749168158,
-0.012246297672390938,
-0.0035190184134989977,
-0.01068845670670271,
0.06036928668618202,
0.019847139716148376,
-0.023237768560647964,
0.02289203368127346,
-0.03131096437573433,
0.02130912058055401,
0.019987305626273155,
-0.0012128405505791306,
-0.008401952683925629,
0.018900735303759575,
-0.028105059638619423,
-0.04976706579327583,
-0.07023587822914124,
0.011974519118666649,
0.07040447741746902,
0.016206122934818268,
0.0461205393075943,
0.013162141665816307,
-0.00108973472379148,
0.004855057690292597,
-0.007656674832105637,
-0.02994152531027794,
0.03849048167467117,
-0.0009585545631125569,
0.0458776131272316,
-0.01251167617738247,
-0.0520189143717289,
0.04791948199272156,
0.049419958144426346,
-0.03257215395569801,
0.020725535228848457,
0.03216998651623726,
0.013167995028197765,
0.048752911388874054,
-0.019156642258167267,
-0.027806945145130157,
0.07093492150306702,
0.00782702025026083,
0.026893604546785355,
-0.018054896965622902,
-0.012891504913568497,
0.0470879003405571,
0.016718873754143715,
0.029649343341588974,
-0.03964497521519661,
-0.044598110020160675,
-0.01622491329908371,
0.02188262902200222,
0.04999157413840294,
-0.035556502640247345,
-0.00327658629976213,
0.03778260946273804,
0.00886103231459856,
-0.006616360507905483,
-0.0014549967600032687,
0.02461407519876957,
-0.04664850980043411,
-0.0022678575478494167,
-0.007132375612854958,
-0.07080980390310287,
0.011966829188168049,
-0.0021851619239896536,
-0.02011774852871895,
0.025095675140619278,
-0.003211228409782052,
-0.008582176640629768,
-0.018969496712088585,
-0.00048263679491356015,
0.012878510169684887,
0.03238765150308609,
-0.015008079819381237,
0.025793593376874924,
-0.012401026673614979,
0.016357505694031715,
0.10941534489393234,
0.043153535574674606,
0.01726936362683773,
-0.04494443163275719,
0.011244073510169983,
0.0049829944036901,
0.0046591563150286674,
-0.05328069254755974,
0.011179654859006405,
0.003269749926403165,
0.008357142098248005,
-0.02770528383553028,
0.059079185128211975,
0.02160983718931675,
-0.008156548254191875,
0.011096911504864693,
-0.0011188106145709753,
-0.051846884191036224,
0.013521059416234493,
0.03893023729324341,
-0.03214709460735321,
0.003085122210904956,
0.011153751984238625,
0.0054933601059019566,
-0.014372237026691437,
0.019674014300107956,
-0.06071453168988228,
-0.03667454794049263,
0.0061702062375843525,
-0.0000494546620757319,
-0.026205403730273247,
0.02988024801015854,
-0.0006298146909102798,
-0.005108793266117573,
-0.01922333799302578,
-0.0075940038077533245,
0.028834503144025803,
-0.010072248987853527,
0.0004170896136201918,
0.05810163915157318,
-0.02288074977695942,
0.00790854450315237,
0.008959776721894741,
0.0029684817418456078,
-0.020022448152303696,
-0.026021620258688927,
-0.034295909106731415,
0.06663072109222412,
-0.04452399164438248,
-0.024157511070370674,
0.018303124234080315,
0.008042801171541214,
0.002356261247768998,
-0.03575733304023743,
0.009430552832782269,
0.01222268771380186,
0.03575023263692856,
-0.02989869937300682,
-0.033225852996110916,
-0.00739887123927474,
0.01320588681846857,
-0.008857312612235546,
-0.015772532671689987,
-0.0532669872045517,
-0.011034256778657436,
0.024986805394291878,
0.009449734352529049,
0.04709674417972565,
-0.015043915249407291,
0.01026209443807602,
-0.03789150342345238,
0.006805841811001301,
-0.055778201669454575,
-0.040466465055942535,
0.007971961982548237,
0.031228313222527504,
0.024949606508016586,
-0.0002456429647281766,
-0.029511911794543266,
-0.007745977956801653,
-0.11379588395357132,
0.032697636634111404,
-0.02882680483162403,
-0.05901634693145752,
-0.0134191382676363,
0.030909040942788124,
0.018786299973726273,
0.056623686105012894,
-0.002151818247511983,
0.005075153429061174,
0.021500395610928535,
0.010735619813203812,
0.011777878738939762,
-0.029051510617136955,
-0.014076017774641514,
0.004419058095663786,
-0.045104820281267166,
0.0005062713171355426,
0.004815582185983658,
-0.017982138320803642,
0.0006206861580722034,
0.030767984688282013,
-0.015543508343398571,
0.03517135605216026,
-0.02962433360517025,
0.019845368340611458,
0.015294035896658897,
-0.05109701305627823,
0.011318733915686607,
0.003983392845839262,
0.024660171940922737,
-0.03888360410928726,
-0.03441489115357399,
-0.02447492629289627,
-0.02344026230275631,
-0.00665223877876997,
0.00862034596502781,
-0.05022610351443291,
-0.017414813861250877,
-0.0026173247024416924,
-0.0070382291451096535,
-0.011208204552531242,
0.026666365563869476,
-0.007182840723544359,
0.03343600407242775,
0.01719859428703785,
0.0023787105455994606,
-0.024965351447463036,
0.00795214343816042,
0.030465397983789444,
-0.018225446343421936,
0.006216945592314005,
0.037770092487335205,
0.00002179584225814324,
-0.010695948265492916,
0.014605981297791004,
0.006489440333098173,
0.03750882297754288,
-0.002783771837130189,
-0.02460468001663685,
0.04946441948413849,
-0.023501906543970108,
-0.037914495915174484,
0.028043650090694427,
0.013567181304097176,
0.017526164650917053,
0.06997525691986084,
0.025346387177705765,
-0.013548756018280983,
0.02929890714585781,
-0.033342596143484116,
0.016167636960744858,
-0.002347958739846945,
-0.04763812944293022,
0.002844196278601885,
-0.001808379776775837,
0.03240898996591568,
0.006625319831073284,
-0.007706712931394577,
0.01228273194283247,
0.004956494085490704,
0.0008812042069621384,
0.02405036985874176,
0.002740182215347886,
0.000488888646941632,
0.038677096366882324,
0.004882899112999439,
0.0045091682113707066,
0.019077278673648834,
0.052187226712703705,
-0.014432201161980629,
0.02699028141796589,
0.03028155118227005,
0.009806063026189804,
-0.07628390192985535,
-0.014486199244856834,
0.008566775359213352,
-0.00944451242685318,
0.025579379871487617,
-0.039377354085445404,
0.012471594847738743,
0.01970818266272545,
-0.09091861546039581,
0.04936307668685913,
-0.025191035121679306,
0.01848999410867691,
-0.00896627176553011,
0.0045836316421628,
-0.03936219587922096,
0.08101769536733627,
0.03658399358391762,
0.026855316013097763,
-0.0037767316680401564,
-0.004922822117805481,
-0.007387201301753521,
-0.03924140706658363,
0.0179757047444582,
0.06274954229593277,
0.024137524887919426,
-0.022029943764209747,
0.057303864508867264,
-0.0342598520219326,
-0.029934540390968323,
0.020110908895730972,
0.0014145722379907966,
-0.01536975335329771,
-0.037481654435396194,
-0.01821940392255783,
-0.038217585533857346,
0.053169745951890945,
0.015386995859444141,
0.004769823048263788,
-0.008447426371276379,
0.009711740538477898,
0.014503329060971737,
-0.0010865433141589165,
-0.001196746132336557,
-0.0010193863417953253,
0.02202911488711834,
-0.01405327208340168,
-0.006895997561514378,
0.104576975107193,
-0.025428446009755135,
0.001966254087164998,
0.004248057026416063,
-0.025722291320562363,
0.024627307429909706,
-0.018151605501770973,
0.029667455703020096,
-0.06148529052734375,
0.011010975576937199,
0.0008036398212425411,
0.018739433959126472,
-0.01569611206650734,
0.007509566377848387,
-0.01405242271721363,
-0.05205989256501198,
0.04615333303809166,
0.029793962836265564,
-0.0514233335852623,
-0.04335273802280426,
-0.026219598948955536,
0.00868314504623413,
0.020076332613825798,
0.019646571949124336,
-0.062033385038375854,
-0.03267282992601395,
0.04137713462114334,
0.004390818066895008,
0.013433876447379589,
-0.045060157775878906,
-0.024421852082014084,
-0.031678617000579834,
-0.05652724206447601,
0.04063811153173447,
0.04179557412862778,
-0.032439399510622025,
0.003416870953515172,
0.00467775808647275,
0.003074675565585494,
-0.02669374644756317,
0.05177932605147362,
0.028763968497514725,
0.024569904431700706,
0.006203715223819017,
-0.01921009086072445,
0.007431511767208576,
-0.032694075256586075,
-0.028436779975891113,
0.0006348806200549006,
-0.006851282902061939,
0.001476049772463739,
0.030693860724568367,
-0.026057545095682144,
-0.0037061781622469425,
0.04379540681838989,
-0.02060054987668991,
0.012586524710059166,
0.02313734032213688,
-0.028689531609416008,
0.04867130145430565,
-0.01413044799119234,
0.009696830995380878,
0.043604545295238495,
-0.000026244690161547624,
0.0018462908919900656,
0.034323327243328094,
-0.018009519204497337,
-0.040960341691970825,
-0.008788260631263256,
-0.037181541323661804,
-0.05044804885983467,
-0.013276265002787113,
0.0032950604800134897,
0.026107724756002426,
-0.005121913272887468,
0.01713320054113865,
0.03704792633652687,
-0.04680335521697998,
-0.044314250349998474,
0.05508384853601456,
0.011667893268167973,
0.018200591206550598,
-0.006704562809318304,
0.02641267515718937,
0.02709455043077469,
0.007094032596796751,
-0.004434024915099144,
0.03981442004442215,
0.05047105252742767,
0.04567918926477432,
0.016858482733368874,
0.04540867358446121,
-0.008341006003320217,
0.03134932368993759,
0.0022943250369280577,
-0.0026627653278410435,
-0.0304630808532238,
0.007506616413593292,
0.027445113286376,
-0.028377901762723923,
0.009013991802930832,
-0.03272479027509689,
-0.033961035311222076,
0.12282394617795944,
-0.019356902688741684,
-0.013033191673457623,
-0.041013453155756,
-0.013682744465768337,
-0.03040994703769684,
-0.015044301748275757,
0.026739807799458504,
0.043848663568496704,
-0.001971517689526081,
0.021110322326421738,
-0.04387042671442032,
0.005476688500493765,
0.022999456152319908,
-0.054656077176332474,
-0.02497708797454834,
0.03216016665101051,
0.006870264653116465,
-0.005171206779778004,
0.0019479462644085288,
-0.03453926369547844,
-0.007476074155420065,
0.023387979716062546,
0.012413612566888332,
0.03380146995186806,
0.005144316237419844,
0.017661694437265396,
-0.01645142026245594,
0.050160158425569534,
-0.05542938783764839,
-0.059930283576250076,
-0.03162400424480438,
0.015301705338060856,
-0.014530947431921959,
-0.019490987062454224
] |
<p>I've been wondering exactly why the elements are distributed the way they are on Earth. The heavier elements have their origins in the centers of stars, or in supernovae. After the death of the stars, you end up with a dust cloud containing the heavier elements. Later, planets form out of these along with new stars.</p>
<p>If the heavier elements were randomly distributed in these explosions, how do we end up with special deposits of minerals on Earth? We have mines and special areas where the concentrations of different materials are higher. For example, we have iron, gold, nickel and uranium mines. Why aren't these materials uniformly distributed? Why isn't the Earth composed of a substance which is a uniform mixture of all the heavy elements? Why does it seem there is sometimes a preference for like materials to clump together?</p>
<p>The nickel and iron mostly make up the Earth's core, which I guess makes sense in terms of them being fairly heavy while comparatively abundant relative to heavier elements, but what about everything near the surface that we observe?</p> | 4,597 | [
-0.04474712535738945,
-0.012133512645959854,
0.004946249537169933,
-0.025116294622421265,
0.06203267350792885,
-0.0025505695957690477,
-0.0409114733338356,
-0.02019774354994297,
0.004241323564201593,
-0.062381815165281296,
0.012401146814227104,
0.03756056725978851,
0.062087785452604294,
0.022272929549217224,
0.02836141176521778,
-0.010695838369429111,
0.03134240210056305,
-0.03777512162923813,
-0.03759100288152695,
-0.016591189429163933,
0.010200371034443378,
-0.006207534112036228,
-0.0008295343141071498,
0.022747233510017395,
-0.03879081457853317,
0.019640177488327026,
-0.015087783336639404,
-0.01691950485110283,
0.04031851887702942,
0.03631366416811943,
0.026716386899352074,
0.0026983865536749363,
0.018256373703479767,
0.03921840339899063,
0.06311468034982681,
0.005305509548634291,
-0.009304299019277096,
-0.019005022943019867,
-0.04357459396123886,
0.04189359024167061,
-0.05972838029265404,
-0.027867557480931282,
-0.028925737366080284,
0.0009068305371329188,
-0.014550858177244663,
0.01712322235107422,
0.02263217605650425,
-0.012092831544578075,
0.04420642554759979,
-0.07067986577749252,
0.02162182703614235,
0.011477550491690636,
0.033542245626449585,
0.04339782893657684,
-0.004067169968038797,
-0.009869449771940708,
0.05538992956280708,
0.042140547186136246,
0.035848118364810944,
-0.021224845200777054,
0.0034719223622232676,
0.0007868027896620333,
-0.02006950043141842,
-0.013256683945655823,
0.008366544730961323,
0.04743197560310364,
-0.015808068215847015,
-0.040923405438661575,
0.015378717333078384,
0.016301264986395836,
0.035040050745010376,
0.02093459665775299,
0.008090948686003685,
-0.0023032077588140965,
-0.008099496364593506,
-0.04803122207522392,
0.08016529679298401,
-0.027644552290439606,
0.04360539838671684,
0.017163429409265518,
0.0006596499588340521,
0.010418222285807133,
0.004316327627748251,
-0.001495018252171576,
0.005104637239128351,
0.033288564532995224,
0.06703486293554306,
-0.012241900898516178,
0.01830168254673481,
0.023563578724861145,
0.009828455746173859,
0.02580113895237446,
0.04531068354845047,
0.00840291939675808,
-0.015818733721971512,
0.000286190421320498,
-0.007759439293295145,
0.022141696885228157,
-0.0026481931563466787,
0.018313562497496605,
0.013520894572138786,
-0.010490036569535732,
0.030496060848236084,
0.07796520739793777,
0.010943494737148285,
-0.028340687975287437,
-0.07802629470825195,
0.00899122841656208,
-0.02865312620997429,
-0.006152006797492504,
-0.010108206421136856,
0.03227386996150017,
0.026552647352218628,
-0.018086260184645653,
0.013905865140259266,
0.006917919963598251,
0.04478072002530098,
-0.05663776025176048,
0.045197512954473495,
0.06933362782001495,
0.015432694926857948,
-0.017785120755434036,
0.03959101438522339,
-0.036931607872247696,
-0.04542809724807739,
0.01337983924895525,
0.016715295612812042,
-0.014074014499783516,
-0.023254720494151115,
0.044141411781311035,
-0.027464980259537697,
-0.0046176426112651825,
0.010347318835556507,
0.0010274320375174284,
0.020785409957170486,
-0.006922196131199598,
-0.10017953813076019,
-0.06409759074449539,
0.0175220537930727,
-0.00008891230390872806,
-0.027947556227445602,
-0.05504867434501648,
-0.0002914127253461629,
0.007839111611247063,
0.04617336392402649,
0.0042875297367572784,
-0.009297071024775505,
-0.0038648906629532576,
0.0375947430729866,
0.023681355640292168,
-0.02590826153755188,
-0.04185357317328453,
0.010625644586980343,
-0.04902544990181923,
0.021775593981146812,
-0.0860082283616066,
0.01824401505291462,
0.004718231502920389,
0.02783150225877762,
-0.029510099440813065,
0.008798382245004177,
-0.025569014251232147,
-0.015877539291977882,
-0.011673078872263432,
0.008174172602593899,
-0.006418975535780191,
0.057047415524721146,
0.053029999136924744,
0.04005640372633934,
0.0402546189725399,
0.02435881644487381,
0.030066831037402153,
0.03983571007847786,
0.07028809934854507,
0.0006917737773619592,
-0.03561658412218094,
-0.001163081149570644,
-0.03433835133910179,
0.007386651821434498,
0.008148894645273685,
-0.026295578107237816,
-0.03146045655012131,
-0.0017388291889801621,
0.016354413703083992,
0.03774203732609749,
0.04976343736052513,
0.03961314260959625,
-0.04807734489440918,
0.027810880914330482,
-0.02045869641005993,
0.003908948507159948,
-0.037167251110076904,
-0.022896267473697662,
-0.0266885943710804,
-0.047523438930511475,
0.01794390194118023,
0.0013288491172716022,
-0.005578888580203056,
-0.004940416198223829,
-0.012072762474417686,
0.025423169136047363,
0.028625058010220528,
0.02115410938858986,
0.0002765445678960532,
-0.0001634173677302897,
0.09319363534450531,
-0.01036515086889267,
0.006060980260372162,
0.033242449164390564,
-0.011415847577154636,
-0.04711833968758583,
-0.017960593104362488,
-0.003713979385793209,
0.00012496071576606482,
0.017710154876112938,
-0.03403628617525101,
-0.006683810614049435,
0.010893989354372025,
0.0087471017614007,
0.02103539928793907,
-0.03713057562708855,
0.13573633134365082,
0.03491083160042763,
-0.014307566918432713,
-0.008731688372790813,
0.04303551837801933,
0.011581898666918278,
0.017732854932546616,
-0.00966533925384283,
-0.01697867549955845,
-0.08961569517850876,
-0.016747642308473587,
0.027957813814282417,
0.026922432705760002,
-0.022280288860201836,
0.01588040590286255,
0.013939518481492996,
0.06297557801008224,
0.02076089382171631,
-0.0013594496995210648,
-0.033936843276023865,
-0.020586088299751282,
0.004889810457825661,
-0.01528090052306652,
0.029530439525842667,
0.03662797063589096,
0.008106490597128868,
0.029994050040841103,
-0.006465198006480932,
-0.05618013069033623,
-0.01980130933225155,
0.00665986118838191,
0.015985548496246338,
0.02049589715898037,
0.002987951273098588,
-0.021216943860054016,
0.022764509543776512,
-0.017209086567163467,
0.015129431150853634,
0.02110910229384899,
0.014009763486683369,
-0.017583006992936134,
-0.04449538514018059,
-0.01908646710216999,
0.011988041922450066,
0.03376171365380287,
-0.020962363108992577,
-0.003582995617762208,
0.014510487206280231,
-0.01620541512966156,
0.0029461446683853865,
-0.00964284222573042,
0.0019012076081708074,
-0.05405740439891815,
0.019020721316337585,
0.041691023856401443,
0.021137507632374763,
-0.012698967941105366,
-0.02273472398519516,
-0.016202721744775772,
-0.03672214224934578,
-0.011137561872601509,
-0.01578272320330143,
0.03751813992857933,
-0.06355441361665726,
0.03515443205833435,
0.004532655235379934,
-0.012963494285941124,
0.04340058192610741,
0.05167675390839577,
0.016203857958316803,
0.0016917166067287326,
0.0000033107749004557263,
-0.038822829723358154,
0.007552360184490681,
0.028527595102787018,
-0.003896919311955571,
-0.005903417244553566,
0.016358070075511932,
0.07888256013393402,
-0.05442618206143379,
-0.006646925583481789,
0.024318484589457512,
-0.05777062103152275,
-0.05543552339076996,
-0.042290814220905304,
-0.0009892380330711603,
-0.03748232126235962,
-0.02177070826292038,
0.0024212487041950226,
0.06402628868818283,
-0.051604483276605606,
-0.03791799768805504,
-0.03177428990602493,
-0.042565084993839264,
-0.017392905429005623,
-0.06325811892747879,
0.04418638348579407,
-0.006074290722608566,
-0.00684136338531971,
0.07490365952253342,
0.057000625878572464,
-0.010381403379142284,
-0.021433332934975624,
0.004463879857212305,
-0.003711218247190118,
0.016052978113293648,
0.06262676417827606,
0.03024500235915184,
0.006764506455510855,
0.00699077732861042,
0.028267694637179375,
0.04519249126315117,
0.028417780995368958,
0.00667179049924016,
-0.022125476971268654,
0.04221706464886665,
0.012310405261814594,
-0.00018246209947392344,
0.024164773523807526,
-0.001737335347570479,
-0.007099051494151354,
0.014675176702439785,
-0.008595345541834831,
0.04801119863986969,
0.02889557182788849,
-0.029871009290218353,
0.014189784415066242,
0.009159475564956665,
0.0017730140825733542,
-0.06490478664636612,
0.03652716428041458,
0.008131682872772217,
-0.004902179352939129,
-0.02092612534761429,
-0.014561488293111324,
0.07381542772054672,
0.003955688327550888,
-0.02569109946489334,
0.0059386431239545345,
0.053983598947525024,
-0.03556062653660774,
-0.015306957066059113,
0.0025979802012443542,
0.02797110006213188,
-0.010013689287006855,
-0.016807714477181435,
0.03175003081560135,
0.046569231897592545,
0.032107576727867126,
0.007663742173463106,
-0.031232798472046852,
-0.04866110160946846,
-0.01061205379664898,
-0.06870783120393753,
-0.0053373356349766254,
0.006320249754935503,
0.03605874627828598,
0.004355650395154953,
0.07482210546731949,
0.016070177778601646,
-0.008515845984220505,
-0.01917959377169609,
-0.01770530827343464,
-0.08293870091438293,
0.007093643769621849,
-0.031098993495106697,
-0.011338473297655582,
-0.01969839446246624,
-0.0028542729560285807,
-0.03514821454882622,
-0.03125356510281563,
-0.03168762847781181,
-0.022274725139141083,
-0.0147605175152421,
-0.043260812759399414,
0.024646546691656113,
-0.02490140125155449,
-0.05397777631878853,
-0.01930449716746807,
0.035350773483514786,
0.0359552800655365,
-0.0033475039526820183,
0.05605513975024223,
-0.018947236239910126,
-0.029953790828585625,
0.01583428867161274,
-0.04066168889403343,
0.001452288357540965,
0.011849195696413517,
0.008330353535711765,
-0.010068867355585098,
0.014824840240180492,
0.0011385433608666062,
-0.0011445716954767704,
0.01208520121872425,
0.0464879535138607,
0.0012969699455425143,
-0.005349769722670317,
-0.01765819638967514,
-0.016497278586030006,
-0.03229152411222458,
0.020521020516753197,
-0.003989610821008682,
-0.03397404029965401,
0.004965722095221281,
0.02655438892543316,
-0.00035749044036492705,
-0.02328016795217991,
0.033182255923748016,
0.025894036516547203,
-0.002895936369895935,
-0.007021698169410229,
-0.017923502251505852,
-0.021190183237195015,
-0.022706154733896255,
0.00582794239744544,
0.026943214237689972,
0.007057972252368927,
0.0062834895215928555,
-0.013292305171489716,
0.018890082836151123,
0.0061770542524755,
-0.016490422189235687,
-0.013665245845913887,
-0.009792651049792767,
0.04301360994577408,
-0.021301398053765297,
-0.0147102577611804,
0.011138571426272392,
0.004167366307228804,
0.06500626355409622,
-0.00800496805459261,
-0.0085734399035573,
-0.04547344893217087,
-0.024214159697294235,
0.011582089588046074,
0.01564800925552845,
-0.04211064428091049,
0.02358000911772251,
-0.04597964510321617,
-0.04420419782400131,
0.03345746546983719,
-0.027465127408504486,
0.031878333538770676,
-0.035799041390419006,
-0.010946463793516159,
0.022676018998026848,
-0.041222140192985535,
0.007271999958902597,
0.015898287296295166,
-0.014668729156255722,
0.025111475959420204,
0.006044539622962475,
0.0040957205928862095,
-0.025748275220394135,
0.03853042051196098,
0.03649357706308365,
0.0269185621291399,
0.0012604830553755164,
0.003487142501398921,
-0.01066361740231514,
-0.009437592700123787,
0.007461496163159609,
-0.07640861719846725,
-0.035356126725673676,
-0.0022258723620325327,
-0.002808295888826251,
0.023894116282463074,
-0.016313791275024414,
-0.07268080860376358,
0.03751356154680252,
0.021374015137553215,
-0.019371232017874718,
-0.03355748578906059,
-0.023888148367404938,
0.05407634750008583,
0.04534795135259628,
0.009288843721151352,
0.02863767370581627,
0.007248518988490105,
-0.02160760760307312,
0.002806029049679637,
-0.04883703961968422,
0.0290924571454525,
-0.027623403817415237,
0.03131066635251045,
-0.005479607731103897,
0.007895450107753277,
-0.008835028856992722,
0.033222831785678864,
0.048613451421260834,
0.004435354378074408,
-0.006054154597222805,
-0.05731463059782982,
0.021590949967503548,
0.008676008321344852,
0.026787471026182175,
0.009800498373806477,
0.011330676265060902,
0.0408647395670414,
0.004014001227915287,
-0.003945809789001942,
0.04876720905303955,
-0.004591088276356459,
0.0048660640604794025,
0.005250278394669294,
-0.013330135494470596,
0.008717510849237442,
-0.07359780371189117,
-0.01318154763430357,
0.012836694717407227,
-0.03595539554953575,
0.059815093874931335,
0.01237932313233614,
0.04052374139428139,
0.0313333235681057,
-0.02981557697057724,
-0.01997094601392746,
-0.019150374457240105,
-0.029825527220964432,
0.03569651395082474,
-0.03765847533941269,
0.02046082355082035,
0.002256333827972412,
0.028257057070732117,
-0.09653361886739731,
-0.04330737888813019,
0.01194682065397501,
0.01067536510527134,
-0.024811312556266785,
-0.053112611174583435,
0.024869659915566444,
0.005366060417145491,
-0.015355885028839111,
0.004591506440192461,
0.03182071074843407,
-0.023828476667404175,
-0.010631212033331394,
0.01837124116718769,
0.0402199923992157,
0.07750798016786575,
-0.030581925064325333,
-0.04105105996131897,
0.029741957783699036,
0.0023512011393904686,
0.027212249115109444,
-0.03570146858692169,
0.02979222685098648,
-0.03884920850396156,
-0.05884171277284622,
0.02516428381204605,
0.023219749331474304,
0.025134259834885597,
-0.019009901210665703,
-0.010138272307813168,
0.030203763395547867,
0.00044709359644912183,
0.00381688610650599,
-0.014099713414907455,
0.047186437994241714,
0.007557603530585766,
-0.008849489502608776,
-0.04095045477151871,
0.015320739708840847,
0.0050852796994149685,
-0.05416024848818779,
0.04089132696390152,
-0.04368229955434799,
0.02413691207766533,
0.009835507720708847,
0.03242048621177673,
0.012267966754734516,
-0.011235899291932583,
0.03315286338329315,
0.00044326248462311924,
0.011846540495753288,
-0.006384484004229307,
-0.0009166878880932927,
0.044480811804533005,
0.0013949136482551694,
-0.009632203727960587,
-0.01004995871335268,
-0.021885083988308907,
0.02640092559158802,
0.04991183802485466,
-0.036512162536382675,
0.01839030720293522,
0.03266723081469536,
-0.014570794068276882,
0.016399072483181953,
-0.06347532570362091,
-0.020993705838918686,
-0.017014818266034126,
-0.045210450887680054,
0.030445197597146034,
-0.007015535142272711,
0.006804932840168476,
0.06233493611216545,
0.06072647497057915,
-0.021963467821478844,
0.026426274329423904,
0.015769939869642258,
-0.01121868472546339,
0.028499210253357887,
0.030330641195178032,
-0.05249672755599022,
0.020235661417245865,
-0.011699330061674118,
0.02651936560869217,
0.0395708866417408,
-0.03970051929354668,
0.0573943667113781,
0.0013660667464137077,
-0.041813213378190994,
-0.04960767179727554,
-0.043224215507507324,
-0.02087184228003025,
0.01854563318192959,
0.018105272203683853,
0.006869103293865919,
-0.024365440011024475,
0.012713942676782608,
0.008298822678625584,
-0.010492302477359772,
-0.04386169835925102,
0.019398106262087822,
-0.07849310338497162,
-0.023818956688046455,
-0.03313598781824112,
-0.0714661106467247,
-0.001632185885682702,
-0.03933921828866005,
-0.058122120797634125,
0.002975663635879755,
-0.03521494194865227,
0.004584473557770252,
0.01382583286613226,
-0.002729460597038269,
-0.03198137506842613,
0.048325106501579285,
0.002293936675414443,
0.025776332244277,
0.0017055502394214272,
-0.007206824142485857,
0.11226637661457062,
0.033694587647914886,
0.004476814065128565,
-0.01443187054246664,
-0.006637842394411564,
-0.013429035432636738,
-0.02000236324965954,
0.015157617628574371,
-0.01764492504298687,
-0.01828579604625702,
0.05507223680615425,
-0.00853877142071724,
0.021149640902876854,
0.016273310407996178,
0.011785351671278477,
0.05558306723833084,
-0.0415651835501194,
-0.0018594932043924928,
-0.0365171805024147,
-0.0034924803767353296,
-0.017075199633836746,
0.01571183279156685,
-0.07923971861600876,
0.04013828560709953,
-0.013662736862897873,
-0.018306031823158264,
-0.02732403762638569,
-0.019496843218803406,
-0.012013872154057026,
0.026549341157078743,
-0.032041020691394806,
-0.008830834180116653,
0.02094442956149578,
-0.061357785016298294,
-0.006326901260763407,
-0.001185061177238822,
0.030102768912911415,
-0.023942967876791954,
0.018785271793603897,
-0.01991259679198265,
0.007355185691267252,
0.02374083176255226,
-0.01187579333782196,
0.04394233599305153,
-0.04029181972146034,
-0.005957677960395813,
-0.03484201431274414,
0.0474364198744297,
-0.0377843864262104,
-0.03208814188838005,
0.0011946106096729636,
-0.007674036547541618,
0.035288188606500626,
-0.006697888486087322,
-0.0008574635139666498,
-0.003958364482969046,
0.03381936624646187,
-0.01654910109937191,
-0.02844456396996975,
0.0046363831497728825,
0.011049416847527027,
-0.0068449899554252625,
0.02108653262257576,
0.018435461446642876,
0.000432320375693962,
-0.0025651922915130854,
-0.02843080833554268,
-0.002739467192441225,
0.005958128720521927,
-0.0018992546247318387,
-0.05701032280921936,
-0.004119144752621651,
-0.050993163138628006,
0.014414796605706215,
0.003064609132707119,
0.031131817027926445,
0.05241021513938904,
0.01980838179588318,
-0.013330659829080105,
-0.009278738871216774,
0.021523185074329376,
0.05620959773659706,
-0.03203940764069557,
-0.030568420886993408,
-0.04546869173645973,
-0.004833763465285301,
-0.022083133459091187,
0.009383147582411766,
-0.02397196926176548,
0.021223710849881172,
-0.006582516711205244,
0.005376383196562529,
0.0054410104639828205,
-0.033684875816106796,
-0.0032779970206320286,
0.021232999861240387,
-0.020082825794816017,
0.021665923297405243,
0.016543500125408173,
0.01755393296480179,
0.03193820267915726,
-0.019791698083281517,
0.03275733068585396,
0.03336222469806671,
-0.008190208114683628,
0.02753659524023533,
0.016742343083024025,
-0.039042819291353226,
-0.016666840761899948,
0.020898859947919846,
-0.027454407885670662,
-0.02653590589761734,
-0.014134824275970459,
-0.03391427546739578,
-0.01601150818169117,
0.005902852863073349,
0.05186174064874649,
-0.011934584006667137,
0.02422432042658329,
-0.05098821967840195,
0.04563241824507713,
-0.02842468023300171,
0.0026047201827168465,
-0.05556826665997505,
0.006745263934135437,
-0.010527272708714008,
-0.020532991737127304,
-0.020083744078874588,
0.026278844103217125,
0.0046805511228740215,
-0.00970086082816124,
0.03351949527859688,
-0.025901485234498978,
0.03711392357945442,
0.02519294247031212,
0.0005801610532216728,
-0.03006434254348278,
0.05969591066241264,
-0.02118646912276745,
0.002938472433015704,
0.020085418596863747,
0.007438345346599817,
-0.06676918268203735,
0.009490610100328922,
-0.022936901077628136,
0.013324914500117302,
0.008260154165327549,
-0.015671242028474808,
-0.02194550260901451,
0.07053516805171967,
-0.025102728977799416,
-0.018334820866584778,
-0.0031512670684605837,
0.04397622123360634,
0.02433491311967373,
0.018538281321525574,
0.010865959338843822,
-0.02978140115737915,
-0.022557079792022705,
0.030053237453103065,
-0.005410864017903805,
0.013089960440993309,
-0.0031535543967038393,
0.0032955165952444077,
-0.06105225160717964,
0.0068171401508152485,
0.02346207946538925,
0.013737425208091736,
0.016804583370685577,
0.03388363495469093,
-0.06369733065366745,
0.07484092563390732,
0.05673104152083397,
-0.024430660530924797,
-0.04795166477560997,
-0.03464978188276291,
-0.008496948517858982,
-0.037897638976573944,
-0.0085458280518651,
-0.03302593156695366,
-0.02187252789735794,
0.02815980277955532,
-0.10670123994350433,
0.020169366151094437,
-0.03349193558096886,
-0.04764995351433754,
-0.032217640429735184,
-0.004541189409792423,
-0.02094944752752781,
0.030307671055197716,
0.02617804892361164,
0.07704196125268936,
0.06197476014494896,
0.00985327735543251,
-0.005622532218694687,
0.023940786719322205,
-0.0271229799836874,
0.00311313197016716,
-0.02702138014137745,
0.020103352144360542,
0.04185076057910919,
0.023829443380236626,
-0.01490228995680809,
0.019073249772191048,
-0.005590491462498903,
0.000027552370738703758,
0.021252473816275597,
-0.012695137411355972,
-0.019260812550783157,
0.03208213672041893,
-0.01611887849867344,
0.002484019845724106,
-0.0023182937875390053,
0.02153756096959114,
0.02855140157043934,
0.032947439700365067,
0.01428914349526167,
0.020063987001776695,
0.04739202931523323,
-0.04325103014707565,
0.021045131608843803,
0.011892044916749,
-0.00016598004731349647,
0.023190192878246307,
0.018208779394626617,
0.05111129581928253,
0.02893805131316185,
0.01894797571003437,
-0.013413485139608383,
-0.017401941120624542,
-0.038410086184740067,
0.008312412537634373,
0.0009019728749990463,
-0.0009280617232434452,
0.04860956221818924,
-0.01753622107207775,
-0.00017150690837297589,
-0.06716574728488922,
0.02662668749690056,
-0.018610643222928047,
-0.013373475521802902,
0.005249754525721073,
0.023172877728939056,
-0.01149932760745287,
-0.0021930313669145107,
-0.029676130041480064,
-0.0328352265059948,
0.06148203834891319,
0.019374024122953415,
0.03607485815882683,
-0.024671019986271858,
-0.04625418782234192,
0.004222394898533821,
-0.03499949723482132,
0.04405081272125244,
-0.055801521986722946,
0.005207065958529711,
-0.030310116708278656,
-0.029451491311192513,
-0.0021295438054949045,
0.02505667693912983,
0.03503616899251938,
0.02003747597336769,
0.02774033509194851,
-0.008898821659386158,
-0.03355007991194725,
0.0677228793501854,
-0.05264604464173317,
0.04603642225265503,
0.03632553666830063,
-0.019201599061489105,
0.017812248319387436,
-0.022805236279964447,
0.006740480661392212,
0.030380431562662125,
0.00497473357245326,
-0.03535984829068184,
0.0026764587964862585,
0.008162115700542927,
0.01760593242943287,
0.04989693686366081,
-0.019973134621977806,
-0.029327096417546272,
0.07600314170122147,
-0.021981604397296906,
0.016533328220248222,
0.03328336402773857,
0.0009021268342621624,
-0.04367706924676895,
0.040622349828481674,
-0.017685050144791603,
-0.042591631412506104,
0.008345263078808784,
0.006989569868892431,
0.044021762907505035,
-0.05124379321932793,
0.028684323653578758,
-0.00017977814422920346,
-0.017124826088547707,
-0.024758033454418182,
0.019221071153879166,
0.00371146178804338,
0.0749901533126831,
0.018609359860420227,
-0.00828556902706623,
-0.020049797371029854,
-0.02785571478307247,
0.004048608709126711,
0.03495188057422638,
0.006226690486073494,
0.004567560274153948,
0.008145094849169254,
-0.006428866181522608,
0.006749496795237064,
0.01271218154579401,
0.004387218039482832,
0.024572569876909256,
-0.06527646631002426,
-0.0013344534672796726,
0.03489476069808006,
-0.021595781669020653,
0.009178133681416512,
0.024919066578149796,
-0.024095015600323677,
0.09324005246162415,
0.012848508544266224,
-0.0034179887734353542,
-0.020306365564465523,
-0.018579181283712387,
0.019297456368803978,
-0.008786892518401146,
-0.037509966641664505,
0.00445086695253849,
0.0017503509297966957,
-0.025694364681839943,
-0.034502893686294556,
0.03906656429171562,
0.04994838312268257,
-0.0017473811749368906,
0.019134096801280975,
-0.020823484286665916,
-0.039727624505758286,
-0.003245556028559804,
0.0045157563872635365,
-0.04735960811376572,
-0.059214457869529724,
0.028944434598088264,
0.03622657433152199,
0.018664177507162094,
0.0170290544629097,
-0.0340711884200573,
-0.02557494305074215,
0.03695147484540939,
-0.06319143623113632,
-0.0073837595991790295,
-0.0604400560259819,
0.026422858238220215,
-0.033043865114450455,
-0.028423026204109192
] |
<blockquote>
<p><em>A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation.</em></p>
</blockquote>
<p>I know that:</p>
<p>Angular momentum is conserved and therefore $\vec{L}=\vec{r} \times \vec{p}=\vec{r} \times m\vec{v}=constant$ and $L=mrv\sin\theta$.</p>
<p>Kepler's $2^{nd}$ law means $\frac{dA}{dt}=constant$</p>
<p>Somehow this comes out to be $dA=(\frac{1}{2})(\frac{L}{m})dt$ but I'm having a hard time getting there.</p>
<blockquote>
<p><em>B) Explain how circular motion can be described as simple harmonic motion.</em></p>
</blockquote>
<p>I know that:</p>
<p>For circular motion
$m\vec{a}=\vec{F}_{c}=-m\frac{v^2}{R}\vec{r}=-m\omega^2R\vec{r}$</p>
<p>However, I'm fairly lost on this equation. Where does the negative sign come from, and where does the $\vec{r}$ come from?</p> | 4,598 | [
-0.036903977394104004,
-0.022954387590289116,
-0.03380424156785011,
0.026147685945034027,
0.06826572865247726,
-0.00980012770742178,
-0.050483714789152145,
-0.015154341235756874,
0.011098838411271572,
-0.028570113703608513,
0.005718003027141094,
0.020980678498744965,
0.04194767773151398,
0.010833241045475006,
0.03606835752725601,
-0.03381478786468506,
0.010626232251524925,
-0.049897272139787674,
0.0015125401550903916,
-0.0008590616635046899,
-0.00945907924324274,
-0.027818845584988594,
0.04167264327406883,
0.013952890411019325,
-0.008099712431430817,
0.0394975021481514,
0.053962528705596924,
-0.011354539543390274,
0.011838946491479874,
0.058315426111221313,
0.012043311260640621,
-0.0036701452918350697,
0.02409888431429863,
0.043031662702560425,
0.022673139348626137,
0.02024877443909645,
-0.04217417165637016,
-0.009795579127967358,
-0.004479245748370886,
0.06059188395738602,
-0.03831244632601738,
-0.01128328312188387,
-0.01369139552116394,
0.05045280233025551,
-0.03311644867062569,
0.017459258437156677,
0.023573147132992744,
0.020772377029061317,
0.06303580105304718,
-0.03805457428097725,
0.07537014037370682,
0.014561770483851433,
0.04125891625881195,
0.011386651545763016,
0.002513796789571643,
-0.00302936602383852,
0.07253960520029068,
0.07508468627929688,
0.015896134078502655,
-0.04239066317677498,
-0.011673148721456528,
-0.0041780234314501286,
-0.017792263999581337,
-0.0015333298360928893,
-0.01950247958302498,
0.01908096857368946,
-0.003266584360972047,
0.0026618961710482836,
0.03201361000537872,
0.037694916129112244,
0.054974254220724106,
0.005837411619722843,
0.00005525106826098636,
-0.03665831312537193,
0.016970185562968254,
-0.05933611840009689,
0.013025715947151184,
0.017642050981521606,
-0.007396680768579245,
0.03390858694911003,
-0.017567604780197144,
0.002438831841573119,
0.010572222992777824,
0.04850856214761734,
-0.01744423247873783,
0.02567504718899727,
0.04707843437790871,
0.03320106118917465,
0.012846206314861774,
0.022414684295654297,
0.0412868931889534,
0.025698702782392502,
0.038701239973306656,
-0.03001335635781288,
-0.022128038108348846,
0.03159352391958237,
-0.009312319569289684,
0.0429479219019413,
0.03141232579946518,
-0.016348982229828835,
-0.010976583696901798,
-0.023464148864150047,
0.03856462612748146,
0.057655368000268936,
-0.0017387813422828913,
-0.025798995047807693,
-0.03250019997358322,
0.000896037498023361,
-0.009468577802181244,
-0.03373955562710762,
-0.03657810017466545,
0.011044100858271122,
0.00817074254155159,
-0.010432742536067963,
-0.004139208700507879,
-0.009223835542798042,
-0.025167783722281456,
0.015383592806756496,
0.04742661863565445,
0.05536763370037079,
0.039251700043678284,
-0.015251749195158482,
0.029978014528751373,
-0.052201587706804276,
-0.05579182505607605,
-0.011036455631256104,
0.012280520051717758,
0.03402961418032646,
-0.005900425836443901,
0.024882584810256958,
0.039154984056949615,
-0.013307813555002213,
-0.04802441969513893,
0.010882229544222355,
0.011309683322906494,
-0.008809858933091164,
-0.10016657412052155,
-0.06303109228610992,
0.021269436925649643,
0.0009193905862048268,
-0.04132962226867676,
-0.06114603951573372,
0.010467219166457653,
0.007304144557565451,
0.0933673158288002,
-0.004035463090986013,
-0.03947301581501961,
0.011892927810549736,
0.04767952859401703,
-0.011674012988805771,
-0.044967226684093475,
-0.012326871044933796,
0.008421770296990871,
-0.026696696877479553,
0.015504300594329834,
-0.07884857058525085,
0.005030762869864702,
0.029635872691869736,
0.020754100754857063,
-0.0177631713449955,
0.08170890808105469,
-0.02573380433022976,
0.0011048850137740374,
0.04551657661795616,
-0.0017113274661824107,
-0.011759299784898758,
0.09245149046182632,
0.008747374638915062,
-0.024478189647197723,
0.06775554269552231,
0.021010255441069603,
0.025702638551592827,
-0.031271792948246,
0.018644245341420174,
0.059290140867233276,
-0.023171687498688698,
-0.010331254452466965,
-0.026900768280029297,
0.022002223879098892,
0.009398067370057106,
-0.05055985972285271,
-0.04802832752466202,
0.004118995275348425,
-0.011151355691254139,
0.011604498140513897,
0.0646040141582489,
0.014239560812711716,
0.02092607319355011,
-0.014676118269562721,
-0.014860991388559341,
0.008096110075712204,
-0.05890033766627312,
0.05387430638074875,
-0.01845170557498932,
-0.04492347687482834,
0.04121864214539528,
0.025016264989972115,
0.04714763164520264,
-0.03450027480721474,
-0.02575007453560829,
-0.014867888763546944,
0.054399993270635605,
0.0011337142204865813,
-0.005097516812384129,
0.03406823053956032,
0.05773123353719711,
0.0441657155752182,
-0.00432481849566102,
-0.019642198458313942,
-0.029496029019355774,
0.00509278941899538,
-0.010424998588860035,
0.008345896378159523,
0.032341524958610535,
0.04477626085281372,
-0.014451143331825733,
-0.015481722541153431,
0.0016186059219762683,
-0.003135316539555788,
0.038782402873039246,
-0.033580172806978226,
0.07206173986196518,
0.048186592757701874,
-0.0015426453901454806,
0.034966811537742615,
0.05673293396830559,
0.0033484932500869036,
-0.007375300861895084,
-0.019763527438044548,
-0.014490902423858643,
-0.029560409486293793,
-0.006407527718693018,
0.04285769164562225,
0.030239615589380264,
-0.031243665143847466,
0.025622345507144928,
0.06543636322021484,
0.02290062978863716,
0.017058899626135826,
0.006794306915253401,
-0.021436063572764397,
-0.031886469572782516,
0.01526983268558979,
0.009550664573907852,
-0.032165613025426865,
0.017866548150777817,
0.04122169315814972,
0.028355317190289497,
0.00845649465918541,
0.018130820244550705,
-0.044881682842969894,
0.03609350696206093,
0.01843242160975933,
0.009672362357378006,
0.03501623123884201,
-0.010076228529214859,
0.0566624253988266,
-0.0033615021966397762,
0.021089667454361916,
0.054007500410079956,
-0.0034514775034040213,
0.019553864374756813,
-0.01761780120432377,
0.011401568539440632,
-0.022080371156334877,
0.0047044591046869755,
0.0069852834567427635,
-0.015195938758552074,
0.011190855875611305,
-0.04347045719623566,
-0.03143524006009102,
-0.0027922908775508404,
-0.027980441227555275,
-0.03249485045671463,
0.009494961239397526,
0.03206739202141762,
0.02432420291006565,
0.0205587949603796,
-0.013490559533238411,
-0.019744623452425003,
-0.023092593997716904,
-0.030231313779950142,
-0.030605481937527657,
0.01408100314438343,
-0.027459774166345596,
0.031649600714445114,
-0.015292954631149769,
-0.011426950804889202,
0.047634270042181015,
0.010380422696471214,
0.01437999028712511,
-0.008336847648024559,
0.016570691019296646,
-0.09368328005075455,
-0.029010092839598656,
-0.030828654766082764,
0.01059853844344616,
-0.03662126883864403,
-0.000629649730399251,
0.05883956328034401,
-0.03576597943902016,
-0.019102327525615692,
-0.007940859533846378,
-0.06287159025669098,
-0.01355491392314434,
-0.020408567041158676,
-0.0137209827080369,
0.0384678989648819,
-0.04932066798210144,
-0.0009107667719945312,
-0.0008308186079375446,
-0.03309985250234604,
0.0032266241032630205,
-0.03155389800667763,
-0.014365261420607567,
0.007229332812130451,
0.0019123235251754522,
0.03264478221535683,
-0.02252843603491783,
-0.038868099451065063,
0.07466409355401993,
0.03477978706359863,
-0.010339207015931606,
-0.016515294089913368,
0.00820703525096178,
-0.013049340806901455,
-0.06079716235399246,
-0.007025351747870445,
0.03942009434103966,
-0.009005351923406124,
0.015765348449349403,
0.008889980614185333,
0.00502864271402359,
0.00022391180391423404,
0.009792913682758808,
-0.004979939665645361,
0.035217493772506714,
0.002665331121534109,
-0.004775507841259241,
0.07540568709373474,
0.010944036766886711,
-0.0013660388067364693,
0.011233470402657986,
0.00035576458321884274,
0.05220840126276016,
0.02089725062251091,
-0.06522169709205627,
0.0021958136931061745,
-0.007920258678495884,
-0.010481410659849644,
-0.005691650323569775,
0.032522451132535934,
-0.00949057936668396,
0.013483181595802307,
0.023117752745747566,
0.0014798769261687994,
0.06943667680025101,
-0.013252092525362968,
-0.013445165008306503,
0.044018689543008804,
0.01604512706398964,
0.012261644005775452,
-0.00799923948943615,
-0.02749757468700409,
0.029951706528663635,
0.01660734787583351,
-0.033311642706394196,
0.015571274794638157,
0.048537734895944595,
0.04309355095028877,
0.011599632911384106,
-0.006599248852580786,
-0.05862979590892792,
0.011200962588191032,
-0.04987586662173271,
-0.027743689715862274,
-0.038225919008255005,
0.05197349190711975,
0.01871464028954506,
0.051904961466789246,
0.02097165770828724,
0.001983323134481907,
0.02786366268992424,
0.0075640687718987465,
-0.06660909950733185,
0.04592651501297951,
-0.02284603752195835,
-0.027382679283618927,
-0.006832415703684092,
0.023278359323740005,
-0.0052687195129692554,
-0.022012554109096527,
-0.028677815571427345,
-0.025374120101332664,
-0.03465117886662483,
-0.034576788544654846,
-0.026778515428304672,
-0.022101949900388718,
-0.05244239792227745,
-0.042399488389492035,
0.03628848120570183,
0.035406965762376785,
-0.035949885845184326,
0.045610878616571426,
0.08124538511037827,
-0.021593844518065453,
-0.0140111418440938,
-0.0439140684902668,
-0.009780094027519226,
-0.0051789130084216595,
0.01445514801889658,
-0.0030312296003103256,
0.011659860610961914,
0.036115679889917374,
0.004063940141350031,
0.010659770108759403,
0.0495428591966629,
0.0076851495541632175,
0.023453200235962868,
-0.02996225468814373,
-0.04020886868238449,
0.03634839504957199,
0.01670208014547825,
0.04339517652988434,
0.009844010695815086,
-0.006664350628852844,
0.03601652383804321,
-0.009128784760832787,
-0.005362522788345814,
0.03998517617583275,
0.01628277637064457,
-0.002278702799230814,
0.01052817702293396,
-0.045825812965631485,
0.009085091762244701,
-0.015813425183296204,
-0.004641552455723286,
0.00221722642891109,
-0.03946203365921974,
-0.0044737281277775764,
-0.031000355258584023,
0.005421394947916269,
-0.009283622726798058,
-0.009244579821825027,
0.014821304939687252,
-0.04155508056282997,
0.03531377390027046,
-0.030363280326128006,
-0.018975893035531044,
0.014400629326701164,
0.03435593843460083,
0.03134164959192276,
-0.025260072201490402,
0.009288430213928223,
-0.07535193115472794,
-0.019008856266736984,
-0.01368845533579588,
0.04591374844312668,
0.016907446086406708,
-0.025458430871367455,
-0.05792782083153725,
-0.07780692726373672,
0.03560636565089226,
-0.009577236138284206,
0.049363985657691956,
-0.050242986530065536,
-0.005471882410347462,
-0.03839332237839699,
-0.04866309463977814,
-0.038471054285764694,
0.003489941358566284,
-0.012511413544416428,
0.017752064391970634,
-0.03392282873392105,
0.005331507418304682,
-0.024828054010868073,
0.008858777582645416,
0.005617628805339336,
0.0407114215195179,
0.023813970386981964,
-0.0357615128159523,
-0.005042775999754667,
0.011668932624161243,
-0.03571939095854759,
-0.07395518571138382,
-0.01581677608191967,
0.0022339331917464733,
-0.027473431080579758,
0.03648654744029045,
-0.06461518257856369,
-0.06624241173267365,
0.01586214080452919,
0.009017111733555794,
-0.017179932445287704,
-0.006295861676335335,
-0.049696601927280426,
0.009754961356520653,
0.015010952018201351,
-0.020644498988986015,
0.0400044210255146,
0.01737494394183159,
-0.014666643925011158,
-0.01754772663116455,
-0.026234356686472893,
0.025954285636544228,
-0.0074777668341994286,
-0.029431015253067017,
-0.04126541316509247,
0.0033014186192303896,
-0.023132607340812683,
0.04176587238907814,
0.010817852802574635,
0.003431989811360836,
-0.03725752606987953,
-0.031066447496414185,
-0.00548138190060854,
0.024193499237298965,
0.0035632033832371235,
-0.024716999381780624,
0.021549062803387642,
-0.006054650526493788,
0.02920643985271454,
-0.008833539672195911,
0.035819072276353836,
-0.028459878638386726,
0.009717290289700031,
0.029846200719475746,
0.010558375157415867,
0.013057299889624119,
-0.027308575809001923,
-0.014009678736329079,
-0.014184759929776192,
-0.056384216994047165,
0.01951448805630207,
0.011483716778457165,
-0.010332812555134296,
0.018015889450907707,
-0.04098229855298996,
-0.027128012850880623,
0.006419762037694454,
-0.012022019363939762,
-0.007208522874861956,
-0.02778553031384945,
0.018443169072270393,
0.04014210030436516,
-0.002257415559142828,
-0.051693279296159744,
-0.04724067449569702,
0.00407525897026062,
-0.0026244986802339554,
-0.01294462475925684,
0.019678838551044464,
-0.006617298815399408,
0.01343765389174223,
-0.024161240085959435,
0.028535693883895874,
0.04812426492571831,
-0.05882038548588753,
-0.009300107136368752,
0.01829366758465767,
0.029119394719600677,
0.06503106653690338,
-0.03775724023580551,
-0.03054877743124962,
0.023112336173653603,
-0.006429559551179409,
-0.009703494608402252,
0.012269224971532822,
0.08878452330827713,
-0.037542618811130524,
-0.053911153227090836,
-0.01374105829745531,
-0.01261805184185505,
0.0255460012704134,
-0.00019889199757017195,
-0.009234583005309105,
0.012811319902539253,
-0.0128335477784276,
-0.02206055074930191,
-0.03650591894984245,
0.007099932059645653,
0.006818105932325125,
0.06194312125444412,
0.003282195422798395,
-0.026610955595970154,
-0.046168211847543716,
-0.03835593909025192,
0.02221921645104885,
-0.017688019201159477,
0.01531180925667286,
-0.014975322410464287,
0.0448266826570034,
-0.01251945085823536,
0.03733760863542557,
0.03679238632321358,
-0.0076271407306194305,
0.01063485722988844,
-0.024434726685285568,
0.007109208032488823,
0.0022616288624703884,
-0.0003928357036784291,
-0.036382514983415604,
-0.05160974711179733,
-0.03940490633249283,
0.015183888375759125,
0.07991813123226166,
-0.018049033358693123,
0.0741906389594078,
0.03548378497362137,
0.0047001466155052185,
-0.014028143137693405,
-0.05107129365205765,
-0.012796260416507721,
-0.031617097556591034,
0.02329229563474655,
0.02265249565243721,
-0.031415071338415146,
0.0005103966686874628,
0.04655848443508148,
0.03820810467004776,
-0.02352898381650448,
-0.045509930700063705,
0.02383315935730934,
0.0028770852368324995,
0.025147248059511185,
0.016880588605999947,
-0.02122136391699314,
0.00942674744874239,
-0.0020053721964359283,
0.058838438242673874,
0.008927276358008385,
-0.00543208746239543,
0.03406403958797455,
0.003404180286452174,
-0.014426641166210175,
-0.031753141433000565,
0.003497073892503977,
-0.042151499539613724,
0.01700853928923607,
0.02706015855073929,
-0.01057324931025505,
-0.010422615334391594,
0.003558834083378315,
0.05377926677465439,
-0.03028085269033909,
-0.00013994803884997964,
-0.031100278720259666,
-0.030419424176216125,
-0.021113764494657516,
-0.030260059982538223,
-0.024502737447619438,
0.022384818643331528,
-0.01932377554476261,
-0.0183541439473629,
-0.008014019578695297,
-0.01907932199537754,
0.018891043961048126,
0.026607023552060127,
0.016015974804759026,
-0.055466119199991226,
0.05510178208351135,
-0.015559750609099865,
-0.015636811032891273,
-0.016674434766173363,
-0.01638704724609852,
0.11101018637418747,
-0.0005330208223313093,
-0.004760285839438438,
-0.048112258315086365,
0.03615592047572136,
-0.0021734987385571003,
0.008402216248214245,
-0.04216741397976875,
-0.0016450812108814716,
-0.004061627667397261,
0.01998106949031353,
0.03380632773041725,
0.04877874627709389,
-0.0020754134748131037,
-0.02125115692615509,
0.044293444603681564,
0.0021133567206561565,
-0.042421553283929825,
-0.0131913423538208,
0.004103121347725391,
-0.038332387804985046,
0.043385863304138184,
-0.05699654296040535,
0.046627528965473175,
-0.055691372603178024,
-0.014432649128139019,
-0.04675913602113724,
-0.03412710875272751,
0.031154567375779152,
0.02656860463321209,
-0.0271415077149868,
0.06520842760801315,
0.011561566032469273,
-0.013369291089475155,
0.004933610558509827,
0.039142709225416183,
0.030697040259838104,
-0.0070528616197407246,
0.027261337265372276,
0.016288720071315765,
-0.021966004744172096,
-0.0008131578797474504,
0.009758532978594303,
-0.0049601104110479355,
-0.04349016025662422,
0.02201789803802967,
-0.042252589017152786,
0.05931591987609863,
-0.0074889142997562885,
-0.003985671792179346,
0.005275968927890062,
0.016902262344956398,
-0.02374912239611149,
-0.046332791447639465,
0.017886554822325706,
0.0028290655463933945,
0.0383225753903389,
-0.04984172433614731,
-0.033144041895866394,
-0.004330894909799099,
-0.0013126933481544256,
0.007998327724635601,
0.0037878232542425394,
-0.02340463548898697,
0.014033118262887001,
-0.02408335916697979,
-0.0034199196379631758,
0.02656104974448681,
-0.0075821829959750175,
-0.00354372663423419,
-0.019337445497512817,
-0.00023450909066013992,
-0.05888807028532028,
0.0009857234545052052,
0.003619937691837549,
0.02825538069009781,
0.01993926614522934,
0.01106257364153862,
-0.023633742704987526,
-0.017533404752612114,
-0.06775065511465073,
0.05495888367295265,
0.01926225610077381,
-0.03918013349175453,
-0.011969504877924919,
-0.019195837900042534,
0.013614253140985966,
0.004417098592966795,
-0.03369157388806343,
0.059145487844944,
-0.0034110674168914557,
0.04702514782547951,
0.019946156069636345,
-0.004064908251166344,
-0.03024340607225895,
0.051044099032878876,
-0.015547486953437328,
-0.014635255560278893,
-0.01862480118870735,
0.023328840732574463,
0.03970224782824516,
-0.007449815981090069,
-0.015286782756447792,
0.023098306730389595,
-0.03839427977800369,
0.0009253063471987844,
0.04106484353542328,
-0.03765644133090973,
0.020080914720892906,
0.002544211922213435,
0.002742297947406769,
-0.04258297383785248,
0.02245272509753704,
-0.013423619791865349,
-0.0341959185898304,
0.000040990675188368186,
0.0008253680425696075,
-0.024188946932554245,
0.048784077167510986,
-0.06938774138689041,
0.023312924429774284,
-0.07338128983974457,
0.009154301136732101,
-0.04136718809604645,
0.020720962435007095,
-0.012906094081699848,
0.004393183160573244,
-0.00951638724654913,
0.042404647916555405,
-0.018935589119791985,
-0.026188082993030548,
0.017356742173433304,
0.016123617067933083,
0.003966759890317917,
0.011756427586078644,
0.019375529140233994,
-0.026297183707356453,
0.06176885962486267,
-0.013580093160271645,
-0.04260608181357384,
0.04854220151901245,
-0.010589956305921078,
-0.05086393281817436,
0.02718348056077957,
-0.01760026626288891,
0.03406196087598801,
0.0034338226541876793,
-0.03188411518931389,
0.008936547674238682,
0.06440185755491257,
0.0012145133223384619,
0.005241733510047197,
-0.0010501401266083121,
-0.04381131753325462,
-0.023208435624837875,
-0.010702589526772499,
0.04855773225426674,
-0.04329782351851463,
0.0031507713720202446,
0.027361605316400528,
0.02935280278325081,
-0.02883758582174778,
0.0167292058467865,
-0.008256779052317142,
-0.0040288157761096954,
0.026735037565231323,
0.04422043636441231,
0.020231004804372787,
0.047288455069065094,
-0.012030965648591518,
0.0035668055061250925,
0.03405570238828659,
0.006777449510991573,
0.0013933224836364388,
-0.0758465975522995,
0.008316272869706154,
-0.029296759516000748,
0.014308949001133442,
0.013575561344623566,
-0.06802928447723389,
-0.0336020365357399,
0.03572557866573334,
-0.0544055700302124,
0.0066131227649748325,
-0.04425165057182312,
-0.006469007581472397,
0.01196813303977251,
0.004852789919823408,
-0.0031545418314635754,
0.031080499291419983,
0.009153204038739204,
0.04079481214284897,
0.02390308864414692,
0.011601641774177551,
-0.018714657053351402,
-0.03031340055167675,
0.011661771684885025,
0.01701943390071392,
-0.0051047406159341335,
0.019451742991805077,
0.03389236703515053,
0.009988401085138321,
-0.027618149295449257,
0.07370154559612274,
-0.055178701877593994,
0.06862043589353561,
-0.003114516381174326,
0.012559275142848492,
-0.020381895825266838,
0.027298439294099808,
-0.0016056594904512167,
-0.0047764587216079235,
-0.04866328462958336,
0.005622961092740297,
0.016175422817468643,
0.02050364390015602,
0.00896456465125084,
-0.002894988749176264,
0.015696126967668533,
-0.052093662321567535,
-0.0072835516184568405,
0.04985148832201958,
-0.0420936718583107,
0.011269360780715942,
-0.011373762041330338,
0.00015719563816674054,
0.01203092560172081,
-0.04055103659629822,
0.023161109536886215,
-0.007107885088771582,
-0.009509525261819363,
0.013861481100320816,
-0.010186267085373402,
-0.001592474291101098,
-0.0017141022253781557,
0.02656736969947815,
-0.03433859348297119,
0.05080469325184822,
-0.03420089930295944,
-0.01722625456750393,
-0.03658568859100342,
-0.003876148257404566,
0.01694922149181366,
0.0003682847018353641,
-0.0003994584549218416,
-0.04476290941238403,
-0.06283944845199585,
0.03782936558127403,
0.011257443577051163,
-0.009291510097682476,
-0.042748142033815384,
-0.027514049783349037,
0.004139706026762724,
-0.06694090366363525,
0.0036463874857872725,
0.02340877614915371,
-0.0372224822640419,
-0.023473285138607025,
-0.037039026618003845,
-0.01142022293061018,
0.021958600729703903,
0.04096901789307594,
0.00854326132684946,
0.022112861275672913,
0.02656516060233116,
-0.03785520792007446,
0.017764557152986526,
-0.057023365050554276,
0.022497471421957016,
-0.0016907162498682737,
-0.0181479100137949,
0.052983950823545456,
-0.010577909648418427,
-0.030074412003159523,
-0.0013414360582828522,
0.001814462710171938,
0.011603085324168205,
0.04820632562041283,
0.030959494411945343,
-0.04703430458903313,
0.04714222997426987,
-0.018492547795176506,
-0.0012385511072352529,
0.08678797632455826,
0.019682465121150017,
0.03242173418402672,
0.03228035569190979,
-0.02664291486144066,
-0.01788068190217018,
0.019798140972852707,
-0.056513700634241104,
-0.031267184764146805,
-0.018914036452770233,
-0.05471331998705864,
0.04647360369563103,
-0.04019582271575928,
-0.010004395619034767,
0.04748686030507088,
-0.00095847510965541,
-0.018047049641609192,
0.009722192771732807,
-0.007493182085454464,
0.03385678678750992,
0.014594832435250282,
0.027172166854143143,
0.012278451584279537,
-0.02733832597732544,
-0.0015955078415572643,
0.02109731361269951,
0.039996594190597534,
0.024659646674990654,
-0.016522981226444244,
0.048023566603660583,
-0.008284072391688824,
0.04374987259507179,
-0.015783293172717094,
0.04086543247103691,
-0.015531064942479134,
0.00861275289207697,
0.017843494191765785,
-0.03686061128973961,
-0.009394199587404728,
0.04589633643627167,
0.011670625768601894,
0.0606827549636364,
-0.016484176740050316,
-0.0007027973770163953,
-0.00915767066180706,
0.009627497754991055,
-0.03917635232210159,
-0.0035427173133939505,
0.005079706199467182,
0.004734545946121216,
0.007283270824700594,
-0.02295510470867157,
-0.028381207957863808,
-0.022651299834251404,
0.02542172186076641,
-0.014480287209153175,
0.04485732316970825,
0.03236653655767441,
-0.002168895909562707,
-0.019905518740415573,
0.001998719060793519,
-0.029842816293239594,
-0.041899215430021286,
0.03330354392528534,
0.03750588372349739,
0.03227875381708145,
-0.014859053306281567,
0.00487901084125042,
-0.0010766781633719802,
0.0421883687376976,
-0.06980366259813309,
-0.04361787438392639,
0.002100815996527672,
0.01354846078902483,
0.01223570853471756,
-0.0296028945595026
] |
<p>Suppose there's some satellite orbiting the earth in circular motion. Suppose there's an asteroid that hits the satellite in the same direction as the instant velocity vector of the satellite. The collision causes the satellite to move faster. And here are my 2 questions:</p>
<p>1) Why will the satellite start moving in an elliptical orbit? Is it because its speed has increased, but the centripetal acceleration hasn't? It seems intuitively right for me, because then the satellite covers larger path before the centripetal acceleration causes the change in the velocity vector direction.</p>
<p>2) However, what confuses me is the fact that the centripetal acceleration is dependent on the velocity ($v^2/r$). On the other hand, since the force of gravity exerted on the satellite by the earth, hasn't changed after the hit (if we neglect asteroid's mass or suppose it just fell down after the hit), because there was no change in the radius (i suppose) of the circular path, there was no change in the centripetal acceleration. So these two arguments contradict each other. Where am I wrong? What I miss here? </p>
<p>Thanks in advance.</p> | 4,599 | [
-0.025629989802837372,
-0.0363733246922493,
-0.02006150595843792,
-0.011669040657579899,
0.018149007111787796,
0.017617428675293922,
-0.016754332929849625,
-0.024008363485336304,
0.039290908724069595,
-0.011928471736609936,
-0.00196061166934669,
0.019243212416768074,
0.04063690826296806,
-0.01866341196000576,
0.025907250121235847,
0.008247013203799725,
-0.02405431866645813,
-0.007899833843111992,
0.01612437702715397,
-0.021519728004932404,
-0.0163884274661541,
-0.027531005442142487,
0.03221757709980011,
-0.02852846123278141,
-0.0068239918909966946,
0.013875177130103111,
0.05181385204195976,
-0.0008157044067047536,
0.0389520488679409,
0.05729064717888832,
0.012996134348213673,
0.007410462945699692,
0.002506426302716136,
0.01918668858706951,
-0.0032320304308086634,
0.016725411638617516,
-0.04082866758108139,
0.008169871754944324,
-0.0012485201004892588,
0.04267849400639534,
-0.04442596435546875,
-0.028286106884479523,
0.010893057100474834,
0.08987615257501602,
-0.02487686462700367,
0.014452093280851841,
0.015486884862184525,
0.007648387923836708,
0.05530613660812378,
-0.04782960191369057,
0.08013449609279633,
-0.03860784322023392,
0.030192703008651733,
0.011956261470913887,
0.005332480184733868,
-0.002985906321555376,
0.07916966080665588,
0.08544401824474335,
-0.023138005286455154,
-0.00573697267100215,
-0.01613597385585308,
-0.0045259371399879456,
-0.011399805545806885,
-0.015939202159643173,
0.007538611069321632,
0.03934942185878754,
-0.023534856736660004,
-0.005101052578538656,
-0.004020608030259609,
0.01591985858976841,
0.03667741268873215,
0.004268266726285219,
-0.02404005639255047,
-0.034354593604803085,
-0.015273590572178364,
-0.019636120647192,
0.051447950303554535,
0.015665685757994652,
0.03844446688890457,
0.0398767814040184,
-0.02828611060976982,
0.01780620962381363,
0.041524555534124374,
0.0457962229847908,
0.02766530029475689,
0.028072280809283257,
0.03279098495841026,
0.03393636643886566,
0.022169819101691246,
0.027876168489456177,
-0.0031719044782221317,
0.0055365292355418205,
0.00018141513282898813,
-0.03647512570023537,
-0.019470101222395897,
0.03084302321076393,
-0.0026861797086894512,
0.07424037903547287,
0.008926880545914173,
0.020534103736281395,
0.01205320842564106,
-0.018135759979486465,
0.028989257290959358,
0.07298583537340164,
-0.0067858318798244,
-0.00586925633251667,
-0.041789811104536057,
0.030606113374233246,
-0.0412379615008831,
-0.04339507222175598,
-0.02124461531639099,
0.034508731216192245,
-0.022968962788581848,
-0.000803482485935092,
0.030436554923653603,
0.003613345790654421,
0.012701204046607018,
-0.001817103591747582,
0.05537844076752663,
0.028926987200975418,
0.07101432234048843,
-0.008873053826391697,
0.01071519311517477,
-0.04268666356801987,
-0.040734030306339264,
-0.009406950324773788,
0.013945399783551693,
-0.01096873264759779,
-0.016088390722870827,
-0.004089097958058119,
-0.0021037408150732517,
-0.008574487641453743,
-0.024193260818719864,
-0.007266075350344181,
0.035453833639621735,
-0.014611917547881603,
-0.0947447419166565,
-0.06427878886461258,
0.04805974289774895,
0.035355087369680405,
0.0001625257427804172,
-0.09950295090675354,
0.02021619863808155,
-0.0038030180148780346,
0.08192270249128342,
-0.0015351244946941733,
-0.008970570750534534,
0.027872320264577866,
0.06874217838048935,
0.029305368661880493,
-0.028022393584251404,
-0.020039254799485207,
0.011914410628378391,
-0.05132849141955376,
0.006165544968098402,
-0.10355137288570404,
0.007870285771787167,
0.005988393910229206,
0.023553963750600815,
-0.007561671547591686,
0.06515680998563766,
-0.033644065260887146,
0.04511094093322754,
0.0003431117220316082,
0.019134365022182465,
0.015171417035162449,
0.06582468003034592,
0.03611607849597931,
-0.017856415361166,
0.028987571597099304,
0.07558012008666992,
0.055593397468328476,
0.010759053751826286,
0.0031552312429994345,
0.07846333086490631,
-0.05181015282869339,
-0.010320383124053478,
-0.0376497246325016,
-0.01070225890725851,
-0.0257905051112175,
-0.007371523417532444,
-0.06762586534023285,
-0.0006192207220010459,
0.010877622291445732,
-0.008464827202260494,
0.078896164894104,
0.03900928795337677,
0.02461259439587593,
-0.003961716778576374,
-0.010146111249923706,
-0.009334993548691273,
-0.05328759178519249,
0.03162480145692825,
-0.007743893191218376,
0.010575976222753525,
0.006868183612823486,
0.020116571336984634,
0.022530578076839447,
-0.01057429239153862,
0.015602829866111279,
-0.0002932910283561796,
0.03077378123998642,
-0.008505132980644703,
-0.03591802343726158,
0.004817924927920103,
0.04776691272854805,
0.00782477855682373,
0.01851554401218891,
-0.027399098500609398,
0.025968221947550774,
0.012151999399065971,
0.02628001756966114,
0.005693336017429829,
0.009071084670722485,
0.0051625133492052555,
0.01663815975189209,
0.017892563715577126,
0.01839469000697136,
-0.0008204869227483869,
0.04980653151869774,
-0.04493773356080055,
0.10401298850774765,
0.07461871206760406,
0.031439438462257385,
0.030276380479335785,
0.06620676070451736,
0.026551058515906334,
-0.008284959942102432,
-0.010469784960150719,
-0.017639797180891037,
-0.03657238930463791,
-0.004975257907062769,
0.020584583282470703,
0.003843550570309162,
-0.02818475291132927,
0.052069198340177536,
0.0642612874507904,
0.049431491643190384,
0.016326265409588814,
0.02019074559211731,
0.016054050996899605,
-0.03627826273441315,
0.015416986308991909,
0.009322735480964184,
-0.01639726385474205,
-0.019542433321475983,
0.004007432144135237,
0.001880544819869101,
0.004365865606814623,
0.007525759283453226,
-0.023472951725125313,
0.025830047205090523,
0.016165468841791153,
0.013646718114614487,
0.021080857142806053,
-0.012260546907782555,
0.06039559841156006,
-0.03086422197520733,
0.03438877314329147,
0.018362846225500107,
-0.012612086720764637,
-0.014477870427072048,
-0.05842847004532814,
0.014903605915606022,
0.011984544806182384,
-0.01126091368496418,
-0.005118258763104677,
-0.0041596004739403725,
0.013321202248334885,
-0.042061276733875275,
-0.020916465669870377,
-0.004407698288559914,
-0.038645047694444656,
-0.05143258720636368,
0.0017537534004077315,
0.028211165219545364,
0.014542737975716591,
0.014405968599021435,
-0.01765577867627144,
-0.0039999717846512794,
-0.0036823139525949955,
-0.05642269179224968,
-0.0015814410289749503,
0.010460861027240753,
-0.05525445565581322,
0.04478355497121811,
-0.07177723944187164,
0.01294997613877058,
0.0385267399251461,
0.00491635175421834,
0.013859251514077187,
0.001743231201544404,
-0.014909938909113407,
-0.04364878311753273,
-0.018871042877435684,
-0.04124404489994049,
-0.01996222883462906,
-0.03670443594455719,
-0.01133114006370306,
0.06119660288095474,
-0.020426101982593536,
0.00795954093337059,
0.013393617235124111,
-0.06321539729833603,
-0.013890535570681095,
-0.016734039410948753,
0.005438466090708971,
0.01917215622961521,
-0.03795846924185753,
-0.003605510573834181,
-0.020247898995876312,
-0.021606557071208954,
-0.01161507610231638,
-0.03109581768512726,
-0.04279715567827225,
0.0076974183320999146,
-0.014020108617842197,
0.0341869592666626,
-0.021091260015964508,
-0.0438685342669487,
0.060904838144779205,
0.019817424938082695,
0.007669209968298674,
-0.04016507789492607,
0.033393494784832,
-0.02546127885580063,
-0.03477321192622185,
0.0026607373729348183,
-0.00810063723474741,
-0.014933554455637932,
-0.022660434246063232,
0.019485844299197197,
0.01496550627052784,
0.01891169883310795,
0.0056123314425349236,
-0.03221862390637398,
0.0035266017075628042,
0.014887278899550438,
0.011858256533741951,
0.003949231002479792,
0.052711281925439835,
0.013203917071223259,
0.018719054758548737,
0.0014419412473216653,
0.05582061782479286,
0.002552625024691224,
-0.07449748367071152,
0.03708801418542862,
-0.0007432093261741102,
-0.003497522557154298,
-0.008058170787990093,
0.02290639840066433,
0.018558837473392487,
0.02123565971851349,
0.024542512372136116,
-0.006583092268556356,
0.03149115666747093,
-0.024037986993789673,
-0.009820635430514812,
0.018174167722463608,
0.028738809749484062,
-0.028762223199009895,
-0.03476022556424141,
-0.0019892766140401363,
-0.020002072677016258,
0.034477561712265015,
-0.0017629769863560796,
0.01728096790611744,
0.0340406708419323,
0.012381281703710556,
0.022695641964673996,
0.0007183529669418931,
-0.05464837700128555,
-0.006360075902193785,
-0.06392212957143784,
-0.009551397524774075,
-0.02034851722419262,
0.03559653460979462,
0.009458422660827637,
0.058922987431287766,
0.018749771639704704,
-0.018298646435141563,
0.0371987447142601,
0.0037734671495854855,
-0.07849729061126709,
0.03838175907731056,
-0.05874347686767578,
-0.03897123783826828,
0.022140538319945335,
0.018447207286953926,
-0.048679936677217484,
-0.027589190751314163,
-0.012615036219358444,
-0.03126394376158714,
-0.013923526741564274,
-0.04224377125501633,
-0.0063587361946702,
-0.03650006651878357,
-0.01947603188455105,
-0.006607645191252232,
0.034935303032398224,
0.03831906616687775,
-0.043628890067338943,
0.0290827676653862,
0.028763487935066223,
-0.04557352513074875,
0.012670486234128475,
-0.02526695653796196,
0.010892965830862522,
0.004885265603661537,
0.0031431487295776606,
0.02203724905848503,
0.022310329601168633,
0.0105970473960042,
0.006174700800329447,
0.003134457627311349,
0.02419373206794262,
0.03686981275677681,
0.017881181091070175,
-0.05290777608752251,
-0.08543560653924942,
-0.0057939765974879265,
-0.02356012910604477,
0.048111267387866974,
0.011326680891215801,
-0.0271467138081789,
0.05186363682150841,
0.0074442364275455475,
0.014248181134462357,
0.03170015290379524,
0.00224177329801023,
0.00895205419510603,
0.009892445988953114,
-0.06216733157634735,
-0.014230766333639622,
-0.028545301407575607,
-0.039945732802152634,
0.01687023602426052,
-0.03978690505027771,
-0.04536553844809532,
0.013425747863948345,
-0.002308584051206708,
-0.010273809544742107,
0.020475074648857117,
-0.009025050327181816,
-0.011297774501144886,
0.02060561254620552,
-0.033225033432245255,
-0.0128707867115736,
0.005011497996747494,
0.024308789521455765,
0.04502050206065178,
-0.012572837993502617,
0.011889715678989887,
-0.05530723184347153,
0.006565277464687824,
0.024931808933615685,
0.04724442586302757,
-0.04291457682847977,
-0.024295596405863762,
-0.057144250720739365,
-0.024893632158637047,
0.028494250029325485,
-0.029216142371296883,
0.03156460076570511,
-0.03495154529809952,
0.0039977142587304115,
-0.01700100116431713,
-0.031665489077568054,
-0.03943353891372681,
0.0071241301484405994,
0.005922216456383467,
0.019289232790470123,
-0.033524543046951294,
0.00023844650422688574,
-0.014148429967463017,
-0.0071049039252102375,
0.0487760566174984,
0.03347597271203995,
0.028059035539627075,
0.0116765471175313,
-0.01724115200340748,
0.003232602495700121,
-0.009587910026311874,
-0.06909583508968353,
-0.027730667963624,
-0.004511908628046513,
-0.010172707960009575,
0.03336236998438835,
-0.037390850484371185,
-0.021454233676195145,
0.06268596649169922,
-0.001984777394682169,
-0.03394173085689545,
-0.0023049332667142153,
-0.03436366096138954,
0.06233706325292587,
0.04952147603034973,
-0.015626978129148483,
0.013492317870259285,
0.0246543250977993,
-0.006863562390208244,
-0.014752455055713654,
-0.038960590958595276,
0.012394052930176258,
-0.03452923521399498,
-0.01917891576886177,
-0.03591449186205864,
0.028867198154330254,
-0.015583934262394905,
0.03158392012119293,
0.023190440610051155,
0.006130624562501907,
-0.04489944130182266,
-0.013644253835082054,
-0.013384411111474037,
0.03443087264895439,
0.000944819999858737,
0.012255753390491009,
-0.009771132841706276,
-0.0047079152427613735,
-0.011349273845553398,
-0.013420479372143745,
0.013149969279766083,
-0.030819859355688095,
-0.024861043319106102,
0.023331591859459877,
0.015870647504925728,
0.003997675143182278,
-0.029960574582219124,
-0.02699480764567852,
0.0026230132207274437,
-0.05223498120903969,
0.06358664482831955,
-0.016205009073019028,
-0.031850241124629974,
0.04109101742506027,
-0.05911730229854584,
-0.012186861597001553,
-0.013608765788376331,
-0.019548457115888596,
0.0045199040323495865,
-0.047445621341466904,
-0.00029838920454494655,
0.02606090158224106,
0.012677857652306557,
-0.07234422862529755,
-0.039418503642082214,
0.02233949303627014,
-0.026584643870592117,
-0.03681290149688721,
-0.006916853599250317,
-0.0038181745912879705,
-0.044229697436094284,
-0.02152610383927822,
0.001087214215658605,
0.05973903834819794,
-0.03321036696434021,
-0.030342500656843185,
0.006462162360548973,
0.01567365601658821,
0.05020662024617195,
-0.020897287875413895,
-0.012961771339178085,
0.00519039761275053,
-0.009132255800068378,
-0.004290021490305662,
0.018233267590403557,
0.12155891954898834,
-0.034673936665058136,
-0.028609564527869225,
-0.013551739044487476,
-0.04955115541815758,
0.006802826654165983,
0.00925515592098236,
-0.0038468290586024523,
0.03897576406598091,
-0.01710832118988037,
-0.008679283782839775,
0.01553914975374937,
0.03315591812133789,
-0.0152567895129323,
0.02135624550282955,
0.02104313112795353,
-0.018359588459134102,
-0.04264608025550842,
-0.027289116755127907,
0.015895675867795944,
0.00477351900190115,
0.03878118470311165,
-0.011521394364535809,
0.06975709646940231,
-0.025415318086743355,
-0.011336438357830048,
-0.00539407879114151,
-0.03808903321623802,
0.018802093341946602,
-0.049372706562280655,
-0.038956861943006516,
0.010892434976994991,
-0.016604837030172348,
-0.04135756939649582,
-0.018795672804117203,
-0.031382083892822266,
0.0178290493786335,
0.08783577382564545,
-0.06317407637834549,
0.04102536290884018,
0.005879511125385761,
0.035096365958452225,
0.007577352691441774,
-0.03013034351170063,
0.014812537468969822,
-0.033687908202409744,
-0.022072939202189445,
0.02762366272509098,
-0.026567367836833,
-0.010277030989527702,
0.017261875793337822,
0.043753888458013535,
-0.008632841520011425,
0.01160286832600832,
0.03793030604720116,
-0.009911901317536831,
0.04256577044725418,
0.00823492556810379,
-0.00419497350230813,
0.006074834149330854,
-0.0037564707454293966,
0.04159557446837425,
0.015624363906681538,
-0.00573100708425045,
0.07875091582536697,
0.021605409681797028,
-0.0025813619140535593,
-0.03540508821606636,
-0.007478734478354454,
-0.053598858416080475,
0.0029058486688882113,
0.02067909948527813,
0.007156473584473133,
0.00636721309274435,
0.016456736251711845,
0.057190537452697754,
0.0027154884301126003,
-0.0004311705706641078,
-0.03628477454185486,
-0.06714086979627609,
-0.03984396904706955,
-0.01298459991812706,
-0.046080540865659714,
0.02420208603143692,
0.0006873897509649396,
-0.02094155363738537,
0.0047539109364151955,
-0.0178059171885252,
0.006004503928124905,
0.04141366854310036,
0.044038984924554825,
-0.011148672550916672,
0.09045974910259247,
-0.03661687299609184,
0.0037869829684495926,
-0.010460938327014446,
-0.016720471903681755,
0.09438793361186981,
0.04710746929049492,
-0.01925016939640045,
-0.013744859024882317,
0.014631387777626514,
-0.013097173534333706,
0.007787064183503389,
-0.05004105344414711,
0.020264236256480217,
0.0026810667477548122,
-0.0021342867985367775,
0.027925821021199226,
0.03777293115854263,
-0.0038180265109986067,
-0.018753020092844963,
0.039987336844205856,
-0.023726779967546463,
-0.04245646670460701,
-0.04491116851568222,
0.026457956060767174,
-0.03111129067838192,
0.0005540369311347604,
-0.01698310673236847,
0.041039325296878815,
-0.05649618059396744,
-0.010735074989497662,
-0.058420099318027496,
-0.04815701022744179,
-0.002895224606618285,
0.00021138746524229646,
-0.0578712560236454,
0.007392656058073044,
0.01941792480647564,
-0.018181810155510902,
-0.0586555190384388,
0.029291601851582527,
0.006661966908723116,
-0.008905182592570782,
0.05494861677289009,
0.009558885358273983,
0.0029102445114403963,
0.006087205372750759,
0.017793621867895126,
0.012751758098602295,
-0.0573187991976738,
0.0246872678399086,
-0.03752317279577255,
0.06806135922670364,
0.001480337232351303,
0.012785624712705612,
0.006690870970487595,
0.017573220655322075,
-0.012985443696379662,
-0.07130689173936844,
0.004763362463563681,
0.028666866943240166,
0.0035944487899541855,
0.0019264239817857742,
0.006119394209235907,
-0.017055492848157883,
0.009915049187839031,
0.010749398730695248,
0.016360782086849213,
0.022352473810315132,
0.01811518333852291,
0.0050576478242874146,
-0.04044822230935097,
0.03828499838709831,
-0.002349520567804575,
-0.0416000671684742,
-0.006016962230205536,
-0.006845085881650448,
-0.034434013068675995,
0.03253593668341637,
0.019395891577005386,
0.026027007028460503,
0.05241021886467934,
-0.014018603600561619,
-0.02075815759599209,
0.012649540789425373,
-0.04857930541038513,
0.024600330740213394,
-0.0012920062290504575,
-0.026089906692504883,
-0.02846345864236355,
0.020939473062753677,
0.03749615699052811,
-0.0009997457964345813,
-0.010083758272230625,
0.017618171870708466,
-0.028705501928925514,
0.03260493278503418,
0.009968017227947712,
-0.028039010241627693,
-0.022111574187874794,
0.03192002326250076,
0.030758086591959,
-0.005803308449685574,
-0.026000311598181725,
0.031161116436123848,
0.0262965876609087,
0.022650713101029396,
-0.025816887617111206,
0.026894494891166687,
-0.015193420462310314,
0.032382506877183914,
0.032348401844501495,
-0.031068358570337296,
-0.01232871226966381,
0.018114939332008362,
0.03431951627135277,
-0.03380292281508446,
-0.013558905571699142,
-0.03301422297954559,
-0.037051741033792496,
0.0011683673365041614,
-0.007407004479318857,
-0.03811831772327423,
0.062403757125139236,
-0.0697336196899414,
0.05113916099071503,
-0.054341670125722885,
0.007673574145883322,
-0.037615202367305756,
0.005854109767824411,
0.010644424706697464,
-0.01875772699713707,
-0.012462171725928783,
0.04159575700759888,
-0.015734966844320297,
-0.05349285155534744,
-0.013435530476272106,
0.004981427453458309,
-0.011981560848653316,
-0.027826597914099693,
0.02029500901699066,
-0.0330156646668911,
0.06288542598485947,
-0.009070824831724167,
-0.014809996820986271,
0.03202798217535019,
-0.023654988035559654,
-0.04353633150458336,
0.015599205158650875,
-0.009542695246636868,
0.04878537729382515,
-0.02511497028172016,
-0.019889555871486664,
-0.003787637921050191,
0.08998929709196091,
-0.018446698784828186,
0.020493123680353165,
0.019774625077843666,
-0.03810039162635803,
-0.02111133374273777,
0.017293039709329605,
0.030525805428624153,
-0.027930675074458122,
0.03568402677774429,
0.04975799843668938,
0.01333187147974968,
-0.015458079054951668,
0.03039972111582756,
-0.009013980627059937,
-0.010469851084053516,
0.030404265969991684,
0.02747984603047371,
0.004977518692612648,
0.03790216147899628,
0.03333248198032379,
-0.02646477520465851,
0.029849881306290627,
0.04525304213166237,
-0.007510462310165167,
-0.07134329527616501,
0.011150334030389786,
-0.019305113703012466,
0.01928560994565487,
0.03637653961777687,
-0.07763732224702835,
0.0073163448832929134,
0.04381178319454193,
-0.05950373411178589,
-0.005223235115408897,
-0.04448404908180237,
-0.013430756516754627,
-0.023737290874123573,
-0.025984913110733032,
-0.008919213898479939,
0.03670312091708183,
0.0719052329659462,
0.03266950696706772,
0.021750206127762794,
-0.003867153776809573,
-0.029062069952487946,
-0.003132106736302376,
0.006120437756180763,
0.0423894077539444,
-0.0054172673262655735,
0.0161324180662632,
0.06459525227546692,
-0.013254950754344463,
0.0025258767418563366,
0.03655505180358887,
0.007205931469798088,
0.02451079525053501,
-0.003136824117973447,
-0.01448063738644123,
0.008073881268501282,
-0.000862921355292201,
0.024623218923807144,
-0.015083583071827888,
0.01767256297171116,
0.026161886751651764,
-0.004003375768661499,
0.026602091267704964,
-0.003954123239964247,
-0.01656017079949379,
0.026765162125229836,
-0.018848473206162453,
-0.023922432214021683,
0.01155785471200943,
0.004578513093292713,
0.009227337315678596,
0.005074624437838793,
0.008201707154512405,
0.009960188530385494,
0.008505577221512794,
0.02422548085451126,
-0.035763539373874664,
-0.012419464997947216,
0.0003507577639538795,
-0.024425361305475235,
-0.01903579756617546,
0.007194488774985075,
-0.01018440444022417,
0.0007070277933962643,
-0.03455079719424248,
-0.008338315412402153,
0.003974820487201214,
-0.03901815786957741,
-0.0034160532522946596,
-0.009920439682900906,
-0.012607579119503498,
-0.04090895503759384,
-0.027090387418866158,
-0.03179054707288742,
0.04409469664096832,
0.009875103831291199,
-0.01918044313788414,
-0.002198200672864914,
-0.017945969477295876,
-0.03149047866463661,
-0.07519683241844177,
0.033710334450006485,
0.008188197389245033,
-0.058502066880464554,
-0.008861220441758633,
-0.0312489066272974,
-0.022510066628456116,
0.005108359269797802,
0.03383690118789673,
0.006437352858483791,
-0.00014955246297176927,
0.040298089385032654,
-0.0033602414187043905,
0.0011748203542083502,
-0.058289021253585815,
-0.0023634096141904593,
-0.0011368778068572283,
-0.023498252034187317,
0.0071691046468913555,
-0.011309717781841755,
-0.02380775846540928,
-0.008198420517146587,
-0.0022360780276358128,
-0.0076930406503379345,
0.04499439895153046,
0.016678571701049805,
-0.042342111468315125,
0.05256839841604233,
0.0078114112839102745,
-0.003479272359982133,
0.08002014458179474,
0.014895987696945667,
0.013272491283714771,
0.03346870839595795,
-0.027994228526949883,
-0.0370933935046196,
0.02759249322116375,
-0.04817499592900276,
-0.004725307691842318,
-0.04031588137149811,
-0.017830852419137955,
0.023207198828458786,
-0.049782924354076385,
0.016915196552872658,
0.049897946417331696,
-0.037384502589702606,
-0.013790062628686428,
0.01302957534790039,
-0.001687113894149661,
0.02481376938521862,
0.010144487954676151,
0.037304673343896866,
0.019147079437971115,
-0.01045673992484808,
0.02177518792450428,
0.006803502328693867,
0.03161853179335594,
0.029499167576432228,
0.009102515876293182,
0.03818873316049576,
0.0031240934040397406,
0.009183833375573158,
-0.015108712948858738,
0.05375643074512482,
-0.017783941701054573,
-0.0230373814702034,
-0.02519853599369526,
-0.017836086452007294,
0.004745952319353819,
0.029320895671844482,
-0.011982777155935764,
0.02828940376639366,
-0.021058348938822746,
0.006920223124325275,
0.016260197386145592,
-0.01940891332924366,
-0.029392704367637634,
-0.007542349398136139,
-0.0037023925688117743,
-0.0014142184518277645,
0.0064742183312773705,
-0.00542390625923872,
-0.00772300036624074,
-0.006660137791186571,
0.0520394928753376,
0.013518824242055416,
0.01959054358303547,
0.012790506705641747,
-0.015945786610245705,
-0.02351633459329605,
-0.03943007439374924,
-0.007709209341555834,
-0.012135093100368977,
0.03882022202014923,
0.05581948161125183,
0.030642516911029816,
-0.013187984935939312,
-0.00745967635884881,
-0.029630407691001892,
0.05948856472969055,
-0.09576292335987091,
-0.0176999568939209,
-0.027625057846307755,
0.032530177384614944,
0.011070363223552704,
-0.021320274099707603
] |
<p>This question is about cosmology and general relativity.</p>
<p>I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read that the universe is infinite.</p>
<ul>
<li>Does it have infinite mass or is it
dishomogeneous? </li>
<li>How can the universe
transition from being finite near the
big bang and infinite 14 billion
years later? Or would an infinite
universe not necessarily have a big
bang at all?</li>
</ul> | 922 | [
-0.04394892603158951,
-0.0347791388630867,
0.020969560369849205,
-0.035431232303380966,
0.07109803706407547,
0.03370751440525055,
-0.03744715452194214,
-0.07832744717597961,
-0.03070780076086521,
-0.016470374539494514,
0.014856725931167603,
0.003723693545907736,
-0.00039437698433175683,
0.01589369960129261,
0.022548172622919083,
0.0017582583241164684,
0.0081322081387043,
-0.011475369334220886,
-0.007116587832570076,
-0.001042158342897892,
0.025566186755895615,
0.028725534677505493,
0.017800522968173027,
0.008502256125211716,
-0.024373522028326988,
0.040901463478803635,
0.0289370846003294,
-0.005193660967051983,
0.05144139379262924,
0.03350268676877022,
-0.005123046226799488,
-0.029998155310750008,
0.01185741275548935,
0.040065567940473557,
0.044333335012197495,
0.0006071212701499462,
-0.015099508687853813,
-0.013236735947430134,
0.0014508417807519436,
-0.01791469007730484,
-0.07335992157459259,
-0.027272073552012444,
-0.009512490592896938,
0.06805603206157684,
-0.01526949554681778,
0.011174287647008896,
-0.011494957841932774,
-0.012830246239900589,
0.024156657978892326,
-0.027889655902981758,
0.05463254079222679,
-0.021373039111495018,
0.07134648412466049,
0.021303744986653328,
0.003183727152645588,
-0.00580320879817009,
0.0949038565158844,
0.07702083140611649,
0.009895640425384045,
-0.055439822375774384,
0.0015626365784555674,
-0.0027420141268521547,
-0.011483184061944485,
-0.03476011008024216,
-0.0075333015993237495,
0.05562075227499008,
-0.004814689978957176,
-0.014597944915294647,
0.01569451205432415,
0.005679147318005562,
0.026822581887245178,
0.0238239336758852,
0.00961424969136715,
-0.01721257157623768,
0.050658706575632095,
-0.009554361924529076,
0.03070647269487381,
-0.007155291736125946,
0.02291964367032051,
0.04125424474477768,
0.01850225031375885,
-0.0003942215407732874,
0.050305772572755814,
0.019405821338295937,
0.01823091320693493,
-0.0014512757770717144,
0.06411869823932648,
0.02006230130791664,
0.004420958925038576,
0.06348064541816711,
0.0039413138292729855,
-0.014666703529655933,
0.023082468658685684,
-0.027082335203886032,
-0.008345642127096653,
0.08192559331655502,
-0.01955718919634819,
0.025750087574124336,
-0.01175097655504942,
-0.0011278969468548894,
0.029719658195972443,
-0.01690750941634178,
0.016949161887168884,
0.07667416334152222,
0.027943618595600128,
-0.023216066882014275,
-0.06927310675382614,
0.0208539217710495,
-0.03997350111603737,
0.0034072729758918285,
-0.014849976636469364,
0.008632663637399673,
-0.011532364413142204,
0.03292353078722954,
-0.004998702555894852,
-0.036454956978559494,
0.0050247833132743835,
-0.02754424326121807,
0.014668697491288185,
0.0739077478647232,
0.033559512346982956,
-0.01406201720237732,
0.003149307332932949,
-0.026465004310011864,
-0.05089188367128372,
-0.010910137556493282,
0.05947166681289673,
-0.009705992415547371,
-0.02652081288397312,
0.04269199073314667,
-0.007989145815372467,
-0.021023163571953773,
0.014212451875209808,
-0.0032027498818933964,
0.03630557656288147,
-0.005057140719145536,
-0.06596239656209946,
-0.045010074973106384,
0.05061665177345276,
-0.0103662284091115,
-0.027746018022298813,
-0.071917325258255,
0.03552684932947159,
0.03470711037516594,
0.024989590048789978,
-0.027569938451051712,
0.0066852206364274025,
-0.0013210645411163568,
0.027921684086322784,
0.005471486132591963,
-0.027121027931571007,
-0.008853551931679249,
-0.011582167819142342,
-0.026288118213415146,
0.03877098113298416,
-0.07927406579256058,
0.01831698976457119,
0.04842951521277428,
0.022191951051354408,
-0.051472458988428116,
0.08653270453214645,
-0.015278754755854607,
-0.003924927208572626,
0.007969132624566555,
0.009362570010125637,
-0.018506433814764023,
0.06780774891376495,
0.04042716696858406,
0.015898089855909348,
0.03412626311182976,
0.019705720245838165,
0.009152260608971119,
0.010180661454796791,
0.02902095764875412,
0.024527013301849365,
-0.03245200216770172,
-0.02048073709011078,
-0.02367851883172989,
-0.01769329607486725,
-0.006554855965077877,
-0.03936678543686867,
-0.017473500221967697,
-0.025335613638162613,
-0.004953806288540363,
0.04192809388041496,
0.013839847408235073,
0.014551778323948383,
0.00992382038384676,
0.0011737640015780926,
-0.044472455978393555,
-0.014693357050418854,
-0.07338499277830124,
-0.012009451165795326,
0.0017516525695100427,
0.009997756220400333,
0.01018208172172308,
0.0393364243209362,
0.000691122142598033,
-0.0613890178501606,
-0.023877263069152832,
0.00028052832931280136,
0.048789236694574356,
-0.002042689360678196,
0.004096667747944593,
0.009657212533056736,
0.05970720201730728,
0.030738113448023796,
-0.008407593704760075,
-0.023903708904981613,
-0.003331806045025587,
-0.020806575194001198,
0.036087725311517715,
-0.008810619823634624,
0.016078798100352287,
-0.04662648215889931,
0.011345716193318367,
-0.0036759984213858843,
0.012498456984758377,
0.01257787924259901,
0.038843002170324326,
-0.006361673586070538,
0.0740727111697197,
0.025379139930009842,
-0.030883507803082466,
-0.004760934505611658,
0.05207109451293945,
-0.006569637916982174,
0.012178407050669193,
-0.03640509396791458,
-0.0038959956727921963,
-0.08206268399953842,
-0.04527514427900314,
0.06476406753063202,
0.02619364857673645,
0.01693904399871826,
0.016496388241648674,
0.02551550604403019,
0.04242567718029022,
0.020656045526266098,
-0.002041405998170376,
-0.028766710311174393,
-0.03696420043706894,
0.022450918331742287,
-0.021310092881321907,
0.04779498651623726,
0.04856942966580391,
0.031000029295682907,
0.005307489074766636,
0.029806451871991158,
-0.031323108822107315,
-0.0008021534886211157,
0.05165601149201393,
0.00747740687802434,
-0.006427074316889048,
-0.0013653766363859177,
-0.06017235293984413,
0.030173351988196373,
-0.013963762670755386,
-0.0016347640193998814,
-0.002095621544867754,
0.010465128347277641,
-0.015690021216869354,
-0.06349010765552521,
0.01593114249408245,
-0.030103925615549088,
0.031724538654088974,
-0.017192095518112183,
-0.03450211137533188,
0.025088906288146973,
-0.040946509689092636,
0.020335860550403595,
0.021363049745559692,
-0.024206319823861122,
-0.04551878571510315,
-0.034753087908029556,
0.011876753531396389,
0.004546295385807753,
0.007379821036010981,
-0.049801744520664215,
-0.01047076378017664,
0.012717027217149734,
-0.030737198889255524,
0.005841006059199572,
0.001337421708740294,
-0.046968139708042145,
0.05829417333006859,
-0.023219551891088486,
-0.014686964452266693,
0.02193867228925228,
-0.0032006551045924425,
0.03391176834702492,
0.02468109503388405,
0.010980403050780296,
-0.0323963388800621,
-0.015661826357245445,
-0.022253675386309624,
0.016934290528297424,
-0.005610585678368807,
-0.00015706497651990503,
0.09093379974365234,
-0.01592576503753662,
-0.06346311420202255,
-0.016028957441449165,
-0.06566900759935379,
-0.03504453971982002,
-0.03044496662914753,
0.008218408562242985,
0.01629732735455036,
-0.03233085572719574,
0.03454206883907318,
0.004185502417385578,
-0.05470019951462746,
0.0032064029946923256,
-0.06761359423398972,
-0.039208002388477325,
0.05235464125871658,
-0.00951396208256483,
0.04698750749230385,
-0.0008399227517656982,
-0.046067412942647934,
0.06242530047893524,
0.05367372930049896,
-0.003252374706789851,
-0.02353801019489765,
0.0078322384506464,
0.028307059779763222,
-0.004828926641494036,
0.02690242789685726,
-0.026360001415014267,
-0.01127693336457014,
-0.038596171885728836,
0.03493235260248184,
0.052236635237932205,
-0.036413609981536865,
-0.027070743963122368,
0.003227032721042633,
0.006397215649485588,
-0.011110188439488411,
0.03526293486356735,
0.035871319472789764,
0.017045319080352783,
-0.02775293029844761,
0.008640844374895096,
-0.017427515238523483,
-0.0033465137239545584,
0.003499184502288699,
-0.04358924180269241,
0.029635591432452202,
0.02586286887526512,
0.0014471540926024318,
-0.04777832701802254,
0.046573102474212646,
0.022792275995016098,
-0.00007782765169395134,
0.022524189203977585,
-0.01995600387454033,
0.04753395915031433,
0.016314096748828888,
-0.001647107768803835,
0.009707153774797916,
0.008194728754460812,
-0.012590494006872177,
-0.01719757169485092,
-0.014619116671383381,
-0.010693266056478024,
0.016792461276054382,
-0.03315037861466408,
-0.022837772965431213,
0.04371374472975731,
0.048183899372816086,
-0.01271404791623354,
-0.04050008952617645,
-0.029885774478316307,
-0.023255005478858948,
-0.06828724592924118,
0.02899504080414772,
-0.030951645225286484,
0.001646446529775858,
0.011634638532996178,
0.06184650585055351,
0.004930797964334488,
0.03221523389220238,
-0.015408720821142197,
0.007849637418985367,
-0.10338371247053146,
-0.009867791086435318,
-0.056947000324726105,
0.012984155677258968,
-0.02478974498808384,
-0.0017334911972284317,
-0.028543418273329735,
0.0005377513589337468,
-0.00454375334084034,
-0.014043653383851051,
-0.025720929726958275,
-0.0286600012332201,
0.012994911521673203,
-0.06176938861608505,
-0.014284015633165836,
-0.014089432545006275,
0.0022502250503748655,
0.05451548844575882,
-0.02996530383825302,
0.05673769861459732,
0.024055596441030502,
0.001495224772952497,
-0.016913190484046936,
0.00418680626899004,
-0.01100881677120924,
0.02739701233804226,
0.03908495232462883,
0.011036733165383339,
0.020122839137911797,
-0.018104201182723045,
0.016475781798362732,
0.05527424067258835,
0.017598940059542656,
-0.00016336482076440006,
0.00042931194184347987,
-0.029528947547078133,
-0.046609360724687576,
0.0012819553958252072,
0.012322928756475449,
0.03795101121068001,
-0.010103996843099594,
-0.014629987068474293,
0.029739264398813248,
0.0038462013471871614,
-0.0164536964148283,
0.05737077817320824,
0.0321863628923893,
-0.020157579332590103,
-0.0047065685503184795,
-0.017215585336089134,
-0.005053855944424868,
-0.06255874782800674,
0.018539980053901672,
0.010400635190308094,
0.015479851514101028,
-0.03998110443353653,
0.039533037692308426,
-0.027281679213047028,
-0.00967346876859665,
-0.02215907908976078,
-0.0387742705643177,
-0.00457775266841054,
0.03244756907224655,
-0.016310175880789757,
-0.009710699319839478,
0.0023478472139686346,
0.04372468218207359,
0.05872729793190956,
0.023371389135718346,
0.01582445576786995,
-0.06816529482603073,
-0.009745589457452297,
0.034517258405685425,
0.007633285131305456,
0.020335495471954346,
-0.01299340557307005,
-0.07519008964300156,
-0.04157501831650734,
0.05574141815304756,
-0.05305476859211922,
0.03143114969134331,
-0.029445873573422432,
0.002961896127089858,
0.008084321394562721,
-0.027598729357123375,
-0.011912773363292217,
0.01870904117822647,
-0.011694086715579033,
-0.007000127341598272,
0.008994990959763527,
0.04018602892756462,
-0.0352993942797184,
0.034351542592048645,
0.019563797861337662,
0.035250224173069,
0.014655769802629948,
0.03858266770839691,
0.03341137245297432,
-0.0028171329759061337,
-0.04103325679898262,
-0.044967230409383774,
0.0231239702552557,
0.024015314877033234,
-0.037291545420885086,
0.03364892676472664,
-0.019177056849002838,
-0.047138553112745285,
0.026577170938253403,
0.009473212994635105,
-0.02399389259517193,
0.00815928541123867,
-0.048463452607393265,
0.030715040862560272,
0.01537376083433628,
-0.016687801107764244,
0.04283105954527855,
0.01622302643954754,
-0.004269347991794348,
0.014977916143834591,
-0.04787106066942215,
0.030787769705057144,
-0.04498356580734253,
-0.012068974785506725,
-0.02179671637713909,
-0.025200922042131424,
-0.050145238637924194,
0.00004608288509189151,
0.007807127665728331,
-0.006391579285264015,
0.002710366854444146,
-0.0664050430059433,
0.028159240260720253,
0.029648397117853165,
0.02891966514289379,
0.005281762219965458,
-0.037666432559490204,
-0.0129533801227808,
0.015814872458577156,
-0.02871408872306347,
0.03524676337838173,
0.013399982824921608,
0.017979655414819717,
0.0054339151829481125,
-0.02983182482421398,
0.030962971970438957,
-0.002480466151610017,
-0.017867831513285637,
0.036893997341394424,
-0.029053552076220512,
0.042971622198820114,
0.004499317146837711,
0.032479774206876755,
-0.0028438197914510965,
-0.06685126572847366,
-0.047032855451107025,
-0.004305963404476643,
-0.01493697240948677,
0.014890467748045921,
-0.0401570126414299,
0.017930269241333008,
0.008615451864898205,
0.04463067650794983,
-0.06754469871520996,
-0.04506942629814148,
0.04751027747988701,
0.0037031190004199743,
-0.020991602912545204,
0.00042685645166784525,
0.04336335137486458,
-0.01957351341843605,
-0.009079805575311184,
-0.02495855838060379,
0.017836585640907288,
-0.03927607089281082,
-0.0029618481639772654,
-0.0005583196762017906,
0.024936312809586525,
0.049338553100824356,
-0.016805250197649002,
-0.016281818971037865,
-0.01178758218884468,
-0.0014870933955535293,
-0.03505599498748779,
-0.012739134952425957,
0.07054610550403595,
-0.017202522605657578,
-0.04593842476606369,
-0.018597129732370377,
-0.0036447711754590273,
0.018336141481995583,
-0.06835224479436874,
0.00010378720617154613,
0.03961222618818283,
-0.02318449504673481,
-0.0022501591593027115,
-0.004413820803165436,
0.011672395281493664,
-0.0045663947239518166,
0.005429429933428764,
-0.021741345524787903,
-0.01377053651958704,
0.024800695478916168,
-0.07460431754589081,
0.03800506144762039,
-0.005897788796573877,
0.016302049160003662,
0.026885611936450005,
0.0351279191672802,
0.00039043507422320545,
-0.03339703381061554,
0.007854655385017395,
-0.07326322048902512,
0.0007020034827291965,
-0.01709183119237423,
0.018142756074666977,
0.013294733129441738,
-0.009402393363416195,
-0.051099639385938644,
-0.03141358122229576,
-0.01721549965441227,
-0.017025182023644447,
0.006770602427423,
0.011975109577178955,
0.01713232509791851,
0.023390397429466248,
-0.01503453217446804,
-0.0021060702856630087,
-0.025802887976169586,
-0.02380102500319481,
0.031855955719947815,
0.0017769901314750314,
0.05027232691645622,
-0.023690303787589073,
-0.011629786342382431,
0.027983160689473152,
0.028738807886838913,
-0.006358861457556486,
0.03516164422035217,
0.03578178584575653,
0.00909531768411398,
0.024615734815597534,
-0.02679447829723358,
-0.045760758221149445,
0.012448284775018692,
-0.02662970870733261,
0.03628777340054512,
0.0031644536647945642,
-0.02493581734597683,
0.02641351893544197,
0.020265644416213036,
0.00404532253742218,
-0.017720719799399376,
0.009489988908171654,
-0.06418855488300323,
-0.013957880437374115,
0.03613375872373581,
0.045530784875154495,
0.016036586835980415,
0.011615038849413395,
0.004287057556211948,
0.0026120522525161505,
-0.018633071333169937,
-0.0004764266195707023,
-0.07554338872432709,
-0.023404613137245178,
-0.038464710116386414,
-0.08166234195232391,
0.04134721681475639,
-0.02027917467057705,
-0.029452547430992126,
-0.021404091268777847,
-0.03777897357940674,
0.010522689670324326,
0.0131000941619277,
0.024811552837491035,
-0.06047888472676277,
0.0354117713868618,
0.013282094150781631,
0.04391874000430107,
-0.014784727245569229,
0.03718903288245201,
0.09102243930101395,
0.054578378796577454,
0.015392284840345383,
-0.03851568326354027,
0.02789205312728882,
-0.021976541727781296,
0.01922541670501232,
-0.04319864884018898,
-0.0029679955914616585,
-0.023558631539344788,
0.041822586208581924,
0.0125187449157238,
0.012485377490520477,
-0.0215289369225502,
-0.019979286938905716,
0.03977358713746071,
-0.03903106972575188,
-0.009707905352115631,
0.00608018459752202,
0.019704408943653107,
-0.00937636848539114,
0.03376264125108719,
-0.044635552912950516,
0.05079111456871033,
-0.011864474043250084,
0.01856253109872341,
-0.041992828249931335,
-0.01377373468130827,
0.002644186606630683,
0.0023478108923882246,
-0.07535538077354431,
0.024627789855003357,
0.008899122476577759,
-0.046865660697221756,
-0.019762516021728516,
-0.001952715334482491,
0.0071342336013913155,
-0.006100358907133341,
0.011225874535739422,
0.025748657062649727,
-0.010219247080385685,
0.013146608136594296,
0.007403447292745113,
-0.008999044075608253,
-0.03174953907728195,
-0.004032673314213753,
-0.004505079239606857,
0.04624442383646965,
-0.04400254413485527,
0.004810608923435211,
-0.01777331903576851,
0.042440515011548996,
0.01750205084681511,
-0.05829056724905968,
0.014810772612690926,
0.04242532327771187,
0.008661339990794659,
-0.006346625275909901,
-0.03803971782326698,
0.0022404748015105724,
0.01577138528227806,
-0.003160814754664898,
0.04652457684278488,
-0.020047888159751892,
-0.022419914603233337,
0.03604605793952942,
-0.02041057124733925,
0.0014601910952478647,
-0.011434637010097504,
-0.006142476573586464,
-0.005094498861581087,
0.014774817042052746,
-0.059989988803863525,
-0.009197654202580452,
0.03698054701089859,
0.007306298241019249,
0.019647499546408653,
0.03224654123187065,
0.030454885214567184,
-0.03133132681250572,
-0.0348069928586483,
0.035635706037282944,
-0.027777714654803276,
-0.031218400225043297,
-0.02168532833456993,
0.001035370398312807,
0.004069085232913494,
0.037237852811813354,
-0.020032303407788277,
0.027807755395770073,
-0.013878013007342815,
0.014826789498329163,
0.017062289640307426,
0.0045209587551653385,
-0.013668826781213284,
0.004792660940438509,
-0.01829984225332737,
0.0193835087120533,
-0.03897426649928093,
0.05420608073472977,
0.060930803418159485,
0.0056076496839523315,
0.010095895268023014,
0.03417866304516792,
-0.008147548884153366,
0.038526929914951324,
0.03223906457424164,
-0.016330763697624207,
0.01683841273188591,
0.020123222842812538,
0.035600192844867706,
-0.017752215266227722,
-0.03176397085189819,
-0.009899410419166088,
0.003184839151799679,
0.008192147128283978,
-0.021879790350794792,
-0.02234814316034317,
0.009097040630877018,
-0.001987636089324951,
0.020906725898385048,
-0.03877045959234238,
-0.007673460058867931,
-0.04476931318640709,
-0.008837622590363026,
0.020432529971003532,
-0.0018099913140758872,
0.0024284422397613525,
0.0549081489443779,
-0.03394906967878342,
-0.03690165653824806,
0.012264309450984001,
-0.021859442815184593,
-0.043126340955495834,
0.012446452863514423,
0.02049478515982628,
-0.019780710339546204,
0.03941573202610016,
0.019411569461226463,
0.001673955819569528,
0.0043323407880961895,
-0.013914315961301327,
-0.03797295689582825,
0.01815969869494438,
0.004911018535494804,
0.046216290444135666,
0.03999217599630356,
-0.02558106556534767,
-0.040568407624959946,
0.05733327940106392,
-0.029347002506256104,
-0.013843018561601639,
-0.030401768162846565,
-0.021101132035255432,
0.02927405945956707,
0.023707132786512375,
0.04414652660489082,
-0.00036771787563338876,
-0.02222859486937523,
0.009227454662322998,
0.014851037412881851,
0.008104359731078148,
-0.023094233125448227,
-0.0031138770282268524,
-0.039262376725673676,
-0.008411991409957409,
-0.011439358815550804,
0.013050523586571217,
0.009641407988965511,
0.04692184925079346,
-0.023896152153611183,
0.04398565739393234,
0.03126484900712967,
-0.013232536613941193,
-0.0935983806848526,
0.0035289155784994364,
0.011752380058169365,
0.008699610829353333,
0.046599842607975006,
-0.0217230636626482,
-0.004898390267044306,
0.02798822708427906,
-0.03504536673426628,
0.041360314935445786,
-0.009351679123938084,
-0.015054231509566307,
-0.05210936442017555,
0.0004875775775872171,
-0.023900054395198822,
0.03368259221315384,
0.058849141001701355,
0.0554075613617897,
-0.008292348124086857,
0.01606724038720131,
-0.03693862631917,
-0.022194156423211098,
-0.00030126050114631653,
0.042503394186496735,
-0.03464224562048912,
0.0022888549137860537,
0.06009138748049736,
-0.024987151846289635,
-0.0027089060749858618,
0.03877560794353485,
0.0003826075990218669,
0.051326826214790344,
0.0018049220088869333,
-0.0016453161370009184,
0.024000318720936775,
0.03218330070376396,
-0.004581076093018055,
0.001974544022232294,
0.010509424842894077,
0.06378660351037979,
0.00904848799109459,
-0.012422729283571243,
0.013581627048552036,
-0.013991142623126507,
-0.001056181499734521,
-0.08569984883069992,
0.019109249114990234,
0.006236317101866007,
-0.00440944405272603,
0.0054965452291071415,
0.014166346751153469,
0.007337296847254038,
0.0059927660040557384,
-0.0379047729074955,
-0.024660242721438408,
-0.030312931165099144,
-0.035740893334150314,
0.04054352268576622,
0.0018313911277800798,
-0.012827723287045956,
0.013413455337285995,
-0.0045912740752100945,
0.020178860053420067,
0.029074441641569138,
0.0010711268987506628,
-0.011513279750943184,
-0.020500337705016136,
-0.011535543948411942,
0.008366677910089493,
-0.010552527382969856,
0.06307010352611542,
-0.01646692492067814,
-0.0422801710665226,
0.03452237695455551,
0.028736425563693047,
0.010333191603422165,
-0.014431490562856197,
-0.06025300547480583,
-0.030160976573824883,
-0.08601609617471695,
0.0009016802650876343,
0.007353954948484898,
-0.00911314133554697,
-0.05720898136496544,
0.003167252754792571,
-0.023103272542357445,
-0.03362498804926872,
0.04404006525874138,
-0.0019586810376495123,
-0.0152352349832654,
0.007393986918032169,
0.005519620142877102,
0.0335652232170105,
-0.050759099423885345,
0.019539153203368187,
0.004965968895703554,
-0.03615434095263481,
-0.004934214521199465,
0.009211761876940727,
-0.009079745039343834,
0.007584356237202883,
0.014624209143221378,
-0.02013377845287323,
0.043695952743291855,
0.01894196681678295,
-0.04691660404205322,
0.04129490628838539,
-0.021301601082086563,
-0.017590941861271858,
0.0540848933160305,
-0.04592224955558777,
0.02767816185951233,
0.05551011115312576,
0.00496556144207716,
-0.05036698281764984,
-0.029606029391288757,
-0.02103201113641262,
0.00846263486891985,
-0.05474478751420975,
-0.005083626136183739,
-0.00693005695939064,
-0.0060582770965993404,
-0.006435043644160032,
0.05401160940527916,
-0.012506844475865364,
-0.01766476221382618,
0.034879375249147415,
-0.007102766074240208,
0.09478909522294998,
-0.042327024042606354,
-0.022346017882227898,
0.041020069271326065,
-0.008895295672118664,
0.01985999196767807,
-0.004083408508449793,
0.04049202799797058,
0.004137798678129911,
0.023570366203784943,
0.035055916756391525,
0.014328135177493095,
-0.006025415845215321,
-0.010685663670301437,
0.043623510748147964,
-0.06503410637378693,
-0.0013515984173864126,
0.0012889730278402567,
-0.019536908715963364,
0.0455317460000515,
0.052488651126623154,
-0.003230202477425337,
0.07556790113449097,
0.0013095797039568424,
0.026221396401524544,
0.005153592675924301,
0.013645310886204243,
-0.042756158858537674,
0.0025736524257808924,
-0.04055385664105415,
0.0355636328458786,
0.002103564329445362,
0.011906757950782776,
-0.018739232793450356,
0.029675712808966637,
0.03915463760495186,
-0.051433905959129333,
0.015171313658356667,
0.02069147862493992,
0.005177353974431753,
-0.0066911811009049416,
0.012408875860273838,
-0.007186634000390768,
-0.035588815808296204,
0.07584568858146667,
0.03557480126619339,
0.02076227031648159,
-0.029370786622166634,
0.0089634470641613,
-0.03947385400533676,
0.06293464452028275,
-0.04145924746990204,
0.0008434051414951682,
-0.04115178436040878,
0.012598703615367413,
-0.017282377928495407,
-0.007017305586487055
] |
<p>Here's something that I've found difficult to wrap my head around. The relationship between the Schwarzschild radius and mass is linear. It's generally known that if you take an object in the universe and squeeze it down to it's Schwarzschild radius, that radius will always be smaller than smaller than the original object's radius. E.x, the sun has 1 solar radius, which is much larger than it's Schwarzschild radius of 3 km.</p>
<p>But if you started calculating Schwarzschild radius for an object with really high mass, things seem to get a bit funky. Take an object that has a mass of $10^{100}$ kilograms. The corresponding Schwarzschild radius for that is $1.48513 \times 10^{73}$ meters. But if we took an object that has the density of the Sun (1410 $kg/m^{-3}$) and tried to find it's radius normally, we end up with a radius of $1.19244 \times 10^{32}$ meters which is smaller than the Schwarzchild radius. How is this possible? I understand that you won't be able to have an object that large enough to even consider this to be "possible", but this still is confusing to me. Are my calculations off?</p> | 4,600 | [
-0.03243621066212654,
-0.013519569300115108,
-0.0019506261451169848,
-0.030153343454003334,
0.039073582738637924,
-0.014099319465458393,
-0.05720169469714165,
-0.038854941725730896,
-0.03343652933835983,
-0.00585993891581893,
0.004692266695201397,
0.011459051631391048,
0.07121261209249496,
0.011114154011011124,
0.048797957599163055,
0.00889597088098526,
-0.04059505835175514,
-0.022689547389745712,
0.01566571369767189,
-0.03775802627205849,
0.038538869470357895,
0.02626141346991062,
0.01872950606048107,
-0.01108829490840435,
-0.005433585029095411,
0.014537149108946323,
-0.010684516280889511,
0.007023617159575224,
0.04370734840631485,
0.04180857911705971,
0.019847553223371506,
-0.018667755648493767,
0.036578137427568436,
0.027881108224391937,
0.03596821054816246,
-0.005145478527992964,
-0.023624518886208534,
-0.033514101058244705,
-0.018952621147036552,
0.06047174334526062,
-0.06471992284059525,
-0.02233707904815674,
-0.03233442083001137,
0.045298654586076736,
-0.02358824945986271,
-0.02300645224750042,
0.0005399758229032159,
-0.03391037881374359,
0.033249381929636,
-0.04896707832813263,
0.06439516693353653,
0.05423368141055107,
0.06375239044427872,
0.02430974319577217,
-0.012260539457201958,
-0.011379257775843143,
0.08792617172002792,
0.04990800842642784,
-0.01933947205543518,
-0.01985696703195572,
-0.03270812705159187,
-0.01264460664242506,
-0.030703550204634666,
0.011594274081289768,
0.009420436806976795,
0.04291347414255142,
-0.04603389650583267,
0.021265646442770958,
0.00891659315675497,
-0.014238506555557251,
0.043787796050310135,
-0.003963344730436802,
-0.014627802185714245,
-0.004991831257939339,
0.00026446336414664984,
-0.015341673977673054,
0.0067972950637340546,
0.007554181851446629,
0.033138811588287354,
0.04571709409356117,
-0.014949546195566654,
0.021870864555239677,
0.048789914697408676,
0.03824609890580177,
0.01749240979552269,
0.010519709438085556,
0.0635136216878891,
0.01633920520544052,
0.013784968294203281,
-0.008327247574925423,
-0.034402165561914444,
-0.0031522619538009167,
0.04650291055440903,
-0.03878714144229889,
-0.019744154065847397,
0.019170882180333138,
-0.0035911970771849155,
0.04911649599671364,
-0.01515863835811615,
-0.009268521331250668,
0.003962959628552198,
-0.015066412277519703,
0.01635214313864708,
0.049837104976177216,
0.03717891871929169,
-0.0503976009786129,
-0.04487030953168869,
0.05662999302148819,
-0.03437013179063797,
-0.03482814505696297,
-0.022993337363004684,
0.00904210563749075,
-0.023258313536643982,
-0.011233746074140072,
0.0363028347492218,
-0.04040093347430229,
0.0314812958240509,
-0.03499331697821617,
0.03370138630270958,
0.04616307094693184,
0.029049687087535858,
-0.0008275300497189164,
0.033665984869003296,
-0.05077049881219864,
-0.04996398836374283,
0.029448935762047768,
0.03970407322049141,
0.014222959987819195,
-0.014355283230543137,
0.01731037348508835,
0.006712109316140413,
-0.017305990681052208,
0.004027075134217739,
0.013447294011712074,
0.05454573035240173,
-0.03641842305660248,
-0.07216902077198029,
-0.04514146223664284,
0.03595733642578125,
0.020853709429502487,
-0.02237715572118759,
-0.054218027740716934,
0.02854309231042862,
0.04185103625059128,
0.08974866569042206,
0.020887555554509163,
-0.01720006763935089,
0.019148115068674088,
0.05421411991119385,
0.0036188075318932533,
-0.01760818623006344,
-0.00018845840531866997,
0.008413953706622124,
-0.044533148407936096,
-0.0015735018532723188,
-0.10049298405647278,
0.02284306474030018,
0.00889789778739214,
0.018292579799890518,
-0.017772577702999115,
0.05015186965465546,
-0.00558754988014698,
0.010891309939324856,
0.007990997284650803,
0.007497449871152639,
-0.013521607965230942,
0.07944406569004059,
0.007462823297828436,
-0.045426927506923676,
0.03852235898375511,
0.02989845909178257,
0.00959747564047575,
0.06935145705938339,
0.03865421935915947,
0.021566731855273247,
-0.021156013011932373,
-0.0007831230177544057,
-0.059807684272527695,
-0.008749901317059994,
0.028261318802833557,
-0.02559339627623558,
-0.032130222767591476,
-0.024888519197702408,
0.015115438960492611,
0.043208565562963486,
0.0379025824368,
-0.0183341633528471,
-0.01577322743833065,
0.010314393788576126,
-0.07579971104860306,
-0.02040296420454979,
-0.04533708095550537,
0.01870938017964363,
0.029414044693112373,
0.022186292335391045,
0.02452290616929531,
0.0030598314478993416,
0.033136073499917984,
-0.0023048720322549343,
-0.018904801458120346,
0.022919591516256332,
0.05283142253756523,
-0.016193054616451263,
-0.00855046696960926,
0.0071921744383871555,
0.05446402356028557,
0.05259866639971733,
-0.00023219265858642757,
-0.011617714539170265,
-0.005686173215508461,
-0.04732876643538475,
0.008268828503787518,
0.020344730466604233,
0.007562620099633932,
-0.03682997450232506,
-0.023556560277938843,
0.02200264111161232,
0.009997515939176083,
-0.0016291881911456585,
0.04509413242340088,
0.0010283739538863301,
0.10126436501741409,
0.05489546060562134,
0.00015629852714482695,
-0.01887180283665657,
0.04236024618148804,
0.013578809797763824,
-0.00011366623220965266,
-0.028204375877976418,
-0.03892979770898819,
-0.06109700724482536,
0.02423669770359993,
-0.004147382918745279,
0.018049875274300575,
-0.028346868231892586,
0.027086151763796806,
0.05062412470579147,
0.03809991851449013,
0.043394785374403,
0.009153014048933983,
-0.03615347668528557,
-0.01401269156485796,
-0.009836751036345959,
-0.004626605659723282,
0.019669996574521065,
0.0035319793969392776,
-0.004429753869771957,
0.01091684028506279,
0.009009849280118942,
-0.012114150449633598,
0.00022739604173693806,
0.005575031507760286,
-0.039030760526657104,
0.008130915462970734,
-0.00615579541772604,
0.0006759946700185537,
0.037281230092048645,
-0.03578341379761696,
0.002693255664780736,
0.05376053974032402,
0.007128436584025621,
-0.013223236426711082,
-0.05151864141225815,
-0.012358983047306538,
0.04381220042705536,
0.005023229401558638,
-0.029243599623441696,
-0.007481459062546492,
-0.007216089870780706,
-0.04469623044133186,
-0.011127863079309464,
-0.0407092422246933,
0.008936691097915173,
-0.04993487149477005,
0.009883913211524487,
0.014680063351988792,
0.026097014546394348,
0.03168534114956856,
-0.018703896552324295,
-0.02028663642704487,
-0.00785586517304182,
-0.018976449966430664,
0.01051050703972578,
0.003139105159789324,
-0.06294877827167511,
-0.004347251262515783,
-0.02006593719124794,
-0.043576907366514206,
0.04402200132608414,
-0.0018440982094034553,
0.006262049078941345,
0.0008740649791434407,
-0.01313359197229147,
-0.03468608111143112,
0.012376761063933372,
-0.043436817824840546,
-0.007158737629652023,
-0.006620325148105621,
0.023534204810857773,
0.044044189155101776,
0.0018311484018340707,
-0.028400398790836334,
0.02179882489144802,
-0.009695511311292648,
-0.020461708307266235,
-0.03722909092903137,
0.008731343783438206,
-0.01625361293554306,
-0.04338424280285835,
0.029129257425665855,
-0.0018993482226505876,
0.009516003541648388,
0.003959622234106064,
-0.023444093763828278,
-0.017724446952342987,
0.02505124732851982,
0.0033182355109602213,
0.011287021450698376,
0.013623211532831192,
-0.039262764155864716,
0.08809593319892883,
-0.004415031988173723,
0.010146268643438816,
-0.04632731154561043,
0.017758378759026527,
0.002858781022951007,
0.007874425500631332,
-0.02330644056200981,
0.03678852319717407,
-0.01470134686678648,
-0.000271909695584327,
0.020882736891508102,
0.019830506294965744,
0.007654867600649595,
-0.009241443127393723,
-0.04250216856598854,
0.005793166812509298,
-0.03151310607790947,
0.02856661006808281,
0.06203716993331909,
-0.01099545881152153,
-0.0076288036070764065,
0.027254579588770866,
-0.027659384533762932,
0.06510042399168015,
-0.0188326183706522,
-0.09238411486148834,
0.011875119991600513,
0.02091163396835327,
0.0019379508448764682,
-0.01238520909100771,
0.018263643607497215,
-0.015463805757462978,
-0.01796381175518036,
0.050130248069763184,
0.0038680732250213623,
0.05078329145908356,
-0.014541855081915855,
-0.013646980747580528,
0.007864520885050297,
0.04726701229810715,
-0.02383008785545826,
-0.01277401763945818,
-0.02411573752760887,
-0.030037157237529755,
0.020960992202162743,
-0.005997100844979286,
-0.0262707881629467,
0.051182087510824203,
0.03576866537332535,
0.007446242496371269,
-0.036212433129549026,
-0.006708463188260794,
-0.007462537381798029,
-0.07336854934692383,
-0.036922093480825424,
0.021296944469213486,
0.01401420310139656,
0.0026957476511597633,
0.017354067414999008,
0.06638108938932419,
-0.002401413396000862,
0.023650022223591805,
-0.025923850014805794,
-0.08810736238956451,
0.013443812727928162,
-0.07563548535108566,
-0.02391035482287407,
-0.02147739939391613,
-0.04021422564983368,
-0.05330655723810196,
-0.016784055158495903,
0.01693701185286045,
-0.003956918139010668,
-0.0009873389499261975,
-0.05804845690727234,
-0.009296673350036144,
-0.016968967393040657,
-0.013211488723754883,
-0.01674877479672432,
0.03569648042321205,
0.023965898901224136,
-0.008313113823533058,
-0.0131612503901124,
-0.0035682886373251677,
-0.028643058612942696,
0.001143910805694759,
-0.0187385194003582,
0.0248306542634964,
0.02296162024140358,
0.037794969975948334,
0.023027632385492325,
0.0022492515854537487,
-0.005472737364470959,
-0.02964724227786064,
0.029444267973303795,
0.039226945489645004,
0.017205100506544113,
-0.006255059968680143,
-0.02253616414964199,
-0.04439700022339821,
-0.015783825889229774,
-0.008172981441020966,
0.06166328117251396,
-0.017415883019566536,
0.033121176064014435,
0.02914116159081459,
-0.001968878321349621,
0.012543200515210629,
0.01745608262717724,
0.04163062945008278,
-0.048938117921352386,
-0.02914791740477085,
-0.053061600774526596,
-0.03466487675905228,
-0.04826968535780907,
-0.01442721951752901,
0.021050160750746727,
-0.02318025566637516,
-0.0318215973675251,
-0.031821805983781815,
0.007762571796774864,
-0.03882066160440445,
-0.007721202913671732,
-0.015413149259984493,
-0.008816744200885296,
0.01814739778637886,
-0.03944845125079155,
0.0027820977848023176,
0.024379229173064232,
0.013178215362131596,
0.07596152275800705,
-0.020346295088529587,
0.012582311406731606,
-0.052737507969141006,
-0.04823723062872887,
0.005500601604580879,
0.018439967185258865,
-0.007632025051862001,
0.0065476843155920506,
-0.07195402681827545,
-0.02237866073846817,
0.04782433062791824,
-0.049408137798309326,
0.02701467275619507,
0.0003478422877378762,
0.03005102463066578,
-0.010011735372245312,
-0.02154637686908245,
0.00904415175318718,
-0.0006860305438749492,
-0.01835326850414276,
-0.018868114799261093,
-0.033923257142305374,
0.029049336910247803,
-0.02394375391304493,
0.00850184541195631,
0.026089059188961983,
0.04672848805785179,
0.011566093191504478,
-0.0287263635545969,
0.0029754627030342817,
-0.014715436846017838,
-0.014345478266477585,
-0.09624128043651581,
-0.01250105444341898,
0.015293236821889877,
-0.028037160634994507,
0.03943343833088875,
-0.02944285050034523,
-0.03326268121600151,
0.03658605366945267,
-0.004130029119551182,
-0.026885030791163445,
-0.009836592711508274,
-0.03320742025971413,
0.04303897172212601,
0.015931198373436928,
-0.027409041300415993,
0.028277959674596786,
-0.01494360901415348,
0.027665287256240845,
0.00026877710479311645,
-0.061204299330711365,
0.0333123654127121,
-0.02887454815208912,
-0.02910495176911354,
-0.03344392403960228,
-0.0023370725102722645,
-0.03622827306389809,
0.06793033331632614,
-0.008554738946259022,
0.0195517148822546,
0.01012252178043127,
-0.014816856011748314,
0.03903580084443092,
0.026469547301530838,
0.007039478048682213,
0.0626494511961937,
-0.009200780652463436,
0.009570468217134476,
0.02030367963016033,
-0.037793491035699844,
0.03194164112210274,
0.010711737908422947,
0.01268119364976883,
0.025937266647815704,
-0.016583655029535294,
0.021204425022006035,
0.014063192531466484,
-0.004357227589935064,
0.02480834163725376,
-0.051706764847040176,
0.05854932591319084,
-0.03405270725488663,
-0.009363660588860512,
0.0009990816470235586,
-0.02454828843474388,
-0.021705387160182,
-0.048690710216760635,
-0.003978169057518244,
0.036593519151210785,
-0.06688916683197021,
0.0026238728314638138,
0.02530364878475666,
0.007152386475354433,
-0.08709269762039185,
-0.010875249281525612,
0.023825636133551598,
0.01877759024500847,
-0.003235196229070425,
-0.015787426382303238,
-0.0030610784888267517,
-0.0204900112003088,
-0.04237474873661995,
-0.015571084804832935,
0.05067472159862518,
-0.03966837376356125,
0.014058122411370277,
-0.008404157124459743,
0.016196422278881073,
0.042791932821273804,
-0.05523999407887459,
-0.020565640181303024,
-0.02568533457815647,
0.03185915946960449,
0.020360149443149567,
0.002915665041655302,
0.05067848041653633,
-0.03446104750037193,
-0.05742473900318146,
-0.03887631371617317,
-0.028660178184509277,
0.025667106732726097,
-0.010173621587455273,
-0.005251334048807621,
0.058099012821912766,
0.03726445138454437,
0.052319806069135666,
0.019547872245311737,
0.02157709375023842,
-0.01832355558872223,
0.017359275370836258,
-0.0076205735094845295,
-0.0288240984082222,
-0.030031735077500343,
-0.04253183305263519,
0.05187240242958069,
0.008082855492830276,
0.027533451095223427,
-0.0020539495162665844,
0.05943400040268898,
-0.001389970420859754,
0.0046384152956306934,
0.0009128193487413228,
-0.046434707939624786,
0.01971960812807083,
0.04097868502140045,
-0.0010164721170440316,
0.034291841089725494,
0.019382918253540993,
-0.0005335730966180563,
-0.015324116684496403,
-0.045299556106328964,
0.0008537853136658669,
0.06401441246271133,
-0.03497691825032234,
0.0245266854763031,
0.00949040986597538,
-0.016305547207593918,
0.02445056103169918,
-0.049012064933776855,
0.0012133211130276322,
0.00013962978846393526,
0.002568481955677271,
0.015620672143995762,
-0.05799470469355583,
-0.018175583332777023,
0.03706446290016174,
0.03245551139116287,
-0.0032138852402567863,
0.005574533715844154,
0.010828436352312565,
0.037127189338207245,
-0.0030792781617492437,
-0.0019940112251788378,
-0.02616535685956478,
0.013566154055297375,
-0.006276267580688,
0.00676680076867342,
0.002061334205791354,
0.04458637163043022,
0.009194218553602695,
0.009287823922932148,
0.046381641179323196,
-0.025639608502388,
-0.05029882863163948,
-0.040157951414585114,
-0.00586082274094224,
0.04363873600959778,
0.017598683014512062,
0.0019002038752660155,
0.0029430375434458256,
0.0029320339672267437,
0.03479517251253128,
0.029794080182909966,
0.011464728973805904,
-0.04515376687049866,
-0.03339401260018349,
-0.034726254642009735,
-0.07019878178834915,
0.03267500549554825,
-0.004837202373892069,
-0.0335538275539875,
0.029345406219363213,
-0.04351142421364784,
0.005114113911986351,
0.05266595259308815,
0.02540264092385769,
-0.002360473619773984,
0.06442835181951523,
0.0027640906628221273,
0.006345713045448065,
-0.01584574207663536,
0.02930409088730812,
0.1042003259062767,
0.0462283194065094,
0.0052510942332446575,
-0.05009012296795845,
0.032137759029865265,
-0.0228346548974514,
-0.005755445454269648,
-0.044194936752319336,
0.04295353963971138,
-0.0018185647204518318,
-0.026554465293884277,
0.010302822105586529,
0.04028675705194473,
-0.01114310696721077,
-0.02826560102403164,
0.04256243631243706,
-0.01870785281062126,
-0.008402934297919273,
0.014796185307204723,
0.04883253574371338,
-0.03342781215906143,
-0.024094073101878166,
0.0007999982917681336,
0.039744455367326736,
-0.033198386430740356,
0.010720746591687202,
-0.06906372308731079,
0.004778319504112005,
-0.013061163946986198,
-0.036899764090776443,
-0.06332318484783173,
0.03755378723144531,
-0.0031662252731621265,
-0.06114515662193298,
-0.01098798867315054,
0.017426643520593643,
0.01824200339615345,
-0.0005046335281804204,
0.0039016231894493103,
0.03817780315876007,
-0.024539846926927567,
0.053419120609760284,
-0.0189992506057024,
0.01433713547885418,
-0.05003264173865318,
-0.01909641921520233,
-0.024722889065742493,
0.04294428601861,
-0.03105434775352478,
0.00044778527808375657,
0.008944257162511349,
0.03333095833659172,
-0.00965126883238554,
-0.055087458342313766,
0.018580907955765724,
-0.019100354984402657,
0.019231293350458145,
0.00712205097079277,
-0.027083536610007286,
0.020132072269916534,
0.04551597684621811,
0.009741545654833317,
0.028481636196374893,
-0.02117849327623844,
0.01804875209927559,
0.03558844327926636,
-0.022664787247776985,
0.026420610025525093,
-0.010944339446723461,
-0.01360925380140543,
-0.01074546854943037,
0.012383801862597466,
-0.04017206281423569,
-0.015084798447787762,
0.03399203345179558,
0.0030581566970795393,
0.04109052196145058,
0.022547820582985878,
0.011165130883455276,
-0.011496967636048794,
-0.053841762244701385,
0.024130942299962044,
-0.031651828438043594,
-0.022071437910199165,
-0.04255262017250061,
-0.010060465894639492,
0.019649688154459,
0.042243797332048416,
-0.024219298735260963,
0.005430353805422783,
-0.012193182483315468,
0.015068513341248035,
-0.028514869511127472,
-0.028646046295762062,
-0.013784519396722317,
0.03392568603157997,
-0.034961119294166565,
0.03593781962990761,
0.008999901823699474,
0.016829993575811386,
0.0367586612701416,
0.011698300950229168,
-0.008679220452904701,
0.025649897754192352,
-0.023839177563786507,
0.004042594227939844,
-0.011803722009062767,
-0.010719852522015572,
-0.0011086107697337866,
0.0012212081346660852,
0.0010284100426360965,
-0.002264247741550207,
-0.03826881945133209,
-0.010908485390245914,
-0.03249930962920189,
-0.007223564200103283,
0.033909354358911514,
-0.00693465257063508,
0.007165652234107256,
0.0015264308312907815,
-0.013529038056731224,
-0.033854104578495026,
-0.02540949359536171,
-0.04668763279914856,
0.028397895395755768,
0.014656017534434795,
-0.03120778687298298,
-0.013125771656632423,
0.01596205309033394,
-0.01415658462792635,
-0.05256463214755058,
0.010191972367465496,
0.020260760560631752,
-0.017424389719963074,
-0.036469604820013046,
0.04442108795046806,
-0.01843980699777603,
0.06867893040180206,
-0.01737350784242153,
-0.016406705603003502,
0.048394300043582916,
-0.054169993847608566,
-0.03901856765151024,
0.0642082467675209,
0.013725860975682735,
0.033355340361595154,
0.009529752656817436,
0.0028350530192255974,
-0.0119519317522645,
0.09627663344144821,
-0.014864730648696423,
-0.00754996482282877,
0.0021675927564501762,
-0.03384178504347801,
-0.013525253161787987,
0.005192987155169249,
0.02171723172068596,
-0.042111627757549286,
0.020225245505571365,
0.044176727533340454,
0.012580642476677895,
-0.026175497099757195,
0.01355087012052536,
0.025101730599999428,
-0.0008502499549649656,
0.026921264827251434,
-0.003596695838496089,
0.004758534021675587,
0.03325808420777321,
0.05404290184378624,
-0.049117062240839005,
0.06140820309519768,
0.07892212271690369,
0.003306789556518197,
-0.09954610466957092,
-0.018269365653395653,
-0.02339254692196846,
-0.006542587652802467,
0.04764966666698456,
-0.061536386609077454,
-0.005169531796127558,
-0.00369832175783813,
-0.03213224560022354,
0.029546773061156273,
-0.046512994915246964,
-0.012815816327929497,
-0.028116311877965927,
-0.045432545244693756,
-0.004579080734401941,
0.030495481565594673,
0.057282641530036926,
0.0615357831120491,
-0.015206740237772465,
0.0007827209774404764,
-0.01002897322177887,
-0.014146300964057446,
-0.023436326533555984,
0.028931409120559692,
-0.007990950718522072,
-0.005637927912175655,
0.05005359649658203,
-0.014623007737100124,
-0.03862231969833374,
0.06611177325248718,
0.00928699690848589,
-0.021111220121383667,
0.03202221170067787,
0.031956978142261505,
0.010672414675354958,
0.006491002161055803,
0.0673399269580841,
0.010888278484344482,
0.002204112708568573,
0.01783468760550022,
0.039491958916187286,
0.006723152007907629,
-0.005894782952964306,
0.01155315525829792,
0.04361618682742119,
-0.03860313072800636,
0.008526860736310482,
0.036658432334661484,
-0.004206961020827293,
0.0025802890304476023,
0.010006650350987911,
0.0045995814725756645,
0.01810925453901291,
-0.03235749900341034,
-0.007345947436988354,
-0.05125969275832176,
-0.0073691136203706264,
0.044169798493385315,
0.025486338883638382,
-0.011623612605035305,
0.024836184456944466,
-0.0013544687535613775,
-0.025672320276498795,
-0.005442900583148003,
-0.023188918828964233,
-0.00775834871456027,
-0.021804826334118843,
0.011566332541406155,
0.013713844120502472,
-0.019170287996530533,
0.03331452235579491,
-0.0575200617313385,
-0.03882356360554695,
0.059188392013311386,
0.012113434262573719,
0.024234632030129433,
-0.024270009249448776,
-0.044761329889297485,
-0.013218139298260212,
-0.04774244502186775,
0.0036744745448231697,
-0.01786138117313385,
-0.016050932928919792,
-0.0453120656311512,
-0.02487875148653984,
-0.0008461379911750555,
-0.025753730908036232,
0.049294691532850266,
-0.012102850712835789,
-0.003607827238738537,
0.011974437162280083,
-0.006361064035445452,
0.019079482182860374,
-0.03502776846289635,
-0.005620255600661039,
0.025983883067965508,
-0.033940110355615616,
-0.002937447279691696,
0.00895788986235857,
-0.0018449696945026517,
0.035512544214725494,
0.028076952323317528,
-0.006981876213103533,
0.042921315878629684,
0.017845220863819122,
0.001683312002569437,
0.052873335778713226,
0.010342424735426903,
0.019386403262615204,
0.05803472176194191,
0.015244117006659508,
0.02078082598745823,
0.041390642523765564,
0.0032870431896299124,
-0.015628233551979065,
0.0196630097925663,
-0.017496762797236443,
0.00464235246181488,
-0.02219095081090927,
-0.029982110485434532,
0.0274528618901968,
-0.04002261161804199,
-0.016583748161792755,
0.0353495255112648,
-0.015866974368691444,
-0.030521182343363762,
0.04344600439071655,
0.008108709007501602,
0.04254075512290001,
-0.015401128679513931,
0.0073796529322862625,
0.01843777485191822,
0.0034084287472069263,
-0.006701677106320858,
0.034905269742012024,
0.04382055252790451,
-0.000690211309120059,
-0.016851037740707397,
0.04639655724167824,
0.008758332580327988,
0.002100866986438632,
-0.01017102599143982,
0.07460150867700577,
-0.029053376987576485,
-0.047544773668050766,
-0.03213215246796608,
-0.025507580488920212,
0.018887287005782127,
-0.0013145379489287734,
-0.025348326191306114,
0.06357903778553009,
0.010428747162222862,
0.0072237653657794,
-0.01365432795137167,
-0.010751522146165371,
-0.020394418388605118,
0.030179599300026894,
-0.009988617151975632,
0.05013809725642204,
-0.00495713297277689,
-0.014676501043140888,
-0.024131078273057938,
0.005280716344714165,
0.04493306204676628,
-0.0010566810378804803,
-0.010383615270256996,
-0.004847787320613861,
-0.00293346238322556,
-0.04146818071603775,
-0.031352005898952484,
-0.008832518011331558,
-0.017256639897823334,
0.037388432770967484,
0.0482826754450798,
0.009382057003676891,
0.031498223543167114,
-0.01359723974019289,
-0.003265561070293188,
0.020544279366731644,
-0.057001493871212006,
-0.05077309533953667,
-0.014012050814926624,
0.024381157010793686,
-0.008975914679467678,
-0.008725968189537525
] |
<p>I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the process described precisely.</p>
<p>Here's the deal: at first there is a nice object, a star. Stars can be nicely modeled by general relativity, nuclear physics and statistical physics combined and very much is known about these models and it can be observed whether they agree with things like light and neutrino fluxes, surface temperature and probably also lot of other stuff I know nothing about.</p>
<p>After the collapse we are left with another nice object, a black hole. We know that <a href="http://en.wikipedia.org/wiki/No-hair_theorem">black holes have no hair</a>.</p>
<p>The question is: what happens in-between? More precisely, between the time when all of the nuclear material has been burned out (and if possible ignore effects like reheating of the star after big enough compression) and the time where there is nothing more than just a black hole.</p>
<blockquote>
<ul>
<li><p>Give a description of what happens during the collapse?</p></li>
<li><p>How does the star "lose its hair"?</p></li>
<li><p>Can the actual collapse be solved analytically?</p></li>
<li><p>At what point is singularity created?</p></li>
</ul>
</blockquote>
<p><strong>Update:</strong> <em>I don't want to know what an outside observer will see. Instead, I'd like to find out what an individual part of the dead star will "feel" when a black hole is about to form near it. In other words, I want a complete solution (ideally analytical, but numerical would be also completely fine)</em></p>
<p>Feel free to assume anything that makes your life easier. Spherical symmetry is definitely fine. Also, if for any reason the questions don't make sense (like Cauchy problem is ill-defined in the presence of the singularity) feel free to interpret them in a way that make them sensible (e.g. assume that black hole is built from D-branes).</p>
<hr>
<p>Also, I have a feeling that what I intended as a simple question at first ended up being pretty complex. If you think it should be split into smaller (and therefore more manageable and answerable) parts, let me know.</p> | 4,601 | [
-0.056217607110738754,
-0.052017152309417725,
0.009714804589748383,
-0.053552042692899704,
0.009415344335138798,
-0.011691578663885593,
-0.06713280826807022,
-0.06223052367568016,
-0.02071213722229004,
-0.0690409392118454,
0.04020790755748749,
0.028043467551469803,
0.035941384732723236,
0.06622476130723953,
-0.00970572978258133,
-0.002879102947190404,
0.005940023344010115,
-0.05796276032924652,
-0.02657141163945198,
-0.014511952176690102,
0.028047485277056694,
-0.004562688525766134,
-0.01952611654996872,
-0.019673693925142288,
-0.013540772721171379,
0.016280582174658775,
0.0192149356007576,
-0.017610330134630203,
-0.006699003744870424,
0.06428719311952591,
-0.029569609090685844,
-0.03539610281586647,
0.016345659270882607,
0.05495457723736763,
0.06285355240106583,
0.0432145819067955,
-0.002207598416134715,
-0.004851820878684521,
-0.0030554526019841433,
0.021117739379405975,
-0.0032610513735562563,
-0.0251638013869524,
-0.01783498376607895,
0.006649745628237724,
-0.03736715018749237,
-0.00208994559943676,
-0.008406457491219044,
0.003922638017684221,
0.02724180929362774,
-0.04841175302863121,
0.04560711979866028,
0.02304430864751339,
0.01814577728509903,
0.007701707072556019,
-0.01218229066580534,
0.0012392352800816298,
0.07764165103435516,
0.08005771785974503,
-0.017832504585385323,
-0.048649199306964874,
-0.02622714266180992,
0.010647888295352459,
-0.0457422100007534,
-0.01481869351118803,
-0.005463948007673025,
0.035031091421842575,
0.007444361690431833,
-0.007393442094326019,
0.04217103496193886,
-0.010109649039804935,
-0.0027050597127527,
-0.008504881523549557,
0.010880030691623688,
0.02862084098160267,
0.020055288448929787,
-0.016383521258831024,
0.028343692421913147,
0.011140570044517517,
0.03437041491270065,
0.041371479630470276,
-0.02791742980480194,
0.009334051050245762,
0.02528703399002552,
0.017555400729179382,
0.008433355018496513,
0.025121772661805153,
0.09551921486854553,
-0.013216582126915455,
0.029065363109111786,
0.03396754711866379,
-0.0011511920019984245,
-0.0013622721889987588,
0.01785069890320301,
-0.035448890179395676,
-0.04865454509854317,
0.026933053508400917,
0.011953587643802166,
0.060703061521053314,
-0.01906830631196499,
-0.024450942873954773,
0.025220228359103203,
0.0014623744646087289,
0.008559582754969597,
0.07496682554483414,
0.032175395637750626,
-0.028187697753310204,
-0.05610091984272003,
-0.004595884121954441,
-0.03031085804104805,
-0.04797448217868805,
-0.04494791105389595,
0.024693725630640984,
-0.006690812297165394,
-0.021619729697704315,
0.009201825596392155,
-0.03462069854140282,
-0.0038342252373695374,
-0.04012630879878998,
0.05002357065677643,
0.04696159437298775,
0.01930808462202549,
0.027937039732933044,
0.010264419950544834,
-0.036254435777664185,
-0.05230052396655083,
0.0013032743008807302,
0.04949745908379555,
-0.02662762813270092,
-0.036560773849487305,
-0.010566153563559055,
-0.015138505958020687,
-0.006768749561160803,
0.05512809008359909,
-0.010044573806226254,
0.012474330142140388,
-0.023082733154296875,
-0.09966607391834259,
-0.040243685245513916,
0.039456382393836975,
0.006706829648464918,
-0.03142230212688446,
-0.03965779021382332,
-0.004223592579364777,
0.028823882341384888,
0.0804033949971199,
-0.021253427490592003,
-0.01748153194785118,
0.009746359661221504,
0.07138673961162567,
0.0071481578052043915,
-0.023592453449964523,
-0.0023833431769162416,
-0.0033831512555480003,
-0.0038971598260104656,
-0.037426434457302094,
-0.04806124046444893,
0.025741633027791977,
0.06203698366880417,
0.017608651891350746,
0.015524578280746937,
0.03902902826666832,
-0.021015450358390808,
0.007851831614971161,
0.0072370548732578754,
-0.022129764780402184,
-0.025030197575688362,
0.06750459223985672,
0.01221416238695383,
-0.03992738947272301,
0.02893640100955963,
-0.0038021232467144728,
0.014616594649851322,
-0.004162953235208988,
0.018903447315096855,
0.03596752882003784,
-0.035285644233226776,
-0.01584937982261181,
-0.030906956642866135,
-0.03422283008694649,
0.006283816881477833,
-0.05238422751426697,
-0.024852804839611053,
-0.006802378688007593,
-0.012723160907626152,
0.021010231226682663,
0.04790734127163887,
0.022264748811721802,
-0.012611190788447857,
0.012998952530324459,
-0.024865170940756798,
-0.00033060822170227766,
-0.07967383414506912,
-0.018050648272037506,
0.015621944330632687,
-0.00028800612199120224,
0.004651207011193037,
0.013721223920583725,
0.025202330201864243,
-0.03789210319519043,
-0.020558025687932968,
0.05427664890885353,
0.06426139175891876,
-0.0013879904290661216,
0.012092079035937786,
0.008115863427519798,
0.058364253491163254,
0.023291749879717827,
-0.008446046151220798,
-0.007288039196282625,
-0.016611386090517044,
-0.012872432358562946,
-0.025791045278310776,
0.0271140243858099,
-0.0002854994381777942,
-0.029023176059126854,
0.012497825548052788,
0.03718367591500282,
-0.0032559598330408335,
0.04207676649093628,
0.013151432387530804,
-0.015513784252107143,
0.0534050427377224,
0.03619983047246933,
0.010519256815314293,
0.021921850740909576,
0.03364596888422966,
0.014928067103028297,
0.018172958865761757,
-0.01629403792321682,
-0.011575819924473763,
-0.023653386160731316,
0.004506729543209076,
0.05835684761404991,
0.02680741809308529,
-0.021851111203432083,
0.02224745601415634,
0.036217860877513885,
0.05221729725599289,
0.024739975109696388,
0.023804614320397377,
-0.03084406815469265,
0.008631718344986439,
-0.009473199024796486,
-0.06136497110128403,
-0.005370376631617546,
0.014159687794744968,
0.0010652083437889814,
0.025735732167959213,
0.0073936702683568,
-0.022766537964344025,
-0.007006078492850065,
0.03932446613907814,
0.03172192722558975,
-0.004845315590500832,
-0.007904584519565105,
-0.032091107219457626,
0.038267794996500015,
0.00851461011916399,
0.004468301776796579,
0.005729710217565298,
0.02202867530286312,
0.010926397517323494,
-0.0644478052854538,
-0.0017931773327291012,
0.021692028269171715,
0.05853160098195076,
0.006544345524162054,
0.003738521598279476,
0.006746876984834671,
-0.012416311539709568,
0.017944863066077232,
0.004836380947381258,
0.01186898723244667,
-0.021194549277424812,
0.011724021285772324,
0.03577518090605736,
0.023952998220920563,
0.021852385252714157,
-0.048172127455472946,
-0.03860785812139511,
-0.016885610297322273,
-0.02062419056892395,
0.007846933789551258,
0.04316284507513046,
-0.0445353202521801,
0.013234799727797508,
-0.028684325516223907,
-0.008948714472353458,
0.005801643710583448,
-0.009411807172000408,
0.03284787759184837,
0.030218232423067093,
-0.005714775994420052,
-0.060811206698417664,
-0.0015247304691001773,
-0.022544648498296738,
-0.015789588913321495,
-0.07077431678771973,
0.029234306886792183,
0.039615221321582794,
0.01537227351218462,
-0.05765325948596001,
0.025143014267086983,
-0.026024017482995987,
-0.06232994794845581,
-0.027142483741044998,
-0.003944690339267254,
0.04058772698044777,
-0.042438119649887085,
0.03306809812784195,
0.00858487281948328,
-0.011749174445867538,
0.005277617368847132,
-0.08195827901363373,
-0.038866471499204636,
0.03443899005651474,
-0.008322110399603844,
0.03826826065778732,
-0.012266555801033974,
-0.01347290724515915,
0.06338311731815338,
-0.010253718122839928,
-0.0025197574868798256,
-0.03348168358206749,
0.030847545713186264,
-0.0014571521896868944,
-0.005072722677141428,
0.004756162874400616,
-0.019459955394268036,
0.013976448215544224,
-0.01781846210360527,
0.03479120507836342,
0.036282557994127274,
-0.0018954172264784575,
0.027027864009141922,
0.026171257719397545,
0.014505007304251194,
0.004232688341289759,
0.012843653559684753,
0.028851881623268127,
0.0048842402175068855,
-0.01889326050877571,
0.046969108283519745,
-0.01260356418788433,
0.04894823580980301,
0.016083337366580963,
-0.06432949751615524,
0.019156407564878464,
-0.007823929190635681,
-0.0021137043368071318,
-0.015666883438825607,
0.03594067320227623,
-0.01358623243868351,
-0.02959870919585228,
0.027546372264623642,
-0.01968494988977909,
0.0743386447429657,
0.017171313986182213,
-0.0029032789170742035,
0.016736162826418877,
0.030919302254915237,
-0.03757932782173157,
-0.027790792286396027,
-0.0035053673200309277,
-0.04207465052604675,
0.011024962179362774,
-0.033323999494314194,
0.029735933989286423,
0.039019741117954254,
0.04708312824368477,
0.03189009055495262,
-0.029226696118712425,
-0.017489098012447357,
-0.018192635849118233,
-0.05164457857608795,
-0.006674061994999647,
-0.005425553768873215,
0.03382450342178345,
-0.0222609993070364,
0.05233713984489441,
0.042325519025325775,
0.04596433416008949,
0.017401162534952164,
0.00678308866918087,
-0.10142096877098083,
0.005928780883550644,
-0.04177321493625641,
0.003751883516088128,
-0.02265743911266327,
0.01214552391320467,
-0.01982017792761326,
0.018104275688529015,
-0.017795056104660034,
-0.018556544557213783,
0.026586508378386497,
-0.05654199421405792,
0.043460194021463394,
-0.02739335224032402,
-0.041945867240428925,
-0.0007277184049598873,
0.06675002723932266,
0.07198811322450638,
-0.0002106086176354438,
0.006231480743736029,
0.007127086166292429,
-0.020649725571274757,
-0.030196333304047585,
-0.0031528857070952654,
0.0036115231923758984,
-0.001879789517261088,
0.05508887395262718,
0.004997625015676022,
0.02264406904578209,
-0.03184516355395317,
-0.016354065388441086,
0.07376062124967575,
0.050421275198459625,
-0.01402982510626316,
-0.014231001026928425,
0.021822577342391014,
-0.05100782960653305,
-0.01715075969696045,
0.000060353522712830454,
0.07527313381433487,
-0.017817668616771698,
-0.013203385286033154,
-0.020102106034755707,
-0.0073832920752465725,
0.006264825351536274,
0.015673445537686348,
0.02883567102253437,
0.015114125795662403,
-0.021068617701530457,
0.0054709892719984055,
-0.02065785601735115,
-0.034099873155355453,
0.029847530648112297,
-0.005095838103443384,
0.00901704654097557,
-0.03978944942355156,
-0.02000548504292965,
0.02285889908671379,
0.007120375521481037,
-0.04035801813006401,
-0.009312023408710957,
0.000014429367183765862,
0.013833770528435707,
-0.04330753535032272,
0.03269459679722786,
0.03847145289182663,
0.06518213450908661,
0.04595773294568062,
0.007725743111222982,
0.019420702010393143,
-0.038231927901506424,
-0.05241130664944649,
0.049831438809633255,
0.04413072392344475,
0.0048922523856163025,
-0.037356629967689514,
-0.09659138321876526,
-0.030671501532197,
0.05335627496242523,
-0.029481174424290657,
0.019190875813364983,
0.021798038855195045,
-0.002973410068079829,
0.01627160608768463,
-0.047523822635412216,
-0.01924397237598896,
0.010083112865686417,
-0.03282547742128372,
0.02053975686430931,
-0.03831765055656433,
0.022619703784585,
0.009478555992245674,
0.020956482738256454,
0.014933332800865173,
0.0291975736618042,
0.02480003610253334,
-0.015541954897344112,
-0.0019035472068935633,
-0.01227662991732359,
-0.03050868585705757,
-0.07624335587024689,
-0.016242418438196182,
-0.007891923189163208,
-0.047475967556238174,
0.06034649536013603,
-0.04414638504385948,
-0.05445864051580429,
0.03279106318950653,
0.00995263084769249,
-0.03002467192709446,
0.03293880447745323,
-0.06840258091688156,
0.025639452040195465,
0.013293330557644367,
-0.019565517082810402,
0.044619541615247726,
0.010869406163692474,
-0.014207126572728157,
0.012331829406321049,
-0.0486723966896534,
-0.005635096691548824,
-0.0233280211687088,
-0.003269634209573269,
-0.017910746857523918,
-0.03868814557790756,
-0.05388135835528374,
0.03753824532032013,
-0.02883477695286274,
-0.0024329330772161484,
0.01248382031917572,
-0.02532261610031128,
0.02108481340110302,
0.00345954904332757,
0.00839699525386095,
0.007490046322345734,
-0.00374824577011168,
0.017869314178824425,
0.028354346752166748,
-0.012200632132589817,
0.021126095205545425,
-0.0019442137563601136,
-0.017501208931207657,
0.04900282993912697,
-0.03219737857580185,
0.014041174203157425,
0.016322018578648567,
-0.01688365451991558,
0.040623005479574203,
-0.03327913209795952,
0.055751536041498184,
-0.02148451842367649,
0.01499891560524702,
0.05442115664482117,
-0.01834036223590374,
-0.0026450916193425655,
-0.03133387118577957,
0.00894120428711176,
0.01765481010079384,
-0.019522009417414665,
-0.007821338251233101,
-0.0008400075021199882,
0.00524702575057745,
-0.05313149094581604,
-0.004653056152164936,
0.04534148424863815,
0.0018839652184396982,
-0.05782203748822212,
-0.02263280563056469,
0.01893709786236286,
-0.01659720577299595,
-0.05204573646187782,
-0.010981522500514984,
-0.007748421747237444,
-0.03422660753130913,
-0.010139644145965576,
0.0095616914331913,
0.0494622103869915,
0.02657848782837391,
-0.02958095446228981,
0.004724215250462294,
-0.013150665909051895,
-0.01239592581987381,
0.018980195745825768,
-0.003317785682156682,
0.041195087134838104,
-0.0016882155323401093,
-0.05774904042482376,
-0.033975180238485336,
0.006792014464735985,
0.013050809502601624,
0.02088208496570587,
0.011572150513529778,
0.016868831589818,
-0.018183084204792976,
-0.010483015328645706,
-0.020104561001062393,
0.014560096897184849,
-0.008287716656923294,
0.036646485328674316,
-0.014876109547913074,
-0.021023275330662727,
0.011169981211423874,
-0.05943158268928528,
0.01408030092716217,
-0.012059415690600872,
0.012028309516608715,
0.0014619268476963043,
0.01187100913375616,
0.0003907356003765017,
-0.028787830844521523,
0.012035653926432133,
-0.040954940021038055,
0.03550250828266144,
0.020530730485916138,
0.005727559793740511,
0.01120471116155386,
-0.005710271652787924,
-0.03784732520580292,
-0.02315882034599781,
-0.0305180661380291,
0.0035028920974582434,
0.07438291609287262,
0.03836024925112724,
0.01300856750458479,
0.007810650393366814,
0.02939944714307785,
-0.0033639066386967897,
-0.033910997211933136,
0.011097636073827744,
-0.00039046606980264187,
0.023715849965810776,
0.0231865793466568,
0.008238370530307293,
-0.0013274452649056911,
0.060222700238227844,
0.03685634210705757,
-0.011399255134165287,
0.06242530420422554,
0.03332678601145744,
0.0003781571867875755,
0.031365811824798584,
-0.042755644768476486,
-0.040652863681316376,
0.015309138223528862,
-0.04452839493751526,
0.036484599113464355,
0.011988361366093159,
0.01467892900109291,
0.009176721796393394,
0.010147524997591972,
0.03258315846323967,
-0.045009199529886246,
-0.020244738087058067,
-0.03135593608021736,
0.01062159426510334,
0.010507563129067421,
-0.027265358716249466,
0.006141334772109985,
0.032960209995508194,
0.005516515579074621,
-0.0075896019116044044,
0.015128730796277523,
-0.0012590335682034492,
-0.05660681799054146,
-0.008222234435379505,
-0.041215263307094574,
-0.07716085016727448,
0.04454817250370979,
0.023057857528328896,
-0.021136581897735596,
0.02662147954106331,
-0.02401665598154068,
0.02530316635966301,
0.018086202442646027,
0.05723821371793747,
-0.01651495136320591,
0.048445023596286774,
-0.02155175618827343,
0.011523229070007801,
-0.05708722025156021,
0.02842823788523674,
0.12611128389835358,
0.026322869583964348,
0.019780617207288742,
-0.05103721097111702,
-0.01237559039145708,
0.013250347226858139,
0.05141746997833252,
-0.03530806303024292,
0.01796082593500614,
-0.02977081388235092,
0.00419712346047163,
0.03797295317053795,
0.061649978160858154,
-0.01764283888041973,
-0.03329364210367203,
0.021932290866971016,
-0.03254573047161102,
-0.009448453783988953,
-0.017831210047006607,
-0.006688657216727734,
0.02031608484685421,
0.02767079323530197,
-0.045846983790397644,
0.04743422195315361,
-0.009900589473545551,
-0.01560993306338787,
-0.04828765243291855,
-0.008974271826446056,
0.029329953715205193,
-0.012738065794110298,
-0.09683801233768463,
0.0070588067173957825,
-0.0004000468470621854,
-0.03117327019572258,
-0.00021050080249551684,
0.012374396435916424,
0.025134388357400894,
-0.03586298227310181,
-0.0032501942478120327,
0.03314095363020897,
0.0033283294178545475,
0.03406713157892227,
0.01762259565293789,
0.011830920353531837,
-0.026555005460977554,
-0.028243867680430412,
-0.026529226452112198,
0.08286672830581665,
-0.028898384422063828,
-0.018870536237955093,
-0.015973059460520744,
-0.004755694419145584,
0.04813653603196144,
-0.023358775302767754,
-0.00010984329128405079,
-0.01723673567175865,
-0.020500274375081062,
-0.011469492688775063,
-0.02151760831475258,
0.028778301551938057,
0.022504586726427078,
0.026111193001270294,
-0.00562472315505147,
-0.0014089271426200867,
0.04118860885500908,
-0.006426951382309198,
-0.04122466593980789,
0.049685653299093246,
0.006717171519994736,
0.015556245110929012,
-0.050061989575624466,
0.006207364611327648,
-0.010188406333327293,
-0.015001415275037289,
0.012022381648421288,
0.004358278587460518,
0.02104026824235916,
0.015810081735253334,
0.01647830381989479,
-0.028226671740412712,
-0.03826596960425377,
0.056889135390520096,
-0.016652008518576622,
-0.03827027603983879,
-0.018001697957515717,
0.0030589804518967867,
-0.008931972086429596,
0.03289233148097992,
-0.0221878495067358,
-0.018491573631763458,
-0.008486688137054443,
0.06307011097669601,
0.012678156606853008,
0.011832328513264656,
0.019653944298624992,
-0.0023398674093186855,
-0.0275643952190876,
0.014307882636785507,
-0.03493631258606911,
0.038795355707407,
0.030012382194399834,
0.009668483398854733,
0.0324004590511322,
0.039635635912418365,
-0.043485376983881,
-0.03972899168729782,
0.0011685144854709506,
-0.004431076813489199,
0.005262176506221294,
0.005313021596521139,
0.027801379561424255,
-0.02875209040939808,
-0.027063516899943352,
-0.031058507040143013,
-0.013653522357344627,
-0.006688347551971674,
0.025436414405703545,
-0.01721639558672905,
0.04969857633113861,
-0.0014440951636061072,
0.03546154499053955,
-0.045889921486377716,
0.012421887367963791,
-0.046599045395851135,
0.004854083061218262,
0.022459357976913452,
-0.027372466400265694,
0.006861565634608269,
0.01710297353565693,
0.016466863453388214,
-0.027597850188612938,
-0.019405215978622437,
0.02238667756319046,
-0.018513871356844902,
0.017973950132727623,
0.0011530275223776698,
-0.01195835042744875,
0.034882090985774994,
0.04982667416334152,
-0.024934593588113785,
0.019287025555968285,
-0.04637500271201134,
-0.044026654213666916,
0.0009695893386378884,
-0.028621362522244453,
0.040332138538360596,
-0.0009991814149543643,
-0.02153042145073414,
-0.0016686570597812533,
0.05338078737258911,
0.0026492548640817404,
-0.029311273247003555,
0.01399107463657856,
-0.024137450382113457,
0.00011049564636778086,
0.0365387499332428,
0.046594880521297455,
-0.02188098430633545,
-0.042946722358465195,
0.0197280365973711,
0.010286596603691578,
-0.05108493193984032,
0.0055324179120361805,
0.015732863917946815,
-0.015333572402596474,
0.015280981548130512,
-0.0021356467623263597,
0.013156394474208355,
0.03845446929335594,
0.05663792043924332,
-0.032633718103170395,
0.050607066601514816,
0.0275216456502676,
-0.022728661075234413,
-0.12136565893888474,
-0.0011434879852458835,
-0.004031140357255936,
0.028074422851204872,
0.016034813597798347,
-0.028324462473392487,
0.0047283414751291275,
0.026106135919690132,
-0.06581379473209381,
0.028259599581360817,
-0.02231833152472973,
0.02497245743870735,
-0.02494858019053936,
-0.005728004965931177,
-0.03211905062198639,
0.01512612123042345,
0.04945196956396103,
0.06240018084645271,
0.0011952181812375784,
0.03168373182415962,
-0.026717878878116608,
-0.024395471438765526,
0.007655304856598377,
0.02262977510690689,
-0.027977842837572098,
-0.024909289553761482,
0.07380189001560211,
-0.005907802376896143,
0.01578446291387081,
0.0032510734163224697,
-0.007153559010475874,
0.03525295481085777,
-0.021630784496665,
-0.02512558363378048,
-0.0037925303913652897,
0.01269232016056776,
0.014655164442956448,
-0.007948469370603561,
0.007632985711097717,
0.0027026983443647623,
0.0002868817246053368,
0.007233235985040665,
0.0026042277459055185,
0.03312903270125389,
0.04154429957270622,
-0.06321051716804504,
-0.020012028515338898,
-0.005436624865978956,
-0.02645799145102501,
0.006163702812045813,
0.002623891457915306,
0.00987608078867197,
-0.003847253741696477,
-0.016010304912924767,
-0.031059162691235542,
-0.030560456216335297,
0.0044524334371089935,
0.023834718391299248,
0.0617934949696064,
0.037082310765981674,
0.029163779690861702,
-0.02173663303256035,
-0.017643578350543976,
0.0020468810107558966,
-0.032325197011232376,
-0.016028286889195442,
-0.010460584424436092,
0.00581353111192584,
-0.04480846971273422,
0.00836598314344883,
0.010208784602582455,
-0.03083273023366928,
-0.01551058143377304,
0.03701203688979149,
0.0391228049993515,
0.012651916593313217,
-0.037707697600126266,
-0.06872952729463577,
-0.03972060605883598,
-0.07596684247255325,
0.007248156704008579,
-0.016721829771995544,
0.005479035433381796,
-0.053815808147192,
-0.03127753734588623,
0.004590683616697788,
0.019523145630955696,
0.03575719892978668,
-0.0035176670644432306,
-0.005634206347167492,
0.03515823557972908,
-0.033413443714380264,
0.013203929178416729,
-0.06395703554153442,
0.019046679139137268,
-0.010562383569777012,
0.015469851903617382,
0.004222961142659187,
-0.010553302243351936,
-0.008887923322618008,
0.007858083583414555,
0.059025660157203674,
-0.0074083153158426285,
0.018775923177599907,
0.016572076827287674,
-0.00836088601499796,
0.055399518460035324,
0.013967861421406269,
-0.011324453167617321,
0.05123201757669449,
0.014559520408511162,
-0.010525906458497047,
0.05692964419722557,
-0.03832459822297096,
-0.007524866610765457,
0.004035320598632097,
0.00926121324300766,
-0.023090098053216934,
-0.035112421959638596,
-0.025137625634670258,
0.006770188920199871,
-0.020018626004457474,
-0.00024975102860480547,
0.039283305406570435,
-0.014924020506441593,
-0.054342370480298996,
0.014747128821909428,
-0.01587037555873394,
0.035950541496276855,
-0.02113245613873005,
-0.01888456381857395,
0.0043968320824205875,
0.0038544314447790384,
-0.009780495427548885,
0.009778899140655994,
0.03869738057255745,
0.021264834329485893,
0.0017971590859815478,
0.003224920015782118,
0.015414672903716564,
-0.0016294437227770686,
-0.036927253007888794,
0.043745532631874084,
-0.04416078329086304,
-0.029127666726708412,
0.037993572652339935,
-0.0026197866536676884,
0.007776828017085791,
0.012118239887058735,
-0.025065608322620392,
0.09764733165502548,
0.027466196566820145,
0.007717925123870373,
0.008901884779334068,
-0.003814967116340995,
-0.040133848786354065,
0.05201452225446701,
-0.007853459566831589,
0.04422026127576828,
-0.010273752734065056,
-0.016926651820540428,
0.017868660390377045,
0.028308583423495293,
0.04427222162485123,
-0.021552521735429764,
-0.002071582479402423,
0.007391397375613451,
-0.009308705106377602,
0.005718786269426346,
-0.0418778695166111,
-0.03424740582704544,
-0.03974880278110504,
0.030485862866044044,
0.015299643389880657,
-0.01169491931796074,
0.02692238613963127,
-0.009654376655817032,
-0.0365704670548439,
0.04629451036453247,
-0.0635700598359108,
-0.03515860438346863,
0.032635170966386795,
0.021598419174551964,
-0.04079083353281021,
-0.04386206343770027
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14074/what-are-the-prerequisites-to-studying-general-relativity">What are the prerequisites to studying general relativity?</a> </p>
</blockquote>
<p>I'am 27 now and i have a burning desire to study math and physics from the ground up and I strongly prefer doing a self study.I want to be a self tutor till i reach certain level.</p>
<p>My question is what is the minimum knowledge needed to read and completely understand the General and Special Theory of Relativity.</p>
<p>As of now my level of math knowledge is basic differential calculus.I also have a basic understanding of Kinematics {One dimensional motion with constant acceleration}</p>
<p>I welcome all possible sugessions,advices and recomendations.</p>
<p>Thank's in Advance</p> | 108 | [
-0.007437484338879585,
-0.03275425359606743,
0.011146221309900284,
-0.006683167535811663,
0.06320848315954208,
-0.0008645237539894879,
-0.024976009503006935,
-0.05678320303559303,
-0.038390014320611954,
-0.03492429107427597,
0.0395662784576416,
-0.0057439343072474,
0.028050780296325684,
0.01720687747001648,
0.04859893396496773,
-0.031018828973174095,
-0.005835023242980242,
-0.04026278480887413,
-0.003389467252418399,
-0.022621389478445053,
0.0009613626752980053,
-0.022091267630457878,
0.0036128105130046606,
0.04918001592159271,
-0.030792785808444023,
0.04946085438132286,
0.014645235612988472,
0.00844175461679697,
0.012290647253394127,
0.05618511885404587,
0.01495968084782362,
0.020197110250592232,
-0.029478834941983223,
0.05025392025709152,
0.010284663178026676,
0.003729321528226137,
-0.03135678172111511,
0.003861445700749755,
0.0035808521788567305,
-0.010339568369090557,
-0.040892016142606735,
-0.014007775112986565,
0.005311432294547558,
0.04456714913249016,
-0.02366488054394722,
0.04488956555724144,
0.013200515881180763,
0.009436888620257378,
0.05106450244784355,
-0.041857264935970306,
0.06029678136110306,
0.03282250091433525,
0.04537663981318474,
0.007827365770936012,
-0.019952619448304176,
-0.013699682429432869,
0.09033465385437012,
0.0630740076303482,
-0.025088733062148094,
-0.03510521352291107,
-0.008143862709403038,
-0.012909932993352413,
0.007497155573219061,
-0.02185042016208172,
-0.020740007981657982,
0.060811810195446014,
-0.041744738817214966,
0.003679124405607581,
0.02675827592611313,
-0.016235951334238052,
0.014452961273491383,
0.0313614159822464,
0.004335735458880663,
0.012584441341459751,
-0.012218499556183815,
-0.018819838762283325,
-0.004757733084261417,
0.004178653936833143,
0.04448550567030907,
0.04660191014409065,
-0.015260766260325909,
0.016623513773083687,
0.014750867150723934,
0.03707106411457062,
0.01771259680390358,
0.0008145365864038467,
0.10886380821466446,
0.03743283078074455,
0.0048802075907588005,
0.009660528041422367,
-0.011027774773538113,
-0.027405057102441788,
0.003946977201849222,
-0.018621815368533134,
-0.02147800475358963,
0.03720872849225998,
0.00457442132756114,
0.03415863960981369,
0.026694264262914658,
-0.05554957315325737,
-0.0031434798147529364,
-0.020789945498108864,
0.009957692585885525,
0.07934674620628357,
0.01117637474089861,
-0.022555628791451454,
-0.04049742966890335,
0.02229401282966137,
-0.011428107507526875,
-0.02588222548365593,
0.02589741162955761,
0.02906082198023796,
-0.028555138036608696,
-0.013447561301290989,
0.022808479145169258,
0.008456221781671047,
0.02478734776377678,
-0.005034381523728371,
0.060839153826236725,
0.031433142721652985,
0.0754208117723465,
-0.03821784257888794,
0.018837375566363335,
0.019756756722927094,
-0.081046923995018,
-0.018156971782445908,
0.04036916792392731,
-0.011419816873967648,
-0.004651615861803293,
-0.0034391151275485754,
-0.0020263195037841797,
-0.03721650689840317,
0.002801547758281231,
0.041578005999326706,
0.023558955639600754,
0.008459464646875858,
-0.11788967996835709,
-0.059885576367378235,
0.04858413338661194,
-0.011273074895143509,
-0.03168099373579025,
-0.08506321161985397,
0.01877463236451149,
0.0003049201040994376,
0.060989346355199814,
-0.015546765178442001,
0.04949803650379181,
-0.004257646389305592,
0.010338669642806053,
-0.009718183428049088,
-0.03605083376169205,
0.003998089116066694,
-0.04476114735007286,
-0.0008629823569208384,
0.01341995783150196,
-0.05887811258435249,
0.03499218448996544,
0.003224054118618369,
-0.007180230692028999,
-0.031913574784994125,
0.09724640846252441,
-0.02149219624698162,
0.00977137591689825,
0.017140740528702736,
-0.016912316903471947,
-0.006834730971604586,
0.06823725998401642,
0.020871086046099663,
0.023989876732230186,
0.05568611994385719,
0.00794882234185934,
0.01889875717461109,
-0.010400581173598766,
0.004152616951614618,
0.0622163750231266,
-0.030843237414956093,
-0.018511369824409485,
0.017654476687312126,
-0.04417186975479126,
-0.008721282705664635,
-0.035885803401470184,
-0.033709533512592316,
-0.0024463371373713017,
-0.0006650288705714047,
0.0037246388383209705,
0.029576361179351807,
0.023230446502566338,
0.01942393183708191,
-0.004158372525125742,
-0.03329183906316757,
0.003261999925598502,
-0.06857549399137497,
-0.008094442076981068,
-0.02685645967721939,
-0.003225648310035467,
0.015915893018245697,
-0.0022790178190916777,
0.0158352293074131,
-0.051783740520477295,
-0.03573694825172424,
0.024763213470578194,
0.041697513312101364,
0.012869693338871002,
-0.012714006938040257,
0.004956000950187445,
0.04210153967142105,
0.06196298450231552,
-0.0063413092866539955,
-0.00014706743240822107,
0.00039279964403249323,
-0.000030945953767513856,
0.030741291120648384,
0.01870059035718441,
0.03104911744594574,
-0.01888011023402214,
0.019441692158579826,
0.0034971239510923624,
0.007112050428986549,
-0.02628517523407936,
0.024424586445093155,
-0.02822772040963173,
0.0494391955435276,
0.005894027184695005,
0.0353645458817482,
-0.005425961688160896,
0.053871627897024155,
0.00814077164977789,
0.04142749682068825,
0.0061655547469854355,
-0.004289604723453522,
-0.05414296314120293,
-0.01430271752178669,
0.04264770820736885,
0.030803661793470383,
-0.045357078313827515,
0.01606259122490883,
0.03942960873246193,
0.05587916448712349,
0.01508406549692154,
-0.003250635229051113,
-0.01665913686156273,
-0.07335487008094788,
-0.01085688266903162,
0.005733731668442488,
-0.005063182674348354,
0.031077053397893906,
0.016418810933828354,
0.04705296829342842,
-0.012874963693320751,
0.031339097768068314,
-0.034587837755680084,
0.049875691533088684,
-0.0076332236640155315,
-0.01088640745729208,
0.027785317972302437,
-0.016787881031632423,
0.08004380762577057,
0.009471019729971886,
-0.0033619736786931753,
0.023044515401124954,
-0.0066833291202783585,
-0.00670769065618515,
0.005363261327147484,
0.012561303563416004,
-0.011130520142614841,
-0.01462399959564209,
-0.013940013013780117,
-0.007755293510854244,
0.019358383491635323,
-0.08398790657520294,
-0.00479162996634841,
0.011977100744843483,
-0.04515986144542694,
-0.04181039705872536,
-0.019445043057203293,
-0.010517735034227371,
0.007914375513792038,
0.019353827461600304,
-0.015340831130743027,
-0.021406762301921844,
0.012875142507255077,
-0.009697886183857918,
0.02414066530764103,
0.005759380757808685,
-0.04301128908991814,
0.03517509251832962,
-0.043256405740976334,
-0.0312054343521595,
0.06217476725578308,
-0.030280735343694687,
0.025675222277641296,
0.019918624311685562,
-0.00651960726827383,
-0.04021421819925308,
-0.020231952890753746,
-0.0190450306981802,
0.01305371057242155,
-0.04633583873510361,
0.008828055113554,
0.0475960299372673,
-0.03114059567451477,
-0.029235895723104477,
-0.00870439037680626,
-0.035767361521720886,
-0.052841249853372574,
-0.02745559625327587,
0.03330012783408165,
0.00278291548602283,
-0.03197728097438812,
0.01739395782351494,
0.0010657671373337507,
-0.033478040248155594,
0.01533189695328474,
-0.05909048393368721,
-0.03452083095908165,
0.037941135466098785,
0.048086900264024734,
0.03428957238793373,
0.009675778448581696,
-0.023421430960297585,
0.037387460470199585,
0.01595589891076088,
-0.024358902126550674,
-0.0536784864962101,
0.013724921271204948,
0.019817747175693512,
-0.015332420356571674,
0.02754122018814087,
0.01764921098947525,
0.01863664761185646,
-0.01848371885716915,
0.06206933781504631,
0.009218469262123108,
0.014508280903100967,
0.004223216790705919,
-0.0002085312153212726,
-0.02811758778989315,
-0.0047960104420781136,
0.034987058490514755,
0.025587402284145355,
0.032493043690919876,
-0.03247752785682678,
-0.0004654863732866943,
-0.0025605489499866962,
0.03803418576717377,
0.01974763534963131,
-0.03951479494571686,
0.07140146940946579,
-0.003171005053445697,
-0.01643518917262554,
-0.009256801567971706,
0.02257438190281391,
-0.005667977035045624,
-0.019932417199015617,
0.04440116882324219,
-0.03997266665101051,
0.028766252100467682,
0.017936881631612778,
0.022598344832658768,
0.010015838779509068,
0.04380502551794052,
-0.025244761258363724,
0.005053775385022163,
-0.02684246562421322,
-0.032057467848062515,
0.007418820634484291,
-0.027305901050567627,
0.011036799289286137,
0.02202802337706089,
0.06060049310326576,
0.006513613276183605,
-0.000027871095880982466,
-0.038084592670202255,
0.0029700887389481068,
-0.08586087822914124,
-0.01486190129071474,
0.01899663545191288,
0.05062778666615486,
-0.027055364102125168,
0.049012720584869385,
0.022735802456736565,
0.0019648047164082527,
0.03648163005709648,
0.006774840410798788,
-0.10767064243555069,
0.060716889798641205,
-0.04954076558351517,
0.011851494200527668,
0.016340216621756554,
0.012504001148045063,
0.004705904982984066,
-0.02186901681125164,
-0.02681889198720455,
-0.02950236201286316,
0.005868478212505579,
-0.04301510378718376,
0.03199486434459686,
-0.016762644052505493,
-0.03429466485977173,
0.011172909289598465,
0.05701536685228348,
0.035208560526371,
-0.011317004449665546,
-0.005222109146416187,
0.07007919251918793,
-0.005478210747241974,
-0.03184043616056442,
0.016292903572320938,
-0.008898844011127949,
0.011704595759510994,
0.02216390147805214,
0.024211132898926735,
-0.017592312768101692,
0.005399674642831087,
0.0007005051011219621,
0.0057772183790802956,
0.030013328418135643,
-0.0016543071251362562,
-0.041522860527038574,
-0.01510861236602068,
-0.05553223565220833,
-0.009876961819827557,
0.005103983450680971,
0.07922998815774918,
0.010240203700959682,
0.008070636540651321,
0.036949899047613144,
-0.01127101294696331,
-0.009336835704743862,
0.017715971916913986,
0.06489016860723495,
-0.03709520772099495,
-0.03716125339269638,
-0.042697228491306305,
-0.06385522335767746,
-0.0637764260172844,
0.007314677815884352,
0.0509328730404377,
0.007709486410021782,
-0.0369524210691452,
0.010656855069100857,
-0.0014172346564009786,
0.012848103418946266,
-0.05523165315389633,
-0.008121288381516933,
0.010373678058385849,
0.07572659850120544,
0.024060670286417007,
-0.03678698092699051,
-0.017459141090512276,
0.020231958478689194,
0.07014332711696625,
-0.055694829672575,
-0.008386261761188507,
-0.051694657653570175,
0.0011434233747422695,
0.010490639135241508,
0.06389924883842468,
-0.0030009986367076635,
0.008337067440152168,
-0.04795835167169571,
-0.012117481790482998,
0.054299600422382355,
-0.04111570864915848,
0.0022886255756020546,
-0.012356001883745193,
-0.029617056250572205,
-0.027562882751226425,
-0.03449254855513573,
-0.011427930556237698,
0.011959319934248924,
-0.015049452893435955,
-0.0004043105582240969,
-0.052365563809871674,
0.042850762605667114,
-0.01725868508219719,
-0.006124137435108423,
-0.010906864888966084,
0.056777674704790115,
0.04154262691736221,
0.011579722166061401,
-0.00038867624243721366,
0.03856328874826431,
-0.013191291131079197,
-0.07904534041881561,
-0.004118959419429302,
-0.003144142683595419,
-0.030245589092373848,
0.006241380702704191,
-0.03379514440894127,
-0.050842005759477615,
0.041890405118465424,
0.03239506110548973,
-0.00957759004086256,
0.016607964411377907,
-0.07766257226467133,
0.008722410537302494,
0.001334325410425663,
0.03329791873693466,
0.009663003496825695,
0.013135740533471107,
-0.04404965043067932,
0.0037151086144149303,
-0.0036091150250285864,
-0.012281321920454502,
-0.027204059064388275,
-0.0038960084784775972,
-0.0036349997390061617,
-0.03013595938682556,
-0.040185440331697464,
0.055761829018592834,
-0.046111393719911575,
-0.024259550496935844,
0.00893800426274538,
-0.018406830728054047,
-0.0010127155110239983,
0.04996092990040779,
0.027878157794475555,
-0.005434677004814148,
-0.009105906821787357,
0.03245364874601364,
-0.00988470483571291,
-0.010972331278026104,
0.029880106449127197,
-0.00373176415450871,
-0.01227117981761694,
0.022540757432579994,
-0.003582705743610859,
0.02356644719839096,
-0.026014801114797592,
-0.03395194187760353,
0.0036059643607586622,
-0.05935421586036682,
0.04697141423821449,
0.020802604034543037,
0.008355489932000637,
0.06614160537719727,
-0.023578550666570663,
-0.02324593812227249,
0.011835004203021526,
0.014464669860899448,
0.04851454123854637,
-0.019871719181537628,
0.00023482234973926097,
0.00435158796608448,
0.0017551493365317583,
-0.05087105557322502,
-0.061353232711553574,
0.03707662969827652,
0.00014980843116063625,
-0.04688866063952446,
-0.029255598783493042,
0.05100536346435547,
-0.058269672095775604,
-0.005423672962933779,
-0.025014040991663933,
0.02048170380294323,
-0.010181262157857418,
-0.006082291714847088,
0.007446906063705683,
0.022888191044330597,
0.02760159596800804,
-0.023652901872992516,
0.031116651371121407,
0.038490813225507736,
-0.024934394285082817,
-0.006341768428683281,
-0.016633348539471626,
0.051503196358680725,
-0.005835745949298143,
-0.029101843014359474,
-0.06934215873479843,
0.02047298103570938,
-0.0059654200449585915,
-0.03112160600721836,
0.009672962129116058,
0.02167809009552002,
-0.005699200555682182,
-0.050934452563524246,
-0.033497098833322525,
0.022097082808613777,
-0.016792146489024162,
0.00903441570699215,
-0.02692355029284954,
0.005650714505463839,
0.01806294545531273,
-0.009502225555479527,
0.06478438526391983,
-0.0041907294653356075,
0.02750074677169323,
-0.02754823863506317,
0.05062840133905411,
0.009119674563407898,
0.010159417055547237,
0.03694543614983559,
-0.016107061877846718,
0.024450229480862617,
-0.02372055873274803,
0.023644637316465378,
0.03563053905963898,
-0.01811755821108818,
-0.026341231539845467,
-0.0608854815363884,
-0.035877883434295654,
-0.0036039608530700207,
0.07313894480466843,
0.01578640192747116,
0.03130991756916046,
0.020426923409104347,
-0.027677061036229134,
-0.0048416368663311005,
-0.0075759077444672585,
-0.00909078773111105,
-0.0018194529693573713,
0.05156959593296051,
0.01994500681757927,
-0.03511422127485275,
-0.03667411580681801,
0.00446289824321866,
0.03661516681313515,
-0.0392753966152668,
0.01790810562670231,
0.03711041435599327,
-0.0024246983230113983,
-0.003629708429798484,
-0.039611782878637314,
-0.028598515316843987,
0.041499607264995575,
0.004832588601857424,
0.04362113028764725,
-0.0079270601272583,
-0.001024259952828288,
0.00913169700652361,
0.03430527076125145,
0.020843710750341415,
-0.023142436519265175,
-0.015565803274512291,
-0.033331625163555145,
0.009297950193285942,
0.03787367418408394,
0.01549911592155695,
-0.02247674949467182,
0.010119724087417126,
0.019413691014051437,
0.0009599402546882629,
0.05344506725668907,
-0.0056903185322880745,
-0.06022163853049278,
-0.006806339602917433,
-0.03038877621293068,
-0.08026931434869766,
0.05545216426253319,
0.022262826561927795,
-0.0452115423977375,
-0.008675822988152504,
-0.021232688799500465,
0.032596245408058167,
0.015479134395718575,
0.03858095407485962,
-0.032647568732500076,
0.05780549347400665,
-0.011081477627158165,
-0.013077490031719208,
-0.01106460951268673,
0.021471625193953514,
0.117713563144207,
0.03612670674920082,
-0.016838084906339645,
-0.07084591686725616,
0.01061475370079279,
0.002336125588044524,
-0.01914319396018982,
-0.02359260432422161,
0.025729821994900703,
-0.03150131180882454,
-0.01501154899597168,
0.02402654103934765,
0.02391621842980385,
-0.004024975001811981,
-0.014625859446823597,
0.05266020447015762,
-0.04373835772275925,
-0.03994130715727806,
-0.03447165712714195,
0.008143278770148754,
-0.017870904877781868,
0.033884063363075256,
-0.002900511957705021,
0.03842240944504738,
-0.01892055571079254,
0.017873555421829224,
-0.05492809787392616,
-0.03759031370282173,
0.027388861402869225,
-0.007748533971607685,
-0.046064592897892,
0.02102280780673027,
0.0021019100677222013,
-0.021333899348974228,
-0.06708771735429764,
0.01910799741744995,
0.03137978911399841,
-0.008566310629248619,
0.013386775739490986,
-0.0009855997050181031,
-0.04634098708629608,
0.011531512252986431,
0.0006130728288553655,
-0.015207423828542233,
-0.026389041915535927,
0.029805542901158333,
-0.02284633368253708,
0.04374224320054054,
-0.02435230277478695,
-0.012337174266576767,
-0.007647220510989428,
0.008642023429274559,
0.008237697184085846,
-0.05301784723997116,
-0.013400938361883163,
0.015293446369469166,
0.032665323466062546,
-0.020716391503810883,
0.0008625516202300787,
-0.03039928711950779,
0.013809419237077236,
-0.0031964422669261694,
0.02789451740682125,
-0.025734633207321167,
-0.04373442754149437,
0.0018391923513263464,
-0.015610241331160069,
0.02220846526324749,
-0.030280856415629387,
-0.006004170514643192,
-0.032462429255247116,
-0.00009674869215814397,
-0.012563697062432766,
-0.005131063982844353,
0.041587334126234055,
0.02670474536716938,
0.022445056587457657,
0.03807539492845535,
-0.013993006199598312,
0.01512615755200386,
-0.02579876407980919,
0.02079572156071663,
-0.043580975383520126,
-0.03261842206120491,
-0.03525486961007118,
-0.01901654154062271,
-0.0013355094706639647,
0.05455793812870979,
0.025542596355080605,
0.019726131111383438,
0.005867162253707647,
0.0020687668584287167,
-0.0036252273712307215,
0.054438963532447815,
0.01669953018426895,
-0.015171481296420097,
-0.017450321465730667,
0.009382318705320358,
-0.03661845996975899,
0.022704211995005608,
0.031184658408164978,
0.0328371599316597,
0.022845862433314323,
0.02602734975516796,
-0.030665136873722076,
-0.007588536012917757,
-0.0023727526422590017,
-0.0284580048173666,
0.0029514722991734743,
0.03587048128247261,
0.059021156281232834,
-0.041279617697000504,
-0.008569037541747093,
-0.005811594892293215,
0.01483825221657753,
-0.005354559514671564,
0.02234106883406639,
0.003965800628066063,
0.06458769738674164,
0.0077971601858735085,
0.03273966163396835,
-0.04931756108999252,
0.011207934468984604,
-0.029422469437122345,
0.043405767530202866,
-0.0014139465056359768,
-0.033688414841890335,
-0.007439094129949808,
0.020048830658197403,
0.014506719075143337,
-0.024561498314142227,
0.020305979996919632,
-0.019693780690431595,
-0.05294039100408554,
-0.02095761150121689,
0.03169601783156395,
-0.03932527080178261,
0.048854175955057144,
-0.0017988064792007208,
-0.008579438552260399,
0.007678984198719263,
-0.05514101684093475,
-0.037621818482875824,
0.03362436592578888,
-0.028037341311573982,
0.022719332948327065,
0.016594525426626205,
-0.04629272595047951,
-0.006436356343328953,
0.07794655859470367,
-0.003167174058035016,
0.023018546402454376,
-0.014248162508010864,
-0.035103991627693176,
-0.004585288930684328,
-0.005031533073633909,
0.04369141161441803,
-0.027875462546944618,
-0.01322550605982542,
0.005093530751764774,
0.00783380214124918,
-0.016746416687965393,
0.01642860844731331,
0.02191474288702011,
-0.0045141978189349174,
-0.028401197865605354,
-0.005687025375664234,
-0.013915767893195152,
0.023249486461281776,
0.022216804325580597,
-0.044591113924980164,
0.02551933191716671,
0.008273614570498466,
0.024033933877944946,
-0.08396501839160919,
0.00629953620955348,
0.015842869877815247,
0.012373008765280247,
0.04294491931796074,
-0.05743718519806862,
0.012247652746737003,
0.0481516532599926,
-0.018239349126815796,
0.01316860318183899,
-0.010605012066662312,
-0.047578390687704086,
0.00982157327234745,
-0.012179315090179443,
0.017305994406342506,
0.030187275260686874,
0.01467413455247879,
0.03241200000047684,
-0.010628760792315006,
0.0029003359377384186,
-0.02207535319030285,
-0.01884985715150833,
-0.01584922894835472,
0.014261724427342415,
-0.04274442046880722,
-0.01116329524666071,
0.0658833310008049,
0.01492379978299141,
-0.012140913866460323,
0.04316779971122742,
0.01552827563136816,
0.02227448672056198,
0.012297553941607475,
0.03638716787099838,
-0.01373511366546154,
0.047847215086221695,
0.047458965331315994,
-0.001975209452211857,
-0.017940832301974297,
0.06394260376691818,
-0.005845452193170786,
0.012378422543406487,
-0.012241526506841183,
0.0014529434265568852,
-0.008455549366772175,
-0.0056307450868189335,
-0.02791028842329979,
0.025511089712381363,
-0.027856677770614624,
-0.03172958269715309,
-0.0013395368587225676,
0.009728834964334965,
-0.02211560495197773,
-0.04473960027098656,
-0.02398015558719635,
-0.03925077244639397,
-0.012196910567581654,
0.0004883504007011652,
0.008190188556909561,
-0.028026189655065536,
0.0027786793652921915,
-0.030530046671628952,
-0.01726723276078701,
0.01420508697628975,
-0.0009606972453184426,
0.014458805322647095,
-0.034430984407663345,
0.0066542793065309525,
0.013584805652499199,
-0.01582511141896248,
0.021157292649149895,
-0.0371362566947937,
0.008442049846053123,
0.054541271179914474,
0.005741599015891552,
0.004016354214400053,
-0.007360375020653009,
-0.01767183467745781,
0.02680162340402603,
-0.06392840296030045,
0.0007155287894420326,
0.0017636932898312807,
0.000727967475540936,
-0.032143428921699524,
-0.014242712408304214,
-0.008781366981565952,
-0.027179375290870667,
0.05329698324203491,
-0.008393635973334312,
0.009757084771990776,
0.024886302649974823,
-0.012579034082591534,
0.00002942624814750161,
-0.04330319166183472,
-0.002479835180565715,
-0.01829238422214985,
-0.04401375353336334,
-0.006155549082905054,
-0.01748649589717388,
0.01790633425116539,
0.00721615320071578,
0.02991059049963951,
0.010979442857205868,
0.025893962010741234,
-0.002447150880470872,
-0.035222381353378296,
0.031378909945487976,
0.03363673761487007,
-0.002829138422384858,
0.03902087360620499,
-0.02612248808145523,
0.001383477239869535,
0.08390069752931595,
-0.016352234408259392,
-0.01254906877875328,
0.01876227930188179,
-0.04050217196345329,
-0.008197999559342861,
-0.0025543011724948883,
-0.01030641607940197,
0.010940993204712868,
-0.05752568319439888,
0.010570325888693333,
0.05506913363933563,
-0.005367874167859554,
-0.006371880415827036,
0.02544533461332321,
0.01918279193341732,
0.001870077452622354,
-0.01918403059244156,
-0.029027767479419708,
0.022444188594818115,
-0.053348395973443985,
-0.022259963676333427,
0.024191556498408318,
0.03134695813059807,
0.003999761305749416,
0.02426273003220558,
0.027881627902388573,
0.013522663153707981,
0.006467022933065891,
-0.019974136725068092,
0.05730332434177399,
-0.01033167727291584,
0.005610950756818056,
0.015138089656829834,
-0.01635841280221939,
-0.016069160774350166,
0.02257242612540722,
-0.010150817222893238,
0.06126890331506729,
-0.017873264849185944,
0.0023217552807182074,
0.006809980608522892,
-0.0036947717890143394,
-0.06648969650268555,
0.02551146410405636,
0.004051574971526861,
0.024677231907844543,
-0.014883838593959808,
0.010727227665483952,
-0.030323881655931473,
-0.012088047340512276,
0.04144362732768059,
-0.018026892095804214,
0.042952828109264374,
0.036303047090768814,
-0.001121352193877101,
0.020357884466648102,
-0.01543801836669445,
-0.03424584120512009,
-0.013217655010521412,
-0.006124579347670078,
0.024571944028139114,
0.005244916304945946,
-0.07501126825809479,
0.014241068623960018,
-0.03814385458827019,
0.04740619659423828,
-0.04867902770638466,
-0.015352006070315838,
-0.04152052849531174,
-0.04372033476829529,
-0.03742587938904762,
0.027777502313256264
] |
<p>Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary energy to climb the hill. </p>
<p>Will it reach the top of the hill in infinite or finite time? </p>
<p>In my proof it needs infinite time and this is quite non-intuitive because, though the particle has the necessary energy to climb the hill, it needs an infinite time. Also if we reverse the time, when the particle is in equilibrium on the top of the hill, it will never go down, therefore this process is time irreversible.</p> | 4,602 | [
-0.026910316199064255,
-0.05189530551433563,
0.000131292748847045,
0.006555792409926653,
0.013034060597419739,
0.015209701843559742,
-0.005147508345544338,
-0.002144051715731621,
-0.05287479609251022,
-0.011703652329742908,
0.04513326287269592,
0.005931374616920948,
0.017776338383555412,
0.01024266891181469,
0.02702423930168152,
0.0036656903102993965,
-0.01140439324080944,
0.00006648764247074723,
-0.030845172703266144,
-0.023906374350190163,
-0.006682910490781069,
0.005275329574942589,
-0.010411228984594345,
-0.007725285831838846,
-0.04067666083574295,
0.011095743626356125,
0.05083335191011429,
0.023968085646629333,
-0.010496629402041435,
0.09047567844390869,
-0.02996417135000229,
0.0074156890623271465,
-0.00426656287163496,
0.030733123421669006,
0.051173362880945206,
0.014739937148988247,
-0.010694841854274273,
-0.030690060928463936,
-0.02549557201564312,
0.013733663596212864,
0.0006121006445027888,
0.008951767347753048,
0.02206709235906601,
0.05424080416560173,
-0.03461826592683792,
0.05090454965829849,
0.03602535277605057,
0.020742660388350487,
0.04798854887485504,
-0.025136513635516167,
0.05719013512134552,
-0.007150327321141958,
0.01928240805864334,
-0.0055128438398242,
0.0412883386015892,
-0.005636625923216343,
0.05241149663925171,
0.06626277416944504,
-0.02161337621510029,
-0.06155120208859444,
-0.014586894772946835,
-0.04719884321093559,
-0.039372872561216354,
0.0026902633253484964,
-0.0264438409358263,
0.016838908195495605,
-0.006469441577792168,
0.011089267209172249,
-0.008074800483882427,
-0.02617163024842739,
0.026901206001639366,
-0.0013569050934165716,
0.04636721312999725,
-0.0005360175855457783,
0.02523788809776306,
-0.006243005860596895,
0.02321501448750496,
0.008660076186060905,
0.006000111345201731,
0.04621525853872299,
-0.0038000657223165035,
0.01984468288719654,
0.023773590102791786,
0.05294842645525932,
0.0141037842258811,
-0.022511309012770653,
0.03670033812522888,
-0.0006225482793524861,
0.026162464171648026,
0.08498891443014145,
0.011292176321148872,
-0.008607417345046997,
0.01410436350852251,
-0.034731827676296234,
-0.0323592945933342,
0.02569720521569252,
-0.012760341167449951,
0.034840915352106094,
-0.007052116561681032,
0.01940474659204483,
0.01956665702164173,
-0.04528836905956268,
0.012382689863443375,
0.0801069363951683,
0.007243907079100609,
-0.00882758665829897,
-0.03145888075232506,
0.021111134439706802,
-0.015363459475338459,
-0.004205680452287197,
-0.08411473035812378,
0.0017267040675505996,
-0.012442867271602154,
0.013271210715174675,
0.006458084098994732,
-0.0420757532119751,
0.010244989767670631,
-0.004885743837803602,
0.03333984687924385,
0.017181897535920143,
0.04409055784344673,
-0.03450463339686394,
0.011478927917778492,
-0.039534710347652435,
-0.05989491194486618,
0.0012693392345681787,
0.05389775335788727,
-0.01268373616039753,
-0.01702485978603363,
-0.0009632777073420584,
-0.006577091291546822,
0.010677902027964592,
0.024680549278855324,
-0.028740139678120613,
0.06759627163410187,
0.003734063357114792,
-0.06670989096164703,
-0.031251776963472366,
0.022761167958378792,
0.002446451922878623,
-0.012851105071604252,
-0.06553284823894501,
0.01160571537911892,
0.04310255125164986,
0.07373230904340744,
-0.0351853147149086,
0.028939493000507355,
-0.008250493556261063,
0.024423032999038696,
-0.014224310405552387,
-0.029546789824962616,
-0.013395545072853565,
0.04782644659280777,
-0.02970845438539982,
-0.03616092726588249,
-0.051780980080366135,
0.07361343502998352,
0.03444119542837143,
0.005081056151539087,
-0.027959497645497322,
0.05584733933210373,
-0.04318072646856308,
0.03174924477934837,
-0.006019477266818285,
-0.03686895594000816,
-0.0003663344250526279,
0.07955801486968994,
0.02942758798599243,
0.01772259548306465,
0.007387146353721619,
0.05356042832136154,
0.038723986595869064,
-0.01188464742153883,
-0.007405025884509087,
0.04406902566552162,
-0.03960951417684555,
-0.038406722247600555,
-0.01344896387308836,
-0.01955002173781395,
0.024791987612843513,
-0.037327080965042114,
-0.04633167386054993,
0.006998030468821526,
0.02033170312643051,
0.0026168886106461287,
0.029254630208015442,
0.003006217535585165,
0.009710256941616535,
-0.01616227999329567,
-0.03837241604924202,
-0.05470190569758415,
-0.0762321799993515,
0.05807848274707794,
0.04183204472064972,
0.006466583348810673,
0.022634921595454216,
0.02576920948922634,
0.006122095510363579,
-0.09522732347249985,
-0.029392965137958527,
-0.01697607710957527,
-0.0014557596296072006,
0.0038996955845505,
-0.02578275091946125,
0.008666449226439,
0.0680570974946022,
0.053867556154727936,
0.03833012282848358,
-0.00770242465659976,
-0.011076617054641247,
-0.009171764366328716,
-0.0066016679629683495,
-0.011194813996553421,
0.03243987634778023,
0.010317121632397175,
0.04199913889169693,
-0.010382317937910557,
-0.004336532671004534,
-0.014754900708794594,
0.006761539727449417,
-0.014903235249221325,
0.06892989575862885,
0.05501691997051239,
0.022210873663425446,
-0.018751094117760658,
0.014196794480085373,
-0.007122127339243889,
0.0027306571137160063,
-0.042356859892606735,
-0.015352164395153522,
-0.05984687805175781,
-0.0026775153819471598,
0.001751090632751584,
0.057427577674388885,
-0.048285339027643204,
-0.003259194316342473,
0.017106952145695686,
0.05132967606186867,
0.011909877881407738,
0.03565618768334389,
-0.012524033896625042,
-0.014102975837886333,
0.04805818572640419,
0.011238058097660542,
0.02813832461833954,
0.0015089036896824837,
0.012961245141923428,
-0.00894949957728386,
-0.013689769431948662,
-0.01432210486382246,
-0.012054728344082832,
0.026304276660084724,
0.028264272958040237,
0.023792671039700508,
0.02433457411825657,
-0.008890794590115547,
0.004851377569139004,
-0.01718353107571602,
-0.003836180316284299,
0.01752188801765442,
-0.01788068376481533,
-0.013653898611664772,
-0.04972844570875168,
-0.015202132053673267,
0.02022952400147915,
0.01602577604353428,
0.007019510958343744,
-0.0015896956901997328,
0.04858522117137909,
-0.004623734392225742,
0.03215152397751808,
-0.05535564199090004,
-0.05708390474319458,
-0.0307381059974432,
-0.028429828584194183,
0.0034086115192621946,
-0.008313830010592937,
0.02044524997472763,
-0.03487025201320648,
-0.03368057310581207,
0.02519974298775196,
-0.029403040185570717,
0.013337337411940098,
0.028716860339045525,
-0.05676504597067833,
0.018091890960931778,
-0.005595318507403135,
-0.04887697845697403,
0.07790953665971756,
0.0188742782920599,
0.0029694295953959227,
0.021234916523098946,
-0.007462515030056238,
-0.061750490218400955,
-0.008055890910327435,
-0.02642122656106949,
0.01675122231245041,
-0.042409539222717285,
0.003576913382858038,
0.04931223392486572,
-0.01670638471841812,
-0.035009052604436874,
0.030869707465171814,
-0.04248281940817833,
-0.007836428470909595,
-0.005351544823497534,
-0.0026175507809966803,
0.024489719420671463,
-0.01331534143537283,
0.04719050973653793,
-0.016216464340686798,
-0.03263227641582489,
0.0008341451757587492,
-0.05976216495037079,
-0.06411433964967728,
0.028909746557474136,
-0.012207306921482086,
0.01982891373336315,
-0.0034611911978572607,
-0.015075433999300003,
0.05000918358564377,
0.06388100236654282,
-0.02019319124519825,
-0.013792349025607109,
-0.035938069224357605,
-0.0025898199528455734,
-0.0006537046865560114,
-0.008315320126712322,
-0.008016317151486874,
-0.030501501634716988,
-0.025893308222293854,
-0.020823100581765175,
0.034373704344034195,
0.030737265944480896,
0.010450523346662521,
-0.015030390582978725,
-0.0027385251596570015,
0.019592059776186943,
0.054003842175006866,
0.023911602795124054,
0.05089275538921356,
-0.040147531777620316,
0.020860856398940086,
0.01012587733566761,
0.058299824595451355,
-0.0013959018979221582,
-0.0417461134493351,
0.08735471218824387,
0.004176485352218151,
0.0312853641808033,
-0.04462380334734917,
0.04933174327015877,
0.010626128874719143,
-0.002172069624066353,
0.006830285768955946,
0.0005516257951967418,
0.0711907222867012,
0.0058569167740643024,
0.018849212676286697,
-0.000632498471532017,
0.07939367741346359,
-0.020991945639252663,
-0.0700453594326973,
0.0001744473702274263,
-0.00907322857528925,
0.03661072626709938,
0.006659848149865866,
-0.009322709403932095,
0.008899103850126266,
0.0038045556284487247,
-0.01373718585819006,
0.030178260058164597,
-0.05596290901303291,
0.009100006893277168,
-0.05224831402301788,
0.01942870393395424,
-0.0023229788057506084,
0.03289300203323364,
-0.0037498895544558764,
0.04582260549068451,
0.003770412877202034,
0.020635994151234627,
0.03404056280851364,
0.01010863296687603,
-0.11214909702539444,
0.020512789487838745,
-0.05339718237519264,
0.004079342819750309,
-0.016602514311671257,
0.02612525410950184,
0.02219289541244507,
0.003265396924689412,
-0.010335968807339668,
0.031716082245111465,
-0.017555447295308113,
-0.04315353184938431,
0.012664984911680222,
-0.06939596682786942,
-0.04887231066823006,
-0.024404866620898247,
-0.007727126125246286,
0.04975917562842369,
-0.025660503655672073,
0.04647196829319,
0.060123804956674576,
-0.05106261745095253,
0.013960744254291058,
0.005594382993876934,
-0.02313959039747715,
0.017180027440190315,
-0.0018220347119495273,
0.012078805826604366,
0.029505407437682152,
0.004845863673835993,
0.011974508874118328,
-0.018561139702796936,
0.008229333907365799,
0.021451052278280258,
-0.008235082030296326,
-0.020166806876659393,
-0.04385046288371086,
0.002129417611286044,
0.010679229162633419,
0.04521562531590462,
0.0030318705830723047,
0.002418923657387495,
-0.026378093287348747,
0.011964554898440838,
-0.00902247242629528,
0.04972899705171585,
0.006474115885794163,
0.01570621319115162,
-0.03350938856601715,
-0.04881030693650246,
-0.02708623744547367,
-0.030561920255422592,
-0.009968193247914314,
-0.022851048037409782,
0.0004475476162042469,
-0.053331442177295685,
0.004273423459380865,
-0.000845501956064254,
0.042565517127513885,
0.02054905891418457,
0.022409379482269287,
-0.006656862795352936,
0.044279154390096664,
0.006313979625701904,
-0.009465442970395088,
0.04434574767947197,
0.04038090258836746,
0.021949850022792816,
0.004209458827972412,
-0.01098936703056097,
-0.07103567570447922,
-0.04839708283543587,
0.06298290193080902,
0.05201626569032669,
-0.0009133681305684149,
-0.0025250569451600313,
-0.05712142586708069,
-0.02512122318148613,
0.053008612245321274,
-0.004864968359470367,
0.01771247200667858,
-0.029112547636032104,
-0.013911456800997257,
-0.01922576315701008,
-0.058085571974515915,
-0.03195197135210037,
0.02690819837152958,
0.0117351608350873,
0.041037626564502716,
-0.018442297354340553,
-0.016726460307836533,
-0.006894065532833338,
-0.030865013599395752,
0.02755321003496647,
0.07750768959522247,
-0.0007048289990052581,
0.03044377826154232,
0.009126110933721066,
-0.00996960699558258,
-0.004028094466775656,
-0.07842683047056198,
0.014606365002691746,
-0.009288460947573185,
-0.03083508089184761,
-0.001509461784735322,
-0.054253384470939636,
-0.07958606630563736,
0.033639147877693176,
0.0204335767775774,
-0.008537114597856998,
0.012846332974731922,
-0.04241630807518959,
0.0462539903819561,
0.009171463549137115,
-0.005214028526097536,
0.02348518930375576,
0.031032510101795197,
-0.02075769193470478,
-0.01752675697207451,
0.012416095472872257,
-0.000054867770813871175,
-0.007259592413902283,
0.008320621214807034,
-0.05484210327267647,
-0.003960855305194855,
-0.04430577903985977,
0.013836489990353584,
0.02368868514895439,
-0.015932105481624603,
-0.017948828637599945,
-0.019266821444034576,
-0.019707171246409416,
0.032226234674453735,
0.01918947882950306,
-0.014092104509472847,
-0.07234255224466324,
0.014383962377905846,
0.04291969910264015,
-0.012174875475466251,
0.007392198778688908,
-0.007052165921777487,
0.004406096413731575,
0.06878483295440674,
-0.006701227277517319,
0.013632645830512047,
-0.01866227388381958,
-0.030558358877897263,
0.015405760146677494,
-0.03540080785751343,
0.027756063267588615,
-0.027798080816864967,
0.011414362117648125,
0.05293611064553261,
-0.039343539625406265,
-0.031822893768548965,
0.007110524922609329,
-0.01371162198483944,
-0.02466708980500698,
-0.05930189788341522,
0.019658386707305908,
0.01751190982758999,
0.003892159089446068,
-0.05971382558345795,
-0.04672614857554436,
0.03764307498931885,
-0.010393401607871056,
-0.05807853117585182,
-0.0009892919333651662,
-0.014569440856575966,
-0.015497250482439995,
-0.0542527511715889,
0.0029665606562048197,
0.028343388810753822,
-0.026048678904771805,
0.01580986939370632,
0.020914847031235695,
0.017457883805036545,
0.03963106498122215,
0.0032023866660892963,
-0.014953204430639744,
0.04678398743271828,
-0.019366109743714333,
-0.06280560791492462,
-0.04619477689266205,
0.05759182572364807,
-0.02519671805202961,
0.006195185240358114,
0.019664501771330833,
-0.025952761992812157,
0.022849902510643005,
-0.006166695151478052,
-0.03223192319273949,
0.05608369782567024,
-0.005551155190914869,
-0.017544448375701904,
0.014611904509365559,
0.011719025671482086,
-0.021182745695114136,
0.006246895994991064,
0.012944711372256279,
-0.027809785678982735,
-0.022399118170142174,
-0.026265176013112068,
0.024872714653611183,
0.008993283845484257,
0.012746637687087059,
-0.002181326039135456,
0.050534386187791824,
-0.05208892375230789,
-0.0170667115598917,
0.008493632078170776,
-0.03944128379225731,
-0.004326213151216507,
-0.009525728411972523,
0.012413771823048592,
-0.0014898345107212663,
-0.05105629190802574,
-0.018147265538573265,
0.00010394382843514904,
-0.01759023405611515,
0.011763660237193108,
0.047169383615255356,
0.003684768220409751,
0.05881321057677269,
0.018176954239606857,
0.03683152422308922,
0.021307887509465218,
-0.005760802421718836,
-0.009279311634600163,
-0.035451557487249374,
0.021124470978975296,
0.0008948871400207281,
0.0021748202852904797,
-0.001414804719388485,
0.05444817245006561,
0.012437124736607075,
-0.024356428533792496,
0.016495686024427414,
0.017622340470552444,
0.01992919109761715,
0.026489565148949623,
-0.008781945332884789,
-0.027294613420963287,
0.00271723885089159,
-0.04155587777495384,
0.06684365123510361,
-0.0195219274610281,
-0.04514928534626961,
0.02321798913180828,
0.05638176202774048,
0.012518100440502167,
-0.030027227476239204,
0.04040513560175896,
-0.04597143456339836,
0.01813535764813423,
-0.0289671178907156,
0.028296079486608505,
0.0017612497322261333,
0.005306479521095753,
0.011513400822877884,
0.007849869318306446,
0.014073485508561134,
-0.03217433765530586,
-0.04258153960108757,
-0.043252527713775635,
-0.02242162823677063,
-0.058571841567754745,
0.021983617916703224,
0.005702620837837458,
-0.024197770282626152,
0.03322111815214157,
-0.024405552074313164,
-0.007950794883072376,
0.0253746397793293,
0.04709162563085556,
0.0026861715596169233,
0.036147408187389374,
-0.009840693324804306,
0.04713054001331329,
-0.045944929122924805,
0.010825319215655327,
0.11643803119659424,
0.04432874917984009,
0.00461356807500124,
-0.047870099544525146,
0.05160100385546684,
-0.002847847528755665,
0.034440573304891586,
-0.028176376596093178,
0.007715065497905016,
0.0094525758177042,
-0.04192835092544556,
0.02260511927306652,
0.0040805828757584095,
-0.03551093116402626,
-0.0040279473178088665,
0.02076493576169014,
-0.05001288652420044,
-0.012123752385377884,
-0.007895016111433506,
0.00788508914411068,
-0.020426608622074127,
0.010919583961367607,
-0.009388412348926067,
-0.0020466146524995565,
-0.04385870322585106,
-0.011115942150354385,
0.004379264544695616,
-0.0676940456032753,
0.027372784912586212,
0.013521500863134861,
-0.04236578568816185,
0.030149750411510468,
0.0325433574616909,
-0.048225708305835724,
-0.017519330605864525,
0.013609402813017368,
-0.025578785687685013,
0.00829544011503458,
0.029757918789982796,
0.053316883742809296,
0.026894569396972656,
0.01893249712884426,
0.010399041697382927,
0.013141519390046597,
-0.00285342731513083,
-0.014706440269947052,
-0.028301559388637543,
0.050845928490161896,
-0.041218582540750504,
0.019146759063005447,
0.004319949075579643,
-0.010126630775630474,
0.01098148338496685,
-0.050664737820625305,
0.01295167300850153,
-0.018145320937037468,
0.03158647194504738,
0.02285711094737053,
0.006871075835078955,
-0.023340068757534027,
-0.013331684283912182,
0.04573427513241768,
0.007157163228839636,
-0.0018689623102545738,
-0.027703579515218735,
0.018984684720635414,
-0.013628670945763588,
0.029916422441601753,
-0.03296806290745735,
-0.031753815710544586,
-0.030295154079794884,
0.0028375552501529455,
-0.04980982467532158,
0.026173753663897514,
0.0042713177390396595,
-0.003191546304151416,
0.004800050985068083,
0.014286126010119915,
-0.019395794719457626,
-0.025469966232776642,
-0.022514386102557182,
0.03462965041399002,
0.014570126309990883,
-0.029167551547288895,
-0.02052280306816101,
-0.023335609585046768,
0.005487361922860146,
0.037544310092926025,
-0.02173449471592903,
0.0015988644445315003,
-0.018471743911504745,
0.0009876280091702938,
0.0025469069369137287,
-0.05718592181801796,
-0.026212522760033607,
0.003042644588276744,
-0.019146565347909927,
0.015733465552330017,
-0.016246125102043152,
0.04547104984521866,
0.011059421114623547,
0.015192622318863869,
-0.033357590436935425,
0.03897090256214142,
-0.007575612515211105,
0.019993923604488373,
0.008953523822128773,
-0.001147311762906611,
0.003874522401019931,
0.014757056720554829,
0.016343440860509872,
-0.025207212194800377,
-0.03213085979223251,
-0.017956452444195747,
0.04557900130748749,
-0.02970203384757042,
-0.006641152780503035,
-0.019853873178362846,
0.032621949911117554,
-0.014105726033449173,
0.04768480360507965,
-0.013265118934214115,
0.011949402280151844,
-0.04578983038663864,
0.01292260643094778,
0.01048364769667387,
0.04324663430452347,
-0.0011132153449580073,
0.06360448896884918,
0.004090953152626753,
-0.033950429409742355,
0.01359180174767971,
0.055850040167570114,
-0.01563708484172821,
-0.039044089615345,
0.025286728516221046,
-0.011115205474197865,
0.06043841689825058,
-0.03407440707087517,
-0.043619148433208466,
-0.00019177781359758228,
-0.024293476715683937,
-0.0323072113096714,
-0.009138543158769608,
0.027697481215000153,
0.007314779330044985,
0.010754554532468319,
0.00522429496049881,
0.015674883499741554,
0.01831880584359169,
0.015202045440673828,
-0.008754229173064232,
-0.008508987724781036,
-0.05836503207683563,
-0.031285762786865234,
-0.012623180635273457,
0.039557792246341705,
-0.008764257654547691,
-0.01688796654343605,
0.0181950144469738,
0.0018185765948146582,
-0.01648814044892788,
-0.026288725435733795,
-0.0034914722200483084,
-0.03736961632966995,
-0.010332086123526096,
0.014867489226162434,
-0.030191700905561447,
0.06540451943874359,
0.04892660304903984,
-0.06278344243764877,
0.01035588700324297,
0.004307731986045837,
-0.01393168792128563,
-0.07405851781368256,
-0.03323908895254135,
0.03689269348978996,
-0.0027820838149636984,
0.043641168624162674,
-0.057269174605607986,
-0.012622352689504623,
0.06066922843456268,
-0.06809860467910767,
0.04099944606423378,
-0.007024621125310659,
0.037078503519296646,
-0.017155420035123825,
-0.018768196925520897,
-0.013117881491780281,
0.04258500412106514,
0.05649079382419586,
0.07564989477396011,
0.0016578992363065481,
0.01286897249519825,
-0.02363777533173561,
-0.03941640257835388,
-0.0032854427117854357,
0.020095359534025192,
-0.027616450563073158,
-0.022462328895926476,
0.056667257100343704,
-0.014230042695999146,
0.031785998493433,
0.0021052074152976274,
-0.03158801794052124,
0.004956744145601988,
0.013282779604196548,
0.020121147856116295,
0.0064197503961622715,
0.02057350054383278,
0.014710798859596252,
0.006034210789948702,
-0.0022949343547225,
0.03545835614204407,
0.00047213229117915034,
0.03350687772035599,
-0.04362238943576813,
-0.01887943223118782,
-0.01678817719221115,
0.005923373159021139,
-0.03801582008600235,
0.06615613400936127,
-0.0229103434830904,
-0.0017999039264395833,
0.006311123259365559,
0.016141235828399658,
-0.0013947328552603722,
0.02626415155827999,
-0.0006861942820250988,
-0.02726040780544281,
-0.01249250490218401,
0.047712065279483795,
-0.00877163652330637,
0.00111028749961406,
-0.011449581943452358,
-0.023645328357815742,
-0.004789771977812052,
0.037621717900037766,
0.0022476757876574993,
-0.026454119011759758,
-0.014523069374263287,
0.03629443421959877,
-0.0037663138937205076,
-0.014127704314887524,
0.035171497613191605,
-0.019878040999174118,
-0.03388991206884384,
-0.01995709538459778,
0.034137241542339325,
0.027711430564522743,
0.0004121742967981845,
-0.0265358779579401,
-0.020459771156311035,
-0.054997190833091736,
0.05081705003976822,
-0.03758881613612175,
0.0008769333944655955,
-0.03800002112984657,
-0.0318266898393631,
0.01031038723886013,
0.002587632741779089,
0.07460574805736542,
-0.04383748769760132,
-0.0034082785714417696,
0.04234648495912552,
-0.005269549321383238,
0.030058294534683228,
-0.015573234297335148,
-0.0019576491322368383,
-0.005960212089121342,
0.016669580712914467,
0.005592037923634052,
0.011025682091712952,
-0.019450901076197624,
0.020207934081554413,
0.04686523228883743,
-0.030061256140470505,
0.036232758313417435,
-0.004266652278602123,
-0.048710208386182785,
0.0455053374171257,
0.03004443645477295,
-0.01581309735774994,
0.06449001282453537,
-0.01863374374806881,
0.040503907948732376,
0.004478173796087503,
-0.04871060699224472,
-0.032932620495557785,
0.03266870602965355,
-0.05135397985577583,
-0.013179146684706211,
-0.03145909309387207,
-0.013316618278622627,
-0.014131033793091774,
-0.042494695633649826,
-0.0243764016777277,
0.030023152008652687,
-0.05629631131887436,
-0.029067430645227432,
0.01360717136412859,
0.0015434296801686287,
0.06246485933661461,
-0.03878067433834076,
-0.0007592386100441217,
0.020944343879818916,
0.01855783350765705,
0.03365844488143921,
0.042489055544137955,
0.05520059913396835,
-0.01627000793814659,
-0.011941781267523766,
0.024481741711497307,
0.002192499116063118,
0.03744504228234291,
0.00466632517054677,
0.030386701226234436,
-0.017708372324705124,
-0.046842243522405624,
0.015348654240369797,
-0.01993388682603836,
-0.006697793025523424,
0.017289742827415466,
-0.010902270674705505,
0.029567776247859,
0.01652808114886284,
0.03106606937944889,
-0.0016895135631784797,
-0.022968119010329247,
-0.03323732689023018,
-0.023259982466697693,
0.017445150762796402,
0.00018466108303982764,
-0.018100857734680176,
-0.050337329506874084,
-0.00023397606855724007,
0.016251327469944954,
0.02805803343653679,
-0.022191446274518967,
0.017899421975016594,
0.02521021105349064,
-0.006733864080160856,
-0.012471417896449566,
-0.048019587993621826,
-0.01269503217190504,
-0.029247626662254333,
0.034961432218551636,
0.05842919275164604,
0.014556884765625,
0.008563359268009663,
0.00325388484634459,
-0.012805051170289516,
0.06605827808380127,
-0.029002109542489052,
0.00406071450561285,
0.00410454859957099,
0.05439380928874016,
-0.0199954342097044,
-0.013632447458803654
] |
<p>I am making a comparation between the photon gas and the ideal classic gas for my Thermodynamics class. The photon gas is defined by the equations:</p>
<p>$$U=aVT^4 $$
$$P=\dfrac{1}{3}aT^4$$</p>
<p>I found this document: <a href="http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf" rel="nofollow">http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf</a> which explain how to find some basic things, like enthalpy and entropy. It says that a great exercise is to compare the Carnot cycle of the photon gas with the Carnot cycle of the ideal gas. According to it, the efficiency is $\eta=1-\frac{T_2}{T_1}$ the same as the ideal gas. I think that this is really interesting for my comparation, so I'm trying to calculate the Carnot cycle efficiency for this gas.</p>
<p>I have no problem with the isothermal process, which is solved in that document:
$$W_{ab}=-\dfrac{1}{3}aT^4\Delta V$$</p>
<p>However, I'm not sure if my result of the adiabatic process is correct. Work is $W=\int PdV$. Now, I can use the photon gas adiabatic equation (see the document) $PV^{4/3}=k$, where $k$ is a constant, to substitute $P$ in work equation, and integrate to obtain:</p>
<p>$$W_{bc} =\dfrac{3}{4}k\left( \dfrac{1}{V_b^3} - \dfrac{1}{V_c^3} \right)$$</p>
<p>I'm not sure if this result is correct. When I try to calculate the efficiency of the cycle, I have:
$$\eta=\dfrac{|W_T|}{|Q_{ab}|}=\dfrac{|W_{ab}+W_{bc}+W_{cd}+W_{da}|}{|Q_{ab}|}$$</p>
<p>where $W_{ab}$,$W_{cd}$ are isothermal and $W_{bc}$,$W_{da}$ are adiabatic. The heat is also defined in the document as:</p>
<p>$$Q_{ab}=\dfrac{4}{3}aT^4\Delta V$$</p>
<p>But with these values I can't obtain the correct expression for the efficiency, or I don't know how to reduce the efficiency expression to obtain what I want. Which is the correct way to calculate adiabatic work in a photon gas? And the Carnot cycle efficiency?</p>
<p>Thank you all for your answers :D</p> | 4,603 | [
0.005707956850528717,
-0.039767488837242126,
-0.005074026063084602,
-0.018521452322602272,
0.042539842426776886,
0.01667909510433674,
-0.049091510474681854,
-0.01200637873262167,
-0.01125264074653387,
-0.0032062295358628035,
0.053348224610090256,
0.03500494733452797,
0.03838907182216644,
0.02849506586790085,
-0.0010202339617535472,
0.006096940021961927,
-0.02465926855802536,
-0.00829655397683382,
0.003820206969976425,
-0.023576848208904266,
-0.006866132840514183,
0.01899201050400734,
0.014821230433881283,
-0.03270978853106499,
-0.04967663437128067,
0.029988054186105728,
0.005134935025125742,
0.01437592227011919,
-0.02745831571519375,
0.036609239876270294,
-0.05312899500131607,
-0.012444848194718361,
0.038999080657958984,
0.018267132341861725,
0.00816099252551794,
0.057761967182159424,
-0.002439863048493862,
-0.03320101276040077,
-0.010595454834401608,
0.04653649777173996,
-0.049233146011829376,
0.0218744408339262,
-0.01064342726022005,
0.007363920100033283,
0.009629270061850548,
0.014979776926338673,
-0.0002913842909038067,
-0.0025186720304191113,
0.029825137928128242,
-0.08289841562509537,
0.04368481785058975,
0.007700380869209766,
0.045341916382312775,
0.031380876898765564,
-0.022488782182335854,
-0.010493847541511059,
0.057117220014333725,
0.09038005769252777,
-0.005614675581455231,
-0.03238961100578308,
-0.03198204189538956,
0.009030208922922611,
-0.01810310035943985,
-0.002700696000829339,
-0.012367025949060917,
0.02513885870575905,
0.035817500203847885,
-0.022475821897387505,
0.04859058931469917,
0.00014271502732299268,
0.042529791593551636,
0.012281776405870914,
0.005630393046885729,
-0.027751412242650986,
0.018027789890766144,
0.014596112072467804,
-0.00759954284876585,
0.026346730068325996,
0.06015457585453987,
0.05499924346804619,
-0.010022624395787716,
0.015722570940852165,
0.018774785101413727,
0.04398969188332558,
-0.01674335077404976,
0.009204579517245293,
0.08087830990552902,
-0.016247199848294258,
0.003737426595762372,
0.03216886892914772,
-0.008289454504847527,
0.045104917138814926,
0.028774572536349297,
-0.008812518790364265,
0.032194193452596664,
0.03231310099363327,
-0.028018712997436523,
0.040723998099565506,
-0.013173914514482021,
-0.05468999221920967,
-0.034650545567274094,
-0.025983715429902077,
0.02197403647005558,
0.10817556828260422,
0.02872535213828087,
-0.036801401525735855,
-0.0431952103972435,
0.03450930118560791,
-0.0005103730945847929,
-0.012081408873200417,
-0.06987837702035904,
0.010399902239441872,
-0.0018677674233913422,
0.0011806586990132928,
-0.018199535086750984,
-0.024011923000216484,
0.00613868935033679,
-0.0250578373670578,
0.05313999578356743,
0.04278210550546646,
0.01914629153907299,
-0.03474266454577446,
0.051870714873075485,
-0.014090986922383308,
-0.03531750664114952,
0.003230367787182331,
0.026321014389395714,
-0.022883815690875053,
-0.012303048744797707,
0.007209070026874542,
-0.012612194754183292,
-0.004521498456597328,
-0.009779647924005985,
0.010616429150104523,
0.013061589561402798,
-0.058167751878499985,
-0.047173332422971725,
-0.04951615631580353,
0.05823887512087822,
0.02955012023448944,
-0.03323693573474884,
-0.06874652206897736,
0.029418108984827995,
0.017937401309609413,
0.06328630447387695,
-0.03822443634271622,
-0.009965579025447369,
-0.01291683316230774,
0.019928012043237686,
-0.007524984888732433,
-0.041451673954725266,
0.005660251248627901,
0.01295334380120039,
-0.016215452924370766,
-0.0033582025207579136,
-0.07354072481393814,
0.03402913734316826,
0.05743761733174324,
0.011189829558134079,
0.005862026009708643,
0.07983336597681046,
-0.004864898975938559,
-0.017231255769729614,
0.011543696746230125,
0.014164390042424202,
-0.03741826117038727,
0.06851226091384888,
0.03566810488700867,
0.03071954846382141,
-0.03869730606675148,
0.002361701801419258,
-0.013855216093361378,
-0.017687585204839706,
-0.01106177642941475,
0.03968973457813263,
-0.035913802683353424,
-0.0013818169245496392,
-0.0039751650765538216,
0.026738977059721947,
0.0452767089009285,
-0.018952200189232826,
-0.01690775528550148,
-0.0012008259072899818,
-0.0008830039878375828,
-0.020268402993679047,
0.05428910255432129,
0.003124230308458209,
0.03595012053847313,
-0.008606971241533756,
-0.046986114233732224,
-0.044693466275930405,
-0.038402386009693146,
-0.02488357201218605,
0.048227306455373764,
-0.011072431690990925,
0.0037979495245963335,
0.004819001071155071,
0.020451270043849945,
0.033850133419036865,
-0.012534472160041332,
-0.016792524605989456,
0.041263777762651443,
0.034581996500492096,
0.008516098372638226,
0.04410552605986595,
0.0689833015203476,
0.05135778710246086,
0.010715263895690441,
0.01233686227351427,
0.011589867062866688,
0.01669849082827568,
0.004700264427810907,
-0.032281700521707535,
0.007739755790680647,
-0.008276297710835934,
-0.017228515818715096,
0.04307505860924721,
0.03171829879283905,
0.005881226155906916,
0.006202262360602617,
-0.00782642513513565,
0.03330288827419281,
0.048053424805402756,
0.017468087375164032,
-0.005941396113485098,
0.023230891674757004,
-0.03806878253817558,
0.05473572015762329,
-0.018549621105194092,
0.004458878189325333,
-0.00913391262292862,
0.010723287239670753,
0.04450564086437225,
0.040300849825143814,
-0.051206763833761215,
0.024644633755087852,
0.04427410662174225,
-0.023965604603290558,
0.030644679442048073,
-0.00729170860722661,
0.01506810262799263,
-0.03123885579407215,
0.05373532325029373,
0.030564967542886734,
0.027237674221396446,
0.04575010761618614,
0.014388689771294594,
0.00002881053660530597,
0.0002956778625957668,
-0.007028117310255766,
-0.018580814823508263,
0.02004977874457836,
-0.02203950099647045,
0.002199248643592,
-0.014851843006908894,
0.007283762563019991,
0.06523820012807846,
-0.04011271893978119,
0.006062382832169533,
0.0315723679959774,
0.005892736371606588,
0.03401648625731468,
-0.002000244800001383,
-0.03963702917098999,
-0.0004891230491921306,
0.011988879181444645,
0.025801561772823334,
-0.01841791160404682,
0.01496861781924963,
-0.009819604456424713,
0.026828737929463387,
-0.0324288085103035,
0.01602807268500328,
-0.04228610545396805,
0.0022866667713969946,
0.022656625136733055,
0.040654126554727554,
-0.01919787935912609,
-0.030501600354909897,
-0.023449834436178207,
0.006460551638156176,
0.00001670163510425482,
0.011105787940323353,
0.01903579756617546,
-0.028862927109003067,
-0.02449803426861763,
-0.01314228679984808,
-0.036043889820575714,
0.025213573127985,
-0.02633669227361679,
-0.016588523983955383,
0.05661559849977493,
-0.005371835548430681,
-0.042791612446308136,
-0.0034448017831891775,
0.0016527230618521571,
-0.01819135993719101,
-0.0453869067132473,
-0.0011345092207193375,
0.04205182194709778,
-0.021305713802576065,
-0.058405231684446335,
0.008569982834160328,
-0.027111375704407692,
-0.08960957825183868,
-0.017232129350304604,
-0.02229480817914009,
0.017549943178892136,
-0.013836534693837166,
0.05285612866282463,
0.04069490358233452,
-0.028966199606657028,
-0.02214541658759117,
-0.06825172901153564,
-0.017438247799873352,
0.028638681396842003,
-0.00830457266420126,
0.025913836434483528,
-0.0059120384976267815,
-0.041613370180130005,
0.054259397089481354,
0.044593654572963715,
-0.012379526160657406,
0.005395522806793451,
-0.011411859653890133,
-0.03752637654542923,
-0.019119812175631523,
-0.002303697867318988,
-0.013918362557888031,
-0.040019549429416656,
-0.0057211327366530895,
-0.018827151507139206,
0.03392811119556427,
0.011918703094124794,
0.027536019682884216,
-0.016706766560673714,
0.01627286896109581,
-0.0420273095369339,
0.009828402660787106,
0.03153263032436371,
-0.021347973495721817,
-0.009101495146751404,
0.020642992109060287,
-0.012876537628471851,
-0.0071273245848715305,
0.02889779582619667,
-0.06384973973035812,
0.06172758713364601,
0.02779199741780758,
-0.0005461801774799824,
-0.04572351276874542,
0.005558154545724392,
-0.026050018146634102,
-0.034754008054733276,
0.01897442154586315,
0.015023688785731792,
0.047323837876319885,
0.019478486850857735,
0.007872185669839382,
0.04336463287472725,
0.042267248034477234,
-0.006099384278059006,
-0.005744929425418377,
0.007639292627573013,
-0.04315691068768501,
0.02819473296403885,
0.007008043583482504,
-0.001189176575280726,
0.041313547641038895,
0.05257444828748703,
0.015028439462184906,
-0.028471458703279495,
-0.01999983750283718,
-0.003998422529548407,
-0.050888191908597946,
-0.013788796029984951,
-0.051738105714321136,
0.06766320765018463,
0.005569479428231716,
0.03406570106744766,
0.013219204731285572,
-0.006541942246258259,
0.044848546385765076,
-0.03909781947731972,
-0.08404777199029922,
0.035175472497940063,
0.02509744092822075,
-0.04974556714296341,
0.016231341287493706,
-0.015323624946177006,
0.00009426489850739017,
-0.034846968948841095,
-0.05244914069771767,
0.006382018327713013,
-0.012870918028056622,
-0.04242982715368271,
0.03982478752732277,
-0.022394215688109398,
-0.015965986996889114,
-0.025809353217482567,
0.0336347259581089,
0.04564455524086952,
0.005136065650731325,
0.00819344725459814,
0.05092629790306091,
-0.029345713555812836,
0.04493045434355736,
-0.014955705963075161,
0.009646992199122906,
0.0467156358063221,
0.051625464111566544,
0.0341540090739727,
0.0037234961055219173,
-0.0028747273609042168,
-0.019629133865237236,
0.00796507578343153,
-0.012206671759486198,
0.021151797845959663,
-0.0457686185836792,
-0.006439450662583113,
-0.02274085208773613,
-0.0011989917838945985,
-0.0066603850573301315,
0.042420510202646255,
-0.014618407003581524,
0.020420651882886887,
-0.004388350993394852,
0.0010402599582448602,
-0.0009097433066926897,
0.036083679646253586,
0.05514756217598915,
-0.05451683700084686,
-0.009045485407114029,
-0.03515181690454483,
-0.0016066191019490361,
0.0021470217034220695,
-0.00781506858766079,
0.03207602724432945,
0.014628874137997627,
-0.05293995141983032,
-0.031586214900016785,
-0.0055850800126791,
0.035006772726774216,
-0.00814904272556305,
-0.0077803852036595345,
0.007546643260866404,
0.003879436757415533,
0.03695444017648697,
-0.03211866691708565,
0.014484638348221779,
0.048220083117485046,
0.02811744436621666,
0.0019126787083223462,
0.015007887966930866,
-0.08330877125263214,
-0.026878217235207558,
0.011244278401136398,
0.024380015209317207,
-0.006124529056251049,
-0.016710272058844566,
-0.02956966683268547,
-0.0023559958208352327,
0.04134511575102806,
-0.026594210416078568,
0.07278469204902649,
-0.013353691436350346,
0.02124965377151966,
0.01288510300219059,
-0.04908905178308487,
-0.01729431562125683,
0.016783885657787323,
0.012331252917647362,
-0.019910383969545364,
-0.049981147050857544,
-0.012321006506681442,
0.01477695070207119,
0.014415394514799118,
0.003868955187499523,
0.047734469175338745,
-0.06084035336971283,
-0.03296460583806038,
0.021168455481529236,
0.032226789742708206,
-0.0457112193107605,
-0.07979204505681992,
0.005496497265994549,
-0.00609514070674777,
-0.0035791138652712107,
0.004432294983416796,
-0.03845938667654991,
-0.06332893669605255,
0.03820847347378731,
-0.0009273846517316997,
-0.03660175949335098,
-0.02389390394091606,
-0.04621289297938347,
0.0399765819311142,
0.004481251817196608,
-0.015796301886439323,
0.07322266697883606,
0.07062063366174698,
-0.05251453071832657,
-0.016208788380026817,
-0.04670180752873421,
0.014327336102724075,
-0.017292441800236702,
-0.007400007918477058,
-0.04641445353627205,
-0.019197750836610794,
0.003615695983171463,
0.032032113522291183,
-0.05759105831384659,
0.04261137172579765,
-0.012430420145392418,
-0.015238741412758827,
0.03288668394088745,
-0.011931395158171654,
0.010209931060671806,
-0.004421132151037455,
-0.04202809929847717,
0.006319625768810511,
-0.009596441872417927,
-0.018393827602267265,
0.02309257909655571,
-0.0005403906689025462,
-0.03683137521147728,
0.015105210244655609,
0.02636159397661686,
0.02958451397716999,
-0.04258456081151962,
-0.017768848687410355,
-0.024951931089162827,
-0.012129509821534157,
0.036309242248535156,
-0.0029716268181800842,
0.028306031599640846,
-0.004037198610603809,
-0.039887942373752594,
-0.037021081894636154,
-0.020781129598617554,
0.014369518496096134,
0.020913459360599518,
-0.030770789831876755,
0.03902703523635864,
-0.0033893322106450796,
-0.013990574516355991,
-0.07194431126117706,
-0.03614598885178566,
0.026026448234915733,
-0.01343008503317833,
-0.02646617218852043,
-0.03219293802976608,
0.006963658146560192,
-0.000713711662683636,
-0.019980059936642647,
0.01623239554464817,
0.045959800481796265,
-0.037463486194610596,
0.0036384444683790207,
-0.016819097101688385,
0.027761535719037056,
0.032036345452070236,
-0.01818935200572014,
-0.03690449893474579,
-0.0017431140877306461,
0.01772584579885006,
-0.043229129165410995,
0.028863007202744484,
0.025743277743458748,
-0.008517210371792316,
-0.03719821199774742,
0.025660723447799683,
0.007409404497593641,
0.047106266021728516,
-0.03384256362915039,
-0.046389300376176834,
0.0414125956594944,
0.016619013622403145,
-0.013274078257381916,
-0.02258133701980114,
0.011007487773895264,
0.012274904176592827,
0.03137830272316933,
-0.005809410475194454,
-0.007958019152283669,
-0.012270990759134293,
-0.03685254231095314,
0.009292669594287872,
-0.03285026177763939,
-0.0203756894916296,
-0.002879111794754863,
0.07337559759616852,
-0.01407464686781168,
0.018504183739423752,
-0.011149149388074875,
-0.01857246458530426,
-0.0056642224080860615,
-0.017366735264658928,
0.013073446229100227,
-0.003119999310001731,
-0.00379559095017612,
-0.028925055637955666,
-0.024635516107082367,
-0.08355686068534851,
-0.010829433798789978,
0.07041092962026596,
0.016361979767680168,
0.07875891029834747,
-0.006712966598570347,
0.02544458955526352,
0.0676984041929245,
-0.04083186760544777,
-0.015327602624893188,
0.023461569100618362,
0.006674529518932104,
0.025204502046108246,
-0.010492349043488503,
-0.0308372862637043,
0.04227346554398537,
0.027693340554833412,
-0.05932309851050377,
0.01776229590177536,
0.014545433223247528,
-0.016421249136328697,
-0.0384947843849659,
-0.014186130836606026,
-0.027612769976258278,
0.041183196008205414,
-0.023977747187018394,
0.04383380711078644,
-0.013701782561838627,
0.003998646978288889,
0.04494509473443031,
0.0075973812490701675,
-0.002151548396795988,
-0.06125162914395332,
0.004630789160728455,
-0.0468946248292923,
-0.008834928274154663,
0.03028847463428974,
-0.013720965944230556,
0.044569164514541626,
0.018062399700284004,
0.04379855841398239,
-0.005799517501145601,
0.03790199011564255,
-0.010273810476064682,
-0.027574285864830017,
0.005780808161944151,
-0.010443628765642643,
-0.04620518907904625,
0.04883309453725815,
-0.028752189129590988,
-0.04047840088605881,
0.007832638919353485,
-0.03452951833605766,
0.0222486462444067,
0.029410304501652718,
0.04156314581632614,
0.03477884829044342,
0.02571636438369751,
0.00033800373785197735,
0.046884264796972275,
-0.005165608134120703,
0.047211334109306335,
0.13624034821987152,
0.03725826367735863,
0.006746035069227219,
-0.030393138527870178,
0.020604874938726425,
-0.04360392689704895,
0.006754788104444742,
-0.03143436089158058,
0.0368446446955204,
-0.02352052368223667,
-0.049866657704114914,
0.02544393204152584,
0.03386780247092247,
-0.03721360117197037,
0.003950872458517551,
0.0050475457683205605,
-0.020191563293337822,
-0.041510000824928284,
0.03866448625922203,
0.04637778177857399,
0.00757046602666378,
0.028206031769514084,
0.008026155643165112,
0.006725843995809555,
-0.04342907294631004,
-0.0010092685697600245,
-0.011160583235323429,
-0.04452795535326004,
0.04857821762561798,
-0.020326636731624603,
-0.032982610166072845,
-0.013324671424925327,
-0.0013908767141401768,
-0.012537148781120777,
0.016831684857606888,
-0.013154497370123863,
0.014758561737835407,
-0.013467922806739807,
0.016703704372048378,
0.032813556492328644,
-0.0009828830370679498,
0.011952311731874943,
0.03526655584573746,
0.04082028567790985,
-0.039116453379392624,
-0.007563354447484016,
-0.02444521151483059,
0.045311376452445984,
-0.01448204554617405,
0.038489967584609985,
-0.03116677515208721,
0.0022799456492066383,
-0.007508058100938797,
-0.04142719879746437,
0.002672079484909773,
-0.0083058662712574,
0.023964891210198402,
-0.03513934090733528,
-0.042665995657444,
-0.03512360155582428,
0.007240245118737221,
0.01063738763332367,
-0.0011984172742813826,
-0.06889595091342926,
-0.006442531943321228,
0.022491777315735817,
-0.013147860765457153,
0.016111360862851143,
-0.07276217639446259,
-0.026104090735316277,
0.014790233224630356,
-0.027695732191205025,
-0.040786053985357285,
-0.027635013684630394,
0.0007826890796422958,
-0.002726054983213544,
0.0592898353934288,
0.03454252704977989,
-0.03649154305458069,
-0.019240541383624077,
-0.09358197450637817,
-0.012381472624838352,
0.013740349560976028,
-0.0407954640686512,
-0.02156720869243145,
0.003572574583813548,
0.02250337041914463,
0.008778638206422329,
0.021126648411154747,
0.007065144833177328,
0.04847614839673042,
0.02803984470665455,
0.048669081181287766,
-0.0027031870558857918,
-0.026195039972662926,
0.03798067569732666,
-0.014161443337798119,
-0.008130578324198723,
0.004185289144515991,
0.014137335121631622,
0.022154005244374275,
-0.0017070559551939368,
-0.02343822456896305,
0.012481000274419785,
-0.014395331032574177,
0.022151650860905647,
-0.011923326179385185,
0.0045806593261659145,
-0.02744673192501068,
0.04301978647708893,
0.027523677796125412,
-0.031933899968862534,
-0.02169438637793064,
-0.035692404955625534,
0.02460477687418461,
-0.04741667956113815,
-0.015597001649439335,
-0.0024492465890944004,
0.021501664072275162,
-0.03445323929190636,
0.004936009179800749,
-0.06629957258701324,
-0.045670103281736374,
-0.004767878446727991,
0.02534259483218193,
0.011975801549851894,
0.047732360661029816,
-0.0159566942602396,
0.026400361210107803,
0.02298745885491371,
0.0015989828389137983,
0.029065104201436043,
0.035917844623327255,
0.004623475484549999,
-0.058620814234018326,
0.012699260376393795,
0.02209741808474064,
0.04867469146847725,
0.019848717376589775,
-0.005925243720412254,
0.029825415462255478,
-0.02202683873474598,
-0.05605829507112503,
0.005064954049885273,
0.02938065491616726,
0.02219828963279724,
0.03988092020153999,
-0.006525400094687939,
-0.017384758219122887,
0.06297395378351212,
-0.03596775606274605,
0.01789151504635811,
-0.018602075055241585,
-0.06148899719119072,
-0.009216482751071453,
0.02215413562953472,
0.007358701433986425,
0.010416855104267597,
0.011521635577082634,
0.02272224612534046,
0.017061306163668633,
-0.022554030641913414,
0.0016359611181542277,
-0.024280330166220665,
-0.045414455235004425,
-0.016156062483787537,
0.016753695905208588,
-0.025544235482811928,
0.0118743646889925,
0.04002496227622032,
0.02608553133904934,
0.031532444059848785,
0.024573324248194695,
-0.0174392182379961,
-0.10670650005340576,
-0.007550018839538097,
-0.024032777175307274,
0.016758190467953682,
0.02796945534646511,
-0.05171455442905426,
0.04515168070793152,
0.029168209061026573,
-0.03404873609542847,
0.025722166523337364,
0.006444467231631279,
-0.010351539589464664,
-0.058708932250738144,
-0.014824294485151768,
-0.028444118797779083,
0.030828360468149185,
0.014399374835193157,
0.005971141625195742,
-0.009135555475950241,
0.028675466775894165,
-0.014217947609722614,
-0.03372161462903023,
0.013290959410369396,
0.021352432668209076,
-0.02092054672539234,
0.019974231719970703,
0.012641181237995625,
-0.013209768570959568,
-0.008642314933240414,
0.02554485760629177,
-0.031503986567258835,
0.030729377642273903,
-0.0016962012741714716,
0.02637851983308792,
-0.02135169692337513,
0.03304602950811386,
0.05432670935988426,
-0.00713065080344677,
0.000515201420057565,
0.005431661382317543,
0.04069361463189125,
0.004264672286808491,
-0.003366154385730624,
0.001971745863556862,
0.052014533430337906,
-0.0008856846252456307,
-0.07373619824647903,
0.06348945945501328,
0.0015468687051907182,
-0.021202053874731064,
-0.00950778741389513,
-0.01936222054064274,
-0.03985102102160454,
-0.01701902598142624,
0.0003879123833030462,
-0.07178205996751785,
0.013297303579747677,
0.02539491467177868,
-0.020765502005815506,
0.02159297652542591,
-0.03874790295958519,
-0.014164270833134651,
-0.01746172085404396,
0.05934819206595421,
0.015448960475623608,
-0.011074758134782314,
-0.031104521825909615,
-0.033304352313280106,
-0.00030174225685186684,
0.001994574908167124,
-0.021291328594088554,
-0.04677712544798851,
-0.03555495664477348,
0.03629656136035919,
0.006917527876794338,
-0.022386591881513596,
-0.036488406360149384,
0.008450482040643692,
-0.03690412640571594,
-0.051152728497982025,
0.0029472194146364927,
-0.031058214604854584,
-0.022724393755197525,
-0.040141984820365906,
0.0001413706922903657,
0.008379727602005005,
0.027687277644872665,
0.038101926445961,
-0.007905744947493076,
-0.04424627497792244,
0.03259620442986488,
-0.005669998005032539,
0.011933586560189724,
-0.05805810168385506,
-0.006911392789334059,
-0.022701077163219452,
0.012338923290371895,
0.024729618802666664,
0.021061871200799942,
-0.05645539239048958,
0.025847746059298515,
0.02520425245165825,
-0.03330037742853165,
-0.008426173590123653,
0.01596195250749588,
-0.01272536814212799,
0.021481245756149292,
-0.011625171639025211,
-0.0232454314827919,
0.038484763354063034,
-0.01211768388748169,
0.03692745044827461,
0.02691139094531536,
-0.009856789372861385,
-0.010623670183122158,
0.020696286112070084,
-0.00830230675637722,
0.009573330171406269,
-0.022502325475215912,
-0.02614099718630314,
0.01957208290696144,
-0.0376761294901371,
0.00621434859931469,
0.009988737292587757,
-0.04847331345081329,
-0.005856991745531559,
0.048133134841918945,
0.009111093357205391,
0.028704093769192696,
-0.028972091153264046,
0.058137260377407074,
-0.0016517541371285915,
0.018744252622127533,
0.015182293951511383,
0.04039662703871727,
0.020167363807559013,
0.020871946588158607,
0.028177767992019653,
-0.003126993542537093,
-0.01723966747522354,
-0.014770377427339554,
0.032203320413827896,
-0.0030027006287127733,
-0.019201455637812614,
-0.012136057019233704,
0.01923390105366707,
-0.015053920447826385,
-0.0024042180739343166,
0.037023793905973434,
0.007996300235390663,
0.07847907394170761,
-0.019395412877202034,
0.025460952892899513,
-0.05119061842560768,
-0.009531845338642597,
-0.051331523805856705,
0.008682611398398876,
0.021667614579200745,
0.031061388552188873,
-0.03427402675151825,
0.004893461707979441,
-0.029248153790831566,
0.024065691977739334,
0.013352733105421066,
-0.05475890263915062,
-0.005604083184152842,
0.03506464511156082,
-0.014254109002649784,
-0.024326564744114876,
-0.008555503562092781,
-0.015004911459982395,
-0.03822522237896919,
-0.017913585528731346,
0.052196528762578964,
0.009984453208744526,
0.05799051746726036,
-0.007815971970558167,
0.021189048886299133,
0.07169781625270844,
-0.013579174876213074,
-0.01939000003039837,
0.022678932175040245,
0.016197439283132553,
0.01038715336471796,
0.012082294560968876
] |
<p>What is the molecular level reason behind the pattern (sine function) of the waves?</p>
<p><img src="http://i.stack.imgur.com/wAoQL.jpg" alt="enter image description here"></p> | 4,604 | [
-0.03614038974046707,
0.01100224070250988,
0.007648073602467775,
-0.037535641342401505,
0.041052963584661484,
0.010068709030747414,
-0.005757450591772795,
-0.033844299614429474,
0.025687385350465775,
-0.02918897196650505,
0.0351601243019104,
0.03848075866699219,
-0.004738491959869862,
0.025698451325297356,
0.0201606135815382,
-0.015002606436610222,
-0.02557205967605114,
-0.030947133898735046,
-0.031170085072517395,
-0.006849849596619606,
-0.029792606830596924,
0.012624274007976055,
-0.026207899674773216,
0.021896544843912125,
-0.045990847051143646,
0.0485641211271286,
0.06781462579965591,
0.021237066015601158,
0.03981407731771469,
0.03708428144454956,
-0.001890176790766418,
-0.03542846441268921,
0.015949489548802376,
0.03208623826503754,
0.017315128818154335,
-0.028293993324041367,
-0.01989651843905449,
-0.019442927092313766,
-0.007529393304139376,
0.03183780610561371,
-0.0031783939339220524,
-0.026127465069293976,
-0.026525013148784637,
0.028382331132888794,
-0.040497101843357086,
-0.011419218964874744,
0.00965904537588358,
-0.014369535259902477,
0.034916382282972336,
-0.08662160485982895,
0.07667059451341629,
-0.011080057360231876,
0.0214463472366333,
-0.007749725133180618,
-0.011551828123629093,
0.0004315936821512878,
0.06843598932027817,
0.042064033448696136,
-0.053258322179317474,
-0.06289980560541153,
0.009094792418181896,
-0.0252497810870409,
-0.00958429928869009,
0.012104323133826256,
-0.03546639531850815,
0.022529078647494316,
-0.0007422671769745648,
-0.07373040169477463,
0.030701102688908577,
0.021417804062366486,
0.0017230985686182976,
-0.008218721486628056,
0.028073986992239952,
-0.051796358078718185,
0.016918133944272995,
-0.036878425627946854,
-0.013531362637877464,
0.007213744334876537,
0.02346758171916008,
0.05330493301153183,
-0.003976715262979269,
0.012235256843268871,
0.0058622220531105995,
0.025199109688401222,
-0.008786789141595364,
0.01413734257221222,
0.08082450181245804,
-0.03579078987240791,
0.008895406499505043,
0.03391902148723602,
0.0029032290913164616,
0.045765604823827744,
0.04499475285410881,
0.056789692491292953,
-0.01838221214711666,
0.029381945729255676,
-0.005917662288993597,
0.020774435251951218,
0.049771830439567566,
-0.02586202323436737,
0.01987001858651638,
-0.0257648266851902,
0.010998315177857876,
0.057398226112127304,
-0.03083082288503647,
-0.01688855141401291,
-0.05587923899292946,
0.03792138025164604,
-0.031126605346798897,
0.0021430153865367174,
-0.014360791072249413,
0.015487910248339176,
-0.006472853012382984,
0.003851344808936119,
-0.006280595902353525,
0.003348025493323803,
0.007889282889664173,
-0.004876692779362202,
0.022611163556575775,
0.08959740400314331,
0.029344648122787476,
-0.03465758636593819,
0.02424563653767109,
0.018614575266838074,
-0.054196424782276154,
-0.007629129104316235,
-0.018488887697458267,
-0.00935429148375988,
-0.023130720481276512,
0.030804412439465523,
-0.0015371617628261447,
-0.015909191220998764,
0.04372740164399147,
-0.012165462598204613,
0.029121318832039833,
-0.011406401172280312,
-0.1338285505771637,
-0.04826750606298447,
0.06356276571750641,
-0.01939169317483902,
0.013087254017591476,
-0.08166655898094177,
0.008855249732732773,
0.025418585166335106,
0.06913286447525024,
-0.019948601722717285,
-0.017903128638863564,
0.0031394530087709427,
0.01972879283130169,
0.00008624957990832627,
0.023468278348445892,
-0.004987603519111872,
0.000007408221790683456,
-0.06071333959698677,
-0.019625123590230942,
-0.01860220357775688,
0.023064497858285904,
0.050987642258405685,
0.013346471823751926,
-0.02653362974524498,
0.028391819447278976,
-0.027406848967075348,
-0.007881877943873405,
0.0230680201202631,
-0.00804265309125185,
-0.04643281549215317,
0.07853302359580994,
0.0184019785374403,
0.001432374818250537,
0.03618413954973221,
-0.040672335773706436,
0.02245189994573593,
-0.013594996184110641,
0.020850738510489464,
-0.004855177830904722,
-0.014549760147929192,
-0.014878441579639912,
-0.02154088020324707,
0.022487914189696312,
-0.002710495376959443,
-0.011570192873477936,
-0.034042805433273315,
0.015574174001812935,
0.027196386829018593,
0.007914554327726364,
0.05084056407213211,
-0.027709925547242165,
-0.024756142869591713,
0.01884419471025467,
-0.07670807093381882,
0.0004853994178120047,
-0.03661986440420151,
0.04624553024768829,
-0.0334479883313179,
-0.04175133630633354,
0.02794579602777958,
0.025304673239588737,
-0.0022178138606250286,
-0.014329753816127777,
-0.010393360629677773,
-0.029596665874123573,
0.025374390184879303,
0.017005300149321556,
0.006845809053629637,
0.03487526997923851,
0.06568485498428345,
0.00037391879595816135,
-0.01353418081998825,
0.02293705940246582,
-0.04219150170683861,
-0.016919072717428207,
0.003906059078872204,
-0.035504721105098724,
0.030077297240495682,
-0.04938993975520134,
0.00162891938816756,
0.021655483171343803,
0.013002006337046623,
-0.014985914342105389,
0.02900620736181736,
-0.07137337327003479,
0.055134985595941544,
0.04603166505694389,
0.035151802003383636,
0.0130893774330616,
0.044418852776288986,
0.006360459607094526,
0.03128444403409958,
0.0022790648508816957,
-0.038777273148298264,
-0.06058545783162117,
-0.003853216301649809,
0.04504420608282089,
0.05047867074608803,
-0.02052958309650421,
-0.008356080390512943,
0.023902786895632744,
0.03902176767587662,
0.039848826825618744,
0.040127672255039215,
0.002747278194874525,
-0.014455312862992287,
0.02642717771232128,
0.022813165560364723,
-0.014570659957826138,
0.006284118164330721,
0.04122896492481232,
0.024674341082572937,
0.011323102749884129,
-0.02458617463707924,
-0.05352175980806351,
0.04365967959165573,
-0.016799209639430046,
0.03343365713953972,
-0.005552420858293772,
-0.0061770109459757805,
0.023907793685793877,
-0.03497797250747681,
0.006415643263608217,
0.010549060069024563,
-0.00987299159169197,
0.0033794590272009373,
-0.023895110934972763,
-0.010920916683971882,
0.005637403577566147,
0.031845469027757645,
-0.052168965339660645,
-0.01787755638360977,
0.029116543009877205,
-0.056474052369594574,
0.015224304050207138,
-0.020210513845086098,
-0.010338380932807922,
0.0010410224786028266,
-0.011100818403065205,
0.06347391754388809,
0.020293328911066055,
0.041748177260160446,
-0.035483602434396744,
-0.03694135323166847,
0.011719074100255966,
-0.03298621624708176,
0.006482883356511593,
-0.0005149655626155436,
-0.017685987055301666,
0.004727529361844063,
-0.009370548650622368,
-0.01380907092243433,
0.04491112008690834,
-0.012501209042966366,
0.002014678902924061,
-0.01041368581354618,
-0.02679676003754139,
-0.051154643297195435,
-0.03934406861662865,
-0.03190844506025314,
0.0480475090444088,
0.009747053496539593,
-0.0005704238428734243,
0.03250446543097496,
-0.032044969499111176,
-0.020005349069833755,
0.027774060145020485,
-0.044541776180267334,
-0.001294261310249567,
0.0011780090862885118,
-0.004863771144300699,
0.015407901257276535,
-0.021371249109506607,
0.01564125157892704,
0.004334545694291592,
-0.07629437744617462,
0.017083952203392982,
-0.052415087819099426,
-0.03323006257414818,
-0.011506271548569202,
-0.01276481430977583,
0.039664383977651596,
-0.017034590244293213,
-0.012825916521251202,
0.04271875321865082,
0.02367527224123478,
-0.05947062745690346,
-0.013905615545809269,
-0.029151324182748795,
-0.04342024773359299,
-0.03184657171368599,
0.03990825638175011,
0.08592979609966278,
0.018689259886741638,
0.034974921494722366,
0.016977675259113312,
0.004046950489282608,
0.0805588811635971,
-0.0044312733225524426,
-0.010565890930593014,
0.030539045110344887,
0.0016982863890007138,
-0.02381124347448349,
0.05503254383802414,
0.005770827643573284,
-0.044714801013469696,
0.01832662895321846,
0.024391690269112587,
-0.0088863680139184,
0.025035643950104713,
-0.07156423479318619,
0.02449440397322178,
0.008850273676216602,
0.0005051203770563006,
-0.059253327548503876,
0.02114802412688732,
0.010608824901282787,
0.01525138970464468,
-0.027589010074734688,
0.016794005408883095,
0.05137820169329643,
-0.004299765918403864,
-0.01997138187289238,
0.034992516040802,
0.018435340374708176,
-0.022480523213744164,
-0.01206230092793703,
0.0074346037581563,
-0.006435059476643801,
0.024296162649989128,
-0.04673350229859352,
-0.051604438573122025,
0.04853262007236481,
0.0020178048871457577,
0.04877669736742973,
0.02707788720726967,
-0.055634334683418274,
-0.0036474999506026506,
-0.07088912278413773,
-0.020026957616209984,
-0.020725376904010773,
0.06293714046478271,
-0.0026203582528978586,
0.11172556132078171,
0.022270403802394867,
0.0377754345536232,
0.012612039223313332,
-0.0006870129145681858,
-0.09269553422927856,
0.014033691957592964,
-0.004395273048430681,
0.0023898202925920486,
-0.031261201947927475,
-0.03196422755718231,
0.0014543479774147272,
-0.012050396762788296,
-0.010192395187914371,
0.004307692404836416,
-0.016176162287592888,
-0.06013650819659233,
-0.00475329952314496,
0.004870449658483267,
0.009283321909606457,
-0.04298504441976547,
0.04612293839454651,
0.004168705083429813,
-0.004288916010409594,
0.007356714922934771,
0.06406767666339874,
-0.01852603070437908,
0.04075847193598747,
-0.007800779305398464,
-0.000529712880961597,
0.006966809276491404,
0.012889152392745018,
0.010129958391189575,
-0.008632998913526535,
-0.007610096596181393,
-0.018674517050385475,
0.010067650116980076,
0.04509114846587181,
0.02874901331961155,
0.01916486583650112,
-0.01809868775308132,
-0.02075396478176117,
0.022356584668159485,
-0.0013100006617605686,
0.043804943561553955,
0.013234869576990604,
0.00263278023339808,
0.009915385395288467,
-0.018215902149677277,
-0.02572532184422016,
0.05703829973936081,
0.040374256670475006,
0.0368342399597168,
-0.007678521331399679,
-0.05237261950969696,
-0.012302578426897526,
-0.021282095462083817,
0.021395621821284294,
0.025559958070516586,
0.004916344303637743,
-0.01667281612753868,
0.02682281658053398,
0.012518152594566345,
0.017395885661244392,
0.011488779447972775,
-0.007234654854983091,
-0.016151798889040947,
0.03287791460752487,
-0.03374924883246422,
0.01794615015387535,
-0.007512280251830816,
0.023100856691598892,
0.05722615122795105,
0.0018234928138554096,
-0.012400195002555847,
-0.0912061408162117,
-0.011826963163912296,
0.009515998885035515,
0.024215176701545715,
-0.010667659342288971,
0.003285214537754655,
-0.07197344303131104,
-0.043845050036907196,
0.030235618352890015,
-0.051750171929597855,
0.038880567997694016,
-0.020019497722387314,
-0.01433852594345808,
-0.04831252247095108,
-0.007161981891840696,
-0.0059818183071911335,
0.0013433144195005298,
0.0009557313751429319,
0.01663537323474884,
-0.0216880701482296,
-0.019922805950045586,
-0.017987580969929695,
0.014386455528438091,
0.009500953368842602,
0.04019124060869217,
0.007885860279202461,
0.00248153880238533,
0.016381144523620605,
0.000011150944374094252,
-0.018910357728600502,
-0.04576227068901062,
0.027669256553053856,
0.014990359544754028,
0.030984139069914818,
0.04294892027974129,
-0.04447883740067482,
-0.046882353723049164,
-0.016090339049696922,
0.0056361667811870575,
0.02014004811644554,
-0.00934196449816227,
-0.02283206768333912,
0.03689529746770859,
0.046717166900634766,
-0.0268744844943285,
0.031173668801784515,
0.0592132993042469,
-0.03252672031521797,
0.006410453002899885,
-0.031072817742824554,
0.02953161485493183,
-0.013863090425729752,
-0.016430489718914032,
-0.03124838136136532,
0.003412590129300952,
-0.04392089322209358,
0.0260747279971838,
-0.021361058577895164,
-0.0036350414156913757,
-0.02993696741759777,
-0.017832349985837936,
-0.00988171435892582,
0.028655461966991425,
0.011167934164404869,
0.0012075616978108883,
0.003147302195429802,
0.052202243357896805,
0.016753172501921654,
-0.025421449914574623,
0.04968470335006714,
-0.048347074538469315,
0.00019870145479217172,
0.045802727341651917,
0.012819184921681881,
0.0013083625817671418,
-0.020795101299881935,
0.00613434286788106,
0.014713247306644917,
-0.07028869539499283,
0.034180935472249985,
-0.02838887646794319,
0.010039214044809341,
0.03582195192575455,
-0.06723830848932266,
-0.0270929466933012,
0.020406484603881836,
-0.04448152333498001,
0.05987268313765526,
-0.007929577492177486,
0.04977140203118324,
-0.016350386664271355,
0.00925472192466259,
-0.043641217052936554,
-0.07015641778707504,
0.04198845848441124,
0.03924113139510155,
-0.02495754137635231,
-0.016438061371445656,
0.03581356257200241,
-0.013450205326080322,
-0.00926516018807888,
0.017187384888529778,
0.01805921271443367,
-0.02985774539411068,
-0.012319247238337994,
0.0236344113945961,
0.0039138575084507465,
0.0789552852511406,
0.01576145552098751,
-0.02601797692477703,
0.045107435435056686,
-0.032038651406764984,
-0.0075058951042592525,
-0.021205436438322067,
0.043808065354824066,
-0.02726333774626255,
-0.037081390619277954,
0.0020048534497618675,
0.004105218220502138,
0.016982341185212135,
-0.025942757725715637,
-0.011449393816292286,
-0.021946638822555542,
0.04407791048288345,
-0.007580381818115711,
-0.03414337709546089,
0.0035375459119677544,
-0.030044347047805786,
0.027507970109581947,
0.010345272719860077,
0.01124541275203228,
-0.06552218645811081,
-0.024357862770557404,
-0.008745258674025536,
0.014796492643654346,
-0.004408485721796751,
0.01746957376599312,
0.0628165677189827,
-0.03180427476763725,
-0.024440422654151917,
0.01864822767674923,
0.0018920385045930743,
0.03556017950177193,
0.0011986251920461655,
0.015513602644205093,
0.01055779680609703,
0.03611340373754501,
-0.028563253581523895,
-0.04254136234521866,
-0.04079485684633255,
-0.007307447958737612,
0.06796111166477203,
-0.03453249856829643,
0.037388864904642105,
0.017737917602062225,
-0.02182406187057495,
-0.003904108889400959,
-0.0169417392462492,
0.0022763842716813087,
-0.0118978600949049,
-0.012590719386935234,
0.008150621317327023,
-0.041550010442733765,
0.029969755560159683,
0.012959531508386135,
0.0033899894915521145,
-0.014283712953329086,
0.022557469084858894,
0.06736042350530624,
0.023657366633415222,
0.002062485320493579,
0.006107797846198082,
-0.048338089138269424,
0.028193389996886253,
-0.029012786224484444,
0.07132155448198318,
-0.006571429315954447,
-0.006099138408899307,
0.02950001321732998,
0.021437715739011765,
-0.005535972770303488,
-0.04580441862344742,
0.047334447503089905,
0.011278034187853336,
0.025544393807649612,
0.04945317655801773,
-0.001354460371658206,
0.023093659430742264,
0.028338700532913208,
0.03021860681474209,
0.029899027198553085,
-0.002297686878591776,
0.01798177883028984,
-0.031057802960276604,
-0.0009007413755171001,
0.010721643455326557,
-0.06221948191523552,
0.0607728473842144,
-0.017707664519548416,
-0.039699800312519073,
0.0013050091220065951,
-0.01274680532515049,
0.03891341760754585,
0.004878126084804535,
0.005004816222935915,
-0.02072755992412567,
0.06751883774995804,
0.02693025954067707,
0.0007945906254462898,
-0.012619349174201488,
-0.0070387134328484535,
0.1162024438381195,
0.04844045266509056,
0.010856803506612778,
-0.07160165905952454,
-0.004893984645605087,
0.0025636693462729454,
0.01909687928855419,
-0.009995678439736366,
0.020694227889180183,
0.0019600747618824244,
0.03278031200170517,
-0.0026925618294626474,
0.03944319114089012,
0.0020784956868737936,
0.047932181507349014,
0.040041740983724594,
-0.041378237307071686,
-0.050208721309900284,
0.0029452191665768623,
-0.0066725024953484535,
0.005975807085633278,
0.032291751354932785,
-0.05120488628745079,
-0.0007489055278711021,
-0.05827535316348076,
-0.04709266871213913,
-0.02454935386776924,
-0.026120346039533615,
0.03473396599292755,
0.020876619964838028,
-0.04919179901480675,
0.004634021781384945,
0.013126392848789692,
-0.006276492960751057,
-0.044693611562252045,
0.037213727831840515,
0.021834757179021835,
-0.02422720193862915,
0.0019917876925319433,
0.02182629518210888,
0.013618672266602516,
-0.0267796590924263,
-0.007441007532179356,
0.009719940833747387,
-0.023241735994815826,
0.016528205946087837,
-0.02569759078323841,
0.043617479503154755,
-0.005500175058841705,
-0.034172844141721725,
-0.013291075825691223,
0.021802993491292,
0.0014205706538632512,
-0.07108627259731293,
-0.014336171559989452,
-0.008432057686150074,
0.030198119580745697,
-0.04528628662228584,
-0.034715622663497925,
-0.006860504858195782,
-0.013190974481403828,
-0.01625652052462101,
0.02656981348991394,
-0.013489451259374619,
-0.016611987724900246,
-0.02261492982506752,
0.016865314915776253,
0.04155019670724869,
-0.04506775364279747,
-0.01209305226802826,
0.003499741666018963,
-0.030019273981451988,
-0.05699281021952629,
-0.024625228717923164,
0.012763992883265018,
0.025815200060606003,
0.052870769053697586,
-0.00032636342803016305,
-0.01675041764974594,
-0.005249639041721821,
-0.051854632794857025,
0.03274930268526077,
-0.0024892776273190975,
-0.03546252101659775,
0.005938701331615448,
-0.010194489732384682,
0.05932876840233803,
0.03407077118754387,
-0.010164753533899784,
0.0397457517683506,
-0.012691802345216274,
-0.00217066309414804,
0.02732682041823864,
-0.02623693272471428,
-0.05902751535177231,
0.02848350629210472,
0.029245922341942787,
-0.005220805760473013,
0.014000522904098034,
0.032876625657081604,
0.01427364069968462,
0.001154557685367763,
0.01821213960647583,
0.05305713042616844,
-0.04367652162909508,
-0.03307719901204109,
-0.03178391605615616,
-0.018192477524280548,
-0.004200720693916082,
0.006525459699332714,
-0.006770572625100613,
-0.0053655351512134075,
-0.033605195581912994,
-0.027945056557655334,
0.004805808886885643,
0.022829703986644745,
0.038646895438432693,
-0.010491669178009033,
-0.00793230626732111,
-0.02081713080406189,
0.004290642216801643,
-0.02127383090555668,
-0.025553546845912933,
-0.05294901132583618,
-0.005232662428170443,
-0.01590319164097309,
-0.022918689996004105,
-0.009892942383885384,
0.04248689115047455,
-0.042322397232055664,
-0.008463123813271523,
0.029527444392442703,
0.05076160281896591,
0.01158386841416359,
0.01330898329615593,
0.01640170067548752,
-0.033162955194711685,
0.02618313953280449,
-0.014295087195932865,
-0.0616617389023304,
-0.0000787883618613705,
-0.0667768195271492,
-0.024495217949151993,
0.008793669752776623,
-0.03670770674943924,
0.003999816253781319,
0.017519241198897362,
0.025402532890439034,
0.047576796263456345,
0.031918372958898544,
0.004538793582469225,
-0.01165566872805357,
0.029402945190668106,
-0.01588156633079052,
0.01505731139332056,
-0.015521031804382801,
-0.019435184076428413,
-0.01591663248836994,
-0.012536115013062954,
0.04537881165742874,
0.013653268106281757,
0.03333800286054611,
-0.00514262868091464,
0.01886608824133873,
-0.043196067214012146,
0.0195044856518507,
0.02345805987715721,
0.007050188258290291,
0.023351619020104408,
0.0012769366148859262,
-0.01233530044555664,
0.033776357769966125,
-0.002786337397992611,
-0.00948258675634861,
-0.07289110124111176,
-0.000282104971120134,
0.026026282459497452,
-0.009545568376779556,
0.02181505784392357,
-0.03794938325881958,
0.014183777384459972,
0.01912265457212925,
-0.08203747123479843,
0.025334343314170837,
-0.0011881114915013313,
0.006837863940745592,
-0.011365738697350025,
0.0017689173109829426,
-0.028816724196076393,
0.047226984053850174,
0.019296418875455856,
0.02438206598162651,
0.03676872327923775,
0.009606930427253246,
-0.013374523259699345,
0.0008640834712423384,
0.017267730087041855,
0.033956147730350494,
0.010615005157887936,
-0.037372298538684845,
0.07351730763912201,
-0.006522933952510357,
-0.0198212843388319,
0.010843181982636452,
-0.019881319254636765,
0.019805867224931717,
0.01916658878326416,
0.018539471551775932,
0.00762710627168417,
0.007623766083270311,
-0.016125356778502464,
-0.04921390116214752,
-0.006040007341653109,
-0.0045917946845293045,
0.004104452673345804,
0.015387707389891148,
0.018526364117860794,
0.004296540282666683,
0.009476217441260815,
-0.04146822914481163,
-0.005711608566343784,
0.010661608539521694,
0.0062864553183317184,
-0.019122615456581116,
-0.024022409692406654,
-0.0031305185984820127,
0.023949317634105682,
-0.027769804000854492,
-0.01832384616136551,
-0.0524837002158165,
0.028206810355186462,
-0.00042275592568330467,
0.02749008499085903,
0.0065450952388346195,
0.014066855423152447,
-0.004215456545352936,
-0.0278768427670002,
0.025039687752723694,
0.010592618025839329,
-0.0076781162060797215,
-0.04416155070066452,
0.013627160340547562,
-0.003956454806029797,
0.011627915315330029,
0.007617694791406393,
-0.01613088697195053,
-0.007144752889871597,
0.037365857511758804,
0.002372140996158123,
-0.0075664641335606575,
0.004982732702046633,
-0.059276506304740906,
-0.03823300451040268,
-0.04830099269747734,
0.04036711901426315,
-0.012622523121535778,
-0.01570972427725792,
-0.0285323578864336,
-0.039346374571323395,
-0.023216957226395607,
0.059443335980176926,
0.06133135035634041,
0.0013769518118351698,
-0.007833554409444332,
-0.019099323078989983,
0.0036509947385638952,
0.02545274794101715,
-0.043528035283088684,
0.011919161304831505,
-0.0009723046678118408,
-0.033465106040239334,
-0.0018219823250547051,
-0.003358595073223114,
-0.0044272844679653645,
0.03232112154364586,
0.0017240303568542004,
-0.007662237621843815,
0.032228633761405945,
-0.04001106694340706,
-0.021819164976477623,
0.003250605659559369,
0.009295576252043247,
-0.03544670715928078,
0.08584953844547272,
-0.00047889319830574095,
-0.005772408563643694,
0.014034523628652096,
-0.020585376769304276,
-0.07902085036039352,
0.012792286463081837,
-0.031197484582662582,
-0.0011328458786010742,
0.022498436272144318,
0.011330824345350266,
0.07068019360303879,
-0.053164053708314896,
-0.001717852777801454,
0.0261534433811903,
-0.027009334415197372,
-0.015398548915982246,
0.08308156579732895,
-0.002278348198160529,
-0.006085406057536602,
-0.0059211072511971,
0.053340159356594086,
-0.008029852993786335,
-0.015413879416882992,
-0.0188098456710577,
0.054920174181461334,
0.038484714925289154,
-0.015089582651853561,
0.0034039674792438745,
0.022954244166612625,
-0.0029458238277584314,
-0.004260350950062275,
0.014020354487001896,
0.018015781417489052,
-0.01876046322286129,
-0.00339428149163723,
0.03848375380039215,
-0.053964048624038696,
-0.0042511033825576305,
0.05312710255384445,
0.013807459734380245,
0.11403091251850128,
-0.038163427263498306,
0.02072075381875038,
-0.0024065342731773853,
0.007832374423742294,
-0.035592544823884964,
-0.005052930675446987,
0.025841470807790756,
0.007007067557424307,
-0.00479893246665597,
0.005795441567897797,
-0.005695999599993229,
-0.006154894828796387,
0.03596644848585129,
-0.045636966824531555,
0.0015963413752615452,
-0.012517508119344711,
-0.009974491782486439,
0.004575057420879602,
0.016178252175450325,
-0.033988967537879944,
-0.030741063877940178,
0.030416348949074745,
0.027751101180911064,
-0.02640431933104992,
0.03002939559519291,
0.02008136175572872,
-0.02728830650448799,
0.04875596985220909,
-0.05041904002428055,
0.003853508969768882,
-0.0010981938103213906,
0.007555914111435413,
-0.029508283361792564,
-0.02873474732041359
] |
<p>Let a wire be shaped according to some even function $y=f(x)$, with $f'(0)=0$ and $f''(0)>0$, and let a bead of negligible size slide frictionlessly on the wire. Let the bead oscillate under the influence of gravity about $x=0$ with amplitude $A$ (i.e., between $x=-A$ and $x=+A$) and frequency $\omega(A)$. Clearly $\omega$ is nearly constant for small $A$; it differs from the frequency $\omega_o$ of simple harmonic motion by at most $O(A^2)$. By choosing $f$ to be a fourth-order polynomial, we could presumably adjust the wire's shape so as to eliminate the errors of order $A^2$ and make $\omega(A)$ constant up to $O(A^4)$. Possibly we could continue this process of approximation and make all the derivatives $d^n\omega/dA^n$ vanish up to some finite $n$, or maybe for all $n$.</p>
<p>If the derivatives can be made to vanish for all $n$, then I think $\omega$ would have to be nonanalytic at $x=0$. It seems impossible that there is any $f$ such that isochrony holds for arbitrarily large $A$. No matter how steep you make the sides, the bead can't do any better than accelerating downward with acceleration $g$. Therefore I think the best $f$ you can find is probably one that blows up to infinity at $|x|$ equal to some $x_{max}$. On dimensional grounds, we would have to have $x_{max}=cL$, where $c$ is a unitless constant and $L=g/\omega_0^2$.</p>
<p>So my multipart question is: (1) Is there a function $f$ that gives $d^n\omega/dA^n=0$ for all $n$? If so, ... (2) How is $f$ characterized, and what is $c$? (3) Is $\omega(A)$ analytic at $x=0$, and if so, what is its radius of convergence to its Taylor series in units of $L$?</p> | 4,605 | [
-0.014699785970151424,
0.014157013967633247,
0.023793671280145645,
-0.021518951281905174,
0.028498493134975433,
-0.019491950049996376,
-0.055542103946208954,
-0.034607838839292526,
0.023013798519968987,
-0.0328790582716465,
0.03751105070114136,
-0.006804896052926779,
0.0342688225209713,
0.022818103432655334,
0.04982352256774902,
-0.010047899559140205,
-0.019737549126148224,
-0.0018377072410658002,
0.013016100972890854,
-0.048198942095041275,
0.019681701436638832,
0.029518773779273033,
-0.02885797619819641,
0.0005189977819100022,
-0.008390448987483978,
-0.026463642716407776,
0.004179871175438166,
-0.02601463347673416,
-0.02217646688222885,
0.07889220863580704,
-0.03946608677506447,
0.004965460859239101,
-0.0050253914669156075,
0.012930731289088726,
0.047436658293008804,
0.049444347620010376,
-0.03523726388812065,
-0.002180848503485322,
0.020022111013531685,
0.037663090974092484,
-0.024027608335018158,
0.009523128159344196,
0.01767088659107685,
0.05628997087478638,
0.0005038343369960785,
0.023583687841892242,
0.029377058148384094,
-0.016991455107927322,
0.08400410413742065,
-0.052148398011922836,
0.04428352415561676,
-0.004771932493895292,
0.018857253715395927,
0.022330541163682938,
-0.006849183235317469,
-0.040924426168203354,
0.05319754034280777,
0.048867907375097275,
-0.0032499940134584904,
-0.058668870478868484,
-0.019454969093203545,
0.0034461813047528267,
-0.00176828948315233,
-0.013789299875497818,
0.009742885828018188,
0.01235116459429264,
0.00011059278040193021,
-0.026041503995656967,
0.014015239663422108,
-0.012477895244956017,
-0.00789135042577982,
-0.010298420675098896,
0.03712746873497963,
-0.022372206673026085,
-0.011858606711030006,
0.012018357403576374,
-0.014373311772942543,
-0.01075971033424139,
0.01866801641881466,
0.004267081618309021,
-0.001833628281019628,
-0.0030585366766899824,
0.022342296317219734,
0.024729302152991295,
-0.003092539729550481,
-0.013495663180947304,
0.03940336033701897,
-0.02224147319793701,
0.03188459947705269,
0.05484383553266525,
0.018048694357275963,
-0.012093720957636833,
0.03746824711561203,
-0.026843063533306122,
0.0033315359614789486,
-0.0012132324045524001,
0.04675421863794327,
-0.003319518407806754,
-0.007157439831644297,
-0.0648515373468399,
-0.021331632509827614,
-0.03547460213303566,
-0.01570132188498974,
0.08508230745792389,
0.03555480018258095,
0.012271593324840069,
0.023369625210762024,
0.016585808247327805,
-0.025464899837970734,
-0.009699717164039612,
-0.03135298565030098,
-0.011785460636019707,
0.01575635001063347,
0.008828070014715195,
0.0031853793188929558,
0.03000555746257305,
0.011636788956820965,
-0.019843552261590958,
-0.0028585796244442463,
0.04439419507980347,
0.01754133030772209,
-0.024393543601036072,
0.036052413284778595,
-0.04395310580730438,
-0.05724212899804115,
0.0031211550813168287,
0.0396367684006691,
0.013728063553571701,
-0.03479306772351265,
-0.0005671812104992568,
0.03404993191361427,
-0.005337165202945471,
0.012582172639667988,
0.01954096369445324,
0.023521218448877335,
-0.017554432153701782,
-0.09911850094795227,
-0.04188268631696701,
0.04395953193306923,
0.007275893818587065,
-0.005823620595037937,
-0.07474876195192337,
-0.04082699120044708,
0.02594599686563015,
0.06353597342967987,
0.005994232837110758,
-0.0014015760971233249,
0.006765344645828009,
0.06079144403338432,
0.01578013226389885,
0.012749433517456055,
0.009544630534946918,
0.0008475069189444184,
-0.058566540479660034,
-0.017302649095654488,
0.0073788342997431755,
0.023189518600702286,
0.014714599587023258,
0.009264000691473484,
-0.03140014410018921,
0.04120539501309395,
-0.011992343701422215,
0.001331531791947782,
-0.016845079138875008,
-0.00610966794192791,
-0.016700075939297676,
0.06486842036247253,
-0.007806240580976009,
-0.01251691859215498,
0.017565961927175522,
-0.01156538538634777,
0.009133283980190754,
-0.019862905144691467,
0.005958501249551773,
0.03532005473971367,
-0.06904545426368713,
-0.021699434146285057,
-0.03640441223978996,
-0.004190211184322834,
-0.016570331528782845,
-0.011272024363279343,
-0.006159840617328882,
0.0033044631127268076,
-0.012134422548115253,
-0.036905962973833084,
0.02761847898364067,
0.0139662716537714,
0.03632261976599693,
0.02121064066886902,
-0.04103397950530052,
-0.008877779357135296,
-0.03127027675509453,
0.04727480933070183,
0.01791747659444809,
-0.033484406769275665,
0.040261149406433105,
-0.016239026561379433,
-0.053326673805713654,
-0.006989152170717716,
-0.017474496737122536,
0.020795002579689026,
0.055452823638916016,
0.036692064255476,
-0.03078637458384037,
-0.004736389499157667,
0.06583287566900253,
0.024615123867988586,
0.022527633234858513,
0.03564302623271942,
-0.00802366342395544,
-0.00975298322737217,
-0.0072816708125174046,
-0.033421244472265244,
0.035496242344379425,
-0.001491702743805945,
0.03021926060318947,
0.04048226773738861,
-0.05731847509741783,
0.019486602395772934,
0.023105867207050323,
-0.05248209834098816,
0.07663726806640625,
0.05191623792052269,
-0.022845298051834106,
-0.0069519151002168655,
0.05767801031470299,
0.0038962913677096367,
0.010318904183804989,
-0.0025756920222193003,
-0.027828402817249298,
-0.06390094757080078,
-0.008232281543314457,
0.0037197908386588097,
0.09778085350990295,
-0.018338628113269806,
0.0041504185646772385,
0.048766862601041794,
0.031104525551199913,
0.01937790773808956,
-0.02172219008207321,
-0.0075221494771540165,
-0.027212753891944885,
0.03215467929840088,
-0.0002965073217637837,
-0.00005141263682162389,
0.021911442279815674,
0.01572444662451744,
0.028659150004386902,
0.026519786566495895,
-0.018429910764098167,
0.001315270084887743,
0.004317911341786385,
0.01613272726535797,
0.002760838018730283,
-0.0033015580847859383,
0.00929449126124382,
0.03694618120789528,
-0.02111615426838398,
0.03146536648273468,
0.030540354549884796,
-0.02118281088769436,
-0.006769390311092138,
-0.0011134155793115497,
-0.0029392214491963387,
0.04054741933941841,
-0.010898211970925331,
-0.017957262694835663,
-0.04850677028298378,
0.039576008915901184,
-0.02620210126042366,
-0.018463661894202232,
-0.05094590038061142,
0.0015366164734587073,
-0.003672676859423518,
0.002039267448708415,
0.025220660492777824,
0.02077462337911129,
0.021812710911035538,
-0.035614561289548874,
-0.005616395268589258,
0.04179765284061432,
-0.0006424929015338421,
0.004894125275313854,
0.04751404747366905,
-0.02672993391752243,
-0.0002971094800159335,
-0.04341117665171623,
-0.03922240808606148,
0.035743702203035355,
0.018057923763990402,
0.031409598886966705,
0.05381157621741295,
0.012355032376945019,
-0.04620462656021118,
-0.016358600929379463,
-0.023021025583148003,
-0.010210714302957058,
-0.07296625524759293,
-0.009107355959713459,
0.010420934297144413,
0.017701735720038414,
-0.017081772908568382,
-0.012596985325217247,
-0.049648988991975784,
-0.028976738452911377,
-0.03904343023896217,
0.006822417490184307,
0.012155639939010143,
-0.006828456185758114,
0.016432246193289757,
-0.015568430535495281,
0.013575479388237,
-0.015532100573182106,
-0.05369667336344719,
-0.059627775102853775,
0.00015274850011337548,
-0.021413704380393028,
0.06796373426914215,
0.022232849150896072,
-0.012243102304637432,
0.060586635023355484,
0.05837210640311241,
-0.032840877771377563,
-0.0291583389043808,
-0.008919932879507542,
-0.010252803564071655,
-0.036841101944446564,
0.015652960166335106,
0.022544322535395622,
-0.01470525935292244,
-0.01563972420990467,
0.012059537693858147,
-0.006649531424045563,
0.020746465772390366,
0.0061048478819429874,
0.022799599915742874,
0.038522087037563324,
0.038558896631002426,
0.04145536944270134,
0.038230475038290024,
-0.004509700462222099,
0.003672800725325942,
0.026058020070195198,
0.0034668338485062122,
-0.012014644220471382,
-0.003830845234915614,
-0.06807508319616318,
0.02943294681608677,
0.00935231801122427,
-0.016706572845578194,
0.0040116095915436745,
0.01344440970569849,
0.0008099814876914024,
-0.042038749903440475,
-0.035577815026044846,
0.012706671841442585,
0.044399652630090714,
0.02234441228210926,
0.03448175638914108,
0.021164150908589363,
0.06268790364265442,
-0.008572118356823921,
0.008058738894760609,
0.007610511966049671,
-0.015930723398923874,
0.015103070996701717,
-0.04631277546286583,
-0.00234928447753191,
0.004639497958123684,
0.0317700020968914,
0.007747679483145475,
0.039619483053684235,
-0.035080742090940475,
0.016261179000139236,
-0.0674859806895256,
-0.025016743689775467,
-0.04329424351453781,
0.03665827587246895,
0.021024160087108612,
0.04158394783735275,
0.01387852430343628,
0.03918728232383728,
-0.017310695722699165,
0.01747194305062294,
-0.12172207981348038,
0.03349390998482704,
-0.06612234562635422,
-0.016977231949567795,
0.0013030832633376122,
0.025821177288889885,
0.016694173216819763,
-0.028545189648866653,
-0.015238592401146889,
-0.003874111222103238,
0.01813228242099285,
-0.073356494307518,
-0.004053868819028139,
-0.02069041319191456,
-0.04863834008574486,
-0.03292020037770271,
0.03864114731550217,
0.061538539826869965,
-0.04007547348737717,
0.04812074452638626,
0.024091850966215134,
-0.022599488496780396,
-0.0035556277725845575,
-0.003908524289727211,
-0.006307330448180437,
0.0107510294765234,
0.0019298811675980687,
-0.030238280072808266,
0.031691499054431915,
0.0009791343472898006,
-0.0032357058953493834,
0.021740231662988663,
0.04682859778404236,
0.014365922659635544,
-0.018521271646022797,
-0.02006007917225361,
-0.03218146413564682,
-0.023937230929732323,
0.027504922822117805,
0.06342200934886932,
0.02081701159477234,
-0.02178906835615635,
0.03760669380426407,
-0.012048330157995224,
0.03221997991204262,
0.021704092621803284,
0.0046594697050750256,
0.00867883488535881,
-0.01852969452738762,
-0.017508285120129585,
-0.03772890940308571,
-0.027875613421201706,
0.01853696070611477,
-0.03880658373236656,
-0.00694702984765172,
0.00554104708135128,
0.01650376059114933,
0.04085269942879677,
0.03521208092570305,
0.014731023460626602,
0.005233356263488531,
0.004972449038177729,
0.0431031696498394,
-0.047120895236730576,
0.004366431385278702,
-0.04297882691025734,
0.02091887779533863,
0.0635685846209526,
0.00888277031481266,
-0.009791191667318344,
-0.10005868971347809,
-0.05584758520126343,
-0.004300899337977171,
0.08268243074417114,
0.022975513711571693,
-0.002986213658004999,
-0.040773238986730576,
-0.03616056963801384,
0.028391342610120773,
0.018696578219532967,
0.05638928338885307,
-0.0028293842915445566,
0.023444226011633873,
-0.02312258817255497,
-0.04298204556107521,
-0.024004993960261345,
-0.03507865592837334,
0.02500382624566555,
-0.020801881328225136,
-0.030953792855143547,
0.008130067028105259,
0.015855662524700165,
0.021249355748295784,
0.023029712960124016,
0.038286760449409485,
-0.0016995260957628489,
-0.0340169295668602,
-0.0035387007519602776,
-0.010100108571350574,
-0.0206557996571064,
-0.08328043669462204,
0.021304236724972725,
0.0028730230405926704,
-0.013769821263849735,
0.011170720681548119,
0.00488866725936532,
-0.034197863191366196,
0.02822434902191162,
-0.01357740256935358,
-0.0005274030263535678,
0.04971574246883392,
-0.019161485135555267,
0.0591803677380085,
0.020642278715968132,
0.03012082353234291,
0.02098054252564907,
0.07216627895832062,
-0.017833389341831207,
-0.023888075724244118,
-0.001728441333398223,
0.036637019366025925,
-0.04305446892976761,
0.03098645992577076,
-0.0286356583237648,
0.005981891881674528,
-0.051940493285655975,
0.01581577956676483,
-0.01253308542072773,
0.01219131425023079,
0.0025519102346152067,
-0.03182123601436615,
0.023809438571333885,
0.05929407849907875,
0.02041485160589218,
0.020125379785895348,
-0.0008618154097348452,
0.031593382358551025,
-0.003926299046725035,
-0.0015082693425938487,
0.000687597319483757,
0.011676850728690624,
0.020149994641542435,
0.06522161513566971,
-0.0525263212621212,
0.002436052542179823,
-0.0237616878002882,
-0.016946842893958092,
-0.016437627375125885,
-0.06346560269594193,
0.08295603096485138,
-0.021018758416175842,
-0.021112775430083275,
0.028006859123706818,
-0.035006243735551834,
-0.009647675789892673,
-0.006741571240127087,
0.000596434052567929,
0.009182760491967201,
-0.06802251189947128,
-0.0262160561978817,
-0.022125354036688805,
0.011249956674873829,
-0.04394189268350601,
-0.032088860869407654,
0.012324745766818523,
-0.009901505894958973,
-0.02905675768852234,
-0.0068987831473350525,
0.03643272444605827,
-0.030204104259610176,
-0.03785456717014313,
0.01771428808569908,
0.02311406098306179,
-0.02637040801346302,
0.05233488976955414,
0.024102527648210526,
0.02222326025366783,
0.0314776636660099,
0.00021104348707012832,
-0.00827590748667717,
0.0011629847576841712,
-0.02382056601345539,
0.004719471093267202,
-0.042899761348962784,
0.026553481817245483,
-0.03128112480044365,
0.004741151817142963,
0.02490285411477089,
-0.00048804227844811976,
0.027744971215724945,
-0.04041413590312004,
-0.02771070785820484,
0.04315316677093506,
0.03583649545907974,
0.02629883401095867,
0.024894392117857933,
-0.01844366081058979,
-0.027781125158071518,
0.026717469096183777,
0.015812410041689873,
-0.005562923848628998,
0.00010143381223315373,
-0.06216461956501007,
0.005843079183250666,
-0.005278250202536583,
0.016771048307418823,
-0.001017724396660924,
0.0596439354121685,
-0.04335855692625046,
-0.05390671268105507,
0.015773434191942215,
0.004244545008987188,
0.051264688372612,
-0.019704381003975868,
0.009163259528577328,
-0.0032513549085706472,
-0.016000760719180107,
-0.06362779438495636,
-0.07177066802978516,
-0.04828525707125664,
0.018766086548566818,
0.09298377484083176,
0.04591285437345505,
0.029975151643157005,
0.0115093057975173,
-0.04087912291288376,
-0.05607613921165466,
-0.02044510282576084,
-0.045896563678979874,
0.02879897505044937,
-0.00699222506955266,
0.03832357004284859,
-0.02462279237806797,
-0.05213634669780731,
0.005526701454073191,
-0.003863431978970766,
-0.04908138886094093,
0.044278886169195175,
0.01705148257315159,
0.019354285672307014,
0.03189190849661827,
-0.027034834027290344,
-0.021528011187911034,
0.029665103182196617,
-0.013432214967906475,
0.04838893935084343,
0.008138502947986126,
-0.00758267380297184,
0.004748185630887747,
0.028242498636245728,
0.039522748440504074,
-0.03373302146792412,
0.000038692607631674036,
-0.070237897336483,
0.018828872591257095,
0.034191861748695374,
0.00034877241705544293,
0.01980765350162983,
-0.0200895257294178,
0.019922643899917603,
-0.005769822280853987,
0.04732591286301613,
-0.027891555801033974,
-0.017949303612113,
0.0313664972782135,
-0.017778636887669563,
-0.05922451987862587,
0.07068467140197754,
0.024405088275671005,
-0.02797582373023033,
0.0370015986263752,
-0.03524119034409523,
0.015797020867466927,
0.05389409512281418,
0.015475952066481113,
-0.010500915348529816,
0.05081387981772423,
-0.04006768390536308,
0.0215990599244833,
-0.030457479879260063,
0.0014024425763636827,
0.15994784235954285,
0.06374846398830414,
-0.0022884204518049955,
-0.034241337329149246,
-0.018006043508648872,
-0.024981532245874405,
0.008914303034543991,
-0.04159359261393547,
-0.01183087844401598,
-0.00958331674337387,
-0.03141968324780464,
-0.01128315832465887,
0.027613496407866478,
-0.05884654074907303,
-0.009243271313607693,
0.02642953209578991,
-0.03314230591058731,
0.0162146408110857,
-0.007229342125356197,
-0.02215869538486004,
0.005873712711036205,
0.02320016920566559,
-0.016151942312717438,
0.003599658142775297,
-0.018606135621666908,
-0.031198585405945778,
-0.02458243817090988,
-0.013846742920577526,
0.025849513709545135,
-0.025497812777757645,
-0.07492031902074814,
-0.007297222502529621,
0.020369572564959526,
-0.06023171544075012,
-0.03486238792538643,
0.03878393396735191,
-0.006883692927658558,
0.007993504405021667,
0.011536630801856518,
0.018949512392282486,
0.014333733357489109,
-0.011646402068436146,
0.02345298044383526,
0.006975618656724691,
-0.015912825241684914,
-0.03043239377439022,
-0.05409771576523781,
0.01763654127717018,
-0.027696719393134117,
-0.011022727936506271,
0.01754886656999588,
-0.021503891795873642,
0.007744211703538895,
-0.03337087109684944,
-0.008689186535775661,
-0.013600648380815983,
0.0487247109413147,
0.005025324411690235,
-0.03379391133785248,
0.032454006373882294,
0.028987562283873558,
0.03902055695652962,
-0.017901981249451637,
-0.02474818006157875,
-0.017411930486559868,
-0.0150232445448637,
0.007695009466260672,
0.0785917192697525,
-0.001587218837812543,
-0.01415372546762228,
-0.011871511116623878,
-0.011763001792132854,
-0.018403688445687294,
0.004473505076020956,
-0.010950198397040367,
0.002193696331232786,
0.041448887437582016,
0.022189898416399956,
-0.029693955555558205,
-0.0041406420059502125,
-0.0283498652279377,
0.023154255002737045,
0.000450872874353081,
0.00445146020501852,
-0.016298329457640648,
-0.024332916364073753,
0.022227022796869278,
0.01195392943918705,
-0.015568377450108528,
0.0059884050861001015,
0.00865030474960804,
0.04615997150540352,
0.024195581674575806,
0.002765484619885683,
-0.03890535235404968,
-0.02063516154885292,
0.005031414330005646,
0.034127380698919296,
0.018996762111783028,
0.023681161925196648,
0.01966606266796589,
-0.0015981897013261914,
-0.024829791858792305,
0.03601064905524254,
-0.0448712483048439,
-0.012893501669168472,
0.0414334237575531,
-0.02040570229291916,
-0.0012834904482588172,
0.05757853016257286,
0.0077709355391561985,
-0.07076860964298248,
-0.055237241089344025,
-0.039074379950761795,
0.019180066883563995,
-0.01552664116024971,
0.04077186435461044,
-0.015869582071900368,
0.03747168183326721,
-0.026314333081245422,
0.008947832509875298,
-0.039796434342861176,
0.007002278231084347,
-0.003801797516644001,
0.019491299986839294,
-0.005483980756253004,
0.027867913246154785,
0.004822193179279566,
0.03546587750315666,
-0.01925940066576004,
-0.03850053995847702,
-0.0035464128013700247,
0.04014725238084793,
0.014451462775468826,
-0.010002344846725464,
0.00023527683515567333,
0.024572985246777534,
0.035874418914318085,
0.01081188302487135,
-0.0383242592215538,
-0.0032992663327604532,
-0.06080859154462814,
-0.05877288058400154,
0.050623293966054916,
0.015177762135863304,
-0.021551139652729034,
0.034484609961509705,
-0.022238094359636307,
-0.013820130378007889,
0.012959273532032967,
-0.029744507744908333,
-0.007597458083182573,
-0.005948066245764494,
-0.027711529284715652,
-0.041349176317453384,
0.0025211255997419357,
-0.024066321551799774,
0.006959198508411646,
0.024937598034739494,
-0.020816022530198097,
0.004218758083879948,
0.01179041899740696,
-0.008854527957737446,
0.052337877452373505,
-0.03317392244935036,
-0.009745541028678417,
0.02541155181825161,
0.044555068016052246,
0.01188524067401886,
0.06532368808984756,
-0.028063103556632996,
0.014888742938637733,
-0.007777273189276457,
-0.029347358271479607,
-0.09990598261356354,
0.01801222190260887,
-0.004646350163966417,
0.014286473393440247,
0.06194126233458519,
-0.03289635851979256,
0.008114004507660866,
-0.0008235974819399416,
-0.05683080479502678,
0.024776101112365723,
-0.05784580484032631,
-0.0035701808519661427,
-0.03209587186574936,
-0.026489028707146645,
-0.051834940910339355,
0.012226958759129047,
0.04943665489554405,
0.05246070772409439,
-0.0013343130704015493,
0.016254998743534088,
-0.04111550748348236,
-0.03132116049528122,
0.019766297191381454,
0.044282253831624985,
-0.013521850109100342,
-0.0042022280395030975,
0.02879425510764122,
-0.025324979797005653,
-0.02569884993135929,
0.04834867641329765,
-0.02109348773956299,
-0.007983291521668434,
-0.06698381155729294,
0.01589386537671089,
0.01661781594157219,
0.04134353995323181,
0.00518193282186985,
-0.007528299931436777,
-0.013899535872042179,
0.026058048009872437,
-0.0058502438478171825,
0.004059191327542067,
-0.040226615965366364,
0.01166197657585144,
0.020969117060303688,
0.0031192838214337826,
-0.027700290083885193,
0.03903743252158165,
-0.0102040134370327,
0.00029863743111491203,
0.01383757870644331,
0.009636079892516136,
0.003388711018487811,
-0.003185494802892208,
-0.049572788178920746,
0.016979217529296875,
-0.02521304041147232,
0.010004664771258831,
0.020839504897594452,
-0.021661849692463875,
0.04112427681684494,
-0.030214885249733925,
-0.014789030887186527,
-0.011698202230036259,
0.0032911794260144234,
-0.016783060505986214,
-0.02461041882634163,
-0.022673526778817177,
-0.03465546667575836,
0.008204925805330276,
0.029022928327322006,
-0.005300735589116812,
-0.00596840213984251,
0.012373420409858227,
-0.020700162276625633,
0.025983646512031555,
-0.02592538110911846,
-0.014133070595562458,
-0.018345583230257034,
-0.0876367911696434,
0.03270091861486435,
-0.02858266979455948,
0.0005446794675663114,
-0.00939711183309555,
-0.052404388785362244,
0.04048018530011177,
0.0513894185423851,
0.0653170645236969,
-0.014904748648405075,
-0.023869866505265236,
0.0254285279661417,
0.022940564900636673,
-0.00005322302968124859,
0.02788698300719261,
0.02324717491865158,
-0.011967104859650135,
0.04938759282231331,
0.015217549167573452,
0.01739032007753849,
-0.014287092722952366,
-0.005876163020730019,
0.01252814382314682,
-0.004293635953217745,
-0.0013350723311305046,
-0.01345525961369276,
-0.03702247142791748,
0.04025304690003395,
0.016004888340830803,
-0.050953056663274765,
0.04934021830558777,
0.011426073499023914,
-0.00022687617456540465,
-0.02253713086247444,
-0.021700453013181686,
-0.08791224658489227,
0.021831786260008812,
0.005723097361624241,
-0.018165625631809235,
-0.059865064918994904,
0.05275106057524681,
0.027583502233028412,
-0.028304437175393105,
0.020849592983722687,
0.05555408447980881,
-0.0014750499976798892,
-0.0323566310107708,
0.036878056824207306,
0.004624411463737488,
0.02512963116168976,
0.01451488770544529,
0.009669679217040539,
0.04712573066353798,
-0.0043879360891878605,
0.014258322305977345,
-0.001312407199293375,
0.015033788047730923,
-0.009623746387660503,
-0.005760539323091507,
0.028811944648623466,
-0.044029418379068375,
0.017025552690029144,
0.004045920912176371,
-0.001591406879015267,
-0.005983332637697458,
-0.029251579195261,
0.004328962415456772,
-0.006488837767392397,
-0.035421222448349,
0.06091631203889847,
0.0029483300168067217,
0.06949429959058762,
0.02305867150425911,
-0.0029416317120194435,
-0.0025071955751627684,
-0.015556694939732552,
0.0033994747791439295,
0.01005704328417778,
-0.029924167320132256,
0.021152058616280556,
-0.04779811203479767,
-0.008720094338059425,
0.006495840847492218,
-0.010405692271888256,
0.008134889416396618,
-0.004416323266923428,
-0.005077205132693052,
0.016678359359502792,
0.021015502512454987,
0.00026893423637375236,
-0.03501385822892189,
-0.03452882543206215,
-0.01813177391886711,
0.03858640789985657,
0.028593122959136963,
0.01731809228658676,
0.004194356966763735,
0.028894968330860138,
-0.02360343188047409,
0.037723299115896225,
-0.035051677376031876,
-0.00822367426007986,
0.009124587289988995,
0.013384174555540085,
0.015426497906446457,
0.01776002161204815
] |
<p>When a ray of ordinary light is passed on the surface of the water the reflected light will be completely polarized( vibrations in one plane).</p>
<p>My question is what will be <strong>plane of vibration in the partially polarized light</strong> that undergoes refraction? <strong>How many planes of vibration</strong> will be there? Deep explanation focusing on the <strong>planes of vibration</strong> of the partially polarized light would be appreciated.</p> | 4,606 | [
-0.001433077035471797,
-0.012191703543066978,
-0.004818971734493971,
0.014596440829336643,
0.03688845783472061,
0.03668709099292755,
-0.014330958016216755,
-0.04485022649168968,
-0.017934473231434822,
-0.03842313215136528,
0.033610571175813675,
0.07176271826028824,
0.04276324436068535,
0.06258499622344971,
0.012201288715004921,
0.013296511955559254,
-0.012337923049926758,
0.0018021524883806705,
-0.0024302497040480375,
-0.0372532419860363,
-0.021008888259530067,
-0.003905324963852763,
-0.010066972114145756,
0.015651749446988106,
-0.03263140842318535,
0.014795358292758465,
0.011979113332927227,
0.004299351945519447,
0.0518324039876461,
-0.0020563313737511635,
0.012682124972343445,
-0.028042905032634735,
-0.0014724942157045007,
0.0318710096180439,
0.02304757572710514,
-0.014992872253060341,
-0.02758023701608181,
-0.00009709688310977072,
-0.02508268691599369,
0.011955778114497662,
0.006891478318721056,
-0.005174529273062944,
-0.02878854051232338,
0.029003111645579338,
-0.018303805962204933,
0.0023263548500835896,
0.05691269040107727,
-0.03188737481832504,
0.04155547171831131,
-0.06429066509008408,
0.06139623373746872,
-0.0023278233129531145,
0.03554752096533775,
0.00739052752032876,
0.00446775509044528,
-0.004809029400348663,
0.07933752983808517,
0.06615953147411346,
-0.011974656954407692,
-0.03889772668480873,
0.00962635688483715,
-0.018245939165353775,
-0.019294660538434982,
-0.0020509129390120506,
-0.0508345291018486,
-0.01050823274999857,
-0.012959838844835758,
-0.038533810526132584,
0.02816358581185341,
0.015882069244980812,
-0.01939443126320839,
-0.004452776163816452,
0.03873010352253914,
-0.02230892702937126,
-0.02530677802860737,
-0.016547057777643204,
0.022859035059809685,
0.0703858956694603,
-0.013676630333065987,
0.010663548484444618,
0.011521972715854645,
0.026950553059577942,
-0.004193153232336044,
0.04892211779952049,
-0.022054748609662056,
-0.03717361390590668,
0.08984329551458359,
0.02596934139728546,
0.028943603858351707,
0.0009492114186286926,
0.015091333538293839,
-0.010610773228108883,
-0.011595726944506168,
0.031666144728660583,
-0.042511358857154846,
-0.035265468060970306,
-0.01105288602411747,
0.047795139253139496,
0.029222100973129272,
-0.04157913848757744,
0.008885460905730724,
-0.009210513904690742,
0.0229879692196846,
0.07004129886627197,
-0.006972347851842642,
0.0031250205356627703,
-0.054109711199998856,
0.00519895413890481,
-0.018034720793366432,
-0.013333001174032688,
0.005740127060562372,
0.05036056041717529,
-0.028559476137161255,
-0.024220706894993782,
-0.034912027418613434,
-0.03392917290329933,
0.019514383748173714,
-0.005754602141678333,
0.07059944421052933,
0.10165327787399292,
0.03725041449069977,
-0.050190236419439316,
-0.008168138563632965,
-0.03956269845366478,
-0.08884720504283905,
0.04833831638097763,
0.031284645199775696,
-0.0056917984038591385,
-0.03716430440545082,
0.027379818260669708,
-0.0019896458834409714,
0.008423957973718643,
0.01800963655114174,
-0.00457947188988328,
0.006934621836990118,
-0.03204197436571121,
-0.09198569506406784,
-0.050759438425302505,
0.05428118258714676,
0.0014305446529760957,
-0.022270191460847855,
-0.04549315944314003,
0.04069884493947029,
0.06382203102111816,
0.08006175607442856,
-0.029827911406755447,
0.047014009207487106,
0.00934508815407753,
0.026640450581908226,
0.005548613611608744,
-0.025489136576652527,
0.00998623389750719,
-0.005269160959869623,
-0.036859285086393356,
-0.004112196620553732,
-0.04407262057065964,
0.0000350791378878057,
0.04459550231695175,
-0.008440566249191761,
-0.023864593356847763,
0.025491999462246895,
-0.04588264226913452,
0.0032410866115242243,
0.026257360354065895,
-0.009439573623239994,
-0.06389063596725464,
0.07659315317869186,
0.010108200833201408,
0.029837118461728096,
0.023949535563588142,
-0.022144397720694542,
0.033213481307029724,
-0.04346218705177307,
0.03466208279132843,
0.015894107520580292,
0.001698396517895162,
-0.0008070767507888377,
-0.00424575200304389,
0.0046998909674584866,
0.0017790538258850574,
-0.019864708185195923,
-0.014701614156365395,
0.009601828642189503,
0.028287069872021675,
-0.005582007113844156,
0.033940039575099945,
-0.00043009163346141577,
-0.01284089870750904,
-0.013776194304227829,
-0.040799930691719055,
-0.008237159810960293,
0.0009585060179233551,
0.02852723002433777,
-0.019237060099840164,
-0.02103497087955475,
-0.010631242766976357,
0.018671197816729546,
0.009173164144158363,
-0.02476336993277073,
-0.005772568751126528,
-0.033778056502342224,
0.04602263867855072,
-0.0009132830891758204,
-0.008905719965696335,
0.05621619522571564,
0.04032399132847786,
0.03263070434331894,
0.012647666968405247,
-0.00572583544999361,
-0.026225022971630096,
0.029086831957101822,
-0.02489909902215004,
-0.015193340368568897,
0.017551658675074577,
-0.03040202334523201,
-0.017505258321762085,
-0.027782587334513664,
0.03864721953868866,
-0.0008125629974529147,
0.012563989497721195,
-0.04122241213917732,
0.06844444572925568,
0.05999772623181343,
0.010894288308918476,
-0.0038278193678706884,
0.031807444989681244,
-0.029831120744347572,
0.006311302538961172,
-0.013732499442994595,
-0.016880592331290245,
-0.03568604215979576,
0.029944563284516335,
0.01500704512000084,
0.017367465421557426,
-0.036138247698545456,
0.026584353297948837,
0.01797070913016796,
0.039843570441007614,
0.04144788160920143,
0.003621625015512109,
-0.02988504245877266,
-0.044195257127285004,
0.02828829735517502,
0.020425204187631607,
0.01047544926404953,
0.008543203584849834,
0.025168200954794884,
0.027273371815681458,
-0.007061701733618975,
-0.014393031597137451,
-0.001216112868860364,
0.03612792119383812,
-0.027923449873924255,
0.05040481686592102,
-0.022557692602276802,
-0.031459227204322815,
0.04126001521945,
-0.04213385656476021,
0.016458189114928246,
0.019621513783931732,
0.005296151619404554,
-0.024146176874637604,
-0.044805530458688736,
-0.000013875725016987417,
0.004117992240935564,
-0.00035481833037920296,
-0.026273347437381744,
-0.030052917078137398,
0.038378406316041946,
-0.04486337676644325,
0.014418390579521656,
-0.028105566278100014,
-0.013492499478161335,
0.009102476760745049,
-0.003420479828491807,
0.07202677428722382,
0.027291733771562576,
0.05440657213330269,
-0.02397037111222744,
-0.038951076567173004,
0.016698691993951797,
-0.019858522340655327,
-0.003289137501269579,
-0.028877370059490204,
-0.05444016307592392,
-0.030792605131864548,
-0.04241941496729851,
-0.0255887471139431,
0.0063556162640452385,
-0.004964475054293871,
-0.03029700368642807,
0.014472480863332748,
0.0011122255818918347,
-0.059976205229759216,
-0.032495830208063126,
-0.044348444789648056,
0.02025531604886055,
-0.06916146725416183,
-0.007685068994760513,
-0.012041487731039524,
0.0027227415703237057,
0.00116289546713233,
-0.0031529986299574375,
-0.020034313201904297,
-0.03606785461306572,
0.0024355060886591673,
-0.029501039534807205,
0.02688436210155487,
-0.041464682668447495,
0.01352138351649046,
0.04568896442651749,
0.0028155301697552204,
0.03079986944794655,
-0.045544661581516266,
-0.05986034497618675,
0.05837088078260422,
0.017766259610652924,
0.06141341105103493,
-0.02043350413441658,
-0.014322451315820217,
0.058689262717962265,
-0.0015228897100314498,
-0.05719161033630371,
-0.022223686799407005,
0.007282234262675047,
-0.003086394164711237,
-0.019405215978622437,
-0.008798344992101192,
0.03458698093891144,
-0.02599431946873665,
0.04192100837826729,
0.019262822344899178,
0.01020304299890995,
0.04188118129968643,
0.02860000543296337,
-0.01554996520280838,
-0.006659374106675386,
0.009562043473124504,
0.03771994635462761,
0.022986454889178276,
0.04412103071808815,
-0.037525516003370285,
-0.009937264025211334,
-0.02038796804845333,
0.024472389370203018,
0.028880298137664795,
-0.017473967745900154,
0.05587400496006012,
0.018792789429426193,
0.025737140327692032,
-0.015751155093312263,
0.044428665190935135,
0.008778774179518223,
0.0010173894697800279,
0.0037409886717796326,
0.008738316595554352,
0.04851458594202995,
-0.013454632833600044,
-0.002800201065838337,
0.01732257381081581,
0.03311983868479729,
-0.018832776695489883,
-0.016535896807909012,
-0.027407102286815643,
-0.0013766235206276178,
0.022211525589227676,
-0.015341444872319698,
-0.017678938806056976,
0.03999119997024536,
0.0029665359761565924,
0.044511474668979645,
-0.011167491786181927,
-0.02856864593923092,
0.04054073989391327,
-0.01551222987473011,
0.005873188842087984,
0.005770581774413586,
0.05649259686470032,
-0.017265351489186287,
0.07023656368255615,
-0.002453072229400277,
0.008952437900006771,
0.037151727825403214,
0.029477842152118683,
-0.058095239102840424,
0.02415146306157112,
-0.01391538791358471,
0.005977690685540438,
0.009213171899318695,
-0.022877994924783707,
-0.011961312033236027,
-0.055188972502946854,
-0.02810903824865818,
-0.009204578585922718,
-0.048244304955005646,
-0.053705837577581406,
0.026850827038288116,
-0.020843327045440674,
-0.016207072883844376,
-0.036325979977846146,
0.030221186578273773,
0.027692614123225212,
-0.01414510514587164,
-0.00111331045627594,
0.0329742468893528,
-0.05502041429281235,
0.02059858851134777,
-0.0025202950928360224,
-0.0023761712945997715,
0.008103077299892902,
0.046640802174806595,
0.013181743212044239,
0.01664496213197708,
0.027505777776241302,
0.0029274579137563705,
-0.018230106681585312,
0.04042157530784607,
0.024626968428492546,
-0.00427330331876874,
-0.012549130246043205,
-0.00716480752453208,
0.023921748623251915,
-0.026900215074419975,
0.05891914665699005,
0.0059325131587684155,
-0.02686368115246296,
0.0003957511216867715,
-0.017203619703650475,
-0.054242219775915146,
0.049079086631536484,
0.023502647876739502,
0.028246764093637466,
0.01936548575758934,
-0.029682843014597893,
-0.001151748583652079,
-0.01582508720457554,
-0.00959336943924427,
0.025938061997294426,
0.020385991781949997,
0.007736777421087027,
0.018985185772180557,
-0.011225493624806404,
0.03084227442741394,
0.008935402147471905,
0.04378844052553177,
-0.07602851837873459,
-0.014543624594807625,
-0.03831067308783531,
-0.00007663261203560978,
-0.026019228622317314,
0.08120471239089966,
0.051520150154829025,
-0.01863994635641575,
-0.03391670435667038,
-0.06927606463432312,
-0.0022048219107091427,
0.030332231894135475,
0.06627002358436584,
0.017107509076595306,
0.008080272004008293,
-0.038132812827825546,
-0.04369653761386871,
0.027816152200102806,
-0.03470786288380623,
-0.001096653752028942,
-0.03675220534205437,
-0.017239507287740707,
-0.013775492087006569,
-0.0022236367221921682,
-0.023516517132520676,
-0.01573496311903,
-0.025723561644554138,
0.034257542341947556,
0.009504000656306744,
-0.005322583485394716,
-0.00037449371302500367,
0.010729721747338772,
0.011807710863649845,
0.04367921128869057,
0.03242648392915726,
-0.011552989482879639,
-0.02272605337202549,
0.010831712745130062,
-0.032591313123703,
-0.07656949013471603,
0.03356119245290756,
0.020366810262203217,
-0.009072604589164257,
0.045349955558776855,
-0.04823974892497063,
-0.05409449338912964,
0.05517791584134102,
0.03560382127761841,
-0.010499375872313976,
0.005974603351205587,
-0.04144665226340294,
-0.0024617579765617847,
-0.010339776054024696,
0.011878957971930504,
0.05324336513876915,
0.032227613031864166,
-0.025673815980553627,
-0.01930978335440159,
-0.004967457614839077,
0.04897681996226311,
-0.03653058782219887,
-0.032736267894506454,
-0.01638104021549225,
-0.016331175342202187,
-0.03446059301495552,
0.05422471836209297,
-0.04756980761885643,
-0.0034167312551289797,
-0.012436558492481709,
-0.04603506252169609,
-0.051589712500572205,
0.043319933116436005,
-0.02513786405324936,
-0.006329183466732502,
-0.004335930570960045,
0.03760633245110512,
0.015104983933269978,
0.022120673209428787,
0.003399004926905036,
-0.05398271977901459,
0.05270116776227951,
0.0332178995013237,
0.024694303050637245,
0.027965521439909935,
-0.03137294948101044,
-0.012712504714727402,
-0.01832439936697483,
-0.053674206137657166,
0.04790906608104706,
0.006784916389733553,
0.024493932723999023,
0.04377095028758049,
-0.09089932590723038,
-0.014960403554141521,
0.030416538938879967,
-0.015208808705210686,
0.04543216899037361,
-0.045104458928108215,
0.029716232791543007,
0.010328033939003944,
0.016172662377357483,
-0.03113759495317936,
-0.057338353246450424,
0.027464915066957474,
0.048958417028188705,
-0.01655806601047516,
-0.004197436384856701,
-0.009867829270660877,
-0.030823031440377235,
-0.028767026960849762,
-0.024428386241197586,
-0.017157914116978645,
-0.020370785146951675,
-0.007039277348667383,
0.026191741228103638,
-0.008243612945079803,
0.047635767608881,
-0.009446587413549423,
-0.030360300093889236,
0.01586943492293358,
-0.044280555099248886,
-0.020203199237585068,
-0.015265877358615398,
0.028940966352820396,
-0.019580937922000885,
-0.04833227023482323,
-0.031247718259692192,
0.027828093618154526,
0.03390347585082054,
-0.011002032086253166,
0.050215210765600204,
-0.0362577885389328,
0.011495268903672695,
-0.04891571030020714,
-0.019818609580397606,
-0.005531728267669678,
0.007145700976252556,
0.009819982573390007,
0.019886091351509094,
0.013256710022687912,
-0.020216897130012512,
-0.04028720036149025,
0.020059091970324516,
-0.022030111402273178,
-0.001806801650673151,
-0.03287322819232941,
0.08381837606430054,
-0.009250953793525696,
0.010660962201654911,
0.010590468533337116,
-0.024129405617713928,
0.007006358355283737,
0.019761666655540466,
-0.007724529132246971,
0.045078590512275696,
0.013343359343707561,
-0.008534998632967472,
-0.05149436369538307,
-0.03310272470116615,
0.002179110888391733,
0.08896633982658386,
-0.01803022250533104,
0.03379077464342117,
0.015526941046118736,
-0.0008696073782630265,
-0.03202880918979645,
-0.0006408313056454062,
-0.017688315361738205,
0.01062268391251564,
-0.010619920678436756,
0.04945278540253639,
-0.0416652150452137,
-0.010017083026468754,
0.00780701357871294,
0.067949578166008,
-0.0015737951034680009,
0.03339175507426262,
0.006191439926624298,
0.02964368276298046,
0.014610517770051956,
-0.019634097814559937,
-0.050057828426361084,
0.011950469575822353,
-0.012592234648764133,
0.04606445133686066,
0.02489706687629223,
0.003727704519405961,
0.057658448815345764,
-0.019785383716225624,
0.0340711735188961,
-0.053122926503419876,
-0.008158699609339237,
-0.017229974269866943,
0.027626320719718933,
-0.016831055283546448,
0.0692366361618042,
-0.014805600047111511,
-0.0002660975733306259,
0.017838625237345695,
-0.005541857797652483,
0.020805269479751587,
0.004735832568258047,
-0.05113009363412857,
-0.023630864918231964,
-0.01671864651143551,
-0.01939140260219574,
0.04903039708733559,
0.0024748656433075666,
-0.016847917810082436,
0.010971039533615112,
-0.022879384458065033,
0.011026749387383461,
0.002063529100269079,
0.046624306589365005,
-0.011244107969105244,
0.01960303820669651,
0.018782347440719604,
0.05434276908636093,
0.037805985659360886,
-0.034386053681373596,
0.13452257215976715,
0.0690663680434227,
0.00941744539886713,
-0.03806328400969505,
-0.007155990228056908,
-0.023090949282050133,
-0.009260128252208233,
-0.031394846737384796,
-0.011481409892439842,
-0.010808868333697319,
0.020881488919258118,
-0.00045565899927169085,
0.03811900317668915,
-0.017367521300911903,
0.010648585855960846,
-0.0027526456397026777,
-0.05755174905061722,
-0.03929801657795906,
0.00788483303040266,
0.004224516451358795,
-0.03882245346903801,
0.05617120489478111,
-0.035907261073589325,
0.0035204726736992598,
-0.013122773729264736,
-0.024618783965706825,
-0.014868738129734993,
-0.02007906138896942,
0.03255734592676163,
-0.012365087866783142,
-0.014179971069097519,
-0.012911997735500336,
-0.015270373784005642,
-0.021884500980377197,
-0.060791365802288055,
0.05165720731019974,
0.028346192091703415,
-0.026550626382231712,
0.013033319264650345,
0.010998358950018883,
-0.03361157700419426,
-0.005597813054919243,
0.03338972106575966,
-0.0013488262193277478,
-0.018376853317022324,
-0.006840984337031841,
-0.002028060145676136,
0.03353431075811386,
-0.009897951036691666,
0.002511027967557311,
-0.035352032631635666,
0.001682316418737173,
0.027429230511188507,
-0.06784851104021072,
-0.012255776673555374,
0.0005348281702026725,
0.0472792312502861,
-0.027440277859568596,
-0.04834867641329765,
0.015499122440814972,
-0.031733859330415726,
0.0017911747563630342,
0.016855640336871147,
-0.02954377420246601,
-0.0015579444589093328,
-0.02046196721494198,
0.006282723043113947,
0.013247820548713207,
0.02240980975329876,
-0.031110528856515884,
-0.053463809192180634,
-0.01639847829937935,
-0.009875145740807056,
-0.01750563085079193,
0.008807548321783543,
0.03244079649448395,
0.011168957687914371,
-0.009683538228273392,
-0.01088724471628666,
-0.013556297868490219,
-0.06231669709086418,
0.02549077197909355,
-0.04038568586111069,
-0.04299619421362877,
0.002185800578445196,
0.0014057527296245098,
0.011615404859185219,
0.05513681098818779,
-0.025206539779901505,
0.02344556339085102,
0.024350065737962723,
-0.006836452521383762,
0.023821953684091568,
-0.031575482338666916,
-0.0196661576628685,
0.0017740254988893867,
-0.004546462092548609,
-0.023331906646490097,
0.011846973560750484,
0.03700727969408035,
0.02828889898955822,
0.02244449034333229,
0.017642170190811157,
0.023180468007922173,
-0.02966064028441906,
-0.014515174552798271,
0.003191144671291113,
-0.02234736829996109,
0.015765685588121414,
0.013845057226717472,
-0.02129235304892063,
-0.07119884341955185,
-0.01522766426205635,
-0.015901684761047363,
-0.016541382297873497,
0.003184008179232478,
-0.0006123679340817034,
0.009823691099882126,
0.012057079933583736,
-0.01016230508685112,
0.0009107706719078124,
-0.023448538035154343,
-0.0210199523717165,
-0.024874210357666016,
0.02848491258919239,
0.028256461024284363,
0.018332496285438538,
-0.04654502868652344,
0.03517536818981171,
-0.002609172835946083,
-0.017343860119581223,
0.02484411559998989,
0.024620119482278824,
0.009148063138127327,
-0.008481859229505062,
0.05871922895312309,
0.00046145424130372703,
0.07600145787000656,
-0.00531086977571249,
-0.026585571467876434,
0.025773417204618454,
-0.07691285014152527,
-0.002425037557259202,
0.024686312302947044,
-0.016562454402446747,
0.05301959812641144,
0.023169126361608505,
0.010233882814645767,
-0.00007352454849751666,
0.04442327469587326,
0.032076939940452576,
0.004302925430238247,
-0.0009589415276423097,
-0.011233672499656677,
0.014979229308664799,
-0.022299259901046753,
0.00613661203533411,
-0.003893994027748704,
-0.0053903632797300816,
0.04797016829252243,
0.00800703838467598,
0.006482507102191448,
-0.011057227849960327,
0.008522800169885159,
-0.008099187165498734,
-0.005021169316023588,
0.020059136673808098,
0.0006056693382561207,
0.010630571283400059,
0.019673852249979973,
-0.024193238466978073,
0.0377923883497715,
0.011587023735046387,
0.021409016102552414,
-0.11446075141429901,
-0.007951115258038044,
0.0023542095441371202,
0.034604962915182114,
0.03694261610507965,
-0.051129765808582306,
0.037312522530555725,
0.05147327110171318,
-0.09068906307220459,
0.011884791776537895,
-0.0036484014708548784,
0.009093504399061203,
-0.0421188659965992,
0.005433525890111923,
-0.02028682269155979,
0.05537762492895126,
0.03793708235025406,
0.0414433479309082,
0.045618679374456406,
0.017048252746462822,
-0.02403697744011879,
-0.03713312745094299,
-0.010811664164066315,
0.0402534157037735,
0.014072336256504059,
-0.004208825062960386,
0.08944140374660492,
-0.0129012456163764,
-0.04633589833974838,
0.02829878032207489,
-0.03292170166969299,
0.013933812268078327,
0.01473441906273365,
-0.004891617689281702,
-0.0066772401332855225,
0.009651059284806252,
0.008798016235232353,
-0.0021687138359993696,
-0.01512913964688778,
0.008005321025848389,
0.01701933518052101,
0.02188281901180744,
-0.004145625047385693,
-0.020034249871969223,
0.028907878324389458,
-0.06399033963680267,
-0.042234960943460464,
0.02374996803700924,
0.002096497220918536,
0.014187201857566833,
0.007444445975124836,
-0.01274458970874548,
0.009601778350770473,
-0.012168548069894314,
-0.01600397378206253,
-0.0577649362385273,
-0.014392591081559658,
0.029245246201753616,
-0.018833722919225693,
-0.027982069179415703,
0.01515214517712593,
-0.0004994899500161409,
-0.0673101544380188,
-0.012935499660670757,
-0.05765346437692642,
-0.0204364862293005,
-0.054004594683647156,
0.004508438520133495,
0.021434778347611427,
-0.0005843781400471926,
0.0042409952729940414,
0.010849792510271072,
-0.041095614433288574,
0.025422463193535805,
0.025396041572093964,
-0.004777739755809307,
-0.019870517775416374,
-0.03170967102050781,
-0.04384288936853409,
-0.06184328719973564,
0.022467443719506264,
0.04069751873612404,
-0.04238881543278694,
-0.03552977368235588,
-0.01885118894279003,
-0.02612406760454178,
0.06095373257994652,
0.042542148381471634,
-0.007702300790697336,
-0.010051663964986801,
-0.025848165154457092,
-0.015055886469781399,
0.042991530150175095,
-0.04432728886604309,
-0.04221052676439285,
-0.008097963407635689,
-0.048328280448913574,
-0.026594381779432297,
0.02226661890745163,
-0.016253458335995674,
-0.00789940170943737,
-0.0026567920576781034,
-0.005324102938175201,
0.0220623891800642,
0.01112879253923893,
-0.0269295834004879,
0.037862520664930344,
-0.008084754459559917,
-0.009598861448466778,
0.04574267566204071,
-0.0115691889077425,
-0.0036021952982991934,
0.019888125360012054,
-0.06856565177440643,
-0.060935866087675095,
-0.02912776917219162,
-0.043564584106206894,
-0.0011607083724811673,
0.018361032009124756,
0.01942860148847103,
0.03703537955880165,
-0.04375964403152466,
0.03735053166747093,
0.02378912828862667,
-0.03818942978978157,
-0.005495683755725622,
0.053512051701545715,
0.0011050836183130741,
0.020244572311639786,
0.011400540359318256,
0.0343158021569252,
-0.006511601619422436,
-0.05124442279338837,
0.023918190971016884,
0.0751577690243721,
0.02484612911939621,
0.019415557384490967,
0.029228955507278442,
0.0007114465697668493,
0.011044619604945183,
0.03433019295334816,
0.019109997898340225,
0.02699950523674488,
-0.023708712309598923,
0.02598341926932335,
0.02339618280529976,
0.000050034941523335874,
-0.03355185687541962,
0.012327947653830051,
0.004576309118419886,
0.057802848517894745,
-0.0264502614736557,
0.02369195967912674,
-0.02471037767827511,
-0.01045299880206585,
-0.00017380017379764467,
0.014784661121666431,
0.050019629299640656,
0.05086963623762131,
-0.029049888253211975,
0.0005731271230615675,
-0.021084463223814964,
-0.007200274616479874,
0.014133775606751442,
-0.023609496653079987,
0.02636820822954178,
0.004009258933365345,
-0.017856542021036148,
-0.0022787987254559994,
-0.017843032255768776,
0.01151361595839262,
0.010868717916309834,
0.031265538185834885,
0.017527634277939796,
0.0014161414001137018,
0.03412424027919769,
0.025480210781097412,
-0.00008663888002047315,
0.027962576597929,
-0.052755437791347504,
0.006412743125110865,
-0.027794845402240753,
0.0335274413228035,
-0.001434973906725645,
-0.02792128548026085
] |
<p>If a future astronaut travelled to Alpha Centauri at a significant percentage of light-speed?
Apart from increased blue shifted radiation from their direction of travel - how would they experience other cosmic radiation? </p>
<p>If the trip took a subject several times faster than an observer on earth. Would the astronaut get less or more time / exposure to cosmic radiation?</p> | 4,607 | [
-0.0015639173798263073,
-0.07794935256242752,
-0.006116973236203194,
-0.04554269090294838,
0.07045897096395493,
0.035782843828201294,
-0.0023395998869091272,
-0.010023625567555428,
-0.01320749893784523,
-0.05957455560564995,
0.007283416576683521,
0.053652580827474594,
0.04305468872189522,
0.005675009451806545,
-0.008312511257827282,
-0.014140798710286617,
-0.012129373848438263,
-0.02725857123732567,
-0.020121553912758827,
-0.03304632008075714,
0.025988714769482613,
-0.0009097869042307138,
0.019448593258857727,
0.0380542017519474,
-0.0587761364877224,
0.02068760246038437,
0.01585140824317932,
0.005139784887433052,
0.011243206448853016,
-0.005484591703861952,
0.014392828568816185,
0.012422415427863598,
0.012649457901716232,
0.03661588951945305,
-0.017339857295155525,
-0.015003005973994732,
-0.04344434663653374,
0.0037207312416285276,
-0.004747353959828615,
0.03240130469202995,
-0.04986894503235817,
-0.022916771471500397,
0.03511655330657959,
0.05880118906497955,
-0.008860451169312,
0.029626313596963882,
-0.004293206613510847,
0.0012790897162631154,
0.049538444727659225,
-0.04587605223059654,
0.04381565749645233,
-0.01108216866850853,
0.028261907398700714,
0.04208260774612427,
0.012885112315416336,
-0.0174157302826643,
0.0888853669166565,
0.08347391337156296,
0.01160894799977541,
-0.022846782580018044,
-0.013865041546523571,
0.005598251707851887,
0.007822358049452305,
0.005992180202156305,
-0.019661180675029755,
0.017246926203370094,
-0.0504513680934906,
-0.03248975798487663,
0.0026089970488101244,
0.03467385470867157,
0.036889251321554184,
0.022484125569462776,
0.014238221570849419,
-0.0018227096879854798,
0.007397851906716824,
-0.040277935564517975,
-0.008976821787655354,
0.023427549749612808,
0.06333863735198975,
0.0056991176679730415,
-0.03604297339916229,
-0.014270385727286339,
0.01464173011481762,
0.030052991583943367,
-0.010306935757398605,
0.01813584379851818,
0.049772314727306366,
-0.0006228714482858777,
-0.003750477684661746,
0.007992789149284363,
0.010596049018204212,
0.025271320715546608,
0.027858836576342583,
0.010783865116536617,
-0.047549810260534286,
0.0080931531265378,
-0.017157310619950294,
0.05480373278260231,
0.0028271167539060116,
-0.009844889864325523,
0.028289053589105606,
0.016802240163087845,
-0.004738876596093178,
0.032554470002651215,
0.011996956542134285,
-0.027148308232426643,
-0.04541575536131859,
-0.009374124929308891,
-0.02825513854622841,
-0.022244451567530632,
-0.05076180025935173,
-0.008991183713078499,
0.022180480882525444,
0.033396657556295395,
0.05934600532054901,
-0.04717689007520676,
0.013187635689973831,
-0.04517852142453194,
0.08895961195230484,
0.0701352134346962,
0.03936399891972542,
-0.0009998360183089972,
0.012654867954552174,
0.02424628473818302,
-0.002119038486853242,
0.029731590300798416,
0.001862857025116682,
-0.027976909652352333,
-0.03728444501757622,
0.012527355924248695,
-0.013934534043073654,
-0.004048568196594715,
0.002174906199797988,
-0.006481594871729612,
0.007765093352645636,
0.004628459457308054,
-0.08078697323799133,
-0.0706682801246643,
0.02334311231970787,
-0.004983976017683744,
-0.01561034843325615,
-0.05578912794589996,
0.02537417784333229,
0.019660480320453644,
0.07705900073051453,
0.01209335494786501,
-0.012565256096422672,
-0.007353035267442465,
0.04042847082018852,
0.03081262670457363,
-0.06841686367988586,
0.025830423459410667,
-0.0196370929479599,
-0.039189353585243225,
0.012979813851416111,
-0.08410026878118515,
-0.023768752813339233,
0.03244568035006523,
-0.0031276834197342396,
-0.0269889198243618,
0.07419922202825546,
-0.018719753250479698,
0.028235824778676033,
-0.023798644542694092,
-0.0065154507756233215,
-0.015541352331638336,
0.09260290861129761,
0.0469297431409359,
0.0023916412610560656,
0.0019294648664072156,
0.042942121624946594,
0.06409434974193573,
0.010714147239923477,
-0.01774860918521881,
0.06234648451209068,
-0.06287026405334473,
-0.0014956025406718254,
0.009705254808068275,
0.0035650180652737617,
-0.015098518691956997,
-0.046742867678403854,
-0.026558630168437958,
-0.001992630073800683,
0.0047648753970861435,
0.03418237343430519,
0.06023215502500534,
-0.00018464903405401856,
-0.03481361269950867,
0.024913551285862923,
-0.01329097617417574,
0.026056833565235138,
-0.03568051755428314,
0.0030925592873245478,
0.023691140115261078,
-0.024947214871644974,
0.006244870834052563,
0.017606036737561226,
0.050984323024749756,
-0.018593475222587585,
-0.047090813517570496,
0.027641713619232178,
0.035731129348278046,
-0.00529984338209033,
-0.0018228876870125532,
-0.004781736526638269,
0.06281084567308426,
0.006959488615393639,
0.021574178710579872,
-0.013944778591394424,
0.04018151015043259,
-0.04759356006979942,
0.024333268404006958,
-0.019754771143198013,
0.04049244150519371,
-0.001650686259381473,
0.019204093143343925,
0.0015132054686546326,
-0.0068164365366101265,
-0.024761097505688667,
0.03594641387462616,
0.0038369055837392807,
0.07139328122138977,
0.026699025183916092,
-0.02164897695183754,
0.014778638258576393,
0.026934165507555008,
0.029791444540023804,
-0.02934904582798481,
-0.007359743118286133,
-0.05115753039717674,
-0.06397237628698349,
-0.030362769961357117,
0.018501732498407364,
-0.0007656459929421544,
-0.029646292328834534,
0.02390626259148121,
-0.0007445181836374104,
-0.0027070841751992702,
0.04812551289796829,
0.018886249512434006,
-0.00019941871869377792,
-0.024279266595840454,
-0.021030675619840622,
0.0032894923351705074,
-0.0035919826477766037,
-0.023829413577914238,
0.02428349107503891,
0.0011902719270437956,
0.008506004698574543,
-0.02196335606276989,
0.005454811733216047,
0.013153989799320698,
-0.02454809844493866,
0.020612724125385284,
-0.0356605239212513,
-0.034143708646297455,
0.038396865129470825,
-0.04141174629330635,
-0.0017829880816861987,
0.046222858130931854,
0.0003511565737426281,
-0.006194867193698883,
-0.011809300631284714,
-0.010219716466963291,
-0.0422414131462574,
0.019749540835618973,
-0.026318440213799477,
-0.0065626767463982105,
0.057008154690265656,
-0.06099137291312218,
0.02353247068822384,
-0.03381011635065079,
0.008316904306411743,
-0.017842523753643036,
-0.005801260005682707,
0.03460446745157242,
0.022795775905251503,
0.0229781661182642,
-0.01403870154172182,
-0.03899389132857323,
0.013997005298733711,
-0.017415527254343033,
-0.013816446997225285,
0.005292822606861591,
-0.042628202587366104,
0.05042189732193947,
-0.025134043768048286,
-0.021492326632142067,
-0.0031813313253223896,
-0.008118491619825363,
-0.0088879419490695,
0.04141153395175934,
-0.03547518700361252,
-0.05320728197693825,
0.015585575252771378,
-0.005881543271243572,
-0.009682446718215942,
-0.03225770592689514,
-0.02327680215239525,
0.07361136376857758,
-0.014925099909305573,
-0.01261088065803051,
0.017763806506991386,
-0.056133028119802475,
0.012079959735274315,
-0.003963224124163389,
0.014096276834607124,
0.017096931114792824,
-0.062080953270196915,
0.04155571386218071,
0.03233712539076805,
-0.06004692241549492,
-0.009835767559707165,
-0.003173349890857935,
-0.0381912961602211,
0.046729959547519684,
0.004740129690617323,
0.018297629430890083,
-0.0410953052341938,
-0.0005267421365715563,
0.045252859592437744,
0.024044686928391457,
0.011503500863909721,
-0.0489819161593914,
-0.00004583666304824874,
-0.026064692065119743,
-0.031291183084249496,
-0.00842795055359602,
0.030037160962820053,
-0.03287264704704285,
-0.026177307590842247,
0.0073058512061834335,
0.03680034726858139,
0.01408085785806179,
0.013547566719353199,
-0.022768715396523476,
-0.013052509166300297,
0.008067176677286625,
0.019231490790843964,
0.008682777173817158,
0.01062138844281435,
-0.029791565611958504,
0.008859054185450077,
-0.012351097539067268,
0.047102537006139755,
0.014715488068759441,
-0.023404555395245552,
0.050516124814748764,
0.03655816242098808,
0.029004722833633423,
0.01578362099826336,
0.024317145347595215,
0.011072871275246143,
0.007747404742985964,
-0.003611563239246607,
-0.005919487681239843,
0.05736834555864334,
-0.007873497903347015,
0.0010631667682901025,
0.054750289767980576,
0.06918275356292725,
0.024183489382267,
-0.03386208787560463,
-0.019538773223757744,
0.020992731675505638,
0.023265769705176353,
-0.04628998041152954,
-0.007470266427844763,
0.029837703332304955,
0.03245891258120537,
-0.0020398059859871864,
0.026228103786706924,
-0.024727553129196167,
-0.00213831989094615,
-0.04923086240887642,
0.003405295079573989,
-0.03121103346347809,
0.059023499488830566,
0.008934231474995613,
0.036768410354852676,
0.02789025381207466,
-0.04589896276593208,
0.017201656475663185,
0.019129952415823936,
-0.0807238519191742,
0.00620898837223649,
-0.01816367357969284,
-0.01940031349658966,
-0.00028323009610176086,
0.0031801906879991293,
0.012429040856659412,
-0.007822557352483273,
-0.018824780359864235,
0.005218448117375374,
-0.014948011375963688,
-0.04179174080491066,
0.04126361384987831,
-0.0326165072619915,
-0.03785121068358421,
-0.05741036310791969,
0.02814096212387085,
0.028056856244802475,
-0.006253228057175875,
-0.0054778726771473885,
0.0009540150640532374,
-0.05600906163454056,
0.005591902881860733,
0.015119210816919804,
0.0075544994324445724,
-0.029297281056642532,
0.05844064801931381,
0.02282106690108776,
-0.01295947004109621,
-0.0520254485309124,
-0.012468625791370869,
0.008932704105973244,
0.012262193486094475,
-0.014108549803495407,
0.00869156513363123,
-0.03118998371064663,
-0.04487358033657074,
-0.024404320865869522,
-0.010184768587350845,
0.025128355249762535,
-0.0018522230675444007,
0.028723644092679024,
0.04147534817457199,
-0.011838771402835846,
-0.034602586179971695,
0.022602995857596397,
0.026277676224708557,
-0.00015364766295533627,
-0.04228011146187782,
0.0015916855772957206,
-0.0062639145180583,
-0.0020768577232956886,
-0.024838628247380257,
0.027448849752545357,
0.007202478125691414,
-0.023944182321429253,
0.03034316562116146,
-0.018459025770425797,
0.006288012955337763,
-0.04778432846069336,
0.01092345267534256,
0.02277497947216034,
0.004966424312442541,
0.012548010796308517,
-0.011189970187842846,
-0.015228417702019215,
0.0332675501704216,
0.06906802207231522,
-0.023335417732596397,
-0.008837458677589893,
-0.052451636642217636,
-0.03319734334945679,
0.007375130895525217,
0.06688601523637772,
0.026351258158683777,
-0.011718065477907658,
-0.0564175620675087,
-0.0042984155006706715,
0.019906945526599884,
-0.03862154856324196,
-0.009637984447181225,
-0.008090614341199398,
0.02185755968093872,
-0.04217086359858513,
-0.046309906989336014,
-0.04893498122692108,
0.03789098560810089,
-0.030241582542657852,
-0.024769240990281105,
-0.0075795878656208515,
0.004958216566592455,
0.005528855137526989,
0.009153262712061405,
0.04369309917092323,
0.058528557419776917,
0.0440572090446949,
0.01379298884421587,
-0.03542624041438103,
0.013496264815330505,
-0.01889899931848049,
-0.03559784218668938,
-0.02113485150039196,
0.020409174263477325,
-0.04146435856819153,
0.056208133697509766,
-0.024805376306176186,
-0.014525501057505608,
0.019741486757993698,
0.014273514971137047,
-0.004939964506775141,
-0.038083914667367935,
-0.07597912847995758,
0.05069660767912865,
0.036654431372880936,
0.009037796407938004,
0.06716813892126083,
-0.002597186481580138,
-0.029254237189888954,
0.006963029038161039,
0.005360088311135769,
0.03968333825469017,
-0.012885267846286297,
0.011840078979730606,
-0.015717623755335808,
-0.03716209903359413,
-0.008158635348081589,
0.05235404148697853,
-0.046719685196876526,
-0.0013690459309145808,
0.02827538549900055,
-0.0457879900932312,
0.01021614484488964,
0.045571744441986084,
0.010682202875614166,
-0.008700060658156872,
-0.05299924686551094,
-0.0026325921062380075,
-0.01530403085052967,
0.01344867143779993,
0.03264743089675903,
-0.019825711846351624,
-0.022614194080233574,
0.015680206939578056,
-0.02187439799308777,
0.009638684801757336,
-0.025395117700099945,
0.00284787081182003,
0.019096393138170242,
-0.04063715040683746,
0.041078876703977585,
-0.0012689896393567324,
-0.0016030827537178993,
-0.00042112081428058445,
-0.03300599008798599,
-0.022219359874725342,
0.05096123367547989,
-0.06577640026807785,
0.024977199733257294,
-0.028920093551278114,
0.048265330493450165,
0.0062559619545936584,
0.00671909935772419,
-0.0755595937371254,
-0.017156656831502914,
0.05037906393408775,
0.0427912212908268,
0.006928524002432823,
-0.03999844565987587,
-0.02158334292471409,
-0.07172389328479767,
-0.02118724025785923,
-0.009252914227545261,
0.038872115314006805,
-0.03001457452774048,
-0.0055753192864358425,
-0.020600637421011925,
0.003717538435012102,
0.008340670727193356,
-0.006445166654884815,
-0.019132064655423164,
0.030403250828385353,
0.0146831925958395,
-0.017058582976460457,
-0.03632078319787979,
0.027112146839499474,
-0.009603790938854218,
-0.04112090915441513,
-0.024155154824256897,
-0.009420404210686684,
0.01023896038532257,
-0.017875999212265015,
0.009740546345710754,
0.04062063246965408,
0.010155691765248775,
-0.02870248816907406,
0.010885688476264477,
0.005939724389463663,
-0.017060136422514915,
0.050982434302568436,
-0.002318569691851735,
-0.017946666106581688,
-0.011979624629020691,
-0.003069578669965267,
0.05155635252594948,
0.02982502058148384,
-0.005583873949944973,
-0.009436821565032005,
0.03620319440960884,
0.020245932042598724,
-0.00404087221249938,
-0.01601237803697586,
0.01664344035089016,
0.03661416471004486,
-0.007562153972685337,
0.031180448830127716,
0.030310507863759995,
-0.011239725165069103,
0.005666555371135473,
-0.00848927441984415,
-0.02368343248963356,
-0.03455161675810814,
0.07169635593891144,
-0.02030557207763195,
0.02853114902973175,
-0.021845968440175056,
0.026728201657533646,
-0.03837636858224869,
-0.041771240532398224,
-0.008776625618338585,
0.006776302121579647,
-0.03928723558783531,
0.008406445384025574,
0.003403033595532179,
-0.03267290070652962,
0.012853700667619705,
0.05243288353085518,
-0.03286350518465042,
0.056827668100595474,
0.038869671523571014,
0.053175970911979675,
0.040454115718603134,
-0.018636509776115417,
-0.01106406282633543,
-0.005848926957696676,
-0.044851936399936676,
0.021153446286916733,
0.023629704490303993,
-0.015226299874484539,
0.05289493128657341,
0.003851147135719657,
0.03518638014793396,
-0.06529886275529861,
-0.039600711315870285,
-0.05264631286263466,
-0.02565562166273594,
0.050284046679735184,
0.03737807646393776,
-0.01495441421866417,
-0.012069528922438622,
0.047250136733055115,
-0.04532161355018616,
-0.01143112313002348,
0.006941508036106825,
-0.05687164515256882,
-0.03820543363690376,
-0.05815409496426582,
-0.00700466288253665,
0.06671197712421417,
0.001343941898085177,
-0.04831079766154289,
0.008742745034396648,
0.002192018087953329,
0.048997651785612106,
0.01124200876802206,
0.05109843984246254,
-0.0018006532918661833,
0.07078347355127335,
-0.01548964623361826,
0.0016601771349087358,
-0.005671224091202021,
0.015528117306530476,
0.10471092164516449,
0.06533193588256836,
-0.025989675894379616,
-0.03743855655193329,
0.016843294724822044,
-0.040384117513895035,
0.034147173166275024,
0.004045774694532156,
-0.01859337091445923,
0.031026193872094154,
0.017634091898798943,
0.0519421249628067,
0.05265034735202789,
-0.01690378598868847,
0.00868744496256113,
0.04562992602586746,
-0.03373502939939499,
0.01165832206606865,
0.007369397673755884,
-0.0013783939648419619,
0.0032417182810604572,
0.030122894793748856,
-0.046077050268650055,
0.022887080907821655,
-0.03798237815499306,
0.04699172452092171,
-0.045859113335609436,
-0.029628030955791473,
0.016589203849434853,
-0.01559001486748457,
-0.05342302471399307,
-0.006432175636291504,
0.0234751645475626,
-0.01873895339667797,
-0.008599530905485153,
0.04049673676490784,
0.05108669400215149,
-0.013593814335763454,
-0.007137020118534565,
0.023625889793038368,
0.01724371500313282,
0.0028274785727262497,
-0.0007496277685277164,
0.004583486821502447,
-0.02012246660888195,
0.020320666953921318,
-0.01718355529010296,
0.06385185569524765,
-0.001811694586649537,
-0.049173031002283096,
-0.0063118888065218925,
0.004332991316914558,
-0.034790243953466415,
-0.0467328242957592,
-0.00023781831259839237,
0.017901480197906494,
-0.04464796558022499,
-0.009004093706607819,
0.0148814357817173,
-0.014289380051195621,
-0.024082396179437637,
0.023488227277994156,
0.03611552715301514,
0.0011993586085736752,
-0.016099439933896065,
-0.0014700460014864802,
-0.015892932191491127,
-0.01726353168487549,
-0.012139461934566498,
-0.04186130315065384,
-0.04838687181472778,
0.004006044007837772,
-0.07707514613866806,
0.023583590984344482,
0.03286076337099075,
0.006201270967721939,
0.011610081419348717,
0.00990097876638174,
-0.009071060456335545,
-0.043071579188108444,
-0.029838811606168747,
0.04791252315044403,
0.010871412232518196,
-0.0054984563030302525,
0.014200935140252113,
0.012058977968990803,
0.02982284314930439,
0.033532559871673584,
-0.0071425545029342175,
-0.010518163442611694,
-0.03308806195855141,
0.06318793445825577,
0.026021772995591164,
0.0038364895153790712,
0.00017751163977663964,
-0.019049884751439095,
-0.02535308711230755,
0.029365675523877144,
-0.044839873909950256,
0.06834691762924194,
0.021523278206586838,
-0.023463374003767967,
-0.005119846202433109,
0.00004107303175260313,
-0.018430331721901894,
0.00505933677777648,
0.032437022775411606,
-0.017568213865160942,
-0.025519955903291702,
0.011321891099214554,
0.04355257377028465,
-0.036943159997463226,
0.013225948438048363,
-0.0724676251411438,
-0.04351680353283882,
-0.02045995369553566,
-0.019367124885320663,
0.01296899002045393,
0.04192668944597244,
0.014298097230494022,
-0.010750923305749893,
0.010621832683682442,
0.05513522028923035,
-0.023490525782108307,
0.04407041519880295,
-0.014813125133514404,
-0.02061951719224453,
0.020995832979679108,
0.023632533848285675,
-0.042919568717479706,
-0.03706522285938263,
0.015132813714444637,
0.000804948853328824,
-0.008050368167459965,
0.006925002206116915,
0.01778951846063137,
0.022147146984934807,
0.07615213096141815,
-0.03788328170776367,
-0.01654885523021221,
0.002144617959856987,
-0.006642946042120457,
-0.041144099086523056,
0.041453734040260315,
-0.05804856866598129,
0.049495212733745575,
-0.017172927036881447,
-0.025451306253671646,
-0.001833140617236495,
0.0833493322134018,
-0.02865506149828434,
-0.028609097003936768,
0.006845533382147551,
-0.014179672114551067,
-0.04978985711932182,
-0.016895951703190804,
0.027271855622529984,
-0.015369956381618977,
-0.01949942670762539,
0.03801802545785904,
0.029723435640335083,
-0.025519274175167084,
0.032832954078912735,
-0.05677400901913643,
-0.026982933282852173,
-0.01921640709042549,
0.004352698568254709,
-0.013270829804241657,
0.013495241291821003,
0.02168426290154457,
-0.036098092794418335,
0.038180314004421234,
0.015006802044808865,
-0.010506190359592438,
-0.10110601037740707,
-0.02068653702735901,
-0.0030123009346425533,
0.02963506430387497,
0.03621271252632141,
-0.02960786409676075,
0.058742403984069824,
0.05171792581677437,
-0.09070044010877609,
0.036294177174568176,
-0.0015340866521000862,
-0.008266715332865715,
-0.017093732953071594,
0.016811488196253777,
0.0031065517105162144,
0.015905380249023438,
0.07960288971662521,
0.011386157013475895,
-0.0060663046315312386,
0.012328403070569038,
-0.0077205984853208065,
-0.05348469689488411,
0.025914419442415237,
0.04483228921890259,
-0.018596326932311058,
0.016768168658018112,
0.07508175075054169,
0.00805404968559742,
-0.011022808030247688,
0.03145068138837814,
0.024737171828746796,
0.011363820172846317,
-0.0026916309725493193,
-0.010664831846952438,
0.019280102103948593,
0.014115352183580399,
-0.03722081333398819,
-0.004226881545037031,
-0.015470484271645546,
0.006014948710799217,
-0.005473852623254061,
-0.011881922371685505,
-0.004834143910557032,
0.010355005972087383,
0.012718490324914455,
-0.013090929947793484,
-0.008701100014150143,
0.028197119012475014,
0.034156717360019684,
-0.006936497520655394,
0.018877433612942696,
0.0128642488270998,
0.02015404775738716,
-0.03605802357196808,
0.00038685923209413886,
-0.06000670790672302,
-0.010027850046753883,
-0.0015363611746579409,
0.006918149534612894,
-0.011325483210384846,
-0.007575494237244129,
-0.03921746090054512,
0.0023089509923011065,
-0.006747931241989136,
-0.00042634576675482094,
0.00654090428724885,
-0.014668229036033154,
-0.0015676963375881314,
-0.027952056378126144,
0.039799947291612625,
0.007964069955050945,
-0.0320749431848526,
-0.015116045251488686,
0.01583387702703476,
0.0005638613365590572,
0.009994357824325562,
-0.0008004062692634761,
-0.01949797198176384,
0.023153088986873627,
-0.06522700935602188,
0.023539811372756958,
-0.019924920052289963,
-0.02241683192551136,
-0.03867703303694725,
-0.01647188514471054,
-0.01842912659049034,
0.03664172440767288,
0.034496791660785675,
0.005604181904345751,
-0.023133061826229095,
0.0187081266194582,
0.012822045013308525,
0.022038372233510017,
-0.07716494798660278,
-0.014952587895095348,
0.0011965474113821983,
-0.04928753525018692,
-0.051857005804777145,
-0.006394409574568272,
-0.017115533351898193,
0.02111288346350193,
0.018166158348321915,
0.03154628723859787,
0.022313063964247704,
0.030265502631664276,
-0.030681917443871498,
0.07034897059202194,
0.05095558613538742,
0.034942224621772766,
0.029134904965758324,
-0.0015799877000972629,
0.020394282415509224,
0.05893344432115555,
0.0020826642867177725,
-0.037272024899721146,
0.01754869893193245,
-0.00829144287854433,
0.009084915742278099,
0.0070467726327478886,
0.0032211760990321636,
-0.012407468631863594,
-0.03288690745830536,
0.04882591590285301,
0.005827923305332661,
-0.03309200704097748,
-0.018428154289722443,
0.02322269417345524,
0.007260425481945276,
0.011097608134150505,
0.021747689694166183,
0.0035071575548499823,
-0.00008862410322763026,
0.0005108812474645674,
-0.04898075386881828,
0.01989796571433544,
-0.028589343652129173,
0.006048949901014566,
0.04791174829006195,
0.007009134627878666,
0.012842336669564247,
-0.0006787489983253181,
0.005694877821952105,
0.01439648773521185,
-0.06443441659212112,
-0.007974940352141857,
0.0156936664134264,
-0.019537150859832764,
0.01919807307422161,
0.024407383054494858,
0.01237411703914404,
0.052614305168390274,
-0.028982948511838913,
0.026237711310386658,
0.003297783201560378,
-0.030890807509422302,
-0.022184591740369797,
0.01552126556634903,
0.005071388557553291,
0.020607613027095795,
-0.02009757049381733,
-0.02060718461871147,
-0.01889740116894245,
-0.018479490652680397,
0.04234848544001579,
-0.060835324227809906,
0.0332120880484581,
0.0009839095873758197,
-0.0430319644510746,
0.0464930459856987,
-0.03135981783270836,
-0.016315745189785957,
-0.012554457411170006,
-0.0017881481908261776,
0.02049429900944233,
0.014837818220257759,
-0.026979371905326843,
-0.01515018381178379,
-0.03379188850522041,
0.04720330238342285,
-0.05635518208146095,
0.01549513079226017,
0.03201163187623024,
0.03229639306664467,
-0.041142743080854416,
-0.0021497129928320646
] |
<p>Wikipedia says:</p>
<blockquote>
<p>It is believed that, due to the extraordinarily small scale of the
universe at the time, quantum effects of gravity dominated physical
interactions.</p>
</blockquote>
<p>But I wonder whether there is any indication that the dimensions of the universe were small at the time rather than being infinite?</p>
<p>Undoubtedly it was very dense but very dense does not necessary mean "small".</p>
<p>Is Wikipedia wrong on this point?</p> | 4,608 | [
-0.009309392422437668,
-0.05749916657805443,
0.01930384710431099,
-0.05015524476766586,
0.08495330065488815,
0.017005261033773422,
-0.041891638189554214,
-0.05213974043726921,
-0.01363091915845871,
-0.047636039555072784,
-0.00026183537556789815,
0.003921270836144686,
0.02825036272406578,
0.009804158471524715,
0.0023550265468657017,
0.009991147555410862,
0.006118968594819307,
0.0022742534056305885,
0.018883422017097473,
-0.03357116878032684,
0.015115804970264435,
0.04482695087790489,
-0.0036862706765532494,
-0.0029936442151665688,
-0.041893716901540756,
0.047042395919561386,
0.039337217807769775,
0.019585901871323586,
0.03061857633292675,
0.03817373514175415,
-0.018663572147488594,
-0.0057620820589363575,
0.024269649758934975,
0.017573460936546326,
0.02510667033493519,
-0.019307667389512062,
-0.01952865906059742,
-0.057320352643728256,
0.02786644734442234,
-0.0015174158615991473,
-0.031244702637195587,
-0.01363864354789257,
-0.007621095981448889,
0.03644116595387459,
0.001044641132466495,
0.054041579365730286,
0.00041801430052146316,
-0.04346254840493202,
0.05372834950685501,
-0.015115589834749699,
0.050910186022520065,
-0.007284399587661028,
0.04451671987771988,
0.02144407294690609,
-0.01416135486215353,
0.007324622943997383,
0.06156199052929878,
0.055153340101242065,
-0.023224325850605965,
-0.0361674465239048,
-0.017635144293308258,
-0.01730659231543541,
-0.0017780838534235954,
0.0038732250686734915,
-0.0053247613832354546,
0.0446942001581192,
-0.01176528725773096,
-0.03855959698557854,
-0.014625678770244122,
-0.008336534723639488,
0.002133320551365614,
0.01861826330423355,
0.04624375328421593,
0.014476318843662739,
0.009601801633834839,
0.0060426294803619385,
0.02175571396946907,
0.009885421022772789,
0.004649773705750704,
0.042914289981126785,
-0.008801372721791267,
-0.01270157191902399,
0.051895685493946075,
0.017313053831458092,
0.03787463530898094,
0.04821746423840523,
0.03684641793370247,
-0.031108353286981583,
-0.02952657826244831,
0.05928695201873779,
-0.03060680255293846,
0.01471637561917305,
0.048858463764190674,
-0.02292831987142563,
-0.04114828631281853,
0.02466651238501072,
0.008539950475096703,
0.052396003156900406,
-0.003243126440793276,
-0.002065381733700633,
0.024622295051813126,
-0.008542085066437721,
-0.0033091045916080475,
0.06334854662418365,
0.028698323294520378,
-0.028942912817001343,
-0.06431171298027039,
0.03448348492383957,
-0.04773535206913948,
-0.000798180466517806,
-0.03634272888302803,
-0.014961249195039272,
0.004996847361326218,
-0.021389087662100792,
0.001218178658746183,
-0.019617028534412384,
0.005324832629412413,
-0.0027792498003691435,
0.07279839366674423,
0.08498913049697876,
0.010714839212596416,
-0.009380976669490337,
0.0016329773934558034,
-0.015258545987308025,
-0.04320422559976578,
0.012099729850888252,
0.024925939738750458,
-0.01271287351846695,
-0.010452569462358952,
0.04711419716477394,
-0.0022351450752466917,
0.028440209105610847,
0.02447069250047207,
0.006126989144831896,
0.06779281795024872,
0.01654832437634468,
-0.07941810041666031,
-0.05559956282377243,
0.054423633962869644,
-0.017486542463302612,
-0.003913691733032465,
-0.07627682387828827,
0.041242994368076324,
-0.012885218486189842,
0.060441579669713974,
0.009707833640277386,
0.037433527410030365,
-0.03329211845993996,
0.027119159698486328,
-0.012727570720016956,
-0.03286257013678551,
-0.020551826804876328,
0.030976638197898865,
-0.012669811025261879,
0.029079411178827286,
-0.09366033971309662,
0.027435598894953728,
0.04341111704707146,
0.035482149571180344,
-0.023965904489159584,
0.057402461767196655,
-0.01958848163485527,
-0.012640821747481823,
-0.007286129519343376,
-0.018331225961446762,
-0.03194171562790871,
0.07054345309734344,
0.00983420480042696,
-0.007061575539410114,
0.02132412977516651,
-0.03501177206635475,
0.02465539425611496,
0.03664442524313927,
0.005913146771490574,
0.011523202061653137,
-0.016813913360238075,
-0.01418724749237299,
0.008692268282175064,
0.00959795992821455,
-0.0009454780956730247,
-0.039737340062856674,
-0.008203098550438881,
0.0023606200702488422,
0.017625192180275917,
0.009987305849790573,
0.06258650869131088,
-0.00939627643674612,
-0.03501357138156891,
-0.03152692690491676,
-0.0254251379519701,
-0.02474222145974636,
-0.04415387287735939,
-0.027717139571905136,
0.0056944917887449265,
-0.012990362010896206,
0.033077389001846313,
0.011080989614129066,
0.04294655844569206,
-0.06907968968153,
-0.03071649931371212,
-0.005982961505651474,
0.025813931599259377,
0.019299596548080444,
-0.023232532665133476,
0.03616179898381233,
0.02601841278374195,
0.05890846252441406,
-0.015342582948505878,
-0.023638693615794182,
0.0011299579637125134,
-0.024219583719968796,
0.042361997067928314,
-0.01377861574292183,
0.03564931079745293,
-0.02373354136943817,
0.00459629762917757,
-0.023055844008922577,
0.0176191758364439,
0.00392160564661026,
0.0393257662653923,
0.0018455033423379064,
0.06768972426652908,
-0.02224077098071575,
0.006757744587957859,
-0.02832764945924282,
0.04228275269269943,
0.008034810423851013,
0.011539075523614883,
0.01150449551641941,
-0.01837928034365177,
-0.0684451311826706,
-0.021485352888703346,
0.02975146658718586,
0.052566662430763245,
-0.026885822415351868,
0.0020878701470792294,
0.03443106636404991,
0.060552068054676056,
-0.01130887120962143,
0.020961124449968338,
-0.03363484516739845,
-0.04984687268733978,
0.0028435748536139727,
-0.004056624602526426,
0.0356745719909668,
0.0012139909667894244,
0.027161914855241776,
0.038936518132686615,
0.00218420522287488,
-0.04531223699450493,
-0.011995233595371246,
0.0007790722884237766,
-0.014184889383614063,
0.02315816842019558,
0.0048616137355566025,
-0.057265736162662506,
0.0010463037760928273,
-0.03754014894366264,
0.018934037536382675,
0.0012831760104745626,
0.00958324410021305,
0.013765565119683743,
-0.06243334710597992,
-0.030510293319821358,
0.0028452682308852673,
0.022039424628019333,
-0.033830657601356506,
-0.00040908012306317687,
0.04007835313677788,
-0.04751595854759216,
-0.014444218017160892,
-0.01767689548432827,
-0.021183663979172707,
-0.035017214715480804,
-0.009466184303164482,
0.017019351944327354,
0.0032478678040206432,
0.001292859436944127,
-0.030224889516830444,
-0.037378523498773575,
-0.011395933106541634,
-0.013879786245524883,
-0.0030873259529471397,
0.03241921588778496,
-0.03648274019360542,
0.02929593063890934,
-0.03533262014389038,
0.013030371628701687,
0.020124297589063644,
-0.0375409871339798,
0.05244259536266327,
0.0174634400755167,
-0.017396394163370132,
-0.005617600400000811,
-0.0006867483607493341,
-0.02635493315756321,
0.03549468144774437,
0.00022662214178126305,
-0.007351886015385389,
0.03037198632955551,
0.005899190437048674,
-0.03316520154476166,
-0.004198066890239716,
-0.0359964556992054,
-0.041005492210388184,
-0.020894264802336693,
0.023422617465257645,
-0.012738018296658993,
-0.025927435606718063,
0.03748684749007225,
0.0004814784333575517,
-0.04159393161535263,
-0.02145533263683319,
-0.05791908875107765,
-0.03715106472373009,
0.036882705986499786,
0.0016219380777329206,
0.04517044126987457,
-0.023831907659769058,
-0.03635723516345024,
0.05700729042291641,
0.02411043271422386,
-0.005836507771164179,
-0.0291246697306633,
0.006073084659874439,
0.011103319935500622,
0.01820794679224491,
0.027143867686390877,
0.004317126236855984,
0.020874418318271637,
0.012473943643271923,
0.03313538804650307,
0.05808502808213234,
0.0012743509141728282,
0.013117309659719467,
-0.02110065333545208,
0.021330377086997032,
-0.02302238531410694,
-0.012455903925001621,
0.033007241785526276,
0.03922554850578308,
-0.04000229015946388,
-0.013405515812337399,
-0.033328909426927567,
0.035848017781972885,
0.006672091782093048,
-0.05434858053922653,
0.03286813199520111,
0.04448889568448067,
0.02705450728535652,
-0.011048581451177597,
-0.011010578833520412,
0.004767134319990873,
-0.000056345110351685435,
0.008733933791518211,
0.017261961475014687,
0.012532409280538559,
-0.010774082504212856,
0.006586242467164993,
-0.018243560567498207,
0.01974915713071823,
-0.01312056090682745,
0.001960419351235032,
0.03051558881998062,
-0.02247433178126812,
0.0512569323182106,
0.003934841603040695,
-0.04785800725221634,
0.03920700401067734,
0.06516425311565399,
0.033585965633392334,
-0.027681389823555946,
-0.024831965565681458,
-0.003990148194134235,
-0.053771913051605225,
-0.002622653730213642,
-0.021003641188144684,
0.003209579037502408,
0.02023768238723278,
0.03611832112073898,
0.04648321494460106,
0.01860075443983078,
-0.014095338992774487,
-0.02954820729792118,
-0.09645642340183258,
-0.025448115542531013,
-0.08269324898719788,
-0.005440020468086004,
0.006617739796638489,
-0.022515837103128433,
-0.03497469052672386,
-0.01368714775890112,
0.011832877062261105,
0.0033939883578568697,
-0.012828802689909935,
-0.0646895319223404,
0.004911992233246565,
-0.005237880162894726,
-0.019393978640437126,
-0.01258949376642704,
0.026418844237923622,
0.02725045382976532,
0.020562350749969482,
0.01879865862429142,
0.046126291155815125,
0.0010397072182968259,
-0.02380620874464512,
0.011206996627151966,
0.01179931964725256,
-0.0024623365607112646,
0.043278422206640244,
-0.006372766103595495,
0.019208092242479324,
-0.03865831717848778,
-0.003305010497570038,
0.06256038695573807,
0.05887733772397041,
-0.0061210752464830875,
0.006250528618693352,
-0.018629200756549835,
-0.011288076639175415,
0.026409974321722984,
-0.0016772992676123977,
0.04367285221815109,
-0.017153235152363777,
0.002423759549856186,
0.03247959539294243,
0.029173284769058228,
-0.006002312060445547,
0.053872544318437576,
0.07311787456274033,
-0.002963428385555744,
-0.05122119188308716,
-0.022987062111496925,
-0.013284408487379551,
-0.03336191177368164,
0.013688266277313232,
0.029208676889538765,
0.018312236294150352,
-0.02431846782565117,
0.01622246764600277,
0.01762126199901104,
-0.005772339645773172,
-0.06378158926963806,
0.00010323029709979892,
-0.009916083887219429,
0.009212655946612358,
-0.02500341832637787,
-0.013747124001383781,
0.012040846049785614,
0.01745194010436535,
0.05056900531053543,
0.005004752427339554,
0.009768576361238956,
-0.05268636718392372,
-0.009867948479950428,
0.0214302409440279,
0.0170731283724308,
0.03565780073404312,
0.01704462058842182,
-0.07895051687955856,
-0.018732264637947083,
0.05179928243160248,
-0.02509218454360962,
0.013093754649162292,
-0.03061528317630291,
0.014692549593746662,
0.0011851424351334572,
-0.011416032910346985,
-0.005776061676442623,
-0.012826496735215187,
-0.0013140069786459208,
0.01951734907925129,
-0.006139236502349377,
0.014340009540319443,
-0.03477310761809349,
-0.0016379161970689893,
0.019441112875938416,
0.025681907311081886,
0.033176008611917496,
0.03455604985356331,
-0.020512208342552185,
0.009345127269625664,
-0.059739042073488235,
-0.05853132903575897,
0.010311951860785484,
-0.012532344087958336,
-0.01931552216410637,
0.027337543666362762,
-0.03469584882259369,
-0.02858729474246502,
0.03868947550654411,
0.01778402179479599,
0.006800022441893816,
0.008029825054109097,
-0.02864808216691017,
0.030978789553046227,
-0.009602850303053856,
-0.03094494715332985,
0.061813950538635254,
0.026211300864815712,
-0.016630757600069046,
0.015035826712846756,
-0.0394146665930748,
0.037504952400922775,
-0.047295790165662766,
0.001922385417856276,
-0.03534992039203644,
-0.013265654444694519,
-0.032995522022247314,
0.050563789904117584,
-0.013820790685713291,
0.017115412279963493,
0.0026760089676827192,
-0.03500402718782425,
0.006285561714321375,
0.021521974354982376,
0.015375002287328243,
-0.005997144617140293,
-0.027453254908323288,
-0.008416795171797276,
0.012165052816271782,
-0.02645142935216427,
0.02750656008720398,
0.034129366278648376,
0.0009587862878106534,
0.015940655022859573,
0.0023096308577805758,
0.039030905812978745,
0.011524154804646969,
-0.021806450560688972,
0.039120230823755264,
-0.022634383291006088,
0.0320606492459774,
-0.017103975638747215,
-0.0228787399828434,
0.014937574975192547,
-0.0726187527179718,
-0.015692319720983505,
-0.043707773089408875,
-0.03730050474405289,
0.04563850536942482,
-0.03769930079579353,
0.05098138377070427,
0.006203793920576572,
0.023314213380217552,
-0.0739348977804184,
-0.03531235456466675,
0.04258783906698227,
0.032815538346767426,
0.009492503479123116,
-0.004879923537373543,
0.013404252007603645,
-0.07798267155885696,
0.0122444499284029,
-0.018452491611242294,
0.043998170644044876,
0.006200735457241535,
-0.010243785567581654,
0.02390800230205059,
0.0160316601395607,
0.017556920647621155,
0.005427297204732895,
-0.03347772732377052,
0.0012748388107866049,
0.004287355113774538,
0.007822253741323948,
-0.010609823279082775,
0.03517540171742439,
-0.048157162964344025,
-0.025014543905854225,
-0.002679292345419526,
-0.01560994517058134,
-0.010568899102509022,
-0.04813024029135704,
-0.01418949943035841,
0.039640363305807114,
-0.014307131059467793,
0.010060192085802555,
-0.014844855293631554,
0.007286001928150654,
-0.016022544354200363,
0.005900339689105749,
-0.012398145161569118,
-0.039000872522592545,
-0.005952219013124704,
-0.02662017196416855,
0.02830774523317814,
-0.017291290685534477,
-0.02532755583524704,
0.015654049813747406,
0.05883936211466789,
0.0231338981539011,
-0.03371746838092804,
0.027951939031481743,
-0.04632435739040375,
-0.013041638769209385,
-0.018259873613715172,
-0.012142796069383621,
0.038428641855716705,
0.044510617852211,
-0.007550397887825966,
-0.03128094971179962,
-0.015668075531721115,
0.004081800114363432,
0.029529383406043053,
-0.0013923298101872206,
0.03023955598473549,
0.018466372042894363,
-0.06721451878547668,
-0.0005661196773871779,
-0.026462361216545105,
-0.04276787117123604,
0.03695792332291603,
0.004332893993705511,
0.029990117996931076,
-0.04448471590876579,
0.0035610098857432604,
0.022223521023988724,
-0.005861146375536919,
-0.00965940672904253,
0.021120797842741013,
0.038909584283828735,
0.0015729464357718825,
-0.013910127803683281,
-0.02683398313820362,
-0.024202238768339157,
0.030019473284482956,
-0.03132691979408264,
0.01811923272907734,
0.00026701815659180284,
-0.014192722737789154,
-0.0025640579406172037,
-0.00624596793204546,
0.00205998751334846,
-0.007180347107350826,
-0.030732911080121994,
-0.02090434357523918,
-0.015110395848751068,
0.051237404346466064,
0.04752194136381149,
-0.008193280547857285,
0.007743890397250652,
-0.0007534218020737171,
0.009753384627401829,
-0.024116702377796173,
0.0362253375351429,
-0.03617619350552559,
-0.025177225470542908,
-0.05823437497019768,
-0.04816051200032234,
0.035216573625802994,
-0.022128110751509666,
-0.03638884797692299,
0.022999310865998268,
-0.03606512024998665,
0.013886221684515476,
0.03662089258432388,
0.01810668595135212,
-0.02944936975836754,
0.04840782284736633,
0.0015591949922963977,
0.000022576656192541122,
-0.020460769534111023,
0.016423098742961884,
0.1298726201057434,
0.0719079002737999,
-0.0016254429938271642,
-0.03593023493885994,
0.0481172576546669,
-0.01446794718503952,
-0.00490537891164422,
-0.05646204948425293,
0.018155910074710846,
-0.0425359383225441,
0.006836067419499159,
0.022744091227650642,
0.06387604027986526,
-0.004347862210124731,
-0.031914230436086655,
0.05292227491736412,
-0.005559984128922224,
-0.05351375415921211,
0.0015497746644541621,
0.045468952506780624,
0.011696487665176392,
0.013119660317897797,
-0.022987795993685722,
0.012071559205651283,
-0.028163684532046318,
0.02247658185660839,
-0.043553922325372696,
-0.022545812651515007,
-0.0018411361379548907,
0.028570374473929405,
-0.08607970923185349,
0.006929753813892603,
0.04873044043779373,
0.0015577550511807203,
-0.042306430637836456,
-0.03858007863163948,
0.030851401388645172,
-0.01808875985443592,
0.009345831349492073,
0.05261877551674843,
-0.0045735943131148815,
0.015589616261422634,
-0.02730882354080677,
0.02062792330980301,
-0.05288520082831383,
-0.008557114750146866,
0.007650092244148254,
0.02974322810769081,
-0.02316792495548725,
0.007929322309792042,
-0.004157370422035456,
0.003323348006233573,
-0.00891780573874712,
-0.05339751020073891,
-0.013765358366072178,
0.005967105273157358,
0.0218623336404562,
-0.02889416553080082,
-0.03635292127728462,
0.009946050122380257,
-0.016369914636015892,
-0.012598060071468353,
0.04704797640442848,
-0.02059285342693329,
0.013094361871480942,
0.03673871234059334,
-0.012599186971783638,
0.007529720198363066,
-0.04179905354976654,
0.019388752058148384,
-0.02611459046602249,
-0.01936899870634079,
-0.066822849214077,
-0.01030865591019392,
0.024270404130220413,
0.061394769698381424,
0.023007575422525406,
0.009456305764615536,
-0.020259030163288116,
-0.023231154307723045,
-0.04048876091837883,
0.023148812353610992,
-0.022440031170845032,
-0.011732219718396664,
-0.011029056273400784,
0.01545546855777502,
0.0061868117190897465,
0.027837863191962242,
-0.04353099316358566,
-0.008155802264809608,
-0.027580033987760544,
-0.003561627585440874,
0.03152397647500038,
-0.010859861969947815,
0.022882839664816856,
-0.013612917624413967,
-0.04469885304570198,
-0.0053209178149700165,
-0.038625821471214294,
-0.002327958820387721,
0.0369160920381546,
-0.028819775208830833,
0.035244595259428024,
0.04633018746972084,
-0.006233708001673222,
0.008503908291459084,
0.031951408833265305,
-0.036326609551906586,
-0.004168959800153971,
0.00841008871793747,
0.06054797023534775,
-0.04819798469543457,
-0.05047807842493057,
-0.0316903255879879,
0.03447089344263077,
0.0033154375851154327,
0.015479324385523796,
-0.018515128642320633,
0.019380291923880577,
-0.012549404054880142,
-0.0016153303440660238,
-0.028161436319351196,
-0.020022112876176834,
-0.028576483950018883,
0.0065355258993804455,
0.0130988834425807,
0.007060847245156765,
0.012363442219793797,
0.02389608882367611,
-0.025442590937018394,
-0.045290108770132065,
0.006893422920256853,
0.0019129315624013543,
-0.05445091053843498,
-0.019893361255526543,
0.02027236856520176,
0.035924289375543594,
0.041797347366809845,
-0.022039927542209625,
-0.004057943820953369,
0.006728392094373703,
-0.05434846878051758,
-0.053867410868406296,
0.07392410933971405,
-0.03498353436589241,
0.019784172996878624,
0.032318856567144394,
0.014780089259147644,
-0.049534838646650314,
0.09161529690027237,
-0.057533763349056244,
-0.0016960985958576202,
0.01164634432643652,
-0.028577199205756187,
0.03947252407670021,
-0.026155048981308937,
-0.006804632022976875,
-0.006293196231126785,
-0.03652661293745041,
0.009105760604143143,
0.00721349660307169,
0.015210200101137161,
-0.03490326926112175,
0.018320396542549133,
-0.006950449664145708,
0.0030851059127599,
-0.008849181234836578,
-0.014322656206786633,
-0.0008541680872440338,
0.05504628270864487,
-0.06502833962440491,
0.03769213333725929,
0.06434421241283417,
0.0013574585318565369,
-0.13370491564273834,
-0.008599836379289627,
-0.019963545724749565,
0.02857516147196293,
0.05965128168463707,
-0.045670703053474426,
0.0059987339191138744,
-0.002884901827201247,
-0.0873912125825882,
0.023373043164610863,
-0.01668185368180275,
-0.039388008415699005,
-0.002091712784022093,
-0.01693798415362835,
0.004872780293226242,
0.03732089698314667,
0.044326603412628174,
0.08823131769895554,
0.020397869870066643,
0.004138851538300514,
-0.023480666801333427,
-0.005965107120573521,
-0.01733229123055935,
0.0356813445687294,
-0.020446887239813805,
0.04231476038694382,
0.055706724524497986,
-0.028609665110707283,
-0.029561106115579605,
0.049669813364744186,
0.01698860339820385,
0.04226889833807945,
-0.002565230941399932,
-0.015441348776221275,
0.015965474769473076,
0.023473529145121574,
0.03787342086434364,
-0.021885881200432777,
-0.006962025072425604,
0.025250617414712906,
-0.02172328718006611,
0.0066933161579072475,
0.04905252903699875,
-0.018988056108355522,
0.023384854197502136,
-0.05592744052410126,
0.02123638615012169,
0.020818041637539864,
-0.0047571114264428616,
0.04433346912264824,
0.0041991714388132095,
-0.015266528353095055,
-0.0041880221106112,
-0.019065918400883675,
-0.0006757420487701893,
-0.0316808745265007,
-0.030043400824069977,
0.007234229240566492,
-0.003064812859520316,
-0.008874225430190563,
0.035275477916002274,
0.02417863719165325,
-0.02539997734129429,
0.008883324451744556,
-0.009857149794697762,
-0.014485389925539494,
-0.029977811500430107,
-0.0035132584162056446,
0.0014664912596344948,
0.008490136824548244,
0.04543382674455643,
-0.029994744807481766,
-0.04603322595357895,
0.041530266404151917,
0.02556340955197811,
0.03590582683682442,
0.005396681372076273,
-0.06471116095781326,
-0.011218423955142498,
-0.05327630043029785,
-0.01644398644566536,
0.023720188066363335,
0.009704926051199436,
-0.019997859373688698,
-0.0074597313068807125,
0.0004418523167259991,
-0.017203843221068382,
0.035066790878772736,
-0.0036822764668613672,
-0.00758766382932663,
-0.020111626014113426,
0.021864965558052063,
0.01729145646095276,
-0.05771942064166069,
-0.0014293940039351583,
0.008120836690068245,
-0.03719191625714302,
0.0031721931882202625,
-0.027609476819634438,
-0.00040077781886793673,
-0.0007212694617919624,
-0.006734360009431839,
0.0028303060680627823,
0.01607193611562252,
0.016205254942178726,
-0.04848003387451172,
0.06291941553354263,
0.02263030968606472,
0.0011499663814902306,
0.06460157781839371,
0.02269546501338482,
-0.000126409693621099,
0.044351086020469666,
0.03606543689966202,
-0.030907699838280678,
0.00157168076839298,
-0.011077341623604298,
-0.019698143005371094,
0.003753627184778452,
0.005798435769975185,
0.003167359624058008,
-0.007087907753884792,
0.008430161513388157,
0.06987986713647842,
0.020259158685803413,
-0.010043525137007236,
0.046837832778692245,
-0.01014192495495081,
0.05732443928718567,
-0.015939975157380104,
-0.01588660664856434,
0.04747649282217026,
0.011157942935824394,
-0.001414212747476995,
0.04298039898276329,
0.04973919689655304,
0.02056535892188549,
0.0032733692787587643,
0.02636178396642208,
0.009562700055539608,
0.003240630030632019,
-0.020967820659279823,
0.013524184934794903,
-0.08077041804790497,
-0.03490147739648819,
0.024866674095392227,
-0.03724953904747963,
0.024442218244075775,
0.0373375341296196,
-0.02841169945895672,
0.07801654189825058,
-0.009191373363137245,
0.017812807112932205,
-0.017336774617433548,
0.005207058507949114,
-0.04531719535589218,
0.033039651811122894,
0.002699485281482339,
0.03036443330347538,
-0.038510534912347794,
-0.004197895061224699,
-0.03664786368608475,
0.012632109224796295,
0.014375980012118816,
-0.040820974856615067,
-0.03357740119099617,
0.008625920861959457,
0.010996274650096893,
0.005621127784252167,
0.04110223054885864,
-0.016330858692526817,
-0.02382507361471653,
0.050621964037418365,
0.051749441772699356,
0.02535388059914112,
-0.037453826516866684,
0.017388559877872467,
-0.014724561013281345,
0.06758876144886017,
-0.04243629798293114,
-0.0034978645853698254,
-0.007136525586247444,
0.046041592955589294,
-0.01067043375223875,
-0.008091106079518795
] |
<p>The media are reporting the commercially sold 128-bit quantum computer from D-Wave</p>
<blockquote>
<p><a href="http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n">http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n</a></p>
</blockquote>
<p>which of course sounds amazing. The gadget is described as something capable of doing quantum annealing</p>
<blockquote>
<p><a href="http://en.wikipedia.org/wiki/Quantum_annealing">http://en.wikipedia.org/wiki/Quantum_annealing</a></p>
</blockquote>
<p>which looks less convincing. I want to ask you what classes of problems the D-Wave computer can actually solve or perform. It can't run Shor's algorithm on 128 qubits, can it?</p> | 528 | [
-0.02277962863445282,
-0.02796584740281105,
-0.019475780427455902,
-0.048332300037145615,
0.06362759321928024,
-0.004644614178687334,
-0.033810023218393326,
-0.038819149136543274,
0.02236926183104515,
-0.025986772030591965,
0.03368503227829933,
0.02742360718548298,
0.006550596095621586,
0.028162194415926933,
-0.005932588595896959,
0.02310549095273018,
0.003630325896665454,
-0.050197139382362366,
-0.031890418380498886,
-0.021946502849459648,
0.0030114855617284775,
0.03267701342701912,
-0.0038664950989186764,
-0.013458914123475552,
0.006463978905230761,
0.011929809115827084,
-0.011690746061503887,
-0.03675239160656929,
-0.0052795871160924435,
0.05608430877327919,
-0.006606285460293293,
-0.03129592537879944,
0.029275286942720413,
0.004004513379186392,
0.016833117231726646,
0.0035908943973481655,
-0.013596541248261929,
-0.016100475564599037,
0.012842816300690174,
0.010108839720487595,
-0.04501589015126228,
0.00397460674867034,
-0.020351547747850418,
0.03997693583369255,
-0.03412255644798279,
0.033991940319538116,
0.006089744158089161,
-0.0719958022236824,
0.013718510046601295,
-0.05950827896595001,
0.056628067046403885,
-0.015525059774518013,
0.020028313621878624,
-0.016221003606915474,
0.020053042098879814,
-0.020442061126232147,
0.08180733025074005,
0.07276535034179688,
-0.01832754537463188,
-0.03550564870238304,
-0.003498395439237356,
0.02052350714802742,
0.011724797077476978,
-0.0038440232165157795,
-0.04891479015350342,
0.01982177421450615,
0.013787416741251945,
0.003955947235226631,
0.0018576522124931216,
-0.019009491428732872,
0.02878114953637123,
0.04005977511405945,
0.034233611077070236,
0.036346565932035446,
0.029064081609249115,
-0.024860922247171402,
-0.0071172453463077545,
0.02078058570623398,
-0.02745652012526989,
0.02125106193125248,
-0.02156047150492668,
-0.013522401452064514,
-0.018802277743816376,
0.031528785824775696,
-0.002544399816542864,
-0.01918174885213375,
0.06338178366422653,
-0.013681689277291298,
-0.013339463621377945,
0.015054341405630112,
0.010899119079113007,
0.012581146322190762,
0.05833158642053604,
-0.0070030223578214645,
-0.05997655168175697,
0.03275439143180847,
0.03164267539978027,
0.02471598982810974,
-0.031217707321047783,
-0.034383486956357956,
-0.00836299080401659,
-0.0029225978069007397,
0.029172955080866814,
0.06968614459037781,
0.0025696498341858387,
0.017666393890976906,
-0.006007819902151823,
0.04553664103150368,
-0.03251336142420769,
0.001036026980727911,
-0.06463854759931564,
0.018225563690066338,
-0.0017795012099668384,
0.014196273870766163,
0.025287000462412834,
-0.025064531713724136,
-0.004604069050401449,
-0.014509898610413074,
0.025107573717832565,
0.04804825410246849,
0.008473176509141922,
-0.05025021359324455,
0.008322254754602909,
-0.05590085685253143,
-0.10141715407371521,
0.030319374054670334,
0.03421981632709503,
-0.03626178950071335,
-0.04179432988166809,
0.04464785382151604,
-0.026075318455696106,
-0.0032005775719881058,
0.005136396270245314,
-0.006852493621408939,
0.009501663967967033,
-0.012350144796073437,
-0.11569713801145554,
-0.0730118378996849,
0.050497766584157944,
0.011126655153930187,
-0.006833305582404137,
-0.08491341769695282,
-0.007612310349941254,
0.03218938410282135,
0.05511333793401718,
-0.011449558660387993,
0.04174359515309334,
0.014209072105586529,
0.041910264641046524,
0.030314063653349876,
-0.013005848973989487,
0.026664311066269875,
0.01483896654099226,
-0.009418747387826443,
-0.012862760573625565,
-0.047921229153871536,
0.024509206414222717,
0.034423377364873886,
-0.018794747069478035,
-0.043590862303972244,
0.01308736763894558,
-0.009753036312758923,
-0.01869863085448742,
-0.013481014408171177,
-0.01998838037252426,
0.00021159528114367276,
0.0734899714589119,
-0.011207019910216331,
0.020756376907229424,
0.026626771315932274,
-0.04392656311392784,
0.01723385788500309,
0.02071359194815159,
0.008683966472744942,
0.0497511625289917,
-0.03603389114141464,
0.005549314431846142,
-0.028451820835471153,
-0.0015581509796902537,
-0.029392223805189133,
0.004191468469798565,
-0.03371066972613335,
0.012594610452651978,
0.04654789716005325,
-0.018956080079078674,
0.039348017424345016,
0.004773931577801704,
0.016964852809906006,
0.03332354873418808,
-0.04019499197602272,
-0.024704786017537117,
-0.05403788760304451,
0.02787969261407852,
0.018342522904276848,
0.01705228164792061,
0.02190358377993107,
-0.018508778885006905,
0.01649429462850094,
-0.006744920276105404,
-0.049439508467912674,
0.012623056769371033,
0.031460244208574295,
0.032764315605163574,
0.013950030319392681,
0.02219121903181076,
0.10066743195056915,
-0.0013166232965886593,
-0.03893190994858742,
0.03960311785340309,
-0.051182352006435394,
-0.012746245600283146,
-0.024442221969366074,
-0.00045747446711175144,
-0.0022739730775356293,
0.023217571899294853,
-0.027739878743886948,
0.010184142738580704,
0.009465084411203861,
-0.030317511409521103,
0.010257051326334476,
-0.03811383619904518,
0.0827355682849884,
0.026877230033278465,
-0.006711716763675213,
-0.004137085750699043,
0.01774541661143303,
0.04443885385990143,
0.016533954069018364,
0.013567989692091942,
-0.006016672123223543,
-0.01781008020043373,
0.0007319719297811389,
0.04450370743870735,
0.012428481131792068,
-0.034118592739105225,
0.033378716558218,
0.008773601613938808,
0.014262450858950615,
0.03757714107632637,
0.00229777698405087,
-0.04642292484641075,
0.034575216472148895,
0.044910505414009094,
0.016547825187444687,
-0.02016630209982395,
-0.00021279499924276024,
0.020584343001246452,
0.019144607707858086,
-0.027387214824557304,
-0.013844749890267849,
-0.011547799222171307,
0.059071388095617294,
-0.03947089612483978,
-0.003328209277242422,
-0.012617596425116062,
-0.04144204035401344,
0.020269660279154778,
-0.019147373735904694,
-0.003575913142412901,
0.032598115503787994,
-0.002238152315840125,
-0.0158845204859972,
0.008044961839914322,
-0.08119368553161621,
0.015661219134926796,
0.021120768040418625,
-0.021709347143769264,
-0.03974872827529907,
0.04531165212392807,
-0.060460761189460754,
0.01682448945939541,
-0.044176287949085236,
0.015437132678925991,
-0.044087570160627365,
0.021914469078183174,
0.013529077172279358,
-0.007110221311450005,
0.0323575884103775,
-0.05090818926692009,
-0.02571595087647438,
0.030341878533363342,
-0.03303263708949089,
0.015371288172900677,
0.02611192688345909,
-0.07899375259876251,
0.022466076537966728,
-0.0058651636354625225,
-0.031110994517803192,
0.017003731802105904,
-0.011966105550527573,
-0.010599492117762566,
-0.004611949436366558,
-0.022560350596904755,
-0.03160311281681061,
-0.007215754594653845,
-0.03755738586187363,
0.061871353536844254,
-0.063400037586689,
-0.01669570803642273,
0.00033557164715602994,
-0.0022837643045932055,
-0.0018413387006148696,
0.0340687558054924,
0.008689913898706436,
-0.010721453465521336,
0.004413899499922991,
-0.02473342977464199,
0.01279823575168848,
-0.022039437666535378,
0.010615929961204529,
0.02151176519691944,
-0.029639922082424164,
0.03416338935494423,
-0.06573719531297684,
-0.08104606717824936,
0.03777378425002098,
-0.020456966012716293,
0.03698870167136192,
0.020317351445555687,
-0.004587316885590553,
0.08498459309339523,
0.027042241767048836,
-0.06777727603912354,
-0.013393310829997063,
0.007506114896386862,
0.0038566538132727146,
-0.03634146973490715,
0.015205330215394497,
0.07715506106615067,
-0.03292848914861679,
0.031048743054270744,
-0.014407191425561905,
0.024584675207734108,
0.042881887406110764,
0.00473254406824708,
-0.03720567002892494,
0.0343068465590477,
-0.0112324059009552,
0.0243870560079813,
0.06963901221752167,
0.02144499309360981,
-0.02736653946340084,
0.021209632977843285,
-0.002173423068597913,
0.030326317995786667,
0.03406532481312752,
-0.021173512563109398,
0.03858020529150963,
0.003298789029940963,
0.024339813739061356,
-0.027341194450855255,
0.023977449163794518,
0.02219841070473194,
0.008068273775279522,
0.02809237129986286,
0.007910293526947498,
0.03202704340219498,
-0.01193851325660944,
0.04952745884656906,
0.01408425159752369,
0.040586717426776886,
-0.01047966256737709,
-0.0007021845085546374,
-0.0007774934056214988,
-0.02859647572040558,
0.043908391147851944,
-0.01498574111610651,
-0.04222644120454788,
0.03550877794623375,
-0.04062287136912346,
0.03551957756280899,
0.011060792952775955,
-0.017491772770881653,
0.02173573710024357,
-0.04137716442346573,
0.005221353378146887,
-0.026044856756925583,
0.06172633171081543,
0.016647815704345703,
0.021782981231808662,
0.012298248708248138,
-0.021456997841596603,
-0.004775687120854855,
-0.006715021561831236,
-0.08562378585338593,
-0.014893312007188797,
-0.037386100739240646,
-0.0014281063340604305,
0.002729032887145877,
-0.025389883667230606,
0.044597234576940536,
-0.017420513555407524,
-0.04773363098502159,
-0.009393228217959404,
0.008558549918234348,
-0.04093345254659653,
0.014459517784416676,
-0.0201492290943861,
-0.013151520863175392,
-0.005156867206096649,
-0.022326821461319923,
0.0004967147251591086,
-0.005955953150987625,
-0.007078809197992086,
0.029407428577542305,
-0.04749147966504097,
-0.01016256120055914,
0.028911398723721504,
0.01847926527261734,
0.003659007837995887,
0.023832546547055244,
0.02043260633945465,
0.06490175426006317,
-0.024426493793725967,
-0.0011764419032260776,
0.013826712965965271,
0.06857229024171829,
-0.04515992850065231,
-0.01958664506673813,
-0.012374996207654476,
-0.052200306206941605,
-0.013782824389636517,
-0.012273721396923065,
0.05749842897057533,
-0.007002011872828007,
0.02844303287565708,
0.049538835883140564,
0.014499720185995102,
-0.024365713819861412,
0.02570509910583496,
0.05632658675312996,
-0.030135834589600563,
0.00608025910332799,
-0.00621945783495903,
-0.03441091999411583,
-0.02760378271341324,
-0.015846312046051025,
0.021074406802654266,
-0.010185317136347294,
0.02275092341005802,
0.03387697413563728,
0.029828203842043877,
-0.0012932518729940057,
-0.01943022571504116,
-0.007656170520931482,
0.017555056139826775,
-0.001423920039087534,
-0.028090352192521095,
0.018110699951648712,
0.006799738854169846,
0.018967129290103912,
0.01751982793211937,
-0.0030220448970794678,
-0.019147047773003578,
-0.07056426256895065,
0.0002785780525300652,
0.0655909851193428,
0.06443726271390915,
0.023213179782032967,
0.027043679729104042,
-0.04140852391719818,
0.006647160742431879,
0.017421716824173927,
-0.028303395956754684,
0.048025742173194885,
0.016958540305495262,
-0.05773868039250374,
-0.026435857638716698,
-0.00010340297740185633,
0.05869107320904732,
-0.008825491182506084,
0.013569307513535023,
0.016481423750519753,
-0.021390512585639954,
-0.006233441177755594,
-0.01135214138776064,
-0.01577848196029663,
0.036374229937791824,
0.04810677468776703,
-0.024579836055636406,
0.010984394699335098,
0.00525636924430728,
0.008854237385094166,
-0.03938242793083191,
-0.08186446875333786,
-0.002014464931562543,
0.0041984086856245995,
-0.07172571867704391,
0.07086338102817535,
-0.021435050293803215,
-0.03730253130197525,
0.05343518778681755,
0.00197122641839087,
-0.00048493375652469695,
-0.0036595913115888834,
-0.02218359336256981,
0.037652045488357544,
0.013478980399668217,
0.015701953321695328,
0.025241823866963387,
0.05122246965765953,
-0.021481990814208984,
0.017159098759293556,
0.015613498166203499,
0.050691209733486176,
-0.0383579358458519,
0.008068262599408627,
-0.007752577308565378,
0.0021214301232248545,
-0.03861327841877937,
0.00617297412827611,
-0.011265434324741364,
0.007115115877240896,
-0.053536515682935715,
0.00540879787877202,
-0.03193219006061554,
0.009495723992586136,
-0.029827313497662544,
0.002130411798134446,
-0.002366237575188279,
0.023541633039712906,
0.017500149086117744,
-0.012664146721363068,
-0.00866613071411848,
-0.03139001131057739,
0.018474185839295387,
0.022710373625159264,
-0.019797801971435547,
0.0041101849637925625,
-0.07879114896059036,
0.004837599582970142,
0.030758513137698174,
-0.05169260501861572,
0.04161199554800987,
-0.025388700887560844,
0.016800109297037125,
0.031175939366221428,
-0.05145739018917084,
-0.01824110373854637,
-0.0025966023094952106,
0.018175141885876656,
-0.013818379491567612,
-0.009529883041977882,
0.02739023044705391,
-0.02617434598505497,
0.01015439908951521,
-0.059974852949380875,
-0.03782478719949722,
0.01987225003540516,
0.02458658441901207,
-0.015314313583076,
0.0026069595478475094,
0.03201058879494667,
-0.023884832859039307,
-0.011934145353734493,
-0.02864363230764866,
-0.003163359360769391,
-0.02340826764702797,
0.024027099832892418,
0.048651475459337234,
0.04140413925051689,
0.04807915538549423,
-0.0002878225641325116,
-0.023527229204773903,
0.005273774266242981,
-0.02588532119989395,
0.0021224881056696177,
0.006929152179509401,
0.004176197573542595,
-0.06694246828556061,
-0.02369980700314045,
-0.0012566009536385536,
0.006891491822898388,
0.000729652470909059,
0.006169664207845926,
0.005715622566640377,
-0.004523041658103466,
0.016101868823170662,
-0.012415881268680096,
0.006302586290985346,
-0.009957295842468739,
0.0024193301796913147,
0.02641344629228115,
0.01240381971001625,
0.008303637616336346,
0.002774243475869298,
-0.02117258496582508,
0.019774526357650757,
0.01970796473324299,
-0.017498932778835297,
0.04769216850399971,
0.09022828191518784,
-0.0028008059598505497,
-0.012003741227090359,
0.02267659455537796,
-0.03752266988158226,
-0.00485517643392086,
-0.006546456832438707,
0.050935544073581696,
-0.02637920156121254,
0.021300531923770905,
-0.009233387187123299,
-0.07586146146059036,
-0.022664064541459084,
0.002033142140135169,
0.06311323493719101,
-0.006129149813205004,
0.0431220605969429,
0.018091456964612007,
0.0007362416363321245,
-0.019545376300811768,
-0.0420551523566246,
0.0016156650381162763,
0.03907525911927223,
-0.02333282306790352,
-0.003219905076548457,
-0.006154852453619242,
-0.006711124908179045,
-0.001949820201843977,
0.026477733626961708,
0.023261966183781624,
0.017614461481571198,
0.03970370814204216,
0.02067071758210659,
-0.003497103927657008,
-0.05294976383447647,
-0.033069197088479996,
0.05198116973042488,
-0.08238496631383896,
0.04288465902209282,
0.0006830843631178141,
0.014646200463175774,
0.0771060660481453,
-0.019457761198282242,
-0.0023138711694628,
-0.050951022654771805,
-0.010099313221871853,
-0.08585909008979797,
0.022115599364042282,
0.024231290444731712,
-0.021598761901259422,
-0.011250220239162445,
-0.034702181816101074,
0.020495928823947906,
0.016584154218435287,
-0.00039769234717823565,
-0.019484642893075943,
-0.05297857150435448,
-0.031304068863391876,
-0.008970406837761402,
-0.06046920642256737,
0.045748110860586166,
0.03728359192609787,
-0.027877194806933403,
0.0008830217411741614,
-0.03636685386300087,
0.09457193315029144,
0.027996093034744263,
0.0052104233764112,
-0.028151951730251312,
0.05260360613465309,
0.0015354366041719913,
0.04344563186168671,
-0.0058895801194012165,
-0.027171732857823372,
0.1214742586016655,
0.04583887383341789,
0.029362307861447334,
-0.09573732316493988,
0.007974404841661453,
-0.009701934643089771,
0.054339561611413956,
0.004936907906085253,
-0.03958211466670036,
0.03606203570961952,
0.02084587700664997,
-0.010119646787643433,
0.04485642910003662,
0.03879455476999283,
0.024338021874427795,
-0.00481827836483717,
-0.06921542435884476,
-0.05320720002055168,
0.010794847272336483,
0.023927057161927223,
0.004347800277173519,
-0.003637786954641342,
-0.016008708626031876,
-0.02016119658946991,
-0.03984897956252098,
-0.026077477261424065,
-0.03228394314646721,
-0.043759822845458984,
0.03758874535560608,
0.05192979425191879,
-0.028521886095404625,
-0.02118775062263012,
-0.047019220888614655,
0.004246197175234556,
0.0002526436001062393,
0.015407951548695564,
0.00019543252710718662,
-0.008459160104393959,
-0.0015127378283068538,
0.06062230095267296,
0.051116883754730225,
-0.013222855515778065,
0.008983572013676167,
0.02695300616323948,
-0.016759634017944336,
0.009199781343340874,
0.0077039506286382675,
0.0255439430475235,
-0.05729304999113083,
-0.026139311492443085,
-0.0019084005616605282,
-0.03734622150659561,
-0.010786350816488266,
-0.06391222029924393,
-0.02566138282418251,
0.02018073946237564,
0.013112516142427921,
0.006465699523687363,
0.01565755344927311,
-0.008449617773294449,
0.03184320405125618,
0.011466517113149166,
0.028381571173667908,
0.0023686622735112906,
-0.006346580106765032,
-0.00021002223365940154,
-0.018117764964699745,
0.02821316570043564,
0.001178221427835524,
-0.013390906155109406,
-0.04952982813119888,
0.007787087932229042,
-0.03261867165565491,
-0.025940820574760437,
-0.0036349177826195955,
0.012670785188674927,
0.03432272747159004,
-0.0026423572562634945,
0.012869877740740776,
-0.012281781993806362,
-0.023158887401223183,
0.011958864517509937,
0.009680302813649178,
-0.004795617423951626,
-0.023398157209157944,
-0.027483748272061348,
0.03176048398017883,
0.010436112992465496,
-0.02543370984494686,
0.028916174545884132,
0.02923205867409706,
0.014833181165158749,
0.013021140359342098,
-0.010940688662230968,
-0.005992457270622253,
-0.014711820520460606,
-0.04170090705156326,
0.004628980997949839,
-0.007574907504022121,
0.03659651428461075,
0.004055018071085215,
-0.002701156074181199,
-0.019602425396442413,
0.050690848380327225,
-0.02622544951736927,
-0.015625903382897377,
-0.0030658612959086895,
-0.023028044030070305,
0.0023295350838452578,
0.00573656614869833,
0.011019384488463402,
-0.021344805136322975,
-0.04763210564851761,
-0.03977931663393974,
-0.020565755665302277,
-0.012741249054670334,
0.02006249874830246,
-0.0556645393371582,
-0.014267700724303722,
0.004730409011244774,
0.024684568867087364,
-0.022109612822532654,
-0.00676953699439764,
-0.007556779310107231,
0.004047095309942961,
-0.03249786049127579,
-0.0050457678735256195,
0.00911035481840372,
0.011686760000884533,
0.011170605197548866,
0.001714978483505547,
0.014376744627952576,
0.06448756158351898,
-0.035416509956121445,
0.008095189929008484,
-0.002201700583100319,
0.017745669931173325,
0.004274448379874229,
-0.03725401684641838,
-0.021573800593614578,
0.06427834182977676,
-0.04933324083685875,
-0.007861997000873089,
0.05319344624876976,
-0.034828972071409225,
-0.018751999363303185,
0.025630729272961617,
-0.00671784020960331,
0.0035665056202560663,
0.021477842703461647,
-0.0012609971454367042,
-0.0073043787851929665,
0.011922229081392288,
-0.03992735967040062,
0.0269074235111475,
0.0008716545416973531,
-0.03144209086894989,
-0.01682920753955841,
-0.04037681967020035,
0.025030503049492836,
0.0710105374455452,
0.009385489858686924,
0.0024427848402410746,
-0.015961555764079094,
0.025981811806559563,
0.032587628811597824,
0.033361513167619705,
-0.00625544972717762,
-0.0026132005732506514,
0.03386732190847397,
0.013582950457930565,
0.039269451051950455,
-0.002345981542021036,
-0.008664469234645367,
-0.07189785689115524,
0.0022538481280207634,
0.03899162635207176,
-0.0060366918332874775,
0.018704185262322426,
-0.05853545293211937,
0.013341092504560947,
0.02631489746272564,
-0.10833266377449036,
0.062417276203632355,
-0.02320123463869095,
0.003472724696621299,
-0.04780574515461922,
0.020733831450343132,
-0.039258360862731934,
0.02699541486799717,
-0.010678383521735668,
0.04751873016357422,
0.031024105846881866,
-0.004527756478637457,
-0.01656152866780758,
-0.02724546380341053,
0.02072341926395893,
0.03907014802098274,
-0.009851312264800072,
0.010134968906641006,
0.0400097481906414,
-0.05030468478798866,
-0.04321683570742607,
0.018577788025140762,
0.004576913081109524,
0.02495099976658821,
-0.00025038779131136835,
0.0035128507297486067,
0.010065725073218346,
0.0399693064391613,
0.028958739712834358,
-0.014627075754106045,
0.0070542809553444386,
-0.0011297205928713083,
0.04235859215259552,
0.06149067357182503,
0.012362557463347912,
0.009517200291156769,
-0.011611513793468475,
-0.029840361326932907,
-0.04193931445479393,
0.034638214856386185,
0.005662058014422655,
0.027544422075152397,
0.002951245289295912,
0.005862504243850708,
0.007972660474479198,
-0.009947284124791622,
0.008958685211837292,
-0.03373286873102188,
0.02018565870821476,
0.013489468954503536,
-0.005074325017631054,
0.005534302443265915,
0.0026692545507103205,
-0.0444984957575798,
-0.020683808252215385,
0.04155045747756958,
-0.003404207993298769,
0.0032228378113359213,
-0.009886756539344788,
0.010291574522852898,
0.01583842560648918,
0.03691432997584343,
0.027640778571367264,
-0.01797841303050518,
-0.021328598260879517,
0.022563926875591278,
-0.026468919590115547,
0.03860171511769295,
0.008319873362779617,
-0.0001778116711648181,
-0.0036917151883244514,
-0.0721944123506546,
0.051926471292972565,
-0.004350070841610432,
0.017051244154572487,
-0.015757838264107704,
0.010107060894370079,
0.004740846808999777,
0.02619759552180767,
0.04438851773738861,
0.0052617453038692474,
-0.00023250016965903342,
0.008855870924890041,
-0.04047860950231552,
0.04117107763886452,
-0.006021369248628616,
0.02296827733516693,
-0.01571655087172985,
0.019800016656517982,
-0.029994944110512733,
0.002222021110355854,
-0.040356483310461044,
0.014082861132919788,
0.052301403135061264,
0.023361943662166595,
-0.022674717009067535,
0.0003952699189539999,
-0.00953371450304985,
0.04190392047166824,
-0.02179362066090107,
0.009625624865293503,
0.04925915226340294,
-0.00304708955809474,
0.0019703449215739965,
0.013170669786632061,
-0.009068620391190052,
-0.033328667283058167,
0.026044968515634537,
-0.026671964675188065,
-0.024933405220508575,
0.007377259898930788,
-0.005969947669655085,
0.061220932751894,
-0.03438182547688484,
-0.0351075641810894,
0.008329974487423897,
0.005543179344385862,
-0.013457302935421467,
0.01443537138402462,
0.008388864807784557,
0.021563880145549774,
-0.03994967043399811,
0.026838788762688637,
0.016650516539812088,
-0.020937461405992508,
-0.020613711327314377,
0.035920239984989166,
0.03764522448182106,
-0.011870346032083035,
0.021421238780021667,
0.06807056069374084,
-0.015172423794865608,
0.025274911895394325,
0.03413908928632736,
0.03158477321267128,
-0.02378750406205654,
-0.027871055528521538,
0.05799657851457596,
-0.017272071912884712,
-0.040270473808050156,
0.023191135376691818,
-0.039754968136548996,
0.03643247112631798,
-0.021387360990047455,
-0.0007289345376193523,
-0.0491332970559597,
-0.006464605685323477,
-0.023688293993473053,
-0.01797553151845932,
-0.004307687282562256,
0.059713128954172134,
-0.04841107875108719,
-0.028311865404248238,
-0.040858782827854156,
0.03195251151919365,
-0.014023863710463047,
-0.03734569996595383,
-0.006524176336824894,
-0.06299582868814468,
0.004752511624246836,
0.0158290546387434,
0.009604289196431637,
-0.02656053751707077,
0.0036715304013341665,
0.02513384260237217,
0.024985304102301598,
-0.028638780117034912,
0.00874157715588808,
0.007695137057453394,
0.005821108352392912,
0.061031144112348557,
-0.03333456441760063,
-0.013312799856066704,
-0.04267551004886627,
0.0016235364601016045,
-0.00625484948977828,
0.003591762622818351
] |
<p>String theory - for example - requires extra spatial dimension. Say for example in 10 dimensional string theory, what theoretically prevents clustering of the extra 6 dimensions in 2 timeless 3 dimensional (infinite) spaces? </p> | 4,609 | [
-0.01584334298968315,
-0.014243713580071926,
-0.01659843698143959,
-0.06394993513822556,
0.030233772471547127,
0.00337815098464489,
-0.029277538880705833,
-0.013060650788247585,
-0.013130992650985718,
-0.03592618927359581,
0.019329700618982315,
0.0072316620498895645,
0.030020279809832573,
0.006506122648715973,
0.014112974517047405,
0.0069237640127539635,
-0.0005578062846325338,
-0.00959271751344204,
-0.004693659022450447,
-0.018789151683449745,
0.002358247060328722,
0.03191068395972252,
0.006758480332791805,
0.012284326367080212,
-0.021701617166399956,
0.03652361035346985,
0.04912828654050827,
0.029993776232004166,
0.03733774647116661,
0.061118364334106445,
0.005137789994478226,
-0.021474894136190414,
0.039561204612255096,
0.051607560366392136,
0.0033714845776557922,
-0.049603722989559174,
-0.020350420847535133,
-0.027149472385644913,
-0.015665089711546898,
0.0002589756331872195,
-0.05958595871925354,
0.004334356635808945,
-0.014583876356482506,
0.060542766004800797,
-0.012789498083293438,
0.0444435179233551,
-0.015785621479153633,
-0.03547556698322296,
0.05458923056721687,
-0.043043848127126694,
0.05360798537731171,
-0.0003642774827312678,
0.01792588271200657,
0.007911148481070995,
0.003113015554845333,
0.005279933102428913,
0.09003369510173798,
0.06748601794242859,
0.001242478028871119,
-0.051227767020463943,
-0.06152060627937317,
-0.0032702600583434105,
0.017455877736210823,
-0.025870680809020996,
-0.029837051406502724,
0.042437970638275146,
-0.018965015187859535,
0.008132917806506157,
0.009802923537790775,
-0.015058129094541073,
-0.002437352668493986,
0.01283703651279211,
0.04758680239319801,
-0.03133198618888855,
0.018696432933211327,
0.001712813158519566,
0.006103035528212786,
0.012103901244699955,
0.057408321648836136,
0.027187852188944817,
-0.0002883131382986903,
-0.0014884306583553553,
0.02955430932343006,
0.011206082068383694,
0.013231970369815826,
-0.003270515939220786,
0.0641210749745369,
-0.036003921180963516,
-0.016231078654527664,
0.08614243566989899,
-0.03746446967124939,
-0.008355475962162018,
0.0645466074347496,
0.011935991235077381,
-0.03560727834701538,
0.0424644760787487,
0.0098977480083704,
0.06662324070930481,
-0.010976923629641533,
0.003699380671605468,
-0.008894684724509716,
-0.017914334312081337,
0.0012828330509364605,
0.05558855086565018,
0.015012995339930058,
-0.02824726514518261,
-0.03998202458024025,
0.013213086873292923,
-0.024510463699698448,
0.012396812438964844,
-0.013880627229809761,
0.006788209546357393,
0.005766171030700207,
0.002775581320747733,
0.050690487027168274,
-0.02068585343658924,
0.02016635611653328,
-0.02355719543993473,
0.03411726653575897,
0.09662918001413345,
0.02505076304078102,
-0.03622741252183914,
0.02074289880692959,
-0.014140347950160503,
-0.0766419768333435,
-0.007541855797171593,
0.036237675696611404,
-0.011828543618321419,
-0.02509426511824131,
0.013382266275584698,
0.011774777434766293,
-0.0015741587849333882,
0.028675230219960213,
-0.005312393885105848,
0.08853276818990707,
0.013899589888751507,
-0.10428283363580704,
-0.028727881610393524,
0.05441584438085556,
-0.014939258806407452,
-0.033084481954574585,
-0.05657165125012398,
0.014616756699979305,
-0.0005169612122699618,
0.08627874404191971,
-0.0016480524791404605,
0.0038138497620821,
0.009759727865457535,
0.023524707183241844,
-0.011433725245296955,
-0.03806144371628761,
-0.028540484607219696,
0.0031713161151856184,
-0.034335747361183167,
0.012419949285686016,
-0.061248477548360825,
0.013145897537469864,
0.025273827835917473,
-0.007353396154940128,
-0.03642700985074043,
0.03512321785092354,
-0.04172191768884659,
0.002093685558065772,
-0.011790362186729908,
-0.012208756990730762,
-0.02005618065595627,
0.05091782659292221,
0.008896508254110813,
-0.009836952202022076,
0.033923350274562836,
-0.007197091821581125,
0.020874647423624992,
0.030580246821045876,
0.057993222028017044,
0.020756598562002182,
0.00577907869592309,
-0.02396625280380249,
0.0022332603111863136,
0.00519527355208993,
0.016646595671772957,
-0.04595772922039032,
-0.025967968627810478,
0.02019520476460457,
0.018929945304989815,
-0.01176977064460516,
0.011457689106464386,
-0.03450559824705124,
-0.008538688533008099,
-0.020220017060637474,
-0.03598419576883316,
-0.017395129427313805,
-0.05728277191519737,
0.008499200455844402,
0.03333764523267746,
-0.018552301451563835,
0.013183651491999626,
-0.00797000527381897,
0.019435429945588112,
-0.05203404650092125,
-0.05713803693652153,
-0.04435324668884277,
0.02023768052458763,
0.01289190910756588,
-0.016021935269236565,
0.017927125096321106,
0.038531918078660965,
0.06125032901763916,
0.002495977794751525,
0.03822913020849228,
0.014586814679205418,
-0.03388938680291176,
-0.018194565549492836,
-0.015779271721839905,
0.024769293144345284,
-0.0397891141474247,
-0.009523710235953331,
0.026366928592324257,
-0.01096933614462614,
-0.03926321491599083,
0.04373069107532501,
0.013010092079639435,
0.0802001878619194,
0.03301779180765152,
0.009584566578269005,
-0.02789071947336197,
0.020224498584866524,
-0.010338962078094482,
-0.0023417791817337275,
-0.0022445048671215773,
-0.06315571069717407,
-0.06004258245229721,
-0.020211556926369667,
0.01516755297780037,
0.053254760801792145,
-0.037401169538497925,
0.046257443726062775,
0.012273591943085194,
0.062217459082603455,
-0.011302503757178783,
0.030557747930288315,
-0.04302234575152397,
-0.015470500104129314,
0.023536788299679756,
-0.019921254366636276,
0.029075415804982185,
0.020880619063973427,
0.04955010488629341,
0.02932133711874485,
-0.026972513645887375,
-0.011972208507359028,
-0.003316932823508978,
0.024220680817961693,
-0.008336642757058144,
-0.010889365337789059,
0.03323876112699509,
0.0028328518383204937,
0.006724504288285971,
-0.02844458632171154,
0.028916504234075546,
0.02339625544846058,
0.030651090666651726,
-0.015174704603850842,
-0.033063363283872604,
-0.021429752930998802,
-0.005573825910687447,
0.04090820252895355,
-0.02156582847237587,
0.012450468726456165,
0.017629407346248627,
-0.017630381509661674,
-0.026712840422987938,
-0.014018489047884941,
-0.0017013020114973187,
-0.027744680643081665,
-0.009438581764698029,
0.07011861354112625,
-0.01314056571573019,
0.05547263100743294,
-0.007012392394244671,
-0.034908149391412735,
-0.020099472254514694,
-0.012635880149900913,
-0.018303148448467255,
-0.019812680780887604,
-0.027432329952716827,
0.04017915949225426,
-0.008568155579268932,
-0.017677372321486473,
0.019800890237092972,
-0.015979137271642685,
0.03795456141233444,
-0.009927814826369286,
-0.01395316980779171,
-0.022934021428227425,
-0.0037365418393164873,
-0.008572586812078953,
0.036329977214336395,
-0.008037733845412731,
0.016503531485795975,
0.06477818638086319,
0.008907582610845566,
-0.04860419034957886,
0.01700483448803425,
-0.04664277657866478,
-0.03212747350335121,
-0.027980685234069824,
0.006882334593683481,
0.007057552225887775,
-0.06775091588497162,
0.029512766748666763,
0.013904214836657047,
-0.06573138386011124,
0.025485582649707794,
-0.025405187159776688,
-0.058185938745737076,
0.0013153755571693182,
-0.015738697722554207,
0.033423054963350296,
-0.018097586929798126,
-0.05004492029547691,
0.04770806059241295,
0.012680799700319767,
-0.029685117304325104,
-0.008651144802570343,
-0.021138695999979973,
-0.004795968998223543,
-0.032755035907030106,
0.039164669811725616,
0.01765313185751438,
-0.00036894145887345076,
-0.0007617320516146719,
0.07370726764202118,
0.03278132528066635,
0.030183259397745132,
-0.021201694384217262,
-0.04378843680024147,
0.000142541088280268,
0.031440023332834244,
0.014048914425075054,
0.01165869552642107,
0.01423716638237238,
-0.0372832827270031,
0.0009545914945192635,
0.0046985214576125145,
0.02476184256374836,
-0.0004498999333009124,
-0.039594464004039764,
0.014894435182213783,
-0.0033680337946861982,
0.04417600482702255,
-0.004515852779150009,
0.022630607709288597,
-0.015654418617486954,
-0.029378844425082207,
0.03945792093873024,
0.008868376724421978,
0.045579999685287476,
-0.0028160361107438803,
0.003064841963350773,
0.00926824938505888,
0.0631292387843132,
-0.011421353556215763,
-0.019288064911961555,
-0.0018845851300284266,
0.019451366737484932,
0.029788797721266747,
-0.011629602871835232,
-0.03279484808444977,
0.03636854514479637,
0.0373227596282959,
0.0005400822847150266,
-0.014876026660203934,
-0.011278826743364334,
-0.007567502558231354,
-0.06505914777517319,
0.017472371459007263,
-0.001760509330779314,
0.04690159857273102,
-0.01854444481432438,
0.0012475023977458477,
0.03150804713368416,
-0.0003285135608166456,
0.004248764365911484,
0.010450663976371288,
-0.06962569802999496,
-0.023836825042963028,
-0.05700934678316116,
0.0007870863773860037,
0.0013106872793287039,
0.022480573505163193,
0.001462495536543429,
-0.018239974975585938,
-0.018324783071875572,
0.008736955001950264,
-0.014161476865410805,
-0.073821522295475,
-0.005196792539209127,
-0.03903200477361679,
0.01583312824368477,
-0.02400643192231655,
0.03604969009757042,
0.04662935435771942,
-0.0018457751721143723,
0.033957310020923615,
0.03449906036257744,
-0.03551377356052399,
-0.005344245117157698,
0.011093433946371078,
0.014182052575051785,
0.009253138676285744,
0.022105827927589417,
0.022249141708016396,
0.015941090881824493,
-0.02693115547299385,
-0.011981386691331863,
0.009405004791915417,
0.020355723798274994,
-0.01092591043561697,
0.019950784742832184,
-0.02237057313323021,
-0.03575754910707474,
-0.007763736415654421,
-0.010413240641355515,
0.0434546023607254,
-0.012713639065623283,
0.009969125501811504,
0.030610429123044014,
0.02619168348610401,
-0.026422705501317978,
0.021738020703196526,
0.05529754236340523,
0.015802359208464622,
-0.0730007067322731,
-0.005779589060693979,
-0.04891582578420639,
-0.012246453203260899,
-0.02886710874736309,
0.011044325307011604,
-0.022652124986052513,
-0.015392068773508072,
0.040112145245075226,
0.0015155458822846413,
-0.022748468443751335,
-0.036779213696718216,
-0.015987999737262726,
0.007171817123889923,
0.007198627106845379,
-0.012833775021135807,
-0.004907254129648209,
-0.015868479385972023,
0.02413525991141796,
0.06314466148614883,
0.041592665016651154,
-0.005968960002064705,
-0.07125519216060638,
-0.002808388788253069,
0.005873485933989286,
0.046218518167734146,
0.00034075643634423614,
-0.02563590742647648,
-0.05497847869992256,
-0.014890123158693314,
0.024090468883514404,
-0.052041977643966675,
-0.0032742167823016644,
-0.04121560603380203,
-0.013967087492346764,
-0.028864407911896706,
-0.006789426319301128,
-0.006276359781622887,
0.00616574427112937,
0.010475020855665207,
0.03883323073387146,
0.0017852965975180268,
0.01429674681276083,
-0.037517670542001724,
0.026947397738695145,
0.011994434520602226,
0.03406937047839165,
0.012519950047135353,
0.030559390783309937,
0.004485025070607662,
0.03902241587638855,
-0.020080866292119026,
-0.0737709030508995,
0.018261173740029335,
0.03223055973649025,
-0.01910209283232689,
0.043991804122924805,
-0.049306709319353104,
-0.03289543092250824,
-0.009122115559875965,
0.014418914914131165,
-0.0007266594911925495,
0.02020343765616417,
0.010975252836942673,
0.0448373407125473,
0.040942270308732986,
0.013728332705795765,
0.02271221950650215,
0.0032390195410698652,
0.012093723751604557,
-0.0020247932989150286,
-0.04488648474216461,
0.025193018838763237,
-0.03636808320879936,
0.03638484328985214,
-0.026414692401885986,
0.00013811343524139374,
-0.05761454254388809,
0.04242623969912529,
-0.046218451112508774,
-0.016178447753190994,
0.025146303698420525,
-0.03282855451107025,
-0.0041531408205628395,
0.04021204262971878,
0.025407051667571068,
-0.011713818646967411,
0.006336689926683903,
0.030609963461756706,
-0.02571139857172966,
-0.004262575879693031,
0.024377046152949333,
-0.0018305329140275717,
-0.02822379767894745,
0.021951949223876,
0.008949619717895985,
0.017424389719963074,
-0.008419044315814972,
0.004116630181670189,
0.02437739074230194,
-0.01993379183113575,
0.04238159582018852,
-0.020438581705093384,
0.0037040894385427237,
0.009068479761481285,
-0.046016424894332886,
-0.02269819565117359,
-0.03826291486620903,
-0.03891516849398613,
0.040447451174259186,
-0.024653153494000435,
0.050964441150426865,
-0.004165150690823793,
0.008032283745706081,
-0.07956061512231827,
-0.043425798416137695,
0.012017729692161083,
0.04457425698637962,
0.010033839382231236,
-0.06215618550777435,
0.0053262668661773205,
-0.052730824798345566,
-0.03642416000366211,
-0.03628832474350929,
0.06323244422674179,
-0.016577009111642838,
-0.030902152881026268,
0.019296200945973396,
0.054257381707429886,
0.028833825141191483,
-0.005420845467597246,
-0.011583398096263409,
0.006755562499165535,
0.009056448936462402,
0.036505017429590225,
-0.01624741405248642,
0.03440234065055847,
-0.035369955003261566,
-0.025120684877038002,
-0.013345053419470787,
-0.01676030270755291,
0.01150425337255001,
-0.06227139011025429,
-0.0021078085992485285,
0.012921452522277832,
0.027310078963637352,
0.025662291795015335,
-0.029673252254724503,
0.03410574793815613,
-0.022684896364808083,
0.009758511558175087,
-0.024154243990778923,
0.0014492057962343097,
-0.029951339587569237,
-0.03750528022646904,
0.04379785805940628,
0.007859699428081512,
-0.03264376148581505,
-0.0029778729658573866,
0.032937902957201004,
0.031116023659706116,
-0.01802356168627739,
0.029203366488218307,
-0.031002305448055267,
0.018213806673884392,
-0.016354087740182877,
0.0003240267396904528,
0.03096998669207096,
0.015827981755137444,
-0.023934300988912582,
-0.060606248676776886,
0.0008979483391158283,
0.028761250898241997,
0.03359903022646904,
-0.055981576442718506,
0.07257027924060822,
0.02610551379621029,
-0.021030496805906296,
-0.02136143110692501,
-0.026749175041913986,
0.001464993110857904,
0.013703547418117523,
0.011883029714226723,
0.03660930320620537,
-0.00025116244796663523,
0.03212163597345352,
0.03512880578637123,
0.05904541164636612,
-0.023565106093883514,
0.051136843860149384,
0.050742924213409424,
0.023918472230434418,
0.0069711762480437756,
-0.04599025100469589,
-0.04178829863667488,
0.05872168391942978,
-0.04766615107655525,
0.011045105755329132,
0.019893581047654152,
-0.006029072217643261,
0.012281731702387333,
0.004607234615832567,
0.007665091194212437,
-0.010403180494904518,
-0.059185829013586044,
-0.03034212626516819,
-0.007091850973665714,
0.03152000159025192,
0.03421267494559288,
0.012251421809196472,
-0.0017444584518671036,
0.016774481162428856,
0.02075314335525036,
-0.0227478239685297,
0.015947250649333,
-0.07255084067583084,
-0.057923197746276855,
-0.04638907313346863,
-0.03059850074350834,
0.04234664887189865,
0.03812295198440552,
-0.0476883128285408,
0.009714903309941292,
-0.034122444689273834,
0.026455149054527283,
0.004192562773823738,
0.053794339299201965,
-0.032312456518411636,
0.03868431597948074,
0.03221341595053673,
0.03201364353299141,
-0.037637416273355484,
0.04074791446328163,
0.09580106288194656,
0.0547017939388752,
0.0233819130808115,
-0.08614305406808853,
0.02618798241019249,
-0.019633827731013298,
-0.011594045907258987,
-0.04904844984412193,
0.025265561416745186,
0.019796432927250862,
0.018544422462582588,
0.011982519179582596,
0.08386868238449097,
0.004708833992481232,
-0.017497625201940536,
0.07663974910974503,
-0.05958636477589607,
-0.05366908013820648,
-0.018703879788517952,
-0.0026521715335547924,
0.033875033259391785,
0.003859905758872628,
-0.06720942258834839,
0.013819567859172821,
0.012675263918936253,
0.012576794251799583,
-0.009372827596962452,
-0.004374917596578598,
0.030057162046432495,
0.01109202578663826,
-0.029886744916439056,
-0.021646782755851746,
0.0152958445250988,
-0.011829163879156113,
-0.05942169949412346,
-0.02170015498995781,
0.016046110540628433,
-0.013886906206607819,
0.00895956251770258,
0.008432854898273945,
0.007826668210327625,
0.043924007564783096,
-0.017333917319774628,
0.01091436855494976,
-0.04135230556130409,
-0.045459114015102386,
-0.0012317883083596826,
0.04621962457895279,
-0.025218619033694267,
-0.00473822234198451,
0.02745830826461315,
0.017951812595129013,
0.0128182889893651,
-0.019931843504309654,
-0.033942483365535736,
0.010912984609603882,
0.026128355413675308,
-0.0007755890837870538,
-0.007187583018094301,
-0.013573472388088703,
0.026103993877768517,
-0.011233005672693253,
0.03275882825255394,
-0.02350122481584549,
0.027994945645332336,
0.023062964901328087,
-0.024300863966345787,
0.01159142516553402,
-0.024055521935224533,
-0.0036291591823101044,
-0.060784317553043365,
0.00629915576428175,
-0.01590736024081707,
0.012027526274323463,
0.005041381344199181,
0.04398490861058235,
0.019357142969965935,
-0.006030551623553038,
0.01319064386188984,
0.013921533711254597,
0.014627535827457905,
0.024893682450056076,
-0.03938446566462517,
-0.022458761930465698,
-0.004656506236642599,
0.01759839616715908,
0.014987434260547161,
0.03627949580550194,
-0.00023540192341897637,
0.00473400903865695,
-0.04479340836405754,
-0.015818053856492043,
0.019541848450899124,
0.0036312886513769627,
-0.006835184060037136,
-0.01589345559477806,
-0.04309222102165222,
-0.0010496509494259953,
0.005307168234139681,
0.021715160459280014,
0.015413773246109486,
-0.040795788168907166,
0.04300151392817497,
0.04821569845080376,
-0.030993428081274033,
0.011490225791931152,
0.027514168992638588,
-0.0463983416557312,
0.00031984495581127703,
0.011787650175392628,
0.020639412105083466,
-0.036265403032302856,
-0.036115095019340515,
-0.0010539855575188994,
-0.008348673582077026,
0.024039611220359802,
0.02973688580095768,
-0.036461833864450455,
0.005249678622931242,
0.014477656222879887,
0.011046607047319412,
-0.049106162041425705,
0.011965841986238956,
-0.045304059982299805,
0.010968996211886406,
-0.0255819670855999,
-0.030378056690096855,
-0.010222206823527813,
-0.012629609555006027,
-0.030255332589149475,
-0.019917035475373268,
0.009705428034067154,
0.0044408924877643585,
-0.008176632225513458,
0.0008914946811273694,
-0.005713301245123148,
0.001322819385677576,
0.04380365461111069,
-0.029385140165686607,
-0.0458819642663002,
0.022513799369335175,
-0.06731542199850082,
-0.06107478216290474,
0.0397254042327404,
-0.04704538360238075,
0.02142323926091194,
0.04262199625372887,
-0.01579667627811432,
-0.03137650713324547,
0.05026441439986229,
-0.022760527208447456,
-0.04520730674266815,
0.024371782317757607,
-0.009392037987709045,
-0.007742290385067463,
-0.004406175576150417,
-0.0013407747028395534,
-0.03639579936861992,
-0.025639746338129044,
0.002978377975523472,
0.048209477216005325,
0.018987957388162613,
-0.05550198256969452,
0.005839423276484013,
0.021992074325680733,
0.04712053760886192,
0.0056435721926391125,
-0.0006644868990406394,
-0.015309643000364304,
0.05888138711452484,
-0.05270720273256302,
0.031892627477645874,
0.039275895804166794,
-0.001346467062830925,
-0.08555524796247482,
-0.018437331542372704,
0.017116380855441093,
0.0050372290425002575,
0.02311006560921669,
-0.04437511786818504,
-0.0138301532715559,
0.007539122365415096,
-0.09368253499269485,
0.07230047881603241,
-0.039026349782943726,
-0.02243930473923683,
-0.04256364703178406,
-0.01524133700877428,
-0.011169699020683765,
0.05070725455880165,
0.0663030594587326,
0.06327261030673981,
-0.032030005007982254,
0.002167740371078253,
-0.010056894272565842,
-0.015828102827072144,
-0.004792629275470972,
0.0033849389292299747,
-0.040017735213041306,
0.007230299990624189,
0.05676775798201561,
-0.02334810420870781,
-0.026011478155851364,
0.02591399848461151,
-0.003233811119571328,
-0.0011430049780756235,
0.046278711408376694,
-0.007240750826895237,
-0.011631937697529793,
-0.010688943788409233,
0.018923146650195122,
-0.017072731629014015,
0.013534614816308022,
0.019228819757699966,
0.01764497719705105,
-0.01285762432962656,
0.010972118936479092,
0.004284518305212259,
-0.010365523397922516,
-0.016640450805425644,
0.025110621005296707,
0.01782824471592903,
-0.02404298447072506,
0.017050066962838173,
0.015272739343345165,
0.03704475983977318,
0.02218024432659149,
-0.009079348295927048,
-0.03642088174819946,
-0.03582381084561348,
-0.025050457566976547,
0.010329730808734894,
0.029638197273015976,
0.000857472128700465,
0.03833425045013428,
-0.032600872218608856,
-0.030254382640123367,
0.004007147625088692,
0.019489727914333344,
0.009244650602340698,
-0.03313366696238518,
-0.013388196006417274,
0.009127269499003887,
0.015476787462830544,
0.02088121883571148,
-0.052712582051754,
0.0010810637613758445,
0.055812034755945206,
0.013434089720249176,
0.038832299411296844,
0.006276164203882217,
-0.062404781579971313,
0.0020782561041414738,
-0.061438266187906265,
0.03687485307455063,
-0.0221305750310421,
0.024653377011418343,
-0.053639158606529236,
-0.01067569199949503,
-0.03433738276362419,
0.05475218966603279,
0.06613147258758545,
0.002986566862091422,
-0.00872957706451416,
0.00369932409375906,
0.022945841774344444,
0.0035643531009554863,
-0.03263430669903755,
-0.005987830925732851,
0.013191472738981247,
-0.02988344430923462,
-0.03514304384589195,
-0.03282908722758293,
0.007103686220943928,
0.0012295112246647477,
0.040570009499788284,
-0.0035254713147878647,
0.027164658531546593,
0.006063540931791067,
-0.030077416449785233,
0.038823578506708145,
0.0016878371825441718,
0.01636500656604767,
0.04410909116268158,
-0.01601836457848549,
0.00127640541177243,
0.007220350671559572,
-0.0118866590783,
0.008915349841117859,
0.034509237855672836,
-0.03306825831532478,
0.009456302039325237,
-0.002474322449415922,
-0.004979399498552084,
0.017805611714720726,
-0.021651722490787506,
-0.012777285650372505,
0.06178460270166397,
-0.004145542159676552,
-0.025149419903755188,
0.050574954599142075,
0.03287922590970993,
0.05166834592819214,
-0.02349011041224003,
-0.0004589043965097517,
0.024431612342596054,
0.04736042022705078,
0.012975878082215786,
0.039444562047719955,
0.03303084895014763,
0.015178005211055279,
0.03628925234079361,
0.0049323346465826035,
-0.004981159698218107,
0.011610934510827065,
-0.01252429373562336,
0.06764019280672073,
-0.05063936114311218,
-0.02205699123442173,
0.007708058692514896,
-0.046905647963285446,
0.03288936987519264,
-0.0026880991645157337,
-0.001209681504406035,
0.08564183861017227,
-0.0029343408532440662,
0.01989702135324478,
0.009932675398886204,
-0.01367175579071045,
-0.032771266996860504,
-0.004539129789918661,
-0.00918674748390913,
0.053572602570056915,
-0.017934132367372513,
-0.012635166756808758,
-0.042731355875730515,
0.022920390591025352,
0.022070711478590965,
-0.017144788056612015,
0.011279400438070297,
-0.009228323586285114,
-0.021115535870194435,
0.023986386135220528,
-0.018533632159233093,
-0.02268616296350956,
-0.03772293031215668,
0.031527791172266006,
0.050850749015808105,
0.04329060763120651,
-0.015973255038261414,
-0.00954507663846016,
-0.02840074896812439,
0.028221184387803078,
-0.06854082643985748,
-0.04502377659082413,
-0.03574708104133606,
0.023377541452646255,
-0.0550248809158802,
0.013079076074063778
] |
<p>Some time far into the future, humans have made the technology breakthroughs to construct decoherence-proof reversible quantum computers with quantum fault tolerance. They have also solved the hard AI problem. They program a quantum conscious being on such a computer and also a two state quantum system. The quantum conscious being is programmed to entangle with the quantum system, measuring it. The rules of the Copenhagen interpretation tell us the state of the quantum system happened. The programmers reverse the program, undoing the measurement, with all the memory wiped clean. Did the quantum system unhappen?</p> | 4,610 | [
-0.00817963108420372,
-0.014989476650953293,
0.01321940403431654,
-0.026006808504462242,
0.03420725092291832,
-0.017056848853826523,
-0.013396329246461391,
-0.03191375732421875,
-0.016289571300148964,
-0.0037526178639382124,
0.021187221631407738,
0.05558659881353378,
0.0006892152014188468,
0.038059432059526443,
-0.01138080283999443,
-0.04100408777594566,
0.03244848549365997,
-0.02972579374909401,
-0.0006627217517234385,
-0.010513986460864544,
0.03239167109131813,
0.011597007513046265,
0.00030998550937511027,
0.017472855746746063,
-0.015162976458668709,
0.010814969427883625,
0.01810402050614357,
-0.026750272139906883,
0.0162863377481699,
0.0474335253238678,
0.0015008815098553896,
-0.03784205764532089,
-0.011766573414206505,
-0.011625215411186218,
0.015635542571544647,
-0.02777188830077648,
0.00421292195096612,
-0.0319114550948143,
0.024822430685162544,
-0.01641876809298992,
0.020189816132187843,
-0.008603861555457115,
-0.006420038640499115,
0.09305603057146072,
-0.028328293934464455,
-0.02164592407643795,
-0.011067072860896587,
-0.0009699768270365894,
-0.0005445596762001514,
-0.05491001158952713,
0.038500066846609116,
-0.00011958307004533708,
0.024954698979854584,
-0.01714925840497017,
-0.010908360593020916,
-0.00772802485153079,
0.0526302307844162,
0.07442671805620193,
0.0240009818226099,
-0.05595238134264946,
-0.013550539501011372,
-0.006223632488399744,
-0.023251594975590706,
0.018921803683042526,
-0.010492985136806965,
0.0031527269165962934,
-0.031097814440727234,
-0.03860383853316307,
0.031724922358989716,
-0.013286466710269451,
0.024219701066613197,
0.0070208837278187275,
0.061375852674245834,
0.004011484328657389,
0.041873522102832794,
0.002403357531875372,
0.028972245752811432,
-0.003182733664289117,
-0.029269009828567505,
0.019311517477035522,
0.012200301513075829,
0.005331413354724646,
0.048539843410253525,
0.048013098537921906,
-0.0005370358121581376,
-0.00908928643912077,
0.0587739422917366,
-0.03826889395713806,
0.006434261333197355,
0.058817148208618164,
0.033616118133068085,
0.01018496509641409,
0.02383088320493698,
-0.009419179521501064,
-0.02373049035668373,
0.0036546937189996243,
-0.0009817349491640925,
0.07739698141813278,
0.016315476968884468,
0.0112442122772336,
0.01564696989953518,
-0.0015490048099309206,
0.027160732075572014,
0.036913979798555374,
0.0056966328993439674,
-0.0055313087068498135,
-0.0011351979337632656,
0.04677265137434006,
-0.007936290465295315,
-0.005837087985128164,
-0.07453295588493347,
0.023080164566636086,
0.011585966683924198,
-0.004101338796317577,
0.027584610506892204,
0.008713925257325172,
-0.02277633547782898,
-0.040595658123493195,
0.04934209585189819,
0.0403444841504097,
0.008020920678973198,
0.009019315242767334,
0.00017713532724883407,
-0.02732803300023079,
-0.01847895048558712,
0.015276786871254444,
0.039240580052137375,
0.005601678509265184,
-0.0457037054002285,
0.02256719395518303,
-0.02320956252515316,
0.003507344052195549,
0.017633771523833275,
0.02116777002811432,
0.06380011141300201,
-0.034967903047800064,
-0.10006588697433472,
-0.07308673858642578,
0.017992764711380005,
-0.006948809139430523,
0.027459243312478065,
-0.07261718809604645,
0.0633222758769989,
0.05010293051600456,
0.10882376879453659,
-0.019393304362893105,
-0.01516824122518301,
0.005338120274245739,
0.00025509012630209327,
0.02725166454911232,
0.0141992112621665,
0.016498412936925888,
-0.022292083129286766,
-0.020868033170700073,
-0.05239754915237427,
-0.07140225172042847,
0.042059820145368576,
0.03658124431967735,
-0.0030762902460992336,
-0.008464747108519077,
0.025043703615665436,
-0.007726671174168587,
-0.001745708053931594,
0.007304378319531679,
-0.04760017246007919,
-0.0642186850309372,
0.0766138881444931,
0.021678706631064415,
-0.0014552901266142726,
0.05552764981985092,
0.002961324527859688,
0.031478315591812134,
0.020244423300027847,
0.008893769234418869,
0.009418519213795662,
-0.05142761394381523,
-0.013964845798909664,
0.002935030497610569,
0.018345747143030167,
-0.015918778255581856,
-0.02092345803976059,
-0.023885652422904968,
-0.015178742818534374,
0.00038888113340362906,
0.03276233375072479,
-0.004523581825196743,
-0.025929108262062073,
-0.03343832492828369,
0.0021175500005483627,
-0.01864539459347725,
-0.05025141313672066,
-0.048890285193920135,
0.026585565879940987,
0.00269063632003963,
0.018062947317957878,
0.022636985406279564,
0.007496772799640894,
0.05580892041325569,
-0.04137715324759483,
-0.03628520667552948,
-0.020336825400590897,
0.003277081297710538,
0.018366975709795952,
0.01632879674434662,
0.03732948377728462,
0.06854233145713806,
0.03766623139381409,
0.013912429101765156,
0.04639824107289314,
-0.0229534562677145,
-0.04715323820710182,
-0.0007031176937744021,
0.006723553873598576,
0.015184633433818817,
-0.018751109018921852,
0.0099314134567976,
0.00714845210313797,
-0.012733718380331993,
-0.02331399731338024,
-0.02683713659644127,
-0.007339552044868469,
0.033176716417074203,
-0.0037683160044252872,
0.01233901921659708,
0.0030857096426188946,
0.033305972814559937,
0.006047029048204422,
-0.036375489085912704,
0.019802676513791084,
-0.020677318796515465,
-0.08183226734399796,
-0.025450147688388824,
-0.03816082701086998,
0.03290903940796852,
-0.013374612666666508,
0.040489889681339264,
0.004699192475527525,
0.0506342388689518,
-0.009377285838127136,
-0.01069970615208149,
-0.06452787667512894,
0.009124492295086384,
0.018812494352459908,
-0.026284953579306602,
0.015372865833342075,
0.005487439222633839,
0.01900624670088291,
0.026034723967313766,
-0.006390709895640612,
-0.020191241055727005,
-0.012886871583759785,
0.02912634238600731,
-0.004204918630421162,
-0.002266014227643609,
-0.013063046149909496,
-0.08098442852497101,
-0.019903799518942833,
0.00899827852845192,
-0.00543645303696394,
0.02392963133752346,
-0.01953417994081974,
-0.0038688385393470526,
-0.06748371571302414,
-0.007375976070761681,
-0.027987975627183914,
0.02112054079771042,
-0.025677470490336418,
-0.015971429646015167,
0.04608512669801712,
0.0003263955295551568,
0.025924736633896828,
-0.0036676276940852404,
0.02864230051636696,
-0.005943662021309137,
0.026990950107574463,
0.005965206306427717,
-0.018136758357286453,
-0.001604585675522685,
-0.004074417985975742,
-0.0332702100276947,
-0.0016905742231756449,
-0.03477045148611069,
0.018460409715771675,
0.014409242197871208,
-0.04342406243085861,
0.02846146933734417,
-0.0036519598215818405,
-0.006614841986447573,
0.023081563413143158,
0.009361542761325836,
0.019663069397211075,
0.028771407902240753,
-0.041789937764406204,
-0.03359580039978027,
-0.026072105392813683,
-0.03613518550992012,
0.0031748879700899124,
-0.006019175983965397,
0.0013609774177893996,
0.027244266122579575,
0.02178354375064373,
-0.01428274903446436,
-0.029001953080296516,
-0.017637919634580612,
-0.012947922572493553,
-0.001239930628798902,
-0.0217710193246603,
0.02753414586186409,
-0.026838740333914757,
0.008049143478274345,
0.02270740270614624,
-0.04513343796133995,
-0.021786348894238472,
-0.051130469888448715,
-0.07513051480054855,
0.03984594717621803,
0.0032264140900224447,
0.03389747068285942,
0.012223162688314915,
0.041167452931404114,
0.04764712229371071,
0.009071511216461658,
-0.012388888746500015,
-0.0007851249538362026,
0.0029304372146725655,
0.02143966220319271,
-0.008959897793829441,
-0.050224240869283676,
0.03156985342502594,
0.009766223840415478,
0.026597153395414352,
-0.030616747215390205,
0.002095163566991687,
0.03261638060212135,
-0.007755683269351721,
-0.02785506285727024,
0.0285082645714283,
0.0321350060403347,
-0.011868595145642757,
0.004632400814443827,
0.009250919334590435,
-0.01729765348136425,
0.02687949500977993,
0.032842475920915604,
0.035766538232564926,
0.018614880740642548,
-0.01645871065557003,
0.0501265786588192,
0.023597627878189087,
0.03404469043016434,
-0.00501658022403717,
0.011848575435578823,
-0.041810326278209686,
-0.001461147447116673,
-0.003673332976177335,
0.010852420702576637,
0.05776987969875336,
-0.009364617057144642,
-0.0012450696667656302,
0.010186676867306232,
0.020832594484090805,
-0.023593798279762268,
-0.05508597567677498,
-0.020019445568323135,
-0.0038908268325030804,
0.008807538077235222,
-0.014784172177314758,
-0.031405311077833176,
0.05464167892932892,
0.021845461800694466,
0.05259960517287254,
0.00871445145457983,
-0.0343221053481102,
-0.04924235865473747,
-0.045643243938684464,
0.015636472031474113,
-0.009353949688374996,
0.02133815921843052,
0.03560736030340195,
0.022869084030389786,
0.025549082085490227,
0.034359484910964966,
-0.03578075394034386,
-0.006002240348607302,
-0.0779462605714798,
-0.006955250632017851,
-0.04148918762803078,
0.028226394206285477,
0.022495044395327568,
0.011073863133788109,
0.03495047241449356,
-0.048916179686784744,
-0.0676269605755806,
0.010352889075875282,
0.002735061338171363,
-0.0690750703215599,
0.0073631261475384235,
-0.026569264009594917,
-0.02283109351992607,
0.007675814907997847,
0.033692773431539536,
0.05309538170695305,
0.0003799555415753275,
0.04066567122936249,
0.044170066714286804,
-0.02637227065861225,
0.0056857578456401825,
0.0024377265945076942,
-0.01563061587512493,
0.0029228872153908014,
0.02707562781870365,
0.027014372870326042,
0.05179937183856964,
-0.012725072912871838,
-0.01444766204804182,
0.018423080444335938,
0.04740246757864952,
-0.016551004722714424,
0.02207062765955925,
-0.020962629467248917,
-0.016054119914770126,
-0.04941633343696594,
0.0074297357350587845,
0.0440802127122879,
0.025477029383182526,
0.04645392671227455,
-0.010820819064974785,
0.04728078097105026,
-0.06466066837310791,
0.027203360572457314,
0.05436034873127937,
-0.014329350553452969,
0.012542977929115295,
-0.012364793568849564,
-0.03983721137046814,
-0.030716875568032265,
-0.016125917434692383,
0.004808005876839161,
-0.014159792102873325,
-0.0008029164746403694,
0.0072134691290557384,
0.04296484217047691,
0.01794615387916565,
-0.04022877290844917,
-0.008146841078996658,
-0.04570630565285683,
-0.002171073341742158,
0.004261350259184837,
0.06129137799143791,
0.019676530733704567,
0.01641058176755905,
0.010900575667619705,
0.0029393290169537067,
-0.006504128221422434,
-0.0648469477891922,
-0.0019277060637250543,
0.04098798334598541,
0.05656212568283081,
0.014457575976848602,
-0.0016158922808244824,
-0.08060649782419205,
-0.0526779405772686,
0.03393762931227684,
-0.012438805773854256,
0.04604777693748474,
0.010132304392755032,
-0.017769915983080864,
-0.035320863127708435,
-0.0014588143676519394,
0.04356313496828079,
0.009530970826745033,
0.029174543917179108,
0.02754322439432144,
0.025971276685595512,
0.007255706936120987,
-0.02332666702568531,
-0.04821497201919556,
0.004216237459331751,
0.036560460925102234,
0.013541384600102901,
0.015474453568458557,
-0.04697984829545021,
-0.002033777302131057,
-0.04075330123305321,
-0.07003042846918106,
0.011728442274034023,
-0.02933935448527336,
-0.04955369979143143,
0.06477522104978561,
-0.00730872992426157,
-0.04737824574112892,
-0.009376514703035355,
-0.004641413222998381,
-0.013393591158092022,
0.009370235726237297,
-0.02874494343996048,
0.03401767835021019,
-0.014236673712730408,
-0.013291203416883945,
0.0311511792242527,
-0.001475540571846068,
-0.027985621243715286,
0.008797900751233101,
-0.0328063927590847,
0.02309335768222809,
-0.02328847348690033,
0.059973277151584625,
-0.01556877139955759,
0.002949325367808342,
-0.013885457068681717,
0.0376020111143589,
-0.002955908654257655,
0.018414869904518127,
0.0008442332036793232,
-0.007488881703466177,
-0.009219934232532978,
-0.013831857591867447,
-0.02053300105035305,
0.011413770727813244,
-0.06181119754910469,
-0.014639988541603088,
-0.03751986101269722,
0.0034556719474494457,
-0.016318004578351974,
-0.010566103272140026,
0.024899769574403763,
0.05210231617093086,
-0.0467362180352211,
0.028343016281723976,
-0.017829185351729393,
-0.023568231612443924,
0.009740792214870453,
-0.02766570635139942,
0.014396741054952145,
-0.012078333646059036,
-0.02612796053290367,
0.0056845820508897305,
-0.0415675975382328,
-0.003098055487498641,
0.01059214398264885,
-0.02242458611726761,
-0.03499390184879303,
-0.030193084850907326,
0.045409563928842545,
0.012130510061979294,
0.01892070472240448,
-0.0543079748749733,
-0.0106645617634058,
-0.0028225036803632975,
0.0048715039156377316,
0.011759474873542786,
-0.026242641732096672,
0.012332279235124588,
0.0004568231524899602,
-0.031120222061872482,
-0.0218229778110981,
0.04250557720661163,
-0.0027381812687963247,
-0.002021616790443659,
0.05104489624500275,
0.0016495350282639265,
0.024433452636003494,
-0.02622964046895504,
0.00618088198825717,
-0.027413384988904,
0.0006912280805408955,
-0.01667019911110401,
-0.010614573024213314,
0.012689933180809021,
-0.0018469113856554031,
-0.0566958524286747,
-0.040221139788627625,
0.020653991028666496,
0.008474031463265419,
-0.022443711757659912,
-0.027039749547839165,
0.014526121318340302,
-0.0011657481081783772,
-0.01350527722388506,
-0.02537732571363449,
-0.05526192486286163,
-0.006080883089452982,
0.01696350798010826,
0.008677939884364605,
-0.045543234795331955,
0.004074921831488609,
-0.03319045156240463,
0.051002874970436096,
0.025285955518484116,
-0.03546725586056709,
0.028332265093922615,
0.02280283346772194,
0.005187643226236105,
-0.023958010599017143,
-0.005806954577565193,
-0.04528243839740753,
0.04914145544171333,
0.004955952521413565,
0.0112878093495965,
-0.003171935211867094,
0.005960560403764248,
-0.03704546019434929,
-0.03700360655784607,
-0.04077386483550072,
-0.01282504852861166,
0.045834705233573914,
-0.0142211327329278,
0.02037362940609455,
0.012922549620270729,
0.03104262240231037,
-0.018879452720284462,
-0.015015344135463238,
-0.02070010080933571,
0.05383211746811867,
0.006836096290498972,
-0.006658501457422972,
-0.02440265193581581,
0.018500976264476776,
0.027211423963308334,
0.04082171246409416,
-0.011410916224122047,
0.013276765123009682,
0.014873253181576729,
0.019793935120105743,
0.008262120187282562,
-0.06635305285453796,
-0.012571963481605053,
0.013910947367548943,
-0.0812612920999527,
0.0224916972219944,
0.011755859479308128,
-0.0324522964656353,
0.013638927601277828,
0.02656429447233677,
0.01919472962617874,
-0.043776873499155045,
-0.0037233582697808743,
-0.08299477398395538,
-0.00157423026394099,
0.029140431433916092,
0.03435547277331352,
0.012159397825598717,
0.013961073011159897,
-0.01939086616039276,
0.04331011325120926,
0.0014828230487182736,
-0.011650923639535904,
-0.07879294455051422,
-0.050691332668066025,
-0.036623891443014145,
-0.005175009369850159,
0.05835657939314842,
0.01593141444027424,
0.013214128091931343,
0.04751722142100334,
-0.011126408353447914,
0.06985051184892654,
0.022310029715299606,
0.05615256726741791,
-0.008599524386227131,
0.05467066913843155,
-0.03540576994419098,
0.06685739010572433,
-0.025176366791129112,
0.025913644582033157,
0.11434942483901978,
0.06839223206043243,
-0.001473776763305068,
-0.07749791443347931,
0.03249406814575195,
-0.0034034033305943012,
0.04398312792181969,
0.016887202858924866,
0.008652526885271072,
-0.004269607365131378,
0.016696682199835777,
0.002909763716161251,
0.004062804859131575,
0.058983877301216125,
0.013160246424376965,
0.030045421794056892,
-0.04669402167201042,
-0.07037562876939774,
0.01916651427745819,
0.007304395083338022,
-0.013353069312870502,
-0.013005092740058899,
-0.004785435739904642,
-0.041338562965393066,
-0.024556687101721764,
-0.00960539374500513,
0.027303172275424004,
0.009614254347980022,
-0.008289222605526447,
0.03792795538902283,
-0.0004451487329788506,
0.025713149458169937,
0.002654690993949771,
0.005206220783293247,
0.0033816779032349586,
0.05827973783016205,
-0.0006955034914426506,
-0.004542838782072067,
-0.0070083546452224255,
0.026116298511624336,
0.06724749505519867,
0.003374051535502076,
0.007991928607225418,
0.00996498204767704,
-0.021973177790641785,
0.001371034188196063,
-0.006625514943152666,
0.037643205374479294,
-0.036916136741638184,
-0.046191804111003876,
-0.01214553415775299,
-0.044287342578172684,
0.0009942766046151519,
0.0006334712961688638,
-0.004907265305519104,
0.027795294299721718,
0.016892338171601295,
-0.01775149442255497,
-0.03260330855846405,
0.02212342992424965,
0.00838463194668293,
-0.04461943358182907,
0.045353252440690994,
-0.031797297298908234,
0.0005089254700578749,
0.005072345491498709,
-0.017817718908190727,
0.024189574643969536,
-0.027941562235355377,
0.02094397135078907,
-0.07328806817531586,
0.01947198435664177,
-0.040768928825855255,
-0.06924960017204285,
0.027629023417830467,
0.012468181550502777,
0.03585975617170334,
-0.02334844134747982,
-0.02614375576376915,
-0.051369812339544296,
-0.03807126730680466,
0.049720291048288345,
-0.02988971211016178,
0.01870390586555004,
-0.023607278242707253,
-0.027874235063791275,
0.02213175594806671,
0.010038730688393116,
-0.010774693451821804,
0.0015845601446926594,
0.03400838375091553,
0.007199098821729422,
0.037643011659383774,
-0.026116173714399338,
-0.0004746262857224792,
0.007683256175369024,
-0.05834222584962845,
-0.026588182896375656,
-0.07904759049415588,
0.03244117274880409,
0.026486575603485107,
-0.015150709077715874,
0.0010464196093380451,
0.022145556285977364,
-0.02743126079440117,
-0.013193273916840553,
0.014610725454986095,
-0.03048841655254364,
-0.059928540140390396,
0.012938451021909714,
0.07167671620845795,
-0.02533266693353653,
-0.03377801924943924,
-0.047013118863105774,
-0.02073577605187893,
-0.02098064124584198,
0.0173334963619709,
-0.026544518768787384,
-0.002660043304786086,
0.023000050336122513,
0.04705052450299263,
-0.0014641215093433857,
-0.003002554178237915,
0.0029405406676232815,
-0.0005856282077729702,
0.018781248480081558,
-0.022655928507447243,
-0.009334731847047806,
0.02868703566491604,
0.021186452358961105,
0.001927111647091806,
0.02204747125506401,
0.013605264015495777,
-0.025925956666469574,
0.029554391279816628,
-0.008982366882264614,
0.00811843667179346,
0.0064723375253379345,
-0.03407331556081772,
-0.04995383322238922,
0.03053577058017254,
-0.030401945114135742,
-0.018673395738005638,
-0.0034512225538492203,
-0.011902408674359322,
0.03205346688628197,
0.05444273352622986,
0.01029993500560522,
-0.014100423082709312,
0.02724650129675865,
-0.050461579114198685,
-0.0006807001191191375,
0.04475170001387596,
-0.005846764892339706,
-0.01888944022357464,
0.03857652470469475,
0.009894907474517822,
-0.023467838764190674,
-0.052614327520132065,
0.054716963320970535,
0.04577583819627762,
0.035709649324417114,
0.046387046575546265,
0.027203762903809547,
-0.0024087014608085155,
0.029781926423311234,
0.02401702292263508,
-0.01278742216527462,
-0.011649999767541885,
0.048200953751802444,
-0.02277953177690506,
0.028554610908031464,
0.0352984257042408,
-0.027979424223303795,
-0.11308646947145462,
0.004396796226501465,
0.012780897319316864,
-0.017276788130402565,
0.06273297965526581,
-0.009638641960918903,
0.06043672934174538,
0.005520305596292019,
-0.0721297338604927,
0.04258172586560249,
-0.01815417781472206,
-0.028247950598597527,
0.011603747494518757,
0.06156489625573158,
-0.0150988744571805,
0.06613291800022125,
0.005296281073242426,
0.024287905544042587,
0.04855276644229889,
0.026639217510819435,
0.008296256884932518,
-0.04188106581568718,
-0.02560790628194809,
0.019364917650818825,
-0.014318606816232204,
-0.020268000662326813,
0.028050130233168602,
-0.04578971862792969,
-0.02746080979704857,
0.0007477065664716065,
-0.029552599415183067,
0.03924151137471199,
-0.03736297786235809,
0.0003627068072091788,
0.030607659369707108,
0.026377003639936447,
0.008314413949847221,
-0.01113682147115469,
0.013295324519276619,
0.006685313303023577,
0.007388629484921694,
-0.0015441724099218845,
0.042962126433849335,
0.005564696155488491,
0.022263303399086,
-0.016037072986364365,
-0.026122337207198143,
0.005898502189666033,
0.023021532222628593,
0.029762044548988342,
-0.004377715289592743,
0.027748331427574158,
-0.013702720403671265,
-0.019275033846497536,
0.008878722786903381,
-0.03676093369722366,
-0.011403205804526806,
0.01824711449444294,
0.031300708651542664,
-0.015245579183101654,
0.002838022308424115,
-0.042403191328048706,
0.007782960310578346,
0.04147869348526001,
-0.003855667309835553,
-0.015614015981554985,
-0.05722205713391304,
0.016123080626130104,
-0.009513997472822666,
0.027838870882987976,
0.00024204610963352025,
-0.04676421359181404,
-0.009991435334086418,
0.027106113731861115,
-0.02281184494495392,
0.042614709585905075,
-0.01960168406367302,
-0.06558878719806671,
-0.013262763619422913,
-0.019742848351597786,
0.008284253999590874,
0.01867053285241127,
0.04043835401535034,
-0.03736589848995209,
-0.013461904600262642,
-0.016734419390559196,
-0.0058138407766819,
0.07031411677598953,
-0.0023082394618541002,
0.00980070699006319,
-0.020013539120554924,
-0.005960120353847742,
0.03967937082052231,
-0.027507446706295013,
0.019026093184947968,
-0.046598613262176514,
0.007343955338001251,
-0.04585368558764458,
-0.019193222746253014,
-0.032729409635066986,
0.014960137195885181,
0.03411705046892166,
0.00462175440043211,
-0.0037071367260068655,
-0.0001974889455595985,
-0.014779007993638515,
0.029532238841056824,
-0.01613711379468441,
0.04366091266274452,
0.07600530982017517,
-0.041353702545166016,
0.06425255537033081,
0.020899698138237,
-0.010525571182370186,
-0.0708685964345932,
0.01847776025533676,
-0.023390881717205048,
-0.025652948766946793,
-0.00318345264531672,
0.003351781517267227,
0.010659639723598957,
-0.03326081484556198,
-0.019864045083522797,
0.0015388820320367813,
-0.03779281675815582,
0.012177559547126293,
0.052071720361709595,
-0.02669711410999298,
0.037998348474502563,
0.0010570933809503913,
0.028095098212361336,
0.009473742917180061,
0.05693989247083664,
0.020361315459012985,
0.04501071572303772,
0.05634133890271187,
0.005811638198792934,
0.022203974425792694,
0.0466763861477375,
-0.039295293390750885,
0.06498081982135773,
-0.00789389107376337,
0.03995390981435776,
-0.032967641949653625,
0.0017940980615094304,
0.05041048303246498,
0.005846121814101934,
-0.02519845776259899,
0.010699992999434471,
-0.013940825127065182,
0.07510736584663391,
-0.022181862965226173,
0.03707113862037659,
0.005369266029447317,
-0.012019455432891846,
-0.019439810886979103,
-0.0034594868775457144,
0.06337364763021469,
0.03796057030558586,
-0.02657949924468994,
-0.0050939274951815605,
-0.013540656305849552,
0.019689133390784264,
0.007779694627970457,
-0.05669588968157768,
0.004410102963447571,
0.005458917934447527,
-0.02239537052810192,
0.016706403344869614,
-0.011783849447965622,
-0.05214959755539894,
-0.05724392086267471,
0.02453489601612091,
-0.0027284908574074507,
-0.009720544330775738,
-0.012382873333990574,
-0.052095819264650345,
-0.009421102702617645,
0.04954147711396217,
-0.030442893505096436,
-0.004736769944429398,
-0.022173162549734116,
0.04925968125462532,
-0.022980432957410812,
-0.033590223640203476
] |
<p>I can find equations to give the force of an electromagnet on a piece of iron when the iron touches the electromagnet. </p>
<p>But what about when the iron is some distance from the electromagnet? Presumably the force depends on the shape/size of the iron piece as well as the location of the piece away from the magnet. </p>
<p>If anybody can tell me how to calculate this, even if I have to write a numerical calculation routine, I would appreciate any direction on this. </p> | 4,611 | [
-0.01895204372704029,
0.002572607947513461,
-0.006260452326387167,
-0.02682744711637497,
0.014168652705848217,
0.027446558699011803,
-0.05100032687187195,
0.007831987924873829,
0.013824189081788063,
-0.003952383995056152,
0.029103105887770653,
0.046280261129140854,
0.06327372789382935,
0.01911827363073826,
0.016941461712121964,
-0.003940497525036335,
-0.02407253161072731,
-0.0326472707092762,
0.009220873937010765,
-0.05347127839922905,
0.0321647934615612,
0.009782222099602222,
0.014445784501731396,
-0.009999734349548817,
-0.018769854679703712,
0.004218030255287886,
0.04725800082087517,
-0.01195697020739317,
0.04058950021862984,
0.052248429507017136,
-0.00863691046833992,
-0.06201481074094772,
0.014265256933867931,
0.03671404719352722,
0.037963081151247025,
0.005871109664440155,
-0.03630979731678963,
-0.03595438972115517,
-0.017328081652522087,
0.023107539862394333,
-0.014420542865991592,
-0.022638386115431786,
-0.01638112962245941,
0.06925865262746811,
-0.020606378093361855,
0.015580627135932446,
-0.017476974055171013,
-0.03156011551618576,
0.057993415743112564,
-0.05830589309334755,
0.08673684298992157,
-0.03503170236945152,
0.062313683331012726,
-0.0017106713494285941,
-0.009020433761179447,
-0.021924052387475967,
0.06109534204006195,
0.036058392375707626,
-0.0004462145152501762,
-0.03723576292395592,
-0.01333808246999979,
-0.010839414782822132,
-0.036868322640657425,
-0.08798837661743164,
-0.03457377851009369,
0.04591787979006767,
-0.01832147315144539,
-0.03815877065062523,
0.012698838487267494,
0.008637144230306149,
0.009561269544064999,
0.026742134243249893,
0.03905605897307396,
-0.02436763420701027,
-0.002336648292839527,
-0.05340081825852394,
0.022164225578308105,
0.016121355816721916,
0.043881114572286606,
0.03876720368862152,
-0.058481283485889435,
0.024518171325325966,
0.07151727378368378,
0.03526048734784126,
0.0053030699491500854,
-0.06864030659198761,
0.055739570409059525,
0.01659547910094261,
0.008035334758460522,
0.009619126096367836,
0.00022255175281316042,
0.037100933492183685,
0.061332058161497116,
-0.017045801505446434,
-0.014545710757374763,
0.017055155709385872,
-0.007868250831961632,
0.04039273411035538,
0.010393839329481125,
-0.01739109866321087,
0.026905056089162827,
-0.025379600003361702,
-0.005997795145958662,
0.06682772189378738,
0.03575088083744049,
-0.04263366386294365,
-0.006370308343321085,
0.02696768380701542,
-0.005311236716806889,
-0.0003741601249203086,
0.01959218457341194,
0.03425069898366928,
0.0008770474814809859,
-0.039321064949035645,
-0.0005230107344686985,
-0.016915258020162582,
-0.00019028996757697314,
-0.04021007940173149,
0.027912039309740067,
0.04686512053012848,
0.005804772954434156,
-0.07393121719360352,
0.002532328013330698,
-0.05368930473923683,
-0.0613974928855896,
0.0332430899143219,
0.03137842193245888,
-0.016217458993196487,
-0.002289876341819763,
0.040889181196689606,
-0.010531977750360966,
-0.026976069435477257,
0.007217499893158674,
-0.013586745597422123,
0.0227444376796484,
-0.002835663501173258,
-0.07411336153745651,
-0.06857994943857193,
0.06727976351976395,
0.00019240837718825787,
0.0172358900308609,
-0.07429523020982742,
0.012073850259184837,
0.03414855897426605,
0.04358578473329544,
0.024169601500034332,
-0.013861638493835926,
-0.026576317846775055,
0.02138264663517475,
0.0017021612729877234,
-0.007980294525623322,
-0.01259579136967659,
-0.010965697467327118,
-0.02505098097026348,
0.010003314353525639,
-0.03398240730166435,
0.029933135956525803,
0.02404770441353321,
-0.025246018543839455,
-0.024494575336575508,
0.057019032537937164,
-0.003541944781318307,
-0.006904206238687038,
0.010473662987351418,
0.016268936917185783,
-0.05932125076651573,
0.07612618058919907,
0.01337870117276907,
0.0035865572281181812,
0.035237886011600494,
0.010273736901581287,
0.011173099279403687,
-0.011340982280671597,
0.01160992868244648,
0.07069877535104752,
-0.018948227167129517,
-0.025954030454158783,
-0.019490277394652367,
0.03229143097996712,
0.016518546268343925,
-0.05417995527386665,
-0.056903306394815445,
0.0010287469485774636,
0.040071215480566025,
0.028847048059105873,
0.04281836003065109,
-0.016498802229762077,
-0.01653675176203251,
-0.034544073045253754,
-0.02965434268116951,
-0.029353979974985123,
-0.06565584987401962,
0.04808451980352402,
-0.01335966121405363,
-0.021793343126773834,
0.0206974558532238,
0.005449151620268822,
0.009740127250552177,
-0.03249096870422363,
-0.05726297199726105,
0.018278006464242935,
-0.005079635418951511,
0.018839113414287567,
0.004074422176927328,
-0.01591365784406662,
0.059295929968357086,
0.07820659130811691,
0.022174641489982605,
0.06419771909713745,
-0.04019381105899811,
-0.03715551644563675,
-0.01812286674976349,
-0.03701825439929962,
-0.0053835720755159855,
0.052493855357170105,
-0.012524251826107502,
0.011495267041027546,
0.00176062504760921,
-0.04477395489811897,
0.012806231155991554,
-0.01435757800936699,
0.0886523649096489,
0.05443373695015907,
0.01701541431248188,
0.017269203439354897,
-0.0037080068141222,
0.023177949711680412,
0.02923865057528019,
0.0029335275758057833,
-0.013834888115525246,
-0.07316628098487854,
0.004177102353423834,
0.008399826474487782,
0.028437739238142967,
-0.02719925343990326,
0.002766064601019025,
0.04276817664504051,
0.01517788227647543,
0.01805560477077961,
0.02063846029341221,
-0.02264438010752201,
-0.01102611143141985,
-0.003590163541957736,
0.01660609431564808,
-0.015493801794946194,
-0.024157769978046417,
0.03561058267951012,
0.03787827864289284,
0.0249796062707901,
0.020577605813741684,
-0.029968885704874992,
0.045634057372808456,
-0.01570184715092182,
0.026675771921873093,
0.017453189939260483,
-0.039817504584789276,
0.062112778425216675,
-0.01636807806789875,
-0.004634729120880365,
-0.01554704736918211,
-0.004339816514402628,
0.0009575133444741368,
-0.014952941797673702,
-0.009177690371870995,
0.023083265870809555,
-0.0263336393982172,
-0.031608499586582184,
-0.009082203730940819,
0.016000833362340927,
-0.028097044676542282,
-0.019846400246024132,
0.0006125965737737715,
-0.009018464013934135,
-0.008997145108878613,
0.0041793412528932095,
0.011386008933186531,
0.02951393835246563,
0.06973576545715332,
-0.010680951178073883,
-0.026911752298474312,
-0.02343934215605259,
-0.016384875401854515,
-0.006130484864115715,
0.0005688226083293557,
-0.034766487777233124,
0.010731149464845657,
-0.03952789679169655,
0.006404798943549395,
0.05105559155344963,
0.004047708585858345,
-0.020977793261408806,
-0.00243604788556695,
0.02722294256091118,
-0.04913179203867912,
0.00028480665059760213,
-0.004737658426165581,
-0.002108040265738964,
-0.03369475156068802,
-0.005606450606137514,
0.03994368016719818,
0.0012111809337511659,
-0.009064234793186188,
0.03576814755797386,
-0.02586892805993557,
-0.013019592501223087,
-0.011763784103095531,
-0.027318717911839485,
0.013748643919825554,
-0.035300396382808685,
0.02187684178352356,
0.015744009986519814,
-0.044110655784606934,
0.024688981473445892,
-0.047536320984363556,
-0.018598755821585655,
0.012376271188259125,
-0.023173129186034203,
0.04321376606822014,
-0.028279850259423256,
-0.027927031740546227,
0.0896923765540123,
-0.008685896173119545,
-0.03273647278547287,
-0.02035435475409031,
-0.01163411047309637,
-0.009908345527946949,
-0.0016546233091503382,
-0.0053094299510121346,
0.03468271717429161,
-0.033159200102090836,
-0.0076064844615757465,
0.006204735022038221,
0.005582196172326803,
0.023678584024310112,
0.012227418832480907,
0.006367926020175219,
-0.011178328655660152,
0.02048655040562153,
-0.04201510176062584,
0.08150050789117813,
0.014493892900645733,
-0.021606041118502617,
0.020326614379882812,
0.02707887627184391,
0.03947289288043976,
0.010201570577919483,
-0.03774995729327202,
0.012482354417443275,
-0.012470382265746593,
-0.004878051578998566,
-0.027425194159150124,
0.04071371257305145,
-0.007407462224364281,
-0.023407381027936935,
0.01484785694628954,
0.025477750226855278,
0.06522833555936813,
-0.03373997285962105,
-0.03758593648672104,
0.05293484404683113,
0.034998852759599686,
-0.022173913195729256,
-0.03937733918428421,
-0.0057010832242667675,
0.0029820960480719805,
0.015051073394715786,
-0.0305638387799263,
-0.010975622572004795,
0.006454652640968561,
0.02080168016254902,
0.039387404918670654,
0.020459933206439018,
-0.020397521555423737,
-0.02079978957772255,
-0.08146046102046967,
-0.014047124423086643,
0.026462966576218605,
0.04791678115725517,
0.00833018496632576,
0.029713477939367294,
0.02934863045811653,
-0.004709792323410511,
0.040191151201725006,
-0.005046362988650799,
-0.08993112295866013,
0.06630992889404297,
-0.05892971530556679,
-0.04397561773657799,
0.010514832101762295,
-0.01578974351286888,
-0.028551194816827774,
-0.01484962459653616,
0.009711142629384995,
-0.016908686608076096,
-0.013998279348015785,
-0.03459908813238144,
0.0017108181491494179,
-0.013237625360488892,
-0.015433217398822308,
0.010749397799372673,
0.022347524762153625,
-0.016396425664424896,
-0.0351150818169117,
-0.0011038914090022445,
0.019222140312194824,
-0.04857167229056358,
-0.020465005189180374,
0.00024402029521297663,
0.022492537274956703,
-0.005347701255232096,
0.03855109587311745,
0.013995368964970112,
-0.0018218258628621697,
-0.033178310841321945,
0.020049571990966797,
0.003569092368707061,
0.03630060330033302,
0.036962416023015976,
-0.00687134824693203,
-0.0451124869287014,
-0.05073761194944382,
-0.03334524482488632,
-0.016402173787355423,
0.0713946670293808,
-0.026347659528255463,
0.007233377546072006,
0.0356496199965477,
-0.0009429972269572318,
-0.03455634042620659,
0.02226637676358223,
0.03232217952609062,
0.06766073405742645,
-0.032995447516441345,
-0.07040460407733917,
0.008532696403563023,
-0.01850896142423153,
0.017213014885783195,
0.014797528274357319,
0.022780539467930794,
-0.01769038289785385,
-0.0020573576912283897,
0.0040003093890845776,
0.012054285034537315,
-0.015493541955947876,
0.0036909719929099083,
0.013300039805471897,
-0.016401061788201332,
-0.027206212282180786,
0.0027876831591129303,
0.0344822034239769,
0.0003755762299988419,
0.05851690098643303,
-0.008405076339840889,
-0.021547483280301094,
-0.09475121647119522,
-0.018053088337183,
0.0628514215350151,
0.017297929152846336,
-0.016512233763933182,
-0.019462330266833305,
-0.025575140491127968,
0.007508962880820036,
0.03878846392035484,
-0.04342356696724892,
0.030035046860575676,
-0.017006928101181984,
0.00936803501099348,
-0.04592673107981682,
-0.014979522675275803,
-0.05463988706469536,
0.007111155427992344,
-0.026161791756749153,
0.019220398738980293,
-0.030229533091187477,
-0.035617224872112274,
0.00915534794330597,
0.029666490852832794,
0.05940762907266617,
0.05777221545577049,
0.014745495282113552,
0.0037387479096651077,
-0.0089705316349864,
-0.005972095299512148,
-0.038710352033376694,
-0.06985638290643692,
0.010453334078192711,
-0.00579865975305438,
-0.0021329561714082956,
0.009700284339487553,
-0.022379187867045403,
-0.02613760344684124,
0.016896501183509827,
-0.006588661577552557,
0.017967216670513153,
-0.029266422614455223,
-0.0189951341599226,
0.04004080593585968,
0.043098822236061096,
-0.008601565845310688,
0.05269325524568558,
0.0010053265141323209,
-0.0005524569423869252,
-0.0049065882340073586,
0.008019235916435719,
0.03516939654946327,
0.019371209666132927,
0.009753035381436348,
-0.03787602484226227,
0.03319782763719559,
-0.041905634105205536,
0.03230461850762367,
-0.04053039476275444,
0.02617541328072548,
-0.02005806565284729,
-0.034285735338926315,
-0.02453427016735077,
0.021005665883421898,
-0.01752530038356781,
-0.005533840972930193,
0.020939283072948456,
-0.008617522194981575,
-0.026360945776104927,
-0.02224317565560341,
0.02948775142431259,
0.013989100232720375,
0.018824230879545212,
-0.005398212932050228,
-0.030819294974207878,
-0.020436296239495277,
-0.0322546549141407,
-0.03218434005975723,
0.027966178953647614,
-0.08412668853998184,
0.04814159497618675,
-0.049920402467250824,
0.013748429715633392,
0.008908872492611408,
-0.03960656002163887,
-0.027996720746159554,
0.007259368896484375,
-0.018393155187368393,
0.05005525052547455,
-0.030919745564460754,
0.0011018839431926608,
0.017581183463335037,
-0.006099710240960121,
-0.0059698959812521935,
-0.0713898316025734,
0.015774555504322052,
0.0015927109634503722,
0.007052428089082241,
-0.028952376917004585,
-0.007696830201894045,
-0.03861050680279732,
-0.017773954197764397,
0.014642389491200447,
0.02359723672270775,
-0.029881225898861885,
0.014033159241080284,
0.041995760053396225,
-0.0453760027885437,
0.06343185156583786,
0.0422886461019516,
-0.03164653107523918,
0.015340598300099373,
-0.020344993099570274,
-0.02987697720527649,
0.01105972658842802,
0.047461364418268204,
-0.0275893434882164,
-0.025785202160477638,
0.02806657738983631,
0.0028567835688591003,
0.03763783350586891,
-0.026801906526088715,
0.009061725810170174,
0.005566395353525877,
0.0435389019548893,
0.009119071997702122,
-0.011192760430276394,
0.03463994711637497,
0.04077117145061493,
0.010409797541797161,
-0.026726089417934418,
-0.023097435012459755,
-0.04762360826134682,
-0.042518872767686844,
-0.031519144773483276,
0.005049379076808691,
0.02908734604716301,
0.0006178648327477276,
0.05412765219807625,
0.0021192498970776796,
0.018280111253261566,
0.021777179092168808,
-0.017368920147418976,
0.04135952889919281,
-0.02974209189414978,
-0.0028621861711144447,
-0.000806460331659764,
0.0061807106249034405,
-0.0047718253917992115,
-0.010745440609753132,
0.01459464617073536,
-0.015290938317775726,
0.048170410096645355,
-0.03581319376826286,
0.07687358558177948,
0.02960888110101223,
-0.0013925599632784724,
-0.007600926328450441,
0.00857591349631548,
-0.005295810755342245,
-0.0015989548992365599,
-0.0010023914510384202,
0.049944136291742325,
-0.0013597600627690554,
-0.0016957692569121718,
0.02440210059285164,
0.0032444919925183058,
-0.03412798419594765,
-0.02949412725865841,
0.007051750086247921,
0.05322905257344246,
0.04746617376804352,
-0.005139076616615057,
-0.02781793102622032,
0.011670785024762154,
-0.001455794321373105,
0.03133484721183777,
-0.0037416075356304646,
-0.02877955511212349,
0.045662879943847656,
0.029797054827213287,
0.013634827919304371,
0.004661647602915764,
-0.030045820400118828,
0.003310171654447913,
0.009423882700502872,
0.0363784059882164,
-0.012287547811865807,
0.0032666902989149094,
0.03659259155392647,
0.009737075306475163,
-0.012769747525453568,
0.01865522563457489,
0.002284831367433071,
-0.049836665391922,
-0.012104145251214504,
-0.06470249593257904,
-0.06577852368354797,
0.030723413452506065,
0.009356475435197353,
-0.033438026905059814,
0.03371882811188698,
-0.025297513231635094,
0.037157945334911346,
0.02582854963839054,
0.00219998462125659,
-0.004880751017481089,
0.10229696333408356,
-0.01925063133239746,
-0.0064409151673316956,
-0.013610600493848324,
0.010304136201739311,
0.09203249216079712,
0.033222876489162445,
0.024046458303928375,
-0.054087039083242416,
0.051130156964063644,
-0.043599627912044525,
-0.023288045078516006,
-0.03190278261899948,
0.012176026590168476,
-0.04510396346449852,
-0.027898192405700684,
0.02920709364116192,
0.01592935621738434,
-0.005907255690544844,
0.0031044785864651203,
0.06504102796316147,
-0.029313936829566956,
-0.02857430838048458,
0.01778789609670639,
0.015119926072657108,
-0.007439080160111189,
-0.006231213454157114,
-0.02801424264907837,
0.0352681502699852,
-0.06515158712863922,
-0.013033512979745865,
-0.03107365034520626,
-0.043629877269268036,
0.023912593722343445,
-0.0007800610037520528,
-0.05408058688044548,
-0.010437441058456898,
-0.013822371140122414,
-0.039365027099847794,
-0.029667221009731293,
0.025726037099957466,
0.059571512043476105,
-0.0019767065532505512,
0.0012041098671033978,
0.019152987748384476,
0.019356010481715202,
0.0270396638661623,
0.014494496397674084,
0.014868603087961674,
-0.041067108511924744,
0.027310390025377274,
-0.03997961804270744,
0.05612780153751373,
0.019246919080615044,
0.02710098773241043,
0.011430718004703522,
0.0458340086042881,
0.031074540689587593,
-0.0326177217066288,
-0.02077765204012394,
0.0003889175713993609,
0.008763899095356464,
-0.022201962769031525,
0.008649293333292007,
0.009731062687933445,
0.07016641646623611,
0.013787176460027695,
0.0033881631679832935,
0.019663693383336067,
-0.01652824506163597,
0.029011942446231842,
0.011068287305533886,
0.03874469920992851,
-0.00989499781280756,
-0.040082499384880066,
-0.024807699024677277,
-0.03712029755115509,
-0.015961362048983574,
0.03626798093318939,
0.010354675352573395,
0.027099493891000748,
0.02638118341565132,
-0.03536098450422287,
-0.027080409228801727,
-0.032073263078927994,
-0.041477449238300323,
0.018298659473657608,
-0.043233394622802734,
0.012272167019546032,
-0.022156910970807076,
0.0016098757041618228,
0.04299933835864067,
0.045473821461200714,
-0.0022840402089059353,
-0.015471374616026878,
0.005114140920341015,
-0.01573352701961994,
-0.00512800645083189,
-0.011194384656846523,
-0.02350478060543537,
-0.0032216294202953577,
-0.04170698672533035,
0.018376674503087997,
0.0009801944252103567,
0.025913605466485023,
0.0259877759963274,
-0.019958190619945526,
0.035011716187000275,
0.029863594099879265,
-0.031539805233478546,
0.009414845146238804,
-0.012737015262246132,
-0.01583598367869854,
-0.014588912017643452,
-0.019622819498181343,
-0.049288030713796616,
-0.054465994238853455,
0.01916476897895336,
-0.042088672518730164,
-0.034634534269571304,
0.0064566778019070625,
0.05686695873737335,
-0.028003163635730743,
0.016050640493631363,
-0.005586965475231409,
0.009415454231202602,
0.004536348860710859,
-0.025518158450722694,
-0.02541404962539673,
-0.028786635026335716,
0.02040737494826317,
-0.009121548384428024,
-0.023755135014653206,
0.021197320893406868,
-0.03146011382341385,
0.028165338560938835,
0.004070194438099861,
0.012779202312231064,
0.03231481462717056,
0.014575259760022163,
0.02598293125629425,
-0.002304817782714963,
0.07107967883348465,
0.0030149437952786684,
-0.001066259341314435,
0.052308082580566406,
-0.029620734974741936,
-0.012835213914513588,
0.04011109843850136,
-0.02240101806819439,
0.021462105214595795,
0.0374024398624897,
-0.007754661608487368,
-0.02815273404121399,
0.05378853529691696,
-0.016714148223400116,
-0.00803398434072733,
-0.022767387330532074,
0.0027553425170481205,
0.023609070107340813,
-0.01068519614636898,
0.007785398978739977,
-0.028097745031118393,
-0.014584933407604694,
-0.013259504921734333,
0.023123225197196007,
0.028688466176390648,
-0.019725924357771873,
0.030448656529188156,
0.04315798357129097,
-0.05187917873263359,
0.03586922213435173,
-0.004058529157191515,
0.02711097151041031,
0.05218290537595749,
-0.006832845509052277,
0.026346703991293907,
-0.0019204228883609176,
-0.004065795335918665,
-0.1017245426774025,
0.004613819532096386,
-0.014951701276004314,
-0.003300780663266778,
0.05988435447216034,
-0.08201861381530762,
0.0011198044521734118,
0.00213542184792459,
-0.06989642232656479,
-0.003434572136029601,
-0.008053964003920555,
-0.017206327989697456,
-0.012018909677863121,
-0.005751123186200857,
0.054184701293706894,
0.046195149421691895,
0.002261745510622859,
0.04270020127296448,
0.026668105274438858,
0.012365845963358879,
-0.031460728496313095,
-0.03586460277438164,
-0.002776547335088253,
0.047060027718544006,
-0.013071216642856598,
0.011735429055988789,
0.05798235535621643,
-0.003876917529851198,
-0.009130994789302349,
0.022335199639201164,
-0.03703362122178078,
0.017094986513257027,
0.0014643552713096142,
0.0088193379342556,
0.02665208838880062,
0.021451814100146294,
-0.02136584371328354,
0.018225904554128647,
0.0009276014752686024,
0.010579929687082767,
-0.023283682763576508,
0.04542914405465126,
-0.020438142120838165,
0.013514157384634018,
0.04102524369955063,
-0.03653526306152344,
0.006691989954560995,
0.03845427185297012,
-0.044367916882038116,
-0.001988719217479229,
-0.015997709706425667,
0.020242666825652122,
0.005002237856388092,
-0.04556789621710777,
0.006508753169327974,
-0.03370163217186928,
-0.008206989616155624,
0.020257828757166862,
-0.018413899466395378,
-0.019809871912002563,
0.02724316157400608,
-0.007533685304224491,
-0.03566044196486473,
0.006071907468140125,
-0.013899252749979496,
-0.012686128728091717,
-0.07302692532539368,
0.02394699677824974,
0.024533316493034363,
-0.007116241380572319,
0.021740512922406197,
-0.04182034358382225,
-0.0161463413387537,
0.029528576880693436,
0.023491980507969856,
-0.011812898330390453,
0.02586015872657299,
-0.013910152949392796,
-0.0007178065134212375,
-0.04527084901928902,
0.019961832091212273,
-0.01412627287209034,
-0.05770741403102875,
-0.029714541509747505,
-0.04505326226353645,
0.016215678304433823,
0.008915514685213566,
0.04875665158033371,
-0.022618986666202545,
-0.016176115721464157,
0.006770469713956118,
-0.02654709853231907,
-0.011001291684806347,
-0.04465917870402336,
0.0022771419025957584,
0.031891532242298126,
-0.007484558504074812,
-0.01039041019976139,
-0.01735018566250801,
0.0015356499934569001,
0.008371197618544102,
0.015653500333428383,
0.027491772547364235,
0.02822699584066868,
-0.03151761740446091,
-0.0582260861992836,
0.016864268109202385,
0.003453946439549327,
-0.0036972113884985447,
0.0338556244969368,
-0.0024265774991363287,
0.008311307989060879,
-0.01071670651435852,
-0.010721503756940365,
-0.05576900392770767,
0.006067919544875622,
-0.055185094475746155,
0.015010257251560688,
-0.022509995847940445,
-0.02494368515908718,
0.050977353006601334,
-0.05810907855629921,
-0.011394551955163479,
0.015746885910630226,
-0.031226053833961487,
0.011500511318445206,
0.05509934946894646,
0.04645548760890961,
0.020087305456399918,
-0.03419781103730202,
0.027057545259594917,
0.022563114762306213,
-0.020474685356020927,
0.004474358633160591,
0.002975220326334238,
0.011331395246088505,
0.01052461564540863,
-0.0006407010951079428,
0.0578654520213604,
0.03162849321961403,
-0.011286391876637936,
0.028758186846971512,
0.014319030568003654,
0.002133978297933936,
-0.03839629143476486,
0.013153454288840294,
-0.005076035391539335,
0.039047952741384506,
0.045395947992801666,
-0.03588827699422836,
0.07848386466503143,
-0.020927997305989265,
0.02758755348622799,
-0.017983274534344673,
0.022422773763537407,
0.027544710785150528,
0.03266201913356781,
0.01937755011022091,
0.026965944096446037,
-0.0282275527715683,
0.009967251680791378,
0.038268957287073135,
-0.0015377082163468003,
0.04086887836456299,
-0.021481165662407875,
0.03927994892001152,
-0.008960297331213951,
0.009641017764806747,
-0.042475130409002304,
-0.022892821580171585,
-0.04530802369117737,
-0.022484323009848595,
0.04216492176055908,
0.013813904486596584,
0.00936258677393198,
0.018986737355589867,
0.0377962552011013,
0.006853143218904734,
0.051011741161346436,
-0.08847056329250336,
-0.02401796169579029,
-0.041286028921604156,
0.052549708634614944,
-0.016217608004808426,
0.021334106102585793
] |
<p>How to estimate the amount of water condensing from air on a surface, given the air's temperature and relative humidity and how they change over time, the surface temperature, material's thermal properites, roughness and whatever else needs to be given about the air and surface?</p>
<p>For my purpose, we may assume the surface starts off dry, but the more general situation would be as interesting. If enough water condenses, it'll form drops and run off - can we account for that? </p>
<p>Are there some fairly simple formulas or rules of thumb? High accuracy is not needed; I'll be happy to get grams per sq meter per second (or whatever) to within a factor of two. (What if we wanted higher accuracy?)</p> | 4,612 | [
-0.024494091048836708,
-0.04388098418712616,
-0.006495967041701078,
0.03130155801773071,
0.05823768675327301,
-0.026468699797987938,
-0.04511311277747154,
-0.017767520621418953,
0.018960261717438698,
-0.023816989734768867,
0.020429184660315514,
0.06447016447782516,
0.03522712364792824,
0.040905408561229706,
-0.010732021182775497,
-0.005540892947465181,
-0.0106214489787817,
-0.03420426696538925,
0.009024468250572681,
-0.007957180961966515,
-0.008562757633626461,
0.005325048230588436,
0.005080458242446184,
0.0046434709802269936,
-0.018482889980077744,
0.025771675631403923,
-0.0012234182795509696,
-0.030454212799668312,
0.02230212651193142,
0.007853533141314983,
-0.023281097412109375,
-0.004639169201254845,
0.028142495080828667,
0.04059405252337456,
0.033842191100120544,
-0.015197978354990482,
-0.03336569294333458,
-0.04416046291589737,
-0.057362452149391174,
0.040957868099212646,
-0.026101164519786835,
-0.01000552624464035,
-0.002826105570420623,
-0.010309039615094662,
-0.01351676881313324,
0.003265485865995288,
0.006986686959862709,
-0.01729494519531727,
0.051202911883592606,
-0.11913726478815079,
0.026484448462724686,
0.019100749865174294,
0.06868849694728851,
0.04006313160061836,
0.0075852577574551105,
0.005551534704864025,
0.08946608006954193,
0.061108555644750595,
-0.0004578950465656817,
-0.0269099622964859,
-0.022566402330994606,
-0.011228764429688454,
-0.012676813639700413,
-0.04812469333410263,
-0.013812136836349964,
0.013898071832954884,
-0.013392720371484756,
-0.03427040949463844,
0.020337484776973724,
-0.021609922870993614,
0.031516943126916885,
-0.022460758686065674,
0.019816717132925987,
0.01107513066381216,
0.013009864836931229,
-0.0014870675513520837,
0.02273564785718918,
0.04222962260246277,
0.03265387937426567,
0.03953896090388298,
-0.007188331335783005,
0.0304967500269413,
0.024122009053826332,
0.022560223937034607,
0.011517864651978016,
-0.03580446168780327,
0.09210597723722458,
-0.012918735854327679,
0.020822469145059586,
0.027594340965151787,
0.023900343105196953,
0.027152985334396362,
0.01528406236320734,
0.012088104151189327,
0.006845722906291485,
-0.031252142041921616,
-0.01603798381984234,
0.039578504860401154,
-0.018748151138424873,
-0.021128032356500626,
-0.007731184829026461,
0.018477316945791245,
0.03408745676279068,
0.07152558118104935,
-0.02381322719156742,
-0.027738729491829872,
-0.029128607362508774,
0.02152327634394169,
0.02201171964406967,
-0.019982287660241127,
-0.033412568271160126,
-0.0019568921998143196,
-0.028635036200284958,
-0.04182657599449158,
-0.010907216928899288,
0.011496865190565586,
0.037397220730781555,
-0.023589788004755974,
0.04308683052659035,
0.05671069025993347,
0.026700813323259354,
-0.017926286906003952,
0.01618707738816738,
-0.014035767875611782,
-0.07618983089923859,
0.010958109982311726,
0.003351078601554036,
-0.03309405595064163,
-0.04774075374007225,
-0.002199857961386442,
-0.009026658721268177,
-0.01596602238714695,
0.02521919645369053,
-0.03973560780286789,
-0.008215985260903835,
-0.03218858316540718,
-0.06928430497646332,
-0.05406644195318222,
0.013992175459861755,
0.011012451723217964,
-0.03821675479412079,
-0.04611382260918617,
0.019899746403098106,
0.009228289127349854,
0.0667339488863945,
-0.00844997726380825,
0.03737517073750496,
-0.015461362898349762,
0.005981628317385912,
-0.015309818089008331,
-0.02939836122095585,
-0.01877920888364315,
0.03448528051376343,
-0.03336304798722267,
-0.01674814149737358,
-0.04081926867365837,
0.02634093537926674,
0.08614906668663025,
0.0014208478387445211,
-0.016783248633146286,
0.05636543780565262,
0.032652854919433594,
-0.0025077126920223236,
0.02163056842982769,
0.022153731435537338,
-0.08653489500284195,
0.026905782520771027,
-0.0021490773651748896,
-0.012739953584969044,
-0.018728822469711304,
0.04066222533583641,
-0.012503169476985931,
-0.005103667266666889,
0.01666860282421112,
0.09701705724000931,
-0.0018582222983241081,
0.0025831470265984535,
-0.028037820011377335,
0.0026102180127054453,
0.032529886811971664,
-0.01656998135149479,
0.0005053300992585719,
0.020738663151860237,
-0.018157606944441795,
0.009913258254528046,
0.020956337451934814,
0.006380261853337288,
-0.04641299694776535,
0.005500440020114183,
-0.050854943692684174,
-0.04540562257170677,
-0.08857003599405289,
0.008025981485843658,
0.0010917680338025093,
0.04049148038029671,
0.00562997255474329,
0.002637491561472416,
0.006319265812635422,
-0.04086128622293472,
-0.0740123987197876,
0.020794853568077087,
0.014047736302018166,
0.029128044843673706,
-0.042540695518255234,
0.0021980665624141693,
0.02078077755868435,
0.04221651330590248,
-0.012918305583298206,
0.020036814734339714,
-0.050283558666706085,
-0.036139681935310364,
-0.062177155166864395,
-0.02497877925634384,
0.01633262075483799,
-0.03187485784292221,
-0.01567370630800724,
0.0377955362200737,
-0.010373745113611221,
0.03191709890961647,
-0.0043624164536595345,
-0.022308602929115295,
0.05876731500029564,
0.07502834498882294,
0.008194727823138237,
-0.02173500321805477,
0.019910410046577454,
0.030150773003697395,
-0.012697793543338776,
0.0018141844775527716,
-0.028805816546082497,
-0.04538115859031677,
-0.029843071475625038,
0.054620902985334396,
0.026749344542622566,
-0.015203600749373436,
-0.011694761924445629,
0.02563437633216381,
0.04944983497262001,
0.062606580555439,
0.012719440273940563,
-0.007328878156840801,
0.007499765604734421,
0.0215345099568367,
0.019026730209589005,
0.01996522955596447,
0.0061724563129246235,
0.026312105357646942,
0.0607169084250927,
0.022619200870394707,
-0.01755419187247753,
-0.024577993899583817,
0.02350982278585434,
0.01877124048769474,
0.04368980601429939,
-0.026459338143467903,
-0.038498107343912125,
0.04979894310235977,
-0.03228110820055008,
-0.015472681261599064,
0.007720065303146839,
0.03267135098576546,
0.04504844546318054,
-0.03302335739135742,
-0.03383804112672806,
0.03297876939177513,
0.00772513123229146,
-0.0167610514909029,
-0.012867419980466366,
0.013580829836428165,
-0.055942680686712265,
0.031577907502651215,
-0.02970673330128193,
-0.004373329225927591,
-0.017530301585793495,
0.02346285991370678,
0.057822711765766144,
0.013097569346427917,
0.03670082241296768,
0.0035606916062533855,
-0.07120810449123383,
-0.008133145980536938,
-0.03125489130616188,
-0.010165845043957233,
0.017022497951984406,
-0.045269619673490524,
0.012735684402287006,
0.009769030846655369,
-0.014583890326321125,
0.06140396371483803,
-0.019290996715426445,
-0.03748185932636261,
0.030835198238492012,
0.02315739169716835,
-0.05472245439887047,
0.005077387671917677,
-0.04252773895859718,
-0.05517302453517914,
-0.03158854693174362,
0.0032603233121335506,
0.004207562189549208,
-0.024184728041291237,
-0.020795190706849098,
0.04264877364039421,
-0.025512656196951866,
-0.0406394824385643,
-0.03481939435005188,
-0.027333131060004234,
-0.004155656788498163,
-0.03605083376169205,
-0.014684213325381279,
0.03953711315989494,
-0.02328246459364891,
-0.016752615571022034,
-0.029648300260305405,
-0.0817750096321106,
0.04850541800260544,
-0.016938071697950363,
0.057700835168361664,
0.011817459017038345,
-0.02253630757331848,
0.08304692804813385,
0.00032643965096212924,
-0.034108877182006836,
0.01659797877073288,
-0.019250042736530304,
0.026349004358053207,
0.00025796820409595966,
-0.026243679225444794,
0.0026762408670037985,
-0.01293054036796093,
0.025803204625844955,
0.03354492038488388,
-0.016751045361161232,
0.021706927567720413,
0.02069983445107937,
0.03978239372372627,
0.009217611514031887,
0.0019236825173720717,
0.0314970500767231,
0.0365271270275116,
0.0016151665477082133,
0.01857692562043667,
0.003032263135537505,
-0.0228899996727705,
0.01669827103614807,
0.018445661291480064,
-0.051477573812007904,
0.029766716063022614,
-0.02040359377861023,
0.0034067737869918346,
-0.053229767829179764,
0.048318151384592056,
-0.036926064640283585,
-0.004459202289581299,
0.02158977836370468,
0.01942404918372631,
0.03002738393843174,
0.026132147759199142,
0.002562434645369649,
0.05332402139902115,
0.08066653460264206,
0.01130913756787777,
-0.013933952897787094,
-0.006404525600373745,
-0.032763224095106125,
-0.009125696495175362,
-0.029171936213970184,
0.006856986787170172,
0.035373613238334656,
0.02020964026451111,
0.023623300716280937,
0.0009028777712956071,
-0.044230032712221146,
-0.011265129782259464,
-0.06428757309913635,
-0.011510483920574188,
-0.02735973708331585,
0.06994582712650299,
-0.02132594585418701,
0.05485890433192253,
0.011920076794922352,
-0.001140375854447484,
0.038001999258995056,
-0.002508341334760189,
-0.054158397018909454,
0.025898858904838562,
-0.008759959600865841,
-0.017096471041440964,
-0.0038655465468764305,
-0.013168510049581528,
0.0013650438049808145,
-0.04276489466428757,
-0.042045097798109055,
-0.0025567945558577776,
0.045424796640872955,
-0.03815099224448204,
0.017433108761906624,
-0.02711937390267849,
-0.04473353549838066,
-0.04025646299123764,
0.036564912647008896,
0.015481117181479931,
-0.008315729908645153,
0.031204229220747948,
0.05931595340371132,
-0.009512146934866905,
-0.047488704323768616,
-0.02803146466612816,
0.02990884892642498,
-0.007163913454860449,
0.018778154626488686,
0.013848756439983845,
0.008320368826389313,
-0.03901531547307968,
0.01916416361927986,
-0.005877065006643534,
0.01712373085319996,
0.0092088608071208,
-0.0029703578911721706,
-0.037321384996175766,
-0.002093815477564931,
-0.006380968727171421,
0.03194388002157211,
0.011400597169995308,
0.0006123434286564589,
0.012365459464490414,
-0.0164127666503191,
-0.01499208901077509,
-0.04667556285858154,
0.04213721677660942,
0.08257374912500381,
0.01572343148291111,
0.020212247967720032,
-0.04868254065513611,
0.023808762431144714,
-0.02014760673046112,
0.030539928004145622,
0.021731287240982056,
0.028858281672000885,
-0.01865242049098015,
-0.025930745527148247,
0.005945191252976656,
-0.03985271230340004,
0.005344364792108536,
0.023615002632141113,
0.04240686073899269,
0.05997404083609581,
0.014046236872673035,
-0.00418822793290019,
-0.00515331095084548,
0.051705244928598404,
0.02274552546441555,
0.030551498755812645,
-0.02526499330997467,
-0.10473047196865082,
-0.035152044147253036,
0.02528904378414154,
0.012233270332217216,
-0.031800366938114166,
-0.025555245578289032,
-0.03315266966819763,
-0.020564816892147064,
0.07642079889774323,
0.011413575150072575,
0.01735737919807434,
-0.006654875352978706,
0.01982259936630726,
-0.01526428572833538,
-0.011768399737775326,
0.014318298548460007,
0.015285097062587738,
-0.001610013423487544,
0.019992325454950333,
0.0012882056180387735,
-0.009087461046874523,
-0.01704680174589157,
0.05032061040401459,
0.02557428553700447,
0.06953556835651398,
0.0064497170969843864,
0.003895488101989031,
-0.024498673155903816,
-0.041112761944532394,
-0.027844585478305817,
-0.06827948242425919,
0.018390560522675514,
-0.02279854379594326,
0.006285548210144043,
0.05165392532944679,
-0.008464745245873928,
-0.008478180505335331,
0.04329821467399597,
0.006124833598732948,
-0.04387093335390091,
-0.00676573533564806,
-0.02765537053346634,
0.020673837512731552,
0.017805190756917,
0.011551843024790287,
0.054146915674209595,
0.011180386878550053,
0.008057559840381145,
0.031015967950224876,
0.0014051055768504739,
0.03740595281124115,
-0.01044734288007021,
-0.02782556042075157,
-0.023813463747501373,
-0.012588794343173504,
-0.03579843416810036,
0.028723563998937607,
-0.014237212017178535,
0.049842897802591324,
-0.007149687502533197,
-0.036198463290929794,
-0.016164986416697502,
-0.007239874452352524,
0.004186559002846479,
-0.034992679953575134,
0.030677927657961845,
0.04989539459347725,
0.0027092203963547945,
-0.019453253597021103,
0.007719152141362429,
0.009440732188522816,
0.020097842440009117,
-0.0019158475333824754,
-0.00021234971063677222,
0.018169119954109192,
-0.042339589446783066,
-0.018258482217788696,
0.015081671997904778,
-0.0008561845170333982,
0.08476974070072174,
-0.02107749693095684,
0.03654904291033745,
0.015935448929667473,
-0.0374298132956028,
0.01554041262716055,
0.03649883717298508,
0.04444028064608574,
0.06007689982652664,
-0.05748515948653221,
-0.0015050964429974556,
0.021058201789855957,
-0.001359627116471529,
-0.05287124216556549,
-0.011782788671553135,
0.049097757786512375,
0.03898891434073448,
-0.029651550576090813,
-0.08836729824542999,
0.011737394146621227,
-0.045608166605234146,
-0.048363540321588516,
0.00967477262020111,
0.025925837457180023,
-0.04380963742733002,
-0.003633912419900298,
0.019770123064517975,
0.011752422899007797,
0.07186298817396164,
-0.03810570389032364,
-0.013143105432391167,
0.009692512452602386,
-0.03628573939204216,
-0.03523319214582443,
0.015172833576798439,
0.010813259519636631,
-0.04180329293012619,
0.002654491690918803,
0.00014908685989212245,
-0.006335975136607885,
0.07201993465423584,
-0.026293402537703514,
0.0018541597528383136,
0.011536451987922192,
0.028241822496056557,
-0.016673782840371132,
0.0009097276488319039,
0.04741663858294487,
0.014794454909861088,
0.029802314937114716,
-0.03767545148730278,
-0.01932526007294655,
0.010081473737955093,
0.013186058960855007,
-0.03307892009615898,
0.008426403626799583,
0.004260470159351826,
-0.01432301476597786,
0.05976446717977524,
-0.018918896093964577,
-0.024876374751329422,
0.02683478407561779,
-0.02415129542350769,
0.019094258546829224,
0.013954795897006989,
-0.0026068647857755423,
0.012294130399823189,
-0.0034918393939733505,
-0.015095409005880356,
-0.0467020645737648,
-0.026619575917720795,
-0.018157348036766052,
0.06758525967597961,
0.011015183292329311,
0.03878561034798622,
0.03842519596219063,
0.026684094220399857,
-0.02389335073530674,
0.00189819629304111,
-0.038467489182949066,
0.04343968257308006,
0.00045744344242848456,
0.023867450654506683,
-0.003392548533156514,
-0.008225451223552227,
-0.025381630286574364,
-0.0033197589218616486,
-0.007272512186318636,
0.013199549168348312,
-0.029070215299725533,
0.019833559170365334,
0.032842375338077545,
-0.049265116453170776,
-0.04692719131708145,
0.030538540333509445,
-0.03709922730922699,
0.027977576479315758,
0.0014951267512515187,
-0.018463734537363052,
0.03500521555542946,
0.009061058051884174,
-0.0033942987211048603,
-0.04399316757917404,
-0.01509916316717863,
-0.029750902205705643,
-0.017325395718216896,
0.022332260385155678,
-0.009716924279928207,
-0.00877339206635952,
0.042130887508392334,
0.0012153256684541702,
-0.015552091412246227,
0.007643846329301596,
0.004698888398706913,
-0.04866231605410576,
0.013089219108223915,
-0.04785322770476341,
-0.05521668866276741,
0.03677491098642349,
0.014552522450685501,
-0.027988148853182793,
0.022473584860563278,
0.00144869030918926,
0.022301223129034042,
-0.007829849608242512,
0.009356217458844185,
0.006647841073572636,
0.027591906487941742,
0.0012709706788882613,
0.0182806309312582,
-0.014037836343050003,
0.04155644029378891,
0.10850007086992264,
0.0663268119096756,
0.01376533042639494,
-0.026946017518639565,
-0.012477456592023373,
0.0030016684904694557,
-0.020057352259755135,
-0.0478617399930954,
0.015839241445064545,
-0.02883860096335411,
0.029322031885385513,
0.02594982273876667,
0.04166250675916672,
-0.027425915002822876,
0.011852276511490345,
0.03399944305419922,
-0.023887045681476593,
-0.006290566176176071,
-0.011626054532825947,
0.027568364515900612,
0.01084044761955738,
0.05713805556297302,
-0.01678062416613102,
0.02846565656363964,
-0.014052139595150948,
-0.017340391874313354,
-0.015698937699198723,
-0.015704942867159843,
0.015867333859205246,
0.0009147530072368681,
-0.04240100085735321,
0.02276783250272274,
0.03669803962111473,
-0.0041898805648088455,
-0.05911466106772423,
0.00333869899623096,
0.0225230623036623,
-0.015524229034781456,
0.00587464589625597,
0.02861238270998001,
0.03468992933630943,
-0.02349928393959999,
0.008379475213587284,
0.018034055829048157,
-0.07404431700706482,
-0.013812516815960407,
-0.04541291296482086,
0.02647792547941208,
-0.029344188049435616,
0.007350466214120388,
-0.004546552896499634,
-0.00017663581820670515,
0.01236768253147602,
-0.048462580889463425,
-0.023206230252981186,
0.019262587651610374,
0.053582724183797836,
-0.05585687607526779,
-0.05030127987265587,
-0.022559398785233498,
0.03021901845932007,
-0.009884752333164215,
0.0038512370083481073,
0.030699074268341064,
-0.022139577195048332,
-0.04127569869160652,
-0.009573899209499359,
0.045084502547979355,
-0.024778855964541435,
-0.030130328610539436,
-0.0373401902616024,
-0.034928932785987854,
-0.01352684386074543,
-0.02729024365544319,
-0.004438154399394989,
-0.008357550948858261,
0.04901210963726044,
-0.011796192266047001,
0.013574942015111446,
-0.01556001789867878,
-0.058762941509485245,
0.015765653923153877,
-0.026996571570634842,
-0.01744743622839451,
-0.06230798363685608,
-0.0012320888927206397,
0.01414231676608324,
0.028038552030920982,
-0.024543726816773415,
0.028424546122550964,
0.014259591698646545,
0.04276767000555992,
0.05161557346582413,
0.004380758386105299,
-0.003529116278514266,
0.027703434228897095,
-0.022829357534646988,
0.039158713072538376,
0.021182453259825706,
0.05309714749455452,
0.037414297461509705,
0.003013337729498744,
0.03073837235569954,
-0.003212832612916827,
-0.0338081456720829,
0.032011713832616806,
-0.017328474670648575,
-0.03608391061425209,
-0.002997735282406211,
-0.006535614375025034,
-0.02343704365193844,
-0.029585039243102074,
-0.012460854835808277,
-0.057220131158828735,
-0.012537992559373379,
-0.01809391751885414,
0.00863052997738123,
-0.012227050960063934,
0.05803654342889786,
-0.007692128419876099,
0.030039794743061066,
-0.02898230217397213,
-0.025826238095760345,
-0.057583753019571304,
0.003229665569961071,
0.009135188534855843,
-0.0014114439254626632,
-0.007834836840629578,
0.004755100235342979,
-0.03247721865773201,
-0.013465139083564281,
0.019547145813703537,
-0.007324925158172846,
0.006136968266218901,
-0.010056478902697563,
0.009311698377132416,
-0.00022773644013796002,
0.08025290071964264,
-0.01796954683959484,
0.011804714798927307,
0.034639839082956314,
-0.009774129837751389,
-0.049028631299734116,
0.030537305399775505,
0.01664493791759014,
0.027706917375326157,
0.04695485159754753,
-0.025299686938524246,
0.011746834963560104,
0.0300967488437891,
-0.013007843866944313,
-0.004781029652804136,
-0.03856057673692703,
0.02273792028427124,
0.008729062974452972,
-0.017778316512703896,
0.021764280274510384,
-0.012674827128648758,
0.00023111997870728374,
0.048246536403894424,
0.004227576311677694,
-0.003456034464761615,
0.007724649738520384,
0.009498844854533672,
-0.08110971748828888,
-0.006289753597229719,
0.028634479269385338,
0.008526422083377838,
0.020696844905614853,
0.028201874345541,
-0.0567566342651844,
0.013285094872117043,
0.008308443240821362,
-0.02635987289249897,
-0.059201449155807495,
0.015572203323245049,
0.009922114200890064,
0.00642967876046896,
0.03606824576854706,
-0.03906456381082535,
0.01927012763917446,
0.03830401226878166,
-0.044065553694963455,
0.019449913874268532,
-0.022566014900803566,
0.012509111315011978,
-0.028418773785233498,
-0.013068625703454018,
0.005244002211838961,
0.004571121651679277,
-0.005594573449343443,
0.043204110115766525,
0.029377246275544167,
0.030347639694809914,
-0.0026647697668522596,
-0.04727405682206154,
-0.008122689090669155,
0.012328550219535828,
-0.009439847432076931,
-0.040435124188661575,
0.023000841960310936,
-0.03562888875603676,
0.007283552549779415,
0.022230610251426697,
-0.03860349953174591,
0.02326333150267601,
-0.04271531105041504,
0.01651633344590664,
-0.015265620313584805,
0.03353011980652809,
0.02442225068807602,
-0.028577499091625214,
-0.003252990311011672,
0.034787971526384354,
0.029160479083657265,
0.0240020714700222,
0.00599195109680295,
0.010674749501049519,
0.031704142689704895,
-0.030903292819857597,
-0.05125943571329117,
0.05109994113445282,
-0.028317293152213097,
-0.032083895057439804,
0.019027242437005043,
-0.02246476337313652,
0.02949575148522854,
-0.014529108069837093,
-0.024112015962600708,
-0.04306216165423393,
-0.0026071136817336082,
0.022880107164382935,
0.02368476428091526,
-0.006495890207588673,
0.0072515374049544334,
-0.01147208921611309,
-0.03172893822193146,
0.023854106664657593,
-0.00010558404756011441,
-0.020135074853897095,
-0.07163965702056885,
-0.028210517019033432,
0.0292793121188879,
-0.04188923537731171,
-0.018024487420916557,
-0.012298677116632462,
-0.030180491507053375,
0.03378559648990631,
-0.007292264606803656,
0.0012854903470724821,
0.030332112684845924,
-0.03987923264503479,
0.004965078551322222,
-0.05463239178061485,
0.03753617778420448,
-0.006544553674757481,
-0.013400474563241005,
-0.007336323615163565,
0.0006199391791597009,
0.021844057366251945,
-0.029180755838751793,
0.06879320740699768,
-0.010727040469646454,
-0.02684161067008972,
-0.010684221051633358,
0.02281336300075054,
0.023713551461696625,
-0.02995915524661541,
0.018344661220908165,
0.0019943928346037865,
-0.032554127275943756,
-0.011916757561266422,
-0.028676223009824753,
-0.0166306234896183,
-0.019253632053732872,
0.03382385894656181,
-0.010750368237495422,
0.010025150142610073,
0.016260527074337006,
-0.01378670148551464,
0.047386087477207184,
0.028233429417014122,
-0.02179684489965439,
0.057426705956459045,
-0.02531082183122635,
0.01010134443640709,
0.03517255559563637,
-0.009050054475665092,
-0.06673145294189453,
0.030363356694579124,
-0.00794918928295374,
-0.006042839959263802,
-0.017803791910409927,
-0.002261654706671834,
0.019535187631845474,
-0.05673576518893242,
0.02995677851140499,
0.009628074243664742,
-0.024411408230662346,
0.01894628442823887,
0.04944685846567154,
0.0016892926068976521,
0.03945948928594589,
-0.004803426098078489,
0.02405228093266487,
0.04878635331988335,
-0.01493084616959095,
-0.03766656294465065,
0.03778153285384178,
0.05329754576086998,
-0.021054266020655632,
0.03292042389512062,
0.020021848380565643,
-0.018714461475610733,
0.021353432908654213,
0.00527430372312665,
0.0043457201682031155,
-0.010896692052483559,
-0.03205273672938347,
0.03462984785437584,
-0.020524822175502777,
-0.008390381932258606,
0.020031295716762543,
-0.044309671968221664,
0.06704907864332199,
0.03292010352015495,
0.003901406889781356,
-0.039498768746852875,
-0.013981785625219345,
-0.017460959032177925,
0.011449461802840233,
-0.023772863671183586,
0.0748111680150032,
0.03410488739609718,
0.00736483046784997,
-0.00006717531505273655,
0.007519627455621958,
-0.01287537720054388,
-0.025544699281454086,
0.05164162442088127,
-0.012566632591187954,
0.023728754371404648,
-0.019584741443395615,
-0.011299730278551579,
-0.01790853776037693,
-0.022876717150211334,
0.049371130764484406,
0.04138393700122833,
0.014463244006037712,
0.05430605635046959,
-0.013236409984529018,
-0.013126668520271778,
0.04135987535119057,
-0.07402033358812332,
-0.01784205250442028,
-0.026182614266872406,
0.013437896966934204,
0.006784277968108654,
-0.04521452635526657
] |
<p>Also the side question is how many Joules is one photon (any between 450-660nm).
Thank you</p>
<p>P.S. I am asking because I want to estimate how much thermal energy should be dissipated by LED when part of known energy is emitted as light.</p>
<p>P.S. Got an answer from Robert. Thank you.
So those 6500 Lumen 100Watt white LED arrays emit about 9 watt of energy in photons alone and rest 91W goes into heat. Not bad.</p> | 4,613 | [
-0.026409853249788284,
-0.035580120980739594,
-0.016400674358010292,
-0.026931680738925934,
0.01838832162320614,
0.0130296116694808,
-0.0497201606631279,
-0.060301534831523895,
0.01814301870763302,
-0.04932509735226631,
0.04428950324654579,
0.05154462158679962,
0.007385793142020702,
0.018234288319945335,
0.009671801701188087,
0.012443001382052898,
-0.00777398468926549,
0.012933355756103992,
0.00891831424087286,
-0.03679164499044418,
-0.02628258615732193,
-0.002282960107550025,
0.020098548382520676,
-0.00830500666052103,
-0.05879835784435272,
0.016284571960568428,
0.018446676433086395,
-0.004937977530062199,
0.009182518348097801,
0.05847751721739769,
-0.026788754388689995,
-0.0470469631254673,
0.021854471415281296,
0.029688851907849312,
0.020198343321681023,
-0.0007357856375165284,
-0.03557050600647926,
-0.03840205818414688,
-0.04665995389223099,
0.0221418309956789,
-0.025550177320837975,
-0.017968375235795975,
0.0028928255196660757,
0.013130121864378452,
0.027213377878069878,
-0.020394157618284225,
-0.024275487288832664,
-0.03540107235312462,
0.04663993418216705,
-0.06438972055912018,
0.05969318002462387,
-0.008254565298557281,
0.06999146193265915,
-0.005921384785324335,
-0.02995946630835533,
0.02090274542570114,
0.06736375391483307,
0.05037202686071396,
-0.011623518541455269,
-0.033080510795116425,
0.0030871995259076357,
0.02888936549425125,
0.009784668684005737,
-0.04736353084445,
0.001716171158477664,
0.013399118557572365,
-0.0077905841171741486,
-0.03163469210267067,
0.038566600531339645,
0.03370962664484978,
0.03540652617812157,
0.008722648024559021,
0.04406299814581871,
0.00765073299407959,
-0.01808871142566204,
-0.02860303781926632,
0.005847040098160505,
0.04980123043060303,
0.038425348699092865,
0.027178827673196793,
-0.029176581650972366,
0.007422277238219976,
0.03376123681664467,
0.05713003873825073,
0.004393840674310923,
-0.01763298735022545,
0.05873355641961098,
-0.015196326188743114,
0.01065094955265522,
-0.0013310638023540378,
0.04249107092618942,
0.0415375679731369,
0.03793950378894806,
0.07101503014564514,
-0.006387049797922373,
0.032240647822618484,
-0.006532144267112017,
0.04676699638366699,
-0.01438229437917471,
-0.04723190888762474,
0.06258586794137955,
0.025906885042786598,
0.04154285416007042,
0.04965107515454292,
-0.020911986008286476,
-0.022543037310242653,
-0.008284238167107105,
0.01990010030567646,
0.003428572788834572,
0.01696142554283142,
-0.03114195540547371,
-0.01276891864836216,
-0.005983735900372267,
-0.019026683643460274,
0.042774830013513565,
-0.01937011070549488,
-0.02348899096250534,
-0.0004617642844095826,
0.04227069765329361,
0.024185022339224815,
-0.02400483936071396,
-0.017697196453809738,
0.026337146759033203,
-0.013870077207684517,
-0.06083130091428757,
0.02348802424967289,
0.014364696107804775,
-0.005519362632185221,
-0.05519026890397072,
0.04477991536259651,
-0.013099459931254387,
-0.03170626610517502,
0.006469348445534706,
-0.021411238238215446,
-0.011798771098256111,
-0.05262282118201256,
-0.027888640761375427,
-0.06832718849182129,
0.02854309417307377,
-0.022618548944592476,
0.028455348685383797,
-0.03944006562232971,
0.03875691816210747,
0.030255496501922607,
0.05692267790436745,
-0.018367819488048553,
0.006054137367755175,
-0.033758752048015594,
0.004449797794222832,
-0.062248509377241135,
-0.043809399008750916,
-0.02096170000731945,
0.005416822154074907,
-0.035826049745082855,
0.0407431535422802,
-0.049759455025196075,
0.05101966857910156,
0.059182681143283844,
-0.013194606639444828,
-0.04929383099079132,
-0.020733803510665894,
0.030580880120396614,
0.02094077132642269,
0.03338032588362694,
0.010894456878304482,
-0.04404883831739426,
0.06499882787466049,
-0.027525292709469795,
0.002566294278949499,
0.051001206040382385,
-0.04673922434449196,
-0.011580594815313816,
0.0006480589509010315,
0.014954826794564724,
0.06593473255634308,
-0.00992660317569971,
0.015870308503508568,
-0.04409906268119812,
0.04581242799758911,
0.009433481842279434,
-0.06861549615859985,
-0.04265422746539116,
0.016588814556598663,
-0.027286622673273087,
0.03246290981769562,
0.026364166289567947,
0.008600424975156784,
-0.03577825799584389,
0.027125254273414612,
-0.017296649515628815,
-0.03169284015893936,
-0.04858919605612755,
0.0028598534408956766,
0.013878828845918179,
-0.020587706938385963,
-0.019801300019025803,
-0.008959630504250526,
0.02482534758746624,
0.002957548014819622,
-0.022827904671430588,
0.004953077062964439,
0.0069535961374640465,
0.00023252901155501604,
-0.03386746719479561,
0.011459734290838242,
0.05811789259314537,
0.055476464331150055,
0.0005741328350268304,
0.010045051574707031,
-0.043424833565950394,
-0.017802303656935692,
-0.007476672995835543,
-0.038473162800073624,
0.0205213725566864,
-0.01936458982527256,
-0.04652689769864082,
-0.0031839795410633087,
-0.012199739925563335,
-0.00491139804944396,
0.017892973497509956,
-0.008357025682926178,
0.07014816254377365,
0.03419257700443268,
-0.012163689360022545,
-0.020525475963950157,
-0.002240680856630206,
-0.03560131415724754,
-0.005292641930282116,
-0.018153131008148193,
-0.026322735473513603,
-0.07611954212188721,
0.019796758890151978,
0.03334251791238785,
-0.013257034122943878,
-0.05098684877157211,
0.02460654452443123,
0.042033202946186066,
0.015971895307302475,
0.029278121888637543,
-0.010907904244959354,
-0.03617937117815018,
0.0033634360879659653,
-0.0010005191434174776,
0.03364932909607887,
-0.018934698775410652,
-0.0016082036308944225,
-0.004702428355813026,
0.043465353548526764,
0.02927187830209732,
-0.0075514717027544975,
-0.03360333666205406,
0.06256068497896194,
0.00653125811368227,
0.04512269049882889,
-0.032219819724559784,
-0.03336143121123314,
0.05457592383027077,
-0.02769823558628559,
0.0062330192886292934,
-0.0026180469430983067,
-0.02746817097067833,
0.029069464653730392,
-0.019645273685455322,
-0.06518054008483887,
-0.002256265375763178,
-0.0028993776068091393,
-0.03423161432147026,
-0.015855692327022552,
0.025715181604027748,
-0.0029030253645032644,
0.0367133729159832,
-0.030619675293564796,
0.023213503882288933,
-0.036252353340387344,
-0.018688786774873734,
0.048627763986587524,
-0.006159050855785608,
0.00527389207854867,
-0.10870741307735443,
-0.061275094747543335,
-0.013036142103374004,
-0.055178746581077576,
0.00766797224059701,
0.0023463803809136152,
-0.05991848558187485,
-0.023291897028684616,
-0.002856522100046277,
-0.023180028423666954,
0.004489129409193993,
-0.013967073522508144,
0.006514058914035559,
0.06416214257478714,
0.004320999141782522,
-0.0580768957734108,
-0.013986564241349697,
-0.004445171449333429,
-0.012700507417321205,
-0.02952374517917633,
-0.0053934501484036446,
0.040560878813266754,
-0.024858664721250534,
-0.056559957563877106,
-0.014543229714035988,
-0.06764940172433853,
-0.026643887162208557,
0.002289771568030119,
-0.014765914529561996,
0.04937896877527237,
-0.0046506766229867935,
0.02146674133837223,
-0.0012655608588829637,
-0.02291027642786503,
0.04229534789919853,
-0.07078815996646881,
-0.04783686250448227,
-0.002537570195272565,
-0.004492667503654957,
0.002651454880833626,
0.0007233312935568392,
-0.029448358342051506,
0.0618591383099556,
0.011956363916397095,
-0.05959039181470871,
-0.019162947311997414,
-0.017413334921002388,
0.014716674573719501,
-0.038763634860515594,
0.013293815776705742,
-0.019498147070407867,
-0.020237823948264122,
-0.007904536090791225,
0.0039492640644311905,
0.028212768957018852,
0.02204093337059021,
0.03149811178445816,
0.02288617566227913,
0.01780886761844158,
-0.020558813586831093,
-0.009632844477891922,
0.02567177452147007,
-0.0194183848798275,
-0.020677875727415085,
0.019764447584748268,
-0.00159777095541358,
0.035824425518512726,
-0.008969155140221119,
-0.021792057901620865,
0.054021205753088,
-0.010664494708180428,
0.012549707666039467,
-0.05217939242720604,
0.007133781909942627,
0.027271173894405365,
0.012521234340965748,
0.004835246596485376,
0.0414683036506176,
0.042254041880369186,
-0.047551531344652176,
-0.0034225357230752707,
0.015477688051760197,
0.056907255202531815,
0.03174708038568497,
-0.02487051859498024,
0.031451184302568436,
0.007835361175239086,
-0.018750615417957306,
-0.01294576283544302,
-0.041553135961294174,
0.046274974942207336,
0.0547960139811039,
0.08039974421262741,
0.018012847751379013,
-0.007795798126608133,
0.0028105215169489384,
-0.07127951085567474,
-0.031118934974074364,
-0.02788020297884941,
0.09114911407232285,
0.006850662175565958,
0.026274830102920532,
0.05160972848534584,
0.019134774804115295,
0.04040570184588432,
-0.006381558254361153,
-0.0937543660402298,
0.016492756083607674,
-0.008804886601865292,
-0.01498461700975895,
-0.010238911025226116,
-0.014652976766228676,
-0.011961719021201134,
-0.040457289665937424,
-0.011049255728721619,
0.019167516380548477,
0.03174598515033722,
-0.03615462779998779,
0.00594826927408576,
-0.009541564621031284,
-0.04085838794708252,
0.001020602649077773,
-0.007502923719584942,
-0.019431907683610916,
-0.016575468704104424,
-0.0016868560342118144,
0.04141080379486084,
-0.0035236563999205828,
0.0008801705553196371,
-0.00922359898686409,
0.02159804105758667,
-0.044025685638189316,
0.04868277534842491,
0.042910218238830566,
0.05543317645788193,
-0.03632708266377449,
0.004624785389751196,
0.010309704579412937,
0.02600754238665104,
0.016488565132021904,
-0.04050225391983986,
-0.010537770576775074,
-0.02405938133597374,
-0.0004277563712093979,
0.030534764751791954,
0.01563711278140545,
-0.01342548243701458,
0.034848231822252274,
0.06610962748527527,
-0.0034112671855837107,
-0.012301587499678135,
0.057012785226106644,
0.02789229527115822,
-0.01393679529428482,
-0.013574770651757717,
-0.01749688759446144,
0.014704281464219093,
-0.010550867766141891,
0.013682830147445202,
0.03135024011135101,
0.03088659979403019,
0.003559473901987076,
-0.007560457568615675,
0.0003581664932426065,
0.009060204960405827,
-0.015414631925523281,
0.0090728048235178,
0.02035599574446678,
0.024059787392616272,
-0.005464902613312006,
-0.022208314388990402,
-0.002926433924585581,
0.044205501675605774,
0.02825365774333477,
-0.018015295267105103,
-0.024999167770147324,
-0.07466548681259155,
0.0025628095027059317,
0.04742027074098587,
0.05989640951156616,
0.0012797609670087695,
-0.000022375057596946135,
-0.025277309119701385,
0.028611063957214355,
0.014690149575471878,
-0.02750120870769024,
0.022792739793658257,
0.0077384356409311295,
0.02903188019990921,
0.01479425374418497,
-0.02563541755080223,
0.005309546831995249,
0.008621866814792156,
-0.00651287566870451,
0.028508523479104042,
-0.02439267747104168,
-0.049765679985284805,
0.0023773708380758762,
0.02584139071404934,
0.0436432845890522,
0.0726243183016777,
-0.02430468052625656,
0.01252265926450491,
0.008642742410302162,
0.02633029781281948,
0.014864928089082241,
-0.04799622669816017,
0.00810029823333025,
0.0012956650462001562,
-0.02518637478351593,
0.048159606754779816,
-0.024933597072958946,
-0.06155218556523323,
0.04084525257349014,
0.05671394243836403,
0.021820448338985443,
-0.048149507492780685,
-0.03484117612242699,
0.03438899666070938,
0.022479819133877754,
0.0011942536802962422,
0.07366229593753815,
0.018935510888695717,
-0.04321296885609627,
0.027721615508198738,
-0.0019657923839986324,
0.06797294318675995,
-0.07099270075559616,
0.006361611653119326,
-0.004298849031329155,
0.0060866354033350945,
0.0172114335000515,
0.06094467639923096,
-0.0443442203104496,
0.021169429644942284,
0.0038228861521929502,
-0.060940276831388474,
-0.004052688367664814,
0.0022302200086414814,
0.023806562647223473,
-0.0011638484429568052,
-0.026505272835493088,
0.050453390926122665,
-0.0024649573024362326,
-0.03565969318151474,
0.010688599199056625,
-0.025978263467550278,
0.032488174736499786,
-0.010258404538035393,
0.003478267230093479,
0.035057686269283295,
-0.060723528265953064,
0.020947257056832314,
0.027243155986070633,
0.006729931104928255,
0.050623416900634766,
0.016123902052640915,
0.058187201619148254,
0.0346573106944561,
-0.08577055484056473,
-0.014729089103639126,
0.0055276332423090935,
-0.0018996520666405559,
0.027082886546850204,
-0.03137305751442909,
0.024859154596924782,
-0.010787266306579113,
-0.02142959088087082,
-0.05231117084622383,
-0.033881139010190964,
-0.0057858857326209545,
0.036820266395807266,
0.00515382643789053,
-0.024649644270539284,
0.00697719119489193,
-0.04243761673569679,
-0.019853200763463974,
0.005008624866604805,
0.006087110843509436,
-0.00915090274065733,
0.0013199499808251858,
0.006765830330550671,
-0.0036794585175812244,
0.013860664330422878,
0.010993219912052155,
-0.03280732408165932,
0.014568501152098179,
0.017524491995573044,
-0.04149112105369568,
0.004457511007785797,
0.03574884682893753,
-0.03019263781607151,
0.00576370395720005,
0.018985431641340256,
-0.030878394842147827,
0.06727463006973267,
-0.004747838247567415,
0.01302576158195734,
0.011719640344381332,
0.0493905246257782,
-0.03864199295639992,
-0.004330007825046778,
0.027706990018486977,
0.012664847075939178,
0.037729714065790176,
0.03560495749115944,
-0.028413252905011177,
-0.012352980673313141,
0.00965779647231102,
0.02791462279856205,
0.009715664200484753,
0.027151769027113914,
0.0018623782088980079,
0.03305988386273384,
0.00006365760782500729,
0.01234314776957035,
0.00155726820230484,
-0.003998375032097101,
0.04884546622633934,
0.004098138771951199,
0.02283274568617344,
0.0000504566341987811,
-0.015986481681466103,
-0.010037017986178398,
-0.06052922084927559,
-0.0394405797123909,
-0.03290794789791107,
0.059086188673973083,
-0.020061567425727844,
0.052598170936107635,
-0.01045557577162981,
-0.011857975274324417,
0.03097473457455635,
-0.021310461685061455,
0.0027612990234047174,
0.02751101180911064,
0.00658893259242177,
0.029042644426226616,
-0.020802661776542664,
-0.03293278440833092,
0.037573352456092834,
0.012197588570415974,
-0.011908972635865211,
0.02359839342534542,
0.0016336020780727267,
0.03246379643678665,
0.0169138852506876,
-0.025490393862128258,
-0.033838238567113876,
-0.0017331622075289488,
-0.029966700822114944,
0.0066774822771549225,
-0.0036973312962800264,
0.01485093031078577,
0.03569038584828377,
-0.010682386346161366,
0.00764832366257906,
-0.01576818712055683,
-0.02084467001259327,
-0.046077366918325424,
0.01709246262907982,
0.015150168910622597,
0.0038354338612407446,
-0.040985144674777985,
0.037339452654123306,
0.007895802147686481,
-0.0019688315223902464,
0.03250932693481445,
-0.004247636999934912,
-0.022118067368865013,
-0.04609757661819458,
0.005126184318214655,
-0.04102223366498947,
0.004923190921545029,
0.015274419449269772,
0.015621338039636612,
-0.013403982855379581,
-0.02090127021074295,
-0.016215255483984947,
-0.006808922626078129,
0.03892269730567932,
0.034880105406045914,
0.05289333313703537,
-0.0014056336367502809,
0.05135128274559975,
-0.021727370098233223,
0.023449363186955452,
0.10127907246351242,
0.043709058314561844,
0.027697918936610222,
-0.07008572667837143,
-0.0009571335976943374,
-0.03285229951143265,
-0.0012728525325655937,
-0.03841328248381615,
0.0186353400349617,
-0.006775551475584507,
0.009689119644463062,
0.04907115548849106,
0.0668317973613739,
-0.009477377869188786,
-0.017178798094391823,
0.007368661928921938,
-0.0026244199834764004,
-0.01239530649036169,
0.07875704020261765,
0.014520873315632343,
-0.009359297342598438,
0.010949918068945408,
-0.04221462830901146,
-0.010552517138421535,
-0.0029581189155578613,
-0.037845317274332047,
0.0008690259419381618,
-0.04037054255604744,
0.04306524991989136,
0.011517961509525776,
-0.02561536245048046,
-0.01792323961853981,
0.017048165202140808,
0.005441228859126568,
-0.03847908228635788,
0.00739577692002058,
0.05399070307612419,
0.00893869623541832,
0.012483367696404457,
0.011520962230861187,
0.03398885950446129,
0.0027491606306284666,
0.02820638194680214,
0.026112498715519905,
-0.050224896520376205,
-0.027721678838133812,
-0.03496987745165825,
0.0008654644479975104,
-0.03478051722049713,
0.026075292378664017,
0.014292660169303417,
-0.004761382471770048,
-0.00512915151193738,
-0.061664026230573654,
0.003490445902571082,
0.025131406262516975,
0.013394667766988277,
0.0023528633173555136,
-0.032674241811037064,
-0.023387739434838295,
0.008607728406786919,
-0.005125502124428749,
0.02296639420092106,
-0.027329932898283005,
0.012857123278081417,
0.012949736788868904,
0.0023213813547044992,
0.0446578748524189,
-0.02025725692510605,
-0.05280911922454834,
0.00017605915491003543,
-0.04075063765048981,
-0.02726292982697487,
-0.03005608543753624,
0.014307251200079918,
-0.0009437000844627619,
-0.014603628776967525,
0.011980054900050163,
-0.020826127380132675,
-0.026653137058019638,
-0.09329390525817871,
0.014546189457178116,
0.013679343275725842,
-0.04961537569761276,
-0.027141159400343895,
0.01379859633743763,
0.046104565262794495,
0.04657258838415146,
0.003274560207501054,
-0.004589500371366739,
-0.0006750429165549576,
0.028083402663469315,
0.015411675907671452,
-0.035046059638261795,
0.017744669690728188,
0.03406830504536629,
-0.041062794625759125,
0.0019517510663717985,
-0.01848038285970688,
0.03373885154724121,
0.0044235833920538425,
-0.009675281122326851,
0.022605013102293015,
0.003997432999312878,
-0.022005625069141388,
-0.021852783858776093,
-0.006051022559404373,
-0.027025027200579643,
-0.004212826024740934,
-0.008036011829972267,
-0.003262251615524292,
-0.02182317152619362,
-0.03096536546945572,
-0.03486575931310654,
0.0016190331662073731,
0.026595789939165115,
-0.010069961659610271,
-0.01996070332825184,
-0.0020567041356116533,
-0.014857389964163303,
-0.007686665281653404,
-0.04865776374936104,
-0.03583454713225365,
-0.0006651427829638124,
0.024396900087594986,
0.03307754173874855,
-0.0036901223938912153,
0.0021803968120366335,
0.026910513639450073,
-0.01997707039117813,
0.010811686515808105,
0.07028239965438843,
0.046207040548324585,
0.02009403705596924,
-0.02703186497092247,
0.0027340734377503395,
0.00807612668722868,
0.05131065100431442,
-0.012459497898817062,
-0.011457106098532677,
0.06290768086910248,
-0.009527616202831268,
-0.05290249362587929,
0.05233142897486687,
-0.014515579678118229,
0.008947819471359253,
0.007058922201395035,
-0.013661427423357964,
-0.021592048928141594,
0.04916052147746086,
0.0017736912705004215,
-0.032688599079847336,
0.006472276523709297,
-0.040107451379299164,
0.0066889445297420025,
0.030387260019779205,
0.007446632254868746,
-0.027872905135154724,
0.016838403418660164,
0.05401671305298805,
0.030149947851896286,
-0.02749653346836567,
0.0047346455976367,
-0.021251333877444267,
0.00666304025799036,
0.010296656750142574,
0.04754741117358208,
-0.012173098511993885,
0.013426530174911022,
0.02781982533633709,
0.021026652306318283,
0.01390301063656807,
-0.011871571652591228,
0.000144341160194017,
-0.0903802216053009,
0.004708772525191307,
-0.03256490081548691,
-0.0040696654468774796,
-0.012927398085594177,
-0.05996640399098396,
0.0387854278087616,
0.019882161170244217,
-0.07621975243091583,
0.0119621055200696,
0.00018378547974862158,
-0.012757591903209686,
-0.052809733897447586,
0.046095773577690125,
-0.00837663747370243,
0.01960121840238571,
0.007078842259943485,
0.05894327536225319,
0.012174000032246113,
0.034455806016922,
-0.010294455103576183,
-0.018178658559918404,
0.018188633024692535,
0.03067498840391636,
-0.009547332301735878,
-0.03231307491660118,
0.026669003069400787,
-0.011674892157316208,
-0.013029178604483604,
0.00033815947244875133,
-0.01648792438209057,
0.010984333232045174,
-0.029070617631077766,
0.05482086166739464,
-0.009746970608830452,
0.041040752083063126,
0.00838974304497242,
-0.03338995203375816,
-0.02182873524725437,
0.012700685299932957,
0.029956497251987457,
-0.0038812237326055765,
-0.009162548929452896,
0.023647217079997063,
0.004822349175810814,
-0.013125217519700527,
-0.030414806678891182,
0.04846538230776787,
0.011506031267344952,
-0.004255303647369146,
0.025372972711920738,
0.007023426238447428,
-0.004612762946635485,
-0.04618716239929199,
0.02471119537949562,
-0.0810767263174057,
-0.008973919786512852,
-0.02257435955107212,
-0.01351943239569664,
-0.00417063944041729,
-0.02902952954173088,
0.022900018841028214,
-0.04161384329199791,
0.026244092732667923,
-0.020920278504490852,
0.010903912596404552,
-0.05579499155282974,
0.01363142766058445,
0.01931675896048546,
0.007985970005393028,
-0.019769765436649323,
-0.047370363026857376,
-0.06435368955135345,
0.042237505316734314,
-0.023875946179032326,
0.024791294708848,
0.03821069747209549,
-0.025499844923615456,
-0.024598348885774612,
-0.04021400585770607,
0.030703360214829445,
0.0010736577678471804,
0.0174263846129179,
-0.07699079066514969,
-0.02911718748509884,
0.008387110196053982,
0.004760146141052246,
0.042910028249025345,
0.007556624710559845,
-0.04449649527668953,
0.0048759933561086655,
-0.0058617922477424145,
0.009693172760307789,
-0.06359744817018509,
0.05033307522535324,
-0.03355661407113075,
-0.011189879849553108,
-0.056249648332595825,
-0.017927469685673714,
0.00303340470418334,
-0.009348051622509956,
0.03587159141898155,
-0.03388544172048569,
-0.02334729954600334,
-0.04667963460087776,
-0.00046105534420348704,
0.024827687069773674,
0.017991213127970695,
0.035472847521305084,
0.07760746777057648,
-0.02234123833477497,
0.01857076957821846,
0.07659457623958588,
-0.02543790452182293,
-0.0456588938832283,
0.027331432327628136,
-0.007935059256851673,
0.02123316377401352,
0.035076916217803955,
0.022520124912261963,
0.056745026260614395,
-0.04196695238351822,
-0.016871143132448196,
0.00868607684969902,
-0.008482009172439575,
-0.013346058316528797,
0.03782765194773674,
-0.018516013398766518,
0.0065957424230873585,
0.01535030547529459,
0.05472810938954353,
0.03611036017537117,
0.017397526651620865,
-0.013280199840664864,
0.022742293775081635,
0.005976477637887001,
-0.012699796818196774,
0.0439784862101078,
-0.005200539715588093,
-0.0005294476286508143,
0.02269446663558483,
-0.019925285130739212,
0.0018335144268348813,
-0.02863280102610588,
-0.01910717971622944,
0.013773208484053612,
0.016598962247371674,
-0.020084181800484657,
0.03366256505250931,
-0.030157582834362984,
0.0748981386423111,
-0.037775248289108276,
0.029779424890875816,
-0.04720860347151756,
-0.02010798640549183,
-0.03460600972175598,
0.00044956919737160206,
0.027228498831391335,
0.06994838267564774,
-0.02570032700896263,
-0.004472275730222464,
0.012651734985411167,
-0.0019360800506547093,
-0.0032232985831797123,
-0.06295716762542725,
0.03112187795341015,
-0.02091030217707157,
0.00864017941057682,
-0.024678708985447884,
0.000360023055691272,
0.007913519628345966,
-0.002774324966594577,
0.00007768100476823747,
0.043580006808042526,
-0.009331848472356796,
0.043877799063920975,
-0.012529841624200344,
0.010384049266576767,
0.05230335146188736,
-0.02373626083135605,
0.0032812769059091806,
-0.013918207958340645,
0.011201538145542145,
0.01400428544729948,
0.0022385409101843834
] |
<p>Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for <a href="http://scholar.google.com/scholar?q=%22cellular+automata%22+physics&hl=en&btnG=Search&as_sdt=2001&as_sdtp=on">"cellular automata" physics</a>.</p>
<p>Google Scholar still gives more than 2.000 results when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22quantum+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"quantum cellular automata"</a>.</p>
<p>But it gives only <a href="http://books.google.com/books?hl=en&lr=&id=sab-9fGPCEcC&oi=fnd&pg=PA1&dq=%22relativistic+cellular+automata%22&ots=rG9eoNgPYh&sig=ZNQpI-0B-0S2358zX9To-h4NtdI#v=onepage&q=%22relativistic%20cellular%20automata%22&f=false">1</a> (one!) result when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22relativistic+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"relativistic cellular automata"</a>, i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.</p>
<blockquote>
<p>How can this be understood? </p>
<p>Why does the concept of QCA seem more
promising than that of RCA?</p>
<p>Are there conceptual or technical barriers for a thorough treatment of RCA?</p>
</blockquote> | 4,614 | [
-0.04302620887756348,
-0.0487511046230793,
0.01127107534557581,
-0.04053924232721329,
0.02017020992934704,
-0.0009691492887213826,
-0.029004964977502823,
-0.047196246683597565,
-0.011849511414766312,
-0.06443555653095245,
0.0650782361626625,
-0.0031101973727345467,
0.07012952864170074,
0.03676491975784302,
0.01541217602789402,
0.010648545809090137,
-0.021804364398121834,
-0.01558747235685587,
-0.02293006330728531,
-0.02983451448380947,
0.04451588913798332,
0.01522222999483347,
-0.0056589823216199875,
0.014078562147915363,
0.00027037100517190993,
0.028035268187522888,
0.02687819115817547,
-0.012585645541548729,
0.004129380453377962,
0.031286418437957764,
-0.04334690049290657,
0.029936015605926514,
-0.007046390790492296,
0.005145960953086615,
0.006622158456593752,
-0.005921597126871347,
-0.013823398388922215,
-0.021650776267051697,
0.04279409721493721,
-0.0150923952460289,
-0.005390615202486515,
-0.017595544457435608,
-0.03517666831612587,
0.050520848482847214,
-0.03713070601224899,
0.06337529420852661,
0.027491403743624687,
-0.010639403015375137,
-0.001721955370157957,
-0.06750570982694626,
0.0548105388879776,
0.021615728735923767,
0.03187800943851471,
-0.0052820066921412945,
0.01110607385635376,
0.0033586870413273573,
0.01907811500132084,
0.0782112330198288,
0.002124482998624444,
-0.03602809086441994,
-0.004668922629207373,
0.004052410367876291,
0.007012850604951382,
-0.024463530629873276,
-0.02455311268568039,
0.09111572802066803,
0.016180364415049553,
-0.03377652168273926,
0.03845345601439476,
-0.026987697929143906,
0.007091469597071409,
-0.011202442459762096,
-0.002972628688439727,
-0.018022911623120308,
0.009219725616276264,
-0.026347817853093147,
-0.011986738070845604,
0.02284133806824684,
0.00035370697150938213,
0.04442059248685837,
-0.00873059593141079,
0.005339844152331352,
-0.020059246569871902,
-0.003943330608308315,
-0.021509282290935516,
-0.005083958152681589,
0.0975852906703949,
-0.03785485029220581,
-0.03839457035064697,
-0.013043919578194618,
-0.03164391592144966,
0.016954652965068817,
0.0294715017080307,
0.022865474224090576,
-0.012357771396636963,
0.05549042299389839,
-0.004344400484114885,
0.024344168603420258,
-0.009027773514389992,
-0.060894645750522614,
-0.05027955397963524,
-0.02991955541074276,
0.010369825176894665,
0.07620427012443542,
-0.028892293572425842,
-0.026276949793100357,
-0.016841094940900803,
0.03821810334920883,
-0.04890991374850273,
0.006482765544205904,
-0.015023315325379372,
0.018736055120825768,
-0.01137547381222248,
0.02604830451309681,
0.017807375639677048,
-0.015398521907627583,
0.01080077700316906,
-0.007685514632612467,
0.02983824722468853,
0.09117383509874344,
0.0270483810454607,
-0.06440959125757217,
-0.0020155529491603374,
-0.030038710683584213,
-0.07446882128715515,
0.005202966276556253,
0.024372488260269165,
-0.009684673510491848,
-0.043484512716531754,
0.015624864026904106,
-0.001813940703868866,
0.0027967507485300303,
-0.00471282796934247,
-0.025984492152929306,
0.05540118366479874,
0.0035701128654181957,
-0.11316205561161041,
-0.058417439460754395,
0.10306654870510101,
0.023997317999601364,
0.019383050501346588,
-0.06390193849802017,
0.00530578289180994,
0.022469060495495796,
0.07441192865371704,
-0.005019430071115494,
0.007296123541891575,
0.024380473420023918,
0.05411841720342636,
-0.004105223808437586,
-0.027145711705088615,
0.034511927515268326,
0.0050353542901575565,
0.005452919285744429,
0.023587271571159363,
-0.054021526128053665,
0.02965344488620758,
0.04022245854139328,
0.01810770481824875,
-0.003848831169307232,
0.0695820227265358,
0.010859227739274502,
-0.004044658504426479,
-0.011784251779317856,
0.024307506158947945,
-0.01655520871281624,
0.06803468614816666,
0.009717359207570553,
0.019990606233477592,
0.014644194394350052,
-0.028401264920830727,
0.006099375430494547,
-0.006872070021927357,
-0.014542683959007263,
0.04239138588309288,
-0.004896792117506266,
0.026795726269483566,
0.003748701186850667,
0.004889161791652441,
0.0032575789373368025,
-0.06821602582931519,
-0.02418951317667961,
-0.04308471083641052,
0.02777579054236412,
0.0021297212224453688,
0.03028884157538414,
-0.033350955694913864,
-0.017688274383544922,
-0.0028279453981667757,
-0.030739743262529373,
-0.01783131994307041,
-0.0575454980134964,
-0.015051810070872307,
-0.01107209362089634,
0.0289749875664711,
0.066579669713974,
-0.04250617325305939,
-0.0007653286447748542,
0.01543465256690979,
-0.007244075648486614,
-0.024193644523620605,
0.010485868901014328,
0.018393339589238167,
0.00032005467801354825,
0.006657733581960201,
0.06313678622245789,
0.037181492894887924,
-0.023626364767551422,
0.01898925006389618,
0.0206720270216465,
-0.022114785388112068,
0.010020848363637924,
-0.021068990230560303,
0.0542011484503746,
-0.019344033673405647,
-0.016282467171549797,
0.018849536776542664,
0.031020265072584152,
-0.0236019566655159,
-0.007115354761481285,
-0.02507747896015644,
0.01950807496905327,
0.03469020500779152,
0.04092181473970413,
0.0009341827244497836,
0.0783865675330162,
-0.004743318073451519,
-0.002426261082291603,
0.0006768789608031511,
-0.017473455518484116,
-0.06108209118247032,
-0.02349264547228813,
0.05594852194190025,
0.021791256964206696,
-0.05092090740799904,
0.03690063953399658,
-0.0019998913630843163,
0.0852322205901146,
0.028020285069942474,
0.033144332468509674,
-0.05327829718589783,
-0.08449501544237137,
0.04619316756725311,
0.009641353040933609,
0.001315656234510243,
0.01332625187933445,
0.008699306286871433,
-0.02939937822520733,
-0.0028910033870488405,
0.010597245767712593,
-0.0042384229600429535,
0.016123928129673004,
-0.007992510683834553,
-0.05116073787212372,
-0.012757684104144573,
-0.03023792803287506,
0.03098313696682453,
0.0010410461109131575,
-0.0006932824617251754,
0.02580558881163597,
0.0022675087675452232,
0.028844527900218964,
-0.03724813833832741,
-0.02575703151524067,
-0.0007031757268123329,
0.009070602245628834,
-0.018969787284731865,
-0.04261363670229912,
0.02375083416700363,
-0.032841023057699203,
0.02922596037387848,
-0.02713613398373127,
-0.014162911102175713,
-0.038420651108026505,
-0.010324523784220219,
0.0013496121391654015,
0.04339129850268364,
0.01107504591345787,
-0.04894037917256355,
-0.001213329960592091,
0.03591341897845268,
0.0011420137016102672,
0.01716412790119648,
0.029387550428509712,
-0.013575864024460316,
0.028717946261167526,
-0.04170748591423035,
-0.044511910527944565,
0.02631205879151821,
-0.04150443524122238,
-0.003175755962729454,
0.015975836664438248,
-0.045354343950748444,
-0.03508272022008896,
-0.006989290006458759,
-0.04025878757238388,
0.026778878644108772,
-0.03919288143515587,
0.019697804003953934,
0.05367385596036911,
0.018365440890192986,
-0.07350461184978485,
-0.017077995464205742,
-0.010705011896789074,
-0.03978360816836357,
0.008138354867696762,
-0.0013112846063449979,
0.021824359893798828,
-0.042591117322444916,
0.03440238535404205,
0.036128293722867966,
-0.03164701536297798,
-0.008304997347295284,
-0.053345970809459686,
-0.0356920026242733,
-0.0015460627619177103,
-0.060299571603536606,
0.06083715707063675,
-0.01279931515455246,
-0.018421506509184837,
0.06453432887792587,
0.00835327710956335,
-0.001854602131061256,
-0.03361368924379349,
0.004833022132515907,
-0.03059929609298706,
-0.06193293258547783,
0.021882347762584686,
0.034655652940273285,
-0.011693473905324936,
-0.0015715499175712466,
-0.0011074582580477,
0.04806464910507202,
0.055618785321712494,
0.006735965609550476,
-0.027490977197885513,
0.0003932058752980083,
-0.029615309089422226,
0.0024990697856992483,
0.015099523589015007,
0.007768531329929829,
-0.026559878140687943,
0.019451087340712547,
-0.022774821147322655,
0.026599036529660225,
-0.0018300452502444386,
-0.06657744944095612,
0.04384611174464226,
0.017754005268216133,
-0.015231098979711533,
-0.04312286898493767,
-0.0011773679871112108,
0.022287264466285706,
-0.016108175739645958,
0.014702183194458485,
0.037229228764772415,
0.0009336598450317979,
0.008575422689318657,
-0.002051047282293439,
0.0033075232058763504,
0.05040896683931351,
-0.03548883646726608,
0.027223164215683937,
-0.01184510625898838,
-0.004910980351269245,
0.0323234423995018,
-0.006734179798513651,
0.0014396145706996322,
0.06117837131023407,
0.0194413885474205,
-0.006730641704052687,
0.01678285375237465,
-0.04190463945269585,
-0.041104283183813095,
-0.03795817866921425,
-0.018765801563858986,
-0.033551666885614395,
0.04826837033033371,
0.011918721720576286,
0.0053410837426781654,
0.00040912468102760613,
-0.0031860002782195807,
-0.013033363036811352,
-0.020639630034565926,
-0.11560118943452835,
-0.0002773749583866447,
-0.027460861951112747,
0.028219502419233322,
0.013703650794923306,
-0.010389069095253944,
0.012658379040658474,
0.006421237718313932,
-0.04664204269647598,
0.00007917291804915294,
0.019145173951983452,
-0.07419532537460327,
0.025343235582113266,
-0.022092873230576515,
-0.02390442043542862,
-0.00848251674324274,
-0.005446618422865868,
0.05289798229932785,
-0.04056894779205322,
0.01146105770021677,
0.03765083849430084,
-0.03736185282468796,
-0.021520651876926422,
-0.01828876882791519,
-0.000604479864705354,
0.060609593987464905,
-0.0030452709179371595,
-0.024456657469272614,
0.0065295081585645676,
-0.028566107153892517,
0.013390553183853626,
0.03804666921496391,
-0.0190870463848114,
0.018705546855926514,
-0.011671495623886585,
-0.012223522178828716,
-0.054835546761751175,
-0.018102087080478668,
-0.009227760136127472,
0.02321959100663662,
0.01993023231625557,
0.04198518022894859,
0.034224580973386765,
0.04170858487486839,
0.01416986808180809,
0.05595633015036583,
0.012629265896975994,
-0.043715253472328186,
-0.03411061689257622,
-0.009651475585997105,
-0.01222493126988411,
-0.04120098426938057,
-0.017859743908047676,
0.03671453893184662,
-0.0010766256600618362,
-0.020802730694413185,
-0.0041404347866773605,
-0.0007234627264551818,
-0.014336470514535904,
-0.05494455248117447,
-0.0018950705416500568,
-0.004521271679550409,
-0.02203982323408127,
-0.022490721195936203,
-0.014760862104594707,
-0.012079541571438313,
0.01810537464916706,
0.013116325251758099,
0.003076395019888878,
0.01843833737075329,
-0.08672870695590973,
-0.025556501001119614,
0.04983751103281975,
0.0538870133459568,
-0.003195747034624219,
0.010254266671836376,
-0.07543348520994186,
-0.022143010050058365,
-0.01992456242442131,
-0.01712563820183277,
0.04358196258544922,
-0.003539865603670478,
-0.0246322900056839,
-0.005761082284152508,
-0.013063209131360054,
0.035435792058706284,
-0.03305688500404358,
0.01611068844795227,
0.021626031026244164,
-0.03070998378098011,
-0.005609570536762476,
0.0019012329867109656,
-0.033065926283597946,
-0.014047330245375633,
-0.013643867336213589,
-0.015205665491521358,
0.048210132867097855,
0.002401270205155015,
0.0020194021053612232,
-0.05954461544752121,
-0.07324423640966415,
0.011557377874851227,
0.017215818166732788,
-0.0021442146971821785,
0.061222679913043976,
-0.03723583370447159,
-0.03892085328698158,
0.030573897063732147,
-0.007390485145151615,
-0.014894233085215092,
-0.048869360238313675,
-0.016216037794947624,
0.046347618103027344,
0.04046713188290596,
-0.018724877387285233,
0.032370876520872116,
0.03304850682616234,
-0.035263918340206146,
-0.007071106228977442,
-0.003157435916364193,
0.041511259973049164,
-0.04574430361390114,
0.006311031524091959,
-0.01869349740445614,
0.01649773307144642,
-0.03009911999106407,
0.05160011723637581,
0.000826057861559093,
0.011172902770340443,
0.00436454126611352,
-0.0012031856458634138,
-0.04528393968939781,
0.05865342542529106,
-0.02544535882771015,
0.009615483693778515,
-0.026369089260697365,
0.012728691101074219,
0.02653469890356064,
-0.005000617820769548,
0.04786403849720955,
-0.011719093658030033,
-0.015549535863101482,
0.03533993661403656,
-0.011693185195326805,
0.016890443861484528,
-0.02435227483510971,
0.012242065742611885,
0.01735561713576317,
-0.05031013861298561,
0.06289692968130112,
-0.015500582754611969,
-0.004225593991577625,
0.036768145859241486,
-0.06616699695587158,
-0.07463658601045609,
0.00966330524533987,
0.007531492039561272,
0.013210335746407509,
0.005645334720611572,
-0.015531008131802082,
0.004300935193896294,
0.02278146706521511,
-0.060575421899557114,
-0.013034901581704617,
0.05117170140147209,
0.02483821101486683,
-0.06169137358665466,
-0.030756037682294846,
-0.0035831774584949017,
-0.012998580001294613,
-0.009895219467580318,
0.00456985691562295,
0.03604186698794365,
-0.057606007903814316,
0.02448604628443718,
0.011462888680398464,
0.03586924076080322,
0.02033301629126072,
0.023259418085217476,
0.005802130792289972,
0.018327811732888222,
0.011094986461102962,
0.026096666231751442,
-0.027072856202721596,
0.018804963678121567,
-0.014495066367089748,
-0.025048434734344482,
-0.0056154062040150166,
0.03287184238433838,
-0.01068408228456974,
-0.020919613540172577,
0.004413149785250425,
0.04767758026719093,
0.006674597505480051,
-0.0013623288832604885,
-0.0027907215990126133,
0.019300075247883797,
0.013857552781701088,
0.014718333259224892,
-0.014999009668827057,
-0.007976075634360313,
-0.004487538710236549,
-0.006010924931615591,
0.010884619317948818,
-0.02295828051865101,
-0.0013816066784784198,
0.0008940542466007173,
0.04903091490268707,
-0.031891245394945145,
-0.012979353778064251,
0.007344568148255348,
-0.0012757009826600552,
0.03989499807357788,
-0.039393167942762375,
0.06151730194687843,
0.007448764517903328,
-0.024900466203689575,
-0.00364050455391407,
-0.03767085075378418,
-0.03802851587533951,
0.02219761721789837,
0.062008362263441086,
0.0008216718561016023,
-0.0019874125719070435,
0.03731604292988777,
-0.0028749650809913874,
0.011335630901157856,
-0.03144168108701706,
0.028576061129570007,
0.032330382615327835,
0.00853013712912798,
0.04152318090200424,
-0.03655378893017769,
-0.009026980958878994,
0.01902114227414131,
0.022913120687007904,
-0.0034667502623051405,
0.012896411120891571,
0.035004958510398865,
0.04081927612423897,
-0.007988819852471352,
-0.014650306664407253,
-0.03616763651371002,
0.06813598424196243,
-0.03366299346089363,
0.029146896675229073,
0.037033576518297195,
-0.030089113861322403,
0.048584938049316406,
0.005300433374941349,
0.021917134523391724,
-0.04230808466672897,
0.0039289649575948715,
-0.08304090797901154,
0.0648101344704628,
0.0009903789032250643,
0.008413710631430149,
0.0030971819069236517,
0.018386080861091614,
0.045186758041381836,
0.01583707705140114,
0.0018782415427267551,
0.01583455689251423,
-0.04564816877245903,
-0.016566455364227295,
-0.04840298369526863,
-0.040428753942251205,
0.01869804784655571,
0.026364624500274658,
-0.03826985880732536,
-0.006664280779659748,
-0.040766362100839615,
0.03031880035996437,
0.028585081920027733,
0.040259696543216705,
-0.0073289112187922,
0.030904902145266533,
-0.027657262980937958,
0.007118313107639551,
-0.047268472611904144,
-0.022973017767071724,
0.15081624686717987,
0.02087617851793766,
0.009759285487234592,
-0.0508478507399559,
0.02314603514969349,
0.025154847651720047,
0.013927381485700607,
-0.03960833698511124,
-0.020501619204878807,
0.011722355149686337,
-0.014819231815636158,
0.026227939873933792,
0.042962901294231415,
0.02038625441491604,
-0.0327320359647274,
0.002400288125500083,
-0.05841710418462753,
-0.054074861109256744,
-0.002136839320883155,
0.017939848825335503,
-0.0009488697978667915,
0.03630390018224716,
0.007853593677282333,
0.01847558282315731,
-0.02057253010571003,
-0.008089290000498295,
-0.02674485556781292,
-0.009496506303548813,
0.02481345646083355,
0.025230368599295616,
-0.06205824017524719,
-0.022304592654109,
0.018708018586039543,
-0.009210663847625256,
-0.016016706824302673,
0.003399429377168417,
0.008338126353919506,
0.015016881749033928,
0.0034238798543810844,
0.009429004043340683,
0.01468739751726389,
-0.0016755175311118364,
0.017625804990530014,
0.03907519578933716,
-0.04460294917225838,
0.022157739847898483,
-0.041032303124666214,
0.052538447082042694,
-0.036967456340789795,
0.0026290961541235447,
-0.008372546173632145,
-0.023211397230625153,
-0.03127725422382355,
0.003798568854108453,
-0.008045769296586514,
-0.010325159877538681,
-0.016757341101765633,
-0.004362356383353472,
0.007849156856536865,
-0.01486431248486042,
0.02382698468863964,
-0.02093789540231228,
0.0408942811191082,
-0.0024492903612554073,
-0.02320794202387333,
-0.0053642564453184605,
-0.002074248157441616,
0.04267905652523041,
-0.024878669530153275,
0.01510538812726736,
-0.04543278366327286,
0.014594361186027527,
-0.05488322675228119,
-0.032996028661727905,
-0.022361917421221733,
-0.007849891670048237,
0.03789278119802475,
0.013783902861177921,
-0.02149367891252041,
-0.024726565927267075,
-0.024107838049530983,
-0.001015183632262051,
-0.010003107599914074,
-0.017839530482888222,
-0.06027193367481232,
0.0057630641385912895,
0.01658581756055355,
0.02310427464544773,
-0.028210997581481934,
0.009376700036227703,
-0.011844455264508724,
-0.005315069574862719,
0.02128574624657631,
-0.00788938719779253,
0.006738724187016487,
-0.01627325639128685,
-0.028139377012848854,
-0.005675486754626036,
-0.004862235859036446,
0.005524786189198494,
0.03015231341123581,
-0.023367807269096375,
0.029341524466872215,
0.053598470985889435,
0.005701952613890171,
0.0016826280625537038,
0.03736073151230812,
-0.02022218145430088,
0.03707404434680939,
0.0355277881026268,
0.03935007378458977,
-0.03455207869410515,
-0.02930593676865101,
0.005809147376567125,
0.018918311223387718,
0.022321602329611778,
0.029059836640954018,
-0.03479226678609848,
0.020616181194782257,
-0.02611214481294155,
0.03517785295844078,
-0.056963007897138596,
-0.006358644925057888,
-0.028328025713562965,
0.026921788230538368,
-0.03168673440814018,
-0.018678057938814163,
-0.015443729236721992,
0.029856421053409576,
0.021783534437417984,
0.015765288844704628,
0.03705209493637085,
0.06160881370306015,
-0.0181240476667881,
0.0076016150414943695,
0.021919161081314087,
-0.00038204086013138294,
0.07519683986902237,
-0.01788233406841755,
-0.03220352157950401,
0.04385000839829445,
-0.03294554725289345,
-0.06698255240917206,
0.01896345429122448,
-0.05787079408764839,
0.002660247264429927,
0.03967525064945221,
-0.0054065510630607605,
0.0055379001423716545,
0.057366713881492615,
-0.005179059691727161,
0.008054244332015514,
0.012882218696177006,
-0.0007125752745196223,
-0.01926233246922493,
-0.0318758524954319,
-0.005536571145057678,
0.01289840042591095,
-0.011153949424624443,
0.026488950476050377,
0.05318792909383774,
-0.004309338517487049,
-0.016037102788686752,
0.00824266392737627,
-0.03442586585879326,
0.03917241841554642,
0.00125414680223912,
0.01652931235730648,
0.01940295845270157,
0.030228793621063232,
-0.0189682450145483,
0.03291149437427521,
0.03975546732544899,
-0.008101518265902996,
-0.08521924167871475,
0.0198456309735775,
-0.009849279187619686,
0.028162088245153427,
0.023247048258781433,
-0.03153245896100998,
0.012808228842914104,
0.03451400622725487,
-0.08156128227710724,
0.02933964878320694,
-0.01148317288607359,
-0.020244436338543892,
-0.02885664999485016,
-0.015594779513776302,
-0.01391515415161848,
0.035377874970436096,
0.024888865649700165,
0.04194724187254906,
0.03137526661157608,
0.01993558555841446,
-0.034993965178728104,
-0.02947602979838848,
0.02615133672952652,
0.04113391041755676,
-0.04863280430436134,
0.0018770711030811071,
0.018566038459539413,
-0.010733295232057571,
-0.026805751025676727,
0.01551665086299181,
0.029151301831007004,
0.01173267513513565,
0.0020521869882941246,
0.011474302969872952,
0.008555186912417412,
0.026921814307570457,
0.04422431066632271,
-0.005286771338433027,
0.008913025259971619,
-0.00934980995953083,
0.019852858036756516,
0.024301744997501373,
0.0037177088670432568,
0.031113984063267708,
0.04998629167675972,
-0.016080597415566444,
-0.020046336576342583,
0.05455692112445831,
-0.025543438270688057,
0.004190327599644661,
-0.005581236910074949,
-0.029091887176036835,
0.007887053303420544,
0.007541229482740164,
-0.010664175264537334,
-0.039957329630851746,
0.001404333277605474,
-0.004562278278172016,
0.010847439058125019,
0.013412406668066978,
0.036091193556785583,
-0.045808643102645874,
-0.008440189063549042,
0.02040422149002552,
-0.0007120233494788408,
-0.002977126045152545,
-0.02691780962049961,
-0.0010306350886821747,
-0.0014635137049481273,
0.03114534728229046,
-0.006952113937586546,
-0.03366629034280777,
-0.033912476152181625,
0.0434221476316452,
0.019787756726145744,
0.02147790603339672,
-0.013548352755606174,
0.004806028213351965,
0.018515676259994507,
-0.0634862408041954,
-0.003357634646818042,
-0.020918479189276695,
0.02393733151257038,
-0.051093727350234985,
-0.03850606828927994,
0.028061451390385628,
0.03644551709294319,
0.05210670083761215,
-0.012205579318106174,
0.0017620250582695007,
-0.010329252108931541,
-0.00742190470919013,
0.03530154749751091,
0.007845137268304825,
-0.016439178958535194,
-0.039412252604961395,
0.010715275071561337,
0.040395159274339676,
-0.019674235954880714,
0.01937822997570038,
0.054329127073287964,
0.04353838786482811,
0.0030737274792045355,
-0.012245459482073784,
-0.010122791863977909,
-0.04666614904999733,
0.05718320235610008,
-0.0004747576604131609,
-0.01408622320741415,
0.09428468346595764,
0.0037083118222653866,
0.036256950348615646,
0.01726337894797325,
0.012024910189211369,
0.023873575031757355,
0.011475118808448315,
-0.04522288963198662,
-0.03952950984239578,
0.026396336033940315,
-0.030926475301384926,
0.023182228207588196,
-0.024973804131150246,
0.011987660080194473,
0.027403585612773895,
-0.0023924862034618855,
-0.015765484422445297,
0.03488694131374359,
0.008447072468698025,
0.011724249459803104,
0.008996739983558655,
0.0336863212287426,
0.013600734993815422,
0.000932403898332268,
-0.01388873066753149,
0.06683521717786789,
-0.007095500361174345,
0.014381876215338707,
0.012798954732716084,
0.04591769352555275,
-0.001720392843708396,
0.021801641210913658,
0.0259249247610569,
0.0027266840916126966,
-0.02387731894850731,
0.008723249658942223,
0.02691161073744297,
-0.017073893919587135,
0.013911042362451553,
-0.002661739010363817,
-0.022860979661345482,
0.09473169595003128,
-0.02624390460550785,
0.010819698683917522,
0.0012773863272741437,
-0.013705640099942684,
-0.02065121755003929,
0.012895743362605572,
-0.008387277834117413,
0.018726475536823273,
-0.019893037155270576,
-0.019315915182232857,
-0.013487141579389572,
0.02832557074725628,
0.008911961689591408,
-0.06308932602405548,
-0.012501843273639679,
0.0071269189938902855,
-0.0028367440681904554,
0.0064134919084608555,
0.005923418328166008,
0.012436477467417717,
-0.007454967126250267,
0.02428789809346199,
0.007372978143393993,
-0.01093376986682415,
-0.026557842269539833,
-0.013077456504106522,
-0.03134723752737045,
0.08194566518068314,
-0.04307258129119873,
-0.04362960904836655,
-0.021023591980338097,
0.006956154480576515,
-0.04100712388753891,
-0.007166640367358923
] |
<blockquote>
<p><strong>Possible Duplicates:</strong><br>
<a href="http://physics.stackexchange.com/questions/14973/what-would-be-the-immediate-effects-if-light-does-not-go-at-the-maximum-speed-pos">What would be the immediate effects if light does not go at the maximum speed possible?</a><br>
<a href="http://physics.stackexchange.com/questions/14968/superluminal-neutrinos">Superluminal neutrinos</a></p>
</blockquote>
<p>I was reading this <a href="http://hosted.ap.org/dynamic/stories/E/EU_BREAKING_LIGHT_SPEED?SITE=AP&SECTION=HOME&TEMPLATE=DEFAULT" rel="nofollow">article</a> about a group of scientist thinking that they might have surpassed the speed of light with neutrinos, and are wanting other groups to check their work.</p>
<p>If their research is proven true, what impact would this finding have on the world of physics?</p> | 83 | [
-0.02416691556572914,
-0.0245500635355711,
-0.018860163167119026,
-0.03322449326515198,
0.06984104216098785,
0.01534886285662651,
-0.0015655752504244447,
-0.05391320586204529,
0.0016411466058343649,
-0.0035008955746889114,
0.07306370139122009,
0.03483663126826286,
0.030363770201802254,
0.02354450337588787,
0.0012748209992423654,
0.026761984452605247,
-0.013604770414531231,
0.014294803142547607,
-0.015621164813637733,
-0.01768745481967926,
-0.029883889481425285,
-0.010080080479383469,
-0.008115943521261215,
0.022897515445947647,
-0.0453936867415905,
0.012930369935929775,
0.005771273281425238,
0.004335926380008459,
-0.005536028183996677,
0.00829245988279581,
0.014299540780484676,
-0.014733725227415562,
0.02459784410893917,
0.00214665406383574,
-0.02536342851817608,
0.04301747679710388,
-0.037589892745018005,
-0.019454311579465866,
0.019655995070934296,
-0.00270936731249094,
-0.025499457493424416,
0.014423864893615246,
0.03140295669436455,
0.007392556872218847,
-0.04479793459177017,
0.052699655294418335,
-0.0015800740802660584,
-0.01933443173766136,
0.0483284667134285,
-0.03834320977330208,
0.03739752620458603,
0.003235742449760437,
0.031104708090424538,
0.013115105219185352,
-0.017779817804694176,
-0.02482331357896328,
0.07507012784481049,
0.07281380146741867,
-0.005132846999913454,
-0.06314143538475037,
0.001864852849394083,
-0.0005241340259090066,
0.020039018243551254,
-0.012575582601130009,
-0.02419414184987545,
0.08516911417245865,
-0.04140327125787735,
0.007807557471096516,
-0.0008548187906853855,
0.02286062017083168,
0.019440513104200363,
0.015782684087753296,
-0.001418879022821784,
0.009257777594029903,
0.005900150164961815,
-0.053684670478105545,
-0.012997131794691086,
-0.0029406489338725805,
0.009966515935957432,
0.0808514803647995,
-0.057753849774599075,
0.016088156029582024,
0.02548997290432453,
0.010928673669695854,
0.017033763229846954,
-0.027620846405625343,
0.07292478531599045,
-0.007986444048583508,
0.0038802686613053083,
-0.0007029031403362751,
0.01279081217944622,
0.0016229512402787805,
-0.0007883089710958302,
0.025788774713873863,
-0.00566072529181838,
0.005691749509423971,
-0.012584246695041656,
0.02435649000108242,
-0.009996862150728703,
-0.028238525614142418,
0.014082580804824829,
-0.009476692415773869,
-0.009274697862565517,
0.03444499149918556,
-0.004444469232112169,
-0.039859697222709656,
-0.015943119302392006,
0.010207366198301315,
-0.05924251675605774,
0.00018047101912088692,
-0.016108831390738487,
-0.013095283880829811,
0.015651632100343704,
0.01798171177506447,
0.0232757106423378,
-0.05644094571471214,
-0.00483772112056613,
-0.02303956262767315,
0.10943327844142914,
0.055555131286382675,
0.028862865641713142,
-0.010581403970718384,
0.01752830483019352,
0.0032846988178789616,
-0.052894942462444305,
0.022062260657548904,
0.011395872570574284,
0.026505818590521812,
-0.03751802444458008,
0.024683717638254166,
-0.025361325591802597,
0.0053422097116708755,
-0.019666090607643127,
-0.04180585965514183,
0.03634875640273094,
-0.020081350579857826,
-0.09646990150213242,
-0.05880042538046837,
0.07839705795049667,
0.0295913927257061,
-0.029110917821526527,
-0.09685888886451721,
-0.022804604843258858,
-0.012952396646142006,
0.07718687504529953,
0.00531652569770813,
0.017415709793567657,
-0.013323117047548294,
0.05442185699939728,
-0.014017445035278797,
0.0022031008265912533,
0.01834832690656185,
-0.0029162790160626173,
0.0004160279640927911,
0.014725680463016033,
-0.06656881421804428,
-0.005869761109352112,
0.02749803103506565,
-0.0021429196931421757,
-0.020297972485423088,
0.0575765036046505,
0.00793384201824665,
0.029647087678313255,
-0.029878167435526848,
-0.016907300800085068,
0.01012857723981142,
0.10264880955219269,
0.029112253338098526,
-0.0356629341840744,
0.04739435762166977,
-0.006024016533046961,
0.03914906084537506,
-0.04950061812996864,
-0.019816521555185318,
0.046440061181783676,
-0.020846642553806305,
0.003611330408602953,
0.0003812977811321616,
0.01489424891769886,
-0.00616416335105896,
-0.01652590185403824,
-0.024391286075115204,
-0.02657209150493145,
-0.0159348975867033,
0.04923722892999649,
0.08343831449747086,
-0.028637384995818138,
-0.012349549680948257,
0.01159641519188881,
-0.0503372848033905,
-0.01880500651896,
-0.06292164325714111,
0.022448593750596046,
0.030437037348747253,
-0.0012135051656514406,
0.0011981192510575056,
-0.0003018470015376806,
0.02630568854510784,
-0.031190503388643265,
-0.015554784797132015,
0.006023856811225414,
0.026493698358535767,
0.04820770397782326,
0.04034274071455002,
0.014754259027540684,
0.029591543599963188,
0.048464737832546234,
-0.04791322350502014,
-0.0038113147020339966,
0.0012274169130250812,
-0.010435537435114384,
0.031224990263581276,
-0.006343596614897251,
0.02357017807662487,
-0.01563456282019615,
0.016764454543590546,
0.02288742922246456,
0.02763843722641468,
-0.03219030797481537,
-0.0027095016557723284,
-0.0005201008170843124,
0.05002254620194435,
0.0016603297553956509,
-0.011590399779379368,
0.019387468695640564,
0.010204528458416462,
0.048389509320259094,
0.003314988687634468,
0.018338292837142944,
-0.04529775306582451,
-0.07499605417251587,
-0.01350621972233057,
0.022436439990997314,
-0.003474700730293989,
-0.07481609284877777,
0.01878977194428444,
0.0006457063718698919,
0.020236505195498466,
0.04152686521410942,
0.0366508923470974,
-0.04062846302986145,
-0.048809900879859924,
0.0059539563953876495,
0.03418319672346115,
0.00025062126223929226,
0.016169114038348198,
0.019620152190327644,
0.03315316513180733,
0.03884455934166908,
0.00493469275534153,
0.0019175827037543058,
0.04453577473759651,
0.00023749665706418455,
-0.026895951479673386,
0.00949819851666689,
-0.01521375309675932,
0.06984151899814606,
0.003477255580946803,
0.0175087321549654,
0.011411238461732864,
0.01573692262172699,
-0.005188362672924995,
-0.032820116728544235,
0.032505035400390625,
0.013457839377224445,
0.017178326845169067,
-0.04210644215345383,
-0.03829767182469368,
0.021426310762763023,
-0.07456688582897186,
0.03780536353588104,
-0.03559115529060364,
-0.02692178264260292,
-0.021346604451537132,
-0.015628591179847717,
0.011089659295976162,
-0.00014263934281188995,
0.057620152831077576,
-0.03592336177825928,
-0.030202563852071762,
0.026462852954864502,
-0.006593522150069475,
0.0007539962534792721,
0.030178256332874298,
-0.02128053456544876,
0.0422058142721653,
-0.026830017566680908,
-0.051737163215875626,
0.02337685227394104,
-0.015291459858417511,
0.021767865866422653,
0.05819322541356087,
-0.050015889108181,
-0.049379538744688034,
-0.009578322991728783,
-0.022797564044594765,
0.023936552926898003,
-0.03626596927642822,
0.0044657038524746895,
0.04642869532108307,
-0.006132777780294418,
-0.030459808185696602,
-0.01138139609247446,
-0.03183846175670624,
-0.008033410646021366,
-0.0007812652038410306,
0.013378155417740345,
-0.00578183401376009,
-0.03722783923149109,
0.0393511988222599,
-0.04650818929076195,
-0.04952196776866913,
0.014235704205930233,
-0.061491984874010086,
-0.06863494962453842,
0.008688516914844513,
-0.00022102499497123063,
0.03689955174922943,
0.0019187444122508168,
-0.024023424834012985,
0.07472265511751175,
0.029177183285355568,
-0.02091919630765915,
-0.0293134693056345,
-0.016344662755727768,
-0.01965360715985298,
-0.04844040796160698,
-0.020001431927084923,
0.01582353562116623,
0.023669453337788582,
0.007708806078881025,
-0.006003171671181917,
0.04350974038243294,
0.028916843235492706,
0.011653013527393341,
-0.002754238434135914,
-0.03005802631378174,
0.012022518552839756,
-0.010182095691561699,
0.014934202656149864,
0.04176802560687065,
-0.018457381054759026,
0.028849348425865173,
0.015927691012620926,
0.015418185852468014,
0.012627295218408108,
-0.04160194471478462,
0.0702456459403038,
0.03956238925457001,
-0.01315134484320879,
-0.00038437251350842416,
0.025976303964853287,
0.0034759510308504105,
-0.019314613193273544,
-0.025654956698417664,
-0.005112438928335905,
0.050464875996112823,
0.013063785620033741,
-0.001302405260503292,
0.02288229763507843,
0.05285263806581497,
-0.022189265117049217,
-0.05009082704782486,
-0.04183460772037506,
0.019241919741034508,
-0.0014218422584235668,
-0.01849338412284851,
-0.027483319863677025,
0.05273760110139847,
0.028267772868275642,
-0.007540027145296335,
-0.02358035370707512,
-0.002079406986013055,
-0.034244656562805176,
-0.041106291115283966,
0.022437570616602898,
-0.037725888192653656,
0.04147098585963249,
0.02770185098052025,
0.042068395763635635,
0.011305480264127254,
0.01289672963321209,
0.005472299177199602,
0.01157438475638628,
-0.0964961126446724,
0.024291126057505608,
-0.07106722891330719,
-0.0289552491158247,
-0.006015090737491846,
-0.013330142945051193,
-0.019683558493852615,
0.002503605792298913,
-0.005574281793087721,
-0.011984280310571194,
0.0022153854370117188,
-0.037878748029470444,
0.020247535780072212,
-0.015800131484866142,
-0.02946195751428604,
0.018062323331832886,
0.02614366076886654,
0.044605277478694916,
-0.018837468698620796,
-0.003663396229967475,
0.013200734741985798,
-0.08514519780874252,
-0.02532590925693512,
-0.03372480720281601,
0.004416182637214661,
0.01345801167190075,
0.04899725690484047,
0.011596753261983395,
-0.009852556511759758,
-0.019826073199510574,
0.00953271146863699,
0.025281621143221855,
0.0039050839841365814,
0.01892179623246193,
-0.0014842106029391289,
-0.05851982161402702,
-0.0074771312065422535,
0.028658950701355934,
0.019095441326498985,
0.06666067987680435,
-0.029316352680325508,
-0.023340370506048203,
0.020715933293104172,
-0.001793088624253869,
0.028268316760659218,
0.03235838934779167,
0.03856177255511284,
0.0019081413047388196,
-0.005680886562913656,
-0.0026122359558939934,
-0.0091581204906106,
-0.0030560623854398727,
0.005350001156330109,
0.009989246726036072,
0.026269640773534775,
-0.015602846629917622,
-0.013992976397275925,
0.0031639609951525927,
0.012778026051819324,
-0.08935031294822693,
0.02146804705262184,
-0.029366817325353622,
-0.03144489601254463,
0.005859811324626207,
-0.004910249263048172,
-0.03421178087592125,
0.043900031596422195,
0.050560031086206436,
-0.04093853011727333,
-0.022510532289743423,
-0.06815561652183533,
0.004651592578738928,
0.03972656652331352,
0.10100237280130386,
-0.024584345519542694,
-0.008877893909811974,
-0.07112522423267365,
0.04067471995949745,
0.04723389819264412,
-0.06557925045490265,
0.046440061181783676,
0.011101904325187206,
0.0025383909232914448,
-0.027825329452753067,
-0.05688614770770073,
-0.017445912584662437,
0.02385484240949154,
-0.004368530120700598,
0.015196491964161396,
-0.010913047939538956,
0.008766049519181252,
0.020258856937289238,
-0.010412941686809063,
0.03638048470020294,
0.045908115804195404,
-0.0311917494982481,
0.03431665897369385,
-0.01918220892548561,
-0.006268933415412903,
-0.04903135076165199,
-0.05637725815176964,
0.0428285151720047,
0.022397583350539207,
-0.01894388161599636,
0.05249691382050514,
-0.04190879315137863,
-0.07380497455596924,
0.058927636593580246,
0.0005955961532890797,
-0.03616773337125778,
-0.011239704675972462,
-0.06743922084569931,
0.033499643206596375,
0.07031378895044327,
-0.00275697885081172,
-0.011677952483296394,
0.02042047679424286,
-0.05331990122795105,
0.0031830056104809046,
-0.0025576655752956867,
0.020207680761814117,
-0.03454569727182388,
-0.0033939445856958628,
0.021275755017995834,
-0.019963353872299194,
-0.07104484736919403,
0.07147528976202011,
-0.00233219051733613,
0.018673531711101532,
0.0035462842788547277,
-0.0076424917206168175,
-0.017737269401550293,
0.0314907543361187,
0.0350673571228981,
0.011250385083258152,
-0.05184051766991615,
0.006771969608962536,
0.013531808741390705,
-0.02381034567952156,
0.04534338787198067,
0.005223035346716642,
0.04721376299858093,
0.01821351982653141,
0.003316025249660015,
0.00809969287365675,
-0.045342352241277695,
-0.02203008532524109,
0.03347139433026314,
-0.07794543355703354,
0.02230648137629032,
0.003209318034350872,
-0.02000408247113228,
0.04067523032426834,
-0.023987524211406708,
-0.03757753595709801,
0.04726357012987137,
-0.0241555143147707,
0.009096750058233738,
-0.041068315505981445,
0.04178028926253319,
0.017285078763961792,
-0.011985771358013153,
-0.038963865488767624,
-0.04161472246050835,
0.04023874178528786,
-0.012192935682833195,
0.004740295000374317,
-0.025021089240908623,
0.006361680570989847,
-0.05299849435687065,
0.00938393548130989,
-0.025967398658394814,
0.03533543273806572,
-0.03463616222143173,
-0.01814238168299198,
-0.004359271377325058,
-0.013916945084929466,
0.030381163582205772,
-0.011874908581376076,
-0.021068690344691277,
0.007918712683022022,
-0.016217082738876343,
-0.005231782328337431,
-0.01204459834843874,
0.019873201847076416,
-0.007602909579873085,
-0.08089998364448547,
-0.019413109868764877,
0.013460957445204258,
0.02800530195236206,
-0.010881826281547546,
0.021974606439471245,
0.02766212448477745,
0.004905728157609701,
-0.026240132749080658,
-0.005603522527962923,
0.01996413618326187,
0.008438218384981155,
0.023463279008865356,
0.02141793631017208,
0.0021469523198902607,
0.0031731389462947845,
-0.03735796734690666,
0.03915560990571976,
0.015478058718144894,
0.014379967004060745,
-0.030543047934770584,
0.037076402455568314,
-0.025836870074272156,
0.0029547964222729206,
0.02546762116253376,
-0.0347343385219574,
0.028233837336301804,
-0.0019130191067233682,
0.014783691614866257,
0.010868176817893982,
-0.034477103501558304,
-0.005536708980798721,
-0.04187794029712677,
-0.027691930532455444,
-0.02646419033408165,
0.06448353081941605,
-0.016118505969643593,
0.009749457240104675,
-0.006941142957657576,
-0.023280512541532516,
-0.012322836555540562,
-0.020658979192376137,
0.031412262469530106,
0.007498335558921099,
0.03641143813729286,
0.028848618268966675,
-0.013648009859025478,
-0.028987908735871315,
0.026676109060645103,
0.05288776382803917,
0.003626114223152399,
0.008599791675806046,
0.033747538924217224,
0.046525515615940094,
0.02520819380879402,
-0.025145020335912704,
-0.01867782697081566,
0.016311077401041985,
-0.05617087334394455,
-0.010727552697062492,
-0.0029937298968434334,
0.009908325038850307,
0.03594239056110382,
-0.031334538012742996,
0.00569072924554348,
0.006712224800139666,
-0.039915598928928375,
-0.03988627716898918,
0.0005197664722800255,
0.016080062836408615,
0.011058511212468147,
0.02161080203950405,
0.017292020842432976,
0.0009411175851710141,
0.0014414250617846847,
0.04382593184709549,
-0.035154227167367935,
-0.06092395633459091,
-0.04001140594482422,
-0.041612789034843445,
-0.025612296536564827,
0.050277918577194214,
0.024287447333335876,
-0.008401001803576946,
0.026658765971660614,
-0.059877362102270126,
-0.003734592581167817,
0.03285198286175728,
0.05096358060836792,
-0.04208219796419144,
0.07487064599990845,
-0.013762357644736767,
0.016272855922579765,
0.001030679210089147,
0.007685192860662937,
0.09441940486431122,
0.041425470262765884,
0.02501821331679821,
-0.06332334131002426,
0.052825573831796646,
0.028591401875019073,
0.007883126847445965,
-0.0190192349255085,
-0.027486002072691917,
-0.03460332751274109,
-0.0029695131815969944,
0.05111539363861084,
0.05220344662666321,
0.018476730212569237,
0.03226947411894798,
-0.009505430236458778,
-0.03272108733654022,
-0.0316927544772625,
0.0325673446059227,
0.02908354066312313,
-0.0040829721838235855,
0.0018566008657217026,
-0.011558103375136852,
0.058862440288066864,
-0.011941565200686455,
-0.02104690670967102,
-0.033934108912944794,
-0.00827658362686634,
0.019805951043963432,
0.0104763712733984,
-0.058826688677072525,
-0.018160482868552208,
0.03105243854224682,
-0.019883200526237488,
-0.05682957544922829,
0.014411973766982555,
0.027711447328329086,
0.013257739134132862,
0.027025997638702393,
0.06393060088157654,
0.040424853563308716,
0.0011898769298568368,
0.03707325831055641,
0.04361070320010185,
-0.07553267478942871,
-0.00006926231435500085,
0.002612378681078553,
0.024378882721066475,
0.0020626848563551903,
-0.009370701387524605,
-0.002006316091865301,
0.007402072194963694,
0.002662572544068098,
-0.02771391160786152,
-0.01902744360268116,
-0.007471240591257811,
-0.01086190901696682,
0.013800096698105335,
0.019041623920202255,
0.004602298606187105,
0.004275151062756777,
0.03219909220933914,
0.016509046778082848,
-0.011904514394700527,
-0.002134527312591672,
-0.004603126551955938,
-0.007004285231232643,
-0.0020776723977178335,
0.0020212747622281313,
-0.007495211437344551,
-0.01690838299691677,
0.027504101395606995,
-0.04028722643852234,
0.0061438013799488544,
0.03562867268919945,
0.024347281083464622,
-0.00603943457826972,
0.028725825250148773,
0.024228768423199654,
-0.055478982627391815,
-0.03086499683558941,
0.041119761765003204,
-0.013380540534853935,
-0.026583479717373848,
0.012975023128092289,
-0.009342885576188564,
0.008194235153496265,
0.0070272814482450485,
-0.008890241384506226,
0.0018689564894884825,
-0.012260174378752708,
0.06795678287744522,
0.0015665385872125626,
0.005965953692793846,
-0.0017901123501360416,
-0.01659145951271057,
-0.012809401378035545,
0.0011966789606958628,
-0.033532414585351944,
0.05255553498864174,
0.020537985488772392,
-0.014900808222591877,
0.048651400953531265,
0.014089329168200493,
-0.01787319965660572,
-0.03619338199496269,
0.06975104659795761,
-0.017311448231339455,
-0.017071176320314407,
0.0036890723276883364,
0.06464546918869019,
0.03013555333018303,
-0.027106529101729393,
0.01577981933951378,
-0.011234988458454609,
0.03004038706421852,
-0.0007412412669509649,
-0.03137604147195816,
0.02889951691031456,
-0.038855623453855515,
-0.000721473537851125,
-0.014578510075807571,
-0.017759844660758972,
-0.002505498705431819,
0.012469535693526268,
-0.0012867136392742395,
-0.035159338265657425,
0.01941903494298458,
0.029529152438044548,
-0.007928723469376564,
-0.009165345691144466,
0.011491134762763977,
0.007662585005164146,
-0.05504254624247551,
0.014488416723906994,
-0.025776730850338936,
0.013480404391884804,
0.034029994159936905,
-0.015648622065782547,
0.010319434106349945,
0.04728174954652786,
-0.018475646153092384,
-0.03973343223333359,
0.052725110203027725,
-0.03852330520749092,
0.022912530228495598,
0.03329945355653763,
-0.030828356742858887,
0.022755270823836327,
0.0784917026758194,
-0.04576339200139046,
-0.018603943288326263,
-0.005278209690004587,
-0.020101623609662056,
-0.027789384126663208,
0.02056058868765831,
0.018073968589305878,
0.006720978766679764,
-0.018219076097011566,
0.043055690824985504,
0.03673355281352997,
-0.013226568698883057,
0.00797177478671074,
-0.001891199848614633,
-0.04078732430934906,
-0.02197410725057125,
-0.02445765770971775,
-0.023668810725212097,
-0.005436577368527651,
0.05848608538508415,
-0.0436064638197422,
0.02444036677479744,
-0.009272336028516293,
0.009319520555436611,
-0.11921043694019318,
0.010471485555171967,
0.006525788456201553,
0.016602952033281326,
0.024683061987161636,
-0.04076617211103439,
0.04374837502837181,
0.028591133654117584,
-0.05581830069422722,
0.0246534813195467,
-0.02694031037390232,
-0.018329761922359467,
-0.047166720032691956,
0.028290094807744026,
-0.010334869846701622,
0.055273525416851044,
0.02771768532693386,
0.039166320115327835,
-0.006026823073625565,
0.037997934967279434,
-0.02589951455593109,
-0.03995947167277336,
0.016316479071974754,
0.03379831835627556,
0.002246492775157094,
-0.0070033930242061615,
0.07441571354866028,
-0.006640027742832899,
-0.0013264137087389827,
0.023473208770155907,
0.008233575150370598,
-0.0008645891794003546,
0.009822160005569458,
0.005607915110886097,
0.022727925330400467,
0.007163160014897585,
0.016685327515006065,
0.015485193580389023,
-0.013558330945670605,
0.021221159026026726,
-0.01115733664482832,
0.053854428231716156,
0.006544833071529865,
-0.001441379776224494,
-0.020336735993623734,
-0.007923942990601063,
-0.013366682454943657,
0.012888903729617596,
-0.02795860357582569,
-0.0158223956823349,
0.002351449802517891,
0.0053929733112454414,
0.0032177504617720842,
-0.04439825564622879,
0.001132040866650641,
-0.03961734473705292,
-0.0007132827304303646,
0.002397929085418582,
0.011347991414368153,
-0.0046529932878911495,
0.017529180273413658,
-0.04148559644818306,
0.007602930534631014,
-0.018925830721855164,
-0.02397926338016987,
-0.012554568238556385,
-0.04979456961154938,
-0.024122433736920357,
-0.002559893298894167,
0.003183837281540036,
0.014472597278654575,
-0.018556954339146614,
-0.0333671048283577,
0.05005769059062004,
0.00997355580329895,
0.0038615211378782988,
0.011412085965275764,
-0.020239295437932014,
-0.01240477990359068,
-0.08167225867509842,
-0.018145941197872162,
-0.0018551575485616922,
0.05013903230428696,
-0.07395235449075699,
0.001999641302973032,
-0.0075205666944384575,
0.026655759662389755,
0.04143659025430679,
0.008655039593577385,
-0.03094947710633278,
0.046502452343702316,
-0.015207064338028431,
-0.02287205681204796,
-0.04315683990716934,
-0.032073426991701126,
0.010514435358345509,
-0.011240888386964798,
-0.009826182387769222,
0.008242905139923096,
0.002461756579577923,
0.00755555322393775,
0.015335001982748508,
0.00197355798445642,
-0.005577262490987778,
0.016950177028775215,
0.002923730993643403,
0.03204522281885147,
0.014595487155020237,
-0.0020267788786441088,
0.04964105784893036,
0.011752858757972717,
0.019369328394532204,
0.020059511065483093,
0.0011515301885083318,
0.0003446798073127866,
0.009203379973769188,
-0.018250860273838043,
0.014995132572948933,
0.006902127061039209,
-0.026237957179546356,
0.0192232858389616,
-0.043484486639499664,
0.0025677720550447702,
0.026320869103074074,
-0.028040286153554916,
-0.013719783164560795,
0.050495974719524384,
0.0013376588467508554,
-0.022618010640144348,
-0.03292292729020119,
0.0060897148214280605,
-0.0007446039235219359,
-0.03475998714566231,
-0.019913604483008385,
0.024211879819631577,
-0.021713778376579285,
0.01716945879161358,
0.017267417162656784,
0.055314525961875916,
0.03231989964842796,
0.02702990174293518,
0.0009693207102827728,
0.04222828149795532,
-0.018376346677541733,
-0.02450902946293354,
0.0009437389089725912,
-0.0036161644384264946,
-0.009983038529753685,
0.03037285804748535,
0.030685391277074814,
0.06994308531284332,
-0.009205789305269718,
0.048370856791734695,
-0.013811711221933365,
-0.0415240153670311,
0.003128143260255456,
0.027112731710076332,
-0.02249976433813572,
0.005600873380899429,
-0.008126918226480484,
0.012754213996231556,
-0.008865603245794773,
0.0002685285289771855,
0.011517000384628773,
-0.06772541254758835,
0.014291047118604183,
-0.01738065481185913,
-0.0033165409695357084,
-0.003000932279974222,
-0.04631469398736954,
-0.0033123239409178495,
0.014436915516853333,
-0.01479437667876482,
-0.001903521129861474,
-0.026806367561221123,
-0.011565345339477062,
-0.033676695078611374,
0.0037475195713341236,
0.02737201564013958,
-0.011649448424577713,
0.0037219389341771603,
-0.016038386151194572,
0.018935151398181915,
-0.0475599579513073,
-0.03727538511157036
] |
<p>How does it make sense to vary the position and the velocity independently?</p>
<p><strong>Edit:</strong></p>
<p>Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics student ask this question when he learns calculus of variations? Does anybody ever answer this question? Ever? If so, please educate me.</p> | 505 | [
0.014009989798069,
0.033517807722091675,
0.02328954078257084,
0.00047220385749824345,
0.05591835081577301,
0.0022044233046472073,
-0.007232836913317442,
-0.010734776966273785,
0.007247802335768938,
-0.016164014115929604,
-0.005692301318049431,
0.07234003394842148,
0.06731957942247391,
-0.006143470294773579,
0.02891695685684681,
0.01833300292491913,
0.04165290668606758,
-0.024173125624656677,
-0.029032820835709572,
0.004120303317904472,
-0.040161602199077606,
0.002491016173735261,
0.014160022139549255,
0.0045846570283174515,
-0.03452211990952492,
0.01434592716395855,
0.007592691108584404,
-0.027088167145848274,
0.01735004410147667,
0.05404852330684662,
-0.04249382019042969,
-0.006313144229352474,
-0.011642832309007645,
0.046752870082855225,
0.03521055728197098,
-0.005286604631692171,
-0.05483754351735115,
-0.004015165846794844,
-0.0008044799906201661,
0.004013190045952797,
-0.04037570208311081,
0.004280296619981527,
-0.014260088093578815,
0.06387069821357727,
-0.04241457208991051,
0.042152296751737595,
0.029596226289868355,
-0.029001668095588684,
0.09541959315538406,
-0.04364008456468582,
0.09000468254089355,
-0.003080021822825074,
0.040948472917079926,
0.04685550555586815,
-0.02967066317796707,
0.011148977093398571,
0.09809652715921402,
0.033593375235795975,
-0.016094937920570374,
-0.03111622855067253,
-0.0021284453105181456,
-0.01750202104449272,
-0.0028250643517822027,
-0.00998110044747591,
-0.019129129126667976,
0.019174344837665558,
-0.005120886955410242,
0.01405785046517849,
0.015889381989836693,
-0.02641419880092144,
0.012796759605407715,
0.007875246927142143,
0.024285130202770233,
-0.016100777313113213,
0.026270411908626556,
-0.032528072595596313,
0.04956849664449692,
0.014636245556175709,
0.02452029287815094,
0.029890963807702065,
-0.0105208745226264,
-0.005450178403407335,
0.0548718087375164,
0.010059039108455181,
-0.004193335771560669,
-0.030441811308264732,
0.05385937914252281,
0.001962621696293354,
0.028436413034796715,
0.029423899948596954,
-0.009146086871623993,
0.009854079224169254,
0.04533304646611214,
0.02163367159664631,
-0.010719656944274902,
0.03158803656697273,
-0.00999147817492485,
0.02265743911266327,
0.007283762097358704,
-0.022085657343268394,
-0.0059317005798220634,
-0.060879845172166824,
0.013429448939859867,
0.05010294169187546,
-0.012782730162143707,
-0.008607160300016403,
0.00326724024489522,
0.0275277066975832,
-0.014939064159989357,
0.0010624985443428159,
-0.008461801335215569,
0.01126046385616064,
0.00849449634552002,
0.005260431207716465,
0.024942023679614067,
-0.008604906499385834,
-0.017843622714281082,
0.01229073852300644,
0.022168079391121864,
0.04953072965145111,
0.046904053539037704,
-0.06888217478990555,
0.034904446452856064,
-0.01583397202193737,
-0.030919266864657402,
0.020362533628940582,
0.024406006559729576,
0.009141143411397934,
-0.03485921397805214,
0.017401941120624542,
-0.01981637254357338,
0.030059264972805977,
0.004287998657673597,
0.03080132231116295,
-0.015605460852384567,
-0.01791890524327755,
-0.11286423355340958,
-0.06961183995008469,
0.05330540984869003,
-0.01820947788655758,
-0.018021905794739723,
-0.08860385417938232,
0.023242734372615814,
0.037386517971754074,
0.07623311877250671,
-0.05010567605495453,
0.004863445181399584,
0.020488765090703964,
-0.003187410533428192,
-0.025323519483208656,
0.011355539783835411,
-0.017787693068385124,
-0.028946034610271454,
-0.05710439383983612,
0.018729060888290405,
-0.06603498011827469,
0.017681896686553955,
0.04468530789017677,
0.008720748126506805,
-0.029100779443979263,
0.04226303845643997,
-0.018943095579743385,
-0.0013875680742785335,
0.015174061991274357,
0.014173362404108047,
-0.01815624162554741,
0.08729703724384308,
0.021793857216835022,
0.023021992295980453,
0.029715821146965027,
0.01444260124117136,
0.02442108280956745,
-0.043561261147260666,
0.021019751206040382,
0.032411128282547,
-0.01798345521092415,
-0.03079327382147312,
0.017690977081656456,
0.0035738253500312567,
-0.0011987194884568453,
-0.05447223037481308,
-0.07191187143325806,
-0.020693885162472725,
0.009821067564189434,
-0.02551320195198059,
0.03918902948498726,
0.013881160877645016,
0.03692006692290306,
-0.015842122957110405,
-0.014881693758070469,
0.003208113368600607,
-0.09422226250171661,
0.034239206463098526,
0.006133249029517174,
-0.012270105071365833,
0.0398159883916378,
0.016800586134195328,
-0.004672500770539045,
-0.026375792920589447,
-0.024638663977384567,
-0.013972293585538864,
0.01041736826300621,
-0.011980390176177025,
-0.03694980591535568,
0.00743094040080905,
0.07096685469150543,
0.03416290879249573,
0.051070135086774826,
0.005018200725317001,
-0.014584881253540516,
-0.017878465354442596,
0.0005334375309757888,
-0.03307969123125076,
0.01419802661985159,
0.01710633747279644,
-0.011975445784628391,
-0.008624469861388206,
0.003503495594486594,
-0.021221106871962547,
0.006914994679391384,
-0.05537328124046326,
0.10824747383594513,
0.056480564177036285,
-0.01532514113932848,
-0.010882006958127022,
0.07719291746616364,
0.000841244705952704,
0.031346481293439865,
0.03585779666900635,
-0.0459258109331131,
-0.04072113707661629,
0.019168540835380554,
-0.006076900754123926,
0.016879389062523842,
-0.017964502796530724,
-0.009820009581744671,
0.04340222850441933,
0.03666529059410095,
0.02581019513309002,
0.021566109731793404,
-0.013497764244675636,
-0.02914995141327381,
0.03401535749435425,
-0.010623769834637642,
0.016596950590610504,
0.017310701310634613,
0.03272119536995888,
0.042300209403038025,
0.020288294181227684,
0.007146098185330629,
-0.012718288227915764,
0.014472064562141895,
-0.011264209635555744,
0.018327608704566956,
0.03176349774003029,
-0.023665906861424446,
0.03719770163297653,
-0.018032139167189598,
0.014163295738399029,
0.04906599968671799,
0.005676023196429014,
-0.00888118613511324,
-0.001231277477927506,
-0.01724083162844181,
0.004068379756063223,
-0.01436796598136425,
-0.03742291405797005,
-0.007548170164227486,
0.028703870251774788,
-0.014596457593142986,
-0.004292833153158426,
-0.04939885810017586,
-0.03597438335418701,
-0.009038533084094524,
-0.006765787955373526,
0.022713737562298775,
0.021111106500029564,
0.012052943930029869,
0.010511494241654873,
-0.03244359791278839,
-0.03309867903590202,
-0.03147429972887039,
-0.025620369240641594,
0.006791098974645138,
-0.039780065417289734,
0.029551975429058075,
-0.024944810196757317,
-0.044657152146101,
0.057388581335544586,
-0.007754208520054817,
0.019365938380360603,
0.012154415249824524,
-0.017718292772769928,
-0.06732670217752457,
-0.02295558713376522,
-0.023278571665287018,
0.004678640048950911,
-0.006766106933355331,
-0.013380643911659718,
0.07067034393548965,
-0.028257273137569427,
-0.017769960686564445,
0.025351887568831444,
-0.07126051932573318,
-0.04406389221549034,
-0.006181559059768915,
0.014304086565971375,
0.03971327468752861,
-0.013124974444508553,
0.0011219168081879616,
0.05670463293790817,
-0.022749163210392,
-0.02059442363679409,
-0.05377570167183876,
-0.055907901376485825,
0.003471852745860815,
-0.007143649272620678,
0.052458345890045166,
-0.01951449364423752,
-0.02334701642394066,
0.08561528474092484,
0.028347665444016457,
-0.034821681678295135,
-0.017773227766156197,
-0.010713386349380016,
-0.024446971714496613,
-0.01084499154239893,
0.033366717398166656,
0.03191027417778969,
-0.03242623805999756,
0.010315567255020142,
0.051730308681726456,
0.014541874639689922,
0.04251422733068466,
0.01772434078156948,
-0.004761162679642439,
-0.04226117581129074,
0.036910563707351685,
-0.01972692646086216,
0.0193264652043581,
0.03618289902806282,
-0.038725148886442184,
-0.0015217027394101024,
0.027035938575863838,
0.06122699752449989,
-0.006295912433415651,
-0.01614772155880928,
0.041953444480895996,
0.019158771261572838,
0.013595485128462315,
-0.029397767037153244,
0.06344650685787201,
-0.01184573769569397,
0.006425610277801752,
-0.01960780657827854,
-0.007614517118781805,
0.03685811907052994,
-0.05305055156350136,
-0.01344616524875164,
0.03814346343278885,
0.03154533728957176,
-0.04716715216636658,
-0.03187451884150505,
0.013431944884359837,
0.03792092204093933,
0.02979237027466297,
-0.025867898017168045,
-0.02349933236837387,
0.03601071983575821,
0.009265205822885036,
0.007698704022914171,
0.0024142644833773375,
-0.07193442434072495,
0.019194886088371277,
-0.07407701760530472,
0.03118331916630268,
0.02576298639178276,
0.03592527657747269,
0.010625910013914108,
0.08076310157775879,
0.01362598780542612,
0.033550165593624115,
0.010811627842485905,
-0.012315075844526291,
-0.07811618596315384,
0.05913233011960983,
-0.026025013998150826,
-0.05137098580598831,
-0.010694208554923534,
-0.006631078198552132,
0.013661692850291729,
-0.055953897535800934,
-0.02115328051149845,
0.014993269927799702,
-0.016425721347332,
-0.04451242834329605,
-0.008731155656278133,
-0.02652384340763092,
-0.04648886248469353,
-0.026252735406160355,
0.01911025494337082,
0.037150535732507706,
-0.008378978818655014,
0.040047354996204376,
0.04562267288565636,
-0.019314846023917198,
-0.006832069251686335,
-0.014301689341664314,
-0.03168438374996185,
0.004905432462692261,
0.028101898729801178,
-0.030259083956480026,
0.02400503121316433,
0.021964017301797867,
0.03142222762107849,
-0.016135266050696373,
0.022005435079336166,
0.03278699517250061,
-0.01934025250375271,
-0.021722687408328056,
-0.057850126177072525,
0.02960231713950634,
0.00468813581392169,
0.0479411818087101,
0.001905822311528027,
0.0030311672016978264,
0.05064009875059128,
0.005024698097258806,
-0.00452154828235507,
0.015670115128159523,
0.04882575571537018,
0.0073657529428601265,
-0.0193680077791214,
-0.03716893121600151,
0.008557811379432678,
-0.018385857343673706,
-0.004946457222104073,
0.008917017839848995,
-0.004739463794976473,
-0.03593505918979645,
-0.010511796921491623,
0.004224049858748913,
0.011947515420615673,
-0.007601827848702669,
0.0028833772521466017,
-0.03800838813185692,
0.014602978713810444,
-0.016827061772346497,
-0.0008627076167613268,
0.003891867119818926,
0.03550409525632858,
0.019816124811768532,
0.009492912329733372,
-0.02507011778652668,
-0.06396480649709702,
-0.019032282754778862,
0.025627952069044113,
0.009443260729312897,
-0.020476127043366432,
0.013035901822149754,
-0.024605123326182365,
-0.04103239253163338,
0.052860479801893234,
-0.033487848937511444,
0.01608012244105339,
-0.005614593159407377,
-0.00609949417412281,
-0.015780359506607056,
-0.03218384459614754,
-0.0341811366379261,
-0.004937074612826109,
-0.04029941186308861,
0.028485296294093132,
-0.013547730632126331,
0.0002834114129655063,
-0.01966932602226734,
0.013145104981958866,
0.036876801401376724,
0.08764330297708511,
0.017026325687766075,
-0.006840806920081377,
-0.03221047669649124,
-0.0036864716093987226,
-0.03644264489412308,
-0.0738365650177002,
0.008371389470994473,
0.019667264074087143,
0.014356551691889763,
0.017250021919608116,
-0.02683420479297638,
-0.06607214361429214,
0.025253431871533394,
0.0012276817578822374,
0.015264730900526047,
0.023857682943344116,
-0.011534814722836018,
-0.00562795577570796,
0.03294656425714493,
0.010116863995790482,
0.02308771200478077,
0.022437743842601776,
-0.028310850262641907,
-0.01976344920694828,
0.008460301905870438,
0.04343893751502037,
-0.02834598906338215,
-0.03778642788529396,
-0.052525125443935394,
0.00797621812671423,
-0.024088840931653976,
0.04858894646167755,
0.021383635699748993,
0.014367848634719849,
-0.022325148805975914,
-0.04252022132277489,
-0.02709447592496872,
0.05429355427622795,
0.054519087076187134,
-0.01826196350157261,
-0.012583760544657707,
0.009647052735090256,
-0.015189905650913715,
-0.01473125722259283,
0.002352375304326415,
0.008278117515146732,
-0.011445329524576664,
0.04048989340662956,
-0.008814102038741112,
0.022282103076577187,
-0.04099934920668602,
-0.038730550557374954,
0.025763683021068573,
-0.07128619402647018,
0.028642525896430016,
-0.00445243576541543,
0.015887964516878128,
0.04390653595328331,
-0.07057461142539978,
-0.0413796566426754,
0.0032721885945647955,
-0.03483186289668083,
0.022513113915920258,
-0.0839320719242096,
0.05043300986289978,
-0.021985121071338654,
0.03819699585437775,
-0.08803673833608627,
-0.05262621492147446,
0.007571293972432613,
0.008941266685724258,
-0.01296967826783657,
-0.0006118403980508447,
0.03600374981760979,
-0.03742013871669769,
-0.036458127200603485,
-0.01773492433130741,
0.029039617627859116,
0.029889950528740883,
-0.02027520351111889,
0.017121318727731705,
0.004799088463187218,
0.06796226650476456,
0.004119195509701967,
0.0012420706916600466,
0.032774679362773895,
-0.03793128579854965,
0.01648038625717163,
-0.0012647353578358889,
0.05718468129634857,
-0.019815020263195038,
-0.010439437814056873,
-0.003444025060161948,
0.013415494002401829,
0.012036525644361973,
-0.013399808667600155,
0.005142670590430498,
0.04280655086040497,
0.032440364360809326,
-0.013017004355788231,
-0.019346196204423904,
0.010072841309010983,
0.0004933164454996586,
0.018674487248063087,
0.02150811441242695,
0.03573222830891609,
-0.009477967396378517,
-0.03512440621852875,
0.00473390007391572,
0.0012667690170928836,
0.0038680443540215492,
-0.006682835519313812,
0.04046817868947983,
-0.011421489529311657,
0.008936508558690548,
0.0036501723807305098,
0.05166938155889511,
0.026254288852214813,
-0.015089237131178379,
-0.030684558674693108,
0.022494060918688774,
0.005376818124204874,
-0.039050936698913574,
-0.014150762930512428,
-0.032834116369485855,
0.01938113570213318,
0.06243018060922623,
-0.04839899390935898,
0.05789279192686081,
0.04425683245062828,
0.02126424014568329,
0.01469338871538639,
-0.006692735478281975,
-0.019955163821578026,
-0.03615410625934601,
-0.006681454833596945,
0.02482428029179573,
-0.0024341170210391283,
-0.0025368197821080685,
0.04446127265691757,
0.04437064006924629,
-0.025072738528251648,
-0.014372280798852444,
0.015388081781566143,
0.011079137213528156,
0.022259609773755074,
0.009248829446732998,
-0.06229651719331741,
0.019325440749526024,
-0.01762782782316208,
0.027264704927802086,
-0.0109931118786335,
-0.021290550008416176,
0.04418596625328064,
-0.02434268593788147,
-0.0050970264710485935,
-0.029820648953318596,
0.00833622831851244,
-0.016689712181687355,
-0.0016721683787181973,
0.021168015897274017,
0.03415216505527496,
0.005905189085751772,
-0.00888906978070736,
0.032458897680044174,
-0.006074422970414162,
-0.013776687905192375,
-0.04026924818754196,
-0.06300463527441025,
-0.041969019919633865,
-0.03518107160925865,
-0.021807212382555008,
0.046663399785757065,
-0.002263557631522417,
-0.05251616612076759,
0.03560902923345566,
0.014118323102593422,
0.014693676494061947,
0.019731061533093452,
0.02029711753129959,
-0.019486049190163612,
0.07244445383548737,
0.00741993635892868,
0.003772658994421363,
-0.0375172384083271,
0.01689954660832882,
0.09575815498828888,
0.04340657219290733,
0.01081936340779066,
-0.046071648597717285,
0.023863617330789566,
-0.028827279806137085,
0.0026330656837671995,
-0.0357971228659153,
0.02793867699801922,
0.0171766709536314,
0.022821689024567604,
-0.00041794474236667156,
0.002635934855788946,
0.024307573214173317,
-0.006023075431585312,
0.033448297530412674,
-0.042646367102861404,
-0.03559335321187973,
-0.02412518672645092,
0.007653369102627039,
-0.025081144645810127,
0.0096850311383605,
-0.030496779829263687,
0.005265211686491966,
-0.038272298872470856,
-0.028875574469566345,
-0.0006228704587556422,
-0.0544399693608284,
0.026580192148685455,
0.024823462590575218,
-0.01833253726363182,
0.014162428677082062,
0.037844493985176086,
-0.020107001066207886,
-0.05848380923271179,
0.058135803788900375,
0.0016088603297248483,
-0.04086975380778313,
-0.017462076619267464,
0.03501138091087341,
0.011213714256882668,
-0.01206907071173191,
0.005800518672913313,
-0.013806143775582314,
-0.028994932770729065,
0.005790018010884523,
-0.04832867160439491,
0.03629440441727638,
-0.0006359464023262262,
0.029325181618332863,
-0.03921913355588913,
0.01830994337797165,
-0.01450490951538086,
-0.0855303406715393,
-0.008688941597938538,
-0.0001324919139733538,
0.024948086589574814,
-0.004131869412958622,
-0.0007029217085801065,
-0.02411821112036705,
0.002348299603909254,
-0.005037217866629362,
0.0024702984374016523,
0.0192558690905571,
0.005603849422186613,
-0.018062807619571686,
-0.000875905912835151,
0.047076981514692307,
-0.02953958883881569,
-0.01412010658532381,
0.0035724560730159283,
-0.014210510067641735,
-0.05296061933040619,
-0.006909621879458427,
0.01996086910367012,
0.008130248636007309,
-0.0038950834423303604,
-0.018454423174262047,
0.010108002461493015,
-0.02444218099117279,
-0.03182128071784973,
0.03651776909828186,
0.007601524703204632,
0.003950141835957766,
-0.014788038097321987,
0.03744325041770935,
0.033277906477451324,
0.03011474758386612,
0.020224077627062798,
0.005369527265429497,
-0.02500089816749096,
0.009083923883736134,
-0.002080395817756653,
-0.020040633156895638,
-0.03192055970430374,
0.02958902157843113,
-0.031606994569301605,
-0.0024093787651509047,
-0.004015276208519936,
0.05090107396245003,
0.020126817747950554,
0.008724191226065159,
-0.01540940161794424,
0.0012828093022108078,
-0.015548549592494965,
0.01974561996757984,
0.05106015503406525,
-0.03107045218348503,
-0.015728069469332695,
0.04325763136148453,
-0.014894175343215466,
-0.027070796117186546,
-0.009941007941961288,
-0.027889523655176163,
0.017860308289527893,
-0.012028343975543976,
0.026272526010870934,
-0.007370679173618555,
0.02391962520778179,
-0.013096467591822147,
0.03359982743859291,
-0.022974340245127678,
0.03721977025270462,
-0.04465626925230026,
0.008934668265283108,
-0.010467718355357647,
0.001773489755578339,
-0.03822306916117668,
-0.002349893329665065,
-0.038527749478816986,
-0.006332766730338335,
0.02526228129863739,
0.02056964859366417,
0.04860830307006836,
-0.01376350037753582,
0.03174024820327759,
0.010542397387325764,
0.042211223393678665,
-0.04542975872755051,
-0.029015837237238884,
0.006508057937026024,
-0.04021506756544113,
-0.048532597720623016,
0.00836543645709753,
-0.014236566610634327,
0.06628140807151794,
0.013162177056074142,
-0.038606029003858566,
-0.012916866689920425,
0.041202884167432785,
0.004690298344939947,
-0.006279396824538708,
0.016261136159300804,
-0.0275482889264822,
-0.006275895982980728,
-0.06418602913618088,
0.01581031084060669,
-0.02239932119846344,
-0.003051161067560315,
0.01827138103544712,
0.0030519107822328806,
0.005555805284529924,
-0.011835768818855286,
0.027563486248254776,
0.038107022643089294,
0.026423541828989983,
0.004339765757322311,
-0.006569283548742533,
0.05089326947927475,
0.03411759063601494,
-0.0041971164755523205,
0.006829992402344942,
0.010710974223911762,
0.03241034597158432,
-0.12769117951393127,
-0.002697716001421213,
-0.010542018339037895,
0.000019418745068833232,
0.03438199311494827,
-0.04382770135998726,
-0.0025546650867909193,
0.03402649983763695,
-0.08534416556358337,
0.012985588982701302,
-0.03201354295015335,
0.00997419934719801,
0.013782567344605923,
-0.004065871704369783,
-0.008751261048018932,
0.08890275657176971,
0.04216878116130829,
0.019321762025356293,
0.019115179777145386,
0.016091663390398026,
-0.004295759368687868,
-0.02420387789607048,
-0.009295695461332798,
0.035513922572135925,
0.0014182704035192728,
-0.002147671999409795,
0.030914759263396263,
-0.004414897412061691,
-0.020617429167032242,
0.023173028603196144,
-0.022605326026678085,
-0.0019567632116377354,
-0.027436913922429085,
0.0033804618287831545,
0.02779114618897438,
0.03857903182506561,
0.009748568758368492,
-0.025208840146660805,
-0.040617432445287704,
0.001503029023297131,
0.004391720984131098,
0.038352396339178085,
0.02339312992990017,
-0.005273099523037672,
0.018310705199837685,
-0.04816066101193428,
-0.02681901305913925,
0.0010561918606981635,
-0.014136035926640034,
-0.009365075267851353,
0.009495094418525696,
0.023027949035167694,
0.005660607013851404,
-0.03906024619936943,
-0.012079999782145023,
-0.037166476249694824,
-0.012442025355994701,
0.03125390782952309,
-0.024000052362680435,
-0.008645801804959774,
-0.004405161831527948,
-0.015275145880877972,
-0.03162208944559097,
-0.015887336805462837,
-0.00402813171967864,
-0.0006551151163876057,
-0.05443781986832619,
0.02228585071861744,
0.015716150403022766,
-0.02929682284593582,
-0.024861542508006096,
-0.019482843577861786,
-0.02171648107469082,
0.017226072028279305,
0.03392206132411957,
0.01914994791150093,
-0.035096075385808945,
-0.03457530960440636,
-0.022572122514247894,
-0.06868588924407959,
0.08167844265699387,
0.00929970946162939,
-0.059959445148706436,
-0.061142757534980774,
-0.05329826474189758,
-0.0034869839437305927,
0.04808361083269119,
0.04019297659397125,
-0.007426353637129068,
-0.007234947755932808,
0.031117433682084084,
0.013919416815042496,
0.01659592054784298,
-0.00435788044705987,
-0.0030656703747808933,
-0.006581295281648636,
-0.022742699831724167,
0.012765840627253056,
0.005791428033262491,
-0.014113853685557842,
0.0025176287163048983,
-0.0012940842425450683,
-0.020360706374049187,
0.048425786197185516,
0.00853029452264309,
-0.01708425208926201,
0.02205272950232029,
0.031157247722148895,
-0.0254108477383852,
0.05668186396360397,
0.001491874922066927,
0.01831418089568615,
0.023129131644964218,
-0.01863197423517704,
-0.04477535933256149,
-0.004851866979151964,
-0.06421219557523727,
-0.030456455424427986,
-0.015988804399967194,
-0.006342717912048101,
0.02973897010087967,
-0.045510485768318176,
0.007178716827183962,
0.04036591202020645,
-0.055514078587293625,
-0.014570605009794235,
0.038789067417383194,
0.04902978241443634,
0.02626592293381691,
-0.0011856366181746125,
0.00510215712711215,
0.007308724336326122,
-0.03059764951467514,
-0.0067702424712479115,
0.016845278441905975,
0.02499975450336933,
0.009004876017570496,
0.01580377109348774,
0.04775523021817207,
-0.0000035751179439103,
0.03341543674468994,
0.021168019622564316,
0.026868456974625587,
0.001856415648944676,
-0.012331398203969002,
-0.01903979294002056,
-0.021185552701354027,
0.00016467092791572213,
0.0222566407173872,
-0.0332108736038208,
0.06103498861193657,
-0.015225172974169254,
-0.008958806283771992,
-0.007650348823517561,
0.02287697046995163,
-0.03011215478181839,
-0.039009951055049896,
0.00960648711770773,
0.04972926527261734,
-0.0066090901382267475,
-0.011846638284623623,
-0.007586623076349497,
-0.019091740250587463,
0.02349061332643032,
-0.040026526898145676,
0.03654807433485985,
-0.009214400313794613,
-0.01935293897986412,
-0.03844110667705536,
0.013995948247611523,
-0.04974943399429321,
0.0011059351963922381,
0.030364323407411575,
0.05157528445124626,
0.04777060076594353,
0.008293564431369305,
-0.027109673246741295,
-0.04707133024930954,
0.05409228801727295,
-0.06443313509225845,
-0.014640230685472488,
-0.03635222092270851,
0.010685598477721214,
0.009241011925041676,
0.019267549738287926
] |
<p>Inspired by <a href="http://physics.stackexchange.com/questions/234/how-should-a-physics-student-study-mathematics">How should a physics student study mathematics?</a> and in the same vein as <a href="http://physics.stackexchange.com/questions/193/best-books-for-mathematical-background">Best books for mathematical background?</a>, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.</p>
<p>In spite of the frivolous nature of this post, I think it can be a valuable resource.</p>
<p>For example:</p>
<hr>
<p><a href="http://rads.stackoverflow.com/amzn/click/0750628960">Course of Theoretical Physics</a> - <strong>L.D. Landau, E.M. Lifshitz.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0805370021">Mathematical Methods of Physics</a> - <strong>Mathews, Walker</strong>. Very nice chapter on complex variables and evaluation of integrals, presenting must-know tricks to solve non-trivial problems. Also contains an introduction to groups and group representations with physical applications.</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/048667164X">Mathematics of Classical and Quantum Physics</a> - <strong>Byron and Fuller.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0471010901">Topics in Algebra</a> - <strong>I. N. Herstein</strong>. Extremely well written, introduce basic concepts in groups, rings, vector spaces, fields and linear transformations. Concepts are motivated and a nice set of problems accompany each chapter (some of them quite challenging).</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0126546568">Partial Differential Equations in Physics</a> - <strong>Arnold Sommerfeld</strong>. Although a bit dated, very clear explanations. First chapter on Fourier Series is enlightening. The ratio interesting information/page is extremely large. Contains discussions on types of differential equations, integral equations, boundary value problems, special functions and eigenfunctions.</p>
<hr> | 4,615 | [
-0.0008908159215934575,
-0.044190794229507446,
0.006188159808516502,
-0.028758317232131958,
0.03325416520237923,
0.024961577728390694,
0.0036220094189047813,
-0.0463373027741909,
-0.01227987464517355,
-0.040362805128097534,
0.07173165678977966,
0.00478989165276289,
0.04408181831240654,
0.043111033737659454,
0.031559497117996216,
0.027184883132576942,
-0.010517805814743042,
-0.07702162861824036,
-0.03855681046843529,
0.02582935243844986,
0.0218268483877182,
0.030363863334059715,
-0.011481334455311298,
0.05846019834280014,
-0.05535915121436119,
0.02978307381272316,
-0.008812435902655125,
0.00047837060992605984,
-0.019547561183571815,
0.06392521411180496,
-0.05794049799442291,
0.011223436333239079,
0.018690165132284164,
-0.018373068422079086,
-0.01669244095683098,
0.02321551740169525,
0.009037339128553867,
-0.008675851859152317,
-0.0008510755724273622,
0.0027670306153595448,
-0.007114347070455551,
0.014518515206873417,
-0.006230268627405167,
0.07151338458061218,
-0.03273596987128258,
0.06687085330486298,
0.0012550436658784747,
-0.006857257802039385,
0.04169338196516037,
-0.04093059524893761,
0.03586071729660034,
-0.009316573850810528,
0.012998159043490887,
0.01903064362704754,
0.00911123026162386,
-0.030006639659404755,
0.03723228722810745,
0.03131873905658722,
0.005340317729860544,
-0.044683318585157394,
0.012693054974079132,
-0.029013115912675858,
-0.010096424259245396,
0.01276511512696743,
-0.03678996488451958,
0.03832028806209564,
0.01383848488330841,
-0.02532235160470009,
0.03227413445711136,
0.0014929909957572818,
0.00348376901820302,
0.036546170711517334,
0.02119060792028904,
-0.02124226652085781,
0.0037549904081970453,
-0.03379468992352486,
-0.0324152335524559,
0.0036387485451996326,
0.01874876581132412,
0.004706729669123888,
-0.022803936153650284,
0.018578149378299713,
0.0038431233260780573,
0.03799978271126747,
0.022693421691656113,
-0.02580215409398079,
0.08892595767974854,
-0.015056272968649864,
-0.05747506394982338,
-0.019662003964185715,
-0.02633797377347946,
-0.018557745963335037,
0.020930398255586624,
-0.004659632686525583,
-0.003904265584424138,
0.02375687099993229,
0.028122514486312866,
0.015767496079206467,
-0.0006098530720919371,
-0.013888731598854065,
-0.016876311972737312,
-0.023773174732923508,
0.025839656591415405,
0.07582128047943115,
0.009774401783943176,
-0.03221385180950165,
-0.034849874675273895,
-0.003573240712285042,
-0.008141797035932541,
-0.01979157142341137,
-0.028889013454318047,
0.043003376573324203,
-0.03486405685544014,
-0.011300420388579369,
-0.02280760183930397,
-0.04636133462190628,
0.024462655186653137,
-0.02311711758375168,
0.030085744336247444,
0.0593290850520134,
0.06343922019004822,
-0.040876634418964386,
0.00859286729246378,
-0.020007112994790077,
-0.10589062422513962,
-0.024878554046154022,
0.05982508137822151,
-0.0064621660858392715,
-0.04555929824709892,
0.05413082242012024,
-0.0189906507730484,
0.039461810141801834,
-0.0037020875606685877,
-0.010123257525265217,
0.031781814992427826,
0.030077138915657997,
-0.09030619263648987,
-0.07523220032453537,
0.05131516233086586,
-0.015314479358494282,
-0.05602918565273285,
-0.025386661291122437,
0.005058410111814737,
0.025681737810373306,
0.06002907454967499,
0.014903767965734005,
0.034550439566373825,
0.0013136848574504256,
0.014241940341889858,
-0.005792488809674978,
-0.03288991376757622,
0.01345121394842863,
-0.02692493237555027,
-0.004476319067180157,
0.027393780648708344,
-0.05015343427658081,
0.017784789204597473,
0.012321623042225838,
0.016103457659482956,
0.007419695612043142,
0.043497949838638306,
0.00041862388025037944,
0.013493197970092297,
-0.023190736770629883,
-0.020574377849698067,
0.03282134234905243,
0.05206325277686119,
0.020284127444028854,
0.02635800838470459,
0.029308343306183815,
-0.04876279458403587,
0.022875411435961723,
-0.052830688655376434,
-0.023127587512135506,
0.026805473491549492,
-0.01110937912017107,
-0.0084152827039361,
0.03480702266097069,
-0.0051025100983679295,
0.016972597688436508,
-0.02341850847005844,
-0.051133885979652405,
-0.025911234319210052,
-0.003364474978297949,
-0.03216864913702011,
0.03472449630498886,
0.057709600776433945,
0.008428176864981651,
0.007724463008344173,
-0.007772660348564386,
-0.009980556555092335,
-0.03352263569831848,
0.02333446592092514,
-0.029695777222514153,
-0.019221985712647438,
0.0573965348303318,
-0.012280374765396118,
-0.011004318483173847,
-0.018707655370235443,
-0.049984823912382126,
0.020519789308309555,
0.020238302648067474,
-0.007342177908867598,
-0.00039891802589409053,
-0.002249723067507148,
0.026142606511712074,
0.03153441473841667,
-0.04034305736422539,
0.016665350645780563,
-0.053290899842977524,
-0.022747600451111794,
0.00900455191731453,
-0.009365713223814964,
0.04708384722471237,
0.0265439972281456,
-0.006005832925438881,
0.010150509886443615,
0.037644483149051666,
-0.04230877012014389,
-0.003096003085374832,
-0.03233054280281067,
0.012158299796283245,
0.016459058970212936,
0.030950922518968582,
-0.0068893819116055965,
0.07496296614408493,
0.03278117999434471,
0.004976172465831041,
0.006904010660946369,
-0.010214644484221935,
-0.023699764162302017,
-0.0026420261710882187,
0.047197725623846054,
0.04395313560962677,
-0.06771013140678406,
0.05534948408603668,
0.021207882091403008,
0.026495320722460747,
0.03569786250591278,
0.013986839912831783,
-0.04762359708547592,
-0.08721660822629929,
0.03432367369532585,
0.002208008663728833,
-0.03307009115815163,
0.02332548052072525,
-0.028233086690306664,
-0.0033486380707472563,
-0.003543333150446415,
0.037172142416238785,
0.004849725402891636,
0.019239893183112144,
0.0024338136427104473,
-0.010060361586511135,
0.015146962366998196,
-0.05576154589653015,
0.02135130576789379,
-0.011398866772651672,
0.013253575190901756,
0.0041845110245049,
-0.01174948550760746,
0.011404763907194138,
-0.032373908907175064,
-0.031617823988199234,
-0.013083023019134998,
-0.029509738087654114,
-0.0005740814958699048,
0.005189524032175541,
0.04846309497952461,
-0.07177427411079407,
-0.01962880976498127,
-0.0043645380064845085,
-0.019191129133105278,
-0.05159519240260124,
-0.02455902099609375,
-0.004451379179954529,
0.022684017196297646,
0.012579333037137985,
-0.033335305750370026,
0.007354589179158211,
0.009289947338402271,
-0.01805058866739273,
-0.003268872620537877,
0.005966792348772287,
-0.035844527184963226,
-0.005862648598849773,
-0.04048784077167511,
-0.05436475947499275,
0.061509888619184494,
-0.00832054577767849,
-0.02340085618197918,
0.04993532598018646,
0.02033020183444023,
-0.05442946031689644,
-0.005610769148916006,
-0.009668085724115372,
0.010386409237980843,
-0.065862275660038,
0.009360355325043201,
0.0700383111834526,
-0.00828277226537466,
-0.03075374662876129,
-0.016462570056319237,
-0.011708669364452362,
-0.05096014216542244,
0.0032657578121870756,
0.006153176538646221,
0.005030243191868067,
-0.027746055275201797,
-0.031063809990882874,
0.03179442137479782,
-0.028789490461349487,
-0.003623001975938678,
-0.08546432107686996,
-0.019581522792577744,
-0.017149537801742554,
0.009580462239682674,
0.036590345203876495,
0.017622020095586777,
0.003522713202983141,
0.09083234518766403,
0.018254170194268227,
-0.04191626235842705,
-0.04117957502603531,
-0.007143734954297543,
0.001602731179445982,
-0.011852657422423363,
0.02169434353709221,
0.05179566890001297,
-0.02457147091627121,
0.009237594902515411,
0.03603023663163185,
0.014433616772294044,
0.017087368294596672,
0.03386719152331352,
0.012013901956379414,
0.03346577286720276,
-0.02415727637708187,
0.009737271815538406,
0.03707233443856239,
0.006230066996067762,
-0.04857708886265755,
-0.0007817542064003646,
-0.01001514121890068,
0.016263950616121292,
0.025431348010897636,
-0.04088630899786949,
0.0596848726272583,
-0.016127916052937508,
0.02785816229879856,
-0.03799876943230629,
0.014959686435759068,
0.0049496483989059925,
-0.04937129467725754,
-0.001307869330048561,
0.011033031158149242,
-0.004513285122811794,
0.01258611585944891,
0.032479602843523026,
0.04175499454140663,
0.08085974305868149,
-0.016619322821497917,
-0.006197127979248762,
-0.006637548096477985,
-0.007195129059255123,
0.01975819282233715,
-0.04513905569911003,
0.0159765537828207,
0.054915692657232285,
0.051907967776060104,
-0.012413923628628254,
0.023771433159708977,
-0.011754467152059078,
-0.012493569403886795,
-0.08657220751047134,
0.0021296644117683172,
-0.04308938607573509,
0.06861455738544464,
-0.006597357336431742,
0.02161218971014023,
0.00722273625433445,
-0.0067650387063622475,
-0.0013981583761051297,
0.015237920917570591,
-0.09268734604120255,
0.012645615264773369,
-0.0011394822504371405,
-0.002301296917721629,
0.032344259321689606,
0.01810012198984623,
-0.0009337321389466524,
0.0005539094563573599,
-0.03544827550649643,
-0.03673688322305679,
0.010280395857989788,
-0.03142130374908447,
-0.0034216283820569515,
-0.038936905562877655,
-0.0546669140458107,
-0.005229762755334377,
0.041320983320474625,
0.06975007802248001,
-0.041754357516765594,
0.030724670737981796,
0.015521051362156868,
-0.03337658569216728,
-0.00480193505063653,
0.01854122243821621,
0.01934542879462242,
-0.0037727353628724813,
0.023127958178520203,
0.012952492572367191,
0.03678883612155914,
-0.024975571781396866,
0.015499014407396317,
0.011655254289507866,
0.03221359848976135,
0.0014684099005535245,
-0.04506560415029526,
-0.0024523502215743065,
-0.035094909369945526,
-0.031220244243741035,
-0.035567838698625565,
0.04128675535321236,
0.009534855373203754,
-0.01762908138334751,
0.05903216823935509,
-0.02603723481297493,
-0.02884569950401783,
0.05080347880721092,
0.030739329755306244,
-0.02902684360742569,
-0.021372705698013306,
0.023427920415997505,
0.0009740028181113303,
-0.025662684813141823,
-0.0176191758364439,
0.005736003164201975,
0.019222501665353775,
-0.008700544945895672,
-0.014277124777436256,
0.002595284255221486,
0.055398520082235336,
-0.0569465272128582,
0.035342540591955185,
-0.012492183595895767,
0.007884837687015533,
0.019472194835543633,
-0.04931642487645149,
-0.004931094124913216,
0.034458644688129425,
0.05092255398631096,
-0.009469936601817608,
-0.013256892561912537,
-0.04112463444471359,
-0.03157433867454529,
0.06889358162879944,
0.07496089488267899,
-0.00873466394841671,
0.0005885070422664285,
-0.049317654222249985,
-0.011681430973112583,
0.0466383621096611,
-0.033643219619989395,
0.03076597861945629,
-0.05029657483100891,
-0.009663558565080166,
-0.037632815539836884,
-0.03767720237374306,
-0.016374699771404266,
0.011127399280667305,
0.017512574791908264,
0.011504078283905983,
-0.013595795258879662,
0.00827045552432537,
-0.005784008651971817,
0.021433593705296516,
0.046189915388822556,
0.02071181870996952,
-0.011720694601535797,
-0.01982060633599758,
0.00798087939620018,
-0.0010707410983741283,
-0.01907449960708618,
-0.059731945395469666,
0.014459156431257725,
0.003957613371312618,
-0.03277237340807915,
0.012370061129331589,
-0.021133974194526672,
-0.023355061188340187,
0.04091833159327507,
0.007430139929056168,
-0.027341188862919807,
-0.011799461208283901,
-0.04159634932875633,
0.031548965722322464,
0.028064681217074394,
0.02306228317320347,
0.026644624769687653,
0.0994955524802208,
-0.06799887865781784,
-0.005170947872102261,
-0.0353243388235569,
0.02868034504354,
-0.008231052197515965,
-0.009862718172371387,
-0.048769935965538025,
-0.07295488566160202,
-0.06865601986646652,
0.04993077367544174,
-0.058118436485528946,
-0.015707818791270256,
-0.016417576000094414,
-0.01397467590868473,
-0.0035863006487488747,
0.0015912761446088552,
-0.012763096019625664,
-0.0030593203846365213,
0.023430779576301575,
0.023200061172246933,
-0.016735965386033058,
-0.000010812434993567877,
0.02766670100390911,
0.006182866636663675,
0.007941428571939468,
0.060785915702581406,
-0.010800556279718876,
0.024831270799040794,
-0.04408048093318939,
-0.010179540142416954,
-0.05035708099603653,
-0.054863832890987396,
0.07305337488651276,
-0.0018278518691658974,
0.03806035965681076,
0.04378066211938858,
-0.017539000138640404,
-0.07145678251981735,
0.03700698912143707,
0.005777870304882526,
-0.02899935655295849,
-0.011388510465621948,
-0.0009939005831256509,
0.004055109340697527,
0.003230151254683733,
0.001366538810543716,
-0.025136085227131844,
-0.015320627950131893,
-0.0031003248877823353,
-0.04337551072239876,
-0.028046444058418274,
0.042209722101688385,
-0.012561899609863758,
0.014923152513802052,
-0.022256234660744667,
0.02683020941913128,
-0.04315314069390297,
-0.014193748123943806,
0.013745958916842937,
0.005838929675519466,
0.03436393290758133,
0.017974799498915672,
-0.018424706533551216,
0.030769111588597298,
0.053507719188928604,
0.007014674134552479,
-0.009308738633990288,
0.01200717780739069,
-0.00832595955580473,
-0.03734145686030388,
-0.008830692619085312,
-0.0011232472024857998,
0.006169850472360849,
-0.046701088547706604,
0.009350230917334557,
0.04302625358104706,
0.008915739133954048,
-0.030890000984072685,
-0.037009865045547485,
0.018996955826878548,
0.004548691213130951,
0.01889669895172119,
0.008099165745079517,
0.02168375253677368,
0.015252551063895226,
-0.0340413823723793,
0.0044529251754283905,
-0.018928028643131256,
0.012347707524895668,
0.016504738479852676,
0.03299126774072647,
-0.0005009653978049755,
-0.000050006008677883074,
0.044974230229854584,
0.01516080740839243,
0.028990687802433968,
-0.03215831518173218,
0.04825928807258606,
0.008842620067298412,
-0.025601821020245552,
-0.007099418435245752,
-0.05600587651133537,
-0.02660825103521347,
-0.014468072913587093,
0.028537122532725334,
0.04927225410938263,
0.011123227886855602,
0.04435434564948082,
-0.03209372237324715,
0.0009817556710913777,
0.02991309203207493,
-0.009426036849617958,
-0.028892619535326958,
0.03964047133922577,
0.03395584225654602,
-0.03658376634120941,
0.011502443812787533,
0.020085865631699562,
0.0413169339299202,
-0.035335902124643326,
-0.015058501623570919,
0.013665410690009594,
0.029982011765241623,
0.02604850009083748,
-0.025933189317584038,
-0.042121876031160355,
0.043419722467660904,
-0.048499442636966705,
0.025029219686985016,
0.019608434289693832,
-0.038019947707653046,
-0.0009560015168972313,
0.01159385684877634,
-0.003795853815972805,
-0.023217009380459785,
-0.008888180367648602,
-0.04996876046061516,
-0.00961375143378973,
0.0015248769195750356,
0.01663472317159176,
-0.03295296058058739,
0.016022169962525368,
0.0393761582672596,
-0.005191928707063198,
0.01528828777372837,
-0.005695872940123081,
-0.04526404291391373,
-0.02389736846089363,
-0.040670499205589294,
-0.05775371938943863,
0.06738962233066559,
0.00916657317429781,
-0.028055330738425255,
0.021649008616805077,
-0.025036374107003212,
0.06911440193653107,
0.014130722731351852,
0.019574135541915894,
-0.02990858256816864,
0.03600545972585678,
-0.03994214907288551,
-0.01967947743833065,
-0.011816638521850109,
-0.04517093300819397,
0.16074256598949432,
0.03989453613758087,
0.020498450845479965,
-0.0334034226834774,
0.02921265736222267,
-0.0027514230459928513,
0.03461330011487007,
-0.025678560137748718,
-0.03985937684774399,
-0.03581051528453827,
0.0023873131722211838,
0.020080232992768288,
0.04723820090293884,
0.016256064176559448,
-0.007171785458922386,
0.012127460911870003,
-0.04938860610127449,
-0.03831736370921135,
-0.002314486773684621,
0.015253507532179356,
0.0074271392077207565,
0.05603634938597679,
-0.020556427538394928,
-0.005823086481541395,
-0.004626081790775061,
-0.000866105139721185,
-0.049129337072372437,
-0.0344557911157608,
0.03742029145359993,
-0.006926567293703556,
-0.013240136206150055,
0.01484150905162096,
0.00014338352775666863,
-0.006538051646202803,
-0.002396221272647381,
0.014621169306337833,
0.06695239245891571,
0.004118186887353659,
0.020995941013097763,
0.019790707156062126,
0.005544613115489483,
-0.013668296858668327,
0.008187671191990376,
0.01943844184279442,
-0.06703232228755951,
0.008812042884528637,
-0.037660159170627594,
0.0427568294107914,
-0.02855672314763069,
0.0043258750811219215,
-0.041033562272787094,
0.012688345275819302,
0.020904412493109703,
-0.0021434887312352657,
0.010421769693493843,
-0.004048095550388098,
0.03534616529941559,
-0.04737759381532669,
-0.009883240796625614,
-0.008490893058478832,
0.030569514259696007,
-0.011132817715406418,
0.03916282579302788,
-0.0012690516887232661,
-0.018553346395492554,
-0.009838053956627846,
-0.012132436968386173,
0.012037551961839199,
-0.03021855279803276,
-0.006131987553089857,
-0.03910664841532707,
0.03147587552666664,
-0.008215712383389473,
-0.004196914378553629,
0.012212458997964859,
0.020736094564199448,
0.018716266378760338,
0.015027694404125214,
0.010515245608985424,
-0.00041316752322018147,
-0.04312524199485779,
0.02623981609940529,
-0.008682736195623875,
-0.018477147445082664,
-0.033744681626558304,
-0.015652712434530258,
-0.014035561122000217,
0.020722005516290665,
0.04574858397245407,
-0.0048370067961514,
0.001053771236911416,
0.043393127620220184,
0.058879684656858444,
0.023966753855347633,
0.006481259595602751,
-0.002646269043907523,
-0.020271437242627144,
0.023923777043819427,
0.023004427552223206,
0.001189032569527626,
0.023944750428199768,
0.004655161872506142,
0.01709328405559063,
0.0345599502325058,
-0.01976005546748638,
-0.013598345220088959,
-0.0025698605459183455,
-0.03783588483929634,
-0.0018387064337730408,
0.05616992339491844,
0.01410732977092266,
-0.028059130534529686,
-0.02276323363184929,
0.03390831872820854,
0.009965870529413223,
-0.031416650861501694,
0.026945261284708977,
0.00010340045992052183,
0.04336531087756157,
-0.04127724841237068,
0.0123699139803648,
-0.05209357663989067,
0.017337976023554802,
-0.0507630817592144,
-0.0015532933175563812,
0.0022101060021668673,
-0.010455746203660965,
-0.03031110018491745,
0.015445427969098091,
0.01944401115179062,
-0.0034928906243294477,
0.015791786834597588,
0.0032825733069330454,
-0.0036987510975450277,
-0.01368013583123684,
0.00015639442426618189,
-0.04208360239863396,
0.020467646420001984,
-0.0059578330256044865,
-0.02792595885694027,
0.023868246003985405,
-0.02761039324104786,
-0.04630483686923981,
0.04028624668717384,
-0.03309352695941925,
0.0007908942643553019,
0.035400256514549255,
-0.030286869034171104,
-0.01623355783522129,
0.02664094604551792,
0.005735199432820082,
-0.024243377149105072,
0.007925908081233501,
-0.02197178266942501,
0.012343131005764008,
-0.0077098216861486435,
0.0020190877839922905,
0.0016336132539436221,
-0.03220989555120468,
0.0028466724324971437,
0.0588403046131134,
0.0005107609904371202,
-0.02027607336640358,
-0.016542717814445496,
-0.02748975344002247,
0.0016625531716272235,
-0.010316597297787666,
-0.009862477891147137,
0.06298264861106873,
0.01395302265882492,
-0.04800163954496384,
0.041406210511922836,
0.0031467205844819546,
0.009263521991670132,
-0.08988883346319199,
-0.00896589457988739,
0.020836982876062393,
0.031963787972927094,
0.047305889427661896,
-0.06108870729804039,
0.028533171862363815,
0.021838385611772537,
-0.08997842669487,
0.035057730972766876,
-0.009371151216328144,
-0.008750207722187042,
0.002882664557546377,
-0.003636712208390236,
-0.012694686651229858,
0.05920010432600975,
-0.03762829676270485,
0.040489986538887024,
0.015806948766112328,
0.009032965637743473,
-0.006142723374068737,
-0.03792835399508476,
-0.016415847465395927,
0.03156217560172081,
-0.024032168090343475,
-0.015358241274952888,
0.018982958048582077,
0.04632178321480751,
-0.05845985189080238,
0.005109837744385004,
0.0028644774574786425,
-0.013209034688770771,
-0.01549813337624073,
0.021925373002886772,
0.001322550349868834,
0.02944955974817276,
0.03215229511260986,
-0.02295118197798729,
0.00014465177082456648,
-0.01519508846104145,
0.020076032727956772,
0.03684225305914879,
0.01339191384613514,
0.02401111088693142,
0.05626636743545532,
-0.010485623963177204,
-0.0442921407520771,
0.05706821382045746,
-0.011222763918340206,
-0.004371162038296461,
0.005266332067549229,
-0.004235320258885622,
-0.0029567342717200518,
-0.03364977613091469,
-0.01767743192613125,
-0.08003228157758713,
0.00018628094403538853,
0.007461621426045895,
-0.019558094441890717,
0.051774103194475174,
0.06979069113731384,
-0.00453373184427619,
-0.025306303054094315,
0.010331425815820694,
0.007583114318549633,
0.0023117067757993937,
-0.015049658715724945,
0.01059821154922247,
0.03183375298976898,
0.017003852874040604,
0.005211805924773216,
-0.013281123712658882,
-0.011334509588778019,
0.004926288966089487,
0.020175814628601074,
0.039167288690805435,
-0.018030324950814247,
-0.011550416238605976,
0.00994470901787281,
-0.04388284683227539,
0.0166341420263052,
0.031535860151052475,
0.033364202827215195,
-0.03429166227579117,
-0.003808164969086647,
0.03621072694659233,
0.01687479391694069,
0.026796262711286545,
-0.00006255285552470013,
-0.0008362422231584787,
0.01530542504042387,
-0.037153150886297226,
0.012869792990386486,
-0.029210306704044342,
0.01640055887401104,
-0.022695938125252724,
0.019842758774757385,
0.021384958177804947,
0.01628676988184452,
-0.03330506756901741,
0.004379861056804657,
0.03699071332812309,
0.0017277644947171211,
0.008348502218723297,
-0.0006249740836210549,
-0.01840873993933201,
0.04511122778058052,
0.02668500691652298,
0.00037681980757042766,
0.032311905175447464,
-0.009724805131554604,
-0.003701252629980445,
0.03610823303461075,
-0.04288365691900253,
0.0009039672440849245,
0.05348275601863861,
-0.0444389283657074,
-0.045700542628765106,
-0.005351991858333349,
-0.019812244921922684,
0.02538689412176609,
-0.06562621891498566,
0.009871935471892357,
0.04521314427256584,
-0.0034350452478975058,
-0.022517455741763115,
0.04012155532836914,
0.03879349306225777,
0.021399272605776787,
0.04473334923386574,
-0.0015698974020779133,
0.02443494275212288,
-0.07917941361665726,
-0.029127268120646477,
0.012627732940018177,
0.0405072383582592,
0.018029874190688133,
0.007292773574590683,
0.017341556027531624,
0.02711133100092411,
-0.01745736598968506,
0.0212735403329134,
0.04239460453391075,
-0.027511075139045715,
0.010033070109784603,
0.03442753478884697,
-0.024949273094534874,
0.0006217306945472956,
0.03785919398069382,
-0.01757068559527397,
0.06506098061800003,
-0.038553182035684586,
0.0014893559273332357,
-0.00163696997333318,
0.01149141974747181,
-0.013090201653540134,
0.017078299075365067,
0.0036066146567463875,
0.051279813051223755,
-0.02265685796737671,
-0.01423199288547039,
-0.03146471828222275,
0.00887339748442173,
-0.0022899042814970016,
-0.04421088844537735,
0.031049735844135284,
0.04327856004238129,
0.004103980492800474,
0.03411370888352394,
0.020673628896474838,
-0.033409763127565384,
-0.021313117817044258,
0.015329833142459393,
0.042164403945207596,
-0.01334749348461628,
-0.04822462424635887,
-0.012481236830353737,
-0.029334964230656624,
0.05500879883766174,
-0.02408788539469242,
0.007624357473105192,
-0.0049016219563782215,
-0.009009674191474915,
-0.017402540892362595,
0.025164393708109856
] |
<p>If a rectangular pan has a constant and uniform temperature $T$ first, then put it in a vacuum. Considering the effect of thermal radiation, the temperature distribution of the rectangular blackbody will change. My question is, will the temperature of the corner be higher than the edge?</p> | 4,616 | [
0.003442625980824232,
-0.06496971100568771,
0.03694029152393341,
-0.01129941362887621,
0.03541388735175133,
0.030853502452373505,
-0.03825030475854874,
-0.00627150060608983,
-0.017711294814944267,
-0.042381107807159424,
0.04047933220863342,
0.02995891124010086,
0.03193875774741173,
0.007161542773246765,
0.02366611547768116,
-0.003108828794211149,
-0.022550929337739944,
-0.004850330762565136,
0.005345465615391731,
-0.028661426156759262,
0.01545300055295229,
0.0556851290166378,
-0.007746534887701273,
-0.018708055838942528,
-0.07173122465610504,
0.01071285828948021,
-0.010716630145907402,
-0.00414798641577363,
0.02227596566081047,
0.058502133935689926,
-0.023519866168498993,
-0.02209898829460144,
0.014673169702291489,
0.006409281864762306,
0.021043702960014343,
-0.050203390419483185,
-0.013661803677678108,
-0.016054682433605194,
-0.04249556362628937,
-0.010423432104289532,
-0.0310899019241333,
-0.03747095167636871,
-0.0038510283920913935,
0.05030720680952072,
0.015447254292666912,
-0.03747231513261795,
0.00993618555366993,
-0.017543595284223557,
0.04040968790650368,
-0.053827814757823944,
0.07332202792167664,
-0.0198977068066597,
0.06306173652410507,
0.04165332764387131,
-0.01903514377772808,
-0.00016175571363419294,
0.06288409233093262,
0.05848142132163048,
-0.004418507684022188,
-0.02303300052881241,
0.01098137628287077,
-0.041945040225982666,
-0.0135686369612813,
-0.00565751176327467,
-0.03801094740629196,
0.01853431947529316,
-0.03295746445655823,
-0.030510421842336655,
-0.03494866192340851,
-0.012402084656059742,
0.009557422250509262,
0.022665726020932198,
0.03463735058903694,
-0.012887408956885338,
-0.013377398252487183,
-0.030945852398872375,
0.025487801060080528,
0.056438054889440536,
0.039107441902160645,
0.036008965224027634,
0.017090534791350365,
0.018277667462825775,
0.05968674272298813,
0.03485839441418648,
0.0034541599452495575,
0.006594519596546888,
0.05310247093439102,
-0.024567753076553345,
0.037963394075632095,
0.055059485137462616,
-0.012113603763282299,
-0.006039711181074381,
0.016355136409401894,
-0.024596378207206726,
-0.012882644310593605,
-0.015204907394945621,
-0.0162905752658844,
0.051141586154699326,
-0.012171751819550991,
-0.0569576695561409,
0.01874074712395668,
0.032165251672267914,
-0.012282492592930794,
0.07235968858003616,
0.023720914497971535,
-0.03908229246735573,
-0.03849053755402565,
0.03764020651578903,
0.019247006624937057,
-0.02356092631816864,
-0.06434959918260574,
0.007510210387408733,
-0.020388342440128326,
0.0028611519373953342,
0.02346043474972248,
-0.044007521122694016,
0.014976020902395248,
-0.0324474573135376,
0.020099032670259476,
0.04901709780097008,
0.0313311442732811,
-0.03025692142546177,
-0.0010017689783126116,
-0.006984913256019354,
-0.045773644000291824,
0.039869338274002075,
0.039270661771297455,
-0.018869983032345772,
-0.042843032628297806,
-0.00450476910918951,
-0.021574586629867554,
-0.020665690302848816,
0.019757594913244247,
-0.007979760877788067,
0.011504806578159332,
-0.017890363931655884,
-0.061908453702926636,
-0.07976473867893219,
0.05308886244893074,
-0.020650159567594528,
-0.025698816403746605,
-0.06841105967760086,
0.010225885547697544,
0.025677142664790154,
0.06849446147680283,
-0.0013220793334767222,
-0.014307213015854359,
-0.02421233057975769,
0.014421551488339901,
0.010374472476541996,
-0.03095046430826187,
0.02057770825922489,
0.015836795791983604,
-0.04349897801876068,
0.006834839470684528,
-0.07502170652151108,
0.027629932388663292,
0.046806227415800095,
-0.019453497603535652,
-0.03267686814069748,
0.05475503206253052,
-0.022792955860495567,
0.032346345484256744,
0.004119995515793562,
-0.005047670099884272,
-0.03938259556889534,
0.11767765134572983,
0.01798374578356743,
0.020589454099535942,
0.0078053344041109085,
0.035256508737802505,
0.022727489471435547,
-0.005230527836829424,
0.0025824757758527994,
0.03486384078860283,
-0.0388743057847023,
-0.006140732206404209,
-0.00866479892283678,
0.05789964273571968,
0.028305793181061745,
-0.06947039812803268,
-0.014341914094984531,
-0.028282612562179565,
-0.007194622419774532,
-0.012363323010504246,
0.0719309002161026,
-0.031887564808130264,
-0.00765795074403286,
-0.0009575660806149244,
-0.06667427718639374,
-0.014268814586102962,
-0.08034741133451462,
0.0030934116803109646,
0.0007715158862993121,
-0.0174997728317976,
-0.011663687415421009,
-0.0009453437523916364,
0.029733940958976746,
-0.02762436494231224,
-0.01692306622862816,
0.023723633959889412,
0.024240978062152863,
0.006105477921664715,
-0.04404676333069801,
0.028074078261852264,
0.040000662207603455,
0.05629972368478775,
-0.017053086310625076,
0.03555102273821831,
-0.04319162294268608,
-0.03763895481824875,
0.03834023326635361,
-0.02822602540254593,
0.005151302553713322,
-0.005268984008580446,
0.01320596318691969,
0.030399184674024582,
0.000541388348210603,
-0.007130888756364584,
0.03821689262986183,
0.00875512883067131,
0.06853347271680832,
-0.00842307135462761,
0.026824530214071274,
0.011380387470126152,
0.04494402930140495,
0.017997540533542633,
0.005188303999602795,
-0.011396563611924648,
-0.03587508201599121,
-0.052762120962142944,
0.02490624040365219,
0.030009789392352104,
0.018229560926556587,
-0.05543489009141922,
0.012428397312760353,
0.02243555523455143,
0.0006358843529596925,
0.007233652751892805,
-0.011605381965637207,
0.012880105525255203,
0.010199007578194141,
0.012211918830871582,
0.002142129000276327,
0.03340138494968414,
-0.010551897808909416,
0.0059269326739013195,
0.021817727014422417,
0.03611466661095619,
-0.006850430741906166,
-0.009020359255373478,
0.026189513504505157,
0.009690397419035435,
0.013900441117584705,
0.005130130797624588,
0.026051752269268036,
0.019799858331680298,
-0.06601608544588089,
-0.006449108477681875,
0.004463811870664358,
0.004659391473978758,
-0.011258680373430252,
-0.04452886804938316,
-0.026511074975132942,
0.04101243242621422,
0.009371625259518623,
-0.014487020671367645,
0.022828785702586174,
0.03740384429693222,
-0.029307760298252106,
0.02528987266123295,
-0.01612035743892193,
0.00024503585882484913,
0.021693816408514977,
0.014207994565367699,
0.06549044698476791,
0.026209788396954536,
0.020337475463747978,
-0.03851580247282982,
-0.01934623159468174,
-0.016496391966938972,
-0.016893502324819565,
-0.013209613040089607,
0.01919870264828205,
-0.05984576418995857,
0.025786086916923523,
-0.03870409354567528,
-0.06006280332803726,
0.026226308196783066,
0.03006977029144764,
0.023684952408075333,
0.025846565142273903,
-0.026654133573174477,
-0.02399533800780773,
-0.0011648311046883464,
-0.012807700783014297,
0.023521853610873222,
-0.07431897521018982,
0.004084629938006401,
0.03758877515792847,
-0.012103035114705563,
-0.011051288805902004,
0.03321922942996025,
-0.036671146750450134,
-0.06973837316036224,
-0.043039727956056595,
-0.005195342469960451,
0.03932884708046913,
-0.011855388060212135,
0.0515519417822361,
0.04438086971640587,
-0.009073195978999138,
-0.006525293458253145,
-0.03466794267296791,
-0.011241967789828777,
0.023504167795181274,
-0.016060471534729004,
0.016319746151566505,
-0.008963225409388542,
-0.0014355686726048589,
0.04575573652982712,
0.030200902372598648,
-0.010931278578937054,
-0.0003602996875997633,
-0.015696199610829353,
-0.037668533623218536,
-0.03703678771853447,
0.013996806927025318,
0.003509605536237359,
0.0029653310775756836,
-0.00011235077545279637,
0.03376740217208862,
0.03413725644350052,
0.022069524973630905,
0.006404179614037275,
-0.03183918818831444,
-0.006543310824781656,
0.017380839213728905,
0.03175876662135124,
0.01897270604968071,
-0.00857056025415659,
0.024625906720757484,
0.011164282448589802,
0.0050158994272351265,
0.019120896235108376,
0.02737712860107422,
-0.07212640345096588,
0.032100412994623184,
0.008285832591354847,
0.012242144905030727,
-0.024768048897385597,
0.052991025149822235,
0.024764014407992363,
0.005494812503457069,
-0.006806304212659597,
0.04099709540605545,
0.04685532674193382,
0.011456872336566448,
0.007065756246447563,
0.045952167361974716,
0.04461601376533508,
-0.014809826388955116,
-0.006709483452141285,
0.0020713224075734615,
-0.015212992206215858,
0.03317031264305115,
-0.0074928440153598785,
-0.011829539202153683,
0.0280417762696743,
0.06836102157831192,
0.033728428184986115,
0.03554365038871765,
-0.03728993237018585,
-0.02526448480784893,
-0.03357086703181267,
-0.052274513989686966,
0.015937440097332,
0.045166950672864914,
0.010202930308878422,
0.027852041646838188,
0.04028036817908287,
0.019031988456845284,
0.052886735647916794,
0.019631361588835716,
-0.09508670121431351,
0.018264032900333405,
-0.02878452092409134,
-0.018645377829670906,
-0.012608018703758717,
0.0015485516050830483,
-0.020170988515019417,
0.010203137993812561,
0.01589852385222912,
0.024269727990031242,
0.007481447421014309,
-0.05639277398586273,
0.03354071453213692,
-0.02400527149438858,
-0.05658988282084465,
-0.0005825904081575572,
0.08315633237361908,
0.0313945971429348,
-0.0401526615023613,
0.014031784608960152,
0.03151148930191994,
-0.0009314320050179958,
0.0030453819781541824,
-0.008575682528316975,
0.032320816069841385,
0.018004050478339195,
0.06301476061344147,
0.015294598415493965,
-0.007371717598289251,
-0.016268743202090263,
0.012711522169411182,
0.027372511103749275,
0.05379321798682213,
-0.009331515058875084,
-0.029661549255251884,
-0.006481225602328777,
-0.061478521674871445,
-0.01544290129095316,
0.0006717276992276311,
0.044827427715063095,
-0.04802784323692322,
-0.018783124163746834,
0.05547941476106644,
-0.006283989176154137,
-0.03450237587094307,
0.013452316634356976,
0.046270404011011124,
0.014580684714019299,
-0.026018261909484863,
-0.019622454419732094,
-0.028326598927378654,
-0.024982957169413567,
-0.02075190283358097,
-0.009975729510188103,
-0.037232398986816406,
-0.04366721212863922,
0.008519235998392105,
0.016103511676192284,
0.018970953300595284,
-0.045794978737831116,
-0.0014243798796087503,
0.016566429287195206,
0.0468808189034462,
-0.0018581829499453306,
-0.01223595067858696,
-0.009392998181283474,
0.006319284439086914,
0.02255581133067608,
-0.015548218972980976,
-0.020053764805197716,
-0.04901222139596939,
-0.007188315968960524,
0.030571091920137405,
0.039845094084739685,
0.01839718595147133,
-0.013417295180261135,
-0.06854498386383057,
0.012976933270692825,
0.062300197780132294,
-0.010665945708751678,
0.033671073615550995,
-0.025389548391103745,
-0.017097346484661102,
-0.02178170718252659,
-0.015008406713604927,
-0.007921927608549595,
0.007863887585699558,
0.009078656323254108,
0.023174792528152466,
-0.05447615310549736,
-0.010196462273597717,
-0.006097278092056513,
0.034993208944797516,
0.06303101032972336,
0.024587400257587433,
0.013338684104382992,
0.027705973014235497,
-0.0011043860577046871,
-0.0052092308178544044,
-0.013065061531960964,
-0.07687275856733322,
0.02901274897158146,
0.015388418920338154,
0.007281254976987839,
0.01946190372109413,
-0.016880754381418228,
0.01109317597001791,
0.03818792477250099,
-0.006898927036672831,
-0.01628136821091175,
0.0016586020356044173,
-0.0036385206039994955,
0.04769615828990936,
0.014366167597472668,
-0.01781943254172802,
0.05602530762553215,
0.05860438197851181,
0.0271043311804533,
-0.00535197276622057,
-0.01402878575026989,
0.054138585925102234,
-0.02018897980451584,
-0.008004645816981792,
-0.02888718992471695,
-0.02403920516371727,
-0.02103620581328869,
0.04009523615241051,
-0.026640184223651886,
0.03278636932373047,
-0.0022498052567243576,
-0.06434711813926697,
-0.003174466546624899,
0.03150394558906555,
0.01670355163514614,
0.018378261476755142,
-0.0121657969430089,
0.01582309789955616,
-0.00029436699696816504,
-0.032499440014362335,
0.014729139395058155,
-0.0052520702593028545,
0.012985741719603539,
0.014433995820581913,
-0.01614084094762802,
0.026181384921073914,
-0.04377445951104164,
-0.010042130947113037,
-0.030583521351218224,
-0.03826863318681717,
0.032702960073947906,
-0.006467342376708984,
0.000607214926276356,
0.043438348919153214,
-0.047459959983825684,
-0.01171001698821783,
0.004300935659557581,
0.00032264654873870313,
0.047338295727968216,
-0.08966071903705597,
0.03837509825825691,
0.05058020353317261,
0.025534529238939285,
-0.07995759695768356,
-0.008769663982093334,
0.003965111915022135,
0.02243419922888279,
0.006082816049456596,
-0.02765546180307865,
-0.03652296960353851,
-0.07386436313390732,
-0.05917666107416153,
-0.005121639929711819,
0.02917449176311493,
0.00943642109632492,
0.0007088725105859339,
0.011275261640548706,
0.003736624727025628,
0.039934709668159485,
0.015318759717047215,
-0.012647191993892193,
0.0036919305566698313,
-0.009335437789559364,
-0.019987594336271286,
0.013769731856882572,
0.03954501822590828,
-0.02251020073890686,
-0.003160677617415786,
0.010069558396935463,
0.021145859733223915,
0.06124896556138992,
0.02677200920879841,
-0.018114633858203888,
0.06063193455338478,
0.048923663794994354,
-0.0031725168228149414,
-0.003755842801183462,
0.05723947286605835,
-0.00274594291113317,
-0.005513692740350962,
0.010212697088718414,
-0.00023390044225379825,
-0.005081671755760908,
-0.0408843457698822,
-0.02741260826587677,
-0.04056107625365257,
0.008218148723244667,
0.006727462634444237,
0.09871555119752884,
-0.0008900074171833694,
-0.001138133928179741,
-0.01792510226368904,
-0.02627738192677498,
0.025116203352808952,
0.02724684402346611,
0.01334622222930193,
-0.03264622390270233,
-0.001384114963002503,
0.007337689399719238,
-0.010275447741150856,
-0.058555133640766144,
-0.03282581642270088,
0.07366658002138138,
-0.013906683772802353,
0.03640563040971756,
0.028675168752670288,
-0.001362498733215034,
-0.0023650284856557846,
-0.013731837272644043,
0.013472954742610455,
0.0058211032301187515,
-0.01166187971830368,
0.027375098317861557,
-0.02521025761961937,
0.01038768794387579,
0.024555709213018417,
0.03887060657143593,
-0.004836787935346365,
0.02889718860387802,
-0.0050611416809260845,
0.007766547612845898,
0.01801558956503868,
-0.0045533981174230576,
-0.025595061480998993,
0.054658569395542145,
-0.02047743834555149,
0.05152866616845131,
-0.029967498034238815,
0.01884452998638153,
0.024438807740807533,
-0.002824783558025956,
0.016374126076698303,
-0.042653851211071014,
-0.038590021431446075,
-0.036094799637794495,
0.03782817721366882,
0.003390772268176079,
0.026124248281121254,
-0.012798367999494076,
0.019503938034176826,
0.03281128406524658,
-0.02318834885954857,
-0.011325294151902199,
-0.024193983525037766,
-0.03139648959040642,
-0.021838471293449402,
-0.058503273874521255,
-0.038513824343681335,
0.021898366510868073,
-0.006585080176591873,
-0.02185557223856449,
0.03381650149822235,
-0.04810094088315964,
-0.003721837652847171,
0.029551494866609573,
0.0550403818488121,
0.008918335661292076,
0.05427704006433487,
0.008896533399820328,
0.03288087621331215,
0.002437360119074583,
0.021871333941817284,
0.11559534072875977,
0.050425030291080475,
0.0020871441811323166,
-0.031225278973579407,
0.015183450654149055,
-0.02267487160861492,
-0.004337158054113388,
-0.030948610976338387,
-0.002150404267013073,
-0.025476694107055664,
-0.017910871654748917,
0.017186664044857025,
0.09037881344556808,
-0.007379054557532072,
0.006524521857500076,
0.015025181695818901,
-0.045128531754016876,
-0.046367257833480835,
0.01747090183198452,
0.03197616711258888,
0.028996160253882408,
0.028125286102294922,
-0.03882583603262901,
0.0028760770801454782,
-0.012381590902805328,
0.01646394096314907,
-0.06104886531829834,
-0.023623868823051453,
0.01791863515973091,
-0.02022727206349373,
-0.06714323908090591,
-0.0033948286436498165,
0.01622180826961994,
-0.04990550875663757,
-0.04218999296426773,
-0.03179452568292618,
0.02249414287507534,
0.004584466107189655,
0.02820008434355259,
0.04544955492019653,
0.027628814801573753,
0.027542799711227417,
0.0363706536591053,
0.042198292911052704,
-0.04031805321574211,
-0.011863951571285725,
0.0018882181029766798,
0.024145765230059624,
0.009486319497227669,
-0.0051821013912558556,
0.010380388237535954,
0.009550056420266628,
-0.008329497650265694,
-0.029979197308421135,
0.00702346907928586,
0.018054964020848274,
0.008738026954233646,
-0.018200086429715157,
-0.025661835446953773,
-0.015778817236423492,
0.07363490015268326,
-0.007293586153537035,
0.0017539780819788575,
0.013589248061180115,
-0.0415077842772007,
0.010177957825362682,
-0.00227211881428957,
0.09681379795074463,
-0.021459370851516724,
-0.027537396177649498,
-0.029569681733846664,
-0.08581992983818054,
-0.024730626493692398,
-0.03415289893746376,
0.010672692209482193,
0.013518263585865498,
0.03208627179265022,
0.005290020257234573,
0.008837775327265263,
0.011519973166286945,
-0.056024082005023956,
0.0084741972386837,
-0.023413874208927155,
-0.0129993986338377,
-0.05077582970261574,
-0.005791800562292337,
0.029893282800912857,
0.043120186775922775,
-0.048792287707328796,
-0.03390764072537422,
0.020437302067875862,
0.012490442022681236,
0.04053255543112755,
-0.0013269816990941763,
0.007471335120499134,
-0.014011390507221222,
-0.019712287932634354,
-0.0018369992030784488,
-0.03016313724219799,
0.0380779467523098,
0.01328316330909729,
-0.0021916222758591175,
-0.0005042619304731488,
-0.001638036803342402,
-0.03282773867249489,
-0.01329765748232603,
0.024686213582754135,
-0.02615356259047985,
0.00863625667989254,
0.01260881032794714,
-0.012235482223331928,
-0.030446942895650864,
-0.04394560679793358,
-0.011033090762794018,
-0.009468575939536095,
-0.02443891204893589,
0.04056944698095322,
-0.025511877611279488,
0.023076247423887253,
-0.0031553623266518116,
0.014025840908288956,
-0.019058987498283386,
-0.04709560051560402,
-0.039967965334653854,
-0.011139106005430222,
0.04176973178982735,
-0.007264174520969391,
-0.013386949896812439,
0.01806814968585968,
-0.0085965720936656,
-0.04011991247534752,
0.00011783360241679475,
0.042577557265758514,
0.018260197713971138,
-0.028850769624114037,
0.0039890785701572895,
-0.02584567852318287,
0.036157816648483276,
-0.007794842589646578,
-0.029894446954131126,
0.04589717090129852,
-0.029397590085864067,
-0.029947573319077492,
0.020775150507688522,
-0.012402929365634918,
0.03546207770705223,
-0.0033686310052871704,
-0.0015648469561710954,
0.012442655861377716,
0.06119966879487038,
-0.027121014893054962,
-0.009952038526535034,
0.04023488610982895,
-0.06559891998767853,
-0.00019104308739770204,
-0.013343139551579952,
0.023106323555111885,
-0.00877164676785469,
-0.005584545433521271,
0.033264342695474625,
0.027291536331176758,
-0.008622415363788605,
-0.032376594841480255,
0.022073496133089066,
-0.0045188856311142445,
-0.003425180446356535,
-0.0021234722808003426,
0.009171167388558388,
0.03847368434071541,
0.06726118922233582,
-0.059858933091163635,
0.06306230276823044,
0.019067823886871338,
-0.018851017579436302,
-0.11468744277954102,
-0.012801246717572212,
0.02087690494954586,
-0.00021495363034773618,
0.04967707023024559,
-0.04699886590242386,
0.024512402713298798,
0.025241903960704803,
-0.040346402674913406,
0.03933247551321983,
0.0047138831578195095,
-0.014929595403373241,
-0.0649537444114685,
-0.015801288187503815,
-0.007210367359220982,
0.03715166822075844,
0.03145987167954445,
0.039293013513088226,
0.009589830413460732,
0.018480051308870316,
-0.024956418201327324,
-0.053220413625240326,
-0.01095682755112648,
0.02493368089199066,
-0.006997411139309406,
-0.013344112783670425,
0.03279217705130577,
0.011008515022695065,
-0.015425656922161579,
-0.006584965158253908,
-0.013227877207100391,
-0.05594130977988243,
-0.030922025442123413,
-0.012965861707925797,
-0.010442620143294334,
0.018538622185587883,
0.016780974343419075,
0.004823802970349789,
-0.001075028907507658,
0.03470520302653313,
0.010770260356366634,
-0.006287010386586189,
-0.0018796442309394479,
0.00010191925684921443,
0.027696510776877403,
-0.031136268749833107,
-0.010391156189143658,
0.014835900627076626,
-0.008510078303515911,
-0.021671628579497337,
0.01605452597141266,
0.003987881820648909,
0.031173856928944588,
-0.025264624506235123,
0.016122831031680107,
-0.027482513338327408,
-0.008225922472774982,
0.00805712305009365,
0.041512299329042435,
0.011380694806575775,
-0.0054448917508125305,
0.0002687556843739003,
-0.023971272632479668,
0.008333188481628895,
0.006553729996085167,
-0.0004650430928450078,
-0.05589858815073967,
-0.024313759058713913,
0.00438287016004324,
-0.005143444985151291,
-0.0011472422629594803,
-0.0810028538107872,
-0.027585485950112343,
-0.018554365262389183,
0.017261987552046776,
0.024259919300675392,
-0.03214889392256737,
0.004924965091049671,
-0.05485643073916435,
-0.02250138483941555,
-0.008277719840407372,
-0.044603269547224045,
-0.011763505637645721,
-0.017046544700860977,
-0.0006996344309300184,
-0.029946083202958107,
0.008180019445717335,
0.02499135583639145,
0.04122726991772652,
-0.025906650349497795,
0.02318202145397663,
-0.02080025151371956,
0.0037640712689608335,
-0.07168827950954437,
0.03390144184231758,
-0.027811121195554733,
-0.040272947400808334,
-0.038222938776016235,
-0.013586186803877354,
0.02432231791317463,
0.012812391854822636,
0.015582404099404812,
-0.04051916301250458,
0.017660457640886307,
-0.02324358932673931,
-0.020465176552534103,
0.014093414880335331,
0.00490149762481451,
-0.008466823026537895,
0.09002462029457092,
-0.00640259450301528,
0.01467844843864441,
0.01222107745707035,
0.010995795950293541,
-0.0425967201590538,
-0.037749506533145905,
-0.023200049996376038,
-0.018195169046521187,
-0.0158845167607069,
0.0224712323397398,
-0.0196884423494339,
-0.04009806737303734,
-0.01087180245667696,
0.03645452484488487,
-0.06779883056879044,
-0.01651083119213581,
0.014237457886338234,
0.024696718901395798,
0.02951839193701744,
-0.03138357400894165,
0.0037607818376272917,
0.02726406790316105,
0.004167449194937944,
0.003939924295991659,
0.0523499920964241,
-0.0025613131001591682,
-0.014936170540750027,
0.024833286181092262,
0.025675233453512192,
-0.025296732783317566,
0.024460725486278534,
-0.0031699351966381073,
0.003980240784585476,
-0.02533813752233982,
-0.029010117053985596,
0.001925490447320044,
0.017757927998900414,
-0.007903644815087318,
-0.0056918226182460785,
-0.01918988674879074,
0.05652899295091629,
0.01180191244930029,
0.006653589196503162,
-0.007952915504574776,
-0.02386374957859516,
-0.0218783151358366,
0.03875913470983505,
0.06180828437209129,
0.043711625039577484,
-0.026406804099678993,
-0.021412227302789688,
0.00099744217004627,
0.007029421161860228,
-0.014288186095654964,
-0.03235837072134018,
-0.015498152002692223,
-0.009507347829639912,
-0.0013343191239982843,
-0.0407630018889904,
-0.009808574803173542,
0.021650122478604317,
-0.023909294977784157,
0.016805704683065414,
0.04894252121448517,
0.06376085430383682,
0.01610368676483631,
-0.009470876306295395,
0.009197582490742207,
0.059947945177555084,
-0.05487758666276932,
-0.05286109820008278,
-0.008192416280508041,
0.0210720244795084,
-0.010497898794710636,
-0.012627570889890194
] |
<p>As the air molecules are environment for carrying sound waves, could stream of photons be environment for carrying electromagnetic waves? What contradictions cause this assumption in the existing theories?</p> | 4,617 | [
-0.023651570081710815,
-0.0321921668946743,
0.012314177118241787,
-0.04327015206217766,
0.02156279794871807,
0.029950585216283798,
-0.0013925067614763975,
-0.02973630093038082,
0.015559791587293148,
-0.0007011766429059207,
0.06856206804513931,
0.038368020206689835,
0.05855489522218704,
0.0126334922388196,
-0.011930473148822784,
-0.0069764056243002415,
-0.014315799809992313,
-0.008874932304024696,
-0.03200075402855873,
-0.023768426850438118,
-0.011674454435706139,
0.06339079886674881,
-0.007069464307278395,
0.041749656200408936,
-0.036129966378211975,
0.036855291575193405,
0.0013390682870522141,
0.008605287410318851,
0.055389586836099625,
0.028652751818299294,
0.007973141968250275,
-0.00242034369148314,
0.0012605783995240927,
0.03383108973503113,
0.013221749104559422,
-0.02279255911707878,
-0.03141016513109207,
-0.01177233550697565,
-0.0021086125634610653,
-0.024444950744509697,
-0.02289680391550064,
-0.028476228937506676,
0.021775713190436363,
0.03574894741177559,
-0.039784375578165054,
-0.015011955983936787,
0.022267917171120644,
-0.019725997000932693,
0.044753484427928925,
-0.08538207411766052,
0.06549966335296631,
-0.011785012669861317,
0.029290255159139633,
0.021950742229819298,
-0.01993742398917675,
0.011883056722581387,
0.08740057051181793,
0.08534365892410278,
0.011676072143018246,
-0.04087284207344055,
0.023239318281412125,
-0.0061279963701963425,
-0.009450833313167095,
-0.009992068633437157,
-0.04178273305296898,
0.0002132243535015732,
-0.021530980244278908,
-0.00005232408511801623,
0.034304678440093994,
0.04333936423063278,
-0.012770935893058777,
-0.010884685441851616,
0.0426858589053154,
0.010712017305195332,
0.035959918051958084,
0.006117943208664656,
0.017963072285056114,
-0.0030823585111647844,
0.047762323170900345,
0.03131205588579178,
0.0383060984313488,
0.004253349266946316,
0.03042508289217949,
-0.01500263623893261,
-0.017281264066696167,
0.0007244725711643696,
0.07621757686138153,
-0.030807163566350937,
-0.016358807682991028,
0.005061732605099678,
0.009949497878551483,
0.0020582140423357487,
0.032243967056274414,
0.025611786171793938,
0.0007663404103368521,
0.010647819377481937,
-0.03372696414589882,
0.04220286011695862,
0.021400805562734604,
-0.0591026246547699,
0.020113259553909302,
0.019367191940546036,
0.0803474560379982,
0.07552448660135269,
-0.0060527268797159195,
-0.048100851476192474,
-0.047386541962623596,
0.05752057954668999,
-0.01993768848478794,
-0.019023826345801353,
-0.04948430880904198,
0.022361554205417633,
-0.010222329758107662,
0.003266450483351946,
0.01565912924706936,
-0.010232321918010712,
0.027310049161314964,
-0.02926775813102722,
0.06585139781236649,
0.11023184657096863,
0.02714395336806774,
-0.05168144777417183,
0.023329468443989754,
-0.012839334085583687,
-0.052364885807037354,
0.008791955187916756,
0.012864183634519577,
-0.0032371720299124718,
-0.04957680404186249,
0.031454235315322876,
-0.0368804894387722,
-0.015875685960054398,
0.017713936045765877,
0.005846663843840361,
0.05043107271194458,
-0.04145614430308342,
-0.1275416910648346,
-0.053354743868112564,
0.01413582731038332,
-0.018651742488145828,
-0.02176685631275177,
-0.05281684547662735,
0.014594553038477898,
0.022922292351722717,
0.076602503657341,
-0.030961472541093826,
0.004631485790014267,
-0.017954498529434204,
0.04635893926024437,
0.009594129398465157,
-0.024405792355537415,
0.015828236937522888,
-0.020289335399866104,
-0.03227867931127548,
0.03174784779548645,
-0.07077928632497787,
0.036796510219573975,
0.028467215597629547,
0.014018049463629723,
-0.042592938989400864,
0.015100006945431232,
-0.025865059345960617,
-0.0037349325139075518,
-0.005520063918083906,
0.013386355713009834,
-0.07072002440690994,
0.054439976811409,
0.031945351511240005,
0.014105080626904964,
0.045594118535518646,
0.027533456683158875,
0.014657058753073215,
0.0034145929384976625,
0.010037248022854328,
0.013621633872389793,
-0.07821925729513168,
-0.02843027375638485,
-0.01205427199602127,
0.013616181910037994,
0.0010821501491591334,
-0.025669466704130173,
-0.015015474520623684,
-0.006149405147880316,
0.025847608223557472,
-0.019218243658542633,
0.02526736445724964,
-0.01177090685814619,
-0.01014751847833395,
-0.014065288938581944,
-0.06620373576879501,
0.006946689914911985,
-0.03243551403284073,
0.059708502143621445,
-0.006604865659028292,
-0.0027637346647679806,
-0.00606144405901432,
0.010214670561254025,
0.010780363343656063,
-0.043346107006073,
-0.02438754215836525,
-0.02355290949344635,
0.038069479167461395,
0.003198688616976142,
0.0010667743626981974,
0.026940539479255676,
0.05939594656229019,
0.04701823368668556,
0.017330190166831017,
0.009897802956402302,
-0.011423678137362003,
-0.05089753493666649,
0.008529527112841606,
-0.02526967227458954,
0.04108155518770218,
0.018279511481523514,
0.0005526540335267782,
0.012665471993386745,
-0.0056269969791173935,
-0.03206714242696762,
0.029600467532873154,
-0.0017838005442172289,
0.046373359858989716,
0.03815298527479172,
0.0163619052618742,
-0.01082620583474636,
0.04819335415959358,
0.015893982723355293,
-0.00913813803344965,
-0.01179974339902401,
-0.0454266183078289,
-0.04514756798744202,
0.04415901005268097,
0.044048890471458435,
0.004340984392911196,
-0.04492645710706711,
0.04528513550758362,
0.0028746339958161116,
0.03271760419011116,
0.020793447270989418,
0.031486984342336655,
-0.010750800371170044,
-0.0710873231291771,
0.012925722636282444,
0.04365698993206024,
0.04206424206495285,
0.0004595220962073654,
0.024118995293974876,
-0.005304817575961351,
-0.006918644532561302,
-0.028683729469776154,
-0.012020356953144073,
0.010455474257469177,
-0.0238303504884243,
0.02016315795481205,
-0.0422842763364315,
-0.022063659504055977,
0.006785770412534475,
-0.052522722631692886,
0.017064962536096573,
0.0013660669792443514,
-0.027535060420632362,
-0.014615767635405064,
0.021919123828411102,
-0.03224732726812363,
-0.0008706834632903337,
-0.007145329844206572,
-0.008890293538570404,
-0.0026161775458604097,
0.04218285530805588,
-0.0683688372373581,
0.00023394872550852597,
-0.025097081437706947,
0.010643036104738712,
-0.012436720542609692,
-0.005763350520282984,
0.036046501249074936,
0.00936718937009573,
0.034280698746442795,
-0.04456714913249016,
-0.03470094874501228,
-0.022982606664299965,
-0.01986967772245407,
-0.07135483622550964,
0.024021897464990616,
-0.02378922887146473,
0.002427947474643588,
-0.029595451429486275,
-0.043528471142053604,
0.023951152339577675,
-0.029663357883691788,
-0.006678819190710783,
0.01493797916918993,
-0.024452725425362587,
-0.03430021181702614,
0.006179922726005316,
-0.04782574251294136,
-0.005686433054506779,
-0.007581599988043308,
-0.003264679806306958,
0.0427701361477375,
-0.017669355496764183,
-0.012154946103692055,
0.01498650386929512,
-0.02245836704969406,
-0.0649833008646965,
-0.009155101142823696,
-0.04184119030833244,
0.009175017476081848,
-0.04051200672984123,
0.04969901964068413,
0.03635644167661667,
-0.058685071766376495,
0.017398886382579803,
-0.035857029259204865,
-0.061196763068437576,
0.04318470507860184,
0.012730305083096027,
0.055841345340013504,
0.006057497579604387,
-0.03280648589134216,
0.03814203292131424,
0.02191808633506298,
-0.06221824884414673,
0.0021135241258889437,
-0.012266627512872219,
-0.012685801833868027,
-0.014452076517045498,
-0.01553993858397007,
0.03245355188846588,
0.01662285253405571,
0.03665759041905403,
0.030176281929016113,
-0.017821134999394417,
-0.009103164076805115,
0.021554674953222275,
-0.03745220974087715,
-0.020412757992744446,
-0.015554359182715416,
0.02084747701883316,
0.05345939099788666,
-0.014206307008862495,
-0.030873341485857964,
-0.004114219918847084,
-0.03182656317949295,
-0.004241612274199724,
0.011230175383388996,
-0.019181998446583748,
0.04873882979154587,
0.0021837593521922827,
0.047597553580999374,
-0.054870232939720154,
0.03826373070478439,
-0.01833491399884224,
0.012643186375498772,
0.007250345777720213,
0.023341426625847816,
0.012093877419829369,
-0.0033586849458515644,
0.004062938038259745,
0.017811529338359833,
0.07295047491788864,
-0.027598919346928596,
-0.023849818855524063,
-0.010493829846382141,
0.011429441161453724,
0.011478720232844353,
-0.007294535171240568,
-0.008279317058622837,
0.054288800805807114,
0.027653684839606285,
0.028657151386141777,
0.049117498099803925,
-0.031039277091622353,
0.003029966028407216,
-0.002271420555189252,
0.028958596289157867,
0.008654357865452766,
0.010520722717046738,
0.0024147985968738794,
0.031308870762586594,
0.027156515046954155,
-0.004172604065388441,
-0.00809240061789751,
-0.018367206677794456,
-0.07251223176717758,
-0.02485312893986702,
-0.013780949637293816,
-0.010248655453324318,
-0.03424936160445213,
-0.028248991817235947,
-0.04860531911253929,
-0.023481277748942375,
-0.02344825677573681,
-0.020696178078651428,
-0.0254866573959589,
-0.08023654669523239,
0.011869983747601509,
-0.03930586203932762,
-0.03653223440051079,
-0.01884240098297596,
0.01861964538693428,
0.023407666012644768,
-0.01870911568403244,
0.018976790830492973,
0.03156653419137001,
-0.0328591987490654,
0.0012582752387970686,
0.00544637581333518,
0.013685139827430248,
-0.012957449071109295,
0.023928914219141006,
0.04853000491857529,
-0.005221530795097351,
-0.02014543116092682,
0.004648922942578793,
-0.0076510426588356495,
0.04148177430033684,
0.013534888625144958,
-0.029042882844805717,
-0.0073822978883981705,
-0.01745799370110035,
-0.02278960309922695,
0.00846714898943901,
0.06473493576049805,
0.006621406879276037,
-0.017807675525546074,
0.015221398323774338,
-0.037962671369314194,
-0.012157394550740719,
0.04458171874284744,
0.0105432802811265,
-0.0014216784620657563,
-0.011904713697731495,
-0.02130613848567009,
0.013511108234524727,
-0.006019762251526117,
-0.027150822803378105,
0.02077021636068821,
-0.0030703393276780844,
-0.004428462125360966,
-0.01752026192843914,
0.0027713661547750235,
0.03007107973098755,
-0.012852785177528858,
-0.01086872536689043,
-0.007928723469376564,
-0.014961780980229378,
0.01197078637778759,
-0.00818110816180706,
-0.027147043496370316,
0.03350114822387695,
0.03857855126261711,
0.017128802835941315,
-0.035531654953956604,
-0.07547666877508163,
-0.017884448170661926,
0.04312321916222572,
0.01986548863351345,
0.03733193129301071,
0.022999441251158714,
-0.008526167832314968,
0.01631707325577736,
-0.002470894018188119,
0.021232912316918373,
0.03694627434015274,
-0.04855988919734955,
-0.007197607774287462,
-0.008185584098100662,
-0.026286521926522255,
0.004524352494627237,
0.024019461125135422,
0.018778949975967407,
-0.012185262516140938,
-0.020521260797977448,
-0.011566512286663055,
-0.01668190024793148,
0.019629549235105515,
0.020100675523281097,
0.04777516424655914,
0.013603521510958672,
0.003557368414476514,
-0.004577504470944405,
0.024295184761285782,
-0.03924970328807831,
-0.04544110968708992,
0.02900499291718006,
0.009585238993167877,
-0.03987502306699753,
0.021030252799391747,
0.010437201708555222,
-0.06254371255636215,
-0.011838644742965698,
0.014750145375728607,
-0.014753414317965508,
-0.02205577865242958,
-0.04957660660147667,
0.02248532511293888,
-0.0014447259018197656,
-0.004863781854510307,
0.0699319988489151,
0.0525825098156929,
-0.032189276069402695,
0.0013529653660953045,
-0.013643396086990833,
0.047620922327041626,
-0.036785926669836044,
0.015687281265854836,
-0.0006636996986344457,
-0.019366512075066566,
0.019368227571249008,
0.07143811136484146,
-0.010381760075688362,
-0.0067292763851583,
0.055294521152973175,
-0.05643618106842041,
-0.012844429351389408,
0.027924545109272003,
-0.018690284341573715,
0.0023330466356128454,
-0.05999790504574776,
0.04952069744467735,
-0.03691572695970535,
0.013737150467932224,
0.03264935314655304,
-0.012639589607715607,
0.016674509271979332,
0.0558711402118206,
0.019170140847563744,
0.02497073821723461,
-0.04705293849110603,
0.008882862515747547,
0.000858455547131598,
-0.04703132063150406,
0.037124041467905045,
-0.020375235006213188,
0.0037579433992505074,
0.04016411677002907,
-0.06688374280929565,
-0.026513053104281425,
0.02543572708964348,
-0.009332914836704731,
0.04451533034443855,
-0.03906220570206642,
0.052201226353645325,
0.006186795886605978,
0.008049631491303444,
-0.07915721833705902,
-0.05568881705403328,
-0.010667319409549236,
0.055244866758584976,
0.02068711258471012,
-0.028342515230178833,
-0.0038907555863261223,
-0.05332113429903984,
-0.012957408092916012,
-0.015085235238075256,
0.016887962818145752,
-0.030404819175601006,
0.006275624968111515,
0.03260831907391548,
0.028267838060855865,
0.031083788722753525,
-0.008725378662347794,
-0.030896559357643127,
0.026981698349118233,
-0.022475436329841614,
0.0012578212190419436,
-0.023321490734815598,
0.019008202478289604,
0.0013252567732706666,
-0.03998314589262009,
0.016854427754878998,
0.016910580918192863,
0.05020122602581978,
-0.030449556186795235,
-0.020199714228510857,
0.03957781195640564,
0.014802170917391777,
-0.008191914297640324,
-0.010571146383881569,
0.039051610976457596,
0.010481701232492924,
0.032247308641672134,
-0.00991874560713768,
-0.0028537821490317583,
-0.016833389177918434,
-0.03604936972260475,
0.04818960279226303,
0.03358547389507294,
-0.0037460983730852604,
0.03705782815814018,
0.05628528073430061,
-0.008840211667120457,
0.0010096237529069185,
0.013799618929624557,
-0.030528344213962555,
0.027996646240353584,
-0.02668522298336029,
0.012802465818822384,
-0.005398444831371307,
0.021302498877048492,
-0.003412216668948531,
-0.043674711138010025,
-0.022286251187324524,
-0.03374568372964859,
0.03865500167012215,
-0.04307396709918976,
0.06271590292453766,
0.02536110393702984,
-0.023711763322353363,
0.00029660353902727365,
-0.01847063936293125,
0.002793959341943264,
0.028532037511467934,
-0.025546064600348473,
0.015948258340358734,
-0.008774716407060623,
0.0015077056596055627,
0.031638119369745255,
0.05335163325071335,
-0.0004104833642486483,
0.006406065076589584,
0.005365965887904167,
0.025198204442858696,
0.021506043151021004,
0.013161363080143929,
-0.027676289901137352,
0.011104021221399307,
-0.07869178056716919,
0.004432868678122759,
0.021661480888724327,
0.018778853118419647,
0.02195814438164234,
-0.001273804111406207,
0.010643300600349903,
-0.0312734991312027,
0.004565209615975618,
-0.03519323468208313,
-0.0038486525882035494,
-0.03312330320477486,
0.036394134163856506,
0.02171509899199009,
-0.001969193806871772,
0.011789713986217976,
0.0030934587121009827,
0.025601452216506004,
0.015823623165488243,
-0.051570191979408264,
-0.039516814053058624,
0.0098574822768569,
-0.023202959448099136,
0.06323961168527603,
-0.008906777948141098,
-0.04533737152814865,
0.02349909581243992,
0.004991916008293629,
0.033784449100494385,
0.004201896954327822,
0.033945534378290176,
-0.007663619238883257,
0.02546173892915249,
0.0032878462225198746,
-0.002351571572944522,
-0.0165700726211071,
0.027680696919560432,
0.12051244080066681,
0.05423260107636452,
0.03347758203744888,
-0.047768484801054,
0.00202923733741045,
-0.0197747889906168,
-0.002988892374560237,
-0.03900734707713127,
0.019777020439505577,
-0.006620222236961126,
0.04659998044371605,
-0.012811160646378994,
0.02691435068845749,
-0.016601484268903732,
0.0007695868262089789,
0.020914677530527115,
-0.05317381024360657,
-0.05351381003856659,
0.020681338384747505,
0.018760686740279198,
-0.0019522529328241944,
0.030298009514808655,
-0.032260771840810776,
0.005736399907618761,
-0.024390961974859238,
-0.01379477884620428,
0.005586101207882166,
-0.028282372280955315,
0.043969687074422836,
-0.03949964791536331,
-0.05669053643941879,
-0.03775420039892197,
0.03215861693024635,
-0.04915553331375122,
-0.030283330008387566,
0.0025210545863956213,
0.016269387677311897,
-0.0131547125056386,
-0.01122686080634594,
-0.015200981870293617,
0.03815498575568199,
-0.01623467542231083,
0.011829349212348461,
0.04628683254122734,
-0.029803870245814323,
-0.010631625540554523,
0.0270099975168705,
0.042804352939128876,
-0.015376011840999126,
0.01883379928767681,
0.010448918677866459,
0.016795681789517403,
-0.0010328376665711403,
-0.0679401382803917,
0.0028318052645772696,
-0.017408475279808044,
0.029603516682982445,
0.027612874284386635,
-0.03783610463142395,
0.008533735759556293,
0.0122472383081913,
0.004071625415235758,
0.026739459484815598,
-0.01772512122988701,
0.009771235287189484,
0.0015353969065472484,
0.0024095610715448856,
0.015319393947720528,
-0.010412092320621014,
-0.012858112342655659,
-0.028414005413651466,
-0.02832392044365406,
-0.04489532485604286,
-0.04312865436077118,
0.06301113963127136,
0.030209701508283615,
0.06456708908081055,
0.033481165766716,
0.007586762774735689,
-0.031057029962539673,
-0.05936732515692711,
-0.004988283384591341,
-0.004885045345872641,
-0.06886476278305054,
-0.017091596499085426,
-0.017082730308175087,
0.007867132313549519,
0.043443597853183746,
-0.0020095251966267824,
-0.015433724038302898,
0.002190324943512678,
0.02929750457406044,
-0.004972029477357864,
-0.019687043502926826,
-0.045501966029405594,
0.008051618002355099,
-0.002728054765611887,
-0.02813061513006687,
0.020395245403051376,
0.03284386545419693,
-0.018217872828245163,
-0.0031962161883711815,
-0.0033739791251719,
0.04755194112658501,
-0.02754511870443821,
-0.027912674471735954,
0.012584495358169079,
-0.0035445813555270433,
0.0185039434581995,
0.023935439065098763,
0.00497248163446784,
-0.039674725383520126,
-0.04449351131916046,
-0.01777869462966919,
-0.006104925647377968,
0.0075475252233445644,
-0.015058792196214199,
-0.0027376562356948853,
0.0356086865067482,
-0.022872794419527054,
0.006639862898737192,
-0.014028389006853104,
-0.002756275236606598,
-0.030860047787427902,
-0.007730127777904272,
-0.02254706434905529,
-0.041662994772195816,
-0.004998939577490091,
0.045081574469804764,
-0.05514712631702423,
-0.017182601615786552,
0.04781251773238182,
0.04840923100709915,
-0.02337375096976757,
0.0027559346053749323,
0.005167866125702858,
0.005557466298341751,
0.05394831299781799,
-0.026023250073194504,
-0.029034368693828583,
0.05697866156697273,
-0.053020868450403214,
-0.044596992433071136,
0.031021926552057266,
0.00045953012886457145,
0.030139602720737457,
0.012529290281236172,
0.03394918143749237,
-0.02566411718726158,
0.04295705258846283,
-0.021466491743922234,
0.028289511799812317,
-0.013679870404303074,
-0.0222233384847641,
-0.007570741232484579,
-0.009954305365681648,
0.0134322140365839,
-0.008036371320486069,
-0.032301317900419235,
0.0273117758333683,
0.00891819316893816,
0.029460908845067024,
0.020328791812062263,
-0.0030655991286039352,
-0.055421553552150726,
0.014078381471335888,
0.031070800498127937,
0.0023355633020401,
0.013459664769470692,
0.015044168569147587,
-0.03928358852863312,
0.053018394857645035,
0.0487101674079895,
-0.021666524931788445,
-0.14593029022216797,
0.01385549083352089,
0.02899702452123165,
-0.0010506031103432178,
0.02467595599591732,
-0.02462369203567505,
0.045006923377513885,
0.0373954251408577,
-0.08068221807479858,
-0.018337219953536987,
0.004702604375779629,
-0.008374377153813839,
-0.022547787055373192,
0.018436631187796593,
-0.014560699462890625,
0.038784608244895935,
0.026058297604322433,
0.05517883226275444,
-0.0054084910079836845,
-0.0018380938563495874,
0.0013513924786821008,
-0.029571061953902245,
-0.05476544797420502,
-0.00010209756874246523,
-0.010050054639577866,
0.01909143477678299,
0.08142751455307007,
-0.0303217601031065,
0.022958625108003616,
0.003647866193205118,
0.01480637863278389,
0.02986578457057476,
0.004189442377537489,
0.028070364147424698,
0.033284761011600494,
0.004255844280123711,
0.00824589654803276,
-0.038569480180740356,
0.005919842515140772,
0.03178883716464043,
0.0019907355308532715,
-0.008229115977883339,
-0.020274000242352486,
-0.02370363660156727,
-0.007467004936188459,
-0.04801320284605026,
-0.05308444797992706,
0.028966296464204788,
-0.0036800361704081297,
-0.05234647914767265,
-0.008754266425967216,
0.019363032653927803,
-0.022254211828112602,
-0.015734121203422546,
-0.007962081581354141,
-0.07459475100040436,
-0.022957852110266685,
-0.009136280976235867,
0.04929329827427864,
-0.035021550953388214,
0.005331268534064293,
0.01521631795912981,
-0.041964415460824966,
0.021115735173225403,
0.00809542741626501,
0.03777468577027321,
-0.02829873561859131,
-0.007243180647492409,
0.015182523056864738,
0.0223174300044775,
-0.0059707085601985455,
-0.05566277727484703,
-0.03808790072798729,
0.014870826154947281,
-0.008906623348593712,
0.058261699974536896,
0.017832055687904358,
-0.016641603782773018,
-0.04488865286111832,
-0.04043057933449745,
0.03500986471772194,
-0.014801138080656528,
0.028315505012869835,
-0.04037481173872948,
0.0001785576023394242,
-0.00238780677318573,
0.05549999326467514,
0.05042955279350281,
0.010015610605478287,
-0.02745378017425537,
0.019310927018523216,
-0.01264216285198927,
0.020479246973991394,
-0.011167926713824272,
0.0041084494441747665,
-0.00613931892439723,
-0.03491206094622612,
0.0072253914549946785,
-0.01226749736815691,
-0.037376631051301956,
0.02431507036089897,
0.03712426871061325,
-0.004376465920358896,
0.036583062261343,
0.005112956743687391,
-0.044243574142456055,
0.04097908362746239,
0.03770994022488594,
0.00009624112135497853,
0.02353283390402794,
-0.0372825562953949,
0.013591377064585686,
0.011386384256184101,
-0.01632254756987095,
-0.055366627871990204,
0.05977015197277069,
-0.005851734429597855,
0.0052392915822565556,
0.010514228604733944,
-0.009469553828239441,
0.042824018746614456,
-0.013170707039535046,
-0.014660736545920372,
0.047617074102163315,
-0.028821604326367378,
0.032950568944215775,
0.056491635739803314,
0.019741207361221313,
0.018322935327887535,
-0.0064798565581440926,
0.038424935191869736,
0.018366968259215355,
-0.028213992714881897,
-0.03086920827627182,
0.02990623377263546,
0.019485386088490486,
-0.007689854130148888,
0.023397628217935562,
0.020978664979338646,
-0.004531021695584059,
0.0353192463517189,
0.018590794876217842,
-0.00007653923239558935,
-0.020523833110928535,
0.002399908611550927,
0.029567178338766098,
0.03862334415316582,
-0.06367885321378708,
0.015020603314042091,
-0.007187141105532646,
0.07098620384931564,
-0.04678254947066307,
0.027407020330429077,
-0.02046469785273075,
-0.014766514301300049,
0.007876605726778507,
0.050772130489349365,
0.012281861156225204,
0.014824640937149525,
0.02197919599711895,
0.040063630789518356,
-0.0012972198892384768,
-0.02050809934735298,
0.0032703678589314222,
-0.04750993102788925,
-0.017231401056051254,
-0.026923391968011856,
-0.01790522411465645,
-0.029752884060144424,
-0.012362956069409847,
0.019093336537480354,
0.008569629862904549,
-0.00431883055716753,
0.02912340685725212,
-0.00484498729929328,
0.0205313079059124,
0.00740842055529356,
-0.035836111754179,
0.037406641989946365,
-0.03141854330897331,
0.025220679119229317,
-0.019340557977557182,
0.05507543310523033,
0.0017772273859009147,
0.004582810681313276
] |
<p>All around I read that buoyancy is numerically equal to the weight of fluid <strong>displaced</strong> by a submerged object, the volume of displaced fluid being equal to that of the <strong>submerged portion</strong> <a href="https://en.wikipedia.org/wiki/Archimedes%27_principle" rel="nofollow" title="Wikipedia - Archimedes' principle">(Wikipedia)</a>. However, thinking about it brought me to believe that such wording is not very good.</p>
<p>Consider the 2D example below of a box being sunk into water.</p>
<p><img src="http://i.stack.imgur.com/gJ5MV.png" alt="Archimedes 1"></p>
<p>In this example, it is clear that the buoyancy is equal to the weight of 4 cm² of water, which is the volume of the submerged box. However, closer inspection reveals that this does not match the displaced volume.</p>
<p><img src="http://i.stack.imgur.com/pBWhx.png" alt="Archimedes 2"></p>
<p>I concluded that the common definition works well when the body of fluid is large compared to the object, such that its surface level does not change significantly upon submersion. In this case, <em>displaced volume</em> matches <em>volume of submerged portion</em>. However, for the more general case (including example above), it would be more accurate to forgo <em>displaced volume</em> and hang on to <em>volume of submerged portion</em> only.</p>
<p>Am I missing something here? Is the original, ubiquitous wording indeed accurate?</p> | 151 | [
-0.018706126138567924,
-0.008548921905457973,
0.02240728959441185,
-0.00017997148097492754,
0.020960532128810883,
-0.037648703902959824,
-0.012607826851308346,
-0.011050508357584476,
0.024266337975859642,
0.004202572163194418,
0.01701241545379162,
0.04767509177327156,
0.06525352597236633,
-0.014185203239321709,
0.014110418036580086,
0.014790388755500317,
0.0038943348918110132,
-0.020977066829800606,
0.005056893918663263,
-0.03252328932285309,
0.0006304642301984131,
0.02095196582376957,
-0.006554917432367802,
0.0015019477577880025,
0.0026523482520133257,
0.025761207565665245,
0.019401967525482178,
-0.012081220746040344,
0.010739677585661411,
0.048295099288225174,
-0.009532605297863483,
-0.012255111709237099,
0.015191718004643917,
-0.0011133344378322363,
0.009946225211024284,
0.006349439267069101,
-0.027193164452910423,
-0.020060360431671143,
-0.013363741338253021,
0.07000192999839783,
0.01730080135166645,
-0.02873118594288826,
0.013307584449648857,
0.07451393455266953,
-0.012080312706530094,
0.013267616741359234,
-0.0016950002172961831,
-0.053514767438173294,
0.009538841433823109,
-0.05678185448050499,
0.0435808002948761,
0.023248082026839256,
0.060966722667217255,
0.02860303595662117,
-0.0064096348360180855,
-0.037647563964128494,
0.0846521258354187,
0.06031905114650726,
-0.026844888925552368,
-0.04739605635404587,
-0.020298631861805916,
0.0259397029876709,
-0.00786332692950964,
-0.02031213976442814,
-0.00880692433565855,
-0.002342988271266222,
-0.025885650888085365,
-0.02436661906540394,
0.03138444945216179,
-0.02258904278278351,
0.0037981958594173193,
-0.005940104369074106,
0.06802599877119064,
-0.012309608981013298,
0.01682708039879799,
-0.011352320201694965,
0.0014565871097147465,
0.04442600533366203,
0.016581129282712936,
0.02081592008471489,
-0.014982461929321289,
-0.00011933178757317364,
0.03449887037277222,
0.01743570901453495,
0.04502050206065178,
-0.025249058380723,
0.049500711262226105,
-0.002601868472993374,
0.041348498314619064,
0.023361865431070328,
-0.007483798544853926,
0.0034223105758428574,
0.03440457582473755,
0.005346172023564577,
0.012936023063957691,
-0.007215416058897972,
-0.01732630655169487,
0.05295421928167343,
0.01821412518620491,
-0.027704447507858276,
0.01613735966384411,
-0.014790954999625683,
0.04499699920415878,
0.07700349390506744,
-0.022087527438998222,
-0.018788671121001244,
-0.03279878944158554,
0.021139616146683693,
0.00678064813837409,
-0.007205416448414326,
-0.02248385176062584,
0.020473524928092957,
-0.03980829566717148,
-0.007668118923902512,
-0.0018102612812072039,
-0.011274455115199089,
0.011922811158001423,
0.01372196339070797,
0.060608137398958206,
0.005518503487110138,
0.037268586456775665,
-0.021072641015052795,
0.016377925872802734,
-0.038558125495910645,
-0.06317585706710815,
0.03785770386457443,
0.02152916043996811,
-0.00754956528544426,
-0.04679213464260101,
0.05077603459358215,
0.023410022258758545,
0.01733173243701458,
0.028649160638451576,
0.022828487679362297,
0.028096672147512436,
0.002854650840163231,
-0.0623307004570961,
-0.05512044206261635,
0.07307940721511841,
0.00856682937592268,
-0.03628278523683548,
-0.051435522735118866,
0.007459679152816534,
0.04389883577823639,
0.06412012130022049,
0.02543470822274685,
0.023370198905467987,
-0.007167566101998091,
0.016057714819908142,
-0.012036729604005814,
-0.009676389396190643,
0.000531029945705086,
0.029998866841197014,
-0.0236531812697649,
-0.005549281369894743,
-0.03902439773082733,
-0.0032334192655980587,
0.017841190099716187,
0.012970350682735443,
-0.017459215596318245,
0.0745411366224289,
-0.006624571979045868,
-0.024808065965771675,
0.020840339362621307,
0.02642090432345867,
-0.023496113717556,
0.05991167947649956,
-0.0048433635383844376,
0.004429624415934086,
0.005181305110454559,
0.02561766281723976,
0.019116565585136414,
-0.02399693801999092,
-0.008344070054590702,
0.051352761685848236,
-0.011348575353622437,
-0.009030599147081375,
-0.05842980742454529,
0.028185464441776276,
0.05275027081370354,
-0.06390970200300217,
-0.042939115315675735,
-0.006277882028371096,
-0.018864549696445465,
-0.007352004759013653,
0.054497238248586655,
-0.00044682889711111784,
-0.030890384688973427,
0.03673894330859184,
-0.05196793004870415,
-0.010455426760017872,
-0.06917417794466019,
0.04017091542482376,
-0.011364365927875042,
0.04007527232170105,
0.021272659301757812,
-0.018418004736304283,
0.019894558936357498,
-0.0523209348320961,
0.019856005907058716,
-0.00630420446395874,
-0.016141068190336227,
0.013693631626665592,
-0.019812779501080513,
0.002132349880412221,
0.019879253581166267,
0.03694096952676773,
0.018579766154289246,
-0.0004798577865585685,
-0.013255152851343155,
-0.018015936017036438,
-0.006225435994565487,
-0.0067986249923706055,
-0.003730771131813526,
-0.00023223101743496954,
-0.01642753556370735,
0.030327165499329567,
0.003864408005028963,
-0.017738953232765198,
0.018358828499913216,
-0.04514104500412941,
0.09897071868181229,
0.04396887123584747,
-0.006893927697092295,
0.001810855814255774,
0.03878137096762657,
0.03455612063407898,
-0.004843256436288357,
-0.007621777709573507,
-0.03729740157723427,
-0.044792596250772476,
0.0003154241421725601,
0.005526079796254635,
0.05247310921549797,
-0.008815644308924675,
0.019088124856352806,
0.0008452677284367383,
0.001624756958335638,
0.03807198628783226,
-0.025810105726122856,
-0.0026550511829555035,
-0.032825153321027756,
0.03447704389691353,
0.03227733075618744,
0.02031412161886692,
0.011557793244719505,
-0.000013412204680207651,
0.026031557470560074,
0.014447787776589394,
-0.021047094836831093,
0.004181071184575558,
0.014772176742553711,
0.02062247507274151,
0.013095629401504993,
-0.07586037367582321,
0.00936200376600027,
0.03067491576075554,
-0.055555351078510284,
-0.009559405967593193,
-0.010138736106455326,
-0.009204411879181862,
-0.000823601963929832,
-0.05538618564605713,
-0.010006360709667206,
0.047349777072668076,
0.016332929953932762,
-0.02104560285806656,
-0.008597083389759064,
0.00892025325447321,
-0.04843535274267197,
-0.01654244028031826,
-0.0639377310872078,
-0.009796788915991783,
0.0052873254753649235,
0.015505748800933361,
0.001030727056786418,
-0.00979677215218544,
0.03450528159737587,
-0.02523566037416458,
-0.005168143194168806,
-0.057465605437755585,
0.002007000846788287,
-0.021439364179968834,
-0.001259766984730959,
-0.07177959382534027,
-0.021496614441275597,
-0.05000390484929085,
-0.031189344823360443,
0.048907019197940826,
-0.018768858164548874,
0.01685904525220394,
0.030241867527365685,
0.010693290270864964,
-0.020980902016162872,
-0.02098100446164608,
-0.04921647533774376,
-0.022755946964025497,
-0.014989534392952919,
-0.011917054653167725,
0.06242736056447029,
-0.02231431007385254,
-0.024416154250502586,
0.03181753307580948,
-0.0498541034758091,
-0.06129239499568939,
-0.02498914673924446,
-0.012012104503810406,
0.03334260359406471,
0.0054790242575109005,
-0.012396140955388546,
0.025831561535596848,
-0.026188557967543602,
-0.013823706656694412,
-0.04105429723858833,
-0.0858064740896225,
0.011162769980728626,
-0.0119983134791255,
0.04807322099804878,
0.002072713803499937,
-0.004069051239639521,
0.11090890318155289,
-0.03520197793841362,
-0.027281271293759346,
0.0037980303168296814,
0.004475634079426527,
0.017524613067507744,
-0.02736423909664154,
-0.017180943861603737,
0.023538365960121155,
-0.03325652331113815,
0.035177722573280334,
-0.032681889832019806,
-0.00857371836900711,
0.04107644781470299,
0.03607800975441933,
-0.00800943374633789,
0.03240750730037689,
0.04301026836037636,
0.004152483772486448,
0.04200861230492592,
0.011501647531986237,
-0.007230440154671669,
0.0030681509524583817,
-0.03415793552994728,
0.03643754497170448,
0.021669715642929077,
-0.024336863309144974,
0.060442179441452026,
-0.00792468711733818,
0.00827910378575325,
0.010576409287750721,
0.03755940869450569,
-0.026185082271695137,
-0.02884829044342041,
0.005446127615869045,
0.01766723394393921,
0.046159617602825165,
0.011598574928939342,
-0.028650062158703804,
0.05568890646100044,
0.03949413448572159,
-0.004228605888783932,
-0.017155800014734268,
-0.00428771274164319,
0.002205846831202507,
0.03501318022608757,
-0.0006567227537743747,
-0.004258079919964075,
0.04850412532687187,
-0.0029412347357720137,
0.03794800862669945,
-0.013973405584692955,
-0.026735223829746246,
-0.021511057391762733,
-0.08187232911586761,
-0.02997482195496559,
0.00879259966313839,
0.060363005846738815,
-0.0024658762849867344,
0.01656779833137989,
0.04649613797664642,
-0.007063562516123056,
0.007292179390788078,
0.05710471794009209,
-0.07517912983894348,
-0.032073307782411575,
-0.022502262145280838,
0.027318986132740974,
-0.007434528321027756,
-0.04793305695056915,
-0.025476625189185143,
-0.06265691667795181,
-0.03296096250414848,
-0.012563514523208141,
0.02567875385284424,
-0.05940327048301697,
0.026717795059084892,
0.014848540537059307,
-0.03917916864156723,
0.004053517710417509,
0.003265929641202092,
0.019627273082733154,
-0.03479050472378731,
0.03635121136903763,
0.032203491777181625,
-0.010011997073888779,
-0.006139158736914396,
-0.02276339754462242,
0.018102413043379784,
0.012518445029854774,
-0.00022113094746600837,
0.01789586991071701,
0.026271648705005646,
-0.03742155805230141,
0.017880991101264954,
0.031534090638160706,
0.01956881955265999,
-0.02702941931784153,
0.019219156354665756,
-0.041956860572099686,
-0.019106317311525345,
-0.007419590838253498,
0.008223214186728,
0.02573353983461857,
0.006556848529726267,
-0.0015200520865619183,
0.013846107758581638,
0.02909771353006363,
0.001809092704206705,
0.0719270408153534,
0.047765687108039856,
0.018104342743754387,
-0.01942651905119419,
-0.04522852227091789,
0.029711492359638214,
-0.041142310947179794,
-0.013888460583984852,
0.03603406995534897,
0.010423103347420692,
-0.003908519167453051,
-0.01221398077905178,
0.014712111093103886,
-0.0036221975460648537,
-0.016508037224411964,
0.02843625098466873,
-0.01501903310418129,
-0.025307996198534966,
-0.04498302936553955,
0.0237114317715168,
0.026918651536107063,
0.009582115337252617,
0.022086866199970245,
0.022558096796274185,
-0.003937524277716875,
-0.06684301793575287,
-0.02741762064397335,
0.04330163076519966,
0.022333120927214622,
0.0138817448168993,
0.016912421211600304,
-0.06259897351264954,
-0.044515080749988556,
0.06750030815601349,
-0.03527022898197174,
0.007012144196778536,
-0.049233295023441315,
0.0246744304895401,
0.011147694662213326,
-0.04464754834771156,
0.015533212572336197,
-0.018620023503899574,
-0.002808589255437255,
0.022044850513339043,
-0.005790314637124538,
0.0169425867497921,
0.036526430398225784,
0.02388051152229309,
0.001795596326701343,
0.05813482776284218,
-0.0006624423549510539,
-0.025367623195052147,
-0.008887400850653648,
0.010877788998186588,
-0.043205805122852325,
-0.035687047988176346,
-0.030520541593432426,
-0.017889540642499924,
0.006899075582623482,
0.003843111451715231,
-0.024061543866991997,
-0.07277106493711472,
0.019759144634008408,
0.010403940454125404,
-0.022909296676516533,
0.0315595418214798,
-0.035610880702733994,
0.044979844242334366,
0.039052173495292664,
0.019407495856285095,
0.045955073088407516,
0.045775145292282104,
-0.03175274655222893,
-0.03111041523516178,
-0.04638255015015602,
0.01080995425581932,
-0.03261585906147957,
-0.047423288226127625,
-0.06292813271284103,
0.01627715304493904,
-0.040687691420316696,
0.018674377351999283,
0.04670342057943344,
-0.012414547614753246,
0.0048568760976195335,
-0.030309908092021942,
0.008271991275250912,
0.011326933279633522,
0.007269375957548618,
0.02107168175280094,
0.017647553235292435,
0.02093023806810379,
0.003826387459412217,
0.0046495068818330765,
-0.005481087602674961,
-0.02147945947945118,
0.009016888216137886,
0.018958067521452904,
0.0036579284351319075,
0.041546355932950974,
-0.001814383896999061,
-0.012544147670269012,
0.041597794741392136,
-0.016506008803844452,
0.07605908811092377,
-0.022837122902274132,
0.026193032041192055,
-0.017571570351719856,
-0.08883143961429596,
-0.0076141939498484135,
-0.01406241487711668,
0.033981505781412125,
0.034169673919677734,
-0.04825514554977417,
0.018010471016168594,
0.03809022158384323,
0.017350444570183754,
-0.04023916274309158,
-0.0259285606443882,
0.035744354128837585,
0.019213445484638214,
-0.005614643916487694,
-0.01743447780609131,
0.013542838394641876,
-0.0165103692561388,
-0.03452431410551071,
0.016429418697953224,
0.037200022488832474,
-0.03948204219341278,
-0.03402711823582649,
0.014254005625844002,
0.026244396343827248,
0.04377828538417816,
-0.024770287796854973,
-0.0009673197055235505,
-0.0344100184738636,
0.010027245618402958,
0.02358563058078289,
0.005159006919711828,
0.06298627704381943,
-0.027569789439439774,
-0.007832703180611134,
-0.029700016602873802,
-0.03521335870027542,
0.06152045726776123,
-0.006537639535963535,
-0.019260816276073456,
0.016277600079774857,
0.007384841330349445,
-0.021875005215406418,
-0.0018179862527176738,
0.028464261442422867,
-0.005968840327113867,
0.0014611121732741594,
-0.0005938474787399173,
-0.0035589318722486496,
0.0004805114003829658,
-0.02916848286986351,
0.02123931795358658,
-0.01917112246155739,
0.013717290945351124,
-0.02299271896481514,
0.06614094227552414,
-0.047176383435726166,
-0.007362276781350374,
0.02198062092065811,
-0.0073318746872246265,
0.048685215413570404,
0.03147081658244133,
-0.016860373318195343,
0.0094457371160388,
0.04391072317957878,
-0.010775651782751083,
-0.03585299476981163,
-0.023859698325395584,
0.026299435645341873,
0.04566457122564316,
-0.02296232059597969,
0.0503995344042778,
0.01613408699631691,
-0.023748718202114105,
0.05741308629512787,
0.005928965751081705,
-0.02903122268617153,
0.024995004758238792,
-0.03752753883600235,
0.046557724475860596,
-0.05577543377876282,
-0.006796997040510178,
0.024734297767281532,
0.004100022371858358,
0.0017255159327760339,
0.007236551493406296,
0.03531264141201973,
-0.0026692154351621866,
-0.03108651004731655,
-0.0037425686605274677,
-0.04216114804148674,
0.06256838887929916,
-0.013561283238232136,
0.02479448914527893,
-0.02646392025053501,
-0.034719884395599365,
0.032481223344802856,
-0.0015538898296654224,
0.005839251913130283,
-0.08462528884410858,
-0.032151542603969574,
0.00419139489531517,
0.004152487963438034,
0.016678759828209877,
0.03128175064921379,
-0.01863577775657177,
0.01590835489332676,
0.040848102420568466,
-0.0022606616839766502,
0.011248216032981873,
-0.020064005628228188,
-0.06403452157974243,
-0.02304856665432453,
-0.06214519217610359,
-0.041733890771865845,
0.033025287091732025,
0.0008964380831457675,
-0.029056107625365257,
0.011664805933833122,
-0.022793790325522423,
0.01199352741241455,
0.04910353943705559,
0.012302827090024948,
-0.03529585525393486,
0.04853404685854912,
-0.02278735302388668,
-0.01637864299118519,
-0.02991754189133644,
-0.01006785873323679,
0.1411300003528595,
0.052381351590156555,
0.020096687600016594,
-0.021594954654574394,
0.026004187762737274,
-0.016546597704291344,
-0.016068153083324432,
-0.027521202340722084,
-0.009566370397806168,
-0.01599312387406826,
0.01928320713341236,
-0.014775754883885384,
0.048754140734672546,
0.01568327657878399,
-0.015109187923371792,
-0.020339656621217728,
-0.021568825468420982,
-0.02194036915898323,
0.021068140864372253,
0.03517543897032738,
-0.059365756809711456,
0.019852720201015472,
-0.018177878111600876,
0.007675928063690662,
-0.0050901202484965324,
-0.024485688656568527,
-0.01133042760193348,
0.001887426245957613,
-0.01579468697309494,
0.011829112656414509,
-0.0477604866027832,
0.006708522327244282,
-0.009653869085013866,
-0.050839442759752274,
-0.04001997411251068,
0.032303158193826675,
0.010969344526529312,
-0.03196905553340912,
0.007464621681720018,
0.023138107731938362,
0.014388329349458218,
0.006814262829720974,
0.035012710839509964,
0.03556055948138237,
-0.04925592616200447,
-0.022855348885059357,
-0.04638103395700455,
0.038107436150312424,
-0.02356093004345894,
-0.007373835425823927,
0.016890721395611763,
-0.02454422041773796,
0.008671995252370834,
-0.08444040268659592,
-0.004933936055749655,
0.031702809035778046,
0.0408271886408329,
0.00278966105543077,
-0.03306471183896065,
0.010765896178781986,
0.028789233416318893,
0.008423703722655773,
-0.0036778999492526054,
0.02550327405333519,
0.007011757232248783,
0.008478772826492786,
0.01846885494887829,
0.04130403324961662,
0.005117620341479778,
0.0289413183927536,
-0.04671652242541313,
-0.0026621567085385323,
-0.03782850503921509,
-0.010417026467621326,
-0.03415130078792572,
0.02805456891655922,
0.005179420113563538,
-0.0046685440465807915,
-0.005244018509984016,
-0.01740136742591858,
-0.08192702382802963,
0.05327276140451431,
-0.0212778951972723,
-0.01792488992214203,
-0.05754844844341278,
0.020519299432635307,
0.020042061805725098,
0.042714640498161316,
-0.021068038418889046,
-0.013438633643090725,
0.013950989581644535,
0.04424688220024109,
-0.014331197366118431,
-0.04255278781056404,
-0.00006808843318140134,
-0.005543667357414961,
-0.005425591021776199,
-0.01187518797814846,
0.028980549424886703,
0.014241592027246952,
0.040150269865989685,
0.010822596959769726,
-0.02453891932964325,
0.048232436180114746,
-0.01855938322842121,
0.026326153427362442,
-0.0017117862589657307,
-0.013280944898724556,
-0.0409354604780674,
0.008639810606837273,
-0.00791993923485279,
-0.01696084812283516,
-0.014732849784195423,
-0.057671356946229935,
-0.03385130316019058,
-0.024951202794909477,
0.02405206859111786,
-0.03183804079890251,
-0.012095107696950436,
-0.027547335252165794,
-0.01780851185321808,
-0.007812458090484142,
-0.042441777884960175,
-0.057122036814689636,
-0.02628784067928791,
0.005206460133194923,
-0.0357651486992836,
-0.06453850865364075,
0.029282396659255028,
-0.0317859947681427,
-0.017268842086195946,
0.0055100941099226475,
-0.029673822224140167,
-0.0015457839472219348,
-0.030714159831404686,
0.015191678889095783,
-0.015661723911762238,
0.050389211624860764,
-0.0288650244474411,
-0.03836585581302643,
0.00392769044265151,
0.032513201236724854,
0.020104749128222466,
0.04061968997120857,
-0.012470907531678677,
-0.010636655613780022,
0.02465490810573101,
0.03626009821891785,
-0.028845977038145065,
0.058702681213617325,
-0.016590947285294533,
0.040332067757844925,
-0.004597023129463196,
-0.04463500156998634,
0.002076324075460434,
-0.007836456410586834,
0.011949650943279266,
-0.0058959415182471275,
-0.031893402338027954,
0.014902173541486263,
0.02109617367386818,
0.04626913368701935,
0.009432705119252205,
0.008672800846397877,
-0.017806818708777428,
0.012443900108337402,
0.019033649936318398,
-0.0013691793428733945,
0.012509124353528023,
0.034801699221134186,
-0.05338068678975105,
-0.011620302684605122,
0.021604789420962334,
0.022929495200514793,
-0.10939641296863556,
-0.009814734570682049,
0.01771058887243271,
0.005765954498201609,
0.03487839549779892,
-0.07651282846927643,
-0.0089240912348032,
0.02406591735780239,
-0.03924698010087013,
0.009195338003337383,
-0.06741143018007278,
0.008273535408079624,
-0.01622704789042473,
-0.014003543183207512,
0.010191901586949825,
0.05827079340815544,
0.0053490884602069855,
-0.008251478895545006,
-0.010492635890841484,
0.010392038151621819,
0.005869729444384575,
-0.027225911617279053,
-0.008068419061601162,
0.04131731018424034,
-0.032015930861234665,
-0.018820082768797874,
0.061824481934309006,
0.005219121929258108,
-0.03688722103834152,
0.030904725193977356,
-0.031064733862876892,
0.0063263047486543655,
0.02575094625353813,
0.012469371780753136,
-0.031408388167619705,
0.022828467190265656,
0.019998472183942795,
0.005290262401103973,
-0.014222517609596252,
0.02700004354119301,
0.030518334358930588,
0.026552649214863777,
-0.025547584518790245,
-0.006589995697140694,
0.014053663238883018,
-0.021415527909994125,
-0.031124407425522804,
0.055212270468473434,
-0.024040155112743378,
0.03403954952955246,
-0.004669150337576866,
-0.010043255984783173,
0.021061785519123077,
-0.022605694830417633,
0.005184595473110676,
-0.04508540406823158,
-0.015577531419694424,
0.06814062595367432,
-0.00336698186583817,
-0.0445304736495018,
-0.005896029528230429,
0.03344200924038887,
-0.022503800690174103,
-0.0004759855510201305,
-0.0073383646085858345,
-0.01518379244953394,
-0.04478076472878456,
-0.022056670859456062,
-0.00389100587926805,
0.004860930610448122,
-0.0034040205646306276,
-0.04373271390795708,
-0.04796028509736061,
0.038787394762039185,
0.03330677002668381,
0.023989306762814522,
0.03107813186943531,
-0.006348713766783476,
-0.027079327031970024,
-0.09474197030067444,
0.05535469576716423,
-0.009602904319763184,
-0.03138400986790657,
-0.020601704716682434,
0.008716244250535965,
0.0440140962600708,
-0.008302401751279831,
0.05393155291676521,
-0.011451560072600842,
-0.009258094243705273,
0.010182788595557213,
-0.011773467995226383,
0.01735365390777588,
0.03484518826007843,
-0.025814644992351532,
0.022773241624236107,
-0.03631505370140076,
0.01795247755944729,
0.02368895895779133,
-0.011013432405889034,
-0.02220230922102928,
0.03452301770448685,
-0.024829549714922905,
0.03787822276353836,
-0.0009688296704553068,
0.0012893951497972012,
0.04719695821404457,
0.026267649605870247,
-0.014039161615073681,
0.07070522010326385,
-0.0006816514069214463,
-0.02065381221473217,
0.038022395223379135,
0.00022520669153891504,
-0.05357164144515991,
0.006568880286067724,
-0.0195612832903862,
-0.004518047906458378,
0.011721128597855568,
-0.014054026454687119,
0.016351915895938873,
-0.02877061627805233,
-0.022743605077266693,
0.04831012338399887,
-0.03366094082593918,
-0.024924390017986298,
0.047036878764629364,
0.03695504739880562,
0.021546924486756325,
-0.025793181732296944,
0.026608288288116455,
0.03263171389698982,
-0.030309725552797318,
0.01647934690117836,
0.025077618658542633,
0.04639353230595589,
0.018187053501605988,
-0.011996435932815075,
0.019020698964595795,
0.006835394538938999,
0.0037185815162956715,
0.041004788130521774,
0.02314595878124237,
-0.030633049085736275,
-0.030154142528772354,
-0.016577227041125298,
-0.009654572233557701,
-0.021207915619015694,
0.010730922222137451,
-0.0157060194760561,
0.07680992782115936,
0.014716100879013538,
-0.004311387427151203,
-0.013808846473693848,
-0.030294092372059822,
0.006919168867170811,
0.04738006740808487,
0.042236749082803726,
0.054867081344127655,
-0.02925759367644787,
-0.016848478466272354,
0.011232887394726276,
-0.0025212406180799007,
0.006332176271826029,
0.018326260149478912,
-0.002790831495076418,
-0.040533263236284256,
0.059378139674663544,
-0.03483746945858002,
-0.020865121856331825,
0.0038814351428300142,
0.011610910296440125,
0.04476523399353027,
0.0512055829167366,
0.04482989385724068,
-0.012638729996979237,
-0.03017905168235302,
-0.035796158015728,
0.062411077320575714,
-0.09425865113735199,
-0.0013716659741476178,
0.011633784510195255,
0.021453799679875374,
0.025341443717479706,
-0.04920931160449982
] |
<p>What are the physics of wind (or any gas flow really) bouncing off surfaces?</p>
<p>If a wind hits a wall directly (in a 90 degree angle) does any of it bounce back? </p>
<p>Are there any similarities with, say, light rays hitting a mirror?</p>
<p>I understand, that the other extreme case is a 0 degree angle in gas pipes, for example, where the surface guides the flow further.</p> | 4,618 | [
-0.03406020626425743,
-0.036144934594631195,
-0.021858887746930122,
0.012110922485589981,
0.024647772312164307,
0.028472235426306725,
-0.023218777030706406,
0.012471363879740238,
0.018731463700532913,
-0.020494330674409866,
0.02362813800573349,
0.06931999325752258,
0.04038330167531967,
0.03085559606552124,
0.024523360654711723,
-0.013644152320921421,
-0.033479101955890656,
-0.021066635847091675,
0.026663288474082947,
-0.010792464017868042,
-0.03201133757829666,
-0.014420539140701294,
0.04219621419906616,
0.012933626770973206,
-0.056284982711076736,
0.019703634083271027,
0.021412700414657593,
-0.032957639545202255,
0.02249998040497303,
-0.026150790974497795,
-0.004183777142316103,
0.01211859006434679,
-0.027845200151205063,
0.008750837296247482,
0.013439244590699673,
-0.002690330147743225,
-0.023890476673841476,
0.006300340406596661,
-0.03438393399119377,
0.0015137901064008474,
-0.02800898440182209,
0.0026701849419623613,
-0.016333065927028656,
0.008800637908279896,
-0.03725166246294975,
-0.022713100537657738,
-0.0306065883487463,
-0.0027734495233744383,
0.049928758293390274,
-0.09623249620199203,
0.03675621747970581,
-0.010451714508235455,
0.03588002547621727,
0.01993589475750923,
0.024005167186260223,
-0.027315637096762657,
0.09611205011606216,
0.060923319309949875,
-0.03595302999019623,
-0.028709571808576584,
0.009396204724907875,
-0.009972973726689816,
-0.060452789068222046,
-0.003700829343870282,
-0.01708933338522911,
0.018192648887634277,
-0.015757938846945763,
-0.05268746241927147,
0.03830660879611969,
0.027140727266669273,
0.006045721471309662,
0.016990885138511658,
0.021388515830039978,
0.007093705236911774,
0.03899111971259117,
-0.006315229460597038,
0.05467572808265686,
0.006135427858680487,
0.0431162528693676,
0.03731595724821091,
0.010547010228037834,
-0.00308629241771996,
0.06693105399608612,
0.015706053003668785,
0.007993243634700775,
-0.019503643736243248,
0.09533814340829849,
-0.016113078221678734,
-0.002940477104857564,
0.015689650550484657,
0.07317152619361877,
-0.008886557072401047,
0.010230125859379768,
0.034978751093149185,
-0.02461136318743229,
0.022289391607046127,
0.014031841419637203,
0.06039804220199585,
0.008065289817750454,
0.0008567572804167867,
-0.06689701974391937,
0.020143412053585052,
0.041030459105968475,
0.054501667618751526,
0.0172725897282362,
0.003177391365170479,
-0.021360090002417564,
0.025888215750455856,
-0.04096115380525589,
0.01273268461227417,
-0.02925785258412361,
0.013087814673781395,
-0.015089370310306549,
-0.038750406354665756,
0.012411670759320259,
-0.017225008457899094,
0.03614006191492081,
-0.0197011549025774,
0.0431552454829216,
0.07971715927124023,
0.017357777804136276,
-0.01460353471338749,
0.012447384186089039,
0.006268470548093319,
-0.0534168966114521,
0.005871634464710951,
0.03602784499526024,
-0.04614729434251785,
-0.03521031513810158,
0.012849640101194382,
-0.019490189850330353,
0.0016307136975228786,
-0.0006609390256926417,
-0.019641868770122528,
0.030096685513854027,
-0.01277855597436428,
-0.11215994507074356,
-0.05033445358276367,
0.043746814131736755,
0.016042310744524002,
-0.019093457609415054,
-0.04896365478634834,
-0.010550069622695446,
0.047083284705877304,
0.0732162594795227,
-0.02270875684916973,
0.004421295132488012,
-0.0343695729970932,
0.02539190836250782,
-0.038263820111751556,
0.0031209890730679035,
0.023042693734169006,
0.013281567953526974,
-0.06384088844060898,
-0.005412222817540169,
-0.023723233491182327,
0.06271443516016006,
0.05718119069933891,
0.012392846867442131,
-0.05243125185370445,
0.039015449583530426,
-0.019044362008571625,
-0.0013808655785396695,
0.006080850958824158,
0.005732403136789799,
-0.019761664792895317,
0.049438707530498505,
0.051774006336927414,
-0.005867285188287497,
0.03792605921626091,
-0.01461110357195139,
-0.006719276309013367,
0.006384183652698994,
-0.005141932051628828,
0.047524549067020416,
-0.02313912846148014,
-0.023685790598392487,
-0.006005884148180485,
0.03628554195165634,
-0.02551265060901642,
-0.01778244972229004,
-0.006726434454321861,
0.012741702608764172,
0.002217617118731141,
0.00650678901001811,
0.010745502077043056,
-0.010453285649418831,
-0.012396151199936867,
0.002205074764788151,
-0.03307675942778587,
-0.035625286400318146,
-0.04677406698465347,
0.0604914166033268,
-0.05801081657409668,
-0.00025075540179386735,
0.007273647002875805,
0.014546982012689114,
-0.006163331214338541,
-0.010095614939928055,
-0.02692415751516819,
0.015829430893063545,
0.023722240701317787,
0.023731930181384087,
-0.013326910324394703,
-0.03277788311243057,
0.026107948273420334,
0.03226841986179352,
0.0024885861203074455,
0.04525512456893921,
-0.0018974167760461569,
-0.011583448387682438,
-0.05422922596335411,
-0.026209471747279167,
-0.019089963287115097,
0.003997035790234804,
-0.00939994677901268,
0.04902477562427521,
-0.0023228793870657682,
-0.00873817689716816,
-0.008325623348355293,
-0.04468424245715141,
0.04534474387764931,
0.07459419965744019,
0.02738952822983265,
0.006861909758299589,
0.017494797706604004,
0.014094042591750622,
-0.03004211187362671,
0.02418782375752926,
-0.022858867421746254,
-0.03164629638195038,
-0.01607804000377655,
0.02816450409591198,
0.006887897849082947,
-0.008941005915403366,
0.011930680833756924,
0.027190139517188072,
0.019390122964978218,
0.0020306799560785294,
0.04258187115192413,
0.01006276160478592,
-0.04756735637784004,
-0.00017597622354514897,
0.012914621271193027,
0.030774736776947975,
-0.00266659096814692,
0.025572659447789192,
0.0300153698772192,
0.01513141393661499,
-0.010587872937321663,
-0.034066930413246155,
0.0057716211304068565,
-0.0039574517868459225,
0.021104009822010994,
-0.013762646354734898,
-0.0346449613571167,
0.06527595221996307,
-0.01295142900198698,
-0.012092332355678082,
0.019119761884212494,
-0.0066408999264240265,
0.017389101907610893,
-0.03263012692332268,
0.01801801659166813,
0.016908634454011917,
-0.014064757153391838,
0.011433742009103298,
-0.0319785475730896,
0.0426776148378849,
-0.05343697592616081,
0.03300866857171059,
-0.0072360229678452015,
-0.005033034365624189,
-0.008424281142652035,
0.005823036190122366,
0.024350225925445557,
0.02858690917491913,
0.044612135738134384,
-0.008260569535195827,
-0.09620509296655655,
0.001510603935457766,
-0.020627880468964577,
-0.03893550857901573,
0.02473287843167782,
-0.0330265611410141,
0.039126526564359665,
-0.040496211498975754,
0.010323076508939266,
0.032758645713329315,
-0.019711846485733986,
-0.020730875432491302,
0.0455453023314476,
0.025047488510608673,
-0.028262503445148468,
0.002358127385377884,
-0.04372359812259674,
0.013706967234611511,
-0.02221093140542507,
0.004533539991825819,
0.03142291679978371,
-0.012734648771584034,
-0.03354315087199211,
0.045930005609989166,
-0.019179394468665123,
-0.054238539189100266,
-0.03829358145594597,
-0.015570135787129402,
0.03231527656316757,
-0.0070390054024755955,
0.0011258921585977077,
0.06547693908214569,
-0.0435999371111393,
-0.028583796694874763,
-0.007789216469973326,
-0.059969693422317505,
0.0019712834618985653,
-0.021587425842881203,
0.04989629238843918,
-0.011945650912821293,
-0.017880510538816452,
0.057144585996866226,
0.010067089460790157,
-0.03693167492747307,
-0.0003229007706977427,
-0.030958309769630432,
-0.0074647823348641396,
-0.02973739616572857,
0.00542115792632103,
0.06713604927062988,
-0.014332538470625877,
0.013020058162510395,
-0.009421126917004585,
0.015401607379317284,
0.022840997204184532,
-0.003416175954043865,
0.0006331261829473078,
-0.03179127722978592,
0.024560755118727684,
0.0011651947861537337,
0.03027944825589657,
-0.01779543049633503,
-0.0559774711728096,
0.033304281532764435,
0.008947069756686687,
0.014217160642147064,
0.041694276034832,
-0.07582354545593262,
0.08231690526008606,
-0.014870907180011272,
0.006794775370508432,
-0.04485214874148369,
0.00861877016723156,
-0.023489713668823242,
0.002560477005317807,
-0.0072016934864223,
0.01753835380077362,
0.05742507800459862,
0.009426740929484367,
0.013190164230763912,
0.021923057734966278,
0.07233738899230957,
-0.015683308243751526,
-0.02885127253830433,
-0.01630668342113495,
-0.019451625645160675,
0.018988782539963722,
-0.005731008481234312,
0.021947940811514854,
0.06616321951150894,
0.03815467283129692,
0.03421054035425186,
0.03597158566117287,
-0.04818617179989815,
0.004112096969038248,
-0.014419231563806534,
-0.004343790002167225,
-0.012814668007194996,
0.04113179072737694,
-0.015925006940960884,
0.0455927737057209,
0.003910958766937256,
0.03426224738359451,
0.01325470581650734,
-0.010178200900554657,
-0.047068722546100616,
0.0079453494399786,
-0.01626669242978096,
-0.02060493640601635,
-0.02777206152677536,
-0.015264141373336315,
-0.0269046351313591,
-0.00845724530518055,
-0.0005451129982247949,
0.005257050972431898,
-0.00882293377071619,
-0.022049976512789726,
0.006274015177041292,
-0.031455397605895996,
-0.07115805894136429,
0.008169294334948063,
0.05383959040045738,
0.012994879856705666,
-0.02426108717918396,
0.05327906087040901,
0.03723845258355141,
-0.03649723902344704,
-0.02755647711455822,
-0.009565377607941628,
0.014443161897361279,
-0.007227055262774229,
0.05782120302319527,
0.025732988491654396,
-0.012594733387231827,
-0.008244061842560768,
0.012566699646413326,
0.011028237640857697,
-0.0015478971181437373,
-0.005831735674291849,
-0.004079221747815609,
-0.02698049321770668,
-0.040805961936712265,
-0.035847824066877365,
-0.0044464231468737125,
0.023898446932435036,
-0.007903228513896465,
-0.039058152586221695,
-0.01694425754249096,
-0.004078684840351343,
-0.012761793099343777,
0.04322919622063637,
0.021323567256331444,
0.02729852683842182,
0.04608330875635147,
-0.04489360749721527,
0.011507494375109673,
0.0027465573512017727,
-0.004749710205942392,
0.004086549859493971,
0.02369578927755356,
-0.022021742537617683,
-0.01320230308920145,
0.01068876776844263,
0.03417551890015602,
-0.0006327709415927529,
0.011771969497203827,
0.0075265043415129185,
0.03009829670190811,
-0.03732292354106903,
-0.006228076759725809,
-0.014470798894762993,
0.05415377765893936,
0.03079008124768734,
0.028453126549720764,
-0.03254931420087814,
-0.06847948580980301,
-0.012424111366271973,
0.03428645431995392,
0.027818720787763596,
-0.030657675117254257,
-0.008781538344919682,
-0.056386977434158325,
0.008920916356146336,
0.012767696753144264,
0.0012576566077768803,
0.00698733190074563,
-0.0544162280857563,
0.015756448730826378,
-0.015789657831192017,
-0.038602497428655624,
0.0010459941113367677,
0.01886139065027237,
0.0065301028080284595,
0.01186662819236517,
-0.029096180573105812,
-0.04921277239918709,
-0.018194597214460373,
0.010761581361293793,
0.0077803004533052444,
0.02614622376859188,
-0.0010842005722224712,
0.019889360293745995,
-0.06212977319955826,
0.02468150109052658,
-0.06374401599168777,
-0.09382742643356323,
0.011491836979985237,
0.0079793157055974,
-0.005015994887799025,
0.037579335272312164,
0.00214362982660532,
-0.02297535352408886,
0.0030491454526782036,
-0.010474931448698044,
-0.012314989231526852,
0.006897546350955963,
-0.012137475423514843,
0.015342175029218197,
0.014568419195711613,
0.014197726733982563,
0.05294722318649292,
0.06363939493894577,
-0.014891484752297401,
-0.02348683960735798,
0.029695091769099236,
0.08811363577842712,
-0.01646234840154648,
-0.020438851788640022,
-0.0603945218026638,
-0.03397208824753761,
-0.012294578365981579,
0.049633145332336426,
0.0008559005800634623,
0.047447480261325836,
0.013866694644093513,
-0.05443071573972702,
-0.02752932533621788,
0.024546727538108826,
0.0008405402186326683,
-0.026294108480215073,
-0.008985256776213646,
0.03394578769803047,
-0.02290567010641098,
-0.03230408579111099,
0.002957848599180579,
0.041494157165288925,
0.016995491459965706,
0.014792156405746937,
-0.012607797048985958,
-0.017222711816430092,
-0.05678854137659073,
0.009281247854232788,
-0.01036116387695074,
-0.04649600759148598,
0.049836672842502594,
-0.00029931802419014275,
-0.004629945382475853,
0.03654041886329651,
-0.017917485907673836,
0.00815953966230154,
0.03724132850766182,
-0.0017991367494687438,
0.03712090849876404,
-0.05544896051287651,
0.015345567837357521,
0.0035190670751035213,
0.014122244901955128,
-0.05311773717403412,
-0.03818367421627045,
0.026601778343319893,
0.040876347571611404,
-0.01461821049451828,
-0.039771247655153275,
-0.030693354085087776,
-0.049717213958501816,
-0.051188867539167404,
0.009056360460817814,
0.016060568392276764,
-0.03523432835936546,
0.001503974199295044,
0.029799792915582657,
0.00959082506597042,
0.04967363551259041,
-0.013937884010374546,
-0.01227490697056055,
0.02286922000348568,
-0.038473062217235565,
-0.016226524487137794,
-0.023805398494005203,
0.027210166677832603,
-0.014341100119054317,
-0.009387035854160786,
-0.0014001003000885248,
-0.0072548361495137215,
0.039303746074438095,
-0.05311556160449982,
0.04878716915845871,
0.004256847780197859,
-0.0023798970505595207,
-0.014913349412381649,
0.006970124784857035,
0.019416166469454765,
0.008143160492181778,
0.04140084609389305,
0.0023195422254502773,
-0.0025214925408363342,
0.003170275129377842,
-0.023497210815548897,
0.013454452157020569,
0.012968150898814201,
0.019211074337363243,
0.019534144550561905,
0.051950640976428986,
-0.014702157117426395,
-0.012522791512310505,
0.008011252619326115,
-0.025917043909430504,
0.052169069647789,
-0.04753926023840904,
0.02211935631930828,
0.026364319026470184,
0.0023530516773462296,
-0.004784355405718088,
-0.059948358684778214,
-0.02592429704964161,
-0.009452695026993752,
0.04130139946937561,
-0.021799219772219658,
0.03967341408133507,
-0.01725071296095848,
-0.011917914263904095,
-0.04406749829649925,
-0.031245430931448936,
0.008305390365421772,
-0.004931621253490448,
0.015543833374977112,
0.04678952693939209,
0.0005983031005598605,
0.013141649775207043,
-0.004284868948161602,
-0.0005918353563174605,
0.02473716251552105,
-0.0157389584928751,
0.0047427075915038586,
0.03281630575656891,
0.05592101439833641,
0.014119246043264866,
-0.016001299023628235,
0.04015897959470749,
-0.04169502109289169,
0.028026070445775986,
-0.006595198065042496,
-0.016828909516334534,
0.050355054438114166,
0.012132111936807632,
-0.01920434832572937,
-0.0651082769036293,
0.016940535977482796,
-0.026004834100604057,
0.0030458057299256325,
0.00785488449037075,
0.005705992225557566,
-0.01739586517214775,
-0.006427522283047438,
0.030383503064513206,
0.006109073758125305,
0.019482582807540894,
0.015078172087669373,
-0.028963884338736534,
-0.0008577355183660984,
-0.020432544872164726,
-0.016779977828264236,
0.048016197979450226,
0.0007347570499405265,
-0.012877890840172768,
0.017119213938713074,
-0.054675180464982986,
0.022888198494911194,
-0.013286910951137543,
0.011626501567661762,
-0.03214257210493088,
0.06040613353252411,
0.016336746513843536,
0.023601919412612915,
-0.028448371216654778,
0.023393278941512108,
0.1096973568201065,
0.03455566614866257,
0.03473610058426857,
-0.011797809042036533,
-0.0347842276096344,
-0.005680915899574757,
-0.007453188765794039,
-0.013626654632389545,
0.018390120938420296,
-0.004023382440209389,
0.025156985968351364,
0.025143198668956757,
0.045353539288043976,
0.025348953902721405,
0.015285898931324482,
0.024622509256005287,
-0.05125880241394043,
-0.014864319004118443,
-0.01783483475446701,
-0.024930080398917198,
-0.018366601318120956,
0.0756630077958107,
-0.05564292147755623,
0.02246498130261898,
-0.006560908164829016,
-0.018205981701612473,
0.01829935424029827,
-0.04466067999601364,
0.05196627974510193,
-0.016346262767910957,
-0.05020016431808472,
0.029659058898687363,
0.01661156490445137,
-0.017301121726632118,
-0.03913969174027443,
0.01966380886733532,
0.033963318914175034,
-0.024783650413155556,
0.025207513943314552,
0.00639744009822607,
0.011356372386217117,
-0.021458804607391357,
0.01703648641705513,
0.031866252422332764,
-0.053548023104667664,
-0.007196767721325159,
-0.02981371246278286,
0.028209466487169266,
-0.018705138936638832,
0.02179405838251114,
-0.03302190825343132,
0.021772975102066994,
0.04437790438532829,
-0.06299850344657898,
-0.015577835962176323,
-0.021582862362265587,
0.05625404790043831,
-0.026152538135647774,
-0.03816341981291771,
-0.014326329343020916,
0.04148469865322113,
-0.004614273086190224,
0.005957544315606356,
0.0038672592490911484,
-0.018004285171628,
0.0019714466761797667,
0.00022330682259052992,
0.06640217453241348,
-0.004765976686030626,
-0.04589340463280678,
-0.04865337908267975,
-0.006766237784177065,
-0.04829224944114685,
-0.010709126479923725,
0.006867086049169302,
0.03736969456076622,
0.02583317831158638,
0.015948500484228134,
-0.014842625707387924,
-0.024186130613088608,
-0.03597687557339668,
0.04754236340522766,
-0.034319546073675156,
-0.02212963066995144,
-0.022364484146237373,
-0.03669134899973869,
0.0333552286028862,
0.0220696572214365,
-0.03528586030006409,
-0.0068563553504645824,
-0.027336502447724342,
0.031542498618364334,
0.012999128550291061,
-0.0044674319215118885,
-0.040431659668684006,
0.0489308200776577,
-0.021520620211958885,
0.013944383710622787,
-0.010037277825176716,
0.049291133880615234,
0.02385740913450718,
-0.006219852715730667,
0.028864938765764236,
0.019976379349827766,
-0.030373958870768547,
-0.018568484112620354,
0.022906705737113953,
-0.02602349780499935,
-0.015058987773954868,
0.0036728812847286463,
0.004090873524546623,
-0.04632740840315819,
-0.03060365840792656,
-0.022071197628974915,
-0.013328026048839092,
-0.015176709741353989,
0.04398684203624725,
-0.014559811912477016,
0.018650773912668228,
-0.04127960652112961,
0.04220316931605339,
-0.03940558061003685,
-0.04030679166316986,
-0.0755508616566658,
0.01909545622766018,
0.0009820872219279408,
-0.004043612163513899,
-0.008360972627997398,
0.03855416178703308,
-0.05348793789744377,
0.017613157629966736,
0.006142119877040386,
0.03016914799809456,
-0.011366127990186214,
0.04099934548139572,
0.019209329038858414,
-0.03173533454537392,
0.028823696076869965,
0.0005077444366179407,
-0.019289899617433548,
0.06326962262392044,
-0.03649578616023064,
-0.09894293546676636,
0.034576136618852615,
0.0020797608885914087,
0.01585022732615471,
0.03593925014138222,
-0.0241857822984457,
-0.014314738102257252,
0.05025062337517738,
0.018909137696027756,
-0.01715819351375103,
-0.031425733119249344,
0.003767518326640129,
0.0006445858161896467,
0.0010752452071756124,
0.05083569511771202,
-0.04059595987200737,
-0.006533753126859665,
0.027391115203499794,
0.016869083046913147,
-0.022808967158198357,
0.048457372933626175,
0.0041308170184493065,
-0.031499043107032776,
-0.03459910675883293,
0.01893533393740654,
0.01658032462000847,
0.0063690138049423695,
0.0403839536011219,
-0.03357623144984245,
0.02912461757659912,
0.007100699935108423,
0.004641949199140072,
-0.10771447420120239,
0.03179522976279259,
0.011874419637024403,
-0.008445469662547112,
0.03233712911605835,
-0.05061441659927368,
0.01214046310633421,
0.063857801258564,
-0.10683178156614304,
-0.0030095267575234175,
0.002585121663287282,
-0.009306435473263264,
-0.030161403119564056,
0.024909362196922302,
0.01274113543331623,
0.022770201787352562,
-0.009552821516990662,
0.03069860115647316,
0.030073005706071854,
0.033675242215394974,
0.009961441159248352,
0.015687158331274986,
-0.030874153599143028,
0.026615334674715996,
-0.01905319280922413,
0.0008640959276817739,
0.05772063508629799,
-0.026680395007133484,
0.013166005723178387,
0.02755064144730568,
-0.011445587500929832,
0.023586029186844826,
-0.0420365035533905,
-0.0043380786664783955,
0.02625725418329239,
0.006375455297529697,
0.0028132011648267508,
0.004675325937569141,
-0.01100258156657219,
0.04013383015990257,
0.022014783695340157,
0.009306736290454865,
-0.0018768199952319264,
-0.01956283114850521,
0.006088033318519592,
-0.05876430496573448,
-0.023725708946585655,
0.009342719800770283,
-0.003370184451341629,
-0.021081887185573578,
-0.0025065639056265354,
0.007399832829833031,
0.021539883688092232,
0.00658106105402112,
-0.0012043733149766922,
-0.07633835077285767,
-0.031233085319399834,
0.012446067295968533,
-0.023153210058808327,
-0.008605015464127064,
0.04357728734612465,
-0.01804719865322113,
-0.02507624961435795,
0.01702713593840599,
-0.033687710762023926,
-0.0013440119801089168,
-0.06322814524173737,
-0.03290941193699837,
0.0005093723302707076,
-0.014108706265687943,
0.010636319406330585,
-0.013461295515298843,
-0.0014595192624256015,
0.001998461550101638,
-0.004374903626739979,
0.061105720698833466,
-0.007523634936660528,
-0.07066311687231064,
-0.028017083182930946,
-0.057452794164419174,
0.03709474578499794,
-0.02042592316865921,
-0.013898569159209728,
-0.07221795618534088,
-0.019771575927734375,
0.03263044357299805,
0.022102992981672287,
0.05126448720693588,
-0.011812757700681686,
-0.0012431995710358024,
0.0041953488253057,
-0.003908362239599228,
0.024386346340179443,
-0.03313645347952843,
0.006494637578725815,
-0.0005011014873161912,
-0.011916633695363998,
-0.004285284783691168,
-0.008523952215909958,
-0.014398752711713314,
0.0005654754932038486,
0.03391556069254875,
0.0036755769979208708,
0.008561665192246437,
-0.01858494058251381,
-0.06639639288187027,
0.052391134202480316,
0.05382556468248367,
-0.021731453016400337,
0.05126350745558739,
-0.02673046663403511,
0.02222168818116188,
0.015698537230491638,
-0.04137536510825157,
-0.04822385311126709,
0.013759120367467403,
-0.031789083033800125,
-0.012872894294559956,
-0.04442048445343971,
-0.014780608005821705,
0.037658385932445526,
-0.03393511101603508,
0.021575070917606354,
-0.01817202754318714,
-0.04048921540379524,
0.018281428143382072,
0.0847257748246193,
0.013986415229737759,
0.01602310501039028,
-0.005435655824840069,
0.007646528072655201,
0.048806387931108475,
-0.018056826665997505,
-0.05348123610019684,
0.059861183166503906,
0.04678325355052948,
-0.006666714791208506,
-0.000483472686028108,
0.041378699243068695,
0.01706395484507084,
0.03886864706873894,
0.0252924095839262,
0.028846614062786102,
-0.017648160457611084,
-0.01786895841360092,
0.025832856073975563,
0.02707807719707489,
-0.04144567996263504,
0.0312841534614563,
-0.017048176378011703,
0.05431821197271347,
-0.00942846667021513,
0.024172507226467133,
-0.01417322177439928,
-0.01573041081428528,
0.016248144209384918,
0.03143582120537758,
-0.01170389074832201,
0.0407903753221035,
0.03409180790185928,
-0.007771863602101803,
-0.015155022963881493,
0.04683372750878334,
0.02709493413567543,
0.0024378476664423943,
0.008367522619664669,
-0.0234039518982172,
0.00656697666272521,
-0.030250808224081993,
-0.026687797158956528,
-0.0008408587309531868,
-0.01262037642300129,
0.021379591897130013,
0.010631765238940716,
0.002396420342847705,
0.051541686058044434,
0.0069062854163348675,
-0.035316694527864456,
0.06373155117034912,
-0.06541252136230469,
0.016641585156321526,
0.0018663706723600626,
0.0550771988928318,
0.0011688274098560214,
-0.003445018082857132
] |
<p>In a Leyden jar, I have read that a charged object is brought in contact with the conductor in contact with the metal inside the jar, thus giving the inner metal a similar charge. And the metal outside the jar then gets an opposite charge.</p>
<p>My question is simply how does the metal outside the jar get the opposite charge, given that there is an insulator in-between?</p>
<p>I hope that someone can give me a clear reply, explaining exactly what happens with the outer metal.</p> | 4,619 | [
-0.04778943210840225,
-0.0401211678981781,
0.016248906031250954,
-0.00975081603974104,
0.026555553078651428,
0.028467733412981033,
-0.019247407093644142,
0.025982055813074112,
0.02532089315354824,
-0.014414974488317966,
0.02898583933711052,
0.02617243491113186,
0.034655965864658356,
0.016057390719652176,
0.022923527285456657,
0.005253776907920837,
-0.002566871466115117,
-0.020044630393385887,
0.02868192456662655,
-0.06486430764198303,
-0.025845317170023918,
0.008650313131511211,
-0.021731512621045113,
-0.0011618785792961717,
-0.04440180957317352,
0.009720005095005035,
0.010806996375322342,
-0.017273126170039177,
0.03488663583993912,
0.019637584686279297,
-0.03455222398042679,
-0.02319132536649704,
-0.020626414567232132,
-0.01757131516933441,
0.05323808267712593,
-0.000543948553968221,
-0.06460575759410858,
-0.06787101179361343,
-0.006201914977282286,
0.028155123814940453,
-0.005812143906950951,
-0.03229948878288269,
0.007315699476748705,
0.04875095933675766,
-0.010100879706442356,
-0.027549922466278076,
0.00716448063030839,
0.00023811240680515766,
0.01842435635626316,
-0.06372614949941635,
0.009590905159711838,
-0.020426029339432716,
0.03760732337832451,
0.05373623967170715,
0.002046840265393257,
0.02072247304022312,
0.09649583697319031,
0.04615561291575432,
0.018098579719662666,
-0.04268324002623558,
-0.014045617543160915,
-0.04424126818776131,
-0.026274424046278,
-0.04120507463812828,
-0.03579512611031532,
0.02636178955435753,
0.03912423178553581,
-0.048732951283454895,
0.017158163711428642,
0.03143736347556114,
0.02704625017940998,
0.018737368285655975,
0.01712687499821186,
-0.007083101663738489,
0.014933057129383087,
-0.01556332129985094,
0.027217041701078415,
0.02360464259982109,
0.01226009987294674,
0.0022287224419414997,
-0.03202508017420769,
-0.007861794903874397,
0.016346760094165802,
0.03285004943609238,
0.004944980144500732,
-0.029334675520658493,
0.055410344153642654,
-0.015424231998622417,
0.01261688582599163,
0.022616736590862274,
0.0069255102425813675,
0.022917194291949272,
0.011120191775262356,
0.0029105311259627342,
-0.029976239427924156,
0.004729714244604111,
-0.017722031101584435,
0.05073568597435951,
-0.0355784073472023,
-0.0009195927414111793,
-0.003308328799903393,
0.028611185029149055,
0.05449272319674492,
0.07383057475090027,
0.02454301342368126,
-0.08283420652151108,
-0.0255736093968153,
-0.0023331695701926947,
0.013181708753108978,
0.017891841009259224,
-0.027765922248363495,
0.01396697387099266,
0.030469227582216263,
-0.016996854916214943,
0.006436477415263653,
-0.034106142818927765,
-0.014141150750219822,
-0.03024986945092678,
0.015642059966921806,
0.03728276118636131,
0.009944654069840908,
-0.012473643757402897,
0.03848638758063316,
-0.041158996522426605,
-0.06560584157705307,
-0.014201519079506397,
-0.0019461900228634477,
0.03211478143930435,
0.011114913038909435,
0.004517382476478815,
-0.003022218821570277,
-0.02652786113321781,
0.019961034879088402,
0.019374700263142586,
0.028829971328377724,
-0.036553140729665756,
-0.10732902586460114,
-0.06586437672376633,
0.02265569567680359,
0.003954981453716755,
-0.02800837531685829,
-0.08158490806818008,
0.016752492636442184,
0.002953365445137024,
0.069664865732193,
0.015201608650386333,
-0.030608590692281723,
-0.014005645178258419,
0.003800520673394203,
0.0349680632352829,
0.02624569647014141,
-0.04019857943058014,
0.018390268087387085,
0.008203491568565369,
0.010264640673995018,
-0.08876403421163559,
0.026070961728692055,
0.02539186365902424,
-0.017910649999976158,
-0.02518037147819996,
0.07504270225763321,
-0.013883790001273155,
0.02710076794028282,
0.03632771968841553,
-0.033550381660461426,
-0.018972214311361313,
0.10629946738481522,
0.007400503847748041,
-0.00838664174079895,
0.032366856932640076,
0.02129255421459675,
0.03887094557285309,
-0.011992822401225567,
0.034943316131830215,
0.04011279717087746,
-0.022249337285757065,
-0.008118709549307823,
-0.02157163806259632,
0.06107941269874573,
-0.029490159824490547,
-0.05429902300238609,
-0.021994872018694878,
0.014467540197074413,
-0.02135017141699791,
0.021718233823776245,
0.010371821001172066,
-0.01600368320941925,
-0.03679979220032692,
-0.01950032450258732,
-0.04180033504962921,
-0.019592508673667908,
-0.0373268686234951,
0.034348975867033005,
0.011113564483821392,
-0.050993017852306366,
0.025456732138991356,
0.007537773810327053,
0.004628852475434542,
-0.0438498929142952,
-0.017285173758864403,
-0.020104361698031425,
0.015955980867147446,
-0.010427175089716911,
-0.001548848464153707,
0.029512731358408928,
0.03618224337697029,
0.03814723715186119,
0.010422633960843086,
0.0015180944465100765,
-0.01362144947052002,
-0.04314455762505531,
-0.011874916031956673,
-0.009864452295005322,
-0.01020605769008398,
0.01615223102271557,
-0.006755822338163853,
0.050092779099941254,
0.010905896313488483,
-0.017731649801135063,
0.04893343523144722,
-0.0157028716057539,
0.06098410487174988,
0.06104346364736557,
0.03072580136358738,
-0.02068604901432991,
0.04933685436844826,
0.001737759099341929,
0.03246741369366646,
0.012487556785345078,
-0.013540483079850674,
-0.07231134176254272,
-0.0033542856108397245,
0.04894378408789635,
-0.00458358833566308,
-0.01855791173875332,
0.01621462032198906,
0.01684914156794548,
0.03062537871301174,
-0.0005969441845081747,
0.014783774502575397,
-0.03007866069674492,
-0.009718366898596287,
0.018876345828175545,
-0.010738158598542213,
0.004655282944440842,
-0.01627599075436592,
0.01070152036845684,
-0.006017555948346853,
0.015762964263558388,
-0.004084921441972256,
-0.020455580204725266,
0.03067675605416298,
-0.011005121283233166,
0.046153724193573,
-0.012533497996628284,
-0.03425846993923187,
0.00022588131832890213,
-0.04850664734840393,
0.020058374851942062,
0.0010011408012360334,
0.028484733775258064,
0.022149620577692986,
-0.025677183642983437,
0.020104769617319107,
0.010207124054431915,
-0.03497655689716339,
-0.0331336073577404,
0.01571519859135151,
0.011104432865977287,
-0.05696025863289833,
0.016362160444259644,
0.00930757075548172,
0.010940276086330414,
-0.004278917331248522,
0.003329431638121605,
0.00831808801740408,
0.024967843666672707,
0.025702156126499176,
0.0029447395354509354,
-0.03284444287419319,
0.015540213324129581,
-0.017656775191426277,
0.0076257712207734585,
0.031182706356048584,
-0.03756938502192497,
0.016774510964751244,
-0.04094838723540306,
-0.05054531991481781,
0.03945378586649895,
0.018228968605399132,
-0.010730400681495667,
0.02875947766005993,
0.007161296904087067,
-0.04321571812033653,
0.019810978323221207,
0.02785288169980049,
-0.01699061505496502,
-0.03282523155212402,
0.01671990565955639,
0.05599268153309822,
0.05331890657544136,
-0.03676999360322952,
-0.011139866895973682,
-0.055569808930158615,
-0.03517911210656166,
-0.018396921455860138,
-0.012169021181762218,
0.014727409929037094,
-0.01175694353878498,
0.01609412394464016,
0.01671718619763851,
-0.03231121599674225,
-0.00838844571262598,
-0.049935098737478256,
-0.007933715358376503,
-0.015156887471675873,
0.027617646381258965,
0.0075166798196733,
-0.03200875595211983,
-0.03965310752391815,
0.06549002975225449,
-0.009306477382779121,
-0.04686293378472328,
-0.02772814780473709,
-0.04838808998465538,
-0.030830707401037216,
-0.01622162014245987,
-0.008455761708319187,
0.06450184434652328,
-0.019318871200084686,
0.040666207671165466,
0.032000813633203506,
0.04804938659071922,
0.011273615062236786,
0.020187871530652046,
0.0309629924595356,
-0.0018072688253596425,
0.052071429789066315,
-0.001406394294463098,
0.05260629206895828,
0.01201606635004282,
-0.02200724370777607,
0.029362237080931664,
0.015400350093841553,
0.001548182568512857,
0.027121728286147118,
-0.03098880872130394,
0.02347324974834919,
0.0025495081208646297,
0.02936404198408127,
-0.023763740435242653,
0.014745688065886497,
-0.030745526775717735,
0.021702054888010025,
0.001770972041413188,
0.021440213546156883,
0.041530024260282516,
-0.034700196236371994,
-0.020248929038643837,
0.04896170273423195,
0.046541694551706314,
-0.03278631344437599,
-0.04658813774585724,
0.026906028389930725,
-0.010711238719522953,
0.0367778055369854,
-0.02794710546731949,
0.005946943536400795,
0.011026311665773392,
0.04314473271369934,
0.010204612277448177,
-0.0012007299810647964,
-0.02455809898674488,
-0.04181051254272461,
-0.04872524365782738,
-0.00645179720595479,
0.011211865581572056,
0.025884123519062996,
-0.022287456318736076,
0.06605415791273117,
0.03974337503314018,
0.03183576837182045,
-0.006826724857091904,
0.013712180778384209,
-0.11194518208503723,
0.03007156029343605,
-0.007573756389319897,
0.009129924699664116,
-0.022363586351275444,
-0.014450549148023129,
-0.04162242263555527,
0.009353789500892162,
-0.016514508053660393,
0.003976108971983194,
-0.04266967251896858,
-0.03041469305753708,
0.03697217255830765,
0.01464807614684105,
-0.020599424839019775,
-0.036258336156606674,
0.028527546674013138,
-0.001779841841198504,
-0.005413045175373554,
-0.016869165003299713,
0.014630774036049843,
-0.01760987378656864,
0.01947043463587761,
-0.015471527352929115,
-0.028004752472043037,
0.03908143937587738,
0.01861387863755226,
0.014222214929759502,
-0.020461123436689377,
-0.01281664613634348,
-0.0059655094519257545,
0.02753915823996067,
0.05487428233027458,
-0.002588055795058608,
-0.05241231620311737,
-0.037106338888406754,
-0.05691739171743393,
-0.029730401933193207,
-0.012150401249527931,
0.08731096237897873,
-0.013534222729504108,
0.01286291889846325,
0.016887666657567024,
0.007205140311270952,
0.007898814044892788,
0.014528997242450714,
0.054523855447769165,
0.03129272162914276,
-0.04894578456878662,
-0.012584399431943893,
-0.021510116755962372,
-0.020529605448246002,
-0.01257438026368618,
0.03915822505950928,
-0.026371236890554428,
0.0035890028811991215,
-0.0017949242610484362,
0.027845807373523712,
0.014678256586194038,
0.01670270413160324,
0.016442663967609406,
-0.016622478142380714,
0.020755134522914886,
-0.04144913703203201,
-0.0036217132583260536,
-0.0013835550053045154,
0.0337064154446125,
0.07054057717323303,
0.011500311084091663,
0.011601193808019161,
-0.0861569494009018,
-0.019082020968198776,
0.051811158657073975,
0.05172717943787575,
-0.04418392479419708,
0.0023948948364704847,
-0.07039117813110352,
-0.015591146424412727,
0.029323967173695564,
-0.02096732147037983,
0.014411966316401958,
-0.022432100027799606,
-0.01347027812153101,
-0.038026243448257446,
-0.017568150535225868,
-0.010226705111563206,
0.004796973895281553,
-0.004622103180736303,
0.022293206304311752,
-0.033635567873716354,
-0.04209072142839432,
-0.01880919560790062,
0.01615745760500431,
0.008526429533958435,
0.02586136758327484,
0.0029952824115753174,
0.035722360014915466,
-0.027558831498026848,
-0.0069879936054348946,
-0.020377445966005325,
-0.054881609976291656,
0.00757143460214138,
-0.015700271353125572,
0.005841987673193216,
0.02424788475036621,
-0.04032273218035698,
-0.053378596901893616,
0.0025094698648899794,
0.008158007636666298,
0.02601979859173298,
-0.032441843301057816,
-0.03791506588459015,
0.02467176876962185,
0.009852631948888302,
-0.007941710762679577,
0.048560213297605515,
-0.012953181751072407,
-0.038442615419626236,
0.013639448210597038,
0.0032896846532821655,
0.05870717763900757,
-0.026509905233979225,
0.00846998579800129,
0.006058228202164173,
0.021724143996834755,
-0.029003649950027466,
0.07646165788173676,
-0.005067536607384682,
0.02995530143380165,
-0.02699171006679535,
-0.02159254625439644,
0.021653873845934868,
0.010689646005630493,
-0.013123851269483566,
-0.012086352333426476,
-0.027933944016695023,
0.02903464436531067,
0.01849566400051117,
-0.03327878192067146,
0.0482163242995739,
-0.0013965180842205882,
0.007065645884722471,
0.04143242537975311,
-0.026386214420199394,
0.03749949112534523,
-0.04042148217558861,
-0.02995304763317108,
-0.006869486533105373,
-0.03378318250179291,
0.009742102585732937,
-0.01879570260643959,
0.0006537533481605351,
0.04250596836209297,
-0.05994131788611412,
-0.038426365703344345,
0.015677165240049362,
-0.04593360424041748,
0.005117148160934448,
-0.09058217704296112,
0.025233663618564606,
0.05647484213113785,
-0.025468312203884125,
-0.07448668032884598,
-0.08039714395999908,
0.030504588037729263,
-0.0005001189419999719,
0.010082816705107689,
-0.018821237608790398,
-0.04219181463122368,
0.019363820552825928,
-0.03794753551483154,
0.0038196477107703686,
0.03811405226588249,
-0.0743030309677124,
0.024484410881996155,
0.0026199305430054665,
0.0067846281453967094,
0.06594099849462509,
0.01207041647285223,
0.002784713637083769,
0.020725607872009277,
-0.045277904719114304,
-0.006249705795198679,
0.002284785732626915,
0.05329067260026932,
-0.01335066370666027,
-0.04114050418138504,
-0.008006364107131958,
0.02663530968129635,
0.05075807496905327,
-0.0034112974535673857,
-0.03394332900643349,
0.025314519181847572,
0.02941710874438286,
-0.011707285419106483,
-0.020131245255470276,
0.03390485420823097,
0.05963166058063507,
0.032160211354494095,
-0.013856964185833931,
0.00897244457155466,
-0.06342694908380508,
-0.03847469761967659,
-0.020261481404304504,
0.014303469099104404,
-0.0014752903953194618,
-0.0060397302731871605,
0.08512015640735626,
-0.037983085960149765,
0.018667304888367653,
0.04552296921610832,
-0.029981398954987526,
0.021580122411251068,
-0.03964769095182419,
0.01864367164671421,
0.03504547104239464,
0.042142949998378754,
-0.004644854925572872,
-0.030383359640836716,
-0.03061758168041706,
-0.020715512335300446,
0.056625742465257645,
0.009631101973354816,
0.06493804603815079,
0.05392215773463249,
0.002652908442541957,
-0.03045433759689331,
-0.00947374477982521,
0.01646164059638977,
0.03214193508028984,
-0.005846903659403324,
0.01821795478463173,
-0.03293455019593239,
0.01908249221742153,
0.025966573506593704,
0.06179807707667351,
-0.0629313737154007,
-0.023141421377658844,
0.03431681543588638,
0.04525132477283478,
0.027458231896162033,
-0.019831739366054535,
-0.03380453959107399,
0.034443438053131104,
-0.016399752348661423,
0.04133215174078941,
0.020762991160154343,
-0.04652641341090202,
0.03548745810985565,
0.013436255045235157,
0.013903467915952206,
-0.016924496740102768,
-0.03125956282019615,
-0.043316129595041275,
0.02689511515200138,
-0.005210807081311941,
0.02338799089193344,
-0.02376279979944229,
0.02033264748752117,
0.01909886673092842,
0.0029354430735111237,
0.00021247711265459657,
-0.000018784350686473772,
-0.035897668451070786,
-0.02134021371603012,
-0.030992159619927406,
-0.006938959937542677,
0.03082149848341942,
-0.008763945661485195,
-0.008968965150415897,
-0.004070915747433901,
-0.034288190305233,
0.025699691846966743,
0.024319643154740334,
0.05059073120355606,
-0.020755240693688393,
0.06289538741111755,
-0.005288142245262861,
0.06255348026752472,
-0.032813165336847305,
0.019690269604325294,
0.10734373331069946,
0.0034928189124912024,
-0.006388396956026554,
-0.0655740350484848,
-0.03206527605652809,
-0.01380929071456194,
0.0028297288808971643,
-0.009018145501613617,
0.02151102013885975,
-0.06218412518501282,
0.01039142906665802,
0.01703854277729988,
0.029377449303865433,
-0.02096474915742874,
0.010853767395019531,
0.025458665564656258,
-0.0051892404444515705,
-0.004295129794627428,
-0.002047321991994977,
0.010341843590140343,
-0.008299930021166801,
-0.002844663802534342,
-0.05733947083353996,
0.012751895934343338,
-0.03471045196056366,
0.008610587567090988,
-0.04340566322207451,
-0.008693891577422619,
0.03493932634592056,
0.009115313179790974,
-0.04591130092740059,
-0.0064179240725934505,
0.014059830456972122,
-0.01617373153567314,
-0.027507003396749496,
0.031133420765399933,
0.03282622992992401,
0.026954786852002144,
-0.009975033812224865,
0.007224824745208025,
0.04130687564611435,
-0.00534783722832799,
0.012853381223976612,
0.036041565239429474,
-0.04407921060919762,
0.010711383074522018,
-0.012428447604179382,
0.04946429654955864,
0.01711718551814556,
0.001384452567435801,
-0.009741033427417278,
0.013048126362264156,
0.031619176268577576,
-0.011125341057777405,
-0.04909108579158783,
-0.010513847693800926,
-0.0020651586819440126,
-0.00973972026258707,
0.009552816860377789,
-0.017534509301185608,
0.028401685878634453,
-0.0008282710332423449,
-0.00986513216048479,
-0.044811446219682693,
-0.013057625852525234,
0.0180470310151577,
-0.007494661025702953,
-0.01114248763769865,
0.021268410608172417,
-0.013662719167768955,
-0.012545895762741566,
-0.02969694696366787,
-0.025161175057291985,
0.004818926565349102,
-0.0028166938573122025,
0.049149587750434875,
0.07476438581943512,
-0.02294878661632538,
-0.0005116810789331794,
0.0417044535279274,
-0.04648648202419281,
0.050406090915203094,
-0.0016759173013269901,
-0.009148010052740574,
-0.04008195921778679,
-0.00852185022085905,
-0.020594419911503792,
0.041549962013959885,
-0.04915384203195572,
0.027494799345731735,
0.024899527430534363,
0.044328898191452026,
0.004571948200464249,
-0.010032701306045055,
-0.010304385796189308,
0.009286055341362953,
-0.03925266116857529,
0.024290315806865692,
-0.008205423131585121,
0.023105667904019356,
-0.006835469510406256,
0.03264674171805382,
0.01695171743631363,
0.029074368998408318,
-0.03930613771080971,
-0.011600429192185402,
0.013078606687486172,
0.01709900051355362,
-0.015223423950374126,
0.005140515509992838,
0.006252748891711235,
-0.017632242292165756,
-0.03539831191301346,
0.020032016560435295,
-0.0391579233109951,
0.009764885529875755,
0.026780109852552414,
-0.025222206488251686,
-0.0031006312929093838,
0.004124229308217764,
0.010658742859959602,
-0.00244208169169724,
-0.008333936333656311,
-0.07883618026971817,
-0.03965917229652405,
0.038704052567481995,
0.0005793366581201553,
0.004418043419718742,
0.02501598745584488,
-0.025915104895830154,
0.015870526432991028,
0.021141769364476204,
0.014068547636270523,
-0.013578549027442932,
0.0032058977521955967,
0.035422101616859436,
-0.020353950560092926,
0.00020974715880583972,
0.004795403685420752,
-0.029078423976898193,
0.04056836664676666,
-0.013912846334278584,
-0.010301601141691208,
-0.025504235178232193,
-0.004625012632459402,
0.01095108687877655,
0.021921396255493164,
-0.02925894223153591,
-0.013319193385541439,
0.06984593719244003,
-0.00647527864202857,
-0.016810758039355278,
-0.025182275101542473,
-0.023329680785536766,
0.0207070205360651,
-0.0018297577043995261,
-0.014644167385995388,
-0.02549353800714016,
-0.010564044117927551,
0.047487352043390274,
-0.015847882255911827,
0.027888843789696693,
-0.009179332293570042,
0.03706325590610504,
0.01040447037667036,
-0.012030905112624168,
0.02202814258635044,
0.026085451245307922,
-0.014105968177318573,
0.06087029352784157,
-0.02137746848165989,
0.03997362405061722,
0.04820847883820534,
0.018097279593348503,
-0.08898763358592987,
-0.02419121190905571,
0.005094268824905157,
0.007359104230999947,
0.021168000996112823,
-0.03147357702255249,
-0.017789602279663086,
0.03340400755405426,
-0.07759685069322586,
0.012765331193804741,
-0.020538736134767532,
-0.03330638259649277,
-0.024182481691241264,
-0.024764226749539375,
-0.023654282093048096,
0.03112832084298134,
0.0138855567201972,
0.03665880486369133,
0.01326234731823206,
0.0062483809888362885,
-0.004351139534264803,
-0.022244893014431,
-0.04990750923752785,
0.0475994274020195,
0.015120521187782288,
0.007659377530217171,
0.05387477949261665,
-0.003924517426639795,
-0.0016628087032586336,
0.013372846879065037,
-0.007353583816438913,
-0.04996837303042412,
-0.0010299587156623602,
0.017501574009656906,
-0.0009417784167453647,
0.0018203635700047016,
-0.05031213536858559,
-0.015372552908957005,
0.01697748526930809,
-0.0012483163736760616,
0.035937968641519547,
0.006958186626434326,
0.0046462113969028,
-0.026247631758451462,
0.028951063752174377,
-0.015319223515689373,
0.036727678030729294,
0.027683742344379425,
-0.03383408859372139,
0.0014266212237998843,
-0.02915782481431961,
0.06297020614147186,
0.03778356686234474,
-0.018284223973751068,
-0.040307026356458664,
-0.05482165142893791,
-0.010134723037481308,
0.03186437860131264,
0.0016205566935241222,
0.014195891097187996,
0.012080389074981213,
-0.010953147895634174,
0.0031204393599182367,
0.007469316013157368,
0.02324015647172928,
-0.014446517452597618,
-0.04719607159495354,
-0.014664921909570694,
0.006414840463548899,
0.0010375528363510966,
0.018207455053925514,
-0.033545996993780136,
-0.03125710040330887,
0.017444992437958717,
0.024506909772753716,
0.058744028210639954,
-0.0019373819231987,
-0.08950778841972351,
-0.0261672493070364,
-0.034709714353084564,
0.03060987964272499,
-0.03276948630809784,
-0.07102720439434052,
-0.006683667190372944,
-0.07071081548929214,
-0.01839553564786911,
0.05728026479482651,
0.089214026927948,
-0.013599681667983532,
-0.031025409698486328,
-0.01083326805382967,
-0.023780807852745056,
0.022374825552105904,
-0.03601979464292526,
0.03460598737001419,
0.01894593983888626,
-0.012229591608047485,
0.03850502148270607,
0.023110076785087585,
-0.02304856851696968,
0.001292425673455,
0.00856170803308487,
-0.029340676963329315,
-0.0073217665776610374,
-0.015550663694739342,
-0.039226796478033066,
0.02094428241252899,
0.0016448339447379112,
0.020641092211008072,
0.1118684932589531,
0.01383040938526392,
0.006496347486972809,
-0.01809435524046421,
0.011833969503641129,
-0.04008565843105316,
0.005200640298426151,
-0.0253364946693182,
0.03252921998500824,
-0.01202374417334795,
0.013418486341834068,
0.017528528347611427,
-0.028160205110907555,
0.027990756556391716,
-0.0088631771504879,
-0.02771773561835289,
-0.025661258026957512,
0.06122097745537758,
0.02858252264559269,
0.03096885047852993,
0.020078061148524284,
0.005359217990189791,
0.005155017599463463,
0.05236797407269478,
-0.011981097050011158,
0.06009187176823616,
0.028454532846808434,
0.028839778155088425,
-0.02272210828959942,
0.05986632779240608,
-0.021522633731365204,
-0.0012008940102532506,
-0.02135845459997654,
0.010366257280111313,
-0.0053754462860524654,
0.0076710619032382965,
-0.0023569781333208084,
-0.016071867197752,
0.02938852459192276,
0.03192603215575218,
-0.021108627319335938,
0.0627640038728714,
-0.04541662335395813,
-0.0002618062135297805,
-0.012184490449726582,
0.05241180211305618,
0.005676930770277977,
0.006578535307198763,
0.017726438120007515,
0.011154763400554657,
-0.013685327023267746,
-0.01855170913040638,
-0.024477742612361908,
0.0017100459663197398,
0.049268513917922974,
-0.005638973321765661,
0.008051995187997818,
0.0010601743124425411,
0.0021560965105891228,
-0.0289008691906929,
-0.021760279312729836,
-0.018824057653546333,
-0.0346057265996933,
-0.008461421355605125,
0.01180906780064106,
0.057253286242485046,
0.006601227913051844,
0.010081339627504349,
-0.03035742975771427,
0.04600239917635918,
-0.04422304779291153,
-0.019703634083271027,
-0.011243662796914577,
0.026345275342464447,
-0.0007339963922277093,
0.03379204124212265
] |
<p>Earlier today, I saw <a href="http://www.orlandosentinel.com/business/nationworld/sns-bc-eu--breakinglightspeed,0,5266439.story">this link</a> on Facebook about neutrinos going faster than the speed of light, and of course, re-posted. Since then, a couple of my friends have gotten into a discussion about what this means (mostly about time-travel), but I don't really know what this really implies. This made me wonder...</p>
<p>What are the biggest and most immediate implications of this potential discovery?</p>
<p><strong>Related:</strong> <a href="http://physics.stackexchange.com/q/14968/3454">Superluminal neutrinos</a></p> | 83 | [
0.0014742352068424225,
-0.06717430800199509,
-0.007619943469762802,
-0.06707265228033066,
0.06781674176454544,
0.01921534352004528,
0.0086390171200037,
-0.0219124723225832,
0.010687809437513351,
-0.04393758624792099,
0.03167853131890297,
0.05941933020949364,
0.017547287046909332,
0.0005034230998717248,
0.0032336812000721693,
0.021755574271082878,
-0.011898635886609554,
0.0009454339160583913,
-0.014144878834486008,
-0.05194908380508423,
0.02134673297405243,
0.012576916255056858,
-0.03735803812742233,
0.02868853695690632,
-0.03364819660782814,
0.03014553338289261,
0.017566151916980743,
0.03432901203632355,
0.007085310760885477,
0.020650610327720642,
0.03722364827990532,
-0.022717310115695,
0.0068022459745407104,
0.018275665119290352,
-0.0193262230604887,
0.007191346026957035,
-0.03188702091574669,
-0.035930898040533066,
0.001809717039577663,
0.02245880663394928,
-0.028024611994624138,
-0.026266682893037796,
0.013222213834524155,
0.036202069371938705,
-0.055651918053627014,
0.018897738307714462,
0.0015402698190882802,
-0.02398640662431717,
0.04323603957891464,
-0.04746819660067558,
0.06325001269578934,
0.012880676425993443,
0.020132219418883324,
-0.0023343118373304605,
-0.014462145045399666,
-0.005636273883283138,
0.08816753327846527,
0.07373590767383575,
-0.008936227299273014,
-0.07400672137737274,
0.010598315857350826,
-0.004587947856634855,
0.012409180402755737,
-0.011871874332427979,
-0.03853994235396385,
0.08332986384630203,
-0.06054822355508804,
-0.0097971111536026,
-0.0037969278637319803,
-0.013586794957518578,
0.017203008756041527,
0.013287536799907684,
0.028628142550587654,
0.016624532639980316,
0.010759305208921432,
-0.05954990163445473,
-0.013272288255393505,
-0.0071683176793158054,
0.009445125237107277,
0.07911030203104019,
-0.03794117271900177,
0.008532132022082806,
0.025279425084590912,
0.03194553405046463,
0.005934425164014101,
-0.011826937086880207,
0.05616171658039093,
-0.03151613473892212,
0.008848127909004688,
0.015555582009255886,
-0.005215733777731657,
0.009705272503197193,
0.017997313290834427,
-0.003867726307362318,
-0.019775686785578728,
0.016853757202625275,
0.012539662420749664,
0.016854997724294662,
-0.003567650681361556,
-0.028159024193882942,
0.023528704419732094,
0.013681572861969471,
0.01815860904753208,
0.037000782787799835,
-0.022921770811080933,
-0.045493144541978836,
-0.0396776907145977,
0.01049752812832594,
-0.039296671748161316,
0.00416693976148963,
-0.047795988619327545,
-0.019160915166139603,
-0.00469915522262454,
0.035325098782777786,
0.027331646531820297,
-0.05613890662789345,
-0.02442658692598343,
-0.024121344089508057,
0.08844806998968124,
0.049816396087408066,
0.01935480162501335,
-0.005959848873317242,
0.023563483729958534,
0.010980495251715183,
-0.05283108353614807,
0.0477786622941494,
0.0038162830751389265,
-0.0005400961963459849,
0.012504861690104008,
0.010858001187443733,
-0.015591013245284557,
-0.0033727698028087616,
0.007231398019939661,
-0.03775737062096596,
0.03599240630865097,
-0.014317570254206657,
-0.10007070004940033,
-0.07033030688762665,
0.09063554555177689,
0.03794647753238678,
-0.05070954188704491,
-0.10223516821861267,
0.0024874310474842787,
-0.016517171636223793,
0.1008867621421814,
0.024970320984721184,
0.0015611762646585703,
-0.0045233420096337795,
0.04626423493027687,
0.016452008858323097,
-0.024853304028511047,
-0.00805277656763792,
0.017092034220695496,
-0.010619763284921646,
0.01605154760181904,
-0.08568975329399109,
-0.0072533925995230675,
0.03579207882285118,
-0.021256661042571068,
-0.035408951342105865,
0.09257344901561737,
-0.005141345784068108,
0.02859956957399845,
-0.010436338372528553,
-0.017751196399331093,
-0.0069251516833901405,
0.09970688819885254,
0.028276408091187477,
-0.04132358357310295,
0.07399146258831024,
0.00887496117502451,
0.05190302059054375,
-0.009479278698563576,
0.016179433092474937,
0.01611652784049511,
-0.027230266481637955,
-0.016630731523036957,
-0.0054275779984891415,
-0.008193545043468475,
-0.017484942451119423,
-0.023856624960899353,
-0.03035297803580761,
-0.028814440593123436,
0.0015173305291682482,
0.05219334363937378,
0.07396865636110306,
-0.041386038064956665,
-0.020052965730428696,
0.02533719874918461,
-0.06535975635051727,
-0.015795070677995682,
-0.07650233060121536,
0.0066003757528960705,
-0.0021901256404817104,
-0.015609599649906158,
0.038321807980537415,
-0.013001920655369759,
0.03172061964869499,
-0.04782009497284889,
-0.02990693226456642,
-0.018547601997852325,
0.04268575459718704,
0.031644705682992935,
0.018711624667048454,
0.01938711851835251,
0.04970419406890869,
0.0014254717389121652,
-0.03869658336043358,
-0.006300964392721653,
0.013733381405472755,
-0.04603596776723862,
0.018976062536239624,
-0.004257948603481054,
0.03050028532743454,
-0.01530434563755989,
0.007813990116119385,
0.015754440799355507,
-0.006052561569958925,
-0.020752137526869774,
0.021817049011588097,
-0.001731658587232232,
0.056931622326374054,
-0.006983949802815914,
0.007699758745729923,
0.01360450778156519,
0.015463140793144703,
0.03718222677707672,
0.0025100368075072765,
0.011149365454912186,
-0.01702403835952282,
-0.06846888363361359,
-0.025304259732365608,
0.027121642604470253,
0.0251357089728117,
-0.028062906116247177,
0.007339754607528448,
-0.0010292727965861559,
0.03546799719333649,
0.03532131016254425,
0.030400294810533524,
-0.04052550718188286,
-0.050401441752910614,
-0.01715150661766529,
0.017306724563241005,
-0.0007765382761135697,
-0.0015746174613013864,
0.017044398933649063,
0.013788264244794846,
0.019877314567565918,
-0.029058536514639854,
-0.01248392928391695,
0.029629075899720192,
-0.014351559802889824,
-0.018249988555908203,
0.014494756236672401,
-0.025182954967021942,
0.03677286580204964,
-0.012232199311256409,
0.012851397506892681,
0.026436083018779755,
0.01209479570388794,
0.021330401301383972,
-0.02151731587946415,
0.016136961057782173,
0.005267833359539509,
0.003183104330673814,
-0.0071976943872869015,
-0.009169358760118484,
0.013539264909923077,
-0.041622765362262726,
0.034051451832056046,
-0.03192322328686714,
-0.03812165930867195,
-0.02299410291016102,
-0.01260366104543209,
-0.012456062249839306,
0.021798938512802124,
0.04060514643788338,
-0.01816224679350853,
-0.06664281338453293,
0.011175155639648438,
-0.04038170725107193,
-0.007861065678298473,
0.05302184075117111,
-0.025141317397356033,
0.058467842638492584,
-0.025665072724223137,
-0.04363235458731651,
0.030632469803094864,
-0.006953579373657703,
0.03009888529777527,
0.00927075743675232,
-0.0394100584089756,
-0.05607784911990166,
-0.026485227048397064,
-0.01757945865392685,
0.020193519070744514,
-0.0323011688888073,
0.0013361710589379072,
0.046715255826711655,
-0.022672321647405624,
-0.039698053151369095,
-0.019800586625933647,
-0.03138815239071846,
-0.038807567209005356,
-0.03505632281303406,
0.020472262054681778,
-0.008044825866818428,
-0.046511292457580566,
0.03428677096962929,
-0.018969321623444557,
-0.04893561825156212,
0.014969754964113235,
-0.03140738978981972,
-0.0760878473520279,
0.04350870102643967,
0.011275514028966427,
0.03210381045937538,
-0.019263774156570435,
-0.020394500344991684,
0.05634633079171181,
0.016935864463448524,
0.010002443566918373,
-0.026210857555270195,
-0.009167477488517761,
0.006713435985147953,
-0.0409151092171669,
0.001192972413264215,
0.043789029121398926,
0.003973336890339851,
0.022039644420146942,
0.0024312357418239117,
0.05164052173495293,
0.03963635116815567,
0.004345796536654234,
-0.014645013958215714,
-0.021476320922374725,
0.004492057953029871,
0.03294662758708,
0.009550199843943119,
-0.0012235483154654503,
-0.012195130810141563,
0.024258019402623177,
-0.00983238872140646,
0.03293979540467262,
0.04942747950553894,
-0.01999822072684765,
0.0591350719332695,
0.04407269507646561,
-0.000978120369836688,
-0.008324776776134968,
0.011315413750708103,
-0.008805173449218273,
-0.0019526469986885786,
-0.01629534177482128,
-0.01103809755295515,
0.0632728636264801,
-0.024560818448662758,
-0.006127595901489258,
0.012587256729602814,
0.0342053659260273,
-0.021453194320201874,
-0.047659602016210556,
-0.030672887340188026,
-0.0004326697380747646,
0.00787047203630209,
-0.011004051193594933,
0.00017533903883304447,
0.04259631410241127,
0.021846983581781387,
-0.012921200133860111,
-0.012909629382193089,
-0.008897566236555576,
-0.026946544647216797,
-0.05431767553091049,
0.008258072659373283,
-0.005994027946144342,
0.03098684921860695,
0.01822890155017376,
0.03460973873734474,
-0.0009676113841123879,
-0.0162203386425972,
0.0170434582978487,
-0.012068165466189384,
-0.07594616711139679,
0.018570363521575928,
-0.056727733463048935,
-0.0024281980004161596,
-0.010296556167304516,
-0.011210856959223747,
-0.00531094940379262,
-0.0037610051222145557,
-0.02373613975942135,
-0.024002062156796455,
-0.003524620784446597,
-0.061656855046749115,
0.013776689767837524,
-0.04834812879562378,
-0.04076387360692024,
0.0013209792086854577,
0.011269787326455116,
0.02197706699371338,
-0.00853512343019247,
-0.012449268251657486,
0.018431030213832855,
-0.08654461055994034,
-0.009123154915869236,
-0.005487862508744001,
0.020202023908495903,
0.023704776540398598,
0.01768627017736435,
0.04808592423796654,
-0.017248475924134254,
-0.03576287627220154,
0.035445768386125565,
0.030038515105843544,
0.011761846020817757,
0.022366536781191826,
-0.004890337120741606,
-0.05091390758752823,
-0.037629369646310806,
0.0033096291590481997,
0.018579401075839996,
0.060807183384895325,
0.024551376700401306,
0.02291487529873848,
0.05768601968884468,
0.007979024201631546,
-0.006529239006340504,
0.035437289625406265,
0.045761529356241226,
-0.004351542331278324,
0.0002930058108177036,
-0.04192239046096802,
-0.024715177714824677,
-0.0017407736741006374,
0.01156837772578001,
0.01736287586390972,
-0.013397579081356525,
-0.023413315415382385,
-0.0032169464975595474,
-0.00362603971734643,
-0.0000268558542302344,
-0.06208861619234085,
0.0030146597418934107,
-0.013677294366061687,
-0.016420729458332062,
0.016257958486676216,
0.0027684480883181095,
-0.043244313448667526,
0.03514876961708069,
0.04592610523104668,
0.004035152494907379,
-0.00025568914134055376,
-0.0813426524400711,
0.0028762114234268665,
0.05016089975833893,
0.06999033689498901,
-0.01432844065129757,
-0.020307812839746475,
-0.05615725368261337,
0.015245976857841015,
0.037487659603357315,
-0.02356366068124771,
0.03652723878622055,
0.02045392245054245,
-0.017340635880827904,
-0.05330710485577583,
-0.029153620824217796,
0.012339277192950249,
0.06459460407495499,
0.0068999994546175,
0.0299327801913023,
-0.009431233629584312,
0.007782532833516598,
-0.009198990650475025,
0.0019050404662266374,
0.025838488712906837,
0.06011207029223442,
0.009914549067616463,
-0.011180117726325989,
0.0021746151614934206,
0.01431557722389698,
0.013956360518932343,
-0.07517234236001968,
0.022797919809818268,
0.03877890482544899,
-0.04040021076798439,
0.0412122942507267,
-0.040137726813554764,
-0.07112596184015274,
0.03842466324567795,
0.01427160482853651,
-0.015451012179255486,
-0.01427167747169733,
-0.054816313087940216,
0.031474992632865906,
0.04850921407341957,
-0.007523160427808762,
-0.0004166602739132941,
0.01906893588602543,
-0.041702114045619965,
0.010437068529427052,
0.020492061972618103,
0.03260952606797218,
-0.013577152974903584,
0.035595186054706573,
0.042783722281455994,
-0.008232506923377514,
-0.04311875253915787,
0.07358159869909286,
-0.0038731107488274574,
0.008685956709086895,
0.01654018834233284,
-0.03513763099908829,
-0.044011276215314865,
0.04687350615859032,
0.02862514927983284,
-0.02183537185192108,
-0.02456716075539589,
-0.0019042460480704904,
0.01995946280658245,
-0.014595013111829758,
0.03709369897842407,
0.007884095422923565,
0.04566238075494766,
0.024058140814304352,
0.033090148121118546,
0.0009585182415321469,
-0.011503716930747032,
-0.025363432243466377,
0.039121098816394806,
-0.04819895699620247,
0.030293578281998634,
0.007531126495450735,
-0.015546157956123352,
0.036311060190200806,
-0.03669808432459831,
-0.027958817780017853,
0.023501388728618622,
-0.04899623990058899,
0.005629835184663534,
-0.05517378821969032,
0.023161418735980988,
0.025937173515558243,
0.024959785863757133,
-0.04277353733778,
-0.05027979984879494,
0.04379812628030777,
-0.014366291463375092,
-0.016559777781367302,
-0.012436145916581154,
-0.012547346763312817,
-0.047500621527433395,
-0.015948299318552017,
-0.008748450316488743,
0.06625127047300339,
-0.0496768057346344,
-0.036692023277282715,
0.011187651194632053,
0.001975839491933584,
0.0644165650010109,
-0.003903639502823353,
-0.01337332371622324,
0.03148447722196579,
0.011814850382506847,
0.00943346880376339,
-0.017018727958202362,
0.05432342737913132,
-0.012964659370481968,
-0.03587033227086067,
-0.03296888992190361,
-0.0035785178188234568,
0.030080072581768036,
-0.03110397420823574,
0.016483690589666367,
0.03129545971751213,
0.012670459225773811,
0.00546921556815505,
-0.0113010723143816,
0.032634954899549484,
0.02462398074567318,
0.03295533359050751,
0.03166317567229271,
0.00712243327870965,
0.014819535426795483,
-0.03331800177693367,
0.06021185591816902,
0.01544636208564043,
0.020170871168375015,
-0.028215501457452774,
0.005460239946842194,
-0.02669043280184269,
-0.006496116518974304,
0.00868280604481697,
-0.039789993315935135,
0.02899838238954544,
0.022121742367744446,
0.025471294298768044,
-0.0032534506171941757,
-0.013531139120459557,
-0.038862839341163635,
-0.03437866270542145,
-0.04663412272930145,
-0.026785705238580704,
0.05937528982758522,
-0.033991195261478424,
0.007754429709166288,
-0.0076872785575687885,
-0.021763090044260025,
0.00038278414285741746,
-0.040931105613708496,
0.01607537269592285,
0.03410272300243378,
0.013275514356791973,
-0.011225583963096142,
-0.032716404646635056,
-0.031327251344919205,
0.03763585165143013,
0.04283508285880089,
0.01576918736100197,
0.011111332103610039,
0.04092797636985779,
0.026700111106038094,
0.019595986232161522,
0.0004566903808154166,
-0.03959378972649574,
0.05738753080368042,
-0.049270227551460266,
-0.0049459077417850494,
0.014047258533537388,
0.01952751912176609,
0.05353337526321411,
-0.03331669792532921,
0.023362312465906143,
-0.015936249867081642,
-0.006305032409727573,
-0.029764387756586075,
-0.04045005142688751,
0.006026926450431347,
0.006904079578816891,
-0.003061696421355009,
-0.02904319390654564,
0.020944830030202866,
0.051901597529649734,
0.02415403351187706,
-0.013009951449930668,
-0.08551626652479172,
-0.045294806361198425,
-0.03162408992648125,
-0.026575906202197075,
0.018317386507987976,
0.004320253152400255,
-0.04257519543170929,
0.01603948511183262,
-0.04002887010574341,
-0.005270648747682571,
0.009788772091269493,
0.03947452828288078,
-0.0297230314463377,
0.06789784878492355,
-0.0028418954461812973,
0.018869850784540176,
0.021638108417391777,
-0.007164482958614826,
0.07321197539567947,
0.036625683307647705,
0.02304472029209137,
-0.05090119317173958,
0.03616677597165108,
-0.007365269120782614,
0.02573232352733612,
-0.017059890553355217,
-0.02108558639883995,
-0.02349238097667694,
0.0027328557334840298,
0.037703271955251694,
0.05580439791083336,
0.040644172579050064,
0.018178122118115425,
0.007235649973154068,
-0.026291141286492348,
-0.01701812446117401,
0.031282689422369,
0.04172232374548912,
-0.005863125901669264,
-0.003595886053517461,
-0.05121918395161629,
0.033277321606874466,
-0.03605864197015762,
-0.02178013324737549,
0.00038471436710096896,
0.0014019248774275184,
0.03668146952986717,
0.0044783721677958965,
-0.045652709901332855,
-0.0212702676653862,
0.014823881909251213,
-0.027209367603063583,
-0.03678829222917557,
0.024976074695587158,
-0.006519517861306667,
0.011954724788665771,
0.02632567286491394,
0.03833968564867973,
0.040802016854286194,
-0.020896341651678085,
-0.006902710068970919,
0.03565346822142601,
-0.07508542388677597,
-0.013604496605694294,
-0.0014795975293964148,
0.03837086260318756,
-0.015555514954030514,
-0.00208849273622036,
0.003293098183348775,
0.026031872257590294,
0.03645716980099678,
-0.036988310515880585,
-0.006790828891098499,
0.0004815920547116548,
-0.020837385207414627,
0.007031574845314026,
0.03238402679562569,
-0.01655219867825508,
-0.00028160930378362536,
-0.008604107424616814,
0.03972308710217476,
0.003376687178388238,
0.013116893358528614,
0.006418692879378796,
-0.021623993292450905,
-0.02149748057126999,
-0.00445543834939599,
-0.0321747325360775,
-0.016884226351976395,
0.03678569570183754,
-0.060746900737285614,
0.008395269513130188,
0.03704642131924629,
0.0033881054259836674,
-0.02160755917429924,
0.014677213504910469,
0.0013636978110298514,
-0.0537593811750412,
-0.02135417051613331,
0.056784890592098236,
-0.024451887235045433,
-0.030150800943374634,
-0.010689766146242619,
-0.004000859335064888,
0.024085549637675285,
0.02960347570478916,
-0.01255485974252224,
0.042768917977809906,
-0.04406169801950455,
0.030096953734755516,
0.018180441111326218,
-0.0207982175052166,
0.004926069639623165,
-0.011174093931913376,
-0.006079012528061867,
0.00418591033667326,
-0.04175512492656708,
0.03516045957803726,
0.018789321184158325,
-0.011239904910326004,
0.03994152694940567,
0.016120100393891335,
-0.009719941765069962,
-0.01860559545457363,
0.033288005739450455,
-0.029617570340633392,
-0.002710438799113035,
-0.022608261555433273,
0.04313141852617264,
0.025572890415787697,
-0.0272968877106905,
-0.03151506185531616,
0.0106015894562006,
0.0028418556321412325,
-0.0009929693769663572,
-0.020456509664654732,
0.02019871398806572,
-0.024310404434800148,
0.025381144136190414,
-0.011289306916296482,
-0.002097764518111944,
-0.0034664389677345753,
0.016718316823244095,
-0.012788436375558376,
-0.03795893117785454,
0.0120093310251832,
0.04346949979662895,
-0.009011494927108288,
-0.00011670123058138415,
0.011948410421609879,
0.021634168922901154,
-0.03223489597439766,
-0.01944727450609207,
0.02221769280731678,
-0.001154510653577745,
0.03856617957353592,
-0.02485699951648712,
-0.017711324617266655,
0.021445050835609436,
-0.011909154243767262,
-0.05430615320801735,
0.07299275696277618,
-0.042481716722249985,
0.013683822937309742,
0.02847384661436081,
-0.008404521271586418,
0.0038812728598713875,
0.06681942939758301,
-0.02916133403778076,
-0.02244577370584011,
0.015498257242143154,
-0.02130669355392456,
-0.02409801259636879,
0.004704565275460482,
0.02905733697116375,
-0.012054170481860638,
-0.013467350043356419,
0.02118351310491562,
0.040386125445365906,
-0.04062383621931076,
0.018072593957185745,
-0.034359581768512726,
-0.0405658483505249,
-0.003434924641624093,
-0.014160973019897938,
0.004883323330432177,
0.0339990071952343,
0.05558343231678009,
-0.04239147529006004,
0.03416813164949417,
0.020887961611151695,
0.02038547396659851,
-0.08219820261001587,
0.00837357435375452,
0.0004520424990914762,
-0.015525694005191326,
0.027571765705943108,
-0.05401880294084549,
0.06603553146123886,
0.027889076620340347,
-0.0438515730202198,
0.02266133762896061,
-0.048266105353832245,
-0.03614448755979538,
-0.03798084706068039,
-0.005927895661443472,
0.008685349486768246,
0.08759982138872147,
0.049923550337553024,
0.03002125397324562,
-0.0020665021147578955,
0.02950945869088173,
-0.02205992490053177,
-0.06360653042793274,
0.018021278083324432,
0.03607338294386864,
0.006451757159084082,
-0.01398920826613903,
0.06345377117395401,
0.0032397147733718157,
-0.0007733521633781493,
0.03158756345510483,
0.026928210631012917,
-0.0022213684860616922,
0.024393152445554733,
0.001413927529938519,
0.03782343491911888,
0.010223626159131527,
-0.004034367389976978,
0.006319237407296896,
-0.017346523702144623,
0.026921847835183144,
0.008211418054997921,
0.058290768414735794,
0.002166423946619034,
0.0004459166375454515,
-0.04497649520635605,
-0.019877441227436066,
-0.0046387603506445885,
-0.0034694033674895763,
-0.00830910261720419,
-0.014738883823156357,
0.02775932289659977,
0.006915911100804806,
0.018660863861441612,
-0.03148952126502991,
0.024761194363236427,
-0.03782181069254875,
-0.02774398773908615,
0.009239032864570618,
0.03523407503962517,
-0.004081430844962597,
0.013196682557463646,
-0.026214076206088066,
-0.0269326064735651,
-0.011194601655006409,
-0.012893515639007092,
0.0067380256950855255,
-0.06677240133285522,
-0.02163851633667946,
0.007173923775553703,
0.003359856316819787,
0.003950207959860563,
-0.019016874954104424,
-0.025411345064640045,
0.040358759462833405,
0.018129412084817886,
0.025065194815397263,
0.012085506692528725,
-0.02649403177201748,
-0.009024210274219513,
-0.06855249404907227,
0.007599990349262953,
-0.01433388888835907,
0.04572252929210663,
-0.0584133006632328,
-0.014216474257409573,
-0.015671856701374054,
0.0068619390949606895,
0.07339076697826385,
-0.02503582462668419,
-0.005664702970534563,
0.0472881942987442,
0.0031474223360419273,
-0.029079029336571693,
-0.048894766718149185,
-0.027970120310783386,
0.009027035906910896,
-0.03116902895271778,
-0.02378818951547146,
-0.003557844553142786,
-0.027311032637953758,
0.027127323672175407,
0.04228027164936066,
0.015091358684003353,
0.006535365246236324,
0.0055760876275599,
0.006943354848772287,
0.03843815624713898,
0.011654519475996494,
0.0020584948360919952,
0.04634104296565056,
-0.008103780448436737,
0.017373938113451004,
0.025333277881145477,
-0.006984566804021597,
-0.02705351822078228,
0.030579643324017525,
0.003309187013655901,
0.015820425003767014,
-0.007613492198288441,
-0.0226574819535017,
0.0011433814652264118,
-0.04724017530679703,
-0.014490054920315742,
0.03592861443758011,
-0.039374466985464096,
0.007521693129092455,
0.0627904087305069,
0.0012473065871745348,
0.0032574147917330265,
-0.01717555895447731,
0.004731117282062769,
0.002864571986719966,
-0.01743307337164879,
-0.02996932528913021,
0.02186896838247776,
0.011784003116190434,
0.009775486774742603,
0.03443560004234314,
0.0033481442369520664,
0.02196040190756321,
0.02727791853249073,
-0.010694700293242931,
0.038958292454481125,
-0.04511125385761261,
-0.01485986728221178,
-0.001980855828151107,
-0.0097699835896492,
0.04507019743323326,
0.027631709352135658,
-0.006055694539099932,
0.06435087323188782,
-0.0031726802699267864,
0.03252406790852547,
-0.006256962660700083,
-0.026767706498503685,
0.011732148937880993,
0.01635114662349224,
-0.027116987854242325,
0.02823346108198166,
-0.013420379720628262,
0.012748999521136284,
0.011346125043928623,
0.0008777622133493423,
0.026104236021637917,
-0.06605713069438934,
0.027155369520187378,
-0.010856306180357933,
-0.013661261647939682,
-0.01970847323536873,
-0.047852836549282074,
0.005831459537148476,
0.015195350162684917,
-0.031244926154613495,
0.015112393535673618,
-0.00008756465103942901,
0.0016580501105636358,
-0.03915611281991005,
0.010571534745395184,
0.041143808513879776,
-0.01909526251256466,
0.01871379464864731,
-0.038004886358976364,
0.016562750563025475,
-0.03678863123059273,
-0.027666736394166946
] |
<p>A teacher of mine told me once that there were no ninth gluon because such a one should be white and interact infinitely far, and no one has been observed. Is there also a theoretical reason?</p> | 4,620 | [
-0.031107017770409584,
-0.018350062891840935,
-0.0032491388265043497,
-0.046285346150398254,
0.041682709008455276,
0.027316618710756302,
-0.03566357493400574,
-0.006709346082061529,
-0.013645648956298828,
-0.038881950080394745,
0.012895416468381882,
0.013918149285018444,
0.03645579144358635,
0.01127762533724308,
-0.0020392516162246466,
0.01774361915886402,
-0.02575337141752243,
0.01675119809806347,
0.012602078728377819,
0.004728373140096664,
0.01924208737909794,
0.036991022527217865,
-0.03083481825888157,
-0.008965341374278069,
-0.001074798870831728,
-0.021180925890803337,
0.013471441343426704,
0.03890592232346535,
0.043181732296943665,
0.06147624924778938,
0.019053172320127487,
-0.013252590782940388,
-0.00294909393414855,
0.04601670801639557,
0.0075162192806601524,
0.006726713385432959,
-0.008381828665733337,
-0.034790024161338806,
-0.022348443046212196,
0.02386503480374813,
-0.03298908472061157,
-0.0744895488023758,
-0.0009024546598084271,
0.038403768092393875,
-0.023060180246829987,
0.023451752960681915,
-0.0014235284179449081,
-0.04070264846086502,
0.09609053283929825,
-0.06673652678728104,
0.025162355974316597,
0.007465575356036425,
0.03328413516283035,
-0.009492003358900547,
0.021313879638910294,
-0.005776789039373398,
0.04406352341175079,
0.04652896150946617,
-0.04277994483709335,
-0.022812070325016975,
-0.02789895236492157,
0.0021497684065252542,
0.027585122734308243,
0.016132326796650887,
-0.006314022932201624,
0.01836814358830452,
-0.007346486672759056,
-0.008985118009150028,
0.0064043267630040646,
-0.01941395364701748,
-0.012538092210888863,
0.023816367611289024,
0.033433545380830765,
0.0021137737203389406,
0.01677376590669155,
-0.0010783430188894272,
-0.005686069373041391,
0.0044392179697752,
0.04425739124417305,
0.022436369210481644,
-0.05148401856422424,
-0.016330184414982796,
0.014625951647758484,
-0.007767908275127411,
0.004227250814437866,
-0.01779780350625515,
0.0357418917119503,
-0.02890443243086338,
-0.009209239855408669,
0.06433670967817307,
-0.020301155745983124,
0.002039260696619749,
0.06601442396640778,
-0.004409041255712509,
-0.022437937557697296,
0.024369357153773308,
0.01489278208464384,
0.027076760306954384,
0.005107318516820669,
-0.018938690423965454,
0.037977032363414764,
-0.01625543087720871,
0.013870660215616226,
0.10386689752340317,
-0.006586250849068165,
-0.008863884024322033,
-0.06068718805909157,
0.028453759849071503,
-0.02513827010989189,
-0.004810923244804144,
-0.014984519220888615,
-0.006799464114010334,
0.018795838579535484,
-0.008148199878633022,
-0.012630388140678406,
-0.02706017531454563,
0.027956577017903328,
0.024775030091404915,
0.06373776495456696,
0.08893369883298874,
0.06286628544330597,
-0.000464003998786211,
-0.006100219674408436,
0.009525574743747711,
-0.042221345007419586,
-0.014669050462543964,
0.0486961230635643,
0.007446859031915665,
-0.011599023826420307,
0.011592782102525234,
0.028869174420833588,
0.020863087847828865,
0.0237564854323864,
-0.028533780947327614,
0.029250677675008774,
-0.04025736451148987,
-0.08308912813663483,
-0.08002209663391113,
0.06637243926525116,
-0.01918015256524086,
-0.043561745434999466,
-0.08143619447946548,
-0.014116532169282436,
0.04220706224441528,
0.11782756447792053,
-0.0005914792418479919,
-0.034413643181324005,
-0.03510444983839989,
0.02998935803771019,
0.004619562067091465,
-0.005069086328148842,
0.005190730094909668,
-0.006073297932744026,
-0.05330231040716171,
-0.0009193563018925488,
-0.10637801140546799,
0.007658496033400297,
0.018003566190600395,
0.017058994621038437,
-0.03196015581488609,
0.05058756470680237,
-0.021992893889546394,
0.024847209453582764,
0.03503860533237457,
-0.0013197455555200577,
-0.044674210250377655,
0.07615967094898224,
0.0027623195201158524,
0.00781786534935236,
0.050673212856054306,
-0.014974069781601429,
0.06796932965517044,
0.03312639147043228,
0.050139714032411575,
-0.009711727499961853,
-0.034460462629795074,
-0.037797749042510986,
-0.03784572333097458,
0.024303728714585304,
-0.028012551367282867,
-0.021130774170160294,
-0.0038133468478918076,
-0.011609033681452274,
0.026072397828102112,
-0.03404201939702034,
0.017474783584475517,
-0.05968239903450012,
-0.015657316893339157,
0.04309428483247757,
-0.03579386696219444,
-0.00618555024266243,
-0.036430470645427704,
0.004342225380241871,
0.03447011113166809,
0.0012524238554760814,
0.038976963609457016,
0.02975260652601719,
0.008625146001577377,
-0.032589901238679886,
-0.044744573533535004,
-0.025707442313432693,
0.0458768792450428,
-0.0006059268489480019,
0.010612063109874725,
0.005173732992261648,
0.019427916035056114,
0.017843319103121758,
-0.026606692001223564,
0.03738727793097496,
-0.014675413258373737,
-0.015396276488900185,
0.006714173126965761,
-0.012782219797372818,
0.003764199558645487,
-0.018987253308296204,
0.01582980901002884,
0.0007725518080405891,
-0.018062809482216835,
-0.000326744542689994,
0.06264127045869827,
-0.044036611914634705,
0.06510939449071884,
0.023223502561450005,
0.00003095842475886457,
-0.005033954977989197,
0.047026991844177246,
0.008393604308366776,
0.009897641837596893,
-0.017965685576200485,
-0.04340359941124916,
-0.061001043766736984,
-0.013860099948942661,
0.022485341876745224,
0.016249600797891617,
-0.04600076377391815,
0.036646369844675064,
0.024973595514893532,
0.06533830612897873,
-0.004522509872913361,
0.04643244668841362,
-0.04408780112862587,
-0.05173445865511894,
-0.007759265601634979,
0.02712825872004032,
0.006596203427761793,
0.01936790719628334,
0.08236237615346909,
0.009916255250573158,
0.004645911976695061,
-0.013933325186371803,
-0.03754666820168495,
0.018345259130001068,
-0.034010227769613266,
-0.002489265287294984,
0.0008652107208035886,
-0.006482481490820646,
0.058680180460214615,
-0.018754584714770317,
0.049661461263895035,
0.009528854861855507,
-0.0382368303835392,
-0.0015120379393920302,
0.006129578221589327,
0.004236089996993542,
0.02449258789420128,
-0.029880747199058533,
-0.06340567767620087,
-0.017239242792129517,
0.030237192288041115,
-0.03476904705166817,
0.009539078921079636,
-0.012668916024267673,
0.01680082082748413,
0.010764782316982746,
0.03470316529273987,
0.01827545277774334,
0.01700468733906746,
-0.003855142742395401,
-0.011006896384060383,
-0.04563138261437416,
0.03511105477809906,
-0.03688004985451698,
0.028794314712285995,
0.04868928715586662,
-0.04611494392156601,
0.018648847937583923,
-0.05443471297621727,
-0.032247964292764664,
0.003591670421883464,
-0.009703757241368294,
0.029102209955453873,
0.02385459840297699,
-0.014291289262473583,
-0.02670973353087902,
-0.01652461290359497,
0.011464400216937065,
-0.0013431673869490623,
-0.03615599498152733,
0.03496268391609192,
0.019442157819867134,
0.016850631684064865,
-0.037219077348709106,
-0.0008195292321033776,
-0.037373900413513184,
-0.05280410498380661,
-0.026255520060658455,
0.03399542346596718,
0.03773394599556923,
-0.04514603316783905,
0.0129312789067626,
-0.0036997459828853607,
-0.016246715560555458,
-0.0035108253359794617,
-0.02602706104516983,
-0.016450969502329826,
0.008232840336859226,
0.018157316371798515,
0.014495348557829857,
0.005467131268233061,
-0.00947850476950407,
0.040990084409713745,
0.05294939503073692,
-0.014215466566383839,
-0.020710555836558342,
-0.022845318540930748,
-0.030677201226353645,
-0.04287009686231613,
0.014876027591526508,
-0.007017191033810377,
0.013428489677608013,
-0.004333715885877609,
0.02119453437626362,
0.059425510466098785,
0.002089299261569977,
0.000879778410308063,
-0.032570403069257736,
0.00567382900044322,
0.024522053077816963,
0.0006707821739837527,
0.036509640514850616,
0.0005304481601342559,
-0.020093174651265144,
-0.028101036325097084,
0.021668430417776108,
0.009840075857937336,
-0.0009366813465021551,
-0.04542886093258858,
0.09908466041088104,
0.012428374961018562,
0.03961014375090599,
0.015284706838428974,
0.003649479476734996,
0.001830677385441959,
-0.015551206655800343,
-0.016272759065032005,
0.008749007247388363,
0.03641635924577713,
-0.0573396198451519,
0.008121484890580177,
0.03579142317175865,
0.026682786643505096,
-0.04283876344561577,
0.007157066836953163,
-0.027873540297150612,
0.00902137067168951,
-0.02178993821144104,
0.010951045900583267,
0.006692060269415379,
0.005516942590475082,
0.03408362716436386,
0.025957485660910606,
-0.01683230884373188,
-0.017370378598570824,
-0.013617726042866707,
-0.02291097678244114,
-0.0017495397478342056,
-0.008925098925828934,
-0.009151418693363667,
0.0007372903637588024,
0.014265436679124832,
0.01600644551217556,
0.03018614649772644,
-0.010817312635481358,
-0.02590990625321865,
-0.09009131044149399,
0.010886743664741516,
-0.051958467811346054,
-0.001503428560681641,
-0.02966257557272911,
-0.012772911228239536,
-0.03140238672494888,
0.006156416609883308,
-0.028121566399931908,
-0.028601810336112976,
-0.007842895574867725,
-0.069809690117836,
0.01737203821539879,
-0.039152298122644424,
-0.057509105652570724,
-0.014500463381409645,
0.01849708892405033,
0.04973125457763672,
-0.002140360651537776,
0.008308276534080505,
0.017328375950455666,
-0.05521774664521217,
-0.04206801578402519,
-0.007050808984786272,
0.025355760008096695,
-0.01575360633432865,
0.002361009828746319,
0.019990671426057816,
0.05630713328719139,
-0.051965031772851944,
-0.04508760944008827,
0.04002504050731659,
0.04380977153778076,
0.03331965208053589,
-0.0004255952371750027,
0.019921397790312767,
-0.0672127977013588,
0.0033897499088197947,
0.0036687729880213737,
0.04889819025993347,
0.01782694272696972,
0.019474074244499207,
0.03773002326488495,
0.015610366128385067,
-0.010192040354013443,
0.0163078885525465,
0.015460391528904438,
0.0007150585297495127,
-0.06505651026964188,
0.01606588438153267,
0.05261240154504776,
-0.006715722382068634,
0.012185901403427124,
-0.012061209417879581,
-0.014375760219991207,
-0.006267484277486801,
0.0009711774182505906,
-0.00265547726303339,
0.004870939999818802,
-0.03227425739169121,
-0.01886597089469433,
0.0006003612070344388,
-0.009933828376233578,
-0.01802222430706024,
-0.026438483968377113,
-0.033207181841135025,
0.05474565178155899,
0.02352985180914402,
0.003253825008869171,
-0.004812206141650677,
-0.04242934659123421,
0.033345311880111694,
0.05050674453377724,
0.06423606723546982,
0.014121174812316895,
-0.032014328986406326,
-0.05348015949130058,
0.003306810511276126,
0.031046172603964806,
-0.021970214322209358,
0.022945506498217583,
-0.06856819987297058,
-0.016934001818299294,
-0.016019314527511597,
0.00411631166934967,
-0.000373332790331915,
0.025798365473747253,
-0.022529566660523415,
-0.018054526299238205,
-0.041542910039424896,
-0.014871161431074142,
-0.010301983915269375,
0.03878684341907501,
0.04234250634908676,
0.034538812935352325,
0.04128256067633629,
0.03652242198586464,
0.002669733017683029,
0.013121363706886768,
-0.01426886860281229,
-0.09276442974805832,
0.030121443793177605,
-0.025245115160942078,
-0.005457696039229631,
0.06966355443000793,
-0.055996160954236984,
-0.05193129554390907,
0.007959430105984211,
0.012500626035034657,
0.01550245936959982,
0.014146699570119381,
-0.045145079493522644,
0.010991683229804039,
0.03290462866425514,
-0.003541838377714157,
0.02973354607820511,
0.03845271095633507,
-0.0194812323898077,
-0.04524998739361763,
-0.015088940970599651,
0.04588041454553604,
-0.016610080376267433,
-0.00034208191209472716,
0.0003179792838636786,
-0.008280079811811447,
-0.00843097735196352,
0.05191424861550331,
-0.02080518752336502,
0.007895290851593018,
0.015868600457906723,
-0.04774068668484688,
-0.011602959595620632,
0.021479591727256775,
-0.0075409444980323315,
-0.0045911455526947975,
-0.011692537926137447,
-0.013346802443265915,
-0.02066650241613388,
0.01411554217338562,
0.036062899976968765,
0.02131517231464386,
-0.021122118458151817,
0.023718517273664474,
-0.001816967036575079,
0.021123018115758896,
-0.03936697170138359,
-0.023117396980524063,
0.034779127687215805,
-0.029603518545627594,
0.03390322998166084,
-0.0011857437202706933,
-0.0012983712367713451,
0.03817271068692207,
-0.06220164895057678,
-0.054822277277708054,
-0.003240373916924,
-0.042564354836940765,
0.03880853205919266,
-0.049045879393815994,
0.019354015588760376,
0.01028535608202219,
0.019570857286453247,
-0.09347681701183319,
-0.00014946181909181178,
0.028764590620994568,
0.04063260927796364,
-0.013509567826986313,
0.0009143108618445694,
-0.004426237661391497,
-0.019833121448755264,
0.007387333083897829,
0.0010176879586651921,
0.05607060343027115,
-0.014130747877061367,
-0.004832716193050146,
-0.0076499516144394875,
0.01772778481245041,
0.022888336330652237,
0.022321397438645363,
-0.03179730102419853,
0.029225913807749748,
-0.010079208761453629,
-0.006403361912816763,
-0.018586894497275352,
0.05043516680598259,
-0.005577515810728073,
-0.005544022191315889,
0.006223628297448158,
-0.025864746421575546,
0.006609008647501469,
-0.0374651700258255,
-0.0016480546910315752,
0.03554356098175049,
0.012394670397043228,
-0.002941723680123687,
-0.016073094680905342,
0.0062515330500900745,
-0.026933861896395683,
-0.012959306128323078,
0.004145344719290733,
-0.029570315033197403,
0.005806164816021919,
-0.01860238052904606,
0.025820953771471977,
0.011931400746107101,
0.010369685478508472,
-0.009389697574079037,
0.05254754796624184,
0.019453145563602448,
-0.06575748324394226,
-0.0013333669630810618,
-0.008510603569447994,
-0.025984765961766243,
-0.02396443858742714,
0.00768525805324316,
-0.027418209239840508,
-0.003013281151652336,
-0.01728513091802597,
-0.03460213914513588,
-0.02050754614174366,
0.04806264489889145,
0.056826792657375336,
-0.032582368701696396,
0.01875787414610386,
-0.02940925769507885,
-0.02453570067882538,
-0.020609037950634956,
-0.021675167605280876,
-0.012605530209839344,
0.03627319261431694,
0.0020974837243556976,
0.0076044718734920025,
-0.01213209331035614,
-0.027862031012773514,
0.012602383270859718,
0.03235800564289093,
0.026173288002610207,
-0.002436538692563772,
0.044154975563287735,
0.01715226285159588,
0.006901612505316734,
0.012754498049616814,
-0.05189589411020279,
0.06573629379272461,
-0.057932958006858826,
0.028074074536561966,
0.025467339903116226,
-0.02832983061671257,
0.014968550764024258,
-0.016232525929808617,
0.011404212564229965,
-0.012715427204966545,
-0.010602176189422607,
-0.04992545768618584,
0.01698978804051876,
0.01931166462600231,
0.043265506625175476,
0.024252599105238914,
-0.01362181082367897,
-0.003292185952886939,
0.054204877465963364,
0.03368385136127472,
0.0030178995802998543,
-0.07406660169363022,
-0.043881114572286606,
-0.018483756110072136,
-0.0303967222571373,
0.03372886776924133,
-0.014986439608037472,
-0.030138099566102028,
-0.005202849395573139,
-0.00621426897123456,
0.005063341464847326,
-0.02905413508415222,
0.03250003978610039,
-0.00857238657772541,
0.026408763602375984,
0.014306255616247654,
0.029805047437548637,
-0.02216772735118866,
0.03989911451935768,
0.1252616047859192,
0.05545775219798088,
0.019323114305734634,
-0.052900657057762146,
0.02144588530063629,
-0.04706989601254463,
-0.002452454762533307,
-0.058100625872612,
0.045057494193315506,
0.028719596564769745,
0.006331500131636858,
-0.016009150072932243,
0.06546002626419067,
-0.004203895106911659,
-0.013626971282064915,
0.07269527018070221,
-0.024128608405590057,
-0.07573606073856354,
0.01156480610370636,
0.049006152898073196,
-0.008065696805715561,
-0.006357902195304632,
-0.027503041550517082,
0.03312961384654045,
0.01798076741397381,
0.01823556423187256,
0.020719343796372414,
-0.04105870798230171,
0.0323672853410244,
0.015549050644040108,
-0.04465746134519577,
0.002634995384141803,
0.03524647653102875,
0.01680711656808853,
-0.08074972033500671,
-0.014933750964701176,
0.006015374790877104,
-0.02015754021704197,
0.021645208820700645,
-0.003873351728543639,
0.01714143715798855,
-0.023567255586385727,
0.009136879816651344,
0.0007872295682318509,
-0.05396454036235809,
-0.03553233668208122,
0.024869468063116074,
0.04359710216522217,
-0.011683820746839046,
-0.01726353168487549,
-0.011622839607298374,
0.015886899083852768,
0.02456664852797985,
-0.030538098886609077,
-0.0470585972070694,
-0.020472630858421326,
0.011451425030827522,
-0.027290737256407738,
-0.015095802955329418,
0.016278130933642387,
0.0003786224697250873,
-0.039451830089092255,
0.01991506665945053,
-0.007573030889034271,
-0.008079071529209614,
0.02814345434308052,
0.003084341064095497,
0.02767893299460411,
0.026272667571902275,
-0.017166078090667725,
-0.007135510910302401,
-0.020595913752913475,
-0.02043231949210167,
-0.03295132517814636,
0.012942175380885601,
0.0017534868093207479,
0.034256961196660995,
0.026540987193584442,
-0.025683877989649773,
-0.02619919367134571,
0.015722252428531647,
0.00882923323661089,
-0.0028428721707314253,
0.010174252092838287,
0.005261734593659639,
-0.007918734103441238,
-0.023960284888744354,
0.03949650004506111,
-0.01403943169862032,
0.006523125804960728,
-0.03458831086754799,
0.03549915924668312,
-0.0016563339158892632,
-0.030864765867590904,
-0.039094846695661545,
-0.022941578179597855,
-0.03653682768344879,
-0.008648661896586418,
-0.024510366842150688,
0.0015958966687321663,
-0.008261583745479584,
0.0027099347207695246,
0.05323899909853935,
0.0037901222240179777,
-0.026170818135142326,
-0.017566664144396782,
0.035357631742954254,
-0.04865682125091553,
0.03309427946805954,
0.0035626583267003298,
0.011638214811682701,
-0.029162464663386345,
-0.06778007745742798,
0.01950746774673462,
0.046736933290958405,
0.05120754614472389,
0.05367293953895569,
-0.023287352174520493,
-0.01438987534493208,
-0.02436153031885624,
0.012799691408872604,
-0.036697495728731155,
-0.02782435156404972,
-0.04716232791543007,
0.01817723922431469,
-0.016325755044817924,
-0.024798857048153877,
-0.0010164622217416763,
0.02619769796729088,
-0.02271152101457119,
-0.007536014076322317,
0.019532999023795128,
0.021489039063453674,
-0.041367702186107635,
-0.04062127321958542,
0.00935464445501566,
0.01218363642692566,
0.03544297069311142,
0.015596071258187294,
-0.0059564183466136456,
0.04987315461039543,
-0.04726086184382439,
-0.09611629694700241,
0.022842029109597206,
-0.012082225643098354,
0.022716661915183067,
0.022811053320765495,
-0.018065303564071655,
-0.013461786322295666,
0.08062105625867844,
-0.03815481439232826,
-0.008401462808251381,
0.0025407481007277966,
0.014324276708066463,
-0.021461060270667076,
-0.04215601459145546,
-0.02368013560771942,
0.0026524451095610857,
-0.004406943917274475,
0.03065486066043377,
0.01712958700954914,
0.013423853553831577,
-0.01818307302892208,
-0.024281088262796402,
0.018719330430030823,
0.01619836874306202,
0.012946834787726402,
0.04835214465856552,
-0.03366214781999588,
0.011151420883834362,
-0.03921898081898689,
0.04670057073235512,
-0.006093436852097511,
0.023193296045064926,
-0.08996102213859558,
0.006824288982897997,
-0.0007448015385307372,
0.0000022207880192581797,
0.046994648873806,
-0.007617977913469076,
0.02270641177892685,
0.04360063746571541,
-0.07749416679143906,
0.03125191479921341,
-0.011668592691421509,
-0.05371367558836937,
-0.04310016706585884,
0.02107645384967327,
0.004122174810618162,
0.06585130095481873,
0.06495610624551773,
0.04710012674331665,
0.029301969334483147,
-0.012926163151860237,
-0.024062439799308777,
-0.029765021055936813,
-0.024497512727975845,
0.028194112703204155,
-0.00008269670070149004,
-0.0042806207202374935,
0.03731207549571991,
-0.007763009984046221,
0.011541143991053104,
0.0009445974719710648,
0.006963890045881271,
0.01145704835653305,
-0.01612943969666958,
0.006966660264879465,
0.011474000290036201,
0.0407271608710289,
0.0495830737054348,
-0.004773247521370649,
-0.020442744717001915,
0.007459515240043402,
0.021275626495480537,
0.04162143915891647,
0.014928647316992283,
0.0284624882042408,
-0.009811410680413246,
-0.03241681307554245,
-0.04431917890906334,
0.005981639958918095,
0.02771133929491043,
-0.0350489467382431,
0.007536682765930891,
-0.011295287869870663,
0.007225921843200922,
-0.031238973140716553,
-0.03311031311750412,
-0.019190678372979164,
-0.034153230488300323,
0.007457253988832235,
0.04639819264411926,
0.01130868960171938,
0.012053007259964943,
-0.00006383096479112282,
-0.015581648796796799,
-0.005074480548501015,
0.02847808599472046,
0.014185887761414051,
-0.0474567636847496,
-0.021167250350117683,
0.00011553759395610541,
0.018057260662317276,
0.015248196199536324,
-0.004533418919891119,
-0.03136502951383591,
0.045747917145490646,
-0.010960821062326431,
0.027384649962186813,
-0.006277001462876797,
-0.051770444959402084,
0.008784670382738113,
-0.04918213188648224,
0.05721140280365944,
0.0170033760368824,
0.06113772466778755,
-0.05086078122258186,
-0.02472224459052086,
0.01433639321476221,
0.0157865472137928,
0.029382051900029182,
0.003595310263335705,
-0.02385612018406391,
0.01394924521446228,
0.024951966479420662,
-0.013461805880069733,
-0.0049966019578278065,
0.002410286571830511,
0.023157835006713867,
-0.0064145298674702644,
-0.035469941794872284,
-0.02929668501019478,
-0.00015549124509561807,
0.03412197157740593,
0.020989300683140755,
-0.005404138471931219,
-0.008843918330967426,
0.026379769667983055,
-0.060549721121788025,
0.07913519442081451,
0.017895670607686043,
-0.013700716197490692,
0.044956646859645844,
0.0006451087538152933,
0.022946787998080254,
0.00820440985262394,
-0.012829947285354137,
-0.06602567434310913,
0.030658192932605743,
-0.019729839637875557,
0.010853325016796589,
-0.010119556449353695,
-0.004148419480770826,
0.024609193205833435,
-0.02863169088959694,
-0.04426886886358261,
0.07138415426015854,
-0.00851875264197588,
-0.013016204349696636,
0.03776979446411133,
0.032496336847543716,
0.026956897228956223,
0.016116302460432053,
0.009164448827505112,
0.012358746491372585,
0.034403298050165176,
-0.0044581894762814045,
0.06057185307145119,
0.011826823465526104,
0.020923564210534096,
0.019888626411557198,
-0.012313741259276867,
-0.005936834961175919,
0.012074717320501804,
0.007670113351196051,
0.015795305371284485,
0.0013529331190511584,
-0.009060618467628956,
0.02033945359289646,
0.009612847119569778,
0.04507092013955116,
-0.0022562702652066946,
-0.0030515010003000498,
0.08508575707674026,
-0.06472747027873993,
0.006941904313862324,
-0.019531136378645897,
-0.010779717937111855,
0.008032998070120811,
0.033489976078271866,
-0.009613829664885998,
0.03519834950566292,
-0.028238670900464058,
-0.012918180786073208,
-0.01706552319228649,
0.024209415540099144,
0.043051570653915405,
-0.030956849455833435,
-0.003919907379895449,
-0.012558501213788986,
-0.002279372187331319,
-0.026400789618492126,
-0.007388291414827108,
-0.011770939454436302,
-0.009717096574604511,
0.016898181289434433,
0.022822672501206398,
0.01685008779168129,
-0.04270113632082939,
-0.011334883980453014,
-0.0444713830947876,
0.05900820717215538,
0.0009859264828264713,
0.021725354716181755,
-0.01808013953268528,
0.017758246511220932,
-0.029016220942139626,
-0.000573806231841445
] |
<p>The derivation for Heat Equation I am reading starts by stating </p>
<p>Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total heat generated inside $[x,x+\Delta x]$ and writes the conservation equation</p>
<p>$$\textit{Total Heat Inside} [x,x+\Delta x]=
cpA \int _{ x}^{x+\Delta x}u(s,t) ds
$$</p>
<p>and later equates net flux across the boundary with</p>
<p>$u_x(x+\Delta x,t) - u_x(x,t)$,</p>
<p>so the heat flow is proportional to the spatial gradient of temperature at both ends. What I dont understand is why is net flux proportional to the spatial gradient, why cant we use the temparature variable $u$ itself to measure the difference? If the temparature difference at both ends is high, then we would expect higher flow from high temparature to low, right? What would be the physical intuition behind this? Was this model arrived at by experimentation?</p>
<p><img src="http://i.stack.imgur.com/d5On3.png" alt="enter image description here"></p> | 4,621 | [
-0.0005430158344097435,
-0.010550867766141891,
-0.014044815674424171,
0.0004392926348373294,
0.017056114971637726,
-0.0024155154824256897,
-0.03630886226892471,
-0.02794569730758667,
-0.0002797548659145832,
0.005799883045256138,
0.0253415796905756,
-0.02559027634561062,
0.03901732340455055,
0.0237133651971817,
0.018118947744369507,
0.0271459948271513,
-0.0005065483856014907,
0.008297845721244812,
0.020346496254205704,
-0.030428728088736534,
-0.03197171539068222,
0.04249633848667145,
-0.02217235043644905,
-0.0012030750513076782,
-0.026820922270417213,
0.02006770297884941,
-0.018322840332984924,
0.004051691386848688,
-0.00406831968575716,
0.061087507754564285,
-0.011961428448557854,
-0.038385119289159775,
-0.0053251502104103565,
0.028183065354824066,
0.02312719076871872,
0.0009553163545206189,
-0.03241685405373573,
-0.02710130251944065,
0.002407144522294402,
0.029829340055584908,
-0.017458679154515266,
-0.0259521696716547,
0.017995374277234077,
0.03489704802632332,
-0.00019683074788190424,
0.007065415848046541,
-0.0022700116969645023,
0.006142999976873398,
0.04713599011301994,
-0.04052278771996498,
0.024998610839247704,
0.020015938207507133,
0.08311948925256729,
0.050002213567495346,
-0.021155571565032005,
0.011689226143062115,
0.04019748419523239,
0.07087601721286774,
-0.01437342632561922,
-0.03705204278230667,
-0.013480107299983501,
-0.017773015424609184,
-0.022004304453730583,
-0.03736862167716026,
0.0015307242283597589,
0.009194794110953808,
0.017148219048976898,
-0.0345752090215683,
-0.009056727401912212,
-0.03405417129397392,
0.007747415918856859,
-0.01506865955889225,
0.0018739200895652175,
0.01993757113814354,
0.019543714821338654,
-0.013005725108087063,
-0.00940022524446249,
0.025618402287364006,
0.028253983706235886,
0.04467730596661568,
0.009946699254214764,
0.007402225863188505,
0.03057119809091091,
0.022260267287492752,
-0.003919515293091536,
-0.009668047539889812,
0.06098324432969093,
0.010512003675103188,
0.028951086103916168,
0.004776631481945515,
0.015469674952328205,
0.02008122391998768,
-0.0030167691875249147,
-0.03232528269290924,
0.01950128935277462,
0.00752305518835783,
0.013906601816415787,
0.016521578654646873,
-0.012835118919610977,
-0.04293591156601906,
-0.03239919990301132,
-0.03719326853752136,
0.004296123515814543,
0.07147485017776489,
0.007969939149916172,
-0.028210647404193878,
-0.034697260707616806,
0.016645103693008423,
0.017604826018214226,
-0.0020235576666891575,
-0.10025084018707275,
0.0020579842384904623,
0.01848444528877735,
0.023320429027080536,
-0.029428349807858467,
-0.021847423166036606,
-0.0043818335980176926,
-0.04895985871553421,
0.0217321515083313,
0.05986132100224495,
0.03195402771234512,
-0.04117071256041527,
0.02165922336280346,
-0.007642474491149187,
-0.0858033299446106,
0.051454026252031326,
0.015488305129110813,
-0.013320821337401867,
-0.020301949232816696,
0.022444890812039375,
-0.01675228774547577,
-0.00027655926533043385,
0.004415565636008978,
0.0182774867862463,
-0.012495657429099083,
0.006503402255475521,
-0.10712897032499313,
-0.051305338740348816,
0.04706602543592453,
-0.013493182137608528,
-0.050248317420482635,
-0.09738162159919739,
-0.018314536660909653,
0.04897585138678551,
0.06550774723291397,
-0.028766803443431854,
-0.008162940852344036,
-0.007862608879804611,
0.008247824385762215,
0.0035534778144210577,
-0.030420761555433273,
-0.027752302587032318,
0.015249370597302914,
-0.015423775650560856,
0.00047886744141578674,
0.007941152900457382,
0.010213511995971203,
0.05740325525403023,
-0.03791883587837219,
-0.02104652114212513,
0.051005974411964417,
0.002968200482428074,
0.001493512187153101,
0.02112364023923874,
0.007297759875655174,
-0.031918175518512726,
0.07872352749109268,
0.008244889788329601,
0.015127690508961678,
0.02498243749141693,
0.018168587237596512,
-0.003639318747445941,
-0.007823457941412926,
0.01046566292643547,
0.009317891672253609,
-0.024546002969145775,
0.012881523929536343,
0.01462593860924244,
-0.041929490864276886,
0.05191666632890701,
-0.03542668744921684,
-0.019224608317017555,
-0.02157571353018284,
-0.005670945625752211,
-0.00025889091193675995,
0.04776039347052574,
0.0006387897883541882,
-0.02835991233587265,
-0.0008937771781347692,
-0.05851311236619949,
-0.044495463371276855,
-0.06349539756774902,
0.023055516183376312,
-0.03810533508658409,
-0.0011592066148295999,
0.014543767087161541,
-0.010041506960988045,
0.019368866458535194,
-0.021611163392663002,
-0.047661080956459045,
0.0287387203425169,
0.03225736692547798,
0.023211326450109482,
0.017237719148397446,
0.00449611758813262,
0.041593682020902634,
0.06122296303510666,
0.01348660048097372,
0.02729695290327072,
-0.036652822047472,
-0.017588332295417786,
0.017656205222010612,
-0.056719038635492325,
0.014194641262292862,
-0.025942010805010796,
-0.05052608624100685,
-0.007702978327870369,
-0.024566730484366417,
-0.001254648552276194,
0.04786275699734688,
-0.02649877406656742,
0.09284312278032303,
0.04760962724685669,
0.014244137331843376,
-0.02591104432940483,
0.026761582121253014,
-0.002022502012550831,
0.07820133864879608,
-0.04506590589880943,
-0.06360508501529694,
-0.03976478427648544,
-0.008871134370565414,
0.04094916954636574,
0.04322248324751854,
-0.03253437206149101,
-0.012710770592093468,
0.0064203208312392235,
0.0074570984579622746,
0.011858146637678146,
0.025843996554613113,
0.03898322954773903,
-0.018064601346850395,
0.03511872887611389,
0.00822175107896328,
0.012694241479039192,
0.02906940132379532,
0.013558870181441307,
0.008693751879036427,
0.051466140896081924,
0.013252299278974533,
-0.006435708608478308,
0.06025156006217003,
-0.0028954860754311085,
0.049923647195100784,
0.0128498999401927,
0.027633868157863617,
0.034660838544368744,
-0.012033115141093731,
0.03293152526021004,
0.035705871880054474,
0.008071104995906353,
0.02630406618118286,
-0.017211617901921272,
-0.005074182990938425,
0.02176465466618538,
0.02472020499408245,
0.011473797261714935,
-0.0038222800940275192,
0.007298044860363007,
-0.013935678638517857,
0.024059319868683815,
-0.019092300906777382,
0.028007332235574722,
-0.03295013681054115,
-0.02790381945669651,
0.04036319628357887,
0.010704818181693554,
0.013325074687600136,
-0.03546527773141861,
-0.03993431106209755,
0.013291614130139351,
0.004010974895209074,
-0.01841622032225132,
0.015188924968242645,
-0.06165904179215431,
0.03229772672057152,
-0.027541356161236763,
-0.03659575432538986,
0.050122976303100586,
-0.0009808930335566401,
0.025717077776789665,
0.004829605109989643,
-0.026950286701321602,
-0.07298853993415833,
-0.012697950005531311,
0.015510342083871365,
0.029715653508901596,
0.006968751084059477,
0.022448375821113586,
0.05942392721772194,
-0.010358654893934727,
-0.057723622769117355,
0.051018476486206055,
-0.02833770029246807,
-0.05351308360695839,
-0.02993192709982395,
0.01382953580468893,
0.003233268391340971,
0.0037399292923510075,
0.04459276422858238,
0.02922561764717102,
-0.058577366173267365,
-0.0332418829202652,
-0.04370442405343056,
-0.021591056138277054,
0.019470706582069397,
-0.012873495928943157,
0.01596556417644024,
-0.029752852395176888,
-0.04196130484342575,
0.05079996958374977,
0.033505070954561234,
-0.037162140011787415,
-0.009927717037498951,
0.005289172288030386,
-0.03733999654650688,
-0.008051685057580471,
0.002074443269520998,
0.019461816176772118,
-0.017541810870170593,
0.021373558789491653,
-0.019820939749479294,
0.09271025657653809,
0.03551708906888962,
0.006199363619089127,
-0.011428648605942726,
0.006987179163843393,
-0.02046499028801918,
-0.0012799825053662062,
0.03633904457092285,
-0.01288454420864582,
-0.02855803072452545,
-0.013559793122112751,
-0.0008989364723674953,
0.029228385537862778,
0.060110777616500854,
-0.04830044135451317,
0.03925538435578346,
0.01879975199699402,
-0.0378287099301815,
-0.06888798624277115,
-0.011757956817746162,
-0.010493130423128605,
-0.03026486001908779,
0.0003000715223606676,
0.038549114018678665,
0.027601223438978195,
-0.0073254648596048355,
-0.017608990892767906,
-0.006869038566946983,
0.030974049121141434,
-0.025121640413999557,
0.0026977239176630974,
-0.021046943962574005,
0.026192063465714455,
0.01914772018790245,
0.006472392939031124,
-0.01624154858291149,
0.03315044566988945,
0.05480384826660156,
0.004959539044648409,
-0.0006574972067028284,
-0.03330608457326889,
-0.027353106066584587,
-0.06650093197822571,
-0.003875227877870202,
0.008886966854333878,
0.06667444854974747,
-0.00325373956002295,
0.0465913861989975,
0.009399129077792168,
0.041219547390937805,
0.01776704378426075,
-0.009872767142951488,
-0.08697804808616638,
-0.014011071063578129,
-0.018609844148159027,
-0.026443693786859512,
-0.020594581961631775,
-0.04284258186817169,
0.026891006156802177,
-0.0186876580119133,
0.015865355730056763,
0.008147211745381355,
0.011646522209048271,
-0.08744803816080093,
0.01619965396821499,
-0.029617242515087128,
-0.018929723650217056,
-0.0354977510869503,
0.01725940965116024,
0.06485491245985031,
-0.06957656145095825,
-0.0037815270479768515,
0.02297806367278099,
-0.004603168927133083,
-0.014465524815022945,
-0.030394678935408592,
-0.023502180352807045,
0.05258449167013168,
0.020762881264090538,
-0.005355517379939556,
0.004003207664936781,
-0.010962529107928276,
0.03044954687356949,
0.05610315501689911,
0.05808659642934799,
-0.023322857916355133,
-0.05102252960205078,
-0.0663408488035202,
-0.057788487523794174,
-0.030015727505087852,
0.03444897383451462,
0.06000645086169243,
0.0020136735402047634,
0.01607607677578926,
0.019544348120689392,
0.025740860030055046,
-0.025109203532338142,
0.020000169053673744,
0.019975677132606506,
0.004210075829178095,
-0.011691199615597725,
-0.032640766352415085,
-0.000790082907769829,
-0.03552781045436859,
-0.022466566413640976,
0.027685822919011116,
0.025998570024967194,
-0.03755071014165878,
-0.008816367015242577,
0.05699022114276886,
0.011171269230544567,
-0.0368298776447773,
0.0034124236553907394,
0.016648871824145317,
0.026453696191310883,
-0.011075505055487156,
0.009750760160386562,
0.03969299793243408,
0.06435400992631912,
0.018122348934412003,
-0.014776690863072872,
0.014067571610212326,
-0.08066277205944061,
-0.05559748411178589,
0.004409896209836006,
0.0121167516335845,
-0.00997376162558794,
-0.005962352268397808,
-0.038227859884500504,
0.01454659178853035,
0.019443701952695847,
0.007527160923928022,
0.04253299906849861,
-0.01909124292433262,
0.02915201149880886,
-0.008075384423136711,
-0.05739202722907066,
-0.008363746106624603,
0.018909461796283722,
-0.005716770421713591,
0.021367909386754036,
-0.029663478955626488,
-0.026571722701191902,
-0.002199161099269986,
0.002859314437955618,
-0.006932290270924568,
0.024347592145204544,
-0.02832300402224064,
-0.003418796928599477,
0.022553151473402977,
0.04037686064839363,
-0.04416864737868309,
-0.06531628966331482,
0.004850750323385,
0.0033122075255960226,
0.020000576972961426,
0.03320629149675369,
-0.022899245843291283,
-0.04078599810600281,
0.04437839612364769,
0.0335802398622036,
-0.012640955857932568,
0.010040154680609703,
-0.030082374811172485,
0.08495979011058807,
0.04469301179051399,
-0.011305700056254864,
0.06841816008090973,
0.03404894843697548,
-0.009084559045732021,
-0.020897945389151573,
0.006502620875835419,
0.04615982621908188,
-0.0208144411444664,
-0.009131145663559437,
-0.04087839648127556,
0.004132639151066542,
-0.007966579869389534,
0.009134447202086449,
-0.019209006801247597,
0.0460854172706604,
-0.03761574253439903,
-0.05671808868646622,
0.02752840146422386,
0.014291016384959221,
0.036345161497592926,
0.007785705383867025,
-0.021911008283495903,
0.017082253471016884,
0.03689519688487053,
-0.03865952789783478,
0.01738305389881134,
-0.007231106515973806,
-0.0007278924458660185,
0.014620031230151653,
-0.00960714090615511,
0.003950299695134163,
-0.013259965926408768,
-0.03105403296649456,
0.02856440097093582,
-0.02056627720594406,
0.01831231825053692,
0.02066277712583542,
0.04221389815211296,
0.021008465439081192,
-0.03484542295336723,
0.006558689754456282,
-0.0023486106656491756,
0.022048495709896088,
-0.0072284541092813015,
-0.06162964552640915,
0.0410270057618618,
0.010727997869253159,
0.04343153536319733,
-0.07121583819389343,
-0.06269274652004242,
0.0038519147783517838,
-0.010267800651490688,
-0.04909972846508026,
-0.038154009729623795,
-0.014730894938111305,
-0.014858914539217949,
-0.03750045597553253,
-0.00866783782839775,
0.037858981639146805,
-0.006716527976095676,
0.0038972788024693727,
0.019725637510418892,
0.047937553375959396,
0.04154454544186592,
0.0006812865613028407,
0.028511732816696167,
-0.023051274940371513,
-0.012931819073855877,
-0.025601914152503014,
-0.0060299476608633995,
0.02192729525268078,
-0.02693934366106987,
-0.02358781360089779,
0.03545380383729935,
0.015522502362728119,
0.09037274122238159,
-0.0024733301252126694,
-0.009884262457489967,
0.009942992590367794,
-0.0015933082904666662,
-0.027976421639323235,
-0.005878170020878315,
0.01823088526725769,
-0.013072829693555832,
-0.0026981353294104338,
0.008765648119151592,
0.014928117394447327,
-0.0175277478992939,
-0.029539037495851517,
0.0250630434602499,
-0.007150168064981699,
-0.0003691501042339951,
0.012708117254078388,
0.061044394969940186,
-0.006130896974354982,
0.015779536217451096,
0.005809039808809757,
0.016395656391978264,
0.042482513934373856,
0.020230496302247047,
0.028611278161406517,
0.0022228891029953957,
-0.017701638862490654,
-0.043433040380477905,
-0.028174879029393196,
-0.04697512835264206,
0.04148853197693825,
0.05302908271551132,
-0.021663840860128403,
0.044728875160217285,
0.03602875769138336,
-0.021022003144025803,
0.032146941870450974,
-0.009793019853532314,
-0.026993194594979286,
0.03253140300512314,
-0.031574320048093796,
0.032788872718811035,
-0.007350155618041754,
-0.046655815094709396,
0.05271874740719795,
0.026589808985590935,
-0.006068840157240629,
0.0180971659719944,
-0.0012218195479363203,
-0.019703008234500885,
0.014264198020100594,
-0.012409267947077751,
-0.03771757334470749,
0.01727108843624592,
0.0043381499126553535,
0.012223143130540848,
-0.0033058521803468466,
-0.011995596811175346,
0.06444302946329117,
-0.01783248409628868,
-0.017464548349380493,
-0.06952253729104996,
-0.0025504534132778645,
-0.06480928510427475,
0.004488092847168446,
0.02568746730685234,
0.018883150070905685,
0.030895568430423737,
0.023572171106934547,
0.032594166696071625,
0.003988249693065882,
-0.004464170895516872,
0.004428028129041195,
-0.04404034465551376,
0.0046118865720927715,
-0.017251543700695038,
-0.01835773140192032,
0.03178533911705017,
-0.013218482956290245,
-0.023457471281290054,
-0.005158219486474991,
-0.034650929272174835,
0.010043131187558174,
0.0201229490339756,
0.008496282622218132,
-0.032853610813617706,
0.08829814940690994,
-0.033165328204631805,
0.013649269938468933,
-0.022914748638868332,
0.018008537590503693,
0.10945455729961395,
0.03717159479856491,
-0.015648184344172478,
-0.023900438100099564,
0.0347675196826458,
-0.02055896818637848,
-0.0303159411996603,
-0.016987837851047516,
0.03349699079990387,
0.014488897286355495,
0.0035930557642132044,
0.02912646159529686,
0.04673338681459427,
-0.020089708268642426,
-0.031604476273059845,
0.033948373049497604,
-0.06382361799478531,
-0.005548024084419012,
0.07560351490974426,
-0.02291254885494709,
-0.02438855729997158,
0.008611347526311874,
-0.011966533958911896,
0.022153686732053757,
-0.01159037183970213,
0.01277147140353918,
-0.01637663133442402,
-0.027684269472956657,
0.023221556097269058,
0.002808433026075363,
-0.046826113015413284,
0.01305605098605156,
0.002915217075496912,
-0.002644109772518277,
-0.05163431912660599,
-0.029179200530052185,
0.030665062367916107,
-0.026055414229631424,
0.0370531789958477,
0.020480716601014137,
0.00784299336373806,
-0.00041154769132845104,
-0.005004359874874353,
0.06589765846729279,
-0.023457523435354233,
-0.03582484647631645,
-0.0370662696659565,
0.06793494522571564,
-0.00424863351508975,
0.01986605115234852,
0.022656947374343872,
0.005475978367030621,
0.011328044347465038,
-0.019450707361102104,
-0.0005301511264406145,
-0.006423566956073046,
0.02228444069623947,
-0.012263663113117218,
-0.040385302156209946,
-0.02533717080950737,
0.04038885608315468,
0.03139045089483261,
0.023107700049877167,
0.012820284813642502,
-0.027411257848143578,
-0.004683980252593756,
-0.007070982363075018,
0.050825078040361404,
-0.013121513649821281,
0.030551422387361526,
-0.04462584853172302,
0.01842126064002514,
-0.028291871771216393,
-0.017738904803991318,
0.010806995443999767,
-0.0052803573198616505,
0.007573699578642845,
0.027936559170484543,
-0.029144855216145515,
0.005969551391899586,
-0.06794454157352448,
0.02382000721991062,
-0.020104045048356056,
0.027238350361585617,
-0.04721227288246155,
0.013514652848243713,
-0.012194018810987473,
0.0687934085726738,
-0.007744993083178997,
-0.021648790687322617,
0.04202723503112793,
0.018961595371365547,
0.02317390963435173,
-0.02420506626367569,
-0.0009793124627321959,
-0.024831632152199745,
-0.04459771141409874,
-0.009617543779313564,
0.044401466846466064,
0.02518555335700512,
0.055294640362262726,
0.0017514978535473347,
-0.0016624744748696685,
0.04791002348065376,
-0.03139539435505867,
0.012910634279251099,
0.018405858427286148,
-0.0032184580340981483,
-0.0038061789236962795,
0.008787233382463455,
-0.024290237575769424,
-0.008513436652719975,
-0.029346825554966927,
-0.025708405300974846,
0.005959177855402231,
0.013344674371182919,
0.003533301642164588,
-0.009139404632151127,
0.001833664602600038,
-0.0346858836710453,
0.045616619288921356,
-0.06002271920442581,
-0.03208876773715019,
-0.06100790202617645,
-0.026361532509326935,
0.008440355770289898,
-0.005572242196649313,
-0.026091523468494415,
0.023373153060674667,
-0.02464967779815197,
-0.04056309536099434,
-0.0003714687773026526,
0.002123055746778846,
-0.0005992838414385915,
-0.04550419747829437,
0.026425132527947426,
0.007670239545404911,
0.009067199192941189,
0.002615240402519703,
-0.054288528859615326,
0.055554766207933426,
-0.032113440334796906,
-0.03813569247722626,
0.009075540117919445,
0.013644615188241005,
0.011664276011288166,
-0.004868586082011461,
0.020576445385813713,
-0.012315208092331886,
0.027011826634407043,
-0.03476742282509804,
-0.010203879326581955,
-0.02897406369447708,
-0.03456616401672363,
-0.016059059649705887,
-0.06101521849632263,
0.040357355028390884,
-0.001433987752534449,
0.03349059075117111,
0.008723651990294456,
-0.0219707228243351,
-0.005923762451857328,
-0.019695201888680458,
0.00811540987342596,
-0.05221199616789818,
0.014801103621721268,
0.0019529300043359399,
0.00833195447921753,
0.014799113385379314,
0.05484021455049515,
-0.015031983144581318,
-0.0069877891801297665,
-0.001958665903657675,
0.008643759414553642,
-0.07256024330854416,
0.01374047715216875,
-0.016035079956054688,
-0.03168807551264763,
0.00428468594327569,
-0.07753370702266693,
0.022655131295323372,
0.033722829073667526,
-0.01874449849128723,
0.0245097316801548,
-0.035645052790641785,
-0.037471603602170944,
-0.0407169945538044,
-0.02249019779264927,
-0.009218409657478333,
0.04870542883872986,
0.05201571434736252,
0.017640603706240654,
-0.001022016629576683,
0.007906734012067318,
0.0051870197057724,
-0.015293235890567303,
-0.012806843966245651,
-0.0019045495428144932,
-0.008012695237994194,
-0.023595787584781647,
0.030394386500120163,
-0.006157201249152422,
-0.010006876662373543,
0.00887330248951912,
-0.0075171575881540775,
-0.04478343948721886,
-0.00018723413813859224,
0.021841134876012802,
0.012216083705425262,
0.024249108508229256,
0.03457148000597954,
0.02008628472685814,
0.028199462220072746,
0.016330070793628693,
0.0015831273049116135,
0.01056942343711853,
-0.008212098851799965,
-0.01876935176551342,
0.042973846197128296,
-0.021635575219988823,
-0.05577448382973671,
0.04145531728863716,
-0.03476038575172424,
-0.01788637973368168,
0.028252772986888885,
-0.024090077728033066,
0.02835557609796524,
-0.026664046570658684,
0.01621825061738491,
-0.01930343545973301,
-0.019453102722764015,
0.04452401399612427,
-0.018096493557095528,
-0.055993497371673584,
-0.0019916228484362364,
0.03454569727182388,
-0.020563185214996338,
0.03412669152021408,
0.003359677502885461,
-0.011430235579609871,
-0.04787395894527435,
-0.028699010610580444,
0.006545922253280878,
-0.044248152524232864,
-0.011667829006910324,
-0.005414885468780994,
-0.03875993937253952,
0.02034669928252697,
0.017699480056762695,
0.03503002971410751,
-0.007814948447048664,
-0.05499618127942085,
-0.02560150995850563,
-0.04161502793431282,
0.043013282120227814,
-0.019622117280960083,
-0.018687037751078606,
-0.041277926415205,
0.000008455586794298142,
-0.03661080449819565,
0.007577191572636366,
0.052739065140485764,
0.0035287102218717337,
-0.04428916424512863,
0.04948568344116211,
0.027999473735690117,
0.03669680282473564,
-0.05169256404042244,
0.02078383043408394,
-0.02571866288781166,
0.01146848313510418,
-0.01768331788480282,
-0.00361711997538805,
0.023772764950990677,
0.07549716532230377,
0.02343812771141529,
-0.03192027285695076,
-0.02033378928899765,
-0.008022498339414597,
-0.016778796911239624,
0.008492841385304928,
-0.005991943646222353,
-0.03073858469724655,
0.07040724903345108,
-0.004880706313997507,
0.017425337806344032,
0.017319032922387123,
-0.008987294510006905,
-0.03720143809914589,
-0.010021837428212166,
0.006401269230991602,
0.016294419765472412,
-0.0099219661206007,
-0.031889013946056366,
0.03486393019556999,
-0.018828753381967545,
-0.008562295697629452,
0.05056854709982872,
-0.06087634712457657,
-0.019855061545968056,
0.05499623715877533,
0.035305798053741455,
-0.006453832611441612,
0.012889609672129154,
0.014183353632688522,
0.002528570359572768,
0.020686766132712364,
-0.009152197279036045,
0.046759381890296936,
0.04826363921165466,
-0.009954496286809444,
0.005897884722799063,
0.028650695458054543,
-0.03752733767032623,
0.024116812273859978,
0.008643021807074547,
-0.002234821440652013,
-0.020454227924346924,
-0.032562706619501114,
0.02288779430091381,
0.006386245600879192,
0.005091240629553795,
0.01594613865017891,
-0.023543117567896843,
0.10131053626537323,
0.01823701150715351,
0.012342258356511593,
-0.028970595449209213,
0.013195155188441277,
0.001694496488198638,
-0.003647909499704838,
0.07037321478128433,
0.07936757057905197,
-0.018535621464252472,
0.006665994878858328,
0.020188946276903152,
-0.0005865398561581969,
-0.013133238069713116,
-0.01072467677295208,
0.019733790308237076,
0.0008181758457794785,
-0.0012747755972668529,
-0.030156660825014114,
-0.01128455065190792,
-0.015274557285010815,
-0.0195058174431324,
0.059149935841560364,
0.045773696154356,
0.029918193817138672,
0.0633859783411026,
-0.02350057102739811,
0.0017615968827158213,
0.06759534776210785,
-0.07016813009977341,
-0.0286187045276165,
-0.00793466530740261,
-0.008042611181735992,
0.013153823092579842,
-0.02427198365330696
] |
<p>I am still struggling with C being a constant and what that implies.
So can an experiment be done to find the resting state for the universe?
Take a device with an observer and a light source and two mirrors, one 10 meters in front and the other 10 meters behind the light source. Now move this through space at some speed. Can’t you determine your speed by using the red/blue shift from the light reflected by the mirrors? Will this allow you to find the resting reference for the entire universe?</p> | 4,622 | [
-0.00313384342007339,
-0.010500341653823853,
-0.001779325888492167,
-0.036316465586423874,
0.08725377172231674,
-0.019283102825284004,
-0.03151089698076248,
-0.03278213366866112,
-0.02929052524268627,
-0.0264144167304039,
-0.011397468857467175,
0.04871298372745514,
0.040599703788757324,
0.004742904100567102,
0.022504232823848724,
0.010054618120193481,
0.0047501446679234505,
-0.002342497231438756,
-0.058814775198698044,
-0.036151520907878876,
0.045969609171152115,
0.03484692424535751,
0.033431276679039,
0.021074211224913597,
-0.012858603149652481,
0.027698028832674026,
-0.018093738704919815,
-0.048511240631341934,
-0.0026520066894590855,
0.040757279843091965,
-0.03061552904546261,
-0.024502398446202278,
-0.013825612142682076,
0.04174882546067238,
0.02005402185022831,
-0.026834873482584953,
0.0071788448840379715,
-0.013629372231662273,
-0.010918100364506245,
0.03557206690311432,
-0.04600851610302925,
-0.032872524112463,
-0.012101192958652973,
0.053323034197092056,
0.0009103236952796578,
-0.0012299752561375499,
0.00048696185695007443,
-0.0041524977423250675,
0.0434352271258831,
-0.06234689801931381,
0.06947854161262512,
-0.03246014565229416,
0.006778471637517214,
0.028617870062589645,
-0.026638904586434364,
-0.014801198616623878,
0.083067387342453,
0.04937933757901192,
0.006348752416670322,
-0.03612150996923447,
-0.029031949117779732,
0.0027327570132911205,
-0.0009031528607010841,
-0.018709445372223854,
-0.015529507771134377,
-0.005722247529774904,
0.015444742515683174,
0.038899630308151245,
0.03215591609477997,
0.003306702710688114,
0.022347845137119293,
0.02383407950401306,
0.054934948682785034,
0.025640500709414482,
0.020633384585380554,
-0.05302193760871887,
0.022894276306033134,
0.004306830000132322,
0.00660464633256197,
0.04468464478850365,
-0.03904459625482559,
0.004245046526193619,
0.019402440637350082,
0.03560091555118561,
-0.008975809440016747,
-0.016531821340322495,
0.06114279478788376,
0.030841195955872536,
0.002825459698215127,
0.034746479243040085,
0.022639216855168343,
-0.028014548122882843,
0.019295845180749893,
0.006369023118168116,
-0.03500970080494881,
0.023271113634109497,
-0.011113026179373264,
0.03659101948142052,
-0.034834835678339005,
-0.03705262020230293,
-0.0012734426418319345,
0.01895769126713276,
0.012124751694500446,
0.04536021873354912,
-0.012355472892522812,
0.0011661072494462132,
-0.020072810351848602,
0.015917828306555748,
-0.0163260605186224,
0.010230825282633305,
-0.04233212769031525,
0.010277029126882553,
-0.007481090724468231,
0.021481642499566078,
0.031243734061717987,
-0.011322288773953915,
0.021766120567917824,
-0.06952031701803207,
0.07149560004472733,
0.020418895408511162,
0.037148021161556244,
-0.013407720252871513,
-0.013021047227084637,
0.011923892423510551,
-0.02389140985906124,
0.03851857781410217,
0.03269515186548233,
0.02504519559442997,
-0.03389231488108635,
0.028911596164107323,
0.026598449796438217,
-0.026166079565882683,
-0.028413325548171997,
0.02360525354743004,
0.022420207038521767,
-0.007077275309711695,
-0.1276969164609909,
-0.09356054663658142,
0.036591704934835434,
-0.0015277753118425608,
-0.03087979555130005,
-0.061234135180711746,
0.02543935738503933,
0.0649854987859726,
0.06567160040140152,
0.0003163181245326996,
-0.023635538294911385,
-0.03928221017122269,
0.018571488559246063,
0.03220120817422867,
0.004551638849079609,
-0.06182438135147095,
-0.007227654568850994,
-0.06373503804206848,
-0.024494487792253494,
-0.04402769356966019,
-0.0056859892792999744,
0.03149435669183731,
-0.008888059295713902,
-0.010244441218674183,
0.03976619616150856,
-0.011670960113406181,
0.012090081349015236,
-0.0016558304196223617,
-0.012686377391219139,
-0.032178573310375214,
0.09109325706958771,
0.02459973283112049,
0.003675872925668955,
-0.0020938278175890446,
0.01632566750049591,
0.05897115543484688,
-0.001313169370405376,
0.00729795079678297,
0.030689096078276634,
-0.06912792474031448,
-0.0041014705784618855,
-0.016562245786190033,
0.010485891252756119,
0.0019504402298480272,
-0.005453922785818577,
-0.03605407848954201,
-0.028498774394392967,
0.007245577871799469,
0.0009666774421930313,
0.06698436290025711,
-0.048982489854097366,
0.0195461455732584,
0.0058092703111469746,
-0.029231024906039238,
0.02371210791170597,
-0.047151390463113785,
0.0020463778637349606,
0.023601872846484184,
0.011035407893359661,
0.007696405053138733,
0.0024487818591296673,
0.06390590220689774,
-0.0436227060854435,
-0.05466165766119957,
-0.0020974082872271538,
0.06665840744972229,
-0.01225997693836689,
0.0060275946743786335,
0.006532931700348854,
0.041178781539201736,
0.017604177817702293,
-0.008862181566655636,
-0.015610783360898495,
-0.018651727586984634,
-0.022134222090244293,
0.04188798740506172,
-0.018679756671190262,
0.0005130644422024488,
0.02081533707678318,
0.025959346443414688,
-0.008856256492435932,
0.040830038487911224,
0.015214590355753899,
0.033282604068517685,
-0.009947150945663452,
0.06159762293100357,
-0.00138955214060843,
-0.014419902116060257,
0.03424152359366417,
0.04140771925449371,
-0.01767004281282425,
-0.013115308247506618,
-0.0012637587497010827,
-0.02060098573565483,
-0.036074090749025345,
-0.01157817430794239,
0.007338658906519413,
-0.0078101386316120625,
-0.0067815026268363,
-0.016446193680167198,
0.04942816495895386,
0.029805008322000504,
0.04696101322770119,
-0.006705714855343103,
-0.01212616078555584,
-0.038671281188726425,
-0.0023369109258055687,
0.014589129015803337,
0.00759125966578722,
0.006709180306643248,
0.016937991604208946,
-0.021128321066498756,
0.014632008038461208,
0.007405110634863377,
-0.003101510228589177,
0.018344677984714508,
0.00010844549251487479,
-0.011329812929034233,
0.00025386529159732163,
-0.02922106720507145,
0.027695849537849426,
-0.020552316680550575,
0.03763879835605621,
0.057006459683179855,
-0.007816965691745281,
-0.0030684168450534344,
-0.04391959682106972,
-0.024347931146621704,
-0.0053906734101474285,
-0.006603396963328123,
-0.03919026628136635,
-0.022615531459450722,
0.033319178968667984,
-0.010106894187629223,
0.02399633079767227,
0.0010591682512313128,
0.008970442228019238,
-0.01441541314125061,
-0.023518582805991173,
-0.024623509496450424,
-0.0038023721426725388,
0.015907717868685722,
-0.026860808953642845,
-0.005254992749541998,
0.010404949076473713,
-0.050893764942884445,
-0.014954207465052605,
0.0024007647298276424,
-0.0512106791138649,
0.009769397787749767,
-0.008969457820057869,
-0.06377997994422913,
-0.0038671342190355062,
-0.014979194849729538,
0.042506057769060135,
0.05670170113444328,
-0.021708345040678978,
-0.07476918399333954,
-0.0023662694729864597,
-0.026428718119859695,
-0.0006468401988968253,
-0.03788064420223236,
0.03745909407734871,
0.044322334229946136,
-0.007841291837394238,
-0.047958724200725555,
-0.014208379201591015,
-0.04083153232932091,
-0.05066214129328728,
0.010526878759264946,
-0.042924873530864716,
0.02012769877910614,
-0.03292447701096535,
0.04725765064358711,
0.0390361063182354,
-0.054756756871938705,
-0.015023693442344666,
-0.03157729282975197,
-0.07589644938707352,
0.07787637412548065,
-0.025497382506728172,
0.05155620723962784,
-0.012536110356450081,
0.010509468615055084,
0.0780099555850029,
0.041285742074251175,
-0.030308198183774948,
-0.040189892053604126,
0.00589939346536994,
0.012357538565993309,
-0.03870801255106926,
-0.04362902790307999,
0.032182030379772186,
-0.03393660858273506,
0.005163485184311867,
0.034748587757349014,
0.027525177225470543,
0.0235332902520895,
0.018056580796837807,
-0.015039248391985893,
0.025676287710666656,
-0.018355395644903183,
0.03901246562600136,
0.04584740102291107,
0.022126879543066025,
-0.013523631729185581,
-0.01828816719353199,
0.0068703643046319485,
0.058450207114219666,
0.00491219200193882,
-0.0297872181981802,
0.035590071231126785,
-0.0007097800262272358,
0.017773104831576347,
-0.017395125702023506,
0.00521433912217617,
0.006480029318481684,
-0.001918390509672463,
-0.008131017908453941,
0.020450152456760406,
0.027013739570975304,
0.015023008920252323,
-0.007272353395819664,
0.016762318089604378,
0.0018201053608208895,
-0.003258167766034603,
-0.04746001958847046,
0.009566093795001507,
-0.019308261573314667,
0.014044485986232758,
-0.05409602075815201,
-0.053360749036073685,
0.06937670707702637,
0.04009922593832016,
0.013344538398087025,
-0.014307110570371151,
-0.05500883609056473,
0.020690713077783585,
-0.04328221082687378,
-0.04206204041838646,
0.04533122479915619,
-0.002095197094604373,
0.02868538908660412,
0.025845004245638847,
0.030322397127747536,
0.0009651869186200202,
-0.009647095575928688,
-0.005560453049838543,
-0.09779821336269379,
0.0013331142254173756,
-0.048563480377197266,
-0.01601404882967472,
0.015297028236091137,
0.010242756456136703,
0.0256186630576849,
-0.02596891112625599,
0.03658817335963249,
-0.03118930570781231,
-0.024793600663542747,
-0.034699223935604095,
-0.0004678039695136249,
-0.01651652157306671,
-0.02760043367743492,
-0.02170921117067337,
0.011479551903903484,
0.06464089453220367,
-0.05414871498942375,
-0.0028557823970913887,
0.0036424442660063505,
-0.030225427821278572,
0.00013994400796946138,
0.005049504339694977,
-0.03382213041186333,
0.027115846052765846,
0.039927348494529724,
0.023226914927363396,
0.03874538466334343,
0.02807091362774372,
0.005299596581608057,
0.010853925719857216,
0.00438592117279768,
-0.00260625290684402,
-0.030073294416069984,
-0.031070047989487648,
-0.03919437155127525,
-0.0001880339696072042,
-0.014043697156012058,
0.05890018865466118,
-0.01996759884059429,
0.021235160529613495,
0.02661138027906418,
0.03047380968928337,
-0.015132080763578415,
0.027689315378665924,
0.04147672280669212,
-0.017451800405979156,
-0.05888139829039574,
-0.033940333873033524,
-0.0020265388302505016,
-0.028864936903119087,
0.023179007694125175,
0.04122651368379593,
-0.014160821214318275,
-0.031000368297100067,
0.01985677145421505,
0.00806721206754446,
0.03144893795251846,
-0.015855416655540466,
0.00924499798566103,
-0.02534373477101326,
0.005703016649931669,
-0.014045728370547295,
0.0016464665532112122,
0.006057703867554665,
0.043550312519073486,
-0.00019851217803079635,
-0.019002340734004974,
-0.0572994239628315,
-0.05548489838838577,
0.0028635216876864433,
0.009673367254436016,
0.01017664186656475,
0.059271588921546936,
-0.019593486562371254,
-0.05143948644399643,
-0.058091383427381516,
0.032779261469841,
-0.03185658156871796,
0.016303258016705513,
-0.014758762903511524,
-0.018910573795437813,
-0.004307583440095186,
-0.01913447491824627,
-0.022379226982593536,
0.0554489940404892,
0.0011620844015851617,
-0.021516814827919006,
-0.005016405135393143,
0.0024453680962324142,
-0.00608624704182148,
-0.00904031377285719,
-0.017003683373332024,
0.012791677378118038,
-0.03408066928386688,
0.002619948470965028,
0.0061571295373141766,
0.04446624591946602,
-0.0026698033325374126,
-0.05634690076112747,
-0.007188489194959402,
0.025023436173796654,
0.009713026694953442,
0.07187998294830322,
0.02266276814043522,
-0.050395771861076355,
0.013997244648635387,
0.01922094263136387,
-0.03459944948554039,
0.022236276417970657,
-0.04475586488842964,
0.0692354291677475,
0.018055463209748268,
-0.021279213950037956,
0.03528662398457527,
-0.0077843028120696545,
-0.012869231402873993,
-0.03270759433507919,
0.03326207771897316,
0.024850817397236824,
-0.0267353318631649,
0.009516793303191662,
-0.0012048411881551147,
-0.027282502502202988,
-0.02049844153225422,
0.028441118076443672,
0.0008794645546004176,
0.006202151533216238,
0.008312993682920933,
-0.01958501525223255,
-0.021532131358981133,
0.010218441486358643,
0.05200859531760216,
0.02518804371356964,
-0.0002918087993748486,
-0.05063574016094208,
0.004838246386498213,
-0.017352649942040443,
0.006904782727360725,
-0.0063271960243582726,
0.011437802575528622,
0.012843326665461063,
-0.007298261392861605,
0.027654843404889107,
-0.02936256118118763,
-0.00884811021387577,
0.018548985943198204,
-0.029221493750810623,
0.04071171209216118,
0.013463479466736317,
0.027013301849365234,
-0.013648086227476597,
-0.03680567443370819,
-0.04775902256369591,
0.002196607645601034,
-0.028226202353835106,
-0.00271974946372211,
-0.061593230813741684,
0.01794569194316864,
-0.007844805717468262,
0.06340499222278595,
-0.08630909770727158,
-0.022060563787817955,
0.01855381391942501,
0.005086147226393223,
0.006374993361532688,
-0.005781643092632294,
0.023534078150987625,
-0.01358060259371996,
-0.013499855995178223,
-0.0250646211206913,
0.043301552534103394,
0.0014383170055225492,
-0.010310284793376923,
-0.0089993542060256,
0.011767979711294174,
0.03371614217758179,
0.02040090039372444,
0.007648381404578686,
0.004869770724326372,
-0.013257318176329136,
-0.00836669746786356,
-0.011201731860637665,
0.05372776836156845,
-0.03535031899809837,
-0.034737106412649155,
-0.03260641172528267,
0.013710489496588707,
0.026401787996292114,
-0.015236493200063705,
-0.007118947803974152,
0.04954466596245766,
-0.022622650489211082,
-0.014177820645272732,
-0.03514128550887108,
-0.0023865040857344866,
-0.01849808730185032,
0.004580401815474033,
0.025177787989377975,
-0.004061909858137369,
-0.014282424934208393,
-0.05291707441210747,
0.057756826281547546,
0.022873971611261368,
-0.015921879559755325,
-0.019484596326947212,
0.05344115197658539,
0.03937320411205292,
-0.06028695032000542,
-0.004923029337078333,
0.03580816462635994,
0.002858869032934308,
-0.014227787964046001,
-0.00849672220647335,
0.005024316720664501,
-0.03135276958346367,
-0.05588692054152489,
-0.007936211302876472,
-0.02060110867023468,
-0.014940476045012474,
0.06133602187037468,
-0.004714734852313995,
0.05815292149782181,
0.0038390643894672394,
-0.027027448639273643,
-0.00850687362253666,
0.024095531553030014,
-0.007832888513803482,
0.006119893863797188,
-0.005539266392588615,
0.01996055245399475,
-0.009339616633951664,
0.0036672574933618307,
0.02662830613553524,
0.05988943576812744,
-0.017306877300143242,
0.008248284459114075,
0.04838818311691284,
0.04273001477122307,
0.022770028561353683,
-0.022786686196923256,
-0.03183118999004364,
0.0412861667573452,
-0.03711418807506561,
0.001143195084296167,
0.012297732755541801,
-0.011969950050115585,
0.01942734606564045,
0.0007230775663629174,
0.005794222466647625,
-0.046895574778318405,
-0.028700090944767,
-0.051815904676914215,
0.001681855763308704,
0.01933826133608818,
0.033863674849271774,
-0.0005138534470461309,
-0.00853794626891613,
-0.013928440399467945,
-0.005539739970117807,
0.03175744786858559,
-0.007455861195921898,
-0.07310684770345688,
-0.06920309364795685,
-0.018745148554444313,
-0.022861575707793236,
0.06853071600198746,
0.028697781264781952,
-0.021321285516023636,
0.023656411096453667,
-0.02555892802774906,
0.046644750982522964,
0.038884710520505905,
0.040305934846401215,
-0.01880405656993389,
0.08278244733810425,
-0.02923004887998104,
-0.017482001334428787,
-0.014258867129683495,
0.006604090332984924,
0.11677096784114838,
0.03231002762913704,
0.0002658702724147588,
-0.08338174968957901,
0.058221179991960526,
-0.013933824375271797,
0.039374906569719315,
-0.04106705263257027,
0.022018486633896828,
0.006749073509126902,
0.05052785947918892,
0.03175096958875656,
0.04112368822097778,
0.01799619570374489,
-0.0017474305350333452,
0.040769536048173904,
-0.01301824115216732,
-0.020512254908680916,
0.05485828220844269,
0.048822756856679916,
-0.03251267969608307,
-0.018783627077937126,
0.01350470632314682,
0.009344708174467087,
-0.02213050052523613,
-0.005775954108685255,
-0.023837629705667496,
-0.020781002938747406,
-0.016206571832299232,
-0.02485458180308342,
-0.029950136318802834,
0.03273378312587738,
0.009706051088869572,
-0.028800373896956444,
-0.06732627749443054,
-0.0011750743724405766,
0.05442720651626587,
0.0019083988154307008,
0.023976191878318787,
0.00896933302283287,
-0.03099299967288971,
0.025470498949289322,
-0.012826806865632534,
-0.030136579647660255,
-0.014639888890087605,
-0.025518078356981277,
-0.02445916086435318,
0.05850919336080551,
-0.014024232514202595,
-0.02449425868690014,
0.005463516339659691,
0.013578078709542751,
-0.004475078079849482,
-0.01675475761294365,
0.010855743661522865,
0.00666383421048522,
0.017303837463259697,
-0.009691446088254452,
0.005387244280427694,
-0.036394134163856506,
0.006778211332857609,
0.02420579455792904,
-0.013749809935688972,
0.012655477039515972,
-0.009970735758543015,
-0.025292756035923958,
-0.002020845888182521,
0.04384021461009979,
0.0070733726024627686,
-0.01359121035784483,
-0.00585568742826581,
-0.004580220207571983,
-0.013949141837656498,
0.020566755905747414,
0.02525484934449196,
-0.009430499747395515,
-0.014010706916451454,
-0.030529554933309555,
0.004576155450195074,
-0.024296218529343605,
-0.05090326815843582,
0.011351165361702442,
-0.04802602529525757,
-0.008487751707434654,
-0.005967260338366032,
-0.0012910064542666078,
0.03506603091955185,
0.06777572631835938,
0.006906274706125259,
-0.015190023928880692,
0.023903654888272285,
0.03919254243373871,
0.01610172539949417,
0.002370061818510294,
0.00703368429094553,
-0.017357012256979942,
-0.020550092682242393,
-0.006429243832826614,
-0.035237859934568405,
0.05722110718488693,
-0.004152639769017696,
0.0036871973425149918,
-0.00046852955711074173,
0.03187042102217674,
-0.03414805606007576,
0.028526468202471733,
0.007661718875169754,
-0.06168079003691673,
-0.0020829711575061083,
0.007714715786278248,
0.03291337564587593,
-0.01969403587281704,
-0.0617293119430542,
-0.040732964873313904,
0.012742232531309128,
-0.027057822793722153,
-0.021930353716015816,
-0.02454346790909767,
-0.0015386902960017323,
-0.020862076431512833,
0.004535883665084839,
-0.07040530443191528,
0.07192280888557434,
-0.01663387194275856,
0.015496082603931427,
0.03959266096353531,
-0.020344961434602737,
-0.002363950479775667,
0.03550613299012184,
-0.012528176419436932,
-0.01544708851724863,
0.015031284652650356,
0.0110431257635355,
0.00923021137714386,
0.021558457985520363,
0.023768646642565727,
0.035921093076467514,
0.017267653718590736,
-0.038317639380693436,
-0.037199005484580994,
0.030239393934607506,
-0.034575849771499634,
-0.027867795899510384,
0.04762672632932663,
-0.033024050295352936,
0.05318855866789818,
0.024173947051167488,
0.019213508814573288,
0.037879668176174164,
0.016421595588326454,
-0.032665934413671494,
0.024020304903388023,
0.010594896972179413,
-0.027717895805835724,
-0.004982348531484604,
0.02322617545723915,
0.06740308552980423,
0.011246894486248493,
-0.013137644156813622,
0.03732876479625702,
0.01367791835218668,
-0.02036581188440323,
0.045036014169454575,
-0.011613896116614342,
-0.02894439361989498,
-0.014374236576259136,
0.00924863014370203,
0.005888008512556553,
0.03964942693710327,
0.024690866470336914,
-0.05751844495534897,
0.03779120743274689,
0.022841697558760643,
0.017711898311972618,
-0.09545327723026276,
-0.002836070489138365,
-0.012611165642738342,
0.01922193169593811,
0.06432922929525375,
-0.026566050946712494,
0.05432640761137009,
0.06117360666394234,
-0.04405514895915985,
0.020952431485056877,
-0.03576448932290077,
-0.044174544513225555,
-0.019144324585795403,
0.030510174110531807,
0.010651428252458572,
0.039531271904706955,
0.054849185049533844,
0.015601811930537224,
0.018835976719856262,
0.006942241918295622,
-0.003852071240544319,
-0.023607557639479637,
0.010293119587004185,
0.007833998650312424,
0.015043141320347786,
0.00024066709738690406,
0.07215432822704315,
-0.0349089652299881,
-0.019084040075540543,
0.036130085587501526,
0.01273337658494711,
0.025249386206269264,
-0.047965746372938156,
0.011548581533133984,
0.015660148113965988,
0.0341508649289608,
0.021680692210793495,
-0.032424673438072205,
-0.014004908502101898,
0.0313793309032917,
0.0038704515900462866,
0.03960715979337692,
0.034115634858608246,
-0.02959028258919716,
0.0017819271888583899,
-0.05954672768712044,
-0.03851812705397606,
0.03263978287577629,
-0.00789385475218296,
0.012658522464334965,
0.048516515642404556,
-0.018995478749275208,
0.013949647545814514,
-0.004488363396376371,
-0.019358258694410324,
-0.07988688349723816,
0.017220621928572655,
0.023888254538178444,
0.000492351595312357,
-0.03857240825891495,
-0.039830729365348816,
-0.0116806635633111,
-0.028690379112958908,
0.04092661663889885,
-0.001850720844231546,
-0.03613206371665001,
-0.03752466291189194,
-0.013913844712078571,
0.00022226276632864028,
-0.023690491914749146,
0.01855986751616001,
-0.022078434005379677,
-0.010945925489068031,
0.04464231804013252,
0.03044511377811432,
-0.008148721419274807,
-0.03695689141750336,
-0.024454424157738686,
-0.004652732517570257,
-0.04965671896934509,
0.004449780564755201,
0.028824230656027794,
0.05084558576345444,
-0.045948583632707596,
-0.006705847103148699,
-0.03754185885190964,
-0.03809276223182678,
0.04693806171417236,
-0.04602402076125145,
0.016859546303749084,
-0.026776820421218872,
-0.014113304205238819,
0.01657695882022381,
-0.05941817909479141,
-0.012858507223427296,
-0.02387799695134163,
-0.03667736053466797,
-0.0006503586191684008,
0.01567354053258896,
0.016678962856531143,
-0.05110626295208931,
0.023635420948266983,
0.03310464695096016,
0.02566441521048546,
0.023386089131236076,
-0.02072809264063835,
0.06207556277513504,
-0.00019782276649493724,
0.010641654022037983,
0.052660003304481506,
0.0011337463511154056,
0.019767560064792633,
0.040997013449668884,
-0.01286457572132349,
-0.03031158819794655,
0.04772990942001343,
-0.01987902633845806,
-0.0005739634507335722,
0.004495007451623678,
-0.007564203348010778,
-0.003726580645889044,
-0.019736912101507187,
-0.031246745958924294,
0.07942985743284225,
-0.04025258123874664,
-0.0020806784741580486,
0.04835335537791252,
-0.023172874003648758,
0.02445147931575775,
-0.007871245965361595,
0.02493034489452839,
0.005302040372043848,
-0.0059422217309474945,
0.0019807603675872087,
0.045807112008333206,
0.025373946875333786,
-0.0047856587916612625,
0.034574564546346664,
0.04539390280842781,
-0.015659091994166374,
0.025134604424238205,
-0.029442762956023216,
0.05116283893585205,
-0.043387219309806824,
-0.005481962114572525,
-0.0071833087131381035,
-0.0033691013231873512,
0.0001927684643305838,
0.02328569069504738,
0.003028156468644738,
0.07139372825622559,
-0.02613752894103527,
-0.006757973227649927,
0.004118638578802347,
-0.009694057516753674,
-0.04057900607585907,
-0.0014408889692276716,
0.010234128683805466,
0.031901948153972626,
0.010655446909368038,
0.014513637870550156,
-0.009618200361728668,
0.006484602112323046,
0.04767313972115517,
-0.05264069139957428,
0.030599869787693024,
-0.006542406976222992,
-0.006818902213126421,
0.013079381547868252,
0.00634829793125391,
-0.04647577181458473,
-0.04463762789964676,
0.02254505828022957,
0.03977407515048981,
0.006652113050222397,
-0.006574607454240322,
0.018318772315979004,
-0.014419455081224442,
0.03202741965651512,
-0.03314896300435066,
-0.027933258563280106,
0.00032373249996453524,
0.03486309200525284,
-0.014797265641391277,
-0.01938473805785179
] |
<p>I know it is hard , but can we transfer the charge on a capacitor plate elsewhere? </p> | 4,623 | [
-0.013290397822856903,
0.014590421691536903,
0.02202875353395939,
0.018223945051431656,
0.006257579196244478,
-0.02564917504787445,
-0.03409331291913986,
0.010421538725495338,
0.044771429151296616,
-0.01903722994029522,
0.011532740667462349,
0.05282459408044815,
0.04929729551076889,
0.019000431522727013,
-0.0057174768298864365,
0.023248089477419853,
-0.023458430543541908,
-0.0019471601117402315,
0.0002230764803243801,
-0.02870762348175049,
-0.01839902624487877,
0.03312980383634567,
-0.009115784429013729,
0.019432026892900467,
0.004653346259146929,
-0.004223154857754707,
0.006040020380169153,
-0.0016466820379719138,
0.02610294707119465,
0.059720125049352646,
-0.023654846474528313,
-0.028945662081241608,
0.02946733869612217,
0.021459924057126045,
0.0473870113492012,
-0.007960016839206219,
-0.03713444992899895,
-0.045962702482938766,
-0.014519434422254562,
-0.013185983523726463,
-0.008544603362679482,
-0.015544450841844082,
0.00026502515538595617,
0.028143087401986122,
-0.016807449981570244,
-0.00039249719702638686,
-0.005941391456872225,
-0.000895306933671236,
0.038849905133247375,
-0.0750904455780983,
0.036748919636011124,
-0.02713974565267563,
0.03706948459148407,
0.053939081728458405,
0.008888405747711658,
0.028047028928995132,
0.0796944871544838,
0.06303811073303223,
-0.007652272470295429,
0.009078005328774452,
-0.0356249138712883,
-0.0008313967264257371,
-0.016909604892134666,
-0.01581914909183979,
-0.04191046208143234,
0.008391753770411015,
0.02479488030076027,
-0.01624530367553234,
-0.01679646410048008,
-0.0031401230953633785,
-0.00974972639232874,
0.06046353653073311,
0.02189645916223526,
-0.012838427908718586,
-0.006511721760034561,
-0.031559258699417114,
0.0271008163690567,
0.0013290834613144398,
0.03432304039597511,
0.027617869898676872,
-0.008268085308372974,
0.03555412217974663,
0.05294869840145111,
0.0338917151093483,
0.007939607836306095,
-0.03246276080608368,
0.04681780934333801,
-0.019816549494862556,
0.049981728196144104,
0.03883124515414238,
-0.0011050800094380975,
-0.02422182261943817,
0.022494833916425705,
0.017319001257419586,
-0.033320892602205276,
0.008283741772174835,
0.01196473091840744,
0.04853051155805588,
0.00784003920853138,
-0.00576378870755434,
0.04492223262786865,
0.006356147583574057,
0.02214006707072258,
0.06310728192329407,
0.011484185233712196,
-0.014488527551293373,
-0.01825569197535515,
0.006356872618198395,
0.04236861318349838,
0.0069302902556955814,
-0.10205160826444626,
0.013602259568870068,
0.0005964486044831574,
-0.0023225676268339157,
0.05358868092298508,
-0.03319385647773743,
0.00008641112799523398,
-0.03931339085102081,
0.032929256558418274,
0.047459926456213,
0.02582702971994877,
-0.0003163142246194184,
0.01595183089375496,
-0.0190905574709177,
-0.07867865264415741,
0.056623175740242004,
-0.017821233719587326,
-0.00933778379112482,
-0.015121636912226677,
0.006973815616220236,
0.009625534527003765,
-0.0035627041943371296,
0.001787414657883346,
-0.027210619300603867,
0.022851748391985893,
-0.016845081001520157,
-0.10082188993692398,
-0.05432073771953583,
0.005846602842211723,
0.03523252159357071,
-0.019720008596777916,
-0.053726259618997574,
0.009234845638275146,
0.027525877580046654,
0.04160119220614433,
0.003502714214846492,
-0.014270742423832417,
-0.012030292302370071,
0.0242407638579607,
0.015537858940660954,
0.026751315221190453,
-0.010048327967524529,
-0.007917068898677826,
-0.0339592769742012,
0.012989825569093227,
-0.05660688132047653,
0.017269644886255264,
0.0369328036904335,
0.017748650163412094,
-0.03361159935593605,
0.06577244400978088,
-0.009798739105463028,
0.007869715802371502,
-0.05153186246752739,
-0.00875928346067667,
-0.02241218276321888,
0.08810237795114517,
0.00814132485538721,
-0.01009743195027113,
0.0028514352161437273,
-0.003373913699761033,
0.04193628951907158,
-0.019624171778559685,
0.009094220586121082,
0.04136748984456062,
-0.043231770396232605,
-0.03767893835902214,
-0.033178433775901794,
0.018734579905867577,
-0.01036200113594532,
-0.033443380147218704,
-0.012148743495345116,
0.03096630610525608,
0.017803288996219635,
0.006160899996757507,
0.05144441872835159,
-0.016217654570937157,
-0.026371804997324944,
-0.024444514885544777,
-0.006497635040432215,
-0.032561834901571274,
-0.035732220858335495,
0.039424289017915726,
-0.011789591982960701,
0.002085129963234067,
0.0035307975485920906,
0.0038778656162321568,
0.013516607694327831,
-0.04284008964896202,
-0.029641209170222282,
0.02652493305504322,
0.0032748698722571135,
-0.020956914871931076,
-0.0031773524824529886,
0.029699161648750305,
0.032596707344055176,
0.036049388349056244,
0.019788868725299835,
0.023425858467817307,
-0.023386714980006218,
0.010378958657383919,
-0.014521006494760513,
-0.011759728193283081,
0.022763893008232117,
-0.0017499687382951379,
-0.004772640764713287,
0.02025650069117546,
0.02530800737440586,
-0.02816867269575596,
0.039050690829753876,
-0.00028089131228625774,
0.09690677374601364,
0.05871015042066574,
0.017300693318247795,
-0.0030409935861825943,
0.03327585756778717,
0.018762053921818733,
0.010762344114482403,
-0.005556456744670868,
-0.052021875977516174,
-0.040858812630176544,
-0.015091155655682087,
0.027981113642454147,
0.012091162614524364,
-0.015440652146935463,
0.015589779242873192,
0.026624038815498352,
-0.003367637749761343,
0.027191676199436188,
-0.008351239375770092,
0.0032291929237544537,
-0.010260002687573433,
0.011401092633605003,
-0.015169025398790836,
-0.0042066555470228195,
-0.008760187774896622,
0.020192643627524376,
0.003632843028753996,
0.004229220561683178,
0.012109965085983276,
0.0021082351449877024,
-0.007864098995923996,
0.003145382972434163,
0.04723601043224335,
0.020424453541636467,
-0.06381329894065857,
0.033307138830423355,
-0.04957917705178261,
0.04971792921423912,
0.014837613329291344,
0.028366757556796074,
0.011653482913970947,
0.009843162260949612,
-0.004497569520026445,
0.02480327896773815,
0.0026726440992206335,
-0.004575984086841345,
0.025543782860040665,
0.05003153532743454,
-0.04708780348300934,
0.050167687237262726,
-0.0038725535850971937,
-0.006229648366570473,
0.015176652930676937,
0.003653265768662095,
0.008519752882421017,
0.0001634052605368197,
0.06581289321184158,
-0.04995151609182358,
-0.021514255553483963,
-0.02876102738082409,
-0.01871492713689804,
-0.015660477802157402,
-0.0035729720257222652,
-0.028779946267604828,
0.014522097073495388,
-0.045742690563201904,
-0.03508799150586128,
0.016396479681134224,
0.024785568937659264,
0.0020246112253516912,
-0.006195780821144581,
-0.0170600563287735,
-0.04846863076090813,
0.017367007210850716,
0.002702151658013463,
0.013386144302785397,
-0.05259839445352554,
0.009364958852529526,
0.05605674907565117,
0.025013400241732597,
-0.04371876269578934,
0.007066975813359022,
-0.002559969201683998,
-0.0421152301132679,
0.03490546718239784,
0.01211283914744854,
0.043349627405405045,
-0.041826095432043076,
0.029899178072810173,
-0.009379418566823006,
-0.04848114773631096,
-0.018949972465634346,
-0.004248180892318487,
-0.04994453117251396,
0.01182499434798956,
-0.0035789948888123035,
0.02901322953402996,
-0.012267102487385273,
-0.02505393885076046,
0.05388376861810684,
0.008765455335378647,
-0.030113697052001953,
0.04013988375663757,
-0.05942460522055626,
-0.020364107564091682,
-0.024973344057798386,
-0.042052388191223145,
0.05051485449075699,
-0.016197867691516876,
0.005785278044641018,
0.02324051409959793,
0.01620744913816452,
0.01741272211074829,
0.01973462663590908,
-0.005824564956128597,
-0.004204114433377981,
0.024541333317756653,
-0.026990152895450592,
0.05444052442908287,
-0.03958176448941231,
-0.03079330176115036,
0.015568598173558712,
0.0203374195843935,
0.009638234972953796,
0.015643447637557983,
-0.011404606513679028,
0.04946320876479149,
-0.007330603897571564,
0.01307126134634018,
-0.03525940328836441,
0.025793442502617836,
0.02170446328818798,
0.013533055782318115,
-0.002647818299010396,
0.051591288298368454,
0.08756893873214722,
-0.015409975312650204,
-0.001957372296601534,
0.06600863486528397,
0.04791264981031418,
-0.030806679278612137,
-0.03193936124444008,
-0.0004220216360408813,
0.011204351671040058,
0.02475045807659626,
0.025829961523413658,
-0.0363713800907135,
0.0336703322827816,
0.004398683551698923,
0.015213869512081146,
0.0356208011507988,
-0.016625676304101944,
0.006364230997860432,
-0.05765112489461899,
0.0153457997366786,
-0.0027507857885211706,
0.024491632357239723,
0.020817382261157036,
0.05190114676952362,
0.0607488676905632,
-0.009045313112437725,
-0.025883104652166367,
0.01543833315372467,
-0.07007168978452682,
-0.005710958037525415,
0.011629518121480942,
0.0004887286340817809,
-0.024940282106399536,
-0.01453343778848648,
0.0005350120482034981,
-0.00445174565538764,
0.0006787432357668877,
-0.031231462955474854,
-0.02088724449276924,
-0.06777116656303406,
0.011282047256827354,
-0.0014510543551295996,
-0.04728437587618828,
-0.030672365799546242,
0.006449359003454447,
0.020660147070884705,
-0.009348777122795582,
-0.011147134937345982,
0.024272488430142403,
-0.037825070321559906,
-0.01781371422111988,
0.0014815160539001226,
0.0015493846731260419,
-0.007574663497507572,
0.03165915980935097,
0.015087727457284927,
0.026508435606956482,
-0.025863399729132652,
-0.01056022010743618,
-0.01014806516468525,
0.05483026057481766,
0.013952231034636497,
-0.04806201905012131,
-0.029273828491568565,
-0.056309234350919724,
-0.03540151193737984,
-0.0021345734130591154,
0.06934758275747299,
-0.02949575148522854,
0.005650512408465147,
0.0058686379343271255,
-0.019207747653126717,
-0.03275304660201073,
0.017568087205290794,
0.061944298446178436,
0.03016333095729351,
-0.01703052408993244,
-0.08107708394527435,
-0.0325617790222168,
-0.0029126496519893408,
0.0035072334576398134,
0.03852659463882446,
0.01423860713839531,
-0.029236186295747757,
-0.013010547496378422,
0.01640184223651886,
0.017049193382263184,
0.0019188857404515147,
0.007997858338057995,
-0.007372333202511072,
0.00862538069486618,
-0.005131109151989222,
0.01640012115240097,
-0.012374022975564003,
-0.01567874103784561,
0.05132368952035904,
0.01708706095814705,
-0.01248822920024395,
-0.08441203087568283,
0.009097792208194733,
0.037056636065244675,
0.05217566341161728,
-0.012670322321355343,
-0.020661525428295135,
-0.0635250136256218,
-0.04825722426176071,
0.050341133028268814,
-0.035378411412239075,
0.012842042371630669,
-0.03884771093726158,
-0.0004803553456440568,
-0.009458692744374275,
-0.039890214800834656,
-0.013695180416107178,
0.0428425669670105,
-0.02569631114602089,
0.02041846327483654,
-0.02448180504143238,
-0.003370599588379264,
-0.0037956442683935165,
0.012935489416122437,
0.06811597943305969,
0.12105224281549454,
0.023887023329734802,
0.0019253853242844343,
-0.039033934473991394,
0.0052846018224954605,
-0.05636809766292572,
-0.0699051097035408,
-0.011377180926501751,
-0.009251604788005352,
-0.02123413421213627,
0.027405111119151115,
-0.009310602210462093,
-0.04487643018364906,
0.0036997690331190825,
-0.005996245425194502,
0.005229214206337929,
0.004901550244539976,
-0.007641134317964315,
0.034252677112817764,
0.05553948134183884,
0.005514293443411589,
0.07967658340930939,
0.02713467739522457,
-0.041229624301195145,
0.012590375728905201,
0.0037837554700672626,
0.03639867156744003,
-0.031874269247055054,
-0.019218578934669495,
0.008630474098026752,
0.014146971516311169,
-0.02825615368783474,
0.031308773905038834,
0.016739621758461,
0.021881576627492905,
-0.007505656685680151,
-0.051583997905254364,
-0.007040949538350105,
0.015899017453193665,
-0.015898868441581726,
0.019148368388414383,
-0.03225082531571388,
0.027534767985343933,
0.011756114661693573,
-0.04077562317252159,
-0.0038882801309227943,
0.004028522875159979,
0.007348279468715191,
0.0103845139965415,
0.0070890807546675205,
-0.006900773383677006,
-0.07204951345920563,
0.00508895656093955,
-0.02900887280702591,
-0.028126021847128868,
0.0698435828089714,
-0.011148600839078426,
0.00009919206058839336,
0.009163948707282543,
-0.09036288410425186,
-0.05925820767879486,
0.055475473403930664,
-0.008365907706320286,
0.009344375692307949,
-0.07365146279335022,
0.040613073855638504,
0.0006700663361698389,
0.00461623864248395,
-0.06527480483055115,
-0.06138312816619873,
-0.0049619534984230995,
0.05555391311645508,
0.013712762854993343,
-0.03204498812556267,
-0.026895876973867416,
-0.007641457486897707,
-0.02696305513381958,
-0.01986604742705822,
0.013498830609023571,
-0.018623894080519676,
0.005293581634759903,
0.029334794729948044,
-0.038266122341156006,
0.07714404165744781,
-0.0001384779898216948,
0.027482954785227776,
0.01891438476741314,
-0.027070285752415657,
-0.028126554563641548,
-0.0460224412381649,
0.026618165895342827,
-0.0379689522087574,
-0.015095147304236889,
0.006566065829247236,
-0.016772542148828506,
0.032111357897520065,
-0.03366265445947647,
-0.04035082459449768,
0.0415332093834877,
0.006641896441578865,
-0.045383255928754807,
0.002591060008853674,
0.040670786052942276,
0.020433008670806885,
-0.0034339972771704197,
0.0074234334751963615,
0.011482153087854385,
-0.05405807122588158,
0.002192608080804348,
-0.018981091678142548,
0.004423064645379782,
0.022954247891902924,
0.001815736060962081,
0.0498187318444252,
-0.02524692192673683,
-0.019745206460356712,
0.07640863209962845,
0.0012888959608972073,
0.0537576898932457,
-0.01725379005074501,
-0.0005033785128034651,
-0.011703438125550747,
-0.008277623914182186,
-0.029300905764102936,
-0.0007250996422953904,
-0.024964364245533943,
-0.02806027978658676,
0.04411351680755615,
0.02625652402639389,
0.07029438018798828,
-0.01904642954468727,
0.003705937648192048,
-0.02132156305015087,
0.009801235049962997,
-0.008983509615063667,
0.012525591067969799,
-0.01607859507203102,
0.026134947314858437,
0.012996640987694263,
0.004590226802974939,
-0.014353794977068901,
0.06964676827192307,
0.008004693314433098,
-0.012314869090914726,
0.015719788148999214,
0.035899028182029724,
0.07157709449529648,
-0.03505543991923332,
-0.05329589545726776,
0.008908862248063087,
-0.055458396673202515,
0.0060191466473042965,
-0.026214390993118286,
-0.07490692287683487,
0.05878445506095886,
-0.006201047450304031,
-0.00598876690492034,
-0.02810453064739704,
-0.03132815659046173,
-0.01988150365650654,
0.006209318991750479,
-0.013498305343091488,
0.0414636991918087,
-0.013334368355572224,
-0.004543666262179613,
0.0513232983648777,
-0.011210883036255836,
0.013128546997904778,
-0.04948481544852257,
-0.08953547477722168,
-0.03683655336499214,
-0.03397627919912338,
-0.00843201857060194,
0.06626982241868973,
0.003532836213707924,
-0.03077278845012188,
0.019853942096233368,
-0.016067180782556534,
0.033725544810295105,
0.004168910440057516,
0.03526047617197037,
-0.023756150156259537,
0.05062238872051239,
-0.012890517711639404,
0.017772672697901726,
-0.028992705047130585,
0.014570998027920723,
0.13627120852470398,
0.037712372839450836,
0.015827197581529617,
-0.05822204425930977,
-0.0007872051210142672,
-0.05716301500797272,
0.0030450704507529736,
-0.051587752997875214,
0.02178877964615822,
-0.028332537040114403,
-0.012277577072381973,
0.019233860075473785,
0.06317681074142456,
0.028367789462208748,
0.04949631169438362,
0.045121800154447556,
-0.02996058762073517,
-0.01804513670504093,
0.020400410518050194,
0.009965760633349419,
0.0001842870842665434,
0.03193579614162445,
-0.036934904754161835,
0.029380250722169876,
-0.05535489693284035,
-0.006296616513282061,
-0.020053187385201454,
-0.018012695014476776,
0.04829322546720505,
-0.0055795335210859776,
0.002652374329045415,
-0.02310410514473915,
0.020896274596452713,
-0.028702644631266594,
-0.020257242023944855,
0.026799539104104042,
0.03156358003616333,
0.00772131746634841,
-0.00020780385239049792,
0.015936164185404778,
0.033438630402088165,
0.005059928633272648,
0.008980012498795986,
-0.0011860181111842394,
-0.025220157578587532,
0.002403469057753682,
-0.024330604821443558,
0.01747019775211811,
-0.021167367696762085,
0.012368562631309032,
0.023108165711164474,
0.011193626560270786,
0.010677929036319256,
-0.05909884721040726,
-0.04786992073059082,
0.023290123790502548,
0.011505994945764542,
0.03981587290763855,
0.01762346364557743,
-0.03291817381978035,
0.04608380049467087,
-0.005214396398514509,
-0.04090138524770737,
-0.00606768811121583,
0.0008332919096574187,
0.017818760126829147,
0.022390179336071014,
0.013671993277966976,
0.0038248368073254824,
-0.054667286574840546,
-0.02720249816775322,
-0.002946015913039446,
-0.030052412301301956,
-0.026502419263124466,
-0.020596619695425034,
0.04310113564133644,
0.007378484588116407,
-0.011594322510063648,
0.009755481965839863,
-0.007819458842277527,
-0.0692458227276802,
0.031267616897821426,
0.017718974500894547,
0.004323961213231087,
-0.026845188811421394,
0.005392804741859436,
0.017147457227110863,
0.07512635737657547,
0.0018844562582671642,
-0.020650384947657585,
-0.010929467156529427,
0.028904112055897713,
0.012606936506927013,
-0.04485054686665535,
-0.030050694942474365,
0.005523997358977795,
-0.06751027703285217,
0.022201983258128166,
-0.023339351639151573,
0.016219334676861763,
0.00817935075610876,
-0.002127966843545437,
0.010505001991987228,
0.011578666046261787,
-0.035701725631952286,
0.02704300545156002,
0.05357496067881584,
-0.012844685465097427,
-0.017036689445376396,
-0.03798715025186539,
0.00986605416983366,
0.015779072418808937,
-0.018462106585502625,
-0.017374200746417046,
0.003384367795661092,
-0.01676536723971367,
0.0316944420337677,
-0.021166451275348663,
-0.0063199871219694614,
-0.03915128856897354,
0.009921528398990631,
-0.035680852830410004,
-0.00693130400031805,
-0.04248032718896866,
-0.02357933297753334,
0.004165836609899998,
-0.010405024513602257,
-0.005228185560554266,
0.021209532395005226,
-0.03474455699324608,
0.031038764864206314,
0.007223213091492653,
0.01875237748026848,
-0.01584058254957199,
0.005549540277570486,
-0.009949171915650368,
0.027943940833210945,
0.030132723972201347,
-0.06103438884019852,
-0.0010654284851625562,
0.07084692269563675,
-0.035315003246068954,
-0.026273246854543686,
-0.02823328971862793,
-0.011788821779191494,
0.030835790559649467,
0.03717757388949394,
-0.013394969515502453,
0.001865284750238061,
0.047330498695373535,
0.0070513030514121056,
-0.04184176027774811,
0.009313809685409069,
-0.021425623446702957,
-0.003432798432186246,
0.02901817485690117,
0.03314216434955597,
-0.043482016772031784,
0.003643751610070467,
0.02841341681778431,
-0.014660126529633999,
0.02316153235733509,
0.002595350844785571,
-0.010456768795847893,
-0.009918195195496082,
0.013328874483704567,
0.030533120036125183,
-0.0035608394537121058,
0.012636927887797356,
0.0538470484316349,
-0.0465603806078434,
0.012908115051686764,
0.03272121772170067,
-0.015298868529498577,
-0.0641646757721901,
-0.041104041039943695,
0.020189492031931877,
-0.017961472272872925,
0.03669990971684456,
-0.02629888616502285,
0.038835979998111725,
-0.0020617092959582806,
-0.10659812390804291,
0.009727167896926403,
-0.02818763628602028,
-0.029903054237365723,
-0.02228798158466816,
0.03309483081102371,
-0.028259916231036186,
0.040784403681755066,
0.0025211437605321407,
0.05565812811255455,
0.003373038489371538,
0.0227240938693285,
0.02495959959924221,
-0.036349136382341385,
-0.033757638186216354,
0.021532241255044937,
0.016078952699899673,
0.008846206590533257,
0.0695977434515953,
-0.053840648382902145,
-0.018358005210757256,
0.0027669728733599186,
-0.009656894952058792,
-0.02860531397163868,
-0.018477121368050575,
0.006780859548598528,
0.016764109954237938,
0.028960328549146652,
-0.011470530182123184,
-0.03432280197739601,
-0.04800410568714142,
-0.01579977571964264,
0.024027863517403603,
0.025423618033528328,
-0.007078150752931833,
0.026208924129605293,
0.03192375600337982,
-0.002786376280710101,
-0.013495655730366707,
-0.01075825747102499,
-0.046680789440870285,
-0.040524665266275406,
0.01234422717243433,
0.029250124469399452,
0.05159779638051987,
-0.01692161150276661,
-0.012783982791006565,
-0.040284208953380585,
-0.00983914639800787,
0.016935762017965317,
-0.004544888157397509,
0.01762809045612812,
0.006552115548402071,
-0.007412900682538748,
-0.007427738048136234,
0.01891719549894333,
0.04305015131831169,
-0.012080946937203407,
-0.041086725890636444,
-0.0033848390448838472,
0.0028523195069283247,
0.023194048553705215,
0.0012235295725986362,
-0.0640544444322586,
-0.021739332005381584,
0.023006843402981758,
-0.006313761230558157,
0.04348168149590492,
0.0053801992908120155,
-0.03959070146083832,
0.0052861706353724,
-0.0507817417383194,
0.03075527586042881,
0.009987509809434414,
-0.00647707050666213,
-0.0043223886750638485,
-0.06003319099545479,
-0.007304197642952204,
0.00923997350037098,
0.0905844196677208,
-0.02247755415737629,
0.007104129996150732,
0.013682776130735874,
-0.0295142512768507,
0.011290076188743114,
-0.06973971426486969,
0.033939775079488754,
0.0314660370349884,
-0.021158885210752487,
0.006661581341177225,
-0.004545840434730053,
-0.03130592033267021,
0.0026258868165314198,
0.023416895419359207,
0.010147136636078358,
0.0049731372855603695,
-0.03435112163424492,
0.0013001087354496121,
0.016767218708992004,
0.013717097230255604,
-0.010906740091741085,
0.07971705496311188,
0.010939588770270348,
0.007742319721728563,
-0.0006634842720814049,
-0.028672337532043457,
-0.005106716882437468,
0.007547460496425629,
-0.06475283205509186,
0.009367860853672028,
-0.06464482843875885,
0.027097979560494423,
0.011885838583111763,
-0.06664412468671799,
-0.0011615216499194503,
0.01917974278330803,
-0.03705981746315956,
-0.020503588020801544,
0.06319432705640793,
0.006322335917502642,
0.01475949864834547,
0.04247426986694336,
-0.012213618494570255,
-0.039931345731019974,
0.02052215114235878,
0.011958440765738487,
0.022319594398140907,
0.02112702652812004,
-0.021728280931711197,
0.02314816042780876,
0.051008254289627075,
0.007438084576278925,
-0.008293772116303444,
0.014450841583311558,
0.023675473406910896,
-0.023794114589691162,
-0.020419660955667496,
0.010133405216038227,
-0.01970587857067585,
-0.009930765256285667,
0.0106428861618042,
-0.038415588438510895,
0.08740513771772385,
-0.015886293724179268,
-0.004933994263410568,
0.015433085151016712,
0.030483929440379143,
0.017892085015773773,
0.013718144968152046,
-0.010299883782863617,
0.024405861273407936,
-0.015086875297129154,
-0.02527676336467266,
-0.01911134086549282,
0.022842789068818092,
0.004775294102728367,
-0.030500292778015137,
0.016881147399544716,
-0.011898543685674667,
0.029901381582021713,
-0.019394714385271072,
0.01744309440255165,
-0.03712158650159836,
-0.010580305941402912,
-0.00877273641526699,
0.031051190569996834,
0.00862972717732191,
0.015822630375623703,
-0.0015095239505171776,
0.012967592105269432,
0.021938012912869453,
-0.059228360652923584,
-0.00932228472083807,
0.0068815965205430984,
0.023068591952323914,
-0.005877446848899126,
0.041188087314367294
] |
<p>The usual "proof" entropy is a state property is like that:</p>
<p>"Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, which is also reversible. Since the cycle is reversible we can write: </p>
<p>$$\int_1^2 \delta Q / T + \int_2^1 \delta Q / T = 0 $$</p>
<p>Now let cycle be completed along path C, but paths B and C represent arbitrary reversible processes. So $\int_2^1 \delta Q / T $ is the same for all reversible paths between states 2 and 1."</p>
<p>My question is, isn't the equation above already assume entropy is a state property? Only if it is a state property it can go around a cycle without changes. How can it be valid to prove entropy is state property if it is already assumed from the beginning?</p> | 4,624 | [
-0.007844211533665657,
-0.004083590116351843,
-0.006064345128834248,
0.026701582595705986,
0.036946505308151245,
-0.029319677501916885,
0.00046148308319970965,
0.026384670287370682,
-0.021481581032276154,
0.007397305686026812,
0.013850311748683453,
0.012510284781455994,
0.03957151621580124,
-0.01267920434474945,
0.03177923709154129,
-0.013595929369330406,
-0.028239235281944275,
0.016940554603934288,
-0.019110191613435745,
-0.01597369834780693,
0.0021262585651129484,
0.02853427082300186,
0.004899914376437664,
-0.007538480684161186,
-0.004608916584402323,
0.04074718430638313,
-0.002042060950770974,
0.0132805947214365,
0.029161246493458748,
0.05281359329819679,
0.009963718242943287,
-0.03617248311638832,
0.008803498931229115,
0.053302984684705734,
0.003937195520848036,
-0.017286939546465874,
-0.03657915070652962,
0.002105278894305229,
0.011128254234790802,
0.020452747121453285,
-0.04033414646983147,
-0.010437541641294956,
-0.003529229201376438,
0.03683296963572502,
-0.021035339683294296,
0.022604161873459816,
0.023142145946621895,
0.023357395082712173,
0.04198547452688217,
-0.046201467514038086,
0.0633147805929184,
-0.003417513333261013,
0.05971788242459297,
0.04356672987341881,
-0.005894648842513561,
0.0008452496840618551,
0.07160443812608719,
0.07662243396043777,
-0.016771893948316574,
-0.02452923357486725,
-0.059804342687129974,
-0.02160746231675148,
0.015833253040909767,
-0.009992895647883415,
-0.052766039967536926,
0.0015763656701892614,
0.029859457165002823,
0.00715440372005105,
0.029226193204522133,
-0.0139279430732131,
-0.04329822584986687,
-0.02307068184018135,
0.03660176694393158,
0.008316193707287312,
0.001284771366044879,
-0.017776459455490112,
0.02349713444709778,
0.009868442080914974,
0.01846369355916977,
0.06071082502603531,
-0.01981823705136776,
0.009259557351469994,
0.008760569617152214,
0.031077619642019272,
-0.005218101665377617,
-0.01738576404750347,
0.07248988747596741,
-0.0040008858777582645,
0.013004771433770657,
0.03942732885479927,
-0.000053951083827996626,
-0.0029950703028589487,
0.00453580729663372,
-0.028444278985261917,
-0.009821226820349693,
0.02210485190153122,
-0.024947762489318848,
0.03852320834994316,
-0.014158596284687519,
-0.03670237958431244,
-0.013429686427116394,
-0.03938358277082443,
0.04915087670087814,
0.04202742874622345,
-0.011914757080376148,
0.004199642688035965,
-0.04365013167262077,
0.040849801152944565,
0.0026270842645317316,
0.010767283849418163,
-0.0600590743124485,
0.0037933948915451765,
0.027133863419294357,
-0.006392315961420536,
-0.0043008760549128056,
-0.008557770401239395,
-0.04533014073967934,
-0.0129005778580904,
0.023131554946303368,
0.05072559788823128,
0.060040030628442764,
-0.012103972025215626,
0.011280257254838943,
-0.03852592408657074,
-0.04427146166563034,
0.049121126532554626,
0.03274936601519585,
-0.017692090943455696,
-0.024307720363140106,
0.0007110870210453868,
0.0032750682439655066,
-0.011729715391993523,
-0.01439504325389862,
0.03072291985154152,
0.04604969173669815,
-0.030576298013329506,
-0.1105089783668518,
-0.05746551230549812,
0.03408365696668625,
0.008033949881792068,
-0.02428317256271839,
-0.06348372995853424,
0.03214371204376221,
0.0524752214550972,
0.0937173143029213,
-0.0304317194968462,
0.026398563757538795,
0.024072522297501564,
0.010159210301935673,
0.02288113348186016,
-0.025479799136519432,
-0.028110040351748466,
-0.0014310686383396387,
-0.02273334190249443,
0.00789004284888506,
-0.03614482283592224,
0.029030153527855873,
0.03281446546316147,
-0.03769997879862785,
-0.026834815740585327,
0.03644093871116638,
-0.024041544646024704,
0.00008474480273434892,
0.0069899060763418674,
0.00893669668585062,
-0.026806728914380074,
0.09586672484874725,
0.005635042674839497,
0.008081612177193165,
0.029563356190919876,
0.05609484016895294,
-0.0060761370696127415,
-0.02575930766761303,
0.031424034386873245,
0.06137004867196083,
-0.06851908564567566,
-0.06249143183231354,
-0.017590215429663658,
-0.038635365664958954,
0.02583562768995762,
-0.005061031319200993,
-0.029339410364627838,
-0.02005133591592312,
0.03241860494017601,
0.012064357288181782,
-0.015953194350004196,
0.0025843316689133644,
0.010470724664628506,
0.03433091193437576,
-0.05059279501438141,
-0.01470485981553793,
-0.04827431961894035,
0.03550560772418976,
0.013497577048838139,
-0.02061116136610508,
0.002541853580623865,
0.0013651809422299266,
0.04302631691098213,
-0.026334229856729507,
-0.019862167537212372,
-0.03019406460225582,
0.025828320533037186,
-0.014768208377063274,
-0.034824762493371964,
0.024963848292827606,
0.03113630786538124,
0.08072775602340698,
-0.014061255380511284,
0.04896837845444679,
-0.013353441841900349,
-0.029115715995430946,
0.017259282991290092,
0.006073468830436468,
0.01278768852353096,
-0.005628345999866724,
-0.0204970370978117,
0.013349221087992191,
0.01274960394948721,
-0.015626726672053337,
0.041680142283439636,
-0.03999394550919533,
0.055871132761240005,
0.05363169312477112,
0.038850847631692886,
-0.011751164682209492,
0.032383084297180176,
0.012022110633552074,
0.020555848255753517,
-0.03363914415240288,
-0.03904414921998978,
-0.03770698606967926,
-0.016038546338677406,
-0.0006159435142762959,
0.018037976697087288,
-0.041596073657274246,
-0.03432178869843483,
0.020245671272277832,
0.05182674899697304,
-0.0036012863274663687,
0.02298126369714737,
0.025419220328330994,
-0.022046653553843498,
0.025623654946684837,
-0.006296051200479269,
0.013407424092292786,
0.0006426720647141337,
0.012841927818953991,
-0.042647793889045715,
0.001168950810097158,
0.03352321311831474,
-0.02158181555569172,
0.01463630236685276,
-0.01045188121497631,
0.014707584865391254,
0.01093250885605812,
0.007834432646632195,
0.037004292011260986,
-0.0036766198463737965,
0.01293120626360178,
0.02123410254716873,
0.0013040951453149319,
0.005457291379570961,
-0.04077206179499626,
0.0016904691001400352,
0.0036705820821225643,
-0.0026087432634085417,
-0.020007317885756493,
-0.029807282611727715,
0.022563602775335312,
0.004031676333397627,
0.0014502122066915035,
0.008013163693249226,
-0.011629101820290089,
-0.05077718198299408,
0.0213867649435997,
0.04511191323399544,
-0.024639809504151344,
0.008896583691239357,
-0.056672077625989914,
-0.027140773832798004,
0.0033845549914985895,
0.015342318452894688,
0.0120412427932024,
0.02779216878116131,
-0.053493939340114594,
0.026284493505954742,
-0.005951911211013794,
-0.04463900998234749,
0.054502569139003754,
-0.019868141040205956,
0.020285556092858315,
-0.025263408198952675,
-0.02534383349120617,
-0.048423223197460175,
0.001983964117243886,
-0.05018243193626404,
0.030733542516827583,
-0.036819398403167725,
-0.009730683639645576,
0.03921850770711899,
0.009100264869630337,
-0.05277707800269127,
0.02403322421014309,
-0.03497592732310295,
-0.04959282651543617,
0.0023182262666523457,
-0.041771434247493744,
0.03021632879972458,
-0.033442117273807526,
0.055874135345220566,
0.026699040085077286,
-0.05856414511799812,
-0.03663299232721329,
-0.04508206248283386,
-0.07947954535484314,
0.02165590226650238,
0.004310490097850561,
0.03357813507318497,
-0.012395189143717289,
-0.04207850620150566,
0.053121861070394516,
0.040047429502010345,
-0.03195550665259361,
0.01788598671555519,
-0.020227806642651558,
0.007183382287621498,
-0.053857769817113876,
-0.018623990938067436,
0.003118070773780346,
-0.019421063363552094,
0.06833747029304504,
-0.014552104286849499,
0.04366905987262726,
0.025034688413143158,
0.0010221186093986034,
-0.038487017154693604,
0.031533680856227875,
0.02353610284626484,
0.03482355549931526,
0.004548370838165283,
0.009430374018847942,
0.0002894258941523731,
0.010141991078853607,
-0.015047047287225723,
0.045728351920843124,
0.019435109570622444,
-0.0403514988720417,
0.06885974854230881,
0.019087327644228935,
0.03983374685049057,
-0.06589578092098236,
0.027297353371977806,
-0.03797347843647003,
-0.0009294363553635776,
0.015122486278414726,
0.022446095943450928,
0.04053741320967674,
0.026891646906733513,
0.016191143542528152,
-0.011641058139503002,
0.003043776610866189,
-0.03528960421681404,
-0.010932015255093575,
-0.017957424744963646,
-0.027112778276205063,
0.029285483062267303,
0.008399114944040775,
-0.018029699102044106,
0.04828223958611488,
0.02123185247182846,
0.007390248589217663,
-0.0187294390052557,
-0.026827238500118256,
-0.015038521029055119,
-0.08133424818515778,
-0.03554147481918335,
0.0008722692145965993,
0.03322027251124382,
-0.0046104672364890575,
0.04829176142811775,
0.02599339559674263,
-0.0003939836460631341,
0.018788335844874382,
-0.0035678765270859003,
-0.10024619102478027,
0.026442082598805428,
-0.026389528065919876,
-0.028301840648055077,
0.030600987374782562,
-0.0073693906888365746,
0.05112644284963608,
-0.02794594317674637,
-0.05448349937796593,
-0.03582204878330231,
-0.007176377344876528,
-0.05906517431139946,
-0.03391575813293457,
-0.0219974797219038,
-0.029653314501047134,
0.00500465277582407,
0.04317884519696236,
0.04366687685251236,
-0.04834714159369469,
0.003222683211788535,
0.04703158140182495,
-0.04025360569357872,
0.002011145232245326,
-0.016445722430944443,
0.01564938761293888,
0.030192334204912186,
0.019223878160119057,
0.07800421118736267,
0.00522560253739357,
0.027002111077308655,
0.011924857273697853,
-0.008565432392060757,
0.04570373520255089,
-0.006875934079289436,
-0.04239669442176819,
0.002388032153248787,
-0.05294221639633179,
-0.021438000723719597,
0.013584201224148273,
0.054573915898799896,
0.019694412127137184,
0.04357391223311424,
0.008506398648023605,
0.021009717136621475,
-0.01917312853038311,
0.03712425008416176,
0.04174948111176491,
-0.02952316217124462,
-0.019193880259990692,
-0.0007955294568091631,
-0.02083040028810501,
-0.046094704419374466,
-0.04323117807507515,
0.025426654145121574,
-0.022578667849302292,
-0.038938988000154495,
0.020789066329598427,
-0.021249225363135338,
0.012307198718190193,
-0.005874068010598421,
0.002089589601382613,
-0.007636867463588715,
0.0227008406072855,
0.0257984958589077,
-0.009204321540892124,
0.024112986400723457,
0.015215250663459301,
-0.019817782565951347,
0.02432607114315033,
-0.0019755165558308363,
-0.0420774444937706,
-0.010117115452885628,
0.02965674363076687,
0.006371689960360527,
-0.014190246351063251,
-0.012127134017646313,
-0.05194004997611046,
-0.05594940483570099,
0.03258296102285385,
0.0286067184060812,
0.03312560170888901,
-0.006828384008258581,
-0.010410716757178307,
-0.00395426107570529,
-0.04741308465600014,
0.006538502871990204,
0.02035992220044136,
0.02082725800573826,
0.01261703111231327,
0.018742792308330536,
0.008232411928474903,
-0.039432037621736526,
-0.03381670266389847,
0.014915145933628082,
0.07501067221164703,
-0.05323156714439392,
-0.00592007115483284,
-0.003625215031206608,
0.06012307107448578,
-0.029585523530840874,
-0.06841164082288742,
0.016377435997128487,
-0.029174383729696274,
0.02065187692642212,
0.0021448282059282064,
-0.024807317182421684,
-0.05132726952433586,
0.034592676907777786,
0.006289670243859291,
-0.021157002076506615,
0.027340762317180634,
0.003946486860513687,
0.057345714420080185,
0.03079622983932495,
-0.002187049947679043,
0.0193642508238554,
0.07214923202991486,
0.0214200671762228,
0.00399367930367589,
-0.0001966250711120665,
0.03417520597577095,
-0.04500829800963402,
-0.008249948732554913,
-0.07138542830944061,
0.023666365072131157,
-0.017451204359531403,
0.03243568167090416,
0.02658805064857006,
0.014339673332870007,
-0.00029838280170224607,
-0.042617253959178925,
-0.0028191632591187954,
0.025024814531207085,
0.03883545100688934,
0.023121284320950508,
0.0001949592842720449,
0.0304364413022995,
0.017235029488801956,
-0.02697533369064331,
0.018942205235362053,
-0.03629031032323837,
-0.01711166650056839,
0.025568518787622452,
0.026766663417220116,
0.019215766340494156,
-0.05093817412853241,
-0.033253878355026245,
-0.027642013505101204,
-0.000696154369506985,
0.030257850885391235,
-0.027955463156104088,
-0.008540692739188671,
0.009520111605525017,
-0.030122295022010803,
-0.007083958014845848,
0.01356007345020771,
-0.017865236848592758,
-0.018085533753037453,
-0.04869493469595909,
0.013065127655863762,
0.034151241183280945,
-0.02136775106191635,
-0.09470702707767487,
-0.06351881474256516,
0.014103025197982788,
-0.02085104212164879,
-0.036020901054143906,
-0.023171018809080124,
0.023522719740867615,
-0.04776616394519806,
-0.01822512596845627,
-0.010742554441094398,
0.03250942379236221,
0.005185065325349569,
-0.0011707980884239078,
0.062176577746868134,
0.04621722176671028,
0.040098413825035095,
0.017330501228570938,
-0.016545189544558525,
-0.01883598230779171,
-0.03972974047064781,
-0.00704485597088933,
0.030799582600593567,
0.023678889498114586,
-0.03561780974268913,
-0.0016512940637767315,
-0.01597977802157402,
0.0027926689945161343,
0.035891033709049225,
-0.0032387706451117992,
-0.01425520796328783,
0.001511697773821652,
-0.022613659501075745,
-0.014455941505730152,
-0.027257245033979416,
0.002238090382888913,
-0.0033946181647479534,
0.009800903499126434,
-0.006359500344842672,
0.008893617428839207,
-0.008242478594183922,
-0.03700421378016472,
-0.0009541670442558825,
-0.004547847434878349,
-0.020814446732401848,
0.0005238693556748331,
0.06895926594734192,
0.004223030526190996,
-0.0023836600594222546,
-0.013325341045856476,
-0.011187543161213398,
0.022601066157221794,
-0.013070207089185715,
0.013843015767633915,
-0.0053950585424900055,
-0.012556414119899273,
-0.03476440906524658,
-0.012420720420777798,
-0.06347937136888504,
0.017443766817450523,
0.044068120419979095,
-0.026300009340047836,
0.03516800329089165,
0.011055600829422474,
0.02253653109073639,
0.007877671159803867,
-0.023799439892172813,
-0.01810331642627716,
0.013980901800096035,
-0.0193647351115942,
0.05416731536388397,
-0.023196730762720108,
-0.017727382481098175,
0.037601277232170105,
0.037170689553022385,
-0.042505428194999695,
-0.015979111194610596,
0.01668684557080269,
-0.010517905466258526,
0.031385794281959534,
0.012269198894500732,
-0.007644395809620619,
0.0362764373421669,
-0.029011022299528122,
0.010295149870216846,
-0.009944341145455837,
0.0031828719656914473,
0.05211782455444336,
-0.02625337988138199,
-0.036243949085474014,
-0.021466350182890892,
-0.01397884450852871,
-0.028166217729449272,
0.02268599160015583,
0.0009845064487308264,
0.032539382576942444,
0.054807599633932114,
-0.019618647173047066,
0.01949705183506012,
0.004247336182743311,
0.011172564700245857,
0.011482340283691883,
-0.045850206166505814,
-0.034811634570360184,
-0.021597398445010185,
-0.03670427203178406,
0.00006765676516806707,
0.012962240725755692,
-0.015110314823687077,
-0.014856119640171528,
-0.020501792430877686,
0.0027844563592225313,
0.05182488635182381,
0.034110963344573975,
-0.009812360629439354,
0.08045442402362823,
-0.002283330075442791,
0.03045051544904709,
-0.03037079982459545,
-0.008857592940330505,
0.08972090482711792,
0.045649416744709015,
-0.0009320417884737253,
-0.07315946370363235,
0.030296340584754944,
0.027778904885053635,
0.02993718348443508,
-0.021604973822832108,
0.06752465665340424,
0.029472922906279564,
-0.010017570108175278,
0.0031883209012448788,
0.025516202673316002,
-0.0027099859435111284,
0.01072721742093563,
0.050763677805662155,
-0.052596405148506165,
-0.03285672888159752,
0.013116182759404182,
0.006311363540589809,
-0.03161138296127319,
0.011509513482451439,
-0.027632368728518486,
-0.019927872344851494,
-0.01849045790731907,
-0.0015691748121753335,
0.00043572814320214093,
-0.038974251598119736,
-0.0012991380644962192,
0.03015868365764618,
-0.02650163136422634,
0.02701643854379654,
0.046790819615125656,
-0.010693410411477089,
-0.028117824345827103,
0.008204867132008076,
0.01999129354953766,
0.0136026069521904,
0.04172743856906891,
0.04479585960507393,
0.03737308457493782,
0.011419106274843216,
-0.006005780305713415,
0.028511976823210716,
-0.04968910291790962,
-0.025802483782172203,
-0.036019254475831985,
0.05710602551698685,
-0.02390359155833721,
0.0022290023043751717,
-0.018608463928103447,
-0.020034445449709892,
-0.019780436530709267,
-0.06400176882743835,
0.0008514397777616978,
-0.01818237639963627,
0.03648857772350311,
0.01024533249437809,
-0.012989426031708717,
-0.04088317230343819,
-0.004674453753978014,
0.004304579459130764,
0.025254251435399055,
-0.017987210303544998,
-0.044411551207304,
0.016432613134384155,
-0.0023155398666858673,
0.031156489625573158,
0.0006727290456183255,
-0.019603943452239037,
0.0009811831405386329,
0.01397156435996294,
-0.05036967992782593,
0.0031125997193157673,
-0.004593455698341131,
-0.009326104074716568,
0.02942725643515587,
0.025393256917595863,
-0.02149655669927597,
0.010179467499256134,
-0.04801159352064133,
-0.0053305658511817455,
-0.012294706888496876,
-0.04485679045319557,
-0.01999339647591114,
-0.00750690558925271,
0.02238081395626068,
0.06950435042381287,
-0.03349488973617554,
-0.032297275960445404,
0.03358294442296028,
0.01180284284055233,
0.013076622039079666,
-0.0238608717918396,
0.021926233544945717,
0.017356183379888535,
-0.016814332455396652,
-0.02644863724708557,
0.004525936208665371,
0.025245577096939087,
0.05811309441924095,
0.027261653915047646,
-0.049106426537036896,
0.02392341010272503,
0.0009139876929111779,
0.0322917103767395,
0.010869164951145649,
-0.022910719737410545,
-0.011516761034727097,
0.029203427955508232,
0.045114025473594666,
-0.017343858256936073,
-0.03154897689819336,
-0.015746580436825752,
0.032846175134181976,
-0.001111831283196807,
-0.02758915163576603,
-0.04287266731262207,
-0.002689852612093091,
-0.04727296158671379,
0.05079096555709839,
-0.059983596205711365,
-0.026400797069072723,
-0.05308373272418976,
-0.010921573266386986,
0.014682040549814701,
0.01134710293263197,
-0.02915284037590027,
0.04485400393605232,
0.025759926065802574,
-0.03783935680985451,
0.036730438470840454,
0.047060322016477585,
-0.010168684646487236,
-0.043780915439128876,
0.025139017030596733,
0.03610106557607651,
0.05604228749871254,
-0.04807484894990921,
-0.039883870631456375,
0.07034419476985931,
-0.016962233930826187,
-0.013013182207942009,
0.028144191950559616,
0.013447681441903114,
0.02592434361577034,
0.01406788732856512,
-0.011872269213199615,
0.0035841641947627068,
0.02431458793580532,
-0.007266436703503132,
0.016155624762177467,
-0.00438122171908617,
-0.038836363703012466,
-0.032838448882102966,
-0.022289633750915527,
-0.006274010520428419,
-0.00527612678706646,
0.019174225628376007,
0.011722827330231667,
0.030792661011219025,
-0.005785897374153137,
-0.01546767819672823,
0.008135436102747917,
-0.010285066440701485,
0.05180941894650459,
0.030031777918338776,
0.004129429347813129,
0.031114721670746803,
0.04172597452998161,
-0.026491379365324974,
0.012242292985320091,
0.022886816412210464,
0.011162970215082169,
-0.053727395832538605,
0.03372051939368248,
-0.011063079349696636,
-0.008083214052021503,
0.035248979926109314,
-0.03648795187473297,
0.042059820145368576,
0.03569246828556061,
-0.049092695116996765,
0.0018191118724644184,
-0.04130825772881508,
-0.005824133288115263,
-0.03803293779492378,
-0.014566942118108273,
-0.07065659761428833,
0.06637396663427353,
0.06648183614015579,
0.040557269006967545,
0.0021180391777306795,
-0.014099754393100739,
-0.02888660691678524,
0.0033483419101685286,
-0.026735736057162285,
-0.010300303809344769,
-0.008512704633176327,
0.0076724509708583355,
0.03700193762779236,
-0.02991728112101555,
-0.02467990480363369,
0.011249035596847534,
-0.03902538865804672,
-0.0117637999355793,
-0.010365490801632404,
0.02084767073392868,
0.023176420480012894,
0.0013083448866382241,
0.037377942353487015,
-0.004475232679396868,
0.005661681294441223,
0.004415365867316723,
0.0207088403403759,
0.01493837870657444,
0.009969270788133144,
-0.023395657539367676,
0.020317358896136284,
-0.02491668239235878,
-0.06118270382285118,
0.02082373946905136,
-0.022704752162098885,
0.0008568394696339965,
0.01381702721118927,
-0.0114784250035882,
0.029032999649643898,
-0.007160875480622053,
0.03346630185842514,
-0.052580419927835464,
0.0012721531093120575,
0.04002750292420387,
-0.013631128706037998,
-0.005842779763042927,
-0.03810364380478859,
0.0077681997790932655,
-0.03858264535665512,
0.06750507652759552,
0.011577336117625237,
-0.04627063125371933,
-0.06388110667467117,
-0.03152724355459213,
-0.02320951409637928,
0.008070151321589947,
-0.015829410403966904,
-0.05239482969045639,
-0.03321778401732445,
0.02575802057981491,
0.019062919542193413,
0.009321337565779686,
-0.02277342975139618,
-0.022467894479632378,
-0.05374843627214432,
-0.06084559112787247,
0.05042194575071335,
0.024692505598068237,
0.021274155005812645,
-0.08056013286113739,
0.011430898681282997,
-0.01562780700623989,
-0.0034564011730253696,
0.04169299826025963,
-0.0048494185321033,
-0.01790221594274044,
0.029250694438815117,
0.02569691091775894,
0.055938057601451874,
-0.006890884600579739,
0.014905964955687523,
-0.08143772184848785,
-0.03804966062307358,
0.019926121458411217,
-0.0028549861162900925,
-0.01470824796706438,
0.013272212818264961,
0.043219391256570816,
-0.03276139870285988,
0.00035053363535553217,
-0.005532887764275074,
-0.015696683898568153,
0.030560756102204323,
-0.01104968972504139,
-0.023897899314761162,
0.06475985795259476,
-0.04375137761235237,
0.020175838842988014,
0.02213430404663086,
-0.02711288444697857,
-0.03549567237496376,
0.04962000995874405,
-0.011963843367993832,
-0.02067684754729271,
-0.01622365601360798,
-0.01996929757297039,
0.012771500274538994,
-0.010575398802757263,
-0.030325716361403465,
0.024420157074928284,
-0.035921841859817505,
0.019233131781220436,
0.03702624887228012,
-0.011302312836050987,
0.03666231781244278,
-0.02532055787742138,
0.021312588825821877,
0.027114063501358032,
0.023603932932019234,
0.007390206214040518,
0.08126968145370483,
0.058154527097940445,
-0.0009094019769690931,
0.009686043485999107,
0.039519019424915314,
-0.03868059068918228,
0.009037443436682224,
0.008996653370559216,
0.05784959718585014,
-0.033236291259527206,
-0.02890297770500183,
0.005626309663057327,
-0.030866200104355812,
0.004825143609195948,
0.027105683460831642,
-0.02008085511624813,
0.05748242884874344,
-0.025830503553152084,
0.0372479148209095,
-0.02270149067044258,
-0.021119417622685432,
-0.026742473244667053,
0.00523833092302084,
0.05179810896515846,
0.04083234816789627,
-0.0022703777067363262,
0.011264636181294918,
-0.000007521440238633659,
-0.008547072298824787,
0.009368610568344593,
-0.02256092242896557,
0.02531624585390091,
0.015544964000582695,
-0.01383865438401699,
-0.012657459825277328,
-0.00816965103149414,
0.012917235493659973,
-0.042699169367551804,
0.031650446355342865,
0.06315108388662338,
0.0344279445707798,
0.008011812344193459,
-0.027797004207968712,
-0.012539146468043327,
0.0739765539765358,
-0.030429929494857788,
-0.011957426555454731,
-0.022321538999676704,
0.05450356379151344,
0.013962360098958015,
-0.022144189104437828
] |
<p>I was doing some simple harmonic motion problems and I came across this <a href="http://i.imgur.com/W2zi40o.jpg" rel="nofollow">picture</a> describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the linear oscillator should not be moving, only changing directions. I'm having a hard time understanding why the acceleration is the greatest at that time (according to these graphs), since there is no velocity change. Is it because acceleration is only the difference in velocity at two different points in time and not one? How exactly does the change in direction affect acceleration?</p>
<p>edit: I found another <a href="http://physics.stackexchange.com/questions/34178/how-can-an-objects-instantaneous-speed-be-zero-and-its-instantaneous-accelerat?rq=1">question</a> that answered my question. haha.</p> | 152 | [
-0.006782280746847391,
-0.017610371112823486,
-0.035529203712940216,
0.007819912396371365,
0.05103973299264908,
-0.002914645941928029,
-0.0257974024862051,
-0.01505183894187212,
-0.006993158720433712,
-0.020019376650452614,
0.0118750324472785,
0.04476970061659813,
0.0679374411702156,
0.015243258327245712,
0.02038818970322609,
0.00098729960154742,
-0.020333079621195793,
-0.03894306346774101,
-0.027805978432297707,
-0.010933654382824898,
0.002444179728627205,
0.016457704827189445,
0.02527792938053608,
0.014805525541305542,
-0.022320859134197235,
0.03349607065320015,
0.039079535752534866,
0.04417258873581886,
0.004520032089203596,
0.05358003079891205,
0.0060590049251914024,
0.0029735227581113577,
-0.018246930092573166,
-0.002348228357732296,
0.05856535583734512,
-0.0022824867628514767,
-0.02333417721092701,
-0.037215594202280045,
0.010044067166745663,
0.03866752237081528,
-0.006861580070108175,
-0.007852653041481972,
-0.020730549469590187,
0.08697047084569931,
-0.04531035199761391,
0.03637763112783432,
0.0432642363011837,
0.01314563024789095,
0.09088386595249176,
-0.01650875248014927,
0.07164780795574188,
-0.011861157603561878,
0.026310520246624947,
0.004104481544345617,
0.03779199346899986,
0.035732563585042953,
0.04135365039110184,
0.05844932049512863,
-0.02542026899755001,
-0.04487453028559685,
0.000008335353413713165,
-0.019722552970051765,
-0.04611743986606598,
-0.005254887044429779,
0.0015060799196362495,
0.024063367396593094,
0.011387601494789124,
-0.008288810960948467,
0.015125405043363571,
0.02115461602807045,
-0.01324558351188898,
0.026668285951018333,
0.008260845206677914,
-0.037230782210826874,
-0.015292075462639332,
-0.045800380408763885,
0.035243645310401917,
0.0052863555029034615,
0.033394504338502884,
0.027976306155323982,
-0.032057084143161774,
-0.0025496878661215305,
0.03738617151975632,
0.027674168348312378,
0.03219480440020561,
-0.026871830224990845,
0.05955042317509651,
0.009065461345016956,
-0.002975968411192298,
0.05213550478219986,
-0.020704103633761406,
0.02902638353407383,
-0.013079027645289898,
-0.02915305271744728,
-0.017607633024454117,
0.03168955072760582,
0.02262718603014946,
0.06924138963222504,
0.028777429834008217,
-0.04350171238183975,
0.023321272805333138,
-0.02585793100297451,
0.03498503938317299,
0.04535377398133278,
0.00445817643776536,
-0.03070017509162426,
-0.015309872105717659,
0.03641478344798088,
-0.035742856562137604,
-0.03860855847597122,
-0.05300638824701309,
0.010774854570627213,
0.028941979631781578,
0.014158457517623901,
-0.002484445460140705,
-0.009777241386473179,
0.018196338787674904,
0.016952088102698326,
0.01536058634519577,
0.015036256983876228,
0.039270926266908646,
-0.06259257346391678,
0.03787475824356079,
-0.002873349469155073,
-0.060154978185892105,
-0.01519390195608139,
-0.014627448283135891,
-0.004013143479824066,
-0.03695371374487877,
0.05169697105884552,
0.0045774090103805065,
-0.012760546058416367,
0.017880043014883995,
-0.013637582771480083,
0.03577551245689392,
-0.012150250375270844,
-0.10405267775058746,
-0.05862005427479744,
0.04398132860660553,
0.01177838072180748,
-0.018235182389616966,
-0.08592332899570465,
-0.012827339582145214,
0.0007620662217959762,
0.07959499210119247,
-0.015331377275288105,
0.006766050588339567,
0.02794257365167141,
0.02489618957042694,
0.023013930767774582,
0.008205096237361431,
-0.005655377171933651,
-0.009806748479604721,
-0.06053640693426132,
0.017871219664812088,
-0.054912712424993515,
-0.0020347002428025007,
0.021646615117788315,
-0.006777440197765827,
-0.02484801970422268,
0.04571892321109772,
-0.005777497310191393,
-0.0003126091614831239,
0.01147693581879139,
-0.015590735711157322,
-0.002140764147043228,
0.10051769018173218,
0.022428885102272034,
-0.040255721658468246,
0.04616091772913933,
0.03044271096587181,
0.0481477752327919,
-0.02196195162832737,
0.02404877170920372,
0.03882693871855736,
-0.019230058416724205,
-0.0433298721909523,
-0.037281811237335205,
0.005711287260055542,
0.008558303117752075,
-0.034481123089790344,
-0.0538448765873909,
-0.019215911626815796,
0.005180431995540857,
-0.004740877542644739,
0.0691925436258316,
-0.01078919880092144,
0.06851145625114441,
-0.01724114455282688,
-0.03750581666827202,
-0.018915507942438126,
-0.08887606114149094,
0.052103105932474136,
-0.008586031384766102,
-0.00820420403033495,
0.02190791442990303,
0.029035430401563644,
0.008963731117546558,
-0.03025100752711296,
0.0019201856339350343,
0.002243656665086746,
0.02179066091775894,
-0.018246464431285858,
-0.037370651960372925,
0.01754777878522873,
0.05683688819408417,
0.025703636929392815,
-0.0010261238785460591,
-0.01046394556760788,
-0.022469371557235718,
0.019543403759598732,
0.050238922238349915,
-0.021743347868323326,
0.019072921946644783,
-0.0040345448069274426,
-0.016168873757123947,
-0.004847703035920858,
-0.002460663905367255,
-0.004936710931360722,
0.040242865681648254,
-0.009011677466332912,
0.0712553858757019,
0.04674956575036049,
-0.02339896932244301,
-0.008950377814471722,
0.05723436549305916,
0.018183253705501556,
0.005837815813720226,
-0.007883415557444096,
-0.016987580806016922,
-0.02390861138701439,
0.018385525792837143,
0.024706711992621422,
0.03229472041130066,
-0.02404790371656418,
-0.0003640364739112556,
0.0326743945479393,
0.06370279937982559,
0.003360885428264737,
0.017789294943213463,
-0.02633843943476677,
-0.0334070585668087,
0.009212428703904152,
0.0034085551742464304,
0.012763837352395058,
0.0009216525359079242,
0.04535116255283356,
0.0022923836950212717,
0.0345526784658432,
0.021733805537223816,
0.01132988277822733,
0.058973539620637894,
-0.0047986796125769615,
0.004854985512793064,
0.03190075233578682,
-0.02782341279089451,
-0.0030794416088610888,
-0.03859719634056091,
0.0270198043435812,
0.017454475164413452,
-0.004083178471773863,
0.00385898444801569,
-0.012835497967898846,
0.01443798840045929,
0.003659583628177643,
0.007196301128715277,
-0.026149943470954895,
0.00032612704671919346,
0.029025359079241753,
-0.020382139831781387,
0.005913848523050547,
-0.039852701127529144,
-0.010724960826337337,
-0.04675667732954025,
-0.025166312232613564,
0.042862068861722946,
0.044622067362070084,
0.02194250375032425,
-0.07966836541891098,
-0.013626644387841225,
-0.019872047007083893,
-0.057725343853235245,
0.026986610144376755,
0.014405742287635803,
-0.03967957943677902,
0.03848610818386078,
-0.03489862009882927,
-0.05973665416240692,
0.0634051039814949,
0.03436917066574097,
0.0005366051918826997,
0.059355705976486206,
-0.021582642570137978,
-0.06840934604406357,
-0.07550400495529175,
-0.061248838901519775,
0.027600213885307312,
-0.03965499624609947,
-0.005229208152741194,
0.045696210116147995,
-0.021610628813505173,
-0.017143556848168373,
0.035238929092884064,
-0.04903290048241615,
-0.005574458744376898,
-0.026574887335300446,
-0.010669298470020294,
0.031209489330649376,
-0.016706714406609535,
-0.005987834185361862,
0.0010171710746362805,
-0.029013369232416153,
-0.016130194067955017,
-0.038386113941669464,
-0.05210632085800171,
-0.015352802351117134,
0.008865490555763245,
0.06488912552595139,
0.004845092538744211,
-0.005641349591314793,
0.056431423872709274,
0.044841017574071884,
-0.022082027047872543,
-0.04855936020612717,
0.017391059547662735,
-0.023225700482726097,
-0.0021036250982433558,
0.010514771565794945,
0.04288634657859802,
-0.018087854608893394,
0.041932471096515656,
0.0038305544294416904,
0.03379189223051071,
0.005376415327191353,
0.02212011069059372,
0.013061164878308773,
-0.03893817216157913,
0.0006576435407623649,
0.005880534183233976,
0.008628202602267265,
0.02426993101835251,
-0.005390152335166931,
0.05135403200984001,
0.014901407063007355,
0.056054405868053436,
0.006517369765788317,
-0.035754647105932236,
0.04839525371789932,
0.002718789968639612,
-0.005009938962757587,
-0.03500310331583023,
0.04458174109458923,
-0.0075293597765266895,
0.046691443771123886,
-0.015111827291548252,
0.02052219770848751,
0.04115317016839981,
0.002436339622363448,
0.022502848878502846,
-0.006293388549238443,
-0.005155001766979694,
-0.03797871991991997,
-0.060079582035541534,
0.016567368060350418,
0.01433652639389038,
0.026515254750847816,
-0.02985702082514763,
-0.03776250407099724,
0.07141698151826859,
-0.0011021657846868038,
0.012606337666511536,
0.010302034206688404,
-0.04684511944651604,
0.009942391887307167,
-0.035190969705581665,
0.007521151565015316,
0.01739085465669632,
0.03052806667983532,
0.01413784734904766,
0.06683608889579773,
0.009421117603778839,
0.03960750624537468,
0.009300553239881992,
-0.005314815789461136,
-0.1004144623875618,
0.05551997944712639,
-0.04235808551311493,
-0.029362870380282402,
0.0004790053062606603,
-0.02200627699494362,
0.0017151578795164824,
-0.025723619386553764,
-0.011862705461680889,
0.001824470586143434,
-0.01478528045117855,
-0.05975718051195145,
-0.0029614591039717197,
-0.030833834782242775,
-0.004859254229813814,
-0.048018891364336014,
0.013211026787757874,
0.014485057443380356,
-0.0371609628200531,
0.04229859635233879,
0.04529120400547981,
-0.0176739152520895,
-0.009035400114953518,
-0.025385497137904167,
-0.007042982615530491,
0.02472284622490406,
0.006802633870393038,
0.011471974663436413,
0.019516263157129288,
-0.0017339938785880804,
0.064059779047966,
-0.00573356356471777,
0.051788315176963806,
0.03780558332800865,
-0.01379826758056879,
-0.02038278616964817,
-0.03182695806026459,
0.015331417322158813,
-0.021789880469441414,
0.03169414401054382,
0.006073335651308298,
0.007902581244707108,
0.03128080070018768,
0.03142739087343216,
0.01766446977853775,
0.026093406602740288,
0.036276914179325104,
-0.010998495854437351,
0.027348704636096954,
-0.0652187168598175,
-0.020116521045565605,
-0.025827907025814056,
-0.005941346753388643,
-0.0019253569189459085,
-0.02148265391588211,
-0.03362195938825607,
0.015788352116942406,
0.027206270024180412,
0.010037679225206375,
0.019886359572410583,
-0.007990709505975246,
-0.011813280172646046,
0.02497357688844204,
0.026058949530124664,
-0.011640061624348164,
0.0031541932839900255,
0.01125417836010456,
0.07221362739801407,
0.0008322198409587145,
-0.029396552592515945,
-0.07088387757539749,
-0.016471968963742256,
0.029016204178333282,
0.0370914451777935,
-0.019101329147815704,
-0.004723681602627039,
-0.022829420864582062,
-0.016609568148851395,
0.03012985549867153,
-0.02749807760119438,
0.053072571754455566,
-0.01197931170463562,
0.008008833974599838,
-0.04052538797259331,
-0.04689284414052963,
-0.018337449058890343,
-0.020984530448913574,
-0.027940362691879272,
0.01871907152235508,
-0.007049053907394409,
-0.01468808762729168,
-0.0037362719886004925,
0.016209576278924942,
0.01180780865252018,
0.04239557683467865,
-0.013166057877242565,
0.010673139244318008,
-0.004249959718436003,
0.02261199988424778,
-0.02743208222091198,
-0.08202408254146576,
0.009967572055757046,
0.01661125011742115,
-0.02054653689265251,
0.02660192735493183,
-0.054655127227306366,
-0.015424561686813831,
0.024112744256854057,
0.011847570538520813,
-0.025404974818229675,
-0.015130209736526012,
-0.017461642622947693,
0.031032321974635124,
0.03334485739469528,
-0.01338997483253479,
0.02387220226228237,
0.0641804113984108,
-0.02203943394124508,
-0.04669372737407684,
0.010036909021437168,
0.02056456170976162,
-0.030437475070357323,
0.010331932455301285,
-0.026515480130910873,
0.02545001357793808,
-0.027942074462771416,
0.0584716871380806,
-0.015228928066790104,
0.02170293964445591,
0.00785012822598219,
-0.014695708639919758,
-0.018556443974375725,
0.04435933008790016,
-0.00874224491417408,
0.015346875414252281,
-0.009091576561331749,
-0.0012376272352412343,
-0.025306038558483124,
-0.039644595235586166,
0.007775991689413786,
-0.029878005385398865,
0.0040953257121145725,
0.07629899680614471,
0.02523042820394039,
0.030514784157276154,
-0.014103730209171772,
-0.00770257692784071,
-0.02092318795621395,
-0.04550562798976898,
0.014391820877790451,
0.00202170480042696,
-0.02091166563332081,
0.016439666971564293,
-0.0507621206343174,
-0.04876470938324928,
-0.015823496505618095,
-0.014761272817850113,
0.0377478152513504,
-0.04197022691369057,
0.021351458504796028,
0.0038727649953216314,
0.02808532305061817,
-0.05754414200782776,
-0.08265537023544312,
0.051402732729911804,
-0.0018524342449381948,
-0.010107938200235367,
-0.02022542618215084,
-0.015601111575961113,
-0.020240023732185364,
-0.004310776479542255,
0.03483792394399643,
0.035814788192510605,
-0.016320625320076942,
-0.02345600537955761,
0.03715583309531212,
-0.011750306002795696,
0.03938218951225281,
0.020352814346551895,
-0.01665354333817959,
0.00018307939171791077,
-0.011160562746226788,
-0.018440935760736465,
0.020552337169647217,
0.09169498831033707,
-0.04048933833837509,
-0.010909542441368103,
-0.01213863119482994,
-0.014242090284824371,
0.059519268572330475,
-0.0015614056028425694,
-0.027179252356290817,
0.03466334939002991,
0.010722316801548004,
-0.01621321402490139,
-0.04686180129647255,
0.02634654939174652,
0.0009046649793162942,
-0.005770001094788313,
0.026393141597509384,
-0.02652193047106266,
-0.03717663511633873,
-0.08279183506965637,
-0.014465109445154667,
0.011251966468989849,
0.021734368056058884,
0.02996072731912136,
0.05124058946967125,
-0.028830286115407944,
-0.009435637854039669,
0.003558663185685873,
-0.018383309245109558,
-0.00667025288566947,
-0.010533742606639862,
-0.010010172612965107,
-0.003133519785478711,
-0.02773013338446617,
-0.03390824422240257,
-0.0034731675405055285,
-0.044048286974430084,
0.024027904495596886,
0.0702371820807457,
-0.007342190016061068,
0.04221035912632942,
0.020326590165495872,
0.02096915990114212,
-0.0023993952199816704,
0.005814619828015566,
-0.0013451020931825042,
-0.01927090808749199,
-0.0020204512402415276,
0.019032107666134834,
-0.04446300491690636,
-0.0057353852316737175,
0.03486890345811844,
0.04370652884244919,
0.015593803487718105,
-0.014321941882371902,
0.058323949575424194,
0.010576844215393066,
0.05032026395201683,
0.022124940529465675,
-0.031641438603401184,
0.015778491273522377,
0.012491717003285885,
0.03959984704852104,
0.01229256670922041,
-0.02691343054175377,
0.029396628960967064,
0.0030611525289714336,
-0.004727751947939396,
-0.05729774013161659,
0.011168891564011574,
-0.05731624737381935,
0.0009717097855173051,
0.00044082471868023276,
0.030850308015942574,
-0.019195115193724632,
0.02004225179553032,
0.05857660248875618,
0.025431767106056213,
0.01930629089474678,
0.010257270187139511,
-0.05224781855940819,
-0.029508179053664207,
-0.00020578844123519957,
-0.018888888880610466,
-0.011876782402396202,
0.0043281614780426025,
-0.03900648280978203,
0.026969512924551964,
-0.042421236634254456,
0.021389566361904144,
-0.00026494619669392705,
0.029987893998622894,
0.007677855901420116,
0.07552842050790787,
0.0022947113029658794,
-0.0022667681332677603,
-0.016700876876711845,
0.011642590165138245,
0.10156500339508057,
0.03757414594292641,
-0.02324514649808407,
-0.020415134727954865,
0.005203446373343468,
-0.001335367327556014,
0.0179568063467741,
-0.024185488000512123,
0.02489149197936058,
0.010036793537437916,
0.006439809687435627,
0.01220325194299221,
0.05198365077376366,
0.009242124855518341,
-0.013624722138047218,
0.02114814706146717,
-0.03253944218158722,
-0.037144023925065994,
-0.03960733860731125,
0.012611930258572102,
0.034866221249103546,
0.005705459974706173,
-0.03463475778698921,
0.03025444597005844,
-0.041069794446229935,
-0.019046993926167488,
-0.027003513649106026,
-0.05233948305249214,
0.02576259709894657,
0.008647666312754154,
-0.042841747403144836,
0.02166472189128399,
0.05051976442337036,
-0.038807034492492676,
-0.08741720765829086,
0.03836274892091751,
0.001990186981856823,
0.007583150174468756,
0.04261479899287224,
0.043891794979572296,
0.0380985364317894,
0.019376486539840698,
0.020341677591204643,
-0.020324118435382843,
-0.03456495702266693,
-0.010290796868503094,
-0.050085656344890594,
0.024386776611208916,
0.012098019011318684,
0.009821831248700619,
-0.021049469709396362,
0.016828561201691628,
-0.02579137310385704,
-0.08712410926818848,
-0.027223611250519753,
0.007825206033885479,
0.049752186983823776,
0.011631257832050323,
0.0014531022170558572,
-0.04247627034783363,
-0.006281367968767881,
0.005707594566047192,
0.009770287200808525,
0.014033081941306591,
-0.018499935045838356,
0.025232087820768356,
-0.029195565730333328,
0.05768544599413872,
-0.024849532172083855,
-0.027802595868706703,
0.03576526790857315,
-0.00428908783942461,
-0.028176210820674896,
-0.011147253215312958,
0.013496407307684422,
0.03643035516142845,
0.04966851696372032,
0.018575938418507576,
-0.004820582922548056,
-0.006270959507673979,
-0.07638250291347504,
-0.01851118728518486,
0.029166962951421738,
-0.026112504303455353,
-0.019172806292772293,
-0.0035996711812913418,
0.054358065128326416,
0.02158028818666935,
-0.02745457924902439,
0.008636349812150002,
-0.013834185898303986,
0.02147940918803215,
-0.004072017502039671,
0.00021221696806605905,
-0.007947896607220173,
0.05390934646129608,
-0.018289295956492424,
0.02322428487241268,
-0.006903605069965124,
0.062434837222099304,
-0.001378434244543314,
-0.0024320059455931187,
-0.0009377276874147356,
0.016469208523631096,
-0.024929843842983246,
-0.022011728957295418,
0.03838326409459114,
-0.026343706995248795,
0.004618700128048658,
0.021297836676239967,
0.011002212762832642,
-0.027755822986364365,
-0.05272766575217247,
-0.013540071435272694,
-0.02192426472902298,
-0.02157232165336609,
0.041674934327602386,
-0.015093005262315273,
0.03416471555829048,
-0.03887693211436272,
0.023972999304533005,
-0.03068147599697113,
-0.0011885144049301744,
-0.045100290328264236,
0.00877708476036787,
0.0208156518638134,
-0.007684607524424791,
-0.023561518639326096,
0.025420062243938446,
-0.026330484077334404,
0.0021181991323828697,
0.0010328043717890978,
0.04021043702960014,
-0.014956353232264519,
-0.022600319236516953,
0.02969137579202652,
-0.01975981704890728,
0.026035791262984276,
-0.02609875798225403,
-0.021347807720303535,
0.03249887377023697,
-0.046703897416591644,
-0.02073170803487301,
0.044186729937791824,
0.001294207526370883,
-0.008873304352164268,
-0.017388194799423218,
-0.019208461046218872,
-0.011595875956118107,
0.06869272887706757,
-0.021661316975951195,
0.0019469489343464375,
0.03148506209254265,
-0.06080659478902817,
-0.03167688101530075,
0.02076338790357113,
-0.023204797878861427,
-0.006820566486567259,
0.004850701428949833,
0.007090989500284195,
0.041134968400001526,
-0.0085465582087636,
-0.01061467919498682,
-0.017375363036990166,
-0.029903972521424294,
0.016819974407553673,
0.036989860236644745,
0.0057869115844368935,
0.034886434674263,
0.0523885078728199,
-0.030259335413575172,
0.04100576043128967,
-0.005050336942076683,
-0.004678604658693075,
-0.08089648187160492,
0.009417696855962276,
0.005469499621540308,
-0.013034024275839329,
0.018402099609375,
-0.058817308396101,
0.020865311846137047,
0.03849941864609718,
-0.06715577095746994,
0.010300533846020699,
-0.0399957112967968,
0.00883719976991415,
-0.035651493817567825,
-0.025238865986466408,
-0.01277223415672779,
0.036598753184080124,
0.04980350658297539,
0.03501369059085846,
0.02336668223142624,
0.00029506866121664643,
-0.01781894639134407,
-0.029004916548728943,
0.00732296472415328,
0.053717490285634995,
-0.00010815246787387878,
0.011042248457670212,
0.02983206696808338,
-0.027746617794036865,
-0.032188575714826584,
0.04037526249885559,
-0.04360860213637352,
-0.010503735393285751,
0.002276192419230938,
0.004045578185468912,
-0.034013669937849045,
0.035472042858600616,
0.0008209669031202793,
-0.013752379454672337,
-0.030417680740356445,
0.009090856648981571,
0.02202938310801983,
0.03085973672568798,
0.008381220512092113,
-0.0008538019610568881,
-0.005071545485407114,
-0.03919530287384987,
-0.04321765899658203,
0.004749922081828117,
0.017341360449790955,
-0.0032938425429165363,
0.02385944128036499,
0.0008761974168010056,
0.02399817854166031,
-0.052766308188438416,
-0.009733387269079685,
-0.007717309053987265,
-0.02146456576883793,
0.05385393649339676,
-0.02583102323114872,
-0.01768561266362667,
-0.016553321853280067,
-0.03626137599349022,
-0.008136347867548466,
-0.010314242914319038,
0.011973081156611443,
-0.008055370301008224,
-0.07473764568567276,
-0.011221433989703655,
0.004440611694008112,
-0.03930317237973213,
-0.021060746163129807,
-0.018588511273264885,
-0.005220495630055666,
0.023519745096564293,
0.0210635457187891,
0.010205531492829323,
0.013211931101977825,
-0.03874991089105606,
-0.03582295775413513,
-0.07858811318874359,
0.0516340471804142,
0.02162844128906727,
-0.029462795704603195,
-0.04776480793952942,
-0.02575541101396084,
-0.01777583546936512,
0.02462981641292572,
0.02960699424147606,
-0.02012743428349495,
-0.03024238906800747,
0.03401251137256622,
-0.021007198840379715,
0.00541294738650322,
-0.0031523823272436857,
-0.004659065045416355,
-0.02091091312468052,
-0.019961373880505562,
0.0334756001830101,
0.00475484412163496,
-0.06244795769453049,
0.0012994176940992475,
0.014032832346856594,
-0.030388975515961647,
0.044679418206214905,
-0.0252496637403965,
-0.018860207870602608,
0.03050469607114792,
0.05314425751566887,
0.0025474857538938522,
0.08254364877939224,
0.008855574764311314,
-0.016029223799705505,
0.014204869046807289,
-0.01794549636542797,
-0.03561639413237572,
0.012676820158958435,
-0.02964620292186737,
0.0024922750890254974,
-0.014519340358674526,
-0.031347207725048065,
0.03435242921113968,
-0.0637316182255745,
-0.009064815938472748,
0.027916574850678444,
-0.017658811062574387,
-0.015918254852294922,
0.011980517767369747,
0.011995812878012657,
0.055636629462242126,
0.005511066876351833,
0.006557267624884844,
0.010251309722661972,
-0.021619783714413643,
0.00648872833698988,
0.03275623545050621,
0.004869161639362574,
0.011415014043450356,
-0.0062252311035990715,
0.06865952908992767,
-0.005462910048663616,
0.031306445598602295,
0.009810695424675941,
0.0393335334956646,
-0.02493230812251568,
0.017311356961727142,
-0.021141408011317253,
-0.03990641608834267,
-0.014274774119257927,
0.02208206057548523,
-0.011633757501840591,
0.028826342895627022,
-0.022967951372265816,
-0.005434650462120771,
0.02478044666349888,
0.008133250288665295,
-0.024401884526014328,
-0.020134305581450462,
-0.01799686811864376,
0.024953031912446022,
-0.019488150253891945,
-0.007707721553742886,
-0.013777167536318302,
-0.014818785712122917,
0.03133448213338852,
-0.054582759737968445,
0.016342641785740852,
0.02424483560025692,
-0.029217762872576714,
-0.013738047331571579,
-0.020466549322009087,
-0.014659992419183254,
-0.02577240765094757,
0.028917372226715088,
0.04572593793272972,
0.02631950005888939,
-0.03287622705101967,
-0.004956083372235298,
-0.03275395929813385,
0.04900446906685829,
-0.05846754461526871,
-0.01758541911840439,
-0.030140960589051247,
0.03554897382855415,
-0.0053013223223388195,
-0.006407288368791342
] |
<p>Isn't speed a relative thing in space? If so, why would the speed of a propellant matter? Why can't a space ship accelerate infinitely?</p> | 4,625 | [
-0.008373877964913845,
-0.005334650166332722,
-0.03571260720491409,
0.00013148901052773,
0.060640349984169006,
0.004698761738836765,
-0.037153296172618866,
0.008063899353146553,
-0.027921460568904877,
-0.03627043589949608,
0.00016447938105557114,
0.05577896535396576,
0.05526217445731163,
-0.003686232026666403,
0.014461232349276543,
0.02140124887228012,
-0.012391403317451477,
0.0004157469957135618,
-0.007886193692684174,
-0.013904153369367123,
0.019110579043626785,
0.0041543771512806416,
0.06735823303461075,
-0.013141552917659283,
-0.0014149114722386003,
0.016693614423274994,
0.027024829760193825,
0.006601041182875633,
0.02513153664767742,
0.02535990998148918,
0.04416053369641304,
0.00522589823231101,
0.014816544018685818,
0.01692255400121212,
0.028308505192399025,
0.010068180039525032,
-0.016250580549240112,
0.001841056626290083,
-0.016238460317254066,
0.019940922036767006,
-0.051681019365787506,
-0.04105883836746216,
-0.006771187297999859,
0.0635775625705719,
-0.02662675641477108,
0.006837471388280392,
0.01500181294977665,
0.003858128795400262,
0.05599668622016907,
-0.0609334260225296,
0.0417620986700058,
-0.012208848260343075,
0.04673142358660698,
0.030285203829407692,
-0.020585523918271065,
0.022747792303562164,
0.09271806478500366,
0.08567429333925247,
-0.01551014930009842,
-0.01670297235250473,
-0.015119796618819237,
0.01657814346253872,
0.007038233336061239,
-0.030546309426426888,
-0.0019721947610378265,
0.0380561426281929,
-0.050190892070531845,
0.0031314471270889044,
0.002492445521056652,
0.009456006810069084,
0.004260319285094738,
0.021995212882757187,
0.0265356432646513,
-0.017086435109376907,
-0.006472536828368902,
-0.01689567230641842,
0.048609573394060135,
-0.006222172640264034,
0.04789802432060242,
0.06831654906272888,
-0.025121349841356277,
0.007078147958964109,
0.023831816390156746,
0.00756573723629117,
0.017059143632650375,
0.017748963087797165,
0.048551641404628754,
0.012919855304062366,
0.02220620959997177,
0.06900778412818909,
-0.0057964748702943325,
0.01064417976886034,
0.00862014852464199,
-0.014560412615537643,
-0.001679669483564794,
0.037427619099617004,
-0.00015558928134851158,
0.04137810692191124,
0.01743469201028347,
-0.010163220576941967,
0.02999003417789936,
-0.016860606148838997,
0.015042454935610294,
0.04647112637758255,
0.000177159090526402,
-0.04372568055987358,
-0.06467435508966446,
0.03492231294512749,
-0.03756338357925415,
-0.010424096137285233,
-0.010616580955684185,
0.032274626195430756,
-0.004794612061232328,
-0.013973218388855457,
0.012829424813389778,
-0.030358871445059776,
0.027550557628273964,
-0.04313946142792702,
0.058222319930791855,
0.06201832368969917,
0.04096190631389618,
-0.019371913745999336,
0.02533579058945179,
0.029631059616804123,
-0.011589054949581623,
0.014644081704318523,
0.0010475368471816182,
-0.042088013142347336,
0.007112948689609766,
-0.011992471292614937,
-0.015477145090699196,
-0.013389633037149906,
-0.003883819794282317,
-0.01996372453868389,
0.049729324877262115,
0.010005911812186241,
-0.0800967887043953,
-0.061830878257751465,
0.044870775192976,
-0.010884175077080727,
-0.03616884723305702,
-0.09436653554439545,
0.012867274694144726,
-0.0015404032310470939,
0.07630941271781921,
-0.03606756776571274,
-0.01296260766685009,
-0.01975715532898903,
0.026057852432131767,
0.01180072408169508,
-0.04655412584543228,
-0.03034331277012825,
-0.005819689482450485,
-0.06816989183425903,
0.03893477842211723,
-0.07521820813417435,
-0.008216462098062038,
0.019365454092621803,
-0.003631736384704709,
-0.029735306277871132,
0.028309529647231102,
-0.060132939368486404,
-0.0012672357261180878,
0.0015656017931178212,
0.0045373523607850075,
-0.0213270615786314,
0.0886484831571579,
0.029042817652225494,
0.012215597555041313,
0.042689248919487,
0.05466919392347336,
0.01750224269926548,
0.019296087324619293,
0.02129560150206089,
0.037818122655153275,
-0.020815802738070488,
-0.03677869215607643,
-0.03162356838583946,
0.001952212885953486,
-0.02336691878736019,
-0.057863496243953705,
-0.05964115634560585,
0.020821303129196167,
-0.0006266596610657871,
-0.009536489844322205,
0.023668954148888588,
0.004320926032960415,
0.02241840586066246,
-0.016433684155344963,
-0.0008303640643134713,
0.007384724915027618,
-0.08490507304668427,
0.02148415520787239,
-0.004044444300234318,
0.0037206942215561867,
0.02339514158666134,
0.016306042671203613,
0.021229244768619537,
-0.05085095390677452,
-0.026579739525914192,
0.015859432518482208,
0.04758283868432045,
-0.004962047096341848,
-0.022880714386701584,
0.033523477613925934,
0.05504390224814415,
0.019092421978712082,
-0.0012169453548267484,
-0.006930561736226082,
0.01951085403561592,
-0.04526456817984581,
0.01655072718858719,
-0.015136762522161007,
-0.007942434400320053,
-0.017025208100676537,
0.00634119613096118,
0.019222792237997055,
-0.010459060780704021,
0.02201513573527336,
0.047821637243032455,
0.002121727680787444,
0.10895367711782455,
0.02183523215353489,
-0.02966965176165104,
0.000434094195952639,
0.024181382730603218,
-0.0017619817517697811,
-0.01306618470698595,
0.021824941039085388,
-0.04639681428670883,
-0.03845631703734398,
-0.012130970135331154,
0.03688833862543106,
0.033485956490039825,
-0.021828003227710724,
0.012390905991196632,
0.03554077818989754,
0.035615451633930206,
0.04829041659832001,
0.03094794787466526,
-0.036816760897636414,
-0.017045890912413597,
0.015918368473649025,
-0.022790543735027313,
0.008972237817943096,
0.013970944099128246,
0.05234217643737793,
0.021228769794106483,
-0.0022646840661764145,
-0.03720991685986519,
-0.010098997503519058,
0.03737068921327591,
0.039222873747348785,
-0.015921223908662796,
0.01329804491251707,
-0.05884818732738495,
0.03457850217819214,
-0.01606295071542263,
0.04406878352165222,
0.018244201317429543,
0.008645577356219292,
0.03333539515733719,
-0.04074487090110779,
-0.010464094579219818,
-0.013156848959624767,
0.00021375060896389186,
-0.02513790689408779,
-0.005473374389111996,
0.037647511810064316,
-0.02926248125731945,
0.027102598920464516,
-0.03415031358599663,
0.01863926649093628,
-0.008184224367141724,
-0.026129793375730515,
0.029545381665229797,
0.007630460429936647,
0.03183532506227493,
-0.01837002858519554,
-0.0369902141392231,
0.011385585181415081,
-0.06998930126428604,
-0.013194859027862549,
-0.017184389755129814,
-0.03371396288275719,
0.04862365871667862,
-0.016957052052021027,
-0.05112646147608757,
0.02523951046168804,
0.006511338520795107,
0.011343322694301605,
0.02170170471072197,
-0.03876163810491562,
-0.0646064430475235,
0.004905741661787033,
-0.04940534383058548,
-0.00293642352335155,
-0.029307642951607704,
0.035499248653650284,
0.0714610144495964,
-0.06313713639974594,
-0.033009763807058334,
0.025714315474033356,
-0.04868880286812782,
-0.027742622420191765,
-0.00008481417171424255,
0.011405796743929386,
0.0311647467315197,
-0.036407746374607086,
0.014773418195545673,
0.01848321035504341,
-0.07250933349132538,
-0.0027799243107438087,
-0.030858544632792473,
-0.03814096003770828,
0.02213980071246624,
0.008317535743117332,
0.04549851268529892,
-0.02505701221525669,
-0.03784286975860596,
0.07586939632892609,
0.04964028671383858,
-0.006283033173531294,
-0.03734032064676285,
-0.010773458518087864,
-0.005850921384990215,
-0.011093106120824814,
0.030685966834425926,
0.020693643018603325,
-0.021495375782251358,
0.0018836958333849907,
0.05950690805912018,
0.03939798101782799,
0.005532370414584875,
-0.00797982793301344,
-0.01077905111014843,
-0.021929018199443817,
0.026736831292510033,
0.012077612802386284,
0.020684292539954185,
0.05283861234784126,
-0.02799840457737446,
0.06012545898556709,
0.02282346785068512,
0.06199880316853523,
-0.007210385054349899,
-0.02933313325047493,
0.057699792087078094,
-0.001709963078610599,
0.011234008707106113,
-0.012338277883827686,
0.057429954409599304,
0.011330191045999527,
0.025532234460115433,
0.010637174360454082,
-0.0020341123454272747,
0.023416781798005104,
0.005512152798473835,
0.013599196448922157,
0.021593015640974045,
0.03019154816865921,
-0.025139622390270233,
-0.01878373511135578,
-0.0143696004524827,
-0.013913195580244064,
-0.015025191009044647,
-0.005865923129022121,
-0.040262963622808456,
0.055664338171482086,
0.03708741441369057,
-0.0008179085562005639,
-0.00897851213812828,
-0.03860507532954216,
0.023954756557941437,
-0.08452563732862473,
0.009326957166194916,
-0.023440778255462646,
0.011592564173042774,
-0.0015720517840236425,
0.07696483284235,
0.014827027916908264,
0.031832680106163025,
-0.004678564146161079,
-0.0035696595441550016,
-0.08947722613811493,
0.005999325308948755,
-0.04638344794511795,
-0.039523106068372726,
-0.01862858422100544,
0.0054390705190598965,
-0.05413132905960083,
-0.04574215039610863,
-0.03207699954509735,
0.006179811432957649,
-0.013313133269548416,
-0.05815333500504494,
0.018953371793031693,
-0.05268101394176483,
-0.04505426809191704,
-0.022579938173294067,
0.015434026718139648,
0.041037417948246,
-0.014384819194674492,
0.024411294609308243,
0.03803468868136406,
-0.029602117836475372,
-0.015523254871368408,
-0.01379839051514864,
-0.015130691230297089,
-0.0003761229454539716,
0.029825497418642044,
0.03266218304634094,
0.010666023008525372,
-0.03020080365240574,
-0.0103212995454669,
0.030659977346658707,
0.028075693175196648,
-0.023526813834905624,
-0.016662610694766045,
-0.05737035721540451,
-0.04739575833082199,
-0.004982959013432264,
0.002448698505759239,
0.030544448643922806,
0.011179886758327484,
-0.0052538057789206505,
0.009319054894149303,
0.012203382328152657,
-0.010100284591317177,
0.02639450505375862,
0.026748379692435265,
0.017419207841157913,
-0.01738038659095764,
-0.03498195856809616,
-0.03826909139752388,
-0.02479800023138523,
-0.03360925614833832,
0.03865576535463333,
-0.009097187779843807,
-0.033771123737096786,
0.004868858493864536,
-0.03738204017281532,
0.0008273705025203526,
-0.013606098480522633,
-0.02492736466228962,
-0.012677830643951893,
-0.00253911130130291,
0.0013028476387262344,
0.012907150201499462,
-0.007085353136062622,
0.01382591761648655,
0.03980487957596779,
-0.012850315310060978,
-0.004436559975147247,
-0.08751092851161957,
0.02174857072532177,
0.016703281551599503,
0.02363077737390995,
-0.018623942509293556,
-0.02072971686720848,
-0.029121113941073418,
-0.0301201231777668,
0.04012739285826683,
-0.02311309054493904,
-0.0022756808903068304,
-0.027581127360463142,
-0.009279219433665276,
-0.0045956759713590145,
-0.010083209723234177,
0.00023712904658168554,
0.03934021666646004,
0.011337549425661564,
-0.02820977382361889,
-0.018200920894742012,
0.03212934359908104,
-0.020315302535891533,
0.01962481066584587,
0.01877436228096485,
0.05634486302733421,
0.015413758344948292,
0.027396539226174355,
-0.009833499789237976,
0.01161620207130909,
-0.02272098697721958,
-0.06629922986030579,
0.0003768376191146672,
0.005948876030743122,
0.00016973938909359276,
0.02498924545943737,
-0.05110742524266243,
-0.036219045519828796,
0.033940382301807404,
0.0026562707498669624,
-0.0251837857067585,
-0.010719065554440022,
-0.03219713270664215,
-0.0004490577266551554,
0.021223854273557663,
0.01941731385886669,
0.03487224876880646,
0.0185945276170969,
-0.013866263441741467,
-0.05315587297081947,
-0.020197195932269096,
0.04414457082748413,
-0.039061758667230606,
0.0004298282728996128,
-0.017212385311722755,
-0.011807611212134361,
-0.04654973745346069,
0.052158523350954056,
0.0017431337619200349,
-0.01313149742782116,
0.005062652286142111,
-0.017769377678632736,
-0.012514030560851097,
0.02213885262608528,
0.044270873069763184,
-0.025301532819867134,
-0.01653655618429184,
0.01028742827475071,
-0.02862798236310482,
-0.04442992061376572,
-0.004636131692677736,
0.013642272911965847,
-0.02515694499015808,
0.04145051911473274,
0.0069640581496059895,
-0.008287771604955196,
-0.0080353869125247,
-0.0054413024336099625,
0.013817841187119484,
-0.01508368831127882,
0.021760329604148865,
-0.010045845061540604,
-0.04408007487654686,
0.010572118684649467,
-0.05571394041180611,
-0.03502508997917175,
-0.004712450318038464,
-0.01409812830388546,
0.0104835769161582,
-0.03964085504412651,
0.03924792632460594,
-0.008094586431980133,
0.03937995061278343,
-0.08605338633060455,
-0.03821668401360512,
0.02428996004164219,
0.018691476434469223,
-0.00365694728679955,
-0.05720851570367813,
0.01716511882841587,
-0.049895480275154114,
-0.03560693562030792,
0.022495748475193977,
0.0642545223236084,
0.002852646168321371,
-0.042108505964279175,
0.0017732692649587989,
0.010876532644033432,
0.0450405515730381,
-0.01140851154923439,
-0.03533688187599182,
0.01123098935931921,
0.002044293098151684,
-0.010525260120630264,
-0.046364907175302505,
0.06438610702753067,
-0.033751048147678375,
-0.020032916218042374,
-0.017161834985017776,
-0.04007730260491371,
0.002396121621131897,
-0.028571439906954765,
0.019385511055588722,
0.0650811418890953,
-0.0009924594778567553,
0.00515361363068223,
-0.003087707795202732,
0.009855189360678196,
-0.012531323358416557,
0.028350502252578735,
0.007518534082919359,
-0.019375573843717575,
-0.02566136047244072,
-0.04506712034344673,
0.037386536598205566,
0.00858770590275526,
0.010706472210586071,
0.0073592280969023705,
0.03581357002258301,
0.014494549483060837,
-0.0026737439911812544,
0.01628764346241951,
-0.010494030080735683,
0.010043470188975334,
-0.023081136867403984,
-0.02255781926214695,
-0.01478914450854063,
-0.01970992423593998,
-0.03230712190270424,
-0.002380262827500701,
0.014134646393358707,
-0.008094606921076775,
0.05423583462834358,
-0.04632394015789032,
0.04221995919942856,
-0.02715972624719143,
-0.016263773664832115,
-0.012036708183586597,
-0.007877099327743053,
-0.025613633915781975,
-0.0052687861025333405,
-0.007786257192492485,
0.003089039120823145,
-0.02413286827504635,
-0.010468401946127415,
0.040871512144804,
0.0544518418610096,
0.025413911789655685,
-0.012246955186128616,
0.043949272483587265,
0.004972426686435938,
0.027499007061123848,
0.017378346994519234,
-0.03511684760451317,
0.012909960001707077,
-0.01870857924222946,
0.014332327991724014,
0.01799212209880352,
-0.003835023147985339,
0.0480707511305809,
-0.005823420360684395,
-0.00827089324593544,
-0.03824285790324211,
-0.013907375745475292,
-0.04013627767562866,
0.0060483599081635475,
-0.0025866825599223375,
0.039397940039634705,
0.018072081729769707,
0.005019040312618017,
0.017690418288111687,
0.004478034097701311,
0.0009573019342496991,
-0.006306478288024664,
-0.061369575560092926,
-0.04378960654139519,
-0.016155079007148743,
-0.032669536769390106,
0.03145159035921097,
0.03234178572893143,
-0.04664207994937897,
-0.0038724548649042845,
-0.017666028812527657,
0.01915753446519375,
-0.020367830991744995,
0.03886640816926956,
-0.03166945278644562,
0.07043827325105667,
0.028744658455252647,
0.01711360365152359,
-0.01181642897427082,
0.02953006699681282,
0.09782049059867859,
0.04024944081902504,
0.00031021685572341084,
-0.04454367235302925,
0.017984772101044655,
-0.048655927181243896,
0.01677677221596241,
-0.028141675516963005,
0.03196222707629204,
0.02622712217271328,
0.02005808800458908,
0.029388947412371635,
0.07754454016685486,
0.004822199698537588,
0.007322581950575113,
0.07432252913713455,
-0.0463331937789917,
-0.014408147893846035,
-0.011312907561659813,
0.011486577801406384,
0.020559916272759438,
0.03543909266591072,
-0.008911598473787308,
0.028436288237571716,
-0.026982037350535393,
0.006667206529527903,
-0.018656516447663307,
-0.045210883021354675,
0.016601767390966415,
0.015250594355165958,
-0.036563560366630554,
0.003015018766745925,
0.023129841312766075,
-0.023075072094798088,
-0.057196345180273056,
0.012544290162622929,
0.030476143583655357,
-0.010486004874110222,
-0.005434510298073292,
-0.004462708253413439,
0.009853590279817581,
0.04594528302550316,
0.0023516009096056223,
-0.00444437563419342,
-0.031370412558317184,
0.020520560443401337,
-0.029676539823412895,
0.03395567834377289,
-0.010821478441357613,
0.022870495915412903,
0.009141470305621624,
0.03770895674824715,
-0.008608805947005749,
-0.08007469028234482,
-0.05132129415869713,
-0.002382400445640087,
0.035987358540296555,
0.0432642325758934,
0.008070377632975578,
-0.04365159943699837,
0.015486365184187889,
-0.004587152507156134,
0.03519957512617111,
0.012460178695619106,
0.0007438387838192284,
0.040137965232133865,
-0.04119570180773735,
0.027543453499674797,
-0.043055400252342224,
-0.03502926975488663,
0.0013383537298068404,
0.002113145077601075,
-0.03571575880050659,
0.00958059448748827,
0.031872499734163284,
0.031170884147286415,
-0.011337527073919773,
-0.012412368319928646,
0.02653188817203045,
-0.010928834788501263,
-0.06337876617908478,
0.0544964000582695,
-0.010089009068906307,
0.0036821472458541393,
-0.021614039316773415,
0.012551750056445599,
0.07159875333309174,
0.037118349224328995,
-0.03808377683162689,
0.02118512988090515,
-0.06506615877151489,
0.0103061618283391,
0.015799012035131454,
0.000691196124535054,
-0.0201485026627779,
0.025055570527911186,
-0.03053756058216095,
0.019128739833831787,
-0.018398283049464226,
0.03968658670783043,
0.058699898421764374,
-0.018185269087553024,
0.00512982252985239,
0.007080879993736744,
-0.04508352279663086,
0.030818749219179153,
0.05712750181555748,
-0.021902885288000107,
-0.0019754597451537848,
0.0034028450027108192,
0.026530634611845016,
0.0005948142497800291,
-0.05377475544810295,
-0.04985395818948746,
0.0018345759017392993,
-0.012967162765562534,
0.022426504641771317,
-0.007148338481783867,
0.004930861294269562,
0.007699029054492712,
0.03307006508111954,
-0.06974007934331894,
0.017628131434321404,
-0.06864731758832932,
0.03835417330265045,
-0.0014335298910737038,
-0.024446524679660797,
-0.01815047115087509,
0.019714822992682457,
-0.06078667193651199,
-0.026343058794736862,
-0.011879882775247097,
-0.0006647594855166972,
-0.003811586881056428,
-0.016350068151950836,
0.01802637428045273,
0.014543870463967323,
0.04615621268749237,
-0.03247993066906929,
-0.014533158391714096,
0.0033581280149519444,
-0.05141832306981087,
-0.062267761677503586,
0.024024471640586853,
-0.03062673844397068,
0.036550916731357574,
0.020512433722615242,
-0.014796260744333267,
-0.025881962850689888,
0.06990958005189896,
-0.030110647901892662,
-0.0033694205339998007,
0.007155235856771469,
-0.022360945120453835,
-0.025360045954585075,
-0.001391859957948327,
0.027399815618991852,
-0.03370067849755287,
-0.017219355329871178,
0.02612312324345112,
0.014768427237868309,
-0.03679583594202995,
0.025934040546417236,
-0.009591609239578247,
0.0024233886506408453,
0.006683055777102709,
0.018956972286105156,
0.00008002724644029513,
0.021449467167258263,
0.020660940557718277,
-0.022432679310441017,
0.043785788118839264,
0.03029450960457325,
-0.0013411404797807336,
-0.09740427136421204,
0.03281784430146217,
-0.032013051211833954,
0.013507324270904064,
0.02319277450442314,
-0.022134654223918915,
-0.003308347426354885,
0.018723513931035995,
-0.07050305604934692,
0.05490214005112648,
-0.061401404440402985,
-0.02646833099424839,
-0.04657180607318878,
-0.010714501142501831,
0.011891748756170273,
0.03907901048660278,
0.06464628875255585,
0.04161454737186432,
-0.003356283064931631,
0.0017387612024322152,
-0.006998888216912746,
0.0200603399425745,
0.011107181198894978,
0.019846374168992043,
-0.0330253504216671,
0.0292665958404541,
0.05297510325908661,
-0.012627853080630302,
0.009088847786188126,
0.019195007160305977,
0.03391231596469879,
0.023459700867533684,
0.0018837840761989355,
0.0074360244907438755,
0.010589119046926498,
0.02156631276011467,
0.01812359318137169,
-0.00020628391939681023,
-0.040638819336891174,
0.03254612535238266,
0.010436078533530235,
0.021751293912529945,
-0.013147354125976562,
0.007006906438618898,
0.027497990056872368,
-0.05819026008248329,
-0.008815060369670391,
-0.0029979480896145105,
-0.018340488895773888,
-0.012074839323759079,
0.02906203828752041,
0.017131907865405083,
0.02681823819875717,
-0.01802377961575985,
0.004608196206390858,
-0.05527155473828316,
-0.03513767942786217,
0.02949896641075611,
-0.030482525005936623,
-0.007156721781939268,
0.005294887349009514,
0.004600118845701218,
0.0011959313414990902,
0.007966497913002968,
0.010317247360944748,
0.023569777607917786,
-0.04160083457827568,
-0.009269002825021744,
-0.004413281567394733,
-0.044494904577732086,
0.005436921492218971,
-0.02811102569103241,
0.005365731660276651,
0.056272223591804504,
0.03645913675427437,
0.032481372356414795,
-0.012765972875058651,
-0.019338510930538177,
-0.02259110100567341,
-0.048078503459692,
0.02053222805261612,
0.00027370458701625466,
-0.0011993376538157463,
-0.07568152993917465,
-0.02545730583369732,
0.022087790071964264,
0.016014376655220985,
0.04974481463432312,
-0.021229365840554237,
0.004829351790249348,
0.023195086047053337,
0.0011918025556951761,
0.0038683759048581123,
-0.04563160613179207,
-0.0027263278607279062,
0.009139377623796463,
-0.05981571972370148,
-0.021797725930809975,
-0.012476778589189053,
-0.03466821834445,
0.007650640793144703,
0.027240348979830742,
0.0007357519934885204,
0.043730802834033966,
0.021004850044846535,
-0.02349642477929592,
0.0621812604367733,
0.030472179874777794,
-0.02264801412820816,
0.05782655254006386,
0.0049580601043999195,
0.031998101621866226,
0.04461251571774483,
-0.013559971004724503,
-0.03936885669827461,
0.017677992582321167,
-0.012781990692019463,
-0.005719969980418682,
-0.0173957422375679,
-0.0027106874622404575,
-0.006216634530574083,
-0.06045160070061684,
0.01951153576374054,
0.07310159504413605,
-0.03665429353713989,
-0.0037017131689935923,
0.04080571234226227,
0.025847455486655235,
0.061506450176239014,
-0.02452918328344822,
0.006162590347230434,
0.02069966495037079,
0.0077507677488029,
-0.0017383248778060079,
0.035840485244989395,
0.031273771077394485,
0.001672730315476656,
0.02490496076643467,
0.04275977611541748,
0.0075976052321493626,
-0.011339502409100533,
0.004614865407347679,
0.04171745851635933,
-0.03608221560716629,
-0.012948570773005486,
0.0001480298233218491,
-0.0545475110411644,
0.038352809846401215,
0.03583093360066414,
-0.017587246373295784,
0.08356834948062897,
-0.012272357940673828,
0.03314628824591637,
0.004970574285835028,
0.02953343652188778,
-0.021370315924286842,
-0.004321593791246414,
-0.016599975526332855,
0.011097838170826435,
0.010030935518443584,
-0.025442617014050484,
-0.00913155172020197,
0.00031324796145781875,
0.05190620571374893,
-0.03279149532318115,
0.007096101995557547,
-0.0011103339493274689,
-0.014601682312786579,
-0.019732754677534103,
-0.018114184960722923,
-0.03051384724676609,
-0.035352494567632675,
0.041324127465486526,
0.02828259952366352,
-0.004093109630048275,
0.00139651820063591,
-0.008062726818025112,
-0.022688910365104675,
0.0567731149494648,
-0.06941267848014832,
0.002255135215818882,
0.0026114305946975946,
0.017432373017072678,
-0.016730571165680885,
0.0074240402318537235
] |
<p>I'm current developing cargo loader software, but i have a little challenge with calculating load for each axle when a cargo is placed on container. I know that all axles will be affected (the nearest ones are the most affected ones of course), and I want to find approximately the value of each load. Here's example scenario in pictures:</p>
<p><img src="http://i.stack.imgur.com/LCqjF.jpg" alt="enter image description here"> </p>
<p>I tried to find loads using balance rules taking each point as a pivot and calculating equation based on that position as below (EDIT: on the following figure in case 4 the 5th axle is pivot, I forgot to show it on figure):</p>
<p><img src="http://i.stack.imgur.com/3AP9g.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/v0D88.jpg" alt="enter image description here"></p>
<p>But I think I have problem with above solution as I could not find F3, F4, F5 in special examples (putting "d" distance values from pivot - P.S in this last picture all "d"s are different distances from pivot in that case - so d3 in the first equation is not equal to d3 in second equation as these both have different distances to different pivots) - for easy calculation you can use Cramer's rule online calculator <a href="http://matrix.reshish.com/cramer.php" rel="nofollow">here</a>.</p>
<p>I tried to solve this problem with moment but I could not done as I'm not good in physics :( I could not find relations between different forces in that case, I had only F1*d1 + F2*d2 + F3*d3 = F4*d4 + F5*d5 and F1 + F2 + F3 + F4 + F5 = mg ===> i got 5 unknowns but only 2 equations :(</p>
<p>So, i need your help! Any suggestions will be appreciated! </p> | 4,626 | [
-0.034482087939977646,
-0.00026054849149659276,
-0.016158604994416237,
-0.0026888512074947357,
0.07646231353282928,
-0.010367454029619694,
-0.009948808699846268,
0.0015365455765277147,
0.0293935127556324,
0.0009933494729921222,
-0.005118185188621283,
0.03597252443432808,
0.03528960421681404,
0.040280912071466446,
0.0048003424890339375,
0.01899518072605133,
0.010812927968800068,
0.013991601765155792,
-0.0021065883338451385,
-0.025008879601955414,
0.01754712127149105,
-0.002534839790314436,
0.023127036169171333,
-0.03867029771208763,
-0.002814294770359993,
0.028368838131427765,
0.0636635273694992,
-0.0590139776468277,
0.002648534718900919,
0.060383640229701996,
-0.015870319679379463,
0.000454609195003286,
0.0000904277476365678,
0.02563517726957798,
0.010723752900958061,
0.03553274646401405,
0.004269447643309832,
0.009076985530555248,
-0.010434085503220558,
0.029127871617674828,
-0.020024411380290985,
0.012666739523410797,
-0.01682411879301071,
0.05938107892870903,
-0.020788976922631264,
0.02227678708732128,
0.027135835960507393,
0.03975822776556015,
0.03155876323580742,
-0.053369756788015366,
0.11866281926631927,
-0.00306724663823843,
0.014643129892647266,
0.03833705931901932,
-0.015905102714896202,
-0.01596822589635849,
0.03130916878581047,
0.06450948119163513,
0.013120898976922035,
-0.03181355819106102,
-0.02563425712287426,
-0.015349043533205986,
-0.001431296463124454,
-0.06735970824956894,
0.01624881848692894,
0.02900037355720997,
0.015115046873688698,
-0.008777142502367496,
0.027134407311677933,
-0.020002491772174835,
-0.03340800479054451,
0.012640794739127159,
0.08642680197954178,
-0.04361419379711151,
0.04386406019330025,
-0.042571812868118286,
0.009201360866427422,
0.00610637292265892,
0.03579876944422722,
0.0013194550992920995,
-0.021788163110613823,
0.007323606871068478,
0.019867245107889175,
0.031399890780448914,
0.02620813250541687,
-0.06683924049139023,
0.03619804605841637,
-0.026950012892484665,
-0.0014503782149404287,
0.016768014058470726,
0.0015821103006601334,
0.009580421261489391,
0.04053075611591339,
-0.004590096417814493,
0.007013541646301746,
0.012893341481685638,
-0.01810518093407154,
0.00045668231905438006,
-0.010137424804270267,
0.011771133169531822,
0.01998707465827465,
-0.08442052453756332,
-0.026453038677573204,
0.05715019628405571,
-0.02576294168829918,
0.008030323311686516,
-0.011800865642726421,
-0.026949724182486534,
0.00480263726785779,
0.004266728647053242,
-0.02621772512793541,
0.011286556720733643,
-0.022247597575187683,
-0.011830369010567665,
-0.06261202692985535,
-0.05131667107343674,
-0.030631782487034798,
-0.011342277750372887,
0.028589405119419098,
0.016963664442300797,
0.016751684248447418,
-0.03208981454372406,
0.0032766517251729965,
-0.017284298315644264,
-0.035562824457883835,
0.007210584357380867,
-0.004035243298858404,
-0.01938902959227562,
0.02003210037946701,
0.04243981093168259,
0.021378858014941216,
0.016805028542876244,
0.03028532676398754,
0.01862717606127262,
-0.037065692245960236,
-0.015401089563965797,
-0.0539073646068573,
-0.05057085305452347,
0.04808007553219795,
-0.03550976514816284,
-0.011623839847743511,
-0.05104012042284012,
-0.012987022288143635,
0.04220609366893768,
0.03326623886823654,
0.0308530256152153,
0.005752976518124342,
0.02096315287053585,
0.031070901080965996,
-0.017419544979929924,
-0.00597124919295311,
0.009487117640674114,
-0.04720958322286606,
0.027463775128126144,
0.014571251347661018,
-0.055659882724285126,
-0.003951380494982004,
0.0014052222250029445,
-0.013245311565697193,
-0.01696435920894146,
0.028707489371299744,
0.010289648547768593,
-0.021687164902687073,
0.007847596891224384,
-0.02576899528503418,
-0.03851179778575897,
0.045738834887742996,
-0.04031400382518768,
-0.0011632535606622696,
0.008031678386032581,
-0.015968821942806244,
-0.012984459288418293,
-0.029505431652069092,
-0.004781327210366726,
0.06593451648950577,
0.00525150541216135,
-0.01540174800902605,
-0.025775346904993057,
0.0115854786708951,
-0.0015249046264216304,
-0.05037946626543999,
-0.0927523523569107,
-0.008690091781318188,
0.0048638200387358665,
-0.008814902044832706,
0.05940444394946098,
-0.0034499429166316986,
0.026415452361106873,
0.05198213458061218,
-0.01687084138393402,
0.008481932803988457,
-0.040899042040109634,
0.029489364475011826,
-0.019864825531840324,
-0.007774756755679846,
0.013948105275630951,
0.007394811138510704,
0.002089649671688676,
-0.0168794896453619,
-0.02043871209025383,
0.01231579203158617,
0.015533903613686562,
0.006211044266819954,
-0.02131224237382412,
0.011950376443564892,
0.059565406292676926,
0.04867146536707878,
0.001791583956219256,
0.010108564980328083,
-0.04096732288599014,
0.01001049391925335,
-0.006112496368587017,
-0.018519489094614983,
0.008924894034862518,
0.026814233511686325,
-0.0010473552392795682,
0.03431086987257004,
0.004028213210403919,
0.026867059990763664,
-0.022543055936694145,
-0.026085272431373596,
0.052897948771715164,
0.059840403497219086,
0.009342390112578869,
0.03553902357816696,
0.019968081265687943,
0.005026109982281923,
0.041265759617090225,
0.021986469626426697,
-0.0233782846480608,
-0.05239441245794296,
-0.023491961881518364,
-0.016383230686187744,
0.05042032152414322,
-0.016890984028577805,
-0.027402644976973534,
0.059833116829395294,
-0.013669131323695183,
0.004215985536575317,
0.03795153647661209,
-0.010402346961200237,
-0.03791724890470505,
0.053409643471241,
0.039157819002866745,
-0.004301403183490038,
0.03216910734772682,
-0.00174824392888695,
0.026924068108201027,
0.0317554734647274,
-0.010682087391614914,
-0.01757313311100006,
-0.012037808075547218,
0.028774116188287735,
0.005090690217912197,
-0.00883863028138876,
-0.011431792750954628,
0.04759908840060234,
-0.00268935551866889,
-0.01763010397553444,
0.08854258060455322,
0.0068575539626181126,
-0.01596204936504364,
0.007220362313091755,
-0.0012879122514277697,
0.017897330224514008,
0.022881822660565376,
-0.02628880739212036,
0.0007775871199555695,
0.01144933607429266,
-0.022446928545832634,
0.0313619002699852,
-0.03299804776906967,
0.0132911941036582,
-0.004062697757035494,
-0.005216026213020086,
0.015299610793590546,
-0.00754518061876297,
0.005968886893242598,
-0.001374635030515492,
0.015367938205599785,
-0.033723633736371994,
-0.030379146337509155,
-0.001845345483161509,
0.003483089152723551,
-0.06898492574691772,
-0.01196607667952776,
-0.027503006160259247,
-0.0012717950157821178,
0.057289548218250275,
0.01737201400101185,
-0.006043777801096439,
0.04694646596908569,
-0.0031052008271217346,
-0.031220855191349983,
-0.036979589611291885,
0.03366236388683319,
0.019902247935533524,
-0.05490880087018013,
0.028291957452893257,
0.05110892280936241,
0.010968533344566822,
-0.050189994275569916,
0.0003273696347605437,
-0.03082050196826458,
-0.03209971636533737,
0.0031644601840525866,
0.012209550477564335,
-0.015117921866476536,
0.010513247922062874,
0.018298203125596046,
-0.0032521544490009546,
0.004563038237392902,
0.01580228842794895,
-0.03455039858818054,
-0.037732698023319244,
0.0013216894585639238,
-0.006358809769153595,
0.009912247769534588,
0.0069402358494699,
-0.014464390464127064,
0.0623483881354332,
0.014264624565839767,
-0.03673887625336647,
-0.05557073652744293,
-0.01135571114718914,
0.0005905081634409726,
-0.03643125295639038,
0.012606121599674225,
0.029716357588768005,
0.025962239131331444,
0.01749991811811924,
-0.02317129448056221,
0.011166990734636784,
0.04402387887239456,
0.008341168984770775,
0.03143354505300522,
0.019429480656981468,
0.007019138894975185,
-0.027290167286992073,
0.06558874249458313,
0.013706682249903679,
0.009082505479454994,
-0.001662936992943287,
0.032267868518829346,
0.033063311129808426,
0.00615720683708787,
-0.08805908262729645,
-0.006258542183786631,
0.008857534267008305,
-0.005370372906327248,
0.01575813814997673,
0.023636525496840477,
0.008082957938313484,
-0.04807768389582634,
-0.008095011115074158,
0.020987780764698982,
0.08606193959712982,
-0.017997365444898605,
-0.01088032778352499,
0.07344523817300797,
0.045175328850746155,
0.003956961445510387,
-0.03256373852491379,
-0.007793749682605267,
-0.00024584357743151486,
0.03045918047428131,
-0.048670198768377304,
-0.03580789268016815,
0.00714515708386898,
0.011075906455516815,
0.03550132364034653,
0.02496553212404251,
-0.0016294780652970076,
0.0239908155053854,
-0.04872260242700577,
-0.044968098402023315,
-0.052363231778144836,
0.07610631734132767,
0.0012307125143706799,
0.050871774554252625,
0.023229820653796196,
-0.014302114024758339,
-0.0034367006737738848,
0.015268177725374699,
-0.07600535452365875,
0.027406271547079086,
0.039221446961164474,
-0.0035957423970103264,
0.02077905274927616,
-0.025885693728923798,
-0.028274938464164734,
-0.07430572807788849,
-0.004340420477092266,
0.015708617866039276,
0.023742130026221275,
-0.06559769064188004,
0.013181866146624088,
0.015358620323240757,
-0.022260261699557304,
0.015133720822632313,
0.013549946248531342,
0.03215572610497475,
-0.013268647715449333,
0.022258615121245384,
0.03102545440196991,
-0.02082078717648983,
-0.008228483609855175,
-0.04318854212760925,
0.02762887254357338,
0.03028722107410431,
0.03136562928557396,
0.011049563065171242,
0.03931431472301483,
-0.023172473534941673,
-0.0233949963003397,
-0.021104754880070686,
0.019603101536631584,
0.03793743997812271,
-0.019085409119725227,
-0.031343504786491394,
-0.030609846115112305,
0.03368151932954788,
-0.012545238249003887,
0.034689679741859436,
-0.054458342492580414,
0.02423913963139057,
0.024455266073346138,
-0.009506101720035076,
-0.00490653095766902,
0.017247522249817848,
0.07639166712760925,
0.03594552353024483,
-0.04002004116773605,
-0.047317951917648315,
-0.0030312491580843925,
-0.039020564407110214,
-0.010177033953368664,
0.019189678132534027,
-0.018068939447402954,
0.021752551198005676,
0.019219527021050453,
0.050717126578092575,
-0.000879446102771908,
-0.01766221784055233,
0.056525543332099915,
0.014442331157624722,
0.029661409556865692,
0.012423673644661903,
0.0003841328725684434,
0.027344539761543274,
0.009613143280148506,
0.065924733877182,
-0.010547257959842682,
0.012361905537545681,
-0.06073087453842163,
0.0018981494940817356,
0.046448878943920135,
0.018077723681926727,
-0.018156779929995537,
0.03704383596777916,
0.000775557360611856,
-0.033671192824840546,
0.03703802824020386,
-0.016661683097481728,
0.05510801076889038,
-0.022524790838360786,
0.032257020473480225,
-0.022364720702171326,
-0.04210403934121132,
-0.06565753370523453,
0.019673747941851616,
-0.01839868538081646,
0.006275599356740713,
-0.017110753804445267,
0.006170520558953285,
0.02385016530752182,
0.05561518669128418,
0.027791159227490425,
0.014932721853256226,
0.03181154653429985,
-0.0033253240399062634,
-0.008263682015240192,
0.04360444098711014,
-0.03185857832431793,
-0.052090875804424286,
0.02281297743320465,
-0.01736697368323803,
-0.04172459989786148,
0.043236155062913895,
-0.05064288154244423,
-0.005422180984169245,
0.04498634114861488,
0.010956737212836742,
0.03308172896504402,
0.0173017717897892,
-0.01924663409590721,
-0.0018797962693497539,
0.06323035061359406,
-0.04159362241625786,
0.03563903272151947,
0.019621221348643303,
-0.045227546244859695,
-0.03044731356203556,
-0.009778764098882675,
0.02362123876810074,
0.017732374370098114,
-0.04424520581960678,
-0.023941557854413986,
0.060517121106386185,
-0.01625204086303711,
0.01862623542547226,
0.006084222812205553,
0.03359111398458481,
-0.02980967052280903,
-0.01257595606148243,
0.002583357971161604,
0.03741529956459999,
0.005009768530726433,
0.012746875174343586,
0.005367068108171225,
0.007458921521902084,
-0.00986182875931263,
-0.01596853882074356,
-0.014116493053734303,
-0.019599420949816704,
0.0019625897984951735,
0.002093101618811488,
-0.025683118030428886,
0.008182240650057793,
-0.02133028395473957,
0.02737695910036564,
0.0007613793131895363,
-0.0012898189015686512,
0.04736403003334999,
0.025172250345349312,
0.024285122752189636,
0.0554334856569767,
-0.01118072122335434,
-0.040775809437036514,
0.06658528000116348,
0.010019608773291111,
0.020098913460969925,
-0.010801217518746853,
0.02001926861703396,
0.017939312383532524,
0.004807986784726381,
-0.01781621016561985,
-0.0004291571967769414,
0.0232778862118721,
-0.01942421868443489,
-0.02898922562599182,
-0.05728424713015556,
-0.05607907474040985,
0.010407323949038982,
-0.05321289226412773,
-0.014463885687291622,
0.06311693042516708,
-0.04747149348258972,
-0.008439467288553715,
0.021069753915071487,
-0.04624874144792557,
0.07746798545122147,
-0.013532537035644054,
-0.016018060967326164,
0.004149640444666147,
0.02994576282799244,
0.0013897332828491926,
0.009644071571528912,
0.012797676958143711,
-0.011226816102862358,
-0.0180358923971653,
0.004803952295333147,
-0.001163805485703051,
0.02176293171942234,
-0.031082337722182274,
0.010276331566274166,
-0.01953451707959175,
0.03659103438258171,
-0.0035387661773711443,
0.003472972195595503,
0.013690207153558731,
0.03477500006556511,
-0.00493776286020875,
-0.011510798707604408,
0.01960121840238571,
0.015509684570133686,
-0.0004986493731848896,
-0.029058018699288368,
-0.04828463867306709,
-0.0360056534409523,
0.024026183411478996,
0.060868676751852036,
0.0019600691739469767,
0.015923364087939262,
0.0014277254231274128,
0.02376404218375683,
0.07477418333292007,
-0.043157998472452164,
0.005237713921815157,
-0.01560916192829609,
0.00705919461324811,
-0.015255901031196117,
-0.044807903468608856,
-0.0580480620265007,
0.05527373403310776,
0.08693971484899521,
-0.027787338942289352,
0.03625338897109032,
0.01625549979507923,
0.0339590385556221,
-0.004017042461782694,
0.008778810501098633,
-0.01618712767958641,
0.009286297485232353,
-0.004684959538280964,
0.06162324920296669,
-0.016817104071378708,
-0.037693873047828674,
-0.0004174517234787345,
0.023407604545354843,
-0.01213446632027626,
-0.030329005792737007,
-0.0021860108245164156,
-0.011092622764408588,
-0.01957150548696518,
-0.026886310428380966,
-0.040655530989170074,
-0.003687865100800991,
0.0017459873342886567,
0.025884592905640602,
0.028824567794799805,
-0.0756625384092331,
0.05621851235628128,
0.03188502416014671,
-0.004977504722774029,
-0.034744743257761,
-0.030792007222771645,
-0.044940218329429626,
0.042226094752550125,
0.045718852430582047,
-0.04899965971708298,
-0.011729626916348934,
0.02264210768043995,
0.05588293820619583,
-0.010616250336170197,
0.006376579403877258,
-0.02742156758904457,
-0.028352515771985054,
0.003765771398320794,
-0.051364295184612274,
-0.06355223059654236,
0.04168545827269554,
-0.01272832602262497,
-0.02058112993836403,
0.022730696946382523,
-0.006254879757761955,
0.024979792535305023,
0.035561077296733856,
0.020766403526067734,
-0.004935116972774267,
0.05539131537079811,
-0.04458773881196976,
-0.012837986461818218,
-0.024630211293697357,
-0.02032935619354248,
0.1553112417459488,
-0.006529034115374088,
-0.0012113613774999976,
-0.02555154822766781,
-0.028049295768141747,
-0.0009718720684759319,
-0.0359465517103672,
-0.06213708594441414,
0.007263882085680962,
-0.005790160037577152,
-0.029156705364584923,
0.003134702332317829,
0.015321901068091393,
-0.01094047911465168,
0.003307673614472151,
0.050687696784734726,
-0.04955766722559929,
-0.03217712417244911,
0.016244057565927505,
0.024824785068631172,
-0.00013153362669982016,
-0.01417422667145729,
-0.033803269267082214,
0.037920992821455,
0.01803019270300865,
-0.027600856497883797,
-0.014717020094394684,
-0.02436956763267517,
0.031603340059518814,
0.031223081052303314,
-0.03172963485121727,
0.05938408523797989,
0.021324925124645233,
-0.020120227709412575,
-0.015099487267434597,
0.05215936899185181,
-0.006181555800139904,
-0.046597760170698166,
-0.02621547132730484,
0.0058624823577702045,
-0.004310720134526491,
-0.02308577671647072,
0.014882227405905724,
-0.018287016078829765,
-0.008581042289733887,
-0.0024283386301249266,
-0.06662366539239883,
0.035438477993011475,
-0.004567763768136501,
-0.01050501223653555,
0.02775665372610092,
-0.002807849319651723,
-0.0004893798613920808,
-0.06706885993480682,
-0.006970010232180357,
0.017694037407636642,
0.043673075735569,
-0.009651821106672287,
-0.015231410972774029,
-0.03186432272195816,
0.02143738977611065,
0.01897300034761429,
0.005925464443862438,
0.02558051608502865,
0.007327698171138763,
-0.017228513956069946,
-0.05675594136118889,
0.09592926502227783,
0.014268888160586357,
-0.007167957257479429,
-0.04129164665937424,
-0.0014721027109771967,
-0.005187851842492819,
-0.04942264035344124,
0.005959438160061836,
0.012952486053109169,
0.0002915009390562773,
0.025753337889909744,
-0.03484220430254936,
-0.0006367850583046675,
-0.06745412945747375,
-0.011827844195067883,
-0.022365685552358627,
-0.008876863867044449,
-0.06929822266101837,
-0.0012336483923718333,
0.02519509382545948,
0.06332193315029144,
0.04988919198513031,
0.0144730219617486,
-0.008359978906810284,
0.03600041940808296,
0.008302532136440277,
-0.02518041804432869,
-0.030996013432741165,
0.034402452409267426,
-0.0031204726547002792,
0.001369419158436358,
-0.025594495236873627,
0.055753134191036224,
0.01230569276958704,
-0.005757749546319246,
0.00738572096452117,
0.039696626365184784,
-0.0004803381743840873,
0.014864567667245865,
0.01605929434299469,
-0.01618514023721218,
0.036124374717473984,
0.0464148111641407,
-0.0348065011203289,
-0.06641191989183426,
-0.009538315236568451,
-0.05810687690973282,
-0.05091216042637825,
-0.0198530163615942,
-0.006852608639746904,
-0.021663811057806015,
-0.027699392288923264,
-0.053881168365478516,
0.02304186299443245,
-0.03581353276968002,
0.0181907769292593,
-0.02681906335055828,
-0.002841697307303548,
-0.05876140668988228,
-0.0012728481087833643,
-0.06719202548265457,
0.013022365048527718,
0.00414264528080821,
0.019676974043250084,
0.0279125664383173,
-0.00010322437447030097,
0.07049530744552612,
-0.053644824773073196,
0.005414705723524094,
0.01896420679986477,
0.040050335228443146,
-0.02428492158651352,
-0.03995007649064064,
0.027226367965340614,
-0.023350557312369347,
-0.0017067380249500275,
0.03967953473329544,
0.00948125496506691,
0.0068481601774692535,
0.012145450338721275,
0.003013437846675515,
-0.021934889256954193,
0.0797935277223587,
-0.017404284328222275,
-0.003576331539079547,
-0.04694512486457825,
-0.003617786103859544,
0.004932560957968235,
0.015928031876683235,
-0.019419649615883827,
-0.029524432495236397,
-0.021802525967359543,
0.017753886058926582,
0.03025943599641323,
0.001556743634864688,
0.020666856318712234,
0.03421682491898537,
0.004438465926796198,
-0.01233880128711462,
-0.007371525280177593,
0.010590148158371449,
0.012665647082030773,
0.01961742341518402,
-0.012739022262394428,
0.004518277943134308,
0.02836022526025772,
0.04659616947174072,
-0.08314498513936996,
-0.029459716752171516,
0.025076821446418762,
0.005156810395419598,
0.05750573053956032,
-0.022507358342409134,
0.002076791599392891,
-0.002987467683851719,
-0.05460895225405693,
0.011503159068524837,
-0.02126220241189003,
-0.003814403433352709,
-0.010931397788226604,
-0.0052757179364562035,
0.010357087478041649,
0.015802757814526558,
0.016359644010663033,
0.008054687641561031,
0.05360648036003113,
0.038309693336486816,
-0.04782501980662346,
-0.05892292410135269,
0.02205272763967514,
0.03646033629775047,
0.007989584468305111,
-0.0422101691365242,
0.021189607679843903,
-0.007124497089534998,
-0.020259834825992584,
0.007523626554757357,
-0.013673386536538601,
-0.024524442851543427,
-0.01228806097060442,
0.03412072733044624,
-0.006854091305285692,
0.06210876628756523,
0.004262522794306278,
0.019236527383327484,
-0.00808225478976965,
-0.02339036762714386,
-0.009541648440063,
0.005608942359685898,
-0.020018426701426506,
0.0011340072378516197,
0.01808386668562889,
-0.04362785816192627,
-0.020251061767339706,
0.01811586506664753,
-0.041139375418424606,
-0.021353434771299362,
0.003130521858111024,
-0.001112528843805194,
-0.023007456213235855,
-0.0297758299857378,
-0.013023091480135918,
-0.021776637062430382,
0.01858910545706749,
0.04430845007300377,
-0.011434433981776237,
-0.006634540390223265,
0.010148031637072563,
-0.010725010186433792,
-0.02944471314549446,
-0.0013313312083482742,
0.003429719479754567,
-0.019186675548553467,
-0.051870040595531464,
-0.030774232000112534,
0.0041455961763858795,
-0.021223198622465134,
-0.022287024185061455,
-0.02109370566904545,
-0.03617827966809273,
0.03113432042300701,
-0.011444863863289356,
-0.02226901613175869,
0.01794961281120777,
0.0315796360373497,
0.005284583196043968,
-0.09745243191719055,
0.022863231599330902,
0.048718396574258804,
-0.1028691828250885,
-0.0049169957637786865,
-0.017514176666736603,
-0.0214398056268692,
0.04038744792342186,
-0.007082587573677301,
-0.019195018336176872,
-0.012670996598899364,
-0.028980787843465805,
-0.03142089024186134,
0.012533821165561676,
-0.007591442205011845,
0.017224835231900215,
-0.004610470496118069,
-0.025905460119247437,
-0.0027089999057352543,
-0.020677566528320312,
0.005515225697308779,
-0.019320230931043625,
-0.014196045696735382,
0.006710432004183531,
-0.002644131425768137,
0.036746155470609665,
-0.017396096140146255,
0.012748746201395988,
0.009576027281582355,
0.0045645213685929775,
0.026791095733642578,
-0.008693721145391464,
0.00728081539273262,
0.020208900794386864,
-0.018642183393239975,
-0.045576997101306915,
0.03745000809431076,
-0.08119004964828491,
0.012527297250926495,
-0.006371101830154657,
-0.007809854112565517,
0.026470821350812912,
-0.07414308935403824,
0.02067018300294876,
0.048064228147268295,
-0.040497761219739914,
0.01073486264795065,
0.035247981548309326,
0.04254991188645363,
0.04177993908524513,
-0.010775341652333736,
0.059906333684921265,
-0.0012807183666154742,
-0.08357356488704681,
0.02790859341621399,
-0.010379364714026451,
0.010181662626564503,
0.008023185655474663,
-0.018442897126078606,
0.06318067759275436,
-0.03329929709434509,
-0.012074521742761135,
-0.004685195162892342,
-0.010235325433313847,
0.004325775895267725,
-0.022742649540305138,
0.018628912046551704,
-0.04649591073393822,
-0.018144337460398674,
0.04401326924562454,
0.009071280248463154,
0.06827376782894135,
-0.018659308552742004,
-0.010695191100239754,
0.01445743627846241,
0.02487388625741005,
0.0006892136880196631,
0.0005075985100120306,
-0.04620141535997391,
0.021945009008049965,
-0.03336569294333458,
0.03995070606470108,
-0.0128287672996521,
-0.020382223650813103,
0.019953522831201553,
-0.000017167632904602215,
0.011216124519705772,
-0.008661585859954357,
0.0238662026822567,
0.010564574971795082,
-0.036061353981494904,
-0.04420583322644234,
-0.011842377483844757,
0.033275701105594635,
0.030062725767493248,
0.013234246522188187,
-0.042648181319236755,
-0.029053296893835068,
-0.012335035018622875,
0.005745171569287777,
-0.00771238561719656,
-0.029755450785160065,
-0.004542460199445486,
0.03165505453944206,
0.008570373058319092,
0.0034216889180243015
] |
<p>The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = 5.00~m$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass $m_2 = 9.40~kg$, initially at rest. The two blocks never touch. Calculate the maximum height to which $m_1$ rises after the elastic collision."</p>
<p><img src="http://i.stack.imgur.com/Uz4To.gif" alt="enter image description here"></p>
<p>This question comes from webassign. On webassign they have a feature called "Watch It;" this feature allows you to see a person solve a problem nearly similar to this one. I feel as though there is an error in what the person says in the video. The person says that the mechanical energy of the block-earth system is conserved, but that wouldn't be true; if we were looking at the block-block system--that is, $m_1$ and $m_2$--the mechanical energy would be conserved. By looking at just the block-earth system, there would be a loss in kinetic energy, because when the two blocks "collide," they apply a force over a distance(work), causing a change in kinetic energy of each block, because the kinetic energy of the moving block is transferred into the other block, which is why the first block doesn't return to its initial height. Is this correct? If not, what am I misunderstanding?</p>
<p>As a result of this contention with what the person said in the video, I am not very certain on how to solve this problem.
EDIT (attempt to solve): </p>
<p>Energy analysis:</p>
<p>$m_1:$ $PE_i=mgh=KE_f$, where $h$ is the height from which it drops.</p>
<p>$KE_i=0~J$; $PE_f=mgh_0$, where $h_0$ is the height is rises to after the collision</p>
<p>$m_2:$ $KE_i=PE_i=PE_f=0~j$; $KE_f=\frac{1}{2}m_2v^2_{f,2}$</p>
<p>Momentum Analysis:</p>
<p>$m_1:$ $\vec{p}_{i,1}=m_1\vec{v}_{i,1}$; $\vec{p}_{f,1}=m_1\vec{v}_{f,1}$</p>
<p>$m_2:$ $\vec{p}_{i,2}=m_2\vec{v}_{i,1}$; $\vec{p}_{f,2}=m_2\vec{v}_{f,2}$</p>
<p>When I set up an equation for change in mechanical energy, and an equation for conservation of momentum, I get two equations, with a lot of unknowns. What did I do wrong?</p> | 44 | [
-0.028050309047102928,
-0.03430159389972687,
-0.05423586815595627,
-0.012444175779819489,
0.022792788222432137,
0.008534574881196022,
-0.047413233667612076,
-0.05234638974070549,
-0.011785043403506279,
-0.02221347950398922,
0.02740754559636116,
0.03195783495903015,
0.039037954062223434,
0.06710420548915863,
0.0268079973757267,
0.021498609334230423,
0.018470628187060356,
0.005271431524306536,
0.018502896651625633,
-0.0318504236638546,
-0.00331669463776052,
-0.014338891953229904,
0.012191698886454105,
0.006943484302610159,
-0.01042714063078165,
0.0014364083763211966,
0.03616783022880554,
-0.04951991140842438,
-0.010870544239878654,
0.05223141610622406,
0.012488951906561852,
-0.041929781436920166,
0.02718537487089634,
-0.008409373462200165,
-0.013347499072551727,
0.023632695898413658,
-0.056764036417007446,
-0.022346513345837593,
0.00042516455869190395,
0.02815626561641693,
-0.01238140556961298,
-0.024031689390540123,
-0.011146575212478638,
0.0331762433052063,
-0.03909507021307945,
0.02196730673313141,
0.01005815900862217,
-0.004287307616323233,
0.08790253102779388,
-0.05371662974357605,
0.0638832375407219,
0.0001979284716071561,
0.05239752680063248,
0.02190271019935608,
-0.0016003731871023774,
-0.027799857780337334,
0.06471250206232071,
0.05259932950139046,
0.0310672540217638,
-0.027835525572299957,
-0.04177592322230339,
-0.006482478231191635,
-0.029661523178219795,
-0.00043467688374221325,
-0.0005433028563857079,
0.023426478728652,
0.0038689044304192066,
0.022358637303113937,
0.04127597063779831,
0.057002175599336624,
0.011624077335000038,
0.005696464795619249,
0.042085833847522736,
-0.03666018694639206,
0.034028682857751846,
-0.0074225254356861115,
0.017311695963144302,
0.03992898017168045,
0.013703863136470318,
0.04271939396858215,
-0.004581047687679529,
0.024930637329816818,
0.0670158788561821,
0.08440109342336655,
0.02179214172065258,
-0.011778238229453564,
0.05163893103599548,
0.012533323839306831,
0.03516007587313652,
0.03858986124396324,
0.029031703248620033,
-0.004152803681790829,
-0.0017383843660354614,
-0.03966957703232765,
0.017274778336286545,
0.029919125139713287,
0.030735021457076073,
0.038976605981588364,
0.0377325713634491,
0.009298947639763355,
-0.002269092481583357,
-0.028043698519468307,
0.023692067712545395,
0.02954273670911789,
0.05198688060045242,
-0.006825473625212908,
-0.020715396851301193,
0.0008795583853498101,
0.00556503189727664,
-0.000742055824957788,
-0.0008189483196474612,
0.022028103470802307,
-0.006680932827293873,
-0.022464675828814507,
0.017022615298628807,
-0.02343624271452427,
-0.016598787158727646,
0.0023242775350809097,
0.048273056745529175,
-0.009519053623080254,
0.055751584470272064,
-0.040490761399269104,
-0.0002921714331023395,
-0.06034388765692711,
-0.06343712657690048,
-0.035958826541900635,
0.0181268397718668,
-0.006531298626214266,
-0.051475487649440765,
0.04560447111725807,
0.04514172300696373,
0.0046311719343066216,
-0.02111808955669403,
-0.0330120250582695,
-0.012518665753304958,
0.024066869169473648,
-0.06475073844194412,
-0.03283873572945595,
0.06418786942958832,
0.028573572635650635,
-0.011791439726948738,
-0.07301996648311615,
-0.01787741295993328,
0.00568679254502058,
0.05910303071141243,
-0.03497457504272461,
0.0035905682016164064,
0.01021894533187151,
0.04202217608690262,
-0.013606385327875614,
0.008646449074149132,
-0.03001096099615097,
-0.029661070555448532,
-0.038318656384944916,
0.0058310204185545444,
-0.07713565230369568,
0.007214410696178675,
0.03051532804965973,
-0.03888091444969177,
-0.0008781144861131907,
0.00597692746669054,
-0.010770756751298904,
0.014914006926119328,
0.0010989477159455419,
-0.015601861290633678,
-0.0217942725867033,
0.05914051830768585,
0.008558981120586395,
0.018564337864518166,
0.02997409738600254,
0.02394755557179451,
0.010410298593342304,
-0.010446199215948582,
0.042938895523548126,
0.020817955955863,
-0.027833150699734688,
-0.004427878186106682,
-0.037055112421512604,
-0.023357363417744637,
-0.027506059035658836,
-0.03624540567398071,
-0.03295841068029404,
-0.021437842398881912,
-0.01562890037894249,
0.017130525782704353,
0.037431277334690094,
-0.0129169262945652,
0.015004285611212254,
-0.011555743403732777,
-0.03318051993846893,
-0.04866759479045868,
-0.07155115157365799,
0.019910413771867752,
-0.02725866250693798,
0.00903690978884697,
-0.011188779957592487,
-0.032092832028865814,
-0.0010415819706395268,
-0.05264968052506447,
0.0222381092607975,
0.038847971707582474,
0.04273243993520737,
0.009909632615745068,
0.01675337180495262,
-0.010709934867918491,
0.08222674578428268,
0.027552083134651184,
0.052032679319381714,
-0.023386739194393158,
-0.03459323197603226,
-0.034231480211019516,
0.002948802663013339,
-0.03384147956967354,
-0.017773889005184174,
0.057637713849544525,
0.008995523676276207,
0.01798165589570999,
-0.0005315204034559429,
-0.009700221009552479,
-0.023088935762643814,
-0.019532786682248116,
0.053801827132701874,
0.031066052615642548,
0.001551939989440143,
0.015622073784470558,
0.014401379972696304,
0.017897238954901695,
0.03103155829012394,
-0.015355109237134457,
-0.009608537890017033,
-0.0437476746737957,
-0.0034549920819699764,
-0.008011161349713802,
0.017628178000450134,
-0.0433722659945488,
0.03054203651845455,
0.009607167914509773,
0.037068359553813934,
0.02370547689497471,
-0.010745396837592125,
0.005047196056693792,
-0.015250861644744873,
0.025692153722047806,
0.03215663880109787,
0.011119628325104713,
0.032402973622083664,
0.0119019178673625,
0.04751259833574295,
-0.03174208104610443,
-0.0011845093686133623,
-0.016586774960160255,
-0.014453915879130363,
-0.005445993971079588,
0.03719962760806084,
-0.017934249714016914,
0.016347220167517662,
0.02602376416325569,
-0.006588782649487257,
0.022245680913329124,
0.0416596494615078,
-0.0028231560718268156,
0.006606150418519974,
-0.07667212188243866,
-0.04013969376683235,
-0.004321610555052757,
-0.00035048832069151103,
0.0068911537528038025,
-0.01301885861903429,
0.03514629974961281,
-0.03592211380600929,
0.014958580955862999,
0.015613239258527756,
-0.02861209027469158,
0.03373429551720619,
0.0121096670627594,
0.006421645171940327,
0.013658002950251102,
0.016467193141579628,
-0.059045761823654175,
0.00440588453784585,
-0.004366828128695488,
-0.018710806965827942,
-0.010468843393027782,
-0.011582572013139725,
-0.0657462477684021,
0.02372121624648571,
-0.057791247963905334,
0.004092490300536156,
0.0728873535990715,
0.02778804674744606,
-0.003537167562171817,
0.06592138856649399,
0.03817550465464592,
-0.045377083122730255,
-0.032555267214775085,
-0.015966692939400673,
-0.010407041758298874,
-0.05384451523423195,
-0.0063291327096521854,
0.06196075677871704,
0.012818475253880024,
-0.03882201761007309,
0.019792752340435982,
-0.07337275892496109,
-0.027150094509124756,
-0.012102815322577953,
-0.017881182953715324,
0.0009696981869637966,
0.005878766067326069,
0.01733545772731304,
-0.028299372643232346,
0.04374237358570099,
-0.0005025212885811925,
-0.04730987548828125,
-0.040160030126571655,
-0.0147659657523036,
-0.026085257530212402,
0.04251356050372124,
-0.0388217456638813,
-0.014330280013382435,
0.11354682594537735,
0.016481440514326096,
0.0037990061100572348,
-0.02149239368736744,
-0.01830255053937435,
0.0260967705398798,
-0.023941636085510254,
-0.023756476119160652,
0.023469241335988045,
0.008415653370320797,
-0.024335619062185287,
0.002068642294034362,
0.03168867528438568,
0.04255395382642746,
-0.015073764137923717,
0.0022877613082528114,
-0.015101680532097816,
-0.0009373629000037909,
0.007072435226291418,
0.05629276856780052,
-0.0007084045209921896,
-0.0020340168848633766,
0.022728968411684036,
-0.010573433712124825,
0.04908725991845131,
-0.014801799319684505,
-0.06925224512815475,
0.07380732893943787,
-0.02775580994784832,
0.011706726625561714,
-0.017231224104762077,
0.0407494492828846,
0.008581954054534435,
-0.014760791324079037,
0.0028936874587088823,
0.02775341272354126,
0.04577580466866493,
0.01601840741932392,
0.0070298658683896065,
0.0188896507024765,
0.024424860253930092,
-0.012962006032466888,
-0.048453330993652344,
-0.021972693502902985,
0.01216750219464302,
0.04126309975981712,
0.023305926471948624,
-0.013408605940639973,
0.010425115935504436,
0.023619970306754112,
0.04153919219970703,
0.016358107328414917,
-0.03347637876868248,
-0.029158474877476692,
-0.053287021815776825,
-0.0004378428857307881,
-0.0016853527631610632,
0.028046052902936935,
-0.025096168741583824,
0.017080098390579224,
-0.0005899462848901749,
0.025174684822559357,
0.027115382254123688,
0.0067579601891338825,
-0.08610619604587555,
0.028063993901014328,
-0.04136800765991211,
-0.03908803313970566,
0.044134873896837234,
-0.02778920903801918,
0.032449644058942795,
-0.0042540160939097404,
0.008928879164159298,
-0.003010357264429331,
0.030221274122595787,
-0.03748895227909088,
-0.007799974642693996,
-0.020309986546635628,
-0.025775529444217682,
-0.010410753078758717,
-0.025114135816693306,
0.040392741560935974,
-0.03492477163672447,
0.018851783126592636,
0.03451772779226303,
-0.027675699442625046,
0.01979169063270092,
-0.004889543168246746,
-0.019388245418667793,
0.037247177213430405,
0.01458335854113102,
-0.03605024144053459,
0.038838133215904236,
-0.0011147372424602509,
-0.0014737144811078906,
0.0171502698212862,
0.04287140071392059,
0.001780935563147068,
0.014057089574635029,
-0.024798506870865822,
-0.015965096652507782,
-0.012993304058909416,
0.00403108773753047,
0.05063365027308464,
-0.053686898201704025,
0.00895712897181511,
-0.0057701123878359795,
0.045977506786584854,
-0.0018537855939939618,
0.07634516805410385,
0.06207215413451195,
0.034051280468702316,
-0.007135886233299971,
-0.06970556080341339,
-0.035029828548431396,
-0.07255198061466217,
-0.019570613279938698,
0.0037019464652985334,
0.00409774761646986,
-0.03520464897155762,
-0.009160812944173813,
0.055761367082595825,
0.05988621339201927,
-0.005894900765269995,
0.06216645985841751,
-0.008097651414573193,
0.002502712421119213,
-0.030641652643680573,
0.015818441286683083,
-0.0044494555331766605,
0.01960902102291584,
0.02997444197535515,
-0.05971312150359154,
0.0069716270081698895,
-0.04132742062211037,
-0.04157610237598419,
0.006685120519250631,
0.041008129715919495,
-0.016153788194060326,
0.011112868785858154,
-0.0597517155110836,
-0.0027166204527020454,
-0.0213198009878397,
-0.026562463492155075,
0.07363945990800858,
0.009721503593027592,
0.06544951349496841,
0.008097953163087368,
0.011116099543869495,
-0.027499757707118988,
-0.046588048338890076,
0.0010336863342672586,
0.026255318894982338,
0.008644264191389084,
-0.003991138655692339,
0.017497600987553596,
0.008131314069032669,
0.032110150903463364,
0.037999071180820465,
-0.0034464688505977392,
0.010345407761633396,
-0.011231616139411926,
-0.022917328402400017,
-0.032248031347990036,
-0.06109129264950752,
0.003819303121417761,
-0.023837395012378693,
-0.06935379654169083,
0.0050554280169308186,
-0.03354744240641594,
-0.08238756656646729,
0.028169600293040276,
-0.016235122457146645,
-0.01207142323255539,
-0.032648634165525436,
0.006091204006224871,
0.045665595680475235,
0.07036905735731125,
-0.02013062685728073,
0.025517944246530533,
0.026890413835644722,
-0.06048860773444176,
0.00809288676828146,
-0.02820035070180893,
0.023434067144989967,
-0.02222961001098156,
0.016587616875767708,
-0.04253092780709267,
0.049305010586977005,
-0.050791576504707336,
-0.007290434092283249,
-0.0031603234820067883,
0.03283558785915375,
-0.026256676763296127,
-0.04837629571557045,
0.015498675405979156,
0.02864709310233593,
-0.015312871895730495,
0.00613559503108263,
-0.03182096406817436,
-0.008526016026735306,
-0.02671903744339943,
-0.01947072520852089,
0.04214870557188988,
0.0012136524310335517,
0.0011194008402526379,
0.022165093570947647,
-0.0057513234205543995,
0.0028002012986689806,
-0.05159294232726097,
-0.011106804013252258,
-0.0045418585650622845,
-0.04189447686076164,
0.029011951759457588,
-0.008382421918213367,
0.028464728966355324,
0.05725330486893654,
-0.006596873514354229,
-0.004846095573157072,
0.022517213597893715,
-0.006234265398234129,
-0.00036330256261862814,
-0.03302522748708725,
-0.011323336511850357,
0.04199552536010742,
-0.002541508059948683,
-0.023059837520122528,
-0.02320747636258602,
0.059223659336566925,
0.025807632133364677,
-0.026075871661305428,
-0.005366850644350052,
-0.03653869777917862,
0.006384197622537613,
-0.026181122288107872,
-0.018012626096606255,
0.035637956112623215,
-0.038105592131614685,
-0.0010563504183664918,
0.028974216431379318,
0.030645420774817467,
0.05270078778266907,
0.013027293607592583,
-0.020121511071920395,
0.019943008199334145,
-0.005611678585410118,
-0.03892792761325836,
-0.028362547978758812,
0.01424899511039257,
-0.02814977802336216,
-0.03512472286820412,
-0.0021677189506590366,
0.008056995458900928,
0.01597737893462181,
-0.011434875428676605,
-0.004380977712571621,
0.06380641460418701,
0.04045085981488228,
-0.0010864968644455075,
0.009762963280081749,
0.04121183976531029,
-0.005300901830196381,
0.026737917214632034,
-0.009272032417356968,
0.009268335998058319,
0.0034594915341585875,
-0.05693209916353226,
0.012876533903181553,
-0.03692575544118881,
0.011989089660346508,
0.028466390445828438,
0.09200235456228256,
-0.03293986618518829,
-0.030816631391644478,
0.024732837453484535,
-0.02770346775650978,
0.016777126118540764,
-0.0309772789478302,
-0.0056767938658595085,
0.028558725491166115,
-0.02035236731171608,
-0.03354489803314209,
-0.019982056692242622,
-0.017595067620277405,
0.021978916600346565,
0.07232634723186493,
-0.022774597629904747,
0.05893668159842491,
-0.021331502124667168,
0.005363705568015575,
0.03013690561056137,
-0.024067794904112816,
0.005511444061994553,
-0.024077339097857475,
0.014320907182991505,
0.03365598991513252,
-0.03381491079926491,
0.0028964783996343613,
0.05301797389984131,
0.03228602185845375,
-0.028386250138282776,
-0.005649625789374113,
0.02153836376965046,
0.018604205921292305,
0.01550984289497137,
-0.06487768143415451,
-0.04949808865785599,
0.016997799277305603,
-0.023574599996209145,
0.041266266256570816,
0.004544563591480255,
-0.011826977133750916,
0.05695171281695366,
0.08997263014316559,
0.00818043015897274,
-0.041501279920339584,
0.009164812043309212,
-0.059815678745508194,
0.04473448544740677,
0.003027902217581868,
0.009728306904435158,
0.018448058515787125,
0.00017574419325683266,
0.022325465455651283,
0.021993277594447136,
0.002646660665050149,
-0.04482775926589966,
-0.07975009083747864,
-0.003983828239142895,
-0.008741147816181183,
-0.054830729961395264,
0.04912910982966423,
0.019487323239445686,
0.01122245378792286,
0.061200156807899475,
-0.04842569679021835,
0.01925564557313919,
0.015015678480267525,
0.04940114542841911,
-0.017123199999332428,
0.05973776429891586,
-0.03367292135953903,
0.044498320668935776,
-0.047542791813611984,
0.011005884036421776,
0.12665818631649017,
0.05389367789030075,
0.03417821601033211,
0.027969885617494583,
0.03726714104413986,
-0.026678333058953285,
-0.02710224874317646,
-0.03997212275862694,
-0.003686684649437666,
0.0027007528115063906,
-0.0023484283592551947,
-0.0153984185308218,
0.007050950080156326,
-0.015002324245870113,
-0.033313050866127014,
0.023945355787873268,
-0.014635604806244373,
-0.019306901842355728,
-0.016612643375992775,
0.008295132778584957,
-0.027226096019148827,
-0.02307586930692196,
-0.0074319723062217236,
0.01520951371639967,
-0.016341784968972206,
-0.018564550206065178,
-0.027268681675195694,
-0.0457870215177536,
0.02964283898472786,
0.002637537894770503,
-0.02240193821489811,
0.013528460636734962,
0.00887499749660492,
-0.03654105216264725,
-0.020682169124484062,
0.023179728537797928,
0.011641277000308037,
0.019211115315556526,
0.02560351975262165,
0.047529760748147964,
-0.006848637014627457,
-0.005833080038428307,
0.049879271537065506,
0.02212601527571678,
-0.046244774013757706,
0.009352616034448147,
-0.06863927841186523,
0.03746136277914047,
-0.020831739529967308,
-0.0016947522526606917,
0.0055421688593924046,
-0.023967120796442032,
0.0026992917992174625,
-0.03142082318663597,
0.005411761347204447,
0.001271429704502225,
0.03221331164240837,
0.018625453114509583,
-0.014209826476871967,
0.007737649139016867,
0.019349070265889168,
0.021277111023664474,
-0.025749802589416504,
-0.011158243753015995,
-0.01282353326678276,
-0.009889344684779644,
0.021899722516536713,
0.06782090663909912,
-0.01027503702789545,
-0.01145127136260271,
-0.03917890414595604,
-0.0308755561709404,
-0.016578471288084984,
-0.025338394567370415,
-0.030793337151408195,
0.05167500302195549,
0.01446562074124813,
0.016416991129517555,
-0.04199066758155823,
-0.05063854157924652,
-0.012630613520741463,
0.03686000034213066,
-0.030107775703072548,
0.004388158675283194,
-0.04089994356036186,
0.0021608511451631784,
0.02388678677380085,
0.03803042322397232,
-0.048216160386800766,
-0.0017638987628743052,
-0.002899449784308672,
0.03830820322036743,
0.0029965932480990887,
-0.02072894014418125,
-0.023127736523747444,
-0.01926056295633316,
-0.05197101831436157,
0.012520776130259037,
-0.020638566464185715,
0.016169201582670212,
0.0039532119408249855,
-0.015148519538342953,
-0.001182998064905405,
0.009896653704345226,
-0.0018916805274784565,
0.024568622931838036,
0.015479933470487595,
-0.042899761348962784,
0.008490505628287792,
0.03502215817570686,
-0.0257974062114954,
-0.012995106168091297,
0.019127776846289635,
0.020396661013364792,
-0.013990690000355244,
0.01175263337790966,
0.05606742948293686,
-0.03431857004761696,
0.01807403936982155,
-0.03447835147380829,
0.055881697684526443,
0.0013884083600714803,
-0.035308193415403366,
0.0015650639543309808,
0.010445679537951946,
0.027312006801366806,
-0.0021037901751697063,
-0.05184666067361832,
0.01689913123846054,
-0.002786804223433137,
0.004509119316935539,
0.00018454212113283575,
0.007062118034809828,
-0.017836984246969223,
-0.025421125814318657,
0.010364187881350517,
0.011787287890911102,
0.04134839400649071,
0.020160159096121788,
-0.020604293793439865,
0.04735872894525528,
-0.006078485865145922,
-0.033242806792259216,
0.012425428256392479,
-0.024099625647068024,
0.02238618955016136,
0.008739070035517216,
-0.03735525161027908,
-0.037268657237291336,
0.0624888651072979,
-0.05144771933555603,
-0.01510088425129652,
-0.018160613253712654,
-0.03261351212859154,
-0.019178515300154686,
-0.021805506199598312,
0.0040987832471728325,
-0.015622874721884727,
0.0077084326185286045,
0.025859517976641655,
0.013788886368274689,
-0.033666376024484634,
-0.02538563869893551,
-0.027536965906620026,
-0.00035622730501927435,
-0.031292665749788284,
0.021115539595484734,
0.01373097114264965,
-0.00011537925456650555,
0.04611605778336525,
0.000833895755931735,
-0.02057243324816227,
-0.0027584622148424387,
-0.03221917152404785,
-0.035084035247564316,
-0.036319851875305176,
0.019599217921495438,
0.0027678997721523046,
0.037957366555929184,
-0.046542100608348846,
0.023984171450138092,
0.024403246119618416,
-0.0604405477643013,
-0.012147478759288788,
-0.023472575470805168,
-0.028621157631278038,
-0.006180925294756889,
-0.011605098843574524,
-0.003009116742759943,
0.018710702657699585,
-0.018217135220766068,
0.05845324695110321,
0.007294840645045042,
0.014536410570144653,
-0.04540487006306648,
-0.008777002803981304,
0.013413405045866966,
0.00001538399919809308,
0.009910620748996735,
0.017393557354807854,
0.0490715466439724,
0.006114504300057888,
0.0042597949504852295,
0.02094302885234356,
-0.021141501143574715,
0.004108312074095011,
-0.01225954294204712,
0.01018906943500042,
-0.010814505629241467,
0.014374830760061741,
-0.026285730302333832,
0.0004916862235404551,
-0.00745757482945919,
-0.009464477188885212,
0.02454298548400402,
0.02278572879731655,
-0.0049204458482563496,
-0.011853814125061035,
0.01845676638185978,
-0.03201119601726532,
-0.018198397010564804,
0.02962615340948105,
-0.035072147846221924,
-0.023465387523174286,
0.01301533728837967,
0.029899079352617264,
0.006193565204739571,
-0.04058259725570679,
-0.033691246062517166,
0.004203828517347574,
0.0015575975412502885,
0.04698612540960312,
-0.03876795992255211,
-0.01623806357383728,
0.02175457961857319,
0.00859815627336502,
0.029846008867025375,
0.0230188500136137,
0.02751578576862812,
-0.06378030776977539,
-0.044846061617136,
-0.018085476011037827,
-0.006944278720766306,
0.005934285931289196,
-0.028441524133086205,
-0.02853010967373848,
-0.05029686167836189,
0.07428368180990219,
0.016995223239064217,
0.054208893328905106,
-0.001501214224845171,
-0.03290281444787979,
-0.009975362569093704,
-0.07434167712926865,
0.04882384091615677,
-0.007024749182164669,
-0.04845060035586357,
-0.029294908046722412,
-0.04605121910572052,
0.028052184730768204,
-0.007144126575440168,
0.05756457895040512,
-0.0038466122932732105,
-0.031205860897898674,
0.037338752299547195,
-0.023265402764081955,
0.02660302445292473,
0.005481982138007879,
0.015255474485456944,
0.008256200700998306,
0.024084217846393585,
0.042865339666604996,
-0.005464623216539621,
0.011810694821178913,
-0.006506254430860281,
0.01881236769258976,
-0.020910248160362244,
-0.013615667819976807,
0.0056135100312530994,
0.01511342916637659,
0.018670447170734406,
-0.008420861326158047,
-0.035225819796323776,
0.07192372530698776,
-0.005139552988111973,
-0.000896136392839253,
0.004895997233688831,
-0.06888334453105927,
-0.04473324865102768,
0.03818410262465477,
-0.04736714065074921,
-0.001484891283325851,
-0.04273303598165512,
-0.04677142947912216,
0.06911227107048035,
-0.041879840195178986,
-0.026786906644701958,
0.04495219141244888,
-0.023588046431541443,
-0.013626547530293465,
0.024961471557617188,
0.026716995984315872,
0.049107298254966736,
-0.010637559927999973,
0.05594291910529137,
0.0026960603427141905,
-0.016221076250076294,
0.030136222019791603,
0.02356491982936859,
0.00806436501443386,
-0.019966110587120056,
-0.013851174153387547,
0.018784960731863976,
0.0260848980396986,
0.02704961970448494,
0.016955005005002022,
0.02391129732131958,
0.024854246526956558,
-0.03317885100841522,
-0.014672892168164253,
-0.00010811789252329618,
-0.0480944998562336,
0.011712154373526573,
-0.029078353196382523,
0.061052106320858,
-0.0028009554371237755,
-0.021067308261990547,
-0.008781899698078632,
0.010486315935850143,
0.003449362004175782,
0.0077420491725206375,
0.010833684355020523,
-0.0028876932337880135,
-0.01701151579618454,
-0.039211928844451904,
0.005491352174431086,
0.01861845888197422,
0.019738130271434784,
0.03300720080733299,
0.02140437625348568,
0.00988831091672182,
0.02735975757241249,
0.026755675673484802,
-0.023174041882157326,
-0.05147884786128998,
-0.04339337348937988,
0.043655455112457275,
-0.0009268373250961304,
-0.008780451491475105,
-0.020454708486795425,
0.004823653027415276,
-0.024980507791042328,
0.02246289886534214,
-0.051545027643442154,
-0.0018760128878057003,
-0.029004914686083794,
0.04883905127644539,
0.0390290766954422,
0.035096388310194016
] |
<p>Ok, so I remember reading that every conservation law has a corresponding symmetry (i.e. conservation of momentum is translational symmetry, conservation of angular momentum is rotational symmetry).</p>
<p>Now conservation of energy is temporal symmetry (you can rewind the tape and it looks exactly the same, but in reverse--you don't get a different "movie" running the tape in reverse).</p>
<p>But I just saw an article here...</p>
<p><a href="http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/" rel="nofollow">http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/</a></p>
<p>...where researchers found violations of time-reversal symmetry.</p>
<p>Now wouldn't that therefore mean that they found processes that create or destroy energy?? Does T-Symmetry violation mean that energy is not being conserved?</p> | 4,627 | [
-0.04037807881832123,
-0.05177238583564758,
-0.006188360508531332,
-0.01226608082652092,
0.05246443673968315,
0.015448600985109806,
-0.02983449399471283,
0.04048515856266022,
-0.011348088271915913,
-0.03296539559960365,
0.0012395859230309725,
0.014527506195008755,
0.008269284851849079,
0.005956534296274185,
0.026255734264850616,
0.019235527142882347,
-0.0235393438488245,
-0.0058966432698071,
-0.019506163895130157,
-0.03926512226462364,
0.010878434404730797,
-0.012649108655750751,
-0.03565734624862671,
0.013057788833975792,
-0.032240837812423706,
0.0384366437792778,
0.02793007902801037,
0.03488297387957573,
0.02482001855969429,
0.046247366815805435,
-0.022047104313969612,
-0.029139110818505287,
0.015992579981684685,
-0.011820744723081589,
-0.008595362305641174,
-0.011558445170521736,
-0.02938590757548809,
-0.06082719936966896,
0.008351591415703297,
0.035250358283519745,
-0.0023836176842451096,
-0.008020768873393536,
-0.023827895522117615,
0.0797685980796814,
-0.053040072321891785,
0.03134120628237724,
-0.014021373353898525,
0.013585144653916359,
0.06705792248249054,
-0.0380399264395237,
0.08004952222108841,
0.020295821130275726,
0.03308703377842903,
-0.015085792168974876,
-0.009933500550687313,
0.019841812551021576,
0.05659143626689911,
0.04133816435933113,
-0.00926132220774889,
-0.06747323274612427,
-0.010340468026697636,
-0.009025970473885536,
0.011871350929141045,
0.008003683760762215,
-0.03520340099930763,
-0.007243421394377947,
0.02144772745668888,
0.0054063317365944386,
0.02139219082891941,
0.004380893427878618,
0.020836837589740753,
-0.0013185933930799365,
0.03465931490063667,
0.009993053041398525,
-0.018470998853445053,
-0.02727055922150612,
0.046349797397851944,
-0.015747833997011185,
0.03508888557553291,
0.04191238060593605,
0.029248109087347984,
0.000789737154264003,
-0.012512369081377983,
0.043897997587919235,
-0.010092680342495441,
-0.0033555857371538877,
0.03596276417374611,
-0.018962880596518517,
-0.0032614211086183786,
0.04261808469891548,
0.011133759282529354,
0.024204129353165627,
0.027387447655200958,
0.006875547114759684,
-0.05421144515275955,
0.013918316923081875,
0.01580186001956463,
0.04610873758792877,
0.0031974317971616983,
-0.020252911373972893,
0.009805153124034405,
-0.0063184704631567,
0.03248697519302368,
0.03745725005865097,
-0.031947292387485504,
-0.04385659843683243,
-0.03483930602669716,
0.030138565227389336,
-0.023008519783616066,
0.029492652043700218,
-0.08789099007844925,
-0.047661133110523224,
-0.004968561697751284,
-0.00891446229070425,
0.02152875065803528,
-0.02977469004690647,
-0.012906264513731003,
-0.009143216535449028,
0.07787834852933884,
0.0654313787817955,
0.05585407465696335,
-0.02644318901002407,
0.042668312788009644,
0.005854969844222069,
-0.09233220666646957,
-0.013812979683279991,
0.043620724231004715,
-0.0023689493536949158,
-0.019520359113812447,
0.03672906756401062,
-0.0003399315173737705,
-0.028394149616360664,
0.012294159270823002,
-0.053010884672403336,
0.06227562204003334,
-0.027994289994239807,
-0.09458402544260025,
-0.06861142814159393,
0.028591347858309746,
0.028103630989789963,
-0.02897533029317856,
-0.08692736178636551,
-0.037292592227458954,
-0.024218767881393433,
0.07910943031311035,
-0.028768157586455345,
0.0017850013682618737,
0.021180640906095505,
0.052910227328538895,
-0.0012303624534979463,
-0.028094960376620293,
-0.003175656544044614,
0.05178091302514076,
-0.03876852989196777,
0.005787938833236694,
-0.05776779353618622,
0.004715150222182274,
0.014420123770833015,
-0.003459389554336667,
0.0068183476105332375,
0.04604091867804527,
-0.02011050283908844,
0.005510507617145777,
0.02774396352469921,
-0.01745830476284027,
-0.01074856985360384,
0.05702340230345726,
-0.00844727735966444,
-0.023848919197916985,
0.02391918934881687,
0.009229104965925217,
0.018080005422234535,
-0.014618536457419395,
0.02663744054734707,
0.02344389259815216,
-0.05071929097175598,
-0.023151254281401634,
0.0036252480931580067,
0.00008567282202420756,
-0.014654583297669888,
-0.04313630238175392,
-0.009851445443928242,
0.009070868603885174,
-0.0071038855239748955,
-0.00565918767824769,
0.05528528615832329,
-0.04170384258031845,
-0.0008437939104624093,
0.002005329355597496,
-0.04212132468819618,
-0.04213586449623108,
-0.06393055617809296,
0.0057938010431826115,
-0.0218333937227726,
-0.014155155047774315,
0.022726017981767654,
0.010763179510831833,
0.057866983115673065,
-0.055065762251615524,
-0.027880676090717316,
0.03502749279141426,
0.027273809537291527,
0.002155581722036004,
0.001975164981558919,
0.016959743574261665,
0.03560761362314224,
0.021032700315117836,
0.009823733940720558,
0.001702969311736524,
0.02404455654323101,
-0.004732528701424599,
0.02150394394993782,
-0.024472009390592575,
0.013065006583929062,
0.029758460819721222,
-0.02571398764848709,
0.00783578772097826,
-0.013213771395385265,
-0.01892412081360817,
0.02565056085586548,
-0.0017222255701199174,
0.03922279551625252,
0.03644699603319168,
0.017780181020498276,
-0.005062656942754984,
0.04704289138317108,
0.004298292566090822,
0.011424411088228226,
-0.02331983670592308,
-0.025388356298208237,
-0.0415043868124485,
-0.029567673802375793,
0.05175016075372696,
0.03460744395852089,
-0.037026919424533844,
0.015404722653329372,
0.007022714242339134,
0.03543385490775108,
0.020703062415122986,
0.030445730313658714,
-0.014963772147893906,
-0.06186518445611,
0.021087385714054108,
0.03806692734360695,
-0.0035677868872880936,
0.023068029433488846,
0.028899163007736206,
-0.034988611936569214,
0.013834251090884209,
0.009653995744884014,
-0.04478331282734871,
0.023639565333724022,
-0.00843604002147913,
0.016984645277261734,
0.031958356499671936,
-0.049692779779434204,
0.0017741479678079486,
-0.01635953038930893,
0.04221843183040619,
0.05149458721280098,
0.009318224154412746,
0.005693004000931978,
-0.029285291209816933,
-0.0008191288216039538,
-0.015815749764442444,
0.011979109607636929,
0.005696108099073172,
-0.017642784863710403,
0.014633318409323692,
-0.005438941065222025,
-0.02112884819507599,
0.005349765531718731,
-0.0026688629295676947,
-0.018044715747237206,
-0.02687276341021061,
0.0141788674518466,
-0.006649200338870287,
0.02816586382687092,
-0.059789855033159256,
-0.021955709904432297,
0.003253565402701497,
-0.03786712512373924,
-0.03321337699890137,
0.028623417019844055,
-0.06149394065141678,
0.04033001512289047,
-0.059421930462121964,
-0.014946873299777508,
0.0405915305018425,
-0.025605227798223495,
0.03836171701550484,
0.02094843238592148,
0.0016428270610049367,
-0.04859459772706032,
0.0008350158459506929,
-0.030230993404984474,
0.019283216446638107,
-0.008641616441309452,
-0.0030259760096669197,
0.03582458570599556,
-0.016622401773929596,
-0.04613275080919266,
0.014848965220153332,
-0.047464221715927124,
-0.025134596973657608,
-0.03248061239719391,
-0.01989271119236946,
0.04338343068957329,
-0.032219208776950836,
0.06807494908571243,
0.015424401499330997,
-0.06986483931541443,
-0.001734126708470285,
-0.03206431120634079,
-0.03310486301779747,
0.004315200261771679,
0.026872217655181885,
0.0371820330619812,
-0.03209378197789192,
-0.058589763939380646,
0.06428249925374985,
0.03870702162384987,
-0.03688102588057518,
0.003479483537375927,
-0.026717016473412514,
-0.005266571883112192,
-0.03307490423321724,
0.008601391687989235,
0.02243622951209545,
0.0018375031650066376,
0.0332723930478096,
-0.0029299466405063868,
0.05121966451406479,
0.018300307914614677,
0.010845670476555824,
-0.06006346270442009,
-0.01452308613806963,
0.02786395512521267,
0.035398636013269424,
0.03261761739850044,
-0.011882496997714043,
-0.02843988686800003,
0.015048671513795853,
0.0013708720216527581,
0.04344918951392174,
0.011645057238638401,
-0.05963907018303871,
0.0657406821846962,
0.017813369631767273,
0.01125373039394617,
-0.026962274685502052,
0.03870030865073204,
-0.017449287697672844,
0.01965540461242199,
0.007590530440211296,
0.0591794028878212,
0.04414374753832817,
-0.01280294917523861,
0.03257119655609131,
0.01685282588005066,
0.05650317296385765,
-0.007686546538025141,
-0.012146255001425743,
-0.019508732482790947,
-0.020137062296271324,
0.03592023625969887,
0.011053984984755516,
-0.03575912117958069,
0.08066200464963913,
0.03547520935535431,
0.04258183762431145,
0.035238925367593765,
-0.06147456541657448,
-0.010565015487372875,
-0.022450771182775497,
0.032015323638916016,
-0.022697925567626953,
0.04211343452334404,
-0.008652951568365097,
0.07242649048566818,
0.030512366443872452,
0.019476866349577904,
0.04333873838186264,
-0.02091969922184944,
-0.054935943335294724,
0.05196540057659149,
-0.027217509225010872,
0.009002943523228168,
-0.002949116053059697,
0.0078041027300059795,
0.012400435283780098,
-0.0010495382593944669,
0.025865428149700165,
0.02405109815299511,
-0.012584179639816284,
-0.0670379102230072,
-0.004851194564253092,
-0.05759793892502785,
-0.04373229667544365,
-0.011835244484245777,
0.04435492306947708,
0.08334974944591522,
-0.04783673956990242,
0.027661960572004318,
0.028029799461364746,
-0.0436873584985733,
0.008669557049870491,
-0.010492727160453796,
0.0263590719550848,
0.02753506414592266,
0.024115780368447304,
0.009624739177525043,
0.02180541679263115,
-0.016557559370994568,
0.009724277071654797,
0.02328561805188656,
0.05060674250125885,
-0.01677696779370308,
0.029825780540704727,
-0.04935082793235779,
-0.027342164888978004,
-0.01763148605823517,
0.04657543823122978,
0.03339093551039696,
0.03202206268906593,
0.02327975444495678,
0.014117578975856304,
0.05395432934165001,
-0.04005831107497215,
0.049834463745355606,
0.035862043499946594,
0.0030820993706583977,
-0.012936869636178017,
-0.05484423041343689,
-0.0019877587910741568,
0.0018140955362468958,
-0.047021348029375076,
-0.007536843419075012,
-0.0035980683751404285,
-0.027968892827630043,
0.034324198961257935,
0.0012955344282090664,
0.003690368263050914,
-0.03396107628941536,
0.020632155239582062,
-0.026185685768723488,
-0.004609697498381138,
0.019532248377799988,
0.006820341572165489,
0.02336699329316616,
0.03417711704969406,
0.03220932185649872,
0.027711443603038788,
0.004223964177072048,
-0.04977311193943024,
0.012322054244577885,
0.02958083339035511,
0.030207060277462006,
-0.003004238707944751,
-0.019509822130203247,
-0.06385567784309387,
-0.022261688485741615,
0.02044292725622654,
-0.02843615785241127,
0.04987280070781708,
-0.019800087437033653,
-0.0027072469238191843,
-0.014570871368050575,
-0.013613302260637283,
0.004172873683273792,
0.02601589448750019,
0.0034819866996258497,
0.012114547193050385,
-0.00020592067448887974,
-0.021052390336990356,
-0.028117312118411064,
-0.007199970073997974,
0.01715249754488468,
0.015046252869069576,
-0.013146589510142803,
-0.0011669851373881102,
-0.009238271042704582,
0.01898818090558052,
-0.011062689125537872,
-0.07486730813980103,
-0.00024790645693428814,
0.0112185999751091,
-0.004696431569755077,
0.07353800535202026,
-0.04923522099852562,
-0.0430075079202652,
-0.0022579559590667486,
0.026380734518170357,
0.006271163932979107,
-0.02811604179441929,
-0.05502753704786301,
0.020437918603420258,
0.04236094653606415,
-0.014820406213402748,
0.04619226232171059,
0.051205165684223175,
-0.0071026841178536415,
-0.01593969576060772,
-2.534678600341067e-8,
0.024862604215741158,
-0.02330525778234005,
0.03887336701154709,
-0.03766852989792824,
-0.000529556826222688,
-0.021239493042230606,
0.0421869121491909,
-0.0038735545240342617,
-0.008977683261036873,
0.0009262648527510464,
-0.002125396393239498,
0.0016737411497160792,
0.044241391122341156,
0.021701695397496223,
-0.03896677866578102,
-0.022577648982405663,
0.023245880380272865,
-0.015145231038331985,
-0.006892824545502663,
-0.0038246808107942343,
-0.009607390500605106,
-0.035020750015974045,
0.052297528833150864,
0.031061816960573196,
0.022866234183311462,
-0.02360064722597599,
-0.05000971630215645,
0.019786808639764786,
0.0020865320693701506,
0.009101311676204205,
-0.03534698858857155,
-0.010082456283271313,
0.019587211310863495,
-0.05061956122517586,
-0.030100243166089058,
0.02892198972404003,
-0.03652726858854294,
0.0063076261430978775,
-0.06786124408245087,
0.03385311737656593,
0.03498373180627823,
0.03333535045385361,
-0.08612853288650513,
-0.049973174929618835,
0.0005562164587900043,
-0.0058075799606740475,
-0.03624280169606209,
-0.010615925304591656,
-0.04251328483223915,
-0.0556815043091774,
-0.04138787463307381,
0.0019362986786291003,
0.026351042091846466,
-0.04142176732420921,
-0.006067244336009026,
0.012769072316586971,
-0.009085415862500668,
0.05922785401344299,
-0.0030185068026185036,
-0.001918913796544075,
0.00682009058073163,
0.0032909081783145666,
-0.023066295310854912,
-0.00017254696285817772,
0.03376997634768486,
-0.006662150379270315,
0.012032405473291874,
0.00924998614937067,
0.02276298962533474,
0.019457411020994186,
-0.011468603275716305,
0.004305543377995491,
0.041103463619947433,
-0.03446560725569725,
0.01807394064962864,
-0.03626593202352524,
0.04426472634077072,
-0.011104648932814598,
0.02369535341858864,
-0.00845386739820242,
-0.03694510832428932,
0.0009454017854295671,
-0.032665785402059555,
0.04326248541474342,
-0.0022394878324121237,
0.029134146869182587,
0.034014638513326645,
0.03675990179181099,
-0.01451676432043314,
-0.012630418874323368,
0.006354965269565582,
-0.04198956489562988,
0.019142592325806618,
-0.017036188393831253,
0.0007288549677468836,
-0.027410609647631645,
-0.003805227344855666,
-0.04002765566110611,
-0.030923400074243546,
0.0070798215456306934,
0.01998668536543846,
0.060073986649513245,
-0.010292516089975834,
0.06903249025344849,
0.0540325865149498,
0.001672400627285242,
-0.008380934596061707,
-0.044289443641901016,
0.03323996812105179,
0.038095083087682724,
0.031702253967523575,
0.010696222074329853,
-0.0217756275087595,
-0.016992265358567238,
0.044985316693782806,
0.037440452724695206,
-0.019569842144846916,
0.02642315998673439,
0.024233553558588028,
0.01764422468841076,
0.007310495246201754,
-0.018956460058689117,
-0.06273893266916275,
0.032565224915742874,
-0.04899223893880844,
0.047688283026218414,
0.0057345046661794186,
0.02764458768069744,
0.013608098961412907,
0.019497517496347427,
0.0021788061130791903,
-0.03271102160215378,
-0.012552035972476006,
-0.06317682564258575,
0.023506660014390945,
-0.01341108325868845,
0.006741198245435953,
-0.01392754353582859,
0.01859801448881626,
0.04874042421579361,
0.018289227038621902,
-0.017382126301527023,
0.0044365860521793365,
-0.06588644534349442,
-0.012884409166872501,
-0.0368703156709671,
0.004908896517008543,
0.04568874463438988,
-0.022127466276288033,
-0.006583159789443016,
-0.011246707290410995,
-0.019087497144937515,
-0.0038255546241998672,
0.0031696155201643705,
0.03121243789792061,
-0.04104381799697876,
0.04588261991739273,
0.005144566763192415,
0.05974101275205612,
-0.03111918270587921,
0.02990518882870674,
0.10110629349946976,
0.04679539054632187,
-0.013128571212291718,
-0.02961864322423935,
0.02163274586200714,
-0.05033840984106064,
0.028276769444346428,
-0.004767416976392269,
0.009652799926698208,
0.011325754225254059,
0.007714835461229086,
-0.00922801997512579,
0.05414516478776932,
0.0406443290412426,
-0.04053857550024986,
0.06886475533246994,
-0.03966420516371727,
-0.021055981516838074,
0.018597545102238655,
0.02412678487598896,
0.002808233955875039,
-0.029901374131441116,
-0.06030726432800293,
0.01020753663033247,
-0.035939861088991165,
-0.020396843552589417,
-0.017765754833817482,
-0.07347681373357773,
-0.010790044441819191,
0.02463209442794323,
-0.01857912354171276,
0.015596354380249977,
0.00523541122674942,
0.010746763087809086,
-0.07839886099100113,
-0.00642547570168972,
-0.0011112828506156802,
0.00753429252654314,
0.04362224042415619,
0.06567522138357162,
0.004836681764572859,
-0.003926146775484085,
0.010473967529833317,
0.02466895990073681,
-0.03319583833217621,
0.0071104238741099834,
-0.004133951384574175,
0.0435795821249485,
-0.007854478433728218,
0.008854052983224392,
-0.02724437601864338,
-0.0349603071808815,
0.012147318571805954,
-0.04393526911735535,
-0.024801144376397133,
-0.025555577129125595,
-0.003970352467149496,
0.0034880966413766146,
0.0077735246159136295,
-0.03492237254977226,
-0.014837806113064289,
-0.011433192528784275,
0.022141925990581512,
-0.017337990924715996,
0.034061871469020844,
0.03770281374454498,
-0.010887590236961842,
0.0424402579665184,
-0.019605964422225952,
-0.029491417109966278,
-0.04148532450199127,
-0.02329881303012371,
-0.055897217243909836,
-0.003612588392570615,
0.03677672892808914,
0.011184296570718288,
0.015629209578037262,
0.0299545768648386,
-0.0003622156218625605,
-0.011271820403635502,
-0.03060854598879814,
0.04952545836567879,
-0.003910901490598917,
-0.03473447635769844,
-0.013572257943451405,
0.010634022764861584,
0.02809801511466503,
0.04372365400195122,
-0.06773976236581802,
0.033829230815172195,
0.004305684939026833,
0.01679154671728611,
0.022402448579669,
-0.005741967353969812,
-0.026635263115167618,
0.008894369006156921,
-0.002353128045797348,
-0.03127385675907135,
-0.02254209853708744,
0.016587931662797928,
0.03013072907924652,
-0.01370091363787651,
0.01327967457473278,
0.01510518230497837,
-0.015317224897444248,
-0.024053841829299927,
0.03207150474190712,
0.003913221415132284,
-0.0031353950034826994,
0.005793431308120489,
0.017799999564886093,
-0.03156096860766411,
-0.021720776334404945,
-0.014907514676451683,
0.03279105946421623,
0.024544812738895416,
-0.012693744152784348,
-0.034746523946523666,
-0.015568530187010765,
-0.07149964570999146,
0.05313633754849434,
-0.037467826157808304,
0.0007660160772502422,
-0.04460599645972252,
0.022741522639989853,
0.00009155427687801421,
-0.001414088997989893,
-0.00977512076497078,
0.049108974635601044,
0.007264003623276949,
-0.012136431410908699,
0.03580460324883461,
0.029001085087656975,
-0.012871412560343742,
-0.007455840706825256,
0.056539081037044525,
0.017602970823645592,
0.0500556156039238,
-0.009961951524019241,
-0.03459629416465759,
0.06061435863375664,
-0.03060767985880375,
-0.03521426394581795,
0.04593173414468765,
-0.013585818000137806,
-0.022663220763206482,
-0.002416397212073207,
0.002843019086867571,
0.004072042182087898,
0.05315164849162102,
-0.042760808020830154,
0.023434940725564957,
0.032059259712696075,
-0.056044988334178925,
-0.04021788388490677,
-0.048633918166160583,
0.023769104853272438,
-0.020631570369005203,
-0.04770222306251526,
0.042097315192222595,
0.031967516988515854,
-0.0020536247175186872,
-0.008304592221975327,
-0.03552764281630516,
-0.004849045537412167,
0.024166926741600037,
0.018100906163454056,
0.005165167152881622,
0.013336371630430222,
0.0774698555469513,
-0.03105463832616806,
-0.012601318769156933,
0.027582935988903046,
-0.009072800166904926,
-0.08298329263925552,
0.03068503923714161,
0.009371581487357616,
-0.013494632206857204,
0.03321347385644913,
-0.04165390878915787,
0.024530993774533272,
0.0025285365991294384,
-0.050800424069166183,
0.03580104932188988,
-0.04479745775461197,
0.00033272491418756545,
-0.03480536863207817,
0.007084546145051718,
-0.004138424061238766,
0.06549879908561707,
0.018051324412226677,
0.05075741559267044,
0.011949433013796806,
0.01779983751475811,
-0.02071717195212841,
-0.02082408219575882,
-0.014341464266180992,
0.02558484859764576,
0.009063140489161015,
-0.004990697372704744,
0.05164765566587448,
-0.00873588863760233,
-0.04816759005188942,
-0.014748558402061462,
0.008276091888546944,
0.0035247167106717825,
-0.034744080156087875,
0.008997444994747639,
0.0040460992604494095,
0.011719891801476479,
0.021804407238960266,
-0.02407643385231495,
0.014545062556862831,
0.020217837765812874,
0.005627044476568699,
0.01979750767350197,
0.04996364191174507,
0.005981623660773039,
-0.0308760367333889,
-0.04007310792803764,
-0.0037049702368676662,
0.047181129455566406,
-0.00792588759213686,
-0.01874116063117981,
0.004723806865513325,
0.0036402777768671513,
0.021877383813261986,
-0.01403809804469347,
-0.004086167551577091,
-0.03427615016698837,
-0.02364899218082428,
0.020938929170370102,
0.022073684260249138,
-0.011547843925654888,
0.007592439651489258,
-0.000669093627948314,
-0.031510356813669205,
0.0434938482940197,
0.004358136560767889,
-0.010368925519287586,
-0.03977050632238388,
0.021281125023961067,
-0.0031157806515693665,
0.007001527119427919,
-0.01728176139295101,
-0.03157085180282593,
-0.014327042736113071,
0.03311024606227875,
0.054166294634342194,
0.033552385866642,
-0.00031002916512079537,
-0.053911324590444565,
-0.0055581689812242985,
-0.05353701114654541,
0.029437940567731857,
-0.02522367611527443,
0.022666065022349358,
-0.044878482818603516,
-0.0026427097618579865,
-0.014254254288971424,
0.021618923172354698,
0.02761685661971569,
0.0012067571515217423,
-0.013101851567626,
0.07791806757450104,
-0.010496087372303009,
-0.01868901029229164,
-0.05005989596247673,
0.017934780567884445,
0.011721828952431679,
0.02088046260178089,
0.014932573772966862,
-0.025111744180321693,
-0.06462651491165161,
0.01777888461947441,
0.028009623289108276,
-0.02785496786236763,
0.000745629717130214,
-0.0062433634884655476,
-0.040514055639505386,
0.04584484547376633,
-0.015072308480739594,
0.0005062859854660928,
0.07486048340797424,
-0.030386347323656082,
0.029280919581651688,
0.025392768904566765,
-0.020772019401192665,
-0.006610037758946419,
0.02382880635559559,
-0.054376088082790375,
-0.02575342357158661,
-0.015376446768641472,
-0.013880930840969086,
0.06355137377977371,
-0.005858227610588074,
0.0030852369964122772,
0.04181474819779396,
-0.04773283749818802,
-0.0016689500771462917,
0.0329761728644371,
0.009768491610884666,
0.03981851041316986,
-0.04679027572274208,
0.031043989583849907,
-0.020299522206187248,
0.03243513032793999,
0.0016471364069730043,
0.05159781500697136,
0.014109240844845772,
0.018384268507361412,
-0.016841506585478783,
-0.026459289714694023,
-0.026749981567263603,
0.008230653591454029,
0.007369219325482845,
0.019013315439224243,
-0.03131138160824776,
-0.00240709469653666,
0.039068255573511124,
-0.0022322454024106264,
0.0065570310689508915,
0.016869651153683662,
-0.008664846420288086,
0.0689612552523613,
-0.019097117707133293,
0.014458107762038708,
-0.025134770199656487,
-0.0016516365576535463,
-0.004006767645478249,
0.004889451898634434,
0.007183501496911049,
0.024550018832087517,
-0.007616820745170116,
-0.023799657821655273,
-0.04633422940969467,
0.024178238585591316,
-0.005100199952721596,
-0.04910571500658989,
0.012591605074703693,
-0.01992669887840748,
-0.011084277182817459,
-0.017746565863490105,
-0.025241844356060028,
-0.033219240605831146,
-0.043726030737161636,
-0.019610609859228134,
0.0198863185942173,
0.015269569121301174,
-0.008753851987421513,
-0.032775454223155975,
-0.01175198145210743,
0.017296014353632927,
-0.04032574221491814,
-0.02110224775969982,
-0.009946586564183235,
0.0324094332754612,
-0.01741090789437294,
0.006747101899236441
] |
<p>What is the orbital motion where both foci are located at one point? I know that an ellipse orbit is motion with two distinct foci.</p> | 4,628 | [
-0.028267428278923035,
-0.020094865933060646,
-0.0003594621375668794,
0.034205224364995956,
0.04593788832426071,
-0.004017459228634834,
-0.009056744165718555,
-0.005312541965395212,
0.015328844077885151,
-0.045249130576848984,
0.029952798038721085,
0.04787670820951462,
0.026241417974233627,
0.025949101895093918,
0.016677888110280037,
0.002642478561028838,
-0.018295718356966972,
0.006629894487559795,
-0.009790990501642227,
-0.010621821507811546,
0.011406511068344116,
-0.0488160140812397,
0.026904171332716942,
0.02720847725868225,
-0.009197515435516834,
0.020171303302049637,
0.04343907907605171,
-0.002185218036174774,
0.02141791768372059,
0.051549673080444336,
-0.043099258095026016,
-0.040851667523384094,
0.012179162353277206,
0.041718244552612305,
0.019427193328738213,
-0.009108866564929485,
-0.02891407534480095,
0.003995366394519806,
-0.02707056701183319,
0.01638634316623211,
-0.033826783299446106,
-0.06576492637395859,
-0.03670334815979004,
0.05355656519532204,
-0.022765755653381348,
0.006569581106305122,
0.001917774323374033,
-0.035201214253902435,
0.07223731279373169,
-0.05651148781180382,
0.08404938131570816,
-0.016401279717683792,
0.037450239062309265,
0.017076164484024048,
0.012003283016383648,
0.02684967592358589,
0.08261411637067795,
0.06139892712235451,
-0.01564718410372734,
-0.03589698672294617,
-0.036834221333265305,
-0.01550888828933239,
0.037250105291604996,
-0.007586223538964987,
-0.036714620888233185,
0.03463663533329964,
-0.012622646056115627,
-0.01922009326517582,
0.011737468652427197,
0.035634130239486694,
-0.025744179263710976,
0.01483143214136362,
0.02249433472752571,
-0.0531972274184227,
-0.0013026081724092364,
-0.046611934900283813,
0.03495420143008232,
-0.01810000091791153,
0.030233031138777733,
0.0023446495179086924,
-0.005413001868873835,
0.014587011188268661,
0.01873389258980751,
-0.006381732877343893,
-0.015448234975337982,
0.005966308992356062,
0.06728009879589081,
-0.02067524380981922,
0.018310025334358215,
0.01025503221899271,
-0.01521097868680954,
0.00949183851480484,
0.049824733287096024,
-0.010113627649843693,
-0.035960059612989426,
0.03250749409198761,
0.0032469690777361393,
0.03045397810637951,
0.0019861047621816397,
-0.017966290935873985,
0.010149545967578888,
-0.05620681494474411,
-0.007370089180767536,
0.09816049039363861,
-0.0011660816380754113,
0.026735134422779083,
-0.01331540197134018,
0.02869323082268238,
-0.012197757139801979,
0.007745290640741587,
-0.013476996682584286,
0.018410874530673027,
0.006921283435076475,
0.03544885665178299,
0.013604536652565002,
0.0012896670959889889,
-0.023232920095324516,
0.013300505466759205,
0.026240583509206772,
0.06931821256875992,
0.06600397080183029,
-0.016062837094068527,
0.018559778109192848,
-0.00018155976431444287,
-0.06113667041063309,
0.01040217000991106,
0.03561459854245186,
0.015737954527139664,
-0.028688356280326843,
0.04314809665083885,
0.023513924330472946,
0.017787354066967964,
0.007793434429913759,
-0.0009661056683398783,
0.003821977647021413,
0.017901679500937462,
-0.0809095948934555,
-0.047047488391399384,
0.05066846311092377,
0.006449877750128508,
-0.002572736470028758,
-0.05149884894490242,
0.025811724364757538,
0.04649339243769646,
0.07294581085443497,
-0.002047206973657012,
-0.04950540512800217,
0.006073195952922106,
0.05036181956529617,
0.0010402905754745007,
-0.019310491159558296,
0.0073356046341359615,
0.00217078416608274,
-0.09226095676422119,
0.005260608159005642,
-0.07403706759214401,
-0.003938888665288687,
0.06082348898053169,
-0.016193322837352753,
-0.03597664833068848,
0.045667387545108795,
-0.03536596894264221,
0.013164374977350235,
0.020363807678222656,
0.04625506326556206,
-0.00016691490600351244,
0.08317971974611282,
0.022013571113348007,
-0.00991053692996502,
0.05884982645511627,
0.016001740470528603,
0.04721258208155632,
-0.002418121788650751,
0.045773886144161224,
0.05181479454040527,
-0.04100228473544121,
-0.037544745951890945,
-0.03736232593655586,
0.023048754781484604,
0.020320003852248192,
-0.03381049633026123,
-0.06625814735889435,
0.012923691421747208,
0.0006638685008510947,
-0.018317893147468567,
0.06397712230682373,
-0.030393267050385475,
0.010763523168861866,
-0.01970704272389412,
-0.03939172625541687,
0.014632819220423698,
-0.0245854239910841,
0.021473759785294533,
-0.031529657542705536,
-0.018983224406838417,
0.022856852039694786,
0.02377285622060299,
0.018495846539735794,
-0.034946054220199585,
-0.01500975526869297,
-0.03392219915986061,
0.014366474002599716,
-0.0034730720799416304,
-0.026548603549599648,
0.037256766110658646,
0.078701451420784,
0.011188891716301441,
0.01773182488977909,
-0.005800101440399885,
-0.016383245587348938,
0.05417705699801445,
-0.043703243136405945,
-0.004308794625103474,
0.03142525255680084,
-0.006966948043555021,
-0.005418221466243267,
-0.03410106897354126,
0.006768449675291777,
-0.03385850414633751,
0.014106747694313526,
-0.05488605052232742,
0.08166533708572388,
0.06349214911460876,
0.024014629423618317,
0.018171116709709167,
0.029191844165325165,
0.02951071783900261,
-0.02028348669409752,
0.025387082248926163,
-0.05164458975195885,
-0.024246754124760628,
0.016988247632980347,
0.03726540133357048,
0.017634164541959763,
-0.02715017832815647,
0.009948291815817356,
0.051763977855443954,
0.06577351689338684,
0.026458920910954475,
0.04026152566075325,
-0.035917844623327255,
-0.019888021051883698,
-0.006703231483697891,
0.008816368877887726,
0.012920268811285496,
0.0028793057426810265,
0.046354107558727264,
-0.0022488972172141075,
0.029304595664143562,
0.019221797585487366,
-0.056821465492248535,
0.05314990505576134,
0.019106905907392502,
0.004253152292221785,
0.006114879157394171,
-0.012474668212234974,
0.015173514373600483,
-0.03462367132306099,
0.040417224168777466,
0.0024761378299444914,
-0.012245372869074345,
0.004785184748470783,
0.01280627865344286,
0.015163963660597801,
0.005969780031591654,
0.015705307945609093,
-0.008028045296669006,
0.00495906500145793,
0.04700728505849838,
-0.048337943851947784,
0.025852540507912636,
-0.035297270864248276,
-0.00988930556923151,
0.021531712263822556,
-0.0007020445773378015,
0.013003263622522354,
0.01033418346196413,
-0.001418180065229535,
-0.017369750887155533,
-0.023420371115207672,
-0.05151624605059624,
-0.04039197787642479,
-0.0002673291601240635,
0.0000754239663365297,
-0.07091948390007019,
0.03128458186984062,
-0.024768041446805,
-0.02900880202651024,
0.04462602734565735,
0.011966085992753506,
-0.02213265188038349,
0.015445725060999393,
0.019385922700166702,
-0.052830904722213745,
-0.00800190307199955,
-0.03978615626692772,
0.025224722921848297,
-0.041859373450279236,
0.006436493713408709,
0.03919301927089691,
-0.020300595089793205,
-0.027327345684170723,
0.023527031764388084,
-0.02171710506081581,
0.0019359143916517496,
-0.017557967454195023,
0.001013896893709898,
0.04749821498990059,
-0.058182958513498306,
0.03953113034367561,
-0.014869888313114643,
0.02069142833352089,
0.014561708085238934,
-0.0397900715470314,
-0.034212712198495865,
0.009695731103420258,
-0.02293715998530388,
-0.019510427489876747,
-0.03858625516295433,
-0.03076026774942875,
0.04215943068265915,
0.017684757709503174,
-0.009139308705925941,
-0.015851080417633057,
0.021188566461205482,
-0.04149265214800835,
0.009668310172855854,
0.03329486399888992,
-0.0030810809694230556,
0.0039314222522079945,
-0.002934899879619479,
0.01941077597439289,
-0.02608102187514305,
0.05549309402704239,
0.013588443398475647,
0.018130049109458923,
0.006381186190992594,
0.010511920787394047,
-0.005219800863415003,
0.0346529446542263,
0.020580871030688286,
-0.024742715060710907,
0.03892367705702782,
0.027213452383875847,
0.02443941868841648,
0.009042748250067234,
-0.020925024524331093,
0.02417502924799919,
-0.023990098387002945,
-0.019625848159193993,
0.020401492714881897,
0.024263588711619377,
0.05148344486951828,
0.023892389610409737,
-0.07981881499290466,
0.057085759937763214,
0.06607041507959366,
-0.022416939958930016,
-0.020431002601981163,
0.03376799449324608,
0.005125951021909714,
-0.01964021660387516,
-0.01401411835104227,
-0.02608351595699787,
-0.006747044622898102,
0.03378986194729805,
-0.019285770133137703,
-0.05925355106592178,
0.050355829298496246,
-0.008845857344567776,
-0.006773252971470356,
0.031280528753995895,
-0.025729944929480553,
0.031217657029628754,
-0.07006486505270004,
0.0030476662795990705,
0.023247424513101578,
0.030124355107545853,
-0.002003179397433996,
0.02063653990626335,
0.00033197010634467006,
0.011336400173604488,
-0.004509695805609226,
0.013033554889261723,
-0.07102402299642563,
0.036087919026613235,
-0.03236418962478638,
-0.035574086010456085,
-0.00017193752864841372,
-0.004522196017205715,
-0.005266972351819277,
-0.009222843684256077,
-0.034035418182611465,
-0.014187125489115715,
-0.0001395093568135053,
-0.025435077026486397,
0.02149984985589981,
-0.018653320148587227,
-0.021154101938009262,
-0.007555605378001928,
0.04960726574063301,
0.020919272676110268,
-0.020309453830122948,
0.04848642647266388,
0.02657359465956688,
-0.007139865309000015,
-0.014088082127273083,
-0.01459761057049036,
0.025485774502158165,
-0.03332632780075073,
0.012030748650431633,
-0.011132235638797283,
0.058334752917289734,
-0.02236141450703144,
0.004476507660001516,
-0.0061690956354141235,
0.0377480685710907,
0.00022699184773955494,
-0.02784239687025547,
-0.029838258400559425,
-0.023772725835442543,
0.004436406772583723,
0.0006273816106840968,
0.06422632187604904,
0.0025472959969192743,
0.0025140722282230854,
0.04425515979528427,
0.013858871534466743,
-0.018702711910009384,
0.05470521003007889,
0.05087233707308769,
0.05063711479306221,
0.012424691580235958,
-0.02929452806711197,
-0.010799524374306202,
-0.02514454908668995,
0.009747819043695927,
0.04019153118133545,
-0.007763460278511047,
-0.030445249751210213,
-0.007146206218749285,
0.006047958508133888,
0.013304627500474453,
-0.019245058298110962,
-0.008719110861420631,
-0.025501612573862076,
0.01697349175810814,
-0.04122098535299301,
-0.022960448637604713,
0.019633520394563675,
0.0011527090100571513,
0.0457339771091938,
0.017436059191823006,
0.01955500803887844,
-0.07979320734739304,
0.015078162774443626,
0.04721957445144653,
-0.019626559689641,
-0.0163633581250906,
-0.004381990525871515,
-0.02347479574382305,
-0.004796258173882961,
0.025538234040141106,
-0.03457554429769516,
0.02809908799827099,
-0.04511147364974022,
-0.001895871595479548,
0.010250340215861797,
-0.028820058330893517,
-0.032800327986478806,
0.005036293528974056,
-0.00826566107571125,
-0.0046647461131215096,
0.001247129519470036,
0.022912602871656418,
-0.007180225104093552,
-0.0008696008590050042,
0.03584101051092148,
0.08182551711797714,
0.04933047294616699,
0.010417568497359753,
-0.009528574533760548,
0.04033324494957924,
-0.015990762040019035,
-0.07782790809869766,
0.0020899937953799963,
0.012287705205380917,
-0.02211618982255459,
0.03692961484193802,
-0.05480887368321419,
-0.02680584043264389,
0.025422463193535805,
-0.008982335217297077,
0.0025165569968521595,
0.006689786911010742,
-0.006133473012596369,
-0.01503368467092514,
0.06155196577310562,
0.04043407738208771,
0.044828109443187714,
-0.023463206365704536,
-0.01746443659067154,
-0.04457956179976463,
-0.02458345517516136,
0.04123663529753685,
-0.027157794684171677,
-0.020807841792702675,
0.0032481877133250237,
0.04859377071261406,
-0.03348228335380554,
0.04703875631093979,
-0.016070913523435593,
-0.0057581039145588875,
-0.00948306918144226,
-0.02195567451417446,
-0.0527203306555748,
0.03992673382163048,
0.031102117151021957,
-0.0069521041586995125,
-0.010902230627834797,
0.013093432411551476,
-0.004028795752674341,
0.005713489837944508,
0.0023412893060594797,
-0.06751672178506851,
0.02103474922478199,
0.02984021231532097,
-0.003558098804205656,
0.0238596573472023,
-0.034118056297302246,
-0.006317957304418087,
-0.002507078228518367,
-0.04593798145651817,
0.049391552805900574,
-0.014109254814684391,
-0.015973350033164024,
0.05000917240977287,
-0.11834479123353958,
-0.05568242073059082,
0.01993655040860176,
0.02283334732055664,
0.03623628243803978,
-0.05729615315794945,
0.030223987996578217,
0.016623731702566147,
0.009047872386872768,
-0.07658696919679642,
-0.06116544455289841,
0.04025443643331528,
0.022087376564741135,
-0.002650827169418335,
-0.036613829433918,
0.033101409673690796,
-0.032042600214481354,
-0.04070448502898216,
0.0018926841439679265,
0.04026765748858452,
-0.026842646300792694,
-0.042042218148708344,
0.00551998196169734,
-0.0014883497497066855,
0.04964108020067215,
0.022275757044553757,
-0.01518501527607441,
0.02114279381930828,
0.0169677771627903,
0.0014134244993329048,
0.01046076137572527,
0.06975571066141129,
-0.007502943743020296,
0.0009580348269082606,
-0.06984610110521317,
-0.02900262176990509,
0.0007346299244090915,
-0.037219174206256866,
-0.015954742208123207,
0.04287867993116379,
0.028191201388835907,
0.017856337130069733,
-0.010527404956519604,
0.004457769449800253,
-0.04203925281763077,
-0.008340478874742985,
-0.0032158060930669308,
0.02585318498313427,
0.016730496659874916,
-0.02815876342356205,
0.004671903792768717,
0.00516330823302269,
-0.04028761386871338,
0.0002758127811830491,
0.0610777847468853,
0.00020255074196029454,
0.018114496022462845,
0.008425404317677021,
0.027239209040999413,
0.0014505282742902637,
-0.026315568014979362,
0.006202626973390579,
0.0017348907422274351,
-0.00033215456642210484,
-0.0405532643198967,
0.012791316024959087,
-0.005946481134742498,
0.023155925795435905,
0.09721602499485016,
-0.051231641322374344,
0.0487176850438118,
0.04181620851159096,
0.02473314478993416,
-0.000456021458376199,
-0.01603538729250431,
0.024717630818486214,
-0.0004932411247864366,
-0.009014200419187546,
0.05222335085272789,
-0.048537082970142365,
-0.011986820958554745,
0.030138671398162842,
0.06894191354513168,
-0.007538233418017626,
0.024312138557434082,
0.01779760792851448,
0.03091222047805786,
0.028996190056204796,
0.008432458154857159,
-0.058957621455192566,
0.03250216320157051,
-0.029502687975764275,
0.050118666142225266,
-0.0035687191411852837,
-0.02083093672990799,
0.04966633394360542,
0.011729689314961433,
0.02658708021044731,
-0.01700492575764656,
-0.03270129859447479,
-0.027407657355070114,
0.03996125981211662,
-0.011096938513219357,
-0.006494258530437946,
0.0091870641335845,
-0.0015553832054138184,
0.04533582925796509,
-0.017255941405892372,
-0.014031019061803818,
-0.032220419496297836,
-0.06266668438911438,
-0.06392349302768707,
-0.028789009898900986,
-0.033770736306905746,
0.0364006832242012,
-0.01814749278128147,
-0.027815569192171097,
0.0030540579464286566,
0.0277944877743721,
-0.034035298973321915,
0.04552260786294937,
0.04284454882144928,
-0.023269779980182648,
0.07352041453123093,
-0.0019579511135816574,
0.016032718122005463,
-0.017967229709029198,
0.009828700684010983,
0.11395291239023209,
0.050493352115154266,
-0.0036257565952837467,
-0.08096471428871155,
-0.000496436667162925,
-0.015500475652515888,
0.009485024958848953,
-0.03645920008420944,
0.024162935093045235,
0.0187224093824625,
0.017364725470542908,
0.02466699667274952,
0.03675930202007294,
0.022510886192321777,
-0.0345359668135643,
0.03012390248477459,
-0.008975451812148094,
-0.0558822862803936,
0.008041453547775745,
0.008228451013565063,
0.014197472482919693,
0.006986849009990692,
-0.048008255660533905,
-0.004419507924467325,
-0.03488394245505333,
-0.021773047745227814,
-0.03591347485780716,
-0.06294578313827515,
0.045958273112773895,
0.04486142471432686,
-0.0082413824275136,
0.0075507014989852905,
0.018104029819369316,
-0.03719615936279297,
-0.03557777777314186,
0.02952108532190323,
-0.001545832259580493,
-0.015190355479717255,
0.004641651175916195,
0.028216417878866196,
0.002590870251879096,
0.006059969775378704,
0.02697073295712471,
-0.0053062825463712215,
-0.04949769005179405,
0.0018964189803227782,
-0.018695011734962463,
0.0071760984137654305,
-0.011669246479868889,
0.02721470780670643,
-0.023676078766584396,
0.0015738782240077853,
-0.023863110691308975,
-0.05756741017103195,
-0.02193387970328331,
-0.022696293890476227,
0.017648305743932724,
-0.020552020519971848,
-0.03309217840433121,
-0.05402868613600731,
-0.02953368052840233,
-0.0030124851036816835,
0.012140204198658466,
0.002642025938257575,
0.024020368233323097,
0.02418239414691925,
-0.005461208056658506,
0.07566782087087631,
0.003167087910696864,
-0.02569286897778511,
-0.002103975508362055,
-0.0001610577164683491,
-0.021951429545879364,
0.0034551587887108326,
0.004865322727710009,
-0.0014236090937629342,
0.014672028832137585,
0.036412980407476425,
-0.04258514568209648,
-0.02066841721534729,
-0.042405854910612106,
0.019480830058455467,
0.023719267919659615,
-0.010882006026804447,
-0.0033623308409005404,
-0.013466091826558113,
0.0741262286901474,
0.024829154834151268,
-0.023379817605018616,
0.028318079188466072,
-0.02189117856323719,
0.02115641161799431,
0.00617798650637269,
-0.03936559706926346,
-0.032685887068510056,
0.007735968567430973,
0.012510155327618122,
-0.039977818727493286,
-0.061699364334344864,
0.06135500594973564,
0.04325907304883003,
-0.00654508825391531,
-0.006351615767925978,
0.007415459956973791,
-0.023513084277510643,
-0.00576765276491642,
0.02519506961107254,
-0.03512103855609894,
-0.013297131285071373,
0.007729444652795792,
-0.011096366681158543,
-0.03967403620481491,
0.002635440556332469,
0.00031005448545329273,
-0.0158293005079031,
-0.007217003032565117,
0.025170860812067986,
-0.05377820506691933,
0.05717410147190094,
-0.013955453410744667,
0.031062742695212364,
-0.01988338865339756,
-0.004862341098487377,
-0.038583315908908844,
0.022158661857247353,
0.027889281511306763,
0.0078015513718128204,
-0.031751491129398346,
0.014077129773795605,
0.011304732412099838,
-0.009991985745728016,
0.02967637963593006,
0.01780158281326294,
0.016026167199015617,
0.019142422825098038,
0.02723056450486183,
-0.00619710236787796,
0.057866960763931274,
-0.018861625343561172,
0.0005851745372638106,
-0.0002890012983698398,
-0.03875894099473953,
-0.03360733389854431,
0.021681876853108406,
-0.026521775871515274,
0.023318767547607422,
0.021571435034275055,
0.016164885833859444,
0.009516175836324692,
0.03153776749968529,
0.0020301456097513437,
-0.04862569272518158,
0.02142804116010666,
-0.007589360699057579,
-0.02781371958553791,
-0.012986976653337479,
-0.0033537631388753653,
-0.009556892327964306,
-0.031068241223692894,
0.011272640898823738,
0.03405337408185005,
-0.02240562066435814,
-0.01939387433230877,
-0.019299112260341644,
-0.009799703024327755,
0.03433902561664581,
0.0036001154221594334,
0.009166152216494083,
0.023830784484744072,
-0.006637854501605034,
-0.015403518453240395,
0.029876885935664177,
0.01451919786632061,
-0.0022517323959618807,
-0.061667367815971375,
-0.02095641754567623,
-0.00319266808219254,
0.0038573010824620724,
0.027215516194701195,
-0.03731166943907738,
-0.023883763700723648,
0.03537825867533684,
-0.052133575081825256,
0.005061938893049955,
-0.010328460484743118,
-0.011472757905721664,
-0.04126827046275139,
-0.03573243319988251,
-0.006428117863833904,
0.06549647450447083,
0.03272384777665138,
0.031484875828027725,
0.00991068035364151,
0.024984056130051613,
-0.05346903204917908,
-0.02288840524852276,
0.007032196968793869,
0.017755327746272087,
-0.016420193016529083,
-0.028078436851501465,
0.0361662395298481,
-0.04020041599869728,
-0.03904680535197258,
0.03145866468548775,
-0.006078408099710941,
0.0032276592683047056,
0.010162950493395329,
-0.004291114397346973,
-0.013003585860133171,
0.012407617643475533,
-0.0124056376516819,
-0.009000294841825962,
-0.03330589085817337,
0.008930937387049198,
0.009478747844696045,
0.03715292736887932,
-0.05154560133814812,
-0.025757258757948875,
0.030105270445346832,
-0.02805480733513832,
-0.05057724565267563,
0.027244484052062035,
-0.008370830677449703,
-0.01483077835291624,
-0.029600944370031357,
-0.02202840894460678,
0.012128896079957485,
-0.03029257245361805,
-0.01271961908787489,
-0.02302480861544609,
-0.00886636134237051,
0.014227134175598621,
-0.034405432641506195,
0.00370030477643013,
0.00105673773214221,
0.016532396897673607,
-0.05449133366346359,
0.04029208421707153,
-0.04233498126268387,
0.0015177541645243764,
-0.06183338165283203,
0.013257483951747417,
0.02316173166036606,
-0.00919545628130436,
-0.025854989886283875,
-0.007869242690503597,
-0.016329450532794,
0.06110147014260292,
-0.02045118249952793,
-0.0137430839240551,
0.021263502538204193,
0.01658283732831478,
-0.015271824784576893,
-0.045605484396219254,
0.04248077794909477,
0.009009549394249916,
-0.0025952269788831472,
-0.03476790338754654,
-0.036508720368146896,
-0.003435731865465641,
0.008557720109820366,
0.029446596279740334,
-0.010236285626888275,
0.017909647896885872,
0.01894477941095829,
0.0074895587749779224,
0.023539872840046883,
-0.02775486372411251,
-0.009807380847632885,
-0.03463611379265785,
-0.05827377364039421,
0.0022097881883382797,
-0.02177472598850727,
-0.04412354528903961,
-0.02792682871222496,
0.024146048352122307,
0.005139535292983055,
0.03357288986444473,
-0.013412951491773129,
0.004603625275194645,
0.024253252893686295,
0.03561192378401756,
0.035300079733133316,
0.0786496102809906,
0.011491505429148674,
-0.017663950100541115,
0.012509656138718128,
-0.04413073509931564,
-0.034175921231508255,
0.01132905762642622,
-0.04040703922510147,
-0.02136959694325924,
-0.017396127805113792,
-0.027269620448350906,
-0.0011868448927998543,
-0.061835598200559616,
-0.026625223457813263,
0.02634725533425808,
-0.040000248700380325,
-0.042129453271627426,
0.029924985021352768,
-0.01771150901913643,
0.0428558886051178,
-0.008341330103576183,
0.010075087659060955,
-0.007798459846526384,
-0.05921235308051109,
0.023660961538553238,
0.006889672018587589,
0.02522415854036808,
0.0194870475679636,
0.021534131839871407,
-0.015352894552052021,
0.02593998610973358,
0.02421949803829193,
-0.018850481137633324,
0.02468247152864933,
-0.007236757315695286,
-0.011920015327632427,
0.03697993606328964,
-0.015359953977167606,
0.02929222397506237,
-0.008942030370235443,
-0.025463201105594635,
0.04231064021587372,
-0.062284231185913086,
0.014323912560939789,
0.0005363761447370052,
0.021057693287730217,
-0.034436073154211044,
-0.02167539857327938,
0.03193755820393562,
0.03191007673740387,
-0.0076631405390799046,
-0.015858713537454605,
0.005054563283920288,
0.006569752469658852,
0.05018529295921326,
-0.03394981846213341,
0.0276583731174469,
-0.010697795078158379,
0.014018182642757893,
-0.0052413251250982285,
0.015295566990971565,
-0.057905763387680054,
-0.028577061370015144,
-0.01303113717585802,
0.044713906943798065,
0.011807202361524105,
-0.004946623928844929,
-0.007816617377102375,
-0.016301322728395462,
0.04211261495947838,
-0.07096239179372787,
-0.017620109021663666,
-0.021058345213532448,
0.028857974335551262,
0.009423215873539448,
0.033195611089468
] |
<p>I have this problem:</p>
<p>A 4.0 kg block is given an initial speed of 8.0 m/s at the bottom of a 20° incline. The
frictional force that retards its motion is 15.0 N. (a) If the block is directed up the
incline, how far does it move before stopping? (b)Will it slide back down the incline? </p>
<p>I've managed to get part (a) which was 4.51m but I'm not sure how to start part (b)..</p>
<p>The coefficient of Kinetic Friction was 0.407</p>
<p>Any ideas?</p> | 4,629 | [
-0.035756561905145645,
-0.015075482428073883,
-0.03958930820226669,
0.03737160935997963,
0.038933660835027695,
0.031076716259121895,
-0.027809496968984604,
-0.012150180526077747,
-0.014836251735687256,
-0.009224490262567997,
0.031061680987477303,
0.03566247969865799,
0.03646358475089073,
0.0336880162358284,
0.009041734039783478,
0.009119488298892975,
-0.02134079486131668,
-0.019869178533554077,
0.03844503313302994,
0.00886237807571888,
-0.020846586674451828,
-0.028567589819431305,
0.013553343713283539,
0.005047934129834175,
0.03397275507450104,
0.01805039867758751,
0.040415190160274506,
-0.03401680663228035,
0.01341316383332014,
0.03738473728299141,
0.016668369993567467,
-0.0405212827026844,
-0.006763321813195944,
-0.0037461540196090937,
0.014799509197473526,
0.05437702685594559,
-0.042836789041757584,
0.00307462178170681,
-0.024531632661819458,
0.02241085097193718,
-0.012785677798092365,
-0.023434780538082123,
-0.011568858288228512,
0.06260090321302414,
0.008138190023601055,
0.034037549048662186,
0.019663307815790176,
0.013288148678839207,
0.05701209977269173,
-0.05165770277380943,
0.08490613847970963,
0.01122975628823042,
0.026206601411104202,
0.031010644510388374,
-0.018099840730428696,
-0.012537881731987,
0.05717281252145767,
0.09518899023532867,
-0.02650492638349533,
-0.04613979533314705,
-0.0012253503082320094,
-0.05014539137482643,
-0.013517961837351322,
-0.0025958239566534758,
-0.014078335836529732,
0.04848812520503998,
-0.058819279074668884,
-0.008495531976222992,
0.036041878163814545,
-0.004957462195307016,
0.02861534059047699,
0.01833527348935604,
0.05068051069974899,
-0.035174380987882614,
0.003619980765506625,
-0.02414238452911377,
0.019757341593503952,
0.019746217876672745,
0.0029130293987691402,
0.054083600640296936,
-0.018846353515982628,
0.012995902448892593,
0.038621339946985245,
0.04951613023877144,
0.007164597511291504,
-0.019902197644114494,
0.035123586654663086,
0.017287341877818108,
0.04790326952934265,
0.04106836020946503,
0.012696929275989532,
-0.024325579404830933,
0.007269205991178751,
0.037484511733055115,
-0.0012617191532626748,
0.04183432087302208,
-0.0004311722586862743,
0.046104684472084045,
0.022238973528146744,
-0.02475900389254093,
-0.030969712883234024,
-0.0003884972829837352,
0.037960417568683624,
0.06154927611351013,
0.009503960609436035,
0.039193276315927505,
-0.044760171324014664,
0.006514725740998983,
-0.0249242652207613,
0.0032189551275223494,
0.0029705059714615345,
0.02271963283419609,
-0.027796098962426186,
-0.011717470362782478,
0.007839352823793888,
-0.033978406339883804,
-0.020432353019714355,
-0.013087569735944271,
0.018321212381124496,
0.018615368753671646,
0.029795436188578606,
-0.007740593049675226,
-0.006876104045659304,
-0.01791505515575409,
-0.04397721216082573,
-0.029851458966732025,
0.019310971722006798,
-0.05367124825716019,
-0.0011620154837146401,
0.029555654153227806,
-0.005020521115511656,
0.015083973295986652,
0.00438798638060689,
-0.02014642022550106,
0.07202687114477158,
0.0057794153690338135,
-0.03645525500178337,
-0.1043892651796341,
0.04855605587363243,
-0.006486020516604185,
-0.03138025477528572,
-0.05170908197760582,
-0.0018018677365034819,
0.015127244405448437,
0.04434475302696228,
-0.00041128078009933233,
0.016291344538331032,
-0.012853555381298065,
0.0226402897387743,
0.013790562748908997,
0.018218442797660828,
-0.021192707121372223,
-0.0036457832902669907,
-0.03435410186648369,
0.006495440378785133,
-0.08863968402147293,
0.0075490134768188,
0.002053458010777831,
-0.019361434504389763,
-0.031527698040008545,
0.025123940780758858,
0.009938721545040607,
-0.017573567107319832,
-0.002048571826890111,
-0.025870006531476974,
-0.005635092966258526,
0.0958009660243988,
0.01420601736754179,
0.011243090964853764,
-0.0015204455703496933,
0.059580691158771515,
-0.0026859669014811516,
-0.04023464769124985,
0.007923658937215805,
0.02739994041621685,
-0.013841007836163044,
-0.02331685461103916,
0.0054292394779622555,
0.00889863632619381,
0.005788594484329224,
-0.010831974446773529,
-0.05814972519874573,
0.010671159252524376,
-0.003075127489864826,
0.0013435741420835257,
0.014275899156928062,
0.008313026279211044,
0.02651095576584339,
-0.009743649512529373,
0.0010778961004689336,
-0.0331626832485199,
-0.06536558270454407,
0.04208473488688469,
-0.0026627539191395044,
0.011355173774063587,
-0.00003470658339210786,
-0.0034434611443430185,
0.006653773598372936,
-0.04893798381090164,
0.011687148362398148,
0.018828466534614563,
0.028819097205996513,
-0.02188223972916603,
-0.008428390137851238,
-0.012393948622047901,
0.06126154959201813,
0.04589151591062546,
-0.023452160879969597,
0.039602719247341156,
-0.03211117908358574,
0.02221110835671425,
-0.019464263692498207,
-0.0226824302226305,
-0.0042113917879760265,
-0.0022743698209524155,
0.005070663522928953,
0.013327270746231079,
0.02055216021835804,
0.012004218064248562,
0.021291902288794518,
-0.026754336431622505,
0.07995231449604034,
0.040331799536943436,
0.0371600016951561,
0.012102673761546612,
0.011213512159883976,
0.010686053894460201,
0.04864724725484848,
-0.014364467933773994,
-0.015093707479536533,
-0.014564471319317818,
-0.007948998361825943,
-0.008901855908334255,
-0.004064395558089018,
-0.048052411526441574,
0.033387962728738785,
0.05849660187959671,
-0.005154764745384455,
0.058558348566293716,
0.0398818738758564,
0.023621635511517525,
-0.024835150688886642,
-0.002921787090599537,
0.013039341196417809,
-0.006600019987672567,
0.030616650357842445,
-0.010721190832555294,
0.013449883088469505,
0.013948224484920502,
-0.019420208409428596,
-0.04113444685935974,
0.008983992040157318,
0.02405068464577198,
0.024391764774918556,
-0.019442502409219742,
-0.06395755708217621,
0.06259054690599442,
0.011780164204537868,
-0.021151045337319374,
0.02946377918124199,
0.026178376749157906,
0.02779812552034855,
-0.06277210265398026,
-0.03941667824983597,
0.01832801289856434,
0.0003384531009942293,
-0.03067811205983162,
-0.0004517057095654309,
0.04965485632419586,
-0.00197148066945374,
0.005270914174616337,
-0.032476793974637985,
0.008788149803876877,
-0.016570087522268295,
-0.010607494041323662,
0.03681977093219757,
-0.008493570610880852,
0.030811062082648277,
-0.034487780183553696,
-0.003096093190833926,
0.0007237439276650548,
-0.04921858757734299,
0.006934696808457375,
-0.018816523253917694,
-0.06245382875204086,
0.014141046442091465,
-0.026513973250985146,
-0.02628452330827713,
0.02701561525464058,
0.03288557380437851,
-0.009604241698980331,
0.028837837278842926,
-0.002804680960252881,
-0.017171116545796394,
-0.012126938439905643,
0.017458774149417877,
-0.014806592836976051,
-0.056166645139455795,
0.013191022910177708,
0.05757155641913414,
-0.009628264233469963,
0.00593549245968461,
0.031652700155973434,
-0.03484160080552101,
-0.02096029557287693,
-0.011009533889591694,
-0.0036037678364664316,
0.002232912229374051,
-0.008239874616265297,
0.009421859867870808,
-0.013592991977930069,
-0.011186680756509304,
0.0016217648517340422,
-0.052999939769506454,
-0.07012910395860672,
-0.006767327431589365,
0.00693068141117692,
0.04059673100709915,
-0.01206885278224945,
0.000980618060566485,
0.06550218164920807,
0.03780444338917732,
-0.03792900592088699,
-0.037735577672719955,
-0.02401108294725418,
0.010709165595471859,
-0.046485740691423416,
-0.01272748876363039,
-0.0012605650117620826,
-0.047207050025463104,
-0.012639682739973068,
-0.05342011898756027,
0.04154068976640701,
0.08632034808397293,
-0.006605086848139763,
0.012350392527878284,
0.009459606371819973,
0.040753453969955444,
-0.030512351542711258,
0.027613617479801178,
0.02574808895587921,
-0.010236275382339954,
0.013936740346252918,
-0.056155141443014145,
0.04333587735891342,
0.005229846574366093,
-0.047212522476911545,
0.02415093407034874,
-0.008327817544341087,
-0.0058112493716180325,
-0.017518915235996246,
0.04151493310928345,
-0.000697683950420469,
0.007681220769882202,
0.000056123764807125553,
0.01083537470549345,
0.04268891364336014,
-0.002600679639726877,
-0.012674794532358646,
0.029197411611676216,
0.014473410323262215,
-0.003026422346010804,
-0.03315926715731621,
-0.016234789043664932,
0.03284154459834099,
0.009762171655893326,
-0.013859348371624947,
0.0020634031388908625,
0.0359414778649807,
0.014190001413226128,
0.022579291835427284,
0.014529495500028133,
-0.03668799251317978,
-0.03044053167104721,
-0.04056200385093689,
0.0013393438421189785,
0.05148981511592865,
0.04239087551832199,
-0.0075040641240775585,
0.03030318208038807,
-0.010078329592943192,
0.030592719092965126,
0.013315222226083279,
0.03243163228034973,
-0.10767941176891327,
0.03890785947442055,
-0.07232526689767838,
-0.08621199429035187,
0.05253790691494942,
-0.0015413722721859813,
0.009813155978918076,
-0.0014845768455415964,
-0.001871755812317133,
0.06296981871128082,
0.03160860389471054,
-0.06569751352071762,
0.013211567886173725,
-0.018703967332839966,
-0.008179978467524052,
-0.007227208930999041,
-0.03407551348209381,
0.023406853899359703,
-0.023320218548178673,
0.017659224569797516,
0.04968445375561714,
-0.0430859699845314,
0.0163723174482584,
0.020432792603969574,
0.024511583149433136,
0.03017064370214939,
0.03632073476910591,
0.034550778567790985,
0.0335688553750515,
-0.03305043280124664,
0.03241083398461342,
0.0002628842194098979,
0.05010790005326271,
0.014064203016459942,
-0.0027349565643817186,
-0.03859114646911621,
-0.0297545213252306,
-0.03461870551109314,
-0.02009069360792637,
0.047892261296510696,
-0.018733764067292213,
0.027056943625211716,
-0.02642715722322464,
0.00032651075161993504,
-0.0546974316239357,
0.04914464056491852,
0.055311787873506546,
0.02129746973514557,
-0.04895835369825363,
-0.0591004341840744,
-0.04597438499331474,
-0.023229174315929413,
-0.0004433922586031258,
0.014711033552885056,
-0.00041962144314311445,
-0.01726447604596615,
-0.0074080112390220165,
0.03941209241747856,
0.0411183163523674,
-0.011830974370241165,
0.08841965347528458,
-0.02414935640990734,
0.02084512636065483,
-0.04697386175394058,
-0.02116420678794384,
-0.023959161713719368,
0.012345761060714722,
0.03435370326042175,
-0.013942821882665157,
0.005489239934831858,
-0.06512842327356339,
0.0003214857424609363,
0.02617461234331131,
0.05837224796414375,
-0.04328567162156105,
0.002421381650492549,
-0.05297532305121422,
-0.04628864303231239,
0.0631217360496521,
-0.02485770732164383,
0.07056524604558945,
-0.03784308210015297,
0.01773231476545334,
-0.004954173229634762,
-0.013088279403746128,
-0.027189815416932106,
-0.018434612080454826,
0.01099963579326868,
0.020944928750395775,
0.0033378072548657656,
-0.03568897396326065,
0.008673111908137798,
0.006499567534774542,
0.07209677994251251,
0.06277645379304886,
-0.007964489981532097,
-0.03806975483894348,
-0.0003305232967250049,
-0.009480474516749382,
-0.030329402536153793,
-0.03344012051820755,
0.015324883162975311,
-0.0253745149821043,
-0.02367604337632656,
-0.017269693315029144,
-0.022850101813673973,
-0.05813080072402954,
0.03594106435775757,
-0.014617612585425377,
-0.03135308623313904,
-0.011282096616923809,
-0.030120890587568283,
0.040931884199380875,
0.03662467002868652,
-0.01397051103413105,
0.014786601066589355,
0.04000338539481163,
-0.014441125094890594,
0.015795838087797165,
-0.03801783174276352,
0.015452612191438675,
0.008363769389688969,
-0.025748230516910553,
-0.029416538774967194,
-0.007834439165890217,
-0.013278212398290634,
0.03336479142308235,
0.013840319588780403,
0.041898831725120544,
-0.030491290614008904,
-0.03859182074666023,
-0.01820451207458973,
0.024880554527044296,
-0.011160067282617092,
-0.01088748313486576,
0.027741694822907448,
-0.01586998626589775,
-0.018668007105588913,
-0.026041081175208092,
0.0018604276701807976,
0.028715871274471283,
0.04436306655406952,
0.01307598501443863,
-0.012650560587644577,
0.0007687789620831609,
-0.042048871517181396,
-0.045868292450904846,
0.006551516707986593,
-0.0828406885266304,
-0.00033851416083052754,
-0.03020387887954712,
0.028293166309595108,
0.050390735268592834,
-0.07171932607889175,
-0.000013897433746024035,
0.03173859417438507,
0.0036077559925615788,
0.002169286832213402,
-0.07511335611343384,
0.050044771283864975,
0.0079501299187541,
0.029042204841971397,
-0.052943579852581024,
-0.031925152987241745,
0.03046305663883686,
0.005143684800714254,
-0.019968349486589432,
-0.010448320768773556,
-0.02917659282684326,
0.00972452200949192,
-0.04033181443810463,
-0.002464753808453679,
0.08184296637773514,
-0.034544751048088074,
-0.008553190156817436,
0.059129953384399414,
0.0035061766393482685,
0.05403386056423187,
0.048727963119745255,
-0.02029598504304886,
0.020414836704730988,
-0.0318746455013752,
-0.033542025834321976,
0.005663663148880005,
0.04017411544919014,
-0.035226963460445404,
0.0005507625755853951,
-0.0021770973689854145,
0.014147389680147171,
0.03620924428105354,
0.03356979787349701,
0.0005668160156346858,
0.021263524889945984,
0.02091125026345253,
-0.0011880387319251895,
-0.06512768566608429,
-0.007000196725130081,
0.010195453651249409,
0.03001079149544239,
0.009314034134149551,
0.027918748557567596,
-0.010341520421206951,
-0.0361858494579792,
0.01563394069671631,
-0.01157071627676487,
0.03500068187713623,
-0.02600799687206745,
0.07392051815986633,
-0.042772673070430756,
0.015717163681983948,
0.02291448786854744,
0.01820388436317444,
0.02594791352748871,
-0.0123427864164114,
-0.025080693885684013,
0.02534216083586216,
-0.03113059140741825,
-0.036953844130039215,
-0.03941246494650841,
-0.021760938689112663,
-0.045905936509370804,
0.049443569034338,
-0.027414554730057716,
0.06815438717603683,
-0.01685408502817154,
0.015748383477330208,
0.006472546607255936,
0.016070067882537842,
0.00860519614070654,
0.002287374809384346,
0.03889317810535431,
0.023890921846032143,
0.019409487023949623,
0.009172141551971436,
0.008148359134793282,
0.003316710703074932,
0.024980908259749413,
-0.007282628677785397,
0.009299403987824917,
0.019250893965363503,
0.041134800761938095,
0.023189213126897812,
-0.033413615077733994,
0.0013231753837317228,
-0.027734581381082535,
0.055417414754629135,
-0.024506941437721252,
-0.03577202185988426,
0.06982836872339249,
0.0331692136824131,
0.02093449980020523,
-0.0376448929309845,
0.01052132248878479,
-0.042219918221235275,
-0.007402684073895216,
0.03541918471455574,
0.02262946404516697,
-0.015557671897113323,
0.033488836139440536,
0.07726269960403442,
0.007983878254890442,
0.028432678431272507,
-0.05279526859521866,
-0.0627853125333786,
0.006015044637024403,
-0.027645854279398918,
-0.07498321682214737,
0.049063604325056076,
0.02366059459745884,
0.007719866931438446,
0.013117584399878979,
-0.009828943759202957,
0.008100644685328007,
0.041393011808395386,
0.043146662414073944,
-0.006495320703834295,
0.047489915043115616,
-0.02790839411318302,
0.0017602553125470877,
-0.027958663180470467,
0.000966634601354599,
0.09366845339536667,
0.07767230272293091,
0.017031632363796234,
-0.012518979609012604,
0.02039683610200882,
-0.023846188560128212,
-0.0013664772268384695,
-0.018281104043126106,
0.005136737134307623,
0.01841397024691105,
-0.02890259586274624,
0.03840629383921623,
0.018141979351639748,
-0.012221958488225937,
0.002666917396709323,
0.02221386507153511,
-0.02315557934343815,
-0.042051393538713455,
-0.030686885118484497,
0.017258353531360626,
-0.002036305610090494,
-0.0035325451754033566,
-0.002074579242616892,
0.005644682329148054,
-0.010504852049052715,
-0.041988346725702286,
-0.06920436769723892,
-0.04894115775823593,
0.005506480112671852,
0.00568818673491478,
-0.0429697223007679,
0.022411571815609932,
0.02019496075809002,
-0.03662317991256714,
-0.008471252396702766,
0.04581749439239502,
-0.014925491996109486,
0.003420044668018818,
0.021955108270049095,
0.01657591201364994,
0.013155018910765648,
-0.009018382988870144,
0.0012291515013203025,
0.00568743422627449,
-0.03620689734816551,
0.004047800321131945,
-0.025631103664636612,
-0.0013243453577160835,
-0.01912725903093815,
-0.0066740731708705425,
0.01929629221558571,
0.007946128956973553,
-0.005594393704086542,
-0.0563349574804306,
0.012056218460202217,
0.006235580891370773,
0.014770859852433205,
-0.017311034724116325,
-0.03234131634235382,
0.0003266620042268187,
0.0056224181316792965,
0.0012546263169497252,
0.00366573641076684,
0.015370728448033333,
-0.014442746527493,
0.0064009130001068115,
0.003080814378336072,
0.0157840047031641,
-0.04908924922347069,
-0.02057425118982792,
-0.024488508701324463,
0.007208041846752167,
-0.050461847335100174,
-0.000432225497206673,
0.013245901092886925,
0.02790830470621586,
0.0024277393240481615,
-0.02883482538163662,
-0.0347287543118,
-0.045114077627658844,
0.008787224069237709,
0.029498111456632614,
-0.011808367446064949,
0.01932304911315441,
-0.023297065868973732,
-0.00470240181311965,
0.01929955929517746,
0.012214460410177708,
-0.030588336288928986,
0.0069543132558465,
0.012983111664652824,
0.0007671132334508002,
0.032907892018556595,
-0.03763771057128906,
-0.021151553839445114,
0.019205234944820404,
-0.03112700767815113,
0.015999259427189827,
-0.0036963894963264465,
0.033321186900138855,
0.034826960414648056,
0.0023158001713454723,
-0.028134459629654884,
0.014727350324392319,
-0.04752856120467186,
0.03631829097867012,
-0.0000027771384338848293,
-0.05214570835232735,
-0.022703170776367188,
0.057873763144016266,
-0.0208725705742836,
-0.03367791697382927,
0.009555742144584656,
-0.01506084855645895,
-0.020466171205043793,
0.033182643353939056,
0.00830053724348545,
-0.013413280248641968,
0.020203614607453346,
-0.04064881429076195,
0.016575798392295837,
-0.016459358856081963,
-0.013556141406297684,
-0.01887739822268486,
-0.025773677974939346,
0.02647685632109642,
0.014086822047829628,
-0.021488718688488007,
-0.002970930188894272,
0.001937266206368804,
-0.004138752352446318,
-0.034159038215875626,
0.03774913400411606,
0.01904723234474659,
-0.009734083898365498,
-0.000936968601308763,
0.005716280080378056,
0.04414139688014984,
0.002823766553774476,
-0.00322261406108737,
0.03446075692772865,
-0.029022324830293655,
-0.0545499213039875,
0.020047981292009354,
-0.015029149129986763,
0.02037774957716465,
0.023796863853931427,
-0.01674148254096508,
0.02760731801390648,
0.07477408647537231,
-0.0057981195859611034,
-0.009346523322165012,
-0.016164302825927734,
-0.06298062950372696,
-0.05095015838742256,
-0.011909007094800472,
-0.025278206914663315,
-0.003361609997227788,
0.011113936081528664,
0.0409439317882061,
0.011733326129615307,
-0.012058882042765617,
-0.007972930558025837,
0.00279177981428802,
-0.010228991508483887,
-0.047038741409778595,
0.03980482369661331,
0.0022620968520641327,
0.014600776135921478,
0.00459484476596117,
-0.003076673485338688,
0.0027110439259558916,
-0.02461889572441578,
0.019869394600391388,
-0.04969412088394165,
-0.03689970821142197,
0.017487045377492905,
0.01502867229282856,
0.062409818172454834,
-0.08367333561182022,
-0.017581095919013023,
0.03829334303736687,
-0.04128812626004219,
-0.01203165389597416,
-0.016570456326007843,
-0.016693640500307083,
-0.0076466393657028675,
0.008868840523064137,
0.0164926890283823,
0.025451015681028366,
-0.01377023570239544,
0.04800491780042648,
0.01751035638153553,
-0.007481270004063845,
-0.03972405567765236,
-0.030289774760603905,
0.05905136093497276,
0.031026668846607208,
0.016062894836068153,
-0.025230370461940765,
0.03644724190235138,
-0.02424754947423935,
0.022317999973893166,
0.025607148185372353,
-0.07976150512695312,
0.032508835196495056,
0.009729874320328236,
-0.01752682588994503,
-0.013134552165865898,
0.06786327064037323,
-0.001771925832144916,
-0.0034183484967797995,
0.011934727430343628,
0.02132050320506096,
-0.002405238337814808,
0.06547829508781433,
-0.037314679473638535,
0.01168948132544756,
0.03734422102570534,
-0.04377574846148491,
-0.023011373355984688,
-0.0038257099222391844,
-0.006940960418432951,
0.0247771255671978,
0.014113484881818295,
-0.016983846202492714,
0.019988901913166046,
-0.0409790575504303,
-0.02382812649011612,
-0.008235453628003597,
-0.006692583207041025,
0.03991866111755371,
-0.07866616547107697,
-0.015291866846382618,
-0.009472893550992012,
0.009450430981814861,
-0.009737065061926842,
-0.002465600147843361,
-0.01596044935286045,
-0.05146123096346855,
-0.07890433073043823,
0.01550402119755745,
-0.0012291815364733338,
-0.043746110051870346,
-0.02574271894991398,
-0.000781288486905396,
-0.0041631548665463924,
0.03445839881896973,
0.017654133960604668,
0.010133800096809864,
0.016823094338178635,
0.013385351747274399,
-0.02929661236703396,
-0.09629368036985397,
0.03550378233194351,
-0.003860349301248789,
-0.041319701820611954,
-0.023831671103835106,
0.029773492366075516,
0.033029474318027496,
-0.020647665485739708,
0.05814007297158241,
-0.04597853124141693,
-0.018078826367855072,
-0.007739060092717409,
-0.021791212260723114,
0.01304645836353302,
-0.016936084255576134,
-0.008161250501871109,
0.0041447291150689125,
-0.011217974126338959,
-0.00022355798864737153,
-0.018940472975373268,
-0.017906542867422104,
-0.016987154260277748,
0.01570492424070835,
-0.0026751658879220486,
0.0038495566695928574,
-0.014823691919445992,
0.013778741471469402,
-0.012838947586715221,
0.03676403686404228,
-0.009850128553807735,
0.0797172337770462,
-0.0020304410718381405,
0.03302175551652908,
0.02725536748766899,
-0.009847375564277172,
-0.06895671039819717,
0.04385075345635414,
-0.02810012735426426,
-0.008772220462560654,
-0.021686438471078873,
-0.022557886317372322,
0.03846031427383423,
-0.07999906688928604,
-0.005371429957449436,
0.011668205261230469,
-0.05801311880350113,
0.006847722455859184,
0.014392245560884476,
0.0552247054874897,
0.0410136803984642,
-0.04855186119675636,
0.029647978022694588,
0.03298822045326233,
-0.026224669069051743,
0.03312569111585617,
0.014128425158560276,
0.0506388396024704,
-0.02519156038761139,
0.0004203403368592262,
0.03391478583216667,
-0.01994585059583187,
0.018073903396725655,
-0.017615411430597305,
0.008612826466560364,
-0.020896265283226967,
-0.01796393096446991,
0.022315779700875282,
-0.013552137650549412,
0.018887870013713837,
0.052269112318754196,
-0.0226858202368021,
0.04506727680563927,
-0.032792773097753525,
0.019234128296375275,
-0.02615806646645069,
-0.004738626070320606,
-0.025252753868699074,
-0.0014684769557788968,
0.040546562522649765,
-0.008888575248420238,
0.009350433945655823,
-0.014905823394656181,
0.024789003655314445,
-0.005691130179911852,
0.03369908407330513,
0.017729315906763077,
0.020278573036193848,
-0.02451866678893566,
0.020685726776719093,
-0.010183872655034065,
0.011791313998401165,
-0.05387084186077118,
-0.04022078588604927,
0.03619394451379776,
0.03381657600402832,
-0.01997804455459118,
0.011166603304445744,
0.008313273079693317,
-0.008427746593952179,
0.06961740553379059,
-0.045512374490499496,
-0.0005902972770854831,
-0.010226908139884472,
0.02094998210668564,
0.005906598176807165,
0.008538232184946537
] |
<p>I have been told that trasverse wave propogates by the oscillation of medium particles in direction perpendicular to propogation.</p>
<p>Consider a wave on a taught string (x-y plane).
What is the mechanism of movement of the same sinosudial function along the string?</p>
<p>Suppose we start moving the particle on one end sinosudialy the how come the next particle also moves sinosudialy? How does elastic force between them does this work?
If we displace the particle, there is some elastic force developed which is at some angle with horizontal so the next particle should move at some angle and its vertical displacement should be less than the previous one. </p>
<p>So how come in a propogating wave all particle rise to the same height?</p> | 4,630 | [
-0.00633418932557106,
-0.021792443469166756,
0.020848585292696953,
-0.049078319221735,
0.049589574337005615,
0.023103823885321617,
-0.01814034767448902,
-0.03461761027574539,
0.0037356072571128607,
-0.05165034905076027,
0.0031992022413760424,
0.04371390491724014,
0.04795341193675995,
0.01289825327694416,
0.02965993620455265,
-0.022362880408763885,
-0.029822414740920067,
0.0026186122559010983,
-0.009290570393204689,
-0.03846755623817444,
-0.01195572130382061,
-0.0038377968594431877,
-0.027584146708250046,
-0.00380190322175622,
0.018100926652550697,
0.0221303328871727,
0.026873627677559853,
0.03260769695043564,
0.01760665513575077,
0.04934743419289589,
0.019283298403024673,
-0.026485830545425415,
-0.009905166923999786,
0.02004092000424862,
0.04288255050778389,
-0.012559865601360798,
-0.038804102689027786,
-0.031223610043525696,
0.0040166438557207584,
-0.006757207680493593,
-0.01276291161775589,
-0.0065717245452106,
-0.02142757922410965,
0.06394192576408386,
-0.028606321662664413,
0.019534967839717865,
0.022622045129537582,
0.0004358497099019587,
0.07881039381027222,
-0.08196437358856201,
0.0482446551322937,
-0.032662227749824524,
0.03693677857518196,
0.00033931012148968875,
0.00833843369036913,
-0.02907712198793888,
0.10702649503946304,
0.05357213318347931,
-0.030596112832427025,
-0.04411865398287773,
0.006297413259744644,
-0.006954289507120848,
-0.02988329343497753,
-0.0232487004250288,
-0.050560902804136276,
0.008171106688678265,
0.0019110909197479486,
-0.0020702744368463755,
0.0156536977738142,
0.005944543052464724,
-0.004290275741368532,
0.006536731030791998,
0.05143708735704422,
-0.02586640976369381,
0.025233756750822067,
0.004749417304992676,
0.02458317205309868,
0.01617353968322277,
0.01249261200428009,
0.04311370104551315,
0.028959380462765694,
-0.000020185230823699385,
0.01217670924961567,
0.06040337681770325,
-0.0027005875017493963,
-0.036850232630968094,
0.06635591387748718,
-0.02699793502688408,
-0.00047275834367610514,
0.034083686769008636,
-0.0035657882690429688,
0.0225636288523674,
0.02062465436756611,
0.04986044019460678,
-0.00915807019919157,
0.016932250931859016,
0.019644159823656082,
0.055049143731594086,
0.038072239607572556,
-0.023431645706295967,
0.03985424339771271,
-0.043279919773340225,
0.03167351707816124,
0.04574226960539818,
0.017035098746418953,
-0.014928377233445644,
-0.05262265354394913,
0.010345476679503918,
-0.09144384413957596,
-0.0401909276843071,
-0.031156156212091446,
0.015701426193118095,
-0.011939695104956627,
0.009874362498521805,
-0.010535603389143944,
0.007273074239492416,
0.009943021461367607,
-0.009045691229403019,
0.06056363135576248,
0.06519705057144165,
0.04466988891363144,
-0.01916508562862873,
0.023309044539928436,
-0.00977410189807415,
-0.06629578769207001,
-0.005539574194699526,
-0.002273190300911665,
-0.01241625938564539,
-0.03179755061864853,
0.03724232688546181,
0.0030654536094516516,
-0.03000250644981861,
0.022812116891145706,
-0.003045847872272134,
0.07062672823667526,
0.04823104664683342,
-0.11621472239494324,
-0.010124717839062214,
0.06575499475002289,
-0.013737180270254612,
0.0032363173086196184,
-0.04387074336409569,
-0.021807285025715828,
0.02556508779525757,
0.06940951198339462,
-0.037699587643146515,
0.009818003512918949,
-0.0030269057024270296,
0.0410417839884758,
-0.018440116196870804,
-0.00792242493480444,
-0.037776343524456024,
-0.011349467560648918,
-0.03931083157658577,
-0.007747602183371782,
-0.02243099920451641,
0.03544604405760765,
0.0458228625357151,
-0.022337429225444794,
-0.030313830822706223,
0.05125891789793968,
-0.023678328841924667,
0.015002964995801449,
0.02287697046995163,
-0.0005189532530494034,
-0.048782337456941605,
0.08349065482616425,
0.016682958230376244,
-0.025778569281101227,
0.015836378559470177,
-0.02590446174144745,
-0.007479178719222546,
-0.02006343938410282,
0.011918270960450172,
0.010225392878055573,
-0.04868799075484276,
-0.03926314041018486,
0.0012088073417544365,
-0.007399886380881071,
0.004522964358329773,
0.002519194735214114,
-0.03556111454963684,
0.00691626500338316,
0.033965062350034714,
0.0012640557251870632,
0.007357897702604532,
-0.0165900606662035,
-0.005385421682149172,
-0.01863921619951725,
-0.0735984519124031,
-0.006834539119154215,
-0.03569315746426582,
0.08197472989559174,
-0.015074040740728378,
0.009166814386844635,
0.013912742957472801,
0.028280213475227356,
-0.020179715007543564,
-0.014566594734787941,
0.011468852870166302,
-0.03803863003849983,
0.03571109473705292,
0.0024479622952640057,
0.0356646403670311,
0.0254477821290493,
0.09075931459665298,
0.011151956394314766,
0.01604987308382988,
0.03003809042274952,
-0.021205874159932137,
-0.008102328516542912,
0.020241573452949524,
-0.027460990473628044,
0.0224299393594265,
-0.024939902126789093,
0.013015372678637505,
0.0014888375299051404,
-0.01683191955089569,
-0.018020646646618843,
0.05488884821534157,
-0.054596949368715286,
0.06310170143842697,
0.06692180782556534,
0.012805424630641937,
-0.004124800208956003,
0.049198951572179794,
-0.04644956439733505,
0.03755108639597893,
0.04975137114524841,
-0.036393217742443085,
-0.031238794326782227,
-0.02023286372423172,
0.010533970780670643,
0.010473595932126045,
-0.02086261846125126,
-0.01850043796002865,
0.021021738648414612,
0.030418142676353455,
0.040151629596948624,
0.05790938064455986,
-0.013434991240501404,
-0.025474177673459053,
0.0018152992706745863,
0.04141334071755409,
-0.0006760058458894491,
0.004881871864199638,
0.02264309488236904,
0.02216780185699463,
-0.004782975185662508,
-0.019414380192756653,
-0.0420750267803669,
0.025263162329792976,
0.0566963367164135,
0.0376591831445694,
-0.0029590651392936707,
-0.030264349654316902,
0.007102282252162695,
-0.03349226713180542,
-0.014337407425045967,
0.01604945957660675,
0.02446851320564747,
-0.018457584083080292,
-0.04109642282128334,
-0.006958776153624058,
0.003987082280218601,
0.011457666754722595,
-0.01712150126695633,
-0.030609864741563797,
0.012795447371900082,
-0.026211559772491455,
-0.004466555081307888,
-0.012682297267019749,
-0.017273854464292526,
-0.0005104529554955661,
-0.020323744043707848,
0.0644885003566742,
0.0658164918422699,
0.04057297110557556,
-0.05133911967277527,
-0.04317169636487961,
0.005595141556113958,
-0.040647827088832855,
0.01338233333081007,
0.005153149366378784,
-0.03943650797009468,
0.017671052366495132,
-0.04604322463274002,
-0.05522381514310837,
0.04613497108221054,
0.0018217976903542876,
-0.019070031121373177,
0.03704504668712616,
-0.008963865227997303,
-0.06606223434209824,
-0.03565797954797745,
-0.04604790732264519,
0.03995942324399948,
-0.0012891574297100306,
0.018532611429691315,
0.047239892184734344,
0.023065870627760887,
-0.0038230279460549355,
-0.0013120548101142049,
-0.05833631008863449,
-0.04866029694676399,
-0.009529881179332733,
-0.012733268551528454,
0.024188879877328873,
-0.0038241290021687746,
0.04341435432434082,
0.0022075390443205833,
-0.04103502258658409,
0.002827058546245098,
-0.032344769686460495,
-0.026973018422722816,
0.006450423039495945,
-0.0030718704219907522,
0.061778511852025986,
0.0011612805537879467,
-0.006834391504526138,
0.06590136885643005,
0.007616973016411066,
-0.059772320091724396,
-0.01798463612794876,
-0.009721959009766579,
-0.02509988285601139,
-0.013247061520814896,
0.03775417059659958,
0.0647488683462143,
-0.03369341418147087,
0.03800216689705849,
0.03327702358365059,
0.02629980258643627,
0.05129716917872429,
0.020703567191958427,
0.0007925903773866594,
-0.016068777069449425,
0.027459952980279922,
0.017974691465497017,
0.04004155471920967,
0.007370870094746351,
-0.04214593395590782,
0.017307177186012268,
0.01342020370066166,
0.014722198247909546,
0.011791934259235859,
-0.007335726637393236,
0.022101527079939842,
0.0219782255589962,
-0.03331505134701729,
-0.03742646425962448,
0.02900933474302292,
0.02169082686305046,
-0.02294001542031765,
0.024573054164648056,
0.007393487263470888,
0.03138309344649315,
0.004324365872889757,
-0.0005813327734358609,
-0.01201056782156229,
0.0006852774531580508,
-0.009859058074653149,
-0.03530031815171242,
-0.03282118961215019,
-0.010409730486571789,
0.018228955566883087,
-0.027705691754817963,
-0.03795408457517624,
0.03945886343717575,
0.011503812856972218,
0.02093110792338848,
0.0009153031860478222,
-0.06019774079322815,
0.006381626706570387,
-0.024018531665205956,
0.001414208090864122,
0.02052251249551773,
0.022193722426891327,
0.02050485461950302,
0.06418338418006897,
0.002779979957267642,
0.01870817318558693,
0.039670731872320175,
-0.008379384875297546,
-0.09162387251853943,
-0.011584351770579815,
-0.06169414147734642,
-0.012923586182296276,
-0.01805323176085949,
-0.014386428520083427,
-0.01885218173265457,
-0.007973222061991692,
-0.02456279844045639,
-0.01945304311811924,
-0.030949579551815987,
-0.045150499790906906,
0.03959396481513977,
-0.05408455431461334,
-0.019636211916804314,
-0.020512953400611877,
0.024994874373078346,
0.018888607621192932,
-0.050624772906303406,
0.014667116105556488,
0.06910093873739243,
-0.04766970872879028,
0.022082218900322914,
-0.02017214708030224,
-0.010052619501948357,
0.020781738683581352,
0.019967565312981606,
0.02448149025440216,
0.02649972215294838,
-0.025770477950572968,
0.009982059709727764,
0.006237035151571035,
0.023801589384675026,
0.02611440233886242,
-0.0077369678765535355,
-0.02899116277694702,
-0.02547614835202694,
0.007678413763642311,
-0.012210666202008724,
0.03977794572710991,
0.02866421453654766,
-0.03713975101709366,
0.03156934678554535,
-0.00005446856812341139,
-0.030417747795581818,
0.0719737559556961,
0.035997774451971054,
0.020286452025175095,
0.02824266254901886,
-0.027883995324373245,
-0.005277467425912619,
-0.012061444111168385,
-0.009893452748656273,
0.011146760545670986,
0.018465274944901466,
-0.03701680526137352,
0.012914566323161125,
0.043048758059740067,
0.029631327837705612,
-0.0029306954238563776,
0.008985178545117378,
-0.04154086485505104,
0.01571674831211567,
-0.02631956711411476,
-0.015151673927903175,
0.0057191443629562855,
0.02980402484536171,
0.0159014780074358,
-0.02668951079249382,
-0.02813849411904812,
-0.06812912970781326,
-0.024917222559452057,
0.015059508383274078,
0.0027302848175168037,
-0.030350150540471077,
0.02744341269135475,
-0.05028699338436127,
-0.04597581550478935,
0.05023609474301338,
-0.035432443022727966,
-0.0018241617362946272,
-0.029986971989274025,
-0.004264387767761946,
-0.012255116365849972,
-0.00296473759226501,
-0.01964867115020752,
0.02336292713880539,
-0.00917905569076538,
-0.004195470828562975,
-0.026102986186742783,
0.007901351898908615,
-0.035218529403209686,
0.017510471865534782,
0.014186873100697994,
0.024933218955993652,
0.01645124889910221,
0.0168000515550375,
0.0013405231293290854,
0.02750239335000515,
-0.013823176734149456,
-0.05514930561184883,
0.021861692890524864,
0.014641552232205868,
-0.009847642853856087,
0.029309429228305817,
-0.01359729003161192,
-0.023697955533862114,
0.011885338462889194,
0.006018409039825201,
-0.024212483316659927,
-0.020443301647901535,
-0.05496992915868759,
0.04675387591123581,
0.029769109562039375,
0.000545332208275795,
0.04376081004738808,
0.04665996506810188,
-0.04671379178762436,
0.005821549333631992,
-0.0017569514457136393,
0.02364879474043846,
-0.020692816004157066,
-0.005176521837711334,
-0.023115569725632668,
0.019540607929229736,
-0.007947567850351334,
0.05434621870517731,
0.012173749506473541,
-0.032509349286556244,
-0.03572455048561096,
0.008588285185396671,
-0.024468205869197845,
0.05339229106903076,
-0.02626626566052437,
-0.0038812148850411177,
0.008856454864144325,
0.052779097110033035,
-0.013584681786596775,
-0.029124153777956963,
0.0032914122566580772,
-0.021673280745744705,
0.0233138557523489,
0.020417045801877975,
0.03299260139465332,
-0.004759097006171942,
-0.03979851305484772,
-0.014392371289432049,
0.03066074289381504,
-0.08201246708631516,
0.02351698838174343,
-0.014730952680110931,
0.03423430770635605,
0.040247850120067596,
-0.03476645424962044,
-0.04793709143996239,
0.006644516717642546,
0.0024516540579497814,
0.06975002586841583,
-0.037773363292217255,
0.013747528195381165,
-0.005638333968818188,
0.022553758695721626,
-0.06339811533689499,
-0.07156249135732651,
0.008756759576499462,
-0.008502178825438023,
0.006293610204011202,
-0.019559074193239212,
0.021123437210917473,
-0.02107781171798706,
-0.013239752501249313,
0.018262412399053574,
-0.000424081867095083,
-0.01566949486732483,
0.013062754645943642,
0.014584891498088837,
0.0026131863705813885,
0.07434980571269989,
0.001728548901155591,
-0.05037486553192139,
0.0068710376508533955,
-0.01888420805335045,
0.01725704036653042,
-0.05164552107453346,
0.04278460517525673,
-0.025226684287190437,
-0.043306395411491394,
0.011526979506015778,
0.01060933992266655,
0.009268614463508129,
-0.018629105761647224,
0.014489484019577503,
0.004711317364126444,
0.047551821917295456,
-0.011887171305716038,
-0.022931981831789017,
0.005299590062350035,
-0.04209291934967041,
0.011828082613646984,
0.002248669508844614,
0.007321247365325689,
-0.07449521124362946,
-0.048465002328157425,
-0.004629958886653185,
0.014266709797084332,
0.0241441298276186,
0.0044306376948952675,
0.049275562167167664,
-0.04255450516939163,
-0.004430843982845545,
0.01852603815495968,
0.014076393097639084,
-0.012414725497364998,
-0.029188401997089386,
-0.00524279847741127,
-0.0023080387618392706,
-0.012996506877243519,
0.011052606627345085,
-0.016183752566576004,
-0.028287623077630997,
0.02135486900806427,
0.05809219181537628,
-0.05106385052204132,
0.056733496487140656,
0.024862393736839294,
-0.007333020213991404,
-0.014728924259543419,
-0.0008702180348336697,
-0.008578981272876263,
-0.01138029433786869,
-0.007605972699820995,
0.01397997047752142,
-0.06505909562110901,
-0.0032528764568269253,
0.020833222195506096,
0.029900450259447098,
-0.02239382639527321,
0.012608478777110577,
0.015058944001793861,
0.008266439661383629,
0.03539445251226425,
-0.021282974630594254,
-0.01847696304321289,
0.02902267314493656,
-0.019716901704669,
0.07787439227104187,
0.0036350039299577475,
-0.007832820527255535,
0.018597403541207314,
0.048415858298540115,
-0.024339554831385612,
-0.050835199654102325,
0.035115040838718414,
-0.032004136592149734,
-0.005503436084836721,
0.008638538420200348,
0.039258308708667755,
0.016072191298007965,
0.020580129697918892,
0.03252877667546272,
0.009671361185610294,
0.04508120194077492,
-0.04091238975524902,
-0.055747561156749725,
-0.03070797398686409,
-0.0223187617957592,
-0.05726221948862076,
0.04940655082464218,
0.003928171470761299,
-0.02753090113401413,
-0.004425321239978075,
-0.020128581672906876,
0.04013371467590332,
-0.004497254267334938,
0.03560110926628113,
-0.02298291027545929,
0.09028027951717377,
-0.00007125599950086325,
0.02408982627093792,
0.003801054786890745,
0.010047446936368942,
0.11288639158010483,
0.03454389423131943,
0.022560400888323784,
-0.03982776775956154,
-0.014301581308245659,
-0.018300438299775124,
-0.0002788248530123383,
-0.04965260997414589,
-0.012527518905699253,
0.053251855075359344,
0.00523033645004034,
-0.0022186930291354656,
0.05061614513397217,
-0.004591837991029024,
0.007710577454417944,
0.041850745677948,
-0.08151649683713913,
-0.07902094721794128,
-0.012376493774354458,
-0.018657997250556946,
-0.016295915469527245,
0.04802917689085007,
-0.03448891267180443,
0.014719435013830662,
-0.02852163463830948,
-0.03128279745578766,
-0.039506252855062485,
-0.06863473355770111,
0.026957256719470024,
-0.003623556112870574,
-0.03365863114595413,
-0.001673526712693274,
0.012313777580857277,
-0.030425572767853737,
-0.05446853116154671,
0.008013485930860043,
0.01778239570558071,
-0.029326535761356354,
0.03426499664783478,
0.01857713982462883,
0.012572692707180977,
0.03405832126736641,
0.03200192004442215,
0.03332212194800377,
-0.008562800474464893,
0.025153759866952896,
-0.0016497093020007014,
0.053832221776247025,
0.008932302705943584,
-0.003257678123190999,
0.011110302992165089,
0.02465549297630787,
-0.005811354611068964,
-0.06001943349838257,
-0.04370666667819023,
-0.00740430410951376,
0.05297917500138283,
-0.032298482954502106,
-0.005177677609026432,
0.0019789491780102253,
-0.010387885384261608,
-0.018734635785222054,
0.028913589194417,
-0.028428155928850174,
0.010508489795029163,
-0.02802988328039646,
-0.004404607228934765,
0.03351321071386337,
-0.026203718036413193,
-0.027740241959691048,
-0.010955746285617352,
-0.0005698617896996439,
-0.04410898685455322,
0.008415830321609974,
0.020920410752296448,
0.04094112664461136,
0.03677917271852493,
0.0017054814379662275,
-0.007850902155041695,
0.00635119155049324,
-0.024158844724297523,
0.01750054396688938,
0.012080477550625801,
-0.02544313110411167,
-0.030339807271957397,
-0.011068199761211872,
0.04897560179233551,
0.06300391256809235,
-0.009841806255280972,
0.01780654676258564,
-0.014208666980266571,
-0.003453741082921624,
0.022169535979628563,
-0.04832516983151436,
-0.049577951431274414,
0.012739724479615688,
0.005280213430523872,
-0.010594756342470646,
0.0019152113236486912,
0.04033142328262329,
0.03777426853775978,
-0.003011461813002825,
-0.03853706270456314,
0.04097878932952881,
-0.058052897453308105,
-0.030789203941822052,
0.005180620588362217,
-0.04034765064716339,
0.028716526925563812,
0.052907440811395645,
0.003737642662599683,
-0.026822324842214584,
-0.026915909722447395,
0.04399912804365158,
0.03349064663052559,
0.004544079303741455,
-0.00044878089101985097,
-0.05142659321427345,
0.018331168219447136,
-0.035614144057035446,
0.01335305254906416,
-0.03083433210849762,
-0.011609651148319244,
-0.049724988639354706,
0.003959699533879757,
-0.007725510746240616,
-0.009514796547591686,
-0.05064346268773079,
0.030046047642827034,
-0.045734941959381104,
-0.03495178744196892,
-0.0037491749972105026,
0.013894962146878242,
0.006863177753984928,
-0.003350696759298444,
0.059698835015296936,
-0.028448091819882393,
0.033446844667196274,
0.0076054600067436695,
-0.027533618733286858,
-0.004023441579192877,
-0.024528415873646736,
-0.05867711454629898,
0.015644770115613937,
-0.03813346475362778,
0.032442864030599594,
0.03510343283414841,
0.0031858570873737335,
0.005289293825626373,
0.042923327535390854,
0.011284939013421535,
-0.0031334548257291317,
-0.007527065463364124,
-0.052763137966394424,
0.012749666348099709,
-0.017924988642334938,
-0.018555594608187675,
0.022055475041270256,
-0.04672834649682045,
0.051701657474040985,
0.03904367610812187,
0.015524715185165405,
0.009033706039190292,
0.024285120889544487,
-0.01604282855987549,
-0.034891657531261444,
0.022178450599312782,
-0.01325591653585434,
0.019866162911057472,
0.049902621656656265,
-0.036517661064863205,
0.02593812346458435,
0.0002292638528160751,
0.016872700303792953,
-0.06471092998981476,
0.020329631865024567,
0.018324606120586395,
0.00047723480383865535,
0.04850076884031296,
-0.023555243387818336,
0.010055222548544407,
0.00946175865828991,
-0.05261994153261185,
0.03671196848154068,
-0.023914242163300514,
-0.00047038847696967423,
-0.007511647418141365,
-0.017945468425750732,
-0.01742807775735855,
0.06074349209666252,
0.026730230078101158,
0.05087483301758766,
0.013326294720172882,
0.012463117949664593,
0.010011247359216213,
-0.01293400302529335,
-0.011263158172369003,
0.03990478441119194,
0.01415521465241909,
0.01597532071173191,
0.0778602808713913,
-0.020979909226298332,
-0.03318005055189133,
0.05015698820352554,
-0.012864450924098492,
0.01577509008347988,
0.0037599478382617235,
0.008952151983976364,
-0.002830455545336008,
0.011068381369113922,
-0.0040601929649710655,
0.0061761424876749516,
-0.0032032851595431566,
0.023068459704518318,
0.013099756091833115,
-0.008713127113878727,
0.013104627840220928,
-0.024114355444908142,
0.006965125910937786,
-0.03790590167045593,
0.013036462478339672,
0.05428096652030945,
-0.005227429326623678,
0.004344236571341753,
0.017080845311284065,
0.013262945227324963,
0.027043461799621582,
0.025569796562194824,
-0.011237597092986107,
-0.018688363954424858,
0.008781574666500092,
0.00438068900257349,
-0.014439206570386887,
-0.03796456754207611,
0.006095622666180134,
0.014555947855114937,
-0.020668279379606247,
0.033444441854953766,
-0.028129005804657936,
0.0035208354238420725,
-0.004911147989332676,
0.003594966372475028,
0.011825981549918652,
0.007572774309664965,
-0.0018214547308161855,
-0.009314809925854206,
-0.019110383465886116,
0.025615781545639038,
0.011731794103980064,
0.02011348120868206,
-0.007589109241962433,
-0.00509378919377923,
-0.04269024357199669,
-0.06715165823698044,
0.07575143128633499,
0.008925056084990501,
-0.026926623657345772,
-0.049906130880117416,
-0.013708533719182014,
0.0015369587345048785,
0.05228835716843605,
0.03161187097430229,
-0.023260939866304398,
-0.004924397449940443,
-0.00046723539708182216,
-0.009696980006992817,
0.025579005479812622,
-0.018819913268089294,
-0.01841932348906994,
0.03525841608643532,
-0.04878611862659454,
-0.02143985964357853,
0.02817220240831375,
-0.04097570478916168,
0.02624141424894333,
0.002687192289158702,
-0.005925123114138842,
0.02593580074608326,
0.0057024648413062096,
-0.0647953525185585,
-0.03370954841375351,
0.033998165279626846,
-0.0226424690335989,
0.0709897056221962,
-0.014469768851995468,
-0.01627010852098465,
-0.003095946041867137,
-0.033511921763420105,
-0.040903303772211075,
0.007928761653602123,
-0.015041236765682697,
0.003156773280352354,
0.004835468251258135,
0.006136465352028608,
0.017772827297449112,
-0.051307108253240585,
-0.03882353752851486,
0.02562018111348152,
-0.04926690831780434,
0.0016575591871514916,
0.03535967320203781,
0.025071095675230026,
0.0172395221889019,
-0.002678866032510996,
0.00983939878642559,
0.015633611008524895,
-0.008590257726609707,
0.012776088900864124,
0.055030956864356995,
-0.005047819577157497,
-0.029840480536222458,
0.01213375199586153,
0.014571497216820717,
0.00047482442460022867,
0.04201493412256241,
0.008789736777544022,
0.017490390688180923,
-0.02370626851916313,
-0.012100686319172382,
-0.011202781461179256,
-0.024295827373862267,
-0.010656867176294327,
0.08833666145801544,
-0.02907845750451088,
0.07748430222272873,
-0.03257511928677559,
0.0446879044175148,
-0.01965736784040928,
0.016128936782479286,
-0.006510023958981037,
0.005404750816524029,
0.01603648252785206,
0.03577415272593498,
-0.006468843203037977,
-0.027058668434619904,
0.0028307558968663216,
-0.0029873051680624485,
0.002669744659215212,
0.001616048626601696,
-0.02030155062675476,
-0.012460476718842983,
-0.034634724259376526,
0.014469803310930729,
-0.01697956770658493,
-0.03207521513104439,
0.005255047231912613,
0.05346614122390747,
0.029756048694252968,
0.007819430902600288,
0.014386768452823162,
0.009908760897815228,
-0.029589632526040077,
0.039249785244464874,
-0.06323150545358658,
0.003979440312832594,
-0.028381308540701866,
-0.0023535664658993483,
-0.04697320982813835,
-0.0018914805259555578
] |
<p>When we send an electromagnetic short wave to the sky, it reflects due to the ionosphere effects. But if we send it horizontally, is it correct that it moves around the surface of the earth, and if it has enough energy, it can return to its first position?</p>
<p>If yes, then how could that happen?</p> | 4,631 | [
-0.03659885749220848,
-0.03306509181857109,
0.0034399975556880236,
0.00813574530184269,
0.06009805575013161,
0.0224841870367527,
-0.032370731234550476,
-0.021451102569699287,
0.008005591109395027,
-0.019120143726468086,
0.008449538610875607,
0.03908165171742439,
0.037375736981630325,
0.024564016610383987,
0.020853884518146515,
0.010814222507178783,
-0.01690666750073433,
0.027409620583057404,
-0.03803064674139023,
-0.04328916221857071,
-0.02466052584350109,
-0.001654312713071704,
-0.006850547157227993,
0.010149325244128704,
-0.013518543913960457,
-0.016741875559091568,
0.04926217719912529,
-0.011094705201685429,
0.03838912025094032,
0.050308097153902054,
0.03298491612076759,
0.006939092185348272,
-0.00846771989017725,
0.0143269719555974,
0.00783693790435791,
-0.014279302209615707,
-0.04114807769656181,
-0.04923843964934349,
0.013835133984684944,
-0.029778869822621346,
0.00871451199054718,
-0.0068980674259364605,
-0.032903265208005905,
0.033764783293008804,
-0.04392734542489052,
-0.008354262448847294,
-0.013748286291956902,
0.00029998584068380296,
0.06171789765357971,
-0.038595009595155716,
0.03382447361946106,
-0.03670935705304146,
0.01049682404845953,
-0.004137384705245495,
-0.000020695570128737018,
-0.0159841850399971,
0.08368130028247833,
0.03296726942062378,
0.0044265505857765675,
-0.005567463114857674,
0.011133636347949505,
-0.023985957726836205,
-0.03998318687081337,
-0.007571404334157705,
-0.0011264360509812832,
0.008249828591942787,
-0.017737828195095062,
0.002865527756512165,
0.005445309914648533,
0.014874391257762909,
0.015286468900740147,
0.006984110455960035,
0.0297156423330307,
0.027385953813791275,
0.05513180419802666,
-0.0009125978103838861,
0.008986851200461388,
-0.02264232560992241,
0.04046345129609108,
0.04072742164134979,
0.004470147658139467,
-0.011897704564034939,
0.01809893362224102,
0.023029301315546036,
0.01360611617565155,
-0.001269640983082354,
0.054213862866163254,
-0.0017519190441817045,
0.02758384868502617,
0.02163192816078663,
0.029451191425323486,
0.031289245933294296,
-0.01189147774130106,
0.008167324587702751,
-0.013357770629227161,
0.05370531976222992,
0.010639047250151634,
0.052521876990795135,
0.008499439805746078,
-0.022307302802801132,
0.020221002399921417,
-0.015106123872101307,
0.037196382880210876,
0.03545428812503815,
0.003753546392545104,
-0.015816571190953255,
-0.03247128054499626,
0.014746889472007751,
-0.05998991057276726,
-0.022731903940439224,
-0.02770264819264412,
-0.0017596848774701357,
-0.004159159027040005,
0.020208977162837982,
0.02089778333902359,
-0.026365667581558228,
0.0286802276968956,
-0.022068504244089127,
0.06703543663024902,
0.07930122315883636,
0.039166197180747986,
0.0053338841535151005,
0.05987156555056572,
-0.010875186882913113,
-0.0319395437836647,
-0.012693416327238083,
-0.013350175693631172,
-0.006437933538109064,
-0.048586923629045486,
-0.005643126089125872,
-0.009326661005616188,
-0.02458823472261429,
-0.002570332260802388,
-0.030775664374232292,
0.03964170813560486,
0.00041493761818856,
-0.11684632301330566,
-0.027179410681128502,
0.011985471472144127,
0.01636890135705471,
-0.009310313500463963,
-0.08451720327138901,
-0.012891487218439579,
0.020315449684858322,
0.0805797129869461,
-0.009105650708079338,
0.020214855670928955,
-0.016887111589312553,
0.06587444245815277,
-0.013980143703520298,
-0.021878451108932495,
-0.027934450656175613,
-0.004886855836957693,
-0.06676080822944641,
0.022698525339365005,
-0.07327014952898026,
0.027873439714312553,
0.035448309034109116,
0.005100475624203682,
-0.01679554395377636,
0.029326368123292923,
-0.02014608308672905,
0.013882207684218884,
-0.008399671874940395,
-0.03256328031420708,
-0.018653474748134613,
0.10127364099025726,
0.051393501460552216,
-0.01775490492582321,
0.005810140632092953,
-0.005735319573432207,
0.009526592679321766,
-0.02081957459449768,
-0.012168017216026783,
0.02918866276741028,
-0.06445827335119247,
0.010881264694035053,
0.0046197036281228065,
0.028425607830286026,
-0.019067928194999695,
-0.009622747078537941,
-0.016274472698569298,
0.033964648842811584,
0.018776055425405502,
0.016340142115950584,
0.04574964568018913,
-0.0231721643358469,
0.01160432118922472,
0.011666174046695232,
-0.030475249513983727,
-0.016591081395745277,
0.03169213980436325,
0.0448005385696888,
-0.0020450945012271404,
0.03684160113334656,
-0.016241561621427536,
0.005146577954292297,
0.0060323989018797874,
-0.008513163775205612,
-0.022545624524354935,
0.0203283429145813,
0.05776037648320198,
0.016767051070928574,
0.011592098511755466,
0.009198307059705257,
0.10456769913434982,
0.025447232648730278,
0.011447401717305183,
-0.009310374036431313,
0.012930996716022491,
-0.01980043388903141,
-0.04104909300804138,
0.003305961610749364,
0.03856242075562477,
0.026688257232308388,
0.020772509276866913,
0.026062926277518272,
0.02410246804356575,
-0.006207017693668604,
-0.009600506164133549,
-0.029072230681777,
0.035846564918756485,
0.06406145542860031,
-0.02411545440554619,
0.029105575755238533,
0.05564495921134949,
0.02738172374665737,
0.01597576215863228,
0.060716498643159866,
-0.05554050952196121,
-0.05460449308156967,
-0.02595885470509529,
0.009499860927462578,
-0.017651809379458427,
-0.02783455140888691,
-0.0021578106097877026,
0.009947726503014565,
0.041811998933553696,
0.032711952924728394,
0.02970893681049347,
-0.002145932288840413,
-0.03964121639728546,
0.031115131452679634,
0.006080814637243748,
0.015831585973501205,
0.02071954496204853,
0.02236432209610939,
0.007778148166835308,
-0.030930906534194946,
-0.00039020361145958304,
0.004420006647706032,
0.005404841620475054,
0.00171037542168051,
-0.008791683241724968,
0.010611546225845814,
-0.04858936369419098,
0.028240276500582695,
-0.04498940333724022,
0.019292622804641724,
0.0114896884188056,
-0.007777984254062176,
0.021516235545277596,
-0.04209303483366966,
0.044117480516433716,
-0.011389442719519138,
-0.014002017676830292,
0.00726365065202117,
-0.011521752923727036,
0.05108950287103653,
-0.04592997580766678,
0.037470877170562744,
-0.03871920332312584,
-0.015470637939870358,
-0.018903646618127823,
-0.04099390655755997,
0.052931711077690125,
0.010859877802431583,
0.026469722390174866,
-0.03853593021631241,
-0.03944844752550125,
-0.006779100280255079,
-0.03843659907579422,
-0.02495747245848179,
0.005174287129193544,
-0.047350380569696426,
0.048198822885751724,
-0.06259453296661377,
-0.02195398323237896,
0.05041748285293579,
0.026197707280516624,
0.012377132661640644,
0.03520579636096954,
-0.014551728963851929,
-0.06279215961694717,
-0.011636344715952873,
-0.05385807156562805,
0.006631848867982626,
-0.008401029743254185,
-0.004815199412405491,
0.0777340978384018,
-0.003691029967740178,
-0.019102226942777634,
-0.003008094383403659,
-0.02410447597503662,
-0.039087262004613876,
0.0014524335274472833,
-0.02388589270412922,
-0.01946129836142063,
-0.027856329455971718,
0.03486030176281929,
-0.0017923908308148384,
-0.062482453882694244,
-0.010996147990226746,
-0.04106371849775314,
-0.057889748364686966,
0.009614315815269947,
-0.017499573528766632,
0.01729944534599781,
-0.013961613178253174,
-0.008274131454527378,
0.04252026230096817,
0.05993009731173515,
-0.013658139854669571,
-0.022231101989746094,
0.004003540612757206,
-0.01606120355427265,
-0.03745608776807785,
0.011339197866618633,
0.03173303231596947,
-0.009260713122785091,
-0.01317747961729765,
-0.02675880864262581,
-0.0033123416360467672,
0.0005928107420913875,
0.014639057219028473,
-0.03184483200311661,
-0.0020837837364524603,
0.01954752765595913,
0.017003266140818596,
0.007387826219201088,
0.009071489796042442,
-0.045615408569574356,
0.021829361096024513,
0.020059870555996895,
0.04565497487783432,
0.03252599760890007,
-0.04874905198812485,
0.04076671972870827,
-0.02619134820997715,
-0.02022775635123253,
-0.029001658782362938,
0.05134367570281029,
0.014838730916380882,
0.00593134481459856,
0.01804320327937603,
0.007950221188366413,
0.08444985747337341,
0.019150929525494576,
-0.023675085976719856,
-0.006741927936673164,
0.06128060445189476,
-0.016780665144324303,
-0.035592690110206604,
-0.03575010225176811,
-0.0036946346517652273,
-0.00011090243060607463,
0.015391459688544273,
-0.04567646235227585,
0.024230044335126877,
0.031815316528081894,
0.020273223519325256,
0.025466786697506905,
-0.04149741679430008,
-0.04278373345732689,
-0.027133692055940628,
0.01874348521232605,
0.009363837540149689,
0.0003765603178180754,
0.003325816011056304,
0.03238588944077492,
0.015997176989912987,
0.03068135306239128,
-0.007409181445837021,
0.014018867164850235,
-0.07240725308656693,
0.006457815412431955,
-0.05016099289059639,
0.00445339223369956,
-0.015856649726629257,
-0.02013951726257801,
-0.047676555812358856,
-0.017852280288934708,
-0.005581721197813749,
-0.003703662659972906,
-0.006322161294519901,
-0.025410925969481468,
-0.006093934178352356,
-0.01519163977354765,
-0.0430915541946888,
-0.016277462244033813,
0.035530027002096176,
0.04132085666060448,
-0.02026429958641529,
-0.0065788025967776775,
0.05072121322154999,
-0.02935517020523548,
-0.02689325250685215,
-0.012370597571134567,
0.0177005548030138,
-0.01045130379498005,
0.002083208877593279,
0.018715178593993187,
-0.0012224353849887848,
-0.03318353369832039,
0.01921187900006771,
0.022762389853596687,
0.0037559540942311287,
0.0022051509004086256,
-0.006098912097513676,
-0.04232947900891304,
-0.032760005444288254,
-0.0056496262550354,
0.017974181100726128,
0.018963202834129333,
-0.0033736140467226505,
0.023899296298623085,
0.021495310589671135,
-0.008928859606385231,
-0.01052643358707428,
0.03267187625169754,
0.03172599524259567,
0.014768553897738457,
0.009657534770667553,
-0.061514101922512054,
0.00813344307243824,
-0.018955474719405174,
-0.01243064645677805,
0.011325057595968246,
-0.04804643243551254,
-0.021917076781392097,
-0.030931731685996056,
0.03574274852871895,
-0.0019406919600442052,
0.01100911758840084,
0.018067432567477226,
-0.032307300716638565,
-0.012408495880663395,
-0.014945808798074722,
-0.015234903432428837,
0.0037327611353248358,
0.03836546465754509,
0.039297521114349365,
0.051069095730781555,
-0.0408988893032074,
-0.08229949325323105,
0.003036417532712221,
0.01559511013329029,
0.018994780257344246,
-0.025209268555045128,
0.0018393758218735456,
-0.10207034647464752,
-0.019335998222231865,
0.016474680975079536,
-0.01564868539571762,
0.034594591706991196,
-0.03099491260945797,
-0.004901386331766844,
0.0063837082125246525,
-0.02872489206492901,
-0.01540467794984579,
0.016333015635609627,
-0.012748808600008488,
0.004774521570652723,
-0.008731499314308167,
-0.0012894171522930264,
0.004037347622215748,
0.038873109966516495,
0.024538936093449593,
0.028711583465337753,
0.006224296987056732,
0.042722295969724655,
-0.02599060721695423,
-0.011459806002676487,
-0.007165742106735706,
-0.08020826429128647,
-0.024472204968333244,
0.027882052585482597,
-0.011865575797855854,
0.04565594717860222,
-0.015063188970088959,
-0.03642109036445618,
0.04098164290189743,
0.028605690225958824,
-0.005896099377423525,
-0.04695365950465202,
-0.05688471719622612,
0.013878758065402508,
0.02348814159631729,
-0.004280919674783945,
0.05475269630551338,
0.028567200526595116,
-0.022280773147940636,
0.007242706138640642,
0.020993368700146675,
0.05622924864292145,
-0.018150679767131805,
0.009151686914265156,
0.014878666959702969,
0.020816614851355553,
-0.031176205724477768,
0.05069556459784508,
0.002476359950378537,
-0.03780790790915489,
0.007911372929811478,
-0.04233062267303467,
-0.04693620279431343,
0.03936029225587845,
-0.0336676649749279,
0.006987725384533405,
-0.04044381529092789,
0.03594430908560753,
-0.031146397814154625,
-0.02828109823167324,
0.005064336583018303,
-0.003162662498652935,
0.030197642743587494,
0.0017382792429998517,
0.022844811901450157,
-0.01607164368033409,
-0.03983968123793602,
0.003559787990525365,
-0.015934890136122704,
-0.04027147963643074,
0.03582137078046799,
-0.000055711541790515184,
-0.010947512462735176,
0.03269554674625397,
-0.07602698355913162,
-0.0053963614627718925,
0.0236530564725399,
-0.0010211082408204675,
-0.015881462022662163,
-0.02972024865448475,
-0.0058433664962649345,
0.02960379235446453,
0.024893267080187798,
-0.07703350484371185,
-0.02776080183684826,
0.015569145791232586,
0.04214496165513992,
-0.0014948388561606407,
-0.04644428938627243,
-0.03190658241510391,
-0.03509156033396721,
-0.05419842526316643,
-0.0018394860671833158,
-0.007461726199835539,
-0.005906648002564907,
0.016916388645768166,
0.025506040081381798,
0.005573066882789135,
0.04858175292611122,
-0.005738208070397377,
-0.019441979005932808,
0.03630031645298004,
-0.0401957631111145,
-0.001558629679493606,
-0.0389978289604187,
0.059158436954021454,
-0.017198223620653152,
-0.06376692652702332,
-0.024969080463051796,
-0.0110519053414464,
-0.002558806212618947,
0.008573691360652447,
-0.06222986429929733,
0.08671681582927704,
-0.014249020256102085,
-0.035903289914131165,
-0.005012085661292076,
0.025112248957157135,
-0.0017858871724456549,
0.030625421553850174,
-0.0036671836860477924,
0.003446893533691764,
-0.04060496389865875,
-0.008489632979035378,
0.025131799280643463,
0.018704110756516457,
0.034157298505306244,
-0.0016813448164612055,
0.05224272236227989,
-0.025344084948301315,
-0.032447636127471924,
0.040475089102983475,
0.034783512353897095,
-0.002327796071767807,
0.010647551156580448,
-0.019542355090379715,
0.02395058609545231,
0.0168140958994627,
-0.003092127852141857,
-0.03417762368917465,
-0.007943771779537201,
0.018386155366897583,
0.05445757135748863,
-0.036550089716911316,
0.04146302118897438,
-0.01588364504277706,
0.05295652523636818,
-0.02829849161207676,
0.00036834581987932324,
0.014378919266164303,
-0.004588930867612362,
0.019644923508167267,
0.012155653908848763,
-0.021778250113129616,
0.034123606979846954,
-0.006372121162712574,
0.08906742185354233,
0.02069064788520336,
-0.012201804667711258,
0.029393795877695084,
0.007652104366570711,
0.01598738133907318,
-0.017747823148965836,
-0.03896855562925339,
0.01201140321791172,
-0.04917197301983833,
0.03405332565307617,
0.0044594272039830685,
-0.002097669057548046,
0.054812151938676834,
0.0123219583183527,
0.017897484824061394,
-0.03979294002056122,
0.004690177738666534,
-0.045493025332689285,
-0.0036825716961175203,
0.0023796118330210447,
0.02873329445719719,
0.012180357240140438,
-0.008692949078977108,
0.044169168919324875,
0.01154350396245718,
0.012796026654541492,
0.023488251492381096,
-0.06013752147555351,
-0.05854158103466034,
-0.03170841932296753,
-0.06151238828897476,
0.10762300342321396,
0.010875504463911057,
0.003972592763602734,
-0.02446231245994568,
-0.036718983203172684,
0.01880064606666565,
0.0474175401031971,
0.052973125129938126,
-0.013535174541175365,
0.03916150704026222,
-0.009973867796361446,
0.008588962256908417,
-0.027001401409506798,
0.01312460470944643,
0.13099972903728485,
0.050919059664011,
0.0005409945733845234,
-0.025836490094661713,
0.027698148041963577,
-0.038388028740882874,
0.012127607129514217,
-0.02591225691139698,
-0.010421047918498516,
-0.010527308098971844,
0.05081745982170105,
0.033916305750608444,
0.013680088333785534,
-0.023586729541420937,
-0.009957044385373592,
0.008631277829408646,
-0.05771121382713318,
-0.007878541015088558,
0.018344158306717873,
-0.013953441753983498,
0.0006274361512623727,
0.043129172176122665,
-0.037260375916957855,
0.01830182410776615,
-0.030166851356625557,
-0.036381177604198456,
0.00898265652358532,
-0.05901244655251503,
0.01325969398021698,
0.01835906319320202,
-0.04488864913582802,
-0.026279984042048454,
0.026746176183223724,
-0.0023786542005836964,
-0.02361597865819931,
0.035270076245069504,
0.02988697588443756,
-0.0041084676049649715,
0.01928454451262951,
0.014844299294054508,
0.01925067789852619,
0.00209632096812129,
0.01294062752276659,
0.016445834189653397,
-0.07403060793876648,
-0.015555884689092636,
-0.013084778562188148,
0.023384638130664825,
0.006617437582463026,
0.006823396310210228,
-0.004551639314740896,
0.007775877136737108,
0.0032424249220639467,
-0.05956584960222244,
0.024713922291994095,
-0.003121216781437397,
0.018674027174711227,
-0.004628886468708515,
-0.018546054139733315,
-0.009153933264315128,
0.0014972665812820196,
-0.002370729111135006,
0.014631434343755245,
0.04595251381397247,
0.00492929108440876,
-0.009923623874783516,
0.023343440145254135,
0.06667858362197876,
-0.004950953647494316,
-0.052691344171762466,
-0.06140496954321861,
-0.01470224093645811,
-0.043812450021505356,
-0.011808332987129688,
0.015346701256930828,
0.028923137113451958,
0.00002739779847615864,
0.015415649861097336,
-0.023265330120921135,
-0.04441126435995102,
-0.05382837727665901,
0.041353967040777206,
0.004781958647072315,
-0.011179345659911633,
-0.012014205567538738,
-0.008557681925594807,
0.04607171565294266,
0.06585092097520828,
0.004319685511291027,
0.004239135421812534,
0.0033057741820812225,
-0.009756697341799736,
0.016216790303587914,
-0.00465902965515852,
-0.04879869520664215,
0.041993398219347,
-0.02142089232802391,
-0.010939648374915123,
-0.011508548632264137,
0.009782633744180202,
0.011949654668569565,
0.025816598907113075,
-0.005294014234095812,
0.00011090733460150659,
-0.04539399966597557,
-0.009231382049620152,
-0.009190918877720833,
-0.0436750091612339,
-0.003165705129504204,
-0.0034053646959364414,
-0.014360318891704082,
-0.0030675914604216814,
-0.02670859545469284,
-0.005821633618324995,
0.021712373942136765,
0.018981190398335457,
0.03958382084965706,
-0.03196099400520325,
0.03505495935678482,
-0.028196562081575394,
0.054522376507520676,
-0.019011080265045166,
0.0118853859603405,
-0.030570512637495995,
0.004301512613892555,
-0.036101631820201874,
-0.030203428119421005,
-0.034219108521938324,
0.022122139111161232,
-0.06486517935991287,
-0.0011984293814748526,
0.03473250940442085,
0.009825093671679497,
0.0005542528815567493,
0.049889542162418365,
0.04754320904612541,
-0.009170341305434704,
0.05021974444389343,
-0.0058244275860488415,
-0.0294085294008255,
0.04304773733019829,
-0.022308271378278732,
-0.06457995623350143,
0.04294896870851517,
-0.05241560935974121,
0.055087294429540634,
0.03249722346663475,
-0.02380625531077385,
0.04402569308876991,
0.06099185347557068,
-0.0020636068657040596,
-0.006503701210021973,
0.0009957877919077873,
-0.02591240592300892,
0.04382956400513649,
0.007879752665758133,
0.041702501475811005,
-0.04418734461069107,
-0.005835495423525572,
0.051364097744226456,
0.02370912954211235,
0.020172247663140297,
-0.0011281354818493128,
-0.023423315957188606,
-0.020521322265267372,
-0.0362793505191803,
0.025919217616319656,
-0.0038996904622763395,
-0.001968018477782607,
0.04766060784459114,
-0.01003285776823759,
0.02424710802733898,
0.008763565681874752,
-0.016783621162176132,
-0.06302143633365631,
-0.0036507707554847,
0.02881646528840065,
0.010890447534620762,
0.04066910222172737,
-0.04161570593714714,
0.004263567738234997,
0.044025737792253494,
-0.07903772592544556,
0.03875487670302391,
0.004764198325574398,
0.00019779284775722772,
-0.039226632565259933,
0.023021509870886803,
-0.01177115086466074,
0.07045931369066238,
0.05044776573777199,
0.043244149535894394,
-0.004522529896348715,
0.01659281738102436,
-0.010205058380961418,
-0.03931534290313721,
-0.020255574956536293,
0.02568911202251911,
0.015497530810534954,
0.0592893585562706,
0.06839268654584885,
-0.04641212895512581,
-0.030162552371621132,
0.05213771015405655,
-0.022233551368117332,
0.045084431767463684,
-0.039682574570178986,
0.003792800009250641,
0.0086870351806283,
0.025600040331482887,
-0.011202008463442326,
-0.011783025227487087,
-0.011811021715402603,
0.02448812872171402,
0.03616776317358017,
0.026625368744134903,
-0.006733166519552469,
-0.01813507080078125,
0.0038156339433044195,
-0.042122937738895416,
-0.036763034760951996,
0.02423361875116825,
-0.0057677943259477615,
-0.009733585640788078,
0.007495664060115814,
0.0007606717408634722,
0.004085874650627375,
0.015980802476406097,
-0.003218947909772396,
-0.045110028237104416,
-0.011960402131080627,
0.0109560526907444,
-0.030790772289037704,
-0.02810014598071575,
0.035275351256132126,
0.01638621650636196,
-0.034111738204956055,
0.06038219481706619,
-0.024203745648264885,
-0.034437742084264755,
-0.03047827072441578,
-0.0002597641432657838,
0.003868373576551676,
0.009615980088710785,
-0.01301135029643774,
0.0128174452111125,
0.0005138980341143906,
0.033812712877988815,
0.02648836001753807,
0.027766769751906395,
0.012392827309668064,
-0.0569266602396965,
-0.03569610044360161,
-0.04444126412272453,
0.04091281816363335,
0.004768182523548603,
-0.01031944714486599,
-0.025506628677248955,
-0.06524212658405304,
-0.002703700214624405,
0.009974158369004726,
0.04494432732462883,
-0.010519938543438911,
0.005524953827261925,
0.03545583784580231,
-0.030346183106303215,
0.033356912434101105,
-0.08788285404443741,
-0.012629247270524502,
0.031137483194470406,
-0.0410926416516304,
-0.007710895035415888,
-0.025420324876904488,
-0.0299488864839077,
0.0008645905763842165,
-0.01218701247125864,
0.0010036897147074342,
0.01971091888844967,
-0.0204046368598938,
-0.019792810082435608,
0.03477735444903374,
0.04251960292458534,
-0.043628714978694916,
0.05602562427520752,
-0.012783529236912727,
-0.02561180666089058,
-0.014500983990728855,
-0.049178242683410645,
-0.02539527416229248,
0.0037867582868784666,
-0.04498642683029175,
0.009640894830226898,
-0.03469588980078697,
0.04313832148909569,
0.041034113615751266,
-0.05145253613591194,
-0.019735882058739662,
0.029380301013588905,
-0.012237245216965675,
0.010618318803608418,
0.0483342707157135,
-0.00956383440643549,
0.014004340395331383,
0.002999753225594759,
0.005116546526551247,
0.027995526790618896,
-0.016506271436810493,
-0.014869953505694866,
0.07529743760824203,
-0.021166617050766945,
-0.043036967515945435,
0.03278380632400513,
0.0020680890884250402,
0.03617355227470398,
0.030376384034752846,
0.01307786162942648,
0.06250020861625671,
-0.022698160260915756,
0.005322423297911882,
0.0316002257168293,
0.02412252314388752,
-0.054348524659872055,
0.02837739884853363,
-0.013504432514309883,
0.030787242576479912,
-0.005052951630204916,
0.009334546513855457,
0.010897469706833363,
-0.011317949742078781,
0.020438816398382187,
0.03744038566946983,
0.00011382874799892306,
0.010704402811825275,
0.033589694648981094,
0.0031013102270662785,
-0.005421718582510948,
-0.0030983001925051212,
0.0022234648931771517,
-0.026322104036808014,
0.007820365019142628,
-0.017002150416374207,
-0.0012560628820210695,
-0.0003769487957470119,
-0.002431883942335844,
-0.04399891942739487,
-0.026586392894387245,
0.001374507904984057,
0.025955425575375557,
-0.0069879647344350815,
0.027294835075736046,
0.0033872334752231836,
-0.022495707497000694,
0.03299857676029205,
-0.06201343610882759,
-0.018167952075600624,
-0.06088472530245781,
0.03403078764677048,
0.012896961532533169,
0.013815036043524742
] |
<p>Thermodynamic buoyancy. I have an air intake for combustion air entering into a basement furnace room. During cold weather, the air enters unchecked (no damper on pipe is allowed). I have this 5 foot vertical pipe, suspended downwards within a 2 foot high box, terminating 12" from the bottom. The cold air spills over the top of the box (combustion appliances are off at this point). How do I create a "cold air trap" like a p-trap (thermal equilibrium)? Would raising the height of the box help?</p> | 4,632 | [
-0.026072517037391663,
-0.024667246267199516,
-0.014669522643089294,
0.018285751342773438,
0.027192607522010803,
0.004105790518224239,
0.0016465520020574331,
-0.031405944377183914,
0.042291704565286636,
-0.012297609820961952,
0.0134740574285388,
0.06537769734859467,
0.01679426059126854,
0.0038183473516255617,
0.02694150060415268,
0.004800880793482065,
-0.004481175914406776,
-0.039337266236543655,
0.021193400025367737,
-0.03637759014964104,
-0.05151147022843361,
0.01652863621711731,
-0.008553260937333107,
0.007050646003335714,
-0.02186770737171173,
0.09105446189641953,
0.017106803134083748,
-0.039332468062639236,
0.03073868528008461,
0.012743568979203701,
-0.02611376903951168,
0.011340229772031307,
-0.007387950085103512,
0.015713341534137726,
0.05092344805598259,
-0.0020889644511044025,
-0.00882048811763525,
0.012561527080833912,
-0.04710523784160614,
0.03172482177615166,
-0.025432702153921127,
-0.015335452742874622,
-0.02275567129254341,
0.014814174734055996,
-0.02421736903488636,
-0.004957456141710281,
0.0198862012475729,
-0.0141077795997262,
0.07915586978197098,
-0.07692256569862366,
0.024403570219874382,
0.003907502628862858,
0.018039949238300323,
0.08422635495662689,
0.01410403661429882,
-0.007718122098594904,
0.061121270060539246,
0.03630585968494415,
-0.024699075147509575,
-0.021030990406870842,
-0.004316004458814859,
-0.015278809703886509,
-0.05508353188633919,
-0.008923765271902084,
-0.016484171152114868,
-0.009817921556532383,
-0.015019431710243225,
-0.0180631335824728,
-0.0168351661413908,
-0.023320043459534645,
0.025604702532291412,
-0.008317556232213974,
-0.0113374600186944,
-0.027286922559142113,
0.027074730023741722,
-0.033860817551612854,
0.011648387648165226,
0.01124773919582367,
0.02788844145834446,
0.005564737133681774,
-0.01122263539582491,
0.003771628485992551,
0.023906799033284187,
0.04289405047893524,
-0.03044593520462513,
-0.02542264387011528,
0.08679838478565216,
-0.030326340347528458,
0.03595592826604843,
0.031230103224515915,
-0.02896501123905182,
0.018432049080729485,
0.02406333014369011,
0.03306138142943382,
-0.021012505516409874,
-0.007977738976478577,
0.028523297980427742,
0.05892893299460411,
0.012504806742072105,
-0.040879733860492706,
0.01353661622852087,
-0.014285839162766933,
0.024842318147420883,
0.08339100331068039,
-0.0007037838222458959,
-0.03301643952727318,
-0.04400554671883583,
-0.004263515584170818,
0.03190436586737633,
0.003968232311308384,
-0.026750441640615463,
-0.026541879400610924,
-0.04160555079579353,
-0.061643633991479874,
0.01635201834142208,
-0.01404260192066431,
0.003278970718383789,
-0.008471427485346794,
0.03440892696380615,
0.005330034997314215,
0.05919036641716957,
-0.007327837869524956,
0.06513125449419022,
-0.012489224784076214,
-0.12172462791204453,
0.018413452431559563,
0.00729187810793519,
-0.02356494590640068,
-0.03201022744178772,
0.05609165504574776,
0.020702769979834557,
-0.020740479230880737,
0.0230337493121624,
-0.038392480462789536,
0.043158724904060364,
-0.0024130314122885466,
-0.09601464867591858,
-0.047299135476350784,
0.05371802672743797,
-0.009042591787874699,
-0.038533587008714676,
-0.06772655993700027,
-0.041452910751104355,
0.03107280284166336,
0.069390669465065,
-0.00035198451951146126,
-0.024484964087605476,
-0.018925892189145088,
0.013377225026488304,
0.004175962880253792,
-0.036044247448444366,
-0.02317037060856819,
0.003996162675321102,
-0.02966316044330597,
-0.022009043022990227,
-0.0374768041074276,
0.03569359704852104,
0.021735860034823418,
-0.014878913760185242,
-0.020367825403809547,
0.02038426138460636,
-0.016151517629623413,
-0.051959797739982605,
0.0024039954878389835,
-0.005692722741514444,
-0.02600419893860817,
0.05888085067272186,
0.007294411770999432,
-0.03957144916057587,
0.019522707909345627,
-0.0026325201615691185,
0.03264213353395462,
-0.008447081781923771,
0.0010671704076230526,
0.028195170685648918,
-0.006724900100380182,
0.023651598021388054,
-0.04026627540588379,
0.013216126710176468,
0.04176684096455574,
-0.03377657011151314,
-0.0025526368990540504,
-0.016484055668115616,
0.008630029857158661,
0.00906360149383545,
0.03710309416055679,
-0.01249940600246191,
-0.02561403252184391,
0.021619750186800957,
-0.05117538571357727,
-0.03662341088056564,
-0.08244650065898895,
0.007325385231524706,
-0.03612527251243591,
-0.0030338361393660307,
-0.011701484210789204,
0.004027960821986198,
0.040788669139146805,
-0.05153123661875725,
0.0026589673943817616,
0.006915913429111242,
0.007714437786489725,
0.04200178012251854,
-0.0039445143193006516,
-0.0020360935013741255,
0.015184471383690834,
0.08647420257329941,
-0.011264464817941189,
0.06184948980808258,
-0.04498176649212837,
-0.006442353595048189,
-0.05964731425046921,
0.0016558915376663208,
-0.028099728748202324,
-0.02538548968732357,
-0.026851868256926537,
0.04082809016108513,
-0.014883553609251976,
0.04084054008126259,
0.016182539984583855,
-0.02312346361577511,
0.0815185010433197,
0.04781598597764969,
0.03284104913473129,
-0.005520839709788561,
0.025837557390332222,
0.027979975566267967,
0.01569773256778717,
-0.00256220530718565,
-0.015158815309405327,
-0.02980796992778778,
-0.01881415955722332,
0.03582264110445976,
0.049811314791440964,
-0.04713710770010948,
0.028018178418278694,
0.034246671944856644,
0.023214828222990036,
0.011005746200680733,
0.027633558958768845,
0.012801042757928371,
-0.009648682549595833,
0.018840862438082695,
0.06141044944524765,
0.04217562451958656,
0.028489748015999794,
0.033010710030794144,
0.002958659315481782,
0.01664433442056179,
-0.005387273151427507,
-0.023843806236982346,
-0.011721409857273102,
0.02309725619852543,
0.005869052838534117,
-0.055232200771570206,
-0.0160028338432312,
0.025388555601239204,
-0.017205648124217987,
0.0036527812480926514,
-0.003086693584918976,
-0.001222458085976541,
0.042525384575128555,
-0.004306648392230272,
-0.010814151726663113,
0.0011780565837398171,
0.03816073760390282,
0.002207494108006358,
0.00235460652038455,
0.036289021372795105,
-0.018140550702810287,
0.005375193431973457,
-0.026918113231658936,
0.042573705315589905,
-0.02178139053285122,
0.03396604210138321,
0.038153909146785736,
-0.017422690987586975,
0.041608408093452454,
-0.027697153389453888,
-0.05773534998297691,
-0.06359037011861801,
-0.01823044754564762,
0.00010606017895042896,
0.02005324885249138,
-0.03626355528831482,
0.002348382258787751,
-0.02533324994146824,
-0.02208416350185871,
0.07706071436405182,
-0.027939900755882263,
0.003468066919595003,
0.05941331759095192,
0.004083759151399136,
-0.03917255625128746,
-0.008317960426211357,
-0.031063228845596313,
0.011636399663984776,
-0.015837064012885094,
0.027209976688027382,
0.052436165511608124,
-0.03532005846500397,
-0.0034476560540497303,
0.04681571573019028,
-0.08958762139081955,
-0.036539677530527115,
-0.01763155311346054,
-0.0038338988088071346,
0.022919468581676483,
-0.004591554868966341,
0.010175595991313457,
0.01712590456008911,
-0.031430330127477646,
-0.004331094212830067,
-0.039806172251701355,
-0.021844392642378807,
-0.002607733476907015,
0.002692470094189048,
0.03630148991942406,
0.0024252403527498245,
0.008959511294960976,
0.09234575182199478,
-0.023758916184306145,
-0.061811745166778564,
-0.03551805764436722,
-0.057410966604948044,
-0.005314019974321127,
-0.023655148223042488,
-0.01698320545256138,
0.061569493263959885,
0.0076360879465937614,
0.021849896758794785,
0.009497142396867275,
-0.007928550243377686,
0.037767332047224045,
0.038820941001176834,
-0.04930241033434868,
0.038958340883255005,
0.004895293153822422,
-0.0052787428721785545,
0.07390143722295761,
-0.013335154391825199,
-0.01954200118780136,
0.005492756143212318,
-0.0157584547996521,
0.03677460178732872,
0.04717310145497322,
-0.044101499021053314,
0.05018576234579086,
-0.005783349275588989,
-0.0018293476896360517,
-0.06873946636915207,
0.025916583836078644,
-0.06667816638946533,
-0.012438103556632996,
-0.04126083478331566,
0.005134601145982742,
0.028299378231167793,
-0.0020707619842141867,
-0.023379886522889137,
0.04177644103765488,
0.08126766234636307,
-0.03235233575105667,
-0.024980910122394562,
0.020118296146392822,
-0.005633351393043995,
0.009058687835931778,
0.03138634189963341,
-0.01581156998872757,
0.05566680431365967,
0.036367904394865036,
0.03901040554046631,
0.044936079531908035,
-0.015018120408058167,
0.03441120684146881,
-0.050680652260780334,
-0.0072762807831168175,
0.004205693956464529,
0.07217197865247726,
-0.02195141278207302,
0.007201990112662315,
-0.005943049676716328,
0.019734296947717667,
0.04955209791660309,
0.012630424462258816,
-0.0613141804933548,
0.005546733736991882,
-0.02807263284921646,
-0.0010823175543919206,
-0.0034130921121686697,
0.004794389940798283,
-0.000506233423948288,
-0.0263547133654356,
0.014715502969920635,
-0.0015659119235351682,
0.0512814074754715,
-0.016165999695658684,
-0.0414971299469471,
0.0093474006280303,
0.002140255179256201,
-0.030916010960936546,
0.03338748216629028,
0.0364096574485302,
-0.04002915695309639,
0.027512414380908012,
0.0038441165816038847,
-0.03129247948527336,
-0.020086130127310753,
0.0030799454543739557,
0.008639735169708729,
0.000047955556510714814,
-0.020672494545578957,
-0.006152718793600798,
0.01671948842704296,
-0.011504648253321648,
-0.008254783228039742,
-0.010096307843923569,
0.02263859286904335,
-0.024534985423088074,
0.028801018372178078,
0.006868705153465271,
-0.0006559524335898459,
-0.03688272088766098,
0.01806681416928768,
0.004995136056095362,
-0.031242869794368744,
0.058729443699121475,
-0.013552766293287277,
-0.03104330785572529,
-0.04344039782881737,
0.054136358201503754,
0.05161476880311966,
0.01162614393979311,
-0.0016445929650217295,
-0.0106647415086627,
0.00043013624963350594,
-0.02381991781294346,
-0.0046260361559689045,
0.013170210644602776,
0.054664548486471176,
-0.04439185932278633,
-0.025952573865652084,
-0.0008883870323188603,
0.03938497602939606,
-0.00017479780944995582,
0.03217542544007301,
0.047413215041160583,
0.019495435059070587,
0.0036140582524240017,
0.011262225918471813,
0.019033506512641907,
-0.0101374052464962,
0.01048334315419197,
-0.00884835235774517,
-0.016562681645154953,
-0.07779252529144287,
-0.041567616164684296,
0.03854941949248314,
0.052371639758348465,
-0.03753902390599251,
0.02244899608194828,
-0.08626598864793777,
-0.015489679761230946,
0.07291010022163391,
-0.016781525686383247,
0.04096327722072601,
-0.05485440045595169,
0.016341589391231537,
0.022201593965291977,
-0.015669429674744606,
-0.018201211467385292,
-0.002460291376337409,
-0.005234589800238609,
0.018454458564519882,
0.007006397470831871,
-0.0503501370549202,
0.03597363084554672,
0.009340803138911724,
0.029378250241279602,
0.02570318803191185,
-0.013150093145668507,
-0.01635047048330307,
-0.02564268559217453,
0.015849439427256584,
-0.035994309931993484,
-0.07772095501422882,
-0.043380483984947205,
0.00758173456415534,
-0.01021872740238905,
0.015571005642414093,
-0.03933943808078766,
-0.017651880159974098,
0.010530146770179272,
-0.004846951458603144,
-0.02797010913491249,
-0.0013053345028311014,
-0.017268424853682518,
0.039444830268621445,
0.041024111211299896,
0.046132221817970276,
0.0564810149371624,
0.04469247907400131,
-0.014052195474505424,
0.015136893838644028,
-0.003012698609381914,
0.05878954008221626,
-0.01072628702968359,
-0.010785342194139957,
-0.03699211776256561,
0.01213515643030405,
-0.026746312156319618,
0.0719333067536354,
0.032369811087846756,
-0.0027124944608658552,
0.03368654102087021,
-0.014922999776899815,
0.05111043155193329,
0.05113586410880089,
0.03292981907725334,
-0.023388510569930077,
0.03939666599035263,
0.01608843170106411,
-0.007170580327510834,
-0.03806246072053909,
0.00009048373613040894,
0.029491210356354713,
0.010433875024318695,
0.019025186076760292,
-0.03480053320527077,
0.018680619075894356,
-0.02721503935754299,
-0.025119584053754807,
-0.03488009423017502,
-0.053142234683036804,
0.08648107200860977,
-0.017154663801193237,
0.0056190211325883865,
0.045709121972322464,
-0.05776648968458176,
-0.014016605913639069,
0.029865076765418053,
0.02768479287624359,
0.03824423998594284,
-0.04463410750031471,
0.06887088716030121,
-0.010523788630962372,
0.001591780805028975,
-0.039081308990716934,
-0.026270709931850433,
0.04335683211684227,
0.03999302163720131,
-0.019804244861006737,
-0.07695647329092026,
-0.030607786029577255,
-0.019624924287199974,
-0.033196303993463516,
0.017290014773607254,
0.023328004404902458,
-0.013311062008142471,
-0.006703909486532211,
0.027343442663550377,
0.018598021939396858,
0.02557571418583393,
0.028939178213477135,
-0.0057912529446184635,
-0.027262702584266663,
-0.024881640449166298,
-0.02791423350572586,
-0.0040594469755887985,
0.02895721048116684,
-0.04349295794963837,
-0.034585583955049515,
0.01174415834248066,
0.005633444059640169,
0.03105314075946808,
-0.010010560043156147,
0.005333480425179005,
0.0037364934105426073,
0.03225617855787277,
-0.02140229009091854,
-0.020387010648846626,
0.05752049386501312,
0.0011750912526622415,
0.029176635667681694,
-0.002488052938133478,
0.001623688847757876,
-0.03908105939626694,
-0.0538908988237381,
-0.002424968173727393,
-0.027915693819522858,
-0.010973631404340267,
0.002494590822607279,
0.04672970622777939,
-0.013838658109307289,
0.00814787670969963,
0.00018245127284899354,
0.02405034564435482,
0.02401154488325119,
0.014053255319595337,
-0.018701203167438507,
0.006126580759882927,
-0.015784231945872307,
-0.014171983115375042,
-0.05259083956480026,
0.0012007418554276228,
0.0023491489700973034,
0.018452676013112068,
-0.02524682506918907,
0.08571738004684448,
0.026583438739180565,
-0.009942715987563133,
0.016658956184983253,
0.013562637381255627,
0.00960572436451912,
0.03667278215289116,
0.00339758419431746,
0.049627259373664856,
-0.0023220134899020195,
-0.039740175008773804,
0.04512988403439522,
0.036789607256650925,
-0.0030444879084825516,
0.008799462579190731,
0.029336649924516678,
0.03424656018614769,
0.024582389742136,
-0.027006685733795166,
-0.023104647174477577,
0.04652352258563042,
-0.007239962927997112,
0.03300229087471962,
-0.01427419763058424,
0.010270503349602222,
0.013200059533119202,
0.023127542808651924,
-0.012487468309700489,
-0.07596372812986374,
-0.027406975626945496,
-0.010722064413130283,
-0.0029598763212561607,
0.024861911311745644,
-0.02257092297077179,
-0.01226959377527237,
0.020420895889401436,
0.02502773143351078,
-0.023187655955553055,
0.0013914244482293725,
0.004395490977913141,
-0.0371343232691288,
0.010632004588842392,
-0.028004461899399757,
-0.019379649311304092,
0.012818633578717709,
0.0058295694179832935,
-0.008264342322945595,
-0.014607513323426247,
-0.0019313471857458353,
-0.015190212987363338,
-0.00025640276726335287,
0.006784344557672739,
-0.005590640939772129,
0.04730570316314697,
-0.010800033807754517,
0.00031669659074395895,
-0.013383332639932632,
-0.005418442655354738,
0.12573212385177612,
0.0470883846282959,
0.023945778608322144,
-0.05112713202834129,
-0.016190625727176666,
-0.01394675299525261,
-0.0036622739862650633,
-0.050459250807762146,
0.005932888016104698,
0.0026553014758974314,
-0.004308765288442373,
0.02697470411658287,
0.04615235701203346,
-0.02302074059844017,
-0.005858393851667643,
0.06534833461046219,
-0.07274943590164185,
-0.0038286473136395216,
0.016312578693032265,
-0.015198311768472195,
-0.020705385133624077,
0.017057307064533234,
-0.0480383038520813,
0.03019133023917675,
-0.021613437682390213,
-0.020589224994182587,
-0.020218487828969955,
-0.06055101752281189,
0.05612652003765106,
0.011516604572534561,
-0.04419896751642227,
0.026039227843284607,
0.011440714821219444,
-0.03296457231044769,
-0.001023333054035902,
-0.012714720331132412,
0.011976425535976887,
-0.022052530199289322,
0.018453866243362427,
0.014098124578595161,
0.038885489106178284,
0.01227288693189621,
-0.0042279870249331,
0.0522671639919281,
-0.007891547866165638,
-0.007678352762013674,
0.0029552262276411057,
0.03505300357937813,
0.0025059343315660954,
-0.025717992335557938,
-0.016473494470119476,
0.031684476882219315,
-0.0064176274463534355,
0.0007398578454740345,
-0.04812037572264671,
-0.02191704511642456,
0.04618046060204506,
-0.02979365736246109,
-0.027012303471565247,
-0.022748786956071854,
0.029070531949400902,
-0.005729610100388527,
-0.013527440838515759,
-0.007303418125957251,
-0.007027925457805395,
0.006127822212874889,
-0.016351735219359398,
0.055454276502132416,
0.01685177907347679,
0.0011662726756185293,
-0.029528623446822166,
-0.01931370049715042,
-0.024742262437939644,
-0.010352042503654957,
-0.02836279571056366,
0.03222839906811714,
-0.01635846495628357,
0.006127229891717434,
0.002350226743146777,
0.004006394185125828,
-0.04337327182292938,
0.028051279485225677,
-0.017556529492139816,
-0.013032577000558376,
-0.0640721470117569,
-0.010115979239344597,
-0.006424759514629841,
0.0757460743188858,
-0.007664069067686796,
-0.023164814338088036,
0.01422890555113554,
0.02620523050427437,
0.007996171712875366,
-0.019828645512461662,
-0.025218099355697632,
0.010387863032519817,
-0.02612997591495514,
0.02372848242521286,
0.05128587782382965,
0.04459020122885704,
0.028769314289093018,
-0.014387129805982113,
0.011071914806962013,
0.0067988005466759205,
-0.04703596234321594,
0.018740950152277946,
-0.0043749199248850346,
-0.0164506658911705,
-0.009183613583445549,
-0.005683880299329758,
-0.01876853033900261,
-0.02492400072515011,
-0.051117897033691406,
-0.009944170713424683,
-0.014986417256295681,
-0.019963765516877174,
0.03364328667521477,
-0.022379135712981224,
0.018597399815917015,
-0.00556891318410635,
0.022473540157079697,
-0.03729226067662239,
0.004007498733699322,
-0.07353680580854416,
-0.014679180458188057,
0.01562543958425522,
-0.0014407122507691383,
-0.06162671744823456,
0.020551025867462158,
-0.0531611442565918,
-0.008436988107860088,
-0.010278573259711266,
0.03025718778371811,
0.004613048397004604,
-0.04802442714571953,
-0.0005203138571232557,
0.016483372077345848,
0.052195798605680466,
-0.03722887486219406,
-0.03548530116677284,
0.042493123561143875,
-0.02518368884921074,
-0.004346159752458334,
0.03858039155602455,
0.003632626263424754,
-0.021372267976403236,
0.03504430875182152,
-0.013511566445231438,
-0.021249819546937943,
0.07563191652297974,
-0.007848703302443027,
-0.016404395923018456,
-0.01291167363524437,
-0.014586997218430042,
-0.030671531334519386,
0.00793534331023693,
0.012039436027407646,
-0.03885404020547867,
-0.040938615798950195,
-0.004924170207232237,
0.01511968020349741,
0.015181228518486023,
-0.030656950548291206,
-0.0040171523578464985,
0.005747505463659763,
-0.032587215304374695,
0.0010118716163560748,
-0.009580546990036964,
0.028233209624886513,
0.02269144542515278,
-0.0539349727332592,
0.015460031107068062,
0.0006597607280127704,
0.01949569210410118,
-0.1091565191745758,
0.014366045594215393,
0.004954539705067873,
-0.038453713059425354,
0.03704512491822243,
-0.027359742671251297,
0.026553945615887642,
0.029407400637865067,
-0.0335356630384922,
-0.010522200725972652,
-0.03869827836751938,
-0.010660254396498203,
-0.03219272196292877,
0.006275664083659649,
0.002802913775667548,
0.044681668281555176,
0.009148428216576576,
0.001595077570527792,
-0.005874833092093468,
0.02620561607182026,
-0.01937042362987995,
-0.02064819447696209,
0.030915552750229836,
0.00856959167867899,
0.0014334481675177813,
-0.014118711464107037,
0.05724579095840454,
-0.03364812210202217,
-0.009959448128938675,
0.04148039594292641,
-0.018675176426768303,
-0.00632070517167449,
0.008555595763027668,
-0.018526121973991394,
-0.043591540306806564,
0.053730111569166183,
0.01661686599254608,
0.034911952912807465,
0.01730218343436718,
0.04868019372224808,
0.03368903324007988,
0.0034128031693398952,
0.003393659135326743,
0.008196428418159485,
-0.00006650322757195681,
-0.014392026700079441,
-0.013475279323756695,
0.05952110141515732,
-0.06091761589050293,
0.01705903932452202,
-0.0022912228014320135,
-0.017542457208037376,
0.018391745164990425,
-0.03837713226675987,
-0.02078022062778473,
-0.0144486790522933,
-0.013459203764796257,
0.04158836603164673,
-0.007643864490091801,
-0.018427859991788864,
-0.018882516771554947,
0.002216375432908535,
-0.01530455518513918,
0.03622555360198021,
0.026677576825022697,
-0.023701343685388565,
-0.02612513117492199,
-0.012805682606995106,
-0.003246383974328637,
-0.01624307967722416,
-0.004342022817581892,
-0.05374467000365257,
-0.003594504902139306,
0.04023023694753647,
0.03896135464310646,
0.007824966683983803,
0.0062468950636684895,
0.0007757910061627626,
-0.010702068917453289,
-0.03128129616379738,
0.041984476149082184,
-0.039424337446689606,
-0.007274425122886896,
-0.004949687514454126,
-0.033851854503154755,
0.015578177757561207,
0.02969038486480713,
0.03528110310435295,
-0.007452994119375944,
-0.02572174370288849,
0.0028186829295009375,
-0.041176870465278625,
0.0347680039703846,
-0.025723300874233246,
0.01978389173746109,
0.03680041432380676,
-0.03685629740357399,
-0.008136797696352005,
-0.024757659062743187,
0.006330124568194151,
-0.030282776802778244,
0.03192564845085144,
0.0032873349264264107,
0.018804023042321205,
-0.006851558107882738,
-0.01636018231511116,
-0.010528091341257095,
0.005820562597364187,
0.012333680875599384,
0.04439247027039528,
-0.012015421874821186,
0.007427832577377558,
0.016465146094560623,
-0.005395148880779743,
-0.003341639880090952,
0.06340513378381729,
-0.04576226323843002,
-0.005882408935576677,
-0.01995505951344967,
-0.03958512097597122,
-0.0068107228726148605,
-0.02276799827814102,
0.009910342283546925,
-0.02513767033815384,
-0.041263505816459656,
-0.00931387860327959,
0.029804876074194908,
0.057538602501153946,
0.024975072592496872,
-0.028995687142014503,
0.04669822007417679,
-0.003965064417570829,
0.008619874715805054,
0.0069122472777962685,
0.05206653103232384,
0.02868405543267727,
0.007729723583906889,
0.04066440835595131,
0.03574379161000252,
0.02443777024745941,
0.04311689734458923,
0.02120799757540226,
-0.006607525981962681,
-0.019399411976337433,
-0.019172390922904015,
0.028398660942912102,
0.004806157201528549,
-0.009631362743675709,
0.04215608537197113,
-0.03469594940543175,
0.02731100283563137,
-0.028359800577163696,
-0.0015945888590067625,
-0.03916361927986145,
0.005735954735428095,
0.02477618306875229,
0.01720121130347252,
0.011561152525246143,
0.0458352267742157,
-0.007014819420874119,
0.049356307834386826,
0.009189424104988575,
0.025202181190252304,
-0.03238648921251297,
0.01204643677920103,
0.023539738729596138,
-0.03422467038035393,
0.017729055136442184,
-0.023887133225798607,
-0.00919936690479517,
-0.03156932070851326,
-0.014696487225592136,
0.016355430707335472,
0.07660051435232162,
0.024632561951875687,
-0.008642991073429585,
-0.016297096386551857,
-0.015356969088315964,
0.04167325794696808,
-0.050723250955343246,
-0.014250200241804123,
-0.023096496239304543,
0.01709803380072117,
-0.00864377710968256,
0.009350568056106567
] |
<p>How is spacetime depicted in quantum field theory?
Is space and time completely separate, and time is just nature of law as in Newtonian mechanics?</p> | 4,633 | [
0.003002046374604106,
-0.04080260172486305,
0.011576687917113304,
-0.009225952439010143,
0.04606149345636368,
0.0021440833806991577,
-0.020395852625370026,
-0.03257042169570923,
-0.0035494770854711533,
-0.000539950851816684,
0.025566445663571358,
0.0068340543657541275,
0.023282472044229507,
-0.013713096268475056,
0.03233414888381958,
0.018715854734182358,
0.017000701278448105,
-0.009949822910130024,
-0.0010824825149029493,
-0.031648531556129456,
0.009388539008796215,
0.03745679184794426,
0.0051107872277498245,
0.03191782906651497,
-0.018132662400603294,
0.03397971764206886,
0.027082672342658043,
0.047447822988033295,
0.01744941435754299,
0.055388081818819046,
-0.0006654249737039208,
-0.052942629903554916,
0.017379973083734512,
0.013958306983113289,
0.01641838811337948,
-0.01824933849275112,
-0.028995200991630554,
-0.05462750419974327,
0.011051771230995655,
-0.03515828400850296,
-0.04552127793431282,
-0.037679921835660934,
-0.010489106178283691,
0.05825190246105194,
-0.045297328382730484,
0.040382932871580124,
-0.01851963996887207,
-0.0005819009384140372,
0.05625571683049202,
-0.03236440569162369,
0.045879095792770386,
0.00965637806802988,
0.011097974143922329,
0.00023940246319398284,
-0.009090163744986057,
0.019339237362146378,
0.07367291301488876,
0.04263383150100708,
0.0041635241359472275,
-0.05401596799492836,
-0.06342555582523346,
-0.009380698204040527,
0.01490253210067749,
-0.02377428114414215,
-0.010481259785592556,
0.015608648769557476,
-0.02110670506954193,
-0.019647348672151566,
-0.007434726692736149,
0.005498484242707491,
-0.02888517826795578,
0.026910770684480667,
0.07028370350599289,
-0.0010039028711616993,
0.0048727854155004025,
-0.0190964974462986,
0.023724256083369255,
-0.0018488269997760653,
0.03541882336139679,
0.006766910199075937,
-0.012531891465187073,
-0.010919853113591671,
0.015136715956032276,
-0.018355371430516243,
-0.017495926469564438,
-0.0032427154947072268,
0.06346335262060165,
-0.0010818646987900138,
-0.01792125403881073,
0.04144176468253136,
-0.04830412566661835,
0.032841410487890244,
0.024355590343475342,
-0.005575490649789572,
-0.03334806486964226,
0.04511011764407158,
0.013716265559196472,
0.019644998013973236,
0.019397234544157982,
-0.00280359061434865,
-0.007582241669297218,
-0.007931947708129883,
0.026588214561343193,
0.04665469005703926,
0.004486109595745802,
0.003532647853717208,
-0.028865665197372437,
0.023021278902888298,
-0.021032702177762985,
-0.001910764491185546,
-0.055247243493795395,
0.014873006381094456,
-0.007425488438457251,
-0.0047334348782896996,
0.024395305663347244,
-0.02342873066663742,
0.009310763329267502,
-0.01234818622469902,
0.05252485349774361,
0.09279997646808624,
0.046937402337789536,
-0.058543264865875244,
0.026405517011880875,
-0.008403738029301167,
-0.05411066114902496,
0.0016125078545883298,
0.0328671969473362,
-0.01237375196069479,
-0.04634285345673561,
0.009499277919530869,
-0.016163231804966927,
-0.004043547436594963,
-0.003440198954194784,
0.011705119162797928,
0.05184813216328621,
-0.01584795117378235,
-0.0969221442937851,
-0.052224479615688324,
0.031081125140190125,
-0.0037305790465325117,
-0.026356404647231102,
-0.04955475777387619,
0.04479479417204857,
0.0002583462919574231,
0.06790459156036377,
0.02155294641852379,
-0.022815383970737457,
0.0184594988822937,
0.027945630252361298,
-0.003675637999549508,
-0.024142185226082802,
0.01966889016330242,
0.01809118688106537,
-0.02203059196472168,
0.017354639247059822,
-0.05181161314249039,
-0.008668516762554646,
0.05564320832490921,
-0.0032709466759115458,
-0.04772041365504265,
0.08247053623199463,
-0.018108220770955086,
0.008606603369116783,
0.02309194579720497,
-0.00997340027242899,
-0.021578464657068253,
0.05836963653564453,
0.002301401924341917,
0.017994076013565063,
0.06504973769187927,
0.02735031396150589,
0.01494421437382698,
0.029361708089709282,
0.03239332139492035,
0.0093880919739604,
-0.021668625995516777,
-0.01359738502651453,
0.04727644473314285,
-0.013469044119119644,
-0.022726422175765038,
-0.058129288256168365,
-0.009350869804620743,
-0.0068401750177145,
0.007374234963208437,
-0.028738543391227722,
0.03998279944062233,
-0.021984869614243507,
0.016841329634189606,
-0.021040188148617744,
-0.0212849248200655,
-0.005062700714915991,
-0.06418583542108536,
0.02414926141500473,
0.0018424921436235309,
-0.01372996624559164,
0.021853361278772354,
0.03893307223916054,
0.034858930855989456,
-0.0919303297996521,
-0.058924123644828796,
-0.03759251534938812,
0.06386572122573853,
-0.03462118282914162,
0.0008642819011583924,
0.02521037496626377,
0.07223207503557205,
0.03375929594039917,
0.01319759339094162,
0.008176148869097233,
-0.0008462257101200521,
-0.0451551117002964,
0.02384915202856064,
-0.012210143730044365,
0.0185451228171587,
-0.010110979899764061,
0.02910873293876648,
-0.007826480083167553,
-0.01296463143080473,
-0.009892421774566174,
0.04048016294836998,
0.0024939021095633507,
0.044121310114860535,
0.013891183771193027,
-0.004621236585080624,
-0.018391743302345276,
0.027109423652291298,
-0.013087844476103783,
-0.0038277998100966215,
0.007712147198617458,
-0.03446894884109497,
-0.01675804890692234,
-0.016346050426363945,
0.04557117819786072,
0.038308076560497284,
-0.000002498655476301792,
-0.003664531046524644,
0.005883478093892336,
0.03977947682142258,
0.025505347177386284,
0.034352630376815796,
-0.03025313839316368,
-0.02538837306201458,
0.0308308694511652,
-0.02698296494781971,
0.044053949415683746,
-0.03413017839193344,
0.01685733161866665,
0.0046628923155367374,
0.017667556181550026,
-0.002437472576275468,
-0.020268796011805534,
0.051868535578250885,
-0.04523998871445656,
0.027799852192401886,
0.03606381639838219,
-0.053861331194639206,
0.007897446863353252,
-0.0035843742080032825,
0.006136588752269745,
0.018944717943668365,
-0.03339548036456108,
-0.01006470900028944,
-0.03838961571455002,
-0.013716530986130238,
0.003315935144200921,
0.009699897840619087,
-0.03148455172777176,
-0.0025966144166886806,
0.028766319155693054,
-0.03788003325462341,
-0.003993269056081772,
-0.023634161800146103,
-0.013779478147625923,
0.007805035449564457,
0.012232165783643723,
0.06140527501702309,
-0.014798503369092941,
0.04222070425748825,
-0.016362112015485764,
-0.03732992708683014,
0.008353863842785358,
-0.018416060134768486,
0.014126602560281754,
0.021458255127072334,
-0.0375911220908165,
0.05790821090340614,
-0.038897790014743805,
-0.061319250613451004,
0.03729269281029701,
-0.02587328664958477,
0.03494048863649368,
0.01619887724518776,
-0.03876221925020218,
-0.016459915786981583,
-0.008805516175925732,
-0.04494402930140495,
0.011139586567878723,
0.012458491139113903,
-0.0007482331711798906,
0.03185487538576126,
-0.021905770525336266,
-0.029238224029541016,
-0.008831518702208996,
-0.01755029521882534,
-0.0491795539855957,
-0.02655147574841976,
0.022752542048692703,
0.0366012342274189,
-0.032210420817136765,
0.009540707804262638,
0.0595330148935318,
-0.07818490266799927,
-0.027824312448501587,
-0.024868618696928024,
-0.033662524074316025,
0.038983386009931564,
0.014721997082233429,
0.02723218873143196,
-0.034551676362752914,
-0.022035283967852592,
0.05592673644423485,
0.035051461309194565,
-0.01093320269137621,
-0.016421906650066376,
-0.012646207585930824,
-0.01963752880692482,
-0.012734867632389069,
0.009110065177083015,
0.013940908014774323,
0.0031652390025556087,
0.024258453398942947,
0.023498181253671646,
0.02942560240626335,
0.001167010748758912,
0.020953325554728508,
-0.01522659882903099,
-0.013709415681660175,
0.001965683652088046,
0.01504085399210453,
0.03614059463143349,
0.0018897923873737454,
-0.03551814705133438,
-0.006269198842346668,
0.008613752201199532,
0.036534082144498825,
0.019207864999771118,
-0.028114620596170425,
0.06867695599794388,
0.009989029727876186,
0.022109298035502434,
-0.021824587136507034,
0.029321273788809776,
-0.02176382765173912,
-0.00939108058810234,
0.007958087138831615,
-0.0015988425584509969,
0.023073110729455948,
0.018025502562522888,
0.018467051908373833,
0.008681723847985268,
0.06158868223428726,
-0.06291235983371735,
-0.03605339676141739,
-0.011530289426445961,
0.018160482868552208,
0.05187428370118141,
-0.036412209272384644,
-0.03191027790307999,
0.039432961493730545,
0.032314594835042953,
0.028116239234805107,
0.020158009603619576,
-0.014735657721757889,
-0.023775393143296242,
-0.07221639156341553,
-0.010694822296500206,
0.03551626205444336,
0.01570206880569458,
0.029904812574386597,
0.05540015175938606,
0.010004140436649323,
0.0063751391135156155,
0.0011133354855701327,
0.006195103749632835,
-0.055910393595695496,
0.01628817617893219,
-0.06397238373756409,
-0.00541754299774766,
-0.02456924319267273,
0.0006520047900266945,
-0.015005857683718204,
-0.013472547754645348,
0.0021186897065490484,
0.010445897467434406,
-0.02590419538319111,
-0.07510800659656525,
-0.016277840360999107,
-0.052211593836545944,
-0.01624896004796028,
-0.03687544912099838,
0.02724689617753029,
0.038916490972042084,
-0.024036945775151253,
0.019862910732626915,
0.07088727504014969,
-0.0046211653389036655,
-0.004617237951606512,
0.029520176351070404,
-0.002074542688205838,
0.032280053943395615,
0.019747218117117882,
0.056960344314575195,
-0.01804112270474434,
-0.03561575710773468,
0.014574894681572914,
0.024029217660427094,
0.06354086846113205,
-0.005824006628245115,
-0.02364400215446949,
-0.012048354372382164,
-0.04918054863810539,
0.013944471254944801,
-0.027211491018533707,
0.06779084354639053,
-0.001837783376686275,
0.007242260966449976,
0.034230902791023254,
0.005578616168349981,
-0.03032827563583851,
0.047660473734140396,
0.03785933554172516,
-0.004105585627257824,
-0.016352346166968346,
-0.02489989623427391,
-0.02057088539004326,
-0.03190048038959503,
-0.007417720276862383,
0.01245724968612194,
0.0012931115925312042,
-0.022705070674419403,
0.025847652927041054,
0.012923418544232845,
0.012994798831641674,
-0.04742278531193733,
0.0019479667535051703,
0.010644789785146713,
-0.010866080410778522,
-0.01789732836186886,
-0.0031264284625649452,
-0.00356777710840106,
0.046702273190021515,
0.05144885927438736,
0.002366210101172328,
-0.012285021133720875,
-0.09266854077577591,
-0.0029505440033972263,
0.038123540580272675,
0.008717339485883713,
0.04312928020954132,
-0.028813505545258522,
-0.05991910770535469,
-0.032395172864198685,
0.045169178396463394,
-0.013056907802820206,
0.012255581095814705,
-0.004635976627469063,
0.008958942256867886,
-0.016803408041596413,
-0.002086790045723319,
0.022417131811380386,
0.034730199724435806,
0.0013884850777685642,
-0.01660691760480404,
0.013718259520828724,
0.01793583482503891,
-0.00806620717048645,
0.03391604870557785,
0.012225637212395668,
0.01595480740070343,
0.05499028414487839,
0.02931421808898449,
-0.0014579694252461195,
0.023323070257902145,
-0.02947954274713993,
-0.07211092114448547,
0.0024749061558395624,
0.04974150285124779,
-0.032058507204055786,
0.026378188282251358,
-0.01440480723977089,
-0.02358263172209263,
0.00846257247030735,
-0.010144871659576893,
0.01106993667781353,
0.015495898202061653,
-0.06299880146980286,
0.03146674111485481,
-0.03348487615585327,
-0.004400752484798431,
0.03781978413462639,
0.03429203853011131,
-0.01811862178146839,
-0.0287220049649477,
-0.008727969601750374,
0.06662954390048981,
-0.009765289723873138,
0.02697928436100483,
-0.05120363086462021,
-0.015171109698712826,
-0.034161511808633804,
0.039260074496269226,
-0.05643931403756142,
-0.01014848705381155,
-0.011912131682038307,
-0.027790145948529243,
-0.035564400255680084,
0.017164282500743866,
0.024137815460562706,
-0.02023966982960701,
-0.024514375254511833,
0.00040632992750033736,
-0.02220917120575905,
-0.024676857516169548,
-0.015420233830809593,
0.01675534062087536,
-0.020247643813490868,
0.010321746580302715,
0.016916874796152115,
0.03546196222305298,
-0.012381025590002537,
-0.028946544975042343,
0.006195530295372009,
-0.055625926703214645,
0.025734607130289078,
-0.018482718616724014,
-0.046974632889032364,
0.012832440435886383,
-0.0740482434630394,
-0.03731275349855423,
-0.018161743879318237,
-0.008939477615058422,
0.02611294388771057,
-0.05557660013437271,
0.024694155901670456,
0.03257746249437332,
0.010932200588285923,
-0.09075406193733215,
-0.06652028858661652,
0.01726127788424492,
0.004225686192512512,
-0.007133927661925554,
-0.025913968682289124,
0.0417012944817543,
-0.06505555659532547,
-0.029683390632271767,
-0.004373544827103615,
0.049805108457803726,
-0.013342969119548798,
-0.028951475396752357,
-0.02345743402838707,
0.01051227655261755,
0.015189534984529018,
0.009578532539308071,
-0.0023673088289797306,
-0.007769649848341942,
0.005178338848054409,
-0.013148616068065166,
-0.013292742893099785,
0.040463391691446304,
-0.005032672546803951,
-0.004340732004493475,
-0.06256499886512756,
0.020404471084475517,
0.000538805325049907,
-0.03794097900390625,
0.034643761813640594,
0.0459100566804409,
0.04355161637067795,
-0.003925385884940624,
-0.026479603722691536,
0.005003680009394884,
0.004836645908653736,
0.06735268980264664,
-0.027467679232358932,
0.003810507943853736,
0.0009368162136524916,
-0.05047430843114853,
0.021330635994672775,
-0.020104113966226578,
0.00841495767235756,
-0.00008533386426279321,
0.02975352853536606,
-0.012074882164597511,
0.009244312532246113,
0.011383865028619766,
-0.027873681858181953,
-0.01288976613432169,
-0.017017055302858353,
0.013565348461270332,
0.02572021074593067,
0.03411981090903282,
-0.01673503965139389,
-0.0018931498052552342,
-0.015317565761506557,
-0.01916326768696308,
0.0435575470328331,
-0.026642020791769028,
0.03141902759671211,
0.04291732981801033,
-0.021866613999009132,
-0.013332556933164597,
-0.026350224390625954,
0.0023347290698438883,
0.02433517575263977,
0.005743536166846752,
0.023607052862644196,
-0.015244872309267521,
0.009993689134716988,
0.054337505251169205,
0.04044048860669136,
-0.027623018249869347,
0.014433730393648148,
0.04686170443892479,
0.016393210738897324,
0.018340228125452995,
0.021418286487460136,
-0.06890329718589783,
0.02714904025197029,
-0.018628817051649094,
0.014615960419178009,
0.0034414478577673435,
-0.01867050863802433,
0.03229935094714165,
-0.006099788472056389,
-0.00009143369970843196,
0.0009491000091657043,
-0.021543283015489578,
-0.05047394335269928,
0.013676227070391178,
-0.006319195963442326,
0.04503414034843445,
0.008482720702886581,
0.02350381575524807,
0.0329304002225399,
-0.0027419296093285084,
0.007446329575031996,
0.03977051004767418,
-0.059448033571243286,
-0.03223131597042084,
-0.053833652287721634,
-0.0427122488617897,
0.05292904004454613,
-0.01859108917415142,
-0.026735864579677582,
-0.0039224037900567055,
-0.014801321551203728,
0.029033513739705086,
-0.02110229805111885,
0.04928838089108467,
-0.05102086067199707,
0.05781872197985649,
0.006452431436628103,
0.027795348316431046,
-0.0025768340565264225,
0.01567276567220688,
0.11393918842077255,
0.033825527876615524,
-0.002835031831637025,
-0.07206132262945175,
0.010103884153068066,
-0.03894345462322235,
0.011524391360580921,
-0.03200804814696312,
0.03550279885530472,
-0.009376179426908493,
0.013111783191561699,
0.01312845479696989,
0.048241183161735535,
0.03605985268950462,
-0.03412254899740219,
0.04958920553326607,
-0.04207489266991615,
-0.040983252227306366,
-0.004767764825373888,
0.03658290579915047,
-0.00033777731005102396,
0.04547635838389397,
-0.03927573189139366,
0.002585066482424736,
-0.02144206501543522,
0.03558778017759323,
-0.01906321570277214,
-0.03982256352901459,
0.022807065397500992,
0.001066124183125794,
-0.033005908131599426,
-0.006951179355382919,
0.0184054896235466,
-0.028896795585751534,
-0.06712877005338669,
-0.001438436796888709,
0.02746138721704483,
0.0022678407840430737,
0.013792628422379494,
0.03734169900417328,
0.010174594819545746,
0.014138755388557911,
-0.01973917707800865,
0.0036663333885371685,
-0.03511084243655205,
0.007912320084869862,
-0.014526637271046638,
0.05216527357697487,
-0.024086009711027145,
-0.00157880038022995,
0.0018064526375383139,
0.0062903156504035,
0.006289721466600895,
-0.0639711245894432,
-0.023394759744405746,
0.004555319901555777,
0.04459315538406372,
0.007262935861945152,
-0.006657661870121956,
-0.03696971386671066,
0.03779751807451248,
-0.01646079309284687,
0.01600024849176407,
0.006525664124637842,
0.005101282615214586,
0.07179369777441025,
0.01294683013111353,
-0.0018568410305306315,
-0.04800335690379143,
-0.0016066570533439517,
-0.023778686299920082,
-0.031727492809295654,
-0.03514440730214119,
-0.014478371478617191,
0.031787361949682236,
0.0537051223218441,
0.02419785037636757,
-0.019972188398241997,
0.0029975639190524817,
-0.0019259130349382758,
-0.05117581784725189,
0.03215821459889412,
-0.02648475207388401,
-0.026907067745923996,
-0.008553176186978817,
0.021593930199742317,
0.050682514905929565,
0.055858489125967026,
-0.046737104654312134,
0.012345056049525738,
-0.03133778274059296,
-0.02433878183364868,
0.03553175926208496,
-0.020130915567278862,
0.01867608353495598,
0.01164652407169342,
0.004921531304717064,
-0.026384275406599045,
-0.06456098705530167,
0.001335875946097076,
0.04480722174048424,
-0.00007486664253519848,
-0.00367002678103745,
0.03361155092716217,
-0.005498066078871489,
0.016157886013388634,
0.03935442864894867,
-0.03665655478835106,
0.0015758041990920901,
0.005221671424806118,
0.016783440485596657,
-0.05039813742041588,
-0.04195554554462433,
-0.02730559930205345,
0.015525316819548607,
-0.00019880136824212968,
0.02953745797276497,
-0.05093063786625862,
0.022307181730866432,
0.0019219869282096624,
0.019656283780932426,
-0.04721207544207573,
0.0019311495125293732,
-0.07879064232110977,
0.0333775170147419,
0.011968780308961868,
-0.06145525351166725,
0.001436687191016972,
0.04144369438290596,
-0.011113343760371208,
-0.013044032268226147,
0.0057251644320786,
0.033184245228767395,
-0.016506370157003403,
0.027442600578069687,
0.048148348927497864,
-0.0021066605113446712,
0.057648979127407074,
0.00611121067777276,
-0.008815556764602661,
0.005598301067948341,
-0.04241613671183586,
-0.07479105144739151,
0.04708832874894142,
-0.016351304948329926,
0.028503678739070892,
0.029391922056674957,
-0.0021814953070133924,
-0.026009630411863327,
0.02996966615319252,
-0.04519166797399521,
-0.009342498145997524,
0.02915961481630802,
-0.05384787172079086,
-0.013889017514884472,
-0.032735928893089294,
0.03263203054666519,
0.02033345215022564,
-0.02867688611149788,
0.020545145496726036,
0.010376941412687302,
0.007046562619507313,
-0.01749327778816223,
0.03635599464178085,
-0.015778400003910065,
0.03256315365433693,
0.048847947269678116,
-0.007668827194720507,
0.01645888201892376,
0.05786534771323204,
-0.028714407235383987,
0.016915051266551018,
0.025567930191755295,
0.018878787755966187,
-0.09048683941364288,
-0.02422277256846428,
0.016132399439811707,
0.010819563642144203,
0.03270823135972023,
-0.027438035234808922,
0.004289815668016672,
0.022123320028185844,
-0.08043701946735382,
0.04881152883172035,
-0.011492344550788403,
-0.03258693590760231,
0.009609791450202465,
-0.009927444159984589,
-0.019488506019115448,
0.09135998040437698,
0.04924704506993294,
0.044530294835567474,
-0.01070687361061573,
0.004876275081187487,
0.02057834528386593,
-0.01733563281595707,
-0.04365818202495575,
0.03482918068766594,
-0.019095834344625473,
-0.01237088069319725,
0.04976864904165268,
-0.008202049881219864,
-0.013088468462228775,
0.026157084852457047,
0.0024894257076084614,
-0.0020826165564358234,
-0.010800261981785297,
-0.009220498614013195,
0.017166614532470703,
0.001512329326942563,
0.017694948241114616,
-0.04390709474682808,
0.018249211832880974,
0.04513775184750557,
0.001798996003344655,
0.012171483598649502,
-0.01273705530911684,
0.01358830090612173,
-0.01180639024823904,
-0.060477033257484436,
-0.0391043983399868,
0.02986636571586132,
0.010902374051511288,
-0.023948490619659424,
-0.03453601896762848,
0.029663674533367157,
0.009767129085958004,
-0.022349542006850243,
0.00622112862765789,
-0.023746268823742867,
-0.0012231116415932775,
0.03955043479800224,
-0.015427525155246258,
-0.018923966214060783,
0.0047310274094343185,
-0.013898549601435661,
-0.025880202651023865,
-0.008246184326708317,
0.0122644929215312,
0.013575744815170765,
-0.05500685051083565,
-0.018013278022408485,
0.020440861582756042,
0.008974727243185043,
0.005800341255962849,
-0.05690887197852135,
-0.022327568382024765,
0.017330212518572807,
0.016993915662169456,
0.015396819449961185,
-0.01952330209314823,
-0.027228031307458878,
-0.02417844533920288,
-0.06406369060277939,
0.019342942163348198,
-0.002496285829693079,
0.0013600836973637342,
-0.0538790263235569,
-0.00934232585132122,
-0.01432880014181137,
0.013476571068167686,
0.03146866336464882,
-0.001238677534274757,
-0.028652993962168694,
-0.014629121869802475,
0.02139250375330448,
0.01723530702292919,
-0.00571174081414938,
-0.020909972488880157,
-0.012059018947184086,
-0.04754651337862015,
0.0008798792841844261,
-0.010942436754703522,
-0.016353610903024673,
0.01811201125383377,
0.014957897365093231,
-0.013895112089812756,
0.029314445331692696,
0.003868894884362817,
-0.057703930884599686,
0.05313246324658394,
0.01691032201051712,
-0.007020025048404932,
0.06480514258146286,
-0.020738700404763222,
0.029136478900909424,
0.06470534205436707,
-0.0024742402601987123,
-0.00949444342404604,
-0.004468834027647972,
-0.040562860667705536,
-0.013393099419772625,
-0.0009131153346970677,
-0.018424266949295998,
0.019120918586850166,
-0.07219696789979935,
-0.021381888538599014,
0.06929495185613632,
-0.024601202458143234,
0.032653652131557465,
0.06473249942064285,
0.007533185184001923,
0.02832263521850109,
0.004212174564599991,
-0.01308569684624672,
0.053822219371795654,
0.030264537781476974,
0.0010032461723312736,
0.03491516411304474,
0.061753660440444946,
0.0009381498675793409,
0.025232037529349327,
0.039142172783613205,
-0.035679034888744354,
0.0283551923930645,
0.01685216650366783,
0.05376603826880455,
-0.04090902954339981,
0.015340839512646198,
0.025199750438332558,
-0.003030757186934352,
0.02352791279554367,
0.017936307936906815,
-0.03247532993555069,
0.06440547108650208,
-0.033302389085292816,
0.002908500609919429,
-0.026086069643497467,
0.0028263619169592857,
-0.02344352938234806,
0.01102378685027361,
0.03037366084754467,
0.044849514961242676,
0.0031338974367827177,
-0.01710587553679943,
-0.025189334526658058,
0.010504870675504208,
0.010717814788222313,
-0.04914020001888275,
-0.004857649561017752,
0.008947828784584999,
-0.01612665504217148,
-0.010372155345976353,
-0.009919092059135437,
-0.03718524053692818,
-0.0227956622838974,
0.0343456044793129,
0.016404345631599426,
0.05174363777041435,
-0.05005515739321709,
0.019561925902962685,
-0.022896500304341316,
0.042595166712999344,
-0.08891702443361282,
0.012429717928171158,
-0.015524797141551971,
0.023778283968567848,
-0.018005944788455963,
0.009357837028801441
] |
<p>This is an ultra-soft question about relatively recent history. While reading some of Mandelstam's papers, I noticed that he cites David John Candlin consistenly whenever he does anything with Grassman path-integral. Everyone else cites Berezin.</p>
<p>So I read Candlin's 1956 paper, and I was stunned to find a complete and correct description of anticommuting variables, presented more lucidly than anywhere else, with a clear definition of Grassman integration, and a proof that it reproduces the Fermionic quantum field. This is clearly the original source of all the Grassman methods. I was stunned that the inventor of this method is quietly buried away.</p>
<p>I wrote the <a href="http://en.wikipedia.org/wiki/David_John_Candlin">Wikipedia page on the guy</a>, but I couldn't find out anything beyond the sketchy stuff I found on an old Princeton staff listing. The fellow doesn't google very well at all.</p>
<p>Here are the questions:</p>
<ul>
<li>Is he still alive? (Hello? Are you there?)</li>
<li>Did he become the experimental physicist David John Candlin in the late 1970s/early 1980s? Or is this someone else with the same name?</li>
<li>Did he get any credit for his discovery?</li>
</ul>
<p>I mean, this is one of the central tools of modern physics, it is used every day by every theorist, and the inventor is never mentioned. It's 50% of the path integral. Why the silence?</p> | 4,634 | [
-0.002852365607395768,
-0.019126687198877335,
0.011393173597753048,
-0.06517145037651062,
0.06701906025409698,
-0.035870667546987534,
-0.026498716324567795,
-0.041798267513513565,
0.0020218382123857737,
-0.03591009974479675,
0.04829449579119682,
-0.013276323676109314,
0.07671062648296356,
0.03310573473572731,
0.021995756775140762,
-0.008324306458234787,
0.008998162113130093,
-0.035633333027362823,
-0.017840834334492683,
-0.005602702964097261,
0.0054528131149709225,
0.03447737544775009,
0.003667621873319149,
-0.020322052761912346,
-0.003899606177583337,
0.0011383958626538515,
-0.0033569952938705683,
0.0024237469770014286,
-0.017770322039723396,
0.05706847459077835,
-0.032952770590782166,
-0.022098427638411522,
0.03460274264216423,
-0.020642930641770363,
0.016564376652240753,
0.012465492822229862,
-0.023344898596405983,
-0.062155064195394516,
0.00828666053712368,
0.016509974375367165,
-0.00593006145209074,
-0.00768326735123992,
-0.015613947063684464,
0.044914741069078445,
-0.035255495458841324,
0.034239038825035095,
0.0025322381407022476,
-0.012034947052598,
0.0829901173710823,
-0.0500280000269413,
0.04630330577492714,
0.002680199919268489,
-0.0043905386701226234,
0.006093498785048723,
-0.026415439322590828,
-0.020397664979100227,
0.041585925966501236,
0.0427326001226902,
-0.006096062250435352,
-0.042935412377119064,
-0.04989352077245712,
-0.015203160233795643,
0.007283809594810009,
0.00807213969528675,
-0.02318788692355156,
0.03603540360927582,
0.04246902838349342,
-0.021223222836852074,
0.041179437190294266,
-0.04215804859995842,
-0.030907144770026207,
-0.00685509666800499,
0.03410838916897774,
-0.009376985020935535,
0.006620131898671389,
0.0051102167926728725,
0.016420934349298477,
0.02630302868783474,
0.0106789106503129,
0.009984740987420082,
-0.02846726030111313,
0.046510715037584305,
0.02223452739417553,
-0.011298424564301968,
0.027578430250287056,
0.015317457728087902,
0.06682416796684265,
-0.023369012400507927,
-0.01789824478328228,
0.04958876967430115,
-0.01893552765250206,
0.020902354270219803,
0.05364470183849335,
0.00708531541749835,
-0.031200876459479332,
0.042761966586112976,
0.04076823964715004,
0.01956012472510338,
-0.023395178839564323,
0.002769641112536192,
-0.021103696897625923,
-0.03402675688266754,
-0.009909260086715221,
0.09906072914600372,
-0.022734660655260086,
-0.021643852815032005,
0.01188728865236044,
0.012515791691839695,
-0.006518630776554346,
-0.029727594926953316,
-0.07751357555389404,
0.02923165261745453,
0.00151151476893574,
0.01043869461864233,
0.0053404150530695915,
-0.00215742876753211,
-0.01677505113184452,
-0.014743438921868801,
0.06279639154672623,
0.0806509256362915,
0.0036396903451532125,
-0.01009924616664648,
0.020142219960689545,
-0.05575110763311386,
-0.053798627108335495,
-0.008166314102709293,
0.03630102053284645,
0.0022305219899863005,
-0.010854721069335938,
0.02096487767994404,
0.049648530781269073,
-0.002357118297368288,
0.0426650233566761,
0.008990658447146416,
0.01264857780188322,
-0.009052958339452744,
-0.10553553700447083,
-0.04568607732653618,
0.04277219623327255,
-0.01115366443991661,
-0.029030218720436096,
-0.07844679057598114,
0.010180391371250153,
0.021646467968821526,
0.09254816174507141,
0.008638694882392883,
0.0069530983455479145,
-0.041052013635635376,
0.010573774576187134,
0.011510110460221767,
-0.03344743698835373,
-0.049867432564496994,
0.02104206383228302,
-0.03366177901625633,
-0.04181533306837082,
-0.03444584086537361,
0.048839274793863297,
0.04027043655514717,
-0.018925869837403297,
-0.03060137666761875,
0.06343214958906174,
0.05454407259821892,
-0.03849240019917488,
-0.0002005147689487785,
0.00011327172978781164,
-0.02438681200146675,
0.07971540093421936,
0.05994090437889099,
-0.0013378914445638657,
0.0011703423224389553,
0.010883990675210953,
0.031671129167079926,
0.0027582021430134773,
0.017929797992110252,
0.04978328198194504,
-0.058868978172540665,
0.005342227406799793,
-0.0022288765758275986,
0.025379428640007973,
0.00990714319050312,
-0.012397578917443752,
-0.012820500880479813,
-0.0021572222467511892,
0.011695926077663898,
0.018972167745232582,
0.04412269964814186,
0.015214772894978523,
0.03644813224673271,
0.018668605014681816,
-0.06127544119954109,
-0.044744543731212616,
-0.02942994423210621,
-0.005406384821981192,
-0.0010206509614363313,
0.0009884374449029565,
0.008989050053060055,
0.009482554160058498,
-0.007820844650268555,
-0.00542863504961133,
-0.050973404198884964,
0.02259138785302639,
0.031315840780735016,
0.04807654768228531,
-0.017531268298625946,
-0.012992794625461102,
0.07667643576860428,
0.06389499455690384,
-0.021448280662298203,
0.03494633361697197,
-0.06945917755365372,
-0.005303895100951195,
0.014136172831058502,
-0.0010661196429282427,
0.02187546342611313,
0.006864660419523716,
0.020362788811326027,
0.00166849116794765,
-0.010371563956141472,
-0.012644530273973942,
0.0017372398870065808,
-0.021121615543961525,
0.021785806864500046,
0.014055434614419937,
-0.011182519607245922,
-0.03244880214333534,
0.07752605527639389,
0.011525899171829224,
-0.005208456888794899,
0.0599394366145134,
-0.01745665818452835,
-0.06676600873470306,
-0.012536799535155296,
0.004243167582899332,
0.022558769211173058,
-0.008931098505854607,
0.011766842566430569,
0.006563004106283188,
0.06124889478087425,
0.005361539777368307,
0.014583834446966648,
-0.0045013041235506535,
-0.034320566803216934,
0.03304692730307579,
0.00016207719454541802,
-0.013622399419546127,
0.03301011398434639,
0.029134806245565414,
-0.004132266156375408,
-0.015769686549901962,
-0.0015756753273308277,
-0.045875195413827896,
-0.024345120415091515,
-0.020844263955950737,
0.005296585615724325,
0.014323375187814236,
-0.006216465961188078,
0.00983583927154541,
-0.014682975597679615,
0.0019119115313515067,
0.018330218270421028,
-0.0028837055433541536,
0.02165672741830349,
-0.030370663851499557,
-0.04320182278752327,
0.022589413449168205,
-0.016728607937693596,
-0.05813649669289589,
-0.0050502922385931015,
0.03666331246495247,
-0.022406866773962975,
0.010085844434797764,
-0.04856494069099426,
0.04332197085022926,
-0.0523783303797245,
0.003136640414595604,
0.0059660617262125015,
0.01978946290910244,
0.05970229208469391,
-0.015958499163389206,
-0.007639651652425528,
0.014325104653835297,
-0.04104592278599739,
0.031103068962693214,
0.0846736878156662,
-0.035164739936590195,
0.003131689503788948,
-0.044245488941669464,
-0.02666492946445942,
0.055343661457300186,
-0.009412121027708054,
-0.027679016813635826,
0.03435197472572327,
-0.012734438292682171,
-0.04579661786556244,
0.017779052257537842,
-0.010547621175646782,
-0.01713583990931511,
-0.04296349361538887,
-0.01278834231197834,
0.002538295229896903,
0.010265223681926727,
-0.039154794067144394,
0.008360394276678562,
-0.021785955876111984,
-0.035450272262096405,
-0.017698273062705994,
-0.041500069200992584,
0.03288711979985237,
-0.015718555077910423,
-0.007281175348907709,
0.027747303247451782,
0.0023134073708206415,
0.012521229684352875,
-0.08875689655542374,
-0.06620544195175171,
0.0004642853164114058,
-0.019210154190659523,
-0.023135719820857048,
0.007531828712671995,
-0.005250915419310331,
0.0232502780854702,
0.03141240403056145,
-0.0993245542049408,
-0.035976432263851166,
0.0002630966482684016,
0.013509491458535194,
-0.021874964237213135,
0.015149226412177086,
0.006267290562391281,
0.025662090629339218,
0.058512426912784576,
0.013300122693181038,
0.006046685855835676,
0.0343744158744812,
0.008821655996143818,
-0.022396009415388107,
-0.0005678918096236885,
-0.015454774722456932,
0.01749603822827339,
0.03893328830599785,
0.016557004302740097,
-0.03251129388809204,
0.03167146071791649,
-0.026502126827836037,
0.012737668119370937,
0.0428619384765625,
-0.011188214644789696,
0.042388949543237686,
0.024513429030776024,
-0.0007866907981224358,
-0.02173604816198349,
0.007068299688398838,
-0.036280546337366104,
-0.04308018088340759,
0.006607745308429003,
-0.013398028910160065,
0.021567944437265396,
-0.011252716183662415,
0.0011988371843472123,
0.035076823085546494,
0.0525345504283905,
-0.04641660675406456,
-0.025029025971889496,
0.02424797974526882,
0.025385059416294098,
0.031711939722299576,
-0.04024102911353111,
-0.03832457959651947,
-0.0014777403557673097,
0.058706898242235184,
-0.0020524952560663223,
-0.017967689782381058,
-0.03318784758448601,
0.0076404414139688015,
-0.040987662971019745,
0.02868938073515892,
-0.026279274374246597,
0.04177791252732277,
-0.007446333300322294,
0.046193525195121765,
-0.0014668232761323452,
0.011399893090128899,
0.029953747987747192,
0.00468679703772068,
-0.10180114209651947,
0.03378841280937195,
-0.024008052423596382,
-0.02401970885694027,
-0.022290825843811035,
0.004478658549487591,
0.04005898907780647,
0.03811435028910637,
-0.034663863480091095,
-0.03936814144253731,
-0.007517467252910137,
-0.05374468117952347,
0.014571474865078926,
-0.05538373440504074,
-0.03801240772008896,
-0.029981277883052826,
0.03371964767575264,
0.04613027349114418,
-0.046253565698862076,
-0.0016040254849940538,
0.05681692436337471,
-0.011031245812773705,
-0.008919976651668549,
-0.06512467563152313,
-0.015316187404096127,
0.02879125438630581,
-0.01027098298072815,
0.03824668377637863,
0.014489398337900639,
-0.029804883524775505,
0.02542182058095932,
0.014683754183351994,
0.04308902844786644,
-0.0031760106794536114,
-0.036965686827898026,
-0.008262474089860916,
0.004286016803234816,
0.04721306264400482,
0.002103345235809684,
0.03241853415966034,
0.00831796508282423,
0.03518037497997284,
0.014483536593616009,
0.05088824778795242,
-0.012675158679485321,
0.05349692329764366,
0.041665662080049515,
-0.01772037334740162,
0.0012843189761042595,
-0.043205827474594116,
0.005542567931115627,
-0.021643973886966705,
0.006080423481762409,
-0.0070516266860067844,
0.03617190942168236,
-0.002078745514154434,
-0.030440809205174446,
0.049832165241241455,
-0.015292590484023094,
-0.02526790089905262,
0.03334438055753708,
-0.0010802238248288631,
-0.007533148396760225,
-0.03221001848578453,
0.01050165668129921,
0.0014606420882046223,
0.03133449703454971,
0.020024755969643593,
0.03408722206950188,
0.00818195752799511,
-0.05627402663230896,
-0.03528192266821861,
0.025898443534970284,
0.05294650048017502,
-0.029683303087949753,
0.02409830316901207,
-0.10232682526111603,
-0.0416310653090477,
0.0324067659676075,
0.011335283517837524,
-0.016449324786663055,
-0.030723217874765396,
-0.026035070419311523,
-0.03435462340712547,
-0.03322306275367737,
-0.025546057149767876,
0.011920645833015442,
0.02020348235964775,
0.04361412674188614,
-0.01637597754597664,
-0.022241339087486267,
-0.037092190235853195,
0.011015958152711391,
-0.019953066483139992,
0.031075211241841316,
-0.018556084483861923,
0.021403206512331963,
0.002771058352664113,
0.019606947898864746,
-0.015546310693025589,
-0.06302141398191452,
0.011407679878175259,
0.009869316592812538,
-0.026381991803646088,
0.018815740942955017,
-0.03880718722939491,
-0.0519135408103466,
0.005961056798696518,
-0.0020032599568367004,
-0.02488800697028637,
0.0025735292583703995,
-0.025357533246278763,
0.04540945217013359,
0.010691502131521702,
-0.01741441711783409,
0.012118524871766567,
0.046806756407022476,
-0.015149401500821114,
-0.00830122921615839,
0.017739111557602882,
0.035717204213142395,
-0.018364103510975838,
0.015505555085837841,
-0.029632147401571274,
-0.0070665376260876656,
-0.04544555023312569,
0.036503568291664124,
-0.026294808834791183,
0.011748671531677246,
-0.03243706002831459,
-0.015842098742723465,
-0.007564101368188858,
-0.0005134798120707273,
-0.011953379958868027,
-0.020081546157598495,
0.005703013855963945,
0.06482177972793579,
0.029101647436618805,
-0.008617570623755455,
-0.005682854913175106,
-0.00244624144397676,
0.01022664550691843,
0.04509976878762245,
0.01661881059408188,
0.009969509206712246,
-0.03985043987631798,
-0.013195245526731014,
-0.005260084755718708,
-0.021792739629745483,
0.02494003251194954,
-0.027484511956572533,
0.010931434109807014,
0.04266028851270676,
-0.042276833206415176,
-0.04013612121343613,
-0.019684923812747,
-0.021274374797940254,
-0.01938053034245968,
-0.06554806232452393,
0.01933416724205017,
0.024455001577734947,
0.012646729126572609,
-0.031682103872299194,
-0.00987346563488245,
0.023116454482078552,
0.037927720695734024,
-0.02978570945560932,
-0.01609664410352707,
0.021068423986434937,
0.0005226964713074267,
0.01539783738553524,
-0.013546760194003582,
0.03162335604429245,
-0.02365667186677456,
-0.013156385160982609,
-0.0005210254457779229,
0.014136438257992268,
0.012626825831830502,
-0.008084788918495178,
0.0020312387496232986,
0.027432376518845558,
-0.015109525062143803,
0.0041631069034338,
0.03430403396487236,
0.035678111016750336,
-0.028115522116422653,
0.002743373392149806,
0.022540519014000893,
0.01806476153433323,
0.010117701254785061,
-0.011808721348643303,
0.022371549159288406,
0.02701139822602272,
-0.004194346256554127,
-0.0037392398808151484,
0.02779551036655903,
-0.009977390058338642,
0.008468338288366795,
-0.008590218611061573,
0.026500245556235313,
0.01730222813785076,
0.00994343776255846,
-0.004841678310185671,
0.003352315165102482,
-0.024303529411554337,
-0.0061443764716386795,
-0.017990462481975555,
0.033768340945243835,
0.02302316576242447,
0.020806824788451195,
0.07199160754680634,
-0.034020476043224335,
0.05961554870009422,
-0.0026564737781882286,
0.009078721515834332,
0.007418233901262283,
-0.0001670035271672532,
0.0030479233246296644,
-0.02234267070889473,
-0.012587206438183784,
0.037185244262218475,
0.03924553468823433,
0.00015043839812278748,
0.02346351556479931,
0.010857734829187393,
-0.004092327319085598,
-0.0016653425991535187,
-0.0015885321190580726,
-0.0066641089506447315,
0.017509227618575096,
-0.01667628064751625,
0.01945759914815426,
-0.02991451881825924,
0.022698061540722847,
0.019773421809077263,
0.03416459262371063,
-0.03439394012093544,
-0.019387349486351013,
-0.0009986200602725148,
0.022311732172966003,
0.023422352969646454,
-0.011220919899642467,
-0.02230742946267128,
0.05487189069390297,
0.0065778945572674274,
0.00616822112351656,
0.03923594951629639,
-0.05424309894442558,
0.035392191261053085,
0.013083606027066708,
0.007226472720503807,
-0.0031504647340625525,
-0.011140693910419941,
-0.034122858196496964,
0.018496107310056686,
0.023821214213967323,
0.0050784507766366005,
0.024460457265377045,
-0.019453847780823708,
0.01949452981352806,
-0.0238365326076746,
0.0015560360625386238,
-0.029811609536409378,
-0.04522515833377838,
-0.005262360442429781,
-0.0477890819311142,
-0.03705884888768196,
0.057542476803064346,
0.016709838062524796,
-0.05148909613490105,
-0.024626143276691437,
-0.04134846851229668,
0.033315785229206085,
-0.02091200090944767,
0.04804713651537895,
-0.02290799841284752,
0.02066156454384327,
-0.029836304485797882,
0.07127873599529266,
-0.008915042504668236,
-0.009815812110900879,
0.1432177573442459,
0.005127835553139448,
0.03050265647470951,
-0.07569106668233871,
-0.05142342671751976,
0.0008739251643419266,
0.0047788494266569614,
0.002773627173155546,
-0.002234135288745165,
-0.0283980593085289,
0.014775741845369339,
0.027387436479330063,
0.028465162962675095,
0.002632786985486746,
0.009687201119959354,
0.031474605202674866,
-0.009142621420323849,
-0.019738849252462387,
0.04588859900832176,
0.01567995548248291,
-0.03140716254711151,
0.004194572567939758,
-0.003533658105880022,
0.0324854776263237,
0.0055103059858083725,
0.04007318615913391,
0.025653671473264694,
-0.047714293003082275,
0.010205117985606194,
0.03979826346039772,
-0.02085288241505623,
-0.009408500976860523,
0.042827293276786804,
-0.0008410692680627108,
-0.02036755532026291,
-0.005646591540426016,
0.05029971897602081,
0.028033539652824402,
0.01566934399306774,
0.05538187921047211,
0.06152939051389694,
-0.046333715319633484,
0.0025165646802634,
0.010276812128722668,
-0.02376890927553177,
-0.006670352537184954,
-0.005533298943191767,
0.05402539670467377,
-0.004745271988213062,
-0.011636346578598022,
-0.010871096514165401,
-0.040922630578279495,
0.029121454805135727,
-0.05747419595718384,
-0.003407038515433669,
0.01103619858622551,
0.05098682641983032,
-0.04558917507529259,
0.014431467279791832,
0.0190044566988945,
0.02867627516388893,
-0.031811296939849854,
-0.019145386293530464,
0.001262367470189929,
-0.04906187951564789,
-0.0009166353847831488,
0.007227646186947823,
0.03951048105955124,
0.0016794059192761779,
-0.027258457615971565,
-0.05027327686548233,
0.0003598845505621284,
-0.05502524971961975,
0.026245618239045143,
0.01654326170682907,
-0.004022140521556139,
0.019581209868192673,
-0.0361056849360466,
0.002620068145915866,
-0.048933301120996475,
-0.03411070257425308,
0.017046155408024788,
-0.012889583595097065,
0.017389243468642235,
0.013488993048667908,
-0.03810902312397957,
0.009134615771472454,
0.036242347210645676,
-0.02710420824587345,
0.015309195965528488,
0.0019800367299467325,
0.030943019315600395,
0.0325855016708374,
-0.009309998713433743,
-0.001260923221707344,
-0.004537464585155249,
-0.053196098655462265,
0.004611264914274216,
-0.040855903178453445,
-0.04720795527100563,
0.012210807763040066,
-0.0017184007447212934,
-0.029647881165146828,
0.031397927552461624,
0.030035296455025673,
0.0012127005029469728,
-0.011286838911473751,
-0.029731910675764084,
-0.021459123119711876,
0.02306349202990532,
0.0400899238884449,
-0.023664657026529312,
-0.052472129464149475,
-0.04311336576938629,
0.01743861846625805,
0.013032444752752781,
0.06171027943491936,
-0.050839487463235855,
-0.01705453358590603,
-0.008568196557462215,
-0.01123928651213646,
-0.057120442390441895,
0.043502215296030045,
-0.036484554409980774,
0.03147607669234276,
-0.017115050926804543,
0.030026502907276154,
-0.021308068186044693,
0.05384878069162369,
-0.009714164771139622,
-0.010475235059857368,
0.03034171089529991,
0.0534391850233078,
-0.05319405719637871,
-0.03192324936389923,
-0.023082895204424858,
0.019268887117505074,
0.06367181986570358,
0.032085370272397995,
-0.024680547416210175,
0.009456406347453594,
-0.033800315111875534,
-0.05458692088723183,
0.06685026735067368,
-0.01732506789267063,
0.008303788490593433,
0.021704168990254402,
-0.05118720233440399,
-0.026952356100082397,
0.00541642727330327,
-0.023271573707461357,
0.003900863928720355,
-0.009352317079901695,
-0.0031925076618790627,
0.004573119804263115,
0.0013279671547934413,
-0.010374589823186398,
-0.0017298562452197075,
0.0017782412469387054,
0.029875921085476875,
0.013772944919764996,
0.0016384233022108674,
0.011499808169901371,
0.031141741201281548,
-0.02657792530953884,
-0.040548160672187805,
-0.0017124186269938946,
-0.03571425750851631,
-0.007977339439094067,
0.07882571965456009,
0.001191718620248139,
0.00192267878446728,
0.016502436250448227,
0.03750031813979149,
-0.08793793618679047,
0.004675812087953091,
-0.0015921479789540172,
0.03671812638640404,
0.027445955201983452,
-0.03884878009557724,
-0.0032505462877452374,
0.01831248588860035,
-0.07362668216228485,
0.06237485632300377,
-0.049808304756879807,
-0.02035715989768505,
-0.049966514110565186,
-0.009122701361775398,
-0.029287870973348618,
0.02381357178092003,
0.01088572945445776,
0.04057363048195839,
0.016302645206451416,
0.01265487540513277,
-0.008549259975552559,
-0.007023376878350973,
-0.021749550476670265,
0.004436630755662918,
-0.026689479127526283,
-0.028500964865088463,
0.03021955117583275,
-0.05100804939866066,
-0.014479792676866055,
0.04588604345917702,
-0.008616944774985313,
-0.030213018879294395,
-0.03861042484641075,
-0.030415117740631104,
0.007128049153834581,
0.02057511918246746,
0.03914665803313255,
-0.03288458660244942,
0.018544266000390053,
0.044862039387226105,
0.019957898184657097,
0.023434046655893326,
0.007977002300322056,
0.0012712531024590135,
0.005761553067713976,
-0.0003987204690929502,
-0.03701233118772507,
0.007606518920511007,
-0.0217596348375082,
-0.009424926713109016,
0.012550558894872665,
0.006153299007564783,
-0.018012769520282745,
-0.020384320989251137,
0.00025162563542835414,
-0.03734670206904411,
-0.019265202805399895,
0.027486151084303856,
0.036650773137807846,
-0.006945716217160225,
0.04814466834068298,
-0.03675750643014908,
-0.021731436252593994,
0.05063534900546074,
0.03465157374739647,
-0.0157802551984787,
0.006374436430633068,
-0.024735471233725548,
-0.0038029004354029894,
0.03583415597677231,
0.050137463957071304,
-0.04211577773094177,
-0.02479434199631214,
-0.007266168016940355,
-0.009496159851551056,
0.016096949577331543,
0.006223268806934357,
-0.05234155058860779,
0.013611490838229656,
-0.04718052223324776,
0.03318381309509277,
0.01497294008731842,
0.03296472877264023,
-0.01156721729785204,
0.0050183129496872425,
0.024093685671687126,
-0.019637737423181534,
0.028588872402906418,
-0.03913062810897827,
-0.012239902280271053,
0.023464733734726906,
0.022854475304484367,
0.008093726821243763,
-0.03725738823413849,
0.03655590862035751,
-0.02522536739706993,
0.012520968914031982,
-0.010642648674547672,
0.024581188336014748,
0.0157463401556015,
0.003971603699028492,
0.016399087384343147,
-0.007675476372241974,
-0.018693730235099792,
-0.01860801689326763,
-0.06533446162939072,
0.03573019057512283,
0.008828462101519108,
0.009952402673661709,
0.035810112953186035,
-0.004137455485761166,
0.020750580355525017,
0.04201848804950714,
-0.03922963887453079,
-0.026344558224081993,
0.05960112810134888,
-0.027505049481987953,
-0.014033930376172066,
-0.012546135112643242,
-0.0038568302989006042,
-0.004565791692584753,
-0.036252621561288834,
-0.01720389910042286,
0.06726834923028946,
-0.016582787036895752,
-0.018320461735129356,
0.053128682076931,
0.005682633724063635,
0.015679981559515,
0.04426373168826103,
0.023918040096759796,
0.04087560623884201,
0.018292943015694618,
-0.06683836132287979,
0.06162722408771515,
0.041175611317157745,
0.022707099094986916,
0.026865050196647644,
0.0144986342638731,
-0.019323615357279778,
0.02282455377280712,
0.011605632491409779,
0.02594616822898388,
-0.06248058006167412,
-0.007550423964858055,
0.04274531453847885,
-0.02654300443828106,
-0.0012507812352851033,
0.021314874291419983,
-0.030697083100676537,
0.07981673628091812,
0.008023479953408241,
-0.002159945899620652,
0.0019360720179975033,
0.004295380786061287,
-0.006708729080855846,
-0.012791047804057598,
0.024332350119948387,
0.03183862939476967,
-0.03183852136135101,
-0.01543711218982935,
-0.05311370640993118,
0.028676794841885567,
0.01978468708693981,
-0.05762458220124245,
0.010945365764200687,
-0.010442636907100677,
0.006631025113165379,
0.01719014160335064,
-0.0019559620413929224,
-0.051095008850097656,
-0.039178114384412766,
0.02862131968140602,
0.021043114364147186,
0.01589576154947281,
-0.02930890955030918,
-0.002729139057919383,
-0.011720653623342514,
0.0636008158326149,
-0.03827599063515663,
-0.032616011798381805,
-0.022619027644395828,
0.03723662346601486,
-0.01946331560611725,
0.029081828892230988
] |
<p>I live in Ireland where serving food on hot plates is considered “good cooking practice” to ensure the food remains warm – I come from France where I have rarely seen it done.</p>
<p>I am wondering if this practice really is useful. I assume it depends on the difference of temperature between the food and the plate, as heat won’t transfer as fast to the plate. But wouldn’t the extra time the food remains above an “acceptable” temperature threshold just be marginal?</p> | 4,635 | [
0.009995490312576294,
-0.013245108537375927,
0.008836894296109676,
-0.013109778054058552,
0.008950459770858288,
0.0004583338741213083,
-0.009132839739322662,
-0.02823691815137863,
0.016800247132778168,
0.04711952805519104,
0.014991606585681438,
0.033873651176691055,
-0.010438431054353714,
-0.02399604395031929,
0.010685660876333714,
0.024427110329270363,
0.039670106023550034,
-0.038171760737895966,
0.0007788169314153492,
-0.004791443236172199,
-0.04276292398571968,
0.001993158832192421,
-0.02227085269987583,
0.0018127376679331064,
-0.03517277538776398,
-0.013911289162933826,
0.004125062841922045,
0.030535908415913582,
0.03578644245862961,
0.03991023451089859,
-0.005764733999967575,
-0.010280884802341461,
0.007986951619386673,
0.0040626744739711285,
0.013410879299044609,
0.00921825971454382,
-0.038211628794670105,
-0.03574349358677864,
-0.0023225736804306507,
0.04341711476445198,
-0.006692743394523859,
-0.04032247141003609,
0.009989975951611996,
0.007977747358381748,
0.01620776578783989,
0.01725027710199356,
-0.02493458054959774,
-0.042782217264175415,
0.026915868744254112,
-0.047056589275598526,
-0.01743340492248535,
-0.003930751699954271,
0.01872621662914753,
0.03882930800318718,
0.021934542804956436,
0.02251749113202095,
0.08432619273662567,
0.026734428480267525,
-0.010589431039988995,
-0.04754899442195892,
-0.000029824763259966858,
-0.019915856420993805,
-0.005534396041184664,
0.018654320389032364,
-0.012798058800399303,
0.016971882432699203,
-0.012802405282855034,
-0.028420113027095795,
0.025257736444473267,
0.04199868068099022,
0.014163165353238583,
0.02772393450140953,
0.02713216096162796,
-0.015890581533312798,
0.010074685327708721,
-0.011652651242911816,
-0.007481296081095934,
0.03093753755092621,
0.030351435765624046,
0.04187026247382164,
0.04652925208210945,
0.0156240900978446,
0.059442225843667984,
0.0703340619802475,
0.0068653179332613945,
0.01098368875682354,
0.08427777886390686,
-0.024301474913954735,
0.03921882435679436,
0.052140265703201294,
-0.022597536444664,
0.014954394660890102,
0.02302020974457264,
0.005521731451153755,
-0.01796163246035576,
-0.009733809158205986,
-0.03353553265333176,
0.021440360695123672,
-0.014434176497161388,
-0.010123389773070812,
-0.02070886641740799,
-0.019518248736858368,
0.0064840372651815414,
0.05023754760622978,
0.0031507371459156275,
-0.02924494445323944,
-0.046319738030433655,
-0.018470725044608116,
0.06309549510478973,
-0.006299663335084915,
-0.10167764872312546,
0.014381705783307552,
-0.007807526737451553,
0.026980796828866005,
0.034225668758153915,
0.010915098711848259,
0.019616760313510895,
0.0007319762371480465,
0.03163045644760132,
0.03062795288860798,
0.03333250433206558,
0.009177225641906261,
0.007492797914892435,
-0.021661534905433655,
-0.10109995305538177,
0.03909747675061226,
-0.009952719323337078,
-0.004383229650557041,
-0.05641847848892212,
0.059003796428442,
0.00899538490921259,
-0.01422985177487135,
0.002675538184121251,
0.0013941496144980192,
-0.02398429624736309,
0.007032047025859356,
-0.052848923951387405,
-0.0281741451472044,
0.06073157861828804,
0.0059518273919820786,
-0.0336381159722805,
-0.06868266314268112,
-0.025150565430521965,
0.012051490135490894,
0.04470529779791832,
0.013307491317391396,
-0.02204202488064766,
-0.03348160535097122,
0.0067509980872273445,
-0.023013148456811905,
-0.028458070009946823,
-0.0015611876733601093,
-0.01599184237420559,
-0.05304482579231262,
0.00948250200599432,
-0.035128116607666016,
0.033237092196941376,
0.03283924236893654,
-0.0015080958837643266,
-0.05204574018716812,
0.01676923967897892,
-0.01917031779885292,
0.010620473884046078,
-0.024377936497330666,
0.0017860078951343894,
-0.0220126211643219,
0.07260000705718994,
-0.02877800352871418,
0.028072718530893326,
-0.028630677610635757,
0.013351467438042164,
0.026068124920129776,
-0.03092363104224205,
0.01420255471020937,
-0.0028812140226364136,
0.0018011822830885649,
0.020536771044135094,
-0.026704400777816772,
0.0407891720533371,
0.019903523847460747,
-0.02910188026726246,
0.01906665600836277,
0.009110387414693832,
0.017083998769521713,
-0.0029684235341846943,
0.07022171467542648,
0.0142744155600667,
-0.0041700867004692554,
0.015284476801753044,
-0.0660819262266159,
-0.050494760274887085,
-0.07918643206357956,
0.011097212322056293,
-0.0019065383821725845,
0.005471027456223965,
-0.0011038106167688966,
-0.0044316076673567295,
0.03863931819796562,
-0.025115426629781723,
-0.019761068746447563,
0.015995388850569725,
-0.02242898941040039,
0.03309248015284538,
-0.07222749292850494,
0.024969646707177162,
0.062245436012744904,
0.03770562261343002,
-0.00931758526712656,
0.0349569171667099,
-0.047309041023254395,
-0.05629517510533333,
-0.01736733876168728,
-0.030931051820516586,
0.019835662096738815,
0.028731921687722206,
-0.031641632318496704,
0.021066363900899887,
0.006418709177523851,
-0.052824199199676514,
0.04965775087475777,
-0.05057007074356079,
0.07791370153427124,
-0.01301142293959856,
0.0001600148534635082,
0.016244390979409218,
0.004230474587529898,
0.01608041487634182,
0.016579490154981613,
0.01728794537484646,
-0.05311312526464462,
-0.054622817784547806,
-0.007932955399155617,
0.05511748790740967,
0.031533464789390564,
-0.03281225264072418,
-0.01012646034359932,
0.025331418961286545,
0.006463396362960339,
0.015296678990125656,
0.02550218068063259,
0.015555578283965588,
-0.036253947764635086,
0.04339718446135521,
0.0015142783522605896,
0.01506007183343172,
0.04669962823390961,
-0.03341255336999893,
-0.010251784697175026,
0.020158953964710236,
0.021804247051477432,
-0.02006274089217186,
0.014648151583969593,
0.032990872859954834,
0.035995762795209885,
-0.018071675673127174,
-0.008928660303354263,
0.04203549399971962,
-0.048260681331157684,
0.06370043009519577,
-0.0009219140047207475,
0.029450776055455208,
0.061042483896017075,
-0.001023822114802897,
-0.02217574417591095,
0.024788668379187584,
0.02779904380440712,
-0.019900629296898842,
-0.014116039499640465,
0.051739975810050964,
-0.02767466939985752,
0.015603756532073021,
-0.08538799732923508,
-0.05176600441336632,
0.033992767333984375,
-0.05971910431981087,
-0.005507333669811487,
-0.021376410499215126,
0.05001908168196678,
-0.035556256771087646,
0.00830167718231678,
-0.017797503620386124,
-0.0117479944601655,
0.0005180425359867513,
-0.031294237822294235,
-0.004396383184939623,
-0.010189816355705261,
0.012217883951961994,
-0.011408970691263676,
0.04706721380352974,
0.008584619499742985,
0.02152206562459469,
0.018567301332950592,
-0.013630989007651806,
-0.04751988872885704,
-0.016238154843449593,
0.01660170406103134,
0.008350996300578117,
-0.012230350635945797,
-0.01819261722266674,
0.023830315098166466,
-0.00018595848814584315,
-0.01697552390396595,
0.021373996511101723,
-0.03840155526995659,
-0.04768987372517586,
-0.024012334644794464,
0.021172670647501945,
0.020533252507448196,
0.029461726546287537,
0.004938795696943998,
0.04736374318599701,
-0.06165086850523949,
-0.03885499760508537,
-0.029773607850074768,
-0.017766835168004036,
0.012417357414960861,
-0.030551521107554436,
0.02297326736152172,
-0.028654877096414566,
-0.029856326058506966,
0.043664734810590744,
0.031928159296512604,
-0.023396451026201248,
-0.0009915918344631791,
-0.020314902067184448,
-0.006630086340010166,
-0.012959909625351429,
0.00009074880654225126,
0.02875654585659504,
-0.03683939576148987,
0.019973795861005783,
0.024526221677660942,
0.016043808311223984,
0.034221623092889786,
0.013292456045746803,
-0.03382248803973198,
-0.021415308117866516,
-0.016775960102677345,
-0.021808229386806488,
-0.0026586311869323254,
0.019612515345215797,
0.007579993922263384,
-0.019396206364035606,
-0.02988705225288868,
0.0706462562084198,
0.026119716465473175,
-0.04495220258831978,
0.06347374618053436,
-0.004759731236845255,
-0.016046632081270218,
-0.048655394464731216,
0.027767378836870193,
0.020532658323645592,
-0.023535408079624176,
-0.018178502097725868,
0.03934919461607933,
0.04924100637435913,
-0.015557208098471165,
0.00647730054333806,
0.051084838807582855,
0.07138775289058685,
0.0056449295952916145,
0.009954433888196945,
0.029856842011213303,
0.024848658591508865,
-0.001349946018308401,
-0.009485688991844654,
-0.004988437984138727,
0.017074840143322945,
0.041887830942869186,
-0.0007279944256879389,
0.001816985895857215,
-0.03350715711712837,
-0.012044310569763184,
-0.10070882737636566,
0.026021169498562813,
0.013359718956053257,
0.011297316290438175,
0.008525309152901173,
0.03017386794090271,
0.01773511990904808,
0.013662484474480152,
0.0043448093347251415,
0.017590191215276718,
-0.050156496465206146,
0.03396075963973999,
-0.0239080972969532,
-0.0270780548453331,
-0.03317131847143173,
-0.049897871911525726,
-0.00928531214594841,
-0.03337927907705307,
0.030437802895903587,
-0.0032035261392593384,
0.006786112207919359,
-0.01729028858244419,
0.006693035364151001,
-0.028525447472929955,
-0.05895364657044411,
-0.012135811150074005,
-0.00199719425290823,
0.03274659812450409,
-0.01647845469415188,
0.009652851149439812,
0.03555281087756157,
-0.009517209604382515,
-0.03283839672803879,
-0.019695745781064034,
-0.009744863025844097,
-0.0008413987816311419,
0.03020809218287468,
-0.009891408495604992,
0.06404073536396027,
-0.04670963063836098,
0.021205192431807518,
0.029641471803188324,
0.034156203269958496,
-0.0142579460516572,
-0.046485017985105515,
-0.04219071567058563,
-0.0286713819950819,
-0.017902256920933723,
0.0375119224190712,
0.03659433871507645,
-0.02212153747677803,
-0.002714643720537424,
0.028529634699225426,
0.011671848595142365,
-0.025596298277378082,
-0.00007626180740771815,
0.028371581807732582,
0.004954266361892223,
0.016369899734854698,
-0.051902517676353455,
-0.004132772795855999,
-0.020720330998301506,
0.018694231286644936,
0.03762814775109291,
0.02462538331747055,
-0.011251951567828655,
0.014528787694871426,
0.007703715469688177,
-0.01511441171169281,
-0.012325892224907875,
0.017550833523273468,
-0.0013620273675769567,
0.013337201438844204,
0.014053143560886383,
0.005410602781921625,
0.028408318758010864,
0.03607727587223053,
0.013005441054701805,
0.007992522791028023,
0.0005608396022580564,
-0.07847762107849121,
0.008051442913711071,
0.053855761885643005,
0.05491829663515091,
-0.0009696785709820688,
0.0003486564091872424,
-0.03532002121210098,
0.004262820351868868,
0.06643001735210419,
-0.003588865976780653,
0.050367582589387894,
-0.054020561277866364,
-0.02953009493649006,
-0.010695723816752434,
-0.028827786445617676,
-0.004117215052247047,
0.006050234194844961,
0.01244780607521534,
0.02355564944446087,
0.006450524553656578,
-0.05080252140760422,
-0.003476815763860941,
-0.007283880840986967,
0.012214405462145805,
-0.018213016912341118,
0.0006520000752061605,
-0.017012862488627434,
0.007335411850363016,
0.011787301860749722,
-0.03267727419734001,
-0.039119139313697815,
-0.02210414968430996,
-0.014521528035402298,
-0.0037896097637712955,
0.0073326583951711655,
-0.002077498473227024,
-0.02852061577141285,
0.034025344997644424,
0.014977779239416122,
-0.009597091004252434,
-0.0018536379793658853,
-0.0023007255513221025,
0.0688716322183609,
0.04349198192358017,
-0.01625247858464718,
0.041674427688121796,
0.04725067690014839,
-0.058906301856040955,
-0.005315190646797419,
0.03596536070108414,
0.014781977981328964,
-0.04653552547097206,
-0.018246686086058617,
-0.057397644966840744,
-0.03628043830394745,
-0.03910383582115173,
0.018960611894726753,
0.022689692676067352,
0.024895314127206802,
0.014065947383642197,
-0.04269419610500336,
-0.012379461899399757,
0.016597945243120193,
0.03162487968802452,
-0.02321058325469494,
-0.05031093582510948,
-0.01345943845808506,
0.004220487084239721,
-0.011119604110717773,
0.018391501158475876,
-0.003868230851367116,
0.05904679745435715,
-0.007239282131195068,
-0.020593049004673958,
-0.0035477273631840944,
-0.02654958702623844,
-0.04151420295238495,
-0.007912089116871357,
-0.020194634795188904,
0.050454821437597275,
0.012379252351820469,
0.012768990360200405,
-0.024595510214567184,
-0.08305687457323074,
0.029567746445536613,
0.03532654792070389,
0.012179873883724213,
0.035142455250024796,
-0.04733851179480553,
0.0460490882396698,
0.0009338608360849321,
0.010886762291193008,
-0.04126875102519989,
0.01192148681730032,
0.03809746727347374,
-0.036988917738199234,
-0.03724848851561546,
-0.056684575974941254,
-0.04061290621757507,
-0.017874963581562042,
-0.055636897683143616,
-0.018882235512137413,
0.04041896387934685,
0.007414041552692652,
-0.0034324636217206717,
-0.022326748818159103,
-0.020864931866526604,
0.07326050847768784,
-0.010340697132050991,
-0.019325461238622665,
0.03409695625305176,
-0.021941393613815308,
-0.02551991678774357,
-0.051559410989284515,
0.03705267235636711,
-0.016392599791288376,
0.032425373792648315,
-0.003950589336454868,
0.01773073337972164,
-0.0033601103350520134,
0.017824864014983177,
-0.020220104604959488,
0.02901083044707775,
0.026089880615472794,
-0.0184226855635643,
-0.021384457126259804,
0.09138821810483932,
-0.0011869289446622133,
0.007976376451551914,
0.016803286969661713,
0.01594841666519642,
0.013400953263044357,
-0.029279479756951332,
0.011359728872776031,
-0.043154384940862656,
0.014777682721614838,
0.02197069488465786,
0.04123660549521446,
-0.033445894718170166,
0.0012655843747779727,
0.006632321048527956,
-0.027334673330187798,
0.029900187626481056,
-0.02413683757185936,
-0.0244077667593956,
-0.005725613795220852,
-0.020646173506975174,
-0.03567536547780037,
-0.006529785692691803,
-0.002992206020280719,
-0.05627530440688133,
0.04133877530694008,
-0.019934484735131264,
0.04167700186371803,
-0.03171170875430107,
-0.020968681201338768,
-0.0018098435830324888,
0.007139390800148249,
-0.0272140521556139,
-0.0030556339770555496,
-0.02105579525232315,
0.011771823279559612,
-0.018037330359220505,
-0.0008663117769174278,
0.038669973611831665,
0.018197350203990936,
0.007604503072798252,
0.004130041692405939,
0.029315276071429253,
0.033044081181287766,
-0.012730001471936703,
-0.03949379548430443,
-0.030580969527363777,
0.02111716754734516,
-0.08497947454452515,
-0.002338926075026393,
-0.03283596783876419,
-0.017513800412416458,
0.01584058627486229,
0.006084275431931019,
0.03742097318172455,
-0.061743684113025665,
0.016081994399428368,
0.023722564801573753,
-0.003033560700714588,
-0.003872200846672058,
-0.027673209086060524,
0.04025787487626076,
-0.01607256941497326,
0.042502302676439285,
0.005704218987375498,
0.010373798198997974,
0.005600098054856062,
-0.025451671332120895,
-0.013060048222541809,
-0.011279027909040451,
0.02187059260904789,
0.05819741636514664,
-0.008804802782833576,
-0.02884671837091446,
-0.014604169875383377,
-0.007709200028330088,
-0.000114796930574812,
0.018476136028766632,
0.045976873487234116,
-0.03666314110159874,
0.09586586803197861,
-0.02513108402490616,
-0.006222178228199482,
0.01173001155257225,
0.028748322278261185,
0.12548404932022095,
0.02882697619497776,
0.014977985993027687,
-0.03799736872315407,
0.022231439128518105,
-0.029582766816020012,
-0.00683910446241498,
-0.034338582307100296,
-0.02013416960835457,
-0.02551165223121643,
-0.007140947040170431,
0.034721482545137405,
0.09879252314567566,
-0.01909588649868965,
0.00026603040168993175,
0.027402609586715698,
-0.008102037943899632,
-0.016522657126188278,
0.03201537951827049,
0.020746033638715744,
0.014875329099595547,
0.017328735440969467,
-0.03844417631626129,
0.004325535614043474,
0.00968959927558899,
-0.010920016095042229,
0.012852729298174381,
0.012571952305734158,
0.014344850555062294,
0.010789657942950726,
-0.03590768203139305,
-0.031028956174850464,
0.014941112138330936,
-0.0467204675078392,
-0.0013182363472878933,
-0.005658517125993967,
0.018148258328437805,
0.011567083187401295,
0.029199525713920593,
0.03093617409467697,
0.010767964646220207,
0.010549158789217472,
0.03762407973408699,
0.01977946050465107,
-0.032818570733070374,
-0.020872021093964577,
-0.011188292875885963,
0.0036127427592873573,
0.0009641453507356346,
-0.007490518968552351,
0.04455525800585747,
-0.04170719161629677,
0.04090304672718048,
0.015210901387035847,
-0.029106831178069115,
0.028145356103777885,
0.011029447428882122,
0.003580864053219557,
-0.04133181273937225,
-0.04741814732551575,
0.04552427679300308,
0.028288614004850388,
0.004481453914195299,
0.04951215535402298,
-0.05757962167263031,
-0.010554378852248192,
0.016749316826462746,
0.032957468181848526,
0.011267252266407013,
-0.02224624715745449,
0.0066108182072639465,
0.0034197126515209675,
-0.03144477307796478,
-0.006532247643917799,
-0.000252285972237587,
0.03049735352396965,
0.03960806876420975,
-0.01808510348200798,
-0.01825808919966221,
-0.04965127632021904,
-0.11097739636898041,
0.026151282712817192,
-0.056236639618873596,
-0.029656408354640007,
-0.0010594583582133055,
-0.03812938928604126,
0.009954719804227352,
0.04306822270154953,
-0.011866360902786255,
-0.0004276858817320317,
0.009458251297473907,
0.05547397956252098,
0.03324397653341293,
-0.013657291419804096,
-0.028200116008520126,
-0.0298931784927845,
-0.06304886937141418,
-0.013175642117857933,
-0.011130835860967636,
0.058191604912281036,
0.020601490512490273,
0.007238408084958792,
0.02504696510732174,
-0.009312060661613941,
0.01221049390733242,
0.027414847165346146,
0.03449777513742447,
-0.02635779418051243,
-0.016263127326965332,
-0.01771656796336174,
-0.006316889077425003,
-0.029030190780758858,
-0.03691001236438751,
-0.000719635165296495,
-0.008711645379662514,
-0.0525941327214241,
0.007617291994392872,
-0.011176065541803837,
0.005614199209958315,
0.0019456271547824144,
0.04560253769159317,
-0.02017960511147976,
0.0045552547089755535,
-0.029881322756409645,
-0.036693025380373,
-0.009645786136388779,
-0.012766240164637566,
-0.016683131456375122,
0.04441036656498909,
-0.011894939467310905,
0.017951371148228645,
0.019583214074373245,
0.007326988968998194,
-0.017890948802232742,
-0.03680974617600441,
0.014738263562321663,
0.011633196845650673,
0.020100386813282967,
-0.05440095439553261,
-0.05494438484311104,
0.04274443909525871,
-0.017436014488339424,
-0.0572466142475605,
0.012711696326732635,
0.010374835692346096,
0.008235462941229343,
0.004771426320075989,
0.018517067655920982,
-0.0072736297734081745,
0.05593699589371681,
0.004704768769443035,
-0.030541643500328064,
0.004989411681890488,
0.022470740601420403,
0.03611573576927185,
0.008409848436713219,
-0.007140669040381908,
-0.029657699167728424,
-0.00797292497009039,
0.03502612188458443,
0.03313158079981804,
0.031239716336131096,
0.03532825782895088,
0.005749114323407412,
-0.016496215015649796,
0.025872131809592247,
-0.02729663997888565,
0.019556671380996704,
0.03406195342540741,
0.06054738536477089,
-0.033152006566524506,
0.004478419199585915,
-0.004942574072629213,
-0.019870292395353317,
-0.04897390305995941,
-0.0029805293306708336,
-0.0017733594868332148,
0.003162318840622902,
0.02133192867040634,
-0.0040914700366556644,
0.050183676183223724,
0.002133480506017804,
-0.028253192082047462,
0.03581023961305618,
0.02440296672284603,
-0.024664033204317093,
-0.08084651082754135,
0.0320466086268425,
-0.030178336426615715,
0.07162237167358398,
-0.0010610886383801699,
0.04317353665828705,
0.038539063185453415,
0.02406378462910652,
-0.004487095400691032,
-0.02860158309340477,
0.03289741277694702,
0.03196115046739578,
-0.008674942888319492,
-0.024121936410665512,
0.06111232191324234,
0.0019391017267480493,
-0.054151322692632675,
-0.003028975334018469,
-0.022640293464064598,
0.022168250754475594,
-0.003571902634575963,
0.011745776981115341,
-0.03360818699002266,
0.0009848468471318483,
0.007430154364556074,
-0.018800372257828712,
-0.012086169794201851,
-0.0041882372461259365,
0.014540085569024086,
0.028346609324216843,
-0.034132763743400574,
0.028236692771315575,
0.047023434191942215,
-0.0051883514970541,
-0.04111650958657265,
0.0033951732330024242,
-0.011009798385202885,
-0.0048865643329918385,
0.021127356216311455,
0.040173906832933426,
0.04944330081343651,
-0.017433729022741318,
0.0031141210347414017,
-0.07944730669260025,
0.02426275983452797,
-0.01770842634141445,
0.03894034028053284,
0.016936665400862694,
-0.005274308379739523,
-0.014008189551532269,
-0.0009225601679645479,
-0.006430281791836023,
0.018768204376101494,
-0.0263889841735363,
-0.007545443717390299,
-0.0207236185669899,
0.019895929843187332,
0.047693610191345215,
-0.06528264284133911,
0.010720465332269669,
-0.027569718658924103,
0.016318773850798607,
0.0000025383005777257495,
0.0717921108007431,
-0.00311875413171947,
0.006313546560704708,
-0.012149159796535969,
-0.0368032306432724,
0.03152589127421379,
-0.01689472794532776,
-0.022252041846513748,
-0.019901493564248085,
-0.03246629238128662,
-0.03320479765534401,
-0.01721636764705181,
0.07322303205728531,
0.0045843543484807014,
0.02590080536901951,
-0.023370901122689247,
0.024954183027148247,
-0.015326790511608124,
-0.06351328641176224,
0.05414646863937378,
-0.04055410251021385,
0.002218054374679923,
-0.000536951411049813,
0.0047051794826984406,
-0.022912954911589622,
-0.0025897491723299026,
0.03063356690108776,
-0.051798246800899506,
0.04167255759239197,
0.004983553197234869,
-0.02351442724466324,
0.05519746243953705,
0.04840177297592163,
-0.016711391508579254,
0.08031287789344788,
-0.043640028685331345,
-0.04012437164783478,
0.030545733869075775,
0.007553396746516228,
-0.055362384766340256,
0.0028738263063132763,
-0.01957191713154316,
0.0011749063851311803,
-0.02929438091814518,
0.004348414018750191,
-0.01230816263705492,
-0.08055989444255829,
-0.0023595388047397137,
0.03639347851276398,
0.004759447183459997,
-0.002659466816112399,
-0.016740722581744194,
0.06330814212560654,
0.022389503195881844,
0.0007309610955417156,
-0.013507090508937836,
-0.018823089078068733,
0.05242381989955902,
0.0034312622155994177,
0.04886484891176224,
0.01623344235122204,
-0.02840372361242771,
0.05997302010655403,
0.003403641516342759,
-0.030068980529904366,
0.052918799221515656,
0.011141817085444927,
0.060906268656253815,
-0.0018694467144086957,
-0.015873413532972336,
-0.019503168761730194,
-0.02037678100168705,
-0.007639297749847174,
0.025642814114689827,
0.0012214749585837126,
0.046997569501399994,
0.014929819852113724,
-0.03412814438343048,
-0.013233968988060951,
-0.02107003517448902,
-0.002071115653961897,
-0.008845650590956211,
0.05729716271162033,
-0.00835486315190792,
-0.03625163808465004,
0.02440030127763748,
0.02520711161196232,
-0.009112956933677197,
0.023692935705184937,
-0.036972176283597946,
0.023321913555264473,
-0.02704089693725109,
0.025457141920924187,
-0.013249167241156101,
-0.05578645318746567,
-0.009134911932051182,
0.0116684939712286,
0.020871762186288834,
0.028253834694623947,
0.0069369301199913025,
0.013330334797501564,
0.014708258211612701,
0.01546761766076088,
0.02660369500517845,
-0.12928105890750885,
-0.009382792748510838,
-0.02146051451563835,
0.025398828089237213,
-0.03352353349328041,
0.02696351520717144
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/29805/richtmyer-meshkov-instability-in-mhd">Richtmyer Meshkov instability in MHD</a> </p>
</blockquote>
<p>The Richtmyer Meshkov instability in Hydrodynamics:-
1) When shock wave interacts with the contact discontinuity, it accumulates the vorticity on the CD
2) This causes the density discontinuity to curl up, and form series of vortices</p>
<p>In application of the longitudinal magnetic field with conducting fluid as the working medium,</p>
<p>1) The RM instability is suppressed
2) Series of new shocks is formed and it carries away the vorticity</p>
<p>My question is ,
what exactly happens in Magneto-Hydrodynamic system?
Why the RM instability is supressed?
How can one get the physical intuition of what is happening at the interface?</p> | 462 | [
-0.00945320725440979,
-0.01927727647125721,
-0.0034109705593436956,
-0.03965502232313156,
0.02211492881178856,
0.023569170385599136,
-0.024484412744641304,
-0.03366151079535484,
-0.0120004927739501,
-0.007961052469909191,
0.036952823400497437,
0.011424398981034756,
0.0648965835571289,
0.01059943251311779,
0.02013993263244629,
-0.007443316280841827,
0.010335510596632957,
-0.040809713304042816,
0.0536811500787735,
-0.003435068065300584,
-0.03639766573905945,
0.008249873295426369,
0.010255992412567139,
-0.010262604802846909,
-0.054301366209983826,
0.003940348979085684,
0.010694604367017746,
0.013220224529504776,
0.039681993424892426,
0.02596851997077465,
-0.006975146476179361,
-0.02655116654932499,
-0.00862100813537836,
-0.037654101848602295,
0.011361858807504177,
0.03240686282515526,
-0.057453371584415436,
-0.030276061967015266,
-0.017266735434532166,
0.012748959474265575,
0.004831557162106037,
-0.020070163533091545,
0.005558859556913376,
0.05969558283686638,
-0.04349574074149132,
-0.019828394055366516,
0.028791168704628944,
0.009114588610827923,
0.03440474718809128,
-0.08035135269165039,
-0.009423693642020226,
0.00267763901501894,
0.07167893648147583,
0.00021432088396977633,
0.0019220986869186163,
-0.009213004261255264,
0.07069434970617294,
0.09821978211402893,
0.0038916259072721004,
-0.022979022935032845,
0.014045906253159046,
-0.0004094065516255796,
-0.015820441767573357,
-0.008192257955670357,
-0.046057745814323425,
0.07796639949083328,
0.002074220683425665,
0.00024973988183774054,
0.03368706256151199,
0.01130935363471508,
-0.015253087505698204,
-0.03646466135978699,
-0.03793789818882942,
0.0017537242965772748,
0.05824267119169235,
-0.0033057467080652714,
0.028085758909583092,
0.015515119768679142,
0.009890425950288773,
0.05430988967418671,
-0.025088302791118622,
0.020225850865244865,
0.010977016761898994,
0.03741797059774399,
0.011502410285174847,
0.007633139379322529,
0.08300060778856277,
0.010434415191411972,
0.033512458205223083,
0.01774556003510952,
-0.019280079752206802,
0.01692405715584755,
0.010792018845677376,
-0.004669124260544777,
-0.017510417848825455,
-0.007638491690158844,
-0.005367287900298834,
0.0438627228140831,
0.02110152691602707,
-0.02287129871547222,
-0.011131158098578453,
-0.003114644903689623,
0.01755143329501152,
0.06371201574802399,
0.016786843538284302,
-0.053291480988264084,
-0.036352261900901794,
0.027864569798111916,
-0.04621828719973564,
-0.03786727041006088,
0.005007994826883078,
0.00971525814384222,
0.009043879806995392,
-0.02141714096069336,
0.018476350232958794,
-0.007737608160823584,
0.026804903522133827,
0.008508564904332161,
0.04072384908795357,
0.07011407613754272,
0.018234504386782646,
-0.038168925791978836,
0.002289530588313937,
-0.012042565271258354,
-0.08222135156393051,
0.0010714944219216704,
0.01818714290857315,
-0.03850896656513214,
-0.003474524710327387,
0.0024716132320463657,
-0.024643130600452423,
-0.01618020236492157,
0.0034865064080804586,
0.04431276395916939,
0.022602533921599388,
-0.03043525293469429,
-0.09507764875888824,
-0.048687756061553955,
0.06426072865724564,
-0.012884406372904778,
-0.01352512463927269,
-0.07013685256242752,
-0.016444949433207512,
0.023152774199843407,
0.093375563621521,
-0.03177022561430931,
-0.020732175558805466,
0.02370276488363743,
0.09037958830595016,
0.012945159338414669,
-0.012039894238114357,
-0.023647276684641838,
-0.012759004719555378,
-0.028162583708763123,
-0.03217049688100815,
-0.0728641003370285,
0.0044804406352341175,
0.052957918494939804,
0.013451042585074902,
-0.00876376498490572,
0.07053571194410324,
-0.010250048711895943,
-0.003974952269345522,
0.007874428294599056,
-0.00768857030197978,
-0.014514456503093243,
0.08024982362985611,
-0.0079182805493474,
0.05778743326663971,
0.0657300278544426,
0.0061841621063649654,
0.0019373068353161216,
-0.02584218606352806,
0.05317075178027153,
0.00029537605587393045,
-0.03736885264515877,
-0.010868160054087639,
-0.011884646490216255,
-0.03260107710957527,
-0.03418934345245361,
-0.04740964248776436,
-0.04993560165166855,
-0.011810657568275928,
-0.03647622838616371,
0.004210188984870911,
0.021388530731201172,
-0.020020263269543648,
-0.007602098863571882,
-0.03121645376086235,
-0.04579358175396919,
-0.03267365321516991,
-0.03976714238524437,
-0.0024886399041861296,
-0.034963469952344894,
-0.019287345930933952,
0.027845215052366257,
-0.024542290717363358,
-0.004755630157887936,
-0.03364965319633484,
-0.022997455671429634,
-0.00502903712913394,
0.026661965996026993,
-0.004958704113960266,
0.009558288380503654,
0.01910323277115822,
-0.000645761436317116,
0.023457463830709457,
-0.005254026968032122,
0.0035590133629739285,
0.017322540283203125,
-0.04921629652380943,
0.026242433115839958,
0.005985395982861519,
0.02542225643992424,
-0.04614873230457306,
-0.028059523552656174,
0.029977181926369667,
0.0038081875536590815,
-0.0055413623340427876,
-0.017213013023138046,
-0.02921050600707531,
0.06017208471894264,
0.07041467726230621,
0.0043870834633708,
0.015850719064474106,
0.03681887313723564,
-0.014952447265386581,
0.008259584195911884,
0.002307698130607605,
0.00021588147501461208,
-0.052337586879730225,
0.009518768638372421,
0.046831753104925156,
0.021222367882728577,
-0.047447655349969864,
0.03608454018831253,
0.03052777238190174,
0.06216498836874962,
0.03517121449112892,
0.04750773683190346,
-0.0015232586301863194,
-0.02974318340420723,
0.0537780337035656,
0.013047941960394382,
-0.02203497476875782,
-0.0036234480794519186,
0.03619812801480293,
0.020746419206261635,
0.020429102703928947,
-0.020896701142191887,
-0.01053172629326582,
0.025528086349368095,
0.0015877261757850647,
-0.020480576902627945,
-0.018488120287656784,
0.006649723742157221,
0.03332630172371864,
-0.011206050403416157,
0.02495933137834072,
0.023456895723938942,
0.03757411614060402,
0.029619747772812843,
-0.05018658563494682,
0.013384980149567127,
0.0008398506906814873,
0.03427835553884506,
0.023862488567829132,
-0.03320193663239479,
0.017199432477355003,
-0.05975879356265068,
-0.030976049602031708,
0.0006721987156197429,
0.005664888769388199,
0.006649866234511137,
-0.0285370871424675,
-0.004699946381151676,
0.03493724390864372,
0.008438583463430405,
-0.00950772687792778,
-0.015278425067663193,
-0.002188951475545764,
-0.016162479296326637,
-0.0111135458573699,
0.03556767478585243,
-0.05381552502512932,
0.021994933485984802,
-0.028456365689635277,
0.004947931971400976,
0.03907495364546776,
0.03195063769817352,
0.024719692766666412,
0.020721565932035446,
-0.02704095095396042,
-0.056756746023893356,
-0.04278681054711342,
-0.03005714900791645,
0.02110448107123375,
-0.018340880051255226,
-0.013736340217292309,
0.07985757291316986,
-0.007212445605546236,
-0.013511762954294682,
-0.003900485811755061,
-0.032481804490089417,
-0.019557330757379532,
0.001760688959620893,
-0.01970488764345646,
0.01819339208304882,
-0.0048431335017085075,
0.023484788835048676,
0.022753167897462845,
-0.03149455413222313,
0.0045528714545071125,
-0.040395621210336685,
-0.02100282721221447,
0.024505717679858208,
-0.05106280371546745,
0.016711916774511337,
-0.04234737902879715,
-0.076036237180233,
0.026924917474389076,
0.001474583288654685,
-0.024343296885490417,
0.00016857474111020565,
0.010877286083996296,
-0.030306454747915268,
-0.010684393346309662,
0.023040013387799263,
0.03107663057744503,
0.010682574473321438,
-0.0012715569464489818,
0.015879245474934578,
0.046588413417339325,
0.028053507208824158,
0.023505808785557747,
-0.0035877106711268425,
0.015018856152892113,
0.008892131969332695,
0.002651029732078314,
0.04313666746020317,
0.012147672474384308,
-0.004716874100267887,
0.03868100792169571,
-0.03205069154500961,
0.023235175758600235,
0.038864750415086746,
-0.04941204935312271,
0.04467613995075226,
0.004260331392288208,
0.0026873883325606585,
-0.037209488451480865,
0.039207324385643005,
-0.008168986067175865,
-0.0047417995519936085,
-0.007555600255727768,
0.006994583178311586,
0.03921867161989212,
-0.035026006400585175,
-0.005895542912185192,
0.030230378732085228,
0.026738116517663002,
-0.023177623748779297,
-0.001065016258507967,
-0.014294004999101162,
-0.026427965611219406,
0.030133696272969246,
-0.03699394688010216,
0.03306077420711517,
0.050731170922517776,
0.011647598817944527,
0.008502811193466187,
-0.017001204192638397,
-0.03207070007920265,
-0.008556020446121693,
-0.06466756016016006,
-0.013658473268151283,
0.015419051051139832,
0.06058533117175102,
0.005802867002785206,
0.06597539037466049,
0.020427512004971504,
0.03244204446673393,
0.031494416296482086,
-0.025430038571357727,
-0.09792777895927429,
0.0006023116875439882,
-0.0020881611853837967,
-0.018384523689746857,
-0.02013576216995716,
-0.03320613503456116,
-0.021504318341612816,
-0.012628861702978611,
-0.006180080119520426,
-0.03351948782801628,
0.009725108742713928,
-0.04891497641801834,
0.02983924001455307,
-0.02411366067826748,
-0.03369409218430519,
-0.02240283042192459,
0.05526350066065788,
0.05948293209075928,
-0.039687760174274445,
0.023461399599909782,
0.029387423768639565,
-0.0391959473490715,
-0.0016903229989111423,
-0.04820619150996208,
-0.017413906753063202,
0.04044235125184059,
0.016942037269473076,
-0.0076918634586036205,
-0.004261061083525419,
-0.020190345123410225,
0.02795136347413063,
0.031543467193841934,
0.03836825117468834,
-0.006109656300395727,
0.011016790755093098,
-0.02705151028931141,
-0.02257092110812664,
-0.013271337375044823,
-0.014144615270197392,
0.07519734650850296,
-0.002653363160789013,
0.004595301114022732,
0.024027368053793907,
0.005028457846492529,
-0.04375341162085533,
0.03343433886766434,
0.030731892213225365,
-0.006615918595343828,
0.02878291718661785,
-0.03518424928188324,
-0.012602247297763824,
-0.041521549224853516,
0.010441931895911694,
0.044767770916223526,
-0.015690919011831284,
-0.029745779931545258,
0.007345361169427633,
0.01304290909320116,
0.02785738743841648,
0.002537610474973917,
-0.004311618395149708,
-0.008233238942921162,
0.023002108559012413,
-0.002990837674587965,
0.004457941744476557,
-0.013588370755314827,
0.03925417363643646,
0.0633419007062912,
-0.019897254183888435,
0.015360790304839611,
-0.08915669471025467,
-0.02855697087943554,
0.014433911070227623,
0.019872406497597694,
-0.03630375489592552,
-0.022745802998542786,
-0.07380589842796326,
0.007231617346405983,
0.02633318305015564,
-0.04380762204527855,
0.014891406521201134,
-0.019631516188383102,
-0.005809890106320381,
-0.04060998931527138,
-0.007154530379921198,
-0.021999236196279526,
-0.004966323729604483,
-0.010253094136714935,
0.024051867425441742,
-0.054613012820482254,
-0.0033141945023089647,
-0.012568637728691101,
0.02107147127389908,
0.009726008400321007,
0.028996573761105537,
-0.014373225159943104,
0.009211848489940166,
-0.019008545204997063,
0.01967238076031208,
-0.031684260815382004,
-0.11058187484741211,
0.016798432916402817,
0.008220798335969448,
0.023128647357225418,
0.026850342750549316,
-0.03604999929666519,
-0.03890078514814377,
0.029308564960956573,
0.03510310873389244,
0.036218710243701935,
0.011081559583544731,
-0.03241845965385437,
0.025529779493808746,
0.06067681312561035,
-0.0281822606921196,
0.020718315616250038,
0.02429724857211113,
-0.020357979461550713,
-0.02320014499127865,
-0.009471888653934002,
0.019325686618685722,
-0.022853463888168335,
-0.025989260524511337,
-0.0020739969331771135,
0.006162306293845177,
-0.03005411848425865,
0.05773131921887398,
-0.04443439468741417,
-0.012304501608014107,
-0.02077745646238327,
0.004730831831693649,
0.019462203606963158,
0.018474634736776352,
-0.01673690229654312,
-0.03677508607506752,
0.008118920028209686,
0.014274055138230324,
0.02749880962073803,
-0.019041048362851143,
0.03459038585424423,
-0.03124941885471344,
-0.012092409655451775,
0.03750450164079666,
-0.019621293991804123,
-0.0020858270581811666,
-0.01857839524745941,
-0.016641251742839813,
-0.014336280524730682,
-0.009491241537034512,
0.03492787852883339,
-0.0003673278843052685,
0.02320113033056259,
-0.010655184276401997,
-0.04792390763759613,
-0.0011325539089739323,
-0.022078288719058037,
0.011676231399178505,
0.024887241423130035,
-0.004889739211648703,
0.05906078964471817,
0.05653540417551994,
0.005080984439700842,
-0.07610239088535309,
-0.08276326954364777,
0.017829827964305878,
-0.025595376268029213,
-0.04242310672998428,
-0.011949571780860424,
-0.011601699516177177,
-0.02720070444047451,
-0.03188600018620491,
0.01978185586631298,
-0.0021631408017128706,
-0.06512705981731415,
-0.010616178624331951,
0.043137118220329285,
0.010916848666965961,
0.02036159858107567,
-0.025082668289542198,
-0.031564563512802124,
0.029522458091378212,
-0.031406138092279434,
0.003398009343072772,
-0.012347742915153503,
0.0299972053617239,
0.00954703614115715,
-0.037956491112709045,
-0.018686845898628235,
-0.01232836488634348,
0.04052680358290672,
0.018832454457879066,
0.03905880078673363,
0.015239022672176361,
0.012463374063372612,
-0.0035047384444624186,
-0.04007032886147499,
0.010824318043887615,
-0.013371317647397518,
0.033108919858932495,
-0.015553067438304424,
0.012630089186131954,
-0.04952116683125496,
-0.03527955710887909,
0.011595195159316063,
-0.015340893529355526,
-0.002916783792898059,
-0.03305603563785553,
0.03940838202834129,
-0.03624800592660904,
-0.009317663498222828,
-0.007094715256243944,
-0.03528209030628204,
0.03512713313102722,
-0.027445634827017784,
-0.0070910160429775715,
0.03630297631025314,
0.03736850619316101,
-0.022425537928938866,
-0.028983954340219498,
-0.06222176551818848,
0.031385283917188644,
0.07304856926202774,
-0.0414370596408844,
0.051521193236112595,
-0.01860363595187664,
-0.03838237747550011,
0.004281461238861084,
-0.022162672132253647,
-0.014158486388623714,
0.0238603875041008,
-0.004774236120283604,
0.04523336514830589,
-0.008765176869928837,
0.025957247242331505,
0.014458410441875458,
0.051564984023571014,
0.001331131556071341,
0.0025159509386867285,
0.02701343037188053,
0.017572641372680664,
0.04351915419101715,
0.028831083327531815,
-0.0606488361954689,
0.0579865500330925,
-0.033551089465618134,
0.022973954677581787,
0.027667896822094917,
0.05119357258081436,
0.05764634907245636,
0.030484991148114204,
0.03237055987119675,
-0.06812643259763718,
0.005069322418421507,
-0.003611577209085226,
0.0047389790415763855,
-0.004287081770598888,
-0.010286318138241768,
0.02529154159128666,
0.026164360344409943,
0.017681604251265526,
-0.011316993273794651,
-0.022283563390374184,
-0.0026857058983296156,
-0.050000980496406555,
-0.018068036064505577,
-0.012540671974420547,
-0.03283701837062836,
0.01895257458090782,
0.006879565306007862,
-0.015014863573014736,
0.009291351772844791,
-0.039053723216056824,
0.022143665701150894,
-0.001419765641912818,
0.015275486744940281,
-0.027369752526283264,
0.08453505486249924,
-0.020490335300564766,
0.04932370036840439,
-0.048628345131874084,
-0.006924745626747608,
0.11068126559257507,
0.028928210958838463,
0.03192046284675598,
-0.09940040111541748,
0.010134929791092873,
0.000658193021081388,
-0.008622810244560242,
-0.0640348345041275,
0.05121273174881935,
0.01835557445883751,
0.0014057389926165342,
0.02370096743106842,
0.04892849177122116,
0.03732322156429291,
0.0375913605093956,
0.0035592836793512106,
-0.04351842775940895,
-0.01859138160943985,
-0.03881758451461792,
-0.016902144998311996,
-0.03785780444741249,
0.010206621140241623,
-0.02208683080971241,
0.01807516999542713,
-0.03221110627055168,
-0.006968893576413393,
-0.043680720031261444,
-0.025946328416466713,
0.011722451075911522,
0.006942382548004389,
-0.0790499672293663,
0.009088775143027306,
-0.019421448931097984,
-0.012002137489616871,
-0.019785312935709953,
0.007925743237137794,
0.02820802479982376,
0.01852617971599102,
-0.00571941863745451,
0.010772478766739368,
-0.010529791004955769,
-0.02909323386847973,
0.003330873791128397,
0.030019644647836685,
-0.035611592233181,
0.009119328111410141,
-0.052145298570394516,
0.05703914165496826,
-0.011720504611730576,
-0.028860609978437424,
-0.00850288849323988,
0.04842047393321991,
0.02656683512032032,
-0.010442406870424747,
-0.02515098825097084,
-0.012776090763509274,
0.005241296254098415,
0.0009140396723523736,
-0.032363977283239365,
-0.011734719388186932,
0.026438070461153984,
-0.017023734748363495,
0.004933027550578117,
-0.04491207003593445,
-0.009425242431461811,
-0.013343984261155128,
-0.00983519572764635,
0.03555028513073921,
0.004751528613269329,
0.0016910264967009425,
-0.05116689205169678,
0.010393033735454082,
-0.03463209047913551,
-0.02007160894572735,
0.0325230248272419,
-0.012521995231509209,
0.026656650006771088,
0.027878288179636,
-0.03281887620687485,
-0.016212154179811478,
-0.053408194333314896,
0.07538018375635147,
-0.005693392362445593,
-0.013862427324056625,
-0.02413320168852806,
-0.002126662526279688,
0.0016114759491756558,
0.04931489750742912,
0.013329618610441685,
-0.000009341246368421707,
-0.010721671395003796,
0.02805442363023758,
-0.018544375896453857,
-0.017755700275301933,
-0.034491654485464096,
-0.015317965298891068,
-0.0447319820523262,
-0.008986594155430794,
0.012077152729034424,
0.0376090407371521,
0.021529242396354675,
0.018248261883854866,
0.03834792599081993,
0.03844992071390152,
0.004202906973659992,
-0.010949446819722652,
0.05995336174964905,
-0.01838298700749874,
0.017427464947104454,
-0.016063034534454346,
0.019707977771759033,
-0.009940959513187408,
-0.013347301632165909,
0.0034517496824264526,
-0.01915735937654972,
0.006580688524991274,
0.005685338284820318,
-0.039389386773109436,
-0.0045946924947202206,
-0.01594782993197441,
0.02538701705634594,
-0.040198151022195816,
-0.048397600650787354,
-0.05439358204603195,
-0.005016754847019911,
-0.012782152742147446,
0.01813008263707161,
-0.007272535003721714,
0.01681390032172203,
-0.000491060724016279,
0.007394723128527403,
-0.005310066509991884,
0.0002891266776714474,
-0.014696451835334301,
0.01152307540178299,
0.05066024512052536,
0.021058090031147003,
0.032780133187770844,
-0.004417767748236656,
-0.025927690789103508,
0.0403895229101181,
-0.028330203145742416,
-0.04768068715929985,
0.0137571319937706,
0.011806321330368519,
0.024280179291963577,
0.030681997537612915,
0.01495498325675726,
-0.054906636476516724,
0.09510406851768494,
0.019347548484802246,
0.015138479880988598,
-0.01847839541733265,
-0.04242845997214317,
0.015083760023117065,
0.011212443932890892,
0.019705593585968018,
-0.009935027919709682,
0.002651795046404004,
0.03190534561872482,
0.05657327547669411,
0.0038021185901015997,
0.0037721635308116674,
0.009025665931403637,
0.016154009848833084,
0.02977973222732544,
-0.003940207418054342,
-0.023030400276184082,
0.04766061529517174,
0.03824930265545845,
-0.00443081883713603,
-0.015416830778121948,
0.006779402960091829,
-0.02039436437189579,
-0.11667519062757492,
-0.015121372416615486,
-0.002058857586234808,
0.021877260878682137,
0.0173057708889246,
-0.04381081834435463,
0.005605932790786028,
0.030248254537582397,
-0.04431837797164917,
-0.013122870586812496,
0.0034585956018418074,
0.021588392555713654,
-0.035860881209373474,
-0.029682761058211327,
-0.01334090530872345,
0.040738485753536224,
0.02933361753821373,
0.012568460777401924,
0.012693056836724281,
0.01961406320333481,
-0.03211557865142822,
0.022166084498167038,
-0.011366253718733788,
0.023708179593086243,
0.0212237685918808,
-0.020507976412773132,
0.08318135887384415,
-0.012566576711833477,
-0.03143962100148201,
0.021129311993718147,
0.009797985665500164,
-0.00026038705254904926,
0.02450018748641014,
0.021656688302755356,
-0.007016843184828758,
-0.010951388627290726,
0.005012840032577515,
0.007093177177011967,
0.03987406566739082,
0.014616299420595169,
0.025821173563599586,
-0.002714532194659114,
0.013516237027943134,
0.009862193837761879,
0.04560088366270065,
-0.010527484118938446,
0.011054247617721558,
0.04898790642619133,
-0.05436433479189873,
-0.011783754453063011,
-0.022937288507819176,
0.006984052713960409,
0.05624726414680481,
-0.003153198165819049,
0.002993618370965123,
-0.0018934888066723943,
-0.0072115506045520306,
0.003019366879016161,
0.04194173961877823,
-0.013372172601521015,
0.028926683589816093,
-0.0022353832609951496,
-0.020365696400403976,
0.007590706925839186,
-0.006555784028023481,
-0.0029075827915221453,
-0.016613265499472618,
-0.015348542481660843,
-0.034680772572755814,
0.019220247864723206,
-0.011242648586630821,
-0.03735293820500374,
-0.025824962183833122,
0.03072601556777954,
0.01471409760415554,
0.03224654495716095,
-0.006152472458779812,
-0.08095335215330124,
-0.02441522292792797,
-0.05151756480336189,
0.02629392221570015,
-0.028446311131119728,
-0.037976425141096115,
-0.02948097325861454,
-0.0490492582321167,
-0.016033902764320374,
-0.00638373801484704,
0.07037580013275146,
0.0481380969285965,
0.01691243425011635,
0.025544488802552223,
0.019366078078746796,
0.03434378653764725,
-0.03010243922472,
0.007940390147268772,
0.009663037955760956,
-0.0031962546054273844,
0.05248849838972092,
-0.015974147245287895,
0.01715303771197796,
0.051184866577386856,
0.045372139662504196,
0.0032421830110251904,
0.029155930504202843,
-0.0060050953179597855,
-0.025642195716500282,
0.0051836916245520115,
-0.013836177065968513,
-0.020492006093263626,
0.052167028188705444,
-0.028369465842843056,
0.0317564383149147,
-0.017552336677908897,
-0.004046290647238493,
-0.016398699954152107,
0.010253483429551125,
-0.02505529671907425,
0.0020409743301570415,
0.002317456528544426,
-0.033896658569574356,
0.028727736324071884,
-0.037475328892469406,
0.02332705818116665,
0.013178532011806965,
-0.0444297157227993,
-0.007627648767083883,
0.08675570040941238,
0.026812445372343063,
0.012420596554875374,
0.0032440326176583767,
0.017501741647720337,
0.005654872395098209,
0.0040871985256671906,
-0.018387900665402412,
0.05369001626968384,
0.02617836743593216,
0.009188980795443058,
0.014657793566584587,
0.015615877695381641,
0.018866926431655884,
0.004669882822781801,
-0.0018008006736636162,
0.02518276683986187,
-0.022528285160660744,
-0.050111643970012665,
0.03488045185804367,
-0.05330934748053551,
-0.0019083399092778563,
0.047856830060482025,
-0.0011208417126908898,
0.10888742655515671,
-0.004374273587018251,
0.015593273565173149,
-0.007767300587147474,
0.010614867322146893,
-0.026566922664642334,
0.00749503867700696,
-0.011950705200433731,
0.052470192313194275,
0.006654240190982819,
0.006570751313120127,
0.021414728835225105,
0.004515591077506542,
0.026542050763964653,
-0.004419813863933086,
0.016159486025571823,
0.021099872887134552,
-0.016409127041697502,
-0.005909672472625971,
0.010629082098603249,
-0.01856072060763836,
-0.0313519649207592,
0.01933610439300537,
0.020678628236055374,
0.00542371766641736,
0.007276578340679407,
-0.019351612776517868,
-0.05271380767226219,
0.02888920158147812,
-0.079042449593544,
-0.027436520904302597,
0.0067763724364340305,
0.0009335531503893435,
-0.022154564037919044,
0.009959339164197445
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.