question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>On calm days, the water in the toilet looks completely still. But when it's rainy and windy out, the water looks like it moves and pulsates. Why is this?</p>
| 8,245 |
[
-0.06219548359513283,
-0.008447575382888317,
-0.01595088094472885,
0.019369857385754585,
0.044265009462833405,
-0.0031685051508247852,
0.006760757882148027,
-0.008342986926436424,
0.0018795874202623963,
-0.007825654931366444,
0.016078822314739227,
0.09102804958820343,
0.006115181837230921,
0.008767703548073769,
0.009350685402750969,
-0.0150855528190732,
0.023166082799434662,
-0.015073532238602638,
-0.014372246339917183,
-0.011631223373115063,
-0.004326643422245979,
-0.011506084352731705,
0.009444699622690678,
0.011281191371381283,
-0.033052198588848114,
0.013191726058721542,
0.03332361578941345,
0.004827504046261311,
0.024832870811223984,
0.020895378664135933,
-0.016191815957427025,
-0.0016171211609616876,
-0.023877007886767387,
0.03306111693382263,
0.02435288019478321,
-0.006282229442149401,
-0.020782971754670143,
-0.004320998676121235,
-0.013368391431868076,
0.04634735733270645,
0.00364512181840837,
-0.03750279173254967,
-0.04271335527300835,
0.03270009160041809,
-0.06356720626354218,
0.007451200392097235,
0.04872964695096016,
0.001504968968220055,
0.0495319664478302,
-0.0499257892370224,
0.04201841354370117,
-0.025089435279369354,
0.01927039586007595,
0.010521030984818935,
-0.011875377036631107,
0.0040107592940330505,
0.07935964316129684,
0.0811670795083046,
-0.03425906226038933,
-0.04641234502196312,
-0.002133465139195323,
0.009160398505628109,
-0.02771133743226528,
-0.020098526030778885,
0.013720756396651268,
-0.0007937658810988069,
-0.0032592983916401863,
-0.038395147770643234,
0.053058963268995285,
-0.0015976836439222097,
-0.0399804525077343,
-0.017059683799743652,
0.05017578974366188,
-0.03763557970523834,
0.0032715387642383575,
-0.031552765518426895,
0.03408662974834442,
0.052657704800367355,
0.029172413051128387,
0.0028581221122294664,
-0.005784468725323677,
0.004014636855572462,
-0.018369272351264954,
0.008820420131087303,
0.014672355726361275,
-0.025680482387542725,
0.07026511430740356,
-0.0011270997347310185,
-0.0018083053873851895,
0.034374941140413284,
0.003329336177557707,
0.0042825075797736645,
-0.004512722138315439,
0.04181800037622452,
0.015787381678819656,
0.018107445910573006,
0.008365115150809288,
0.027745626866817474,
0.03051396645605564,
-0.03531603887677193,
0.0033403874840587378,
-0.01572933793067932,
0.02848588302731514,
0.0635991171002388,
0.024541903287172318,
-0.020785817876458168,
-0.048977941274642944,
0.03525138273835182,
-0.054967839270830154,
0.0028005007188767195,
-0.031177187338471413,
-0.050613537430763245,
-0.002127821557223797,
-0.02007235959172249,
-0.014034000225365162,
-0.034990668296813965,
0.007947620935738087,
-0.012673919089138508,
0.01320387702435255,
0.08487407863140106,
0.007213386707007885,
0.0028829530347138643,
0.014197730459272861,
-0.031251270323991776,
-0.07358445972204208,
0.07667382061481476,
-0.004442599136382341,
-0.039964690804481506,
-0.05166611447930336,
0.03761041909456253,
-0.005335283000022173,
-0.0021789863239973783,
0.02652139961719513,
-0.015279478393495083,
0.033540304750204086,
0.011630764231085777,
-0.11447597295045853,
-0.062037210911512375,
0.03100157156586647,
-0.005960558541119099,
-0.036499179899692535,
-0.06758077442646027,
-0.010783222503960133,
0.06459397077560425,
0.07757008075714111,
-0.02249974198639393,
0.010469915345311165,
0.03727403283119202,
0.031438715755939484,
0.006142812315374613,
-0.03496704623103142,
-0.0013839767780154943,
0.032268837094306946,
-0.02602226287126541,
0.015068063512444496,
-0.048630453646183014,
0.004280839581042528,
0.04271729663014412,
0.008405436761677265,
-0.036265965551137924,
0.03970889374613762,
0.01346698310226202,
-0.022664356976747513,
-0.00713826110586524,
-0.0028813034296035767,
-0.038844965398311615,
0.04760101065039635,
0.018298069015145302,
0.024644626304507256,
0.015264024026691914,
0.001657621469348669,
0.026191983371973038,
-0.006182347424328327,
0.022602392360568047,
0.001514266710728407,
-0.01921207271516323,
-0.005518705118447542,
0.0321400947868824,
0.005989160388708115,
0.011291529051959515,
0.005705462768673897,
-0.005168150179088116,
-0.024710893630981445,
0.04389439895749092,
-0.011329984292387962,
0.02699742093682289,
-0.03055337257683277,
-0.043220024555921555,
0.012089397758245468,
-0.07788125425577164,
0.015818214043974876,
-0.060950055718421936,
0.01631474867463112,
-0.022418484091758728,
0.02769727259874344,
0.005762537010014057,
0.017548419535160065,
0.00470343604683876,
-0.015224017202854156,
0.025048358365893364,
0.031021108850836754,
0.021352190524339676,
0.007104677613824606,
-0.021307168528437614,
-0.013492329977452755,
0.03197784721851349,
0.02421705611050129,
-0.0018071987433359027,
0.013117752969264984,
-0.0052164457738399506,
-0.005215918645262718,
-0.007384241092950106,
-0.025041058659553528,
0.004569611512124538,
-0.03477595001459122,
-0.03822580352425575,
0.009855628944933414,
0.0012908827047795057,
0.040983233600854874,
0.0029924509581178427,
-0.014895947650074959,
0.05169334262609482,
0.06329696625471115,
-0.05798901617527008,
0.025390027090907097,
0.015295689925551414,
-0.01316365972161293,
-0.010330363176763058,
0.01583987846970558,
-0.04384758323431015,
-0.018083954229950905,
-0.029300082474946976,
0.00956274475902319,
0.023558560758829117,
0.018207496032118797,
0.02210863307118416,
0.013046861626207829,
0.053725145757198334,
0.004090277478098869,
0.04014518857002258,
0.04636571928858757,
-0.007157820276916027,
0.001277677365578711,
0.004072218202054501,
0.02128358744084835,
0.04175422713160515,
0.03987560421228409,
0.0065592811442911625,
0.027659021317958832,
-0.04111773893237114,
-0.04586545377969742,
-0.0005096904933452606,
-0.019846685230731964,
0.026902444660663605,
-0.039033930748701096,
-0.04281780123710632,
0.013925918377935886,
-0.027145082131028175,
-0.03894480690360069,
-0.00019151806191075593,
0.010408188216388226,
0.022590333595871925,
-0.01786929927766323,
-0.013093006797134876,
0.004436589311808348,
0.010476440191268921,
-0.012357727624475956,
-0.015978367999196053,
0.03973586857318878,
-0.048151396214962006,
0.032363735139369965,
-0.048287518322467804,
0.0006665326072834432,
-0.012988709844648838,
0.008309774100780487,
0.05497899278998375,
0.025469675660133362,
0.043871428817510605,
-0.01658002845942974,
-0.057634107768535614,
0.019263816997408867,
-0.01633039303123951,
-0.04086653143167496,
-0.010478352196514606,
-0.048563435673713684,
0.04825141653418541,
0.03208291530609131,
-0.018770264461636543,
0.05649864301085472,
-0.007070018909871578,
0.010977049358189106,
-0.002782310824841261,
-0.005251706577837467,
-0.03499723970890045,
-0.016087321564555168,
-0.059804998338222504,
0.029580067843198776,
-0.0012728049186989665,
-0.020959412679076195,
0.052430275827646255,
-0.013080150820314884,
-0.03029397502541542,
0.03727762773633003,
-0.0025489316321909428,
-0.03902990743517876,
0.012115838006138802,
-0.006549591198563576,
0.018551113083958626,
-0.02855631336569786,
-0.02240559086203575,
0.008314784616231918,
-0.043106235563755035,
-0.00005090137346996926,
-0.02706451527774334,
-0.0506938211619854,
0.0036400642711669207,
0.011199881322681904,
0.07656112313270569,
0.00426959153264761,
-0.046441640704870224,
0.029283886775374413,
-0.000030504790629493073,
-0.037142567336559296,
-0.012396808713674545,
-0.025342417880892754,
-0.03542446717619896,
-0.06023189797997475,
0.011406873352825642,
0.08538304269313812,
0.018576309084892273,
0.04077146202325821,
0.009026087820529938,
0.005363999400287867,
0.034365903586149216,
0.014108872041106224,
-0.03608274832367897,
-0.04264633730053902,
-0.0032027901615947485,
-0.010652030818164349,
-0.00749983498826623,
-0.016184041276574135,
-0.030248580500483513,
-0.01023946050554514,
-0.020010199397802353,
-0.012834767811000347,
0.045520294457674026,
-0.01359959039837122,
0.06415652483701706,
-0.015682360157370567,
0.002546718344092369,
-0.057778894901275635,
0.034135233610868454,
-0.025538498535752296,
0.00919031910598278,
-0.03788710758090019,
-0.03502826765179634,
0.054413191974163055,
0.009259848855435848,
-0.004024861846119165,
0.039682384580373764,
0.04265257343649864,
-0.00662331935018301,
-0.027057550847530365,
0.011325147934257984,
-0.01819142885506153,
0.05702994391322136,
-0.0356106273829937,
-0.010038339532911777,
0.09646470099687576,
-0.029117537662386894,
-0.0037547305691987276,
0.017193734645843506,
-0.04923154413700104,
0.002866971306502819,
-0.04037317633628845,
0.007223749067634344,
0.03793326020240784,
0.025625497102737427,
0.013806075789034367,
0.04830266907811165,
0.004531004466116428,
0.01969706267118454,
-0.005890746600925922,
-0.018999049440026283,
-0.03404278680682182,
-0.004235728643834591,
-0.01787584461271763,
0.006444670259952545,
-0.02292361855506897,
-0.019485415890812874,
-0.0458281971514225,
-0.03126305341720581,
-0.019251449033617973,
0.0022215137723833323,
-0.0054822382517158985,
-0.01475326344370842,
0.02234552428126335,
-0.018493080511689186,
-0.04248485341668129,
-0.016952326521277428,
0.02009943686425686,
-0.020169690251350403,
-0.0018326343270018697,
0.03209235891699791,
0.0191664919257164,
-0.0026634824462234974,
0.015438464470207691,
-0.02085673250257969,
-0.01340715866535902,
0.015547617338597775,
0.011367393657565117,
0.02965393103659153,
-0.0031788269989192486,
-0.014685118570923805,
0.004369757138192654,
0.007161782123148441,
0.018216894939541817,
-0.013376621529459953,
0.007963686250150204,
-0.025636954233050346,
0.006873039528727531,
-0.000853681587614119,
0.01351896021515131,
0.017911454662680626,
-0.006916576996445656,
0.007370103616267443,
-0.027619464322924614,
0.00910788495093584,
-0.013076270930469036,
0.030315203592181206,
0.04748483747243881,
0.013097363524138927,
0.009104426950216293,
-0.04469899460673332,
0.025797508656978607,
-0.013943647965788841,
0.004409074783325195,
-0.0027845846489071846,
0.022150075063109398,
-0.007479493040591478,
0.02959546260535717,
0.020801348611712456,
-0.010469619184732437,
-0.003699276363477111,
-0.019178779795765877,
0.023458827286958694,
0.003476220415905118,
-0.031856682151556015,
0.03243502601981163,
0.013857852667570114,
0.05724668875336647,
0.03224228695034981,
0.008118762634694576,
-0.03735627233982086,
-0.07970334589481354,
-0.010548191145062447,
0.05633314326405525,
0.014963682740926743,
-0.02898944355547428,
-0.0318550206720829,
-0.0963289886713028,
-0.04400677978992462,
0.03317930921912193,
-0.014120849780738354,
-0.010808514431118965,
-0.000799219124019146,
-0.012448280118405819,
-0.018284913152456284,
-0.01509884838014841,
-0.007049176841974258,
0.012278921902179718,
-0.025177698582410812,
0.021445777267217636,
-0.00966652948409319,
-0.010460604913532734,
-0.03228183835744858,
0.034945450723171234,
0.0024699787609279156,
0.012913449667394161,
0.021119000390172005,
0.03392612934112549,
-0.02120065502822399,
0.019576124846935272,
-0.06814102828502655,
-0.06855031847953796,
0.023376798257231712,
0.011714142747223377,
-0.004409280139952898,
0.06089427322149277,
-0.02528253197669983,
-0.008329760283231735,
-0.02961784414947033,
-0.026177382096648216,
-0.017158063128590584,
0.004061697516590357,
-0.05121041089296341,
0.007309108041226864,
0.0053319176658988,
0.008294763043522835,
0.02523929998278618,
0.03509381413459778,
-0.024744944646954536,
-0.04247719794511795,
0.013536324724555016,
0.05570994317531586,
-0.05778952315449715,
-0.01660037972033024,
-0.0046612233854830265,
-0.01582294888794422,
-0.04655676335096359,
0.07314661890268326,
0.009369893930852413,
0.02306097373366356,
0.030052481219172478,
-0.011402792297303677,
-0.03742289915680885,
0.03562223166227341,
0.03543808311223984,
-0.028432507067918777,
0.026583874598145485,
-0.0003097910957876593,
0.011350646615028381,
-0.031150387600064278,
0.024199046194553375,
-0.03479240834712982,
0.01743522472679615,
0.05809051916003227,
-0.0023979574907571077,
0.00987935345619917,
-0.04650989919900894,
-0.015683036297559738,
0.04562553018331528,
-0.003196078585460782,
0.03497626259922981,
-0.019428392872214317,
0.0022724876180291176,
0.05165122076869011,
-0.05483052134513855,
0.002427118830382824,
0.021593935787677765,
-0.008128581568598747,
0.02244015410542488,
-0.026162676513195038,
0.042858123779296875,
0.04751012101769447,
0.015219009481370449,
-0.045339155942201614,
-0.06484347581863403,
0.057557012885808945,
0.040448036044836044,
-0.0210000928491354,
-0.026278268545866013,
0.006171911954879761,
-0.019925301894545555,
-0.038179509341716766,
-0.013742188923060894,
-0.011882299557328224,
-0.019643915817141533,
0.020635467022657394,
-0.00017716824368108064,
0.01283955853432417,
0.06968960165977478,
-0.015932196751236916,
0.03278658166527748,
0.003970571327954531,
-0.08104761689901352,
-0.028915729373693466,
-0.021545011550188065,
0.05318588763475418,
-0.01493151392787695,
-0.017245052382349968,
0.020663682371377945,
-0.00855332612991333,
0.045779380947351456,
-0.015246348455548286,
0.012919759377837181,
0.0266487505286932,
0.03471233695745468,
0.009611659683287144,
-0.005508290138095617,
0.02290673553943634,
-0.006258821114897728,
0.045302681624889374,
0.005526342894881964,
-0.006061696447432041,
0.010038685984909534,
-0.03836148604750633,
0.01050700806081295,
0.022973190993070602,
-0.06691253185272217,
-0.00469661969691515,
0.06537428498268127,
-0.036003708839416504,
0.013421728275716305,
0.01540707889944315,
0.005890827160328627,
0.03820740804076195,
0.03477191925048828,
-0.001924669835716486,
0.013547463342547417,
0.02018657885491848,
-0.021406902000308037,
-0.02572164684534073,
-0.03260468319058418,
-0.01170100923627615,
0.02539726532995701,
-0.055892474949359894,
0.044999074190855026,
0.011159922927618027,
-0.005335698369890451,
0.004422313999384642,
0.002220845315605402,
-0.02724812738597393,
0.016548004001379013,
-0.015312770381569862,
0.031067267060279846,
-0.014567410573363304,
-0.0066810958087444305,
0.009983510710299015,
0.05826755240559578,
0.03444715589284897,
0.03643428161740303,
0.04471764340996742,
0.01424141600728035,
-0.0033170594833791256,
-0.007574738468974829,
-0.0625745952129364,
0.022716622799634933,
-0.006783088203519583,
0.04431351646780968,
0.014242655597627163,
-0.03915529325604439,
0.025460943579673767,
-0.006026408635079861,
-0.033956378698349,
-0.05243837833404541,
0.014792348258197308,
-0.046861711889505386,
-0.0157975722104311,
0.01519787311553955,
0.031370121985673904,
-0.00790775939822197,
0.012417570687830448,
0.016954174265265465,
0.002039185957983136,
-0.0011028751032426953,
-0.0334618054330349,
-0.03201161324977875,
0.0062157148495316505,
-0.026957593858242035,
-0.02138681150972843,
0.034145891666412354,
-0.034826550632715225,
-0.03179461508989334,
0.015829255804419518,
-0.03319893404841423,
0.008238072507083416,
-0.0160761047154665,
0.005588619504123926,
-0.01045234128832817,
0.028864393010735512,
-0.009434167295694351,
-0.022404445335268974,
-0.00025935316807590425,
0.02085566148161888,
0.15081539750099182,
0.005667983088642359,
0.03039209358394146,
-0.038687948137521744,
0.012278239242732525,
0.003295067697763443,
0.005482698790729046,
-0.024740222841501236,
0.025028130039572716,
0.021290212869644165,
0.04811255633831024,
0.016046611592173576,
0.044032420963048935,
0.028330912813544273,
0.004197805188596249,
0.04003207013010979,
-0.0351228304207325,
-0.011938107199966908,
0.012329308316111565,
0.007616567425429821,
-0.026314184069633484,
0.028079232200980186,
-0.05288549140095711,
0.06030292436480522,
-0.012003730982542038,
-0.00021199206821620464,
-0.01616096682846546,
-0.06173093616962433,
0.017875496298074722,
0.00010171148460358381,
-0.07508246600627899,
0.06174490228295326,
0.013573057018220425,
-0.02141282707452774,
-0.034732695668935776,
0.06527004390954971,
0.03209105134010315,
-0.046991121023893356,
0.028414778411388397,
-0.022325176745653152,
0.02723117545247078,
-0.002319863298907876,
-0.028050629422068596,
0.0033132024109363556,
-0.027980998158454895,
0.010044539347290993,
-0.04280439764261246,
0.002585342153906822,
0.053367651998996735,
0.005657361354678869,
-0.018349405378103256,
0.008693479001522064,
-0.01746656745672226,
-0.08060672134160995,
-0.024417588487267494,
-0.004926049616187811,
0.006117629818618298,
-0.0036450971383601427,
-0.04505165293812752,
-0.020999187603592873,
-0.004070657305419445,
0.016230033710598946,
-0.0041479445062577724,
-0.007730541750788689,
-0.01712982915341854,
-0.004566356539726257,
0.018933340907096863,
0.024538321420550346,
0.009217238053679466,
0.016956035047769547,
0.0024162367917597294,
-0.01419826690107584,
-0.021865908056497574,
-0.02848237007856369,
0.015110352076590061,
0.012450739741325378,
0.01591639034450054,
0.04257258400321007,
-0.04471322149038315,
-0.011705239303410053,
-0.06949684768915176,
0.05256402865052223,
-0.0023671442177146673,
-0.005001037381589413,
-0.028581691905856133,
-0.01371725182980299,
0.03546178713440895,
0.020138872787356377,
-0.006454128306359053,
0.001853113528341055,
-0.010480240918695927,
0.057615261524915695,
-0.008364652283489704,
-0.028022829443216324,
0.00009227779082721099,
0.010131903924047947,
0.026456108316779137,
-0.0014308312674984336,
-0.00963803380727768,
0.03670336678624153,
0.039853427559137344,
0.022795064374804497,
-0.018789764493703842,
0.022996170446276665,
-0.026310492306947708,
-0.017966093495488167,
0.0305223036557436,
-0.019299374893307686,
-0.04821440204977989,
0.01017867773771286,
0.009167023934423923,
-0.027564220130443573,
-0.024753965437412262,
-0.05464674159884453,
0.0003195689932908863,
-0.012546604499220848,
0.024691889062523842,
0.003014089772477746,
0.019997477531433105,
-0.020000388845801353,
0.052139099687337875,
-0.03570921719074249,
-0.0378626249730587,
-0.10809846222400665,
-0.010630072094500065,
0.01655975729227066,
-0.025931281968951225,
-0.033624935895204544,
0.03611225262284279,
-0.039675869047641754,
-0.03519095480442047,
0.012970074079930782,
0.009608558379113674,
0.004418145399540663,
0.06329919397830963,
0.08536592870950699,
-0.006195873953402042,
0.04957731068134308,
-0.0156821571290493,
-0.05679357424378395,
0.045188140124082565,
-0.03122059628367424,
-0.04389084130525589,
0.04276536405086517,
-0.013044842518866062,
0.00914000440388918,
0.023763781413435936,
-0.02499798685312271,
0.035698819905519485,
0.04535950347781181,
-0.03388117626309395,
0.006623321212828159,
-0.018238384276628494,
0.023429786786437035,
0.024815788492560387,
-0.009947742335498333,
0.02048874832689762,
-0.015326154418289661,
-0.03935050219297409,
0.0673288106918335,
0.03634943440556526,
0.02686861902475357,
0.0048804800026118755,
-0.03478618338704109,
-0.054812148213386536,
0.02702927030622959,
-0.007709190249443054,
0.022116566076874733,
0.004792788531631231,
0.003173526842147112,
-0.03860928490757942,
-0.010143782943487167,
-0.023189203813672066,
0.006606162991374731,
-0.10994645953178406,
0.06870797276496887,
-0.02291017584502697,
-0.008367901667952538,
0.048119235783815384,
-0.019514886662364006,
0.0035265800543129444,
0.05503615736961365,
-0.04207305982708931,
-0.0162116140127182,
-0.024904191493988037,
-0.013831921853125095,
-0.04618353769183159,
0.040472738444805145,
-0.003917742054909468,
0.056536052376031876,
0.048393189907073975,
0.008654777891933918,
0.0004331907257437706,
0.03846925124526024,
0.019599169492721558,
0.01597246155142784,
0.00003301863762317225,
0.035284969955682755,
0.009923836216330528,
0.02247666008770466,
0.041270479559898376,
-0.027428727596998215,
-0.015322046354413033,
0.031075017526745796,
-0.06336977332830429,
-0.0008212149259634316,
-0.023511726409196854,
0.0058312611654400826,
0.006355618126690388,
0.006893624551594257,
0.027248330414295197,
0.00720315333455801,
-0.022060787305235863,
0.008219849318265915,
0.018824299797415733,
0.0567430779337883,
0.014637633226811886,
-0.010340397246181965,
-0.017990881577134132,
-0.039512794464826584,
-0.048668526113033295,
-0.007421091198921204,
-0.021051837131381035,
-0.011513478122651577,
0.021143632009625435,
-0.010038656182587147,
0.028351686894893646,
0.003757164813578129,
-0.01097631175071001,
-0.03093409165740013,
0.03825407847762108,
-0.0013643469428643584,
-0.0031807217746973038,
-0.02425924502313137,
0.05385652929544449,
0.01941021904349327,
-0.02670181356370449,
-0.026963086798787117,
0.00008689548121765256,
-0.011452004313468933,
-0.027014335617423058,
-0.021769719198346138,
-0.012140507809817791,
0.007192614953964949,
-0.0017825181130319834,
-0.013748399913311005,
-0.012986033223569393,
0.032318949699401855,
0.015060651116073132,
0.01816224865615368,
0.03965652361512184,
-0.05583338439464569,
-0.04462302848696709,
-0.06390748172998428,
0.04811741039156914,
0.023964431136846542,
-0.020852968096733093,
-0.04019004851579666,
0.014654100872576237,
-0.03498942777514458,
0.06038981303572655,
0.0396733433008194,
0.013949038460850716,
0.0028827369678765535,
0.029659420251846313,
-0.006976919714361429,
0.011781731620430946,
-0.02810930274426937,
-0.024242829531431198,
-0.030322188511490822,
-0.04335006698966026,
0.034426603466272354,
-0.01091025024652481,
0.026515673846006393,
-0.0022633906919509172,
0.037711840122938156,
-0.00020902561664115638,
0.04380304366350174,
0.00933577585965395,
-0.006919751409441233,
0.03606313094496727,
0.013486380688846111,
-0.05085373297333717,
0.07864993065595627,
0.0025630472227931023,
0.006506360601633787,
0.006880317814648151,
-0.013248423114418983,
-0.03206560015678406,
0.04049431160092354,
0.016232963651418686,
0.02764364518225193,
0.021772071719169617,
-0.054067205637693405,
0.014413842000067234,
-0.0645899698138237,
0.03789542615413666,
0.006221410818397999,
-0.03850702941417694,
0.003831378184258938,
0.042910728603601456,
0.005413773003965616,
-0.01171048078685999,
0.004488059319555759,
0.0031248610466718674,
0.04243021830916405,
0.011729005724191666,
-0.01658935286104679,
0.044999439269304276,
0.019864454865455627,
0.013866275548934937,
0.009160496294498444,
0.021423056721687317,
0.006732584442943335,
0.02284267172217369,
0.013922291807830334,
0.0451154001057148,
0.015746504068374634,
-0.045518387109041214,
-0.021759608760476112,
-0.026908235624432564,
-0.011965986341238022,
0.0013040037592872977,
0.0013186136493459344,
0.07124456763267517,
-0.01047094538807869,
-0.0025802254676818848,
-0.01558848936110735,
0.019391896203160286,
-0.0033239959739148617,
0.00005417958527687006,
0.03049341030418873,
0.009337354451417923,
0.039448898285627365,
-0.009160330519080162,
-0.03598204627633095,
0.014854599721729755,
-0.016180193051695824,
-0.02621527947485447,
0.022404512390494347,
-0.022153060883283615,
0.022995857521891594,
-0.012498361058533192,
-0.007842843420803547,
-0.02362186461687088,
-0.045210063457489014,
0.031069805845618248,
-0.023777203634381294,
0.030932923778891563,
0.0027710027061402798,
-0.04413016512989998,
-0.019702550023794174,
0.06381046772003174,
-0.08603034913539886,
-0.010711886920034885,
0.02237844094634056,
0.00788758136332035,
0.0083768917247653,
-0.028860826045274734
] |
<p>I heard a saying that <a href="http://en.wikipedia.org/wiki/Exotic_R4" rel="nofollow">$\mathbb{R}^4$</a> having infinitely many differential structures which are not diffeomorphic to each other has a relationship with Yang-Mills field. Does anyone can explain it, and give me some references.</p>
| 8,246 |
[
0.021001815795898438,
-0.007888464257121086,
0.023336181417107582,
-0.03304024040699005,
0.006954611744731665,
0.028921164572238922,
-0.007911949418485165,
0.001913275569677353,
-0.01060287281870842,
-0.07225213199853897,
-0.02867778018116951,
0.017646869644522667,
0.06420191377401352,
-0.000690567132551223,
-0.018604839220643044,
0.0034133719746023417,
0.005164477974176407,
0.01040088664740324,
0.004729221574962139,
-0.03162198141217232,
0.01887628622353077,
0.015692293643951416,
-0.019402803853154182,
-0.01983286812901497,
-0.004154456779360771,
0.02630235254764557,
-0.011795046739280224,
0.007204335182905197,
-0.018532833084464073,
0.034453604370355606,
0.013785993680357933,
-0.004885427188128233,
0.032214514911174774,
0.01955893449485302,
0.02542075142264366,
0.01345193199813366,
-0.019737135618925095,
0.0021972369868308306,
-0.008355305530130863,
0.0090398658066988,
-0.034693945199251175,
-0.05683498829603195,
-0.021177085116505623,
0.06780005991458893,
-0.012394004501402378,
0.0245890524238348,
0.004895905032753944,
-0.023640673607587814,
0.09144490212202072,
-0.023780932649970055,
0.08858508616685867,
0.009588785469532013,
0.011731366626918316,
0.0072137583047151566,
0.026295296847820282,
0.013357575051486492,
0.03144311159849167,
0.051294922828674316,
-0.04553766921162605,
-0.04073091223835945,
-0.06470748782157898,
-0.019066790118813515,
0.0038417938631027937,
-0.02754947729408741,
-0.03629939630627632,
0.0394173301756382,
0.00940997339785099,
0.008356100879609585,
0.0184326209127903,
-0.04038097336888313,
0.0023373132571578026,
0.006886642891913652,
0.026326892897486687,
-0.020437145605683327,
0.013334742747247219,
0.008975156582891941,
-0.007607754319906235,
-0.007690550293773413,
-0.010842949151992798,
0.01270383596420288,
0.0022754345554858446,
0.018692413344979286,
0.001627066871151328,
0.0038705263286828995,
0.03297528624534607,
-0.018525853753089905,
0.041784800589084625,
0.006071262527257204,
0.011372256092727184,
0.07150182127952576,
0.0038940527010709047,
-0.004015833139419556,
0.05702914297580719,
-0.01198116410523653,
-0.043417200446128845,
0.03858112171292305,
0.02212865650653839,
0.048368919640779495,
-0.021689221262931824,
-0.03434066101908684,
-0.023051545023918152,
-0.032381877303123474,
-0.0060696532018482685,
0.07383919507265091,
0.0029574036598205566,
-0.006955376360565424,
-0.04382411390542984,
0.009125306271016598,
-0.03601836413145065,
0.009526395238935947,
-0.02209887094795704,
0.04041370376944542,
-0.007904872298240662,
-0.023630082607269287,
-0.016227131709456444,
-0.03326229751110077,
-0.005945609416812658,
0.012177296914160252,
0.012969113886356354,
0.09246364235877991,
0.03721074387431145,
-0.046967972069978714,
0.026737423613667488,
-0.016390016302466393,
-0.03952477127313614,
0.036294542253017426,
0.06601332128047943,
-0.021114427596330643,
0.012083927169442177,
-0.012346412986516953,
0.037585895508527756,
0.0006341539556160569,
-0.0320841483771801,
0.02413928136229515,
0.027251435443758965,
-0.019725553691387177,
-0.07037831097841263,
-0.043010272085666656,
0.05100201442837715,
0.005738495383411646,
-0.003478357568383217,
-0.06029760465025902,
0.020196879282593727,
-0.006421156693249941,
0.08229237049818039,
-0.011008581146597862,
0.012666761875152588,
0.03153292462229729,
0.02501291036605835,
0.00026571081252768636,
0.0032465383410453796,
-0.005768397822976112,
-0.023381289094686508,
-0.06899505853652954,
-0.026493193581700325,
-0.06924071162939072,
0.031174272298812866,
0.014982231892645359,
0.01714318059384823,
-0.0010660814587026834,
0.03389821946620941,
0.00445000221952796,
0.013629424385726452,
0.06267723441123962,
0.0035990187898278236,
-0.027913426980376244,
0.0610409677028656,
-0.03754470869898796,
0.028722086921334267,
0.033261992037296295,
-0.03248274698853493,
0.04325084388256073,
-0.004305571783334017,
0.08402187377214432,
0.0285413209348917,
-0.008659164421260357,
-0.003152254270389676,
-0.0037833680398762226,
0.005153011530637741,
0.0021049214992672205,
-0.05887901782989502,
-0.030044550076127052,
-0.0019632582552731037,
-0.003493714379146695,
0.0027307551354169846,
0.04500652849674225,
0.01590922474861145,
-0.01811286062002182,
0.02170179784297943,
-0.05755911022424698,
-0.00355965131893754,
-0.03852539509534836,
0.011436893604695797,
-0.017409028485417366,
-0.012679179199039936,
-0.0020856731571257114,
0.017966855317354202,
-0.007379957940429449,
-0.028714116662740707,
-0.00791239645332098,
-0.01972648873925209,
0.006675816606730223,
0.028325095772743225,
0.004410984460264444,
0.009649009443819523,
0.021916670724749565,
0.022259879857301712,
-0.0036570546217262745,
0.05921695753931999,
-0.037730321288108826,
-0.0204075388610363,
0.015094616450369358,
-0.02220875956118107,
0.02907363511621952,
-0.002102307975292206,
-0.023995868861675262,
0.019746460020542145,
0.005432730540633202,
-0.021320601925253868,
0.05038157105445862,
-0.05937005579471588,
0.05365792661905289,
0.020992066711187363,
0.032158926129341125,
-0.004990202374756336,
0.03988701477646828,
0.012679534032940865,
0.018696589395403862,
-0.026136403903365135,
-0.04250681772828102,
-0.03802097216248512,
-0.002172661479562521,
0.03609619662165642,
0.041376836597919464,
-0.04372033104300499,
0.00855859462171793,
0.0006812004139646888,
0.09197033941745758,
-0.004962639417499304,
0.030067041516304016,
-0.026264118030667305,
-0.019592761993408203,
0.041420917958021164,
-0.007526869885623455,
0.0171520933508873,
0.019407764077186584,
0.020944062620401382,
0.006420988589525223,
0.01255022082477808,
-0.017756152898073196,
-0.027806181460618973,
0.05778328701853752,
-0.03363047540187836,
0.022042371332645416,
0.024709666147828102,
0.001965033123269677,
0.06260872632265091,
-0.023550504818558693,
0.03902913257479668,
0.04808742552995682,
-0.011369767598807812,
0.013015415519475937,
-0.0034461747854948044,
-0.004696985706686974,
0.009962978772819042,
-0.0010080857900902629,
-0.043704044073820114,
-0.03957530856132507,
0.024608232080936432,
-0.04864675924181938,
-0.014581166207790375,
-0.01268333662301302,
-0.06005808338522911,
-0.05273965746164322,
0.00927349366247654,
0.013241928070783615,
0.05153600499033928,
0.030447186902165413,
-0.01809781603515148,
-0.035687051713466644,
0.05585690960288048,
-0.034187138080596924,
-0.02471400983631611,
0.018637949600815773,
-0.03835369646549225,
0.0268736332654953,
-0.03834741190075874,
-0.004547731019556522,
0.05305759236216545,
-0.027072038501501083,
0.019034288823604584,
-0.004094347823411226,
-0.0002107149630319327,
-0.005438864231109619,
-0.011392579413950443,
0.003731884527951479,
0.01166284829378128,
-0.021333947777748108,
-0.034074071794748306,
0.03623426333069801,
-0.028259441256523132,
-0.008967647328972816,
-0.001448582741431892,
-0.06853727996349335,
-0.025370514020323753,
0.025120966136455536,
0.00499158538877964,
0.006903636734932661,
-0.0027494998648762703,
0.046693816781044006,
-0.03004808910191059,
-0.04165865480899811,
-0.00411391444504261,
-0.05515819415450096,
-0.06899227946996689,
0.021280275657773018,
0.025242790579795837,
0.009165054187178612,
0.03372114896774292,
-0.04952142387628555,
0.07888390123844147,
0.021655600517988205,
-0.025468729436397552,
-0.02410746179521084,
-0.01715775951743126,
-0.010308793745934963,
-0.024933530017733574,
0.029539817944169044,
0.01903119683265686,
-0.009100453928112984,
-0.0020321295596659184,
0.057511281222105026,
0.029745319858193398,
-0.0037737905513495207,
-0.018407031893730164,
-0.008043264970183372,
-0.00664007430896163,
0.01629002019762993,
-0.028060300275683403,
0.04265328869223595,
0.011771215125918388,
-0.018948767334222794,
-0.022240761667490005,
0.007651244290173054,
0.031929753720760345,
0.028404757380485535,
-0.05578005313873291,
0.04250611737370491,
0.005948470905423164,
0.006576686166226864,
0.024009961634874344,
0.03855961188673973,
0.004963372368365526,
-0.033722613006830215,
0.0064003667794167995,
0.026760585606098175,
0.03639909625053406,
-0.02108638547360897,
-0.00350549747236073,
-0.0029857880435884,
0.011441200040280819,
-0.05006779357790947,
0.023389512673020363,
-0.05170467495918274,
0.006986699998378754,
0.03019656613469124,
-0.005798657890409231,
-0.016226835548877716,
0.04223113879561424,
0.017402077093720436,
0.0026296060532331467,
0.01390526257455349,
-0.012847630307078362,
0.04334982857108116,
-0.06288657337427139,
0.02254589833319187,
-0.03070610575377941,
0.030774960294365883,
0.005357894115149975,
-0.0035031288862228394,
0.015705911442637444,
0.012959637679159641,
0.013854102231562138,
-0.011373652145266533,
-0.07516995072364807,
0.017229624092578888,
-0.01514313742518425,
0.01476278342306614,
-0.03628752380609512,
-0.040268901735544205,
0.044098176062107086,
0.03693254292011261,
-0.08116953074932098,
-0.016595695167779922,
-0.021399687975645065,
-0.08770865201950073,
0.04984736070036888,
-0.03894009068608284,
-0.048666421324014664,
-0.028193728998303413,
0.03821546956896782,
0.06823240220546722,
-0.021620575338602066,
-0.013546965084969997,
0.009693516418337822,
-0.028719587251544,
-0.02397211268544197,
-0.006148187443614006,
0.014117494225502014,
-0.000620901002548635,
0.040634915232658386,
-0.007023883517831564,
0.01921752654016018,
-0.0018290620064362884,
0.006882667075842619,
0.020131269469857216,
0.03344530984759331,
-0.007020866498351097,
-0.011859865859150887,
-0.012515646405518055,
-0.04044774919748306,
0.022594476118683815,
-0.0012894487008452415,
0.051066309213638306,
0.02043522521853447,
0.002603237982839346,
0.024239668622612953,
0.022874537855386734,
-0.005679014604538679,
-0.017477981746196747,
0.020541774109005928,
0.018022501841187477,
-0.04766715317964554,
-0.04184303432703018,
0.02577252872288227,
-0.0038291967939585447,
0.026176434010267258,
-0.002833861857652664,
-0.00660510640591383,
-0.03706779330968857,
0.014004460535943508,
0.0190016720443964,
-0.01611277274787426,
-0.0019589783623814583,
-0.01614113710820675,
-0.034561313688755035,
0.0021010723430663347,
-0.021925322711467743,
-0.016417590901255608,
-0.008562130853533745,
0.06722111254930496,
0.07357852160930634,
0.022947877645492554,
-0.022335756570100784,
-0.09990435093641281,
0.013477024622261524,
0.03652690351009369,
0.025647960603237152,
-0.006145121064037085,
0.01930290088057518,
-0.03326807916164398,
0.030603719875216484,
0.034326765686273575,
0.006490260362625122,
0.01947479322552681,
-0.028934400528669357,
-0.02379555255174637,
-0.025519177317619324,
0.0041828397661447525,
0.009372493252158165,
0.008535935543477535,
-0.023793010041117668,
0.01277730893343687,
-0.010127877816557884,
0.026749948039650917,
-0.0287320613861084,
0.01795821078121662,
0.016179891303181648,
0.04235979914665222,
0.06373829394578934,
0.005799067206680775,
0.0005818819627165794,
0.03732332959771156,
-0.028888029977679253,
-0.029476303607225418,
0.018521495163440704,
0.00026111199986189604,
-0.032717835158109665,
0.0632425993680954,
-0.06845716387033463,
0.0016736203106120229,
0.009670328348875046,
0.02908727340400219,
0.04353459179401398,
0.03225383907556534,
-0.03993122652173042,
-0.014745933003723621,
0.03420666977763176,
0.023162996396422386,
0.04053542762994766,
0.04125453159213066,
0.001948042307049036,
0.00250208075158298,
0.014947718940675259,
0.05464846268296242,
-0.0382109098136425,
-0.0183695200830698,
-0.003868137951940298,
-0.00041897810297086835,
-0.03787515312433243,
0.037526752799749374,
-0.04453688859939575,
0.015052241273224354,
-0.011368698440492153,
-0.03715719282627106,
-0.008884110487997532,
0.0046961503103375435,
0.01937936618924141,
-0.08386766165494919,
-0.028289368376135826,
0.044577062129974365,
0.010650682263076305,
0.0029882437083870173,
0.002815634710714221,
-0.005653007421642542,
-0.014698791317641735,
0.031014280393719673,
0.00541424797847867,
0.018712254241108894,
-0.03046524152159691,
-0.003641546005383134,
0.0343976654112339,
-0.04817313328385353,
-0.001766982371918857,
-0.008404913358390331,
-0.019303159788250923,
0.041900668293237686,
-0.05422482267022133,
-0.017745424062013626,
-0.035157542675733566,
-0.01568652130663395,
0.008856160566210747,
-0.04404303804039955,
0.00043099457980133593,
-0.02323824167251587,
-0.002177616348490119,
-0.0762384682893753,
-0.04161506146192551,
0.04443054646253586,
0.00903381034731865,
-0.02236712910234928,
-0.03418075665831566,
-0.0027077787090092897,
-0.07133883982896805,
-0.04459246248006821,
0.010874437168240547,
0.04878463223576546,
-0.05830507352948189,
0.012994817458093166,
0.04179970175027847,
0.027903128415346146,
0.04241012781858444,
0.00472512049600482,
-0.021836884319782257,
0.0427531935274601,
0.010095752775669098,
0.00405854219570756,
-0.024593105539679527,
0.018778620287775993,
-0.007960965856909752,
0.01042037270963192,
-0.024815959855914116,
-0.03130065277218819,
-0.020186103880405426,
-0.030744245275855064,
-0.011197227984666824,
0.022979864850640297,
0.028560878708958626,
0.024561788886785507,
-0.0644158199429512,
-0.0025955720338970423,
-0.021792886778712273,
0.014753513038158417,
-0.007880698889493942,
0.017998553812503815,
0.009257076308131218,
-0.07329760491847992,
0.051492735743522644,
-0.02130798064172268,
0.019404498860239983,
0.007581767160445452,
0.06245861575007439,
0.009119427762925625,
-0.04747922345995903,
-0.015632420778274536,
-0.008809930644929409,
-0.03373004123568535,
-0.01038525439798832,
0.01917131617665291,
-0.032533857971429825,
0.012991526164114475,
-0.02741282433271408,
-0.0656740739941597,
0.00020606358884833753,
-0.004694012459367514,
0.04843233898282051,
-0.032686468213796616,
0.06856532394886017,
0.04514932632446289,
-0.0248856283724308,
-0.004485351964831352,
-0.006459738593548536,
-0.021570298820734024,
0.021258559077978134,
-0.0014964534202590585,
0.0395689494907856,
-0.06810074299573898,
-0.016688793897628784,
0.0012867378536611795,
0.0701274499297142,
-0.010059351101517677,
0.03832701966166496,
0.009314654394984245,
-0.009310649707913399,
0.005488238763064146,
0.015023130923509598,
-0.07148810476064682,
0.08020246028900146,
-0.02457212284207344,
0.04417027160525322,
0.02291315607726574,
-0.009364551864564419,
0.009285393171012402,
0.03928307443857193,
0.027433540672063828,
-0.0034399444703012705,
-0.04245639964938164,
-0.022447675466537476,
0.047075580805540085,
0.039022237062454224,
0.027482468634843826,
0.0041941567324101925,
0.008783996105194092,
0.001127463998273015,
0.032984327524900436,
0.028227364644408226,
0.01131304632872343,
-0.03427079692482948,
-0.017700884491205215,
-0.05848846212029457,
-0.01765628159046173,
0.04188833385705948,
-0.02778972126543522,
-0.010818949900567532,
-0.05935750529170036,
-0.030575880780816078,
0.01579410210251808,
-0.032680071890354156,
0.023278748616576195,
-0.012824894860386848,
0.027251843363046646,
-0.0044510685838758945,
0.027112530544400215,
-0.031209897249937057,
0.04515650495886803,
0.11103208363056183,
0.05187327042222023,
0.0050005535595119,
-0.0509326197206974,
0.0012652414152398705,
-0.012235447764396667,
0.004291653633117676,
-0.05711235851049423,
0.0038018233608454466,
-0.028757557272911072,
0.024815602228045464,
-0.0005158051499165595,
0.0689336284995079,
0.015542375855147839,
0.009580441750586033,
0.0545891597867012,
-0.020546017214655876,
-0.030674828216433525,
-0.0090110432356596,
0.008960242383182049,
-0.012381534092128277,
-0.012247750535607338,
-0.07115515321493149,
0.021708808839321136,
0.013724942691624165,
0.03454207256436348,
-0.009574953466653824,
-0.04012024775147438,
-0.0005673491978086531,
0.050524916499853134,
-0.0023513748310506344,
-0.01455102302134037,
-0.00021633724099956453,
0.005320427007973194,
-0.029545869678258896,
0.00007885044760769233,
0.010551786981523037,
-0.009646546095609665,
0.049857378005981445,
0.06103161349892616,
0.006953638046979904,
-0.0001224071893375367,
0.031053490936756134,
0.051634207367897034,
-0.05347297713160515,
-0.005116076674312353,
0.004093313589692116,
0.020734649151563644,
-0.02845669724047184,
0.008701521903276443,
-0.025317436084151268,
-0.019044961780309677,
0.017999235540628433,
-0.02596333995461464,
-0.02326376922428608,
-0.021298052743077278,
-0.011581544764339924,
-0.046904899179935455,
-0.02589268982410431,
-0.007647575810551643,
0.02845776081085205,
-0.023382950574159622,
0.038322895765304565,
-0.02925127185881138,
-0.0065162405371665955,
-0.010575284250080585,
-0.014497344382107258,
0.040848229080438614,
-0.005338591989129782,
-0.016271160915493965,
-0.0268075093626976,
-0.00927339494228363,
-0.005756792612373829,
-0.009588080458343029,
-0.020190341398119926,
0.03618020564317703,
0.03909870609641075,
0.007995960302650928,
-0.0561315156519413,
-0.0012060041772201657,
-0.012033897452056408,
0.0036604800261557102,
0.0035593602806329727,
0.027377186343073845,
-0.03792176768183708,
0.00625305762514472,
-0.012066084891557693,
0.017287923023104668,
-0.038195960223674774,
-0.008172214031219482,
-0.015477263368666172,
0.033547598868608475,
-0.00228894897736609,
-0.002479173708707094,
0.006541929207742214,
-0.006120803765952587,
-0.030947722494602203,
-0.008463393896818161,
-0.0026665660552680492,
0.01050647348165512,
0.013162259943783283,
-0.015270602889358997,
-0.011208375915884972,
0.03212246298789978,
-0.013626092113554478,
0.009425814263522625,
0.042984168976545334,
-0.013385341502726078,
0.02722308225929737,
0.0012249099090695381,
-0.009542012587189674,
-0.0494842566549778,
0.007568945176899433,
-0.0011712344130501151,
-0.022357182577252388,
-0.04293510317802429,
0.020708022639155388,
-0.018874969333410263,
-0.024962134659290314,
-0.004259954206645489,
0.012366480194032192,
-0.04649285972118378,
-0.01227449718862772,
-0.06702587753534317,
0.04635234922170639,
-0.006006270181387663,
0.025222022086381912,
-0.012277424335479736,
0.03211274370551109,
-0.004990460816770792,
-0.03946739807724953,
0.009199714288115501,
-0.015425783582031727,
-0.04592420533299446,
0.0019681171979755163,
0.016379037871956825,
0.017291728407144547,
0.012168891727924347,
0.023053143173456192,
-0.01295649353414774,
0.01983192190527916,
-0.04830849543213844,
-0.03336193785071373,
0.00906822644174099,
-0.008641626685857773,
0.020231187343597412,
0.028017939999699593,
-0.01385191548615694,
-0.015075312927365303,
0.044212959706783295,
0.003172894474118948,
-0.006226169876754284,
-0.006944788154214621,
-0.02069728448987007,
0.009443116374313831,
-0.025580907240509987,
0.016656851395964622,
-0.007752193603664637,
-0.005416618660092354,
-0.00960069615393877,
0.014856172725558281,
-0.011334110051393509,
-0.040236491709947586,
0.01735656149685383,
0.001074011903256178,
-0.006254544481635094,
-0.026662111282348633,
0.022471126168966293,
0.05013333261013031,
0.07012253999710083,
-0.028372522443532944,
0.006762864999473095,
0.0020256093703210354,
0.02839779667556286,
-0.06132255867123604,
-0.005524693988263607,
0.018529850989580154,
0.003964883740991354,
0.0572986826300621,
-0.0487169586122036,
0.01356933917850256,
-0.00461578369140625,
-0.08935035020112991,
0.017317965626716614,
-0.02723074145615101,
-0.023740792647004128,
-0.055592555552721024,
-0.002319410676136613,
0.003680030582472682,
0.06647486984729767,
0.06516013294458389,
0.026043163612484932,
-0.0063755810260772705,
-0.00026780518237501383,
-0.02357848547399044,
0.013852962292730808,
-0.02029622159898281,
0.021628672257065773,
0.025463152676820755,
-0.04759994149208069,
0.06235530599951744,
0.0062798564322292805,
-0.053758762776851654,
0.04657098650932312,
0.007218742277473211,
0.0074525452218949795,
0.01567688398063183,
-0.002792098093777895,
0.03910186141729355,
0.02372155152261257,
0.02119864523410797,
0.00625385669991374,
-0.04022563248872757,
-0.03305583447217941,
0.03224432095885277,
0.0008936149533838034,
-0.01959792524576187,
-0.007769985590130091,
0.013798077590763569,
-0.026969164609909058,
-0.022941678762435913,
0.03349889814853668,
-0.02572428062558174,
-0.009806891903281212,
-0.02212822437286377,
-0.04019472748041153,
-0.004377513192594051,
-0.046587809920310974,
0.010426053777337074,
-0.026367416605353355,
0.00785758625715971,
0.014161193743348122,
-0.004692721180617809,
0.021469641476869583,
0.07360945641994476,
-0.016789140179753304,
-0.04564284905791283,
0.010415426455438137,
0.036226410418748856,
0.025814011693000793,
-0.054588887840509415,
0.004644796252250671,
-0.02565552107989788,
-0.013880792073905468,
-0.007841598242521286,
-0.029237737879157066,
-0.026276778429746628,
0.026385826990008354,
0.04307970032095909,
0.00702078640460968,
-0.00724510382860899,
-0.03661857545375824,
0.020212914794683456,
-0.03835363686084747,
0.0632748231291771,
0.023097801953554153,
-0.002918199636042118,
-0.03073612041771412,
0.017003221437335014,
0.02938774973154068,
0.017235852777957916,
0.049074724316596985,
-0.051235854625701904,
0.01267456915229559,
0.052319616079330444,
0.03828226029872894,
0.00045045747538097203,
-0.03375469148159027,
-0.020290112122893333,
0.01641240529716015,
-0.01165325939655304,
0.013724911957979202,
-0.0010307689663022757,
0.014552203007042408,
-0.005313574802130461,
-0.017974229529500008,
-0.017444614320993423,
0.022271757945418358,
0.04063207656145096,
-0.06893248111009598,
0.023757727816700935,
0.02661486342549324,
-0.029562927782535553,
0.057659901678562164,
-0.023470096290111542,
0.011235327459871769,
0.007469126023352146,
-0.034797169268131256,
0.004046477843075991,
0.034280382096767426,
-0.038090456277132034,
0.02088332735002041,
-0.010152499191462994,
-0.03679130971431732,
0.04159196466207504,
-0.01814000867307186,
-0.012825863435864449,
0.05711940675973892,
-0.018208647146821022,
-0.014677999541163445,
0.08053356409072876,
0.008971075527369976,
0.0710071474313736,
-0.006302318070083857,
-0.033318113535642624,
0.011997748166322708,
-0.00020474620396271348,
0.006810009945183992,
0.023424189537763596,
0.016478609293699265,
0.01823916845023632,
-0.039331886917352676,
0.03494013845920563,
-0.013560888357460499,
-0.00933876447379589,
-0.00841474998742342,
0.0555805042386055,
-0.032301165163517,
0.008929149247705936,
0.0069303628988564014,
0.013928067870438099,
0.02622126415371895,
0.05763799697160721,
-0.04574793949723244,
0.0928569808602333,
-0.015217659994959831,
-0.009978055953979492,
-0.0318545326590538,
0.01626656949520111,
-0.018843229860067368,
0.03273393586277962,
0.037465985864400864,
0.04340321570634842,
-0.01822437159717083,
0.015134381130337715,
-0.020418697968125343,
-0.008653691038489342,
-0.016140151768922806,
-0.03419909253716469,
0.033369652926921844,
-0.033918239176273346,
0.017951393499970436,
0.043575841933488846,
-0.009817290119826794,
-0.017199913039803505,
-0.0195192601531744,
0.03893512114882469,
0.005522857420146465,
0.053904153406620026,
-0.008223559707403183,
-0.023800548166036606,
-0.022512564435601234,
0.025035517290234566,
-0.06560785323381424,
-0.029345301911234856,
-0.035304777324199677,
0.013612017035484314,
-0.0017637854907661676,
-0.024163495749235153
] |
<ol>
<li><p>How does one derive the superconformal algebra? </p></li>
<li><p>Especialy how to argue the existence of the operator $S$ which doesn't exist either in either the supersymmetric algebra or the conformal algebra? </p></li>
<li><p>What is the explanation of the convention of choosing If $J _ \alpha ^\beta$ as a generator of $SU(2) \times SU(2)$ and $R^A _B$ and $r$ are the generators of the $U(m)$ R-symmetry ( $m \neq 4$)? How does one get these $R$ and $r$? </p></li>
<li><p>One further defines $R_1, R_2$ and $R_3$ as the generators of the Cartan subalgebra of $SU(4)$ (the $N=4$ R-symmetry group) where these are defined such that $R_k$ has $1$ on the $k^{th}$ diagonal entry and $-1$ on the $(k+1)^{th}$ diagonal entry. </p></li>
</ol>
<p>Using the above notation apparently one of the $Q-S$ commutation looks like,</p>
<p>$\{ S^A_\alpha , Q^\beta _B\} = \delta ^A_B J^\beta _\alpha + \delta ^\beta _\alpha R^A_B + \delta ^A_B \delta ^\beta _\alpha (\frac{H}{2} + r \frac{4-m}{4m})$</p>
<p>I would like to know how the above comes about and why the above equation implies the following equation (..each of whose sides is defined as $\Delta$) </p>
<p>$2\{ Q_4 ^- , S^4_ - \} = H - 3J_3 + 2\sum _{k=1} ^ 3 \frac{k}{4} R_k$ </p>
<p>I can't understand how to get the second of the above equations from the first of the above and why is this $\Delta$ an important quantity. </p>
<p>{Is there any open source online reference available which explains the above issues? </p>
| 8,247 |
[
-0.021334633231163025,
-0.0007365234196186066,
0.031295012682676315,
-0.03741444647312164,
0.04512578248977661,
0.02044779434800148,
-0.056525275111198425,
-0.03800562769174576,
0.018043017014861107,
-0.0630953386425972,
-0.018220877274870872,
0.003308143699541688,
0.048770032823085785,
0.02002335898578167,
-0.0033087374176830053,
0.006173905450850725,
-0.002666938118636608,
-0.036343175917863846,
-0.012630526907742023,
0.00019820267334580421,
0.051598768681287766,
0.02466512657701969,
0.014201905578374863,
0.0036852373741567135,
0.006248384714126587,
0.02760392054915428,
0.02052408643066883,
0.02445284090936184,
0.01693921908736229,
0.056750524789094925,
0.0016381515888497233,
-0.022174352779984474,
0.04328221082687378,
0.0348777249455452,
-0.02784852311015129,
0.03082328662276268,
-0.0036345927510410547,
-0.014872130006551743,
0.01100616529583931,
0.04117562621831894,
-0.05544114112854004,
-0.030692994594573975,
-0.033742379397153854,
0.01470243837684393,
-0.024615122005343437,
-0.004564131144434214,
-0.025178251788020134,
-0.006747768260538578,
0.020242761820554733,
-0.07035022228956223,
0.10406512022018433,
0.06102824956178665,
0.0075486390851438046,
0.0017865663394331932,
-0.016856800764799118,
0.006656645331531763,
0.024231087416410446,
0.06775557994842529,
0.026622282341122627,
-0.06775795668363571,
-0.02795044705271721,
-0.030962616205215454,
-0.013259428553283215,
-0.0025343638844788074,
-0.01626371033489704,
0.011529739014804363,
0.03645981848239899,
0.04801548644900322,
0.00826689600944519,
-0.021557174623012543,
0.02107582613825798,
0.002686668187379837,
0.02442147023975849,
-0.02054692432284355,
0.037352271378040314,
-0.005300821270793676,
-0.045915503054857254,
-0.0005193345132283866,
0.03307715803384781,
0.009801232255995274,
-0.010211650282144547,
0.04753238335251808,
-0.0017190823564305902,
-0.017893413081765175,
-0.01021664496511221,
0.00456865131855011,
0.05703912302851677,
0.03383444622159004,
0.019126879051327705,
0.01187701616436243,
-0.015658985823392868,
0.018185298889875412,
0.027357662096619606,
-0.015866342931985855,
-0.02326819859445095,
0.048514265567064285,
0.01661449298262596,
0.054052360355854034,
0.0017203058814629912,
-0.051232416182756424,
-0.034167636185884476,
-0.037372611463069916,
-0.0035726067144423723,
0.09132552146911621,
0.017243292182683945,
0.019792167469859123,
-0.03558429330587387,
0.023238347843289375,
-0.025903627276420593,
-0.02378389984369278,
-0.041382987052202225,
0.016131088137626648,
-0.030054721981287003,
-0.003355732886120677,
-0.015547240152955055,
-0.004276967607438564,
0.00925370678305626,
0.0076328301802277565,
0.050958409905433655,
0.06024337559938431,
0.026500100269913673,
-0.015615029260516167,
-0.012174506671726704,
-0.016259489580988884,
-0.05026858299970627,
0.005643256474286318,
0.03337680548429489,
0.025403404608368874,
-0.03404868766665459,
0.0007370671373791993,
0.05679413303732872,
-0.021121082827448845,
-0.0070420620031654835,
0.01451050117611885,
0.013526895083487034,
-0.006605689413845539,
-0.08364614844322205,
-0.06703706085681915,
0.062101155519485474,
-0.002965616760775447,
-0.0251664649695158,
-0.06244410201907158,
-0.005292015615850687,
0.04362546280026436,
0.07243141531944275,
-0.011488259769976139,
0.02241925150156021,
0.050424955785274506,
0.009589019231498241,
0.04193549603223801,
0.0025077892933040857,
-0.022363919764757156,
-0.03417423740029335,
-0.03973778709769249,
-0.03530052304267883,
-0.03136812523007393,
0.03048396110534668,
0.015081256628036499,
0.000706164282746613,
0.000685611623339355,
0.09130562841892242,
0.02682463452219963,
0.003007404739037156,
0.04669696465134621,
0.012208270840346813,
-0.03413370996713638,
0.04861464723944664,
0.013298110105097294,
-0.01012708805501461,
0.024194220080971718,
-0.014229820109903812,
0.011101311072707176,
0.0003116742882411927,
0.04494941979646683,
-0.0008191950037144125,
-0.04590325430035591,
-0.012272320687770844,
-0.042991142719984055,
-0.018992196768522263,
-0.02804894931614399,
-0.03320939093828201,
-0.03244609013199806,
-0.004997284617275,
0.04731123894453049,
0.004995744209736586,
0.010361362248659134,
0.010372397489845753,
-0.02062414027750492,
0.0057261353358626366,
-0.058533988893032074,
-0.005414445418864489,
-0.05368419736623764,
-0.010471689514815807,
0.02571270987391472,
-0.026148388162255287,
0.03960416465997696,
0.0439610630273819,
-0.03512903302907944,
0.026916900649666786,
-0.03676772117614746,
0.01380955334752798,
0.058287329971790314,
0.01030751597136259,
0.009750476107001305,
0.029123734682798386,
0.04589543119072914,
0.03679318353533745,
-0.001175808603875339,
0.05054747685790062,
-0.019893597811460495,
-0.013716115616261959,
0.02153130993247032,
0.008715856820344925,
0.02529272437095642,
-0.018485374748706818,
0.018430979922413826,
0.011350764892995358,
-0.003990274854004383,
-0.021732574328780174,
0.019626012071967125,
-0.0503724180161953,
0.022657426074147224,
0.03129831328988075,
0.02099067158997059,
-0.005862430203706026,
0.056624025106430054,
0.021538691595196724,
0.058699507266283035,
-0.028762808069586754,
-0.02511332370340824,
-0.06542758643627167,
-0.0027924703899770975,
0.02209681272506714,
0.013378473930060863,
-0.05289590731263161,
0.03017815202474594,
0.023367680609226227,
0.0364423431456089,
-0.00047893685405142605,
-0.002377570839598775,
0.0052782027050852776,
0.01750994846224785,
0.006801536772400141,
-0.016513647511601448,
-0.024992480874061584,
0.021259330213069916,
-0.03367919474840164,
-0.036534473299980164,
-0.0004662606806959957,
-0.023162655532360077,
-0.07469034940004349,
0.030681326985359192,
-0.02783135510981083,
-0.020513026043772697,
0.019844330847263336,
-0.024413764476776123,
0.06163380295038223,
-0.00878828950226307,
0.032416075468063354,
0.06618933379650116,
0.009675000794231892,
0.030121518298983574,
0.0012062513269484043,
-0.032093439251184464,
0.010529874823987484,
0.007188946008682251,
0.0017069184686988592,
-0.03623796999454498,
0.010558790527284145,
-0.013707535341382027,
-0.010576815344393253,
-0.007904929108917713,
-0.012974669225513935,
0.02055135741829872,
-0.0008704770589247346,
-0.012751213274896145,
0.017651265487074852,
0.031854577362537384,
-0.031923551112413406,
0.014207852073013783,
0.04847417026758194,
0.0052411314100027084,
0.03496643528342247,
0.03929086774587631,
-0.03656616061925888,
0.011690796352922916,
-0.08539318293333054,
-0.02656027488410473,
0.058610402047634125,
0.01895485445857048,
-0.021536244079470634,
-0.01570889912545681,
-0.030396372079849243,
-0.01663118042051792,
-0.05394921824336052,
0.025758495554327965,
0.013821279630064964,
-0.07009942829608917,
0.00692766672000289,
0.045600526034832,
-0.005415137391537428,
-0.0217844657599926,
0.002083156257867813,
-0.055217038840055466,
-0.03733666613698006,
0.0035474668256938457,
-0.020163001492619514,
0.019246848300099373,
-0.011813907884061337,
0.029097529128193855,
-0.0071844314225018024,
-0.008626451715826988,
-0.0025746070314198732,
-0.021894313395023346,
-0.03561444953083992,
0.006816317792981863,
-0.019770730286836624,
0.04007815942168236,
0.017081577330827713,
-0.06052987650036812,
0.10202514380216599,
0.02194644697010517,
-0.009517502039670944,
-0.003671971382573247,
0.0375690832734108,
-0.034764256328344345,
-0.034997593611478806,
0.026086846366524696,
0.026224182918667793,
0.0026873808819800615,
0.043190035969018936,
0.01928594708442688,
0.05179530009627342,
0.029116448014974594,
-0.045610759407281876,
-0.05553487688302994,
0.030660182237625122,
0.009766398929059505,
0.02746523544192314,
0.057283613830804825,
-0.04878763481974602,
0.0193192046135664,
-0.011621188372373581,
0.016407597810029984,
0.001319071394391358,
-0.012063178233802319,
-0.0657220333814621,
0.012302117422223091,
-0.022847581654787064,
0.010259022936224937,
0.008954877965152264,
0.06746120005846024,
0.0017394284950569272,
-0.044005509465932846,
-0.0013397670118138194,
0.003931927960366011,
0.025882719084620476,
-0.031716763973236084,
0.03297974541783333,
0.008771797642111778,
0.03331853449344635,
-0.036535877734422684,
-0.013300532475113869,
0.005649161990731955,
-0.014247423969209194,
0.014434721320867538,
-0.022728437557816505,
-0.018216852098703384,
0.032687604427337646,
0.035554513335227966,
-0.019843420013785362,
-0.00456919614225626,
-0.050053633749485016,
-0.0174611397087574,
-0.05164913088083267,
-0.01604950800538063,
-0.04895586892962456,
0.046115897595882416,
-0.016700580716133118,
0.062439873814582825,
0.02632329612970352,
-0.0034504602663218975,
-0.0001220940612256527,
-0.011225285939872265,
-0.0545518659055233,
-0.012261537835001945,
-0.037440791726112366,
0.018852734938263893,
-0.0014402797678485513,
-0.03162063658237457,
0.03581516072154045,
0.007548520341515541,
-0.05086686462163925,
-0.026846330612897873,
-0.028496993705630302,
-0.030398810282349586,
0.032193686813116074,
-0.027369536459445953,
-0.052991777658462524,
-0.01628945954144001,
0.019908539950847626,
0.07840240746736526,
-0.01395877543836832,
-0.008074377663433552,
0.05719352886080742,
-0.025437168776988983,
0.038441985845565796,
-0.02116106078028679,
0.032709185034036636,
0.004625074099749327,
-0.006658531725406647,
0.02167609892785549,
-0.00260101817548275,
-0.010743611492216587,
-0.044296491891145706,
-0.005994639825075865,
0.05481123924255371,
-0.0150433499366045,
-0.03256165608763695,
0.010815734043717384,
-0.047841109335422516,
0.00533956428989768,
-0.01167422067373991,
0.0581321083009243,
-0.020324774086475372,
0.015832163393497467,
0.04346271976828575,
0.003614239627495408,
-0.023388076573610306,
0.04244178161025047,
0.0559057742357254,
-0.0032186778262257576,
-0.044450148940086365,
-0.026376647874712944,
0.0004963201354257762,
-0.019878406077623367,
-0.03391439840197563,
-0.009184660390019417,
-0.013574964366853237,
-0.04904700070619583,
0.023587191477417946,
0.012054597958922386,
0.01997782289981842,
-0.0339822880923748,
0.033372506499290466,
0.015701884403824806,
-0.03011111542582512,
0.016108868643641472,
-0.010178915224969387,
0.018576905131340027,
0.03310539573431015,
0.01101425290107727,
-0.008657890371978283,
0.01389404945075512,
0.0026335706934332848,
-0.013981525786221027,
0.03313978388905525,
0.012256648391485214,
-0.012487323954701424,
-0.0008909249445423484,
-0.06025787442922592,
-0.015968501567840576,
0.028482086956501007,
-0.032441817224025726,
0.0636574923992157,
0.009997637011110783,
0.015730135142803192,
-0.02241549827158451,
-0.01756695844233036,
-0.009871316142380238,
0.01552756130695343,
-0.01290625799447298,
0.02097679115831852,
-0.023543627932667732,
0.004032492637634277,
-0.023367803543806076,
0.014009770937263966,
0.03401106968522072,
0.02117037959396839,
0.011866825632750988,
0.0009847256587818265,
0.0005174749530851841,
0.04309513792395592,
-0.014747412875294685,
-0.055913470685482025,
0.0074369041249156,
0.005363463424146175,
-0.024055300280451775,
0.013719256035983562,
-0.04602418839931488,
-0.03207332268357277,
-0.010738582350313663,
0.0047588050365448,
0.048703912645578384,
0.02041594125330448,
-0.058787666261196136,
0.05257038772106171,
0.05211364105343819,
-0.013076037168502808,
0.02354184351861477,
0.02038123458623886,
-0.026254691183567047,
-0.004992569796741009,
-0.024153204634785652,
-0.011924492195248604,
-0.0031556414905935526,
0.009022276848554611,
-0.037404172122478485,
-0.0010529509745538235,
-0.02221040241420269,
0.024901611730456352,
-0.051531679928302765,
-0.014768464490771294,
0.018092738464474678,
-0.025414852425456047,
-0.0340009368956089,
0.017676038667559624,
-0.017832450568675995,
-0.01495244912803173,
0.003753300290554762,
0.01585354469716549,
0.06258463859558105,
-0.0112948352470994,
0.0256867166608572,
-0.020193638280034065,
-0.015027332119643688,
0.015431797131896019,
-0.009594704955816269,
-0.005542856641113758,
-0.030193418264389038,
-0.013793960213661194,
0.012361177243292332,
-0.050924308598041534,
0.04100096970796585,
-0.005647612735629082,
-0.011215409263968468,
-0.011866376735270023,
-0.04145412892103195,
-0.05692629516124725,
-0.00601730914786458,
-0.019300496205687523,
-0.021754052489995956,
-0.014281387440860271,
-0.0021981257013976574,
0.051378022879362106,
-0.025603560730814934,
-0.06947237998247147,
-0.007479939144104719,
0.0263720341026783,
0.02929033897817135,
-0.0345195047557354,
0.005388210061937571,
0.009906299412250519,
-0.016515951603651047,
-0.02469022199511528,
0.02272546850144863,
0.06831474602222443,
-0.055071886628866196,
0.01134546846151352,
0.02778959460556507,
0.07039163261651993,
0.03459848463535309,
-0.0186292827129364,
-0.018709171563386917,
0.023619938641786575,
-0.01927972212433815,
0.03341012820601463,
0.013876261189579964,
0.00013504779781214893,
-0.007584268227219582,
-0.041756704449653625,
-0.01571812853217125,
-0.01916274055838585,
0.02441064454615116,
-0.012859520502388477,
-0.006498332601040602,
0.0017750781262293458,
0.04869449883699417,
0.033128704875707626,
-0.04398101568222046,
-0.015803208574652672,
0.00881972722709179,
0.020374583080410957,
-0.0122299175709486,
0.0035202624276280403,
-0.01999247632920742,
-0.008828788064420223,
0.020124897360801697,
-0.056486740708351135,
-0.003459826810285449,
-0.008674518205225468,
0.0822393000125885,
0.0004260915447957814,
0.017774198204278946,
0.004186348523944616,
-0.013629322871565819,
-0.00009374300861964002,
-0.011460286565124989,
0.04276563599705696,
0.030795037746429443,
-0.016002224758267403,
0.022000741213560104,
-0.032203804701566696,
-0.057524655014276505,
0.013209385797381401,
0.05609464645385742,
-0.021201811730861664,
0.04617670178413391,
0.037119533866643906,
-0.029855836182832718,
0.00834648497402668,
-0.018668074160814285,
-0.0019286328461021185,
0.020114939659833908,
-0.016701040789484978,
0.007564673665910959,
-0.08132483065128326,
-0.0020321556366980076,
0.01178442407399416,
0.039664577692747116,
-0.025585569441318512,
-0.0067713139578700066,
0.03179267421364784,
0.059951186180114746,
-0.006191442720592022,
-0.023851364850997925,
-0.07716064900159836,
0.06479868292808533,
-0.022815275937318802,
0.0243631973862648,
0.0157354436814785,
-0.028069710358977318,
-0.012173635885119438,
0.04565532132983208,
0.001314580556936562,
-0.045320190489292145,
-0.00315597141161561,
-0.039903104305267334,
0.045656587928533554,
0.05079084262251854,
-0.0017943239072337747,
0.017744945362210274,
-0.010549790225923061,
0.03137766569852829,
0.00007589270535390824,
0.036329954862594604,
-0.00003647868288680911,
-0.024841519072651863,
-0.0033346768468618393,
-0.017079973593354225,
-0.05367279425263405,
0.050863321870565414,
-0.018053477630019188,
0.008512726984918118,
-0.03961304575204849,
-0.01679205149412155,
0.02232677862048149,
0.04225906357169151,
0.02742180787026882,
-0.040233056992292404,
0.05018896609544754,
-0.030215468257665634,
0.04219214245676994,
-0.002039195504039526,
0.02671707421541214,
0.11586423218250275,
0.06281037628650665,
0.02098603919148445,
-0.07529421150684357,
0.02632792294025421,
-0.007412376347929239,
0.01905619353055954,
-0.02074248157441616,
0.0441707968711853,
-0.009018965065479279,
-0.020205939188599586,
-0.016251331195235252,
0.05777490511536598,
-0.04304540157318115,
-0.00026643776800483465,
0.03933775797486305,
-0.0530925877392292,
-0.04155878722667694,
-0.01022883877158165,
0.02801460213959217,
-0.01254354789853096,
0.024187907576560974,
-0.041277315467596054,
0.018999198451638222,
0.004402773454785347,
-0.011251282878220081,
-0.06766963750123978,
-0.03662964329123497,
0.012232363224029541,
-0.001189653412438929,
-0.01688433066010475,
0.035242095589637756,
0.007943626493215561,
-0.005159800872206688,
0.0006938139558769763,
0.018652984872460365,
-0.0002757761103566736,
-0.04786553606390953,
0.05274903029203415,
0.028177399188280106,
0.002368965419009328,
-0.0003130882396362722,
0.03677678108215332,
0.047502923756837845,
-0.056453198194503784,
0.0059710172936320305,
-0.040272075682878494,
0.03652094304561615,
-0.056278496980667114,
-0.01582038588821888,
-0.007187324576079845,
0.016343114897608757,
0.006280945148319006,
-0.03440175950527191,
-0.0037296924274414778,
-0.021179284900426865,
-0.005555041134357452,
-0.048417579382658005,
0.02302015945315361,
0.006855345331132412,
0.03715892881155014,
-0.007495754864066839,
0.021413782611489296,
-0.01689670793712139,
-0.028517141938209534,
0.006374729331582785,
-0.005153221543878317,
0.013550780713558197,
0.005478546489030123,
0.01251224335283041,
-0.02359619550406933,
0.011193578131496906,
-0.03242321312427521,
0.005143109243363142,
-0.008670797571539879,
0.04255552962422371,
0.08008673042058945,
0.04474359378218651,
-0.011219455860555172,
-0.03255018964409828,
-0.030336495488882065,
-0.007701701484620571,
-0.02050124853849411,
-0.006702268961817026,
-0.003887799335643649,
-0.02639235556125641,
0.03688004985451698,
0.0712704136967659,
-0.05158304423093796,
0.010471976362168789,
0.0024711007717996836,
0.02580331824719906,
0.03596014156937599,
-0.044862810522317886,
-0.02767787128686905,
0.025516804307699203,
-0.06717687100172043,
0.0034512882120907307,
-0.019103918224573135,
-0.023670963943004608,
0.04732152819633484,
0.004179221577942371,
-0.00768430856987834,
0.07211815565824509,
-0.0030830251052975655,
-0.028603505343198776,
0.0006167695391923189,
-0.0354972742497921,
0.01585402898490429,
0.01787448488175869,
0.021466830745339394,
0.0008991527720354497,
-0.01651335135102272,
0.029566295444965363,
0.010684655047953129,
0.030950995162129402,
0.00924433022737503,
-0.044294919818639755,
-0.05316529422998428,
-0.0017196503467857838,
-0.005463685840368271,
-0.04444907605648041,
0.013753136619925499,
-0.02111942321062088,
0.031623389571905136,
-0.023079996928572655,
0.04043350741267204,
-0.02565525658428669,
0.04032542556524277,
-0.0035711040254682302,
-0.009612945839762688,
-0.012138447724282742,
0.024067025631666183,
-0.010712213814258575,
-0.004984427243471146,
-0.007517900317907333,
0.01811840943992138,
-0.009006700478494167,
0.029406165704131126,
-0.03772326558828354,
-0.00813846942037344,
-0.02688300423324108,
-0.05062507092952728,
0.014117332175374031,
0.02376871183514595,
0.006997722666710615,
0.04690314456820488,
-0.039350297302007675,
-0.041655972599983215,
0.014304950833320618,
-0.04079420864582062,
0.004833899904042482,
-0.007455292623490095,
-0.028518397361040115,
-0.014655105769634247,
-0.027216332033276558,
-0.017900491133332253,
0.020119020715355873,
0.00811267551034689,
-0.004707476124167442,
0.030993536114692688,
-0.053548380732536316,
-0.029500018805265427,
0.009969164617359638,
0.006249644793570042,
-0.00830705463886261,
0.0158550888299942,
0.0299654770642519,
0.009249699302017689,
0.024101795628666878,
-0.01553072314709425,
0.039985667914152145,
0.018512241542339325,
-0.0048571801744401455,
-0.05738437920808792,
-0.012247302569448948,
0.025482870638370514,
0.015147499740123749,
0.06700488924980164,
-0.07334262132644653,
0.03177381679415703,
0.028276657685637474,
-0.04625183343887329,
0.04571988433599472,
-0.046763379126787186,
-0.0027773925103247166,
-0.030347004532814026,
-0.017063768580555916,
-0.024672534316778183,
0.055290840566158295,
0.007266569882631302,
0.01781015284359455,
-0.005001198500394821,
0.016416460275650024,
-0.00003976674270234071,
-0.019595978781580925,
-0.018313361331820488,
-0.014294485561549664,
0.03262900561094284,
-0.01808580383658409,
0.053895339369773865,
-0.006971264723688364,
-0.02724556438624859,
0.0436391606926918,
0.010381979867815971,
0.009380643256008625,
-0.009883482940495014,
0.06031596288084984,
0.023583928123116493,
0.03231649845838547,
0.043519411236047745,
0.002520888578146696,
-0.0037234239280223846,
-0.02342047356069088,
0.034961506724357605,
0.014676446095108986,
0.001959859160706401,
-0.009243897162377834,
-0.01608469896018505,
-0.034137941896915436,
-0.027564601972699165,
0.01208762638270855,
-0.04006539285182953,
-0.03892917558550835,
-0.013584695756435394,
-0.0416177436709404,
0.005090442486107349,
-0.009149395860731602,
0.029610875993967056,
0.00048305836389772594,
0.050421178340911865,
0.019215216860175133,
0.02383664809167385,
-0.00004371823160909116,
0.05836733803153038,
-0.019175231456756592,
-0.029436271637678146,
0.05635051056742668,
0.012436768971383572,
-0.04183884710073471,
-0.04218617081642151,
0.00493445573374629,
-0.012534975074231625,
0.01879648119211197,
-0.005433277226984501,
-0.04366521164774895,
-0.01171266008168459,
0.0015307094436138868,
-0.0040060426108539104,
0.026900606229901314,
-0.053359705954790115,
-0.057468168437480927,
-0.002748737344518304,
-0.055087607353925705,
0.0569930337369442,
0.01833018846809864,
-0.03676054626703262,
-0.002180407987907529,
-0.0052639190107584,
-0.00724288634955883,
0.013176563195884228,
0.06337656825780869,
0.002408413914963603,
-0.02166663110256195,
0.052145980298519135,
-0.010759934782981873,
0.05057337135076523,
-0.028560250997543335,
0.004062573425471783,
0.040640588849782944,
-0.0054457541555166245,
0.008793002925813198,
0.014920659363269806,
0.0007479623891413212,
0.03063587285578251,
-0.005765601992607117,
-0.014016092754900455,
0.0077128843404352665,
0.014451093040406704,
-0.05123006924986839,
-0.0037394054234027863,
-0.02710886485874653,
-0.05226104333996773,
0.0526060052216053,
0.010357472114264965,
0.009621082805097103,
0.05194714292883873,
-0.03169010579586029,
-0.01618191786110401,
-0.013189036399126053,
-0.004586354363709688,
-0.019592953845858574,
0.0022368915379047394,
-0.04586571082472801,
0.061465296894311905,
-0.02240876667201519,
-0.014418871141970158,
0.03355606645345688,
-0.049594804644584656,
-0.023105328902602196,
0.0759306401014328,
-0.00300446804612875,
0.026199083775281906,
0.04333497956395149,
0.007525037974119186,
0.00810168031603098,
-0.004005118738859892,
0.03970428556203842,
0.03795633092522621,
-0.0017204092582687736,
0.011798728257417679,
-0.004943114705383778,
0.01674523390829563,
0.017033498734235764,
0.016110120341181755,
-0.03158130124211311,
-0.000920135120395571,
-0.019676843658089638,
0.004761374555528164,
0.034636907279491425,
-0.051622211933135986,
0.010120990686118603,
0.03482529893517494,
-0.02396184764802456,
0.08311235904693604,
-0.02064618468284607,
0.0079141054302454,
-0.04121289774775505,
0.015735117718577385,
-0.03539332374930382,
-0.0019322680309414864,
-0.004929562099277973,
0.01317614410072565,
-0.010367462411522865,
0.002313700970262289,
-0.02997017651796341,
-0.004445139318704605,
0.026028592139482498,
-0.013739953748881817,
-0.013951382599771023,
0.040913596749305725,
-0.015249144285917282,
-0.0016715204110369086,
-0.04032626003026962,
0.0009985588258132339,
-0.01556146889925003,
0.046142611652612686,
0.002549423137679696,
-0.027193497866392136,
0.002742598531767726,
-0.00913285743445158,
-0.019096214324235916,
0.01430483628064394,
0.005957767833024263,
-0.04562942311167717,
0.007464300841093063,
0.0355391651391983,
0.01128483098000288,
0.0077520702034235
] |
<p>In the photoelectric effect there is a threshold frequency that must be exceeded, to observe any electron emission, I have two questions about this.</p>
<p>I) <strong>Lower than threshold</strong>:
What happen with lesser frequency/energy photons? I mean there is no energy transferred? If some energy were transferred, (and it must be transfered quantized), how can be experimentally known it was quantized, if there is no electron emission?</p>
<p>II) <strong>Intensity dependence</strong>: There is any known dependency with intensity? (I mean a dependency not about the number of electrons <em>(I am already aware of this)</em> but about the energy of them) I thought energy of electron emited was independent with intensity, but then I found this link <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-3WN77X7-16&_user=10&_coverDate=06/17/1996&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=4d0612bde6536d59f730cd066af81c23&searchtype=a" rel="nofollow" title="dependency with intensity">dependency with intensity</a> (is a paper to buy that I haven't read) but relates energy with intensity.</p>
| 8,248 |
[
-0.02920808643102646,
-0.024386312812566757,
0.018159544095396996,
-0.011252925731241703,
0.003945931326597929,
0.00006846872565802187,
-0.026377830654382706,
-0.025890788063406944,
0.04596809670329094,
-0.03736628592014313,
0.04820776730775833,
0.019953235983848572,
0.03212013840675354,
0.03336019441485405,
0.010645291768014431,
0.01635524071753025,
-0.02642282098531723,
-0.026655711233615875,
-0.0019058817997574806,
-0.013265681453049183,
-0.04098106548190117,
0.05091208964586258,
-0.0033265352249145508,
-0.00412584887817502,
-0.045878320932388306,
0.028118282556533813,
0.018001215532422066,
0.030963057652115822,
0.010038022883236408,
0.04916203394532204,
-0.0255857203155756,
-0.029582316055893898,
-0.0050801862962543964,
-0.006860523484647274,
-0.015163717791438103,
0.021964361891150475,
-0.04155748337507248,
-0.054899439215660095,
0.03891843929886818,
0.00167169445194304,
-0.01733085885643959,
0.007417437620460987,
-0.006281544454395771,
0.04632452502846718,
-0.03969430923461914,
-0.026045899838209152,
0.01971418969333172,
-0.02444857358932495,
0.04526040703058243,
-0.05876624956727028,
0.020183850079774857,
-0.013801648281514645,
0.030820520594716072,
0.026402223855257034,
0.0051959967240691185,
-0.018963536247611046,
0.059789787977933884,
0.08754534274339676,
0.0033163391053676605,
-0.05538081377744675,
-0.04677632451057434,
-0.029404718428850174,
-0.014782097190618515,
-0.02149594947695732,
-0.045730382204055786,
0.043015919625759125,
-0.020678415894508362,
-0.038162365555763245,
0.045386891812086105,
0.014850531704723835,
0.020545441657304764,
0.012169498018920422,
0.026312416419386864,
0.0027934270910918713,
0.03112015128135681,
-0.0042570484802126884,
0.05209987983107567,
0.0042144679464399815,
0.030165188014507294,
0.06272619217634201,
-0.00902086216956377,
0.018316688016057014,
0.018674012273550034,
0.02639082632958889,
0.018900815397500992,
-0.015913227573037148,
0.07715945690870285,
-0.025825323536992073,
0.01958170160651207,
-0.004137933719903231,
-0.02726028673350811,
0.006036701146513224,
0.0365762859582901,
0.017664693295955658,
-0.024676555767655373,
0.02551756054162979,
-0.0021250334102660418,
0.061120204627513885,
-0.026902928948402405,
-0.006334169302135706,
0.03833983838558197,
0.003484675195068121,
0.02074512280523777,
0.08760789781808853,
-0.003677085507661104,
0.004629280883818865,
-0.020802007988095284,
0.020253989845514297,
-0.0004653865471482277,
-0.008943009190261364,
-0.0040588341653347015,
0.010428798384964466,
-0.01334093976765871,
0.00012632152356673032,
0.005152247846126556,
-0.012660386972129345,
0.027639834210276604,
-0.02292998880147934,
0.07191941142082214,
0.05895758420228958,
0.01745218224823475,
-0.006416418123990297,
0.01933346502482891,
-0.014424633234739304,
-0.04251797869801521,
0.009922735393047333,
0.04619178920984268,
-0.013906898908317089,
-0.033687274903059006,
0.06128250062465668,
-0.021919971331954002,
-0.012884752824902534,
-0.0008963308064267039,
-0.04021535441279411,
0.030731357634067535,
0.000986876548267901,
-0.0852699875831604,
-0.04646318778395653,
0.04304993525147438,
0.004090250004082918,
-0.015228024683892727,
-0.06079517677426338,
0.028487149626016617,
0.03426816314458847,
0.07032902538776398,
-0.017297783866524696,
-0.020412765443325043,
-0.0250755213201046,
0.04496631398797035,
0.038908861577510834,
-0.021758921444416046,
0.022237805649638176,
0.014689991250634193,
-0.02884613536298275,
-0.0022255766671150923,
-0.04142794758081436,
0.03643061965703964,
0.029940638691186905,
0.01126819010823965,
-0.005501690320670605,
0.09418544918298721,
-0.007126599084585905,
-0.005693953949958086,
-0.0021079755388200283,
0.032624129205942154,
-0.015253088437020779,
0.09134389460086823,
0.021088216453790665,
0.0017490877071395516,
0.02689584344625473,
-0.001092769904062152,
0.03111124038696289,
0.014642786234617233,
0.011670985259115696,
-0.0010157290380448103,
-0.07017406076192856,
-0.036958545446395874,
-0.027349963784217834,
0.013601593673229218,
-0.016656024381518364,
-0.04352331534028053,
-0.029358526691794395,
-0.024003764614462852,
0.022942306473851204,
0.0071345907635986805,
0.06613170355558395,
-0.0031945891678333282,
-0.007252516690641642,
-0.009057186543941498,
-0.020344307646155357,
0.00048053593491204083,
-0.050131507217884064,
0.0022933315485715866,
-0.0055983662605285645,
-0.025376489385962486,
0.030349232256412506,
-0.0614018514752388,
-0.02931799925863743,
0.018927311524748802,
-0.0018735264893621206,
-0.0018938767025247216,
0.026029100641608238,
-0.0043526096269488335,
0.00406523747369647,
0.04655783250927925,
0.04433669149875641,
0.019339095801115036,
0.03529394790530205,
0.0121544124558568,
-0.024664705619215965,
-0.030177945271134377,
0.013275937177240849,
-0.007646019104868174,
0.021045226603746414,
0.028403237462043762,
-0.016428863629698753,
0.000049486658099340275,
-0.01944129355251789,
-0.01807764172554016,
0.03726259618997574,
-0.014929138123989105,
0.05327115207910538,
0.0370989628136158,
0.011676780879497528,
-0.005378955975174904,
0.04384448751807213,
0.02997192181646824,
0.008168900385499,
-0.021617870777845383,
-0.025739209726452827,
-0.05565100908279419,
0.005540078971534967,
0.05066785216331482,
0.005743644665926695,
-0.033608101308345795,
0.0187558364123106,
0.0170406773686409,
0.0033216425217688084,
0.00976232998073101,
0.036067329347133636,
-0.030194317921996117,
-0.025680677965283394,
0.039016395807266235,
0.014765428379178047,
-0.004998161923140287,
0.021596167236566544,
0.017827404662966728,
0.003160678781569004,
0.01565183699131012,
0.004156174138188362,
-0.001528911292552948,
0.03981733322143555,
-0.009126557968556881,
-0.025365609675645828,
-0.023099850863218307,
0.005072237458080053,
0.053048357367515564,
-0.04022078961133957,
0.028511283919215202,
0.03283151984214783,
-0.021992290392518044,
0.008350031450390816,
-0.005907432176172733,
-0.02309519425034523,
0.03186856582760811,
-0.02917199581861496,
-0.025516323745250702,
-0.0172598697245121,
0.0004955570911988616,
-0.04813690483570099,
0.03478997200727463,
-0.012066143564879894,
-0.03591744229197502,
-0.041599877178668976,
-0.020252373069524765,
0.024266060441732407,
0.02954021468758583,
0.0413583442568779,
-0.07464861869812012,
-0.03934786468744278,
-0.011165643110871315,
-0.04606049135327339,
0.03849988058209419,
0.025004113093018532,
0.013658682815730572,
-0.030915526673197746,
-0.04247632622718811,
-0.058751583099365234,
0.0725831687450409,
-0.04374844953417778,
0.013175895437598228,
0.004438533913344145,
-0.03386359661817551,
-0.0399511456489563,
-0.017723342403769493,
0.007767944596707821,
-0.004598365630954504,
-0.034645356237888336,
-0.030784649774432182,
0.06358425319194794,
-0.026179803535342216,
-0.00001644037001824472,
0.029800569638609886,
0.009920253418385983,
-0.036781445145606995,
0.007562813814729452,
0.0238746739923954,
0.0031171103473752737,
-0.012782206758856773,
0.051122792065143585,
0.0072910841554403305,
-0.035712115466594696,
-0.027354871854186058,
-0.06683903932571411,
-0.0623321607708931,
0.03605256974697113,
-0.019100582227110863,
0.016525307670235634,
-0.02602415531873703,
-0.053137701004743576,
0.044403258711099625,
0.023986922577023506,
-0.011060445569455624,
-0.03906881809234619,
-0.016828471794724464,
-0.019050931558012962,
-0.009363073855638504,
-0.00360710546374321,
0.014239008538424969,
0.022693132981657982,
0.005198564846068621,
0.02561350166797638,
0.04436403512954712,
0.0026348759420216084,
0.01733134128153324,
-0.007557256147265434,
0.03296845406293869,
-0.0020743042696267366,
-0.003549473127350211,
0.016641980037093163,
0.01981917768716812,
-0.0336727648973465,
0.016885623335838318,
0.0006959786987863481,
-0.0026090345345437527,
0.03809376060962677,
-0.07498272508382797,
0.038442518562078476,
0.01705748774111271,
-0.013509142212569714,
-0.025087835267186165,
0.019612932577729225,
0.02660129778087139,
0.010620967485010624,
0.010934877209365368,
0.011445102281868458,
0.03487219288945198,
-0.023461271077394485,
-0.0021121110767126083,
0.027835942804813385,
0.03951262682676315,
-0.013888878747820854,
-0.04093259200453758,
0.006246487144380808,
0.007664765231311321,
0.013284089975059032,
-0.00946633517742157,
-0.025984026491642,
0.043397434055805206,
-0.005271159112453461,
0.044429272413253784,
0.014681984670460224,
0.0047855982556939125,
-0.026549680158495903,
-0.02903815172612667,
0.006267676129937172,
-0.028193244710564613,
0.07009895890951157,
0.04482291638851166,
0.05242905020713806,
0.04351586475968361,
0.007882733829319477,
-0.007977742701768875,
0.00879628211259842,
-0.09703612327575684,
-0.00003852365261991508,
-0.008563498966395855,
-0.02903568185865879,
-0.019994407892227173,
0.012392976321280003,
-0.02942596562206745,
-0.03520425409078598,
-0.031705014407634735,
-0.010613830760121346,
0.02424571104347706,
-0.03199426457285881,
-0.0025374277029186487,
-0.03212818130850792,
-0.015923861414194107,
-0.05138232931494713,
0.03382512554526329,
0.00499850045889616,
-0.015769343823194504,
0.00894877314567566,
0.04699033498764038,
-0.05549921840429306,
0.011858678422868252,
-0.03306524455547333,
-0.01528660487383604,
0.010603765957057476,
0.03797103464603424,
0.01716768555343151,
0.015352721326053143,
-0.016857871785759926,
0.0015022063162177801,
0.03621699661016464,
0.04588071629405022,
0.0384880006313324,
-0.006144977640360594,
-0.05044010654091835,
-0.023253977298736572,
0.0031549260020256042,
-0.00025645570713095367,
0.05769803002476692,
-0.00691865012049675,
0.012019666843116283,
0.024695122614502907,
-0.030677298083901405,
-0.04035605862736702,
0.05655336380004883,
0.03705723583698273,
-0.025450851768255234,
-0.027316158637404442,
-0.04482949152588844,
0.013302772305905819,
-0.02201477810740471,
0.01188618503510952,
0.0200081504881382,
-0.004659442696720362,
-0.00638324161991477,
-0.03265709802508354,
0.025551022961735725,
0.012619320303201675,
-0.011082213371992111,
-0.039580248296260834,
0.003071921644732356,
-0.00042990653309971094,
-0.01789194904267788,
-0.029960012063384056,
0.0018722729291766882,
-0.014637131243944168,
0.051192980259656906,
0.004754543304443359,
0.018769748508930206,
-0.09342730045318604,
-0.016467614099383354,
0.0348360501229763,
0.05586400628089905,
-0.01756473071873188,
-0.007033538073301315,
-0.05697150155901909,
0.008431777358055115,
-0.011181042529642582,
-0.03622245416045189,
0.015028322115540504,
-0.02070997655391693,
0.032941047102212906,
-0.03253825753927231,
-0.04362139850854874,
0.0013852681731805205,
0.025000987574458122,
0.04302576556801796,
0.020295582711696625,
-0.030584760010242462,
-0.009674971923232079,
0.00757905188947916,
-0.009680158458650112,
0.04805680736899376,
0.06948436796665192,
-0.023581063374876976,
-0.012758062221109867,
0.010592118836939335,
0.013255410827696323,
-0.02548261545598507,
-0.11613065749406815,
0.0010743277380242944,
-0.015051278285682201,
0.029513109475374222,
0.07714200019836426,
-0.04545462876558304,
-0.03060190938413143,
0.01408296823501587,
0.02052447572350502,
-0.03369791805744171,
-0.01611867919564247,
-0.02932041324675083,
0.07860544323921204,
0.03308344632387161,
-0.014453432522714138,
0.06127716228365898,
0.05546897277235985,
-0.048046354204416275,
0.027912957593798637,
0.006273423321545124,
0.04686432704329491,
-0.025036070495843887,
0.024711664766073227,
-0.03531524911522865,
0.031105386093258858,
-0.01245835516601801,
0.06064944341778755,
0.007834097370505333,
0.023429017513990402,
-0.012483535334467888,
-0.009237829595804214,
-0.009280943311750889,
0.03466983139514923,
-0.01514813769608736,
0.016793644055724144,
-0.041981104761362076,
0.03536750003695488,
-0.03863687813282013,
-0.025880448520183563,
0.00857437215745449,
0.0066753351129591465,
-0.006846425123512745,
0.004400318954139948,
0.00554833235219121,
0.02031739614903927,
-0.05637945979833603,
-0.010312925092875957,
0.01711435429751873,
-0.046617258340120316,
0.06002730131149292,
0.003353134961798787,
0.010046270675957203,
-0.011690609157085419,
-0.036982499063014984,
-0.041096031665802,
0.03713352233171463,
-0.01128295250236988,
0.061998870223760605,
-0.02991858497262001,
0.03572150692343712,
-0.010932975448668003,
0.008220057003200054,
-0.053266603499650955,
-0.033404652029275894,
0.02383926510810852,
0.05519310012459755,
-0.037697117775678635,
0.003533759154379368,
0.013167117722332478,
-0.05372917279601097,
-0.01775776967406273,
0.005783369764685631,
0.01763327047228813,
-0.048340000212192535,
-0.024761367589235306,
-0.0010885070078074932,
-0.010697750374674797,
0.022029170766472816,
-0.030948828905820847,
0.00022921636991668493,
-0.010319509543478489,
-0.0014573067892342806,
-0.030923645943403244,
-0.014950180426239967,
0.024569526314735413,
-0.014588617719709873,
-0.04550064727663994,
-0.015676818788051605,
0.0014031532919034362,
0.012501428835093975,
-0.03311722353100777,
-0.03936532139778137,
0.06360355019569397,
0.043593429028987885,
-0.004057867918163538,
0.0004363105399534106,
0.024751560762524605,
0.003988990094512701,
0.03031950443983078,
0.019983483478426933,
-0.01274930126965046,
-0.03371419012546539,
-0.02788114920258522,
0.016775380820035934,
-0.013935556635260582,
0.00860994029790163,
0.013399813324213028,
0.0696171298623085,
-0.020053023472428322,
0.02176828682422638,
0.016094665974378586,
0.01454979833215475,
0.024506276473402977,
-0.037866365164518356,
0.002824889263138175,
0.006486163008958101,
0.0031649325974285603,
-0.020473377779126167,
-0.024982331320643425,
-0.06073710322380066,
-0.019328655675053596,
0.05353294312953949,
-0.010182385332882404,
0.02714814990758896,
-0.004287519957870245,
-0.03721744194626808,
-0.009655029512941837,
-0.013938664458692074,
-0.010096336714923382,
0.0010512713342905045,
0.014785467647016048,
0.008806739002466202,
-0.010940284468233585,
-0.023180628195405006,
0.031014472246170044,
0.04838349670171738,
-0.0407399907708168,
0.04099304974079132,
0.021162962540984154,
0.035162318497896194,
0.029412301257252693,
-0.04675605893135071,
-0.046085961163043976,
0.06714688241481781,
-0.04523875564336777,
0.021593276411294937,
0.029634153470396996,
-0.02479020692408085,
0.06095396354794502,
0.006460561882704496,
0.004340741783380508,
-0.043960705399513245,
-0.02183046191930771,
-0.06011953949928284,
0.04971352219581604,
-0.002054077573120594,
0.0184957142919302,
-0.027675127610564232,
0.007766796741634607,
0.021753868088126183,
-0.00020198003039695323,
0.009601873345673084,
-0.0014350423589348793,
-0.056936729699373245,
-0.031916115432977676,
-0.05288708955049515,
-0.015670599415898323,
0.0430384986102581,
-0.039773136377334595,
-0.033882297575473785,
0.030975954607129097,
-0.05159803107380867,
0.026929575949907303,
0.04573964327573776,
0.046748217195272446,
-0.006130958441644907,
0.06969863176345825,
-0.02694656327366829,
0.0007601852994412184,
-0.00933495070785284,
0.026256877928972244,
0.12384175509214401,
0.08524058759212494,
0.01491551287472248,
-0.05651932209730148,
0.01024280022829771,
-0.02273617312312126,
0.040322400629520416,
-0.018152615055441856,
0.011853175237774849,
-0.029553765431046486,
0.0021307903807610273,
0.014141754247248173,
0.06930570304393768,
0.010074910707771778,
0.0353287048637867,
0.025441935285925865,
-0.04845977574586868,
-0.029439197853207588,
0.03607385978102684,
0.017311083152890205,
0.005629258695989847,
0.01343892328441143,
-0.03673272207379341,
-0.0011455186177045107,
-0.05258861184120178,
-0.02503269910812378,
-0.046242598444223404,
-0.007967079058289528,
0.026048721745610237,
-0.032835256308317184,
-0.03261640667915344,
-0.03549416363239288,
0.02593616396188736,
-0.001979645574465394,
-0.02070711739361286,
-0.006184256635606289,
0.013543237932026386,
0.0005826720152981579,
0.012577635236084461,
0.00586995342746377,
-0.010331572033464909,
-0.034357111901044846,
0.028088131919503212,
0.02416761964559555,
-0.017881378531455994,
-0.011946147307753563,
-0.00726876687258482,
0.06556570529937744,
0.00020352819410618395,
-0.008649946190416813,
-0.012186228297650814,
0.007007501553744078,
-0.0014222386525943875,
-0.02776310406625271,
-0.005654090084135532,
0.022548573091626167,
-0.006986354943364859,
-0.01228462252765894,
0.0013058121548965573,
-0.06669826060533524,
0.02477240189909935,
-0.0071341609582304955,
0.0031025719363242388,
0.022125381976366043,
-0.00043172124424017966,
-0.00032927197753451765,
-0.01030847616493702,
0.04859403520822525,
-0.011605454608798027,
-0.006492170970886946,
0.00511249341070652,
-0.018028568476438522,
-0.036807749420404434,
-0.05543384328484535,
0.00629293592646718,
0.014745403081178665,
0.049038778990507126,
0.00850760005414486,
-0.02569448947906494,
-0.015562610700726509,
-0.06414689868688583,
0.009685533121228218,
0.0444209910929203,
-0.0033438196405768394,
0.00044878190965391695,
0.014088181778788567,
0.04768737405538559,
0.012824425473809242,
-0.012311694212257862,
0.024320172145962715,
0.015774201601743698,
-0.012662188149988651,
0.05435122549533844,
-0.0694299265742302,
-0.01876056008040905,
0.007832477800548077,
0.026822887361049652,
-0.021057939156889915,
-0.025137383490800858,
0.018523816019296646,
-0.03152237460017204,
0.007682102266699076,
0.03129127249121666,
0.0185670405626297,
-0.02244519628584385,
-0.010989584028720856,
0.0306103378534317,
-0.020053090527653694,
0.010394010692834854,
0.005115541163831949,
0.017526384443044662,
-0.0034971325658261776,
-0.044660504907369614,
-0.02961275540292263,
0.003976492211222649,
-0.001965447561815381,
0.018973082304000854,
-0.0138297900557518,
0.031025798991322517,
-0.01237430889159441,
0.024549929425120354,
0.00034192114253528416,
-0.034012410789728165,
-0.008023074828088284,
-0.004066247493028641,
0.0040504345670342445,
0.002231795573607087,
-0.009223069995641708,
0.034667007625103,
-0.015401170589029789,
-0.0626986175775528,
0.013061638921499252,
0.04270045459270477,
-0.02407372184097767,
0.002430243417620659,
-0.015622619539499283,
-0.022433817386627197,
0.04886959493160248,
-0.012807715684175491,
-0.05339641124010086,
0.039707113057374954,
-0.04964100196957588,
-0.03582004830241203,
0.03743898123502731,
-0.024024415761232376,
0.016452232375741005,
0.045076653361320496,
-0.015284334309399128,
-0.02878931537270546,
0.0715436339378357,
0.0207503754645586,
-0.020975444465875626,
0.029366519302129745,
-0.03558337315917015,
-0.026725033298134804,
0.021530423313379288,
0.011089379899203777,
0.005990426521748304,
0.033727411180734634,
0.050255801528692245,
0.03361521661281586,
0.026044968515634537,
-0.010420435108244419,
-0.00022782967425882816,
-0.0358424186706543,
0.017247511073946953,
0.013083640486001968,
0.022436175495386124,
0.031627848744392395,
0.0314793661236763,
-0.03617506101727486,
0.014345590025186539,
-0.02525859884917736,
0.017138389870524406,
-0.08823661506175995,
-0.005770996678620577,
-0.005068876314908266,
0.028979813680052757,
0.030665913596749306,
-0.029832053929567337,
0.005362868309020996,
-0.009128585457801819,
-0.08501337468624115,
0.011334122158586979,
0.015705876052379608,
-0.021439874544739723,
-0.03765828162431717,
0.013928326778113842,
-0.053580958396196365,
0.016088243573904037,
-0.0019562679808586836,
0.056263990700244904,
0.019823133945465088,
0.03582853078842163,
-0.0016407460207119584,
-0.031827379018068314,
-0.019715074449777603,
0.03246007487177849,
0.0266715157777071,
-0.005412181839346886,
0.05858726054430008,
-0.035430487245321274,
-0.016006214544177055,
0.04025143384933472,
0.003926090896129608,
-0.0020727745722979307,
-0.009765928611159325,
0.018222613260149956,
-0.006258899345993996,
0.034742362797260284,
0.020768601447343826,
-0.014643787406384945,
0.01712050288915634,
0.02292151376605034,
0.006799810566008091,
0.035523563623428345,
0.002833588281646371,
0.020909396931529045,
0.030262034386396408,
-0.014197209849953651,
-0.0539165660738945,
0.03494708612561226,
-0.01861065998673439,
-0.021106138825416565,
0.025975579395890236,
0.02351287752389908,
0.02969234250485897,
-0.022535433992743492,
0.02431543357670307,
-0.05372520908713341,
-0.009745093062520027,
-0.0016781615559011698,
0.011195450089871883,
0.03448868542909622,
0.020472615957260132,
-0.029715215787291527,
-0.01668848656117916,
0.029237359762191772,
-0.003751827869564295,
-0.016528597101569176,
-0.050329260528087616,
-0.009541801176965237,
-0.007397655863314867,
0.016760963946580887,
-0.0027170779649168253,
-0.04109993577003479,
-0.07593366503715515,
0.0017174697713926435,
-0.03547234088182449,
0.027909602969884872,
-0.01615780219435692,
-0.00226103188470006,
0.009498964063823223,
-0.08121040463447571,
0.028495540842413902,
0.0005170427029952407,
0.02888491004705429,
-0.045815952122211456,
-0.01302255503833294,
0.003366258693858981,
0.009500371292233467,
0.04620977118611336,
-0.0014737246092408895,
-0.039126865565776825,
0.009126052260398865,
-0.03456772118806839,
0.020026186481118202,
-0.039172422140836716,
0.02111698128283024,
-0.015299294143915176,
-0.003414655802771449,
-0.032310601323843,
-0.02472900226712227,
-0.029717933386564255,
0.04645494744181633,
0.02191060408949852,
0.01905636303126812,
0.013003638945519924,
-0.021585486829280853,
-0.02770126424729824,
0.05311368405818939,
-0.017182447016239166,
-0.015282745473086834,
0.06658226996660233,
0.002865292364731431,
0.02808256819844246,
0.035400182008743286,
-0.0095262685790658,
-0.017486384138464928,
0.034891389310359955,
-0.01977953501045704,
0.01115349493920803,
0.020173639059066772,
0.012609974481165409,
0.04122381657361984,
-0.06216040253639221,
0.0076055764220654964,
0.02703136019408703,
-0.02899278700351715,
-0.0025622467510402203,
0.0721464455127716,
0.016621295362710953,
0.018694011494517326,
0.02029081992805004,
0.018962135538458824,
-0.012899098917841911,
-0.00988102424889803,
-0.0333809033036232,
0.032181043177843094,
0.0010422650957480073,
0.00810987502336502,
0.061769768595695496,
0.012424568645656109,
-0.002508895006030798,
-0.0545223206281662,
0.005943141411989927,
0.023771850392222404,
-0.03522317111492157,
-0.03148190304636955,
0.01751093566417694,
0.012474770657718182,
-0.006903469562530518,
0.02577325329184532,
-0.01668523997068405,
0.033598966896533966,
-0.012333588674664497,
-0.0040876604616642,
-0.00838787667453289,
-0.03935590758919716,
-0.031129170209169388,
0.03837985545396805,
0.009697199799120426,
0.06590145081281662,
-0.00520072178915143,
-0.004650955554097891,
-0.03387116640806198,
0.01536769513040781,
-0.005956687033176422,
-0.05959286913275719,
-0.002685238141566515,
-0.020618194714188576,
-0.051887158304452896,
0.005951299797743559,
0.020477507263422012,
-0.01294142659753561,
-0.005384795367717743,
0.010579372756183147,
0.01718299649655819,
0.00025271589402109385,
-0.02430480159819126,
-0.024291271343827248,
0.0017091832123696804,
0.06016652286052704,
-0.05273274704813957,
0.007213828153908253,
-0.02242802083492279,
0.01036823634058237,
-0.04313590005040169,
-0.016633765771985054
] |
<p><img src="http://i.stack.imgur.com/WNlBP.png" alt="enter image description here"></p>
<p>In my book equation for two advanced wave which created this static wave are
$$y_1=asin{\frac{2\pi}{\lambda}(vt+x)} $$
$$y_2=asin{\frac{2\pi}{\lambda}(vt-x)} $$</p>
<p>and equation for static wave is derived by adding this two equation: $\ Y=y_1+y_2$</p>
<p>Q1: Though this two wave comes from opposite direction why it is added rather then subtracted? Shouldn't it be $\ Y=y_1-y_2$</p>
<p>Q2: Why sign of $\ x$ is opposite for two equation though it is said that it's the distance of the particular point from the reference and whose displacement for the wave is $\ y$ </p>
| 8,249 |
[
0.005120071116834879,
0.000006685305379505735,
-0.002699266653507948,
0.03481510654091835,
0.04002741724252701,
0.01223381794989109,
-0.024852752685546875,
0.0017610196955502033,
0.030544618144631386,
-0.0015922292368486524,
0.013190464116632938,
0.03786775842308998,
0.05727219581604004,
0.06564174592494965,
0.05159250646829605,
0.03207932785153389,
0.009633958339691162,
-0.012051746249198914,
-0.018809884786605835,
-0.0007963046082295477,
-0.022804126143455505,
-0.005977334454655647,
0.030839214101433754,
0.018918422982096672,
-0.016127029433846474,
0.044878654181957245,
0.05169631913304329,
0.00699484022334218,
0.008354025892913342,
0.00799464713782072,
-0.005019017960876226,
-0.03660665079951286,
-0.007126694079488516,
0.006936520803719759,
0.01939624734222889,
-0.017689257860183716,
0.013206611387431622,
-0.046929940581321716,
0.030080977827310562,
0.0407116524875164,
-0.00014609098434448242,
0.026562461629509926,
-0.032666511833667755,
0.04688282683491707,
-0.04129040613770485,
0.010660187341272831,
0.0012128378730267286,
0.011218673549592495,
0.034777313470840454,
-0.017906133085489273,
0.05008048191666603,
-0.008640242740511894,
0.045571163296699524,
0.020694535225629807,
0.02361140586435795,
0.028859378769993782,
0.07034473866224289,
0.02484949119389057,
-0.027064409106969833,
-0.053468257188797,
0.015414181165397167,
-0.011284811422228813,
-0.02003907971084118,
-0.027525797486305237,
0.009625902399420738,
0.017097091302275658,
-0.026492862030863762,
-0.0003297908406239003,
-0.004213824402540922,
-0.03650860860943794,
0.02024451270699501,
-0.020528120920062065,
-0.0071044787764549255,
-0.050097160041332245,
0.03458388149738312,
-0.02811886928975582,
-0.03317231312394142,
0.012340939603745937,
-0.007065160665661097,
0.037112269550561905,
0.03341294825077057,
0.0279043260961771,
0.016103720292448997,
0.023649418726563454,
0.01660812832415104,
-0.03255396708846092,
0.06893808394670486,
0.01887599006295204,
0.008817087858915329,
0.040296632796525955,
0.0034942259080708027,
0.016629967838525772,
0.016571510583162308,
-0.023510988801717758,
-0.0072800773195922375,
0.017663322389125824,
-0.01649908348917961,
0.035030581057071686,
0.04944734275341034,
-0.014380987733602524,
0.0071266028098762035,
-0.02652573399245739,
0.03028448112308979,
0.0944717675447464,
-0.01611766591668129,
-0.00892544537782669,
-0.01682257652282715,
0.05259563773870468,
-0.017476633191108704,
-0.024028021842241287,
-0.029436863958835602,
0.0032934981863945723,
-0.016508683562278748,
0.024009136483073235,
-0.019396081566810608,
0.015138981863856316,
0.018225466832518578,
-0.0471644252538681,
0.04144531860947609,
0.0555756613612175,
0.04259677603840828,
-0.03908061608672142,
0.007265796884894371,
0.014790304005146027,
-0.0425071194767952,
-0.016296150162816048,
0.029142191633582115,
-0.011319013312458992,
-0.052157603204250336,
0.03697638586163521,
0.036070141941308975,
0.0011019607773050666,
0.0037923678755760193,
0.018237771466374397,
0.028496528044342995,
0.02497195266187191,
-0.11526922881603241,
-0.06108585372567177,
0.015016857534646988,
-0.013191532343626022,
0.013394870795309544,
-0.09032346308231354,
-0.020026598125696182,
0.041047222912311554,
0.07082175463438034,
-0.02231426164507866,
-0.019185954704880714,
0.014580398797988892,
0.024501081556081772,
0.017337577417492867,
-0.012968555092811584,
-0.0347084142267704,
-0.009782600216567516,
-0.05709352716803551,
-0.023338984698057175,
-0.06877843290567398,
-0.01939123310148716,
0.028813228011131287,
-0.03846396505832672,
0.008696927689015865,
0.04893683269619942,
-0.002582430373877287,
-0.023822937160730362,
0.035519637167453766,
-0.023743346333503723,
-0.06139130890369415,
0.055145204067230225,
0.0023313150741159916,
-0.04135066270828247,
0.061060644686222076,
-0.031489383429288864,
0.03154388815164566,
-0.020655974745750427,
-0.016915274783968925,
0.023534296080470085,
-0.038578279316425323,
0.001211628783494234,
-0.04042036086320877,
-0.013740932568907738,
0.020753294229507446,
-0.042795129120349884,
-0.05782027915120125,
-0.021897833794355392,
0.018259605392813683,
0.022941652685403824,
0.08900119364261627,
-0.02309557795524597,
0.007822045125067234,
0.010244662873446941,
-0.028662852942943573,
0.0057319155894219875,
-0.026926960796117783,
0.04069185256958008,
0.0290524922311306,
-0.013531159609556198,
0.020387206226587296,
0.03460872173309326,
0.03054153360426426,
-0.022608492523431778,
-0.0006977642187848687,
0.025609059259295464,
0.04719297215342522,
0.018830014392733574,
-0.005983287002891302,
0.07098571956157684,
0.059687282890081406,
0.03091810829937458,
0.030583061277866364,
0.023714831098914146,
-0.05172280967235565,
0.004000093787908554,
0.0208599753677845,
-0.024020014330744743,
0.02639768086373806,
-0.00231886631809175,
-0.012354706414043903,
0.022290527820587158,
-0.02943345345556736,
0.011680557392537594,
0.007380809169262648,
-0.04160822182893753,
0.07044418156147003,
0.07049721479415894,
0.008588584139943123,
0.022592224180698395,
0.03870311379432678,
-0.02668176405131817,
0.06076309457421303,
0.015686288475990295,
-0.029611559584736824,
-0.04564596340060234,
-0.015706786885857582,
0.016694655641913414,
0.00638074753805995,
-0.026387443765997887,
0.02152230776846409,
0.009915527887642384,
0.0310878474265337,
0.042725492268800735,
0.023832213133573532,
0.013543442822992802,
-0.05685745179653168,
0.04854568466544151,
0.04735647886991501,
-0.016318993642926216,
0.026680251583456993,
0.047998055815696716,
0.01292330026626587,
-0.0078174052760005,
0.002600523177534342,
-0.015107613988220692,
0.05759778991341591,
0.011890671215951443,
0.025814838707447052,
0.005850562360137701,
0.006999246776103973,
0.047688618302345276,
-0.0274956077337265,
0.022440442815423012,
0.020348351448774338,
-0.02182714454829693,
-0.0025706994347274303,
0.008727711625397205,
0.047851160168647766,
-0.013391693122684956,
-0.01688832975924015,
-0.01785195991396904,
-0.050784915685653687,
0.023998621851205826,
-0.05997378006577492,
-0.00548350578173995,
-0.04008523374795914,
-0.05530758574604988,
0.009159720502793789,
-0.03251383453607559,
0.06553416699171066,
0.028786003589630127,
0.05868886783719063,
-0.03335011005401611,
-0.04066568240523338,
0.011855724267661572,
-0.02156788296997547,
0.0057044923305511475,
0.006841555237770081,
-0.028302287682890892,
0.011050700210034847,
-0.06726240366697311,
-0.01818062923848629,
0.04121710732579231,
-0.001252444228157401,
0.01616494357585907,
0.01630070060491562,
-0.02080814354121685,
-0.06230683624744415,
-0.040671076625585556,
-0.07528318464756012,
0.00982034020125866,
0.012985646724700928,
-0.005207231733947992,
0.042833440005779266,
0.008151745423674583,
-0.012674382887780666,
0.020510010421276093,
-0.023099277168512344,
-0.007126973941922188,
0.004883007612079382,
-0.033643726259469986,
0.013444083742797375,
-0.006480325013399124,
0.021406041458249092,
-0.019249550998210907,
-0.017143217846751213,
0.03868738189339638,
-0.06456713378429413,
-0.05965796113014221,
0.03523526340723038,
-0.0034528011456131935,
0.06304358690977097,
-0.007161984220147133,
-0.03385106846690178,
0.08437628298997879,
0.015628386288881302,
-0.0006354887736961246,
-0.004143087193369865,
0.034459225833415985,
-0.014005678705871105,
-0.014254461973905563,
-0.017180513590574265,
0.037304166704416275,
0.02155064418911934,
0.07147709280252457,
-0.004998180083930492,
0.020084697753190994,
0.051520563662052155,
0.019672321155667305,
-0.008324760012328625,
-0.011561601422727108,
0.01661542057991028,
0.03278348967432976,
0.0559866689145565,
-0.015640387311577797,
-0.03660668432712555,
-0.022092804312705994,
0.0106666823849082,
0.013523206114768982,
0.024344472214579582,
-0.03138543665409088,
0.04451039806008339,
0.005319376941770315,
0.008202445693314075,
-0.04952475056052208,
0.037372246384620667,
0.010550698265433311,
-0.0009764485293999314,
-0.02210499718785286,
0.02913993038237095,
0.038202639669179916,
-0.022046847268939018,
0.02090158313512802,
0.013055425137281418,
0.05625104531645775,
-0.000832168385386467,
-0.04470241069793701,
0.006766770966351032,
0.017191393300890923,
0.041343022137880325,
-0.0015056334668770432,
-0.020886525511741638,
0.028425347059965134,
0.04152676463127136,
-0.02793988026678562,
0.027431748807430267,
-0.01762385293841362,
0.004157596733421087,
-0.02367248386144638,
-0.05317782610654831,
-0.0011832596501335502,
0.04029618203639984,
-0.02856532856822014,
0.05238834768533707,
0.03865060955286026,
0.01741345040500164,
0.04466255381703377,
-0.007957885041832924,
-0.05941775441169739,
0.004456411115825176,
-0.017329435795545578,
-0.04319452866911888,
0.005602071061730385,
0.01923408918082714,
0.005222477484494448,
-0.033853091299533844,
-0.03266578167676926,
-0.014176194556057453,
-0.03716336935758591,
-0.049298565834760666,
0.026362409815192223,
-0.02267811819911003,
-0.032616034150123596,
-0.020035669207572937,
0.058872420340776443,
0.004229302983731031,
-0.06946943700313568,
-0.003249027067795396,
0.05489695444703102,
-0.009792513214051723,
0.0018976719584316015,
-0.03910871595144272,
-0.029339604079723358,
-0.018566204234957695,
-0.023104317486286163,
0.04449202120304108,
0.032529719173908234,
-0.045419104397296906,
-0.0075746942311525345,
0.009963826276361942,
0.03770139068365097,
0.03385058045387268,
-0.026798190549016,
-0.03201722726225853,
-0.00005405663250712678,
-0.01951502077281475,
-0.056863654404878616,
0.05679171532392502,
0.046009328216314316,
0.033267080783843994,
-0.0071306838653981686,
-0.0070365541614592075,
-0.01925794780254364,
0.03757065534591675,
0.01617298647761345,
-0.0225305687636137,
0.02646772935986519,
-0.03150470554828644,
0.010913604870438576,
-0.029980722814798355,
-0.026130935177206993,
0.02905208431184292,
-0.03721641004085541,
-0.030240314081311226,
-0.013810359872877598,
0.03644443675875664,
0.019932370632886887,
0.005910530220717192,
0.024433325976133347,
-0.027473686262965202,
-0.025017814710736275,
-0.0013027220265939832,
-0.014332463033497334,
0.018563635647296906,
0.03252929821610451,
0.04356412589550018,
-0.025144340470433235,
-0.03065558522939682,
-0.08838922530412674,
-0.05463356897234917,
0.004552673548460007,
0.028281833976507187,
0.026881448924541473,
-0.00393249373883009,
-0.07278824597597122,
-0.04725455492734909,
0.018033575266599655,
-0.00025503552751615644,
0.04137609899044037,
-0.013968361541628838,
-0.01124225277453661,
0.0018146013608202338,
-0.02733585238456726,
-0.07437898218631744,
0.005658347625285387,
-0.009927072562277317,
-0.001105212140828371,
-0.0332861989736557,
-0.02306811884045601,
-0.004122158978134394,
-0.019846010953187943,
-0.012804213911294937,
0.029119079932570457,
-0.012533625587821007,
-0.0278493519872427,
-0.026235193014144897,
0.020860157907009125,
-0.01223666500300169,
-0.027171162888407707,
0.0076994155533611774,
0.006729789078235626,
0.03479232266545296,
0.0534532256424427,
-0.007671026978641748,
-0.024669842794537544,
0.021095948293805122,
0.003701898269355297,
0.010547425597906113,
-0.0010097401682287455,
-0.0198855958878994,
0.0319528803229332,
0.05672742426395416,
-0.011456409469246864,
0.04727134481072426,
0.018536634743213654,
-0.048006441444158554,
0.007457507774233818,
-0.02826138585805893,
0.019733209162950516,
-0.04462115094065666,
-0.016961943358182907,
-0.03214506804943085,
0.011410108767449856,
-0.014253097586333752,
0.06753068417310715,
0.02217881754040718,
0.02395600825548172,
-0.032361164689064026,
0.013484276831150055,
0.02615794725716114,
0.015733906999230385,
-0.013517515733838081,
0.025014827027916908,
0.008082026615738869,
0.0310722254216671,
0.031318314373493195,
-0.01474471390247345,
0.012426079250872135,
-0.011953763663768768,
-0.010054260492324829,
0.007262503728270531,
0.04056664928793907,
0.018881021067500114,
-0.00978701189160347,
-0.01108582317829132,
0.003873741952702403,
-0.04433818534016609,
-0.0019729072228074074,
-0.014013404957950115,
0.0135396309196949,
0.005610951688140631,
-0.06404320150613785,
-0.058133140206336975,
0.004331961274147034,
-0.00782814435660839,
0.016035819426178932,
-0.01266593299806118,
0.05007919296622276,
0.05536700040102005,
0.0412035696208477,
-0.04785452410578728,
-0.025762682780623436,
-0.013767817057669163,
-0.011680576018989086,
-0.023508967831730843,
-0.019345860928297043,
0.034978482872247696,
-0.02041231095790863,
-0.026652442291378975,
0.021229317411780357,
0.005869204644113779,
-0.036950815469026566,
-0.035139307379722595,
0.04258013144135475,
0.016998233273625374,
0.014315412379801273,
-0.013594940304756165,
-0.014825250022113323,
0.019804103299975395,
-0.022118210792541504,
-0.0019897243473678827,
-0.005531614646315575,
0.050431400537490845,
-0.007002327125519514,
-0.03925171121954918,
-0.008865166455507278,
-0.04055660963058472,
0.0062266006134450436,
-0.03611995652318001,
-0.014415834099054337,
-0.015495531260967255,
0.025840966030955315,
-0.034368496388196945,
-0.03750574216246605,
-0.02001335844397545,
-0.020858533680438995,
0.02724023535847664,
0.008162680082023144,
-0.018869571387767792,
-0.05353266000747681,
-0.047526948153972626,
0.005115307401865721,
0.01581941545009613,
-0.033736974000930786,
-0.015378717333078384,
0.06457193195819855,
-0.040958110243082047,
0.03239082172513008,
-0.0011195347178727388,
0.044059690088033676,
0.038199421018362045,
-0.027994312345981598,
-0.012077689170837402,
0.030385373160243034,
0.005008107516914606,
-0.0053037009201943874,
-0.013098427094519138,
-0.04941659793257713,
0.056345101445913315,
0.10572781413793564,
-0.006942104082554579,
0.07943860441446304,
0.009248601272702217,
0.011423169635236263,
-0.017444787546992302,
-0.010473792441189289,
-0.006115812808275223,
-0.0003210296272300184,
-0.04013059288263321,
0.009192656725645065,
-0.06244577094912529,
-0.01814931444823742,
0.010307670570909977,
0.012375797145068645,
0.0040384926833212376,
-0.034744393080472946,
-0.020128842443227768,
0.03248348459601402,
-0.05701626464724541,
0.010849401354789734,
-0.020506566390395164,
0.014581725001335144,
0.02951779030263424,
0.038039036095142365,
-0.00741791445761919,
-0.02715430036187172,
0.04705631732940674,
0.018198920413851738,
-0.028408026322722435,
-0.07318506389856339,
-0.013112352229654789,
-0.04466121643781662,
-0.004090200178325176,
0.042993780225515366,
0.014809501357376575,
0.022865833714604378,
0.018247505649924278,
0.029927851632237434,
-0.0001486724941059947,
0.029258260503411293,
-0.023670431226491928,
-0.08116322755813599,
-0.017421618103981018,
-0.006511436775326729,
-0.029794063419103622,
0.033830560743808746,
-0.009002749808132648,
-0.04070527106523514,
0.02353707328438759,
-0.04722164198756218,
0.039329882711172104,
0.04483408480882645,
0.013758664019405842,
-0.015967335551977158,
0.0657891258597374,
-0.04845577850937843,
0.024098925292491913,
-0.027960482984781265,
-0.005932124797254801,
0.1332923173904419,
0.02436259016394615,
0.025562023743987083,
-0.04481436312198639,
0.007216629572212696,
-0.019159730523824692,
0.019022583961486816,
-0.01840219646692276,
0.020184790715575218,
-0.0008066001464612782,
0.008101954124867916,
0.03219139575958252,
0.05662422999739647,
0.004802708979696035,
-0.0250470582395792,
0.018183721229434013,
-0.04691856727004051,
-0.05655134469270706,
-0.0008631513337604702,
-0.0025098673067986965,
-0.004755453206598759,
0.03442515432834625,
0.009665888734161854,
0.022585509344935417,
-0.01313774660229683,
0.0007390949758701026,
-0.060857295989990234,
-0.03126524016261101,
0.035563692450523376,
0.00701708160340786,
-0.05322490632534027,
0.014736843295395374,
0.008601203560829163,
-0.03432857245206833,
-0.029965387657284737,
0.036677855998277664,
0.02964959852397442,
-0.050752244889736176,
0.03625849261879921,
0.009511664509773254,
0.02664978988468647,
-0.01866690255701542,
0.018307123333215714,
0.0047280979342758656,
-0.05157649889588356,
-0.0006160461925901473,
0.0012650522403419018,
0.0481187142431736,
0.03337416797876358,
0.0006737904623150826,
-0.02351781353354454,
0.03886284679174423,
-0.005818947218358517,
-0.024852383881807327,
-0.00860543642193079,
-0.005909340921789408,
0.038228075951337814,
-0.02997218817472458,
0.022245803847908974,
-0.052037063986063004,
-0.0007126881973817945,
0.021460844203829765,
0.018086688593029976,
0.045336950570344925,
-0.031087065115571022,
-0.0009799092076718807,
0.010072775185108185,
0.07203572988510132,
0.03168509155511856,
-0.016069049015641212,
-0.0474630706012249,
0.012702204287052155,
-0.016522446647286415,
-0.02059325948357582,
-0.0192808136343956,
0.012965133413672447,
0.02464258298277855,
0.02445225417613983,
-0.030234182253479958,
-0.023690804839134216,
-0.05354798212647438,
0.0228876993060112,
0.00475216843187809,
-0.021959463134407997,
0.026369526982307434,
-0.04196591302752495,
0.00024296135234180838,
0.02995985373854637,
-0.030774440616369247,
0.009293434210121632,
0.03302501514554024,
0.025468675419688225,
0.00401900103315711,
-0.017194854095578194,
-0.056292932480573654,
0.021884145215153694,
-0.041587863117456436,
-0.013122223317623138,
-0.028320368379354477,
0.014978869818150997,
0.037840329110622406,
-0.005183050874620676,
0.03587539866566658,
0.05134280025959015,
-0.032918576151132584,
-0.032976165413856506,
0.021695228293538094,
-0.013033860363066196,
0.021405206993222237,
0.02833881974220276,
0.010425180196762085,
-0.023520201444625854,
-0.004821891896426678,
0.015044636093080044,
0.007301802281290293,
0.03065449371933937,
0.010350524447858334,
-0.03885088860988617,
0.02620810829102993,
-0.013056698255240917,
0.01186967734247446,
-0.07002391666173935,
-0.01958666928112507,
-0.025273120030760765,
0.012681643478572369,
-0.009175515733659267,
-0.0017990279011428356,
-0.012493384070694447,
0.04769909754395485,
-0.02234833315014839,
-0.018151305615901947,
0.013794192112982273,
-0.0006046566413715482,
-0.013522044755518436,
-0.00015524540503975004,
-0.015215042978525162,
-0.02845284529030323,
0.032841287553310394,
-0.009295061230659485,
-0.043567873537540436,
-0.0033654258586466312,
-0.0005522898281924427,
-0.027250798419117928,
0.036912281066179276,
-0.0010997087229043245,
0.02111777663230896,
0.043382082134485245,
0.008039929904043674,
0.004654655233025551,
0.04677465185523033,
0.01912318915128708,
0.0054702614434063435,
-0.03346100077033043,
-0.05298544839024544,
-0.008030918426811695,
-0.020230354741215706,
-0.04041089490056038,
-0.018768543377518654,
-0.011942584067583084,
0.0324944444000721,
0.00626713503152132,
-0.012567903846502304,
-0.019108500331640244,
-0.007726920302957296,
-0.015402479097247124,
-0.0063253832049667835,
0.01875181309878826,
-0.0315018892288208,
0.014018919318914413,
-0.01946779526770115,
-0.013989741913974285,
0.01575874537229538,
0.02363252267241478,
0.0013450561091303825,
-0.06751145422458649,
-0.017780421301722527,
0.024373726919293404,
0.013919969089329243,
0.022005872800946236,
-0.04101453348994255,
-0.00430386234074831,
0.02794630080461502,
-0.049036286771297455,
0.010110560804605484,
-0.01717342995107174,
0.0022564693354070187,
-0.021487750113010406,
-0.008017132990062237,
0.025387639179825783,
0.06280628591775894,
0.013795997016131878,
0.030773000791668892,
0.018481338396668434,
0.019620245322585106,
-0.004922351334244013,
-0.035211022943258286,
-0.02342170476913452,
-0.00429189158603549,
0.029460061341524124,
0.012219512835144997,
0.04630492627620697,
-0.03430546447634697,
-0.006665173918008804,
0.03908805549144745,
-0.019072631374001503,
-0.0005038083181716502,
0.034418635070323944,
0.05921041965484619,
-0.037177205085754395,
0.011286844499409199,
0.006647236179560423,
-0.01813625358045101,
-0.005411053542047739,
-0.002491228748112917,
0.020138945430517197,
-0.002855293219909072,
0.006684425752609968,
-0.014803031459450722,
0.0070541477762162685,
-0.07042703032493591,
-0.013562297448515892,
0.03800390288233757,
-0.017573494464159012,
-0.030722206458449364,
0.001159405685029924,
-0.007806089706718922,
0.027111833915114403,
-0.021464645862579346,
0.00047115664347074926,
-0.038754891604185104,
-0.01887194998562336,
0.028545858338475227,
-0.013995114713907242,
-0.020444083958864212,
-0.001742116641253233,
-0.0007225206354632974,
-0.05268209055066109,
0.007196236401796341,
0.010072861798107624,
0.002728356746956706,
-0.07052072137594223,
0.03187594935297966,
-0.003211768576875329,
-0.0023583800066262484,
0.011597590520977974,
0.0032225355971604586,
-0.03703958913683891,
0.01900627464056015,
-0.02443884126842022,
-0.015297339297831059,
-0.020310157909989357,
-0.03006720170378685,
-0.025036849081516266,
-0.017650431022047997,
0.01823621429502964,
0.0518932119011879,
-0.05452528968453407,
-0.03110503777861595,
-0.019064657390117645,
-0.010138160549104214,
0.05872271582484245,
0.04145115241408348,
0.03327658027410507,
-0.03502805158495903,
0.011662416160106659,
-0.024612605571746826,
0.0008867229335010052,
-0.03592471405863762,
-0.03378408029675484,
0.010255476459860802,
0.004800187423825264,
0.06159931793808937,
0.03273798152804375,
-0.027706822380423546,
0.031257789582014084,
0.008930729702115059,
-0.015787316486239433,
0.04208730161190033,
0.01673518307507038,
-0.04171845316886902,
-0.04082783684134483,
0.013080422766506672,
-0.013962220400571823,
0.09339538216590881,
-0.010577782057225704,
0.0030516530387103558,
0.020543547347187996,
-0.057439230382442474,
-0.04670193791389465,
0.02052830159664154,
-0.01861274242401123,
-0.02502354606986046,
0.006815183442085981,
-0.008486144244670868,
0.03806150704622269,
-0.05627540126442909,
-0.045759979635477066,
0.03093278780579567,
-0.022588929161429405,
-0.022405600175261497,
0.0438266284763813,
0.021359765902161598,
-0.024774517863988876,
0.006928321905434132,
0.031551193445920944,
0.0020400420762598515,
-0.035656847059726715,
0.04348690062761307,
0.0195987056940794,
0.013474891893565655,
0.03480467200279236,
-0.0021134354174137115,
0.02375905029475689,
-0.004845971241593361,
0.021812165156006813,
0.0006731629837304354,
0.024849113076925278,
0.004085508640855551,
0.04264146834611893,
0.004969567060470581,
-0.013084677048027515,
-0.037606533616781235,
0.03734440356492996,
0.002227674936875701,
0.022953568026423454,
-0.04076758399605751,
0.024185439571738243,
0.00448332354426384,
-0.0012702126987278461,
-0.026756364852190018,
-0.012854058295488358,
-0.0283631794154644,
0.020752109587192535,
-0.009667164646089077,
-0.0033457563258707523,
0.025417223572731018,
-0.024691401049494743,
-0.01909228228032589,
-0.015354782342910767,
0.022376373410224915,
0.028452759608626366,
-0.022388869896531105,
0.031028665602207184,
-0.013078168034553528,
-0.04868870973587036,
-0.0042405566200613976,
0.03754277154803276,
0.05272173136472702,
-0.01591416448354721,
0.012222294695675373,
-0.027074236422777176,
-0.0024570287205278873,
0.029827291145920753,
-0.06490129232406616,
-0.03333142027258873,
0.009435442276299,
0.004253096412867308,
0.004076285287737846,
-0.024453533813357353
] |
<p>Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?</p>
| 272 |
[
-0.013899468816816807,
-0.020591149106621742,
-0.026624659076333046,
-0.028780397027730942,
0.021811392158269882,
-0.021151607856154442,
-0.04620404168963432,
-0.01959351822733879,
-0.03263029456138611,
-0.03391152620315552,
0.013601094484329224,
0.033636853098869324,
0.05961162596940994,
-0.011821637861430645,
0.0013220907421782613,
0.009047691710293293,
-0.038783617317676544,
0.015552970580756664,
0.013562063686549664,
-0.02203523740172386,
0.017768902704119682,
0.029789533466100693,
0.020601529628038406,
0.002723837271332741,
-0.015585624612867832,
-0.03343747556209564,
0.06902282685041428,
-0.012050863355398178,
0.03734227642416954,
0.0404299758374691,
0.011586422100663185,
-0.014440404251217842,
0.011578816920518875,
0.05971010401844978,
0.021759485825896263,
-0.003057006513699889,
-0.050796154886484146,
-0.028670942410826683,
-0.023113388568162918,
0.02973358705639839,
-0.0440007746219635,
-0.05423371493816376,
-0.0360470749437809,
0.04761061072349548,
-0.016584236174821854,
0.006230018101632595,
-0.0007844928186386824,
-0.012731037102639675,
0.03795642778277397,
-0.06319721788167953,
0.06575122475624084,
-0.01622345857322216,
0.0526592843234539,
0.018291788175702095,
-0.03550608083605766,
-0.01162706594914198,
0.09117745608091354,
0.060798268765211105,
-0.022107519209384918,
-0.03613411635160446,
-0.03596489503979683,
0.014170029200613499,
-0.0279000885784626,
-0.007900536991655827,
-0.010778752155601978,
0.014320441521704197,
0.0005562485312111676,
-0.02458086423575878,
0.0310618057847023,
0.01918935775756836,
0.011236323043704033,
0.02129899151623249,
-0.007147729862481356,
-0.017403598874807358,
-0.04536813870072365,
-0.032115738838911057,
-0.0025219651870429516,
-0.031376004219055176,
0.04619259387254715,
0.029342269524931908,
-0.05225249007344246,
0.018489036709070206,
0.05731997266411781,
0.041409723460674286,
0.018500084057450294,
0.016239475458860397,
0.06741776317358017,
-0.001518520643003285,
-0.006498255766928196,
0.024992408230900764,
0.008960707113146782,
0.010392109863460064,
0.010953746736049652,
-0.04303361102938652,
-0.032090917229652405,
0.015026033855974674,
0.007504758425056934,
0.04891031235456467,
0.014464229345321655,
-0.014677147381007671,
0.0056496718898415565,
0.005239212419837713,
-0.010761171579360962,
0.08853296935558319,
0.03104500100016594,
-0.018064254894852638,
-0.018950581550598145,
0.03640447184443474,
-0.035071782767772675,
-0.04634633660316467,
-0.044367387890815735,
-0.0013667349703609943,
-0.04949859529733658,
-0.0496806874871254,
0.03813347965478897,
-0.006310520227998495,
-0.0006464083562605083,
-0.025034641847014427,
0.028145069256424904,
0.07577136158943176,
0.03865116462111473,
0.015233236365020275,
0.014037087559700012,
-0.019148165360093117,
0.008379219099879265,
0.04891650751233101,
0.06206769868731499,
-0.03495638817548752,
-0.03472797945141792,
-0.02198350988328457,
-0.010700898244976997,
-0.039190348237752914,
-0.013285089284181595,
-0.003377014771103859,
0.01715829037129879,
-0.009154502302408218,
-0.08412732183933258,
-0.047582920640707016,
0.03312263637781143,
-0.009260003454983234,
-0.01323575060814619,
-0.04776152968406677,
0.005383522715419531,
0.0016230206238105893,
0.08510536700487137,
0.003216299694031477,
0.012835070490837097,
0.021523546427488327,
0.06009724363684654,
-0.02308732271194458,
-0.019128955900669098,
0.027057284489274025,
0.007672804407775402,
-0.04942185431718826,
-0.02901570312678814,
-0.08083925396203995,
0.0020449229050427675,
0.02861112169921398,
0.017295140773057938,
-0.03334857523441315,
0.05240260809659958,
-0.008797756396234035,
0.023633422330021858,
0.00936064776033163,
-0.016360504552721977,
-0.04480922967195511,
0.04734059050679207,
0.018754499033093452,
-0.022453170269727707,
0.02804642729461193,
-0.0010225799633190036,
0.03488646075129509,
0.030917730182409286,
-0.008330192416906357,
0.030347583815455437,
-0.057118937373161316,
0.022187910974025726,
-0.04652516543865204,
0.0005930360057391226,
-0.011905076913535595,
-0.018011027947068214,
-0.053669653832912445,
0.004793445114046335,
-0.017238875851035118,
-0.013602572493255138,
0.05972300469875336,
-0.030311832204461098,
-0.009724417701363564,
-0.008732346817851067,
-0.05640246346592903,
0.02732529304921627,
-0.03655892238020897,
0.03661610186100006,
0.002965728286653757,
0.0026003350503742695,
-0.007558029145002365,
0.040948666632175446,
0.05821632221341133,
-0.031896550208330154,
-0.03348236903548241,
0.016632625833153725,
0.04902830719947815,
-0.01899799332022667,
0.004084543325006962,
-0.001337342313490808,
0.04970022663474083,
0.03080068901181221,
0.004407256375998259,
0.00834674946963787,
0.026637326925992966,
-0.036619290709495544,
-0.007257444784045219,
-0.017972955480217934,
0.033580176532268524,
-0.004233167972415686,
-0.006599431857466698,
0.04497753828763962,
-0.008553549647331238,
0.030940115451812744,
0.02682187780737877,
-0.02925630286335945,
0.0654630959033966,
0.047742102295160294,
0.016858695074915886,
0.023000696673989296,
0.03728875145316124,
0.04087972268462181,
-0.02203810028731823,
0.008968496695160866,
0.002404517261311412,
-0.011893970891833305,
0.0019543273374438286,
0.05170237645506859,
0.03480500355362892,
-0.05015455558896065,
0.009228341281414032,
0.07637757062911987,
0.03017526865005493,
0.02792567014694214,
0.03238525614142418,
-0.0129218939691782,
-0.025253193452954292,
0.038898419588804245,
-0.003318596398457885,
0.0013541420921683311,
-0.0028831257950514555,
0.031192075461149216,
0.02154608443379402,
-0.026340188458561897,
0.037931911647319794,
-0.05854598060250282,
0.03082612343132496,
-0.006054701283574104,
-0.009224670007824898,
0.02052498050034046,
-0.021776162087917328,
0.03608608618378639,
-0.041497085243463516,
0.014237483032047749,
0.012511077336966991,
-0.0182499922811985,
0.016597749665379524,
-0.004274293314665556,
0.005109273362904787,
0.02091960608959198,
-0.01030989270657301,
-0.008701936341822147,
0.0025763458106666803,
0.054036978632211685,
-0.05499405786395073,
0.014157885685563087,
-0.035974230617284775,
0.02435869537293911,
-0.017165903002023697,
-0.00501957256346941,
0.013879307545721531,
0.02388017438352108,
0.03949352353811264,
0.02150718867778778,
-0.008859463036060333,
0.02029537968337536,
-0.02185291051864624,
-0.04704034700989723,
0.040695879608392715,
-0.029665622860193253,
0.02405237779021263,
-0.032345037907361984,
-0.03042702004313469,
0.05648038908839226,
-0.020317450165748596,
0.011870545335114002,
0.016000086441636086,
-0.018147481605410576,
-0.023179814219474792,
-0.009366771206259727,
-0.03805221617221832,
-0.014007392339408398,
-0.05859653279185295,
0.02613062784075737,
0.037059757858514786,
0.00037909363163635135,
-0.01997767575085163,
0.0221917275339365,
-0.0002563471789471805,
-0.03306196630001068,
0.00706453388556838,
0.019329383969306946,
0.01736547239124775,
-0.06601335853338242,
0.020187003538012505,
-0.02330472320318222,
-0.05634087696671486,
0.0043935407884418964,
-0.03062204085290432,
-0.008723217993974686,
0.0556798130273819,
-0.014610286802053452,
0.03405987471342087,
-0.0046428050845861435,
-0.04243248701095581,
0.0814407616853714,
-0.002694468479603529,
0.005600153934210539,
-0.023971455171704292,
-0.03515592962503433,
-0.029527390375733376,
-0.01654019206762314,
-0.00841033086180687,
0.04222039505839348,
-0.006949635222554207,
-0.026113886386156082,
0.03814565762877464,
-0.005831123795360327,
0.013166936114430428,
-0.001864511170424521,
-0.017619865015149117,
-0.0064605106599628925,
-0.003511778311803937,
0.003821253078058362,
0.058303382247686386,
-0.0203905887901783,
-0.022448107600212097,
0.025244977325201035,
0.005046585109084845,
0.04509362578392029,
0.006195928435772657,
-0.06342390179634094,
0.0490088053047657,
-0.013311196118593216,
0.018756158649921417,
0.0080923642963171,
0.036470454186201096,
-0.01263023167848587,
0.009850749745965004,
0.01613573729991913,
0.04414309188723564,
0.030935026705265045,
0.020206425338983536,
-0.025262724608182907,
0.027155879884958267,
0.07276950776576996,
-0.025239653885364532,
-0.03377669304609299,
-0.025180788710713387,
-0.023800164461135864,
0.03380409628152847,
-0.015150129795074463,
-0.019151605665683746,
0.022589074447751045,
0.0014980339910835028,
0.026478033512830734,
0.014630110934376717,
-0.03875603526830673,
0.006510686129331589,
-0.09637897461652756,
-0.02725735865533352,
-0.024393770843744278,
0.036256320774555206,
-0.02721191570162773,
0.035167451947927475,
0.006376433186233044,
0.027835996821522713,
0.020274385809898376,
-0.017170947045087814,
-0.08453771471977234,
0.018408317118883133,
-0.05336610600352287,
-0.04226742684841156,
-0.0015092547982931137,
-0.0047586094588041306,
-0.03207821398973465,
-0.029756249859929085,
-0.02489718608558178,
-0.02707977034151554,
0.006090224254876375,
-0.06904864311218262,
0.02093278244137764,
-0.004905996844172478,
-0.013784278184175491,
0.009977908805012703,
0.04557019844651222,
0.015499846078455448,
-0.02563829906284809,
0.00866595096886158,
0.0237836092710495,
-0.011526661925017834,
-0.022906167432665825,
0.0061748698353767395,
0.021231498569250107,
-0.029631583020091057,
0.03065093792974949,
0.012939673848450184,
0.014691541902720928,
-0.028643405064940453,
-0.02329745702445507,
0.020043112337589264,
0.020941531285643578,
0.007000231184065342,
0.001795368269085884,
-0.020926935598254204,
-0.06002330780029297,
-0.007397009991109371,
0.012670003809034824,
0.06533754616975784,
-0.015454637818038464,
0.008434191346168518,
0.025815537199378014,
0.0002148784842574969,
0.002433229936286807,
0.00484352046623826,
0.03829193860292435,
0.02051910199224949,
-0.031462155282497406,
-0.06099068373441696,
-0.0019202769035473466,
-0.014950740151107311,
0.0083314822986722,
0.014945040456950665,
-0.008947339840233326,
-0.059453677386045456,
0.014749267138540745,
0.009998688474297523,
0.001540385652333498,
-0.017214460298419,
-0.0002600325387902558,
0.013340638019144535,
0.04615388438105583,
-0.03972639515995979,
0.05616798996925354,
0.02833695337176323,
0.04277050495147705,
0.046146318316459656,
0.022777194157242775,
-0.013140803202986717,
-0.08958498388528824,
-0.014222651720046997,
0.030471088364720345,
0.028882676735520363,
0.024012472480535507,
-0.031523484736680984,
-0.07038714736700058,
0.007352312561124563,
0.07084167003631592,
-0.0081412885338068,
0.033096082508563995,
0.012168949469923973,
0.02687300555408001,
-0.011220204643905163,
-0.02161237597465515,
0.009884792380034924,
0.04242270439863205,
-0.02877853624522686,
-0.01692013256251812,
-0.03606640174984932,
0.02049979381263256,
0.018759040161967278,
0.05010846629738808,
0.0396253876388073,
0.06647137552499771,
0.05945948138833046,
0.009554159827530384,
-0.004065583925694227,
0.0022232993505895138,
-0.06641989946365356,
-0.07650699466466904,
-0.005990315694361925,
0.023597536608576775,
-0.03527617081999779,
0.03872545808553696,
-0.03478020429611206,
-0.018052859231829643,
0.01492577139288187,
-0.021967468783259392,
-0.02124771848320961,
0.0056322007440030575,
-0.051715653389692307,
-0.003308685962110758,
0.031633805483579636,
0.000740431307349354,
0.05929992347955704,
0.02214369736611843,
0.012710179202258587,
-0.0029640670400112867,
-0.004903363063931465,
0.040149230509996414,
-0.037806760519742966,
-0.024680808186531067,
0.02056979387998581,
-0.010469061322510242,
-0.029046015813946724,
0.006916526705026627,
-0.01031032856553793,
0.025758827105164528,
0.039628732949495316,
-0.009532780386507511,
-0.025348806753754616,
0.010485386475920677,
0.004628573078662157,
-0.005196929909288883,
-0.0003701856767293066,
0.024020064622163773,
-0.03468663990497589,
-0.043140143156051636,
0.013700407929718494,
0.030217120423913002,
-0.012504269368946552,
0.03331528976559639,
-0.00890103355050087,
-0.010815798304975033,
-0.016177596524357796,
-0.016871625557541847,
0.02136133797466755,
-0.03353370353579521,
0.09025084227323532,
-0.03999106213450432,
-0.008575506508350372,
0.010667826980352402,
-0.05576262250542641,
-0.005494869779795408,
0.012653771787881851,
0.007778844330459833,
0.03366062045097351,
-0.02379854954779148,
0.002032229909673333,
0.05162208527326584,
0.012212530709803104,
-0.06526611000299454,
-0.007182625122368336,
0.04982326179742813,
0.018486542627215385,
0.03141581267118454,
-0.024196309968829155,
0.020468819886446,
-0.06890825182199478,
-0.03207765147089958,
-0.0221874937415123,
0.032691679894924164,
-0.04545724019408226,
0.0027962226886302233,
-0.021693706512451172,
0.0048489817418158054,
0.012147199362516403,
-0.023594699800014496,
-0.04258069396018982,
0.02743217907845974,
-0.015240705572068691,
0.010075966827571392,
-0.015658309683203697,
0.06061997264623642,
-0.02443927899003029,
-0.021163182333111763,
-0.016940483823418617,
-0.025521254166960716,
0.03277009725570679,
0.01126649510115385,
0.019184134900569916,
0.08202581107616425,
0.002260165521875024,
0.022957205772399902,
-0.00948240328580141,
0.024295354261994362,
-0.03300810232758522,
0.036357585340738297,
-0.022579343989491463,
-0.01649317517876625,
-0.04000858962535858,
-0.02234523557126522,
0.02348656952381134,
0.022767432034015656,
-0.011750283651053905,
-0.024258354678750038,
0.06894040107727051,
0.021500635892152786,
-0.07335492968559265,
-0.008460781536996365,
-0.015757514163851738,
0.008385342545807362,
0.007088882848620415,
0.03055613487958908,
0.009518739767372608,
-0.007372959516942501,
-0.014339367859065533,
-0.036884158849716187,
-0.005160316824913025,
-0.0010751503286883235,
0.09514431655406952,
-0.0441153384745121,
0.0528494231402874,
0.008784020319581032,
-0.004782664589583874,
-0.0240972638130188,
-0.0230253916233778,
0.008331014774739742,
0.004122848156839609,
-0.013004743494093418,
0.03007645718753338,
0.008732371963560581,
-0.0029162743594497442,
0.018452579155564308,
0.033863458782434464,
-0.005043982993811369,
0.05335197225213051,
0.011922817677259445,
0.015281552448868752,
0.03756536915898323,
0.013040997087955475,
-0.023279409855604172,
-0.00024538367870263755,
-0.05476072430610657,
0.04417729750275612,
-0.006157125812023878,
-0.01221716683357954,
0.03799145668745041,
-0.002556553576141596,
0.031171070411801338,
-0.018969910219311714,
-0.03249508515000343,
-0.036982014775276184,
0.013149606063961983,
-0.003428868018090725,
-0.010627112351357937,
0.011181429959833622,
0.024443427100777626,
0.030356096103787422,
0.0277435053139925,
0.02655387856066227,
0.012022793292999268,
-0.04630858078598976,
-0.023411892354488373,
-0.028824500739574432,
-0.0665966272354126,
0.0485483855009079,
0.028111876919865608,
-0.026449818164110184,
0.025986360386013985,
0.005995248444378376,
0.006352405995130539,
0.034371212124824524,
0.048419516533613205,
-0.009554661810398102,
0.10387994349002838,
-0.042204249650239944,
-0.0039031957276165485,
-0.024307874962687492,
0.010587689466774464,
0.1003054603934288,
0.0313199944794178,
0.022453904151916504,
-0.0634089782834053,
0.0026811405550688505,
-0.032911915332078934,
-0.00034059686004184186,
-0.046588998287916183,
0.02081316150724888,
-0.016912192106246948,
-0.010664132423698902,
0.017361514270305634,
0.05265277624130249,
0.00304975057952106,
-0.069784976541996,
0.04707661271095276,
-0.017859606072306633,
-0.009201432578265667,
0.005897179711610079,
0.030430404469370842,
0.011182406917214394,
0.003499835031107068,
-0.038506604731082916,
0.042481016367673874,
-0.04654041677713394,
0.005843323655426502,
-0.03697384148836136,
-0.010834642685949802,
-0.015820201486349106,
-0.039603859186172485,
-0.08629690855741501,
-0.001401997054927051,
0.005518757738173008,
-0.01310129277408123,
-0.04171213135123253,
0.02234766073524952,
0.0035813439171761274,
-0.023385630920529366,
0.00986495241522789,
0.014261307194828987,
-0.002146362792700529,
0.027364905923604965,
0.012244613841176033,
-0.008041473105549812,
-0.029494300484657288,
0.04205814003944397,
-0.014065390452742577,
0.013067284598946571,
-0.02323359251022339,
0.014147274196147919,
0.007783068809658289,
-0.005114739295095205,
-0.018602559342980385,
-0.06393704563379288,
-0.007985631935298443,
-0.015630556270480156,
-0.01865062676370144,
0.017784276977181435,
-0.02585081197321415,
0.017401712015271187,
0.014470036141574383,
0.02349191904067993,
0.02882387489080429,
0.003231628565117717,
0.021746300160884857,
0.025547441095113754,
-0.0014604859752580523,
0.07756107300519943,
-0.046630099415779114,
-0.022948255762457848,
-0.021530935540795326,
-0.02054501324892044,
-0.04658334329724312,
0.009090784005820751,
0.01973256655037403,
0.007758244406431913,
0.007582462392747402,
0.01034696213901043,
0.011482302099466324,
-0.028486665338277817,
-0.057642772793769836,
0.028543977066874504,
-0.0419948510825634,
-0.018350960686802864,
-0.0009096467983908951,
-0.00696933176368475,
0.04102056846022606,
0.014496898278594017,
-0.001663330476731062,
0.009370021522045135,
-0.02376639097929001,
0.024904878810048103,
0.021201711148023605,
-0.03142007440328598,
-0.019747057929635048,
-0.005237811245024204,
-0.013975387439131737,
0.010572430677711964,
-0.013948912732303143,
0.015444745309650898,
0.040806662291288376,
-0.009529057890176773,
-0.02463148906826973,
0.032590437680482864,
-0.0356084480881691,
0.027795610949397087,
0.015128543600440025,
-0.02804495580494404,
-0.022742215543985367,
0.014916620217263699,
-0.014180568978190422,
-0.040173936635255814,
-0.0030497214756906033,
-0.04702746868133545,
-0.027173206210136414,
0.007344208657741547,
0.045327264815568924,
-0.03300093114376068,
0.0389261431992054,
0.015590361319482327,
0.01258059497922659,
-0.04869154095649719,
-0.0015787385636940598,
-0.03598640486598015,
0.02559950388967991,
-0.00010024398943642154,
-0.02874046377837658,
-0.007495264057070017,
0.00484152277931571,
-0.0288026574999094,
0.00463862856850028,
-0.004867190960794687,
0.018281064927577972,
0.00552784139290452,
0.024568580090999603,
0.028725340962409973,
-0.026274405419826508,
0.04983789473772049,
0.010072288103401661,
-0.0176690760999918,
0.0420963354408741,
-0.05031035095453262,
-0.05587294325232506,
0.04608723521232605,
-0.048590101301670074,
0.04485132917761803,
0.01701071485877037,
-0.057640090584754944,
-0.006828372832387686,
0.056441277265548706,
-0.026408560574054718,
-0.011704221367835999,
0.01771826669573784,
0.0045214248821139336,
-0.006748107261955738,
-0.002861926332116127,
0.04578479379415512,
-0.04676390811800957,
0.009390443563461304,
0.05902082845568657,
0.009188828989863396,
-0.02273859828710556,
0.012886689975857735,
0.01930277794599533,
-0.020199397578835487,
0.006839186418801546,
0.01745002157986164,
-0.00731501542031765,
0.025808067992329597,
0.044235941022634506,
-0.05904902145266533,
0.019153714179992676,
0.036468543112277985,
0.02208350971341133,
-0.08781659603118896,
-0.013546902686357498,
-0.012155449949204922,
-0.01625177264213562,
0.03800292685627937,
-0.05607081949710846,
0.02835555374622345,
0.0020600848365575075,
-0.06055813655257225,
0.0030092396773397923,
-0.04190531000494957,
0.01958812214434147,
-0.026146424934267998,
-0.004118115641176701,
0.03172820806503296,
0.00820126198232174,
0.048077888786792755,
0.01117322500795126,
-0.03460429608821869,
0.001787621877156198,
-0.012774343602359295,
-0.039491187781095505,
0.014147802256047726,
0.0029117371886968613,
-0.008991221897304058,
-0.006258772220462561,
0.037398144602775574,
0.00904290471225977,
-0.021710488945245743,
0.011424969881772995,
0.035621143877506256,
0.02440805360674858,
-0.013190790079534054,
0.006868375930935144,
0.006652941927313805,
0.007404005620628595,
0.01849350892007351,
-0.039023056626319885,
-0.010036056861281395,
0.0013637664960697293,
-0.006679485086351633,
0.031761154532432556,
-0.029360994696617126,
0.02024795301258564,
0.00578733254224062,
-0.02193501777946949,
-0.035030297935009,
0.041899532079696655,
-0.02885730378329754,
-0.020466243848204613,
-0.010727251879870892,
0.001155214267782867,
0.011595985852181911,
-0.030386118218302727,
-0.0019753947854042053,
-0.07929956167936325,
0.01406863983720541,
0.018371421843767166,
0.004756248090416193,
-0.002738298149779439,
0.018051283434033394,
0.017191709950566292,
0.0007454349542967975,
-0.006034557241946459,
-0.03912567347288132,
0.02441161498427391,
-0.05647002533078194,
0.007469013333320618,
-0.01973869651556015,
-0.014191998168826103,
-0.0019630715250968933,
-0.0655319020152092,
0.018364641815423965,
0.03638981655240059,
0.003555759321898222,
0.0017464340198785067,
0.02812071330845356,
-0.045783884823322296,
-0.008535100147128105,
-0.06309929490089417,
0.009067497216165066,
-0.003456762060523033,
0.009233537130057812,
-0.008633741177618504,
-0.03768794238567352,
0.0019243605202063918,
-0.02280905842781067,
0.036038026213645935,
-0.008108852431178093,
-0.0006239546346478164,
0.048076678067445755,
-0.004845861345529556,
-0.011134942062199116,
-0.06694632023572922,
0.016922147944569588,
-0.028210271149873734,
-0.05794304981827736,
-0.0009427687036804855,
-0.017058582976460457,
-0.004103266634047031,
0.006112148519605398,
0.011664182879030704,
0.012968847528100014,
0.05168824642896652,
0.02321365848183632,
0.009726778604090214,
0.049114570021629333,
0.04376009479165077,
0.016822287812829018,
0.03645686060190201,
0.02340690605342388,
0.01274630893021822,
0.030566925182938576,
-0.005836936645209789,
-0.01168929785490036,
0.0309696514159441,
-0.01751922257244587,
-0.009189383126795292,
-0.03891698271036148,
-0.02406315878033638,
-0.005969791207462549,
-0.04281049594283104,
-0.008442442864179611,
0.07536452263593674,
-0.0419258251786232,
0.01671498455107212,
0.010832220315933228,
0.015173752792179585,
0.02395792119204998,
-0.009320275858044624,
0.007842729799449444,
0.04222714900970459,
0.009747719392180443,
-0.02917713299393654,
0.03136000409722328,
0.030265824869275093,
0.005259535275399685,
0.0029985220171511173,
0.03118540719151497,
0.009775030426681042,
0.0008641842287033796,
0.024889854714274406,
0.026610545814037323,
-0.030284391716122627,
-0.05412428453564644,
-0.0019867641385644674,
-0.011269711889326572,
0.034222833812236786,
0.021209245547652245,
-0.009627986699342728,
0.06840497255325317,
-0.0015789616154506803,
0.01112629845738411,
-0.011688913218677044,
-0.018952181562781334,
0.008618956431746483,
0.04640526324510574,
0.016764862462878227,
0.05660698190331459,
-0.005792711395770311,
-0.022872138768434525,
-0.0020346848759800196,
0.0050784931518137455,
0.022545401006937027,
-0.02439267374575138,
0.009592866525053978,
-0.00012319798406679183,
0.037007465958595276,
-0.02070150338113308,
-0.040477924048900604,
-0.031205419450998306,
-0.04890057444572449,
0.01956368423998356,
0.024803372099995613,
0.02736186608672142,
0.023996204137802124,
-0.002766895107924938,
-0.023633860051631927,
0.030385402962565422,
-0.06277865171432495,
-0.032555460929870605,
-0.004977740813046694,
0.051508430391550064,
-0.022221792489290237,
0.01159853208810091
] |
<p>Recently, I read in the journal <a href="http://www.nature.com/news/stephen-hawking-there-are-no-black-holes-1.14583">Nature</a> that Stephen Hawking wrote a paper claiming that black holes do not exist. How is this possible? Please explain it to me because I didn't understand what he said.</p>
<p>References:</p>
<ol>
<li><p>Article in Nature News: <a href="http://dx.doi.org/doi:10.1038/nature.2014.14583"><em>Stephen Hawking: 'There are no black holes'</em></a> (Zeeya Merali, January 24, 2014).</p></li>
<li><p>S. Hawking, <em>Information Preservation and Weather Forecasting for Black Holes,</em> <a href="http://arxiv.org/abs/1401.5761">arXiv:1401.5761</a>.</p></li>
</ol>
| 763 |
[
-0.046529371291399,
-0.049110617488622665,
0.006630400195717812,
-0.0517781600356102,
0.03267017379403114,
-0.014863645657896996,
-0.03999578207731247,
0.0016906560631468892,
-0.048396527767181396,
-0.03335438668727875,
0.019153015688061714,
0.01854138821363449,
0.042110417038202286,
0.037575602531433105,
0.0037822953891009092,
0.012578235939145088,
-0.026845693588256836,
0.003960023168474436,
-0.003162153996527195,
-0.01201798114925623,
0.027092337608337402,
0.03684181720018387,
0.009460770525038242,
0.016050251200795174,
-0.011677257716655731,
0.009407786652445793,
-0.025286514312028885,
0.02917632646858692,
0.020263923332095146,
0.04049043357372284,
-0.00847479049116373,
-0.016955439001321793,
-0.01397428847849369,
0.033228833228349686,
-0.016081493347883224,
-0.015215329825878143,
-0.03681037575006485,
-0.0008460203534923494,
-0.003045555204153061,
-0.006575134117156267,
0.009862019680440426,
-0.04423736035823822,
0.015463542193174362,
0.06504683196544647,
-0.06954141706228256,
0.0024085002951323986,
0.026628931984305382,
-0.04005616530776024,
0.027656005695462227,
-0.06258806586265564,
0.030464082956314087,
-0.004577750340104103,
0.04800328612327576,
0.044364165514707565,
-0.03172321245074272,
0.02659444697201252,
0.08240256458520889,
0.09760735183954239,
-0.042023397982120514,
-0.04655762389302254,
-0.020367786288261414,
-0.0313095822930336,
0.02210630103945732,
-0.002907942747697234,
0.001873389701358974,
0.059661250561475754,
-0.017367703840136528,
0.0003488661313895136,
0.011778169311583042,
-0.010178417898714542,
0.021660836413502693,
-0.02578768879175186,
-0.011607328429818153,
0.002751866588369012,
-0.002642629900947213,
-0.06192411109805107,
0.018865957856178284,
-0.01974538527429104,
0.020565731450915337,
0.07151398807764053,
-0.01097839791327715,
0.000337639736244455,
0.05006417632102966,
-0.007253033574670553,
-0.0053192321211099625,
-0.001227441942319274,
0.10215935111045837,
0.015501204878091812,
0.028918853029608727,
0.005611490923911333,
-0.013855429366230965,
-0.008444207720458508,
0.03316020220518112,
-0.04253525286912918,
-0.016331087797880173,
0.021877074614167213,
0.004466810263693333,
0.027220293879508972,
-0.05328187346458435,
-0.036580890417099,
-0.0000034875238270615228,
0.018137233331799507,
0.034308064728975296,
0.07263399660587311,
0.004186768550425768,
-0.03671355918049812,
-0.05729314684867859,
0.028238199651241302,
-0.04673808068037033,
-0.00908044632524252,
-0.0511472150683403,
0.008955518715083599,
0.01612015813589096,
-0.031198512762784958,
-0.00048440491082146764,
-0.03265520557761192,
0.0024093997199088335,
-0.01389079075306654,
0.03195309638977051,
0.07667015492916107,
0.028232812881469727,
-0.014396551065146923,
0.0037179687060415745,
-0.031511805951595306,
-0.05240270867943764,
0.03499748185276985,
0.039930310100317,
0.0009332436020486057,
-0.023961056023836136,
0.020639576017856598,
-0.01060773991048336,
0.02345103584229946,
0.017843885347247124,
0.05382787436246872,
0.025091039016842842,
-0.04036980867385864,
-0.13045097887516022,
-0.035942405462265015,
0.08020982146263123,
-0.00994921289384365,
-0.010846317745745182,
-0.04797176271677017,
-0.01516081765294075,
0.023161213845014572,
0.06854043155908585,
0.007015742361545563,
0.015532189980149269,
0.03235927224159241,
0.01570373773574829,
0.00851490069180727,
-0.03551434725522995,
0.029032109305262566,
0.002525239484384656,
-0.029997484758496284,
0.00032790255500003695,
-0.05830136686563492,
0.018506387248635292,
0.024162614718079567,
0.0018293674802407622,
-0.03901924192905426,
0.06419294327497482,
0.0009397262474521995,
0.0033967909403145313,
0.015019872225821018,
-0.022983349859714508,
-0.011858324520289898,
0.06472864001989365,
0.022118350490927696,
-0.0032284811604768038,
0.07261127233505249,
0.016330629587173462,
0.044109851121902466,
-0.000426010403316468,
0.05895380303263664,
0.02207094430923462,
-0.03906021639704704,
-0.002621299121528864,
-0.013784436509013176,
-0.003233574330806732,
-0.01392570324242115,
-0.04852116107940674,
0.005488731898367405,
0.02997009828686714,
-0.0004549721197690815,
0.013836275786161423,
0.05599220469594002,
-0.017961878329515457,
-0.001664643525145948,
0.011556639336049557,
-0.061034996062517166,
-0.012263307347893715,
-0.09450031071901321,
0.023186465725302696,
-0.006690839771181345,
0.03479719161987305,
0.03317209705710411,
0.011889678426086903,
0.023320510983467102,
-0.018347304314374924,
-0.01129431277513504,
0.02126648835837841,
0.03626907244324684,
0.021482180804014206,
-0.01736350543797016,
-0.0012820352567359805,
0.046514298766851425,
0.04726972430944443,
-0.023598331958055496,
0.005187795963138342,
-0.020568856969475746,
-0.03934778273105621,
0.0005814373726025224,
-0.008671322837471962,
-0.007418920285999775,
-0.0054887752048671246,
-0.02320566214621067,
0.02458946593105793,
0.029166771098971367,
-0.010579763911664486,
0.025092609226703644,
-0.024919308722019196,
0.0472697876393795,
-0.007530752569437027,
0.0032463818788528442,
-0.009285863488912582,
0.02380506880581379,
0.00959332101047039,
0.003506673965603113,
0.0067906505428254604,
-0.007773406803607941,
-0.06490714102983475,
0.022134974598884583,
0.05874108150601387,
0.025942597538232803,
-0.025390686467289925,
0.024796217679977417,
0.01881217584013939,
0.03654368966817856,
0.007212540600448847,
0.037173543125391006,
-0.002946777269244194,
-0.019230449572205544,
0.02627851627767086,
-0.0008031768375076354,
0.011029849760234356,
0.038943223655223846,
0.054754819720983505,
0.004967242479324341,
0.02310316078364849,
-0.006754622329026461,
-0.026177361607551575,
0.06655281782150269,
-0.04259691759943962,
0.0055702258832752705,
0.0017053255578503013,
0.0015462100272998214,
0.016412509605288506,
-0.026945114135742188,
0.002501604612916708,
0.004827439785003662,
-0.010810389183461666,
-0.030138473957777023,
-0.05163101851940155,
0.00743108568713069,
-0.009267947636544704,
0.018970835953950882,
-0.033601466566324234,
-0.013616683892905712,
0.003149803727865219,
-0.051893968135118484,
-0.00597829045727849,
-0.02197284996509552,
-0.030213819816708565,
-0.04491917043924332,
0.025193270295858383,
0.03458155319094658,
-0.004906976129859686,
0.01919524557888508,
-0.0077223279513418674,
-0.045186907052993774,
0.024288572371006012,
-0.03158039227128029,
-0.012022359296679497,
0.02701735869050026,
-0.03269843012094498,
-0.0018039257265627384,
-0.013984336517751217,
-0.025503145530819893,
0.07216203212738037,
-0.04041852802038193,
0.0014025300042703748,
-0.0017608619527891278,
-0.037785839289426804,
-0.02566499635577202,
0.0002284842630615458,
-0.03839275613427162,
0.010241877287626266,
0.002006739377975464,
-0.013869965448975563,
0.042105644941329956,
-0.02448565885424614,
-0.003908606246113777,
0.031093260273337364,
-0.010704504325985909,
-0.05098215490579605,
0.00816851481795311,
0.005143558606505394,
0.0008835092303343117,
-0.0573863722383976,
0.014470902271568775,
0.016738446429371834,
-0.03815300390124321,
0.013202529400587082,
-0.04933807626366615,
-0.06100849062204361,
0.01950223371386528,
0.0043524159118533134,
0.01958819106221199,
-0.0036048535257577896,
-0.030867833644151688,
0.04774312674999237,
0.012613807804882526,
-0.020055511966347694,
-0.019344903528690338,
-0.030395936220884323,
-0.006439086515456438,
-0.012447685934603214,
-0.014871944673359394,
0.03113839216530323,
0.011669193394482136,
0.0028783397283405066,
0.018383242189884186,
-0.001624629832804203,
0.022103201597929,
0.0046416292898356915,
-0.02293643169105053,
-0.06361179798841476,
-0.020083323121070862,
0.018819766119122505,
0.04357228800654411,
0.008226345293223858,
-0.03870554640889168,
-0.005073533859103918,
-0.012424164451658726,
0.05388208478689194,
0.04195064678788185,
-0.051861781626939774,
0.027033966034650803,
0.016826266422867775,
0.030605832114815712,
-0.05798669904470444,
0.023088831454515457,
-0.021960271522402763,
-0.017220718786120415,
0.0007114752079360187,
-0.012758087366819382,
0.04917790740728378,
0.015204386785626411,
-0.008867107331752777,
0.017878346145153046,
0.03128116577863693,
-0.040665604174137115,
-0.0037959825713187456,
-0.048625387251377106,
-0.026033231988549232,
0.010685868561267853,
0.008570900186896324,
0.01009207870811224,
0.045154377818107605,
0.033381666988134384,
-0.004115371499210596,
0.0013855613069608808,
-0.02226950228214264,
0.00828155130147934,
-0.04987800493836403,
0.015380959026515484,
-0.011559328064322472,
0.028959864750504494,
-0.002703581005334854,
0.02333579957485199,
0.002272706013172865,
0.000378363678464666,
0.023457588627934456,
-0.008457873947918415,
-0.04521630331873894,
-0.004489709157496691,
-0.02588941901922226,
-0.029640616849064827,
0.0037504059728235006,
-0.031567927449941635,
-0.014025687240064144,
-0.016883106902241707,
-0.013397403061389923,
-0.01626913622021675,
-0.004485434386879206,
-0.06433041393756866,
-0.00020786495588254184,
-0.021768439561128616,
-0.007324100472033024,
-0.006677503231912851,
0.03179874271154404,
0.04725085571408272,
-0.02902889810502529,
0.013888919726014137,
0.0218536127358675,
-0.02265501394867897,
-0.03620421513915062,
0.010682184249162674,
0.003901056246832013,
0.008529423736035824,
0.016972536221146584,
0.02195594273507595,
0.008590619079768658,
-0.009158104658126831,
0.02751731686294079,
0.039302289485931396,
0.053441304713487625,
-0.00843394361436367,
0.013957032933831215,
-0.038312993943691254,
-0.03313978388905525,
0.006643122993409634,
0.012420732527971268,
0.051858026534318924,
-0.027578512206673622,
0.02073562704026699,
0.020281193777918816,
0.003318595699965954,
-0.0011880878591910005,
0.009409422986209393,
0.03649691864848137,
-0.004430900793522596,
0.009564497508108616,
-0.035138800740242004,
-0.04322127625346184,
-0.027001837268471718,
-0.02111666277050972,
0.0405518114566803,
0.001750723458826542,
-0.027767207473516464,
0.00790238007903099,
0.009938448667526245,
-0.01425272598862648,
-0.030318371951580048,
-0.010087224654853344,
0.00904139131307602,
0.0199525598436594,
-0.02840624563395977,
0.028477240353822708,
0.024172281846404076,
0.08636024594306946,
0.036286283284425735,
0.01736067421734333,
-0.02376941218972206,
-0.0807814970612526,
0.0016015784349292517,
0.04163900390267372,
0.04087460786104202,
0.030160430818796158,
-0.018173454329371452,
-0.0662701204419136,
-0.005459981970489025,
0.042506251484155655,
-0.011704547330737114,
0.03598221018910408,
-0.02026541344821453,
0.02422822080552578,
-0.006508642807602882,
-0.027025213465094566,
0.03383678197860718,
0.006416282616555691,
-0.029520351439714432,
0.048308130353689194,
0.024528905749320984,
0.011504917405545712,
-0.00956694781780243,
-0.021994397044181824,
-0.005869879387319088,
0.07182174921035767,
-0.0005511093768291175,
0.021045077592134476,
0.002648456022143364,
0.0025952032301574945,
-0.028060385957360268,
-0.08334706723690033,
-0.022875797003507614,
0.002205903409048915,
-0.04137156158685684,
0.06174261122941971,
-0.028165364637970924,
-0.051391005516052246,
0.026950620114803314,
0.00442122807726264,
-0.031882453709840775,
0.0038539113011211157,
-0.07238252460956573,
-0.035138681530952454,
0.024528948590159416,
-0.010126421228051186,
0.02693980000913143,
0.017427099868655205,
-0.008689415641129017,
0.0044156932272017,
-0.04711677506566048,
0.04577678442001343,
-0.033616889268159866,
-0.0001847110834205523,
-0.01687624864280224,
0.026926646009087563,
-0.05094938352704048,
0.025378825142979622,
0.007234513759613037,
0.026838364079594612,
0.022207578644156456,
-0.03338909149169922,
-0.05324920266866684,
0.007401247974485159,
0.019970018416643143,
-0.005196277052164078,
-0.02003282494843006,
0.043969061225652695,
-0.01595171168446541,
-0.03370071202516556,
0.012592836283147335,
-0.0008857477805577219,
-0.014017441309988499,
0.044160015881061554,
0.005774913355708122,
0.011888200417160988,
-0.03304322808980942,
-0.028624121099710464,
0.060656558722257614,
-0.03429659456014633,
0.030757900327444077,
-0.0011178411077708006,
-0.017445560544729233,
0.04229278489947319,
-0.05330970883369446,
-0.02654620073735714,
-0.024365466088056564,
0.003606832353398204,
0.02608264423906803,
-0.07957570254802704,
0.02725985273718834,
0.05476927012205124,
0.010349924676120281,
-0.06779836118221283,
-0.028964456170797348,
0.054864462465047836,
0.027739612385630608,
-0.04028584435582161,
-0.026216693222522736,
0.05115451291203499,
-0.051030807197093964,
-0.03723655641078949,
-0.03523053228855133,
0.007962312549352646,
-0.03576439991593361,
-0.024378009140491486,
0.02113674208521843,
0.0139924893155694,
0.03676498308777809,
-0.009489554911851883,
-0.032458506524562836,
0.00022420837194658816,
0.003041884396225214,
0.0018144104396924376,
-0.03847289830446243,
0.03198356181383133,
-0.012627053074538708,
-0.029855726286768913,
-0.04405219852924347,
-0.0029038540087640285,
0.007418584078550339,
-0.013574850745499134,
0.03711682930588722,
0.028325768187642097,
0.019671129062771797,
0.00491413613781333,
-0.022647082805633545,
0.020943569019436836,
-0.051614779978990555,
0.026508066803216934,
-0.03209438547492027,
0.0015822574496269226,
0.017423514276742935,
-0.027573231607675552,
0.049341823905706406,
-0.007813943549990654,
0.024121226742863655,
0.0035188801120966673,
0.04898390173912048,
0.030096903443336487,
0.020785538479685783,
-0.025451622903347015,
-0.05790282040834427,
0.03208775445818901,
0.03234949707984924,
0.03591317683458328,
0.0016383602051064372,
-0.010570588521659374,
-0.016667256131768227,
-0.02826313115656376,
-0.015525390394032001,
0.04164675250649452,
0.08802853524684906,
-0.0008043756242841482,
0.006451822351664305,
0.031740058213472366,
-0.012476759031414986,
-0.004163977690041065,
-0.05401427298784256,
0.02014024555683136,
0.021828221157193184,
0.012589962221682072,
0.021046046167612076,
0.00011735755833797157,
-0.004310564137995243,
0.04920271411538124,
0.04785880446434021,
0.02596905268728733,
0.014909625984728336,
0.038618188351392746,
0.008442561142146587,
-0.021812213584780693,
0.011986826546490192,
-0.027833016589283943,
0.0503057986497879,
-0.027133574709296227,
0.03804803639650345,
0.02557547762989998,
0.009446398355066776,
0.015388055704534054,
-0.030160890892148018,
0.02170966938138008,
-0.035899125039577484,
-0.035547249019145966,
-0.05322756990790367,
0.006689226720482111,
-0.011624885722994804,
-0.01576477289199829,
0.014572879299521446,
-0.012138859368860722,
-0.0040234727784991264,
0.022798674181103706,
0.015201758593320847,
-0.0006078229635022581,
-0.06668810546398163,
-0.024844439700245857,
-0.03841428458690643,
-0.01604682207107544,
0.06914649158716202,
0.04223060980439186,
-0.03033556416630745,
0.000047513000026810914,
0.0025833139661699533,
0.019511530175805092,
0.029494918882846832,
0.05008865147829056,
-0.013462829403579235,
0.04772926867008209,
0.014447330497205257,
0.009544948115944862,
-0.032326750457286835,
0.0052438038401305676,
0.10736832022666931,
0.07449550181627274,
0.02131037227809429,
-0.05070456489920616,
0.02570391818881035,
0.0062132226303219795,
0.01484261266887188,
-0.031005864962935448,
0.05598825961351395,
-0.0412091389298439,
0.03437313064932823,
-0.0022611573804169893,
0.027329975739121437,
-0.014376209117472172,
-0.03773723170161247,
0.052153076976537704,
-0.040644239634275436,
-0.00648796372115612,
-0.03917590528726578,
0.01745876669883728,
0.0010836995206773281,
-0.007847254164516926,
-0.0597420297563076,
0.025131361559033394,
0.0019608575385063887,
-0.0383211150765419,
-0.01810809038579464,
-0.027050519362092018,
-0.0067808544263243675,
0.001981894252821803,
-0.04971373453736305,
-0.004475685767829418,
0.023897482082247734,
-0.01519793551415205,
-0.0006800412083975971,
-0.010043518617749214,
0.007626514881849289,
-0.006980599369853735,
0.04425067827105522,
0.05720531567931175,
-0.000599296239670366,
-0.026005906984210014,
0.005921465344727039,
0.028568675741553307,
-0.043238043785095215,
-0.008188861422240734,
-0.021279234439134598,
0.05268911272287369,
-0.053274620324373245,
-0.0026407630648463964,
-0.02926444448530674,
-0.00807061418890953,
-0.0011391197331249714,
-0.031091388314962387,
-0.005287937819957733,
0.011775964871048927,
0.0014201690210029483,
-0.028637951239943504,
-0.0463830828666687,
-0.009930931963026524,
0.00423678383231163,
0.002239325549453497,
0.035710662603378296,
0.04562760889530182,
0.01937483623623848,
0.00031515309819951653,
-0.014150397852063179,
0.0001551960885990411,
-0.028241874650120735,
0.027643730863928795,
-0.06148424744606018,
0.001138816587626934,
-0.019334783777594566,
-0.0231490358710289,
-0.0029817894101142883,
0.0014379770727828145,
0.02596108242869377,
0.007378512527793646,
0.01946774125099182,
-0.013555972836911678,
-0.05509921908378601,
0.02359827607870102,
-0.006682500708848238,
-0.018601706251502037,
-0.0056607979349792,
-0.005968917161226273,
-0.02830674685537815,
0.014832217246294022,
-0.011304968036711216,
-0.007371011655777693,
0.018531112000346184,
-0.014044491574168205,
0.02538246661424637,
-0.012418278492987156,
-0.005042267497628927,
0.009633834473788738,
-0.05567450076341629,
-0.0041631171479821205,
-0.010677819140255451,
0.023902874439954758,
0.04795408621430397,
0.0323810875415802,
0.016675354912877083,
0.04642229154706001,
-0.0223857294768095,
-0.032654594630002975,
0.03841473162174225,
-0.03646495193243027,
0.036833398044109344,
0.029103700071573257,
0.03755800798535347,
-0.029565710574388504,
-0.03257778659462929,
-0.0011094819055870175,
0.015615303069353104,
0.015313689596951008,
0.02449844777584076,
-0.023445017635822296,
0.02661115676164627,
0.010000795125961304,
0.03366732597351074,
-0.05327432230114937,
-0.006319686770439148,
-0.0513732023537159,
0.04031426087021828,
-0.004108380991965532,
-0.006308571435511112,
-0.027005810290575027,
0.02798393927514553,
0.0030070405919104815,
-0.023037917912006378,
0.021923374384641647,
0.007386732380837202,
-0.046943262219429016,
0.009726475924253464,
0.01001596450805664,
-0.0025959641207009554,
0.0430121123790741,
0.004924514330923557,
-0.06193801015615463,
0.04922236502170563,
-0.03681281954050064,
-0.06556644290685654,
0.032165300101041794,
-0.014152356423437595,
0.010391635820269585,
0.03950269892811775,
-0.04426918178796768,
-0.012393510900437832,
0.062218885868787766,
-0.028484730049967766,
-0.0007198378443717957,
-0.017614541575312614,
0.013615366071462631,
0.0013755944091826677,
0.014369547367095947,
0.009470803663134575,
-0.020243853330612183,
-0.031074972823262215,
0.0312343779951334,
0.01601254753768444,
0.01781493052840233,
-0.011431222781538963,
0.02343379519879818,
-0.011275894939899445,
-0.010812225751578808,
-0.008319290354847908,
0.005356209818273783,
-0.009052134118974209,
0.07408127188682556,
-0.04579829052090645,
0.07547268271446228,
0.008363960310816765,
0.01642213761806488,
-0.12275560200214386,
0.01638341322541237,
0.02637440897524357,
0.0016258434625342488,
0.025055481120944023,
-0.03499068692326546,
0.021021492779254913,
0.01538889016956091,
-0.0686996579170227,
0.01813495345413685,
-0.04005703702569008,
-0.033687397837638855,
-0.03212578594684601,
0.00019947561668232083,
-0.019515326246619225,
0.05354974418878555,
0.0694674402475357,
0.014271996915340424,
-0.010161522775888443,
-0.006732131354510784,
-0.008933372795581818,
-0.024813372641801834,
-0.025432711467146873,
0.016573503613471985,
-0.004893757868558168,
-0.009626494720578194,
0.07388707250356674,
-0.00871487706899643,
-0.010578148998320103,
0.048101358115673065,
-0.004087425302714109,
-0.0045157927088439465,
0.006737773306667805,
0.02650180645287037,
0.024279270321130753,
0.0047346483916044235,
0.01768743246793747,
0.000212759172427468,
0.004136340692639351,
0.005898196250200272,
0.009369872510433197,
0.02426202781498432,
0.017700931057333946,
-0.0005446139839477837,
-0.028930827975273132,
-0.05015679448843002,
-0.06047479063272476,
0.002319566672667861,
-0.004454444162547588,
0.00034720631083473563,
0.022666797041893005,
0.029073914512991905,
0.006504354998469353,
-0.011793063022196293,
-0.016207121312618256,
-0.03942129760980606,
-0.0058205765672028065,
0.0475090928375721,
0.01775505766272545,
-0.002498550107702613,
0.011487042531371117,
-0.02246720902621746,
-0.040344852954149246,
0.03301587700843811,
0.004804551135748625,
-0.004867203067988157,
-0.059809911996126175,
-0.003224501386284828,
0.004022589419037104,
0.005667863413691521,
-0.006108843721449375,
-0.023160967975854874,
-0.018740003928542137,
0.022885344922542572,
0.003390671918168664,
0.009724438190460205,
-0.017662974074482918,
-0.04886819049715996,
-0.03661036863923073,
-0.053894493728876114,
0.035993169993162155,
-0.003885942278429866,
0.053234510123729706,
-0.050067778676748276,
-0.04387088865041733,
-0.004467729479074478,
0.0012232193257659674,
0.03816920146346092,
0.002093913033604622,
0.0059961299411952496,
0.02482648566365242,
0.0009041042067110538,
-0.0013069396372884512,
-0.04513375088572502,
0.01890493929386139,
-0.0007042006473056972,
-0.03528319671750069,
-0.022493762895464897,
-0.02077099308371544,
-0.006261256989091635,
0.028786469250917435,
0.06386115401983261,
-0.0015514498809352517,
0.06238090246915817,
0.024434268474578857,
-0.02304002083837986,
0.04125455394387245,
0.04569143429398537,
-0.023265568539500237,
0.05788816884160042,
-0.0145194036886096,
0.024043578654527664,
0.04280750826001167,
0.025334760546684265,
-0.012856253422796726,
0.05218162760138512,
-0.024210304021835327,
-0.006876364815980196,
0.006271490827202797,
-0.03173024207353592,
0.04063430428504944,
-0.03622324764728546,
-0.015674933791160583,
0.04753554239869118,
0.002196751767769456,
-0.006417917553335428,
0.051181744784116745,
-0.015896013006567955,
0.044801291078329086,
0.0049422262236475945,
-0.012580592185258865,
-0.0067266616970300674,
0.0013701909920200706,
-0.028916794806718826,
0.047431737184524536,
0.023460712283849716,
0.0025388028007000685,
0.023823490366339684,
0.04551844671368599,
-0.020811665803194046,
0.04180015251040459,
-0.025891395285725594,
0.09706921875476837,
-0.01794629730284214,
-0.02493496611714363,
-0.014943563379347324,
0.0005843968247063458,
-0.015980737283825874,
0.020268969237804413,
-0.02513582818210125,
0.07849869132041931,
-0.007175997365266085,
0.003636864712461829,
-0.02288527972996235,
-0.015904728323221207,
-0.0346866101026535,
0.04288038611412048,
0.019315987825393677,
0.05769071355462074,
0.016202222555875778,
-0.03284016251564026,
0.013184973038733006,
0.017132751643657684,
0.03079918585717678,
-0.02654007449746132,
0.00940284039825201,
-0.008942783810198307,
-0.021948320791125298,
0.008258707821369171,
-0.016200315207242966,
0.008647838607430458,
-0.0034839760046452284,
0.023573897778987885,
0.00145240081474185,
0.004114306066185236,
-0.008795298635959625,
-0.02596507966518402,
-0.03648504987359047,
0.051127247512340546,
-0.04401571303606033,
0.001071991864591837,
-0.022875646129250526,
0.019402453675866127,
-0.039926107972860336,
-0.02234639599919319
] |
<p>When we like to produce known forces, we know that standard weights acting vertically on a object creates a known force. Now, what are the other methods to generate forces with accuracy. It is a DIY experiment I like to do, so any apparatus which uses simple devices like coils, motors, stepper/servo motors, or similar things would be great to try. </p>
<p>So guys, if you have any ideas, please let me know. Cheers.</p>
| 8,250 |
[
-0.02260080724954605,
-0.02914111688733101,
-0.017283296212553978,
-0.028216766193509102,
0.03675895184278488,
-0.018560372292995453,
-0.01741720922291279,
-0.01683318056166172,
0.029359862208366394,
-0.039780598133802414,
0.02822032943367958,
0.04213114455342293,
0.035699740052223206,
0.027745932340621948,
0.029075006023049355,
-0.008356750942766666,
-0.012161602266132832,
-0.028099358081817627,
-0.0027130180969834328,
-0.02072569541633129,
-0.039958830922842026,
-0.006650089286267757,
-0.029484951868653297,
-0.0015046807238832116,
-0.010177248157560825,
0.027147065848112106,
0.0572686642408371,
-0.010847724042832851,
0.018610481172800064,
0.06287544965744019,
-0.024230865761637688,
-0.02635018900036812,
-0.015078477561473846,
0.04281717911362648,
0.024848392233252525,
-0.006428695749491453,
-0.037771087139844894,
-0.02708042599260807,
-0.023979883641004562,
0.029676763340830803,
-0.07354354113340378,
0.02977060340344906,
-0.03640933334827423,
0.035646844655275345,
-0.012099909596145153,
0.01204250194132328,
-0.01447602454572916,
-0.021744659170508385,
0.05353647843003273,
-0.059660814702510834,
0.040399182587862015,
0.027909474447369576,
0.035716451704502106,
0.03703787550330162,
0.007741487119346857,
-0.0013330818619579077,
0.07077141851186752,
0.0227240938693285,
-0.017778785899281502,
-0.04369343817234039,
-0.009563039056956768,
0.0007820930331945419,
-0.03382859379053116,
-0.07947160303592682,
-0.03196509927511215,
0.047851018607616425,
-0.027818825095891953,
-0.007955879904329777,
0.04406553879380226,
-0.021093541756272316,
0.024044418707489967,
0.029327768832445145,
0.014551149681210518,
0.01793771982192993,
-0.02360837161540985,
-0.04086454212665558,
0.00911114364862442,
0.007027050014585257,
0.02061603032052517,
0.03917866572737694,
-0.027744891121983528,
0.014015472494065762,
0.011541531421244144,
0.04644906148314476,
0.004530611913651228,
-0.035890623927116394,
0.03321143612265587,
-0.004353832919150591,
-0.0038065831176936626,
0.008739076554775238,
-0.011143505573272705,
0.006732393521815538,
0.03754055127501488,
-0.005955372471362352,
0.001611820887774229,
-0.015567240305244923,
-0.01039789617061615,
0.03828103840351105,
0.023833397775888443,
-0.03998947516083717,
0.031479835510253906,
-0.03040657378733158,
-0.008121256716549397,
0.09357830137014389,
-0.0002835807972587645,
-0.027467695996165276,
0.034227266907691956,
0.010949047282338142,
-0.01221995148807764,
0.007076568901538849,
0.014688407070934772,
-0.020087571814656258,
0.0033946416806429625,
-0.0046682413667440414,
0.007778896018862724,
-0.006703297607600689,
0.0014465469866991043,
-0.023054007440805435,
0.06647849082946777,
0.05565208941698074,
0.006194534711539745,
-0.04032164439558983,
0.04893733188509941,
-0.03715633600950241,
-0.01521577313542366,
-0.0000039866154111223295,
0.043355707079172134,
-0.02420935221016407,
-0.020279936492443085,
0.04889366775751114,
0.035040874034166336,
-0.01763400435447693,
-0.01220596581697464,
-0.00199727900326252,
0.04038956016302109,
0.009517960250377655,
-0.09330543875694275,
-0.06995800137519836,
0.040056515485048294,
-0.021814614534378052,
-0.009002849459648132,
-0.05090082809329033,
0.015302364714443684,
0.04787784814834595,
0.016220102086663246,
0.03966524824500084,
-0.0004598373780027032,
-0.012566767632961273,
0.02329546958208084,
0.0036253235302865505,
0.0031577476765960455,
-0.008282512426376343,
-0.015239857137203217,
-0.02251369319856167,
-0.02706565335392952,
-0.04908563941717148,
0.04545699805021286,
-0.010310889221727848,
0.008054718375205994,
-0.01753119006752968,
0.04590817913413048,
-0.03439769521355629,
-0.019416334107518196,
0.021782776340842247,
0.017672451213002205,
-0.03775642067193985,
0.048591457307338715,
-0.0032418963965028524,
-0.0201839879155159,
0.008310704492032528,
-0.019532937556505203,
0.02026856504380703,
0.06562565267086029,
-0.008551177568733692,
0.06260353326797485,
-0.03876189887523651,
-0.03280693665146828,
-0.008963370695710182,
0.03695810213685036,
0.015119100920855999,
-0.043472737073898315,
-0.02193906158208847,
0.013923532329499722,
-0.0023617350962013006,
-0.004716084338724613,
0.05785888060927391,
-0.0028142596129328012,
0.0043499101884663105,
0.015095984563231468,
-0.04559534788131714,
0.012799437157809734,
-0.05967259407043457,
0.02547444775700569,
0.010876921005547047,
-0.02169184200465679,
0.02435314655303955,
0.005566898267716169,
0.012898550368845463,
-0.007510166149586439,
-0.03755170851945877,
-0.01530229952186346,
0.022588679566979408,
0.027043228968977928,
0.007072947919368744,
0.018838997930288315,
0.021834643557667732,
0.03742670640349388,
-0.004566659685224295,
0.025940395891666412,
-0.019293537363409996,
-0.031659696251153946,
-0.007140308618545532,
-0.05645538121461868,
0.0016592578031122684,
0.0010985617991536856,
-0.0014613851672038436,
0.040478307753801346,
-0.010231627151370049,
-0.013521227054297924,
0.03507029637694359,
-0.01920371875166893,
0.09529953449964523,
0.06084389612078667,
0.013458467088639736,
0.023860139772295952,
0.04667867720127106,
0.02046235091984272,
0.02051575295627117,
-0.011955426074564457,
-0.01930062472820282,
-0.074947290122509,
-0.008254355750977993,
0.0289697777479887,
-0.002802339382469654,
-0.039829641580581665,
0.03757433593273163,
0.030759520828723907,
0.007234353572130203,
0.04457252472639084,
0.031953755766153336,
0.0016531484434381127,
-0.02490122988820076,
0.023299580439925194,
0.07049483805894852,
0.031049620360136032,
0.05650206282734871,
0.02405143715441227,
0.0556182861328125,
0.013628019951283932,
0.0552409328520298,
0.008580418303608894,
0.015752995386719704,
-0.022263089194893837,
0.00809136126190424,
0.005822459235787392,
-0.042194757610559464,
0.027323080226778984,
0.004241641610860825,
0.011253375560045242,
0.010149406269192696,
-0.00044608584721572697,
-0.009929516352713108,
0.01189613901078701,
0.002496000612154603,
0.04451187700033188,
0.0009014622191898525,
-0.026958873495459557,
-0.028058022260665894,
0.02753618359565735,
-0.03468384966254234,
0.003526592394337058,
-0.016874022781848907,
0.0016000536270439625,
-0.03861173242330551,
-0.0087199117988348,
0.02986990474164486,
0.002437432063743472,
0.06599653512239456,
-0.023127635940909386,
-0.018590591847896576,
-0.024828914552927017,
-0.0356578603386879,
0.026959296315908432,
0.014570804312825203,
-0.04564393684267998,
-0.005530273541808128,
-0.04264233261346817,
-0.02958860993385315,
0.0708962231874466,
-0.02197510562837124,
-0.000584169290959835,
0.03635019809007645,
0.0167455542832613,
-0.011367564089596272,
-0.004642047919332981,
-0.030838191509246826,
0.0016263659344986081,
-0.008033743128180504,
0.011900408193469048,
0.01667281985282898,
-0.009946164675056934,
-0.04845412075519562,
0.07041472941637039,
-0.04622333496809006,
-0.009685693308711052,
-0.010606500320136547,
0.017115673050284386,
0.008258881978690624,
-0.047265153378248215,
0.029446711763739586,
0.024839241057634354,
-0.028455324470996857,
-0.0040484266355633736,
-0.04587091505527496,
-0.026439718902111053,
-0.007171574514359236,
-0.0021628933027386665,
0.04891045391559601,
-0.005051289219409227,
-0.03964781016111374,
0.08833496272563934,
-0.007007713429629803,
-0.05954389646649361,
-0.050852689892053604,
-0.02314714342355728,
-0.005252713803201914,
-0.05486515909433365,
0.01961049810051918,
0.008432832546532154,
-0.05182066932320595,
0.03593577817082405,
0.02957623079419136,
-0.03934705629944801,
0.04113331809639931,
0.03539672866463661,
0.02399943768978119,
-0.021393246948719025,
0.002785033779218793,
-0.036594685167074203,
0.08135849982500076,
0.002964264713227749,
-0.0325540266931057,
-0.006339737214148045,
0.020818952471017838,
0.03726112097501755,
0.008852679282426834,
-0.040954966098070145,
0.011799458414316177,
0.004828614182770252,
-0.020641446113586426,
-0.027234679087996483,
0.004613200668245554,
-0.0012552288826555014,
-0.013042180798947811,
-0.001161895110271871,
0.03765147179365158,
0.022855883464217186,
-0.020038889721035957,
-0.00987322349101305,
0.05599807947874069,
0.041317228227853775,
-0.016497664153575897,
-0.015318159013986588,
-0.017281830310821533,
0.0024496589321643114,
0.02686423622071743,
0.004056265112012625,
0.008679802529513836,
0.041358619928359985,
0.023538267239928246,
0.022994929924607277,
0.044232890009880066,
0.00456986716017127,
-0.003633194137364626,
-0.05469665676355362,
0.010343248955905437,
-0.03576309233903885,
0.050302501767873764,
-0.0017334623262286186,
0.08249212801456451,
0.016200734302401543,
0.00344036309979856,
-0.008920916356146336,
-0.014331686310470104,
-0.09637254476547241,
0.059066712856292725,
-0.023238642141222954,
-0.04587898403406143,
0.026793427765369415,
-0.020000936463475227,
-0.03022007644176483,
-0.02490147203207016,
-0.01111842505633831,
-0.015039836056530476,
0.015308696776628494,
-0.006778449285775423,
-0.005192184820771217,
-0.005070128943771124,
-0.06305336207151413,
-0.02142372913658619,
0.021132372319698334,
0.0016876386944204569,
-0.036297380924224854,
0.014913680963218212,
-0.013818499632179737,
-0.008413000963628292,
-0.009217114187777042,
-0.019701221957802773,
-0.013091023080050945,
-0.0033554674591869116,
0.028788287192583084,
0.014852357096970081,
0.029861930757761,
-0.023499736562371254,
-0.01239723153412342,
-0.001062055234797299,
0.06284846365451813,
0.03280710056424141,
-0.005248586181551218,
-0.04745086282491684,
-0.0535501092672348,
-0.0172222051769495,
0.018143409863114357,
0.01894160732626915,
-0.015216061845421791,
0.009931175038218498,
0.0029878043569624424,
0.0030495082028210163,
-0.0329190157353878,
0.036248236894607544,
0.054543495178222656,
-0.007635387592017651,
-0.009048929437994957,
-0.04952152445912361,
-0.010423966683447361,
-0.007840384729206562,
-0.0500127449631691,
0.019419031217694283,
-0.0036248669493943453,
-0.0038541657850146294,
-0.006095957942306995,
0.032845403999090195,
0.013922857120633125,
-0.009509609080851078,
0.04470602050423622,
-0.006587817799299955,
0.03525090590119362,
-0.01975168101489544,
0.011883008293807507,
0.022985398769378662,
0.013167968019843102,
0.04530370235443115,
0.008065997622907162,
-0.0413811132311821,
-0.11260819435119629,
0.008508357219398022,
0.03792985528707504,
0.0250990130007267,
-0.059177130460739136,
0.002464319346472621,
0.003967964090406895,
-0.04554333537817001,
0.04373479261994362,
-0.044446974992752075,
0.03607141226530075,
-0.02126946859061718,
0.02353636361658573,
-0.02262214571237564,
0.010491019114851952,
-0.04009387642145157,
-0.0005458325613290071,
-0.038282718509435654,
0.01902097277343273,
-0.00905985850840807,
-0.018024582415819168,
0.011822463944554329,
0.03533313423395157,
0.06378206610679626,
0.06008812412619591,
0.026326004415750504,
-0.015911856666207314,
-0.004248214885592461,
0.009084817953407764,
-0.05418964475393295,
-0.06521245092153549,
-0.023215193301439285,
-0.0001922780938912183,
-0.023769497871398926,
0.040011223405599594,
0.004511681385338306,
-0.07989465445280075,
0.018663844093680382,
-0.045578502118587494,
0.028444048017263412,
0.009207958355545998,
0.0006942405016161501,
0.006017768289893866,
0.054568350315093994,
0.03957816958427429,
0.04962670058012009,
0.037791136652231216,
-0.014284662902355194,
-0.0036810380406677723,
0.024051351472735405,
0.009925157763063908,
-0.0034801512956619263,
-0.026173138990998268,
-0.030523454770445824,
0.041872475296258926,
-0.03160863369703293,
0.02592344395816326,
0.008191270753741264,
0.038022443652153015,
-0.009978598915040493,
-0.04021034017205238,
-0.010431245900690556,
0.05901458486914635,
0.038170620799064636,
-0.004370423033833504,
0.04214904457330704,
0.017359428107738495,
0.009457850828766823,
-0.021424410864710808,
-0.021139053627848625,
0.0750260204076767,
0.015219798311591148,
-0.022141311317682266,
-0.014420214109122753,
0.012205488979816437,
-0.039873261004686356,
0.002408206695690751,
0.05391726642847061,
-0.053631823509931564,
0.11080727726221085,
0.005984203424304724,
0.03248264268040657,
-0.01015948224812746,
-0.06829225271940231,
-0.042912449687719345,
0.03618204593658447,
-0.008951064199209213,
0.05763961747288704,
-0.03289156034588814,
0.001861683325842023,
-0.036864377558231354,
-0.007444178219884634,
-0.03550957515835762,
-0.04516633599996567,
0.01077960804104805,
0.029958002269268036,
0.03560485318303108,
-0.003137851133942604,
0.010545291006565094,
-0.04177554324269295,
-0.02607416920363903,
-0.015291406773030758,
0.06559237837791443,
-0.013414534740149975,
0.008624660782516003,
0.0037611820735037327,
-0.03099546581506729,
0.02949441969394684,
0.010289628989994526,
-0.028465762734413147,
-0.02661982923746109,
-0.01602296531200409,
0.011860349215567112,
0.013834147714078426,
0.01643359661102295,
-0.04250327870249748,
-0.009188256226480007,
0.05278553068637848,
0.032121315598487854,
0.02082762122154236,
-0.017317192628979683,
0.051411982625722885,
0.05730712413787842,
0.04524145647883415,
-0.022115888074040413,
-0.014286122284829617,
0.03983287140727043,
-0.007514425087720156,
0.011794425547122955,
-0.007460275664925575,
0.0064704203978180885,
-0.037453148514032364,
-0.033625464886426926,
0.006374535616487265,
-0.002468118676915765,
-0.0025135590694844723,
-0.028659407049417496,
0.06545483320951462,
-0.0034713533241301775,
0.002904430963099003,
0.016008617356419563,
-0.007458891719579697,
0.023500263690948486,
0.009817011654376984,
0.031679362058639526,
0.012144031934440136,
0.015474059619009495,
-0.02379549667239189,
-0.02410181052982807,
-0.0010408946545794606,
0.015226401388645172,
0.08649516850709915,
-0.021526578813791275,
0.10830853134393692,
0.044314321130514145,
0.01374431885778904,
-0.013240835629403591,
0.0025464389473199844,
-0.028292635455727577,
-0.021896935999393463,
-0.0068014939315617085,
0.03375799208879471,
0.004160108044743538,
0.01999051682651043,
-0.0014717064332216978,
0.005719421897083521,
0.004573574755340815,
0.02289745956659317,
0.04177628457546234,
0.07354260236024857,
0.0032633987721055746,
-0.04501693323254585,
-0.032234299927949905,
0.019290855154395103,
-0.03271957486867905,
0.04145502671599388,
0.012940564192831516,
-0.013207686133682728,
0.01873577944934368,
-0.02135596051812172,
-0.009494188241660595,
-0.022114967927336693,
-0.019243119284510612,
-0.04354972019791603,
0.01211134996265173,
0.03328707814216614,
-0.017111869528889656,
-0.023395854979753494,
0.00942808948457241,
0.03622037172317505,
0.006928165443241596,
0.01818210259079933,
-0.026771849021315575,
-0.07271423935890198,
-0.019993264228105545,
-0.0277261883020401,
-0.06129416078329086,
0.023227225989103317,
-0.010686908848583698,
-0.045615680515766144,
0.02600039727985859,
-0.003083429764956236,
0.053292617201805115,
0.02197732776403427,
-0.015776393935084343,
-0.021308833733201027,
0.03181467205286026,
-0.04428961127996445,
-0.00010030595876742154,
-0.007260159123688936,
0.0357767716050148,
0.10032504051923752,
0.04592861235141754,
0.030327429994940758,
-0.04512128233909607,
0.0007542855455540121,
-0.0351371131837368,
0.00026149433688260615,
-0.013726495206356049,
0.04641300067305565,
-0.017392771318554878,
0.0035353335551917553,
-0.020848143845796585,
0.04088979586958885,
-0.05307316407561302,
0.03517817705869675,
0.05860274285078049,
-0.011208551935851574,
-0.030666816979646683,
-0.007975239306688309,
-0.002677490469068289,
-0.006473097950220108,
-0.0035586347803473473,
-0.01450334768742323,
0.029210953041911125,
-0.041907887905836105,
-0.03825338929891586,
-0.005839251913130283,
-0.040001265704631805,
0.021857459098100662,
0.031123830005526543,
-0.04318346083164215,
0.012458878569304943,
-0.008043885231018066,
-0.002104029292240739,
-0.06362131983041763,
0.027462907135486603,
-0.01621120050549507,
-0.012659146450459957,
-0.000007864156032155734,
0.023400159552693367,
0.019861221313476562,
-0.005216061603277922,
-0.03414299711585045,
-0.016380736604332924,
-0.017839541658759117,
0.0014485855353996158,
-0.06475607305765152,
0.039776843041181564,
-0.043707504868507385,
0.01986129954457283,
-0.010934611782431602,
0.002641155384480953,
-0.027332859113812447,
-0.0070435176603496075,
-0.025307534262537956,
0.01610507257282734,
0.009558782912790775,
-0.05398093909025192,
-0.01545814611017704,
-0.007645919919013977,
0.04646740108728409,
-0.004178515635430813,
-0.006948203779757023,
0.0015093834372237325,
0.012632878497242928,
0.014524145051836967,
0.00917856115847826,
0.05444846302270889,
-0.029230110347270966,
-0.034224312752485275,
-0.00023239899019245058,
-0.022797130048274994,
-0.04027354717254639,
0.022809501737356186,
-0.013273052871227264,
0.03534407168626785,
0.007077740039676428,
-0.0002862087276298553,
-0.025771206244826317,
0.0015344008570536971,
-0.03267774358391762,
0.033381447196006775,
-0.030833572149276733,
-0.006655652076005936,
-0.02841118536889553,
0.00865392480045557,
0.018015246838331223,
0.029771870002150536,
0.020497038960456848,
0.007324639707803726,
0.014729795046150684,
0.00014712009578943253,
0.015333311632275581,
-0.04510001465678215,
-0.03819077089428902,
0.0066122389398515224,
-0.004780271090567112,
-0.009923416189849377,
0.006391375325620174,
0.021389324218034744,
0.04326601326465607,
-0.016771767288446426,
0.026574283838272095,
0.003173980861902237,
-0.006787709426134825,
0.026613062247633934,
0.021546006202697754,
-0.03274309262633324,
0.0024351151660084724,
-0.016093367710709572,
-0.0029920984525233507,
-0.0424833707511425,
-0.02883969061076641,
-0.017205284908413887,
-0.03146775811910629,
-0.0020848673302680254,
0.034411393105983734,
-0.01291571743786335,
0.007479862775653601,
-0.026348881423473358,
0.021709825843572617,
-0.030623184517025948,
0.021461986005306244,
-0.030424313619732857,
-0.022944513708353043,
-0.020935386419296265,
-0.011348159983754158,
-0.01576741226017475,
0.0029198816046118736,
-0.024105031043291092,
0.003948645666241646,
0.03005952760577202,
0.009340961463749409,
0.008125627413392067,
-0.011912817135453224,
0.030852902680635452,
-0.017235886305570602,
-0.0013105024117976427,
-0.003000326920300722,
-0.02585519663989544,
0.03771247714757919,
-0.045026522129774094,
-0.024239635095000267,
0.017129145562648773,
-0.013422313146293163,
0.0064702993258833885,
0.056793708354234695,
-0.036685314029455185,
0.03872356936335564,
0.0400894470512867,
-0.008334392681717873,
-0.010534349828958511,
-0.025264540687203407,
0.026787834241986275,
-0.0013058151816949248,
0.049034737050533295,
0.028193166479468346,
-0.04107721522450447,
-0.008350534364581108,
0.008026979863643646,
0.02227400802075863,
0.024118073284626007,
-0.046797480434179306,
0.047735121101140976,
0.011759144254028797,
0.007040339522063732,
0.04589853435754776,
-0.02149711549282074,
0.014048736542463303,
0.02831583097577095,
-0.04492403566837311,
-0.0020908908918499947,
-0.01940448023378849,
-0.0042126779444515705,
-0.07740416377782822,
-0.041116971522569656,
-0.025256797671318054,
-0.02464134432375431,
0.03839360177516937,
-0.03512176126241684,
-0.008828302845358849,
0.04252028837800026,
-0.069298654794693,
0.007431337144225836,
-0.009889379143714905,
-0.01638568751513958,
0.01637808233499527,
-0.03234684839844704,
0.03259953483939171,
0.0283958800137043,
-0.01591232791543007,
0.04130668193101883,
0.002357976511120796,
-0.004719018470495939,
-0.022119246423244476,
-0.024450937286019325,
0.02772851288318634,
0.025045879185199738,
0.022504430264234543,
-0.01898491010069847,
0.04424203559756279,
-0.018353549763560295,
-0.03152885660529137,
0.043610621243715286,
0.0014533144421875477,
0.03947247937321663,
-0.015944400802254677,
0.005583393853157759,
-0.0551060289144516,
0.06105814874172211,
-0.02517075650393963,
0.001734438119456172,
-0.014814467169344425,
0.03305917978286743,
-0.0008244760683737695,
0.05249437317252159,
-0.02577347494661808,
0.022943487390875816,
0.07837019115686417,
-0.030873212963342667,
-0.022663498297333717,
0.058365002274513245,
-0.03442685306072235,
-0.0142127126455307,
0.020450664684176445,
-0.010145116597414017,
0.029153630137443542,
-0.0241845715790987,
-0.0015939796576276422,
-0.05170449987053871,
0.014732979238033295,
-0.0062650577165186405,
-0.013161085546016693,
-0.01714925467967987,
0.03402182087302208,
-0.005430306773632765,
-0.004742339253425598,
0.009311288595199585,
-0.0009346658480353653,
-0.03686622157692909,
-0.06271927058696747,
-0.003804546082392335,
0.006100696045905352,
-0.001172086107544601,
-0.0010291693033650517,
-0.04719221964478493,
-0.04264053329825401,
0.05556844174861908,
0.013668152503669262,
-0.0025954321026802063,
0.012087773531675339,
-0.01951928436756134,
-0.012385149486362934,
-0.054957784712314606,
0.07720180600881577,
-0.00007043007644824684,
-0.042681436985731125,
-0.04764516279101372,
0.0037084573414176702,
0.012613472528755665,
-0.02061004750430584,
0.027270376682281494,
-0.022616999223828316,
-0.009323936887085438,
0.007463229354470968,
-0.004509703256189823,
0.00029032633756287396,
-0.019691716879606247,
0.017428794875741005,
0.0006297953659668565,
-0.03276863694190979,
-0.02462044730782509,
0.01318423543125391,
-0.006361799780279398,
0.026773806661367416,
0.002657502656802535,
-0.0008692803094163537,
0.0018846361199393868,
-0.04184841364622116,
-0.03149821236729622,
0.025998808443546295,
0.006926355883479118,
-0.0019153001485392451,
0.041529834270477295,
-0.007063735742121935,
0.01453513652086258,
-0.01733912155032158,
-0.04462992027401924,
-0.0025317431427538395,
0.04780351743102074,
-0.0301279965788126,
0.023345040157437325,
-0.06825121492147446,
0.006742504891008139,
0.026481468230485916,
-0.04035366326570511,
-0.014389196410775185,
0.013494156301021576,
-0.029404716566205025,
0.0077197132632136345,
0.032172247767448425,
0.021223759278655052,
-0.01174448523670435,
-0.019602250307798386,
0.03646783158183098,
0.011156451888382435,
-0.019018391147255898,
-0.00039694184670224786,
0.0321345254778862,
0.0371340848505497,
0.0009033401147462428,
-0.0009516818099655211,
0.07037441432476044,
-0.018110251054167747,
0.025594284757971764,
0.01596701517701149,
0.018712632358074188,
-0.02297939546406269,
-0.01684981770813465,
-0.031033525243401527,
-0.035510752350091934,
0.02255908027291298,
0.006045693531632423,
-0.04370832070708275,
0.08882959187030792,
-0.04018455371260643,
-0.018107548356056213,
-0.056675221771001816,
0.0008510539191775024,
0.029070716351270676,
-0.04437720403075218,
-0.02799410931766033,
0.05801061540842056,
-0.003947391174733639,
-0.013946679420769215,
-0.024001669138669968,
0.012703136540949345,
0.026623982936143875,
0.016523020341992378,
0.02921426296234131,
0.00009112067345995456,
0.03351170942187309,
-0.042369384318590164,
-0.03230390325188637,
-0.0631549134850502,
-0.01689966581761837,
0.05890011414885521,
0.02322770096361637,
0.025979608297348022,
0.009989676997065544,
-0.014253617264330387,
-0.01808546669781208,
0.02798500657081604,
-0.05746910348534584,
-0.016061333939433098,
-0.017903771251440048,
0.030010735616087914,
0.013314692303538322,
0.03803207725286484
] |
<p>Say there is a satellite polar-orbiting the Earth at 600km.
How much would the satellite be dragged additionally due to dragging force?</p>
<p>Such that $$ \Omega = \dfrac{r_s \alpha r c}{\rho^2(r^2 + \alpha^2) + r_s \alpha^2 r sin^2 \theta}$$</p>
<p>such that:</p>
<p>$r_s = \dfrac{2GM}{c^2}$ is the Schwarzchild radius.</p>
<p>$\alpha = \dfrac{J}{Mc}$ </p>
<p>$\rho^{2} = r^{2} + \alpha^{2} \cos^{2} \theta$ </p>
<p>$\Delta = r^{2} - r_{s} r + \alpha^{2}$</p>
<p>I'm a bit confused how I'm supposed to use this formula as $\Omega$ denotes angular speed not distance doesn't it?</p>
<p>Thank you so much for any help</p>
| 272 |
[
-0.029455244541168213,
-0.00020652292005252093,
-0.007623615674674511,
-0.013602223247289658,
0.030129998922348022,
-0.01108924113214016,
-0.05814339965581894,
-0.029557617381215096,
0.007726951036602259,
-0.03488416597247124,
0.016457902267575264,
0.030796999111771584,
0.05267168954014778,
0.007105513475835323,
-0.003059960901737213,
0.027349483221769333,
-0.04890010133385658,
0.03306969627737999,
0.02912628836929798,
-0.01834304817020893,
0.05415770411491394,
0.00794335175305605,
0.03485073149204254,
-0.013896678574383259,
0.019903162494301796,
0.02035021036863327,
0.051597580313682556,
0.00897484365850687,
0.035384103655815125,
0.03912004828453064,
0.02216188795864582,
0.005678306799381971,
0.022665033116936684,
0.020607242360711098,
0.033198267221450806,
0.02495000883936882,
-0.070859894156456,
0.008439315482974052,
-0.006846695672720671,
0.07531455159187317,
-0.030057629570364952,
-0.02806009165942669,
-0.014881392009556293,
0.05401003360748291,
-0.011228331364691257,
-0.004906577058136463,
0.0013304525054991245,
-0.018780233338475227,
0.04065695405006409,
-0.054439716041088104,
0.058873362839221954,
-0.03140966221690178,
0.045356012880802155,
0.016340071335434914,
-0.005727347917854786,
-0.014243042096495628,
0.07098335772752762,
0.033196501433849335,
-0.036532990634441376,
-0.03441664204001427,
-0.022188112139701843,
-0.03213929384946823,
-0.013163232244551182,
-0.023844758048653603,
-0.010085799731314182,
0.027034752070903778,
-0.03738606721162796,
-0.014454648829996586,
0.026183540001511574,
0.029263461008667946,
0.04069145396351814,
0.026943126693367958,
-0.007730310782790184,
-0.03747928515076637,
-0.010793685913085938,
-0.05801759287714958,
-0.012603371404111385,
0.03413384407758713,
0.02326919324696064,
0.022444676607847214,
-0.0350484624505043,
0.0290973000228405,
0.01784384436905384,
0.05600947514176369,
0.027641352266073227,
-0.007381768431514502,
0.05315638706088066,
0.00577635457739234,
-0.004682150203734636,
0.027475111186504364,
0.006696066819131374,
0.009238896891474724,
0.0003604748344514519,
-0.02255537174642086,
-0.014089569449424744,
0.022337451577186584,
0.008483121171593666,
0.05817022919654846,
0.0023466134443879128,
-0.008568122051656246,
0.00447755167260766,
-0.0496005155146122,
-0.028693871572613716,
0.07723084837198257,
0.013363824225962162,
0.010612948797643185,
-0.018957925960421562,
-0.0008572600199840963,
-0.0008014809573069215,
-0.0287723857909441,
-0.016085470095276833,
0.015406502410769463,
0.002382804173976183,
-0.032176095992326736,
-0.0010008284589275718,
0.011891540139913559,
-0.023495087400078773,
0.03589622676372528,
0.028283553197979927,
0.06433121860027313,
0.03445902094244957,
0.0220029316842556,
0.024711163714528084,
-0.014374295249581337,
-0.03781559690833092,
0.06030862778425217,
0.01776122860610485,
-0.008046239614486694,
-0.03897598758339882,
-0.002438449999317527,
0.024292776361107826,
-0.014711176976561546,
-0.03271131590008736,
-0.014963841997087002,
0.05077993497252464,
0.004501668736338615,
-0.08654915541410446,
-0.05686183646321297,
0.004299604799598455,
0.009855750948190689,
0.009947487153112888,
-0.05507834628224373,
0.01812645047903061,
0.015895342454314232,
0.08602818846702576,
0.020871024578809738,
-0.006060652434825897,
0.03143354132771492,
0.021364562213420868,
-0.00823103729635477,
-0.037285663187503815,
-0.008772806264460087,
-0.01990225724875927,
-0.07877729833126068,
0.0030306028202176094,
-0.09664438664913177,
0.00011594241368584335,
0.017988471314311028,
0.00878422986716032,
-0.005641866009682417,
0.0249219611287117,
0.008729456923902035,
0.013081037439405918,
-0.005156571976840496,
-0.02379126101732254,
-0.04401412606239319,
0.10046642273664474,
-0.0009664943208917975,
0.00042998220305889845,
0.053366631269454956,
0.011695528402924538,
0.019229553639888763,
-0.02396385185420513,
-0.006189445964992046,
0.040727950632572174,
-0.022470060735940933,
-0.0046424721367657185,
-0.026083696633577347,
-0.027510082349181175,
0.02121335081756115,
-0.05532621592283249,
-0.072994664311409,
0.0007427218370139599,
0.025592803955078125,
0.024508036673069,
0.06164141371846199,
-0.005604424048215151,
-0.0052040740847587585,
0.004156654234975576,
-0.05851222574710846,
0.027069322764873505,
-0.011523730121552944,
0.04627223312854767,
-0.02830413356423378,
-0.007834919728338718,
0.03617037832736969,
0.009146792814135551,
0.020582353696227074,
0.0005936033558100462,
-0.009541664272546768,
0.019497759640216827,
0.03611215949058533,
-0.00805529672652483,
-0.021444084122776985,
0.037567682564258575,
0.06694480776786804,
0.02521062269806862,
0.02810726687312126,
-0.003323291428387165,
0.008826225996017456,
0.0035104237031191587,
-0.025476394221186638,
-0.006150797940790653,
0.022352540865540504,
0.014603201299905777,
0.0054499125108122826,
0.010276230052113533,
-0.010716698132455349,
0.025407491251826286,
0.028992902487516403,
-0.006682177074253559,
0.0933486819267273,
0.05244971811771393,
-0.0029615741223096848,
0.05120118707418442,
0.03330416977405548,
0.022722871974110603,
-0.01148614939302206,
-0.013439586386084557,
-0.006105213426053524,
-0.028825722634792328,
0.014347545802593231,
0.048358093947172165,
-0.0021496263798326254,
-0.07080550491809845,
-0.01070417370647192,
0.066228948533535,
0.03287489339709282,
0.027969567105174065,
0.0028830342926084995,
-0.00009838023834163323,
-0.014783656224608421,
0.03636961057782173,
0.001936272601597011,
-0.015366978012025356,
0.0003936013672500849,
-0.013686100952327251,
-0.011544703505933285,
0.010671505704522133,
-0.011340135708451271,
-0.0371210053563118,
0.06175342574715614,
0.004672196228057146,
0.018025286495685577,
0.02656514197587967,
0.0033677208703011274,
0.06902548670768738,
-0.02047782763838768,
0.014927728101611137,
0.030370555818080902,
-0.022651292383670807,
0.020782122388482094,
-0.0363345630466938,
-0.006672333460301161,
0.01553248893469572,
0.00044332031393423676,
-0.03159983828663826,
0.0027504165191203356,
0.012893987819552422,
-0.046559564769268036,
-0.040920570492744446,
-0.011912026442587376,
0.016996312886476517,
-0.048420000821352005,
-0.01978185772895813,
0.033113837242126465,
0.01763763092458248,
0.05389152839779854,
-0.008776008151471615,
0.0046610403805971146,
0.0008486004662699997,
0.0040282877162098885,
-0.017967751249670982,
0.02271147072315216,
-0.03911943733692169,
0.030129432678222656,
-0.04934195801615715,
-0.0001251112116733566,
0.054452333599328995,
-0.008684531785547733,
-0.044441334903240204,
0.00815655943006277,
-0.005237146746367216,
-0.05065850913524628,
-0.05369936674833298,
-0.0009887937922030687,
0.004547412041574717,
-0.06390595436096191,
-0.01398477889597416,
0.038012340664863586,
-0.008345094509422779,
-0.006893452722579241,
0.009305093437433243,
-0.06250718981027603,
-0.028437482193112373,
0.0121531393378973,
0.01127663068473339,
0.0241977721452713,
-0.06980293989181519,
0.042111240327358246,
-0.04149245098233223,
-0.01806032657623291,
0.008921398781239986,
-0.03890561684966087,
-0.034511543810367584,
0.032794758677482605,
-0.023638224229216576,
0.03557681664824486,
-0.0021237004548311234,
-0.05737914890050888,
0.11486276239156723,
0.004225964657962322,
-0.0049216593615710735,
-0.03788535296916962,
0.012393984012305737,
-0.02489815279841423,
-0.016099946573376656,
-0.019306061789393425,
0.017228100448846817,
-0.015778087079524994,
-0.04317976534366608,
0.010456223972141743,
0.038213979452848434,
0.011720867827534676,
-0.00972870271652937,
0.004069566261023283,
-0.007754328195005655,
0.00795399583876133,
-0.01899394765496254,
0.09060652554035187,
0.02528179995715618,
-0.005150573328137398,
0.02835202030837536,
-0.014848687686026096,
0.042502906173467636,
-0.01308525912463665,
-0.09100190550088882,
0.017754755914211273,
-0.024901041761040688,
-0.03302152827382088,
0.04979020729660988,
0.05868895724415779,
0.029381129890680313,
-0.013320457190275192,
0.01710297353565693,
0.009694923646748066,
0.018244856968522072,
-0.025041522458195686,
-0.04258253425359726,
0.044764816761016846,
0.04365408793091774,
-0.008554033003747463,
-0.0315466932952404,
-0.037690866738557816,
0.009538531303405762,
0.03213012218475342,
-0.054508768022060394,
-0.04791681468486786,
0.006053842604160309,
-0.008110999129712582,
0.03921280801296234,
-0.010878771543502808,
-0.03867311403155327,
0.0025536175817251205,
-0.08969534933567047,
-0.025074852630496025,
-0.04830717295408249,
0.05757107958197594,
-0.03233817219734192,
0.037481144070625305,
0.03384591266512871,
0.011036507785320282,
0.05073840916156769,
0.024513771757483482,
-0.05589977651834488,
0.036506008356809616,
-0.0406268872320652,
-0.0534636490046978,
0.0065766130574047565,
0.016110504046082497,
-0.003610384650528431,
-0.03877226635813713,
0.01025648694485426,
-0.00514280004426837,
0.030659593641757965,
-0.05443936586380005,
-0.001877706847153604,
-0.027104802429676056,
-0.009639477357268333,
0.015954555943608284,
0.0638386607170105,
0.015600678510963917,
-0.034698549658060074,
0.023781200870871544,
0.050441842526197433,
-0.0256479661911726,
-0.004167140461504459,
-0.04598695784807205,
-0.033912286162376404,
-0.012631694786250591,
0.0064719184301793575,
0.045476850122213364,
0.01636074297130108,
-0.0046343752183020115,
-0.023690542206168175,
0.0011803042143583298,
0.007815572433173656,
0.011493323370814323,
0.01012066937983036,
-0.018455293029546738,
-0.05947422608733177,
0.004315320402383804,
0.008006474934518337,
0.055415041744709015,
-0.01777220331132412,
-0.02038879320025444,
0.021052708849310875,
-0.033021438866853714,
0.0065840380266308784,
0.013127077370882034,
0.03064585290849209,
0.002544993767514825,
-0.03552507236599922,
-0.05290605500340462,
-0.028743909671902657,
-0.02295602671802044,
-0.036966949701309204,
0.05116809159517288,
-0.003690737299621105,
-0.058056991547346115,
-0.027465619146823883,
-0.007788129150867462,
-0.0029748377855867147,
-0.02636869065463543,
0.01971624046564102,
0.017172856256365776,
0.00994278583675623,
-0.014014109969139099,
-0.0007114377222023904,
0.018150504678487778,
0.02973962388932705,
0.05264975130558014,
-0.018589820712804794,
0.007408641744405031,
-0.06753938645124435,
-0.020716017112135887,
0.02469770610332489,
0.02932325005531311,
-0.004267431795597076,
-0.01588490791618824,
-0.024024030193686485,
-0.002520811976864934,
0.04142516478896141,
-0.033093225210905075,
0.07048992067575455,
0.007948378100991249,
0.03502407297492027,
-0.008421513251960278,
-0.04186450317502022,
-0.046134304255247116,
0.0236924160271883,
-0.021654726937413216,
0.011720122769474983,
-0.061044614762067795,
-0.0023856740444898605,
0.00958151463419199,
0.019671764224767685,
0.016004065051674843,
0.06370361149311066,
0.012586629018187523,
-0.04722031578421593,
-0.019308768212795258,
0.0016120392829179764,
-0.03742045536637306,
-0.050896819680929184,
-0.00041851261630654335,
-0.00604333495721221,
-0.010561554692685604,
0.03640711307525635,
-0.040561873465776443,
-0.04518578574061394,
0.011892151087522507,
0.013912179507315159,
-0.02122536115348339,
-0.034430645406246185,
-0.05008392408490181,
0.03438565135002136,
0.04685448482632637,
-0.01252567395567894,
0.015386330895125866,
0.027866840362548828,
0.003191030817106366,
-0.010876010172069073,
-0.006443255580961704,
0.037123385816812515,
-0.00813538208603859,
-0.031652044504880905,
-0.014384456910192966,
0.010376286692917347,
-0.031334418803453445,
0.02767086774110794,
-0.033146098256111145,
0.042264748364686966,
-0.038010742515325546,
-0.06022188812494278,
-0.005782818887382746,
0.02944042906165123,
-0.0009026540792547166,
0.0031133617740124464,
0.009591679088771343,
-0.002992676105350256,
0.0020475368946790695,
-0.04037602245807648,
-0.008714200928807259,
0.006764530204236507,
0.009714805521070957,
0.026218032464385033,
0.000038179627154022455,
-0.024108070880174637,
-0.0242365263402462,
-0.009567957371473312,
0.0047215926460921764,
-0.06705257296562195,
0.06835871189832687,
-0.041707299649715424,
-0.0068979025818407536,
0.027083300054073334,
-0.06845272332429886,
-0.04131847247481346,
-0.010625071823596954,
-0.020273543894290924,
0.016354545950889587,
-0.05784003064036369,
-0.02484455145895481,
0.030127184465527534,
0.023076428100466728,
-0.04734558239579201,
-0.034668341279029846,
0.027373798191547394,
0.014563925564289093,
0.0334407202899456,
-0.0032141930423676968,
0.010769210755825043,
-0.015690505504608154,
-0.01900470443069935,
-0.018847739323973656,
0.060544081032276154,
-0.028770245611667633,
0.030012987554073334,
-0.007019310258328915,
0.01842021942138672,
0.04084507375955582,
-0.016615986824035645,
-0.028416769579052925,
0.037080660462379456,
0.008237655274569988,
0.038772378116846085,
-0.00480579724535346,
0.0867493748664856,
-0.01869996264576912,
-0.06263574957847595,
-0.037781722843647,
-0.015340674668550491,
0.028250517323613167,
0.009191145189106464,
-0.011549723334610462,
0.03929070010781288,
0.032259177416563034,
0.023747529834508896,
-0.006554928608238697,
-0.007811712566763163,
0.004222227726131678,
0.03628816828131676,
0.0178065225481987,
-0.02131631039083004,
-0.054350029677152634,
-0.008088953793048859,
-0.027921399101614952,
0.014323920011520386,
0.026076845824718475,
-0.020770352333784103,
0.0846376121044159,
-0.01438125316053629,
-0.02609226107597351,
0.019432995468378067,
0.005857204552739859,
-0.0010759913129732013,
0.03885961323976517,
0.007301877718418837,
0.0153432572260499,
-0.0028346292674541473,
0.0028781029395759106,
0.0035524440463632345,
-0.041205763816833496,
-0.01157162431627512,
0.11215899884700775,
-0.05295681953430176,
0.02774103544652462,
0.0005595705006271601,
0.0014831146690994501,
-0.004215226508677006,
-0.015020308084785938,
-0.017122432589530945,
-0.006868131458759308,
0.012884518131613731,
0.04129628464579582,
-0.02354993298649788,
-0.018686439841985703,
0.023017851635813713,
0.04309653490781784,
-0.03503827378153801,
-0.0027263930533081293,
0.0014380342327058315,
0.02755727991461754,
0.01025453582406044,
-0.011168895289301872,
-0.006354335695505142,
0.027535244822502136,
-0.005143509246408939,
0.041486430913209915,
0.015003007836639881,
-0.011641179211437702,
0.0650533139705658,
0.034107428044080734,
0.030178580433130264,
-0.05323005095124245,
-0.012773009017109871,
-0.015537464059889317,
-0.002457811962813139,
0.029879266396164894,
-0.030092570930719376,
-0.011446607299149036,
-0.010028406977653503,
0.039526719599962234,
0.02441100776195526,
0.06073610857129097,
-0.020552314817905426,
-0.029879122972488403,
-0.011694851331412792,
-0.008948973380029202,
-0.07166701555252075,
0.004370450507849455,
0.014214334078133106,
0.02008376084268093,
0.010169806890189648,
0.006139481905847788,
0.006987936794757843,
0.0697561502456665,
0.015238679014146328,
-0.01422661729156971,
0.10993210971355438,
-0.03528687730431557,
-0.00511180842295289,
-0.002660976257175207,
-0.009294034913182259,
0.09380100667476654,
0.02151503972709179,
-0.012731501832604408,
-0.05744434893131256,
0.025348246097564697,
-0.03363478183746338,
0.01886782795190811,
-0.06972067803144455,
-0.008950111456215382,
-0.014584052376449108,
-0.0033508038613945246,
0.005812843330204487,
0.06336513161659241,
-0.01884462684392929,
-0.027224645018577576,
0.00396043062210083,
-0.00584245752543211,
-0.0160970501601696,
-0.0065841167233884335,
-0.010739180259406567,
-0.017135659232735634,
-0.007585263345390558,
-0.0009551190887577832,
0.03469298034906387,
-0.014726454392075539,
0.0218123160302639,
-0.04151943698525429,
-0.014210093766450882,
0.0081148911267519,
0.011784889735281467,
-0.07310104370117188,
0.047151945531368256,
-0.012230169028043747,
-0.012605475261807442,
-0.021916579455137253,
0.04006512090563774,
0.024194978177547455,
-0.02804214507341385,
0.03430742770433426,
0.0550396591424942,
-0.011043400503695011,
0.018588686361908913,
0.04370833933353424,
-0.024353180080652237,
-0.03918708860874176,
0.01998167298734188,
-0.0296634528785944,
0.04618808999657631,
-0.018346179276704788,
0.001188394846394658,
0.012560190632939339,
0.01392681710422039,
-0.03047490119934082,
-0.08902478963136673,
0.006672409828752279,
0.0010332611855119467,
-0.0023802025243639946,
-0.010418858379125595,
-0.026342526078224182,
0.034748759120702744,
0.0100451884791255,
0.037513311952352524,
0.04766691476106644,
-0.009338563308119774,
-0.004768910817801952,
-0.012882381677627563,
-0.0037734624929726124,
0.07425492256879807,
-0.004379164893180132,
-0.025583451613783836,
0.009728620760142803,
0.028796369209885597,
-0.04660975933074951,
0.034107353538274765,
0.03349834680557251,
-0.008644841611385345,
0.029421469196677208,
-0.00007913495937827975,
-0.02347787283360958,
-0.036048803478479385,
-0.05255981534719467,
0.025716714560985565,
0.002496052999049425,
-0.006881473120301962,
-0.03639286383986473,
-0.015973100438714027,
0.03317844867706299,
0.029439080506563187,
-0.012890142388641834,
0.0006809408660046756,
-0.019670747220516205,
0.05483444407582283,
0.003990246448665857,
-0.01934249885380268,
-0.05004492402076721,
0.010541806928813457,
-0.03897181898355484,
0.017126424238085747,
0.015850486233830452,
0.022220609709620476,
0.0463319756090641,
0.00346056348644197,
-0.03504861518740654,
0.004786998964846134,
-0.014722909778356552,
0.02239355631172657,
0.023405760526657104,
-0.0423019640147686,
-0.020632049068808556,
0.002118973759934306,
-0.009974689222872257,
-0.036849457770586014,
0.024885479360818863,
-0.004323100205510855,
-0.017184657976031303,
0.02540074661374092,
0.010331066325306892,
-0.03654033690690994,
0.030088111758232117,
-0.018666448071599007,
0.009850737638771534,
-0.039042335003614426,
0.025992589071393013,
-0.018247805535793304,
0.012773160822689533,
-0.003209189511835575,
0.021363699808716774,
-0.05094971880316734,
0.01211150735616684,
-0.03639303520321846,
-0.00537630682811141,
-0.02529923804104328,
0.031258437782526016,
0.010794385336339474,
-0.03200997784733772,
-0.00760243833065033,
-0.017878703773021698,
0.05357520654797554,
-0.044600702822208405,
-0.0011157229309901595,
0.034005746245384216,
-0.03668714314699173,
-0.03682365640997887,
0.02238357439637184,
-0.016322625800967216,
0.05633586272597313,
-0.017870651558041573,
-0.021290332078933716,
-0.006363246124237776,
0.06790164858102798,
-0.01738351210951805,
-0.01550127100199461,
-0.02636939100921154,
0.008320825174450874,
-0.004835319705307484,
-0.016995979472994804,
0.012304040603339672,
-0.03294605761766434,
0.038502223789691925,
0.023216068744659424,
0.034225404262542725,
-0.01964695379137993,
0.011358978226780891,
-0.001525662955828011,
0.018857309594750404,
-0.022283755242824554,
0.02950327843427658,
-0.014204085804522038,
0.02455201931297779,
0.005175906233489513,
-0.03054959513247013,
0.00680511724203825,
0.023834645748138428,
0.008270311169326305,
-0.03629132732748985,
0.008299117907881737,
-0.03424542024731636,
-0.005808315705507994,
0.05412793532013893,
-0.06279092282056808,
0.030612047761678696,
0.0382833331823349,
-0.08241710811853409,
-0.00537464814260602,
-0.03828728571534157,
0.021260764449834824,
-0.015761829912662506,
-0.007394627667963505,
0.010511580854654312,
0.03392469882965088,
0.06215076893568039,
0.006071992218494415,
-0.014134682714939117,
-0.014303709380328655,
-0.018915029242634773,
-0.031486861407756805,
0.03806602209806442,
0.021479783579707146,
0.0005929344333708286,
-0.01365876104682684,
0.017896026372909546,
-0.012249336577951908,
-0.010462074540555477,
0.016510948538780212,
-0.02691183239221573,
0.022847706452012062,
-0.002324337838217616,
0.01295756921172142,
-0.001261106925085187,
-0.012755212374031544,
0.00429126201197505,
-0.029042324051260948,
0.006779055576771498,
0.009432334452867508,
0.01504040788859129,
0.02441938780248165,
-0.021319817751646042,
-0.022184057161211967,
0.022617971524596214,
-0.014475016854703426,
-0.022128738462924957,
0.045431483536958694,
-0.02007857710123062,
0.010377706028521061,
0.020245760679244995,
-0.014408147893846035,
0.007743152789771557,
-0.05383884534239769,
-0.012301940470933914,
-0.0741853341460228,
0.010767098516225815,
0.021930402144789696,
-0.010227792896330357,
-0.003410633187741041,
0.001900310511700809,
0.006011140998452902,
-0.045164089649915695,
-0.014167187735438347,
-0.03203907981514931,
-0.020003987476229668,
-0.017711929976940155,
-0.004851148463785648,
-0.006081886123865843,
-0.02372630126774311,
0.0108901746571064,
-0.030595898628234863,
0.00014123866276349872,
0.04410911723971367,
0.010253933258354664,
0.00015880346472840756,
0.0167522132396698,
-0.00825284980237484,
0.001758426078595221,
-0.05771974101662636,
0.017461547628045082,
0.014736585319042206,
-0.03740382567048073,
-0.006620864849537611,
-0.02921574003994465,
0.004627099726349115,
0.005736622493714094,
0.051041267812252045,
-0.023547079414129257,
0.01010188553482294,
0.013809519819915295,
-0.021558554843068123,
-0.00965815782546997,
-0.06082968786358833,
0.02016068808734417,
0.016575248911976814,
-0.032399822026491165,
0.002032676711678505,
0.019726967439055443,
0.020056916400790215,
-0.004154103808104992,
-0.0027188067324459553,
0.020241476595401764,
0.0580737367272377,
0.0189711581915617,
-0.022154532372951508,
0.01648523658514023,
0.0009983343770727515,
0.021118199452757835,
0.04599343612790108,
0.006075006444007158,
0.006027911324054003,
0.048520322889089584,
-0.0017979573458433151,
-0.013134465552866459,
0.028359292075037956,
-0.026996446773409843,
-0.009822096675634384,
-0.021489502862095833,
-0.022998688742518425,
0.033269234001636505,
-0.04436538740992546,
0.003147516865283251,
0.040189024060964584,
-0.040419936180114746,
-0.018154097720980644,
0.0341603122651577,
0.006712209898978472,
0.031708456575870514,
-0.02518974244594574,
0.01479821465909481,
0.060803547501564026,
-0.013864688575267792,
-0.019441068172454834,
0.016697553917765617,
0.01760847307741642,
0.035748954862356186,
0.021316558122634888,
0.05372601002454758,
0.03197399526834488,
0.024909332394599915,
0.001931834383867681,
0.031029915437102318,
0.015294787473976612,
-0.01127015333622694,
-0.005168829578906298,
-0.008093629963696003,
0.007017343770712614,
0.05077486112713814,
0.002833553357049823,
0.059117723256349564,
-0.013954107649624348,
-0.013554422184824944,
-0.0165266003459692,
-0.006197142880409956,
-0.03373494744300842,
0.03311850503087044,
0.00780965993180871,
0.020375972613692284,
-0.010166100226342678,
-0.040994614362716675,
-0.016499854624271393,
-0.03290391340851784,
0.06764326244592667,
-0.017091872170567513,
0.01324065774679184,
-0.0031644816044718027,
-0.005498890765011311,
-0.009208735078573227,
-0.041706837713718414,
-0.013761702924966812,
-0.0063283564522862434,
0.044184986501932144,
0.003237145021557808,
0.021088099107146263,
-0.014951711520552635,
0.013723108917474747,
0.00784321129322052,
0.0400342121720314,
-0.06847570091485977,
-0.03241803124547005,
0.01757311262190342,
0.024009445682168007,
-0.031721267849206924,
0.013958325609564781
] |
<p>This is a statement from Giamarchi's book on Quantum Physics in 1D:</p>
<p>"For a single-particle in a cosine potential, the slightest amount of
tunneling between two cosine minima leads to conduction bands, for
example, and restores the translational symmetry. However, our
sine-Gordon problem is a two-dimensional (one space one time) problem.
In that case it is well-known that instantons with a finite action
(instanton) that would connect two cosine minima cannot exist
(Rajaraman, 1982). There is thus no restoring of symmetry and the
field is truly locked in one of the minima. This is of course related
to the Mermin-Wagner theorem stating that in two (classical) dimensions it is
impossible to break a continuous symmetry but one can break a discrete one."</p>
<p>The potential concerns us here of a scalar field $\Phi$ is:
$$
g \cos(\beta \;\Phi)
$$</p>
<p>I wonder how to <strong>show this statement</strong>: </p>
<blockquote>
<p>"It is well-known that <strong>instantons</strong> with a
finite action (instanton) that would <strong>connect two cosine minima cannot
exist</strong> (Rajaraman, 1982) ... the field is truly <strong>locked in one of the minima</strong>."</p>
</blockquote>
<p><strong>Question</strong>: </p>
<p>(1) Are "there" any criteria or conditions when the field will be locked in one of the minima? Such as $g>g_c$ and certain values of $\beta$? </p>
<p>(2) how to <strong>show this statement</strong>? How is the instanton analysis done here?</p>
<p>ps. I read Rajaraman book and S Coleman on instantons. So please do not post an answer for recommending just the Refs. Thanks. :)</p>
<p>NEW Edit NOTE: I suppose we are talking about this kind of 1+1D bosonic action:
$$
\frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi
+ g \cos(\beta_{}^{} \cdot\Phi_{})
$$</p>
<p>Ref:</p>
<p>(1) Rajaraman 1982, Solitons and Instantons, Volume 15: An Introduction to Solitons and Instantons in Quantum Field Theory (North-Holland Personal Library)</p>
<p>(2) Thierry Giamarchi, Quantum Physics in One Dimension</p>
<p>(3) S Coleman, Aspects of Symmetry</p>
| 8,251 |
[
0.0009077813010662794,
0.0012370843905955553,
-0.007475084159523249,
-0.03254968672990799,
0.025363489985466003,
0.018738260492682457,
-0.039110101759433746,
-0.05256813392043114,
0.023667914792895317,
-0.046223726123571396,
0.06561493128538132,
0.02141820825636387,
0.032280560582876205,
0.05290014669299126,
-0.027348369359970093,
0.018160756677389145,
-0.004661345388740301,
-0.04234606772661209,
-0.0332656092941761,
-0.027783161029219627,
-0.027050793170928955,
0.020954366773366928,
-0.030814461410045624,
0.006740712560713291,
0.0025226494763046503,
-0.011986338533461094,
-0.0018751085735857487,
0.01330210454761982,
-0.04711112380027771,
0.05187429115176201,
-0.054039791226387024,
-0.05921969562768936,
0.009735966101288795,
0.021694203838706017,
0.007379317656159401,
-0.016857394948601723,
-0.042345765978097916,
-0.044484693557024,
0.0071656652726233006,
0.005600597709417343,
-0.003946330398321152,
0.02019924856722355,
-0.03282018378376961,
0.019173884764313698,
-0.02906375378370285,
0.03910968825221062,
0.02405174821615219,
-0.0006670983275398612,
0.08117958903312683,
-0.045012325048446655,
0.015351833775639534,
-0.008841240778565407,
0.011226974427700043,
-0.012440611608326435,
0.0019382009049877524,
-0.010592030361294746,
0.05507291480898857,
0.03734854236245155,
-0.00941947940737009,
-0.047513145953416824,
-0.037424154579639435,
-0.021526608616113663,
-0.015338034369051456,
0.013002526015043259,
-0.005534614436328411,
0.04754161462187767,
0.03379727527499199,
-0.018870774656534195,
0.006566823925822973,
-0.035419076681137085,
0.023533998057246208,
0.012422621250152588,
0.011603130958974361,
-0.0030105924233794212,
0.019435463473200798,
0.0034001341555267572,
-0.02666299045085907,
0.016262440010905266,
0.007640830706804991,
0.053840335458517075,
-0.02261546440422535,
0.012362535111606121,
0.02927556075155735,
-0.005176631733775139,
-0.032483574002981186,
-0.041071753948926926,
0.07384750247001648,
-0.01961866021156311,
-0.01101928111165762,
0.0580742321908474,
0.023864267393946648,
-0.003699043532833457,
-0.004855604842305183,
-0.03807052597403526,
-0.05895393341779709,
0.011339851655066013,
0.02997196651995182,
0.028316862881183624,
-0.033713437616825104,
0.0045752874575555325,
-0.061037253588438034,
-0.02805311605334282,
-0.004591044504195452,
0.050380706787109375,
-0.005193370394408703,
0.016351642087101936,
0.023986298590898514,
0.03410117328166962,
-0.00291730766184628,
-0.016003867611289024,
-0.05681132525205612,
0.00002538402986829169,
-0.007126026786863804,
0.027384256944060326,
-0.017206910997629166,
0.01820058375597,
-0.003162272972986102,
-0.02399168349802494,
0.0635422095656395,
0.0626119002699852,
0.04575416073203087,
-0.04622768610715866,
-0.0070878081023693085,
-0.03002026304602623,
-0.06473443657159805,
0.013091113418340683,
0.03610264137387276,
0.03864552080631256,
-0.03104349784553051,
-0.001158244675025344,
0.05751820653676987,
0.021889954805374146,
0.001183537533506751,
0.008407323621213436,
0.05503052473068237,
-0.032036617398262024,
-0.10052688419818878,
-0.048425182700157166,
0.07876016944646835,
0.0043800147250294685,
-0.005382198374718428,
-0.07933568209409714,
-0.01290505938231945,
-0.009757897816598415,
0.07462628930807114,
-0.045582953840494156,
0.022736862301826477,
0.007872053422033787,
-0.007299763150513172,
0.02475547231733799,
-0.006648570764809847,
0.03527139872312546,
-0.01186735276132822,
-0.0364765003323555,
-0.049645956605672836,
-0.00833636149764061,
0.07175716757774353,
0.004982509650290012,
0.01741231046617031,
0.006880852393805981,
0.04870094358921051,
-0.01950988546013832,
-0.006900365464389324,
-0.004367947578430176,
-0.014131957665085793,
-0.01976104825735092,
0.05556454509496689,
-0.01092079933732748,
0.024869700893759727,
0.0560772567987442,
-0.050409700721502304,
0.03324391320347786,
-0.008088591508567333,
0.0049523357301950455,
0.01393063273280859,
-0.05604954808950424,
-0.0014640350127592683,
0.011205893941223621,
-0.011154167354106903,
-0.02100576087832451,
-0.02924765832722187,
-0.011314859613776207,
0.0010390614625066519,
0.031037811189889908,
-0.026982570067048073,
0.03746778517961502,
0.016995346173644066,
0.0025647899601608515,
-0.01306135207414627,
-0.0433710552752018,
-0.015748122707009315,
-0.06538133323192596,
-0.02873859740793705,
0.031532853841781616,
-0.03296350687742233,
0.04259083792567253,
0.023129954934120178,
0.024520253762602806,
-0.023728253319859505,
-0.017607945948839188,
-0.015525156632065773,
0.022399824112653732,
0.024553118273615837,
0.009643174707889557,
0.040984392166137695,
0.005596109665930271,
0.04834367334842682,
0.010918963700532913,
0.0465485155582428,
-0.004243912175297737,
0.022058071568608284,
-0.00999202486127615,
-0.02441331557929516,
0.04536222293972969,
0.036176878958940506,
0.016688166186213493,
0.03667200729250908,
-0.019890470430254936,
-0.048295240849256516,
-0.0011590260546654463,
-0.016592517495155334,
0.005214198026806116,
0.029670074582099915,
-0.012577911838889122,
-0.043399810791015625,
0.048271141946315765,
0.006727080792188644,
0.012371421791613102,
0.007641883566975594,
-0.006248867139220238,
-0.03392563760280609,
-0.005505112931132317,
0.03256325051188469,
0.06039420887827873,
-0.006873426027595997,
0.001996362116187811,
0.04998042806982994,
0.025195669382810593,
0.03959989175200462,
-0.0018193558789789677,
-0.027822811156511307,
-0.05448783189058304,
0.05540559068322182,
0.014046136289834976,
-0.002786852652207017,
0.034754447638988495,
0.03550857678055763,
-0.011758293025195599,
-0.0054553961381316185,
0.0009756764047779143,
0.0010508771520107985,
0.020768212154507637,
-0.019201474264264107,
-0.0025129560381174088,
0.0009374782093800604,
0.01505495049059391,
0.06740500032901764,
-0.0061084916815161705,
0.05725084990262985,
0.024209488183259964,
-0.033068615943193436,
-0.02637898176908493,
-0.03981989994645119,
0.011525359004735947,
0.02026735432446003,
-0.02220883034169674,
-0.03043074533343315,
-0.042097508907318115,
0.020614678040146828,
-0.05824139714241028,
0.014196841046214104,
-0.0004918684135191143,
-0.017467275261878967,
0.01266161072999239,
-0.030949667096138,
0.03750166669487953,
-0.00018939058645628393,
0.037579379975795746,
-0.051359858363866806,
0.010205979458987713,
-0.009686200879514217,
0.023109249770641327,
0.013313207775354385,
0.019806865602731705,
-0.02610546536743641,
0.021525098010897636,
-0.0669204592704773,
0.0005875476635992527,
0.01840176247060299,
-0.006912815850228071,
0.006540792062878609,
0.008258355781435966,
-0.004141227342188358,
-0.06331060826778412,
-0.025899849832057953,
-0.025837702676653862,
0.0362883061170578,
-0.06920723617076874,
0.012679739855229855,
0.042485374957323074,
0.015484328381717205,
-0.07039054483175278,
0.005998535547405481,
-0.004152956884354353,
-0.030742380768060684,
-0.01405389979481697,
-0.009387019090354443,
0.00414916081354022,
-0.03669923171401024,
0.019615132361650467,
-0.0053194486536085606,
0.009451228193938732,
0.006635433528572321,
-0.0675223246216774,
-0.022508200258016586,
0.0024499676655977964,
-0.017043761909008026,
0.025902150198817253,
-0.015079153701663017,
-0.036623768508434296,
0.10377827286720276,
0.02443031594157219,
-0.03987714275717735,
0.006960759870707989,
0.029394151642918587,
-0.03568635508418083,
-0.0019318235572427511,
0.006566260475665331,
0.030693242326378822,
0.007215819787234068,
0.004515764769166708,
0.0364827886223793,
0.023534409701824188,
0.05391817167401314,
-0.030506987124681473,
-0.029400981962680817,
0.013279196806252003,
-0.013540185056626797,
0.010849501937627792,
0.011202994734048843,
0.011040125973522663,
-0.00011047368752770126,
0.006753059569746256,
-0.00024863987346179783,
0.01049443893134594,
0.022465670481324196,
-0.022577039897441864,
0.03441111370921135,
-0.010801068507134914,
0.023809872567653656,
-0.0095973564311862,
0.04971766099333763,
0.03866640850901604,
-0.06914567947387695,
0.0034135107416659594,
0.02900560572743416,
0.01346496120095253,
-0.015382061712443829,
0.010057765990495682,
0.01665332168340683,
0.03872041404247284,
-0.026895739138126373,
-0.016619745641946793,
0.017107680439949036,
0.03695526346564293,
0.03907095640897751,
-0.03950474038720131,
-0.0298165250569582,
0.015683427453041077,
0.04662039503455162,
0.011460738256573677,
0.015717938542366028,
-0.01719735935330391,
-0.03682306781411171,
-0.03234925493597984,
0.0005663558840751648,
-0.022626522928476334,
0.07780170440673828,
-0.004971116781234741,
0.05238277092576027,
0.036205608397722244,
0.02522023767232895,
0.004209489561617374,
-0.0010150839807465672,
-0.1031113862991333,
0.04329966381192207,
-0.011088112369179726,
-0.005750693380832672,
-0.024488506838679314,
-0.03683372214436531,
-0.010099138133227825,
0.0027169000823050737,
-0.040540020912885666,
-0.03230641409754753,
-0.0197860449552536,
-0.0788138210773468,
0.0305031668394804,
-0.021400529891252518,
-0.023803578689694405,
-0.024363406002521515,
0.02008550800383091,
0.0885784775018692,
-0.04342092201113701,
-0.0021925088949501514,
0.017572999000549316,
-0.022387368604540825,
0.017609713599085808,
-0.013090638443827629,
0.020544210448861122,
0.052215464413166046,
0.05858880281448364,
-0.0017837440827861428,
0.013871286995708942,
0.0023976280353963375,
-0.03724532201886177,
0.02847416140139103,
0.06664823740720749,
0.031191952526569366,
0.02364940568804741,
-0.02853085845708847,
-0.025126812979578972,
0.008100656792521477,
0.033253345638513565,
0.05711650848388672,
-0.012513894587755203,
-0.0031788391061127186,
0.02615426294505596,
-0.0018150846008211374,
-0.024636412039399147,
0.02964441105723381,
0.05206488072872162,
-0.006894164718687534,
-0.02136284112930298,
-0.03172400966286659,
-0.04319613799452782,
-0.01498424168676138,
0.011215251870453358,
-0.003848076332360506,
-0.010024869814515114,
-0.0178980715572834,
0.0026032086461782455,
0.039694350212812424,
0.03879009187221527,
-0.04500405862927437,
0.012945368885993958,
0.00866714771836996,
-0.011121025308966637,
0.00010578567889751866,
0.00863895658403635,
0.006039139814674854,
0.02528662607073784,
0.07444478571414948,
0.024740932509303093,
0.008435480296611786,
-0.03426090255379677,
-0.03802310302853584,
0.024940261617302895,
0.041962262243032455,
0.013821913860738277,
-0.003164964960888028,
-0.0614493303000927,
-0.015581452287733555,
0.025581926107406616,
-0.015573094598948956,
0.014673045836389065,
0.0030068804044276476,
-0.00522954948246479,
-0.02926257811486721,
-0.06408348679542542,
-0.04241236671805382,
0.035917624831199646,
0.02164280042052269,
-0.01407383568584919,
-0.036598023027181625,
-0.015998942777514458,
0.017883431166410446,
-0.0012821126729249954,
-0.03448815271258354,
0.042722199112176895,
0.01239261869341135,
0.05691448226571083,
0.04232768714427948,
0.007293951231986284,
-0.020786862820386887,
-0.09846340864896774,
0.03952183946967125,
-0.0029272979591041803,
0.007913804613053799,
0.029225626960396767,
-0.04160059243440628,
-0.050044164061546326,
0.016710495576262474,
0.019354738295078278,
-0.001850184053182602,
0.03284826502203941,
-0.06369436532258987,
0.05446304380893707,
0.029733873903751373,
0.008225111290812492,
0.03088393062353134,
-0.007496149279177189,
-0.05614769086241722,
-0.05304436385631561,
0.002774855587631464,
0.03446158394217491,
-0.024677131325006485,
-0.01975967362523079,
-0.02925100550055504,
-0.021437205374240875,
-0.061139389872550964,
0.012001877650618553,
0.007142240647226572,
-0.02203022874891758,
0.010412726551294327,
0.010990289971232414,
0.010847567580640316,
0.010397590696811676,
-0.01251030433923006,
-0.018256932497024536,
-0.033923033624887466,
0.0365823470056057,
-0.001749798422679305,
-0.027692146599292755,
0.033982548862695694,
-0.02435116283595562,
0.000860448635648936,
0.06685088574886322,
-0.032469868659973145,
-0.01688976027071476,
-0.056981999427080154,
-0.007440804038196802,
-0.04621021822094917,
-0.06011325493454933,
0.04515378922224045,
0.02216671220958233,
-0.009349342435598373,
0.01553361490368843,
-0.024960579350590706,
-0.03168216720223427,
0.036206718534231186,
-0.003579405602067709,
-0.03177621588110924,
-0.010610905475914478,
-0.0026896100025624037,
0.03511815518140793,
0.033695995807647705,
-0.05785548314452171,
-0.032197967171669006,
0.02390478365123272,
0.029979407787322998,
-0.04217229411005974,
-0.019473155960440636,
-0.01612154021859169,
-0.0373174212872982,
-0.04269172623753548,
0.010222389362752438,
-0.01007585134357214,
-0.04568551480770111,
0.01774641126394272,
0.03520442172884941,
0.05556569993495941,
0.05343078076839447,
-0.0008049978059716523,
0.0015227171825245023,
0.02224772423505783,
-0.041174303740262985,
-0.011766654439270496,
0.004587478935718536,
-0.008997539058327675,
-0.007246652618050575,
-0.041016705334186554,
-0.027267055585980415,
0.001410636119544506,
0.005447874311357737,
-0.0024320906959474087,
-0.01470057014375925,
0.035036250948905945,
-0.041981495916843414,
0.011567855253815651,
-0.04059026762843132,
-0.018511787056922913,
0.01559311430901289,
0.049063701182603836,
-0.01121203601360321,
0.011508418247103691,
-0.017943881452083588,
-0.04197554290294647,
0.020168036222457886,
0.014647833071649075,
-0.01949911005795002,
-0.012351637706160545,
0.051091015338897705,
-0.02270480990409851,
-0.010097583755850792,
-0.004556820262223482,
-0.039502762258052826,
0.009057266637682915,
-0.01559442188590765,
0.05083388462662697,
0.023784905672073364,
-0.0010286739561706781,
-0.04983455687761307,
-0.0321984700858593,
-0.010638788342475891,
0.02521594613790512,
0.04554276540875435,
0.008923879824578762,
0.0067228456027805805,
-0.0019037071615457535,
-0.021261097863316536,
-0.014824955724179745,
0.02385629527270794,
0.005140151362866163,
0.047155994921922684,
-0.008961567655205727,
0.020359370857477188,
-0.06780228763818741,
-0.010554373264312744,
0.05972976237535477,
0.018823526799678802,
-0.032358717173337936,
-0.0009306215797550976,
0.014798707328736782,
0.03391570970416069,
0.005995301064103842,
-0.010885853320360184,
-0.03688265010714531,
0.04082449898123741,
0.0034678149968385696,
0.05215424299240112,
0.02740526758134365,
0.022706883028149605,
0.0030278379563242197,
0.022089220583438873,
0.04614194110035896,
-0.008267927914857864,
-0.042356181889772415,
-0.04031446948647499,
0.02671230584383011,
0.007863301783800125,
0.0019026787485927343,
0.031565193086862564,
-0.0157031137496233,
0.04884469881653786,
0.002679523779079318,
0.0074883257038891315,
-0.040011242032051086,
0.0034502067137509584,
0.0010571444872766733,
-0.03276883810758591,
-0.03384961187839508,
0.06335826963186264,
-0.004244385752826929,
-0.031928978860378265,
0.043362341821193695,
-0.010564765892922878,
0.02623721957206726,
0.010162423364818096,
0.020944226533174515,
-0.014497008174657822,
0.05003578960895538,
-0.0038307637441903353,
0.04352092370390892,
-0.0224654208868742,
0.015523186884820461,
0.14699624478816986,
0.09735549986362457,
-0.0022584025282412767,
-0.06351686269044876,
0.015815546736121178,
-0.014243485406041145,
0.008886326104402542,
-0.029158171266317368,
0.04507877305150032,
-0.0048661138862371445,
-0.017873767763376236,
0.014332977123558521,
0.07654125243425369,
-0.01100868545472622,
-0.011677362956106663,
0.023008272051811218,
-0.03688117489218712,
-0.02540614828467369,
0.002557622268795967,
0.027437733486294746,
-0.0014475618954747915,
-0.01815827749669552,
-0.012834842316806316,
0.0203247033059597,
-0.0115132387727499,
0.010472836904227734,
-0.047216810286045074,
-0.02459050342440605,
0.0619380846619606,
0.01628369279205799,
-0.02578992396593094,
-0.00754013005644083,
0.017182642593979836,
-0.020397499203681946,
-0.029213910922408104,
-0.014186174608767033,
0.0008130833739414811,
0.03219401463866234,
0.02079392783343792,
0.08286857604980469,
-0.032228734344244,
0.006962355226278305,
0.032094888389110565,
0.032979097217321396,
-0.02573273330926895,
-0.03771441429853439,
-0.0377533845603466,
0.05186951905488968,
-0.04670262709259987,
-0.018485432490706444,
0.00965418852865696,
-0.009119966998696327,
0.011437776498496532,
0.00626304792240262,
-0.01932435855269432,
-0.03027917630970478,
0.018127672374248505,
-0.02185186557471752,
-0.004534802865236998,
-0.011716323904693127,
0.029293294996023178,
0.014589007943868637,
-0.003450580406934023,
-0.04286331683397293,
-0.04746145382523537,
-0.01223566010594368,
0.004730992019176483,
0.0625661239027977,
0.011590628884732723,
0.009459448978304863,
0.01643982343375683,
0.021426646038889885,
-0.01766853779554367,
-0.010577994398772717,
0.006966413930058479,
-0.004703679587692022,
0.022477785125374794,
0.02454206347465515,
-0.0021041978616267443,
-0.03140579164028168,
-0.0318375863134861,
0.008176103234291077,
-0.015755988657474518,
-0.023915298283100128,
0.01455809734761715,
-0.014923425391316414,
0.01610913872718811,
0.05263678729534149,
-0.0316786989569664,
-0.0029922318644821644,
-0.013077409006655216,
0.06760016828775406,
0.045725107192993164,
-0.02706543728709221,
-0.01845208741724491,
-0.01546902023255825,
-0.06433022022247314,
-0.003415631828829646,
-0.01323598064482212,
0.009731036610901356,
0.023557953536510468,
0.02014266513288021,
0.0006710083107464015,
0.02100626565515995,
0.006184902973473072,
-0.0027578184381127357,
0.046224597841501236,
-0.031587865203619,
0.011750880628824234,
0.026912542060017586,
0.02988974004983902,
-0.01119235809892416,
-0.02107921615242958,
-0.00018235556490253657,
0.02071325108408928,
0.014436761848628521,
-0.0093543017283082,
-0.03235483914613724,
0.01935577020049095,
0.02197287790477276,
0.004303342662751675,
-0.0362543947994709,
-0.018715249374508858,
-0.03713731840252876,
0.024599887430667877,
-0.020960327237844467,
0.028748059645295143,
0.011287215165793896,
0.04146769642829895,
-0.0000030846597383060725,
-0.023741472512483597,
-0.0005160372238606215,
0.010741611011326313,
-0.0063037932850420475,
0.029064476490020752,
0.005034744739532471,
0.007085164077579975,
0.024520685896277428,
0.021572677418589592,
-0.026435747742652893,
0.00925382785499096,
-0.024989061057567596,
-0.06048007681965828,
0.012793924659490585,
-0.03843335807323456,
0.006379656959325075,
0.021146852523088455,
-0.03491005301475525,
-0.029227131977677345,
0.017253762111067772,
-0.013358496129512787,
-0.002609609393402934,
0.00024673689040355384,
-0.033789582550525665,
0.018418217077851295,
-0.0479368232190609,
-0.007351142354309559,
-0.0033862139098346233,
-0.003021037206053734,
-0.014959149993956089,
0.01115147303789854,
0.01863744668662548,
-0.01971019059419632,
-0.00977315567433834,
-0.03277016803622246,
0.04702194035053253,
0.02154204435646534,
0.006810400635004044,
0.02892635017633438,
0.04970370978116989,
-0.012633748352527618,
0.006746463477611542,
-0.0023323106579482555,
-0.009585573337972164,
-0.06883548200130463,
-0.024711962789297104,
0.02077903039753437,
0.0005234696436673403,
0.04674630984663963,
-0.033964309841394424,
0.026706332340836525,
0.026789525523781776,
-0.08104630559682846,
-0.013313514180481434,
-0.028033453971147537,
0.00843534991145134,
-0.03734513372182846,
-0.025893960148096085,
-0.02993852272629738,
0.05012167990207672,
0.009569653309881687,
0.02579996921122074,
-0.03265038877725601,
0.0454711839556694,
-0.01567692495882511,
-0.004601205233484507,
0.016326436772942543,
0.04139668494462967,
-0.004902790300548077,
0.01779300533235073,
0.08019112050533295,
-0.038243118673563004,
-0.03956098482012749,
0.02273532934486866,
-0.033790770918130875,
-0.014945697039365768,
-0.00434507243335247,
0.021602483466267586,
0.008946016430854797,
-0.009635157883167267,
0.03513665124773979,
0.02951485477387905,
-0.006944528315216303,
-0.021756745874881744,
0.007387999445199966,
0.007646515499800444,
0.0053962217643857,
-0.008988032117486,
0.01571674458682537,
-0.012456288561224937,
-0.02807612717151642,
-0.005802168045192957,
-0.03962552547454834,
-0.025025073438882828,
-0.024905802682042122,
-0.00442016264423728,
-0.0035075079649686813,
0.011010191403329372,
-0.0256334375590086,
-0.010874933563172817,
-0.015733469277620316,
-0.0028938520699739456,
0.05406022071838379,
0.030521567910909653,
-0.003776197088882327,
-0.029574722051620483,
-0.03523840755224228,
0.05186204984784126,
0.06265798956155777,
-0.025231167674064636,
-0.06502886861562729,
-0.022752853110432625,
0.036072611808776855,
0.018834104761481285,
0.02083538845181465,
-0.02682632766664028,
0.007983599789440632,
0.017834721133112907,
0.00411301339045167,
0.03149230778217316,
-0.06378528475761414,
-0.011029679328203201,
0.023093752562999725,
-0.03995247557759285,
0.009268923662602901,
0.025207819417119026,
0.0038280291482806206,
-0.015884768217802048,
-0.039801113307476044,
0.022729400545358658,
0.042252592742443085,
0.03147511929273605,
-0.03596207872033119,
-0.02731933444738388,
0.07798788696527481,
-0.012874205596745014,
0.01583695411682129,
-0.011819560080766678,
-0.006742869503796101,
0.011009001173079014,
0.004401978105306625,
0.013048057444393635,
0.015082888305187225,
-0.007723884657025337,
0.015365147963166237,
0.0253144521266222,
0.004634486511349678,
0.03424087166786194,
-0.006708348635584116,
-0.008161614648997784,
0.03770563751459122,
0.0037184625398367643,
-0.0006687436252832413,
0.04818493500351906,
-0.009792730212211609,
-0.006081536877900362,
-0.003910352475941181,
-0.07127460837364197,
-0.02283257246017456,
-0.009662800468504429,
-0.040166355669498444,
-0.021284926682710648,
0.005597200244665146,
-0.014011939987540245,
0.011974706314504147,
-0.03676025569438934,
0.0006923889159224927,
0.03782038390636444,
-0.008813613094389439,
-0.0178461205214262,
0.07724393904209137,
0.01547385472804308,
0.028280755504965782,
-0.001321682007983327,
0.01644018478691578,
0.008033683523535728,
0.011781429871916771,
0.03927068039774895,
0.02996884472668171,
-0.0016456436133012176,
0.007563834078609943,
-0.009384348057210445,
0.01747237704694271,
0.009495480917394161,
0.0032232902012765408,
0.004572434350848198,
0.03942880406975746,
-0.010647003538906574,
0.009475838392972946,
0.04712217301130295,
-0.010084787383675575,
-0.0528813898563385,
0.0004888313123956323,
-0.007225308567285538,
0.10638953745365143,
-0.04134051874279976,
0.020144769921898842,
-0.018986757844686508,
0.028605123981833458,
-0.00890278909355402,
0.0011481537949293852,
0.008983445353806019,
0.05013369768857956,
-0.01355269830673933,
-0.017544923350214958,
-0.018532801419496536,
0.0011683552293106914,
-0.0076713222078979015,
-0.07797729969024658,
-0.04039721190929413,
0.03980403020977974,
0.007202097214758396,
-0.010082941502332687,
-0.006923006847500801,
-0.02602570317685604,
-0.003786441870033741,
0.021401187404990196,
-0.03616093099117279,
-0.000030974337278166786,
-0.03161705285310745,
0.003668830031529069,
0.0026618295814841986,
0.07709012925624847,
-0.04964013770222664,
-0.028969092294573784,
-0.01963520422577858,
-0.004061949905008078,
-0.025045879185199738,
0.02232014574110508
] |
<p>Assume "The Big Crunch" scenario (the universe will collapse to a singularity). In this case, I think of the entire universe as an isolated system; in the "Big Crunch" scenario, it seems to me gravity itself would act as the "walls" of the system, keeping all the matter and energy inside. Thus, by the second law of thermodynamics, entropy will increase. However, it seems to decrease (everything is being smashed together).</p>
<p>I know black holes get around this through the emission of Hawking radiation, but this is the emission of radiation from black holes to the universe. In the big crunch scenario, by definition, there is no universe for the radiation to escape to because the universe itself is collapsing, taking all radiation with it.</p>
| 8,252 |
[
-0.034887637943029404,
-0.03679949790239334,
0.021185897290706635,
-0.005095881409943104,
0.0031288263853639364,
0.03410648927092552,
-0.021704981103539467,
-0.020801974460482597,
0.006093495991080999,
-0.05757993087172508,
-0.03643762692809105,
0.02781744860112667,
0.006794891320168972,
0.005971502047032118,
0.0072924732230603695,
0.004314989782869816,
-0.05261731520295143,
-0.006036881357431412,
0.0021124372724443674,
-0.030868656933307648,
0.03494815155863762,
0.047621339559555054,
-0.02144913375377655,
0.003314839443191886,
-0.05870790034532547,
0.02229955792427063,
0.00620057201012969,
0.010481981560587883,
0.03427618741989136,
0.03508307784795761,
0.0021912415977567434,
-0.006705931853502989,
-0.023511109873652458,
0.05453598499298096,
0.036998260766267776,
-0.01884903386235237,
-0.034024037420749664,
-0.028693757951259613,
-0.013342815451323986,
-0.026155561208724976,
-0.06874337047338486,
-0.04529016464948654,
-0.011750544421374798,
0.02997477725148201,
-0.07029417902231216,
0.000006698438028251985,
0.008841301314532757,
0.013067097403109074,
0.045840419828891754,
-0.05571024864912033,
0.025214040651917458,
-0.003037805203348398,
0.04224306717514992,
0.044563278555870056,
-0.02377471514046192,
0.02759372442960739,
0.09559354931116104,
0.06362508982419968,
-0.034080374985933304,
-0.0278654582798481,
-0.03028782270848751,
0.002635740675032139,
-0.04290279000997543,
-0.00032624774030409753,
-0.008974925614893436,
0.04990539699792862,
0.0011741284979507327,
-0.03329750522971153,
0.013975925743579865,
0.024774517863988876,
0.005432872101664543,
0.012242683209478855,
0.013670741580426693,
-0.008968085050582886,
0.03094286099076271,
-0.01763329654932022,
0.022796358913183212,
-0.012526346370577812,
0.029706832021474838,
0.027914535254240036,
-0.004905807785689831,
-0.017014579847455025,
0.07822120189666748,
0.05242159590125084,
0.019792655482888222,
0.03626158833503723,
0.08091667294502258,
-0.03365969657897949,
0.001922711613588035,
0.045565828680992126,
-0.0022011075634509325,
0.0025435753632336855,
0.04821643605828285,
-0.016914954409003258,
-0.04480718821287155,
0.01628640666604042,
-0.011892985552549362,
0.06288161873817444,
-0.004946345463395119,
-0.025838712230324745,
0.013332013972103596,
0.03194991871714592,
0.02625611610710621,
0.08299112319946289,
0.04496512934565544,
-0.023804688826203346,
-0.07327824831008911,
0.005351944826543331,
-0.0147877037525177,
-0.028792964294552803,
-0.06474103033542633,
0.002016696846112609,
0.004466554149985313,
-0.04494969919323921,
0.011649547144770622,
-0.02984507568180561,
-0.0028750579804182053,
-0.02918379008769989,
0.03752675652503967,
0.08887270092964172,
0.04601411521434784,
0.0043289028108119965,
0.03263509273529053,
-0.03849010542035103,
-0.05724632740020752,
0.037496015429496765,
0.05082959681749344,
-0.042406100779771805,
-0.06570817530155182,
0.020889664068818092,
-0.0389232411980629,
-0.00656858691945672,
0.004551815800368786,
-0.010760496370494366,
0.04442921280860901,
-0.03588103875517845,
-0.09176716953516006,
-0.0464087650179863,
0.053651805967092514,
0.0018836638191714883,
-0.004543740767985582,
-0.019199268892407417,
0.015297205187380314,
0.039306432008743286,
0.08236784487962723,
0.007008058484643698,
-0.009814227931201458,
-0.015230459161102772,
0.02544611692428589,
0.008581220172345638,
-0.034384336322546005,
0.006058963481336832,
-0.001069952268153429,
-0.034261543303728104,
0.016619844362139702,
-0.09535935521125793,
0.005130781326442957,
0.039863672107458115,
0.006123717408627272,
-0.03095267526805401,
0.0436856672167778,
-0.017540814355015755,
0.016565456986427307,
-0.009531035088002682,
-0.012834888882935047,
-0.016517819836735725,
0.08629220724105835,
0.0090249665081501,
0.001002888660877943,
0.04508063197135925,
0.06349562108516693,
0.02307490073144436,
0.013421100564301014,
-0.005028417333960533,
-0.0014674218837171793,
-0.060453176498413086,
-0.013898057863116264,
-0.04571416601538658,
0.006947288289666176,
-0.018670570105314255,
-0.033381883054971695,
-0.022106949239969254,
-0.0061567495577037334,
-0.0329912044107914,
0.030374737456440926,
0.02004908211529255,
0.0033412021584808826,
-0.04642634838819504,
-0.004943131469190121,
-0.01278663333505392,
-0.01204756274819374,
-0.07837074995040894,
0.014552541077136993,
0.020822104066610336,
-0.011044434271752834,
-0.025517135858535767,
0.038430437445640564,
0.06524669378995895,
-0.029773712158203125,
-0.02435201406478882,
-0.014268043451011181,
0.028682226315140724,
-0.031254321336746216,
-0.0004334932309575379,
-0.004261461552232504,
0.036169592291116714,
0.06135941669344902,
-0.0037994403392076492,
0.021671712398529053,
0.009147776290774345,
-0.018924662843346596,
0.027353797107934952,
-0.006087533663958311,
0.006822944153100252,
-0.019852666184306145,
0.0001232895883731544,
0.016563471406698227,
0.017326069995760918,
0.02349037677049637,
0.025976376608014107,
-0.023316437378525734,
0.08003231137990952,
0.03434891626238823,
0.03542545065283775,
-0.013425689190626144,
0.03736618533730507,
0.008443339727818966,
-0.017016177996993065,
-0.04341603070497513,
-0.038886506110429764,
-0.04695066437125206,
0.000983443227596581,
0.033995360136032104,
0.007473111152648926,
-0.022530274465680122,
0.0271694865077734,
0.03933054953813553,
0.019232701510190964,
-0.02581676095724106,
0.01064863707870245,
-0.017989598214626312,
-0.0012932408135384321,
0.004512865096330643,
-0.005179638508707285,
0.04096473008394241,
-0.0010611958568915725,
0.04640411213040352,
-0.0029900858644396067,
-0.004302250687032938,
-0.012835717760026455,
0.011180387809872627,
0.02369050122797489,
0.039672255516052246,
0.045986466109752655,
-0.01551233883947134,
-0.027746088802814484,
0.022313931956887245,
-0.02572440914809704,
-0.005027624312788248,
0.017171012237668037,
0.005349928513169289,
-0.00019612883625086397,
-0.06936212629079819,
0.0027564330957829952,
-0.017094429582357407,
0.009256154298782349,
-0.03796045109629631,
-0.019222494214773178,
0.02542021870613098,
-0.0564606711268425,
-0.0036587135400623083,
0.02685035765171051,
-0.002662090817466378,
-0.03611870855093002,
-0.011495928280055523,
0.027850253507494926,
-0.002810238627716899,
0.018675535917282104,
-0.0359862856566906,
-0.049069978296756744,
-0.017199089750647545,
-0.03913462162017822,
-0.03593440726399422,
0.03076910227537155,
-0.0407080352306366,
0.02615439146757126,
-0.029935399070382118,
-0.03953849896788597,
0.04664982855319977,
-0.035170067101716995,
0.04403142258524895,
0.020904289558529854,
-0.014992553740739822,
-0.037669211626052856,
0.012535156682133675,
-0.016596265137195587,
0.009726212359964848,
-0.031854938715696335,
-0.00190693826880306,
0.08628471195697784,
-0.008047878742218018,
-0.053540799766778946,
-0.021225569769740105,
-0.07171840220689774,
-0.06404584646224976,
-0.03094119019806385,
0.018174730241298676,
0.010121774859726429,
-0.012160194106400013,
0.035343557596206665,
0.03339270502328873,
-0.05030990391969681,
-0.034050680696964264,
-0.033371321856975555,
-0.05821259692311287,
0.03498432785272598,
0.012248468585312366,
0.011764663271605968,
-0.04241679981350899,
-0.048668477684259415,
0.02946583181619644,
0.021010378375649452,
-0.01093096099793911,
-0.01238225121051073,
-0.015240124426782131,
0.008740478195250034,
-0.01940540410578251,
-0.008786757476627827,
-0.022166699171066284,
0.03688836470246315,
0.01895791105926037,
0.03813692182302475,
0.04331650957465172,
-0.01837032288312912,
-0.008312460035085678,
-0.019185295328497887,
0.0051416209898889065,
0.033366911113262177,
0.0036678665783256292,
0.025820650160312653,
0.010334013029932976,
-0.0374995693564415,
0.012616834603250027,
-0.007175736594945192,
0.016868561506271362,
0.013814892619848251,
-0.048923272639513016,
0.030910836532711983,
0.015787675976753235,
0.05137614905834198,
-0.05127611756324768,
0.02016259916126728,
-0.020529061555862427,
0.00698574585840106,
0.024861646816134453,
0.01111071277409792,
0.07443958520889282,
0.01086458470672369,
0.014398564584553242,
-0.02470124512910843,
0.047208722680807114,
-0.03216351196169853,
0.01743474416434765,
-0.0008625957416370511,
-0.007025659549981356,
0.011400808580219746,
0.007603159639984369,
0.024177666753530502,
0.050217077136039734,
0.01657356135547161,
0.008621875196695328,
-0.002326399087905884,
-0.019337736070156097,
0.012856834568083286,
-0.07175087183713913,
-0.006167169194668531,
-0.018613548949360847,
0.051961950957775116,
0.013951567001640797,
0.023659635335206985,
0.035829588770866394,
0.025122979655861855,
0.029384534806013107,
-0.019592605531215668,
-0.08081414550542831,
0.021837806329131126,
-0.053311534225940704,
-0.021090757101774216,
0.0307554192841053,
0.0014588907361030579,
-0.013762478716671467,
0.009400075301527977,
-0.014062450267374516,
0.004844511393457651,
-0.003223072038963437,
-0.07686449587345123,
-0.017955806106328964,
-0.04327227175235748,
-0.03468138352036476,
0.012007704004645348,
0.04186023026704788,
0.04180965945124626,
-0.015784138813614845,
-0.028297951444983482,
0.028586313128471375,
-0.003918537870049477,
0.015356055460870266,
0.014454836957156658,
0.02268207259476185,
0.0115195969119668,
0.016386419534683228,
0.027970416471362114,
-0.008513365872204304,
0.011768634431064129,
-0.0038678431883454323,
0.06344088912010193,
0.013423152267932892,
-0.028728105127811432,
-0.023065699264407158,
-0.007843107916414738,
-0.03376072272658348,
-0.03916659951210022,
-0.020363038405776024,
0.030185271054506302,
-0.007346723228693008,
0.0260393675416708,
0.02304273471236229,
0.01250788290053606,
-0.0002641070750541985,
0.02120937593281269,
0.0808817520737648,
-0.020472867414355278,
-0.04557283967733383,
0.0167104322463274,
-0.05009421706199646,
-0.018549853935837746,
-0.04128951579332352,
-0.0009096402209252119,
-0.013609168119728565,
-0.06702735275030136,
0.030603256076574326,
-0.007220849860459566,
0.021151263266801834,
-0.027795126661658287,
-0.02612449787557125,
0.029116617515683174,
0.058658063411712646,
-0.0162579957395792,
0.0138626703992486,
0.02598833106458187,
0.044100768864154816,
0.0402996651828289,
-0.011744282208383083,
0.009644370526075363,
-0.0505976565182209,
-0.015243187546730042,
0.02131255529820919,
0.02946137823164463,
0.036796633154153824,
-0.033424053341150284,
-0.05224921181797981,
-0.02959524840116501,
0.04961682856082916,
-0.00826929695904255,
0.042741406708955765,
0.00885673239827156,
0.008336336351931095,
0.03391152247786522,
-0.03864850103855133,
0.01853725127875805,
0.018095942214131355,
-0.039316412061452866,
0.001534745329990983,
0.014225734397768974,
0.0170002244412899,
-0.03698781877756119,
0.01570669375360012,
-0.00021136052964720875,
0.041295625269412994,
0.001160927931778133,
0.009759677574038506,
0.020915156230330467,
0.023691600188612938,
-0.011880112811923027,
-0.04753366485238075,
0.012909515760838985,
-0.00305146723985672,
-0.06678412854671478,
0.04651276767253876,
-0.028915120288729668,
-0.005718313157558441,
0.006557303946465254,
0.01666981354355812,
0.0017222898313775659,
0.004376934375613928,
-0.02498811110854149,
0.02481355518102646,
0.03213199973106384,
0.010395724326372147,
0.03382958844304085,
0.03794363886117935,
0.01736087165772915,
0.04095037654042244,
-0.03720470145344734,
0.04009896516799927,
-0.053677283227443695,
-0.007618234492838383,
-0.03543509915471077,
0.004624110646545887,
-0.025174107402563095,
0.04731500893831253,
-0.016082486137747765,
0.006093879695981741,
0.012330790981650352,
-0.04655328020453453,
0.015411578118801117,
-0.002773604355752468,
0.00043848087079823017,
0.009829945862293243,
-0.012244676239788532,
0.04592885076999664,
0.004882029257714748,
-0.0165436789393425,
0.0125464191660285,
-0.012160904705524445,
-0.025907741859555244,
0.04996098205447197,
-0.024528784677386284,
0.027660785242915154,
0.0036746677942574024,
-0.02488829381763935,
0.023051613941788673,
-0.01801958866417408,
0.03505135700106621,
-0.009529712609946728,
-0.02384219877421856,
0.023289058357477188,
-0.04248261824250221,
-0.020235935226082802,
-0.02658933587372303,
-0.007571593392640352,
0.0015506880590692163,
-0.02189958281815052,
0.021462002769112587,
0.016764096915721893,
-0.012387705035507679,
-0.10060284286737442,
-0.030133729800581932,
0.021151289343833923,
-0.010939829982817173,
0.011776674538850784,
-0.03311479091644287,
0.00651395320892334,
-0.07302957773208618,
-0.016689471900463104,
-0.013168363831937313,
0.001607140526175499,
-0.014068586751818657,
0.02306487038731575,
-0.004975531715899706,
0.020081594586372375,
-0.004343940876424313,
0.01186968944966793,
-0.032611727714538574,
0.010537347756326199,
0.010086663998663425,
-0.0009748907759785652,
0.017322616651654243,
0.06001856178045273,
-0.016117801889777184,
-0.0041432492434978485,
-0.016572192311286926,
-0.01810210756957531,
0.02662709914147854,
-0.01232382282614708,
-0.014929036609828472,
0.036495331674814224,
0.02229856327176094,
-0.018124021589756012,
0.00019141907978337258,
0.03697909414768219,
-0.01588558219373226,
0.010247575119137764,
-0.00754398200660944,
-0.0131729980930686,
0.022833608090877533,
-0.06933505088090897,
0.012173464521765709,
-0.0057862079702317715,
0.007567656226456165,
0.002163308672606945,
0.06492196023464203,
0.058612141758203506,
-0.04592873156070709,
-0.024901624768972397,
-0.032579999417066574,
0.02307121641933918,
-0.00627800403162837,
0.032298214733600616,
0.016260823234915733,
0.008574475534260273,
-0.02025018446147442,
-0.042649757117033005,
-0.0497821569442749,
-0.014278527349233627,
0.058025527745485306,
-0.035923950374126434,
0.03982536494731903,
0.016131088137626648,
-0.0019933332223445177,
0.0026723856572061777,
-0.061612870544195175,
0.018847670406103134,
0.04381170868873596,
-0.0005684306961484253,
0.013639806769788265,
-0.006561764981597662,
-0.018496621400117874,
0.02932477928698063,
0.01872929185628891,
-0.033629294484853745,
0.03683968633413315,
0.028081176802515984,
0.03224710375070572,
0.02408505044877529,
-0.02433997206389904,
-0.0362589992582798,
0.02935406193137169,
-0.07021607458591461,
0.039032138884067535,
0.018905704841017723,
0.014937651343643665,
0.018905943259596825,
-0.009668633341789246,
0.017809337005019188,
-0.046151354908943176,
-0.04120299220085144,
-0.04818876087665558,
0.011237900704145432,
-0.01593921333551407,
0.027619270607829094,
0.010374422185122967,
0.021245082840323448,
0.021491220220923424,
0.01376850251108408,
-0.005521330051124096,
0.02489418163895607,
-0.0783262699842453,
-0.02678479440510273,
-0.02942781150341034,
-0.048194315284490585,
0.02954568713903427,
0.02516757696866989,
-0.010217363014817238,
-0.018250055611133575,
-0.02564794197678566,
-0.023353230208158493,
-0.0021744489204138517,
0.05655807629227638,
0.007139524910598993,
0.06842654943466187,
0.00007071833533700556,
0.013827490620315075,
-0.01998685486614704,
0.013440624810755253,
0.1071055606007576,
0.059525035321712494,
-0.008658572100102901,
-0.06471341848373413,
-0.021257000043988228,
-0.022653618827462196,
0.009015033952891827,
-0.013779389671981335,
0.019476717337965965,
0.004684279207140207,
0.013012212701141834,
0.04551174119114876,
0.05779346078634262,
-0.0005956034874543548,
-0.05562423914670944,
0.04098103940486908,
-0.04975121468305588,
-0.010156631469726562,
0.027532123029232025,
0.039633557200431824,
-0.0031954573933035135,
0.00828804261982441,
-0.03350409120321274,
-0.00654548080638051,
-0.019182493910193443,
0.019000379368662834,
-0.0433722622692585,
-0.027983408421278,
0.019039224833250046,
-0.022385483607649803,
-0.04586589336395264,
-0.002896346151828766,
-0.009423473849892616,
-0.04499359056353569,
0.0010073540033772588,
-0.0023126432206481695,
0.046105142682790756,
0.002071295166388154,
-0.0031853048130869865,
0.0007320238510146737,
0.012302279472351074,
0.0121223796159029,
-0.0024146386422216892,
0.0005387885612435639,
-0.013404677622020245,
0.008048776537179947,
0.01604396104812622,
0.05794277414679527,
-0.020599933341145515,
0.021403325721621513,
0.012818644754588604,
0.025065738707780838,
0.021475527435541153,
-0.0222424678504467,
0.030208542943000793,
0.0034938391763716936,
0.01429673656821251,
-0.0036441960837692022,
-0.04849975183606148,
-0.003887629834935069,
0.002691179048269987,
-0.0060869306325912476,
0.031609684228897095,
-0.0092384098097682,
0.008003617636859417,
0.029224060475826263,
-0.014698530547320843,
0.05055560544133186,
-0.032744914293289185,
0.007358407601714134,
-0.04143015295267105,
-0.0064276354387402534,
-0.05929916352033615,
-0.006424629595130682,
0.030170584097504616,
0.02705160342156887,
0.004773731343448162,
0.013295920565724373,
0.03403501585125923,
-0.010129732079803944,
-0.01481102779507637,
0.03136981278657913,
-0.0067191533744335175,
-0.03769197314977646,
-0.01387225091457367,
0.013789098709821701,
0.0008532440406270325,
0.05500487610697746,
0.010660683736205101,
-0.03690517693758011,
0.02550101839005947,
0.013565796427428722,
0.021435681730508804,
0.012807955034077168,
0.011713432148098946,
-0.010462678968906403,
-0.04912211745977402,
-0.014175301417708397,
-0.004603203386068344,
0.01883763261139393,
0.02211466059088707,
0.0017679408192634583,
0.0284881629049778,
0.03196844458580017,
-0.010378128848969936,
0.02408425323665142,
0.017685692757368088,
-0.0258040688931942,
-0.0003229804860893637,
0.02686501480638981,
-0.009458903223276138,
-0.020638378337025642,
-0.02191476710140705,
-0.016748785972595215,
0.011139512993395329,
-0.019957974553108215,
0.029561538249254227,
-0.04061906784772873,
0.03701767325401306,
-0.011777777224779129,
0.06089060753583908,
-0.06558120995759964,
0.01213936135172844,
-0.06185169145464897,
-0.0059504699893295765,
0.04765770584344864,
0.0039627267979085445,
-0.0008701547631062567,
0.05030404031276703,
-0.00994870811700821,
-0.06196262687444687,
0.02653351239860058,
0.04087802395224571,
-0.03499544784426689,
0.00950220599770546,
0.029457764700055122,
-0.0017185152973979712,
0.055880773812532425,
0.008374114520847797,
0.010147498920559883,
0.029256273061037064,
-0.0349118672311306,
-0.04857755824923515,
0.013076278381049633,
-0.016366934403777122,
0.01764700748026371,
0.007468593306839466,
-0.040092576295137405,
-0.0669398084282875,
0.0684322789311409,
-0.007104779127985239,
-0.0017271747346967459,
-0.002575912047177553,
-0.03742389380931854,
-0.009182779118418694,
-0.008877279236912727,
0.018190452829003334,
-0.025458768010139465,
-0.02019951492547989,
0.005808040499687195,
0.00016266221064142883,
-0.015385075472295284,
-0.019499333575367928,
-0.023628516122698784,
-0.03484916687011719,
0.006063241045922041,
-0.014919809065759182,
-0.015086136758327484,
0.033165089786052704,
0.06796851009130478,
-0.04887857660651207,
0.025045163929462433,
0.0543871745467186,
0.009464746341109276,
-0.10651733726263046,
0.009210747666656971,
0.026799289509654045,
-0.007227614987641573,
0.02532588690519333,
-0.016270771622657776,
0.018828226253390312,
0.014450328424572945,
-0.06693463027477264,
0.011537707410752773,
-0.029196828603744507,
-0.003055550390854478,
-0.020953357219696045,
0.020436367020010948,
-0.020230328664183617,
0.03196655213832855,
0.07133505493402481,
0.0657612755894661,
-0.005870777647942305,
-0.007838679477572441,
-0.03226146101951599,
-0.01523979939520359,
-0.00886560045182705,
0.009050547145307064,
-0.008006410673260689,
0.023883111774921417,
0.05484217032790184,
-0.019233038648962975,
-0.009859584271907806,
0.0022130555007606745,
-0.02322772704064846,
-0.02147180400788784,
-0.017874713987112045,
0.010588927194476128,
0.0382588729262352,
0.014560945332050323,
0.002201182534918189,
-0.016689524054527283,
0.0018683748785406351,
0.029434215277433395,
0.013270711526274681,
-0.0015799644170328975,
0.002780153416097164,
0.00008428518776781857,
-0.00510913971811533,
-0.014615765772759914,
0.006973030511289835,
0.014081860892474651,
0.010095023550093174,
0.0010430667316541076,
0.0073880101554095745,
0.02183322235941887,
0.0219881534576416,
0.0035837795585393906,
-0.011798598803579807,
-0.06390466541051865,
-0.02784397080540657,
0.010999685153365135,
0.03660055249929428,
0.00041626027086749673,
0.011439921334385872,
0.015288490802049637,
-0.009791906923055649,
0.0007459413027390838,
-0.02122555300593376,
-0.01206660084426403,
-0.03607361763715744,
-0.02535225823521614,
-0.0296021718531847,
0.029423147439956665,
0.013747417367994785,
-0.07785869389772415,
-0.026143280789256096,
0.04754461348056793,
0.004826409742236137,
0.020593861117959023,
-0.005689631216228008,
-0.057920604944229126,
-0.04604364186525345,
-0.0458049438893795,
0.029086152091622353,
-0.016142310574650764,
0.03982449695467949,
-0.0517609566450119,
-0.034139543771743774,
-0.019388869404792786,
-0.006853482685983181,
0.03963319584727287,
-0.009060785174369812,
-0.004915066063404083,
0.010836978442966938,
-0.00453619658946991,
0.04424569755792618,
-0.040790922939777374,
0.01953163556754589,
-0.006007450167089701,
-0.028640644624829292,
-0.0004237844841554761,
0.0034120853524655104,
-0.009494171477854252,
0.01238497719168663,
0.06501845270395279,
-0.024845024570822716,
0.040318071842193604,
-0.006643814966082573,
-0.02417738549411297,
0.03886813297867775,
0.012441960163414478,
-0.00823188479989767,
0.040012337267398834,
-0.0378483310341835,
0.02003069967031479,
0.051261648535728455,
0.014380892738699913,
-0.018325304612517357,
0.06448730081319809,
-0.007416653446853161,
0.014212050475180149,
0.0017317058518528938,
-0.004188356921076775,
0.009037282317876816,
-0.02106577530503273,
-0.016120867803692818,
0.031187256798148155,
-0.04597180709242821,
0.013095916248857975,
0.017571834847331047,
0.010693296790122986,
0.044034358114004135,
-0.0252993144094944,
0.012989239767193794,
0.029939452186226845,
0.05028223246335983,
-0.03641738370060921,
0.06488935649394989,
0.040941525250673294,
0.006134118884801865,
0.027449361979961395,
0.009405397810041904,
-0.029184605926275253,
0.021888190880417824,
0.0012915327679365873,
0.019086886197328568,
-0.09977585077285767,
-0.01089749950915575,
0.0007216494414024055,
0.004399729892611504,
0.01790218986570835,
0.019157232716679573,
-0.035379573702812195,
0.05575936660170555,
0.0007780606974847615,
0.023603668436408043,
-0.00765327038243413,
-0.023584039881825447,
-0.04165599122643471,
0.025210756808519363,
-0.004707358777523041,
0.05917402356863022,
0.02402244322001934,
-0.006253029219806194,
-0.013646700419485569,
-0.0070340889506042,
0.027812723070383072,
-0.020351625978946686,
0.024497220292687416,
-0.013114129193127155,
-0.012934809550642967,
-0.026997210457921028,
0.013624691404402256,
-0.005255550146102905,
-0.028216293081641197,
0.04489320144057274,
0.030529271811246872,
0.028796067461371422,
0.0018545225029811263,
-0.02786196582019329,
-0.008832467719912529,
0.03922364488244057,
-0.00841011106967926,
0.0291104968637228,
-0.00762706296518445,
0.027217460796236992,
-0.032082878053188324,
-0.0222888495773077
] |
<p>I'm a very visual learner and I would like to know if the diagram representing the Schwarzschild solution is altered at all when the torsion tensor is non zero.</p>
<p>Of particular interest - what is the graphical form of a metric with no curvature and the full range of torsion values?</p>
| 8,253 |
[
-0.005962676368653774,
0.01450755912810564,
-0.009087884798645973,
-0.020815586671233177,
0.03806881234049797,
0.02277398854494095,
-0.04669458791613579,
-0.013651754707098007,
-0.0684288889169693,
-0.045283831655979156,
-0.00954642053693533,
0.0011440968373790383,
0.024013977497816086,
0.022246479988098145,
0.013495873659849167,
-0.021770784631371498,
-0.026963388547301292,
-0.011451136320829391,
-0.028345409780740738,
-0.03647240623831749,
0.00007430317054968327,
-0.008116849698126316,
-0.016342811286449432,
0.00602765241637826,
-0.013437094166874886,
0.02733798511326313,
0.017659582197666168,
-0.025908812880516052,
0.01861536130309105,
0.043307896703481674,
-0.056741081178188324,
0.0014753425493836403,
0.020289352163672447,
0.04057502746582031,
0.061692651361227036,
-0.008045163005590439,
-0.04340330883860588,
-0.01914164051413536,
-0.0069282944314181805,
-0.012520869262516499,
-0.015490862540900707,
-0.005125651601701975,
-0.02612607181072235,
0.06054724007844925,
-0.00968984141945839,
-0.015093810856342316,
0.020443366840481758,
-0.004498437978327274,
0.050032295286655426,
-0.04422946274280548,
0.08570486307144165,
0.008220722898840904,
0.032881222665309906,
0.011099993251264095,
-0.009309545159339905,
0.007752879522740841,
0.0522332638502121,
0.06949158012866974,
-0.012712661176919937,
-0.048951517790555954,
-0.021080682054162025,
-0.0006620625499635935,
-0.027228863909840584,
-0.017005326226353645,
-0.011474615894258022,
0.051802217960357666,
0.023354167118668556,
-0.01335377898067236,
0.04010159522294998,
-0.0021262841764837503,
-0.020838608965277672,
0.010784687474370003,
0.00004824654388357885,
-0.023344609886407852,
-0.01540748868137598,
-0.03882267698645592,
0.019593926146626472,
0.008036293089389801,
0.02547207474708557,
0.039051469415426254,
-0.018462341278791428,
-0.00296903308480978,
0.050693199038505554,
0.04879924654960632,
-0.005810179281979799,
0.029607119038701057,
0.05749665945768356,
0.016377080231904984,
0.026254691183567047,
0.04029029980301857,
-0.005973441991955042,
-0.019196217879652977,
-0.006160646677017212,
-0.032524533569812775,
-0.033995985984802246,
0.021993467584252357,
-0.006775121670216322,
0.05137629434466362,
0.0001856018352555111,
-0.039492297917604446,
-0.0200163796544075,
0.011442436836659908,
0.002324007684364915,
0.045989520847797394,
0.037387993186712265,
0.01399457361549139,
-0.051359135657548904,
0.0017490418395027518,
-0.04869598522782326,
-0.01434488408267498,
-0.016604389995336533,
-0.012876996770501137,
-0.024713288992643356,
-0.003263721941038966,
0.015614638105034828,
-0.06384876370429993,
0.016273649409413338,
-0.04952799156308174,
0.03937884420156479,
0.05324066802859306,
0.0438556931912899,
-0.0037253156770020723,
0.04806515574455261,
-0.044511158019304276,
-0.06998991221189499,
-0.0014072677586227655,
0.061961133033037186,
-0.0006459060241468251,
0.002689979737624526,
0.008313599042594433,
-0.015528237447142601,
0.008761500008404255,
0.002748670056462288,
-0.006545396987348795,
0.030281076207756996,
-0.03699946403503418,
-0.07273668050765991,
-0.058459289371967316,
-0.0033258106559515,
0.02429194189608097,
-0.007335373666137457,
-0.032877758145332336,
-0.015061387792229652,
0.054469797760248184,
0.06550929695367813,
-0.015608681365847588,
0.01791391335427761,
-0.0007770806550979614,
0.032223377376794815,
-0.021750163286924362,
-0.013114812783896923,
0.02523629367351532,
0.008787239901721478,
-0.05122509226202965,
0.007133388426154852,
-0.11618183553218842,
-0.013217239640653133,
0.038579538464546204,
-0.006159570533782244,
-0.042331986129283905,
0.03875667229294777,
-0.025363992899656296,
0.0387214720249176,
0.02412278763949871,
-0.05238649249076843,
0.007008452899754047,
0.0915176048874855,
-0.01577039249241352,
0.004322289489209652,
0.013790851458907127,
0.011152260936796665,
0.011587025597691536,
0.028320591896772385,
0.014533902518451214,
0.04917500540614128,
-0.005637111142277718,
0.02238323912024498,
-0.030080484226346016,
0.028510887175798416,
0.013717393390834332,
-0.03676052764058113,
-0.006573664024472237,
-0.032592736184597015,
0.025623882189393044,
-0.006991262547671795,
0.028005527332425117,
-0.022305361926555634,
-0.0076639847829937935,
0.023874949663877487,
-0.03657325729727745,
0.003347207559272647,
-0.018403630703687668,
0.027508296072483063,
-0.0012975978897884488,
-0.01982646994292736,
0.015371843241155148,
0.018835818395018578,
0.003985524643212557,
-0.03275885432958603,
-0.00778482249006629,
0.02250516787171364,
0.05133099481463432,
-0.01317757461220026,
-0.05487458035349846,
0.0208725668489933,
0.031998831778764725,
0.05271614342927933,
-0.012640617787837982,
-0.010704142041504383,
-0.04782497510313988,
-0.003082111943513155,
0.0020641530863940716,
0.02599230408668518,
0.039539989084005356,
-0.009000945836305618,
0.03946876525878906,
-0.028859412297606468,
0.04529597610235214,
-0.010703926905989647,
0.020795322954654694,
-0.038237739354372025,
0.08535478264093399,
0.06730977445840836,
0.010194336995482445,
-0.008955201134085655,
0.018347684293985367,
0.0013893831055611372,
0.035395774990320206,
0.018570175394415855,
-0.025567924603819847,
-0.035331789404153824,
0.013860293664038181,
0.019719185307621956,
0.012732320465147495,
-0.06277097761631012,
0.012734311632812023,
0.063965804874897,
0.016162019222974777,
-0.02012825757265091,
-0.010621062479913235,
-0.01403772085905075,
-0.05215341970324516,
0.008997843600809574,
0.011488153599202633,
0.004777174908667803,
0.004261106718331575,
0.025469977408647537,
0.025266453623771667,
0.02118968404829502,
0.012309949845075607,
-0.0020000527147203684,
0.022850150242447853,
-0.03632642701268196,
0.00739882979542017,
0.035962458699941635,
0.016767071560025215,
0.08415878564119339,
0.017860276624560356,
-0.0185542032122612,
0.0719316378235817,
-0.007451991084963083,
-0.026127509772777557,
-0.007100920658558607,
-0.005277439020574093,
0.040783412754535675,
0.0007830150425434113,
-0.003435528837144375,
-0.009834825992584229,
0.02648271434009075,
-0.041726939380168915,
0.022010086104273796,
-0.032422441989183426,
-0.015317948535084724,
-0.04592721536755562,
-0.005037381779402494,
0.04704985022544861,
0.023540068417787552,
0.002273889724165201,
-0.03817475959658623,
-0.0604446716606617,
0.01157701388001442,
0.01792241260409355,
0.007378817535936832,
0.03599622845649719,
-0.05079904943704605,
0.012152974493801594,
-0.05030529573559761,
-0.01743350550532341,
0.028933873400092125,
-0.011673656292259693,
0.01913817971944809,
0.019623061642050743,
-0.02355722337961197,
-0.013619454577565193,
-0.018042854964733124,
-0.026811817660927773,
0.02495318464934826,
-0.04969048872590065,
0.015337559394538403,
0.04486696422100067,
0.028530551120638847,
-0.04093116149306297,
0.03946414962410927,
-0.02153654582798481,
-0.051649317145347595,
-0.003208274720236659,
0.02353578805923462,
0.007477602455765009,
-0.02237042598426342,
0.004278051201254129,
0.024207912385463715,
-0.02742287702858448,
0.019238827750086784,
-0.038489267230033875,
-0.04857872799038887,
0.03141727298498154,
0.009718636982142925,
0.009063920006155968,
-0.020293770357966423,
-0.06595094501972198,
0.05343024432659149,
0.022527461871504784,
-0.003062301781028509,
-0.04496501758694649,
0.009304888546466827,
0.005863196216523647,
-0.025776732712984085,
0.016528384760022163,
0.019558709114789963,
-0.014986991882324219,
-0.011225500144064426,
0.00025995291071012616,
0.07848937809467316,
0.004127804189920425,
0.04646438732743263,
-0.021736619994044304,
0.017582053318619728,
0.01930229924619198,
0.007168775424361229,
0.027508290484547615,
0.024231618270277977,
-0.02188812382519245,
-0.010322383604943752,
-0.0004711192159447819,
0.060147859156131744,
-0.008170866407454014,
-0.035572975873947144,
0.024653863161802292,
-0.0011523982975631952,
0.026719162240624428,
-0.011333294212818146,
0.02607308141887188,
-0.029227981343865395,
0.0036630865652114153,
-0.001074473257176578,
0.00017760794435162097,
0.05215434357523918,
-0.004358268808573484,
-0.006199520081281662,
-0.017288852483034134,
0.006441018544137478,
-0.057294175028800964,
0.018662352114915848,
0.026797715574502945,
-0.0214425940066576,
0.06004997715353966,
-0.03366437554359436,
0.0011370740830898285,
0.042256440967321396,
0.05206107720732689,
0.0006075489800423384,
-0.006708132568746805,
-0.03206709027290344,
0.02640153095126152,
-0.06521020829677582,
-0.016610972583293915,
-0.016228090971708298,
0.03088250197470188,
0.011288362555205822,
0.011669415980577469,
0.009920885786414146,
0.029564144089818,
0.0037384785246104,
0.0003215143224224448,
-0.07708035409450531,
0.020383788272738457,
-0.05826083943247795,
-0.016390500590205193,
0.020698722451925278,
-0.008947274647653103,
0.0027018659748136997,
-0.03788071870803833,
-0.0033994936384260654,
0.012592930346727371,
0.009477265179157257,
-0.0746014416217804,
0.015114057809114456,
-0.015761058777570724,
-0.02119515836238861,
-0.03347139060497284,
0.044453442096710205,
0.00785016268491745,
-0.013462604023516178,
-0.024066030979156494,
0.020372658967971802,
0.00963691994547844,
0.015055558644235134,
0.00819431059062481,
0.015582236461341381,
-0.0008560054702684283,
0.03695400059223175,
0.013423452153801918,
0.004618363454937935,
-0.028809858486056328,
-0.0036106393672525883,
0.023811157792806625,
0.07159063220024109,
-0.014891274273395538,
-0.008141773752868176,
0.005117520224303007,
-0.05466565117239952,
-0.0516214519739151,
-0.016931552439928055,
0.06570443511009216,
-0.03598863631486893,
0.026704862713813782,
-0.0020415799226611853,
-0.010955513454973698,
0.012245068326592445,
-0.010628098621964455,
0.046730801463127136,
-0.01610909402370453,
-0.0437384732067585,
-0.04212011769413948,
-0.042886581271886826,
-0.029856408014893532,
-0.027558524161577225,
-0.0020485753193497658,
0.04272788017988205,
-0.05101633071899414,
-0.0036092610098421574,
0.016536816954612732,
0.02799784392118454,
-0.003210522001609206,
-0.013017569668591022,
0.028119221329689026,
0.012859001755714417,
-0.008243833668529987,
0.0368635393679142,
0.07773096859455109,
0.02084270492196083,
0.06573802977800369,
-0.0013626199215650558,
-0.0038405130617320538,
-0.04211778938770294,
-0.01874815672636032,
0.032569460570812225,
0.05019085109233856,
0.019181301817297935,
-0.018338117748498917,
-0.08722462505102158,
-0.02741696685552597,
0.03940111771225929,
-0.020968912169337273,
0.026442833244800568,
0.010586095042526722,
0.01890251785516739,
-0.05229036882519722,
0.0013421319890767336,
-0.027332687750458717,
0.03801681846380234,
-0.025452204048633575,
-0.00605602515861392,
-0.005025711841881275,
0.043976228684186935,
0.011444666422903538,
0.010071678087115288,
-0.01553184911608696,
0.05828072130680084,
0.06431221961975098,
-0.01814138889312744,
0.006346527952700853,
-0.006049199961125851,
-0.01939489133656025,
-0.0805545374751091,
-0.005959714762866497,
0.03476203978061676,
-0.034649476408958435,
0.035482969135046005,
0.005818837787955999,
-0.04252828285098076,
0.03653954714536667,
0.02415381744503975,
-0.005701407324522734,
0.02662460319697857,
-0.05983670428395271,
0.03089965507388115,
0.00732137355953455,
-0.017781879752874374,
0.01800871267914772,
0.04138302803039551,
0.03909812495112419,
0.0006755677750334144,
-0.039384640753269196,
0.06108061224222183,
-0.030802935361862183,
-0.005268485751003027,
-0.00580995250493288,
0.01554399449378252,
-0.046824388206005096,
0.020739462226629257,
-0.0018122285837307572,
0.04783829674124718,
-0.008457104675471783,
0.007412704639136791,
0.017350874841213226,
0.02296726405620575,
-0.0014004433760419488,
0.012665804475545883,
0.017473723739385605,
-0.008108840323984623,
0.006394736934453249,
-0.027537424117326736,
-0.0067268298007547855,
-0.02871881052851677,
-0.03168322518467903,
0.046795595437288284,
0.02449355088174343,
0.025203004479408264,
-0.01356544904410839,
-0.005977805238217115,
0.004331924486905336,
-0.03695105016231537,
0.055759698152542114,
-0.00004771880776388571,
-0.0006158854812383652,
0.04577042534947395,
-0.009951861575245857,
0.01608330011367798,
-0.004241127520799637,
-0.012065412476658821,
0.020218389108777046,
-0.048981308937072754,
0.018090877681970596,
0.03163382038474083,
0.015544976107776165,
-0.0661270022392273,
-0.06528186053037643,
0.01436450146138668,
0.019770996645092964,
-0.032952141016721725,
0.024938389658927917,
0.005878502503037453,
-0.013841429725289345,
-0.03231192007660866,
0.0016868769889697433,
0.054638560861349106,
-0.03856728598475456,
0.005915925372391939,
-0.0016310455976054072,
0.015051951631903648,
0.04296904057264328,
-0.012579470872879028,
-0.01767658442258835,
0.018755685538053513,
-0.0016295453533530235,
-0.007870964705944061,
0.013746418990194798,
0.0447826012969017,
-0.02259388007223606,
-0.05065165087580681,
-0.06706616282463074,
0.028639087453484535,
0.024966098368167877,
0.017672881484031677,
0.012873399071395397,
0.015799768269062042,
0.008744156919419765,
0.010576329194009304,
-0.041148364543914795,
-0.01874389313161373,
-0.05135110393166542,
0.004148864187300205,
-0.024612460285425186,
-0.004018249921500683,
0.007968345656991005,
-0.057656168937683105,
0.0018164035864174366,
0.02574480138719082,
0.014234812930226326,
-0.010274238884449005,
0.07742942869663239,
0.042784322053194046,
-0.043597400188446045,
-0.021738216280937195,
-0.05806072801351547,
-0.013234348967671394,
0.03083846904337406,
-0.002099335892125964,
0.01097233034670353,
0.0004925061948597431,
-0.027045344933867455,
-0.026757612824440002,
-0.03854972869157791,
-0.002267448930069804,
0.10065887868404388,
0.0037740180268883705,
0.03406904637813568,
0.026739545166492462,
-0.010710641741752625,
-0.007714113220572472,
-0.031066829338669777,
-0.005642850883305073,
-0.004891541320830584,
0.020523644983768463,
0.038524117320775986,
-0.0248662568628788,
-0.00854511372745037,
0.028110403567552567,
0.04699282720685005,
-0.011194488033652306,
0.04009187966585159,
0.005260751582682133,
-0.009041479788720608,
0.05330899357795715,
-0.013338306918740273,
-0.048195261508226395,
0.01544356532394886,
0.0025586734991520643,
0.0706309974193573,
0.008537055924534798,
0.012542184442281723,
0.020816627889871597,
0.025176245719194412,
0.022596945986151695,
0.0066020251251757145,
-0.04843689128756523,
-0.06502468138933182,
0.030463634058833122,
-0.004101426340639591,
0.0011605130275711417,
-0.026551881805062294,
0.010692124255001545,
0.04190375655889511,
-0.008747534826397896,
0.0007052336586639285,
0.005089599173516035,
-0.03822382539510727,
0.02005627192556858,
0.005430783610790968,
-0.02614484913647175,
0.0493159219622612,
0.020721618086099625,
-0.029055915772914886,
0.016774334013462067,
-0.025790026411414146,
0.01393871195614338,
0.011256717145442963,
0.028752818703651428,
0.009171470068395138,
0.06285638362169266,
-0.03888801857829094,
0.024026064202189445,
-0.02598673850297928,
-0.0038471876177936792,
0.13131357729434967,
0.058741506189107895,
0.009121465496718884,
-0.05994807556271553,
0.002182831522077322,
-0.026015639305114746,
-0.005112987477332354,
-0.03782954439520836,
0.06445964425802231,
-0.024929802864789963,
-0.033542972058057785,
0.02233695425093174,
0.04565265029668808,
-0.022782428190112114,
-0.014895424246788025,
0.06160333752632141,
-0.036461327224969864,
-0.024198435246944427,
0.00914517417550087,
0.030096352100372314,
0.0063741253688931465,
-0.0015307122375816107,
-0.051429979503154755,
0.02355840802192688,
-0.017222190275788307,
0.008817741647362709,
-0.07064042240381241,
-0.041690632700920105,
0.013283290900290012,
0.012234434485435486,
-0.05649349093437195,
0.010053535923361778,
0.04057643935084343,
-0.00557744363322854,
-0.035083457827568054,
-0.004696275573223829,
0.029271578416228294,
-0.01733810268342495,
0.033222176134586334,
0.052496038377285004,
-0.0055233570747077465,
-0.0096944160759449,
0.0055094435811042786,
0.011693025007843971,
-0.032024938613176346,
0.017624076455831528,
-0.009716556407511234,
0.024449219927191734,
-0.015700479969382286,
0.014592107385396957,
-0.016051990911364555,
0.014681857079267502,
0.009999323636293411,
-0.07050427794456482,
-0.0388738177716732,
-0.020129626616835594,
0.017506714910268784,
0.014726812019944191,
-0.03296655789017677,
0.027762068435549736,
0.012814962305128574,
0.057179536670446396,
0.04189809039235115,
-0.012991470284759998,
-0.0022880674805492163,
0.01883099041879177,
-0.03844158351421356,
0.07851433008909225,
0.0015870488714426756,
-0.01812354288995266,
0.007288145832717419,
-0.040959812700748444,
0.0050729624927043915,
-0.024381786584854126,
0.004693296272307634,
0.03992078825831413,
0.018929140642285347,
0.017192456871271133,
-0.006161134224385023,
0.013843262568116188,
-0.03367907181382179,
0.026498546823859215,
-0.016421526670455933,
-0.0018412882927805185,
-0.017368873581290245,
0.025723418220877647,
0.040401067584753036,
0.04557691514492035,
-0.005064327735453844,
0.011010654270648956,
0.02720138430595398,
0.006906221155077219,
-0.014675075188279152,
-0.025893939658999443,
-0.012537574395537376,
0.03006141260266304,
-0.06904244422912598,
-0.008252986706793308,
-0.023757262155413628,
-0.005124338436871767,
0.03970875218510628,
0.0165691077709198,
-0.005688659381121397,
0.021177539601922035,
-0.01161191612482071,
-0.0007952397572807968,
-0.015297042205929756,
-0.030823856592178345,
0.008257987909018993,
-0.00821420457214117,
-0.005107097327709198,
-0.049444977194070816,
-0.016023941338062286,
-0.02004239894449711,
-0.0015875345561653376,
0.007073453161865473,
0.023951685056090355,
-0.015288312919437885,
0.01819477416574955,
-0.03164999932050705,
-0.015846390277147293,
-0.033072806894779205,
-0.007785010617226362,
-0.02439788542687893,
-0.00399138405919075,
0.018525009974837303,
0.0012508558575063944,
0.020412331447005272,
0.00968337431550026,
-0.025975512340664864,
-0.005988352466374636,
0.008743629790842533,
0.029078245162963867,
-0.011061511933803558,
-0.04434127360582352,
0.026927992701530457,
-0.00038210692582651973,
0.03747434914112091,
-0.005021147429943085,
-0.040461186319589615,
0.013377237133681774,
-0.03139029070734978,
-0.009501319378614426,
0.031668771058321,
0.008017211221158504,
0.0007555516203865409,
-0.006781614385545254,
-0.024003170430660248,
-0.02613813988864422,
0.06667686253786087,
-0.015772979706525803,
-0.01904817670583725,
0.02903405949473381,
-0.03126312419772148,
-0.0012738598743453622,
-0.0036022691056132317,
0.01636551320552826,
-0.03049004264175892,
-0.014967142604291439,
0.012546226382255554,
0.023085976019501686,
-0.026728473603725433,
-0.021085456013679504,
0.019669607281684875,
-0.03132878243923187,
-0.0006595271406695247,
0.019031787291169167,
-0.005359185393899679,
0.036640714854002,
0.044923022389411926,
-0.01835520565509796,
0.0376095175743103,
0.032481372356414795,
0.020558219403028488,
-0.12904834747314453,
-0.017977911978960037,
0.014189322479069233,
0.011744734831154346,
0.04481292888522148,
-0.07354909181594849,
0.009714982472360134,
0.01562652178108692,
-0.05056612193584442,
0.06698223948478699,
-0.0351424403488636,
-0.03885800391435623,
-0.03436257690191269,
-0.0224284790456295,
-0.014610596932470798,
0.06852744519710541,
0.08279270678758621,
0.04344848543405533,
-0.013232783414423466,
-0.013908823020756245,
-0.059745971113443375,
0.02610773593187332,
0.0031518128234893084,
0.008406948298215866,
-0.0025410179514437914,
-0.024233676493167877,
0.020228978246450424,
0.015891101211309433,
-0.05857236310839653,
0.008947961963713169,
-0.006141200195997953,
-0.016009656712412834,
-0.014280861243605614,
-0.018592821434140205,
-0.0024746942799538374,
0.017731385305523872,
0.04548368230462074,
-0.00769991846755147,
-0.0177842415869236,
-0.013910247012972832,
-0.018692567944526672,
0.011876072734594345,
-0.02704651467502117,
0.03546462208032608,
-0.004806854296475649,
-0.07051365077495575,
-0.04314183443784714,
0.02164875529706478,
-0.013858913443982601,
-0.03752121329307556,
-0.018594324588775635,
0.004456882830709219,
0.02013368345797062,
-0.014887076802551746,
-0.019940080121159554,
-0.0497429184615612,
-0.010763105005025864,
0.04499071463942528,
-0.005726562812924385,
0.018321692943572998,
0.023604871705174446,
-0.020234202966094017,
-0.03702910616993904,
0.005684415809810162,
-0.009700206108391285,
-0.016966650262475014,
-0.05558912083506584,
0.004700907506048679,
-0.03230728954076767,
-0.006028071045875549,
0.02665749192237854,
-0.025830460712313652,
0.00999645795673132,
0.06516075134277344,
0.025586474686861038,
0.008287964388728142,
0.0013727796031162143,
-0.05700670927762985,
-0.02273629978299141,
-0.053571805357933044,
0.021787725389003754,
-0.016570933163166046,
-0.022620804607868195,
-0.032795947045087814,
-0.00508419843390584,
-0.018214596435427666,
0.036835405975580215,
0.024007553234696388,
-0.02918270416557789,
0.02251681126654148,
-0.005870495922863483,
-0.030856136232614517,
0.006749553140252829,
-0.06445757299661636,
0.007619014009833336,
0.0033319848589599133,
-0.031738150864839554,
0.018438922241330147,
0.01864224672317505,
0.0024077307898551226,
0.03322083503007889,
0.038584254682064056,
-0.023404477164149284,
0.03650030866265297,
-0.01763339713215828,
-0.012777619995176792,
0.022637883201241493,
0.0392981581389904,
-0.019941074773669243,
0.08060121536254883,
0.015305220149457455,
-0.018567174673080444,
0.022827699780464172,
-0.006626469548791647,
-0.004093109630048275,
0.027084944769740105,
-0.030160140246152878,
0.005880918353796005,
-0.0033391048200428486,
-0.05954578146338463,
0.031198818236589432,
-0.030114157125353813,
0.021714147180318832,
0.04574773833155632,
-0.027204645797610283,
-0.020118586719036102,
0.019377268850803375,
0.0014684470370411873,
0.0405663400888443,
-0.024012265726923943,
-0.013668827712535858,
0.0032609368208795786,
-0.021228311583399773,
0.04524369165301323,
0.01602793298661709,
0.0198773592710495,
0.03238939493894577,
-0.043340954929590225,
-0.021010244265198708,
-0.06822937726974487,
0.036046404391527176,
-0.008200840093195438,
0.04480687901377678,
-0.013231771066784859,
-0.0037887319922447205,
0.043222568929195404,
-0.006420801859349012,
0.012466341257095337,
-0.00767927523702383,
-0.01121816411614418,
0.045727506279945374,
0.0021725366823375225,
0.010436008684337139,
-0.04362371563911438,
-0.0005397931090556085,
-0.03688093274831772,
0.04815760999917984,
0.025404727086424828,
0.06788408756256104,
-0.006270922254770994,
-0.037485815584659576,
-0.011163365095853806,
-0.020566601306200027,
0.044737085700035095,
-0.020504849031567574,
0.01718343421816826,
-0.028917433694005013,
-0.007135834079235792,
-0.005602055694907904,
-0.00878707692027092,
-0.039328161627054214,
-0.014293540269136429,
0.02239459753036499,
0.014755547977983952,
0.047153495252132416,
-0.0182036180049181,
-0.0007155514904297888,
-0.0298872459679842,
0.023564014583826065,
-0.049448542296886444,
-0.02804209478199482,
-0.02388763800263405,
0.02141410857439041,
0.004826338961720467,
-0.006125956308096647
] |
<p>In certain books like David Griffiths electrodynamics , he treats current as a vector in some places. Moreover certain problems like current in a strip are often dealt with by taking current components. I am having a difficult time understanding this.
After going through books and dealing with problems,i think that when current flows in a wire, of negligible dimensions, it is bound to flow along a line, so we treat it as scalar. But when we talk about current in a strip or in a volume, we can take components of current.Is it so?</p>
| 273 |
[
-0.006763413082808256,
0.01611700840294361,
-0.002842843532562256,
-0.050951577723026276,
0.03357774019241333,
0.029017433524131775,
-0.014792535454034805,
0.027049964293837547,
0.005381046794354916,
-0.0175580233335495,
0.009863370098173618,
-0.002362270141020417,
0.09249389171600342,
-0.008335897698998451,
0.03971618041396141,
0.006332984659820795,
0.005767629947513342,
0.008391588926315308,
-0.0019676308147609234,
-0.039869844913482666,
-0.013037843629717827,
0.04444177821278572,
0.030897144228219986,
-0.024397127330303192,
0.009047117084264755,
0.03818568214774132,
0.011378861032426357,
0.02938948944211006,
-0.003117996035143733,
0.025023620575666428,
-0.014205568470060825,
-0.03646334260702133,
-0.03643723577260971,
-0.007298280950635672,
0.021007142961025238,
0.0028738391119986773,
-0.028185144066810608,
-0.026259630918502808,
-0.016547584906220436,
-0.005174682941287756,
-0.04554671049118042,
0.0011450003366917372,
0.03323207423090935,
0.052803415805101395,
-0.03820164129137993,
0.040267713367938995,
0.017945842817425728,
-0.013770253397524357,
-0.0016794451512396336,
-0.0720740482211113,
0.05537920817732811,
0.02468918263912201,
0.06684896349906921,
0.02434331364929676,
0.013205285184085369,
0.0012877762783318758,
0.050953175872564316,
0.059687525033950806,
-0.026668835431337357,
-0.019044822081923485,
-0.019812971353530884,
-0.016598688438534737,
-0.035277582705020905,
-0.07862033694982529,
-0.00867451075464487,
0.02648869901895523,
-0.013811159878969193,
-0.003558004042133689,
-0.019620483741164207,
-0.007174482569098473,
-0.012693691998720169,
0.019790256395936012,
-0.008031153120100498,
-0.0011564379092305899,
-0.016750376671552658,
-0.008462614379823208,
0.0345497764647007,
0.008821511641144753,
0.0523536317050457,
0.020394692197442055,
-0.01863967441022396,
0.01913183555006981,
0.01725231297314167,
0.016119465231895447,
0.024911612272262573,
-0.03274848684668541,
0.05279106646776199,
-0.007614091970026493,
0.0026156585663557053,
0.01800781488418579,
-0.012991664931178093,
0.025690805166959763,
0.025808749720454216,
0.0060226875357329845,
-0.027147825807332993,
0.03350358456373215,
0.017661431804299355,
0.03806307911872864,
0.014967908151447773,
-0.03556792438030243,
-0.016589723527431488,
0.019084788858890533,
0.0410957895219326,
0.0746932104229927,
0.008512107655405998,
-0.015745479613542557,
-0.007665758021175861,
0.01336709875613451,
-0.015572985634207726,
-0.0036176254507154226,
-0.04161393642425537,
0.021888351067900658,
0.03226114809513092,
0.04827294126152992,
0.006796051282435656,
-0.006658504251390696,
0.027237502858042717,
-0.02137582190334797,
0.07378228008747101,
0.05330721288919449,
-0.001747791888192296,
-0.0568503811955452,
0.03240795060992241,
0.0034691074397414923,
-0.0719149187207222,
0.02905295044183731,
0.008057799190282822,
-0.016101326793432236,
-0.005530453287065029,
0.028270261362195015,
-0.011937040835618973,
0.008515114895999432,
0.0015998446615412831,
0.031407907605171204,
0.023412281647324562,
-0.028988724574446678,
-0.09658461809158325,
-0.05718759819865227,
0.03715834766626358,
0.0016267833998426795,
-0.008129604160785675,
-0.07421805709600449,
-0.024628646671772003,
0.0324222557246685,
0.05660983920097351,
-0.01907096803188324,
0.004542653914541006,
0.010321252979338169,
0.021000640466809273,
-0.004310148302465677,
-0.03904017433524132,
-0.000028219701562193222,
-0.0012282021343708038,
-0.01730564422905445,
-0.008837140165269375,
-0.039807576686143875,
0.014730789698660374,
0.026527101173996925,
0.02246234007179737,
-0.031275276094675064,
0.03056151606142521,
-0.0574704073369503,
-0.0017154391389340162,
0.04360002651810646,
-0.03487740829586983,
-0.01633215881884098,
0.0449550598859787,
0.006466913968324661,
0.040032487362623215,
0.03778314217925072,
0.036049917340278625,
0.0021703867241740227,
-0.022432919591665268,
0.016823414713144302,
0.07401201874017715,
-0.04448799416422844,
-0.02669936791062355,
-0.010561071336269379,
0.03326699510216713,
0.010182572528719902,
-0.022913124412298203,
-0.06850815564393997,
0.0022516611497849226,
0.006728284526616335,
-0.005133519880473614,
0.054897163063287735,
0.018060430884361267,
-0.012809043750166893,
-0.025552917271852493,
-0.015437289141118526,
0.0027457410469651222,
-0.030031580477952957,
0.021270152181386948,
0.0041610971093177795,
-0.025856146588921547,
0.04483777657151222,
-0.018532926216721535,
-0.007146739400923252,
-0.04250016808509827,
-0.03217698261141777,
0.00962120946496725,
0.027753479778766632,
-0.03049679473042488,
-0.04663591831922531,
-0.012662580236792564,
0.018108297139406204,
0.02621210180222988,
0.015209647826850414,
0.04579900577664375,
-0.012816332280635834,
-0.025786466896533966,
-0.010458270087838173,
-0.009868663735687733,
0.032202091068029404,
0.05448473244905472,
-0.020886380225419998,
0.0020692485850304365,
0.005623198114335537,
4.0899715259001823e-7,
0.07305392622947693,
0.00022831854585092515,
0.05039425194263458,
0.05373732000589371,
0.009854008443653584,
-0.010637951083481312,
0.027443738654255867,
-0.0156863983720541,
-0.031728748232126236,
-0.007885615341365337,
-0.031799085438251495,
-0.039625439792871475,
0.03931811824440956,
0.06249212101101875,
0.021093910560011864,
-0.04811178520321846,
-0.027647020295262337,
0.03207981213927269,
0.026642870157957077,
0.031101038679480553,
0.01435268484055996,
-0.027763698250055313,
-0.030683351680636406,
0.014542078599333763,
0.017935648560523987,
-0.010827874764800072,
-0.023251058533787727,
0.026782920584082603,
0.012235335074365139,
0.05297430232167244,
-0.016674723476171494,
-0.02186724916100502,
0.03663385286927223,
-0.0289764404296875,
0.002495040185749531,
0.015874119475483894,
-0.01791292242705822,
0.05324922502040863,
-0.045844122767448425,
0.03379342332482338,
0.003987894859164953,
-0.008570496924221516,
0.003843397367745638,
-0.022589679807424545,
-0.0016209699679166079,
0.024327721446752548,
-0.0036952963564544916,
-0.022852366790175438,
-0.029453080147504807,
0.029827535152435303,
-0.03207121416926384,
0.011709405109286308,
-0.03128420189023018,
0.007431089878082275,
-0.04692266881465912,
-0.0027466961182653904,
0.05353739112615585,
-0.021069683134555817,
0.06974098831415176,
-0.02953125163912773,
-0.03995448723435402,
-0.011376315727829933,
-0.03305933251976967,
0.011067301034927368,
0.04510928690433502,
-0.0441037118434906,
0.03417414426803589,
-0.06351320445537567,
-0.03938184306025505,
0.04863514006137848,
0.017327234148979187,
0.028064001351594925,
0.024747801944613457,
-0.02297290787100792,
-0.05809031426906586,
0.018836749717593193,
0.0013254155637696385,
0.04803700000047684,
-0.011012702248990536,
0.022032639011740685,
0.0687117949128151,
-0.03432057797908783,
-0.03320948779582977,
0.003810188500210643,
-0.03265242278575897,
-0.06606560200452805,
-0.029530445113778114,
-0.03406873717904091,
0.0071735321544110775,
-0.018973365426063538,
0.025666065514087677,
0.035911381244659424,
-0.05028717592358589,
-0.003277681302279234,
-0.04212294518947601,
-0.014633368700742722,
-0.020688531920313835,
-0.023927737027406693,
0.03681090101599693,
0.004267759155482054,
-0.045048292726278305,
0.08431477099657059,
0.02366749197244644,
-0.056025706231594086,
-0.008778983727097511,
0.017288118600845337,
-0.046316083520650864,
-0.031215883791446686,
0.04087240621447563,
0.055194541811943054,
-0.009795541875064373,
0.0060580093413591385,
-0.012554315850138664,
0.03772406652569771,
0.028400318697094917,
0.019059672951698303,
-0.014568538405001163,
0.03501660376787186,
0.01732039637863636,
-0.0005909557803533971,
0.030332742258906364,
0.013113020919263363,
-0.04545900225639343,
0.01367009337991476,
-0.010388744994997978,
0.0453837513923645,
0.06058957427740097,
0.01173796784132719,
0.03832375630736351,
-0.013382316567003727,
0.031227150931954384,
-0.04315882548689842,
0.0028494710568338633,
0.013727284967899323,
0.02087465114891529,
0.022367103025317192,
0.013086485676467419,
-0.011323203332722187,
-0.04127831012010574,
-0.022402934730052948,
0.012621038593351841,
0.03637576848268509,
-0.0386984683573246,
-0.023471148684620857,
0.006606066133826971,
0.004405196290463209,
0.027218645438551903,
-0.03668500483036041,
-0.009896832518279552,
0.047956231981515884,
0.02751082181930542,
-0.014225653372704983,
0.009113030508160591,
-0.017454255372285843,
0.001739581930451095,
-0.07815850526094437,
-0.021102214232087135,
0.03799210861325264,
0.03722480684518814,
0.00936711672693491,
0.02176746539771557,
-0.005507492460310459,
0.02320757880806923,
-0.014245082624256611,
-0.004082315135747194,
-0.08304101228713989,
-0.01925382949411869,
-0.022579096257686615,
0.000014016596651345026,
-0.04087187722325325,
-0.031645361334085464,
-0.005209265276789665,
-0.024349911138415337,
-0.03159176558256149,
0.006575154140591621,
-0.0351078137755394,
-0.042137470096349716,
0.038834985345602036,
-0.0020219585858285427,
-0.02637048438191414,
-0.03869419917464256,
0.016717640683054924,
0.05104461684823036,
-0.06292001157999039,
0.01037165429443121,
0.031002745032310486,
-0.023015519604086876,
0.009501158259809017,
-0.000659269979223609,
0.0041508921422064304,
0.03291858732700348,
0.0026784923393279314,
0.018474267795681953,
-0.012820814736187458,
-0.045228976756334305,
0.04127894714474678,
0.025245636701583862,
0.07065735757350922,
-0.005901075899600983,
-0.049759019166231155,
-0.03125690296292305,
-0.07436738908290863,
-0.04084679111838341,
-0.012666357681155205,
0.05239720642566681,
0.02928633987903595,
0.007343592122197151,
0.03238922730088234,
0.014761731959879398,
-0.008803702890872955,
0.029620995745062828,
0.0383048914372921,
0.01760072261095047,
-0.038604315370321274,
-0.06136172264814377,
0.025534290820360184,
-0.022652050480246544,
0.003220226615667343,
0.03985317796468735,
-0.013235310092568398,
-0.0380609929561615,
-0.01777271181344986,
0.031512513756752014,
0.021658167243003845,
-0.024394776672124863,
0.011775346472859383,
0.03433820977807045,
-0.00122847652528435,
0.007379770744591951,
0.004136297851800919,
0.024927671998739243,
0.03765200078487396,
0.035626549273729324,
0.0029261040035635233,
-0.020786570385098457,
-0.08651236444711685,
-0.03105052374303341,
0.03997885808348656,
0.022693784907460213,
-0.01786697283387184,
-0.01092675793915987,
-0.03542838990688324,
0.0029663254972547293,
0.05614546686410904,
-0.01968616247177124,
0.008184514008462429,
-0.043970949947834015,
-0.035340506583452225,
-0.022783562541007996,
-0.0622834675014019,
-0.005464385729283094,
0.008665126748383045,
0.006551030091941357,
0.04210468754172325,
-0.02890281192958355,
-0.01128308940678835,
-0.011862530373036861,
-0.006413527298718691,
0.019482307136058807,
0.04651324078440666,
0.001254910952411592,
0.007136985659599304,
0.02011222392320633,
0.039249274879693985,
-0.024346182122826576,
-0.08750693500041962,
0.005943772848695517,
0.02869775891304016,
0.016097180545330048,
0.03264683485031128,
-0.01650218479335308,
-0.029486767947673798,
0.0013630163157358766,
-0.0045658922754228115,
0.014136227779090405,
0.007029047701507807,
-0.03777741268277168,
0.05109040439128876,
-0.0036923286970704794,
-0.017141908407211304,
0.04293164983391762,
0.011472338810563087,
-0.011919905431568623,
-0.035916153341531754,
-0.002765227574855089,
0.05893674120306969,
-0.010337136685848236,
0.01976022496819496,
-0.04541276767849922,
-0.003533565904945135,
-0.016530023887753487,
0.08287932723760605,
-0.0031539902556687593,
0.0010409801034256816,
-0.023398440331220627,
-0.02074512466788292,
-0.007557723671197891,
-0.0026259126607328653,
0.029139667749404907,
-0.042324602603912354,
-0.023338982835412025,
0.040611542761325836,
0.003370962105691433,
-0.0365431122481823,
0.016449546441435814,
-0.03245425596833229,
-0.0076770237646996975,
0.06113724038004875,
-0.01100831851363182,
-0.02675372175872326,
-0.015126883052289486,
-0.0063302465714514256,
0.019852515310049057,
-0.04113639146089554,
0.03895032778382301,
-0.03812668099999428,
-0.023944972082972527,
0.0019962156657129526,
-0.03221723064780235,
-0.025532539933919907,
0.015321115031838417,
-0.022143283858895302,
0.005118147004395723,
-0.07823891937732697,
0.04418234899640083,
0.0481489859521389,
0.04177805781364441,
-0.07504526525735855,
-0.06670023500919342,
0.004312028177082539,
-0.0006694532930850983,
-0.019626552239060402,
-0.015430350787937641,
0.016385678201913834,
-0.013983516953885555,
-0.04367436468601227,
-0.00999275129288435,
0.042797863483428955,
-0.030809491872787476,
-0.01395360566675663,
0.026240650564432144,
0.026454996317625046,
0.04237023741006851,
-0.005960829555988312,
0.0013243876164779067,
0.024561000987887383,
-0.010125262662768364,
-0.00727382255718112,
-0.023296819999814034,
0.025311164557933807,
-0.015902847051620483,
-0.012778538279235363,
0.020184224471449852,
-0.00971935223788023,
0.022735821083188057,
0.0007378021255135536,
0.019618302583694458,
0.036745961755514145,
-0.017624611034989357,
-0.02638116106390953,
0.010961608961224556,
0.010697576217353344,
0.023756161332130432,
0.013089319691061974,
-0.0003104351053480059,
-0.018694600090384483,
-0.04158778116106987,
-0.03178856894373894,
0.022960137575864792,
0.019196053966879845,
0.028441915288567543,
0.007294401526451111,
0.028376221656799316,
-0.037558309733867645,
-0.016663407906889915,
0.02185608632862568,
0.00026751396944746375,
0.02466115541756153,
0.003909306135028601,
0.03041328676044941,
-0.015646139159798622,
0.006959843449294567,
-0.015608977526426315,
-0.029049301519989967,
0.003501641098409891,
0.025815609842538834,
0.025904692709445953,
-0.00328848953358829,
0.04350556433200836,
0.01916690357029438,
-0.020624611526727676,
0.010261068120598793,
-0.009350436739623547,
-0.04464779794216156,
0.02802484855055809,
-0.021987207233905792,
0.03310587629675865,
-0.020199386402964592,
-0.008946242742240429,
0.000059239780966890976,
0.01781574636697769,
-0.03477777913212776,
-0.009733892977237701,
0.037317488342523575,
0.022498708218336105,
0.038326557725667953,
0.045525532215833664,
-0.017299221828579903,
0.028607869520783424,
-0.011116180568933487,
-0.00299887266010046,
-0.006050006952136755,
-0.005704719107598066,
0.07361657172441483,
-0.022112786769866943,
-0.00577884167432785,
-0.04510020464658737,
-0.03614223375916481,
-0.007333903107792139,
0.012967350892722607,
-0.009643755853176117,
0.010700044222176075,
-0.012543713673949242,
0.027925075963139534,
0.05723945423960686,
-0.00012053820682922378,
0.011120060458779335,
0.018136490136384964,
-0.045943520963191986,
-0.00007694177475059405,
-0.05752432718873024,
-0.02475769817829132,
0.05439246445894241,
0.025087593123316765,
-0.030760755762457848,
-0.046257805079221725,
-0.02443764917552471,
0.01188627164810896,
0.02081151492893696,
0.012032856233417988,
-0.01685883104801178,
0.05500837042927742,
-0.01242156233638525,
0.02062203735113144,
-0.0446016751229763,
0.0037545454688370228,
0.10791145265102386,
0.04588888958096504,
-0.008593828417360783,
-0.056988127529621124,
0.021997803822159767,
-0.059904661029577255,
0.013925259932875633,
-0.035553980618715286,
0.048071376979351044,
-0.013354607857763767,
0.031427107751369476,
0.024579918012022972,
0.03717542067170143,
-0.008472864516079426,
0.00524600176140666,
0.05261100456118584,
-0.05615679919719696,
-0.02618386410176754,
0.012103646993637085,
0.033929068595170975,
-0.015910176560282707,
0.042615268379449844,
-0.05129782110452652,
0.01068102940917015,
-0.007363858167082071,
-0.0022097090259194374,
-0.02621198631823063,
0.004568909760564566,
0.06088607385754585,
-0.005702261347323656,
-0.08139456063508987,
-0.014251147396862507,
0.03937899321317673,
-0.053240347653627396,
-0.029098860919475555,
0.007687990553677082,
0.05692031979560852,
0.011086995713412762,
0.02903711050748825,
0.013892021961510181,
0.011753295548260212,
0.004500720649957657,
0.031224757432937622,
0.04448500648140907,
-0.04636300355195999,
-0.022697437554597855,
-0.0538923442363739,
0.054762452840805054,
0.004395527299493551,
0.02444656565785408,
0.02380545251071453,
0.04910220205783844,
0.024860283359885216,
-0.05844579637050629,
-0.01986788399517536,
-0.015491317957639694,
0.0242328904569149,
0.030714282765984535,
-0.018500344827771187,
-0.03190741315484047,
0.03269185498356819,
-0.012207574211061,
0.014268928207457066,
0.02429552562534809,
-0.03773897886276245,
0.029416540637612343,
0.013889600522816181,
0.011889355257153511,
-0.005170037969946861,
-0.020305592566728592,
-0.027789631858468056,
0.007906290702521801,
-0.01617158018052578,
-0.017337214201688766,
0.016706829890608788,
0.01841607876121998,
-0.008842818439006805,
-0.0475572906434536,
-0.011137580499053001,
0.047368306666612625,
-0.07115565240383148,
0.034913092851638794,
0.0034607015550136566,
-0.016146987676620483,
0.003921582829207182,
0.03495717793703079,
0.0005197332939133048,
0.048183854669332504,
-0.024718409404158592,
-0.019202131778001785,
0.021075554192066193,
0.014340149238705635,
0.026928916573524475,
-0.012293479405343533,
-0.02402281016111374,
-0.012000137940049171,
-0.046578072011470795,
-0.011383402161300182,
0.013549228198826313,
0.002573838224634528,
0.019074684008955956,
-0.0009332724148407578,
-0.05254945158958435,
0.05596855655312538,
0.01852991431951523,
0.004965615924447775,
0.03748365864157677,
-0.02142593078315258,
0.027355113998055458,
0.013792559504508972,
0.018576983362436295,
-0.06582801789045334,
-0.023485567420721054,
-0.054038625210523605,
0.01886228285729885,
0.014293207786977291,
0.029251703992486,
-0.022708289325237274,
-0.0033027827739715576,
-0.03145596757531166,
0.029412351548671722,
-0.00727100670337677,
-0.01012955978512764,
-0.03526647388935089,
0.005361040122807026,
0.01775132305920124,
-0.0024630283005535603,
-0.01909918710589409,
0.012569568119943142,
-0.020616965368390083,
-0.004556913394480944,
0.005247780587524176,
0.04836828261613846,
0.005839709658175707,
-0.0016387990908697248,
-0.007647273130714893,
0.010319999419152737,
0.020101482048630714,
-0.0024310541339218616,
-0.036543868482112885,
0.034663133323192596,
-0.030862318351864815,
-0.010138352401554585,
0.03278443589806557,
0.021499907597899437,
-0.004966819193214178,
0.01741850934922695,
0.023884475231170654,
-0.017368527129292488,
0.023104315623641014,
-0.005025799851864576,
0.01138676330447197,
0.008016052655875683,
-0.031504809856414795,
-0.018907656893134117,
-0.02989443764090538,
-0.012994371354579926,
0.022564420476555824,
0.011565176770091057,
-0.007614259608089924,
0.008327648974955082,
0.01817987859249115,
-0.020513784140348434,
-0.007220698520541191,
0.019230807200074196,
0.006815748754888773,
0.06522316485643387,
-0.005614689085632563,
0.028561310842633247,
0.05605790391564369,
-0.026006804779171944,
0.015027464367449284,
0.009675061330199242,
-0.0023604368325322866,
-0.09898000955581665,
-0.018001506105065346,
0.013988719321787357,
0.016417663544416428,
0.012247716076672077,
-0.05969146266579628,
-0.0407458171248436,
0.017956819385290146,
-0.06676028668880463,
0.003471162635833025,
-0.038964129984378815,
-0.01990342140197754,
-0.061546895653009415,
-0.02268528938293457,
0.00209414167329669,
0.07361123710870743,
0.023794200271368027,
0.014552679844200611,
-0.009380986914038658,
-0.004390813875943422,
-0.013524484820663929,
-0.05716025084257126,
-0.025602784007787704,
0.018802471458911896,
-0.03853648155927658,
-0.04767772927880287,
0.03691192343831062,
-0.030915234237909317,
-0.012187106534838676,
-0.0008579364512115717,
-0.008088795468211174,
-0.010118278674781322,
0.010223914869129658,
0.020176870748400688,
0.00956717785447836,
0.0393245667219162,
0.012043329887092113,
0.0090080127120018,
-0.005240303929895163,
0.03446335718035698,
0.00892714411020279,
-0.010855692438781261,
-0.02520916610956192,
-0.030798818916082382,
0.0368066281080246,
-0.06821606308221817,
-0.019825393334031105,
0.034654323011636734,
-0.03398742899298668,
0.000029805680242134258,
-0.015696611255407333,
0.00409096060320735,
0.017351767048239708,
-0.01091682631522417,
0.04127709940075874,
-0.06928515434265137,
-0.03374113515019417,
0.0416075773537159,
-0.032785236835479736,
0.03534679859876633,
-0.008172630332410336,
0.000018242692021885887,
-0.022290410473942757,
0.031513672322034836,
0.022682925686240196,
0.016597500070929527,
-0.06705526262521744,
-0.004416653420776129,
-0.0025910825934261084,
-0.04131859913468361,
0.014910967089235783,
-0.062271200120449066,
-0.0017028236761689186,
0.007638432085514069,
0.03935626521706581,
0.023625293746590614,
-0.0043489690870046616,
-0.03514491021633148,
-0.03540734946727753,
-0.014888258650898933,
0.05727596953511238,
-0.002806814154610038,
-0.028351929038763046,
-0.01090021338313818,
-0.03483814001083374,
-0.008619568310678005,
0.028400730341672897,
0.04491903632879257,
-0.01686217449605465,
-0.012162616476416588,
0.04022548347711563,
-0.006073981057852507,
0.05572313070297241,
-0.04550525173544884,
-0.012760243378579617,
0.004322192631661892,
0.0014689991949126124,
0.0314866304397583,
0.019807253032922745,
-0.040301986038684845,
-0.0003791640338022262,
-0.00164196384139359,
0.01603659987449646,
0.017986102029681206,
-0.047559671103954315,
-0.04042637720704079,
0.03842741623520851,
0.042204245924949646,
0.0001398111053276807,
0.06909564882516861,
-0.0226829145103693,
0.014875730499625206,
-0.00334371579810977,
-0.02676231786608696,
-0.024383436888456345,
0.004268958233296871,
-0.011417023837566376,
0.031874749809503555,
-0.008544493466615677,
0.021800734102725983,
0.05920245498418808,
-0.022925710305571556,
-0.02539609745144844,
0.03083672747015953,
-0.012756590731441975,
-0.000980525161139667,
0.07248958200216293,
0.014334926381707191,
-0.005439332686364651,
-0.021668946370482445,
0.01856537163257599,
0.03979947790503502,
-0.0007498016930185258,
-0.019710931926965714,
0.020541435107588768,
0.054557736963033676,
0.02333945967257023,
-0.01824324019253254,
0.05977776274085045,
-0.002744820900261402,
0.018203193321824074,
0.012095967307686806,
0.02332621067762375,
-0.02224498614668846,
-0.000039814465708332136,
0.013578633777797222,
-0.011355175636708736,
0.0012218101182952523,
0.005881627090275288,
-0.03973390534520149,
0.10511402785778046,
-0.05138285458087921,
0.0028411217499524355,
-0.025422323495149612,
-0.004398223478347063,
-0.0070261163637042046,
0.030634041875600815,
0.01802160032093525,
0.05098303034901619,
-0.007691684179008007,
-0.044534627348184586,
-0.037003397941589355,
-0.031098775565624237,
0.04772218316793442,
-0.044346921145915985,
0.030762149021029472,
-0.01661013439297676,
0.0025117220357060432,
-0.032165542244911194,
0.0034223636612296104,
0.00879044458270073,
-0.0066432892344892025,
-0.0020577881950885057,
0.012699948623776436,
0.024494187906384468,
-0.002051470335572958,
-0.007248995825648308,
-0.037310175597667694,
0.05968039855360985,
-0.08205334097146988,
-0.028162583708763123,
-0.005602193530648947,
0.04195116087794304,
0.024728022515773773,
0.028338350355625153
] |
<p>I don't quite get the practical use of a <a href="http://en.wikipedia.org/wiki/Capacitor" rel="nofollow">capacitor</a>. The theory is fine, but in simple words please explain how, why and where capacitors are used? Is there any other equivalent circuit for capacitors? From what I have learnt capacitors are used to store charge, but how does that make it useful in electric appliances?</p>
| 8,254 |
[
-0.03339983895421028,
-0.012784885242581367,
-0.013156467117369175,
-0.0004392205155454576,
0.029359877109527588,
-0.0009050897788256407,
0.004182955250144005,
-0.002634600503370166,
0.028672844171524048,
-0.024201519787311554,
-0.02709386684000492,
0.07587895542383194,
0.042050473392009735,
0.01826634258031845,
0.02905300259590149,
0.007304063532501459,
0.013452356681227684,
-0.03219321742653847,
-0.01175395492464304,
-0.009284308180212975,
-0.001757310121320188,
0.006775313057005405,
0.005314375273883343,
0.0417427197098732,
-0.0031136253383010626,
0.02563103288412094,
0.029862593859434128,
-0.015493640676140785,
0.0515621043741703,
0.028176624327898026,
-0.011865840293467045,
-0.03433728590607643,
-0.021273687481880188,
0.028018292039632797,
0.03174910321831703,
-0.024942070245742798,
-0.012906361371278763,
-0.05044598877429962,
-0.01851765066385269,
0.03200802579522133,
-0.0202406644821167,
-0.02564890868961811,
-0.01387743093073368,
0.009764546528458595,
-0.03262986242771149,
-0.005155934486538172,
0.0030598328448832035,
-0.04377788305282593,
0.008962264284491539,
-0.11272057145833969,
0.06081123277544975,
-0.004413324408233166,
0.0390811450779438,
0.060099709779024124,
0.011482157744467258,
0.050265297293663025,
0.061454255133867264,
0.05576935037970543,
-0.05147140845656395,
-0.043110184371471405,
-0.016583619639277458,
-0.013767854310572147,
-0.03313322365283966,
-0.03735409304499626,
-0.002359614707529545,
0.06063341721892357,
0.022291049361228943,
-0.017516888678073883,
0.03662922605872154,
-0.0033462652936577797,
0.029413262382149696,
0.011906366795301437,
0.006587933748960495,
-0.0324842669069767,
0.011256788857281208,
-0.021033355966210365,
0.021934861317276955,
0.0046112933196127415,
0.04705313593149185,
0.05232466012239456,
0.006089828442782164,
0.00828586332499981,
0.04533998668193817,
0.03245681896805763,
0.026427609845995903,
-0.0190107561647892,
0.05737682059407234,
-0.011584071442484856,
0.03717301785945892,
0.008613795973360538,
-0.002476586028933525,
0.00624097278341651,
0.023652458563447,
-0.01942361332476139,
-0.026864755898714066,
0.03363689407706261,
-0.005415796302258968,
0.06346824765205383,
0.0022079532500356436,
-0.012654612772166729,
0.0459812693297863,
0.0030297914054244757,
0.041451774537563324,
0.05438155308365822,
0.0017984005389735103,
-0.03779015317559242,
-0.037203386425971985,
0.011577967554330826,
0.03202846273779869,
-0.01699008420109749,
-0.05747586488723755,
0.01655999757349491,
0.02209952101111412,
0.016494443640112877,
0.04361145198345184,
-0.03667273744940758,
0.028478238731622696,
0.010212186723947525,
0.037066515535116196,
0.03223485127091408,
0.02156531810760498,
-0.02510702982544899,
0.014418250881135464,
-0.026721740141510963,
-0.07807579636573792,
0.024581387639045715,
-0.030192624777555466,
0.0022475721780210733,
0.003896358422935009,
0.04090446978807449,
-0.03021080605685711,
-0.030531272292137146,
0.004543160554021597,
-0.01113587711006403,
0.056231539696455,
-0.05260268598794937,
-0.09207264333963394,
-0.03696529567241669,
0.024335872381925583,
0.008984304964542389,
-0.03251880407333374,
-0.07333854585886002,
0.027880646288394928,
0.005085803102701902,
0.04898061975836754,
0.014336762949824333,
-0.023669803515076637,
-0.0039692712016403675,
0.007260237354785204,
0.02686978690326214,
-0.044412486255168915,
-0.04437783733010292,
0.02610747329890728,
-0.019580360502004623,
0.022655246779322624,
-0.05640815943479538,
0.028899800032377243,
0.03613242879509926,
0.02006400004029274,
-0.046965014189481735,
0.056114599108695984,
-0.0006240248330868781,
-0.05866486579179764,
0.014830926433205605,
-0.04324167221784592,
-0.024438519030809402,
0.0739811584353447,
-0.013430406339466572,
0.005214986391365528,
0.04367447644472122,
0.013300983235239983,
0.03211893513798714,
0.019215118139982224,
0.023183070123195648,
0.054110683500766754,
-0.013329852372407913,
-0.03661142662167549,
-0.0219670869410038,
0.03221573680639267,
-0.004184299148619175,
-0.031883299350738525,
-0.020722176879644394,
0.02526485174894333,
0.01023942045867443,
0.01392290461808443,
0.03441326320171356,
-0.012674384750425816,
-0.041187386959791183,
-0.007148687727749348,
-0.05107511952519417,
-0.03538994491100311,
-0.07982949912548065,
0.04876358434557915,
-0.03727247565984726,
-0.007186063565313816,
0.01935163326561451,
0.01320149376988411,
0.021638644859194756,
-0.0589434988796711,
-0.002653330098837614,
-0.0023394275922328234,
0.019271312281489372,
-0.011309431865811348,
-0.004083507694303989,
0.027399882674217224,
0.02288205735385418,
0.024710072204470634,
-0.011126858182251453,
0.021087011322379112,
-0.012054243125021458,
-0.010105101391673088,
-0.022097526118159294,
-0.008794156834483147,
0.011404006741940975,
0.00278868293389678,
-0.013160010799765587,
0.022008007392287254,
-0.0010415042052045465,
-0.00021236094471532851,
0.04743623733520508,
-0.006569347344338894,
0.07660892605781555,
0.05135525390505791,
-0.01867947168648243,
-0.0019216884393244982,
0.01636786200106144,
0.008871144615113735,
0.0039291600696742535,
0.005702577531337738,
-0.008975488133728504,
-0.06218278035521507,
0.020745722576975822,
0.03990387171506882,
0.038196783512830734,
-0.045549556612968445,
0.004126456566154957,
0.033152688294649124,
0.017805082723498344,
0.0468766987323761,
-0.0020854801405221224,
-0.019211331382393837,
0.014936039224267006,
-0.01107533648610115,
0.0032700567971915007,
0.005600176751613617,
-0.007952801883220673,
-0.000008921295375330374,
0.019512716680765152,
0.026104208081960678,
-0.0015421748394146562,
-0.014386419206857681,
0.04700833931565285,
-0.016627509146928787,
0.06316700577735901,
0.031117917969822884,
-0.04490155354142189,
0.018220869824290276,
-0.054092761129140854,
0.006451339460909367,
-0.007336737122386694,
0.00003239038051106036,
0.04198304936289787,
0.0004813079722225666,
-0.000004797457222593948,
0.013327096588909626,
0.004282926209270954,
-0.02110784687101841,
-0.036970362067222595,
0.004634249955415726,
-0.02420598268508911,
0.029549049213528633,
0.017713259905576706,
-0.027489176020026207,
-0.01879659853875637,
0.008390075527131557,
0.009767934679985046,
-0.004579897969961166,
0.08154933154582977,
-0.02149137854576111,
-0.037411462515592575,
-0.02083701826632023,
-0.06266254186630249,
-0.005784591659903526,
-0.043734367936849594,
-0.03922292962670326,
0.007430736906826496,
-0.028390072286128998,
-0.01963142864406109,
0.05115073546767235,
0.022152911871671677,
0.016748502850532532,
-0.01889929175376892,
-0.021601824089884758,
-0.050098441541194916,
-0.008523129858076572,
0.0053980667144060135,
0.03955154865980148,
-0.026576725766062737,
-0.004948226269334555,
0.048139721155166626,
-0.021607086062431335,
-0.022505465894937515,
0.00868042279034853,
-0.06095346435904503,
-0.057014379650354385,
-0.00404654024168849,
-0.012914440594613552,
0.026195425540208817,
-0.041063643991947174,
-0.001302467193454504,
0.02213854342699051,
-0.07040664553642273,
-0.029210444539785385,
-0.018585704267024994,
-0.052900590002536774,
0.014672163873910904,
-0.005711991339921951,
0.05022469535470009,
0.018609289079904556,
-0.034391921013593674,
0.06454501301050186,
-0.000786477467045188,
-0.04658786207437515,
0.01950776018202305,
-0.047080546617507935,
-0.025981148704886436,
-0.01734006404876709,
0.010256553068757057,
0.07518048584461212,
-0.02725115977227688,
0.0032380931079387665,
0.03454897552728653,
0.011948714032769203,
0.04371633380651474,
0.011504199355840683,
0.0023785841185599566,
-0.010082069784402847,
0.014721664600074291,
-0.02078241854906082,
0.04979043826460838,
-0.004479751456528902,
-0.04064227640628815,
0.008919409476220608,
0.0056217024102807045,
0.020358508452773094,
0.039471227675676346,
-0.0005648898659273982,
0.034948576241731644,
-0.016578279435634613,
-0.0025425166822969913,
-0.044973500072956085,
0.019840994849801064,
-0.013876228593289852,
0.006887985393404961,
0.010402883403003216,
0.031077811494469643,
0.042534396052360535,
-0.031468458473682404,
0.0024469513446092606,
0.025195160880684853,
0.03048158995807171,
-0.04184360429644585,
-0.01820969022810459,
-0.0017147957114502788,
-0.01696830615401268,
-0.0004472553846426308,
0.006791912950575352,
-0.019090747460722923,
0.06835319846868515,
0.024018945172429085,
0.011349748820066452,
0.01990896463394165,
-0.034542515873909,
0.014709893614053726,
-0.052490174770355225,
0.01629701443016529,
0.005843244958668947,
0.035755086690187454,
-0.011909878812730312,
0.061261456459760666,
0.019089635461568832,
0.0008189385407604277,
0.008837481029331684,
0.002386858221143484,
-0.07653582841157913,
0.011147433891892433,
-0.01455608382821083,
0.015915479511022568,
-0.025507239624857903,
0.012909656390547752,
0.03750104457139969,
0.002978942124173045,
-0.035914961248636246,
-0.02475646696984768,
0.0014422001549974084,
-0.04668450355529785,
0.03403368592262268,
0.01459133718162775,
-0.008813681080937386,
-0.05186595022678375,
-0.017811940982937813,
0.01747901737689972,
0.004231398459523916,
-0.007130852900445461,
0.03424974903464317,
-0.02894364856183529,
-0.009177791886031628,
0.02454567141830921,
-0.021645504981279373,
0.051994625478982925,
-0.0143264876678586,
0.03266344964504242,
0.018782351166009903,
0.007255062460899353,
0.010135652497410774,
0.0135565847158432,
0.06240185350179672,
0.0007784274639561772,
-0.039673179388046265,
-0.01582854799926281,
-0.05917324125766754,
-0.036620836704969406,
-0.03745516762137413,
0.04013976454734802,
-0.00012183478975202888,
-0.0012976375874131918,
0.017535602673888206,
-0.002326441928744316,
-0.0011522503336891532,
0.04190607741475105,
0.05008983984589577,
0.02867833524942398,
-0.028700578957796097,
-0.06883727014064789,
-0.010130386799573898,
-0.03878585249185562,
0.02324894443154335,
0.03287014737725258,
-0.014204398728907108,
-0.04818190261721611,
-0.004952375311404467,
0.01239235233515501,
-0.01310656312853098,
-0.002898380160331726,
0.011370939202606678,
0.04042273014783859,
0.02033459208905697,
0.007337313145399094,
-0.004789463710039854,
-0.0009073130204342306,
0.006300752051174641,
0.03955525904893875,
0.009381833486258984,
-0.009838275611400604,
-0.09826096892356873,
0.008782069198787212,
0.05975998565554619,
0.043994732201099396,
-0.05599495396018028,
-0.01896492764353752,
-0.040985725820064545,
-0.011262490414083004,
0.06804947555065155,
-0.0594167560338974,
0.006298617459833622,
-0.0496600866317749,
-0.005093554500490427,
-0.024651316925883293,
-0.0009490272495895624,
0.031619906425476074,
0.026487533003091812,
-0.018279844895005226,
0.024409571662545204,
-0.0049616009928286076,
-0.004240245558321476,
-0.03984122723340988,
-0.0008145130705088377,
0.03834467753767967,
0.08680438995361328,
0.009448417462408543,
0.010535404086112976,
0.01394676323980093,
0.03285879269242287,
-0.009703717194497585,
-0.06181541457772255,
-0.01812395267188549,
-0.006016100756824017,
-0.01175775472074747,
0.004285238683223724,
-0.01263763289898634,
-0.030635273084044456,
-0.046927742660045624,
-0.013480328023433685,
0.0008401628583669662,
-0.006759352050721645,
-0.01394890807569027,
0.028951171785593033,
0.022377662360668182,
-0.03327450528740883,
0.043077725917100906,
0.023501813411712646,
-0.03421012684702873,
-0.010754634626209736,
0.0005605675396509469,
0.02766318991780281,
-0.009074279107153416,
-0.010443350300192833,
-0.005633865483105183,
0.012793206609785557,
-0.042868562042713165,
0.0466829314827919,
-0.02353857457637787,
0.032808613032102585,
-0.03254474699497223,
-0.04251305013895035,
-0.01407337374985218,
0.03378354758024216,
0.0014800013741478324,
-0.025986218824982643,
-0.03084930032491684,
0.013912217691540718,
0.01789332740008831,
-0.03406352549791336,
-0.003435769584029913,
0.015297185629606247,
0.03246410936117172,
0.016187602654099464,
-0.003173551522195339,
-0.0008611110388301313,
-0.03286939114332199,
-0.018329594284296036,
0.04509172588586807,
-0.03114926442503929,
0.055585891008377075,
-0.0012886944459751248,
-0.01161886379122734,
0.013084822334349155,
-0.07247010618448257,
-0.08499404788017273,
0.0382629819214344,
0.0018261424265801907,
0.024101298302412033,
-0.05531234294176102,
0.0403299517929554,
0.004855496808886528,
0.00934076402336359,
-0.051044873893260956,
-0.05810091644525528,
0.035061366856098175,
0.022717799991369247,
0.013546263799071312,
0.006416626740247011,
0.0012225944083184004,
0.003626229939982295,
-0.021262189373373985,
0.008175039663910866,
0.03624184429645538,
-0.0383012630045414,
-0.0010103255044668913,
0.003367655212059617,
-0.004201115109026432,
0.0673670694231987,
0.033726729452610016,
-0.01974288560450077,
0.009348616935312748,
-0.034375306218862534,
-0.020091587677598,
-0.02996431104838848,
0.03152163326740265,
-0.035291265696287155,
-0.02983265183866024,
0.0019327953923493624,
-0.0009969058446586132,
0.04072805494070053,
-0.011327812448143959,
0.0005403071409091353,
0.020657433196902275,
0.04569556564092636,
-0.030178144574165344,
-0.050400037318468094,
0.029728403314948082,
-0.009813574142754078,
0.014878207817673683,
0.027119338512420654,
-0.0031530193518847227,
-0.06858354806900024,
-0.01074262522161007,
0.01232132688164711,
0.002674082526937127,
0.007792682386934757,
0.011595400981605053,
0.04516703635454178,
-0.00839833915233612,
0.0208718441426754,
0.025542303919792175,
-0.0032517604995518923,
0.025468258187174797,
0.021525580435991287,
-0.003744528628885746,
-0.00646042637526989,
0.012098148465156555,
-0.0212651789188385,
-0.008225622586905956,
-0.039988934993743896,
-0.016177386045455933,
0.06082012876868248,
-0.0007976924534887075,
0.05700754001736641,
0.03732294589281082,
-0.032197367399930954,
-0.009968283586204052,
-0.017580753192305565,
-0.01577327400445938,
0.02436833642423153,
-0.0005611996748484671,
0.007462328765541315,
-0.0069510736502707005,
0.0010789859807118773,
0.032008301466703415,
0.011949781328439713,
0.014353244565427303,
-0.012005075812339783,
0.04734698683023453,
0.06774937361478806,
0.02122279815375805,
0.0007761475862935185,
-0.040575381368398666,
0.04255373030900955,
-0.02810191921889782,
0.0014826413244009018,
0.016733162105083466,
-0.034900352358818054,
0.049768928438425064,
0.005061998497694731,
-0.012094248086214066,
-0.045811641961336136,
-0.0009475338156335056,
-0.03223717212677002,
0.02694367617368698,
0.00298285111784935,
-0.010626395232975483,
-0.013883822597563267,
0.00021047922200523317,
0.01893152855336666,
-0.0056857517920434475,
0.05030529573559761,
-0.01151848305016756,
-0.06175685673952103,
-0.0029778291936963797,
-0.0076111918315291405,
-0.014262599870562553,
0.028471361845731735,
0.027269480749964714,
-0.025233374908566475,
-0.0031025323551148176,
-0.025417406111955643,
0.027200261130928993,
0.0047623165883123875,
0.015149085782468319,
-0.015484647825360298,
0.06751785427331924,
-0.012346690520644188,
-0.002700008684769273,
-0.015035501681268215,
-0.010989131405949593,
0.1253693848848343,
0.007777865044772625,
-0.025915082544088364,
-0.0907968208193779,
-0.020881829783320427,
-0.011232534423470497,
0.015006904490292072,
-0.038015395402908325,
0.01219570729881525,
0.005554054863750935,
0.026255086064338684,
0.018905553966760635,
0.03707098215818405,
0.00541255809366703,
0.06619328260421753,
0.06102057173848152,
-0.02423444762825966,
-0.03432762622833252,
-0.01601388305425644,
0.011302342638373375,
-0.009425134398043156,
0.03503155708312988,
-0.03924311324954033,
0.03276811167597771,
-0.06068810075521469,
-0.031336601823568344,
-0.027056705206632614,
0.010137215256690979,
0.04023272171616554,
0.00453784829005599,
-0.017839323729276657,
0.02239813096821308,
-0.006738645490258932,
-0.013365395367145538,
-0.035761572420597076,
0.027178196236491203,
0.030858874320983887,
0.02585163526237011,
-0.009467636235058308,
-0.0059313587844371796,
0.04231078550219536,
-0.03083692118525505,
0.021302800625562668,
0.014098021201789379,
-0.05711594223976135,
-0.026142675429582596,
-0.038687530905008316,
0.015537726692855358,
0.0072269681841135025,
0.0009374736109748483,
0.000628335983492434,
0.04303060844540596,
-0.0005615036352537572,
-0.03498523309826851,
-0.0507083460688591,
-0.01542663387954235,
0.03643697872757912,
-0.012648841366171837,
-0.0213299747556448,
-0.06411213427782059,
0.020170146599411964,
-0.02620420791208744,
0.01984749548137188,
-0.01804262213408947,
-0.004267942160367966,
0.02178041823208332,
-0.028732459992170334,
-0.02775224857032299,
-0.009966092184185982,
-0.024827204644680023,
-0.005859171971678734,
-0.004979229532182217,
-0.042316585779190063,
-0.02441699616611004,
0.02140085957944393,
0.03106265887618065,
0.028604330494999886,
-0.038695111870765686,
0.010702496394515038,
0.02825985476374626,
-0.059882327914237976,
0.03840475156903267,
-0.004189939238131046,
-0.01697552017867565,
-0.0156832505017519,
0.008778837509453297,
0.045860566198825836,
0.04433448612689972,
0.0022870656102895737,
0.03055957891047001,
-0.020412465557456017,
-0.0303941760212183,
0.005873948335647583,
-0.009052110835909843,
-0.015113058499991894,
0.04321370646357536,
-0.05616078898310661,
0.008534213528037071,
0.0032991745974868536,
0.026999814435839653,
0.038745585829019547,
-0.009837230667471886,
-0.004948199260979891,
0.0066801318898797035,
-0.026402205228805542,
-0.011041324585676193,
0.005502517335116863,
-0.04561945050954819,
0.019972912967205048,
-0.00682953791692853,
0.021526683121919632,
-0.007850391790270805,
-0.031310100108385086,
-0.023188874125480652,
0.015343032777309418,
-0.036404818296432495,
0.05123530700802803,
-0.00940000917762518,
0.01848692260682583,
-0.03253436088562012,
0.06542254984378815,
-0.047180578112602234,
-0.025537947192788124,
-0.052565015852451324,
-0.0182973463088274,
0.024605417624115944,
0.0023547294549643993,
-0.002986540086567402,
0.0224545206874609,
-0.002601919462904334,
0.01630987413227558,
0.014604722149670124,
0.028202151879668236,
-0.015380830504000187,
-0.011574515141546726,
-0.00905274786055088,
0.012259704992175102,
0.029024016112089157,
-0.06744576245546341,
-0.04040270671248436,
0.0589296892285347,
-0.008682104758918285,
-0.05210854113101959,
-0.01760036312043667,
0.004591077566146851,
0.018733171746134758,
0.031901996582746506,
0.003910913597792387,
-0.0037837778218090534,
0.03729316219687462,
-0.006233677733689547,
0.015477760694921017,
-0.01706610433757305,
-0.018318738788366318,
-0.0006676033372059464,
0.03589963540434837,
-0.005872056353837252,
-0.03816499933600426,
0.025991948321461678,
0.023942241445183754,
0.05685420334339142,
0.025790244340896606,
-0.03677866607904434,
0.020499439910054207,
0.021361468359827995,
-0.005838135257363319,
0.010466938838362694,
-0.0009995405562222004,
0.018198395147919655,
0.05021948739886284,
-0.043804705142974854,
0.026571158319711685,
0.015133104287087917,
-0.0015503003960475326,
-0.059649210423231125,
-0.0034980818163603544,
-0.010984753258526325,
-0.026335474103689194,
0.013961248099803925,
-0.01769362948834896,
-0.022785212844610214,
0.024079011753201485,
-0.03680921345949173,
-0.016162468120455742,
-0.0443425215780735,
-0.03583332896232605,
0.007623976096510887,
-0.010666374117136002,
-0.0006606715032830834,
0.058360859751701355,
0.010186324827373028,
0.025135353207588196,
0.01644434966146946,
-0.025851435959339142,
0.0218492578715086,
-0.04051041603088379,
-0.003363455878570676,
0.07220947742462158,
0.0006223352393135428,
-0.008069595322012901,
0.08343818038702011,
-0.04899630695581436,
-0.009017445147037506,
0.044918403029441833,
0.013798960484564304,
-0.015599771402776241,
0.0030812460463494062,
0.011364773847162724,
-0.023904604837298393,
0.06670592725276947,
0.023911865428090096,
-0.03151298686861992,
-0.06663623452186584,
-0.02223276160657406,
0.05886853113770485,
0.022981097921729088,
0.02251341938972473,
0.019817790016531944,
0.02005583606660366,
-0.031157253310084343,
-0.025359580293297768,
-0.00960657000541687,
-0.015247546136379242,
-0.031038425862789154,
0.008558711968362331,
0.0026557890232652426,
0.02052825316786766,
-0.015752606093883514,
0.00396305974572897,
-0.03181103616952896,
-0.04918922856450081,
0.025692183524370193,
-0.01036402303725481,
0.04266762733459473,
0.0032873523887246847,
0.0008801773656159639,
-0.011601279489696026,
0.034127380698919296,
0.05101645737886429,
-0.018404144793748856,
-0.06593392789363861,
0.005337014328688383,
0.00034241314278915524,
-0.029281742870807648,
-0.002034454606473446,
-0.02573426440358162,
-0.009408739395439625,
0.0334244929254055,
0.009282772429287434,
-0.023487523198127747,
-0.004752494394779205,
-0.0680738165974617,
-0.019027702510356903,
-0.04367111250758171,
0.07236727327108383,
0.010924462229013443,
-0.022791773080825806,
-0.04327862337231636,
-0.03533971309661865,
0.006454370450228453,
0.026052871719002724,
0.07688932865858078,
-0.0338093638420105,
-0.0034603842068463564,
-0.006263064686208963,
-0.003945601172745228,
0.027568913996219635,
-0.07245674729347229,
0.02160467766225338,
0.031311895698308945,
-0.027482636272907257,
-0.008730619214475155,
-0.013417992740869522,
-0.03199833258986473,
0.0005952786887064576,
0.0586923323571682,
-0.0012622528010979295,
0.0045891935005784035,
-0.043577417731285095,
0.004618993494659662,
0.0517493411898613,
0.05174386873841286,
-0.021810786798596382,
0.07949898391962051,
0.0040986607782542706,
0.019197657704353333,
0.0253111831843853,
-0.00448522949591279,
-0.023899873718619347,
-0.003125283168628812,
0.006118857767432928,
0.04260734096169472,
-0.04128263518214226,
0.0015426499303430319,
0.027083810418844223,
-0.04658655449748039,
-0.03648070991039276,
0.03510662540793419,
-0.03518829494714737,
-0.011406096629798412,
0.07490082830190659,
0.006478555500507355,
0.016547031700611115,
-0.011916144751012325,
-0.006602147594094276,
-0.016700278967618942,
0.012624753639101982,
0.00674865860491991,
0.02860231138765812,
0.05333814024925232,
-0.029279809445142746,
0.008572694845497608,
0.02541782148182392,
-0.013597363606095314,
0.017391983419656754,
0.0136213144287467,
0.03898638114333153,
-0.043657805770635605,
-0.03636046126484871,
0.000022096985048847273,
-0.03526169806718826,
0.01785595528781414,
0.028261862695217133,
-0.045473359525203705,
0.06925906985998154,
-0.0375535823404789,
-0.015078196302056313,
0.030619213357567787,
0.005750749260187149,
-0.015837756916880608,
-0.026772277429699898,
-0.006918034050613642,
0.0171732809394598,
-0.008272701874375343,
0.02034502662718296,
0.004788544028997421,
-0.005624511744827032,
0.06633831560611725,
-0.020933007821440697,
0.02337019145488739,
-0.003331754356622696,
-0.0013441485352814198,
-0.025303104892373085,
0.002713582944124937,
-0.03418362885713577,
-0.03212125226855278,
0.022023409605026245,
0.05071282759308815,
0.025858581066131592,
0.025238659232854843,
-0.008965395390987396,
0.018246714025735855,
0.05638064816594124,
-0.06433538347482681,
-0.0019812241662293673,
-0.007336215581744909,
-0.007894197478890419,
-0.01744544506072998,
0.01006374228745699
] |
<p>I am trying to calculate
$$Z = \int\limits_{\phi(\beta) = \phi(0) =0} D \phi\ e^{-\frac{1}{2} \int_0^{\beta} d\tau \dot{\phi}^2}$$
without transforming it to the <a href="http://en.wikipedia.org/wiki/Matsubara_frequency" rel="nofollow">Matsubara frequency space</a>, I can show that $Z = \sqrt{\frac{1}{2\pi \beta}}$. However, I have a problem in obtaining the same result in the Matsubara frequency space:
\begin{equation}
\phi (\tau) = \frac{1}{\sqrt{\beta}} \left( \sum_{n} \phi_n \ e^{i\omega_n\tau} \right),
\end{equation}
with $\sum_n \phi_n =0, \omega_n = \frac{2\pi n}{\beta}$. And
\begin{equation}
Z = \int \prod_n D\phi_n\ \delta\left(\sum_n \phi_n\right)\ e^{-\frac{1}{2} \sum_n \phi_n \phi_{-n} \omega_n^2 }
\end{equation}
which, I think, vanishes. </p>
<p>I guess the problem lies in the measure. Any comments?</p>
<p>Info: I write the Schulman's derivation in imaginary time here.
\begin{eqnarray}
Z &=& \int\limits_{\phi(0) =\phi(\beta) = 0} D\phi(\tau) e^{-\frac{1}{2}\int_0^{\beta}d\tau\dot{\phi}^2}\\
&=& \text{lim}_{N \rightarrow \infty} (\frac{1}{2\pi \epsilon})^{(N+1)/2} \int d\phi_1
\dots d\phi_N e^{-\frac{1}{2\epsilon} \sum_{i =0}^N (\phi_{i+1} -\phi_i)^2}
\end{eqnarray}</p>
<p>Then, we can use the identity
\begin{equation}
\int_{-\infty}^{\infty} du \sqrt{\frac{a}{\pi}} e^{-a(x-u)^2}\sqrt{\frac{b}{\pi}} e^{-b(u -y)^2} = \sqrt{\frac{ab}{\pi(a+b)}} e^{-\frac{ab}{a+b}(x-y)^2}
\end{equation}
to evaluate the sum to be
\begin{equation}
Z = \sqrt{\frac{1}{2\pi \beta}}.
\end{equation}</p>
| 8,255 |
[
0.021295806393027306,
-0.03232898563146591,
0.024691034108400345,
-0.03688418120145798,
0.02611726149916649,
-0.02801244892179966,
-0.057248152792453766,
-0.02250373177230358,
-0.007472188211977482,
-0.030342165380716324,
0.046865202486515045,
-0.005625459365546703,
0.03528456389904022,
0.013473217375576496,
0.018085027113556862,
0.01062246784567833,
-0.050160132348537445,
0.0014645080082118511,
-0.05202503129839897,
-0.019937876611948013,
0.009541202336549759,
0.0260433629155159,
0.015229354612529278,
-0.024975648149847984,
-0.04214121773838997,
0.03128309175372124,
-0.006629578303545713,
0.017639070749282837,
-0.03344346582889557,
0.03165030479431152,
-0.026719678193330765,
-0.018405858427286148,
0.008657843805849552,
0.04641969874501228,
0.011185826733708382,
0.017231838777661324,
-0.04914158210158348,
-0.016330372542142868,
-0.0035676120314747095,
-0.018189655616879463,
-0.009312094189226627,
-0.013943860307335854,
-0.0230856966227293,
0.025136657059192657,
-0.03477346897125244,
0.0012088519288226962,
0.0005750676500611007,
-0.025152165442705154,
0.05566450208425522,
-0.05389656499028206,
0.07017247378826141,
-0.0029971350450068712,
0.009503151290118694,
-0.009371575899422169,
-0.0083415312692523,
-0.025424774736166,
0.07126393914222717,
0.06385057419538498,
0.026841403916478157,
-0.06015143170952797,
-0.011031004600226879,
-0.02739417366683483,
0.011911177076399326,
-0.015558342449367046,
-0.011022941209375858,
0.04956582188606262,
0.05529535934329033,
-0.017905643209815025,
0.02384323999285698,
0.00029656619881279767,
0.04208957403898239,
0.003455114085227251,
0.00426972983404994,
-0.01195190753787756,
0.00468853022903204,
-0.001780985970981419,
0.0029297492001205683,
0.023855168372392654,
0.009308208711445332,
0.05135327950119972,
-0.029184050858020782,
0.02580438181757927,
0.013531925156712532,
0.002278587082400918,
0.051196224987506866,
-0.012188317254185677,
0.06250713765621185,
-0.004550199024379253,
-0.017199473455548286,
0.023028304800391197,
0.00511598726734519,
0.037100136280059814,
0.04936739057302475,
-0.04918603226542473,
-0.03549458086490631,
0.06392340362071991,
0.005066695157438517,
0.024650920182466507,
-0.029137732461094856,
-0.028723062947392464,
-0.015270520001649857,
-0.034968502819538116,
0.0062919240444898605,
0.06431122869253159,
0.0051321485079824924,
-0.006174733396619558,
-0.041258927434682846,
-0.007034930866211653,
-0.03307464346289635,
-0.06348572671413422,
-0.04042264446616173,
0.0400085411965847,
-0.005223134532570839,
0.011922926642000675,
-0.0006615492166019976,
0.004325656685978174,
-0.011481824330985546,
0.006973933894187212,
0.02083759941160679,
0.06782568991184235,
0.013507788069546223,
-0.02388419397175312,
0.014818294905126095,
-0.03508906811475754,
-0.06278802454471588,
-0.014492825604975224,
0.01969248801469803,
0.011971011757850647,
-0.04453883320093155,
0.02374912239611149,
0.039257798343896866,
-0.007179189473390579,
0.04221079871058464,
0.027488328516483307,
0.03194129839539528,
-0.009051770903170109,
-0.050291698426008224,
-0.012593238614499569,
0.04452047124505043,
-0.04908313974738121,
0.002190269995480776,
-0.07027912884950638,
0.005484327208250761,
0.016225654631853104,
0.06399628520011902,
0.04289540648460388,
0.02424991875886917,
-0.015281928703188896,
0.06963741034269333,
0.02312430739402771,
-0.04692506790161133,
-0.05155611410737038,
-0.0378812775015831,
-0.007809747010469437,
0.014348515309393406,
-0.009977156296372414,
0.015668805688619614,
0.016922172158956528,
0.007573505863547325,
0.008126954548060894,
0.04941818118095398,
0.012703217566013336,
0.010074284859001637,
-0.004020616412162781,
0.014759514480829239,
-0.03397413715720177,
0.04083583131432533,
0.0009165379451587796,
-0.0009769909083843231,
0.0023436411283910275,
-0.019129179418087006,
0.005214058328419924,
-0.01835218258202076,
0.04518229141831398,
0.03831800818443298,
-0.054543234407901764,
-0.018203601241111755,
-0.011251995339989662,
0.024593526497483253,
-0.008849666453897953,
-0.008455614559352398,
-0.007574642077088356,
-0.056885965168476105,
0.038894861936569214,
0.013517338782548904,
0.04982438310980797,
-0.0051884278655052185,
-0.00638897018507123,
-0.024644076824188232,
-0.0368073433637619,
-0.0016937651671469212,
-0.025832263752818108,
-0.004341283813118935,
0.006454484071582556,
-0.035906676203012466,
0.04494350403547287,
-0.006227185949683189,
0.015602624975144863,
0.007542026229202747,
-0.011673718690872192,
-0.00984546821564436,
0.018137559294700623,
0.03317449241876602,
-0.036692697554826736,
0.02160620503127575,
0.044627707451581955,
0.039552196860313416,
-0.01136030163615942,
0.021110255271196365,
-0.018799444660544395,
-0.010773583315312862,
-0.019531842321157455,
-0.010721097700297832,
0.06162191182374954,
-0.004879852756857872,
-0.006697319447994232,
0.019577572122216225,
-0.04778057336807251,
-0.018901685252785683,
0.017450518906116486,
-0.06030726432800293,
0.030636945739388466,
0.07721373438835144,
-0.010208605788648129,
0.019573787227272987,
0.03840570151805878,
0.003136321669444442,
0.004569199867546558,
-0.0038336494471877813,
-0.016143424436450005,
-0.017216496169567108,
0.01499975100159645,
0.051445066928863525,
0.06621730327606201,
-0.011345159262418747,
-0.019959932193160057,
0.06296189874410629,
0.011676045134663582,
0.05029723793268204,
0.004424953833222389,
-0.010531713254749775,
-0.053615063428878784,
0.016513803973793983,
-0.003415531711652875,
0.01779394969344139,
-0.00266287918202579,
0.06098313629627228,
-0.01729683391749859,
0.029543792828917503,
-0.040233172476291656,
-0.01908912882208824,
0.01899205520749092,
-0.017621539533138275,
-0.029115786775946617,
-0.016521282494068146,
0.019402053207159042,
0.029692957177758217,
0.006947474554181099,
0.01836455799639225,
0.03334347903728485,
-0.0002890148607548326,
0.007638039067387581,
0.006356245372444391,
-0.040217768400907516,
0.032725296914577484,
0.01933089643716812,
0.015677856281399727,
-0.0538625605404377,
0.022355424240231514,
-0.014260448515415192,
-0.015771670266985893,
0.021491924300789833,
-0.016354849562048912,
0.03958947956562042,
0.006687897723168135,
0.021415727213025093,
0.02843780629336834,
-0.03154883161187172,
-0.022335879504680634,
-0.026539485901594162,
0.022200368344783783,
0.02558480016887188,
0.047052524983882904,
0.044143497943878174,
-0.0691344290971756,
-0.02114861272275448,
0.0002786827099043876,
-0.008748405613005161,
0.018024608492851257,
-0.006474551744759083,
-0.007884632796049118,
0.02068968676030636,
-0.004975108429789543,
-0.07798619568347931,
-0.032292500138282776,
-0.007975129410624504,
-0.015758352354168892,
-0.04880371689796448,
0.011112064123153687,
0.050577085465192795,
0.007313207257539034,
-0.05171314626932144,
0.017671115696430206,
-0.030919769778847694,
-0.0712597668170929,
-0.015729131177067757,
-0.026762492954730988,
0.06447535753250122,
-0.052557408809661865,
0.030400363728404045,
-0.020910412073135376,
-0.005157578736543655,
-0.007532578893005848,
-0.05341162160038948,
-0.04070480912923813,
0.007560939062386751,
0.009403289295732975,
0.007090062368661165,
0.035938240587711334,
-0.02642100676894188,
0.093182772397995,
0.01873975805938244,
-0.0012290673330426216,
0.0011754020815715194,
0.03955831751227379,
0.007791487965732813,
-0.06856009364128113,
-0.01895158924162388,
0.01621982455253601,
-0.017145996913313866,
0.03765525668859482,
-0.010702533647418022,
0.046222835779190063,
0.0566619336605072,
0.0066653951071202755,
0.00760658597573638,
0.029716545715928078,
-0.009192891418933868,
0.045986030250787735,
0.04064223915338516,
-0.000003147968527628109,
0.02008698135614395,
0.02758379653096199,
0.015680063515901566,
0.0381435826420784,
-0.021273722872138023,
-0.07372536510229111,
0.04035106301307678,
-0.0026004360988736153,
-0.0023524598218500614,
-0.012747886590659618,
0.025882862508296967,
0.0176797267049551,
-0.03453468158841133,
-0.04771116003394127,
-0.021944338455796242,
0.03831935301423073,
-0.02664686180651188,
-0.0014530752087011933,
0.038157109171152115,
0.004085923545062542,
0.023179151117801666,
0.014916402287781239,
-0.006428636610507965,
0.028750408440828323,
0.03452657163143158,
-0.04463255777955055,
-0.01975180022418499,
-0.02443927712738514,
0.06484994292259216,
-0.013991245068609715,
-0.02501261793076992,
-0.015731653198599815,
-0.022952405735850334,
-0.01286787074059248,
0.006111066788434982,
-0.03796255961060524,
0.05158037319779396,
0.033114656805992126,
0.03891364857554436,
0.0029119362588971853,
-0.007260290905833244,
-0.011630202643573284,
-0.026182450354099274,
-0.07024423778057098,
-0.004939594771713018,
-0.012879814021289349,
-0.008953135460615158,
-0.035527415573596954,
-0.012952664867043495,
0.0038436134345829487,
-0.004360623192042112,
0.0034859608858823776,
-0.04035026207566261,
0.0009157503372989595,
-0.07308456301689148,
0.0175058264285326,
-0.06398870795965195,
-0.0378158763051033,
-0.036003436893224716,
0.06014937534928322,
0.030635960400104523,
-0.0032412533182650805,
-0.02114611677825451,
0.031833209097385406,
-0.05515184998512268,
0.030425647273659706,
-0.052039578557014465,
-0.0018208192195743322,
-0.009273510426282883,
0.025424784049391747,
0.016091350466012955,
0.033953431993722916,
0.021960122510790825,
0.021534428000450134,
0.013486677780747414,
0.039981942623853683,
0.007295388728380203,
-0.012273749336600304,
0.0076111494563519955,
-0.03364706039428711,
0.00779171846807003,
0.003117720130831003,
0.05865748971700668,
0.024231312796473503,
0.00876277219504118,
0.040287792682647705,
0.010623596608638763,
0.03378523886203766,
0.013574693351984024,
0.008328425697982311,
-0.000747335609048605,
0.00604674918577075,
-0.06342080980539322,
-0.006865975446999073,
-0.0494111143052578,
-0.01603490114212036,
-0.03177087381482124,
-0.016189271584153175,
-0.016340339556336403,
-0.017763489857316017,
-0.019830841571092606,
-0.015665676444768906,
0.046243976801633835,
-0.02894654870033264,
0.013843775726854801,
-0.020523305982351303,
0.013535486534237862,
-0.015534242615103722,
0.0017971376655623317,
0.03938237950205803,
0.04765739291906357,
0.030464427545666695,
0.020394621416926384,
-0.046010926365852356,
-0.03960857167840004,
0.010904228314757347,
0.015127511695027351,
0.028169648721814156,
-0.028370782732963562,
-0.060028284788131714,
-0.05881108343601227,
0.0358901247382164,
-0.012041330337524414,
0.05122556537389755,
-0.027707168832421303,
-0.0050503904931247234,
-0.008678304962813854,
-0.053169313818216324,
-0.02948426455259323,
0.01103869080543518,
0.002044005086645484,
0.01210249587893486,
-0.03808141499757767,
-0.004436560906469822,
-0.01897474378347397,
0.013219407759606838,
-0.0252568069845438,
0.03606374189257622,
0.001985252136364579,
-0.0007878206088207662,
0.01315704919397831,
0.024063274264335632,
-0.028484616428613663,
-0.08993174135684967,
0.03707102686166763,
0.003753653261810541,
0.01321330014616251,
0.023793326690793037,
-0.039573077112436295,
-0.07079166173934937,
0.03966522589325905,
0.02109450288116932,
0.025877181440591812,
0.014279468916356564,
-0.03588775545358658,
0.02976217307150364,
0.021454406902194023,
0.007222985383123159,
0.05816650390625,
0.043941620737314224,
-0.026313461363315582,
0.0367305651307106,
-0.02032112143933773,
-0.0005114207160659134,
-0.017069922760128975,
-0.01600760966539383,
-0.03181923180818558,
-0.009910580702126026,
-0.04653197526931763,
0.0518646314740181,
-0.02790837176144123,
0.00597543828189373,
0.018862957134842873,
0.013627314008772373,
0.050647586584091187,
0.014836161397397518,
-0.05343468114733696,
0.02142297476530075,
0.034571293741464615,
0.025798199698328972,
0.04406397044658661,
-0.02791348285973072,
0.018246030434966087,
-0.015163606032729149,
0.0004526835400611162,
0.00907990150153637,
-0.00297333812341094,
0.036946166306734085,
0.007622640114277601,
-0.013653399422764778,
0.03333747759461403,
-0.03278050199151039,
-0.008376514539122581,
-0.004186365753412247,
0.017977338284254074,
0.03409629315137863,
-0.02603088691830635,
-0.04403035715222359,
-0.01441700104624033,
-0.006680724676698446,
0.000037457444705069065,
-0.010730370879173279,
-0.03222397714853287,
0.05993800610303879,
0.021526755765080452,
-0.05794147029519081,
-0.03761175647377968,
0.025164924561977386,
-0.005833509843796492,
0.021244769915938377,
-0.04270116984844208,
-0.009304777719080448,
0.021183766424655914,
-0.03397209197282791,
0.035470835864543915,
0.037847187370061874,
-0.011567363515496254,
0.017503071576356888,
0.010904503986239433,
0.0348004586994648,
0.05619420111179352,
-0.01374762412160635,
0.007995632477104664,
0.007749058771878481,
-0.0012246305122971535,
-0.017172733321785927,
0.022235460579395294,
0.0664089024066925,
-0.03146383911371231,
0.0014624671312049031,
-0.006513820495456457,
-0.0129372114315629,
-0.018985604867339134,
0.011605951003730297,
-0.04709979146718979,
0.017964832484722137,
0.03230760991573334,
0.028939085081219673,
0.006749436724931002,
-0.02424514852464199,
0.02836933732032776,
-0.005628163926303387,
-0.007487535011023283,
-0.04508452117443085,
-0.04056677594780922,
0.0011267615482211113,
0.004648115020245314,
-0.003664301009848714,
0.004046950489282608,
-0.030588023364543915,
0.019063757732510567,
0.023417357355356216,
-0.020425017923116684,
-0.009976147674024105,
-0.011714707128703594,
0.020228104665875435,
-0.005530267488211393,
-0.011149993166327477,
0.013374839909374714,
-0.011828755959868431,
-0.040844667702913284,
0.0014238336589187384,
-0.0623047836124897,
0.02474389038980007,
0.0711263045668602,
0.04217822104692459,
0.006220090202987194,
0.0005582629819400609,
0.01718663051724434,
-0.009703327901661396,
-0.032383739948272705,
-0.023818233981728554,
0.04004306346178055,
-0.02367514744400978,
0.01833975315093994,
-0.04613792896270752,
-0.02136458083987236,
0.024669544771313667,
0.009923852980136871,
-0.011584564112126827,
0.0361410491168499,
0.024144014343619347,
0.05483989790081978,
0.0027545420452952385,
-0.009438350796699524,
-0.054114729166030884,
0.015630947425961494,
-0.049465447664260864,
0.034904491156339645,
-0.02871575951576233,
-0.004032214172184467,
-0.006175327580422163,
0.04210149869322777,
0.0028399357106536627,
-0.007223771419376135,
0.00006581765046576038,
0.003197836223989725,
0.014859647490084171,
0.0069992211647331715,
-0.00798861775547266,
-0.0015699757495895028,
-0.008421044796705246,
0.025796711444854736,
-0.009904848411679268,
0.03503752872347832,
-0.010983959771692753,
-0.01783817633986473,
0.026129426434636116,
-0.05696721002459526,
-0.06863913685083389,
0.0704825222492218,
0.02159426361322403,
0.011659951880574226,
-0.0018576581496745348,
-0.02418808452785015,
0.01831107772886753,
0.029460055753588676,
-0.027306439355015755,
-0.01372681837528944,
0.03657154366374016,
0.015771815553307533,
0.012427250854671001,
-0.013207022100687027,
0.010451600886881351,
0.14020226895809174,
0.04355880245566368,
0.004998252727091312,
-0.03228551149368286,
0.020768042653799057,
-0.024204084649682045,
0.02275071106851101,
-0.04533710703253746,
-0.008595469407737255,
-0.017382599413394928,
-0.024715304374694824,
0.024574831128120422,
0.10297834873199463,
0.0163243617862463,
-0.016358541324734688,
0.01803443394601345,
-0.030501609668135643,
-0.029729705303907394,
0.03404051810503006,
0.00481504388153553,
-0.045067451894283295,
-0.028815364465117455,
-0.007392363157123327,
0.03328275680541992,
-0.05362548679113388,
0.02213084138929844,
-0.0631323903799057,
0.006429939065128565,
-0.016535744071006775,
-0.014141431078314781,
-0.03406902030110359,
-0.02298540249466896,
0.01812550239264965,
-0.04644040763378143,
0.05702022463083267,
0.013497690670192242,
-0.00016170309390872717,
-0.01233053021132946,
0.03331359103322029,
0.0409599132835865,
0.014069169759750366,
0.022030532360076904,
0.014879855327308178,
0.0170131865888834,
-0.026063235476613045,
-0.04049744829535484,
-0.018851950764656067,
0.07475174218416214,
-0.01981309987604618,
0.008908028714358807,
-0.032893404364585876,
0.012058532796800137,
0.026080507785081863,
-0.08092346042394638,
-0.02727370895445347,
-0.03707636520266533,
-0.00023308703384827822,
-0.04206318035721779,
-0.000081478530773893,
-0.013343948870897293,
0.0005967331235297024,
0.04495464265346527,
0.002107541775330901,
-0.015527221374213696,
-0.012609315104782581,
0.013444068841636181,
0.018902240321040154,
0.02607070840895176,
0.00639740377664566,
-0.03541213274002075,
0.023710913956165314,
0.0011709451209753752,
-0.04049452394247055,
-0.023101139813661575,
-0.03292567655444145,
-0.021380692720413208,
0.039239946752786636,
-0.019398611038923264,
-0.021466964855790138,
-0.04280440881848335,
-0.055318888276815414,
0.007538286037743092,
-0.0067307837307453156,
-0.03503858298063278,
-0.011461635120213032,
-0.043196264654397964,
0.010001786053180695,
0.0584799200296402,
0.000634849420748651,
-0.009177656844258308,
-0.010227972641587257,
0.0316748321056366,
0.05703157186508179,
-0.005172253120690584,
-0.05634460970759392,
-0.010005151852965355,
-0.024454476311802864,
0.014898650348186493,
-0.024148115888237953,
0.017670003697276115,
0.023209571838378906,
0.047883182764053345,
-0.0023717996664345264,
0.03447483852505684,
-0.012866546399891376,
-0.028831012547016144,
-0.0006849189521744847,
-0.04094134271144867,
0.0012593161081895232,
0.04874261096119881,
0.04071667045354843,
-0.01743726246058941,
0.01899292878806591,
-0.01787916012108326,
0.03151066601276398,
-0.030680321156978607,
0.03938848152756691,
-0.05883633717894554,
-0.0013642662670463324,
-0.017740478739142418,
-0.01913125440478325,
0.008861719630658627,
0.005095511209219694,
-0.032103169709444046,
0.0219954214990139,
-0.01406365167349577,
0.043055690824985504,
-0.02015308476984501,
0.07127226144075394,
-0.032438747584819794,
-0.0017393236048519611,
0.026741016656160355,
0.05456632375717163,
-0.028744248673319817,
-0.02723441831767559,
0.0303938165307045,
-0.018044548109173775,
0.007073709275573492,
0.0239123348146677,
-0.02791484445333481,
0.03563861921429634,
-0.025190485641360283,
-0.041671592742204666,
0.019093653187155724,
0.03196517378091812,
0.01265435479581356,
0.041422002017498016,
-0.009608715772628784,
-0.04282126575708389,
0.027726858854293823,
-0.009969090111553669,
-0.028099991381168365,
-0.024852538481354713,
-0.06610842794179916,
0.015765396878123283,
-0.020965861156582832,
0.01871589571237564,
0.002430870197713375,
0.012978501617908478,
0.000016191914255614392,
0.03407234326004982,
-0.008798479102551937,
-0.0210578553378582,
0.0006732415640726686,
-0.03483373671770096,
0.016560139134526253,
0.035712793469429016,
0.01815207302570343,
-0.015008575282990932,
0.07501422613859177,
0.007074682042002678,
-0.024065647274255753,
-0.030718401074409485,
0.0035363193601369858,
-0.09051695466041565,
-0.03358343616127968,
0.0002684671198949218,
0.03125813975930214,
0.03478386998176575,
-0.05196227878332138,
0.013076306320726871,
0.0016921376809477806,
-0.06142265349626541,
0.05538823455572128,
-0.01754811219871044,
0.003907941281795502,
-0.037035610526800156,
-0.02564425580203533,
-0.027914803475141525,
0.0068859802559018135,
0.06948878616094589,
0.04764244705438614,
0.007421825546771288,
0.029009222984313965,
-0.022549189627170563,
-0.01720799133181572,
-0.005767821799963713,
0.03740774467587471,
0.03175291419029236,
-0.02875486947596073,
0.04830919951200485,
-0.0069952732883393764,
0.007619480136781931,
0.04268350824713707,
0.009397484362125397,
-0.0016823344631120563,
-0.005369915161281824,
0.022426897659897804,
0.046651944518089294,
0.052557311952114105,
0.007413203828036785,
0.026094555854797363,
0.016737770289182663,
-0.02155020646750927,
0.05133631080389023,
-0.03231506794691086,
-0.04484749212861061,
-0.00014033571642357856,
0.0248351339250803,
0.0052297357469797134,
-0.05817157030105591,
0.00978170707821846,
0.00686570443212986,
-0.008985172025859356,
0.02620306983590126,
-0.04439781606197357,
0.01239450927823782,
-0.03363360837101936,
0.025190921500325203,
-0.06654816120862961,
-0.009173962287604809,
0.027082866057753563,
0.02648538537323475,
-0.02331451140344143,
-0.023787066340446472,
-0.0011274946155026555,
-0.050902511924505234,
0.030170701444149017,
0.029949994757771492,
-0.04205687716603279,
-0.05465727299451828,
-0.04925558343529701,
-0.026585016399621964,
0.02407085709273815,
0.036963947117328644,
-0.001694600796326995,
-0.027917560189962387,
0.025998981669545174,
-0.0229656882584095,
0.020422140136361122,
-0.029444631189107895,
-0.032672494649887085,
0.0017724500503391027,
-0.06027047708630562,
0.0030019166879355907,
0.005323778837919235,
-0.034886304289102554,
0.0006779063842259347,
-0.022896837443113327,
-0.004127840977162123,
0.024962812662124634,
0.033950671553611755,
-0.01146847102791071,
-0.012867281213402748,
-0.009170467033982277,
-0.01346334908157587,
0.045752644538879395,
-0.05409028008580208,
-0.0007031538989394903,
-0.0034024573396891356,
-0.02059638313949108,
0.009571033529937267,
0.034353479743003845,
-0.010627235285937786,
0.016073837876319885,
0.03717600926756859,
-0.001443640561774373,
0.013908011838793755,
0.015724381431937218,
-0.0492728054523468,
0.052240028977394104,
-0.005612567532807589,
-0.0029951813630759716,
0.04508723318576813,
-0.04001999646425247,
0.044392671436071396,
0.010242493823170662,
-0.027628205716609955,
-0.034362342208623886,
-0.013619528152048588,
-0.010575764812529087,
-0.023195140063762665,
-0.011641428805887699,
0.02454986423254013,
0.009539319202303886,
0.013304620049893856,
-0.038097985088825226,
0.04560763016343117,
0.015144085511565208,
0.0012543165357783437,
0.04291539266705513,
-0.013788221403956413,
0.037621207535266876,
0.04239919036626816,
0.015897559002041817,
0.015598319470882416,
0.0017473887419328094,
0.050916753709316254,
0.025290267542004585,
0.0035933845210820436,
-0.019001493230462074,
0.01446409523487091,
0.030962178483605385,
-0.03099590539932251,
0.01890644058585167,
-0.03856281191110611,
0.017902132123708725,
-0.0010146890999749303,
-0.01917264051735401,
0.028612297028303146,
-0.01828550361096859,
-0.022951073944568634,
0.03619927912950516,
0.005305613856762648,
0.07401483505964279,
-0.032129086554050446,
0.07481718808412552,
0.008129945024847984,
0.022725623100996017,
-0.049803536385297775,
0.027553904801607132,
0.009530553594231606,
0.05399187281727791,
-0.0248472411185503,
-0.0035598392132669687,
-0.058811988681554794,
0.017436860129237175,
0.002223691903054714,
-0.06373490393161774,
-0.04209691286087036,
0.06140292063355446,
-0.009011771529912949,
0.01970050111413002,
-0.0013570914743468165,
-0.005571122281253338,
-0.042020801454782486,
0.010493705980479717,
0.04223465174436569,
0.013346599414944649,
0.013504723086953163,
-0.027914946898818016,
-0.02912900596857071,
0.05463637411594391,
-0.016601651906967163,
-0.005447447765618563,
0.008668106980621815,
0.004873605910688639,
-0.022220967337489128,
0.003843089798465371
] |
<p>If it does have a pH, I mean. Though I don't see why it shouldn't have it.</p>
<p>Both the <a href="http://en.wikipedia.org/wiki/Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" rel="nofollow">Brønsted-Lowry</a> and <a href="http://en.wikipedia.org/wiki/Lewis_acids_and_bases" rel="nofollow">Lewis</a> definitions of acid have to do with the ability of a substance to accept, or provide protons or pairs of electrons in certain reactions.</p>
<p>I got interested into this when I learned that the electric charges for antimatter particles are the opposite of those for matter particles (i.e.: positively charged positrons orbiting around negatively charged antiprotons).</p>
<p>So I was thinking... If I mixed anti-hydrogen chloride with anti-sodium hydroxide to make anti-salt, it would be the anti-HCl that would be donating negative charged ions, and the anti-NaOH that would be providing the positive charges.</p>
<p>Does that mean that the pH of a matter substance and its antimatter counterpart are reversed in relation to each other? Would anti-LSD be a base instead of an acid?</p>
<p><strong>Edit:</strong> I understand that getting matter in contact with antimatter will cause anihilation. I know that trying to neutralize an antimatter acid with a matter base <strike>would be great fun</strike> would never work. While asking this question I had a "bizarro" anti-matter world in mind. I was thinking, for example, how some anti-lemmon battery would work, since the anti-ions would be going in different ways when compared to a lemon battery in our matter world.</p>
| 8,256 |
[
-0.029757246375083923,
0.0022538190241903067,
-0.003007354447618127,
0.0026046177372336388,
0.03436567634344101,
-0.005485645495355129,
-0.006389794405549765,
0.032862886786460876,
-0.00024964410113170743,
-0.012292210943996906,
0.03439147397875786,
0.04757453128695488,
0.052572719752788544,
0.04508750140666962,
-0.0003908134822268039,
0.01420285739004612,
0.001955124782398343,
-0.029083827510476112,
0.0110033443197608,
-0.00813364703208208,
0.06970909982919693,
0.002185485791414976,
0.014536455273628235,
0.011936681345105171,
-0.013691389001905918,
0.07225321978330612,
-0.007518989033997059,
-0.03183257579803467,
0.017655231058597565,
0.04831252992153168,
0.023486563935875893,
-0.06276620179414749,
0.01453922875225544,
-0.016708670184016228,
0.014333534054458141,
-0.010710246860980988,
0.010947709903120995,
-0.008217585273087025,
-0.0020480388775467873,
0.036571815609931946,
-0.0006017726263962686,
-0.02280612662434578,
0.0280949454754591,
0.050383005291223526,
-0.05785433202981949,
0.00492637325078249,
-0.01643064059317112,
-0.007830601185560226,
0.029486773535609245,
-0.06509627401828766,
0.03437693789601326,
0.04604015871882439,
0.008377165533602238,
0.019674470648169518,
-0.017846694216132164,
0.00994967296719551,
0.07235120981931686,
0.039789579808712006,
0.011940152384340763,
-0.08227495849132538,
-0.009558488614857197,
-0.006746613420546055,
0.0041783759370446205,
0.005841952282935381,
-0.06278843432664871,
0.02047787234187126,
0.01984460838139057,
-0.02831125445663929,
0.023650070652365685,
0.039436858147382736,
0.029692787677049637,
0.00680693332105875,
-0.021486787125468254,
0.012486238963901997,
0.0025034055579453707,
-0.055597636848688126,
0.01453425269573927,
0.01999521628022194,
-0.0064932783134281635,
0.03486583009362221,
-0.043734706938266754,
0.01580890826880932,
-0.010546807199716568,
0.03453397750854492,
0.006095459219068289,
-0.016469916328787804,
0.04657813906669617,
-0.007074348162859678,
0.0005572817171923816,
0.04607454687356949,
0.02215927466750145,
0.004356409888714552,
0.02787838876247406,
0.0263984352350235,
-0.013184999115765095,
0.010227616876363754,
-0.007096602115780115,
0.06327741593122482,
-0.00020979423425160348,
0.04131980240345001,
-0.041330210864543915,
0.02939285896718502,
0.023370156064629555,
0.043475352227687836,
0.0020941710099577904,
-0.07141982764005661,
-0.007690568920224905,
0.002304653637111187,
0.01561857108026743,
0.0070066009648144245,
-0.03492223098874092,
0.02916775271296501,
0.026773257181048393,
-0.02718133106827736,
-0.011048206128180027,
-0.0633494183421135,
0.015356513671576977,
-0.025064576417207718,
0.05506535619497299,
0.043061718344688416,
0.03834313526749611,
-0.01364546362310648,
0.028163177892565727,
-0.01647120714187622,
-0.038998909294605255,
-0.04047422483563423,
-0.006740820128470659,
0.012784688733518124,
0.005323231685906649,
-0.020711731165647507,
-0.005817766301333904,
-0.021232012659311295,
0.027330948039889336,
-0.02298426255583763,
0.05971154198050499,
-0.030516481027007103,
-0.07737080752849579,
-0.07104622572660446,
-0.006090455688536167,
0.008159133605659008,
-0.046612560749053955,
-0.058583296835422516,
0.0016224842984229326,
-0.0016669770702719688,
0.059404511004686356,
0.005244072992354631,
-0.03159894421696663,
0.0019464129582047462,
0.01356230117380619,
0.04600143805146217,
0.005307743791490793,
0.014842004515230656,
0.023359734565019608,
-0.04272306710481644,
-0.03478633239865303,
-0.07363564521074295,
0.040566783398389816,
-0.0013401996111497283,
0.012134340591728687,
-0.0065007684752345085,
0.051946695894002914,
-0.01927335374057293,
0.006079039536416531,
0.002928003668785095,
-0.028798967599868774,
-0.04347629100084305,
0.06504251062870026,
0.014215120114386082,
-0.021871458739042282,
0.017676658928394318,
-0.010472376830875874,
0.06445729732513428,
-0.004986828658729792,
0.022314980626106262,
0.06547021120786667,
-0.015004755929112434,
-0.03645459935069084,
-0.05399736389517784,
0.03777933493256569,
-0.009757989086210728,
-0.04312404990196228,
-0.009659934788942337,
-0.03310341015458107,
0.0129953408613801,
0.024573560804128647,
0.018406368792057037,
-0.014018910005688667,
0.013545493595302105,
0.03205563500523567,
-0.03297088295221329,
0.003271834459155798,
-0.07787515968084335,
0.005295589566230774,
-0.0022683122660964727,
-0.039511825889348984,
0.0444396510720253,
0.03192136436700821,
0.03940695896744728,
-0.027638332918286324,
-0.011174120008945465,
-0.05200856178998947,
0.02962515503168106,
-0.008949716575443745,
0.008617904968559742,
0.026739442721009254,
0.04739171639084816,
0.0016721648862585425,
-0.027259109541773796,
-0.0008597674313932657,
0.012276709079742432,
-0.007105204276740551,
-0.01816479116678238,
-0.016735853627324104,
-0.009327842853963375,
0.010975059121847153,
-0.008404131047427654,
0.010982166044414043,
-0.009539720602333546,
0.007780454587191343,
0.049437299370765686,
-0.017299549654126167,
0.08736443519592285,
0.04927929490804672,
-0.009065423160791397,
0.011546402238309383,
0.026396671310067177,
0.027163976803421974,
0.027719486504793167,
-0.01663353480398655,
-0.026188910007476807,
-0.04277265816926956,
0.012250391766428947,
-0.006169307976961136,
0.013521361164748669,
-0.04369128495454788,
0.024983974173665047,
-0.0004988772561773658,
0.005660965573042631,
0.02529097907245159,
0.011848490685224533,
-0.005851572845131159,
-0.05071531608700752,
0.009649725630879402,
0.00013692495122086257,
0.024186832830309868,
0.00045685115037485957,
0.019914835691452026,
0.004877529572695494,
0.0022528599947690964,
-0.030215876176953316,
-0.007278629578649998,
-0.008329981938004494,
-0.027795955538749695,
0.012311850674450397,
0.011086461134254932,
-0.048055000603199005,
0.029022015631198883,
-0.02196582593023777,
0.04081346467137337,
0.0143617894500494,
0.0018854043446481228,
-0.012470540590584278,
-0.034242600202560425,
-0.020376021042466164,
-0.012906868942081928,
0.007670835591852665,
-0.03699076920747757,
0.0024224070366472006,
0.029246199876070023,
-0.06445880979299545,
0.0003857005503959954,
-0.003413659520447254,
0.04452449083328247,
-0.022841578349471092,
0.009521565400063992,
-0.010697738267481327,
0.014743741601705551,
0.03306657075881958,
0.02366115339100361,
0.0031589469872415066,
0.02002725377678871,
-0.04014457017183304,
0.005121716298162937,
0.0044191800989210606,
0.005444417707622051,
-0.010622861795127392,
-0.01996794156730175,
-0.03590182960033417,
0.014994124881923199,
0.003274385817348957,
-0.018876126036047935,
0.008003860712051392,
-0.04175915569067001,
-0.03906707838177681,
0.01428960170596838,
-0.013897571712732315,
0.0029125167056918144,
-0.026575226336717606,
-0.006296077277511358,
-0.007007031235843897,
0.04157935082912445,
-0.023432815447449684,
0.00649601174518466,
-0.04440193995833397,
-0.0224972702562809,
-0.007922378368675709,
-0.008092078380286694,
0.01675403118133545,
-0.0020690017845481634,
0.03198689594864845,
0.06750241667032242,
-0.03891010209918022,
-0.01386412512511015,
-0.07042992860078812,
-0.048397500067949295,
0.003523668274283409,
0.04651474207639694,
0.006943220272660255,
-0.019890476018190384,
0.0035859134513884783,
0.06474470347166061,
0.0321677103638649,
-0.09271707385778427,
-0.004564642906188965,
0.0020229010842740536,
-0.014220217242836952,
-0.03773879632353783,
0.015998009592294693,
0.022928308695554733,
0.03134296089410782,
0.02787655033171177,
0.03075570985674858,
0.04237140342593193,
0.011357631534337997,
0.0031013668049126863,
-0.030047329142689705,
-0.03168068081140518,
0.03779391571879387,
0.017177963629364967,
0.033735230565071106,
-0.0027099980507045984,
-0.0020610301289707422,
0.014733751304447651,
0.032393887639045715,
0.06146717444062233,
0.007606421131640673,
-0.024550121277570724,
0.03361843526363373,
0.011269581504166126,
0.049224019050598145,
-0.014513490721583366,
0.01295461505651474,
-0.04141148924827576,
0.024830419570207596,
0.02986525185406208,
0.03204945847392082,
0.03474650904536247,
-0.009333214722573757,
0.0070593878626823425,
0.03020976297557354,
0.05581005662679672,
-0.06986439973115921,
-0.04257503151893616,
0.023044774308800697,
0.0089799789711833,
0.004078878555446863,
-0.01636120304465294,
0.022521894425153732,
0.016889195889234543,
0.012433764524757862,
0.02408679947257042,
0.030044417828321457,
-0.007863657549023628,
0.024199344217777252,
-0.08354812115430832,
-0.0028552948497235775,
0.010099959559738636,
0.03789781779050827,
-0.026105528697371483,
0.0691804364323616,
0.018493421375751495,
0.004872848745435476,
-0.023784345015883446,
0.0009077927679754794,
-0.07253195345401764,
0.04602854698896408,
-0.029290247708559036,
-0.0010777342831715941,
-0.033577512949705124,
-0.03290268033742905,
-0.008714734576642513,
-0.019684376195073128,
-0.029871243983507156,
0.011857843957841396,
-0.028020769357681274,
-0.06592300534248352,
0.018145935609936714,
-0.030580300837755203,
0.01450119074434042,
-0.0133836530148983,
0.03516004607081413,
0.0363168939948082,
0.015457335859537125,
-0.002364163985475898,
-0.002794903004541993,
-0.04112222418189049,
0.015551384538412094,
-0.03596347197890282,
0.02053963951766491,
0.039798662066459656,
0.015543698333203793,
0.038277022540569305,
0.02056206576526165,
0.016273031011223793,
0.013539309613406658,
-0.029019175097346306,
0.04914124682545662,
-0.014032038860023022,
0.008357755839824677,
-0.006731591187417507,
-0.08120597898960114,
-0.009346626698970795,
0.023009171709418297,
0.04270348697900772,
-0.04487984627485275,
0.050466421991586685,
-0.038595959544181824,
0.006094453390687704,
-0.007846647873520851,
0.06026138365268707,
0.07996247708797455,
0.008199716918170452,
-0.025495462119579315,
-0.05466476455330849,
-0.043118156492710114,
0.00967408251017332,
0.023756464943289757,
0.039536502212285995,
-0.00690980302169919,
-0.011991927400231361,
-0.018840275704860687,
-0.0034375544637441635,
0.047492653131484985,
-0.0296059288084507,
0.00809035450220108,
-0.052158161997795105,
0.0383855402469635,
-0.03171711042523384,
0.011667133308947086,
-0.021010294556617737,
0.03626549616456032,
0.027275849133729935,
-0.005713540595024824,
0.019412804394960403,
-0.08899779617786407,
0.02346235327422619,
0.036419037729501724,
0.06513311713933945,
-0.01716841198503971,
-0.05033925175666809,
-0.039240557700395584,
-0.01037681382149458,
0.048929985612630844,
-0.02651810273528099,
0.048567768186330795,
-0.0064593227580189705,
0.012499343603849411,
-0.0015627540415152907,
-0.013923771679401398,
-0.0006647451082244515,
0.012889044359326363,
-0.02104025147855282,
-0.0035170726478099823,
-0.0007878665346652269,
-0.015615710988640785,
-0.016792520880699158,
-0.0034977300092577934,
0.011536716483533382,
0.01603134535253048,
-0.017213089391589165,
-0.001195068471133709,
0.021755779162049294,
0.0041434671729803085,
0.0006929882219992578,
-0.06734974682331085,
0.0021964991465210915,
0.010235963389277458,
-0.02705324813723564,
0.04574958235025406,
-0.011710246093571186,
0.003092947881668806,
0.044728003442287445,
-0.012926007620990276,
-0.011846628971397877,
-0.0016235384391620755,
-0.03826095163822174,
-0.0018991485703736544,
-0.002127521438524127,
0.023337043821811676,
0.027507739141583443,
0.003689644392579794,
-0.011349214240908623,
-0.02276826836168766,
-0.025915609672665596,
-0.01977360062301159,
-0.03437681496143341,
0.016478965058922768,
-0.010914932936429977,
0.004751742817461491,
-0.042503420263528824,
0.057799726724624634,
-0.005378146655857563,
0.01414584368467331,
0.007913317531347275,
-0.0007200708496384323,
-0.040938958525657654,
-0.002604139968752861,
-0.00042391917668282986,
-0.0044207097962498665,
-0.0038027779664844275,
0.02315262146294117,
0.009010165929794312,
-0.012089117430150509,
0.029220160096883774,
-0.03666166961193085,
-0.005307293031364679,
0.026040121912956238,
-0.017435045912861824,
0.03576518967747688,
0.00034935312578454614,
-0.02800016477704048,
0.015532806515693665,
-0.035876840353012085,
0.010700047016143799,
0.004388135392218828,
-0.011060267686843872,
0.01896667666733265,
-0.07506800442934036,
-0.017169449478387833,
0.07348866760730743,
-0.03604492172598839,
-0.0299665704369545,
-0.047719649970531464,
0.030908145010471344,
0.012111339718103409,
0.00191895617172122,
-0.07244841009378433,
-0.08737482875585556,
0.05107347294688225,
0.05035695061087608,
-0.030856788158416748,
-0.03627621382474899,
-0.03666917607188225,
0.008655893616378307,
0.0016431472031399608,
0.021152310073375702,
0.07428807765245438,
-0.07246442139148712,
-0.019170014187693596,
0.03595145419239998,
-0.019702672958374023,
0.029964040964841843,
0.010097021237015724,
-0.025672994554042816,
0.013448495417833328,
-0.03959216549992561,
0.03543706610798836,
0.01749269664287567,
0.013903947547078133,
-0.018819209188222885,
-0.022289810702204704,
-0.010027488693594933,
0.007837606593966484,
0.03570321574807167,
-0.03195895627140999,
-0.011384096927940845,
-0.012791440822184086,
-0.011368266306817532,
-0.03297077864408493,
-0.01714061014354229,
0.02451951429247856,
-0.017200808972120285,
0.010834033600986004,
-0.030665060505270958,
-0.007760584354400635,
-0.010510193184018135,
-0.04447243735194206,
-0.002270509023219347,
0.03053172305226326,
-0.006952252238988876,
-0.006826472468674183,
0.05198202654719353,
-0.008238032460212708,
-0.0316426120698452,
0.03313691169023514,
-0.016862090677022934,
0.06623850017786026,
-0.018428515642881393,
-0.00799570418894291,
0.026957595720887184,
-0.00273976381868124,
-0.014147554524242878,
-0.05318547785282135,
0.004138810560107231,
0.01844494789838791,
0.03958830609917641,
0.03155943751335144,
0.01573251374065876,
0.008126736618578434,
-0.0000651201480650343,
-0.018670443445444107,
-0.03468308597803116,
0.0059584686532616615,
0.038129016757011414,
0.020016983151435852,
0.05841265991330147,
-0.026194369420409203,
0.009834984317421913,
0.020396681502461433,
0.0498279333114624,
-0.013564818538725376,
-0.03461041674017906,
0.056997157633304596,
0.02043112926185131,
0.016300398856401443,
0.0025247724261134863,
-0.06336212158203125,
0.042962245643138885,
-0.04070685803890228,
0.04924066737294197,
0.01188557781279087,
-0.06075113266706467,
0.03828111290931702,
0.002305969363078475,
0.04891958087682724,
-0.0782279297709465,
-0.05024782940745354,
-0.021493498235940933,
0.00018318399088457227,
0.016984516754746437,
0.033957984298467636,
-0.02337954193353653,
-0.000621657760348171,
0.0498436838388443,
-0.007702741771936417,
0.022356819361448288,
-0.003648242447525263,
-0.04831109195947647,
-0.0052924370393157005,
-0.003046787343919277,
-0.024349676445126534,
0.018686724826693535,
-0.038203172385692596,
-0.0005183823523111641,
0.0026205801405012608,
-0.0272869560867548,
0.057136375457048416,
0.023275746032595634,
0.007415405008941889,
-0.006505146156996489,
0.03783869743347168,
-0.019173618406057358,
0.042423833161592484,
-0.004177923314273357,
0.008003512397408485,
0.13474401831626892,
0.023421388119459152,
-0.00017188173660542816,
-0.07378683984279633,
0.011503234505653381,
-0.005089026875793934,
0.01710563898086548,
0.0002840880770236254,
-0.0013174045598134398,
0.0006962668267078698,
0.0010701494757086039,
-0.00804198533296585,
0.03505038842558861,
0.010252583771944046,
-0.010385311208665371,
0.06416656076908112,
-0.03823811933398247,
-0.038499657064676285,
-0.006439098622649908,
-0.02232392132282257,
-0.05381253734230995,
0.00017051296890713274,
-0.04441823810338974,
0.029734153300523758,
0.02829318307340145,
0.017525920644402504,
-0.005964931100606918,
-0.010575122199952602,
0.03047032654285431,
0.061509665101766586,
-0.021677907556295395,
-0.002914021722972393,
-0.012378119863569736,
-0.0076869456097483635,
-0.019045861437916756,
0.027154725044965744,
0.059814948588609695,
0.005302106961607933,
-0.012841650284826756,
0.036101676523685455,
0.042681384831666946,
0.03526441380381584,
0.000965696235653013,
0.027635857462882996,
-0.03451300412416458,
0.0031013276893645525,
-0.008740789256989956,
0.023686764761805534,
-0.004902465734630823,
-0.030230266973376274,
-0.0007512009469792247,
0.00923180766403675,
0.0642554834485054,
-0.037582311779260635,
-0.036792345345020294,
-0.020065035670995712,
0.00975389126688242,
0.00790560245513916,
-0.014385215938091278,
0.002330282237380743,
0.04144112393260002,
0.012053280137479305,
0.009475874714553356,
-0.021238623186945915,
0.02874637581408024,
-0.0014293920248746872,
-0.02325991354882717,
0.0004124738334212452,
0.02677212655544281,
-0.015418966300785542,
-0.042054783552885056,
0.0006418908596970141,
-0.0428355447947979,
-0.033455900847911835,
0.024965764954686165,
0.06780413538217545,
0.056019145995378494,
0.012724547646939754,
0.004443759098649025,
-0.023139018565416336,
-0.02570568583905697,
0.04876099154353142,
-0.016246385872364044,
-0.023798832669854164,
0.013658887706696987,
-0.02045474201440811,
0.019901398569345474,
0.019181540235877037,
-0.030216814950108528,
-0.02177257463335991,
-0.00024672667495906353,
0.028427379205822945,
0.015463418327271938,
-0.02168641798198223,
-0.022592682391405106,
0.00963672623038292,
-0.06638212502002716,
-0.003569340333342552,
0.010862748138606548,
0.029004869982600212,
-0.012795062735676765,
-0.020838111639022827,
-0.009086323902010918,
0.0008398044155910611,
0.0032779749017208815,
-0.01036873646080494,
0.02866201288998127,
-0.0016980802174657583,
-0.027311932295560837,
0.014697450213134289,
-0.021210219711065292,
-0.04215564951300621,
-0.03399312496185303,
-0.033986303955316544,
-0.010070408694446087,
0.00001521105514257215,
0.023777417838573456,
0.007177583873271942,
-0.014212706126272678,
-0.030864529311656952,
-0.014864535070955753,
-0.004022905603051186,
0.013001264072954655,
-0.06397397816181183,
-0.015034032054245472,
-0.03539295867085457,
0.008038200438022614,
0.009304116480052471,
0.027950823307037354,
-0.03180471807718277,
-0.009421410970389843,
0.015723107382655144,
0.04374479129910469,
-0.03475652635097504,
-0.02397931180894375,
0.019797630608081818,
0.02354694902896881,
0.020693153142929077,
-0.025499114766716957,
-0.026514165103435516,
0.03342481702566147,
-0.03973755985498428,
-0.024910109117627144,
-0.011326035484671593,
-0.039557695388793945,
0.015137896873056889,
0.030679157003760338,
-0.023918379098176956,
-0.0033928377088159323,
0.0677606537938118,
-0.00878210924565792,
-0.013085059821605682,
0.017735913395881653,
-0.051058776676654816,
-0.035618431866168976,
-0.0060829841531813145,
-0.028395753353834152,
-0.01023791916668415,
0.014944767579436302,
0.04217914119362831,
0.008591790683567524,
-0.0258040614426136,
0.029968226328492165,
-0.025222767144441605,
0.009416713379323483,
0.0263002160936594,
-0.007261733524501324,
-0.007790022529661655,
-0.03958272561430931,
0.01034923829138279,
-0.02781054936349392,
0.03559349104762077,
0.0673094391822815,
0.04046595096588135,
-0.09811384975910187,
0.01757013611495495,
0.03015000931918621,
-0.04055827111005783,
0.017837628722190857,
-0.049801722168922424,
0.019313568249344826,
-0.008731859736144543,
-0.10322396457195282,
-0.03579820692539215,
-0.055112455040216446,
-0.026339825242757797,
-0.033084530383348465,
-0.006341326050460339,
-0.02238168753683567,
0.018795445561408997,
-0.021124210208654404,
0.048195019364356995,
0.030422305688261986,
-0.0342930406332016,
-0.006920395884662867,
-0.02592301368713379,
-0.01236919779330492,
0.04095340892672539,
0.014154946431517601,
0.007581888698041439,
0.04754488542675972,
-0.06140048801898956,
-0.016948813572525978,
0.015308027155697346,
-0.00935266725718975,
0.01359192281961441,
-0.012248366139829159,
0.03023490682244301,
-0.025732623413205147,
0.018298782408237457,
-0.0518505834043026,
-0.02443581260740757,
-0.004346570931375027,
0.0459413044154644,
0.05148569867014885,
0.04573005437850952,
0.005666655953973532,
-0.007747164461761713,
-0.01261143572628498,
-0.0022616786882281303,
-0.0035764561034739017,
0.013395335525274277,
-0.0010750116780400276,
-0.014351923950016499,
-0.03877044469118118,
0.05453023687005043,
-0.001842646161094308,
-0.02856067568063736,
-0.03585527464747429,
-0.017658254131674767,
0.017571689561009407,
0.039386942982673645,
-0.008510956540703773,
0.005024968646466732,
0.03342289850115776,
-0.01548825018107891,
-0.018257489427924156,
0.005438470747321844,
-0.012580715119838715,
-0.01214560866355896,
-0.043518684804439545,
-0.022721627727150917,
0.0008843557443469763,
0.04563827067613602,
-0.0016596540808677673,
-0.040590450167655945,
-0.014197081327438354,
0.04722972959280014,
0.00005682578557753004,
0.03533913567662239,
-0.0008892857003957033,
-0.062479160726070404,
0.02425978146493435,
-0.024375809356570244,
0.012686329893767834,
-0.012697308324277401,
0.038827430456876755,
-0.0350629985332489,
-0.019811807200312614,
0.05179273709654808,
0.020309753715991974,
0.06680469214916229,
-0.02565094456076622,
-0.039711061865091324,
-0.020758090540766716,
-0.013833446428179741,
-0.019699236378073692,
0.008193344809114933,
-0.0045754979364573956,
-0.0025806135963648558,
-0.027972251176834106,
0.031360071152448654,
0.011592281050980091,
-0.032948099076747894,
0.019855253398418427,
0.04122983291745186,
-0.02424437180161476,
-0.024399107322096825,
-0.013343959115445614,
-0.05065806582570076,
0.04074258357286453,
-0.016915999352931976,
0.023866787552833557,
0.08541993796825409,
0.045467786490917206,
-0.004918558057397604,
0.03633705899119377,
-0.004809749778360128,
-0.04489080235362053,
0.04578143358230591,
-0.004353557713329792,
-0.002206702483817935,
0.028904074802994728,
-0.02994801104068756,
0.030434388667345047,
-0.028783701360225677,
0.01498385425657034,
0.006297334097325802,
-0.024118904024362564,
-0.005958595313131809,
0.06598909944295883,
0.013216355815529823,
0.07192078977823257,
-0.006096236407756805,
0.02143273502588272,
-0.00867832638323307,
0.09301280230283737,
-0.027548305690288544,
0.03823485225439072,
0.036426037549972534,
0.029834089800715446,
-0.01318985316902399,
0.03971248120069504,
-0.011908715590834618,
0.019086744636297226,
0.024814434349536896,
0.05629071965813637,
-0.007361045107245445,
0.03273691609501839,
0.03858849033713341,
-0.010749109089374542,
0.08112440258264542,
0.005074885208159685,
-0.013587354682385921,
0.05649104341864586,
-0.04829416796565056,
0.005739287007600069,
-0.04697943106293678,
-0.0015387822641059756,
-0.030090557411313057,
0.022066915407776833,
-0.011592173017561436,
0.013705054298043251,
-0.007407667115330696,
-0.0503838025033474,
-0.024105170741677284,
-0.004817167762666941,
0.012077676132321358,
-0.032144442200660706,
0.014586455188691616,
-0.0006926796049810946,
-0.006926083005964756,
0.0005731828277930617,
-0.025842998176813126,
-0.02916092798113823,
-0.03211740776896477,
0.00020143052097409964,
0.01871894858777523,
0.03177165612578392,
0.0011736004380509257,
-0.005343744996935129,
-0.005226215813308954,
0.05399639159440994,
-0.025529183447360992,
-0.042307183146476746,
0.0009356689406558871,
0.01314569916576147,
-0.027440140023827553,
0.0006903625326231122
] |
<p>From the question "<a href="http://physics.stackexchange.com/questions/79152/why-is-the-absolute-zero-273-15">Why is the absolute zero -273.15ºC?</a>" I understood that 1°C is the 100th part of the difference of melting and boiling temperature of water (this is my high school physics, maybe there is a more accurate definition). So we linked the value of 1°C to a physical quantity.</p>
<p>Then we measure another physical quantity (the absolute zero) and it turns out this is exactly 273.15°C less the melting temperature of water. So how come those two quantities have a rational ratio?</p>
<p>If we look at other constants (gravitational, <a href="http://en.wikipedia.org/wiki/Planck_length" rel="nofollow">Planck</a> or whatever) they all are irrational, aren't they?</p>
<p>What did I miss? Is it because the melting point of water is not exactly 0°C (maybe something really close to 0 like 0.000565...)?</p>
| 8,257 |
[
0.008580080233514309,
-0.046731170266866684,
0.0034073188435286283,
-0.0217746589332819,
0.007282280828803778,
0.018919894471764565,
-0.030528217554092407,
-0.00479107303544879,
-0.03779851272702217,
-0.010550406761467457,
0.048884183168411255,
0.0510624460875988,
0.028399454429745674,
0.02649279497563839,
0.03569855913519859,
-0.004935798235237598,
-0.002454515313729644,
-0.029088960960507393,
0.005927823483943939,
-0.023541266098618507,
0.04337485879659653,
0.028367742896080017,
-0.003769747680053115,
-0.014476737007498741,
0.0010888357646763325,
-0.00654281210154295,
0.041481100022792816,
0.026918496936559677,
0.05438166856765747,
0.04352458193898201,
0.0010327112395316362,
-0.04840538650751114,
0.02646268531680107,
-0.010002406314015388,
0.02836897037923336,
0.02456362545490265,
0.022430211305618286,
0.003441308857873082,
-0.03337652608752251,
0.016147689893841743,
-0.03331771120429039,
-0.02815472148358822,
-0.02209567092359066,
0.01979585364460945,
-0.012311967089772224,
-0.011317434720695019,
0.046256449073553085,
-0.05379893630743027,
0.03720758110284805,
-0.07469045370817184,
0.032236985862255096,
0.03571876138448715,
0.028706109151244164,
0.03763791173696518,
0.020472880452871323,
0.0027457084506750107,
0.10075986385345459,
0.05008022487163544,
-0.04985196515917778,
-0.08085561543703079,
-0.029044391587376595,
-0.023001905530691147,
0.0018648543627932668,
0.02800809033215046,
0.010166610591113567,
0.047926709055900574,
0.009913593530654907,
-0.026111075654625893,
0.03476811200380325,
-0.022798702120780945,
0.03484839200973511,
0.030283883213996887,
0.02238079532980919,
-0.007375061046332121,
0.031163526698946953,
-0.04388382285833359,
0.012669279240071774,
0.03132542595267296,
0.042679015547037125,
0.0826234295964241,
-0.03876008465886116,
0.009924281388521194,
0.04152403771877289,
0.02600703202188015,
0.015378020703792572,
-0.0008923925925046206,
0.0376141183078289,
-0.04400055482983589,
0.02559327892959118,
0.057004861533641815,
-0.01240329910069704,
0.010823455639183521,
0.010655120015144348,
0.033194322139024734,
-0.007184523623436689,
0.010370980948209763,
0.010139544494450092,
0.049145735800266266,
-0.007692746352404356,
-0.021646462380886078,
0.017189284786581993,
0.010677351616322994,
0.03156832233071327,
0.04057818278670311,
-0.003370631253346801,
-0.013217759318649769,
-0.03980541229248047,
0.01374849397689104,
-0.026667438447475433,
-0.023631151765584946,
-0.011568319983780384,
0.02167080156505108,
0.01508372463285923,
-0.00417930306866765,
0.009393647313117981,
-0.05254917964339256,
-0.0007700080168433487,
-0.04937109351158142,
0.055484551936388016,
0.02881637215614319,
0.016156649217009544,
0.0017584452871233225,
0.01945391297340393,
-0.009898735210299492,
-0.035152893513441086,
0.014294954016804695,
-0.003293860936537385,
0.0006015226244926453,
-0.02030358463525772,
0.0019827084615826607,
-0.044915974140167236,
0.0024460921995341778,
0.009650607593357563,
-0.01714525744318962,
0.07188987731933594,
-0.01764937862753868,
-0.07785562425851822,
-0.06293369084596634,
0.06048697978258133,
0.015139669179916382,
-0.03269197791814804,
-0.1069064661860466,
0.04672418534755707,
0.021920867264270782,
0.055851180106401443,
0.04632537066936493,
0.022110115736722946,
-0.035893697291612625,
-0.0196676068007946,
0.056388869881629944,
-0.0029332332778722048,
-0.013045127503573895,
0.02209068089723587,
-0.03931325301527977,
-0.0014000401133671403,
-0.04538353160023689,
0.02279389277100563,
0.05026767775416374,
0.006003167945891619,
0.006433101370930672,
0.0231081061065197,
-0.015166856348514557,
-0.03902722895145416,
0.03712129220366478,
-0.013605375774204731,
-0.008955264464020729,
0.09300963580608368,
-0.017295217141509056,
-0.03437922149896622,
0.01416768878698349,
-0.004523167386651039,
0.01908836141228676,
0.02317153662443161,
0.022591523826122284,
0.045102156698703766,
-0.01657227985560894,
0.0060417549684643745,
-0.053833696991205215,
0.015408491715788841,
0.0304704699665308,
-0.05188393592834473,
-0.034526001662015915,
0.005431957542896271,
0.01673031598329544,
-0.0022819063160568476,
0.04698706045746803,
-0.024613216519355774,
-0.010432387702167034,
0.027431046590209007,
-0.02302822470664978,
0.004608214367181063,
-0.04394114762544632,
0.008275642991065979,
0.03290557116270065,
0.005309644155204296,
0.008918890729546547,
0.012788028456270695,
-0.008454867638647556,
-0.03754832595586777,
-0.020076550543308258,
0.039173562079668045,
0.022933071479201317,
0.02598361112177372,
-0.02236899361014366,
0.020900053903460503,
0.06144334748387337,
0.03357914090156555,
-0.021854575723409653,
-0.006362294312566519,
-0.03452138975262642,
0.003965235780924559,
-0.006247055716812611,
-0.039911482483148575,
0.02736058086156845,
-0.014053190127015114,
-0.007567870430648327,
0.011959358118474483,
-0.0026801663916558027,
-0.014867846854031086,
0.040858831256628036,
-0.02254878357052803,
0.06194303557276726,
0.007456946652382612,
0.0045788949355483055,
0.013466021977365017,
0.0625082477927208,
0.027634840458631516,
0.0003673406026791781,
-0.015000094659626484,
-0.03452432528138161,
-0.05566698685288429,
0.0015266098780557513,
0.0420040488243103,
0.015131581574678421,
-0.018987365067005157,
0.006522740703076124,
0.014911663718521595,
0.07960231602191925,
0.016815582290291786,
0.007320585660636425,
-0.006208140403032303,
0.0034673232585191727,
-0.01856537163257599,
-0.014505511149764061,
-0.004030813928693533,
0.014871854335069656,
0.016463395208120346,
-0.0031413626857101917,
0.020798470824956894,
-0.0178684014827013,
-0.02557130716741085,
0.06063322722911835,
-0.009666568599641323,
0.036317288875579834,
0.01917136088013649,
-0.007351910695433617,
-0.0025636041536927223,
-0.04624127224087715,
0.011936167255043983,
-0.007437851745635271,
-0.008907628245651722,
-0.030661066994071007,
-0.05247080326080322,
-0.016929317265748978,
-0.0065110838040709496,
0.020087622106075287,
-0.04482659697532654,
0.0020192794036120176,
0.010407942347228527,
-0.03707991540431976,
-0.03711092844605446,
-0.03601996973156929,
-0.0004766829952131957,
-0.008658160455524921,
0.01354896742850542,
0.03507349640130997,
0.03253915533423424,
0.023917756974697113,
-0.05682539939880371,
-0.02624720148742199,
-0.0019106573890894651,
-0.09475672990083694,
-0.015787634998559952,
-0.01096905954182148,
-0.02046242170035839,
0.003758385544642806,
0.018156692385673523,
-0.014451336115598679,
0.000572374789044261,
-0.006448240950703621,
0.04503440484404564,
-0.003534835297614336,
-0.018457874655723572,
-0.015092186629772186,
-0.002305894158780575,
-0.04306607320904732,
0.0028020257595926523,
-0.0080289700999856,
0.011691492050886154,
0.05603206157684326,
-0.046632420271635056,
-0.031335312873125076,
0.00010779684089357033,
-0.03259165212512016,
-0.027262292802333832,
0.009889420121908188,
-0.010843019932508469,
-0.0020169243216514587,
-0.00854648370295763,
-0.037462182343006134,
0.03415030241012573,
-0.0587405227124691,
0.0003683379618450999,
-0.04375539347529411,
-0.08613570779561996,
0.012380464933812618,
-0.0016754820244386792,
0.050907380878925323,
0.010029017925262451,
-0.01635422557592392,
0.03374578058719635,
0.022721685469150543,
-0.043564923107624054,
-0.057036709040403366,
0.017815833911299706,
0.0015837334794923663,
-0.009088504128158092,
0.006998274475336075,
0.059970710426568985,
0.0008286814554594457,
0.01743239536881447,
0.03140230476856232,
0.07189314067363739,
0.013707934878766537,
-0.002172314329072833,
0.0022738927509635687,
-0.020316755399107933,
0.011883718892931938,
0.000021731937522417866,
0.0314098559319973,
0.018911555409431458,
-0.006421681959182024,
0.028568558394908905,
-0.019541103392839432,
0.057036351412534714,
0.02372458204627037,
-0.03367430344223976,
0.024088498204946518,
-0.0018245140090584755,
0.041527315974235535,
-0.0400422140955925,
0.04519525542855263,
-0.02633015811443329,
-0.018343202769756317,
0.014967198483645916,
0.030783485621213913,
0.021144744008779526,
-0.03734457120299339,
-0.019844098016619682,
0.028746023774147034,
0.05676211416721344,
-0.034009899944067,
-0.008823089301586151,
-0.0001611600018804893,
-0.006516033783555031,
0.0017125073354691267,
-0.02940714731812477,
-0.017683204263448715,
0.03869202360510826,
0.01880321279168129,
0.05818663910031319,
0.0016835632268339396,
-0.0629165917634964,
-0.017146343365311623,
-0.059808943420648575,
-0.04840655252337456,
-0.007678042631596327,
0.04625733569264412,
-0.017380917444825172,
0.06960109621286392,
0.03321125730872154,
0.028329091146588326,
0.0029649054631590843,
0.004312589764595032,
-0.09211403876543045,
0.02395820990204811,
-0.07350466400384903,
-0.04226749390363693,
-0.008175145834684372,
-0.019403740763664246,
-0.005546430591493845,
-0.015371440909802914,
-0.027190925553441048,
0.008265428245067596,
-0.007771081291139126,
-0.05607050657272339,
-0.006659321486949921,
-0.01681102253496647,
-0.025858653709292412,
-0.03827566280961037,
0.0027168639935553074,
0.041275136172771454,
-0.03953969106078148,
0.016840949654579163,
0.03951818123459816,
0.016316762194037437,
-0.01872229389846325,
-0.013836347497999668,
0.022743437439203262,
0.043633680790662766,
0.03765649348497391,
0.02911343239247799,
-0.007593953050673008,
-0.028972169384360313,
0.01655527390539646,
0.024429619312286377,
0.047976743429899216,
0.02601221762597561,
-0.01887492649257183,
-0.024248069152235985,
-0.04068775102496147,
0.018449822440743446,
-0.054168086498975754,
0.03175532445311546,
-0.0367567203938961,
0.00010376954742241651,
0.02703765593469143,
-0.01895003765821457,
0.0018335687927901745,
0.050099581480026245,
0.05680816248059273,
-0.013962655328214169,
-0.0212705098092556,
-0.03607636317610741,
-0.011547941714525223,
-0.04280507564544678,
0.016179518774151802,
0.031498782336711884,
0.019645776599645615,
0.004071512725204229,
-0.018318265676498413,
0.03814471513032913,
-0.01655038632452488,
-0.014164152555167675,
0.021321218460798264,
0.011553769931197166,
0.033908504992723465,
-0.04227185249328613,
-0.015795737504959106,
-0.02210669219493866,
0.011069457978010178,
0.04728442057967186,
-0.01615876331925392,
-0.03220546990633011,
-0.08413327485322952,
0.021104497835040092,
-0.003979216795414686,
0.06217876821756363,
0.001662298571318388,
0.013158558867871761,
-0.03725237771868706,
-0.013736301101744175,
0.04179961234331131,
-0.03329673036932945,
0.05283195152878761,
-0.013704986311495304,
0.01660153828561306,
-0.024619726464152336,
-0.010384646244347095,
0.007767852861434221,
0.017737768590450287,
0.01833920180797577,
0.035583291202783585,
-0.017947817221283913,
0.0008879650849848986,
-0.00012218723713885993,
0.025065138936042786,
0.013462519273161888,
0.029519928619265556,
-0.015001105144619942,
-0.004537578672170639,
0.04134877026081085,
-0.01689780503511429,
-0.012351014651358128,
-0.07206496596336365,
0.0011191292433068156,
-0.033441584557294846,
0.013694338500499725,
0.01565507799386978,
-0.03637943044304848,
-0.04695241153240204,
0.02421146258711815,
0.012687133625149727,
-0.017330609261989594,
0.0008639204897917807,
-0.03878815099596977,
0.03125868737697601,
0.018553156405687332,
-0.01357088889926672,
0.011837041936814785,
0.04959144443273544,
-0.018253037706017494,
0.015944845974445343,
-0.05033767223358154,
0.015447515994310379,
-0.019602959975600243,
-0.007039293181151152,
-0.014162711799144745,
-0.011032691225409508,
-0.06869221478700638,
0.03148966282606125,
0.008775724098086357,
0.005541605409234762,
-0.04489903151988983,
-0.04237024113535881,
-0.02872559055685997,
-0.015958817675709724,
0.015853380784392357,
0.025726070627570152,
0.019845832139253616,
0.03558224439620972,
-0.0050402916967868805,
-0.0320107564330101,
0.013088569045066833,
-0.010801544412970543,
-0.007692994084209204,
0.04827083274722099,
0.00716455327346921,
0.04746120050549507,
0.02045055478811264,
-0.010084068402647972,
0.005482457112520933,
-0.051984887570142746,
-0.000027018362743547186,
-0.04108783230185509,
0.0031183366663753986,
0.014345085248351097,
-0.013691249303519726,
-0.02600730024278164,
-0.015754366293549538,
0.005474231205880642,
0.05689176917076111,
-0.07351859658956528,
0.03277498483657837,
0.03966384381055832,
0.028605710715055466,
-0.06558781117200851,
-0.046844858676195145,
0.04002590849995613,
0.018360711634159088,
-0.03378790616989136,
-0.01904664747416973,
-0.004263347014784813,
-0.002309803618118167,
0.008126365952193737,
0.014022397808730602,
0.045967794954776764,
-0.017748575657606125,
-0.04370077699422836,
-0.011078108102083206,
0.03442408889532089,
0.05192060023546219,
-0.027505747973918915,
-0.033033039420843124,
0.003696588333696127,
-0.0016115730395540595,
-0.046184178441762924,
0.036870554089546204,
0.07999458909034729,
-0.04055196791887283,
-0.04525143653154373,
-0.00827767699956894,
-0.04607219249010086,
-0.011497375555336475,
0.01321045495569706,
-0.03225185349583626,
0.01443821843713522,
0.019829047843813896,
-0.0029446566477417946,
-0.029356401413679123,
0.03218900039792061,
0.03985440358519554,
0.0018637815956026316,
-0.013070201501250267,
0.0162997767329216,
-0.025776272639632225,
-0.056143466383218765,
0.0039233798161149025,
0.023409251123666763,
0.010195327922701836,
-0.0024819080717861652,
0.06785701960325241,
-0.0022805514745414257,
-0.02684655785560608,
0.024300508201122284,
-0.0315319299697876,
0.03341370448470116,
0.04492790251970291,
-0.0050321053713560104,
-0.03409487009048462,
0.01810396835207939,
-0.005717164371162653,
-0.018269333988428116,
-0.06395713984966278,
0.02254483476281166,
0.032575879245996475,
0.006028318777680397,
0.04202590882778168,
-0.00001953081118699629,
-0.01945309527218342,
0.008151538670063019,
-0.004751552827656269,
-0.03035159409046173,
0.021972276270389557,
-0.009673677384853363,
0.015459775924682617,
-0.03418350592255592,
0.0027434234507381916,
0.03144702687859535,
0.06392744183540344,
-0.015986977145075798,
-0.004214765504002571,
0.034783218055963516,
0.046513140201568604,
-0.02200641855597496,
0.024152884259819984,
-0.01330194529145956,
0.05348612740635872,
-0.008213558234274387,
0.009818678721785545,
0.005570051725953817,
-0.02248634211719036,
0.02223963290452957,
-0.02412654459476471,
0.006268633529543877,
-0.06732333451509476,
-0.036902885884046555,
-0.01928151771426201,
0.02214440517127514,
0.02423371747136116,
0.05271514132618904,
0.0116960434243083,
0.007072712294757366,
0.003341089701279998,
0.026203185319900513,
0.011233272962272167,
0.019442696124315262,
-0.03766244649887085,
-0.014721381478011608,
-0.05317861586809158,
-0.06099768728017807,
0.033206138759851456,
0.0006330896867439151,
-0.0660911500453949,
0.03874272108078003,
-0.04540161415934563,
0.02044663392007351,
0.001146998954936862,
0.0064341723918914795,
-0.04193530231714249,
0.015316156670451164,
0.03274577111005783,
0.0010449474211782217,
-0.038938257843256,
0.005077849142253399,
0.11395853757858276,
0.06736113876104355,
-0.0045943958684802055,
-0.05872320756316185,
0.025044554844498634,
0.01289571076631546,
0.027094615623354912,
-0.03589523211121559,
0.008499384857714176,
-0.020849699154496193,
0.05913533642888069,
0.040428947657346725,
0.04781030863523483,
0.02438269555568695,
-0.005363063886761665,
0.017575740814208984,
-0.022488921880722046,
-0.02549234963953495,
0.020189912989735603,
0.03718823194503784,
-0.008460146375000477,
-0.01039233710616827,
-0.022786343470215797,
0.04484621807932854,
-0.043190665543079376,
-0.016942264512181282,
-0.04485558718442917,
-0.0064750243909657,
0.02129233255982399,
-0.01515616662800312,
-0.05499269440770149,
0.04887048527598381,
0.0012988827656954527,
-0.01007941085845232,
-0.02000807598233223,
0.04598642885684967,
0.04780164733529091,
0.007468998432159424,
-0.03050992637872696,
0.01836334727704525,
0.033145513385534286,
-0.01715235598385334,
-0.010149200446903706,
0.01739673689007759,
-0.06284185498952866,
-0.00764734810218215,
-0.027353014796972275,
0.008621055632829666,
0.018179479986429214,
-0.005202110856771469,
-0.008745482191443443,
0.009216354228556156,
-0.04197516664862633,
-0.0270504429936409,
0.011615384370088577,
0.0190745759755373,
0.04079499840736389,
-0.010996903292834759,
-0.04538143053650856,
-0.007893940433859825,
0.023830337449908257,
-0.0095974775031209,
0.015147501602768898,
0.015545434318482876,
-0.001688772113993764,
-0.017490984871983528,
0.002386766718700528,
0.019484085962176323,
-0.02905283495783806,
-0.019873809069395065,
-0.0015771210892125964,
-0.007598267402499914,
-0.037431396543979645,
-0.0282849483191967,
-0.015482579357922077,
0.008500498719513416,
0.06995519995689392,
0.005610643420368433,
0.009700542315840721,
-0.005987037904560566,
-0.0033972705714404583,
0.019110441207885742,
-0.0022990896832197905,
-0.024785500019788742,
-0.01639823243021965,
-0.021965647116303444,
0.004716303199529648,
0.021278273314237595,
-0.05114803835749626,
-0.003882572753354907,
0.005013866815716028,
-0.003340694820508361,
0.007447860203683376,
0.00918773002922535,
0.014970021322369576,
0.0238198209553957,
-0.06381069123744965,
-0.014510429464280605,
0.0076638939790427685,
0.02457171119749546,
0.03993883356451988,
0.04167303442955017,
0.03093608096241951,
0.04021277651190758,
-0.028948437422513962,
0.021958505734801292,
0.04233721271157265,
-0.003907892853021622,
-0.018755726516246796,
0.023898160085082054,
-0.014332887716591358,
-0.04185853525996208,
-0.06422464549541473,
-0.010870235040783882,
0.04612566530704498,
-0.0014701440231874585,
0.024710271507501602,
-0.048276521265506744,
0.010362590663135052,
0.000389565946534276,
-0.0052044568583369255,
-0.06666058301925659,
-0.011772830970585346,
-0.08085117489099503,
-0.010698947124183178,
0.000557420717086643,
0.005784950219094753,
-0.0028171930462121964,
-0.009987695142626762,
-0.009047856554389,
-0.00745416758581996,
0.06772314012050629,
0.03965368494391441,
-0.00181311194319278,
-0.04311895743012428,
0.023236732929944992,
0.017393724992871284,
0.01877196691930294,
-0.06635777652263641,
-0.03625461831688881,
0.026768619194626808,
-0.05596279725432396,
-0.04197708144783974,
0.027901124209165573,
-0.011994556523859501,
-0.005203669890761375,
0.0391540564596653,
0.01046188548207283,
0.02365853264927864,
0.0603318028151989,
-0.003324730321764946,
0.03622080385684967,
-0.0036070893984287977,
-0.021299287676811218,
0.010834276676177979,
0.007257365621626377,
-0.020345112308859825,
0.0035835036542266607,
-0.009746428579092026,
0.05998934060335159,
0.04765433818101883,
-0.025658031925559044,
0.02771669812500477,
-0.007041045464575291,
-0.008385825902223587,
-0.02169903926551342,
0.025856683030724525,
0.017892615869641304,
0.0246841199696064,
0.006880831439048052,
-0.04386284947395325,
0.024985967203974724,
-0.020795656368136406,
0.03617012873291969,
-0.06909701973199844,
-0.007307957857847214,
-0.002449090126901865,
0.01868412084877491,
0.007764121983200312,
-0.010907516814768314,
-0.012516475282609463,
0.043173618614673615,
-0.0653626099228859,
-0.01503929402679205,
-0.04003997519612312,
-0.01763814687728882,
-0.02771964855492115,
0.01637260802090168,
-0.013031739741563797,
0.02290533110499382,
0.03459359332919121,
0.007585003040730953,
0.012298805639147758,
-0.00793076679110527,
-0.003244500607252121,
-0.04075610637664795,
-0.009906301274895668,
0.014260023832321167,
-0.026283053681254387,
-0.03171682730317116,
0.03752011060714722,
0.0019505404634401202,
-0.021842854097485542,
0.023880930617451668,
-0.05429983511567116,
-0.008075667545199394,
0.014463935047388077,
0.05665040388703346,
0.016377294436097145,
0.04628903046250343,
-0.007799570914357901,
-0.0025630665477365255,
-0.0421563982963562,
0.012780118733644485,
0.0488717146217823,
0.03241518512368202,
0.014300587587058544,
-0.0029754226561635733,
0.012732649222016335,
-0.036592237651348114,
-0.02669108845293522,
-0.006674840115010738,
-0.013875124976038933,
0.034216612577438354,
0.008022913709282875,
0.0299838874489069,
0.00696158641949296,
-0.03991727903485298,
0.008305083028972149,
-0.036501385271549225,
-0.014842589385807514,
0.06316135078668594,
0.0024090129882097244,
0.025563182309269905,
-0.023772520944476128,
0.0014518779935315251,
0.006895900703966618,
0.00005923322169110179,
0.01982671581208706,
-0.029471086338162422,
-0.040965400636196136,
-0.022097034379839897,
0.025691883638501167,
0.0005378288333304226,
0.0245394017547369,
-0.015417098067700863,
-0.0184894111007452,
0.04718751460313797,
0.015769632533192635,
0.008915314450860023,
-0.023958178237080574,
-0.02782564051449299,
-0.03970561549067497,
-0.07533702254295349,
0.03324161842465401,
-0.021543556824326515,
0.0252543855458498,
-0.03651091828942299,
-0.006308254320174456,
-0.039326924830675125,
0.013798731379210949,
0.03909270465373993,
0.0317852683365345,
0.008506005629897118,
0.001698311883956194,
-0.04026837274432182,
0.040210384875535965,
-0.05616418644785881,
0.007848847657442093,
-0.0065882569178938866,
-0.012167204171419144,
0.024142015725374222,
-0.00926627404987812,
-0.01777486689388752,
-0.008783933706581593,
0.01928684487938881,
-0.017855551093816757,
0.02294754609465599,
-0.003986832685768604,
-0.004548639990389347,
0.03746461868286133,
-0.011493007652461529,
-0.01010392140597105,
0.07567489892244339,
0.004551399499177933,
0.01930197887122631,
0.018771082162857056,
0.0044473763555288315,
-0.053678806871175766,
0.04022535681724548,
-0.0011731891427189112,
0.013873274438083172,
-0.0051501039415597916,
-0.007571088150143623,
0.026656562462449074,
-0.0297244843095541,
0.014437503181397915,
0.030974131077528,
-0.04201576113700867,
-0.018991690129041672,
0.009450362995266914,
-0.010820632800459862,
0.01863473653793335,
-0.005977672524750233,
0.06347797811031342,
0.009844073094427586,
-0.026482515037059784,
0.014620695263147354,
0.04173034429550171,
0.05463545396924019,
0.0007237959653139114,
0.04556502774357796,
0.041893117129802704,
0.006974183954298496,
0.0371895395219326,
0.01575419306755066,
0.023151153698563576,
-0.03391066938638687,
-0.014465762302279472,
0.02433558739721775,
-0.035002436488866806,
0.010524870827794075,
0.023838583379983902,
-0.0005952385254204273,
0.1046360656619072,
0.0027166602667421103,
0.01928049325942993,
-0.03859061375260353,
0.01704823225736618,
0.006374632008373737,
0.005560832563787699,
-0.005979579873383045,
0.011697102338075638,
-0.03940719738602638,
-0.0341244675219059,
-0.009947902522981167,
0.001952964230440557,
0.0077210464514791965,
-0.04005983844399452,
0.004720460623502731,
-0.020388664677739143,
-0.020183125510811806,
-0.0324893482029438,
-0.006563277915120125,
-0.03692395240068436,
-0.028548169881105423,
0.05337813124060631,
0.02280420809984207,
0.001264834078028798,
0.0073671904392540455,
-0.07096955180168152,
-0.01223838236182928,
0.04332930967211723,
-0.046726275235414505,
-0.03847226873040199,
0.024285176768898964,
0.025677483528852463,
-0.011344666592776775,
-0.06426508724689484
] |
<p>I am trying to find the moment of intia about its centre of a sector of a circle of radius $a$, mass $m$ and angle $\pi/3$. I have found the answer it is $\frac{1}{2}ma^2$ but originally tried a method that was unsuccessful and don't know why this is the case. This involved finding the moment of interia of elementry rods about the centre, length $a$ and width $a\;\delta\theta$, using $p$ as mass per unit area. I then tried to integrate the moment of inertia of these rods from $\theta=0$, to $\theta=\pi/3$. Which gave me an answer that did not lead to the correct result. Please can you explain why? I have shown my workings bellow but they are not very clear:
<img src="http://i.stack.imgur.com/Qs91b.jpg" alt="enter image description here"></p>
| 8,258 |
[
0.01165005099028349,
-0.005477009806782007,
-0.0331253707408905,
-0.026707934215664864,
0.0467991977930069,
-0.012757441028952599,
-0.06482367217540741,
-0.04955659434199333,
0.019709184765815735,
-0.022600699216127396,
0.05414627864956856,
0.035829607397317886,
0.069910429418087,
0.04572509974241257,
0.02481873333454132,
0.016160733997821808,
-0.007299480494111776,
-0.003582611447200179,
0.00034573214361444116,
-0.03562097251415253,
-0.010925676673650742,
0.0010523954406380653,
0.0007366198697127402,
-0.03126233071088791,
-0.027304671704769135,
0.013393555767834187,
0.011766606010496616,
-0.020859936252236366,
-0.009448133409023285,
0.07561038434505463,
-0.03999171406030655,
-0.011324006132781506,
0.023762786760926247,
0.0060178181156516075,
0.007802511099725962,
0.007519412320107222,
-0.012122880667448044,
-0.007050498854368925,
0.0035084679257124662,
0.08544676005840302,
-0.013885332271456718,
-0.019138120114803314,
0.01664615422487259,
0.013011051341891289,
-0.009644169360399246,
0.026437561959028244,
-0.03952745720744133,
-0.009093062952160835,
0.03648510202765465,
-0.052076298743486404,
0.09713134169578552,
0.017858417704701424,
0.04474017769098282,
0.05592591315507889,
-0.00315604149363935,
-0.02612137794494629,
0.04939078539609909,
0.0335373692214489,
-0.046150028705596924,
-0.03133663907647133,
-0.004452110733836889,
-0.016040854156017303,
0.004060134291648865,
-0.03604261949658394,
-0.012671512551605701,
-0.024900956079363823,
-0.012354067526757717,
-0.007722401525825262,
0.025787873193621635,
0.02071000635623932,
0.014005829580128193,
0.005446604918688536,
0.04406026378273964,
-0.016464564949274063,
-0.015936395153403282,
-0.030899105593562126,
0.02147899754345417,
0.020757053047418594,
0.04331878200173378,
0.017236215993762016,
0.010665260255336761,
0.029419129714369774,
0.046155307441949844,
0.02730131335556507,
0.015026275999844074,
0.0021876872051507235,
0.0687943696975708,
0.0013604057021439075,
-0.01293074432760477,
0.002027279930189252,
-0.01632721722126007,
0.003855764400213957,
0.01985054276883602,
-0.0045646862126886845,
0.02433650754392147,
0.05321114882826805,
0.0074408454820513725,
0.055833518505096436,
0.015040548518300056,
-0.015499981120228767,
0.02766621857881546,
-0.015907471999526024,
0.025954732671380043,
0.06487299501895905,
-0.011118165217339993,
-0.002913211937993765,
-0.018121447414159775,
0.011228865012526512,
-0.01758248545229435,
-0.03869707137346268,
-0.02179831452667713,
0.046351611614227295,
-0.004498593974858522,
0.003998864442110062,
0.000007445661594829289,
-0.006735160015523434,
-0.022853899747133255,
-0.011370974592864513,
0.04857378825545311,
0.006159341428428888,
0.028485655784606934,
-0.05125551298260689,
0.024842357262969017,
-0.055877555161714554,
-0.07254042476415634,
0.029372867196798325,
-0.0029743441846221685,
0.03232035040855408,
-0.05106063187122345,
0.013174161314964294,
0.01586083509027958,
-0.01798066310584545,
0.014722825959324837,
-0.00010736706462921575,
0.000565391790587455,
-0.030946310609579086,
-0.08340036123991013,
-0.05613354966044426,
0.03949891775846481,
0.005637968424707651,
-0.021249940618872643,
-0.07929790019989014,
-0.03459211066365242,
0.07144027203321457,
0.08990225940942764,
0.020034685730934143,
0.00247782445512712,
0.018112674355506897,
0.08658355474472046,
-0.011253814212977886,
-0.04979486018419266,
-0.026921261101961136,
-0.02547447569668293,
-0.01076776348054409,
-0.01764259859919548,
-0.059029195457696915,
0.017943624407052994,
0.01522384025156498,
0.01220926083624363,
-0.021534979343414307,
0.010026204399764538,
-0.009722254239022732,
0.03200623765587807,
0.003087404416874051,
-0.010457569733262062,
-0.030279630795121193,
0.07650907337665558,
0.012338646687567234,
-0.020778855308890343,
0.031521040946245193,
0.031563129276037216,
0.017336394637823105,
-0.022179601714015007,
0.01866954378783703,
0.0705818459391594,
-0.04294782131910324,
-0.0079739298671484,
-0.013060426339507103,
-0.0015754210762679577,
0.010525859892368317,
-0.037980396300554276,
-0.059863969683647156,
-0.0016639700625091791,
0.018584301695227623,
0.016943857073783875,
0.1044694259762764,
0.002312556141987443,
-0.03604276478290558,
0.0195942185819149,
-0.015590708702802658,
-0.0057059163227677345,
-0.043291956186294556,
0.03846162185072899,
-0.013842294923961163,
-0.03380728140473366,
-0.004724978934973478,
-0.0061551895923912525,
0.014629662036895752,
-0.034189753234386444,
0.028135033324360847,
-0.006865197792649269,
0.0202198326587677,
-0.0010418168967589736,
-0.027148980647325516,
0.05012764781713486,
0.046592727303504944,
0.030964264646172523,
-0.021671025082468987,
-0.006525307893753052,
-0.00992580782622099,
-0.006144440267235041,
0.007072851061820984,
-0.015486749820411205,
0.027592889964580536,
0.012877791188657284,
-0.011342526413500309,
0.027342576533555984,
-0.007783729583024979,
-0.011844748631119728,
0.0578395277261734,
0.008841533213853836,
0.10332741588354111,
0.0040974183939397335,
0.00155582872685045,
0.04339775815606117,
0.02543824166059494,
0.015366881154477596,
0.02261933498084545,
-0.020841330289840698,
-0.027748126536607742,
-0.054772213101387024,
-0.0256209559738636,
0.026540657505393028,
0.04782066121697426,
-0.054525647312402725,
-0.02390819787979126,
0.024254580959677696,
0.014623952098190784,
0.021981166675686836,
0.004611550830304623,
-0.03136836737394333,
-0.02350991778075695,
0.01550751831382513,
0.05008356645703316,
-0.06195642799139023,
0.01745852455496788,
0.015438436530530453,
0.017024673521518707,
0.03772632032632828,
0.017843276262283325,
-0.005221290048211813,
0.04402042552828789,
-0.011846421286463737,
0.02871764823794365,
0.021031416952610016,
0.01926843822002411,
0.05537205934524536,
-0.030122928321361542,
0.034343451261520386,
0.03881435841321945,
0.035190433263778687,
0.006460755597800016,
-0.022964471951127052,
-0.014969334937632084,
0.022548507899045944,
0.01827581226825714,
-0.030334265902638435,
-0.02519911155104637,
0.00509857852011919,
-0.011187450960278511,
0.01536867767572403,
-0.020038586109876633,
-0.03255407512187958,
-0.023728638887405396,
-0.011330189183354378,
0.006357433274388313,
0.05838742479681969,
0.03809642046689987,
-0.024257609620690346,
0.02417396567761898,
-0.0031927970703691244,
0.010878014378249645,
0.019460873678326607,
-0.010883225128054619,
-0.05317145958542824,
0.0011243799235671759,
-0.02558073215186596,
-0.011517020873725414,
0.028553295880556107,
0.02107839286327362,
0.01089378260076046,
-0.015088187530636787,
-0.01121837180107832,
-0.06594535708427429,
0.01007966510951519,
-0.002432033885270357,
-0.0010667379247024655,
-0.026565056294202805,
-0.0066675059497356415,
0.02032305672764778,
-0.007005284074693918,
-0.019066544249653816,
0.020665226504206657,
-0.05592344328761101,
-0.022258510813117027,
-0.030154328793287277,
0.051794636994600296,
0.04597066715359688,
-0.020366398617625237,
0.019471246749162674,
-0.006682885345071554,
0.02220972813665867,
0.003878827439621091,
-0.04878365248441696,
0.0009000948048196733,
-0.032815124839544296,
-0.013317568227648735,
0.016303909942507744,
0.00723009929060936,
-0.03857263922691345,
0.06863231956958771,
0.01620108261704445,
-0.03417078033089638,
0.014480207115411758,
0.007084319833666086,
-0.04689990356564522,
-0.04741748794913292,
-0.0075796241872012615,
0.008430150337517262,
-0.03868469223380089,
0.01784553751349449,
0.006920470390468836,
0.03679606691002846,
0.04358844459056854,
0.03881991654634476,
-0.0187697596848011,
0.061595089733600616,
0.002480874303728342,
-0.006908940151333809,
0.04859830439090729,
0.05846806615591049,
0.020583296194672585,
0.020666006952524185,
-0.016883380711078644,
0.03007066436111927,
-0.023233607411384583,
-0.062271807342767715,
0.028572577983140945,
-0.03939642757177353,
0.01002576481550932,
-0.02095017395913601,
0.05261281505227089,
0.005150134675204754,
-0.01456121914088726,
0.015536474995315075,
0.0013854517601430416,
0.06339755654335022,
-0.0019698275718837976,
0.005831417627632618,
0.0736984983086586,
-0.007841382175683975,
0.03337989002466202,
-0.016161231324076653,
-0.034266047179698944,
0.00445170933380723,
-0.007223974913358688,
-0.0024995729327201843,
-0.02325708046555519,
0.03035069815814495,
0.049650609493255615,
0.016151251271367073,
-0.015261776745319366,
-0.031476929783821106,
0.004844976123422384,
-0.02393282763659954,
-0.020649483427405357,
-0.043045613914728165,
0.05714112147688866,
-0.003101795446127653,
0.03817116841673851,
0.04174581170082092,
-0.01902596466243267,
-0.02824181318283081,
0.015253148972988129,
-0.06276442110538483,
0.052451372146606445,
-0.028265733271837234,
-0.023582270368933678,
0.004656252451241016,
-0.010930686257779598,
-0.017062297090888023,
-0.03959821164608002,
-0.006954290438443422,
-0.037836648523807526,
-0.03303541988134384,
-0.05187857151031494,
-0.008990133181214333,
-0.055780984461307526,
-0.0005759534542448819,
-0.01729622296988964,
0.05969375744462013,
0.04125158488750458,
-0.015468625351786613,
0.02339085191488266,
0.04587066173553467,
-0.0559433177113533,
-0.018086936324834824,
-0.05155619606375694,
-0.011254554614424706,
-0.0010997087229043245,
0.035138264298439026,
0.044819753617048264,
0.0052505359053611755,
-0.00030021672137081623,
-0.025331519544124603,
-0.012908648699522018,
0.0813969150185585,
0.002125475322827697,
-0.014135466888546944,
-0.036809369921684265,
-0.0519915334880352,
0.003597402712330222,
0.0067195529118180275,
0.03434666246175766,
-0.027219373732805252,
0.0055888742208480835,
0.03392903506755829,
-0.006033164449036121,
-0.0237333495169878,
0.039828553795814514,
0.03275938704609871,
0.03243487700819969,
-0.04230378195643425,
-0.10036946833133698,
-0.037047822028398514,
-0.02356834150850773,
-0.03184276074171066,
0.011036458425223827,
-0.020777227357029915,
-0.008512596599757671,
-0.036737024784088135,
0.036516182124614716,
0.00014866347191855311,
0.028467632830142975,
0.024277852848172188,
-0.006074965000152588,
0.01969159208238125,
0.006258873734623194,
-0.028039000928401947,
-0.005467609968036413,
-0.01357060857117176,
0.043837159872055054,
0.017408372834324837,
0.016838885843753815,
-0.03641660511493683,
-0.01194024458527565,
0.04463301599025726,
0.054839059710502625,
-0.03991523012518883,
-0.004678403493016958,
-0.05457420274615288,
-0.008248573169112206,
0.01677308790385723,
-0.05627984181046486,
0.03042471967637539,
-0.027821725234389305,
-0.014980907551944256,
-0.017199473455548286,
-0.047166697680950165,
-0.06366420537233353,
0.0028124325908720493,
-0.008414298295974731,
0.023439621552824974,
-0.07669511437416077,
-0.004823436960577965,
-0.02097104862332344,
-0.010626026429235935,
0.04158635810017586,
0.015598869882524014,
-0.001917436020448804,
-0.007906793616712093,
-0.0033585906494408846,
0.03764263167977333,
-0.02356092631816864,
-0.06097796559333801,
0.006009859498590231,
-0.007739658001810312,
0.007038443814963102,
-0.009154604747891426,
-0.04394359886646271,
-0.056126587092876434,
0.05027211830019951,
-0.008224175311625004,
0.01984539069235325,
0.0027291078586131334,
-0.007425196934491396,
0.0004281331493984908,
0.03417346253991127,
-0.01143350638449192,
0.0643148273229599,
0.05371365696191788,
-0.010750536806881428,
-0.03125948831439018,
-0.04137358069419861,
0.03563292324542999,
0.009903864935040474,
-0.04017455503344536,
-0.043940696865320206,
0.02616189233958721,
-0.01716756820678711,
0.03829986974596977,
0.026460623368620872,
0.03414272516965866,
-0.03203393891453743,
-0.01627386547625065,
0.007408536039292812,
0.02288299985229969,
0.019618984311819077,
0.028126833960413933,
-0.004021079745143652,
0.012533326633274555,
0.01683157868683338,
-0.025462253019213676,
0.02701326459646225,
-0.02327566035091877,
0.00008444405830232427,
0.02485262230038643,
0.024396885186433792,
0.02668214589357376,
-0.04764166846871376,
-0.02939448691904545,
-0.02406320720911026,
-0.019147776067256927,
0.04641088843345642,
-0.04810753092169762,
0.028224727138876915,
0.016907621175050735,
-0.06031274050474167,
-0.05014929547905922,
-0.0035612608771771193,
-0.005172841250896454,
0.060456596314907074,
-0.044800322502851486,
-0.025807365775108337,
-0.0036200075410306454,
0.006277256645262241,
-0.020650414749979973,
-0.03016011416912079,
-0.0016051235143095255,
0.0352618433535099,
-0.011364423669874668,
-0.013951858505606651,
-0.036854494363069534,
0.004468396306037903,
-0.04580599442124367,
0.001197375706396997,
0.060868095606565475,
-0.047903500497341156,
0.013198581524193287,
-0.008071093820035458,
0.011209447868168354,
0.06718768179416656,
-0.032285839319229126,
-0.005760390777140856,
0.014898959547281265,
-0.006804947275668383,
-0.033513206988573074,
0.011324345134198666,
0.04213952645659447,
-0.03491584584116936,
-0.04613051936030388,
0.007107983808964491,
0.0027248440310359,
0.050081539899110794,
0.0189928337931633,
-0.003858323674649,
0.01213899441063404,
-0.0020917735528200865,
0.0028987457044422626,
0.020287923514842987,
0.03747154772281647,
0.05353628098964691,
-0.0017644409090280533,
-0.014503651298582554,
-0.011691422201693058,
-0.048985518515110016,
-0.0028764628805220127,
0.056429117918014526,
-0.022159354761242867,
-0.005406783893704414,
-0.015108190476894379,
0.0507953055202961,
-0.028753452003002167,
0.026639392599463463,
0.003376843174919486,
0.02079491876065731,
0.03861897066235542,
0.007619194220751524,
-0.017565837129950523,
0.003569310065358877,
0.010948839597404003,
-0.017818082123994827,
-0.01618078723549843,
-0.05621275305747986,
0.032641105353832245,
0.06258350610733032,
-0.02113455906510353,
0.03403906896710396,
0.02346010133624077,
0.016176516190171242,
-0.002286799717694521,
-0.03754045069217682,
-0.03610922396183014,
-0.010043543763458729,
0.005765260197222233,
0.015592575073242188,
-0.025763580575585365,
-0.002820354886353016,
0.03487398475408554,
0.037767812609672546,
-0.037219349294900894,
-0.01735256239771843,
-0.006548609118908644,
0.009216221049427986,
-0.023291680961847305,
0.009520742110908031,
-0.026061344891786575,
0.02352147363126278,
0.004999013151973486,
0.03860548138618469,
-0.024270588532090187,
-0.04121308773756027,
0.054383065551519394,
0.021250640973448753,
-0.028750961646437645,
-0.029186950996518135,
0.039855945855379105,
-0.006146923638880253,
0.03657522052526474,
0.04115226864814758,
-0.0035565393045544624,
-0.01845887117087841,
-0.0032335049472749233,
0.022089840844273567,
-0.023566938936710358,
0.020679153501987457,
-0.01119717676192522,
-0.0312788300216198,
-0.02984185330569744,
-0.03597551956772804,
-0.06669691205024719,
0.061696965247392654,
-0.028698183596134186,
-0.013041463680565357,
0.03846387937664986,
-0.028372449800372124,
0.01795615628361702,
0.0059652975760400295,
-0.006512990687042475,
-0.014117500744760036,
0.09822724014520645,
0.010209896601736546,
0.01272634044289589,
-0.012650424614548683,
0.03258254751563072,
0.10568895190954208,
0.033521924167871475,
-0.004726829472929239,
-0.07417955249547958,
0.034450095146894455,
0.009458478540182114,
0.040517475455999374,
-0.031236981973052025,
-0.014835381880402565,
-0.00506520876660943,
-0.0232215728610754,
0.011162225157022476,
0.0344819575548172,
-0.03711982071399689,
-0.013274244964122772,
0.036615848541259766,
-0.014128240756690502,
-0.05017027631402016,
-0.014596547931432724,
-0.007069037761539221,
-0.009746894240379333,
-0.013070622459053993,
-0.040647804737091064,
0.0460381917655468,
-0.04097125679254532,
-0.004228727426379919,
-0.024099254980683327,
-0.02116367593407631,
0.0018874604720622301,
0.011125747114419937,
-0.046283479779958725,
-0.004528159741312265,
0.001909072743728757,
-0.024675441905856133,
-0.02446957305073738,
0.007248538080602884,
0.008669635280966759,
-0.004617675673216581,
0.03344971314072609,
0.0030709311831742525,
-0.002503257477656007,
0.0027746204286813736,
0.01592591591179371,
0.01112137921154499,
-0.060439880937337875,
-0.03790506348013878,
0.005225460045039654,
0.04470953717827797,
0.014903114177286625,
0.0027025460731238127,
0.006014125421643257,
-0.015467232093214989,
-0.045095331966876984,
-0.031205132603645325,
0.026622729375958443,
-0.027835311368107796,
-0.013710572384297848,
-0.027413932606577873,
-0.006552348379045725,
-0.016145355999469757,
0.0014990870840847492,
-0.0007327532512135804,
0.028491578996181488,
-0.030771201476454735,
-0.012758655473589897,
-0.017917361110448837,
0.0011648490326479077,
0.024781042709946632,
-0.02641219273209572,
-0.005288697313517332,
0.014437174424529076,
-0.03625032678246498,
-0.03627299889922142,
-0.012433911673724651,
-0.0027972806710749865,
0.0046781315468251705,
0.01833794079720974,
0.015901412814855576,
-0.021091949194669724,
-0.02074776031076908,
-0.03448232635855675,
-0.009336072020232677,
-0.00992631632834673,
0.021985061466693878,
-0.04222562164068222,
-0.02477889321744442,
0.02642160654067993,
0.03598611429333687,
0.0015273563330993056,
0.0010034294100478292,
-0.028863195329904556,
0.017074236646294594,
0.011544077657163143,
-0.006730604916810989,
-0.03231881931424141,
-0.011083542369306087,
-0.01793571375310421,
0.045237284153699875,
-0.04261285439133644,
-0.024970456957817078,
0.012565593235194683,
0.04477338120341301,
-0.008209232240915298,
0.010273018851876259,
0.0006331144249998033,
0.006287859287112951,
-0.015200256370007992,
-0.02490360476076603,
0.012969894334673882,
0.01295282132923603,
0.01435899455100298,
-0.03344595804810524,
0.005338672548532486,
-0.005499879363924265,
-0.02779429778456688,
-0.030358148738741875,
0.05920908600091934,
-0.005710077006369829,
0.020322619006037712,
-0.0546303391456604,
-0.010958959348499775,
-0.021152658388018608,
-0.015485692769289017,
-0.03295997157692909,
-0.021644169464707375,
-0.0009836546378210187,
0.004883919842541218,
-0.05448131635785103,
0.031081771478056908,
0.010032727383077145,
-0.018892260268330574,
0.022030211985111237,
0.014824706129729748,
-0.03280968591570854,
-0.038038160651922226,
0.0176335908472538,
0.0032597193494439125,
0.052356913685798645,
-0.009868594817817211,
-0.007286980282515287,
0.06369462609291077,
-0.010262096300721169,
-0.03405024856328964,
0.007381277158856392,
-0.009848122484982014,
0.03587663546204567,
0.015359725803136826,
-0.04308829456567764,
-0.019019439816474915,
0.049276065081357956,
-0.008231079205870628,
-0.027833791449666023,
0.003834072733297944,
-0.01023299340158701,
0.012491165660321712,
-0.006711436901241541,
0.011281678453087807,
-0.022708836942911148,
-0.005463007837533951,
0.04265744611620903,
0.03682990372180939,
-0.023466147482395172,
-0.023097120225429535,
0.0136331832036376,
0.0063864486292004585,
-0.005850067362189293,
0.04007219523191452,
0.03193463757634163,
0.056590184569358826,
0.05228929594159126,
-0.02482321299612522,
0.03274020552635193,
-0.041722267866134644,
0.005431772209703922,
-0.08394622057676315,
-0.014118826016783714,
-0.02039942517876625,
0.020230477675795555,
0.054509237408638,
-0.061691418290138245,
0.0036653303541243076,
0.036117587238550186,
-0.05240153893828392,
-0.017711488530039787,
-0.02202761545777321,
-0.050644420087337494,
-0.04349355027079582,
-0.05532176047563553,
-0.01056838408112526,
0.01975170150399208,
0.02777198515832424,
0.021299879997968674,
0.04058977961540222,
0.0192209854722023,
-0.05215054377913475,
-0.006462640594691038,
0.007545654661953449,
0.0533030703663826,
-0.0303102508187294,
-0.0032511462923139334,
0.02605840377509594,
-0.013319063931703568,
-0.04515153169631958,
0.03831013664603233,
-0.02368020825088024,
0.006133731920272112,
0.014288571663200855,
0.03294401988387108,
-0.02299792692065239,
0.05619819089770317,
0.01911509409546852,
0.016198646277189255,
0.0043246266432106495,
0.011385396122932434,
0.013971660286188126,
0.013295898213982582,
-0.04290996491909027,
-0.0028552121948450804,
0.03285974636673927,
-0.0381525382399559,
-0.05445166304707527,
-0.0011830867733806372,
-0.005880915094166994,
-0.008750177919864655,
0.005105296149849892,
-0.00782278086990118,
-0.0016778084682300687,
-0.06738405674695969,
0.041802745312452316,
-0.03761141747236252,
0.038459666073322296,
0.05062423273921013,
-0.0016951531870290637,
0.032314639538526535,
-0.010917630977928638,
0.047998491674661636,
-0.01016492024064064,
0.027185771614313126,
0.00004083317253389396,
-0.03236008062958717,
-0.017689993605017662,
-0.007786950096487999,
0.021272173151373863,
0.003978355787694454,
-0.01837776042521,
-0.021260377019643784,
-0.04992631822824478,
-0.0018647018587216735,
0.0040184068493545055,
-0.026903212070465088,
0.012252314947545528,
0.007346872705966234,
-0.03442075103521347,
-0.0941402018070221,
0.031358543783426285,
0.0038905832916498184,
-0.05642257258296013,
-0.017395170405507088,
-0.011945797130465508,
0.0027973263058811426,
0.016360821202397346,
0.057763904333114624,
-0.0030267771799117327,
0.005680347792804241,
0.02301974408328533,
-0.014131974428892136,
0.0199121106415987,
-0.007022645324468613,
-0.007185910362750292,
-0.004403096158057451,
-0.006257195957005024,
0.014453031122684479,
-0.018589278683066368,
0.04300305247306824,
0.014149660244584084,
-0.02682795375585556,
-0.001323995180428028,
0.02725832909345627,
0.010681519284844398,
-0.02677788771688938,
0.03736423701047897,
-0.03359944373369217,
-0.0013210177421569824,
0.0754755288362503,
0.02493351139128208,
0.013613189570605755,
0.03349996730685234,
-0.03727066516876221,
-0.03092307411134243,
0.023244129493832588,
-0.018910041078925133,
-0.004923615138977766,
-0.003482275875285268,
0.034638166427612305,
0.014124919660389423,
-0.03719497472047806,
0.010252987034618855,
0.03656554967164993,
-0.00970070157200098,
-0.01593831740319729,
0.02364439330995083,
0.014779006130993366,
0.05474037304520607,
-0.001871625892817974,
0.06303275376558304,
0.03954260051250458,
-0.016550501808524132,
0.04943268373608589,
0.03290710598230362,
0.025066668167710304,
0.010641094297170639,
-0.040704287588596344,
0.036750711500644684,
-0.020355263724923134,
-0.02712942473590374,
-0.03976743295788765,
0.027020594105124474,
0.0006134290597401559,
-0.03731543943285942,
0.002252383856102824,
-0.047740638256073,
0.027457796037197113,
0.024427784606814384,
-0.006832509767264128,
0.06205086410045624,
0.01633927784860134,
0.03552040457725525,
0.0065787420608103275,
0.004613534081727266,
0.014689411967992783,
0.01646612025797367,
0.037034712731838226,
0.015679506585001945,
-0.03376930207014084,
-0.01314595527946949,
-0.017351219430565834,
-0.006540162488818169,
0.030806127935647964,
0.012518355622887611,
0.0271782074123621,
0.037230733782052994,
0.025662222877144814,
-0.018350204452872276,
-0.05485978722572327,
0.005072365514934063,
-0.028466831892728806,
0.04415176436305046,
0.057060010731220245,
0.04983586072921753,
0.005894044414162636,
-0.0073019894771277905,
-0.01022990234196186,
0.0821743905544281,
-0.0379781499505043,
-0.029020920395851135,
-0.009725748561322689,
0.03113422356545925,
0.019687814638018608,
-0.032595694065093994
] |
<p>I have a system, where there are ball bearings on the pistons that clamp the metal plate with special dents for ball bearings. The system should be precise, because it is used for microscopy. It also should be as noiseless as possible. It also should be fast, so the impact at high velocity is inevitable.</p>
<p>I've thought of introducing some resin coating, but it will reduce the rigidity. Are there any solutions for this problem? Is there any strong relationship between sound and rigidity? I believe that there may be some rigid materials that somehow don't favor phonons.</p>
| 8,259 |
[
-0.026082677766680717,
-0.03201134875416756,
0.025631507858633995,
-0.04549013823270798,
0.008835545741021633,
-0.008925752714276314,
-0.01574479416012764,
-0.005529699381440878,
0.01014709286391735,
0.009911004453897476,
0.04217999428510666,
0.03207926079630852,
0.03717375174164772,
0.02380562387406826,
0.001550506567582488,
-0.04824398085474968,
0.007798557635396719,
-0.047640323638916016,
-0.02347106672823429,
-0.02199576050043106,
0.007490264251828194,
-0.0018619863549247384,
0.003605462843552232,
0.005287496838718653,
-0.007150907069444656,
0.03603890910744667,
-0.014342035166919231,
-0.049725089222192764,
0.0269733015447855,
-0.0026626987382769585,
-0.04124123230576515,
0.02078901417553425,
-0.012213642708957195,
-0.01150926761329174,
0.049369003623723984,
0.015468843281269073,
-0.040379978716373444,
0.00602783402428031,
-0.030391110107302666,
0.02361868880689144,
-0.07511565089225769,
-0.0038016936741769314,
0.024192163720726967,
0.032043952494859695,
-0.0008905240683816373,
0.006693012546747923,
0.02233036980032921,
-0.02657543122768402,
0.035092126578092575,
-0.050003234297037125,
0.04685639590024948,
-0.0020559385884553194,
0.041743528097867966,
0.04952109977602959,
-0.0031186065170913935,
-0.02276482619345188,
0.07204216718673706,
0.09719938039779663,
-0.030996719375252724,
-0.0340907908976078,
0.03893611952662468,
-0.02277246117591858,
-0.016579054296016693,
-0.0031439962331205606,
-0.024792883545160294,
0.010611013509333134,
-0.027592116966843605,
-0.02925378829240799,
0.05235638469457626,
-0.0058821686543524265,
0.002504250966012478,
-0.03564831241965294,
0.034288909286260605,
-0.037175655364990234,
-0.005704197101294994,
-0.045911382883787155,
0.0204742643982172,
0.03485293313860893,
0.015372850932180882,
0.02185932733118534,
-0.003881505923345685,
-0.02205760031938553,
0.014798375777900219,
0.06552224606275558,
-0.009331922046840191,
-0.014502276666462421,
0.02979494258761406,
-0.02720472775399685,
0.012962859123945236,
0.036570802330970764,
0.014606683515012264,
-0.0023844074457883835,
0.052435051649808884,
0.018098391592502594,
0.0044456589967012405,
-0.005697544664144516,
0.019257716834545135,
0.0556115061044693,
0.023719927296042442,
-0.03556303679943085,
-0.01417324598878622,
0.014153245836496353,
0.04205400496721268,
0.09255584329366684,
-0.02811618335545063,
-0.022002846002578735,
-0.03063385933637619,
-0.007022126577794552,
-0.01489570178091526,
0.006298664957284927,
-0.025793977081775665,
-0.022419173270463943,
-0.021737538278102875,
0.004667873028665781,
0.008313038386404514,
-0.006903310306370258,
0.002518261782824993,
-0.008241505362093449,
0.024674691259860992,
0.08150254935026169,
0.029005879536271095,
-0.029700689017772675,
0.026398679241538048,
-0.03378134220838547,
-0.04770369082689285,
0.002418696880340576,
0.04071371629834175,
-0.04866394028067589,
-0.008418358862400055,
0.025061115622520447,
0.048539113253355026,
-0.024322081357240677,
0.021320289000868797,
-0.047599464654922485,
0.05893823504447937,
-0.04014364629983902,
-0.059722062200307846,
-0.06657108664512634,
0.07481634616851807,
0.02233208157122135,
-0.011941864155232906,
-0.08241278678178787,
0.025111045688390732,
0.02940511889755726,
0.0728762149810791,
-0.003085620701313019,
-0.005145195871591568,
0.02854997105896473,
0.021770169958472252,
0.00027203105855733156,
0.020944444462656975,
-0.03810755908489227,
-0.01427369099110365,
-0.006166669074445963,
0.03338739648461342,
-0.045307889580726624,
0.030593182891607285,
0.00444506760686636,
0.0011200470617040992,
-0.026997819542884827,
-0.008975571021437645,
-0.033199287950992584,
-0.015488089062273502,
0.0186151210218668,
0.0016073795268312097,
-0.04287875443696976,
0.029698193073272705,
-0.016318241134285927,
0.014065803028643131,
0.018261656165122986,
0.004534078761935234,
0.003894572611898184,
0.020613893866539,
0.013774283230304718,
-0.00005500245970324613,
-0.034667063504457474,
-0.011371452361345291,
-0.0056339288130402565,
-0.0021709830034524202,
0.016125105321407318,
-0.03943338617682457,
-0.02138715609908104,
0.013738105073571205,
-0.011905304156243801,
-0.0022694615181535482,
0.021655531600117683,
0.041924167424440384,
0.01081489585340023,
0.043780338019132614,
-0.02596353366971016,
-0.01759311370551586,
-0.06985165923833847,
0.03726239874958992,
-0.03820696845650673,
-0.01488130446523428,
0.04356568306684494,
-0.022182567045092583,
-0.03645094111561775,
-0.018046943470835686,
0.0015506240306422114,
0.03910434991121292,
-0.02146300859749317,
0.02940390259027481,
0.004531872924417257,
-0.02052345499396324,
0.025173667818307877,
0.010347278788685799,
-0.013477370142936707,
-0.008883320726454258,
0.011213526129722595,
-0.007000804878771305,
-0.005302275065332651,
-0.06394422799348831,
0.0025988598354160786,
-0.028411773964762688,
-0.005889700260013342,
0.03916052356362343,
-0.05575031787157059,
0.013662726618349552,
-0.020098956301808357,
-0.014667046256363392,
0.07902175933122635,
0.035416074097156525,
-0.04444165527820587,
0.01741877943277359,
0.033316776156425476,
0.012587242759764194,
0.02404545247554779,
0.004786050412803888,
-0.012710319831967354,
-0.07578862458467484,
0.001537807285785675,
0.02153913304209709,
0.038052644580602646,
-0.0497918501496315,
0.04382498189806938,
0.03415830805897713,
0.008808647282421589,
0.05354057997465134,
-0.00796812679618597,
-0.01608886383473873,
-0.05426353961229324,
0.05221576988697052,
0.005652525927871466,
0.021739233285188675,
0.012439175508916378,
0.013335813768208027,
0.004257554654031992,
0.025131838396191597,
-0.016439499333500862,
0.01945696584880352,
0.027830958366394043,
0.023192478343844414,
0.03236003220081329,
0.003824300365522504,
-0.061906956136226654,
-0.0009178242762573063,
-0.007849755696952343,
0.017149601131677628,
0.014006247743964195,
0.0017645524349063635,
0.03386352211236954,
-0.015792978927493095,
0.020186522975564003,
-0.01816689968109131,
0.014555134810507298,
0.0035269756335765123,
-0.030235515907406807,
0.044508807361125946,
-0.06687819212675095,
-0.022718213498592377,
-0.009893381036818027,
-0.009665094316005707,
0.020422641187906265,
-0.025758318603038788,
0.043499745428562164,
0.026937469840049744,
0.010710225440561771,
-0.012008965015411377,
0.0034525629598647356,
0.008300845511257648,
-0.03806276246905327,
-0.006017109379172325,
0.032991379499435425,
-0.027481233701109886,
-0.011712083593010902,
-0.016473213210701942,
-0.024153415113687515,
0.0034552374854683876,
-0.022121872752904892,
0.01942785084247589,
0.031675420701503754,
0.010155074298381805,
-0.049728523939847946,
-0.01581500470638275,
-0.009967019781470299,
-0.01924194023013115,
-0.06497018784284592,
0.015216702595353127,
0.0212125014513731,
0.041421689093112946,
0.011118752881884575,
-0.0062049082480371,
-0.03575294092297554,
-0.005627673119306564,
-0.007157341111451387,
-0.012431570328772068,
0.010744745843112469,
-0.0471588559448719,
0.003250100649893284,
0.03499182313680649,
-0.012813650071620941,
-0.01770772598683834,
-0.031201843172311783,
-0.024808034300804138,
0.025841880589723587,
-0.0016769367503002286,
0.0964871495962143,
-0.006551974453032017,
-0.016438649967312813,
0.07462087273597717,
0.022032825276255608,
-0.029131775721907616,
-0.035670846700668335,
-0.0789676085114479,
0.0010960269719362259,
-0.05801769718527794,
0.0032710011582821608,
0.059543121606111526,
-0.01673412322998047,
0.027517957612872124,
0.03445254638791084,
-0.00398115674033761,
0.01007143221795559,
0.035290516912937164,
-0.01684482954442501,
0.0013483072398230433,
0.016045590862631798,
-0.01634073071181774,
0.052674487233161926,
0.04727822542190552,
-0.04092784598469734,
0.00835968367755413,
-0.022954922169446945,
-0.0046132286079227924,
0.025492506101727486,
-0.09730708599090576,
0.03112873062491417,
-0.0034441519528627396,
-0.00004960489968652837,
-0.03126685321331024,
0.004398755729198456,
0.0014283546479418874,
-0.004850543104112148,
-0.02618751861155033,
0.03321889042854309,
0.007013039663434029,
0.012345549650490284,
0.002098497236147523,
0.05708691105246544,
0.04029928147792816,
0.009706961922347546,
-0.00820410717278719,
-0.01883331872522831,
-0.0043486044742167,
0.018711673095822334,
-0.009483822621405125,
0.02471015229821205,
0.0188230462372303,
-0.012021197937428951,
0.037221141159534454,
0.03873825445771217,
-0.03059232607483864,
0.006214780267328024,
-0.05430377647280693,
-0.0007058889605104923,
-0.017577895894646645,
0.05787508934736252,
-0.006616912316530943,
0.04824631288647652,
0.03644223138689995,
0.017604388296604156,
0.012872060760855675,
-0.027712183073163033,
-0.08580689132213593,
0.007899666205048561,
-0.023830309510231018,
-0.02633671462535858,
0.021804912015795708,
-0.009842148050665855,
-0.06279224902391434,
-0.018101779744029045,
-0.02024035155773163,
-0.005746465642005205,
0.046150971204042435,
-0.06836624443531036,
0.04387795925140381,
-0.016909126192331314,
-0.03248398378491402,
-0.010899159125983715,
0.03018687665462494,
0.00551255140453577,
0.0023234181571751833,
0.036249447613954544,
-0.0037607275880873203,
-0.00990897137671709,
0.009530345909297466,
-0.006469205021858215,
0.019568856805562973,
0.01692773774266243,
0.030559826642274857,
0.009549705311655998,
0.011533591896295547,
0.005804010201245546,
-0.012190675362944603,
0.02343582920730114,
0.034597933292388916,
0.021836010739207268,
0.0067659164778888226,
-0.04048413783311844,
-0.021389910951256752,
-0.05147819593548775,
0.023438984528183937,
0.059815824031829834,
-0.027273105457425117,
-0.03448934108018875,
-0.008212747052311897,
-0.019873959943652153,
-0.02870071306824684,
-0.010871805250644684,
0.0030817678198218346,
0.03976244479417801,
-0.021233994513750076,
-0.05563514679670334,
-0.05240672454237938,
0.004787610378116369,
-0.011335862800478935,
-0.022209925577044487,
0.049735426902770996,
-0.012220427393913269,
0.013565740548074245,
0.011601226404309273,
0.006511818151921034,
-0.020098473876714706,
0.03944524750113487,
-0.001282346318475902,
0.004957494791597128,
-0.012645636685192585,
0.03482082113623619,
0.01537268701940775,
0.0421505942940712,
0.039607517421245575,
0.026416078209877014,
-0.05061306431889534,
-0.055918414145708084,
-0.0017547004390507936,
0.012121758423745632,
0.04144063591957092,
-0.010272101499140263,
0.002438875148072839,
-0.02474266104400158,
-0.06601160019636154,
0.04801125079393387,
-0.00733994459733367,
0.028209593147039413,
-0.022995999082922935,
0.016761215403676033,
-0.0226457379758358,
-0.032883696258068085,
-0.029170379042625427,
-0.011661423370242119,
-0.012898799031972885,
0.0059209405444562435,
-0.0209468062967062,
-0.028146294876933098,
-0.001130297314375639,
-0.018873704597353935,
0.03696952015161514,
0.04161229357123375,
-0.014381066896021366,
-0.012035753577947617,
-0.013080520555377007,
-0.010676695965230465,
-0.024246875196695328,
-0.07281410694122314,
0.02331169880926609,
-0.0025166268460452557,
0.00015472376253455877,
-0.00722384313121438,
-0.03619494289159775,
-0.0208671186119318,
0.038550108671188354,
-0.004612228367477655,
-0.013925162144005299,
0.01225486770272255,
-0.024837512522935867,
0.009345315396785736,
0.015024553053081036,
0.025659415870904922,
0.03580351918935776,
0.03604971617460251,
-0.03330330550670624,
0.021770648658275604,
-0.00791616179049015,
-0.00789257325232029,
-0.04622812941670418,
0.01923610456287861,
-0.007024337537586689,
0.0429689846932888,
-0.043511006981134415,
-0.025320235639810562,
0.01850917749106884,
0.03650901839137077,
0.008201966062188148,
-0.0319083146750927,
0.013813911005854607,
0.02565094828605652,
-0.0022670014295727015,
-0.010524964891374111,
0.006545129232108593,
0.052259597927331924,
-0.013112661428749561,
-0.0038000766653567553,
-0.009834174066781998,
0.016496799886226654,
0.012154927477240562,
0.04440479353070259,
-0.04790513589978218,
0.02279038541018963,
-0.06001729145646095,
-0.03791061416268349,
0.007914411835372448,
-0.04095291718840599,
0.08924964815378189,
-0.021131228655576706,
0.060163550078868866,
0.050107650458812714,
-0.03984837606549263,
0.05276404693722725,
0.04434508830308914,
-0.036756325513124466,
0.05520845204591751,
-0.08282802253961563,
-0.0036437916569411755,
-0.03155186027288437,
0.031235288828611374,
-0.015389160253107548,
-0.04556840658187866,
0.013253533281385899,
0.03606981411576271,
-0.0057329717092216015,
-0.03292422741651535,
0.0003728788869921118,
-0.010793762281537056,
-0.025144631043076515,
0.056967850774526596,
-0.0029328707605600357,
-0.010132083669304848,
0.004782552365213633,
0.0627126395702362,
-0.01927683688700199,
0.037860650569200516,
-0.0020790635608136654,
-0.0072422209195792675,
0.0031873981934040785,
-0.021860752254724503,
-0.028260933235287666,
-0.035206954926252365,
0.04998016729950905,
-0.026259800419211388,
-0.03862367570400238,
-0.01601874828338623,
0.028356080874800682,
-0.003993431106209755,
0.011557855643332005,
0.03037978522479534,
0.014095641672611237,
0.0186918955296278,
-0.016540834680199623,
-0.015079917386174202,
0.03697269782423973,
0.004048905335366726,
-0.000841221131850034,
-0.03163325786590576,
0.0322519950568676,
-0.04500485211610794,
-0.06255263835191727,
0.008192015811800957,
0.004489700775593519,
0.019984794780611992,
-0.02431940659880638,
0.04560123756527901,
0.0047814869321882725,
-0.0059267510659992695,
0.026285039260983467,
-0.04328735172748566,
0.07129252701997757,
-0.011477820575237274,
0.013559899292886257,
-0.02341679483652115,
-0.011895539239048958,
0.0071067591197788715,
-0.019458094611763954,
-0.024573281407356262,
-0.03144198656082153,
0.053832076489925385,
-0.027563368901610374,
0.07188516855239868,
0.044706206768751144,
-0.013582581654191017,
-0.036184605211019516,
-0.01738692633807659,
-0.014514325186610222,
0.012775726616382599,
-0.04230279102921486,
0.04436963424086571,
-0.01551770605146885,
-0.026173744350671768,
0.016402479261159897,
0.0347442626953125,
0.004129603039473295,
-0.0037562805227935314,
0.0211225226521492,
0.023506129160523415,
0.02075863629579544,
-0.03755950927734375,
-0.011454857885837555,
0.0161416158080101,
-0.05501000955700874,
0.0557415708899498,
0.02324395440518856,
-0.0028653426561504602,
0.06390340626239777,
0.05484985560178757,
0.01669076271355152,
-0.019565608352422714,
0.015467971563339233,
-0.05606428161263466,
0.030177002772688866,
0.009740591049194336,
-0.012057909741997719,
0.012756282463669777,
0.0006080606253817677,
0.013731339015066624,
0.03463795408606529,
0.05005015432834625,
-0.04759581759572029,
-0.037728771567344666,
0.014674697071313858,
-0.01777396723628044,
-0.03429492190480232,
0.07044145464897156,
-0.006559042725712061,
-0.030105233192443848,
0.04056714102625847,
-0.0004352934192866087,
0.06034041941165924,
-0.0049886577762663364,
-0.005158626940101385,
-0.014796651899814606,
0.042680464684963226,
-0.007714817766100168,
0.009097041562199593,
-0.028845787048339844,
0.05835406482219696,
0.1228981539607048,
0.05525636672973633,
0.06264055520296097,
0.001924106851220131,
0.021868644282221794,
0.016441188752651215,
-0.0038518207147717476,
-0.01980993151664734,
0.018273698166012764,
0.021432405337691307,
-0.010167819447815418,
-0.026773929595947266,
0.06750381737947464,
-0.029863804578781128,
-0.016430728137493134,
0.04053325578570366,
-0.030752167105674744,
0.008776447735726833,
-0.028628282248973846,
0.0005718989414162934,
0.023326167836785316,
0.01698865368962288,
-0.019498081877827644,
-0.0011994695523753762,
-0.038776297122240067,
-0.050057798624038696,
-0.03862788900732994,
-0.061880242079496384,
0.031685296446084976,
-0.010152528062462807,
-0.0010808873921632767,
0.028421564027667046,
0.02472296915948391,
0.0023406974505633116,
-0.04807581380009651,
0.030430424958467484,
-0.010419776663184166,
0.0030905120074748993,
0.02433081343770027,
-0.006353754550218582,
0.028191018849611282,
0.003646233817562461,
-0.015423434786498547,
-0.002323330380022526,
-0.03050120733678341,
0.006057164166122675,
-0.04322342202067375,
0.04107292369008064,
-0.005110622383654118,
0.014197115786373615,
0.0027676967438310385,
0.02905913069844246,
0.026746390387415886,
-0.030588246881961823,
0.0005776227335445583,
0.021727653220295906,
0.033147212117910385,
0.00666471291333437,
-0.05801600590348244,
0.024610912427306175,
0.025951560586690903,
0.014747333712875843,
-0.014409631490707397,
-0.024415848776698112,
0.01998726651072502,
-0.007631293963640928,
0.011588983237743378,
0.023114947602152824,
-0.04050643742084503,
-0.013647752813994884,
-0.039375487715005875,
0.014736098237335682,
-0.040403708815574646,
0.005875931587070227,
-0.024789931252598763,
0.04762878641486168,
0.03320400416851044,
-0.0005753577570430934,
-0.0026840546634048223,
-0.03564535826444626,
-0.04244983568787575,
0.06771639734506607,
-0.031104596331715584,
-0.014014716260135174,
-0.03511980175971985,
-0.024767933413386345,
-0.0030105228070169687,
0.013439293019473553,
-0.0435914620757103,
-0.007425910793244839,
-0.0012597237946465611,
0.027155209332704544,
0.03626957908272743,
0.004455619025975466,
-0.013982153497636318,
-0.025336645543575287,
-0.028171153739094734,
0.051170121878385544,
0.02153828553855419,
0.04823921620845795,
0.017526034265756607,
-0.010943293571472168,
0.03759210556745529,
0.02931676246225834,
-0.026949064806103706,
-0.015266899019479752,
0.01113146636635065,
-0.02344721183180809,
-0.03595493361353874,
0.011130883358418941,
0.022093510255217552,
-0.06520013511180878,
-0.04310297966003418,
-0.04229535162448883,
-0.028499439358711243,
-0.04789511114358902,
0.033782847225666046,
-0.006385378539562225,
0.044129885733127594,
-0.02279502898454666,
-0.005781939718872309,
-0.028612308204174042,
0.041261591017246246,
0.0010012860875576735,
-0.008520686998963356,
0.007247290574014187,
0.032613784074783325,
-0.0371573306620121,
0.02112327516078949,
-0.02338295243680477,
-0.006252271123230457,
0.011066834442317486,
0.007588760461658239,
0.009080000221729279,
0.003466882975772023,
0.0002168460632674396,
-0.011431805789470673,
0.012255233712494373,
-0.01980466954410076,
0.02048494666814804,
0.027067871764302254,
-0.06127607822418213,
-0.04809059202671051,
0.008057037368416786,
-0.0026316263247281313,
-0.013751245103776455,
0.02480737492442131,
0.003981059417128563,
-0.0008350145071744919,
0.06625361740589142,
-0.02800399623811245,
-0.025758879259228706,
0.007127848453819752,
0.015130499377846718,
0.005229332484304905,
0.01569177955389023,
0.06959991157054901,
-0.04837917536497116,
-0.00204920070245862,
0.023258337751030922,
0.02298031374812126,
0.006231732200831175,
0.016066117212176323,
-0.007659464608877897,
-0.037665955722332,
0.0016029548132792115,
-0.010530177503824234,
0.016764365136623383,
0.01788974553346634,
0.023983098566532135,
-0.025860615074634552,
0.004558337852358818,
0.03008940815925598,
-0.026084130629897118,
-0.07970044761896133,
-0.013642997480928898,
-0.03202018514275551,
-0.03088669665157795,
0.030357113108038902,
-0.024076534435153008,
0.05176680535078049,
0.013799261301755905,
-0.07717033475637436,
0.017635928466916084,
-0.04853411391377449,
-0.03483512997627258,
-0.06353539228439331,
-0.0051730480045080185,
-0.026570947840809822,
0.028860826045274734,
0.00026411956059746444,
0.0097737405449152,
0.03200320899486542,
0.03130989149212837,
-0.02604065276682377,
-0.00173410854768008,
0.025428205728530884,
-0.00867372751235962,
0.018346361815929413,
0.0017640978330746293,
0.06316845118999481,
-0.0385630838572979,
-0.020649345591664314,
0.02565232664346695,
-0.004836836364120245,
0.01956588588654995,
-0.02086958847939968,
0.026407752186059952,
0.02150263823568821,
0.025081828236579895,
-0.0019421001197770238,
0.010287824086844921,
0.018179351463913918,
-0.011629912070930004,
0.017726687714457512,
0.00821522157639265,
-0.02580646239221096,
0.04693949967622757,
0.025056611746549606,
-0.011166349053382874,
0.004255262203514576,
-0.012516990303993225,
-0.007474266923964024,
0.029976828023791313,
0.014525802806019783,
0.028075166046619415,
-0.000809786026366055,
-0.013163654133677483,
-0.03749532997608185,
-0.012309418059885502,
0.00924103893339634,
0.010971088893711567,
0.0543602891266346,
-0.005809804890304804,
0.02598327025771141,
-0.026773575693368912,
0.0027717191260308027,
-0.05717800185084343,
0.011200942099094391,
-0.05223766714334488,
-0.052021440118551254,
-0.028968054801225662,
-0.013727542944252491,
0.010743005201220512,
-0.05474087595939636,
0.006573287304490805,
-0.010354967787861824,
0.06490156054496765,
-0.010871096514165401,
0.046957824379205704,
0.01621200516819954,
-0.019208304584026337,
-0.031693581491708755,
-0.09373842924833298,
0.0060919830575585365,
-0.0011539343977347016,
-0.020891761407256126,
-0.013016396202147007,
-0.057990286499261856,
0.020086616277694702,
0.03366710618138313,
0.07767342031002045,
0.011198816820979118,
-0.014597473666071892,
0.022624054923653603,
-0.036209069192409515,
0.0022124326787889004,
-0.006510458420962095,
0.0031532091088593006,
-0.03359522297978401,
0.04811711981892586,
-0.003989321179687977,
0.005184621550142765,
-0.019478552043437958,
-0.005352491047233343,
0.05440831929445267,
-0.04396413266658783,
-0.00037916150176897645,
0.008684630505740643,
-0.04870840162038803,
0.012894672341644764,
-0.0017000463558360934,
0.014812988229095936,
0.05539432913064957,
-0.02691151760518551,
0.03259073197841644,
0.022019075229763985,
-0.043078113347291946,
-0.07554526627063751,
0.04614962264895439,
-0.03748223930597305,
-0.02176680602133274,
-0.02986362762749195,
0.0061708493158221245,
0.019269516691565514,
-0.034391872584819794,
0.04034408554434776,
0.028483007103204727,
-0.037849560379981995,
-0.025322141125798225,
0.008733696304261684,
0.02455187775194645,
0.014810538850724697,
0.00806001853197813,
0.03498665988445282,
-0.006811443250626326,
-0.0009327134466730058,
-0.00047906325198709965,
0.010231904685497284,
0.004493371583521366,
0.010272668674588203,
0.014800755307078362,
0.030758628621697426,
-0.022516988217830658,
0.04354189708828926,
0.026054218411445618,
0.0259097870439291,
-0.0014384679961949587,
-0.0013511348515748978,
0.01916229911148548,
0.007322199176996946,
-0.01277224626392126,
0.009569360874593258,
-0.0038460404612123966,
0.08732371032238007,
-0.018970245495438576,
-0.027490787208080292,
-0.06599897146224976,
-0.01649397984147072,
-0.00018143541819881648,
0.0021252918522804976,
0.0002137019473593682,
0.01899568736553192,
-0.06822586059570312,
0.04137985780835152,
-0.03413781896233559,
0.038789600133895874,
0.0481623038649559,
-0.025317812338471413,
-0.020275689661502838,
-0.0033027995377779007,
0.006667429115623236,
0.005085486453026533,
0.021630587056279182,
-0.05415378883481026,
0.006592852994799614,
0.04387059062719345,
0.0330129973590374,
-0.006850545760244131,
0.021308185532689095,
0.0027992601972073317,
-0.05913319066166878,
0.02699161134660244,
-0.0419812947511673,
0.004849105142056942,
0.00979587435722351,
0.0230303555727005,
-0.01447302009910345,
0.057429321110248566
] |
<p>Is there a vibratory rate at which my hand would just pass right through the object and it could not be perceived by touch anymore?</p>
| 8,260 |
[
-0.020320454612374306,
-0.044471729546785355,
0.016958987340331078,
-0.03060195967555046,
0.012567720375955105,
-0.025323443114757538,
-0.04449397698044777,
0.0017264543566852808,
0.008175327442586422,
0.002129800384864211,
-0.006796043831855059,
0.07062137871980667,
0.035486139357089996,
0.00030812586192041636,
0.0005141374422237277,
-0.03903285041451454,
0.008342576213181019,
-0.014795202761888504,
-0.01516504492610693,
-0.02180880308151245,
-0.020097659900784492,
-0.013786238618195057,
-0.016566202044487,
0.019624678418040276,
-0.02190641686320305,
-0.0017026180867105722,
0.03817998990416527,
-0.018466519191861153,
0.023193394765257835,
0.015388639643788338,
-0.016381967812776566,
-0.009239651262760162,
-0.01680845208466053,
0.030735576525330544,
0.05824044346809387,
-0.005335514899343252,
-0.05704079195857048,
-0.016310667619109154,
-0.010598274879157543,
0.0294039323925972,
-0.03367139399051666,
0.01478803064674139,
-0.0022026582155376673,
0.05864784121513367,
0.002727598650380969,
0.013824018649756908,
0.022361058741807938,
-0.03135509043931961,
0.05110863968729973,
-0.021320795640349388,
0.0761861801147461,
-0.018510669469833374,
0.023420268669724464,
0.009783675894141197,
-0.014248957857489586,
0.003295269561931491,
0.09154025465250015,
0.06088729575276375,
-0.0590021125972271,
-0.025042327120900154,
-0.015935633331537247,
0.004252797458320856,
-0.04001729562878609,
-0.03280056640505791,
-0.021559637039899826,
0.014144071377813816,
-0.04265705123543739,
-0.024901214987039566,
0.03351987525820732,
0.0031790677458047867,
-0.015074927359819412,
0.010471392422914505,
0.06297249346971512,
0.018981654196977615,
0.01405383925884962,
-0.044825032353401184,
0.04518483951687813,
0.028804145753383636,
-0.00014066720905248076,
0.06783851981163025,
-0.0407877042889595,
-0.010311122983694077,
0.018033871427178383,
0.0671091079711914,
0.032745521515607834,
-0.031237924471497536,
0.07074623554944992,
-0.0288968775421381,
-0.0017817153129726648,
0.05791228264570236,
-0.011065899394452572,
-0.033648621290922165,
0.039656419306993484,
0.035204604268074036,
-0.024764586240053177,
-0.01127855759114027,
0.00022806401830166578,
0.04718417674303055,
0.022035548463463783,
-0.053933363407850266,
0.003254236886277795,
0.013445432297885418,
0.039791934192180634,
0.048855360597372055,
0.020126797258853912,
-0.04272991046309471,
-0.0038719004951417446,
0.02109682746231556,
0.0029066656716167927,
-0.009697342291474342,
-0.023303356021642685,
-0.02413426898419857,
-0.0007177434745244682,
0.00778602622449398,
0.027353527024388313,
0.008784612640738487,
-0.02357676811516285,
-0.04043613746762276,
0.034625567495822906,
0.07166332006454468,
0.03733326494693756,
-0.0603952594101429,
0.035936981439590454,
-0.04574502259492874,
-0.03143373131752014,
0.02929960936307907,
0.033986397087574005,
-0.012739383615553379,
-0.04021027684211731,
-0.008404407650232315,
-0.0009060160955414176,
-0.03924611955881119,
0.0388985201716423,
-0.05002471059560776,
0.027262980118393898,
-0.012116972357034683,
-0.08738747984170914,
-0.08516144007444382,
0.0646851658821106,
0.012070025317370892,
-0.05467376112937927,
-0.09247851371765137,
0.022739047184586525,
0.04446224495768547,
0.039500679820775986,
0.025105901062488556,
-0.0436873622238636,
-0.020961346104741096,
0.05036713182926178,
0.0013747059274464846,
-0.014343980699777603,
-0.026592392474412918,
0.0017888617003336549,
-0.042031180113554,
0.02417163923382759,
-0.026202453300356865,
0.01094796508550644,
0.06956472992897034,
0.01952185668051243,
-0.031666100025177,
0.005700582638382912,
-0.018128272145986557,
-0.02669808454811573,
0.00930726621299982,
-0.015421923249959946,
-0.06334351748228073,
0.06706087291240692,
0.014539478346705437,
-0.004937404301017523,
0.013175942935049534,
0.05096918344497681,
0.019775286316871643,
-0.008558967150747776,
0.04485447704792023,
0.014327596873044968,
-0.04298330098390579,
0.0227701086550951,
-0.015245003625750542,
-0.015174388885498047,
-0.010077561251819134,
-0.02796447090804577,
-0.03284984454512596,
0.009257233701646328,
0.00935677532106638,
-0.0012720878003165126,
0.010425359942018986,
-0.025311725214123726,
-0.013732310384511948,
-0.023653261363506317,
-0.03672567382454872,
-0.032802145928144455,
-0.0081558246165514,
0.037321653217077255,
0.0050965044647455215,
-0.0016762356972321868,
-0.0016448261449113488,
0.019439762458205223,
0.022647799924016,
-0.051510073244571686,
-0.010279982350766659,
-0.0030713973101228476,
0.004830787889659405,
0.03567465767264366,
-0.028926460072398186,
-0.037956904619932175,
0.04632362350821495,
0.031015075743198395,
0.0026312004774808884,
0.027892261743545532,
-0.012569180689752102,
-0.03439763933420181,
0.012310010381042957,
-0.0006318225641734898,
0.055562615394592285,
0.010282373055815697,
0.00639509130269289,
0.004972620401531458,
-0.01821994036436081,
-0.021689385175704956,
0.031395718455314636,
-0.008881829679012299,
0.0702577531337738,
0.026828844100236893,
-0.005512664094567299,
-0.01667832024395466,
-0.006867912132292986,
0.011361287906765938,
-0.030240453779697418,
-0.01032479852437973,
-0.04925352334976196,
-0.05499155819416046,
0.00964035838842392,
0.02841479703783989,
0.008241461589932442,
-0.0015600291080772877,
0.010632619261741638,
0.0022405232302844524,
0.040399231016635895,
0.05055016279220581,
0.0060258712619543076,
0.02858268842101097,
-0.037979140877723694,
-0.019024530425667763,
0.0029622018337249756,
0.009934918954968452,
0.0010465706000104547,
-0.005356189329177141,
0.031356461346149445,
0.021776407957077026,
0.0064324368722736835,
0.011972736567258835,
0.0005315479356795549,
0.01486898958683014,
0.01730305887758732,
-0.0030126869678497314,
-0.01828373223543167,
0.030000191181898117,
-0.040815506130456924,
0.006354923360049725,
0.011843010783195496,
0.008021487854421139,
-0.006749874912202358,
-0.007980805821716785,
-0.0007859863108024001,
0.017161430791020393,
0.027180185541510582,
0.007051706314086914,
-0.022625427693128586,
0.04404819756746292,
-0.01801009476184845,
-0.019442768767476082,
-0.0011225639609619975,
0.03985719382762909,
0.0014241471653804183,
-0.0034258475061506033,
0.031580209732055664,
0.04438566416501999,
0.051568835973739624,
-0.01973641850054264,
-0.024005088955163956,
0.01270687859505415,
-0.019563976675271988,
0.013775739818811417,
-0.0036137818824499846,
-0.03141346946358681,
-0.03943915665149689,
-0.011952697299420834,
-0.028148071840405464,
0.011974049732089043,
-0.02149730548262596,
-0.014894858933985233,
0.0098256291821599,
-0.008443277329206467,
-0.09073852002620697,
0.008664042688906193,
-0.0031941323541104794,
0.014309520833194256,
-0.046702153980731964,
0.028355883434414864,
0.01876760460436344,
0.019669296219944954,
-0.02552844025194645,
0.014443268068134785,
-0.020361190661787987,
-0.0412028543651104,
-0.015486296266317368,
-0.02404617890715599,
0.005458618514239788,
-0.029668105766177177,
-0.01052295882254839,
0.0028966600075364113,
-0.02078627608716488,
0.022852255031466484,
-0.027988722547888756,
-0.03246475011110306,
0.05649523064494133,
0.021741803735494614,
0.05582902580499649,
0.01254535187035799,
0.004444427322596312,
0.0891125425696373,
0.03592771664261818,
-0.0378456711769104,
0.00577657762914896,
-0.04224264249205589,
0.003584107616916299,
-0.030817661434412003,
0.0016920221969485283,
0.04245619475841522,
-0.025457333773374557,
0.011112065985798836,
0.02682013437151909,
0.022066542878746986,
0.029365703463554382,
-0.022602064535021782,
0.005424052942544222,
-0.008791203610599041,
0.007799607701599598,
-0.017170345410704613,
-0.014889408834278584,
0.014214505441486835,
-0.04133477434515953,
0.010360728949308395,
0.006462611258029938,
0.055155619978904724,
0.051968228071928024,
-0.012543563731014729,
0.07016777992248535,
-0.005598438438028097,
0.013310935348272324,
0.03748312219977379,
0.012094985693693161,
0.010124302469193935,
0.003953596111387014,
-0.05332466959953308,
0.054162535816431046,
0.056383166462183,
-0.007081456016749144,
0.004922893829643726,
0.03392098844051361,
0.03376626595854759,
0.0172436386346817,
-0.00179701903834939,
0.00666336202993989,
0.0323672741651535,
0.02921929582953453,
-0.0023850081488490105,
-0.02773023024201393,
0.016217805445194244,
0.0074004121124744415,
0.0439981184899807,
0.007506069261580706,
-0.01623835787177086,
0.009317471645772457,
-0.03751981258392334,
-0.007742848247289658,
0.00897958967834711,
0.004399977624416351,
0.007758143823593855,
0.02949538454413414,
0.0471196286380291,
0.030297894030809402,
-0.03478509932756424,
0.015281924046576023,
-0.0818350613117218,
0.03534572571516037,
-0.06904730945825577,
-0.01639784686267376,
-0.008236292749643326,
-0.0005386754055507481,
-0.029502805322408676,
-0.002761385403573513,
-0.03796298801898956,
-0.007303259801119566,
-0.009273499250411987,
-0.05587563291192055,
-0.006573440507054329,
0.00287017528899014,
0.019779616966843605,
-0.015062305144965649,
0.00308929942548275,
0.009009040892124176,
-0.005418024957180023,
0.029928624629974365,
0.01352138165384531,
0.018665539100766182,
0.022213559597730637,
-0.013436995446681976,
-0.026650020852684975,
-0.05041838437318802,
0.038112152367830276,
-0.01738245226442814,
0.0002787862904369831,
-0.03405863791704178,
0.0053990306332707405,
-0.02159598469734192,
0.04848438501358032,
-0.00016360385052394122,
-0.0313553586602211,
-0.04171163961291313,
-0.07808325439691544,
-0.009707702323794365,
0.018322337418794632,
0.083851158618927,
-0.009270540438592434,
0.017561281099915504,
0.01500637549906969,
0.008770584128797054,
-0.04193445295095444,
0.026705319061875343,
-0.005768134258687496,
0.016729796305298805,
-0.02521076425909996,
-0.056033141911029816,
0.00404930068179965,
0.012970149517059326,
0.010797022841870785,
0.01400297973304987,
0.028898490592837334,
-0.014142493717372417,
-0.002313939156010747,
-0.027187475934624672,
0.033952273428440094,
-0.032043807208538055,
0.006449394393712282,
-0.01649703085422516,
-0.030075963586568832,
-0.04623067378997803,
0.011695461347699165,
0.03475039824843407,
0.015449161641299725,
0.03936128318309784,
-0.02623973786830902,
-0.0031523413490504026,
-0.09158843755722046,
-0.023237621411681175,
0.02745353989303112,
0.006612452212721109,
-0.008474119007587433,
0.021294118836522102,
-0.030765997245907784,
-0.03582801669836044,
0.03881901502609253,
-0.01338429655879736,
0.009587541222572327,
-0.0723295584321022,
0.018401669338345528,
-0.08383128046989441,
-0.028820408508181572,
-0.02546696737408638,
0.0011722760973498225,
-0.005384582094848156,
-0.02905876561999321,
0.026996782049536705,
-0.03138553351163864,
0.009324911050498486,
-0.003847906133159995,
0.027783339843153954,
0.04945334792137146,
0.03364668786525726,
0.018775155767798424,
-0.020467866212129593,
-0.0016554080648347735,
-0.05272620543837547,
-0.0487128309905529,
0.016127919778227806,
0.021026497706770897,
-0.0140620656311512,
0.02148684859275818,
-0.0003823962470050901,
-0.024302124977111816,
0.06887733191251755,
0.001420838525518775,
0.014241986908018589,
0.005065086297690868,
-0.03803270310163498,
0.04793653264641762,
0.024426452815532684,
-0.008575979620218277,
0.029213765636086464,
0.007258511148393154,
-0.018695246428251266,
0.0083065340295434,
0.0057450239546597,
0.0509859062731266,
-0.01158461719751358,
0.003931600134819746,
-0.003536999924108386,
0.0008471590117551386,
-0.047887083142995834,
0.048974644392728806,
-0.01297858078032732,
0.03765210136771202,
0.012967205606400967,
-0.039397794753313065,
-0.025843588635325432,
0.027674812823534012,
0.007423705887049437,
-0.0033221228513866663,
0.010692992247641087,
-0.01773005537688732,
-0.03198627382516861,
-0.0036003177519887686,
0.005527363624423742,
-0.016859935596585274,
0.03368144854903221,
0.07159611582756042,
-0.012394513934850693,
0.016896219924092293,
-0.058932751417160034,
-0.019181091338396072,
-0.004928430076688528,
-0.04505050182342529,
0.03903007507324219,
-0.047306422144174576,
-0.002348326612263918,
0.0356411449611187,
-0.041821546852588654,
0.020386286079883575,
0.024904988706111908,
-0.02523866482079029,
0.06960044056177139,
-0.027209872379899025,
0.035438865423202515,
-0.014490480534732342,
0.017353372648358345,
-0.058790698647499084,
-0.06727444380521774,
0.06122240051627159,
0.0585782416164875,
-0.00641960185021162,
-0.011969602666795254,
-0.03551338240504265,
-0.031647153198719025,
-0.04122360423207283,
0.02806130237877369,
0.021023640409111977,
0.023731784895062447,
0.04268234968185425,
0.037397559732198715,
-0.002635003300383687,
0.03560105338692665,
0.008456585928797722,
-0.039533235132694244,
0.013875375501811504,
-0.016987474635243416,
-0.028662431985139847,
-0.015535873360931873,
0.07153426855802536,
-0.05770767480134964,
-0.025622418150305748,
0.007175407372415066,
-0.04373330995440483,
0.051191769540309906,
0.0002458511444274336,
0.005003335885703564,
0.03630852326750755,
-0.011539330706000328,
0.014261276461184025,
-0.01881841942667961,
0.06544790416955948,
0.016901150345802307,
-0.0006860751309432089,
-0.015656933188438416,
-0.027990370988845825,
-0.030924154445528984,
-0.05384527146816254,
0.03382522240281105,
0.03210236877202988,
0.01426419522613287,
0.006875642575323582,
0.06474880874156952,
-0.028634287416934967,
-0.012687915936112404,
0.0023745037615299225,
-0.032480668276548386,
0.030657727271318436,
-0.01824827678501606,
-0.027110915631055832,
-0.02870299480855465,
-0.015367499552667141,
-0.032349687069654465,
-0.016773628070950508,
-0.03106764145195484,
-0.028551863506436348,
0.053763777017593384,
-0.02877233549952507,
0.024311073124408722,
-0.018275322392582893,
-0.04182532802224159,
-0.013168012723326683,
0.016785675659775734,
-0.03018864057958126,
0.0037373253144323826,
-0.02916829288005829,
0.016615532338619232,
-0.006707586348056793,
0.02083279937505722,
-0.0009328652522526681,
0.02914820797741413,
-0.02825315296649933,
0.0202114786952734,
0.03002948872745037,
0.04318346083164215,
0.062228236347436905,
-0.0511251799762249,
0.014065222814679146,
-0.01755429431796074,
-0.07972707599401474,
0.029759081080555916,
0.011363353580236435,
0.00803106278181076,
-0.006498248316347599,
-0.0035996490623801947,
-0.01374086458235979,
-0.0008974898373708129,
-0.016681721433997154,
-0.023650143295526505,
0.001094750128686428,
-0.006013514474034309,
0.0360255241394043,
0.01825702004134655,
-0.02248861826956272,
-0.00021496214321814477,
-0.02505195513367653,
0.026436490938067436,
0.0067151449620723724,
-0.028692910447716713,
-0.00686793215572834,
-0.031170379370450974,
-0.018453475087881088,
0.04264453798532486,
-0.0038919595535844564,
-0.017286425456404686,
0.03939242288470268,
-0.032046906650066376,
0.03538234531879425,
0.00938054732978344,
0.04217514023184776,
0.01592789776623249,
0.1101621761918068,
0.004875145386904478,
0.006051781587302685,
-0.02646373212337494,
0.05657314881682396,
0.13123764097690582,
0.044870827347040176,
0.0008822961826808751,
0.011968649923801422,
0.04083452373743057,
-0.03416185453534126,
-0.04858929663896561,
-0.01880224235355854,
0.02808307856321335,
-0.013603060506284237,
0.0016405603382736444,
0.012225985527038574,
0.06530655920505524,
0.017165346071124077,
0.0068092686124145985,
0.04129026457667351,
-0.006551128812134266,
0.025895092636346817,
0.0005653473199345171,
0.018782900646328926,
0.0020663042087107897,
-0.013276174664497375,
-0.01330074854195118,
0.02149287424981594,
-0.025383908301591873,
-0.014973253011703491,
0.010709425434470177,
-0.04088295251131058,
0.037234045565128326,
-0.013326553627848625,
-0.01802079938352108,
-0.003016482573002577,
0.04634501785039902,
-0.02573084644973278,
-0.042820848524570465,
0.008692177012562752,
0.049638405442237854,
0.01927008107304573,
0.014348402619361877,
0.04634837061166763,
0.005902071949094534,
0.020849475637078285,
0.028003133833408356,
0.008570644073188305,
-0.04481523483991623,
-0.013262440450489521,
-0.04284397512674332,
-0.00774820102378726,
0.010532107204198837,
0.00968799740076065,
0.015805745497345924,
-0.022371472790837288,
-0.014065541326999664,
-0.031001850962638855,
-0.032089002430438995,
-0.0006737781222909689,
0.0019339596619829535,
0.02604774385690689,
-0.013533961959183216,
0.012972522526979446,
0.006798478774726391,
0.033571235835552216,
0.025276264175772667,
-0.026588302105665207,
-0.007131281774491072,
0.001388341886922717,
0.032358262687921524,
0.015000538900494576,
-0.010838093236088753,
-0.05452875792980194,
0.03107132576406002,
-0.023318598046898842,
-0.04431914538145065,
0.007857237011194229,
-0.03104403242468834,
0.04356562718749046,
0.0337543748319149,
-0.023321298882365227,
-0.053272608667612076,
-0.071262426674366,
-0.02558550052344799,
0.045694876462221146,
-0.02279598079621792,
-0.0038030820433050394,
0.016463521867990494,
-0.0228356271982193,
0.02017880789935589,
0.032249484211206436,
-0.0424613282084465,
-0.009265181608498096,
-0.020117059350013733,
0.05002332851290703,
0.023618394508957863,
-0.005435241386294365,
-0.026094580069184303,
0.0005886198487132788,
-0.030806800350546837,
0.061518628150224686,
-0.024278229102492332,
0.061725348234176636,
0.017789166420698166,
-0.012365985661745071,
0.02498638816177845,
-0.009575971402227879,
-0.03626098483800888,
-0.017258167266845703,
-0.0022398829460144043,
-0.045967016369104385,
-0.030465291813015938,
0.003638348076492548,
0.024412965402007103,
-0.016200168058276176,
-0.05687073990702629,
-0.08045580983161926,
-0.00034190481528639793,
-0.03512970730662346,
0.06315000355243683,
0.024231290444731712,
0.01970820128917694,
-0.010448184795677662,
-0.020537519827485085,
-0.016269944608211517,
-0.019375212490558624,
-0.048622410744428635,
-0.005541178863495588,
-0.026061521843075752,
0.014347514137625694,
0.024338824674487114,
0.03788413852453232,
-0.04706640541553497,
0.027109883725643158,
0.0024127685464918613,
0.021334199234843254,
-0.01105921994894743,
-0.019307754933834076,
0.038931041955947876,
0.006084003951400518,
0.018355008214712143,
0.003043054835870862,
-0.03781493008136749,
0.05287791043519974,
-0.03833751380443573,
-0.02599216252565384,
0.03766598179936409,
-0.029945198446512222,
0.025892941281199455,
0.0084734121337533,
-0.01461759116500616,
0.001362365554086864,
0.09733659774065018,
0.009984316304326057,
0.012298737652599812,
0.01702398620545864,
0.02189803309738636,
-0.0226396806538105,
0.020709335803985596,
0.025585249066352844,
-0.006190806161612272,
-0.04240475594997406,
0.03492697700858116,
-0.01986796408891678,
0.019595559686422348,
-0.0009202143992297351,
0.02181144990026951,
-0.026015251874923706,
0.009436354041099548,
0.02830134704709053,
0.025347677990794182,
0.012735859490931034,
0.024675238877534866,
-0.010616772808134556,
0.009598590433597565,
0.03630993887782097,
-0.012604493647813797,
-0.10340256989002228,
-0.022131241858005524,
-0.04203669726848602,
0.03233521804213524,
0.06568669527769089,
-0.06111203134059906,
0.04980261251330376,
0.01241858396679163,
-0.05335257574915886,
0.038186002522706985,
-0.0076073044911026955,
-0.03765706717967987,
-0.04261629283428192,
0.017626501619815826,
-0.014211640693247318,
-0.005988069344311953,
0.03365105390548706,
0.03556806221604347,
0.01119163166731596,
0.02444503828883171,
-0.05743807181715965,
-0.01162191852927208,
0.01976591907441616,
0.039407216012477875,
-0.0222189798951149,
-0.006134930998086929,
0.059730228036642075,
-0.04091624170541763,
-0.010524691082537174,
0.009579136036336422,
-0.01999901421368122,
0.0384896844625473,
-0.0027436090167611837,
0.01840500347316265,
0.034576416015625,
0.00889770220965147,
0.02573496103286743,
-0.004302255343645811,
-0.02165018394589424,
0.011787482537329197,
-0.009216699749231339,
0.026648836210370064,
-0.04086671024560928,
0.009243819862604141,
-0.001944340649060905,
-0.034599095582962036,
-0.0422268845140934,
-0.026510749012231827,
-0.03365488722920418,
0.0033624544739723206,
0.03294503316283226,
0.001986101269721985,
0.0429345928132534,
-0.018847867846488953,
-0.017447780817747116,
-0.043423015624284744,
0.0022189340088516474,
0.026481103152036667,
-0.026364924386143684,
-0.01881122961640358,
0.020185695961117744,
-0.001971112797036767,
-0.0291331447660923,
-0.0211293064057827,
0.02485893853008747,
-0.018337950110435486,
-0.07991080731153488,
-0.04792686924338341,
0.014229162596166134,
0.006903632543981075,
0.002980748424306512,
0.002677649725228548,
-0.0198373906314373,
0.03731405362486839,
0.03738582134246826,
0.01800684817135334,
0.03752566874027252,
0.0014019120717421174,
-0.01411795150488615,
-0.05864185094833374,
0.02235528640449047,
-0.0037028398364782333,
-0.005715525709092617,
-0.03409740328788757,
-0.02195696160197258,
0.00708978483453393,
-0.017730597406625748,
0.09229724109172821,
-0.023418694734573364,
-0.012982421554625034,
-0.0011572663206607103,
0.0063868374563753605,
0.00175444595515728,
-0.01559892576187849,
-0.011600733734667301,
-0.01488636713474989,
-0.017619702965021133,
-0.010503907687962055,
0.013033988885581493,
-0.027707427740097046,
-0.04157273471355438,
0.005591554567217827,
0.024579057469964027,
0.004443471319973469,
-0.004876366350799799,
-0.021230263635516167,
0.052037566900253296,
0.023433033376932144,
0.016222497448325157,
0.031522996723651886,
-0.026468243449926376,
0.0032057093922048807,
-0.018768087029457092,
-0.030748285353183746,
-0.0776490867137909,
0.036036793142557144,
-0.028502698987722397,
0.005256791599094868,
-0.009710036218166351,
-0.014888633973896503,
0.007228157017379999,
-0.00365322083234787,
-0.007973561994731426,
0.037969447672367096,
0.018155602738261223,
0.001047857804223895,
0.03790343180298805,
0.015439444221556187,
0.045014139264822006,
-0.004163880832493305,
-0.004021519795060158,
0.020659007132053375,
-0.03454180061817169,
-0.0019350103102624416,
0.010643701069056988,
-0.01927139423787594,
-0.02233319729566574,
-0.014745953492820263,
-0.005112352780997753,
0.013158767484128475,
0.03359173983335495,
0.02624678984284401,
0.032947540283203125,
-0.0045819394290447235,
-0.03837373107671738,
0.010761030949652195,
0.013111933134496212,
-0.01981249637901783,
0.022430630400776863,
-0.01144974585622549,
0.09087955951690674,
0.025264497846364975,
0.007066468242555857,
-0.014650721102952957,
-0.00859851948916912,
-0.005503878928720951,
0.011491987854242325,
0.03519265726208687,
0.008981136605143547,
-0.037389617413282394,
-0.013841363601386547,
-0.023420581594109535,
-0.009489393793046474,
0.037294719368219376,
-0.062350086867809296,
0.017143819481134415,
0.0008143830928020179,
0.0125513207167387,
-0.010461941361427307,
-0.036352816969156265,
-0.02441774308681488,
-0.02402171678841114,
0.031573113054037094,
0.02566492184996605,
0.000329440226778388,
0.005297400057315826,
0.04125181958079338,
0.0060777366161346436,
0.053744103759527206,
-0.07140062004327774,
0.02644461952149868,
-0.003928325138986111,
0.05860050767660141,
0.008052932098507881,
0.012665687128901482
] |
<p>Please,kindly help me; my teacher assigned me problem set, and she never went over anything about interferometers in class. Also, there is almost no information about about how to solve interferometer problems in my book. I have no idea how to set this problem up, and I have no intuition concerning how I should solve it...
Can someone help me set this problem up and explain it? I know if this example is solved, I will be able to solve the rest of the problems:</p>
<p>Sodium D lines, of wavelength(a)=589.0 nanometers and wavelength(b)=589.6 nanometers are used on a <a href="http://en.wikipedia.org/wiki/Michelson_interferometer" rel="nofollow">Michelson interferometer</a>. When the first mirror moves, these lines periodically appear and disappear. Explain, in detail, this phenomenon and write an equation that would allow you to know how much the mirror must move to make the lines reappear and disappear one time.</p>
| 8,261 |
[
0.0018687850097194314,
-0.016171185299754143,
-0.0452963151037693,
0.016668912023305893,
0.0567309632897377,
0.008411217480897903,
-0.021577367559075356,
-0.03240804001688957,
0.005811577662825584,
0.010852147825062275,
0.05124795064330101,
0.0484425313770771,
0.03767678514122963,
0.02795177511870861,
0.014159340411424637,
0.012964659370481968,
-0.029089387506246567,
-0.03735661879181862,
-0.01880253665149212,
-0.02668694406747818,
-0.013914414681494236,
0.013116931542754173,
0.027301739901304245,
-0.022807711735367775,
-0.028977196663618088,
0.029514793306589127,
0.0027545818593353033,
-0.01647055149078369,
0.04551974684000015,
0.022940294817090034,
-0.019015533849596977,
-0.02535831741988659,
0.008532034233212471,
0.007042236160486937,
0.0020995968952775,
0.0356132797896862,
-0.0027182414196431637,
0.0014426599955186248,
-0.010576595552265644,
0.026029756292700768,
-0.021389121189713478,
0.027200274169445038,
-0.008416474796831608,
0.04329325258731842,
-0.008318942971527576,
-0.0377972349524498,
0.03226644545793533,
-0.011479123495519161,
0.03465578332543373,
-0.06029155105352402,
0.09806528687477112,
-0.012162567116320133,
0.057654786854982376,
0.022214634343981743,
-0.015573686920106411,
-0.030645018443465233,
0.07023423910140991,
0.0836181715130806,
-0.01570678874850273,
-0.03475823253393173,
-0.02412348799407482,
-0.003984260372817516,
-0.04564256966114044,
-0.0026414289604872465,
-0.02690145932137966,
0.018019547685980797,
-0.011073296889662743,
-0.01901588775217533,
0.05365106835961342,
0.02661416307091713,
0.013986359350383282,
0.015844285488128662,
0.05432521179318428,
-0.024023620411753654,
0.0027529275976121426,
-0.041745301336050034,
0.000728026672732085,
0.038695015013217926,
0.018643904477357864,
0.05615110322833061,
-0.00046618125634267926,
0.04684622958302498,
0.017601078376173973,
0.03061293065547943,
0.022446976974606514,
-0.03502703830599785,
0.08502035588026047,
0.005459451116621494,
0.004451367538422346,
0.0024400020483881235,
0.0016800384037196636,
0.03164098411798477,
0.04073705896735191,
0.023344475775957108,
-0.035591185092926025,
0.005118686240166426,
-0.008538838475942612,
0.05535723268985748,
0.008450406603515148,
-0.019183531403541565,
0.014664126560091972,
-0.024511929601430893,
0.01999463327229023,
0.0593210868537426,
-0.010754108428955078,
-0.0034096434246748686,
-0.034252967685461044,
0.019535956904292107,
-0.02157425321638584,
-0.007279545068740845,
-0.02662121318280697,
0.03448936343193054,
-0.008755713701248169,
0.01758887805044651,
-0.000520449539180845,
-0.02804475463926792,
-0.036123357713222504,
-0.001155711361207068,
0.0432853139936924,
0.0710877999663353,
0.017449816688895226,
-0.012889922596514225,
0.034042954444885254,
0.002868291223421693,
-0.06666410714387894,
-0.002639650832861662,
0.006301695480942726,
-0.010858544148504734,
-0.03591029345989227,
0.04299652576446533,
-0.018161889165639877,
0.0012799837859347463,
0.0021025969181209803,
-0.027512485161423683,
0.05709061399102211,
-0.022770846262574196,
-0.10077302902936935,
-0.08937554061412811,
0.04789390787482262,
-0.016251325607299805,
0.00033749602152965963,
-0.07282733917236328,
0.004427302163094282,
0.05672598257660866,
0.10034478455781937,
-0.00397271104156971,
-0.01164252869784832,
-0.008306764997541904,
0.023950878530740738,
-0.030194737017154694,
-0.009621253237128258,
-0.01988985575735569,
0.01985093206167221,
-0.046447984874248505,
-0.010139144025743008,
-0.0647284984588623,
-0.007099837530404329,
0.05370272696018219,
-0.018320279195904732,
-0.041872765868902206,
0.02137451060116291,
0.007579182740300894,
0.0009324242128059268,
0.013096259906888008,
-0.008117537014186382,
-0.026470042765140533,
0.08162201941013336,
0.02104996331036091,
-0.023352675139904022,
0.07452032715082169,
0.009926809929311275,
0.038208797574043274,
-0.03325611725449562,
0.026286877691745758,
0.013839904218912125,
0.0044775898568332195,
0.0084117716178298,
0.03092166595160961,
-0.019911710172891617,
0.05281665548682213,
-0.009023051708936691,
-0.023500900715589523,
0.022300055250525475,
0.021154478192329407,
0.013824274763464928,
0.025982584804296494,
-0.005656912922859192,
0.020903289318084717,
-0.011679322458803654,
-0.03286710008978844,
-0.011781408451497555,
-0.004391300957649946,
0.031371306627988815,
-0.017524374648928642,
-0.016176782548427582,
-0.01368024293333292,
0.0029335306026041508,
-0.006203345954418182,
-0.022373557090759277,
-0.0502043291926384,
-0.005562819540500641,
0.01171946246176958,
0.004027172457426786,
-0.0011736482847481966,
0.042502012103796005,
0.06416204571723938,
0.04659689590334892,
-0.0332178957760334,
0.018621595576405525,
-0.056047290563583374,
0.049616552889347076,
-0.012345923110842705,
-0.007635314483195543,
0.01698293164372444,
0.011349204927682877,
0.01371876522898674,
-0.012850155122578144,
0.01957506313920021,
0.011287493631243706,
0.016895996406674385,
-0.03747282177209854,
0.03733684495091438,
0.048025671392679214,
0.021964188665151596,
-0.0015609964029863477,
0.014394823461771011,
0.010613461956381798,
0.036370649933815,
0.0026306260842829943,
-0.05797206237912178,
-0.06144547834992409,
-0.0025706884916871786,
-0.023352067917585373,
0.01161628682166338,
-0.02388397790491581,
0.011639416217803955,
0.05787153169512749,
0.010399101302027702,
0.01592874899506569,
0.017146015539765358,
-0.032906126230955124,
-0.022147875279188156,
0.0036262325011193752,
0.013314384035766125,
-0.0064261117950081825,
0.024520952254533768,
0.006171425338834524,
0.018717758357524872,
0.00845780223608017,
-0.01263500191271305,
-0.009432182647287846,
0.023713739588856697,
-0.010052014142274857,
0.026066264137625694,
0.010676170699298382,
0.00108565844129771,
0.05219990015029907,
-0.012541530653834343,
0.03138215094804764,
0.05408599227666855,
-0.019698241725564003,
0.010566115379333496,
-0.04299582168459892,
0.006167617626488209,
0.014550464227795601,
-0.005062533542513847,
-0.008102738298475742,
-0.01573396660387516,
0.022552503272891045,
-0.004436910152435303,
0.02018008939921856,
-0.0020561490673571825,
0.002375225303694606,
-0.026560340076684952,
0.007960109040141106,
0.0073208995163440704,
0.015815094113349915,
0.0661814957857132,
-0.04418519139289856,
-0.027715550735592842,
-0.007711188867688179,
-0.045588865876197815,
0.005124130751937628,
-0.014687062241137028,
-0.026077205315232277,
0.010651546530425549,
0.009385323151946068,
-0.021659132093191147,
0.036392759531736374,
0.01076352410018444,
-0.00003819164339802228,
0.0027709342539310455,
-0.017277134582400322,
-0.05775335431098938,
-0.024186518043279648,
-0.005383264739066362,
-0.004297097213566303,
-0.03926295042037964,
0.025699693709611893,
0.034279223531484604,
0.00982171855866909,
-0.011479156091809273,
0.001202817540615797,
-0.05553087219595909,
-0.029086921364068985,
-0.022504160180687904,
-0.016848772764205933,
0.012313777580857277,
-0.019427917897701263,
0.01518299337476492,
-0.014896663837134838,
-0.013061141595244408,
0.013183045201003551,
-0.052007291465997696,
-0.06308753788471222,
0.014700588770210743,
-0.008632151409983635,
0.010801892727613449,
-0.02479938417673111,
-0.019788483157753944,
0.06741306930780411,
0.023300696164369583,
-0.06697823852300644,
0.000033510452340124175,
0.00949329137802124,
-0.010484766215085983,
-0.03851558640599251,
0.0355047732591629,
0.03603976592421532,
-0.05977720022201538,
0.01727430149912834,
0.006017175503075123,
0.01716798171401024,
0.05974822863936424,
0.023132069036364555,
0.015079733915627003,
-0.006099677179008722,
0.014274383895099163,
0.008013922721147537,
0.0521421916782856,
0.03728862851858139,
-0.03399595990777016,
0.0031236200593411922,
-0.01342551875859499,
0.042399052530527115,
0.009652674198150635,
-0.058994535356760025,
0.01619037240743637,
0.001339507638476789,
-0.01492838654667139,
-0.02642589621245861,
0.008473025634884834,
0.030012022703886032,
0.0137422364205122,
-0.013376076705753803,
-0.014101308770477772,
0.03700367361307144,
-0.002589307026937604,
-0.026290331035852432,
0.046947918832302094,
0.007229912094771862,
0.015091083012521267,
-0.02175801247358322,
-0.02516501024365425,
-0.0036207428202033043,
0.004974585957825184,
-0.07434912770986557,
-0.02933451719582081,
0.03761120140552521,
0.03950365632772446,
0.039556603878736496,
-0.03334450349211693,
-0.042875491082668304,
0.002765286946669221,
-0.06911640614271164,
-0.003760415129363537,
-0.0049632093869149685,
0.0436628982424736,
0.012364348396658897,
0.02189948596060276,
0.0411984883248806,
0.029760096222162247,
0.03155363351106644,
-0.03227692469954491,
-0.08722319453954697,
0.0691874697804451,
-0.013115441426634789,
-0.028835780918598175,
-0.0137200728058815,
-0.0013461591443046927,
0.01893041282892227,
-0.05368606746196747,
-0.013378022238612175,
-0.019980866461992264,
0.023609302937984467,
-0.06890590488910675,
-0.006076727993786335,
-0.0121952835470438,
-0.016575215384364128,
-0.044697150588035583,
0.03955616429448128,
0.025494184345006943,
-0.023073645308613777,
0.013845643028616905,
0.04786481335759163,
-0.02177780494093895,
-0.016783101484179497,
0.002051372779533267,
-0.04243079572916031,
0.03487019240856171,
0.050096601247787476,
0.022187180817127228,
0.037886302918195724,
-0.01953284628689289,
0.014786685816943645,
0.0241690706461668,
0.026664791628718376,
-0.003172541270032525,
-0.02606039121747017,
-0.021633686497807503,
-0.03564300760626793,
-0.0032765937503427267,
-0.0033541263546794653,
0.09874957799911499,
-0.015017244033515453,
-0.02233535796403885,
0.024913964793086052,
-0.011305972933769226,
-0.028767233714461327,
0.06232871860265732,
0.02646566554903984,
0.029440373182296753,
0.009971238672733307,
-0.0313410721719265,
0.0004226850578561425,
-0.034062884747982025,
0.019719086587429047,
0.0444088950753212,
0.006017932668328285,
0.0017022558022290468,
-0.008309531956911087,
0.025506721809506416,
0.03018615022301674,
-0.00026740581961348653,
0.009941661730408669,
-0.02115306816995144,
-0.022341972216963768,
-0.009709087200462818,
-0.02298590913414955,
0.008972364477813244,
0.05436639115214348,
0.045669350773096085,
-0.021295109763741493,
0.018407568335533142,
-0.10946016013622284,
-0.012598195113241673,
0.024576233699917793,
0.026301227509975433,
-0.0008823127718642354,
-0.0012795707443729043,
-0.044919274747371674,
-0.004603725858032703,
0.0500413216650486,
-0.057504404336214066,
0.04104559123516083,
-0.011239965446293354,
0.009438666515052319,
-0.02819432131946087,
-0.018582699820399284,
0.002230498706921935,
0.00979602336883545,
-0.017868248745799065,
0.01734175533056259,
-0.012385650537908077,
-0.006615549325942993,
0.0035426539834588766,
0.01483119372278452,
0.05466119945049286,
0.04412012919783592,
0.003542466787621379,
-0.043800339102745056,
0.03618542104959488,
0.012586312368512154,
-0.049649834632873535,
-0.05263330414891243,
0.03407677635550499,
-0.03810194134712219,
-0.023704305291175842,
0.07002738118171692,
-0.03176514431834221,
-0.031226979568600655,
0.028701839968562126,
0.02505275048315525,
-0.020684244111180305,
-0.047924429178237915,
-0.01444951817393303,
0.011558336205780506,
0.029743380844593048,
-0.01932334154844284,
0.05282008275389671,
0.034187499433755875,
0.020506398752331734,
0.0051198191940784454,
0.007141001522541046,
0.030021559447050095,
-0.013278823345899582,
-0.01648120954632759,
-0.014519521966576576,
0.0030538307037204504,
-0.029870416969060898,
0.06573236733675003,
-0.030954662710428238,
-0.018999066203832626,
-0.024993686005473137,
-0.019243231043219566,
0.000029134966098354198,
0.02712910808622837,
-0.005541796796023846,
0.01351273525506258,
-0.0011527861934155226,
-0.004625882487744093,
0.04610622674226761,
-0.042937666177749634,
0.015672927722334862,
-0.016350794583559036,
-0.0005851880996488035,
0.0027962946332991123,
0.010063265450298786,
0.03375448286533356,
-0.018149442970752716,
-0.04029790684580803,
0.007488110568374395,
-0.07183106988668442,
0.007396814413368702,
-0.025873543694615364,
0.038006626069545746,
0.05847327038645744,
-0.06472177058458328,
-0.034178122878074646,
0.007313209120184183,
-0.006150775123387575,
0.017069565132260323,
-0.05326319858431816,
0.007927724160254002,
0.018071237951517105,
0.017239421606063843,
-0.04718686267733574,
-0.03501012548804283,
0.030919229611754417,
0.009380914270877838,
-0.04270307347178459,
0.025584101676940918,
-0.007914680987596512,
0.038389258086681366,
-0.03033670037984848,
-0.005443739704787731,
-0.006574725266546011,
-0.019325759261846542,
-0.0272834412753582,
0.04031231999397278,
0.016136858612298965,
0.07565345615148544,
-0.016839100047945976,
-0.01132226549088955,
-0.019208498299121857,
-0.041775740683078766,
-0.02227078378200531,
-0.024250810965895653,
0.027632620185613632,
-0.03208281099796295,
-0.08214841783046722,
-0.018041018396615982,
0.022992974147200584,
0.041440289467573166,
-0.016073089092969894,
0.005155771505087614,
-0.02377135120332241,
0.039985064417123795,
-0.005807394161820412,
-0.03760450705885887,
0.002303899032995105,
-0.02122102677822113,
0.03705877065658569,
0.020710129290819168,
0.028789743781089783,
-0.006839097011834383,
-0.022660888731479645,
-0.003195403842255473,
0.0008343395893462002,
-0.009128366596996784,
-0.02010307088494301,
0.08019373565912247,
-0.018289880827069283,
-0.00893985666334629,
0.03289085999131203,
-0.010972409509122372,
-0.009836463257670403,
-0.023428259417414665,
-0.0002561991277616471,
-0.008435913361608982,
0.011785900220274925,
-0.020721986889839172,
-0.058522045612335205,
-0.02195674367249012,
-0.011339793913066387,
0.07301884144544601,
-0.021297801285982132,
0.05189890041947365,
0.022412531077861786,
0.02069568820297718,
0.020427776500582695,
-0.018089178949594498,
-0.03792480379343033,
-0.013309266418218613,
0.041451346129179,
0.008043976500630379,
-0.058232102543115616,
-0.011748618446290493,
0.00856017041951418,
0.04624813795089722,
0.026216791942715645,
0.002215663203969598,
0.011497428640723228,
0.03908216208219528,
0.009134318679571152,
0.011620820499956608,
-0.031211476773023605,
0.010983186773955822,
0.018109358847141266,
0.0503414161503315,
0.004283912945538759,
0.006463985424488783,
0.03204502910375595,
0.019429922103881836,
0.049589503556489944,
-0.03213059902191162,
-0.015833957120776176,
-0.033062759786844254,
0.005025397054851055,
0.0025660162791609764,
0.007859958335757256,
0.008775006048381329,
0.020405501127243042,
-0.008702313527464867,
0.021395724266767502,
0.0338357575237751,
-0.04921553656458855,
-0.04148009791970253,
-0.03293931111693382,
-0.016497207805514336,
-0.06251406669616699,
0.08994537591934204,
-0.032136254012584686,
-0.043044302612543106,
0.026068666949868202,
0.001532296184450388,
0.02638821490108967,
0.030458342283964157,
0.03024805337190628,
-0.023531168699264526,
0.06928819417953491,
-0.014486972242593765,
0.028914326801896095,
0.01814878173172474,
0.022032495588064194,
0.08314401656389236,
0.023217473179101944,
0.019788099452853203,
-0.05441118776798248,
0.01224098913371563,
-0.02443026192486286,
0.011543664149940014,
-0.04462122917175293,
0.03658080846071243,
-0.015965677797794342,
0.04845865070819855,
0.010879967361688614,
0.008834796026349068,
-0.003238704986870289,
0.010214976035058498,
0.02227405272424221,
-0.04456563666462898,
-0.032082512974739075,
0.012027227319777012,
-0.010468601249158382,
0.006190669722855091,
0.045963190495967865,
-0.0564434789121151,
0.04190491512417793,
-0.03548896312713623,
-0.029132410883903503,
-0.014451905153691769,
-0.018479717895388603,
0.025637591257691383,
-0.006001889239996672,
-0.027403919026255608,
0.06510262936353683,
0.017888551577925682,
-0.02684929221868515,
-0.025939082726836205,
0.03868795931339264,
0.006258384324610233,
-0.020411577075719833,
0.027485301718115807,
0.03793703392148018,
-0.019062452018260956,
-0.015712609514594078,
0.04737917333841324,
0.0054101464338600636,
-0.02980165369808674,
-0.0072790184058249,
-0.013060311786830425,
0.07395753264427185,
0.0011608158238232136,
-0.04075881093740463,
-0.015136918053030968,
0.01705360785126686,
0.004714495502412319,
-0.07425782829523087,
-0.04250652715563774,
-0.01453386154025793,
-0.023699963465332985,
-0.038793809711933136,
-0.024125341325998306,
-0.004964121617376804,
0.006806208286434412,
0.036414772272109985,
0.007430769503116608,
-0.003583542536944151,
0.04261995479464531,
-0.020883535966277122,
0.0004409046669024974,
0.045919254422187805,
-0.03666054084897041,
0.0049458276480436325,
-0.012396389618515968,
0.018976720049977303,
-0.016499437391757965,
-0.0047292690724134445,
0.014689548872411251,
0.03181829676032066,
0.012607821263372898,
0.0011914995266124606,
-0.030528556555509567,
-0.024542342871427536,
-0.05847307667136192,
0.0034040790051221848,
-0.016798267140984535,
-0.05141224339604378,
-0.010000635869801044,
-0.0029934290796518326,
0.04779411107301712,
0.03857921436429024,
0.000605153851211071,
0.017436616122722626,
0.0333828330039978,
0.0013697503600269556,
0.03119875118136406,
-0.015003741718828678,
-0.030166804790496826,
-0.033429328352212906,
-0.01642111875116825,
-0.009655466303229332,
-0.009166658855974674,
0.040938135236501694,
0.02394995465874672,
-0.00178072031121701,
0.04495159164071083,
0.03246043995022774,
-0.04297817125916481,
-0.014909972436726093,
-0.015546988695859909,
-0.06036008894443512,
0.039576251059770584,
-0.010488674975931644,
0.036473412066698074,
-0.04144148901104927,
-0.015225499868392944,
-0.001194785931147635,
-0.008418658748269081,
0.028836965560913086,
0.0204553734511137,
-0.029488123953342438,
0.019053569063544273,
-0.008313104510307312,
0.017184196040034294,
-0.0386863611638546,
0.020578259602189064,
-0.04296010732650757,
-0.005235019605606794,
0.0023499017115682364,
0.024054650217294693,
-0.03398456424474716,
0.05170142650604248,
-0.024054784327745438,
-0.034243401139974594,
-0.0025695529766380787,
0.04614819958806038,
0.011095604859292507,
-0.010609608143568039,
0.030018649995326996,
-0.0017500568646937609,
0.02916635386645794,
-0.02126137539744377,
-0.038717132061719894,
0.04011239483952522,
-0.038792699575424194,
-0.024263951927423477,
0.009528592228889465,
-0.020391248166561127,
0.023671025410294533,
0.02618648298084736,
-0.02135534957051277,
-0.00896134041249752,
0.0354730598628521,
-0.0004288157797418535,
-0.005806621629744768,
-0.018235744908452034,
-0.040725432336330414,
0.010975331999361515,
-0.02322264015674591,
-0.013477470725774765,
0.002892265794798732,
0.010079536586999893,
0.004057650454342365,
0.07789745926856995,
0.010821879841387272,
0.025675205513834953,
0.0000018249837694384041,
0.015436438843607903,
0.004612752236425877,
-0.005471815355122089,
0.003453304525464773,
0.02211911231279373,
0.022840002551674843,
-0.024114297702908516,
-0.011954735033214092,
-0.00009290818707086146,
0.037184227257966995,
-0.07833100110292435,
0.03559388220310211,
-0.02085866406559944,
0.016795076429843903,
0.026635680347681046,
-0.04636033996939659,
0.005699971225112677,
0.04881443455815315,
-0.04835924878716469,
0.02948853373527527,
-0.06689925491809845,
-0.04349788650870323,
-0.034317050129175186,
-0.006488591432571411,
-0.010854334570467472,
0.04049857705831528,
0.048905834555625916,
0.03163820132613182,
0.031876251101493835,
0.015592862851917744,
-0.02235732413828373,
-0.05429275706410408,
0.023696882650256157,
0.021893709897994995,
0.015017904341220856,
-0.018337475135922432,
0.022230224683880806,
-0.011613629758358002,
-0.00043363365693949163,
0.05790664255619049,
-0.052183013409376144,
0.030631214380264282,
-0.011767936870455742,
-0.01312293577939272,
0.012197460979223251,
0.001984536414965987,
-0.005394297651946545,
0.001685950206592679,
0.001524441409856081,
-0.030795952305197716,
-0.0017543387366458774,
0.009637058712542057,
0.03674947842955589,
0.002135955262929201,
0.04320475086569786,
-0.0823780745267868,
-0.015607534907758236,
0.015070359222590923,
0.02579953335225582,
0.03580676391720772,
0.015112950466573238,
-0.003196076489984989,
0.012586811557412148,
-0.05437736585736275,
-0.030181964859366417,
-0.05040434002876282,
0.001119673834182322,
0.012500787153840065,
0.010949986055493355,
-0.019604114815592766,
0.0017733430722728372,
0.005534702446311712,
-0.05286872014403343,
0.05852595344185829,
-0.05143291503190994,
-0.05059202387928963,
-0.03253645822405815,
-0.010072816163301468,
0.013817192986607552,
-0.018339883536100388,
-0.011903186328709126,
-0.004107349552214146,
-0.05984686315059662,
0.03814489021897316,
0.0027422215789556503,
-0.0002455298963468522,
-0.028808804228901863,
-0.06497368216514587,
-0.040386706590652466,
-0.06596697866916656,
0.03880377858877182,
0.005867695435881615,
-0.005903573706746101,
-0.04345392435789108,
-0.027198486030101776,
-0.026469001546502113,
0.05798704922199249,
0.04319598525762558,
-0.0035682995803654194,
-0.004733683541417122,
0.015723586082458496,
-0.027609016746282578,
0.01573917455971241,
-0.057963766157627106,
0.00981514435261488,
0.023730890825390816,
-0.003248233115300536,
-0.021529559046030045,
-0.0017671294044703245,
-0.00019242333655711263,
0.005442987661808729,
0.0004925559624098241,
0.01924016885459423,
0.04037245362997055,
0.041035328060388565,
-0.03051656484603882,
-0.029636425897479057,
-0.02406851015985012,
-0.001782055594958365,
0.03658352047204971,
0.009295818395912647,
0.023954350501298904,
0.01898285001516342,
-0.014014160260558128,
-0.06765166670084,
-0.0008249052916653454,
-0.045528843998909,
0.03930755332112312,
-0.028005795553326607,
-0.011475549079477787,
0.02146824635565281,
-0.06797968596220016,
-0.0012388125760480762,
0.005628091748803854,
-0.021345391869544983,
-0.0405779629945755,
0.04354468360543251,
0.009533590637147427,
0.02399495057761669,
-0.028154628351330757,
0.036082781851291656,
0.003515085903927684,
-0.0024587090592831373,
-0.0227197352796793,
0.056972697377204895,
0.024382520467042923,
0.013048842549324036,
0.05628537759184837,
0.02268313243985176,
-0.007505145389586687,
0.00556736858561635,
-0.011993968859314919,
0.010403168387711048,
0.024810034781694412,
0.006542131304740906,
0.020698633044958115,
-0.01118334662169218,
-0.05068088695406914,
0.04442942515015602,
0.008363468572497368,
0.0560247004032135,
-0.03902862221002579,
0.062480729073286057,
-0.0018522256286814809,
-0.004589226096868515,
0.0028527206741273403,
0.003129673656076193,
0.004259518813341856,
0.008395245298743248,
-0.01082255132496357,
0.02312207780778408,
-0.0030000677797943354,
0.00945779774338007,
-0.0061104996129870415,
-0.05085795745253563,
0.023424549028277397,
-0.015985192731022835,
-0.03867567330598831,
-0.020051438361406326,
0.015665946528315544,
-0.018154658377170563,
-0.030095186084508896,
0.029365386813879013,
0.030899250879883766,
-0.042296916246414185,
-0.015232191421091557,
0.010029797442257404,
-0.01189360674470663,
0.06077363342046738,
-0.04780508205294609,
-0.022696277126669884,
-0.025542644783854485,
0.03305358812212944,
-0.027611523866653442,
-0.020024839788675308
] |
<p>Considering that speed increases weight and the proton is going at almost the speed of light, I would like to know how much a speeding proton would weigh in the LHC.</p>
| 8,262 |
[
-0.018254628404974937,
-0.028776012361049652,
-0.022124018520116806,
-0.05605887249112129,
0.05925489589571953,
0.028087066486477852,
-0.027573373168706894,
-0.018924875184893608,
-0.031102625653147697,
-0.03312932327389717,
0.042883727699518204,
0.05020507797598839,
0.04651322960853577,
-0.008343489840626717,
-0.0008260885952040553,
0.03443161025643349,
0.018895458430051804,
0.0037356349639594555,
-0.004512771964073181,
-0.029900340363383293,
0.034541886299848557,
0.007796630263328552,
0.030641060322523117,
0.02952573262155056,
-0.025240140035748482,
0.013632694259285927,
0.025308560580015182,
-0.002803162205964327,
0.017653649672865868,
0.0668739303946495,
-0.02044212631881237,
-0.02036801166832447,
0.043843287974596024,
0.023037957027554512,
0.04305237531661987,
-0.02199501357972622,
-0.020873086526989937,
-0.04617636650800705,
-0.027871467173099518,
0.023733118548989296,
-0.03991184011101723,
-0.012506278231739998,
-0.013823253102600574,
0.034272607415914536,
0.00751221738755703,
0.027709700167179108,
-0.013551837764680386,
-0.00020675454288721085,
0.06816700100898743,
-0.08094443380832672,
0.06917637586593628,
0.0032771120313555002,
0.008783523924648762,
0.005661191418766975,
-0.014836518093943596,
-0.01565123349428177,
0.0576554611325264,
0.05659061670303345,
-0.026162825524806976,
-0.05081143230199814,
-0.031066255643963814,
0.0039276015013456345,
0.034758489578962326,
-0.038947943598032,
0.008230200037360191,
-0.000225706011406146,
-0.047792818397283554,
-0.004526042845100164,
0.02453635260462761,
0.018737997859716415,
0.053214386105537415,
0.017530327662825584,
0.03604891523718834,
0.0004782337346114218,
0.012384378351271152,
-0.030766628682613373,
0.02517971396446228,
0.053866248577833176,
0.026004083454608917,
0.03653601557016373,
-0.057165682315826416,
0.008093650452792645,
0.02897445484995842,
0.022491823881864548,
-0.014767237938940525,
-0.030638238415122032,
0.03884485363960266,
-0.02274397201836109,
-0.024450933560729027,
0.05224326625466347,
-0.03805810213088989,
-0.004150167107582092,
0.008942333050072193,
0.019018245860934258,
0.01234170701354742,
0.01635628752410412,
-0.006156517658382654,
0.047845326364040375,
0.007800076622515917,
-0.007410501595586538,
0.0400860458612442,
0.022037670016288757,
-0.0080493139103055,
0.0742596834897995,
0.004768023267388344,
-0.006869264412671328,
-0.014863505959510803,
0.015521294437348843,
-0.028225919231772423,
-0.019532140344381332,
-0.03520204871892929,
-0.019376039505004883,
-0.003598975483328104,
-0.02077428065240383,
0.011704524978995323,
-0.05840926244854927,
0.015498392283916473,
-0.03702130541205406,
0.08867201209068298,
0.04297250136733055,
0.027794620022177696,
-0.012802992016077042,
-0.00424596294760704,
0.0016069491393864155,
-0.037646662443876266,
0.017725395038723946,
0.054559238255023956,
-0.006560164503753185,
-0.028703579679131508,
0.027666764333844185,
-0.03128588944673538,
-0.01959950104355812,
0.012494471855461597,
-0.018771490082144737,
0.03742717206478119,
-0.007438022177666426,
-0.09387459605932236,
-0.06684616208076477,
0.025379728525877,
-0.0022468429524451494,
-0.0452168732881546,
-0.07320386916399002,
-0.007995888590812683,
0.015241570770740509,
0.04823380708694458,
-0.018796397373080254,
0.0061634075827896595,
-0.002228804398328066,
0.039058927446603775,
0.018859634175896645,
-0.008143836632370949,
-0.011660411022603512,
-0.0014467750443145633,
-0.02649315632879734,
0.011609574779868126,
-0.06039329245686531,
-0.011708894744515419,
0.050132621079683304,
-0.02720371074974537,
-0.034741781651973724,
0.021313659846782684,
-0.030355842784047127,
0.03958582505583763,
-0.010995030403137207,
-0.013093170709908009,
-0.02562049590051174,
0.035287968814373016,
0.01819724403321743,
-0.016508782282471657,
0.004577220883220434,
0.0070136962458491325,
0.013885816559195518,
0.008251719176769257,
-0.027528705075383186,
0.06375234574079514,
-0.020380644127726555,
-0.03728807345032692,
-0.0038780905306339264,
0.01655239798128605,
-0.01179449912160635,
-0.04076894372701645,
-0.03592494875192642,
-0.011362118646502495,
-0.013563056476414204,
-0.0007325845654122531,
0.02855515666306019,
-0.012269861996173859,
-0.0058633191511034966,
0.004698553122580051,
-0.041004352271556854,
-0.017268583178520203,
-0.07338667660951614,
0.0011045453138649464,
0.009063915349543095,
0.030258163809776306,
0.043261125683784485,
0.026291964575648308,
-0.0057621425949037075,
-0.01642840914428234,
0.0015886020846664906,
-0.0017671639798209071,
0.05729345977306366,
-0.007488020695745945,
-0.022345414385199547,
-0.013419917784631252,
0.03329416364431381,
0.027721218764781952,
-0.021652482450008392,
0.00833298359066248,
0.013378256931900978,
-0.038328442722558975,
0.010411509312689304,
-0.03847258538007736,
-0.01055471133440733,
0.0035960180684924126,
0.025724267587065697,
0.009616364724934101,
-0.026657279580831528,
-0.01284986361861229,
0.03842102363705635,
0.007738151121884584,
0.09879178553819656,
0.021783875301480293,
-0.008155572228133678,
0.019090428948402405,
0.034338053315877914,
-0.0021355992648750544,
0.011950472369790077,
-0.024100493639707565,
-0.024955755099654198,
-0.0282151997089386,
-0.030624423176050186,
0.030777927488088608,
0.04219739884138107,
-0.03258124366402626,
0.008834808133542538,
0.0376085489988327,
0.04847663640975952,
0.0325070358812809,
-0.007226941175758839,
-0.050026923418045044,
-0.08139578998088837,
0.011948715895414352,
0.009063968434929848,
-0.026875758543610573,
-0.015736199915409088,
0.01177903264760971,
0.009017802774906158,
0.016348954290151596,
-0.007166246417909861,
-0.0016653654165565968,
0.0059806485660374165,
0.005936090834438801,
-0.010110780596733093,
0.011190676130354404,
-0.08269179612398148,
0.058782827109098434,
-0.010307702235877514,
0.04455401375889778,
0.012387804687023163,
-0.03441033512353897,
0.0020278263837099075,
-0.03540848195552826,
-0.014424057677388191,
-0.004650657530874014,
0.01575174741446972,
-0.028520317748188972,
0.0020984699949622154,
0.032842472195625305,
-0.05304805189371109,
0.06211628019809723,
-0.015441504307091236,
0.022246619686484337,
0.01805407553911209,
0.0259880181401968,
0.025976188480854034,
-0.012382260523736477,
0.03820914775133133,
-0.038651321083307266,
-0.020897895097732544,
0.041225288063287735,
-0.04606682062149048,
0.012135664001107216,
0.031127968803048134,
-0.05639961361885071,
0.019735343754291534,
-0.027027040719985962,
-0.04575696215033531,
0.02003023959696293,
-0.02533629909157753,
0.015453055500984192,
0.04895223304629326,
-0.029428398236632347,
-0.025131307542324066,
-0.005490486975759268,
-0.0037088787648826838,
0.00018921607988886535,
-0.029150232672691345,
0.0340154767036438,
0.039366524666547775,
0.026559732854366302,
-0.03819506987929344,
0.007249188609421253,
-0.017114244401454926,
-0.024589795619249344,
-0.01208946667611599,
-0.005569712724536657,
-0.00737124215811491,
-0.046020109206438065,
0.030730105936527252,
0.042610060423612595,
-0.031570304185152054,
0.009443860501050949,
-0.019408458843827248,
-0.0315597727894783,
0.05723663792014122,
0.009099312126636505,
0.05137887969613075,
-0.020069491118192673,
-0.045873209834098816,
0.08867353945970535,
0.023426569998264313,
-0.04347005486488342,
-0.03999410942196846,
-0.009938741102814674,
0.00718309823423624,
-0.032870102673769,
0.0002825160918291658,
0.026288608089089394,
-0.029269330203533173,
-0.015123466029763222,
0.04863899201154709,
0.008696966804564,
-0.0027503129094839096,
0.01778288185596466,
0.00266257394105196,
-0.004599273204803467,
-0.00812217965722084,
0.04389217495918274,
0.055910687893629074,
0.00445152772590518,
-0.03130391240119934,
0.03206469491124153,
-0.0063997660763561726,
0.04849079251289368,
-0.022997522726655006,
-0.039569173008203506,
0.082542784512043,
0.0480816625058651,
0.014697265811264515,
-0.02428770810365677,
-0.012594463303685188,
0.008133653551340103,
-0.011404425837099552,
0.018617672845721245,
0.013384711928665638,
0.02621518261730671,
0.002776695415377617,
0.002098715864121914,
0.02893049456179142,
0.08386649936437607,
-0.00794711709022522,
-0.044161438941955566,
-0.007164588663727045,
-0.02222319133579731,
0.031163755804300308,
-0.0224077757447958,
-0.0473049134016037,
0.03239910677075386,
0.019253842532634735,
-0.001956967171281576,
-0.0033775053452700377,
0.005823726300150156,
-0.005740045104175806,
-0.07232031971216202,
-0.02554960735142231,
0.03625984862446785,
0.011930717155337334,
0.028189077973365784,
0.07787945121526718,
0.019833454862236977,
-0.016183795407414436,
0.01981031522154808,
-0.008754974231123924,
-0.09150346368551254,
0.01067519560456276,
-0.055838655680418015,
-0.005667696241289377,
-0.013849307782948017,
-0.007796172518283129,
-0.04698909819126129,
-0.03638623654842377,
0.004760935436934233,
-0.037362005561590195,
0.008327856659889221,
-0.010995735414326191,
0.03780011087656021,
-0.01482337061315775,
-0.0229039266705513,
0.0047706239856779575,
0.04998460039496422,
0.019480997696518898,
-0.016001492738723755,
0.0007171464967541397,
0.006250421050935984,
-0.02718624658882618,
-0.031100112944841385,
0.005874456372112036,
0.0410567931830883,
-0.036443404853343964,
0.041158247739076614,
0.03240298107266426,
0.0073768929578363895,
-0.061733413487672806,
0.012014498934149742,
0.0035606350284069777,
0.01476998906582594,
0.007946591824293137,
-0.028070347383618355,
-0.013869198970496655,
-0.04145076870918274,
-0.026659101247787476,
-0.0009995149448513985,
0.021327879279851913,
-0.023923804983496666,
-0.018900366500020027,
0.03483278304338455,
-0.02048947662115097,
0.0009434272069483995,
0.04394537955522537,
0.07158314436674118,
0.0030957330018281937,
-0.020524151623249054,
-0.05387114733457565,
0.015164067037403584,
0.009851254522800446,
-0.021253235638141632,
0.012729009613394737,
0.0074416399002075195,
-0.014253692701458931,
0.039171162992715836,
-0.014707596972584724,
0.028242038562893867,
-0.0350063256919384,
0.012980562634766102,
0.016893722116947174,
0.015951287001371384,
-0.00008058168896241114,
0.004050340969115496,
0.0033537468407303095,
0.026201214641332626,
0.020477985963225365,
-0.015809420496225357,
-0.018394766375422478,
-0.08734609931707382,
-0.03872301056981087,
0.01551442127674818,
0.06596207618713379,
-0.03436659649014473,
-0.03848833218216896,
-0.005193768534809351,
0.011902851052582264,
0.08220893889665604,
-0.027264762669801712,
0.008645282126963139,
0.0052664615213871,
0.021187564358115196,
0.018337704241275787,
0.0037641313392668962,
-0.006069375202059746,
0.03227139636874199,
-0.033038653433322906,
-0.014129501767456532,
-0.04326450824737549,
-0.017834393307566643,
-0.019906284287571907,
0.023882251232862473,
0.04283943399786949,
0.04115516319870949,
0.00298058963380754,
0.05374123528599739,
-0.006949062459170818,
0.003089774399995804,
-0.018050171434879303,
-0.07883451879024506,
0.025047345086932182,
0.01650516502559185,
-0.01096681784838438,
0.022860325872898102,
-0.02695927955210209,
-0.04731706529855728,
0.01888068951666355,
0.005156511906534433,
-0.005364056210964918,
-0.006035841070115566,
-0.09468523412942886,
0.044744037091732025,
0.04073774069547653,
0.015660803765058517,
0.031233085319399834,
0.018466603010892868,
-0.011848917230963707,
-0.0072894529439508915,
0.00021443354489747435,
0.05014393478631973,
-0.038017913699150085,
0.02028602920472622,
-0.006139691453427076,
0.010560903698205948,
-0.05023526772856712,
0.05896155536174774,
-0.01038852334022522,
0.042725879698991776,
0.01903236098587513,
-0.06288968771696091,
-0.05401597172021866,
-0.005024726036936045,
0.01578560099005699,
-0.021000413224101067,
-0.007443900220096111,
0.007056672126054764,
-0.009688813239336014,
-0.035903122276067734,
-0.001184496795758605,
0.018666671589016914,
-0.0060602640733122826,
-0.020653115585446358,
-0.017748497426509857,
0.027945073321461678,
-0.008044537156820297,
-0.00804161187261343,
0.03893830627202988,
-0.02398674003779888,
0.05747399479150772,
-0.02098694257438183,
-0.0162761602550745,
-0.0029171956703066826,
-0.08879885822534561,
-0.0461798794567585,
0.02201995439827442,
-0.018030034378170967,
0.019901614636182785,
-0.06308691948652267,
0.0073825703002512455,
-0.016603786498308182,
0.010679895058274269,
-0.04650087282061577,
-0.0131094790995121,
0.043444763869047165,
0.006597855594009161,
0.01599949598312378,
-0.015028946101665497,
0.01683320477604866,
-0.046310655772686005,
-0.04366161301732063,
-0.04452148824930191,
0.03230256214737892,
-0.04585771635174751,
0.0015258481726050377,
-0.014894683845341206,
-0.0036298693157732487,
0.040651556104421616,
0.010994444601237774,
-0.02529687061905861,
-0.01255018264055252,
0.00684224721044302,
-0.01896667666733265,
-0.040123291313648224,
0.04755641147494316,
-0.013100790791213512,
-0.028722969815135002,
0.023603355512022972,
-0.03677242249250412,
0.03922484815120697,
-0.04130995646119118,
0.0034687684383243322,
0.03983428329229355,
0.044845882803201675,
-0.005183517932891846,
0.03415055200457573,
0.03382505476474762,
0.005822999402880669,
0.05238073691725731,
-0.016569338738918304,
0.006816321052610874,
0.0033032058272510767,
-0.020003778859972954,
0.02283034473657608,
0.016395527869462967,
0.011478330940008163,
-0.01619425229728222,
0.001018627779558301,
0.022534919902682304,
-0.03735873103141785,
0.01022938173264265,
-0.059242092072963715,
0.014250150881707668,
-0.009318521246314049,
0.017891239374876022,
0.026326153427362442,
-0.03137443959712982,
0.018248848617076874,
-0.02870943769812584,
-0.034944746643304825,
-0.05631447955965996,
0.047967329621315,
0.0059332768432796,
0.050192710012197495,
-0.03361263498663902,
-0.014479149132966995,
-0.0006037718267180026,
0.02238200604915619,
-0.0024380965624004602,
0.01950530894100666,
0.03519529476761818,
0.013212873600423336,
-0.0047811828553676605,
-0.017719238996505737,
0.04293098300695419,
0.020041130483150482,
-0.00018620358605403453,
0.024321725592017174,
0.047806259244680405,
0.006394116207957268,
0.031040653586387634,
-0.049758270382881165,
-0.04325040057301521,
0.017753966152668,
0.0027085684705525637,
0.013584794476628304,
-0.013377975672483444,
-0.035497602075338364,
0.06659800559282303,
-0.0039287470281124115,
0.007669241167604923,
-0.008622844703495502,
-0.018340514972805977,
-0.0547560453414917,
-0.018535494804382324,
0.03044837713241577,
-0.004075462464243174,
-0.025584673509001732,
0.014852242544293404,
0.018252801150083542,
0.03884643688797951,
0.021665796637535095,
0.00880452711135149,
-0.05800351873040199,
-0.031092658638954163,
-0.02089560404419899,
-0.05614017695188522,
0.03612523898482323,
0.018122775480151176,
0.01036047376692295,
0.020897259935736656,
0.006217914633452892,
0.00905359536409378,
0.004862312693148851,
0.029994599521160126,
-0.026940787211060524,
0.0607437789440155,
-0.02078614942729473,
0.019402839243412018,
-0.03887208551168442,
0.01548492070287466,
0.10450287163257599,
0.05449537932872772,
0.04495170712471008,
-0.05019636079668999,
0.013413953594863415,
-0.030025070533156395,
0.022343574091792107,
-0.027592981234192848,
0.01350640319287777,
-0.003838850185275078,
-0.0007923956145532429,
-0.010427647270262241,
0.04152930900454521,
-0.028539590537548065,
0.0029924071859568357,
0.048745088279247284,
-0.0010209910105913877,
-0.006181544624269009,
0.005142597947269678,
0.059206657111644745,
-0.00839975755661726,
0.023079175502061844,
-0.022701362147927284,
0.03440923988819122,
0.0020585355814546347,
0.014401807449758053,
-0.04101000353693962,
-0.06584776937961578,
0.003678390523418784,
-0.01678972691297531,
-0.05907350406050682,
0.0033199938479810953,
-0.000753924367018044,
-0.02957947552204132,
-0.056180648505687714,
0.024914033710956573,
0.03244676813483238,
0.006302317138761282,
-0.0067308745346963406,
0.017074745148420334,
0.0413808599114418,
0.024757642298936844,
-0.01210799254477024,
0.0156489759683609,
-0.04701504111289978,
-0.006596940569579601,
-0.0046606301330029964,
0.008594576269388199,
-0.007269320543855429,
-0.0008259008754976094,
0.009923967532813549,
0.030636273324489594,
-0.03087460994720459,
-0.043153561651706696,
-0.00480550667271018,
0.01407325267791748,
0.02280268631875515,
0.026464875787496567,
0.03089809976518154,
0.006360901985317469,
0.029515566304326057,
-0.017776785418391228,
0.021690573543310165,
0.00964359100908041,
0.01163449976593256,
0.013549715280532837,
-0.00272957282140851,
0.021933361887931824,
-0.014449172653257847,
-0.016729114577174187,
-0.0026799137704074383,
0.011897731572389603,
-0.06395955383777618,
-0.010306142270565033,
0.011095983907580376,
0.02850521169602871,
0.012689915485680103,
0.008754728361964226,
0.01594850793480873,
-0.042600251734256744,
-0.04285157471895218,
0.05673731490969658,
-0.006270093377679586,
-0.037781644612550735,
-0.03501791134476662,
0.0013708519982174039,
0.02267938107252121,
0.01350498292595148,
-0.032983213663101196,
-0.005995652638375759,
-0.02807885780930519,
0.034797362983226776,
-0.010535444132983685,
-0.06026960536837578,
0.031506896018981934,
0.02533513493835926,
-0.020684771239757538,
0.020697057247161865,
-0.005270783789455891,
0.013090012595057487,
0.03613020107150078,
-0.016405444592237473,
0.003596232272684574,
0.014181858859956264,
-0.008316143415868282,
0.014646339230239391,
0.03812983259558678,
-0.039756085723638535,
0.007603142876178026,
0.0025713141076266766,
0.012124301865696907,
-0.060811977833509445,
-0.03957292065024376,
-0.0310128852725029,
-0.009407664649188519,
-0.010919928550720215,
0.024224894121289253,
-0.009600639343261719,
0.01787908747792244,
-0.009252222254872322,
-0.0025273689534515142,
-0.0027176039293408394,
0.03284093365073204,
-0.04441893473267555,
0.025087030604481697,
-0.009617307223379612,
-0.01182479690760374,
-0.006554733961820602,
0.031626760959625244,
-0.04665054753422737,
-0.010615484789013863,
0.0037774096708744764,
-0.0007150872843340039,
-0.02604508027434349,
-0.02337944507598877,
0.02732628770172596,
0.004849440883845091,
0.029689878225326538,
-0.03558551147580147,
-0.00881626270711422,
0.035687196999788284,
-0.04327169433236122,
-0.0292788278311491,
0.047578372061252594,
-0.022470014169812202,
0.013476677238941193,
0.040086496621370316,
-0.030564693734049797,
-0.021480193361639977,
0.053342677652835846,
-0.03898784890770912,
-0.007604365237057209,
0.008144741877913475,
-0.015701884403824806,
-0.018432404845952988,
-0.00042900373227894306,
0.005223189014941454,
0.010646763257682323,
0.005346738267689943,
0.056332867592573166,
0.012606644071638584,
-0.061892326921224594,
0.04777462035417557,
-0.04142752289772034,
-0.018314093351364136,
0.032223161309957504,
-0.010055151768028736,
-0.01043586153537035,
0.0017979997210204601,
0.04468053579330444,
-0.06179139018058777,
0.028905700892210007,
-0.008512790314853191,
-0.019247502088546753,
-0.10792750865221024,
-0.02671952359378338,
-0.005860379431396723,
0.004584348760545254,
0.06585933268070221,
-0.033032625913619995,
0.05446833744645119,
0.03866170719265938,
-0.08991338312625885,
0.02545572817325592,
-0.03857022151350975,
-0.026650646701455116,
-0.03027450293302536,
-0.04288668930530548,
-0.007814341224730015,
0.06089593097567558,
0.030821599066257477,
0.0705852285027504,
0.030875807628035545,
0.007196337915956974,
0.0001902776857605204,
-0.04116801545023918,
-0.014233393594622612,
0.024347882717847824,
-0.002856140024960041,
-0.015248400159180164,
0.059605661779642105,
-0.014697384089231491,
-0.0045236083678901196,
0.042802706360816956,
0.043563295155763626,
0.006672854069620371,
-0.01260298304259777,
0.047646794468164444,
0.021364960819482803,
0.06477772444486618,
-0.0017428949940949678,
0.017529187723994255,
-0.0065122912637889385,
0.03101101517677307,
-0.006252134218811989,
0.016053704544901848,
0.0021951706148684025,
0.023693405091762543,
-0.009114221669733524,
-0.012838184833526611,
0.0036177774891257286,
0.040533483028411865,
-0.02749631367623806,
0.009448647499084473,
-0.020424271002411842,
0.001313137705437839,
0.010045907460153103,
-0.03749510645866394,
-0.001961363246664405,
-0.009433689527213573,
0.03891279175877571,
0.04732207581400871,
-0.0061683738604187965,
-0.018320051953196526,
0.030269915238022804,
-0.020189642906188965,
0.02031480334699154,
-0.010416075587272644,
0.006546961143612862,
-0.013829194009304047,
-0.055769093334674835,
-0.003033849410712719,
0.032364372164011,
0.021961143240332603,
0.01412971317768097,
-0.07364615797996521,
-0.05294523760676384,
0.034995466470718384,
0.00227750139310956,
0.03628157451748848,
0.004940236918628216,
-0.013272016309201717,
0.01742030307650566,
-0.07315106689929962,
-0.0011014018673449755,
0.012439843267202377,
0.04141511395573616,
-0.014000698924064636,
-0.023025168105959892,
-0.0034247380681335926,
0.03517348691821098,
0.06404786556959152,
0.0010604263516142964,
-0.03226374462246895,
0.004639855585992336,
-0.004805877339094877,
0.00936900731176138,
-0.032405830919742584,
-0.029831312596797943,
-0.02008744888007641,
-0.03947979211807251,
-0.01239134930074215,
-0.019225899130105972,
0.012680668383836746,
0.010545925237238407,
0.04242519661784172,
0.029584618285298347,
0.002095138654112816,
-0.02247999608516693,
-0.011979932896792889,
0.06534972041845322,
-0.015764320269227028,
0.021132387220859528,
0.04986773803830147,
0.011108155362308025,
0.03572908788919449,
0.026512717828154564,
-0.02944209985435009,
-0.03648090362548828,
0.01246363203972578,
-0.03205724433064461,
-0.0010048019466921687,
0.001964871073141694,
0.0055508241057395935,
-0.005851552821695805,
-0.05484619364142418,
0.027322102338075638,
0.0230553075671196,
-0.01674194447696209,
-0.04585237801074982,
0.038736820220947266,
0.04133739694952965,
0.03305243328213692,
0.029557926580309868,
0.002808387391269207,
0.035392094403505325,
-0.005444041453301907,
0.004831383470445871,
0.03434286639094353,
0.02141079679131508,
-0.00509691284969449,
0.024696476757526398,
0.04468910023570061,
0.017280900850892067,
-0.011141621507704258,
0.04894086718559265,
0.015327190980315208,
-0.03440290316939354,
-0.04452391713857651,
-0.0028066772501915693,
-0.05258664861321449,
0.06496085971593857,
0.025377051904797554,
-0.020114833489060402,
0.09092193841934204,
-0.019754931330680847,
0.006714419461786747,
-0.026220940053462982,
-0.01607295498251915,
0.018862957134842873,
-0.0005707826931029558,
-0.02587152272462845,
0.046059586107730865,
-0.016068752855062485,
-0.02626911550760269,
0.01875770092010498,
-0.0031410546507686377,
0.006615843623876572,
-0.06620406359434128,
-0.004928506910800934,
0.01902133785188198,
-0.0075742583721876144,
-0.03804779052734375,
-0.022277744486927986,
-0.027500517666339874,
0.003318048780784011,
0.018354594707489014,
0.02654922939836979,
0.01872781291604042,
0.01254549715667963,
0.007106900215148926,
-0.018058907240629196,
0.013449974358081818,
-0.03517039120197296,
0.018686136230826378,
-0.033192235976457596,
0.012395200319588184,
-0.02075381949543953,
-0.00031711632618680596
] |
<p>We are building an addition on our home that will allow us to build a basement home theater room with some level of flexibility regarding its size and shape. I've been reading somewhat conflicting information about room dimensions and shapes to provide optimal acoustics, and few sources seem to directly cite a scientific basis for guidelines. I kind of get the feeling that this is more art than science.</p>
<p>My first question would be--how reliable is room modeling software (or manual calculations) in providing an accurate acoustic room response? Simulation has the allure of helping optimize room shape, but only if it's a good predictor. </p>
<p>I've read conflicting guidelines regarding whether or not angling a wall, or multiple walls might help minimize standing wave problems, and that they certainly complicate the analysis. I've read in some places that room dimension formulas are valid and other places that they're not. It seems pretty universally accepted that dimensions shouldn't be near multiples of each other. Are there current best practices for room design that are universally accepted? </p>
<p>For reference, the room interior width is constrained to be 11'11", length can be up to 23', and height can be as large as reasonably excavated in a home basement (6 to 10 ft).</p>
| 8,263 |
[
-0.03302174061536789,
-0.04407505691051483,
-0.01630103960633278,
-0.04808715358376503,
0.06643399596214294,
0.011868462897837162,
0.0020550440531224012,
-0.031068215146660805,
0.03282136470079422,
-0.010531416162848473,
0.01154404878616333,
0.025773199275135994,
0.05721036344766617,
0.026848167181015015,
0.018779676407575607,
0.0031114157754927874,
0.02893519215285778,
-0.0070115658454597,
-0.0014217898715287447,
-0.02509966306388378,
-0.021411435678601265,
0.026200933381915092,
0.0007199893589131534,
-0.018714170902967453,
-0.020266177132725716,
0.06147635355591774,
0.05695129185914993,
-0.00627873744815588,
-0.015719668939709663,
0.008008671924471855,
0.014515439979732037,
-0.008603659458458424,
0.005963590927422047,
0.07236482948064804,
0.040381982922554016,
-0.026293113827705383,
-0.030687987804412842,
-0.0029105432331562042,
-0.004305694252252579,
0.037626028060913086,
0.003917742986232042,
0.026719408109784126,
0.015261861495673656,
0.0037037900183349848,
-0.04603356868028641,
0.00509480107575655,
-0.02450217679142952,
-0.04271114617586136,
0.044802047312259674,
-0.06786233931779861,
0.057533539831638336,
0.03128352761268616,
0.04041455313563347,
0.029100948944687843,
0.022780774161219597,
0.014637196436524391,
0.05103456601500511,
0.04743149131536484,
0.011191453784704208,
-0.07208554446697235,
0.0015478029381483793,
-0.002254712162539363,
-0.01710175722837448,
-0.03534859046339989,
-0.009136417880654335,
0.020934568718075752,
0.009574412368237972,
0.02083554118871689,
-0.011760917492210865,
-0.044094596058130264,
-0.00839587114751339,
0.03168242424726486,
0.05756455659866333,
-0.0015830458141863346,
0.02143351547420025,
-0.02279837243258953,
0.022142840549349785,
0.036857474595308304,
0.029255464673042297,
0.005227134563028812,
-0.021609870716929436,
-0.005128683056682348,
0.021303482353687286,
0.027261391282081604,
0.0022536450996994972,
-0.026494832709431648,
0.029657047241926193,
-0.034296561032533646,
-0.031323593109846115,
-0.02014564350247383,
0.019920241087675095,
0.02147429995238781,
0.05107368156313896,
-0.004285638686269522,
-0.014677013270556927,
-0.00422216160222888,
0.014425043016672134,
0.102951280772686,
0.014026853255927563,
-0.024005930870771408,
-0.0001316586130997166,
0.0039047268219292164,
0.00027714623138308525,
0.032508306205272675,
-0.007543488405644894,
-0.0200542863458395,
-0.029261082410812378,
0.024501698091626167,
0.006752556189894676,
-0.020818114280700684,
-0.034000214189291,
0.023938188329339027,
0.0010168645530939102,
0.007780592888593674,
0.004746009595692158,
-0.038357727229595184,
0.012725714594125748,
-0.008648569695651531,
0.04534268379211426,
0.042159710079431534,
0.047203391790390015,
-0.041997089982032776,
0.027750661596655846,
-0.05442187935113907,
-0.06975334137678146,
-0.015547693707048893,
0.0038059281650930643,
-0.024636035785079002,
-0.08615881949663162,
0.07297944277524948,
0.05975324660539627,
0.021577173843979836,
0.013117145746946335,
-0.0037534222938120365,
0.02757248468697071,
-0.004555678926408291,
-0.04531826451420784,
-0.07160038501024246,
0.015715217217803,
-0.010871917009353638,
-0.022801604121923447,
-0.06337317824363708,
-0.03960472717881203,
0.03257278725504875,
0.06300720572471619,
-0.01210386585444212,
0.005936797242611647,
-0.0028902392368763685,
0.04605157673358917,
-0.004899999126791954,
-0.06511381268501282,
0.03274654597043991,
-0.04121997579932213,
0.037154585123062134,
0.015661899000406265,
-0.06988837569952011,
0.04651032015681267,
0.005200931336730719,
-0.0021739196963608265,
-0.018610313534736633,
0.057337358593940735,
0.006506275851279497,
-0.07771440595388412,
0.013089200481772423,
-0.003380886046215892,
-0.0358368344604969,
0.052705246955156326,
-0.027032535523176193,
-0.023186150938272476,
0.015184774994850159,
-0.0027317635249346495,
-0.03352915868163109,
0.04270249605178833,
0.0012839923147112131,
0.00511673791334033,
0.015519528649747372,
0.03729001805186272,
-0.029074285179376602,
0.03169193118810654,
0.021379511803388596,
-0.02469463087618351,
-0.028574960306286812,
-0.003626816673204303,
0.015870947390794754,
-0.0076412782073020935,
0.02438918873667717,
-0.026906996965408325,
0.006622220389544964,
0.04560323804616928,
-0.0059304144233465195,
-0.033062949776649475,
-0.05068721994757652,
0.05905580520629883,
-0.02032875269651413,
0.019335737451910973,
0.015936771407723427,
0.01631203666329384,
0.02354440838098526,
-0.0188019797205925,
-0.009314346127212048,
0.0039001619443297386,
-0.017335768789052963,
0.03803937882184982,
0.0050209215842187405,
0.01676476001739502,
0.040657903999090195,
0.03789736330509186,
-0.04588647186756134,
0.022935129702091217,
-0.046813178807497025,
-0.041375260800123215,
-0.004882821813225746,
-0.015140300616621971,
0.03264833241701126,
0.02618221566081047,
-0.03631536290049553,
-0.004480465315282345,
-0.036253418773412704,
-0.03599266707897186,
0.012809615582227707,
0.002866465598344803,
0.056914277374744415,
0.055678486824035645,
0.004986912477761507,
0.008579747751355171,
0.03778360038995743,
-0.012373210862278938,
-0.022505350410938263,
0.012985522858798504,
-0.0114104263484478,
-0.08512070029973984,
0.0018259626813232899,
0.08949396759271622,
-0.018246272578835487,
0.004953938070684671,
0.02723800577223301,
0.003960905596613884,
0.01954379305243492,
0.0662204697728157,
0.028789779171347618,
-0.030589021742343903,
-0.04837508872151375,
-0.004842706955969334,
0.046637993305921555,
0.06007416918873787,
0.012278459966182709,
0.025200264528393745,
0.03086625412106514,
0.000038944239349802956,
-0.038137879222631454,
0.007747121155261993,
0.011360349133610725,
0.02837895043194294,
0.006949260365217924,
-0.03019525669515133,
-0.007574756629765034,
0.023243939504027367,
-0.034084271639585495,
0.0035234452225267887,
0.03219227492809296,
-0.006418720819056034,
-0.011918767355382442,
-0.0173757616430521,
0.0235405545681715,
0.025810660794377327,
-0.003849057015031576,
-0.0180051289498806,
0.0350053571164608,
0.03586127236485481,
-0.04293765127658844,
0.009396398440003395,
-0.05787954106926918,
-0.0196674931794405,
-0.014509535394608974,
-0.022407812997698784,
0.03270494565367699,
-0.02256537415087223,
0.04742037132382393,
0.0023799031041562557,
-0.010311977937817574,
-0.0465395413339138,
-0.022892728447914124,
-0.0049863471649587154,
0.023643624037504196,
-0.03509699925780296,
-0.002736810827627778,
-0.04042121022939682,
-0.01245040912181139,
0.003185197478160262,
-0.008663743734359741,
0.009014289826154709,
0.02772991545498371,
0.025210408493876457,
-0.08586721122264862,
-0.03065396100282669,
0.017125671729445457,
0.04935501888394356,
-0.00003143587673548609,
-0.016157833859324455,
0.020199861377477646,
0.018385397270321846,
-0.04207557067275047,
0.02078177034854889,
-0.021172387525439262,
-0.018810708075761795,
-0.025832878425717354,
-0.0096439179033041,
-0.020100168883800507,
0.0001507642591604963,
-0.03544365614652634,
0.031908705830574036,
-0.048347145318984985,
-0.0064221653155982494,
-0.030336707830429077,
-0.06088412553071976,
-0.005283194128423929,
-0.02778046764433384,
0.10621695220470428,
0.01779029704630375,
-0.01002969779074192,
0.0770416110754013,
-0.0024473872035741806,
-0.018288269639015198,
-0.022004378959536552,
-0.00014706625370308757,
0.017573030665516853,
-0.05803778022527695,
0.047944076359272,
0.06756284087896347,
-0.008386731147766113,
0.05150841549038887,
0.00998732727020979,
-0.012904336676001549,
0.02742573246359825,
0.020332230255007744,
-0.013760052621364594,
0.016772229224443436,
-0.004567379597574472,
-0.01998569816350937,
0.04563647881150246,
0.01871161162853241,
0.030194126069545746,
-0.002487264107912779,
-0.06886600703001022,
-0.0188430342823267,
0.021532690152525902,
-0.06692756712436676,
0.01423789095133543,
-0.03943987935781479,
-0.0028674639761447906,
-0.03295908123254776,
-0.021830251440405846,
-0.018624134361743927,
-0.023236840963363647,
-0.014110982418060303,
0.03050031140446663,
-0.0003177082980982959,
-0.0007106906268745661,
-0.01939782314002514,
-0.002238145563751459,
0.027846449986100197,
-0.001326396712101996,
-0.03298552706837654,
0.011276702396571636,
-0.008036321960389614,
0.013637589290738106,
0.013893142342567444,
-0.015588385052978992,
0.05986767262220383,
0.016194457188248634,
0.019056372344493866,
-0.004735204391181469,
-0.06631499528884888,
-0.003761929925531149,
-0.05025877803564072,
0.018392641097307205,
-0.07221486419439316,
0.04519787058234215,
-0.024080995470285416,
-0.004395229741930962,
0.0078011308796703815,
-0.01842406392097473,
0.01686055026948452,
-0.007243115454912186,
-0.07477675378322601,
-0.0325845405459404,
-0.03140939399600029,
0.022538410499691963,
0.008198484778404236,
-0.008317878469824791,
-0.017734380438923836,
0.0032647422049194574,
-0.02051513083279133,
-0.023633094504475594,
0.026494594290852547,
-0.03472490981221199,
0.001984523143619299,
-0.03450110927224159,
-0.04937300086021423,
0.007909671403467655,
0.027921117842197418,
-0.019555849954485893,
-0.022433897480368614,
0.02887851372361183,
0.03401467576622963,
-0.008730779401957989,
-0.035237107425928116,
0.009343761019408703,
0.05036844685673714,
-0.01372492779046297,
0.05560031160712242,
0.028021469712257385,
0.01730968989431858,
-0.057471856474876404,
0.014199070632457733,
-0.009267846122384071,
0.022742746397852898,
-0.010037320666015148,
-0.007982124574482441,
-0.005241434555500746,
-0.01966172456741333,
0.005173540208488703,
0.007084143813699484,
0.022275548428297043,
0.002545630559325218,
-0.007712691556662321,
0.04554031044244766,
0.020966900512576103,
-0.046448323875665665,
0.01167357712984085,
0.019147321581840515,
-0.021334752440452576,
-0.036409422755241394,
-0.039297208189964294,
-0.015978287905454636,
-0.012119506485760212,
-0.013839565217494965,
-0.026715394109487534,
0.014215805567800999,
-0.008724067360162735,
0.017884353175759315,
0.007893686182796955,
-0.03106357902288437,
-0.04019096493721008,
0.05035777762532234,
0.021972758695483208,
0.01667769066989422,
-0.01749163307249546,
0.01218640897423029,
0.004284970462322235,
-0.0055845254100859165,
0.050761960446834564,
0.02990245260298252,
-0.02629532665014267,
-0.055543359369039536,
-0.016438577324151993,
0.012688593938946724,
0.031053153797984123,
0.004249962978065014,
0.054293252527713776,
-0.028001895174384117,
-0.05180034413933754,
0.013580301776528358,
0.027444757521152496,
0.01188579574227333,
-0.03440943732857704,
0.019808733835816383,
-0.025595277547836304,
-0.010364366695284843,
-0.0018265204271301627,
-0.019628111273050308,
0.02634362317621708,
0.024037819355726242,
-0.03492553159594536,
-0.002263616770505905,
-0.0027735489420592785,
0.04320717975497246,
0.02007555216550827,
0.00841241329908371,
-0.0027089575305581093,
-0.01085740514099598,
0.0327037088572979,
0.012861243449151516,
-0.004852209705859423,
-0.020125126466155052,
-0.028920233249664307,
0.02465796284377575,
0.009926233440637589,
0.028616739436984062,
0.005243752617388964,
-0.0234703179448843,
0.031030962243676186,
0.018966110423207283,
-0.018711945042014122,
0.01700769178569317,
0.047135815024375916,
0.03770964965224266,
-0.0003753003547899425,
0.03205332159996033,
0.04711678996682167,
0.02416922152042389,
0.0018676117761060596,
0.017114166170358658,
0.02142069861292839,
0.02413938008248806,
-0.00538601353764534,
0.014333821833133698,
-0.043018490076065063,
-0.013564498163759708,
-0.052114345133304596,
0.0362490713596344,
-0.0122583769261837,
0.05547873303294182,
-0.0074773854576051235,
-0.03736678138375282,
0.01722492277622223,
0.06644222885370255,
0.007671618368476629,
0.025494195520877838,
0.02948533557355404,
0.015480535104870796,
-0.02258242294192314,
-0.023791184648871422,
-0.007389174774289131,
-0.03283020108938217,
0.03433585539460182,
0.060365691781044006,
-0.02513568475842476,
0.007901664823293686,
-0.02865847386419773,
-0.01543029211461544,
0.00029486900893971324,
-0.06486079841852188,
0.0826086774468422,
-0.030922364443540573,
0.048130325973033905,
0.0264931321144104,
-0.05343015864491463,
0.01496065966784954,
0.016430890187621117,
-0.014306005090475082,
0.04591123387217522,
-0.011666418984532356,
0.029271895065903664,
-0.003102687420323491,
0.024154625833034515,
-0.027704594656825066,
0.009492946788668633,
0.0005295865703374147,
0.029575008898973465,
-0.048322346061468124,
-0.05471525713801384,
-0.0035152756609022617,
-0.016137707978487015,
-0.02879742532968521,
-0.015958158299326897,
0.05826294794678688,
-0.028109628707170486,
-0.013688083738088608,
0.049620527774095535,
0.029575712978839874,
0.09346483647823334,
0.01395447738468647,
0.018399571999907494,
-0.018247608095407486,
-0.02844845876097679,
0.011796467006206512,
-0.0018541250610724092,
0.02954307571053505,
-0.024215340614318848,
-0.024035362526774406,
0.004182606004178524,
0.03126135095953941,
0.05441110581159592,
-0.03526824712753296,
0.024629702791571617,
0.0031377673149108887,
-0.010497038252651691,
0.007639803923666477,
-0.0027361868415027857,
0.03870396688580513,
-0.03996315971016884,
0.04185320436954498,
-0.0389968603849411,
0.003172416938468814,
-0.033229760825634,
0.01276902575045824,
-0.028085464611649513,
0.017249325290322304,
0.00646593514829874,
0.01422822754830122,
0.04200030863285065,
0.0054216934368014336,
-0.01572417840361595,
0.009170744568109512,
-0.03613689914345741,
0.04108734428882599,
-0.014398804865777493,
0.016819579526782036,
0.007711184676736593,
0.022426847368478775,
-0.008058217354118824,
-0.07480532675981522,
-0.03907644376158714,
0.0017719961469992995,
0.014284847304224968,
-0.027291562408208847,
0.03151973709464073,
0.04198182001709938,
-0.03002222254872322,
-0.027231914922595024,
-0.026410408318042755,
-0.006746327038854361,
-0.004592347424477339,
-0.008428344503045082,
0.09660083800554276,
-0.02867601253092289,
-0.02532072737812996,
-0.008821629919111729,
0.02104056254029274,
0.021207429468631744,
-0.00008018904190976173,
-0.015277864411473274,
0.008439757861196995,
0.00947586353868246,
-0.022608410567045212,
-0.017544401809573174,
0.04721532016992569,
-0.07935449481010437,
-0.003038377035409212,
0.0062326532788574696,
0.05257013440132141,
0.0254666730761528,
0.034461844712495804,
-0.02233804017305374,
-0.03121214359998703,
0.008515647612512112,
-0.0196500476449728,
0.011420910246670246,
0.026211360469460487,
0.02959735132753849,
-0.025421438738703728,
-0.01269577443599701,
0.05451163277029991,
-0.00867386069148779,
0.01380101963877678,
-0.015690771862864494,
-0.0723099336028099,
-0.016137689352035522,
-0.003721732646226883,
-0.03396733105182648,
0.0279846154153347,
0.012150299735367298,
-0.03330884128808975,
0.027543310075998306,
-0.06246976926922798,
0.0002207787911174819,
-0.016161443665623665,
0.0071395584382116795,
-0.010235709138214588,
0.039429210126399994,
-0.02501736208796501,
-0.0031575444154441357,
-0.01764490269124508,
0.02017287164926529,
0.15882089734077454,
0.05959916114807129,
0.04448511451482773,
-0.0416763499379158,
0.018096165731549263,
-0.011473574675619602,
-0.014916243962943554,
-0.022672468796372414,
0.009934713132679462,
0.010396839119493961,
0.023478668183088303,
0.024405915290117264,
0.05775746330618858,
0.006927561014890671,
-0.014999416656792164,
0.026280811056494713,
0.0016727135516703129,
-0.0480559878051281,
0.03878244012594223,
0.007083103060722351,
-0.008884363807737827,
-0.012215989641845226,
-0.009066056460142136,
0.012074694037437439,
-0.017398379743099213,
0.0014216105919331312,
-0.024536503478884697,
-0.04381759464740753,
0.035358261317014694,
0.032729219645261765,
-0.024193821474909782,
-0.011918708682060242,
-0.025791507214307785,
-0.0036722319200634956,
-0.029727481305599213,
0.006969135254621506,
0.0014604413881897926,
-0.02943030558526516,
-0.008422374725341797,
0.0436665341258049,
0.018159570172429085,
-0.03138136863708496,
0.011206535622477531,
0.028186969459056854,
-0.030952638015151024,
-0.010517364367842674,
-0.004134766757488251,
-0.0006040541338734329,
0.021648559719324112,
-0.037234000861644745,
-0.002199568087235093,
0.024561814963817596,
0.03439364954829216,
-0.04834970831871033,
-0.0028494275175035,
0.022719135507941246,
0.022236302495002747,
-0.02479707822203636,
-0.005580488126724958,
-0.005707196891307831,
0.024374956265091896,
0.035022005438804626,
-0.013452277518808842,
0.02335207909345627,
0.01634621061384678,
-0.030476871877908707,
-0.04900621995329857,
0.06811012327671051,
0.03668118268251419,
-0.027516737580299377,
-0.06621610373258591,
0.017850326374173164,
-0.05090682953596115,
-0.006268134340643883,
-0.014941809698939323,
0.030052613466978073,
0.034396082162857056,
0.022259291261434555,
0.009278692305088043,
-0.01095040887594223,
-0.04782066494226456,
0.023308778181672096,
-0.03361133113503456,
-0.04244202747941017,
-0.04414571076631546,
-0.01509427186101675,
0.021704699844121933,
0.021028228104114532,
-0.019288664683699608,
-0.018233776092529297,
-0.011841283179819584,
0.013453550636768341,
0.0005544130108319223,
-0.019883258268237114,
-0.003648436861112714,
-0.006226344499737024,
-0.04460819065570831,
-0.012894895859062672,
0.02669641003012657,
0.03497505560517311,
-0.0036349031142890453,
-0.010429082438349724,
0.019768081605434418,
0.02893204800784588,
-0.038529474288225174,
0.0225639920681715,
-0.038163650780916214,
-0.06034668907523155,
0.01218978688120842,
-0.0018925576005131006,
0.00665646605193615,
-0.04203394800424576,
-0.030199438333511353,
-0.03381190076470375,
-0.02428213134407997,
-0.006986703258007765,
-0.0002117062540492043,
-0.041065655648708344,
0.040799472481012344,
-0.016863685101270676,
-0.013365757651627064,
-0.025327634066343307,
0.024192754179239273,
0.004898461513221264,
0.0032100824173539877,
-0.02764633670449257,
0.011155317537486553,
-0.012640086002647877,
-0.030893003568053246,
-0.05517634376883507,
-0.06331009417772293,
-0.010542078875005245,
-0.019076520577073097,
0.013231346383690834,
0.028411749750375748,
-0.020195385441184044,
-0.01489010639488697,
0.055189695209264755,
-0.028174307197332382,
-0.028035329654812813,
0.022031893953680992,
-0.016062337905168533,
-0.03664851188659668,
0.011147084645926952,
-0.03105335682630539,
-0.009233064949512482,
0.016091952100396156,
0.014109457843005657,
0.005668817553669214,
0.008379606530070305,
-0.024747010320425034,
-0.014084589667618275,
-0.029706785455346107,
0.005694526247680187,
0.02662850171327591,
-0.02476336807012558,
0.03262807056307793,
-0.025237709283828735,
-0.027221478521823883,
-0.0022456191945821047,
0.04324466735124588,
0.015639211982488632,
0.010930185206234455,
-0.001432237564586103,
-0.04386970400810242,
0.004745576996356249,
-0.011636849492788315,
0.004611409269273281,
-0.005595664493739605,
0.030636776238679886,
-0.033178336918354034,
0.043355103582143784,
0.03160206601023674,
-0.016276702284812927,
-0.07893350720405579,
-0.006436140276491642,
0.006863190792500973,
-0.01873382180929184,
0.0078058140352368355,
-0.06587128341197968,
0.010095825418829918,
0.027640463784337044,
-0.05591081082820892,
0.032859787344932556,
-0.018824785947799683,
-0.0153831010684371,
-0.04647751525044441,
-0.022406388074159622,
0.016802942380309105,
-0.006186502519994974,
0.011996729299426079,
-0.009696622379124165,
-0.0330745168030262,
0.005033188033849001,
-0.006825222633779049,
-0.019935570657253265,
0.04951907694339752,
0.024611378088593483,
-0.030587924644351006,
0.028601843863725662,
0.029879635199904442,
-0.005641476716846228,
-0.031217539682984352,
0.035749197006225586,
0.011571207083761692,
0.008670796640217304,
-0.008037113584578037,
-0.009695982560515404,
-0.012949044816195965,
0.04169679060578346,
0.07028382271528244,
0.02656419388949871,
-0.03298448026180267,
0.019029177725315094,
0.002504526637494564,
0.02093563973903656,
-0.007893320173025131,
0.00335046392865479,
0.01905880495905876,
-0.002305173547938466,
0.018124697729945183,
0.03102402202785015,
-0.018611792474985123,
0.011689867824316025,
-0.027888702228665352,
-0.008964935317635536,
0.015454672276973724,
-0.004583778325468302,
0.035393569618463516,
-0.01688356325030327,
-0.05657031014561653,
0.038354795426130295,
0.02943422459065914,
-0.023405838757753372,
0.007253968622535467,
0.02263016439974308,
-0.03191729262471199,
0.02845115028321743,
-0.006207158789038658,
-0.027985749766230583,
-0.0435231477022171,
-0.03698146715760231,
0.0041299122385680676,
-0.007569870445877314,
0.006998624186962843,
-0.03095494955778122,
-0.029359975829720497,
0.02356656827032566,
0.009240638464689255,
0.05921845883131027,
0.0154320253059268,
-0.036424074321985245,
-0.015788070857524872,
-0.0026101041585206985,
0.07442615181207657,
0.009363963268697262,
-0.01154010184109211,
-0.04535986855626106,
-0.009265543892979622,
0.03270473703742027,
0.00013998999202158302,
0.0687495619058609,
0.03151516243815422,
-0.016254935413599014,
-0.0024656825698912144,
-0.04114789515733719,
0.015903571620583534,
-0.02404301054775715,
-0.002381565049290657,
0.06323277950286865,
-0.020627038553357124,
-0.028228171169757843,
-0.019203338772058487,
0.022576231509447098,
-0.00263775116764009,
0.02976994588971138,
-0.03590121492743492,
0.044384200125932693,
0.0030601276084780693,
-0.028845371678471565,
0.04198072478175163,
0.03604599088430405,
-0.004253504332154989,
0.06721918284893036,
-0.03929736837744713,
-0.027534445747733116,
0.00685378210619092,
-0.030300339683890343,
-0.03282695636153221,
-0.002755344845354557,
-0.041931942105293274,
0.005268103908747435,
-0.022204143926501274,
0.03144143521785736,
0.045309606939554214,
0.005827951245009899,
-0.015174531377851963,
0.0651906356215477,
-0.0466875359416008,
0.007504891604185104,
0.047791656106710434,
0.05572102218866348,
0.019477983936667442,
-0.020319398492574692,
-0.009663915261626244,
0.049057215452194214,
-0.01821536384522915,
-0.003199626225978136,
-0.010847724042832851,
0.013444804586470127,
-0.0009140775073319674,
0.0055914041586220264,
0.06950385123491287,
-0.0063117207027971745,
0.03891532123088837,
0.027531513944268227,
0.047322917729616165,
-0.0020290666725486517,
-0.005245275795459747,
0.008288931101560593,
0.020378228276968002,
-0.06849091500043869,
0.02086876891553402,
-0.04115705192089081,
0.09302917122840881,
0.01807078719139099,
-0.014805792830884457,
0.0027585786301642656,
-0.017902007326483727,
-0.00010635678336257115,
-0.01253445167094469,
-0.015197682194411755,
0.03274000063538551,
-0.022289007902145386,
0.015613594092428684,
-0.004959543235599995,
-0.001595660112798214,
0.02780008316040039,
-0.05946013331413269,
0.010297774337232113,
-0.0004954540054313838,
0.018588412553071976,
-0.015152164734899998,
-0.03299413621425629,
-0.014926502481102943,
-0.005199382547289133,
0.06405600905418396,
0.06947530061006546,
-0.0015061390586197376,
0.016498124226927757,
-0.01816343329846859,
-0.012244575656950474,
0.04868151620030403,
-0.10176661610603333,
-0.006385782267898321,
-0.0077195484191179276,
-0.0009574646246619523,
0.013780145905911922,
0.0237722247838974
] |
<p>I'm having a little trouble with wrapping my head around a part of a method which is fairly 'new' in some fashions to me. I imagine it should be fairly obvious, but I am not seeing something at the moment.</p>
<p>Let's take the Lagrangian density to be </p>
<p>$$\mathcal{ L}={1\over{2}}\left(\mu\dot{\phi}^2-Y(\partial_x\phi)^2\right),$$</p>
<p>where $\mu$ is mass density of rod and $Y$ is Young's modulus.</p>
<p>One "should" be able to put this into the equation</p>
<p>$${\partial\over \partial t}\left({\partial \mathcal{L}\over{\partial(\partial_t \phi)}}\right)+{\partial\over \partial x}\left({\partial \mathcal{L}\over{\partial(\partial_x \phi)}}\right)={\partial \mathcal{L}\over{\partial \phi}}$$</p>
<p>to get the equation of motion for the rod
$$\mu\ddot\phi=Y\partial_{xx}\phi,$$
right?</p>
<p>The trouble is I'm not exactly seeing where to go with the LHS of the E-L equation applied to $\mathcal L$ at the moment. I'm hoping someone would be so kind as to demonstrate that in a few lines.</p>
| 8,264 |
[
-0.002484925091266632,
0.017571771517395973,
0.012512247078120708,
-0.011094973422586918,
-0.004595975857228041,
-0.024684738367795944,
-0.031075583770871162,
-0.007246505003422499,
0.0174447949975729,
-0.014742632396519184,
0.04296994209289551,
0.038468532264232635,
0.1054859608411789,
0.046762868762016296,
0.056977249681949615,
0.005708028562366962,
0.0032114116474986076,
0.02933875471353531,
0.006652279291301966,
-0.06602975726127625,
-0.011142265051603317,
-0.029134495183825493,
-0.01621665433049202,
-0.015276902355253696,
-0.033841535449028015,
0.056583184748888016,
-0.007878044620156288,
-0.01730666309595108,
0.002565032569691539,
0.07773169875144958,
-0.020487280562520027,
-0.04804860055446625,
0.01351856254041195,
-0.00660156412050128,
0.03183302283287048,
0.021497325971722603,
-0.07589605450630188,
-0.034404389560222626,
0.026620525866746902,
0.01025889627635479,
-0.0420999675989151,
-0.0015662553487345576,
0.0008879250381141901,
0.05885900929570198,
-0.00974124576896429,
0.04579634964466095,
0.01052128616720438,
0.0056812940165400505,
0.09629299491643906,
-0.04051358625292778,
0.08156295865774155,
0.028277238830924034,
0.015379061922430992,
0.0305593591183424,
-0.04435766488313675,
-0.01507569756358862,
0.04062051698565483,
0.05709618702530861,
-0.0024757448118180037,
-0.04056946560740471,
-0.02270747348666191,
-0.014150265604257584,
0.0018468205817043781,
-0.03975994139909744,
0.026452315971255302,
0.0026173049118369818,
0.018453475087881088,
-0.0037555054295808077,
0.0343477725982666,
-0.014759141951799393,
-0.007927453145384789,
-0.00856084655970335,
0.02388687990605831,
0.005845601204782724,
0.01132150087505579,
-0.020380042493343353,
-0.007771877106279135,
0.029413489624857903,
-0.026966053992509842,
0.017957771196961403,
-0.013752850703895092,
0.01760667935013771,
0.028509458526968956,
0.04287184774875641,
-0.04420771077275276,
-0.022192785516381264,
0.06856541335582733,
0.018418895080685616,
0.006404257845133543,
0.013929067179560661,
0.023485852405428886,
0.015473926439881325,
0.03607133403420448,
0.01609559915959835,
-0.0037170734722167253,
0.04069479927420616,
0.025608962401747704,
0.0469452366232872,
0.019426265731453896,
0.020195191726088524,
0.0023304708302021027,
-0.03187735006213188,
0.03888849914073944,
0.061467356979846954,
-0.031384408473968506,
-0.04975229129195213,
-0.03493453934788704,
-0.013400232419371605,
0.007537480443716049,
-0.052178118377923965,
-0.024520665407180786,
0.03248673304915428,
-0.015065019950270653,
0.002018149010837078,
-0.0034994101151823997,
-0.016664909198880196,
0.0024098677095025778,
-0.013583009131252766,
0.03243090584874153,
0.02299756556749344,
0.0220605731010437,
-0.012016388587653637,
0.04731874167919159,
-0.00444002915173769,
-0.08848404139280319,
0.03588555380702019,
0.057598624378442764,
-0.007697741501033306,
-0.03045191429555416,
0.023550665006041527,
0.0047644879668951035,
0.013704794459044933,
0.0010981698287650943,
-0.010287928394973278,
0.00887940265238285,
-0.022881725803017616,
-0.08611071109771729,
-0.04242337495088577,
0.0023445154074579477,
0.033769652247428894,
-0.028523718938231468,
-0.055385999381542206,
-0.03836723044514656,
0.03478580340743065,
0.054876960813999176,
-0.024630054831504822,
-0.005699560511857271,
0.019637135788798332,
0.03273381292819977,
-0.026129990816116333,
-0.0077153355814516544,
-0.054429542273283005,
-0.012298393994569778,
-0.05007748305797577,
0.011571638286113739,
-0.06947139650583267,
0.014524077996611595,
0.010706010274589062,
-0.010100780054926872,
-0.01111721619963646,
0.09402648359537125,
-0.016441158950328827,
0.02142263390123844,
0.0017661219462752342,
0.0010615837527438998,
-0.009591442532837391,
0.049368686974048615,
0.008435348980128765,
0.005006026942282915,
0.06373961269855499,
-0.0008577011758461595,
-0.0006143224309198558,
-0.03156095743179321,
0.01311817578971386,
0.049535561352968216,
-0.029407940804958344,
-0.03114158846437931,
-0.026477040722966194,
-0.011953474953770638,
0.012171427719295025,
-0.026229869574308395,
-0.07167179137468338,
-0.014495854265987873,
-0.03778396174311638,
0.018820354714989662,
0.035678308457136154,
0.01952473632991314,
0.006445146631449461,
0.0002717372262850404,
-0.05582049861550331,
-0.07427351921796799,
-0.05441335216164589,
0.03169573098421097,
0.005622294265776873,
-0.024390920996665955,
0.02226155996322632,
-0.02337639592587948,
0.023144373670220375,
-0.007577904965728521,
-0.018947748467326164,
-0.010129698552191257,
0.040442246943712234,
-0.010608376003801823,
0.0014848086284473538,
0.010312668047845364,
0.043859951198101044,
0.01079577673226595,
0.005866766907274723,
0.014733396470546722,
-0.031125545501708984,
-0.024057267233729362,
-0.00028820388251915574,
0.019800718873739243,
0.024631163105368614,
0.004221150651574135,
-0.01704832911491394,
0.004074257332831621,
-0.04234896972775459,
-0.006021557375788689,
0.010560216382145882,
-0.05093731731176376,
0.053685758262872696,
0.0650455430150032,
-0.008884218521416187,
0.022392461076378822,
0.06754475831985474,
-0.03357338532805443,
0.030245130881667137,
0.0030006947927176952,
-0.032830361276865005,
-0.004849342163652182,
0.007511482574045658,
0.018587911501526833,
0.05386817082762718,
-0.023930344730615616,
0.008767623454332352,
0.050684768706560135,
0.005926407873630524,
0.004199056886136532,
0.044592566788196564,
-0.04220466688275337,
-0.033850133419036865,
0.05308248847723007,
0.04563172906637192,
-0.04617472365498543,
-0.025362111628055573,
0.015679901465773582,
0.02586827240884304,
0.024544553831219673,
-0.014688212424516678,
-0.03355283662676811,
0.04884186014533043,
-0.009894147515296936,
-0.000886077934410423,
-0.022843167185783386,
-0.018409131094813347,
0.07311058789491653,
-0.026047617197036743,
0.07105038315057755,
0.017472034320235252,
-0.027258388698101044,
0.0013681489508599043,
-0.06009366363286972,
0.011218143627047539,
-0.008422279730439186,
0.02490643970668316,
-0.014761841855943203,
-0.009087933227419853,
0.017338966950774193,
-0.033764664083719254,
-0.03418122977018356,
-0.014973933808505535,
-0.031902071088552475,
-0.028541503474116325,
0.013687564060091972,
0.004466419108211994,
0.013855069875717163,
0.003161435015499592,
-0.03861078992486,
-0.047765813767910004,
-0.019796520471572876,
0.028516249731183052,
0.03567137196660042,
0.011191464960575104,
-0.06728748232126236,
-0.02034376747906208,
-0.03484233841300011,
-0.008268020115792751,
0.031064648181200027,
0.019942542538046837,
-0.02175236865878105,
-0.01246724370867014,
0.007671393919736147,
-0.09158801287412643,
-0.01181017979979515,
-0.012782338075339794,
-0.014042102731764317,
-0.005950596649199724,
0.012937317602336407,
0.038669511675834656,
0.006734970957040787,
-0.0013361426535993814,
-0.011311887763440609,
-0.05562553554773331,
-0.015053516253829002,
-0.02080770581960678,
0.01316014863550663,
-0.004397130571305752,
-0.003445762675255537,
0.032464176416397095,
0.047516364604234695,
0.018490634858608246,
0.01823057420551777,
-0.05915696173906326,
-0.020853975787758827,
0.02526642195880413,
0.018595082685351372,
0.04111102223396301,
-0.014009352773427963,
-0.029170755296945572,
0.10347772389650345,
0.0357639417052269,
-0.05321536585688591,
-0.04608224332332611,
0.012273653410375118,
-0.0031581090297549963,
-0.03368237242102623,
0.020723911002278328,
0.027401762083172798,
-0.029858103021979332,
0.019183481112122536,
0.0075498465448617935,
-0.010547907091677189,
0.024021144956350327,
0.028334693983197212,
0.04505069553852081,
0.002146410057321191,
-0.005983762908726931,
0.0029717159923166037,
0.05275341123342514,
0.011680963449180126,
-0.0032754861749708652,
0.026840349659323692,
-0.03084864653646946,
0.035614337772130966,
-0.0035073435865342617,
-0.0730774849653244,
0.04498257488012314,
0.028731564059853554,
-0.06102064251899719,
-0.01228323858231306,
0.04202652350068092,
0.02022506855428219,
-0.026033183559775352,
-0.007571106776595116,
0.007013676688075066,
0.01951037161052227,
0.007245604880154133,
-0.014385898597538471,
0.0403573140501976,
-0.01074931025505066,
-0.02793039381504059,
-0.024974681437015533,
-0.012488876469433308,
-0.02240576036274433,
0.0228058323264122,
-0.026024911552667618,
-0.03816220164299011,
0.0446154847741127,
0.004939135629683733,
0.010661082342267036,
-0.03358200937509537,
-0.02287917584180832,
0.02385806106030941,
-0.0859789252281189,
-0.004567012656480074,
-0.010368798859417439,
0.044350843876600266,
0.022452767938375473,
0.06568853557109833,
0.021624984219670296,
0.030411573126912117,
0.019349049776792526,
0.039463020861148834,
-0.08626174181699753,
0.026694610714912415,
-0.02225734479725361,
-0.019288688898086548,
-0.0013813000405207276,
0.02567318081855774,
0.03967619687318802,
-0.02079732157289982,
-0.0210108682513237,
-0.0022880889009684324,
-0.025198133662343025,
-0.07410251349210739,
-0.002698185620829463,
-0.05837251991033554,
0.0016368598444387317,
-0.016962707042694092,
0.01111363060772419,
0.03507969155907631,
0.005230557639151812,
0.0030065071769058704,
0.04673303663730621,
-0.02179170399904251,
-0.02788974903523922,
-0.044613584876060486,
0.002787172794342041,
0.016931701451539993,
0.01567106880247593,
-0.0260145366191864,
0.017731139436364174,
0.000775629305280745,
0.05112747475504875,
-0.025720160454511642,
0.04878412187099457,
0.052123572677373886,
-0.0015902124578133225,
-0.025745438411831856,
-0.02151298150420189,
-0.004128880333155394,
0.028836838901042938,
0.07309692353010178,
-0.00666311290115118,
0.0255779679864645,
0.04479258507490158,
0.009763018228113651,
0.004574939142912626,
0.04577149823307991,
0.017290808260440826,
0.02227606251835823,
0.00030397018417716026,
-0.06494490802288055,
0.03160487115383148,
-0.022104855626821518,
0.010896630585193634,
0.005179551430046558,
-0.00984978023916483,
0.01320570893585682,
0.00038561969995498657,
0.045777078717947006,
0.01275340560823679,
0.038967303931713104,
0.01867048814892769,
-0.026346342638134956,
0.012371624819934368,
0.008105926215648651,
-0.013094245456159115,
0.03264550119638443,
0.033205196261405945,
0.036749448627233505,
0.0062990314327180386,
0.034185610711574554,
-0.07434165477752686,
-0.04727104306221008,
0.042344000190496445,
0.04056844487786293,
-0.009031755849719048,
0.009807048365473747,
-0.07941451668739319,
-0.049106664955616,
0.035187240689992905,
-0.02028760313987732,
0.022835748270154,
-0.02383851818740368,
0.0014231570530682802,
0.03565281629562378,
-0.04312824085354805,
-0.03982196003198624,
-0.004128406289964914,
-0.005183632951229811,
-0.0025099667254835367,
-0.036288585513830185,
0.02285599149763584,
-0.01709352433681488,
0.018810492008924484,
0.012698208913207054,
0.057337790727615356,
-0.006526482757180929,
-0.06334114819765091,
-0.02610177733004093,
0.023327117785811424,
-0.014051015488803387,
-0.07708840817213058,
-0.0166153647005558,
0.03063276968896389,
-0.0061538321897387505,
0.02565985918045044,
-0.023272328078746796,
-0.02791234478354454,
0.055146098136901855,
0.03714372217655182,
-0.011814611032605171,
-0.0006669802241958678,
-0.03688288480043411,
0.01046296488493681,
0.037739530205726624,
0.01677829399704933,
0.05427047237753868,
0.03502621501684189,
-0.013568605296313763,
0.014484470710158348,
-0.030985152348876,
0.012922187335789204,
0.014537275768816471,
0.02888016775250435,
-0.06183905154466629,
0.03576373681426048,
-0.015512353740632534,
0.049244292080402374,
-0.013683494180440903,
0.019143540412187576,
-0.06113521754741669,
-0.03660861402750015,
0.009897680953145027,
0.03361674025654793,
-0.0006584673537872732,
-0.006249243393540382,
0.00098482146859169,
0.03473120927810669,
0.03193707764148712,
-0.022203130647540092,
0.00350689934566617,
0.007033329922705889,
0.011691478081047535,
0.03905580937862396,
0.015412247739732265,
0.049841947853565216,
0.0037083658389747143,
-0.026058288291096687,
0.026918301358819008,
-0.0643773078918457,
0.07933882623910904,
0.006449713371694088,
0.03162557631731033,
0.008964989334344864,
-0.0047921654768288136,
-0.0321124866604805,
-0.0010377977741882205,
0.0005094204097986221,
0.006452385801821947,
-0.013901827856898308,
-0.01994144357740879,
0.011466313153505325,
-0.028883008286356926,
-0.06344031542539597,
-0.0625002384185791,
-0.0008876800420694053,
-0.023424742743372917,
-0.0191421490162611,
-0.02273593470454216,
-0.009217826649546623,
-0.01928221434354782,
-0.02203955501317978,
0.012598070316016674,
0.033079247921705246,
0.00006312768528005108,
0.013068951666355133,
0.013629191555082798,
0.01579934172332287,
0.030914703384041786,
-0.02520488202571869,
-0.0011674724519252777,
-0.006422714795917273,
-0.024076607078313828,
-0.013738930225372314,
0.0018659703200682998,
0.053268298506736755,
-0.0053953928872942924,
-0.03802552446722984,
-0.024940770119428635,
0.024402957409620285,
0.03668057173490524,
-0.02107107825577259,
-0.040675438940525055,
-0.00008299005276057869,
0.020059600472450256,
-0.023170510306954384,
-0.009477691724896431,
0.0005397603381425142,
-0.00510960491374135,
0.00996397528797388,
0.007683174684643745,
0.003290049731731415,
-0.02344411052763462,
-0.03140527009963989,
0.046764031052589417,
-0.005419065244495869,
0.0034508847165852785,
-0.0005237755831331015,
0.06845858693122864,
-0.022419942542910576,
-0.002691431436687708,
0.06118008494377136,
0.016314124688506126,
0.04759318381547928,
0.019956501200795174,
0.009052080102264881,
0.009698525071144104,
0.006686593871563673,
-0.048782676458358765,
-0.03766295686364174,
-0.012669628486037254,
0.006592286750674248,
0.06846880167722702,
-0.02600274235010147,
0.04757240414619446,
0.011245944537222385,
-0.019260670989751816,
0.012528649531304836,
0.016431551426649094,
-0.05556785315275192,
0.005805297754704952,
-0.02799404039978981,
0.07277189940214157,
-0.013606560416519642,
-0.002306766342371702,
0.02412443980574608,
0.03463003411889076,
-0.028561092913150787,
0.008037969470024109,
0.02056950330734253,
0.020999999716877937,
-0.013837014324963093,
-0.009541234001517296,
-0.052076928317546844,
0.03326211869716644,
-0.0070702326484024525,
0.050190504640340805,
-0.044830888509750366,
-0.025449354201555252,
0.06988558918237686,
0.022707605734467506,
0.01439469214528799,
-0.012471229769289494,
0.001339527196250856,
-0.013388989493250847,
0.02256300300359726,
0.03281005099415779,
-0.004249080084264278,
0.027798272669315338,
0.033098913729190826,
0.031719472259283066,
-0.006554480642080307,
0.017911851406097412,
-0.0028961068019270897,
-0.023022238165140152,
-0.020274758338928223,
-0.0398564450442791,
-0.06000248342752457,
0.05124456807971001,
0.014112796634435654,
0.02224166877567768,
0.02307966910302639,
0.010067524388432503,
0.004392222501337528,
0.02571510337293148,
0.04085380211472511,
-0.025417545810341835,
0.09134747087955475,
0.016864633187651634,
0.003154287813231349,
-0.04374632611870766,
-0.00836793053895235,
0.10604412853717804,
0.04813693091273308,
0.025203919038176537,
-0.06462548673152924,
-0.0036912839859724045,
-0.03174227103590965,
-0.014938863925635815,
-0.04515592381358147,
-0.0034130180720239878,
-0.021107101812958717,
0.008635364472866058,
-0.025402018800377846,
0.05436026304960251,
-0.0028892364352941513,
-0.016363102942705154,
0.024742987006902695,
-0.010997862555086613,
0.0017445271369069815,
0.0007330408552661538,
-0.00021699912031181157,
0.0018119963351637125,
-0.009095166809856892,
-0.031454261392354965,
0.021377237513661385,
0.0018069817451760173,
0.0007052542641758919,
-0.048593003302812576,
-0.08698271214962006,
0.011607498861849308,
-0.013358348049223423,
-0.03815942630171776,
0.005146692041307688,
-0.018872695043683052,
-0.046549346297979355,
0.004544090013951063,
-0.007536477874964476,
0.010692053474485874,
-0.035625383257865906,
0.05592061206698418,
0.041187629103660583,
-0.009031255729496479,
0.018429212272167206,
0.024808384478092194,
0.027966946363449097,
-0.011182659305632114,
0.0027782414108514786,
-0.006589884404093027,
0.06507403403520584,
-0.0022110166028141975,
0.021065691486001015,
0.006254827603697777,
-0.004346702713519335,
-0.005872870795428753,
-0.0525694265961647,
-0.00717463344335556,
-0.0108974389731884,
0.030146436765789986,
0.011381887830793858,
0.0049244496040046215,
-0.010263399221003056,
-0.04877671226859093,
0.0021755509078502655,
0.005656143184751272,
0.020793795585632324,
0.01864822767674923,
-0.018623599782586098,
-0.00833879690617323,
-0.011229608207941055,
-0.014782673679292202,
-0.026661116629838943,
-0.04376118630170822,
-0.04021112993359566,
-0.022238407284021378,
-0.026721207424998283,
-0.006708087399601936,
0.004440420772880316,
0.01095106266438961,
-0.021861594170331955,
-0.01542938407510519,
-0.045027151703834534,
-0.09737367928028107,
0.006976344622671604,
-0.0013233139179646969,
-0.023794742301106453,
-0.032168276607990265,
-0.0024722199887037277,
0.0015662231016904116,
0.04135775566101074,
0.010021244175732136,
-0.007427643518894911,
-0.025509988889098167,
0.03264113515615463,
0.0028713359497487545,
-0.0476892851293087,
-0.0679117813706398,
-0.01724180020391941,
0.0005876527866348624,
0.02550927735865116,
0.013036437332630157,
-0.00026214317767880857,
-0.015578416176140308,
0.03498225286602974,
0.0016138615319505334,
0.0398535318672657,
-0.001010584062896669,
-0.016585268080234528,
-0.014685677364468575,
-0.008077356964349747,
-0.0020811932627111673,
0.011704042553901672,
0.003854131791740656,
-0.02870204858481884,
0.002274948637932539,
-0.02197771891951561,
-0.04950649291276932,
0.0011541470885276794,
0.009734047576785088,
-0.02680133655667305,
0.0010382302571088076,
-0.024772366508841515,
-0.0016292334767058492,
-0.027314774692058563,
0.03407314419746399,
-0.009976459667086601,
0.011522645130753517,
-0.01200611237436533,
0.002939097350463271,
-0.037722181528806686,
0.032792408019304276,
-0.053810372948646545,
-0.007120013236999512,
0.0059895701706409454,
0.02791500650346279,
0.0008973624790087342,
-0.0015395039226859808,
0.026747243478894234,
-0.0025630660820752382,
0.030942747369408607,
0.02982746809720993,
-0.016141707077622414,
0.0016508413245901465,
-0.031066158786416054,
-0.011958427727222443,
0.033836375921964645,
0.01571972295641899,
0.030725067481398582,
0.05260731652379036,
-0.023102734237909317,
-0.013491479679942131,
0.025930287316441536,
0.00948344636708498,
-0.017940884456038475,
-0.0035804526414722204,
-0.03248318284749985,
-0.01372280903160572,
-0.02303219772875309,
-0.0029087509028613567,
-0.015220408327877522,
-0.0008234682027250528,
0.027495339512825012,
0.04942068085074425,
-0.04645021632313728,
0.0011595567921176553,
0.028877606615424156,
0.030113155022263527,
0.016360599547624588,
0.001390080084092915,
0.0029164981096982956,
0.01751679927110672,
0.05995843932032585,
0.013660067692399025,
-0.017741568386554718,
0.012009997852146626,
0.005860315170139074,
-0.07746189832687378,
0.005931027699261904,
-0.026606421917676926,
0.013737056404352188,
0.023829760029911995,
-0.05910096317529678,
-0.0012430474162101746,
0.002405542880296707,
-0.04118223860859871,
-0.006387610454112291,
-0.024924971163272858,
0.013554594479501247,
-0.016278963536024094,
-0.031734053045511246,
-0.00809033028781414,
0.03505884110927582,
0.030408041551709175,
0.03495291620492935,
0.00040584910311736166,
0.024064620956778526,
-0.000468670972622931,
-0.023453809320926666,
0.010385176166892052,
0.0353991724550724,
0.013254400342702866,
-0.029066480696201324,
0.0787416622042656,
-0.014176598750054836,
-0.04569627717137337,
-0.009416249580681324,
0.01660730317234993,
0.02661086991429329,
0.022228354588150978,
0.04774469882249832,
0.005768556613475084,
0.01318269968032837,
0.01563337817788124,
-0.012359345331788063,
-0.013033375144004822,
0.023143921047449112,
0.01741526648402214,
0.012610319070518017,
-0.04465955123305321,
-0.012196014635264874,
0.028778012841939926,
-0.018485184758901596,
-0.023534657433629036,
0.06334973871707916,
-0.028306808322668076,
0.03278162330389023,
0.0034471412654966116,
0.006368871778249741,
-0.00533201964572072,
-0.04196897894144058,
0.014593778178095818,
-0.026064330711960793,
-0.015822838991880417,
0.03570612147450447,
0.010669798590242863,
-0.008057801052927971,
0.027312027290463448,
0.03588271141052246,
-0.05099423974752426,
0.024100560694932938,
-0.018148716539144516,
0.020251411944627762,
-0.07282083481550217,
-0.00047001068014651537,
-0.011742690578103065,
-0.019917966797947884,
-0.007888893596827984,
-0.01861325092613697,
-0.041913870722055435,
0.017493898048996925,
-0.004195143468677998,
-0.012175250798463821,
0.006964548956602812,
0.004258242901414633,
0.01788197085261345,
-0.03922589495778084,
-0.0015276947524398565,
0.019478898495435715,
-0.048616744577884674,
-0.018827514722943306,
-0.03264700993895531,
0.02033867873251438,
0.0403447225689888,
0.0651039332151413,
-0.013538462109863758,
-0.030267316848039627,
0.043610528111457825,
-0.005722372326999903,
-0.011207222007215023,
-0.017112761735916138,
0.011905685998499393,
-0.004425182938575745,
-0.005457985680550337,
0.006345933768898249,
0.02792247384786606,
-0.05790148675441742,
0.020262669771909714,
0.03155015408992767,
0.021324777975678444,
0.012106303125619888,
-0.029883628711104393,
-0.04972707852721214,
0.025276491418480873,
-0.005685767624527216,
-0.0008205216727219522,
0.03371249511837959,
0.007459585554897785,
-0.006164820399135351,
0.0268417801707983,
-0.03987722843885422,
-0.06646635383367538,
0.05963127687573433,
-0.056447744369506836,
-0.026477133855223656,
-0.01050843670964241,
0.025029903277754784,
-0.0002407028223387897,
-0.03391330689191818,
-0.021135836839675903,
0.025277072563767433,
-0.036716729402542114,
-0.04637850821018219,
0.06508785486221313,
0.023177370429039,
0.05258942395448685,
-0.02024579979479313,
0.012403655797243118,
0.03652996942400932,
-0.02525457926094532,
0.017367497086524963,
0.013669339939951897,
0.03517290577292442,
-0.0015292512252926826,
-0.003419708227738738,
0.031042983755469322,
-0.030990419909358025,
0.013888930901885033,
-0.010711926966905594,
0.0429149754345417,
-0.052270058542490005,
0.00957676861435175,
0.006701251957565546,
-0.022996509447693825,
-0.0024401741102337837,
0.003929264843463898,
-0.05326247215270996,
0.04103649780154228,
-0.03437552973628044,
0.01189745869487524,
-0.008565512485802174,
0.0072557744570076466,
0.0026501130778342485,
0.02376817725598812,
0.011959336698055267,
0.0631113275885582,
0.02229074388742447,
0.017622319981455803,
-0.04184964671730995,
-0.0328625850379467,
0.037223055958747864,
-0.023709790781140327,
0.008957043290138245,
0.00972270593047142,
0.003348728409036994,
0.0494188517332077,
-0.05361295863986015,
-0.015145108103752136,
-0.026666710153222084,
0.005329174920916557,
0.034724198281764984,
0.00629808846861124,
-0.03714698180556297,
-0.01097937859594822,
-0.0058630164712667465,
0.0370037779211998,
-0.05887235701084137,
-0.02485612779855728,
0.0015389920445159078,
0.0142064169049263,
-0.002869108458980918,
-0.020644987002015114
] |
<p>I remember being in my college dorm, watching a film with a friend. His computer wasn't loud enough and we couldn't hear properly. So he took his earphones and put them on a electric guitar coil. He then plugged his guitar to his amp and voilà, we could listen through the amp.</p>
<p>Why on earth did this work? </p>
| 8,265 |
[
-0.01585620455443859,
-0.04117203876376152,
0.0036845537833869457,
-0.09198582917451859,
-0.007260315120220184,
0.04638691246509552,
-0.00041622601565904915,
0.03577855974435806,
0.004208772908896208,
0.02657945454120636,
0.04431439936161041,
0.05323093757033348,
0.06549951434135437,
-0.017910214141011238,
0.012383819557726383,
-0.02855638973414898,
0.04012513533234596,
0.00280145020224154,
-0.018323533236980438,
-0.04082907736301422,
-0.04198387637734413,
0.0641331598162651,
-0.059657540172338486,
-0.003936851862818003,
0.006037569604814053,
-0.0004025061789434403,
0.02078557200729847,
-0.007825745269656181,
0.018069487065076828,
0.02013440430164337,
-0.015016667544841766,
-0.011773359961807728,
0.018804481253027916,
0.00822287704795599,
0.03161206468939781,
-0.047727249562740326,
-0.03232428804039955,
-0.0023980906698852777,
0.03065577708184719,
0.023709798231720924,
0.021105188876390457,
0.027739010751247406,
0.0015263311797752976,
0.039141830056905746,
-0.035606786608695984,
0.002838641172274947,
0.0393315888941288,
-0.03813222423195839,
0.0035650806967169046,
-0.06845447421073914,
0.047661274671554565,
-0.02177877351641655,
0.020266922190785408,
0.04332230985164642,
0.032363999634981155,
0.03708807751536369,
0.08986318856477737,
0.03948643058538437,
-0.008432818576693535,
-0.040661588311195374,
-0.006235161330550909,
0.008201910182833672,
-0.058961186558008194,
0.012759574688971043,
-0.016196051612496376,
0.03661877289414406,
0.035734519362449646,
-0.011986727826297283,
0.040314942598342896,
-0.029034283012151718,
-0.02429194375872612,
0.013463316485285759,
0.03531821444630623,
-0.004877688828855753,
0.020928334444761276,
-0.030617766082286835,
-0.005165550392121077,
-0.01935506984591484,
0.025066852569580078,
0.03358813375234604,
-0.03492949530482292,
-0.0031423650216311216,
0.024977602064609528,
0.04420480504631996,
0.013460308313369751,
-0.008639573119580746,
0.0837981179356575,
-0.027150247246026993,
-0.02262730896472931,
0.015525085851550102,
0.0027914955280721188,
0.02438833937048912,
0.03420427441596985,
0.031279079616069794,
0.0015137779992073774,
0.029070211574435234,
0.003394001629203558,
0.055356353521347046,
0.05004151910543442,
-0.07060161978006363,
0.046111639589071274,
0.021801762282848358,
0.027753528207540512,
0.05822458863258362,
-0.0038854749873280525,
-0.0422188825905323,
-0.006778581999242306,
0.033140555024147034,
-0.033461593091487885,
0.01091387402266264,
-0.0385640412569046,
0.021234886720776558,
0.036433637142181396,
-0.008244819939136505,
0.0468086339533329,
-0.0018598783062770963,
-0.018950343132019043,
-0.04172477498650551,
0.04932834580540657,
0.04309811443090439,
0.007646666374057531,
-0.0006451552617363632,
0.02573946863412857,
-0.033787842839956284,
-0.05260242894291878,
0.0051344106905162334,
-0.02744179591536522,
-0.002915013115853071,
-0.028489932417869568,
0.01145247183740139,
-0.03437905013561249,
-0.028537046164274216,
-0.0151562774553895,
-0.010008462704718113,
0.06369615346193314,
0.0025178641080856323,
-0.0958016961812973,
-0.06004329398274422,
0.041523199528455734,
-0.029469020664691925,
0.01319961529225111,
-0.07166143506765366,
-0.010386326350271702,
0.043861765414476395,
0.0690176710486412,
-0.000536177889443934,
-0.002527275588363409,
-0.012690123170614243,
0.017470229417085648,
0.01181490533053875,
0.0064093368127942085,
-0.025834811851382256,
-0.03233008459210396,
0.007046915125101805,
0.028984136879444122,
-0.03668167442083359,
0.037568703293800354,
0.014635622501373291,
-0.015369913540780544,
-0.019958626478910446,
0.04383070766925812,
-0.043746598064899445,
-0.0541960634291172,
0.005355128087103367,
-0.05402538180351257,
-0.035526178777217865,
0.0412859208881855,
0.010772496461868286,
-0.02823481149971485,
0.030895814299583435,
-0.021912334486842155,
0.04987950995564461,
0.0522824265062809,
0.003624255768954754,
-0.03460727632045746,
-0.04041535407304764,
0.01792658120393753,
-0.02157832495868206,
0.011502138338983059,
0.00914798490703106,
0.01180267333984375,
-0.024500081315636635,
0.04509960114955902,
0.0401543453335762,
0.013125387951731682,
0.0599004290997982,
0.015025056898593903,
-0.040318600833415985,
-0.022951092571020126,
-0.0033060654532164335,
0.015477597713470459,
-0.037766147404909134,
0.05509061738848686,
-0.040807921439409256,
-0.013380604796111584,
-0.005902451928704977,
0.004263387527316809,
0.021366648375988007,
-0.03244318440556526,
-0.008329961448907852,
0.020135752856731415,
-0.012878394685685635,
0.02818627469241619,
0.010684126988053322,
0.0009870595531538129,
0.09016474336385727,
0.03497695550322533,
-0.003710055723786354,
0.06911970674991608,
-0.004927851725369692,
-0.04823218658566475,
0.024435706436634064,
-0.0013224971480667591,
0.037129078060388565,
-0.030722517520189285,
-0.0020158973056823015,
-0.007671881001442671,
-0.02049226686358452,
-0.03053433634340763,
0.05547456443309784,
-0.026226457208395004,
0.047088250517845154,
0.03841902315616608,
0.019279630854725838,
0.010813585482537746,
0.02730279229581356,
0.01775222271680832,
0.029107728973031044,
0.0019096574978902936,
-0.013309171423316002,
-0.06546701490879059,
0.006350191775709391,
0.06136498972773552,
0.02433061972260475,
-0.0018172019626945257,
0.024295564740896225,
-0.010700793005526066,
0.026441169902682304,
0.03108246624469757,
0.041264381259679794,
0.008944565430283546,
-0.004169507417827845,
-0.013207484036684036,
0.01079325471073389,
0.00493205850943923,
0.01745724119246006,
0.032938484102487564,
0.022274086251854897,
0.019260110333561897,
0.012736418284475803,
-0.014584706164896488,
0.022817110642790794,
-0.0027677572797983885,
0.037356484681367874,
0.006980010308325291,
-0.03751368820667267,
-0.005727696232497692,
-0.0488998182117939,
0.0038242971058934927,
-0.020127547904849052,
0.03304952755570412,
-0.019628582522273064,
-0.0022405616473406553,
0.00505414791405201,
-0.006176468450576067,
0.034379974007606506,
0.0069314357824623585,
0.005105065647512674,
0.05592756345868111,
-0.021472902968525887,
0.004368514288216829,
-0.008287929929792881,
0.02132023125886917,
-0.05062439665198326,
0.031792934983968735,
-0.007714647334069014,
0.013807257637381554,
0.022530805319547653,
-0.04613000899553299,
-0.04997849091887474,
-0.03792186453938484,
-0.0055054668337106705,
0.01000779215246439,
0.021263154223561287,
0.013449890539050102,
-0.013804390095174313,
0.010359340347349644,
0.002771734958514571,
0.011446776799857616,
-0.00008856911881593987,
-0.01622084341943264,
0.0018688086420297623,
-0.04134027287364006,
-0.05329272523522377,
-0.00348839838989079,
0.0051237111911177635,
0.040856387466192245,
-0.00820243451744318,
-0.0035629458725452423,
0.05512324348092079,
0.015334042720496655,
-0.003644917393103242,
-0.002942277817055583,
-0.054601337760686874,
-0.03955870866775513,
0.05382690206170082,
-0.04177665710449219,
0.012223698198795319,
-0.04926840960979462,
0.022388868033885956,
-0.025995174422860146,
-0.05101454257965088,
-0.017506549134850502,
-0.030620016157627106,
-0.025949819013476372,
0.0022519377525895834,
0.012769908644258976,
0.032247934490442276,
0.007980653084814548,
-0.02553807571530342,
0.0058702933602035046,
-0.006405139807611704,
-0.07291264086961746,
-0.018723171204328537,
-0.0062264022417366505,
-0.012143081985414028,
-0.058934930711984634,
0.030843479558825493,
0.12050630897283554,
-0.022817092016339302,
0.0412755012512207,
0.026403510943055153,
-0.0015190707053989172,
0.03447161614894867,
0.04571652412414551,
-0.036673907190561295,
-0.027866169810295105,
0.0010900113265961409,
-0.034806687384843826,
0.046315111219882965,
0.009491032920777798,
-0.042283523827791214,
0.00668358476832509,
0.0002908403112087399,
0.014509614557027817,
0.04733255133032799,
-0.0130327632650733,
0.03483535721898079,
-0.01693275198340416,
0.008692925795912743,
-0.05156370997428894,
0.03290232643485069,
-0.0027120402082800865,
-0.0043145581148564816,
-0.01838863268494606,
0.041877392679452896,
0.0024163934867829084,
-0.014565947465598583,
-0.0236179418861866,
-0.00946478359401226,
0.024867333471775055,
-0.059130433946847916,
-0.05587904900312424,
0.00050826818915084,
0.019919490441679955,
0.00026670066290535033,
-0.00976861733943224,
-0.03717151656746864,
0.06077417731285095,
0.03677010536193848,
-0.005078004207462072,
0.005381311289966106,
-0.03308473899960518,
-0.01600576564669609,
-0.0741850882768631,
0.026354575529694557,
-0.030741292983293533,
0.007510754745453596,
-0.00035588251193985343,
0.08336493372917175,
0.00122668722178787,
0.00963974092155695,
-0.011956698261201382,
-0.04410744830965996,
-0.0699935257434845,
0.007987386547029018,
-0.024217573925852776,
-0.0420120470225811,
-0.024498483166098595,
-0.0030855650547891855,
0.002061030827462673,
-0.002065498847514391,
-0.028847433626651764,
-0.0357455350458622,
-0.02859097719192505,
-0.04816313460469246,
-0.005569589789956808,
0.004581942688673735,
-0.0628599151968956,
-0.03977498039603233,
0.021154632791876793,
0.05142425745725632,
0.02334469184279442,
0.000535705650690943,
-0.02099926397204399,
-0.057413216680288315,
-0.025913288816809654,
-0.009102873504161835,
-0.008095113560557365,
-0.00778236472979188,
0.02118871919810772,
0.04914715141057968,
0.022757308557629585,
-0.03888148069381714,
0.0050719790160655975,
0.00034694335772655904,
0.0695527121424675,
-0.01591888815164566,
-0.02888188511133194,
-0.045952484011650085,
-0.05168582871556282,
-0.03843355551362038,
-0.010925043374300003,
0.03970663994550705,
0.0011431336170062423,
0.012591594830155373,
-0.004860305227339268,
0.0031624031253159046,
-0.0327034555375576,
-0.000026707075448939577,
0.01603439822793007,
-0.00009889905049931258,
-0.029159871861338615,
-0.03691156581044197,
-0.04465535283088684,
-0.022458605468273163,
0.006827107630670071,
-0.0018997261067852378,
-0.00827212817966938,
-0.01532741915434599,
-0.0284006018191576,
0.023479508236050606,
0.0007119773072190583,
0.001510846777819097,
0.0020597781985998154,
-0.029007982462644577,
0.00638221949338913,
-0.015600613318383694,
0.01100129634141922,
0.008095935918390751,
0.029462385922670364,
0.06428270787000656,
-0.015298383310437202,
-0.07640700787305832,
-0.0877656489610672,
0.02913001738488674,
0.010165681131184101,
0.04233875125646591,
-0.00775704812258482,
0.01576751098036766,
-0.040363676846027374,
-0.05700983479619026,
0.009386763907968998,
-0.00003907929203705862,
0.035106759518384933,
-0.03331200033426285,
0.006706209387630224,
-0.04650929942727089,
-0.03786724433302879,
0.028559403494000435,
0.011367793194949627,
-0.016070883721113205,
-0.0032138517126441,
-0.018113702535629272,
-0.06413231045007706,
-0.01676836609840393,
0.009043939411640167,
0.049374356865882874,
0.016881320625543594,
-0.002148861065506935,
0.024568192660808563,
-0.01952364854514599,
0.04250659793615341,
-0.03314955532550812,
-0.042871471494436264,
-0.015643225982785225,
-0.02279810607433319,
-0.029174549505114555,
0.034684423357248306,
-0.007132427766919136,
-0.04019571840763092,
0.018190978094935417,
0.0019639458041638136,
0.020060621201992035,
-0.012473398819565773,
-0.02609197422862053,
0.01873433217406273,
0.014536792412400246,
0.009095783345401287,
0.049368396401405334,
0.012290249578654766,
-0.018166454508900642,
0.011062460020184517,
0.003680725581943989,
0.03345420956611633,
-0.0113789401948452,
0.03770865127444267,
0.016926215961575508,
0.027318663895130157,
-0.027434051036834717,
0.051306940615177155,
-0.006983375642448664,
0.01832856796681881,
-0.01556409988552332,
-0.026794172823429108,
-0.03694736212491989,
0.03508274629712105,
-0.03462725877761841,
-0.03692489117383957,
-0.009150569327175617,
0.008342310786247253,
0.0030589825473725796,
-0.03240214288234711,
0.027408722788095474,
-0.006448136176913977,
-0.003726476337760687,
0.06025528907775879,
0.007140244822949171,
0.027232103049755096,
-0.03406903147697449,
-0.0010934678139165044,
0.021864887326955795,
-0.04098997637629509,
0.025920800864696503,
-0.06536374241113663,
-0.014562145806849003,
0.010375924408435822,
-0.041228994727134705,
-0.028306154534220695,
0.007425930351018906,
0.0013464119983837008,
0.061758529394865036,
-0.014291757717728615,
0.020265143364667892,
0.0028372735250741243,
0.0001026232130243443,
-0.03337576985359192,
-0.04954999312758446,
0.03572827950119972,
0.028825700283050537,
0.019938768818974495,
-0.0025642085820436478,
-0.02077234908938408,
0.026240985840559006,
-0.03950178995728493,
0.008217878639698029,
0.005601776298135519,
-0.020530784502625465,
0.027951540425419807,
0.04714159667491913,
0.005113564431667328,
0.05281311273574829,
0.01810973696410656,
-0.029067713767290115,
0.011014873161911964,
-0.05783194303512573,
0.0011069810716435313,
-0.0028712444473057985,
0.0046061500906944275,
-0.02386200614273548,
-0.025993958115577698,
0.018858948722481728,
-0.005313987378031015,
0.026912709698081017,
-0.014107870869338512,
0.000573868106584996,
0.012019007466733456,
-0.004613931756466627,
-0.004665021318942308,
-0.0275140218436718,
0.032956041395664215,
-0.006137286778539419,
-0.0019662196282297373,
0.00006448269414249808,
-0.003331830259412527,
-0.06474542617797852,
-0.01675320416688919,
0.010739237070083618,
0.0300009585916996,
0.009733958169817924,
-0.016280045732855797,
0.07632410526275635,
-0.01866614632308483,
-0.033941805362701416,
0.023583918809890747,
-0.03867408260703087,
0.03636642172932625,
-0.015961159020662308,
-0.00890664104372263,
0.001680653658695519,
0.024351660162210464,
-0.014243134297430515,
-0.020332898944616318,
0.0029797751922160387,
-0.025209715589880943,
0.042952489107847214,
-0.0029124084394425154,
0.03716129809617996,
0.03686985746026039,
-0.023813551291823387,
-0.009782040491700172,
-0.01414314191788435,
-0.00044711315422318876,
0.015133509412407875,
-0.041991788893938065,
0.012759968638420105,
0.014144090935587883,
0.01906750351190567,
0.027011986821889877,
0.00410029012709856,
0.013190515339374542,
0.004118418786674738,
0.04517504945397377,
0.04221528768539429,
-0.00643458915874362,
0.04481891170144081,
-0.024564819410443306,
0.03054332174360752,
-0.06196598336100578,
0.005763811059296131,
-0.011506718583405018,
0.028540974482893944,
0.027958180755376816,
-0.03040684573352337,
-0.025450976565480232,
-0.047387175261974335,
0.02160109020769596,
-0.04261532798409462,
-0.032162874937057495,
0.03127916529774666,
0.023401059210300446,
0.05019320547580719,
-0.013591645285487175,
0.04624098166823387,
0.008060372434556484,
0.016821205615997314,
0.008837380446493626,
-0.06244046986103058,
-0.02844618447124958,
-0.002327653346583247,
-0.03080950863659382,
0.05339832231402397,
0.02098105475306511,
-0.03273081034421921,
0.0521724596619606,
-0.029648199677467346,
0.0067487419582903385,
0.007201529573649168,
0.026620639488101006,
-0.03507376089692116,
0.05839131772518158,
-0.0015458299312740564,
0.018496137112379074,
-0.00010046984243672341,
-0.024353763088583946,
0.128474161028862,
0.009846638888120651,
0.03067677654325962,
-0.04971398413181305,
0.024220936000347137,
-0.03925354406237602,
0.01634838990867138,
-0.011152198538184166,
0.023908259347081184,
-0.0186323132365942,
0.03891512751579285,
-0.006829629186540842,
0.038776546716690063,
0.05775599181652069,
0.028324156999588013,
0.05521642044186592,
-0.014406261965632439,
-0.008805367164313793,
-0.0008135681273415685,
-0.016447270289063454,
-0.002890186384320259,
-0.01479617040604353,
-0.03876185789704323,
-0.018873412162065506,
-0.03871648758649826,
-0.024140536785125732,
0.00685327872633934,
-0.026329275220632553,
0.07776294648647308,
0.005279926583170891,
-0.04174172878265381,
0.025444407016038895,
0.01871536485850811,
-0.0021198121830821037,
0.006491075735539198,
0.029220864176750183,
0.06411158293485641,
0.033669646829366684,
-0.02184215374290943,
0.010529144667088985,
0.051237206906080246,
-0.012331963516771793,
-0.04490656778216362,
0.013060079887509346,
-0.006476706359535456,
-0.034236326813697815,
-0.00933073554188013,
0.0005503350985236466,
0.01562401745468378,
-0.026897137984633446,
-0.00719359191134572,
-0.00038820886402390897,
0.0033957497216761112,
-0.0010139503283426166,
-0.06750597059726715,
-0.0014803470112383366,
0.0012566751101985574,
-0.012404887937009335,
0.007476347964257002,
-0.01646372303366661,
0.0185394249856472,
0.006050884258002043,
0.010348140262067318,
-0.004684294108301401,
0.02121942676603794,
0.017148923128843307,
-0.02160344459116459,
-0.03692222386598587,
-0.0006694752373732626,
-0.01219980139285326,
-0.06438436359167099,
-0.012605094350874424,
-0.045276280492544174,
0.02037852071225643,
-0.007812317460775375,
0.02738654613494873,
0.03466850891709328,
0.01812887005507946,
-0.006155859213322401,
-0.02643738128244877,
-0.03811065852642059,
0.04004143923521042,
0.0025281987618654966,
-0.012968935072422028,
-0.021797096356749535,
-0.021925320848822594,
-0.003277404233813286,
-0.005391690880060196,
0.01123740617185831,
0.0034999584313482046,
0.011310819536447525,
0.02842012606561184,
-0.0023649048525840044,
-0.0012169721303507686,
-0.05760892853140831,
-0.0030354235786944628,
-0.01286266464740038,
0.008479572832584381,
0.042128413915634155,
0.05560849979519844,
0.0018121590837836266,
-0.010500642471015453,
0.0018193431897088885,
0.025343874469399452,
-0.0599948950111866,
-0.014286312274634838,
0.018674593418836594,
0.017170697450637817,
0.023363763466477394,
0.02012193389236927,
0.04233773797750473,
-0.027917757630348206,
-0.012591591104865074,
-0.01930016092956066,
0.014805963262915611,
0.02815379574894905,
0.006911438889801502,
0.02796110138297081,
0.02214300073683262,
-0.00816044770181179,
0.019670547917485237,
-0.007025477010756731,
0.018134864047169685,
-0.04605531319975853,
-0.015623039565980434,
-0.03710927814245224,
-0.009859966114163399,
-0.030032362788915634,
0.033925458788871765,
-0.03032909333705902,
-0.03463887423276901,
0.001946476986631751,
0.020055271685123444,
-0.030777374282479286,
-0.019909653812646866,
-0.015626119449734688,
0.032379381358623505,
0.005604674573987722,
-0.031074006110429764,
-0.04392334073781967,
0.044672641903162,
-0.04880441352725029,
0.005668812897056341,
0.018802804872393608,
0.013490828685462475,
0.014859471470117569,
0.0014689089730381966,
-0.02553112804889679,
0.010111585259437561,
0.04594296216964722,
-0.026643818244338036,
-0.023810848593711853,
0.002721300581470132,
0.015948306769132614,
0.008878624998033047,
0.027986332774162292,
-0.048688631504774094,
0.0015925243496894836,
-0.013452648185193539,
0.023699942976236343,
0.016070231795310974,
0.06794361025094986,
0.02380773052573204,
0.03438866510987282,
0.011949949897825718,
0.012815129943192005,
0.02505498006939888,
0.013241388835012913,
0.00993996299803257,
0.039889413863420486,
-0.008029906079173088,
0.037301674485206604,
0.00854061171412468,
-0.01909353770315647,
-0.07363516837358475,
0.0070832259953022,
0.006546648684889078,
0.003889621002599597,
0.047929227352142334,
-0.0393696203827858,
0.02639719843864441,
0.001140229869633913,
-0.06659083813428879,
0.009325851686298847,
0.0025995434261858463,
-0.07127757370471954,
-0.00888150930404663,
0.011973022483289242,
0.0094534270465374,
0.016095176339149475,
0.048881176859140396,
0.027766140177845955,
-0.0035051528830081224,
-0.017400261014699936,
-0.012488743290305138,
-0.026130927726626396,
0.023230627179145813,
0.009041570127010345,
-0.005894091911613941,
0.0506831556558609,
0.05849118530750275,
-0.04328780993819237,
-0.017283402383327484,
0.041761063039302826,
-0.014583520591259003,
-0.005048625636845827,
0.02189241535961628,
0.03793295845389366,
0.023626916110515594,
0.03927135095000267,
0.010696984827518463,
0.004363671410828829,
-0.017900414764881134,
0.0247797891497612,
0.05643258988857269,
0.001156394719146192,
0.0013574233744293451,
-0.039719223976135254,
0.01075410470366478,
0.01382284052670002,
-0.014724845997989178,
0.003303281730040908,
-0.034444961696863174,
0.004519558046013117,
0.02063600905239582,
0.034921590238809586,
-0.012523166835308075,
-0.03410609811544418,
-0.04718758910894394,
-0.027325976639986038,
-0.04688337445259094,
0.037043239921331406,
0.012639566324651241,
0.015775516629219055,
0.015234182588756084,
-0.013656946830451488,
-0.0124907111749053,
0.015924537554383278,
0.04614702984690666,
-0.017513936385512352,
-0.03641980141401291,
-0.0041314903646707535,
-0.004161675926297903,
0.03263105824589729,
0.022152116522192955,
-0.037783730775117874,
0.0071478430181741714,
0.008531258441507816,
0.027901917695999146,
0.037170059978961945,
0.03416959196329117,
-0.05557653680443764,
0.01909906044602394,
-0.024791283532977104,
0.07643963396549225,
-0.0026669108774513006,
-0.002848132513463497,
-0.05192200839519501,
-0.0403728149831295,
0.011473644524812698,
0.05996863171458244,
0.07925857603549957,
0.009710224345326424,
-0.004575526341795921,
0.00987460557371378,
0.0015399983385577798,
0.026446698233485222,
-0.04772231727838516,
0.03619144856929779,
0.03591146320104599,
-0.01785638928413391,
-0.010305331088602543,
0.018765540793538094,
-0.028503594920039177,
-0.00808272697031498,
0.03015834279358387,
-0.018498068675398827,
0.05365404114127159,
-0.026788897812366486,
0.007857992313802242,
0.012638923712074757,
0.02588307298719883,
-0.016625525429844856,
0.03167151287198067,
-0.016189511865377426,
-0.00014321363414637744,
-0.017601272091269493,
-0.015385545790195465,
-0.05559880658984184,
0.04076193645596504,
-0.04704876244068146,
0.05052480846643448,
-0.048532769083976746,
-0.007838667370378971,
0.003821799997240305,
-0.015702536329627037,
-0.02040020190179348,
0.015042572282254696,
-0.034142155200242996,
-0.029149798676371574,
0.06045375019311905,
-0.004627993796020746,
0.0006523139891214669,
-0.0184328593313694,
0.0304495207965374,
-0.02392544224858284,
-0.0002804107207339257,
-0.03076273389160633,
0.04965116083621979,
0.012553101405501366,
-0.01570742018520832,
-0.03688006475567818,
0.049437351524829865,
-0.0048219733871519566,
0.010072131641209126,
-0.0022542753722518682,
0.02308843471109867,
-0.038088180124759674,
-0.03936322033405304,
-0.00995350070297718,
-0.07642856240272522,
-0.019889604300260544,
0.0474357008934021,
-0.050263889133930206,
0.10034839063882828,
-0.020828893408179283,
0.01786966063082218,
0.046673547476530075,
0.0013698302209377289,
0.01365593634545803,
-0.011902418918907642,
-0.015597301535308361,
-0.0010782490717247128,
-0.04231380671262741,
-0.014401739463210106,
-0.01905835047364235,
-0.0582011342048645,
0.047822825610637665,
-0.035919759422540665,
0.013091628439724445,
0.0056161233223974705,
-0.01803590916097164,
0.006709563545882702,
0.0014845035038888454,
-0.003815603908151388,
-0.009533054195344448,
0.03991329297423363,
0.016367506235837936,
-0.06824712455272675,
-0.017239326611161232,
-0.007501537911593914,
-0.035136234015226364,
0.06589657813310623,
-0.07479546964168549,
0.007357992231845856,
-0.023445257917046547,
0.020337216556072235,
0.026802079752087593,
-0.005424383096396923
] |
<p>Is there any interacting quantum field theory of massless fields with helicity $\pm 1$ which can be expressed entirely locally in terms of the field strength F<sub>μν</sub> with no reference to vector potentials at all? Clearly, quantum electrodynamics doesn't fall into this category. The Aharonov-Bohm effect is the reason.</p>
<p>Classically, it's easy to come up with many such theories, but unfortunately, they happen to be nonrenormalizable. But do asymptotically safe models exist?</p>
| 8,266 |
[
-0.023095708340406418,
-0.014170431531965733,
0.004331796430051327,
-0.022052619606256485,
0.046651922166347504,
0.025472141802310944,
-0.028022630140185356,
-0.033923495560884476,
0.027073029428720474,
-0.03233664110302925,
0.027453819289803505,
-0.0007902070065028965,
0.051148660480976105,
0.03765483573079109,
0.008455147966742516,
0.009518361650407314,
0.004922471009194851,
0.0050445133820176125,
-0.021084042266011238,
-0.04119738191366196,
-0.02401602454483509,
0.05273416265845299,
0.019006723538041115,
0.019456397742033005,
0.007062344346195459,
-0.006916624493896961,
0.016334572806954384,
0.01446817722171545,
-0.017807140946388245,
0.07490172982215881,
-0.014048188924789429,
-0.05208389833569527,
-0.010100213810801506,
0.02746932953596115,
-0.003721782471984625,
0.021538903936743736,
0.009249641560018063,
-0.04227867349982262,
-0.003262697719037533,
-0.0063765752129256725,
-0.049059122800827026,
-0.07487726211547852,
-0.0061888848431408405,
0.0665295422077179,
-0.008706456050276756,
0.03857313096523285,
-0.011749662458896637,
0.004719120915979147,
0.11156570911407471,
-0.03847968578338623,
0.026735182851552963,
-0.0036251109559088945,
0.02391180768609047,
0.004435489885509014,
0.011131112463772297,
-0.024871421977877617,
0.054329756647348404,
0.05400975048542023,
-0.0015042612794786692,
-0.062838613986969,
-0.0809682235121727,
-0.023775609210133553,
0.012085110880434513,
-0.045245446264743805,
-0.0030280915088951588,
0.03537154197692871,
-0.012331590056419373,
-0.01012100838124752,
0.018908124417066574,
-0.010243580676615238,
-0.04043648764491081,
0.011882294900715351,
0.009283088147640228,
-0.0006112083210609853,
0.0008105282904580235,
0.03376422077417374,
-0.004096507094800472,
-0.009975392371416092,
0.0023124676663428545,
0.016813483089208603,
-0.04226960241794586,
0.019294878467917442,
0.026579152792692184,
0.005818451289087534,
0.016900960355997086,
-0.007538751699030399,
0.05204758793115616,
0.0005623350734822452,
0.0015037939883768559,
0.04999189451336861,
-0.04371882975101471,
-0.00312747317366302,
0.03625787794589996,
-0.03516753390431404,
-0.04918849468231201,
0.03468137979507446,
0.016389500349760056,
0.009426840580999851,
-0.0030131477396935225,
0.007506825961172581,
-0.028642280027270317,
0.0032371319830417633,
-0.018181651830673218,
0.06762891262769699,
0.0017715173307806253,
-0.028758561238646507,
-0.004679120145738125,
-0.01787739060819149,
-0.03683941066265106,
0.009058225899934769,
-0.03794567659497261,
0.012637024745345116,
0.0005455415812321007,
-0.0066309114918112755,
0.010015054605901241,
-0.04938749969005585,
-0.023437874391674995,
-0.02719447948038578,
0.05452408641576767,
0.08045565336942673,
0.06800203025341034,
-0.023461105301976204,
0.017193801701068878,
-0.07262303680181503,
-0.049006883054971695,
-0.020801043137907982,
0.024449225515127182,
0.013708132319152355,
-0.046981219202280045,
0.026574162766337395,
0.018346436321735382,
-0.020186951383948326,
-0.012875747866928577,
0.019235793501138687,
0.04365689679980278,
-0.05289655923843384,
-0.03398635983467102,
-0.038950640708208084,
0.02326084114611149,
-0.024595221504569054,
-0.014481857419013977,
-0.0337773859500885,
-0.010777176357805729,
0.027654439210891724,
0.13243468105793,
0.007671430241316557,
0.029713202267885208,
0.014538794755935669,
0.048607178032398224,
0.016652043908834457,
-0.016432633623480797,
-0.0480339489877224,
-0.0014890681486576796,
-0.024970412254333496,
-0.018693232908844948,
-0.057118628174066544,
0.040484052151441574,
0.03727853670716286,
0.015245882794260979,
0.011430821381509304,
0.0721273422241211,
-0.03050851821899414,
0.0519404374063015,
-0.0007289584609679878,
-0.02706596627831459,
0.0032400295604020357,
0.058930449187755585,
0.004061670508235693,
0.03272487223148346,
0.05418241769075394,
-0.01800903119146824,
-0.0009781093103811145,
0.006895571947097778,
0.02978879027068615,
0.058418408036231995,
-0.034913741052150726,
0.0008887614822015166,
-0.017082558944821358,
0.022897889837622643,
0.01891334354877472,
-0.027980303391814232,
-0.015981776639819145,
-0.04494990035891533,
-0.004789350088685751,
-0.031672339886426926,
0.0563041977584362,
-0.002615410601720214,
-0.029559966176748276,
0.014512275345623493,
-0.021962396800518036,
-0.008225059136748314,
-0.04437416046857834,
0.007056528236716986,
0.03532061725854874,
-0.0028579682111740112,
0.08972529321908951,
0.007382871583104134,
0.009448855184018612,
-0.04200027137994766,
-0.033416833728551865,
-0.029761284589767456,
0.02015053667128086,
-0.024041593074798584,
0.01520252414047718,
0.0185129102319479,
0.016269054263830185,
0.03809596970677376,
0.005997446831315756,
0.06263961642980576,
-0.016144467517733574,
-0.07649928331375122,
-0.004893156699836254,
-0.0219007208943367,
0.03616614639759064,
0.007177583407610655,
0.002096242504194379,
0.0043010045774281025,
-0.025702545419335365,
0.00040546973468735814,
0.01961270533502102,
-0.01006154716014862,
0.042057763785123825,
0.01057283952832222,
0.009278332814574242,
0.01989026740193367,
0.058201197534799576,
0.01228852104395628,
-0.012140058912336826,
-0.028415925800800323,
-0.023451318964362144,
-0.04936440661549568,
0.010313272476196289,
0.09763788431882858,
0.03661712631583214,
-0.030379492789506912,
0.0060319253243505955,
0.031824205070734024,
0.039801765233278275,
0.03684592247009277,
0.025668462738394737,
-0.06783241033554077,
-0.03701195493340492,
0.038643404841423035,
-0.01839013397693634,
0.022336378693580627,
0.00974294263869524,
0.0445089191198349,
0.012302461080253124,
-0.002878516213968396,
0.019631067290902138,
-0.01815428026020527,
0.024847419932484627,
-0.03188403695821762,
0.008423213846981525,
-0.02060520462691784,
-0.02893994376063347,
0.019742516800761223,
-0.008651301264762878,
0.031210940331220627,
-0.012476852163672447,
-0.05657251179218292,
0.006259507033973932,
-0.019804339855909348,
-0.006769272033125162,
0.06049397587776184,
-0.009000676684081554,
0.000651758920866996,
-0.04117092117667198,
0.02177157998085022,
-0.04634355381131172,
0.0020074951462447643,
-0.03685852885246277,
-0.028069157153367996,
0.008994489908218384,
0.025322705507278442,
0.03434860706329346,
0.00038084317930042744,
0.03437364101409912,
-0.03880910202860832,
-0.027024898678064346,
0.06590578705072403,
-0.0340738520026207,
0.03744636848568916,
0.0673784539103508,
-0.015874411910772324,
-0.005928393453359604,
-0.05931544303894043,
-0.02434375509619713,
0.052361395210027695,
-0.0006183384684845805,
0.013696888461709023,
-0.008348047733306885,
0.003773014759644866,
-0.03084765188395977,
-0.0004212791391182691,
-0.03017154522240162,
-0.009709197096526623,
-0.023163946345448494,
-0.004215842112898827,
0.01374830212444067,
0.005451364442706108,
-0.014059050008654594,
0.021575752645730972,
-0.010424388572573662,
-0.03277624398469925,
-0.04133095592260361,
0.0385211817920208,
0.022404052317142487,
-0.020580630749464035,
0.059811946004629135,
0.026802588254213333,
-0.05498846620321274,
-0.03128986433148384,
-0.0580921545624733,
-0.010213380679488182,
0.007954460568726063,
-0.013980253599584103,
0.019298890605568886,
0.018000494688749313,
-0.03829684481024742,
0.06282753497362137,
-0.00041457233601249754,
-0.035090137273073196,
-0.0206983033567667,
-0.009979807771742344,
-0.0033198301680386066,
-0.001120609580539167,
0.016160763800144196,
0.00269806245341897,
0.0012092427350580692,
0.02567342482507229,
-0.00031464290805161,
-0.002896552672609687,
-0.0004798532754648477,
0.033386874943971634,
-0.03690849617123604,
0.022561559453606606,
-0.02295362949371338,
-0.008551138453185558,
0.04209174960851669,
0.018429117277264595,
-0.03935571387410164,
-0.02846195362508297,
0.0246001984924078,
-0.030445406213402748,
0.04855455830693245,
-0.013169923797249794,
0.07661747932434082,
0.012045038864016533,
0.032818179577589035,
-0.029258020222187042,
0.024136805906891823,
-0.02410801313817501,
-0.015643682330846786,
-0.0165718924254179,
0.028193973004817963,
0.03338877111673355,
0.015318640507757664,
0.005354638677090406,
-0.010107913054525852,
0.041939474642276764,
-0.06828933954238892,
0.005181693471968174,
-0.0076121254824101925,
0.006328936666250229,
0.008013245649635792,
-0.019930044189095497,
-0.00735394237563014,
0.014598325826227665,
0.0166785828769207,
0.02734324522316456,
-0.02588008902966976,
0.001647063996642828,
0.01769023761153221,
-0.02846541441977024,
-0.0015099344309419394,
-0.056313201785087585,
0.00690430635586381,
0.03265484794974327,
0.03378552570939064,
0.021243596449494362,
0.009604441933333874,
-0.008575831539928913,
0.028727274388074875,
-0.08294949680566788,
0.03275429829955101,
-0.0014958828687667847,
0.008406633511185646,
-0.04706230014562607,
-0.0030228549148887396,
-0.026293983682990074,
-0.01283922977745533,
-0.03715753182768822,
-0.031381186097860336,
-0.026559272781014442,
-0.033855028450489044,
0.00781607162207365,
-0.033703822642564774,
-0.07127644866704941,
-0.014902504161000252,
0.04639415442943573,
0.04747087135910988,
-0.05812333896756172,
0.0196323674172163,
0.0034346363972872496,
-0.0659126415848732,
-0.016695890575647354,
-0.030964775010943413,
0.042708441615104675,
0.0018934672698378563,
0.02166803367435932,
0.029406828805804253,
0.018654894083738327,
-0.027196738868951797,
-0.0121651915833354,
0.0328504703938961,
0.04907818138599396,
0.021850742399692535,
0.011270961724221706,
0.004796852823346853,
-0.05340811610221863,
-0.025388961657881737,
0.004765170626342297,
0.05392175912857056,
0.011408076621592045,
0.009108268655836582,
0.04354381933808327,
-0.002267195377498865,
-0.04087246209383011,
-0.006879904307425022,
0.037649307399988174,
0.005682399496436119,
-0.030852630734443665,
-0.0276853796094656,
-0.0028735955711454153,
0.010661732405424118,
0.008351130411028862,
0.009972342289984226,
-0.05112423375248909,
-0.004232331644743681,
0.012440136633813381,
0.015109150670468807,
0.018455134704709053,
-0.043940044939517975,
-0.0032351831905543804,
0.008215050213038921,
-0.020503226667642593,
-0.035921305418014526,
-0.01324948575347662,
-0.012810605578124523,
0.048797812312841415,
0.06413055211305618,
0.02255788818001747,
0.014963756315410137,
-0.09110676497220993,
0.009383155964314938,
0.03976276516914368,
0.03510669991374016,
0.031181927770376205,
-0.011365080252289772,
-0.019656499847769737,
-0.019574681296944618,
0.07575967907905579,
-0.007267842534929514,
0.004498125985264778,
0.017720360308885574,
-0.02927444688975811,
-0.015207788906991482,
-0.03376961871981621,
-0.06569948047399521,
0.00941163208335638,
0.013995117507874966,
-0.025853319093585014,
-0.047469839453697205,
0.013407931663095951,
0.004830966237932444,
0.04143218323588371,
-0.006357980892062187,
0.016533588990569115,
0.05380519852042198,
-0.010374143719673157,
0.0007749937940388918,
0.01838412694633007,
-0.020052021369338036,
-0.07696864008903503,
-0.003351474180817604,
0.02116278000175953,
0.0011381858494132757,
0.028806839138269424,
-0.0481489896774292,
-0.07679922878742218,
0.022019585594534874,
-0.0017496153013780713,
0.0016093940939754248,
0.027500269934535027,
-0.026814283803105354,
0.05572127923369408,
-0.01542650070041418,
0.020091932266950607,
0.02925894409418106,
0.05145685374736786,
-0.0262683667242527,
-0.04086294397711754,
-0.00533309206366539,
0.013711889274418354,
-0.031499989330768585,
0.016801027581095695,
-0.05600430816411972,
0.02004358172416687,
-0.0391668826341629,
0.026957346126437187,
-0.01973797008395195,
0.016375109553337097,
-0.0193316750228405,
-0.04060094803571701,
-0.029458103701472282,
-0.001677103340625763,
-0.024450965225696564,
-0.03925567492842674,
-0.010824054479598999,
0.008034474216401577,
0.0034986985847353935,
-0.015084600076079369,
0.015031067654490471,
0.015750862658023834,
0.0015157152665778995,
0.018038930371403694,
-0.004170338623225689,
-0.013430509716272354,
-0.012897511944174767,
-0.010260647162795067,
-0.0005086925229988992,
-0.06536345183849335,
0.0412069633603096,
-0.002749640727415681,
0.0007909767446108162,
0.0013133141910657287,
-0.062376927584409714,
-0.010823720134794712,
0.012406029738485813,
-0.009057638235390186,
0.013687985949218273,
0.01907244510948658,
-0.010896888561546803,
-0.008015632629394531,
0.003951931372284889,
-0.04241805151104927,
-0.03308289498090744,
0.01588999480009079,
-0.009681029245257378,
0.011483725160360336,
-0.02841527946293354,
0.0016565249534323812,
-0.033665575087070465,
-0.01731417514383793,
0.0027237902395427227,
0.04018121957778931,
-0.01538792997598648,
0.030428996309638023,
0.02216297946870327,
0.04604938626289368,
-0.009359821677207947,
0.011445862241089344,
-0.003372608684003353,
0.027474988251924515,
-0.023831238970160484,
0.02484188973903656,
0.0030521980952471495,
0.035046130418777466,
-0.021674174815416336,
-0.004948000889271498,
-0.002527577569708228,
-0.02963852323591709,
0.010367156006395817,
0.011102167889475822,
0.011889218352735043,
0.05791885033249855,
0.0156319011002779,
0.009085305966436863,
-0.00040481804171577096,
-0.004291899502277374,
0.005481358617544174,
0.04832181707024574,
-0.025026706978678703,
-0.005183270666748285,
-0.016940874978899956,
-0.023688718676567078,
0.05689317733049393,
-0.01845368929207325,
-0.009249831549823284,
0.01139947958290577,
0.010124864056706429,
-0.0017306292429566383,
-0.03916393592953682,
0.026343051344156265,
0.009956717491149902,
0.003152896650135517,
-0.014913232997059822,
0.023574935272336006,
0.005134920123964548,
0.03751613572239876,
-0.01898963749408722,
-0.07650170475244522,
-0.0044439733028411865,
0.002368076704442501,
0.04059072583913803,
0.011324364691972733,
0.042890746146440506,
0.00721063744276762,
-0.012471325695514679,
-0.02898179553449154,
-0.029842184856534004,
-0.02623322419822216,
0.029217088595032692,
-0.0007521172519773245,
0.05830775201320648,
-0.032493364065885544,
0.019274363294243813,
0.036169279366731644,
0.04898039251565933,
-0.028104962781071663,
0.007591065019369125,
0.023476939648389816,
0.012969459407031536,
0.03455440700054169,
-0.02267051860690117,
-0.06022254377603531,
0.04384491220116615,
-0.0393347404897213,
0.017356151714920998,
0.037000615149736404,
-0.004089630674570799,
0.03007313795387745,
0.013332120142877102,
0.022639784961938858,
0.02084830217063427,
-0.026523407548666,
-0.005218358710408211,
0.007909881882369518,
0.026567501947283745,
-0.009746422059834003,
-0.021823324263095856,
-0.011115950532257557,
0.042551711201667786,
0.017933014780282974,
-0.011900682933628559,
-0.007265612483024597,
-0.05734886974096298,
-0.012981236912310123,
-0.03052802011370659,
-0.041479095816612244,
0.05249762162566185,
0.03269113227725029,
-0.023182418197393417,
0.032519225031137466,
-0.009395689703524113,
-0.01268571987748146,
0.014494060538709164,
0.0018869274063035846,
-0.009337563998997211,
0.00964080449193716,
-0.026288233697414398,
0.02161394990980625,
-0.02891160547733307,
-0.016994448378682137,
0.11489308625459671,
0.04562794044613838,
0.02860945463180542,
-0.058432310819625854,
0.012230588123202324,
-0.04239415004849434,
-0.0027524337638169527,
-0.04879417642951012,
0.02225765772163868,
-0.007536187302321196,
-0.03326527401804924,
0.0027610210236161947,
0.08482611179351807,
0.010291551239788532,
0.018202144652605057,
0.07975166290998459,
-0.022583110257983208,
-0.022294513881206512,
-0.03639354556798935,
0.013004119507968426,
-0.015090111643075943,
0.0013428560923784971,
-0.041127920150756836,
0.0007538438658230007,
-0.02953365445137024,
0.0275263711810112,
-0.014727211557328701,
-0.027301670983433723,
0.013119002804160118,
-0.0077461195178329945,
-0.050249818712472916,
-0.014795643277466297,
0.0004370837996248156,
0.0011075864313170314,
-0.03461165726184845,
0.004312099423259497,
0.02639564499258995,
-0.01078085694462061,
0.03000863641500473,
0.015185396187007427,
-0.043991293758153915,
0.018818216398358345,
0.030495047569274902,
0.004023860674351454,
-0.030284153297543526,
-0.023045124486088753,
-0.052030786871910095,
0.039428722113370895,
-0.011340377852320671,
0.03932548686861992,
0.004685979336500168,
-0.010355562902987003,
0.03891262784600258,
0.010112248361110687,
-0.00086324627045542,
-0.0030279739294201136,
0.02260216698050499,
0.006154174916446209,
0.008602184243500233,
-0.02744242548942566,
0.04827018082141876,
0.02058030292391777,
-0.004312728065997362,
-0.0262023713439703,
-0.04261184483766556,
0.03667082637548447,
0.0028277765959501266,
0.04611385986208916,
0.01706157810986042,
-0.017175981774926186,
0.013638613745570183,
0.0016318467678502202,
-0.019829178228974342,
0.014777043834328651,
-0.0025399813894182444,
-0.006135889329016209,
0.05134020745754242,
0.018017949536442757,
0.019937224686145782,
0.01478556264191866,
-0.08441609144210815,
-0.002198172500357032,
-0.028739415109157562,
-0.03997493535280228,
0.0031530759297311306,
-0.0037538865581154823,
0.011310565285384655,
0.03112124465405941,
0.002316955476999283,
-0.015829503536224365,
-0.02788364887237549,
0.03661121055483818,
0.010061490349471569,
-0.025108054280281067,
-0.02967933379113674,
-0.011573487892746925,
-0.03658226877450943,
-0.007533438969403505,
-0.01058544497936964,
-0.016420092433691025,
0.034135498106479645,
0.010448005981743336,
-0.008111515082418919,
0.04321535676717758,
-0.013596434146165848,
-0.006378120742738247,
0.034072812646627426,
-0.027001850306987762,
-0.014282847754657269,
0.015164259821176529,
0.016846537590026855,
-0.053653839975595474,
-0.06192999705672264,
0.01929236575961113,
-0.023382039740681648,
0.0014058502856642008,
0.029159149155020714,
-0.0448516421020031,
-0.016101406887173653,
-0.014780187048017979,
0.03954879567027092,
-0.034986462444067,
0.0033846383448690176,
-0.03527884930372238,
0.019396936520934105,
0.004929018672555685,
-0.0013277807738631964,
0.01219500508159399,
0.025767242535948753,
-0.012840285897254944,
0.014368853531777859,
0.0290635097771883,
-0.007723796647042036,
-0.026544390246272087,
0.01965562254190445,
0.0018931690137833357,
0.01637246087193489,
0.023195957764983177,
0.019782282412052155,
-0.05972534418106079,
0.05219085514545441,
-0.035897545516490936,
-0.0671902447938919,
0.021008359268307686,
-0.013580158352851868,
0.04744550958275795,
0.0546727329492569,
-0.01982269249856472,
-0.05456069856882095,
0.03563559055328369,
-0.01690230891108513,
0.003386866766959429,
0.02306261844933033,
-0.02259049005806446,
0.004897866863757372,
-0.018706081435084343,
0.010574966669082642,
0.010585399344563484,
-0.02958543412387371,
0.014306762255728245,
0.022371847182512283,
0.026406802237033844,
-0.013485884293913841,
0.046417947858572006,
0.0058553386479616165,
0.053367193788290024,
0.016994895413517952,
-0.02171630598604679,
0.005962839350104332,
0.057084303349256516,
-0.03925376012921333,
0.04082999378442764,
0.019811075180768967,
0.005954952444881201,
-0.11829594522714615,
-0.037145595997571945,
0.009637524373829365,
0.033786434680223465,
0.056688226759433746,
-0.051529642194509506,
0.01915925182402134,
0.002138437470421195,
-0.11217832565307617,
0.0053844270296394825,
-0.01026833988726139,
-0.00008763693767832592,
-0.009882169775664806,
-0.011519129388034344,
-0.02572241798043251,
0.047344859689474106,
0.0043363263830542564,
0.04107394441962242,
-0.01048481184989214,
0.029922595247626305,
-0.008809149265289307,
0.003529003355652094,
-0.01657225750386715,
0.034140694886446,
0.0020090285688638687,
-0.020944025367498398,
0.06847389042377472,
-0.026725079864263535,
-0.029155973345041275,
0.01964777335524559,
-0.006205932702869177,
-0.032202139496803284,
-0.021305426955223083,
0.0064111207611858845,
0.029936911538243294,
0.037049125880002975,
0.003882969729602337,
-0.011434538289904594,
0.013372507877647877,
0.017173560336232185,
0.0050649456679821014,
0.05210702121257782,
-0.03486679866909981,
0.007184869609773159,
-0.005519401747733355,
-0.03750650957226753,
-0.04375583305954933,
0.0648241639137268,
-0.024444323033094406,
-0.028563251718878746,
-0.01872234418988228,
-0.004466523882001638,
-0.003129407996311784,
0.005165509879589081,
0.03728238865733147,
-0.03235683590173721,
-0.002988434163853526,
0.014465718530118465,
-0.006619372870773077,
0.018909482285380363,
0.05533387511968613,
-0.01626376435160637,
0.00018262685625813901,
0.015302623622119427,
0.03367716819047928,
0.00887568574398756,
-0.028957093134522438,
-0.018559230491518974,
0.03318913280963898,
0.01947578601539135,
0.011039496399462223,
-0.04717942327260971,
-0.035419173538684845,
-0.01503324881196022,
0.007869604974985123,
0.056591156870126724,
-0.0278721135109663,
-0.011218302883207798,
0.004923748318105936,
-0.06965924054384232,
0.030639775097370148,
0.008133440278470516,
0.04333467036485672,
0.011416526511311531,
-0.05700765177607536,
0.0071877604350447655,
-0.014276828616857529,
0.06111299246549606,
-0.009193876758217812,
-0.0420234277844429,
0.05693447217345238,
-0.01106646191328764,
0.00588251231238246,
-0.010659274645149708,
-0.017300862818956375,
-0.0035209376364946365,
-0.018830012530088425,
0.014906594529747963,
0.0026554912328720093,
0.008619981817901134,
0.03456230089068413,
-0.001874656300060451,
0.016882508993148804,
-0.008196631446480751,
0.007847408764064312,
-0.0571419857442379,
0.04921030253171921,
0.009973332285881042,
-0.02326492965221405,
0.05257206782698631,
0.005828725639730692,
0.04244937375187874,
0.006347839720547199,
-0.016936486586928368,
-0.0032037468627095222,
0.019308891147375107,
-0.058388832956552505,
-0.0279543437063694,
-0.009724760428071022,
0.0381334125995636,
0.019592786207795143,
-0.023554008454084396,
0.033790502697229385,
0.04699213057756424,
-0.03611323609948158,
-0.0248135756701231,
0.04704027995467186,
-0.0033847277518361807,
0.04597987234592438,
0.026776449754834175,
-0.0063507286831736565,
0.032359443604946136,
0.0029705865308642387,
0.0115654356777668,
0.028474781662225723,
0.04460238665342331,
-0.0015852316282689571,
0.015872735530138016,
0.028648819774389267,
-0.03360113874077797,
-0.0013760261936113238,
0.021464545279741287,
0.01851741597056389,
0.022336654365062714,
-0.002855858998373151,
0.020337233319878578,
-0.01792502962052822,
-0.012385180220007896,
0.019734852015972137,
-0.02243993990123272,
0.0812358483672142,
-0.009721269831061363,
-0.011688828468322754,
-0.05135336518287659,
0.012797944247722626,
0.003661048598587513,
0.005341776181012392,
0.006884345319122076,
0.051033128052949905,
-0.01619873382151127,
-0.03520171716809273,
-0.02190685272216797,
-0.00010234225919703022,
-0.020764093846082687,
-0.07485456764698029,
0.015104458667337894,
0.04292459040880203,
-0.0014683761401101947,
-0.02224995754659176,
-0.03809879347681999,
-0.019149400293827057,
-0.011108039878308773,
-0.009648334234952927,
0.04823915287852287,
0.026224201545119286,
-0.012604526244103909,
0.017679650336503983,
-0.042600128799676895,
0.020071813836693764,
-0.07953678071498871,
0.04594719782471657,
-0.02625097706913948,
0.014977042563259602,
-0.0125435134395957,
0.005214300472289324
] |
<p>For a single point mass :
$\tau=F_{t}r=ma_tr=(m r^2)\alpha = I\alpha$</p>
<p>For multiple point masses bound together : $\sum \tau_i = (m_ir_i^2)\alpha = I\alpha$</p>
<p>But how do we go from that to $I\alpha = F_tr_{app} $ (for the multiple masses case), where $r_{app}$ is the point where force is applied? That is saying that the entire sum of torques of individual masses $\sum \tau_i$ is physically equivalent to (i.e. produces the same angular acceleration of the bound rigid object as) a single torque $F_tr_{app}$ applied to the point $r_{app}$. (Or putting it another way, that applying a single force $F_t r_{app}$ will result in many $F_{t\_i}$ forces on each mass element such that $\sum F_{t\_i}r_{i}$ will be equal to $I\alpha$.)</p>
<p>Every place I've looked for a derivation just jumps from $\sum \tau_i =I\alpha$, to $\tau=I\alpha$, as if they are the same thing.</p>
| 8,267 |
[
-0.037945251911878586,
0.02826014533638954,
-0.0213436521589756,
-0.04706121236085892,
0.026919938623905182,
0.015187390148639679,
-0.0196074265986681,
-0.0004225414013490081,
-0.0030098811257630587,
-0.008468495681881905,
0.03257396072149277,
0.017800230532884598,
0.08482564985752106,
0.00791206955909729,
0.014187237247824669,
-0.0013633884955197573,
-0.005014998838305473,
0.003607021179050207,
-0.017410771921277046,
-0.031582772731781006,
0.013957579620182514,
0.010005984455347061,
0.029452387243509293,
-0.024071358144283295,
0.011241720989346504,
0.03553830832242966,
0.015009271912276745,
-0.026905234903097153,
0.007720993831753731,
0.04182196408510208,
-0.026529347524046898,
0.010303658433258533,
-0.023574190214276314,
0.016804244369268417,
0.018704866990447044,
0.015279460698366165,
-0.041816841810941696,
0.005158609710633755,
0.004915587138384581,
0.04390373080968857,
-0.07742605358362198,
-0.026613568887114525,
-0.03237703815102577,
0.021743640303611755,
-0.013287614099681377,
0.02522135339677334,
-0.040051110088825226,
0.0037197794299572706,
0.036895375698804855,
-0.039389267563819885,
0.08711622655391693,
0.00843675434589386,
0.03622112423181534,
0.03799046576023102,
-0.03704381361603737,
-0.004665199667215347,
0.062192030251026154,
0.02824185974895954,
-0.011146037839353085,
-0.04714318737387657,
-0.023954732343554497,
-0.031494513154029846,
0.007358101662248373,
-0.0436813160777092,
-0.01695181243121624,
0.0668952539563179,
0.00471586175262928,
-0.004993973299860954,
0.02647232450544834,
0.013132883235812187,
0.016912953928112984,
-0.0034322827123105526,
0.035257305949926376,
-0.026526130735874176,
-0.021697085350751877,
-0.010284241288900375,
0.02185070514678955,
-0.016849014908075333,
0.03500670567154884,
0.027376171201467514,
-0.00931162852793932,
0.026193775236606598,
0.0931096002459526,
0.05659825727343559,
0.02568444237112999,
-0.03236515074968338,
0.05081402137875557,
0.014637310989201069,
0.027026738971471786,
0.022825589403510094,
0.020115891471505165,
0.013188951648771763,
0.03282010927796364,
-0.022303305566310883,
-0.02631072700023651,
0.04175708815455437,
0.019823169335722923,
0.03573736548423767,
-0.022865979000926018,
0.00908184889703989,
0.029049132019281387,
-0.006475923582911491,
-0.0014801669167354703,
0.05040730535984039,
0.013181271962821484,
0.011002883315086365,
-0.03359128534793854,
-0.02079346776008606,
-0.04679432883858681,
-0.022101348266005516,
-0.059130407869815826,
-0.0036310774739831686,
-0.02683282271027565,
0.004345840308815241,
0.0002566699404269457,
-0.009314297698438168,
0.000028683445634669624,
0.03536754101514816,
0.07182518392801285,
0.04627777636051178,
0.010029242374002934,
-0.016679242253303528,
0.017801236361265182,
-0.06187944486737251,
-0.04735216498374939,
0.047807399183511734,
-0.002024182816967368,
-0.04080852493643761,
-0.03167007118463516,
0.013207361102104187,
0.049463510513305664,
-0.04201258346438408,
-0.012870950624346733,
0.021493704989552498,
0.015567238442599773,
-0.048959460109472275,
-0.08114872872829437,
-0.026842201128602028,
0.03521677106618881,
-0.00008206335769500583,
-0.012564808130264282,
-0.0380803607404232,
0.014784610830247402,
0.02590496651828289,
0.07947412133216858,
0.03084751032292843,
0.0032969128806144,
0.019906993955373764,
0.03851718828082085,
-0.013225425034761429,
-0.02462265081703663,
-0.02032744139432907,
-0.017049431800842285,
-0.015744902193546295,
-0.02486897073686123,
-0.09542492777109146,
0.04929246008396149,
0.0343245305120945,
0.008360857143998146,
0.01284082606434822,
0.05046938359737396,
-0.008632315322756767,
0.0003601510252337903,
0.032733552157878876,
0.0071631004102528095,
-0.01099921204149723,
0.05684317648410797,
-0.0025773546658456326,
-0.029672307893633842,
0.059815458953380585,
0.03139296919107437,
0.00396876921877265,
-0.006203182972967625,
0.05850253999233246,
0.0292334146797657,
-0.05359172448515892,
-0.018913615494966507,
-0.009320731274783611,
-0.01997341960668564,
0.04310242831707001,
-0.05318911746144295,
-0.06691418588161469,
0.011423750780522823,
-0.01578862965106964,
0.0028238517697900534,
0.042446598410606384,
-0.012231452390551567,
0.0008309041149914265,
-0.025992199778556824,
-0.052906330674886703,
0.012630095705389977,
-0.09055060148239136,
0.013296268880367279,
-0.0486251562833786,
-0.03520084172487259,
0.05242367088794708,
0.02172231674194336,
0.01916412077844143,
-0.015751032158732414,
-0.04108613356947899,
-0.016111014410853386,
0.022326888516545296,
0.02371438592672348,
0.0017525061266496778,
0.01661449298262596,
0.04773653671145439,
0.026615919545292854,
0.04983445629477501,
0.017880013212561607,
-0.022560497745871544,
-0.01791338436305523,
-0.009672429412603378,
-0.029431680217385292,
0.033902958035469055,
0.0337386317551136,
-0.0015364590799435973,
-0.006025437265634537,
-0.040662724524736404,
-0.01282420288771391,
0.03241623193025589,
-0.019995369017124176,
0.06241273507475853,
0.08985348045825958,
0.028171362355351448,
0.009074987843632698,
0.054217781871557236,
-0.003003899473696947,
0.005720421671867371,
-0.03199348971247673,
-0.03291650116443634,
-0.017566539347171783,
-0.008399917744100094,
0.0008293053251691163,
0.08233562111854553,
-0.04210377112030983,
0.028933942317962646,
0.06306295841932297,
0.05979238450527191,
0.00872509554028511,
0.02287367172539234,
-0.027504928410053253,
0.0038802537601441145,
0.022636715322732925,
0.01294784341007471,
-0.000036726669350173324,
-0.021988991647958755,
0.01449424959719181,
0.004925477784126997,
0.013205048628151417,
0.022464999929070473,
-0.006151585839688778,
0.03502488508820534,
-0.02043355442583561,
0.009948402643203735,
0.03180753439664841,
-0.026913251727819443,
0.018249614164233208,
0.004658339079469442,
0.03163785859942436,
0.03296912834048271,
0.00022502304636873305,
-0.03722715750336647,
-0.04065779224038124,
0.00033444439759477973,
0.026766333729028702,
-0.035147953778505325,
0.0014147545443847775,
-0.022485554218292236,
0.026839729398489,
-0.037018898874521255,
0.0030353718902915716,
-0.02613705024123192,
-0.024069268256425858,
-0.019933534786105156,
0.008589520119130611,
-0.005950439255684614,
0.006471717264503241,
0.028446348384022713,
-0.037580542266368866,
0.003390942234545946,
-0.01967312954366207,
-0.04712255671620369,
0.007873911410570145,
0.03028336726129055,
-0.0559622123837471,
0.011729753576219082,
-0.046001970767974854,
-0.015854939818382263,
0.07627258449792862,
0.00952153094112873,
-0.032969579100608826,
-0.003996124025434256,
0.014674074947834015,
-0.05308989807963371,
-0.03344975411891937,
0.010797305963933468,
-0.027767036110162735,
-0.055561613291502,
0.016094813123345375,
0.03471533954143524,
-0.02179000899195671,
-0.02754799835383892,
0.004889016505330801,
-0.04208766296505928,
-0.001872101565822959,
0.02301519736647606,
-0.045557525008916855,
0.02409737929701805,
-0.015891633927822113,
0.002955440431833267,
0.05657857283949852,
-0.02504362352192402,
-0.01184359472244978,
-0.05121392384171486,
-0.0400993637740612,
0.0042511895298957825,
-0.013335643336176872,
0.07258279621601105,
0.02435104362666607,
-0.05341928452253342,
0.09610915929079056,
0.005726323463022709,
-0.026403598487377167,
-0.03212827444076538,
0.02409692108631134,
0.0009589307010173798,
-0.01091995369642973,
-0.009649988263845444,
0.00393872894346714,
-0.04316358640789986,
0.015098286792635918,
0.013877153396606445,
-0.003470220835879445,
0.06064542755484581,
0.00452266214415431,
0.022261379286646843,
-0.0025336015969514847,
0.004765570629388094,
-0.03251098468899727,
0.04221649840474129,
0.030905574560165405,
0.013919603079557419,
-0.001039695693179965,
0.025616394355893135,
0.023785490542650223,
-0.01829124055802822,
-0.07355599850416183,
0.01888309046626091,
0.0037845373153686523,
-0.02547738514840603,
-0.020846815779805183,
0.04509252309799194,
-0.012578779831528664,
-0.04289424419403076,
-0.018809454515576363,
0.05264532193541527,
0.040518127381801605,
-0.06317389756441116,
-0.0138807138428092,
0.06210153177380562,
0.03986753895878792,
-0.0105767622590065,
-0.03930606693029404,
-0.014071288518607616,
0.009395161643624306,
0.0194710586220026,
-0.04284593462944031,
-0.0064620329067111015,
0.023612501099705696,
0.0019262481946498156,
0.05205737054347992,
0.0027999936137348413,
-0.028662443161010742,
0.03641495481133461,
-0.05552094429731369,
-0.009916380979120731,
-0.04344671219587326,
0.05557961016893387,
0.005187332630157471,
0.0401298813521862,
0.02580086514353752,
0.028086494654417038,
0.024556327611207962,
0.002765854587778449,
-0.06505623459815979,
0.027027897536754608,
-0.012334365397691727,
-0.04811996966600418,
0.012406887486577034,
-0.00029788108076900244,
-0.016442973166704178,
-0.04239359870553017,
-0.001318987924605608,
-0.02442934922873974,
-0.0039672935381531715,
-0.05307888984680176,
0.008035515435039997,
-0.03426621854305267,
-0.009339239448308945,
0.003432124387472868,
0.043037451803684235,
0.0584539994597435,
-0.01727289706468582,
0.015966301783919334,
0.025417586788535118,
-0.047430239617824554,
0.006999583914875984,
-0.049828674644231796,
0.015650171786546707,
-0.001791103626601398,
-0.03518371656537056,
0.048330217599868774,
0.04687628149986267,
0.007854118943214417,
0.014893870800733566,
-0.020555682480335236,
0.07320301979780197,
0.027698298916220665,
-0.06352854520082474,
-0.013612492009997368,
-0.0656200721859932,
-0.01161616574972868,
0.0008014884078875184,
0.05457276105880737,
0.007234921678900719,
-0.017717434093356133,
0.030137380585074425,
0.033142898231744766,
0.005814871750771999,
0.05133450776338577,
0.00950558390468359,
0.03099081479012966,
-0.0339341014623642,
-0.07488145679235458,
-0.016208931803703308,
-0.00625997269526124,
0.0025185630656778812,
0.030138306319713593,
-0.024972930550575256,
-0.031056666746735573,
-0.0038237206172198057,
0.012441468425095081,
-0.005163799040019512,
-0.018929846584796906,
-0.008369175717234612,
-0.04225235432386398,
0.016164125874638557,
-0.025876328349113464,
-0.015011715702712536,
0.015611853450536728,
0.022250117734074593,
0.02147056721150875,
0.004607480484992266,
0.027601908892393112,
-0.08197984099388123,
-0.014869702979922295,
-0.0037307573948055506,
-0.022247333079576492,
-0.015533892437815666,
0.03357653319835663,
0.007136404048651457,
-0.030763156712055206,
0.046495601534843445,
-0.031068209558725357,
0.05899655073881149,
0.019480085000395775,
0.03502182289958,
-0.004269519355148077,
-0.020035559311509132,
-0.032920919358730316,
0.0004397851589601487,
-0.006896876264363527,
0.024219021201133728,
-0.016612689942121506,
0.01145873125642538,
0.0075303190387785435,
-0.003312483662739396,
0.0285168569535017,
0.02975560538470745,
0.03345606103539467,
-0.022906752303242683,
-0.02430473454296589,
0.05104693025350571,
-0.007715938147157431,
-0.060751475393772125,
-0.012478845193982124,
0.015314106829464436,
-0.01684473641216755,
-0.000264104048255831,
-0.07346206903457642,
-0.04305311664938927,
0.03914784640073776,
0.007687909994274378,
0.020560864359140396,
0.024053016677498817,
-0.05078286677598953,
0.038686614483594894,
0.04730100929737091,
0.014771596528589725,
0.064096599817276,
0.011581694707274437,
-0.03231321647763252,
-0.005890620872378349,
-0.0019600423984229565,
0.01608918234705925,
0.0012512512039393187,
-0.025756940245628357,
-0.05095219239592552,
0.06127547472715378,
-0.01913263648748398,
0.05233815684914589,
0.011017863638699055,
0.027755163609981537,
0.00631369324401021,
-0.02141580730676651,
-0.013924158178269863,
0.055314816534519196,
-0.004875146318227053,
-0.0028064288198947906,
0.016523141413927078,
0.04352918639779091,
0.008938807062804699,
-0.013367596082389355,
-0.0015238079940900207,
0.005816454999148846,
0.013217039406299591,
0.007064984180033207,
0.006864033639431,
0.04225293546915054,
-0.016672533005475998,
-0.018261095508933067,
0.04460307955741882,
-0.03478715941309929,
0.06626784056425095,
0.008524702861905098,
0.006420707795768976,
0.015680907294154167,
-0.034315310418605804,
-0.02750544250011444,
-0.0002462254196871072,
-0.006890480872243643,
0.023000570014119148,
-0.024973629042506218,
-0.0027165694627910852,
0.007102970965206623,
-0.0173146054148674,
-0.02254466339945793,
-0.031794238835573196,
0.0071507832035422325,
0.017488623037934303,
-0.0008405850385315716,
-0.00274853827431798,
0.023607930168509483,
-0.022553376853466034,
-0.023197419941425323,
0.005077654495835304,
0.08965596556663513,
-0.03474137932062149,
-0.006668203044682741,
0.024300318211317062,
0.016802499070763588,
0.042248379439115524,
-0.009963592514395714,
-0.0310234185308218,
0.0030977234710007906,
-0.018379325047135353,
0.03897383064031601,
0.030477775260806084,
0.08123896270990372,
-0.028628429397940636,
0.004502808675169945,
-0.03832395002245903,
-0.02614038810133934,
0.024186693131923676,
0.029669849202036858,
0.027146557345986366,
-0.016453910619020462,
0.025585085153579712,
0.0032174743246287107,
-0.048341136425733566,
0.006293667014688253,
0.031970568001270294,
0.042788244783878326,
0.00820254534482956,
0.018154161050915718,
-0.028339723125100136,
-0.02705630101263523,
0.015741100534796715,
0.006320627871900797,
0.009079397656023502,
0.017459353432059288,
0.05051151663064957,
-0.028082190081477165,
0.02835208736360073,
0.023770378902554512,
0.003756917081773281,
0.04614637419581413,
0.005651759449392557,
-0.017576558515429497,
0.028257040306925774,
-0.02310076542198658,
-0.020381372421979904,
-0.026178443804383278,
-0.028384970501065254,
0.05739628151059151,
0.06897715479135513,
-0.059592340141534805,
0.06382628530263901,
0.051126059144735336,
-0.01691012643277645,
-0.020843349397182465,
-0.027605049312114716,
0.008754861541092396,
-0.006605899427086115,
0.017213698476552963,
0.0514114685356617,
-0.04544739052653313,
-0.025031747296452522,
0.03540666028857231,
0.03922972455620766,
-0.048493582755327225,
-0.04061899706721306,
0.013319081626832485,
0.004975317046046257,
-0.03668991103768349,
-0.012216491624712944,
-0.01257595606148243,
0.022999970242381096,
-0.001900914590805769,
0.030706731602549553,
0.024307003244757652,
-0.025023458525538445,
0.04187475144863129,
0.016063207760453224,
0.041069138795137405,
-0.05536631494760513,
-0.015291701070964336,
-0.038535233587026596,
0.05865515395998955,
0.02842513658106327,
-0.017591506242752075,
0.002505748299881816,
0.0055410536006093025,
0.04518924281001091,
-0.02388097159564495,
-0.0057719312608242035,
-0.026329217478632927,
-0.00026106179575435817,
-0.017398184165358543,
-0.03566449135541916,
-0.048918068408966064,
0.028251606971025467,
-0.011112541891634464,
-0.04060405492782593,
0.017879316583275795,
-0.028336038812994957,
0.026204204186797142,
0.022669661790132523,
0.01338954083621502,
-0.022663172334432602,
0.08693315088748932,
-0.023233402520418167,
0.021779419854283333,
-0.014197242446243763,
-0.02757411077618599,
0.11621659249067307,
0.0369223989546299,
0.03579398989677429,
-0.03501243516802788,
0.018190091475844383,
-0.025594715029001236,
-0.026290271431207657,
-0.02312944270670414,
0.015126599930226803,
0.013765577226877213,
0.0018334205960854888,
0.014489645138382912,
0.0590328611433506,
-0.023996278643608093,
-0.012928984127938747,
0.05006583034992218,
-0.028687264770269394,
-0.009352879598736763,
-0.00554383359849453,
-0.003341344418004155,
0.014341820031404495,
-0.021895183250308037,
-0.026153910905122757,
0.016636081039905548,
-0.022784775123000145,
0.03377898037433624,
0.0058954148553311825,
-0.030656570568680763,
0.014953691512346268,
0.00205160491168499,
-0.04980628192424774,
0.012141991406679153,
0.002754323882982135,
-0.0406174473464489,
-0.014086593873798847,
0.04789000004529953,
0.0004311372176744044,
-0.027908755466341972,
0.030802728608250618,
0.03685370460152626,
0.0007111797458492219,
-0.00007356048445217311,
-0.0030086087062954903,
0.011718165129423141,
-0.014509626664221287,
0.00710831256583333,
-0.044453490525484085,
0.04410957917571068,
-0.05694931373000145,
0.01823524758219719,
0.012595128268003464,
0.006476372946053743,
-0.012270085513591766,
-0.061044733971357346,
0.01227641012519598,
-0.01673976704478264,
0.02366652339696884,
-0.01818270795047283,
0.012036420404911041,
-0.023281455039978027,
0.007759725674986839,
0.01375882513821125,
-0.023316500708460808,
-0.015854032710194588,
-0.008197598159313202,
-0.008926392532885075,
0.007590642664581537,
0.054536592215299606,
-0.024378592148423195,
-0.0006633027805946767,
-0.05160742998123169,
-0.00932011753320694,
-0.022868990898132324,
-0.017555708065629005,
-0.022657915949821472,
0.012317282147705555,
0.03316285088658333,
-0.015906931832432747,
-0.005864139646291733,
-0.02159181237220764,
-0.05425421521067619,
-0.012971516698598862,
-0.03109692595899105,
-0.01645289920270443,
0.0023255771957337856,
-0.016764231026172638,
0.00044650895870290697,
0.0585375614464283,
-0.03358696028590202,
0.025141330435872078,
-0.015800490975379944,
0.0441400483250618,
0.005508359521627426,
-0.023448098450899124,
-0.030338764190673828,
0.023889098316431046,
0.00933024287223816,
0.00398982735350728,
-0.012824330478906631,
0.00009440298890694976,
0.039765533059835434,
-0.005278116557747126,
-0.018092095851898193,
0.06706936657428741,
0.029392603784799576,
-0.002185449469834566,
0.021841812878847122,
0.024036860093474388,
0.015860656276345253,
0.04200996458530426,
-0.025180412456393242,
-0.06421202421188354,
0.02666977234184742,
-0.011145183816552162,
-0.060835983604192734,
-0.015423495322465897,
0.015362422913312912,
-0.022348720580339432,
0.01565445214509964,
-0.04806973785161972,
-0.000797525979578495,
-0.04257040098309517,
0.018761759623885155,
-0.05492071807384491,
0.01764426752924919,
0.012998124584555626,
-0.009805816225707531,
-0.0480082631111145,
0.006262138020247221,
-0.025861825793981552,
-0.017181361094117165,
0.028571296483278275,
0.0031237832736223936,
-0.0044158389791846275,
-0.00468548433855176,
0.015150563791394234,
-0.0175025537610054,
0.03731665760278702,
0.0016914971638470888,
-0.01876218058168888,
0.016046298667788506,
-0.015721896663308144,
-0.03704644367098808,
0.035104900598526,
-0.008841614238917828,
0.017994830384850502,
0.019829846918582916,
-0.005220807157456875,
-0.03129943832755089,
0.047603122889995575,
-0.025456439703702927,
-0.02177756279706955,
-0.012365507893264294,
0.005662387236952782,
-0.034353360533714294,
-0.03564200550317764,
0.050491638481616974,
-0.03146086260676384,
0.02278108522295952,
-0.0094691701233387,
0.0463654026389122,
-0.047873105853796005,
-0.019183628261089325,
0.007411415688693523,
-0.0011544282315298915,
-0.005616113543510437,
0.031072093173861504,
0.04072469472885132,
0.0015534734120592475,
0.036674756556749344,
-0.01201101765036583,
-0.025661734864115715,
-0.0003126308147329837,
0.0359155535697937,
-0.06907166540622711,
-0.02620960772037506,
-0.009115454740822315,
-0.015468019992113113,
-0.0014632840175181627,
-0.009569530375301838,
-0.02715197391808033,
0.005730390548706055,
-0.06841001659631729,
-0.010301776230335236,
-0.04008389636874199,
0.021431775763630867,
-0.00041269531357102096,
0.008628125302493572,
-0.015223713591694832,
0.04688487574458122,
0.0014300772454589605,
0.03826053440570831,
-0.0014821627410128713,
0.0189058780670166,
-0.016350993886590004,
-0.019219160079956055,
0.005077564623206854,
0.03960208222270012,
-0.006488804705440998,
-0.018423793837428093,
0.07446954399347305,
0.00667453370988369,
-0.04394567012786865,
0.021914757788181305,
-0.00939224287867546,
-0.01681332476437092,
-0.01966402865946293,
0.028461381793022156,
-0.0032076186034828424,
0.039281781762838364,
-0.046017762273550034,
-0.01970512978732586,
-0.01832076720893383,
0.04589929059147835,
0.00037431390956044197,
0.024592459201812744,
-0.03819737583398819,
-0.008121469989418983,
0.0364064984023571,
-0.03381306678056717,
0.00985797867178917,
-0.01906234212219715,
-0.02587038278579712,
-0.03359777480363846,
-0.007269024848937988,
0.008946118876338005,
-0.01212308369576931,
-0.04157876595854759,
0.020257141441106796,
-0.025843091309070587,
0.009234034456312656,
0.03155722841620445,
-0.006479514762759209,
-0.013950098305940628,
0.004065799992531538,
0.013884632848203182,
-0.020059213042259216,
0.0047855069860816,
0.008215573616325855,
-0.02432633936405182,
-0.0845872163772583,
-0.005989828146994114,
0.031559593975543976,
-0.033705320209264755,
-0.04658636450767517,
-0.04428098350763321,
-0.02184431627392769,
0.012327700853347778,
0.01434004120528698,
-0.012187882326543331,
0.007023301441222429,
-0.016511991620063782,
0.00716943945735693,
-0.06018916517496109,
0.013022569008171558,
0.0046975272707641125,
-0.02058478258550167,
-0.016185324639081955,
-0.03920159861445427,
-0.0017294184071943164,
-0.0027420357801020145,
0.03858568146824837,
0.008711514063179493,
-0.014585058204829693,
0.03452006354928017,
-0.01819698140025139,
0.0006184530793689191,
0.0006386045133695006,
0.009236653335392475,
-0.013434292748570442,
-0.0040552350692451,
0.00627541309222579,
-0.027716014534235,
0.0011776096653193235,
-0.02547944150865078,
0.015268086455762386,
-0.0060212258249521255,
0.035550106316804886,
-0.02538246475160122,
-0.024778148159384727,
0.016972120851278305,
0.028832932934165,
0.011702589690685272,
0.05054975301027298,
0.0024070395156741142,
0.031355757266283035,
0.026986638084053993,
-0.038573358207941055,
-0.02782239392399788,
0.03808861970901489,
-0.01687769964337349,
-0.00940112303942442,
-0.04229000583291054,
-0.005498883780092001,
-0.006472307723015547,
-0.0352768637239933,
0.008854357525706291,
0.03492330387234688,
-0.025277413427829742,
-0.040581442415714264,
0.03804497420787811,
0.019588083028793335,
0.012939915992319584,
0.0034218544606119394,
0.03333365172147751,
0.024213485419750214,
-0.04812924563884735,
0.020635277032852173,
0.013855036348104477,
0.05352597311139107,
0.03702618181705475,
-0.02705511450767517,
0.035466574132442474,
-0.03335193172097206,
0.03641045466065407,
-0.008823073469102383,
0.02727985940873623,
0.004072266165167093,
-0.04000641405582428,
0.002081227023154497,
-0.025810914114117622,
0.017271490767598152,
0.027593538165092468,
-0.009318564087152481,
0.08556048572063446,
-0.01573140174150467,
-0.004843113943934441,
-0.006769345607608557,
0.012876125052571297,
0.016349993646144867,
-0.019638679921627045,
-0.015750672668218613,
0.06655094027519226,
-0.0245394054800272,
-0.0011082253186032176,
-0.0371507965028286,
-0.034950703382492065,
0.048822592943906784,
-0.009719612076878548,
0.0133672459051013,
0.02256930246949196,
0.014402967877686024,
0.006102359853684902,
-0.03274468332529068,
-0.05254262685775757,
-0.010801003314554691,
0.02834746241569519,
0.0124449348077178,
0.03917919471859932,
-0.002226057928055525,
-0.0473598949611187,
-0.022967878729104996,
0.04814090207219124,
-0.08677193522453308,
-0.04582132399082184,
-0.024784786626696587,
0.03788478672504425,
0.021327396854758263,
0.008379061706364155
] |
<p>Are there any materials exploring intermediate levels (of any sub-subject) which give plain English descriptions along side formulas/equations//diagrams/notations?</p>
| 8,268 |
[
-0.013934754766523838,
-0.0425233319401741,
-0.009580107405781746,
0.018397539854049683,
0.02734629437327385,
0.024955086410045624,
-0.013103741221129894,
-0.011002923361957073,
0.0073261200450360775,
-0.06524868309497833,
0.017171885818243027,
0.01968500018119812,
0.04410086199641228,
0.018082601949572563,
0.02991759590804577,
0.01522578950971365,
-0.016585679724812508,
-0.010621643625199795,
-0.02441881038248539,
-0.02517538145184517,
0.02305411919951439,
-0.04623386263847351,
-0.019860778003931046,
0.03206013888120651,
0.01651565171778202,
0.0348191075026989,
0.0239313505589962,
-0.03143591433763504,
0.020123396068811417,
0.03021794930100441,
0.01018413808196783,
-0.0009076383430510759,
-0.006231856066733599,
-0.0069547914899885654,
0.021468723192811012,
-0.010043567977845669,
0.004774518311023712,
-0.06687618792057037,
-0.004230705089867115,
-0.010223842225968838,
-0.04372043162584305,
0.00811903364956379,
-0.0052956221625208855,
0.026632245630025864,
-0.011890718713402748,
0.029631348326802254,
-0.03497124835848808,
-0.026292847469449043,
0.011289006099104881,
-0.06236988678574562,
0.0439324751496315,
0.05448446422815323,
0.04691949114203453,
0.05323103815317154,
0.00213799811899662,
0.018712040036916733,
0.05383218824863434,
0.052314966917037964,
-0.017692793160676956,
-0.041913170367479324,
-0.011314461939036846,
-0.030570996925234795,
-0.00040010767406784,
-0.03961490839719772,
-0.04841162636876106,
0.03344440832734108,
-0.0044596241787076,
0.003522427985444665,
0.024824952706694603,
0.026096442714333534,
0.00032672303495928645,
0.0033029455225914717,
0.06407389789819717,
0.004957702476531267,
0.01854201965034008,
-0.04601888358592987,
0.02837522327899933,
0.012425124645233154,
0.014461890794336796,
0.053678251802921295,
-0.010059252381324768,
-0.004900296218693256,
0.009724250063300133,
0.004359424579888582,
-0.025944704189896584,
-0.003589669708162546,
0.07663413137197495,
0.0008452405454590917,
-0.00033150604576803744,
0.025852777063846588,
-0.018645120784640312,
-0.013822250068187714,
0.025544699281454086,
-0.01330447569489479,
-0.03125647082924843,
-0.012775035575032234,
0.0027931847143918276,
0.024428021162748337,
0.00869601871818304,
-0.03190796449780464,
0.04899061471223831,
0.0003882046730723232,
0.04334275424480438,
0.08200588822364807,
0.027395786717534065,
-0.01985003612935543,
-0.03737113997340202,
-0.007025123108178377,
0.03636058419942856,
-0.021882882341742516,
0.03930726647377014,
0.01615271344780922,
0.005579429678618908,
0.04907799884676933,
-0.0147959403693676,
-0.054558850824832916,
-0.0003808849724009633,
-0.010651961900293827,
0.05224955826997757,
0.042798932641744614,
0.06145056337118149,
-0.046306367963552475,
0.04731661453843117,
0.0017308199312537909,
-0.10858429223299026,
0.0015994393033906817,
0.023299848660826683,
-0.03067927248775959,
-0.04243261367082596,
0.0570976659655571,
0.03210495412349701,
0.012551150284707546,
0.021947450935840607,
-0.03140628710389137,
0.04770291969180107,
0.007197934668511152,
-0.03012669086456299,
-0.06102145463228226,
0.01839657500386238,
-0.010807367973029613,
-0.03011549636721611,
-0.058540184050798416,
0.02733284793794155,
0.05635256692767143,
0.02913730777800083,
0.004003874491900206,
0.0004307898343540728,
-0.010905132628977299,
-0.0005663703777827322,
0.0041087656281888485,
-0.01877034269273281,
-0.024691244587302208,
0.033316902816295624,
-0.00663286866620183,
0.038138460367918015,
-0.0570107102394104,
0.027089923620224,
0.046446386724710464,
0.01381782814860344,
-0.021760033443570137,
0.04781234636902809,
-0.0004757560964208096,
-0.004301161039620638,
0.01894453354179859,
0.008063316345214844,
-0.017971837893128395,
0.046815626323223114,
-0.029804041609168053,
0.03167010098695755,
0.02106538414955139,
0.04056777060031891,
-0.006294958293437958,
0.011407219804823399,
0.0006698423530906439,
0.04334350302815437,
-0.019223563373088837,
-0.01779552362859249,
0.02697109989821911,
0.010716158896684647,
-0.015146405436098576,
-0.04385093227028847,
-0.026264410465955734,
0.005981347989290953,
0.0367182195186615,
-0.01713128387928009,
0.0031363547313958406,
0.0015274863690137863,
-0.012784750200808048,
0.0023071460891515017,
-0.05937978997826576,
-0.008491037413477898,
-0.028236640617251396,
0.044766299426555634,
-0.020057808607816696,
-0.021214334294199944,
0.04856950417160988,
-0.022288283333182335,
0.051742468029260635,
-0.04419724643230438,
-0.023849239572882652,
-0.0017987738829106092,
0.020566729828715324,
-0.0008723571081645787,
-0.05382966995239258,
0.012932008132338524,
0.018087269738316536,
0.04452667385339737,
-0.03196406736969948,
0.03705734387040138,
-0.028746310621500015,
0.006635759025812149,
-0.021686214953660965,
-0.01776112988591194,
0.05490632355213165,
0.0121835395693779,
-0.006069501396268606,
0.013369490392506123,
0.0021402272395789623,
0.03542132303118706,
0.05839252471923828,
-0.05843435600399971,
0.05237884446978569,
0.05568576604127884,
0.06791891902685165,
0.017202889546751976,
0.04237247630953789,
0.026360468938946724,
-0.00042300240602344275,
-0.0010227393358945847,
-0.03187790885567665,
-0.004114158451557159,
-0.035244718194007874,
0.02404438704252243,
0.01196969486773014,
-0.07218250632286072,
0.042900118976831436,
0.03532782196998596,
0.02156699076294899,
0.040806736797094345,
0.055702805519104004,
0.0013755927793681622,
-0.04185508191585541,
-0.0038304394111037254,
0.012930616736412048,
0.009927873499691486,
0.07017888128757477,
0.002445546444505453,
0.0549154169857502,
-0.014384432695806026,
0.03305579721927643,
-0.005753661040216684,
0.01706775277853012,
0.00936820451170206,
0.005337757524102926,
0.024100307375192642,
-0.03190366178750992,
0.0579959861934185,
-0.05395267903804779,
0.029265688732266426,
-0.030360059812664986,
0.018203360959887505,
-0.02165459468960762,
0.019084064289927483,
-0.009825710207223892,
0.026574868708848953,
-0.006939534563571215,
-0.017202284187078476,
-0.015336169861257076,
0.03780777007341385,
-0.03452561795711517,
0.029270756989717484,
-0.030358625575900078,
0.011076755821704865,
-0.01751560904085636,
-0.051649101078510284,
0.006299229804426432,
-0.017893237993121147,
0.04816754534840584,
-0.04228305071592331,
-0.009171376936137676,
-0.015109241008758545,
-0.007566479966044426,
0.049999725073575974,
-0.009082863107323647,
-0.03245421126484871,
0.03808086737990379,
-0.009534684009850025,
-0.08007588237524033,
0.08257757127285004,
-0.024183198809623718,
-0.028814323246479034,
0.025398684665560722,
-0.02129739709198475,
-0.028377046808600426,
0.008937548846006393,
-0.017652226611971855,
-0.012694272212684155,
-0.049117181450128555,
0.011494900099933147,
0.04151222109794617,
-0.02243734709918499,
-0.023323724046349525,
0.0009658749331720173,
-0.025122495368123055,
-0.03869974985718727,
-0.03080003336071968,
0.003954696003347635,
-0.01771242544054985,
-0.014824261888861656,
-0.005394733045250177,
0.025477373972535133,
-0.04691299423575401,
-0.004996895790100098,
-0.03835836425423622,
-0.08803121745586395,
0.0017234475817531347,
0.030278997495770454,
0.02065546065568924,
0.0013561842497438192,
-0.02165486477315426,
0.0600263774394989,
-0.0053046587854623795,
-0.05241421237587929,
-0.04063597694039345,
-0.012505719438195229,
0.0474935844540596,
-0.035815414041280746,
0.011120151728391647,
0.014302265830338001,
-0.024889511987566948,
0.007635634392499924,
0.01538790948688984,
0.013558325357735157,
0.04478488489985466,
0.03303011879324913,
0.01115727610886097,
0.0372551828622818,
0.01654554344713688,
-0.009503004141151905,
0.03865238279104233,
0.010379692539572716,
-0.0770401656627655,
-0.004158482421189547,
0.009359415620565414,
0.031054681167006493,
0.03824278339743614,
-0.014998635277152061,
0.04259640723466873,
0.0034384483005851507,
-0.03529595956206322,
-0.025780342519283295,
0.030925408005714417,
0.013862992636859417,
-0.021527599543333054,
-0.0040350710041821,
0.04260527342557907,
0.012311224825680256,
-0.017377711832523346,
0.035768743604421616,
0.042338404804468155,
0.020383596420288086,
-0.0695936307311058,
0.0009623191435821354,
0.004725102335214615,
0.01255603414028883,
0.028297655284404755,
0.005627651698887348,
-0.0011546905152499676,
0.06499982625246048,
0.018462901934981346,
0.013197919353842735,
0.020192619413137436,
-0.02507663518190384,
0.03447851166129112,
-0.07571283727884293,
-0.03349655494093895,
-0.044902488589286804,
0.03577101230621338,
-0.016806429252028465,
0.048612285405397415,
-0.009627604857087135,
0.015079175122082233,
0.012099554762244225,
0.04911462590098381,
-0.07702267169952393,
-0.022111129015684128,
-0.043525420129299164,
0.03868364542722702,
0.011907297186553478,
0.03815220296382904,
-0.021648148074746132,
-0.017111744731664658,
-0.07135570049285889,
-0.009188443422317505,
0.023260457441210747,
-0.020721454173326492,
0.012566937133669853,
-0.01862022839486599,
-0.006547636352479458,
-0.002611069008708,
-0.000523522263392806,
0.006098717916756868,
-0.04117697477340698,
-0.013763882219791412,
0.02271519973874092,
-0.004622408654540777,
0.0012870760401710868,
-0.06381960213184357,
-0.009846608154475689,
0.009939922019839287,
0.011013844050467014,
0.014716397039592266,
0.028915470466017723,
-0.034774135798215866,
0.014855222776532173,
-0.01847301423549652,
0.06221114099025726,
-0.04002838954329491,
-0.01467334944754839,
-0.008485711179673672,
-0.016237054020166397,
-0.016789831221103668,
0.019018687307834625,
0.0317794606089592,
-0.034296490252017975,
0.03660368546843529,
0.002952724462375045,
-0.006142466329038143,
-0.053579699248075485,
0.08807399868965149,
-0.010851076804101467,
-0.010501943528652191,
-0.04011618718504906,
-0.01266137883067131,
-0.04760083183646202,
-0.04391007125377655,
-0.02912459522485733,
-0.0033258271869271994,
0.030363382771611214,
-0.008416665717959404,
0.00208300887607038,
0.019173841923475266,
0.011925175786018372,
-0.01985308900475502,
0.014699893072247505,
-0.016772659495472908,
-0.001048654317855835,
0.0008954172371886671,
-0.042744435369968414,
0.016913337633013725,
0.0287549439817667,
0.03188782185316086,
-0.003838647622615099,
-0.004275837913155556,
-0.061844345182180405,
0.008786754682660103,
0.0384831540286541,
0.031289998441934586,
-0.013390285894274712,
0.027682753279805183,
-0.0381942018866539,
-0.06825311481952667,
0.04171263426542282,
-0.00019989980501122773,
0.004269512835890055,
-0.05466284230351448,
-0.01831892505288124,
-0.059310413897037506,
0.006257554516196251,
0.005195633042603731,
-0.010263131000101566,
0.010595000348985195,
0.026706857606768608,
0.02136865258216858,
0.05966438353061676,
-0.042716287076473236,
0.03137299418449402,
0.053797900676727295,
0.01819366216659546,
0.020011402666568756,
-0.0212043859064579,
0.034031517803668976,
0.0016546646365895867,
-0.02552594244480133,
-0.05973643437027931,
0.005485744681209326,
0.009754804894328117,
0.022809701040387154,
0.015436306595802307,
-0.0005345352692529559,
-0.04643808677792549,
0.00646273884922266,
0.02968723326921463,
-0.005049203522503376,
-0.026035264134407043,
-0.01203700341284275,
0.06021640822291374,
0.01859177276492119,
0.0427846685051918,
0.026727814227342606,
0.01666019856929779,
-0.027321234345436096,
-0.0032171953935176134,
0.0037471242249011993,
0.03962064906954765,
-0.023624377325177193,
-0.025166213512420654,
-0.04251503571867943,
-0.023060191422700882,
-0.04436469450592995,
0.060303352773189545,
-0.009799253195524216,
0.010331178084015846,
-0.0240497849881649,
-0.040587883442640305,
-0.025042060762643814,
-0.007417178712785244,
-0.019647616893053055,
-0.020807914435863495,
-0.03043999895453453,
0.0034891669638454914,
-0.0020200414583086967,
-0.03402731567621231,
0.02996615320444107,
-0.018161283805966377,
0.008384705521166325,
0.010522675700485706,
-0.006315183825790882,
0.03188618645071983,
-0.0744749903678894,
-0.009205460548400879,
0.009247422218322754,
-0.04020598903298378,
0.06746655702590942,
-0.020660897716879845,
0.025116775184869766,
0.01820114068686962,
-0.03954630717635155,
-0.05496247857809067,
0.03873005509376526,
-0.01003541424870491,
-0.03863956034183502,
0.004617438185960054,
0.010494960471987724,
-0.009232230484485626,
-0.021591253578662872,
-0.0217253677546978,
-0.07796893268823624,
0.01729515939950943,
-0.0004830548423342407,
-0.01118595153093338,
-0.022702805697917938,
0.034524690359830856,
-0.007777135819196701,
-0.012718741782009602,
0.03911778703331947,
0.05726073682308197,
-0.03363386541604996,
0.02211931347846985,
0.013715135864913464,
-0.012663055211305618,
0.04290462285280228,
0.021242525428533554,
0.011989018879830837,
-0.010680459439754486,
0.023506557568907738,
0.0064082336612045765,
0.004539744928479195,
0.004648104310035706,
-0.015897467732429504,
0.008468549698591232,
-0.034780826419591904,
0.03759694844484329,
0.040419694036245346,
-0.03570631518959999,
0.0015317295910790563,
0.04310332611203194,
-0.008088593371212482,
-0.008787044323980808,
-0.04073604196310043,
0.021402087062597275,
0.0005696438602171838,
0.022576022893190384,
-0.03256531432271004,
-0.005266471300274134,
-0.03691880777478218,
-0.041565872728824615,
0.024997975677251816,
-0.0011379066854715347,
0.015690159052610397,
-0.020770009607076645,
0.06028374284505844,
0.008182206191122532,
-0.027406996116042137,
0.0601499117910862,
0.007158336695283651,
-0.021512703970074654,
-0.0029662454035133123,
-0.0042158132418990135,
0.047914981842041016,
0.020945537835359573,
-0.015285320580005646,
-0.06038902699947357,
-0.007810072973370552,
-0.016911234706640244,
0.01095651090145111,
-0.011966747231781483,
0.07039482146501541,
0.04269193485379219,
-0.03179566189646721,
-0.01901291497051716,
-0.03534654527902603,
-0.032988760620355606,
0.0057379077188670635,
0.020072802901268005,
0.083381786942482,
-0.04099937528371811,
0.006779041141271591,
-0.011573676951229572,
0.047120604664087296,
-0.021673642098903656,
0.02024770714342594,
0.023013409227132797,
0.005168947856873274,
0.0010648693423718214,
-0.046454936265945435,
-0.05127676948904991,
0.03410704806447029,
-0.019747208803892136,
0.02437729574739933,
0.00034846304333768785,
-0.02717047929763794,
0.025820406153798103,
0.03127001225948334,
0.009491629898548126,
-0.03818574920296669,
-0.010149288922548294,
-0.03074800781905651,
0.053306400775909424,
0.013234629295766354,
-0.006263635121285915,
-0.029574217274785042,
0.022598953917622566,
0.020046064630150795,
-0.05581052601337433,
0.002700305311009288,
-0.012836313806474209,
-0.041386112570762634,
-0.04546507075428963,
-0.01908533088862896,
-0.039236150681972504,
0.035102032124996185,
-0.011997065506875515,
0.02081308513879776,
-0.02375648356974125,
-0.03940455615520477,
0.019808568060398102,
0.008310631848871708,
0.016465310007333755,
-0.028659457340836525,
0.062494758516550064,
-0.010316905565559864,
-0.007114737760275602,
-0.003755792509764433,
-0.0004389825917314738,
0.16021688282489777,
0.03380339965224266,
-0.005545045714825392,
-0.07371225208044052,
0.030871892347931862,
0.012291820719838142,
0.03521239385008812,
-0.026182519271969795,
-0.004294106736779213,
-0.008989102207124233,
0.001854433212429285,
-0.026989245787262917,
0.09661971777677536,
-0.032247982919216156,
0.020238453522324562,
0.05007293447852135,
-0.03371443971991539,
-0.02554134465754032,
0.00970282033085823,
-0.002783945994451642,
-0.017548108473420143,
0.05424457788467407,
-0.030292021110653877,
0.019245469942688942,
0.015956664457917213,
-0.034834980964660645,
-0.019923008978366852,
-0.033421967178583145,
0.08731383830308914,
0.031231703236699104,
-0.04532371833920479,
0.007419995032250881,
0.026216715574264526,
-0.0005772094591520727,
-0.008129866793751717,
0.022415917366743088,
0.02096228487789631,
-0.0018177039455622435,
0.013105052523314953,
0.018518026918172836,
0.027203349396586418,
0.01962169073522091,
0.025702955201268196,
0.009696751832962036,
-0.03645801544189453,
-0.010713460855185986,
-0.013644457794725895,
0.001711800810880959,
-0.03073194995522499,
-0.014505129307508469,
-0.026278173550963402,
-0.01083147618919611,
-0.0025440887548029423,
-0.02611996792256832,
-0.018412692472338676,
0.02916041389107704,
0.005268340464681387,
-0.045302823185920715,
0.001567295053973794,
-0.009139379486441612,
0.02045365236699581,
-0.030944112688302994,
0.018137909471988678,
-0.01887522079050541,
-0.045512378215789795,
0.007818379439413548,
-0.03362236171960831,
0.02525983564555645,
-0.023228323087096214,
-0.04809187725186348,
-0.01391240581870079,
0.026775188744068146,
0.013540364801883698,
-0.017706304788589478,
0.011868536472320557,
0.029745325446128845,
0.010932856239378452,
0.0002892653283197433,
-0.06495588272809982,
0.033620137721300125,
0.012245585210621357,
0.0303314458578825,
0.021528419107198715,
-0.007722984068095684,
0.016812730580568314,
-0.02511061169207096,
0.020203670486807823,
0.013559570536017418,
-0.014676196500658989,
0.027873272076249123,
-0.024165522307157516,
0.01712406799197197,
0.04145107418298721,
-0.026560690253973007,
0.0006807643221691251,
0.00613881042227149,
-0.01893596351146698,
0.024468019604682922,
0.0020954974461346865,
0.03300859034061432,
0.013935133814811707,
-0.007033159956336021,
-0.011814874596893787,
0.06250733137130737,
-0.004980520810931921,
0.011815046891570091,
-0.004162496887147427,
-0.03892095014452934,
0.029447942972183228,
0.0037734750658273697,
0.04957665130496025,
0.027609463781118393,
0.007112604100257158,
-0.047634419053792953,
0.0067553273402154446,
-0.023283701390028,
0.02003604918718338,
-0.02817092090845108,
0.014711307361721992,
-0.03595787659287453,
0.001677089836448431,
-0.0048881168477237225,
0.027178935706615448,
-0.03619172424077988,
-0.02071957290172577,
0.0051076156087219715,
-0.025368884205818176,
-0.0055336966179311275,
0.017421890050172806,
-0.018722251057624817,
-0.011027032509446144,
0.037712566554546356,
-0.0038948359433561563,
-0.033039480447769165,
-0.009944331832230091,
-0.0005081930430606008,
-0.012535675428807735,
0.030544299632310867,
-0.015160681679844856,
-0.05072401836514473,
-0.01710566133260727,
0.00021664453379344195,
-0.042700864374637604,
0.011006421409547329,
0.016774166375398636,
0.008047997020184994,
0.036634668707847595,
-0.023012535646557808,
-0.015131769701838493,
0.05844210833311081,
0.003002682700753212,
0.0019293060759082437,
0.005793803371489048,
0.001110845129005611,
0.018857503309845924,
-0.01631227135658264,
0.027990426868200302,
-0.027114026248455048,
-0.045041605830192566,
-0.01816113106906414,
0.023426877334713936,
0.021776733919978142,
-0.01981969177722931,
0.037786055356264114,
-0.016037385910749435,
0.018374770879745483,
0.02529529482126236,
0.0017607177142053843,
0.030337616801261902,
0.001930969301611185,
-0.017169272527098656,
0.03134111687541008,
0.016515638679265976,
0.01980374939739704,
-0.07060272246599197,
-0.014559082686901093,
0.01955617591738701,
0.049510810524225235,
0.046055905520915985,
-0.0705234557390213,
0.015185825526714325,
0.0047161635011434555,
-0.06909472495317459,
0.017173973843455315,
-0.03343135863542557,
-0.04118388518691063,
-0.014937504194676876,
-0.03215678036212921,
-0.0044313957914710045,
0.03967244550585747,
-0.01637892611324787,
0.042025867849588394,
-0.007136000785976648,
-0.022886570543050766,
0.0008361267391592264,
0.007512151729315519,
-0.01439952477812767,
-0.002884929534047842,
-0.008068189956247807,
-0.03315162658691406,
0.03126624599099159,
-0.021142898127436638,
-0.043069686740636826,
0.039248641580343246,
0.013324870727956295,
0.013720645569264889,
-0.006462447810918093,
0.022606858983635902,
-0.021783027797937393,
0.04238026216626167,
-0.0001312296953983605,
-0.025213101878762245,
-0.019574103876948357,
-0.003326412523165345,
-0.012831130996346474,
0.03374820202589035,
0.007513571996241808,
-0.004412516485899687,
0.033213675022125244,
-0.0032529281452298164,
-0.04293476417660713,
0.048414986580610275,
-0.06132159009575844,
-0.030818412080407143,
-0.013208643533289433,
-0.037015676498413086,
0.029306253418326378,
-0.03877949342131615,
0.026149380952119827,
-0.04813780635595322,
-0.023408709093928337,
-0.021085968241095543,
-0.0014175869291648269,
-0.008861485868692398,
0.026685884222388268,
0.01960449106991291,
-0.002650347538292408,
-0.003915447276085615,
0.03208717703819275,
0.014333939179778099,
-0.03654848411679268,
-0.005261927377432585,
0.012668455950915813,
0.006278459448367357,
0.005167259834706783,
-0.017028309404850006,
-0.017630083486437798,
0.022586848586797714,
-0.0009610424749553204,
0.020767511799931526,
0.003934514243155718,
-0.03583703935146332,
0.032672129571437836,
-0.01476539857685566,
0.06628470867872238,
0.019630515947937965,
0.015734978020191193,
-0.0021738100331276655,
-0.014246828854084015,
0.024490918964147568,
-0.009654264897108078,
0.047240763902664185,
-0.028274966403841972,
-0.018906939774751663,
0.002572986762970686,
-0.0014153714291751385,
0.031209422275424004,
0.00017444760305806994,
0.010997484438121319,
-0.01910710521042347,
-0.06102572754025459,
-0.004208105616271496,
-0.01986026205122471,
0.0038700364530086517,
0.013590141199529171,
0.012775039300322533,
0.033609963953495026,
0.0003624313685577363,
-0.05776206776499748,
-0.018266642466187477,
0.0013534813188016415,
0.049621690064668655,
-0.047013841569423676,
0.032584864646196365,
-0.0038887823466211557,
-0.019019698724150658,
0.022073663771152496,
-0.02475622296333313,
-0.04210667312145233,
0.03849099203944206,
0.0006067266222089529,
0.004626006819307804,
-0.002136936876922846,
-0.0010775132104754448,
0.011102482676506042,
-0.053206637501716614,
-0.013221842236816883,
-0.024196360260248184,
-0.05745353922247887,
-0.03708579018712044,
0.06160580739378929,
0.02603769861161709,
0.01050583552569151,
-0.025268075987696648,
-0.03083551488816738,
0.03784044086933136,
-0.0311031024903059,
-0.005148246418684721,
0.03934924304485321,
0.03325335681438446,
0.027296951040625572,
-0.01094685960561037,
0.023918502032756805,
-0.009247488342225552,
0.017798466607928276,
0.02682603895664215,
0.05268435552716255,
-0.013879787176847458,
-0.002079593250527978,
0.04639095813035965,
-0.0212709903717041,
0.02918904274702072,
-0.005355178844183683,
0.007523851003497839,
0.07520943135023117,
-0.026688039302825928,
0.012447155080735683,
-0.06966041028499603,
0.06389201432466507,
-0.04040968418121338,
-0.024789202958345413,
0.03829312324523926,
0.026628464460372925,
-0.01394010428339243,
-0.0009889878565445542,
-0.03470864146947861,
-0.00003981245026807301,
0.032746799290180206,
-0.042840782552957535,
0.023117726668715477,
-0.02755190245807171,
-0.029686948284506798,
0.05398429557681084,
0.0008047158480621874,
-0.05009245127439499,
-0.04525149613618851,
0.05919747054576874,
0.027349116280674934,
0.024330325424671173,
-0.04194190725684166,
0.0036870224867016077,
-0.017697704955935478,
0.07941979914903641,
-0.0726039856672287,
0.00620997091755271,
-0.027207277715206146,
-0.011012307368218899,
-0.01825321651995182,
0.008465005084872246
] |
<p>I want to compute the viscosity of argon at different temperatures. What is <a href="http://en.wikipedia.org/wiki/Viscosity#Gases" rel="nofollow">Sutherland's constant</a> of argon?</p>
| 8,269 |
[
0.0031326620373874903,
-0.009123342111706734,
-0.029189415276050568,
-0.01684730127453804,
0.02205737866461277,
0.002911386312916875,
-0.025022262707352638,
-0.005140805151313543,
-0.018611671403050423,
-0.034509897232055664,
0.06245207041501999,
0.05712214112281799,
0.031874220818281174,
0.01598268188536167,
0.005692873615771532,
-0.0036356367636471987,
0.008760414086282253,
0.008426371030509472,
0.037432923913002014,
-0.006483679171651602,
-0.012052137404680252,
-0.033751171082258224,
-0.0038181045092642307,
0.021849673241376877,
-0.008467109873890877,
0.05324719846248627,
0.03618406876921654,
0.015635672956705093,
0.03154663369059563,
0.0422574020922184,
-0.0036097357515245676,
-0.02460024505853653,
0.029421010985970497,
0.016698427498340607,
0.00810896884649992,
0.006512389983981848,
-0.04301822930574417,
0.003674908308312297,
-0.027975110337138176,
0.03492541238665581,
-0.030444897711277008,
-0.008604228496551514,
-0.007688934449106455,
0.051496438682079315,
-0.004857408348470926,
-0.0046068779192864895,
0.03090660832822323,
-0.03499559685587883,
0.038818854838609695,
-0.08213470876216888,
0.05894996225833893,
-0.006207381375133991,
0.05796530097723007,
0.027681969106197357,
-0.01710052788257599,
0.006369943730533123,
0.04490847513079643,
0.06405007839202881,
-0.030078178271651268,
-0.053656600415706635,
0.012890839949250221,
-0.005558856762945652,
-0.006883448455482721,
-0.03209580481052399,
-0.022462163120508194,
0.030390935018658638,
-0.027095140889286995,
-0.033429376780986786,
0.002395455026999116,
0.02546452172100544,
0.0051324632950127125,
0.0048388526774942875,
0.03206542879343033,
-0.04671997204422951,
0.01721104234457016,
-0.020977934822440147,
0.0052450550720095634,
0.015665093436837196,
0.016029076650738716,
0.055659420788288116,
-0.013650122098624706,
0.010399853810667992,
0.04072358459234238,
-0.003282784717157483,
-0.036750808358192444,
-0.002394641749560833,
0.09066321700811386,
-0.006428385619074106,
-0.0015372654888778925,
0.048976581543684006,
-0.017638619989156723,
0.001777543919160962,
0.04614271968603134,
0.01926630735397339,
0.023763382807374,
0.013465429656207561,
-0.02967679500579834,
0.059288375079631805,
-0.00833310279995203,
-0.040363609790802,
0.0054760160855948925,
-0.018433155491948128,
-0.014551584608852863,
0.0988735482096672,
-0.0015603448264300823,
-0.02683623507618904,
-0.034968968480825424,
-0.015457021072506905,
0.0046976045705378056,
-0.02760554663836956,
-0.0325448140501976,
-0.007980220019817352,
-0.04277818277478218,
-0.026592953130602837,
-0.006271584890782833,
-0.034898269921541214,
0.005968044977635145,
-0.01179058849811554,
0.02203953079879284,
0.06317446380853653,
0.04078080877661705,
-0.022665960714221,
0.03249073401093483,
-0.013526779599487782,
-0.10567795485258102,
0.03039412945508957,
0.017470311373472214,
-0.01004724856466055,
-0.012764438055455685,
0.031127311289310455,
-0.018378479406237602,
-0.033062081784009933,
-0.03688962385058403,
-0.007608204614371061,
0.04270586371421814,
-0.003602837910875678,
-0.07144962251186371,
-0.08304549008607864,
0.021549833938479424,
0.004654495976865292,
-0.02046964503824711,
-0.037540923804044724,
0.004099758807569742,
0.021308107301592827,
0.0790204256772995,
0.021094193682074547,
0.023110948503017426,
-0.009360491298139095,
0.032802291214466095,
-0.01884925179183483,
-0.022137237712740898,
-0.004381740465760231,
0.01914083957672119,
-0.04994354397058487,
-0.004290753044188023,
-0.05037159100174904,
0.0018330051098018885,
0.025555532425642014,
-0.028587250038981438,
-0.013926312327384949,
0.03727992624044418,
-0.02966812252998352,
-0.012122614309191704,
0.007939713075757027,
-0.015430818311870098,
-0.030010050162672997,
0.07572814077138901,
0.02559114433825016,
0.002545516239479184,
0.011197240091860294,
-0.02405782788991928,
0.008310866542160511,
-0.028580332174897194,
-0.007273805793374777,
0.088924840092659,
0.02859737165272236,
-0.012671126052737236,
-0.00181186490226537,
-0.02007266692817211,
0.052998125553131104,
-0.03807622566819191,
-0.018934553489089012,
0.000001082675908037345,
-0.003012159839272499,
-0.018541377037763596,
0.03762420266866684,
0.006921929772943258,
0.031022844836115837,
0.016067368909716606,
-0.05558668449521065,
-0.03866880014538765,
-0.0383019745349884,
0.030051153153181076,
-0.031479571014642715,
0.0044220928102731705,
0.013965471647679806,
0.01740977354347706,
0.029753854498267174,
0.014326811768114567,
-0.059029072523117065,
-0.014717375859618187,
0.031953006982803345,
0.05119836702942848,
-0.006255009211599827,
0.007121183443814516,
0.01881452091038227,
0.03263702243566513,
-0.044396668672561646,
0.027082165703177452,
-0.02712380886077881,
0.0030138292349874973,
-0.021701570600271225,
-0.041103165596723557,
0.023894768208265305,
-0.03717430680990219,
-0.011370022781193256,
0.0203702449798584,
0.0024126002099364996,
0.00782793015241623,
0.018958216533064842,
-0.018975326791405678,
0.07260657101869583,
0.03020884282886982,
0.026377659291028976,
-0.009542769752442837,
0.02730085328221321,
-0.020120052620768547,
-0.009707283228635788,
0.011761090718209743,
-0.013450763188302517,
-0.018693696707487106,
-0.006789136677980423,
0.038305558264255524,
0.04127945005893707,
-0.03950567916035652,
-0.01823488250374794,
0.05320291221141815,
0.03110898658633232,
0.04860059544444084,
0.029995746910572052,
-0.009988890960812569,
-0.020774254575371742,
-0.0008500280673615634,
0.007100829854607582,
0.021362869068980217,
0.027841992676258087,
0.015243479050695896,
0.05985628813505173,
0.07747069746255875,
0.013497480191290379,
-0.045809056609869,
0.03727656602859497,
0.002508152974769473,
0.0029337911400943995,
0.012960071675479412,
-0.007688487414270639,
0.04736713692545891,
-0.028626782819628716,
-0.011263624764978886,
0.03012227453291416,
0.0023318687453866005,
0.03162652999162674,
0.011161409318447113,
-0.012305974029004574,
0.037314414978027344,
-0.0025399995502084494,
-0.011809284798800945,
-0.012934455648064613,
0.00009823883010540158,
-0.019046245142817497,
0.02640361152589321,
-0.023869022727012634,
0.02489190548658371,
-0.044984012842178345,
-0.0001778670703060925,
-0.0011681508040055633,
0.008117207325994968,
0.014816291630268097,
-0.024547794833779335,
-0.03701968491077423,
0.009082125499844551,
-0.048179369419813156,
-0.02402936853468418,
-0.004045713692903519,
-0.043587274849414825,
0.008388345129787922,
0.009782030247151852,
-0.03710030019283295,
0.01866653375327587,
-0.029454320669174194,
-0.020865626633167267,
0.0638553574681282,
-0.03290938958525658,
-0.04006178304553032,
0.004320694599300623,
-0.02009512297809124,
0.0321696437895298,
-0.03553055599331856,
0.028951069340109825,
0.038280341774225235,
-0.03313364461064339,
-0.03437824547290802,
0.018223145976662636,
-0.04726368933916092,
-0.04173062741756439,
-0.044958677142858505,
-0.016680555418133736,
0.026297692209482193,
-0.04683820530772209,
-0.017886940389871597,
0.0434560663998127,
-0.048272036015987396,
-0.008349798619747162,
-0.01730327680706978,
-0.04171065241098404,
0.02145298197865486,
0.017290327697992325,
0.02045716531574726,
-0.01949426718056202,
-0.026461651548743248,
0.03576657176017761,
0.006386937107890844,
-0.034053985029459,
-0.02835853211581707,
-0.01959964632987976,
-0.015073917806148529,
-0.02431310899555683,
0.019209282472729683,
0.013475094921886921,
-0.05458967760205269,
-0.01218112651258707,
0.005007508210837841,
0.02701532654464245,
0.051521722227334976,
0.034344788640737534,
0.028880851343274117,
0.012252992950379848,
0.014610877260565758,
-0.026102662086486816,
0.10075693577528,
0.017229393124580383,
-0.02873402088880539,
0.04925138130784035,
-0.005467815790325403,
0.05133543908596039,
0.04577164724469185,
-0.03657171130180359,
0.033065006136894226,
0.00022670321050100029,
-0.025018369778990746,
-0.01782211661338806,
-0.0031581143848598003,
-0.029264729470014572,
-0.011884862557053566,
0.0009864948224276304,
0.04253173619508743,
0.008388102054595947,
0.0000574275545659475,
0.005174524150788784,
0.043795399367809296,
0.051332324743270874,
-0.0032112132757902145,
-0.022030232474207878,
-0.03209741786122322,
-0.0514514334499836,
0.03168508782982826,
-0.04537685215473175,
-0.03982728719711304,
0.05626197159290314,
0.024184690788388252,
0.028745144605636597,
-0.025206368416547775,
-0.0441969595849514,
0.014838800765573978,
-0.07964332401752472,
0.006680730730295181,
-0.0007490165298804641,
0.06400775164365768,
-0.0023221829906105995,
0.06854121387004852,
0.01803860440850258,
0.040508512407541275,
0.040419820696115494,
0.011751927435398102,
-0.07859325408935547,
0.06254363059997559,
-0.020152131095528603,
-0.007521003484725952,
0.0031081493943929672,
-0.01989552192389965,
0.00589745445176959,
-0.030525125563144684,
0.027071982622146606,
0.01299088541418314,
-0.017622338607907295,
-0.021063875406980515,
0.01905127801001072,
-0.01901240646839142,
0.008994772098958492,
0.0011342548532411456,
0.06606242805719376,
0.021085107699036598,
-0.003627757541835308,
0.040183763951063156,
0.03920668363571167,
-0.010853995569050312,
-0.028159737586975098,
-0.0018859257688745856,
0.014395504258573055,
0.02289723791182041,
0.037876807153224945,
0.015438257716596127,
0.025321677327156067,
-0.005304893013089895,
-0.0009085942292585969,
0.0009435705724172294,
0.028099235147237778,
-0.01796555705368519,
0.023153718560934067,
-0.03365938365459442,
-0.049886517226696014,
-0.010626567527651787,
-0.003224237821996212,
0.029919706284999847,
-0.012260877527296543,
0.027797870337963104,
0.00635880883783102,
-0.021196728572249413,
-0.03754941746592522,
0.010153139010071754,
0.048987001180648804,
-0.010126120410859585,
-0.03380570933222771,
-0.016821173951029778,
0.007882378995418549,
0.0075289164669811726,
-0.0005609652143903077,
0.026730861514806747,
0.04150647297501564,
-0.03372541442513466,
-0.018370335921645164,
0.018652677536010742,
0.003136418294161558,
-0.015216977335512638,
0.0058973911218345165,
0.013961905613541603,
0.0253811776638031,
-0.012828625738620758,
-0.027805780991911888,
0.0048002819530665874,
0.011951551772654057,
0.010354767553508282,
-0.015505880117416382,
-0.024647558107972145,
-0.10524599254131317,
0.009362279437482357,
0.0425710491836071,
0.06655111163854599,
-0.010981676168739796,
0.009796352125704288,
-0.048797059804201126,
0.002179505303502083,
0.07896694540977478,
-0.017737532034516335,
0.04459318518638611,
-0.03160152956843376,
0.0012154855066910386,
0.01878480054438114,
-0.027478594332933426,
-0.011617581360042095,
0.027241285890340805,
-0.0016953570302575827,
0.013083037920296192,
-0.052669283002614975,
-0.0018673886079341173,
-0.006578641012310982,
-0.01664947159588337,
0.011824368499219418,
0.06639343500137329,
0.0017205890035256743,
0.009389459155499935,
0.018714841455221176,
0.004505777265876532,
-0.02445034310221672,
-0.06238522753119469,
-0.0032594671938568354,
0.00964713841676712,
0.0016424366040155292,
0.011944806203246117,
-0.022988272830843925,
-0.044403448700904846,
0.013402898795902729,
0.011074838228523731,
-0.02412007376551628,
0.00986335426568985,
-0.0076672108843922615,
0.05602972209453583,
0.04023012891411781,
-0.011508329771459103,
0.02621358633041382,
0.057098206132650375,
0.0039182608015835285,
-0.010982966050505638,
-0.049775633960962296,
0.05570115149021149,
0.0004381148610264063,
-0.017734741792082787,
-0.004769651219248772,
-0.0011031656758859754,
-0.029776835814118385,
0.039756156504154205,
-0.030411018058657646,
0.02388177067041397,
-0.02081301063299179,
-0.011977019719779491,
-0.000249523640377447,
-0.008076269179582596,
0.015343003906309605,
-0.033670444041490555,
0.041299864649772644,
0.0034359602723270655,
-0.023431362584233284,
-0.027526922523975372,
0.026675382629036903,
0.01219498086720705,
-0.018790286034345627,
0.025139732286334038,
-0.01203781459480524,
0.010510222986340523,
-0.023641373962163925,
-0.025179866701364517,
0.0030003287829458714,
-0.012433337047696114,
0.03956703469157219,
-0.012458009645342827,
0.04421619325876236,
-0.005245823413133621,
-0.061873115599155426,
-0.02304648794233799,
0.028448054566979408,
0.012381995096802711,
0.03684055805206299,
-0.057500895112752914,
0.031667519360780716,
-0.017390424385666847,
0.014281149953603745,
-0.07761044800281525,
-0.05800019949674606,
0.03314420208334923,
0.041849903762340546,
-0.032212842255830765,
-0.038061052560806274,
-0.01934133842587471,
-0.019832026213407516,
-0.025299418717622757,
0.01341940090060234,
0.06376030296087265,
-0.017338037490844727,
-0.008523112162947655,
-0.003316691843792796,
0.010648977942764759,
0.06383729726076126,
0.03788250684738159,
0.0019943667575716972,
-0.01747221313416958,
-0.03178197517991066,
-0.036442093551158905,
0.024704180657863617,
0.04985649511218071,
-0.024772092700004578,
-0.027704695239663124,
0.027726786211133003,
0.013577369041740894,
0.019598079845309258,
-0.01269536092877388,
0.004139111377298832,
-0.004351157229393721,
-0.004244251176714897,
0.02101818285882473,
-0.014569774270057678,
0.025064369663596153,
-0.03780984506011009,
0.05554339662194252,
-0.023571103811264038,
-0.03569754958152771,
-0.05186673253774643,
-0.03803722932934761,
-0.04197308048605919,
0.017908263951539993,
0.01549503393471241,
0.005816403776407242,
0.06382840126752853,
-0.02340041659772396,
-0.02290571853518486,
0.014493186958134174,
-0.02224605716764927,
0.03964041545987129,
0.00819597952067852,
-0.012771617621183395,
-0.005883920006453991,
-0.006775336340069771,
-0.029735557734966278,
-0.03895685449242592,
-0.06036541238427162,
0.015596942976117134,
0.07746288925409317,
-0.022283654659986496,
0.040800608694553375,
0.005734028294682503,
-0.007265704683959484,
0.03833039849996567,
0.011971846222877502,
-0.03977128490805626,
0.020861199125647545,
0.016392171382904053,
0.01960410177707672,
0.020487360656261444,
-0.012457882054150105,
-0.006834585685282946,
0.026683762669563293,
-0.017336104065179825,
0.026718026027083397,
0.01096249558031559,
0.01699821837246418,
0.0038101307582110167,
-0.03988349810242653,
-0.027457691729068756,
0.06669659912586212,
0.020770249888300896,
0.06379815936088562,
-0.02146814577281475,
-0.01956208609044552,
0.04898076876997948,
-0.022515343502163887,
0.03135095536708832,
-0.01102115586400032,
-0.023947840556502342,
-0.0027782246470451355,
-0.01060070376843214,
0.0023695165291428566,
-0.030211128294467926,
0.004476329777389765,
0.04767133295536041,
0.023660045117139816,
0.0013696576934307814,
0.025028273463249207,
-0.010405936278402805,
-0.0387619212269783,
0.026315605267882347,
-0.006976030766963959,
-0.06761462986469269,
0.03410768508911133,
0.06908451020717621,
-0.04295286908745766,
0.004520891699939966,
0.04239549860358238,
-0.015728289261460304,
0.006237986963242292,
0.02513783983886242,
0.005111402831971645,
0.08319016546010971,
-0.017809119075536728,
0.026175444945693016,
-0.04556204006075859,
0.04310690239071846,
0.11261865496635437,
0.030636271461844444,
0.016531290486454964,
-0.035193249583244324,
0.0037654952611774206,
-0.02082519792020321,
0.017303112894296646,
-0.02876620925962925,
0.0037503845524042845,
-0.014474600553512573,
-0.0172832403331995,
0.05629550293087959,
0.022739289328455925,
-0.0011980037670582533,
0.013211257755756378,
0.043597523123025894,
-0.024955762550234795,
-0.015433699823915958,
-0.007873148657381535,
0.01653372123837471,
-0.015967078506946564,
0.038462720811367035,
-0.04641164839267731,
0.01650157757103443,
-0.03853439539670944,
-0.018139606341719627,
-0.03851626068353653,
-0.040209781378507614,
0.034891095012426376,
0.024632466956973076,
-0.03847621753811836,
0.011653273366391659,
-0.0008663535700179636,
-0.013900557532906532,
-0.03997739031910896,
0.004558117128908634,
0.0736243724822998,
-0.0192172322422266,
-0.011960219591856003,
0.024337753653526306,
-0.013984022662043571,
0.0181709174066782,
-0.023698100820183754,
0.026580099016427994,
-0.02566693350672722,
-0.022848743945360184,
-0.005145920440554619,
0.011167624965310097,
0.016969256103038788,
0.030203474685549736,
-0.0037508050445467234,
0.027273694053292274,
-0.005658725742250681,
-0.02799002081155777,
-0.01832396350800991,
-0.00013374026457313448,
0.03678670898079872,
-0.05025313422083855,
-0.009068267419934273,
-0.03464464098215103,
-0.001797644654288888,
-0.01724732294678688,
0.033449552953243256,
-0.012384884990751743,
-0.031472429633140564,
-0.004380640108138323,
-0.036788903176784515,
0.041480518877506256,
-0.054123423993587494,
-0.04463908076286316,
-0.008167478255927563,
-0.012736642733216286,
-0.04831307753920555,
-0.03007863648235798,
0.02703140303492546,
0.009557795710861683,
0.024060340598225594,
-0.016704997047781944,
-0.00985005684196949,
-0.005354867782443762,
-0.07617403566837311,
0.034672994166612625,
-0.006191427819430828,
0.002266945317387581,
-0.055274125188589096,
-0.015568890608847141,
0.05440168082714081,
0.016917312517762184,
-0.009962128475308418,
-0.025025933980941772,
-0.0018718800274655223,
-0.011953792534768581,
0.06572290509939194,
-0.029368504881858826,
-0.03979414701461792,
-0.0080810422077775,
-0.05469442158937454,
-0.026679106056690216,
0.0032768447417765856,
0.08961731195449829,
0.04746251553297043,
0.013896592892706394,
-0.006939574144780636,
0.0023471976164728403,
-0.05751673877239227,
0.030127257108688354,
-0.010557953268289566,
-0.015195757150650024,
-0.009049824438989162,
0.011310608126223087,
-0.01549930777400732,
-0.052880845963954926,
-0.04235178604722023,
-0.04712994396686554,
0.02328806184232235,
0.01586197130382061,
0.009065413847565651,
0.004036480560898781,
0.024717826396226883,
0.0014312485000118613,
-0.001574473106302321,
-0.042579881846904755,
-0.008333234116435051,
-0.04676724225282669,
-0.03235127404332161,
0.002826854819431901,
0.03201819211244583,
0.003853216767311096,
0.0001362842449452728,
-0.006676036864519119,
0.014086427167057991,
0.02724878117442131,
0.029898108914494514,
0.01436376292258501,
-0.04794114828109741,
0.018041089177131653,
-0.012162260711193085,
0.06301283836364746,
-0.028298791497945786,
-0.045997295528650284,
0.045989081263542175,
-0.04166136682033539,
-0.049868691712617874,
0.014366278424859047,
-0.01857997290790081,
0.01973930560052395,
0.028452130034565926,
-0.006114736199378967,
-0.013696379959583282,
0.0782819390296936,
-0.010618436150252819,
-0.015323110856115818,
-0.02255435846745968,
-0.020746983587741852,
0.014810252003371716,
-0.011404906399548054,
-0.010532991029322147,
-0.0002732755965553224,
0.0049440134316682816,
0.041677076369524,
0.038404449820518494,
0.005084655247628689,
0.0038950860034674406,
0.013545062392950058,
0.0011832542950287461,
-0.015399252064526081,
0.0443156398832798,
-0.01747496798634529,
0.0540614053606987,
0.03093075193464756,
-0.028338002040982246,
0.03914647921919823,
0.020311476662755013,
0.020701153203845024,
-0.09920851141214371,
0.01043748203665018,
-0.0006749334279447794,
0.008847647346556187,
0.04991382360458374,
-0.05437258258461952,
0.02183796651661396,
0.02761927805840969,
-0.0286004226654768,
-0.001743091270327568,
-0.01277164276689291,
0.0002466212026774883,
-0.03333715721964836,
-0.01986026205122471,
0.015194201841950417,
0.07551026344299316,
0.03791183978319168,
0.034166958183050156,
0.035507023334503174,
-0.011624004691839218,
-0.020698092877864838,
-0.04138689488172531,
0.021484125405550003,
0.02198856696486473,
-0.018603269010782242,
-0.02154483273625374,
0.029826637357473373,
-0.012772280722856522,
-0.014056441374123096,
0.052056171000003815,
-0.033378858119249344,
0.03145537152886391,
-0.0020928476005792618,
-0.01357959397137165,
-0.0002783830277621746,
0.003950520418584347,
0.01744801364839077,
-0.011609516106545925,
-0.013132474385201931,
0.03502831608057022,
0.004963831510394812,
0.03082200139760971,
-0.012133294716477394,
0.0162389874458313,
0.02777835540473461,
-0.047245629131793976,
-0.05359439551830292,
0.04236551746726036,
0.001420948188751936,
-0.018820390105247498,
0.0019636021461337805,
-0.03131057694554329,
0.01864001341164112,
-0.048663824796676636,
0.00705898879095912,
-0.028564320877194405,
-0.008703790605068207,
0.06252408772706985,
-0.00018279292271472514,
0.0011436374625191092,
-0.00393966818228364,
-0.02096416801214218,
-0.03439332917332649,
0.04379171133041382,
-0.0326353944838047,
0.004127009771764278,
-0.021228482946753502,
-0.01951463147997856,
0.012252848595380783,
-0.0077802217565476894,
0.004022032953798771,
-0.030160028487443924,
-0.02188655361533165,
0.011469508521258831,
0.02208324335515499,
-0.009742128662765026,
-0.01753412000834942,
-0.031056685373187065,
-0.005896694026887417,
-0.04599110782146454,
-0.0013970134314149618,
-0.02026779018342495,
-0.003948303405195475,
-0.034196190536022186,
-0.024493670091032982,
-0.0027452954091131687,
0.0125012481585145,
0.05282333493232727,
-0.034734729677438736,
0.032759591937065125,
-0.024023957550525665,
0.011172587051987648,
-0.012213206849992275,
-0.05002807453274727,
0.005646390374749899,
0.010615733452141285,
-0.036612529307603836,
-0.01307392492890358,
0.0015887029003351927,
-0.016640491783618927,
0.01450147945433855,
0.020542563870549202,
-0.0008727371459826827,
0.0056436434388160706,
-0.020948613062500954,
-0.03896995261311531,
0.013059446588158607,
0.021261580288410187,
-0.053268592804670334,
0.0592946894466877,
-0.04025300592184067,
-0.024744393303990364,
0.015176252461969852,
0.011738808825612068,
-0.01987820863723755,
0.01761513017117977,
-0.02169322781264782,
-0.0128196245059371,
0.034334395080804825,
-0.0274354275316,
0.00140459428075701,
-0.07551242411136627,
0.01772930659353733,
0.006328767631202936,
-0.06123373657464981,
-0.02814532443881035,
0.06496793031692505,
0.04205187410116196,
0.04461470991373062,
-0.00814251508563757,
-0.010965333320200443,
0.008677870035171509,
0.000494390435051173,
-0.014843960292637348,
0.04184994474053383,
0.03575027734041214,
0.016761502251029015,
0.02514829859137535,
0.004514453466981649,
0.004323837347328663,
0.04708521440625191,
0.0092124929651618,
0.01811356656253338,
-0.030603723600506783,
-0.042884450405836105,
-0.0028295309748500586,
-0.026238644495606422,
0.025175675749778748,
0.04664386063814163,
-0.01649467647075653,
0.09065800160169601,
-0.0269281268119812,
0.02877415157854557,
-0.012867577373981476,
0.039573684334754944,
-0.03552115708589554,
0.01071599218994379,
-0.0027655523736029863,
0.032143834978342056,
-0.019899407401680946,
-0.012752346694469452,
0.01638660952448845,
-0.003768984228372574,
0.032115593552589417,
-0.04679419472813606,
0.00037064330535940826,
-0.016115985810756683,
0.022583836689591408,
-0.03655267134308815,
-0.015692081302404404,
-0.02536798268556595,
0.00874948687851429,
0.0069377548061311245,
0.053079381585121155,
-0.0034955800510942936,
0.02310388721525669,
-0.003094310639426112,
-0.027419520542025566,
0.05867611989378929,
-0.07602772116661072,
-0.009414716623723507,
-0.011428844183683395,
-0.010507079772651196,
-0.018911899998784065,
0.017426172271370888
] |
<p>A 6500-kg helicopter accelerates upward at 0.60 m/s² while lifting a 1200-kg car.
(a) What is the lift force exerted by the air on the rotors?<br>
(b) What is the tension in the cable (ignore its mass) that connects the car to the helicopter?</p>
| 8,270 |
[
-0.03340675309300423,
-0.02346625365316868,
-0.05567501485347748,
0.0023647856432944536,
0.031533289700746536,
-0.014494801871478558,
-0.007803656160831451,
-0.03555377572774887,
0.00648746220394969,
-0.04417720437049866,
0.06886807829141617,
0.05053774639964104,
0.023252282291650772,
0.008853592909872532,
0.011649620719254017,
-0.020079955458641052,
-0.014203432947397232,
-0.029949460178613663,
0.02094678394496441,
0.03582427650690079,
-0.025322332978248596,
-0.008418910205364227,
0.03142988309264183,
0.02113194763660431,
-0.028717584908008575,
0.050706177949905396,
0.046861160546541214,
-0.029436277225613594,
0.04195817559957504,
0.047725412994623184,
-0.03004566580057144,
-0.03309433162212372,
0.01642559841275215,
0.04226628318428993,
0.040926605463027954,
0.019620871171355247,
-0.05475478246808052,
-0.0024915041867643595,
-0.04804764688014984,
0.013183558359742165,
0.013627714477479458,
0.005180263426154852,
0.01694674603641033,
0.06478557735681534,
-0.0071416255086660385,
0.04405050724744797,
-0.00930896308273077,
-0.012098634615540504,
0.03615887835621834,
-0.07292922586202621,
0.06181564927101135,
-0.014245864935219288,
0.010788344778120518,
0.04186667129397392,
-0.007427365519106388,
-0.013688646256923676,
0.03043266572058201,
0.05145096033811569,
-0.030216233804821968,
-0.03593810275197029,
0.008385706692934036,
0.0019256604136899114,
-0.046884406358003616,
-0.013293877243995667,
-0.05390677601099014,
0.03875625506043434,
-0.051706645637750626,
-0.018101908266544342,
0.06871306896209717,
-0.0002767440746538341,
0.001178893493488431,
0.00819147564470768,
0.04714234173297882,
-0.03713338449597359,
0.014577403664588928,
-0.028211088851094246,
-0.0063864924013614655,
0.024302246049046516,
0.03289457783102989,
0.058548398315906525,
-0.026680752635002136,
0.0101077975705266,
0.033146247267723083,
0.05337879806756973,
0.038178469985723495,
-0.0264853797852993,
0.07547105103731155,
0.004345092922449112,
-0.0031496151350438595,
-0.005933729000389576,
0.009140306152403355,
-0.01177932508289814,
-0.006186781916767359,
-0.024269716814160347,
0.004642881453037262,
0.040096480399370193,
0.010889053344726562,
0.0507357195019722,
0.007535075768828392,
-0.02831338904798031,
-0.0015716197667643428,
-0.03080812282860279,
0.031522419303655624,
0.07971394807100296,
-0.017099393531680107,
0.0064859590493142605,
0.005270525347441435,
0.023424291983246803,
-0.01552328560501337,
-0.01752527430653572,
-0.05355394259095192,
0.00926766823977232,
-0.015690196305513382,
-0.02938588336110115,
-0.025022592395544052,
-0.030102478340268135,
0.030516162514686584,
0.013871605508029461,
0.04556824266910553,
0.019333651289343834,
0.05936345085501671,
-0.020278405398130417,
0.01747742109000683,
0.004037162289023399,
-0.02875887043774128,
0.013239323161542416,
0.0027588163502514362,
-0.030433665961027145,
-0.028380900621414185,
0.05002136528491974,
-0.03341367468237877,
0.0031107603572309017,
-0.02598314918577671,
0.01788877509534359,
0.0319451242685318,
-0.004542573355138302,
-0.11286081373691559,
-0.07554880529642105,
0.002593524754047394,
-0.0008380580693483353,
-0.006377358455210924,
-0.046977002173662186,
0.03309169411659241,
0.04719669744372368,
0.07330146431922913,
-0.015641098842024803,
0.025738494470715523,
0.010348175652325153,
-0.0057981559075415134,
-0.020243197679519653,
0.019352711737155914,
-0.02050703391432762,
-0.015871770679950714,
-0.015791963785886765,
0.0029537014197558165,
-0.05417810380458832,
-0.00048046893789432943,
0.026543358340859413,
0.005544582381844521,
-0.047579094767570496,
0.01901767961680889,
0.03132753074169159,
0.0015590604161843657,
-0.020962845534086227,
-0.021846365183591843,
-0.009372362866997719,
0.010257243178784847,
-0.004133010283112526,
0.008339396677911282,
0.05700285732746124,
-0.02164853736758232,
0.029169680550694466,
-0.029582109302282333,
0.003879992524161935,
0.03692216798663139,
-0.029025394469499588,
-0.00028248727903701365,
-0.028657549992203712,
0.0151996910572052,
0.018672166392207146,
-0.025862161070108414,
-0.045971259474754333,
-0.016878845170140266,
0.025234846398234367,
0.010231309570372105,
0.03587793558835983,
0.020536988973617554,
-0.03136739134788513,
0.000872206233907491,
-0.024726733565330505,
-0.011635423637926579,
-0.0350724458694458,
0.025498557835817337,
-0.002312309108674526,
-0.038396693766117096,
0.00030423415591940284,
-0.0010589894372969866,
0.015829352661967278,
-0.05696937441825867,
0.009806793183088303,
-0.00872826762497425,
0.0004932570154778659,
0.015819638967514038,
0.039893489331007004,
0.03299364447593689,
0.07796771079301834,
0.07034080475568771,
0.015020993538200855,
0.03640883415937424,
0.004274547100067139,
-0.03607384115457535,
-0.005019038915634155,
-0.026961063966155052,
-0.014760526828467846,
0.006902047898620367,
0.026171406731009483,
0.027311056852340698,
0.005636278074234724,
-0.014708035625517368,
0.054963186383247375,
-0.02793925441801548,
0.060925066471099854,
0.04539164528250694,
0.03609247878193855,
0.0041657485999166965,
0.03211204707622528,
0.00862808246165514,
0.020133865997195244,
-0.004077071323990822,
0.0016147849382832646,
-0.053720708936452866,
0.009892195463180542,
0.03213312104344368,
0.027625272050499916,
-0.07400277256965637,
-0.015544830821454525,
0.03649095073342323,
0.032587870955467224,
0.04093175008893013,
0.024721328169107437,
-0.029313305392861366,
-0.05936708673834801,
0.01333469245582819,
0.007825396955013275,
-0.01437073852866888,
0.010559212416410446,
-0.0018564154161140323,
0.05327776446938515,
0.03147279843688011,
0.004627082496881485,
-0.003205556422472,
0.032126184552907944,
0.008197805844247341,
0.016829369589686394,
-0.0259588323533535,
-0.016237620264291763,
0.05402649939060211,
0.003338724607601762,
-0.01231988426297903,
0.006884617730975151,
-0.01613498665392399,
0.012357786297798157,
-0.0004763737670145929,
-0.02393917553126812,
0.04783724248409271,
-0.04823101684451103,
-0.009648025035858154,
-0.00976325199007988,
0.04250183328986168,
-0.04626671224832535,
0.0031874049454927444,
-0.03646664693951607,
-0.007835792377591133,
-0.02810998633503914,
0.00322530185803771,
0.01850275881588459,
-0.021432839334011078,
0.06016664579510689,
-0.006617280654609203,
-0.016030501574277878,
0.00960579700767994,
-0.05308379977941513,
-0.000909001100808382,
-0.011224514804780483,
-0.05838490277528763,
0.005639206152409315,
0.004175468813627958,
-0.02552352473139763,
0.06656379997730255,
0.01421547681093216,
-0.03429163247346878,
0.04657436162233353,
0.020226111635565758,
-0.008955604396760464,
0.002581373555585742,
-0.024804050102829933,
0.03325014188885689,
-0.007166038267314434,
-0.023942407220602036,
0.025544971227645874,
-0.004616472404450178,
0.022049371153116226,
0.055107682943344116,
-0.08958498388528824,
-0.022245699539780617,
-0.02155892550945282,
-0.023604607209563255,
-0.014160708524286747,
-0.007008241955190897,
0.011709213256835938,
-0.015785548835992813,
-0.04177117347717285,
0.0168021060526371,
-0.06807788461446762,
-0.02816924639046192,
-0.008230386301875114,
-0.03250358626246452,
0.04359685257077217,
-0.00256383721716702,
-0.05039137229323387,
0.06899008899927139,
-0.015189132653176785,
-0.024026384577155113,
-0.021288493648171425,
-0.04406450688838959,
-0.011479546315968037,
-0.005267408676445484,
0.01570727862417698,
0.034570448100566864,
-0.007999183610081673,
-0.014461544342339039,
0.057559434324502945,
-0.01030135527253151,
0.03200482949614525,
-0.005334946326911449,
-0.028537075966596603,
0.0014245411148294806,
0.007408022880554199,
0.01295438315719366,
0.10091663897037506,
0.008536113426089287,
0.02194247581064701,
0.033157628029584885,
-0.009444796480238438,
0.03755715861916542,
-0.015287855640053749,
-0.014446347951889038,
0.06191783398389816,
0.00018597459711600095,
0.02269420027732849,
-0.0142899164929986,
0.07211688905954361,
0.028056541457772255,
-0.016076525673270226,
0.01957918517291546,
-0.014728275127708912,
0.03119128756225109,
-0.03196020796895027,
-0.03355170041322708,
0.043241292238235474,
0.08632906526327133,
-0.047675274312496185,
-0.06236836314201355,
0.02261391468346119,
0.008618855848908424,
0.03116304986178875,
-0.04702048376202583,
-0.03295845165848732,
0.03927350044250488,
0.029107218608260155,
0.034409403800964355,
0.013905791565775871,
-0.02586992457509041,
0.014968269504606724,
-0.08517295122146606,
-0.014038397930562496,
-0.023680677637457848,
0.037302952259778976,
0.008887425065040588,
0.08163581788539886,
0.013947436586022377,
0.03290856257081032,
0.03682033345103264,
0.045248061418533325,
-0.05351967737078667,
0.035396743565797806,
-0.02336118370294571,
-0.0557403489947319,
0.002427258063107729,
-0.021849919110536575,
0.031275197863578796,
-0.05307156965136528,
-0.004874248988926411,
0.0008946901652961969,
0.003054568078368902,
-0.04394586756825447,
0.03609197959303856,
-0.044370535761117935,
-0.028692297637462616,
0.030717946588993073,
-0.004789829254150391,
0.06233135610818863,
0.014845221303403378,
0.032221775501966476,
0.10235238820314407,
-0.02632264420390129,
0.007086592726409435,
-0.008557947352528572,
-0.022532643750309944,
-0.047781556844711304,
0.02561378665268421,
-0.007883085869252682,
0.0418022982776165,
-0.011115134693682194,
0.006458199117332697,
0.017133697867393494,
0.004785461816936731,
-0.000028970678613404743,
0.010629542171955109,
-0.02635490521788597,
-0.08283396810293198,
-0.03150079399347305,
-0.022058645263314247,
0.034211914986371994,
-0.043840426951646805,
0.013290002010762691,
0.012867122888565063,
-0.019729601219296455,
-0.004274872597306967,
0.08110743761062622,
0.04223134368658066,
0.009184186346828938,
-0.00861699040979147,
-0.007395369000732899,
-0.006210772320628166,
-0.04149099439382553,
-0.01273279543966055,
0.06787183880805969,
0.015175260603427887,
-0.01269877701997757,
-0.020524093881249428,
0.06437854468822479,
-0.0040216161869466305,
-0.0010426517110317945,
0.03658660128712654,
0.007809013593941927,
0.008800256066024303,
0.008639608509838581,
-0.00278960051946342,
-0.0029231663793325424,
0.030856484547257423,
0.06924591958522797,
0.007904475554823875,
-0.04469411075115204,
-0.11369775980710983,
-0.05853426456451416,
0.04106525704264641,
0.017082255333662033,
-0.0448622852563858,
-0.005510922521352768,
-0.031034694984555244,
0.008530803956091404,
0.04297259449958801,
-0.02095947228372097,
0.05464326590299606,
-0.014552277512848377,
0.024146538227796555,
-0.0007335582631640136,
0.017004407942295074,
-0.04948786646127701,
0.026181811466813087,
-0.008107136934995651,
0.009975854307413101,
-0.006465987302362919,
0.004374082665890455,
0.013275153934955597,
0.005560588091611862,
0.05926676094532013,
0.043807502835989,
0.029512790963053703,
-0.023311566561460495,
-0.027177317067980766,
-0.016432765871286392,
-0.05283298343420029,
-0.022143030539155006,
0.003983018919825554,
0.008719158358871937,
-0.04558011144399643,
0.03365691006183624,
-0.04423170164227486,
-0.04131092503666878,
-0.0025007466319948435,
-0.003019933123141527,
0.006695646792650223,
0.02523668110370636,
-0.023580092936754227,
0.014450468122959137,
0.06286963820457458,
0.01688237674534321,
0.052836060523986816,
0.0386071614921093,
-0.03264660760760307,
0.030862480401992798,
-0.002982762409374118,
0.031993113458156586,
0.02281513623893261,
-0.01932615414261818,
0.009329554624855518,
0.023789888247847557,
-0.04981685057282448,
0.03215450420975685,
-0.025487754493951797,
0.03600408136844635,
-0.043183162808418274,
-0.03923625126481056,
-0.0024266496766358614,
0.03924689069390297,
-0.017318684607744217,
-0.023294245824217796,
-0.016386020928621292,
0.002867494011297822,
-0.01238051988184452,
-0.037473782896995544,
-0.0026221720036119223,
-0.010036315768957138,
-0.021687215194106102,
-0.016332805156707764,
-0.031200001016259193,
0.015752093866467476,
-0.02749888226389885,
-0.014610182493925095,
0.007278006989508867,
-0.07726852595806122,
0.05026647076010704,
-0.012764747254550457,
0.012121070176362991,
0.019831592217087746,
-0.03085077367722988,
-0.014769620262086391,
0.017303604632616043,
0.030516233295202255,
0.033482056111097336,
-0.015626488253474236,
0.032871000468730927,
-0.020865116268396378,
-0.0328872911632061,
-0.026605000719428062,
-0.05976913869380951,
0.04482010751962662,
0.057589154690504074,
0.023944895714521408,
-0.044560499489307404,
0.007983855903148651,
-0.004575186409056187,
-0.0031152283772826195,
-0.032996103167533875,
0.03377361223101616,
-0.03590204566717148,
0.03187268599867821,
0.021705757826566696,
-0.0027886363677680492,
0.04067631810903549,
-0.013270135968923569,
0.009227774105966091,
0.024488240480422974,
-0.02083621546626091,
-0.01486844290047884,
-0.00030549682560376823,
0.015849245712161064,
-0.019669990986585617,
-0.006791734602302313,
0.038691870868206024,
-0.012446405366063118,
0.041360173374414444,
-0.010663379915058613,
0.010862139984965324,
0.062484223395586014,
0.01888967491686344,
0.006052929908037186,
0.008237242698669434,
-0.007502852473407984,
-0.00975148007273674,
0.05353604257106781,
-0.024391693994402885,
-0.01842307299375534,
-0.022904174402356148,
-0.037429869174957275,
0.0037012556567788124,
0.028342334553599358,
-0.003912627696990967,
0.009415815584361553,
0.03940790519118309,
-0.02563823014497757,
-0.010378899984061718,
-0.005984863732010126,
0.03229977935552597,
0.0458950474858284,
0.0009203426307067275,
-0.016812825575470924,
0.0535203218460083,
-0.013024981133639812,
-0.0006937921280041337,
-0.02443942241370678,
-0.01484317984431982,
0.0036927128676325083,
0.06331642717123032,
-0.02719276398420334,
0.04401550441980362,
-0.023488933220505714,
0.0021910665091127157,
-0.006696279160678387,
-0.028153592720627785,
-0.01313780713826418,
-0.00031286454759538174,
0.01807272434234619,
0.02008187398314476,
-0.007901657372713089,
0.03171518072485924,
0.03597164899110794,
0.024063993245363235,
-0.0005692637641914189,
-0.020622970536351204,
0.03491803631186485,
0.028992662206292152,
0.019544929265975952,
-0.03160298615694046,
-0.011599965393543243,
0.009434611536562443,
-0.009683705866336823,
0.06509615480899811,
-0.0027229248080402613,
0.005338707473129034,
0.06723573058843613,
0.033321503549814224,
0.03351443260908127,
-0.03736960515379906,
-0.004759940784424543,
-0.023801861330866814,
-0.04364345595240593,
-0.01665935292840004,
-0.009501690044999123,
0.01899278350174427,
0.011062153615057468,
0.023894725367426872,
0.005456527695059776,
0.038347028195858,
-0.03147106617689133,
-0.023486193269491196,
0.004642650485038757,
-0.012531169690191746,
-0.07340870797634125,
0.03205454349517822,
0.026684807613492012,
-0.04717788100242615,
0.07251288741827011,
0.0055472878739237785,
0.033684469759464264,
0.0224783793091774,
0.02839326113462448,
-0.013317668810486794,
0.05420328676700592,
-0.05437652766704559,
0.010317441076040268,
-0.014250442385673523,
0.013384280726313591,
0.07353118062019348,
0.025436092168092728,
0.010993939824402332,
-0.03877663612365723,
0.02396278642117977,
-0.003063059179112315,
-0.00312455534003675,
-0.07772315293550491,
0.002968616783618927,
-0.015664609149098396,
-0.0031277684029191732,
0.017422687262296677,
0.0362127311527729,
-0.026031741872429848,
-0.015408490784466267,
0.019126415252685547,
-0.012262593023478985,
-0.008335585705935955,
-0.02643692120909691,
0.03347155079245567,
0.0063148364424705505,
0.0071573383174836636,
-0.01453995332121849,
0.0003810892812907696,
-0.039904359728097916,
-0.014177422039210796,
-0.014639697037637234,
-0.02423251047730446,
0.03414008021354675,
-0.015998877584934235,
-0.04518599063158035,
0.02648318186402321,
0.01626608520746231,
-0.022951677441596985,
-0.03899587690830231,
0.022997209802269936,
0.007063800003379583,
0.007355884183198214,
-0.006269868463277817,
0.007645701058208942,
0.016607007011771202,
0.003620460629463196,
0.0008202549070119858,
-0.018149683251976967,
-0.06839197874069214,
-0.004874482750892639,
-0.03231840953230858,
0.031908437609672546,
-0.01979730650782585,
0.007917442359030247,
-0.010642044246196747,
-0.03048105724155903,
0.006105121690779924,
-0.02854490838944912,
-0.019612982869148254,
-0.019065244123339653,
-0.019381964579224586,
-0.028344471007585526,
-0.0700143501162529,
-0.03610272705554962,
0.024931272491812706,
0.01860920898616314,
0.01106968242675066,
0.006040052976459265,
-0.015973586589097977,
0.020364295691251755,
-0.02268296852707863,
0.05659990385174751,
-0.025292284786701202,
0.0011401907540857792,
-0.0011008442379534245,
-0.011946146376430988,
-0.019421253353357315,
-0.013362896628677845,
0.015459601767361164,
0.031151065602898598,
0.01962624303996563,
-0.009228714741766453,
-0.0028147404082119465,
-0.02734002284705639,
-0.04090569168329239,
0.023497112095355988,
0.0207410529255867,
-0.009713457897305489,
-0.03303293138742447,
-0.015294890850782394,
-0.006973435636609793,
0.05556197836995125,
0.016282597556710243,
0.014519590884447098,
0.006599775981158018,
0.03826295956969261,
-0.019758988171815872,
-0.052609194070100784,
-0.03290983662009239,
0.014740235172212124,
-0.05363867059350014,
0.005767290014773607,
0.019756166264414787,
0.04149232059717178,
0.04438963532447815,
0.020362531766295433,
-0.009656879119575024,
0.01735798642039299,
-0.024746747687458992,
0.015339699573814869,
0.0483056902885437,
-0.035312023013830185,
0.0018286729464307427,
0.032743025571107864,
0.0067229908891022205,
-0.05828604847192764,
-0.008211236447095871,
-0.00990904401987791,
-0.02227059379220009,
-0.002779484959319234,
-0.008262845687568188,
-0.004509252030402422,
-0.009756733663380146,
-0.045919500291347504,
0.0016921615460887551,
-0.032086703926324844,
0.016269491985440254,
-0.031114179641008377,
0.01305762492120266,
-0.008848374709486961,
-0.012940495274960995,
-0.020448928698897362,
0.007584611419588327,
-0.06853251904249191,
0.04677168279886246,
-0.0000957647425821051,
-0.023635754361748695,
0.017178213223814964,
-0.02227964997291565,
-0.03257985785603523,
0.0031967940740287304,
0.0344257690012455,
-0.010774297639727592,
-0.03133629262447357,
0.05684421584010124,
-0.03853056952357292,
-0.005922582931816578,
0.018751244992017746,
0.021033111959695816,
0.013496221974492073,
0.027220238000154495,
-0.026229804381728172,
-0.006538620218634605,
0.034784749150276184,
-0.02444867603480816,
-0.00989675521850586,
-0.02156033180654049,
-0.018814031034708023,
-0.02186726965010166,
-0.032133638858795166,
-0.014362049289047718,
-0.018986374139785767,
-0.016949577257037163,
0.01666523888707161,
0.05639021098613739,
-0.024239741265773773,
-0.00489327497780323,
0.03726402297616005,
0.029654575511813164,
-0.00041650005732662976,
0.030424604192376137,
-0.0033060035202652216,
0.028352990746498108,
0.046742893755435944,
-0.034153107553720474,
0.0031978939659893513,
0.016568783670663834,
0.009247029200196266,
-0.10567337274551392,
-0.031081244349479675,
0.0038639786653220654,
-0.005767805967479944,
0.03785346448421478,
-0.029162926599383354,
-0.012278526090085506,
0.03776085376739502,
-0.07423657923936844,
-0.02876666560769081,
-0.007205396890640259,
0.03268740326166153,
-0.014676316641271114,
0.004209859296679497,
0.03337882086634636,
0.03302103653550148,
-0.03483980521559715,
0.04631134122610092,
0.04171176254749298,
-0.026855478063225746,
-0.005514222662895918,
-0.021545451134443283,
0.028191866353154182,
0.025777848437428474,
-0.005526144988834858,
-0.03179895132780075,
0.018127895891666412,
-0.01913432590663433,
0.006555800326168537,
-0.002629391383379698,
-0.0430295467376709,
0.04810597747564316,
-0.01300245150923729,
-0.008546191267669201,
0.025606246665120125,
0.011958361603319645,
-0.03557256981730461,
-0.008224021643400192,
-0.024169430136680603,
0.03073255717754364,
-0.003996915649622679,
0.01650194078683853,
-0.017068782821297646,
0.013424558565020561,
0.017222415655851364,
-0.01989125646650791,
-0.021467505022883415,
0.05974593013525009,
-0.045289553701877594,
-0.025046460330486298,
-0.0013698498951271176,
0.009978723712265491,
-0.030876437202095985,
-0.024086955934762955,
-0.008866447024047375,
-0.028347156941890717,
-0.003043792210519314,
-0.001213624607771635,
-0.03343562036752701,
-0.03392229229211807,
0.022317547351121902,
-0.015207021497189999,
0.008078126236796379,
-0.003179907100275159,
0.0054194992408156395,
-0.007356195244938135,
-0.018604647368192673,
0.010237934067845345,
0.0164980199187994,
-0.008779853582382202,
0.01353492122143507,
-0.06358698010444641,
-0.016256146132946014,
0.02443886362016201,
0.04566555097699165,
0.03411830961704254,
0.024640141054987907,
-0.013447574339807034,
-0.01112088467925787,
-0.07504063844680786,
0.007023036014288664,
0.017232190817594528,
-0.022076481953263283,
-0.0313413105905056,
-0.04551418870687485,
-0.007202889770269394,
0.023436682298779488,
0.04217122495174408,
0.009028064087033272,
-0.03317916393280029,
0.012674621306359768,
-0.019703328609466553,
0.004651880823075771,
-0.02362169325351715,
0.018462523818016052,
0.010506425984203815,
-0.041426967829465866,
-0.0017955793300643563,
0.006082459352910519,
-0.00031785128521732986,
0.015882819890975952,
0.010410215705633163,
0.004273565486073494,
0.06441163271665573,
0.017175201326608658,
-0.020046835765242577,
-0.004823625553399324,
0.03697444126009941,
-0.026680639013648033,
0.053677722811698914,
-0.01490469928830862,
0.037892330437898636,
0.006141252350062132,
-0.00784506369382143,
-0.016216862946748734,
0.05665909871459007,
-0.06691278517246246,
0.006070575211197138,
0.00116504798643291,
-0.03212756663560867,
0.03517531603574753,
-0.07478541880846024,
0.017080897465348244,
0.009053226560354233,
-0.055439505726099014,
-0.0019058776088058949,
0.008148714900016785,
0.04536261409521103,
0.02964126504957676,
-0.014910268597304821,
0.03236611932516098,
0.02627544105052948,
-0.03927126154303551,
0.02631385624408722,
0.00953078456223011,
0.029441500082612038,
-0.018752453848719597,
-0.023661768063902855,
0.06152211129665375,
-0.014286983758211136,
0.017357707023620605,
-0.007125756703317165,
-0.019907070323824883,
-0.012080063112080097,
-0.052882708609104156,
-0.027584059163928032,
-0.011958233080804348,
0.006879050750285387,
0.032594580203294754,
-0.010651878081262112,
0.059358060359954834,
-0.033507995307445526,
-0.002187290694564581,
0.024474648758769035,
0.035835109651088715,
0.02819828875362873,
0.01049252413213253,
0.01989709585905075,
0.02547297812998295,
-0.005233935546129942,
-0.03261299803853035,
0.004570074379444122,
-0.007722653914242983,
0.005998186767101288,
-0.006524174939841032,
-0.001499697333201766,
-0.027424735948443413,
-0.014135725796222687,
-0.05594709888100624,
-0.04526621848344803,
-0.01904342509806156,
-0.006981691345572472,
0.05841409042477608,
0.040538638830184937,
-0.03687890246510506,
-0.05264579504728317,
0.003614465706050396,
-0.010579726658761501,
0.047991082072257996,
-0.04149020463228226,
0.009611373767256737,
-0.018869994208216667,
0.023934930562973022,
-0.0149792255833745,
0.002267050789669156
] |
<p>I should preface this by admitting that my physics background is rather weak so I beg you to keep that in mind in your responses. I work in mathematics (specifically probability theory) and a paper my adviser asked me to read dealt with a discrete approximation to the random Schrödinger operator $\Delta + V(x,\omega)$ where $V$ is some random function. The physical meaning of this object is completely beyond me at this point and I was hoping that someone here could shed some light on it.</p>
<p>The basic issues I am trying to work through now are what this actually models (one professor said something about 'disordered media') and whether there are physical reasons to believe that there should be universality of spectral statistics if one makes some kind of reasonable assumptions about the behavior of $V$. I know that proving the last statement rigorously is a major open question in mathematics, so I do want to emphasize that I am really just looking for a little hand-waving to help understand what is going on. </p>
<p>Based on a few explicitly solvable classes of discrete approximations in the limit, I want to say that universality should hold for some broad classes of $V$, depending on the rate of decay of $V$ since the limiting spectral statistics from the discrete approximations seem to have that property if everything is taken to be independent. I have been told that this is a somewhat common phenomenon in the study of Schrödinger operators, though again I don't really understand what is going on here.</p>
<p>Anything would help: links to good write-ups on the random (or not random) Schrödinger operator, a toy example that is illuminating, a suggestion on good papers to read--anything really.</p>
<p>Thanks :)</p>
| 8,271 |
[
-0.016332464292645454,
-0.05263141542673111,
0.015603036619722843,
-0.06435684114694595,
0.02951914630830288,
0.01080211903899908,
-0.03529427573084831,
-0.04367504268884659,
0.020440809428691864,
-0.06474006921052933,
0.024277128279209137,
0.016064094379544258,
0.0641118660569191,
-0.0027469806373119354,
0.032819222658872604,
0.020772680640220642,
-0.024781109765172005,
-0.03043670393526554,
-0.025459634140133858,
-0.013042168691754341,
0.025871839374303818,
0.0354311466217041,
0.04276609420776367,
-0.006481609307229519,
-0.036145202815532684,
0.0007558810175396502,
-0.009677696973085403,
0.019503500312566757,
0.03681785613298416,
0.057996343821287155,
-0.016158249229192734,
-0.004439390264451504,
-0.004641622770577669,
0.05904163792729378,
0.0055963764898478985,
0.007926958613097668,
-0.04017461836338043,
-0.047609150409698486,
0.01024174690246582,
-0.002142966026440263,
-0.05179294943809509,
-0.016443878412246704,
-0.023050785064697266,
0.023966172710061073,
0.0006983874482102692,
-0.011348343454301357,
0.011739743873476982,
-0.055928997695446014,
0.056051626801490784,
-0.018114838749170303,
0.06918050348758698,
-0.0059036328457295895,
0.06301423162221909,
0.03658595308661461,
0.006057324819266796,
0.01323269959539175,
0.06590604037046432,
0.07451928406953812,
-0.0035747603978961706,
-0.011505511589348316,
0.0029408724512904882,
-0.03358220309019089,
-0.008253873325884342,
-0.0014830977888777852,
-0.029543181881308556,
0.020327292382717133,
-0.017865395173430443,
-0.04575755447149277,
0.004702318925410509,
-0.028218520805239677,
0.018735889345407486,
0.02405271865427494,
0.05293995514512062,
-0.01581951603293419,
0.031966567039489746,
0.023158123716711998,
0.01657751016318798,
0.029594436287879944,
0.015201007016003132,
0.017107542604207993,
-0.034332238137722015,
-0.014443554915487766,
0.0015162307536229491,
0.014008350670337677,
0.0022555000614374876,
-0.031099412590265274,
0.06379086524248123,
-0.0331258587539196,
0.0036663529463112354,
0.04448793828487396,
-0.028967900201678276,
0.019589589908719063,
0.006675709970295429,
-0.0038999917451292276,
-0.10162463784217834,
0.023540310561656952,
0.025323182344436646,
0.04980091005563736,
0.00381550588645041,
-0.0367186963558197,
-0.009979546070098877,
-0.051835544407367706,
0.025661969557404518,
0.08182103931903839,
-0.0363316535949707,
-0.013306285254657269,
-0.05672796815633774,
0.003943643998354673,
-0.012358269654214382,
-0.03279659524559975,
-0.009004969149827957,
0.004630703013390303,
0.018110966309905052,
0.015032917261123657,
-0.015356302261352539,
0.008413759991526604,
0.003378041321411729,
-0.03533006086945534,
0.05432088300585747,
0.08637794107198715,
0.022411977872252464,
-0.034315623342990875,
0.032828189432621,
-0.06390642374753952,
-0.036104217171669006,
0.020296048372983932,
0.038956884294748306,
-0.016170751303434372,
-0.06472179293632507,
0.023630836978554726,
0.006880307570099831,
-0.008405044674873352,
0.03174089267849922,
0.0060760509222745895,
0.04612485319375992,
-0.05543214827775955,
-0.09524252265691757,
-0.04393409565091133,
0.03680578991770744,
-0.026025844737887383,
0.0018906882032752037,
-0.06294224411249161,
0.0024476360995322466,
0.0314779207110405,
0.05171776935458183,
-0.012755407020449638,
0.04106630012392998,
0.0008322044741362333,
0.01406013872474432,
0.029300715774297714,
-0.0022473353892564774,
-0.03724166750907898,
-0.007070083171129227,
-0.019918933510780334,
0.008586553856730461,
-0.056041426956653595,
0.02169855497777462,
0.003323793411254883,
0.015171566046774387,
-0.019108155742287636,
0.07341659814119339,
-0.03227980062365532,
0.0034524418879300356,
0.005642982665449381,
0.03191555663943291,
-0.03801964223384857,
0.08497756719589233,
0.025878295302391052,
0.03815894201397896,
0.023137448355555534,
-0.007266174536198378,
0.01116714347153902,
0.043693333864212036,
0.05845547467470169,
0.03139957785606384,
-0.02411465346813202,
0.01671616919338703,
-0.003481183899566531,
-0.010756193660199642,
0.02469632960855961,
-0.028260519728064537,
-0.010417325422167778,
-0.007072288542985916,
0.013493908569216728,
0.002102125436067581,
0.04272470995783806,
0.012617237865924835,
0.009922276251018047,
0.00492900051176548,
-0.05733807012438774,
0.016743702813982964,
-0.046220000833272934,
0.034204185009002686,
0.039170172065496445,
0.0006038077408447862,
0.0626959428191185,
0.008322559297084808,
0.016041917726397514,
0.007939793169498444,
-0.04154127463698387,
-0.0288284569978714,
-0.004461259115487337,
0.022001029923558235,
-0.033581990748643875,
0.03755732253193855,
0.045491356402635574,
0.041733335703611374,
-0.007111691404134035,
0.0541522279381752,
-0.011890840716660023,
-0.0572582483291626,
0.011134685948491096,
-0.01633433811366558,
0.04273326322436333,
0.0053441328927874565,
0.003745672758668661,
0.008959067054092884,
-0.041505418717861176,
-0.020355066284537315,
0.013108383864164352,
-0.03276646509766579,
0.025993041694164276,
0.04543296620249748,
0.015635157003998756,
-0.07269688695669174,
0.06621772795915604,
0.0066777667962014675,
0.00000675669571137405,
-0.008615843951702118,
-0.06092485412955284,
-0.06072055548429489,
0.026905210688710213,
0.06366855651140213,
0.06976813822984695,
-0.026949157938361168,
0.008988434448838234,
0.021254878491163254,
0.06422886997461319,
0.062189675867557526,
-0.008700902573764324,
-0.0386185459792614,
0.006998956203460693,
0.013827825896441936,
-0.006989277433604002,
0.027387697249650955,
0.01377187855541706,
-0.00612197769805789,
-0.010069996118545532,
0.018343079835176468,
-0.018999429419636726,
-0.01025409996509552,
0.0057433657348155975,
-0.011501970700919628,
-0.00035757277510128915,
-0.024508479982614517,
-0.020367136225104332,
0.03626231849193573,
-0.02672240138053894,
0.0021488936617970467,
0.04120184853672981,
-0.021435357630252838,
0.027184294536709785,
-0.06318450719118118,
-0.032720718532800674,
0.05852705240249634,
0.016362592577934265,
-0.05672632157802582,
-0.027269460260868073,
0.008472836576402187,
0.03040880151093006,
-0.01539151556789875,
-0.03407549858093262,
-0.006028174422681332,
-0.027984783053398132,
0.026643913239240646,
0.04273808375000954,
0.001284299069084227,
0.017120789736509323,
-0.03343512862920761,
-0.031366460025310516,
0.014222384430468082,
-0.016742315143346786,
-0.004162952769547701,
0.01639741286635399,
-0.016072653234004974,
0.0186235960572958,
-0.027547677978873253,
-0.013627087697386742,
0.02160160057246685,
0.017516300082206726,
-0.0052198790945112705,
-0.0418444387614727,
-0.033016007393598557,
-0.06233607977628708,
-0.006053771823644638,
0.007900248281657696,
0.007578868884593248,
-0.039668966084718704,
0.004202334675937891,
0.05799342319369316,
-0.01905685104429722,
-0.018598809838294983,
0.026279563084244728,
-0.006297154352068901,
-0.05728845298290253,
-0.033374685794115067,
-0.022416092455387115,
0.03302782028913498,
-0.04737825691699982,
0.04928159713745117,
0.028223223984241486,
-0.049262385815382004,
-0.03753124549984932,
-0.06564926356077194,
-0.056800540536642075,
0.011539717204868793,
-0.01550859771668911,
0.022885121405124664,
0.013471190817654133,
-0.021712686866521835,
0.0731874406337738,
0.021621188148856163,
-0.004883129615336657,
0.003970032557845116,
0.016705816611647606,
-0.0029925312846899033,
0.012259081937372684,
0.007637981791049242,
0.027969736605882645,
-0.013436877168715,
0.03545162454247475,
0.0036728805862367153,
0.039513278752565384,
0.017185157164931297,
-0.0034125633537769318,
-0.02234829030930996,
0.04828033968806267,
0.00502805644646287,
-0.006500841584056616,
0.01905839703977108,
0.013483664020895958,
-0.03264094144105911,
-0.009763998910784721,
-0.021100662648677826,
0.029892362654209137,
0.01348924171179533,
-0.06534679979085922,
0.059625785797834396,
0.029738089069724083,
0.025805721059441566,
-0.03978528454899788,
0.046871256083250046,
-0.0009290200541727245,
-0.03460857644677162,
0.0033355113118886948,
0.02499937266111374,
0.042195599526166916,
-0.0038648254703730345,
0.021290414035320282,
0.01359943114221096,
0.049604810774326324,
-0.01963680237531662,
-0.017089543864130974,
-0.007114761043339968,
0.017748480662703514,
0.0022607597056776285,
-0.029443390667438507,
-0.019747480750083923,
0.041433729231357574,
0.005577498115599155,
0.03263459354639053,
-0.0584869459271431,
-0.03892810270190239,
-0.003579749958589673,
-0.03467930108308792,
0.008141671307384968,
-0.03216404840350151,
0.03813127428293228,
0.005476284772157669,
0.03787454590201378,
0.019189078360795975,
0.0214201882481575,
0.02170589566230774,
0.007434125989675522,
-0.060012489557266235,
-0.007293348200619221,
-0.01335187442600727,
-0.004812679719179869,
-0.028711169958114624,
0.007598060183227062,
0.015492451377213001,
-0.005480858497321606,
-0.04498878866434097,
-0.01143453735858202,
0.010838852263987064,
-0.07262097299098969,
-0.0046045514754951,
-0.028870631009340286,
-0.03823656588792801,
-0.024849731475114822,
-0.005101044662296772,
0.014939154498279095,
-0.006429338362067938,
-0.010877657681703568,
0.0024119073059409857,
-0.011543669737875462,
-0.008915677666664124,
-0.045491188764572144,
0.01219064462929964,
0.02082797884941101,
-0.020743215456604958,
0.0552840530872345,
0.030842941254377365,
-0.01604674756526947,
0.019483530893921852,
0.019505254924297333,
0.0696251392364502,
0.02723998762667179,
-0.020966893061995506,
0.029885027557611465,
-0.055178117007017136,
-0.008663746528327465,
0.016706453636288643,
0.03375168517231941,
0.007412465754896402,
0.004118442069739103,
0.04664672911167145,
-0.001358683337457478,
-0.04843698814511299,
0.007960449904203415,
0.026062997058033943,
-0.03713206574320793,
-0.0029484101105481386,
-0.03098829835653305,
0.006371632684022188,
-0.003278637770563364,
0.011408069171011448,
0.012727710418403149,
-0.02452610433101654,
0.008194397203624249,
0.012361500412225723,
0.018514510244131088,
0.0033206455409526825,
-0.039952538907527924,
-0.049965642392635345,
-0.016884589567780495,
-0.0035206093452870846,
-0.021379098296165466,
-0.013710848055779934,
0.013832813128829002,
0.025308484211564064,
0.03818622976541519,
0.031711358577013016,
0.0077252695336937904,
-0.057516708970069885,
-0.00876996573060751,
0.0289845559746027,
0.013149012811481953,
-0.010547560639679432,
0.005014452151954174,
-0.03652371093630791,
-0.0012765335850417614,
0.051005903631448746,
0.009437820874154568,
0.0006986373919062316,
0.013468062505126,
-0.05075082555413246,
0.006678496953099966,
-0.05084997043013573,
0.003426516428589821,
0.023102443665266037,
0.03462832421064377,
0.03214925155043602,
-0.047249935567379,
-0.016441144049167633,
-0.05317619442939758,
0.03418773040175438,
0.011186806485056877,
0.07330746948719025,
-0.008022687397897243,
-0.005957427434623241,
0.0010306917829439044,
0.010050673969089985,
-0.004045302513986826,
-0.07046680152416229,
0.005736933089792728,
0.013897618278861046,
0.021206708624958992,
0.030941996723413467,
-0.03256049007177353,
-0.07270950078964233,
0.0374491810798645,
0.007500887848436832,
-0.03624862805008888,
0.011101088486611843,
-0.02415338158607483,
0.05739155039191246,
0.032166920602321625,
0.0042065707966685295,
0.04335930198431015,
0.053554512560367584,
0.01749645546078682,
-0.01773623749613762,
-0.0239888746291399,
0.06127200648188591,
-0.03280966356396675,
0.008883326314389706,
-0.061254311352968216,
-0.00946572981774807,
-0.015583549626171589,
0.04909520596265793,
-0.011433255858719349,
0.0026856078766286373,
-0.0063309739343822,
-0.04510095715522766,
-0.008266051299870014,
0.022721748799085617,
0.003290877677500248,
0.008792745880782604,
0.0010302329901605844,
0.010629481635987759,
-0.01707659661769867,
-0.01055151131004095,
-0.003519624937325716,
-0.009251074865460396,
-0.011953270994126797,
0.03655888885259628,
-0.014444854110479355,
-0.013142499141395092,
-0.04713665321469307,
-0.00234040804207325,
-0.0037914603017270565,
-0.07992945611476898,
0.017026780173182487,
-0.004712253343313932,
0.028705647215247154,
-0.009655628353357315,
-0.03579486906528473,
0.002137875184416771,
-0.01421426609158516,
-0.005761106498539448,
0.02728855051100254,
-0.01081889495253563,
-0.02996351756155491,
-0.008673184551298618,
0.012680528685450554,
-0.08277877420186996,
-0.06255056709051132,
-0.0020531450863927603,
0.014871779829263687,
-0.032106876373291016,
-0.04004599526524544,
0.04767924174666405,
-0.04645945504307747,
-0.007555386051535606,
0.020576834678649902,
0.03452013432979584,
-0.006195863708853722,
-0.015836266800761223,
0.023888545110821724,
0.03524792939424515,
0.058557599782943726,
-0.01188074890524149,
-0.011211234144866467,
0.0076496778056025505,
-0.033535074442625046,
0.0036337736528366804,
-0.004535053391009569,
0.05188393220305443,
-0.04894479364156723,
-0.03401695564389229,
-0.02677285671234131,
-0.005735521204769611,
0.02386932447552681,
-0.024576641619205475,
-0.02967737801373005,
0.01450872328132391,
-0.001680249348282814,
0.03460812568664551,
0.009311447851359844,
0.0040644025430083275,
0.009831098839640617,
0.018655577674508095,
0.02223757468163967,
0.03042171150445938,
-0.028217658400535583,
-0.04762959107756615,
0.041074685752391815,
0.004185079131275415,
-0.02378930151462555,
0.03942429646849632,
0.04528479278087616,
-0.0020931458566337824,
0.026089983060956,
0.015156435780227184,
-0.003108524950221181,
-0.009931451641023159,
0.010722635313868523,
0.027184968814253807,
0.0182900819927454,
-0.01277184672653675,
-0.002255828818306327,
-0.05682775005698204,
-0.05471184477210045,
0.04079343006014824,
0.027239318937063217,
-0.0074629634618759155,
0.017955811694264412,
0.030606048181653023,
0.0007340300362557173,
-0.021627219393849373,
-0.034469470381736755,
-0.03715438023209572,
0.006769739557057619,
-0.028231311589479446,
0.025213535875082016,
-0.03171396255493164,
-0.003177003003656864,
0.006529408972710371,
0.03371312841773033,
0.008522889576852322,
0.01201703306287527,
0.012977588921785355,
0.022483959794044495,
0.038393694907426834,
-0.015610702335834503,
-0.013177345506846905,
0.05508057028055191,
-0.01567552238702774,
0.03080867975950241,
0.01679929904639721,
-0.009518424049019814,
0.026483498513698578,
0.016880786046385765,
0.023427387699484825,
-0.028106611222028732,
-0.02237601764500141,
-0.038930803537368774,
0.03814408928155899,
0.0053329020738601685,
0.026429206132888794,
0.06083523854613304,
-0.013204417191445827,
0.0032912224996834993,
0.044418029487133026,
0.04091627523303032,
-0.004611213691532612,
-0.07544635236263275,
0.000691235123667866,
-0.004144397564232349,
-0.062236811965703964,
0.04765696078538895,
0.008476557210087776,
-0.014654678292572498,
0.0036397946532815695,
-0.06161800026893616,
0.03190995752811432,
0.005839275196194649,
0.004591486882418394,
-0.017453748732805252,
0.0473475344479084,
0.02390306629240513,
0.04552232846617699,
0.029883289709687233,
0.012167065404355526,
0.08971939980983734,
0.06272931396961212,
0.01738753356039524,
-0.06077222898602486,
-0.015941627323627472,
-0.011987882666289806,
0.008796476759016514,
-0.04204600304365158,
0.0033298637717962265,
0.018055476248264313,
-0.0326685756444931,
-0.021430926397442818,
0.03915715962648392,
0.005078976508229971,
-0.008200638927519321,
0.04049324616789818,
-0.06043332442641258,
-0.02870495431125164,
0.01932527869939804,
-0.011817718856036663,
0.020650865510106087,
0.0009454044047743082,
-0.015265151858329773,
0.037890978157520294,
-0.026584254577755928,
-0.009692062623798847,
-0.060643769800662994,
0.012585627846419811,
0.028481442481279373,
0.007610730826854706,
0.002065628068521619,
-0.02160177379846573,
0.011778012849390507,
0.003197396406903863,
-0.017148518934845924,
0.014253436587750912,
0.02724570780992508,
0.0091499462723732,
0.039207156747579575,
0.026019465178251266,
-0.022047488018870354,
-0.0017028627917170525,
0.042203497141599655,
0.011081005446612835,
-0.022540200501680374,
-0.06189192831516266,
-0.03334208205342293,
0.05942580848932266,
-0.025247547775506973,
0.011926808394491673,
-0.005999872460961342,
-0.007314041722565889,
0.00032171214115805924,
-0.051002733409404755,
-0.009649456478655338,
-0.0060509201139211655,
0.037857722491025925,
-0.017911570146679878,
0.010986313223838806,
-0.011267987079918385,
0.005493447184562683,
0.001613282598555088,
0.02433127537369728,
-0.006625599227845669,
-0.023956958204507828,
-0.014382170513272285,
-0.02176748774945736,
0.00025548003031872213,
0.0030025180894881487,
-0.030279768630862236,
-0.007488991133868694,
0.005954031366854906,
-0.03736879676580429,
-0.012691470794379711,
-0.001906015444546938,
0.005399087443947792,
0.05309809371829033,
0.01710405759513378,
0.002329387469217181,
0.0027515359688550234,
-0.09792407602071762,
0.014847787097096443,
-0.016621608287096024,
-0.028165889903903008,
-0.004106227774173021,
-0.011215021833777428,
-0.002231368562206626,
0.018073176965117455,
0.0001994673948502168,
0.012489410117268562,
-0.021597499027848244,
0.02277333103120327,
0.008821018040180206,
-0.01786164380609989,
-0.027616877108812332,
-0.00924907810986042,
-0.06439358741044998,
0.025074832141399384,
-0.004726733081042767,
-0.02882799133658409,
0.012799747288227081,
-0.012981097213923931,
0.015958847478032112,
0.04493606463074684,
-0.03220907226204872,
0.004246060270816088,
0.0033608197700232267,
-0.0633990690112114,
0.03833077847957611,
0.02626161091029644,
-0.008489911444485188,
-0.013012981973588467,
-0.05298977717757225,
-0.014728447422385216,
0.030771372839808464,
0.001376694766804576,
-0.0024604559876024723,
-0.020085586234927177,
-0.015895744785666466,
-0.02260676585137844,
0.03788544237613678,
-0.028492208570241928,
-0.026838915422558784,
-0.02591237612068653,
0.018746569752693176,
0.01941845752298832,
0.00635835574939847,
-0.0019625432323664427,
0.00887224543839693,
0.029374463483691216,
-0.03042907454073429,
0.03899732232093811,
0.043119922280311584,
0.00456738518550992,
-0.028918379917740822,
0.01642160303890705,
-0.02288202941417694,
0.054007094353437424,
-0.00752235297113657,
-0.0633309856057167,
0.05132223293185234,
-0.03479954972863197,
-0.04652031138539314,
0.020944159477949142,
-0.03283582255244255,
0.02031109854578972,
0.037395600229501724,
-0.02142040804028511,
-0.019719071686267853,
0.06345964968204498,
-0.02824685350060463,
-0.00853897538036108,
-0.0005964560550637543,
-0.012235607020556927,
-0.012555376626551151,
0.02417970634996891,
0.009536675177514553,
0.03361881151795387,
0.013393411412835121,
0.011332045309245586,
0.05295712873339653,
-0.004152402281761169,
0.002048376016318798,
0.027119316160678864,
-0.012770842760801315,
0.040430158376693726,
0.02613709680736065,
0.0336398184299469,
0.010395601391792297,
0.058191560208797455,
-0.03879169747233391,
0.04437999427318573,
0.03720810264348984,
-0.0011096516391262412,
-0.11387120187282562,
-0.017619524151086807,
0.02118777483701706,
0.03181985765695572,
0.00806086789816618,
-0.051600925624370575,
-0.015068160369992256,
0.01093229278922081,
-0.050165239721536636,
0.025359954684972763,
-0.017229439690709114,
-0.017725203186273575,
-0.05513943359255791,
0.022173771634697914,
-0.0728265792131424,
0.008624495007097721,
0.020689982920885086,
0.044042427092790604,
0.017326703295111656,
0.03370337188243866,
-0.027733827009797096,
-0.007895050570368767,
-0.015483519993722439,
0.043859634548425674,
-0.007644467521458864,
0.03132094815373421,
0.03981255367398262,
-0.01405810285359621,
-0.019655488431453705,
0.026925651356577873,
0.013118681497871876,
-0.016885310411453247,
0.0011217092396691442,
0.029225165024399757,
-0.010115105658769608,
-0.00406645517796278,
0.033487603068351746,
-0.007743293885141611,
-0.006991683039814234,
0.0036010511685162783,
0.04117566719651222,
0.029782427474856377,
-0.024853412061929703,
-0.002420094795525074,
0.021472709253430367,
-0.04298371076583862,
-0.018980154767632484,
0.05367986112833023,
0.010488537140190601,
0.011106079444289207,
0.013370458967983723,
0.0020301195327192545,
0.0137063292786479,
0.008234226144850254,
0.04064590483903885,
-0.051823414862155914,
-0.03373601660132408,
0.026431627571582794,
0.04547375068068504,
0.0077471863478422165,
0.01435541920363903,
-0.03078409656882286,
-0.04191824048757553,
-0.0017180136637762189,
0.0016867684898898005,
-0.022710012272000313,
-0.03321234509348869,
-0.0026869582943618298,
-0.001192570198327303,
0.03789142519235611,
0.0027159887831658125,
-0.024601494893431664,
-0.03482414782047272,
0.008679822087287903,
-0.01814286597073078,
0.024213841184973717,
-0.056527525186538696,
-0.04086025804281235,
-0.06272908300161362,
-0.07841779291629791,
0.04161945357918739,
0.004529894329607487,
-0.012007595971226692,
-0.042126547545194626,
0.005216002929955721,
0.004046119749546051,
0.03884239122271538,
0.03240014985203743,
0.008410402573645115,
-0.022105351090431213,
0.014312505722045898,
0.007734684273600578,
0.028471335768699646,
-0.017960891127586365,
-0.0010688458569347858,
-0.02384333685040474,
0.013485188595950603,
-0.034213315695524216,
-0.007804887369275093,
0.008370224386453629,
0.00728653883561492,
0.031088724732398987,
-0.010672527365386486,
-0.038858551532030106,
0.005595293361693621,
-0.05131300538778305,
0.08288536220788956,
0.010807787999510765,
-0.0014821419026702642,
0.04590306058526039,
-0.022255446761846542,
0.03693555295467377,
-0.004584159702062607,
0.009171415120363235,
-0.018695274367928505,
0.008758440613746643,
-0.026025623083114624,
-0.016474341973662376,
0.004235394764691591,
0.022368190810084343,
-0.005888426676392555,
-0.01869591325521469,
-0.004459036979824305,
0.028087684884667397,
-0.04231438785791397,
-0.02639792114496231,
0.028609624132514,
0.016857698559761047,
0.03406132757663727,
0.011699795722961426,
-0.0035172507632523775,
0.04905279725790024,
0.05504114553332329,
0.0006460544536821544,
0.045744817703962326,
0.049146220088005066,
-0.0016197850927710533,
0.050580739974975586,
-0.0034937774762511253,
-0.04023969545960426,
0.029222598299384117,
-0.003154634265229106,
-0.01525095384567976,
-0.06693800538778305,
0.014927241951227188,
0.05330405384302139,
0.0011048989836126566,
-0.053704939782619476,
0.016571437940001488,
-0.007634588051587343,
0.08465810865163803,
0.005470286589115858,
0.018645059317350388,
-0.04553947225213051,
-0.014618471264839172,
0.017028555274009705,
0.02061028778553009,
0.006962483748793602,
0.0027987563516944647,
-0.03380511328577995,
0.030294807627797127,
-0.012167582288384438,
0.01898859441280365,
0.03295043110847473,
-0.04911700263619423,
0.004158474039286375,
-0.0028073471039533615,
-0.029912611469626427,
-0.008138198405504227,
-0.005163270980119705,
-0.007337518967688084,
-0.008796886540949345,
-0.005793056450784206,
0.048234276473522186,
0.026593098416924477,
0.0026041839737445116,
-0.021916188299655914,
-0.01246376521885395,
0.04768123850226402,
-0.05937657877802849,
0.003887566737830639,
-0.04752938821911812,
0.026425490155816078,
-0.012629234232008457,
-0.01236544456332922
] |
<p>Relativistic mass $\displaystyle m(v)=\frac{m_o}{\sqrt{(1-(v/c)^2}}$ </p>
<p>$m_o$ = mass of object measured at rest<br>
$c$ = speed of light ($3\times 10^8\;m/s$)<br>
$v$ = speed</p>
<p>If the total relativistic energy of an object is given by $E=mc^2$, then find the second-order Taylor approximation of $E(v)$. The zeroth-order term is called the "rest energy." What is the second-order term usually called?</p>
| 8,272 |
[
-0.017590714618563652,
-0.07174830138683319,
0.016147704795002937,
-0.017487000674009323,
0.04416492208838463,
0.019054098054766655,
-0.03979458659887314,
-0.057297054678201675,
-0.007487634662538767,
-0.047621771693229675,
0.03014366701245308,
0.03580223023891449,
0.05799024552106857,
0.02803667075932026,
0.016901616007089615,
0.016623303294181824,
0.01879987306892872,
-0.0235590860247612,
-0.038999930024147034,
-0.016649087890982628,
0.014347563497722149,
-0.016411367803812027,
0.015427639707922935,
0.027739232406020164,
-0.021594898775219917,
0.040941592305898666,
0.045098677277565,
0.0023007290437817574,
0.05072186514735222,
0.03321311995387077,
-0.045004650950431824,
-0.012227375991642475,
-0.009805341251194477,
0.011526067741215229,
0.03310635685920715,
0.04349735379219055,
-0.011621164157986641,
-0.028803735971450806,
0.016865048557519913,
0.026819342747330666,
-0.03181394934654236,
-0.04322660714387894,
0.012715214863419533,
0.016026131808757782,
-0.024037694558501244,
0.01372136827558279,
0.027869921177625656,
-0.036718446761369705,
0.05140987038612366,
-0.017690572887659073,
0.0656147450208664,
0.016692550852894783,
0.02271362766623497,
-0.006653251126408577,
-0.023646155372262,
-0.00962789636105299,
0.052045270800590515,
0.06468822807073593,
-0.0006429057684727013,
-0.040987998247146606,
-0.017393553629517555,
-0.0037066142540425062,
-0.01368927862495184,
0.0066020190715789795,
0.03771110624074936,
0.03245484083890915,
-0.001315486733801663,
0.01560181099921465,
0.02621745504438877,
0.004210295155644417,
0.016966845840215683,
0.00024224072694778442,
0.024069245904684067,
-0.03201542794704437,
0.008206585422158241,
-0.027491725981235504,
0.007214367389678955,
0.01290934719145298,
0.03162155672907829,
0.02996116131544113,
-0.006922226399183273,
0.008274714462459087,
0.05699043348431587,
0.04307554289698601,
-0.0022563813254237175,
0.005509910639375448,
0.06747009605169296,
0.04623831436038017,
0.004492986015975475,
0.02002517506480217,
0.010443137027323246,
0.036630235612392426,
0.010002336464822292,
-0.037012744694948196,
0.00029859112692065537,
0.04179416969418526,
-0.028143715113401413,
0.03048563562333584,
0.0011262637563049793,
-0.0035010625142604113,
-0.017461592331528664,
0.008881285786628723,
0.009240792132914066,
0.07752931863069534,
0.017543533816933632,
-0.05368383601307869,
-0.06447454541921616,
0.005051771178841591,
-0.05031704902648926,
-0.0115217175334692,
-0.013408550061285496,
-0.005273005925118923,
0.0031659191008657217,
0.007501001935452223,
-0.022814486175775528,
-0.01927572675049305,
0.018379218876361847,
0.002591104945167899,
0.06302858889102936,
0.03478751704096794,
0.03609204292297363,
-0.008021308109164238,
0.006359536666423082,
0.00508887367323041,
-0.0757572203874588,
0.02160547487437725,
0.03213805705308914,
-0.046288177371025085,
-0.049334537237882614,
0.01092261727899313,
-0.006147895008325577,
-0.017385657876729965,
-0.029049808159470558,
0.004058323800563812,
0.011750010773539543,
-0.02073904126882553,
-0.09397736191749573,
-0.06895683705806732,
-0.00042907841270789504,
-0.009372497908771038,
-0.005373709835112095,
-0.052309054881334305,
0.022811144590377808,
0.05459332466125488,
0.07593556493520737,
0.019723569974303246,
-0.027304913848638535,
-0.026770934462547302,
0.05631589889526367,
-0.022160422056913376,
0.003640060778707266,
-0.04369307681918144,
0.0012757991207763553,
-0.013157594949007034,
0.027056023478507996,
-0.07167325913906097,
-0.03375740721821785,
0.032894060015678406,
-0.012332161888480186,
-0.010501005686819553,
0.08785396069288254,
-0.029568884521722794,
-0.023919662460684776,
0.0070779770612716675,
-0.026084423065185547,
-0.013443730771541595,
0.039104215800762177,
0.007200474385172129,
0.0341268926858902,
0.05589456483721733,
0.033105332404375076,
0.0437810942530632,
0.0009351578773930669,
0.04117407649755478,
0.03745497018098831,
-0.049394648522138596,
-0.048814237117767334,
-0.032875906676054,
0.0015208744443953037,
0.02443300001323223,
-0.055675920099020004,
-0.06367305666208267,
0.014058352448046207,
0.00928728748112917,
0.006667830981314182,
0.023868901655077934,
0.001629308215342462,
0.022347768768668175,
0.0010034013539552689,
-0.011647465638816357,
0.02437431365251541,
-0.034868501126766205,
0.026036709547042847,
0.00225419201888144,
-0.0014763701474294066,
-0.02617538347840309,
0.0037425626069307327,
0.01631910540163517,
-0.017887087538838387,
0.011187885887920856,
0.0008766603423282504,
0.07944627106189728,
-0.011972525157034397,
0.004205469042062759,
0.03067845292389393,
0.046355150640010834,
0.04470142349600792,
-0.01696859672665596,
-0.026661593466997147,
-0.012316038832068443,
-0.04658197611570358,
-0.017235200852155685,
-0.0065836976282298565,
0.03529725596308708,
-0.03447903320193291,
0.002584954723715782,
0.007765414658933878,
-0.010544337332248688,
0.014874238520860672,
0.04607469588518143,
0.015737660229206085,
0.033188510686159134,
0.051456522196531296,
0.005886180326342583,
-0.0013212014455348253,
0.032882627099752426,
-0.008838022127747536,
0.03580150008201599,
-0.03157322481274605,
-0.0013516274048015475,
-0.032096702605485916,
-0.025278622284531593,
0.04244374483823776,
0.04086889326572418,
-0.060835547745227814,
0.026650287210941315,
0.06377469748258591,
0.039995621889829636,
0.05988454818725586,
0.004070598632097244,
-0.05386822670698166,
-0.06353271752595901,
0.03657901659607887,
0.008626020513474941,
-0.015567938797175884,
0.0320509634912014,
0.0490061491727829,
0.006097764708101749,
0.008081828244030476,
0.02693275734782219,
0.004938006401062012,
0.030428892001509666,
0.02025536634027958,
-0.01399165764451027,
0.009943660348653793,
-0.07231064140796661,
0.030249452218413353,
-0.038687948137521744,
0.03371874988079071,
0.006146259140223265,
-0.02028643526136875,
0.01092537771910429,
-0.018392056226730347,
-0.023446952924132347,
-0.007731892168521881,
-0.017676517367362976,
0.013911792077124119,
-0.015857545658946037,
0.025761647149920464,
-0.055709484964609146,
-0.01925070583820343,
-0.016323963180184364,
-0.023529216647148132,
-0.029832879081368446,
-0.0076254988089203835,
0.03259401023387909,
-0.0055482042953372,
0.032522521913051605,
-0.013832307420670986,
-0.030914369970560074,
-0.0070898993872106075,
-0.05056408792734146,
-0.029156498610973358,
-0.008680853992700577,
-0.03091706708073616,
0.04888014867901802,
-0.006966857239603996,
-0.06624586880207062,
0.008752554655075073,
0.03565641865134239,
0.010503004305064678,
0.07184494286775589,
-0.0013562795938923955,
-0.059667784720659256,
0.01997382752597332,
-0.003955288790166378,
-0.039863232523202896,
-0.03657035902142525,
0.0046396092511713505,
0.04370413348078728,
-0.001364006893709302,
-0.03783591836690903,
0.010924275033175945,
-0.053183771669864655,
0.003184181172400713,
-0.011145392432808876,
-0.013891184702515602,
0.04846136271953583,
-0.023442339152097702,
0.04396117106080055,
0.006104171741753817,
0.0074761491268873215,
0.01574261486530304,
-0.055560581386089325,
-0.03833543509244919,
0.018121981993317604,
-0.018855778500437737,
0.03158634901046753,
0.004780691582709551,
-0.02165009081363678,
0.08055147528648376,
0.0285634845495224,
-0.006942535284906626,
-0.02799743413925171,
-0.00040504863136447966,
0.05100245401263237,
-0.023859640583395958,
0.0034594666212797165,
-0.003468343522399664,
-0.02050097845494747,
-0.05530707165598869,
0.007181315682828426,
0.02817722037434578,
0.028981724753975868,
0.001914618769660592,
0.011148220859467983,
0.007471111603081226,
-0.004592034965753555,
-0.035758115351200104,
0.051996488124132156,
-0.009606343694031239,
-0.03596522659063339,
0.03436856344342232,
0.011049971915781498,
0.0660308226943016,
0.011008631438016891,
-0.024514520540833473,
0.03667369484901428,
0.014673665165901184,
-0.00975373387336731,
-0.01172205712646246,
0.04789843037724495,
0.0008460985263809562,
-0.04629049450159073,
0.005133983213454485,
-0.017460143193602562,
0.02023373730480671,
0.009228686802089214,
-0.011597961187362671,
0.0065293144434690475,
0.07245512306690216,
-0.017044944688677788,
-0.03416740521788597,
-0.02802724577486515,
0.005181177984923124,
-0.013731351122260094,
-0.05661068856716156,
0.0009141821647062898,
0.03180808946490288,
0.024676330387592316,
0.03314922749996185,
0.009977269917726517,
-0.027537979185581207,
-0.007044362369924784,
-0.05751383677124977,
-0.02522718533873558,
-0.025432467460632324,
0.031938791275024414,
-0.023738672956824303,
0.055501729249954224,
0.016049286350607872,
0.029162026941776276,
0.05147193744778633,
0.01673131063580513,
-0.0656755194067955,
0.03173549473285675,
-0.015471450984477997,
-0.009920746088027954,
0.001172472140751779,
0.038202233612537384,
-0.03936764597892761,
-0.02535061538219452,
0.02620851807296276,
-0.017693420872092247,
0.002342707710340619,
-0.00858218688517809,
0.030371857807040215,
-0.03809970244765282,
-0.030917229130864143,
0.02982291392982006,
-0.0008060872787609696,
0.05282532051205635,
-0.010753979906439781,
0.01477040071040392,
0.04004243016242981,
-0.00918715912848711,
0.0006127433734945953,
-0.030928608030080795,
-0.04730867221951485,
0.01780535653233528,
0.023264218121767044,
0.03726712241768837,
-0.0016866669757291675,
-0.0030950522050261497,
0.022243034094572067,
0.0005688295350410044,
0.057435207068920135,
-0.0006884710746817291,
-0.008634570054709911,
-0.014943521469831467,
-0.003351195715367794,
0.004735492169857025,
-0.022728215903043747,
0.03981046751141548,
-0.02827460877597332,
0.029313335195183754,
-0.02270607091486454,
-0.0050912173464894295,
-0.010311931371688843,
0.04863075539469719,
0.042153049260377884,
-0.009011218324303627,
-0.03010559268295765,
-0.04766758531332016,
0.01363331824541092,
-0.04513471573591232,
-0.006090026348829269,
0.00092399149434641,
0.018033228814601898,
-0.021990779787302017,
0.023468395695090294,
-0.010638335719704628,
0.0104559026658535,
-0.024281414225697517,
-0.007994219660758972,
-0.002507206052541733,
0.027501458302140236,
-0.021170493215322495,
-0.02303885482251644,
-0.0547960102558136,
0.013914328999817371,
0.06204679608345032,
-0.024533988907933235,
0.010810893960297108,
-0.07533033937215805,
-0.011866685003042221,
0.013721063733100891,
0.06447267532348633,
-0.0063868323341012,
-0.01704934984445572,
-0.056144967675209045,
-0.01397586427628994,
0.02216547355055809,
-0.029786819592118263,
0.02445758506655693,
-0.033403508365154266,
0.009277360513806343,
-0.04124369099736214,
-0.023185918107628822,
-0.048505749553442,
0.0027761096134781837,
-0.018475212156772614,
-0.013384459540247917,
-0.008335423655807972,
0.023199722170829773,
-0.003425008151680231,
0.01767522282898426,
0.035352785140275955,
0.017201686277985573,
0.003525919048115611,
0.003914630971848965,
-0.015908120200037956,
-0.0013304924359545112,
-0.04324512928724289,
-0.06267837435007095,
-0.02674802765250206,
0.005533745512366295,
-0.03266336768865585,
0.025808652862906456,
-0.0387570895254612,
-0.05036681517958641,
0.003975058905780315,
0.013594754040241241,
-0.04216185584664345,
-0.021073218435049057,
-0.049885597079992294,
0.03388417884707451,
0.032103992998600006,
-0.014100098982453346,
0.05823691934347153,
0.029407989233732224,
-0.004919788800179958,
-0.01075652800500393,
-0.04244367033243179,
0.016882987692952156,
0.0018622230272740126,
0.0006900618318468332,
-0.011543819680809975,
-0.015674754977226257,
-0.04795777425169945,
0.04379258304834366,
-0.01637096516788006,
0.030411722138524055,
0.002745213685557246,
-0.006046258844435215,
-0.03108837455511093,
0.05633402615785599,
-0.004302935674786568,
0.018885990604758263,
0.0015898292185738683,
-0.012767530977725983,
-0.01739312708377838,
0.0157952718436718,
0.01565886102616787,
0.016713591292500496,
0.014759480021893978,
0.02412988618016243,
0.003894959343597293,
0.06606870889663696,
-0.018995016813278198,
0.023500753566622734,
0.046015653759241104,
-0.06825795024633408,
0.04334073141217232,
0.01588827557861805,
-0.01237619761377573,
0.007331492844969034,
-0.017282553017139435,
-0.045854099094867706,
0.009093781001865864,
0.0009310443419963121,
-0.016014613211154938,
-0.027853786945343018,
0.008820041082799435,
0.05193658173084259,
0.038322702050209045,
-0.04746450483798981,
-0.028901714831590652,
0.03909856081008911,
-0.023834867402911186,
0.0011829077266156673,
0.007802268024533987,
0.007655701134353876,
-0.0211750827729702,
-0.02179563231766224,
0.017934201285243034,
0.07988494634628296,
-0.009788831695914268,
-0.007775465026497841,
-0.04445692524313927,
0.009612458758056164,
0.010333308950066566,
0.0038556731306016445,
-0.05297236517071724,
0.010324249975383282,
-0.003743533045053482,
-0.010034903883934021,
0.02870035730302334,
0.08657412230968475,
-0.007222623564302921,
-0.005846792366355658,
-0.02351907268166542,
0.023512711748480797,
-0.0047965627163648605,
0.0243862085044384,
-0.010840845294296741,
0.0677923634648323,
0.05474693700671196,
-0.018778806552290916,
-0.013827829621732235,
0.022466441616415977,
0.021814260631799698,
0.05681510269641876,
0.0057932185009121895,
-0.0022613550536334515,
-0.05752073973417282,
-0.042124196887016296,
0.03631068766117096,
0.013124240562319756,
0.023391129449009895,
-0.032121963798999786,
0.07849304378032684,
-0.02073942869901657,
0.01969982497394085,
0.004702725447714329,
-0.0064181974157691,
0.00019759428687393665,
-0.006660970393568277,
-0.012663139961659908,
0.021291028708219528,
0.012227324768900871,
-0.021935729309916496,
0.01866202801465988,
-0.016508925706148148,
-0.011792308650910854,
0.09625128656625748,
-0.020515156909823418,
0.07151360809803009,
-0.005111983511596918,
-0.021276799961924553,
0.013153055682778358,
-0.029766926541924477,
-0.06111321598291397,
-0.02506764978170395,
-0.01276159007102251,
0.04281056299805641,
-0.009871989488601685,
-0.029548397287726402,
0.024248724803328514,
0.0600571483373642,
-0.03618329390883446,
0.010282432660460472,
0.02736882120370865,
0.0351693220436573,
-0.007320580538362265,
-0.04540032893419266,
-0.01799895614385605,
0.023247241973876953,
-0.022130262106657028,
0.013090120628476143,
0.011395493522286415,
-0.0003890118096023798,
0.03496747836470604,
-0.0009877994889393449,
0.02211024798452854,
-0.04626398906111717,
0.0073559158481657505,
-0.06547866761684418,
0.013647819869220257,
0.00854749046266079,
-0.017183298245072365,
-0.01490417867898941,
-0.007547034882009029,
-0.004531019367277622,
0.002498376416042447,
0.028463993221521378,
-0.01949986442923546,
-0.046763140708208084,
-0.013743150047957897,
-0.014262313954532146,
-0.04615648835897446,
0.03415713459253311,
-0.0060511184856295586,
-0.01723243109881878,
0.0034478793386369944,
-0.015109545551240444,
0.026068396866321564,
0.035392362624406815,
0.02644575573503971,
-0.022249704226851463,
0.0478573739528656,
0.0076942541636526585,
-0.03346759080886841,
0.016088854521512985,
0.010121450759470463,
0.12090999633073807,
0.04069406911730766,
0.014281305484473705,
-0.027090750634670258,
0.028333134949207306,
-0.02488401159644127,
0.01854834146797657,
-0.04502471536397934,
0.004073088523000479,
-0.025856396183371544,
0.031525131314992905,
0.025237057358026505,
0.025689763948321342,
-0.02395670861005783,
-0.0022065129596740007,
0.027479320764541626,
-0.009124789386987686,
-0.04987426474690437,
-0.018213044852018356,
0.0162843968719244,
-0.02134694904088974,
0.02866024523973465,
-0.003336576744914055,
0.028653576970100403,
-0.020966647192835808,
-0.007007274776697159,
-0.024640290066599846,
-0.032578740268945694,
0.023328760638833046,
-0.013998002745211124,
-0.027597906067967415,
0.03770502284169197,
0.016369236633181572,
0.009541426785290241,
-0.02305242419242859,
0.05063193663954735,
0.04409285634756088,
0.015524552203714848,
0.018171098083257675,
0.004877645056694746,
-0.005528632551431656,
0.017387431114912033,
0.010659961961209774,
0.03512302786111832,
-0.07358453422784805,
0.023279305547475815,
-0.0306785199791193,
0.03218305855989456,
-0.02104124240577221,
-0.020610079169273376,
-0.005791428033262491,
-0.00328652560710907,
-0.004393395502120256,
-0.02614882029592991,
-0.000686893064994365,
-0.0033901091665029526,
-0.0046273497864604,
0.0057886079885065556,
-0.010523413307964802,
-0.05687228962779045,
0.00943280104547739,
-0.013075622729957104,
0.007314909715205431,
0.015392121858894825,
0.010608246549963951,
-0.02805209532380104,
-0.0018630613340064883,
0.05731469392776489,
-0.02580459788441658,
-0.0054372153244912624,
0.01795499213039875,
-0.04888732731342316,
-0.04246737062931061,
0.0009630030253902078,
-0.009650476276874542,
0.020619096234440804,
0.028459371998906136,
-0.011069530621170998,
-0.0009907068451866508,
-0.07242171466350555,
-0.08353922516107559,
0.012952854856848717,
-0.004755428526550531,
-0.01762048900127411,
-0.03132383152842522,
0.0020848317071795464,
-0.004431086126714945,
0.03051479533314705,
-0.0255501177161932,
0.030421359464526176,
0.02002202533185482,
0.019746558740735054,
-0.013904256746172905,
-0.004938883241266012,
-0.018925989046692848,
0.01988418772816658,
0.013528227806091309,
-0.017061349004507065,
-0.03600813448429108,
0.012577665038406849,
0.011627551168203354,
0.024568084627389908,
-0.0010559868533164263,
-0.0034282964188605547,
-0.03940875828266144,
0.012277371250092983,
0.03237878531217575,
-0.023296188563108444,
0.034721069037914276,
0.027415921911597252,
0.011443016119301319,
-0.04629352688789368,
0.005302226636558771,
-0.02096889540553093,
-0.015601021237671375,
-0.03431185334920883,
0.05008834972977638,
-0.03459731489419937,
0.0018861867720261216,
-0.03776330500841141,
0.014617828652262688,
-0.05265098810195923,
0.02185487188398838,
-0.021884961053729057,
0.05275416746735573,
-0.008098904974758625,
-0.03167764097452164,
-0.03504788503050804,
0.016836412250995636,
-0.00038688763743266463,
0.016588125377893448,
0.008470614440739155,
0.016980983316898346,
-0.008787315338850021,
-0.022995082661509514,
-0.007134177256375551,
0.005121686030179262,
0.04701479896903038,
-0.006905487738549709,
-0.029049213975667953,
0.018875431269407272,
-0.0603746734559536,
-0.03774026036262512,
0.015781152993440628,
0.002769595943391323,
0.03267022594809532,
0.0150305712595582,
-0.02421615831553936,
0.003321420168504119,
0.056777406483888626,
-0.04060884565114975,
-0.050211820751428604,
-0.008508953265845776,
-0.06342111527919769,
0.006570948753505945,
0.03441966697573662,
0.022991467267274857,
-0.0069647072814404964,
-0.017543276771903038,
0.05717471241950989,
-0.0003323848941363394,
-0.03353434056043625,
0.01819659397006035,
0.021053330972790718,
-0.021998055279254913,
0.011478682048618793,
0.011366620659828186,
0.030681166797876358,
0.01686621829867363,
0.048904016613960266,
-0.005827574525028467,
0.05882791057229042,
0.00016778020653873682,
-0.015910916030406952,
-0.10473158210515976,
-0.009904398582875729,
-0.03163382411003113,
0.016810830682516098,
0.02474764920771122,
-0.010377515107393265,
0.019198894500732422,
0.014318142086267471,
-0.03373420238494873,
0.0480908639729023,
-0.020716698840260506,
-0.002303025685250759,
0.00879127811640501,
-0.0041444068774580956,
-0.03051115572452545,
0.05566773936152458,
0.038261257112026215,
0.04161321371793747,
0.053523194044828415,
-0.008269141428172588,
0.0017925555584952235,
-0.034819215536117554,
0.027246663346886635,
0.041651833802461624,
-0.008773396722972393,
-0.0391388013958931,
0.05520555004477501,
-0.041764210909605026,
0.005143186543136835,
0.051901888102293015,
0.018471498042345047,
0.02470216155052185,
-0.05067523196339607,
0.019653460010886192,
-0.016649337485432625,
0.031130831688642502,
0.008968552574515343,
-0.026810387149453163,
-0.02423790842294693,
0.009036807343363762,
0.02241693064570427,
0.015059486031532288,
-0.017841491848230362,
-0.029806142672896385,
0.04555802792310715,
-0.008448782376945019,
-0.045588281005620956,
0.06153228506445885,
-0.02586038038134575,
-0.06455767899751663,
0.009551399387419224,
-0.006121613085269928,
-0.020549291744828224,
-0.015714548528194427,
-0.004440054297447205,
-0.04901919886469841,
-0.01495139580219984,
0.025764981284737587,
-0.03830880671739578,
-0.029375191777944565,
0.013687402941286564,
0.024171076714992523,
0.00924751814454794,
0.0038463918026536703,
-0.00841850508004427,
-0.020928747951984406,
-0.03226138651371002,
-0.020094169303774834,
0.0533699132502079,
0.011989383026957512,
-0.017532924190163612,
-0.006629049777984619,
-0.022910404950380325,
0.09154339879751205,
0.0034413388930261135,
-0.011679409071803093,
-0.01683780364692211,
-0.02288183942437172,
0.004113195929676294,
-0.0758628323674202,
0.008680169470608234,
0.03566642478108406,
-0.023020684719085693,
-0.0396050326526165,
-0.024445125833153725,
0.0058185332454741,
0.011626209132373333,
0.07930751889944077,
0.03497065231204033,
-0.04084336757659912,
-0.019780831411480904,
-0.011586401611566544,
0.01405477523803711,
-0.061192259192466736,
-0.0217830128967762,
-0.008399100042879581,
-0.03403529152274132,
0.0054692430421710014,
0.02036217227578163,
-0.031785499304533005,
0.008869718760251999,
0.009580529294908047,
0.012166323140263557,
0.020531540736556053,
-0.0065657878294587135,
0.0010044729569926858,
0.03000938519835472,
0.006577641703188419,
-0.03363918140530586,
0.07690928876399994,
-0.002090821973979473,
0.055534977465867996,
0.0425715446472168,
-0.027422256767749786,
-0.026398641988635063,
-0.009648707695305347,
-0.022578218951821327,
-0.017134249210357666,
-0.03209162876009941,
-0.04019630700349808,
0.028888441622257233,
-0.046062879264354706,
0.016249574720859528,
0.056915879249572754,
-0.03502410650253296,
-0.017374124377965927,
0.06112578511238098,
0.03947426378726959,
0.042354874312877655,
0.021732043474912643,
0.029847148805856705,
-0.012646829709410667,
-0.03331812843680382,
0.006906823255121708,
0.03665613383054733,
0.03511775657534599,
-0.011257361620664597,
0.019723471254110336,
0.041562046855688095,
-0.028091084212064743,
-0.029249295592308044,
-0.01280624233186245,
-0.0051096174865961075,
-0.021086135879158974,
-0.027090461924672127,
0.018739184364676476,
-0.02529636025428772,
0.03355121985077858,
0.02217303030192852,
-0.013765745796263218,
0.06271108239889145,
-0.00898920651525259,
0.02491101622581482,
-0.03276190534234047,
0.0022771970834583044,
-0.01596103422343731,
0.019833754748106003,
0.0013576127821579576,
0.04478554055094719,
0.038588996976614,
0.0050339591689407825,
-0.031207285821437836,
-0.04377880319952965,
0.016280341893434525,
-0.028628967702388763,
0.027437100186944008,
0.023890569806098938,
0.0034130665007978678,
-0.038346581161022186,
-0.00010605930583551526,
-0.0338471382856369,
-0.05820348113775253,
0.015030888840556145,
0.029757805168628693,
0.011815167032182217,
-0.004873140249401331,
0.0010322565212845802,
-0.005528468172997236,
0.04228980839252472,
-0.06892485916614532,
-0.01465810276567936,
-0.010849211364984512,
-0.017417825758457184,
-0.02253197506070137,
-0.030181409791111946
] |
<p>Framework</p>
<p>If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T.</p>
<p>Question</p>
<p>With a rocket, could you launch the cable from the surface of the Earth without exceeding the tensile strength T?</p>
<p><img src="http://i.stack.imgur.com/TJsxr.jpg" alt="enter image description here"></p>
| 8,273 |
[
-0.0168780367821455,
0.020396091043949127,
0.011567872948944569,
-0.0037683809641748667,
0.01996992528438568,
0.013650069944560528,
-0.007094714790582657,
-0.025778528302907944,
0.019587652757763863,
-0.012995237484574318,
0.05282038822770119,
0.02968384511768818,
0.009861699305474758,
-0.005269119516015053,
-0.0020502335391938686,
0.0028348304331302643,
-0.004133363254368305,
-0.017671484500169754,
-0.026187125593423843,
-0.013379824347794056,
0.011757325381040573,
-0.0002126451872754842,
-0.03825676813721657,
0.021273016929626465,
0.0011979300761595368,
0.025727123022079468,
0.06794716417789459,
-0.02701367437839508,
-0.011066680774092674,
0.05730604752898216,
-0.028736863285303116,
-0.0009655125322751701,
0.01650841534137726,
0.001136648585088551,
0.04860198497772217,
0.02088213339447975,
-0.02930937148630619,
-0.011948536150157452,
0.00184948171954602,
0.02231650799512863,
0.011887559667229652,
-0.003509612288326025,
-0.011057635769248009,
0.03627757728099823,
-0.006706456653773785,
0.03875691443681717,
-0.013977046124637127,
-0.018866131082177162,
0.05362004414200783,
-0.017527662217617035,
0.00848477240651846,
-0.038879185914993286,
-0.015512503683567047,
0.009481918066740036,
0.002237003529444337,
-0.020077915862202644,
0.0847909078001976,
0.03199344873428345,
0.01762513816356659,
-0.043361175805330276,
0.0004463341028895229,
-0.014263029210269451,
-0.03636421263217926,
-0.04543839022517204,
-0.012366444803774357,
0.05402413010597229,
-0.0025224185083061457,
-0.0037660778034478426,
0.009821552783250809,
-0.040159597992897034,
-0.03041749633848667,
-0.04474373161792755,
-0.013455496169626713,
-0.03223627433180809,
0.03266650438308716,
-0.04476282373070717,
-0.0017416866030544043,
-0.0006197542534209788,
0.03836624324321747,
0.05784932151436806,
-0.009862947277724743,
-0.03227037936449051,
0.006805744022130966,
0.04197997599840164,
0.04404563829302788,
0.01165902428328991,
0.07516695559024811,
-0.012738785706460476,
0.010491074062883854,
0.02348841354250908,
0.021889079362154007,
-0.030460739508271217,
-0.008608624339103699,
-0.00943025853484869,
0.009557371027767658,
0.009745155461132526,
0.011426367796957493,
0.01307495217770338,
-0.01480033528059721,
0.018429415300488472,
-0.020042186602950096,
-0.04488576576113701,
0.017300574108958244,
0.05405304580926895,
0.009216190315783024,
-0.010436000302433968,
-0.017773598432540894,
-0.021243024617433548,
-0.014433179050683975,
0.0053973025642335415,
-0.0034683914855122566,
0.013670843094587326,
-0.019386982545256615,
-0.015192952938377857,
0.0010086651891469955,
-0.024265943095088005,
0.02689696103334427,
-0.020850496366620064,
0.04194481298327446,
0.009376785717904568,
0.02863449603319168,
0.001369599369354546,
0.06448088586330414,
-0.025317292660474777,
-0.041772447526454926,
0.006274427752941847,
0.01767941564321518,
-0.00772892078384757,
0.01579597033560276,
0.013500413857400417,
-0.0016570574371144176,
0.005698387045413256,
-0.029976991936564445,
0.014397400431334972,
0.05508977919816971,
0.015054375864565372,
-0.08587861806154251,
-0.06222845986485481,
0.062139615416526794,
0.051891934126615524,
0.0008911725599318743,
-0.03536244481801987,
0.03291954845190048,
0.033978838473558426,
0.030670983716845512,
-0.010018075816333294,
0.028332509100437164,
0.011888445354998112,
-0.009321991354227066,
0.007536112330853939,
-0.014737671241164207,
-0.014129923656582832,
-0.018479079008102417,
-0.050511714071035385,
-0.011326942592859268,
-0.06185213476419449,
0.018302390351891518,
0.006172523368149996,
0.034838076680898666,
-0.0031960755586624146,
0.05354513227939606,
-0.019760075956583023,
0.0075435820035636425,
0.014728310517966747,
-0.024364229291677475,
-0.008404060266911983,
0.0683082565665245,
0.026923872530460358,
-0.004241690970957279,
0.04425831511616707,
0.0054375184699893,
-0.02245696634054184,
0.02744324505329132,
-0.0401223860681057,
0.014054879546165466,
-0.04741466045379639,
0.0007959612412378192,
-0.03664775937795639,
0.0018419980769976974,
-0.006621302105486393,
-0.059322960674762726,
-0.02056208625435829,
-0.03064795769751072,
0.017551930621266365,
0.04105433449149132,
0.06113027036190033,
0.04337069392204285,
-0.011998072266578674,
0.03119349293410778,
-0.017109563574194908,
-0.00682349456474185,
-0.01051046047359705,
0.04318145290017128,
0.011176438070833683,
-0.014477308839559555,
-0.020103583112359047,
-0.031606968492269516,
0.0020386534743010998,
-0.03730836883187294,
0.019439928233623505,
-0.008122456260025501,
0.03766167163848877,
0.030892251059412956,
0.04338690638542175,
0.02545604482293129,
0.09538929164409637,
0.047530438750982285,
0.04454183205962181,
0.006879533175379038,
-0.022508714348077774,
-0.045659683644771576,
-0.02062848024070263,
-0.04621424153447151,
0.02137388102710247,
0.03498758375644684,
0.014266583137214184,
0.009641948156058788,
0.00518888421356678,
-0.00470018433406949,
0.05903022363781929,
-0.03862886503338814,
0.08810557425022125,
0.05767448991537094,
-0.024227324873209,
0.035267941653728485,
-0.01247661467641592,
0.019916756078600883,
0.03641272336244583,
0.029148386791348457,
0.0193009115755558,
-0.06487258523702621,
-0.024180790409445763,
0.01722184754908085,
0.0195670947432518,
-0.04732697457075119,
0.03378933668136597,
0.01625845767557621,
0.0227536428719759,
0.01893187128007412,
0.026595523580908775,
0.003745210589841008,
-0.028588298708200455,
0.0033422301057726145,
0.018756292760372162,
0.0191199891269207,
-0.0003129107935819775,
-0.043001193553209305,
0.010226240381598473,
0.0006641778163611889,
-0.02134130708873272,
0.06612292677164078,
0.03297494724392891,
-0.005486124195158482,
-0.016303203999996185,
-0.0324186310172081,
-0.012081132270395756,
0.05445396900177002,
-0.011285226792097092,
0.02432856895029545,
0.04802187532186508,
-0.011174734681844711,
-0.015278340317308903,
-0.04910820350050926,
0.0013401268515735865,
0.014194849878549576,
-0.005724667105823755,
-0.0027172251138836145,
-0.04243534803390503,
0.0458776019513607,
-0.03455272316932678,
-0.029157744720578194,
-0.06987065076828003,
-0.030206875875592232,
-0.031472429633140564,
0.014545143581926823,
0.020653173327445984,
-0.0120852654799819,
0.04916507378220558,
-0.030255604535341263,
0.008578049018979073,
-0.015051708556711674,
-0.01595696620643139,
-0.015726396813988686,
-0.0149054741486907,
-0.0331314355134964,
-0.0072242263704538345,
-0.001954532228410244,
0.011623065918684006,
0.04704875126481056,
0.03337906301021576,
-0.015037694945931435,
0.02674616500735283,
0.03721968084573746,
0.006413135677576065,
-0.017764948308467865,
-0.046459536999464035,
0.01629837043583393,
-0.031799182295799255,
-0.02872723713517189,
0.04342649132013321,
-0.003303227247670293,
-0.015499930828809738,
0.055741291493177414,
-0.09145097434520721,
-0.023676851764321327,
-0.006014508195221424,
0.02729957364499569,
-0.006895174738019705,
0.00790407694876194,
0.0006056777201592922,
0.005411280319094658,
-0.00830707885324955,
0.015090908855199814,
-0.0979369580745697,
-0.04565167799592018,
-0.03991758078336716,
0.000014556158930645324,
0.038304101675748825,
0.0008318895124830306,
-0.027898672968149185,
0.09979518502950668,
0.0048324172385036945,
-0.04289792478084564,
-0.06119408831000328,
-0.03331002593040466,
0.0017514892388135195,
-0.06790798157453537,
0.03738899901509285,
-0.008826114237308502,
-0.030702674761414528,
-0.05326760560274124,
0.018092380836606026,
0.028779489919543266,
0.01712185889482498,
-0.0058094714768230915,
0.01702839508652687,
-0.022963039577007294,
0.025968706235289574,
-0.021725229918956757,
0.060378655791282654,
0.03903893008828163,
-0.025097914040088654,
0.013629436492919922,
-0.026209859177470207,
0.05320873484015465,
0.010117835365235806,
-0.08880163729190826,
0.0036181865725666285,
0.0110915033146739,
-0.0017542112618684769,
-0.053086042404174805,
0.05356135219335556,
0.004173428751528263,
-0.027223240584135056,
-0.022601407021284103,
-0.026991235092282295,
0.029213719069957733,
0.00425437418743968,
-0.019474225118756294,
0.021578947082161903,
0.06166301667690277,
-0.03897298872470856,
-0.000277815357549116,
0.012824300676584244,
0.028979366645216942,
0.009614088572561741,
-0.011545813642442226,
-0.025776637718081474,
0.019434139132499695,
0.015706416219472885,
0.03630298376083374,
0.05413173511624336,
0.0035014322493225336,
-0.01982751116156578,
-0.07303748279809952,
-0.02393241971731186,
-0.0048796567134559155,
0.04934218153357506,
-0.007435513194650412,
0.04253903031349182,
0.010927747003734112,
0.046042852103710175,
0.012035519815981388,
0.03699173405766487,
-0.08132526278495789,
-0.02165556512773037,
-0.06048549339175224,
-0.03338290750980377,
0.003848522435873747,
-0.02077125385403633,
-0.03269413113594055,
-0.03140496835112572,
-0.02976076863706112,
0.012552670203149319,
0.011256115511059761,
-0.062313444912433624,
0.05460628122091293,
-0.002118076663464308,
0.009616379626095295,
0.005920982453972101,
0.012969103641808033,
0.06328141689300537,
-0.021676890552043915,
0.01399164367467165,
0.033870961517095566,
-0.00408799247816205,
0.027646208181977272,
0.010987582616508007,
0.0014884374104440212,
-0.010279047302901745,
0.008089018054306507,
-0.04270806908607483,
0.030870428308844566,
-0.004710328299552202,
0.0008238505106419325,
-0.0038955118507146835,
0.019321737810969353,
0.023643573746085167,
0.04321864992380142,
-0.01386343501508236,
-0.04696742072701454,
-0.01584957167506218,
0.005444074049592018,
0.00719318026676774,
-0.04752305522561073,
-0.0071496921591460705,
0.011285150423645973,
-0.015229031443595886,
0.006030287127941847,
0.044736795127391815,
0.042422302067279816,
-0.007448242977261543,
-0.0245803315192461,
-0.0129946768283844,
-0.0005916249938309193,
-0.0615851990878582,
-0.023893799632787704,
-0.03020327351987362,
0.026935400441288948,
-0.0047405376099050045,
0.020091209560632706,
0.024061962962150574,
-0.022672105580568314,
-0.03726218268275261,
0.0005779284983873367,
0.0056514800526201725,
0.028516238555312157,
-0.02715694159269333,
0.009607880376279354,
-0.005503905471414328,
0.002827055286616087,
0.054474011063575745,
0.011745932511985302,
-0.024052951484918594,
-0.08763565868139267,
-0.03254068270325661,
0.05177111551165581,
0.04248198866844177,
-0.005534059833735228,
-0.026534924283623695,
-0.07060511410236359,
-0.01761910878121853,
0.03764237090945244,
-0.0025252613704651594,
0.045859891921281815,
-0.023017844185233116,
0.03597990423440933,
-0.039854541420936584,
-0.0361996591091156,
-0.04928571358323097,
-0.024457572028040886,
-0.004171333741396666,
-0.0009316387586295605,
0.008444861508905888,
0.056486520916223526,
0.033542752265930176,
0.03462105989456177,
0.02327844500541687,
0.009872299619019032,
0.00888032279908657,
-0.004643814638257027,
-0.02929750457406044,
-0.033123619854450226,
-0.05596672743558884,
-0.06237267702817917,
0.008627330884337425,
0.04066241532564163,
0.005752911791205406,
0.004502468276768923,
-0.04205125570297241,
-0.04202329367399216,
0.0662492886185646,
0.006046348251402378,
-0.00832783617079258,
0.029481656849384308,
-0.049175944179296494,
0.033374834805727005,
0.05146355554461479,
-0.0003292613837402314,
0.02464989386498928,
0.06352811306715012,
-0.011920343153178692,
0.00984499417245388,
-0.016826361417770386,
-0.004201916046440601,
-0.032843299210071564,
-0.004483300261199474,
-0.030688058584928513,
0.02433887869119644,
-0.04394504800438881,
0.030419593676924706,
-0.009841992519795895,
0.031682468950748444,
-0.0023526446893811226,
-0.005983384791761637,
0.01813344471156597,
0.006754777859896421,
0.027789512649178505,
-0.013316115364432335,
0.020334623754024506,
0.013487144373357296,
-0.0436444953083992,
-0.02789667248725891,
0.007667182013392448,
-0.007765898481011391,
0.012782102450728416,
-0.015700872987508774,
-0.011498937383294106,
0.01649296097457409,
0.003539105411618948,
-0.010141138918697834,
0.010372823104262352,
-0.06874030083417892,
0.07653901726007462,
-0.03086431324481964,
0.00003005474354722537,
0.008889562450349331,
-0.035814084112644196,
0.005208521615713835,
0.031276728957891464,
0.01654580421745777,
0.01382235623896122,
0.017790181562304497,
0.033514782786369324,
-0.00935025978833437,
-0.03468683362007141,
-0.04183544963598251,
-0.018861569464206696,
0.038315318524837494,
0.024595746770501137,
-0.04024875909090042,
-0.022013409063220024,
-0.005143621005117893,
0.01304299384355545,
-0.018171532079577446,
0.004121066071093082,
0.05324186384677887,
-0.04442916437983513,
-0.0016873114509508014,
0.022778429090976715,
0.010167467407882214,
0.035848233848810196,
-0.01238557230681181,
-0.0004759414296131581,
-0.010907945223152637,
0.0006229210994206369,
0.014471144415438175,
-0.07147052884101868,
0.022636281326413155,
-0.029759278520941734,
-0.043506890535354614,
-0.009986493736505508,
0.00110655277967453,
0.0016231508925557137,
0.0035336471628397703,
-0.03969602659344673,
0.03307472914457321,
-0.023512357845902443,
-0.049054715782403946,
-0.03491871431469917,
0.00795405451208353,
0.014466740190982819,
0.017601296305656433,
-0.01806296780705452,
0.04683395475149155,
-0.03156176954507828,
-0.044215116649866104,
-0.006636385340243578,
-0.030778363347053528,
0.004218747839331627,
0.018695710226893425,
0.07388810068368912,
-0.03817758336663246,
0.0035526819992810488,
0.015074732713401318,
0.01201064046472311,
0.021874936297535896,
0.001444944180548191,
-0.03206998482346535,
0.01724027469754219,
0.019100792706012726,
-0.06449548155069351,
-0.016497869044542313,
0.009824328124523163,
0.00947511475533247,
0.04971378296613693,
-0.04884905740618706,
0.030565593391656876,
0.04104440286755562,
-0.02021719515323639,
0.02174069546163082,
-0.00047633214853703976,
-0.0018118382431566715,
-0.0014292339328676462,
0.027927013114094734,
0.04753008112311363,
-0.029036276042461395,
-0.010288666933774948,
0.06311880797147751,
0.046775028109550476,
-0.02482573501765728,
0.014010175131261349,
0.02444055862724781,
0.009508354589343071,
0.02403872460126877,
-0.06656448543071747,
-0.019618960097432137,
-0.0056735677644610405,
-0.031585969030857086,
0.00597874540835619,
0.03153788298368454,
-0.006971117574721575,
0.02629713900387287,
0.041054561734199524,
0.012372680939733982,
-0.013606822118163109,
-0.0035778868477791548,
-0.017109110951423645,
0.019351640716195107,
-0.010176612064242363,
0.0180401261895895,
0.020574694499373436,
-0.017408372834324837,
0.04397985339164734,
-0.02663995325565338,
0.04223095253109932,
-0.005098862107843161,
-0.03457384184002876,
-0.005275656469166279,
-0.01852189563214779,
-0.032176803797483444,
0.06788776069879532,
0.029846303164958954,
-0.03148442506790161,
0.0381760336458683,
-0.025631500408053398,
0.04525749757885933,
0.03715619072318077,
0.05081871524453163,
-0.05309421569108963,
0.07099823653697968,
-0.010277432389557362,
-0.01622115634381771,
-0.01589335687458515,
0.024640481919050217,
0.13565558195114136,
0.08206803351640701,
-0.0013871946139261127,
-0.01044102106243372,
-0.045214295387268066,
-0.010910903103649616,
-0.03208247199654579,
-0.017633967101573944,
0.003292056731879711,
-0.0030433996580541134,
-0.013509701937437057,
0.06254039704799652,
0.049154818058013916,
-0.03957924246788025,
-0.017901703715324402,
0.030366290360689163,
-0.07685308903455734,
-0.015116664581000805,
-0.024606309831142426,
-0.0052927578799426556,
-0.027957892045378685,
0.0006549789104610682,
-0.005723079200834036,
0.042417459189891815,
-0.03844060003757477,
-0.012245340272784233,
-0.04924515634775162,
-0.03083208203315735,
0.02954346314072609,
0.0022157952189445496,
-0.035696983337402344,
-0.009640209376811981,
-0.0022830916568636894,
-0.006019716151058674,
-0.015955910086631775,
0.010397776030004025,
-0.01274800393730402,
-0.0036377031356096268,
0.008975678123533726,
0.05920024216175079,
0.005763383582234383,
-0.0045007457956671715,
-0.007452713325619698,
0.019562697038054466,
-0.0392465814948082,
0.025251012295484543,
-0.04966296628117561,
-0.0034167582634836435,
-0.009071607142686844,
0.005932975094765425,
-0.019650336354970932,
-0.004205518402159214,
0.006967220921069384,
-0.05231636390089989,
-0.02294309251010418,
0.011395457200706005,
0.028211629018187523,
0.00029138365061953664,
-0.01962672919034958,
-0.025062182918190956,
0.010002891533076763,
0.02431490831077099,
0.016544025391340256,
-0.008930235169827938,
-0.007566631305962801,
0.007683080621063709,
0.016991959884762764,
0.05160878598690033,
-0.01834595575928688,
-0.010568474419414997,
-0.0507749505341053,
-0.04547079652547836,
-0.0008622997556813061,
0.014588012360036373,
0.03137533739209175,
0.06442371010780334,
0.03835553303360939,
-0.007151652127504349,
0.00974707119166851,
-0.040012337267398834,
-0.006162318866699934,
0.048433709889650345,
-0.014573653228580952,
0.0068850526586174965,
-0.02671428583562374,
-0.012344191782176495,
0.018099965527653694,
0.053533848375082016,
0.005859629716724157,
0.016532069072127342,
-0.027494288980960846,
0.041439685970544815,
0.030417801812291145,
-0.02747364155948162,
-0.027564890682697296,
-0.001969716278836131,
-0.028173601254820824,
0.03152686730027199,
-0.012651744298636913,
0.030281975865364075,
0.07845219224691391,
0.018394317477941513,
-0.022750576958060265,
0.010106274858117104,
-0.050845757126808167,
-0.003499043406918645,
0.03797939047217369,
-0.026431314647197723,
-0.02297980710864067,
0.01078537106513977,
-0.009795659221708775,
-0.03737698495388031,
0.008165854029357433,
-0.0030197538435459137,
-0.05201350897550583,
0.04714145511388779,
0.013903792016208172,
-0.030330516397953033,
0.015569320879876614,
-0.013667887076735497,
0.02112864889204502,
-0.04946300759911537,
0.011317203752696514,
-0.060751110315322876,
-0.030131353065371513,
-0.003209070535376668,
-0.012178651988506317,
-0.01648555137217045,
0.04580535739660263,
-0.07449305057525635,
-0.031129280105233192,
0.015161557123064995,
-0.004665260203182697,
0.00620131753385067,
-0.04425244405865669,
-0.021107567474246025,
-0.023850591853260994,
0.037601470947265625,
0.0068231201730668545,
-0.016750186681747437,
-0.003791357157751918,
-0.01843515783548355,
-0.005487468559294939,
0.01205459889024496,
-0.029627179726958275,
0.05338994041085243,
0.03816763311624527,
-0.03288590908050537,
0.014337623491883278,
0.035472650080919266,
0.003412329824641347,
-0.007318854797631502,
-0.008416745811700821,
-0.004539909772574902,
0.0313018336892128,
-0.016430500894784927,
-0.02303725853562355,
-0.02382398024201393,
-0.006687816698104143,
-0.004243071656674147,
0.032180845737457275,
0.006374371238052845,
0.0031828461214900017,
0.016793202608823776,
-0.008081747218966484,
-0.03502993285655975,
0.013095732778310776,
0.0018510405207052827,
0.0027946794871240854,
-0.01666191779077053,
0.00143651501275599,
0.012730761431157589,
-0.003453414421528578,
0.026181839406490326,
-0.09984598308801651,
-0.008128614164888859,
-0.012678234837949276,
-0.01367918960750103,
0.025149742141366005,
-0.056058987975120544,
0.023435967043042183,
0.03494810312986374,
-0.08205736428499222,
0.04701724275946617,
-0.002825942123308778,
-0.02376808412373066,
-0.05436946824193001,
0.02592802606523037,
0.0039047054015100002,
0.053346291184425354,
0.00004807643199455924,
0.05212496593594551,
-0.0017726137302815914,
0.02676168829202652,
-0.0600719079375267,
0.020926473662257195,
-0.01225503720343113,
0.035369206219911575,
-0.014292572624981403,
0.008673500269651413,
0.04844072833657265,
0.0008335667080245912,
-0.0012763129780068994,
-0.00795359443873167,
-0.01614757440984249,
0.023659322410821915,
-0.0018601174233481288,
0.013628995977342129,
0.04927622526884079,
0.019061535596847534,
0.0023092622868716717,
0.010128808207809925,
-0.015259278006851673,
0.011429432779550552,
-0.009915105067193508,
0.020014507696032524,
-0.007433158345520496,
0.01133868657052517,
0.036032285541296005,
-0.023010067641735077,
-0.018703831359744072,
0.04197748005390167,
-0.017006099224090576,
0.01371105294674635,
0.0011891830945387483,
0.005053333006799221,
0.012603799812495708,
-0.009864332154393196,
-0.008041624911129475,
-0.0502353310585022,
0.004324663896113634,
0.04594476893544197,
-0.027810465544462204,
-0.020195160061120987,
0.010459836572408676,
-0.01523249689489603,
-0.0016517611220479012,
-0.01661195605993271,
-0.019975891336798668,
-0.02610095590353012,
-0.03675299510359764,
0.017393823713064194,
0.024082854390144348,
-0.019931437447667122,
-0.0061485725454986095,
-0.012880099005997181,
0.009233054704964161,
0.03805895894765854,
0.03454570472240448,
0.04087783396244049,
0.030282434076070786,
-0.02898971363902092,
0.011693053878843784,
-0.09412631392478943,
0.026974741369485855,
-0.02429565228521824,
-0.02630763128399849,
-0.05319037288427353,
-0.0410529300570488,
0.023057349026203156,
0.05850204825401306,
0.03485923632979393,
-0.0100454892963171,
-0.004771600943058729,
0.007198025472462177,
0.001645638607442379,
0.007643670309334993,
-0.06859753280878067,
0.03406934812664986,
0.02476484328508377,
-0.022595319896936417,
0.008306050673127174,
-0.02098979987204075,
0.002657019766047597,
-0.0004883448709733784,
0.013323895633220673,
-0.020392684265971184,
0.019647913053631783,
0.01130230724811554,
-0.040568653494119644,
0.026699312031269073,
-0.006442269776016474,
-0.020920680835843086,
0.06323221325874329,
0.006229477934539318,
0.005449523217976093,
-0.0068085468374192715,
0.007730245590209961,
-0.010136694647371769,
0.0614878311753273,
-0.06987441331148148,
0.001036995672620833,
-0.024993430823087692,
-0.02168303355574608,
0.011746820993721485,
-0.03782085329294205,
-0.03102092631161213,
0.05052809789776802,
-0.0296784620732069,
0.0027919411659240723,
0.04408327862620354,
0.009911349043250084,
0.03759956359863281,
-0.06924296170473099,
0.030823227018117905,
0.042594052851200104,
-0.04167485237121582,
-0.011452540755271912,
-0.004819084890186787,
0.0333351269364357,
-0.058450620621442795,
0.010282911360263824,
0.036055780947208405,
0.0068640802055597305,
0.005121780093759298,
0.02594100683927536,
0.044012103229761124,
-0.03902747854590416,
-0.023451896384358406,
0.0059474981389939785,
-0.001747951959259808,
0.01909790374338627,
0.04252840206027031,
-0.04711803421378136,
0.051161423325538635,
0.01612640917301178,
0.01090485043823719,
-0.013011731207370758,
0.03187232464551926,
0.022050239145755768,
0.03405752778053284,
0.026662522926926613,
0.028753332793712616,
-0.018505100160837173,
0.0031282780691981316,
0.0022280365228652954,
-0.003202165011316538,
0.057154811918735504,
-0.012453485280275345,
0.033487170934677124,
-0.014165781438350677,
0.02075531706213951,
-0.008845002390444279,
-0.0258354302495718,
-0.052748192101716995,
0.01773962937295437,
0.07241567224264145,
0.0013450158294290304,
-0.00043810586794279516,
-0.04019016772508621,
-0.008708675391972065,
-0.014452444389462471,
0.018933173269033432,
-0.011314157396554947,
0.021300239488482475,
-0.027346882969141006,
0.01866241917014122,
-0.015354194678366184,
-0.0007455135346390307
] |
<blockquote>
<p>A thin plank of mass $M$ and length $l$ is pivoted at one end. The plank is released at 60$^{\circ}$ from the vertical. What is the magnitude and direction of the force on the pivot when the plank is horizontal?</p>
</blockquote>
<p>I have a doubt: does the pivot exert an upwards force on the plank when the plank is horizontal? I think the answer to this is yes, because:</p>
<p>The torque on the plank about the pivot, when the plank is horizontal, is</p>
<p>$$\tau=\frac{Mgl}{2}$$</p>
<p>And the plank's angular acceleration at that point will be</p>
<p>$$\alpha=\frac{\tau}{I}=\frac{3g}{2l}$$</p>
<p>So the vertical acceleration of the plank's CM will be</p>
<p>$$a=\alpha R=\frac{3g}{4} $$</p>
<p>Therefore, the upwards force exerted by the pivot on the plank is</p>
<p>$$F_{up}=\frac{mg}{4}$$</p>
<p>Is this reasoning ok for this case? (I'm doubtful of this part because there was <a href="http://www.physicsforums.com/showthread.php?t=444827" rel="nofollow">a post on PF</a> where this force was not mentioned.)</p>
| 8,274 |
[
-0.04539067670702934,
-0.014104373753070831,
-0.03692737594246864,
-0.0026871461886912584,
0.041914332658052444,
0.01254094485193491,
0.005096964072436094,
0.0057129585184156895,
0.029677623882889748,
-0.02626202628016472,
0.023585516959428787,
0.03028208203613758,
0.0685696229338646,
0.06058565154671669,
0.0007331424858421087,
-0.007320287171751261,
0.016088226810097694,
-0.021782923489809036,
0.014001257717609406,
-0.004985561594367027,
-0.03788585215806961,
0.01477360725402832,
-0.035280492156744,
-0.00039173642289824784,
-0.026152225211262703,
0.005934196524322033,
0.05690394714474678,
-0.0015173335559666157,
-0.0010703776497393847,
0.041445542126894,
-0.006099190562963486,
0.032133813947439194,
-0.013594056479632854,
-0.010411642491817474,
0.02715471386909485,
0.010275645181536674,
-0.014522523619234562,
0.00926732923835516,
0.019467590376734734,
0.017707459628582,
-0.025595063343644142,
0.04645409435033798,
-0.041093114763498306,
0.04886494576931,
-0.044584792107343674,
0.00031573529122397304,
-0.01332437340170145,
0.0036687981337308884,
0.04154708608984947,
-0.029017768800258636,
0.04381577670574188,
0.0022573666647076607,
0.02212637849152088,
0.007564347703009844,
0.02607012540102005,
-0.01602770760655403,
0.04770553112030029,
0.03766447678208351,
-0.017833225429058075,
-0.027467433363199234,
-0.014934319071471691,
-0.00531633710488677,
-0.029405537992715836,
-0.037499360740184784,
-0.02525229938328266,
0.04094294086098671,
-0.03388862684369087,
-0.03095969744026661,
0.024528896436095238,
-0.027762722223997116,
-0.00219050538726151,
-0.008698871359229088,
0.020980998873710632,
-0.011588655412197113,
-0.021443337202072144,
-0.03442297875881195,
0.008895443752408028,
0.020700177177786827,
-0.008021161891520023,
0.04353678598999977,
-0.009885587729513645,
0.02212655171751976,
0.04455256834626198,
0.040463440120220184,
0.02152705378830433,
-0.022648729383945465,
0.07346157729625702,
0.004992078989744186,
0.028464334085583687,
0.042385537177324295,
0.03073844499886036,
0.01688915677368641,
-0.017779117450118065,
0.02247139811515808,
-0.014210231602191925,
0.018848540261387825,
0.021662293002009392,
0.053481683135032654,
0.0047376747243106365,
0.03414811193943024,
0.007474194280803204,
-0.014471693895757198,
-0.011127018369734287,
0.07355586439371109,
0.00468446547165513,
-0.022656789049506187,
-0.024479512125253677,
0.010433536022901535,
-0.02671136148273945,
-0.049759626388549805,
-0.04251992329955101,
0.024682188406586647,
-0.03905526176095009,
-0.022140905261039734,
-0.010082759894430637,
-0.020863108336925507,
-0.008536401204764843,
-0.005633227061480284,
0.055538393557071686,
0.024770764634013176,
0.029832391068339348,
-0.021883590146899223,
0.005372794810682535,
-0.02883836440742016,
-0.05392366647720337,
0.030222170054912567,
0.025678105652332306,
-0.038379114121198654,
-0.041390519589185715,
0.06897483021020889,
0.05748339369893074,
0.004876557271927595,
-0.013098486699163914,
-0.018967434763908386,
0.041756946593523026,
-0.0011186914052814245,
-0.10376168042421341,
-0.061660464853048325,
0.05027850344777107,
0.028493426740169525,
-0.03409349173307419,
-0.09472043812274933,
-0.03014565445482731,
0.04138001799583435,
0.06596196442842484,
-0.002380594378337264,
0.012598474510014057,
-0.014255720190703869,
0.000610064365901053,
-0.03138528764247894,
-0.018231241032481194,
-0.0001741871819831431,
-0.006402738392353058,
-0.042069174349308014,
-0.012011411599814892,
-0.08752536028623581,
0.02759629115462303,
-0.004579609725624323,
0.02185620181262493,
-0.044067345559597015,
0.050084665417671204,
-0.007238538004457951,
-0.007090933620929718,
0.01619703322649002,
-0.0034275243524461985,
-0.029256051406264305,
0.07489214092493057,
-0.013767299242317677,
-0.009146247059106827,
0.05137256905436516,
0.01753617450594902,
-0.0009134116698987782,
-0.01750960201025009,
0.004499896429479122,
0.03132697194814682,
-0.0328107513487339,
-0.03423355519771576,
-0.03407343104481697,
0.04178494215011597,
0.009380836971104145,
-0.02650444582104683,
-0.046341393142938614,
-0.030035046860575676,
0.0006099169258959591,
0.01627160981297493,
0.05771894007921219,
0.013188674114644527,
-0.005562119651585817,
-0.02161419205367565,
-0.052237819880247116,
0.017204729840159416,
-0.05536825582385063,
0.06602215021848679,
-0.011095114052295685,
0.003687460906803608,
0.012765363790094852,
-0.007806210312992334,
0.03484034538269043,
-0.037211447954177856,
0.006524112541228533,
-0.009002362377941608,
0.016038062050938606,
0.006501579191535711,
0.008009654469788074,
0.005219668615609407,
0.057049646973609924,
0.00795560423284769,
0.02412145584821701,
0.0007553291507065296,
-0.027343755587935448,
-0.013674052432179451,
0.0056929378770291805,
-0.01856347545981407,
0.020744815468788147,
0.02719465084373951,
0.016871720552444458,
0.03039459139108658,
-0.016241982579231262,
-0.00767815625295043,
0.07017111033201218,
-0.03162989020347595,
0.08925492316484451,
0.0422825813293457,
0.01745433174073696,
0.028993837535381317,
0.04259651526808739,
-0.005110600497573614,
0.0008570842328481376,
-0.010882990434765816,
0.00859356950968504,
-0.042623523622751236,
0.0009784272406250238,
0.0032720123417675495,
0.047165289521217346,
-0.019997505471110344,
0.05135912075638771,
0.028551101684570312,
-0.004609098192304373,
-0.01592504419386387,
0.04714125022292137,
-0.003880165284499526,
-0.04307287186384201,
0.026107337325811386,
0.014193420298397541,
0.011651463806629181,
0.04786813631653786,
-0.003209637710824609,
0.016567973420023918,
0.00262290402315557,
0.019120289012789726,
-0.0007926610414870083,
0.024868730455636978,
0.023029357194900513,
0.04658995196223259,
0.012737507000565529,
-0.027568640187382698,
0.05261312797665596,
-0.026481613516807556,
0.0007436839514411986,
0.024597901850938797,
-0.018890023231506348,
-0.007583364378660917,
-0.03309404477477074,
-0.008897828869521618,
0.006854787468910217,
0.006140321493148804,
-0.007414869964122772,
-0.037213414907455444,
0.04248175397515297,
-0.03710143268108368,
-0.010606450960040092,
-0.05469128489494324,
-0.024217326194047928,
0.021835241466760635,
0.002929933601990342,
0.018879985436797142,
0.025590257719159126,
0.06518209725618362,
-0.0341518335044384,
-0.013390579260885715,
-0.016121570020914078,
-0.02580195479094982,
-0.0005650228704325855,
-0.01666310243308544,
-0.04510369896888733,
0.007460679393261671,
-0.01649394817650318,
-0.029323682188987732,
0.05820547416806221,
0.023003125563263893,
0.003022435586899519,
0.005189038347452879,
0.012567790225148201,
-0.04952049255371094,
-0.008244384080171585,
-0.010576763190329075,
0.008862543851137161,
-0.04969485104084015,
-0.03811925649642944,
0.031700555235147476,
-0.00876452773809433,
0.008302695117890835,
0.04951161891222,
-0.03942517191171646,
-0.046200208365917206,
0.03116963617503643,
0.02725905179977417,
0.00442676804959774,
0.005689047742635012,
-0.014870340004563332,
0.016492070630192757,
-0.013005643151700497,
0.02504269778728485,
-0.08430929481983185,
-0.04185004532337189,
-0.003618307411670685,
-0.03195680305361748,
0.02717731148004532,
0.01031085941940546,
-0.056814033538103104,
0.09461963176727295,
0.009803172200918198,
-0.020714230835437775,
-0.02803458459675312,
-0.026979191228747368,
-0.004124537575989962,
-0.05018142610788345,
0.011593371629714966,
-0.014080848544836044,
-0.03542177379131317,
0.0030471112113445997,
-0.014002361334860325,
-0.022763622924685478,
0.008717590942978859,
0.038847245275974274,
0.027655063197016716,
0.004632582888007164,
-0.005743745248764753,
-0.04994097724556923,
0.07154726982116699,
0.004545648582279682,
0.022672325372695923,
0.005220307502895594,
0.0015618272591382265,
0.030650869011878967,
0.020054707303643227,
-0.05407693609595299,
0.05610985681414604,
0.0034676087088882923,
-0.02794361487030983,
-0.018273834139108658,
0.06273594498634338,
0.02160218544304371,
-0.012381693348288536,
0.023928172886371613,
0.012465853244066238,
0.043153729289770126,
0.0007821206818334758,
-0.006858157925307751,
0.1008421927690506,
0.030788861215114594,
0.01591670513153076,
-0.024198036640882492,
0.013559351675212383,
-0.012176941148936749,
0.04035920649766922,
-0.035282351076602936,
-0.0073537700809538364,
0.011019370518624783,
0.02915833704173565,
0.04492249712347984,
0.008406534790992737,
-0.030745821073651314,
0.002840733388438821,
-0.07799094915390015,
0.02538920007646084,
-0.03573421388864517,
0.04595699533820152,
0.015524634160101414,
0.053762778639793396,
0.02290482260286808,
-0.0017515562940388918,
0.011188209988176823,
0.022671956568956375,
-0.0758228525519371,
0.016585661098361015,
-0.02594602294266224,
-0.014866603538393974,
0.01509985513985157,
-0.004433741793036461,
-0.023068120703101158,
-0.012317737564444542,
-0.0022545387037098408,
0.005298182833939791,
-0.004364798776805401,
-0.04593817889690399,
0.023417122662067413,
-0.008417477831244469,
-0.03837598115205765,
0.033574074506759644,
-0.014074541628360748,
0.030455520376563072,
-0.025857754051685333,
0.04728582128882408,
0.041976526379585266,
-0.025038106366991997,
0.019697895273566246,
-0.03481132164597511,
0.006857729982584715,
-0.01028735563158989,
-0.011121805757284164,
0.006334347650408745,
0.02395259030163288,
0.005217284429818392,
0.02414008229970932,
0.003705275012180209,
0.038125429302453995,
0.02083541452884674,
-0.012521343305706978,
-0.05000687763094902,
-0.05688723921775818,
-0.014272601343691349,
-0.004015111364424229,
0.02727985382080078,
-0.030872534960508347,
-0.004723936785012484,
0.009070941247045994,
0.005593131761997938,
-0.010611963458359241,
0.07435989379882812,
0.05282937362790108,
0.03977500647306442,
0.004026737064123154,
-0.050178609788417816,
-0.015541392378509045,
-0.020177405327558517,
-0.028039710596203804,
-0.005224244203418493,
-0.03361271321773529,
0.018938949331641197,
-0.0037651113234460354,
0.016931956633925438,
0.008071227930486202,
0.01891842857003212,
0.04882685840129852,
-0.039724379777908325,
0.043324023485183716,
-0.03788449615240097,
-0.004548007622361183,
0.010387754999101162,
0.05942080169916153,
0.055320750921964645,
0.03191404417157173,
-0.030777767300605774,
-0.04399429261684418,
0.004379176069051027,
0.02672853320837021,
0.05893270671367645,
-0.07528874278068542,
0.009635815396904945,
-0.04669704660773277,
-0.0019916824530810118,
0.028571970760822296,
-0.027538737282156944,
0.057962190359830856,
-0.034632839262485504,
0.0504009872674942,
-0.023615600541234016,
0.013922558166086674,
-0.050037652254104614,
-0.023186931386590004,
-0.020270202308893204,
-0.0011882733087986708,
-0.01306752860546112,
-0.00018965196795761585,
-0.018022771924734116,
0.020458580926060677,
0.05622851476073265,
-0.013410084880888462,
0.027219751849770546,
-0.018015924841165543,
-0.0231295395642519,
0.013137551955878735,
-0.06495200842618942,
-0.07801572978496552,
-0.017450738698244095,
-0.0058137900196015835,
-0.020528806373476982,
0.008700934238731861,
-0.034670256078243256,
-0.06713651865720749,
0.027529854327440262,
0.011396653950214386,
0.021317508071660995,
0.011802293360233307,
-0.007275806274265051,
0.011149933561682701,
0.058137502521276474,
-0.029359890148043633,
0.058064766228199005,
0.06571483612060547,
-0.02112988755106926,
-0.024239063262939453,
0.0027197818271815777,
0.03152398392558098,
-0.001110991695895791,
0.01449666079133749,
-0.027319174259901047,
0.034427665174007416,
-0.012419120408594608,
0.045890066772699356,
0.01564190164208412,
0.044169533997774124,
-0.023213664069771767,
-0.05091030150651932,
-0.02413525991141796,
0.015109339728951454,
-0.00021809566533192992,
-0.026610199362039566,
-0.0013458315515890718,
0.00437704985961318,
-0.004955763928592205,
-0.005402918439358473,
0.017409393563866615,
0.030589934438467026,
0.027416998520493507,
0.0024778936058282852,
0.008464467711746693,
0.010946936905384064,
-0.023233596235513687,
0.011678438633680344,
-0.013098509050905704,
-0.050225239247083664,
0.05248435586690903,
-0.010805093683302402,
0.008837474510073662,
0.026670122519135475,
-0.037144340574741364,
-0.02437959797680378,
0.020071035251021385,
-0.026163989678025246,
0.007328469306230545,
-0.016678359359502792,
0.03213471174240112,
0.00290078017860651,
0.0032824554946273565,
-0.01786249689757824,
-0.03301025182008743,
0.012311723083257675,
0.016189545392990112,
0.014949114061892033,
-0.0013307904591783881,
-0.018796419724822044,
-0.00005396722553996369,
-0.03609097748994827,
-0.0002491227351129055,
0.06665214896202087,
-0.019613226875662804,
-0.000715005153324455,
0.020582351833581924,
0.005226563662290573,
0.06575749814510345,
-0.009124340489506721,
-0.023036058992147446,
-0.021386152133345604,
-0.017690012231469154,
-0.035349320620298386,
-0.028215372934937477,
0.039892200380563736,
-0.024658124893903732,
-0.03691103309392929,
0.006595325656235218,
0.014461851678788662,
0.02863050438463688,
-0.0019526316318660975,
-0.009938209317624569,
0.05398191511631012,
0.043221790343523026,
-0.015104182064533234,
-0.013886061497032642,
0.0693662092089653,
0.015174660831689835,
0.03698669373989105,
-0.0014375043101608753,
0.02094486728310585,
-0.022230256348848343,
-0.039742063730955124,
0.019091138616204262,
-0.02515162155032158,
0.006088725291192532,
-0.0021176934242248535,
0.06933291256427765,
-0.0383622981607914,
0.028724782168865204,
0.03465908765792847,
0.033289432525634766,
0.0523897223174572,
0.004183126613497734,
-0.0060465577989816666,
0.01910344511270523,
-0.02254015952348709,
-0.042779114097356796,
-0.02419053018093109,
0.0018484840402379632,
0.019821448251605034,
0.04950227588415146,
-0.026602838188409805,
0.049659211188554764,
-0.007749768439680338,
-0.011231597512960434,
5.21176332313189e-7,
-0.006727534346282482,
0.030444979667663574,
-0.030232474207878113,
0.015123647637665272,
0.024608064442873,
-0.04246491566300392,
0.02552892453968525,
0.05064906179904938,
0.025087952613830566,
-0.029238305985927582,
-0.029590733349323273,
0.038278549909591675,
-0.016402004286646843,
0.006961386650800705,
-0.0063003189861774445,
-0.052566640079021454,
0.036126215010881424,
-0.029274938628077507,
0.04145348444581032,
-0.007927430793642998,
-0.06443923711776733,
0.058380380272865295,
0.02020510844886303,
0.032574817538261414,
-0.045367009937763214,
0.0033646041993051767,
-0.025456808507442474,
-0.011480109766125679,
0.0014684320194646716,
0.009927324950695038,
-0.027142155915498734,
0.0016689593903720379,
0.07596098631620407,
0.01346647273749113,
0.016544733196496964,
-0.057609304785728455,
-0.0511145144701004,
-0.04971903935074806,
-0.03361418843269348,
-0.052862346172332764,
0.027930930256843567,
-0.020343998447060585,
-0.035504601895809174,
0.03634098917245865,
-0.06157071143388748,
0.021266549825668335,
0.029508071020245552,
0.05487149581313133,
-0.032948605716228485,
0.06744229793548584,
-0.05947044864296913,
-0.019184963777661324,
-0.022860798984766006,
-0.00122649350669235,
0.12151608616113663,
0.04532253369688988,
0.024337010458111763,
-0.0372842401266098,
0.019616296514868736,
-0.03422193229198456,
-0.012907842174172401,
-0.03380972892045975,
-0.009608842432498932,
-0.029826704412698746,
0.01592143625020981,
-0.0009685211698524654,
0.05761367455124855,
-0.03668021038174629,
0.011407457292079926,
0.06299248337745667,
0.0010770098306238651,
-0.039124343544244766,
0.004112467169761658,
0.011646031402051449,
0.0030914517119526863,
-0.005715927109122276,
-0.022909192368388176,
0.045802731066942215,
-0.01391777116805315,
-0.03756137564778328,
-0.006672816816717386,
-0.03578104078769684,
0.013914618641138077,
-0.007769982796162367,
-0.06788024306297302,
-0.021536024287343025,
0.027052145451307297,
-0.017420707270503044,
-0.020828066393733025,
0.04704279080033302,
-0.012212092988193035,
-0.0434364415705204,
0.03594880551099777,
0.050481293350458145,
-0.008586741983890533,
0.019948866218328476,
0.05082152038812637,
0.016309263184666634,
-0.07135791331529617,
0.008015270344913006,
-0.02911795862019062,
0.016556832939386368,
-0.013937734998762608,
0.007847503758966923,
-0.0037977902684360743,
0.0002349359419895336,
0.0005016365321353078,
-0.0779009610414505,
0.010013164021074772,
0.013192053884267807,
0.03596971556544304,
-0.010383622720837593,
-0.020071696490049362,
-0.021748099476099014,
0.011082833632826805,
0.014311675913631916,
-0.027539139613509178,
0.0035621821880340576,
-0.01345201674848795,
-0.009022644720971584,
-0.01272329967468977,
0.03973669931292534,
-0.027545595541596413,
-0.03276535123586655,
-0.04386923834681511,
0.004815053194761276,
-0.020306820049881935,
0.02651898004114628,
-0.013950059190392494,
0.04113611578941345,
0.041217394173145294,
0.020210033282637596,
-0.022786282002925873,
-0.03802540525794029,
-0.06585008651018143,
0.015955710783600807,
-0.02207084745168686,
-0.0054679387249052525,
-0.018659276887774467,
-0.00567089905962348,
0.007605846039950848,
0.016833052039146423,
-0.00020189966016914696,
0.020498469471931458,
0.012014161795377731,
0.03874209150671959,
0.005010473076254129,
-0.03546356037259102,
-0.03214925900101662,
0.02428930252790451,
-0.006836694665253162,
-0.02036406844854355,
-0.026409216225147247,
-0.002689055632799864,
0.0189066044986248,
0.03317370265722275,
0.004598379600793123,
0.03079376555979252,
-0.005893644876778126,
-0.021497147157788277,
0.05531755089759827,
0.0062211318872869015,
0.018808621913194656,
0.04415863752365112,
0.0018319773953408003,
-0.04618868604302406,
-0.016517313197255135,
-0.005692547187209129,
-0.012005911208689213,
-0.024766983464360237,
-0.00894938874989748,
-0.05224395543336868,
-0.0004610467003658414,
-0.06986193358898163,
0.0025272993370890617,
-0.049395978450775146,
0.0006148057873360813,
-0.015168754383921623,
-0.00534484488889575,
0.0024534156545996666,
-0.022283468395471573,
-0.02377508580684662,
0.04221538081765175,
-0.028074584901332855,
-0.010245619341731071,
-0.0008090540650300682,
0.028943192213773727,
-0.01394460629671812,
-0.021529601886868477,
0.006022686138749123,
-0.00993420835584402,
0.03459520265460014,
0.002589355455711484,
-0.040728602558374405,
0.045910682529211044,
-0.0019121599616482854,
-0.008928418159484863,
0.04564846307039261,
0.009388290345668793,
0.031137332320213318,
0.013818271458148956,
-0.02814261056482792,
0.009064314886927605,
0.06670460850000381,
-0.011807911098003387,
-0.0054795630276203156,
-0.032576784491539,
-0.01259906217455864,
-0.00013170654710847884,
-0.017135953530669212,
-0.014606365002691746,
-0.026589034125208855,
0.001439060433767736,
0.019565094262361526,
0.0153855225071311,
-0.02362573705613613,
-0.0011614119866862893,
0.016685163602232933,
-0.016503438353538513,
-0.02677619643509388,
-0.010581355541944504,
0.0013483203947544098,
0.008939588442444801,
0.04391069710254669,
-0.0034249990712851286,
0.010290360078215599,
-0.0033335841726511717,
-0.009405001066625118,
-0.09341637790203094,
-0.02285631187260151,
0.0026669122744351625,
0.006619008257985115,
0.030178528279066086,
-0.026801029220223427,
-0.018062127754092216,
0.030119145289063454,
-0.06715097278356552,
-0.035844288766384125,
-0.026101527735590935,
-0.011348329484462738,
-0.006953205913305283,
-0.006515884771943092,
0.008061918430030346,
0.028233885765075684,
-0.008195551112294197,
0.02401590719819069,
0.007872608490288258,
0.005995160434395075,
-0.012453635223209858,
-0.03960651904344559,
0.04271068051457405,
0.06339007616043091,
-0.005872516427189112,
-0.011847388930618763,
0.05966688692569733,
-0.015527378767728806,
-0.03861609101295471,
0.04020630195736885,
-0.008278092369437218,
0.05178132653236389,
0.019906742498278618,
0.0060804300010204315,
-0.03171665221452713,
0.02099701762199402,
-0.006976285483688116,
0.0022949855774641037,
-0.04234832152724266,
0.04227237403392792,
0.009325490333139896,
0.036290403455495834,
-0.03921248018741608,
-0.01569201797246933,
0.030296115204691887,
-0.053090233355760574,
-0.03010939620435238,
-0.020069345831871033,
-0.0796983614563942,
0.02193412370979786,
-0.008784384466707706,
0.0046317498199641705,
-0.009208676405251026,
-0.04681125283241272,
0.011383270844817162,
-0.023282820358872414,
0.006365206558257341,
0.01056481059640646,
-0.02306140400469303,
-0.020559541881084442,
-0.0042190104722976685,
0.017631929367780685,
0.027295049279928207,
-0.0070459009148180485,
-0.031113548204302788,
0.007226092740893364,
-0.08184122294187546,
-0.014927476644515991,
-0.025870172306895256,
-0.030592888593673706,
0.003497838508337736,
-0.03243236988782883,
-0.017094295471906662,
0.03957749158143997,
-0.007674733176827431,
0.03457392752170563,
0.02885102853178978,
0.008799082599580288,
0.0075373463332653046,
-0.07331013679504395,
0.06704087555408478,
0.03580643981695175,
-0.06174497678875923,
-0.011074176989495754,
-0.018060607835650444,
-0.003260830184444785,
0.0377114936709404,
0.03699260950088501,
0.013792211189866066,
-0.013987057842314243,
0.033790312707424164,
-0.030875742435455322,
-0.031071994453668594,
-0.028724266216158867,
0.014642156660556793,
0.024248993024230003,
-0.0016630201134830713,
-0.012145914137363434,
-0.03663391247391701,
-0.027048885822296143,
0.0038281490560621023,
0.006440615747123957,
0.027821846306324005,
0.06993141025304794,
0.0011968564940616488,
-0.0070956372655928135,
0.007306933403015137,
0.013265307992696762,
-0.008666054345667362,
0.05829306319355965,
0.019361287355422974,
0.033337660133838654,
0.025713207200169563,
-0.05349597707390785,
-0.04336227476596832,
0.03904614970088005,
-0.0028156153857707977,
-0.0060000941157341,
-0.023348353803157806,
0.0027829071041196585,
0.00040031439857557416,
-0.06489957869052887,
-0.012802405282855034,
0.010882812552154064,
-0.045753348618745804,
0.00018719572108238935,
-0.010027727112174034,
0.028138738125562668,
0.037847235798835754,
-0.052833303809165955,
0.04331693798303604,
0.04468180239200592,
-0.04877280816435814,
-0.006180751137435436,
0.013352904468774796,
0.038166288286447525,
-0.017737165093421936,
-0.013476242311298847,
0.047594599425792694,
0.02545345202088356,
0.013111990876495838,
0.031021639704704285,
0.009983552619814873,
0.0053201522678136826,
-0.004230804741382599,
-0.007203193847090006,
-0.0065298909321427345,
-0.00026615275419317186,
0.054020728915929794,
0.002900729887187481,
0.05652409791946411,
0.007167635951191187,
-0.0029057725332677364,
-0.007658918853849173,
0.002174601424485445,
0.007594660855829716,
0.02318786457180977,
0.012314273044466972,
0.008079481311142445,
-0.006823533680289984,
-0.016375921666622162,
-0.044139452278614044,
-0.009092123247683048,
0.03911307081580162,
-0.004421003628522158,
-0.013663757592439651,
-0.012886594980955124,
0.030314290896058083,
0.0028486575465649366,
-0.020385004580020905,
-0.03084149770438671,
-0.011749065481126308,
0.05927061289548874,
-0.007308279164135456,
0.007285458035767078,
-0.029735242947936058,
0.003904437180608511,
0.0016307772602885962,
0.05179455503821373,
-0.03702715411782265,
-0.011902972124516964,
-0.029600443318486214,
0.03100847825407982,
-0.001891410443931818,
0.01495056226849556
] |
<p><a href="http://earthtech.org/publications/davis_STAIF_conference_2.pdf" rel="nofollow">The Alcubierre Warp Drive in Higher Dimensional
Spacetime</a> (H. G. White & E. W. Davis), among other sources, proposes that the x-axis symmetry paradox for Alcubierre-style warp drives can be resolved by interpreting the warp field as producing a scalar boost on a pre-existing velocity. If that is the case, how can it obey frame invariance?
In other words, how does the boost "know" which velocity, in which inertial frame, it's supposed to be multiplying?</p>
| 8,275 |
[
0.00024765077978372574,
-0.011503569781780243,
-0.03219076991081238,
-0.018068261444568634,
0.042182911187410355,
0.008358525112271309,
-0.011084377765655518,
0.03997787460684776,
-0.013367305509746075,
-0.009311133995652199,
-0.014723889529705048,
0.019961293786764145,
0.07330352813005447,
0.034577492624521255,
0.03153648599982262,
0.014749922789633274,
-0.000732134678401053,
0.023805247619748116,
0.0074829226359725,
-0.024394862353801727,
0.009533843025565147,
0.005429475102573633,
-0.008415011689066887,
-0.006235290784388781,
-0.006101593840867281,
-0.016830142587423325,
0.02503277361392975,
0.0019442163174971938,
0.0028062432538717985,
0.04857364669442177,
0.013918962329626083,
-0.018339477479457855,
0.008036747574806213,
0.05651707574725151,
-0.021852869540452957,
-0.02419707365334034,
-0.006964019034057856,
-0.0486573725938797,
0.05098293349146843,
0.03175203874707222,
-0.054036181420087814,
0.0055169458501040936,
0.004748254548758268,
0.09556645154953003,
0.028292754665017128,
0.03299492225050926,
-0.026938363909721375,
0.001268006395548582,
0.05917377769947052,
-0.035998325794935226,
0.09981339424848557,
0.0003080259484704584,
0.012708546593785286,
0.013798769563436508,
-0.02462528645992279,
0.004447275772690773,
0.0607917495071888,
0.022842930629849434,
0.004689195659011602,
-0.021374447271227837,
-0.018602056428790092,
-0.01713385060429573,
-0.018389644101262093,
-0.029636770486831665,
-0.039708398282527924,
-0.0005617696442641318,
-0.028978243470191956,
-0.031101249158382416,
-0.010806296020746231,
-0.019659848883748055,
0.0294231865555048,
0.047120675444602966,
0.008194036781787872,
-0.010516024194657803,
0.006889264564961195,
-0.01987169124186039,
0.003325553610920906,
-0.00476907379925251,
0.06963276863098145,
0.020175324752926826,
0.019603677093982697,
-0.02833917737007141,
0.02099805697798729,
0.04378199204802513,
0.016499033197760582,
-0.010776153765618801,
0.049235083162784576,
0.011700691655278206,
-0.010193717665970325,
0.04022607207298279,
-0.016914477571845055,
-0.011822417378425598,
0.01782013662159443,
-0.016061218455433846,
-0.03661613166332245,
0.04941249266266823,
-0.00571757135912776,
0.048278212547302246,
0.007653431501239538,
-0.03322960436344147,
-0.024939948692917824,
-0.034190040081739426,
-0.010038184002041817,
0.0493285171687603,
0.011672301217913628,
0.02144186943769455,
0.01313033327460289,
0.02899704873561859,
-0.06000630930066109,
-0.016611499711871147,
-0.050429414957761765,
0.001081580761820078,
0.005669503007084131,
0.012982641346752644,
0.01734192669391632,
-0.044074032455682755,
-0.005829308647662401,
-0.028038378804922104,
0.024196553975343704,
0.042755916714668274,
0.03451114892959595,
0.03790814056992531,
0.025270933285355568,
0.00038257380947470665,
-0.04007705673575401,
0.006684164050966501,
0.011868143454194069,
-0.01997518539428711,
0.005411691032350063,
-0.0011261870386078954,
-0.002550570061430335,
-0.0746510699391365,
-0.020899465307593346,
-0.010961371473968029,
0.026272067800164223,
0.021030724048614502,
-0.0939393937587738,
-0.07378395646810532,
0.08853621035814285,
0.031452592462301254,
0.0070847515016794205,
-0.08026318997144699,
0.002285650698468089,
0.030790163204073906,
0.09185791015625,
-0.02558896318078041,
-0.012037385255098343,
-0.002440833719447255,
0.03665962815284729,
-0.0003879331052303314,
-0.016998976469039917,
-0.01102039311081171,
-0.01981857791543007,
-0.04140443354845047,
-0.002524480689316988,
-0.04196183755993843,
-0.0015696099726483226,
0.010933942161500454,
0.00046741741243749857,
-0.014245172031223774,
0.061205606907606125,
0.0008072647615335882,
0.00618812395259738,
0.027396107092499733,
0.016306282952427864,
-0.012691895477473736,
0.08032985776662827,
0.012523945420980453,
-0.008167380467057228,
0.022422417998313904,
-0.04768473654985428,
0.017519524320960045,
-0.0014947861200198531,
0.021918348968029022,
0.05651578679680824,
-0.04091300070285797,
0.0004704572493210435,
0.01485987938940525,
-0.013989808969199657,
-0.058775804936885834,
-0.043686434626579285,
-0.07050712406635284,
-0.002723034005612135,
-0.05807720124721527,
0.02925250306725502,
0.04548247158527374,
-0.026913130655884743,
0.030648428946733475,
0.010263278149068356,
-0.04618038237094879,
0.005192201118916273,
-0.07248471677303314,
0.003484533168375492,
0.008889037184417248,
-0.024447346106171608,
0.04850567504763603,
-0.008168011903762817,
0.03203483670949936,
0.01704002171754837,
0.0049444460310041904,
0.002656912663951516,
0.026443688198924065,
0.012080485001206398,
0.0060304077342152596,
-0.01129232533276081,
0.010548573918640614,
0.030986111611127853,
0.016453098505735397,
-0.0016233832575380802,
0.014982268214225769,
-0.047024697065353394,
-0.00003936702705686912,
0.004126477986574173,
0.008338449522852898,
-0.02039145678281784,
0.006399236619472504,
-0.0035295644775032997,
0.010334247723221779,
0.0004379011515993625,
0.035073183476924896,
-0.012762174941599369,
0.06883541494607925,
0.046118009835481644,
0.014477649703621864,
0.026844099164009094,
0.035821594297885895,
-0.012048350647091866,
-0.01293448731303215,
0.019032137468457222,
-0.03956517577171326,
-0.021710462868213654,
-0.036236945539712906,
-0.016967758536338806,
0.035847071558237076,
-0.013694437220692635,
0.014843513257801533,
0.03956722840666771,
0.028309917077422142,
0.029950084164738655,
0.0002609502407722175,
-0.02924814634025097,
-0.04330706596374512,
0.02557973563671112,
-0.018594559282064438,
0.037727635353803635,
0.0010582611430436373,
0.0414838083088398,
0.019032655283808708,
-0.01290462352335453,
0.003147219540551305,
-0.01927242986857891,
0.004909929819405079,
0.004564076196402311,
-0.019001532346010208,
0.0036697997711598873,
-0.004086633212864399,
0.017026523128151894,
0.016630588099360466,
0.030393406748771667,
0.051604267209768295,
0.028032919391989708,
0.013496976345777512,
-0.018377233296632767,
0.01416277140378952,
0.0015138194430619478,
-0.026724644005298615,
0.026777802035212517,
-0.042776525020599365,
0.019341055303812027,
-0.03147965669631958,
0.0624389685690403,
-0.06998519599437714,
0.0018588941311463714,
0.0070082275196909904,
-0.011779239401221275,
-0.005220863036811352,
0.017280878499150276,
0.02793978899717331,
-0.027574801817536354,
-0.014447328634560108,
0.004200886469334364,
-0.013229019939899445,
0.005996436811983585,
0.04499359428882599,
-0.049114204943180084,
0.03339946269989014,
-0.07190035283565521,
-0.06758500635623932,
0.03373844176530838,
0.010896698571741581,
0.06314478814601898,
0.0067506819032132626,
-0.0006977223674766719,
-0.07181375473737717,
0.011371348984539509,
-0.05384448915719986,
-0.00487468671053648,
-0.0158943310379982,
0.0012505461927503347,
0.04236737638711929,
-0.029180914163589478,
-0.050610560923814774,
0.018257124349474907,
-0.005908726714551449,
-0.01809321530163288,
0.003144752001389861,
0.014352609403431416,
-0.0070703295059502125,
-0.04716216400265694,
0.04277382418513298,
0.02695905975997448,
-0.007918084971606731,
-0.0013638854725286365,
-0.0013270920608192682,
-0.05790485441684723,
0.004693809896707535,
-0.0004828212840948254,
0.04049853980541229,
0.005573583301156759,
-0.0380713976919651,
0.05579781159758568,
0.030339017510414124,
-0.006451718509197235,
-0.06992152333259583,
-0.0015274822944775224,
0.009538165293633938,
-0.05111802741885185,
0.03521140664815903,
0.040197283029556274,
0.007688557263463736,
0.02433156967163086,
0.05343148857355118,
0.0010494423331692815,
0.0520734079182148,
-0.005510000046342611,
-0.03179429471492767,
-0.008667975664138794,
0.028420737013220787,
0.05542220547795296,
0.013367915526032448,
0.005940656177699566,
-0.03796526417136192,
0.0028453501872718334,
0.012876860797405243,
0.017168570309877396,
0.006469169165939093,
-0.028526226058602333,
0.0156460702419281,
0.04505762830376625,
-0.01220479141920805,
-0.007185665890574455,
0.016841089352965355,
0.003378393594175577,
0.014499581418931484,
0.020050128921866417,
0.009681044146418571,
0.0010987588902935386,
-0.02488904446363449,
0.025743912905454636,
0.013804479502141476,
0.009730659425258636,
-0.04921583831310272,
0.009390824474394321,
0.0008198688155971467,
-0.016001900658011436,
-0.00667638098821044,
-0.032039280980825424,
-0.03359586000442505,
0.06504688411951065,
0.0077915070578455925,
-0.017283989116549492,
0.030774783343076706,
-0.0029872518498450518,
0.027584124356508255,
-0.07027124613523483,
0.007245433051139116,
0.01580890826880932,
0.024043774232268333,
-0.015247836709022522,
0.056492533534765244,
0.016200708225369453,
0.006957281846553087,
-0.034821927547454834,
-0.006381700746715069,
-0.08663002401590347,
0.01598464511334896,
-0.05379858613014221,
-0.0037200499791651964,
-0.017349744215607643,
-0.02583020180463791,
-0.004528289195150137,
-0.045572325587272644,
-0.010970029048621655,
-0.03046129085123539,
0.00663281325250864,
-0.0657995417714119,
0.024153931066393852,
-0.01860845275223255,
-0.06345918029546738,
-0.02777305617928505,
0.013050423003733158,
0.08080240339040756,
-0.028088979423046112,
0.0502735897898674,
0.0442703552544117,
-0.05538543686270714,
-0.0032454284373670816,
0.008290299214422703,
0.022237537428736687,
0.011844290420413017,
-0.010434217751026154,
-0.006482132710516453,
-0.004099688492715359,
-0.05083426088094711,
-0.010744010098278522,
0.019811205565929413,
0.053721796721220016,
0.007559662219136953,
0.000031226281862473115,
-0.03454241901636124,
-0.02947891317307949,
-0.020917071029543877,
0.01776903122663498,
0.049277715384960175,
-0.011397377587854862,
0.00018414830265101045,
0.06051190197467804,
0.06592504680156708,
-0.0009899957804009318,
0.03506024181842804,
0.0787193700671196,
-0.016292443498969078,
-0.021082831546664238,
-0.04625876620411873,
0.005590106826275587,
-0.003087392309680581,
-0.007158681750297546,
0.011628597043454647,
0.00825960747897625,
0.017672108486294746,
0.001047516125254333,
0.01715937815606594,
-0.009816144593060017,
-0.03221067041158676,
0.02646622620522976,
-0.03976231440901756,
0.018369145691394806,
0.019739171490073204,
0.03853265196084976,
-0.007151119410991669,
0.021444695070385933,
0.04095935449004173,
0.03412269428372383,
-0.006680496968328953,
-0.07352393865585327,
-0.026895808055996895,
-0.0035272843670099974,
0.002628426533192396,
0.028666691854596138,
-0.0025754219386726618,
-0.07130274176597595,
-0.016411282122135162,
0.04613850638270378,
-0.016091300174593925,
0.038368433713912964,
0.008004200644791126,
-0.0012966158101335168,
-0.05007784441113472,
-0.0037009352818131447,
-0.0243962612003088,
0.0076531944796442986,
-0.008900034241378307,
-0.01221728790551424,
-0.0029636286199092865,
0.014104955829679966,
-0.014880209229886532,
0.004758410155773163,
0.0006160043412819505,
0.02294466271996498,
0.045217834413051605,
0.021099010482430458,
-0.014031920582056046,
0.04362456873059273,
-0.0099716205149889,
-0.0858757346868515,
-0.010668004862964153,
0.02704215981066227,
-0.03475690633058548,
0.06445363163948059,
-0.04249468445777893,
-0.033533744513988495,
0.028095396235585213,
-0.011315692216157913,
-0.004878716077655554,
0.016864413395524025,
-0.05694599449634552,
-0.009908362291753292,
0.009073197841644287,
0.006531224120408297,
0.04386024922132492,
0.012424286454916,
-0.037702012807130814,
-0.004671545699238777,
0.01293084118515253,
0.018795577809214592,
-0.04077625274658203,
0.007605058141052723,
-0.016998939216136932,
0.004131299909204245,
-0.047162264585494995,
0.07000286132097244,
-0.00013327639317139983,
0.01770804077386856,
-0.004686070140451193,
-0.00041351537220180035,
0.005437642335891724,
0.046144142746925354,
-0.013299968093633652,
0.0006417197873815894,
-0.0016230721957981586,
0.04191488027572632,
-0.024960331618785858,
-0.02618546225130558,
0.024288276210427284,
0.017204975709319115,
0.021712779998779297,
0.02907712571322918,
0.016163889318704605,
0.015067756175994873,
0.002493091393262148,
0.038661424070596695,
0.040537137538194656,
-0.03917921707034111,
0.034088123589754105,
0.006217166781425476,
0.0030877694953233004,
-0.0077054244466125965,
0.010063119232654572,
-0.019191928207874298,
0.00409787567332387,
-0.0058186291716992855,
0.01668560318648815,
-0.031436335295438766,
-0.01387635525316,
0.012881370261311531,
0.028495294973254204,
-0.1158943921327591,
-0.053899455815553665,
-0.012932761572301388,
0.005694155115634203,
-0.0026013071183115244,
-0.05902944877743721,
-0.01588497683405876,
-0.07579562067985535,
-0.029010338708758354,
-0.020774036645889282,
0.04055436700582504,
-0.023138336837291718,
-0.010106448084115982,
0.0037873312830924988,
-0.008489526808261871,
-0.01228377316147089,
-0.04309952259063721,
-0.014299580827355385,
0.0028973084408789873,
-0.019375531002879143,
0.00843653455376625,
-0.019405536353588104,
0.0350654236972332,
-0.029894975945353508,
-0.018577896058559418,
-0.04266664758324623,
0.004442252684384584,
-0.025134610012173653,
-0.02757672220468521,
0.023354176431894302,
0.050940606743097305,
-0.012600538320839405,
0.020047880709171295,
-0.046555303037166595,
-0.005342820659279823,
-0.0373796783387661,
0.022314127534627914,
0.0095100412145257,
-0.010088689625263214,
-0.015728216618299484,
-0.0061141615733504295,
0.04186299443244934,
0.008975695818662643,
-0.005704586394131184,
-0.00578933535143733,
0.02896266244351864,
-0.04797988757491112,
-0.0009438018314540386,
0.023598965257406235,
0.0042116292752325535,
0.04690259322524071,
-0.0062619540840387344,
-0.009974989108741283,
0.009469919838011265,
-0.03288722038269043,
-0.06157626584172249,
-0.02927716076374054,
0.00006304978160187602,
0.014211281202733517,
0.07383103668689728,
-0.044301655143499374,
0.019599201157689095,
0.024740055203437805,
-0.06941476464271545,
-0.030861297622323036,
-0.0271957628428936,
0.002407647203654051,
0.005234358366578817,
-0.04505883902311325,
0.040954671800136566,
0.017074955627322197,
-0.020418576896190643,
0.03985076770186424,
0.05382918193936348,
0.004586801398545504,
-0.014466696418821812,
0.07990135997533798,
0.03463561832904816,
0.03394776210188866,
-0.003093983046710491,
-0.0034973390866070986,
0.08696843683719635,
-0.02659655548632145,
-0.009318414144217968,
0.0058455397374928,
0.01929423213005066,
0.03129114583134651,
0.023743396624922752,
-0.004264445509761572,
-0.020641561597585678,
-0.01547392550855875,
-0.05054043233394623,
0.020444151014089584,
0.022189034149050713,
0.017419783398509026,
0.025762557983398438,
-0.008882908150553703,
0.04881341755390167,
0.012468747794628143,
0.008350998163223267,
-0.03549579530954361,
-0.0367862768471241,
-0.011748285964131355,
-0.028132963925600052,
0.003140051383525133,
0.030470386147499084,
0.034765273332595825,
-0.04814471676945686,
-0.017206033691763878,
-0.013695471920073032,
0.046102289110422134,
0.014886075630784035,
0.05763443931937218,
-0.019100317731499672,
0.08023731410503387,
-0.058831002563238144,
-0.0004824054194614291,
-0.046708639711141586,
-0.016397729516029358,
0.12294431030750275,
0.05316094681620598,
0.005178671795874834,
-0.05802251771092415,
0.02701851911842823,
-0.0037338228430598974,
-0.005085080396384001,
-0.03724747896194458,
0.012134462594985962,
0.0029863694217056036,
0.015442856587469578,
0.019346844404935837,
0.052715886384248734,
0.022293562069535255,
-0.03972845897078514,
0.0006992185371927917,
-0.06944718211889267,
0.002831145655363798,
-0.024097448214888573,
0.008374889381229877,
0.01673726551234722,
-0.017340607941150665,
-0.04858187213540077,
0.019675660878419876,
-0.017593350261449814,
0.016655333340168,
-0.04454314336180687,
-0.015039955265820026,
-0.003183534601703286,
0.02765599824488163,
-0.014811353757977486,
0.002882335102185607,
0.005692922510206699,
-0.0029469921719282866,
-0.01587391085922718,
-0.0030377982184290886,
-0.0035577130038291216,
-0.01203012652695179,
0.05032529681921005,
0.02820729836821556,
0.03564971312880516,
0.02212453819811344,
-0.020684553310275078,
0.00956509355455637,
-0.023150894790887833,
0.030470630154013634,
-0.003591143758967519,
0.032716140151023865,
-0.0007529021240770817,
-0.0000012228734931341023,
-0.003778068581596017,
-0.027387352660298347,
-0.006530091632157564,
-0.053995825350284576,
-0.03772548958659172,
-0.0008317162282764912,
0.009089013561606407,
0.0486828051507473,
-0.029991399496793747,
0.0012393621727824211,
0.045762404799461365,
0.002261947840452194,
0.021917494013905525,
0.00848099123686552,
0.0009985131910070777,
-0.0012533213011920452,
-0.021710356697440147,
0.03482440114021301,
0.001499708043411374,
-0.018305515870451927,
-0.04812714830040932,
-0.0072643328458070755,
-0.02858377806842327,
0.011750215664505959,
0.028590362519025803,
-0.034345705062150955,
0.01620381698012352,
0.003297594841569662,
-0.0061220889911055565,
-0.009986494667828083,
-0.05345972254872322,
-0.004797482863068581,
-0.02339779958128929,
-0.0039039875846356153,
0.005903101526200771,
-0.016874894499778748,
0.028297897428274155,
0.035643257200717926,
-0.02848566509783268,
0.014627316035330296,
-0.018330160528421402,
0.015663454309105873,
-0.0006831337232142687,
-0.02210235968232155,
-0.0008033164776861668,
-0.0033608044032007456,
-0.01663939468562603,
-0.04470596835017204,
-0.05518580228090286,
0.009054495953023434,
0.030505819246172905,
0.035883400589227676,
-0.013631375506520271,
0.014981904998421669,
-0.031341198831796646,
-0.0022942577488720417,
0.06057559698820114,
-0.01775227300822735,
-0.003289078129455447,
0.015222876332700253,
0.022869674488902092,
-0.046167585998773575,
-0.016055868938565254,
-0.01634838804602623,
-0.030784152448177338,
-0.03309871628880501,
0.0461314432322979,
-0.02066689543426037,
-0.022364908829331398,
-0.0019893329590559006,
0.00206385413184762,
-0.015720924362540245,
-0.016530048102140427,
0.010989157482981682,
0.019635770469903946,
0.005793489050120115,
-0.03601128235459328,
-0.011354918591678143,
0.025313256308436394,
-0.04882439970970154,
-0.00265515292994678,
-0.001818753546103835,
-0.00778349582105875,
-0.015614030882716179,
0.023086121305823326,
0.02100066840648651,
-0.0034457275178283453,
0.01894496940076351,
-0.01796911470592022,
-0.03507770597934723,
0.003804892534390092,
-0.02068696916103363,
-0.041439127177000046,
0.08295948058366776,
0.005398837849497795,
-0.003144509857520461,
0.015505346469581127,
-0.023792609572410583,
-0.02132849395275116,
0.03585156798362732,
-0.02240902930498123,
-0.00505431042984128,
0.03268834576010704,
-0.02296540141105652,
0.015439804643392563,
0.02010195329785347,
0.019825713708996773,
-0.06093134358525276,
-0.0174786988645792,
0.03772201016545296,
0.01691499911248684,
-0.016928771510720253,
0.012223828583955765,
-0.03322568163275719,
0.0003988435782957822,
0.032317113131284714,
-0.015401467680931091,
0.009374473243951797,
0.014592946507036686,
0.05646686628460884,
-0.004410221241414547,
-0.01412911619991064,
0.014949791133403778,
0.024387361481785774,
-0.1235828623175621,
0.010151886381208897,
0.0030625162180513144,
0.032612938433885574,
0.0497841015458107,
-0.06919447332620621,
-0.000938952318392694,
0.03634445369243622,
-0.07113003730773926,
-0.000837714527733624,
-0.013181637972593307,
-0.021686429157853127,
-0.0658024251461029,
-0.0042711724527180195,
0.0007746628834865987,
0.05406942218542099,
0.04426943510770798,
0.023070864379405975,
0.004628383554518223,
0.009579064324498177,
-0.008659372106194496,
-0.039626024663448334,
-0.00613770168274641,
0.026327472180128098,
0.011737633496522903,
0.0028519288171082735,
0.04680684581398964,
0.0005736717721447349,
-0.03037239983677864,
0.023705730214715004,
0.03349015489220619,
0.010813449509441853,
-0.03941952437162399,
0.026867376640439034,
0.014843782410025597,
0.015442353673279285,
-0.002101354533806443,
-0.02167407236993313,
-0.00539654353633523,
0.004428336396813393,
0.02596629224717617,
0.033780720084905624,
-0.009461279027163982,
-0.018300773575901985,
0.014740072190761566,
-0.0323527529835701,
-0.015443414449691772,
0.05151776224374771,
-0.022225821390748024,
-0.028476519510149956,
0.011899840086698532,
0.01704641617834568,
0.024968314915895462,
-0.01878289319574833,
0.014118349179625511,
-0.05540723726153374,
-0.008157964795827866,
0.03296409919857979,
-0.01905614696443081,
-0.022232085466384888,
0.0025610970333218575,
-0.04795971140265465,
-0.022475596517324448,
0.014184114523231983,
-0.026411529630422592,
0.03206740692257881,
-0.04944571852684021,
-0.012446862645447254,
-0.0261106975376606,
-0.0077577573247253895,
0.03276890516281128,
-0.03475859388709068,
0.007590625900775194,
0.06881359219551086,
0.020484307780861855,
0.06720167398452759,
-0.00947251170873642,
-0.04886776581406593,
-0.02610352821648121,
-0.05124947428703308,
0.038311876356601715,
0.027217132970690727,
-0.026670942083001137,
0.0032194326631724834,
-0.021899132058024406,
0.012933638878166676,
0.0101652005687356,
0.04446057602763176,
0.04119541868567467,
-0.025996847078204155,
0.05190499126911163,
0.007164157927036285,
0.002864610170945525,
-0.03393128141760826,
0.005202054046094418,
-0.0027450465131551027,
-0.030164426192641258,
-0.036561429500579834,
-0.0013204518472775817,
-0.032469917088747025,
-0.00119804497808218,
-0.020365746691823006,
0.029423868283629417,
0.031132055446505547,
0.03450397402048111,
-0.0612553209066391,
0.03575010597705841,
0.002112027956172824,
-0.0018967733485624194,
0.04018447548151016,
0.017044899985194206,
-0.02227214351296425,
0.046045541763305664,
-0.0021074642427265644,
-0.048238445073366165,
0.0044950079172849655,
-0.03890031576156616,
-0.0138280363753438,
0.006314100231975317,
0.004464634228497744,
-0.007210730575025082,
-0.03786950930953026,
0.00391785753890872,
0.06209414452314377,
-0.018017228692770004,
-0.01928125135600567,
0.04666653275489807,
0.020750852301716805,
0.029803095385432243,
0.005028698593378067,
0.0025636395439505577,
0.005050558131188154,
-0.002421060809865594,
0.000020028290236950852,
0.03698974847793579,
0.009354333393275738,
0.027963416650891304,
-0.002676896285265684,
0.06367389112710953,
-0.012376882135868073,
0.00954514741897583,
-0.016387540847063065,
0.03018357791006565,
-0.03729861602187157,
-0.02732325717806816,
-0.018970150500535965,
-0.04530683904886246,
0.04959060996770859,
0.04503558576107025,
-0.00872092880308628,
0.09701423346996307,
-0.03221992403268814,
0.006031470373272896,
-0.010746346786618233,
0.01921871118247509,
0.006006921641528606,
0.009375120513141155,
-0.025021232664585114,
0.04611266031861305,
-0.021321918815374374,
-0.0032496138010174036,
-0.00604840787127614,
0.001964073395356536,
0.04366869479417801,
-0.010358523577451706,
-0.00250595947727561,
0.0019748746417462826,
-0.016453338786959648,
0.060297537595033646,
-0.037556931376457214,
-0.02589564397931099,
-0.031362276524305344,
0.011581097729504108,
0.026939721778035164,
0.06090079993009567,
-0.02683999203145504,
-0.017958229407668114,
-0.039002273231744766,
0.04399910196661949,
-0.06032964959740639,
-0.025245700031518936,
-0.005840921308845282,
0.022880898788571358,
-0.010262264870107174,
0.021186381578445435
] |
<p>Let me first believe that the ${\cal N}=2$ Landau-Ginzburg theory does in the IR flow to a non-trivial fixed point and that if the potential is of the form $\Phi ^k$ then the central charge of the CFT at that fixed point is indeed $3(1-\frac{2}{k})$. </p>
<ul>
<li><p>Given the above, how does it somehow obviously follow (by Zamlodchikov's c-theorem?) that if I had the potential as any homogeneous function of degree $k$ in say $n$ scalar chiral fields then the central charge at the similar fixed point will be $3n(1-\frac{2}{k})$? </p></li>
<li><p>I have seen some quite terse arguments but I want to know if there is a simple intuitive way to see that the above theory does have a non-trivial IR fixed point (the claim that I initially started off believing). </p></li>
<li><p>Now its also true that the CFT at this fixed point is infact a minimal model and that apprently follows from some representation theory of the ${\cal N}=2$ superconformal algebra. Can someone kindly give me a reference to that? </p></li>
<li><p>Finally are there known generalizations of this construction to higher supersymmetries or higher diemensions? </p></li>
</ul>
| 8,276 |
[
-0.011073713190853596,
0.01145252026617527,
0.02137446217238903,
-0.03232906013727188,
0.02440289407968521,
-0.014088449999690056,
-0.05110105499625206,
-0.03405212610960007,
-0.00320477900095284,
-0.07461947947740555,
0.030909229069948196,
-0.0033551412634551525,
0.05400020256638527,
0.019925925880670547,
0.006112935487180948,
0.01720857247710228,
-0.0036459090188145638,
-0.018237203359603882,
0.008394861593842506,
-0.017576875165104866,
0.01729740761220455,
0.06760475784540176,
0.009772212244570255,
0.00201035151258111,
-0.014400927349925041,
0.0054550995118916035,
-0.00602846872061491,
0.011332391761243343,
0.03910452872514725,
0.08345291018486023,
-0.019212111830711365,
-0.030495483428239822,
-0.017518168315291405,
-0.003318056697025895,
-0.010588753037154675,
0.020033476874232292,
-0.0146623644977808,
-0.018764324486255646,
0.011283940635621548,
-0.0027436146046966314,
-0.046293288469314575,
-0.010503909550607204,
-0.029555698856711388,
0.04332539066672325,
-0.016243012621998787,
0.007254039868712425,
-0.03612188622355461,
-0.013322273269295692,
0.06095542758703232,
-0.0674256682395935,
0.03299056738615036,
0.039220668375492096,
-0.012890191748738289,
0.003088913392275572,
0.0062026078812778,
-0.052856385707855225,
0.05293901637196541,
0.08051835745573044,
0.03439171239733696,
-0.03189782425761223,
-0.0594048798084259,
-0.03956962376832962,
-0.006238883826881647,
-0.019897786900401115,
-0.03284193575382233,
0.024130836129188538,
0.009861067868769169,
0.0012097918661311269,
-0.008501230739057064,
-0.022192614153027534,
-0.020108148455619812,
0.054978832602500916,
-0.02049848437309265,
-0.02506926842033863,
0.0409601554274559,
-0.007251909468322992,
-0.0007246793247759342,
-0.02818962000310421,
0.014864947646856308,
0.04669070243835449,
-0.06344802677631378,
0.029308181256055832,
0.0046109952963888645,
0.030584659427404404,
0.012218373827636242,
-0.01346124429255724,
0.08339086174964905,
0.004031251184642315,
0.001344537828117609,
0.060050979256629944,
-0.057814206928014755,
-0.009829407557845116,
0.04309498891234398,
-0.041458263993263245,
-0.04109391197562218,
0.017574718222022057,
0.016552217304706573,
0.04896305873990059,
-0.015456313267350197,
-0.0007752756937406957,
-0.04886436089873314,
-0.011882846243679523,
-0.01600753888487816,
0.07812994718551636,
-0.0052774203941226006,
0.007045888341963291,
-0.03282535448670387,
0.005579562392085791,
-0.028219351544976234,
-0.02588546834886074,
-0.07400732487440109,
0.011799651198089123,
-0.011039243079721928,
-0.0014988565817475319,
0.004610538948327303,
-0.027020782232284546,
-0.02678150124847889,
-0.03945067524909973,
0.05575842782855034,
0.08195726573467255,
0.05171201750636101,
-0.012273420579731464,
0.0005868507432751358,
-0.023750770837068558,
-0.06863495707511902,
0.02969258837401867,
0.03892713412642479,
0.012879799120128155,
-0.024075454100966454,
-0.011623281054198742,
0.032821159809827805,
0.02742559276521206,
0.01485136616975069,
0.013890530914068222,
0.03222694993019104,
-0.03350118175148964,
-0.06224220246076584,
-0.04842999950051308,
0.050041064620018005,
-0.03568283095955849,
-0.013024551793932915,
-0.07913635671138763,
-0.03077278845012188,
0.0367705374956131,
0.09264473617076874,
-0.03824516385793686,
0.017060941085219383,
0.008381372317671776,
0.029620174318552017,
0.04314948990941048,
-0.030840927734971046,
-0.007232198491692543,
0.007913620211184025,
-0.04222525283694267,
-0.052679643034935,
-0.04362122341990471,
0.07314317673444748,
0.031254734843969345,
0.01852528750896454,
-0.03997733071446419,
0.09180089831352234,
-0.029640287160873413,
0.0230819433927536,
0.014114775694906712,
0.020019391551613808,
0.0013726233737543225,
0.07342410087585449,
0.008812760934233665,
0.03723527118563652,
0.02543252520263195,
-0.011304527521133423,
0.041806016117334366,
0.045820578932762146,
0.05072271078824997,
0.06454001367092133,
-0.041005995124578476,
-0.00581252621486783,
-0.013804417103528976,
0.00661906274035573,
0.007480771746486425,
-0.0164639949798584,
-0.024402905255556107,
-0.01006958819925785,
-0.001733038923703134,
-0.013165011070668697,
0.039675869047641754,
-0.046814415603876114,
-0.011275960132479668,
0.018661918118596077,
-0.07542790472507477,
0.013696449808776379,
-0.031662192195653915,
-0.019265567883849144,
0.002125872764736414,
-0.011504419147968292,
0.05264519155025482,
0.012227063998579979,
0.0012192217400297523,
0.0059889680705964565,
-0.037477921694517136,
0.01350630633533001,
0.015257996506989002,
-0.009326794184744358,
-0.01274071354418993,
0.041951365768909454,
-0.010715420357882977,
0.020582573488354683,
-0.01015546265989542,
0.046426866203546524,
-0.020160600543022156,
-0.017875248566269875,
0.034916818141937256,
0.01726650819182396,
0.049899570643901825,
-0.0008987330365926027,
0.027174627408385277,
-0.007591393310576677,
0.04506984353065491,
0.021365540102124214,
0.030887505039572716,
-0.026619447395205498,
0.0740731805562973,
0.0421249158680439,
-0.023463014513254166,
-0.003985230810940266,
0.04382268711924553,
0.0025842918548732996,
-0.01204504445195198,
-0.0018568244995549321,
-0.00543720368295908,
-0.07289689034223557,
-0.01346619613468647,
0.03802206367254257,
0.07293590158224106,
-0.0255855992436409,
-0.001343531534075737,
0.011386697180569172,
0.028225701302289963,
0.03193497285246849,
-0.006670319475233555,
-0.024313686415553093,
-0.04424497112631798,
-0.00025229781749658287,
0.016954174265265465,
0.00017184444004669785,
-0.0037689029704779387,
0.032294128090143204,
-0.027636568993330002,
0.00624754698947072,
-0.007072063162922859,
-0.07663610577583313,
0.015358916483819485,
-0.04474114999175072,
-0.02854563668370247,
0.020495714619755745,
0.0037969781551510096,
0.03552062436938286,
0.004557280335575342,
0.04637297987937927,
0.040834423154592514,
-0.031965818256139755,
0.003152554389089346,
-0.03829441964626312,
0.01681627705693245,
0.07366414368152618,
-0.014789707958698273,
-0.006401261780411005,
-0.018049756065011024,
0.011734419502317905,
-0.03608071431517601,
-0.021601075306534767,
-0.020651057362556458,
-0.0002742731012403965,
-0.010751044377684593,
0.02939620241522789,
-0.007214500568807125,
-0.013458438217639923,
0.015026875771582127,
-0.060740876942873,
-0.0030515671242028475,
0.07288598269224167,
0.007076452486217022,
0.029640335589647293,
0.03321363404393196,
-0.02259819582104683,
0.017105305567383766,
-0.051346976310014725,
-0.027099918574094772,
0.02517816610634327,
-0.009252726100385189,
0.03846803680062294,
-0.04286424443125725,
-0.026909595355391502,
-0.013911478221416473,
0.0026585322339087725,
-0.005479402374476194,
0.03920907899737358,
-0.07901476323604584,
0.024174874648451805,
0.06804188340902328,
0.01611921563744545,
-0.033717334270477295,
0.041723232716321945,
-0.0032177886459976435,
-0.018489325419068336,
-0.0027915420942008495,
0.020270507782697678,
0.015131712891161442,
-0.04520391300320625,
0.047832150012254715,
-0.016775397583842278,
-0.0642654150724411,
0.021865928545594215,
-0.0618320032954216,
-0.01244121603667736,
0.018733978271484375,
-0.009511129930615425,
0.027855508029460907,
0.0090176435187459,
-0.08293526619672775,
0.04411691799759865,
0.025353698059916496,
-0.044036347419023514,
-0.03729899600148201,
0.011822984553873539,
0.002771876286715269,
0.014061630703508854,
0.021732982248067856,
0.05677336826920509,
-0.046816010028123856,
0.031175263226032257,
0.02265969291329384,
0.05262657254934311,
0.05110419541597366,
0.012986271642148495,
-0.011160635389387608,
0.03417601063847542,
-0.0020261213649064302,
-0.007621204946190119,
0.04538409784436226,
-0.016117319464683533,
-0.0197663102298975,
-0.029631169512867928,
0.008753088302910328,
-0.006495688110589981,
0.05880211666226387,
-0.012929546646773815,
0.058234479278326035,
-0.005623141303658485,
0.03464077413082123,
0.00980175007134676,
0.017474355176091194,
0.014335189014673233,
-0.04031815752387047,
-0.002408559899777174,
0.02000700868666172,
0.019452478736639023,
-0.03520210087299347,
0.023549534380435944,
0.014046892523765564,
0.010059740394353867,
-0.06568253040313721,
-0.03934994712471962,
-0.02025522105395794,
-0.021870004013180733,
-0.00208485359326005,
-0.005256465636193752,
-0.01276512909680605,
-0.011327752843499184,
0.015199080109596252,
0.02752631902694702,
-0.00765798008069396,
-0.01933777518570423,
0.01503735315054655,
-0.02361280284821987,
-0.007710824720561504,
-0.005741563625633717,
0.013422921299934387,
0.01548095140606165,
0.03157227858901024,
0.0031707696616649628,
0.0205166507512331,
-0.0071328748017549515,
0.012410792522132397,
-0.09227660298347473,
-0.027072032913565636,
-0.007597025949507952,
0.013100332580506802,
0.007763528265058994,
-0.02387111261487007,
0.00612038467079401,
0.007187423296272755,
-0.04078422486782074,
-0.015409478917717934,
-0.018120190128684044,
-0.014258029870688915,
0.049073196947574615,
-0.04079873859882355,
-0.02782289683818817,
-0.018639393150806427,
0.02824976295232773,
0.055708613246679306,
-0.050942808389663696,
-0.0286818016320467,
0.004532070830464363,
-0.03553314879536629,
-0.00258638896048069,
-0.017796169966459274,
0.062146879732608795,
0.009775912389159203,
0.03132667392492294,
0.02636704035103321,
-0.009157237596809864,
-0.024343423545360565,
0.0012901410227641463,
-0.005849864799529314,
0.013917366974055767,
0.0029813754372298717,
-0.015588236972689629,
0.020113535225391388,
-0.06261353939771652,
-0.020195085555315018,
-0.001813017181120813,
0.06075085327029228,
0.03579043969511986,
0.02607543207705021,
0.03964652866125107,
0.005235387943685055,
-0.01755305379629135,
0.015565898269414902,
0.049076978117227554,
-0.027638006955385208,
-0.040491607040166855,
-0.0453537292778492,
-0.03331654146313667,
0.0007915131864137948,
-0.013188425451517105,
0.012542521581053734,
-0.00864739716053009,
-0.019306298345327377,
0.01046508364379406,
0.026255076751112938,
0.002870921976864338,
-0.03029439225792885,
-0.01712660677731037,
0.00892554596066475,
-0.010465364903211594,
0.012493405491113663,
0.0055993469431996346,
0.013121422380208969,
0.038818664848804474,
0.035772792994976044,
0.016974637284874916,
-0.0052865175530314445,
-0.08314606547355652,
0.0035414888989180326,
0.0049466961063444614,
0.005854348186403513,
0.0025470934342592955,
-0.012785383500158787,
-0.05320286750793457,
-0.005982326343655586,
0.03278356418013573,
-0.012741874903440475,
0.011004802770912647,
0.030439181253314018,
-0.019080178812146187,
-0.017893582582473755,
-0.04026838392019272,
0.0144423833116889,
0.033580102026462555,
0.01635391265153885,
0.030465932562947273,
-0.03866979852318764,
-0.001487260451540351,
-0.007672299165278673,
0.01978123001754284,
0.013902468606829643,
0.043450728058815,
0.0398809015750885,
0.008059537038207054,
0.016750406473875046,
0.061186350882053375,
-0.01726621575653553,
-0.08032295107841492,
0.011471157893538475,
0.007066107355058193,
0.030972765758633614,
0.005963734816759825,
-0.019052745774388313,
-0.052433498203754425,
-0.006658339872956276,
0.016246411949396133,
-0.0003823339648079127,
0.04375670477747917,
-0.05275190994143486,
0.05502242594957352,
0.02788640931248665,
0.013335559517145157,
0.03543756529688835,
0.048209358006715775,
-0.015336422249674797,
-0.04533860459923744,
0.005084095057100058,
0.029337292537093163,
0.016027163714170456,
0.020587824285030365,
-0.025400539860129356,
0.05005701258778572,
-0.026711029931902885,
0.04461336508393288,
-0.025518234819173813,
-0.01631157658994198,
-0.00748153543099761,
0.012232321314513683,
-0.036828260868787766,
0.0034501408226788044,
-0.006032480858266354,
-0.008090456947684288,
-0.0042636762373149395,
0.03380414843559265,
0.022513044998049736,
-0.005521316546946764,
0.020398903638124466,
-0.010466539300978184,
-0.005302873905748129,
0.011761995032429695,
-0.006874614395201206,
0.017318513244390488,
-0.03891061246395111,
-0.002857687883079052,
0.010483392514288425,
-0.05608169361948967,
0.043562810868024826,
-0.011730005033314228,
-0.01428274717181921,
-0.024168692529201508,
-0.033441800624132156,
-0.033776067197322845,
0.006661750841885805,
0.005104267969727516,
-0.017000794410705566,
-0.0073962402530014515,
-0.014015785418450832,
0.022716861218214035,
0.009928534738719463,
-0.05558396875858307,
-0.02248055301606655,
0.008571821264922619,
0.0039007384330034256,
-0.013677706941962242,
-0.020060107111930847,
-0.02060540020465851,
-0.00908209290355444,
-0.03414992615580559,
0.0279118362814188,
0.07234621047973633,
-0.033371422439813614,
-0.018910085782408714,
0.02168724313378334,
0.03821778669953346,
0.016486918553709984,
0.001695055398158729,
-0.023672286421060562,
0.019881879910826683,
-0.031096288934350014,
-0.011714518070220947,
0.0035340164322406054,
0.038375891745090485,
-0.01900169625878334,
-0.017531709745526314,
0.012815631926059723,
-0.044066302478313446,
0.04864463210105896,
-0.01546191144734621,
-0.018102556467056274,
0.024454699829220772,
0.011199958622455597,
0.02927754446864128,
-0.028837798163294792,
-0.02077343873679638,
-0.014665927737951279,
0.010773960500955582,
-0.018949102610349655,
0.014304275624454021,
0.0000687076899339445,
-0.050196077674627304,
0.05739988759160042,
-0.01662864349782467,
-0.011976746842265129,
-0.00880962610244751,
0.045896366238594055,
0.02138587459921837,
-0.052131883800029755,
-0.00487876869738102,
-0.029309505596756935,
0.0026726655196398497,
0.025276053696870804,
0.025223148986697197,
0.011264839209616184,
-0.013725100085139275,
-0.007052623201161623,
-0.03516773506999016,
-0.02730569988489151,
0.04479413107037544,
0.04222985357046127,
0.004954030737280846,
0.05505707114934921,
-0.025408532470464706,
-0.011553122662007809,
0.011114649474620819,
0.006244696211069822,
0.011659202165901661,
-0.0024861888960003853,
-0.013068120926618576,
0.039095353335142136,
-0.06867226213216782,
-0.00813550315797329,
0.05751495808362961,
0.03361964598298073,
-0.012284358032047749,
0.022806808352470398,
0.07343339920043945,
-0.03171703964471817,
0.04319104552268982,
-0.019312027841806412,
-0.05869586393237114,
0.10307776927947998,
-0.023933131247758865,
0.05096891149878502,
0.05127691850066185,
-0.02313745766878128,
0.020085575059056282,
0.017649762332439423,
0.002515536267310381,
-0.007694735191762447,
-0.012100737541913986,
-0.03764866665005684,
0.005345763172954321,
0.02003927156329155,
0.002705532591789961,
-0.010818076319992542,
-0.007056768052279949,
0.03720863536000252,
-0.004717053379863501,
0.00941470917314291,
0.0015073760878294706,
-0.042918428778648376,
0.0025264655705541372,
-0.007927521131932735,
-0.011171018704771996,
0.029170585796236992,
0.010762546211481094,
-0.019320838153362274,
0.0193366426974535,
-0.032785315066576004,
-0.009254444390535355,
0.011649565771222115,
0.03283492848277092,
-0.006268078461289406,
0.05065305158495903,
-0.002031647600233555,
0.046400636434555054,
-0.022446103394031525,
0.011161528527736664,
0.1347518414258957,
0.09130775183439255,
-0.013391304761171341,
-0.11891075223684311,
0.02398563362658024,
-0.015276096761226654,
-0.013167358934879303,
-0.0295467097312212,
0.02492952160537243,
0.007740833330899477,
-0.041656240820884705,
-0.02381269633769989,
0.06998897343873978,
-0.02180987223982811,
0.004674010910093784,
0.02481902949512005,
-0.014160113409161568,
-0.056963540613651276,
0.006245575845241547,
0.005827840883284807,
-0.015429080463945866,
0.002532079815864563,
-0.030354157090187073,
0.03711920604109764,
0.008694315329194069,
0.010851455852389336,
-0.029308956116437912,
-0.040781170129776,
0.019340351223945618,
0.00724463164806366,
-0.019688179716467857,
-0.004776614252477884,
-0.015507861040532589,
-0.009045949205756187,
-0.030689524486660957,
0.0174740981310606,
-0.02485213428735733,
0.009959489107131958,
0.015568058006465435,
0.03779285028576851,
0.012266859412193298,
0.01580716297030449,
0.00837610475718975,
0.03109860047698021,
-0.04363849759101868,
-0.04469425231218338,
-0.04717439413070679,
0.012543323449790478,
-0.022729558870196342,
-0.020297793671488762,
-0.0014617785345762968,
0.0019425872014835477,
0.03431398421525955,
-0.017027486115694046,
0.0017919749952852726,
0.0008727220119908452,
0.032651387155056,
-0.023104891180992126,
0.006398167461156845,
0.0019622142426669598,
0.007482963614165783,
0.011813676916062832,
-0.01677398756146431,
0.0033293513115495443,
-0.01102342177182436,
0.03589694947004318,
-0.003144053975120187,
0.05413404852151871,
0.022071022540330887,
-0.02306961454451084,
0.0030798318330198526,
0.007023002952337265,
-0.035343099385499954,
0.0034223217517137527,
-0.0049097537994384766,
0.011029301211237907,
0.06800182163715363,
0.007864320650696754,
-0.00009241724183084443,
-0.0018304262775927782,
-0.04166349396109581,
-0.002503237221390009,
-0.0006778102251701057,
0.002068751258775592,
-0.02423846162855625,
-0.022936973720788956,
0.015418834052979946,
0.03470590338110924,
-0.0009486372000537813,
-0.0014292204286903143,
-0.026684097945690155,
0.07547826319932938,
-0.0008628958603367209,
-0.03427894040942192,
-0.02606148272752762,
-0.04388739913702011,
-0.06208440661430359,
0.037390634417533875,
-0.029706433415412903,
-0.008801792748272419,
-0.00038771238178014755,
0.02255767583847046,
-0.006473845336586237,
0.07276149094104767,
-0.020783204585313797,
0.00907120481133461,
0.005882240831851959,
-0.011465398594737053,
0.04476524516940117,
0.025364985689520836,
0.03664638102054596,
0.006493041291832924,
-0.04592938348650932,
0.021851008757948875,
-0.004015689715743065,
0.018899384886026382,
0.02389758639037609,
-0.085127092897892,
-0.03762416914105415,
-0.014760496094822884,
-0.02688421867787838,
-0.0670008510351181,
0.00827911589294672,
-0.017603157088160515,
0.04329866170883179,
-0.0006317009683698416,
0.023742657154798508,
-0.002802463248372078,
0.01573297195136547,
-0.0061781988479197025,
-0.039385147392749786,
0.003439639462158084,
-0.012722235172986984,
-0.031349875032901764,
-0.027875741943717003,
0.024559922516345978,
0.02729230746626854,
0.0020481101237237453,
-0.03343723341822624,
-0.020857177674770355,
0.02020132541656494,
-0.03316696733236313,
-0.044310372322797775,
0.03621502220630646,
-0.016132766380906105,
0.003356916131451726,
0.029173586517572403,
-0.00778482249006629,
-0.014380142092704773,
0.016381075605750084,
0.00393068790435791,
0.0030324107501655817,
0.008772694505751133,
-0.02620902843773365,
0.009538241662085056,
-0.0012753315968438983,
0.01194773055613041,
-0.0033831398468464613,
-0.005011608824133873,
0.033818814903497696,
0.05576268583536148,
-0.020285241305828094,
-0.006618362385779619,
-0.002957626711577177,
-0.017223689705133438,
-0.016469739377498627,
0.025144560262560844,
-0.011721371673047543,
-0.003635913599282503,
0.039890944957733154,
-0.038157980889081955,
0.010435806587338448,
-0.020403197035193443,
0.0025164757389575243,
-0.08777421712875366,
-0.04814974591135979,
-0.002216953784227371,
0.02721772901713848,
0.03677111864089966,
-0.050553858280181885,
0.021805118769407272,
0.007415949832648039,
-0.04764057695865631,
0.03600962832570076,
-0.046871721744537354,
-0.02213386259973049,
-0.023302040994167328,
-0.028400592505931854,
-0.05051040276885033,
0.04825204610824585,
0.03183102235198021,
0.009780583903193474,
-0.0013473149156197906,
0.008825009688735008,
-0.014385579153895378,
-0.0025679715909063816,
-0.006781074684113264,
-0.0010535509791225195,
0.003900193842127919,
-0.030166007578372955,
0.060559529811143875,
-0.006226604804396629,
-0.035459306091070175,
0.03438612446188927,
0.012954041361808777,
-0.02222965471446514,
0.010597585700452328,
0.01857808232307434,
0.020647788420319557,
0.0434485524892807,
0.023916590958833694,
0.017842210829257965,
0.014786157757043839,
-0.006365492474287748,
0.056168895214796066,
0.02833450771868229,
-0.025359589606523514,
-0.024381589144468307,
0.01386810839176178,
-0.0007244485314004123,
0.0025730710476636887,
0.054660726338624954,
-0.04189006984233856,
-0.011682159267365932,
-0.01489641796797514,
-0.04248901829123497,
-0.005676672328263521,
0.0006211639265529811,
0.02777641825377941,
-0.02489093877375126,
0.00589988986030221,
0.011087181977927685,
0.05044913291931152,
0.0020618424750864506,
0.021667612716555595,
0.0017315235454589128,
-0.033647291362285614,
0.014562571421265602,
0.03237713500857353,
0.008111302740871906,
-0.04486052319407463,
-0.04409419372677803,
-0.019772134721279144,
0.009752152487635612,
0.016110945492982864,
-0.032409898936748505,
-0.029278092086315155,
0.01517785619944334,
-0.009481338784098625,
0.026237180456519127,
-0.007437841035425663,
-0.04417124763131142,
0.0025390060618519783,
-0.07768026739358902,
0.03322150185704231,
0.013909737579524517,
0.02413312718272209,
-0.012158184312283993,
-0.025155192241072655,
-0.030064096674323082,
-0.003488922957330942,
0.07226940989494324,
-0.022393502295017242,
-0.008224943652749062,
0.034875400364398956,
0.014132611453533173,
0.02816312573850155,
-0.023656407371163368,
-0.014080775901675224,
0.005592327564954758,
-0.01206954289227724,
0.0009571598493494093,
0.007896129973232746,
-0.02111060358583927,
0.021568940952420235,
0.02145455591380596,
-0.00007328663195949048,
-0.002547107171267271,
-0.0017840842483565211,
-0.046230923384428024,
0.0046460554003715515,
-0.008453602902591228,
-0.011687603779137135,
0.04690191522240639,
0.005845482926815748,
0.014220291748642921,
0.03278158977627754,
-0.0051802718080580235,
-0.019212935119867325,
0.027757376432418823,
-0.03701600059866905,
0.002128252061083913,
-0.03716004267334938,
-0.002991038141772151,
0.031803276389837265,
-0.06282927095890045,
0.010592103935778141,
0.03337614983320236,
-0.030114974826574326,
-0.046895794570446014,
0.06931514292955399,
-0.003062059171497822,
0.041389934718608856,
0.030514124780893326,
-0.0364508330821991,
0.012986808083951473,
-0.015768835321068764,
0.04747666046023369,
0.03273684158921242,
0.03777823597192764,
0.009229586459696293,
-0.00006209385901456699,
0.011769397184252739,
-0.02723538503050804,
-0.010945204645395279,
-0.009255960583686829,
0.024953698739409447,
-0.013881039805710316,
-0.027863461524248123,
0.05327126756310463,
-0.027923228219151497,
0.023094551637768745,
-0.0029469046276062727,
-0.020561056211590767,
0.0993700623512268,
-0.004035796970129013,
0.0012096690479665995,
-0.03280709683895111,
-0.002417130395770073,
-0.013795837759971619,
0.019026795402169228,
0.008752218447625637,
0.055625494569540024,
-0.010648754425346851,
-0.00597262941300869,
-0.020723063498735428,
0.0018630558624863625,
0.012359032407402992,
-0.0617702417075634,
-0.007489880546927452,
-0.005644442513585091,
-0.009534928947687149,
-0.03420596942305565,
-0.02398984134197235,
-0.0218441653996706,
-0.013745415024459362,
-0.003290558001026511,
0.01391162071377039,
0.015991810709238052,
0.007143345195800066,
0.014526132494211197,
-0.01720869168639183,
0.03743205964565277,
-0.03699572756886482,
-0.005156778264790773,
-0.013288484886288643,
-0.0009661098010838032,
-0.010609862394630909,
0.016536585986614227
] |
<p>What don't we know about how electricity and/or magnetism works?</p>
| 8,277 |
[
-0.06578724086284637,
-0.0029950174503028393,
0.01562620885670185,
-0.041500043123960495,
0.04692515358328819,
-0.0011945465812459588,
-0.03284034505486488,
-0.010445487685501575,
-0.017131756991147995,
-0.012249921448528767,
0.03252166509628296,
0.05250125750899315,
0.012624790892004967,
0.022500164806842804,
0.009478767402470112,
0.006109357345849276,
0.009447078220546246,
-0.012188218533992767,
0.010267571546137333,
0.003429366508498788,
-0.027334876358509064,
0.01416096556931734,
-0.017390470951795578,
0.03563215583562851,
-0.004645875189453363,
0.01586396060883999,
0.02288275770843029,
0.006033401004970074,
0.027897601947188377,
0.05533555895090103,
0.03451899066567421,
-0.01321932952851057,
0.02918321266770363,
0.023060988634824753,
0.012797344475984573,
-0.0029411399737000465,
-0.0351841039955616,
-0.046400539577007294,
-0.017210079357028008,
0.0370282344520092,
-0.01221569161862135,
-0.03234505280852318,
-0.011091886088252068,
0.03329389542341232,
-0.06634395569562912,
0.008425386622548103,
0.005838553886860609,
-0.030882103368639946,
0.05096139386296272,
-0.09082409739494324,
0.03104781173169613,
-0.00014816856128163636,
0.004512615967541933,
0.03669986128807068,
0.010104195214807987,
0.006207196973264217,
0.09477417916059494,
0.06324036419391632,
-0.00814068503677845,
-0.0792982280254364,
-0.01221625879406929,
-0.011447349563241005,
0.006367724388837814,
-0.047167595475912094,
-0.04548998177051544,
0.06806249916553497,
-0.004387900233268738,
-0.030641403049230576,
0.03923281654715538,
0.01033005304634571,
0.017496857792139053,
0.04203416779637337,
0.012185436673462391,
0.040390435606241226,
0.019814560189843178,
-0.04067188873887062,
0.017357604578137398,
-0.012292762286961079,
0.045038703829050064,
0.05632352828979492,
-0.01664409041404724,
-0.01313131581991911,
0.01552256103605032,
0.04097733646631241,
-0.007295774761587381,
-0.01759400963783264,
0.05673576146364212,
0.002848084084689617,
0.0162908174097538,
-0.002246874151751399,
0.0019173703622072935,
-0.016428768634796143,
0.022799236699938774,
-0.015762468799948692,
-0.019882136955857277,
0.02356884442269802,
-0.003069985657930374,
0.029409922659397125,
0.024169571697711945,
-0.019281286746263504,
0.04525816813111305,
0.03104005567729473,
0.038482487201690674,
0.05628814548254013,
0.017471620813012123,
-0.056864745914936066,
-0.007367296144366264,
0.011633723974227905,
-0.013484503142535686,
-0.0026859294157475233,
-0.013676322065293789,
0.032877400517463684,
0.0037717195227742195,
-0.008831760846078396,
0.010394170880317688,
0.008675574325025082,
0.013188219629228115,
-0.033669132739305496,
0.052970532327890396,
0.06767667829990387,
-0.0026601669378578663,
-0.03692163527011871,
0.012688085436820984,
-0.03579162433743477,
-0.06073857098817825,
-0.0203117523342371,
0.02427353896200657,
-0.004623502492904663,
-0.025074560195207596,
0.022977493703365326,
-0.008405942469835281,
0.002751426538452506,
-0.02166864275932312,
-0.003794090123847127,
0.025650309398770332,
0.010448330081999302,
-0.10749248415231705,
-0.058155689388513565,
0.027246788144111633,
-0.006657589226961136,
-0.04878877475857735,
-0.058618396520614624,
-0.003258317708969116,
0.005837628152221441,
0.07412037253379822,
-0.010755964554846287,
-0.009734220802783966,
-0.010490791872143745,
0.040206052362918854,
0.01103183999657631,
-0.01646067015826702,
-0.0019170223968103528,
0.0035641915164887905,
-0.011015083640813828,
0.011221741326153278,
-0.054245661944150925,
0.03203074261546135,
0.015030919574201107,
-0.0212856512516737,
-0.029977308586239815,
0.03943214938044548,
-0.00065510073909536,
-0.004860790446400642,
0.003801798215135932,
-0.02464139834046364,
-0.03257180005311966,
0.07947909086942673,
0.012408179230988026,
0.0434030145406723,
0.04379745572805405,
-0.009140321984887123,
0.031612783670425415,
0.011275144293904305,
0.030938798561692238,
0.042119160294532776,
-0.030847815796732903,
-0.0425729863345623,
0.0031630133744329214,
0.01633896306157112,
-0.019321206957101822,
-0.045774973928928375,
-0.009422004222869873,
0.03101676143705845,
0.014933379366993904,
-0.01634608954191208,
0.06453165411949158,
-0.008438914082944393,
-0.020029691979289055,
0.005047397222369909,
-0.03692254796624184,
-0.016443612053990364,
-0.06613477319478989,
0.012367527931928635,
-0.01850210502743721,
-0.018725940957665443,
0.026940524578094482,
-0.009888936765491962,
0.03139646723866463,
-0.045424073934555054,
-0.044578488916158676,
0.020261390134692192,
0.03026607446372509,
0.013969413004815578,
-0.007316183764487505,
0.01568155735731125,
0.0543370395898819,
0.040189847350120544,
-0.009520130231976509,
0.03371388465166092,
-0.03844331577420235,
-0.061035845428705215,
-0.0017733246786519885,
-0.019240602850914,
0.035355906933546066,
0.058730192482471466,
-0.022048108279705048,
0.01953166536986828,
0.005776611622422934,
-0.031655848026275635,
0.037249356508255005,
0.0036279510241001844,
0.0839415043592453,
0.014348190277814865,
0.010879680514335632,
0.0035321626346558332,
0.060281604528427124,
0.010283870622515678,
-0.00419540936127305,
0.0008158444543369114,
-0.001291765714995563,
-0.0551251582801342,
-0.005269539076834917,
0.05356912687420845,
-0.013615005649626255,
-0.026748625561594963,
0.03333098068833351,
-0.02194107323884964,
0.0782511830329895,
0.010038968175649643,
0.014045308344066143,
-0.026987209916114807,
-0.032751746475696564,
0.0033786059357225895,
-0.0020282550249248743,
-0.01445638108998537,
0.031100302934646606,
0.058748919516801834,
0.029742702841758728,
0.010281670838594437,
0.01977522112429142,
-0.03700701892375946,
0.06335777789354324,
-0.04083583503961563,
-0.0008243180927820504,
0.005383843556046486,
-0.03574238717556,
0.03279241919517517,
-0.033004939556121826,
-0.001110630459152162,
-0.015390866436064243,
0.014984608627855778,
-0.009695093147456646,
0.01603117026388645,
-0.02832549810409546,
0.003957035485655069,
-0.022025734186172485,
-0.010835280641913414,
0.0016183137195184827,
0.032412637025117874,
-0.029855042695999146,
0.006007869262248278,
-0.007672831416130066,
0.0005294716684147716,
-0.03583201766014099,
-0.022116290405392647,
-0.006268972996622324,
0.011581146158277988,
0.047919370234012604,
-0.03441810980439186,
-0.03610990196466446,
0.0043335361406207085,
-0.031851351261138916,
0.029511405155062675,
0.038304682821035385,
-0.03465589880943298,
0.03718871623277664,
-0.005866006016731262,
-0.02212672308087349,
0.049177590757608414,
0.004066970199346542,
0.008655511774122715,
0.006520381197333336,
-0.01651112362742424,
-0.023047851398587227,
0.017309360206127167,
0.0016224619466811419,
0.006627948023378849,
-0.0317133292555809,
-0.004233078099787235,
0.026254968717694283,
-0.03454212471842766,
-0.0010553245665505528,
0.028001118451356888,
-0.0251304991543293,
-0.033402785658836365,
0.016385627910494804,
-0.002247310010716319,
0.0242244154214859,
-0.0305886659771204,
0.016528252512216568,
0.0019949213601648808,
-0.0746544748544693,
-0.0004653753712773323,
-0.030970415100455284,
-0.020117642357945442,
0.0065739089623093605,
-0.011651390232145786,
0.03277847170829773,
-0.018962489441037178,
-0.03653915598988533,
0.04023485630750656,
-0.02090795524418354,
-0.023524755612015724,
-0.00944096315652132,
-0.04782663658261299,
-0.03683633357286453,
-0.015598049387335777,
0.027979474514722824,
0.08527076244354248,
-0.011900622397661209,
-0.007966174744069576,
0.022470232099294662,
0.020706037059426308,
-0.010918093845248222,
0.026723535731434822,
0.0015596983721479774,
0.019752804189920425,
0.008653335273265839,
0.0007488922565244138,
0.04898100718855858,
-0.004972402472048998,
-0.020373377948999405,
0.030753158032894135,
0.007067302241921425,
0.03421839326620102,
0.010644081048667431,
-0.013433539308607578,
0.06355514377355576,
-0.008564701303839684,
0.008292505517601967,
-0.038262125104665756,
0.05855526030063629,
-0.03494638577103615,
-0.003944464959204197,
-0.015780167654156685,
0.001151901320554316,
0.06744478642940521,
-0.0030966445337980986,
0.0018354578642174602,
0.037154171615839005,
0.026088636368513107,
-0.03884282335639,
-0.014536473900079727,
-0.0029061848763376474,
0.009811134077608585,
-0.012605398893356323,
-0.014938040636479855,
-0.003235558047890663,
0.07191108912229538,
0.045670073479413986,
0.005443220026791096,
0.015227976255118847,
-0.008489771746098995,
-0.021152054890990257,
-0.05619189888238907,
0.011199855245649815,
-0.020499201491475105,
0.022669240832328796,
0.0032829681877046824,
0.04851776361465454,
0.02552485279738903,
0.0315222442150116,
-0.029611151665449142,
0.005592839326709509,
-0.07398095726966858,
0.026220614090561867,
-0.05559084564447403,
-0.029287289828062057,
-0.02941359579563141,
0.006593001075088978,
-0.0008647536742500961,
0.0065763527527451515,
-0.0024067810736596584,
-0.05125715211033821,
-0.019233863800764084,
-0.03980410099029541,
-0.013469133526086807,
-0.036565106362104416,
-0.04278738424181938,
-0.024094000458717346,
0.013166802003979683,
0.017755070701241493,
-0.026906512677669525,
0.02058328129351139,
0.01754399575293064,
-0.010746586136519909,
0.005282523110508919,
-0.0362657830119133,
-0.003459693631157279,
0.02081890217959881,
0.016819138079881668,
0.01684373803436756,
-0.006428244989365339,
-0.032005082815885544,
-0.028897657990455627,
0.006818060763180256,
0.05953444913029671,
0.009328377433121204,
-0.010523440316319466,
-0.02815808728337288,
-0.04271555319428444,
-0.01664198935031891,
-0.016334667801856995,
0.07871363312005997,
-0.024603886529803276,
0.02480160817503929,
0.021479710936546326,
-0.005345483776181936,
-0.001289197476580739,
0.0010848445817828178,
0.017227422446012497,
0.006401773076504469,
-0.030031288042664528,
-0.044210284948349,
0.0007714444654993713,
-0.04560456424951553,
-0.01669018343091011,
0.015303511172533035,
-0.010861586779356003,
0.017581390216946602,
-0.003391345264390111,
0.0029576015658676624,
-0.00797942653298378,
0.00954026635736227,
-0.0008784547098912299,
0.006836937740445137,
-0.01737690530717373,
0.018933529034256935,
0.0021125455386936665,
0.028930911794304848,
0.013458522036671638,
0.03553799167275429,
-0.02266736887395382,
-0.036257464438676834,
-0.07476012408733368,
0.01363085675984621,
0.03604889288544655,
0.041436098515987396,
-0.02431515045464039,
-0.020005568861961365,
-0.07682079076766968,
-0.009835192933678627,
0.044225431978702545,
-0.04252973198890686,
0.0015438912669196725,
-0.042314425110816956,
-0.028230465948581696,
-0.05839348956942558,
-0.022362995892763138,
-0.01986328884959221,
0.010462377220392227,
-0.005991241429001093,
0.049404628574848175,
-0.0015951956156641245,
-0.006909745279699564,
-0.0011396706104278564,
0.03268950805068016,
0.042936164885759354,
0.05090317502617836,
0.01625508815050125,
0.041625380516052246,
-0.01666584610939026,
0.027540698647499084,
-0.019046306610107422,
-0.09335388988256454,
-0.006319948472082615,
-0.023344997316598892,
-0.041695673018693924,
0.07940535247325897,
-0.0007338457508012652,
-0.07096685469150543,
0.016389284282922745,
-0.0256904698908329,
0.010364685207605362,
-0.03464134782552719,
-0.052859023213386536,
0.006724498234689236,
0.03174855560064316,
0.022761724889278412,
0.06646209955215454,
0.028261063620448112,
-0.0686313584446907,
0.000034492659324314445,
-0.01386119145900011,
0.03216581791639328,
0.006946838926523924,
0.0011352826841175556,
-0.002867434872314334,
0.011832186952233315,
-0.014990897849202156,
0.06777939945459366,
-0.0007462195353582501,
-0.009119502268731594,
-0.023104166612029076,
-0.030713314190506935,
-0.035596467554569244,
0.027666229754686356,
0.014885691925883293,
-0.027269525453448296,
-0.010388518683612347,
0.024586303159594536,
-0.02437073364853859,
-0.006323853507637978,
0.05372418463230133,
-0.0027531518135219812,
0.007010421250015497,
0.01770418882369995,
-0.007173183839768171,
-0.018363626673817635,
-0.04893261194229126,
-0.018208669498562813,
0.005304938647896051,
-0.04629223048686981,
0.06701353937387466,
-0.008032838813960552,
-0.013127095066010952,
0.022802887484431267,
-0.0522579625248909,
-0.055307939648628235,
-0.0012557391310110688,
0.0022461137268692255,
0.06398072093725204,
-0.040836211293935776,
0.03884809464216232,
-0.017318375408649445,
-0.0018943761242553592,
-0.025921106338500977,
-0.0663115382194519,
0.017402056604623795,
0.0324162133038044,
-0.00864669680595398,
-0.007538203150033951,
0.021356748417019844,
-0.01365701761096716,
-0.024280443787574768,
0.011456106789410114,
0.03175823763012886,
-0.042702462524175644,
0.02070312574505806,
0.004328708164393902,
0.008226413279771805,
0.054030150175094604,
-0.0074647874571383,
-0.02102792076766491,
0.047203171998262405,
-0.04709707573056221,
0.012026529759168625,
-0.00521492213010788,
0.019580869004130363,
-0.008689744397997856,
-0.04596484825015068,
0.01335813943296671,
0.006814081221818924,
0.024532847106456757,
-0.05335633084177971,
0.020899508148431778,
0.03392815589904785,
0.036055147647857666,
-0.02339348755776882,
-0.028592923656105995,
0.053003523498773575,
0.016823802143335342,
0.019909674301743507,
-0.007689064368605614,
0.00398151483386755,
-0.03418804705142975,
-0.019041981548070908,
0.049319811165332794,
0.030549509450793266,
-0.015204107388854027,
-0.008957916870713234,
0.05506493151187897,
-0.009424894116818905,
0.005154239945113659,
0.044781751930713654,
0.0038696436677128077,
0.035794246941804886,
-0.017359353601932526,
0.02127128280699253,
-0.00958448275923729,
0.011447143740952015,
-0.04136146605014801,
-0.024522090330719948,
-0.01630324497818947,
-0.00700517138466239,
0.048448994755744934,
-0.009681078605353832,
0.08029346168041229,
-0.00851310696452856,
-0.03641418740153313,
-0.012771234847605228,
-0.01741095259785652,
-0.01997440680861473,
0.030043169856071472,
-0.004226120188832283,
0.0020403696689754725,
-0.0017690707463771105,
0.03619452938437462,
0.04035443812608719,
0.04439561441540718,
-0.029410382732748985,
-0.022127067670226097,
0.03335820138454437,
0.028993984684348106,
0.06336423754692078,
-0.005417646374553442,
-0.06004566699266434,
0.05247355252504349,
-0.04364326596260071,
0.00420853728428483,
-0.005311749875545502,
-0.018479321151971817,
0.0617542527616024,
-0.029921310022473335,
0.0051091634668409824,
-0.000512775732204318,
-0.014139742590487003,
-0.024160414934158325,
-0.00323868403211236,
0.006854476407170296,
0.021421458572149277,
-0.005414812825620174,
0.0020875916816294193,
-0.0052876900881528854,
-0.013995734043419361,
-0.005674199666827917,
0.029411153867840767,
-0.09211338311433792,
-0.024665039032697678,
-0.010646441951394081,
-0.03280676528811455,
0.06085161864757538,
0.022052738815546036,
-0.005843282211571932,
0.010223560966551304,
-0.0222697202116251,
0.05708317831158638,
0.014487961307168007,
0.02889745496213436,
-0.0576019287109375,
0.04389575496315956,
-0.04445285350084305,
0.024061014875769615,
-0.04415905848145485,
-0.004615059122443199,
0.11801557242870331,
0.008657634258270264,
0.024492595344781876,
-0.06813929229974747,
0.007934868335723877,
-0.053171295672655106,
0.0015597058227285743,
-0.008432656526565552,
0.029552016407251358,
-0.017447542399168015,
0.062117286026477814,
-0.0002745352394413203,
0.04800991341471672,
0.010413607582449913,
0.008216270245611668,
0.04680955037474632,
-0.040387820452451706,
-0.0359206460416317,
0.018502483144402504,
0.012908772565424442,
-0.011896489188075066,
0.017896391451358795,
-0.05443276837468147,
0.015412384644150734,
-0.06263656914234161,
0.01417425088584423,
-0.006260480731725693,
-0.03951018303632736,
0.04848385602235794,
0.0010461776982992887,
-0.053619153797626495,
0.004627987742424011,
0.033017780631780624,
-0.012642827816307545,
-0.02697441168129444,
0.039404407143592834,
0.05432477965950966,
-0.0011699170572683215,
0.0034524546936154366,
0.0015477337874472141,
0.028567524626851082,
0.007850132882595062,
-0.007476153317838907,
0.021154945716261864,
-0.05582835525274277,
-0.011156843975186348,
-0.0299538541585207,
0.03298371657729149,
-0.035440102219581604,
0.03063734993338585,
0.01663394086062908,
0.013674226589500904,
-0.013916684314608574,
-0.02609238401055336,
-0.02788187377154827,
-0.01897607371211052,
0.002450501313433051,
-0.009140637703239918,
0.009651949629187584,
-0.006175971124321222,
0.02340046688914299,
-0.013752621598541737,
0.037070583552122116,
-0.02359052561223507,
-0.0009972064290195704,
0.010617827996611595,
0.024973224848508835,
0.014400631189346313,
-0.01528053730726242,
-0.017444400116801262,
-0.04694404453039169,
-0.040532078593969345,
-0.02244868315756321,
-0.017305487766861916,
0.014613335020840168,
0.03739112988114357,
0.020348653197288513,
-0.021333657205104828,
-0.013622782193124294,
-0.004282835870981216,
-0.0268594641238451,
0.05899203196167946,
0.03299495205283165,
0.0008894010679796338,
-0.031080840155482292,
-0.001185016706585884,
0.023416711017489433,
0.041126225143671036,
-0.022668682038784027,
0.019124940037727356,
0.006641567684710026,
-0.0016501842765137553,
0.0040253084152936935,
0.00651364354416728,
-0.020636772736907005,
0.010008378885686398,
-0.015551457181572914,
0.006128789857029915,
0.005437792278826237,
0.02636655792593956,
0.023971501737833023,
0.0062707336619496346,
0.024688849225640297,
0.03141968697309494,
-0.02384175732731819,
-0.022419270128011703,
0.03590114787220955,
-0.031996190547943115,
-0.026801912114024162,
-0.005752286408096552,
0.010687840171158314,
-0.02167472615838051,
-0.025150781497359276,
-0.03987906500697136,
-0.018346864730119705,
0.012662987224757671,
0.05271225795149803,
-0.01647031307220459,
-0.019934987649321556,
0.006165225058794022,
0.05965125933289528,
-0.022905545309185982,
0.006813879124820232,
-0.06348895281553268,
-0.01562249381095171,
-0.033669352531433105,
-0.025743061676621437,
0.021059656515717506,
0.0004399141180329025,
-0.009720724076032639,
0.01182794664055109,
0.021515628322958946,
0.020439131185412407,
-0.014472299255430698,
0.0014637894928455353,
-0.004952724557369947,
0.0023013066966086626,
0.01740911230444908,
-0.04165195673704147,
-0.04486784711480141,
0.05189523473381996,
-0.02286151982843876,
-0.04772211238741875,
-0.0015417084796354175,
-0.021956060081720352,
0.012977492064237595,
0.03950522094964981,
-0.036917779594659805,
0.010398361831903458,
0.05515903979539871,
-0.031726207584142685,
0.01377518568187952,
-0.007703306153416634,
0.00019169787992723286,
-0.011558451689779758,
0.012058427557349205,
0.005990009289234877,
-0.05129307135939598,
-0.027698175981640816,
0.03344029560685158,
0.028364453464746475,
0.02399473637342453,
-0.023312591016292572,
0.0268566831946373,
0.000827386393211782,
0.04204823076725006,
0.04877811670303345,
0.003415478626266122,
-0.0004709910717792809,
0.038006655871868134,
-0.01969948597252369,
0.047134220600128174,
0.014346860349178314,
0.001464339205995202,
-0.10371589660644531,
0.0013737436383962631,
0.006804963573813438,
-0.024364197626709938,
0.023155473172664642,
-0.021572310477495193,
0.014134116470813751,
0.0403994545340538,
-0.09700773656368256,
0.03639901056885719,
-0.017234405502676964,
-0.06309124827384949,
0.006050055846571922,
0.013277354650199413,
-0.0012610219419002533,
0.06129130721092224,
0.01644776575267315,
0.04712497442960739,
-0.02240002155303955,
-0.0206606462597847,
-0.014313632622361183,
0.004838626831769943,
-0.044816117733716965,
0.014746854081749916,
0.002717522205784917,
0.011337915435433388,
0.032878290861845016,
-0.01647215522825718,
-0.007584274280816317,
0.02123473957180977,
0.006790068466216326,
0.029681047424674034,
0.006797731854021549,
0.012018426321446896,
0.01804119534790516,
0.03391275554895401,
0.015631454065442085,
-0.026071952655911446,
0.005312748719006777,
0.01319197379052639,
0.011219684034585953,
0.06108172982931137,
0.011183981783688068,
0.007442318368703127,
0.013388664461672306,
-0.01432027481496334,
0.007599292788654566,
-0.02160661295056343,
-0.05050540342926979,
-0.012203250080347061,
-0.006493230815976858,
0.05681609362363815,
0.009554938413202763,
-0.02187388576567173,
0.001202997867949307,
-0.04168917238712311,
-0.029195601120591164,
0.008450867608189583,
0.01904580183327198,
0.026082027703523636,
0.047915637493133545,
-0.03028015047311783,
0.003678370965644717,
-0.001911856816150248,
0.023327253758907318,
0.029780149459838867,
-0.030610008165240288,
0.023600678890943527,
0.024621913209557533,
0.02785344235599041,
0.02082645706832409,
-0.05898405984044075,
-0.051227208226919174,
0.034701526165008545,
0.0309256911277771,
0.02351507544517517,
0.010948787443339825,
-0.0719192624092102,
-0.015314862132072449,
-0.045419588685035706,
0.07246660441160202,
-0.025303399190306664,
-0.015959490090608597,
-0.03301034867763519,
-0.023026224225759506,
0.008378585800528526,
-0.0013808609219267964,
0.06384015083312988,
-0.016072513535618782,
-0.015538020059466362,
0.02219311334192753,
-0.009499057196080685,
0.027160851284861565,
-0.029370367527008057,
0.022374529391527176,
-0.01055771391838789,
-0.03369943052530289,
-0.00006470090011134744,
-0.03220836818218231,
-0.011409103870391846,
0.01460227556526661,
0.01128007099032402,
0.0034406448248773813,
0.019109247252345085,
-0.028141258284449577,
-0.023430339992046356,
0.038137130439281464,
0.03382163867354393,
-0.05301371589303017,
0.04163901135325432,
-0.020610298961400986,
0.03200436383485794,
-0.0060729472897946835,
-0.00875452347099781,
-0.025718456134200096,
0.03479287773370743,
-0.013518388383090496,
0.012183895334601402,
-0.009998668916523457,
-0.0316556952893734,
0.0562027171254158,
-0.03822676092386246,
-0.01322701945900917,
0.03232382982969284,
-0.026316458359360695,
0.0003182282380294055,
0.03047129511833191,
-0.00224994751624763,
0.019358355551958084,
-0.022980989888310432,
0.007085306104272604,
0.017769256606698036,
-0.0016604035627096891,
-0.023496976122260094,
0.036968108266592026,
0.03454409912228584,
-0.0009630059939809144,
-0.0050416565500199795,
0.06496971845626831,
-0.02179044857621193,
0.0032919030636548996,
-0.0005634148837998509,
0.05699841305613518,
-0.027405044063925743,
-0.04332464560866356,
-0.0012016090331599116,
-0.03132998198270798,
-0.00608027633279562,
0.02469731867313385,
-0.02117305062711239,
0.11675244569778442,
-0.024723589420318604,
0.012935157865285873,
-0.004987115506082773,
0.014413713477551937,
0.027423091232776642,
-0.01824333891272545,
-0.005158599000424147,
0.02787487581372261,
0.003963097929954529,
-0.01476240623742342,
-0.05309836566448212,
0.026783499866724014,
0.04947487637400627,
-0.03726649656891823,
0.026828721165657043,
-0.019119877368211746,
0.00011856546916533262,
-0.013618262484669685,
-0.009644151665270329,
-0.06245952099561691,
-0.024137074127793312,
0.04408036172389984,
0.02101808972656727,
0.030047707259655,
-0.0456363670527935,
-0.011206556111574173,
-0.037418562918901443,
0.047871872782707214,
-0.07059177756309509,
-0.006034834310412407,
-0.053233642131090164,
0.016349876299500465,
-0.025655632838606834,
-0.00869378075003624
] |
<p>What is the connection between Planck's constant and gravity? Why is the Planck scale the natural scale for quantum gravity? I would have though the scale would be related to G, not h. </p>
| 8,278 |
[
-0.008776665665209293,
-0.02122168429195881,
0.0057578119449317455,
-0.008838054724037647,
0.033428847789764404,
0.03517943248152733,
-0.006630558054894209,
-0.01903771422803402,
-0.00370846432633698,
-0.042090047150850296,
0.0014237354043871164,
0.008430242538452148,
0.022930165752768517,
0.004083217587321997,
0.020268913358449936,
-0.007913582026958466,
-0.009105290286242962,
-0.003288727020844817,
-0.022852299734950066,
-0.03100907802581787,
0.0006659099017269909,
0.03787609562277794,
0.029836418107151985,
0.003880897304043174,
-0.009163637645542622,
0.001959639834240079,
0.022825676947832108,
0.013941247016191483,
0.024437200278043747,
0.060985464602708817,
-0.0017740137409418821,
-0.018390517681837082,
0.013629460707306862,
0.031418606638908386,
-0.00645109498873353,
-0.0007914029993116856,
-0.009442186914384365,
-0.006793830543756485,
-0.022332748398184776,
-0.003568322630599141,
-0.06298712641000748,
-0.04317336156964302,
-0.0025511919520795345,
0.039237137883901596,
-0.03198753297328949,
0.018557032570242882,
0.0061024329625070095,
-0.021630648523569107,
0.03994866460561752,
-0.062430448830127716,
0.042309146374464035,
0.01773640140891075,
0.02633756771683693,
0.01755421794950962,
-0.008090331219136715,
0.01415392104536295,
0.10720519721508026,
0.06053434684872627,
-0.008627520874142647,
-0.05993089824914932,
-0.04204324632883072,
-0.0399116612970829,
0.004374796990305185,
-0.025734305381774902,
0.002079979283735156,
0.07068610191345215,
-0.023193923756480217,
-0.019068295136094093,
0.00823630578815937,
0.010958186350762844,
0.005709197372198105,
0.04071280360221863,
0.05094847083091736,
-0.014447535388171673,
0.015554885379970074,
-0.017036737874150276,
0.013434265740215778,
0.014407791197299957,
0.03419144079089165,
0.04597721993923187,
-0.005985436961054802,
0.014493563212454319,
0.04382483288645744,
0.04730077460408211,
0.0038165156729519367,
0.005979642271995544,
0.08033151924610138,
-0.023541871458292007,
-0.01145126111805439,
0.05991864576935768,
-0.03506824001669884,
0.01971004158258438,
0.046998098492622375,
-0.013053404167294502,
-0.01644892618060112,
0.02992786467075348,
-0.01491157803684473,
0.00938087236136198,
0.0037913250271230936,
-0.003211061470210552,
0.03212136775255203,
-0.03490616753697395,
-0.0005831779562868178,
0.06461236625909805,
0.017152246087789536,
-0.04052168130874634,
-0.04437235742807388,
0.0175306536257267,
-0.012060577981173992,
-0.01027394738048315,
-0.02554529719054699,
0.006671604234725237,
-0.001710055279545486,
-0.01878761500120163,
0.025451788678765297,
-0.031072773039340973,
0.01891302317380905,
-0.03716333210468292,
0.06593383848667145,
0.057370204478502274,
0.014667026698589325,
-0.022555971518158913,
0.016451844945549965,
0.0086520342156291,
-0.0344434417784214,
0.02269687131047249,
0.039834339171648026,
-0.03767085820436478,
-0.014730371534824371,
0.018445748835802078,
-0.02414008043706417,
-0.023011771962046623,
-0.0072737461887300014,
0.018722310662269592,
0.04228276386857033,
-0.01967233419418335,
-0.10204260796308517,
-0.06564740836620331,
0.0462428517639637,
-0.00036802716203965247,
-0.024129027500748634,
-0.06342607736587524,
0.032888203859329224,
0.03217829391360283,
0.07620596140623093,
0.02513856068253517,
0.002188306301832199,
-0.017221134155988693,
0.008856723085045815,
0.018295705318450928,
-0.016777439042925835,
-0.03865089640021324,
0.033137932419776917,
-0.039381127804517746,
0.00031923249480314553,
-0.06622789055109024,
-0.01706639491021633,
0.0212263073772192,
-0.0028905158396810293,
-0.041128918528556824,
0.08033567667007446,
-0.022258514538407326,
-0.01795339025557041,
-0.008205111138522625,
-0.011146445758640766,
-0.030805837363004684,
0.0629262924194336,
0.0038451526779681444,
0.00004255697422195226,
0.029856622219085693,
0.0033644824288785458,
0.009404268115758896,
0.03965681418776512,
0.028892628848552704,
0.0019846444483846426,
-0.02781643718481064,
-0.0285850428044796,
-0.034615468233823776,
0.01403121743351221,
-0.00017046942957676947,
-0.020229123532772064,
-0.029108110815286636,
-0.020116811618208885,
0.005278776399791241,
0.010080091655254364,
0.01704852096736431,
-0.02445039339363575,
-0.004425899125635624,
-0.020238621160387993,
-0.04804838448762894,
0.007150729186832905,
-0.07621244341135025,
0.023469315841794014,
0.026730109006166458,
-0.0038989163003861904,
0.020809758454561234,
0.027978215366601944,
0.007718738168478012,
-0.041529931128025055,
-0.0437396802008152,
0.014202045276761055,
0.05278812721371651,
-0.008919967338442802,
-0.02481624111533165,
0.03270604461431503,
0.0801532119512558,
0.045963797718286514,
0.010605329647660255,
0.030691279098391533,
-0.0033727900590747595,
-0.05639493837952614,
0.04704796150326729,
-0.01822851225733757,
-0.00452471524477005,
-0.01938016712665558,
0.036729082465171814,
0.00711295148357749,
-0.014317154884338379,
-0.010479338467121124,
0.0434134379029274,
-0.039693381637334824,
0.07026638090610504,
0.017259769141674042,
-0.011239703744649887,
-0.004016249440610409,
0.04363054409623146,
0.0009902724996209145,
0.0044497959315776825,
-0.02292916737496853,
-0.022763874381780624,
-0.047170210629701614,
0.004075381439179182,
0.018221257254481316,
0.05821724981069565,
-0.02728600986301899,
-0.007789531722664833,
0.01986239291727543,
0.05465826764702797,
0.023887265473604202,
0.028319498524069786,
-0.014702440239489079,
-0.02246958576142788,
0.01234279852360487,
-0.008524676784873009,
0.024863993749022484,
-0.00006435311661334708,
0.02476520463824272,
0.052799880504608154,
0.026500819250941277,
-0.0381096750497818,
-0.029440728947520256,
0.031308140605688095,
0.004737586248666048,
0.023903610184788704,
0.025822844356298447,
-0.002781225834041834,
0.04139748215675354,
-0.03920082375407219,
0.017370566725730896,
0.021985480561852455,
-0.029160983860492706,
-0.00792067963629961,
-0.055234745144844055,
-0.06594330817461014,
0.019288716837763786,
0.004105544649064541,
-0.030963778495788574,
-0.020370077341794968,
0.015133094042539597,
-0.04394415393471718,
0.00484252255409956,
-0.03639809042215347,
-0.007928638719022274,
-0.017023449763655663,
0.004423900041729212,
-0.010102728381752968,
0.005896399728953838,
0.04487099125981331,
-0.022893767803907394,
-0.0584583580493927,
0.026094600558280945,
-0.04886409267783165,
-0.009325751103460789,
-0.010314015671610832,
-0.028141867369413376,
0.013515654020011425,
-0.00823542382568121,
-0.025838365778326988,
0.03862980753183365,
-0.022191757336258888,
0.0525304451584816,
0.002368420362472534,
-0.010967685841023922,
-0.012687369249761105,
0.019973361864686012,
-0.03416438028216362,
0.013119038194417953,
0.0014435891062021255,
0.017641717568039894,
0.045451097190380096,
-0.03445352986454964,
-0.030413681641221046,
0.022328786551952362,
0.012869000434875488,
-0.057607393711805344,
-0.01874721236526966,
-0.010403024964034557,
-0.016480250284075737,
-0.027111805975437164,
0.006457424256950617,
0.018607325851917267,
-0.10540267825126648,
-0.016551893204450607,
-0.023754818364977837,
-0.04378305375576019,
0.0564488060772419,
-0.018517641350626945,
0.03416076675057411,
-0.012527125887572765,
-0.024857524782419205,
0.07303702086210251,
0.04228028282523155,
0.007026616483926773,
-0.041134968400001526,
-0.010412435047328472,
0.0045361896045506,
-0.02105773240327835,
0.017876900732517242,
0.034244365990161896,
0.021931150928139687,
0.010779517702758312,
0.04086097329854965,
0.037640903145074844,
0.02644001692533493,
0.004597322549670935,
-0.018893739208579063,
-0.020009644329547882,
0.0009788243332877755,
0.003277776762843132,
0.049288515001535416,
0.02948949486017227,
-0.04027929902076721,
0.030003096908330917,
0.015248170122504234,
0.04255347698926926,
-0.0136879812926054,
-0.0210307314991951,
0.0596604160964489,
0.0163879431784153,
0.028429090976715088,
-0.049034032970666885,
-0.00095431535737589,
0.005677394103258848,
-0.018183650448918343,
0.024155328050255775,
0.017697881907224655,
0.03268047422170639,
-0.011162733659148216,
-0.008930140174925327,
0.020881295204162598,
0.03406161442399025,
-0.01246232446283102,
-0.037819754332304,
0.028088349848985672,
0.00040034440462477505,
0.02444210834801197,
-0.014108615927398205,
-0.01980038359761238,
0.04439142346382141,
0.04335418716073036,
0.04582292586565018,
-0.01795247755944729,
-0.0731051042675972,
-0.008400464430451393,
-0.05014669895172119,
-0.016580263152718544,
0.003046702826395631,
0.023858631029725075,
-0.014826962724328041,
0.05538889020681381,
0.0413583368062973,
0.019202282652258873,
0.01431832741945982,
0.001118738786317408,
-0.09934881329536438,
0.020438198000192642,
-0.0837484747171402,
-0.019795434549450874,
-0.021585071459412575,
-0.016544144600629807,
-0.01895817555487156,
-0.0155910924077034,
-0.014377436600625515,
-0.024157170206308365,
-0.013672693632543087,
-0.03410983458161354,
0.010441191494464874,
-0.023602236062288284,
-0.03617312014102936,
-0.012958645820617676,
-0.018753712996840477,
0.027588583528995514,
0.005943914409726858,
0.011901711113750935,
0.05673439800739288,
-0.0098798843100667,
0.003733130404725671,
0.016858994960784912,
0.008716791868209839,
0.017965659499168396,
0.030930079519748688,
0.01533528696745634,
-0.006637505255639553,
0.008267413824796677,
0.003799581667408347,
0.01782352104783058,
0.04080434888601303,
0.00731956260278821,
-0.017917538061738014,
-0.017214523628354073,
-0.031370650976896286,
-0.016974514350295067,
-0.01835324615240097,
0.04222880303859711,
-0.02753833867609501,
0.010957133956253529,
0.05095824599266052,
-0.001124364323914051,
-0.027654318138957024,
0.03727760538458824,
0.06919208914041519,
0.013111195527017117,
-0.05430945008993149,
-0.039557911455631256,
-0.0398307740688324,
-0.04534785449504852,
-0.003354389686137438,
0.010898672044277191,
-0.006263188552111387,
-0.038338035345077515,
0.019779901951551437,
0.045587748289108276,
0.016102492809295654,
-0.016379401087760925,
-0.031100638210773468,
0.02770201675593853,
0.05492542311549187,
-0.03816141560673714,
0.0019124721875414252,
-0.03400975093245506,
0.05814647302031517,
0.05377922207117081,
-0.04128709062933922,
-0.013746739365160465,
-0.10858704894781113,
-0.003291398286819458,
0.01290034968405962,
0.017847420647740364,
-0.00010293411469319835,
-0.006879640277475119,
-0.03865642845630646,
-0.02772320806980133,
0.05944795161485672,
-0.020585766062140465,
0.008224476128816605,
-0.0345943421125412,
-0.0033951099030673504,
-0.023763790726661682,
0.0083298459649086,
0.0118219880387187,
0.020074760541319847,
-0.000516825239174068,
0.014539886265993118,
-0.02618139609694481,
0.03501065447926521,
-0.04148390516638756,
0.04284178465604782,
0.004911807831376791,
0.04164644330739975,
0.03200962021946907,
-0.018045982345938683,
0.009122883901000023,
-0.005870924796909094,
-0.02635211870074272,
-0.0885893926024437,
-0.005212272051721811,
0.0024950311053544283,
-0.006661398336291313,
0.007053724490106106,
-0.03190918639302254,
-0.02484489604830742,
-0.010709104128181934,
-0.0020449915900826454,
-0.00006608542753383517,
0.007902048528194427,
-0.0018706481205299497,
0.05122101679444313,
0.03727758675813675,
-0.018505264073610306,
0.029815062880516052,
0.002779544098302722,
-0.02895437367260456,
-0.03422128036618233,
-0.03801875561475754,
0.06236717477440834,
-0.045709822326898575,
-0.003234552452340722,
-0.014960641041398048,
-0.0016088106203824282,
-0.05866914615035057,
0.03114100731909275,
-0.00862672459334135,
0.005283119156956673,
-0.01809895969927311,
-0.047604918479919434,
-0.02603614144027233,
-0.005387402605265379,
0.010254093445837498,
-0.007243541534990072,
0.031014224514365196,
0.02098667062819004,
0.032760798931121826,
-0.04392987862229347,
0.008750738576054573,
0.040825556963682175,
-0.02006077766418457,
0.002984382212162018,
-0.010949745774269104,
0.0057618762366473675,
-0.0017199404537677765,
-0.02322356030344963,
0.03968697041273117,
-0.032681554555892944,
-0.004093062598258257,
-0.031593188643455505,
-0.02069384604692459,
0.0217291247099638,
-0.03636520728468895,
-0.03699037432670593,
-0.018031425774097443,
-0.031098712235689163,
0.04142829775810242,
-0.06654993444681168,
0.03537624701857567,
0.018798895180225372,
0.03252565115690231,
-0.09035389125347137,
-0.011756179854273796,
0.02839469164609909,
-0.000551086210180074,
0.014461162500083447,
-0.018524937331676483,
0.029560524970293045,
-0.05800146609544754,
-0.01573125459253788,
-0.013803377747535706,
0.05748621001839638,
-0.02199428528547287,
-0.004790766630321741,
-0.019757678732275963,
0.017828654497861862,
0.03010057657957077,
-0.014373473823070526,
-0.02177823893725872,
0.005747836548835039,
0.014005744829773903,
-0.030831653624773026,
-0.014200006611645222,
0.06608515977859497,
-0.02290261909365654,
-0.020181434229016304,
0.0015671269502490759,
-0.03229966014623642,
0.0039274245500564575,
-0.03660419583320618,
-0.02109741047024727,
0.04647913575172424,
0.03735734894871712,
0.0014404325047507882,
-0.006291380152106285,
0.030263574793934822,
-0.03003745526075363,
0.06712985783815384,
-0.009085715748369694,
-0.010613367892801762,
-0.014561591669917107,
-0.02125232107937336,
0.041721951216459274,
0.011098220013082027,
-0.0010345509508624673,
0.014650327153503895,
0.0497204028069973,
0.013705087825655937,
-0.0331166572868824,
0.007175636012107134,
-0.028336720541119576,
-0.003957077860832214,
-0.006887855939567089,
0.012603665702044964,
0.00632984796538949,
0.021136749535799026,
-0.016039414331316948,
-0.02479485608637333,
-0.028698572888970375,
-0.013523142784833908,
0.05188825726509094,
-0.013722782023251057,
0.04558897763490677,
-0.004148141480982304,
-0.03034290112555027,
0.013088291510939598,
-0.016150986775755882,
-0.01166133675724268,
0.016855238005518913,
0.011485014110803604,
0.002056690864264965,
-0.010980742983520031,
0.016460977494716644,
0.03534098342061043,
0.05822912976145744,
-0.021338675171136856,
0.0016918606124818325,
0.032715581357479095,
0.04842560738325119,
-0.019251598045229912,
-0.01964135468006134,
-0.05772271379828453,
0.056280817836523056,
-0.009608413092792034,
0.027709657326340675,
-0.010166711173951626,
-0.025459524244070053,
0.02255762182176113,
-0.0037712715566158295,
-0.022061021998524666,
-0.022900188341736794,
-0.022634003311395645,
-0.02433018386363983,
0.025561800226569176,
0.03037070482969284,
0.008684090338647366,
-0.005813496187329292,
0.00839836522936821,
0.007989434525370598,
0.003195967059582472,
-0.010793975554406643,
0.015048814006149769,
-0.053703419864177704,
-0.027223384007811546,
-0.06440023332834244,
-0.054827991873025894,
0.03384195640683174,
0.011427845805883408,
-0.05943842604756355,
0.02577277272939682,
-0.024209124967455864,
0.028354942798614502,
-0.002460574498400092,
0.014104082249104977,
-0.008478831499814987,
0.07048225402832031,
-0.006915789097547531,
-0.02204287238419056,
-0.02415032684803009,
-0.001452527940273285,
0.1112435907125473,
0.04918455332517624,
-0.01266347523778677,
-0.07954121381044388,
0.037957217544317245,
-0.011846854351460934,
0.008044932968914509,
-0.038312993943691254,
0.005566706880927086,
-0.011632746085524559,
0.015703389421105385,
-0.005577189847826958,
0.050128575414419174,
0.01996804028749466,
-0.007716663647443056,
0.08009886741638184,
-0.027856314554810524,
-0.0373108834028244,
0.015391814522445202,
0.03563190624117851,
0.008754171431064606,
0.0033829896710813046,
-0.025706293061375618,
0.03350573778152466,
-0.046006448566913605,
0.003164609195664525,
-0.024784279987215996,
-0.016947319731116295,
-0.0064941756427288055,
0.0004880396299995482,
-0.05415307357907295,
0.00676136976107955,
0.0036018157843500376,
-0.03375420719385147,
-0.033890821039676666,
0.01083318144083023,
0.032904308289289474,
0.00011084553261753172,
0.006282241083681583,
-0.014139377512037754,
-0.003907752223312855,
0.018361246213316917,
-0.007141202222555876,
-0.003835189389064908,
-0.048123352229595184,
0.015909582376480103,
-0.013517023995518684,
0.028824247419834137,
-0.012846998870372772,
0.02258318103849888,
0.02285856567323208,
-0.002394425217062235,
-0.0257460605353117,
-0.03221486508846283,
-0.018539827316999435,
-0.01601606234908104,
0.05670967698097229,
-0.021656638011336327,
-0.04239625856280327,
-0.027450839057564735,
0.029064582660794258,
-0.014967151917517185,
0.04106523469090462,
-0.009540637023746967,
0.0054821134544909,
0.02786681428551674,
-0.013325600884854794,
0.023790741339325905,
-0.0392439067363739,
-0.03263875097036362,
0.009149277582764626,
-0.01876847632229328,
-0.06706179678440094,
-0.03037886507809162,
0.00806098710745573,
0.03321581333875656,
0.04086410254240036,
0.011712368577718735,
0.0011872759787365794,
-0.024407926946878433,
-0.03207380697131157,
0.03772873431444168,
-0.02501346729695797,
-0.015790576115250587,
-0.044105805456638336,
-0.006961693987250328,
0.03813304007053375,
0.04350215569138527,
-0.016446275636553764,
0.03187458962202072,
-0.023410219699144363,
-0.02882014401257038,
0.035758040845394135,
-0.017420418560504913,
0.027198761701583862,
0.031200988218188286,
-0.028023559600114822,
-0.022435374557971954,
-0.013849901966750622,
-0.006491855718195438,
0.03243076801300049,
0.016601599752902985,
-0.0028106842655688524,
0.009172668680548668,
-0.03963746875524521,
0.029233593493700027,
0.02504875510931015,
-0.01263685803860426,
-0.008161569014191628,
0.03976535424590111,
0.01571560651063919,
-0.05492314696311951,
-0.042965102940797806,
-0.03486401587724686,
0.007152577396482229,
-0.01493702083826065,
0.03326631709933281,
-0.023501340299844742,
0.03369078040122986,
-0.016466857865452766,
0.057326577603816986,
-0.06292673200368881,
-0.016436750069260597,
-0.06447587162256241,
0.028365517035126686,
0.010707933455705643,
-0.010053112171590328,
0.02700706757605076,
0.008604696951806545,
-0.009336077608168125,
-0.0029547035228461027,
0.025879399850964546,
0.05090221017599106,
0.013547243550419807,
0.010305690579116344,
0.018964670598506927,
-0.008993699215352535,
0.047436200082302094,
-0.009274170733988285,
-0.01645975559949875,
0.05834013596177101,
-0.044336557388305664,
-0.05645867437124252,
0.05641348287463188,
-0.0068568279966712,
0.021700266748666763,
0.022011011838912964,
-0.046893924474716187,
-0.018504591658711433,
0.028416147455573082,
-0.032284192740917206,
-0.0031229176092892885,
-0.0003301626129541546,
-0.03783893585205078,
-0.03992009535431862,
0.0070122117176651955,
-0.0014592118095606565,
0.004133159760385752,
0.01735256239771843,
0.04606425389647484,
0.01573549211025238,
-0.011655928567051888,
0.01788584142923355,
0.04418041184544563,
-0.032768454402685165,
0.005885764490813017,
0.03230717033147812,
-0.006604434456676245,
0.025281870737671852,
0.052331119775772095,
-0.06426940113306046,
0.016331421211361885,
0.03834189847111702,
0.018361510708928108,
-0.07883753627538681,
0.005025641527026892,
-0.004772758577018976,
0.001111324061639607,
0.0612899549305439,
-0.03172893449664116,
0.021711159497499466,
0.01120372861623764,
-0.055646296590566635,
0.04114890843629837,
-0.0338139571249485,
-0.028273239731788635,
0.012944590300321579,
-0.013714153319597244,
0.012779065407812595,
0.061648860573768616,
0.03871677815914154,
0.041690465062856674,
0.01733112335205078,
0.006458792835474014,
-0.0027006762102246284,
-0.04618028923869133,
-0.013197805732488632,
0.005277184769511223,
-0.02673814259469509,
-0.02601080760359764,
0.06313595175743103,
0.03397709131240845,
-0.00343459565192461,
0.03692871704697609,
-0.003990797325968742,
-0.01555524580180645,
-0.0023923239205032587,
0.02524474821984768,
0.03977764770388603,
0.04935808107256889,
0.013210766948759556,
-0.015848955139517784,
-0.02468620240688324,
0.04391321539878845,
0.03108006715774536,
0.05880618840456009,
0.0065879542380571365,
-0.000950069515965879,
0.009270129725337029,
-0.06272031366825104,
-0.022309748455882072,
0.0187170822173357,
-0.005642910022288561,
0.0011239155428484082,
-0.009720739908516407,
0.0025249915197491646,
0.0036518084816634655,
-0.04065443202853203,
0.010251686908304691,
-0.043893083930015564,
-0.0492156483232975,
0.04657771810889244,
-0.011433570645749569,
-0.008186062797904015,
0.013588656671345234,
-0.006638823077082634,
-0.014592518098652363,
0.0036204950883984566,
0.021471768617630005,
0.013280635699629784,
-0.0389842614531517,
0.0020397957414388657,
0.010113679803907871,
0.0031624548137187958,
0.01306496374309063,
-0.048442840576171875,
-0.03670359402894974,
0.05483366921544075,
-0.014678515493869781,
0.019496150314807892,
-0.027166835963726044,
-0.030991461127996445,
-0.040054019540548325,
-0.050863366574048996,
0.031212035566568375,
-0.0027305851690471172,
-0.0020037642680108547,
-0.01830872893333435,
-0.01691768504679203,
-0.019922133535146713,
-0.0012820960255339742,
0.07801211625337601,
-0.03299440070986748,
-0.019777005538344383,
-0.006102170329540968,
-0.0021420049015432596,
0.03423169627785683,
-0.057385075837373734,
0.01802052929997444,
-0.01076164934784174,
-0.0290677510201931,
-0.01005819346755743,
-0.009460640139877796,
-0.0007863938808441162,
0.023245053365826607,
-0.009053055197000504,
0.0026219382416456938,
0.05885059013962746,
-0.00731049757450819,
-0.012318105436861515,
0.07810202986001968,
0.028948815539479256,
-0.02923000603914261,
0.06469897925853729,
-0.004145406652241945,
0.03888660669326782,
0.0477265827357769,
0.015483370050787926,
-0.01520105917006731,
0.021480323746800423,
-0.007447896990925074,
-0.0067879012785851955,
0.010244537144899368,
0.0415770448744297,
0.014532815665006638,
-0.03658416494727135,
-0.034697115421295166,
0.050954826176166534,
-0.04847743734717369,
-0.0017409271094948053,
0.04186083748936653,
0.015116997994482517,
0.02048625238239765,
-0.00450675655156374,
-0.007566364482045174,
0.049237288534641266,
-0.0028112579602748156,
0.021279528737068176,
0.05315010994672775,
0.074955515563488,
-0.013114508241415024,
0.007993699051439762,
0.030794253572821617,
-0.011926037259399891,
0.015643320977687836,
0.022586336359381676,
0.030098961666226387,
-0.04467162862420082,
-0.05832519754767418,
0.006224985234439373,
-0.0038704678881913424,
0.0326777882874012,
0.023916300386190414,
-0.01274057850241661,
0.09304407238960266,
-0.0276767760515213,
0.005710513796657324,
0.004437695723026991,
0.005257786717265844,
0.00336488732136786,
-0.0008198812138289213,
-0.019179804250597954,
0.03855286166071892,
-0.003603594843298197,
0.0006865860777907073,
-0.01808433048427105,
0.012444468215107918,
-0.003621012670919299,
-0.03576827794313431,
0.023765677586197853,
0.02755102515220642,
-0.004435167647898197,
-0.011868304572999477,
0.01563531532883644,
-0.03657631203532219,
-0.041285984218120575,
0.03783925250172615,
0.04033779352903366,
0.008650104515254498,
0.0008421399397775531,
-0.0075444504618644714,
-0.010695276781916618,
0.025440333411097527,
-0.08176252990961075,
-0.019268233329057693,
-0.006951234769076109,
0.008661016821861267,
-0.021175088360905647,
0.004297761246562004
] |
<p>The quark composition of the neutral pion ($\pi^0$) is $\frac{u\bar{u} - d\bar{d}}{\sqrt{2}}$. What does this actually mean?</p>
<p>I think it's bizarre that a particle doesn't have a definite composition. There's a difference of 2 MeV between the quark masses and I don't understand how this can be ignored. If I were to somehow manage to make a bound state of an up and an anti-up quark, what would it be? Would it be a variation on the neutral pion or would it somehow transform into the mixture?</p>
| 8,279 |
[
0.018774978816509247,
-0.027405520901083946,
-0.002556625520810485,
-0.028947116807103157,
0.013066262938082218,
0.03389080986380577,
-0.011044144630432129,
-0.043487828224897385,
-0.007534124422818422,
-0.018427198752760887,
0.0178095530718565,
0.005633059423416853,
0.039436519145965576,
-0.0061119794845581055,
-0.008407842367887497,
0.024287568405270576,
0.030321035534143448,
-0.01683974638581276,
-0.022277461364865303,
-0.044034577906131744,
0.0066433800384402275,
0.04807927832007408,
0.03053036332130432,
0.021348953247070312,
-0.016040008515119553,
0.036324575543403625,
0.01484709233045578,
-0.0003720507666002959,
0.012684605084359646,
0.055062226951122284,
0.001496068318374455,
-0.04708580672740936,
0.033564046025276184,
0.009346584789454937,
0.04075514152646065,
0.011407201178371906,
-0.0020117859821766615,
-0.051064714789390564,
-0.025981595739722252,
0.029003292322158813,
-0.07919247448444366,
-0.03269921988248825,
0.008708282373845577,
0.00513848103582859,
-0.02053547464311123,
-0.010937613435089588,
0.023644983768463135,
-0.05504796653985977,
0.06586603075265884,
-0.06762706488370895,
0.042693719267845154,
0.05728452652692795,
0.03270196542143822,
0.013965201564133167,
-0.005486383568495512,
-0.018852919340133667,
0.06446424871683121,
0.07184230536222458,
0.020178312435746193,
-0.019745562225580215,
-0.010248557664453983,
-0.017735252156853676,
-0.031214814633131027,
-0.0026219335850328207,
-0.03253118693828583,
0.030914871022105217,
-0.017090819776058197,
0.015132172033190727,
-0.015034173615276814,
-0.04054819792509079,
0.057934243232011795,
-0.004025334492325783,
-0.002669030334800482,
-0.03980452939867973,
0.037250809371471405,
-0.015276228077709675,
0.006802317686378956,
0.01903209649026394,
0.007868900895118713,
0.03982924669981003,
-0.01256245095282793,
0.007465184200555086,
0.021021151915192604,
-0.008464731276035309,
-0.007934942841529846,
-0.0015735714696347713,
0.045008327811956406,
-0.011160939000546932,
-0.041382044553756714,
0.07852410525083542,
0.0012716851197183132,
0.007183276116847992,
0.029071461409330368,
0.0011606237385421991,
0.0016498435288667679,
-0.0024091172963380814,
0.003390576923266053,
0.02664101868867874,
-0.0205671526491642,
-0.01454752404242754,
-0.016550451517105103,
0.0055095176212489605,
0.021817287430167198,
0.09203680604696274,
0.002791988430544734,
-0.011032091453671455,
-0.020181244239211082,
-0.015126356855034828,
-0.02089918963611126,
-0.01098110992461443,
-0.02151276171207428,
-0.0034875166602432728,
-0.02813221514225006,
0.0010275592794641852,
-0.011350877583026886,
-0.02855394221842289,
0.007097532507032156,
-0.03586675599217415,
0.06562826037406921,
0.007318409625440836,
0.04894956201314926,
-0.012498157098889351,
0.0289491955190897,
-0.030450068414211273,
-0.0615767166018486,
0.003214157884940505,
0.01136027742177248,
0.029679853469133377,
-0.03363766893744469,
-0.0019236200023442507,
-0.019388241693377495,
0.029379207640886307,
0.007474183104932308,
0.021754980087280273,
0.016974814236164093,
-0.028238676488399506,
-0.08124522864818573,
-0.052483778446912766,
-0.00585510628297925,
-0.022374380379915237,
-0.04970669746398926,
-0.1159905195236206,
-0.03642261400818825,
0.03656325861811638,
0.04383384808897972,
-0.01689131371676922,
-0.014248345047235489,
-0.012111641466617584,
0.01104126125574112,
0.03282881900668144,
0.02273077517747879,
-0.04203515872359276,
-0.0407366044819355,
-0.04080284759402275,
0.016951873898506165,
-0.029957860708236694,
0.02501010149717331,
0.04131856933236122,
-0.00841610413044691,
-0.004278560169041157,
0.05698145925998688,
-0.018754301592707634,
0.02638320066034794,
0.04863140732049942,
-0.010231061838567257,
-0.010167653672397137,
0.04892498254776001,
0.008967572823166847,
-0.0007316399132832885,
0.050280094146728516,
0.004252977203577757,
0.02392549067735672,
0.03404202684760094,
0.029339224100112915,
0.0803123340010643,
-0.001884874771349132,
-0.07356639206409454,
-0.06153851002454758,
0.016845818608999252,
-0.014980060048401356,
-0.0326523594558239,
-0.03664248436689377,
-0.01196589320898056,
0.03720920532941818,
-0.004233025014400482,
0.02387639321386814,
0.009977027773857117,
-0.011559261940419674,
0.034309517592191696,
-0.06366151571273804,
-0.007127910386770964,
-0.03551055118441582,
-0.0288800410926342,
-0.020447760820388794,
-0.02597982995212078,
0.04089091718196869,
0.002015449106693268,
-0.014602817595005035,
-0.013386364094913006,
-0.03996294364333153,
0.014828478917479515,
0.015443351119756699,
0.02470850944519043,
0.009776775725185871,
0.01925010420382023,
0.023984065279364586,
0.015207343734800816,
0.013910538516938686,
-0.01249778550118208,
-0.03432418406009674,
-0.022559361532330513,
-0.04252920299768448,
-0.018188990652561188,
0.012953239493072033,
-0.008776084519922733,
0.03288782760500908,
0.010025570169091225,
-0.03219222649931908,
0.0055338130332529545,
0.026913337409496307,
-0.02826627530157566,
0.08191680908203125,
0.019327610731124878,
-0.014560669660568237,
-0.011851370334625244,
0.0441523902118206,
-0.0026805116795003414,
0.03704037144780159,
-0.03535350039601326,
-0.012593434192240238,
-0.028675250709056854,
-0.018362127244472504,
0.06013006344437599,
0.02905920334160328,
-0.034618474543094635,
0.02120259776711464,
0.016183065250515938,
0.02288724295794964,
0.002024428453296423,
0.015131992287933826,
-0.03883051499724388,
-0.03035757504403591,
0.059328410774469376,
-0.004826209042221308,
-0.016959073022007942,
0.039841797202825546,
0.02188694477081299,
0.01531412173062563,
-0.007562984712421894,
-0.032746389508247375,
-0.061524830758571625,
0.04738041013479233,
-0.026760226115584373,
0.032597195357084274,
0.011784347705543041,
-0.04043314605951309,
0.013450788334012032,
-0.03847561776638031,
0.06307170540094376,
0.03543644770979881,
-0.023439845070242882,
-0.014410654082894325,
0.003974143415689468,
-0.02001175284385681,
-0.0004968245630152524,
0.042020540684461594,
-0.01107835303992033,
0.005775222089141607,
0.015894586220383644,
-0.047516368329524994,
0.007575149182230234,
0.005195497069507837,
-0.034186262637376785,
-0.01920599676668644,
-0.01975778490304947,
0.040771953761577606,
0.05403764545917511,
0.00989951379597187,
-0.03706032782793045,
-0.02253202348947525,
0.036276888102293015,
-0.027648070827126503,
0.00935573410242796,
0.02956189401447773,
-0.025189226493239403,
0.012937409803271294,
-0.06682903319597244,
-0.006106645334511995,
0.0060389102436602116,
0.005048694089055061,
-0.00025144233950413764,
0.004900483880192041,
-0.035581011325120926,
-0.03424130007624626,
-0.013204188086092472,
0.008583568036556244,
-0.004355177283287048,
-0.017177388072013855,
0.01130486186593771,
0.00985245406627655,
0.019712524488568306,
-0.043069735169410706,
0.04023842141032219,
-0.055264364928007126,
-0.03819652646780014,
-0.0035580466501414776,
0.0221556443721056,
0.0698419138789177,
0.0037078424356877804,
0.05555674061179161,
0.07186232507228851,
-0.05360746383666992,
0.05062160640954971,
-0.05063661187887192,
-0.0410902313888073,
-0.01366165466606617,
0.014546822756528854,
0.04024510458111763,
0.014896499924361706,
-0.02909492515027523,
0.10055626183748245,
0.011874374002218246,
-0.04263396933674812,
0.009805884212255478,
0.02004261501133442,
-0.022986195981502533,
-0.016954602673649788,
0.030502673238515854,
0.02251811884343624,
-0.014729397371411324,
-0.0016134257894009352,
0.022031143307685852,
0.061568714678287506,
0.031633466482162476,
0.017296448349952698,
-0.029062515124678612,
0.028829244896769524,
0.031001215800642967,
-0.0021638968028128147,
0.03145645931363106,
0.011971276253461838,
-0.025976425036787987,
-0.008371109142899513,
0.01835222914814949,
0.053541116416454315,
0.047172367572784424,
-0.004731023218482733,
0.08333469182252884,
0.0027789059095084667,
-0.01721648871898651,
-0.012080230750143528,
0.04416777938604355,
-0.03566442430019379,
-0.032616231590509415,
-0.0013495036400854588,
-0.030605368316173553,
0.028759241104125977,
-0.009517188183963299,
0.014121940359473228,
0.05066749081015587,
0.05027705803513527,
-0.03318244591355324,
-0.018651442602276802,
0.002820787252858281,
0.003963788039982319,
-0.011656029149889946,
-0.022275932133197784,
0.0026633425150066614,
0.0366704948246479,
0.025352302938699722,
0.02072330005466938,
-0.017412913963198662,
-0.014710298739373684,
-0.02987988106906414,
-0.05745723098516464,
-0.03436284884810448,
-0.016401760280132294,
0.007293335162103176,
-0.01079806499183178,
0.0726892501115799,
-0.002808638848364353,
-0.010592595674097538,
-0.014958764426410198,
-0.0022772529628127813,
-0.06521762162446976,
0.0117491465061903,
-0.04787590727210045,
-0.0056387996301054955,
-0.04113360866904259,
-0.004073610994964838,
-0.05018480122089386,
-0.01643754541873932,
-0.039660800248384476,
0.015513541176915169,
-0.01716575399041176,
-0.013007139787077904,
0.04786764830350876,
-0.03594087064266205,
-0.004011985845863819,
-0.018964480608701706,
0.0006163807702250779,
0.05255519971251488,
0.0076170689426362514,
0.003336003515869379,
-0.0012624837690964341,
-0.026652760803699493,
-0.011087456718087196,
-0.04036916792392731,
0.007176945451647043,
0.015290946699678898,
0.03314642980694771,
0.014132422395050526,
0.05019168183207512,
0.013602761551737785,
-0.006767326965928078,
0.02447136864066124,
0.0649385005235672,
0.004808326717466116,
-0.016630234196782112,
-0.01023645605891943,
-0.06462392956018448,
-0.03950786218047142,
0.0063652535900473595,
0.026002081111073494,
-0.00807874370366335,
0.020950227975845337,
0.008680185303092003,
0.02091388963162899,
-0.007742771413177252,
0.020799292251467705,
0.07217513769865036,
0.032184187322854996,
-0.011439620517194271,
-0.07797398418188095,
0.009888393804430962,
-0.015171377919614315,
-0.003257418517023325,
-0.0647394135594368,
-0.01134912297129631,
-0.02107391133904457,
0.019579963758587837,
0.02727310173213482,
0.01775944232940674,
-0.01743479259312153,
-0.02600220963358879,
-0.05567840486764908,
0.002563707297667861,
-0.043989527970552444,
-0.004685682710260153,
0.005470502655953169,
0.0707525685429573,
0.03299814462661743,
0.042633939534425735,
0.005973626859486103,
-0.0429336279630661,
0.002062831539660692,
0.024220677092671394,
0.07217136770486832,
0.01946832984685898,
-0.023805469274520874,
-0.031237730756402016,
-0.01938205026090145,
0.0330570824444294,
-0.018819261342287064,
0.010584714822471142,
-0.030803052708506584,
-0.016482463106513023,
-0.010512926615774632,
-0.017910221591591835,
-0.020284656435251236,
0.04853639751672745,
0.007818072102963924,
0.007626872509717941,
-0.05229012668132782,
-0.011923179030418396,
-0.03139285370707512,
0.061255041509866714,
0.043550167232751846,
0.022575946524739265,
0.004630727227777243,
0.016566302627325058,
0.03469573333859444,
-0.0261459369212389,
-0.022546252235770226,
-0.09600827842950821,
-0.009776321239769459,
0.010798311792314053,
0.04306346923112869,
0.031960323452949524,
-0.02116372063755989,
-0.05256742984056473,
-0.009027908556163311,
0.022965505719184875,
0.01221307273954153,
0.009692620486021042,
-0.07229946553707123,
0.05455775931477547,
0.040679555386304855,
0.004954731557518244,
0.024239499121904373,
0.020980525761842728,
-0.05381320044398308,
-0.02144858054816723,
-0.04779404029250145,
0.04152616485953331,
-0.002013097982853651,
0.00965491496026516,
-0.04373573511838913,
-0.01021168939769268,
-0.010093593038618565,
0.002461784752085805,
-0.00968092493712902,
0.056290894746780396,
0.0016896084416657686,
-0.05218643695116043,
-0.024324210360646248,
0.011487363837659359,
-0.006697060074657202,
-0.021693730726838112,
-0.002760431030765176,
0.010364972054958344,
0.016285285353660583,
0.00967411044985056,
0.022876041010022163,
-0.023889601230621338,
-0.008709854446351528,
0.00482196593657136,
-0.014194376766681671,
0.026256989687681198,
-0.012493375688791275,
-0.053122151643037796,
0.02014360949397087,
-0.0365748293697834,
0.03537540137767792,
-0.025520892813801765,
0.010589796118438244,
0.022625043988227844,
-0.07741472870111465,
-0.03413967415690422,
0.015669776126742363,
-0.008591135032474995,
0.012585300952196121,
-0.037773676216602325,
0.013935282826423645,
0.006639245897531509,
0.030660636723041534,
-0.0665656328201294,
-0.02534129098057747,
0.00915445014834404,
-0.009499847888946533,
-0.025937680155038834,
-0.039623014628887177,
-0.01969466172158718,
0.01363386120647192,
-0.01117588859051466,
-0.02099962718784809,
0.05545520782470703,
-0.025234341621398926,
-0.008027903735637665,
-0.01888788491487503,
0.0584629662334919,
0.05001131445169449,
-0.01734762266278267,
-0.009160737507045269,
0.024723675101995468,
0.00407709926366806,
0.01421284582465887,
0.06328155100345612,
0.06129233166575432,
-0.020946374163031578,
-0.02324341982603073,
-0.000757853442337364,
0.009949472732841969,
0.01202366966754198,
-0.031699538230895996,
0.03018900938332081,
0.022082393988966942,
0.027427485212683678,
0.06541626155376434,
0.016460347920656204,
0.01791413687169552,
0.009980852715671062,
0.003318634582683444,
-0.01238330826163292,
0.007892576977610588,
-0.051108408719301224,
-0.025183340534567833,
0.07554665207862854,
-0.03214624524116516,
0.01454237662255764,
0.019051620736718178,
0.024323098361492157,
0.023526929318904877,
-0.04352205619215965,
0.01933973655104637,
-0.008621356450021267,
-0.003061617026105523,
0.014783617109060287,
0.005535196978598833,
0.04090245068073273,
-0.0012770147295668721,
-0.014728741720318794,
-0.010202418081462383,
-0.010289719328284264,
-0.01296690572053194,
0.009366448037326336,
-0.0004523795796558261,
0.04576679319143295,
0.009445725940167904,
0.005457397550344467,
-0.020264985039830208,
-0.002443792764097452,
-0.051902592182159424,
0.013911517336964607,
-0.02490704134106636,
0.012368422001600266,
-0.019299466162919998,
-0.008861980400979519,
0.007924028672277927,
0.04456297680735588,
-0.004270382225513458,
-0.015789814293384552,
0.058259181678295135,
0.014997070655226707,
0.01687018759548664,
-0.004780046176165342,
-0.04201826825737953,
0.04386571794748306,
-0.03185831382870674,
0.014261974953114986,
0.0060737356543540955,
-0.025493111461400986,
0.06735352426767349,
0.0065248263999819756,
0.021521687507629395,
-0.03335195034742355,
-0.0004433249414432794,
-0.04434344545006752,
0.03531443700194359,
0.03872544318437576,
0.014922523871064186,
-0.0037712876219302416,
0.03249377757310867,
0.030751317739486694,
0.016603734344244003,
0.02059466950595379,
0.01165781170129776,
-0.053849171847105026,
-0.06003445014357567,
-0.03496506065130234,
-0.0467926524579525,
0.017500923946499825,
-0.0777818113565445,
-0.0004782788164447993,
-0.00213591824285686,
-0.010140860453248024,
0.027150319889187813,
-0.030469603836536407,
0.003538012970238924,
-0.051146190613508224,
0.02926863729953766,
-0.013175487518310547,
0.03441998362541199,
-0.0024528272915631533,
0.007962259463965893,
0.11537832021713257,
0.03409396857023239,
0.010601820424199104,
-0.059160638600587845,
0.0012827174505218863,
-0.025311937555670738,
0.013071143999695778,
-0.0002828061406034976,
0.02556302770972252,
0.04698781296610832,
0.031369782984256744,
0.005031652748584747,
0.049202337861061096,
0.012079011648893356,
-0.0035110025200992823,
0.06686481833457947,
-0.002093325601890683,
-0.06806541234254837,
0.0028027123771607876,
0.02324884943664074,
-0.044505298137664795,
0.012087184935808182,
-0.02122952789068222,
0.022709716111421585,
0.006894013378769159,
0.024995926767587662,
-0.030344944447278976,
-0.04053250700235367,
-0.0003951718972530216,
-0.013896745629608631,
-0.04633837565779686,
-0.005045014899224043,
-0.004766971338540316,
0.017574366182088852,
-0.016048891469836235,
-0.011345341801643372,
-0.018167885020375252,
-0.019240373745560646,
-0.0026879936922341585,
0.011069118045270443,
0.022079959511756897,
-0.025934088975191116,
-0.007910403423011303,
-0.009557550773024559,
-0.03299500048160553,
-0.008996034041047096,
0.003913019318133593,
0.04915618896484375,
-0.05368146672844887,
-0.020714350044727325,
0.01756833679974079,
0.03846411779522896,
0.025057749822735786,
-0.03969954326748848,
0.01653388887643814,
0.010988475754857063,
0.022253043949604034,
-0.03265831246972084,
-0.003687850898131728,
-0.009771694429218769,
0.060965098440647125,
0.0005499557009898126,
0.012733529321849346,
0.018148621544241905,
0.004017396830022335,
-0.029986508190631866,
-0.02369394153356552,
0.05392326042056084,
0.018592385575175285,
-0.013893408700823784,
-0.01895386539399624,
0.025452766567468643,
-0.02758820727467537,
-0.030662452802062035,
0.009565838612616062,
0.016551613807678223,
0.06884677708148956,
-0.007719768676906824,
-0.002609799150377512,
-0.00642688712105155,
-0.03178945183753967,
0.06178228557109833,
-0.010968339629471302,
-0.005516428500413895,
-0.021484065800905228,
0.0051773409359157085,
-0.008199641481041908,
0.05420638993382454,
-0.012681637890636921,
0.037110600620508194,
-0.012914424762129784,
0.04078303277492523,
-0.013564076274633408,
-0.020964836701750755,
-0.02337583899497986,
0.038180872797966,
-0.0327402725815773,
0.0009044154430739582,
-0.014556189067661762,
0.006603512912988663,
0.005911530461162329,
0.010525751858949661,
0.017505085095763206,
0.023616043850779533,
-0.026624659076333046,
0.0017994798254221678,
0.0420956127345562,
-0.029878739267587662,
-0.006866938900202513,
-0.012452944181859493,
0.010682978667318821,
0.0005303336074575782,
-0.012532959692180157,
-0.0332820862531662,
-0.02334769442677498,
0.013463180512189865,
0.03350673243403435,
-0.007832598872482777,
-0.02371184714138508,
-0.014450102113187313,
-0.02112562209367752,
0.01308788824826479,
0.005185713060200214,
-0.028803838416934013,
0.013498280197381973,
-0.026566769927740097,
0.011453557759523392,
0.0034393887035548687,
-0.0010216757655143738,
0.005466448608785868,
-0.015844758599996567,
0.019189247861504555,
0.01117912121117115,
-0.038588106632232666,
-0.018091224133968353,
0.01142969448119402,
0.009613806381821632,
0.0012058198917657137,
-0.011996936984360218,
-0.03424040600657463,
0.04670269787311554,
-0.012660373002290726,
-0.049360424280166626,
0.022030707448720932,
0.022873559966683388,
0.027133939787745476,
0.012424062937498093,
-0.028635358437895775,
-0.02908073365688324,
0.040951382368803024,
-0.032564762979745865,
-0.011012302711606026,
-0.029292142018675804,
-0.0189280454069376,
-0.0007062814547680318,
-0.01888962835073471,
-0.01993771269917488,
-0.010194712318480015,
-0.007212200667709112,
0.03709530830383301,
0.01762968674302101,
-0.008756902068853378,
0.024849822744727135,
-0.034203026443719864,
-0.00413493812084198,
0.02898108959197998,
0.022826654836535454,
0.04976845160126686,
-0.001382759539410472,
0.030082935467362404,
0.010516325011849403,
0.030659116804599762,
0.005428994540125132,
-0.0015184602234512568,
-0.07319166511297226,
-0.02925369143486023,
0.035248976200819016,
-0.026291517540812492,
0.043316327035427094,
-0.05176856741309166,
0.0024138547014445066,
0.02842526324093342,
-0.05174608528614044,
0.012642511166632175,
-0.08794353902339935,
-0.04829436168074608,
-0.035803746432065964,
-0.020048700273036957,
-0.03319771960377693,
0.06280595064163208,
0.0029747230000793934,
0.03043654002249241,
0.02102971449494362,
0.016748132184147835,
0.005146570038050413,
-0.00885035376995802,
-0.0027971328236162663,
0.0003209656570106745,
0.00624883733689785,
-0.016039181500673294,
0.08161041140556335,
-0.023815395310521126,
-0.017683232203125954,
0.026092255488038063,
0.01176446583122015,
-0.013122676871716976,
-0.02138865739107132,
0.020469360053539276,
0.008995677344501019,
0.01729949191212654,
0.009141236543655396,
0.020274925976991653,
-0.01593313179910183,
0.011003419756889343,
0.06344573944807053,
0.04447678104043007,
-0.018582185730338097,
-0.005159158259630203,
-0.005275429226458073,
-0.03170100972056389,
-0.021349459886550903,
0.056338053196668625,
-0.07600541412830353,
0.008746285922825336,
0.01422976516187191,
0.02295500598847866,
-0.005114642903208733,
-0.010241478681564331,
-0.0009667804115451872,
-0.02191639132797718,
0.008436258882284164,
0.015131195075809956,
0.03806566447019577,
0.038969043642282486,
0.0023229739163070917,
0.0043855104595422745,
-0.0039255935698747635,
0.023258712142705917,
0.03311244025826454,
-0.032774824649095535,
-0.015832655131816864,
-0.028171256184577942,
-0.0028574506286531687,
0.028465237468481064,
0.046829238533973694,
-0.015508845448493958,
-0.047331325709819794,
-0.0021660877391695976,
-0.005040853284299374,
0.013767173513770103,
-0.03570028766989708,
-0.055642854422330856,
0.01286619808524847,
-0.02403796650469303,
0.05827433615922928,
0.029449142515659332,
-0.0021487893536686897,
-0.011628220789134502,
-0.01932554319500923,
-0.04222901910543442,
0.029391521587967873,
0.03022024966776371,
0.04111311212182045,
-0.025369422510266304,
0.026743143796920776,
-0.012536215595901012,
0.0104792769998312,
-0.0037868123035877943,
-0.0033581836614757776,
-0.00386019516736269,
-0.026141319423913956,
0.004576663952320814,
0.012086254544556141,
-0.0039939298294484615,
0.031605325639247894,
0.04576803371310234,
0.00004226717646815814,
-0.02108665555715561,
0.011161199770867825,
-0.0538463331758976,
0.07964825630187988,
-0.03179684281349182,
0.004159609787166119,
0.061451613903045654,
-0.00855468213558197,
0.013828132301568985,
0.039824504405260086,
-0.030790384858846664,
-0.0664111077785492,
0.02162793092429638,
0.02953764609992504,
-0.02459287829697132,
0.008525282144546509,
0.0008989066700451076,
0.04266896843910217,
-0.02684236690402031,
0.0003479896695353091,
0.042696207761764526,
-0.030785055831074715,
-0.029506953433156013,
0.03732655569911003,
0.05169862136244774,
0.07641399651765823,
0.00816099438816309,
0.010496227070689201,
0.036492664366960526,
-0.0016132986638695002,
0.010687537491321564,
0.02635076269507408,
0.008246279321610928,
0.04566959664225578,
-0.012729265727102757,
0.017519986256957054,
-0.0172837246209383,
-0.005659603979438543,
0.004783309530466795,
0.04723328724503517,
-0.042054612189531326,
-0.00647580623626709,
0.01994672790169716,
-0.031205592676997185,
0.024248231202363968,
0.019132111221551895,
-0.04926262050867081,
0.08381665498018265,
-0.0395367331802845,
0.01965572126209736,
-0.037946801632642746,
0.0008540460839867592,
-0.01037619262933731,
-0.005153127945959568,
-0.004390399903059006,
0.06425163894891739,
0.024665620177984238,
-0.03922609984874725,
-0.04094522446393967,
0.0015777972294017673,
0.02575237862765789,
-0.041517991572618484,
0.0005113407387398183,
0.018766185268759727,
-0.011910933069884777,
-0.04011404514312744,
-0.013612416572868824,
-0.0494033545255661,
-0.030004166066646576,
0.05976521596312523,
0.01011833269149065,
0.019393889233469963,
-0.00893124844878912,
-0.04147912189364433,
-0.056134145706892014,
0.03264859318733215,
-0.01685021072626114,
-0.048558562994003296,
-0.043613843619823456,
0.02243211306631565,
-0.03068859502673149,
-0.024354390799999237
] |
<p>If you push a bar magnet inside a solenoid, a current is produced. But why is that? I mean, the wire is being moved <em>along</em> the magnetic field, so taking the cross product:</p>
<p>$\vec{F} = I\vec{V}\times\vec{B} = I|\vec{V}||\vec{B}|\sin\theta\hat{n}$</p>
<p>Here, the angle between the velocity of the charge in the wires and the magnetic field is essentially zero. So there is no force on the charges in the wire and hence no current. But that does not correspond to reality. Why? </p>
<p><img src="http://i.stack.imgur.com/q1nly.jpg" alt="enter image description here"></p>
| 8,280 |
[
-0.030765922740101814,
0.00608739722520113,
0.0005856279749423265,
-0.012152035720646381,
0.033734407275915146,
0.011318591423332691,
-0.05117282643914223,
0.020006055012345314,
-0.004409796558320522,
0.0009690236183814704,
0.040017470717430115,
0.025132643058896065,
0.04865618422627449,
0.031742170453071594,
0.020310116931796074,
0.028449542820453644,
0.022537581622600555,
-0.00964941456913948,
0.009069249965250492,
0.013342147693037987,
-0.00832332856953144,
0.05879352614283562,
0.01957685872912407,
0.017507879063487053,
0.02730213664472103,
0.0059224688448011875,
0.02536126784980297,
0.0035016790498048067,
-0.016371382400393486,
0.065023273229599,
0.003989504650235176,
-0.02287580631673336,
-0.033961549401283264,
-0.028111539781093597,
0.0074239163659513,
0.0193968266248703,
-0.010247549042105675,
-0.04587128758430481,
-0.006584126502275467,
0.0275509525090456,
0.0025476107839494944,
0.03197285160422325,
-0.014630483463406563,
0.05332247167825699,
-0.03605825826525688,
-0.013135571964085102,
0.0008333317819051445,
0.022637374699115753,
0.06313358247280121,
-0.04527457803487778,
0.054030582308769226,
-0.03050033003091812,
0.030239049345254898,
0.018036063760519028,
-0.004678833764046431,
-0.025974364951252937,
0.07443903386592865,
0.027723342180252075,
-0.010372698307037354,
-0.03503798320889473,
0.018495433032512665,
-0.025251975283026695,
-0.019586073234677315,
-0.056214138865470886,
0.000780376314651221,
0.049250341951847076,
0.0025030949618667364,
0.010534700937569141,
0.018919682130217552,
0.016342708840966225,
0.03992198035120964,
0.009048846550285816,
-0.006284039467573166,
-0.01918770931661129,
0.014657070860266685,
-0.016849756240844727,
0.04980666562914848,
0.006369957700371742,
0.05780816823244095,
0.050059724599123,
-0.05377829074859619,
-0.0057940357364714146,
0.03511135280132294,
0.06216062977910042,
0.022957423701882362,
-0.023637475445866585,
0.03619375079870224,
-0.009992876090109348,
0.01985551044344902,
0.02821270376443863,
-0.0008646033238619566,
0.03153770789504051,
-0.0007373748230747879,
-0.016937298700213432,
0.012362522073090076,
0.051613226532936096,
0.0014972618082538247,
0.05638132244348526,
-0.0024596427101641893,
-0.05998282507061958,
-0.0019597443751990795,
0.0023672208189964294,
-0.0064582377672195435,
0.0686376690864563,
-0.022280655801296234,
-0.006443476770073175,
0.029621152207255363,
0.0019334172829985619,
-0.03189423307776451,
-0.008501909673213959,
-0.04875228554010391,
0.012476149946451187,
0.032217416912317276,
0.015955684706568718,
-0.024128440767526627,
-0.04265797883272171,
0.012458741664886475,
0.00009314147609984502,
0.021819625049829483,
0.05524936690926552,
-0.0044694519601762295,
-0.04711928963661194,
-0.0135334562510252,
-0.026739098131656647,
-0.04180871322751045,
-0.02544037066400051,
-0.0015216588508337736,
-0.0038909190334379673,
0.020710943266749382,
0.03578292950987816,
-0.01815432496368885,
-0.033882517367601395,
0.016492152586579323,
0.020514091476798058,
0.040555667132139206,
-0.025843890383839607,
-0.10232602804899216,
-0.04667261615395546,
0.04668727517127991,
-0.0026085644494742155,
0.002803761512041092,
-0.07854963839054108,
-0.007526428904384375,
-0.00681718485429883,
0.08973740041255951,
-0.006018915679305792,
0.00823570229113102,
-0.019584719091653824,
0.05033956468105316,
0.003632282605394721,
0.01710529811680317,
-0.025602636858820915,
-0.0005806944682262838,
-0.01914810761809349,
-0.026646826416254044,
-0.016852648928761482,
0.0391816608607769,
0.018207164481282234,
-0.0024476274847984314,
-0.03240761160850525,
0.03257788345217705,
-0.01943339593708515,
0.00651204027235508,
0.01016351580619812,
-0.03047005832195282,
-0.010059209540486336,
0.05661039426922798,
0.009168515913188457,
0.006877853535115719,
0.05380373075604439,
0.012468482367694378,
0.029426779597997665,
-0.010719605721533298,
0.013501239009201527,
0.028998320922255516,
-0.04464453086256981,
-0.04232123866677284,
-0.03913447633385658,
0.037323758006095886,
-0.011065131053328514,
-0.05265205353498459,
-0.04258657246828079,
-0.05373357981443405,
0.007486679125577211,
-0.004217429086565971,
0.06144358217716217,
0.023127462714910507,
0.00605213176459074,
-0.002481287345290184,
0.0030673802830278873,
-0.036117441952228546,
-0.051532644778490067,
0.041161686182022095,
-0.007871733047068119,
-0.04571177810430527,
0.026647599413990974,
0.01987740397453308,
0.026934493333101273,
-0.027656670659780502,
-0.005766779184341431,
-0.012355194427073002,
0.021767912432551384,
-0.024158315733075142,
0.0012988770613446832,
-0.005170883145183325,
0.05803530663251877,
0.03331949561834335,
0.012446061708033085,
-0.0020809017587453127,
-0.01251722127199173,
-0.027133554220199585,
-0.016422009095549583,
-0.020359788089990616,
-0.002341634128242731,
0.033295925706624985,
-0.013535541482269764,
0.04637157917022705,
-0.006591468118131161,
-0.019315985962748528,
0.046705592423677444,
0.007200179155915976,
0.11494471877813339,
0.04794396087527275,
-0.023924050852656364,
0.033737897872924805,
0.05742694064974785,
0.017923709005117416,
0.0006201552459970117,
-0.0177978053689003,
-0.030583877116441727,
-0.06213017925620079,
-0.005359078757464886,
0.03870978578925133,
0.0027773494366556406,
-0.0416412390768528,
0.01287047564983368,
-0.006087281741201878,
0.045033976435661316,
0.000643183768261224,
0.03400548920035362,
-0.030404839664697647,
-0.0323825478553772,
0.01517120748758316,
0.020883532240986824,
-0.02640196494758129,
0.022556854411959648,
0.021816400811076164,
0.030725592747330666,
0.05118853226304054,
-0.011660557240247726,
-0.02845083177089691,
0.052906882017850876,
-0.002893395023420453,
0.013721931725740433,
0.037239570170640945,
-0.03227477893233299,
0.06327466666698456,
0.003017335431650281,
0.023007463663816452,
-0.03762337565422058,
0.0066163744777441025,
0.01668403670191765,
-0.006619773339480162,
0.0039275516755878925,
-0.0016650378238409758,
-0.04400932788848877,
-0.016364961862564087,
-0.02991480380296707,
0.029661307111382484,
-0.05787578225135803,
0.006611762568354607,
-0.03457880765199661,
-0.02064324915409088,
-0.03560250997543335,
-0.032529402524232864,
-0.0017785952659323812,
0.031998418271541595,
0.062008343636989594,
-0.03482087329030037,
-0.0192925613373518,
-0.0064119310118258,
-0.03228658810257912,
0.027447134256362915,
0.03612760454416275,
-0.025528928264975548,
0.014827245846390724,
-0.05059468001127243,
-0.004080511629581451,
0.05173215642571449,
0.025876067578792572,
-0.006790960673242807,
0.01942388340830803,
-0.02484660968184471,
-0.06750941276550293,
-0.020887501537799835,
-0.04434497281908989,
0.022583022713661194,
-0.025881707668304443,
0.005539668723940849,
0.03416597843170166,
-0.011464307084679604,
-0.008630269207060337,
0.006658401805907488,
-0.030567195266485214,
-0.03529294580221176,
0.011982467025518417,
0.00869020540267229,
0.027041323482990265,
-0.01820623129606247,
0.041622258722782135,
0.003976328298449516,
-0.025314833968877792,
-0.013488920405507088,
-0.03985368087887764,
0.015282481908798218,
-0.010017520748078823,
-0.01660451479256153,
0.030501000583171844,
-0.006963201332837343,
-0.058683156967163086,
0.07284460216760635,
0.019277529790997505,
-0.036171071231365204,
-0.02173726074397564,
-0.033664166927337646,
-0.015233217738568783,
-0.05599966645240784,
0.026106519624590874,
0.058569833636283875,
-0.018924087285995483,
0.0059702773578464985,
-0.007773563731461763,
0.04713211581110954,
-0.000045478860556613654,
0.035035695880651474,
0.00007175838982220739,
-0.00554222147911787,
0.028896113857626915,
0.004520044662058353,
0.06583521515130997,
-0.0011140161659568548,
-0.0303031112998724,
0.014104064553976059,
0.02477952465415001,
0.037770938128232956,
0.0309902410954237,
-0.03556063771247864,
0.03913460299372673,
0.030766500160098076,
0.02944469451904297,
-0.0646672397851944,
0.06345853954553604,
-0.00916654709726572,
-0.005547529552131891,
-0.007625658996403217,
0.03304077312350273,
0.042602360248565674,
-0.00733077060431242,
0.017183680087327957,
0.024618180468678474,
-0.004467145074158907,
-0.047032520174980164,
-0.02504541538655758,
-0.028325699269771576,
-0.01773924008011818,
0.002825905801728368,
-0.008655186742544174,
0.028772341087460518,
0.020252089947462082,
0.06352455168962479,
0.027165446430444717,
0.0012595931766554713,
0.0027469212654978037,
-0.028062788769602776,
-0.03956274315714836,
0.007882396690547466,
0.007417169865220785,
0.023237479850649834,
0.011311337351799011,
0.07049570232629776,
-0.007892932742834091,
0.010832942090928555,
0.0035211958456784487,
-0.016846276819705963,
-0.10358864814043045,
0.030850503593683243,
-0.011624108068645,
-0.021648967638611794,
0.004105343483388424,
-0.02826978638768196,
-0.038278207182884216,
-0.015938667580485344,
0.0024135462008416653,
-0.009625005535781384,
-0.02188108116388321,
-0.03925564885139465,
-0.011161737143993378,
-0.01436944305896759,
-0.028273237869143486,
-0.022185130044817924,
-0.01593112014234066,
0.0502655915915966,
-0.05245353281497955,
0.019268518313765526,
-0.010627451352775097,
-0.005868593696504831,
-0.007971566170454025,
-0.04166528582572937,
-0.017302442342042923,
-0.0009000207064673305,
0.016001153737306595,
0.014010375365614891,
0.007759231608361006,
-0.04861736297607422,
0.016207464039325714,
0.029238851740956306,
0.032172609120607376,
0.02828288823366165,
-0.0065374234691262245,
-0.0359748974442482,
-0.0789942592382431,
-0.01802886836230755,
-0.015099206939339638,
0.05715975910425186,
0.027134060859680176,
0.0012367379385977983,
0.03881978243589401,
-0.02085117995738983,
0.0132410554215312,
0.01065792329609394,
0.03063938207924366,
0.0357220284640789,
0.003341016359627247,
-0.05000339820981026,
-0.014357710257172585,
-0.03116029128432274,
-0.04561004415154457,
0.018319759517908096,
-0.031878143548965454,
-0.025739405304193497,
-0.04346904531121254,
0.020884830504655838,
0.03986117243766785,
0.010079403407871723,
0.041779208928346634,
0.01655842550098896,
0.0016935269813984632,
-0.0017500849207863212,
-0.002890921663492918,
0.022339437156915665,
0.03355799987912178,
0.05365519970655441,
-0.02107914537191391,
-0.025859536603093147,
-0.08681202679872513,
-0.0004372909606900066,
0.04681466147303581,
0.020654303953051567,
-0.020815784111618996,
-0.01242020446807146,
-0.04459712281823158,
-0.048896424472332,
0.03778839111328125,
-0.04368818551301956,
0.030921312049031258,
-0.008171400055289268,
-0.011358295567333698,
-0.043115030974149704,
-0.056384578347206116,
-0.040746308863162994,
0.03217573091387749,
-0.038254838436841965,
0.05912085250020027,
-0.028651872649788857,
-0.034670691937208176,
0.025547657161951065,
-0.013654756359755993,
0.04029696062207222,
0.014270173385739326,
0.005576332565397024,
0.019675077870488167,
0.004966639913618565,
0.04353928938508034,
-0.019704293459653854,
-0.103556327521801,
0.024912791326642036,
-0.026407741010189056,
0.018658144399523735,
0.04553953558206558,
-0.01600855402648449,
-0.043365493416786194,
0.0036325848195701838,
-0.002676532603800297,
0.03267102316021919,
0.0038180146366357803,
-0.06073695048689842,
0.014800057746469975,
0.034913115203380585,
0.0012770587345585227,
0.02215328812599182,
0.015941057354211807,
-0.0010356722632423043,
-0.004408104345202446,
-0.016950637102127075,
0.03774309530854225,
0.014329858124256134,
0.013395230285823345,
-0.021328197792172432,
0.02634011209011078,
-0.018217163160443306,
0.04505952075123787,
-0.016045305877923965,
-0.011690356768667698,
-0.022688383236527443,
-0.0030566207133233547,
-0.013881396502256393,
0.015393893234431744,
-0.004449528641998768,
-0.015038462355732918,
-0.011357326991856098,
0.04278116673231125,
0.014641053043305874,
-0.038827940821647644,
0.008452361449599266,
-0.006566973403096199,
-0.01677078567445278,
0.018604548647999763,
-0.003738155821338296,
-0.020900655537843704,
-0.019390305504202843,
-0.005482372362166643,
0.002705763792619109,
-0.07516343146562576,
0.04094682261347771,
-0.017455020919442177,
0.010043937712907791,
0.00008267330122180283,
-0.0467398576438427,
-0.04360595718026161,
0.005239664111286402,
-0.028747044503688812,
0.015921328216791153,
-0.0680837631225586,
0.00034473277628421783,
0.04225273057818413,
0.022863389924168587,
-0.0292334146797657,
-0.0846899002790451,
-0.005101651418954134,
-0.022324377670884132,
0.014046384952962399,
0.015427474863827229,
-0.023468421772122383,
0.0027931872755289078,
-0.05776706710457802,
0.02574409916996956,
0.004378300625830889,
-0.02435522899031639,
0.02581304870545864,
0.04203145205974579,
-0.0077346377074718475,
0.055512264370918274,
-0.007852482609450817,
-0.021321190521121025,
0.016639066860079765,
-0.0228956937789917,
-0.003814679803326726,
0.015996519476175308,
0.02991354465484619,
-0.012226816266775131,
-0.026469530537724495,
0.01249485369771719,
0.0109188137575984,
0.019449857994914055,
-0.0033135388512164354,
0.046614810824394226,
0.04385770857334137,
0.019201617687940598,
0.012275361455976963,
0.006483470089733601,
0.0443548709154129,
0.04359481483697891,
0.0030614228453487158,
-0.00583156943321228,
-0.00715102581307292,
-0.10409915447235107,
-0.02532610483467579,
0.022760922089219093,
-0.00611488614231348,
0.020123908296227455,
-0.036792196333408356,
0.05624506622552872,
-0.03346196189522743,
-0.02165871299803257,
0.03175574168562889,
-0.004928261507302523,
-0.03008348122239113,
-0.010283870622515678,
-0.011525857262313366,
-0.005481620319187641,
-0.011857135221362114,
-0.04108310118317604,
0.017504366114735603,
-0.009399646893143654,
0.010467395186424255,
0.0796445831656456,
0.0035596401430666447,
0.05423368513584137,
-0.03194732964038849,
-0.027669042348861694,
-0.02573324739933014,
0.0002983366430271417,
-0.018214251846075058,
0.018701257184147835,
0.007489577867090702,
-0.007187478709965944,
0.014710457995533943,
-0.010730819776654243,
0.032738097012043,
0.04184656962752342,
-0.03927506133913994,
-0.02977672405540943,
0.06280743330717087,
0.040510836988687515,
0.05341886729001999,
0.018840385600924492,
-0.011977099813520908,
0.02462722361087799,
-0.019561149179935455,
0.02825682796537876,
0.0031841204036027193,
-0.02118520438671112,
0.06758555769920349,
0.020995086058974266,
0.0008132424554787576,
-0.028568539768457413,
-0.03242090344429016,
0.0004105817060917616,
0.014208349399268627,
-0.0046186381950974464,
-0.014479085803031921,
-0.015272549353539944,
0.014384646899998188,
0.035627033561468124,
-0.015158760361373425,
0.02050160989165306,
0.008194989524781704,
-0.0762995034456253,
-0.013610663823783398,
-0.01725410670042038,
-0.03218362107872963,
0.07579314708709717,
-0.010422027669847012,
-0.0410640574991703,
-0.0149826155975461,
-0.04393838346004486,
0.01833442971110344,
0.037826813757419586,
0.0064419833943247795,
-0.0219008419662714,
0.040125809609889984,
-0.031282708048820496,
0.017922300845384598,
-0.038949403911828995,
0.011900200508534908,
0.11978518962860107,
-0.0034103551879525185,
0.030954156070947647,
-0.06273872405290604,
0.003310536267235875,
-0.05365236476063728,
-0.017941735684871674,
0.006609056610614061,
0.018357986584305763,
-0.00869294349104166,
0.00902709923684597,
0.006490769330412149,
0.04457501322031021,
-0.01046266220510006,
-0.004120038356631994,
0.03339291736483574,
-0.019562996923923492,
-0.023521147668361664,
-0.029424065724015236,
0.004872745834290981,
0.004496716894209385,
0.02427511475980282,
-0.046114854514598846,
0.0006063536275178194,
-0.02900048904120922,
-0.031791746616363525,
-0.01590261049568653,
-0.04333754628896713,
0.04049137979745865,
-0.003955453634262085,
-0.021985411643981934,
0.023979321122169495,
0.00439691636711359,
-0.022863900288939476,
-0.044169772416353226,
0.02104332111775875,
0.02703344263136387,
0.022515973076224327,
0.02810390293598175,
0.006213681306689978,
0.01714402250945568,
0.008069378323853016,
0.02028975449502468,
0.018908964470028877,
-0.0325675904750824,
0.0360882394015789,
-0.025940528139472008,
0.04039789363741875,
-0.014481214806437492,
-0.001400328823365271,
0.0046517737209796906,
0.019968289881944656,
0.015527053736150265,
-0.041663940995931625,
-0.01594485528767109,
0.010704483836889267,
0.03582541272044182,
0.002463902346789837,
-0.03166276216506958,
-0.03519321233034134,
0.03178362548351288,
0.004981242585927248,
0.016914675012230873,
0.02126222662627697,
-0.03851352259516716,
0.01990329846739769,
0.031758688390254974,
0.05320052430033684,
0.010898085311055183,
-0.009051724337041378,
-0.027267728000879288,
-0.018815048038959503,
-0.012636658735573292,
0.006004112306982279,
0.014248293824493885,
0.03182762861251831,
0.0013983063399791718,
-0.019322749227285385,
-0.012882818467915058,
0.006718385498970747,
-0.02405015006661415,
0.058169107884168625,
0.026956971734762192,
-0.018973110243678093,
-0.006675417535007,
-0.007747222203761339,
-0.01800878532230854,
0.0429658405482769,
-0.013934407383203506,
-0.007726503536105156,
0.014726358465850353,
0.03135215863585472,
0.030775435268878937,
0.003276881529018283,
-0.05359523743391037,
0.012236586771905422,
-0.006397940684109926,
0.01734280027449131,
0.019477469846606255,
-0.00048362871166318655,
0.016587546095252037,
0.020692003890872,
-0.030452081933617592,
0.04600311443209648,
0.008761241100728512,
-0.026678213849663734,
0.03311273828148842,
-0.006526411976665258,
0.020585650578141212,
-0.008503331802785397,
-0.01758021116256714,
-0.03869162127375603,
0.006402547471225262,
-0.012866750359535217,
0.001488859299570322,
0.004527067765593529,
0.046634722501039505,
-0.04960845783352852,
0.002860227832570672,
-0.018102824687957764,
0.054066866636276245,
-0.021633842960000038,
-0.00430268282070756,
-0.026710527017712593,
-0.01939755119383335,
0.0037810609210282564,
0.02793217822909355,
-0.03829652816057205,
0.042950693517923355,
-0.016571540385484695,
0.006638039369136095,
0.01618224009871483,
0.009098163805902004,
-0.02447982132434845,
0.03128065541386604,
0.01676967740058899,
0.030483737587928772,
-0.011200307868421078,
-0.005304216407239437,
-0.047665294259786606,
0.04472531005740166,
-0.0015330760506913066,
-0.03431577607989311,
0.02560938335955143,
-0.007968602702021599,
0.018181446939706802,
0.0374186635017395,
-0.02751612290740013,
-0.029482180252671242,
0.03225119039416313,
-0.020726988092064857,
0.022828884422779083,
-0.020996473729610443,
-0.030961474403738976,
0.01675039902329445,
-0.011266202665865421,
-0.013266000896692276,
-0.01978440210223198,
0.009239173494279385,
-0.01181146688759327,
-0.010786600410938263,
0.01291231531649828,
-0.020703548565506935,
0.014949887990951538,
0.035218290984630585,
-0.03245465084910393,
0.061733756214380264,
-0.01943081244826317,
-0.0180452112108469,
0.03188314661383629,
-0.024600300937891006,
0.026195509359240532,
-0.015305586159229279,
0.003315199865028262,
-0.09367258101701736,
-0.02108055353164673,
0.007191515062004328,
-0.0030210951808840036,
0.035800181329250336,
-0.04136204719543457,
-0.04046683385968208,
0.04282050579786301,
-0.11125204712152481,
-0.012956995517015457,
-0.028500422835350037,
-0.0525682158768177,
-0.02182029001414776,
-0.02825026772916317,
0.011149405501782894,
0.07621551305055618,
0.04317893832921982,
0.06589329987764359,
-0.009032330475747585,
-0.014143558219075203,
-0.015220386907458305,
-0.03153930976986885,
-0.02968636155128479,
0.028956284746527672,
-0.0029097602237015963,
0.060715142637491226,
0.05895725265145302,
-0.03207682445645332,
-0.009000727906823158,
0.01700403541326523,
-0.01302727684378624,
-0.0057737804017961025,
0.00555918226018548,
-0.0006354752113111317,
0.012802123092114925,
0.0717056468129158,
-0.019214017316699028,
-0.01176631823182106,
0.010527039878070354,
0.01873801089823246,
0.026220006868243217,
0.02617173083126545,
-0.017006704583764076,
0.012740639969706535,
0.0447193905711174,
-0.027625801041722298,
-0.017808308824896812,
-0.006874022539705038,
-0.04685698449611664,
0.016229568049311638,
0.036578014492988586,
0.03913760185241699,
0.001937519758939743,
0.014415214769542217,
0.013102596625685692,
-0.020758287981152534,
-0.03617946803569794,
0.008732053451240063,
-0.036094050854444504,
0.02022811584174633,
0.01869841292500496,
-0.002091367496177554,
0.002355973469093442,
0.00539758987724781,
0.007094766944646835,
-0.024849848821759224,
-0.057174623012542725,
-0.007104441523551941,
0.03048940747976303,
-0.013484087772667408,
0.02822340838611126,
-0.0454145222902298,
-0.018692923709750175,
0.03240089863538742,
0.030994346365332603,
0.017397861927747726,
-0.0064552826806902885,
-0.034365758299827576,
-0.042363379150629044,
-0.033408574759960175,
0.02533765882253647,
-0.00580980721861124,
-0.04813753813505173,
-0.0443795807659626,
-0.054763611406087875,
-0.02479647658765316,
0.029328079894185066,
0.06485848128795624,
-0.007110669277608395,
-0.023043856024742126,
0.03714499995112419,
-0.02305411919951439,
0.02528720535337925,
-0.05775150656700134,
0.003017531940713525,
-0.008899944834411144,
0.002806070726364851,
0.03365973383188248,
0.004583158064633608,
-0.025506457313895226,
0.0004017646424472332,
-0.0008768812986090779,
-0.012127346359193325,
-0.0012317238142713904,
-0.022319989278912544,
-0.04419062286615372,
0.048483360558748245,
0.007276605814695358,
-0.0035588606260716915,
0.06193538010120392,
-0.0033767696004360914,
0.017387712374329567,
-0.007261461112648249,
-0.006393718998879194,
-0.04567404463887215,
0.03612971678376198,
-0.013195106759667397,
0.0008398018544539809,
-0.07255732268095016,
0.00621919147670269,
0.05171569436788559,
-0.01866755075752735,
-0.0026004298124462366,
0.029015449807047844,
-0.03545036166906357,
-0.013884223066270351,
0.009207225404679775,
0.0053441585041582584,
0.03599056228995323,
-0.029587071388959885,
0.030899973586201668,
0.002626718720421195,
0.01471132505685091,
0.029055500403046608,
0.05229433253407478,
-0.0074691250920295715,
-0.0006550628459081054,
-0.02378777600824833,
0.07860735058784485,
-0.02104848437011242,
0.024981046095490456,
0.0434403195977211,
0.05204005911946297,
-0.036841437220573425,
-0.01813490502536297,
-0.014243779703974724,
-0.01760842464864254,
0.016400020569562912,
0.021561352536082268,
-0.03957522287964821,
0.08317476511001587,
-0.030873117968440056,
-0.0015586280496791005,
-0.015732260420918465,
0.019409222528338432,
0.017845530062913895,
-0.009899262338876724,
0.009494539350271225,
0.031209146603941917,
-0.030328016728162766,
-0.03482017293572426,
-0.021850598976016045,
-0.007871122099459171,
0.04572125896811485,
0.008833571337163448,
-0.0014904406853020191,
0.003809138899669051,
-0.033265963196754456,
-0.0537346675992012,
-0.02094910852611065,
-0.0455358512699604,
-0.016933884471654892,
0.05204097181558609,
0.03347776457667351,
-0.05942877382040024,
-0.02290346659719944,
0.020823435857892036,
-0.01804654859006405,
0.052519652992486954,
-0.0593169741332531,
-0.020856693387031555,
-0.0305682010948658,
0.04807521775364876,
0.015661276876926422,
0.022783517837524414
] |
<p>Sometimes I may come up with an equation in mind, so I want to search for the related material. It may be the case that I learn it before but forget the name, or, there is no name for the equation yet. In this case, I may be able to recall a reference book. Searching in Internet can be a fast way though.</p>
<p>However, there are cases that I get some idea and equations (maybe a modified one) myself. So I want to know whether there are any other people working on it before. Because of the vagueness, it is difficult to search it by keywords because I do not know the 'name' of this idea: it is either too board or no results.</p>
<p>I can try to search google scholar, arxiv and maybe the prola, but there is no support of equation pattern matching. For example, entering ∇⋅V in google give you no useful results (it is better if you input the 'divergence of potential').</p>
<p>Is there any good way to search papers in this case? It is even better that I can use the combination of equations and keywords.</p>
<p><strong>Edit</strong>: Another reason is that Mathematician should have done some deep analysis on the related mathematical topics. Yet it is difficult to know their results because there is a gap between the terms used in physics and mathematics. It would be really useful if we can find and learn their results.</p>
| 8,281 |
[
-0.02185644395649433,
0.034520331770181656,
-0.009417260996997356,
-0.03334622085094452,
0.003859694814309478,
0.007926342077553272,
-0.022247521206736565,
-0.024828337132930756,
0.030427277088165283,
-0.027509300038218498,
0.03361889347434044,
-0.00651349825784564,
0.06372807174921036,
-0.011047182604670525,
0.014365332201123238,
0.039481036365032196,
0.006553744897246361,
-0.006804654840379953,
-0.011937929317355156,
-0.025913307443261147,
0.010071533732116222,
-0.006345525849610567,
-0.017641635611653328,
0.05074149742722511,
-0.007897550240159035,
0.03289823979139328,
0.012762474827468395,
-0.014089620672166348,
-0.03581910580396652,
0.06210410222411156,
0.004760535433888435,
-0.02604605443775654,
0.0015123055782169104,
0.041406210511922836,
0.004571983125060797,
0.03053225949406624,
-0.027293840423226357,
-0.051748018711805344,
0.009228292852640152,
0.009721610695123672,
-0.03420339897274971,
-0.016043884679675102,
0.0189887136220932,
0.04678867384791374,
-0.03724175691604614,
0.03024751879274845,
0.02449115365743637,
-0.033933404833078384,
0.017869623377919197,
-0.06326518207788467,
0.03120284155011177,
0.014041967689990997,
0.045130643993616104,
0.04793506860733032,
-0.03059324435889721,
-0.022476885467767715,
0.05307670310139656,
0.06762489676475525,
0.0017640929436311126,
-0.06935116648674011,
-0.000989135936833918,
0.01545195747166872,
-0.001846902770921588,
-0.03230854123830795,
-0.05104701593518257,
0.0816081240773201,
0.002383973216637969,
-0.02922864444553852,
0.04661859571933746,
-0.037749119102954865,
-0.015574212186038494,
0.000686130253598094,
0.05850304663181305,
-0.014181298203766346,
0.033455003052949905,
-0.04155127704143524,
-0.04142671450972557,
0.020681330934166908,
0.0291789248585701,
0.053000129759311676,
-0.014393187128007412,
0.0032933142501860857,
0.00588041078299284,
0.026166053488850594,
-0.01897934079170227,
-0.013713492080569267,
0.07584577798843384,
-0.04858170822262764,
-0.018935611471533775,
-0.0020208503119647503,
-0.00443615484982729,
0.020397111773490906,
0.03878847509622574,
-0.010856250301003456,
0.003775013377889991,
0.010008865036070347,
0.027609841898083687,
0.01615462452173233,
0.022824440151453018,
-0.02162976935505867,
-0.013128610327839851,
-0.05354195088148117,
-0.038051992654800415,
0.07811404764652252,
0.01321737002581358,
-0.006178510375320911,
-0.03474809601902962,
0.0003420640423428267,
-0.045237328857183456,
-0.002205983502790332,
0.026012366637587547,
0.022826669737696648,
-0.013674136251211166,
0.022864026948809624,
-0.04114728793501854,
-0.032082267105579376,
0.01468808576464653,
-0.0368264801800251,
0.07384278625249863,
0.08397284895181656,
0.017946947365999222,
-0.03647688031196594,
0.039125628769397736,
-0.03935396671295166,
-0.06616995483636856,
0.008716624230146408,
0.050249017775058746,
0.00005476638762047514,
-0.043687477707862854,
0.03745274990797043,
-0.008165604434907436,
-0.008084549568593502,
0.003682185895740986,
-0.004555928520858288,
0.018725281581282616,
0.02554655447602272,
-0.08646775782108307,
-0.06975286453962326,
0.04105681553483009,
0.01699988543987274,
-0.038646150380373,
-0.04283802583813667,
0.029507284983992577,
0.01827319711446762,
0.06807998567819595,
-0.007883627898991108,
0.018079262226819992,
0.005203319247812033,
-0.0019390644738450646,
-0.01017837319523096,
-0.006537868175655603,
-0.03270217031240463,
-0.010079148225486279,
-0.007379334885627031,
0.005292007699608803,
-0.027317171916365623,
0.010215804912149906,
0.017765263095498085,
-0.009713278152048588,
0.01862999051809311,
0.06956830620765686,
-0.01774800382554531,
0.009724966250360012,
0.02412361279129982,
0.028764817863702774,
-0.03357154503464699,
0.07012585550546646,
-0.0010558277135714889,
0.03497835993766785,
-0.0021659573540091515,
0.011218102648854256,
0.0351482518017292,
-0.0015339930541813374,
-0.03828651085495949,
0.05223222076892853,
-0.04603178799152374,
-0.009157765656709671,
0.019663985818624496,
-0.012550931423902512,
0.007629729807376862,
-0.011921334080398083,
-0.05716434866189957,
-0.015558026731014252,
0.002742613200098276,
-0.015915783122181892,
0.037151601165533066,
0.02672218717634678,
-0.020254312083125114,
0.026726750656962395,
-0.03637151047587395,
0.005600186064839363,
-0.05710016191005707,
0.012174694798886776,
-0.023225732147693634,
-0.005402463488280773,
0.041070327162742615,
0.0003895394620485604,
0.0009228092385455966,
-0.005940835922956467,
-0.01668093167245388,
0.0015752878971397877,
0.013161923736333847,
-0.011506337672472,
0.0038392592687159777,
-0.019021660089492798,
0.044754210859537125,
0.016787806525826454,
-0.009162325412034988,
0.04165642708539963,
-0.019210830330848694,
-0.030539536848664284,
-0.012146088294684887,
-0.022219929844141006,
0.01823393814265728,
-0.0049201613292098045,
0.0013526943512260914,
0.010372002609074116,
-0.008048104122281075,
-0.026362000033259392,
0.005363250616937876,
-0.0578688345849514,
0.046978659927845,
0.0740901306271553,
0.05430775508284569,
-0.023851100355386734,
0.05388319492340088,
0.01992151513695717,
0.04377942532300949,
0.027819456532597542,
-0.0156459528952837,
-0.06958722323179245,
-0.028453228995203972,
0.024831894785165787,
0.051140014082193375,
-0.05878118798136711,
0.032748907804489136,
0.04265885055065155,
-0.00364755024202168,
0.015041577629745007,
0.019609345123171806,
-0.015177121385931969,
-0.05229470878839493,
0.045582566410303116,
0.039481088519096375,
-0.002536688232794404,
0.010068478062748909,
0.007188680116087198,
0.009063874371349812,
0.0257661584764719,
-0.02292781136929989,
-0.010084287263453007,
0.0297302957624197,
0.03661907836794853,
-0.0085474057123065,
0.0036344544496387243,
-0.029340727254748344,
0.05038159713149071,
-0.015507779084146023,
0.037512145936489105,
0.01793288253247738,
-0.0032193739898502827,
0.02322964370250702,
-0.017062481492757797,
-0.018240420147776604,
0.03224532678723335,
-0.005493050906807184,
-0.012771855108439922,
-0.005250096786767244,
0.03356907516717911,
-0.04932484030723572,
0.005628852639347315,
0.010277027264237404,
-0.013004925101995468,
-0.040658432990312576,
-0.025810912251472473,
-0.028403660282492638,
0.009703525342047215,
0.027413196861743927,
-0.01307565625756979,
-0.0031430935487151146,
0.01925082504749298,
-0.0027915353421121836,
0.015743833035230637,
0.029149027541279793,
-0.006825004238635302,
0.03484295308589935,
-0.051117006689310074,
-0.042704686522483826,
0.03656048700213432,
-0.01877974160015583,
0.03340952843427658,
0.03805534541606903,
-0.0034792867954820395,
-0.04903124272823334,
-0.02448977343738079,
-0.018567262217402458,
0.0268088411539793,
-0.008320186287164688,
0.004326082766056061,
0.049041327089071274,
-0.02246508188545704,
-0.0717884972691536,
0.014778230339288712,
-0.02969658561050892,
-0.06628166884183884,
-0.022116877138614655,
-0.003771172370761633,
0.023566797375679016,
-0.011538009159266949,
0.02456837147474289,
0.0259537473320961,
-0.018383635208010674,
-0.033246368169784546,
-0.08496309816837311,
-0.0456630177795887,
0.019082846119999886,
0.00013591136666946113,
0.025068167597055435,
-0.010480962693691254,
-0.021628204733133316,
0.10549385845661163,
0.015281633473932743,
-0.02851901389658451,
-0.06489036232233047,
0.01509937085211277,
-0.013494369573891163,
-0.01663793809711933,
0.01470479927957058,
-0.0034499308094382286,
-0.006213488057255745,
-0.006247734185308218,
0.012101933360099792,
0.03708741441369057,
0.04286789149045944,
0.023526150733232498,
-0.008333664387464523,
0.017479145899415016,
-0.005249048583209515,
-0.02302548475563526,
0.04380872845649719,
0.017266638576984406,
-0.043336138129234314,
-0.0007677839021198452,
0.014484208077192307,
0.026465587317943573,
0.01893925666809082,
-0.07759502530097961,
0.03004259616136551,
0.008425898849964142,
-0.027220390737056732,
-0.05360843241214752,
0.0246720090508461,
0.023460963740944862,
-0.020397629588842392,
0.01843489147722721,
0.030356619507074356,
0.017200198024511337,
-0.004511176608502865,
0.006141976919025183,
0.03805394098162651,
0.02346288599073887,
-0.06460690498352051,
-0.009038632735610008,
-0.029141351580619812,
-0.004486780147999525,
0.009695678949356079,
-0.035334762185811996,
0.0026739612221717834,
0.02054961584508419,
0.051278576254844666,
-0.010735902935266495,
0.012329624965786934,
-0.03403936326503754,
-0.0014976058155298233,
-0.08562451601028442,
-0.016148194670677185,
-0.03819837421178818,
0.09273959696292877,
-0.005872515961527824,
0.05387244001030922,
0.0005659024463966489,
0.021412426605820656,
0.018284842371940613,
0.007626072037965059,
-0.09320268034934998,
0.02140013314783573,
-0.03404539078474045,
-0.02876274660229683,
0.005814776755869389,
0.010088158771395683,
-0.008381092920899391,
-0.038036733865737915,
-0.03628404811024666,
0.005417147185653448,
0.025069771334528923,
-0.057483915239572525,
-0.0044418214820325375,
-0.034300412982702255,
-0.0461958684027195,
-0.002290490549057722,
-0.0019667043816298246,
0.05409369245171547,
-0.006666671950370073,
0.0544959157705307,
0.048074353486299515,
-0.019628556445240974,
-0.02256038226187229,
-0.030958328396081924,
-0.007216236088424921,
0.02808322384953499,
0.023041630163788795,
-0.04456949606537819,
0.022904817014932632,
-0.001165687688626349,
0.0015678730560466647,
0.003433879232034087,
0.02889030985534191,
0.005756580736488104,
-0.008144681341946125,
-0.0015394820366054773,
-0.03271974250674248,
0.0016752397641539574,
0.0007576443022117019,
0.04101121425628662,
-0.009907140396535397,
-0.01167918648570776,
-0.006718223914504051,
0.02935950644314289,
-0.01857374794781208,
0.0300818532705307,
0.07202278822660446,
0.008423908613622189,
-0.023744827136397362,
-0.01160004734992981,
0.0011854436015710235,
-0.03702070564031601,
-0.019247112795710564,
-0.009139941073954105,
0.007418593857437372,
-0.008134778589010239,
-0.044566888362169266,
0.0194975845515728,
0.04503722861409187,
-0.03150945156812668,
0.02120232582092285,
-0.016061924397945404,
-0.04105513542890549,
-0.015824344009160995,
-0.01390589028596878,
0.024061106145381927,
0.03769658878445625,
0.04703858122229576,
-0.0486825630068779,
0.028107771649956703,
-0.06054408475756645,
0.014069237746298313,
0.06102471798658371,
0.0552297867834568,
-0.015952274203300476,
-0.01608479954302311,
-0.07632600516080856,
-0.020487308502197266,
0.01428459957242012,
-0.02907395176589489,
0.009190486744046211,
-0.044570811092853546,
-0.015370609238743782,
-0.000978799071162939,
-0.05734485387802124,
-0.026443209499120712,
0.026977013796567917,
0.003964778035879135,
0.022418534383177757,
-0.03275592252612114,
0.0009891701629385352,
0.005857671145349741,
0.023351341485977173,
-0.0028460705652832985,
0.020315982401371002,
0.014636806212365627,
0.0008387070847675204,
-0.006325270980596542,
-0.005560913123190403,
-0.03669988363981247,
-0.09021207690238953,
-0.001957469619810581,
-0.007083582226186991,
-0.009843368083238602,
0.028844114392995834,
-0.03555796667933464,
-0.048218850046396255,
0.02103041671216488,
-0.010685945861041546,
-0.013308181427419186,
-0.016818510368466377,
-0.03494621813297272,
0.014094623737037182,
0.07880771160125732,
0.05291832983493805,
0.056520041078329086,
0.05090857669711113,
0.007168380077928305,
-0.015787644311785698,
0.006356863304972649,
0.011759240180253983,
-0.019391126930713654,
-0.00008909089956432581,
-0.04945368692278862,
-0.012162127532064915,
-0.07306862622499466,
0.03665723651647568,
-0.028617817908525467,
0.02910528890788555,
-0.023828614503145218,
-0.011891231872141361,
-0.024961356073617935,
0.013363356702029705,
0.0069362991489470005,
-0.03008309006690979,
0.026699699461460114,
0.034577034413814545,
0.02980787120759487,
0.01497446559369564,
0.026298198848962784,
0.014611420221626759,
-0.022652259096503258,
0.017246441915631294,
-0.0032305573113262653,
-0.00402219919487834,
-0.001294220914132893,
-0.006507918704301119,
0.03599526733160019,
-0.03452923893928528,
0.052200693637132645,
0.0010297981789335608,
0.009857366792857647,
0.04887038469314575,
-0.056417953222990036,
-0.059006936848163605,
0.012285122647881508,
0.023041438311338425,
-0.01509957853704691,
-0.030611269176006317,
0.00829655583947897,
0.0033431958872824907,
-0.008036875165998936,
-0.02924937754869461,
-0.052644383162260056,
0.013162906281650066,
-0.017087899148464203,
-0.030445104464888573,
-0.014501133933663368,
-0.00014796142932027578,
0.0014007680583745241,
-0.0072734663262963295,
0.00219824630767107,
0.035198163241147995,
-0.01514985878020525,
-0.0118021285161376,
0.004587193951010704,
0.045683469623327255,
0.015463911928236485,
-0.014890570193529129,
0.014854214154183865,
0.01836937479674816,
0.012712218798696995,
0.041127268224954605,
0.027071816846728325,
0.03955242782831192,
-0.005439729895442724,
-0.04139291122555733,
-0.028617728501558304,
0.012538797222077847,
0.001206607441417873,
-0.012853176333010197,
0.020449457690119743,
0.03667706996202469,
-0.0027600745670497417,
-0.033869124948978424,
-0.0025479199830442667,
0.018049132078886032,
-0.02001054957509041,
0.018992077559232712,
0.010664272122085094,
-0.020993264392018318,
0.026968272402882576,
-0.013603707775473595,
0.02750282920897007,
-0.003639772068709135,
-0.05277235433459282,
-0.03734029084444046,
0.06472581624984741,
-0.031002210453152657,
-0.032641954720020294,
0.06550152599811554,
0.03880437836050987,
0.03619980812072754,
-0.01812058873474598,
0.02492816373705864,
-0.026826320216059685,
0.0023105586878955364,
-0.0291474349796772,
-0.06331677734851837,
-0.01055885385721922,
-0.003557725576683879,
0.08215588331222534,
-0.0010011718841269612,
0.05863163620233536,
0.031130028888583183,
-0.031380802392959595,
0.014052143320441246,
0.019645916298031807,
0.008114944212138653,
0.014311672188341618,
-0.005334606859833002,
0.04370452091097832,
-0.038005802780389786,
0.03563089296221733,
0.0460343211889267,
0.03047177940607071,
-0.03359193727374077,
-0.02440580166876316,
0.005784612149000168,
0.032110076397657394,
0.0382346510887146,
-0.04423731192946434,
-0.03350643441081047,
0.02886114828288555,
-0.06352337449789047,
0.04122055694460869,
0.0014659672742709517,
-0.04712516441941261,
0.04314384236931801,
0.00255193910561502,
-0.01574721373617649,
-0.03689495846629143,
-0.004699761979281902,
-0.014328712597489357,
0.011201365850865841,
0.051325034350156784,
-0.005147644318640232,
0.02623474784195423,
0.012399238534271717,
0.03984179347753525,
0.01485350914299488,
-0.009890884160995483,
-0.0040833610109984875,
-0.05154740437865257,
-0.021524552255868912,
-0.051669660955667496,
-0.04971591755747795,
0.044355664402246475,
0.012248042039573193,
-0.01907963864505291,
-0.01185121014714241,
-0.006099984049797058,
0.04627283662557602,
0.025176910683512688,
0.025170981884002686,
-0.05425906926393509,
0.04071921482682228,
-0.035788219422101974,
0.013906181789934635,
-0.018466802313923836,
0.000583477143663913,
0.12742000818252563,
0.03299425169825554,
0.0586618073284626,
-0.0584576278924942,
0.00733362790197134,
0.004264044109731913,
-0.00694479513913393,
-0.025446081534028053,
0.052286434918642044,
-0.022334836423397064,
0.01431252807378769,
0.017104357481002808,
0.04283754527568817,
0.02300330623984337,
0.013451711274683475,
0.03947582468390465,
-0.0771690085530281,
-0.028616202995181084,
0.04136158525943756,
-0.0023069262970238924,
-0.007491524331271648,
0.037358928471803665,
0.011780970729887486,
0.026425743475556374,
-0.026662398129701614,
-0.011297939345240593,
-0.01983886957168579,
-0.04057478904724121,
0.060536354780197144,
0.010870066471397877,
-0.03603588044643402,
0.038200899958610535,
-0.007029675878584385,
0.005245465785264969,
-0.010956956073641777,
0.013581565581262112,
0.04584509879350662,
0.001339680515229702,
-0.00551481731235981,
0.03725869208574295,
0.0279950313270092,
0.013050246983766556,
-0.010087377391755581,
-0.02897886373102665,
-0.01116414275020361,
0.027793684974312782,
-0.04036347195506096,
0.07104746997356415,
-0.026787010952830315,
0.01273910328745842,
-0.003481260035187006,
-0.0020499820820987225,
0.02692859061062336,
-0.01899532973766327,
-0.020076286047697067,
-0.005607184022665024,
-0.001923754927702248,
-0.03533611074090004,
0.014883494935929775,
-0.010814812034368515,
0.03611195832490921,
0.008086523972451687,
0.008463066071271896,
-0.021253660321235657,
-0.04305538907647133,
-0.0010110241128131747,
0.004911753349006176,
0.018802959471940994,
-0.02799452841281891,
-0.018487224355340004,
-0.025952402502298355,
-0.020528217777609825,
-0.028095319867134094,
-0.037651609629392624,
0.010409660637378693,
0.006406949833035469,
0.027504004538059235,
-0.019279297441244125,
-0.027276569977402687,
-0.025873329490423203,
-0.06163809075951576,
0.03050771728157997,
-0.011524898000061512,
0.005243651103228331,
-0.03190792724490166,
0.010332445614039898,
0.004569167736917734,
0.0365215465426445,
0.02348129078745842,
-0.02055991441011429,
0.0009998889872804284,
0.037371404469013214,
0.04075097665190697,
0.012286340817809105,
-0.04106413200497627,
-0.003912205807864666,
-0.05062832310795784,
0.0012352365301921964,
0.02158874273300171,
-0.011006646789610386,
0.026549778878688812,
0.012236218899488449,
0.04254935309290886,
0.04359385371208191,
-0.01078636571764946,
0.03579863905906677,
0.005581149831414223,
-0.030006516724824905,
-0.0035559097304940224,
0.017650889232754707,
0.011368303559720516,
0.006189000327140093,
0.02066756971180439,
-0.0128758130595088,
0.004539949353784323,
0.009040510281920433,
0.04809803515672684,
-0.0505637563765049,
0.02685578167438507,
-0.014387652277946472,
0.024689679965376854,
-0.029890133067965508,
0.023137010633945465,
-0.06694779545068741,
-0.013635678216814995,
-0.0061920881271362305,
-0.03226257860660553,
-0.013775349594652653,
0.028589142486453056,
-0.012509170919656754,
-0.000970821944065392,
0.02516845241189003,
0.03027912974357605,
-0.016916504129767418,
0.020146530121564865,
0.032416630536317825,
-0.03658481314778328,
0.03197653591632843,
-0.007680940441787243,
-0.03676866739988327,
0.001893949112854898,
-0.040390972048044205,
-0.04946267604827881,
0.025915296748280525,
0.0017856897320598364,
0.01971331052482128,
0.02921793796122074,
-0.010051539167761803,
-0.032080043107271194,
0.05005292594432831,
0.0038248877972364426,
0.013485290110111237,
0.021686922758817673,
-0.023092513903975487,
0.004942263942211866,
-0.01950726844370365,
0.03201458975672722,
-0.026379477232694626,
-0.009902752004563808,
-0.01485837809741497,
0.03223847225308418,
0.015912210568785667,
-0.037064649164676666,
0.041050005704164505,
0.019970262423157692,
0.020809154957532883,
0.021764833480119705,
-0.03713078796863556,
0.03350694105029106,
0.033484090119600296,
-0.019946785643696785,
-0.0057595777325332165,
0.02540242299437523,
0.03390024974942207,
-0.1016344428062439,
0.004387234803289175,
0.026639798656105995,
0.0369160957634449,
0.02490023709833622,
-0.06609033793210983,
0.012726189568638802,
0.025438379496335983,
-0.056727927178144455,
0.04118599370121956,
0.0013832282274961472,
-0.0003393624210730195,
-0.0009546610526740551,
0.021041203290224075,
-0.001771960873156786,
0.048890385776758194,
0.039697859436273575,
0.04651283472776413,
0.022151049226522446,
-0.003235683310776949,
-0.0011453692568466067,
-0.010933673940598965,
-0.011560452170670033,
0.02012225240468979,
-0.009795665740966797,
-0.018239673227071762,
0.03714771568775177,
0.007527428679168224,
-0.042012088000774384,
-0.015904128551483154,
0.006886015180498362,
-0.022144345566630363,
-0.007638227194547653,
0.039003439247608185,
-0.0062059140764176846,
0.034796204417943954,
0.02871488220989704,
-0.024122709408402443,
-0.007159051951020956,
0.0009656649781391025,
-0.021201621741056442,
0.07310082018375397,
0.014623962342739105,
0.008256801404058933,
0.025076162070035934,
-0.012179369106888771,
-0.05567137524485588,
0.05227471888065338,
-0.024850638583302498,
-0.02049659751355648,
0.00025694063515402377,
-0.015938302502036095,
-0.012995473109185696,
0.016976671293377876,
-0.01200474239885807,
-0.03236943855881691,
0.009589189663529396,
-0.00882112979888916,
-0.009556586854159832,
0.009908313862979412,
0.05314132943749428,
-0.04709435626864433,
-0.038658589124679565,
0.03531932458281517,
-0.03529924154281616,
-0.00787398125976324,
-0.03995528072118759,
-0.01359782088547945,
-0.0026320612523704767,
-0.03648895025253296,
-0.0042657735757529736,
-0.041775695979595184,
-0.018185116350650787,
0.049420565366744995,
0.005009092856198549,
-0.004321408458054066,
-0.0036804492119699717,
-0.030025800690054893,
0.019906893372535706,
-0.06004234775900841,
0.0284884013235569,
-0.0070415339432656765,
-0.008757254108786583,
-0.008257902227342129,
-0.003217922290787101,
-0.005001713056117296,
-0.001107542309910059,
0.012317121028900146,
-0.053495172411203384,
-0.015657756477594376,
0.02372530847787857,
-0.03719814121723175,
0.03376098349690437,
-0.010297304950654507,
0.0011729842517524958,
-0.008798555471003056,
0.025923756882548332,
0.004239227157086134,
0.015530142933130264,
0.024776363745331764,
0.047838013619184494,
0.03565152361989021,
0.013879876583814621,
0.02714073844254017,
0.011090809479355812,
-0.048371076583862305,
0.034117765724658966,
0.04821692034602165,
-0.016937654465436935,
0.06348840147256851,
-0.006511730141937733,
0.008851178921759129,
0.007179945707321167,
-0.010888094082474709,
-0.03670472279191017,
0.028404586017131805,
-0.05077943578362465,
-0.04119427129626274,
0.02579597756266594,
-0.04369805380702019,
0.02002270333468914,
-0.05061047151684761,
-0.0317939929664135,
0.03977290913462639,
-0.012042336165904999,
-0.020613696426153183,
0.04219309240579605,
0.014064204879105091,
-0.007078746799379587,
-0.007414969149976969,
0.035743314772844315,
0.0328085832297802,
-0.036513518542051315,
-0.04415552690625191,
0.015571204014122486,
0.019435713067650795,
-0.018934791907668114,
0.015913814306259155,
0.02263561636209488,
0.03499552235007286,
-0.03979799523949623,
0.018431998789310455,
0.04164731502532959,
-0.051330115646123886,
0.0006812073988839984,
0.005708442069590092,
0.02420976385474205,
-0.0020862629171460867,
-0.012593728490173817,
-0.028676945716142654,
0.06801918894052505,
-0.012201520614326,
0.015062974765896797,
-0.00949991587549448,
0.03633158281445503,
-0.04546684771776199,
-0.006260905880481005,
-0.019518088549375534,
0.00816416461020708,
0.01596851646900177,
0.0028408460784703493,
-0.024633221328258514,
0.005262088030576706,
0.022085953503847122,
-0.040394965559244156,
-0.017787765711545944,
0.018079562112689018,
-0.0006994661525823176,
0.011010786518454552,
0.007528688758611679,
-0.037985652685165405,
-0.02141309157013893,
0.058585625141859055,
0.00921866949647665,
0.007037756033241749,
-0.03263334184885025,
-0.01963884010910988,
-0.024665527045726776,
0.059723034501075745,
-0.06534808874130249,
-0.0036662123166024685,
-0.03139923885464668,
-0.016753822565078735,
-0.0195330698043108,
-0.033657848834991455
] |
<p>Suppose you take a loop of string and place it on the surface of a liquid, the string should become taut due to surface tension. How would you be able to calculate the tension in the loop of string?</p>
<p>My main difficulty in solving this problem is the direction in which surface tension force act on the thread - perpendicular or tangential at any point on the thread?</p>
| 8,282 |
[
-0.018451262265443802,
0.0033170897513628006,
-0.018808631226420403,
-0.012504817917943,
0.010742624290287495,
-0.012471199035644531,
-0.016514169052243233,
-0.011782113462686539,
0.01018624659627676,
0.013718015514314175,
0.022387158125638962,
0.047123853117227554,
0.01949600875377655,
0.03214262053370476,
0.03173423931002617,
-0.0010155144846066833,
0.00753144221380353,
-0.04011917486786842,
0.013919125311076641,
-0.006057706195861101,
-0.008786982856690884,
0.018746517598628998,
-0.015097497031092644,
-0.003734152065590024,
-0.016385067254304886,
0.019495820626616478,
0.0308825820684433,
-0.026389185339212418,
0.035643987357616425,
0.04420195892453194,
-0.006460106000304222,
-0.0454222671687603,
0.03376470133662224,
0.011578865349292755,
0.04007827490568161,
0.04812050238251686,
-0.02588469535112381,
-0.015368742868304253,
-0.038118600845336914,
0.027298269793391228,
0.0004397396987769753,
-0.016131803393363953,
-0.009806686080992222,
0.02160673402249813,
-0.02739815227687359,
0.021355006843805313,
-0.013896261341869831,
-0.03240710124373436,
0.043424785137176514,
-0.08330707252025604,
0.05817239359021187,
0.005586895626038313,
0.04652917757630348,
0.029163870960474014,
-0.015519958920776844,
0.00432298518717289,
0.043221864849328995,
0.04508974403142929,
-0.041365157812833786,
-0.06575105339288712,
-0.024341825395822525,
0.02332289144396782,
-0.036275483667850494,
-0.03450433537364006,
-0.015482792630791664,
-0.007886302657425404,
-0.029670149087905884,
-0.02031197026371956,
0.022134365513920784,
-0.0077890753746032715,
-0.047444503754377365,
-0.004466998856514692,
0.05068217217922211,
0.013415027409791946,
-0.017332572489976883,
-0.025585278868675232,
0.011491089127957821,
0.04934709891676903,
0.013208701275289059,
0.05834351107478142,
-0.021033063530921936,
0.009209669195115566,
0.050855472683906555,
0.061625462025403976,
0.026866648346185684,
-0.05353224650025368,
0.06015815958380699,
-0.0006914763944223523,
0.004976876545697451,
0.039065781980752945,
0.024814292788505554,
0.009835124015808105,
-0.02632223814725876,
0.01608208753168583,
-0.022958306595683098,
-0.014837759546935558,
-0.010761359706521034,
0.030810147523880005,
0.015184801071882248,
-0.013980437070131302,
0.021727845072746277,
-0.017844557762145996,
-0.006678376812487841,
0.0987468957901001,
0.042158838361501694,
-0.007704199757426977,
-0.0017182710580527782,
0.021644800901412964,
-0.004466497804969549,
-0.028261074796319008,
-0.049899861216545105,
-0.030888110399246216,
-0.03018351085484028,
-0.04118570685386658,
-0.003081435104832053,
-0.027102574706077576,
0.0012355735525488853,
-0.029257867485284805,
0.0328877754509449,
0.05585591495037079,
0.009522322565317154,
-0.05617918446660042,
0.06069935858249664,
-0.0073714409954845905,
-0.04965615272521973,
0.03839016705751419,
0.024965519085526466,
-0.05891035497188568,
-0.024374449625611305,
0.025551991537213326,
-0.006422832608222961,
-0.022761549800634384,
0.010251588188111782,
0.04053153097629547,
0.05512761324644089,
-0.008363821543753147,
-0.088398776948452,
-0.06248364597558975,
0.08858594298362732,
-0.00420814985409379,
-0.010667960159480572,
-0.05239193141460419,
0.016404446214437485,
0.05743120238184929,
0.06745656579732895,
-0.00305354967713356,
0.04031091183423996,
0.0021130063105374575,
-0.024126116186380386,
-0.007097350433468819,
-0.015869922935962677,
-0.036284200847148895,
0.0067207096144557,
-0.058406781405210495,
-0.02062022127211094,
-0.030137423425912857,
0.00394836999475956,
0.048211775720119476,
0.010472702793776989,
-0.01545623317360878,
0.06294146180152893,
0.01691192202270031,
0.023815304040908813,
0.042671505361795425,
-0.007592631038278341,
-0.04985775053501129,
0.06845666468143463,
-0.003259459510445595,
-0.01215271558612585,
0.025118272751569748,
-0.012169793248176575,
-0.013097441755235195,
-0.02312786504626274,
-0.007460278458893299,
0.05986151471734047,
-0.05318790674209595,
-0.026624642312526703,
0.0022719362750649452,
0.014792492613196373,
-0.002292542951181531,
-0.023667192086577415,
-0.036473535001277924,
-0.014345387928187847,
0.030225738883018494,
0.03728245198726654,
0.058033887296915054,
-0.017304886132478714,
-0.032504625618457794,
-0.025431910529732704,
-0.018984917551279068,
-0.011856467463076115,
-0.03850158676505089,
0.03178096190094948,
-0.017178962007164955,
-0.027987519279122353,
0.0031816421542316675,
-0.013758682645857334,
0.030847370624542236,
-0.06671912223100662,
-0.028957702219486237,
-0.027999356389045715,
0.04033751040697098,
0.006978430785238743,
0.015752920880913734,
0.00987708754837513,
0.05166275054216385,
0.04092095047235489,
0.023746784776449203,
0.01199636422097683,
-0.05822307616472244,
-0.007919940166175365,
-0.023852558806538582,
-0.04377514123916626,
0.027377814054489136,
0.020544137805700302,
-0.026440905407071114,
0.006197751499712467,
-0.02250279299914837,
0.008668854832649231,
0.03745914250612259,
-0.03800615295767784,
0.05979836359620094,
0.051254332065582275,
0.02327352948486805,
0.03708455711603165,
-0.011184897273778915,
0.005710602272301912,
-0.0040091765113174915,
0.05041661113500595,
-0.037402570247650146,
-0.04523015767335892,
0.018946759402751923,
0.009997911751270294,
0.031722698360681534,
-0.03611580282449722,
-0.027501214295625687,
0.027941472828388214,
0.027169134467840195,
0.011551829054951668,
0.045280374586582184,
-0.021079931408166885,
-0.024715827777981758,
-0.008364918641746044,
0.01773901656270027,
-0.004972709808498621,
0.010843166150152683,
0.02689731866121292,
0.05520850792527199,
0.04420272633433342,
-0.0032527451403439045,
-0.006017631851136684,
0.02512616105377674,
-0.003040498588234186,
0.026688776910305023,
0.013570379465818405,
-0.018557261675596237,
0.055057868361473083,
-0.05127941071987152,
0.010550047270953655,
0.016191335394978523,
0.009201989509165287,
0.005368705838918686,
-0.009401150979101658,
0.002915829885751009,
0.007101475726813078,
-0.021649254485964775,
-0.0019701786804944277,
-0.025116225704550743,
0.021879112347960472,
-0.02987120859324932,
0.017721669748425484,
-0.015357820317149162,
0.01003867108374834,
-0.0065450845286250114,
0.0207697544246912,
0.0592365637421608,
0.021372800692915916,
0.02553359605371952,
-0.0285703893750906,
-0.02021528035402298,
0.013948952779173851,
-0.04386842995882034,
-0.007991512306034565,
-0.00961178820580244,
-0.06176281347870827,
0.0010533375898376107,
0.002823803573846817,
-0.029915472492575645,
0.05298655852675438,
0.002611523261293769,
-0.00156652950681746,
0.007709062192589045,
0.016111014410853386,
-0.023579899221658707,
-0.014743836596608162,
-0.04532534256577492,
0.021488314494490623,
-0.010304381139576435,
-0.009496990591287613,
0.01368267647922039,
0.004802875220775604,
-0.015448174439370632,
0.03757040947675705,
-0.04237674921751022,
-0.051001276820898056,
-0.004131863359361887,
-0.0011337226023897529,
0.01658189296722412,
-0.010164134204387665,
0.008338740095496178,
0.016466572880744934,
-0.04187193885445595,
0.016434116289019585,
-0.09489288181066513,
-0.023444032296538353,
-0.013542378321290016,
-0.005881592631340027,
0.02397281490266323,
0.005699019879102707,
-0.06363004446029663,
0.06730634719133377,
0.0007003048667684197,
-0.0778869092464447,
0.018000733107328415,
-0.02218635380268097,
-0.022499239072203636,
-0.04451524466276169,
0.030203456059098244,
0.004016353283077478,
-0.038793839514255524,
-0.003001746255904436,
0.021742960438132286,
0.054361000657081604,
0.07167943567037582,
0.01181692536920309,
0.017682038247585297,
0.002231798367574811,
-0.001976346829906106,
0.014534291811287403,
0.06311117857694626,
0.01614277996122837,
0.02155367285013199,
-0.011392218060791492,
0.014055226929485798,
0.009999701753258705,
0.0360950343310833,
-0.030982082709670067,
0.034833770245313644,
0.013113281689584255,
0.015418385155498981,
-0.018623149022459984,
0.03343115374445915,
-0.023780671879649162,
-0.02044118382036686,
0.04238983243703842,
0.012392530217766762,
0.045241206884384155,
-0.029843270778656006,
-0.009975295513868332,
0.06548807770013809,
0.06117299571633339,
-0.016150735318660736,
-0.0676758885383606,
0.0020887553691864014,
-0.02821294404566288,
0.034430503845214844,
-0.07333341985940933,
-0.03929748386144638,
0.02688978612422943,
0.01842675171792507,
0.01191383320838213,
-0.02253067120909691,
-0.049119651317596436,
0.007577482610940933,
-0.08179422467947006,
-0.0024304697290062904,
0.014668627642095089,
0.07131437957286835,
0.005870507564395666,
0.026142511516809464,
0.03877381607890129,
0.04767446219921112,
0.031096648424863815,
0.02342354692518711,
-0.08655554801225662,
0.020481867715716362,
-0.03583046793937683,
-0.011221090331673622,
-0.01599537953734398,
0.0021127047948539257,
0.0012816392118111253,
-0.03189936652779579,
0.004469291772693396,
-0.006513840984553099,
0.006618646904826164,
-0.04657170921564102,
0.046631839126348495,
0.0013167491415515542,
0.007341329008340836,
-0.007158457767218351,
0.05673550069332123,
0.030479544773697853,
-0.02334783412516117,
0.05766824632883072,
0.027158604934811592,
-0.015492621809244156,
0.01367090456187725,
-0.010739617981016636,
-0.011008812114596367,
0.0052629797719419,
0.014417177997529507,
0.026409706100821495,
0.024969274178147316,
0.015043897554278374,
0.015959979966282845,
-0.010334758087992668,
0.053536321967840195,
0.032104916870594025,
0.007060856558382511,
0.0038643116131424904,
-0.08876882493495941,
-0.009230617433786392,
-0.014028751291334629,
0.06992064416408539,
0.02967943623661995,
0.024637607857584953,
0.01890435256063938,
-0.03445451706647873,
-0.05324913561344147,
0.06106280907988548,
0.05283017456531525,
0.03093448467552662,
-0.015773717314004898,
-0.03343556448817253,
0.0033740901853889227,
-0.029594747349619865,
0.02214210107922554,
-0.004654468968510628,
0.027736429125070572,
-0.02289055660367012,
-0.016341788694262505,
0.05386446416378021,
-0.009883985854685307,
-0.015092138200998306,
-0.0032625801395624876,
-0.004920155741274357,
0.046443723142147064,
-0.03502780199050903,
0.011681562289595604,
0.04304424300789833,
0.021855423226952553,
0.019919399172067642,
-0.01899597980082035,
-0.014124982059001923,
-0.06730212271213531,
-0.042244523763656616,
0.04949519783258438,
0.03296244889497757,
-0.01137281209230423,
-0.027315879240632057,
-0.04288165643811226,
-0.013930057175457478,
0.06652462482452393,
-0.028477540239691734,
0.016155198216438293,
-0.0277559831738472,
0.014565793797373772,
-0.03559337556362152,
-0.02062436379492283,
-0.03145935758948326,
0.03288590535521507,
-0.023879745975136757,
0.03234969079494476,
-0.03320905938744545,
0.00944465771317482,
-0.03454134613275528,
0.005180534441024065,
0.008685659617185593,
0.0021686283871531487,
0.0243220254778862,
-0.010240527801215649,
0.010114341042935848,
0.01296582818031311,
-0.047554414719343185,
-0.056747257709503174,
0.0401485450565815,
0.0043431674130260944,
0.021077200770378113,
0.008110284805297852,
-0.025915710255503654,
-0.0767117366194725,
0.017702383920550346,
0.010597296059131622,
0.020460424944758415,
0.014261112548410892,
-0.009604140184819698,
0.013676350004971027,
0.05105738714337349,
-0.006985099986195564,
0.05702437832951546,
0.023312371224164963,
-0.035316046327352524,
-0.02600809931755066,
0.0008822735399007797,
0.002895737998187542,
-0.023981444537639618,
-0.03528878837823868,
0.0007548996363766491,
0.007218275219202042,
-0.051841966807842255,
0.020538821816444397,
-0.018447814509272575,
0.008229599334299564,
0.0047390032559633255,
-0.014514907263219357,
-0.025339676067233086,
0.0017798148328438401,
0.030252575874328613,
-0.037355903536081314,
0.02097625471651554,
-0.014221874997019768,
-0.007362739183008671,
-0.0035076334606856108,
0.0033425732981413603,
-0.013884590938687325,
-0.0004586509021464735,
0.013011679984629154,
-0.013561681844294071,
-0.003931456245481968,
0.016631152480840683,
-0.02220102585852146,
-0.007167817559093237,
-0.0561416856944561,
0.05372868850827217,
-0.028046298772096634,
0.007731751538813114,
0.015200680121779442,
-0.026309089735150337,
0.005639915354549885,
-0.03691115230321884,
-0.03390784189105034,
0.04512501507997513,
-0.05263232812285423,
0.027735533192753792,
0.013532837852835655,
-0.005609202664345503,
-0.0467304065823555,
-0.05912783741950989,
0.04642583802342415,
0.010957603342831135,
-0.039195138961076736,
-0.019126873463392258,
0.022520840167999268,
-0.009358426555991173,
-0.00028940607444383204,
0.019887041300535202,
0.007351446431130171,
-0.06603346765041351,
-0.019540274515748024,
0.028429051861166954,
-0.004218180663883686,
0.07893697172403336,
0.0037588884588330984,
0.020074907690286636,
0.013097728602588177,
-0.06689069420099258,
-0.022800534963607788,
-0.038000717759132385,
0.016102468594908714,
-0.02202131412923336,
-0.03996804729104042,
0.01222455408424139,
-0.018030567094683647,
0.04403218626976013,
0.008419105783104897,
0.007393523119390011,
-0.010093764401972294,
0.06645102798938751,
-0.02648746408522129,
-0.017322413623332977,
-0.0068632070906460285,
0.013577122241258621,
0.05592469498515129,
-0.012834852561354637,
-0.0034385931212455034,
-0.04964945465326309,
0.015322869643568993,
-0.01141307596117258,
0.031332872807979584,
-0.04668493568897247,
0.007569777779281139,
0.09135182201862335,
-0.017605111002922058,
-0.009525740519165993,
0.041815634816884995,
-0.01426420547068119,
0.030038733035326004,
0.01981757953763008,
-0.0212780199944973,
0.023408271372318268,
0.03759823739528656,
-0.03191356360912323,
-0.06689144670963287,
-0.005349962506443262,
0.02454407513141632,
0.06770504266023636,
-0.04559165984392166,
0.028992535546422005,
0.05157722532749176,
0.0010329530341550708,
0.008338803425431252,
0.011145622469484806,
-0.05102793499827385,
-0.021561849862337112,
0.013833112083375454,
-0.018483880907297134,
-0.03131573647260666,
0.024801859632134438,
0.02900322712957859,
0.011477603577077389,
-0.05161565542221069,
-0.0027844044379889965,
0.03869426250457764,
0.014300571754574776,
0.003998543601483107,
0.017585523426532745,
-0.06773781031370163,
0.013695476576685905,
-0.006464056205004454,
0.040086377412080765,
-0.02427736297249794,
-0.00861035380512476,
0.038273923099040985,
0.013944989070296288,
0.011396657675504684,
-0.028778888285160065,
0.005318438168615103,
0.012217232957482338,
-0.009872597642242908,
-0.0009003867162391543,
0.00038412981666624546,
0.013005685061216354,
0.05208948627114296,
0.042752452194690704,
-0.004846262279897928,
0.04756021499633789,
-0.029785769060254097,
-0.05329059809446335,
0.013746406883001328,
-0.010516377165913582,
-0.03512246906757355,
0.07346899062395096,
0.016033031046390533,
-0.032903894782066345,
0.03370901569724083,
0.000770671118516475,
0.034341856837272644,
0.017807643860578537,
0.026047714054584503,
-0.021457156166434288,
0.07802889496088028,
-0.010244295001029968,
0.015112575143575668,
-0.010352341458201408,
0.039093270897865295,
0.08366535604000092,
0.05127293989062309,
0.02394319884479046,
-0.07575282454490662,
0.00742372265085578,
-0.0007993225008249283,
-0.013668375089764595,
-0.03597104549407959,
0.024500520899891853,
0.014566805213689804,
0.020969059318304062,
0.05408778786659241,
0.026476331055164337,
-0.04462447017431259,
0.013770954683423042,
0.04961463436484337,
-0.05889701098203659,
-0.0392020009458065,
0.0002381874801358208,
-0.0032534210477024317,
-0.015834320336580276,
0.04879416897892952,
-0.05648530647158623,
0.02432485669851303,
-0.030374018475413322,
-0.021309593692421913,
-0.04209540784358978,
-0.013601810671389103,
0.03663026914000511,
-0.007176848128437996,
-0.06024518609046936,
-0.01629720814526081,
-0.009111586958169937,
-0.01611822098493576,
-0.054285719990730286,
0.022017640992999077,
0.027197783812880516,
-0.021345989778637886,
0.007484559901058674,
-0.008876489475369453,
-0.0007074509048834443,
0.0026166464667767286,
0.000865653099026531,
0.03120557963848114,
-0.05902430787682533,
-0.01594546250998974,
-0.0200907401740551,
0.003812708193436265,
0.023135516792535782,
-0.0005922650452703238,
0.009778979234397411,
-0.024002261459827423,
0.01850290037691593,
-0.03393632546067238,
-0.014192630536854267,
-0.00043936228030361235,
0.05449303239583969,
-0.016142219305038452,
0.017402296885848045,
-0.010306403040885925,
0.005042521748691797,
-0.00006652487354585901,
-0.007444781716912985,
0.009533064439892769,
-0.009555709548294544,
-0.012288972735404968,
0.009276741184294224,
0.04547477141022682,
-0.024782901629805565,
-0.025232812389731407,
-0.015359442681074142,
-0.04297342896461487,
-0.01163997408002615,
0.027142195031046867,
0.02476576901972294,
0.009727763943374157,
0.03355866298079491,
-0.002189508406445384,
-0.008653624914586544,
0.009811059571802616,
-0.021159961819648743,
0.051434800028800964,
-0.020268693566322327,
0.0017859713407233357,
-0.039663199335336685,
0.0014482091646641493,
0.03630533069372177,
0.02737189084291458,
-0.00001057059762388235,
0.023020485416054726,
0.011542596854269505,
-0.0120161771774292,
0.022194754332304,
-0.017039630562067032,
-0.03989522159099579,
-0.05055266618728638,
-0.02225625514984131,
-0.007323196157813072,
-0.011046148836612701,
0.013386714272201061,
0.04268449544906616,
0.026756232604384422,
-0.02348441444337368,
0.02321593463420868,
-0.04488530382514,
0.0031309761106967926,
-0.020744454115629196,
-0.010037303902208805,
-0.020924394950270653,
0.010528492741286755,
-0.008011075668036938,
-0.06586936116218567,
-0.0021669049747288227,
-0.007940197363495827,
-0.019226953387260437,
0.04844463989138603,
0.03021344542503357,
-0.030908865854144096,
0.0420898012816906,
-0.0028186547569930553,
-0.0024072660598903894,
-0.06714317202568054,
0.008806516416370869,
-0.07872150093317032,
-0.03531812131404877,
0.0013715546810999513,
0.01990652084350586,
-0.0287611186504364,
0.02643861249089241,
-0.06760817021131516,
-0.020071227103471756,
0.00632599089294672,
0.006822615396231413,
0.04423940181732178,
-0.006771705579012632,
0.058907683938741684,
0.00783983338624239,
0.0184013769030571,
-0.009896451607346535,
-0.03466634824872017,
0.039408404380083084,
-0.03374242037534714,
-0.010305128060281277,
0.01296383049339056,
-0.01290969830006361,
0.039351366460323334,
0.03655559942126274,
-0.023320823907852173,
0.010390938259661198,
0.022367136552929878,
0.021367272362113,
0.0018736846977844834,
-0.012635220773518085,
-0.04617980867624283,
0.023312075063586235,
-0.051563914865255356,
0.004021583590656519,
-0.0005723990616388619,
0.0074149384163320065,
-0.0039711035788059235,
0.04803144186735153,
-0.001863071694970131,
0.004776617046445608,
0.04196828603744507,
0.03293322026729584,
-0.007087899371981621,
0.0545155331492424,
-0.033584147691726685,
0.0165843665599823,
0.03212205320596695,
-0.028880668804049492,
0.0023597595281898975,
-0.013222647830843925,
-0.01946605183184147,
-0.10076028108596802,
0.01530633494257927,
0.002045895205810666,
-0.007520279381424189,
0.025605376809835434,
-0.04438213258981705,
-0.005861245095729828,
0.04538103565573692,
-0.042378753423690796,
-0.0052568488754332066,
-0.04705343395471573,
0.006667372304946184,
-0.007124543655663729,
0.00548563664779067,
-0.03184584900736809,
0.05615716800093651,
0.0024092872627079487,
0.03595989942550659,
0.02685014344751835,
-0.006290953140705824,
-0.017893914133310318,
-0.009936489164829254,
0.010928588919341564,
0.030157048255205154,
0.0013177122455090284,
-0.020328858867287636,
0.03736502677202225,
-0.025981532409787178,
0.013753820210695267,
-0.013243842869997025,
-0.03514999896287918,
0.015806645154953003,
-0.005457808263599873,
0.016052696853876114,
-0.003692660015076399,
0.01213406678289175,
-0.024227885529398918,
-0.013218707405030727,
-0.025534093379974365,
0.03136221691966057,
-0.011406735517084599,
0.022780241444706917,
0.0007219054386951029,
0.009894978255033493,
-0.0006623882218264043,
-0.04411165788769722,
-0.032867252826690674,
0.039136555045843124,
-0.0315084233880043,
0.00762526597827673,
-0.003778275800868869,
-0.014203122816979885,
0.05801824852824211,
-0.04000069573521614,
-0.01807486079633236,
-0.02532067894935608,
0.017750544473528862,
0.013060922734439373,
0.006078831851482391,
-0.04017363861203194,
0.023095261305570602,
0.015954386442899704,
-0.01693141646683216,
0.016552759334445,
-0.02059021405875683,
-0.009527653455734253,
-0.056295089423656464,
0.011309246532619,
0.02754906564950943,
-0.01615430787205696,
-0.01710723713040352,
-0.01658753491938114,
0.014871349558234215,
0.06722329556941986,
0.012793491594493389,
-0.01609381102025509,
0.011988240294158459,
-0.03876291960477829,
0.0035178798716515303,
-0.05878577381372452,
0.024921121075749397,
0.003923444077372551,
-0.02585623972117901,
0.001335327047854662,
-0.005400240421295166,
0.0347953625023365,
0.05968660116195679,
0.023585598915815353,
0.005140010267496109,
-0.012891153804957867,
0.019138285890221596,
-0.025483936071395874,
-0.016961362212896347,
-0.005536581855267286,
-0.009525168687105179,
0.005180615931749344,
-0.03944915905594826,
0.011028737761080265,
-0.03693076968193054,
0.0035522240214049816,
0.0036851437762379646,
0.029139040037989616,
0.012526540085673332,
0.016534892842173576,
-0.014605749398469925,
-0.034181516617536545,
0.0035703550092875957,
-0.01683753728866577,
-0.01799573376774788,
0.0738939493894577,
0.004651670344173908,
0.003475676756352186,
-0.006829546764492989,
-0.007801981642842293,
-0.05197302997112274,
0.0403880774974823,
-0.060897450894117355,
0.03671547397971153,
-0.01807498373091221,
-0.04686233773827553,
0.018274391070008278,
-0.040084972977638245,
0.0006446271436288953,
0.005526776425540447,
-0.032066699117422104,
0.020297329872846603,
0.0341431088745594,
-0.023865653201937675,
-0.008698387071490288,
-0.03345916420221329,
0.03880656883120537,
0.05243641883134842,
-0.0101064657792449,
0.0030537827406078577,
0.02608700469136238,
0.07223287224769592,
0.012964300811290741,
-0.03911353275179863,
0.01564486138522625,
-0.0058503709733486176,
0.055950362235307693,
0.030953245237469673,
-0.02805040217936039,
-0.017548851668834686,
-0.045655135065317154,
0.03749746084213257,
-0.01759730651974678,
-0.01362907700240612,
0.02365819364786148,
-0.014561069197952747,
0.06309586018323898,
-0.014668482355773449,
0.022336352616548538,
-0.007565874140709639,
0.004901631269603968,
0.0210174098610878,
0.021358385682106018,
-0.01204663049429655,
0.026164531707763672,
0.01575528457760811,
-0.031239433214068413,
0.023868992924690247,
-0.001170485746115446,
-0.00014075892977416515,
-0.014729473739862442,
0.033814579248428345,
-0.0019235857762396336,
0.003437153995037079,
-0.02785327471792698,
-0.01873612217605114,
-0.031804159283638,
-0.0027605139184743166,
0.0538213737308979,
0.009817413054406643,
0.0015284459805116057,
0.028183912858366966,
0.006966917775571346,
-0.01916716992855072,
0.07120140641927719,
-0.02703666500747204,
-0.018410667777061462,
-0.004876460414379835,
0.005175411235541105,
0.012162555009126663,
-0.02217690832912922
] |
<p>I understand that in electrostatics all charges are 'static' due to equal forces acting upon them. This then leads to the fact that the arising electric field must be perpendicular to the metals surface at the surface. What i don't understand is what force is counteracting the electric field. I have read that there is a potential well but am not sure how this works. Could someone point me in the right direction? Thanks.</p>
| 8,283 |
[
-0.030545370653271675,
-0.0021734449546784163,
0.00724902143701911,
-0.00038898299681022763,
-0.0018801767146214843,
-0.002764876000583172,
0.01838395558297634,
0.003456622362136841,
-0.006992719601839781,
-0.007815688848495483,
0.02631450444459915,
0.028040992096066475,
0.05990399420261383,
0.006049820221960545,
0.015630139037966728,
-0.0007011974230408669,
-0.013260847888886929,
-0.03282669559121132,
0.01171392947435379,
-0.027860861271619797,
-0.007028310559689999,
0.014393880032002926,
0.009480999782681465,
0.0334455743432045,
-0.030596619471907616,
0.01099686324596405,
0.03832593187689781,
0.002918680664151907,
0.022404376417398453,
0.044343527406454086,
-0.015576512552797794,
-0.06383033096790314,
-0.016996057704091072,
0.03482286259531975,
0.034329310059547424,
0.008089987561106682,
-0.0029322111513465643,
-0.03742252290248871,
-0.03899478167295456,
0.027384329587221146,
-0.005398035980761051,
-0.0026809589471668005,
0.013137838803231716,
0.049936722964048386,
-0.02708684653043747,
-0.016306700184941292,
0.009953971020877361,
-0.00975289847701788,
0.04639787971973419,
-0.07433383166790009,
0.027169978246092796,
-0.0061610047705471516,
0.06856223940849304,
0.03035975806415081,
0.013609267771244049,
-0.003154839389026165,
0.07790012657642365,
0.043598588556051254,
-0.012687630020081997,
-0.059736669063568115,
-0.0247383750975132,
0.0014028839068487287,
-0.028918245807290077,
-0.05292372778058052,
-0.02831176482141018,
0.06456796079874039,
-0.023959385231137276,
-0.055010125041007996,
0.028223266825079918,
0.02718142606317997,
-0.01194800529628992,
0.009585808031260967,
0.015559978783130646,
-0.015823230147361755,
-0.008584816940128803,
-0.050204798579216,
0.010145568288862705,
-0.0038416169118136168,
0.003439749591052532,
0.016050418838858604,
-0.021937193349003792,
-0.013152486644685268,
0.01302874181419611,
0.0763835683465004,
0.01258886232972145,
-0.016889706254005432,
0.052952300757169724,
-0.014640498906373978,
0.017247721552848816,
0.008753490634262562,
-0.029448946937918663,
0.03069884143769741,
0.019354086369276047,
-0.005875611212104559,
-0.03678392991423607,
-0.016221530735492706,
-0.006593161262571812,
0.03923313319683075,
0.0005830766167491674,
0.021106459200382233,
0.03834925591945648,
-0.008578270673751831,
0.003795202588662505,
0.049800239503383636,
0.005942914634943008,
-0.03551991656422615,
-0.020342212170362473,
0.03317476809024811,
-0.0011401247465983033,
-0.013882563449442387,
-0.04871269315481186,
0.03375617787241936,
0.021775206550955772,
-0.022882895544171333,
0.009478204883635044,
-0.04270852357149124,
0.0038075465708971024,
0.0008765825186856091,
0.038396019488573074,
0.050593458116054535,
0.005894079804420471,
-0.06652039289474487,
0.04317571967840195,
-0.017407380044460297,
-0.0724392756819725,
-0.013025658205151558,
0.005023292265832424,
0.008877413347363472,
0.010588614270091057,
0.023161467164754868,
-0.0041937194764614105,
-0.02777217887341976,
0.0005016218638047576,
0.015822360292077065,
0.07544645667076111,
-0.007663584779947996,
-0.10520491749048233,
-0.0288431067019701,
0.04077846556901932,
-0.03870593011379242,
-0.004243858158588409,
-0.04961429908871651,
-0.019655723124742508,
0.009448573924601078,
0.04235682636499405,
0.010265792720019817,
-0.02855534851551056,
0.000658442557323724,
0.02226039208471775,
0.022021444514393806,
-0.02245386317372322,
-0.02926376834511757,
0.006140425335615873,
-0.0014764688676223159,
0.017509980127215385,
-0.03694950044155121,
0.04114200547337532,
0.005938461981713772,
0.00022586974955629557,
-0.040552880614995956,
0.03391976282000542,
-0.0057043894194066525,
0.005157858598977327,
0.01548679918050766,
-0.01707066036760807,
-0.00715968944132328,
0.0770232155919075,
-0.001716060098260641,
-0.033151861280202866,
0.06337804347276688,
0.014789711683988571,
0.0366068109869957,
0.01711943931877613,
0.02289232425391674,
0.030784115195274353,
-0.04541800916194916,
-0.019893750548362732,
-0.05958172678947449,
0.03779987990856171,
0.0028389899525791407,
-0.048970043659210205,
-0.04601794481277466,
0.041522301733493805,
0.0042822654359042645,
-0.02057933807373047,
0.05104738846421242,
-0.015959788113832474,
-0.016526194289326668,
-0.05473848059773445,
-0.02145611122250557,
-0.03767046332359314,
-0.0716567113995552,
0.06344929337501526,
0.008994849398732185,
-0.04117843881249428,
0.021978819742798805,
0.03273538127541542,
0.01505803968757391,
-0.06332207471132278,
-0.05266707018017769,
-0.01118811871856451,
0.03513581305742264,
-0.016118299216032028,
-0.004883746150881052,
0.02900712564587593,
0.03189999982714653,
0.05355898290872574,
0.025630587711930275,
0.0751459002494812,
-0.011139802634716034,
0.000987707986496389,
-0.0033534355461597443,
-0.03213375061750412,
0.03890888765454292,
0.02423032745718956,
-0.01921551488339901,
0.004747861064970493,
-0.00758947990834713,
0.01291625015437603,
0.054676663130521774,
-0.021373387426137924,
0.06859137117862701,
0.03605553135275841,
0.015992749482393265,
-0.030841318890452385,
0.03894718736410141,
-0.0038939942605793476,
-0.003535460215061903,
0.004099035635590553,
-0.044687848538160324,
-0.042902495712041855,
0.01148328185081482,
0.04248515143990517,
0.0021469825878739357,
-0.06193405017256737,
0.018490202724933624,
0.02775939181447029,
0.018275950103998184,
0.039283402264118195,
0.03676523268222809,
-0.044199444353580475,
-0.027913684025406837,
0.030619187280535698,
0.01651173084974289,
-0.027772825211286545,
0.001432097633369267,
0.03344447538256645,
0.04564967006444931,
-0.0034712995402514935,
0.003004564670845866,
-0.03015010803937912,
0.03156358748674393,
-0.012808064930140972,
0.056495267897844315,
-0.009290406480431557,
-0.06874106079339981,
0.021479545161128044,
-0.01149204932153225,
0.03814633563160896,
-0.007870243862271309,
-0.0011429626028984785,
0.01032515149563551,
-0.04398719221353531,
0.003715499769896269,
0.020160527899861336,
-0.02899349480867386,
-0.022814035415649414,
-0.00551703292876482,
0.03107110783457756,
-0.038291480392217636,
-0.003062888514250517,
0.004640891682356596,
-0.000472461135359481,
-0.017114464193582535,
-0.01808934099972248,
0.019569098949432373,
0.020892713218927383,
0.07266194373369217,
-0.0034197820350527763,
-0.03330216556787491,
-0.007464979775249958,
-0.05839769169688225,
-0.00024711800506338477,
0.0010737982811406255,
-0.026304155588150024,
-0.01591523364186287,
-0.012301581911742687,
-0.03167453035712242,
0.06939863413572311,
0.024312293156981468,
0.02248399704694748,
0.015471121296286583,
-0.004436987452208996,
-0.023752370849251747,
0.029337575659155846,
-0.046710092574357986,
0.02134884148836136,
-0.008846992626786232,
0.006679619196802378,
0.02090424671769142,
0.016393400728702545,
0.0033543026074767113,
0.024795573204755783,
-0.03997344523668289,
-0.03822006285190582,
-0.011283347383141518,
-0.0015428863698616624,
0.014849908649921417,
-0.004297122359275818,
0.022560395300388336,
0.027184192091226578,
-0.06823250651359558,
0.012499889358878136,
-0.033752039074897766,
-0.025461681187152863,
0.0025278348475694656,
-0.0055284081026911736,
-0.0034532516729086637,
-0.04605855792760849,
-0.05569859966635704,
0.06789588928222656,
0.008492999710142612,
-0.04029327630996704,
-0.0051673902198672295,
-0.047210633754730225,
-0.013747108168900013,
-0.031094077974557877,
0.02199927158653736,
0.028116118162870407,
-0.023747161030769348,
0.016022436320781708,
-0.005174621939659119,
0.04649907723069191,
0.017868878319859505,
-0.018322622403502464,
0.005770054180175066,
-0.025561194866895676,
0.004929485730826855,
0.027938174083828926,
0.05250532925128937,
-0.00837253499776125,
-0.03009747713804245,
-0.014238458126783371,
0.01554072555154562,
0.044888854026794434,
0.04971083626151085,
-0.01102356519550085,
0.03325142338871956,
-0.029812559485435486,
0.053594768047332764,
-0.04631197825074196,
0.02166534774005413,
-0.019922321662306786,
-0.000909787486307323,
0.040907278656959534,
-0.00739169679582119,
0.052562471479177475,
-0.037685319781303406,
-0.009918375872075558,
0.04503737762570381,
0.03163423389196396,
-0.03424318507313728,
-0.02917744591832161,
-0.001221447833813727,
-0.02424750104546547,
0.018166543915867805,
-0.013330266810953617,
-0.046151719987392426,
0.023238038644194603,
0.02090492844581604,
0.003209583694115281,
0.02616732195019722,
-0.032340649515390396,
-0.029735997319221497,
-0.06478390097618103,
0.017705382779240608,
0.03670719638466835,
0.04427189379930496,
-0.029498718678951263,
0.04278791323304176,
0.027725068852305412,
0.02090885117650032,
0.036830611526966095,
0.02671392448246479,
-0.0652245357632637,
0.050831787288188934,
-0.021533118560910225,
-0.012519254349172115,
-0.006815856322646141,
-0.018143223598599434,
-0.03207986056804657,
0.009562365710735321,
-0.02737598493695259,
0.006032399367541075,
-0.021161388605833054,
-0.06869612634181976,
-0.008097963407635689,
-0.01802053488790989,
-0.02689485251903534,
-0.036459993571043015,
0.03424147143959999,
0.03096965327858925,
-0.0617973692715168,
-0.0007750022923573852,
0.03595858812332153,
-0.027421481907367706,
-0.012959363870322704,
-0.020548950880765915,
-0.00067600590409711,
0.02859942987561226,
0.01758970506489277,
0.02861749567091465,
0.001682073692791164,
0.00467093288898468,
-0.00639911275357008,
-0.007918555289506912,
0.06018029525876045,
0.029400205239653587,
0.014842617325484753,
-0.0410967692732811,
-0.06847073882818222,
-0.019038593396544456,
-0.044402193278074265,
0.07170340418815613,
-0.00785196665674448,
0.022697247564792633,
0.042111579328775406,
0.025376614183187485,
-0.0141535559669137,
0.04360141605138779,
0.07020200788974762,
0.07146384567022324,
-0.0067842258140444756,
-0.03142169862985611,
-0.004461462143808603,
-0.05114744231104851,
-0.00283940602093935,
0.0423838309943676,
-0.011164291761815548,
-0.016449807211756706,
-0.0018211302813142538,
0.03743975609540939,
0.001827585743740201,
0.011835388839244843,
0.00968100968748331,
-0.02407034859061241,
0.03613527491688728,
-0.037357036024332047,
-0.017161037772893906,
0.03229384496808052,
0.009557539597153664,
0.04986570030450821,
0.0061650024726986885,
-0.02164679579436779,
-0.08355257660150528,
-0.01860005594789982,
0.053097840398550034,
0.006511286366730928,
-0.021352078765630722,
-0.009285124018788338,
-0.060936227440834045,
0.0028158666100353003,
0.06254196912050247,
-0.02428613416850567,
0.0007505649700760841,
-0.03525377810001373,
0.014279135502874851,
-0.013552349992096424,
0.0060282559134066105,
-0.027770815417170525,
0.0061576589941978455,
-0.0019371163798496127,
0.010695432312786579,
0.017039356753230095,
-0.009667388163506985,
-0.017017319798469543,
0.003058055182918906,
-0.003486072877421975,
0.02326524630188942,
0.02057231403887272,
0.007733874022960663,
0.022260863333940506,
0.009860333986580372,
-0.009246131405234337,
-0.08717956393957138,
0.01826178841292858,
0.013219557702541351,
0.00980427023023367,
0.03061261959373951,
-0.030154183506965637,
-0.028689831495285034,
0.006098794750869274,
-0.018387626856565475,
0.00029589611222036183,
0.00292117684148252,
0.001122873742133379,
0.021658968180418015,
0.03840871527791023,
-0.001089513418264687,
0.0721881240606308,
-0.015046871267259121,
-0.02019614353775978,
-0.03600604832172394,
0.007889147847890854,
0.04619445279240608,
-0.009903927333652973,
-0.032933857291936874,
-0.026428069919347763,
0.026758618652820587,
-0.018579896539449692,
0.03868367522954941,
-0.04572730511426926,
0.005103429779410362,
-0.023389650508761406,
-0.02801256999373436,
-0.0073805684223771095,
0.017816923558712006,
-0.0059659737162292,
0.003039260860532522,
0.012144547887146473,
0.02014850080013275,
0.0013519558124244213,
-0.033450931310653687,
-0.01727209985256195,
-0.001393275335431099,
-0.003918135073035955,
-0.00660340953618288,
-0.005682260729372501,
0.0032782722264528275,
-0.008580613881349564,
-0.04519641026854515,
0.02533191815018654,
-0.07020015269517899,
0.04781939834356308,
-0.022406460717320442,
-0.0013659681426361203,
0.005369829013943672,
-0.0800049751996994,
-0.036857783794403076,
0.02786756120622158,
0.0034322107676416636,
0.028907837346196175,
-0.05489345267415047,
0.0547432117164135,
0.047088295221328735,
0.016397254541516304,
-0.07662540674209595,
-0.07188116759061813,
0.01809944026172161,
0.04117179289460182,
0.005502020008862019,
-0.015488718636333942,
-0.018908511847257614,
0.024692147970199585,
-0.04838896915316582,
0.041010867804288864,
0.014546644873917103,
-0.02906910702586174,
0.005661427043378353,
0.025257593020796776,
0.011189650744199753,
0.05812186002731323,
0.010563352145254612,
-0.009125552140176296,
0.02170531265437603,
-0.030497366562485695,
-0.0026596826501190662,
-0.009505822323262691,
0.048423148691654205,
-0.0016059138579294086,
-0.025147490203380585,
-0.006217240355908871,
-0.03211727738380432,
0.04883754253387451,
-0.019530348479747772,
0.015350529924035072,
0.0023525755386799574,
0.037974562495946884,
-0.029747866094112396,
-0.023967817425727844,
0.020073993131518364,
0.012383900582790375,
0.06288488209247589,
-0.0028553989250212908,
-0.012343671172857285,
-0.056427858769893646,
-0.03653363138437271,
0.009612789377570152,
0.019607137888669968,
0.014318377710878849,
-0.0144937289878726,
0.07467979192733765,
0.002216809196397662,
0.012977253645658493,
0.009730018675327301,
-0.015830950811505318,
0.034977108240127563,
-0.035773731768131256,
0.034187138080596924,
0.017272694036364555,
0.02692350558936596,
-0.005868585780262947,
-0.03609233349561691,
-0.00003573204230633564,
0.023233989253640175,
0.06671055406332016,
-0.07361551374197006,
0.042454130947589874,
0.03909335657954216,
-0.0003101151087321341,
-0.009206786751747131,
-0.03342887759208679,
-0.02768055722117424,
0.01845685951411724,
0.0018549617379903793,
0.0004959270590916276,
-0.02292417734861374,
0.05366254597902298,
0.024780388921499252,
0.04704982414841652,
0.004496248438954353,
-0.00483799260109663,
0.02988370694220066,
0.038216542452573776,
0.040633562952280045,
0.0037061255425214767,
-0.031604982912540436,
0.05286497250199318,
-0.013378273695707321,
0.05080278217792511,
0.0039741783402860165,
-0.03410552442073822,
0.04678994417190552,
-0.009933133609592915,
0.018441038206219673,
-0.015631653368473053,
-0.04972273111343384,
0.0006012986414134502,
0.044031232595443726,
-0.015284189023077488,
0.011157060973346233,
-0.025616900995373726,
0.05390746518969536,
-0.013003596104681492,
0.022074198350310326,
0.025795424357056618,
0.021275606006383896,
-0.053761012852191925,
-0.030009765177965164,
-0.056174978613853455,
-0.024839013814926147,
0.029981236904859543,
0.011615992523729801,
-0.04047111049294472,
0.023338988423347473,
-0.02350698597729206,
0.04212239757180214,
0.012369666248559952,
0.02041204646229744,
-0.010133109986782074,
0.05026037245988846,
0.016341358423233032,
0.034027133136987686,
-0.030111100524663925,
-0.011590986512601376,
0.10471288859844208,
0.04729375243186951,
0.028231477364897728,
-0.07612020522356033,
-0.003660224610939622,
-0.04026680812239647,
-0.005840754602104425,
-0.033889248967170715,
0.019366366788744926,
-0.04632209241390228,
0.020272955298423767,
0.01807893067598343,
0.0339171476662159,
-0.013762823306024075,
0.01727423071861267,
0.06859496235847473,
-0.024614522233605385,
-0.046890731900930405,
-0.003536419477313757,
0.039133220911026,
-0.021702541038393974,
0.020506521686911583,
-0.051925159990787506,
0.04276631772518158,
-0.05650115758180618,
-0.019277220591902733,
-0.0322129987180233,
-0.022321384400129318,
0.01484835147857666,
0.02163073793053627,
-0.045436348766088486,
-0.003033075015991926,
-0.027423204854130745,
-0.01569496840238571,
-0.052529215812683105,
0.01939801499247551,
0.03995982185006142,
0.0006065065390430391,
0.0018406864255666733,
-0.009595912881195545,
0.013602488674223423,
0.021435571834445,
0.007341840770095587,
0.005548091605305672,
-0.04055853188037872,
0.01147698238492012,
-0.01656109094619751,
0.032883886247873306,
-0.02260352298617363,
0.0197556484490633,
-0.009089955128729343,
0.013914071954786777,
0.00036348364665172994,
-0.008494511246681213,
-0.05655214935541153,
-0.04286826401948929,
0.013293642550706863,
-0.006271853111684322,
-0.022715799510478973,
-0.03284456953406334,
0.023430893197655678,
-0.013643947429955006,
-0.011079123243689537,
-0.014508724212646484,
0.00033647846430540085,
0.015537946484982967,
-0.011069875210523605,
0.02040460892021656,
-0.0006857875268906355,
-0.04606226086616516,
-0.004228971898555756,
-0.03428631275892258,
-0.04165114834904671,
0.005950938444584608,
0.015804212540388107,
0.04948036000132561,
0.028243446722626686,
-0.010013638064265251,
-0.005146034061908722,
0.02437729388475418,
-0.068724125623703,
0.06159288436174393,
-0.018757645040750504,
-0.0013387101935222745,
-0.015439342707395554,
-0.00522517878562212,
0.03460818901658058,
0.04269105941057205,
-0.024992460384964943,
0.027392981573939323,
0.016991524025797844,
-0.00900910422205925,
-0.00270205014385283,
-0.0379914790391922,
-0.02097983844578266,
0.007214773446321487,
-0.03489406406879425,
0.0033409185707569122,
0.0017561342101544142,
-0.011817832477390766,
0.02082756906747818,
0.018581615760922432,
0.013419607654213905,
0.059776969254016876,
-0.05454448238015175,
0.017647508531808853,
-0.004262110218405724,
-0.016825469210743904,
-0.009516172111034393,
0.02178454026579857,
0.0039442298002541065,
-0.050822190940380096,
-0.019584806635975838,
-0.008101517334580421,
0.00975609477609396,
-0.0029041802044957876,
0.041457030922174454,
-0.038343705236911774,
0.024731630459427834,
0.002909930655732751,
0.009142241440713406,
-0.06332306563854218,
-0.02723809890449047,
-0.08322259038686752,
0.002607895527034998,
0.03970949724316597,
0.02992859110236168,
-0.026153448969125748,
0.0060262419283390045,
-0.015603956766426563,
0.002491296734660864,
-0.0010873094433918595,
0.01987704075872898,
0.020774679258465767,
0.015231640078127384,
0.060802388936281204,
-0.01008588820695877,
0.062159232795238495,
-0.00519936066120863,
0.0017426381818950176,
0.03566049411892891,
-0.03076745942234993,
-0.07117080688476562,
0.026265330612659454,
-0.0018939642468467355,
0.022395407781004906,
0.022170616313815117,
-0.0018489058129489422,
-0.018012745305895805,
0.044231951236724854,
-0.0003862472658511251,
0.02853364869952202,
-0.040404971688985825,
-0.023578599095344543,
-0.0005165300099179149,
-0.026893148198723793,
-0.015332337468862534,
-0.025543304160237312,
0.00421380577608943,
0.01977163553237915,
0.015251259319484234,
-0.01888829469680786,
-0.02524552494287491,
0.017115291208028793,
-0.01691601425409317,
-0.02302010916173458,
0.05194604769349098,
-0.016612939536571503,
0.014314649626612663,
0.054126836359500885,
-0.012995870783925056,
0.011560875922441483,
0.0383295938372612,
0.01809656247496605,
-0.08191777020692825,
-0.007834686897695065,
-0.005907365586608648,
0.0023334783036261797,
0.012182638980448246,
-0.0462755486369133,
-0.029116520658135414,
0.024689188227057457,
-0.0884193703532219,
-0.0015280286315828562,
-0.01797248050570488,
-0.012138119898736477,
0.022903956472873688,
-0.030120305716991425,
0.027387086302042007,
0.03960404172539711,
0.0015560573665425181,
0.04013826325535774,
0.035095199942588806,
-0.010001455433666706,
0.0012244083918631077,
-0.018822116777300835,
-0.02051810920238495,
0.043425023555755615,
0.0038793424610048532,
-0.024066008627414703,
0.06551089137792587,
-0.022616654634475708,
-0.002826950279995799,
0.020958345383405685,
-0.028189485892653465,
-0.009718874469399452,
-0.0006626174435950816,
0.03189760074019432,
-0.009346863254904747,
0.0002466500154696405,
-0.035017624497413635,
-0.00934857502579689,
-0.02565661445260048,
0.004219783935695887,
0.026952747255563736,
0.021628206595778465,
0.010373672470450401,
-0.010958810336887836,
0.050557900220155716,
-0.029450058937072754,
-0.025234399363398552,
0.033507443964481354,
-0.024793429300189018,
0.009484915062785149,
-0.0010300176218152046,
0.03522849455475807,
0.04424944147467613,
-0.03548707813024521,
-0.018860407173633575,
-0.05212312936782837,
-0.008074052631855011,
0.013669284991919994,
0.0007468406693078578,
-0.005505111999809742,
0.0405198410153389,
0.008740383200347424,
-0.02665337733924389,
-0.00421417411416769,
0.006459253840148449,
-0.0051408917643129826,
-0.045787710696458817,
0.022400736808776855,
0.021201789379119873,
-0.04849588871002197,
0.01890537701547146,
-0.031994398683309555,
-0.007656405214220285,
0.031674619764089584,
0.005709977354854345,
-0.0027790062595158815,
-0.00970066525042057,
-0.07409413158893585,
-0.012268035672605038,
-0.031951915472745895,
0.027957648038864136,
0.00010322329762857407,
-0.06574444472789764,
-0.009385299868881702,
-0.0547548308968544,
0.013319234363734722,
0.01784384623169899,
0.052685774862766266,
-0.04497656598687172,
0.0022213587071746588,
0.029410919174551964,
-0.012285323813557625,
0.026554543524980545,
-0.06988440454006195,
0.0015065817860886455,
0.027862466871738434,
-0.02766011655330658,
-0.007462380453944206,
0.005853583104908466,
0.012181481346487999,
0.04028434306383133,
0.007683057803660631,
-0.006331020500510931,
0.005451708100736141,
-0.02105710096657276,
-0.029932904988527298,
0.013784580864012241,
0.017133070155978203,
0.01100461557507515,
0.06693030148744583,
-0.018993105739355087,
-0.0005129337660036981,
-0.004108980298042297,
-0.018198782578110695,
0.010631907731294632,
0.03274804353713989,
-0.029299434274435043,
0.03238626569509506,
-0.027692947536706924,
0.004862657748162746,
0.03355859965085983,
-0.03355545923113823,
-0.0229180958122015,
0.00998343899846077,
-0.0035532109905034304,
0.006001125555485487,
0.07443789392709732,
-0.001824375824071467,
0.030296361073851585,
-0.004795411601662636,
0.015388250350952148,
-0.0005729254335165024,
0.026764430105686188,
0.01248528715223074,
0.038064926862716675,
0.02204069495201111,
0.0004362736362963915,
-0.0076856594532728195,
0.06978367269039154,
0.009105751290917397,
0.026772189885377884,
0.012601856142282486,
0.00023850431898608804,
-0.023257702589035034,
-0.003910997416824102,
-0.0012205424718558788,
0.0016975506441667676,
0.022770384326577187,
0.003273238893598318,
-0.0034586566034704447,
0.08788575232028961,
-0.05343670770525932,
0.004777359310537577,
0.0004085767432115972,
0.030019065365195274,
0.01308611873537302,
-0.01912565529346466,
0.0007693550433032215,
0.024770140647888184,
-0.02822859399020672,
-0.05904929339885712,
-0.011247003450989723,
0.03506499528884888,
0.003071798710152507,
-0.004634201992303133,
0.036909379065036774,
-0.003085704520344734,
-0.01617227867245674,
-0.04206361994147301,
0.015324991196393967,
-0.0403389073908329,
0.013577929697930813,
0.023437565192580223,
0.044138528406620026,
0.014083399437367916,
0.026109477505087852,
0.027763528749346733,
-0.027840182185173035,
0.031813476234674454,
-0.07036758959293365,
-0.054673533886671066,
-0.005199859384447336,
0.009463019669055939,
0.002365462016314268,
0.033562809228897095
] |
<p>I learned that a quantum system has an "overall state", a vector in a Hilbert space. That Hilbert space can be decomposed in a basis of "basic states". For example if in the Universe there is only a free electron with its own spin, and I pick an axis $z$, there is an infinite basis of "position+spin", let's say $|(0,0,0);1/2>, |(0,0,0);-1/2>, |(0.1,0,0);1/2>\ldots$</p>
<p>I cannot obviously write all possible positions, but that was to give the idea. Some $\psi (\vec{r},s)$ contains the coefficients for all the elements of this basis and is given. This is the "overall state" of my "one-electron Universe"</p>
<p>I was said that there is "measurement" that makes the $\psi$ collapse to one of the "basic states" and can give the observer the result (position + spin in the $z$ axis)</p>
<p>Since a measurement involves an interaction with some sort of detector I figured out that I would need QFT (the possibility to have multiple particles and interaction) to understand measurement and add a detector into my Universe. I thought that the dynamic of the interaction between the particles of the detector and the electron could act in a way that the $\psi$ collapsed (I hoped that even in QFT there was something analogous to the original $\psi$ of the electron).</p>
<p>Now I couldn't study QFT but from what I grasped it is much more complicated and the reason of the collapsing of the wave function is not explained by an "interaction". The wave function itself is subjective and <a href="http://motls.blogspot.it/2012/11/why-subjective-quantum-mechanics-allows.html?m=1" rel="nofollow">depends on the knowledge of the observer</a>.</p>
<p>So I am lead to believe that QFT does not contain anything that explains the collapse of the wave function. Is it true?</p>
<p>I know that I presented a rather subjective view. I hope that they are shared by many and that an answer that points out my misunderstandings could help others. I think that many people in the quest for a more "classical" explanation of QM resort to thinking that when they would see how the interactions work "really" so as to describe a fully fledged measurement equipment (photons, QED, QCD...) they would figure that out.</p>
| 8,284 |
[
0.03197413682937622,
0.00618480471894145,
0.030723245814442635,
-0.050361067056655884,
0.022059960290789604,
0.017727145925164223,
-0.05262809991836548,
-0.027999822050333023,
0.012852940708398819,
-0.04565133899450302,
0.04086766019463539,
0.01645376719534397,
0.022090822458267212,
0.0025096172466874123,
0.0074181207455694675,
0.040747836232185364,
-0.013476825319230556,
0.0030452548526227474,
-0.030819809064269066,
-0.047383010387420654,
0.03350365161895752,
0.042089641094207764,
0.007407989352941513,
0.0060997917316854,
-0.0008463591220788658,
0.022847924381494522,
-0.024940811097621918,
0.019993962720036507,
0.028250176459550858,
0.07188473641872406,
-0.030469991266727448,
-0.05158694088459015,
-0.007423305418342352,
0.015147953294217587,
0.06176631897687912,
-0.013557272031903267,
-0.02400590479373932,
-0.021371040493249893,
0.01580240949988365,
0.018809380009770393,
-0.03769274428486824,
-0.03253670781850815,
-0.037282392382621765,
0.02911560796201229,
-0.04227418825030327,
-0.032494448125362396,
-0.002233043545857072,
0.0155372628942132,
0.05027153715491295,
-0.0506945475935936,
0.024850070476531982,
0.0038325146306306124,
0.05802182853221893,
0.007512849289923906,
-0.002186502330005169,
-0.016352644190192223,
0.0882386863231659,
0.056582629680633545,
-0.007892088033258915,
-0.03908227011561394,
-0.01029839925467968,
-0.016932882368564606,
-0.006805603392422199,
-0.030284333974123,
-0.023935817182064056,
0.0058058579452335835,
0.002998534357175231,
0.014227112755179405,
-0.015978559851646423,
-0.019813861697912216,
0.031858012080192566,
0.014228965155780315,
-0.014306903816759586,
-0.009325116872787476,
-0.012067033909261227,
-0.0038703319150954485,
0.029912201687693596,
0.006710091605782509,
0.03210468217730522,
0.025335412472486496,
-0.020487822592258453,
-0.008758500218391418,
0.024494290351867676,
0.035345546901226044,
0.011579587124288082,
-0.021429169923067093,
0.0726703628897667,
-0.014949855394661427,
0.007356108166277409,
0.04486920312047005,
-0.053934480994939804,
-0.003846020670607686,
0.06518498063087463,
-0.033933937549591064,
-0.05363764986395836,
0.021511495113372803,
0.00863355677574873,
0.05226270481944084,
0.011692894622683525,
-0.038755349814891815,
-0.006696648895740509,
-0.01584472693502903,
-0.013707512989640236,
0.08074203878641129,
-0.028411636129021645,
-0.015647567808628082,
-0.03427743911743164,
0.018461067229509354,
0.0030324694234877825,
-0.04327917471528053,
-0.002628765068948269,
0.05944138020277023,
-0.0069200992584228516,
0.04599085822701454,
-0.006030101794749498,
-0.030342040583491325,
-0.024773402139544487,
-0.03346679359674454,
0.059163037687540054,
0.06481140851974487,
0.02865007147192955,
-0.03433459624648094,
-0.035429153591394424,
-0.03861434757709503,
-0.06336929649114609,
-0.005531856790184975,
0.02510954812169075,
-0.021077949553728104,
-0.020926102995872498,
0.01667010225355625,
0.003401201218366623,
-0.001787005690857768,
0.03826133906841278,
0.02772163785994053,
0.031230658292770386,
-0.030059298500418663,
-0.1295129954814911,
-0.035423729568719864,
0.03877370432019234,
-0.019254446029663086,
-0.02279585227370262,
-0.037980735301971436,
-0.0013475397136062384,
0.04562778025865555,
0.05918629840016365,
-0.017163868993520737,
0.01062775682657957,
0.03242206200957298,
0.030797341838479042,
0.035624708980321884,
-0.021481633186340332,
-0.02797897346317768,
-0.029765767976641655,
-0.049080368131399155,
-0.030275825411081314,
0.010579250752925873,
0.04625767096877098,
0.03236585855484009,
-0.0001477007317589596,
0.001153776072897017,
0.04971851035952568,
0.011697931215167046,
-0.014635969884693623,
0.04270637407898903,
-0.008191782981157303,
-0.010220827534794807,
0.0836591050028801,
-0.012083947658538818,
0.005520033184438944,
0.07566361874341965,
-0.02695336565375328,
-0.019264647737145424,
-0.005955434869974852,
0.03422488272190094,
0.021663326770067215,
-0.02831997722387314,
-0.06017359718680382,
-0.04895895719528198,
-0.008316341787576675,
-0.0384676493704319,
-0.031747762113809586,
-0.018532810732722282,
-0.04685818403959274,
0.015052962116897106,
0.020041583105921745,
0.029193414375185966,
-0.0014371192082762718,
-0.02020556852221489,
0.0012058016145601869,
-0.045954588800668716,
-0.010044371709227562,
-0.04921485111117363,
-0.027605999261140823,
0.018064627423882484,
-0.019673706963658333,
0.011679224669933319,
-0.014325810596346855,
0.0061085522174835205,
-0.03580024093389511,
-0.06049688905477524,
-0.033703338354825974,
0.030263280496001244,
0.01854751817882061,
-0.0010706933680921793,
-0.0016464064829051495,
0.05516235902905464,
0.04181207716464996,
0.0022925296798348427,
0.00404545571655035,
-0.0041262684389948845,
-0.023349493741989136,
0.013580948114395142,
-0.011429660022258759,
0.021074756979942322,
0.02389986626803875,
-0.002083960920572281,
0.026163293048739433,
0.005415541585534811,
-0.007676164153963327,
0.04147849604487419,
-0.03889518976211548,
0.0648149698972702,
0.030348271131515503,
-0.04235559701919556,
-0.000350204820279032,
0.03570307046175003,
0.02708606794476509,
-0.003413592232391238,
-0.0037040975876152515,
-0.023916136473417282,
-0.07377354800701141,
-0.033072493970394135,
0.0650140792131424,
0.04241943359375,
-0.031143687665462494,
0.020951852202415466,
0.015063898637890816,
0.01009457465261221,
0.01710055209696293,
0.0044782827608287334,
-0.014244703575968742,
-0.02305859513580799,
-0.014966733753681183,
-0.031674377620220184,
0.022276928648352623,
0.027069436386227608,
0.031139755621552467,
0.012126787565648556,
0.010185962542891502,
-0.01102298405021429,
-0.019906511530280113,
0.02108790911734104,
-0.030597295612096786,
0.015697037801146507,
-0.006470027845352888,
-0.026541730388998985,
-0.014282908290624619,
-0.01895258203148842,
0.043109212070703506,
0.019094083458185196,
-0.024667173624038696,
-0.004384098574519157,
-0.033852484077215195,
-0.021321874111890793,
-0.010370224714279175,
0.016211258247494698,
-0.04935246333479881,
-0.028517626225948334,
0.019419265910983086,
-0.03425396606326103,
-0.037797704339027405,
0.002720409305766225,
-0.014669318683445454,
0.004602957516908646,
-0.0015397397801280022,
0.04648786038160324,
0.010644176974892616,
-0.014493710361421108,
-0.0757506787776947,
-0.041065432131290436,
0.006065442692488432,
-0.016298167407512665,
0.03505915030837059,
0.0600106380879879,
-0.0744030773639679,
-0.006046134978532791,
-0.07613135129213333,
-0.04105104133486748,
0.02159029431641102,
-0.004035762511193752,
0.02345452457666397,
-0.02386721409857273,
-0.007786386180669069,
-0.04955362528562546,
-0.03035334311425686,
-0.027756167575716972,
-0.014191030524671078,
-0.0402275025844574,
0.006140436977148056,
0.06453429907560349,
0.0023741554468870163,
-0.04714199900627136,
-0.014949998818337917,
-0.02773723565042019,
-0.0448017418384552,
-0.01563933491706848,
-0.0149530079215765,
0.028440039604902267,
-0.03596507012844086,
0.03458457067608833,
0.01668473333120346,
-0.01294158585369587,
-0.017429403960704803,
-0.0635763481259346,
-0.05728628858923912,
0.012410650961101055,
0.024333827197551727,
0.030393024906516075,
-0.0045515005476772785,
-0.01740969531238079,
0.07825031876564026,
-0.005857990588992834,
-0.03362324833869934,
-0.010070696473121643,
0.024076949805021286,
0.012243757024407387,
-0.018231339752674103,
0.005075103137642145,
0.013210236094892025,
0.002148591447621584,
0.051626745611429214,
-0.016565794125199318,
0.020943330600857735,
-0.00945210363715887,
0.02877870760858059,
0.004188852850347757,
0.030279703438282013,
0.01084255799651146,
0.006103712134063244,
0.055608391761779785,
0.01972455531358719,
-0.016049649566411972,
-0.006954435724765062,
0.03589301556348801,
-0.001906369929201901,
0.023696722462773323,
-0.0482923686504364,
0.055689819157123566,
0.03254677727818489,
0.011282972060143948,
-0.006196506787091494,
0.015201380476355553,
-0.007675467524677515,
-0.028150763362646103,
-0.005644139368087053,
0.019511912018060684,
0.01565692201256752,
0.019234299659729004,
0.02715211734175682,
0.050402410328388214,
0.001086774980649352,
-0.033546630293130875,
-0.034335147589445114,
0.009435565210878849,
0.0007558947545476258,
0.035261090844869614,
-0.002324261935427785,
-0.028923798352479935,
0.031628333032131195,
0.06764823198318481,
0.024228237569332123,
-0.017091190442442894,
-0.010060563683509827,
-0.005553978029638529,
-0.015240839682519436,
-0.02504725381731987,
-0.003636392764747143,
0.048264551907777786,
0.004474901594221592,
0.046977024525403976,
0.007312348578125238,
-0.009572663344442844,
-0.02897496521472931,
0.007604380138218403,
-0.1023232489824295,
-0.013757526874542236,
-0.006131683476269245,
-0.01426195353269577,
-0.019270341843366623,
-0.020108629018068314,
0.05014779046177864,
-0.016141975298523903,
-0.0026725733187049627,
-0.034167803823947906,
-0.024451706558465958,
-0.058198023587465286,
0.01984269730746746,
-0.017224090173840523,
-0.01964316889643669,
-0.03053978644311428,
0.07067219167947769,
0.061702318489551544,
-0.02284364029765129,
-0.013246290385723114,
0.0003584515943657607,
-0.029278231784701347,
0.011834890581667423,
-0.013502019457519054,
-0.011366937309503555,
0.0510871447622776,
0.027449864894151688,
0.046665165573358536,
0.02634071558713913,
-0.01264635194092989,
0.021115742623806,
0.029327593743801117,
0.08202773332595825,
-0.017021413892507553,
-0.025121096521615982,
0.018818266689777374,
-0.0008484610007144511,
0.005352940876036882,
-0.015057023614645004,
0.07218998670578003,
-0.004659726750105619,
-0.01427275687456131,
0.028607571497559547,
-0.0030454129446297884,
-0.004603509325534105,
0.021403098478913307,
0.03347012773156166,
0.0013820613967254758,
-0.001270972890779376,
0.0011759779881685972,
-0.014048296958208084,
-0.02903142012655735,
0.015257608145475388,
0.0003911683743353933,
0.016982199624180794,
-0.0013970701256766915,
0.008134833537042141,
0.03746655583381653,
0.031069714576005936,
-0.02624453976750374,
0.007524686865508556,
-0.01591624692082405,
0.007486283779144287,
0.01795841008424759,
-0.012789738364517689,
-0.024944357573986053,
0.03146001324057579,
0.022860625758767128,
-0.007151035126298666,
0.0011660661548376083,
-0.04679809510707855,
-0.012054281309247017,
0.01865221932530403,
0.01985783688724041,
0.027111154049634933,
-0.011090000160038471,
-0.031771469861269,
-0.06104958802461624,
0.03930992633104324,
-0.03783125430345535,
0.038840144872665405,
-0.018797049298882484,
-0.01405996736139059,
-0.05258066579699516,
-0.04465959966182709,
-0.04203798994421959,
0.00892463605850935,
-0.019261155277490616,
0.003960838541388512,
-0.042661402374506,
0.01395618449896574,
-0.009517135098576546,
0.01438464131206274,
-0.0015306038549169898,
0.012992584146559238,
0.003833208931609988,
-0.003940010908991098,
0.020992176607251167,
0.018658487126231194,
-0.012173833325505257,
-0.08152372390031815,
0.014964737929403782,
0.01119135320186615,
0.002806591335684061,
0.009298015385866165,
-0.008709341287612915,
-0.04121627286076546,
0.019303984940052032,
-0.0037099234759807587,
0.002560617635026574,
0.03411586582660675,
-0.07108878344297409,
0.06199759617447853,
0.022529926151037216,
0.003284385660663247,
0.04428751394152641,
0.005284032318741083,
-0.007960979826748371,
0.01424411591142416,
-0.008299262262880802,
-0.0033898467663675547,
-0.03588715195655823,
0.006069281604140997,
-0.02442752756178379,
0.004590542521327734,
-0.014391837641596794,
0.05674521252512932,
-0.01662478968501091,
0.004212821833789349,
-0.032955288887023926,
-0.04171644151210785,
-0.017028411850333214,
-0.004056162666529417,
-0.04255877062678337,
0.002148751402273774,
-0.04634101688861847,
-0.003983563743531704,
-0.009273926727473736,
-0.046617746353149414,
-0.02195882797241211,
0.019556783139705658,
0.008442654274404049,
0.03773752227425575,
-0.02465633861720562,
0.05059507489204407,
-0.032250210642814636,
-0.02081490494310856,
0.021593235433101654,
-0.04589921236038208,
0.02669386751949787,
-0.02260342612862587,
-0.0037638801150023937,
0.028628624975681305,
-0.05549798533320427,
-0.0682554841041565,
0.00572067778557539,
-0.0005520080449059606,
-0.012583988718688488,
0.012134362012147903,
-0.030972739681601524,
0.009607179090380669,
0.0033700959756970406,
-0.06297983974218369,
-0.014617269858717918,
-0.008829420432448387,
-0.01644565910100937,
-0.005828228313475847,
-0.007494219578802586,
0.0166204571723938,
-0.01368890143930912,
-0.0016676221275702119,
-0.013354409486055374,
-0.012297401204705238,
-0.03817000612616539,
0.011625446379184723,
0.016277052462100983,
0.026357054710388184,
0.012881984934210777,
-0.0129771763458848,
0.000006827188371971715,
0.011423412710428238,
-0.007539719808846712,
0.006435281131416559,
0.026547746732831,
0.01785341650247574,
0.00001559376141813118,
-0.05259638652205467,
-0.03141612932085991,
0.008882579393684864,
0.0030795966740697622,
-0.009663553908467293,
-0.010204965248703957,
0.008187055587768555,
0.006453886162489653,
-0.0031521390192210674,
-0.014146961271762848,
-0.023907754570245743,
0.025872958824038506,
0.017828060314059258,
0.003629640443250537,
-0.0014355240855365992,
-0.04066630080342293,
-0.08148554712533951,
0.02564394846558571,
-0.030449122190475464,
-0.005259943660348654,
0.017199918627738953,
0.03972943499684334,
0.01741260662674904,
0.001851029577665031,
0.024738747626543045,
-0.02546713501214981,
-0.010721664875745773,
-0.026025915518403053,
0.014784462749958038,
0.026712864637374878,
0.023274192586541176,
-0.02759256213903427,
-0.014467896893620491,
-0.04214009642601013,
0.004844624549150467,
0.03096027672290802,
0.038786616176366806,
0.020359426736831665,
0.03073190338909626,
-0.00510427774861455,
-0.01669716089963913,
-0.013004561886191368,
0.003803668776527047,
0.016373762860894203,
0.025930803269147873,
0.03634488210082054,
-0.03630826622247696,
0.00795031525194645,
0.01645987667143345,
0.050476353615522385,
-0.017648400738835335,
-0.008530174382030964,
0.03179531171917915,
0.0248271357268095,
0.029262369498610497,
-0.015225397422909737,
-0.044334717094898224,
0.05157055705785751,
-0.03530425578355789,
0.013421212323009968,
-0.0013739492278546095,
0.013916527852416039,
0.004510947968810797,
0.035624392330646515,
0.05942295491695404,
-0.026934735476970673,
-0.014203446917235851,
-0.03286287561058998,
0.017353573814034462,
0.011058926582336426,
0.008578137494623661,
-0.007096379529684782,
-0.00574391009286046,
0.022227374836802483,
-0.010384817607700825,
0.027747105807065964,
0.036322858184576035,
-0.05939437448978424,
0.007871666923165321,
-0.05218358710408211,
-0.037305496633052826,
0.047290682792663574,
-0.015871455892920494,
-0.03024168498814106,
-0.0027417531237006187,
-0.048934146761894226,
0.06178119778633118,
0.032635025680065155,
0.041962310671806335,
-0.045728541910648346,
0.030930211767554283,
0.004942478146404028,
0.028736749663949013,
-0.027903525158762932,
-0.017842916771769524,
0.1419212520122528,
0.05677006393671036,
-0.007434706669300795,
-0.036402955651283264,
-0.007019788026809692,
-0.00352880684658885,
0.04001310467720032,
-0.00518443901091814,
0.032455772161483765,
0.006892101373523474,
0.0038236237596720457,
-0.008992992341518402,
0.06774792820215225,
0.00925159640610218,
-0.01871589757502079,
0.0556119829416275,
-0.06288314610719681,
-0.048031121492385864,
-0.027479050680994987,
0.013853296637535095,
-0.015624997206032276,
0.002891771262511611,
-0.060030024498701096,
0.011325331404805183,
-0.029261421412229538,
0.0041323089972138405,
-0.01728433556854725,
-0.012647300958633423,
0.0014709059614688158,
-0.018838664516806602,
-0.05566545948386192,
0.005572590511292219,
-0.010300911031663418,
-0.016840681433677673,
-0.025216663256287575,
0.011066787876188755,
0.017797717824578285,
-0.008990339934825897,
0.03066262975335121,
0.018926581367850304,
0.00846019759774208,
0.01401207223534584,
0.004777409601956606,
-0.0027576431166380644,
-0.054193165153265,
0.0033888069447129965,
-0.0032078931108117104,
0.10089711099863052,
-0.01458713598549366,
-0.01925424113869667,
-0.026929043233394623,
-0.023555194959044456,
0.0065351491793990135,
-0.03505052626132965,
-0.018254922702908516,
-0.007373030297458172,
0.034912560135126114,
-0.015679093077778816,
0.014372971840202808,
-0.01422905083745718,
0.03436608240008354,
-0.020067477598786354,
0.0078854626044631,
-0.00637821527197957,
-0.023391012102365494,
0.005034847650676966,
-0.015557009726762772,
0.027739597484469414,
0.03633008897304535,
0.002948976354673505,
-0.013776703737676144,
-0.020856797695159912,
-0.01709805801510811,
-0.026213185861706734,
0.031179560348391533,
0.0032524082344025373,
0.02916027046740055,
0.022701965644955635,
0.04277954623103142,
-0.02336387149989605,
-0.03989666700363159,
0.02109125629067421,
-0.04420104995369911,
-0.008320570923388004,
0.007132305763661861,
-0.00015163421630859375,
-0.011267480440437794,
0.05924396961927414,
-0.015867820009589195,
-0.025101857259869576,
0.016107384115457535,
0.03144702687859535,
0.021592967212200165,
-0.013646035455167294,
-0.00009694314940134063,
0.03312896192073822,
-0.012055875733494759,
0.03860846534371376,
-0.05241062119603157,
0.015265296213328838,
0.018055250868201256,
0.02278313972055912,
0.01826627179980278,
0.04074179008603096,
-0.025011885911226273,
-0.028836868703365326,
0.0046821944415569305,
-0.03798745200037956,
0.013491448946297169,
0.025427555665373802,
0.06377945095300674,
-0.05871659889817238,
-0.030684150755405426,
0.006835499778389931,
0.013558081351220608,
-0.018136709928512573,
0.029345741495490074,
-0.03116210736334324,
-0.017106492072343826,
-0.0007276819669641554,
-0.003928264137357473,
-0.0066107469610869884,
-0.007837126031517982,
-0.04146542400121689,
0.007261416409164667,
-0.02120475471019745,
0.008250914514064789,
-0.01689484715461731,
0.009671732783317566,
0.016823945567011833,
-0.022969095036387444,
0.013012299314141273,
0.024498621001839638,
-0.07490935921669006,
0.00534262228757143,
0.03972116485238075,
0.03585607931017876,
0.0113499965518713,
0.0070332493633031845,
0.00812575127929449,
0.026061587035655975,
-0.04325252026319504,
-0.023153290152549744,
0.06698872148990631,
0.027705758810043335,
0.03163645416498184,
0.044692378491163254,
-0.007842945866286755,
-0.03312584385275841,
0.007517640013247728,
0.009066442959010601,
0.006713086739182472,
0.0022751588840037584,
-0.023971695452928543,
-0.016547955572605133,
0.004418442025780678,
0.04703604802489281,
0.0004162569821346551,
-0.019471343606710434,
0.0337909571826458,
0.008654391393065453,
0.015764808282256126,
0.025254491716623306,
0.013034931384027004,
-0.01075071468949318,
0.022361310198903084,
0.0313497930765152,
-0.0491386242210865,
0.00826431717723608,
0.04024764895439148,
-0.06817513704299927,
0.04079030826687813,
0.037470173090696335,
0.017191383987665176,
-0.09737329930067062,
-0.009762978181242943,
0.00905066542327404,
0.03489042446017265,
0.02470729872584343,
-0.009236141107976437,
0.016395077109336853,
0.02578512392938137,
-0.08325883001089096,
0.0492747500538826,
-0.012004069983959198,
0.011294044554233551,
-0.014766201376914978,
-0.02124917320907116,
-0.05099679157137871,
0.05195746570825577,
0.018418392166495323,
0.06162990629673004,
0.026900531724095345,
0.02142108604311943,
-0.010406898334622383,
-0.025487644597887993,
-0.020781787112355232,
0.033763956278562546,
-0.04387756064534187,
-0.019888242706656456,
0.11202595382928848,
-0.04338065907359123,
0.01565922237932682,
0.015322868712246418,
0.015034334734082222,
0.012041622772812843,
-0.0240632314234972,
-0.0034652117174118757,
0.0341540090739727,
0.05041946470737457,
0.009585625492036343,
-0.009732156060636044,
0.0063190218061208725,
-0.005177950486540794,
0.05183340981602669,
0.016971303150057793,
0.033582501113414764,
-0.013650449924170971,
-0.0008801775984466076,
-0.04929543659090996,
-0.0141326654702425,
0.009596506133675575,
0.03054341860115528,
0.023811640217900276,
0.019549353048205376,
0.03797847032546997,
-0.005958687048405409,
0.0018843330908566713,
-0.01457581203430891,
-0.02138788439333439,
-0.031562477350234985,
0.02231091633439064,
0.020046977326273918,
-0.009744933806359768,
0.00253485469147563,
-0.021097099408507347,
-0.015562379732728004,
0.043209176510572433,
0.011699624359607697,
-0.0018821344710886478,
-0.06104676052927971,
-0.01876632310450077,
0.0015527313807979226,
-0.0015958438161760569,
0.05723275616765022,
-0.017218759283423424,
-0.0222289077937603,
-0.019224170595407486,
-0.01668773964047432,
-0.0010066269896924496,
-0.018546653911471367,
-0.03197378292679787,
-0.00544018903747201,
-0.09473509341478348,
0.03512480482459068,
0.03075934760272503,
0.010803500190377235,
-0.012482118792831898,
-0.03259913995862007,
0.0010436364682391286,
-0.012885910458862782,
0.07228457927703857,
0.002991756424307823,
-0.011441197246313095,
0.0068955435417592525,
0.004579497966915369,
0.04124614968895912,
-0.049243856221437454,
0.004377894103527069,
-0.012877115979790688,
-0.003291843691840768,
-0.013678978197276592,
-0.03792046010494232,
0.0014801598154008389,
0.013943320140242577,
0.03491835296154022,
0.005718741565942764,
0.007074692286550999,
-0.03179910406470299,
-0.031858302652835846,
0.07910573482513428,
-0.012817254289984703,
0.0004931009607389569,
0.05020046606659889,
-0.013459596782922745,
0.050387799739837646,
0.07459763437509537,
-0.0238660778850317,
-0.029256099835038185,
0.007391965948045254,
-0.010666231624782085,
-0.01049334742128849,
0.009105014614760876,
-0.00122584099881351,
0.03213028609752655,
-0.023506823927164078,
-0.03639516979455948,
0.028415583074092865,
-0.0011159724090248346,
-0.04048369079828262,
0.051328372210264206,
-0.023711180314421654,
0.05827448144555092,
-0.008632971905171871,
0.03481632098555565,
0.005444747861474752,
0.003666798584163189,
0.031303536146879196,
0.034673310816287994,
0.028500055894255638,
0.010955835692584515,
0.018624240532517433,
0.06710660457611084,
0.023485463112592697,
0.01067195925861597,
0.03235507011413574,
0.05118179693818092,
-0.018331198021769524,
0.04011227935552597,
0.004062002990394831,
-0.020253829658031464,
-0.01390714943408966,
-0.0004375468706712127,
-0.014894158579409122,
0.10867507755756378,
-0.01882009021937847,
-0.011121457442641258,
-0.012095761485397816,
0.02019771747291088,
-0.03723684325814247,
0.03954016789793968,
0.03702257201075554,
0.05762316659092903,
-0.025976404547691345,
-0.015101511031389236,
-0.034679289907217026,
0.037793632596731186,
0.025390198454260826,
-0.043033067137002945,
0.022862104699015617,
0.012865548953413963,
-0.007965237833559513,
0.01771451346576214,
-0.000973826099652797,
-0.0008689394453540444,
-0.050243496894836426,
0.0446184016764164,
0.03180214390158653,
0.00031766280881129205,
-0.04978577047586441,
-0.003868513973429799,
-0.07816895097494125,
0.04970176890492439,
-0.02303844317793846,
-0.0147259421646595,
0.019179921597242355,
0.04501434788107872,
-0.013638410717248917,
0.0019962945953011513
] |
<p>I've been looking at LIGO figures for <a href="https://dcc.ligo.org/public/0002/T0900288/003/AdvLIGO%20noise%20curves.pdf">gravitational wave sensitivity here</a> and it seem to be displayed in an adimensional strain ratio (which I assume that is more or less equivalent to metric perturbation $h_{\mu \nu}/g_{\mu \nu}$, correct me if I'm wrong)</p>
<p>What I'm wondering is how can I convert this sensitivity measure into something like watts/area, as a measure of energy density flux of gravitational waves.</p>
| 8,285 |
[
0.01166863925755024,
0.008403818123042583,
0.014346283860504627,
-0.035597145557403564,
0.06193278357386589,
0.023408586159348488,
-0.03151390329003334,
-0.05799063667654991,
0.03427063673734665,
-0.029974814504384995,
0.02372509241104126,
0.01441871840506792,
0.08556342124938965,
0.023571446537971497,
0.0069512114860117435,
-0.0383472703397274,
-0.0036878292448818684,
-0.019275512546300888,
-0.020947786048054695,
-0.06262309849262238,
0.021428681910037994,
0.011473639868199825,
0.000843130808789283,
-0.03012794628739357,
-0.005464383866637945,
0.03867758437991142,
0.051578033715486526,
0.004031708464026451,
0.013058927841484547,
0.06858231872320175,
-0.031073786318302155,
-0.03306485339999199,
0.007944541051983833,
0.02568700723350048,
-0.011129948310554028,
0.004992919974029064,
-0.0379149504005909,
-0.020397992804646492,
-0.020242417231202126,
0.0400683768093586,
-0.04482971504330635,
-0.022683190181851387,
-0.027316560968756676,
0.041325513273477554,
-0.028838831931352615,
-0.012649163603782654,
0.024286208674311638,
-0.026172040030360222,
0.06442376971244812,
-0.06026773527264595,
0.08860335499048233,
0.041746776551008224,
0.05650748685002327,
0.06329166889190674,
-0.014414224773645401,
0.013132055290043354,
0.0724412128329277,
0.06634211540222168,
-0.0015873381635174155,
-0.02963358536362648,
-0.01413903571665287,
-0.008688569068908691,
-0.022355761379003525,
-0.035995204001665115,
0.006445991341024637,
0.03712043538689613,
-0.0525023378431797,
-0.022775551304221153,
0.030861418694257736,
0.022491365671157837,
0.030865315347909927,
-0.0017295378493145108,
0.016600966453552246,
-0.04352007433772087,
-0.021988103166222572,
-0.017116403207182884,
-0.0069744461216032505,
0.004729573614895344,
0.030607707798480988,
0.05316498130559921,
-0.025299903005361557,
-0.0032068477012217045,
0.038398269563913345,
0.0809243842959404,
0.008223678916692734,
-0.015134181827306747,
0.04729466512799263,
-0.04712944105267525,
-0.00516027957201004,
0.017870843410491943,
-0.00026561185950413346,
-0.009431891143321991,
0.03141271322965622,
0.015546709299087524,
-0.03882001340389252,
0.0152077442035079,
0.011927337385714054,
0.02876339666545391,
-0.015546062961220741,
-0.008640591986477375,
0.014375896193087101,
0.00046807859325781465,
-0.0028400190640240908,
0.060793474316596985,
0.029806552454829216,
-0.024469489231705666,
-0.04699500650167465,
0.01077569555491209,
-0.04322146624326706,
0.00342379417270422,
-0.0421413853764534,
-0.004256857093423605,
-0.015183410607278347,
-0.025292642414569855,
0.03966836258769035,
-0.032142601907253265,
-0.015039248391985893,
-0.01935786008834839,
0.04865609109401703,
0.07319270819425583,
0.07038912922143936,
0.008044356480240822,
0.0374813936650753,
-0.04369863495230675,
-0.048388514667749405,
0.020145945250988007,
0.04730796441435814,
-0.005432204343378544,
-0.04495890811085701,
0.008565597236156464,
0.0053520286455750465,
-0.034526094794273376,
0.01729171723127365,
-0.00951986201107502,
0.010977980680763721,
-0.02113247849047184,
-0.0817372053861618,
-0.06257147341966629,
0.04035105183720589,
5.987704980725539e-7,
-0.004026890732347965,
-0.06301809847354889,
0.004797528963536024,
0.05114299803972244,
0.05603589490056038,
0.04259277507662773,
0.02446185238659382,
-0.010219542309641838,
0.05054089054465294,
0.008218679577112198,
-0.047694090753793716,
-0.005139934364706278,
-0.015464584343135357,
-0.040579456835985184,
0.01369360089302063,
-0.042122840881347656,
-0.03222593665122986,
0.025256944820284843,
-0.025290576741099358,
-0.018087532371282578,
0.08809855580329895,
-0.005728045478463173,
-0.013092770241200924,
0.037472330033779144,
-0.015666838735342026,
-0.019429003819823265,
0.07035718858242035,
0.012983468361198902,
-0.027888793498277664,
0.022897994145751,
-0.010116631165146828,
-0.032689835876226425,
0.013291753828525543,
-0.001421948429197073,
0.04023093357682228,
-0.023043500259518623,
0.005202634260058403,
-0.04503561183810234,
0.005848753731697798,
0.019781984388828278,
-0.020248979330062866,
-0.04876051843166351,
-0.027836086228489876,
-0.009281661361455917,
0.017078522592782974,
0.024724913761019707,
-0.02701878547668457,
-0.007280954159796238,
-0.0012610466219484806,
-0.0629989504814148,
-0.014387816190719604,
-0.0340137742459774,
0.008317405357956886,
0.0344383642077446,
0.01542553212493658,
0.020143266767263412,
0.012536956928670406,
-0.0017675907583907247,
-0.0033019722905009985,
-0.05033394694328308,
0.01387808844447136,
0.02697306126356125,
0.029315374791622162,
-0.0006218765047378838,
0.022053400054574013,
0.021722061559557915,
0.02985738217830658,
0.016389260068535805,
0.03490374982357025,
-0.026415230706334114,
-0.039617933332920074,
-0.012039787136018276,
-0.04041401296854019,
0.014092677272856236,
-0.01275449339300394,
-0.016710055992007256,
-0.004459750838577747,
-0.02065589465200901,
0.01547376997768879,
0.03315870836377144,
0.001212631119415164,
0.05929630994796753,
0.0462731271982193,
0.0004850159748457372,
0.020232466980814934,
0.03157893568277359,
-0.010407581925392151,
0.028905807062983513,
-0.017963998019695282,
-0.0005101101123727858,
-0.05535576492547989,
0.03156924247741699,
0.034894026815891266,
-0.003099588444456458,
-0.040162842720746994,
0.00016168771253433079,
0.07555072754621506,
0.0011643640464171767,
0.037603892385959625,
0.009171814657747746,
-0.03214253485202789,
-0.036829009652137756,
0.016377946361899376,
0.055398691445589066,
-0.0037676654756069183,
-0.009444551542401314,
0.00847326498478651,
0.06915964931249619,
0.010118863545358181,
-0.00507692527025938,
0.019085584208369255,
0.03577525541186333,
-0.05909562110900879,
0.009691650979220867,
-0.012006943114101887,
0.009400381706655025,
0.006804241798818111,
-0.02347017452120781,
0.011948809958994389,
0.04536343365907669,
-0.02310044690966606,
-0.009236827492713928,
-0.005304083693772554,
0.00029607483884319663,
-0.002807486103847623,
0.015031184069812298,
-0.0030813312623649836,
-0.015678485855460167,
0.017856473103165627,
-0.027607053518295288,
0.025535115972161293,
-0.020078221336007118,
-0.008299533277750015,
-0.05079590529203415,
0.017731472849845886,
0.03982606530189514,
0.02617480792105198,
0.020029831677675247,
-0.026778431609272957,
-0.05233991891145706,
0.04014621302485466,
0.0011959162075072527,
0.002789218444377184,
-0.008723842911422253,
-0.02876574918627739,
-0.01914704591035843,
-0.04330245777964592,
-0.012766174972057343,
-0.006827767007052898,
-0.021439960226416588,
0.016183989122509956,
0.005240401718765497,
0.0010147517314180732,
-0.03241138905286789,
-0.002156319562345743,
-0.0403406135737896,
-0.012653592973947525,
0.029804391786456108,
0.019332360476255417,
0.056776873767375946,
0.010230924934148788,
-0.030680887401103973,
0.00780200632289052,
-0.017937714233994484,
0.0030018012039363384,
-0.027306826785206795,
0.005721480119973421,
-0.014679008163511753,
-0.0234662052243948,
0.05162639543414116,
0.030242908746004105,
-0.06952593475580215,
0.001316901296377182,
-0.06955162435770035,
-0.026477457955479622,
0.019191108644008636,
0.013226350769400597,
0.04453318193554878,
0.031202562153339386,
-0.05346795171499252,
0.07758444547653198,
0.03257472440600395,
-0.012446465902030468,
-0.014187055639922619,
-0.005788101814687252,
0.04980296641588211,
-0.05914166197180748,
-0.00468309223651886,
0.008795707486569881,
0.016983527690172195,
0.0277763269841671,
0.006512219551950693,
0.029920000582933426,
0.04453744366765022,
0.030649662017822266,
-0.015310599468648434,
0.01107566524296999,
-0.006263889372348785,
0.009866943582892418,
0.054845307022333145,
0.011861377395689487,
-0.027841102331876755,
0.022139783948659897,
-0.01321468222886324,
-0.0032553221099078655,
0.009200038388371468,
-0.052884791046381,
0.028824379667639732,
0.006918967701494694,
-0.007735101971775293,
-0.05213044583797455,
0.007492702919989824,
0.00017801859939936548,
0.0011876787757501006,
0.02621704712510109,
0.03857516869902611,
0.04968439042568207,
-0.006478644907474518,
-0.031969379633665085,
0.02160952426493168,
0.03322824835777283,
0.02406102605164051,
-0.03331536427140236,
0.006671018432825804,
0.002795834094285965,
0.009105549193918705,
-0.007444929797202349,
-0.020690489560365677,
0.05698266625404358,
0.029293954372406006,
0.010064874775707722,
-0.027666926383972168,
-0.026271304115653038,
0.009439353831112385,
-0.07200122624635696,
-0.045733146369457245,
0.0030574575066566467,
0.05156859755516052,
0.012666670605540276,
0.019021647050976753,
0.05529186874628067,
0.01755366288125515,
0.029901282861828804,
-0.024094464257359505,
-0.08107409626245499,
0.03803567960858345,
-0.04214469715952873,
-0.02447429485619068,
0.025742972269654274,
-0.03165365010499954,
-0.05262241140007973,
-0.04465522617101669,
-0.03983427211642265,
-0.017889317125082016,
0.02093908004462719,
-0.04000383988022804,
0.007871481589972973,
0.018339183181524277,
-0.005068992730230093,
-0.053351156413555145,
0.07618654519319534,
0.028261052444577217,
-0.02603851445019245,
-0.0082442257553339,
0.025104913860559464,
-0.02676614560186863,
-0.015187104232609272,
0.027496371418237686,
0.011083952151238918,
-0.05069347470998764,
0.03587871417403221,
0.023841721937060356,
0.029795777052640915,
-0.046578940004110336,
0.010586787015199661,
0.05296725779771805,
0.014529435895383358,
0.024637622758746147,
-0.026107152923941612,
-0.038070306181907654,
-0.03814328834414482,
-0.031493354588747025,
0.028100788593292236,
0.06983902305364609,
0.024658210575580597,
-0.03252727538347244,
0.019585156813263893,
-0.0025091420393437147,
-0.01714194566011429,
0.034739427268505096,
0.04156533628702164,
-0.008041584864258766,
-0.029447166249155998,
-0.05331544205546379,
-0.0014021008973941207,
-0.01769581437110901,
-0.0333765409886837,
0.024306247010827065,
0.00011179975263075903,
-0.02070317417383194,
0.013304637745022774,
0.013940413482487202,
-0.004879378713667393,
-0.017682259902358055,
-0.005997937638312578,
0.00018788613670039922,
0.03208719193935394,
-0.010385501198470592,
-0.002188412705436349,
0.018908295780420303,
0.0672980397939682,
0.038234204053878784,
0.0072402385994791985,
-0.0044035883620381355,
-0.1183595210313797,
-0.024359503760933876,
0.03859926015138626,
0.020617034286260605,
0.010719994083046913,
-0.03294629976153374,
-0.04489372670650482,
-0.0016139780636876822,
0.024692783132195473,
-0.024862155318260193,
0.03682772442698479,
0.036169081926345825,
0.026859939098358154,
0.010750374756753445,
-0.000151117768837139,
0.01083854865282774,
0.035010311752557755,
-0.0034648082219064236,
0.004781554918736219,
-0.041723936796188354,
0.029563533142209053,
0.0026316384319216013,
0.012891082093119621,
-0.024692527949810028,
0.046877216547727585,
0.015247195027768612,
-0.020928414538502693,
-0.008537276647984982,
0.0005774822784587741,
-0.012704601511359215,
-0.08256600797176361,
0.0070953876711428165,
-0.01939556747674942,
0.006226068828254938,
0.038561854511499405,
-0.004222674295306206,
-0.012517677620053291,
0.034069281071424484,
0.02449546754360199,
0.017440037801861763,
-0.002531494479626417,
-0.052036136388778687,
0.0865476131439209,
0.0422988161444664,
0.007493185810744762,
0.060835447162389755,
0.02961399406194687,
-0.006970422808080912,
0.011770077981054783,
0.012535272166132927,
0.02482357621192932,
-0.05924287438392639,
-0.02106747031211853,
-0.00859625730663538,
-0.008771933615207672,
-0.05792943760752678,
0.030665569007396698,
-0.004243870731443167,
0.043035805225372314,
0.03404447063803673,
-0.011148112826049328,
-0.028900543227791786,
0.026608670130372047,
0.007310926914215088,
-0.008068695664405823,
0.045703522861003876,
0.05568920820951462,
-0.004111932590603828,
0.002403706545010209,
0.040031548589468,
-0.045142367482185364,
-0.004391226451843977,
0.03828666731715202,
-0.0067338184453547,
0.02416093461215496,
-0.012129628099501133,
0.0013323079328984022,
0.04902265965938568,
-0.034991275519132614,
0.04613298922777176,
-0.0419357605278492,
-0.008242558687925339,
-0.013030354864895344,
-0.03423560410737991,
-0.012114810757339,
-0.016917197033762932,
0.0020501224789768457,
0.018066423013806343,
-0.037122294306755066,
0.02805298939347267,
0.017584480345249176,
0.02141426131129265,
-0.07745122164487839,
0.016651269048452377,
0.03745314106345177,
0.006307639647275209,
-0.014678306877613068,
-0.05038853734731674,
-0.0016872816486284137,
-0.03796673193573952,
-0.01677403226494789,
-0.015682833269238472,
0.03721132501959801,
-0.0834382176399231,
0.01835019513964653,
-0.028813207522034645,
0.021158967167139053,
0.043600939214229584,
-0.05056405067443848,
0.00035237587871961296,
0.03010266087949276,
0.03288242593407631,
-0.0069416179321706295,
-0.006347634829580784,
0.02757137455046177,
-0.05145913362503052,
-0.02492380514740944,
-0.03090491332113743,
-0.025981830433011055,
0.02784035913646221,
-0.005145234055817127,
-0.02052164264023304,
0.021222667768597603,
0.006768181920051575,
-0.008380462415516376,
-0.01062368880957365,
0.020626405254006386,
-0.04730749502778053,
-0.013151860795915127,
-0.031108982861042023,
-0.02843782864511013,
-0.05083280801773071,
-0.0054811337031424046,
0.01635734923183918,
0.01930239424109459,
0.024350527673959732,
-0.022651826962828636,
0.07217064499855042,
-0.013990519568324089,
-0.04163409769535065,
0.003256382653489709,
-0.03824106976389885,
0.01763957180082798,
0.008816620334982872,
0.027120506390929222,
0.01580624096095562,
-0.00923167821019888,
-0.048382051289081573,
-0.04481718689203262,
-0.06469743698835373,
-0.05756061151623726,
0.08254595100879669,
0.0004207552701700479,
0.04563423618674278,
0.030565345659852028,
-0.03670557588338852,
0.04813266545534134,
-0.03842813894152641,
-0.022600146010518074,
0.029523765668272972,
0.0023299269378185272,
0.013496375642716885,
-0.015584118664264679,
-0.04370053485035896,
0.027002492919564247,
0.020343584939837456,
-0.029064280912280083,
0.03837265819311142,
0.007571401074528694,
0.06492748856544495,
-0.007494524586945772,
-0.027747830376029015,
-0.03749249503016472,
0.01584753394126892,
-0.020828422158956528,
0.04526631161570549,
-0.006607473827898502,
0.007119722198694944,
0.01090955175459385,
0.03623269498348236,
0.009325442835688591,
-0.013832289725542068,
-0.027410894632339478,
-0.05919354408979416,
0.04099753126502037,
0.06478622555732727,
-0.020379504188895226,
-0.02408936619758606,
0.038445666432380676,
0.0443081371486187,
-0.015141469426453114,
-0.0002712758141569793,
0.040733832865953445,
-0.0349125973880291,
-0.014437663368880749,
-0.034555885940790176,
-0.06962127983570099,
0.021846286952495575,
-0.002338967751711607,
-0.045812640339136124,
0.051586125046014786,
0.004955152049660683,
0.02882751263678074,
-0.00782670360058546,
0.022512098774313927,
-0.022784316912293434,
0.0717814490199089,
-0.04614618793129921,
0.006111327558755875,
-0.02181643433868885,
-0.008669235743582249,
0.1210360899567604,
0.07319671660661697,
0.009558750316500664,
-0.04044089838862419,
0.028146907687187195,
0.002889974508434534,
-0.0028272520285099745,
-0.04981118068099022,
0.008595633320510387,
-0.008162279613316059,
-0.022626560181379318,
0.027141520753502846,
0.07018354535102844,
-0.015438510105013847,
-0.014540162868797779,
0.060657769441604614,
0.009654071182012558,
0.00150920485612005,
0.05024966597557068,
0.032029200345277786,
-0.012446741573512554,
0.012166276574134827,
-0.010588984936475754,
0.04100170359015465,
0.006694707088172436,
-0.003912196960300207,
-0.042444948107004166,
-0.015866979956626892,
0.0005232830299064517,
-0.041793279349803925,
-0.07104223221540451,
0.013600190170109272,
-0.027944425120949745,
0.010967290960252285,
-0.004528556019067764,
0.02308489754796028,
0.02781047858297825,
-0.004066160414367914,
-0.013706358149647713,
0.026362203061580658,
0.0011492099147289991,
0.0034051858820021152,
-0.03384634479880333,
0.006954084150493145,
-0.01902647502720356,
-0.012919403612613678,
-0.005337533075362444,
0.05596000328660011,
0.014222826808691025,
-0.014594844542443752,
-0.010508193634450436,
0.03635195642709732,
-0.02174680307507515,
-0.01970848999917507,
0.028954755514860153,
0.0011052348418161273,
0.025938039645552635,
0.002102442318573594,
-0.029679490253329277,
-0.006143077276647091,
0.013510674238204956,
-0.009737913496792316,
0.030786922201514244,
0.01655777543783188,
-0.0002907699963543564,
0.00551907904446125,
-0.02694479562342167,
0.04972604662179947,
-0.023268025368452072,
-0.027510246261954308,
-0.00529479468241334,
-0.016276273876428604,
-0.037595655769109726,
-0.011709790676832199,
0.0032518915832042694,
0.020969942212104797,
0.02120370976626873,
0.01844732090830803,
-0.007587265223264694,
-0.03701033815741539,
-0.0538448765873909,
0.01704486832022667,
-0.02621300332248211,
-0.029113488271832466,
-0.0037463349290192127,
0.018984654918313026,
0.01804310269653797,
0.032508134841918945,
0.01548054814338684,
-0.011031151749193668,
0.004012304823845625,
-0.01707320287823677,
-0.009253762662410736,
-0.03524654731154442,
-0.006480433978140354,
0.010440466925501823,
-0.021109556779265404,
-0.024929460138082504,
0.009709016419947147,
0.019058363512158394,
0.002886551897972822,
-0.0032026360277086496,
0.007021829020231962,
0.017993319779634476,
-0.03841075673699379,
-0.00568043440580368,
0.01904727891087532,
-0.019184643402695656,
0.021517202258110046,
-0.018934840336441994,
0.015250924974679947,
-0.03336586803197861,
-0.0123177170753479,
-0.036843299865722656,
-0.018262533470988274,
-0.0002928727481048554,
0.02902824617922306,
0.0006461045704782009,
0.026051897555589676,
0.024536997079849243,
-0.012865414842963219,
-0.03244202956557274,
-0.007355263456702232,
-0.030245419591665268,
-0.02772572822868824,
0.007586881052702665,
-0.008793380111455917,
0.02728320099413395,
0.020507853478193283,
-0.01442059874534607,
-0.0358550138771534,
0.03583289310336113,
0.01856067031621933,
-0.01316319964826107,
0.01227134745568037,
0.03366178274154663,
-0.005382239818572998,
0.055231861770153046,
0.017045825719833374,
-0.031006433069705963,
0.0294650811702013,
-0.04464906081557274,
-0.034878622740507126,
0.059398967772722244,
-0.005289657041430473,
0.018517080694437027,
0.027911139652132988,
-0.033349089324474335,
0.0004886156530119479,
0.06057985499501228,
0.0074982596561312675,
0.010671673342585564,
0.02253597043454647,
0.010012897662818432,
-0.018972601741552353,
-0.004931419622153044,
0.02652834542095661,
-0.007876215502619743,
0.0504874587059021,
0.03246918320655823,
0.0024110397789627314,
-0.015077093616127968,
0.007130318786948919,
0.005194205325096846,
-0.05341791361570358,
-0.010567130520939827,
-0.005361116956919432,
-0.012793373316526413,
0.026457592844963074,
0.03518959879875183,
-0.07128999382257462,
-0.011272306554019451,
0.0011490143369883299,
0.05716738849878311,
-0.10674763470888138,
-0.011454688385128975,
-0.02025361731648445,
-0.0071275494992733,
0.043068092316389084,
-0.07061237096786499,
0.05297679454088211,
-0.010720730759203434,
-0.029760563746094704,
0.005669659469276667,
-0.016108300536870956,
-0.0005266512162052095,
-0.01926453225314617,
0.014740551821887493,
-0.02335810288786888,
0.04142599180340767,
0.009625393897294998,
0.03321029618382454,
0.01752469316124916,
0.013052602298557758,
0.0033271980937570333,
-0.021212710067629814,
0.005458079744130373,
0.011347516439855099,
0.011066139675676823,
-0.02339119277894497,
0.056134529411792755,
-0.007618062663823366,
-0.01940915919840336,
0.013238772749900818,
-0.02519860677421093,
0.006571976467967033,
-0.004308332689106464,
0.010032317601144314,
-0.0009716720087453723,
0.021710053086280823,
0.024336058646440506,
-0.042877763509750366,
-0.010069034993648529,
-0.0031203508842736483,
-0.008455288596451283,
-0.004300667438656092,
-0.011393492110073566,
0.019039807841181755,
0.03040977381169796,
-0.04553154110908508,
-0.036839842796325684,
0.03705960139632225,
-0.015560053288936615,
0.018125619739294052,
-0.01406499557197094,
-0.03535046800971031,
0.02860364131629467,
-0.06403645873069763,
0.03015458770096302,
-0.04953137785196304,
0.005763554945588112,
0.03936086967587471,
-0.02892586775124073,
-0.00949480477720499,
-0.020753148943185806,
0.012908636592328548,
-0.004665125627070665,
0.011642644181847572,
-0.01780475117266178,
-0.04603850096464157,
-0.03774605691432953,
0.012012453749775887,
-0.019375810399651527,
0.01548064686357975,
-0.004726117476820946,
-0.018145237118005753,
-0.022778473794460297,
0.03856434300541878,
-0.007876879535615444,
0.0033365334384143353,
-0.02130817249417305,
-0.02221238985657692,
-0.030043447390198708,
-0.07143472135066986,
0.005553626921027899,
0.030557982623577118,
0.00028466625371947885,
0.007750974036753178,
-0.0006448346539400518,
0.007239579223096371,
-0.003159433603286743,
0.02392253279685974,
0.006115172058343887,
-0.015966132283210754,
0.020064454525709152,
-0.00943722389638424,
0.006197469774633646,
-0.04356074333190918,
0.01194384042173624,
-0.01327485404908657,
-0.03273341432213783,
-0.014125639572739601,
0.000056650318583706394,
0.008665330708026886,
0.018012017011642456,
0.02361435443162918,
0.022329557687044144,
-0.022625906392931938,
-0.029407018795609474,
-0.019265618175268173,
0.04488673433661461,
-0.013160410337150097,
0.011079247109591961,
0.08157290518283844,
0.007370627950876951,
-0.021329322829842567,
0.04733093082904816,
0.015096153132617474,
-0.019398123025894165,
0.05389579385519028,
-0.0009599475306458771,
-0.004841262940317392,
0.008814781904220581,
0.017314231023192406,
0.019243557006120682,
-0.055133968591690063,
-0.03619534149765968,
0.043737996369600296,
-0.03909633308649063,
-0.027369707822799683,
0.008939896710216999,
-0.00040686337160877883,
-0.017169654369354248,
0.030099408701062202,
0.008969433605670929,
0.007234754506498575,
0.007812924683094025,
-0.018474962562322617,
0.031475555151700974,
0.04253290593624115,
0.026908334344625473,
0.0058295633643865585,
0.02928229793906212,
-0.018634648993611336,
0.008020672015845776,
0.0014609028585255146,
0.018451696261763573,
-0.039835814386606216,
-0.032326217740774155,
0.01262109074741602,
-0.003628139616921544,
-0.019605115056037903,
0.030943937599658966,
-0.007993878796696663,
0.05769035592675209,
-0.010139751248061657,
-0.02780775912106037,
-0.015165543183684349,
-0.03353119641542435,
-0.004865327849984169,
0.04116686061024666,
0.02440621890127659,
0.09167023748159409,
-0.002119086217135191,
0.021857040002942085,
0.012404588051140308,
-0.012191761285066605,
0.008443700149655342,
-0.07158961892127991,
-0.007734739221632481,
0.011632909998297691,
0.006955187767744064,
0.010620379820466042,
-0.007864682003855705,
-0.046251870691776276,
-0.017983628436923027,
-0.009987340308725834,
-0.002577245468273759,
0.036117397248744965,
0.0035663419403135777,
-0.04326184466481209,
-0.032284945249557495,
0.019566183909773827,
-0.06120511144399643,
-0.025974778458476067,
-0.010458049364387989,
-0.010465814732015133,
-0.012376825325191021,
-0.00277036614716053
] |
<p>We have 12 different 'notes' per octave on a musical keyboard. They are set up so that every 'note' (A, B,C etc) is a second harmonic of the same 'note' in the next higher octave. With this ratio in place, it seems that everything on a keyboard should be divided up into equal groups of 2,3,4 or 6. However, the keyboard seems to be divided up into groups of 5 and 7 (one group of 2 black & 3 white keys, and another group of 3 black & 4 white keys). This does not make much sense to me. However, when I play scales, the layout is very helpful. I'm guessing that the design of the scale is related to physics and therefor the layout of the keys must be too. What is the connection between physics, scales and the layout of the piano keyboard?</p>
| 8,286 |
[
-0.026159530505537987,
-0.015862954780459404,
-0.024699075147509575,
-0.030621064826846123,
0.019993498921394348,
0.004488019272685051,
0.0036665501538664103,
-0.00026655776309780777,
0.0014655513223260641,
-0.025287099182605743,
-0.0111873559653759,
-0.00009904982289299369,
0.033184394240379333,
0.005674744490534067,
0.02540256641805172,
-0.012511947192251682,
0.0012197309406474233,
-0.006393738556653261,
-0.005558256059885025,
-0.002798745408654213,
-0.020228732377290726,
0.009579433128237724,
-0.011462274938821793,
-0.006774602923542261,
-0.014250658452510834,
0.021069157868623734,
0.01836583949625492,
-0.0021215237211436033,
0.051581550389528275,
0.00882205180823803,
0.06216040998697281,
-0.008389915339648724,
0.028190046548843384,
0.02701019123196602,
0.0456046387553215,
0.007356394547969103,
0.009242454543709755,
-0.02502361871302128,
-0.0471612885594368,
0.0242211502045393,
-0.07370050996541977,
0.008014766499400139,
-0.02879473567008972,
-0.010805148631334305,
-0.021332385018467903,
0.00622204877436161,
0.011184778064489365,
-0.02493405155837536,
0.023650947958230972,
-0.06980931758880615,
0.11986595392227173,
0.025276286527514458,
0.022328386083245277,
0.05229376256465912,
-0.006073829717934132,
0.02048517018556595,
0.07346945255994797,
0.09029151499271393,
-0.018742583692073822,
-0.06418890506029129,
-0.028306473046541214,
-0.028179841116070747,
-0.003177845850586891,
0.020433468744158745,
-0.003966827876865864,
0.04762287065386772,
-0.04745747894048691,
0.009820831008255482,
0.013508275151252747,
0.02577982097864151,
0.00515738083049655,
0.04886981099843979,
0.0686669871211052,
-0.05823855847120285,
-0.0010164061095565557,
-0.040732886642217636,
0.05065765231847763,
0.004112048074603081,
0.012039266526699066,
-0.0034832884557545185,
-0.01760331727564335,
0.010643860325217247,
-0.0002460372634232044,
0.04872000217437744,
-0.002803943119943142,
-0.02412523329257965,
0.05149262771010399,
-0.05366044491529465,
0.019196823239326477,
0.04900074377655983,
0.016668958589434624,
0.021968219429254532,
0.04830961674451828,
-0.02169509418308735,
-0.026661274954676628,
0.02768668718636036,
-0.011796247214078903,
0.004186312202364206,
0.01351088285446167,
-0.004656197968870401,
0.05514680966734886,
-0.0018954547122120857,
-0.008988422341644764,
0.07558555155992508,
0.01657944917678833,
-0.011765203438699245,
-0.052648112177848816,
0.036442287266254425,
0.004773544147610664,
0.025354811921715736,
0.00007661199197173119,
-0.02399185672402382,
0.018365507945418358,
0.023352351039648056,
0.02020876854658127,
-0.009197760373353958,
-0.0011349708074703813,
-0.004591022152453661,
0.04673055186867714,
0.06282699853181839,
0.023889709264039993,
-0.05179378762841225,
0.02455892600119114,
0.02005206048488617,
-0.03366507217288017,
0.008760890923440456,
-0.004514291416853666,
-0.02758469060063362,
-0.029186921194195747,
0.017219513654708862,
0.017404286190867424,
0.001485257176682353,
0.0140653345733881,
0.014355530962347984,
0.012409578077495098,
-0.030408822000026703,
-0.08849244564771652,
-0.04110657796263695,
0.04768206179141998,
0.015399100258946419,
-0.04697069525718689,
-0.06603186577558517,
0.022704213857650757,
0.04253728315234184,
0.0832744613289833,
0.025250397622585297,
0.0025273500941693783,
-0.0015589726390317082,
0.04105519875884056,
0.017629388719797134,
-0.02226799540221691,
-0.001454634009860456,
-0.036984365433454514,
-0.05374660715460777,
0.040746916085481644,
-0.01817587949335575,
0.009610616602003574,
0.02367771416902542,
0.012358486652374268,
-0.04801897704601288,
0.016482628881931305,
-0.028564026579260826,
-0.03839874267578125,
-0.0064225029200315475,
-0.006430142093449831,
-0.01315456721931696,
0.02757127210497856,
-0.010959310457110405,
-0.00463124318048358,
0.03405960649251938,
0.014401395805180073,
0.0026968074962496758,
0.0010690954513847828,
0.030855996534228325,
0.028657883405685425,
-0.0004293608944863081,
0.005451188422739506,
-0.03187861666083336,
0.027385050430893898,
-0.011115058325231075,
-0.03963024914264679,
-0.04902220517396927,
0.0016390024684369564,
0.014020081609487534,
0.0061787632293999195,
0.02578910067677498,
-0.009031097404658794,
0.0014942296547815204,
0.010122420266270638,
-0.027146678417921066,
-0.022968195378780365,
-0.07044048607349396,
0.03040180541574955,
-0.016558827832341194,
-0.005804662127047777,
0.06297997385263443,
0.00912601500749588,
0.036743491888046265,
0.024355780333280563,
0.0271990355104208,
-0.007634230889379978,
0.015262873843312263,
0.005543864332139492,
-0.031178433448076248,
0.0222157035022974,
0.06581064313650131,
-0.007272729650139809,
0.02732875943183899,
0.05869309976696968,
-0.015198617242276669,
-0.03843305632472038,
0.03148806840181351,
-0.009546737186610699,
0.03417499363422394,
-0.02178208716213703,
0.017326824367046356,
-0.01176108792424202,
0.019661135971546173,
-0.010185244493186474,
0.05151676386594772,
-0.020836710929870605,
0.08285534381866455,
0.03291665017604828,
-0.031477686017751694,
0.01953204907476902,
0.023213697597384453,
-0.018009651452302933,
0.009974834509193897,
0.00975284818559885,
-0.06083592772483826,
-0.06179116293787956,
0.007550250738859177,
0.038148634135723114,
0.029560990631580353,
-0.026538725942373276,
0.020072996616363525,
0.029813289642333984,
0.053594090044498444,
0.025965988636016846,
0.014602920971810818,
-0.03334523364901543,
-0.02613605558872223,
0.003854174865409732,
0.010193019174039364,
0.06479161977767944,
0.015625692903995514,
0.014937752857804298,
0.01785667985677719,
-0.015604887157678604,
-0.0357513353228569,
-0.0004810199898201972,
0.014347760006785393,
0.025574594736099243,
0.027883529663085938,
-0.008089818991720676,
0.002205746481195092,
0.028192847967147827,
-0.024536119773983955,
0.02300049364566803,
0.013591745868325233,
0.0011394150787964463,
-0.014135883189737797,
-0.00275988201610744,
-0.03967365622520447,
0.004533060826361179,
0.013171166181564331,
-0.026554005220532417,
-0.012964018620550632,
0.019913336262106895,
-0.04766096547245979,
0.006067275069653988,
-0.014720169827342033,
0.017604855820536613,
0.006647967267781496,
0.004912077449262142,
0.014619676396250725,
0.0014677183935418725,
0.06234382465481758,
-0.04060309752821922,
-0.00983614195138216,
0.022843657061457634,
-0.029933089390397072,
0.029317732900381088,
-0.01964687928557396,
-0.060866471379995346,
-0.011033499613404274,
-0.03785267844796181,
-0.01433481927961111,
0.04165530577301979,
-0.012585106305778027,
0.032445572316646576,
-0.022539401426911354,
0.0004621969419531524,
-0.04894689470529556,
-0.011580408550798893,
-0.037923894822597504,
0.023710304871201515,
0.011426580138504505,
-0.0155100729316473,
0.03292244300246239,
0.008269178681075573,
-0.01769350841641426,
0.02877373807132244,
-0.03881898522377014,
-0.014669101685285568,
-0.005356906447559595,
0.01565544866025448,
-0.03159491717815399,
-0.021278243511915207,
-0.005964085925370455,
0.016453517600893974,
-0.03258117288351059,
-0.046006541699171066,
-0.01955711655318737,
-0.02974109910428524,
0.0018287640996277332,
-0.00526219978928566,
0.07149071991443634,
0.017821133136749268,
0.004066884983330965,
0.09467672556638718,
0.030909011140465736,
-0.0315638966858387,
-0.031112834811210632,
0.018315188586711884,
0.020324939861893654,
-0.0390247106552124,
0.03135538846254349,
0.08010800927877426,
0.008653112687170506,
0.040442515164613724,
0.02241399511694908,
0.0533372238278389,
0.06038178130984306,
-0.054538458585739136,
-0.039798203855752945,
0.02115148864686489,
-0.011425086297094822,
-0.0243405532091856,
0.03365344554185867,
-0.004210673272609711,
-0.005277426913380623,
0.004792401567101479,
-0.008801783435046673,
0.006180909927934408,
0.009009508416056633,
-0.038768965750932693,
0.028428955003619194,
-0.00023784066434018314,
0.01748403161764145,
-0.04613722860813141,
-0.0030362012330442667,
0.007336460053920746,
-0.02267303317785263,
0.0176955908536911,
0.029960008338093758,
0.04466941952705383,
-0.03152357041835785,
-0.003093066858127713,
0.031192505732178688,
0.00792523380368948,
-0.023148352280259132,
-0.025714382529258728,
-0.003043730743229389,
0.01878119632601738,
0.025910424068570137,
-0.0027834270149469376,
-0.02704504132270813,
0.017206329852342606,
0.00808339286595583,
0.04509073123335838,
-0.024643508717417717,
-0.0356815829873085,
0.015946069732308388,
-0.046286795288324356,
-0.03269631043076515,
-0.015192276798188686,
0.03390158340334892,
0.0003770124458242208,
0.027838610112667084,
0.010832753032445908,
0.03353828564286232,
-0.004383035469800234,
0.012402140535414219,
-0.104780413210392,
0.004352369345724583,
-0.038082439452409744,
0.00990199949592352,
-0.02776404842734337,
0.012664579786360264,
-0.013077897019684315,
-0.04637538641691208,
-0.045522540807724,
-0.027675790712237358,
-0.007839987985789776,
-0.03874882683157921,
0.0039047410245984793,
-0.023236025124788284,
-0.026013582944869995,
0.0029581699054688215,
0.009624131955206394,
-0.015557988546788692,
-0.026324797421693802,
0.025331510230898857,
0.03223733976483345,
0.009431707672774792,
-0.02098194509744644,
0.014631028287112713,
0.03773265331983566,
-0.03621058538556099,
0.010814615525305271,
0.024152053520083427,
0.055835917592048645,
-0.0028564392123371363,
-0.028519906103610992,
-0.015882384032011032,
0.03903468698263168,
-0.020305249840021133,
-0.014024104923009872,
0.03188324719667435,
-0.027157390490174294,
0.012631012126803398,
-0.0033196888398379087,
0.013267074711620808,
0.0024673298466950655,
0.002988695167005062,
0.03710844740271568,
0.0042813499458134174,
-0.020920543000102043,
0.030755864456295967,
0.0443427637219429,
-0.008792057633399963,
-0.05804871395230293,
-0.06262987852096558,
-0.043370481580495834,
-0.04708101227879524,
-0.0128075135871768,
0.011852581053972244,
0.006517443805932999,
0.025726746767759323,
0.06376320123672485,
0.03733351454138756,
-0.027885358780622482,
-0.029839282855391502,
0.02614004723727703,
-0.020147960633039474,
0.028734855353832245,
-0.016661757603287697,
0.009781267493963242,
0.006521314848214388,
0.024211706593632698,
0.048742156475782394,
0.0017404702957719564,
-0.05395073443651199,
-0.06770524382591248,
-0.00648622028529644,
-0.021243548020720482,
-0.00292336312122643,
-0.022220918908715248,
0.028631996363401413,
-0.024756191298365593,
-0.0475437231361866,
0.026688868179917336,
-0.023627839982509613,
0.04675634950399399,
-0.02126966416835785,
0.021061556413769722,
-0.07058174908161163,
0.009835285134613514,
0.019579585641622543,
0.013808140531182289,
0.002458045491948724,
0.024134838953614235,
-0.01588008925318718,
0.004511588253080845,
-0.06124809384346008,
0.04479445517063141,
0.029322773218154907,
0.017262691631913185,
-0.017782580107450485,
-0.00453796936199069,
-0.013792745769023895,
-0.0013995139161124825,
-0.0500023253262043,
-0.05004182085394859,
0.024153204634785652,
-0.004530488979071379,
0.002528047887608409,
0.04818595200777054,
-0.03421015292406082,
-0.03906294330954552,
0.019454242661595345,
0.0442759208381176,
0.06232419237494469,
0.02825496904551983,
0.01610695943236351,
0.059634510427713394,
0.025627771392464638,
0.015101518481969833,
-0.0011807653354480863,
0.04455149546265602,
-0.04631685093045235,
-0.024275915697216988,
-0.007809983566403389,
0.026653746142983437,
-0.04149245843291283,
0.004370816517621279,
-0.0008710763067938387,
-0.013789379969239235,
-0.0625658854842186,
0.066643126308918,
-0.018627136945724487,
0.061659086495637894,
-0.04509039595723152,
-0.09271621704101562,
-0.04453258961439133,
-0.001657741260714829,
0.01672726310789585,
-0.0010038865730166435,
0.057928141206502914,
0.055181581526994705,
0.004496342968195677,
-0.0117682795971632,
0.009857220575213432,
-0.0155543964356184,
0.006971965078264475,
0.017261704429984093,
-0.010889649391174316,
-0.0009820424020290375,
-0.02968670055270195,
-0.024246875196695328,
0.018658172339200974,
-0.04460969939827919,
0.04282240569591522,
-0.028892114758491516,
-0.011505323462188244,
0.049426548182964325,
-0.0778244361281395,
-0.03979271277785301,
0.016972040757536888,
-0.006064283195883036,
0.032985590398311615,
-0.028098415583372116,
0.03570970520377159,
0.027396338060498238,
0.019011039286851883,
-0.08059666305780411,
-0.03476235270500183,
0.009409255348145962,
0.02571602538228035,
0.015561198815703392,
-0.003057332243770361,
0.029334278777241707,
-0.033739443868398666,
-0.04822159558534622,
0.02674172632396221,
0.014122100546956062,
-0.019427990540862083,
-0.019683947786688805,
-0.010347764939069748,
-0.01294566411525011,
0.03531937301158905,
0.0011698411544784904,
-0.014055920764803886,
-0.0038030939176678658,
-0.011253589764237404,
0.03195091709494591,
-0.030371367931365967,
0.04991314560174942,
-0.05058996006846428,
0.01985190436244011,
0.010192018933594227,
0.0008197840652428567,
0.05208256095647812,
-0.0058509050868451595,
0.005652775522321463,
-0.011188642121851444,
0.035091500729322433,
0.012391811236739159,
-0.03331337869167328,
0.012598825618624687,
0.00825544074177742,
0.022019265219569206,
-0.009836319833993912,
-0.02949698641896248,
-0.01280858926475048,
-0.0349176824092865,
0.011884803883731365,
0.0001227060129167512,
-0.013772115111351013,
0.041537538170814514,
0.06517846882343292,
0.026982324197888374,
-0.00788967590779066,
0.017976628616452217,
-0.04446076229214668,
-0.0005446369759738445,
0.019168879836797714,
0.009081141091883183,
-0.016482168808579445,
0.02864072658121586,
-0.01603589579463005,
-0.02332427352666855,
-0.019334513694047928,
-0.005272677168250084,
0.05374656245112419,
-0.023568788543343544,
0.03993677720427513,
0.02981651946902275,
-0.035994548350572586,
-0.019875217229127884,
0.013509136624634266,
-0.024497218430042267,
-0.024330107495188713,
-0.003519524121657014,
0.06270379573106766,
-0.06903816014528275,
-0.012578303925693035,
0.020005641505122185,
0.048101358115673065,
0.0038539923261851072,
0.049434270709753036,
0.05944839492440224,
0.03672211617231369,
0.0009423649171367288,
-0.011318273842334747,
-0.05811706930398941,
0.05206301435828209,
-0.04236627370119095,
0.05004655197262764,
0.012531046755611897,
0.008669125847518444,
0.014429787173867226,
0.032191839069128036,
-0.05989496037364006,
-0.07787004113197327,
-0.018882159143686295,
0.0068419617600739,
0.009343328885734081,
0.027002496644854546,
0.007362194359302521,
-0.00282603083178401,
-0.022757617756724358,
0.026475509628653526,
0.005244225263595581,
-0.026855535805225372,
0.011551921255886555,
-0.0735333189368248,
-0.028140217065811157,
-0.06087652966380119,
-0.053726937621831894,
0.035431452095508575,
-0.013928618282079697,
-0.038277193903923035,
-0.0014140489511191845,
-0.021153686568140984,
0.02496541477739811,
0.002909551141783595,
0.023344410583376884,
-0.023511381819844246,
0.060492273420095444,
0.01733357273042202,
0.0068649351596832275,
-0.016837161034345627,
-0.022556930780410767,
0.1291036456823349,
0.05114147067070007,
0.0010794872650876641,
-0.014206756837666035,
0.02652718313038349,
0.007950141094624996,
-0.011617820709943771,
-0.010243069380521774,
0.02853437513113022,
-0.01140142697840929,
0.040250152349472046,
-0.02233164757490158,
0.11124769598245621,
0.024806221947073936,
0.025779932737350464,
0.08088963478803635,
-0.014220882207155228,
-0.01618548482656479,
0.002296863589435816,
0.022086359560489655,
0.019062994047999382,
0.020103588700294495,
-0.037999965250492096,
-0.006463118363171816,
-0.028178879991173744,
-0.005106640048325062,
-0.025187071412801743,
-0.045533474534749985,
0.04539638012647629,
0.035905759781599045,
-0.002321732696145773,
0.041570354253053665,
0.0005273357965052128,
-0.00988234393298626,
-0.041067153215408325,
0.005593784153461456,
0.006632501725107431,
-0.016928870230913162,
0.010254060849547386,
0.021652759984135628,
-0.004361901432275772,
0.007223428692668676,
0.014008495025336742,
-0.018181774765253067,
-0.053578343242406845,
-0.019308142364025116,
-0.03200163319706917,
0.011738992296159267,
0.0017812299774959683,
-0.033652812242507935,
-0.010540132410824299,
0.00878207292407751,
-0.01267791073769331,
-0.06133949011564255,
-0.03935421258211136,
-0.02265133708715439,
0.024358289316296577,
-0.03799028694629669,
-0.020310446619987488,
0.0014973606448620558,
0.014099158346652985,
0.0032347540836781263,
-0.005276199895888567,
0.014812974259257317,
0.0004645444278139621,
0.015827178955078125,
-0.010799175128340721,
0.028379257768392563,
-0.004108304623514414,
-0.005211723502725363,
0.01981249265372753,
0.016027117148041725,
-0.07048288732767105,
-0.03363217040896416,
-0.017362741753458977,
0.057613953948020935,
0.01853482984006405,
0.034318093210458755,
-0.006865766830742359,
-0.0018443557200953364,
-0.03934455290436745,
0.048216596245765686,
-0.004969918634742498,
-0.028753409162163734,
0.009767154231667519,
-0.01937773823738098,
0.035845935344696045,
0.02720646746456623,
-0.03317157179117203,
0.021467985585331917,
-0.008220254443585873,
-0.025079544633626938,
-0.008917584083974361,
-0.01966344565153122,
0.02159709483385086,
0.028396697714924812,
-0.016027256846427917,
0.018147379159927368,
0.01609531044960022,
0.05238765478134155,
-0.01010246854275465,
0.00475551700219512,
0.02953646332025528,
0.039275798946619034,
-0.01500440202653408,
0.010967898182570934,
0.01770431362092495,
-0.07645255327224731,
-0.023214468732476234,
0.016528068110346794,
-0.0024661615025252104,
-0.06902231276035309,
-0.08887159079313278,
-0.02951204590499401,
-0.038131117820739746,
-0.018697870895266533,
0.00012064049224136397,
-0.01756930537521839,
-0.010470960289239883,
-0.007369807455688715,
-0.0006080333259887993,
-0.03291352093219757,
0.006206279154866934,
-0.008027839474380016,
0.02964961715042591,
-0.006675162818282843,
-0.03313342481851578,
-0.028520608320832253,
0.03896498307585716,
-0.036797888576984406,
-0.0185093991458416,
-0.0005496933008544147,
0.008654005825519562,
0.03577418997883797,
-0.006852198392152786,
0.014746217057108879,
-0.020729022100567818,
0.04796278849244118,
-0.041330400854349136,
-0.021367285400629044,
0.02433166466653347,
-0.06688196212053299,
-0.054363444447517395,
0.05851168558001518,
-0.014010298997163773,
0.002769344486296177,
0.02137536182999611,
0.030819332227110863,
0.016852669417858124,
0.03332209214568138,
-0.03603101894259453,
-0.009265068918466568,
-0.0023476078640669584,
-0.005695665255188942,
-0.00047245080349966884,
-0.02395067922770977,
0.008127960376441479,
-0.05109289661049843,
-0.014711675234138966,
0.034169070422649384,
0.02747539058327675,
0.008787475526332855,
-0.037138503044843674,
0.016143325716257095,
-0.022626399993896484,
0.03702550381422043,
-0.007949785329401493,
0.037326015532016754,
0.004910911899060011,
0.004759898409247398,
-0.05442306399345398,
0.04221678152680397,
0.025754088535904884,
-0.012339829467236996,
-0.018351776525378227,
-0.020623305812478065,
-0.0008597863488830626,
-0.00800069235265255,
0.03611753508448601,
-0.02659129537642002,
0.0021796098444610834,
-0.0021764503326267004,
-0.08104711025953293,
0.008605357259511948,
-0.04965982213616371,
-0.022163931280374527,
-0.03798982501029968,
-0.021074099466204643,
-0.0018155775032937527,
0.017480479553341866,
0.03704908862709999,
0.03887692466378212,
0.026191461831331253,
-0.006722192279994488,
-0.026760805398225784,
-0.027865365147590637,
-0.009613494388759136,
0.019968176260590553,
-0.014224888756871223,
-0.001553943264298141,
0.037773001939058304,
-0.0002441607357468456,
-0.040184322744607925,
0.035608816891908646,
-0.016803180798888206,
-0.010163925588130951,
-0.003651477862149477,
-0.008219284005463123,
-0.019360987469553947,
0.02990269474685192,
0.0037422531750053167,
0.003705258946865797,
-0.016029948368668556,
0.007054521236568689,
0.023046236485242844,
0.027986183762550354,
0.03681102395057678,
0.024837931618094444,
0.03831600025296211,
-0.05045009031891823,
-0.013821104541420937,
-0.008293244987726212,
-0.02221619337797165,
-0.0011858218349516392,
0.0014618475688621402,
0.021011468023061752,
0.025202620774507523,
-0.04641512781381607,
0.005145493429154158,
-0.011465009301900864,
-0.04636286199092865,
0.010334587655961514,
0.014840777963399887,
0.008347097784280777,
0.025418534874916077,
0.023860357701778412,
0.008797707036137581,
-0.035762619227170944,
0.04968060925602913,
0.045333605259656906,
-0.02179531380534172,
-0.0065813628025352955,
0.01997154951095581,
-0.018125735223293304,
0.007092000916600227,
-0.003323520766571164,
0.022389639168977737,
0.0353570319712162,
0.002384766936302185,
0.02718946523964405,
-0.041996389627456665,
-0.03280027583241463,
0.0017494026105850935,
-0.03295420482754707,
0.01985313557088375,
0.047725435346364975,
-0.016001462936401367,
-0.04080314561724663,
0.013064105994999409,
-0.03515337035059929,
0.027980156242847443,
0.027650687843561172,
0.011126461438834667,
-0.0024652753490954638,
-0.021411053836345673,
-0.01894461363554001,
0.06975390017032623,
-0.04540412127971649,
-0.018902674317359924,
-0.008329515345394611,
-0.03603070601820946,
0.0008977159159258008,
-0.024161122739315033,
-0.025775834918022156,
-0.006715946365147829,
0.021419759839773178,
-0.008256091736257076,
0.02372126840054989,
-0.00952762458473444,
-0.012089907191693783,
0.015103206038475037,
0.033749230206012726,
-0.016308395192027092,
0.06686628609895706,
-0.03322900831699371,
-0.0012729302980005741,
0.008822253905236721,
-0.03296871483325958,
-0.05700252950191498,
0.0490185022354126,
-0.06854307651519775,
0.003838972421362996,
-0.018323864787817,
0.00008123910083668306,
0.05081796273589134,
-0.026081128045916557,
0.0021027964539825916,
0.032223813235759735,
-0.01258873287588358,
-0.028278976678848267,
0.030417677015066147,
0.011939906515181065,
0.0166582390666008,
0.013989660888910294,
-0.020302027463912964,
0.019186493009328842,
-0.010403800755739212,
-0.0062469979748129845,
0.012603823095560074,
0.051613111048936844,
0.011335211805999279,
-0.040761448442935944,
0.023417724296450615,
-0.03811779245734215,
0.038729261606931686,
0.0350009985268116,
0.03289354220032692,
-0.03550334647297859,
-0.025008417665958405,
0.017232026904821396,
-0.020548099651932716,
-0.011282384395599365,
0.03734912723302841,
-0.001491367002017796,
0.07695462554693222,
-0.014361660927534103,
-0.0036314656026661396,
-0.03461701050400734,
0.002620234852656722,
-0.009931858628988266,
-0.00972349476069212,
-0.005821213126182556,
0.03308054432272911,
-0.050881654024124146,
-0.005422163289040327,
-0.05580808222293854,
0.021111810579895973,
0.025470152497291565,
-0.05130824074149132,
0.021593520417809486,
0.015452522784471512,
-0.009307322092354298,
0.034075114876031876,
0.009151156060397625,
-0.052100762724876404,
-0.027475371956825256,
0.08132414519786835,
0.019795920699834824,
0.014325925149023533,
-0.005255468189716339,
-0.03246800974011421,
-0.007056398782879114,
0.026722926646471024,
-0.040582988411188126,
-0.022326283156871796,
-0.0033264178782701492,
0.007765247952193022,
0.006615626625716686,
0.01933315023779869
] |
<p>While travelling in the train on the sunset, I have noticed the strange phenomenon. The shadows of the lonely trees and lampposts, that stay along the railroad, are moving on the wall in the same direction as the train. I tried my artist talents to express the situation as a picture:</p>
<p><img src="http://i.stack.imgur.com/ua8gY.png" alt="descriptive picture"></p>
<p>As far as I understand, the shadows should move in an opposite direction.</p>
<h2>Update #1</h2>
<p>I have found the evidence video - and converted it into an animated gif:</p>
<p><img src="http://i.stack.imgur.com/zQFqg.gif" alt="animated gif"></p>
<p>The shadow runs on the left wall - from the the camera point of view. So, from the man's point of view, the shadow moves in the direction of the train, if it's observed on the wall behind the camera.</p>
| 8,287 |
[
-0.02343394234776497,
-0.08787953108549118,
-0.022664546966552734,
0.0011050773318856955,
0.033297162503004074,
0.018181106075644493,
-0.0039775012992322445,
-0.003227977314963937,
-0.03874248266220093,
-0.007106690667569637,
0.02933516725897789,
0.04149623587727547,
0.042714305222034454,
0.08569394797086716,
0.04273311421275139,
-0.01700144074857235,
0.014661413617432117,
0.02074372209608555,
-0.024411384016275406,
-0.0510750412940979,
-0.008917995728552341,
0.01934443600475788,
0.012579894624650478,
0.006231819745153189,
0.006863286718726158,
-0.005692074075341225,
0.036657340824604034,
0.008422518149018288,
0.014082943089306355,
0.03458092361688614,
-0.054283272475004196,
-0.0025997632183134556,
-0.011995408684015274,
0.033957477658987045,
0.026726139709353447,
-0.01575290597975254,
-0.016582971438765526,
0.0020817925687879324,
-0.009405393153429031,
-0.0030735007021576166,
0.031992897391319275,
-0.01231558807194233,
-0.000736542628146708,
0.06498311460018158,
-0.04457114636898041,
0.008017042651772499,
0.013489232398569584,
-0.008983313106000423,
0.045548371970653534,
-0.06593233346939087,
0.07648415863513947,
-0.013304000720381737,
0.004952196031808853,
-0.010190700180828571,
0.013493950478732586,
-0.014901606366038322,
0.02237371914088726,
0.06217854470014572,
-0.003915075212717056,
-0.01633046753704548,
-0.02332429029047489,
-0.030956698581576347,
-0.03542085364460945,
0.03637906536459923,
-0.042086709290742874,
-0.002607224276289344,
0.009055810049176216,
-0.02375696413218975,
0.044487472623586655,
-0.01543246116489172,
-0.024001380428671837,
-0.024707380682229996,
0.05531352385878563,
-0.011944708414375782,
0.01779492013156414,
-0.05708072707056999,
0.04315848648548126,
0.0643998384475708,
0.020761117339134216,
-0.0006991839618422091,
0.02778802067041397,
-0.01322942040860653,
0.014818879775702953,
0.014918103814125061,
0.01764182560145855,
-0.023178111761808395,
0.10394486784934998,
-0.005543149076402187,
0.006106520537286997,
0.03199674189090729,
0.00816634763032198,
0.021317997947335243,
0.032359570264816284,
0.02646847441792488,
-0.0065165371634066105,
-0.011559666134417057,
0.006604716647416353,
0.057383663952350616,
0.024180201813578606,
-0.006011162884533405,
-0.0022837414871901274,
-0.0056761824525892735,
0.03965209051966667,
0.061883311718702316,
-0.0076614138670265675,
0.02696838788688183,
-0.006796517409384251,
0.028031358495354652,
0.01838448829948902,
0.003235823707655072,
-0.05736277624964714,
0.010365759953856468,
0.05812295153737068,
0.020006414502859116,
0.003802026156336069,
-0.008098668418824673,
0.007759917061775923,
-0.014102879911661148,
0.019385499879717827,
0.061388589441776276,
0.04361403360962868,
-0.03594284877181053,
0.040122244507074356,
-0.06239733844995499,
-0.05746592953801155,
0.016047082841396332,
0.03321028873324394,
-0.047890059649944305,
-0.03075450286269188,
0.04986311122775078,
0.06258628517389297,
-0.015893667936325073,
0.0006547687808051705,
-0.013550451956689358,
0.05050501599907875,
0.009835781529545784,
-0.11659733951091766,
-0.05503208562731743,
0.036693274974823,
-0.00452512688934803,
0.035683587193489075,
-0.09240753948688507,
-0.005676128901541233,
0.02635769732296467,
0.060078129172325134,
-0.013522980734705925,
0.016335012391209602,
0.02595464326441288,
-0.00006689641304546967,
-0.033116333186626434,
0.01778489165008068,
0.007359951268881559,
-0.005524144507944584,
-0.04533197358250618,
0.02681252546608448,
-0.0372287817299366,
0.015928814187645912,
0.04496483877301216,
-0.0397280678153038,
-0.03973817080259323,
0.06580036878585815,
0.024813968688249588,
-0.0023251036182045937,
0.01721634343266487,
-0.00847657024860382,
-0.017556851729750633,
0.06376223266124725,
0.0037164173554629087,
-0.038696229457855225,
-0.025262830778956413,
0.04558343067765236,
0.05907329544425011,
-0.005211313720792532,
0.00007766410271869972,
0.04140995815396309,
-0.04116281494498253,
-0.02446676231920719,
-0.0031802670564502478,
-0.0027134304400533438,
-0.0011358025949448347,
-0.008635920472443104,
-0.08068643510341644,
0.005782531574368477,
-0.009918509051203728,
0.03782656043767929,
0.037554118782281876,
-0.00674366345629096,
0.021822815760970116,
0.04888753592967987,
-0.06095448508858681,
-0.03446982800960541,
-0.03642333671450615,
0.03841395303606987,
-0.03231758251786232,
-0.022819949313998222,
-0.05874011293053627,
-0.0004917894257232547,
0.04539426043629646,
-0.033629924058914185,
-0.007335883565247059,
-0.02829844132065773,
0.015403641387820244,
0.04873671382665634,
-0.002319775288924575,
-0.026241770014166832,
0.04656187817454338,
0.023984314873814583,
0.01466657780110836,
-0.0062601882964372635,
-0.03939453139901161,
-0.016972804442048073,
-0.017165007069706917,
0.017533358186483383,
-0.026617998257279396,
0.010188388638198376,
-0.006617145612835884,
0.020786209031939507,
-0.004325103480368853,
0.0010689360788092017,
0.03336915001273155,
-0.03701738640666008,
0.02036627009510994,
0.02462897263467312,
-0.006674627773463726,
0.010391110554337502,
0.03562789782881737,
0.02061794511973858,
0.005541302729398012,
0.026723939925432205,
-0.03536367788910866,
-0.040118202567100525,
-0.03335394337773323,
0.024943051859736443,
-0.03584771230816841,
-0.03057510405778885,
0.03661584481596947,
-0.0032327244989573956,
0.044458139687776566,
-0.0063071358017623425,
0.019771669059991837,
-0.0009798579849302769,
-0.03252303600311279,
-0.021517593413591385,
0.026484735310077667,
0.0423387847840786,
0.001110511482693255,
0.01797219179570675,
0.0125370929017663,
-0.010596944019198418,
0.01112398225814104,
-0.06269679218530655,
0.019893506541848183,
-0.013673115521669388,
0.07080903649330139,
0.0005982517614029348,
-0.007882724516093731,
0.03312847763299942,
-0.03523697704076767,
0.0008604278555139899,
0.023620205000042915,
-0.01526076253503561,
0.0068246303126215935,
0.0019484058720991015,
-0.0242825485765934,
0.013729368336498737,
0.03399493917822838,
-0.03811367228627205,
-0.02303127944469452,
0.03930003568530083,
-0.024656031280755997,
0.02412995509803295,
-0.010381931439042091,
-0.03344280645251274,
-0.025134308263659477,
0.02213781699538231,
0.017531419172883034,
0.02639797329902649,
0.005545548163354397,
-0.041537586599588394,
-0.049160026013851166,
-0.00795703288167715,
-0.021928520873188972,
0.006140479352325201,
0.03660919889807701,
-0.04080267995595932,
0.030193571001291275,
0.009910151362419128,
-0.013307461515069008,
0.049509383738040924,
0.009413046762347221,
0.03527000546455383,
0.04047427698969841,
-0.009998926892876625,
-0.0686318650841713,
-0.04501430317759514,
-0.04500201717019081,
0.011725366115570068,
-0.053647398948669434,
-0.02262934297323227,
0.05388667806982994,
-0.0011714108986780047,
-0.021515198051929474,
0.03487851470708847,
-0.034226253628730774,
-0.01198496762663126,
0.002836753847077489,
0.01733696646988392,
0.023186519742012024,
-0.008433155715465546,
0.02146550454199314,
-0.012195850722491741,
-0.0049294959753751755,
0.03320084884762764,
-0.04585530236363411,
-0.06702560186386108,
0.010318784974515438,
0.04617372155189514,
0.015378111973404884,
-0.032761696726083755,
0.0027228326071053743,
0.0561584010720253,
0.037039048969745636,
-0.05487459897994995,
-0.0467219203710556,
-0.03447902575135231,
-0.02274004928767681,
-0.000688775849994272,
-0.016191426664590836,
0.05308075621724129,
0.00320043764077127,
0.04378434643149376,
0.018984945490956306,
0.04115273803472519,
0.029074152931571007,
-0.0001774273841874674,
-0.037205103784799576,
0.0064172036945819855,
-0.015773829072713852,
0.0018562136683613062,
0.04509500786662102,
0.030851207673549652,
-0.06100351735949516,
0.019035914912819862,
-0.0504457987844944,
0.005748449359089136,
-0.0022281515412032604,
-0.03143024817109108,
0.04133401811122894,
0.018704403191804886,
0.0320148803293705,
-0.02641155570745468,
0.04882458969950676,
-0.015071731992065907,
0.03330647572875023,
-0.031787410378456116,
0.0033605769276618958,
0.06314939260482788,
-0.010179916396737099,
-0.0025955571327358484,
0.01607431471347809,
0.007410872727632523,
-0.016738567501306534,
-0.02714597061276436,
-0.018957538530230522,
-0.026461470872163773,
0.022750668227672577,
-0.018678179010748863,
-0.04995252192020416,
0.06085354462265968,
0.024894537404179573,
0.0066915154457092285,
0.01264492142945528,
-0.039821043610572815,
-0.026778917759656906,
-0.04357001185417175,
0.0187277402728796,
-0.00878369901329279,
0.04827028140425682,
0.0007165880524553359,
0.04206445813179016,
0.017727313563227654,
0.020833879709243774,
0.02608170546591282,
0.02374698407948017,
-0.08739785850048065,
-0.007283321116119623,
0.007078163325786591,
0.024370083585381508,
-0.011140982620418072,
-0.002905832603573799,
0.016303008422255516,
-0.005526036489754915,
-0.0067354668863117695,
0.003752046264708042,
0.0019412558758631349,
-0.055648840963840485,
-0.012624883092939854,
-0.004267626907676458,
-0.033555932343006134,
-0.02809193730354309,
0.0066526117734611034,
0.032013654708862305,
-0.04588475450873375,
0.018879219889640808,
0.025502553209662437,
-0.013558425009250641,
-0.040139928460121155,
-0.052082475274801254,
0.022680183872580528,
0.029014362022280693,
0.02172967419028282,
0.006805631332099438,
-0.00934362132102251,
-0.05469799041748047,
0.017291508615016937,
0.004411141853779554,
0.006033141631633043,
-0.01339135691523552,
-0.005077584646642208,
0.003215086180716753,
-0.0006135274306870997,
0.003406847594305873,
0.01871616020798683,
0.034337300807237625,
0.009373717941343784,
0.042426157742738724,
0.007498498074710369,
0.033860377967357635,
-0.014030015096068382,
0.03272003307938576,
0.03980979695916176,
0.016697831451892853,
-0.0037481491453945637,
-0.06643873453140259,
0.024818094447255135,
-0.027287133038043976,
-0.009196698665618896,
-0.004316081292927265,
-0.001482629682868719,
-0.001342429080978036,
0.014021799899637699,
0.03295714780688286,
-0.004542908631265163,
-0.0067683011293411255,
0.03834065422415733,
-0.028249740600585938,
0.04736042022705078,
0.0012407033937051892,
0.016104117035865784,
0.006715088617056608,
0.005881575867533684,
0.013030365109443665,
0.010426359251141548,
-0.03936352580785751,
-0.07235118746757507,
-0.025221697986125946,
0.06176947057247162,
0.02410770207643509,
0.00357897044159472,
0.019916994497179985,
-0.03503936901688576,
0.02144128829240799,
0.006599129643291235,
0.009724155999720097,
0.029735252261161804,
-0.02076759748160839,
-0.026221944019198418,
-0.00856610108166933,
-0.029625732451677322,
0.00937647931277752,
0.022146275267004967,
-0.03216049447655678,
0.02614072524011135,
-0.026663104072213173,
-0.028564104810357094,
0.01219685934484005,
0.004270607139915228,
0.029064562171697617,
0.028067005798220634,
0.005835307762026787,
0.008772080764174461,
-0.02197791449725628,
0.047250896692276,
-0.056091226637363434,
-0.0500197559595108,
0.023798415437340736,
-0.005849036388099194,
0.001425727503374219,
0.032314859330654144,
-0.05143176019191742,
-0.008053597062826157,
-0.011496901512145996,
-0.00978738721460104,
-0.0189549271017313,
-0.02606363222002983,
-0.06948833167552948,
-0.001090132282115519,
0.05916927754878998,
0.004351989831775427,
0.05125864967703819,
0.034839995205402374,
0.0078091989271342754,
0.035141799598932266,
0.010014630854129791,
0.03573112189769745,
-0.013184327632188797,
0.0032807327806949615,
-0.02783520333468914,
0.023679768666625023,
-0.05533439293503761,
0.027274074032902718,
-0.0040975878946483135,
0.042725179344415665,
-0.01566505990922451,
-0.02816806174814701,
-0.04445279762148857,
0.010505360551178455,
-0.025190966203808784,
-0.003929927479475737,
-0.033422842621803284,
-0.015513904392719269,
-0.023392561823129654,
-0.02856229804456234,
-0.0052620111964643,
-0.025539763271808624,
0.0063081649132072926,
0.024083513766527176,
-0.030385812744498253,
-0.005605127662420273,
-0.04360263794660568,
0.012592603452503681,
-0.005636989139020443,
-0.10000663995742798,
0.021371182054281235,
-0.0245547816157341,
0.03051876649260521,
0.08860298991203308,
-0.02630649134516716,
-0.032124388962984085,
0.018894122913479805,
-0.00220884894952178,
0.020141003653407097,
-0.05403745174407959,
-0.009971384890377522,
0.005669149570167065,
-0.013645954430103302,
-0.03635631129145622,
-0.06864224374294281,
0.024116452783346176,
-0.0031285714358091354,
-0.03286353498697281,
-0.03561707213521004,
-0.030439497902989388,
0.005664775613695383,
-0.029442472383379936,
-0.0404697060585022,
0.030802782624959946,
0.005550204776227474,
-0.0011039841920137405,
0.025053944438695908,
-0.011568698100745678,
0.08380576968193054,
0.004916013218462467,
0.018857022747397423,
-0.005023288540542126,
-0.046421244740486145,
-0.04679293558001518,
0.024953318759799004,
0.08083798736333847,
-0.020598337054252625,
-0.03376345336437225,
0.006689941976219416,
0.01359131745994091,
0.018285971134901047,
-0.002025892725214362,
0.0009016092517413199,
0.013581217266619205,
0.043865468353033066,
0.012455202639102936,
-0.03516586869955063,
0.046675827354192734,
0.03977475315332413,
-0.01210755854845047,
0.0007256795070134103,
0.022027162835001945,
-0.007198243401944637,
-0.044932492077350616,
0.011645547114312649,
0.016334911808371544,
-0.030643630772829056,
0.004254417028278112,
0.07014981657266617,
0.015356700867414474,
-0.0061103785410523415,
0.015575090423226357,
0.011652783490717411,
0.03101354092359543,
-0.04995208606123924,
0.015098556876182556,
-0.01792849227786064,
-0.006849953904747963,
-0.05699773132801056,
0.007602958008646965,
0.006522234063595533,
-0.015913670882582664,
0.03084610588848591,
-0.01628364622592926,
0.037174493074417114,
0.014338895678520203,
-0.0110652856528759,
0.021861158311367035,
0.01604342833161354,
-0.0069961328990757465,
-0.004853542428463697,
0.022784719243645668,
0.03450734168291092,
-0.05444694310426712,
0.02533194236457348,
0.015118628740310669,
0.04747956618666649,
-0.006025759503245354,
-0.009310743771493435,
0.02235054224729538,
0.03004883974790573,
0.030156448483467102,
0.02253938838839531,
-0.012558107264339924,
0.027241472154855728,
0.015221470035612583,
0.03965597599744797,
0.018645118921995163,
-0.01677277311682701,
0.08528505265712738,
0.0032400074414908886,
0.01525101438164711,
-0.04302908480167389,
-0.016190215945243835,
-0.05456814914941788,
0.028078339993953705,
-0.007196621038019657,
0.014748581685125828,
-0.002652958733960986,
0.019133178517222404,
0.037208396941423416,
0.002345446264371276,
0.03149314969778061,
-0.03753412887454033,
-0.07747475802898407,
-0.03371935337781906,
-0.020489037036895752,
-0.025519534945487976,
0.049891967326402664,
-0.027147309854626656,
-0.0060147750191390514,
0.014793681912124157,
-0.05517367646098137,
-0.032806478440761566,
0.014773508533835411,
0.01021836418658495,
0.00010882990318350494,
0.0315488800406456,
-0.014257913455367088,
0.07955043017864227,
-0.03451043367385864,
0.0354798249900341,
0.11918672919273376,
0.009976544417440891,
0.014733600430190563,
-0.04439615458250046,
-0.0045410096645355225,
-0.010651320219039917,
-0.010824602097272873,
-0.0219754409044981,
0.041759029030799866,
0.0031054983846843243,
-0.012971943244338036,
-0.013168015517294407,
0.03305966407060623,
0.031065382063388824,
-0.029389142990112305,
0.0438908152282238,
-0.04882636293768883,
-0.05849052220582962,
0.020353328436613083,
-0.02351640723645687,
-0.01667439192533493,
-0.019706720486283302,
-0.06733991205692291,
0.01246991939842701,
-0.013205542229115963,
-0.007246518507599831,
0.004576022271066904,
-0.08562599122524261,
0.06541669368743896,
0.00033013452775776386,
-0.008724679239094257,
0.02781829982995987,
0.039491355419158936,
-0.05055664852261543,
-0.049828022718429565,
-0.024741148576140404,
0.01852729171514511,
-0.0246538445353508,
0.020148150622844696,
0.03595278412103653,
0.04077129811048508,
-0.022602712735533714,
0.01726449839770794,
-0.01632470078766346,
-0.009296996518969536,
-0.023913845419883728,
-0.013068859465420246,
0.02763095684349537,
0.050393663346767426,
0.0003620008355937898,
0.004842041991651058,
0.0018445814494043589,
-0.005914877634495497,
-0.0611100047826767,
0.016393765807151794,
0.008937649428844452,
0.035988613963127136,
0.016185304149985313,
-0.02703716605901718,
-0.023603025823831558,
0.02123449184000492,
0.0032084882259368896,
0.02378096431493759,
0.0537363700568676,
0.02337864227592945,
-0.05596344918012619,
-0.020643997937440872,
0.06503841280937195,
-0.009717111475765705,
-0.04232057183980942,
-0.026391085237264633,
-0.005628000013530254,
-0.012758605182170868,
-0.00022317921684589237,
0.014300070703029633,
0.005604083184152842,
0.002157448558136821,
-0.020828193053603172,
-0.029239071533083916,
-0.004972866270691156,
-0.022409949451684952,
0.037485744804143906,
-0.012976306490600109,
0.00716750742867589,
0.0033463179133832455,
-0.015690887346863747,
0.061489008367061615,
-0.0004726085753645748,
-0.02780299074947834,
-0.022197047248482704,
-0.00026358492323197424,
0.05185249447822571,
0.011489294469356537,
-0.03337507322430611,
-0.04456634074449539,
0.004001939203590155,
-0.00938522256910801,
-0.02033339999616146,
-0.031291794031858444,
0.016558699309825897,
0.022616837173700333,
-0.005130560602992773,
0.020383218303322792,
0.03082473762333393,
-0.026019494980573654,
0.014315027743577957,
-0.0012321232352405787,
-0.007277785800397396,
-0.015243458561599255,
-0.009830305352807045,
-0.021354669705033302,
-0.020185424014925957,
0.0009657086338847876,
0.013598131015896797,
-0.013700940646231174,
0.018221251666545868,
0.04838976636528969,
-0.043398499488830566,
0.020654870197176933,
-0.013640173710882664,
0.05095277726650238,
0.005744047928601503,
-0.043662410229444504,
-0.0666046068072319,
0.0067578088492155075,
-0.013290323317050934,
-0.004432886838912964,
-0.07777878642082214,
0.044201482087373734,
-0.0006906166090629995,
-0.03363771364092827,
0.03374118730425835,
0.010532362386584282,
-0.033204153180122375,
0.03338920697569847,
0.002707832958549261,
0.006265905685722828,
0.0037818006239831448,
0.004914891440421343,
-0.0184642244130373,
0.06397190690040588,
0.004834958352148533,
-0.04025862738490105,
0.018586963415145874,
-0.013634768314659595,
0.009243194945156574,
-0.009609771892428398,
-0.013049080967903137,
0.030635003000497818,
0.030671894550323486,
0.0015870120842009783,
0.005942278541624546,
-0.004399322438985109,
-0.009879249148070812,
0.014137336052954197,
-0.015649262815713882,
-0.017971958965063095,
-0.030831340700387955,
-0.041611090302467346,
0.0024604550562798977,
0.056695032864809036,
-0.0014373348094522953,
0.02907019667327404,
-0.01974331960082054,
0.011745613999664783,
-0.005526501685380936,
-0.025672947987914085,
0.006236854009330273,
0.030181506648659706,
0.013032467104494572,
-0.054315365850925446,
-0.004221029579639435,
-0.0020723191555589437,
0.00936184823513031,
-0.04155091568827629,
-0.015021579340100288,
0.018624119460582733,
-0.004947153385728598,
0.035593707114458084,
-0.052089642733335495,
0.03662122040987015,
0.04882393777370453,
-0.04861397296190262,
0.006833902094513178,
-0.010205931961536407,
-0.018135977908968925,
-0.02169572189450264,
-0.003430055920034647,
-0.03959176316857338,
0.030840879306197166,
0.008830212987959385,
0.05734630301594734,
0.019869279116392136,
0.019046489149332047,
-0.007645768113434315,
-0.04246955364942551,
0.007413921877741814,
0.04038231447339058,
0.029736727476119995,
-0.005869561340659857,
0.04280783236026764,
-0.005794217344373465,
0.007855234667658806,
0.03901923447847366,
0.007431101053953171,
0.019659170880913734,
-0.007741680834442377,
0.03363288566470146,
0.001979734282940626,
0.04089701175689697,
-0.00759022356942296,
-0.0025120587088167667,
-0.02656828612089157,
-0.020367788150906563,
0.033150576055049896,
0.03599881753325462,
0.02392308972775936,
-0.03104584477841854,
-0.02907148003578186,
-0.022238995879888535,
-0.006524598225951195,
0.043710462749004364,
-0.034439053386449814,
-0.00388408824801445,
-0.019610773772001266,
-0.006440978497266769,
0.0020882710814476013,
-0.024232396855950356,
-0.005669484380632639,
-0.020464042201638222,
-0.010296652093529701,
-0.006879858206957579,
-0.02072867564857006,
-0.018314233049750328,
0.017939819023013115,
0.01296931691467762,
-0.04135514795780182,
-0.029806174337863922,
-0.030599351972341537,
-0.04480404034256935,
-0.01696494221687317,
0.0022472820710390806,
0.010309216566383839,
0.050878413021564484,
0.01926255412399769,
-0.022801034152507782,
-0.035333529114723206,
0.004519696347415447,
0.014334608800709248,
-0.0042302776128053665,
0.002757489215582609,
-0.027940712869167328,
-0.026709934696555138,
-0.02646692655980587,
0.08142336457967758,
0.01316069532185793,
-0.025130588561296463,
-0.051820989698171616,
0.007051692809909582,
0.013103999197483063,
0.027276961132884026,
0.05125891789793968,
-0.035993389785289764,
-0.020035136491060257,
0.02581605315208435,
-0.028012050315737724,
0.006549034733325243,
-0.025982555001974106,
-0.021081561222672462,
-0.0046843839809298515,
-0.034449998289346695,
0.02337053045630455,
-0.04049690440297127,
-0.032338131219148636,
0.01329141203314066,
0.044365886598825455,
-0.011595199815928936,
0.012349463999271393,
-0.02247239463031292,
-0.034061357378959656,
-0.024182379245758057,
0.024227086454629898,
-0.012621334753930569,
0.01623213104903698,
0.038930609822273254,
-0.005259789526462555,
0.02161538042128086,
-0.01837298646569252,
-0.037486232817173004,
0.019093479961156845,
-0.03881065919995308,
-0.016692042350769043,
-0.01566045545041561,
-0.029481269419193268,
0.08815838396549225,
-0.05672873929142952,
-0.0032734842970967293,
0.01319033745676279,
-0.024245386943221092,
0.03497830405831337,
0.044589728116989136,
0.014157792553305626,
0.01361050084233284,
0.013908887282013893,
0.04373738914728165,
0.013443308882415295,
0.020878365263342857,
0.03325454890727997,
0.009233658201992512,
-0.028096068650484085,
-0.005836762022227049,
0.03974863514304161,
0.01417095959186554,
0.0076918951235711575,
0.026641374453902245,
0.012120971456170082,
0.007456873077899218,
0.027286430820822716,
0.02023264952003956,
0.029839394614100456,
-0.019485710188746452,
-0.03905325382947922,
0.011601327918469906,
-0.021397430449724197,
0.07693782448768616,
-0.004830764606595039,
0.029858697205781937,
0.026500074192881584,
-0.007642560638487339,
-0.008550471626222134,
-0.0006274661864154041,
0.04020872339606285,
-0.023731453344225883,
0.01851748116314411,
-0.023389670997858047,
0.019385509192943573,
0.030388545244932175,
-0.004406848922371864,
-0.044968027621507645,
0.027652032673358917,
-0.06479735672473907,
-0.03164902329444885,
0.007545293774455786,
-0.021925706416368484,
-0.03178718686103821,
0.0006539690657518804,
0.03158199042081833,
0.0065332758240401745,
0.0047971694730222225,
-0.027380600571632385,
-0.012050855904817581,
-0.032394878566265106,
0.0717424750328064,
-0.10064350813627243,
-0.04836774617433548,
-0.007752350997179747,
0.04215673357248306,
0.012295288033783436,
-0.026068594306707382
] |
<p>What I mean by effective in the question refers to the time and space requirements for sending information over a quantum communications channel. Having read "Mike and Ike" but doing no independent research on the question, my initial impression is that a channel using an effect from quantum field theory e.g. quantum electrodynamics would be more powerful over a narrower range of algorithms than an "ordinary" or "vanilla" quantum computer i.e. one that derived information from its steady-state behavior e.g. quantum electrostatics. </p>
<p>Are there any quantum information theorists working on proving whether this is true or false? </p>
<p>EDIT:</p>
<p>Allow me to quote from the portion of the book the provoked the question (p.6):</p>
<blockquote>
<p>At the time of writing it is not clear whether Deutsch’s notion of a Universal Quantum
Computer is sufficient to efficiently simulate an arbitrary physical system. Proving
or refuting this conjecture is one of the great open problems of the field of quantum
computation and quantum information. It is possible, for example, that some effect of
quantum field theory or an even more esoteric effect based in string theory, quantum
gravity or some other physical theory may take us beyond Deutsch’s Universal Quantum
Computer, giving us a still more powerful model for computation. At this stage, we
simply don’t know.</p>
</blockquote>
<p>I simply assume that a more powerful model of computation would give rise to a more efficient communications channel. Unless there has been a proof of the universality of a Universal Quantum Computer it seems that whoever said 'quantum is quantum' is very much getting ahead of themselves. </p>
<p>Now, with all that being said, I reiterate my previous question: are there any quantum information theorists working on proving whether this is true or false? </p>
| 8,288 |
[
-0.011930028907954693,
-0.049188144505023956,
-0.002722521312534809,
-0.04952169954776764,
0.031182000413537025,
0.008336917497217655,
-0.00856582261621952,
-0.04945700615644455,
0.005083789583295584,
-0.011341826990246773,
0.022663798183202744,
0.04084846004843712,
0.04068923741579056,
0.025248417630791664,
0.001683166716247797,
0.002065257867798209,
-0.021788323298096657,
-0.005618000403046608,
-0.025654379278421402,
-0.013332134112715721,
0.0028283726423978806,
0.06031578406691551,
0.010653854347765446,
0.020001165568828583,
-0.007737082429230213,
0.01169679593294859,
0.011193385347723961,
0.0027521883603185415,
-0.007199570536613464,
0.061675675213336945,
0.01412700954824686,
-0.02140176296234131,
0.03928219527006149,
0.05139573663473129,
0.0317707434296608,
0.02540893666446209,
-0.04238606244325638,
-0.03904237598180771,
0.036686383187770844,
-0.02041756920516491,
-0.021308748051524162,
-0.03443465381860733,
0.010144244879484177,
0.023441189900040627,
-0.014748494140803814,
0.036555081605911255,
-0.0052899522706866264,
-0.04124916344881058,
0.038482438772916794,
-0.030771994963288307,
0.04693371430039406,
-0.008289258927106857,
0.018401969224214554,
-0.008261342532932758,
0.010425413958728313,
-0.0034998846240341663,
0.08762586116790771,
0.07379689812660217,
0.00745867844671011,
-0.011956064030528069,
-0.03707367181777954,
0.014207183383405209,
0.004757355898618698,
-0.028413740918040276,
-0.027865616604685783,
0.020436517894268036,
-0.015125203877687454,
-0.011481449007987976,
0.02614038810133934,
-0.005036939866840839,
-0.028133368119597435,
0.03581611067056656,
0.021555528044700623,
0.02639547362923622,
0.032023292034864426,
0.006666854489594698,
-0.008274167776107788,
0.00791850220412016,
-0.019869443029165268,
0.06814271956682205,
-0.022900529205799103,
-0.0035812300629913807,
0.006150033790618181,
0.04238174110651016,
0.00577995041385293,
-0.007480456959456205,
0.05765046179294586,
-0.04612456262111664,
-0.024105709046125412,
0.034552473574876785,
-0.030268600210547447,
-0.008537545800209045,
0.024656103923916817,
-0.010767234489321709,
-0.024051962420344353,
0.004846351221203804,
0.012303122319281101,
0.02699117362499237,
0.0005890124011784792,
-0.018095124512910843,
0.009591837413609028,
-0.03858937695622444,
0.01568816974759102,
0.06466048210859299,
0.014978374354541302,
-0.003882220247760415,
-0.03794153779745102,
0.027954014018177986,
-0.013988430611789227,
-0.01806436851620674,
-0.035084545612335205,
-0.006879640743136406,
-0.005989951081573963,
0.014711013995110989,
0.013959060423076153,
-0.04844210296869278,
0.017360996454954147,
-0.03184902295470238,
0.06686330586671829,
0.06600905954837799,
0.04676438495516777,
-0.04456023499369621,
0.03840465843677521,
-0.05602698400616646,
-0.006413511000573635,
0.04334557056427002,
0.02654934860765934,
-0.014828096143901348,
-0.03599291294813156,
0.03294863551855087,
0.0013689332408830523,
-0.009431119076907635,
-0.017758572474122047,
0.0016624487470835447,
0.033940140157938004,
-0.027950609102845192,
-0.09909850358963013,
-0.04487401247024536,
0.03957304731011391,
0.0021949983201920986,
0.0009283283143304288,
-0.07284753769636154,
0.028905656188726425,
0.05983815714716911,
0.03768979385495186,
-0.0031395924743264914,
0.04639923572540283,
-0.011819959618151188,
0.01985376887023449,
0.0251925066113472,
-0.031047163531184196,
-0.0005713928258046508,
0.011456497944891453,
-0.015068677254021168,
0.014631061814725399,
-0.053756266832351685,
0.011934882961213589,
0.02967061661183834,
-0.019555307924747467,
-0.02585633471608162,
0.08945762366056442,
-0.014999264851212502,
0.013094743713736534,
0.0036610644310712814,
-0.0012567401863634586,
-0.023985769599676132,
0.09013988822698593,
0.017311634495854378,
0.06463263928890228,
0.007215369958430529,
-0.005339986179023981,
0.010969956405460835,
0.044424958527088165,
-0.004696521908044815,
0.03971084952354431,
-0.0581350177526474,
-0.02025807462632656,
-0.016113659366965294,
-0.008774952962994576,
-0.021245772019028664,
-0.003143713343888521,
-0.024313246831297874,
-0.007267140783369541,
-0.021806251257658005,
0.0030957087874412537,
0.023179544135928154,
-0.017974963411688805,
-0.017234427854418755,
0.0011560427956283092,
-0.04637454077601433,
-0.03407107666134834,
-0.045274246484041214,
0.039482153952121735,
0.032757729291915894,
0.009254274889826775,
-0.0013669333420693874,
0.011758611537516117,
0.002919047139585018,
0.003403926733881235,
-0.06185876578092575,
-0.04052687808871269,
0.021622929722070694,
0.02311454899609089,
0.02733551897108555,
0.04176655784249306,
0.04783312603831291,
0.023419775068759918,
-0.014979983679950237,
0.034744758158922195,
0.0056571695022284985,
-0.0661604106426239,
0.017011594027280807,
0.008749792352318764,
0.04646800085902214,
0.004294237121939659,
0.008968506008386612,
0.03261531889438629,
-0.01962430588901043,
-0.017243826761841774,
-0.016300734132528305,
-0.03205229714512825,
0.07181863486766815,
0.010389406234025955,
0.018275994807481766,
0.009027604013681412,
0.033640481531620026,
0.029871392995119095,
-0.010773582383990288,
0.04417409375309944,
-0.03888491913676262,
-0.059653643518686295,
-0.014043724164366722,
0.02639991044998169,
0.03809947520494461,
-0.050095085054636,
0.033384084701538086,
0.0007970243459567428,
0.05181917920708656,
0.030191820114850998,
0.00626373291015625,
-0.036566361784935,
0.009981609880924225,
0.03640250489115715,
0.018073903396725655,
0.0020730840042233467,
0.02226695418357849,
0.029774703085422516,
0.005670201499015093,
-0.04341241717338562,
-0.020115656778216362,
-0.03599878028035164,
0.01792089268565178,
-0.02049987204372883,
0.011961724609136581,
-0.03480713441967964,
-0.058019593358039856,
-0.010449587367475033,
-0.033651892095804214,
0.0011173677630722523,
0.005601239390671253,
-0.025232335552573204,
0.02725074253976345,
-0.025293786078691483,
-0.03847648948431015,
0.03820757567882538,
-0.0066460976377129555,
-0.02067597396671772,
0.011874510906636715,
0.0407269150018692,
-0.0437154546380043,
0.04492337629199028,
-0.023255595937371254,
0.013317438773810863,
-0.01916537806391716,
0.029618481174111366,
0.030478626489639282,
-0.024306437000632286,
0.030570097267627716,
-0.02937656082212925,
-0.02254329062998295,
-0.010532302781939507,
-0.012131932191550732,
-0.01227573025971651,
0.01761757582426071,
-0.06159423664212227,
0.010771486908197403,
-0.024386590346693993,
-0.036434825509786606,
0.04366784915328026,
-0.05418805032968521,
-0.010288323275744915,
-0.010999058373272419,
-0.03169209137558937,
-0.01886913739144802,
0.009909497573971748,
-0.04955865070223808,
0.022532939910888672,
-0.02607034333050251,
0.014959825202822685,
0.03096184693276882,
0.014079263433814049,
-0.013237767852842808,
-0.0001353789120912552,
-0.016401004046201706,
-0.03580722585320473,
0.0064062862657010555,
-0.0012912002857774496,
0.0038124637212604284,
-0.0609673336148262,
0.026920069009065628,
0.006484854966402054,
-0.03811761736869812,
-0.009620696306228638,
-0.056027602404356,
-0.07106869667768478,
0.044108662754297256,
-0.008170990273356438,
0.02164475992321968,
-0.01342098694294691,
-0.034172121435403824,
0.037344932556152344,
0.026398569345474243,
-0.043663956224918365,
0.01786782406270504,
-0.006657160818576813,
-0.004986472427845001,
-0.007854040712118149,
0.014269865117967129,
0.02934911847114563,
-0.011004793457686901,
0.01821080595254898,
0.03278594836592674,
0.013196980580687523,
0.01557877566665411,
0.008102752268314362,
-0.028289074078202248,
0.0064696273766458035,
0.006791579071432352,
-0.024099476635456085,
0.031474050134420395,
0.02657254971563816,
-0.07504452764987946,
-0.00967787578701973,
0.006878118962049484,
0.013823380693793297,
0.04852649196982384,
-0.013867993839085102,
0.040929533541202545,
0.03091874159872532,
0.05324220657348633,
-0.0002668573579285294,
0.04076661542057991,
-0.0531000979244709,
-0.0312969908118248,
0.006702701095491648,
0.0382428802549839,
-0.01067594438791275,
0.014484576880931854,
0.009029591456055641,
0.006049640476703644,
0.04866722226142883,
-0.03973647952079773,
-0.002083976287394762,
-0.03282216563820839,
-0.05132560059428215,
0.01950925961136818,
-0.01845623180270195,
-0.041635554283857346,
0.026751114055514336,
0.011723481118679047,
0.011952530592679977,
0.025266487151384354,
-0.005014344118535519,
-0.0047319489531219006,
-0.024152003228664398,
-0.0031510547269135714,
-0.0259140245616436,
0.03527176380157471,
0.014849646016955376,
0.03835839405655861,
0.008931970223784447,
0.003272694768384099,
-0.020694922655820847,
-0.0024845879524946213,
-0.0931212306022644,
-0.00687366584315896,
-0.02259429357945919,
-0.015456962399184704,
0.05691327154636383,
-0.03273710608482361,
0.0030004200525581837,
-0.017156707122921944,
-0.07335293292999268,
0.007825758308172226,
0.025988396257162094,
-0.0792267844080925,
0.006518927868455648,
0.0026534576900303364,
-0.07104817777872086,
-0.024651063606142998,
0.02518116682767868,
0.005057087168097496,
-0.014485719613730907,
0.009816113859415054,
0.008086808025836945,
-0.05131254345178604,
-0.001048409496434033,
0.007313326001167297,
0.029372796416282654,
0.037041567265987396,
0.007982670329511166,
0.03410855308175087,
0.04162875562906265,
-0.033992961049079895,
-0.011907340958714485,
0.0411500483751297,
0.034289319068193436,
-0.024993568658828735,
-0.022866351529955864,
0.007433237507939339,
-0.05670694261789322,
-0.015399596653878689,
0.027707869186997414,
0.055183328688144684,
0.015233784914016724,
0.01967868022620678,
0.03770052269101143,
0.02352912165224552,
-0.005777587182819843,
0.05147575959563255,
0.08024174720048904,
-0.022043593227863312,
-0.03411856293678284,
-0.018483135849237442,
-0.03301454707980156,
-0.017322849482297897,
0.01824420876801014,
0.04145433008670807,
0.0016281084390357137,
0.027552271261811256,
0.037424203008413315,
-0.008548343554139137,
-0.020774997770786285,
-0.038621533662080765,
-0.013917464762926102,
-0.007637379225343466,
0.009095891378819942,
-0.014214853756129742,
0.00809017475694418,
-0.02795853093266487,
0.03568870946764946,
0.010269495658576488,
0.01708124205470085,
-0.007327540311962366,
-0.07591161876916885,
-0.016189590096473694,
0.050855591893196106,
0.049838241189718246,
0.0002310324925929308,
0.025569429621100426,
-0.04813076928257942,
0.005715059582144022,
0.0292590893805027,
-0.011877700686454773,
0.03182598948478699,
0.008947259746491909,
-0.008357386104762554,
-0.01536400057375431,
0.013221798464655876,
0.040019262582063675,
-0.010201703757047653,
0.038159891963005066,
-0.007263711653649807,
0.015302170999348164,
0.023795288056135178,
-0.04951174557209015,
0.011922632344067097,
0.03818255662918091,
0.04749952256679535,
0.0043952264823019505,
0.023815056309103966,
-0.0018052635714411736,
-0.0012135623255744576,
-0.05564434453845024,
-0.10108869522809982,
0.04350614175200462,
-0.00034992778091691434,
-0.033101070672273636,
0.01625806652009487,
-0.04110099375247955,
-0.0185855720192194,
0.019832924008369446,
-0.01659734919667244,
-0.014604291878640652,
-0.017392130568623543,
-0.03488628938794136,
0.07006838172674179,
-0.006867832504212856,
0.005350858438760042,
0.01981147937476635,
0.03807101026177406,
-0.04914596676826477,
0.006210551597177982,
0.0008834907202981412,
0.034396957606077194,
-0.03926867991685867,
0.04878202825784683,
-0.04016688093543053,
0.053921014070510864,
-0.010287841781973839,
0.015185208059847355,
-0.01446607243269682,
-0.0020673705730587244,
-0.0267961286008358,
-0.01646967977285385,
-0.0527997724711895,
-0.005647043231874704,
-0.032571882009506226,
-0.027222296223044395,
-0.04902098700404167,
0.023098798468708992,
-0.03028864599764347,
-0.016523582860827446,
0.015658479183912277,
-0.026130886748433113,
0.01194265577942133,
0.008180487900972366,
0.014741810038685799,
0.011428243480622768,
-0.02618858404457569,
-0.007578663062304258,
-0.005128242075443268,
-0.05386633053421974,
0.043057218194007874,
-0.012513131834566593,
-0.028712576255202293,
0.040918752551078796,
-0.07359201461076736,
0.004413361195474863,
0.01312091201543808,
0.0010952067095786333,
0.0013608202571049333,
-0.016397707164287567,
-0.007011827547103167,
-0.0193768460303545,
-0.011755554936826229,
-0.07250943779945374,
-0.0703020915389061,
0.01063713151961565,
0.016320405527949333,
0.02276408113539219,
-0.015443209558725357,
0.014433497563004494,
-0.01710386946797371,
-0.010465781204402447,
-0.03916634991765022,
0.059702496975660324,
0.011333340778946877,
0.021516378968954086,
0.02992015704512596,
0.02238423191010952,
0.010181461460888386,
0.015484977513551712,
0.019776970148086548,
0.007833902724087238,
0.00392579473555088,
0.023478545248508453,
-0.008068617433309555,
0.026545973494648933,
-0.010034210048615932,
-0.02969062514603138,
-0.005217251367866993,
-0.016015008091926575,
0.030575696378946304,
-0.005428211763501167,
0.0030907706823199987,
0.030376151204109192,
0.0321325808763504,
-0.0028258170932531357,
0.02101842314004898,
-0.03037666715681553,
-0.013447281904518604,
0.05689667910337448,
-0.018107596784830093,
-0.0023812316358089447,
0.007721113506704569,
-0.05127210170030594,
0.03244686499238014,
0.0232022013515234,
-0.03081103041768074,
0.016143949702382088,
0.05233057215809822,
0.013438536785542965,
-0.006131396163254976,
0.007536258082836866,
-0.04311595484614372,
-0.013531866483390331,
-0.01103016547858715,
0.029828717932105064,
-0.0351257361471653,
0.009215449914336205,
0.010904688388109207,
-0.04951009526848793,
-0.019732598215341568,
0.025890197604894638,
0.06317990273237228,
0.004748061764985323,
0.03587828576564789,
0.03776785358786583,
0.01672855019569397,
-0.03356365114450455,
-0.029562054201960564,
-0.024840345606207848,
0.023720402270555496,
0.006829823832958937,
0.020663119852542877,
-0.020588817074894905,
0.001346204779110849,
0.032821349799633026,
0.047920674085617065,
-0.003983428701758385,
0.01697131246328354,
0.03509417176246643,
0.007021418772637844,
0.010825921781361103,
-0.0495438426733017,
-0.03851791098713875,
0.02087567001581192,
-0.0982123538851738,
0.004513968247920275,
0.008707343600690365,
-0.008973866701126099,
0.02643699385225773,
0.0005645985365845263,
0.001988383010029793,
-0.010614139027893543,
-0.0035861723590642214,
-0.06447451561689377,
0.010540285147726536,
-0.034393973648548126,
0.041474711149930954,
0.010572290048003197,
-0.006279094610363245,
0.0195260401815176,
0.0040549226105213165,
0.039931830018758774,
0.018544696271419525,
-0.1171708032488823,
-0.05672812461853027,
-0.0314502976834774,
-0.03891751542687416,
0.06510094553232193,
0.02367224358022213,
-0.0404992550611496,
0.03232656791806221,
-0.050885915756225586,
0.03683347627520561,
0.0004321737214922905,
0.05186743289232254,
-0.018931662663817406,
0.05360570549964905,
-0.02182464674115181,
0.060464080423116684,
-0.002868024865165353,
-0.029043598100543022,
0.08422432094812393,
0.05562233179807663,
-0.006391790695488453,
-0.05008986219763756,
0.005730010569095612,
-0.029789511114358902,
0.004594752565026283,
-0.040604010224342346,
0.005287288688123226,
0.015219736844301224,
0.02138018049299717,
0.010748164728283882,
0.051337260752916336,
0.009377001784741879,
-0.010075232945382595,
0.039622582495212555,
-0.05676407366991043,
-0.03346032649278641,
0.018307846039533615,
0.03567494824528694,
0.012861822731792927,
-0.008102085441350937,
-0.014700347557663918,
0.022778216749429703,
-0.04450429230928421,
-0.011536624282598495,
0.000422260636696592,
0.02380625158548355,
0.015505580231547356,
0.018792686983942986,
-0.0623631589114666,
-0.006543795578181744,
-0.008896983228623867,
-0.01732746511697769,
-0.050671420991420746,
0.009465290233492851,
0.017038952559232712,
0.0052032750099897385,
0.002717941300943494,
0.06398952752351761,
0.004447644576430321,
0.000027920948923565447,
0.005487010348588228,
0.0110519053414464,
-0.05417782440781593,
0.015042671002447605,
-0.033122383058071136,
0.004159992560744286,
-0.01721128076314926,
0.01173082273453474,
-0.0009306597639806569,
-0.00717264786362648,
-0.02129732072353363,
-0.026395104825496674,
-0.009211117401719093,
0.006417524069547653,
0.026427747681736946,
-0.0010525848483666778,
-0.031397055834531784,
0.006406026892364025,
0.02831895276904106,
-0.005536608397960663,
-0.0016351178055629134,
-0.0016554812900722027,
-0.03887762874364853,
0.006712708622217178,
-0.015092861838638783,
-0.014015179127454758,
0.002775858622044325,
-0.02186427265405655,
-0.025937628000974655,
-0.008890483528375626,
-0.038675907999277115,
-0.01958088018000126,
0.020686075091362,
-0.010749480687081814,
0.020175008103251457,
-0.016916392371058464,
0.013501335866749287,
0.022167759016156197,
-0.047066185623407364,
0.0053961495868861675,
-0.00967210903763771,
0.015361608006060123,
0.002159166382625699,
-0.02024581842124462,
0.015850631520152092,
0.02043035253882408,
-0.02922419086098671,
0.02506677620112896,
0.024433119222521782,
-0.003328146180137992,
0.03770539164543152,
-0.028954416513442993,
-0.03519153594970703,
-0.014016116969287395,
-0.04154214262962341,
0.027225768193602562,
-0.034007322043180466,
0.017322348430752754,
0.00180850550532341,
0.007302166894078255,
-0.0289464108645916,
0.03698774799704552,
-0.004805567674338818,
0.02548592910170555,
0.005248899571597576,
-0.033472269773483276,
-0.019748816266655922,
0.024107318371534348,
0.04426884651184082,
-0.02458156645298004,
-0.0385330468416214,
-0.01174756046384573,
0.02359858714044094,
-0.008590015582740307,
-0.021113775670528412,
-0.02398345246911049,
0.01696096733212471,
-0.014929918572306633,
0.05745718255639076,
-0.03436802700161934,
-0.0005138636915944517,
-0.0027643239591270685,
0.05141638219356537,
0.004576908424496651,
-0.002963524078950286,
0.014442091807723045,
0.02507411129772663,
0.0005028634332120419,
-0.03086928278207779,
0.02089981734752655,
0.016427673399448395,
-0.034061264246702194,
0.0008882045513018966,
-0.001700466382317245,
0.04575398191809654,
0.049456119537353516,
-0.007788710296154022,
-0.03250239044427872,
0.0516187809407711,
-0.039526406675577164,
-0.03231966122984886,
0.04976104944944382,
-0.02908739633858204,
0.011359816417098045,
0.055553071200847626,
0.006418206263333559,
-0.025805950164794922,
0.013244097121059895,
-0.01841697096824646,
0.024992935359477997,
0.011847049929201603,
0.0005992679507471621,
-0.01750623807311058,
0.011678717099130154,
-0.009504850953817368,
-0.00810134969651699,
-0.026085007935762405,
0.03593849390745163,
0.029484907165169716,
0.01589643396437168,
0.01838999055325985,
0.0005609501386061311,
-0.017103152349591255,
0.022705202922225,
0.05005860701203346,
-0.013406573794782162,
-0.01258944533765316,
0.05282415822148323,
-0.03311207517981529,
0.03177222982048988,
0.024698518216609955,
-0.013545713387429714,
-0.12389109283685684,
0.015412934124469757,
0.0016776559641584754,
0.018495261669158936,
0.027572959661483765,
-0.028603065758943558,
0.06002804636955261,
-0.004418244119733572,
-0.0917956754565239,
0.044313687831163406,
-0.024553092196583748,
-0.008547828532755375,
-0.0037273832131177187,
0.009621522389352322,
-0.08025981485843658,
0.019849298521876335,
0.010596564039587975,
0.01547847781330347,
0.019028067588806152,
0.00768444687128067,
0.020457185804843903,
-0.030134063214063644,
-0.029913313686847687,
0.022802097722887993,
-0.028637494891881943,
0.025877898558974266,
0.047896530479192734,
-0.03651370108127594,
-0.02112501673400402,
0.020856162533164024,
-0.01345126610249281,
0.008208172395825386,
-0.03639402613043785,
-0.005881253629922867,
0.03663447126746178,
-0.02454591542482376,
0.029970495030283928,
-0.04527638852596283,
0.014285351149737835,
0.014169448986649513,
0.008912639692425728,
0.05885148048400879,
0.002022881992161274,
0.009015078656375408,
-0.0031181015074253082,
-0.010960645973682404,
-0.03684969246387482,
0.0363023541867733,
0.0053225792944431305,
-0.013235469348728657,
0.017089348286390305,
0.03332646191120148,
-0.004414618480950594,
-0.02761196903884411,
0.0008372343145310879,
-0.07064153254032135,
-0.011432720348238945,
0.0074935960583388805,
0.07634039223194122,
-0.009524921886622906,
0.01233634538948536,
-0.017109235748648643,
-0.010230815969407558,
0.0024229593109339476,
0.019513221457600594,
0.021697673946619034,
-0.038857754319906235,
-0.03943862020969391,
-0.005598302930593491,
0.03886920586228371,
0.051056522876024246,
-0.07575578987598419,
-0.03786816820502281,
0.06262236833572388,
0.0011382143711671233,
0.02600889839231968,
-0.03148290887475014,
-0.01375043485313654,
-0.0187153872102499,
-0.04005957767367363,
0.0348934680223465,
0.004595563746988773,
0.05449462682008743,
-0.03507468104362488,
-0.02754104696214199,
-0.010904306545853615,
0.02360563352704048,
0.07514575868844986,
0.006059195380657911,
-0.018205955624580383,
0.027438228949904442,
0.01751391589641571,
0.020036032423377037,
-0.02451985329389572,
0.01517869159579277,
-0.04823579639196396,
-0.020001117140054703,
-0.046407997608184814,
-0.04456767067313194,
-0.002898133359849453,
0.0510563999414444,
0.0225497055798769,
0.01682363636791706,
-0.004301850683987141,
-0.022467056289315224,
-0.019966470077633858,
0.07872793078422546,
0.03603319451212883,
0.02295970357954502,
0.0640435740351677,
0.02249087765812874,
0.02019265666604042,
0.009187092073261738,
-0.010034950450062752,
-0.024264326319098473,
0.045100271701812744,
-0.009085660800337791,
0.01149437204003334,
-0.0299321711063385,
0.019876880571246147,
0.0016506446991115808,
-0.02988702990114689,
-0.013390435837209225,
0.054525453597307205,
-0.03127918764948845,
0.010022432543337345,
0.050723206251859665,
-0.021200617775321007,
0.01764846220612526,
-0.01068079099059105,
0.00542836869135499,
0.02268526516854763,
0.00047309440560638905,
-0.018323780968785286,
0.05428040027618408,
0.039677709341049194,
-0.011725638061761856,
0.0576222725212574,
0.029671890661120415,
-0.046583108603954315,
0.06571152061223984,
0.008987979963421822,
-0.003028357867151499,
-0.012580033391714096,
-0.018268274143338203,
0.032100796699523926,
0.0006692690076306462,
-0.05772346258163452,
0.02625858411192894,
-0.011460276320576668,
0.07469093054533005,
-0.010495549067854881,
-0.0007313353125937283,
-0.015736352652311325,
-0.021369876340031624,
-0.0066735632717609406,
-0.0048773507587611675,
0.017367055639624596,
0.015422305092215538,
-0.046663038432598114,
-0.009487849660217762,
-0.014381811022758484,
-0.007807003799825907,
0.017655376344919205,
-0.048185769468545914,
0.00043690510210581124,
-0.005435446742922068,
-0.019054584205150604,
-0.0081824054941535,
-0.018606122583150864,
-0.023284073919057846,
-0.017641210928559303,
0.02868250012397766,
0.018741270527243614,
0.01571953110396862,
0.010874342173337936,
-0.042012836784124374,
0.01004918571561575,
0.09577345848083496,
-0.03803347051143646,
0.025799568742513657,
-0.057869475334882736,
-0.0021627862006425858,
-0.00016605867131147534,
0.019324686378240585
] |
<p>Ignoring for the moment the experimental necessity of eliminating the gluon singlet state, the nine "raw" gluon color components form two quite distinct sets. The first set consists of the six (color,anti-other-color) components:</p>
<blockquote>
<p>$r\overline{g}$, $r\overline{b}$, $g\overline{b}$, $g\overline{r}$, $b\overline{r}$, $b\overline{g}$</p>
</blockquote>
<p>The second set consists of the three (color,anti-color) components:</p>
<blockquote>
<p>$r\overline{r}$, $g\overline{g}$, $b\overline{b}$</p>
</blockquote>
<p>Only the first six components are needed to explain color flipping in hadrons and mesons. The second smaller group cannot change quark colors since they are net neutral in color.</p>
<p>So: For gluon exchanges between quarks in hadrons and mesons, is the role of the three gluon color-anticolor components purely attractive or repulsive? That is, are these three components more closely analogous to the photons of the electromagnetic force, which similarly carry no net electric charge?</p>
<p>Popular explanations, even ones by very good physicists, seem usually to skip over the existence of these two distinct groups, and instead describe only the color-changing consequences of the first group of gluon color components.</p>
<p>Finally, are there experimental implications of in the existence of these two groups? For example, would gluons that happen to carry mostly color-anticolor charge generate identifiably different jets from gluons that carry mostly color-anti-other-color charge?</p>
<p>This is a well-studied area, of course, so I suspect I just haven't been looking in the right places.</p>
| 8,289 |
[
-0.01792619377374649,
0.006888013798743486,
0.0032887423876672983,
-0.029149021953344345,
0.029041005298495293,
0.07653248310089111,
-0.03304539993405342,
-0.0040978072211146355,
-0.0076993792317807674,
-0.05163668468594551,
0.01882363297045231,
-0.012507070787250996,
0.04148152843117714,
-0.006615915335714817,
0.0007939559873193502,
0.019792698323726654,
-0.001438761129975319,
-0.02548929490149021,
0.022126972675323486,
-0.014750444330275059,
0.025965485721826553,
0.03561117872595787,
-0.024608658626675606,
-0.004519983194768429,
-0.0141134699806571,
0.03842006251215935,
0.010797075927257538,
0.02627289481461048,
0.04040930047631264,
0.029871659353375435,
0.0039902012795209885,
-0.026276307180523872,
-0.035880137234926224,
0.004030004143714905,
-0.009699513204395771,
0.02330596372485161,
0.00712523702532053,
-0.02997451275587082,
-0.04268302395939827,
-0.007019024342298508,
-0.04906283691525459,
-0.02478097751736641,
-0.02159176766872406,
0.014308683574199677,
-0.02157783694565296,
-0.012870989739894867,
-0.04877848923206329,
0.02104739286005497,
0.08984265476465225,
-0.09162802994251251,
0.030139466747641563,
0.027289148420095444,
0.031997714191675186,
-0.0020553888753056526,
-0.021258806809782982,
-0.02333684265613556,
0.06695296615362167,
0.06311351805925369,
0.004488973878324032,
-0.04196923226118088,
-0.006153041031211615,
-0.002337756333872676,
0.007283964194357395,
0.006378384307026863,
-0.04552040621638298,
0.05521481856703758,
0.011929835192859173,
0.009665781632065773,
0.0185321606695652,
-0.013118306174874306,
0.016795581206679344,
0.024641292169690132,
-0.0066126505844295025,
0.01663089729845524,
0.013813796453177929,
-0.024715222418308258,
0.01034987810999155,
0.020365191623568535,
0.030923116952180862,
0.037672024220228195,
-0.04781879484653473,
0.012523656710982323,
-0.024011902511119843,
0.04149536415934563,
0.02188756875693798,
-0.028026234358549118,
0.05614638328552246,
-0.0317971296608448,
0.0020971333142369986,
0.008057622238993645,
0.0006214433815330267,
0.018842557445168495,
0.009692843072116375,
0.030267512425780296,
-0.05089106783270836,
0.04230867326259613,
-0.007366601377725601,
0.008222738280892372,
-0.01638164557516575,
0.0035359046887606382,
0.01359042339026928,
0.0032861283980309963,
0.018988123163580894,
0.09631913155317307,
-0.018692711368203163,
-0.01629658043384552,
-0.03268040344119072,
-0.011934301815927029,
-0.004465565551072359,
0.001632904284633696,
-0.009841597639024258,
-0.02709667943418026,
0.01815299317240715,
-0.03950706869363785,
0.016787854954600334,
-0.04638588801026344,
0.018184715881943703,
0.009783814661204815,
0.08497406542301178,
0.07334373146295547,
0.06240849941968918,
-0.029388874769210815,
-0.015318152494728565,
-0.009372000582516193,
-0.029670467600226402,
-0.025438454002141953,
0.02549942024052143,
0.005365828052163124,
-0.01602189801633358,
0.008714690804481506,
0.00008923045243136585,
-0.0225539468228817,
0.024921979755163193,
0.01028330810368061,
0.0009530563256703317,
-0.032207392156124115,
-0.10706490278244019,
-0.06524727493524551,
0.03655843436717987,
-0.036419082432985306,
-0.03224503621459007,
-0.05799579992890358,
-0.04882045090198517,
0.02492513693869114,
0.07494688779115677,
-0.054913654923439026,
-0.012683169916272163,
-0.024242466315627098,
0.05382366105914116,
0.011285053566098213,
-0.044038835912942886,
-0.003640725277364254,
-0.01533627137541771,
-0.031227096915245056,
-0.028040753677487373,
-0.07144158333539963,
0.020381763577461243,
0.02515767514705658,
0.0015320429811254144,
0.010955302976071835,
0.10782551765441895,
-0.04197387397289276,
-0.019593527540564537,
0.024966295808553696,
-0.011927482672035694,
-0.02311018295586109,
0.0617685429751873,
0.017186284065246582,
0.0010764383478090167,
0.05344807729125023,
0.006408036220818758,
0.041884422302246094,
0.006794298999011517,
0.042326271533966064,
0.010284622199833393,
-0.02479090355336666,
-0.03303045779466629,
-0.01194512564688921,
-0.0034279136452823877,
-0.050447218120098114,
-0.017625045031309128,
-0.029975280165672302,
-0.00786990113556385,
-0.011080769822001457,
0.012226147577166557,
0.04486832767724991,
-0.03297170251607895,
-0.026662996038794518,
0.04225139319896698,
-0.054955411702394485,
-0.02491793781518936,
-0.0565081350505352,
0.01670750603079796,
-0.009165198542177677,
-0.05736329033970833,
0.02938329242169857,
0.02126424014568329,
0.003602992044761777,
0.026721766218543053,
-0.05150959640741348,
0.003622263204306364,
0.07564620673656464,
0.014152060262858868,
0.01132055651396513,
-0.01691371016204357,
-0.0011685779318213463,
0.008725729770958424,
-0.007210114039480686,
0.015174749307334423,
-0.021523306146264076,
-0.045017607510089874,
0.027255699038505554,
-0.03424879163503647,
0.035591572523117065,
-0.01736903004348278,
-0.016508229076862335,
0.0020718604791909456,
-0.0022983853705227375,
0.00806030910462141,
0.06980455666780472,
-0.05080468952655792,
0.045493680983781815,
0.00197783880867064,
-0.02456561289727688,
0.0002610906376503408,
0.06607085466384888,
0.006845579948276281,
0.02248593047261238,
-0.01286768727004528,
-0.0038278657011687756,
-0.024428511038422585,
-0.02746770903468132,
0.044382914900779724,
0.019246380776166916,
-0.034434471279382706,
0.04166924208402634,
-0.002620092825964093,
0.05293313041329384,
0.005738577339798212,
0.016207769513130188,
-0.0014314401196315885,
-0.047516897320747375,
0.0013972148299217224,
0.03829638659954071,
-0.014853055588901043,
-0.021443555131554604,
0.016400909051299095,
-0.009616340510547161,
-0.004638581536710262,
0.0031782686710357666,
0.0034835319966077805,
0.04159108176827431,
0.003678874811157584,
-0.008601154200732708,
-0.022796526551246643,
-0.04126506298780441,
0.06311867386102676,
-0.03001369535923004,
0.04149036481976509,
0.014805817045271397,
-0.004339980892837048,
-0.011166160926222801,
0.028574150055646896,
-0.015404908917844296,
-0.010421764105558395,
-0.018339164555072784,
-0.014299499802291393,
-0.007380705792456865,
0.0008993151132017374,
-0.04098990187048912,
0.02501482330262661,
-0.00473501393571496,
0.015937564894557,
-0.02950998954474926,
0.007934844121336937,
-0.005321964621543884,
-0.0009032925008796155,
0.017946647480130196,
-0.04021187871694565,
-0.028410349041223526,
0.04885723069310188,
-0.001231772592291236,
-0.007077113259583712,
0.062013931572437286,
-0.009721845388412476,
0.004281459376215935,
-0.1084524542093277,
-0.007474089041352272,
0.02958396077156067,
-0.02675384096801281,
-0.0178920179605484,
0.005390397273004055,
-0.005643951706588268,
-0.04831618443131447,
0.0010899410117417574,
-0.009755747392773628,
0.014407215639948845,
-0.01642250455915928,
-0.010214714333415031,
0.06559312343597412,
-0.005777320358902216,
-0.015761924907565117,
-0.009212976321578026,
-0.047259364277124405,
-0.04758751019835472,
0.014713317155838013,
0.020220771431922913,
0.007963692769408226,
-0.024305613711476326,
0.0002535736421123147,
0.022308189421892166,
-0.08159279078245163,
-0.0009278629440814257,
-0.022795727476477623,
-0.03524310514330864,
-0.028790436685085297,
0.025149110704660416,
0.013632181100547314,
0.03168955072760582,
-0.016653772443532944,
0.04334422945976257,
0.0227475818246603,
-0.031120628118515015,
0.008912203833460808,
-0.019101716578006744,
-0.051613640040159225,
-0.029578376561403275,
0.02171347104012966,
0.014730051159858704,
0.04941210150718689,
0.03038545697927475,
0.00413821917027235,
0.028295988216996193,
-0.006222351919859648,
0.02513069100677967,
-0.01667848788201809,
0.01675298810005188,
0.039465438574552536,
-0.009447985328733921,
0.033985428512096405,
0.017409348860383034,
-0.00520304823294282,
0.008407281711697578,
0.028510617092251778,
-0.0057591949589550495,
0.007439273875206709,
-0.014632741920650005,
0.09263638406991959,
0.014125793240964413,
0.045090194791555405,
0.006849218625575304,
0.027703169733285904,
-0.015381895937025547,
-0.0129622183740139,
0.017227454110980034,
-0.005871314089745283,
0.01770835928618908,
-0.044644273817539215,
0.00688884686678648,
0.022904520854353905,
0.05835305526852608,
-0.04881497845053673,
-0.025332752615213394,
-0.02570953778922558,
-0.006102577317506075,
0.04294608160853386,
-0.022246232256293297,
0.01771978661417961,
0.036189641803503036,
0.02084474451839924,
0.032989874482154846,
0.01113175693899393,
-0.036559514701366425,
-0.012657145038247108,
-0.04887911304831505,
0.02185993455350399,
-0.0037687919102609158,
0.03548722341656685,
0.003062052186578512,
0.04666845127940178,
-0.00112240482121706,
0.030560927465558052,
-0.012369350530207157,
-0.006201574578881264,
-0.09306652098894119,
0.014414944685995579,
-0.031235404312610626,
0.01279999129474163,
-0.03866884484887123,
-0.026044556871056557,
0.000951073772739619,
-0.015442844480276108,
-0.06471693515777588,
-0.02204306609928608,
-0.004597209393978119,
-0.027317579835653305,
0.040369436144828796,
-0.06710534542798996,
-0.053204555064439774,
-0.004469272214919329,
0.01625337451696396,
0.044380832463502884,
-0.03505324944853783,
-0.016686206683516502,
-0.00935341790318489,
-0.05567455664277077,
-0.010449637658894062,
-0.0185123011469841,
0.02073058858513832,
0.007181570865213871,
0.017677882686257362,
0.046957291662693024,
0.03847899287939072,
-0.014925370924174786,
-0.00706678070127964,
0.05742128938436508,
0.029000693932175636,
0.022869311273097992,
-0.031222648918628693,
0.02163224294781685,
-0.06391533464193344,
-0.010105148889124393,
0.010153592564165592,
0.07275571674108505,
0.01555834524333477,
-0.009686137549579144,
0.038738299161195755,
0.049159932881593704,
-0.013454215601086617,
0.026581870391964912,
0.03941032662987709,
0.04028959944844246,
-0.043228629976511,
-0.039034154266119,
0.039799515157938004,
0.011600322090089321,
0.014856365509331226,
0.004433657508343458,
-0.0024605286307632923,
-0.0083133764564991,
-0.002234002808108926,
0.013682642951607704,
0.022866245359182358,
-0.03400690108537674,
-0.015619675628840923,
0.012310195714235306,
0.01780310645699501,
-0.012247405014932156,
0.02714969404041767,
-0.009685421362519264,
0.08686990290880203,
0.03565060347318649,
-0.0014279468450695276,
0.015227445401251316,
-0.0324295312166214,
0.03951989486813545,
0.05778830498456955,
0.060928281396627426,
-0.041720449924468994,
-0.03214490786194801,
-0.04630580544471741,
0.0179015900939703,
0.007079834118485451,
-0.026695795357227325,
0.040681011974811554,
-0.04199272394180298,
-0.025562195107340813,
-0.017920738086104393,
-0.01943765953183174,
-0.029823822900652885,
0.04651686176657677,
-0.024711662903428078,
0.008675799705088139,
-0.04034895822405815,
-0.0245436429977417,
0.006068124435842037,
0.03962941840291023,
0.04469194635748863,
0.02627076394855976,
-0.014560496434569359,
0.029609810560941696,
0.017141399905085564,
-0.0017604246968403459,
-0.004161464516073465,
-0.11396989226341248,
0.009895398281514645,
0.0014170889044180512,
0.008773725479841232,
0.10186144709587097,
-0.05907290428876877,
-0.030421705916523933,
-0.02088611200451851,
0.029494311660528183,
0.024055510759353638,
0.03368065133690834,
-0.0530746653676033,
0.012166704051196575,
0.039346061646938324,
-0.004128727130591869,
0.045063894242048264,
0.008715900592505932,
-0.03194349631667137,
-0.024733278900384903,
-0.006873242557048798,
0.016656434163451195,
-0.020738298073410988,
-0.0049966792576014996,
0.013862136751413345,
-0.0074548982083797455,
-0.016273407265543938,
0.05600105971097946,
-0.010865486226975918,
0.015764042735099792,
0.03292360529303551,
-0.036219023168087006,
-0.0439411997795105,
-0.009532609954476357,
-0.020802898332476616,
0.007117873523384333,
0.02474479377269745,
0.01700216345489025,
-0.013196632266044617,
0.024255501106381416,
0.042424120008945465,
-0.0019104080274701118,
0.0018970220116898417,
0.02119077928364277,
-0.025234820321202278,
0.0002975657698698342,
-0.02640165202319622,
0.004748054780066013,
-0.005679783411324024,
-0.01589127816259861,
0.03507961705327034,
-0.013516396284103394,
0.0009570569382049143,
0.042340923100709915,
-0.03560347482562065,
-0.02704385668039322,
0.031884852796792984,
-0.014075432904064655,
0.0042350138537585735,
-0.039723560214042664,
0.03852098435163498,
0.014918269589543343,
-0.000020541860067169182,
-0.07686430215835571,
-0.01620008423924446,
0.02253727614879608,
0.03108029253780842,
-0.045512501150369644,
-0.011350910179316998,
-0.0051828185096383095,
-0.017403582111001015,
0.0015858078841120005,
0.003513831179589033,
0.062288135290145874,
-0.03817204385995865,
0.004146181978285313,
0.006289476063102484,
0.042415302246809006,
0.037486232817173004,
-0.010310504585504532,
-0.02083956077694893,
0.021875053644180298,
-0.02472739852964878,
0.032433513551950455,
0.016258740797638893,
0.05762995406985283,
0.008105938322842121,
-0.02737950161099434,
0.032357264310121536,
0.0025135439354926348,
0.011085164733231068,
-0.02639024890959263,
-0.021931175142526627,
0.026335420086979866,
-0.00040024463669396937,
-0.015393979847431183,
-0.005924777127802372,
0.013497614301741123,
-0.008451799862086773,
0.01037515513598919,
0.006423658225685358,
0.008396166376769543,
-0.003982292953878641,
-0.04220399633049965,
0.05264081433415413,
0.014072767458856106,
-0.009605064056813717,
0.031388863921165466,
0.05638578534126282,
0.016006479039788246,
-0.0554637648165226,
0.014733914285898209,
-0.027440261095762253,
0.023114873096346855,
-0.03206382319331169,
0.04677256941795349,
-0.011565158143639565,
-0.020581157878041267,
0.004221480805426836,
-0.02458622120320797,
-0.013013473711907864,
0.018426064401865005,
0.060708388686180115,
-0.013083751313388348,
0.043591197580099106,
-0.007414697669446468,
-0.02840910293161869,
-0.020404718816280365,
-0.027126438915729523,
0.0011406332487240434,
0.016347089782357216,
0.027161583304405212,
0.03731326386332512,
-0.026318121701478958,
-0.000358125485945493,
-0.01527418103069067,
0.024707812815904617,
-0.022239236161112785,
-0.004867515526711941,
0.059627026319503784,
0.024889450520277023,
0.03150178864598274,
-0.017306463792920113,
-0.038946401327848434,
0.05676209181547165,
-0.0633668452501297,
0.0029908998403698206,
0.025713128969073296,
-0.01623912714421749,
0.019733082503080368,
0.0004909143317490816,
0.03325556218624115,
-0.011423139832913876,
-0.028424471616744995,
-0.045535363256931305,
0.030781567096710205,
-0.008306835778057575,
0.0375744067132473,
0.0007765435730107129,
-0.01563924551010132,
0.04010565206408501,
0.01652134209871292,
0.030418559908866882,
-0.013363661244511604,
-0.06789963692426682,
-0.026490800082683563,
-0.012788564898073673,
-0.02525581419467926,
0.056824155151844025,
-0.03463030233979225,
-0.027857445180416107,
0.0015641397330909967,
-0.03238699585199356,
0.02813134901225567,
0.0056255585514009,
0.002606532536447048,
-0.02315894141793251,
0.01927049085497856,
-0.030456501990556717,
0.009037578478455544,
-0.01323284674435854,
-0.0000434786852565594,
0.13947159051895142,
0.04771457239985466,
0.025540631264448166,
-0.06923244148492813,
0.006069228518754244,
-0.041926562786102295,
0.00784975104033947,
-0.03883973881602287,
0.029825374484062195,
-0.010080942884087563,
0.017797397449612617,
-0.006571910344064236,
0.07084919512271881,
0.02334671840071678,
-0.014802621677517891,
0.028706364333629608,
-0.03731387481093407,
-0.051825474947690964,
0.007172997575253248,
0.0301943589001894,
-0.008304646238684654,
-0.011734046041965485,
-0.037181612104177475,
-0.011106238700449467,
0.017872925847768784,
0.009049377404153347,
0.008326500654220581,
-0.05805670842528343,
-0.004976199008524418,
0.008624223992228508,
-0.032042134553194046,
0.003593931905925274,
0.0013796641724184155,
-0.0057837399654090405,
-0.020156534388661385,
0.01369627844542265,
0.015211465768516064,
-0.03310165926814079,
0.02313178777694702,
-0.007673530839383602,
0.03331020101904869,
-0.02951328456401825,
0.04900608956813812,
0.019698847085237503,
-0.055653054267168045,
-0.04513761028647423,
-0.015483058989048004,
0.0392112135887146,
-0.020749807357788086,
-0.017802657559514046,
-0.021349677816033363,
0.004306096583604813,
0.004380124621093273,
-0.046825118362903595,
-0.03357541561126709,
-0.01854097843170166,
0.03274456411600113,
-0.022955743595957756,
-0.006384967360645533,
-0.015188501216471195,
0.02400549314916134,
-0.03596551716327667,
0.012161227874457836,
-0.025399496778845787,
-0.004040436819195747,
-0.006259831599891186,
0.012310890480875969,
0.06405024975538254,
0.042489245533943176,
-0.027366599068045616,
-0.04679202660918236,
-0.001725660404190421,
-0.02670910954475403,
-0.040508728474378586,
0.04394069314002991,
0.05221718177199364,
0.027127480134367943,
0.010852604173123837,
-0.013213751837611198,
-0.012197471223771572,
-0.05735204741358757,
0.020921187475323677,
-0.010379002429544926,
-0.004530266392976046,
-0.00622628815472126,
-0.02513597533106804,
0.011475535109639168,
0.02683258429169655,
0.026264453306794167,
0.0041922698728740215,
-0.013022862374782562,
0.05790688470005989,
-0.02449687011539936,
-0.007923326455056667,
-0.007240752689540386,
-0.004194675944745541,
-0.02849053218960762,
-0.0386999137699604,
0.015771830454468727,
0.03125429153442383,
-0.02387269213795662,
0.01466912217438221,
0.0023970322217792273,
0.026665914803743362,
0.018206708133220673,
-0.02475297451019287,
0.0612083375453949,
-0.012639513239264488,
0.01859109103679657,
-0.003348730970174074,
-0.0019699677359312773,
-0.04264859855175018,
-0.06536991894245148,
-0.0029129963368177414,
-0.009033212438225746,
0.030466949567198753,
0.0036350262816995382,
-0.02848401479423046,
-0.034574031829833984,
-0.03463180735707283,
0.030710948631167412,
-0.024124838411808014,
-0.037208255380392075,
-0.04858292266726494,
-0.005964996293187141,
-0.03721601143479347,
-0.030103357508778572,
0.0027145647909492254,
0.017799364402890205,
-0.01685059443116188,
-0.00515794800594449,
0.029763849452137947,
0.008414213545620441,
-0.020522912964224815,
-0.024184202775359154,
-0.015755102038383484,
0.017490528523921967,
0.045979514718055725,
-0.0036310774739831686,
-0.0280938558280468,
0.03476462885737419,
-0.04290531203150749,
-0.03803569823503494,
0.03550170361995697,
-0.023567894473671913,
0.015064775012433529,
0.019981417804956436,
-0.014350476674735546,
-0.005554370582103729,
0.05760307237505913,
-0.0021087026689201593,
-0.00005979044362902641,
0.006479864474385977,
0.006440844386816025,
-0.010073291137814522,
-0.059851616621017456,
0.012331860139966011,
0.011056842282414436,
0.0003541172482073307,
0.03704962879419327,
-0.0027970238588750362,
-0.02565658651292324,
0.0095061045140028,
-0.02720736339688301,
-0.014505974017083645,
0.031310874968767166,
0.013942415826022625,
0.04887379705905914,
-0.02628849819302559,
0.004680429585278034,
-0.011280970647931099,
0.054131194949150085,
-0.003858935320749879,
0.023210057988762856,
-0.09911177307367325,
-0.0027398266829550266,
0.03310747817158699,
-0.016674669459462166,
0.02331249788403511,
-0.060149360448122025,
0.020396770909428596,
0.026206787675619125,
-0.06513481587171555,
0.021738076582551003,
-0.033301617950201035,
-0.04062172397971153,
-0.03752579540014267,
0.0046098437160253525,
-0.04296373948454857,
0.022681990638375282,
0.012402348220348358,
-0.010318528860807419,
0.02451060712337494,
0.004294542595744133,
-0.031437743455171585,
-0.021469004452228546,
-0.0076038590632379055,
0.030294857919216156,
0.021026646718382835,
-0.024704709649086,
0.0923226922750473,
0.009202254004776478,
-0.00540577620267868,
-0.0052832188084721565,
0.020380035042762756,
0.0196552574634552,
-0.03454715386033058,
0.002453488064929843,
-0.004622671753168106,
0.028840970247983932,
0.0349402017891407,
0.006089233327656984,
-0.016230851411819458,
0.005807515699416399,
0.035796552896499634,
0.059028688818216324,
-0.027844656258821487,
0.029365580528974533,
-0.02071228250861168,
-0.03115689940750599,
-0.0100800646468997,
0.014810372143983841,
-0.039734166115522385,
-0.0347912535071373,
0.0044934069737792015,
0.02828676626086235,
-0.008419016376137733,
-0.0033325019758194685,
-0.0021368800662457943,
-0.06231147050857544,
-0.023470567539334297,
0.014103938825428486,
0.029193883761763573,
0.03557243198156357,
0.020154094323515892,
-0.0018165821675211191,
0.010823087766766548,
-0.022999761626124382,
0.0021106996573507786,
0.032101888209581375,
-0.039603978395462036,
-0.005477145779877901,
0.02043854631483555,
0.025144172832369804,
0.008820030838251114,
-0.04739352688193321,
-0.01995232328772545,
0.033443156629800797,
-0.00454585999250412,
0.02688741125166416,
-0.02201022021472454,
-0.04804101586341858,
0.01122402586042881,
-0.042805202305316925,
0.02165166661143303,
0.037994831800460815,
0.023187128826975822,
-0.015168088488280773,
-0.022963399067521095,
-0.013258557766675949,
0.013346373103559017,
0.055869825184345245,
-0.0023552454076707363,
-0.052676696330308914,
0.03536147251725197,
0.03801186382770538,
0.0007780882297083735,
-0.017081934958696365,
-0.0022022798657417297,
-0.009260333143174648,
0.0338810458779335,
-0.03772462531924248,
-0.01703176274895668,
-0.017104433849453926,
0.04026028513908386,
0.03408970683813095,
-0.014697970822453499,
-0.011959061026573181,
0.005664072465151548,
-0.042713623493909836,
0.08187170326709747,
-0.01572732999920845,
0.005914248991757631,
0.02661188878118992,
0.019749682396650314,
0.03705635294318199,
0.02103736810386181,
-0.029408855363726616,
-0.04053639993071556,
0.021986255422234535,
0.02416790835559368,
-0.00036111444933339953,
0.001838488271459937,
-0.03220704197883606,
0.03571844473481178,
-0.03665906935930252,
0.018080001696944237,
0.025885364040732384,
-0.010265177115797997,
-0.014220020733773708,
0.06826017796993256,
0.03154594451189041,
0.028174864128232002,
0.005302350968122482,
0.0014086567098274827,
0.018809916451573372,
0.00993137713521719,
0.0010843937052413821,
0.03128235414624214,
0.024428633973002434,
0.05379664897918701,
-0.0054468088783323765,
0.005355033092200756,
-0.004541239235550165,
0.009584883227944374,
0.052603546530008316,
0.009283636696636677,
0.007555651944130659,
-0.0038921257946640253,
0.03716105595231056,
0.034413788467645645,
0.04707879573106766,
-0.0034306803718209267,
-0.011212042532861233,
0.0758461058139801,
-0.06571807712316513,
-0.01076444610953331,
-0.04062184318900108,
0.0011485647410154343,
0.0016991236479952931,
0.0290435291826725,
0.0014568514889106154,
0.05281520634889603,
-0.013574671931564808,
-0.010289162397384644,
-0.023027390241622925,
-0.00936344638466835,
0.01414748840034008,
-0.025782465934753418,
0.02211122214794159,
-0.02550490014255047,
0.0023637122940272093,
-0.016571536660194397,
-0.030544036999344826,
0.0006843468290753663,
-0.027215199545025826,
-0.01719178445637226,
0.010628565214574337,
0.03451871871948242,
-0.008538755588233471,
0.005161795765161514,
-0.035456061363220215,
0.049233272671699524,
-0.017129002138972282,
0.00227140705101192,
-0.00957805197685957,
0.02522430196404457,
-0.015904076397418976,
-0.019369617104530334
] |
<p>I'm trying to recall some fact that I learned in my college materials science class, where we learned concepts like stress vs. strain. </p>
<p>I remember that materials like metal have a breaking point, and if an applied stress produces a force higher than the breaking point, the metal will break. Or something like that.</p>
<p>Now, I distinctly remember my professor showing some real-world engineering failure where a metal was used in a structure (in an airplane or bridge), and it broke even through the stress never went above the breaking point. Rather, the metal broke due to repeated use of the structure. What is this principle?</p>
| 8,290 |
[
-0.02757982723414898,
-0.01637459546327591,
0.015291373245418072,
-0.05740131437778473,
0.018538104370236397,
0.027312487363815308,
-0.011221841908991337,
0.007692903280258179,
0.02570810541510582,
-0.039972636848688126,
0.04954047501087189,
0.05791911855340004,
0.03787434101104736,
-0.011295528151094913,
-0.0048987772315740585,
-0.0005973579827696085,
0.006984034553170204,
-0.044376760721206665,
0.00552807142958045,
-0.0016727838665246964,
0.002641742816194892,
-0.04382174089550972,
-0.0418877974152565,
0.0004620248801074922,
-0.016902783885598183,
0.004684397950768471,
0.029221855103969574,
0.01488874014467001,
0.06643097847700119,
0.039906762540340424,
-0.011434759944677353,
-0.030671264976263046,
-0.01270376518368721,
0.01889657974243164,
0.02140634134411812,
0.010935420170426369,
-0.015002984553575516,
-0.03765338286757469,
-0.013715945184230804,
0.023447226732969284,
-0.011649450287222862,
-0.0010946497786790133,
0.010098122991621494,
0.06334433704614639,
-0.04985019564628601,
0.002113919472321868,
0.014356279745697975,
-0.05244924873113632,
0.030994603410363197,
-0.011141938157379627,
0.03921432048082352,
-0.045853082090616226,
0.04561164975166321,
0.020363111048936844,
0.02361140586435795,
-0.01823708601295948,
0.07376338541507721,
0.04266643524169922,
-0.018217269331216812,
-0.06912364810705185,
-0.05080233886837959,
-0.027357468381524086,
-0.03258983790874481,
-0.01191872451454401,
-0.03931621462106705,
0.06802784651517868,
-0.036581769585609436,
-0.0670703798532486,
0.02890363708138466,
0.00670774606987834,
-0.01808180660009384,
0.007929974235594273,
0.0406649187207222,
-0.011308560147881508,
-0.006941439583897591,
-0.04717002063989639,
0.018641658127307892,
-0.02123003825545311,
0.014151783660054207,
0.07672354578971863,
-0.009906681254506111,
0.03660557419061661,
0.016154607757925987,
0.061338599771261215,
-0.015754492953419685,
-0.0487414114177227,
0.09549874812364578,
-0.012357850559055805,
0.018438424915075302,
0.01171075738966465,
0.00921717844903469,
-0.007165429648011923,
0.011877098120748997,
0.006789964623749256,
-0.03747804835438728,
0.008407087065279484,
-0.013687191531062126,
0.0444345623254776,
-0.017599282786250114,
0.025127073749899864,
0.02714596875011921,
-0.016183026134967804,
0.055592264980077744,
0.05568382889032364,
0.007035921327769756,
-0.059338588267564774,
-0.010026776231825352,
0.011051569133996964,
0.008670137263834476,
0.015397385694086552,
-0.022172793745994568,
0.010013162158429623,
0.02942812629044056,
0.007304350379854441,
0.01635235920548439,
0.01579419896006584,
0.022941535338759422,
-0.023117784410715103,
0.069929338991642,
0.04402681067585945,
0.0338987335562706,
-0.028335217386484146,
0.03880131244659424,
-0.018881015479564667,
-0.05360562354326248,
0.013662222772836685,
0.010068933479487896,
-0.03258905187249184,
0.004357641562819481,
0.03870736062526703,
0.00691304262727499,
-0.008382202126085758,
-0.01785111427307129,
0.013223688118159771,
0.0631456971168518,
-0.01757047511637211,
-0.09870392829179764,
-0.046815983951091766,
0.05501494184136391,
0.04213133826851845,
-0.029810378327965736,
-0.059840619564056396,
0.03694405406713486,
0.001097906962968409,
0.06534552574157715,
0.0368259996175766,
-0.0007231422350741923,
-0.025076836347579956,
0.02537977136671543,
0.033993784338235855,
-0.018709026277065277,
0.010452569462358952,
0.025320544838905334,
-0.014262469485402107,
0.0020467296708375216,
-0.08316503465175629,
-0.01148128416389227,
0.018743067979812622,
-0.009944237768650055,
-0.04259293153882027,
0.06324605643749237,
-0.03829162195324898,
0.0010844063945114613,
-0.000007225357876450289,
-0.01839160919189453,
-0.00587166752666235,
0.09559064358472824,
0.002513667568564415,
-0.0030439661350101233,
0.07435489445924759,
0.06160854920744896,
0.005018580239266157,
0.01579395867884159,
0.05361296609044075,
0.023031922057271004,
-0.05760304629802704,
0.025073247030377388,
-0.03407702594995499,
-0.001801281701773405,
0.007220524828881025,
-0.06148994341492653,
-0.022323712706565857,
0.029744429513812065,
-0.005024177487939596,
-0.008485889993607998,
0.05859548598527908,
-0.024312280118465424,
-0.006168394815176725,
0.01624210923910141,
-0.012640903703868389,
0.0007814239943400025,
-0.04756292328238487,
0.05146607756614685,
-0.047098178416490555,
-0.007658901158720255,
0.020412268117070198,
-0.003785630688071251,
0.020321661606431007,
-0.06201125681400299,
-0.011093558743596077,
-0.004106004722416401,
-0.007903316989541054,
-0.005220130085945129,
0.009695210494101048,
0.023087428882718086,
0.015164348296821117,
-0.003004613798111677,
0.034015484154224396,
0.027588019147515297,
-0.032915811985731125,
-0.011585080064833164,
0.019579656422138214,
-0.024832356721162796,
0.01344076544046402,
0.007874337956309319,
-0.018558235839009285,
0.028909672051668167,
-0.05965939909219742,
0.005508510395884514,
0.050371892750263214,
-0.009560473263263702,
0.05138843134045601,
0.044233910739421844,
-0.0032072740141302347,
-0.008925236761569977,
0.02155398577451706,
-0.01913577876985073,
0.011964487843215466,
-0.03096599131822586,
-0.013519244268536568,
-0.044847168028354645,
0.0175517238676548,
0.05860085412859917,
0.023614030331373215,
-0.026416298002004623,
0.003865372622385621,
-0.009467276744544506,
0.029401663690805435,
0.02886253222823143,
0.06359748542308807,
-0.028435077518224716,
-0.008178316988050938,
-0.01089923083782196,
0.025447199121117592,
0.02271679975092411,
0.0164629053324461,
0.0067659844644367695,
0.0429617278277874,
0.010437358170747757,
0.004195210058242083,
0.013720853254199028,
0.02956235781311989,
-0.006139985751360655,
0.01817113347351551,
0.02270006388425827,
-0.040908537805080414,
0.03011743351817131,
-0.03061315417289734,
0.001514757750555873,
0.0287187397480011,
-0.0011030650930479169,
0.011328039690852165,
-0.061556193977594376,
0.010225224308669567,
0.030066538602113724,
0.020261963829398155,
-0.03521527349948883,
0.0029549768660217524,
0.02324686385691166,
-0.007239433005452156,
-0.003688085125759244,
-0.03642227128148079,
-0.013542452827095985,
-0.010494022630155087,
-0.0042633474804461,
-0.017423013225197792,
0.0019445937359705567,
0.0659642443060875,
-0.026055335998535156,
-0.024936126545071602,
-0.013329574838280678,
-0.0846051350235939,
0.0060821655206382275,
0.00010201854456681758,
-0.021802211180329323,
0.01806197501718998,
-0.002188480459153652,
-0.01160102616995573,
0.04589555785059929,
0.01603499986231327,
0.022427106276154518,
0.029425986111164093,
0.00652133347466588,
-0.027329443022608757,
0.012540305964648724,
-0.036900583654642105,
0.010242355056107044,
-0.008192619308829308,
-0.036877259612083435,
0.03835402429103851,
-0.002437931252643466,
-0.02159137651324272,
0.0652788057923317,
-0.04794155806303024,
-0.05003433674573898,
-0.050518013536930084,
-0.017382925376296043,
-0.017461363226175308,
-0.020458176732063293,
0.019465727731585503,
0.03659510239958763,
-0.043556034564971924,
-0.03914160653948784,
-0.020398998633027077,
-0.04978674650192261,
-0.016496552154421806,
-0.024557825177907944,
0.03379997983574867,
-0.017250102013349533,
-0.03487822040915489,
0.07485871016979218,
-0.007242359220981598,
-0.04544036090373993,
-0.01177855022251606,
-0.04137846454977989,
0.034430187195539474,
-0.0258330088108778,
0.02439771592617035,
0.034661199897527695,
-0.006978977005928755,
0.03958369418978691,
0.008369513787329197,
0.05247489735484123,
0.012952820397913456,
0.027523880824446678,
-0.019622845575213432,
-0.057058993726968765,
0.009743471629917622,
-0.016508297994732857,
0.013845162466168404,
0.028811318799853325,
-0.03767960146069527,
0.03954864293336868,
0.012597396969795227,
0.06112414225935936,
0.016674146056175232,
-0.05800040811300278,
0.03821433335542679,
-0.018572920933365822,
-0.008797776885330677,
-0.04674554988741875,
0.0441008098423481,
-0.006314178463071585,
-0.003037272021174431,
0.007113658357411623,
0.02111629769206047,
0.023691831156611443,
-0.034823495894670486,
-0.02020714245736599,
0.02918417938053608,
0.012245384976267815,
-0.03788246214389801,
-0.003032604930922389,
-0.009970464743673801,
-0.002359301084652543,
0.024451596662402153,
-0.011221237480640411,
-0.011350360698997974,
0.03816213458776474,
0.00492902472615242,
0.03128550946712494,
-0.011822540313005447,
-0.043572988361120224,
0.00966417696326971,
-0.06251462548971176,
-0.043223295360803604,
0.02644169144332409,
0.03058835305273533,
-0.010157575830817223,
0.06059219315648079,
0.0533633828163147,
0.023643461987376213,
0.05737089738249779,
-0.021198080852627754,
-0.08830653876066208,
0.03882401064038277,
-0.03535298630595207,
-0.015405287966132164,
-0.007345059420913458,
-0.016316888853907585,
-0.011212721467018127,
-0.047665975987911224,
-0.035088974982500076,
-0.013819906860589981,
-0.005961436312645674,
-0.04260169714689255,
0.03163421154022217,
-0.03934187442064285,
-0.024168824777007103,
0.010098190978169441,
-0.0032577377278357744,
0.026763588190078735,
-0.03765614330768585,
-0.0017307027010247111,
0.04012923687696457,
-0.028122102841734886,
-0.00326529354788363,
-0.018598563969135284,
0.006065456196665764,
0.02793794497847557,
0.012809217907488346,
0.012036807835102081,
0.021204223856329918,
-0.015230797231197357,
0.007623993791639805,
0.0018614736618474126,
0.03882254660129547,
0.022473856806755066,
0.00010814002598635852,
-0.05057329684495926,
-0.020837148651480675,
-0.005547483451664448,
0.001093960483558476,
0.025950677692890167,
-0.005807157605886459,
0.023692509159445763,
0.014337738044559956,
0.019543591886758804,
-0.05093918368220329,
0.03811539337038994,
0.042109448462724686,
0.0265202634036541,
-0.007968001998960972,
-0.039155926555395126,
-0.007013489492237568,
-0.028666572645306587,
-0.017547795549035072,
0.011686934158205986,
-0.008347940631210804,
-0.03480784595012665,
0.01869644969701767,
0.03651455044746399,
-0.0007064954261295497,
-0.013415679335594177,
0.014814749360084534,
-0.008531341329216957,
-0.021553879603743553,
0.022054549306631088,
-0.026982195675373077,
0.008144557476043701,
0.015603669919073582,
0.05308934301137924,
0.03982795402407646,
-0.008002202957868576,
-0.07333756238222122,
-0.00833171047270298,
0.04213125258684158,
-0.0030062671285122633,
-0.033849768340587616,
0.0008436929201707244,
-0.010967941954731941,
-0.055600885301828384,
0.04435548558831215,
-0.022385258227586746,
0.015176670625805855,
-0.0341915637254715,
0.03875941410660744,
-0.052762001752853394,
-0.021377230063080788,
-0.031396619975566864,
-0.003404262475669384,
0.007715748623013496,
0.035678498446941376,
-0.005757851060479879,
0.00994891207665205,
0.0061083221808075905,
0.012899958528578281,
0.01881873793900013,
0.029685745015740395,
0.002346522407606244,
-0.020974038168787956,
-0.027627184987068176,
0.041998233646154404,
-0.029233288019895554,
-0.08139794319868088,
-0.010509946383535862,
0.029016762971878052,
0.0009763010893948376,
0.012524168007075787,
-0.038822952657938004,
-0.05325011536478996,
0.05923278629779816,
0.0068344902247190475,
0.01383249368518591,
0.018776562064886093,
0.007511924020946026,
0.009677741676568985,
0.0542011521756649,
-0.02375606819987297,
0.03265450522303581,
0.021600766107439995,
0.012910447083413601,
-0.001759088016115129,
-0.002630643779411912,
0.05085126310586929,
-0.0045439014211297035,
0.016946688294410706,
-0.024944761767983437,
0.012707737274467945,
-0.03939065709710121,
0.03667367622256279,
0.004120235797017813,
0.025649698451161385,
-0.020119264721870422,
-0.030516916885972023,
0.019131885841488838,
-0.0051619368605315685,
0.017168888822197914,
-0.015471997670829296,
0.02712107077240944,
0.03447748348116875,
-0.020406708121299744,
-0.00749702425673604,
-0.019680004566907883,
0.015685265883803368,
-0.024282464757561684,
0.005784118082374334,
-0.0282936729490757,
0.013739798218011856,
-0.04344412684440613,
-0.05314868688583374,
0.045964840799570084,
-0.042945947498083115,
0.04955950379371643,
-0.032286033034324646,
0.026313845068216324,
0.006135022267699242,
-0.017690084874629974,
-0.0006093408446758986,
0.019460592418909073,
-0.001576733193360269,
0.0323929525911808,
-0.022753646597266197,
0.032576754689216614,
0.008696191012859344,
0.025239642709493637,
-0.044999852776527405,
-0.05120871961116791,
0.051407553255558014,
0.028434552252292633,
-0.05069628730416298,
0.004257151857018471,
-0.0020676495041698217,
0.01996002346277237,
-0.05423133447766304,
0.009802186861634254,
0.054739080369472504,
-0.034876879304647446,
-0.036006614565849304,
0.02373833768069744,
-0.008655142970383167,
0.06609012931585312,
-0.04549432173371315,
-0.04881776124238968,
-0.008874770253896713,
0.0022229694295674562,
-0.020862890407443047,
-0.03674069792032242,
0.046271912753582,
-0.027310766279697418,
0.006013147532939911,
0.00011253703996771947,
-0.011623091995716095,
0.04224780946969986,
-0.030696026980876923,
0.030578473582863808,
0.031446974724531174,
-0.00008770577551331371,
0.0015916344709694386,
-0.006354998331516981,
0.05617093667387962,
0.035687707364559174,
0.02001999504864216,
0.0003360263945069164,
0.021965060383081436,
-0.03233911469578743,
-0.04209605231881142,
0.0017924775602295995,
0.00038682305603288114,
0.013964800164103508,
0.0038018501363694668,
0.059456758201122284,
-0.029111474752426147,
-0.025359898805618286,
-0.01182213332504034,
-0.06160677969455719,
0.011213134974241257,
0.006289222743362188,
0.0053534116595983505,
0.020832505077123642,
0.01722765900194645,
-0.046509746462106705,
-0.012306402437388897,
-0.014656986109912395,
0.02699701488018036,
0.04023837670683861,
-0.051605142652988434,
0.04175982624292374,
0.04431840032339096,
0.004532560706138611,
0.036858998239040375,
-0.013794809579849243,
-0.014904127456247807,
0.031070737168192863,
-0.034667447209358215,
0.05878875404596329,
-0.007975522428750992,
-0.00853491760790348,
0.021254125982522964,
0.03978287801146507,
-0.03321405127644539,
-0.00382118858397007,
0.014155566692352295,
0.011330706998705864,
0.02721780352294445,
-0.028755629435181618,
-0.03330159932374954,
0.05748531594872475,
-0.040002573281526566,
0.017966564744710922,
0.005497885402292013,
-0.003563537960872054,
0.032640136778354645,
-0.0015073175309225917,
0.008280938491225243,
-0.04600857198238373,
-0.007967558689415455,
-0.025142529979348183,
0.024477001279592514,
-0.02798989973962307,
-0.024384617805480957,
0.020937075838446617,
0.03712664172053337,
0.010316312313079834,
0.005001945421099663,
-0.011122486554086208,
-0.011419461108744144,
-0.047211647033691406,
-0.017637398093938828,
-0.040405504405498505,
-0.025488143786787987,
-0.0062914337031543255,
-0.0030645704828202724,
-0.04507730156183243,
0.026772363111376762,
-0.03243791684508324,
0.03463539853692055,
-0.013820953667163849,
0.03360821679234505,
-0.010940520092844963,
0.07124041020870209,
-0.0012011752696707845,
0.02503005973994732,
0.004107310436666012,
-0.000740777759347111,
0.12334788590669632,
0.048991501331329346,
0.0024384346324950457,
-0.04049742594361305,
0.015864461660385132,
-0.021547311916947365,
-0.04711979627609253,
-0.0162363201379776,
0.002619473496451974,
-0.00178137409966439,
0.01859370805323124,
0.020798882469534874,
0.06814402341842651,
0.013239553198218346,
0.0033967511262744665,
0.06528976559638977,
-0.006307229399681091,
0.01346245314925909,
-0.005866232793778181,
0.028058016672730446,
-0.03843936324119568,
-0.010393350385129452,
-0.017248647287487984,
0.01693044789135456,
-0.01075015589594841,
-0.025416327640414238,
-0.005522475112229586,
-0.030491545796394348,
0.05022754892706871,
0.006429404020309448,
0.016179624944925308,
0.006594715174287558,
-0.015302160754799843,
-0.0049941749311983585,
-0.025775747373700142,
0.008445949293673038,
0.019260074943304062,
0.019868813455104828,
0.0060174972750246525,
-0.006875503342598677,
0.00800234917551279,
0.004365071188658476,
-0.0032207907643169165,
0.01582193933427334,
-0.017664415761828423,
-0.012318318709731102,
-0.04864095523953438,
0.03311998397111893,
-0.008272288367152214,
0.018806276842951775,
-0.010003231465816498,
-0.031566571444272995,
0.027385249733924866,
0.007647832855582237,
-0.058627787977457047,
0.0071417889557778835,
-0.00293469219468534,
-0.01885833591222763,
-0.03237181529402733,
-0.02667221426963806,
0.011692102998495102,
-0.02680925466120243,
0.013202318921685219,
-0.0005189907969906926,
-0.029443420469760895,
0.05524619668722153,
0.008271859958767891,
0.03339504450559616,
-0.009999646805226803,
0.0018167283851653337,
-0.029106533154845238,
-0.013211848214268684,
-0.025174492970108986,
0.009614181704819202,
-0.003088385099545121,
0.03453177213668823,
0.04461715742945671,
-0.01429966650903225,
0.0019881390035152435,
-0.009288124740123749,
-0.013634324073791504,
0.061716772615909576,
-0.02763962186872959,
-0.026687655597925186,
-0.030984964221715927,
0.015367207117378712,
0.008871734142303467,
0.06238040328025818,
-0.0005001192330382764,
-0.015034965239465237,
-0.012426177971065044,
0.001156143145635724,
0.02300221100449562,
-0.0470644012093544,
-0.014949560165405273,
-0.0054439278319478035,
-0.03203693404793739,
0.002360372804105282,
-0.006901253946125507,
0.03445815294981003,
0.04619637504220009,
-0.015940606594085693,
0.009421596303582191,
0.043697185814380646,
-0.018051831051707268,
-0.01691153645515442,
0.07126401364803314,
-0.02132341079413891,
0.012622898444533348,
-0.008438152261078358,
0.02897663600742817,
-0.05633591115474701,
-0.031486671417951584,
-0.003955212887376547,
-0.042649608105421066,
-0.04437624290585518,
0.04383057728409767,
0.009143372066318989,
0.018543798476457596,
-0.010820455849170685,
-0.00311693805269897,
-0.04555791988968849,
-0.04243842139840126,
-0.04462006315588951,
-0.0317157618701458,
0.019927723333239555,
0.005308200139552355,
-0.060643270611763,
0.025694511830806732,
0.002990683075040579,
0.0034066825173795223,
0.005964451003819704,
0.0295364111661911,
0.018532751128077507,
-0.0010401143226772547,
0.028644973412156105,
-0.018414977937936783,
0.05275868996977806,
-0.006863337010145187,
0.01026340015232563,
0.031193932518363,
-0.008963292464613914,
-0.03660344332456589,
0.028593305498361588,
-0.024602433666586876,
-0.0001385603245580569,
0.010563519783318043,
0.01555070374161005,
0.0022053737193346024,
0.06822244077920914,
0.0032926579006016254,
-0.00010245306475553662,
-0.018960507586598396,
0.0029725064523518085,
-0.019118933007121086,
-0.020411444827914238,
0.0026999122928828,
-0.0005741099594160914,
0.010284880176186562,
-0.008366409689188004,
0.0030597157310694456,
0.012675037607550621,
0.004661982879042625,
0.04654906317591667,
-0.013004926033318043,
-0.0018460318678990006,
0.026991471648216248,
0.016742568463087082,
0.023038167506456375,
0.0788026750087738,
-0.03406248986721039,
0.03738341107964516,
0.022751865908503532,
0.005725578870624304,
-0.08118462562561035,
-0.00015501999587286264,
-0.015142683871090412,
-0.00946416798979044,
-0.010963456705212593,
0.008512180298566818,
0.039441823959350586,
0.02327360212802887,
-0.05751364305615425,
0.008680945262312889,
-0.03426061570644379,
-0.068320132791996,
-0.020515520125627518,
0.006312744691967964,
-0.004388977773487568,
0.05222979187965393,
0.01628941483795643,
0.030570844188332558,
0.051337260752916336,
0.04216347262263298,
-0.020789669826626778,
0.005826363805681467,
0.007788443006575108,
0.017401577904820442,
-0.008525918237864971,
-0.011531728319823742,
0.05375218763947487,
-0.014961862936615944,
-0.06354565173387527,
0.018366465345025063,
-0.04066910967230797,
0.004567067604511976,
0.030778249725699425,
0.007365951780229807,
-0.028652619570493698,
0.02170684188604355,
-0.017087748274207115,
-0.004489230457693338,
-0.01189242210239172,
-0.008960476145148277,
-0.008941196836531162,
0.0005274917930364609,
-0.02930753491818905,
0.011809858493506908,
0.025936653837561607,
-0.015606141649186611,
-0.035374559462070465,
0.03831030800938606,
-0.012160392478108406,
-0.016283651813864708,
0.024438049644231796,
0.009929053485393524,
0.03088098019361496,
-0.01708051562309265,
0.0009988737292587757,
-0.045086074620485306,
-0.019433585926890373,
0.043028220534324646,
0.038302671164274216,
0.01332659088075161,
0.03331148251891136,
-0.02655179426074028,
-0.003460324602201581,
-0.018764842301607132,
0.002320623490959406,
-0.05761192739009857,
-0.09493892639875412,
-0.005168435163795948,
0.014967447146773338,
-0.01510548498481512,
-0.048187609761953354,
-0.01699093170464039,
-0.01952589862048626,
0.03201349824666977,
0.03915311023592949,
0.02739371918141842,
0.027310242876410484,
-0.06669402122497559,
-0.017481988295912743,
-0.10228268057107925,
0.06258245557546616,
-0.03893093392252922,
0.008773619309067726,
-0.04328254237771034,
-0.052218422293663025,
-0.01290266402065754,
0.013106850907206535,
0.04249776154756546,
-0.01399880088865757,
0.014459449797868729,
-0.000597307865973562,
-0.00041397049790248275,
0.013548214919865131,
-0.03230363503098488,
0.015976419672369957,
0.002521952847018838,
-0.020415274426341057,
-0.012572148814797401,
0.001131757628172636,
-0.00662908935919404,
-0.0032239719294011593,
0.022356830537319183,
-0.008474663831293583,
0.012302703224122524,
-0.0077725304290652275,
-0.002983981976285577,
0.03148064762353897,
0.03223924711346626,
-0.00814118329435587,
0.07610149681568146,
-0.05844051018357277,
0.03089553490281105,
-0.004745613783597946,
-0.01570644974708557,
-0.041177671402692795,
0.0470796637237072,
-0.03734149783849716,
0.022186392918229103,
-0.014141135849058628,
0.011085564270615578,
0.017605412751436234,
-0.08506935834884644,
0.012039868161082268,
0.011272107250988483,
-0.03346090391278267,
-0.0013086330145597458,
0.0232525821775198,
0.017282316461205482,
0.0168344397097826,
-0.05049300193786621,
-0.03619491681456566,
0.010429934598505497,
0.004083910956978798,
-0.018178755417466164,
0.04235566779971123,
0.023850521072745323,
-0.016577135771512985,
0.01729191653430462,
0.03970806300640106,
-0.03205554932355881,
-0.012221603654325008,
-0.0032280082814395428,
0.026274945586919785,
-0.031423747539520264,
-0.04235633835196495,
-0.027786735445261,
-0.033509209752082825,
0.032102979719638824,
0.019422292709350586,
-0.014884578064084053,
0.08656375855207443,
-0.009436165913939476,
0.011821601539850235,
-0.016323162242770195,
0.022746630012989044,
0.02378031238913536,
-0.005186736583709717,
0.011479906737804413,
0.06094904616475105,
-0.0071487026289105415,
-0.0035769089590758085,
0.002928490284830332,
0.0328323170542717,
0.038348518311977386,
0.02541743591427803,
0.02932194620370865,
-0.01952999457716942,
-0.008723710663616657,
-0.04536652937531471,
-0.0003192872100044042,
-0.07507726550102234,
0.0057651749812066555,
0.025759520009160042,
0.01774546131491661,
-0.004030904732644558,
0.03373280540108681,
-0.024219641461968422,
-0.014442122541368008,
0.02295522205531597,
-0.0875476524233818,
0.004429744090884924,
-0.03138706460595131,
0.053927287459373474,
-0.03509197756648064,
-0.019018977880477905
] |
<p>I've played with this idea for years, and haven't really been able to eliminate it. So, perhaps someone here can point to simple experimental evidence that would do so.</p>
<p>Here's the issue: Antimatter of course annihilates ordinary matter, but the more precise statement is that antiparticles annihilate <em>the same types</em> of particles.</p>
<p>That means that you <em>can</em> mix antimatter with matter without it going boom, as long as you only allow one of each type in the mix. For example, positrons (anti-electrons) can pass through interior of a neutron at low speed without causing annihilations for the simple reason quarks and electrons cannot pair off for annihilation.</p>
<p>All of which leads to this delightfully non-standard line of thought: If what we call electrons were actually anti-particles, would we even be able to tell?</p>
<p>A more precise way to express that is this: If <em>all</em> negatively charged particles had the internal chirality of antimatter, and all positively charged particles that of matter, would the resulting transformed theory lead to paradoxes or contradictions with the Standard Model? Or would it instead produce an experimentally isomorphic theory that describes what we see just as accurately as the Standard Model?</p>
<blockquote>
<p>(The neutrinos of course have no charges, so their affiliations would be determined by their associations with the electron types.)</p>
</blockquote>
<p>So my question is this: Would reclassifying the chirality of particles so that "pro" always means positive particles and "anti" always means negative particles result in a version of the Standard Model that is experimentally isomorphic to known results, or would it instead produce one or more clear contradictions or paradoxes?</p>
<p>One final note that's too much fun not to mention: a workable pro="+"/anti="-" theory would convert the mystery of why matter dominates over antimatter into a mystery of the particle mix came out so asymmetrically.</p>
| 8,291 |
[
-0.03280009329319,
0.011247459799051285,
0.018914436921477318,
-0.045750800520181656,
0.04525773227214813,
0.023822544142603874,
-0.023491911590099335,
0.002053861040621996,
0.010488872416317463,
0.0012634501326829195,
0.03521706536412239,
0.00866672769188881,
0.05879542976617813,
0.026438411325216293,
0.013739372603595257,
0.021976342424750328,
-0.02466569095849991,
-0.013937524519860744,
-0.010909617878496647,
-0.056007735431194305,
0.028256505727767944,
0.005506489425897598,
0.023403307422995567,
0.015759039670228958,
-0.02724110148847103,
0.04766406491398811,
0.011131283827126026,
-0.013944033533334732,
0.009722838178277016,
0.03312529996037483,
0.01563812978565693,
-0.00869759265333414,
0.040051162242889404,
0.006046140566468239,
0.028018785640597343,
-0.008329330943524837,
0.02549310401082039,
-0.04400699958205223,
-0.001563421101309359,
0.030219782143831253,
-0.007724311668425798,
-0.014884911477565765,
-0.0032259784638881683,
0.047588251531124115,
-0.0389457643032074,
0.011831887066364288,
-0.01585586741566658,
0.01002571266144514,
0.05394720658659935,
-0.09048137813806534,
0.04669489711523056,
0.036584410816431046,
0.038087423890829086,
0.008355522528290749,
-0.012373577803373337,
-0.018944375216960907,
0.09296015650033951,
0.058043669909238815,
0.00020685585332103074,
-0.06463592499494553,
-0.021287189796566963,
-0.011882097460329533,
0.01070671807974577,
-0.005023987963795662,
-0.03943658247590065,
0.04751943051815033,
0.009476718492805958,
0.0017786783864721656,
0.016281118616461754,
0.008683381602168083,
0.017579782754182816,
0.0008955087978392839,
-0.005270556081086397,
0.033680062741041183,
0.008286656811833382,
-0.03951997309923172,
0.04066692665219307,
0.018510306254029274,
-0.0015828473260626197,
0.038206491619348526,
-0.023327022790908813,
0.017939427867531776,
0.008162174373865128,
0.03137057647109032,
0.0039430358447134495,
-0.0245734341442585,
0.05233455449342728,
-0.005049397703260183,
-0.02458052895963192,
0.04486003518104553,
-0.028790324926376343,
-0.010108238086104393,
0.04843264818191528,
0.015653394162654877,
-0.04293062537908554,
0.036829639226198196,
-0.01673639565706253,
0.038969822227954865,
-0.0005810351576656103,
0.002454579807817936,
-0.008767214603722095,
0.03801039606332779,
0.04192856326699257,
0.02983018010854721,
0.0054452503100037575,
-0.033307019621133804,
-0.02538355626165867,
0.029699621722102165,
-0.005951720755547285,
-0.015280683524906635,
-0.01611034944653511,
-0.005902810953557491,
-0.012993655167520046,
-0.01725233532488346,
0.012663100846111774,
-0.043487004935741425,
0.009580407291650772,
-0.0627337247133255,
0.051954321563243866,
0.04369386285543442,
0.04294118285179138,
-0.004252786748111248,
0.015558836050331593,
-0.028081437572836876,
-0.057944342494010925,
-0.016192598268389702,
0.013140025548636913,
0.03074863739311695,
0.002632945543155074,
0.006948503199964762,
-0.0013801527675241232,
-0.023515915498137474,
0.035866525024175644,
-0.05201654136180878,
0.07194120436906815,
-0.012619302608072758,
-0.08082573115825653,
-0.09086612612009048,
0.005748098716139793,
-0.017574042081832886,
-0.07570715248584747,
-0.08050774782896042,
-0.03740077093243599,
0.019661344587802887,
0.09111961722373962,
-0.004359089769423008,
-0.03457164391875267,
0.022450465708971024,
0.017887447029352188,
0.05366669222712517,
0.011249648407101631,
-0.006648259237408638,
0.005959778092801571,
-0.03744535893201828,
-0.033653732389211655,
-0.040982626378536224,
0.023552071303129196,
-0.006030965596437454,
-0.008106311783194542,
0.0025846369098871946,
0.04594401270151138,
0.004984765779227018,
0.014414356090128422,
0.0018554585985839367,
-0.015505664981901646,
-0.02977660484611988,
0.09485425055027008,
0.035346515476703644,
-0.03958680480718613,
0.021739087998867035,
0.027988435700535774,
0.035674337297677994,
0.005104131065309048,
0.03554382920265198,
0.05712529644370079,
-0.029585406184196472,
-0.02890877239406109,
-0.0435444638133049,
-0.0006570076220668852,
-0.018942508846521378,
-0.03559079393744469,
-0.022426078096032143,
-0.02979162149131298,
0.02441590093076229,
0.034833408892154694,
0.022824937477707863,
-0.016495587304234505,
-0.04157039523124695,
0.05333032086491585,
-0.05905049294233322,
-0.013775080442428589,
-0.08902011811733246,
-0.019208766520023346,
-0.011343171820044518,
-0.01782296411693096,
0.03852788358926773,
0.026071390137076378,
0.013118725270032883,
-0.027489207684993744,
-0.028537316247820854,
-0.021313857287168503,
0.0403033047914505,
0.019256016239523888,
0.019612662494182587,
0.0033108110073953867,
0.004843622446060181,
0.04129130393266678,
-0.05274144932627678,
0.00929421279579401,
0.028504420071840286,
-0.02938256226480007,
0.008418087847530842,
-0.022622568532824516,
0.000320121762342751,
0.019542399793863297,
0.019438449293375015,
0.03274574503302574,
-0.007110205013304949,
-0.010979298502206802,
0.061448827385902405,
-0.012614856474101543,
0.0771380215883255,
-0.005087309516966343,
-0.012728179804980755,
-0.023457787930965424,
0.02949625439941883,
0.04124009981751442,
0.028764786198735237,
-0.010398863814771175,
-0.01611447148025036,
-0.04171149060130119,
-0.0015798961976543069,
0.024688487872481346,
0.02689618058502674,
-0.05314053222537041,
0.048784926533699036,
-0.01498418115079403,
0.0039662085473537445,
-0.0026093991473317146,
0.02023993618786335,
-0.030446941033005714,
-0.06404139846563339,
-0.0004746424965560436,
-0.025498323142528534,
0.026531590148806572,
0.0011650375090539455,
0.04211600124835968,
-0.04046684503555298,
-0.03644449636340141,
-0.008093693293631077,
-0.024950720369815826,
0.016713488847017288,
0.01584223471581936,
-0.0074133798480033875,
0.0033070349600166082,
-0.07919949293136597,
0.01627124845981598,
0.01463154423981905,
0.02080235257744789,
0.002169504063203931,
-0.020148567855358124,
-0.01914622075855732,
-0.01812194101512432,
0.019633516669273376,
0.022929538041353226,
0.0018985634669661522,
0.012055768631398678,
0.004213877022266388,
0.01165222842246294,
-0.07180274277925491,
0.0031147655099630356,
-0.01101990882307291,
0.005572390742599964,
-0.013541150838136673,
0.029699532315135002,
0.009787365794181824,
0.0029919492080807686,
0.04999540001153946,
-0.027703164145350456,
-0.038949303328990936,
0.01886412501335144,
-0.009792891331017017,
0.029935330152511597,
0.07521623373031616,
-0.02211056463420391,
0.015048257075250149,
-0.07363787293434143,
-0.03483862057328224,
0.014366647228598595,
-0.010148374363780022,
0.011214662343263626,
-0.015724364668130875,
-0.026577210053801537,
-0.039536550641059875,
-0.003676365362480283,
-0.03330419957637787,
-0.02525562420487404,
-0.03414062783122063,
-0.01020901184529066,
0.03680409491062164,
0.013761681504547596,
-0.018469681963324547,
-0.020563393831253052,
-0.027469219639897346,
-0.06409367173910141,
0.00623438972979784,
-0.02305351197719574,
0.02105800434947014,
-0.026684077456593513,
0.03141877427697182,
0.03191886469721794,
-0.05541015788912773,
0.02447686344385147,
-0.040453098714351654,
-0.049579888582229614,
-0.017432086169719696,
0.004863244481384754,
0.012551243416965008,
0.04802786558866501,
-0.03003319539129734,
0.056890714913606644,
0.02847335860133171,
-0.061426613479852676,
-0.03131961449980736,
0.014020114205777645,
-0.0344969779253006,
-0.00642468873411417,
0.010944790206849575,
0.05014253780245781,
0.0038842689245939255,
0.037687141448259354,
0.020509397611021996,
0.044383615255355835,
-0.012175995856523514,
0.017967086285352707,
-0.04665423929691315,
0.011218328028917313,
-0.004439018666744232,
0.014432505704462528,
0.026228029280900955,
-0.008047152310609818,
-0.014459885656833649,
0.021804075688123703,
0.009938488714396954,
0.027971824631094933,
0.04727889969944954,
-0.03625871613621712,
0.06631859391927719,
0.01580648124217987,
0.04254414886236191,
-0.00788254477083683,
0.012240582145750523,
-0.00944438949227333,
-0.005598004441708326,
0.0061339414678514,
0.029988907277584076,
0.030169304460287094,
-0.018182668834924698,
0.0059705390594899654,
0.041536327451467514,
0.04143714904785156,
-0.019624661654233932,
-0.035816069692373276,
-0.006347503047436476,
0.020916376262903214,
-0.002011694712564349,
0.001851039589382708,
0.03158612176775932,
0.04503148794174194,
0.01350890938192606,
0.02206760086119175,
0.0325121246278286,
-0.007804251275956631,
0.003308940911665559,
-0.02241758070886135,
-0.000261389504885301,
-0.025157125666737556,
0.026056036353111267,
0.015350566245615482,
0.06771428883075714,
0.025159893557429314,
-0.02564554661512375,
-0.03800252452492714,
0.011830518953502178,
-0.07194782793521881,
0.01785406284034252,
-0.03566629812121391,
0.00875182170420885,
-0.037266794592142105,
-0.011767641641199589,
-0.020175158977508545,
-0.027681980282068253,
-0.03346491605043411,
-0.016062786802649498,
-0.03987126424908638,
-0.04477693885564804,
0.03263401985168457,
-0.052452027797698975,
-0.03779881075024605,
-0.013061605393886566,
0.02850559540092945,
0.06595015525817871,
-0.010809390805661678,
0.002266018185764551,
-0.00004562761387205683,
-0.04183279722929001,
0.009567582979798317,
-0.03700888901948929,
0.036704011261463165,
0.005132482387125492,
0.04171978682279587,
0.03222944959998131,
0.02046596072614193,
-0.02832026034593582,
-0.013736145570874214,
-0.00601153913885355,
0.030439164489507675,
0.003928486257791519,
0.026589561253786087,
-0.03413008525967598,
-0.06152427941560745,
-0.041993990540504456,
0.030865006148815155,
0.05124286562204361,
0.015523923560976982,
0.02962576411664486,
0.013642403297126293,
0.02057505026459694,
-0.013929515145719051,
0.03908253088593483,
0.07840688526630402,
0.016142314299941063,
-0.03620505705475807,
-0.03744306042790413,
-0.03480793908238411,
0.0183650441467762,
0.02574990689754486,
0.011515672318637371,
0.001561579410918057,
-0.006053858436644077,
0.01271519623696804,
0.018386632204055786,
0.003950953483581543,
-0.05385942384600639,
0.0008689607493579388,
-0.04637192189693451,
0.0270802341401577,
-0.029959969222545624,
0.017889896407723427,
-0.013817578554153442,
0.0428716205060482,
0.026468096300959587,
-0.005000597331672907,
0.004156552255153656,
-0.0805291160941124,
0.00413108104839921,
0.06816709041595459,
0.08124814182519913,
-0.023604219779372215,
-0.02900119312107563,
-0.0630359873175621,
-0.0019833268597722054,
0.050281163305044174,
-0.027380788698792458,
0.011187597177922726,
-0.016127318143844604,
-0.0000034920399230031762,
-0.026379911229014397,
-0.020405463874340057,
-0.008896185085177422,
0.03315585106611252,
0.022045647725462914,
-0.011037803255021572,
-0.03797344118356705,
-0.024955594912171364,
-0.03157629072666168,
0.015028842724859715,
0.03904079645872116,
0.0378631129860878,
-0.010043012909591198,
0.03160537779331207,
0.019022783264517784,
0.002294510370120406,
-0.02209564670920372,
-0.08442865312099457,
-0.01881062239408493,
0.012470580637454987,
-0.0019377284916117787,
0.04679252579808235,
-0.03732363507151604,
-0.04592137783765793,
-0.031073149293661118,
-0.003948686178773642,
-0.010543365962803364,
-0.013667802326381207,
-0.0653826966881752,
0.06220247223973274,
0.016525501385331154,
-0.007017695810645819,
0.009096183814108372,
0.006069452501833439,
-0.006252137478441,
-0.0017076022922992706,
-0.0640268325805664,
0.010169525630772114,
-0.012788365595042706,
0.0017593401717022061,
-0.007436207961291075,
0.008248791098594666,
-0.025203149765729904,
0.03949986398220062,
-0.0007901933277025819,
0.0374886728823185,
0.011555266566574574,
-0.03690678998827934,
-0.02881903201341629,
-0.04435544088482857,
-0.025785164907574654,
0.0064207701943814754,
-0.020279088988900185,
0.007117035333067179,
-0.015100952237844467,
-0.02157539129257202,
0.017594188451766968,
0.0014143016887828708,
0.015689196065068245,
0.005581189412623644,
-0.02074023149907589,
0.03522878512740135,
-0.041520509868860245,
-0.01610426791012287,
0.023080861195921898,
-0.03509917110204697,
0.030333857983350754,
-0.0036754156462848186,
-0.008735653012990952,
0.012331529520452023,
-0.06553851068019867,
-0.055563054978847504,
0.04969967156648636,
-0.00500207394361496,
0.008333590812981129,
-0.018288834020495415,
0.02510301023721695,
0.02196265570819378,
-0.004021374974399805,
-0.06736217439174652,
-0.039140019565820694,
0.011733746156096458,
-0.0030402170959860086,
-0.007392807863652706,
-0.01966981031000614,
-0.032307591289281845,
0.00864869263023138,
-0.015787724405527115,
-0.0049315267242491245,
0.05424928292632103,
-0.04544324055314064,
-0.02202562987804413,
0.03169388696551323,
-0.002129366621375084,
0.03874150291085243,
-0.02054818533360958,
-0.035633064806461334,
0.006919653620570898,
-0.03265542909502983,
0.024693714454770088,
0.0528557114303112,
0.027646390721201897,
-0.003176986938342452,
-0.041523851454257965,
0.024057598784565926,
-0.003628656268119812,
0.01959390565752983,
-0.037735600024461746,
-0.00941801443696022,
0.009284048341214657,
0.014303718693554401,
-0.012866402044892311,
0.016500387340784073,
0.033760689198970795,
-0.008533877320587635,
0.034378983080387115,
0.019421551376581192,
0.012432513758540154,
-0.025910355150699615,
-0.03747069463133812,
0.06817541271448135,
-0.004553643986582756,
0.008351081982254982,
-0.004359838552772999,
-0.000928728433791548,
-0.004911452531814575,
-0.017733929678797722,
0.036654092371463776,
-0.03394418582320213,
0.04650947079062462,
-0.019294289872050285,
0.014324488118290901,
-0.012252436950802803,
-0.0070609417743980885,
0.005663443356752396,
-0.04575579985976219,
-0.02041672170162201,
0.017255917191505432,
0.01408523041754961,
-0.00008357270417036489,
0.01209317147731781,
0.0013835398713126779,
0.003159557469189167,
-0.019185392186045647,
-0.04570210352540016,
0.03765670210123062,
0.006903339643031359,
0.003953089937567711,
0.008475563488900661,
-0.00111101393122226,
-0.0037841247394680977,
0.019044239073991776,
0.04559944197535515,
-0.0223161019384861,
0.01084106508642435,
0.03324197977781296,
0.029431529343128204,
-0.00018158569582737982,
-0.01853341795504093,
-0.037154749035835266,
0.05939900130033493,
-0.06666552275419235,
0.014969139359891415,
-0.00011376421025488526,
-0.016410931944847107,
0.017309902235865593,
-0.01902918703854084,
0.03156496584415436,
0.003960586152970791,
-0.04837195947766304,
-0.0562484972178936,
-0.0008922697743400931,
-0.0005501077976077795,
-0.0010583698749542236,
-0.045009709894657135,
0.01158455852419138,
0.05335855111479759,
-0.007179689593613148,
0.02229677513241768,
-0.04244321212172508,
-0.09952624142169952,
0.007632143795490265,
-0.04505861923098564,
-0.0023484209086745977,
0.05634085461497307,
-0.02812127210199833,
-0.0009396395180374384,
-0.00024046342878136784,
-0.02710474655032158,
0.007680993527173996,
0.026574375107884407,
0.03360360115766525,
-0.052770696580410004,
0.002744238590821624,
-0.02827640250325203,
0.020940324291586876,
-0.011558551341295242,
0.0116958599537611,
0.11828164756298065,
0.04032690450549126,
0.03248625993728638,
-0.04500621184706688,
0.02156916633248329,
-0.021473729982972145,
0.007120305672287941,
-0.009061040356755257,
0.02913365140557289,
-0.0062029180116951466,
-0.000007619744792464189,
-0.02319827862083912,
0.0723244920372963,
0.04746824502944946,
-0.021490806713700294,
0.08633939921855927,
-0.02265605889260769,
-0.04920722916722298,
0.00757258478552103,
0.008439779281616211,
-0.028079377487301826,
-0.008378439582884312,
-0.035197529941797256,
0.04549781233072281,
-0.004126803018152714,
0.016836032271385193,
-0.011484935879707336,
-0.02764751762151718,
0.017166228964924812,
0.03288916498422623,
-0.037288766354322433,
-0.015837226063013077,
0.036652036011219025,
-0.01678861305117607,
-0.0052643874660134315,
-0.0033412708435207605,
-0.00844268687069416,
-0.007789330556988716,
0.060838986188173294,
0.01184898056089878,
0.05333925783634186,
0.023978710174560547,
0.01933986507356167,
0.011295763775706291,
-0.07591379433870316,
0.010706682689487934,
0.011446364223957062,
0.034138765186071396,
0.013338742777705193,
-0.02833651751279831,
0.026444755494594574,
0.0002666758082341403,
0.02983672544360161,
-0.02789520099759102,
-0.03378945216536522,
-0.03989091515541077,
0.005275328643620014,
0.01454668864607811,
0.014986017718911171,
-0.021254470571875572,
0.05303853005170822,
-0.024252142757177353,
0.014255089685320854,
-0.021977663040161133,
0.007204908411949873,
-0.021980736404657364,
-0.018508430570364,
0.008172376081347466,
0.03327282518148422,
-0.028276534751057625,
-0.045366834849119186,
0.013781984336674213,
-0.04033210501074791,
0.032768938690423965,
0.042524371296167374,
0.038420043885707855,
0.048517417162656784,
0.026045195758342743,
0.014748482964932919,
-0.018568633124232292,
-0.020874856039881706,
0.04345879703760147,
-0.0013320347061380744,
-0.01427303534001112,
0.008173765614628792,
-0.00737480353564024,
0.021932659670710564,
0.06595112383365631,
-0.044078562408685684,
-0.010944321751594543,
0.010328792966902256,
0.030499303713440895,
-0.01826159842312336,
-0.04125049337744713,
-0.02730863355100155,
-0.008544831536710262,
-0.013988147489726543,
0.020567044615745544,
-0.0012397391255944967,
0.03732019662857056,
0.022103291004896164,
-0.021948041394352913,
-0.00841503031551838,
0.033603861927986145,
0.0020221297163516283,
-0.0346626378595829,
0.0547197125852108,
-0.011903520673513412,
-0.010252275504171848,
0.01528919953852892,
0.02648857794702053,
-0.0031250116880983114,
-0.0373251736164093,
-0.019146693870425224,
-0.002778052119538188,
-0.01650336943566799,
0.013652469962835312,
-0.02503686584532261,
-0.010606306605041027,
-0.03574780002236366,
-0.010733666829764843,
-0.01766108348965645,
0.007297338917851448,
-0.060366466641426086,
0.0030889627523720264,
-0.038335978984832764,
-0.03234628215432167,
0.026375729590654373,
0.055613256990909576,
-0.00975042674690485,
-0.031314484775066376,
0.02386571280658245,
0.031356073915958405,
-0.03472832962870598,
-0.018408508971333504,
0.0076458449475467205,
0.03121069259941578,
0.030926892533898354,
-0.014052195474505424,
0.004551062826067209,
0.05996762588620186,
-0.02730989083647728,
-0.059336088597774506,
0.022372165694832802,
-0.02186506800353527,
0.012898992747068405,
-0.01660821959376335,
-0.019181732088327408,
-0.0011624161852523685,
0.06021527573466301,
-0.04667113721370697,
-0.022751275449991226,
0.011853163130581379,
-0.026427345350384712,
-0.03516371548175812,
-0.017314689233899117,
0.026748700067400932,
0.013716490939259529,
-0.011341819539666176,
0.05149604752659798,
0.008251740597188473,
0.00014823190576862544,
0.0027837955858558416,
-0.02463434264063835,
-0.015512729063630104,
0.04021314159035683,
0.011892487294971943,
0.007367691025137901,
-0.03958151862025261,
0.023972956463694572,
-0.03141201660037041,
0.04704643413424492,
0.017342643812298775,
0.009325062856078148,
-0.08900029212236404,
-0.02108813263475895,
0.03244174271821976,
0.0054644327610731125,
0.014308852143585682,
-0.04153500124812126,
0.03873378783464432,
0.022377662360668182,
-0.06770384311676025,
-0.006389860529452562,
-0.04171007126569748,
-0.036318570375442505,
-0.039893098175525665,
-0.017540819942951202,
-0.054486751556396484,
0.026325667276978493,
0.009219769388437271,
0.038324061781167984,
0.016843322664499283,
0.0016799570294097066,
-0.030037948861718178,
-0.014917276799678802,
-0.029653804376721382,
0.0014060498215258121,
0.0054693701677024364,
-0.01110560167580843,
0.04535066708922386,
-0.01858803816139698,
-0.006586122792214155,
0.056327786296606064,
0.009253702126443386,
-0.004487089347094297,
-0.005509546026587486,
0.002578441984951496,
0.020766403526067734,
0.0015019976999610662,
0.03839118406176567,
0.005891741253435612,
0.00003739032763405703,
0.04606955125927925,
0.027464762330055237,
0.04941178113222122,
0.01977001130580902,
-0.024401964619755745,
-0.044743746519088745,
-0.014760885387659073,
0.01074975449591875,
0.028780972585082054,
-0.024074314162135124,
-0.010512721724808216,
-0.029507219791412354,
0.04671742022037506,
-0.004346121568232775,
0.020090976729989052,
-0.0009152086568064988,
-0.027324194088578224,
0.009684949181973934,
-0.004733412992209196,
0.05197342485189438,
0.0013081913348287344,
0.03580852597951889,
-0.02386840246617794,
-0.018787093460559845,
-0.015625640749931335,
0.027743088081479073,
0.00817343033850193,
-0.0006905522895976901,
-0.012173503637313843,
0.028371460735797882,
0.05601232126355171,
0.013518602587282658,
-0.051273006945848465,
-0.02301911637187004,
0.033665481954813004,
-0.007754852529615164,
0.05934673920273781,
0.010604430921375751,
-0.05917195603251457,
0.012822804972529411,
-0.060461610555648804,
0.016715137287974358,
-0.002861499786376953,
0.05054556205868721,
-0.04009571298956871,
-0.014766978099942207,
-0.02919311821460724,
0.01128795649856329,
0.05649483948945999,
-0.0013516286853700876,
-0.03409240022301674,
0.004305456764996052,
-0.030701037496328354,
0.00005286890882416628,
-0.020491892471909523,
-0.013332042843103409,
0.0037255962379276752,
-0.01042561698704958,
0.0034897709265351295,
-0.005558469332754612,
-0.030910318717360497,
0.03317748382687569,
0.0387212298810482,
-0.027160555124282837,
-0.03973991423845291,
0.034265827387571335,
-0.07109814882278442,
0.0494069829583168,
-0.013255343772470951,
0.01862170919775963,
0.07729779183864594,
0.017124975100159645,
0.02576797641813755,
0.0291980542242527,
-0.01951918937265873,
-0.020557278767228127,
0.027238205075263977,
-0.016863707453012466,
-0.021850377321243286,
-0.014797473326325417,
0.008647686801850796,
0.034714486449956894,
-0.0007032856810837984,
0.030275240540504456,
0.02150002121925354,
0.004120997153222561,
0.007538836449384689,
0.026977229863405228,
0.027102280408143997,
0.038099292665719986,
0.0062179649248719215,
-0.01130453497171402,
0.005087882746011019,
0.04841649532318115,
-0.01278179232031107,
0.03614499047398567,
0.021272433921694756,
0.04636087641119957,
-0.016179785132408142,
0.04672744497656822,
0.017672691494226456,
0.02781790681183338,
0.019093094393610954,
0.029373686760663986,
0.021132200956344604,
0.024092376232147217,
0.02947329543530941,
-0.026795638725161552,
0.08264447748661041,
0.018341578543186188,
-0.01146792620420456,
0.06950326263904572,
-0.011319169774651527,
0.025860918685793877,
-0.008103915490210056,
-0.024863533675670624,
-0.005740731954574585,
0.020573163405060768,
0.01654539816081524,
0.04359057545661926,
-0.03623609244823456,
-0.03667715936899185,
-0.059043895453214645,
0.008551069535315037,
0.022373195737600327,
-0.05719451233744621,
0.010279511101543903,
-0.0005005861748941243,
-0.032370273023843765,
-0.01195590291172266,
-0.017512960359454155,
-0.017177850008010864,
-0.014947433024644852,
0.014138665981590748,
0.03591100871562958,
0.014481746591627598,
-0.018043195828795433,
-0.04073319956660271,
-0.004419222474098206,
0.011723198927938938,
-0.008150315843522549,
-0.0158051960170269,
-0.009524313732981682,
0.031288474798202515,
-0.014080516993999481,
-0.03168299049139023
] |
<p>If we have a kilometer long million slit light source and make an observation on a slit at one of the ends, will the interference pattern fully collapse or partially collapse? is there any delay in the propagation of the collapse or is the collapse instant?</p>
<p>Link to multiple slits.</p>
<p><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslidi.html#c3" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslidi.html#c3</a></p>
<p>Additional information.
I am thinking that if Alice is at one end, point A and is looking at the pattern on the wall from the million slits. Bob is at the other end a kilometer away at point B. Bob then makes an observation to detect if a photon is going through a slit. Wouln't Alice see the pattern on the wall disappear? </p>
<p>My understanding of how this is not faster than light in the 2 slit experiment is because the change in light travels from the slit to the wall at c after the instant collapse. In the multiple slit though the collapse travels a lot further instantly and then the change in light travels at c from the slits to the wall. For Alice that is. Where is my mistake?</p>
| 8,292 |
[
-0.04008379951119423,
-0.02353379689157009,
-0.026393776759505272,
-0.041178662329912186,
0.0416121631860733,
-0.0020453152246773243,
-0.035173650830984116,
-0.04852728173136711,
-0.004804711788892746,
-0.0019554197788238525,
0.0352335125207901,
0.05336173623800278,
-0.016519712284207344,
0.04469340667128563,
0.020456479862332344,
0.01884545013308525,
-0.009768281131982803,
-0.022923627868294716,
-0.016104338690638542,
-0.04972280561923981,
-0.028163818642497063,
0.014731691218912601,
-0.007784060202538967,
-0.019875777885317802,
-0.03477584943175316,
0.03422432020306587,
0.01185783464461565,
0.002035860437899828,
0.03491371124982834,
0.03943357989192009,
-0.027287734672427177,
-0.017839141190052032,
-0.01079433225095272,
-0.0027917425613850355,
0.004061089362949133,
0.028500108048319817,
-0.03560830280184746,
-0.026140619069337845,
0.034719884395599365,
0.0006769225583411753,
0.011557494290173054,
0.0069669210352003574,
-0.011368349194526672,
0.043164271861314774,
-0.04248812794685364,
-0.015942389145493507,
0.025208529084920883,
-0.008610554039478302,
0.0391891784965992,
-0.06271474063396454,
0.05442911759018898,
0.007614761125296354,
0.051067546010017395,
0.004441714845597744,
-0.015814606100320816,
-0.02368110604584217,
0.08223465085029602,
0.05996419116854668,
-0.013070669956505299,
-0.02919723466038704,
-0.0002267369709443301,
0.016683591529726982,
-0.00202423008158803,
-0.05365597829222679,
-0.01829175092279911,
0.06151820346713066,
-0.021834420040249825,
-0.03574663773179054,
0.023056156933307648,
-0.00942649319767952,
-0.0010904533555731177,
-0.006872421130537987,
0.04055485501885414,
0.014212707988917828,
0.03377464413642883,
-0.037732355296611786,
-0.002741711214184761,
0.038561854511499405,
0.03417987376451492,
0.062011029571294785,
-0.02234152890741825,
0.049814239144325256,
0.05277389660477638,
0.045104507356882095,
0.028057442978024483,
-0.0017116644885390997,
0.06483369320631027,
-0.0014538561226800084,
-0.009817075915634632,
0.023882415145635605,
-0.023049695417284966,
0.04205542057752609,
0.023833366110920906,
0.013789747841656208,
0.017111899331212044,
0.02867218106985092,
0.00679319491609931,
0.04973398149013519,
0.005033714231103659,
-0.005098050460219383,
-0.017692403867840767,
0.0037127214018255472,
0.00037432240787893534,
0.030782943591475487,
0.019613133743405342,
-0.015933256596326828,
-0.04423748701810837,
0.04270735755562782,
-0.04620280861854553,
0.0007627521408721805,
-0.025099046528339386,
0.013082331046462059,
-0.009491675533354282,
0.029658399522304535,
0.004777468740940094,
-0.03826238960027695,
-0.0010812247637659311,
-0.006083171349018812,
0.049488365650177,
0.05511308088898659,
0.0366206094622612,
-0.03689844161272049,
-0.01585402339696884,
-0.05259644240140915,
-0.08588068187236786,
0.023599186912178993,
0.0014395418111234903,
-0.012886077165603638,
-0.02981010265648365,
0.036845650523900986,
0.007063979748636484,
-0.0011060107499361038,
0.020415015518665314,
-0.013525065965950489,
0.03636498749256134,
-0.01983766071498394,
-0.12701034545898438,
-0.09321541339159012,
0.04936450719833374,
0.008899936452507973,
-0.020830703899264336,
-0.07279325276613235,
-0.007175848353654146,
0.03313519060611725,
0.09273269772529602,
-0.014571642503142357,
-0.00004575760613079183,
-0.0074807871133089066,
0.009542993269860744,
-0.010415008291602135,
-0.026200659573078156,
-0.012508765794336796,
0.02825133688747883,
-0.002231236081570387,
-0.020237985998392105,
-0.034971170127391815,
0.0053602587431669235,
0.05593288317322731,
0.03367231786251068,
-0.016613539308309555,
0.05810413137078285,
-0.014729036949574947,
-0.006401014514267445,
0.0018435277743265033,
-0.02909287065267563,
-0.026300134137272835,
0.11983731389045715,
0.013734916225075722,
0.015246732160449028,
0.026056084781885147,
0.037840645760297775,
0.024157030507922173,
-0.06086154282093048,
-0.03501751646399498,
0.012384839355945587,
0.012851179577410221,
-0.019134677946567535,
-0.006065636873245239,
0.009046094492077827,
0.003363001858815551,
-0.021224748343229294,
-0.04701802507042885,
-0.03861076012253761,
-0.002848686883226037,
0.02337162382900715,
0.0436280257999897,
-0.022945843636989594,
-0.006177803967148066,
-0.017984023317694664,
-0.05607449263334274,
-0.039279595017433167,
-0.03455837070941925,
0.0006279125227592885,
0.03755197301506996,
-0.0012017161352559924,
0.0014883604599162936,
-0.03122403472661972,
-0.007132716942578554,
0.017912494018673897,
-0.035153456032276154,
-0.022309450432658195,
0.04611310362815857,
0.003784880740568042,
-0.0132836839184165,
0.010582677088677883,
0.08005551993846893,
0.04233979061245918,
-0.018358273431658745,
0.018312975764274597,
-0.029058728367090225,
0.008251432329416275,
0.02608110010623932,
0.011349758133292198,
0.01592080295085907,
0.0049993363209068775,
0.03047974780201912,
0.03086135908961296,
0.03325095400214195,
0.01939425617456436,
0.016306811943650246,
-0.03301743045449257,
0.08518930524587631,
0.04972919076681137,
-0.0035297556314617395,
0.004157138988375664,
0.013546789065003395,
0.0028379501309245825,
0.0015592706622555852,
-0.0004464804951567203,
-0.03913532942533493,
-0.05863064527511597,
-0.034809309989213943,
-0.02115747518837452,
-0.01080640684813261,
-0.03458574786782265,
0.0313054621219635,
-0.0008060430991463363,
0.03498595207929611,
0.01965472102165222,
-0.009087630547583103,
0.0007573990733362734,
-0.048397574573755264,
0.005986950360238552,
-0.01855500601232052,
-0.024421604350209236,
0.011541979387402534,
0.02925454080104828,
0.002417386043816805,
-0.011878037825226784,
-0.04643027484416962,
-0.011198633350431919,
-0.013689898885786533,
-0.021157322451472282,
0.024497006088495255,
-0.017590077593922615,
-0.0281910989433527,
0.036160584539175034,
-0.021078936755657196,
0.01579209975898266,
0.027066484093666077,
-0.008215115405619144,
0.005794046446681023,
-0.06935512274503708,
-0.008390889503061771,
-0.016100047156214714,
0.003947136923670769,
-0.018289661034941673,
-0.03523753210902214,
0.032234568148851395,
-0.03296245262026787,
0.03152923285961151,
-0.0035662807058542967,
-0.0052081020548939705,
-0.0490574948489666,
0.010037205182015896,
0.023262208327651024,
0.01458106841892004,
0.03795421123504639,
-0.08300875127315521,
-0.057126134634017944,
-0.015398659743368626,
-0.03502436727285385,
0.034985750913619995,
0.003910810220986605,
0.005264227278530598,
0.06955961138010025,
-0.022618427872657776,
-0.010791151784360409,
0.020139774307608604,
-0.03642516955733299,
0.003897852497175336,
0.012143006548285484,
-0.013144426979124546,
-0.03742913529276848,
-0.056715745478868484,
-0.003745786380022764,
0.01835482008755207,
-0.011803785338997841,
-0.004103807266801596,
0.05040851607918739,
0.02119883894920349,
-0.034601181745529175,
0.0008328441763296723,
-0.04520578309893608,
-0.023363206535577774,
-0.03603791818022728,
-0.006037806626409292,
0.01107343751937151,
-0.021855445578694344,
0.0013260048581287265,
0.014348187483847141,
-0.031843651086091995,
0.009399871341884136,
-0.025152070447802544,
-0.08396998792886734,
0.032243140041828156,
-0.004500039387494326,
0.03732703626155853,
-0.04796981438994408,
-0.02191951312124729,
0.07676949352025986,
0.02081354334950447,
-0.0019690701737999916,
-0.04219632223248482,
0.039960671216249466,
0.017150769010186195,
-0.005113994237035513,
0.008040817454457283,
0.021645771339535713,
-0.01107154693454504,
0.02872268483042717,
0.0003888416395056993,
0.01711706630885601,
0.06542687863111496,
0.03167344629764557,
0.014524267986416817,
-0.000550302502233535,
-0.02301194705069065,
-0.020347734913229942,
0.048881445080041885,
0.041163019835948944,
-0.022199247032403946,
0.007993150502443314,
-0.015410897321999073,
-0.007542261388152838,
0.015460426919162273,
-0.028882216662168503,
0.040213245898485184,
0.00190774817019701,
0.03685056045651436,
-0.0465441532433033,
0.024500032886862755,
-0.02100549079477787,
-0.008126267232000828,
0.00302960560657084,
-0.030945103615522385,
0.0806274339556694,
-0.009595715440809727,
-0.005136473570019007,
0.04604177176952362,
0.023150134831666946,
-0.01916305534541607,
-0.04214400425553322,
0.00874404888600111,
-0.010747203603386879,
0.03195926174521446,
-0.04817766696214676,
-0.03192655369639397,
0.05518157407641411,
0.04340151324868202,
0.033956319093704224,
-0.021711325272917747,
-0.020411893725395203,
-0.024877658113837242,
-0.03929150477051735,
0.014634930528700352,
-0.005750699900090694,
0.0766611322760582,
0.053593672811985016,
0.026989076286554337,
0.03921973332762718,
-0.005220512859523296,
0.01545894704759121,
-0.01725420169532299,
-0.08137241750955582,
0.023021318018436432,
-0.039320461452007294,
-0.04014754295349121,
-0.017123088240623474,
-0.038018617779016495,
0.02396547794342041,
-0.013909906148910522,
0.0029470790177583694,
0.004289465956389904,
-0.011170923709869385,
-0.05892648920416832,
-0.007807902060449123,
-0.03052930347621441,
-0.0005527517641894519,
-0.03217242658138275,
0.047868452966213226,
0.048755571246147156,
0.020187783986330032,
0.006416159216314554,
0.01778852380812168,
-0.05272238701581955,
0.010325971990823746,
0.010322009213268757,
-0.015380810014903545,
0.00038979481905698776,
0.021792246028780937,
0.025741100311279297,
0.006364918313920498,
-0.04711756110191345,
0.01228757668286562,
0.06246243044734001,
0.013509603217244148,
-0.006585102993994951,
-0.019674357026815414,
0.012242074124515057,
0.00901071261614561,
0.01721506007015705,
-0.03435966745018959,
0.07607293874025345,
-0.007430866826325655,
-0.010660648345947266,
0.0067927041091024876,
0.013379007577896118,
0.0008885346469469368,
0.06185015290975571,
0.054759763181209564,
-0.006754461210221052,
0.003477495163679123,
-0.03192488104104996,
-0.039913684129714966,
-0.023819124326109886,
0.001358393463306129,
0.0002872295444831252,
0.01682906039059162,
-0.027851935476064682,
-0.0016967639094218612,
0.03890801593661308,
0.004299600142985582,
-0.0160695668309927,
0.0090293288230896,
-0.045471757650375366,
-0.029051965102553368,
0.009008144028484821,
0.031231753528118134,
-0.02094707451760769,
0.014041203074157238,
0.02356235682964325,
0.012183964252471924,
-0.006299223750829697,
-0.05689476430416107,
-0.036445215344429016,
0.013186661526560783,
0.08139269053936005,
0.0030197352170944214,
0.03081033006310463,
-0.07506939768791199,
-0.02234131284058094,
0.04501375928521156,
-0.05670572817325592,
0.022297080606222153,
0.006556438747793436,
0.002635128563269973,
-0.035291384905576706,
-0.03410432115197182,
-0.011421158909797668,
0.0043218364007771015,
-0.0291408970952034,
0.034603189677000046,
0.00963426474481821,
-0.0015642907237634063,
-0.017545899376273155,
0.011519727297127247,
0.007001672871410847,
0.029918722808361053,
0.004059041850268841,
0.015534390695393085,
0.008286966010928154,
-0.026367563754320145,
-0.04077943414449692,
-0.05703384056687355,
0.039105139672756195,
-0.024958746507763863,
-0.02315158024430275,
0.05740053206682205,
-0.01856893301010132,
-0.021006474271416664,
0.009679526090621948,
0.02660815790295601,
0.011161317117512226,
0.01085674948990345,
-0.03176995739340782,
0.02346673794090748,
0.010080111213028431,
-0.011553517542779446,
0.03028084523975849,
0.012712884694337845,
0.0057408311404287815,
0.043432921171188354,
-0.015414468944072723,
0.06040092557668686,
-0.028241071850061417,
0.02550426498055458,
-0.03595709055662155,
-0.010955343022942543,
-0.030501170083880424,
0.056998394429683685,
-0.03516645357012749,
0.021160153672099113,
-0.010336512699723244,
-0.02467517927289009,
0.014812233857810497,
-0.005197303835302591,
0.017055142670869827,
0.039762552827596664,
-0.06182112172245979,
-0.012692690826952457,
0.04188796132802963,
-0.02806304581463337,
0.010624866001307964,
-0.015448842197656631,
0.008435335010290146,
0.054444342851638794,
0.006808090023696423,
0.01897674985229969,
-0.02623489499092102,
-0.0033741085790097713,
0.005741820205003023,
-0.057552091777324677,
0.014480077661573887,
-0.0012855705572292209,
0.002455113921314478,
0.006835100706666708,
-0.03091340698301792,
-0.03473115712404251,
-0.020612657070159912,
-0.012374542653560638,
-0.00005731932833441533,
-0.06162719801068306,
0.07524633407592773,
0.009151669219136238,
0.0002993112721014768,
-0.0656852051615715,
-0.02388783171772957,
0.0017688014777377248,
-0.019694605842232704,
-0.010358240455389023,
0.007886247709393501,
-0.02486828900873661,
-0.006005564704537392,
0.0035991312470287085,
-0.009166368283331394,
0.021429600194096565,
-0.05582064017653465,
0.005240149330347776,
0.01921798475086689,
0.014668579213321209,
0.062107134610414505,
0.015161048620939255,
-0.02673061564564705,
0.0025974493473768234,
-0.03832521289587021,
-0.02778714895248413,
0.01073460839688778,
0.053767766803503036,
-0.03160833939909935,
-0.05385012552142143,
-0.027190612629055977,
0.007592618931084871,
0.02477884106338024,
-0.01155516505241394,
0.01894213631749153,
0.018746323883533478,
0.024417027831077576,
-0.03197643160820007,
0.018405869603157043,
-0.017445791512727737,
0.01661943830549717,
0.007240686099976301,
0.0006497369613498449,
0.0006498036091215909,
0.007217803969979286,
-0.06120053306221962,
0.019164904952049255,
0.01601148210465908,
-0.0042951577343046665,
-0.008267506957054138,
0.026179030537605286,
0.015530675649642944,
-0.01850517839193344,
-0.006171870045363903,
-0.026544226333498955,
0.005497894715517759,
-0.030976789072155952,
0.00003070324601139873,
0.010058756917715073,
-0.0006451350636780262,
-0.043973833322525024,
-0.023394787684082985,
-0.01184143777936697,
0.004318560007959604,
0.05148101970553398,
-0.020305972546339035,
0.03143947198987007,
-0.032179392874240875,
0.0024026089813560247,
0.011396038345992565,
-0.03638674318790436,
0.000672089634463191,
0.01165846362709999,
0.052785392850637436,
0.030811207368969917,
-0.03334427252411842,
-0.0015755650820210576,
0.04768500104546547,
0.06805885583162308,
-0.0077926418744027615,
0.025408070534467697,
0.047164708375930786,
0.02497672475874424,
0.026768147945404053,
-0.018977882340550423,
-0.01389173325151205,
0.04226457327604294,
-0.04578088968992233,
0.007100893184542656,
-0.016847891733050346,
0.014523717574775219,
0.03360986337065697,
0.022198643535375595,
0.007804143242537975,
-0.017404263839125633,
-0.019192665815353394,
-0.056391578167676926,
-0.012366077862679958,
0.0006464034668169916,
0.0282167736440897,
-0.006563495844602585,
-0.004591531585901976,
0.04663403332233429,
0.02010907605290413,
0.02503032609820366,
-0.03324827179312706,
-0.0640484094619751,
-0.04806603863835335,
-0.0549638569355011,
-0.02060096710920334,
0.05732707306742668,
0.020691627636551857,
-0.013864454813301563,
0.029140472412109375,
-0.009989101439714432,
0.0170182753354311,
0.013634981587529182,
0.03356398642063141,
-0.01628270000219345,
0.024840330705046654,
0.003202152671292424,
0.02858917787671089,
-0.028413478285074234,
0.009206723421812057,
0.11418220400810242,
0.042118437588214874,
0.00812691729515791,
-0.06177081540226936,
0.014791887253522873,
-0.009686026722192764,
0.03222508355975151,
-0.030054792761802673,
0.019776057451963425,
-0.025854794308543205,
-0.01918734796345234,
0.05589770898222923,
0.040884681046009064,
0.015594963915646076,
-0.01164747029542923,
0.006845218129456043,
0.0037950766272842884,
-0.045788221061229706,
-0.0044806660152971745,
0.023397520184516907,
0.00829991139471531,
-0.010098905302584171,
-0.020230641588568687,
0.04137329384684563,
-0.028754116967320442,
-0.018353966996073723,
0.010439964942634106,
0.003232633462175727,
0.013668487779796124,
0.0068265823647379875,
-0.05569443851709366,
-0.0033939930144697428,
0.005255604162812233,
-0.04246096685528755,
-0.003965368960052729,
0.022960828617215157,
0.03068728744983673,
-0.020418517291545868,
0.03408275172114372,
0.07524298131465912,
0.029189903289079666,
-0.016148198395967484,
0.01978481560945511,
0.015926744788885117,
-0.059497810900211334,
-0.017959704622626305,
-0.020972158759832382,
0.05478253960609436,
-0.014306632801890373,
-0.01966656558215618,
0.021638555452227592,
-0.025397151708602905,
0.014676610939204693,
-0.05465778708457947,
0.00007971184822963551,
0.0011526846792548895,
-0.017425023019313812,
-0.01643628068268299,
-0.007372046820819378,
-0.0436989963054657,
0.00656840531155467,
-0.013091078959405422,
-0.028391307219862938,
0.026370717212557793,
0.009456065483391285,
-0.018286606296896935,
0.006771618500351906,
0.0348532535135746,
-0.029020486399531364,
-0.007828627713024616,
-0.0024658830370754004,
-0.0008572117076255381,
-0.006835258565843105,
-0.02433067560195923,
0.0030892384238541126,
0.021089818328619003,
0.028649643063545227,
-0.023040901869535446,
-0.021979769691824913,
-0.03169019892811775,
-0.05834782496094704,
0.016489816829562187,
-0.02529560960829258,
-0.030416734516620636,
-0.006014910526573658,
0.026900948956608772,
0.05553802475333214,
0.023487018421292305,
-0.01959993690252304,
0.0263371579349041,
-0.017753707244992256,
0.027793606743216515,
0.03220631182193756,
-0.003884565783664584,
-0.03161151334643364,
-0.03395256772637367,
-0.00940658338367939,
0.01784573309123516,
-0.02825513482093811,
0.021491557359695435,
0.015505390241742134,
0.01078309491276741,
0.04459941014647484,
0.04282407462596893,
-0.007033706177026033,
-0.02670270763337612,
-0.022902771830558777,
-0.02093779854476452,
0.022714629769325256,
0.004031739197671413,
0.05453553423285484,
-0.01043455395847559,
-0.03912638500332832,
-0.046880997717380524,
0.0015286465641111135,
0.0011793052544817328,
0.024014195427298546,
-0.031358201056718826,
0.020015545189380646,
-0.0008693728013895452,
0.004712145309895277,
-0.03577983379364014,
0.016961777582764626,
-0.034827183932065964,
0.010463502258062363,
0.007930470630526543,
-0.017874326556921005,
-0.019700638949871063,
0.03675488382577896,
-0.023233739659190178,
-0.029313674196600914,
0.015579779632389545,
0.021723035722970963,
-0.041239552199840546,
0.005906121339648962,
0.01850510947406292,
0.032690003514289856,
0.04006628319621086,
0.01793268322944641,
-0.0350271500647068,
0.03401589393615723,
-0.03958561271429062,
-0.045784033834934235,
0.0422508530318737,
-0.015236019156873226,
0.026204485446214676,
0.02282378263771534,
-0.005001922603696585,
-0.013336311094462872,
0.04556648060679436,
0.0028494889847934246,
-0.02106369473040104,
0.029267095029354095,
-0.03985100984573364,
0.02249099314212799,
-0.011823661625385284,
0.011378519237041473,
-0.019546005874872208,
0.00952543132007122,
0.05744592472910881,
0.021034546196460724,
0.0074894423596560955,
0.03705780208110809,
-0.026943987235426903,
-0.019008558243513107,
0.034384217113256454,
-0.008748658001422882,
-0.021561045199632645,
0.011268455535173416,
0.07171619683504105,
-0.02617415226995945,
0.03971593827009201,
-0.012668722309172153,
0.022759905084967613,
-0.09256339073181152,
0.030796123668551445,
0.017250653356313705,
0.03736487403512001,
0.010561538860201836,
-0.027948688715696335,
0.013906268402934074,
0.0839310958981514,
-0.06206991896033287,
-0.00864197127521038,
-0.029454898089170456,
0.014955095946788788,
-0.024280667304992676,
-0.003363903844729066,
-0.027567720040678978,
0.03596151992678642,
0.02402271144092083,
0.03943412005901337,
-0.02189800888299942,
0.039930425584316254,
-0.0451311320066452,
-0.018819741904735565,
-0.0013192454352974892,
0.032523348927497864,
-0.013180485926568508,
-0.00543937785550952,
0.07835961878299713,
-0.009923006407916546,
0.020962920039892197,
0.02399723418056965,
-0.03690468892455101,
0.037991203367710114,
-0.002899190643802285,
-0.050440579652786255,
0.018271252512931824,
-0.006665704306215048,
-0.011878632940351963,
-0.009817278012633324,
0.006658007390797138,
0.020915137603878975,
0.016617391258478165,
0.013739343732595444,
0.003916999790817499,
0.00992891751229763,
-0.0008987654582597315,
-0.02641121670603752,
-0.0049897669814527035,
0.009374115616083145,
0.020197847858071327,
0.0016359139699488878,
0.009515326470136642,
-0.007426410913467407,
0.04560130462050438,
-0.006036074832081795,
-0.03014393150806427,
-0.04281672090291977,
-0.02284974418580532,
0.04530853033065796,
0.013505066744983196,
-0.019060196354985237,
0.0002144044265151024,
-0.018825218081474304,
-0.007638938259333372,
0.031136561185121536,
0.008627058006823063,
-0.0025275941006839275,
-0.017293982207775116,
-0.03978046402335167,
-0.0244356170296669,
0.02654653787612915,
0.01769341714680195,
-0.03984762355685234,
-0.03344330936670303,
0.009827368892729282,
-0.005919507704675198,
0.002377820201218128,
-0.004286633338779211,
-0.012769287452101707,
-0.028405319899320602,
-0.09699460119009018,
0.01999492011964321,
-0.021117491647601128,
-0.004358751233667135,
-0.06500151008367538,
-0.022976849228143692,
-0.01717550866305828,
0.04207323491573334,
0.0747733935713768,
0.015289838425815105,
0.02596358396112919,
0.022772924974560738,
-0.011034288443624973,
0.024901632219552994,
-0.051347725093364716,
-0.035348717123270035,
-0.028945380821824074,
-0.005923772230744362,
-0.014590617269277573,
-0.01904316060245037,
0.0177414882928133,
0.020765220746397972,
0.032548822462558746,
0.008474241942167282,
0.030392954126000404,
-0.03210083022713661,
-0.01920318603515625,
0.012723138555884361,
-0.01463212352246046,
-0.00574463652446866,
0.06608519703149796,
0.001705350587144494,
0.04184584319591522,
0.0298785287886858,
-0.0005896803340874612,
-0.04186432808637619,
0.007073958870023489,
-0.05964522063732147,
0.026552734896540642,
0.022608885541558266,
-0.02161938138306141,
0.005060052033513784,
-0.0512731671333313,
0.011212104000151157,
0.0034269315656274557,
-0.016345951706171036,
-0.028520667925477028,
0.06709733605384827,
0.005206086207181215,
0.05002932250499725,
-0.022208182141184807,
0.06455595791339874,
0.028862908482551575,
-0.01091576088219881,
-0.016095126047730446,
0.05052502453327179,
0.014406362548470497,
-0.0047319806180894375,
0.03910527750849724,
0.07328115403652191,
0.012645595706999302,
-0.018705300986766815,
-0.021544864401221275,
0.03169427067041397,
0.007493630517274141,
-0.028504012152552605,
-0.006645120680332184,
-0.009024328552186489,
-0.011045998893678188,
0.02608666941523552,
-0.027736080810427666,
0.07380102574825287,
-0.018296891823410988,
0.05557794123888016,
0.022391468286514282,
-0.008987635374069214,
-0.04970640689134598,
0.048218268901109695,
0.009898263961076736,
0.03290366008877754,
-0.003476174082607031,
0.005739891901612282,
-0.028318176046013832,
-0.00677039148285985,
0.018566524609923363,
-0.06409395486116409,
-0.013331718742847443,
-0.024166245013475418,
-0.03506851941347122,
-0.0036887635942548513,
0.014932531863451004,
-0.000998961622826755,
-0.01924903504550457,
0.028459731489419937,
-0.006763812620192766,
-0.03546527028083801,
-0.023264680057764053,
0.022875551134347916,
0.02078479342162609,
0.06856955587863922,
-0.0558353029191494,
0.024112090468406677,
-0.042816177010536194,
0.041342612355947495,
0.002949124202132225,
-0.0014139647828415036
] |
<p>Consider two bodies orbiting each other.</p>
<p>As the Universe expands would the distance between them increase?</p>
<p>Most people say that a gravitationally bound system will not expand with the Universe. They say that such a system is not described by the FRW solution.</p>
<p>But surely one could consider two orbiting bodies that are sufficiently far away that the spacetime between them could be approximately described by the FRW solution? In this case the recession velocity would be of the same order as the orbit velocity.</p>
| 8,293 |
[
0.000154909779666923,
-0.032921019941568375,
0.02189061790704727,
0.009800918400287628,
0.0009998707100749016,
0.0020491403993219137,
-0.05584929510951042,
-0.04000784829258919,
0.014827197417616844,
-0.023108545690774918,
-0.004921273794025183,
-0.0006160405464470387,
0.038779474794864655,
-0.01137993298470974,
0.005887329112738371,
-0.017194831743836403,
-0.021723540499806404,
0.004557961598038673,
-0.01847389154136181,
-0.01603396236896515,
0.04761819913983345,
0.013324156403541565,
0.04844249412417412,
0.016474423930048943,
0.0035328080412000418,
-0.0032347128726541996,
0.019978085532784462,
-0.04409399256110191,
0.023312300443649292,
0.05372818559408188,
0.0007034671725705266,
-0.017778845503926277,
-0.01902506686747074,
0.0639212429523468,
0.01924441196024418,
0.008135232143104076,
-0.06899292767047882,
-0.02615921013057232,
-0.006356993690133095,
-0.0003396421088837087,
-0.0517144650220871,
-0.015295367687940598,
0.0035459452774375677,
0.05836248770356178,
0.0062647066079080105,
0.014582863077521324,
0.004425158724188805,
-0.00570659851655364,
0.03945848345756531,
-0.035021305084228516,
0.043875258415937424,
0.0009740762179717422,
0.04654775559902191,
0.009244478307664394,
-0.012247792445123196,
-0.025760553777217865,
0.11479069292545319,
0.07210154086351395,
-0.015790021046996117,
-0.024258598685264587,
-0.020565912127494812,
0.0017847729614004493,
-0.013212429359555244,
0.003408796386793256,
0.008252447471022606,
0.05951281264424324,
-0.03347305208444595,
0.004383102059364319,
-0.0005442071123979986,
0.02277049794793129,
0.015161924064159393,
0.009260017424821854,
0.028531616553664207,
-0.029105661436915398,
0.04418453946709633,
-0.020379062741994858,
0.01852067932486534,
0.03430363908410072,
0.017732979729771614,
0.032209545373916626,
-0.014810279943048954,
-0.0009437795961275697,
0.04857791215181351,
0.028438765555620193,
0.0020505653228610754,
0.025368379428982735,
0.032415080815553665,
0.016159620136022568,
0.00495567824691534,
0.048988573253154755,
0.04871591553092003,
0.03514573350548744,
0.050814371556043625,
-0.03314322233200073,
0.029236124828457832,
0.05482373386621475,
0.010409663431346416,
0.02898971177637577,
0.011411428451538086,
0.004390212241560221,
-0.003025500103831291,
-0.02789691649377346,
-0.030729180201888084,
0.06308887898921967,
0.03534896671772003,
-0.026751719415187836,
-0.06032337248325348,
0.014244955033063889,
-0.05758729577064514,
-0.03749724477529526,
-0.03418196365237236,
-0.006771001033484936,
-0.034088265150785446,
-0.00020021390810143203,
0.03378655016422272,
-0.01801774837076664,
-0.02874245122075081,
-0.033844053745269775,
0.022429216653108597,
0.0697498470544815,
0.05386842414736748,
0.02213278040289879,
-0.01824767515063286,
-0.024236397817730904,
-0.03067331574857235,
0.047173187136650085,
0.04701095446944237,
-0.03047257661819458,
-0.02700764499604702,
0.021430816501379013,
-0.005804792046546936,
-0.002933711977675557,
0.009177488274872303,
-0.011415722779929638,
0.02737124264240265,
0.022771699354052544,
-0.08905155956745148,
-0.04070711508393288,
0.06706850230693817,
0.03593428432941437,
0.020219027996063232,
-0.054840072989463806,
0.02670443244278431,
0.02308468706905842,
0.11546638607978821,
0.03499250486493111,
-0.012019696645438671,
0.01258253213018179,
0.06384216248989105,
-0.012688287533819675,
-0.00999757181853056,
-0.029479455202817917,
0.018118130043148994,
-0.05514008179306984,
0.005036922171711922,
-0.09485148638486862,
-0.006820933427661657,
0.0544750802218914,
0.027332380414009094,
-0.02654733695089817,
0.0618872232735157,
-0.024806663393974304,
0.017985284328460693,
-0.03927682340145111,
-0.010521063581109047,
-0.029318392276763916,
0.0709540918469429,
0.02438679337501526,
-0.011155863292515278,
0.06258348375558853,
0.0054239570163190365,
0.022857021540403366,
-0.00886533036828041,
0.01241033710539341,
0.07015824317932129,
-0.029596107080578804,
-0.02571769431233406,
-0.015497921966016293,
-0.004823945928364992,
-0.014228560030460358,
-0.02756153978407383,
-0.034771356731653214,
-0.0406738817691803,
-0.02644352614879608,
0.021393289789557457,
0.02791517972946167,
0.006369961425662041,
0.03786235302686691,
-0.021126525476574898,
-0.04282465577125549,
-0.014328604564070702,
-0.07786032557487488,
-0.01194806769490242,
-0.003005518112331629,
-0.006877224892377853,
0.020120611414313316,
0.022757288068532944,
0.010691864416003227,
-0.01333815697580576,
-0.030766397714614868,
-0.04327188804745674,
0.028406918048858643,
-0.027121907100081444,
0.009180468507111073,
0.005527455825358629,
0.09985317289829254,
0.041725531220436096,
0.01612824946641922,
0.0000053046255743538495,
-0.027915487065911293,
-0.0447198785841465,
0.017264124006032944,
-0.006811785511672497,
0.028233300894498825,
-0.008952545002102852,
0.018045218661427498,
-0.0007642494165338576,
-0.007502556778490543,
0.01672002300620079,
0.014943864196538925,
-0.013693609274923801,
0.057226818054914474,
0.07310941815376282,
0.011064945720136166,
0.012233784422278404,
0.02925913967192173,
-0.0016407114453613758,
0.013514255173504353,
-0.010579151101410389,
-0.0404529869556427,
-0.06485020369291306,
-0.029995927587151527,
0.011042232625186443,
0.028595073148608208,
-0.018051965162158012,
0.029805483296513557,
0.05392593517899513,
0.04056116193532944,
0.006110482849180698,
-0.00823427364230156,
0.02109401859343052,
-0.057674773037433624,
0.013376226648688316,
0.03226856142282486,
0.025314848870038986,
-0.0017935612704604864,
0.04046538844704628,
0.006623314693570137,
0.03488431125879288,
-0.010014872066676617,
-0.015167413279414177,
0.008937287144362926,
0.06829386949539185,
0.0026906842831522226,
-0.0015626519452780485,
-0.01564161293208599,
0.008565572090446949,
0.002283205511048436,
0.0033961469307541847,
0.01585550047457218,
-0.013580217026174068,
-0.010063710622489452,
-0.032554078847169876,
-0.005976301617920399,
0.019425179809331894,
-0.025129634886980057,
-0.012585167773067951,
-0.03549720346927643,
0.026162831112742424,
-0.08346235752105713,
-0.00654068635776639,
-0.023924577981233597,
-0.029263796284794807,
-0.022362414747476578,
-0.014790612272918224,
0.0023243860341608524,
0.0487782247364521,
0.02688668854534626,
-0.01397790014743805,
-0.022608445957303047,
0.026309175416827202,
-0.003074780572205782,
-0.045013267546892166,
0.002222870010882616,
-0.03696097433567047,
0.06018930673599243,
0.013315738178789616,
-0.03390790894627571,
-0.0093059241771698,
0.012209759093821049,
0.023059263825416565,
-0.0036569503135979176,
0.002098014811053872,
-0.0396241694688797,
-0.03785121440887451,
-0.021487189456820488,
-0.005655042361468077,
-0.038133226335048676,
-0.006966048385947943,
0.08717252314090729,
-0.0020809287670999765,
-0.036751169711351395,
-0.018357740715146065,
-0.06258057057857513,
-0.013347338885068893,
-0.007813473232090473,
-0.005841065663844347,
0.012796927243471146,
-0.027244750410318375,
0.014462631195783615,
-0.002519916044548154,
-0.04289606586098671,
-0.02196681685745716,
-0.08930125832557678,
-0.043502334505319595,
0.041017260402441025,
-0.002993953414261341,
0.052748747169971466,
-0.02605578862130642,
-0.0343935526907444,
0.07023749500513077,
0.026433182880282402,
0.011875980533659458,
-0.027653399854898453,
0.030027808621525764,
0.014428742229938507,
0.0076081170700490475,
0.004682514350861311,
0.01742306910455227,
-0.0043126968666911125,
-0.030428046360611916,
0.032017119228839874,
0.048795055598020554,
0.011306783184409142,
0.03999965637922287,
-0.02399677038192749,
-0.02221827022731304,
0.04157180339097977,
0.024398604407906532,
0.046138834208250046,
-0.0028137152548879385,
0.017547594383358955,
0.016407256945967674,
-0.0027873909566551447,
0.049620307981967926,
0.015895485877990723,
-0.05524527654051781,
0.020254265516996384,
0.011231368407607079,
0.02552053891122341,
0.008963321335613728,
0.04212646558880806,
0.011112341657280922,
-0.007722874172031879,
-0.02476416528224945,
0.00006792398926336318,
0.06466714292764664,
-0.01827995665371418,
-0.00044476790935732424,
-0.017901970073580742,
0.012600753456354141,
0.004490208346396685,
-0.03308212757110596,
0.015391414985060692,
-0.03460197523236275,
0.01984206773340702,
-0.021300649270415306,
-0.006783290300518274,
0.019171573221683502,
0.00863761454820633,
-0.018181856721639633,
-0.014836682006716728,
-0.026958364993333817,
0.007155295927077532,
-0.05590824782848358,
-0.02423224411904812,
0.0019611374009400606,
0.017129741609096527,
0.04358813539147377,
0.030840998515486717,
-0.008797375485301018,
0.0010396318975836039,
0.02712426707148552,
0.01627250202000141,
-0.08103836327791214,
0.0010195673676207662,
-0.05259168520569801,
-0.032690029591321945,
0.005839924793690443,
-0.001859939773567021,
-0.05685729160904884,
0.007330245804041624,
0.01037606131285429,
-0.05742230638861656,
-0.03120652586221695,
-0.05919218435883522,
0.006788385566323996,
-0.014750910922884941,
-0.04439328610897064,
0.010860131122171879,
0.02378854528069496,
0.06603563576936722,
-0.02498595230281353,
0.04432107135653496,
0.037062324583530426,
-0.007065517362207174,
-0.039950478821992874,
-0.01727561093866825,
0.021771395578980446,
-0.005578010343015194,
0.031540073454380035,
0.0033354584593325853,
0.02552023157477379,
-0.027781791985034943,
0.002360802609473467,
0.03449425846338272,
-0.007553339935839176,
0.025013292208313942,
0.0024980169255286455,
-0.009522555395960808,
-0.03857756033539772,
-0.02157597616314888,
-0.002625655848532915,
0.05909539386630058,
0.009767486713826656,
0.025065893307328224,
0.07369422167539597,
0.0034085542429238558,
0.01520408783107996,
0.010020334273576736,
0.0627620667219162,
-0.018750593066215515,
-0.020926272496581078,
-0.01291049923747778,
-0.032998066395521164,
-0.010244081728160381,
-0.0052344719879329205,
0.006750568747520447,
-0.014985562302172184,
-0.05026637017726898,
0.012015987187623978,
-0.02676965482532978,
0.027610018849372864,
-0.05849805101752281,
0.004403943195939064,
-0.03362441062927246,
0.00402428163215518,
-0.03330061957240105,
-0.007494554854929447,
0.01931641437113285,
0.025373924523591995,
0.03453103452920914,
-0.030123349279165268,
0.004006851464509964,
-0.09937842190265656,
0.00457401666790247,
0.008938676677644253,
0.005683547351509333,
0.0020109403412789106,
-0.011134879663586617,
-0.060989733785390854,
-0.05172114446759224,
0.04338826984167099,
-0.03532208129763603,
0.025192370638251305,
-0.007117582019418478,
-0.02973378263413906,
-0.020174192264676094,
-0.02909749560058117,
-0.014337783679366112,
0.0037722992710769176,
-0.04197787120938301,
-0.02550392411649227,
0.014228690415620804,
0.04963470622897148,
-0.023082353174686432,
0.03254134580492973,
0.007421668618917465,
0.05793244391679764,
0.030105173587799072,
-0.017449762672185898,
0.011692699044942856,
-0.008885033428668976,
-0.011124268174171448,
-0.037183377891778946,
0.03544441610574722,
0.033405810594558716,
-0.04258812218904495,
0.01671041175723076,
0.01005038432776928,
-0.005691432859748602,
0.024413468316197395,
-0.027429677546024323,
-0.01849639043211937,
0.002841492183506489,
-0.029546843841671944,
0.050346795469522476,
0.0434877946972847,
-0.0012737332144752145,
0.06680849939584732,
0.03303986415266991,
-0.0020772446878254414,
-0.021348563954234123,
-0.018237506970763206,
0.03704649955034256,
-0.05781015381217003,
0.01030142791569233,
-0.008021188899874687,
0.03299853205680847,
-0.01094342116266489,
0.05074756592512131,
-0.00765109620988369,
0.01837487891316414,
0.001843988779000938,
-0.026564255356788635,
-0.010461491532623768,
0.03531618416309357,
-0.002166750840842724,
0.06789892166852951,
0.022344347089529037,
0.00020073451742064208,
-0.012113576754927635,
0.005919995717704296,
0.022524671629071236,
-0.02295796014368534,
0.000004704301318270154,
0.033496733754873276,
-0.004734048154205084,
0.04657901078462601,
0.004536892287433147,
-0.006055939942598343,
0.044630106538534164,
-0.03893345221877098,
0.0468241348862648,
-0.03049711138010025,
-0.02370607666671276,
0.027761384844779968,
-0.01778297685086727,
-0.01113014854490757,
0.010290409438312054,
-0.02696671523153782,
-0.011349658481776714,
-0.03697873651981354,
0.01676967367529869,
0.044088881462812424,
0.01312820240855217,
-0.08370301127433777,
-0.016621921211481094,
0.016877155750989914,
-0.014847713522613049,
0.034246232360601425,
-0.0011198162101209164,
0.017106082290410995,
-0.06267393380403519,
0.027380820363759995,
-0.043555717915296555,
0.04297474026679993,
-0.0074181281961500645,
-0.045251015573740005,
0.0022158781066536903,
-0.0004117671342100948,
0.0481429249048233,
0.0026595063973218203,
0.020537009462714195,
0.011338810436427593,
-0.008347022347152233,
0.0023680326994508505,
0.016359400004148483,
0.05657165125012398,
-0.04861615598201752,
-0.054424185305833817,
-0.03480418398976326,
-0.036879971623420715,
-0.008681035600602627,
-0.025119280442595482,
-0.04831203073263168,
0.04104594513773918,
0.032458797097206116,
0.02886662818491459,
-0.019675714895129204,
0.05484906584024429,
-0.024483025074005127,
0.01597588323056698,
-0.0034365630708634853,
-0.0033788406290113926,
0.002039297018200159,
-0.04924774169921875,
0.011383354663848877,
0.011576348915696144,
-0.014951950870454311,
0.019867539405822754,
0.06910377740859985,
0.006429493427276611,
-0.05684567987918854,
0.020816413685679436,
0.01712978072464466,
0.031093396246433258,
-0.015823017805814743,
-0.008041326887905598,
0.03338800370693207,
0.004357797559350729,
-0.0394207164645195,
-0.03300672024488449,
-0.018712269142270088,
0.0028216461651027203,
0.07240737229585648,
-0.04899182170629501,
0.015223933383822441,
-0.00830864254385233,
-0.030640477314591408,
-0.006556377280503511,
-0.0528130941092968,
0.01958893984556198,
0.011956822127103806,
-0.016222316771745682,
0.017838777974247932,
-0.044715516269207,
-0.001885286415927112,
-0.027191728353500366,
0.06643743067979813,
-0.027985477820038795,
0.0039054667577147484,
0.017979541793465614,
0.0000529069293406792,
0.008237618021667004,
-0.017983775585889816,
-0.02165256254374981,
0.04097563773393631,
0.00043086428195238113,
0.009013858623802662,
0.011010166257619858,
-0.016880817711353302,
0.0647299736738205,
0.023086145520210266,
0.04172874987125397,
-0.028521865606307983,
-0.005728317890316248,
-0.02648119069635868,
0.020145373418927193,
0.007776609156280756,
0.021720722317695618,
0.03381572663784027,
-0.010359647683799267,
0.00905140582472086,
0.038095228374004364,
0.04318885877728462,
-0.005648076068609953,
-0.05013478174805641,
-0.018682289868593216,
-0.039959441870450974,
-0.04899666830897331,
0.039259083569049835,
0.00824519619345665,
-0.026975270360708237,
0.0020647060591727495,
-0.024401120841503143,
0.008573345839977264,
0.03328712657094002,
0.0180232934653759,
-0.003345032688230276,
0.07830068469047546,
-0.015920663252472878,
0.008337881416082382,
0.0010499913478270173,
0.017911167815327644,
0.10678299516439438,
0.0177189651876688,
0.013743605464696884,
-0.043641943484544754,
0.01780575141310692,
-0.003459315747022629,
-0.019627340137958527,
-0.06022878736257553,
0.009269465692341328,
-0.014028533361852169,
0.002959855832159519,
0.029628289863467216,
0.018210062757134438,
-0.021136892959475517,
-0.046957019716501236,
0.025782905519008636,
-0.03685552999377251,
-0.025811240077018738,
0.02735474891960621,
0.02137969620525837,
-0.003654786618426442,
0.02550477348268032,
-0.015290459617972374,
0.0012176973978057504,
-0.013382025063037872,
0.011368460953235626,
-0.03270219638943672,
0.004129226319491863,
-0.00224978756159544,
-0.02739397995173931,
-0.0843900665640831,
0.027987021952867508,
0.00663057342171669,
-0.03281920775771141,
-0.014268591068685055,
0.049829255789518356,
-0.0043821451254189014,
-0.016863074153661728,
0.002430357038974762,
0.02824619598686695,
-0.025079568848013878,
0.032068658620119095,
0.022005168721079826,
0.010495471768081188,
-0.048398423939943314,
0.041584696620702744,
-0.0035041016526520252,
0.041236311197280884,
-0.019264765083789825,
-0.014355418272316456,
0.02423987165093422,
0.013093453831970692,
-0.00899669248610735,
-0.040821827948093414,
-0.0053639644756913185,
0.01642407849431038,
0.028782041743397713,
-0.015167003497481346,
-0.007927841506898403,
-0.02348354458808899,
-0.007671423256397247,
0.010783037170767784,
0.0100815799087286,
-0.011929414235055447,
0.015397123992443085,
0.04077865928411484,
0.025205913931131363,
0.08649400621652603,
-0.01091591827571392,
-0.005345546640455723,
-0.03522241860628128,
0.036413099616765976,
-0.051469676196575165,
0.016416899859905243,
0.019112981855869293,
0.009691139683127403,
0.0028336462564766407,
0.016903620213270187,
0.030757343396544456,
-0.047167908400297165,
-0.023357359692454338,
0.0436701737344265,
0.009297926910221577,
-0.0008838915382511914,
-0.045867688953876495,
0.007857764139771461,
-0.0056167407892644405,
0.012216702103614807,
-0.013700363226234913,
-0.011548150330781937,
-0.046528927981853485,
0.04196681082248688,
0.035477977246046066,
0.0034082576166838408,
-0.02149227261543274,
-0.0005285859224386513,
-0.008905082941055298,
-0.03132066875696182,
-0.04075838625431061,
0.017073234543204308,
0.04115352779626846,
-0.013733897358179092,
-0.004805658478289843,
-0.006686088629066944,
-0.03422829508781433,
0.010788179002702236,
0.0333072692155838,
-0.014160851016640663,
-0.005135081242769957,
0.0207632165402174,
-0.010775675997138023,
-0.010290578007698059,
0.0006998588214628398,
-0.018216151744127274,
-0.014762689359486103,
-0.02410142682492733,
0.020559506490826607,
-0.02478005923330784,
0.04302028939127922,
-0.023247532546520233,
0.04153445363044739,
-0.05599198490381241,
0.0038995761424303055,
-0.03947499021887779,
0.0072939409874379635,
0.0032712940592318773,
-0.030278280377388,
0.033917155116796494,
0.020062604919075966,
-0.044015951454639435,
-0.009789087809622288,
0.02921031042933464,
0.021496973931789398,
-0.017228413373231888,
0.016600321978330612,
0.014933274127542973,
-0.017069227993488312,
0.030283397063612938,
-0.0113163311034441,
-0.029829908162355423,
0.04098384454846382,
-0.059306517243385315,
-0.07147369533777237,
0.03052624873816967,
-0.02457556501030922,
0.05069144815206528,
-0.022061217576265335,
-0.023809723556041718,
-0.033379677683115005,
0.049248822033405304,
-0.028385674580931664,
-0.01876172423362732,
0.001623311429284513,
-0.021826181560754776,
0.027632808312773705,
-0.007064878940582275,
-0.014018739573657513,
-0.0020839322824031115,
0.029571546241641045,
-0.0031573448795825243,
0.029612751677632332,
-0.0076722195371985435,
0.00493821082636714,
-0.025440122932195663,
-0.01751883514225483,
-0.010411558672785759,
-0.016763366758823395,
0.00862925499677658,
0.027889125049114227,
0.03060576319694519,
-0.021838268265128136,
-0.009371628053486347,
0.039863042533397675,
0.022371118888258934,
-0.10184385627508163,
0.012896858155727386,
0.011556954123079777,
0.0008290080586448312,
0.03726738691329956,
-0.04058625176548958,
0.005584044381976128,
-0.0031159764621406794,
-0.07501477748155594,
0.07283281534910202,
-0.036539096385240555,
0.005413062870502472,
-0.01733224280178547,
0.005783948581665754,
0.015950484201312065,
0.07303937524557114,
0.060458164662122726,
0.0504043772816658,
-0.03175024315714836,
0.00012151817645644769,
-0.014611544087529182,
-0.045214418321847916,
0.008610904216766357,
0.009646371006965637,
-0.04346538707613945,
-0.025468014180660248,
0.04837673902511597,
0.020120471715927124,
-0.017460506409406662,
0.01963774859905243,
-0.0018680888460949063,
0.0023160960990935564,
-0.0065130251459777355,
-0.016934523358941078,
0.019306521862745285,
0.007422075141221285,
0.00635609682649374,
0.007438755128532648,
-0.023485945537686348,
0.022624701261520386,
-0.004015163518488407,
0.030934175476431847,
-0.020880214869976044,
-0.03417801111936569,
0.03142465278506279,
-0.042103786021471024,
-0.009062817320227623,
0.05289909243583679,
-0.026900751516222954,
0.022846756502985954,
-0.016861718147993088,
-0.004724237136542797,
-0.009613287635147572,
-0.013267843052744865,
-0.016913622617721558,
-0.01204728800803423,
-0.03371583670377731,
0.03223738074302673,
-0.013119555078446865,
-0.01758207567036152,
0.05555594712495804,
-0.0017511441837996244,
-0.00543719157576561,
-0.023726079612970352,
-0.03365165740251541,
0.016554400324821472,
-0.0024319447111338377,
-0.02660266123712063,
0.014367557130753994,
0.016923656687140465,
-0.02578071877360344,
-0.015517085790634155,
-0.03147553652524948,
0.06553295999765396,
0.008644522167742252,
-0.005454476457089186,
0.002915742341428995,
-0.009744181297719479,
-0.06599457561969757,
-0.08599519729614258,
0.0046601747162640095,
0.002569881733506918,
-0.0067094662226736546,
-0.03307797387242317,
-0.00646495446562767,
-0.017147909849882126,
-0.030067486688494682,
0.057764120399951935,
-0.004419292788952589,
-0.02408202737569809,
0.002479495946317911,
0.009053165093064308,
0.02921069599688053,
-0.052245691418647766,
0.007105380296707153,
0.007344990968704224,
-0.013030576519668102,
0.014697318896651268,
-0.007539717946201563,
-0.02859792858362198,
0.023045478388667107,
0.00975134875625372,
-0.0070916712284088135,
0.041926946491003036,
0.025741705670952797,
-0.060764651745557785,
0.03216208517551422,
0.016200387850403786,
0.0325591042637825,
0.02975422516465187,
-0.015009979717433453,
0.006933622993528843,
0.013642240315675735,
0.0034584123641252518,
-0.04121695086359978,
0.022692862898111343,
-0.05842860788106918,
-0.011073242872953415,
-0.011719614267349243,
-0.023242590948939323,
-0.004303335677832365,
-0.05269552394747734,
-0.044421616941690445,
0.05759120360016823,
-0.034534938633441925,
0.01398592721670866,
0.046316567808389664,
0.000374127906979993,
0.036004215478897095,
-0.01751535013318062,
-0.007616742514073849,
0.04381398856639862,
-0.02678946778178215,
-0.0177572313696146,
0.02061844989657402,
0.01546830590814352,
0.018407749012112617,
0.0011978838592767715,
0.02989642694592476,
-0.008835292421281338,
0.028091395273804665,
0.019759763032197952,
0.024132991209626198,
-0.038816217333078384,
0.009374965913593769,
0.008728919550776482,
0.0195578932762146,
0.014437681995332241,
0.02580873668193817,
-0.027311570942401886,
0.06797292083501816,
-0.019404707476496696,
0.029425742104649544,
-0.04186227172613144,
-0.014894313178956509,
-0.049093469977378845,
0.04376133903861046,
-0.017972905188798904,
0.010741585865616798,
0.010595982894301414,
0.025842970237135887,
-0.001647171680815518,
-0.008219217881560326,
-0.0012473395327106118,
-0.02976568602025509,
-0.006371480878442526,
0.012451032176613808,
-0.013191835954785347,
-0.00644569331780076,
0.005363571457564831,
-0.03838031366467476,
0.012581193819642067,
0.06319893151521683,
0.025278883054852486,
0.03155059739947319,
-0.014941195026040077,
0.03072650358080864,
-0.028978005051612854,
0.014619534835219383,
-0.0385909378528595,
-0.013490727171301842,
-0.019584041088819504,
0.010179338976740837,
-0.01830960437655449,
-0.05604297295212746
] |
<p>According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$
What I want to do is to get a equation of solitary wave (solition) from the above Lagrangian which will lead for solving many solitary problems like life-time, dimension analysis etc.
My confusion is choosing the potential because it may vary and depend on the author's selection. What are the physical constraints on choosing an appropriate potential?
Another rather technical expectation is solitary wave is nonlinear equation so how will I write down the equation as 2nd order differential equation with respect to time?</p>
| 8,294 |
[
-0.010913941077888012,
-0.024206776171922684,
-0.00031139477505348623,
0.024865252897143364,
0.009414589032530785,
-0.007220925763249397,
-0.031998131424188614,
-0.028032561764121056,
0.006230614613741636,
-0.02865538001060486,
0.057448286563158035,
-0.005469535477459431,
0.05576920509338379,
-0.005700767505913973,
0.03371947258710861,
0.01677360013127327,
-0.02717101387679577,
-0.001558982185088098,
-0.017110522836446762,
0.003055431181564927,
0.004653117153793573,
0.006982746534049511,
-0.009058458730578423,
0.011036636307835579,
-0.024031970649957657,
0.03216299042105675,
-0.006961135193705559,
0.03370219096541405,
-0.008205161429941654,
0.06925208866596222,
-0.039829354733228683,
-0.04595378786325455,
0.01652037352323532,
0.055855296552181244,
0.011330747976899147,
0.016026338562369347,
-0.056136634200811386,
-0.0707697942852974,
-0.028668487444519997,
-0.00995804462581873,
-0.032488055527210236,
-0.006267696153372526,
0.005314950365573168,
0.05212324112653732,
-0.0455293245613575,
0.028343867510557175,
0.007800106890499592,
-0.014069696888327599,
0.024524807929992676,
-0.04781284183263779,
0.051977626979351044,
0.03992866352200508,
0.04868587478995323,
0.006182888522744179,
0.01203914824873209,
-0.007174501195549965,
0.05383113771677017,
0.062038298696279526,
-0.0024667156394571066,
-0.05498865619301796,
-0.063353531062603,
-0.0020201520528644323,
0.000024317012503161095,
-0.05958651378750801,
0.0034755603410303593,
0.023808497935533524,
0.01168566569685936,
0.0029142831917852163,
0.032930485904216766,
-0.01643879897892475,
-0.014197214506566525,
-0.02529332973062992,
0.042467150837183,
0.005351981148123741,
0.018283061683177948,
-0.011193324811756611,
-0.033308740705251694,
-0.01041692029684782,
-0.008059117011725903,
0.012204057537019253,
-0.013515443541109562,
0.03660998493432999,
0.013958307914435863,
0.03184342011809349,
-0.030181406065821648,
-0.03955933079123497,
0.05780811235308647,
0.022500591352581978,
0.017053380608558655,
0.01148525346070528,
-0.01726066879928112,
0.011818145401775837,
0.05141386389732361,
-0.01062319241464138,
-0.006139285862445831,
0.009656570851802826,
0.03727668896317482,
0.049972668290138245,
0.010221758857369423,
-0.02275276370346546,
-0.021524328738451004,
-0.01458943821489811,
-0.0018253477755934,
0.0656316801905632,
0.008291498757898808,
-0.01858455501496792,
-0.02613145112991333,
0.013788248412311077,
-0.028866011649370193,
-0.009398581460118294,
-0.009885766543447971,
0.0072030178271234035,
-0.00027277908520773053,
0.006627287250012159,
0.004989808425307274,
-0.03503820300102234,
0.002863617381080985,
-0.042902395129203796,
0.07856534421443939,
0.06710348278284073,
0.016427703201770782,
-0.03510177135467529,
0.07784513384103775,
-0.01827983930706978,
-0.050517551600933075,
0.015460839495062828,
0.04341398924589157,
0.0027624033391475677,
-0.025387801229953766,
0.0014159089187160134,
0.026534656062722206,
0.010219398885965347,
0.010011719539761543,
0.028189001604914665,
0.03891725093126297,
-0.04230301454663277,
-0.11435512453317642,
-0.05389663577079773,
-0.013575776480138302,
-0.005169513635337353,
-0.017083682119846344,
-0.06918683648109436,
0.00035295719862915576,
0.03145091235637665,
0.08318072557449341,
-0.018690284341573715,
0.018238553777337074,
0.026818634942173958,
0.03828506916761398,
0.006626752205193043,
-0.017260845750570297,
-0.012857743538916111,
0.005679743830114603,
-0.02450953796505928,
0.012517719529569149,
-0.04277052357792854,
-0.0006644289824180305,
0.02199295535683632,
0.014534353278577328,
-0.016952726989984512,
0.09930986911058426,
-0.03258785605430603,
0.015402032062411308,
0.02923400141298771,
-0.0030539636500179768,
-0.019650187343358994,
0.08476381748914719,
-0.028832759708166122,
0.029230982065200806,
0.024042189121246338,
0.009761985391378403,
0.028180699795484543,
-0.00776620302349329,
0.028389224782586098,
0.03467920050024986,
-0.034543365240097046,
-0.02524792030453682,
-0.007563198450952768,
0.001671336591243744,
0.008612534962594509,
-0.02094086818397045,
-0.06650149822235107,
-0.0257558673620224,
0.00038735437556169927,
-0.0335988849401474,
0.013192351907491684,
0.008059988729655743,
0.01042240671813488,
-0.03456444665789604,
-0.06183517724275589,
-0.023936353623867035,
-0.043121304363012314,
0.027925951406359673,
0.027241839095950127,
0.014793054200708866,
0.054551318287849426,
0.009880516678094864,
0.022718366235494614,
-0.03779781237244606,
-0.020421085879206657,
-0.021651463583111763,
0.05643636733293533,
-0.00826358888298273,
0.0060526723973453045,
0.030801044777035713,
0.033700115978717804,
0.0036347713321447372,
0.015850968658924103,
0.034247562289237976,
-0.015628475695848465,
-0.023168930783867836,
-0.0013723219744861126,
-0.001157909631729126,
0.051155444234609604,
-0.01865409128367901,
0.0033266539685428143,
0.0008180090808309615,
0.012746202759444714,
0.006598121952265501,
0.04569689929485321,
-0.02579541876912117,
0.06506719440221786,
0.0650399923324585,
0.012758119963109493,
0.008221840485930443,
0.05613633990287781,
-0.025561748072504997,
0.015632543712854385,
0.0001115228224080056,
-0.040779054164886475,
-0.016880100592970848,
0.015307710506021976,
0.01803106628358364,
0.06003657728433609,
-0.03196309506893158,
0.022542525082826614,
0.01798943243920803,
0.011603917926549911,
0.09024032950401306,
0.02329469844698906,
-0.053749751299619675,
-0.049271706491708755,
0.06668879091739655,
0.026479339227080345,
-0.023958967998623848,
-0.010187928564846516,
0.04652249068021774,
0.0035482149105519056,
0.010434693656861782,
-0.027931947261095047,
-0.018922695890069008,
0.04262363910675049,
-0.03322989121079445,
0.012871007435023785,
-0.020202219486236572,
-0.01386662945151329,
0.049298979341983795,
-0.03171461448073387,
0.03793984651565552,
0.049566518515348434,
-0.037431150674819946,
0.0025469022803008556,
-0.0517873540520668,
0.0035102139227092266,
0.015369328670203686,
-0.009787064045667648,
-0.008960114791989326,
-0.026848962530493736,
0.027368180453777313,
-0.046084385365247726,
-0.001517346827313304,
0.0010036065941676497,
-0.024388575926423073,
-0.04470991715788841,
0.002950841560959816,
0.032074667513370514,
0.00007113155879778787,
0.00559532456099987,
0.026751108467578888,
-0.04714452475309372,
0.02623624913394451,
0.011946574784815311,
0.018760252743959427,
0.02743316814303398,
-0.04059798642992973,
-0.004406292922794819,
-0.042511697858572006,
-0.027970049530267715,
0.0841112732887268,
-0.006264492403715849,
0.0680767074227333,
0.008567743003368378,
-0.018436048179864883,
-0.06387320905923843,
-0.03403303399682045,
-0.03235575556755066,
0.023531077429652214,
0.005732931662350893,
-0.020914817228913307,
0.03819822147488594,
0.016828157007694244,
-0.05919665843248367,
0.013243966735899448,
-0.05391738936305046,
-0.02850957401096821,
-0.013353763148188591,
0.01478734239935875,
0.01346274372190237,
-0.04205095395445824,
0.036528222262859344,
0.04189573600888252,
0.0033473121002316475,
0.03567000478506088,
-0.06881237030029297,
-0.021578339859843254,
0.02876046858727932,
-0.01873091608285904,
0.028385497629642487,
-0.014927873387932777,
-0.03861430659890175,
0.07844039797782898,
0.0314490869641304,
-0.013025355525314808,
-0.018464285880327225,
0.01295218151062727,
-0.0015179518377408385,
-0.01860976405441761,
0.027537379413843155,
0.00938333384692669,
-0.00411455100402236,
0.013002182357013226,
0.01414512936025858,
0.006902957335114479,
0.03184257820248604,
0.02704601362347603,
0.0011567740002647042,
0.018658991903066635,
0.0015265516703948379,
0.009349712170660496,
0.0276049692183733,
-0.01074706856161356,
-0.011377754621207714,
0.04024370014667511,
-0.00905704963952303,
0.004928405862301588,
0.014833705499768257,
-0.03039306402206421,
0.03983999788761139,
0.0100840013474226,
-0.013731316663324833,
-0.024801788851618767,
0.036909181624650955,
-0.008014391176402569,
-0.03600974753499031,
0.008954661898314953,
-0.016133928671479225,
0.027358712628483772,
-0.01488276943564415,
0.00790484994649887,
0.02385016530752182,
0.02706066519021988,
-0.024414250627160072,
-0.028529291972517967,
-0.037583816796541214,
-0.005610048305243254,
0.021771075204014778,
-0.011930850334465504,
-0.004087486770004034,
0.03864969685673714,
0.005704732611775398,
-0.008195648901164532,
-0.05741603672504425,
-0.03238838165998459,
0.003365604905411601,
-0.055626049637794495,
-0.028093766421079636,
0.012935019098222256,
0.055416759103536606,
-0.00867314450442791,
0.039216767996549606,
0.012804821133613586,
0.017474059015512466,
0.045741088688373566,
0.02105499804019928,
-0.04839125648140907,
0.03180688992142677,
-0.03810356929898262,
-0.020367007702589035,
0.013895224779844284,
0.017404573038220406,
-0.025706343352794647,
-0.0023036468774080276,
-0.015177001245319843,
0.008065777830779552,
-0.02424718253314495,
-0.06192554533481598,
0.026747139170765877,
-0.040878601372241974,
-0.017895573750138283,
-0.0567404143512249,
0.0363006517291069,
-0.00010702465078793466,
-0.007703214418143034,
-0.0033564711920917034,
0.046591658145189285,
0.021029943600296974,
-0.020786482840776443,
0.0005857929936610162,
-0.028047075495123863,
0.005995640531182289,
0.015516030602157116,
0.005001656711101532,
-0.007554211188107729,
-0.012036553584039211,
0.02683369815349579,
0.01180539932101965,
0.03715519607067108,
-0.0024469459895044565,
0.03212299942970276,
-0.004183605313301086,
-0.031552113592624664,
-0.003022372256964445,
0.002999495016410947,
0.06758382171392441,
0.03493016958236694,
0.00024633423890918493,
0.00940046925097704,
-0.020495055243372917,
-0.003720188280567527,
0.03945363685488701,
0.047813210636377335,
-0.011542209424078465,
-0.02468658797442913,
-0.03134646266698837,
-0.002042139181867242,
-0.022142037749290466,
0.004460947588086128,
0.0024307160638272762,
-0.015023687854409218,
-0.03749093413352966,
0.01610773429274559,
-0.0038248978089541197,
0.009547482244670391,
-0.015779664739966393,
-0.017809657379984856,
0.01673606038093567,
0.03149726241827011,
0.01715230755507946,
-0.031270384788513184,
0.004640334751456976,
0.06663314253091812,
0.040427420288324356,
0.00754659716039896,
0.016832871362566948,
-0.06751134991645813,
-0.04845112934708595,
0.01854831352829933,
0.01257467269897461,
0.012458761222660542,
-0.014939703047275543,
-0.06496233493089676,
-0.028908489271998405,
0.03409172594547272,
-0.011653045192360878,
0.0230705589056015,
0.02103586308658123,
0.006354289595037699,
0.014480886049568653,
0.008989586494863033,
-0.017851434648036957,
0.03665263205766678,
0.02463938668370247,
0.017878003418445587,
-0.011659144423902035,
0.03246397525072098,
0.005518130958080292,
0.03748415783047676,
-0.031116152182221413,
0.09723761677742004,
0.0035192405339330435,
0.0009110026876442134,
0.0024721212685108185,
0.008452573791146278,
-0.03144276142120361,
-0.043767765164375305,
-0.01985151134431362,
0.02087421342730522,
-0.001818200689740479,
-0.011464112438261509,
-0.002320006489753723,
-0.03669244796037674,
0.025809485465288162,
0.03551827371120453,
-0.0012758467346429825,
0.0020096669904887676,
-0.05097309499979019,
-0.005752302706241608,
0.019072437658905983,
-0.012656177394092083,
0.07841405272483826,
0.05404312536120415,
-0.009133863262832165,
-0.02139320969581604,
-0.05618893727660179,
0.039221107959747314,
-0.022028349339962006,
0.0034302626736462116,
-0.030439140275120735,
0.03182631731033325,
-0.05500907078385353,
0.05803517997264862,
-0.02653610333800316,
0.009820602834224701,
-0.017368558794260025,
-0.0019925632514059544,
-0.036858249455690384,
0.035532545298337936,
0.03800266981124878,
-0.027398645877838135,
0.00036507315235212445,
0.017435843124985695,
0.027883918955922127,
-0.012615280225872993,
-0.002325578359887004,
-0.03630540147423744,
0.007723532151430845,
0.05711197853088379,
-0.006501953117549419,
0.029457127675414085,
0.005137930624186993,
-0.025807617232203484,
0.05226742476224899,
-0.04333948343992233,
0.04026256501674652,
0.028302578255534172,
-0.022131221368908882,
0.025824440643191338,
-0.05399429798126221,
-0.05125494673848152,
0.005442334339022636,
0.014338050968945026,
0.026729010045528412,
-0.05443327873945236,
0.026007192209362984,
0.02755824849009514,
0.01497745793312788,
-0.10286770015954971,
-0.037512920796871185,
-0.0015593839343637228,
-0.04625045508146286,
-0.0440501868724823,
-0.008538060821592808,
0.027312571182847023,
-0.035221971571445465,
-0.02076820097863674,
0.015929752960801125,
0.06009801849722862,
-0.00481323292478919,
-0.014894205145537853,
-0.025107378140091896,
0.03280338644981384,
0.008448165841400623,
-0.011398994363844395,
0.01109405979514122,
0.0039237127639353275,
-0.028949256986379623,
-0.0013097758637741208,
-0.012472850270569324,
0.04904969036579132,
-0.028180940076708794,
-0.003996033221483231,
-0.03689013794064522,
-0.02365216240286827,
0.04823620989918709,
-0.014717898331582546,
0.01878826692700386,
0.043018072843551636,
0.022831810638308525,
-0.0016851426335051656,
-0.014443241991102695,
-0.0058297631330788136,
-0.007786275818943977,
0.03328883647918701,
0.0026180322747677565,
-0.03613649308681488,
-0.035792138427495956,
-0.034405115991830826,
0.034756872802972794,
-0.015427224338054657,
-0.019246075302362442,
0.0023152916692197323,
0.05672666057944298,
-0.006171373650431633,
-0.0016702645225450397,
0.037356629967689514,
0.007920041680335999,
-0.001464769709855318,
0.01261619571596384,
-0.002168315229937434,
0.030312275514006615,
0.029963631182909012,
-0.04234667867422104,
-0.01686357706785202,
-0.014322496019303799,
0.04294257611036301,
0.06869124621152878,
-0.0203339084982872,
0.03164581209421158,
-0.0014227012870833278,
0.0017362922662869096,
-0.008918478153645992,
0.000041119143133983016,
-0.020549288019537926,
0.0115820849314332,
0.005513077601790428,
0.03581946715712547,
-0.015941832214593887,
-0.00901524256914854,
0.010161350481212139,
-0.009582902304828167,
-0.017079146578907967,
0.044805578887462616,
0.029193799942731857,
0.024600544944405556,
-0.0023107773158699274,
-0.01170315407216549,
-0.03985173627734184,
0.03961196169257164,
-0.04465603455901146,
0.04823405295610428,
0.012745277024805546,
-0.039282213896512985,
0.028701946139335632,
-0.007759586907923222,
-0.01807272620499134,
-0.037356458604335785,
0.019955160096287727,
-0.016069920733571053,
0.00898787658661604,
0.0581403523683548,
-0.021093852818012238,
0.033323198556900024,
0.0523037351667881,
0.02066466398537159,
0.002852145815268159,
0.03405339643359184,
0.00821637362241745,
-0.06058599054813385,
-0.013313116505742073,
-0.06076125428080559,
-0.09021581709384918,
0.044263675808906555,
0.0204815324395895,
-0.01208311878144741,
-0.01169290579855442,
-0.021718699485063553,
0.022688036784529686,
0.015213871374726295,
0.03058069571852684,
-0.01681305654346943,
0.07981158792972565,
0.0023214872926473618,
-0.006677768658846617,
-0.024862099438905716,
0.0003911797539331019,
0.11798030138015747,
0.10315757244825363,
-0.005014369264245033,
-0.09209655970335007,
0.0036434009671211243,
-0.01016149204224348,
-0.0043420675210654736,
-0.0625765398144722,
0.043582700192928314,
0.006993135903030634,
-0.03443671762943268,
-0.008785523474216461,
0.05017572641372681,
-0.022577840834856033,
0.010810181498527527,
0.03941032290458679,
-0.01960589736700058,
-0.05828890576958656,
0.02779056504368782,
0.000927565386518836,
-0.008263614028692245,
-0.0015898110577836633,
0.0017570715863257647,
0.03665081784129143,
0.004950358532369137,
0.045661747455596924,
-0.02214016765356064,
-0.04642290621995926,
0.05480421334505081,
-0.05752208083868027,
-0.031085090711712837,
-0.027986548840999603,
-0.008625809103250504,
-0.008344447240233421,
-0.0037500981707125902,
-0.007824787870049477,
-0.016242921352386475,
-0.03526013717055321,
0.03309477120637894,
0.02533661387860775,
0.009379221126437187,
0.019237497821450233,
0.029658129438757896,
0.0005848337896168232,
-0.020788472145795822,
-0.006248144898563623,
-0.020532267168164253,
0.06704080104827881,
-0.005278189666569233,
-0.000884464243426919,
0.013261587359011173,
-0.0007728914497420192,
0.011628744192421436,
-0.015560212545096874,
-0.03627823665738106,
-0.021289510652422905,
0.07324835658073425,
-0.0014029002049937844,
-0.005586534272879362,
-0.027819272130727768,
-0.024095958098769188,
0.001019410789012909,
0.02053552120923996,
-0.016602106392383575,
-0.0034475841093808413,
-0.010532171465456486,
-0.013505162671208382,
-0.00853871088474989,
-0.01668413355946541,
-0.025441225618124008,
-0.02427626959979534,
-0.03258344158530235,
-0.03222358971834183,
-0.004358589183539152,
0.02805119752883911,
0.023070113733410835,
-0.0005789428832940757,
-0.019085153937339783,
-0.011579133570194244,
-0.02517036907374859,
-0.08236196637153625,
0.03425107151269913,
0.015046507120132446,
-0.004958390258252621,
-0.024353371933102608,
0.009441827423870564,
0.0026614083908498287,
0.051002904772758484,
0.003084484487771988,
0.005435624159872532,
-0.008937699720263481,
-0.0032270909287035465,
0.01688207872211933,
-0.05131101980805397,
-0.020304713398218155,
-0.0029880243819206953,
-0.02637593448162079,
0.007229628972709179,
-0.04327994957566261,
-0.027751529589295387,
-0.008039369247853756,
0.008247800171375275,
-0.005271458066999912,
0.045117441564798355,
-0.0053315856494009495,
-0.014728312380611897,
0.037163540720939636,
-0.02009054645895958,
-0.0048843068070709705,
0.0140119893476367,
0.02152763120830059,
-0.025025634095072746,
-0.04262693226337433,
-0.01575687900185585,
0.0061780912801623344,
-0.001038125716149807,
-0.006142039317637682,
-0.03956275060772896,
-0.011645752005279064,
-0.02276439219713211,
0.00007239740079967305,
-0.03865165263414383,
-0.008503725752234459,
-0.04233144596219063,
0.04598434269428253,
-0.02302130125463009,
-0.014236357994377613,
-0.04035560041666031,
0.021069912239909172,
-0.013288754969835281,
0.005181995686143637,
-0.025343870744109154,
0.001354321837425232,
-0.034399744123220444,
0.025659382343292236,
0.021300919353961945,
-0.020897362381219864,
0.05614306032657623,
0.010779425501823425,
-0.03032969869673252,
-0.005697160959243774,
-0.041919901967048645,
-0.04016726091504097,
0.031150517985224724,
0.014910230413079262,
0.03927027806639671,
0.02442272938787937,
0.012500510551035404,
-0.017064770683646202,
0.07777313888072968,
-0.010428626090288162,
0.003595201298594475,
-0.027484772726893425,
-0.048053644597530365,
-0.03022812493145466,
-0.019650574773550034,
-0.021139390766620636,
-0.0035214521922171116,
0.007226082496345043,
-0.009443307295441628,
0.01092566642910242,
0.009950839914381504,
-0.04416877031326294,
0.015629546716809273,
0.007292252499610186,
0.0345083586871624,
0.011290136724710464,
-0.012201584875583649,
0.032734036445617676,
0.07197534292936325,
0.006743490695953369,
0.008896179497241974,
0.01390122715383768,
0.0033239389304071665,
-0.08708623051643372,
-0.00477001303806901,
0.027160244062542915,
0.024179354310035706,
0.06505130231380463,
-0.05459665134549141,
0.012925214134156704,
0.0021007107570767403,
-0.017638565972447395,
-0.01982700079679489,
-0.03470947593450546,
0.020544175058603287,
0.03190673887729645,
-0.02693295106291771,
-0.01721387542784214,
0.08454371243715286,
0.0517677403986454,
0.015163186006247997,
0.003732152748852968,
-0.012795647606253624,
0.029162876307964325,
0.0005059523391537368,
0.0076674120500683784,
0.057222381234169006,
0.003602940123528242,
-0.00984331127256155,
0.08326559513807297,
-0.014146775007247925,
-0.0700150579214096,
0.02991773933172226,
-0.024203462526202202,
-0.016773393377661705,
0.0063364687375724316,
0.05592593178153038,
-0.02806197665631771,
0.029713084921240807,
0.03717152774333954,
-0.035115476697683334,
-0.009705225005745888,
0.012427860870957375,
0.011591015383601189,
-0.004862042609602213,
-0.005313485860824585,
-0.019464697688817978,
0.011859782971441746,
-0.0294860377907753,
-0.04791047424077988,
0.07094191014766693,
-0.02724473737180233,
-0.03816618025302887,
0.0036696612369269133,
-0.044999830424785614,
0.018507031723856926,
-0.0004651762719731778,
-0.0011663053883239627,
-0.03870255500078201,
0.010875971056520939,
0.023375272750854492,
0.004760792013257742,
0.00054282380733639,
0.033493053168058395,
-0.03005724400281906,
-0.053583696484565735,
0.017647476866841316,
0.007279186509549618,
-0.009301482699811459,
-0.08021115511655807,
-0.017729103565216064,
-0.033539775758981705,
-0.035598285496234894,
-0.012228094041347504,
-0.014790358021855354,
-0.043882813304662704,
0.040938131511211395,
0.008378494530916214,
0.030889613553881645,
0.013601791113615036,
-0.02152656391263008,
0.012363427318632603,
-0.05915037542581558,
0.018481792882084846,
0.020032312721014023,
-0.01833108812570572,
0.006589243188500404,
-0.02424800582230091,
-0.007980668917298317,
0.03725844994187355,
0.03432510048151016,
-0.03585759550333023,
-0.027722755447030067,
0.021715322509407997,
-0.013888997957110405,
0.008493605069816113,
-0.018198257312178612,
-0.04375465214252472,
0.002254931256175041,
-0.0010410858085379004,
-0.005401920061558485,
0.05143025144934654,
-0.019810283556580544,
0.028826110064983368,
0.005412639584392309,
0.021019963547587395,
0.018675683066248894,
0.03545202314853668,
-0.031294532120227814,
0.014628377743065357,
0.019268730655312538,
-0.019582098349928856,
0.03344974294304848,
-0.018742753192782402,
0.013996480964124203,
0.0014047435251995921,
-0.03598371148109436,
-0.03695021569728851,
0.024398181587457657,
-0.05608977749943733,
-0.007650877349078655,
0.007262446917593479,
-0.035462748259305954,
0.03396621346473694,
-0.09000421315431595,
-0.026705903932452202,
0.023098763078451157,
0.00628290930762887,
-0.001561250421218574,
0.031562067568302155,
-0.0017803924856707454,
0.006747924257069826,
0.011609490029513836,
0.015825476497411728,
0.021156124770641327,
0.021485360339283943,
-0.0127868028357625,
0.014820822514593601,
0.013567425310611725,
0.011226399801671505,
0.0315222293138504,
0.004352834541350603,
-0.0017924560233950615,
0.036109115928411484,
0.014596612192690372,
0.031066058203577995,
-0.030693000182509422,
0.004388774279505014,
0.007102619856595993,
-0.01047109067440033,
-0.0018659193301573396,
-0.005190999247133732,
-0.021593041718006134,
0.05354464054107666,
-0.023037247359752655,
0.023105263710021973,
-0.03777053952217102,
0.0027275588363409042,
-0.04876880347728729,
0.024209078401327133,
0.015589006245136261,
0.07041103392839432,
-0.0041090864688158035,
0.01865207776427269,
-0.014497005380690098,
0.004255729261785746,
0.01789740100502968,
-0.0611092671751976,
0.011189370416104794,
0.02477726712822914,
-0.008422764018177986,
-0.004827170167118311,
-0.02508815936744213,
-0.03593405336141586,
-0.014106214046478271,
0.0023555990774184465,
0.02340109646320343,
0.011348637752234936,
-0.012156326323747635,
0.007141708396375179,
-0.019061943516135216,
0.06644164025783539,
-0.05054932460188866,
-0.0380404032766819,
-0.0022076773457229137,
-0.01835319586098194,
-0.028814909979701042,
0.011223480105400085
] |
<p>I know the <a href="http://en.wikipedia.org/wiki/Richter_magnitude_scale" rel="nofollow">Richter magnitude scale</a> is often used for measuring the strength of earthquakes. At the same time, explosive/destructive releases of energy are often quoted in equivalent amounts of TNT. Is there some way to relate these two scales? Or are they not equivalent?</p>
<p>It's especially confusing since the Richter scale doesn't seem to go very high. Is a magnitude 8 earthquake really only 4 times worse than a magnitude 2? Or would converting these numbers to TNT equivalents be more revealing?</p>
| 8,295 |
[
-0.042658790946006775,
-0.04989216476678848,
-0.019054275006055832,
-0.015653029084205627,
0.03489011153578758,
0.02460435964167118,
0.022630324587225914,
-0.038942042738199234,
0.05157742276787758,
-0.008616510778665543,
0.008263327181339264,
0.040092334151268005,
0.02117271162569523,
0.002260399516671896,
0.00507710874080658,
0.009799422696232796,
-0.05214302986860275,
-0.015580521896481514,
0.021901564672589302,
-0.045617133378982544,
0.001796542084775865,
-0.013288063928484917,
-0.0008928763563744724,
-0.006503150332719088,
-0.028238920494914055,
0.04452703893184662,
0.03408702462911606,
-0.007678916212171316,
0.03724184259772301,
0.03361009806394577,
0.028003264218568802,
-0.023356787860393524,
0.031924568116664886,
0.023274486884474754,
0.012979836203157902,
0.016501743346452713,
-0.029754826799035072,
-0.0014137126272544265,
-0.043168455362319946,
0.06299664825201035,
-0.015820477157831192,
-0.02764476090669632,
-0.0002611455274745822,
0.03970486670732498,
-0.054666902869939804,
0.02169903926551342,
-0.048326678574085236,
-0.056097693741321564,
0.0077484119683504105,
-0.054040633141994476,
0.05361853912472725,
0.02926008589565754,
0.02104405127465725,
0.04751741886138916,
0.003131122561171651,
0.03038172237575054,
0.07878269255161285,
0.0699736475944519,
-0.028426753357052803,
-0.07198086380958557,
-0.024981942027807236,
-0.010464946739375591,
0.014017004519701004,
-0.02901349775493145,
-0.0020469885785132647,
0.07804465293884277,
-0.012820111587643623,
-0.037518031895160675,
0.042178310453891754,
0.025807682424783707,
0.002154387766495347,
0.005066059995442629,
0.04309350997209549,
-0.014679263345897198,
-0.020963318645954132,
-0.02587134949862957,
0.023740217089653015,
0.025878561660647392,
0.0013616614742204547,
0.04500381276011467,
-0.011378657072782516,
0.022627977654337883,
0.036761101335287094,
0.05946384370326996,
0.02517145685851574,
0.014069103635847569,
0.059207119047641754,
-0.012687132693827152,
0.019939308986067772,
0.011825816705822945,
0.009836195968091488,
-0.02045428566634655,
0.012757687829434872,
-0.025086816400289536,
-0.004590237513184547,
0.0029678046703338623,
0.0022541950456798077,
0.047578420490026474,
0.03803253546357155,
0.019884586334228516,
0.031910549849271774,
-0.017830166965723038,
0.031073493883013725,
0.04623723402619362,
0.010603251866996288,
-0.040931448340415955,
-0.03688753396272659,
-0.007274152245372534,
-0.005109279882162809,
0.011336131021380424,
-0.028446657583117485,
0.004042925778776407,
0.03664682060480118,
-0.007665090728551149,
0.0024120095185935497,
0.00610623462125659,
0.006941724568605423,
0.018348820507526398,
0.026999471709132195,
0.022916577756404877,
0.04638585075736046,
-0.04361094906926155,
0.036804839968681335,
-0.04050961136817932,
-0.05423074960708618,
-0.011985027231276035,
0.02450830116868019,
-0.0376599095761776,
-0.030605776235461235,
0.05802498012781143,
0.014286191202700138,
-0.012779035605490208,
-0.013381900265812874,
-0.033173106610774994,
0.05002746358513832,
-0.019619401544332504,
-0.06069735810160637,
-0.08213357627391815,
0.027834726497530937,
0.02189464308321476,
-0.03567493334412575,
-0.0794588178396225,
-0.003251072484999895,
0.009187933057546616,
0.005174827761948109,
0.03608324006199837,
0.0296908188611269,
0.02763296477496624,
0.032134056091308594,
0.008123287931084633,
-0.029323633760213852,
0.004541847854852676,
0.01790126971900463,
-0.04586669057607651,
0.011750947684049606,
-0.06474196910858154,
0.0014137510443106294,
0.013954957947134972,
-0.013771971687674522,
-0.009155387058854103,
0.05369894951581955,
-0.0026167489122599363,
-0.03036811202764511,
0.0041481200605630875,
0.026804503053426743,
-0.009173098020255566,
0.08718786388635635,
-0.005460758693516254,
-0.04392116144299507,
0.0496307834982872,
0.017963040620088577,
-0.02073417603969574,
0.044235728681087494,
0.019739532843232155,
0.025397000834345818,
-0.018074089661240578,
-0.01895766332745552,
-0.08627131581306458,
0.024607595056295395,
0.02832098677754402,
-0.029312020167708397,
-0.020302994176745415,
-0.0070975604467093945,
-0.005903015378862619,
0.04194074124097824,
0.045946113765239716,
-0.0014616246335208416,
-0.039846666157245636,
0.011948023922741413,
-0.02063611149787903,
-0.037731483578681946,
-0.052552055567502975,
0.03598720207810402,
-0.013689707033336163,
0.03023494966328144,
0.01055870484560728,
-0.0104951998218894,
0.003379630856215954,
-0.03659353405237198,
0.021449994295835495,
0.0011182584566995502,
0.041593872010707855,
-0.01510572899132967,
-0.018448064103722572,
-0.0034850675147026777,
0.058293335139751434,
0.028076279908418655,
-0.00009006404434330761,
0.030506473034620285,
-0.022801173850893974,
-0.045164577662944794,
0.015606534667313099,
-0.036231085658073425,
0.002872592769563198,
0.014776124618947506,
-0.04565633460879326,
-0.008068816736340523,
-0.008066130802035332,
-0.014995310455560684,
0.03342686966061592,
-0.022045012563467026,
0.06143300607800484,
0.04480898752808571,
0.00543180713430047,
-0.0144263980910182,
0.0031282908748835325,
0.015946490690112114,
0.014340291731059551,
-0.02705780416727066,
-0.012270158156752586,
-0.054718177765607834,
0.015018315985798836,
0.044799238443374634,
0.03295880928635597,
-0.04504310339689255,
0.005060381721705198,
0.07704838365316391,
0.01970389112830162,
0.013186031021177769,
0.014118240214884281,
-0.01656157150864601,
-0.02584051340818405,
-0.016228489577770233,
0.018410665914416313,
-0.010237711481750011,
0.01746673323214054,
-0.0003599867632146925,
0.03520473092794418,
-0.012790513224899769,
-0.027364831417798996,
0.01536725927144289,
0.04725294187664986,
-0.020162155851721764,
0.005795232020318508,
-0.012836094945669174,
-0.0256375540047884,
0.0793422982096672,
-0.0173483993858099,
0.04388279467821121,
0.014000787399709225,
-0.012270254082977772,
0.004831463564187288,
0.00011507983435876667,
-0.006087018642574549,
0.02903493121266365,
-0.02063840441405773,
-0.022472603246569633,
-0.007242955733090639,
0.025417262688279152,
-0.03163957968354225,
-0.0034222458489239216,
0.01744861714541912,
0.002070009708404541,
-0.060352057218551636,
0.019109446555376053,
0.03422001376748085,
-0.006287417374551296,
0.04543126001954079,
-0.028851762413978577,
-0.028313420712947845,
0.001108393189497292,
-0.06796067208051682,
-0.020600933581590652,
0.007184561342000961,
-0.017997553572058678,
0.014209872111678123,
-0.032203443348407745,
-0.014680096879601479,
0.02614419534802437,
-0.003437821287661791,
0.01966673508286476,
0.050090912729501724,
0.004755011294037104,
-0.02981398068368435,
0.03147365152835846,
-0.008311702869832516,
-0.005698349792510271,
0.0015668923733755946,
-0.015998834744095802,
0.052798375487327576,
-0.04387351870536804,
-0.022322632372379303,
-0.001478630001656711,
-0.049921322613954544,
-0.012405897490680218,
-0.03306807205080986,
0.025560766458511353,
-0.002289291936904192,
-0.010478370822966099,
-0.005557904485613108,
0.03173569589853287,
-0.06292691081762314,
-0.02791130170226097,
-0.05602208524942398,
-0.046569474041461945,
0.024545816704630852,
-0.012756258249282837,
0.07734996825456619,
0.015189382247626781,
-0.06379947811365128,
0.0714988112449646,
0.02974504791200161,
0.003616068512201309,
-0.009375210851430893,
-0.006557619199156761,
-0.0002502159040886909,
0.008807145990431309,
-0.0029094566125422716,
0.007546673063188791,
0.045299988240003586,
0.0239602942019701,
-0.008316531777381897,
0.04156475141644478,
0.05113072693347931,
0.011362911202013493,
0.024590888991951942,
-0.006428088527172804,
0.031323522329330444,
0.009385122917592525,
0.022986166179180145,
0.01921936869621277,
-0.034675534814596176,
0.00668182922527194,
-0.0020978853572160006,
0.03887014836072922,
0.009831675328314304,
-0.015504302456974983,
0.016439728438854218,
0.040458522737026215,
-0.015821583569049835,
-0.062001679092645645,
0.028645005077123642,
-0.021708887070417404,
0.05260678753256798,
-0.0036513397935777903,
0.06187981367111206,
0.04670606926083565,
0.007909243926405907,
-0.027672167867422104,
0.0036169704981148243,
0.04807065799832344,
-0.008972649462521076,
-0.028659390285611153,
0.0023680790327489376,
0.03142663091421127,
0.03271779417991638,
0.017340701073408127,
0.008638477884232998,
0.04422535002231598,
0.0005594455869868398,
0.02493663690984249,
0.03665031120181084,
0.008480963297188282,
0.01051232498139143,
-0.07943467795848846,
-0.007675577886402607,
-0.02691870555281639,
0.035542331635951996,
-0.004129472188651562,
0.05214141309261322,
0.014186246320605278,
0.018380174413323402,
0.045263174921274185,
-0.00045072860666550696,
-0.07238709181547165,
0.01925051212310791,
-0.06529354304075241,
-0.021283911541104317,
-0.0015696658520027995,
-0.010979972779750824,
-0.017892170697450638,
-0.0024313684552907944,
-0.046167150139808655,
-0.021631840616464615,
0.01547758188098669,
-0.06643630564212799,
0.03381745144724846,
-0.0006995453150011599,
0.01723656989634037,
0.015975970774888992,
0.04097222536802292,
0.0065096355974674225,
-0.014283611439168453,
0.029667137190699577,
0.026865189895033836,
-0.009555723518133163,
0.01401128526777029,
-0.00691811740398407,
0.010109907016158104,
0.02184402197599411,
0.034176427870988846,
-0.009870407171547413,
0.04951528459787369,
0.015084446407854557,
-0.001312499400228262,
0.019746746867895126,
0.030334535986185074,
0.036285847425460815,
-0.006367611698806286,
-0.0687461569905281,
-0.04491936042904854,
0.004275641869753599,
0.023001333698630333,
0.03074893355369568,
-0.0032469488214701414,
0.03449418023228645,
0.006042984314262867,
0.010383366607129574,
-0.014491606503725052,
0.05574153736233711,
0.020145421847701073,
-0.03809095174074173,
-0.005938006564974785,
-0.05851660296320915,
-0.010138914920389652,
-0.017200849950313568,
-0.022976022213697433,
0.005039751995354891,
0.007379499729722738,
-0.02146206982433796,
0.006653809919953346,
0.05508169159293175,
0.006773747969418764,
-0.04361395537853241,
0.017792273312807083,
0.014714968390762806,
0.013577272184193134,
-0.021485326811671257,
-0.015483280643820763,
-0.014484747312963009,
0.037024833261966705,
0.03173920139670372,
0.007405911572277546,
-0.019506515935063362,
-0.0799049362540245,
-0.009135987609624863,
0.019506346434354782,
0.01352760847657919,
-0.022964539006352425,
-0.03899790346622467,
-0.031405653804540634,
-0.009340926073491573,
0.032450221478939056,
0.001017743139527738,
0.03989982604980469,
-0.010785380378365517,
0.02355414256453514,
-0.017654333263635635,
-0.007564964704215527,
0.02255122736096382,
0.022439157590270042,
-0.0019214204512536526,
0.03724544867873192,
-0.0006535256979987025,
0.020318951457738876,
-0.026211649179458618,
-0.00010014473082264885,
0.06741105020046234,
0.037951529026031494,
0.0024272389709949493,
-0.038006432354450226,
-0.02533910796046257,
0.0006545915966853499,
-0.010829788632690907,
-0.016881275922060013,
-0.022739890962839127,
-0.0020119724795222282,
-0.041139744222164154,
0.05468792840838432,
-0.03612400218844414,
-0.021202867850661278,
0.022568995133042336,
0.02347852662205696,
-0.028991036117076874,
-0.006364332512021065,
-0.017188774421811104,
0.07936426997184753,
0.06268151104450226,
0.004406174644827843,
0.07019173353910446,
0.051483821123838425,
0.008712940849363804,
0.02764659747481346,
-0.014518882147967815,
0.027386199682950974,
-0.042316775768995285,
0.0010899942135438323,
-0.017899498343467712,
0.03395712748169899,
-0.04176338016986847,
0.045705221593379974,
-0.019602881744503975,
0.033473480492830276,
0.005902100820094347,
-0.018545879051089287,
0.00001311167397943791,
0.01400474552065134,
0.014736915938556194,
0.02296694926917553,
-0.0018248730339109898,
0.023414216935634613,
-0.001504017855040729,
-0.03586268052458763,
0.0054551479406654835,
0.007898527197539806,
-0.0006684068939648569,
0.0165298730134964,
-0.057680826634168625,
0.023621201515197754,
-0.034467827528715134,
-0.01365254633128643,
0.04826334863901138,
-0.0486520417034626,
0.05979711934924126,
-0.012448354624211788,
-0.008622434921562672,
0.018992817029356956,
-0.04032507911324501,
-0.035626091063022614,
0.00006421237776521593,
0.019444456323981285,
0.02689165621995926,
-0.06630858778953552,
0.06267435848712921,
0.03001900017261505,
-0.009917674586176872,
-0.0418299175798893,
-0.010382075794041157,
0.04289402440190315,
-0.008313151076436043,
0.002713722176849842,
-0.01777922734618187,
0.014105885289609432,
0.008373688906431198,
-0.017865203320980072,
-0.02208048850297928,
0.08423919975757599,
-0.007255947217345238,
-0.01728757843375206,
0.007210712414234877,
-0.02317550592124462,
0.06770407408475876,
-0.015221877954900265,
-0.03242886811494827,
0.006331787444651127,
0.009372475557029247,
-0.013707973062992096,
-0.01704172044992447,
0.05286715179681778,
-0.043472178280353546,
-0.014774231240153313,
-0.0018402753630653024,
-0.012550245970487595,
0.03592356666922569,
-0.02028009667992592,
0.008554832078516483,
0.007066166959702969,
0.03217090666294098,
-0.026702729985117912,
-0.030383514240384102,
0.028052596375346184,
0.0007137898355722427,
0.036760587245225906,
-0.04248723015189171,
-0.020549042150378227,
-0.03533441945910454,
-0.02769646979868412,
-0.024938812479376793,
0.004091793205589056,
0.023911576718091965,
-0.010300632566213608,
0.05422060191631317,
0.015117467381060123,
-0.012834548018872738,
-0.01148298755288124,
-0.01218945812433958,
0.03510012850165367,
-0.018068872392177582,
0.004699993878602982,
0.0014822229277342558,
0.040300820022821426,
-0.042358770966529846,
-0.05224121734499931,
-0.02805325575172901,
0.00952926930040121,
0.05102517455816269,
-0.05680222064256668,
0.03746641427278519,
0.04804306477308273,
-0.018353929743170738,
0.03276754543185234,
-0.04057078808546066,
0.008869118057191372,
-0.01732574962079525,
-0.015770668163895607,
0.03650779277086258,
-0.036858733743429184,
0.008452539332211018,
0.005141116678714752,
0.04809864982962608,
0.004132065922021866,
0.021003739908337593,
-0.0022492394782602787,
0.035155102610588074,
-0.01761993207037449,
-0.04195057600736618,
-0.04649671912193298,
0.04860101267695427,
-0.03453599661588669,
0.016267292201519012,
0.014561223797500134,
0.0002923420106526464,
0.04562732204794884,
-0.021054686978459358,
-0.03057447448372841,
-0.05365611985325813,
0.0039858706295490265,
-0.036016084253787994,
0.017085997387766838,
0.008198528550565243,
0.003414090722799301,
-0.02202453650534153,
0.021298052743077278,
0.017166027799248695,
0.010705242864787579,
0.010013874620199203,
0.0010966501431539655,
-0.0880299061536789,
-0.0070066750049591064,
-0.018295491114258766,
-0.06885390728712082,
-0.009980101138353348,
-0.033522311598062515,
-0.03789449483156204,
0.03069986216723919,
-0.07039462774991989,
0.024342725053429604,
-0.01944357343018055,
0.02128945291042328,
-0.007626623846590519,
0.0836714580655098,
-0.009105014614760876,
-0.0025780268479138613,
-0.014572403393685818,
-0.0017862488748505712,
0.10353251546621323,
0.06318128108978271,
-0.015253668650984764,
-0.05869963765144348,
0.003252650611102581,
-0.010702081955969334,
0.03159429505467415,
-0.019623931497335434,
-0.02301670052111149,
0.03242234140634537,
0.013440602459013462,
0.013797336257994175,
0.07355431467294693,
-0.01889943704009056,
-0.017390910536050797,
0.07298034429550171,
0.015314902178943157,
-0.033371035009622574,
-0.0031265062279999256,
0.04352446272969246,
-0.012085807509720325,
-0.025103073567152023,
-0.043675538152456284,
0.0224568173289299,
-0.011166747659444809,
-0.011750079691410065,
0.00031205089180730283,
-0.028805050998926163,
0.009093099273741245,
0.016719255596399307,
-0.06164149194955826,
0.0007739831344224513,
0.02653612568974495,
-0.02192845195531845,
-0.029086345806717873,
0.05349581316113472,
0.02252034656703472,
0.004325998015701771,
0.0041030473075807095,
0.007896683178842068,
-0.006119739729911089,
-0.015939438715577126,
0.006098427809774876,
0.030739005655050278,
-0.05385390669107437,
-0.01468350738286972,
-0.03744437173008919,
-0.0069226170890033245,
0.014241439290344715,
0.03354847803711891,
-0.008715756237506866,
0.01036596018821001,
0.005118349101394415,
-0.0340258851647377,
-0.017170226201415062,
0.006236230954527855,
0.026088528335094452,
-0.027547823265194893,
-0.024714341387152672,
-0.06664372980594635,
0.010172235779464245,
-0.02811654470860958,
0.038787730038166046,
0.01780431903898716,
0.02694656141102314,
0.008376003243029118,
-0.046529900282621384,
0.022268131375312805,
-0.024154577404260635,
-0.043798260390758514,
0.0021119089797139168,
-0.0026597760152071714,
-0.06890089064836502,
-0.026046132668852806,
-0.027764316648244858,
0.033092088997364044,
0.05203225836157799,
0.029976002871990204,
-0.013842571526765823,
-0.02983919158577919,
-0.02662782184779644,
0.04876561835408211,
-0.03515303134918213,
-0.034405265003442764,
0.003613595385104418,
-0.03324060142040253,
0.056138940155506134,
-0.008227061480283737,
-0.010363531298935413,
0.0538761168718338,
-0.025603724643588066,
-0.008417312055826187,
0.04202066734433174,
-0.03642251715064049,
0.008270363323390484,
0.04711137339472771,
-0.02122856117784977,
-0.014431613497436047,
0.013200927525758743,
0.016821060329675674,
0.018806392326951027,
-0.04628366231918335,
0.02078554965555668,
0.004712617490440607,
-0.015843285247683525,
-0.007307856809347868,
0.0009265744010917842,
-0.04275452345609665,
-0.029427004978060722,
0.02684006467461586,
0.013748837634921074,
0.008926104754209518,
-0.027510149404406548,
-0.05319741740822792,
-0.0023963695857673883,
0.001955947373062372,
-0.0010779544245451689,
-0.01653251424431801,
0.007000885903835297,
-0.04640785977244377,
0.037301138043403625,
-0.026338063180446625,
-0.027667587623000145,
-0.023952417075634003,
-0.0030208758544176817,
0.0012588457902893424,
-0.025092585012316704,
-0.02020072191953659,
0.022854357957839966,
-0.030738716945052147,
-0.00980160292237997,
0.008353441953659058,
0.020568834617733955,
-0.023138301447033882,
-0.01943601295351982,
-0.006848825607448816,
-0.007332650478929281,
0.07117079943418503,
-0.015343825332820415,
-0.008494996465742588,
0.046622324734926224,
-0.021895524114370346,
-0.05989906191825867,
0.058818500488996506,
-0.010908403433859348,
0.014743231236934662,
0.014656017534434795,
-0.01483332272619009,
-0.042601440101861954,
0.09423099458217621,
-0.026348425075411797,
-0.012636740691959858,
0.005540030542761087,
-0.015126358717679977,
-0.013117598369717598,
0.021515624597668648,
-0.013961986638605595,
-0.011578359641134739,
0.0015348313609138131,
0.007731032557785511,
0.02008151076734066,
0.019755754619836807,
-0.01879139617085457,
-0.011176426894962788,
-0.04727497696876526,
0.001385536976158619,
0.006635655649006367,
-0.011497016996145248,
0.040557555854320526,
0.04138343781232834,
-0.03552340343594551,
0.008546422235667706,
-0.008071472868323326,
0.006845980416983366,
-0.07172372937202454,
0.02250988408923149,
-0.02674678899347782,
-0.02166897989809513,
0.022905739024281502,
-0.07280749827623367,
0.05161299929022789,
-0.0009523454937152565,
-0.04128018021583557,
-0.05195256322622299,
-0.01613837480545044,
-0.05342765897512436,
-0.017031660303473473,
0.0071702804416418076,
0.020209064707159996,
0.04471839964389801,
0.03468898683786392,
0.053695157170295715,
0.02063138037919998,
0.003525318345054984,
-0.06445739418268204,
0.009399248287081718,
-0.007306380663067102,
0.0076048970222473145,
0.03788887709379196,
-0.012687438167631626,
0.060320593416690826,
-0.06556975841522217,
-0.019043264910578728,
0.046271923929452896,
-0.04604630917310715,
0.020752187818288803,
0.005346636287868023,
0.020491713657975197,
-0.020126555114984512,
0.009507738053798676,
-0.004700003191828728,
-0.01678331196308136,
-0.017949657514691353,
0.023839367553591728,
-0.005347344558686018,
0.055922750383615494,
0.002061545616015792,
-0.016771944239735603,
0.025225365534424782,
-0.023667970672249794,
0.0077666714787483215,
0.0339064858853817,
0.002589805983006954,
-0.009115476161241531,
-0.01860670931637287,
-0.03003137931227684,
0.0585547536611557,
-0.013848861679434776,
0.017101138830184937,
-0.023756118491292,
-0.01580940932035446,
0.04516104981303215,
-0.028938962146639824,
-0.0026694706175476313,
0.03909226506948471,
0.01743490807712078,
-0.02841097302734852,
-0.01869443617761135,
0.012460976839065552,
-0.017540067434310913,
-0.03705628961324692,
0.0029707523062825203,
0.01856449991464615,
-0.008877155371010303,
-0.013273583725094795,
-0.028388403356075287,
-0.05634155496954918,
0.05524379760026932,
-0.013059155084192753,
0.03275023400783539,
0.013748999685049057,
-0.003351793857291341,
-0.006737357471138239,
-0.06914470344781876,
0.020202118903398514,
0.0246628075838089,
-0.0010587051510810852,
-0.041636813431978226,
-0.022808371111750603,
0.05049021914601326,
-0.008153648115694523,
0.032371629029512405,
0.0012971970718353987,
-0.0265446025878191,
0.014391050674021244,
-0.03180718049407005,
0.013144455850124359,
-0.05281369760632515,
-0.0073045468889176846,
0.007922619581222534,
-0.04294133558869362,
0.006359095685184002,
-0.011991193518042564,
-0.02927302196621895,
0.013949594460427761,
0.0326000452041626,
0.003206533845514059,
-0.010228748433291912,
-0.05151383578777313,
0.01564794033765793,
0.06816188991069794,
-0.009545396082103252,
-0.028864137828350067,
0.07167454063892365,
-0.002979719778522849,
0.024394866079092026,
0.010972128249704838,
-0.011367494240403175,
-0.00817619077861309,
0.05845015123486519,
-0.015472759492695332,
0.013581037521362305,
0.017620833590626717,
-0.023486532270908356,
0.023397911339998245,
-0.029274387285113335,
-0.03959432244300842,
0.02514614537358284,
0.009110139682888985,
-0.000180184913915582,
0.030844034627079964,
0.04797772690653801,
0.024953613057732582,
-0.02208407036960125,
0.018164677545428276,
0.005585112608969212,
0.005816214252263308,
-0.0017205331241711974,
-0.013214441947638988,
0.03994398191571236,
0.0025106214452534914,
0.005936607718467712,
0.009750545024871826,
-0.03518379479646683,
-0.017073994502425194,
0.03677701950073242,
0.025406155735254288,
-0.03298047557473183,
-0.0557832345366478,
0.006496076937764883,
-0.007364075630903244,
0.02222464606165886,
0.04747071489691734,
-0.01911007985472679,
0.03417452424764633,
0.007772375829517841,
-0.009059049189090729,
-0.027453966438770294,
-0.010283315554261208,
-0.022569844499230385,
-0.017117084935307503,
-0.01706310361623764,
-0.010182024911046028,
-0.013383490033447742,
0.041784290224313736,
-0.0024409950710833073,
0.0072470237500965595,
0.027611183002591133,
-0.06111721694469452,
0.0004147689323872328,
-0.04030836746096611,
0.01601218804717064,
-0.023760057985782623,
-0.01643279567360878,
-0.026454759761691093,
-0.025442885234951973,
0.04960298910737038,
0.04126604646444321,
-0.016474807634949684,
0.023819714784622192,
-0.03354240208864212,
0.009886818006634712,
0.03051677905023098,
-0.08525878190994263,
-0.0012313929619267583,
-0.041300468146800995,
0.0018201932543888688,
-0.031239895150065422,
-0.02372804470360279
] |
<p>I am reading a material about the degree of freedom for linear n-atom molecule and nonlinear n-atom molecule. Here is my analysis for a diatomic molecule, if there are two atoms, we have to use 3 coordinates to describe the translational motion, 2 coordinates about the rotation and 1 for vibration, so total will be 6 degree of freedom for diatomic molecule. According to the equipartition theorem of the energy, when there are N molecule, each degree of freedom share $kT/2$ energy, so total $$E = 6\times \frac{NkT}{2}$$ and the heat capacitor is
$$
C = \frac{dE}{dT} = 3Nk
$$</p>
<p>But in other book, it said that the heat capacitor for diatomic molecule is $\frac{7Nk}{2}$. I am googleing the issue and someone said the vibration energy consists of kinetic energy and potential energy so there are actually 7 degree of freedom instead of 6. Is this statement correct?</p>
<p>It is pretty confusing because in the wiki <a href="http://en.wikipedia.org/wiki/Degrees_of_freedom_%28physics_and_chemistry%29" rel="nofollow">http://en.wikipedia.org/wiki/Degrees_of_freedom_%28physics_and_chemistry%29</a>, it states that the linear N-atom molecule has 3 positions, 2 rotations and 3N-5 vibrations so total 3N degree of freedom, if N=2, then we will have 6 degree of freedom instead of 7. So which conclusion is correct?</p>
<p>BTW, what's the main difference between the linear and nonlinear n-atom molecule?</p>
| 8,296 |
[
-0.0314028225839138,
-0.01211911253631115,
0.0037138506304472685,
0.0034475296270102262,
0.048390477895736694,
-0.0031378089915961027,
-0.04799152910709381,
-0.03729967027902603,
-0.01899646781384945,
-0.05199973285198212,
0.014862271957099438,
0.004720885306596756,
0.017939368262887,
0.021035902202129364,
0.015761541202664375,
0.04870635271072388,
-0.03106660395860672,
-0.019986780360341072,
-0.020062660798430443,
-0.01593102142214775,
-0.0174558125436306,
0.022910887375473976,
-0.019836267456412315,
-0.013612048700451851,
-0.0394890271127224,
0.04363245144486427,
-0.010237623006105423,
0.014166637323796749,
0.052008725702762604,
0.021187905222177505,
-0.009700274094939232,
-0.029223790392279625,
0.0398770272731781,
-0.0005862379330210388,
0.004857578780502081,
0.010774429887533188,
-0.03353608027100563,
-0.021232668310403824,
-0.028307562693953514,
0.0137188620865345,
-0.03580907732248306,
-0.0024215197190642357,
-0.039140406996011734,
0.029589831829071045,
-0.03973372280597687,
0.016227595508098602,
0.01596382074058056,
-0.029195377603173256,
0.02365966886281967,
-0.05735841020941734,
0.10159444063901901,
-0.0004772993561346084,
0.026504140347242355,
-0.0004488084523472935,
-0.02156210131943226,
-0.00355964875780046,
0.04123839735984802,
0.050112541764974594,
-0.023355962708592415,
-0.03360637649893761,
-0.01943417638540268,
-0.03624066337943077,
0.009804663248360157,
0.019025243818759918,
-0.02044701762497425,
0.03072381019592285,
0.01614159531891346,
-0.02290019765496254,
0.041897907853126526,
0.036110058426856995,
0.022955385968089104,
0.004608762450516224,
0.022698262706398964,
-0.044457823038101196,
0.008648544549942017,
-0.021747224032878876,
0.012372116558253765,
-0.010458480566740036,
0.04683137685060501,
0.010604768991470337,
-0.031225403770804405,
0.03332503139972687,
0.02810739539563656,
0.017253369092941284,
0.017301635816693306,
-0.042003002017736435,
0.04772191867232323,
0.026379138231277466,
0.03155158832669258,
0.022932318970561028,
-0.000024674736778251827,
0.022535894066095352,
0.019260097295045853,
0.03686187043786049,
-0.020661450922489166,
0.030912118032574654,
0.0014431962044909596,
0.04211430251598358,
-0.0004913033917546272,
-0.015484986826777458,
-0.017611512914299965,
-0.011501481756567955,
0.06232472509145737,
0.054849546402692795,
0.010298287495970726,
-0.052064135670661926,
-0.02560739777982235,
-0.011193598620593548,
0.01740480400621891,
-0.007553401868790388,
-0.03374568745493889,
0.01913359761238098,
0.008890959434211254,
-0.007236302364617586,
-0.008382899686694145,
-0.003193506272509694,
-0.006265317089855671,
0.014691509306430817,
0.037227123975753784,
0.08961044251918793,
0.018143218010663986,
-0.032435983419418335,
0.017150340601801872,
-0.011706368066370487,
-0.054315198212862015,
0.011734263971447945,
0.021045159548521042,
0.007503490895032883,
-0.031064799055457115,
0.05192514881491661,
-0.009204481728374958,
-0.014752655290067196,
0.019788071513175964,
-0.0013760440051555634,
0.010094909928739071,
-0.008049651980400085,
-0.10137107223272324,
-0.02650507353246212,
0.04436933249235153,
-0.023493720218539238,
-0.01509707048535347,
-0.07740958034992218,
0.04033627733588219,
0.024646729230880737,
0.07766671478748322,
-0.013247888535261154,
-0.01194378174841404,
-0.020475570112466812,
0.008502542041242123,
0.011975065805017948,
-0.002020094310864806,
-0.06189226731657982,
0.0032243228051811457,
-0.06483094394207001,
0.004606893286108971,
-0.04482622072100639,
0.07320530712604523,
0.06439413875341415,
0.03857078403234482,
-0.017388034611940384,
0.07760608196258545,
-0.00793195329606533,
-0.02083747461438179,
0.019430287182331085,
0.02753935009241104,
-0.028644448146224022,
0.06153516843914986,
-0.007305511739104986,
0.022790243849158287,
0.013079420663416386,
0.007369436789304018,
0.028944138437509537,
-0.03723977133631706,
0.06368492543697357,
0.05986090004444122,
-0.012140494771301746,
-0.008030956611037254,
-0.034617140889167786,
0.01094982773065567,
-0.0005614093970507383,
-0.050280578434467316,
-0.02341865934431553,
0.005913689266890287,
0.004978499375283718,
-0.021155524998903275,
0.024826154112815857,
0.008655071258544922,
0.027564628049731255,
-0.012993275187909603,
-0.0346423014998436,
-0.01679760031402111,
-0.05032157525420189,
0.03663889691233635,
-0.005762520246207714,
-0.05685051158070564,
0.02817988395690918,
0.03806215524673462,
0.026771672070026398,
-0.014386361464858055,
-0.0019175371853634715,
0.014938155189156532,
0.0379677377641201,
0.004307340830564499,
-0.02034398727118969,
0.06668595969676971,
0.060376863926649094,
0.01460382342338562,
0.041248779743909836,
0.021098867058753967,
-0.008549184538424015,
-0.0077601224184036255,
0.020031947642564774,
-0.007888070307672024,
0.00013472292630467564,
0.015816589817404747,
0.0015525399940088391,
-0.005001355893909931,
0.028878750279545784,
-0.02742570824921131,
0.04136398434638977,
-0.0348498560488224,
0.03892839327454567,
0.04349235072731972,
-0.0002536277170293033,
0.011016841046512127,
0.04397302120923996,
0.000631247996352613,
0.03541475534439087,
-0.007261328864842653,
-0.003813334973528981,
-0.04422139748930931,
0.032713714987039566,
0.03031747043132782,
0.019183482974767685,
-0.08310849964618683,
-0.016807787120342255,
0.04323052987456322,
0.010099796578288078,
0.02254454791545868,
-0.006580590270459652,
-0.007168937474489212,
-0.014816638082265854,
0.025084644556045532,
-0.006648198701441288,
0.016236139461398125,
-0.007201860658824444,
0.013726404868066311,
0.027680283412337303,
0.03163312375545502,
0.023283028975129128,
-0.02572379633784294,
0.049844227731227875,
-0.009422482922673225,
0.015803083777427673,
0.018388161435723305,
-0.01875513419508934,
0.03258595988154411,
0.0005596966948360205,
0.02550986222922802,
0.028422299772500992,
-0.024298230186104774,
0.036528654396533966,
0.003710147924721241,
-0.009797276929020882,
0.007725859060883522,
-0.014016767032444477,
-0.013135625049471855,
-0.03474855795502663,
0.009563954547047615,
-0.028067266568541527,
0.0003432397497817874,
-0.026456937193870544,
0.022482186555862427,
-0.003014101181179285,
-0.0076922099106013775,
0.03823362663388252,
-0.00008720330515643582,
0.05362767353653908,
-0.016510529443621635,
-0.009818405844271183,
-0.029448792338371277,
-0.019873658195137978,
-0.0042788321152329445,
0.0012823486467823386,
-0.08130316436290741,
-0.0007103660027496517,
-0.02593732811510563,
-0.031793832778930664,
0.061900634318590164,
-0.03021676279604435,
0.022187083959579468,
0.005027199629694223,
-0.0055857254192233086,
-0.08044478297233582,
-0.03208747133612633,
0.008719202131032944,
0.016968443989753723,
-0.05293137580156326,
-0.030609287321567535,
0.027133364230394363,
-0.04538334906101227,
0.0016950819408521056,
0.0322524830698967,
-0.04301748424768448,
-0.023193636909127235,
0.003945054952055216,
-0.007425461895763874,
0.035861991345882416,
-0.005742883309721947,
0.038479115813970566,
0.037415094673633575,
-0.017833245918154716,
-0.02387944795191288,
-0.050218433141708374,
-0.05015765503048897,
0.043010011315345764,
0.002258451422676444,
0.040766846388578415,
0.005601691547781229,
-0.021282104775309563,
0.05447523295879364,
0.004986884538084269,
-0.07102631777524948,
0.04888887330889702,
0.0005502196145243943,
-0.017720654606819153,
-0.027963409200310707,
0.007678469177335501,
0.025811558589339256,
0.02844594605267048,
0.0023849245626479387,
0.005618134047836065,
0.018190080299973488,
0.0418720543384552,
-0.04838486760854721,
0.006898350547999144,
0.015779215842485428,
-0.005337955895811319,
-0.0024187592789530754,
0.07089624553918839,
0.008465206250548363,
-0.03531213477253914,
0.04572589322924614,
-0.017899220809340477,
0.012128841131925583,
0.032225366681814194,
-0.0848623514175415,
0.041593585163354874,
0.04209262877702713,
0.023727107793092728,
-0.04292232543230057,
0.019014017656445503,
0.013681570999324322,
-0.01016085222363472,
0.020473847165703773,
0.05168186128139496,
0.048303451389074326,
-0.015333788469433784,
-0.014966927468776703,
0.02542952261865139,
-0.0030656978487968445,
0.007623453624546528,
-0.01812705397605896,
0.007276165299117565,
-0.000037679954402847216,
-0.007422981318086386,
0.003993762191385031,
-0.041301220655441284,
0.04150494933128357,
0.01655283384025097,
0.028186481446027756,
0.020481303334236145,
-0.035411491990089417,
0.026560194790363312,
-0.030081771314144135,
0.007721062283962965,
-0.0037953618448227644,
0.051373761147260666,
-0.025118552148342133,
0.04203732684254646,
-0.005645431578159332,
0.01642189361155033,
0.01976885087788105,
-0.008660943247377872,
-0.04215644299983978,
0.01906123012304306,
-0.019630897790193558,
-0.047895532101392746,
0.024607328698039055,
0.0013363308971747756,
-0.00008016417268663645,
-0.024175627157092094,
-0.02386418916285038,
0.007176211103796959,
-0.012705429457128048,
-0.046032000333070755,
-0.0034874286502599716,
-0.04686615243554115,
0.017468111589550972,
0.000018240751160192303,
0.06217784434556961,
0.024606190621852875,
-0.06897669285535812,
-0.0041587776504457,
0.046903710812330246,
-0.01630299538373947,
-0.020998205989599228,
0.006696728523820639,
0.00042961747385561466,
0.0027245329692959785,
0.019056392833590508,
0.015270432457327843,
-0.0034337984398007393,
0.05787448212504387,
-0.00948470737785101,
-0.012036836706101894,
0.02987050823867321,
-0.007213730830699205,
-0.023372648283839226,
-0.012682288885116577,
-0.02881055697798729,
0.025739647448062897,
-0.006657291203737259,
0.08611241728067398,
0.014044924639165401,
0.014023207128047943,
-0.001287361141294241,
-0.004742141347378492,
-0.018283434212207794,
0.053345005959272385,
0.007929898798465729,
0.0034102341160178185,
-0.012479305267333984,
-0.05996242165565491,
-0.007745981682091951,
-0.00024870873312465847,
-0.006391711067408323,
0.021655797958374023,
0.016331816092133522,
-0.035206299275159836,
-0.000190884864423424,
0.017279401421546936,
0.02027260884642601,
-0.014760024845600128,
0.0196384210139513,
-0.007916372269392014,
0.06770437210798264,
-0.0003879982396028936,
-0.021714920178055763,
0.037549469619989395,
-0.009421974420547485,
0.042181406170129776,
0.023892126977443695,
-0.02069464698433876,
-0.05927681177854538,
-0.007351426873356104,
-0.0008866771240718663,
0.008962977677583694,
-0.047119323164224625,
0.021724380552768707,
-0.056540876626968384,
-0.0018094872357323766,
0.00553619721904397,
-0.04784407466650009,
0.025158608332276344,
0.0018107666401192546,
0.013630903325974941,
-0.019637268036603928,
-0.02703898400068283,
-0.0045379591174423695,
0.010558384470641613,
0.009959707036614418,
0.022404909133911133,
-0.030846374109387398,
-0.0009548299130983651,
0.006168997846543789,
-0.022131042554974556,
0.04009805992245674,
0.05479345843195915,
-0.015225948765873909,
-0.010358115658164024,
0.024498049169778824,
0.037892844527959824,
-0.017036406323313713,
-0.0488288588821888,
0.009476077742874622,
-0.000128908985061571,
0.006486827973276377,
0.03343033790588379,
-0.08442586660385132,
-0.015666015446186066,
0.006921572610735893,
0.017984185367822647,
-0.02708267606794834,
-0.037945326417684555,
-0.032709937542676926,
0.06396880000829697,
0.029264817014336586,
-0.03247380256652832,
0.05803162604570389,
0.018458358943462372,
-0.020349601283669472,
0.025009959936141968,
-0.04160138592123985,
0.03636922314763069,
-0.006783406250178814,
-0.0009075631969608366,
-0.04257335513830185,
0.004061098676174879,
-0.029130946844816208,
0.05301907658576965,
-0.018620705232024193,
0.047956060618162155,
-0.03631307929754257,
-0.013599894009530544,
0.009242772124707699,
0.024292875081300735,
0.02386513352394104,
0.012020712718367577,
-0.014965319074690342,
0.04203857108950615,
0.004194635897874832,
-0.01684989035129547,
0.013922463171184063,
0.0009636975009925663,
-0.002640899270772934,
0.03932114318013191,
-0.02148643508553505,
0.022800536826252937,
-0.041906099766492844,
-0.029907535761594772,
0.001518575823865831,
-0.062176432460546494,
0.008318407461047173,
0.007382525596767664,
-0.0014300689799711108,
0.03538190573453903,
-0.04188724607229233,
-0.045357901602983475,
-0.0027685381937772036,
-0.018295858055353165,
0.006510801147669554,
-0.03621551766991615,
0.02311251126229763,
0.0023973463103175163,
0.02168426290154457,
-0.0482320562005043,
-0.04429560527205467,
0.0033040603157132864,
-0.016017213463783264,
-0.019590875133872032,
-0.004624797031283379,
0.010193457826972008,
-0.006862070877104998,
-0.0200833510607481,
0.025301681831479073,
0.05137500539422035,
0.007838024757802486,
-0.019853588193655014,
0.00635427376255393,
0.03405867889523506,
0.02778100036084652,
-0.00822257436811924,
-0.014342648908495903,
-0.007672657258808613,
0.01605047658085823,
-0.020239392295479774,
-0.006598781328648329,
0.05786193907260895,
-0.010817875154316425,
-0.010864763520658016,
-0.007045383099466562,
0.007697824388742447,
0.04878056421875954,
-0.003744271816685796,
-0.027423057705163956,
-0.010167313739657402,
0.008607365190982819,
-0.03590291365981102,
-0.024219807237386703,
0.03327328711748123,
-0.01767263188958168,
0.010118833743035793,
0.004385192878544331,
-0.008560077287256718,
-0.02920381724834442,
-0.05925367772579193,
-0.023926133289933205,
0.02393772080540657,
0.01515724416822195,
0.021288501098752022,
0.08086613565683365,
0.009224043227732182,
0.046150341629981995,
0.006769676227122545,
-0.024433277547359467,
0.0012687542475759983,
0.00821349211037159,
0.006776722613722086,
-0.024864647537469864,
-0.011021285317838192,
-0.021725265309214592,
-0.04770055413246155,
-0.06126350909471512,
0.06873786449432373,
0.046892471611499786,
-0.0496164932847023,
0.029002346098423004,
0.037088971585035324,
0.020923197269439697,
-0.005925467237830162,
-0.02407626248896122,
0.009794117882847786,
-0.0006276433705352247,
-0.0010381429456174374,
0.04973272606730461,
-0.05284860357642174,
-0.047248098999261856,
0.04358452558517456,
0.049493834376335144,
-0.03702792152762413,
0.026698371395468712,
0.04120662063360214,
0.02292695641517639,
-0.01680522970855236,
-0.012636312283575535,
-0.04149813577532768,
0.03405681252479553,
-0.020473826676607132,
0.08192244172096252,
0.03585199639201164,
0.006932437885552645,
0.014749039895832539,
0.042780835181474686,
0.007168891374021769,
-0.06731927394866943,
-0.041846275329589844,
-0.02201813831925392,
0.041456177830696106,
0.018346793949604034,
-0.00027029996272176504,
-0.029687002301216125,
0.005693110637366772,
0.03585279360413551,
-0.002794153057038784,
0.019822802394628525,
0.00821099616587162,
-0.0470707081258297,
-0.01943107321858406,
-0.006126157473772764,
-0.04709543287754059,
0.03598817065358162,
-0.028974616900086403,
-0.04806654900312424,
0.029514450579881668,
-0.005201964173465967,
0.05239935219287872,
0.03003218211233616,
0.05133724957704544,
0.01992459036409855,
0.09812016040086746,
-0.011779704131186008,
0.005774063058197498,
-0.013481741771101952,
0.03602994978427887,
0.1470964401960373,
0.027872785925865173,
-0.01722646690905094,
-0.033987242728471756,
0.0037792150396853685,
0.033548254519701004,
-0.012702497653663158,
-0.01462809182703495,
-0.019153662025928497,
0.027234070003032684,
0.03307178616523743,
-0.01157762948423624,
0.03604479506611824,
-0.007017551455646753,
-0.003075668588280678,
0.014582237228751183,
-0.00378328375518322,
-0.04410975053906441,
-0.01490710023790598,
-0.009204660542309284,
0.02475704811513424,
-0.017215518280863762,
-0.009966365993022919,
-0.019905872642993927,
0.011042073369026184,
0.01921785995364189,
-0.04783444479107857,
-0.04428555816411972,
0.04825519397854805,
0.03628234565258026,
-0.0250044334679842,
-0.005567410495132208,
0.007544530555605888,
-0.004666259046643972,
-0.026182077825069427,
0.02317744866013527,
0.021170014515519142,
-0.007998047396540642,
-0.00048466285807080567,
0.033829718828201294,
-0.012900064699351788,
-0.016571633517742157,
0.046394385397434235,
-0.01443373505026102,
-0.050969623029232025,
0.0028966995887458324,
-0.03937646746635437,
0.00019599949882831424,
-0.00231081061065197,
-0.002892283722758293,
-0.007302111946046352,
-0.005185496062040329,
-0.013378183357417583,
-0.062114473432302475,
-0.01811637356877327,
-0.01064365915954113,
0.036973726004362106,
-0.028876634314656258,
-0.026213264092803,
-0.05611865967512131,
-0.013694857247173786,
-0.01631993241608143,
-0.014016612432897091,
-0.013165131211280823,
-0.004587429575622082,
0.03821268677711487,
0.02212640829384327,
0.0015773598570376635,
-0.03283560276031494,
-0.0013213215861469507,
-0.004337464924901724,
-0.010095485486090183,
-0.03073262982070446,
-0.03168061375617981,
0.015075632371008396,
0.020110536366701126,
0.058435168117284775,
-0.009721659123897552,
-0.00487681245431304,
-0.0066216387785971165,
-0.0611887201666832,
0.0064104050397872925,
0.02583528310060501,
-0.029160600155591965,
0.016779132187366486,
0.018421005457639694,
0.0540812611579895,
0.009483883157372475,
-0.03543601185083389,
0.05220703408122063,
0.010225057601928711,
-0.014981978572905064,
0.040453940629959106,
-0.02134643867611885,
0.021003665402531624,
0.01023171842098236,
-0.05565822124481201,
0.008942708373069763,
-0.013501147739589214,
0.032887618988752365,
0.031590234488248825,
0.0284282136708498,
-0.0008851877064444125,
-0.00979902409017086,
-0.008085286244750023,
-0.013881605118513107,
0.0008971926290541887,
-0.027751076966524124,
-0.005043443292379379,
0.05749117210507393,
-0.0010426915250718594,
-0.055391520261764526,
-0.057045307010412216,
-0.02433578483760357,
-0.019451536238193512,
-0.000549030548427254,
0.011398171074688435,
-0.03301709145307541,
0.009608275257050991,
-0.01723395101726055,
-0.013216371648013592,
-0.026621833443641663,
0.0029193994123488665,
-0.005419296678155661,
0.013051173649728298,
0.027879031375050545,
0.026659352704882622,
-0.03864916041493416,
-0.003923493903130293,
-0.01951979473233223,
0.0028111629653722048,
0.03416568785905838,
0.0224518571048975,
0.005991763900965452,
-0.05393923819065094,
0.021873166784644127,
-0.029565827921032906,
0.06876000761985779,
-0.039447035640478134,
0.00357634574174881,
0.02371061034500599,
-0.044275637716054916,
-0.039150580763816833,
-0.012679483741521835,
-0.011541004292666912,
0.016779744997620583,
0.02149454690515995,
0.026751568540930748,
-0.009931047447025776,
0.049361828714609146,
-0.05765940621495247,
0.009473909623920918,
-0.016452187672257423,
-0.04921337962150574,
-0.047709014266729355,
-0.051472246646881104,
-0.02091275341808796,
-0.05634789541363716,
-0.0014600546564906836,
0.07814596593379974,
0.0686328336596489,
-0.0336957648396492,
-0.027027221396565437,
0.019490428268909454,
0.005373111926019192,
-0.002219534246250987,
0.03394065052270889,
0.036703646183013916,
0.023173974826931953,
0.05525391176342964,
-0.026734506711363792,
0.004177967552095652,
0.03878319263458252,
0.03934112936258316,
-0.09347537159919739,
-0.040533360093832016,
-0.006977532524615526,
0.00035626208409667015,
0.010630549862980843,
-0.041551295667886734,
-0.0074247210286557674,
0.01735754869878292,
-0.0578560009598732,
-0.013881050981581211,
-0.01695537194609642,
0.0024596021976321936,
-0.025469636544585228,
-0.007846429944038391,
-0.021597569808363914,
0.04284569248557091,
0.03600649908185005,
0.03573794662952423,
0.010698987171053886,
0.011367491446435452,
-0.026418669149279594,
-0.010877357795834541,
0.008564876392483711,
0.029215101152658463,
0.00971118826419115,
-0.0689193606376648,
0.059593312442302704,
-0.025545120239257812,
-0.059178002178668976,
0.059683822095394135,
-0.06193254515528679,
-0.030943123623728752,
-0.009776459075510502,
-0.015258568339049816,
-0.01844426989555359,
0.021512355655431747,
0.02530800551176071,
-0.018958652392029762,
-0.013813367113471031,
-0.016285855323076248,
0.02166902832686901,
0.012960520572960377,
0.021440990269184113,
-0.021539926528930664,
0.04020964726805687,
-0.03036869876086712,
-0.0430636927485466,
0.049133364111185074,
-0.016805943101644516,
0.0019838290754705667,
0.017558777704834938,
-0.0017207571072503924,
-0.01542497705668211,
-0.06038736179471016,
0.005976133048534393,
-0.03576289489865303,
-0.022923802956938744,
0.021652737632393837,
0.012451901100575924,
0.02356770820915699,
-0.0072465138509869576,
0.00368509441614151,
-0.010675860568881035,
0.010740881785750389,
0.024935351684689522,
-0.0042394110932946205,
-0.07149352878332138,
0.002046135952696204,
0.013076512143015862,
-0.03790378198027611,
-0.015770860016345978,
-0.055290576070547104,
-0.046008478850126266,
0.062395527958869934,
0.04821990057826042,
-0.014244567602872849,
-0.005109572783112526,
-0.03675748407840729,
-0.021016526967287064,
-0.07435127347707748,
0.01782790757715702,
0.019037548452615738,
0.011562393978238106,
-0.04561237990856171,
0.0005302726058289409,
0.016672618687152863,
0.0008223751210607588,
0.04854624345898628,
-0.006331395823508501,
-0.02523382566869259,
0.003155320882797241,
-0.026996176689863205,
0.03294704481959343,
-0.015506766736507416,
-0.0036849959287792444,
0.01271637063473463,
-0.006802082993090153,
-0.013865888118743896,
-0.013870740309357643,
-0.04756098985671997,
0.016780361533164978,
0.014697128906846046,
-0.02145424298942089,
0.03668878600001335,
-0.0022995388135313988,
-0.020672494545578957,
0.025582535192370415,
0.01588757149875164,
0.0017701098695397377,
0.03911877050995827,
-0.04651400446891785,
0.009922548197209835,
0.0617840439081192,
-0.013793263584375381,
-0.03908020257949829,
-0.009942748583853245,
-0.0022933410946279764,
-0.009142059832811356,
-0.040329206734895706,
-0.026817893609404564,
0.049412671476602554,
-0.04950175806879997,
0.018570538610219955,
0.061460986733436584,
-0.037379566580057144,
-0.015819359570741653,
0.031011659651994705,
0.0021283503156155348,
0.04073556885123253,
-0.013331441208720207,
0.039131950587034225,
0.02558092586696148,
-0.01854678802192211,
0.0284565482288599,
0.03444908559322357,
0.04282042011618614,
0.0008796464535407722,
-0.009877015836536884,
0.0007612350163981318,
-0.02146276831626892,
0.04524581879377365,
0.0023217902053147554,
0.015600866638123989,
-0.059903789311647415,
-0.011689918115735054,
0.052899863570928574,
0.014655116014182568,
-0.0030575518030673265,
0.04359300807118416,
-0.015471342019736767,
0.08247260004281998,
-0.023771824315190315,
0.010827177204191685,
-0.018640335649251938,
0.0021500687580555677,
-0.004062167834490538,
-0.01772267185151577,
-0.015324680134654045,
0.021469447761774063,
-0.02373918704688549,
0.012763083912432194,
-0.04747036471962929,
-0.012683878652751446,
0.05026685819029808,
-0.06335365772247314,
-0.0026217480190098286,
-0.01344904862344265,
-0.022774584591388702,
-0.0160665400326252,
-0.010944748297333717,
0.003955964930355549,
-0.019131481647491455,
0.041949667036533356,
0.024940770119428635,
-0.011363629251718521,
-0.04652266949415207,
-0.03254281356930733,
0.018944278359413147,
0.0615299716591835,
-0.03327524662017822,
-0.030428115278482437,
-0.008050200529396534,
-0.0090253334492445,
0.003642602823674679,
0.007027756422758102
] |
<p>Are Cartan structural equations equivalent to Einstein's equations
$$G_{\mu\nu}=T_{\mu\nu}$$
and why (in the case of torsionless geometries, of course)? Does it also apply with a non-null cosmological constant?</p>
| 8,297 |
[
-0.02050885558128357,
-0.015568653121590614,
-0.028716592118144035,
-0.05215747281908989,
0.02923254854977131,
0.027291035279631615,
-0.04735764116048813,
-0.01286400482058525,
-0.012612126767635345,
-0.05949331820011139,
-0.012060471810400486,
0.0157939326018095,
0.04026605933904648,
-0.006233842112123966,
-0.007697298191487789,
0.010333158075809479,
-0.058222539722919464,
0.043010711669921875,
-0.031329523772001266,
-0.05606875196099281,
0.013642295263707638,
0.025517983362078667,
-0.017080482095479965,
-0.0003752626071218401,
-0.008962723426520824,
0.03217930719256401,
0.03321618214249611,
-0.0037649390287697315,
0.017591150477528572,
0.04315046966075897,
-0.032239947468042374,
0.0022885920479893684,
-0.027577539905905724,
0.040461912751197815,
0.003437898587435484,
-0.02786989137530327,
-0.008207797072827816,
-0.017267003655433655,
-0.020011095330119133,
-0.010052142664790154,
-0.06733225286006927,
-0.03163008764386177,
-0.04653538763523102,
0.01977093145251274,
0.0013538026250898838,
0.02471891976892948,
-0.018258729949593544,
0.029958507046103477,
0.053800877183675766,
-0.04307781159877777,
0.10147924721240997,
0.005118730012327433,
0.003395695937797427,
0.019473163411021233,
-0.03258269280195236,
-0.0032427061814814806,
0.06454464793205261,
0.048760440200567245,
-0.019972896203398705,
-0.03345310315489769,
-0.017622536048293114,
-0.01757579855620861,
0.028467053547501564,
-0.0327676497399807,
0.020482337102293968,
0.049029506742954254,
0.0022992424201220274,
0.021217700093984604,
0.027264408767223358,
-0.012950252741575241,
-0.01976555399596691,
0.00796111673116684,
0.0112503282725811,
-0.015520147047936916,
-0.02223222330212593,
-0.004991361405700445,
-0.0023776127491146326,
-0.0026810658164322376,
0.031232036650180817,
0.04913454130291939,
-0.026345625519752502,
-0.005808240734040737,
0.032368361949920654,
0.015405393205583096,
-0.020437944680452347,
0.005038426723331213,
0.05499039962887764,
-0.022486064583063126,
0.028190776705741882,
0.029778005555272102,
0.016682066023349762,
-0.03545590490102768,
0.05196160450577736,
-0.033692773431539536,
-0.025169575586915016,
0.017341729253530502,
0.009963170625269413,
0.01678645610809326,
0.016836779192090034,
-0.012915818020701408,
-0.006544818170368671,
-0.005960042588412762,
-0.032901961356401443,
0.08359454572200775,
0.00903345923870802,
-0.01849474012851715,
-0.013037296012043953,
-0.004881916102021933,
-0.03081262670457363,
0.013773877173662186,
-0.017035475000739098,
-0.008768650703132153,
-0.05389058217406273,
0.011070090346038342,
0.04984299838542938,
-0.0126132657751441,
0.02139274775981903,
-0.05663208290934563,
0.05136578902602196,
0.07310407608747482,
0.0676211342215538,
0.011252354830503464,
0.0053438711911439896,
-0.021210279315710068,
-0.05874250456690788,
-0.0030989297665655613,
0.04172457754611969,
-0.0026970382314175367,
-0.004245331045240164,
-0.006085444241762161,
0.03226735070347786,
-0.0351596437394619,
0.011343535035848618,
0.009248028509318829,
0.04103868082165718,
0.015015476383268833,
-0.06062900647521019,
-0.07149135321378708,
0.026774222031235695,
0.0062563456594944,
-0.025047168135643005,
-0.03239170089364052,
-0.010333087295293808,
0.0175411868840456,
0.08170667290687561,
0.033255502581596375,
0.006662093102931976,
0.026972908526659012,
0.05205613002181053,
-0.019746145233511925,
-0.04176190868020058,
-0.012088336981832981,
-0.002146057551726699,
-0.04049878567457199,
-0.04067793861031532,
-0.07885634899139404,
0.014040034264326096,
0.03532193973660469,
-0.011630821041762829,
-0.008785335347056389,
0.0739748477935791,
-0.008848934434354305,
0.00870368629693985,
0.02609843946993351,
-0.02326776087284088,
-0.026571879163384438,
0.026063520461320877,
-0.007299347314983606,
0.0012239821953698993,
0.0377558134496212,
0.011881259270012379,
0.010215953923761845,
0.03021678887307644,
0.022000446915626526,
0.004636690486222506,
-0.03228259086608887,
-0.017666852101683617,
-0.006032448261976242,
0.0043098218739032745,
0.040731191635131836,
-0.009003179147839546,
-0.015878699719905853,
-0.0025198161602020264,
-0.010456533171236515,
-0.016351871192455292,
0.02232297882437706,
-0.008218162693083286,
-0.013450725935399532,
0.01604391634464264,
-0.04011964797973633,
0.03207293525338173,
-0.07326661050319672,
-0.009734872728586197,
0.016846656799316406,
0.001051020808517933,
0.020621076226234436,
0.03293026238679886,
0.0007417068118229508,
-0.033157024532556534,
-0.02827915921807289,
0.001921244664117694,
0.04221638664603233,
-0.033078428357839584,
-0.010474652983248234,
0.024895256385207176,
0.008101875893771648,
0.056794799864292145,
-0.042553361505270004,
0.0328998938202858,
-0.034310631453990936,
-0.02305424027144909,
0.01754836179316044,
0.007764137350022793,
0.020674895495176315,
-0.04809204116463661,
0.003706712508574128,
0.005403539165854454,
-0.009090707637369633,
-0.01736249215900898,
0.08812662214040756,
-0.05979225039482117,
0.04437527433037758,
0.04420514032244682,
0.021867871284484863,
0.016170859336853027,
0.07514548301696777,
0.00015933338727336377,
0.04898354411125183,
-0.02190844714641571,
-0.024016790091991425,
-0.027304871007800102,
-0.034081511199474335,
0.0414157472550869,
0.05751240625977516,
-0.04100456461310387,
0.017705747857689857,
0.03081337735056877,
0.05209359526634216,
0.007873035036027431,
0.012547768652439117,
-0.03527316078543663,
-0.06614932417869568,
0.011175709776580334,
-0.004982633050531149,
0.01988328993320465,
0.0339495986700058,
0.0008640720043331385,
0.03291887044906616,
-0.0027989791706204414,
-0.009111089631915092,
0.011540072038769722,
0.03474265709519386,
-0.0037867757491767406,
-0.0543803833425045,
0.03301331400871277,
0.000001782928279681073,
0.03957377374172211,
-0.012086382135748863,
0.038676727563142776,
0.04288451746106148,
0.0025629429146647453,
-0.03526157885789871,
-0.020768336951732635,
0.01175445131957531,
0.00639327522367239,
-0.0112618962302804,
0.007404876407235861,
-0.032636839896440506,
0.021275026723742485,
-0.023094112053513527,
-0.017557337880134583,
-0.0053809997625648975,
-0.0355369858443737,
-0.021556932479143143,
-0.002347636967897415,
-0.006829246412962675,
0.004766563884913921,
0.05135020241141319,
-0.031957224011421204,
-0.020966865122318268,
0.034761425107717514,
0.000650041620247066,
-0.013925393112003803,
0.02682391367852688,
-0.037321705371141434,
0.036774590611457825,
-0.0037038493901491165,
-0.014015539549291134,
0.009943941608071327,
-0.020732440054416656,
0.02610832080245018,
-0.006834517698734999,
-0.01604781672358513,
-0.04279540479183197,
-0.03461699187755585,
-0.006518240552395582,
-0.006162725389003754,
-0.028748026117682457,
0.0389232374727726,
0.04433860257267952,
0.014077316038310528,
-0.028151201084256172,
-0.01377788931131363,
-0.040245190262794495,
-0.06613617390394211,
-0.017323030158877373,
0.034320127218961716,
-0.010560735128819942,
-0.042562417685985565,
0.026730844751000404,
0.0440225750207901,
-0.05001591891050339,
0.014630681835114956,
-0.07487105578184128,
-0.024609969928860664,
0.06682631373405457,
-0.014071906916797161,
0.044694073498249054,
0.049873270094394684,
-0.04457151144742966,
0.07953929156064987,
0.03675992786884308,
-0.03066379576921463,
-0.023966435343027115,
-0.006977507378906012,
0.011030834168195724,
-0.05006388574838638,
-0.006987873464822769,
0.003473128192126751,
0.03439553827047348,
0.026950282976031303,
0.07453971356153488,
0.005450870841741562,
-0.009896655566990376,
0.0166432186961174,
-0.007229403592646122,
-0.020155424252152443,
0.013343232683837414,
0.00043525989167392254,
0.028212284669280052,
0.007989942096173763,
-0.013952385634183884,
0.017985345795750618,
0.0400577113032341,
0.04010872542858124,
0.0035173874348402023,
-0.06111876294016838,
0.058099690824747086,
-0.0085999621078372,
0.005418318789452314,
-0.01879214309155941,
0.029066652059555054,
-0.008537398651242256,
0.003332264721393585,
0.001404044684022665,
0.03366050496697426,
0.04467102140188217,
-0.009466179646551609,
0.023338304832577705,
0.012409849092364311,
0.008164550177752972,
-0.019692493602633476,
0.018337396904826164,
0.010113178752362728,
-0.025491084903478622,
0.03058929741382599,
-0.010792550630867481,
0.00965455174446106,
0.061516713351011276,
0.036018006503582,
0.011509712785482407,
0.004175534006208181,
-0.029137728735804558,
0.00263129360973835,
-0.07271674275398254,
0.012629000470042229,
-0.03181371092796326,
0.00897134281694889,
0.008380589075386524,
0.018542110919952393,
0.008110089227557182,
-0.003452578792348504,
0.012317153625190258,
0.01075457688421011,
-0.07382556796073914,
0.006843442562967539,
-0.06474877893924713,
0.015096047893166542,
0.013306532986462116,
0.007773080840706825,
-0.012569529004395008,
-0.00955723412334919,
-0.022604037076234818,
-0.043990544974803925,
0.008210933767259121,
-0.07516607642173767,
0.017965856939554214,
-0.05224604904651642,
-0.050428036600351334,
0.013270662166178226,
0.043655842542648315,
0.041206344962120056,
-0.02675880305469036,
-0.014450530521571636,
0.05441245436668396,
-0.013191932812333107,
-0.0037518262397497892,
-0.01977795548737049,
0.032915666699409485,
-0.018824469298124313,
0.009188337251543999,
0.016009647399187088,
0.023674940690398216,
-0.031394120305776596,
0.010575265623629093,
0.03956284746527672,
0.04578288644552231,
0.002075563184916973,
-0.006490983068943024,
-0.040962327271699905,
-0.053079377859830856,
-0.0431547649204731,
-0.005026682745665312,
0.03694188967347145,
0.007600190117955208,
-0.03379444032907486,
0.04411868378520012,
0.002789346734061837,
0.012982940301299095,
0.04752079397439957,
0.058074951171875,
0.02928880788385868,
-0.051700666546821594,
-0.05398830771446228,
-0.03362207114696503,
-0.005698824767023325,
0.00937190093100071,
0.032723091542720795,
-0.01598796434700489,
-0.05701971426606178,
0.022110113874077797,
-0.0009655219037085772,
-0.009749694727361202,
-0.0192724522203207,
-0.03219327703118324,
0.02889798767864704,
0.013506476767361164,
0.015433037653565407,
0.017253097146749496,
0.012987225316464901,
0.05299573391675949,
0.022856449708342552,
0.009639449417591095,
-0.004888264462351799,
-0.06335243582725525,
0.017117410898208618,
-0.002486105775460601,
-0.008865738287568092,
-0.010791744105517864,
-0.03942922502756119,
-0.06503904610872269,
0.0036623284686356783,
0.04605333134531975,
-0.028931329026818275,
-0.00006991754344198853,
0.013472146354615688,
0.004507933743298054,
-0.022516194730997086,
0.012604821473360062,
-0.022397726774215698,
0.032738104462623596,
-0.0012928229989483953,
-0.020976880565285683,
-0.047774702310562134,
0.026511818170547485,
-0.01667868345975876,
0.03765309602022171,
-0.005976102314889431,
0.02264823019504547,
0.049923524260520935,
-0.00006390491762431338,
-0.003943874500691891,
0.021435923874378204,
0.01456843689084053,
-0.06753911823034286,
0.002533902879804373,
0.026307279244065285,
-0.028060393407940865,
-0.004075715783983469,
-0.019749680534005165,
-0.015690529718995094,
0.037758611142635345,
0.008260981179773808,
0.011600579135119915,
0.055271558463573456,
-0.054093148559331894,
0.020714040845632553,
0.026042897254228592,
-0.026763012632727623,
0.008983866311609745,
-0.0005980145069770515,
0.0004882045614067465,
-0.02711714617908001,
-0.04638933762907982,
0.03340870141983032,
-0.06961700320243835,
-0.029484782367944717,
0.006030420307070017,
0.015222670510411263,
-0.026252930983901024,
0.03301477059721947,
-0.0004152352921664715,
0.03137805685400963,
-0.0003785468579735607,
-0.0021017855033278465,
-0.020626327022910118,
0.02615518867969513,
0.01663108356297016,
-0.006925278343260288,
0.017041485756635666,
0.00635925866663456,
0.03133869171142578,
-0.039864279329776764,
0.014880668371915817,
0.0017207321943715215,
-0.02288079634308815,
0.024815700948238373,
0.02174830064177513,
0.011547952890396118,
-0.03143860772252083,
-0.006358987186104059,
0.04073137789964676,
-0.011628616601228714,
0.03649294003844261,
-0.010805228725075722,
-0.013710606843233109,
0.035452865064144135,
-0.015557311475276947,
-0.022381849586963654,
0.0076990132220089436,
-0.0071751209907233715,
0.02741805650293827,
-0.023425137624144554,
0.01681840792298317,
0.02776559442281723,
-0.0020096830558031797,
-0.09900201112031937,
-0.008062295615673065,
0.02594446949660778,
0.0071916705928742886,
-0.022027311846613884,
0.009491337463259697,
0.005652164109051228,
-0.05968448147177696,
-0.006816482171416283,
-0.006760132499039173,
0.0798303559422493,
-0.03004608303308487,
-0.008650689385831356,
-0.030849020928144455,
0.05600820109248161,
0.0114375539124012,
-0.03532898798584938,
0.013957827351987362,
0.016450392082333565,
-0.010059227235615253,
0.019968772307038307,
0.0009587969398126006,
0.06358562409877777,
-0.006190984044224024,
-0.024409297853708267,
-0.0443752147257328,
-0.030817028135061264,
0.023624684661626816,
0.01461117435246706,
-0.018333962187170982,
0.03719708323478699,
0.006864504888653755,
-0.03478068858385086,
-0.007242504041641951,
0.011180759407579899,
-0.009223774075508118,
0.018814969807863235,
-0.010883309878408909,
-0.012627660296857357,
0.006629190873354673,
-0.022744033485651016,
0.06902740150690079,
-0.018272412940859795,
0.0050673712976276875,
0.010005967691540718,
0.053517427295446396,
0.020530369132757187,
-0.02989882044494152,
0.010752124711871147,
-0.006350145675241947,
0.03378627449274063,
0.0011217625578865409,
-0.0036994139663875103,
0.02762892283499241,
-0.007344607263803482,
-0.043821707367897034,
-0.054020099341869354,
-0.004802427254617214,
0.03901475667953491,
0.08002272248268127,
-0.013481220230460167,
0.03537246957421303,
0.004041841719299555,
-0.032209500670433044,
0.0012275953777134418,
-0.01033126749098301,
-0.01595493033528328,
0.012860976159572601,
0.016399994492530823,
0.04173868149518967,
-0.05118705704808235,
-0.011694078333675861,
0.012839079834520817,
0.05251943692564964,
-0.006095288321375847,
0.03564627096056938,
0.001662495662458241,
0.03847800940275192,
-0.028653491288423538,
-0.019225016236305237,
-0.04466425999999046,
0.05411173030734062,
-0.017218170687556267,
0.055492497980594635,
0.006710912100970745,
0.0007752969395369291,
-0.013043731451034546,
0.04296785220503807,
0.034590862691402435,
0.0024449278134852648,
-0.022915108129382133,
-0.03996749222278595,
0.03843969851732254,
0.04453318193554878,
0.01230622362345457,
0.0079807685688138,
0.01123184897005558,
0.02678508125245571,
-0.018944278359413147,
0.020086517557501793,
0.008816453628242016,
-0.032211314886808395,
-0.012112106196582317,
-0.028472580015659332,
-0.026761561632156372,
0.02368440479040146,
0.004691760987043381,
-0.01976282335817814,
0.022416219115257263,
-0.019569622352719307,
-0.0055048200301826,
0.01174341980367899,
0.043685078620910645,
-0.019175751134753227,
0.05278380960226059,
-0.04310128465294838,
-0.016510168090462685,
-0.058350320905447006,
-0.002373938448727131,
0.1146141067147255,
0.04434217885136604,
0.023766694590449333,
-0.06659775972366333,
0.03293253108859062,
-0.010608246549963951,
-0.00346956355497241,
-0.04501837119460106,
0.04089935123920441,
0.003919398877769709,
-0.038257747888565063,
0.007034845184534788,
0.08275782316923141,
-0.024955103173851967,
-0.02746523544192314,
0.06045972555875778,
-0.04923679307103157,
-0.03297586739063263,
-0.008711039088666439,
0.017496054992079735,
0.017519015818834305,
-0.014702966436743736,
-0.025563443079590797,
0.022042257711291313,
0.0014702081680297852,
0.03337946906685829,
-0.02733726054430008,
-0.01701052486896515,
-0.015859518200159073,
0.003942764829844236,
-0.07828821241855621,
0.006008611060678959,
-0.00032091495813801885,
-0.03443242609500885,
-0.03806087002158165,
-0.01661696471273899,
0.0006626244285143912,
0.012283342890441418,
0.05993955582380295,
0.030267788097262383,
0.005631367675960064,
0.027157146483659744,
0.000787440687417984,
0.00672684283927083,
-0.030455976724624634,
0.017742179334163666,
-0.025162164121866226,
0.023963643237948418,
-0.01605241559445858,
0.04108915477991104,
0.018697021529078484,
-0.01104254275560379,
0.031532369554042816,
-0.012470538727939129,
-0.024280507117509842,
-0.0006853249506093562,
-0.016331836581230164,
-0.035870328545570374,
-0.0038136218208819628,
-0.01932976022362709,
0.02567524090409279,
0.002683652099221945,
0.04125244542956352,
-0.01073283888399601,
-0.004272526130080223,
0.030602501705288887,
-0.015742914751172066,
0.06858895719051361,
0.004093113820999861,
0.00010185910650761798,
-0.002394511131569743,
-0.06069472059607506,
-0.022931242361664772,
-0.027931759133934975,
0.005472075659781694,
0.0035066124983131886,
0.024344487115740776,
-0.011632565408945084,
0.03204349800944328,
0.0053072343580424786,
-0.04615795612335205,
-0.005493387579917908,
-0.017791302874684334,
0.0004702876613009721,
-0.006447061896324158,
0.02649294212460518,
0.007257015444338322,
0.01913936622440815,
-0.0020180190913379192,
0.03615421801805496,
-0.026255030184984207,
-0.0041863988153636456,
0.005190643481910229,
-0.058730922639369965,
-0.01033936720341444,
0.023698903620243073,
-0.024785814806818962,
-0.02480829693377018,
-0.02211800217628479,
-0.01638796553015709,
0.02946378104388714,
0.05568873509764671,
-0.0017882403917610645,
0.05539606884121895,
0.01625153236091137,
-0.02138853445649147,
0.026221230626106262,
-0.050455935299396515,
0.029343197122216225,
0.014417778700590134,
0.031644001603126526,
-0.023878615349531174,
-0.03398718684911728,
-0.024498669430613518,
-0.010674894787371159,
0.026639752089977264,
-0.0047387187369167805,
-0.023818906396627426,
0.006457657553255558,
-0.021099261939525604,
0.011800171807408333,
-0.053314484655857086,
-0.0069158561527729034,
-0.040217600762844086,
0.029755787923932076,
0.01739172264933586,
-0.006310655735433102,
0.029616212472319603,
0.03024297021329403,
-0.0439639687538147,
-0.023294007405638695,
0.022909311577677727,
0.000252187077421695,
-0.021897638216614723,
-0.019739756360650063,
0.007082793395966291,
-0.0154275419190526,
0.023242151364684105,
-0.0027982397004961967,
-0.06064571440219879,
0.018573524430394173,
-0.00021644230582751334,
-0.030569743365049362,
0.023736968636512756,
-0.005913509521633387,
0.012200435623526573,
0.02772103250026703,
-0.05494173243641853,
-0.0009690634906291962,
0.0702618807554245,
-0.05886556953191757,
0.0048370445147156715,
0.05419185385107994,
-0.036295052617788315,
-0.016866303980350494,
-0.041198477149009705,
0.040230512619018555,
0.02527689002454281,
-0.007899920456111431,
0.025521956384181976,
0.03167000785470009,
-0.00391349894925952,
0.0054540797136723995,
0.026307405903935432,
-0.04451550543308258,
-0.05529263988137245,
-0.023431042209267616,
0.0353580042719841,
-0.026002727448940277,
0.06666184961795807,
-0.03857787698507309,
0.04010554030537605,
0.07363231480121613,
0.0600837878882885,
-0.09293314814567566,
-0.000600901897996664,
0.03403698652982712,
0.025355814024806023,
0.06407913565635681,
-0.05111951008439064,
0.020854799076914787,
0.0023966000881046057,
-0.051630351692438126,
0.005915878806263208,
-0.03585606813430786,
0.006260199006646872,
-0.017745109274983406,
-0.03722550719976425,
0.008977219462394714,
0.06304675340652466,
0.03030335158109665,
0.03244918957352638,
-0.039382658898830414,
0.03422578424215317,
-0.040706440806388855,
-0.009570779278874397,
-0.032610636204481125,
0.010737380012869835,
-0.024664567783474922,
-0.031844303011894226,
0.07916906476020813,
-0.004061833489686251,
-0.03568687289953232,
-0.00022892987180966884,
0.018148940056562424,
0.009542861953377724,
0.0017422593664377928,
-0.006367586553096771,
0.021856088191270828,
0.007848038338124752,
0.033574461936950684,
-0.008894211612641811,
-0.027025867253541946,
0.02892220951616764,
-0.019183125346899033,
0.04006269946694374,
-0.037656791508197784,
-0.01804135926067829,
-0.02617299184203148,
-0.04809695854783058,
-0.020069897174835205,
0.013331407681107521,
-0.03493700921535492,
-0.02456403337419033,
-0.02290109172463417,
0.008091465570032597,
0.005682243499904871,
-0.0204477459192276,
0.0058903987519443035,
-0.04842536523938179,
0.005266895983368158,
0.05989906191825867,
-0.00708270026370883,
0.00027838320238515735,
0.036630719900131226,
-0.001735989935696125,
-0.012051300145685673,
0.0032619612757116556,
0.04659048467874527,
0.017317743971943855,
-0.04547947272658348,
0.025152022019028664,
0.0005605020560324192,
-0.012657892890274525,
0.004353359341621399,
-0.04634492099285126,
-0.025013517588377,
0.052128806710243225,
-0.001687609008513391,
0.029304638504981995,
0.0036159397568553686,
-0.06475049257278442,
-0.011363478377461433,
-0.055679067969322205,
0.016514956951141357,
-0.0046905516646802425,
0.012647991999983788,
-0.03139064833521843,
-0.010013650171458721,
-0.00760931521654129,
0.00920010730624199,
0.061033762991428375,
-0.01970748044550419,
-0.019587475806474686,
0.04126423969864845,
-0.0184593815356493,
0.00476908078417182,
-0.03748590871691704,
-0.001481511164456606,
0.006613614037632942,
-0.014457283541560173,
0.030112607404589653,
0.014000139199197292,
-0.01045914925634861,
0.01740350015461445,
0.02716357819736004,
-0.035430263727903366,
0.05705209821462631,
0.016346562653779984,
-0.017127173021435738,
0.032150112092494965,
0.004927245434373617,
-0.012496231123805046,
0.08200761675834656,
-0.005452193785458803,
0.010255699045956135,
0.0525149330496788,
-0.023896805942058563,
-0.017003817483782768,
0.029531802982091904,
-0.04343670606613159,
-0.026270495727658272,
-0.023132380098104477,
0.004391760565340519,
0.0007702233269810677,
-0.022120334208011627,
0.011237158440053463,
0.0565345324575901,
-0.025226904079318047,
-0.008905375376343727,
0.023890946060419083,
-0.0019303493900224566,
0.027183230966329575,
0.014145342633128166,
0.006879725493490696,
0.038381099700927734,
0.014645482413470745,
0.038197264075279236,
0.05760052055120468,
0.037879638373851776,
0.011669440194964409,
-0.0627405196428299,
-0.024475565180182457,
-0.04039201885461807,
0.017208052799105644,
-0.00619506137445569,
0.051566071808338165,
-0.022026805207133293,
-0.04786224290728569,
-0.0006390275084413588,
0.010090391151607037,
0.042123373597860336,
0.006601467728614807,
-0.005485064350068569,
0.0848630890250206,
-0.027278808876872063,
-0.009221214801073074,
-0.028488533571362495,
0.007603259291499853,
-0.047886207699775696,
0.03354533761739731,
-0.0010348139330744743,
0.025305988267064095,
0.00022475914738606662,
-0.02412712574005127,
-0.004834531806409359,
-0.007160063832998276,
0.0004969920846633613,
-0.04120415821671486,
-0.009227628819644451,
0.009027577005326748,
-0.005694152321666479,
0.01804744079709053,
-0.04667074605822563,
-0.024041639640927315,
-0.00540120666846633,
0.009167295880615711,
0.009393704123795033,
0.01044047437608242,
-0.018242813646793365,
0.000009354936992167495,
-0.026579950004816055,
0.04039569944143295,
-0.08371428400278091,
-0.019191136583685875,
-0.013281933031976223,
0.014062698930501938,
-0.00787843856960535,
-0.041787516325712204
] |
<p>Why are the charges of atoms in a molecule not invariant under the rotations of the molecule? </p>
<p>My intuition is that the charges should not change under the rotation of the molecule, because their relative positions do not change. But I was told that they can change. </p>
| 8,298 |
[
-0.05071123689413071,
0.02364092320203781,
-0.0005202043103054166,
-0.010265019722282887,
0.03212672099471092,
0.002877744846045971,
-0.05176033824682236,
0.013883032836019993,
0.017011556774377823,
-0.052281565964221954,
0.07220621407032013,
0.04507242888212204,
0.033587127923965454,
0.04269344359636307,
-0.010980992577970028,
-0.010178182274103165,
-0.004877859260886908,
-0.01591588370501995,
-0.012807618826627731,
0.033155810087919235,
-0.006483913864940405,
0.030008694157004356,
0.012997860088944435,
0.011782118119299412,
-0.028521409258246422,
0.027340944856405258,
0.01974082551896572,
-0.013076375238597393,
0.06934081763029099,
0.04133612662553787,
-0.03654821962118149,
-0.024344224482774734,
0.027906347066164017,
-0.00017258597654290497,
0.01154649443924427,
-0.0074449763633310795,
-0.0034859355073422194,
-0.01014618668705225,
-0.03139125928282738,
0.012353996746242046,
-0.037561748176813126,
-0.004453527275472879,
-0.025045599788427353,
0.04880348965525627,
-0.03359846770763397,
0.015035249292850494,
-0.0075327628292143345,
0.028263429179787636,
0.06131771579384804,
-0.0687689483165741,
0.08418557047843933,
0.008096863515675068,
0.036495618522167206,
0.03781590610742569,
-0.01089475117623806,
0.0037703439593315125,
0.05527794361114502,
0.06358635425567627,
-0.0355236753821373,
-0.02108469232916832,
-0.02854268066585064,
-0.06981849670410156,
0.0381213054060936,
0.011860854923725128,
-0.03180216997861862,
0.002919201273471117,
0.01775044947862625,
-0.04938162863254547,
0.04732503741979599,
0.016824470832943916,
0.0003927656798623502,
0.008306560106575489,
-0.011532559059560299,
-0.028430186212062836,
-0.006364457309246063,
-0.042026352137327194,
0.02981863170862198,
-0.0041651735082268715,
0.051193442195653915,
0.02886282280087471,
-0.00027087112539447844,
0.023130089044570923,
0.0319710448384285,
0.002531760837882757,
-0.0003095628344453871,
-0.04158174619078636,
0.041553325951099396,
-0.004178439732640982,
0.026355857029557228,
0.04132053628563881,
0.014636829495429993,
0.0113728828728199,
0.002532976446673274,
0.004924447275698185,
0.014620056375861168,
0.033153388649225235,
-0.0016192169860005379,
0.06180848181247711,
0.006554671097546816,
0.01845993474125862,
0.0009384560398757458,
-0.00440721632912755,
0.027433695271611214,
0.02496078796684742,
-0.01382893230766058,
-0.0247843898832798,
-0.04126536846160889,
0.008836203254759312,
0.010264239273965359,
-0.018975406885147095,
-0.02972923405468464,
0.005229103844612837,
-0.014088793657720089,
0.011920730583369732,
0.02241532690823078,
-0.027019033208489418,
-0.008857977576553822,
-0.024770576506853104,
0.02442578598856926,
0.05630870163440704,
0.01503548864275217,
-0.028121134266257286,
-0.008938114158809185,
-0.01575528271496296,
-0.04269349202513695,
-0.011221279390156269,
0.04148982837796211,
0.012005009688436985,
-0.027242306619882584,
-0.000058436966355657205,
0.01629176177084446,
-0.033969614654779434,
0.03666185215115547,
-0.02602211758494377,
0.03848531097173691,
0.005451312754303217,
-0.116458460688591,
-0.04808235913515091,
0.02008865401148796,
0.010668289847671986,
-0.02089928463101387,
-0.10956304520368576,
-0.02143970876932144,
0.020775998011231422,
0.07900287210941315,
-0.019375858828425407,
-0.01772589236497879,
0.007057830225676298,
0.028131088241934776,
0.011092886328697205,
0.019106032326817513,
-0.023677213117480278,
0.015950433909893036,
-0.04008565843105316,
-0.028583301231265068,
-0.046553999185562134,
0.026851342990994453,
0.029972463846206665,
0.018849579617381096,
-0.013060410507023335,
0.019336475059390068,
-0.035203516483306885,
-0.012376035563647747,
0.01648394763469696,
0.0026112578343600035,
-0.016074994578957558,
0.06546967476606369,
0.019758673384785652,
-0.004484822973608971,
0.03430071473121643,
0.013054552488029003,
0.051026586443185806,
-0.03615061938762665,
0.03615998104214668,
0.05928732082247734,
-0.02762710489332676,
-0.026543445885181427,
-0.03201979026198387,
0.0337558388710022,
-0.011130566708743572,
-0.054015010595321655,
-0.02027389220893383,
-0.01282312162220478,
0.005750059150159359,
0.00229251547716558,
0.0026734345592558384,
-0.013910642825067043,
0.013853101991117,
-0.009672424755990505,
-0.05438387766480446,
0.003957720939069986,
-0.06516129523515701,
0.02070562168955803,
-0.01929345168173313,
-0.04249226674437523,
0.02963379956781864,
0.044280216097831726,
0.011019141413271427,
-0.020841188728809357,
-0.017877645790576935,
-0.008914177305996418,
0.025035684928297997,
-0.008552107028663158,
-0.01538305263966322,
0.005692989099770784,
0.050125885754823685,
0.043018829077482224,
0.01717277616262436,
-0.00021898580598644912,
0.01529910508543253,
-0.02056307904422283,
0.04343218356370926,
-0.0005285488441586494,
0.002113866386935115,
-0.004655393306165934,
-0.00439608795568347,
0.024767275899648666,
0.03048938512802124,
0.0014611883088946342,
0.06603594124317169,
-0.006422257982194424,
0.07120481878519058,
0.042737171053886414,
-0.02560524269938469,
0.0327155664563179,
0.07502409815788269,
0.00795172993093729,
0.013395193964242935,
-0.005915169138461351,
-0.050928402692079544,
-0.045678675174713135,
-0.012224210426211357,
0.021801725029945374,
0.05445321276783943,
-0.03783281520009041,
0.0005629322840832174,
0.036743417382240295,
0.04824443906545639,
0.026459187269210815,
0.00013741181464865804,
0.0049521238543093204,
-0.06490369886159897,
0.018981996923685074,
-0.03722800314426422,
0.03515094518661499,
-0.0056026470847427845,
0.02675873413681984,
-0.013133102096617222,
0.038202717900276184,
0.0038598773535341024,
-0.02394294925034046,
0.03930220380425453,
-0.003811843227595091,
0.014303452335298061,
0.03631274029612541,
-0.04092709720134735,
0.0027076357509940863,
-0.0031365409959107637,
0.018363788723945618,
-0.0021708994172513485,
-0.0035337875597178936,
-0.007436301093548536,
-0.024655310437083244,
0.009962612763047218,
0.009915877133607864,
-0.0032219630666077137,
-0.004552783444523811,
-0.0001125460839830339,
0.02103789895772934,
-0.044803861528635025,
0.02224436216056347,
0.002479656832292676,
0.007522665895521641,
0.018824290484189987,
0.006401996128261089,
0.04609937220811844,
0.017140517011284828,
0.015657581388950348,
-0.024925848469138145,
-0.031249240040779114,
0.0012603059876710176,
-0.031776633113622665,
0.0068714814260602,
0.03568924963474274,
-0.01756683550775051,
0.00997147150337696,
-0.03247648850083351,
-0.02607767842710018,
0.023041028529405594,
-0.010815180838108063,
0.0034188050776720047,
0.0245230533182621,
0.01950165629386902,
-0.039258476346731186,
0.003193072509020567,
-0.012659869156777859,
0.0026169149205088615,
-0.028667869046330452,
-0.016019586473703384,
0.06174091994762421,
-0.04008602723479271,
0.006464803591370583,
0.03703279048204422,
-0.04083651304244995,
-0.037836696952581406,
0.016533730551600456,
-0.01678851805627346,
0.009197910316288471,
0.0025989417918026447,
0.00056248321197927,
0.024789368733763695,
-0.04558118060231209,
-0.027387483045458794,
-0.030544636771082878,
-0.02539421245455742,
0.023281993344426155,
-0.010630887001752853,
0.05951235443353653,
-0.014535397291183472,
-0.001479131169617176,
0.07915214449167252,
0.01621442660689354,
-0.04371006414294243,
0.00003102334449067712,
-0.036637917160987854,
-0.050898175686597824,
-0.022079968824982643,
0.006724173203110695,
0.03532080724835396,
0.0016176544595509768,
0.02288096584379673,
0.025882121175527573,
0.023129982873797417,
0.03207053989171982,
-0.010507678613066673,
-0.0291795302182436,
0.03627222031354904,
0.01715826243162155,
0.023695675656199455,
0.042822521179914474,
0.008870440535247326,
-0.021081749349832535,
-0.010374052450060844,
0.042865145951509476,
0.00027949182549491525,
0.016384785994887352,
-0.08817373216152191,
0.08435606956481934,
-0.0261066947132349,
0.052752453833818436,
-0.0315859355032444,
0.06013116613030434,
-0.005911474581807852,
-0.01645800471305847,
0.004687676206231117,
0.04581070318818092,
0.04413015767931938,
-0.03186361491680145,
0.00009759615932125598,
0.05023837089538574,
0.03683943673968315,
-0.02409154362976551,
-0.007516366895288229,
0.011739213019609451,
-0.022408420220017433,
0.04635046049952507,
-0.04610997438430786,
-0.04283488914370537,
0.03647759184241295,
0.010824422352015972,
0.030710628256201744,
0.005535100121051073,
-0.06947113573551178,
-0.0158142801374197,
-0.060611676424741745,
0.0109056131914258,
-0.004010140895843506,
0.043876633048057556,
0.0067545878700912,
0.07460702210664749,
0.022565197199583054,
0.017107561230659485,
-0.043039172887802124,
-0.008275747299194336,
-0.06559491902589798,
0.013868284411728382,
-0.02086821384727955,
0.00016235785733442754,
-0.04314442723989487,
-0.004382004961371422,
-0.02131703309714794,
-0.03113155998289585,
-0.004228197503834963,
-0.04975071921944618,
-0.026808932423591614,
-0.029642023146152496,
-0.007080406881868839,
-0.038738347589969635,
0.00001215315660374472,
-0.034619882702827454,
0.06942150741815567,
0.02713865414261818,
-0.02989105135202408,
0.03559652715921402,
0.02825954370200634,
-0.029936794191598892,
0.023320931941270828,
-0.03327342867851257,
0.008801761083304882,
0.005011382978409529,
0.01696115918457508,
0.027583491057157516,
-0.02788388542830944,
0.003540516598150134,
-0.0360761322081089,
-0.00015013717347756028,
0.028255611658096313,
0.021176932379603386,
-0.008312918245792389,
-0.014452370814979076,
-0.04668933525681496,
-0.006917116232216358,
-0.004885647911578417,
0.060744140297174454,
0.006523826625198126,
0.01982823759317398,
0.008443736471235752,
0.00672248937189579,
-0.012371113523840904,
0.022695057094097137,
0.03599614277482033,
0.07347721606492996,
-0.026560738682746887,
-0.04176874831318855,
0.011434117332100868,
-0.016551490873098373,
-0.004902195185422897,
0.033981725573539734,
-0.03170326352119446,
-0.023646313697099686,
-0.026132503524422646,
0.0010039849439635873,
-0.013762709684669971,
-0.019305653870105743,
0.0008838303619995713,
-0.03500131517648697,
0.04476109519600868,
0.0007778082508593798,
0.04003496840596199,
0.019588567316532135,
-0.0004672840004786849,
0.04419167339801788,
0.024908535182476044,
-0.011566572822630405,
-0.07612477242946625,
0.011968382634222507,
0.014141375198960304,
0.010232445783913136,
-0.0309488195925951,
0.012921782210469246,
-0.03987327218055725,
-0.0032824978698045015,
0.043477922677993774,
-0.06509911268949509,
0.04421110451221466,
-0.0006827396573498845,
-0.012997752986848354,
-0.013959541916847229,
-0.029664291068911552,
-0.008476569317281246,
0.00397757301107049,
-0.00360425328835845,
0.011743973940610886,
-0.025418851524591446,
-0.0016195843927562237,
-0.017131786793470383,
0.0008628611103631556,
0.037420839071273804,
0.03937629237771034,
0.004875208251178265,
0.021509341895580292,
0.012892388738691807,
0.016361096873879433,
-0.022946570068597794,
-0.06960616260766983,
0.002758815186098218,
0.015983007848262787,
0.03274490684270859,
0.043384213000535965,
-0.05984525755047798,
-0.07645665109157562,
-0.017846575006842613,
-0.030197039246559143,
0.007829347625374794,
-0.012381048873066902,
-0.03134188801050186,
0.0022584814578294754,
0.040312837809324265,
-0.025812875479459763,
0.05187082290649414,
0.03774997964501381,
-0.010150039568543434,
0.014679054729640484,
-0.0478840209543705,
0.035653479397296906,
-0.01889736019074917,
0.010697399266064167,
-0.03817443549633026,
0.018215645104646683,
-0.017274225130677223,
0.04551215097308159,
-0.0026666184421628714,
0.016733864322304726,
0.013578158803284168,
-0.008991565555334091,
-0.006072843912988901,
0.013778175227344036,
0.014215296134352684,
0.016877226531505585,
-0.024753283709287643,
0.020159762352705002,
-0.009687760844826698,
-0.01542561873793602,
0.04270941764116287,
0.018124883994460106,
-0.02903764694929123,
0.02033909410238266,
-0.04470871016383171,
0.0038531275931745768,
-0.05158476158976555,
0.0001020719573716633,
-0.027919474989175797,
-0.03093496896326542,
0.018876906484365463,
-0.004824765957891941,
-0.03155463561415672,
0.03462290018796921,
-0.05191972479224205,
-0.037045709788799286,
0.043589700013399124,
-0.0304945670068264,
0.020264282822608948,
-0.04122919216752052,
0.0484343096613884,
0.014115484431385994,
0.020389072597026825,
-0.06048562377691269,
-0.06062270700931549,
0.0017552856588736176,
0.037431418895721436,
-0.015831807628273964,
-0.017761435359716415,
0.014605903998017311,
0.020095014944672585,
-0.04298197850584984,
-0.001547877094708383,
0.04257772117853165,
-0.025608772411942482,
-0.0025410912930965424,
0.05269701033830643,
0.020152321085333824,
0.08632867783308029,
-0.07011334598064423,
-0.0008508660248480737,
0.01052057184278965,
-0.07016205042600632,
-0.0031179944053292274,
-0.0094597227871418,
0.03131277859210968,
-0.01417102012783289,
-0.05854545906186104,
-0.004809977952390909,
0.0013702396536245942,
0.02732163481414318,
-0.015502738766372204,
-0.010354510508477688,
0.010673354379832745,
-0.024700144305825233,
-0.007235855795443058,
-0.004118700046092272,
0.01078273169696331,
-0.03088284097611904,
0.028157301247119904,
-0.029992101714015007,
0.0206608809530735,
-0.018852435052394867,
-0.04528801143169403,
-0.004132196307182312,
0.04185393825173378,
0.011161967180669308,
0.018031638115644455,
0.06112292408943176,
-0.014359583146870136,
-0.010774454101920128,
0.03881732374429703,
-0.014487756416201591,
0.04598241671919823,
0.017435481771826744,
-0.012566923163831234,
-0.009287912398576736,
-0.010280500166118145,
-0.021535996347665787,
-0.04124316945672035,
-0.008205819875001907,
0.02837899886071682,
0.05940168350934982,
0.020966263487935066,
0.06304734945297241,
0.014946986921131611,
-0.00572571437805891,
-0.023234955966472626,
-0.022776013240218163,
-0.010567676275968552,
0.014768237248063087,
-0.0008967534522525966,
0.011120068840682507,
-0.021297598257660866,
0.013024026528000832,
0.0277473833411932,
0.05224227160215378,
-0.028191810473799706,
0.009619269520044327,
0.059428367763757706,
0.002443175995722413,
0.003645658493041992,
0.009945143014192581,
-0.04912038892507553,
0.023606831207871437,
-0.039945024996995926,
0.06288237869739532,
-0.014909639954566956,
-0.029300864785909653,
0.043553728610277176,
-0.01966669224202633,
0.030125249177217484,
-0.02716556191444397,
-0.015294517390429974,
-0.008061411790549755,
0.012822628952562809,
-0.011917912401258945,
0.0185075830668211,
-0.03184850513935089,
0.026931878179311752,
0.05148601531982422,
-0.011983860284090042,
-0.014120885170996189,
-0.001660030335187912,
-0.030566329136490822,
0.008275537751615047,
-0.003473967779427767,
-0.03481629490852356,
0.05094389244914055,
-0.004077489022165537,
-0.016759466379880905,
-0.001699815853498876,
0.0028038539458066225,
0.00987539254128933,
0.02700311876833439,
0.023760292679071426,
-0.013513712212443352,
0.04313339665532112,
-0.006645635236054659,
0.018979903310537338,
-0.02861114591360092,
-0.003615918103605509,
0.10617553442716599,
0.025210890918970108,
0.016186844557523727,
-0.05305705964565277,
0.015307849273085594,
-0.006047992967069149,
0.003910597413778305,
-0.010902277193963528,
0.03661243990063667,
-0.006064809858798981,
0.0717075765132904,
-0.04069904610514641,
0.029144341126084328,
0.001004836056381464,
0.006766186095774174,
0.03665316477417946,
-0.023597339168190956,
-0.015858419239521027,
-0.012187890708446503,
0.0024524093605577946,
0.009208825416862965,
0.022806435823440552,
-0.07823221385478973,
0.0286624263972044,
-0.059883277863264084,
-0.022095123305916786,
-0.048670195043087006,
-0.03519998490810394,
0.004723476245999336,
0.0004045110254082829,
-0.036579497158527374,
0.0101100979372859,
0.028400743380188942,
-0.024124551564455032,
-0.06484510749578476,
0.05644688755273819,
0.025165030732750893,
-0.0013837224105373025,
0.004635980352759361,
0.023849088698625565,
0.029504990205168724,
0.006188662257045507,
0.028113866224884987,
0.013846460729837418,
-0.05682501196861267,
-0.007078243885189295,
-0.03686654195189476,
0.0176252368837595,
-0.024102451279759407,
-0.004160159267485142,
-0.011177939362823963,
-0.0030303087551146746,
-0.01764158345758915,
-0.08540428429841995,
-0.02663707174360752,
-0.009466330520808697,
0.014114859513938427,
0.021455932408571243,
-0.017316900193691254,
-0.04268893972039223,
0.012302464805543423,
-0.010843155905604362,
0.0003717926738318056,
-0.02035418152809143,
-0.003464092966169119,
0.02981278859078884,
0.017415909096598625,
0.01227239053696394,
-0.029417166486382484,
-0.0017875628545880318,
-0.02395152673125267,
-0.025091612711548805,
-0.0497918576002121,
-0.03254412114620209,
-0.017191564664244652,
0.030148101970553398,
0.07688287645578384,
-0.028500299900770187,
0.0040319920517504215,
-0.0019026801455765963,
-0.08921042829751968,
0.010079986415803432,
-0.013209720142185688,
-0.028407292440533638,
-0.0049894144758582115,
0.016961146146059036,
0.06070808693766594,
0.0233876071870327,
-0.04899938404560089,
0.03280150145292282,
-0.007849114947021008,
0.008943218737840652,
0.005441484972834587,
-0.017815548926591873,
0.000994736677967012,
0.02513900026679039,
-0.04294052720069885,
0.011943873018026352,
0.0014205784536898136,
0.02682727575302124,
0.038024574518203735,
-0.0008687894442118704,
0.004746968857944012,
0.042046383023262024,
-0.004077467601746321,
0.010715853422880173,
0.05360184609889984,
0.015031973831355572,
-0.00750214047729969,
0.03639912232756615,
-0.00990368239581585,
-0.04971938952803612,
-0.05840416997671127,
-0.029736438766121864,
0.0006750246975570917,
0.02349279820919037,
0.03375229239463806,
-0.01361230667680502,
-0.031399741768836975,
-0.02397158183157444,
0.040293242782354355,
-0.033760905265808105,
-0.024522582069039345,
-0.05787305161356926,
0.011169965378940105,
-0.02567952498793602,
0.004248953890055418,
-0.031268589198589325,
0.010666307993233204,
-0.02053171955049038,
0.00342101464048028,
0.0731397196650505,
0.028354493901133537,
0.0026719518937170506,
-0.030430007725954056,
0.01232127845287323,
-0.014249801635742188,
0.06588774919509888,
-0.03421612083911896,
-0.0326075442135334,
0.026289604604244232,
-0.017399761825799942,
-0.03699694201350212,
-0.021250752732157707,
-0.037447839975357056,
-0.005833834875375032,
0.022698869928717613,
0.023771073669195175,
0.015299693681299686,
0.03554384037852287,
-0.031154677271842957,
-0.004878797102719545,
0.021358339115977287,
-0.015122119337320328,
-0.01548545341938734,
-0.03413844853639603,
0.0069954716600477695,
-0.04646468907594681,
-0.019002104178071022,
0.04456498101353645,
0.0219874270260334,
-0.003823317587375641,
-0.0019045063527300954,
-0.009223666973412037,
0.02008090913295746,
0.0024887537583708763,
0.04714594781398773,
0.021476464346051216,
0.007530194241553545,
0.05722859129309654,
-0.04664589464664459,
0.056321777403354645,
0.009184681810438633,
-0.0005860297824256122,
-0.07446658611297607,
0.005243259482085705,
0.02141064777970314,
-0.004353128839284182,
0.007673636078834534,
-0.019122231751680374,
-0.0200648196041584,
0.054273344576358795,
-0.12421432882547379,
-0.004991060122847557,
-0.05315263941884041,
-0.0029970002360641956,
-0.002651525428518653,
-0.030815081670880318,
-0.02912263013422489,
0.03576154634356499,
0.01315713208168745,
0.035433411598205566,
0.014035903848707676,
0.005384156480431557,
-0.013513459824025631,
-0.0007702460861764848,
-0.023631557822227478,
0.03891764581203461,
0.0024012711364775896,
-0.006159105803817511,
0.02885870635509491,
0.02095305547118187,
-0.020548958331346512,
-0.005635659676045179,
-0.02370319701731205,
-0.006653624586760998,
0.0014100107364356518,
0.010682526044547558,
0.024007955566048622,
0.010511343367397785,
-0.004032349679619074,
-0.010306363925337791,
-0.013852291740477085,
0.006751063745468855,
0.018024777993559837,
0.026652732864022255,
-0.0014787509571760893,
-0.004977528937160969,
0.009847397916018963,
-0.04743392392992973,
-0.0471838004887104,
0.010316697880625725,
-0.0023418134078383446,
-0.007086559198796749,
-0.02132049947977066,
0.044093791395425797,
-0.008583600632846355,
-0.014952532947063446,
-0.0023484656121581793,
-0.03331927955150604,
0.002004574751481414,
0.0410446934401989,
0.006533402483910322,
0.05427674204111099,
0.03358745202422142,
-0.006281774025410414,
0.0015036655822768807,
0.034898966550827026,
0.007962534204125404,
-0.013754323124885559,
-0.08942607045173645,
0.00976273138076067,
0.028339173644781113,
-0.01145326066762209,
-0.019296105951070786,
-0.038371164351701736,
-0.01742563024163246,
0.05041246488690376,
0.03550225868821144,
0.0005987602053210139,
-0.01062790211290121,
-0.08948361128568649,
0.000813145306892693,
-0.08088768273591995,
0.029507488012313843,
-0.008793476037681103,
-0.00570187671110034,
-0.039372339844703674,
-0.0420847088098526,
-0.033940479159355164,
0.004935748875141144,
0.05760838836431503,
0.028105271980166435,
-0.014140987768769264,
0.00464090658351779,
-0.0095432223752141,
0.033436935395002365,
-0.036953993141651154,
0.0019346186891198158,
-0.010060297325253487,
-0.000755072629544884,
0.05119160935282707,
-0.04327240213751793,
-0.0589008666574955,
0.039435867220163345,
0.013420014642179012,
-0.02866487205028534,
0.03735256940126419,
0.006690145004540682,
-0.03928337246179581,
0.052871569991111755,
0.009046884253621101,
-0.0026912400498986244,
0.06116397678852081,
0.01831028051674366,
0.025613268837332726,
0.04414492845535278,
0.000745889323297888,
-0.05225471779704094,
0.016259396448731422,
-0.0425683818757534,
-0.019389808177947998,
-0.024280089884996414,
-0.015545866452157497,
0.05836021900177002,
-0.008598042652010918,
0.023663286119699478,
0.039969008415937424,
-0.034395452588796616,
-0.009158235974609852,
0.031372565776109695,
0.002232048660516739,
0.02464482933282852,
0.016181299462914467,
0.05145827680826187,
0.025269513949751854,
0.009553199633955956,
0.020618589594960213,
0.03589431568980217,
0.0438004732131958,
0.005272556096315384,
0.02226562798023224,
0.03238582983613014,
0.003957904875278473,
-0.00006791623309254646,
0.038055676966905594,
0.02262679487466812,
-0.011039172299206257,
-0.011469925753772259,
0.02022845856845379,
-0.016480524092912674,
0.03818618878722191,
-0.0012913173995912075,
-0.029321294277906418,
0.06460360437631607,
-0.03706445172429085,
0.022372150793671608,
-0.012971322983503342,
0.009841092862188816,
-0.024593332782387733,
0.010913812555372715,
-0.003396093612536788,
0.031158704310655594,
-0.014212042093276978,
-0.016054071485996246,
-0.043820030987262726,
0.010624385438859463,
0.012673917226493359,
-0.02317575365304947,
0.014919684268534184,
0.009107181802392006,
0.00509278941899538,
-0.051505982875823975,
0.019082868471741676,
-0.02107788622379303,
-0.012604930438101292,
0.019672434777021408,
0.019844289869070053,
0.0213118065148592,
0.013005109503865242,
-0.012888316065073013,
-0.05460691452026367,
0.045097772032022476,
-0.049571286886930466,
-0.0468992255628109,
-0.016643080860376358,
0.012492978014051914,
-0.03974131494760513,
-0.0072571090422570705
] |
<p>Does the <a href="http://en.wikipedia.org/wiki/General_topology" rel="nofollow">general topology</a> of Minkowski space-time change under a Lorentz transformation? Open balls in $\mathbb{R}^{4}$ (with the standard topology) are not invariant under Lorentz transformations. Does this mean for example that observers in one reference frame would have different notions of convergence, continuity etc?</p>
<p>Note: I'm asking from the perspective of a curious undergraduate who just finished introductory analysis and modern physics. Please answer appropriately.</p>
| 8,299 |
[
-0.06587908416986465,
-0.005441049113869667,
0.016712980344891548,
-0.007614876609295607,
0.034904029220342636,
0.05457720533013344,
0.007659762166440487,
-0.03480738401412964,
-0.02744671329855919,
-0.019446006044745445,
0.03682844713330269,
0.016289856284856796,
0.04376774653792381,
0.011151744052767754,
0.019439226016402245,
-0.013592994771897793,
-0.026228774338960648,
-0.027744462713599205,
-0.03426780924201012,
-0.026119204238057137,
0.007632482796907425,
0.00664075743407011,
0.031880252063274384,
-0.007800683844834566,
-0.04523104056715965,
0.00562594598159194,
0.004167146515101194,
-0.007374366279691458,
0.019272862002253532,
0.06282052397727966,
-0.019650833681225777,
-0.027721606194972992,
-0.013486366719007492,
0.05064944177865982,
0.003431144170463085,
0.0002008510346058756,
-0.06841430813074112,
-0.030234212055802345,
0.01396691333502531,
-0.004300530068576336,
-0.047929346561431885,
-0.034780800342559814,
-0.03494952991604805,
0.05805161967873573,
-0.028327396139502525,
0.004162485711276531,
0.0012136467266827822,
0.011782870627939701,
0.0639800950884819,
-0.03793464973568916,
0.08962179720401764,
0.012497963383793831,
0.030764548107981682,
0.012629903852939606,
-0.0036020814441144466,
-0.011685667559504509,
0.07004022598266602,
0.06822989135980606,
-0.022666655480861664,
-0.026104532182216644,
-0.02408912405371666,
-0.022808212786912918,
0.02876763418316841,
-0.028116827830672264,
-0.02956707589328289,
0.04018998146057129,
-0.044585105031728745,
-0.0214408989995718,
0.018073225393891335,
-0.011905288323760033,
-0.023451726883649826,
0.026233242824673653,
0.03866646811366081,
0.00004219208494760096,
0.008505623787641525,
-0.012183006852865219,
0.018109049648046494,
-0.004627055022865534,
0.06806935369968414,
0.04990658909082413,
-0.021155433729290962,
-0.00404759868979454,
0.006440918892621994,
0.015194405801594257,
0.04190520569682121,
-0.008857987821102142,
0.03006555512547493,
-0.00811526644974947,
0.01652590185403824,
0.06722613424062729,
0.00956899393349886,
-0.020913878455758095,
0.0300641767680645,
-0.027079936116933823,
-0.028250716626644135,
0.07372184842824936,
-0.023005817085504532,
0.058617670089006424,
0.0012293403269723058,
-0.020141610875725746,
0.030084878206253052,
-0.019038619473576546,
0.005001374054700136,
0.033760108053684235,
-0.003953910898417234,
-0.015440731309354305,
-0.05114253982901573,
0.05640764161944389,
-0.02725488692522049,
-0.016734227538108826,
-0.031131427735090256,
0.013506962917745113,
-0.01960943266749382,
0.029272254556417465,
0.036139246076345444,
-0.06260504573583603,
-0.0048218159936368465,
-0.005629072897136211,
0.008921274915337563,
0.06420332938432693,
0.06705353409051895,
-0.03512001782655716,
0.007173687219619751,
-0.02938825823366642,
-0.06275764852762222,
0.007552606984972954,
0.03877256065607071,
-0.030656564980745316,
-0.007615362294018269,
0.02413775958120823,
-0.005447157192975283,
-0.0077766538597643375,
0.014908641576766968,
0.03902963548898697,
0.041556987911462784,
-0.03708900511264801,
-0.1144307553768158,
-0.040271494537591934,
0.03868652880191803,
0.010926863178610802,
-0.013613136485219002,
-0.09318245947360992,
0.02485775016248226,
0.009212549775838852,
0.04932761937379837,
-0.007993858307600021,
-0.004952925257384777,
0.026881370693445206,
0.038468994200229645,
0.012796244584023952,
-0.04585617780685425,
0.02508077584207058,
0.006933402735739946,
-0.048562463372945786,
0.016656164079904556,
-0.04523826390504837,
0.009443508461117744,
0.030391588807106018,
0.025614524260163307,
-0.05765737593173981,
0.060010332614183426,
0.021281499415636063,
0.019453497603535652,
-0.0033920530695468187,
0.004732264205813408,
0.0011925817234441638,
0.08406820893287659,
-0.004997523035854101,
-0.0044977692887187,
0.006261710077524185,
0.029795240610837936,
0.02793913148343563,
-0.030073042958974838,
0.061966780573129654,
0.03137597069144249,
-0.00992360059171915,
-0.022675568237900734,
-0.006157995201647282,
0.011994664557278156,
-0.019515633583068848,
-0.04875268042087555,
0.009936593472957611,
-0.027006611227989197,
-0.05610749498009682,
-0.031112294644117355,
0.06878878176212311,
0.012511525303125381,
-0.00548554677516222,
-0.008847267366945744,
-0.06691993772983551,
0.029656164348125458,
-0.08220142871141434,
0.010815072804689407,
-0.0247783362865448,
-0.013235270045697689,
0.005219707265496254,
-0.01262583490461111,
0.04178118333220482,
-0.035528942942619324,
-0.019475441426038742,
-0.02665047161281109,
0.042773984372615814,
-0.029690736904740334,
-0.04410886764526367,
0.004601259715855122,
0.037546321749687195,
0.04196840524673462,
-0.00923879723995924,
-0.013871227391064167,
-0.015107718296349049,
-0.023828910663723946,
0.045664314180612564,
0.011164727620780468,
0.03752359375357628,
0.011988723650574684,
0.012805693782866001,
-0.00802700873464346,
0.03543132543563843,
-0.04457618296146393,
0.061999980360269547,
-0.02961108833551407,
0.07644417881965637,
0.023161346092820168,
-0.022598296403884888,
-0.005806633271276951,
0.04645399749279022,
0.017621099948883057,
0.0140910679474473,
-0.02418835647404194,
-0.03818875178694725,
-0.024095378816127777,
-0.001920082955621183,
0.01913348212838173,
0.044721007347106934,
-0.05302822217345238,
0.023255739361047745,
-0.00676873791962862,
0.03750661015510559,
-0.012114906683564186,
0.013701471500098705,
0.004857222083956003,
-0.04573127254843712,
-0.020007841289043427,
-0.016585974022746086,
0.037991754710674286,
-0.0027722972445189953,
0.008943828754127026,
0.021349767223000526,
0.011426163837313652,
-0.003907989710569382,
0.009889962151646614,
0.006047298666089773,
-0.03643394634127617,
-0.026265542954206467,
-0.019839543849229813,
0.010642566718161106,
0.025419672951102257,
-0.011291115544736385,
0.021964726969599724,
0.01705593802034855,
0.027824681252241135,
-0.02380075491964817,
-0.03652053326368332,
-0.003326232312247157,
0.01584201119840145,
-0.011760782450437546,
-0.02181396819651127,
0.01062651164829731,
0.017572974786162376,
-0.04983653128147125,
0.009417528286576271,
0.005471589509397745,
0.006106965709477663,
-0.03248195722699165,
0.012495625764131546,
0.01236681081354618,
0.0037846514023840427,
0.008684216998517513,
-0.02435317263007164,
-0.03627687320113182,
-0.016805535182356834,
0.013194780796766281,
0.0015341652324423194,
0.03468984365463257,
-0.018167005851864815,
0.053149931132793427,
0.01971481367945671,
-0.015091325156390667,
0.01398552767932415,
-0.003688588971272111,
0.04207409918308258,
0.0532502718269825,
0.008820933289825916,
-0.04261542856693268,
0.014749368652701378,
-0.011755021288990974,
0.0327734649181366,
0.009291163645684719,
0.027880296111106873,
0.058403875678777695,
-0.01477323193103075,
-0.02389714866876602,
0.008809730410575867,
-0.05142652243375778,
-0.06931920349597931,
-0.0353577584028244,
-0.017165418714284897,
0.047453440725803375,
-0.0040953014977276325,
0.03277895599603653,
0.02296716347336769,
-0.04723921790719032,
-0.016426315531134605,
-0.01390827540308237,
-0.035400357097387314,
0.027056455612182617,
-0.021186085417866707,
0.03804779797792435,
-0.0003435258404351771,
-0.03101445361971855,
0.0481940321624279,
0.05116723105311394,
-0.027936046943068504,
-0.0447508729994297,
0.009027362801134586,
-0.022848594933748245,
-0.034145381301641464,
-0.00727972062304616,
0.010450311005115509,
0.013385521247982979,
0.027091918513178825,
0.05429970100522041,
0.02367381937801838,
0.023315582424402237,
0.036499954760074615,
0.019502341747283936,
-0.005367734935134649,
0.005005657207220793,
0.0012560520553961396,
0.018878191709518433,
0.03307225555181503,
-0.0055773695930838585,
-0.03263980150222778,
-0.007497606333345175,
0.024967389181256294,
0.02899755723774433,
-0.02240675315260887,
0.07470499724149704,
0.008728127926588058,
-0.02210819348692894,
-0.0012087906943634152,
0.034201182425022125,
-0.006719399243593216,
-0.0036899130791425705,
-0.008927051909267902,
0.01134358998388052,
0.03376094996929169,
0.008924534544348717,
0.014858614653348923,
0.05461522936820984,
0.026039164513349533,
-0.04642394930124283,
0.02148747444152832,
0.025724539533257484,
0.021283438429236412,
0.06339631229639053,
-0.018558412790298462,
-0.030448943376541138,
0.036503057926893234,
0.01964012160897255,
0.00010827904770849273,
0.022178133949637413,
-0.053564466536045074,
0.01945812627673149,
-0.0605737678706646,
-0.009422671049833298,
0.0034938915632665157,
0.03638054430484772,
0.004865220747888088,
0.033923666924238205,
0.023498142138123512,
-0.008334062993526459,
0.00126199412625283,
-0.016096945852041245,
-0.0732962042093277,
0.02568068541586399,
-0.05668042600154877,
-0.038343992084264755,
-0.009400137700140476,
-0.015490366145968437,
0.011660060845315456,
0.017748652026057243,
0.0028259940445423126,
-0.024984514340758324,
-0.030601700767874718,
-0.0886547639966011,
0.02899397723376751,
-0.031003711745142937,
-0.045927420258522034,
-0.0014454424381256104,
0.04383961111307144,
0.051491882652044296,
-0.00004769361112266779,
0.044309332966804504,
0.01304889377206564,
-0.03879764303565025,
0.020864121615886688,
-0.014040963724255562,
0.01759492978453636,
0.00701187364757061,
0.024459965527057648,
0.03315110132098198,
0.008741963654756546,
-0.02361287549138069,
0.03762584924697876,
0.01297613326460123,
0.03589220717549324,
-0.014810658991336823,
-0.03549685701727867,
-0.03353608772158623,
-0.06179911643266678,
-0.03344991058111191,
0.002843828173354268,
0.07453255355358124,
-0.0025259223766624928,
0.015712961554527283,
0.02189808338880539,
0.02110658399760723,
-0.0018132395343855023,
0.007787090260535479,
0.02060915343463421,
-0.008120340295135975,
-0.002136882394552231,
-0.025031697005033493,
-0.015508062206208706,
-0.01817617192864418,
-0.01821720227599144,
0.04554517939686775,
-0.0023071591276675463,
-0.034000299870967865,
0.014757801778614521,
0.0022856551222503185,
0.008336926810443401,
-0.0247078537940979,
-0.005436438601464033,
0.005615553352981806,
0.04486905410885811,
0.019896669313311577,
0.002226849552243948,
-0.0116750942543149,
0.02410198748111725,
0.07662060111761093,
0.016450529918074608,
-0.015112190507352352,
-0.06321506202220917,
-0.013417527079582214,
0.032021574676036835,
0.0030726613476872444,
0.03429296612739563,
0.0016149230068549514,
-0.043536026030778885,
-0.03256915882229805,
0.06432034820318222,
-0.019477777183055878,
0.008182118646800518,
-0.008778311312198639,
-0.012602042406797409,
-0.034324098378419876,
-0.03213311359286308,
0.006379543803632259,
-0.017209898680448532,
-0.022334370762109756,
0.011520964093506336,
-0.01879865862429142,
0.012404067441821098,
0.00936770811676979,
0.010024514980614185,
0.018075430765748024,
0.01657726615667343,
0.0050393142737448215,
0.05187612771987915,
-0.01839001663029194,
0.03510097786784172,
-0.03947073593735695,
-0.06472202390432358,
0.017671335488557816,
0.05568790063261986,
-0.02608763985335827,
0.03507673740386963,
-0.013329201377928257,
-0.012756071984767914,
0.005487221293151379,
-0.01971002109348774,
-0.007717300206422806,
0.031767647713422775,
-0.005603656638413668,
0.016689501702785492,
0.001042419346049428,
-0.007101904600858688,
0.026193326339125633,
0.012128210626542568,
0.02694244310259819,
0.016442211344838142,
-0.007141587324440479,
0.05623627081513405,
-0.025076890364289284,
0.016739653423428535,
0.005262603983283043,
-0.03680282086133957,
-0.021937167271971703,
0.0680093988776207,
-0.019226133823394775,
0.0005329593550413847,
0.02753995917737484,
-0.020684320479631424,
0.0212642140686512,
0.01688493974506855,
0.0021832298953086138,
0.010467895306646824,
-0.008548596873879433,
0.013020225800573826,
-0.023146463558077812,
-0.02607157453894615,
0.02980145439505577,
-0.0012621928472071886,
-0.007110347039997578,
0.02048085629940033,
-0.021864017471671104,
0.04034997522830963,
-0.0380488745868206,
-0.026306364685297012,
0.0076213120482862,
-0.0527166947722435,
0.03389877825975418,
0.009586852043867111,
-0.010817235335707664,
0.037414390593767166,
-0.06254319101572037,
-0.03552313894033432,
-0.02360229566693306,
-0.013521297834813595,
0.024354523047804832,
-0.05888767167925835,
0.01824915036559105,
0.014405644498765469,
0.0034346177708357573,
-0.07589752972126007,
-0.06628350913524628,
0.025269638746976852,
-0.0028742249123752117,
-0.005592093337327242,
-0.026145216077566147,
0.014533971436321735,
-0.0449698306620121,
-0.019264137372374535,
-0.041090015321969986,
0.017293361946940422,
-0.03206907585263252,
-0.01979493536055088,
0.018016427755355835,
-0.006980667356401682,
0.06494993716478348,
-0.007161527406424284,
0.011419335380196571,
0.008494195528328419,
0.017181750386953354,
-0.0011792700970545411,
-0.013153095729649067,
0.063114695250988,
-0.01041056215763092,
-0.019102204591035843,
-0.015808405354619026,
-0.024034179747104645,
-0.002814557170495391,
-0.045222461223602295,
0.0020820950157940388,
0.047256410121917725,
0.0038806975353509188,
0.023555932566523552,
-0.007804002612829208,
-0.02702218107879162,
-0.006011627614498138,
0.007962082512676716,
-0.02141864039003849,
0.008332010358572006,
0.03179395571351051,
-0.08214110881090164,
0.04240676388144493,
0.00045194802805781364,
0.014065192081034184,
0.00360120995901525,
0.023152848705649376,
0.009082615375518799,
-0.015315603464841843,
0.018990492448210716,
-0.012538895010948181,
0.012564205564558506,
-0.019770989194512367,
0.018105434253811836,
-0.018705036491155624,
0.0005812488961964846,
-0.03440123423933983,
-0.04570911452174187,
-0.040145426988601685,
0.0024138870649039745,
0.04543841630220413,
-0.017840171232819557,
0.03988869488239288,
0.08105028420686722,
-0.01624384894967079,
-0.007933242246508598,
-0.03248709812760353,
0.05682859942317009,
0.03297562524676323,
-0.018777189776301384,
0.016334455460309982,
-0.0157470740377903,
0.007179935462772846,
0.03228137642145157,
0.02588477171957493,
-0.03048957884311676,
0.03388658165931702,
0.02697911113500595,
0.012389866635203362,
0.025815105065703392,
0.03300957754254341,
-0.04220118373632431,
0.020172346383333206,
-0.02632995881140232,
0.01912532187998295,
-0.02099165879189968,
0.0035978311207145452,
0.027637900784611702,
0.005409709643572569,
0.04037455841898918,
-0.009850660338997841,
-0.026404736563563347,
-0.048034701496362686,
-0.010765441693365574,
0.02011922560632229,
0.03337518870830536,
-0.014251258224248886,
-0.008647406473755836,
0.04141998663544655,
-0.006988163571804762,
0.02054610103368759,
-0.035923104733228683,
-0.0586242750287056,
-0.0264817476272583,
-0.0464649461209774,
-0.02975894883275032,
0.03839729353785515,
-0.006064190529286861,
-0.018757367506623268,
-0.024855701252818108,
-0.03723066672682762,
0.009574384428560734,
0.04205206781625748,
0.04877655208110809,
-0.036737341433763504,
0.07378201931715012,
-0.01157782319933176,
-0.01107704732567072,
-0.020864861086010933,
0.011700105853378773,
0.10856878012418747,
0.03944294899702072,
0.0006128628156147897,
-0.06296108663082123,
-0.0034935306757688522,
-0.017643455415964127,
0.011300026439130306,
-0.05699734389781952,
0.02335481531918049,
-0.007114817854017019,
0.01849147118628025,
0.0290572177618742,
0.06286988407373428,
0.01793994940817356,
-0.032027117908000946,
0.061994198709726334,
-0.0433230996131897,
-0.03799949213862419,
0.010626844130456448,
0.030337918549776077,
-0.01797996275126934,
0.026847567409276962,
-0.034100715070962906,
0.05864030495285988,
-0.03073098510503769,
0.024637728929519653,
-0.02843453921377659,
-0.01103999838232994,
0.011317637749016285,
0.016769705340266228,
-0.03675882890820503,
0.025886673480272293,
0.014996049925684929,
-0.0324426107108593,
-0.07275068759918213,
-0.007587567903101444,
0.030323047190904617,
0.013938458636403084,
0.0209247637540102,
0.047870147973299026,
0.0037113758735358715,
0.021005826070904732,
0.016686636954545975,
-0.013626624830067158,
-0.043787624686956406,
0.008208406157791615,
-0.034510016441345215,
0.033169448375701904,
0.010375057347118855,
0.011862371116876602,
-0.004513187799602747,
0.0004100388032384217,
0.002461789408698678,
-0.08301638811826706,
-0.020149890333414078,
-0.0121107567101717,
0.023965058848261833,
0.042904071509838104,
-0.01745985820889473,
-0.022944621741771698,
0.018541885539889336,
-0.02653181552886963,
-0.0006393533549271524,
-0.052596304565668106,
-0.014116451144218445,
-0.002486930461600423,
-0.00047488248674198985,
0.012928363867104053,
-0.006261143367737532,
-0.013367223553359509,
-0.04074491560459137,
-0.022204242646694183,
-0.012645182199776173,
-0.02076832205057144,
0.005418090615421534,
0.01655000075697899,
0.0673992857336998,
0.002400347962975502,
0.013442650437355042,
0.03734558820724487,
-0.07768276333808899,
-0.017123082652688026,
-0.019506022334098816,
-0.02271677367389202,
-0.014089889824390411,
-0.004589130636304617,
0.028633922338485718,
0.04295244812965393,
-0.0074815647676587105,
-0.03937366232275963,
-0.005079325754195452,
0.0011187901254743338,
0.019926052540540695,
-0.022528650239109993,
0.02758042700588703,
0.013997186906635761,
-0.0004522653471212834,
-0.0020057738292962313,
-0.054855018854141235,
0.04757154732942581,
0.05158170312643051,
0.013839133083820343,
-0.020411057397723198,
0.0346636101603508,
0.020556338131427765,
0.030079180374741554,
0.015293991193175316,
-0.006558621767908335,
-0.0023828712292015553,
0.01603429578244686,
0.021827470511198044,
-0.04501572996377945,
-0.028542177751660347,
-0.044860828667879105,
0.009030832909047604,
-0.01673990674316883,
-0.005998889449983835,
-0.007764255627989769,
-0.0048103369772434235,
-0.018514055758714676,
-0.003556903451681137,
-0.017209453508257866,
-0.012536143884062767,
-0.044207263737916946,
-0.024410758167505264,
0.012328536249697208,
-0.022096779197454453,
0.04250582307577133,
0.01705080457031727,
-0.020951470360159874,
-0.04305766150355339,
0.038546450436115265,
0.008556291460990906,
-0.03893215209245682,
-0.014168617315590382,
0.006091974209994078,
0.0010705959284678102,
0.03954031690955162,
-0.012402310967445374,
-0.053629349917173386,
0.03629620745778084,
-0.05697229504585266,
-0.044355764985084534,
0.04627927392721176,
-0.023604651913046837,
0.039607878774404526,
0.021760428324341774,
-0.006488454528152943,
-0.019426662474870682,
0.06283243000507355,
0.002268752781674266,
0.03017534129321575,
0.029842467978596687,
-0.03605625405907631,
0.007873406633734703,
0.016896819695830345,
0.05025209113955498,
0.001651297090575099,
-0.010885107330977917,
-0.0066965254954993725,
0.034629229456186295,
0.0037086198572069407,
-0.04133361577987671,
-0.00481096375733614,
-0.05813894048333168,
-0.010742051526904106,
0.007129653822630644,
0.01644277386367321,
0.06370415538549423,
0.05098186805844307,
-0.04023071005940437,
-0.0005379559588618577,
0.03504322096705437,
-0.0060992795042693615,
-0.1223558858036995,
0.012453275732696056,
0.010556142777204514,
-0.004799962043762207,
0.010799859650433064,
-0.03979012370109558,
0.0420658104121685,
0.057269658893346786,
-0.05932538956403732,
0.02252812869846821,
-0.0008277360466308892,
-0.027888856828212738,
-0.04401812702417374,
-0.011662439443171024,
-0.0018821123521775007,
0.051631178706884384,
0.044086478650569916,
0.03272005543112755,
-0.0004774473200086504,
0.011312904767692089,
-0.044791460037231445,
-0.00007656589150428772,
-0.030625250190496445,
0.024222025647759438,
-0.008971811272203922,
-0.03616834059357643,
0.03637683019042015,
0.008732108399271965,
-0.05070428550243378,
0.02837677113711834,
-0.002131605986505747,
-0.027083002030849457,
0.0008422419778071344,
-0.0030099155846983194,
0.03477572649717331,
-0.0037993264850229025,
0.03495746850967407,
0.005307457409799099,
-0.009312892332673073,
0.05550771579146385,
0.013821946457028389,
-0.02390996739268303,
-0.02309737540781498,
-0.020453641191124916,
0.0056239040568470955,
-0.07399241626262665,
-0.028122326359152794,
0.00786367803812027,
-0.01621902547776699,
-0.004338047467172146,
-0.030090318992733955,
-0.0056186034344136715,
0.0029505116399377584,
-0.001177205704152584,
0.004459911957383156,
-0.045559659600257874,
-0.021729089319705963,
0.06795193254947662,
0.006705642212182283,
0.0010349373333156109,
0.00946983601897955,
-0.007516347337514162,
-0.011219131760299206,
0.004360836930572987,
-0.012506322003901005,
-0.005659529473632574,
-0.04124396666884422,
-0.002276067389175296,
-0.00934805627912283,
-0.00834459438920021,
0.010746174491941929,
-0.05420374870300293,
-0.008993599563837051,
0.037718795239925385,
0.04774416610598564,
0.006554633378982544,
0.01803862862288952,
-0.0277370847761631,
-0.046302586793899536,
-0.05461534485220909,
0.008688858710229397,
0.018370386213064194,
-0.015438085421919823,
-0.030392952263355255,
0.030669720843434334,
-0.05133550614118576,
0.018429573625326157,
0.05621738359332085,
-0.0015914369141682982,
0.025618618354201317,
0.024377623572945595,
0.0028305479791015387,
0.012434296309947968,
-0.061821285635232925,
-0.005453935358673334,
-0.03849828988313675,
-0.01563849486410618,
0.009977315552532673,
-0.012972759082913399,
-0.010225649923086166,
0.013840918429195881,
-0.017717279493808746,
-0.009889242239296436,
0.035981420427560806,
-0.024090223014354706,
-0.050028350204229355,
0.046383969485759735,
0.042752742767333984,
-0.007710475940257311,
0.05344073846936226,
-0.013257760554552078,
0.01094056200236082,
0.02117225155234337,
0.000955166993662715,
0.011872907169163227,
0.014126278460025787,
-0.017206678166985512,
-0.012201550416648388,
-0.01249309629201889,
-0.013261158019304276,
-0.007337639108300209,
-0.023097779601812363,
-0.022616328671574593,
0.04821962118148804,
-0.008402136154472828,
-0.03822220861911774,
0.03925754874944687,
0.02186707966029644,
0.027093160897493362,
-0.03314443677663803,
-0.0278969444334507,
0.020534075796604156,
0.004396346863359213,
0.009601081721484661,
0.049193400889635086,
0.0246826633810997,
0.0018589471001178026,
-0.001998852239921689,
0.029726771637797356,
-0.021047649905085564,
0.010211254470050335,
0.008038812316954136,
0.08169732242822647,
-0.012445214204490185,
0.00479474663734436,
-0.018748747184872627,
-0.02073702961206436,
0.01995811238884926,
0.024908699095249176,
-0.02432280220091343,
0.04637935757637024,
-0.03184168413281441,
-0.005602335557341576,
-0.0031571106519550085,
0.015457943081855774,
-0.04695799946784973,
0.03763152286410332,
0.031411394476890564,
0.02507796883583069,
-0.0006877356790937483,
-0.0038716639392077923,
-0.03818465769290924,
0.004447457380592823,
0.0286871250718832,
-0.02813323773443699,
0.021877087652683258,
0.003515467746183276,
0.014962928369641304,
0.0007310372893698514,
0.02279321849346161,
-0.036363597959280014,
-0.031964730471372604,
0.03326260298490524,
0.020245645195245743,
0.07042735069990158,
-0.039007578045129776,
-0.01077857706695795,
-0.04834144562482834,
0.059564366936683655,
-0.07595428824424744,
-0.000544160429853946,
-0.015531684271991253,
0.020008936524391174,
-0.032973457127809525,
0.00881381705403328
] |
<p>I know that standing waves in a simple harmonic system occur when the "echo" of a wave overlaps completely with the original wave at a certain point in time, doubling the amplitude. And then, because both waves have the same speed and frequency but opposite direction, they move away from eachother until they cancel eachother out, and then keep moving until they overlap again to amplify the signal. </p>
<p>But what happens halfway between two harmonics? Would it be like a half standing wave, or would the signal cancel out?</p>
| 8,300 |
[
0.02092384733259678,
-0.035188086330890656,
0.019850434735417366,
-0.017904018983244896,
0.004497642163187265,
0.013070749118924141,
-0.012299776077270508,
-0.04338453337550163,
0.03539399802684784,
0.0009944860357791185,
0.033553678542375565,
0.0385500006377697,
0.03617589920759201,
0.0031502624042332172,
0.02502298168838024,
-0.0007513082236982882,
-0.018366316333413124,
-0.044370412826538086,
-0.009541851468384266,
-0.036398906260728836,
-0.02327006869018078,
0.008591794408857822,
0.0066793556325137615,
-0.001376795582473278,
-0.062653549015522,
0.01669273152947426,
0.03869098052382469,
0.017484251409769058,
0.02876446396112442,
0.03603575751185417,
0.003918914124369621,
-0.04679425060749054,
-0.024427203461527824,
0.06719318777322769,
0.02990654669702053,
0.007160081993788481,
-0.04038238525390625,
-0.04769255593419075,
-0.0029872991144657135,
0.042282477021217346,
-0.028436968103051186,
0.033016446977853775,
-0.03725828602910042,
0.03209635242819786,
-0.04586412012577057,
-0.024235378950834274,
0.02729513682425022,
-0.020315568894147873,
0.0632973313331604,
-0.05419116094708443,
0.05540226772427559,
0.009356138296425343,
0.026312410831451416,
0.0041364822536706924,
0.03078315034508705,
0.0463106706738472,
0.07030143588781357,
0.07806096971035004,
0.005814235657453537,
-0.06385917216539383,
-0.02106582373380661,
-0.01835586316883564,
-0.046430349349975586,
-0.028955107554793358,
-0.03997980058193207,
0.03934980556368828,
0.0031591211445629597,
-0.029454154893755913,
0.022211551666259766,
-0.01567598059773445,
-0.0188465416431427,
-0.002339709782972932,
0.04278365895152092,
-0.06632271409034729,
0.020334862172603607,
-0.05742153525352478,
0.045653630048036575,
0.000570033211261034,
-0.006142377387732267,
0.03499205410480499,
-0.002412803005427122,
-0.01045127771794796,
-0.019004488363862038,
0.07186989486217499,
-0.017963625490665436,
-0.016897795721888542,
0.07254583388566971,
-0.007433059625327587,
-0.019621143117547035,
0.025447584688663483,
0.006109081208705902,
0.013550040312111378,
0.02897951565682888,
0.01227012649178505,
-0.03971167281270027,
0.016363253816962242,
0.012223577126860619,
0.058626286685466766,
0.05757841840386391,
-0.013407474383711815,
0.044721782207489014,
-0.037610821425914764,
0.05469389259815216,
0.06789525598287582,
0.02227894961833954,
-0.024891018867492676,
-0.06288058310747147,
0.019747145473957062,
-0.02180827036499977,
0.012587323784828186,
-0.03566674515604973,
0.011267642490565777,
0.015109998174011707,
0.0021764342673122883,
0.02170003391802311,
0.02159722149372101,
0.025936372578144073,
-0.016406306996941566,
0.04740290716290474,
0.060541458427906036,
0.03646283596754074,
-0.01774931140244007,
0.0022216036450117826,
0.0008184988982975483,
-0.07406354695558548,
-0.0002287411771249026,
-0.006668645888566971,
-0.035105735063552856,
-0.07127632945775986,
0.049548715353012085,
0.021066511049866676,
-0.008467152714729309,
0.010021205060184002,
-0.02321368269622326,
0.05388617143034935,
-0.011620509438216686,
-0.0723106861114502,
-0.04611600562930107,
0.02636055462062359,
-0.031033962965011597,
-0.009209899231791496,
-0.09893731772899628,
0.0011106280144304037,
0.05072157084941864,
0.09090312570333481,
0.004241759888827801,
-0.004610167350620031,
-0.005009915214031935,
0.03586445748806,
0.035200171172618866,
-0.00959960650652647,
-0.02710084058344364,
0.006641607265919447,
-0.013452302664518356,
0.027046572417020798,
-0.03634633496403694,
0.011646637693047523,
0.030391113832592964,
-0.013228880241513252,
-0.009370791725814342,
0.0515296533703804,
-0.0007721541915088892,
-0.025588661432266235,
0.021645167842507362,
-0.05860362946987152,
-0.025755546987056732,
0.10905584692955017,
-0.015160603448748589,
-0.03924248740077019,
0.03391626849770546,
-0.006470173597335815,
0.01808038540184498,
-0.021868053823709488,
0.05404198542237282,
0.021289817988872528,
-0.0014690059470012784,
-0.00913129560649395,
-0.019068360328674316,
0.02555134706199169,
0.02084360457956791,
-0.030719535425305367,
-0.04226063936948776,
0.02046957053244114,
0.05813569948077202,
-0.009592532180249691,
0.026804829016327858,
-0.013058834709227085,
0.010886534117162228,
-0.01086124312132597,
-0.044022057205438614,
-0.00758802006021142,
-0.04365278780460358,
0.017127709463238716,
0.004401967860758305,
-0.02834307588636875,
0.018219374120235443,
0.048656851053237915,
0.04037386551499367,
-0.06632062792778015,
-0.03147638961672783,
-0.011011425405740738,
0.025170253589749336,
0.01015796884894371,
-0.017055995762348175,
0.039815932512283325,
0.06679574400186539,
0.026932507753372192,
0.016366492956876755,
0.04226761311292648,
-0.018294624984264374,
0.00865885429084301,
-0.00876870471984148,
-0.006424587685614824,
0.05500881001353264,
-0.02996688149869442,
0.0060380203649401665,
-0.004401324782520533,
-0.009042439050972462,
0.018067684024572372,
0.021869687363505363,
-0.024458589032292366,
0.04373236000537872,
0.05791454762220383,
-0.024661771953105927,
-0.006773280445486307,
0.011154133826494217,
0.0070910267531871796,
0.008291775360703468,
0.01013797614723444,
-0.03548557311296463,
-0.020756568759679794,
-0.007632295601069927,
0.05030414089560509,
0.004842568188905716,
-0.010729342699050903,
0.018286297097802162,
0.009847762994468212,
0.03126157075166702,
0.06678950041532516,
0.028597086668014526,
0.00392694678157568,
-0.02103150449693203,
0.0032144219148904085,
0.006526296027004719,
0.004221932962536812,
0.0030191047117114067,
0.06247768551111221,
0.007767697796225548,
0.0064269984140992165,
-0.005877647548913956,
-0.054894402623176575,
0.027825141325592995,
0.006281947251409292,
0.04403494670987129,
-0.025763479992747307,
-0.025578303262591362,
0.014502367004752159,
0.004414656665176153,
0.009186040610074997,
0.006917168851941824,
-0.022290151566267014,
-0.0023603339213877916,
-0.013665654696524143,
0.02313879504799843,
-0.009333833120763302,
0.005075240507721901,
-0.02116207964718342,
-0.027203956618905067,
0.010106213390827179,
-0.06539129465818405,
0.005739549174904823,
-0.026797624304890633,
-0.017992112785577774,
0.014750869013369083,
-0.031542904675006866,
0.06820757687091827,
0.018424896523356438,
0.08138646185398102,
-0.05072852596640587,
-0.0462113618850708,
-0.007469472009688616,
-0.04398706927895546,
0.0405317060649395,
-0.0009577452437952161,
-0.014581207185983658,
-0.007349906489253044,
-0.04946332424879074,
-0.018260514363646507,
0.02410266362130642,
0.0033022568095475435,
0.015207997523248196,
0.010578354820609093,
-0.05956070125102997,
-0.061679743230342865,
-0.04128965362906456,
-0.026639902964234352,
0.02126489207148552,
-0.034184060990810394,
0.006605926901102066,
0.03864513710141182,
0.033418480306863785,
-0.04040636867284775,
0.010645654052495956,
0.002088662702590227,
-0.025522733107209206,
-0.014326917938888073,
0.0045157731510698795,
0.02812066301703453,
-0.07177533954381943,
0.04814162850379944,
-0.029412653297185898,
-0.05483807995915413,
0.02027265541255474,
-0.03031686134636402,
-0.04636996239423752,
0.026644596830010414,
0.002644103951752186,
0.05096740648150444,
0.008137039840221405,
-0.04573524743318558,
0.06287336349487305,
-0.025287838652729988,
0.01639309525489807,
0.000025992141672759317,
0.006971235852688551,
0.0103068295866251,
0.02474035881459713,
0.03460367023944855,
0.042452793568372726,
-0.020235413685441017,
0.03734435886144638,
-0.011812116019427776,
0.012326923198997974,
0.07156352698802948,
0.009504429064691067,
0.016616128385066986,
-0.015458234585821629,
0.00037112957215867937,
0.03089733235538006,
0.032763492316007614,
-0.00849851593375206,
-0.014074180275201797,
0.02561679109930992,
-0.0028334958478808403,
0.0038492348976433277,
0.016344117000699043,
-0.03799036890268326,
0.0438363216817379,
-0.02634279802441597,
-0.015934770926833153,
-0.037185072898864746,
0.05394876375794411,
0.040362484753131866,
0.021989988163113594,
-0.05220382288098335,
0.024976305663585663,
0.06032377853989601,
-0.02032097429037094,
-0.01636401005089283,
0.0007059862837195396,
0.03191152587532997,
-0.045833032578229904,
-0.017938019707798958,
-0.005557228345423937,
-0.00816583726555109,
0.03250224143266678,
-0.024801645427942276,
-0.04994640499353409,
0.06675645709037781,
0.0073995282873511314,
-0.005865118000656366,
0.02564161643385887,
-0.03606737405061722,
-0.03615911304950714,
-0.06662213802337646,
-0.015231841243803501,
-0.003926839679479599,
0.01599215716123581,
-0.013277401216328144,
0.05817287042737007,
0.03761925548315048,
0.039377808570861816,
0.0314444899559021,
0.016733340919017792,
-0.06531601399183273,
-0.005638680886477232,
-0.033042654395103455,
-0.01042262278497219,
-0.01806824654340744,
0.022677714005112648,
0.0017342184437438846,
0.004832015372812748,
-0.043973032385110855,
-0.03635717183351517,
-0.026471944525837898,
-0.06044258549809456,
0.014032594859600067,
-0.0076212333515286446,
-0.011092926375567913,
-0.013444634154438972,
0.011528060771524906,
-0.01912141963839531,
-0.009847460314631462,
0.0008437164360657334,
0.0187179297208786,
-0.020494628697633743,
0.019182750955224037,
0.0045968955382704735,
-0.01182826329022646,
0.0037118783220648766,
-0.0014005322009325027,
0.044310063123703,
0.05344393476843834,
-0.012619963847100735,
-0.005541285965591669,
0.011473015882074833,
0.08266487717628479,
0.015216970816254616,
0.006620822474360466,
0.012427428737282753,
-0.015461317263543606,
-0.021470321342349052,
-0.025628138333559036,
0.04634014517068863,
-0.019638163968920708,
-0.01589844562113285,
-0.0209632758051157,
0.017154453322291374,
-0.03530409559607506,
0.06898117810487747,
0.03683933988213539,
0.032960280776023865,
-0.0011405438417568803,
-0.068287692964077,
-0.013621330261230469,
-0.03228641301393509,
-0.012966546230018139,
0.007231592200696468,
-0.041260313242673874,
0.007134882267564535,
0.006915010046213865,
0.01271914690732956,
0.04520175978541374,
-0.00031885248608887196,
0.01742023043334484,
-0.0033717395272105932,
-0.008741043508052826,
-0.027281293645501137,
-0.019872067496180534,
-0.0028435217682272196,
0.02954200468957424,
0.048607297241687775,
0.0089078638702631,
0.0014197810087352991,
-0.07363907247781754,
-0.0054990085773169994,
0.036251794546842575,
0.01429765298962593,
-0.019747721031308174,
0.02728898450732231,
-0.04880329966545105,
-0.05301306024193764,
0.024007698521018028,
-0.02524825558066368,
0.03571230173110962,
-0.042060863226652145,
-0.03254428133368492,
-0.013452202081680298,
0.0139057207852602,
-0.02454741671681404,
0.011059966869652271,
-0.00190652662422508,
0.01705011911690235,
-0.026340030133724213,
-0.03646152839064598,
-0.004121791105717421,
0.028028715401887894,
-0.006251539569348097,
0.04835600405931473,
-0.001571801956743002,
-0.007022515404969454,
0.010260021314024925,
0.02975280210375786,
-0.021046232432127,
-0.05424253270030022,
0.0008815494365990162,
0.011836080811917782,
-0.03018045239150524,
0.04875687137246132,
-0.016001680865883827,
-0.023852145299315453,
0.019321026280522346,
0.033657949417829514,
0.030945751816034317,
-0.004286083392798901,
0.020938342437148094,
0.06093856319785118,
0.026584986597299576,
0.015112500637769699,
0.06363868713378906,
0.04272455349564552,
-0.013708312064409256,
-0.023995395749807358,
0.03545273095369339,
0.05142767354846001,
-0.02903011254966259,
-0.00706397695466876,
-0.0006789177423343062,
-0.019506113603711128,
-0.0694526806473732,
0.07299618422985077,
-0.03491462767124176,
0.015351478010416031,
0.010444405488669872,
-0.012693810276687145,
0.011458451859652996,
0.027058305218815804,
-0.016173752024769783,
0.0077585275284945965,
-0.0015167766250669956,
0.024339934810996056,
-0.01216253824532032,
-0.021223394200205803,
0.007730321492999792,
-0.015009589493274689,
0.01760890707373619,
0.025314562022686005,
-0.011025629937648773,
0.010993951000273228,
-0.0452582910656929,
0.014854924753308296,
0.024826260283589363,
-0.01950962096452713,
0.023961877450346947,
-0.0434880256652832,
-0.007017984054982662,
0.001892207539640367,
-0.03984682261943817,
-0.03365996852517128,
0.04293300211429596,
-0.02628103643655777,
0.027302931994199753,
-0.03673281893134117,
0.07262156158685684,
0.05918540805578232,
0.0036806585267186165,
-0.05906159058213234,
-0.06534408032894135,
0.04305833578109741,
0.042966339737176895,
-0.020901085808873177,
-0.01825091801583767,
0.006441342178732157,
-0.0009509481023997068,
-0.02167961560189724,
0.007876113057136536,
0.0031289500184357166,
-0.04719958081841469,
-0.013645092025399208,
-0.008373145014047623,
-0.02452107146382332,
0.020495649427175522,
0.005876386072486639,
-0.03322271630167961,
0.010518922470510006,
-0.025179285556077957,
-0.03015032224357128,
-0.019010845571756363,
0.06460817158222198,
-0.023350536823272705,
-0.013732222840189934,
-0.016040295362472534,
-0.01784908026456833,
0.012433723546564579,
-0.04769424349069595,
-0.05487445369362831,
0.008983383886516094,
0.008248034864664078,
0.03588470444083214,
-0.013993454165756702,
0.003646814962849021,
-0.02197553589940071,
0.023259080946445465,
-0.001778693520464003,
-0.018447456881403923,
-0.005981578957289457,
-0.03552977740764618,
-0.02565823495388031,
0.00904896017163992,
-0.025375042110681534,
-0.047018762677907944,
0.05701151117682457,
-0.00998457707464695,
0.007457680534571409,
0.0023800726048648357,
-0.015080941841006279,
0.025664597749710083,
-0.023071445524692535,
0.018437828868627548,
0.02480427362024784,
0.010187323205173016,
-0.011949039995670319,
-0.03484073653817177,
-0.023400677368044853,
-0.027058128267526627,
0.07634472101926804,
-0.05217568203806877,
0.025141283869743347,
0.035451021045446396,
-0.0040496354922652245,
-0.014054479077458382,
-0.018321512266993523,
-0.012593712657690048,
-0.01749810203909874,
0.009560362435877323,
0.0372273251414299,
-0.04723018407821655,
-0.003918719477951527,
0.010143606923520565,
0.07957431674003601,
0.008557518944144249,
0.043115727603435516,
0.035234324634075165,
0.04275309294462204,
0.022022459656000137,
0.03660006448626518,
-0.030634742230176926,
0.03818134963512421,
-0.031070822849869728,
0.04070008173584938,
0.0275289174169302,
0.01197026390582323,
0.04438592121005058,
0.020432794466614723,
0.02855944260954857,
-0.05892311409115791,
0.0013431318802759051,
-0.03532771021127701,
0.015803368762135506,
-0.015548501163721085,
0.008995217271149158,
0.019162461161613464,
-0.0069909291341900826,
0.016674170270562172,
0.018811432644724846,
0.007899614050984383,
-0.011561195366084576,
-0.030164960771799088,
-0.03531189635396004,
-0.010380666702985764,
-0.03416728973388672,
0.01246781088411808,
-0.003668063785880804,
-0.021540077403187752,
0.019138634204864502,
-0.020823601633310318,
0.012768393382430077,
-0.0021590206306427717,
0.004707442596554756,
-0.036166392266750336,
0.05026177316904068,
0.045662496238946915,
0.03205076977610588,
-0.00968141295015812,
0.0031858538277447224,
0.13585785031318665,
0.04270557686686516,
0.019016539677977562,
-0.061884380877017975,
0.013144266791641712,
-0.022814569994807243,
0.024909885600209236,
-0.03843458741903305,
-0.018750716000795364,
-0.010039213113486767,
-0.007458268199115992,
0.02923627197742462,
0.06307405978441238,
-0.005388658028095961,
0.018291490152478218,
0.0491594597697258,
-0.010000830516219139,
-0.017872372642159462,
0.016590049490332603,
0.007495718076825142,
-0.017291810363531113,
0.0239255428314209,
-0.031506188213825226,
0.012638997286558151,
-0.021265989169478416,
-0.00029189002816565335,
-0.047403205186128616,
-0.05969620123505592,
0.03765901178121567,
0.054845888167619705,
-0.046144213527441025,
0.02189689129590988,
-0.005990090314298868,
-0.007851243019104004,
-0.0067701926454901695,
0.04329203814268112,
0.02415004000067711,
0.004481540527194738,
-0.02442862093448639,
0.011624613776803017,
0.04343317449092865,
0.00395132414996624,
0.009871596470475197,
0.019494736567139626,
-0.025410152971744537,
-0.0017229964723810554,
0.00041828915709629655,
0.03252401575446129,
0.018184533342719078,
-0.009692269377410412,
-0.0225822813808918,
-0.012228304520249367,
0.010029877535998821,
-0.019587887451052666,
-0.009259359911084175,
0.007667758036404848,
0.012576923705637455,
-0.02110886573791504,
0.006841938477009535,
-0.027598103508353233,
0.020038623362779617,
0.028981752693653107,
0.00017663641483522952,
-0.003822164610028267,
-0.03768863156437874,
0.00533283781260252,
-0.013248095288872719,
0.04011846333742142,
0.002925158478319645,
-0.06252056360244751,
-0.010774640366435051,
0.007360453251749277,
-0.05021650344133377,
-0.004490818828344345,
0.012758739292621613,
0.007513995282351971,
0.03022751584649086,
0.026549765840172768,
-0.05871997028589249,
-0.01958581991493702,
-0.06753384321928024,
0.04108917713165283,
0.015748942270874977,
-0.02541828155517578,
0.00042314507300034165,
-0.008518047630786896,
0.03024945594370365,
0.017131343483924866,
-0.05178787186741829,
0.022029228508472443,
-0.0023943032138049603,
0.015333209186792374,
0.015116352587938309,
-0.05956938490271568,
-0.014698304235935211,
0.03778095543384552,
0.010696396231651306,
-0.0040984791703522205,
-0.0173928365111351,
0.026497172191739082,
0.02552628703415394,
0.024416813626885414,
0.016513420268893242,
0.03617195785045624,
-0.05177334323525429,
-0.0442812405526638,
-0.021198023110628128,
-0.031225595623254776,
-0.0139518016949296,
0.01836887001991272,
0.029417648911476135,
-0.05986306816339493,
-0.031493544578552246,
0.0009415976237505674,
0.008637147024273872,
-0.004176478832960129,
0.019635280594229698,
-0.0188904982060194,
0.02143711782991886,
0.024996275082230568,
-0.0007687779143452644,
0.005740093998610973,
-0.02218996174633503,
-0.05561939999461174,
0.0061234887689352036,
0.011710884049534798,
0.011129775084555149,
-0.011841642670333385,
-0.00401837145909667,
-0.021502135321497917,
-0.04405185952782631,
0.03304847329854965,
0.022022243589162827,
0.02853967435657978,
0.025210503488779068,
0.03055677004158497,
-0.023867757990956306,
-0.0011584139429032803,
0.0013849131064489484,
-0.030590804293751717,
0.03889026120305061,
-0.02094408869743347,
-0.025827400386333466,
0.03386610001325607,
0.005738823674619198,
0.00844911951571703,
0.013102165423333645,
0.0013206457952037454,
0.02057056687772274,
0.021981174126267433,
0.03062533587217331,
-0.0019352593226358294,
-0.028478706255555153,
-0.019898556172847748,
-0.013818339444696903,
0.03177642077207565,
0.012310069054365158,
-0.0072254096157848835,
-0.03576616197824478,
0.023161612451076508,
0.053866058588027954,
-0.02724405936896801,
-0.004761171992868185,
-0.029926396906375885,
-0.051225561648607254,
0.005428447388112545,
0.008282072842121124,
-0.008105265907943249,
0.03756231069564819,
0.024034149944782257,
0.008471549488604069,
0.023289566859602928,
0.00011983281729044393,
-0.0018744179978966713,
-0.08987749367952347,
-0.01903248019516468,
0.005178841296583414,
-0.012373428791761398,
0.007832244969904423,
-0.012248417362570763,
-0.015559213235974312,
0.040727727115154266,
-0.09262055903673172,
-0.012603385373950005,
-0.011996584944427013,
-0.019505532458424568,
-0.02120174653828144,
0.009164489805698395,
-0.02496587485074997,
0.002942920196801424,
0.005285502877086401,
0.03776869550347328,
0.0035878736525774,
-0.015747757628560066,
-0.04608792066574097,
-0.014828747138381004,
-0.00017389967979397625,
0.034305933862924576,
0.0064000035636126995,
0.017968809232115746,
0.06783182919025421,
-0.033806126564741135,
-0.02674579806625843,
0.0703556165099144,
-0.06634876877069473,
0.016332296654582024,
-0.024439217522740364,
0.005151162855327129,
-0.013356983661651611,
0.02076549641788006,
-0.03388158604502678,
0.005339012946933508,
0.0006895935512147844,
-0.0010653812205418944,
0.05240628495812416,
0.02757461927831173,
-0.02052650786936283,
-0.023115050047636032,
0.02801039256155491,
-0.020684974268078804,
-0.04012705385684967,
0.048634279519319534,
-0.019091976806521416,
0.013178825378417969,
-0.014657081104815006,
0.022635865956544876,
0.02960912697017193,
-0.03127405792474747,
0.004177711438387632,
-0.013688606210052967,
-0.03589250147342682,
-0.014818602241575718,
0.012051713652908802,
-0.028887800872325897,
0.016391200944781303,
-0.032238513231277466,
-0.024139130488038063,
0.05322539806365967,
-0.003940128721296787,
-0.03160084784030914,
-0.069501131772995,
-0.0580783486366272,
-0.006700567435473204,
0.0036036872770637274,
0.030026668682694435,
-0.020780226215720177,
-0.012017576023936272,
0.028710873797535896,
0.0345708429813385,
0.029349716380238533,
-0.01693933829665184,
-0.04851153865456581,
-0.05163656547665596,
-0.06353409588336945,
0.037116777151823044,
0.003852789755910635,
0.011245427653193474,
-0.04804535210132599,
-0.007450018543750048,
0.0035068707074970007,
0.00038723641773685813,
0.04621891677379608,
0.029320688918232918,
0.004901823587715626,
0.010555648244917393,
-0.045437268912792206,
0.024406662210822105,
-0.02957402728497982,
-0.029747532680630684,
-0.0005145978066138923,
-0.01094136480242014,
-0.008613502606749535,
-0.018143819645047188,
-0.026100339367985725,
0.01354326494038105,
0.02264108695089817,
-0.024855591356754303,
0.028143659234046936,
-0.0353555791079998,
-0.02659275010228157,
0.019875846803188324,
0.041030239313840866,
-0.05444665998220444,
0.04931119829416275,
-0.008640001527965069,
-0.009708079509437084,
0.01222404558211565,
-0.04513232782483101,
-0.070211261510849,
0.007559939753264189,
-0.007200708147138357,
0.018433796241879463,
-0.013050387613475323,
0.00905941054224968,
0.016937538981437683,
-0.03235188499093056,
-0.007200479507446289,
0.01920517161488533,
-0.007192875724285841,
0.023638635873794556,
0.05150346830487251,
0.025326469913125038,
0.010966096073389053,
-0.018296580761671066,
0.009298673830926418,
0.006009229458868504,
0.02495081163942814,
0.023271750658750534,
-0.00009673000749899074,
-0.020052684471011162,
0.02071780152618885,
0.000308025861158967,
-0.010900866240262985,
0.01839430257678032,
0.018588518723845482,
-0.003978749271482229,
0.012424526736140251,
-0.003121007001027465,
-0.0165459755808115,
0.0006689930451102555,
-0.03278862312436104,
0.012976924888789654,
0.04550120607018471,
0.022434070706367493,
0.06898622214794159,
-0.0218855831772089,
0.049707572907209396,
-0.01847764477133751,
0.014324975199997425,
0.00208028475753963,
-0.042760275304317474,
0.01496243104338646,
0.02109518274664879,
-0.035060081630945206,
-0.014571791514754295,
-0.0012855249224230647,
0.010441591031849384,
0.03744271397590637,
-0.044981375336647034,
0.031243061646819115,
-0.04044359549880028,
-0.0016816339921206236,
0.017933150753378868,
-0.0008770438143983483,
-0.04282242804765701,
0.017033254727721214,
0.04846016690135002,
0.043266620486974716,
-0.006293496582657099,
0.03416527435183525,
-0.009460242465138435,
-0.023568162694573402,
0.017493365332484245,
-0.07107585668563843,
-0.0066903880797326565,
-0.012144450098276138,
0.002939569065347314,
-0.008653108030557632,
-0.017558852210640907
] |
<p>Suppose a plasma has characteristic frequency $\omega_p$. Since </p>
<p>$$n = \sqrt{\left(1-\frac{\omega_p^2}{\omega^2}\right)} $$</p>
<p>For $\omega<\omega_p$, the refractive index will be imaginary - which corresponds to absorption of light.</p>
<p>For $\omega > \omega_p$, the refractive index will be real.</p>
<p>Suppose plasma frequency is $9\: \mathrm{MHz}$. Why is it that AM radio waves ($\sim 1\: \mathrm{MHz}$) are able to be transmitted further than FM radio waves ($\sim 100\: \mathrm{MHz}$)? Isn't that counter-intuitive?</p>
| 8,301 |
[
-0.009095495566725731,
-0.057261958718299866,
0.02267594262957573,
-0.02025979571044445,
0.06480922549962997,
0.006913532968610525,
-0.01810499280691147,
-0.020762138068675995,
-0.024651356041431427,
-0.02134968712925911,
0.034557782113552094,
0.015608824789524078,
0.05127445608377457,
-0.005291356705129147,
0.006697759963572025,
0.027413789182901382,
-0.02512531727552414,
0.015987224876880646,
0.00349608575925231,
-0.010796966962516308,
-0.02574828639626503,
0.04448477178812027,
0.0068316082470119,
0.010668760165572166,
-0.05311407148838043,
0.04301915690302849,
0.017828909680247307,
0.00901266559958458,
0.05928207188844681,
0.006080167833715677,
0.014251887798309326,
0.03245038539171219,
0.030726011842489243,
0.0022288651671260595,
0.016000786796212196,
0.0273920726031065,
-0.04917025938630104,
-0.02163029834628105,
0.002040232066065073,
-0.008665041998028755,
-0.026736102998256683,
-0.028422795236110687,
-0.009787285700440407,
0.010428148321807384,
-0.008151233196258545,
-0.011527701281011105,
0.02169491909444332,
-0.013076720759272575,
0.04515015333890915,
-0.0345722995698452,
0.052362773567438126,
-0.013500005006790161,
0.06719766557216644,
0.00227930536493659,
0.0058752307668328285,
-0.02060309238731861,
0.09370994567871094,
0.0872906967997551,
0.001884758472442627,
-0.05176330730319023,
0.0054689813405275345,
0.013922314159572124,
-0.027132127434015274,
0.0061330972239375114,
-0.0020984241273254156,
0.017983263358473778,
-0.0037862120661884546,
-0.03840821981430054,
0.009971225634217262,
0.05705483257770538,
0.005468438379466534,
-0.0033813538029789925,
-0.022445162758231163,
-0.003913290333002806,
-0.009951028041541576,
-0.017184162512421608,
-0.01121206022799015,
0.024919752031564713,
0.07343745976686478,
0.02472853474318981,
-0.008644801564514637,
-0.012375714257359505,
0.01506622415035963,
0.021370146423578262,
0.009733660146594048,
-0.031354449689388275,
0.03131798282265663,
-0.003774258540943265,
0.030204130336642265,
0.049275677651166916,
-0.03285345435142517,
0.019670438021421432,
0.002560376189649105,
0.007968085817992687,
0.0018877494148910046,
0.027073482051491737,
-0.010871457867324352,
0.03307505324482918,
-0.0025261598639190197,
-0.02410508133471012,
-0.001008418039418757,
-0.019535135477781296,
0.05837876349687576,
0.06499399244785309,
0.012217506766319275,
-0.04297350347042084,
-0.06269881874322891,
0.01953100599348545,
-0.029864897951483727,
0.02811923809349537,
0.013811630196869373,
0.018026577308773994,
0.03211885690689087,
0.030635695904493332,
0.03313582390546799,
-0.03818317875266075,
0.04675060138106346,
-0.04090509191155434,
0.06367465108633041,
0.12160616368055344,
0.027582822367548943,
0.018868453800678253,
0.019368989393115044,
-0.022090880200266838,
-0.08364991843700409,
0.0075744399800896645,
-0.007703763898462057,
0.003907674457877874,
-0.00871055107563734,
-0.03502509742975235,
-0.006798668764531612,
-0.019515981897711754,
0.032475631684064865,
-0.00812858622521162,
0.038540564477443695,
-0.002303176326677203,
-0.09068997949361801,
-0.05629054084420204,
-0.009441830217838287,
-0.021470708772540092,
0.010115205310285091,
-0.08969735354185104,
0.04714391380548477,
0.02193276211619377,
0.07333538681268692,
-0.015911320224404335,
-0.007762331981211901,
-0.016869202256202698,
0.04324254393577576,
0.02477077953517437,
-0.009759362787008286,
-0.00492461584508419,
0.009721384383738041,
-0.03360191732645035,
0.00777528015896678,
-0.07155254483222961,
0.009470787830650806,
0.00997589435428381,
-0.01248677633702755,
-0.023076815530657768,
0.045229218900203705,
-0.03029317781329155,
-0.0007865902734920382,
0.004528017248958349,
-0.01608552783727646,
-0.017988640815019608,
0.09138532727956772,
0.023579066619277,
0.012234905734658241,
0.03883211687207222,
-0.004119782708585262,
0.020311545580625534,
0.012604090385138988,
0.01172466017305851,
0.033655162900686264,
-0.039541494101285934,
-0.014137815684080124,
-0.02976207807660103,
-0.006262592505663633,
0.009962962009012699,
-0.01170724630355835,
-0.05031560733914375,
0.02434159815311432,
0.041392289102077484,
0.013803800567984581,
0.04947983846068382,
-0.018026694655418396,
0.03193819150328636,
0.04575743526220322,
-0.060611918568611145,
-0.0174831785261631,
0.004140747711062431,
0.04626883566379547,
0.03397948294878006,
-0.0062734331004321575,
-0.0015549203380942345,
-0.02590463124215603,
-0.017812591046094894,
-0.007435972336679697,
-0.04537631943821907,
0.003569395514205098,
0.05337461456656456,
0.03878899663686752,
-0.032483458518981934,
0.023623699322342873,
0.05973571166396141,
-0.0067034256644546986,
-0.03361722081899643,
0.011639240197837353,
-0.030509337782859802,
-0.033366892486810684,
-0.009216422215104103,
-0.027089660987257957,
0.020002570003271103,
0.0125510198995471,
-0.026462508365511894,
0.03115079551935196,
-0.002232756931334734,
-0.021140318363904953,
0.05657756328582764,
-0.028762396425008774,
0.043733466416597366,
0.04900256544351578,
0.04121917858719826,
0.009195716120302677,
0.06442072242498398,
0.002092901850119233,
-0.006071596406400204,
0.01680685393512249,
-0.014823110774159431,
-0.04431001469492912,
-0.015403413213789463,
0.04969270899891853,
0.03346863016486168,
-0.050455491989851,
0.03653283417224884,
0.02882586605846882,
0.05173677206039429,
0.05831164866685867,
0.04351246356964111,
0.013743385672569275,
-0.060804154723882675,
0.020410604774951935,
-0.012473897077143192,
-0.0034577788319438696,
0.0013047840911895037,
0.010951271280646324,
-0.016639938578009605,
0.018283501267433167,
-0.022580014541745186,
0.00746825011447072,
0.021214963868260384,
0.021030211821198463,
-0.005420076660811901,
0.03321346640586853,
-0.004769358318299055,
0.023829886689782143,
-0.06416268646717072,
0.0037947646342217922,
0.04313047230243683,
-0.012036404572427273,
0.017814304679632187,
0.002148853149265051,
0.025199219584465027,
-0.0049194227904081345,
-0.0037765330635011196,
-0.030910346657037735,
-0.006339721847325563,
0.01579112745821476,
-0.0680045634508133,
-0.008551775477826595,
-0.014595522545278072,
0.022455869242548943,
-0.017122946679592133,
-0.016492411494255066,
0.029418282210826874,
0.02353755570948124,
0.030010996386408806,
-0.026149528101086617,
-0.05890674144029617,
0.020485317334532738,
-0.037357598543167114,
0.003142274683341384,
0.013006527908146381,
0.020554475486278534,
-0.003052755957469344,
-0.027283934876322746,
-0.039738431572914124,
0.020602550357580185,
0.000050999773520743474,
-0.021213840693235397,
-0.01702679879963398,
-0.06894293427467346,
-0.05401827394962311,
-0.02254410833120346,
-0.02819087542593479,
0.006301235873252153,
-0.01666330359876156,
-0.030697910115122795,
0.07062515616416931,
-0.012571058236062527,
-0.017378004267811775,
-0.018513761460781097,
-0.02531011402606964,
-0.04525771737098694,
0.010096035897731781,
-0.002044669119641185,
-0.0006399251869879663,
-0.02573888935148716,
0.018401779234409332,
0.00668942229822278,
-0.055959176272153854,
0.018869856372475624,
-0.028646938502788544,
-0.05034901946783066,
0.03235609829425812,
-0.005261578597128391,
0.047988761216402054,
-0.012972701340913773,
-0.027624623849987984,
0.0408855639398098,
0.05565834045410156,
-0.004318449180573225,
-0.004527641460299492,
0.0015950686065480113,
-0.02037830278277397,
-0.06571772694587708,
0.0029503065161406994,
0.05449084937572479,
-0.04008760675787926,
0.022438256070017815,
0.04757029190659523,
0.045607391744852066,
0.03639183193445206,
0.03818400204181671,
0.009619805961847305,
-0.003832027083262801,
-0.032925013452768326,
-0.016458017751574516,
0.06482270359992981,
0.020282873883843422,
-0.00806246604770422,
0.03322646766901016,
-0.010564046911895275,
-0.004880072083324194,
0.031205663457512856,
-0.06083085760474205,
0.020506946370005608,
0.009403213858604431,
0.04503155127167702,
-0.02895888313651085,
0.04843702167272568,
0.017139755189418793,
0.014554807916283607,
-0.014382189139723778,
0.011540485545992851,
0.03571150824427605,
-0.02943609282374382,
-0.025104952976107597,
0.025023000314831734,
0.014795280992984772,
-0.03291235864162445,
-0.0018111823592334986,
-0.00862791482359171,
-0.03121354803442955,
0.021558841690421104,
-0.039233285933732986,
-0.010077401995658875,
0.03331179916858673,
0.028315290808677673,
0.018632464110851288,
-0.04048041254281998,
-0.015576319769024849,
-0.03184102475643158,
-0.04595181718468666,
-0.030379725620150566,
-0.013362850993871689,
0.07355275750160217,
-0.02245451882481575,
0.06571633368730545,
0.033602647483348846,
0.030254140496253967,
-0.0004799943999387324,
-0.002600537845864892,
-0.08881992101669312,
-0.007481493055820465,
-0.022081485018134117,
-0.030521485954523087,
-0.02643297053873539,
-0.008183367550373077,
-0.02286377176642418,
0.0042985486797988415,
0.0057178582064807415,
-0.0035949177108705044,
-0.016409702599048615,
-0.03229798004031181,
0.00047304684994742274,
-0.023702923208475113,
-0.05149155110120773,
-0.045811787247657776,
0.029770266264677048,
0.02075004205107689,
-0.02001989632844925,
0.013415427878499031,
0.026098651811480522,
-0.04004264622926712,
-0.019287703558802605,
-0.024597186595201492,
-0.001269965199753642,
0.02505873143672943,
0.02455548197031021,
0.05627695471048355,
0.009821014478802681,
-0.006288173142820597,
0.015233206562697887,
0.02338581718504429,
0.0407174751162529,
0.009483872912824154,
0.00455430056899786,
0.006869904696941376,
-0.029810883104801178,
-0.04297339543700218,
-0.03345320746302605,
0.06677671521902084,
-0.007627944927662611,
-0.024271603673696518,
0.03989822417497635,
-0.0385546013712883,
0.004541449714452028,
-0.0027296538464725018,
-0.0395919494330883,
0.013576052151620388,
0.011975988745689392,
-0.014827322214841843,
0.002010912634432316,
-0.03838508948683739,
0.00729838153347373,
-0.008211306296288967,
0.0014776579337194562,
0.0034713121131062508,
-0.0036978863645344973,
0.026416877284646034,
-0.012502329424023628,
0.021100614219903946,
0.014822613447904587,
-0.009912783280014992,
-0.014466660097241402,
-0.030957192182540894,
-0.005602457094937563,
-0.014031129889190197,
0.039525341242551804,
0.042245037853717804,
0.002245560986921191,
-0.03442097082734108,
-0.10204395651817322,
0.03468408063054085,
0.006799519062042236,
0.057112108916044235,
0.027286553755402565,
-0.014495721086859703,
-0.07103326171636581,
-0.030410971492528915,
-0.011563342995941639,
-0.007029854226857424,
0.0445457324385643,
-0.038211047649383545,
0.00328084290958941,
-0.02202272228896618,
-0.03267335146665573,
-0.01752205565571785,
0.02435809001326561,
0.06111222878098488,
-0.0032919326331466436,
-0.0754738375544548,
-0.006144557613879442,
-0.020992139354348183,
0.024909187108278275,
0.04570411518216133,
0.025772571563720703,
-0.038857512176036835,
-0.02066642791032791,
0.0010078806662932038,
0.025896046310663223,
-0.04340042918920517,
-0.05968629941344261,
-0.02557273767888546,
0.038432616740465164,
0.021073877811431885,
0.032164450734853745,
-0.02367362007498741,
-0.061607472598552704,
0.032642871141433716,
0.0300580020993948,
-0.01637282781302929,
0.003101686481386423,
-0.001969239441677928,
0.060130856931209564,
0.00557316467165947,
-0.01586100645363331,
0.05346420407295227,
0.02297823317348957,
0.018517768010497093,
0.032292407006025314,
-0.014107069931924343,
0.03172329440712929,
-0.028496088460087776,
0.006173319648951292,
-0.0005206307396292686,
-0.00887769553810358,
-0.026929371058940887,
0.060256797820329666,
0.025249764323234558,
-0.014002964831888676,
0.00416873162612319,
-0.014577910304069519,
0.017259087413549423,
0.004911208525300026,
-0.018346965312957764,
-0.006288278382271528,
-0.004555203951895237,
0.023943712934851646,
-0.010066913440823555,
-0.006919349078088999,
0.02825281210243702,
-0.019468234851956367,
0.004736609756946564,
0.032856158912181854,
0.020707303658127785,
0.009783515706658363,
-0.03694574162364006,
0.0070055630058050156,
-0.005513570737093687,
-0.025264238938689232,
0.03203491121530533,
-0.042690228670835495,
0.01651431806385517,
-0.0031301104463636875,
-0.04180901125073433,
-0.02378384955227375,
-0.00848447997123003,
0.0021900732535868883,
0.017175370827317238,
-0.03452926129102707,
0.00591656006872654,
0.01672912947833538,
-0.017865490168333054,
-0.047240737825632095,
-0.004770892672240734,
0.019314303994178772,
0.018948903307318687,
-0.03797977790236473,
-0.013498433865606785,
-0.024761822074651718,
-0.017407776787877083,
-0.049362584948539734,
-0.0031080562621355057,
0.026289111003279686,
-0.05766579136252403,
-0.046343494206666946,
0.009677795693278313,
-0.0024985976051539183,
0.035662468522787094,
-0.03288767859339714,
-0.048163823783397675,
0.030809303745627403,
-0.05307278037071228,
0.01476334035396576,
0.003205743618309498,
0.03708191215991974,
-0.011607836000621319,
-0.02434215508401394,
-0.012103254906833172,
-0.06090601161122322,
0.01988442987203598,
0.03225157409906387,
-0.0027144253253936768,
0.05144786462187767,
-0.010336490347981453,
-0.00426601292565465,
0.011741961352527142,
0.017578376457095146,
0.019467463716864586,
0.03158160671591759,
-0.014727318659424782,
0.01417671050876379,
-0.08010466396808624,
-0.018610116094350815,
0.03361118212342262,
-0.009102686308324337,
0.0357058085501194,
-0.015256163664162159,
0.05316612869501114,
-0.04912587255239487,
0.0032465672120451927,
-0.003554859897121787,
0.011295771226286888,
0.02127266488969326,
-0.003415820887312293,
-0.01658746972680092,
0.017430678009986877,
0.04178615286946297,
-0.008329849690198898,
-0.04642943665385246,
-0.0732504203915596,
-0.0023440616205334663,
0.03763418272137642,
-0.013186325319111347,
0.05901644751429558,
-0.015755750238895416,
-0.015650039538741112,
-0.02212085761129856,
0.0013158668298274279,
-0.0002208609221270308,
0.002275582868605852,
-0.002660994650796056,
0.029288528487086296,
-0.01661001332104206,
0.0012914000544697046,
0.015442738309502602,
0.07028017193078995,
0.008588051423430443,
-0.009611249901354313,
0.02517511323094368,
0.06585487723350525,
0.015193362720310688,
-0.009372428059577942,
-0.02379237674176693,
0.06484542787075043,
-0.05329465866088867,
0.05055905133485794,
0.010123031213879585,
0.013324381783604622,
0.0570879802107811,
0.007828496396541595,
-0.0012997012818232179,
-0.05059477686882019,
0.0057714092545211315,
-0.010125272907316685,
-0.00000933543014980387,
0.03739257529377937,
0.008005095645785332,
0.009031716734170914,
-0.04436120390892029,
0.05134722590446472,
0.007562435697764158,
0.03844553232192993,
0.030512766912579536,
-0.03885577991604805,
-0.031127622351050377,
-0.0006788050523027778,
-0.06969935446977615,
0.029472287744283676,
-0.009976879693567753,
-0.026906268671154976,
0.03002113290131092,
-0.050965920090675354,
0.03035287745296955,
0.03193466365337372,
0.008359572850167751,
-0.01469834428280592,
0.05166744440793991,
0.014482295140624046,
0.02578725852072239,
0.006317379418760538,
-0.0037457565777003765,
0.11979035288095474,
0.062271326780319214,
0.007607892155647278,
-0.023454392328858376,
0.0026961159892380238,
-0.041928984224796295,
0.05918927118182182,
-0.05049435421824455,
0.027008896693587303,
-0.04115188866853714,
0.031130731105804443,
0.06866421550512314,
0.06069595366716385,
0.036292724311351776,
0.030494220554828644,
0.011855906806886196,
-0.05621221289038658,
-0.023103317245841026,
-0.001814239309169352,
0.005256288684904575,
-0.02332814782857895,
0.018146369606256485,
0.010144440457224846,
0.05319793522357941,
-0.0330667607486248,
0.016990650445222855,
-0.030121399089694023,
-0.028900688514113426,
0.032862018793821335,
-0.057867929339408875,
-0.045697081834077835,
-0.011011912487447262,
0.01928977109491825,
-0.05036197602748871,
-0.004460264928638935,
0.026320869103074074,
0.037295836955308914,
0.005869789514690638,
-0.027733905240893364,
-0.0049408311024308205,
0.007952798157930374,
-0.013078635558485985,
-0.01378721371293068,
0.027643082663416862,
-0.051511455327272415,
-0.008550357073545456,
-0.024256791919469833,
0.026551516726613045,
-0.02166001684963703,
-0.008495795540511608,
-0.003452251898124814,
0.0198067594319582,
-0.032125137746334076,
-0.03479710966348648,
0.002033436670899391,
0.02690519019961357,
0.008355667814612389,
0.000679793709423393,
0.012861179187893867,
-0.06825564801692963,
0.01721956580877304,
-0.008359203115105629,
0.006352091673761606,
0.007870154455304146,
-0.007418457418680191,
0.00014089288015384227,
0.01066336315125227,
0.02522292174398899,
-0.00528344651684165,
-0.04037971422076225,
-0.039934076368808746,
0.020504118874669075,
-0.02911752462387085,
-0.027965059503912926,
0.0018664572853595018,
0.018961159512400627,
0.058827806264162064,
0.013127563521265984,
-0.013463888317346573,
-0.037526823580265045,
-0.07411059737205505,
0.032281361520290375,
0.014578158035874367,
-0.04602990671992302,
-0.02250068634748459,
-0.05054231733083725,
-0.007588118314743042,
0.01778307743370533,
-0.011275632306933403,
-0.015642967075109482,
-0.006868175696581602,
0.03686121106147766,
0.024699142202734947,
-0.04019976407289505,
-0.05574023351073265,
-0.0028290392365306616,
-0.02443312294781208,
-0.007433624472469091,
0.024108076468110085,
0.03526792675256729,
0.03151874616742134,
0.013547633774578571,
0.03592287003993988,
0.01717633381485939,
-0.06924979388713837,
-0.005490276496857405,
-0.007263461593538523,
-0.005078836344182491,
0.009781190194189548,
0.03157768398523331,
-0.00465133273974061,
-0.010320419445633888,
-0.05966506525874138,
-0.01567850075662136,
-0.0016484581865370274,
0.018523169681429863,
0.032666973769664764,
0.004367178305983543,
0.008686582557857037,
-0.00221194326877594,
-0.018485764041543007,
-0.05770806223154068,
-0.00896945409476757,
-0.04538969695568085,
0.022067014127969742,
-0.015046382322907448,
-0.00691430177539587,
-0.03506666421890259,
0.02365933358669281,
-0.0316658578813076,
0.003903732867911458,
0.03987128287553787,
0.00793514121323824,
-0.014759312383830547,
0.020686490461230278,
0.020901162177324295,
-0.005910077597945929,
0.02421386167407036,
-0.04191338270902634,
-0.0045019048266112804,
0.044148821383714676,
-0.04076208546757698,
-0.05912492051720619,
0.019656244665384293,
-0.0098318662494421,
0.029797421768307686,
0.015154066495597363,
0.00046786878374405205,
-0.014528155326843262,
0.07991888374090195,
0.001773179043084383,
-0.013088018633425236,
-0.016359897330403328,
-0.0031551767606288195,
0.02167273871600628,
-0.010788521729409695,
0.014199611730873585,
-0.0204943660646677,
0.03987159952521324,
0.04118245840072632,
0.03700026497244835,
0.0009481597226113081,
0.048259198665618896,
0.004871100187301636,
-0.010097134858369827,
-0.0031207369174808264,
0.027000587433576584,
0.005656352732330561,
0.016416965052485466,
0.015391755849123001,
0.004383352119475603,
0.040717270225286484,
0.010424979962408543,
0.012838847935199738,
-0.06981498748064041,
-0.0258801206946373,
0.004483208525925875,
0.01898634433746338,
0.029958024621009827,
-0.056927409023046494,
0.022134456783533096,
0.01757139526307583,
-0.09767318516969681,
-0.037768442183732986,
-0.017036546021699905,
-0.010795451700687408,
-0.052460987120866776,
-0.000036496403481578454,
-0.04250720515847206,
0.023002805188298225,
0.029548119753599167,
-0.003386029042303562,
-0.0010136524215340614,
0.007255963981151581,
-0.0028130742721259594,
-0.03167775645852089,
-0.009122290648519993,
0.014291437342762947,
-0.021243685856461525,
0.008153648115694523,
0.03956267610192299,
-0.012789634056389332,
0.014689323492348194,
0.02882044017314911,
-0.003997539170086384,
-0.004525415599346161,
0.0174215417355299,
0.044108010828495026,
0.00826706551015377,
0.010619740933179855,
0.001448149560019374,
-0.02714597061276436,
-0.03783046454191208,
0.00891536008566618,
0.02057194523513317,
-0.0038439619820564985,
-0.02142508514225483,
-0.010205116122961044,
0.028253775089979172,
-0.029417943209409714,
0.025842435657978058,
-0.021580617874860764,
-0.013229405507445335,
0.0032743883784860373,
0.003079760819673538,
0.005135042127221823,
-0.015633367002010345,
-0.02568723075091839,
0.030102329328656197,
-0.0751843973994255,
-0.012752648442983627,
0.024134214967489243,
0.0375264510512352,
-0.018715739250183105,
-0.03834601864218712,
0.007044916041195393,
-0.03371313586831093,
0.0473308227956295,
0.020860856398940086,
-0.004742306191474199,
-0.010907799005508423,
-0.01990773156285286,
0.00024161982582882047,
0.06448183953762054,
0.01837310940027237,
-0.01542187575250864,
-0.04309885576367378,
0.02439594268798828,
-0.013248666189610958,
0.007093819789588451,
0.005313420668244362,
-0.03692161291837692,
0.0007963381940498948,
-0.056162960827350616,
0.010586532764136791,
-0.01965201087296009,
0.019660094752907753,
-0.02761032246053219,
-0.05996033549308777,
-0.0484762005507946,
0.055752672255039215,
0.05577037110924721,
0.021848976612091064,
0.005966093856841326,
0.014103236608207226,
-0.020989691838622093,
0.005557321012020111,
-0.05250651389360428,
-0.004431965295225382,
0.0002900602703448385,
-0.021976221352815628,
0.0037124210502952337,
0.0014587477780878544,
-0.007267945911735296,
0.014789177104830742,
0.00971495546400547,
0.011810376308858395,
-0.005059880670160055,
0.018973547965288162,
-0.03654072433710098,
0.01639893278479576,
0.02276887744665146,
-0.018180500715970993,
0.05345873534679413,
-0.012389741837978363,
0.0014825385296717286,
0.013627895154058933,
-0.005728346761316061,
-0.0269438736140728,
0.010776631534099579,
-0.022523054853081703,
0.034188948571681976,
-0.011650605127215385,
0.020887264981865883,
0.02227736823260784,
-0.05414227768778801,
0.025174755603075027,
0.014306088909506798,
-0.05797761678695679,
-0.018592095002532005,
0.041066594421863556,
0.019147643819451332,
0.022346006706357002,
0.02214478887617588,
0.00364169804379344,
-0.019451133906841278,
-0.019189199432730675,
-0.03595646098256111,
0.048081666231155396,
0.006837077438831329,
-0.020580356940627098,
0.05903538316488266,
0.04678575322031975,
0.021029295399785042,
0.005083379335701466,
-0.0025950814597308636,
0.051351599395275116,
-0.02613845467567444,
-0.020587917417287827,
-0.003750430652871728,
-0.026555124670267105,
-0.005737605504691601,
0.06681860983371735,
0.014625128358602524,
0.05819376930594444,
-0.024045724421739578,
0.048220209777355194,
0.02297314442694187,
0.0026385800447314978,
-0.0405864380300045,
0.006396677810698748,
0.010512564331293106,
0.008554973639547825,
-0.005651107057929039,
-0.025305353105068207,
-0.005522427149116993,
-0.026936151087284088,
0.029630189761519432,
-0.06351646780967712,
-0.01645086146891117,
-0.020883828401565552,
-0.03331734240055084,
-0.0017338958568871021,
-0.009464397095143795,
0.01311532687395811,
0.0011498710373416543,
-0.01118833664804697,
0.03443317487835884,
0.0379568450152874,
0.0001342877367278561,
-0.005663285497575998,
0.004356526304036379,
0.04121706262230873,
-0.07111415266990662,
0.011918551288545132,
-0.007743967697024345,
0.000352315983036533,
-0.009139945730566978,
-0.012422679923474789
] |
<p>Does wavelength change with distance? How do they know that the change in wavelength can only be caused by the change of speed of the object to the observer? What about noises, distortions, and interferences as the light moves away from the source to the observer? Or perhaps it travelled through some unknown medium that changed its wavelength.</p>
<p>I'm asking this question to understand why redshift is being used to tell how fast a galaxy is moving away from an observer.</p>
<p>Please explain in plain English. I'm not a physics major.</p>
| 8,302 |
[
-0.007434250321239233,
-0.0394999124109745,
0.016029948368668556,
-0.023925069719552994,
0.059038497507572174,
0.018036462366580963,
-0.029451923444867134,
-0.009970592334866524,
0.006119414232671261,
-0.02720428816974163,
-0.01865055039525032,
0.04635782539844513,
0.04217555373907089,
-0.0026712503749877214,
0.040228117257356644,
0.04484856128692627,
-0.009806257672607899,
0.01123213954269886,
-0.03388991206884384,
-0.023808244615793228,
-0.0005498802638612688,
0.015346494503319263,
0.017451882362365723,
-0.0006469633663073182,
-0.03421539440751076,
-0.009342413395643234,
0.01228952407836914,
0.04684319719672203,
0.04254579171538353,
0.04663758724927902,
0.04038426652550697,
0.0009629325941205025,
-0.010319345630705357,
0.05689845234155655,
0.004389419220387936,
-0.012616286054253578,
-0.02600722946226597,
-0.018892375752329826,
-0.014583652839064598,
0.014703625813126564,
-0.045707397162914276,
0.006963232532143593,
0.016421491280198097,
0.04409921169281006,
-0.03838687390089035,
0.022896666079759598,
-0.0014488429296761751,
0.00025946417008526623,
0.059319447726011276,
-0.013503980822861195,
0.07080874592065811,
-0.034143466502428055,
0.024246450513601303,
0.025619378313422203,
-0.028880398720502853,
0.02212653122842312,
0.10825446248054504,
0.06371460855007172,
-0.05069999769330025,
-0.010393843986093998,
-0.024661963805556297,
-0.010508840903639793,
0.02197222411632538,
-0.012835538014769554,
-0.0030848116148263216,
0.010814212262630463,
-0.007293818984180689,
-0.0020637977868318558,
-0.0011767302639782429,
0.02489921636879444,
0.019117025658488274,
-0.006973172537982464,
0.030579080805182457,
-0.016811199486255646,
0.0073657166212797165,
-0.04881129041314125,
0.0010347494389861822,
0.02419123239815235,
0.022116443142294884,
0.03811315819621086,
-0.03520786762237549,
0.007411360740661621,
0.0004987003630958498,
-0.014498399570584297,
0.01266250479966402,
-0.028857585042715073,
0.07704302668571472,
0.006069083232432604,
0.007137248758226633,
0.02585073560476303,
-0.019124288111925125,
0.018500421196222305,
0.011055400595068932,
-0.014963222667574883,
-0.007246375549584627,
0.03501516208052635,
-0.0063483514823019505,
0.045580968260765076,
0.022802777588367462,
-0.042536359280347824,
0.03520205616950989,
-0.0079165855422616,
0.017733067274093628,
0.04111001640558243,
-0.02291887439787388,
-0.025443503633141518,
-0.06385165452957153,
0.011741423979401588,
-0.03802768513560295,
0.004074186086654663,
-0.004594749305397272,
0.0022323245648294687,
0.014881106093525887,
-0.0030594414565712214,
0.00852072425186634,
-0.014123876579105854,
0.0014844749821349978,
-0.012503968551754951,
0.07600455731153488,
0.060156647115945816,
0.03344437852501869,
-0.046237651258707047,
-0.009059285745024681,
0.013836212456226349,
-0.012816849164664745,
0.02035999670624733,
0.014502591453492641,
-0.015120320953428745,
-0.009188245050609112,
0.02581877075135708,
-0.01257133949548006,
-0.023783642798662186,
0.00274186534807086,
0.0018763369880616665,
0.00436036754399538,
0.002004356821998954,
-0.13123619556427002,
-0.09260612726211548,
0.02606532722711563,
0.01772307977080345,
0.01656048558652401,
-0.07814725488424301,
-0.010763131082057953,
0.011486331932246685,
0.08380182087421417,
-0.0023451943416148424,
0.005688565317541361,
-0.024057552218437195,
0.016585567966103554,
-0.015439200215041637,
-0.009934628382325172,
-0.02217629738152027,
-0.004210543818771839,
-0.02440585009753704,
0.017839767038822174,
-0.08552078902721405,
-0.04422709345817566,
0.02685306966304779,
-0.02102881297469139,
-0.0451495461165905,
0.07170511037111282,
-0.01596064493060112,
-0.014965685084462166,
0.041487351059913635,
0.0076715536415576935,
-0.014318142086267471,
0.10267796367406845,
0.00812022015452385,
-0.020732203498482704,
0.0385812483727932,
0.011036140844225883,
0.023357797414064407,
-0.014164436608552933,
0.004781566560268402,
0.018328802660107613,
-0.018518738448619843,
-0.038194458931684494,
-0.0041529531590640545,
0.017046978697180748,
-0.011519932188093662,
-0.03070307895541191,
-0.016852525994181633,
-0.0028030136600136757,
0.0032727851066738367,
0.0025248124729841948,
0.0315522663295269,
-0.0056961653754115105,
0.02709105610847473,
0.02778308093547821,
-0.042854975908994675,
0.018021151423454285,
-0.0325574092566967,
0.03650723770260811,
0.009584903717041016,
0.010188546031713486,
0.005765989422798157,
0.021366333588957787,
0.025902599096298218,
-0.024676216766238213,
-0.040521662682294846,
0.019081486389040947,
0.04651402682065964,
-0.014894325286149979,
-0.005695246625691652,
0.029970720410346985,
0.06341847032308578,
0.05469823628664017,
0.010499846190214157,
0.003069327212870121,
-0.01795070618391037,
-0.028763527050614357,
0.021044567227363586,
-0.01227410789579153,
0.009522057138383389,
-0.0274191927164793,
0.022802885621786118,
-0.023084178566932678,
-0.006304203998297453,
0.005320907570421696,
0.035051897168159485,
-0.027266165241599083,
0.0783119946718216,
0.02261868305504322,
-0.016433265060186386,
0.006818566471338272,
0.034552305936813354,
-0.01929253339767456,
0.038216330111026764,
-0.008770516142249107,
-0.06067991256713867,
-0.0755479484796524,
-0.04419582337141037,
0.015173519030213356,
0.02047136053442955,
0.012014121748507023,
-0.014547081664204597,
-0.0016884295037016273,
0.03724571317434311,
0.04285292699933052,
0.03258919343352318,
-0.0185418538749218,
-0.050989408046007156,
-0.01878196932375431,
0.009373210370540619,
0.013753230683505535,
0.0050685894675552845,
0.06111147254705429,
0.010310078039765358,
0.01919209584593773,
-0.02081921696662903,
0.0050101131200790405,
0.058416277170181274,
0.023677833378314972,
0.02634310908615589,
-0.00032979363459162414,
-0.028180258348584175,
0.020099254325032234,
-0.007420265581458807,
0.018030690029263496,
0.010241284966468811,
-0.000860365224070847,
0.0026128063909709454,
-0.05059291422367096,
0.0020914217457175255,
0.005476276855915785,
0.004424359183758497,
-0.05171367898583412,
0.016711797565221786,
0.013137727975845337,
-0.031879723072052,
0.01875982992351055,
-0.02901015430688858,
0.00632324256002903,
-0.0131620392203331,
-0.01034524291753769,
0.03721044585108757,
0.028577715158462524,
0.0623338483273983,
-0.031667403876781464,
-0.04810115322470665,
0.015808213502168655,
-0.030244100838899612,
-0.010005511343479156,
0.010956564918160439,
0.001394227729178965,
0.0291658453643322,
-0.01494902465492487,
-0.026478368788957596,
0.03129640594124794,
-0.034413520246744156,
0.01009550504386425,
0.01633959636092186,
-0.013669801875948906,
-0.048103924840688705,
0.0019199680536985397,
-0.024870028719305992,
0.006658549420535564,
0.013174161314964294,
0.020779188722372055,
0.026092005893588066,
-0.0361604318022728,
-0.00981579627841711,
0.02531149983406067,
-0.06079845875501633,
-0.015791678801178932,
-0.009027862921357155,
0.005057146307080984,
-0.004245297517627478,
-0.04917444288730621,
0.03143037483096123,
0.012703312560915947,
-0.07137124240398407,
0.015143134631216526,
-0.019650135189294815,
-0.0368204191327095,
0.05414649471640587,
-0.0238575991243124,
0.022904805839061737,
-0.04862336814403534,
0.00028846284840255976,
0.06998971849679947,
0.03878141939640045,
-0.040722984820604324,
-0.03260336071252823,
0.006557615008205175,
-0.02186822146177292,
-0.03811720013618469,
0.0341852568089962,
0.04108640179038048,
0.004621448460966349,
0.02542608045041561,
0.023951681330800056,
0.028976721689105034,
0.03737221285700798,
0.011017559096217155,
-0.014614680781960487,
-0.013389771804213524,
-0.0038084862753748894,
0.005701825488358736,
0.05342761054635048,
0.04193393513560295,
-0.044453930109739304,
0.023096300661563873,
-0.015327328816056252,
0.05757926031947136,
0.00010751422814792022,
-0.026942504569888115,
0.044667959213256836,
0.02555253356695175,
-0.017766650766134262,
-0.02100401371717453,
0.02982969582080841,
0.007149897050112486,
0.01302746869623661,
0.0083687799051404,
-0.017666952684521675,
0.03384267911314964,
0.016407694667577744,
-0.01483747735619545,
0.014459017664194107,
0.029124341905117035,
-0.013304597698152065,
-0.004567279946058989,
-0.0008525741286575794,
-0.04208263009786606,
0.021048670634627342,
-0.05084563046693802,
-0.021972814574837685,
0.0102691650390625,
0.008042353205382824,
-0.021470922976732254,
-0.012731138616800308,
-0.029316119849681854,
-0.008947118185460567,
-0.03746026009321213,
-0.01618254743516445,
0.03681445121765137,
0.012857911176979542,
-0.005907400045543909,
0.08483535051345825,
0.027766799554228783,
0.03220184147357941,
0.018007248640060425,
-0.028776876628398895,
-0.07015698403120041,
0.03862856328487396,
-0.0601346418261528,
-0.04484055936336517,
-0.020236242562532425,
-0.020928576588630676,
-0.03971432149410248,
-0.03766553848981857,
0.009795217774808407,
-0.016850976273417473,
-0.020696112886071205,
-0.036831069737672806,
-0.002650846028700471,
0.0007259814301505685,
-0.04383989796042442,
-0.04764266684651375,
0.03081662394106388,
0.01203130278736353,
0.00630608294159174,
0.025987762957811356,
0.019460204988718033,
-0.0027353919576853514,
-0.02106372080743313,
-0.019503384828567505,
-0.015546301379799843,
0.025469647720456123,
0.024652646854519844,
0.045036397874355316,
0.00287565216422081,
-0.03599710389971733,
0.04265888035297394,
0.020099828019738197,
0.031672365963459015,
-0.015042806975543499,
-0.024924419820308685,
-0.020423177629709244,
-0.048861730843782425,
-0.007317852694541216,
-0.021465864032506943,
0.057797808200120926,
-0.012919126078486443,
0.0017354413866996765,
0.03430286794900894,
-0.045606013387441635,
-0.04472767934203148,
0.02304702438414097,
0.033618468791246414,
-0.026709189638495445,
-0.024997442960739136,
-0.03077266365289688,
-0.0014494647039100528,
-0.012291837483644485,
-0.009259950369596481,
0.01569567620754242,
0.01546800322830677,
-0.0037938272580504417,
0.02158517576754093,
0.013198236003518105,
0.03137072175741196,
-0.03506799042224884,
-0.03408854082226753,
-0.0019528731936588883,
0.0035070746671408415,
-0.0077902101911604404,
0.029948340728878975,
-0.009346618317067623,
0.05788738280534744,
0.055854517966508865,
-0.03989087790250778,
0.007968132384121418,
-0.0758456140756607,
-0.010541209019720554,
-0.004737858194857836,
0.043452173471450806,
0.0023507147561758757,
-0.021617747843265533,
-0.04266709089279175,
-0.035584475845098495,
0.04103367030620575,
-0.006606052629649639,
0.027019236236810684,
-0.010267617180943489,
-0.0004830535617657006,
-0.012177309952676296,
0.003907213918864727,
-0.008166019804775715,
0.015961533412337303,
-0.006455243099480867,
0.0007499111234210432,
-0.025204507634043694,
0.01519748754799366,
-0.03953412175178528,
-0.005008522886782885,
0.018379760906100273,
0.052386574447155,
-0.002474755048751831,
0.01202323753386736,
-0.024890407919883728,
0.004123322665691376,
-0.0074059502221643925,
-0.04554278776049614,
0.01850336603820324,
0.024340854957699776,
0.01688113994896412,
0.042703382670879364,
-0.0047746384516358376,
-0.03656329587101936,
0.015826646238565445,
0.02201182395219803,
-0.03290358558297157,
-0.00014289161481428891,
-0.00970357283949852,
0.024698110297322273,
0.021670706570148468,
-0.007029518019407988,
0.07244161516427994,
0.018228735774755478,
0.007044774014502764,
0.01768754981458187,
-0.012048550881445408,
0.06688088178634644,
-0.0455712154507637,
-0.009713374078273773,
-0.0008925714064389467,
-0.004285162780433893,
-0.038421012461185455,
0.061235323548316956,
0.025736849755048752,
-0.00900175329297781,
0.01592179574072361,
-0.03878070414066315,
-0.022624796256422997,
0.024663740769028664,
-0.003502829698845744,
0.035002365708351135,
-0.021134043112397194,
0.011027397587895393,
-0.029202423989772797,
-0.030007660388946533,
0.009335742332041264,
0.04080739989876747,
-0.007446256000548601,
0.008962007239460945,
0.0020011255983263254,
0.04454164579510689,
-0.012613498605787754,
-0.008121090941131115,
0.03055705316364765,
-0.05087891221046448,
0.019505692645907402,
-0.00003828603439615108,
-0.016140254214406013,
0.017574189230799675,
-0.0676773265004158,
-0.05438933148980141,
-0.010004795156419277,
-0.05888807401061058,
0.029150914400815964,
-0.05169426277279854,
0.0360037162899971,
0.006424423772841692,
0.04685870558023453,
-0.09066209197044373,
-0.01712646894156933,
0.023648913949728012,
0.011640409007668495,
-0.022585388273000717,
0.002411164343357086,
0.048132024705410004,
-0.05662274360656738,
-0.002207505516707897,
-0.028581948950886726,
0.044403303414583206,
0.011796127073466778,
-0.02546938881278038,
0.0037635304033756256,
0.002336855512112379,
0.05159544199705124,
-0.009154511615633965,
-0.011669616214931011,
-0.01853233575820923,
0.0016314800595864654,
0.00411227298900485,
-0.009031273424625397,
0.07108081132173538,
-0.015021785162389278,
-0.048087701201438904,
-0.02341524325311184,
-0.018574189394712448,
-0.016307560727000237,
-0.06853364408016205,
-0.012346116825938225,
0.009722271002829075,
0.028018999844789505,
0.0192414578050375,
-0.010875380598008633,
0.04045909643173218,
-0.03182272985577583,
0.019432950764894485,
0.002018532482907176,
0.002887758892029524,
-0.03864385932683945,
-0.0189408827573061,
0.021052710711956024,
0.0008475288050249219,
0.05308175086975098,
0.005452415905892849,
0.026865003630518913,
0.004644060041755438,
-0.004537343978881836,
0.00813837070018053,
-0.026023168116807938,
0.018620364367961884,
-0.04461323842406273,
-0.0025235258508473635,
0.021600259467959404,
0.02812848426401615,
-0.018627837300300598,
-0.009482065215706825,
-0.013948037289083004,
-0.021013949066400528,
0.08576561510562897,
0.0007075886824168265,
0.06688173860311508,
0.025590896606445312,
-0.011588864028453827,
-0.01204766146838665,
-0.03612037003040314,
0.0028031044639647007,
-0.010686327703297138,
-0.017694473266601562,
0.007620186544954777,
-0.029166189953684807,
0.008581055328249931,
0.012377027422189713,
0.03387179225683212,
-0.009913994930684566,
-0.0017613987438380718,
0.027668815106153488,
0.028458373621106148,
0.025700634345412254,
-0.022183509543538094,
-0.026476237922906876,
0.01325375959277153,
-0.02388336881995201,
0.01742321066558361,
0.016612177714705467,
0.013683529570698738,
0.05887781083583832,
0.004721316043287516,
0.025329727679491043,
-0.04399308189749718,
0.005292691756039858,
-0.05299675837159157,
-0.026736659929156303,
0.02365562878549099,
0.046566661447286606,
0.026614710688591003,
-0.0045227170921862125,
-0.0070773037150502205,
-0.013109869323670864,
0.0068162898533046246,
-0.010962588712573051,
-0.06533953547477722,
-0.04256860539317131,
-0.02685558795928955,
-0.037104055285453796,
0.05631193146109581,
-0.012777790427207947,
-0.05935234948992729,
-0.004162108525633812,
-0.02983168698847294,
0.016409989446401596,
0.024399055168032646,
0.020110532641410828,
-0.030772102996706963,
0.0795140489935875,
-0.018933666869997978,
0.02488688938319683,
-0.0009183420916087925,
0.03422703221440315,
0.08688440918922424,
0.048312362283468246,
0.0136478953063488,
-0.034875571727752686,
0.005688280798494816,
-0.03311134874820709,
0.020797863602638245,
-0.0437517873942852,
0.029856540262699127,
-0.000023232996682054363,
0.0364488884806633,
0.011854609474539757,
0.06368332356214523,
0.014397604390978813,
-0.044335123151540756,
0.06063303351402283,
-0.03841502591967583,
-0.015706835314631462,
0.017491979524493217,
0.0001874831796158105,
0.00732582900673151,
0.034644950181245804,
-0.018161075189709663,
0.015583405271172523,
-0.0446566604077816,
-0.014001820236444473,
-0.008750125765800476,
-0.031520526856184006,
0.006902804598212242,
0.01667364500463009,
-0.05953666940331459,
0.008330706506967545,
0.028486015275120735,
-0.01744893752038479,
-0.0728871300816536,
0.04292477294802666,
0.04533261060714722,
-0.03859526664018631,
0.006613807287067175,
0.02769913151860237,
0.02114003710448742,
0.013302018865942955,
-0.020970603451132774,
0.0049182516522705555,
-0.0026515612844377756,
-0.011465874500572681,
-0.024329273030161858,
0.03515871614217758,
0.018372366204857826,
-0.009746003895998001,
0.012019759975373745,
0.019212942570447922,
-0.037524666637182236,
-0.06708722561597824,
0.0028509413823485374,
0.0384710468351841,
0.0025982081424444914,
-0.008684223517775536,
-0.02355576865375042,
0.01516615878790617,
0.02735712379217148,
0.003335303859785199,
0.013045924715697765,
0.02680758200585842,
0.007778840139508247,
-0.021286355331540108,
0.009182283654808998,
0.011053135618567467,
-0.029263606294989586,
-0.019563715904951096,
-0.016349975019693375,
0.028220005333423615,
-0.06223401799798012,
0.014167026616632938,
0.03767235204577446,
0.025552840903401375,
0.00777923921123147,
-0.014603838324546814,
0.012051967903971672,
-0.0221850723028183,
-0.07913857698440552,
0.000117892624984961,
-0.045432139188051224,
-0.027664637193083763,
-0.010292847640812397,
0.017800819128751755,
0.055801838636398315,
0.02106412500143051,
-0.001968428259715438,
0.016370782628655434,
-0.009483478032052517,
0.000022317812181427144,
0.03062126599252224,
-0.03362850472331047,
0.012010766193270683,
0.029881006106734276,
-0.018022574484348297,
-0.0004229199548717588,
-0.028533579781651497,
0.05179999768733978,
0.03628440573811531,
0.011010599322617054,
0.004296411760151386,
0.004041831009089947,
-0.05168266221880913,
0.026155566796660423,
0.025414735078811646,
-0.015231291763484478,
0.007959515787661076,
-0.011556833982467651,
0.01960678957402706,
-0.022613340988755226,
-0.031521026045084,
-0.05148959904909134,
-0.022529419511556625,
0.013959419913589954,
0.008399723097682,
-0.03141353279352188,
0.04680124297738075,
-0.0006408640765585005,
0.01902187056839466,
-0.04962599277496338,
0.0018857630202546716,
-0.013557666912674904,
0.02862662449479103,
-0.01249365322291851,
-0.04082125425338745,
0.013973632827401161,
0.02796579897403717,
-0.04155688360333443,
-0.09168796986341476,
0.014011112041771412,
0.023731308057904243,
0.014974660240113735,
0.030811473727226257,
0.014874720945954323,
-0.014769169501960278,
0.027186060324311256,
-0.008726763539016247,
0.004215190652757883,
0.013554191216826439,
-0.04134572669863701,
-0.030555669218301773,
0.055017925798892975,
-0.026597941294312477,
0.04649775102734566,
0.01743064820766449,
0.007868156768381596,
0.009680205956101418,
0.038357000797986984,
-0.0008871440077200532,
-0.008876372128725052,
0.003114338731393218,
-0.03479339927434921,
0.00887977983802557,
0.0002480227267369628,
0.02259770594537258,
0.005034775007516146,
-0.009816939942538738,
0.03905872255563736,
0.010644533671438694,
0.007876413874328136,
0.037866052240133286,
0.00882547814399004,
-0.02695533074438572,
-0.0001655167288845405,
0.012150014750659466,
0.0030574777629226446,
0.03773799538612366,
0.04023264721035957,
-0.018217315897345543,
0.06783560663461685,
0.02920716255903244,
-0.022544527426362038,
-0.12547825276851654,
0.017756976187229156,
0.03663976863026619,
0.03553394973278046,
0.04372298717498779,
-0.07055693119764328,
0.023265495896339417,
0.033510055392980576,
-0.07720448076725006,
0.016140243038535118,
-0.039925992488861084,
-0.017170531675219536,
-0.0011546715395525098,
-0.007727786898612976,
0.004175602458417416,
0.03941016271710396,
0.06356322020292282,
0.03999662026762962,
0.00046407844638451934,
0.008385902270674706,
-0.01877133920788765,
-0.01767578162252903,
-0.01400675531476736,
0.02187611348927021,
0.01177662331610918,
0.007465840317308903,
0.046900056302547455,
-0.013690149411559105,
0.009325762279331684,
0.035000428557395935,
-0.010266188532114029,
0.02399107813835144,
-0.006945868954062462,
-0.017140261828899384,
0.03142904117703438,
0.002267488045617938,
-0.014925815165042877,
-0.03765108808875084,
-0.030857307836413383,
0.04854344576597214,
-0.011218531057238579,
0.005682921968400478,
0.010123809799551964,
-0.04059609770774841,
0.005891722161322832,
-0.08459325134754181,
0.00021631200797855854,
-0.0016272495267912745,
0.01970735564827919,
0.015362399630248547,
0.025518644601106644,
0.022996889427304268,
-0.000006885473339934833,
-0.030022650957107544,
-0.00607209000736475,
-0.04803963750600815,
-0.025259511545300484,
0.04115499556064606,
0.037224180996418,
-0.048844240605831146,
-0.01995009556412697,
-0.014658499509096146,
-0.018881535157561302,
0.006059207487851381,
-0.037589024752378464,
-0.0016758093843236566,
-0.035232387483119965,
0.005925352685153484,
0.005345828365534544,
-0.017054053023457527,
0.01969906874001026,
-0.01815875619649887,
-0.038386229425668716,
0.03140828013420105,
-0.01909869909286499,
-0.008727609179913998,
-0.044382695108652115,
-0.029881766065955162,
-0.03920912742614746,
-0.06769739836454391,
0.04404269903898239,
0.02943924441933632,
-0.006796047557145357,
-0.08051890879869461,
-0.012326412834227085,
-0.04024548456072807,
0.020873017609119415,
0.08380961418151855,
0.004712787922471762,
-0.018808556720614433,
-0.006863923743367195,
-0.012066083960235119,
0.003364658448845148,
-0.04714486747980118,
0.00896636862307787,
-0.009924684651196003,
-0.034952063113451004,
-0.049065638333559036,
-0.010033011436462402,
-0.017693452537059784,
0.026844635605812073,
-0.0031514563597738743,
0.010066648945212364,
0.056320447474718094,
-0.0008619300788268447,
-0.05045732483267784,
0.0476078987121582,
0.018356604501605034,
-0.004972982220351696,
0.061133116483688354,
0.0022165237460285425,
0.0013204986462369561,
0.03677460923790932,
0.003391778329387307,
-0.05097123235464096,
0.016291435807943344,
-0.034240104258060455,
-0.0017755681183189154,
0.011843889951705933,
0.025928767397999763,
0.015361964702606201,
-0.06452400982379913,
0.006514993496239185,
0.026287207379937172,
-0.02563450299203396,
-0.018733907490968704,
0.05641951411962509,
0.018109982833266258,
0.0020986064337193966,
-0.01423417218029499,
-0.012933973222970963,
0.004369368311017752,
0.016507474705576897,
-0.01859508641064167,
0.06178824231028557,
0.01605885475873947,
0.008887385949492455,
0.042982205748558044,
0.029564011842012405,
0.0011788251576945186,
-0.01173595990985632,
0.004222133196890354,
0.05831105634570122,
-0.033572591841220856,
-0.0014536078087985516,
-0.013319549150764942,
-0.017014574259519577,
0.026822874322533607,
0.08186344802379608,
-0.0308669563382864,
0.08411726355552673,
-0.0669979602098465,
0.019284123554825783,
-0.004831889644265175,
0.015040469355881214,
-0.03359956294298172,
0.0018087874632328749,
-0.004678087774664164,
0.010062306188046932,
-0.003354370826855302,
0.016318537294864655,
0.006892069708555937,
0.00845730397850275,
0.029205970466136932,
-0.05495120584964752,
0.010037455707788467,
0.018728353083133698,
-0.054108768701553345,
-0.005608730483800173,
0.021139604970812798,
-0.022247739136219025,
-0.007259571924805641,
0.026353852823376656,
0.04006060212850571,
0.009899468161165714,
0.014480849727988243,
0.00342865870334208,
-0.03881685063242912,
0.028645191341638565,
-0.0903676226735115,
0.0018794992938637733,
-0.0272646676748991,
0.019891921430826187,
-0.03200533241033554,
-0.03728881850838661
] |
<p>In Peskin's QFT book page 294, he formally addressed the quantization of EM field,</p>
<blockquote>
<p>$$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$
Now that we have the functional integral quantization method at our command, let us apply it to the derivation of this expression.<br>
Consider the functional integral<br>
$$\int DAe^{iS[A]},$$</p>
</blockquote>
<p>Actually I expected to see how he would derive the generating functional $\int DAe^{i(S[A]+J^\mu A_\mu)}$ from the canonical quantization before proceeding on to introduce the Faddeev-Popov trick. </p>
<p>So is there a way to do this derivation, i.e., from the operator formalism using Hamiltonian, or we must presume the validity of this path integral as a starting point, which is probably what Peskin did(I guess)?</p>
| 8,303 |
[
0.04008452966809273,
-0.027162520214915276,
0.0278471652418375,
-0.036813486367464066,
0.027390742674469948,
-0.007983016781508923,
-0.03526777774095535,
-0.028424551710486412,
0.007295481860637665,
-0.02027713507413864,
0.021017130464315414,
0.013654000125825405,
0.09304346889257431,
0.019220983609557152,
-0.024511564522981644,
0.02917061746120453,
-0.017608873546123505,
-0.0341772697865963,
0.004925376735627651,
-0.02512594498693943,
-0.022654658183455467,
0.0805346891283989,
-0.031029891222715378,
-0.04234278202056885,
0.017373312264680862,
-0.007280972320586443,
-0.006517552770674229,
0.01259413082152605,
-0.0073815821669995785,
0.08186063170433044,
-0.014990823343396187,
-0.05360779911279678,
0.014489145018160343,
0.005788327194750309,
-0.00245532370172441,
0.03592007979750633,
-0.017416492104530334,
-0.029862208291888237,
-0.004098040983080864,
0.04033522680401802,
-0.029888855293393135,
-0.017596449702978134,
-0.05213196948170662,
0.052463289350271225,
-0.018115900456905365,
0.035344447940588,
-0.02454547770321369,
0.00036931983777321875,
0.06674996018409729,
-0.04875122755765915,
0.07625512778759003,
0.010043121874332428,
0.004882873967289925,
0.033857136964797974,
-0.030869996175169945,
-0.030680552124977112,
0.049413200467824936,
0.04455884173512459,
0.027593117207288742,
-0.03159180283546448,
-0.036094069480895996,
-0.03347497805953026,
0.011552445590496063,
-0.046950940042734146,
0.03357003256678581,
-0.021793220192193985,
0.03524497151374817,
-0.03530831262469292,
0.04112774133682251,
-0.01879296265542507,
-0.013038331642746925,
0.02509099617600441,
0.045021411031484604,
-0.00021416992240119725,
0.05202389135956764,
0.0019079879857599735,
0.009325142949819565,
0.008094504475593567,
0.03546837344765663,
0.001254271948710084,
0.008178086020052433,
0.009035727009177208,
-0.0036387736909091473,
0.03860337659716606,
0.03524474799633026,
-0.02174665406346321,
0.05229784548282623,
-0.016302751377224922,
-0.03633973002433777,
-0.013546106405556202,
-0.028681812807917595,
-0.007059890311211348,
0.03889346867799759,
-0.016858140006661415,
-0.027718082070350647,
0.0553891696035862,
0.03331660479307175,
0.07923226058483124,
-0.019298143684864044,
-0.01154516264796257,
-0.019304312765598297,
-0.018951890990138054,
-0.025575121864676476,
0.04718966782093048,
0.02700773999094963,
0.004226522520184517,
-0.030386030673980713,
0.015099656768143177,
-0.01711040735244751,
-0.04400351643562317,
-0.04730113595724106,
0.025279656052589417,
-0.039310041815042496,
-0.01895034871995449,
-0.02713642083108425,
0.014874889515340328,
-0.0004023048095405102,
-0.011321709491312504,
0.036239273846149445,
0.046841565519571304,
0.03140382841229439,
0.0013614670606330037,
0.03747803345322609,
-0.03548640385270119,
-0.05740971490740776,
0.031068291515111923,
0.034839678555727005,
0.026441100984811783,
-0.036687470972537994,
0.015821071341633797,
0.018783003091812134,
-0.012135252356529236,
-0.009390387684106827,
0.010653987526893616,
-0.017075704410672188,
-0.034921903163194656,
-0.06885422021150589,
-0.030782951042056084,
0.04479509964585304,
-0.042317889630794525,
0.04043463245034218,
-0.0460711270570755,
0.0010452078422531486,
0.0307181254029274,
0.087602898478508,
-0.015463628806173801,
-0.0029329294338822365,
-0.01638202741742134,
0.014494272880256176,
-0.0017751040868461132,
-0.0326966866850853,
-0.07478579133749008,
-0.021731602028012276,
-0.029777009040117264,
-0.024617241695523262,
-0.023574739694595337,
0.04872105270624161,
0.060672543942928314,
0.019857356324791908,
-0.002498338930308819,
0.09431811422109604,
-0.00722033716738224,
0.006291511934250593,
0.008175899274647236,
0.005987955257296562,
-0.02470254711806774,
0.07192090898752213,
0.05495420843362808,
0.008233367465436459,
0.04503193870186806,
-0.02575773373246193,
0.04287561774253845,
0.0031951768323779106,
0.02832680754363537,
0.029918396845459938,
-0.041940346360206604,
-0.0009427570039406419,
-0.006911845877766609,
0.03341663256287575,
-0.02640160359442234,
0.01823614165186882,
-0.030998902395367622,
-0.010078540071845055,
0.0031481420155614614,
-0.017605502158403397,
-0.006180034019052982,
0.02107047103345394,
0.029332533478736877,
0.002530299359932542,
-0.05952030047774315,
-0.02016201987862587,
-0.06527569144964218,
0.03303252533078194,
0.02468688413500786,
-0.05219796672463417,
0.022855347022414207,
-0.025899451225996017,
0.03476759418845177,
0.0033085497561842203,
-0.0718042403459549,
-0.023029521107673645,
0.02309270203113556,
0.010762125253677368,
0.011952787637710571,
0.02253839746117592,
0.05872573330998421,
0.015773728489875793,
0.014626837335526943,
0.048481475561857224,
-0.02884642407298088,
-0.025658436119556427,
0.025675391778349876,
-0.0010795765556395054,
0.011933453381061554,
0.008558791130781174,
-0.006495350506156683,
-0.007532431278377771,
-0.025604616850614548,
-0.01610448583960533,
0.01824493333697319,
-0.052965857088565826,
0.021260295063257217,
0.08525759726762772,
0.02106972597539425,
0.004855749662965536,
0.03914060816168785,
-0.014430839568376541,
0.0299773421138525,
0.021464411169290543,
-0.03855741769075394,
-0.01684541068971157,
-0.03160925954580307,
0.039141930639743805,
0.009033516980707645,
-0.027050631120800972,
0.00943325087428093,
0.020606476813554764,
-0.009044972248375416,
0.05104587972164154,
0.016209308058023453,
0.002851917641237378,
0.007261892780661583,
0.012055515311658382,
0.004900538828223944,
-0.03344278410077095,
-0.02420373074710369,
-0.002919896272942424,
-0.021004917100071907,
-0.009658627212047577,
0.010575826279819012,
-0.032554592937231064,
0.0015529118245467544,
-0.02643570490181446,
0.018886666744947433,
0.008118191733956337,
-0.05388505011796951,
0.012351423501968384,
-0.018290555104613304,
0.05354919284582138,
0.0014194080140441656,
-0.020680198445916176,
-0.003924267832189798,
-0.035730525851249695,
-0.059349238872528076,
0.021279655396938324,
-0.01904783584177494,
-0.021992594003677368,
-0.043009333312511444,
0.015318882651627064,
-0.009132090024650097,
-0.01127095427364111,
-0.011601773090660572,
0.009107470512390137,
0.0013015087461099029,
0.010634828358888626,
0.024385826662182808,
0.012824272736907005,
0.029105020686984062,
-0.023247510194778442,
-0.023233767598867416,
0.006679213605821133,
-0.027808360755443573,
0.03825780376791954,
0.06736043840646744,
-0.0242457315325737,
-0.010413066484034061,
-0.044354915618896484,
-0.032485779374837875,
0.05630533769726753,
0.0032188119366765022,
-0.02498609386384487,
0.00048542063450440764,
-0.004856271669268608,
-0.03745424374938011,
-0.033726464956998825,
0.01678244210779667,
0.0029814098961651325,
-0.01006644032895565,
-0.03307017311453819,
0.02164524421095848,
-0.0011016366770491004,
-0.05209587514400482,
0.02097512222826481,
0.015594225376844406,
-0.034017711877822876,
0.00289272447116673,
-0.0040269349701702595,
0.022616134956479073,
-0.05547725781798363,
0.010717752389609814,
0.02426746115088463,
-0.027610426768660545,
-0.004224658012390137,
-0.06489123404026031,
0.00041994344792328775,
0.04698775336146355,
-0.0116049125790596,
0.022460661828517914,
-0.026904422789812088,
-0.039390843361616135,
0.08409363031387329,
0.04505385830998421,
-0.02120303362607956,
-0.008013991639018059,
0.005061848554760218,
0.01695392094552517,
-0.021266909316182137,
-0.024888314306735992,
0.011233796365559101,
-0.012920179404318333,
0.0333140566945076,
0.012797771021723747,
0.022764042019844055,
0.037382423877716064,
-0.01773293875157833,
-0.03585408627986908,
0.03689784184098244,
-0.041960399597883224,
0.020455798134207726,
0.04173607379198074,
0.0016347659984603524,
0.010942414402961731,
0.0013326186453923583,
-0.029023127630352974,
-0.0017632967792451382,
0.014757776632905006,
-0.04277947545051575,
0.07411287724971771,
0.014575794339179993,
-0.01613990217447281,
-0.05021486058831215,
0.02348029799759388,
-0.014097201637923717,
-0.04307489097118378,
0.006179597694426775,
0.03407023847103119,
-0.01781396009027958,
-0.02914956957101822,
0.014925694093108177,
0.03088250942528248,
0.01207165140658617,
-0.006521198432892561,
-0.04926908761262894,
-0.005562823265790939,
-0.030596356838941574,
0.014288877137005329,
-0.0010793507099151611,
-0.017174098640680313,
0.03873642906546593,
0.039821431040763855,
-0.0017975128721445799,
-0.023845218122005463,
-0.04215778782963753,
-0.006674178410321474,
-0.056462451815605164,
-0.013712274841964245,
-0.007231933530420065,
0.05282225459814072,
0.04581345245242119,
0.025921987369656563,
-0.0019104904495179653,
0.011147024109959602,
-0.014138835482299328,
0.018114915117621422,
-0.07434878498315811,
-0.007513874210417271,
0.01265084557235241,
-0.00964202918112278,
-0.0025101574137806892,
-0.046165257692337036,
0.0293640848249197,
-0.004737126640975475,
-0.07537814974784851,
-0.017369691282510757,
-0.019307762384414673,
-0.03608214110136032,
0.010330934077501297,
-0.03826366737484932,
-0.0658947303891182,
-0.04277573898434639,
0.0005917144007980824,
0.05756775662302971,
-0.05130487307906151,
-0.017638154327869415,
0.03425364941358566,
-0.024733226746320724,
0.004065162502229214,
-0.007011988665908575,
0.010216467082500458,
0.00142201641574502,
0.007984410971403122,
0.017196398228406906,
0.002548899967223406,
-0.024481160566210747,
-0.01390901394188404,
0.012216046452522278,
0.09942754358053207,
0.028081029653549194,
-0.03550577536225319,
-0.02376665361225605,
-0.06726600974798203,
0.005479465704411268,
0.025875724852085114,
0.07061531394720078,
-0.0032890536822378635,
-0.023738548159599304,
0.04352613165974617,
0.021473577246069908,
-0.02298656292259693,
0.020417500287294388,
0.07289909571409225,
0.026733510196208954,
-0.01026827935129404,
-0.06321963667869568,
0.02018505334854126,
-0.008303378708660603,
0.003921275958418846,
-0.00023223999596666545,
0.015399892814457417,
-0.008674966171383858,
-0.013790000230073929,
0.019289465621113777,
0.01231269259005785,
-0.0283340010792017,
0.018620219081640244,
0.029456283897161484,
0.01711368001997471,
0.003129083663225174,
0.010868323035538197,
0.021951261907815933,
0.06788716465234756,
0.004598839208483696,
-0.01944619044661522,
-0.013110870495438576,
-0.06915099173784256,
-0.012027129530906677,
0.027081286534667015,
0.0038484856486320496,
0.018735641613602638,
0.009438428096473217,
-0.06132713705301285,
-0.028469841927289963,
0.020829128101468086,
0.02887236885726452,
0.012173699215054512,
0.015858663246035576,
0.025990603491663933,
-0.01778854802250862,
-0.01849883422255516,
-0.039352674037218094,
0.05246861279010773,
0.008064583875238895,
-0.0057596671395003796,
-0.036270078271627426,
-0.001020793803036213,
-0.0155350212007761,
0.02783976122736931,
0.005920628551393747,
0.050001759082078934,
0.039184365421533585,
-0.011032726615667343,
0.010531815700232983,
0.029696863144636154,
-0.03404511511325836,
-0.08633308857679367,
0.010027825832366943,
0.010745381005108356,
0.0030899473931640387,
0.02568172849714756,
-0.014736669138073921,
-0.012506252154707909,
0.012282868847250938,
0.011253265663981438,
-0.010768859647214413,
0.005065480712801218,
-0.06590840220451355,
0.0727912187576294,
-0.011534109711647034,
0.0029685795307159424,
0.035014767199754715,
-0.0033479006960988045,
-0.014843445271253586,
0.00926563423126936,
-0.008795661851763725,
0.03552982583642006,
-0.013662069104611874,
-0.0036983531899750233,
-0.0328340120613575,
0.004732908681035042,
-0.04697443172335625,
0.015344125218689442,
-0.038351185619831085,
0.007846287451684475,
-0.01982148550450802,
-0.05024302378296852,
-0.026984699070453644,
-0.02414889819920063,
-0.02644340880215168,
-0.03157154098153114,
0.013698196038603783,
0.029726583510637283,
0.050698451697826385,
-0.012515839189291,
0.018785905092954636,
-0.03132256120443344,
0.0163884274661541,
0.06212925538420677,
-0.015215711668133736,
0.018692201003432274,
-0.023130230605602264,
-0.0363558866083622,
0.0034392583183944225,
-0.013594345189630985,
0.013078015297651291,
0.0013946631224825978,
-0.0061201490461826324,
-0.012750547379255295,
-0.024215957149863243,
-0.0333060696721077,
-0.02537173591554165,
-0.005676331464201212,
0.012102533131837845,
-0.027612734586000443,
1.977999630753402e-7,
0.000389577733585611,
-0.008941518142819405,
-0.09409048408269882,
0.006190863903611898,
-0.028599970042705536,
-0.010536342859268188,
-0.022141650319099426,
-0.030392272397875786,
0.004302185960114002,
-0.028673699125647545,
-0.024981163442134857,
0.00973694771528244,
0.07041283696889877,
-0.016253292560577393,
0.02575857564806938,
0.006719767581671476,
0.0359201654791832,
0.04057149589061737,
0.0015588745009154081,
0.012526526115834713,
-0.0019282727735117078,
-0.029528137296438217,
0.0014809052227064967,
-0.004847403150051832,
0.0602099783718586,
-0.014898158609867096,
-0.004079751204699278,
0.0004262654110789299,
-0.023736270144581795,
0.013626161031425,
-0.0072518265806138515,
-0.0005482441047206521,
0.01849520578980446,
0.017328713089227676,
0.011654670350253582,
-0.02221204899251461,
-0.021468283608555794,
0.007569962181150913,
0.006015543360263109,
0.020439228042960167,
0.032514143735170364,
-0.05163015052676201,
0.021315155550837517,
0.04572856053709984,
-0.005537937395274639,
0.009624693542718887,
-0.007439273409545422,
0.055210214108228683,
-0.04149569571018219,
0.019271153956651688,
0.07005057483911514,
0.0008389127324335277,
0.008463318459689617,
-0.012844878248870373,
-0.0010356943821534514,
0.018918829038739204,
-0.016123095527291298,
-0.002590141026303172,
-0.03213007003068924,
-0.07759126275777817,
0.006501996889710426,
0.05144031345844269,
-0.033615417778491974,
0.017963169142603874,
0.00529449200257659,
0.001842876081354916,
-0.007710047531872988,
0.01772346906363964,
-0.02682369388639927,
0.02193703129887581,
0.0005974367377348244,
0.056373778730630875,
-0.04914213716983795,
0.019622039049863815,
0.04072614386677742,
0.04514259845018387,
-0.05014001578092575,
0.034876108169555664,
0.020946979522705078,
0.023258119821548462,
0.008890435099601746,
0.024697082117199898,
-0.05786528438329697,
0.05580247566103935,
-0.052815910428762436,
0.044760074466466904,
-0.01446604635566473,
-0.003127455245703459,
0.009520341642200947,
0.019709454849362373,
-0.01952287368476391,
0.011623007245361805,
-0.010565970093011856,
-0.03581768646836281,
0.022751199081540108,
0.014895036816596985,
0.03410111367702484,
0.03500736132264137,
-0.009500752203166485,
0.02939782291650772,
-0.04511844739317894,
-0.0026019937358796597,
0.021844614297151566,
-0.012677120976150036,
0.031436629593372345,
-0.057665105909109116,
-0.0649290531873703,
0.053665146231651306,
-0.03094247169792652,
-0.0022101253271102905,
0.006276486441493034,
0.003843618556857109,
0.03775625675916672,
0.010853548534214497,
0.02741861902177334,
-0.021887075155973434,
0.07451514899730682,
0.004449125844985247,
0.0005737110041081905,
-0.011126416735351086,
0.0034513205755501986,
0.12451045960187912,
0.058822713792324066,
0.01242822129279375,
-0.06773524731397629,
-0.018547458574175835,
0.0029993713833391666,
0.025331616401672363,
-0.05077994614839554,
0.03458591178059578,
-0.03377658501267433,
-0.02106405794620514,
-0.0312346238642931,
0.07083888351917267,
-0.002937780227512121,
0.01072987262159586,
0.03868778049945831,
-0.05279889702796936,
-0.04609863832592964,
0.05198928713798523,
-0.006665606517344713,
-0.054590653628110886,
-0.010523281991481781,
-0.03898779675364494,
-0.0031204104889184237,
-0.03051901049911976,
0.03323284909129143,
-0.03200963884592056,
-0.03382660448551178,
0.00616820203140378,
0.004227594938129187,
-0.040228985249996185,
0.004076351877301931,
0.021866653114557266,
0.02800186537206173,
0.002267130883410573,
-0.025877850130200386,
0.008724730461835861,
-0.006541682872921228,
0.04131976142525673,
0.04517325386404991,
0.022872120141983032,
-0.015428554266691208,
0.009673682041466236,
0.014399703592061996,
0.010674056597054005,
0.005938500631600618,
-0.013710045255720615,
0.07915990799665451,
-0.0103332893922925,
-0.0020672320388257504,
-0.0037613091990351677,
-0.06757701933383942,
0.011825471185147762,
-0.03079022653400898,
0.013969674706459045,
-0.016075287014245987,
0.04154432564973831,
-0.024639949202537537,
0.023107709363102913,
-0.02834942936897278,
0.028511978685855865,
0.0011879957746714354,
0.004310219082981348,
-0.013210180215537548,
-0.00884129200130701,
0.0001665700983721763,
0.027550337836146355,
-0.003344748169183731,
-0.01875164918601513,
-0.03281732648611069,
-0.023456834256649017,
-0.018328366801142693,
-0.02854023687541485,
-0.009824790060520172,
0.006862552370876074,
0.007976739667356014,
0.057660941034555435,
-0.025017699226737022,
0.002234644489362836,
-0.021281899884343147,
-0.04239094629883766,
0.010737976990640163,
-0.022065499797463417,
0.0059211584739387035,
-0.017344167456030846,
0.02667914517223835,
0.03882337361574173,
0.08255897462368011,
-0.02163941040635109,
-0.009227821603417397,
0.018616672605276108,
0.06555813550949097,
0.06001167371869087,
-0.02922777645289898,
0.004432723857462406,
0.00206219800747931,
-0.013032334856688976,
0.02439773455262184,
-0.03454289957880974,
-0.020882533863186836,
0.012206027284264565,
-0.015177370980381966,
-0.01664145104587078,
-0.008353052660822868,
-0.01569725200533867,
-0.002410552930086851,
0.007911006920039654,
-0.006756477523595095,
-0.006731001660227776,
0.017566926777362823,
-0.0142627889290452,
-0.020349429920315742,
-0.002672650618478656,
0.027212992310523987,
0.01982254534959793,
-0.018232615664601326,
0.024609144777059555,
-0.052016835659742355,
-0.015209754928946495,
-0.014910795725882053,
0.018476247787475586,
-0.03502207249403,
0.023380953818559647,
-0.031574688851833344,
0.030518701300024986,
-0.013950341381132603,
0.008146202191710472,
-0.02252577617764473,
0.028324920684099197,
-0.005277982912957668,
-0.022623073309659958,
0.014642867259681225,
0.015868360176682472,
-0.008548676036298275,
0.02935541234910488,
0.007613527122884989,
-0.023180868476629257,
0.031422827392816544,
0.006112275179475546,
-0.0028422183822840452,
0.015137596987187862,
-0.06072187423706055,
-0.018701912835240364,
0.04084066301584244,
-0.008456270210444927,
0.04303183779120445,
0.037048645317554474,
-0.02643773704767227,
-0.02416016347706318,
0.011838862672448158,
-0.0016755416290834546,
-0.023350443691015244,
0.010868336074054241,
-0.05346016585826874,
-0.03507525846362114,
-0.021113235503435135,
0.026405807584524155,
0.026487315073609352,
-0.008038079366087914,
0.014920877292752266,
-0.0071933092549443245,
-0.010437634773552418,
-0.02946813404560089,
0.018637074157595634,
0.0011562919244170189,
0.016585519537329674,
0.0004317459533922374,
0.0006602304056286812,
0.005328609142452478,
0.028993630781769753,
0.00406773341819644,
-0.040222253650426865,
-0.024727901443839073,
-0.003426430281251669,
-0.0855732262134552,
-0.020207254216074944,
-0.004554188810288906,
0.0321018360555172,
0.05807562544941902,
-0.022737106308341026,
0.005715584848076105,
0.026324402540922165,
-0.0771162137389183,
0.011223998852074146,
-0.004444055259227753,
0.005419121589511633,
0.01868477463722229,
0.015822676941752434,
-0.031651951372623444,
0.0624014288187027,
0.020293286070227623,
0.03648015856742859,
-0.010270305909216404,
0.003995291888713837,
0.008918712846934795,
0.005972324870526791,
-0.007952054031193256,
0.01074533723294735,
0.037128519266843796,
-0.015218849293887615,
0.10901821404695511,
-0.031118016690015793,
-0.05177554488182068,
0.04530051350593567,
0.0028639144729822874,
0.013880094513297081,
-0.012014688923954964,
0.016647562384605408,
0.03844655677676201,
0.022937612608075142,
0.0015921577578410506,
0.0009639178169891238,
0.03138107806444168,
-0.024116089567542076,
0.015555146150290966,
0.04002960026264191,
-0.023994024842977524,
-0.004938306752592325,
0.026273377239704132,
-0.016863593831658363,
-0.04561397805809975,
0.039877232164144516,
-0.02189645729959011,
-0.021756093949079514,
-0.013839563354849815,
-0.028065823018550873,
-0.004822050221264362,
-0.0034160518553107977,
0.04770928993821144,
-0.009940513409674168,
0.012138799764215946,
0.008352120406925678,
-0.023991648107767105,
-0.027539119124412537,
0.020866498351097107,
0.025435931980609894,
-0.0367540568113327,
0.05514814704656601,
0.025357484817504883,
-0.02114999108016491,
-0.027060426771640778,
-0.017647456377744675,
-0.0004519362119026482,
-0.0031124637462198734,
-0.01639443077147007,
-0.05496150627732277,
-0.046275895088911057,
-0.007371465675532818,
0.00006677951023448259,
0.05577751249074936,
-0.0060928924940526485,
-0.015196661464869976,
0.026416560634970665,
-0.05773685500025749,
0.03307754546403885,
0.02739592082798481,
-0.0024750027805566788,
-0.022231198847293854,
-0.014437793754041195,
0.040884554386138916,
0.0021547747310250998,
0.025800615549087524,
-0.01300301868468523,
-0.023075707256793976,
0.002848922275006771,
0.001643206225708127,
0.04443902522325516,
-0.05314015969634056,
-0.008069664239883423,
0.0016898689791560173,
0.011324744671583176,
-0.013858053833246231,
-0.006509253289550543,
-0.03398967161774635,
0.03869134187698364,
-0.0020004883408546448,
0.008698518387973309,
-0.008368611335754395,
0.006170192733407021,
-0.03725781664252281,
0.05831329524517059,
0.011734290048480034,
0.014373261481523514,
0.06665666401386261,
-0.007651729974895716,
0.012469564564526081,
0.0475885309278965,
-0.055210474878549576,
-0.007075200323015451,
0.007466059643775225,
-0.037692539393901825,
-0.049397535622119904,
-0.015461462549865246,
-0.02316996082663536,
0.03788934275507927,
-0.021665027365088463,
0.015495258383452892,
0.04448724538087845,
-0.042927924543619156,
-0.01583816483616829,
0.05647262930870056,
-0.01279410533607006,
0.032654985785484314,
0.055047500878572464,
0.015315080992877483,
0.059672463685274124,
0.029076701030135155,
-0.001014122855849564,
0.018430978059768677,
0.03720870241522789,
-0.035807427018880844,
0.004291784018278122,
0.009033679962158203,
0.004970619920641184,
0.008396316319704056,
0.022843634709715843,
0.012610070407390594,
-0.05265543609857559,
0.008326982147991657,
0.0468900203704834,
-0.0386989526450634,
0.009120526723563671,
0.02439923770725727,
-0.06645940989255905,
0.07970402389764786,
-0.002879499923437834,
0.020481491461396217,
-0.0014841397060081363,
0.021728647872805595,
-0.02298610843718052,
0.01569732092320919,
0.03876769542694092,
0.0476546473801136,
-0.03347562626004219,
0.0007191727054305375,
-0.020693665370345116,
-0.0033237433526664972,
0.01009390875697136,
-0.04088500142097473,
-0.0327591747045517,
0.0439128614962101,
-0.05578594654798508,
0.004298232961446047,
-0.03823387995362282,
0.009652500040829182,
0.0002115568786393851,
0.006294370163232088,
0.020314184948801994,
-0.002337572630494833,
0.011648891493678093,
-0.009556328877806664,
-0.03999658674001694,
0.07142498344182968,
-0.05794240161776543,
0.03617923706769943,
0.0017401229124516249,
-0.014801888726651669,
0.007181167136877775,
-0.0011171455262228847
] |
<p>I'm wondering on what principles Noether's theorem foots. More precisely:</p>
<p><em>The action is a functional on the fields only. Why do we consider then variations of the space time too? In principle careful considerations, however, seem to untangle them as special field variations. So what's going on here truly?</em></p>
| 8,304 |
[
-0.00508672883734107,
-0.0068504768423736095,
0.02591339498758316,
-0.023044101893901825,
0.03386112302541733,
0.014581414870917797,
-0.0316363088786602,
-0.033133383840322495,
-0.02944483794271946,
-0.008916391059756279,
0.007114517968147993,
-0.007042884360998869,
0.0669134184718132,
0.027333727106451988,
0.009626575745642185,
-0.026446856558322906,
0.023030852898955345,
-0.01830359734594822,
-0.03041031025350094,
-0.0296244565397501,
-0.011062016710639,
0.03834042698144913,
-0.04213249310851097,
0.017852436751127243,
-0.03755093365907669,
-0.02034047432243824,
-0.013844039291143417,
0.0021525162737816572,
0.03671710193157196,
0.06435760110616684,
-0.020694416016340256,
-0.03336527198553085,
-0.03599228337407112,
0.04252469539642334,
0.01946907304227352,
0.0075347828678786755,
-0.030416171997785568,
-0.014244726859033108,
0.010328810662031174,
-0.01643425039947033,
-0.019791200757026672,
-0.01747375912964344,
-0.019506793469190598,
0.04194355756044388,
-0.04928421974182129,
0.035862356424331665,
0.008224188350141048,
-0.0022136156912893057,
0.05748002603650093,
-0.054469410330057144,
0.07958430796861649,
0.005776493344455957,
-0.0023819676134735346,
-0.00004766092752106488,
-0.03312525898218155,
0.015884585678577423,
0.05985727161169052,
0.050687652081251144,
0.008687409572303295,
-0.054657526314258575,
-0.062124740332365036,
-0.011185123585164547,
-0.007136452477425337,
-0.03863144665956497,
-0.016130341216921806,
0.018695993348956108,
0.01982378028333187,
-0.004750428721308708,
0.026376990601420403,
-0.011417240835726261,
-0.006230924744158983,
0.015094843693077564,
0.029003063216805458,
0.00323244440369308,
-0.0046908240765333176,
0.002595827216282487,
0.03305047005414963,
-0.041892096400260925,
0.039515282958745956,
0.02719089388847351,
0.00011767971591325477,
0.0059684403240680695,
0.03428659215569496,
0.014469116926193237,
-0.0035333235282450914,
-0.025623923167586327,
0.04805196449160576,
-0.0003443026798777282,
0.008598045445978642,
0.017191778868436813,
-0.0021036711987107992,
-0.006085040979087353,
0.011858753859996796,
-0.023865889757871628,
-0.034049052745103836,
0.0359591580927372,
0.016904156655073166,
0.023189470171928406,
-0.026512060314416885,
-0.019463280215859413,
-0.010239802300930023,
-0.007441285531967878,
0.022080419585108757,
0.03858095780014992,
0.001631861086934805,
-0.0015461421571671963,
-0.04350685700774193,
0.029921775683760643,
-0.02641650289297104,
0.0006599178304895759,
-0.05518793687224388,
0.021458066999912262,
-0.008392119780182838,
0.0060348063707351685,
0.01258908212184906,
-0.020043157041072845,
0.022994281724095345,
-0.0038980008102953434,
0.0373702198266983,
0.049988605082035065,
0.054200295358896255,
-0.0015059404540807009,
0.030308621004223824,
0.014883526600897312,
-0.05468999594449997,
0.023698478937149048,
0.05514281243085861,
0.003457780694589019,
-0.027200551703572273,
-0.0008126698085106909,
-0.003016349393874407,
0.002135014394298196,
-0.016757965087890625,
0.08117979019880295,
0.020301837474107742,
-0.02651958540081978,
-0.12517844140529633,
-0.05981060862541199,
0.03154957666993141,
-0.020184088498353958,
-0.037305742502212524,
-0.021893953904509544,
0.028980152681469917,
0.02406845986843109,
0.08233141154050827,
-0.0022624677512794733,
0.015526958741247654,
0.022834505885839462,
0.01924603432416916,
0.03042907826602459,
-0.01484840176999569,
-0.015597095713019371,
-0.006803020369261503,
-0.06674452871084213,
-0.027108030393719673,
-0.0622720941901207,
0.026701737195253372,
0.03523432835936546,
0.021720942109823227,
-0.046018086373806,
0.08792093396186829,
0.004911750555038452,
-0.003627994330599904,
0.005493910983204842,
-0.006668885704129934,
0.0024733846075832844,
0.047954902052879333,
-0.00006339126412058249,
0.036061808466911316,
0.04131579026579857,
0.022762900218367577,
0.05935866758227348,
-0.010261989198625088,
0.06415626406669617,
0.025888623669743538,
-0.03812992572784424,
-0.008905217051506042,
0.01194804348051548,
-0.009627506136894226,
0.012930280528962612,
-0.042190395295619965,
-0.014569848775863647,
0.012721139006316662,
0.020350893959403038,
-0.04168035462498665,
0.03319304436445236,
-0.010823016054928303,
-0.0059849959798157215,
0.004186335485428572,
-0.02728867158293724,
-0.01802344247698784,
-0.09362322837114334,
0.018065599724650383,
-0.019107049331068993,
-0.042486269026994705,
0.028871450573205948,
0.024396192282438278,
0.02197863720357418,
-0.06056017801165581,
-0.04235197231173515,
-0.000689760665409267,
0.046827249228954315,
0.007965401746332645,
-0.015266134403645992,
0.038761287927627563,
0.0447114072740078,
0.016211675480008125,
0.03397662192583084,
0.04788634181022644,
-0.0022302549332380295,
-0.00849513802677393,
0.03781035915017128,
-0.009633292444050312,
-0.0013129382859915495,
0.020339874550700188,
0.0051386007107794285,
0.009367874823510647,
-0.025086309760808945,
-0.021373765543103218,
0.04643905162811279,
-0.03557225689291954,
0.06896936148405075,
0.04379376769065857,
-0.005503552034497261,
-0.0013096973998472095,
0.03995075076818466,
-0.012414572760462761,
0.006293088663369417,
0.0197649784386158,
-0.012094303034245968,
-0.022419385612010956,
0.006101059261709452,
0.044196609407663345,
0.03728805109858513,
-0.005115860141813755,
-0.011144758202135563,
0.03797180950641632,
0.04503611475229263,
0.030607052147388458,
0.03259878605604172,
-0.004408007953315973,
-0.03332991153001785,
0.0036154240369796753,
0.010571995750069618,
0.016105735674500465,
0.000049682585085975006,
0.03488460183143616,
-0.003988474141806364,
0.00015740390517748892,
0.012095911428332329,
-0.029519738629460335,
0.03491426631808281,
-0.032577965408563614,
0.055626653134822845,
0.014705887995660305,
-0.013099988922476768,
0.007015809416770935,
-0.014905951917171478,
0.06493957340717316,
0.05481357127428055,
-0.0021880646236240864,
-0.0004999361699447036,
-0.03686763718724251,
-0.006793882232159376,
0.03898037597537041,
-0.03862129524350166,
-0.04108571261167526,
-0.007852683775126934,
0.02311818301677704,
-0.021621497347950935,
-0.010411671362817287,
-0.03412070870399475,
-0.02716301567852497,
-0.021992307156324387,
-0.006013497244566679,
0.018909703940153122,
-0.01781005598604679,
0.024676833301782608,
0.011832105927169323,
-0.02775348350405693,
-0.00011019332305295393,
-0.029960621148347855,
0.009567315690219402,
0.04752543196082115,
-0.047627758234739304,
0.006663849111646414,
-0.04163829982280731,
-0.03132147714495659,
0.061046671122312546,
0.00774762686342001,
0.045286186039447784,
0.007622091099619865,
-0.005031634122133255,
-0.04238981381058693,
-0.023340800777077675,
-0.029291659593582153,
0.01920955255627632,
-0.012055054306983948,
0.008529896847903728,
0.03858811408281326,
-0.01651192642748356,
-0.0230670478194952,
0.02234315499663353,
-0.01265911478549242,
-0.061420880258083344,
-0.02780362404882908,
0.022295674309134483,
0.022618481889367104,
-0.045864831656217575,
0.021461715921759605,
0.036234330385923386,
-0.06271907687187195,
-0.031456537544727325,
-0.02074490301311016,
-0.03874211385846138,
0.009953496977686882,
-0.025035196915268898,
0.04075249657034874,
-0.0392899326980114,
-0.06340453028678894,
0.07960250228643417,
0.036522816866636276,
-0.027825092896819115,
-0.0042151203379035,
-0.017312025651335716,
-0.00923695508390665,
-0.016354838386178017,
0.011805734597146511,
0.01506907120347023,
-0.009046505205333233,
0.03841676563024521,
0.039420053362846375,
0.02369915135204792,
0.026786545291543007,
0.032466161996126175,
-0.04306540638208389,
-0.00006789489998482168,
0.022602736949920654,
0.013838166370987892,
0.04596007987856865,
0.006914226338267326,
-0.010432170704007149,
-0.00580442463979125,
0.005512526258826256,
0.02858460322022438,
0.017360754311084747,
-0.04694976285099983,
0.038585443049669266,
0.019266903400421143,
0.01610160432755947,
-0.032719485461711884,
0.023094626143574715,
-0.026407454162836075,
-0.026450296863913536,
0.010065201669931412,
0.0010402887128293514,
0.02021368406713009,
-0.045625485479831696,
-0.013916634023189545,
-0.0008655957644805312,
0.05179135501384735,
-0.06908480823040009,
-0.03954779729247093,
0.003585912985727191,
-0.01679336465895176,
0.025346074253320694,
-0.016618819907307625,
-0.006104668602347374,
0.028831079602241516,
0.027524825185537338,
0.022839514538645744,
0.013584362342953682,
-0.040456049144268036,
-0.00463563809171319,
-0.0667976588010788,
-0.00039283616933971643,
0.018532389774918556,
0.0423784963786602,
0.017143310979008675,
0.060135260224342346,
0.007024470251053572,
0.02458203211426735,
0.006303598638623953,
-0.0020787962712347507,
-0.07911357283592224,
0.04194195196032524,
-0.008568905293941498,
-0.03162648156285286,
0.016263803467154503,
-0.027544720098376274,
-0.012777351774275303,
-0.01166102197021246,
-0.014287819154560566,
-0.03968840092420578,
-0.03097751922905445,
-0.07332475483417511,
-0.0021232287399470806,
-0.03286414593458176,
-0.027376318350434303,
-0.044302452355623245,
0.03723246231675148,
0.038493670523166656,
-0.024689508602023125,
-0.015637153759598732,
0.04699622467160225,
-0.03698309510946274,
-0.023605862632393837,
0.005825396627187729,
-0.004879026673734188,
0.00431156437844038,
0.024631764739751816,
0.009475518018007278,
-0.006945171859115362,
-0.0032539679668843746,
0.02173261158168316,
0.02516435831785202,
0.07943833619356155,
0.03328438475728035,
0.005696356762200594,
-0.026062246412038803,
-0.02742796391248703,
-0.009385640732944012,
0.01832515560090542,
0.08047561347484589,
0.01795377768576145,
-0.012869047001004219,
0.040293093770742416,
0.017530445009469986,
-0.0150052011013031,
0.023653164505958557,
0.041821472346782684,
-0.0016310397768393159,
-0.05041477829217911,
-0.03867875412106514,
-0.009415664710104465,
-0.054687198251485825,
-0.00018233196169603616,
0.013133466243743896,
-0.01335311308503151,
-0.032156169414520264,
-0.02450181171298027,
0.009231939911842346,
0.004191890358924866,
-0.007629879750311375,
-0.012388795614242554,
0.028772305697202682,
-0.015164533630013466,
0.009893449023365974,
-0.01460034679621458,
0.022864865139126778,
0.037511132657527924,
0.0631847083568573,
0.0048636808060109615,
-0.009384691715240479,
-0.07869579643011093,
-0.016353080049157143,
0.0590071827173233,
0.0337950624525547,
0.016790373250842094,
-0.001064622774720192,
-0.0414433553814888,
-0.022128451615571976,
0.03684304282069206,
-0.03856750950217247,
0.0090042594820261,
0.0204064529389143,
0.013489381410181522,
-0.024968905374407768,
-0.016727270558476448,
-0.021812546998262405,
0.027591153979301453,
-0.007862485013902187,
0.02113424986600876,
-0.01306820847094059,
0.004238818772137165,
-0.005688573699444532,
0.003106559393927455,
0.006562096066772938,
0.0372844897210598,
0.05792578309774399,
0.013518460094928741,
-0.015599471516907215,
0.04013661667704582,
-0.044365983456373215,
-0.07153812050819397,
-0.016184918582439423,
0.06677667051553726,
0.004050487652420998,
0.0209983941167593,
-0.016205118969082832,
-0.05786748602986336,
0.00623517669737339,
-0.005946408491581678,
-0.00895112194120884,
0.01877521723508835,
-0.038084208965301514,
0.01585604064166546,
0.03902105614542961,
0.01853868179023266,
0.03793242946267128,
0.030439451336860657,
-0.02257927693426609,
-0.005334090441465378,
-0.0000123833769976045,
0.034180305898189545,
0.005343069788068533,
0.014656788669526577,
-0.04074816405773163,
-0.012975404039025307,
-0.029721589758992195,
0.0682530328631401,
-0.011169182136654854,
-0.0003419448621571064,
-0.008870560675859451,
-0.031008735299110413,
-0.04245372116565704,
0.023529650643467903,
0.027024179697036743,
-0.002887811278924346,
-0.021769504994153976,
0.023036932572722435,
0.004219638183712959,
0.014461064711213112,
0.021098913624882698,
0.008662921376526356,
-0.032762378454208374,
0.030065521597862244,
0.02866235189139843,
0.03340300917625427,
-0.01609417237341404,
-0.028167827054858208,
0.014921948313713074,
-0.020551061257719994,
0.025160057470202446,
0.013030887581408024,
-0.02558699995279312,
0.0365581251680851,
-0.039304524660110474,
-0.030313443392515182,
-0.022459372878074646,
-0.034433331340551376,
0.02095283567905426,
-0.039074745029211044,
0.013167699798941612,
0.029404565691947937,
0.018922103568911552,
-0.10519246011972427,
-0.06075024604797363,
0.030290715396404266,
0.00008653294207761064,
-0.04665938764810562,
-0.007271358743309975,
-0.002869527554139495,
-0.03710543364286423,
-0.04162045940756798,
0.007397792302072048,
0.04955466836690903,
-0.030434129759669304,
0.0116187809035182,
0.008900067768990993,
0.02784736640751362,
0.05132647231221199,
-0.023508362472057343,
0.00598768750205636,
0.022101454436779022,
-0.012616541236639023,
-0.0031794975511729717,
-0.021748853847384453,
0.056413110345602036,
-0.009356597438454628,
-0.012229517102241516,
-0.03341491520404816,
0.015471449121832848,
0.017782101407647133,
-0.023421401157975197,
0.007199173793196678,
0.04705134406685829,
0.015106996521353722,
-0.004322872031480074,
-0.04226570948958397,
-0.007428744342178106,
-0.025458812713623047,
0.07281474024057388,
-0.008047685958445072,
0.005315027199685574,
-0.004041919019073248,
-0.03557484596967697,
0.016984986141324043,
0.0023724474012851715,
0.007228671107441187,
0.0017233883263543248,
0.05330711603164673,
-0.008332686498761177,
-0.009979238733649254,
0.01717362180352211,
-0.007094926666468382,
-0.001193152624182403,
-0.020314231514930725,
0.013994649983942509,
0.015442040748894215,
0.011558123864233494,
-0.026622425764799118,
-0.006513552740216255,
-0.02212550677359104,
0.03204057365655899,
0.06713871657848358,
-0.011355787515640259,
0.030277539044618607,
0.023676883429288864,
-0.037286385893821716,
-0.006898775696754456,
-0.02415931038558483,
-0.011427443474531174,
-0.019689610227942467,
0.017490526661276817,
0.026182373985648155,
0.001016451045870781,
0.033714670687913895,
0.06740544736385345,
0.04799991846084595,
-0.047350745648145676,
0.017227454110980034,
0.04025939851999283,
0.017246056348085403,
0.04603283852338791,
0.01198198925703764,
-0.06958209723234177,
0.01171239372342825,
-0.03254426270723343,
0.030157901346683502,
0.017763348296284676,
0.02212102897465229,
0.05507008358836174,
-0.014974795281887054,
0.00394901167601347,
0.00536833330988884,
-0.01973492093384266,
-0.03420354425907135,
0.01094158086925745,
-0.02291659079492092,
0.03446260839700699,
-0.0002454781497363001,
0.004782367963343859,
0.08153270184993744,
-0.010920562781393528,
-0.011853320524096489,
0.03485947102308273,
-0.053723759949207306,
-0.01975846104323864,
-0.04639359563589096,
-0.035116493701934814,
0.060226764529943466,
-0.016253095120191574,
-0.053295109421014786,
-0.012159867212176323,
0.002273579128086567,
0.010045765899121761,
0.03617356717586517,
0.05022016912698746,
-0.008694990538060665,
0.07271241396665573,
0.01894192397594452,
0.016173919662833214,
0.019471721723675728,
0.009774318896234035,
0.11390761286020279,
0.03562408313155174,
-0.024180032312870026,
-0.07755357027053833,
0.027717875316739082,
-0.04172438383102417,
-0.02175961062312126,
-0.017352648079395294,
0.01722443662583828,
-0.0011850734008476138,
0.006918352097272873,
0.0474696010351181,
0.00891381036490202,
-0.030172524973750114,
-0.03355898708105087,
0.05217793956398964,
-0.029163986444473267,
-0.023077799007296562,
0.02129163034260273,
0.008115890435874462,
0.011065798811614513,
0.02712155133485794,
-0.031171754002571106,
-0.019512122496962547,
-0.03131398931145668,
0.018375881016254425,
-0.007696095388382673,
-0.0736633837223053,
0.03218403086066246,
0.020151035860180855,
-0.04469870775938034,
-0.0016102419467642903,
0.005641571246087551,
-0.023144196718931198,
-0.08374013751745224,
-0.02275286614894867,
-0.005180054344236851,
-0.0044615124352276325,
0.0369824655354023,
0.04646416753530502,
0.017104988917708397,
-0.0036453146021813154,
0.0006427139160223305,
0.040815651416778564,
-0.029596107080578804,
-0.008323059417307377,
-0.0359308123588562,
0.04175196960568428,
-0.013970566913485527,
0.0036323885433375835,
-0.005837761797010899,
-0.011580388061702251,
0.028406314551830292,
-0.0717548355460167,
-0.015166309662163258,
-0.023917658254504204,
0.0076109180226922035,
0.011395863257348537,
-0.032788101583719254,
-0.012643520720303059,
-0.021143194288015366,
-0.0027740218210965395,
0.01910603791475296,
-0.01951686106622219,
0.0031520663760602474,
0.01003353577107191,
0.003864951664581895,
-0.004575103521347046,
-0.008866788819432259,
-0.013511043973267078,
-0.0007501168875023723,
-0.009565290063619614,
-0.024955492466688156,
0.01992487534880638,
-0.012624801136553288,
0.01612921431660652,
0.02091539092361927,
-0.03169950097799301,
-0.0045371451415121555,
0.004467853344976902,
-0.036890432238578796,
0.006519589107483625,
-0.03774944320321083,
-0.002425873652100563,
-0.012658534571528435,
0.029011597856879234,
0.007098441943526268,
0.04401654005050659,
-0.003701044712215662,
0.019302211701869965,
-0.030886167660355568,
0.0019521036883816123,
0.023985987529158592,
0.0010002428898587823,
-0.006686226464807987,
-0.003945257980376482,
-0.015575106255710125,
-0.047352954745292664,
-0.024088485166430473,
0.002814078703522682,
0.02484065853059292,
0.023646585643291473,
0.004478811286389828,
0.04426850378513336,
-0.016516875475645065,
0.014552474021911621,
0.012286683544516563,
-0.01938137412071228,
0.028283633291721344,
0.024592984467744827,
-0.007089679595082998,
-0.061473309993743896,
-0.012221143580973148,
-0.018040047958493233,
0.030099809169769287,
0.0072042993269860744,
0.03831262141466141,
-0.023233355954289436,
0.0007469073752872646,
-0.028944483026862144,
0.02369234524667263,
-0.04271312803030014,
0.0027706429827958345,
-0.05800613760948181,
0.06347180902957916,
0.017013151198625565,
0.0024493171367794275,
-0.023162847384810448,
0.03442579135298729,
-0.014448918402194977,
-0.062209807336330414,
0.015481703914701939,
0.010551854968070984,
-0.01409947220236063,
0.021954089403152466,
0.03875851631164551,
0.005783969536423683,
0.04614714905619621,
-0.004075086209923029,
-0.04782690480351448,
0.01091853529214859,
-0.056174684315919876,
-0.0660804957151413,
0.0410335548222065,
-0.02281947061419487,
0.006850576028227806,
0.008141941390931606,
-0.02856559306383133,
-0.017556410282850266,
0.026409510523080826,
-0.01683942787349224,
-0.0008061971166171134,
-0.005041634663939476,
-0.015295456163585186,
-0.0007441696361638606,
-0.043428994715213776,
0.03452116623520851,
-0.019413230940699577,
-0.027001474052667618,
0.01730157434940338,
0.010545182041823864,
-0.023963170126080513,
-0.012964163906872272,
0.012223508208990097,
-0.022572824731469154,
0.01628587767481804,
0.016057612374424934,
0.0022737905383110046,
0.0201102364808321,
0.102342389523983,
-0.042164146900177,
0.02093472331762314,
0.0011433957843109965,
0.009486140683293343,
-0.08837931603193283,
-0.026882020756602287,
-0.006055936217308044,
0.024281438440084457,
0.03706851974129677,
-0.0434417761862278,
0.03555997833609581,
0.013384267687797546,
-0.0396219864487648,
0.042299140244722366,
-0.023338017985224724,
-0.03755398467183113,
-0.016264373436570168,
-0.008825315162539482,
-0.026298025622963905,
0.10149455815553665,
0.03155137225985527,
0.024910571053624153,
0.03853114694356918,
0.0017948504537343979,
-0.005426308140158653,
-0.04153482988476753,
-0.022429203614592552,
0.01595914177596569,
-0.0201719943434,
-0.013015171512961388,
0.0567244328558445,
0.020116642117500305,
-0.07160251587629318,
0.020995767787098885,
-0.01631920598447323,
-0.0142276082187891,
-0.00354967312887311,
0.0063889347948133945,
0.028476454317569733,
-0.0021845486480742693,
-0.00293313548900187,
-0.03688368201255798,
-0.024393413215875626,
0.03491489216685295,
0.02835351601243019,
0.006789073813706636,
-0.011157695204019547,
0.026569902896881104,
0.03432832285761833,
-0.06152302771806717,
-0.026571080088615417,
0.03418194130063057,
-0.010479717515408993,
-0.030525103211402893,
-0.018145564943552017,
0.027848295867443085,
-0.00036181879113428295,
-0.016075357794761658,
-0.010271682403981686,
-0.0276988185942173,
-0.007425835821777582,
0.0587129183113575,
-0.024503611028194427,
-0.000850366021040827,
0.025982974097132683,
-0.033722419291734695,
-0.038533564656972885,
0.017849314957857132,
0.03447515517473221,
0.005866599269211292,
-0.0562894232571125,
0.011717456392943859,
-0.013246743008494377,
-0.039114151149988174,
-0.01238291710615158,
-0.03656215965747833,
-0.019887935370206833,
-0.0025506443344056606,
0.03938296437263489,
-0.00040453282417729497,
-0.04004278406500816,
-0.039080530405044556,
0.004514418542385101,
-0.06847288459539413,
0.011308702640235424,
-0.016730444505810738,
-0.00440515810623765,
-0.04419584572315216,
-0.020163455978035927,
-0.01744385063648224,
0.006798828952014446,
0.013966354541480541,
-0.01081879623234272,
-0.02041512168943882,
0.015173858031630516,
0.019220657646656036,
0.020999658852815628,
-0.01749529130756855,
0.012661813758313656,
-0.009414348751306534,
-0.032211657613515854,
0.00731299165636301,
-0.025340626016259193,
-0.026203719899058342,
0.004940237384289503,
0.01727995090186596,
-0.023610776290297508,
0.06680555641651154,
0.004408901557326317,
-0.04627154394984245,
0.059849951416254044,
0.019286274909973145,
0.0009654670138843358,
0.027571676298975945,
-0.036063723266124725,
0.023627830669283867,
0.047339990735054016,
-0.04009409621357918,
-0.01841394416987896,
0.007460558321326971,
-0.06643837690353394,
-0.019423633813858032,
-0.005896253045648336,
-0.01008594036102295,
0.03442804142832756,
-0.0316128171980381,
-0.013453050516545773,
0.09501928091049194,
-0.04050130024552345,
0.011896687559783459,
0.08666283637285233,
0.013463561423122883,
0.019467348232865334,
-0.002406537299975753,
-0.003146461211144924,
0.0195369441062212,
0.007228214293718338,
-0.00832589715719223,
0.048834655433893204,
0.02097599022090435,
-0.004266025498509407,
-0.008299938403069973,
0.03512415289878845,
-0.021637745201587677,
0.024652602151036263,
0.006683806888759136,
0.05705584958195686,
-0.05193880945444107,
-0.019894063472747803,
0.007896488532423973,
-0.02297838032245636,
0.026831461116671562,
0.04561270773410797,
-0.03309892490506172,
0.08086942136287689,
-0.028869276866316795,
-0.0028769581113010645,
-0.009020423516631126,
-0.005650840699672699,
-0.02470451034605503,
-0.013010240159928799,
0.03872360661625862,
0.06113239377737045,
-0.0020993456710129976,
0.004000051412731409,
0.0204059649258852,
0.014790553599596024,
0.005098335444927216,
-0.03400132432579994,
0.02042265236377716,
-0.010228529572486877,
-0.0114776361733675,
-0.0037418007850646973,
-0.008312140591442585,
-0.04300371930003166,
0.009238498285412788,
0.03487684577703476,
0.01245650090277195,
0.0700782835483551,
0.002865128219127655,
-0.0031072066631168127,
-0.04354860633611679,
0.024341264739632607,
-0.05161455646157265,
-0.007904785685241222,
-0.02524404413998127,
0.03327135369181633,
-0.004646142013370991,
-0.009582322090864182
] |
<p>What is the rigorous justification of <a href="http://en.wikipedia.org/wiki/Wick_rotation" rel="nofollow">Wick rotation</a> in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a convincing proof that it can be done at the level of path integral.</p>
<p>How do we know for sure that Minkowski action and Euclidean action lead to the equivalent physical result? Is there an example where they differ by e.g. a contribution from a pole not taken into account while performing Wick rotation?</p>
| 8,305 |
[
-0.0068465350195765495,
0.02515842765569687,
-0.0018021335126832128,
-0.024002784863114357,
0.03688759356737137,
0.00532712833955884,
-0.013564139604568481,
-0.043528493493795395,
-0.018549932166934013,
-0.022418443113565445,
-0.014027782715857029,
0.01251212041825056,
0.05341988429427147,
-0.0025105811655521393,
0.0028877556324005127,
-0.0162193700671196,
0.024270374327898026,
-0.019373755902051926,
0.018545255064964294,
-0.033967796713113785,
-0.03738454356789589,
0.057904522866010666,
-0.0005885363207198679,
-0.028673941269516945,
-0.020550046116113663,
0.016056202352046967,
0.02582734450697899,
0.009745984338223934,
-0.010498679243028164,
0.07751558721065521,
-0.029879018664360046,
-0.009480983018875122,
0.03253490477800369,
0.04564804956316948,
-0.0051310062408447266,
0.01372463721781969,
-0.01241363026201725,
-0.024025866761803627,
-0.004639567341655493,
-0.0008749586995691061,
-0.03686103969812393,
0.005373939406126738,
-0.04894779995083809,
0.0234480369836092,
-0.004840307403355837,
0.04148101806640625,
-0.013519655913114548,
0.011567329987883568,
0.06784668564796448,
-0.07849949598312378,
0.037652045488357544,
0.00768235232681036,
0.0351966992020607,
0.02064567431807518,
0.016522251069545746,
-0.008100262843072414,
0.06823910027742386,
0.03744657710194588,
-0.04252573475241661,
-0.05962202325463295,
-0.06545750796794891,
-0.04546596482396126,
0.005267428234219551,
-0.029948676005005836,
0.021729709580540657,
-0.013972912915050983,
0.031979672610759735,
0.0007146246498450637,
0.01818915456533432,
-0.022080956026911736,
-0.0056699966080486774,
0.00975007750093937,
0.030657272785902023,
-0.006309330929070711,
-0.017049064859747887,
0.004346149042248726,
0.028754008933901787,
0.008712274953722954,
0.04766453057527542,
0.037893470376729965,
-0.022793661803007126,
0.0016788822831586003,
0.005680004600435495,
0.006914922036230564,
0.007850837893784046,
-0.0009819925762712955,
0.06067075580358505,
0.0020043966360390186,
-0.017845695838332176,
0.04487477242946625,
-0.013317739591002464,
-0.009236489422619343,
0.03345928713679314,
0.008269749581813812,
-0.037507012486457825,
0.03970583900809288,
0.019547713920474052,
0.035923607647418976,
-0.02319261245429516,
0.005880740936845541,
-0.05044825002551079,
-0.01744840294122696,
-0.014534820802509785,
0.06440623849630356,
0.012365487404167652,
0.00307701388373971,
-0.007508753798902035,
0.06341981887817383,
-0.026172317564487457,
-0.016009289771318436,
-0.06935419887304306,
0.02073608711361885,
-0.014934681355953217,
-0.0212737787514925,
-0.02312408573925495,
-0.03594901040196419,
-0.019677111878991127,
-0.027472013607621193,
0.052715808153152466,
0.08197019249200821,
0.058287106454372406,
-0.055846381932497025,
0.008352882228791714,
-0.034529007971286774,
-0.054827164858579636,
0.00909520499408245,
0.02831244096159935,
-0.027257433161139488,
-0.028597941622138023,
-0.015692654997110367,
0.027435610070824623,
-0.01914498396217823,
0.020327158272266388,
0.03271235153079033,
0.024673353880643845,
-0.03794730082154274,
-0.10364855825901031,
-0.053496334701776505,
0.042346540838479996,
0.004920412320643663,
0.0061181094497442245,
-0.07883260399103165,
0.009200189262628555,
0.04005218297243118,
0.11364976316690445,
-0.0022795412223786116,
0.011180545203387737,
-0.018528589978814125,
0.027845967561006546,
0.0023563983850181103,
-0.0261237770318985,
-0.04817652329802513,
0.03149973601102829,
-0.048607274889945984,
-0.04783007502555847,
-0.053611110895872116,
0.02429637499153614,
0.051773570477962494,
-0.006200718693435192,
-0.030553964897990227,
0.0462225116789341,
-0.018304232507944107,
-0.0020730721298605204,
0.014537530951201916,
0.00234962091781199,
-0.001822403515689075,
0.06917381286621094,
0.012663541361689568,
-0.014275419525802135,
0.01136050745844841,
-0.03203007951378822,
0.031746700406074524,
0.0005396746564656496,
0.02082839049398899,
0.052311357110738754,
-0.032451264560222626,
0.009535006247460842,
-0.0006812793435528874,
0.022705839946866035,
-0.0026950999163091183,
-0.026755841448903084,
-0.016421975567936897,
-0.0628226026892662,
-0.0034866444766521454,
-0.021361568942666054,
0.016712265089154243,
-0.011569528840482235,
0.011967366561293602,
-0.003646501339972019,
-0.058921344578266144,
-0.017165353521704674,
-0.05702365189790726,
0.02806434966623783,
0.032137058675289154,
-0.0324394553899765,
0.003618444548919797,
0.01600988581776619,
0.02932741865515709,
-0.040220025926828384,
-0.048018261790275574,
-0.012991918250918388,
0.02767401561141014,
-0.013726879842579365,
-0.015785876661539078,
0.009662985801696777,
0.03750796616077423,
0.046590808779001236,
-0.02203986793756485,
0.04238413646817207,
-0.0194496288895607,
-0.016709009185433388,
-0.011837088502943516,
-0.02497732825577259,
-0.00016022101044654846,
0.016226354986429214,
-0.0072237723506987095,
0.007382066920399666,
0.0009847155306488276,
-0.00875747762620449,
0.04166898503899574,
-0.017302460968494415,
0.07435382902622223,
0.06762103736400604,
-0.008734313771128654,
-0.03312710300087929,
0.04767106473445892,
-0.011131140403449535,
0.000983618781901896,
0.03058355674147606,
-0.06038409471511841,
-0.04384930059313774,
-0.004296144470572472,
0.04672261327505112,
0.034599363803863525,
-0.04372549057006836,
0.002855621511116624,
0.017477557063102722,
0.0467432364821434,
-0.014178982935845852,
0.046355582773685455,
-0.006182176060974598,
0.004958008881658316,
0.005935148801654577,
-0.012586927972733974,
0.013224859721958637,
-0.008857039734721184,
0.04771525412797928,
-0.022006375715136528,
-0.0037937648594379425,
0.026186635717749596,
-0.07567557692527771,
0.03358509764075279,
-0.05790901184082031,
0.014032263308763504,
0.014478299766778946,
0.0031672162003815174,
0.017772510647773743,
-0.01711944304406643,
0.04407322779297829,
-0.008818007074296474,
-0.009735172614455223,
-0.005592589266598225,
-0.05802519619464874,
-0.01291259378194809,
0.026744546368718147,
-0.009234837256371975,
-0.017063744366168976,
-0.022281013429164886,
0.012013603001832962,
-0.016850702464580536,
0.007605873513966799,
-0.033684141933918,
-0.012657439336180687,
-0.01237083412706852,
-0.0057436502538621426,
0.012339265085756779,
0.010553620755672455,
0.026977619156241417,
-0.011124452576041222,
-0.03232451155781746,
0.008993200957775116,
0.00384450051933527,
0.006358310580253601,
0.04270549863576889,
-0.05315963178873062,
0.005244877655059099,
-0.03310063108801842,
-0.01305372454226017,
0.08137892186641693,
-0.04225492477416992,
0.004582585766911507,
0.0002636156277731061,
-0.0030814793426543474,
-0.038807403296232224,
-0.0018589190440252423,
-0.00810531247407198,
0.02446913905441761,
0.00020087574375793338,
-0.010560509748756886,
0.018076270818710327,
-0.030317338183522224,
-0.08850596100091934,
0.05902852863073349,
0.015838876366615295,
-0.06290464848279953,
0.014226428233087063,
-0.01433827355504036,
0.053301773965358734,
-0.02407267689704895,
0.033478762954473495,
-0.0173460952937603,
-0.04296261444687843,
-0.005254832562059164,
-0.046441931277513504,
-0.008321749046444893,
0.02148418128490448,
-0.005292063113301992,
0.013378902338445187,
0.005650240462273359,
-0.04294428601861,
0.07739361375570297,
0.06783463805913925,
-0.04838981479406357,
-0.007460908964276314,
0.008430411107838154,
-0.01527087390422821,
0.010607563890516758,
-0.0182416420429945,
0.012057780288159847,
-0.006856131367385387,
0.05767202004790306,
0.03225702419877052,
0.01733977720141411,
0.01924389787018299,
0.014260592870414257,
-0.01998887024819851,
0.024188945069909096,
0.006058006547391415,
0.011743113398551941,
0.014631770551204681,
0.023696530610322952,
-0.018718821927905083,
0.019223863258957863,
0.009931563399732113,
0.010244045406579971,
0.020652402192354202,
-0.06709180027246475,
0.08420827984809875,
0.014847475104033947,
0.006912827491760254,
-0.021000608801841736,
0.038620930165052414,
-0.024742988869547844,
-0.05342359468340874,
0.010743672959506512,
0.0244876928627491,
0.011806637980043888,
0.007265857886523008,
0.03003283403813839,
0.004894826095551252,
0.05171527713537216,
-0.008540217764675617,
-0.01985522173345089,
-0.009039175696671009,
-0.01056800689548254,
0.050589121878147125,
-0.027157457545399666,
-0.058211490511894226,
0.05639500170946121,
0.03272249922156334,
0.005221906583756208,
-0.0062661306001245975,
-0.047198716551065445,
-0.014078990556299686,
-0.07708824425935745,
0.012183134444057941,
-0.020137937739491463,
0.03673292696475983,
-0.0066978819668293,
0.016692740842700005,
0.016037452965974808,
0.008318787440657616,
-0.0005005346611142159,
-0.009750026278197765,
-0.0840417668223381,
0.02692461386322975,
-0.011327644810080528,
-0.018843190744519234,
-0.025401843711733818,
-0.027491621673107147,
0.004387945402413607,
-0.005489617120474577,
-0.01981024257838726,
-0.03371421620249748,
-0.03629593551158905,
-0.04086507111787796,
0.007722166832536459,
-0.029595090076327324,
-0.020757853984832764,
-0.02312469482421875,
0.05041158199310303,
0.06663979589939117,
-0.04087800905108452,
0.035183053463697433,
0.02146037109196186,
-0.03767215460538864,
0.012995429337024689,
-0.008323500864207745,
0.01980617456138134,
0.00804548617452383,
0.0018498828867450356,
0.050529155880212784,
0.005296308547258377,
0.008764230646193027,
-0.0007556402706541121,
0.004840357229113579,
0.06918972730636597,
-0.0023820106871426105,
-0.03121637925505638,
-0.0015357560478150845,
-0.06256292760372162,
-0.005762574262917042,
-0.023926693946123123,
0.0867442935705185,
-0.004671829286962748,
-0.001934449770487845,
0.033427875488996506,
0.007511241361498833,
-0.03356452286243439,
0.018254665657877922,
0.06012066826224327,
0.00021268564159981906,
-0.02435622178018093,
-0.033516667783260345,
-0.007784431800246239,
0.018493441864848137,
0.008338683284819126,
0.01700959913432598,
-0.0030998000875115395,
-0.020898202434182167,
-0.001984034199267626,
0.0095963841304183,
0.030092310160398483,
-0.019288210198283195,
0.03509397804737091,
0.012619027867913246,
0.05161328241229057,
0.013399127870798111,
0.02139466255903244,
0.003169109346345067,
0.016868354752659798,
0.07170172035694122,
0.02270713821053505,
-0.0006390142370946705,
-0.038345325738191605,
-0.012165076099336147,
0.05642370507121086,
0.030545173212885857,
0.01258938293904066,
0.004104262683540583,
-0.013844037428498268,
-0.004682500846683979,
0.03022216446697712,
0.00972544401884079,
-0.005775042809545994,
-0.010835159569978714,
-0.00966484472155571,
-0.030123189091682434,
-0.027456866577267647,
-0.004519789945334196,
0.025100572034716606,
-0.018714699894189835,
0.001440374180674553,
-0.05521092936396599,
-0.027324313297867775,
-0.02147817052900791,
0.024844622239470482,
-0.0007603117846883833,
0.028483977541327477,
0.023281583562493324,
0.024485314264893532,
-0.008173794485628605,
0.023670000955462456,
-0.029701294377446175,
-0.07791157811880112,
-0.006899645552039146,
0.02364715188741684,
-0.025467559695243835,
0.027875488623976707,
-0.011241848580539227,
-0.057811953127384186,
-0.014100453816354275,
-0.01550112385302782,
0.006403036415576935,
0.030790699645876884,
-0.024345049634575844,
-0.0017573682125657797,
0.01809883862733841,
0.009638619609177113,
0.05624125152826309,
0.009750391356647015,
-0.006627083756029606,
-0.027680810540914536,
0.010474947281181812,
0.05418487638235092,
-0.020651867613196373,
0.005156606435775757,
-0.05208737030625343,
-0.015091443434357643,
-0.0398963987827301,
0.020143592730164528,
-0.024816183373332024,
0.01240362785756588,
-0.007199308834969997,
-0.03179832175374031,
-0.03464581444859505,
0.017684530466794968,
0.015795094892382622,
-0.007171554956585169,
-0.01484712678939104,
0.02088969387114048,
0.029679149389266968,
-0.033428777009248734,
0.0063634347170591354,
0.04659732058644295,
-0.015391364693641663,
0.01980597898364067,
-0.00598353473469615,
0.015021627768874168,
-0.00770233990624547,
-0.023903081193566322,
-0.013916386291384697,
-0.0245565976947546,
0.016832077875733376,
-0.017077550292015076,
-0.02707046829164028,
0.005557819735258818,
-0.0269973985850811,
-0.025665616616606712,
0.006346537731587887,
-0.030413884669542313,
0.04703045263886452,
-0.057673607021570206,
0.0018543818732723594,
0.013042188249528408,
0.005348891951143742,
-0.05911392718553543,
-0.04985682666301727,
0.018412165343761444,
0.004932646173983812,
-0.021837156265974045,
-0.025846874341368675,
-0.005813026335090399,
-0.03676499426364899,
-0.02759633958339691,
0.01202480960637331,
0.04688623920083046,
-0.034351374953985214,
0.01762710139155388,
0.018261577934026718,
0.061801258474588394,
0.036546748131513596,
-0.04517293721437454,
-0.0038306554779410362,
0.011181429028511047,
-0.03126687929034233,
-0.0430419035255909,
-0.014491204172372818,
0.04087512940168381,
-0.025531480088829994,
-0.050190068781375885,
-0.03176553174853325,
-0.008848772384226322,
0.01282910630106926,
0.012553706765174866,
-0.006600708235055208,
0.024154556915163994,
0.013459011912345886,
0.03598180413246155,
-0.024891581386327744,
-0.0005358849884942174,
-0.004275160375982523,
0.0444670170545578,
-0.010937166400253773,
0.016680844128131866,
-0.022809693589806557,
-0.03558402508497238,
0.024800900369882584,
0.017186492681503296,
-0.012505103833973408,
0.008859643712639809,
0.04514126107096672,
-0.02542414702475071,
0.008782065473496914,
0.03170035406947136,
-0.022673076018691063,
-0.017978841438889503,
-0.0006740025710314512,
0.01794525235891342,
0.01821794919669628,
-0.0011933859204873443,
-0.025354936718940735,
-0.04539269953966141,
-0.05167554318904877,
0.011765376664698124,
0.050080448389053345,
-0.02763202227652073,
0.040793124586343765,
0.04677929729223251,
-0.0082284240052104,
-0.017120838165283203,
0.014066806994378567,
-0.013495399616658688,
0.021233361214399338,
-0.0017978916876018047,
0.025916242972016335,
-0.0517120398581028,
0.009799737483263016,
0.033018484711647034,
0.04206660017371178,
-0.03989788144826889,
0.0023077339865267277,
0.030378013849258423,
0.001349730766378343,
0.027314497157931328,
0.033956680446863174,
-0.026577182114124298,
0.07088617980480194,
-0.0181795172393322,
0.04583299905061722,
-0.032895103096961975,
-0.0044012186117470264,
0.02921326458454132,
-0.011380757205188274,
0.0065053668804466724,
0.009668951854109764,
-0.03396950662136078,
-0.05334017053246498,
0.007799059618264437,
0.019384054467082024,
0.017982078716158867,
0.003892869921401143,
-0.01297813281416893,
0.045297615230083466,
0.005036463029682636,
0.012862912379205227,
0.014585345983505249,
-0.03988376632332802,
-0.04658721014857292,
-0.03412821516394615,
-0.05071644484996796,
0.051515862345695496,
-0.024727145209908485,
-0.03640596568584442,
-0.0006398055120371282,
-0.03663823381066322,
0.010558664798736572,
0.006146655883640051,
0.02562742866575718,
-0.016437988728284836,
0.07891298085451126,
0.006057102233171463,
0.03927605599164963,
-0.009622111916542053,
0.008590060286223888,
0.11045430600643158,
0.032048549503088,
-0.0017222255701199174,
-0.08813086152076721,
-0.0007788279326632619,
0.0039059410337358713,
-0.0004641916893888265,
-0.03526932746171951,
0.04266816005110741,
-0.0009621531935408711,
0.006982710678130388,
0.0025829216465353966,
0.05777578055858612,
0.014588815160095692,
-0.046921614557504654,
0.0368293859064579,
-0.054878897964954376,
-0.06160198152065277,
0.010953076183795929,
0.01606481894850731,
-0.025566376745700836,
0.010753528214991093,
-0.05006752908229828,
0.007383759133517742,
-0.0445755273103714,
0.019158346578478813,
-0.007220506202429533,
-0.014159267768263817,
0.00921596959233284,
-0.0016033434076234698,
-0.022612713277339935,
-0.002779170870780945,
0.007662528194487095,
-0.007177426945418119,
-0.044188566505908966,
0.016336897388100624,
0.010062112472951412,
-0.022799067199230194,
0.04902522265911102,
0.07213852554559708,
0.016372881829738617,
0.007367991842329502,
0.0017675432609394193,
0.026146160438656807,
-0.050368983298540115,
-0.020934702828526497,
0.007513168267905712,
0.054171498864889145,
-0.0156788919121027,
-0.023789918050169945,
0.01933622546494007,
-0.03191934898495674,
0.00185966060962528,
-0.04153341427445412,
0.001751159317791462,
-0.010355810634791851,
0.07379361242055893,
0.005817077588289976,
0.015151748433709145,
-0.014590714126825333,
0.02267354167997837,
-0.011183750815689564,
0.009608672931790352,
-0.05654168874025345,
-0.014260770753026009,
-0.011820905841886997,
0.011561322025954723,
0.047886922955513,
-0.02440062165260315,
-0.006913983263075352,
-0.020970873534679413,
-0.005129223223775625,
-0.018638338893651962,
-0.012347636744379997,
-0.0056158374063670635,
-0.003678308567032218,
0.07405620813369751,
-0.009581833146512508,
-0.00040050296229310334,
0.002520980080589652,
-0.057255424559116364,
0.022937126457691193,
-0.0295740757137537,
-0.004833637736737728,
-0.020084813237190247,
-0.002561342203989625,
0.05874386057257652,
0.04023415595293045,
-0.0029306705109775066,
0.0018982270266860723,
-0.01709906756877899,
-0.004828162025660276,
0.031938206404447556,
-0.022205444052815437,
-0.011723593808710575,
0.018535180017352104,
-0.015259741805493832,
-0.021242206916213036,
-0.014533055014908314,
-0.024809455499053,
0.04400501027703285,
0.0038619418628513813,
-0.016529899090528488,
0.01898251473903656,
-0.0005253839772194624,
-0.026847323402762413,
0.007841930724680424,
-0.02453320473432541,
-0.01691254787147045,
0.01005132682621479,
0.0009234054596163332,
-0.05973050370812416,
-0.032065823674201965,
-0.019306929782032967,
0.021709492430090904,
-0.020719166845083237,
0.04250698909163475,
-0.0332123264670372,
0.0013381975004449487,
-0.013834871351718903,
0.032259345054626465,
-0.024694977328181267,
-0.022096922621130943,
-0.0627531111240387,
0.015324552543461323,
-0.009939772076904774,
0.011724237352609634,
0.005989194381982088,
0.007749761454761028,
0.00874696858227253,
-0.03960832953453064,
0.032429084181785583,
0.023972950875759125,
-0.008726172149181366,
0.020472612231969833,
0.00566058000549674,
-0.015379805117845535,
0.01966228149831295,
-0.0018850299529731274,
-0.01920233480632305,
0.027028461918234825,
-0.06826101243495941,
-0.043177515268325806,
0.03274890035390854,
-0.01621077209711075,
0.0354606918990612,
0.019057361409068108,
-0.014963211491703987,
-0.007985163480043411,
0.02034078910946846,
0.00892628077417612,
-0.04646996036171913,
-0.007435667794197798,
-0.044317927211523056,
-0.019148821011185646,
-0.038441725075244904,
0.04470178484916687,
-0.013512604869902134,
0.0015345229767262936,
0.0367753766477108,
0.039127252995967865,
-0.012190168723464012,
-0.0026023273821920156,
0.04782341420650482,
0.005222326144576073,
0.03059214912354946,
0.022497298195958138,
0.01320744026452303,
0.044205646961927414,
0.04990465193986893,
-0.02646060660481453,
0.03721281513571739,
-0.00009525626228423789,
0.019651362672448158,
-0.09357821941375732,
-0.03520234674215317,
-0.010233358480036259,
0.018688512966036797,
0.03627734258770943,
-0.04598291590809822,
0.032714273780584335,
0.036046672612428665,
-0.10410849750041962,
0.025657542049884796,
-0.038064464926719666,
-0.021502070128917694,
-0.033916641026735306,
-0.0066654565744102,
-0.006582433823496103,
0.06338302046060562,
0.04622086137533188,
0.016568498685956,
0.017425939440727234,
0.002579203573986888,
0.008392935618758202,
0.0020637118723243475,
-0.016459794715046883,
0.00022271109628491104,
-0.022362180054187775,
-0.024682849645614624,
0.07904760539531708,
0.02163374237716198,
-0.01863349974155426,
0.020635096356272697,
-0.010841668583452702,
-0.01113178301602602,
-0.010913055390119553,
0.03418487310409546,
0.030309760943055153,
0.0023934203200042248,
0.011272956617176533,
0.007979089394211769,
-0.02245556004345417,
0.0141115328297019,
0.027811473235487938,
0.014265291392803192,
-0.02538394182920456,
-0.0018967713695019484,
0.006058397702872753,
-0.03722040727734566,
-0.005046491511166096,
0.053720347583293915,
0.0036591612733900547,
-0.021547293290495872,
-0.03334614634513855,
-0.017806624993681908,
0.02471725456416607,
0.0015532620018348098,
0.014529927633702755,
-0.040319859981536865,
0.013741862960159779,
0.04385346546769142,
0.015553212724626064,
-0.009639721363782883,
0.016527673229575157,
-0.018494851887226105,
-0.03593110293149948,
0.04273822158575058,
0.009099525399506092,
-0.004644935950636864,
-0.05080491676926613,
-0.020702142268419266,
0.014646938070654869,
-0.009090648964047432,
0.034710515290498734,
-0.03395654633641243,
-0.022552834823727608,
-0.0013132888125255704,
0.02685556747019291,
0.02758883871138096,
-0.01210823841392994,
-0.01943361572921276,
-0.038496289402246475,
-0.02962677925825119,
0.02911129780113697,
-0.0011360596399754286,
0.009132139384746552,
-0.03724426031112671,
-0.014058951288461685,
0.01810871809720993,
-0.000619224738329649,
0.05612511187791824,
0.007908749394118786,
-0.025831962004303932,
0.029071426019072533,
-0.0014775360468775034,
0.009753180667757988,
-0.045680124312639236,
-0.020953012630343437,
-0.018909776583313942,
-0.018629446625709534,
0.0015411712229251862,
-0.016821613535284996,
-0.015712236985564232,
0.04371757432818413,
0.015129291452467442,
-0.011004450730979443,
0.021379055455327034,
0.004899291321635246,
-0.02910599112510681,
0.057615071535110474,
0.012517696246504784,
0.037094127386808395,
0.06726980209350586,
0.02301372028887272,
0.032149504870176315,
0.03960579261183739,
-0.029900703579187393,
-0.006284448783844709,
0.01834309846162796,
-0.04444568231701851,
-0.04670778661966324,
0.007416674867272377,
-0.015374747104942799,
0.011210422962903976,
-0.03486448898911476,
-0.008113212883472443,
0.027727968990802765,
-0.0356147326529026,
-0.010765896178781986,
0.058645933866500854,
0.014208311215043068,
0.05179017782211304,
-0.004898147191852331,
0.03826425224542618,
0.046383004635572433,
0.04346634820103645,
0.030895547941327095,
0.05166862532496452,
0.06310603022575378,
-0.0089632673189044,
0.013930032961070538,
0.020683569833636284,
0.011926824226975441,
0.022197775542736053,
0.016147471964359283,
0.05896758288145065,
-0.048722606152296066,
0.0009263766696676612,
0.05835772305727005,
-0.035552237182855606,
0.02813962660729885,
0.008661392144858837,
-0.04166831821203232,
0.0795191302895546,
-0.0359048955142498,
0.033662211149930954,
-0.008574254810810089,
0.030019348487257957,
-0.044458020478487015,
-0.012111717835068703,
0.014088623225688934,
0.08209427446126938,
-0.005123310722410679,
0.005435782019048929,
-0.017761211842298508,
0.008772237226366997,
-0.015123562887310982,
-0.03507297858595848,
0.008837257511913776,
0.05642075091600418,
-0.038541071116924286,
-0.0038683912716805935,
-0.0382126085460186,
-0.002230357611551881,
-0.009913601912558079,
-0.000902752683032304,
0.047813232988119125,
0.04944658279418945,
0.007181473076343536,
-0.02077982947230339,
-0.035953961312770844,
0.0567568801343441,
-0.04368581622838974,
-0.008745777420699596,
0.00007447013922501355,
0.03488260880112648,
-0.011440511792898178,
0.009173206984996796
] |
<p>The universe is expanding in the 3 spatial dimensions, could it not also be expanding in time dimension. In other words, are we stuck in 3 dimensions because we are riding the "bow wave" of the big bang in the time dimension, stuck on a 3d plane perpendicular to our world lines in spacetime? Think of a 3d-printer, are we on the upper surface of the printed object with new time being added continuously.</p>
<p>Would this mean that the quantum foam is the moment when the universe comes into existence, that the collapse of wave functions is when probability becomes reality? In that way there would be no need for the many worlds interpretation of quantum physics. Ahead of now is "outside" the universe i.e. there is nothing so the extra quantum states never "existed" in any sense, they were only ever mathematical probabilities. The act of observation is simply being in the now and that's why quantum systems are different depending on where you measure them - it's a different locus of the 3 spatial dimensions and "now".</p>
<p><strong>Update</strong></p>
<p>I don't believe that this is a duplicate question. After some discussion elsewhere it turns out that what I am describing is the Evolving Block Universe. It is well (and more formally) described by South African cosmologist George Ellis in this paper:</p>
<p><a href="http://arxiv.org/abs/gr-qc/0605049" rel="nofollow">http://arxiv.org/abs/gr-qc/0605049</a></p>
<p>There is also a YouTube presentation, recorded in 2012, here:</p>
<p><a href="http://www.youtube.com/watch?v=It6Me78dal8" rel="nofollow">http://www.youtube.com/watch?v=It6Me78dal8</a></p>
| 274 |
[
0.025722021237015724,
-0.014521508477628231,
0.050414957106113434,
-0.08409310132265091,
0.06699532270431519,
-0.0030747917480766773,
-0.03774551302194595,
-0.027193814516067505,
0.010985711589455605,
-0.038958750665187836,
-0.010509449988603592,
0.02785198576748371,
0.016225123777985573,
0.0318596288561821,
0.028674695640802383,
0.03642640635371208,
0.029488015919923782,
-0.022899487987160683,
-0.0005486459122039378,
-0.033581990748643875,
0.026653725653886795,
0.060370661318302155,
0.011587854474782944,
0.0123277073726058,
-0.01883254386484623,
0.010656722821295261,
0.04888107255101204,
-0.010114087723195553,
0.056459903717041016,
0.039735421538352966,
-0.028703778982162476,
-0.04016111418604851,
-0.025317827239632607,
0.013188492506742477,
0.015001540072262287,
-0.010467931628227234,
-0.021290022879838943,
-0.039913810789585114,
0.00010394223500043154,
-0.008042974397540092,
-0.022824201732873917,
0.03816405311226845,
-0.026809614151716232,
0.06015406921505928,
-0.020917357876896858,
0.02034164033830166,
0.00197291886433959,
0.007777685299515724,
0.05128925293684006,
-0.024719370529055595,
0.061088018119335175,
-0.037594281136989594,
0.018974995240569115,
0.01631714031100273,
-0.021336257457733154,
-0.00610537501052022,
0.09807359427213669,
0.05600787326693535,
0.00039844357524998486,
0.0000291538453893736,
-0.05255091190338135,
0.0004446899110917002,
0.02405957318842411,
-0.023734087124466896,
-0.015778854489326477,
0.03347789868712425,
-0.01637250930070877,
0.0048903170973062515,
-0.032240793108940125,
-0.017687557265162468,
-0.025425080209970474,
0.0027594028506428003,
0.04616178572177887,
-0.016506049782037735,
0.02261495776474476,
-0.008575230836868286,
0.009998624213039875,
-0.005913829430937767,
0.03389781340956688,
0.028596308082342148,
0.01822996512055397,
-0.028787991032004356,
0.03963412344455719,
0.022275876253843307,
0.014522116631269455,
0.01731932908296585,
0.051162607967853546,
-0.052982669323682785,
-0.023171009495854378,
0.04948795959353447,
-0.015503455884754658,
0.03136899322271347,
0.06145146116614342,
-0.024286972358822823,
-0.02303176559507847,
0.02849053218960762,
0.018072009086608887,
0.04158737137913704,
0.009767071343958378,
-0.02403891645371914,
0.0054609389044344425,
-0.009383761323988438,
0.019367586821317673,
0.05672255530953407,
0.011986508965492249,
0.0013028830289840698,
-0.03599622845649719,
0.01997665874660015,
-0.008583791553974152,
-0.02809782698750496,
-0.06135866418480873,
0.030257485806941986,
0.0000354055009665899,
-0.006792097352445126,
-0.02428578771650791,
-0.025685874745249748,
0.024698318913578987,
-0.02633954957127571,
0.0527365580201149,
0.08923695236444473,
0.01884906180202961,
-0.017374102026224136,
0.007773074321448803,
-0.022736405953764915,
-0.08756580948829651,
-0.0012171966955065727,
0.019468585029244423,
-0.028279995545744896,
-0.03198562562465668,
0.05709022656083107,
0.011456077918410301,
-0.03032369166612625,
0.04203769937157631,
-0.008700110018253326,
0.06475450843572617,
0.02093297801911831,
-0.11774273961782455,
-0.03999088332056999,
0.05210976302623749,
0.009255852550268173,
-0.013198002241551876,
-0.04280881956219673,
0.0163728017359972,
0.007015544921159744,
0.07755284011363983,
-0.023907486349344254,
-0.02126111276447773,
0.0258961021900177,
0.058729562908411026,
-0.017681360244750977,
-0.04333337023854256,
0.012420540675520897,
0.0014885232085362077,
-0.0419900082051754,
-0.022400224581360817,
-0.05004235729575157,
-0.0007026353268884122,
0.03773580119013786,
-0.003683896269649267,
-0.02498224750161171,
0.054581888020038605,
-0.00735039496794343,
-0.0195463914424181,
-0.028711795806884766,
-0.044964034110307693,
-0.037169165909290314,
0.0810248851776123,
0.0065786028280854225,
0.006441623438149691,
0.02896971069276333,
-0.010025856085121632,
0.02329779788851738,
-0.01537584699690342,
0.0275783259421587,
0.002566620474681258,
-0.022295508533716202,
-0.02227741666138172,
0.0055653671734035015,
-0.011765725910663605,
-0.007754948455840349,
-0.029242755845189095,
-0.0274130180478096,
-0.00024352440959773958,
-0.030232053250074387,
0.03795885294675827,
0.015916334465146065,
-0.003029217943549156,
0.0018371870974078774,
-0.0075990185141563416,
-0.0639570876955986,
-0.0006598687032237649,
-0.06903183460235596,
-0.023312587291002274,
-0.0014267769875004888,
0.007278716191649437,
-0.009446301497519016,
0.009128808975219727,
0.005070152226835489,
-0.05233903229236603,
-0.0463632270693779,
0.0007102168165147305,
0.05949784070253372,
0.010172341018915176,
-0.00957745686173439,
0.01072489470243454,
0.040552083402872086,
0.0031688970047980547,
-0.013499832712113857,
-0.018040310591459274,
-0.009840969927608967,
0.005981545429676771,
0.04450048506259918,
-0.04657919704914093,
0.01575048267841339,
-0.028348200023174286,
0.011005743406713009,
0.03643175587058067,
0.007534742821007967,
-0.008435684256255627,
-0.017625613138079643,
-0.032099150121212006,
0.04193342477083206,
0.02160397358238697,
0.006790357641875744,
-0.03366211801767349,
0.046258699148893356,
-0.008435150608420372,
0.01969527080655098,
0.017948096618056297,
-0.01568901538848877,
-0.05091527849435806,
-0.01595798321068287,
0.014860589057207108,
0.0625106617808342,
0.011478953063488007,
0.036801114678382874,
0.01994624361395836,
0.035473283380270004,
-0.00155534571968019,
-0.005160204134881496,
0.006882950663566589,
-0.03339214622974396,
-0.020242296159267426,
0.023053715005517006,
0.022206146270036697,
0.006073790602385998,
0.033272530883550644,
-0.010716094635426998,
-0.022338256239891052,
-0.050728343427181244,
-0.03230344131588936,
-0.0002934835501946509,
-0.01093190349638462,
-0.0025366104673594236,
-0.0036360290832817554,
-0.017014969140291214,
-0.0024971277453005314,
-0.02498115412890911,
-0.009105830453336239,
0.01819356344640255,
0.010045117698609829,
-0.008268735371530056,
-0.05895793437957764,
-0.04734150692820549,
-0.026440013200044632,
0.03805557265877724,
-0.04646864905953407,
-0.04280642792582512,
0.05318279191851616,
-0.061015643179416656,
0.015345157124102116,
-0.006787652615457773,
-0.014345628209412098,
0.0013211482437327504,
-0.0014096746454015374,
0.017687667161226273,
0.002886728150770068,
0.03461350128054619,
-0.076567143201828,
-0.05639118328690529,
0.018308648839592934,
-0.004332948941737413,
0.04158499836921692,
0.01170877180993557,
-0.052280303090810776,
0.04827529191970825,
-0.02581106871366501,
-0.03136969357728958,
0.01774141937494278,
-0.026983829215168953,
-0.0036823211703449488,
0.03960622847080231,
-0.019669512286782265,
-0.011360451579093933,
-0.010256420820951462,
-0.0115813622251153,
0.01169788371771574,
-0.003498116973787546,
0.007354337256401777,
0.07677707076072693,
-0.01034714374691248,
-0.047428812831640244,
-0.015371379442512989,
-0.0279205534607172,
-0.06365698575973511,
-0.020294854417443275,
0.02895195595920086,
-0.017726683989167213,
-0.044224709272384644,
0.03503734618425369,
0.01251097209751606,
0.007885784842073917,
-0.02129421941936016,
-0.03621550276875496,
-0.06996068358421326,
0.024033676832914352,
-0.023628411814570427,
0.0727938711643219,
-0.052453845739364624,
-0.0014121653512120247,
0.07407965511083603,
0.030210506170988083,
0.00038666953332722187,
0.006605254951864481,
-0.003351135877892375,
0.007045600563287735,
-0.04998708516359329,
-0.0006908415234647691,
0.008996077813208103,
-0.01404647994786501,
0.032458413392305374,
0.012374511919915676,
0.04499346762895584,
0.04743046686053276,
0.007661193143576384,
-0.003672275459393859,
0.040951572358608246,
0.01503541599959135,
0.03699522837996483,
0.07085894793272018,
0.01039408054202795,
-0.01797306537628174,
-0.0033470953349024057,
-0.033452004194259644,
0.0015869045164436102,
0.016398733481764793,
-0.045658696442842484,
0.06084200367331505,
0.003395783482119441,
0.012021503411233425,
-0.007131989113986492,
0.006518940906971693,
-0.0015071206726133823,
-0.028895698487758636,
0.009550068527460098,
0.020662514492869377,
0.05364220589399338,
0.001774356234818697,
0.06795146316289902,
0.0240549985319376,
-0.01912429928779602,
-0.014579765498638153,
0.006193486042320728,
-0.00850629061460495,
0.008409044705331326,
0.05224933102726936,
-0.0030196052975952625,
-0.02097984030842781,
0.049247074872255325,
0.03752526640892029,
-0.005684119649231434,
0.012749514542520046,
-0.015135468915104866,
-0.009663662873208523,
-0.03434526175260544,
-0.021547766402363777,
0.046897634863853455,
0.03762771189212799,
0.045801207423210144,
0.026297247037291527,
-0.0015047985361889005,
-0.006026857066899538,
0.0005569919012486935,
-0.017945127561688423,
-0.08776011317968369,
-0.04745502024888992,
-0.024619951844215393,
0.005404457915574312,
-0.00887905340641737,
-0.014231276698410511,
0.01559857651591301,
-0.01099215168505907,
-0.02287328615784645,
0.0009736848878674209,
-0.013098831288516521,
-0.0863640308380127,
0.0018403474241495132,
-0.03887699171900749,
-0.009784426540136337,
-0.004415161907672882,
0.03171364590525627,
0.06956414133310318,
-0.005557028576731682,
0.006481465417891741,
0.02191917970776558,
-0.03023526258766651,
0.02475164085626602,
0.04997583478689194,
-0.004261203110218048,
0.04532681405544281,
0.02127315104007721,
0.03024161048233509,
0.02474360540509224,
-0.024056797847151756,
0.037989530712366104,
0.0414787158370018,
0.017146790400147438,
-0.014886347576975822,
-0.025060154497623444,
-0.013101470656692982,
-0.002771473489701748,
-0.004313151352107525,
0.010684903711080551,
0.051022469997406006,
0.01696207746863365,
-0.009303536266088486,
0.01906806044280529,
0.025495024397969246,
-0.018611600622534752,
0.030808400362730026,
0.048505477607250214,
-0.04585973918437958,
0.0030347860883921385,
-0.005696574691683054,
-0.05379051715135574,
-0.03497229516506195,
-0.02545597217977047,
0.016848191618919373,
-0.021467797458171844,
-0.032931216061115265,
0.01710130274295807,
0.011809367686510086,
0.005385274533182383,
-0.008197746239602566,
0.021711168810725212,
-0.00798459816724062,
0.0033597222063690424,
-0.024730384349822998,
-0.0015702523523941636,
-0.008097154088318348,
0.07036519795656204,
0.029260769486427307,
0.004390017595142126,
0.016362503170967102,
-0.06478383392095566,
-0.016117731109261513,
-0.003958625718951225,
0.019559869542717934,
0.03278353810310364,
-0.005991557613015175,
-0.07798947393894196,
-0.037305306643247604,
0.029090726748108864,
-0.037664953619241714,
0.02395879477262497,
0.010935223661363125,
-0.025286683812737465,
-0.01255431491881609,
-0.019508037716150284,
0.05107700452208519,
-0.04558819159865379,
0.0017877499340102077,
0.013678842224180698,
0.016930140554904938,
0.011912330985069275,
0.011941983364522457,
0.017532946541905403,
0.02004598267376423,
0.03188697248697281,
-0.007719418033957481,
0.012598848901689053,
-0.012078695930540562,
-0.005604320205748081,
-0.011237207800149918,
-0.07177665084600449,
0.0478711873292923,
0.0050412509590387344,
-0.03307171165943146,
0.03435737267136574,
-0.017806390300393105,
-0.024316109716892242,
-0.029973238706588745,
-0.012739697471261024,
0.0003204435051884502,
0.030214684084057808,
0.013634870760142803,
0.02777765691280365,
-0.012520788237452507,
-0.0026415851898491383,
0.00976200308650732,
0.03807469829916954,
0.01626192033290863,
0.0025271906051784754,
-0.010291878134012222,
0.04344465583562851,
-0.04872191697359085,
0.053766265511512756,
-0.03078189305961132,
-0.017666956409811974,
-0.023943442851305008,
0.019659239798784256,
-0.0038657598197460175,
-0.01845547929406166,
0.020679228007793427,
-0.028142163529992104,
0.009142616763710976,
0.0029784739017486572,
0.003989282995462418,
0.007468789350241423,
-0.029720580205321312,
-0.010231309570372105,
-0.014900460839271545,
-0.013606894761323929,
0.013848384842276573,
0.00894874520599842,
0.011882420629262924,
0.024658137932419777,
0.023323209956288338,
0.031929176300764084,
-0.049156203866004944,
-0.0005816248012706637,
-0.0035120565444231033,
-0.012326784431934357,
0.010134040378034115,
-0.00794258899986744,
0.024975918233394623,
0.013557259924709797,
-0.01877153478562832,
-0.030574055388569832,
-0.01615598239004612,
-0.02045332081615925,
0.015629125759005547,
-0.021435189992189407,
0.0183009784668684,
0.004758636467158794,
0.02665971964597702,
-0.0838155522942543,
-0.02936912328004837,
0.025869345292448997,
0.027830073609948158,
-0.02450442872941494,
-0.025528065860271454,
0.004068974405527115,
-0.04169227182865143,
-0.015699267387390137,
-0.017501091584563255,
0.04178808256983757,
-0.037044983357191086,
-0.021031735464930534,
0.011332658119499683,
0.02666807919740677,
0.04790407419204712,
-0.014550416730344296,
-0.0045153358951210976,
0.0015947591746225953,
0.002930196700617671,
-0.0012991848634555936,
-0.016036370769143105,
0.011627407744526863,
-0.019867854192852974,
0.0039540850557386875,
-0.0016001836629584432,
-0.02139524184167385,
0.0018999178428202868,
-0.04537098482251167,
-0.01935657672584057,
0.044074054807424545,
0.018427139148116112,
0.0033599669113755226,
-0.03779489919543266,
0.020150965079665184,
-0.02358606643974781,
-0.009650449268519878,
-0.013980217278003693,
0.0019631541799753904,
0.021541953086853027,
-0.06526853889226913,
0.026923291385173798,
-0.04200834408402443,
-0.0043280767276883125,
-0.010636785067617893,
0.02183605544269085,
0.01828472875058651,
-0.03869539871811867,
0.02442965842783451,
-0.04490065947175026,
0.005238739773631096,
-0.011024102568626404,
0.0002582846791483462,
0.010675680823624134,
-0.012083805166184902,
-0.03068365529179573,
-0.05980430170893669,
-0.036236636340618134,
0.04745103046298027,
0.0298309288918972,
-0.015001627616584301,
0.04253252595663071,
0.017946824431419373,
-0.029600532725453377,
-0.011083744466304779,
-0.03998201712965965,
-0.008159427903592587,
0.002858072752133012,
0.000754841195885092,
0.00457282830029726,
-0.06003037095069885,
0.029913628473877907,
0.032602403312921524,
0.05307075381278992,
-0.006417217198759317,
0.05339406430721283,
0.03947196900844574,
0.008661061525344849,
0.0524948351085186,
-0.023762190714478493,
-0.03784659132361412,
0.05407804250717163,
-0.02005605958402157,
0.023094242438673973,
0.01371676567941904,
-0.007142519578337669,
0.051096946001052856,
0.0052026621997356415,
-0.009242267347872257,
-0.02795596420764923,
0.005812162533402443,
-0.07457917183637619,
0.006172258406877518,
-0.0013600366655737162,
0.04309005290269852,
0.008124461397528648,
0.0005762013024650514,
0.06575983017683029,
0.001585672260262072,
0.009638716466724873,
0.0006247960845939815,
-0.07278672605752945,
-0.03180297091603279,
-0.001094724633730948,
-0.0025728726759552956,
0.053092941641807556,
0.00168638676404953,
-0.014820176176726818,
-0.004003019537776709,
-0.04078038036823273,
0.014210330322384834,
0.012684705667197704,
0.09382783621549606,
-0.04307197034358978,
0.08207140862941742,
0.001310644787736237,
0.03832084685564041,
-0.05529226362705231,
0.015260367654263973,
0.12157366424798965,
0.07704739272594452,
0.03317281976342201,
-0.04646669328212738,
0.02914334647357464,
-0.0205825362354517,
0.030711129307746887,
-0.05914929881691933,
0.005031137727200985,
-0.016887802630662918,
0.0024211215786635876,
-0.002882129978388548,
0.06338279694318771,
0.021856054663658142,
-0.02470233477652073,
0.009263455867767334,
-0.0412013940513134,
-0.05429494008421898,
-0.021364830434322357,
0.02663298137485981,
0.03384096175432205,
-0.021056272089481354,
-0.0392758883535862,
0.036593981087207794,
0.005195446312427521,
-0.007973824627697468,
-0.0000740866016712971,
-0.027895567938685417,
0.027279982343316078,
-0.010702285915613174,
-0.040651991963386536,
0.017112331464886665,
-0.009807387366890907,
-0.05409538373351097,
-0.04279004782438278,
0.029755428433418274,
-0.0067170546390116215,
-0.0036782396491616964,
0.04144641011953354,
0.04091735929250717,
0.04302297532558441,
-0.011102373711764812,
-0.019559547305107117,
0.020442327484488487,
-0.0323290191590786,
-0.032406922429800034,
0.005516702309250832,
0.05977146327495575,
-0.03748595342040062,
-0.02397187054157257,
-0.014906189404428005,
-0.023617353290319443,
0.02194266952574253,
-0.045883938670158386,
0.01336150523275137,
0.003697393462061882,
0.05027642846107483,
0.025695135816931725,
-0.007467519957572222,
-0.00017038098303601146,
-0.015926377847790718,
0.003722617868334055,
0.013073218986392021,
0.012086491100490093,
0.014588185586035252,
0.019747089594602585,
-0.011829842813313007,
0.055498261004686356,
0.012332150712609291,
0.01760345883667469,
-0.05669194832444191,
0.020613225176930428,
-0.060458049178123474,
-0.02719760872423649,
0.029221339151263237,
0.027109775692224503,
0.017414042726159096,
0.00046478770673274994,
0.015825150534510612,
-0.01419967319816351,
-0.03339838236570358,
0.006503135431557894,
-0.04227408766746521,
-0.01967673748731613,
-0.003412568010389805,
0.005665410775691271,
0.05627292022109032,
0.0280996672809124,
-0.025542743504047394,
-0.03310702368617058,
-0.005817823112010956,
0.017126744613051414,
0.02012757770717144,
-0.012544209137558937,
-0.025733977556228638,
0.02309214510023594,
-0.012688536196947098,
-0.021055014804005623,
-0.055193666368722916,
0.004285668488591909,
0.008779039606451988,
-0.021653415635228157,
0.01656724326312542,
0.03346544876694679,
0.016830258071422577,
-0.032741084694862366,
0.005750081967562437,
-0.03561899811029434,
0.028189759701490402,
0.02283155359327793,
0.030372103676199913,
-0.01122189499437809,
-0.02193751558661461,
-0.0173343438655138,
0.019385261461138725,
-0.022564610466361046,
0.032632749527692795,
-0.025450244545936584,
0.0005318119656294584,
-0.00948710460215807,
0.007262608502060175,
-0.0076799336820840836,
0.010374641045928001,
-0.03438151255249977,
-0.010466622188687325,
-0.01475486345589161,
-0.008749610744416714,
-0.017818717285990715,
0.01626567915081978,
-0.011381251737475395,
-0.04082130640745163,
0.01838645339012146,
-0.0061251879669725895,
-0.07369775325059891,
-0.00047292598173953593,
0.009086287580430508,
0.03219987079501152,
0.022463608533143997,
0.002001360058784485,
-0.03963784500956535,
0.007894575595855713,
-0.07013856619596481,
-0.04222483932971954,
0.04465658217668533,
-0.008694768883287907,
0.019673345610499382,
0.029925109818577766,
0.007084687240421772,
-0.022554241120815277,
0.025593411177396774,
-0.004636761732399464,
0.004567731637507677,
0.013137823902070522,
-0.02182454988360405,
-0.006751189008355141,
-0.011643292382359505,
0.03481490910053253,
0.02629987522959709,
0.0012246230617165565,
0.028077775612473488,
0.03263167291879654,
0.02201090380549431,
-0.0009565943037159741,
-0.013721968978643417,
-0.04211711138486862,
-0.04025658965110779,
0.015018926933407784,
-0.00860148761421442,
0.020019598305225372,
0.07400453835725784,
-0.06049283593893051,
0.026356354355812073,
0.03290572762489319,
-0.003361573675647378,
-0.10916201025247574,
-0.012909209355711937,
0.035203415900468826,
0.013594008982181549,
0.03626725822687149,
-0.025007782503962517,
0.059598878026008606,
0.04423047974705696,
-0.11994937062263489,
0.04765515774488449,
0.0054384623654186726,
-0.001188297988846898,
-0.00603546854108572,
0.0040068430826067924,
-0.037591353058815,
0.06789959222078323,
0.03524664044380188,
0.060605790466070175,
0.002931060502305627,
0.006144617218524218,
-0.05597968399524689,
-0.037877824157476425,
-0.0025606120470911264,
0.042094070464372635,
0.0031883646734058857,
0.02319192700088024,
0.04373195394873619,
-0.036655791103839874,
0.0040879035368561745,
0.02840672805905342,
-0.007862536236643791,
-0.010532254353165627,
-0.01838180422782898,
-0.0020584475714713335,
0.019418809562921524,
-0.007641399744898081,
0.041752856224775314,
-0.005778847727924585,
0.010619215667247772,
0.03313214331865311,
0.02306312881410122,
0.001282957149669528,
0.026922348886728287,
0.004843359347432852,
-0.0065935272723436356,
-0.0723026916384697,
-0.002626500790938735,
0.010954752564430237,
0.014748293906450272,
0.044023849070072174,
0.008906255476176739,
0.023890400305390358,
0.012430229224264622,
0.013216663151979446,
-0.006298975087702274,
-0.02646559476852417,
-0.023033158853650093,
0.013962313532829285,
0.02537243627011776,
-0.039542101323604584,
-0.012583808042109013,
-0.023965338245034218,
-0.019480234012007713,
0.02668067067861557,
-0.04199243709445,
-0.004895949270576239,
-0.030814295634627342,
-0.059447094798088074,
-0.003153278725221753,
0.004373305477201939,
0.027946311980485916,
-0.012476596981287003,
-0.04671956226229668,
0.07778174430131912,
-0.017435934394598007,
0.02407144196331501,
0.01242028083652258,
-0.03875502943992615,
-0.027815725654363632,
-0.08281651884317398,
0.035478685051202774,
0.010026693344116211,
0.009627834893763065,
-0.044534314423799515,
-0.009717020206153393,
0.006778189912438393,
0.01812688075006008,
0.05774256959557533,
0.006084648426622152,
0.020205380395054817,
-0.0004440349875949323,
-0.0023690599482506514,
0.035489171743392944,
0.009921724908053875,
-0.0064546577632427216,
0.021072717383503914,
0.00929111149162054,
0.000495773390866816,
-0.011916553601622581,
0.0031110302079468966,
0.013037794269621372,
0.06436798721551895,
-0.025245267897844315,
0.028641432523727417,
-0.016622984781861305,
-0.03189373016357422,
0.0339382030069828,
-0.0076746041886508465,
-0.018713125959038734,
0.039960846304893494,
-0.010196995921432972,
-0.006996772717684507,
0.027223389595746994,
-0.02123899944126606,
-0.02582075446844101,
0.017460254952311516,
0.005992430727928877,
0.009524772875010967,
-0.012296057306230068,
-0.0031339493580162525,
0.018403204157948494,
-0.003910457249730825,
-0.04637451842427254,
0.018206411972641945,
-0.019301339983940125,
0.024360759183764458,
0.04435603320598602,
-0.002834588522091508,
0.02951289340853691,
-0.03478259593248367,
-0.01957547292113304,
-0.006277310661971569,
-0.002588704228401184,
0.012988219037652016,
0.03141647204756737,
0.06473129242658615,
-0.0022380531299859285,
0.02877340093255043,
0.035392969846725464,
-0.00864072423428297,
-0.0010480221826583147,
0.0018890552455559373,
0.027512887492775917,
-0.03973628208041191,
0.008476654067635536,
0.011984898708760738,
0.0007180379470810294,
-0.015616139397025108,
0.0019123941892758012,
-0.02254844270646572,
0.06604725867509842,
0.007953407242894173,
0.0019144021207466722,
0.012789115309715271,
-0.006114394869655371,
-0.04276105761528015,
0.01939360611140728,
-0.010143393650650978,
0.05157003179192543,
-0.05732886120676994,
-0.04294557869434357,
-0.03580131381750107,
0.020666589960455894,
-0.007897036150097847,
-0.02228323183953762,
-0.0012688857968896627,
-0.009715763852000237,
-0.006497721653431654,
0.01846960373222828,
-0.020719921216368675,
-0.005219803191721439,
-0.023997364565730095,
0.05681760236620903,
0.024597950279712677,
0.006916150450706482,
-0.04259168729186058,
0.017876792699098587,
-0.04260573908686638,
0.0508795827627182,
-0.02906796522438526,
0.01123008318245411,
-0.026421599090099335,
0.045040518045425415,
-0.016419943422079086,
-0.008737534284591675
] |
<p>I've been struggling with a detail in Second Quantization which I really need to clear out of my head. If I expand the S-matrix of a theory with an interaction Hamiltonian $ H_I(x) $ then I have</p>
<p>$$ S - 1= \int^{+\infty}_{-\infty} d^4x\, H_I(x) + \int^{+\infty}_{-\infty} \int^{+\infty}_{-\infty} d^4 x\, d^4 y\, T[ H_I(x) \, H_I(y) ] + ... $$</p>
<p>where the T operator is unnecessary in the first term. Now, if I choose a $ \overline{\psi}(x)\psi(x) $ theory for example, the first term gives some contributions which I can calculate most easily by doing the expansion $ \psi(x) = \psi^+(x) + \psi^-(x) $, which is the essence of Wick's theorem. I know the contributions in this example will be trivial, but the point is Wick's theorem is not defined for the same spacetime points and everywhere I see, what everyone says is that since the T operator in the first term can be there, then when substituting $ H_I(x) $ we simply retain the operator and use Wick's theorem like the spacetime points were different and impose x=y at the end, but this doesn't make any sense since the operators T are different. Basically it is assumed implicitly that</p>
<p>$$ \overline{\psi}(x)\,\psi(x) = T[ \overline{\psi}(x)\,\psi(x) ] $$</p>
<p>in the first term of $ S-1 $, but the time ordering operators aren't even the same, since this one has a minus sign in its definition. The point is, the first term will always be</p>
<p>$$ \int^{+\infty}_{-\infty} d^4x\, H_I(x) $$</p>
<p>independently if I chose to put there the T operator (without the minus sign) or not, so for fermions I should have $\overline{\psi}(x)\,\psi(x)$ there and not $T[ \overline{\psi}(x)\,\psi(x) ]$, since they are not the same as far as I can see.</p>
| 8,306 |
[
0.030981525778770447,
-0.006486109923571348,
0.028003709390759468,
-0.048114340752363205,
0.024277808144688606,
-0.006999022793024778,
-0.038891084492206573,
-0.01566898822784424,
-0.01789136417210102,
-0.022315695881843567,
0.027606850489974022,
-0.009505785070359707,
0.0562327578663826,
-0.006770762614905834,
0.020323576405644417,
0.021282151341438293,
-0.010524649173021317,
-0.005873110145330429,
-0.007940374314785004,
-0.02050917223095894,
-0.011966012418270111,
0.013684785924851894,
-0.024586353451013565,
0.002587315160781145,
-0.01305322628468275,
0.032478902488946915,
-0.012520121410489082,
0.017878158017992973,
0.0004185778379905969,
0.07985015958547592,
-0.032814186066389084,
-0.023020777851343155,
0.020679950714111328,
0.035283226519823074,
0.020861919969320297,
0.0017145229503512383,
-0.01855398528277874,
-0.02895820140838623,
0.0352681465446949,
-0.022378111258149147,
-0.020359916612505913,
-0.029159100726246834,
-0.02357914112508297,
0.03916977718472481,
0.00500201340764761,
0.04410247504711151,
0.016186656430363655,
-0.005083139985799789,
0.05869082361459732,
-0.05808966979384422,
0.07703445106744766,
0.02170214243233204,
0.023418083786964417,
0.028337866067886353,
-0.015557055361568928,
0.002251822268590331,
0.0479106642305851,
0.04229355975985527,
0.015402354300022125,
-0.04156449809670448,
-0.04948829859495163,
-0.029996177181601524,
0.03744889050722122,
-0.019771255552768707,
0.01836749166250229,
-0.01837056502699852,
0.027974391356110573,
0.0002762462245300412,
0.024264009669423103,
-0.06018112972378731,
0.028073228895664215,
-0.027752865105867386,
0.040744610130786896,
-0.030651355162262917,
-0.0182475782930851,
0.014250824227929115,
0.01238733995705843,
0.01652899943292141,
0.0528612956404686,
0.006017463747411966,
0.010295839980244637,
0.0321582593023777,
0.016388552263379097,
-0.007091081701219082,
-0.0033120897132903337,
-0.00865320023149252,
0.03696371614933014,
-0.002777495188638568,
0.014694705605506897,
0.04735051468014717,
-0.04669027030467987,
0.014075164683163166,
0.038849372416734695,
-0.023418551310896873,
0.012039185501635075,
0.027329741045832634,
-0.0004198468814138323,
0.020693447440862656,
-0.00904127862304449,
0.009803082793951035,
-0.0292006004601717,
-0.05859716981649399,
-0.007638576906174421,
0.08026091009378433,
0.0103183938190341,
-0.014553261920809746,
-0.04269292205572128,
0.022702056914567947,
-0.008218837901949883,
-0.022143172100186348,
-0.06000223755836487,
0.019652530550956726,
-0.02545401081442833,
0.01482410728931427,
-0.041804227977991104,
-0.023495065048336983,
0.0025222855620086193,
-0.010721582919359207,
0.04009028896689415,
0.05559299886226654,
0.04949360340833664,
-0.01965899020433426,
0.036973465234041214,
-0.015389791689813137,
-0.04993436858057976,
0.0008122764411382377,
0.04121429845690727,
-0.019053850322961807,
-0.007186968345195055,
-0.0029441043734550476,
0.058616433292627335,
0.006807313766330481,
0.021426919847726822,
0.025825437158346176,
0.007573137525469065,
-0.020171064883470535,
-0.0956534594297409,
-0.039382632821798325,
0.03566247224807739,
-0.03213491290807724,
0.00558469770476222,
-0.05704878270626068,
-0.014179924502968788,
0.03953807055950165,
0.09731677919626236,
-0.005145119968801737,
0.011702153831720352,
0.00826070923358202,
0.020869510248303413,
0.0320153571665287,
0.00443480396643281,
-0.028139282017946243,
0.00631345622241497,
-0.04939970746636391,
-0.01910766027867794,
-0.05279592052102089,
0.009581447578966618,
0.06908244639635086,
-0.046628423035144806,
-0.0031635768245905638,
0.10549066960811615,
-0.015033043920993805,
-0.013863829895853996,
0.03924821317195892,
0.01781833916902542,
-0.038754262030124664,
0.01163242757320404,
0.0034168779384344816,
0.007653768174350262,
0.023705508559942245,
-0.024090664461255074,
-0.003741975175216794,
-0.02388148196041584,
0.022451555356383324,
0.022389093413949013,
-0.02823370322585106,
0.007532513700425625,
-0.029527215287089348,
-0.02455402910709381,
-0.0072609055787324905,
-0.008435015566647053,
-0.05287807434797287,
-0.02751428633928299,
0.009768538177013397,
-0.010795128531754017,
-0.0004087490669917315,
-0.01887487806379795,
0.027198942378163338,
-0.013338816352188587,
-0.02908886782824993,
-0.02387819066643715,
-0.04747271537780762,
-0.010550868697464466,
0.04087211191654205,
-0.010784775018692017,
0.023489275947213173,
0.016864443197846413,
0.01354600302875042,
0.03286076709628105,
-0.03013145923614502,
-0.01649458147585392,
0.041120320558547974,
0.010922913439571857,
-0.004616892896592617,
0.04650890454649925,
0.02632344327867031,
0.031119616702198982,
0.015465250238776207,
0.027182703837752342,
-0.011733051389455795,
-0.025348616763949394,
0.011559417471289635,
-0.00984339602291584,
0.022908324375748634,
0.006103388965129852,
-0.030472680926322937,
0.0015532695688307285,
0.0013233585050329566,
-0.02082662843167782,
0.033342983573675156,
-0.050841011106967926,
0.040620021522045135,
0.05927976593375206,
-0.03264913707971573,
-0.056690897792577744,
0.05121223255991936,
-0.018127990886569023,
0.05932549387216568,
-0.02421923540532589,
-0.0471719354391098,
-0.04000876098871231,
-0.029340635985136032,
0.018741466104984283,
0.04906675964593887,
-0.005989822093397379,
-0.0177213903516531,
0.025873690843582153,
-0.006497958675026894,
0.03874469920992851,
0.03320785611867905,
-0.0024410178884863853,
-0.043975576758384705,
0.048400044441223145,
-0.014871497638523579,
0.009170844219624996,
-0.00910459365695715,
0.020606497302651405,
-0.01773763634264469,
0.017009980976581573,
0.00019388552755117416,
-0.004047475755214691,
0.0008239495800808072,
-0.05486218258738518,
0.02863696962594986,
0.003907297272235155,
0.02060176245868206,
0.0005579906282946467,
0.011341182515025139,
0.05263318866491318,
0.04032487794756889,
-0.009749757125973701,
-0.002486292039975524,
-0.048654600977897644,
-0.01927301473915577,
0.021947257220745087,
-0.01900009997189045,
-0.027607202529907227,
-0.015253369696438313,
0.020236298441886902,
-0.05101096257567406,
0.01116096694022417,
-0.01687515340745449,
-0.02966548502445221,
-0.03171249106526375,
-0.01873055100440979,
0.03362106904387474,
0.032592590898275375,
0.028747878968715668,
-0.04206893965601921,
0.020054897293448448,
0.008157993666827679,
-0.001604100107215345,
0.02155241370201111,
0.015805376693606377,
-0.04986695945262909,
-0.029006578028202057,
-0.06732792407274246,
-0.01652238517999649,
0.07211974263191223,
-0.006490296684205532,
-0.011483689770102501,
-0.022632230073213577,
-0.00520657654851675,
-0.04480371251702309,
-0.023950515314936638,
-0.044744428247213364,
0.009577609598636627,
-0.03960094228386879,
-0.020988954231142998,
0.0379420705139637,
0.013663182035088539,
-0.05660298466682434,
0.02389473095536232,
-0.0014517068630084395,
-0.03334265202283859,
-0.01100362278521061,
-0.0104446429759264,
0.05271097645163536,
-0.006488467566668987,
0.015270977281033993,
0.004974392708390951,
-0.019421424716711044,
-0.013136724941432476,
-0.05528531223535538,
-0.029284192249178886,
0.04395865276455879,
0.01674991101026535,
0.028230110183358192,
-0.0009973510168492794,
-0.03290398791432381,
0.0994851142168045,
0.05530426651239395,
0.03398171067237854,
-0.009050076827406883,
0.017493242397904396,
-0.008746892213821411,
0.0022100782953202724,
0.004577190149575472,
0.009426848962903023,
0.01110045425593853,
0.03087868168950081,
0.02469339780509472,
0.009488053619861603,
0.026130370795726776,
0.004540915600955486,
-0.002900924300774932,
0.031034553423523903,
0.008006312884390354,
0.027361495420336723,
0.046490561217069626,
-0.015813950449228287,
-0.0030960794538259506,
-0.0002753050357569009,
-0.03054988384246826,
-0.0018276515183970332,
0.014492284506559372,
-0.01763894222676754,
0.07065197080373764,
0.014771275222301483,
-0.02825348451733589,
-0.002665823558345437,
0.02192387916147709,
-0.014150434173643589,
-0.03152025118470192,
-0.055158812552690506,
0.015507222153246403,
0.019122375175356865,
-0.004546137060970068,
0.029150351881980896,
0.029982643201947212,
0.009199702180922031,
-0.027739981189370155,
-0.01739773154258728,
-0.004767104052007198,
-0.03839511051774025,
0.049475979059934616,
-0.036132700741291046,
-0.06480946391820908,
0.0183758232742548,
0.029043374583125114,
-0.02283835969865322,
-0.017933163791894913,
-0.021702095866203308,
-0.019215090200304985,
-0.012981032021343708,
0.01901654340326786,
-0.02814747393131256,
0.0548287108540535,
0.007150476798415184,
0.02678845264017582,
0.032893165946006775,
0.014151621609926224,
0.010472193360328674,
-0.008581540547311306,
-0.04714043065905571,
0.01559457741677761,
0.018253613263368607,
-0.02004711702466011,
-0.014254230074584484,
0.023369085043668747,
0.040379345417022705,
-0.045706212520599365,
-0.023072905838489532,
-0.0045401547104120255,
-0.04109378159046173,
-0.05732213705778122,
0.03590508550405502,
-0.01818056032061577,
-0.039975158870220184,
-0.01982010342180729,
0.0377599336206913,
0.056747596710920334,
-0.026322046294808388,
-0.0029462832026183605,
0.016222259029746056,
-0.01922442764043808,
0.017930053174495697,
-0.027842054143548012,
-0.013338137418031693,
0.047174885869026184,
0.006496923044323921,
0.045263439416885376,
0.02437097206711769,
-0.01971767656505108,
-0.002355022821575403,
0.024884246289730072,
0.08569072932004929,
-0.0069534615613520145,
-0.05132203549146652,
-0.005057670176029205,
-0.04640791192650795,
-0.020324667915701866,
0.0278126522898674,
0.09310451149940491,
0.0005083593423478305,
0.002677714917808771,
0.03225455805659294,
0.012546023353934288,
-0.007997680455446243,
0.017774008214473724,
0.022280285134911537,
0.0008702657651156187,
0.010972418822348118,
-0.06360423564910889,
0.023141710087656975,
-0.027449531480669975,
0.0313996784389019,
-0.007290545850992203,
0.0005513107753358781,
-0.02428494393825531,
0.016925476491451263,
0.01336814183741808,
0.044233083724975586,
-0.014102328568696976,
0.01749005913734436,
-0.000005405076535680564,
0.01757984794676304,
0.02901872806251049,
-0.015739355236291885,
0.01422844734042883,
-0.003162354463711381,
0.030680129304528236,
0.011872727423906326,
0.02641870453953743,
-0.060316842049360275,
-0.033036988228559494,
0.03008691594004631,
0.04780874773859978,
0.04487255960702896,
-0.008137156255543232,
-0.06652934849262238,
-0.036772821098566055,
0.027498427778482437,
0.01986996829509735,
0.008321375586092472,
-0.0078877629712224,
0.000311422161757946,
0.009001733735203743,
-0.049465328454971313,
-0.0508965328335762,
0.03989379480481148,
-0.00898926891386509,
0.041436780244112015,
-0.022379307076334953,
-0.009206498973071575,
-0.030888665467500687,
0.013236375525593758,
0.013242433778941631,
0.05960356444120407,
-0.006170881446450949,
-0.006545085925608873,
-0.017239147797226906,
0.04082496464252472,
-0.01880742982029915,
-0.05517319589853287,
0.030402980744838715,
0.01834065094590187,
-0.03043023869395256,
0.042666442692279816,
-0.0017711177933961153,
-0.011009718291461468,
0.038404226303100586,
0.008051028475165367,
-0.02518083155155182,
0.0325879342854023,
-0.026406949386000633,
0.029937244951725006,
0.04310184717178345,
0.011658154428005219,
0.03753987327218056,
0.043194662779569626,
-0.006200532894581556,
0.02019120380282402,
-0.005395796149969101,
0.017527876421809196,
-0.02627989463508129,
0.026519495993852615,
-0.039844438433647156,
0.007887806743383408,
-0.04652120918035507,
-0.0016541802324354649,
-0.022573616355657578,
0.021757425740361214,
-0.02168690226972103,
-0.010879579931497574,
0.001488909823819995,
0.008875501342117786,
-0.011534882709383965,
-0.0065786452032625675,
-0.019758734852075577,
0.011122670024633408,
0.03461161628365517,
-0.020784003660082817,
0.007748841308057308,
0.009188316762447357,
-0.02990267425775528,
0.042402494698762894,
0.01343186292797327,
0.04154600948095322,
-0.01775740645825863,
-0.02177654579281807,
0.0002460961986798793,
-0.023052988573908806,
-0.017733745276927948,
-0.004715296905487776,
-0.01506191398948431,
-0.013384134508669376,
0.007834569551050663,
-0.032675765454769135,
-0.01029348187148571,
-0.023880120366811752,
-0.01485977228730917,
-0.06628984212875366,
-0.01012483611702919,
0.02820761315524578,
0.008369611576199532,
-0.09503389894962311,
-0.032937560230493546,
0.008216716349124908,
-0.03853422775864601,
-0.0519414097070694,
-0.053148310631513596,
0.029520653188228607,
-0.03185324743390083,
-0.011996349319815636,
-0.01922716200351715,
0.01886163465678692,
-0.012713336385786533,
-0.003311525797471404,
0.000554228201508522,
0.046746645122766495,
0.030816778540611267,
-0.03438223525881767,
0.018372710794210434,
0.01500428095459938,
-0.01601315289735794,
-0.030800580978393555,
-0.004820441827178001,
0.007692067418247461,
-0.023657726123929024,
-0.014903852716088295,
0.00006767985178157687,
-0.017073579132556915,
-0.01224740780889988,
-0.013674688525497913,
-0.008917592465877533,
0.014017530716955662,
0.03899471089243889,
0.01445571519434452,
-0.03385752812027931,
-0.019444234669208527,
-0.0076656825840473175,
0.013583493418991566,
0.011147909797728062,
0.01991870254278183,
-0.03536480292677879,
-0.036756470799446106,
0.0009284191764891148,
-0.04139851778745651,
-0.01927587389945984,
0.003376457141712308,
0.06514309346675873,
0.006821233779191971,
0.024743853136897087,
0.05444631353020668,
-0.023650603368878365,
0.018997985869646072,
0.009703006595373154,
-0.0158406849950552,
0.010938936844468117,
-0.018492713570594788,
-0.014967241324484348,
-0.023403262719511986,
-0.06492859870195389,
0.052896685898303986,
0.04864136874675751,
0.013783970847725868,
0.032023608684539795,
0.014889209531247616,
-0.019455838948488235,
0.00998381432145834,
-0.00005440602035378106,
0.0010020192712545395,
0.05464530363678932,
-0.020022422075271606,
0.024586038663983345,
-0.035876963287591934,
-0.028998838737607002,
0.010843882337212563,
0.04753042012453079,
-0.07332306355237961,
0.015905747190117836,
0.010428303852677345,
-0.025856245309114456,
0.01762196607887745,
-0.017775464802980423,
-0.040258828550577164,
0.02528974786400795,
-0.018803322687745094,
0.041994012892246246,
-0.024538416415452957,
-0.010999173857271671,
0.03698815032839775,
0.0267097856849432,
0.00289885513484478,
-0.03065609186887741,
-0.037101421505212784,
-0.06268198788166046,
0.0018349732272326946,
0.004648383241146803,
0.0002967172476928681,
0.04772551357746124,
0.033315032720565796,
0.009408017620444298,
0.02890191413462162,
0.029711131006479263,
-0.009746121242642403,
-0.04478687793016434,
-0.01508056465536356,
-0.044725675135850906,
-0.06378810852766037,
0.04904593899846077,
-0.020530542358756065,
-0.0472925528883934,
0.007531274575740099,
-0.04153306409716606,
0.03779677674174309,
0.012018079869449139,
0.026925530284643173,
-0.024448338896036148,
0.052092038094997406,
0.009222296066582203,
0.021305900067090988,
0.0029913350008428097,
0.021730437874794006,
0.15013794600963593,
0.06126251816749573,
-0.01602214016020298,
-0.06224098056554794,
-0.031989701092243195,
0.011270732618868351,
0.020799219608306885,
-0.0521172396838665,
0.021102288737893105,
0.000836044258903712,
-0.02622619830071926,
-0.03992483764886856,
0.04570234939455986,
0.006325764115899801,
-0.03558025509119034,
0.04745936393737793,
-0.07902230322360992,
-0.027983644977211952,
0.02607211470603943,
0.015212995931506157,
-0.004914074204862118,
-0.012617570348083973,
-0.04629097878932953,
-0.013592926785349846,
-0.036461830139160156,
0.06651121377944946,
-0.029278384521603584,
-0.04459476098418236,
0.005808908026665449,
0.024757344275712967,
-0.044458553194999695,
0.026639170944690704,
-0.009817248210310936,
-0.022462278604507446,
-0.020555971190333366,
-0.0044483100064098835,
0.02016681805253029,
-0.021906796842813492,
0.007338317576795816,
0.02833494357764721,
0.001861131633631885,
-0.020900504663586617,
0.010351171717047691,
0.029409145936369896,
-0.01715060882270336,
-0.01789388619363308,
-0.009409761056303978,
0.06953524053096771,
0.004211300518363714,
-0.03484971821308136,
0.0038233096711337566,
-0.018865369260311127,
0.027884166687726974,
-0.03338966146111488,
-0.003277470590546727,
0.006397421471774578,
0.051164913922548294,
-0.010250530205667019,
0.021237961947917938,
-0.036775168031454086,
-0.013223530724644661,
-0.012906787917017937,
-0.019249767065048218,
-0.006571609526872635,
-0.0029618856497108936,
-0.010810649022459984,
-0.0017632119124755263,
0.02318822219967842,
-0.005786259658634663,
-0.01551345270127058,
-0.025395235046744347,
0.010685743764042854,
-0.026403067633509636,
-0.04976296052336693,
-0.006864029448479414,
0.002595027908682823,
0.056131694465875626,
0.017218362540006638,
-0.009901067242026329,
-0.05462126433849335,
-0.044805653393268585,
-0.001593963010236621,
0.006475720088928938,
-0.0298765879124403,
0.008928992785513401,
-0.021145060658454895,
0.039841845631599426,
0.06395027786493301,
-0.006269307341426611,
0.007139862049371004,
0.037695545703172684,
0.012249958701431751,
0.044766057282686234,
-0.025399159640073776,
-0.03388319909572601,
0.025715267285704613,
-0.0002908837341237813,
-0.01562521606683731,
-0.03411348909139633,
-0.027306921780109406,
0.035203855484724045,
-0.02655845694243908,
0.019326316192746162,
0.02635950595140457,
0.0048711891286075115,
-0.009847132489085197,
0.018868496641516685,
-0.030986938625574112,
0.0064563266932964325,
0.04989807307720184,
0.017657127231359482,
-0.035548776388168335,
-0.010665771551430225,
-0.031162787228822708,
0.05540340766310692,
-0.014481579884886742,
0.003935675602406263,
-0.05198433995246887,
-0.02906637266278267,
0.012713450007140636,
0.026154542341828346,
0.0006289690500125289,
0.008157451637089252,
-0.031372930854558945,
0.04947208613157272,
-0.014371683821082115,
0.01771075464785099,
0.021127279847860336,
0.028047336265444756,
0.006793167442083359,
-0.015330016613006592,
0.017956119030714035,
0.02435712330043316,
-0.03396258503198624,
-0.007380479481071234,
-0.013744356110692024,
0.00739530473947525,
0.03317079320549965,
0.036598049104213715,
-0.025142498314380646,
-0.005377373658120632,
-0.05638810992240906,
-0.04276719689369202,
0.048134882003068924,
0.05149681493639946,
0.01825963333249092,
0.059671513736248016,
-0.007163112983107567,
-0.03941581770777702,
0.0459686741232872,
-0.03283961862325668,
-0.006193410139530897,
0.019516227766871452,
-0.0441836453974247,
0.004780617542564869,
-0.03241606056690216,
0.027539599686861038,
0.020962949842214584,
0.015269722789525986,
0.006288634147495031,
0.01050191093236208,
-0.012627138756215572,
-0.008379754610359669,
0.016373710706830025,
-0.007891250774264336,
0.06456460803747177,
-0.0012783475685864687,
-0.04443003982305527,
0.04263961687684059,
0.06229382008314133,
-0.022902796044945717,
0.0013308234047144651,
0.014003649353981018,
0.014357705600559711,
-0.10244105011224747,
-0.03005523793399334,
-0.01499098725616932,
0.04371361806988716,
0.052519604563713074,
0.0010146991116926074,
0.028714902698993683,
0.011012688279151917,
-0.04110225662589073,
0.05804716423153877,
-0.028420867398381233,
0.023367878049612045,
-0.02997782826423645,
-0.008595187216997147,
-0.04273856803774834,
0.0685705617070198,
0.06084193289279938,
0.035738296806812286,
-0.013645523227751255,
0.022001851350069046,
-0.010054616257548332,
-0.03761541098356247,
-0.01038352120667696,
0.016347559168934822,
0.007902231998741627,
-0.029420634731650352,
0.06445889174938202,
0.0029881091322749853,
-0.023875214159488678,
-0.00013356511772144586,
0.04503975063562393,
-0.028575479984283447,
-0.0122502027079463,
0.05337989330291748,
0.02460707724094391,
0.03460255265235901,
0.02352842316031456,
-0.020754164084792137,
0.026094960048794746,
0.006747864652425051,
0.011155706830322742,
0.002132031135261059,
0.012512861751019955,
-0.012491987086832523,
-0.017845168709754944,
-0.05113459378480911,
-0.011337912641465664,
0.04763307049870491,
0.013560829684138298,
-0.006700003053992987,
-0.04092446714639664,
-0.017369573935866356,
0.028067871928215027,
0.0023716113064438105,
-0.008400200866162777,
-0.019494514912366867,
-0.01973719894886017,
0.06950514018535614,
-0.02240723930299282,
-0.0065613784827291965,
-0.021221084520220757,
-0.042183127254247665,
-0.051849767565727234,
0.04007871076464653,
0.016550540924072266,
0.0019023558124899864,
-0.03277801722288132,
-0.028028730303049088,
-0.0057702818885445595,
0.03822036460042,
-0.023698030039668083,
0.000004427755357028218,
-0.07077103108167648,
0.008198400028049946,
-0.013154543936252594,
-0.00014899334928486496,
-0.03711160272359848,
-0.03495106101036072,
0.006936978083103895,
-0.06925144791603088,
0.02202601172029972,
0.01966290920972824,
-0.02290646731853485,
-0.01043013483285904,
0.02756974659860134,
0.000535841565579176,
0.03600390627980232,
0.05277477577328682,
-0.0038922750391066074,
-0.03809512406587601,
0.056153710931539536,
0.019053103402256966,
0.0176971685141325,
-0.031747084110975266,
0.006446520332247019,
0.03288871794939041,
0.04581814259290695,
0.011586424894630909,
0.000017323111023870297,
-0.026149582117795944,
0.044691052287817,
-0.027884820476174355,
-0.023496950045228004,
0.019543200731277466,
-0.0002074055519187823,
-0.03547854721546173,
0.042179837822914124,
-0.01839364692568779,
0.011946037411689758,
0.07063362747430801,
0.0018280791118741035,
0.023110829293727875,
0.06600816547870636,
-0.03547050058841705,
-0.03557191416621208,
-0.038626790046691895,
-0.03589240089058876,
-0.010755001567304134,
0.006487805861979723,
-0.005297601688653231,
0.01171150989830494,
-0.025038762018084526,
-0.007929874584078789,
0.026794543489813805,
-0.00632996903732419,
-0.042892467230558395,
0.057565122842788696,
0.03249293193221092,
0.047204598784446716,
0.006386700551956892,
0.007846811786293983,
0.020726803690195084,
0.006238325498998165,
0.040432482957839966,
0.025147119536995888,
0.01674317941069603,
0.009889447130262852,
0.012939090840518475,
-0.018419811502099037,
-0.011113947257399559,
0.016819149255752563,
0.017498156055808067,
-0.017836015671491623,
-0.03949357196688652,
0.011485736817121506,
0.051457151770591736,
-0.03214731067419052,
0.0062402598559856415,
0.021979816257953644,
-0.01443664263933897,
0.07880338281393051,
-0.029057081788778305,
0.03043142519891262,
-0.03127386420965195,
0.013854051940143108,
-0.04018191248178482,
0.029326599091291428,
-0.011894149705767632,
0.05880791321396828,
-0.0543178953230381,
-0.022432168945670128,
-0.032593242824077606,
-0.01569542847573757,
-0.01801520399749279,
-0.08582396805286407,
-0.03246590122580528,
0.023503517732024193,
0.010623198002576828,
-0.003965691197663546,
-0.05099710077047348,
-0.013876065611839294,
-0.016256174072623253,
0.02243509702384472,
0.057177867740392685,
0.02620870992541313,
-0.03627600148320198,
-0.017946414649486542,
-0.04310494288802147,
0.042289137840270996,
-0.018264630809426308,
0.014548764564096928,
0.02191588468849659,
0.008709708228707314,
-0.016315588727593422,
-0.013872603885829449
] |
<p>If one travels in a spaceship at speed V, the time elapsed for the traveller relative to an observer on earth is dilated by,</p>
<p>$$ t' = t(1 - v^2/c^2)^{1/2} $$</p>
<p>Does this mean that a space traveller, who gradually accelerated to a speed very close to the speed of light can then travel 10 billion light years in a few minutes?</p>
<p>Relative to the travelling observer, does this mean that effectively there is no speed limit? Even though this can be translated as a space contraction, what difference does that make - the traveller effectively travelled 10 billion light years in say 6 minutes - meaning an effective speed of 100 billion light years per hour (876 trillion times the speed of light). </p>
<p>Does this mean that time travel into the future is possible? Would it be possible for a traveller making a round trip away and back to earth to travel to the year 3000 in 5 years?</p>
| 8,307 |
[
0.008180574513971806,
-0.03984644263982773,
-0.004124441184103489,
-0.02831220254302025,
0.08427861332893372,
-0.009845242835581303,
-0.027199571952223778,
-0.023855680599808693,
-0.021281959488987923,
-0.04299061372876167,
0.023164264857769012,
0.07574827969074249,
0.01655595749616623,
0.01753486879169941,
-0.002385564614087343,
0.008201474323868752,
-0.0008592696976847947,
-0.013729438185691833,
-0.020006293430924416,
-0.014138898812234402,
0.03408610820770264,
0.009749329648911953,
0.0001953863975359127,
0.019848376512527466,
-0.03835821896791458,
0.004234931897372007,
0.019860699772834778,
0.0023727351799607277,
-0.0006365415174514055,
0.06249139830470085,
-0.018747886642813683,
-0.013095802627503872,
0.006445744074881077,
0.015462146140635014,
0.0016009740065783262,
0.010609397664666176,
-0.02487989515066147,
-0.0360855869948864,
0.015415141358971596,
0.024017933756113052,
-0.03658464923501015,
0.011918563395738602,
0.021030031144618988,
0.06906856596469879,
0.00116763508412987,
0.020595619454979897,
0.0170477032661438,
-0.008100212551653385,
0.02397266961634159,
-0.04831478372216225,
0.05815640836954117,
-0.016115449368953705,
0.014702649787068367,
0.0023470004089176655,
0.004433630034327507,
-0.00754156056791544,
0.0987403616309166,
0.08374625444412231,
-0.010744440369307995,
-0.023549500852823257,
0.01931021176278591,
0.012182005681097507,
0.014266661368310452,
-0.001792742288671434,
-0.014739216305315495,
0.022219492122530937,
-0.03293053060770035,
0.0026046799030154943,
-0.0031847760546952486,
-0.048861827701330185,
0.015636974945664406,
-0.01456503476947546,
0.01982441172003746,
0.008950748480856419,
0.030548198148608208,
-0.05021826922893524,
0.02110716514289379,
0.011295325122773647,
0.04865933209657669,
0.08043310046195984,
0.01142392959445715,
0.006039328407496214,
0.04310131445527077,
0.05075175315141678,
0.03288387507200241,
-0.0003915066772606224,
0.057826247066259384,
-0.010620509274303913,
0.028134772554039955,
0.042268384248018265,
-0.0014573021326214075,
0.025435272604227066,
0.026098206639289856,
-0.010272559709846973,
-0.0058463215827941895,
0.03905944153666496,
0.012634269893169403,
0.052088361233472824,
0.00008334073208970949,
-0.00423094630241394,
-0.016036290675401688,
-0.038654159754514694,
0.007922491990029812,
0.03693287819623947,
0.0025056300219148397,
-0.02838670089840889,
-0.039904575794935226,
0.01481611654162407,
-0.02700154297053814,
-0.013436844572424889,
-0.03937486186623573,
-0.01505948044359684,
-0.00030440319096669555,
0.044744301587343216,
0.0044073970057070255,
-0.029567502439022064,
0.021498223766684532,
-0.05892535671591759,
0.07210234552621841,
0.035651955753564835,
0.022058462724089622,
-0.008074706420302391,
0.009999825619161129,
0.007837185636162758,
-0.05679880827665329,
0.014932756312191486,
-0.0041008517146110535,
0.0009101690957322717,
-0.005555051378905773,
0.03132506087422371,
0.00902754720300436,
-0.05151645839214325,
0.008923543617129326,
0.003645937191322446,
0.05507498234510422,
0.009296869859099388,
-0.10495550185441971,
-0.06551466882228851,
0.04872443526983261,
0.014120862819254398,
-0.010056935250759125,
-0.056563299149274826,
0.06842266768217087,
-0.006538413465023041,
0.09112980961799622,
0.013652848079800606,
-0.010930914431810379,
0.01291034184396267,
0.017709245905280113,
0.015009389258921146,
-0.05716327950358391,
0.01123717799782753,
0.000837513362057507,
-0.043385207653045654,
0.01845654472708702,
-0.08651144057512283,
0.00011880033707711846,
0.04429611936211586,
0.012538738548755646,
-0.028208274394273758,
0.05886678770184517,
0.007210094481706619,
0.0073065063916146755,
0.000948892324231565,
-0.02572707273066044,
0.003775764023885131,
0.08699578791856766,
0.020307965576648712,
-0.01212754100561142,
0.02569381147623062,
0.03199021890759468,
0.03524863347411156,
0.01646067015826702,
0.002941514365375042,
0.029505040496587753,
-0.030888546258211136,
-0.008328127674758434,
0.008481626398861408,
-0.024555815383791924,
0.02080458030104637,
-0.038238827139139175,
-0.02718259207904339,
-0.022475143894553185,
-0.020148664712905884,
0.041575539857149124,
0.0630495697259903,
-0.009201585315167904,
0.026687467470765114,
-0.02526799403131008,
-0.044859521090984344,
-0.012765699066221714,
-0.052955109626054764,
0.014815722592175007,
0.0506698340177536,
0.012425243854522705,
0.009618113748729229,
-0.04732412472367287,
0.0335371270775795,
-0.04815029725432396,
-0.03169091045856476,
-0.016920046880841255,
0.04263468086719513,
0.023400846868753433,
-0.04713650420308113,
0.02266874350607395,
0.06941606104373932,
0.06003192067146301,
-0.01928764395415783,
0.0008808579877950251,
0.006143113598227501,
-0.07136811316013336,
0.0134843485429883,
-0.004122086334973574,
0.050020571798086166,
-0.0017654069233685732,
0.012407432310283184,
0.031860996037721634,
0.030679676681756973,
-0.010246709920465946,
0.029474902898073196,
-0.013261036947369576,
0.10220374166965485,
0.058253757655620575,
-0.008254509419202805,
0.009470813907682896,
0.016437141224741936,
0.005763229914009571,
-0.0018831109628081322,
0.019615860655903816,
-0.03369222208857536,
-0.046371717005968094,
-0.03016936220228672,
0.017173506319522858,
0.033995334059000015,
-0.02008778229355812,
0.015802206471562386,
0.03386835753917694,
0.017546920105814934,
0.020021630451083183,
0.000825137656647712,
-0.03627694770693779,
-0.0347798615694046,
-0.00588732585310936,
-0.001121707959100604,
-0.019136609509587288,
0.012416325509548187,
0.022519197314977646,
0.01212735753506422,
-0.0007241903804242611,
-0.01559420395642519,
0.017368922010064125,
0.0017271141987293959,
0.015054854564368725,
-0.002277044113725424,
0.03110339306294918,
-0.03886280581355095,
0.017872557044029236,
-0.024739887565374374,
0.014326509088277817,
0.03898559883236885,
0.020942190662026405,
0.02803242951631546,
-0.041566088795661926,
-0.010370355099439621,
-0.009549267590045929,
0.007159603759646416,
-0.008852357044816017,
-0.03672398254275322,
0.029053498059511185,
-0.02944944053888321,
0.013430215418338776,
-0.038304854184389114,
0.017386462539434433,
-0.0115974685177207,
-0.011691874824464321,
0.02989533729851246,
0.024089336395263672,
0.019844697788357735,
-0.022525595501065254,
-0.027539262548089027,
0.008451664820313454,
-0.03709981217980385,
0.004915920086205006,
-0.002929095644503832,
-0.03581887483596802,
0.06332459300756454,
-0.004336996469646692,
-0.05681898444890976,
0.04225322604179382,
0.008633043617010117,
0.012559256516397,
0.052849411964416504,
-0.010874539613723755,
-0.06644590944051743,
-0.006563169881701469,
-0.026637021452188492,
-0.000059144564147572964,
-0.01927320659160614,
0.00023438027710653841,
0.053835343569517136,
0.0017224709736183286,
-0.04548485949635506,
0.014112557284533978,
-0.05904368683695793,
-0.02806079015135765,
-0.03566529601812363,
0.012881388887763023,
-0.000535931030754,
-0.04514302685856819,
0.011715480126440525,
0.013262162916362286,
-0.024868378415703773,
0.017649486660957336,
-0.05728687345981598,
-0.036910876631736755,
0.02057981863617897,
0.005174217280000448,
0.05782113969326019,
-0.02690752036869526,
-0.038536474108695984,
0.08043171465396881,
0.049196016043424606,
0.011716736480593681,
-0.0696926862001419,
-0.00022874154092278332,
0.0008443320984952152,
0.0017918094526976347,
0.003004856174811721,
0.02243698388338089,
-0.05231095105409622,
-0.012149324640631676,
0.030191605910658836,
0.027972029522061348,
0.02625902369618416,
0.019687023013830185,
-0.0014145402237772942,
0.015663310885429382,
-0.02641616202890873,
0.030976947396993637,
0.030596798285841942,
0.018419304862618446,
-0.054258082062006,
0.013009932823479176,
-0.04254372417926788,
0.0467524491250515,
0.02845754846930504,
-0.04995708167552948,
0.05781395360827446,
0.037426695227622986,
0.012355241924524307,
-0.016304897144436836,
0.03618174046278,
0.012219113297760487,
-0.005041423253715038,
-0.004717861767858267,
0.002221561037003994,
0.030233504250645638,
-0.016460638493299484,
-0.009940678253769875,
0.00367932952940464,
0.048345763236284256,
0.012121428735554218,
-0.029245439916849136,
0.011990710161626339,
-0.016361568123102188,
0.035572540014982224,
-0.04424527287483215,
-0.007112834602594376,
0.06785257905721664,
0.05334039404988289,
0.002778585534542799,
-0.0010599354282021523,
-0.008606751449406147,
-0.009299988858401775,
-0.08357628434896469,
-0.02322551980614662,
-0.022267792373895645,
0.034869369119405746,
0.02561636082828045,
0.023754362016916275,
0.015725675970315933,
-0.010272913612425327,
0.02259664051234722,
0.012508811429142952,
-0.05804198980331421,
0.014752272516489029,
-0.02898128516972065,
-0.03986157849431038,
-0.02539617009460926,
0.026625797152519226,
-0.007088076323270798,
-0.0073609063401818275,
-0.0080126216635108,
-0.0383402444422245,
-0.013660416007041931,
-0.0795515924692154,
0.007220172323286533,
-0.013364759273827076,
-0.0341842882335186,
-0.007647586055099964,
-0.01776292733848095,
0.04372365400195122,
-0.008068990893661976,
0.0278752651065588,
0.0313897430896759,
-0.0417570024728775,
0.00596314063295722,
0.015791215002536774,
-0.007856862619519234,
0.023379316553473473,
0.026698119938373566,
0.01929479092359543,
0.010483445599675179,
-0.04271776229143143,
0.02717800997197628,
0.04655284434556961,
0.009053779765963554,
0.006558031775057316,
0.014034023508429527,
-0.05038567632436752,
-0.019889051094651222,
-0.027586957439780235,
0.03469523787498474,
0.034556567668914795,
0.008784457109868526,
0.031614966690540314,
0.04911268129944801,
0.001883070101030171,
-0.014747098088264465,
0.013474945910274982,
0.033462148159742355,
-0.03862382099032402,
-0.015780339017510414,
-0.015823058784008026,
-0.02579142153263092,
-0.00319662899710238,
-0.007140215951949358,
-0.019064337015151978,
0.0025826937053352594,
-0.025640225037932396,
-0.0024803527630865574,
0.005252641625702381,
0.0015728529542684555,
-0.03362440690398216,
0.020776504650712013,
0.013862351886928082,
0.004234041087329388,
0.03494640067219734,
0.01767217181622982,
0.008937099017202854,
0.008964904583990574,
0.03602040559053421,
-0.013449142687022686,
-0.014479637145996094,
-0.08607827126979828,
-0.016614839434623718,
0.014691418968141079,
0.06656873226165771,
-0.003550519235432148,
0.001459728111512959,
-0.05236147344112396,
-0.018679853528738022,
0.019550016149878502,
-0.02173321321606636,
0.005684792995452881,
0.0020785548258572817,
-0.014407654292881489,
-0.0246526338160038,
-0.02569691836833954,
0.004507371690124273,
0.008552768267691135,
-0.010055964812636375,
0.01044635009020567,
0.0010606825817376375,
0.03800240531563759,
0.007841513492166996,
-0.009498441591858864,
0.022214042022824287,
0.056624636054039,
0.0062684169970452785,
-0.018948780372738838,
-0.010246740654110909,
0.02818063646554947,
-0.043433114886283875,
-0.0627121552824974,
0.008294680155813694,
0.03627157583832741,
-0.042129114270210266,
0.045436710119247437,
-0.03395400568842888,
-0.04846177622675896,
0.03628431633114815,
-0.010900100693106651,
-0.018178150057792664,
-0.009992546401917934,
-0.03723304718732834,
0.03328992426395416,
0.025498177856206894,
-0.007203221786767244,
0.017294475808739662,
0.031504206359386444,
-0.017485203221440315,
0.02207227423787117,
-0.002481251023709774,
0.016820795834064484,
-0.030426492914557457,
0.03213032707571983,
0.0024462577421218157,
0.0034971367567777634,
-0.012642187997698784,
0.04195724055171013,
-0.047544926404953,
-0.014117887243628502,
-0.01341691892594099,
-0.022062046453356743,
-0.005499434191733599,
0.03591254726052284,
0.052497636526823044,
0.012862280942499638,
-0.036948125809431076,
-0.017494741827249527,
0.010454919189214706,
-0.037884559482336044,
0.016134601086378098,
0.03916648402810097,
0.013784585520625114,
0.032463595271110535,
0.016440166160464287,
-0.012100969441235065,
0.009346898645162582,
0.030321167781949043,
0.016572026535868645,
-0.03020191192626953,
0.061254989355802536,
-0.009481330402195454,
0.010851253755390644,
0.015960916876792908,
-0.014482175931334496,
-0.03560531511902809,
0.013379333540797234,
-0.022005481645464897,
0.009136800654232502,
-0.06571590155363083,
0.030282404273748398,
0.014469570480287075,
0.014554215595126152,
-0.07081515341997147,
-0.006963842548429966,
0.04580346867442131,
0.0008026412106119096,
-0.0363008938729763,
-0.016602635383605957,
-0.016566932201385498,
-0.04785105213522911,
-0.03349864482879639,
-0.03624754399061203,
0.0532248318195343,
-0.019819747656583786,
-0.02247174084186554,
-0.020242080092430115,
-0.005483132787048817,
0.0492350272834301,
0.0008799677598290145,
-0.005227652844041586,
-0.017630981281399727,
-0.0024817041121423244,
0.01882323808968067,
-0.03252793103456497,
0.027393072843551636,
-0.037230800837278366,
-0.056601766496896744,
-0.010154977440834045,
0.011452908627688885,
0.01711403764784336,
-0.031812869012355804,
-0.010305971838533878,
0.07169869542121887,
-0.008053387515246868,
-0.016696663573384285,
0.008227726444602013,
0.023829234763979912,
-0.009328747168183327,
0.01313430443406105,
-0.006046614143997431,
0.015101881697773933,
-0.010699746198952198,
-0.019672976806759834,
0.04204437509179115,
0.002679515862837434,
-0.015501056797802448,
-0.013772142119705677,
0.03860575705766678,
-0.0039524189196527,
-0.0068459175527095795,
0.014369955286383629,
0.0031036045402288437,
0.01851779595017433,
-0.02238117717206478,
-0.040416982024908066,
0.012310364283621311,
-0.017805343493819237,
-0.043927811086177826,
-0.000644884305074811,
-0.011192157864570618,
-0.01006692461669445,
0.051622048020362854,
-0.008336901664733887,
0.04758962616324425,
-0.013216936029493809,
-0.0039048411417752504,
-0.004619934596121311,
-0.034824907779693604,
-0.02101709321141243,
-0.018262311816215515,
0.007811408955603838,
0.015584892593324184,
-0.03908395394682884,
-0.03261089324951172,
0.03524754196405411,
0.032896071672439575,
-0.006743811070919037,
-0.003364860313013196,
0.02383076585829258,
0.0013568674912676215,
0.03882390260696411,
-0.0305137000977993,
-0.03503516688942909,
0.023480799049139023,
-0.040353868156671524,
0.00582506787031889,
0.006525891367346048,
0.005459228530526161,
0.051953837275505066,
0.006684931460767984,
0.019220946356654167,
-0.03483794629573822,
-0.012821673415601254,
-0.05523572489619255,
-0.03473810479044914,
0.02187214232981205,
0.0184091217815876,
-0.00017580899293534458,
-0.03149333968758583,
0.03997780382633209,
-0.00688463868573308,
-0.00041414439328946173,
-0.00930806715041399,
-0.053382616490125656,
-0.04278695210814476,
-0.03537774831056595,
-0.028006630018353462,
0.037406619638204575,
0.009877976030111313,
-0.036722153425216675,
-0.020627304911613464,
-0.022898340597748756,
-0.0026322926860302687,
-0.01909162849187851,
0.04312213882803917,
-0.004534074105322361,
0.0959753692150116,
-0.005658916663378477,
0.021674880757927895,
-0.026809992268681526,
0.02099910005927086,
0.08925770223140717,
0.03746561333537102,
-0.019250595942139626,
-0.036528512835502625,
0.019880862906575203,
-0.016758201643824577,
0.029523152858018875,
-0.03683209419250488,
0.023812493309378624,
-0.02083951234817505,
0.0023873201571404934,
0.04282231628894806,
0.04756241291761398,
-0.026444928720593452,
-0.03241662681102753,
0.02947811968624592,
-0.03867536410689354,
-0.028789138421416283,
-0.009386040270328522,
0.01608079858124256,
-0.005155531689524651,
0.01258645486086607,
0.019854795187711716,
0.036823056638240814,
-0.05287982523441315,
0.006236397195607424,
-0.06384824216365814,
-0.0036845935974270105,
0.010648101568222046,
-0.01585356704890728,
-0.054338403046131134,
-0.0002383368118898943,
0.029514750465750694,
-0.02710319124162197,
-0.03342375159263611,
-0.010507178492844105,
0.015819791704416275,
-0.006412539631128311,
0.005985102150589228,
0.07873910665512085,
-0.007203914225101471,
-0.0021405513398349285,
0.010922478511929512,
0.017709335312247276,
-0.06295692920684814,
0.00905335508286953,
-0.030548401176929474,
0.03196880593895912,
0.004065392538905144,
0.00034068350214511156,
0.006531643681228161,
0.013207688927650452,
0.010081198066473007,
-0.03481443598866463,
-0.01804344728589058,
0.032785795629024506,
0.007932176813483238,
0.025705263018608093,
-0.011512087658047676,
-0.037725865840911865,
-0.008954906836152077,
0.015698110684752464,
0.02465427853167057,
-0.0012452389346435666,
0.007549045607447624,
0.019610898569226265,
-0.010953345336019993,
0.013816354796290398,
-0.045314449816942215,
-0.007650763727724552,
-0.041145697236061096,
0.02943224087357521,
-0.0527496263384819,
0.01518111303448677,
0.03411273658275604,
0.03243369981646538,
0.012554208748042583,
0.0007102719391696155,
0.009527511894702911,
-0.019650807604193687,
-0.06188935413956642,
0.048754122108221054,
-0.025354895740747452,
-0.0011366019025444984,
-0.017253991216421127,
0.0313379168510437,
0.04966497793793678,
0.013997593894600868,
-0.036662738770246506,
0.03778699412941933,
-0.06209269165992737,
0.05758792534470558,
0.028598465025424957,
0.006658435799181461,
-0.003546216757968068,
-0.019731629639863968,
-0.00882077869027853,
0.015326141379773617,
-0.014299344271421432,
0.051204852759838104,
0.06760068982839584,
-0.027922416105866432,
-0.0010655670193955302,
-0.022297970950603485,
-0.003344679716974497,
0.015322646126151085,
0.04300256446003914,
-0.033292658627033234,
0.01624920405447483,
-0.009388863109052181,
0.05180957540869713,
-0.007976529188454151,
-0.004950747359544039,
-0.01827126368880272,
-0.023849375545978546,
-0.02109689638018608,
-0.007519701030105352,
0.013662298209965229,
0.05573121830821037,
-0.007196033839136362,
-0.015415697358548641,
-0.06475923955440521,
0.010254952125251293,
-0.03394386172294617,
0.03899110481142998,
-0.0258930753916502,
-0.011983218602836132,
0.015491995960474014,
0.018788229674100876,
-0.01856333762407303,
-0.030174439772963524,
0.03110874630510807,
0.0210157111287117,
-0.02053716592490673,
-0.020474594086408615,
0.006998731289058924,
-0.001594984671100974,
0.01945502497255802,
-0.05455499514937401,
-0.053808651864528656,
0.007851691916584969,
-0.012305526994168758,
-0.04628197103738785,
0.059818197041749954,
-0.0015124744968488812,
0.05124737322330475,
0.027443237602710724,
0.005795647855848074,
-0.030262721702456474,
0.06105858460068703,
-0.023584682494401932,
-0.02371407300233841,
0.038601458072662354,
-0.033303119242191315,
-0.016575470566749573,
-0.023170892149209976,
0.007825019769370556,
0.01640596240758896,
-0.01570555567741394,
0.0031097333412617445,
0.011963730677962303,
-0.009581639431416988,
0.037308938801288605,
-0.024205511435866356,
-0.04038213938474655,
-0.013550999574363232,
0.019875813275575638,
-0.03159167245030403,
0.053831547498703,
0.05628606304526329,
-0.01462562195956707,
0.031171653419733047,
0.01711791567504406,
-0.01654600165784359,
-0.1173478364944458,
-0.0059468490071594715,
0.00807730108499527,
0.03487400710582733,
0.03293484076857567,
-0.039762943983078,
0.044119976460933685,
0.03401075676083565,
-0.07522857189178467,
0.0450388565659523,
-0.016651848331093788,
-0.0030126681085675955,
-0.01582423783838749,
0.019124481827020645,
0.0026265622582286596,
0.06805392354726791,
0.04221661388874054,
0.029948627576231956,
-0.009887374006211758,
0.04399648681282997,
-0.030043868348002434,
-0.05672157555818558,
0.002379685640335083,
0.00730900140479207,
-0.03410946950316429,
0.0030222011264413595,
0.05222814902663231,
-0.015645217150449753,
-0.018072374165058136,
0.013547662645578384,
0.034314583986997604,
0.07544437795877457,
-0.004222712945193052,
-0.010004326701164246,
0.022095100954174995,
0.008197194896638393,
0.05203884840011597,
0.0037653292529284954,
-0.0343494787812233,
0.047223180532455444,
-0.022982412949204445,
0.01566031388938427,
-0.002619070466607809,
-0.0245496965944767,
0.023285124450922012,
-0.03363684192299843,
0.008810216560959816,
0.03238476812839508,
-0.008592996746301651,
0.00031315197702497244,
0.04863777384161949,
0.005432730074971914,
-0.01762806624174118,
-0.012500593438744545,
-0.002202926902100444,
-0.040898557752370834,
-0.013723587617278099,
0.02622823975980282,
-0.004175571259111166,
-0.044923193752765656,
0.01760214939713478,
-0.031853292137384415,
-0.027597704902291298,
0.016094159334897995,
-0.009282181970775127,
0.018678337335586548,
-0.023581398651003838,
0.0018764472333714366,
0.029729170724749565,
-0.015691304579377174,
0.017188003286719322,
-0.009747128933668137,
-0.0036891750060021877,
0.016048520803451538,
0.014993433840572834,
0.010269531980156898,
-0.0012170866830274463,
-0.022343946620821953,
-0.019821276888251305,
-0.0408175066113472,
0.012206854298710823,
-0.03669415041804314,
-0.001220262493006885,
-0.04365406185388565,
-0.060590069741010666,
-0.033964235335588455,
0.004957813769578934,
0.07579995691776276,
-0.028662072494626045,
0.005461047403514385,
0.006808467209339142,
0.006734485272318125,
0.013623437844216824,
-0.08669713884592056,
-0.0010956631740555167,
-0.004104055464267731,
-0.05726684629917145,
-0.011694880202412605,
-0.022994406521320343,
-0.04833406209945679,
-0.015482336282730103,
0.04912830889225006,
-0.005094751715660095,
0.037958431988954544,
0.04701919108629227,
-0.04253961890935898,
0.04771612957119942,
0.0377395860850811,
0.010816838592290878,
0.050625115633010864,
-0.00885778572410345,
0.03653121739625931,
0.0476263053715229,
-0.021750466898083687,
-0.03972789645195007,
-0.014028158038854599,
-0.05544201284646988,
-0.022537821903824806,
-0.017372773960232735,
-0.011422892101109028,
-0.006855024956166744,
-0.044643111526966095,
0.012116484344005585,
0.051022034138441086,
-0.040384989231824875,
0.01688031107187271,
0.04596156254410744,
0.014962609857320786,
0.023470409214496613,
-0.03661922365427017,
0.01608973741531372,
0.00710630789399147,
-0.005470578558743,
-0.0201296154409647,
0.005860027391463518,
0.028820203617215157,
-0.023037049919366837,
0.025440745055675507,
0.03442483767867088,
0.024380026385188103,
0.027585219591856003,
-0.034000787883996964,
0.040176618844270706,
-0.06424397975206375,
-0.0013851779513061047,
0.009846617467701435,
-0.03570270910859108,
0.035812463611364365,
0.033366985619068146,
-0.020961621776223183,
0.07951949536800385,
-0.03046158328652382,
0.026426512748003006,
0.015848053619265556,
-0.015854524448513985,
-0.05473986640572548,
0.0068991766311228275,
0.016284655779600143,
-0.002622365253046155,
-0.004223243333399296,
-0.010334638878703117,
-0.008542698808014393,
0.018396496772766113,
0.025689154863357544,
-0.060167428106069565,
-0.024383584037423134,
-0.02190941572189331,
-0.03923029825091362,
-0.018327519297599792,
-0.019805602729320526,
-0.020720576867461205,
0.0015026516048237681,
0.021097416058182716,
0.019844364374876022,
-0.015083682723343372,
-0.018246250227093697,
0.015017145313322544,
0.011140004731714725,
0.037890173494815826,
-0.08584559708833694,
-0.0015644717495888472,
-0.03866885229945183,
0.007888034917414188,
-0.02612302452325821,
-0.053352873772382736
] |
<p>I want to know how to calculate the normal modes from a Lagrangian.
I make the T (kinetic energy matrix) and U (potential energy matrix), and then I calculate the determinant of $|T-\omega ^2 U|$ (with omega as the angular speed). This way I find the $\omega$'s but I dont know how to find the normal modes.
Are they just the eigenvectors of the $T-\omega ^2 U$?</p>
| 8,308 |
[
0.007963108830153942,
-0.01701725274324417,
-0.011127404868602753,
0.008472008630633354,
0.017687678337097168,
-0.002299309941008687,
-0.01621328666806221,
-0.02726098522543907,
0.010105622000992298,
-0.04351328685879707,
-0.005337806884199381,
0.0037096375599503517,
0.04721292853355408,
-0.00044801062904298306,
0.04087475314736366,
-0.005720500834286213,
-0.05789605900645256,
-0.0012628824915736914,
-0.023143725469708443,
-0.016323117539286613,
-0.012318014167249203,
-0.03983309492468834,
0.024201486259698868,
-0.024926265701651573,
-0.012113979086279869,
0.03260623291134834,
0.022731833159923553,
0.008669979870319366,
0.003321226919069886,
0.019472135230898857,
-0.006251388695091009,
-0.01914576068520546,
0.033951740711927414,
0.016992976889014244,
-0.01843992993235588,
0.005054919049143791,
-0.03822566941380501,
0.009944361634552479,
-0.023335326462984085,
-0.004567814990878105,
-0.04320719838142395,
-0.03499023616313934,
-0.03581281378865242,
0.0669354572892189,
-0.00748201971873641,
0.0066330465488135815,
0.0033989723306149244,
-0.01515952218323946,
0.039646439254283905,
-0.03615809231996536,
0.11130887269973755,
-0.00005536998651223257,
0.029438843950629234,
0.03430616483092308,
-0.00478037865832448,
-0.020847786217927933,
0.0720045417547226,
0.046868614852428436,
0.006717366632074118,
-0.06704959273338318,
0.016711995005607605,
-0.04555485397577286,
-0.01959330588579178,
-0.017186438664793968,
-0.03135225176811218,
0.013310117647051811,
-0.008584346622228622,
-0.016088759526610374,
0.042686548084020615,
-0.007411431986838579,
-0.014521606266498566,
0.02200448513031006,
0.018003661185503006,
-0.021229006350040436,
-0.020664962008595467,
-0.020969906821846962,
0.023730164393782616,
0.026291975751519203,
0.015087245032191277,
0.017505280673503876,
0.035557821393013,
0.017060188576579094,
0.001460594474337995,
0.024782033637166023,
-0.044074006378650665,
-0.025774074718356133,
0.0509248822927475,
-0.0127842016518116,
0.016281181946396828,
0.06665855646133423,
-0.009409264661371708,
-0.0015471894294023514,
0.021707633510231972,
-0.01773988828063011,
-0.011728692799806595,
0.03453995659947395,
0.007620816584676504,
0.028332045301795006,
0.015964874997735023,
-0.019215112552046776,
0.010760387405753136,
-0.06120547652244568,
-0.00043724608258344233,
0.06716437637805939,
-0.011207154020667076,
0.00014867394929751754,
-0.04762019217014313,
0.04165470227599144,
-0.012203467078506947,
-0.02604295313358307,
-0.0487421452999115,
0.011744423769414425,
-0.03624223172664642,
-0.007179098203778267,
0.006395337637513876,
-0.03345606476068497,
0.007134505081921816,
-0.03318718820810318,
0.027858158573508263,
0.05359450355172157,
0.0476563386619091,
-0.027562810108065605,
0.022904181852936745,
-0.007068012375384569,
-0.0595298707485199,
0.02175229787826538,
0.04849231243133545,
0.023487336933612823,
-0.0075220633298158646,
-0.030636370182037354,
-0.029347894713282585,
-0.01634274236857891,
0.017451085150241852,
0.013334674760699272,
0.033451732248067856,
-0.01368402224034071,
-0.08798882365226746,
-0.024499045684933662,
0.021418098360300064,
-0.020817430689930916,
-0.01260905247181654,
-0.06403665989637375,
-0.026611587032675743,
0.03198106214404106,
0.046677298843860626,
0.015251435339450836,
0.019111795350909233,
0.0027728737331926823,
0.030380938202142715,
-0.006528924684971571,
-0.008919076062738895,
-0.030738789588212967,
-0.04008548706769943,
-0.04401857405900955,
0.027230704203248024,
-0.04510745778679848,
-0.010385936126112938,
-0.0013485564850270748,
-0.001916798879392445,
0.013675691559910774,
0.06659307330846786,
-0.007009914144873619,
0.014437676407396793,
0.038027647882699966,
0.003010773565620184,
-0.05009206756949425,
0.040802180767059326,
-0.023890187963843346,
0.001738860155455768,
0.028611822053790092,
-0.004388079978525639,
0.0007304321625269949,
-0.005898977164179087,
0.02841746248304844,
0.05284930393099785,
-0.01421667542308569,
-0.04982699081301689,
-0.014630909077823162,
0.03144358843564987,
-0.0018342710100114346,
-0.039346884936094284,
-0.03584239259362221,
0.018149729818105698,
-0.004017457365989685,
-0.018617544323205948,
0.07931006699800491,
-0.0017954400973394513,
-0.0019463412463665009,
0.0019867487717419863,
-0.05386938527226448,
0.006867939606308937,
-0.04376887157559395,
0.05447247624397278,
-0.021459681913256645,
-0.009579755365848541,
0.028456319123506546,
0.023285020142793655,
0.056166645139455795,
-0.017283763736486435,
-0.021760376170277596,
-0.010176768526434898,
0.05941010266542435,
-0.0012512506218627095,
-0.02457873523235321,
0.03660428151488304,
0.0023028957657516003,
0.04297779127955437,
0.019145984202623367,
0.05119653418660164,
-0.024886781349778175,
-0.01072350237518549,
-0.003729987656697631,
-0.04900746047496796,
0.02723846770823002,
0.010549948550760746,
-0.013155417516827583,
-0.000880039413459599,
-0.024902431294322014,
-0.0053787799552083015,
-0.0008110654889605939,
-0.03301972895860672,
0.05287709832191467,
0.06875735521316528,
0.002792187500745058,
-0.02294905297458172,
0.043420299887657166,
-0.005572499707341194,
0.0424652136862278,
0.005418984219431877,
0.009981973096728325,
-0.045794472098350525,
-0.040648203343153,
0.05945100262761116,
0.04440236836671829,
-0.0914226770401001,
0.01256009005010128,
0.03879253566265106,
-0.00028895249124616385,
0.04402444511651993,
0.012669428251683712,
-0.03536180406808853,
-0.04529603570699692,
0.03789815679192543,
0.04485740140080452,
-0.03066878393292427,
-0.020221441984176636,
0.037971995770931244,
0.03684825450181961,
0.014066056348383427,
-0.01598411612212658,
-0.04534048214554787,
0.08089792728424072,
-0.010551358573138714,
-0.004146101884543896,
-0.001998629653826356,
-0.037910688668489456,
0.0775068998336792,
0.014058917760848999,
0.06343512237071991,
0.03905260190367699,
-0.02178526483476162,
-0.027807092294096947,
0.009731567464768887,
0.012613968923687935,
0.0322437509894371,
-0.0014396855840459466,
-0.03426895663142204,
-0.005343415774405003,
0.02215326763689518,
-0.026381582021713257,
0.02276257425546646,
-0.011328102089464664,
-0.005146730225533247,
-0.043682362884283066,
0.018139958381652832,
0.026751121506094933,
0.004697474185377359,
0.01840975508093834,
-0.0011740211630240083,
-0.05939914286136627,
0.01600773259997368,
0.01027039997279644,
-0.030003800988197327,
0.03925611451268196,
-0.07147268205881119,
0.028212927281856537,
-0.06527204811573029,
-0.022743012756109238,
0.011732056736946106,
-0.010739154182374477,
0.02681923657655716,
0.024913815781474113,
-0.023953592404723167,
-0.029014069586992264,
-0.01569380983710289,
0.010238570161163807,
0.010382981970906258,
-0.022537706419825554,
0.015490017831325531,
0.030128004029393196,
-0.006367034278810024,
0.009832835756242275,
0.0063569373451173306,
-0.06295996904373169,
-0.03481331467628479,
0.007243795786052942,
-0.004722886253148317,
0.055772606283426285,
-0.018600964918732643,
0.03173360973596573,
0.014433398842811584,
-0.044406820088624954,
0.058444730937480927,
-0.058070193976163864,
0.003977279644459486,
0.010132876224815845,
0.02022695541381836,
0.050284434109926224,
0.029872952029109,
-0.023873023688793182,
0.10662361979484558,
0.028480326756834984,
-0.058436062186956406,
-0.0019814472179859877,
-0.005498531274497509,
-0.016272949054837227,
-0.045457880944013596,
0.025543689727783203,
0.009504358284175396,
0.02173362486064434,
0.044590309262275696,
0.01996009051799774,
0.0010128869907930493,
0.03721393272280693,
0.0071115391328930855,
-0.031242871657013893,
0.014418641105294228,
0.009444082155823708,
0.007434342987835407,
0.04507540166378021,
-0.020240118727087975,
-0.011829559691250324,
0.007331551983952522,
0.015391029417514801,
0.043661221861839294,
0.00706010265275836,
-0.06664518266916275,
0.040094707161188126,
0.012461700476706028,
-0.018757816404104233,
-0.016659555956721306,
0.03560604527592659,
-0.0006570510449819267,
-0.02163451537489891,
-0.019588185474276543,
0.04118569195270538,
0.026652874425053596,
-0.0030201058834791183,
0.024313831701874733,
0.04864775016903877,
0.02773912250995636,
-0.004398040473461151,
-0.005861655343323946,
-0.02345246449112892,
-0.009459135122597218,
0.014573103748261929,
-0.0266557727009058,
-0.06256473809480667,
0.04294615238904953,
0.01244364120066166,
0.038342274725437164,
0.005786029621958733,
-0.0294384453445673,
0.014789598993957043,
-0.0544569231569767,
-0.003471184289082885,
-0.007164701819419861,
0.03418787941336632,
-0.015418088994920254,
0.054984625428915024,
0.004716785158962011,
0.025328287854790688,
0.029639316722750664,
-0.008046591654419899,
-0.04154541715979576,
0.036822978407144547,
-0.07899073511362076,
-0.04972953721880913,
0.007300355937331915,
0.02014181949198246,
0.043222252279520035,
-0.014178292825818062,
-0.004817106295377016,
0.015663867816329002,
-0.013473214581608772,
-0.08251270651817322,
0.0000992529749055393,
-0.044640377163887024,
-0.023356201127171516,
-0.026058334857225418,
-0.005554767791181803,
0.04590127617120743,
-0.0053658150136470795,
-0.008207238279283047,
0.0529896579682827,
-0.02416311390697956,
0.03039841167628765,
-0.031285665929317474,
-0.006744251120835543,
0.007448077667504549,
0.009120172820985317,
0.04108148440718651,
0.018322987481951714,
0.03541390597820282,
-0.01532574649900198,
-0.013539238832890987,
0.05879950523376465,
0.008568143472075462,
0.002034686738625169,
-0.012275097891688347,
-0.02794809080660343,
0.012558631598949432,
-0.0018113626865670085,
0.07119127362966537,
-0.03646141290664673,
0.020562831312417984,
0.020782383158802986,
0.006196135189384222,
-0.02389129251241684,
0.03495493158698082,
0.04357835277915001,
0.042781341820955276,
-0.029366178438067436,
-0.08666227012872696,
-0.008757209405303001,
-0.03683185577392578,
-0.025402767583727837,
-0.024537403136491776,
-0.029290683567523956,
-0.016673749312758446,
0.053305789828300476,
0.014401495456695557,
-0.004101924132555723,
0.025896485894918442,
0.025620928034186363,
-0.0015592329436913133,
0.03244877979159355,
-0.006978131365031004,
-0.008217014372348785,
0.020657261833548546,
0.047067467123270035,
0.03409747779369354,
-0.016871875151991844,
0.020426495000720024,
-0.059524234384298325,
0.011516325175762177,
0.013076662085950375,
0.008656209334731102,
0.02850988879799843,
-0.027722250670194626,
-0.029534732922911644,
-0.04289381951093674,
0.05353879556059837,
-0.009884019382297993,
0.052952397614717484,
0.023653890937566757,
0.012927045114338398,
-0.009343203157186508,
0.00040751314372755587,
-0.040002282708883286,
0.012523866258561611,
0.006627684459090233,
-0.030594993382692337,
-0.028068505227565765,
-0.010959379374980927,
-0.04146769642829895,
0.03415054455399513,
0.008966774679720402,
0.053145214915275574,
0.009210843592882156,
-0.01005922444164753,
-0.005882943514734507,
0.021805336698889732,
-0.020539598539471626,
-0.05749499052762985,
-0.03931266441941261,
0.04663289338350296,
-0.019618695601820946,
0.02379414811730385,
-0.030540362000465393,
-0.04607018083333969,
0.032346099615097046,
0.025505436584353447,
0.02011972665786743,
0.021440112963318825,
-0.047073058784008026,
0.02661888487637043,
0.0229666605591774,
0.005167585797607899,
0.031706031411886215,
0.04385348781943321,
-0.010153667069971561,
-0.03516440838575363,
-0.031269825994968414,
0.05469651520252228,
-0.013949464075267315,
-0.017838647589087486,
-0.019229209050536156,
0.02272861823439598,
0.016200756654143333,
0.015715859830379486,
-0.018414324149489403,
0.030421841889619827,
-0.04152778536081314,
-0.05524585396051407,
-0.021888231858611107,
0.06435061991214752,
0.034427542239427567,
-0.03742710500955582,
0.038806281983852386,
0.010161110199987888,
-0.0030221324414014816,
-0.012090139091014862,
0.009098638780415058,
-0.056859392672777176,
0.01733451895415783,
0.035147495567798615,
0.003390041645616293,
0.032045528292655945,
-0.051370322704315186,
-0.02552417851984501,
0.016867008060216904,
-0.04830333963036537,
0.02981838956475258,
-0.007896275259554386,
-0.011666069738566875,
0.008840617723762989,
-0.035764049738645554,
-0.03760597109794617,
0.015645386651158333,
0.0033717623446136713,
0.01720285601913929,
-0.019690509885549545,
0.04235783591866493,
0.015546226873993874,
0.01940159685909748,
-0.07188855111598969,
-0.04036308452486992,
-0.00712150614708662,
0.007725769188255072,
-0.000602761167101562,
-0.037689998745918274,
0.0010858633322641253,
-0.04085394740104675,
-0.023412523791193962,
0.022266890853643417,
-0.005341567099094391,
-0.01096006203442812,
0.00171002431306988,
0.013086441904306412,
0.01429547369480133,
0.041183385998010635,
-0.004975136835128069,
-0.012053290382027626,
0.007630450185388327,
-0.016895761713385582,
-0.024616438895463943,
0.024733275175094604,
0.059862371534109116,
-0.02539111115038395,
0.011237368918955326,
-0.014893927611410618,
-0.0027172034606337547,
0.05680768936872482,
-0.024702198803424835,
-0.003716419218108058,
0.03727034851908684,
0.0071190050803124905,
0.025811363011598587,
-0.01652599312365055,
-0.009231758303940296,
0.0008129914640448987,
0.021814314648509026,
0.017146047204732895,
-0.010338698513805866,
-0.013974144123494625,
-0.04687961935997009,
0.04625159502029419,
-0.010035413317382336,
0.020782938227057457,
0.0088398028165102,
0.042767398059368134,
-0.0072400737553834915,
0.021296938881278038,
-0.021019799634814262,
0.005713789723813534,
0.012289105914533138,
0.01816771924495697,
0.022130519151687622,
0.04322115704417229,
-0.017759690061211586,
-0.019912859424948692,
-0.06322069466114044,
-0.03749037906527519,
0.02454051375389099,
0.07904160767793655,
-0.008112017065286636,
0.02335573360323906,
0.03452038764953613,
-0.0065169865265488625,
-0.02746439352631569,
0.020502427592873573,
-0.0017319280887022614,
0.035915277898311615,
-0.00886557437479496,
0.04330829903483391,
-0.03866857662796974,
0.001284792902879417,
-0.003635792527347803,
0.03356510400772095,
-0.04469241946935654,
0.021265732124447823,
0.004997937474399805,
0.04762823507189751,
-0.003610537387430668,
0.039409950375556946,
-0.04587850347161293,
0.01458647195249796,
-0.022280676290392876,
0.06365188211202621,
-0.008519688621163368,
-0.027253098785877228,
0.04545114189386368,
0.056549377739429474,
0.004586647730320692,
-0.010922906920313835,
0.000530945893842727,
-0.00221383199095726,
0.058396633714437485,
0.03817063942551613,
0.005673391744494438,
-0.021625278517603874,
0.025908973067998886,
0.06444389373064041,
-0.0026320458855479956,
0.030465206131339073,
0.013672574423253536,
-0.04155482351779938,
-0.015703843906521797,
-0.059198182076215744,
-0.053753986954689026,
0.009738263674080372,
-0.0037454997655004263,
-0.007546624168753624,
0.02063209004700184,
-0.013825537636876106,
0.015323184430599213,
0.02523161843419075,
0.05498525872826576,
-0.03885062411427498,
0.07797997444868088,
-0.008515475317835808,
0.012188003398478031,
0.0117521146312356,
-0.011363744735717773,
0.11541074514389038,
0.07998937368392944,
0.0041160727851092815,
-0.07438846677541733,
-0.012529849074780941,
-0.01520585361868143,
0.00022841559257358313,
-0.03317028284072876,
0.012420587241649628,
-0.0075025190599262714,
0.003208341309800744,
-0.009470910765230656,
0.05315953120589256,
-0.01178132276982069,
0.014307101257145405,
0.05498581752181053,
-0.01644086092710495,
-0.04180171713232994,
0.02169310674071312,
0.032758209854364395,
-0.043726544827222824,
-0.008445093408226967,
-0.02630574069917202,
0.06544721871614456,
-0.041673168540000916,
-0.011032571084797382,
-0.03440375253558159,
-0.04272474721074104,
0.023164665326476097,
-0.014733255840837955,
-0.02824150212109089,
0.0005586419138126075,
0.021513797342777252,
0.006337266881018877,
-0.02465328946709633,
0.006454534363001585,
0.005875132046639919,
-0.008801308460533619,
0.06722694635391235,
0.00686798058450222,
-0.005372135434299707,
0.029877781867980957,
0.03863813728094101,
-0.016780313104391098,
-0.023342203348875046,
-0.03703122213482857,
0.004127172753214836,
0.05105968937277794,
-0.006775255780667067,
0.023105444386601448,
-0.04261600226163864,
0.016252955421805382,
0.0009975400753319263,
-0.038080185651779175,
-0.0011959484545513988,
-0.03811822831630707,
0.04662381485104561,
-0.03333733230829239,
0.0021614213474094868,
-0.03434816002845764,
0.008004710078239441,
0.011668405495584011,
0.00695324782282114,
-0.006713658571243286,
0.030448921024799347,
0.02128268964588642,
-0.011956984177231789,
0.04055597260594368,
0.0031638683285564184,
-0.030682789161801338,
-0.0322977639734745,
-0.05620522052049637,
-0.03165683150291443,
-0.014991138130426407,
-0.0025637063663452864,
0.01912344992160797,
0.0026194199454039335,
-0.002481317613273859,
-0.02153468132019043,
-0.037415120750665665,
-0.09152057766914368,
-0.00018392821948509663,
-0.007576753851026297,
-0.03337787091732025,
0.002377752447500825,
0.0021707783453166485,
0.02350320667028427,
0.04857904836535454,
-0.018244683742523193,
0.027584660798311234,
0.03437524288892746,
0.027521293610334396,
0.00716335279867053,
-0.01566268689930439,
-0.05784112960100174,
0.016884462907910347,
-0.022365588694810867,
0.010768968611955643,
-0.020067503675818443,
0.0028928702231496572,
0.02576497197151184,
0.023894544690847397,
-0.025261960923671722,
0.016056809574365616,
-0.04819232225418091,
0.0036734973546117544,
0.010783206671476364,
-0.04658592492341995,
0.024822380393743515,
0.017808236181735992,
-0.003788952948525548,
-0.023039555177092552,
-0.026133263483643532,
0.00688381539657712,
-0.022613631561398506,
0.002543678041547537,
0.023001132532954216,
-0.01564471796154976,
-0.012906141579151154,
-0.02729053422808647,
0.02163880318403244,
-0.06091151386499405,
0.013093956746160984,
-0.019256815314292908,
0.04733807593584061,
0.01965053379535675,
0.012871249578893185,
-0.06488943099975586,
0.02464793063700199,
0.021715490147471428,
0.0018379439134150743,
0.002616029465571046,
0.03131446614861488,
0.012326940894126892,
-0.03759220615029335,
0.008229458704590797,
-0.010184586979448795,
0.05876397341489792,
-0.005074250977486372,
-0.014811347238719463,
0.021137479692697525,
-0.02964300848543644,
-0.012299024499952793,
0.01875247247517109,
0.0041804504580795765,
0.033864036202430725,
0.026677371934056282,
-0.02904040738940239,
-0.002820246620103717,
0.019135983660817146,
-0.04077939689159393,
-0.014369812794029713,
0.00631246343255043,
-0.035868264734745026,
-0.059807851910591125,
-0.024192677810788155,
0.013723580166697502,
-0.024142351001501083,
0.0017950215842574835,
0.007608403917402029,
0.02337079681456089,
-0.027048183605074883,
-0.0051640658639371395,
0.01578289084136486,
0.032196905463933945,
0.008661380037665367,
0.0297867264598608,
0.02222239039838314,
0.023731734603643417,
0.06859683245420456,
0.013771151192486286,
0.006909629795700312,
0.0060953665524721146,
0.023878449574112892,
-0.07934480160474777,
0.023988518863916397,
-0.0027599050663411617,
-0.0023768406827002764,
0.08578170090913773,
-0.04605896398425102,
0.005119658540934324,
0.04601401090621948,
-0.025797950103878975,
-0.011104132048785686,
-0.03548477962613106,
0.020166434347629547,
-0.02819223143160343,
0.002798778237774968,
0.008689033798873425,
0.018241897225379944,
0.039993371814489365,
0.005401591770350933,
0.02285386249423027,
0.009139101020991802,
-0.0007254832307808101,
-0.000093916904006619,
-0.0004543852701317519,
0.037105992436409,
0.023491153493523598,
-0.020703453570604324,
0.0450286939740181,
-0.028098629787564278,
-0.04458203166723251,
-0.010655000805854797,
0.02069094032049179,
-0.02835751697421074,
-0.037980690598487854,
0.03096591867506504,
0.007299242075532675,
0.0028360579162836075,
0.029903914779424667,
0.00953461043536663,
-0.01186372246593237,
-0.004444597288966179,
0.010808730497956276,
0.0005441242828965187,
-0.03779240697622299,
-0.015490537509322166,
0.007968458347022533,
-0.05714523419737816,
-0.066640205681324,
0.021547412499785423,
-0.01649310812354088,
-0.02094818651676178,
-0.011469632387161255,
-0.0257799681276083,
-0.0031009558588266373,
-0.0506887286901474,
0.004569374490529299,
-0.04692015051841736,
-0.0000625382672296837,
0.04966619983315468,
-0.02141823247075081,
0.010425964370369911,
0.018886132165789604,
-0.005885636899620295,
-0.04710783064365387,
0.030431540682911873,
0.021674156188964844,
-0.0172126367688179,
-0.08188964426517487,
-0.017287179827690125,
-0.00017168899648822844,
-0.036223337054252625,
-0.023474261164665222,
-0.018369460478425026,
-0.02633694000542164,
0.041349008679389954,
0.016307607293128967,
-0.009716277942061424,
-0.013917009346187115,
-0.03543310612440109,
0.0048509989865124226,
-0.019253863021731377,
-0.0067752813920378685,
0.030375385656952858,
-0.041530340909957886,
-0.015736104920506477,
0.016249412670731544,
0.004255023784935474,
0.028864605352282524,
-0.000846215698402375,
0.001378903049044311,
0.0264494139701128,
0.01595986634492874,
-0.005416072905063629,
0.046062156558036804,
-0.02491585724055767,
0.001710559707134962,
-0.04175190627574921,
-0.062332816421985626,
0.0073208995163440704,
-0.02968188188970089,
0.016966216266155243,
0.03383496403694153,
0.024108000099658966,
-0.021847359836101532,
-0.021497296169400215,
-0.006228829734027386,
-0.016176672652363777,
0.0521174892783165,
-0.015372212044894695,
-0.004852988291531801,
0.06774233281612396,
-0.018196163699030876,
0.020903270691633224,
0.05448174476623535,
-0.058338139206171036,
-0.009718727320432663,
0.036517031490802765,
-0.058252252638339996,
-0.01700986735522747,
-0.021241888403892517,
-0.02596118673682213,
0.03765803948044777,
-0.0459647960960865,
0.00022641883697360754,
0.05727222189307213,
-0.02432386204600334,
-0.005265495739877224,
0.03252197802066803,
0.004584081005305052,
0.016722578555345535,
-0.004499932751059532,
0.017220553010702133,
0.0546732172369957,
-0.02314991131424904,
0.03175266087055206,
0.06593934446573257,
0.020351536571979523,
-0.0006398268160410225,
-0.03634168952703476,
-0.002448722720146179,
-0.046808093786239624,
0.039569295942783356,
-0.01598641462624073,
0.0012000618735328317,
-0.05013369023799896,
-0.019582504406571388,
0.00643538823351264,
-0.014869877137243748,
0.028226181864738464,
0.010381358675658703,
-0.025617698207497597,
0.03667972609400749,
-0.05714105814695358,
-0.013026759959757328,
-0.0272990595549345,
-0.020518600940704346,
-0.03274034336209297,
0.005484908819198608,
0.015779852867126465,
0.02634655497968197,
-0.024003753438591957,
0.02055715210735798,
-0.04456502944231033,
-0.011135457083582878,
0.02389027178287506,
-0.047858547419309616,
0.00008298351895064116,
0.008437243290245533,
0.0039026199374347925,
0.0254825372248888,
-0.019749201834201813,
-0.02449239231646061,
-0.04763467237353325,
0.008525535464286804,
0.04318959265947342,
0.040220070630311966,
-0.026444213464856148,
-0.015074286609888077,
-0.012114498764276505,
0.038322076201438904,
-0.06245595961809158,
-0.0011530722258612514,
-0.03478407487273216,
0.01939130574464798,
-0.015695078298449516,
0.03673270344734192
] |
<p>Let's have <a href="http://en.wikipedia.org/wiki/Wick%27s_theorem" rel="nofollow">Wick's theorem</a> in following form:
for fields
$$
A_{i}(x) ~=~ A_{i}^{+}(x) + A_{i}^{-}(x),
$$
where first summand contains creation operator and the second contains destruction one, is a fair to say
$$ \tag{1}
T(A_{1}...A_{n}) ~=~ \sum_{k}(-1)^{\sigma}\overline{A_{i_{1}}A_{i_{2}}}~\overline{A_{i_{3}}A_{i_{4}}}\ldots \overline{A_{i_{2k - 1}}A_{i_{2k}}}: A_{i_{2k+1}}...A_{i_{n}}:,
$$
where contractions are denoted with an overline
$$
\overline{A_{i_{1}}(x)A_{i_{2}}(y)} ~=~ \langle | T(A_{i_{1}}(x)A_{i_{2}}(y))|\rangle ~=~ -iD^{c}(x - y),
$$</p>
<p>and normal order is</p>
<p>$$
: A_{i_{k}}(x)A_{i_{k + 1}}(y): ~=~ A^{+}_{i_{k}}(x)A^{+}_{i_{k + 1}}(y) + A^{+}_{i_{k}}(x)A^{-}_{i_{k + 1}}(y) + A^{-}_{i_{k}}(x)A^{-}_{i_{k + 1}}(y) + A^{+}_{i_{k + 1}}(x)A^{-}_{i_{k}}(y).
$$</p>
<p>In the beginning of proof of this theorem one says that permutation of fields in the left and right side of $(1)$ doesn't change it. Why this statement is correct?</p>
| 8,309 |
[
-0.016402117908000946,
-0.027067823335528374,
0.045103784650564194,
-0.039172615855932236,
0.005984026473015547,
-0.024372462183237076,
-0.03747718408703804,
-0.02454700693488121,
-0.017264939844608307,
-0.04151718318462372,
0.05388061702251434,
-0.020074786618351936,
0.05360871180891991,
0.04641524702310562,
0.0010817521251738071,
-0.012538574635982513,
-0.027368595823645592,
0.011142333969473839,
-0.02338329143822193,
-0.0006080128368921578,
0.010402260348200798,
0.034892503172159195,
-0.040016282349824905,
0.0120648592710495,
-0.03004414774477482,
0.0261504165828228,
0.006831117440015078,
-0.027757255360484123,
-0.016991358250379562,
0.08226921409368515,
-0.05571234971284866,
-0.027168458327651024,
-0.022348856553435326,
-0.0032672330271452665,
0.043762803077697754,
0.026047827675938606,
0.018241148442029953,
-0.01200290210545063,
0.05050089210271835,
-0.004331125877797604,
-0.016689743846654892,
-0.0238483939319849,
-0.037924788892269135,
0.020071854814887047,
-0.02754313126206398,
0.0028495111037045717,
0.0015164436772465706,
-0.01776443049311638,
0.05872321128845215,
-0.01084886398166418,
0.055831845849752426,
-0.01403606403619051,
-0.02090880461037159,
0.006793519482016563,
-0.02057955414056778,
-0.024578478187322617,
0.015750234946608543,
0.021735962480306625,
0.008022463880479336,
-0.05699366331100464,
-0.025451023131608963,
-0.046395398676395416,
0.02671201340854168,
0.00492853531613946,
-0.0065715922974050045,
-0.012873843312263489,
0.022369354963302612,
-0.0007624812424182892,
0.03263193368911743,
-0.04236414283514023,
0.016054872423410416,
-0.016376113519072533,
0.006090697832405567,
-0.031110385432839394,
-0.00367986923083663,
-0.004883568733930588,
0.01911461539566517,
-0.005503566935658455,
0.0379561185836792,
0.045246671885252,
0.03712642565369606,
0.032307907938957214,
-0.020964255556464195,
0.0002457548107486218,
0.03304971009492874,
-0.00582208763808012,
0.08059801906347275,
-0.030039720237255096,
0.027283720672130585,
0.011948931030929089,
0.021844344213604927,
-0.07010998576879501,
0.05669691413640976,
-0.01601051539182663,
-0.027539480477571487,
0.033339083194732666,
-0.0021914129611104727,
-0.0007174811325967312,
-0.0030127372592687607,
-0.004730083514004946,
-0.039485905319452286,
-0.0583546943962574,
0.003916225861757994,
0.07516045868396759,
0.02689782902598381,
0.001016647438518703,
-0.02517540752887726,
0.0006365865701809525,
-0.03203093633055687,
-0.0359649620950222,
-0.04282260313630104,
0.005103818606585264,
-0.04198693484067917,
0.007342763710767031,
-0.03588711470365524,
0.0014056348009034991,
0.018911734223365784,
-0.01763094589114189,
0.037530168890953064,
0.0785679966211319,
0.08296015113592148,
0.00028499250765889883,
0.03313267603516579,
-0.05186571553349495,
-0.04810714349150658,
0.028799477964639664,
0.04755641147494316,
-0.009410208091139793,
-0.04592881351709366,
0.006428412161767483,
0.06247333809733391,
0.019547414034605026,
0.027341686189174652,
0.00996167678385973,
0.023962877690792084,
0.004691320937126875,
-0.07961438596248627,
-0.07781332731246948,
0.029581347480416298,
-0.0164186991751194,
0.02555125392973423,
-0.07405877858400345,
-0.008489920757710934,
0.026085302233695984,
0.0730869472026825,
0.01979919709265232,
0.03617820888757706,
-0.005950910039246082,
0.009066427126526833,
0.036673545837402344,
0.006028345320373774,
-0.05449594929814339,
0.030015818774700165,
-0.04597797989845276,
-0.05977382883429527,
-0.052699409425258636,
0.023645054548978806,
0.03039827197790146,
-0.03471463546156883,
-0.02731354348361492,
0.045081522315740585,
-0.011925685219466686,
-0.025207947939634323,
0.029650557786226273,
0.02129707857966423,
-0.03961189463734627,
0.02987240068614483,
0.05758701637387276,
0.017751000821590424,
0.02037089504301548,
-0.031547777354717255,
0.04100615158677101,
-0.01634800247848034,
0.04528558999300003,
0.03621535003185272,
-0.035286612808704376,
0.03339727595448494,
-0.06335975229740143,
0.010415736585855484,
0.053206998854875565,
-0.038049183785915375,
-0.028247997164726257,
-0.06370268762111664,
0.015380481258034706,
0.013604081235826015,
-0.017334578558802605,
0.0067549291998147964,
0.04980851709842682,
0.04155248403549194,
-0.06997736543416977,
-0.007895463146269321,
-0.04318878427147865,
0.013248161412775517,
0.05495581403374672,
-0.012296617962419987,
0.018523752689361572,
-0.012246686965227127,
0.01404944621026516,
0.024226415902376175,
-0.0071136304177343845,
0.017341164872050285,
0.007512248121201992,
0.029653502628207207,
-0.027877384796738625,
0.011817306280136108,
-0.0021448007319122553,
0.035560719668865204,
-0.018221022561192513,
0.04590345919132233,
-0.026761312037706375,
-0.02746056765317917,
0.01082556415349245,
0.0024240182247012854,
0.0267897117882967,
0.03683461993932724,
-0.003984995651990175,
0.022371115162968636,
0.02462823875248432,
-0.01597723923623562,
0.015398314222693443,
-0.055766522884368896,
0.032948534935712814,
0.07376401126384735,
0.013845647685229778,
-0.025390274822711945,
0.04354485869407654,
-0.0066370549611747265,
-0.006739449687302113,
-0.011114905588328838,
-0.05377127602696419,
-0.028212808072566986,
-0.031181951984763145,
0.03036588802933693,
0.07705798000097275,
-0.02964125946164131,
0.0069189551286399364,
0.004805439151823521,
0.023586349561810493,
-0.010396120138466358,
0.03787832334637642,
-0.014461581595242023,
-0.012000742368400097,
0.005654264707118273,
-0.0036863924469798803,
0.04076364263892174,
0.002783739473670721,
-0.007203106768429279,
-0.00813441351056099,
0.0008374897297471762,
0.018833015114068985,
-0.017416322603821754,
0.012479959055781364,
-0.03662942722439766,
0.01256980188190937,
0.011150538921356201,
0.014401082880795002,
0.00646059587597847,
-0.008222954347729683,
0.0354263111948967,
0.0252249576151371,
-0.013491768389940262,
-0.013118930160999298,
-0.01651451177895069,
0.005625054705888033,
0.02422390878200531,
-0.034184206277132034,
-0.009391693398356438,
-0.03571704402565956,
0.0371658019721508,
-0.00136190268676728,
0.01742733083665371,
-0.0075599499978125095,
-0.0528833381831646,
-0.0477323941886425,
-0.025213945657014847,
0.004909870680421591,
0.03152058273553848,
0.04243031516671181,
-0.05015408620238304,
0.01366683840751648,
0.0017672569956630468,
0.005803469568490982,
0.048738960176706314,
0.011009530164301395,
-0.04554756358265877,
-0.02021244540810585,
-0.007965276017785072,
-0.005707011092454195,
0.05396827310323715,
-0.046842917799949646,
-0.026507165282964706,
0.00810540746897459,
0.02959192730486393,
-0.054805874824523926,
-0.01214069314301014,
-0.03410358354449272,
-0.015525640919804573,
-0.04356560483574867,
-0.005780444946140051,
0.029755426570773125,
-0.002279799897223711,
-0.08485456556081772,
0.012403802946209908,
0.009010769426822662,
-0.03869739919900894,
-0.0022573722526431084,
-0.029208490625023842,
0.008469539694488049,
-0.0002874604251701385,
0.03146781027317047,
-0.023170527070760727,
-0.024130763486027718,
-0.010534819215536118,
-0.05894611030817032,
-0.048633936792612076,
0.007541486527770758,
-0.010037930682301521,
0.04255025461316109,
-0.009595154784619808,
-0.04263361543416977,
0.09087438881397247,
0.06931886821985245,
-0.022778406739234924,
-0.05096248537302017,
0.01884349063038826,
-0.0008316922467201948,
-0.01451331377029419,
-0.015118395909667015,
0.012484208680689335,
0.005850968882441521,
0.07920719683170319,
0.049235738813877106,
0.03896718844771385,
0.05742572993040085,
-0.0005471893236972392,
-0.014205832965672016,
0.05569818243384361,
0.004284542053937912,
-0.005314371548593044,
0.029230616986751556,
-0.008312004618346691,
-0.027722103521227837,
0.014190861023962498,
-0.03426287695765495,
0.006158226169645786,
0.024254338815808296,
-0.045568548142910004,
0.03297486528754234,
-0.028562532737851143,
-0.0034515871666371822,
0.00999864935874939,
0.029605597257614136,
-0.026638224720954895,
-0.048050105571746826,
-0.029718616977334023,
0.04306839406490326,
-0.018929647281765938,
-0.03097756765782833,
0.0228195171803236,
0.012420358136296272,
0.03745870292186737,
-0.028375068679451942,
0.009316523559391499,
-0.02095883898437023,
-0.04554726183414459,
0.026494530960917473,
-0.061482664197683334,
-0.056417565792798996,
-0.008994260802865028,
0.016246788203716278,
-0.05445760861039162,
0.0028472919948399067,
-0.006066267378628254,
-0.028631828725337982,
-0.014188378117978573,
-0.016151782125234604,
-0.02897125855088234,
0.03415066748857498,
0.03146802634000778,
0.020320096984505653,
0.018147053197026253,
0.011457517743110657,
0.0007857506279833615,
-0.006293320097029209,
-0.05413558706641197,
-0.020865730941295624,
0.007872483693063259,
0.003425869857892394,
0.029547853395342827,
0.005106084980070591,
0.03296880051493645,
0.010757491923868656,
-0.019260406494140625,
-0.034321051090955734,
-0.010920747183263302,
-0.05754905566573143,
0.010183751583099365,
-0.032050032168626785,
-0.07629053294658661,
-0.003836794989183545,
0.02093420922756195,
0.0762716606259346,
-0.04204139485955238,
0.01929040066897869,
-0.008192762732505798,
-0.022414442151784897,
0.0006925354246050119,
-0.04372815042734146,
0.016242699697613716,
0.05418398603796959,
-0.009586891159415245,
0.03396882489323616,
0.030372895300388336,
-0.01605376787483692,
-0.004333799704909325,
-0.0034916677977889776,
0.04582203924655914,
0.0058443075977265835,
-0.02862112782895565,
-0.0002340764767723158,
-0.053841616958379745,
-0.028771288692951202,
0.029661374166607857,
0.06336753815412521,
0.03617335483431816,
0.014502758160233498,
0.04932580515742302,
0.016472913324832916,
-0.00012585287913680077,
-0.004761967808008194,
0.01913299597799778,
0.003107947064563632,
0.009172029793262482,
-0.025078056380152702,
0.004789682570844889,
0.04448598623275757,
0.012466097250580788,
-0.016645636409521103,
-0.007204052992165089,
-0.007099140901118517,
0.022316740825772285,
0.014747700653970242,
0.02137911505997181,
-0.006062865722924471,
0.04878402501344681,
-0.03842549026012421,
-0.008833195082843304,
0.006044476758688688,
-0.008931664749979973,
0.016744399443268776,
0.0032043512910604477,
0.043719153851270676,
0.043939437717199326,
0.017822647467255592,
-0.045900627970695496,
-0.01150199119001627,
0.049704570323228836,
0.052893102169036865,
0.041457127779722214,
0.03603183478116989,
-0.007671835366636515,
-0.02791942097246647,
0.013483569025993347,
0.02050098218023777,
0.014331669546663761,
-0.013439233414828777,
-0.003483003005385399,
-0.00267326133325696,
-0.034780923277139664,
-0.044106077402830124,
0.046952467411756516,
0.02028740383684635,
-0.010124091058969498,
-0.002175391186028719,
0.024010704830288887,
-0.018829572945833206,
-0.02292165718972683,
0.006434015464037657,
-0.007446888834238052,
-0.009191029705107212,
-0.03333864361047745,
0.0018276567570865154,
0.030883044004440308,
0.0001609309547347948,
-0.031033340841531754,
0.028839249163866043,
0.01800294779241085,
-0.021173276007175446,
0.04037674143910408,
-0.010419322177767754,
-0.016944216564297676,
0.014794704504311085,
0.02289983630180359,
-0.01418951153755188,
0.06327646225690842,
-0.039828017354011536,
0.04663410037755966,
0.05226409435272217,
-0.013696721754968166,
0.027538960799574852,
0.0396885871887207,
-0.025660471990704536,
0.010757851414382458,
-0.004162701312452555,
0.01661994308233261,
-0.011308208107948303,
0.041859161108732224,
-0.01665290631353855,
0.012521002441644669,
-0.01610291749238968,
0.02133355103433132,
-0.01283975224941969,
0.007207327056676149,
-0.042166613042354584,
0.003689490957185626,
0.013963785953819752,
0.021086204797029495,
-0.0183330699801445,
0.007322016172111034,
-0.00363969337195158,
0.03137873485684395,
0.025569504126906395,
-0.007717707194387913,
0.011628678999841213,
-0.02369030751287937,
0.03035898320376873,
0.016771037131547928,
-0.026256190612912178,
0.04514289274811745,
-0.05760923773050308,
-0.024492820724844933,
-0.011834916658699512,
-0.027563709765672684,
0.009503033943474293,
0.017376355826854706,
-0.003900574753060937,
-0.005600465927273035,
0.012847121804952621,
-0.014282639138400555,
0.019855476915836334,
-0.02345386892557144,
-0.01218547485768795,
-0.009645768441259861,
-0.0043884809128940105,
0.024269534274935722,
-0.006455708760768175,
-0.08179870992898941,
-0.01760958507657051,
-0.012697597034275532,
-0.05404156073927879,
-0.05626941844820976,
-0.003431274089962244,
0.01789036951959133,
-0.011509658768773079,
-0.0342005118727684,
-0.012689109891653061,
0.010043272748589516,
-0.0202243123203516,
0.008066647686064243,
0.02942739613354206,
0.0008603449095971882,
0.009357038885354996,
0.018768683075904846,
0.030885856598615646,
0.0029259249567985535,
-0.001217699726112187,
-0.00374342012219131,
0.019947540014982224,
0.013506494462490082,
-0.034307029098272324,
-0.014999117702245712,
-0.007667554076761007,
-0.02794078178703785,
0.010728312656283379,
-0.029124487191438675,
-0.04811739921569824,
0.002324291504919529,
0.02711084857583046,
0.019134430214762688,
-0.005725945811718702,
0.004469507839530706,
0.004307449795305729,
0.006690144073218107,
-0.008585808798670769,
-0.021169252693653107,
-0.02525172010064125,
-0.02443094551563263,
-0.031776152551174164,
0.0015660444041714072,
-0.023403968662023544,
0.011630579829216003,
0.037826113402843475,
-0.01393432542681694,
0.004651625175029039,
0.032514676451683044,
-0.01211843267083168,
0.03760875388979912,
-0.021804338321089745,
0.008770191110670567,
-0.007252317853271961,
-0.004666366148740053,
-0.02447848953306675,
-0.010532598942518234,
-0.05494794622063637,
0.029954690486192703,
0.045789748430252075,
0.018145283684134483,
0.023440979421138763,
0.04489179328083992,
-0.021084770560264587,
0.006437624804675579,
0.01952333375811577,
-0.006844277959316969,
0.013777990825474262,
-0.00012719383812509477,
0.034161277115345,
-0.08090212941169739,
-0.008567115291953087,
0.01185233797878027,
0.032414812594652176,
-0.05471805855631828,
-0.007757824379950762,
-0.012424638494849205,
-0.024704404175281525,
0.02821752429008484,
-0.053141992539167404,
-0.04948752745985985,
0.048463303595781326,
-0.010673466138541698,
0.057325948029756546,
0.016954097896814346,
-0.0016779671423137188,
-0.00022373416868504137,
-0.003269494976848364,
0.023620013147592545,
-0.030584318563342094,
-0.05400810390710831,
-0.07903934270143509,
0.025549830868840218,
-0.020216353237628937,
0.01918654888868332,
-0.00618057232350111,
0.02312341332435608,
0.0030415416695177555,
-0.006716544274240732,
0.04108571261167526,
-0.020186226814985275,
-0.01849241554737091,
-0.02754242718219757,
-0.03368700295686722,
-0.05556759238243103,
0.03146195411682129,
-0.012905405834317207,
-0.05709453299641609,
0.009897775016725063,
-0.04896891117095947,
0.0027366681024432182,
0.03444010764360428,
0.027989154681563377,
0.002182439900934696,
0.03744424507021904,
0.0008184323087334633,
0.02775806374847889,
-0.014942956157028675,
0.0075773876160383224,
0.15993206202983856,
0.05000286176800728,
0.025395486503839493,
-0.07932969182729721,
-0.023740829899907112,
0.030492255464196205,
-0.03602837026119232,
-0.014522949233651161,
-0.0377928651869297,
-0.01891179196536541,
-0.042243946343660355,
-0.0075761862099170685,
0.044223394244909286,
0.0032020702492445707,
-0.02457987703382969,
0.01205945760011673,
-0.04055820405483246,
-0.027993647381663322,
0.006515863351523876,
-0.012453336268663406,
-0.016546955332159996,
0.014472593553364277,
-0.030988138169050217,
0.0015633600996807218,
-0.013556142337620258,
0.018119681626558304,
-0.03150344267487526,
-0.024340739473700523,
0.011259862221777439,
0.007577753625810146,
-0.004370523616671562,
0.018852556124329567,
-0.0037537054158747196,
0.010003787465393543,
0.013053938746452332,
-0.01946442574262619,
0.013441828079521656,
-0.03845017030835152,
0.019618337973952293,
0.05275799334049225,
0.03422127664089203,
-0.02984510362148285,
0.027627581730484962,
0.02217525616288185,
-0.012538793496787548,
-0.02997133508324623,
-0.011547790840268135,
0.012098892591893673,
0.016402654349803925,
0.015893466770648956,
-0.003075977321714163,
-0.03842642158269882,
0.026228975504636765,
0.011625069193542004,
-0.0024954781401902437,
-0.00228337780572474,
0.020389258861541748,
-0.03763362020254135,
0.009868985041975975,
-0.013636408373713493,
-0.017229631543159485,
-0.0384928435087204,
-0.01605997048318386,
0.002352694282308221,
-0.0007475704187527299,
-0.028228595852851868,
-0.004268713295459747,
0.0679633840918541,
0.03050616942346096,
0.0023751193657517433,
-0.0797630324959755,
0.01166544109582901,
-0.009690746665000916,
-0.02723025716841221,
-0.02231665328145027,
-0.012657664716243744,
0.08804657310247421,
0.04235677793622017,
-0.01881573721766472,
-0.017432546243071556,
-0.032180942595005035,
0.00017113535432145,
-0.02282189205288887,
-0.011163037270307541,
-0.03661862388253212,
-0.02716631069779396,
0.024028899148106575,
0.006236500106751919,
0.030803658068180084,
-0.007460970897227526,
0.03214900940656662,
0.06969830393791199,
0.04174099862575531,
0.0015591068658977747,
-0.014787683263421059,
-0.018052805215120316,
-0.011920653283596039,
-0.027870910242199898,
-0.0025375550612807274,
-0.013541758060455322,
0.03379635140299797,
0.011355845257639885,
0.04326474294066429,
0.04021801799535751,
-0.029547836631536484,
-0.014217674732208252,
0.04051770642399788,
-0.010508372448384762,
0.007124889176338911,
0.0487775094807148,
0.007263804320245981,
-0.04406922310590744,
0.005980826914310455,
-0.021318931132555008,
0.010597690008580685,
0.009349669329822063,
0.0330357626080513,
-0.037948526442050934,
-0.004134710878133774,
0.03620655834674835,
0.03663869574666023,
-0.027594048529863358,
0.000487310258904472,
-0.0017466042190790176,
0.017282966524362564,
0.0006125824875198305,
0.042926158756017685,
-0.0058903442695736885,
0.006465896964073181,
0.040949732065200806,
-0.020951325073838234,
0.04431905224919319,
0.0023042538668960333,
-0.013332822360098362,
-0.009799537248909473,
-0.02380160428583622,
0.028876440599560738,
0.05326186493039131,
0.008080968633294106,
-0.016739707440137863,
-0.011940698139369488,
-0.03586459532380104,
0.01678747870028019,
0.02677084505558014,
0.007160594221204519,
0.010134410113096237,
0.051489077508449554,
0.016133299097418785,
-0.030238894745707512,
0.056659262627363205,
-0.02314596436917782,
-0.025101253762841225,
0.002082657301798463,
-0.025289062410593033,
0.028940953314304352,
0.000959653640165925,
0.05765022337436676,
0.014073419384658337,
-0.01592271961271763,
-0.023302126675844193,
0.06191857159137726,
-0.008424006402492523,
-0.0066696349531412125,
0.0269303135573864,
-0.01313132606446743,
0.004985203966498375,
-0.04060961306095123,
-0.0436423122882843,
0.06217760592699051,
0.037062011659145355,
-0.01985054463148117,
0.03660667687654495,
0.0009183816728182137,
-0.00735423294827342,
-0.08251740038394928,
-0.03634708374738693,
0.007004252634942532,
0.05203365534543991,
0.057675786316394806,
-0.02386045642197132,
0.0013139217626303434,
-0.03351601958274841,
-0.0817270502448082,
0.012558816000819206,
-0.05699870362877846,
-0.007025343365967274,
-0.04819108545780182,
-0.0029222890734672546,
-0.07413213700056076,
0.05997836962342262,
0.022472543641924858,
0.04552401974797249,
0.006670447066426277,
0.06813458353281021,
-0.04909023270010948,
-0.010243038646876812,
-0.050314415246248245,
-0.013576983474195004,
0.042687512934207916,
-0.048449598252773285,
0.05084386095404625,
0.019356001168489456,
0.0036222278140485287,
0.02284417487680912,
0.008501731790602207,
-0.024914229288697243,
-0.017195595428347588,
0.06427204608917236,
0.03409742936491966,
0.039990562945604324,
0.01496568787842989,
0.010274247266352177,
0.028104281052947044,
-0.013265086337924004,
0.005700734909623861,
0.019697705283761024,
-0.005372319836169481,
0.006132930982857943,
0.039009083062410355,
-0.027133643627166748,
-0.020032798871397972,
0.04413418471813202,
-0.0013960360083729029,
-0.015655865892767906,
-0.020167751237750053,
-0.007829204201698303,
-0.003320678137242794,
0.050448156893253326,
0.005865264218300581,
0.009337757714092731,
0.012935505248606205,
0.022280244156718254,
0.049596596509218216,
-0.02695840783417225,
0.03097396157681942,
-0.02849603444337845,
-0.04118289798498154,
0.010053973644971848,
-0.0035637831315398216,
0.024472851306200027,
-0.03734119236469269,
0.015602631494402885,
-0.009589362889528275,
0.04170391336083412,
0.013229100964963436,
0.016013329848647118,
-0.023865317925810814,
-0.005710097961127758,
0.009820198640227318,
0.024160128086805344,
-0.04385612532496452,
-0.039894428104162216,
0.04065576195716858,
-0.03737631067633629,
0.03746533766388893,
0.012243350967764854,
0.026375822722911835,
-0.02885320410132408,
-0.026750586926937103,
0.012465563602745533,
0.006688418332487345,
0.039397116750478745,
-0.024257773533463478,
-0.031201591715216637,
0.015824757516384125,
0.026851145550608635,
0.009262822568416595,
-0.01256299577653408,
0.013530926778912544,
-0.018439168110489845,
0.035469621419906616,
0.04579409956932068,
-0.011267184279859066,
-0.018907247111201286,
0.025687869638204575,
0.02314653992652893,
-0.030087973922491074,
-0.020940331742167473,
0.0013171978062018752,
-0.042187731713056564,
-0.0030755687039345503,
-0.0007430305704474449,
-0.008272976614534855,
0.09256615489721298,
0.008840711787343025,
0.008672554977238178,
0.0417296402156353,
-0.037270523607730865,
-0.023777339607477188,
0.017257383093237877,
-0.02874651737511158,
0.005023182835429907,
-0.02759339101612568,
-0.035356681793928146,
0.02511415258049965,
-0.011108714155852795,
-0.015105883590877056,
0.023165613412857056,
0.003806358203291893,
-0.04715786874294281,
0.05464126169681549,
0.01376305427402258,
0.05859041586518288,
0.024470236152410507,
0.0077060312032699585,
-0.005629333201795816,
0.000263341935351491,
0.01740439236164093,
0.01475577987730503,
-0.018843989819288254,
-0.020026013255119324,
-0.011727356351912022,
-0.03598382696509361,
-0.02111496776342392,
0.027972830459475517,
-0.008486252278089523,
0.0178240779787302,
-0.0450826920568943,
0.01540048886090517,
0.054095521569252014,
-0.025113262236118317,
0.04247660934925079,
0.015447164885699749,
-0.02628554217517376,
0.11201673746109009,
-0.002689520362764597,
0.03870203718543053,
-0.026447320356965065,
-0.002858951687812805,
-0.05989324301481247,
-0.014154085889458656,
-0.006287621799856424,
0.03336409479379654,
-0.05103417858481407,
0.001728085451759398,
-0.022245435044169426,
0.015526305884122849,
-0.0027237841859459877,
-0.0718650296330452,
-0.03773927688598633,
0.02488892525434494,
-0.016203001141548157,
0.035912781953811646,
-0.030720865353941917,
-0.04794211685657501,
-0.025332113727927208,
0.015444345772266388,
0.03490053862333298,
0.02923911064863205,
-0.0012572517152875662,
-0.006615791469812393,
-0.028134772554039955,
0.015688961371779442,
0.003254347713664174,
0.00953703187406063,
-0.009833777323365211,
0.007196040824055672,
-0.004721271805465221,
-0.033253345638513565
] |
<p>In non-relativistic QM, the position of a particle is an observable. In QFT, fields are the observables. However, particles must have some sort of position, otherwise we wouldn't see pictures like the ones below. What is the (linear, Hermitian) operator that describes what we are observing?</p>
<p>I've tried considering making a "local" version of $N = \int dk\, a^+ a^- = \int dx \, \phi^+(x) \phi^-(x)$</p>
<p>by replacing this with $N_R =\int dx \, f(x) \phi^+ \phi^-$ where $f$ is some function that is concentrated in the localized region $R$. However, this is not Hermitian!</p>
<p><img src="http://i.stack.imgur.com/b3YlF.jpg" alt="enter image description here"></p>
| 8,310 |
[
-0.004048839211463928,
0.01194027904421091,
0.004223555326461792,
-0.01612108387053013,
0.03244619444012642,
-0.0037312349304556847,
-0.04668794572353363,
-0.07316923886537552,
-0.003995280247181654,
-0.0642622858285904,
0.0159270279109478,
0.008206554688513279,
0.05243900790810585,
0.012414608150720596,
-0.018694709986448288,
0.014467653818428516,
-0.04304414615035057,
-0.0301261804997921,
-0.035956017673015594,
-0.044302403926849365,
-0.03081722930073738,
0.06328541785478592,
0.0028358306735754013,
0.01820819079875946,
-0.004589678719639778,
0.023175952956080437,
0.017017241567373276,
0.016899507492780685,
0.029609421268105507,
0.05915705859661102,
-0.014599458314478397,
-0.04375191032886505,
-0.0042797583155334,
0.01603117771446705,
0.027659008279442787,
-0.0027311681769788265,
-0.03516477346420288,
-0.032783143222332,
0.02051914483308792,
0.00024210780975408852,
-0.03331705182790756,
-0.02957463264465332,
0.009840773418545723,
0.04494086652994156,
-0.019842632114887238,
-0.0016254165675491095,
0.03013751283288002,
-0.016296356916427612,
0.07300707697868347,
-0.06946617364883423,
0.0546085350215435,
0.024546589702367783,
0.019657403230667114,
0.0354715958237648,
-0.010190542787313461,
-0.025427905842661858,
0.052074726670980453,
0.08335820585489273,
0.002371558453887701,
-0.04382600635290146,
-0.045061782002449036,
-0.013233895413577557,
-0.0053681726567447186,
-0.03657004237174988,
-0.01907934993505478,
0.00011991198698524386,
0.03158912435173988,
0.004812223836779594,
-0.015312666073441505,
0.0006326765287667513,
-0.025898180902004242,
0.011410650797188282,
0.044604163616895676,
-0.0614856481552124,
-0.011120987124741077,
-0.020198572427034378,
-0.0018557171570137143,
-0.01047980785369873,
0.035738255828619,
-0.010168644599616528,
-0.026647690683603287,
0.013130336068570614,
0.015554007142782211,
0.0005746266688220203,
0.0174932312220335,
0.02347644977271557,
0.058333560824394226,
0.005396538879722357,
-0.011189962737262249,
0.04814843088388443,
-0.043510861694812775,
0.016544902697205544,
0.062295980751514435,
-0.01612623780965805,
-0.024656478315591812,
-0.02439163252711296,
0.02922874316573143,
0.018943553790450096,
0.030626608058810234,
-0.017725102603435516,
-0.006029464304447174,
-0.023993229493498802,
0.012427366338670254,
0.09341917932033539,
-0.02718512713909149,
-0.03961501643061638,
-0.039961256086826324,
0.005271232221275568,
0.00860226433724165,
0.023572679609060287,
-0.08733440190553665,
0.035020288079977036,
-0.005568304564803839,
0.02398565039038658,
0.04144803062081337,
-0.007959430105984211,
-0.03126531466841698,
-0.018501041457057,
0.03790394216775894,
0.07700250297784805,
0.052571263164281845,
-0.028525590896606445,
0.05646819621324539,
-0.05122708901762962,
-0.03979508578777313,
0.03587518632411957,
0.024269744753837585,
-0.01118415780365467,
-0.040781669318675995,
0.004776706453412771,
0.023009760305285454,
0.01068560779094696,
0.018032507970929146,
-0.001918311812914908,
0.04869726672768593,
-0.03487703576683998,
-0.09115614742040634,
-0.036788854748010635,
0.03048575296998024,
-0.0051382603123784065,
-0.007578003220260143,
-0.06693347543478012,
-0.029897205531597137,
0.06091410294175148,
0.0982440784573555,
-0.0012288714060559869,
-0.019486194476485252,
0.02991856262087822,
0.0026805636007338762,
0.01284212339669466,
0.022675685584545135,
-0.0011219368316233158,
-0.04110893979668617,
-0.054388873279094696,
-0.003967770375311375,
-0.04432377219200134,
0.03341387212276459,
0.027996517717838287,
0.00826982781291008,
-0.03518255427479744,
0.09864027798175812,
0.012530307285487652,
0.01863732375204563,
-0.0009856104152277112,
0.013669896870851517,
-0.01616779901087284,
0.08652311563491821,
0.026179511100053787,
0.015127119608223438,
0.009275601245462894,
0.008381028659641743,
0.01915890909731388,
0.008011040277779102,
0.02723456546664238,
0.062221985310316086,
-0.02831117995083332,
-0.007404071278870106,
-0.021196095272898674,
-0.006281944457441568,
0.015775786712765694,
-0.015909692272543907,
-0.04479045420885086,
0.006683118641376495,
-0.0034786276519298553,
-0.028839800506830215,
0.03123105876147747,
-0.00977662205696106,
0.004645571578294039,
0.01695922389626503,
-0.03168754652142525,
0.01709907501935959,
-0.03929579630494118,
-0.004995095543563366,
0.03525765985250473,
0.0008341158390976489,
0.039074402302503586,
0.04467502236366272,
-0.013831974938511848,
-0.021590586751699448,
-0.07338929921388626,
0.009842286817729473,
0.024188967421650887,
0.011737794615328312,
0.016443846747279167,
0.028804004192352295,
0.021338636055588722,
0.021498799324035645,
-0.011506197042763233,
0.03312307596206665,
-0.027566364035010338,
0.0010713337687775493,
-0.018235504627227783,
-0.015093883499503136,
0.03173770383000374,
-0.022528760135173798,
0.007384196389466524,
-0.007313922978937626,
0.00903791468590498,
0.0029930768068879843,
-0.011704210191965103,
-0.024306312203407288,
0.053395356982946396,
-0.017213715240359306,
-0.008293546736240387,
0.004871094133704901,
0.031624410301446915,
0.009314896538853645,
0.012108441442251205,
-0.020805243402719498,
-0.07545986026525497,
-0.03576432913541794,
0.016895610839128494,
0.0379457101225853,
0.028423946350812912,
-0.0501575767993927,
0.019551072269678116,
0.018271639943122864,
0.03926403075456619,
0.025164231657981873,
0.0149887315928936,
-0.040590837597846985,
-0.00884220376610756,
-0.009078769944608212,
0.03689207881689072,
0.0026952389162033796,
-0.012451348826289177,
0.009056506678462029,
-0.004524311050772667,
0.03575246036052704,
0.0022847983054816723,
-0.02232341095805168,
0.020075775682926178,
-0.05619228631258011,
0.035524435341358185,
-0.024713875725865364,
-0.02412792481482029,
0.019208285957574844,
-0.011082668788731098,
0.02824527956545353,
0.00820327177643776,
-0.05179063603281975,
-0.02182159386575222,
-0.013394076377153397,
-0.011245292611420155,
0.055953461676836014,
0.0167164858430624,
-0.01576934941112995,
0.0031081754714250565,
0.033322930335998535,
-0.03855214640498161,
-0.005282282363623381,
-0.03898446261882782,
0.024051852524280548,
-0.005538207478821278,
-0.0042363302782177925,
0.044983506202697754,
0.02936241403222084,
-0.008106091059744358,
-0.026489028707146645,
-0.03475072979927063,
0.00024858524557203054,
-0.03339493274688721,
0.04929608851671219,
0.07852719724178314,
-0.05287995561957359,
0.02039305493235588,
-0.07397379726171494,
-0.011044478043913841,
0.02697184309363365,
-0.0011969930492341518,
0.005289390683174133,
-0.02872662991285324,
-0.03687981143593788,
-0.06338527798652649,
-0.015203339979052544,
-0.03933454677462578,
0.012266024947166443,
-0.04373810440301895,
0.007585635408759117,
0.036397725343704224,
-0.019920147955417633,
-0.01830078475177288,
0.03018222376704216,
-0.02943604812026024,
-0.038146086037158966,
-0.009858902543783188,
0.024929426610469818,
0.0310361310839653,
-0.018057337030768394,
0.03925713524222374,
0.04141739010810852,
-0.013789013028144836,
0.009120534174144268,
-0.06727726012468338,
-0.04282315820455551,
-0.017259562388062477,
0.0064882016740739346,
0.014701894484460354,
0.0096086785197258,
0.0019842288456857204,
0.07764303684234619,
0.03035038709640503,
-0.033601731061935425,
-0.02878478914499283,
-0.0003455174737609923,
-0.04062044620513916,
-0.04107068479061127,
-0.00450250506401062,
0.017548197880387306,
-0.012572274543344975,
0.04277097061276436,
-0.020749345421791077,
-0.012546154670417309,
0.03601435199379921,
0.0626404732465744,
-0.028714619576931,
0.047554824501276016,
-0.025739798322319984,
-0.0017925839638337493,
0.0926499292254448,
-0.007772716693580151,
-0.02419879287481308,
-0.020060978829860687,
-0.007099837530404329,
-0.029546938836574554,
0.009863276034593582,
-0.03178178891539574,
0.04403229430317879,
0.006609788630157709,
0.002782357158139348,
0.011940602213144302,
-0.012710419483482838,
-0.015972377732396126,
-0.026998240500688553,
-0.027150170877575874,
-0.023926155641674995,
0.0037390112411230803,
0.029750537127256393,
0.04200988635420799,
0.00725231459364295,
0.03427999094128609,
-0.05573881417512894,
-0.01036106888204813,
0.0015796661609783769,
-0.017942633479833603,
0.03048773854970932,
-0.0009151059784926474,
-0.06067109480500221,
0.015535438433289528,
0.009085005149245262,
0.021456696093082428,
0.018134403973817825,
-0.02377268858253956,
-0.0018167732050642371,
-0.018658587709069252,
0.007337851449847221,
0.007288226392120123,
0.03443383798003197,
0.05998988822102547,
0.04235891252756119,
0.035617996007204056,
-0.017886554822325706,
0.022072702646255493,
-0.0005616217385977507,
-0.0683465451002121,
0.026178255677223206,
-0.0025186005514115095,
-0.04133983328938484,
0.007800234016031027,
-0.031188707798719406,
-0.00873220432549715,
-0.015823030844330788,
0.003084440715610981,
0.010310614481568336,
-0.024512672796845436,
-0.06336834281682968,
-0.007867234759032726,
-0.018270907923579216,
-0.03594714403152466,
-0.04832767695188522,
0.02201608009636402,
0.02038438804447651,
-0.03911994397640228,
0.020068248733878136,
0.03783976286649704,
-0.043442629277706146,
0.010946579277515411,
-0.016357671469449997,
-0.004947302397340536,
0.024671504274010658,
0.0030958845745772123,
0.026881186291575432,
0.021108955144882202,
-0.0450240857899189,
0.013269233517348766,
0.03393681347370148,
0.07922401279211044,
-0.023578638210892677,
-0.031153852120041847,
0.021261420100927353,
-0.008628861047327518,
0.0022636125795543194,
0.008815851993858814,
0.06794548034667969,
0.007216667756438255,
0.01351347379386425,
0.03471485897898674,
0.01580858789384365,
-0.013642393052577972,
0.005386072210967541,
-0.0010531971929594874,
0.024091331288218498,
0.0037413083482533693,
-0.06348033994436264,
0.024840960279107094,
0.01664351113140583,
0.016205476596951485,
-0.009772120043635368,
-0.025253528729081154,
0.004433371126651764,
-0.0018504969775676727,
0.03632688894867897,
0.020262451842427254,
-0.016656816005706787,
0.007628368213772774,
-0.0077431476674973965,
-0.03632272779941559,
-0.03484681248664856,
-0.0031520696356892586,
-0.003680064808577299,
0.03996824100613594,
0.0360737070441246,
0.025074398145079613,
0.020344529300928116,
-0.08796446025371552,
-0.012978536076843739,
0.04997290298342705,
0.017513487488031387,
0.03823374584317207,
-0.020877361297607422,
-0.028161950409412384,
-0.024107320234179497,
0.07027781009674072,
-0.031207699328660965,
0.04054888337850571,
0.004464711993932724,
-0.012793606147170067,
-0.019101040437817574,
-0.0666644349694252,
-0.03690332546830177,
0.02214357629418373,
-0.013930032029747963,
-0.019464876502752304,
-0.042692117393016815,
-0.004171879030764103,
-0.022343376651406288,
0.014695611782371998,
-0.007905303500592709,
0.05476352944970131,
0.026638852432370186,
-0.012548227794468403,
-0.0016418263548985124,
0.01285205502063036,
-0.008095351979136467,
-0.08500564098358154,
0.042894452810287476,
0.02243133634328842,
0.014808597974479198,
0.03186134621500969,
-0.006377723999321461,
-0.0447472408413887,
-0.01064846757799387,
0.0008591857040300965,
-0.012546590529382229,
0.042685963213443756,
-0.058317165821790695,
0.07798388600349426,
0.030741361901164055,
0.02852405235171318,
0.04394756257534027,
0.026088083162903786,
-0.010339607484638691,
0.0018786840373650193,
-0.011384212411940098,
0.004236752633005381,
-0.008656500838696957,
-0.00817443523555994,
-0.030151518061757088,
-0.013126878067851067,
-0.01601524092257023,
0.03652559220790863,
-0.02878376469016075,
0.036867208778858185,
-0.012824498116970062,
-0.02772337943315506,
-0.024375692009925842,
0.026738764718174934,
-0.0475383922457695,
-0.008149085566401482,
0.014493043534457684,
-0.0041133021004498005,
0.03240160644054413,
-0.023094112053513527,
-0.019940916448831558,
-0.0032546143047511578,
-0.015143281780183315,
0.04566071182489395,
0.0007809769595041871,
0.03075445629656315,
-0.021403437480330467,
-0.03782986104488373,
-0.012581804767251015,
-0.07908976823091507,
0.04215257987380028,
-0.0005386221455410123,
-0.001086856471374631,
0.004609798546880484,
-0.07670209556818008,
-0.05580493435263634,
0.011464932933449745,
0.0009882401209324598,
-0.0010826376965269446,
-0.039087485522031784,
-0.0009641280048526824,
0.034761425107717514,
0.00746919633820653,
-0.04467184096574783,
-0.031321167945861816,
-0.011829471215605736,
-0.0032144056167453527,
-0.0125358821824193,
-0.012196626514196396,
0.028671782463788986,
0.006604316178709269,
0.012430302798748016,
0.022657178342342377,
0.018187422305345535,
-0.01792280375957489,
0.01729605346918106,
0.02973545342683792,
0.03163467347621918,
0.024511706084012985,
-0.016660792753100395,
0.008456983603537083,
0.014651120640337467,
-0.003697814652696252,
-0.003036919981241226,
0.015407099388539791,
0.040933601558208466,
-0.034497883170843124,
-0.013111722655594349,
-0.04544008895754814,
0.01662902534008026,
0.030450548976659775,
0.011568188667297363,
0.01462114043533802,
0.030863480642437935,
0.053329020738601685,
0.01857726275920868,
0.001904550357721746,
-0.027544410899281502,
0.021811002865433693,
-0.010177407413721085,
0.006160195451229811,
0.004695808049291372,
0.0034726730082184076,
-0.051066476851701736,
0.038826651871204376,
-0.013116931542754173,
-0.004715106915682554,
-0.0005786019028164446,
0.023401498794555664,
-0.006048509385436773,
0.006263052579015493,
0.04685956984758377,
0.007782622706145048,
0.017039889469742775,
-0.02595439925789833,
0.024083560332655907,
0.013267646543681622,
0.014472328126430511,
-0.026073109358549118,
-0.03151808679103851,
-0.05173112452030182,
0.015451985411345959,
0.052714187651872635,
0.01590353064239025,
0.048557452857494354,
0.002645686734467745,
0.014415248297154903,
-0.022762995213270187,
0.025539979338645935,
-0.02388637699186802,
0.02793734148144722,
0.005933010019361973,
0.01993255317211151,
-0.037557944655418396,
0.010978888720273972,
0.00346016394905746,
0.05763890594244003,
-0.019114067777991295,
0.024292802438139915,
-0.0039041819982230663,
0.06572703272104263,
0.047867126762866974,
0.007930398918688297,
-0.03838762640953064,
0.0354297049343586,
-0.02052103914320469,
0.03241993114352226,
0.024715976789593697,
-0.025685910135507584,
0.014043290168046951,
-0.005618543829768896,
0.03594609722495079,
-0.0007929872372187674,
-0.007317655719816685,
-0.06244952976703644,
-0.007950274273753166,
-0.007051000837236643,
0.008953188546001911,
-0.031659647822380066,
0.004401156213134527,
0.03860059008002281,
0.008282620459794998,
0.00624428503215313,
-0.008808755315840244,
-0.08164991438388824,
-0.0064709363505244255,
-0.05643778294324875,
-0.037364985793828964,
0.035963594913482666,
-0.035265978425741196,
-0.050281599164009094,
0.010422772727906704,
-0.00506227882578969,
0.03302343562245369,
0.009011211805045605,
0.007452977821230888,
-0.01815647818148136,
0.025889424607157707,
0.020010685548186302,
0.00510767474770546,
-0.009752131067216396,
0.002012083074077964,
0.11700543016195297,
0.053741589188575745,
0.013392515480518341,
-0.03607235476374626,
-0.03907303884625435,
-0.017789024859666824,
0.006572203245013952,
-0.0022613571491092443,
0.0286448672413826,
0.001297318609431386,
-0.022298535332083702,
-0.02401062287390232,
0.06028870493173599,
0.028144847601652145,
0.007582877296954393,
0.054723963141441345,
-0.041275277733802795,
-0.07038074731826782,
0.01100127026438713,
0.0056994943879544735,
0.011213238351047039,
-0.0043530547991395,
-0.04923204705119133,
0.023445038124918938,
-0.035472579300403595,
0.015346984378993511,
-0.020290298387408257,
-0.030141929164528847,
0.0152161605656147,
-0.018892984837293625,
-0.045670606195926666,
-0.026406241580843925,
-0.031034978106617928,
-0.022057155147194862,
-0.01713770255446434,
0.020803948864340782,
0.02042461931705475,
-0.013325579464435577,
0.06271738559007645,
0.010216609574854374,
0.01270219124853611,
-0.018169857561588287,
-0.002233710139989853,
-0.018023960292339325,
-0.032259080559015274,
-0.014006809331476688,
-0.03606062009930611,
0.06715758144855499,
-0.03487648442387581,
-0.010961221531033516,
0.006304510869085789,
0.010085875168442726,
-0.03370734676718712,
-0.051305148750543594,
-0.014122623018920422,
-0.0054292017593979836,
0.008969255723059177,
0.002850920893251896,
0.0008202919270843267,
-0.030986221507191658,
0.015225229784846306,
0.03298260644078255,
-0.008646477945148945,
-0.01577799580991268,
0.004128367640078068,
0.01071170810610056,
-0.013708947226405144,
0.05453632026910782,
0.017065996304154396,
-0.010066747665405273,
-0.026847530156373978,
-0.021058646962046623,
-0.00424120482057333,
-0.020554549992084503,
0.01598065160214901,
0.019144810736179352,
0.04868590831756592,
0.019260860979557037,
0.03793278709053993,
-0.002657056087628007,
-0.05598049983382225,
-0.00622795382514596,
-0.05480893701314926,
-0.02281908318400383,
0.01133676990866661,
0.004971591290086508,
0.03572124242782593,
0.06705670058727264,
-0.02771277166903019,
-0.013812397606670856,
-0.0034604896791279316,
0.019555145874619484,
0.04010307416319847,
-0.036000583320856094,
-0.01388204749673605,
-0.00512296287342906,
-0.021081387996673584,
0.00001754935146891512,
-0.01974918693304062,
-0.027450891211628914,
0.01181830558925867,
-0.0021499779541045427,
0.0237782783806324,
0.04863591492176056,
-0.03324202448129654,
-0.030398627743124962,
-0.011587841436266899,
-0.038194410502910614,
0.01187041960656643,
0.016192952170968056,
0.004100542049854994,
-0.08312518149614334,
-0.032955996692180634,
-0.018586819991469383,
0.0047855922020971775,
-0.004194578621536493,
0.007080081384629011,
-0.002435694681480527,
-0.023053567856550217,
-0.0069058118388056755,
0.02227937802672386,
0.005551702342927456,
0.03205345198512077,
-0.047743912786245346,
0.029978716745972633,
-0.031508300453424454,
-0.0006385527085512877,
-0.032170459628105164,
0.0348588302731514,
0.010101746767759323,
-0.016394736245274544,
0.01119405310600996,
0.0031170090660452843,
-0.014640134759247303,
0.026574410498142242,
0.008778863586485386,
-0.00004637743404600769,
0.031032029539346695,
0.03910321742296219,
-0.021430164575576782,
0.01639745943248272,
-0.04627756401896477,
-0.05038432776927948,
0.04843657463788986,
0.01837032102048397,
0.013897516764700413,
0.06506668776273727,
0.011544618755578995,
0.007951625622808933,
0.005597625859081745,
-0.009647268801927567,
-0.024041760712862015,
0.003661074209958315,
-0.025018151849508286,
-0.010516137816011906,
-0.04380643740296364,
0.011309587396681309,
-0.018317965790629387,
-0.01266730297356844,
0.01204964704811573,
0.03490028157830238,
0.018871471285820007,
-0.004008641000837088,
0.010676845908164978,
-0.026706896722316742,
0.04139116778969765,
-0.015397656708955765,
-0.0033426207955926657,
-0.000028109916456742212,
0.021698109805583954,
-0.05711710453033447,
0.010155891999602318,
0.0306087639182806,
0.0039270962588489056,
-0.0941777154803276,
-0.012043430469930172,
0.02191309817135334,
-0.01171142514795065,
0.045766402035951614,
-0.056650418788194656,
0.02615128457546234,
0.027533015236258507,
-0.0692685917019844,
0.05759395658969879,
-0.011029385030269623,
-0.006433454807847738,
-0.0007256139651872218,
0.00010056995233753696,
-0.0355844609439373,
0.05707108974456787,
-0.001688101445324719,
0.05292467027902603,
0.00045018602395430207,
0.021966533735394478,
-0.012884028255939484,
-0.003141076071187854,
-0.006019007880240679,
-0.0033500599674880505,
0.021957343444228172,
-0.019159791991114616,
0.08269486576318741,
-0.03293146938085556,
0.00028872990515083075,
0.04179294407367706,
-0.05874806270003319,
-0.025327716022729874,
-0.019640350714325905,
0.005735752172768116,
0.009258515201508999,
0.02275555394589901,
0.04961511492729187,
-0.0043409052304923534,
0.018661709502339363,
-0.010271529667079449,
0.045777734369039536,
0.057424142956733704,
-0.012354552745819092,
0.005129569210112095,
0.0019847529474645853,
-0.022320596501231194,
-0.020310064777731895,
0.03466878831386566,
0.0093920873478055,
0.0011767962714657187,
0.019048267975449562,
0.0007047097315080464,
-0.0014577703550457954,
-0.029963331297039986,
-0.013658298179507256,
-0.02502039447426796,
0.0051540182903409,
-0.009823170490562916,
0.0165233314037323,
-0.05166914686560631,
-0.0031448022928088903,
-0.011896227486431599,
-0.0643448755145073,
0.02529175952076912,
0.030921753495931625,
0.00527924345806241,
-0.02730311080813408,
-0.013508881442248821,
0.019763542339205742,
-0.006810958031564951,
0.024564070627093315,
-0.022405993193387985,
-0.029791831970214844,
0.003574494505301118,
-0.03043803945183754,
0.012348726391792297,
-0.0047502839006483555,
-0.007705254014581442,
-0.02052030712366104,
-0.09296621382236481,
0.0334818996489048,
0.05736469477415085,
0.024162549525499344,
-0.004327817820012569,
-0.02876436896622181,
-0.00772145576775074,
0.01460774801671505,
0.06577272713184357,
0.021008286625146866,
-0.030042514204978943,
0.04197036847472191,
-0.006708282046020031,
0.02026996575295925,
-0.020531829446554184,
-0.01585480198264122,
0.01174350269138813,
0.024665389209985733,
-0.020773785188794136,
-0.003810774302110076,
-0.039146170020103455,
0.03549923747777939,
0.03951825201511383,
0.019415277987718582,
-0.0443195104598999,
-0.00010603994451230392,
-0.07069295644760132,
0.050089187920093536,
-0.020205453038215637,
0.018914474174380302,
0.053430311381816864,
0.010274143889546394,
0.00020357672474347055,
0.033154334872961044,
-0.02691659703850746,
-0.010137002915143967,
-0.012802460230886936,
-0.04395485296845436,
-0.03047042153775692,
0.018172187730669975,
0.002880445448681712,
0.035250306129455566,
-0.043927695602178574,
-0.0252617709338665,
0.033020902425050735,
-0.029398130252957344,
-0.015713226050138474,
0.06852173060178757,
0.010278549045324326,
0.01588497683405876,
0.05622516945004463,
0.022853637114167213,
0.024718808010220528,
0.0262872576713562,
-0.003555657109245658,
0.04586547985672951,
-0.0024302667006850243,
-0.0002287214301759377,
0.04382887855172157,
0.009404259733855724,
-0.012533399276435375,
0.04140039160847664,
0.005984575487673283,
0.0618806891143322,
-0.025339433923363686,
0.024943217635154724,
0.03377372398972511,
-0.008723432198166847,
-0.018376706168055534,
0.00830014143139124,
-0.037890318781137466,
0.1082649752497673,
-0.006562672555446625,
0.0013180574169382453,
-0.02996138483285904,
0.025025002658367157,
0.011199556291103363,
0.017970668151974678,
0.01310429535806179,
0.04250321909785271,
-0.03184029459953308,
-0.001422349363565445,
-0.0164212416857481,
0.01926913484930992,
0.011006900109350681,
-0.0376882441341877,
0.001967699034139514,
0.016454918310046196,
-0.04673410952091217,
0.0045457324013113976,
-0.028793716803193092,
-0.031210998073220253,
-0.01692691072821617,
0.025889167562127113,
0.041539985686540604,
0.03342973068356514,
-0.012018860317766666,
0.002196094486862421,
-0.036440037190914154,
0.046996574848890305,
-0.06180891767144203,
0.002383628860116005,
0.0028158840723335743,
-0.0017939630197361112,
-0.00139094318728894,
-0.01794956624507904
] |
<p>I would like to know if Archimedes law take in equation the lack of matter. Fluid density at 1. An object with density of 0 (or near 0) is put in liquid, it's fixed. The external sphere where liquid is inside is fixed too. The lack of matter change the attraction in all the sphere itself, no ? Density change with depth, no ? How forces can be calculate ?</p>
<p><img src="http://i.stack.imgur.com/Jn1KB.jpg" alt="e"></p>
| 8,311 |
[
-0.02069508284330368,
-0.0023161815479397774,
-0.013664343394339085,
-0.006009542383253574,
0.027001073583960533,
-0.042528677731752396,
-0.04326783865690231,
0.0016596385976299644,
-0.019111687317490578,
-0.033032260835170746,
-0.0004547589924186468,
0.030980288982391357,
0.05856303870677948,
0.035271961241960526,
0.03930369019508362,
0.008090009912848473,
0.0011776547180488706,
-0.017621658742427826,
0.016061674803495407,
-0.04229314625263214,
-0.025215473026037216,
0.030161073431372643,
0.017145222052931786,
0.012148862704634666,
-0.01879306323826313,
0.031042024493217468,
0.0013290556380525231,
-0.02549945004284382,
0.025859467685222626,
0.03283928707242012,
0.0188706424087286,
-0.02743881568312645,
0.01967894658446312,
-0.0021258529741317034,
0.027784056961536407,
0.008782738819718361,
-0.019911305978894234,
-0.021578514948487282,
-0.011644148267805576,
0.0297824926674366,
-0.015691019594669342,
-0.01161649078130722,
0.0075743733905255795,
0.049769289791584015,
-0.006766058038920164,
0.014524826779961586,
0.04927445203065872,
-0.017197230830788612,
0.06252720206975937,
-0.07301674783229828,
0.03364650160074234,
0.02890668250620365,
0.07684564590454102,
0.04993288964033127,
0.0172868724912405,
-0.04824622720479965,
0.04936489835381508,
0.04710322618484497,
-0.02290204167366028,
-0.05606294423341751,
-0.03181583434343338,
0.021335063502192497,
-0.006017955485731363,
-0.018225111067295074,
0.009866641834378242,
0.006842303089797497,
-0.02767423912882805,
-0.0146096246317029,
0.02606894075870514,
-0.0006108048255555332,
0.020218467339873314,
0.005744610447436571,
0.04875117167830467,
0.007389270234853029,
0.009807172231376171,
0.004533369094133377,
0.02396422065794468,
-0.014368572272360325,
-0.007696494460105896,
0.04133305326104164,
-0.007371342740952969,
-0.011448634788393974,
0.04866327345371246,
0.042435914278030396,
0.0291083212941885,
-0.034574441611766815,
0.03527935594320297,
-0.0015923952450975776,
0.054147254675626755,
0.030126284807920456,
-0.02925841696560383,
-0.02267804741859436,
0.010581296868622303,
-0.02460228092968464,
-0.02443157322704792,
-0.010339139960706234,
-0.0032490859739482403,
0.05455686151981354,
0.0015458498382940888,
-0.02977157011628151,
0.012185941450297832,
-0.0004489865677896887,
0.0010916192550212145,
0.10375628620386124,
0.011167813092470169,
-0.02555549517273903,
-0.032304417341947556,
0.011019593104720116,
-0.02074950933456421,
0.029152503237128258,
0.016820579767227173,
0.011950998567044735,
-0.003811122849583626,
-0.05802064388990402,
-0.015750965103507042,
-0.028453847393393517,
0.021973930299282074,
-0.038220878690481186,
0.05592569708824158,
0.026621080935001373,
0.051510587334632874,
-0.03214654326438904,
-0.004618419334292412,
-0.01517662312835455,
-0.0512038879096508,
0.03080471232533455,
0.009196082130074501,
-0.030778909102082253,
-0.03179284557700157,
0.04488290473818779,
-0.025789901614189148,
0.031725335866212845,
0.004251208622008562,
0.04656204953789711,
0.052227433770895004,
0.003047544276341796,
-0.059762485325336456,
-0.040027327835559845,
0.08575073629617691,
-0.014228763058781624,
-0.0072542401030659676,
-0.04293128475546837,
0.017083458602428436,
0.03667225316166878,
0.07811177521944046,
-0.006601117085665464,
0.03250795230269432,
0.00039822745020501316,
0.027042439207434654,
-0.008767017163336277,
-0.029432468116283417,
0.019965508952736855,
0.02337583526968956,
-0.05674995481967926,
-0.006854697596281767,
-0.05610198900103569,
0.023587530478835106,
0.029662592336535454,
0.0016501120990142226,
-0.03570770472288132,
0.07779081910848618,
-0.023908989503979683,
-0.008975636214017868,
0.028929777443408966,
0.00690902816131711,
-0.056212168186903,
0.059332799166440964,
-0.031037457287311554,
0.027069775387644768,
0.03451354801654816,
0.011613006703555584,
0.04359531030058861,
-0.02834393084049225,
0.0033606335055083036,
0.04184558242559433,
-0.0017092584166675806,
-0.02136022411286831,
-0.03326718881726265,
0.019728204235434532,
0.0521484799683094,
-0.051301393657922745,
-0.015009419061243534,
-0.023894917219877243,
-0.0106938062235713,
-0.0004812364641111344,
0.037418901920318604,
0.004321490414440632,
-0.0025278262328356504,
0.0006488722865469754,
-0.02803836390376091,
0.01980215311050415,
-0.08909095078706741,
0.018291402608156204,
-0.02576843649148941,
0.013073278591036797,
0.02994997799396515,
0.017646238207817078,
0.010481800884008408,
-0.03563598170876503,
0.016817504540085793,
-0.0323210172355175,
-0.0191549863666296,
-0.0024031910579651594,
-0.02600633166730404,
0.03025149181485176,
0.022728536278009415,
0.022208133712410927,
0.020951615646481514,
-0.006243633106350899,
-0.024004438892006874,
0.004433636553585529,
-0.01814422197639942,
0.0016838638111948967,
0.01353632751852274,
-0.0008512748754583299,
0.021936286240816116,
0.042227648198604584,
0.004121862351894379,
0.000264711823547259,
0.025898803025484085,
-0.023581933230161667,
0.1138993427157402,
0.052349623292684555,
-0.003607056802138686,
0.016201665624976158,
0.04356765002012253,
0.01210237480700016,
-0.0015168843092396855,
0.009058180265128613,
-0.01779242232441902,
-0.059522002935409546,
-0.017990631982684135,
0.007209284696727991,
0.04614005610346794,
-0.0032182717695832253,
0.011123668402433395,
0.023389965295791626,
0.000987977720797062,
0.04040884971618652,
-0.016085144132375717,
-0.033198241144418716,
-0.04563191160559654,
0.024486390873789787,
0.05610525235533714,
0.01754942163825035,
-0.007733487989753485,
0.04781785607337952,
0.025937750935554504,
0.0365186482667923,
-0.03831665962934494,
-0.007078487426042557,
0.010470674373209476,
-0.015109485015273094,
0.015873074531555176,
-0.04952963441610336,
-0.013197033666074276,
0.009898582473397255,
-0.01703673228621483,
0.007280978374183178,
0.0071006654761731625,
0.040239155292510986,
-0.02515084110200405,
-0.07614569365978241,
-0.00504371989518404,
0.037095263600349426,
0.00827452726662159,
-0.020195499062538147,
-0.055913787335157394,
0.011327417567372322,
-0.0645502582192421,
-0.007604263257235289,
0.00804886408150196,
-0.021950120106339455,
-0.03310953825712204,
-0.006504537537693977,
0.022199619561433792,
-0.011582490056753159,
-0.002786290366202593,
-0.01772071234881878,
-0.02187524177134037,
-0.025188380852341652,
-0.0006125125801190734,
-0.029100140556693077,
0.026103751733899117,
-0.05073202773928642,
0.03230489045381546,
-0.0218160729855299,
0.004153808578848839,
0.046084925532341,
-0.004440519958734512,
0.027301901951432228,
0.041053880006074905,
-0.006850031204521656,
-0.012930327095091343,
-0.019282566383481026,
-0.06502202898263931,
-0.021090460941195488,
-0.007771284319460392,
0.03409319743514061,
0.018816258758306503,
0.0024923961609601974,
-0.030327055603265762,
-0.016510246321558952,
-0.06412205845117569,
-0.06350026279687881,
-0.015452668070793152,
0.020116262137889862,
0.009446486830711365,
-0.05393257364630699,
0.020026464015245438,
0.008637391962110996,
-0.03517678380012512,
0.0070780604146420956,
-0.035265546292066574,
-0.05761128291487694,
0.045752350240945816,
0.0013461452908813953,
0.03845137357711792,
-0.00725790299475193,
-0.039592403918504715,
0.07424099743366241,
0.012625478208065033,
-0.0632217526435852,
-0.031261004507541656,
0.004790007136762142,
-0.003283072030171752,
-0.020617183297872543,
0.019092116504907608,
0.048746731132268906,
-0.016605548560619354,
0.009106988087296486,
0.017780672758817673,
0.001029685139656067,
0.014870810322463512,
0.019819075241684914,
0.027609139680862427,
0.021635277196764946,
0.048070650547742844,
-0.0008529736660420895,
0.05823725461959839,
0.0029468857683241367,
0.005611849017441273,
-0.010618982836604118,
-0.006380266044288874,
0.050476402044296265,
0.037889108061790466,
-0.02657955326139927,
0.0501541867852211,
0.02600179798901081,
0.016929272562265396,
0.008239219896495342,
0.018842114135622978,
-0.014341101050376892,
-0.015914011746644974,
0.03468765318393707,
0.0005701102199964225,
0.031271643936634064,
0.019865956157445908,
-0.02042509615421295,
0.07017799466848373,
0.025872880592942238,
-0.03098180517554283,
-0.05377581715583801,
0.005827011074870825,
0.014728885143995285,
0.050646860152482986,
-0.018896568566560745,
0.009437843225896358,
0.029101338237524033,
-0.019179604947566986,
0.05387183278799057,
0.003065674100071192,
-0.0072447992861270905,
-0.015107757411897182,
-0.05587780475616455,
-0.00887746550142765,
-0.010429732501506805,
0.04004952311515808,
0.0016013531712815166,
0.040094196796417236,
0.0003424632886890322,
0.038067497313022614,
0.007755781523883343,
0.024694712832570076,
-0.09116298705339432,
0.0014901920221745968,
-0.013752804137766361,
-0.012088607996702194,
-0.012861255556344986,
-0.01786690019071102,
-0.03613700717687607,
-0.05880829691886902,
-0.004833717364817858,
-0.026506192982196808,
-0.001663049915805459,
-0.054773565381765366,
-0.0007886051316745579,
-0.009716636501252651,
-0.02092282474040985,
-0.017368823289871216,
0.037857141345739365,
-0.010716049000620842,
-0.032554712146520615,
0.03307255357503891,
0.015619565732777119,
-0.007452745456248522,
0.0008147453190758824,
-0.014775654301047325,
-0.007930219173431396,
0.020975317806005478,
0.034147631376981735,
0.023354634642601013,
0.03170288726687431,
-0.03337685763835907,
0.02692219242453575,
0.04555470496416092,
0.030882209539413452,
-0.01719546690583229,
0.04383700340986252,
-0.048052482306957245,
-0.045569855719804764,
-0.022159047424793243,
-0.009875591844320297,
0.02484511397778988,
-0.017294319346547127,
-0.00012964080087840557,
-0.0016710077179595828,
-0.04640056565403938,
0.0033273103181272745,
0.04210207238793373,
0.0666450634598732,
0.02682713232934475,
-0.009687164798378944,
-0.04281357303261757,
0.0019966219551861286,
-0.06180734559893608,
0.029224181547760963,
0.05242643877863884,
0.033954232931137085,
-0.031016720458865166,
-0.006345979403704405,
0.009143403731286526,
0.02103009819984436,
-0.026044199243187904,
-0.04809700325131416,
0.010052893310785294,
0.0004912075237371027,
-0.02403305284678936,
-0.011220183223485947,
0.042735226452350616,
0.037348195910453796,
0.025925183668732643,
-0.01143148448318243,
0.002724324818700552,
-0.08726636320352554,
-0.019101401790976524,
0.04963422566652298,
0.03366532176733017,
0.011713696643710136,
0.02775689959526062,
-0.08035650104284286,
-0.04784121364355087,
0.07130298763513565,
-0.022258305922150612,
0.0020823620725423098,
-0.030156243592500687,
0.051234111189842224,
0.02182808704674244,
-0.05080851539969444,
-0.02756752073764801,
0.005340142175555229,
-0.03721959516406059,
0.00914926826953888,
-0.020685799419879913,
0.01778147742152214,
0.01398694608360529,
0.017970634624361992,
0.015316606499254704,
0.027441726997494698,
0.01445872150361538,
0.01566055417060852,
0.006241299211978912,
-0.01160033792257309,
-0.019308054819703102,
-0.08365745097398758,
-0.00318503868766129,
-0.009316660463809967,
0.01270485483109951,
0.01387804839760065,
-0.053410936146974564,
-0.061991605907678604,
-0.0004269091004971415,
0.020325783640146255,
-0.0016868646489456296,
0.002700804965570569,
-0.03393672779202461,
0.0020354818552732468,
0.004505887161940336,
-0.00988905131816864,
0.02526417002081871,
0.04450235515832901,
-0.013384363614022732,
-0.04816742241382599,
-0.04510881379246712,
-0.004617000930011272,
-0.016830628737807274,
-0.03691370040178299,
-0.030065638944506645,
0.010594590567052364,
-0.03360065817832947,
0.022826062515378,
0.01835859939455986,
0.001033999491482973,
0.0028405182529240847,
-0.00966233853250742,
0.008700227364897728,
0.04983524605631828,
0.020143626257777214,
0.019194580614566803,
-0.012762139551341534,
-0.008193074725568295,
0.016442544758319855,
-0.01771007478237152,
0.006905427668243647,
0.0017684641061350703,
0.006022530607879162,
0.007558623794466257,
-0.010834348388016224,
0.038037996739149094,
0.0030830332543700933,
-0.022409562021493912,
-0.006505858618766069,
-0.032513827085494995,
0.06941401958465576,
-0.0015214630402624607,
0.04725921154022217,
0.01193251833319664,
-0.05940663442015648,
0.011103639379143715,
-0.04376335069537163,
-0.022494865581393242,
0.038318049162626266,
-0.018738912418484688,
0.00016157919890247285,
0.030828185379505157,
-0.006027768831700087,
-0.07155314087867737,
-0.06506477296352386,
0.009278926998376846,
0.011538988910615444,
-0.010833689011633396,
-0.030277196317911148,
0.016735022887587547,
-0.03201455995440483,
-0.031453147530555725,
0.03930521011352539,
0.012363324873149395,
-0.04311039298772812,
-0.022547582164406776,
0.03494575619697571,
-0.007477006874978542,
0.03491806983947754,
0.001967131393030286,
-0.021118907257914543,
-0.02508619800209999,
-0.004167775623500347,
0.018687820062041283,
-0.011854256503283978,
0.03429937735199928,
-0.03151437267661095,
-0.009302526712417603,
-0.021906057372689247,
-0.04569540172815323,
0.04469313099980354,
-0.018804213032126427,
0.01576412282884121,
-0.0026508248411118984,
0.021972814574837685,
-0.014327337965369225,
-0.01947985403239727,
-0.011116680689156055,
-0.0040596527978777885,
0.012756587006151676,
0.015679307281970978,
-0.00576417613774538,
-0.04293598234653473,
-0.04024186730384827,
0.02352154441177845,
-0.04640490189194679,
0.008093715645372868,
-0.008545322343707085,
0.07576511055231094,
0.01899484544992447,
-0.01996716298162937,
0.013099751435220242,
0.00786899495869875,
0.02511022798717022,
-0.01952972263097763,
-0.04487590491771698,
0.0077976989559829235,
0.0417512021958828,
-0.01770624704658985,
-0.030918490141630173,
-0.02930222637951374,
0.02710999920964241,
0.04584003984928131,
0.004979283083230257,
0.04814733937382698,
0.017417730763554573,
-0.004825450014322996,
0.003467975649982691,
0.0199959147721529,
-0.019818035885691643,
0.04154730960726738,
-0.005193344783037901,
0.03260340169072151,
-0.04854638874530792,
0.013012630864977837,
0.029100609943270683,
0.022684410214424133,
-0.01624583825469017,
0.017069565132260323,
0.05700274556875229,
-0.0024778307415544987,
0.016978560015559196,
-0.007334424648433924,
-0.0475861057639122,
0.052860409021377563,
-0.016184333711862564,
0.049839332699775696,
-0.053602434694767,
-0.030545396730303764,
0.05184167996048927,
0.030488086864352226,
-0.01007844414561987,
-0.04699182137846947,
-0.05164092779159546,
-0.009751192294061184,
0.032738763839006424,
0.04296332597732544,
0.03156980872154236,
-0.00947518553584814,
0.0076516782864928246,
0.022613106295466423,
-0.005245010368525982,
-0.007186276838183403,
0.010192280635237694,
-0.0664699599146843,
0.014216870069503784,
-0.037797730416059494,
-0.02759658172726631,
0.013304349966347218,
0.007603352423757315,
-0.032455336302518845,
-0.0057264589704573154,
0.0002549130003899336,
0.025309016928076744,
0.0577344112098217,
0.018862253054976463,
-0.021500391885638237,
0.0631318911910057,
-0.012972691096365452,
0.017445601522922516,
-0.028348131105303764,
0.01161231379956007,
0.12519973516464233,
0.024859284982085228,
0.01675175502896309,
-0.05218959599733353,
-0.009508302435278893,
-0.022042592987418175,
-0.009213745594024658,
-0.0496206171810627,
0.014838754199445248,
-0.02744906023144722,
0.009486913681030273,
0.012053119018673897,
0.03575856611132622,
0.006119161378592253,
-0.037806104868650436,
0.03616131842136383,
-0.04061698541045189,
-0.060317352414131165,
-0.028924139216542244,
0.003980568610131741,
-0.04476449638605118,
0.051226306706666946,
-0.02142181061208248,
0.0074347746558487415,
-0.01655493676662445,
-0.02847474254667759,
-0.04140142723917961,
-0.024538299068808556,
0.011124959215521812,
0.02520548738539219,
-0.06973983347415924,
0.024570904672145844,
-0.008400306105613708,
-0.03903227671980858,
-0.04580129310488701,
0.022658182308077812,
-0.007746560499072075,
-0.03347388282418251,
-0.0014348553959280252,
0.02684040553867817,
-0.008146454580128193,
0.004257729277014732,
0.006156443152576685,
0.01694844849407673,
-0.04588702693581581,
-0.005687063559889793,
-0.028111854568123817,
0.057979583740234375,
-0.00819934532046318,
0.004130091518163681,
0.035512231290340424,
-0.006094076205044985,
-0.006298020947724581,
-0.06216063350439072,
-0.01648576371371746,
-0.009142950177192688,
0.022976554930210114,
-0.0011575077660381794,
-0.03667682781815529,
-0.00006716685311403126,
0.008705253712832928,
0.012413468211889267,
0.02851034328341484,
0.017574943602085114,
0.028623154386878014,
0.009022379294037819,
0.006378318183124065,
0.056602925062179565,
-0.03422915190458298,
-0.00795517023652792,
-0.04180905967950821,
-0.015490937978029251,
-0.0347982682287693,
-0.011179070919752121,
-0.013310355134308338,
0.03930693864822388,
0.02395995892584324,
0.019466886296868324,
-0.0025054991710931063,
0.004911924246698618,
-0.045238591730594635,
0.0387873537838459,
-0.03983260318636894,
0.00020896192290820181,
-0.039609652012586594,
0.01638384908437729,
0.014953003264963627,
0.04586992412805557,
-0.02358773909509182,
-0.0367916002869606,
0.013303657993674278,
0.004854170605540276,
-0.02857663668692112,
-0.011811763979494572,
-0.036302730441093445,
0.005994688719511032,
-0.0484207421541214,
0.01972397044301033,
0.008330712094902992,
0.0039183758199214935,
0.04423884302377701,
-0.010762296617031097,
0.020099477842450142,
0.0643930584192276,
-0.018149808049201965,
0.03196907788515091,
-0.01662832871079445,
0.00028494259458966553,
-0.006172037683427334,
0.005810007452964783,
0.002389497822150588,
-0.016079997643828392,
-0.026568731293082237,
-0.05139588192105293,
0.009664375334978104,
-0.020515035837888718,
0.024603506550192833,
-0.03307082876563072,
-0.0097060427069664,
-0.0014497718075290322,
-0.012139237485826015,
-0.008805761113762856,
-0.00272070593200624,
-0.0336383692920208,
-0.03297469764947891,
0.026636697351932526,
-0.007817721925675869,
-0.022401895374059677,
0.04331906884908676,
-0.019055290147662163,
-0.018213005736470222,
0.002464469987899065,
-0.033387284725904465,
0.0070204040966928005,
-0.017591392621397972,
0.033208250999450684,
-0.017246607691049576,
0.05288557708263397,
-0.013563565909862518,
-0.033438827842473984,
-0.0008452959591522813,
-0.02603885531425476,
-0.032189659774303436,
0.034003403037786484,
-0.008292530663311481,
0.015490790829062462,
0.05407939478754997,
0.005508716683834791,
-0.025383781641721725,
0.08811042457818985,
0.001361967297270894,
0.0313640758395195,
-0.004719719290733337,
-0.07334446907043457,
0.0029811931308358908,
-0.014945019967854023,
0.03310314938426018,
-0.012333895079791546,
-0.03107067197561264,
0.04356607794761658,
0.03874605521559715,
0.035067569464445114,
-0.029433723539114,
0.026938853785395622,
-0.015973465517163277,
-0.011618508957326412,
0.048410285264253616,
-0.011641662567853928,
0.029836740344762802,
0.048534102737903595,
-0.036021191626787186,
0.03722744807600975,
0.021860910579562187,
0.0071065654046833515,
-0.1108306422829628,
-0.028563519939780235,
0.0034211110323667526,
0.013011663220822811,
0.03615532070398331,
-0.06598851084709167,
0.008180346339941025,
0.011320102028548717,
-0.05171867832541466,
-0.006688385736197233,
-0.05869126319885254,
-0.011664720252156258,
-0.021009987220168114,
-0.0001911039580591023,
0.012875249609351158,
0.06431341916322708,
-0.008281425572931767,
0.0460519976913929,
0.01379221398383379,
0.001299893599934876,
0.006573233753442764,
-0.013311835005879402,
-0.021884294226765633,
0.04712057113647461,
-0.026835093274712563,
0.020356833934783936,
0.0033133283723145723,
-0.008533087559044361,
-0.028145425021648407,
0.0017916696378961205,
-0.013981470838189125,
0.023760907351970673,
0.007000657729804516,
0.06259852647781372,
-0.019697099924087524,
0.024213090538978577,
-0.014078604057431221,
0.02886023372411728,
-0.014832762070000172,
0.06176832318305969,
0.005455626640468836,
0.007410295307636261,
-0.03669704496860504,
0.009176861494779587,
0.005843782797455788,
-0.03153945505619049,
-0.022052543237805367,
0.03443297743797302,
-0.028877079486846924,
0.02406276762485504,
-0.020515641197562218,
-0.015869295224547386,
0.00011977719987044111,
-0.01038173958659172,
-0.02329583652317524,
-0.026979753747582436,
0.03464706614613533,
0.06271626055240631,
0.027058344334363937,
-0.04245086759328842,
0.013297480531036854,
0.027815425768494606,
-0.02400761842727661,
-0.003425433998927474,
0.010829666629433632,
-0.009859076701104641,
-0.04423659294843674,
-0.00951674859970808,
-0.0004435475857462734,
-0.008358601480722427,
0.018610307946801186,
-0.017005030065774918,
-0.03441256657242775,
0.025920020416378975,
0.016234101727604866,
0.00025055333389900625,
0.02482110820710659,
-0.042343489825725555,
-0.006235226523131132,
-0.057164277881383896,
0.046743493527173996,
-0.01915782503783703,
-0.021227465942502022,
-0.02570313960313797,
0.014246041886508465,
-0.008836816065013409,
0.001773049938492477,
0.0302838496863842,
0.0005675344727933407,
0.010791348293423653,
-0.004176182206720114,
-0.0004628266324289143,
0.0015899712452664971,
0.005240319762378931,
-0.010843515396118164,
-0.006308306474238634,
-0.02248806692659855,
0.006945924833416939,
0.027983076870441437,
-0.01535007357597351,
-0.012029066681861877,
0.028750650584697723,
-0.03917540982365608,
0.024139663204550743,
-0.002896052086725831,
-0.05696570500731468,
0.03893338516354561,
0.025757072493433952,
-0.005966543219983578,
0.100890152156353,
-0.012845596298575401,
0.009526669047772884,
0.017025433480739594,
-0.030084025114774704,
-0.029739441350102425,
0.04904186353087425,
-0.04248252883553505,
0.021332290023565292,
-0.01904800534248352,
-0.03547880798578262,
0.015039357356727123,
-0.011997309513390064,
0.02015908621251583,
0.043841488659381866,
-0.04660164564847946,
-0.03324677422642708,
0.04620292782783508,
0.010709060356020927,
0.06152741238474846,
-0.051703210920095444,
0.014660135842859745,
-0.000599769817199558,
-0.007167358882725239,
0.02415366843342781,
0.040813032537698746,
0.056129202246665955,
-0.007219621911644936,
-0.027384458109736443,
0.04357605054974556,
0.03649381548166275,
0.0017397920601069927,
0.03287303075194359,
0.013533668592572212,
-0.014161551371216774,
-0.03349854797124863,
-0.0022101132199168205,
-0.04199199378490448,
0.00924728624522686,
0.0017144387820735574,
0.017672613263130188,
0.08755304664373398,
-0.04495249688625336,
0.007750054355710745,
-0.010556299239397049,
-0.02831474132835865,
-0.013987441547214985,
0.037186264991760254,
-0.005497694946825504,
0.059189021587371826,
-0.012810704298317432,
-0.043765973299741745,
0.025057082995772362,
-0.01852067932486534,
0.004947797395288944,
0.02955801784992218,
0.019639136269688606,
-0.0005967135657556355,
0.014092864468693733,
0.004348513670265675,
0.020923670381307602,
-0.02617695927619934,
-0.019697053357958794,
0.061615414917469025,
0.026367472484707832,
0.024808960035443306,
-0.010771152563393116,
-0.002014583209529519,
-0.045080699026584625,
0.08122172951698303,
-0.027657996863126755,
-0.03870905935764313,
-0.020862506702542305,
0.018302448093891144,
0.0029697632417082787,
-0.018326103687286377
] |
<p>Recently I saw some videos of non-newtonian (shear-thickening) fluids like corn starch mixed with water(sometimes known as oobleck), where the fluid is placed on top of a speaker cone and starts to create odd shapes as it becomes thicker in some places.
Now I wondered what would happen in the following situation:</p>
<p>Suppose a room with reflective walls is fully filled with such a fluid. On one side of the room a sound is produced by a speaker. On the other side of the room is a microphone. How will a sound wave propagate through such a substance? Does the fluid increase its viscosity before, during or after a wave moves through it? What will the speed-of-sound be in such a case? I've read that the speed of sound is much faster in solids than in liquids, but how is that for this kind of substance?</p>
| 8,312 |
[
0.0071344501338899136,
-0.06083748862147331,
0.004956299439072609,
-0.040018822997808456,
0.018750231713056564,
0.01756572537124157,
-0.006862863432615995,
-0.027547189965844154,
-0.019521798938512802,
-0.024999961256980896,
0.006371235009282827,
0.05029049515724182,
0.06712161749601364,
-0.007571675814688206,
0.022298498079180717,
-0.02590343914926052,
0.017375078052282333,
0.006278038490563631,
0.012558318674564362,
-0.04162086173892021,
0.009034073911607265,
0.011403833515942097,
-0.00022533649462275207,
-0.0005823097308166325,
0.004088053945451975,
0.01961791142821312,
0.011716957204043865,
0.0063512749038636684,
0.02622951939702034,
-0.012643192894756794,
0.04712451621890068,
-0.014902071096003056,
-0.02671399712562561,
0.011006630957126617,
0.03725069761276245,
0.009560839273035526,
-0.0571165606379509,
-0.003769614966586232,
-0.005648432765156031,
0.025131911039352417,
-0.036518145352602005,
-0.008295970037579536,
0.03755198046565056,
0.03957367315888405,
-0.028302861377596855,
-0.007530715316534042,
0.028986109420657158,
-0.0506492480635643,
0.018137462437152863,
-0.06745264679193497,
0.0704864040017128,
0.03004426322877407,
0.02152443490922451,
0.04579620808362961,
0.001530634704977274,
0.03992191329598427,
0.061121609061956406,
0.07737455517053604,
0.012798380106687546,
-0.06309092789888382,
0.02538270875811577,
0.009127631783485413,
-0.04998210445046425,
-0.016430292278528214,
-0.0427401103079319,
0.0023662082385271788,
-0.02395903319120407,
-0.03298838809132576,
0.024760186672210693,
0.008711396716535091,
-0.025276275351643562,
0.0005550780333578587,
0.06151333451271057,
-0.0061029912903904915,
0.035629644989967346,
-0.007157078478485346,
-0.006619923748075962,
0.04496896266937256,
0.004732377827167511,
-0.007613808382302523,
-0.009516706690192223,
-0.03145860880613327,
0.00014906347496435046,
0.042339831590652466,
-0.02228579670190811,
-0.03367722034454346,
0.03712158650159836,
-0.012159374542534351,
0.020537296310067177,
0.03364213928580284,
-0.01732303574681282,
-0.012952065095305443,
0.01336281280964613,
0.016389921307563782,
0.009976053610444069,
-0.02279440313577652,
-0.024153389036655426,
0.06759777665138245,
0.055021900683641434,
-0.050908349454402924,
0.008785457350313663,
0.0017605533357709646,
0.04536675289273262,
0.09482226520776749,
0.006481495685875416,
-0.06744427233934402,
-0.048357874155044556,
0.023919975385069847,
-0.029578210785984993,
-0.035693779587745667,
-0.009894187562167645,
-0.010525498539209366,
0.0013949864078313112,
-0.017002813518047333,
0.012922891415655613,
-0.042264122515916824,
0.008528942242264748,
-0.022068466991186142,
0.05840800702571869,
0.06804613023996353,
0.053377389907836914,
-0.006399218924343586,
0.0550396703183651,
-0.05183695629239082,
-0.06402907520532608,
0.02942783199250698,
-0.006894049234688282,
-0.05109667405486107,
-0.0503927543759346,
0.011557020246982574,
0.003961585927754641,
0.006405593361705542,
-0.004798016510903835,
-0.03702600300312042,
0.03887622803449631,
-0.032107844948768616,
-0.05588831007480621,
-0.04683489352464676,
0.06447475403547287,
-0.0363929457962513,
-0.022545795887708664,
-0.08409372717142105,
0.006520457565784454,
0.0021736917551606894,
0.060893990099430084,
-0.0010380320018157363,
0.0007601604447700083,
0.019792256876826286,
0.07860951125621796,
0.005624018609523773,
-0.03655123710632324,
-0.020164452493190765,
-0.040295012295246124,
0.004322890657931566,
0.03726780042052269,
-0.05977893993258476,
0.012586764059960842,
0.019480546936392784,
0.027912795543670654,
-0.05779815465211868,
0.033046968281269073,
-0.062226079404354095,
0.009985844604671001,
0.03888304531574249,
-0.007303876802325249,
-0.0612398162484169,
0.07931674271821976,
0.03390893340110779,
0.0018149729585275054,
0.004889455623924732,
0.03026686981320381,
-0.008150110952556133,
0.012070096097886562,
-0.015445874072611332,
0.03295908123254776,
-0.01286027580499649,
0.014301853254437447,
0.017177574336528778,
0.013573633506894112,
0.011199303902685642,
0.0019151675514876842,
0.005343219731003046,
0.015696918591856956,
0.010644007474184036,
0.02615654468536377,
0.017577610909938812,
0.002681742887943983,
0.01832783780992031,
0.03276218846440315,
-0.05262336879968643,
0.007057866547256708,
-0.022603632882237434,
0.06130132079124451,
-0.024224910885095596,
0.004415254108607769,
0.043901313096284866,
0.000246384966885671,
0.04969773069024086,
-0.027451282367110252,
0.015543957240879536,
-0.012235172092914581,
0.0034108366817235947,
0.018714426085352898,
-0.009636146947741508,
-0.012339891865849495,
0.05481275916099548,
0.0011558390688151121,
-0.022361844778060913,
-0.014978601597249508,
0.019993050023913383,
-0.04664892330765724,
-0.0028673354536294937,
-0.013946371152997017,
0.04040400683879852,
-0.056167714297771454,
-0.0035198242403566837,
0.03910894691944122,
0.005230755545198917,
0.01818159595131874,
0.00643259147182107,
-0.026620307937264442,
0.030205359682440758,
0.07296156138181686,
0.000233434620895423,
0.01642308197915554,
0.024890730157494545,
-0.0032739548478275537,
-0.026103559881448746,
0.02167280949652195,
-0.03201083093881607,
-0.053107522428035736,
-0.02395898476243019,
0.029685506597161293,
0.04329030588269234,
-0.030558187514543533,
-0.019463663920760155,
0.011770069599151611,
0.03404328227043152,
0.07635903358459473,
0.017851771786808968,
-0.0026058065705001354,
-0.05034183710813522,
0.020356714725494385,
0.022351866587996483,
0.0019254760118201375,
0.016502419486641884,
0.0020727808587253094,
0.020998859778046608,
0.046913232654333115,
-0.012195775285363197,
-0.0018854791997000575,
-0.028144611045718193,
0.04040564224123955,
0.03795561194419861,
-0.012480584904551506,
-0.04394067823886871,
-0.002425471553578973,
-0.021631035953760147,
-0.03311316296458244,
0.02941209077835083,
0.01551098469644785,
-0.012005427852272987,
-0.03490925580263138,
-0.004290583543479443,
0.018937915563583374,
0.02439218759536743,
-0.02504749782383442,
-0.029617933556437492,
0.027554219588637352,
-0.04094279929995537,
0.01028955727815628,
0.01262386329472065,
0.013857454061508179,
0.0021810985635966063,
0.01998676359653473,
0.017264502122998238,
-0.026998817920684814,
0.02895343117415905,
-0.03370828181505203,
-0.02008523792028427,
-0.016943642869591713,
-0.05660722777247429,
-0.028810856863856316,
0.0002901773841585964,
-0.04181404039263725,
0.026517022401094437,
-0.05840418115258217,
-0.03382982686161995,
0.01818200573325157,
-0.006108966656029224,
-0.0029867119155824184,
0.025679053738713264,
-0.032413192093372345,
-0.05215717479586601,
-0.005763231310993433,
0.014208532869815826,
0.04234978184103966,
-0.07266432046890259,
0.022819940000772476,
0.04173683375120163,
-0.005572446621954441,
-0.01878574676811695,
0.018182575702667236,
-0.029414119198918343,
-0.04315623268485069,
-0.020213093608617783,
-0.016230890527367592,
0.04309166595339775,
-0.06438307464122772,
0.0007221262203529477,
0.0281370859593153,
-0.0609063021838665,
-0.008747905492782593,
-0.03209790587425232,
-0.04794377461075783,
0.050487421452999115,
0.00533262686803937,
0.05579888075590134,
0.007418183609843254,
-0.03183600306510925,
0.01268259808421135,
-0.0005217083962634206,
-0.050128258764743805,
-0.01679113321006298,
-0.006356398109346628,
-0.010569506324827671,
-0.0750206783413887,
0.019075844436883926,
0.06898268312215805,
-0.04927991330623627,
-0.0006531343678943813,
0.040424805134534836,
0.00845946092158556,
0.045799244195222855,
0.032344747334718704,
-0.012575390748679638,
-0.01454415824264288,
0.017240010201931,
0.013298739679157734,
0.04597316309809685,
0.007928385399281979,
-0.04359220340847969,
0.015906017273664474,
-0.017119022086262703,
0.01289138663560152,
0.05002870410680771,
-0.02881081961095333,
0.027012646198272705,
0.01670151948928833,
-0.02834928408265114,
-0.06822019070386887,
0.03473919630050659,
-0.03617231920361519,
0.05107139050960541,
0.00981205701828003,
0.008137870579957962,
0.005039911717176437,
0.015433993190526962,
0.02077009156346321,
0.004366864450275898,
0.03605654090642929,
0.004222246818244457,
-0.043726541101932526,
-0.021297626197338104,
-0.0023280465975403786,
0.0322042852640152,
-0.027849840000271797,
-0.0008052984485402703,
0.045250024646520615,
-0.015521924011409283,
-0.014177410863339901,
-0.013020513579249382,
-0.03701058775186539,
-0.004480044357478619,
-0.03107091225683689,
0.001334420987404883,
0.004977092612534761,
0.00455927848815918,
-0.002403438789770007,
0.09233196079730988,
0.01983269676566124,
0.02057354338467121,
0.035002440214157104,
-0.01301212515681982,
-0.06779353320598602,
0.005832166410982609,
-0.003237406723201275,
-0.0003861000295728445,
-0.03382554650306702,
-0.013517007231712341,
-0.01774486154317856,
-0.030362790450453758,
-0.0052258619107306,
0.018077721819281578,
-0.010786086320877075,
-0.06452404707670212,
0.01966117136180401,
-0.025698542594909668,
-0.025878017768263817,
-0.03316435590386391,
0.039157576858997345,
0.0028275656513869762,
-0.026109473779797554,
0.03532814607024193,
0.00663579860702157,
-0.034798480570316315,
0.018257705494761467,
-0.02425617352128029,
-0.00351916765794158,
0.021641889587044716,
0.024994876235723495,
0.046799514442682266,
0.010386510752141476,
-0.018489602953195572,
0.07430499792098999,
0.0255118478089571,
0.05371915176510811,
-0.03360218554735184,
-0.020399151369929314,
-0.03027375042438507,
-0.06627269834280014,
-0.00489346869289875,
-0.004362584091722965,
0.049627017229795456,
0.008509398438036442,
-0.008166691288352013,
-0.015197424218058586,
-0.010055027902126312,
-0.008254311047494411,
0.019747508689761162,
0.024044277146458626,
0.011238393373787403,
-0.05793572589755058,
-0.06316643208265305,
-0.0407993420958519,
-0.027395933866500854,
0.0017209568759426475,
0.0035251544322818518,
0.05004937946796417,
0.01258033886551857,
0.02415706217288971,
-0.004742148332297802,
-0.00007394390559056774,
-0.005506299901753664,
-0.018776463344693184,
0.008728569373488426,
-0.010104365646839142,
-0.015703992918133736,
-0.008496453054249287,
-0.0012492560781538486,
0.010363169945776463,
0.01645895279943943,
-0.029456187039613724,
-0.01806666888296604,
-0.08727452903985977,
-0.0013141310773789883,
0.007734328508377075,
0.016926705837249756,
-0.02735937014222145,
0.026361657306551933,
-0.04437948018312454,
-0.03545709699392319,
0.029830822721123695,
0.005590447690337896,
0.004197700414806604,
-0.01888199895620346,
-0.00048634939594194293,
-0.02120933309197426,
-0.012594158761203289,
-0.0096619613468647,
0.03384869918227196,
-0.014663999900221825,
-0.021079514175653458,
-0.027256637811660767,
-0.013943405821919441,
0.002744299126788974,
0.03477942571043968,
0.028241101652383804,
0.013159949332475662,
-0.008889037184417248,
0.003927802201360464,
0.025606974959373474,
0.019769743084907532,
-0.01996835507452488,
-0.03802070766687393,
0.02778022363781929,
0.030255068093538284,
-0.03418882563710213,
0.0343896821141243,
-0.031681839376688004,
-0.044432539492845535,
0.033277496695518494,
0.03113436885178089,
-0.0035633216612040997,
0.007489833980798721,
-0.009141645394265652,
0.049418460577726364,
-0.021036287769675255,
-0.0059827580116689205,
0.03217288479208946,
0.04116763919591904,
0.012423585169017315,
-0.010589494369924068,
-0.00024062328157015145,
0.04646128788590431,
-0.00250583840534091,
0.02105090208351612,
0.002253960585221648,
0.007435633800923824,
-0.032754525542259216,
0.050219565629959106,
0.02300053834915161,
0.02142789401113987,
-0.020206725224852562,
-0.018187016248703003,
-0.0008130771457217634,
0.04627472534775734,
0.00809470284730196,
-0.019208118319511414,
0.013063804246485233,
0.05328004062175751,
0.04127288609743118,
-0.0016229936154559255,
-0.003799469443038106,
-0.011449244804680347,
-0.006981112528592348,
0.05166224017739296,
-0.010847920551896095,
0.00840593222528696,
-0.0106946537271142,
-0.0121886832639575,
0.021291717886924744,
-0.033931486308574677,
0.05118131637573242,
-0.0011907784501090646,
0.029461976140737534,
0.022167561575770378,
-0.06142062321305275,
0.03166113793849945,
0.046611253172159195,
-0.03335489705204964,
0.029674837365746498,
-0.06052044406533241,
-0.001063742209225893,
0.0031569842249155045,
0.01711096242070198,
-0.024642005562782288,
-0.037203025072813034,
0.03146883845329285,
0.056648820638656616,
0.00804935023188591,
-0.02139255590736866,
-0.010124709457159042,
-0.05195172503590584,
-0.017307329922914505,
0.014246344566345215,
0.014755652286112309,
-0.033547960221767426,
0.011152727529406548,
0.027581727132201195,
0.0015888626221567392,
0.046227797865867615,
0.017160968855023384,
-0.0012900104047730565,
-0.012518786825239658,
-0.04417966306209564,
0.006249000318348408,
-0.014290308579802513,
0.05729990452528,
-0.031303007155656815,
-0.016389131546020508,
-0.03669312968850136,
0.009588446468114853,
0.04294971376657486,
-0.004142974503338337,
0.04158434644341469,
-0.005263775587081909,
0.010192576795816422,
-0.006406804081052542,
-0.02008112147450447,
0.0077309515327215195,
0.01293850690126419,
0.014584466814994812,
-0.027923481538891792,
-0.02833678387105465,
-0.04666063189506531,
-0.009670866653323174,
-0.008909926749765873,
0.04439961165189743,
0.024393819272518158,
-0.04346877336502075,
0.07088197767734528,
-0.03510938584804535,
-0.0073088062927126884,
0.02429424785077572,
-0.026892714202404022,
0.06854739040136337,
-0.009418490342795849,
-0.024495722725987434,
-0.01099839061498642,
-0.001957281958311796,
-0.007557522505521774,
-0.020449962466955185,
-0.04123101010918617,
-0.010963136330246925,
0.0561043806374073,
-0.05364616587758064,
0.016384301707148552,
0.04394315183162689,
-0.03153062239289284,
-0.01055290549993515,
-0.01856943406164646,
-0.04204125702381134,
0.010616345331072807,
-0.058635491877794266,
0.0409289188683033,
-0.018045101314783096,
-0.026302160695195198,
0.01620621234178543,
0.03228830546140671,
-0.007463737390935421,
0.002519164700061083,
0.038745831698179245,
0.04249291121959686,
0.014652764424681664,
-0.005453754682093859,
-0.010767127387225628,
0.02497122995555401,
-0.06527824699878693,
0.034067414700984955,
-0.011268624104559422,
-0.015855593606829643,
0.05847124755382538,
0.0461726039648056,
0.02448994852602482,
-0.04774883762001991,
0.01891389861702919,
-0.05402979254722595,
0.01950506493449211,
0.0038280796725302935,
0.02166612260043621,
0.01150076650083065,
-0.004725192207843065,
0.005727744661271572,
0.01207425445318222,
0.013505164533853531,
-0.012848756276071072,
-0.0823264941573143,
-0.002472714288160205,
0.023621654137969017,
-0.021474940702319145,
0.014365560375154018,
0.016684515401721,
-0.05271798372268677,
0.06075993925333023,
-0.036194805055856705,
0.016080405563116074,
-0.025154104456305504,
0.008820570074021816,
-0.0023183010052889585,
0.04620799794793129,
-0.00018097952124662697,
0.024863798171281815,
-0.016692770645022392,
0.032911840826272964,
0.09581176191568375,
0.01860494539141655,
0.02608077973127365,
-0.0658453181385994,
0.014124668203294277,
-0.023985201492905617,
0.022607456892728806,
-0.048066820949316025,
0.015590525232255459,
0.005877186544239521,
0.009431381709873676,
-0.008052820339798927,
0.06837575137615204,
0.006522896233946085,
0.024287790060043335,
0.021924512460827827,
-0.03457808494567871,
-0.0016537474002689123,
-0.008089755661785603,
0.0018740565283223987,
-0.04390810802578926,
0.03447754681110382,
-0.048562753945589066,
-0.0014018340734764934,
-0.01781364530324936,
-0.022438090294599533,
-0.024264678359031677,
-0.02846735157072544,
0.015022370964288712,
-0.005263293161988258,
-0.05427319556474686,
0.032454825937747955,
-0.024705814197659492,
-0.03764837980270386,
-0.053229693323373795,
0.04619503393769264,
0.02025190182030201,
-0.02243262343108654,
-0.010839625261723995,
0.014450316317379475,
0.024889076128602028,
-0.001272384892217815,
-0.00112480903044343,
0.023757528513669968,
-0.011891527101397514,
-0.0022684347350150347,
0.0015610110713168979,
0.015805542469024658,
0.020171109586954117,
-0.014211071655154228,
-0.005191779229789972,
0.04978153109550476,
0.02793785184621811,
-0.04451674968004227,
0.00495626637712121,
0.007895903661847115,
0.01289554312825203,
0.005662709940224886,
0.024179676547646523,
0.009612210094928741,
-0.010274028405547142,
0.041871339082717896,
0.00360875204205513,
0.015725327655673027,
0.017884105443954468,
-0.021556373685598373,
-0.021999768912792206,
0.038381434977054596,
-0.003022377146407962,
-0.023561323061585426,
-0.026131831109523773,
0.03304484486579895,
-0.03920382261276245,
0.036111604422330856,
-0.005715749226510525,
0.033124152570962906,
0.02181852050125599,
-0.019721990451216698,
-0.009026588872075081,
0.0007973350584506989,
-0.0484604574739933,
0.056231286376714706,
0.0016428716480731964,
-0.0004874263540841639,
-0.030432336032390594,
-0.033345337957143784,
0.018108582124114037,
0.009217937476933002,
-0.03644701838493347,
-0.038520850241184235,
-0.021270878612995148,
0.029199345037341118,
0.03462672978639603,
-0.03311602398753166,
-0.02289997600018978,
-0.013878576457500458,
0.015105794183909893,
-0.04354775696992874,
0.014576418325304985,
0.06572096049785614,
0.021609235554933548,
0.007503051310777664,
0.005481350235641003,
0.019803248345851898,
-0.04844237118959427,
0.009308832697570324,
-0.00227451347745955,
-0.02885941043496132,
-0.02926645427942276,
0.009929941035807133,
0.004814689978957176,
-0.0020946799777448177,
-0.056691352277994156,
0.00020103895803913474,
-0.010478372685611248,
-0.009304558858275414,
0.018504181876778603,
-0.016199368983507156,
-0.0039554620161652565,
-0.012980308383703232,
-0.0008470105240121484,
-0.017469435930252075,
0.01814800687134266,
-0.033280570060014725,
0.013696600683033466,
0.00664987787604332,
0.018091101199388504,
-0.0029674083925783634,
0.052173513919115067,
-0.0671464055776596,
-0.03725161403417587,
-0.018991418182849884,
0.026029450818896294,
0.029755376279354095,
-0.024199683219194412,
0.0315893292427063,
-0.03178535774350166,
0.013295846991240978,
0.008425803855061531,
-0.06416182965040207,
0.04223988950252533,
-0.036339253187179565,
-0.056161753833293915,
0.02114362269639969,
-0.001614919165149331,
0.018413396552205086,
-0.003862033598124981,
0.022460350766777992,
-0.0015428015030920506,
0.06116770580410957,
-0.03190255165100098,
0.02286212146282196,
0.003484168089926243,
-0.04312903434038162,
-0.020699935033917427,
0.020449960604310036,
0.06920831650495529,
-0.0009359226678498089,
0.020528916269540787,
0.062379442155361176,
0.035140689462423325,
-0.035530008375644684,
0.036165062338113785,
0.015656234696507454,
-0.0666433572769165,
0.013659062795341015,
0.030797401443123817,
0.010724346153438091,
-0.007824377156794071,
0.09976718574762344,
-0.034646324813365936,
0.019921425729990005,
0.03194218501448631,
-0.018273593857884407,
-0.11426408588886261,
0.019834212958812714,
0.014677543193101883,
-0.025544751435518265,
0.003480779705569148,
-0.05731220170855522,
0.03161870315670967,
0.0020629737991839647,
-0.06813699752092361,
0.02438676729798317,
-0.039102889597415924,
-0.015590771101415157,
-0.07362398505210876,
0.02208777517080307,
-0.032210249453783035,
0.015914354473352432,
0.026796748861670494,
0.006284607108682394,
0.0045671588741242886,
0.024999545887112617,
-0.026389405131340027,
0.0054877521470189095,
0.008023795671761036,
0.004903493449091911,
0.030570248141884804,
0.01613052561879158,
0.061949167400598526,
-0.02602611482143402,
-0.035225506871938705,
0.009087005630135536,
-0.006546938791871071,
0.003110585967078805,
0.0022351101506501436,
-0.016285372897982597,
0.021841153502464294,
0.00003169459887431003,
0.00482421088963747,
0.005864206701517105,
-0.004169841296970844,
0.04662074148654938,
0.008822946809232235,
0.007746008690446615,
-0.01884024776518345,
-0.016254832968115807,
-0.0017236614366993308,
-0.021298905834555626,
-0.0034271276090294123,
0.022338559851050377,
-0.029077930375933647,
-0.016949651762843132,
0.031889401376247406,
0.008350777439773083,
0.02862323448061943,
0.0005436654901131988,
0.017562704160809517,
-0.037690866738557816,
0.017208071425557137,
0.018721960484981537,
0.054171547293663025,
-0.03877789527177811,
-0.002214813604950905,
0.0027403910644352436,
0.02967483550310135,
-0.04392202943563461,
-0.026525404304265976,
-0.03176301345229149,
-0.020443368703126907,
-0.042838357388973236,
-0.03967763110995293,
-0.0038743873592466116,
-0.0001671454665483907,
0.010522514581680298,
0.005094383377581835,
0.058590665459632874,
0.045507170259952545,
0.05406517907977104,
0.029211802408099174,
-0.02899581752717495,
-0.04867444187402725,
-0.056085966527462006,
0.017953261733055115,
-0.0020514787174761295,
-0.02851274609565735,
-0.017836717888712883,
0.025551246479153633,
0.01445571519434452,
0.061236798763275146,
0.07775279879570007,
0.02599242329597473,
0.0050240070559084415,
0.01129540428519249,
-0.029816502705216408,
0.002498697256669402,
-0.0092025026679039,
-0.017295267432928085,
0.02594238892197609,
-0.030186662450432777,
0.002820041961967945,
0.0035240263678133488,
0.015252179466187954,
0.0029856606852263212,
0.041306111961603165,
-0.011059528216719627,
0.020457429811358452,
-0.02086951956152916,
-0.0324140265583992,
0.0316411629319191,
0.043992433696985245,
-0.04726891219615936,
0.07301553338766098,
-0.05296555161476135,
-0.037168920040130615,
-0.0010768186766654253,
-0.007506486494094133,
-0.05593197047710419,
0.021255940198898315,
-0.01010294258594513,
0.015429126098752022,
-0.020224256440997124,
-0.029428618028759956,
0.004838547669351101,
-0.008418030105531216,
-0.013485623523592949,
0.002272279467433691,
-0.06420635432004929,
0.019757110625505447,
0.05484200268983841,
0.04196469858288765,
0.0096180010586977,
0.007713422179222107,
-0.023851696401834488,
0.016200389713048935,
0.035613272339105606,
-0.04027509316802025,
0.05577128380537033,
0.03845880180597305,
-0.004856679122895002,
-0.017472531646490097,
0.013666855171322823,
-0.011033564805984497,
0.0151206711307168,
-0.005441570188850164,
-0.00010727417975431308,
-0.0204925499856472,
-0.01780964620411396,
-0.006011846009641886,
-0.039704181253910065,
0.0033895925153046846,
0.02469189092516899,
0.0019075841410085559,
0.0856190100312233,
-0.008651623502373695,
0.0027663582004606724,
-0.00555826211348176,
-0.01208886131644249,
0.016616765409708023,
-0.011432643979787827,
0.032937776297330856,
0.0014205803163349628,
0.004420725628733635,
-0.009016039781272411,
-0.007314683403819799,
-0.02997964434325695,
0.02857489511370659,
-0.038271769881248474,
0.00553981214761734,
-0.0011340833734720945,
-0.0018076011911034584,
0.027678662911057472,
-0.032619234174489975,
-0.004102809354662895,
0.012325302697718143,
0.036043401807546616,
0.025599591434001923,
0.0027039668057113886,
0.009978463873267174,
0.0057574911043047905,
-0.003355338703840971,
0.05600634589791298,
-0.06910969316959381,
-0.022420834749937057,
0.018429303541779518,
0.05653994530439377,
-0.01331066619604826,
0.02204773761332035
] |
<p>If a body is resting on the ground, the Normal force equals its weight. If I keep putting another body on top of it, eventually the body will start moving into the ground until the new Normal equals the total weight of the body. I can add more weight on top and the body will move further into the ground. So it appears that the denser the object gets, the more the Normal force. </p>
<p>So my question is 3 folds:</p>
<ol>
<li><p>Is it accurate to say that the normal force depends on the density of the object that the reference object is sitting on? </p></li>
<li><p>It appears that when the body starts moving into the ground, the equation at any given time t will be Mg - N(t) = Ma where M is the total mass which essentially says that the force that the ground feels on it at time t is N which will keep changing with time and become Mg at some point where acceleration becomes 0? </p></li>
<li><p>If I draw a free-body diagram of an object moving horizontally forward(just to distinguish from backward) because of force applied on it, I will have two forces - The external force applied on it and the force of friction resisting its motion and the equation will be<br>
F - $\mu$mg = ma or<br>
F = m($\mu$g + a)<br>
When I draw the free body diagram of the person pushing the object, I will have three forces - the reaction from the body that is being pushed, the force of friction in the forward direction and the force applied by the person in the opposite direction to his/her movement (a kick backwards). The equation for the person will be<br>
$\mu$Mg -R -F$_{b}$ = Ma or<br>
R = M($\mu$g -a) - F$_{b}$<br>
It would seem that perhaps the reaction to Force F will not be the same as F. Shouldn't action and reaction be the same? </p></li>
</ol>
| 8,313 |
[
-0.0341079942882061,
-0.012083019129931927,
0.002369735622778535,
-0.0032230056822299957,
0.03066958114504814,
-0.0020958324894309044,
-0.006080913357436657,
-0.0080880057066679,
0.002235714579001069,
-0.02706538513302803,
-0.019618676975369453,
0.009856052696704865,
0.05853872001171112,
0.016093838959932327,
0.028616366907954216,
-0.01905464194715023,
-0.01201207097619772,
-0.03229774162173271,
0.011704572476446629,
-0.008954981341958046,
-0.014857818372547626,
0.0011787420371547341,
0.04507308825850487,
-0.03137773647904396,
-0.0041716620326042175,
0.014417297206819057,
0.00288529135286808,
-0.03634218871593475,
0.01992899924516678,
0.053607236593961716,
-0.012099656276404858,
0.0005999461282044649,
-0.020790088921785355,
-0.01669955626130104,
0.05406610295176506,
0.046422600746154785,
-0.009992496110498905,
-0.013089594431221485,
-0.005048313643783331,
0.02665216475725174,
-0.03937498852610588,
0.013714161701500416,
-0.0025305948220193386,
0.0502043180167675,
-0.06266587972640991,
0.027309859171509743,
0.01572190225124359,
-0.00550976162776351,
0.0652950331568718,
-0.06427742540836334,
0.09129542112350464,
-0.017108995467424393,
0.056214671581983566,
0.05238032713532448,
0.001853322726674378,
-0.044435471296310425,
0.07027331739664078,
0.06586597859859467,
-0.0028885824140161276,
-0.04543608799576759,
0.003849895903840661,
-0.04864955320954323,
-0.05500165373086929,
-0.006042770110070705,
0.022909026592969894,
0.040961261838674545,
-0.030332516878843307,
-0.0018171250121667981,
0.02247106283903122,
-0.0009805115405470133,
-0.004381333943456411,
0.012456987053155899,
0.038728516548871994,
-0.028901202604174614,
-0.0049135442823171616,
-0.0025711962953209877,
0.059944700449705124,
0.010077260434627533,
0.009905483573675156,
0.038104355335235596,
-0.026165641844272614,
0.020170917734503746,
0.03650509938597679,
0.05976675823330879,
0.04042915254831314,
-0.0215848907828331,
0.05563933029770851,
0.004023095592856407,
0.0013487815158441663,
0.04095759242773056,
-0.003013279987499118,
0.029759690165519714,
-0.0044668554328382015,
-0.025571897625923157,
-0.016107844188809395,
0.04583106189966202,
-0.011133352294564247,
0.036545973271131516,
0.02291392907500267,
-0.00020486237190198153,
-0.010335376486182213,
-0.030600234866142273,
0.011356506496667862,
0.04354959353804588,
0.011133385822176933,
-0.010090244933962822,
-0.06531926989555359,
-0.022944603115320206,
-0.020943941548466682,
0.0026153111830353737,
-0.0420064702630043,
-0.0005485606379806995,
-0.04030896723270416,
-0.010418393649160862,
0.010105838999152184,
-0.013599366880953312,
0.0022102794609963894,
-0.006482625845819712,
0.05281127989292145,
0.015810135751962662,
0.027507305145263672,
-0.0349515937268734,
0.02631615847349167,
-0.04984447732567787,
-0.05778791010379791,
-0.014729835093021393,
0.024237388744950294,
-0.02445921301841736,
-0.02718515135347843,
0.03557982295751572,
0.014403651468455791,
-0.0227231215685606,
0.0016418680315837264,
-0.01459562312811613,
0.054274071007966995,
-0.0035668043419718742,
-0.07490045577287674,
-0.034278951585292816,
0.04442941024899483,
0.0074973683804273605,
0.030656488612294197,
-0.09485968947410583,
-0.029008472338318825,
0.03993108496069908,
0.046604495495557785,
0.010322638787329197,
-0.00960499793291092,
-0.011104156263172626,
0.046196386218070984,
-0.004496841225773096,
0.015401212498545647,
-0.03572830185294151,
-0.010432844050228596,
-0.041115596890449524,
-0.018692752346396446,
-0.09690888226032257,
0.058850277215242386,
0.01926424168050289,
-0.0034171848092228174,
-0.004858859349042177,
0.06565570831298828,
-0.02052336558699608,
-0.015409378334879875,
0.004168688785284758,
-0.041502658277750015,
-0.003414832754060626,
0.05750005319714546,
0.009525172412395477,
-0.018034303560853004,
0.03679516911506653,
0.054964445531368256,
0.02785230427980423,
-0.013860908336937428,
0.030154582113027573,
0.031101839616894722,
-0.03340788558125496,
-0.006463594734668732,
-0.026397528126835823,
-0.007593766786158085,
-0.00740522425621748,
-0.020135847851634026,
-0.028864912688732147,
-0.04159069433808327,
0.006350906100124121,
0.023473486304283142,
-0.0011057949159294367,
0.0162394717335701,
0.023715775460004807,
-0.019073687493801117,
-0.03881751000881195,
-0.04145985469222069,
-0.11245347559452057,
0.04827045276761055,
-0.00864002201706171,
0.004128092434257269,
0.008270390331745148,
0.028497053310275078,
0.04214527830481529,
-0.035261690616607666,
-0.02619137428700924,
0.00527041545137763,
0.016454875469207764,
-0.002307285089045763,
-0.03611376881599426,
0.01512820739299059,
0.05845407024025917,
0.009155183099210262,
0.00416897376999259,
-0.0010369839146733284,
-0.03663868457078934,
-0.01667071133852005,
0.018114766106009483,
-0.04147942364215851,
0.005711758974939585,
0.013700908981263638,
0.026210131123661995,
0.005214788485318422,
-0.0041435291059315205,
-0.00795502308756113,
0.03752289339900017,
-0.017738686874508858,
0.05087883770465851,
0.06761261075735092,
-0.017228374257683754,
-0.006747257895767689,
0.023659203201532364,
0.017447633668780327,
0.0005406609270721674,
0.006758242845535278,
-0.02509419247508049,
-0.05217349901795387,
-0.05202605575323105,
-0.02980428747832775,
-0.0035545912105590105,
-0.02106448821723461,
0.030895467847585678,
0.044773928821086884,
0.026567991822957993,
0.030732667073607445,
0.014517979696393013,
0.010191500186920166,
-0.05407468229532242,
-0.00014896881475578994,
0.03809179738163948,
0.001920344540849328,
0.002809941302984953,
-0.015097860246896744,
0.03551652655005455,
-0.01947558857500553,
-0.02783813513815403,
0.020393475890159607,
0.01183486171066761,
0.01193204429000616,
0.02167324721813202,
0.016094805672764778,
-0.04644541069865227,
0.030143387615680695,
0.009175480343401432,
0.03834502398967743,
0.046012114733457565,
-0.012592642568051815,
-0.022918665781617165,
-0.07581666857004166,
-0.034645818173885345,
0.016822226345539093,
0.014449921436607838,
-0.01068548671901226,
0.004314698278903961,
0.037413470447063446,
-0.03504801541566849,
-0.02072726935148239,
-0.03781132772564888,
0.004143812693655491,
-0.03607828915119171,
0.010661532171070576,
-0.012015974149107933,
0.008083443157374859,
0.040561504662036896,
-0.028989527374505997,
0.009343533776700497,
0.009062394499778748,
-0.01758466474711895,
0.024004938080906868,
-0.009433134458959103,
-0.044627804309129715,
-0.01327778585255146,
-0.055217988789081573,
-0.048288825899362564,
0.024164235219359398,
0.04549491032958031,
0.005476346239447594,
0.06157257780432701,
0.0037821561563760042,
-0.040055204182863235,
-0.032852184027433395,
-0.01268923468887806,
-0.03388672694563866,
0.02015581913292408,
-0.01455899141728878,
0.045070547610521317,
0.0002920601691585034,
-0.005683925934135914,
0.013134281150996685,
-0.04701095074415207,
-0.05557069182395935,
-0.0413399413228035,
-0.015798378735780716,
-0.0010891573037952185,
-0.007496417034417391,
-0.014418204315006733,
0.043213341385126114,
-0.031995989382267,
-0.010448780842125416,
-0.06553176045417786,
-0.02362351305782795,
0.016612838953733444,
-0.007032456807792187,
0.11011912673711777,
0.010260408744215965,
-0.04597627371549606,
0.09760170429944992,
0.05447124317288399,
-0.01390071865171194,
-0.03280609846115112,
-0.004095963202416897,
-0.008059564977884293,
-0.07470791041851044,
-0.00215681130066514,
0.01734582521021366,
-0.016596553847193718,
-0.0019478105241432786,
0.005564047023653984,
0.010104173794388771,
0.015204103663563728,
0.013507787138223648,
-0.017402565106749535,
0.023435065522789955,
0.03195573762059212,
-0.012842902913689613,
0.031704943627119064,
0.03233884647488594,
0.004656401462852955,
0.020410481840372086,
-0.030414510518312454,
0.05659951642155647,
-0.02341102808713913,
-0.05677669122815132,
0.07781057804822922,
0.012498723343014717,
0.00396403344348073,
-0.056531526148319244,
0.03848779574036598,
0.012326909229159355,
-0.04321460798382759,
-0.010266697034239769,
0.02550504170358181,
0.03400304168462753,
-0.023246388882398605,
-0.00753589766100049,
0.03846927732229233,
0.034749891608953476,
-0.018648695200681686,
-0.08671163767576218,
0.015080433338880539,
0.010097365826368332,
0.017045924440026283,
-0.05564559996128082,
0.005256930366158485,
0.011399177834391594,
0.021910572424530983,
0.03650251030921936,
0.001999930012971163,
-0.03057991713285446,
-0.003235351061448455,
-0.07501242309808731,
-0.032537706196308136,
0.008008797653019428,
0.035912033170461655,
-0.02220802567899227,
0.04056324064731598,
-0.0029180736746639013,
0.006057274993509054,
0.05544241890311241,
0.016304731369018555,
-0.1090431660413742,
0.035201240330934525,
-0.04313703253865242,
-0.009449413977563381,
0.02253616787493229,
-0.004092333372682333,
-0.0038658007979393005,
-0.022374199703335762,
-0.02985590510070324,
0.013408455066382885,
0.021337304264307022,
-0.0646045133471489,
-0.014692960307002068,
-0.05194864049553871,
-0.03275531157851219,
0.00043616045149974525,
0.017039069905877113,
0.015197927132248878,
-0.01810319535434246,
0.03341411054134369,
0.032059647142887115,
-0.01152962539345026,
-0.010111724026501179,
-0.039638929069042206,
-0.018490727990865707,
0.02470845729112625,
0.015909215435385704,
0.026116542518138885,
0.025587307289242744,
-0.017425300553441048,
0.031087206676602364,
0.007738876156508923,
0.02232237160205841,
0.030141698196530342,
-0.017879802733659744,
-0.02341345138847828,
-0.06697463989257812,
-0.05214233323931694,
0.017398949712514877,
0.023113347589969635,
-0.01850350946187973,
0.010429850779473782,
-0.007381632458418608,
0.004095439333468676,
0.028301574289798737,
0.05757870152592659,
0.04005483165383339,
-0.011189610697329044,
-0.034697216004133224,
-0.049130335450172424,
-0.009200027212500572,
-0.030573952943086624,
-0.006133994087576866,
0.024147620424628258,
0.013080824166536331,
-0.0206700898706913,
0.01907459832727909,
0.019408732652664185,
0.057885028421878815,
0.02730168215930462,
-0.006052790209650993,
-0.0114439120516181,
0.01143268495798111,
0.004590870346873999,
0.010267270728945732,
-0.011937721632421017,
0.05573902651667595,
0.05201055854558945,
-0.03009267896413803,
-0.021964646875858307,
-0.06472166627645493,
-0.023901566863059998,
0.03135080263018608,
0.0041718329302966595,
0.0125587098300457,
0.022029660642147064,
-0.022970203310251236,
-0.02295331098139286,
0.026947369799017906,
-0.02737034112215042,
0.03554308041930199,
-0.012245112098753452,
0.047813087701797485,
-0.003298672614619136,
-0.033242300152778625,
-0.06036549061536789,
-0.0193768497556448,
-0.03305508941411972,
0.007494786754250526,
-0.017766067758202553,
0.013504860922694206,
-0.0040710135363042355,
0.018639851361513138,
-0.002378472127020359,
0.03140012174844742,
-0.014596426859498024,
-0.023492911830544472,
-0.0231862124055624,
-0.017882395535707474,
-0.029523557052016258,
-0.08351187407970428,
-0.034222811460494995,
-0.013542105443775654,
0.005063008051365614,
-0.01792830601334572,
-0.011733639054000378,
-0.055388882756233215,
0.014806638471782207,
0.0024333472829312086,
-0.03600603714585304,
-0.015326154418289661,
-0.030067970976233482,
0.061725735664367676,
0.03085831180214882,
-0.017225975170731544,
0.017515230923891068,
-0.004334823694080114,
0.02144438773393631,
-0.001391753670759499,
0.00009573419811204076,
0.007018663454800844,
0.022076189517974854,
0.032356295734643936,
-0.0419052354991436,
0.0053048026748001575,
-0.034993864595890045,
0.043668799102306366,
0.003603231394663453,
0.014065220952033997,
-0.020349839702248573,
-0.045576587319374084,
0.005006413906812668,
0.02330675721168518,
-0.003371103201061487,
0.05410755053162575,
0.03692587837576866,
-0.02718059904873371,
0.010454198345541954,
0.0044015562161803246,
-0.005413122475147247,
-0.0012711299350485206,
0.02029801346361637,
0.04883882775902748,
0.005150460638105869,
0.037807807326316833,
-0.01555320993065834,
-0.02815404161810875,
0.004954288713634014,
-0.04529590159654617,
0.043153535574674606,
0.02380758337676525,
0.02989780344069004,
0.04004484415054321,
-0.023085881024599075,
0.0038659926503896713,
0.020121099427342415,
-0.026577474549412727,
-0.0032265521585941315,
-0.02405591309070587,
0.022997746244072914,
0.022505629807710648,
0.04531355947256088,
-0.0342957004904747,
-0.03886706754565239,
0.03585837781429291,
-0.01728198677301407,
-0.005579599644988775,
-0.015394279733300209,
0.00610130513086915,
0.001674104598350823,
-0.04630588740110397,
0.03931263089179993,
0.0759885236620903,
-0.027438262477517128,
-0.02109404280781746,
0.0510779544711113,
0.015888884663581848,
0.032211873680353165,
-0.004954248666763306,
-0.02830263413488865,
-0.04037841036915779,
-0.004506789613515139,
-0.024137945845723152,
-0.0205747839063406,
0.047110412269830704,
-0.04037611931562424,
-0.015055646188557148,
-0.018967630341649055,
-0.029119865968823433,
0.061098385602235794,
-0.006981614511460066,
-0.014603890478610992,
0.04126964136958122,
0.010377197526395321,
0.003414626931771636,
-0.03997282683849335,
0.030435649678111076,
0.026813136413693428,
0.040679920464754105,
0.01252173725515604,
0.01458263024687767,
-0.023127427324652672,
-0.007922947406768799,
0.01825593039393425,
0.010536938905715942,
0.014845049940049648,
0.00691359955817461,
0.08499959856271744,
0.002377383643761277,
0.0016033693682402372,
0.0006788115133531392,
-0.037007637321949005,
0.08558312803506851,
-0.003128407057374716,
-0.04382699728012085,
0.03440186753869057,
0.004734480287879705,
-0.009281886741518974,
0.000985773396678269,
-0.023077262565493584,
-0.01174312736839056,
0.04348204284906387,
-0.028767094016075134,
0.07709404826164246,
0.03538535162806511,
0.008055165410041809,
0.0003584254300221801,
0.0020982257556170225,
-0.003994505386799574,
-0.022644294425845146,
0.0014276630245149136,
0.04670381173491478,
-0.056773193180561066,
0.005745664704591036,
0.045244667679071426,
0.017335666343569756,
-0.04116924852132797,
0.0035383799113333225,
0.029468495398759842,
-0.0013265961315482855,
0.030507707968354225,
-0.027743978425860405,
-0.020691797137260437,
0.04811697080731392,
-0.013607787899672985,
0.043190356343984604,
0.0064019327983260155,
-0.04919282719492912,
0.05883801355957985,
0.05927637591958046,
0.003959667403250933,
-0.03494878485798836,
-0.0013372390531003475,
-0.023112617433071136,
-0.009175663813948631,
-0.0015775148058310151,
0.019695384427905083,
-0.005750305950641632,
-0.009238911792635918,
0.03157117962837219,
-0.0207308791577816,
0.004007657524198294,
0.008834630250930786,
-0.06346539407968521,
-0.014994105324149132,
-0.02939237467944622,
-0.041481129825115204,
0.02250491827726364,
-0.036181509494781494,
-0.04076533019542694,
0.03545837104320526,
-0.030903633683919907,
0.04119912162423134,
0.009655128233134747,
0.013049491681158543,
-0.006625779904425144,
0.08947352319955826,
-0.03571755439043045,
0.013168318197131157,
-0.01551392488181591,
0.004857371561229229,
0.12549591064453125,
0.042015984654426575,
0.023094024509191513,
-0.024171927943825722,
-0.022828593850135803,
-0.03262663632631302,
-0.0042744288221001625,
0.013578692451119423,
0.008324149064719677,
0.03297937661409378,
-0.006309296935796738,
-0.008517147041857243,
0.040077343583106995,
-0.024942029267549515,
-0.04913588613271713,
0.06648987531661987,
-0.017130451276898384,
-0.03431367129087448,
0.005245449021458626,
0.02010364457964897,
-0.019536202773451805,
0.00892577413469553,
0.013903629034757614,
0.022448396310210228,
0.02258649282157421,
0.0015491588274016976,
-0.0022338456474244595,
-0.022085728123784065,
0.01466723158955574,
-0.022256243973970413,
-0.08249866217374802,
0.025735272094607353,
0.01070860680192709,
-0.040599118918180466,
-0.03926105797290802,
0.03863712400197983,
0.010158676654100418,
-0.055288057774305344,
0.017156243324279785,
0.05290347337722778,
0.009531195275485516,
0.03225364908576012,
0.03549761325120926,
-0.012843256816267967,
-0.046191710978746414,
0.02187720686197281,
-0.03863963112235069,
0.05578331649303436,
-0.027175970375537872,
-0.00020685243362095207,
0.020719287917017937,
0.011005483567714691,
0.022284768521785736,
-0.02778886817395687,
-0.01648293063044548,
0.00012805554433725774,
0.05997500941157341,
0.009860722348093987,
0.015608242712914944,
-0.0018154011340811849,
0.00896231085062027,
0.04346582666039467,
-0.025382906198501587,
0.012470684014260769,
0.019060827791690826,
0.03249826282262802,
0.004800526425242424,
0.044439300894737244,
-0.02824302762746811,
-0.00213194009847939,
-0.04672515392303467,
-0.008039810694754124,
-0.04036102071404457,
-0.001569146290421486,
0.0023064669221639633,
0.06121411547064781,
0.034033600240945816,
0.0019888062961399555,
0.013281970284879208,
-0.049593232572078705,
-0.04256761446595192,
0.027308369055390358,
-0.02150775119662285,
0.015079915523529053,
-0.030849386006593704,
-0.012612602673470974,
-0.00552178593352437,
0.053552284836769104,
0.004088700283318758,
0.004993801470845938,
0.024243302643299103,
0.03972442075610161,
0.01777241751551628,
-0.028357796370983124,
-0.031768232583999634,
0.02680528163909912,
-0.02929433062672615,
0.01828549988567829,
-0.010857149958610535,
0.0040250979363918304,
0.004378392361104488,
0.006523405201733112,
-0.007266268599778414,
0.03327786549925804,
0.008176823146641254,
0.014596087858080864,
0.021505294367671013,
-0.020482970401644707,
0.009770079515874386,
0.030462656170129776,
0.007383494637906551,
-0.01998039148747921,
-0.026183487847447395,
-0.004781671799719334,
-0.0029661820735782385,
-0.034988660365343094,
0.008645562455058098,
-0.018242647871375084,
0.0010295126121491194,
-0.0358576774597168,
0.041258931159973145,
-0.004224126692861319,
-0.004605107940733433,
-0.057612769305706024,
-0.024962469935417175,
0.048675306141376495,
-0.005958541762083769,
-0.011611862108111382,
0.039471469819545746,
-0.007784034591168165,
0.019982587546110153,
-0.0002553662343416363,
0.006078445818275213,
0.0002667269727680832,
-0.007332451641559601,
0.010359351523220539,
-0.01834695041179657,
0.04426165670156479,
0.008471802808344364,
-0.004537730477750301,
0.025106506422162056,
-0.032356515526771545,
-0.048939529806375504,
0.03478251397609711,
0.01739717274904251,
0.01398355420678854,
0.005176339764147997,
-0.01775408908724785,
0.0010204426944255829,
0.07129092514514923,
-0.018852490931749344,
-0.004081551916897297,
-0.008598390966653824,
-0.025040140375494957,
-0.05094488337635994,
-0.03282758966088295,
0.017260050401091576,
0.006491855718195438,
0.005360250826925039,
0.013949970714747906,
-0.0024858831893652678,
-0.02474074438214302,
-0.001903204945847392,
0.015779519453644753,
-0.016241874545812607,
-0.035126522183418274,
0.012941579334437847,
0.01968039758503437,
0.038010962307453156,
0.02747713029384613,
-0.016524601727724075,
-0.0012312490725889802,
0.008023669011890888,
0.000035002001823158935,
-0.1079227551817894,
-0.01781228929758072,
0.02168024517595768,
-0.0132388761267066,
0.02734384872019291,
-0.054012756794691086,
-0.017351234331727028,
0.010212366469204426,
-0.08065848797559738,
0.004559214226901531,
-0.02839594893157482,
-0.014761745929718018,
0.013803972862660885,
-0.006440252531319857,
0.044301312416791916,
0.025929931551218033,
-0.0005756390746682882,
0.0404122918844223,
-0.0060567306354641914,
0.0013408975210040808,
-0.034217651933431625,
-0.003941357135772705,
0.027669545263051987,
0.041358817368745804,
-0.009522013366222382,
-0.005139961373060942,
0.05013366788625717,
-0.03499773517251015,
-0.04062547907233238,
0.004750783089548349,
-0.028159959241747856,
0.03665556758642197,
-0.023867137730121613,
-0.0003941822506021708,
-0.031233802437782288,
0.006398869678378105,
0.011557463556528091,
-0.005724741145968437,
0.03140893951058388,
0.052538663148880005,
0.010545849800109863,
0.03538772091269493,
-0.0396357998251915,
0.0025728577747941017,
-0.001152395037934184,
-0.04799949377775192,
-0.02888054959475994,
0.01609877496957779,
-0.002151952125132084,
-0.0055024828761816025,
0.0022641702089458704,
-0.0016426298534497619,
0.010430118069052696,
0.005410070065408945,
-0.00795438140630722,
-0.044884420931339264,
0.011886798776686192,
0.04159640148282051,
-0.012310624122619629,
-0.012346251867711544,
0.030727023258805275,
0.013784256763756275,
0.009263063780963421,
-0.011039904318749905,
-0.0228725653141737,
-0.03829577565193176,
-0.05227496474981308,
-0.023855194449424744,
-0.0025490056723356247,
-0.025064509361982346,
-0.03434821963310242,
-0.036591339856386185,
-0.02642090432345867,
0.04039373621344566,
0.024317605420947075,
0.006632369942963123,
0.010792109183967113,
-0.06231642886996269,
-0.039480168372392654,
-0.07534793764352798,
0.030617330223321915,
0.024453746154904366,
-0.030653513967990875,
-0.03653622418642044,
-0.005548629444092512,
-0.005503869615495205,
-0.008977016434073448,
0.060558442026376724,
0.006539502646774054,
0.0015726684359833598,
-0.0025702568236738443,
-0.007204126566648483,
0.03599477931857109,
-0.04487919062376022,
0.000927773246075958,
0.004236309323459864,
0.016156097874045372,
0.022684747353196144,
0.020536547526717186,
-0.017191529273986816,
-0.002056361874565482,
0.007341282907873392,
-0.01958460547029972,
0.015266908332705498,
-0.005114289000630379,
-0.009420429356396198,
0.03300393000245094,
0.04549098014831543,
-0.010502415709197521,
0.04796141758561134,
-0.02753475122153759,
0.017987726256251335,
0.045161377638578415,
-0.048041049391031265,
-0.051104914397001266,
0.03839715197682381,
-0.0009294520132243633,
-0.012235485017299652,
-0.012660160660743713,
-0.016163740307092667,
0.00567167904227972,
-0.04576050862669945,
-0.003848414868116379,
0.01351726334542036,
-0.0128775704652071,
-0.010592053644359112,
0.017500819638371468,
0.050701163709163666,
0.026533259078860283,
-0.034322552382946014,
0.024134742096066475,
0.013166888616979122,
0.003737708320841193,
0.01076928898692131,
-0.0021232429426163435,
0.019860034808516502,
-0.02852439135313034,
-0.01926947571337223,
0.06284062564373016,
0.0015922203892841935,
0.03738989681005478,
0.018825115635991096,
0.02209015190601349,
-0.02532959170639515,
0.010059214197099209,
0.006990831810981035,
0.020109405741095543,
0.03502015769481659,
0.0053781806491315365,
0.012067077681422234,
0.04821733385324478,
-0.02404949814081192,
-0.011285175569355488,
0.010654046200215816,
0.0006453997921198606,
-0.0016138259088620543,
0.015375416725873947,
-0.0077178808860480785,
0.01535092294216156,
-0.02273925580084324,
-0.007530738599598408,
-0.013395030982792377,
0.006384385749697685,
0.04752827435731888,
0.019967982545495033,
0.00042989818030036986,
0.035488300025463104,
-0.001851174863986671,
-0.000011412131243559998,
0.0020939090754836798,
-0.02899639867246151,
-0.01584768295288086,
0.07582937926054001,
0.05066503956913948,
-0.0012746331049129367,
-0.019263137131929398,
0.0025209560990333557,
-0.0163597222417593,
0.05101672187447548,
-0.05530682951211929,
-0.06116726994514465,
-0.04950008913874626,
0.03896399214863777,
0.029172522947192192,
-0.020430395379662514
] |
<p>Recently a "U" shaped scratch appeared on my car's front tire. It looks like someone rolled past a curb and scraped it. This has led me to the following problem:</p>
<p>Generate a plot (ideally polar) of a scratch pattern on a tire given tire radius and the ground height of a protrusion. Assume the protrusion is a single point and remains stationary while the tire rolls past. Also assume that the tire rolls straight past the protrusion, which scratches the side of the tire (i.e. hubcap, trim, etc).</p>
<p>If I wasn't so rusty on this material I would have taken a stab at it myself. So, any help in setting up and solving this problem would be greatly appreciated.</p>
| 8,314 |
[
-0.03297245502471924,
-0.019963672384619713,
0.011971480213105679,
0.05116340145468712,
0.02283664047718048,
-0.026411768049001694,
-0.024857062846422195,
0.014473236165940762,
0.01558029092848301,
-0.019655674695968628,
0.0048696985468268394,
0.0821542963385582,
0.022652851417660713,
0.039580587297677994,
0.013989478349685669,
-0.03662287816405296,
-0.02775857038795948,
-0.05180324986577034,
0.02122551016509533,
-0.02217179164290428,
-0.011910093948245049,
-0.029651029035449028,
0.02642790786921978,
-0.006428729277104139,
-0.009926453232765198,
0.026572320610284805,
0.05065819248557091,
-0.01326755154877901,
0.007971787825226784,
0.04981877654790878,
-0.049009665846824646,
0.007528289221227169,
-0.0006069321534596384,
0.014077247120440006,
0.04324931278824806,
0.0162349846214056,
-0.04024262726306915,
0.0015245884424075484,
-0.05874393507838249,
0.027831271290779114,
-0.02913016267120838,
0.00723271444439888,
-0.006307083182036877,
0.05865193158388138,
-0.025110885500907898,
0.017202377319335938,
0.020201824605464935,
-0.001291401800699532,
0.04695882648229599,
-0.04609118402004242,
0.07411505281925201,
-0.03771313652396202,
0.025016600266098976,
0.02251299098134041,
-0.03237316757440567,
-0.007741284556686878,
0.06589803099632263,
0.08133896440267563,
0.0017366979736834764,
-0.025284720584750175,
-0.034905243664979935,
-0.03040837123990059,
-0.03274412080645561,
-0.026894427835941315,
-0.059433721005916595,
0.025307005271315575,
-0.023383833467960358,
-0.03523031622171402,
0.0232263021171093,
-0.04336150363087654,
-0.0008341881330125034,
0.008161778561770916,
0.018934372812509537,
-0.0208046343177557,
-0.005206819623708725,
-0.057674579322338104,
0.002200912917032838,
0.022710079327225685,
0.01011179480701685,
0.013890624977648258,
0.006170330103486776,
0.0064751808531582355,
0.04030928760766983,
0.053239792585372925,
0.003924700431525707,
-0.00704998429864645,
0.06481929123401642,
-0.00012977617734577507,
0.019270630553364754,
0.045022815465927124,
0.01834675669670105,
-0.00850538071244955,
0.045540113002061844,
0.0018044635653495789,
-0.0051841773092746735,
0.006533219013363123,
-0.03460261598229408,
0.03501497581601143,
-0.003364281728863716,
-0.012072515673935413,
-0.009655588306486607,
-0.02858920395374298,
0.029156610369682312,
0.05624593794345856,
0.003840337973088026,
-0.012106535024940968,
0.02945406548678875,
0.00952434167265892,
0.034027114510536194,
-0.023370960727334023,
-0.01593010127544403,
0.04671226441860199,
-0.004694199189543724,
-0.011666101403534412,
-0.007726716343313456,
0.006039015017449856,
-0.008312854915857315,
-0.012646481394767761,
0.007288504857569933,
0.040414959192276,
0.02484877221286297,
-0.06437595933675766,
0.02453300729393959,
-0.04683588445186615,
-0.04727073013782501,
-0.020851824432611465,
0.037179529666900635,
-0.012213741429150105,
-0.029578736051917076,
0.027689065784215927,
-0.020022446289658546,
-0.034970130771398544,
0.040578823536634445,
-0.021622013300657272,
0.023056671023368835,
-0.019802775233983994,
-0.06714588403701782,
-0.04839889705181122,
0.0013375732814893126,
0.02236768789589405,
0.015142128802835941,
-0.0596688874065876,
0.009338309057056904,
0.02588837221264839,
0.05475795269012451,
0.01519044954329729,
0.00460792938247323,
0.026571309193968773,
0.03410578891634941,
-0.008846791461110115,
0.015125026926398277,
-0.01439336035400629,
-0.03265964612364769,
-0.05747425928711891,
0.01042212639003992,
-0.03870055079460144,
0.026645682752132416,
0.006934576202183962,
-0.005402328912168741,
-0.025571634992957115,
0.02037012204527855,
0.011186514981091022,
0.03556877002120018,
0.00019776602857746184,
-0.03658672794699669,
-0.009548974223434925,
0.07057387381792068,
-0.0007964334799908102,
-0.004683992825448513,
0.025218497961759567,
-0.0007899649208411574,
0.03165001422166824,
0.021153133362531662,
0.0072497115470469,
0.06969752162694931,
-0.04283575341105461,
0.009895210154354572,
-0.009642371907830238,
0.008191446773707867,
0.02893814444541931,
-0.03304522484540939,
-0.019656507298350334,
0.004166952800005674,
-0.0018820660188794136,
0.009038969874382019,
0.02808554098010063,
-0.005389714613556862,
-0.020426437258720398,
0.060665570199489594,
-0.004378015175461769,
-0.047863464802503586,
-0.04974374547600746,
0.020513055846095085,
-0.012869996950030327,
-0.008716423995792866,
-0.0008944383589550853,
0.01786765269935131,
0.03940880298614502,
-0.033054497092962265,
-0.02954675629734993,
0.006521111354231834,
0.033026766031980515,
0.04603470861911774,
-0.0683569386601448,
-0.010870142839848995,
0.02611294388771057,
0.03469038009643555,
-0.013173418119549751,
0.01763380877673626,
-0.056259263306856155,
0.00749714532867074,
-0.010596933774650097,
-0.04454397037625313,
-0.001064583659172058,
-0.033337149769067764,
0.03160887584090233,
0.018905261531472206,
0.019082192331552505,
0.01566152088344097,
0.02119281515479088,
-0.051432788372039795,
0.05733909830451012,
0.1003202274441719,
0.041444648057222366,
0.0065703969448804855,
-0.012833599001169205,
-0.028510460630059242,
0.0365607813000679,
-0.009080370888113976,
-0.027495142072439194,
-0.04485829174518585,
-0.001234630704857409,
0.05531303957104683,
0.02466762252151966,
-0.03441717475652695,
-0.0041384631767869,
0.07921560108661652,
0.024716094136238098,
0.03657837212085724,
0.05998096987605095,
0.014078882522881031,
0.021298103034496307,
0.01946437917649746,
0.022906947880983353,
0.023783458396792412,
-0.06435773521661758,
-0.008245442062616348,
0.015631506219506264,
0.013661537319421768,
-0.050222430378198624,
-0.04976622387766838,
0.018578944727778435,
-0.005174471531063318,
0.018028104677796364,
0.0008995551033876836,
-0.013793175108730793,
0.07244642823934555,
0.006398526020348072,
0.00007256233948282897,
0.03598790615797043,
0.0023712788242846727,
0.007076125126332045,
-0.014909075573086739,
0.004211924504488707,
0.04991189017891884,
0.04341639205813408,
-0.03445480763912201,
-0.03909819573163986,
0.0269890446215868,
-0.024145277217030525,
0.026982035487890244,
-0.027745436877012253,
-0.02957881987094879,
0.016059452667832375,
0.04516840726137161,
0.032751813530921936,
0.030809491872787476,
0.014156512916088104,
0.0009619014454074204,
-0.0373586006462574,
-0.009741140529513359,
0.0026111064944416285,
-0.007929706946015358,
0.011371931992471218,
-0.06255368888378143,
-0.009195015765726566,
0.003976190462708473,
0.0002742708311416209,
0.038700252771377563,
0.03437812253832817,
-0.03438912332057953,
0.02287500910460949,
0.015260154381394386,
-0.04006459563970566,
-0.03294687718153,
-0.049378179013729095,
0.021301759406924248,
-0.06068138778209686,
-0.012957198545336723,
0.03372790291905403,
0.004046365153044462,
-0.025952719151973724,
0.06518110632896423,
-0.035694561898708344,
0.023526670411229134,
-0.0225420743227005,
-0.013073033653199673,
0.010343671776354313,
0.005713135469704866,
-0.011820650659501553,
-0.014811496250331402,
-0.013909620232880116,
-0.019688649103045464,
-0.04451362416148186,
-0.06058252230286598,
-0.005325172562152147,
-0.01424180157482624,
0.037919171154499054,
-0.01462617702782154,
-0.00394083047285676,
0.045679885894060135,
0.01840132102370262,
-0.050029587000608444,
-0.04553264379501343,
-0.024543004110455513,
0.003730070311576128,
-0.018727364018559456,
0.0014235398266464472,
0.011687167920172215,
-0.0033760436344891787,
-0.0032343543134629726,
0.005376547574996948,
0.014790304005146027,
0.05925751477479935,
0.06745585799217224,
-0.014910280704498291,
-0.009097781032323837,
-0.019956663250923157,
-0.00909674447029829,
0.021970339119434357,
0.07100291550159454,
-0.02765451744198799,
0.010923570953309536,
0.017555374652147293,
0.03199770674109459,
0.012670869939029217,
-0.019579198211431503,
-0.0024753136094659567,
-0.0067501007579267025,
0.013191157951951027,
-0.019516972824931145,
0.039739321917295456,
0.0049248444847762585,
0.0006688928115181625,
-0.05029035732150078,
0.021035367622971535,
0.061543434858322144,
0.005671690218150616,
0.009139327332377434,
0.049244146794080734,
0.026986341923475266,
-0.029616672545671463,
-0.008206703700125217,
-0.031003771349787712,
-0.02340574562549591,
-0.011558338068425655,
-0.06000426411628723,
0.016690053045749664,
0.034575626254081726,
0.01115589588880539,
0.04228857904672623,
0.04225276783108711,
-0.06779085099697113,
0.017382251098752022,
-0.06924410909414291,
-0.021942419931292534,
-0.028059635311365128,
0.054494306445121765,
-0.006547657772898674,
0.03230581805109978,
0.012236255221068859,
-0.009219513274729252,
0.00581287732347846,
0.011317810975015163,
-0.08253644406795502,
0.05904332175850868,
0.0053737168200314045,
-0.009286428801715374,
-0.009144250303506851,
-0.010090451687574387,
-0.015907837077975273,
-0.03937975689768791,
0.041519347578287125,
0.03887902572751045,
-0.0016929912380874157,
-0.05242908373475075,
0.023828202858567238,
-0.0032251703087240458,
-0.01554066687822342,
-0.04124932363629341,
0.030571550130844116,
0.06194791570305824,
-0.04165710136294365,
0.02079695649445057,
0.03878352791070938,
-0.014313839375972748,
0.00795380212366581,
-0.034991007298231125,
0.0067197298631072044,
-0.02566659264266491,
0.047276195138692856,
-0.02348966710269451,
0.010476472787559032,
0.03194904699921608,
0.010218463838100433,
-0.0019937437027692795,
0.02764761447906494,
0.029872920364141464,
-0.019609879702329636,
-0.01683628186583519,
-0.054128583520650864,
-0.0036483623553067446,
0.010001705028116703,
0.029006168246269226,
-0.06836473941802979,
-0.00335554382763803,
0.03594377264380455,
0.008992394432425499,
-0.04824654385447502,
0.011758903972804546,
0.08072463423013687,
0.039586905390024185,
-0.0014254163252189755,
-0.07940761744976044,
-0.03421295806765556,
0.005272058770060539,
0.00476866913959384,
0.032237812876701355,
-0.018926972523331642,
-0.005601119250059128,
-0.006201480980962515,
0.024110695347189903,
-0.03061661869287491,
-0.03231034800410271,
0.01607242226600647,
-0.030228236690163612,
0.04966093227267265,
-0.036228280514478683,
-0.021524149924516678,
0.030319616198539734,
0.02933822199702263,
0.04691556096076965,
0.02443310059607029,
-0.04265672340989113,
-0.08845233917236328,
0.015768960118293762,
0.039294540882110596,
0.009747940115630627,
-0.002240514848381281,
-0.04687673971056938,
-0.029320305213332176,
-0.004799992777407169,
0.05207043141126633,
-0.05777614563703537,
0.032192207872867584,
-0.01943284645676613,
0.007288394495844841,
-0.01984488032758236,
-0.030220860615372658,
-0.07137248665094376,
0.03588009998202324,
-0.01976042240858078,
0.024836283177137375,
-0.010712938383221626,
-0.05080636590719223,
-0.03826691210269928,
0.025797639042139053,
-0.006064290180802345,
0.05810161679983139,
0.028742149472236633,
-0.0024736111517995596,
-0.03907785937190056,
-0.008913637138903141,
-0.00196895026601851,
-0.04873356595635414,
-0.013972899876534939,
0.008705017156898975,
0.01251211017370224,
0.011699817143380642,
-0.007781331427395344,
0.01646505482494831,
0.031196726486086845,
-0.008424176834523678,
0.01351536437869072,
0.0008042148547247052,
-0.029074301943182945,
0.020848842337727547,
0.031635962426662445,
0.030093995854258537,
0.059722501784563065,
0.049637168645858765,
0.048545386642217636,
0.0017953811911866069,
-0.016881655901670456,
0.021070711314678192,
0.03620896488428116,
-0.05837690830230713,
-0.030548661947250366,
0.0000822939837235026,
-0.04833017289638519,
0.002255177590996027,
-0.00863846205174923,
0.01728714443743229,
-0.057333532720804214,
-0.012838572263717651,
-0.027525465935468674,
0.014270971529185772,
0.012566464953124523,
0.0005440616514533758,
0.04270672798156738,
-0.0162295401096344,
0.026652179658412933,
0.003501883242279291,
-0.018170220777392387,
-0.016733935102820396,
0.002329065930098295,
0.02104722149670124,
-0.006266543176025152,
-0.032487574964761734,
-0.008649580180644989,
-0.013675794005393982,
-0.012402926571667194,
-0.05677932873368263,
0.06453638523817062,
-0.022387925535440445,
0.06115499138832092,
0.04628489166498184,
-0.06548221409320831,
0.031119992956519127,
0.06419043987989426,
0.024035725742578506,
0.0496441014111042,
-0.06504879891872406,
0.009144083596765995,
0.007268507033586502,
0.01086740754544735,
-0.017485082149505615,
-0.08931015431880951,
0.03808857128024101,
0.02933160960674286,
-0.03376428037881851,
-0.007381201721727848,
-0.02915952540934086,
0.008869769982993603,
-0.05874029919505119,
-0.00830397754907608,
0.046664923429489136,
-0.0038728469517081976,
0.007101207971572876,
0.01332701276987791,
0.010010446421802044,
0.056485604494810104,
-0.020138021558523178,
0.012221048586070538,
0.023448748514056206,
-0.034462664276361465,
-0.03882516920566559,
-0.005806117318570614,
0.042612090706825256,
-0.05129076912999153,
-0.0005890533793717623,
-0.017659330740571022,
0.00486214691773057,
0.03288845717906952,
-0.002429200569167733,
-0.00793517753481865,
0.012279313057661057,
0.03252331539988518,
-0.018399571999907494,
-0.032647307962179184,
0.008424665778875351,
0.012397188693284988,
-0.025322325527668,
-0.019652266055345535,
-0.006970343180000782,
0.007316178642213345,
-0.01848643273115158,
0.010694416239857674,
0.037834446877241135,
0.0032850736752152443,
-0.018373997882008553,
0.046985432505607605,
0.004719683900475502,
-0.023341285064816475,
0.031784579157829285,
-0.019387489184737206,
0.006030483171343803,
-0.011617273092269897,
0.014245407655835152,
0.044744763523340225,
0.013603324070572853,
-0.019861755892634392,
-0.01877683587372303,
-0.005143603775650263,
0.0012511505046859384,
0.05313828960061073,
0.0010259398259222507,
0.02247697114944458,
0.0786537304520607,
0.020869435742497444,
-0.019896522164344788,
0.009642055258154869,
-0.05444364622235298,
0.01506874430924654,
0.01709291711449623,
0.061762094497680664,
-0.008665674366056919,
0.0419074185192585,
0.00030376360518857837,
0.0012831937056034803,
0.021296676248311996,
0.033490389585494995,
0.008101292885839939,
0.01869664154946804,
0.026823105290532112,
0.009531846269965172,
-0.0452519953250885,
-0.014526688493788242,
-0.016481474041938782,
0.057922039180994034,
0.016523374244570732,
-0.026185795664787292,
0.06636723130941391,
0.03090796060860157,
0.014211395755410194,
-0.01886863261461258,
0.00437134550884366,
-0.027742477133870125,
0.007739841006696224,
0.00918575655668974,
-0.0033548627980053425,
0.00908749457448721,
0.037723954766988754,
0.015390907414257526,
-0.016128767281770706,
0.03979625552892685,
-0.056682977825403214,
-0.0313788466155529,
-0.0053557478822767735,
-0.037210140377283096,
-0.030967438593506813,
0.043462123721838,
0.018328692764043808,
-0.005491900257766247,
0.06455574929714203,
-0.03471601381897926,
0.020179839804768562,
0.019179444760084152,
0.05820564553141594,
-0.0002640013408381492,
0.07441415637731552,
-0.01004109438508749,
0.011416459456086159,
-0.006937780417501926,
-0.013929147273302078,
0.11739466339349747,
0.07168641686439514,
0.031446948647499084,
-0.059149060398340225,
0.0016765022883191705,
-0.03174477443099022,
-0.019597357138991356,
-0.021034205332398415,
0.026280445978045464,
-0.008450756780803204,
-0.006989619228988886,
0.04046880081295967,
0.05105769261717796,
-0.011771928519010544,
0.02415863797068596,
0.07234226912260056,
-0.030344879254698753,
-0.004515620414167643,
-0.019990574568510056,
-0.007576356176286936,
-0.030065564438700676,
0.035924505442380905,
-0.03386538848280907,
0.0012622441863641143,
0.00007707665645284578,
-0.04492306709289551,
-0.05801749601960182,
-0.04769132286310196,
0.0022447637747973204,
0.015966493636369705,
-0.01747140660881996,
0.03391857445240021,
-0.009665107354521751,
-0.008019310422241688,
-0.03676656633615494,
-0.005794443655759096,
-0.00018508698849473149,
-0.0010652381461113691,
0.03303302824497223,
0.043798670172691345,
0.029823370277881622,
-0.001411859062500298,
0.00005496157973539084,
-0.00041084419353865087,
-0.01727280765771866,
0.0058234333992004395,
-0.07366622239351273,
0.06277547776699066,
-0.017924243584275246,
0.00005730825796490535,
-0.014505279250442982,
0.008285705000162125,
0.029526980593800545,
-0.035440873354673386,
0.013695898465812206,
-0.0007769237854517996,
0.01798560470342636,
-0.03525564819574356,
-0.04264805093407631,
0.020953292027115822,
0.034489452838897705,
0.04027275741100311,
-0.0024963871110230684,
0.008087792433798313,
-0.03978218883275986,
-0.018547803163528442,
0.0014361245557665825,
0.06931157410144806,
-0.027807103469967842,
-0.02720598503947258,
0.0006108786910772324,
-0.028324130922555923,
-0.01586797833442688,
-0.009970461018383503,
0.0035789799876511097,
0.02859485149383545,
0.019489968195557594,
-0.0013230472104623914,
-0.015992378816008568,
0.02460339479148388,
-0.0064498609863221645,
0.03698715567588806,
-0.03322932869195938,
-0.04009311646223068,
-0.041198648512363434,
-0.015268518589437008,
0.04214620217680931,
0.026194319128990173,
-0.02544831857085228,
-0.012387029826641083,
-0.008001421578228474,
0.05841146782040596,
-0.00003040509545826353,
-0.010177992284297943,
-0.0022668763995170593,
0.035120364278554916,
-0.04504043236374855,
0.023217689245939255,
-0.0013262589927762747,
0.00507848896086216,
0.033813949674367905,
0.009822120890021324,
-0.005305586848407984,
0.02459457889199257,
-0.030851371586322784,
0.020874211564660072,
0.008918375708162785,
-0.06635665148496628,
-0.021609129384160042,
-0.017653442919254303,
-0.021357515826821327,
-0.043520379811525345,
-0.010169360786676407,
-0.004000470042228699,
-0.04355035349726677,
-0.032868392765522,
0.007953428663313389,
-0.04663177952170372,
0.026968425139784813,
-0.05623668432235718,
0.008695300668478012,
-0.04648594930768013,
0.011264011263847351,
-0.02798137255012989,
-0.0031739857513457537,
0.027975095435976982,
0.008734549395740032,
-0.005366200115531683,
0.02408534474670887,
-0.04405593499541283,
0.007940273731946945,
-0.008956817910075188,
0.006008374039083719,
0.004002029076218605,
0.03769958019256592,
0.041233550757169724,
-0.002636532299220562,
0.02402716502547264,
-0.015035907737910748,
-0.007506849244236946,
0.043314699083566666,
-0.04348484426736832,
-0.05854365602135658,
-0.003294807393103838,
-0.009167509153485298,
0.02757967822253704,
0.0038776854053139687,
-0.003521815873682499,
0.03279729560017586,
0.03937968984246254,
0.012413069605827332,
-0.03751828521490097,
0.0040545277297496796,
0.029455680400133133,
0.013349826447665691,
-0.015436926856637001,
0.004854989238083363,
-0.041239891201257706,
-0.00452177319675684,
-0.00042318322812207043,
0.0155038982629776,
-0.03576141595840454,
-0.016463832929730415,
0.010020291432738304,
0.00008690269169164822,
-0.013562579639256,
0.011128298006951809,
0.012561144307255745,
0.04446576535701752,
0.02635585516691208,
-0.03698526322841644,
-0.016334427520632744,
-0.024381713941693306,
-0.019633647054433823,
-0.05900929495692253,
-0.029458608478307724,
0.007949119433760643,
-0.005579380318522453,
0.042564135044813156,
-0.07358592003583908,
-0.012939848937094212,
0.05964361131191254,
-0.04654499888420105,
0.0037857431452721357,
-0.02333153411746025,
-0.002612933749333024,
-0.024693084880709648,
0.006639175582677126,
-0.0032212031073868275,
-0.0005437665386125445,
0.04393775016069412,
0.058279454708099365,
0.05408826470375061,
-0.0035111065953969955,
-0.05853753909468651,
0.014905664138495922,
0.0379820391535759,
0.012106204405426979,
0.016609925776720047,
-0.013989186845719814,
0.0333942174911499,
-0.005917408037930727,
-0.005009585991501808,
0.012147320434451103,
-0.035663776099681854,
-0.011236819438636303,
-0.00477232551202178,
0.0008146153413690627,
0.014708776958286762,
0.03158397972583771,
-0.000296353071462363,
-0.012776591815054417,
-0.01776573620736599,
-0.00969124399125576,
-0.0011241250904276967,
0.03250943124294281,
-0.013559488579630852,
0.0181413646787405,
0.02110856957733631,
0.00309615395963192,
-0.047228891402482986,
0.01422932930290699,
-0.02032450959086418,
-0.015000030398368835,
-0.005457742139697075,
0.0037165002431720495,
0.009507846087217331,
-0.04914454370737076,
-0.008562065660953522,
-0.011224585585296154,
0.0141910957172513,
0.017492985352873802,
-0.030851511284708977,
0.006742831785231829,
0.01730670966207981,
-0.02092229388654232,
-0.06010444089770317,
-0.002326731337234378,
-0.029195737093687057,
-0.06128229945898056,
-0.08437267690896988,
0.028053700923919678,
0.004732478875666857,
-0.043232839554548264,
0.00143724016379565,
0.003946211654692888,
0.00694007333368063,
0.017533238977193832,
-0.0175312627106905,
-0.00028117772308178246,
0.059352170675992966,
-0.015438562259078026,
-0.023590954020619392,
-0.049404487013816833,
0.04024394601583481,
0.007108236663043499,
-0.03787985071539879,
-0.04274711757898331,
-0.018890324980020523,
0.007714761421084404,
0.020507968962192535,
0.01604502461850643,
-0.02984256111085415,
-0.007609847467392683,
0.004544494673609734,
-0.017425626516342163,
0.02913377434015274,
0.000632748007774353,
0.037988126277923584,
-0.006954233627766371,
-0.02007156051695347,
0.00695832772180438,
0.015195432119071484,
0.005794997792690992,
0.029940946027636528,
0.011902358382940292,
0.018366046249866486,
0.012999004684388638,
-0.0016070737037807703,
-0.0585387647151947,
-0.007436741143465042,
0.009858524426817894,
-0.015510166995227337,
0.06922287493944168,
0.042928941547870636,
0.02525932900607586,
0.0008317197789438069,
-0.0035361095797270536,
-0.03096572495996952,
0.03136561065912247,
-0.0593298077583313,
-0.036324623972177505,
-0.03398997336626053,
0.004262148402631283,
0.0492369681596756,
-0.06786110252141953,
0.01924319937825203,
-0.026375271379947662,
-0.029609110206365585,
-0.010957535356283188,
0.006707893218845129,
0.023633260279893875,
0.038911815732717514,
-0.031216947361826897,
0.013679335825145245,
-0.011006741784512997,
-0.03310168907046318,
0.010746250860393047,
0.009975922293961048,
0.006755568087100983,
-0.03825134411454201,
-0.01637253351509571,
0.02334246225655079,
-0.02148868329823017,
0.027679279446601868,
-0.005288625601679087,
0.0644681304693222,
0.019147401675581932,
0.004528861027210951,
-0.004708672408014536,
-0.03375989571213722,
0.020705612376332283,
0.012888600118458271,
-0.03745045140385628,
0.02147683873772621,
-0.007481236010789871,
0.025869326665997505,
-0.017620131373405457,
-0.03969530388712883,
-0.029351402074098587,
0.03616153821349144,
-0.00051549740601331,
0.01705874130129814,
0.01183856651186943,
-0.02715138904750347,
0.003654113970696926,
0.029044125229120255,
0.03287685289978981,
0.012938086874783039,
0.031945258378982544,
-0.00993924867361784,
-0.013103743083775043,
-0.03536711260676384,
-0.004436690825968981,
-0.022105690091848373,
-0.013511943630874157,
0.04184721037745476,
0.01645464077591896,
-0.015611149370670319,
-0.005239794030785561,
0.017958389595150948,
-0.008207670412957668,
0.06603489071130753,
-0.08996491134166718,
-0.01081548910588026,
-0.011115373112261295,
0.017209509387612343,
0.014990830793976784,
-0.020491259172558784
] |
<p>After Apollo 11 first landed on the Moon in 1969, there have been conspiracy theories that this never really happened and that it was all a hoax. In 2010 NASA released photos from its Lunar Reconnaissance Orbiter (LRO) mission of some landing sites which showed both a lunar lander and footprints (as dark trails).</p>
<p>The question is, how big (aperture) of a telescope would you theoretically need on earth to see the lunar module or even better, the dark trail of footprints? What about from orbit, without the atmosphere, would a smaller diameter scope work, how big would it need to be?</p>
| 822 |
[
0.01509406603872776,
-0.051621221005916595,
0.0027994748670607805,
-0.03688380494713783,
0.03519868850708008,
0.015067662112414837,
-0.022685829550027847,
-0.04879557713866234,
-0.006098569370806217,
-0.03708237037062645,
-0.010918186977505684,
0.04615936055779457,
0.032738909125328064,
-0.007387777324765921,
-0.02106551267206669,
0.0031036909203976393,
-0.0035916739143431187,
-0.00751277431845665,
-0.0038552419282495975,
-0.03129834681749344,
0.024011364206671715,
0.008886389434337616,
0.05069902166724205,
0.0015801454428583384,
-0.005076529458165169,
0.029919641092419624,
0.04345836117863655,
-0.01578202098608017,
0.028379760682582855,
0.03711942210793495,
-0.017297428101301193,
0.03158051520586014,
0.06104724854230881,
0.024428868666291237,
-0.0027913202065974474,
0.0015372352208942175,
-0.008166552521288395,
-0.024481255561113358,
-0.017123833298683167,
0.007468807511031628,
-0.018078867346048355,
-0.006730939727276564,
0.01938854716718197,
0.043941207230091095,
-0.03594712167978287,
0.005118677392601967,
-0.023534102365374565,
-0.06037481501698494,
0.03537259250879288,
-0.07206948846578598,
0.029516471549868584,
-0.00893124658614397,
0.045992232859134674,
0.050131671130657196,
-0.0099611422047019,
-0.009351927787065506,
0.06295663863420486,
0.07804178446531296,
0.00008859152876539156,
-0.034045811742544174,
-0.040178801864385605,
0.018230240792036057,
0.018832601606845856,
-0.009402534924447536,
0.001548533677123487,
-0.017428256571292877,
-0.04724152013659477,
0.0048499032855033875,
0.023363225162029266,
0.040986932814121246,
0.0325334370136261,
0.014551485888659954,
0.04369451105594635,
0.042184337973594666,
-0.01123142335563898,
-0.04401885345578194,
0.04205866903066635,
0.02717185579240322,
0.030548695474863052,
0.025909096002578735,
0.007764126639813185,
0.03864869102835655,
0.03064250946044922,
-0.0005482056294567883,
0.03251318633556366,
0.03005826473236084,
0.07720351219177246,
0.00009089350351132452,
-0.015396218746900558,
0.0019872253760695457,
0.0010332190431654453,
0.039362676441669464,
0.025899764150381088,
-0.0013902571517974138,
0.002056938363239169,
0.027048185467720032,
-0.025769971311092377,
0.06345780193805695,
0.02263728156685829,
-0.009170384146273136,
0.008357062935829163,
0.013199458830058575,
0.0039833830669522285,
0.06302483379840851,
0.024923378601670265,
0.02244795486330986,
-0.006721514742821455,
0.013202959671616554,
-0.0006031287484802306,
0.018257657065987587,
-0.025962334126234055,
0.03831255063414574,
0.02744949981570244,
0.005255179014056921,
-0.017968397587537766,
-0.0038749962113797665,
0.00964308436959982,
-0.0485859178006649,
0.053916335105895996,
0.06887812167406082,
0.03105143830180168,
0.013026908971369267,
-0.003047398291528225,
-0.024907777085900307,
-0.04512961953878403,
0.042470782995224,
0.02096279338002205,
-0.021432414650917053,
-0.014714980497956276,
0.02619115263223648,
0.004666336812078953,
0.004110344219952822,
0.02322681061923504,
0.01169258076697588,
0.03612154722213745,
-0.0033423411659896374,
-0.0631626769900322,
-0.07934293895959854,
0.031775373965501785,
0.008885817602276802,
0.007020784541964531,
-0.06110144034028053,
0.01820731908082962,
0.030042901635169983,
0.06824438273906708,
-0.003042636439204216,
0.003079537767916918,
0.017863048240542412,
0.013669022358953953,
-0.029721500352025032,
-0.06252457201480865,
0.008975964970886707,
-0.0067140161991119385,
-0.024224011227488518,
-0.0006477019051089883,
-0.06387574970722198,
0.020862029865384102,
0.03702293336391449,
-0.019063178449869156,
-0.08127398788928986,
0.03673382103443146,
-0.013096773996949196,
0.013327572494745255,
-0.021129988133907318,
-0.02526438795030117,
-0.05358244106173515,
0.0711260735988617,
0.029193608090281487,
-0.007502242457121611,
0.0057900091633200645,
0.026386583223938942,
-0.007002824451774359,
0.044256217777729034,
-0.015624254941940308,
0.047861143946647644,
-0.05096687749028206,
-0.018294235691428185,
-0.029005516320466995,
0.022323649376630783,
0.016201695427298546,
-0.029449649155139923,
-0.01551726646721363,
0.01129597146064043,
0.019756631925702095,
0.039287254214286804,
0.0521189421415329,
-0.0054617878049612045,
-0.003550854278728366,
0.015874803066253662,
0.01882932148873806,
-0.03318855166435242,
-0.030392874032258987,
-0.020295506343245506,
0.04500127211213112,
0.026790011674165726,
0.009316546842455864,
-0.012267056852579117,
-0.004242482129484415,
0.013772784732282162,
0.018512072041630745,
0.033645644783973694,
0.02429352141916752,
0.003052948974072933,
-0.0010006149532273412,
-0.004313998855650425,
0.082527756690979,
0.035491932183504105,
-0.007270898204296827,
0.00013222062261775136,
-0.031222043558955193,
-0.015372656285762787,
-0.022156301885843277,
-0.04147905483841896,
0.027415361255407333,
0.021001644432544708,
0.024599894881248474,
0.014510254375636578,
0.009482630528509617,
0.014652584679424763,
0.04328151419758797,
0.02768762968480587,
0.07605773955583572,
0.04290317744016647,
-0.0029362374916672707,
0.004130748100578785,
-0.021916162222623825,
0.01830555871129036,
-0.019174471497535706,
0.005752215161919594,
-0.017331313341856003,
-0.09051898121833801,
-0.04156285524368286,
0.013157272711396217,
0.008025403134524822,
-0.016613714396953583,
0.011981858871877193,
0.03141113370656967,
0.034890592098236084,
0.03146479278802872,
0.02748524211347103,
-0.023544661700725555,
-0.020711051300168037,
-0.030662812292575836,
0.00018217324395664036,
-0.0035126409493386745,
0.01631568744778633,
-0.005830289330333471,
0.020373044535517693,
0.03382366523146629,
-0.043821897357702255,
-0.023572402074933052,
0.012220525182783604,
0.003970347344875336,
-0.01197110116481781,
-0.02758808620274067,
-0.00045944523299112916,
0.03599092736840248,
0.002905610715970397,
-0.004397892858833075,
-0.011388332583010197,
-0.023432757705450058,
-0.00727479811757803,
-0.08054816722869873,
-0.016357388347387314,
0.01505435723811388,
0.030012449249625206,
-0.0019019696628674865,
-0.008199320174753666,
0.04304260015487671,
-0.047386784106492996,
0.020272865891456604,
-0.039206087589263916,
-0.008377100341022015,
0.0029959643725305796,
0.04080924019217491,
0.049660615622997284,
-0.040884118527173996,
0.022072190418839455,
-0.01838405802845955,
-0.05996488779783249,
-0.010127381421625614,
-0.0014164666645228863,
0.01930955983698368,
0.006577441934496164,
-0.047859176993370056,
0.009440284222364426,
-0.01932234689593315,
-0.0033184210769832134,
0.029259510338306427,
0.006718574091792107,
0.023504501208662987,
-0.0018752811010926962,
-0.023449644446372986,
-0.03199457749724388,
-0.008653700351715088,
0.01160378847271204,
-0.012493036687374115,
-0.01757761836051941,
-0.018205543980002403,
0.043166544288396835,
0.014499464072287083,
-0.026522478088736534,
0.006687377113848925,
-0.03688443452119827,
-0.006400520447641611,
0.003993699327111244,
0.017558375373482704,
-0.009696753695607185,
-0.03301616013050079,
0.014328578487038612,
-0.016371430829167366,
-0.022340338677167892,
0.0258655808866024,
-0.03306971862912178,
-0.035418782383203506,
0.040007591247558594,
-0.008593528531491756,
0.023831717669963837,
-0.001754244090989232,
-0.0019682683050632477,
0.05171765387058258,
0.045155324041843414,
0.02243468537926674,
-0.050714120268821716,
0.005079510156065226,
0.035012949258089066,
-0.043591905385255814,
0.014433566480875015,
0.013076454401016235,
-0.0007575696217827499,
0.04141667112708092,
-0.02268838882446289,
-0.009678073227405548,
-0.01874365471303463,
0.04820303991436958,
-0.007191810756921768,
-0.018233144655823708,
-0.004224258940666914,
-0.009524083696305752,
0.04771299660205841,
0.05491706728935242,
-0.02494642324745655,
0.016274571418762207,
-0.04692061245441437,
0.028999386355280876,
0.03107985109090805,
-0.05552400276064873,
0.009425592608749866,
0.00506212841719389,
-0.02241015061736107,
0.016204049810767174,
0.010317645967006683,
0.010433966293931007,
0.019191188737750053,
-0.021375959739089012,
-0.013829491101205349,
0.055792246013879776,
0.022342197597026825,
-0.06925944983959198,
0.012876329012215137,
0.026388123631477356,
0.011843519285321236,
-0.04825303331017494,
-0.0024823364801704884,
-0.010245565325021744,
-0.007227757945656776,
-0.020529871806502342,
-0.03778699040412903,
0.0204426571726799,
0.021159373223781586,
0.025184161961078644,
0.012511889450252056,
-0.0006953737465664744,
-0.03528076410293579,
-0.024169575423002243,
-0.019492607563734055,
-0.03688695654273033,
0.025995412841439247,
0.04188476875424385,
-0.016212143003940582,
0.022136669605970383,
0.006894493475556374,
0.017696330323815346,
0.010530039668083191,
-0.07958418130874634,
0.0023567050229758024,
-0.03396366536617279,
-0.06555980443954468,
-0.03673354536294937,
0.04062792286276817,
-0.013401600532233715,
-0.02783176861703396,
-0.021272599697113037,
-0.007778962608426809,
0.04368065670132637,
-0.03656291961669922,
0.023394640535116196,
0.01981722190976143,
-0.016593391075730324,
-0.024055421352386475,
0.08308170735836029,
0.02996218018233776,
0.030390320345759392,
0.034076157957315445,
-0.031807538121938705,
-0.025289570912718773,
-0.036024294793605804,
0.01348414458334446,
0.03177005425095558,
-0.06082858517765999,
0.05306922271847725,
0.02032111957669258,
0.024442430585622787,
-0.047720227390527725,
0.003480285871773958,
-0.0051832497119903564,
0.033411744982004166,
-0.04081905633211136,
0.03271516039967537,
-0.037335604429244995,
-0.022422844544053078,
0.0094577232375741,
0.03577903285622597,
0.014996661804616451,
-0.05884412303566933,
0.0036833384074270725,
0.04329903796315193,
-0.03922359645366669,
-0.014003001153469086,
0.011907804757356644,
-0.0038819042965769768,
-0.004093891475349665,
0.008571527898311615,
-0.03337325155735016,
-0.009530303999781609,
-0.042970240116119385,
-0.0036860143300145864,
0.03209823742508888,
0.02207336761057377,
-0.05010755732655525,
-0.010779104195535183,
0.03184865787625313,
0.014398408122360706,
-0.06718283891677856,
0.03290790319442749,
-0.029795151203870773,
0.028751203790307045,
-0.042643316090106964,
-0.010864621959626675,
0.019179657101631165,
0.03012865222990513,
0.0531233586370945,
0.013608813285827637,
-0.02647976577281952,
-0.06368041783571243,
-0.010785742662847042,
-0.0008604628965258598,
0.05284091830253601,
-0.013971220701932907,
-0.019283894449472427,
-0.0526704341173172,
-0.020354434847831726,
0.0198398157954216,
-0.025877181440591812,
0.009260387159883976,
-0.04451899230480194,
0.035860829055309296,
-0.011681005358695984,
-0.01005883514881134,
-0.008995076641440392,
0.003050441388040781,
-0.0084030507132411,
0.011880583129823208,
-0.049163345247507095,
-0.005049471277743578,
-0.015532832592725754,
0.044747494161129,
0.05212539806962013,
0.051660455763339996,
0.05376230552792549,
0.016337241977453232,
0.009979233145713806,
-0.01722162589430809,
-0.04414099454879761,
-0.05246012285351753,
-0.03058088757097721,
-0.0016030279221013188,
-0.04381084442138672,
0.039096999913454056,
-0.03446132317185402,
-0.0288771353662014,
0.030413422733545303,
0.026326343417167664,
-0.001953371800482273,
-0.03675614297389984,
-0.039406199008226395,
-0.03536606580018997,
0.047050509601831436,
0.013276450335979462,
0.05537793040275574,
0.007116112858057022,
0.009059932082891464,
0.06307180970907211,
-0.004154311027377844,
0.02351158671081066,
-0.042870260775089264,
-0.01722034253180027,
0.0036340777296572924,
0.0016649756580591202,
-0.05478038638830185,
0.030722318217158318,
-0.03727339208126068,
0.03754555806517601,
0.030184879899024963,
-0.06067889556288719,
-0.03485148400068283,
0.040553297847509384,
-0.02274838462471962,
0.03614325076341629,
0.026832761242985725,
0.05708232894539833,
0.032024167478084564,
-0.026674920693039894,
0.003597379894927144,
-0.005622983444482088,
0.03062538243830204,
0.012665996327996254,
0.017938580363988876,
0.016759656369686127,
-0.012526116333901882,
0.03033817932009697,
0.019251275807619095,
-0.02452019415795803,
0.10135768353939056,
-0.018254831433296204,
-0.013142388314008713,
0.019970929250121117,
-0.0505736842751503,
-0.011950505897402763,
0.01996261440217495,
-0.04075904190540314,
0.03564341366291046,
-0.08468379825353622,
0.0034843110479414463,
0.019571583718061447,
-0.011690346524119377,
-0.04416489228606224,
0.009199333377182484,
0.001179977087303996,
0.04160813242197037,
-0.007485903333872557,
0.0019623420666903257,
-0.03504611551761627,
0.0007181871333159506,
-0.03727488964796066,
-0.007751900237053633,
0.03761126473546028,
-0.011610268615186214,
-0.028324665501713753,
-0.005667803809046745,
-0.002174660097807646,
0.041833072900772095,
0.0037432394456118345,
-0.024059727787971497,
0.0020231723319739103,
-0.02808823622763157,
-0.04338425397872925,
-0.00707661546766758,
0.01996138133108616,
-0.0650889202952385,
-0.04592921957373619,
-0.04159240424633026,
-0.02185584045946598,
-0.0006212383159436285,
-0.003195591736584902,
-0.019153406843543053,
0.03408736363053322,
0.029725894331932068,
0.01765216886997223,
-0.012060311622917652,
0.034173350781202316,
-0.051601994782686234,
0.049520477652549744,
-0.0069940765388309956,
-0.004111496731638908,
-0.010595054365694523,
-0.034271128475666046,
0.005965051706880331,
0.01853748969733715,
0.013009756803512573,
-0.013277503661811352,
0.028724538162350655,
0.012598102912306786,
-0.011011522263288498,
0.03797077015042305,
0.00007090160215739161,
0.024978606030344963,
-0.0136973662301898,
0.03736705332994461,
0.03701531141996384,
0.00871925801038742,
-0.020554272457957268,
-0.06317100673913956,
-0.010824371129274368,
-0.022354256361722946,
0.033519718796014786,
-0.039448030292987823,
-0.008745511993765831,
-0.0011350990971550345,
-0.019548295065760612,
-0.015220391564071178,
-0.03644977882504463,
-0.016298333182930946,
0.02504650130867958,
0.019994594156742096,
0.030931832268834114,
-0.028168775141239166,
-0.008703373372554779,
0.016942428424954414,
0.04462286829948425,
0.010692186653614044,
0.03473944216966629,
0.02594771608710289,
0.034067049622535706,
0.008046855218708515,
-0.030495544895529747,
-0.021136902272701263,
0.00386047619394958,
-0.032497845590114594,
0.03946038335561752,
-0.003660774091258645,
0.010188459418714046,
0.04443947970867157,
0.008331438526511192,
-0.005511274095624685,
-0.02244851551949978,
-0.04394880682229996,
-0.07366175204515457,
0.006806796416640282,
0.0621175579726696,
0.05156295746564865,
-0.024082543328404427,
-0.03186770901083946,
0.007847490720450878,
-0.011514348909258842,
0.00867405068129301,
-0.013130959123373032,
-0.07289419323205948,
-0.05456981435418129,
-0.021565157920122147,
-0.04007536545395851,
0.04343424737453461,
-0.00020107015734538436,
-0.01133656594902277,
0.009559903293848038,
-0.043093133717775345,
0.001970128156244755,
0.039682164788246155,
0.0703570619225502,
-0.0486188605427742,
0.046540386974811554,
-0.02746153064072132,
0.019518239423632622,
-0.0159552413970232,
0.03325763717293739,
0.12953414022922516,
0.07030672580003738,
0.0006087562069296837,
-0.05406936630606651,
-0.022683775052428246,
-0.050127264112234116,
-0.0007450754637829959,
-0.005714180413633585,
0.0457015223801136,
-0.027159644290804863,
0.011761881411075592,
-0.020623791962862015,
0.0062550995498895645,
-0.0331927128136158,
-0.033715274184942245,
0.018908699974417686,
-0.0002413357433397323,
-0.006109987385571003,
0.01620384491980076,
-0.004678681492805481,
-0.031292419880628586,
0.011885372921824455,
-0.017320644110441208,
0.0068652876652777195,
-0.018766025081276894,
-0.015754928812384605,
-0.03145188093185425,
-0.030420290306210518,
0.025801174342632294,
0.02023192308843136,
-0.04478740692138672,
0.034061599522829056,
-0.00011903121776413172,
-0.021574100479483604,
-0.01564028300344944,
0.03046122007071972,
0.02409042976796627,
0.0013017517048865557,
0.035659678280353546,
0.05133618041872978,
0.006141101010143757,
-0.0001177089216071181,
-0.018889423459768295,
-0.00754612497985363,
-0.052211422473192215,
-0.03946593776345253,
-0.011791985481977463,
0.0403565876185894,
-0.0031349314376711845,
0.004905313719063997,
-0.007943304255604744,
-0.010742167942225933,
-0.008591240271925926,
-0.060047589242458344,
0.00814222265034914,
0.04419859126210213,
0.02991725504398346,
-0.025963446125388145,
-0.04472154378890991,
0.02512199804186821,
0.03087945096194744,
0.015123667195439339,
0.015454722568392754,
0.015366233885288239,
0.03257064148783684,
-0.02708498388528824,
-0.017731253057718277,
0.06483728438615799,
-0.018079383298754692,
-0.0553276464343071,
-0.07416430115699768,
0.029172269627451897,
-0.06342169642448425,
0.02384369447827339,
0.013350940309464931,
0.03211462125182152,
0.0198057908564806,
0.04863215610384941,
-0.014401419088244438,
-0.03338313102722168,
-0.021411890164017677,
0.01039065234363079,
-0.03306591510772705,
-0.007159666623920202,
-0.007786166854202747,
0.014948626980185509,
0.041534535586833954,
-0.0021750819869339466,
-0.03234662115573883,
-0.008349666371941566,
0.012401201762259007,
0.009441113099455833,
0.01395430974662304,
-0.01981716975569725,
-0.010232115164399147,
0.02185695990920067,
-0.01893053948879242,
-0.000059187983424635604,
-0.0023403118830174208,
0.017895139753818512,
0.004299293737858534,
-0.011887737549841404,
0.0050178151577711105,
-0.014686726033687592,
-0.048971809446811676,
0.016129381954669952,
0.015263848938047886,
-0.03641851246356964,
-0.011703386902809143,
-0.0002841138339135796,
0.05065784603357315,
-0.058431439101696014,
-0.043198246508836746,
-0.06261447072029114,
-0.0028432728722691536,
0.03443121165037155,
-0.007968965917825699,
-0.013781609013676643,
0.030330738052725792,
-0.004715869203209877,
0.025510791689157486,
-0.03546128049492836,
0.03116038627922535,
-0.01490072812885046,
0.034132152795791626,
0.008376594632863998,
0.015132686123251915,
-0.022362397983670235,
0.036549162119627,
-0.04022541642189026,
-0.07552355527877808,
-0.00367739237844944,
0.007526197005063295,
-0.0006422983133234084,
0.03854930400848389,
-0.007427881471812725,
0.0018093854887410998,
0.05371968448162079,
-0.0026098533999174833,
-0.006812123581767082,
0.04818233475089073,
-0.029813038185238838,
-0.06458640098571777,
0.04249546304345131,
-0.02157922089099884,
0.04450931027531624,
0.014201786369085312,
0.0064514875411987305,
-0.025360427796840668,
0.062113333493471146,
-0.024251211434602737,
-0.05487075075507164,
0.01837245561182499,
0.012345784343779087,
0.0010622295085340738,
0.0036993410903960466,
0.045974250882864,
-0.024517690762877464,
0.003766898065805435,
0.03027842752635479,
-0.021602382883429527,
-0.030055081471800804,
0.03737812489271164,
0.0020208011846989393,
-0.02237348072230816,
-0.0020577008835971355,
-0.01277744397521019,
-0.012188219465315342,
0.00984971970319748,
0.022893639281392097,
-0.02143150009214878,
0.07590074837207794,
0.06036914512515068,
-0.0037460913881659508,
-0.04842730984091759,
0.004136051516979933,
-0.025830401107668877,
0.032696682959795,
0.015082484111189842,
-0.07357418537139893,
-0.01441771537065506,
0.08380430191755295,
-0.04257700592279434,
0.005209853406995535,
-0.023764414712786674,
-0.04647049680352211,
-0.0687962993979454,
0.03846891224384308,
-0.008235891349613667,
-0.008285894989967346,
0.037703242152929306,
0.03323628380894661,
-0.0037969474215060472,
0.019906869158148766,
0.0031425547786056995,
-0.028956927359104156,
0.013613719493150711,
0.009991749189794064,
-0.057236913591623306,
0.026635857298970222,
0.04293579235672951,
-0.04160408303141594,
0.01252614427357912,
0.026684166863560677,
0.007012256421148777,
0.047728754580020905,
-0.03836732357740402,
0.0038361400365829468,
0.004638012498617172,
0.014799920842051506,
0.04035808891057968,
0.0013487412361428142,
-0.0022551401052623987,
0.01577177084982395,
-0.02729877643287182,
0.015598352998495102,
0.04250063747167587,
-0.0029709571972489357,
-0.014432883821427822,
-0.04275713488459587,
-0.0016176165081560612,
0.013548259623348713,
0.01362442597746849,
-0.021034300327301025,
0.00328167830593884,
-0.0005302377394400537,
0.005718526430428028,
-0.033537499606609344,
-0.00652165524661541,
-0.03839493915438652,
-0.0176236554980278,
-0.0036036537494510412,
-0.0010812418768182397,
0.006301429122686386,
-0.011905809864401817,
-0.05460863187909126,
-0.05722326040267944,
0.015403174795210361,
-0.0386841744184494,
-0.02603958360850811,
-0.03740773722529411,
0.0010347107890993357,
0.010253406129777431,
0.01902996376156807,
0.05024543032050133,
-0.010779078118503094,
0.003629362443462014,
0.035220757126808167,
-0.03243358060717583,
0.023961031809449196,
0.039394132792949677,
-0.03796796873211861,
-0.015942130237817764,
-0.0376054048538208,
0.03058646433055401,
0.02785906009376049,
0.013235660269856453,
-0.05232831835746765,
-0.011697395704686642,
0.009120849892497063,
0.016644231975078583,
0.015978604555130005,
0.004249068908393383,
-0.0041998266242444515,
0.013583756983280182,
-0.021960990503430367,
0.0036662686616182327,
-0.04757228121161461,
0.02024003677070141,
0.009039019234478474,
-0.03279479965567589,
-0.008226141333580017,
-0.03423697501420975,
-0.0011482079280540347,
0.023347994312644005,
0.04661004990339279,
0.003023581113666296,
0.032195109874010086,
-0.002442261204123497,
-0.00025921757332980633,
0.06184951961040497,
0.044143129140138626,
0.0015374119393527508,
0.07802482694387436,
0.013617241755127907,
0.013155966997146606,
-0.01845862716436386,
-0.01693597063422203,
-0.011293378658592701,
0.012208453379571438,
-0.058323152363300323,
0.0038294903934001923,
0.005508325062692165,
-0.024136019870638847,
0.026028385385870934,
-0.031933434307575226,
-0.011708059348165989,
0.037540335208177567,
-0.0015572303673252463,
-0.0030786304268985987,
0.04614322632551193,
-0.020377667620778084,
0.046767957508563995,
-0.0380648672580719,
0.04336172342300415,
0.04625033214688301,
-0.014260760508477688,
-0.06517720967531204,
-0.01312097255140543,
0.017738593742251396,
-0.028070693835616112,
0.017658526077866554,
0.028209129348397255,
0.00913690123707056,
0.003914287779480219,
-0.02035386674106121,
0.0434311106801033,
-0.0051155053079128265,
-0.018159326165914536,
0.0189230777323246,
-0.026374196633696556,
-0.009567709639668465,
0.01756221242249012,
0.0001002061617327854,
0.08904397487640381,
0.021058745682239532,
0.009920849464833736,
-0.019244689494371414,
-0.03827795758843422,
-0.03629099205136299,
0.0445382297039032,
-0.007364328019320965,
-0.00046397565165534616,
0.018451742827892303,
0.005387149751186371,
0.017968682572245598,
0.01873241923749447,
0.06506120413541794,
-0.05289967358112335,
0.018082620576024055,
-0.028175458312034607,
0.0003533405251801014,
-0.0007158180815167725,
-0.04877254739403725,
-0.01599893532693386,
-0.0179733969271183,
0.023548485711216927,
0.020982781425118446,
-0.02676381543278694,
0.00801995862275362,
-0.020007271319627762,
-0.010218458250164986,
0.03706575557589531,
-0.09203371405601501,
-0.008899993263185024,
-0.01956349052488804,
0.04289276897907257,
0.008168844506144524,
-0.019679773598909378
] |
<p>As the title explains, </p>
<ol>
<li>How does a comet form?</li>
<li>What are the elements, what is a comet composed of? </li>
<li>Why didn't they become part of planets, moons or asteroids?</li>
</ol>
| 8,315 |
[
-0.03818587213754654,
-0.020473480224609375,
0.033429574221372604,
-0.005360590294003487,
0.04102964326739311,
0.010779633186757565,
-0.055064767599105835,
-0.041345223784446716,
0.015764953568577766,
-0.03950878605246544,
0.03698843717575073,
0.03547085076570511,
0.003917706198990345,
0.03824614733457565,
-0.027373086661100388,
0.012215686030685902,
0.005186285823583603,
-0.02592790685594082,
0.007927230559289455,
-0.005213078577071428,
-0.00759224034845829,
-0.022853773087263107,
0.01843438297510147,
0.024360818788409233,
-0.021916791796684265,
0.01929951272904873,
0.04099934920668602,
-0.004849969409406185,
0.05324505642056465,
0.03970621898770332,
0.019696859642863274,
-0.008329130709171295,
0.02438001148402691,
-0.013568037189543247,
0.004625827074050903,
-0.017295079305768013,
0.007919897325336933,
0.011401917785406113,
-0.007093293126672506,
0.0032420039642602205,
-0.002566309180110693,
-0.019990835338830948,
0.009682412259280682,
0.018582811579108238,
-0.04671718180179596,
0.012960182502865791,
-0.0066615380346775055,
-0.018432868644595146,
0.03937678411602974,
-0.07712855190038681,
0.01159022469073534,
0.012094737961888313,
0.018154224380850792,
0.036461394280195236,
0.008660303428769112,
0.031544316560029984,
0.0679745152592659,
0.0811801552772522,
0.006245383992791176,
-0.00483621284365654,
-0.014403034932911396,
-0.044887132942676544,
0.00960093829780817,
-0.01943304017186165,
-0.06398022174835205,
0.036884840577840805,
-0.0315576009452343,
-0.022533496841788292,
-0.005258770193904638,
0.040518295019865036,
0.05067693442106247,
0.0037681793328374624,
-0.032808247953653336,
0.014313715510070324,
-0.005298658274114132,
-0.01698080636560917,
0.03882414102554321,
0.0009490777156315744,
0.06052538380026817,
0.05252170190215111,
0.014031223952770233,
0.03115777298808098,
0.01818178780376911,
-0.041093990206718445,
0.01927732490003109,
0.01698320545256138,
0.09565997868776321,
-0.019285067915916443,
0.003995844163000584,
-0.017194367945194244,
0.02155316434800625,
0.010293841361999512,
0.030704373493790627,
0.004110593348741531,
-0.0023883034009486437,
0.02489924058318138,
-0.0004829129029531032,
0.028670551255345345,
-0.012764538638293743,
-0.02879541926085949,
0.034087277948856354,
0.0008922308916226029,
0.035020072013139725,
0.036875780671834946,
0.01665819063782692,
-0.013005680404603481,
-0.06403591483831406,
0.027888813987374306,
-0.01818101294338703,
-0.010954489931464195,
0.01866535283625126,
0.03657162934541702,
-0.006421161815524101,
-0.015148271806538105,
0.005050669424235821,
0.018096132203936577,
0.027125516906380653,
-0.034824032336473465,
0.03740871697664261,
0.05307453125715256,
0.02872944250702858,
-0.004883952904492617,
0.016776669770479202,
-0.00691952696070075,
-0.028320815414190292,
-0.034897807985544205,
-0.03547525405883789,
0.01704617217183113,
0.024310801178216934,
0.03468009829521179,
-0.022477908059954643,
-0.017154861241579056,
0.027006274089217186,
0.016662050038576126,
0.01672966033220291,
0.018046783283352852,
-0.0722954049706459,
-0.02525257132947445,
0.006104807835072279,
0.010456252843141556,
-0.048432692885398865,
-0.06217002123594284,
0.02167564444243908,
0.004557533655315638,
0.037454720586538315,
-0.022331595420837402,
-0.02440885826945305,
0.033840619027614594,
0.033408284187316895,
0.00019802246242761612,
-0.00494940672069788,
-0.01522640697658062,
-0.01707499846816063,
-0.05512627959251404,
0.0019196573412045836,
-0.05451593175530434,
0.03489793464541435,
0.029456183314323425,
0.02259870618581772,
-0.020037174224853516,
0.020514436066150665,
-0.044795069843530655,
-0.010313371196389198,
0.011262563988566399,
0.015836814418435097,
-0.023003796115517616,
0.0765460878610611,
0.06385401636362076,
-0.044903773814439774,
0.05599326267838478,
0.016096798703074455,
0.049556490033864975,
0.021194657310843468,
0.046127595007419586,
0.029016559943556786,
-0.032021936029195786,
-0.06242860108613968,
-0.01279258169233799,
0.011661973781883717,
-0.004480169154703617,
-0.044044870883226395,
-0.009353052824735641,
0.0012469019275158644,
0.02009424939751625,
0.024717018008232117,
0.05398581922054291,
0.03578595072031021,
-0.009362543001770973,
-0.024343101307749748,
-0.058350637555122375,
-0.030996205285191536,
-0.071141317486763,
0.0003900722076650709,
-0.027209294959902763,
-0.030058616772294044,
0.0034997216425836086,
0.021250437945127487,
0.025145431980490685,
-0.0280501376837492,
-0.01667875610291958,
-0.012509637512266636,
0.042626045644283295,
0.012739764526486397,
-0.004106765612959862,
0.022743873298168182,
0.10021299868822098,
0.033912062644958496,
-0.010800212621688843,
-0.022527365013957024,
-0.004759861622005701,
-0.01697729341685772,
-0.05318300053477287,
0.01716596446931362,
-0.015683403238654137,
-0.024869166314601898,
-0.03354942798614502,
0.017318755388259888,
0.004462499637156725,
0.0049301628023386,
0.0334366075694561,
0.011060219258069992,
0.08758825808763504,
0.01406185608357191,
-0.01671847701072693,
0.0011886483989655972,
0.02360771782696247,
0.037043724209070206,
0.030930709093809128,
0.021506417542696,
-0.031582243740558624,
-0.05865122377872467,
-0.029417309910058975,
0.03464408591389656,
0.013351399451494217,
-0.050349507480859756,
0.03594101965427399,
-0.0016625735443085432,
0.024663429707288742,
-0.0004311423690523952,
0.01265932060778141,
-0.03102230466902256,
-0.013619503006339073,
0.02003014273941517,
-0.009106210432946682,
0.01320978719741106,
0.007944077253341675,
0.033521246165037155,
0.01092491578310728,
-0.012804824858903885,
-0.012673594988882542,
-0.03855051472783089,
0.06253225356340408,
0.010842245072126389,
-0.004892074037343264,
0.011794701218605042,
-0.039189863950014114,
0.05204543098807335,
-0.02196049503982067,
-0.02742946334183216,
0.0025207505095750093,
0.03057984635233879,
-0.00802108645439148,
-0.007246151566505432,
-0.012809636071324348,
-0.01630488596856594,
0.020786378532648087,
-0.013134071603417397,
0.00009606929233996198,
0.04415253922343254,
-0.03395882248878479,
0.04433923214673996,
0.01426551304757595,
-0.032017190009355545,
-0.02150963805615902,
0.0021462931763380766,
0.016884082928299904,
0.03244658187031746,
0.002478100825101137,
-0.01923312246799469,
-0.030871715396642685,
-0.027625856921076775,
-0.03335922583937645,
-0.04702731966972351,
0.02034463733434677,
-0.06387284398078918,
0.048711735755205154,
-0.02268119342625141,
0.013962618075311184,
0.027389567345380783,
0.01323027815669775,
-0.01642501913011074,
0.001988707110285759,
-0.03256124258041382,
-0.03413236141204834,
0.00842494796961546,
-0.01690792664885521,
-0.01588902436196804,
-0.03161407262086868,
0.025346413254737854,
0.029559658840298653,
-0.026692766696214676,
0.017377503216266632,
0.033474553376436234,
-0.06173423305153847,
-0.020466355606913567,
-0.005196452606469393,
-0.011904179118573666,
0.02262483909726143,
-0.0018662072252482176,
0.0052041588351130486,
0.02839616872370243,
-0.03349792957305908,
0.039993323385715485,
-0.041310813277959824,
-0.028262481093406677,
-0.0025654903147369623,
-0.02609184943139553,
0.010123747400939465,
0.004453807137906551,
-0.04638710990548134,
0.05473927780985832,
0.011087094433605671,
-0.03910636901855469,
-0.012808513827621937,
0.003295502858236432,
-0.018707774579524994,
-0.02170703560113907,
0.024014271795749664,
-0.0025020958855748177,
0.0006229359423741698,
-0.025653433054685593,
0.028868142515420914,
0.009832490235567093,
0.00720634451135993,
-0.01655549183487892,
-0.020425541326403618,
-0.02046327479183674,
0.009594119153916836,
0.008355753496289253,
-0.0013505954993888736,
0.04158185049891472,
0.02070252038538456,
0.03351745381951332,
-0.011687122285366058,
0.0686117634177208,
0.03130829334259033,
-0.03466108441352844,
0.01171825546771288,
-0.024791577830910683,
-0.0023439826909452677,
-0.009465964511036873,
0.05117993429303169,
-0.022753389552235603,
0.01878601685166359,
0.0036998135037720203,
0.03074727952480316,
0.05089104548096657,
0.02016008086502552,
-0.028638655319809914,
0.01946384832262993,
0.037788864225149155,
-0.027866996824741364,
-0.021295394748449326,
-0.003742906264960766,
-0.010320041328668594,
-0.008162706159055233,
0.024541320279240608,
0.038627468049526215,
0.03604447469115257,
0.008669533766806126,
0.03297713026404381,
-0.0004398175806272775,
-0.021542061120271683,
0.01889128051698208,
-0.07441814243793488,
0.019297270104289055,
0.013870247639715672,
0.02441525273025036,
-0.020169800147414207,
0.10750677436590195,
-0.014809593558311462,
0.015385507605969906,
-0.005855824798345566,
-0.021093320101499557,
-0.06845152378082275,
0.0008158087730407715,
-0.03589943051338196,
-0.029556265100836754,
-0.04314060136675835,
0.02828570269048214,
-0.015786148607730865,
-0.008407780900597572,
0.003648436162620783,
-0.01427835039794445,
-0.02168050967156887,
-0.011731334961950779,
0.03283601999282837,
-0.04879598692059517,
-0.03075827658176422,
-0.009262584149837494,
0.031804006546735764,
0.04781461879611015,
0.015125934034585953,
0.021073224022984505,
0.05435297638177872,
-0.00954405590891838,
-0.019133931025862694,
-0.021273085847496986,
-0.013451149687170982,
-0.016419511288404465,
0.031035741791129112,
-0.009493292309343815,
0.004355312325060368,
-0.0020275739952921867,
-0.005655164364725351,
0.005282176658511162,
0.03690705448389053,
0.008930585347115993,
0.0005840714438818395,
-0.027387993410229683,
-0.029370775446295738,
0.01388853881508112,
0.004863399546593428,
0.016039395704865456,
-0.02385726384818554,
0.0009970134124159813,
0.009326355531811714,
-0.015838302671909332,
-0.017724627628922462,
0.032059259712696075,
0.04309719800949097,
0.01966959424316883,
0.0014938426902517676,
-0.015539715066552162,
-0.022396795451641083,
-0.04722010716795921,
-0.011864209547638893,
0.027313297614455223,
0.0018048981437459588,
-0.010627683252096176,
0.016871297731995583,
-0.002649374306201935,
-0.01073647290468216,
-0.0005790082504972816,
-0.017796894535422325,
-0.0261851716786623,
0.029292825609445572,
-0.06565993279218674,
0.015054875984787941,
0.017153793945908546,
0.05989750847220421,
0.06293405592441559,
-0.03009658120572567,
-0.029973968863487244,
-0.07532539963722229,
-0.01779436133801937,
0.03632733225822449,
0.051604658365249634,
-0.04937434569001198,
-0.007733414880931377,
-0.08432825654745102,
-0.015428423881530762,
0.08956529945135117,
-0.03758708015084267,
0.0037406282499432564,
-0.03630479425191879,
-0.012213782407343388,
0.014795232564210892,
0.007088645361363888,
0.03021916188299656,
0.009760615415871143,
0.01119761448353529,
0.06173010915517807,
-0.011213112622499466,
-0.02383115142583847,
-0.0068363831378519535,
0.013111220672726631,
0.039246562868356705,
0.06062055379152298,
-0.01012871228158474,
0.04660717025399208,
-0.008918289095163345,
-0.024496963247656822,
-0.01114014070481062,
-0.08120577782392502,
-0.014949043281376362,
-0.01638057455420494,
-0.018442941829562187,
0.03303955867886543,
-0.03778931498527527,
-0.08052331209182739,
-0.005769565235823393,
0.0017879345687106252,
-0.020755885168910027,
-0.026430070400238037,
-0.05025864019989967,
0.00257486617192626,
0.03428269922733307,
-0.009837421588599682,
0.05714815482497215,
0.017369426786899567,
-0.03647924214601517,
-0.017769409343600273,
-0.08049210906028748,
-0.0021284851245582104,
0.000395068695070222,
0.0013335738331079483,
-0.0010985014960169792,
0.010682161897420883,
-0.037603382021188736,
0.045242518186569214,
0.014922966249287128,
-0.022063160315155983,
0.030463404953479767,
-0.022057928144931793,
0.006371716037392616,
0.04753028228878975,
0.012770123779773712,
0.012530875392258167,
-0.015137319453060627,
0.04646993428468704,
-0.007379189133644104,
0.03218630701303482,
0.059136927127838135,
-0.02250802330672741,
0.008115662261843681,
-0.023125741630792618,
-0.025440694764256477,
0.019125904887914658,
-0.061556026339530945,
-0.023178862407803535,
0.027045616880059242,
-0.0460885725915432,
0.05376698821783066,
-0.007386883720755577,
-0.0036227956879884005,
0.05343296378850937,
-0.09333856403827667,
-0.005770830903202295,
0.016819853335618973,
-0.0035674567334353924,
0.0381646528840065,
-0.032573286443948746,
0.03407149016857147,
0.013189380057156086,
0.02586768940091133,
-0.06534112989902496,
-0.016507945954799652,
0.022820860147476196,
0.022966794669628143,
-0.03758474811911583,
-0.045242276042699814,
0.0517999641597271,
-0.024080218747258186,
-0.012620982713997364,
0.00832333043217659,
0.021419158205389977,
-0.052597977221012115,
-0.027027316391468048,
0.03692059963941574,
0.015713350847363472,
0.07430477440357208,
-0.011148561723530293,
-0.0034054687712341547,
0.046913716942071915,
-0.008991841226816177,
0.021695749834179878,
-0.034432511776685715,
0.028772393241524696,
-0.016737261787056923,
-0.06165923550724983,
-0.0059816595166921616,
0.0028690495528280735,
0.04139070585370064,
-0.04404359310865402,
0.005778147839009762,
0.03421293571591377,
0.0087028993293643,
-0.025027630850672722,
-0.021616466343402863,
0.041735999286174774,
-0.02521723322570324,
0.004374321550130844,
-0.012364319525659084,
0.02520367130637169,
-0.009996950626373291,
-0.030722543597221375,
0.027715010568499565,
-0.03583616763353348,
0.035594746470451355,
-0.009798228740692139,
0.04899350181221962,
-0.0200574342161417,
-0.006435358431190252,
0.03661475330591202,
-0.03362323343753815,
0.03080371394753456,
0.011890554800629616,
-0.011339646764099598,
0.025513654574751854,
0.002841879380866885,
-0.005390309263020754,
-0.005659885238856077,
-0.029518449679017067,
-0.02386954426765442,
0.04603039100766182,
-0.019725872203707695,
-0.0015926315682008862,
-0.0132408132776618,
0.005839676130563021,
0.0012786748120561242,
-0.04299139231443405,
-0.009164735674858093,
-0.0072183758020401,
0.015821022912859917,
0.015875181183218956,
-0.029754189774394035,
0.013588648289442062,
0.018323929980397224,
0.055592797696590424,
-0.014209688641130924,
-0.0012194780865684152,
0.03814346343278885,
-0.01406029798090458,
-0.006340087857097387,
-0.00887172482907772,
-0.04133947193622589,
0.017614202573895454,
-0.007325220853090286,
0.046726424247026443,
-0.0035673545207828283,
-0.009681317023932934,
0.05995951220393181,
-0.013184241950511932,
0.009207393042743206,
-0.008863030932843685,
0.00183593831025064,
-0.009862439706921577,
0.04256999120116234,
0.060147982090711594,
0.00983456615358591,
-0.01768406666815281,
0.020195022225379944,
0.008751670829951763,
-0.004345327615737915,
-0.013229452073574066,
-0.006266613956540823,
-0.0758477970957756,
-0.03382043540477753,
0.001812101574614644,
-0.051593534648418427,
-0.00028694537468254566,
-0.016192996874451637,
0.019931688904762268,
0.006294920574873686,
-0.011907046660780907,
0.005415113642811775,
-0.002060264116153121,
0.043444614857435226,
-0.04688277468085289,
0.03216252848505974,
-0.017948182299733162,
-0.010780160315334797,
-0.035579778254032135,
0.02936139889061451,
0.13259610533714294,
0.04323023185133934,
0.03126014024019241,
-0.06304261833429337,
0.022246351465582848,
-0.011966385878622532,
0.015001291409134865,
0.007976289838552475,
0.03332219272851944,
-0.010378909297287464,
0.055576834827661514,
0.003522049868479371,
0.02115531452000141,
-0.005793037358671427,
0.04654710739850998,
0.016070589423179626,
-0.04698270186781883,
-0.046402089297771454,
-0.02892259880900383,
-0.012456703931093216,
-0.03709039092063904,
0.032248418778181076,
-0.04017748311161995,
0.007256990764290094,
-0.0011343053774908185,
-0.021760333329439163,
-0.04594014212489128,
-0.05548261106014252,
0.013317951932549477,
0.00016573032189626247,
-0.027454568073153496,
0.013600433245301247,
0.02185451239347458,
-0.015239695087075233,
-0.034251824021339417,
0.03425951674580574,
0.004202026408165693,
-0.025827957317233086,
-0.004686771426349878,
-0.01786375604569912,
0.022643238306045532,
0.004478806629776955,
-0.03420700132846832,
0.02347719483077526,
-0.04672989249229431,
-0.022046446800231934,
-0.005561468191444874,
0.04159653186798096,
-0.03250250220298767,
0.004629419185221195,
-0.053206730633974075,
0.040578391402959824,
0.003305235179141164,
-0.034992679953575134,
-0.0061927493661642075,
0.013866596855223179,
0.014581513591110706,
-0.036367375403642654,
-0.06516176462173462,
-0.012681537307798862,
0.007504610810428858,
-0.04893888160586357,
0.024083517491817474,
0.016752932220697403,
0.035300660878419876,
0.027555163949728012,
-0.0398128442466259,
-0.027119368314743042,
0.009056312032043934,
0.04094281420111656,
-0.069879911839962,
0.009864266030490398,
-0.054847847670316696,
-0.034955818206071854,
0.04172593355178833,
0.04066626355051994,
0.023571515455842018,
0.02216997742652893,
0.012179321609437466,
-0.03977138176560402,
-0.028704358264803886,
0.07218655198812485,
0.030478430911898613,
-0.03682558238506317,
-0.018539942800998688,
-0.007243630476295948,
0.031595610082149506,
0.01042483001947403,
-0.029928801581263542,
0.0638040229678154,
-0.025710325688123703,
0.0050042071379721165,
-0.0019465286750346422,
0.005033641587942839,
0.0030250202398747206,
0.07138771563768387,
-0.008605516515672207,
0.01394050382077694,
-0.013896889984607697,
0.06186304986476898,
0.03668868541717529,
0.00237271748483181,
0.013368464075028896,
0.02810709923505783,
-0.03576174005866051,
0.0174403116106987,
0.03456556424498558,
-0.020997298881411552,
-0.0017691906541585922,
0.03094201348721981,
0.009465561248362064,
-0.01459562312811613,
-0.029676072299480438,
-0.019645877182483673,
-0.04059670865535736,
0.018692709505558014,
0.05206020921468735,
-0.05351119115948677,
0.03890932351350784,
-0.02427355945110321,
0.06409566104412079,
-0.02456854283809662,
0.011910492554306984,
-0.06049491465091705,
0.010943316854536533,
0.006965679116547108,
-0.018627749755978584,
-0.029952548444271088,
0.006824952084571123,
-0.01986713334918022,
-0.00334170856513083,
0.04498988389968872,
-0.0167264174669981,
0.0023761705961078405,
-0.012778964824974537,
-0.02117183618247509,
-0.036350470036268234,
0.058517854660749435,
-0.04158556088805199,
-0.035370390862226486,
-0.0023025658447295427,
-0.05031625181436539,
-0.06343112140893936,
-0.04864681512117386,
-0.029347732663154602,
0.024613769724965096,
0.03224973380565643,
0.004075732547789812,
-0.0010185521095991135,
0.05626123771071434,
-0.03785576671361923,
-0.02669680491089821,
0.00232708384282887,
0.012944095768034458,
0.003927112091332674,
0.013853820040822029,
0.015268051065504551,
-0.022990157827734947,
-0.01599121280014515,
0.054102543741464615,
0.007705599069595337,
0.04063577950000763,
-0.023119570687413216,
-0.0015287704300135374,
-0.030686089769005775,
0.009895045310258865,
0.018230166286230087,
0.03702571988105774,
0.011714337393641472,
-0.012193835340440273,
-0.011808720417320728,
0.05888957902789116,
0.014049370773136616,
-0.028044696897268295,
-0.07511024922132492,
0.012372756376862526,
-0.015091110952198505,
-0.021047813817858696,
0.04996564984321594,
-0.03714967519044876,
0.009907187893986702,
0.05360684171319008,
-0.07912696152925491,
0.04539896175265312,
-0.027577968314290047,
-0.0027500628493726254,
-0.00648667523637414,
-0.022966016083955765,
-0.026656074449419975,
0.06786561757326126,
0.011056385934352875,
0.031459253281354904,
0.005527721252292395,
0.031681131571531296,
0.00595858134329319,
-0.028442131355404854,
-0.021374328061938286,
0.018657797947525978,
-0.010195069946348667,
-0.0039649405516684055,
0.05551169440150261,
-0.0066536120139062405,
-0.006505312863737345,
0.04019726812839508,
-0.010356063023209572,
0.013597564771771431,
0.012870355509221554,
0.0023365491069853306,
0.003172461176291108,
-0.023106031119823456,
-0.021955138072371483,
-0.0019154202891513705,
-0.012392250820994377,
0.02979404479265213,
0.015277286060154438,
0.024027111008763313,
0.0487012080848217,
-0.029419351369142532,
0.04734259471297264,
-0.019535880535840988,
-0.016105545684695244,
0.0024638124741613865,
-0.012759361416101456,
0.016553018242120743,
0.0027341290842741728,
0.000015942065147100948,
0.01681574061512947,
-0.0028873065020889044,
-0.020687654614448547,
-0.008785439655184746,
0.02498580329120159,
0.01294788159430027,
-0.015491925179958344,
-0.019835900515317917,
0.038799647241830826,
-0.0373939611017704,
-0.01952264830470085,
-0.00044331778190098703,
0.009560677222907543,
0.007004770450294018,
0.00044449648703448474,
0.054208070039749146,
0.04330117627978325,
0.014901239424943924,
0.000251912948442623,
-0.02070646919310093,
-0.033837754279375076,
0.05016622319817543,
-0.004797772038727999,
0.022406818345189095,
-0.03034219890832901,
-0.08834927529096603,
-0.02007770538330078,
-0.030290964990854263,
0.029881412163376808,
-0.035502683371305466,
-0.04758354648947716,
-0.036534614861011505,
-0.017425067722797394,
-0.026984326541423798,
0.0011636224808171391,
0.04382973536849022,
0.007636380847543478,
0.006379798054695129,
-0.0046654948964715,
0.002177722053602338,
0.030043581500649452,
-0.045975539833307266,
0.029039479792118073,
0.02471020072698593,
-0.014330589212477207,
0.029559414833784103,
-0.03999573737382889,
-0.03994545340538025,
0.04891366884112358,
0.048721689730882645,
-0.03266400843858719,
0.030515607446432114,
-0.00528233777731657,
-0.011399790644645691,
0.04186517372727394,
0.0144395986571908,
-0.014647277072072029,
0.06323876231908798,
-0.016360558569431305,
0.009254036471247673,
0.024674251675605774,
-0.0137721486389637,
-0.0007615567883476615,
0.002859649946913123,
-0.05256829783320427,
-0.022911449894309044,
-0.02267446182668209,
-0.037023190408945084,
0.015971582382917404,
-0.06193659082055092,
0.028912251815199852,
0.009930700995028019,
-0.012192713096737862,
0.0008228100487031043,
0.05299454554915428,
0.008503841236233711,
0.049725256860256195,
-0.007576378062367439,
-0.014548948034644127,
0.016002565622329712,
-0.037000622600317,
-0.01364001166075468,
0.03052244707942009,
0.001723882625810802,
0.021435216069221497,
-0.0005006791325286031,
0.014705763198435307,
0.034106943756341934,
0.023949606344103813,
0.009221978485584259,
0.022126296535134315,
-0.006977166514843702,
-0.013094057328999043,
0.022383801639080048,
-0.010719748213887215,
0.01310774590820074,
0.02249748446047306,
-0.026183107867836952,
0.0938618928194046,
-0.017715109512209892,
0.06490395963191986,
-0.025629447773098946,
0.02694125287234783,
-0.027209214866161346,
0.002731599844992161,
-0.029132287949323654,
0.02145601063966751,
-0.0003772990021388978,
-0.028198905289173126,
-0.03695973381400108,
0.02111116796731949,
0.044884346425533295,
-0.004489329643547535,
0.023706788197159767,
-0.0076396591030061245,
0.0182903204113245,
-0.005508154630661011,
0.03206074982881546,
-0.04474417120218277,
-0.0326734334230423,
-0.0056299916468560696,
0.04744889214634895,
-0.007799448911100626,
0.004689517896622419,
-0.000910404953174293,
-0.06285124272108078,
0.010223962366580963,
-0.06284599006175995,
-0.020627954974770546,
-0.056415192782878876,
0.03272703289985657,
-0.052197374403476715,
-0.020738279446959496
] |
<p>I am a newbie in water system design but I am currently faced with the exact situation below on my land, and I need to know whether gravity alone is sufficient in order to fill Tank 2 from Tank 1, as I already experienced backflow.</p>
<p>Please have a look at this image:</p>
<p><img src="http://img819.imageshack.us/img819/184/qhzf.png" alt="enter image description here" title="My current water system situation"></p>
<p><em>Note: let's not worry about how Tank 1 is being filled as it probably does not matter - I just made sure I never used a pipe diameter smaller than 0.5" between Tank 1 and Tank 2.</em></p>
<p>As you can see:</p>
<ul>
<li><p>My water source is the overflow of Tank 1</p></li>
<li><p>I have put a 1" diameter pipe in the first 'downhill' section of my path</p></li>
<li><p>The second, longest section of the path is a pipe of 0.5" diameter</p></li>
<li><p>The system is 'powered' through gravity alone</p></li>
</ul>
<p><strong>Questions</strong></p>
<ul>
<li><p>Is there any missing variable (eg path length?) on my drawing in order to resolve this system? (What are the important variables?)</p></li>
<li><p>The flow at the source (the overflow of Tank 1) can be nearly 0. How does this variable influence the system? (Can a larger flow at the source help going up the 'uphill' sections between the tanks?)</p></li>
<li><p>Is the 'head' variable important at all?</p></li>
<li><p>I used a bigger pipe for the first section in an attempt to 'make more weight' and create sufficient pressure to go up the small uphill that follows. Should I limit the use of that bigger pipe strictly to the downhill section, and does it actually make sense to have used a bigger pipe at all?</p></li>
</ul>
| 8,316 |
[
0.003954700659960508,
-0.028058145195245743,
-0.009533140808343887,
0.05696159601211548,
0.031069515272974968,
-0.024658434092998505,
-0.02343524992465973,
-0.043204110115766525,
0.035830989480018616,
-0.00949935708194971,
0.014231003820896149,
0.03389347717165947,
0.025263847783207893,
0.00828184187412262,
0.0367363765835762,
0.02294197678565979,
0.018635863438248634,
-0.007771388161927462,
0.03934594616293907,
-0.019618386402726173,
-0.038410548120737076,
0.009293626062572002,
0.04728109762072563,
0.010362168774008751,
-0.009838523343205452,
0.057178813964128494,
0.03154315799474716,
-0.017986252903938293,
-0.02276344783604145,
0.01063531357795,
0.006491214502602816,
-0.029877755790948868,
-0.013897975906729698,
0.03856702521443367,
0.022768007591366768,
0.022408435121178627,
-0.021336764097213745,
-0.01965891197323799,
0.0003953377017751336,
0.014181612059473991,
-0.01547218207269907,
0.006433131173253059,
0.016112668439745903,
0.0033273911103606224,
-0.0034031991381198168,
0.014456849545240402,
0.014324143528938293,
0.0023072371259331703,
0.029795629903674126,
-0.08314057439565659,
0.0176785197108984,
0.0464254729449749,
0.06295168399810791,
0.05239342898130417,
0.03651927784085274,
-0.023755332455039024,
0.057613253593444824,
0.08745753765106201,
0.005353754386305809,
-0.02123723179101944,
-0.010748470202088356,
0.016213631257414818,
-0.05088290944695473,
-0.028105612844228745,
-0.00824980903416872,
-0.008499483577907085,
-0.011977939866483212,
0.01635402999818325,
-0.026271020993590355,
-0.0354229137301445,
0.039671339094638824,
-0.011383479461073875,
0.04181092232465744,
-0.006116172298789024,
0.04112604632973671,
-0.03130609914660454,
0.010574331507086754,
0.03780689463019371,
0.029671767726540565,
0.03271555155515671,
-0.013285723514854908,
0.015161527320742607,
0.035677555948495865,
0.03817892074584961,
0.045442670583724976,
0.008113402873277664,
0.019772252067923546,
0.016826843842864037,
0.017341477796435356,
0.004893193952739239,
-0.01786860264837742,
0.021220626309514046,
0.02907519042491913,
0.014326492324471474,
0.021652309224009514,
0.00008822995732771233,
-0.011550724506378174,
0.02529826946556568,
0.00021005050803069025,
0.003928113263100386,
-0.007765333168208599,
-0.06123191490769386,
0.007529667112976313,
0.08648660778999329,
0.02376846969127655,
-0.013823463581502438,
0.02145417034626007,
-0.009619737043976784,
-0.021273024380207062,
-0.003088477998971939,
-0.03425072133541107,
-0.01042792946100235,
0.02580634318292141,
-0.05748521164059639,
-0.03138473629951477,
-0.02341204509139061,
-0.0020377624314278364,
-0.0164274200797081,
0.04129880666732788,
-0.0006999876932241023,
0.04899653047323227,
-0.014720537699759007,
0.011941575445234776,
-0.03486798703670502,
-0.038656044751405716,
0.016013408079743385,
-0.023323336616158485,
0.010320923291146755,
-0.004665194544941187,
0.04928109422326088,
0.011383087374269962,
0.02385052479803562,
0.0030023609288036823,
-0.0055351946502923965,
0.05398854985833168,
0.021994981914758682,
-0.08038362115621567,
-0.062020812183618546,
0.040352217853069305,
-0.003728357842192054,
0.012372973375022411,
-0.05147167667746544,
0.009539403952658176,
0.052891023457050323,
0.05335823819041252,
-0.01741740293800831,
0.009353410452604294,
0.03142477571964264,
0.0157446451485157,
-0.006140668410807848,
-0.002971767680719495,
0.015027505345642567,
-0.0009614243754185736,
-0.020485149696469307,
-0.014110597781836987,
-0.06482996791601181,
0.036410585045814514,
0.021167444065213203,
-0.008023856207728386,
-0.02684963122010231,
0.04030401632189751,
0.011675126850605011,
0.02901548705995083,
0.024776464328169823,
-0.002866035792976618,
-0.010345928370952606,
0.037516795098781586,
0.015169041231274605,
-0.011264637112617493,
0.0314786396920681,
0.007734647952020168,
0.0028148991987109184,
0.01928761415183544,
0.007842780090868473,
0.04808256775140762,
0.0065922364592552185,
0.005859654396772385,
-0.0582907535135746,
0.0012718922225758433,
0.03387627378106117,
0.000441286334535107,
-0.03838441148400307,
-0.044513460248708725,
0.009443560615181923,
0.041453272104263306,
0.01822122000157833,
0.026256171986460686,
-0.020405810326337814,
0.015046758577227592,
-0.027333034202456474,
-0.01924583502113819,
-0.0011729559628292918,
0.015135487541556358,
-0.03237399086356163,
-0.006558029446750879,
-0.02135332301259041,
0.008089780807495117,
0.02777409367263317,
-0.024472352117300034,
-0.0037911999970674515,
0.05240420624613762,
0.012229859828948975,
0.01545542012900114,
-0.0008032404584810138,
0.015468325465917587,
0.07227302342653275,
0.036468833684921265,
-0.01431831531226635,
-0.001191086252219975,
0.00005622298704111017,
-0.026002930477261543,
-0.017719749361276627,
-0.012632915750145912,
0.0046003516763448715,
-0.02811882272362709,
-0.00721190357580781,
0.006315413862466812,
0.046580564230680466,
0.0187912005931139,
0.007980338297784328,
-0.05155492573976517,
0.12110598385334015,
0.07116498798131943,
-0.028065122663974762,
0.0033641960471868515,
0.009878813289105892,
0.015935568138957024,
0.014207473956048489,
-0.013270948082208633,
-0.014957672916352749,
-0.03608919307589531,
-0.015924697741866112,
0.0014784550294280052,
-0.03435229882597923,
0.0021181271877139807,
0.004337179008871317,
0.027191927656531334,
-0.022433290258049965,
0.02568424493074417,
0.02904476597905159,
0.01070820540189743,
0.014423073269426823,
0.01400310080498457,
0.059280239045619965,
0.004967115819454193,
0.03939441591501236,
0.005721632856875658,
0.026684649288654327,
0.010290990583598614,
-0.05560196563601494,
-0.020991815254092216,
0.005036431364715099,
0.024031266570091248,
0.01882447861135006,
-0.025991883128881454,
0.005073834676295519,
0.04590407386422157,
-0.0389665886759758,
-0.02620869316160679,
0.05631152167916298,
-0.0006643490050919354,
0.013414844870567322,
-0.0690176859498024,
-0.0020248175133019686,
-0.018768759444355965,
0.022121548652648926,
0.007637204136699438,
-0.013161937706172466,
0.028159555047750473,
-0.04470911622047424,
0.04405144602060318,
-0.04190724715590477,
-0.03464812412858009,
-0.034543223679065704,
-0.01276053674519062,
0.046333108097314835,
0.0022411388345062733,
0.04728906974196434,
-0.04990005120635033,
-0.02450711838901043,
-0.029453562572598457,
0.02296368032693863,
-0.02370205894112587,
-0.009848184883594513,
-0.06778337806463242,
0.0008615723345428705,
-0.02555415965616703,
0.01751823164522648,
0.05926769971847534,
0.009788280352950096,
-0.01403758954256773,
0.011981605552136898,
0.006528247147798538,
-0.0038599453400820494,
-0.038182035088539124,
-0.061192337423563004,
0.017677176743745804,
0.005929650738835335,
0.0135304881259799,
0.05631505325436592,
0.019558781757950783,
-0.06745943427085876,
0.026229606941342354,
-0.04426640272140503,
-0.019778328016400337,
-0.018060779199004173,
0.047285690903663635,
-0.004900059197098017,
-0.003577109891921282,
-0.0012648931005969644,
0.011248242110013962,
-0.03968008980154991,
-0.03050008974969387,
-0.03755088523030281,
-0.06347484141588211,
0.018154483288526535,
0.01406834740191698,
0.06791575253009796,
-0.004173316992819309,
-0.027194906026124954,
0.056809764355421066,
-0.01620095781981945,
-0.05086831748485565,
-0.0444980151951313,
-0.007647454272955656,
0.017802605405449867,
-0.015210558660328388,
-0.007333206944167614,
0.06283460557460785,
-0.00045071187196299434,
-0.016473539173603058,
0.009518079459667206,
0.03236996755003929,
0.05909806862473488,
0.01655835472047329,
0.037557218223810196,
0.0003723356348928064,
0.03756365180015564,
-0.009090140461921692,
0.03508739918470383,
0.00906107947230339,
-0.030016887933015823,
-0.002665766282007098,
-0.05585852637887001,
0.03250598907470703,
0.016214614734053612,
-0.026488617062568665,
0.019506115466356277,
-0.0005529280169866979,
0.012748977169394493,
-0.03031570464372635,
-0.008565186522901058,
-0.004302462562918663,
-0.027165407314896584,
0.010869844816625118,
0.006791928317397833,
0.09136824309825897,
-0.00745210750028491,
-0.02693762816488743,
0.0575513020157814,
0.036768462508916855,
-0.040729012340307236,
-0.04830770939588547,
-0.00140837871003896,
0.010664619505405426,
0.0238538458943367,
0.013263334520161152,
0.000254217186011374,
0.02983446978032589,
0.018245849758386612,
-0.019206413999199867,
0.016324149444699287,
-0.01449945755302906,
-0.007602909579873085,
-0.07230784744024277,
-0.0028265323489904404,
-0.025960195809602737,
0.06536304205656052,
-0.019708015024662018,
0.05058515444397926,
0.007805445231497288,
0.02291683852672577,
0.0006672202725894749,
-0.009476179257035255,
-0.0644044503569603,
-0.0010700731072574854,
-0.027269477024674416,
-0.01615593582391739,
0.037651658058166504,
-0.037159934639930725,
-0.044210437685251236,
-0.05487063527107239,
-0.009203615598380566,
-0.008992603048682213,
0.028416365385055542,
-0.024259421974420547,
0.04479001834988594,
-0.030840856954455376,
-0.018996985629200935,
-0.0015184126095846295,
0.009089569561183453,
-0.004638209473341703,
-0.0234860647469759,
0.07354023307561874,
0.019570158794522285,
0.005116677843034267,
-0.01814570464193821,
-0.005031449254602194,
-0.0003340297262184322,
0.024192409589886665,
0.04419035091996193,
0.02433822676539421,
0.051484137773513794,
-0.019860224798321724,
-0.012031513266265392,
-0.005994492210447788,
0.04399780556559563,
-0.020958589389920235,
0.0338350348174572,
-0.008427808992564678,
0.007363215554505587,
-0.018840476870536804,
0.029390627518296242,
0.013684805482625961,
-0.01918233372271061,
-0.0070755574852228165,
0.00478376355022192,
-0.060560956597328186,
-0.03083360753953457,
0.04121759906411171,
0.024928022176027298,
0.04009165242314339,
-0.010203135199844837,
-0.061660636216402054,
-0.04574872553348541,
-0.0380469374358654,
-0.01274892408400774,
0.030830422416329384,
0.052081722766160965,
-0.03975329175591469,
-0.021429885178804398,
0.0394887700676918,
0.014801230281591415,
0.0012920633889734745,
0.04172737896442413,
0.000009480279913987033,
0.036582302302122116,
0.005181905813515186,
0.006947380490601063,
0.006766855251044035,
0.005630690138787031,
0.02062801830470562,
-0.012773203663527966,
0.021835021674633026,
-0.07097490131855011,
-0.08479337394237518,
0.037752699106931686,
0.04425021633505821,
-0.020586909726262093,
0.018702324479818344,
-0.04518180713057518,
-0.04938054829835892,
0.025273602455854416,
-0.005481645464897156,
0.01935444585978985,
-0.02671944908797741,
0.040480781346559525,
-0.01743883080780506,
-0.05576769635081291,
-0.017697002738714218,
0.02143971621990204,
-0.043436966836452484,
0.0035522705875337124,
-0.01989874057471752,
-0.00041152737685479224,
0.024045230820775032,
0.015240422450006008,
0.02051434852182865,
0.055435508489608765,
-0.019670702517032623,
-0.030939612537622452,
0.0005766601534560323,
0.04085284844040871,
-0.007403072901070118,
-0.06544261425733566,
-0.011040144599974155,
-0.061850763857364655,
0.0061293900944292545,
0.023832296952605247,
-0.009907788597047329,
-0.03160078078508377,
0.04263027384877205,
0.005161656066775322,
-0.012251927517354488,
-0.00018934777472168207,
0.006449772045016289,
-0.003829208668321371,
0.032644640654325485,
0.00008728428656468168,
0.037251703441143036,
0.019362181425094604,
-0.039143145084381104,
-0.02444746531546116,
-0.05542031303048134,
0.01951289363205433,
-0.02163509838283062,
-0.04658093303442001,
-0.06562303006649017,
0.001408467534929514,
-0.04869506135582924,
0.013563340529799461,
0.018558477982878685,
0.02626338042318821,
-0.012155506759881973,
-0.029611647129058838,
0.03153691813349724,
0.009580269455909729,
0.0157090425491333,
-0.022812575101852417,
-0.03438470512628555,
0.02408546581864357,
0.03330620378255844,
0.0072221714071929455,
-0.0022230639588087797,
-0.009686444886028767,
0.014643648639321327,
0.01856270618736744,
-0.04919266700744629,
-0.024895062670111656,
-0.0216745063662529,
-0.005939303897321224,
0.007204578723758459,
-0.027103351429104805,
0.048050835728645325,
0.0253248643130064,
0.047287262976169586,
0.029376497492194176,
-0.01702810265123844,
-0.007013890892267227,
0.06919201463460922,
0.006699779536575079,
-0.03339235857129097,
-0.017034832388162613,
0.01659630797803402,
0.04426701366901398,
0.03867180272936821,
-0.010279913432896137,
-0.023679325357079506,
0.017105797305703163,
0.01335995364934206,
0.003712504170835018,
-0.01808866672217846,
-0.04373226314783096,
-0.009871432557702065,
-0.04756598174571991,
-0.014493681490421295,
0.04832394793629646,
-0.02199721336364746,
0.0075709936209023,
0.008352345786988735,
0.03376217931509018,
0.07853201776742935,
-0.006967263296246529,
0.020224880427122116,
0.01439677644520998,
-0.04051807522773743,
-0.010512193664908409,
-0.03728003427386284,
0.006288531236350536,
-0.03257044404745102,
-0.015242674387991428,
-0.004078454803675413,
0.029505757614970207,
0.03974887728691101,
-0.02504594251513481,
0.005867587868124247,
-0.013674438931047916,
0.011567965149879456,
-0.04949437081813812,
-0.0114557184278965,
0.0065366532653570175,
0.0074954889714717865,
0.006120889447629452,
-0.03643030300736427,
-0.014515609480440617,
-0.04859994351863861,
-0.047787707298994064,
-0.02052113227546215,
-0.03499846160411835,
-0.03182841092348099,
-0.01320555154234171,
0.059136055409908295,
0.001700127962976694,
-0.013459681533277035,
-0.01085467729717493,
-0.014511163346469402,
0.04427158832550049,
-0.004974366631358862,
-0.02054959163069725,
0.006111844442784786,
-0.006961964536458254,
-0.008156608790159225,
-0.020245946943759918,
-0.03185494616627693,
-0.024771779775619507,
0.04631924629211426,
0.00388488476164639,
0.03285659849643707,
-0.009762495756149292,
-0.005040804855525494,
0.03778119012713432,
-0.004332708194851875,
-0.021932197734713554,
-0.004085558466613293,
-0.0012863725423812866,
0.04827689751982689,
-0.019919751212000847,
-0.020105410367250443,
0.029636086896061897,
-0.009325101971626282,
0.03372562676668167,
-0.008344884030520916,
0.015532301738858223,
0.00798328872770071,
-0.0017460075905546546,
-0.059138912707567215,
-0.046722277998924255,
0.0402129702270031,
-0.018729954957962036,
0.017710138112306595,
-0.026403801515698433,
-0.024171529337763786,
0.07498133182525635,
0.030210724100470543,
-0.034777913242578506,
-0.0750904381275177,
0.02752937749028206,
-0.026875728741288185,
-0.018183624371886253,
0.010728524066507816,
0.010549528524279594,
-0.00554408086463809,
0.04441516473889351,
0.032293058931827545,
0.0014531476190313697,
0.045494548976421356,
-0.044108327478170395,
-0.04100843146443367,
0.010325976647436619,
-0.031227223575115204,
-0.05925384536385536,
0.02773025445640087,
0.009500991553068161,
-0.026804916560649872,
0.04104423150420189,
-0.030723074451088905,
-0.011441698297858238,
-0.028359215706586838,
0.007611841894686222,
-0.018404996022582054,
0.06427361071109772,
-0.04859693720936775,
0.03467891737818718,
-0.011417247354984283,
-0.005488561931997538,
0.14429987967014313,
0.04269254952669144,
0.017860446125268936,
-0.014851490035653114,
0.02469886653125286,
-0.005972281098365784,
0.02968410961329937,
-0.024677082896232605,
0.033475615084171295,
0.000055549775424879044,
-0.006990169174969196,
0.003772098571062088,
0.00029961575637571514,
-0.03748733177781105,
-0.005933730863034725,
0.07467328757047653,
-0.043998416513204575,
-0.02758307382464409,
0.03314315527677536,
-0.00715048611164093,
-0.03204035758972168,
0.014677241444587708,
-0.03298691660165787,
0.052724480628967285,
-0.020747067406773567,
0.00999834667891264,
-0.029849963262677193,
-0.03591688349843025,
0.03650972619652748,
0.008405814878642559,
-0.06521294265985489,
0.016564680263400078,
-0.01972043514251709,
-0.02000040002167225,
-0.023278454318642616,
0.010704925283789635,
-0.01693778857588768,
-0.057514265179634094,
-0.0157385915517807,
0.03651358187198639,
-0.018194761127233505,
0.009241687133908272,
-0.001875151414424181,
0.040465932339429855,
-0.05089404061436653,
0.022615481168031693,
-0.05004839226603508,
0.029770324006676674,
0.027459926903247833,
0.009282467886805534,
-0.0019017898011952639,
0.05027683079242706,
0.029977411031723022,
-0.05561355501413345,
-0.02374122478067875,
0.0014885349664837122,
0.03141745924949646,
0.004893716890364885,
-0.016569441184401512,
0.008955410681664944,
-0.020178386941552162,
0.013921117410063744,
-0.002515413099899888,
-0.0026510353200137615,
-0.017529448494315147,
0.001492387498728931,
-0.011621491983532906,
0.07296723872423172,
0.03401312232017517,
-0.032894477248191833,
-0.053428057581186295,
0.03661677986383438,
-0.020120350643992424,
0.01997365616261959,
0.006560251582413912,
0.029352029785513878,
-0.005244554486125708,
0.029182961210608482,
-0.03193316608667374,
-0.012601884081959724,
-0.02963237278163433,
0.049883995205163956,
-0.003722929395735264,
-0.0006891184020787477,
-0.03769703209400177,
-0.001392059726640582,
-0.036770619451999664,
0.05875406786799431,
0.03952908143401146,
-0.029641365632414818,
-0.0041627222672104836,
0.06361765414476395,
0.006368791684508324,
-0.04568091034889221,
-0.005899813491851091,
-0.008963470347225666,
-0.057719748467206955,
-0.009358982555568218,
0.008620652370154858,
0.02236088179051876,
-0.0014639812288805842,
0.026017550379037857,
-0.01185823418200016,
0.025937333703041077,
-0.001727722818031907,
0.03800394758582115,
0.009792806580662727,
-0.017096908763051033,
-0.014977792277932167,
-0.03003361076116562,
0.020337194204330444,
-0.04381529986858368,
-0.0005496765370480716,
-0.0010911592980846763,
0.0005335609894245863,
0.007960768416523933,
0.00004018880645162426,
-0.04000543802976608,
-0.00744436914101243,
-0.04557682201266289,
0.034152671694755554,
-0.013621652498841286,
0.011986078694462776,
-0.05715738236904144,
-0.04069847986102104,
-0.010378663428127766,
0.0011913005728274584,
-0.05036384239792824,
0.04907897859811783,
-0.01836118847131729,
0.007207309827208519,
-0.003152946475893259,
0.0017860528314486146,
0.007714745122939348,
-0.020226001739501953,
0.04427351430058479,
-0.003767543938010931,
0.040788065642118454,
-0.03289216011762619,
-0.05048529431223869,
0.019491491839289665,
0.04325917363166809,
-0.023835090920329094,
0.009462936781346798,
0.015407437458634377,
0.04653360694646835,
0.004498121794313192,
-0.058314964175224304,
-0.021162288263440132,
0.05611122027039528,
0.014212762005627155,
0.01897668093442917,
-0.03594592586159706,
0.0067091891542077065,
0.002068341476842761,
-0.0014106049202382565,
-0.00985207874327898,
-0.01977522112429142,
0.021790731698274612,
0.005809684284031391,
0.04159599170088768,
0.013267946429550648,
-0.028465820476412773,
0.0040168603882193565,
-0.007758801802992821,
-0.002749080304056406,
-0.006055191624909639,
-0.04291730746626854,
0.03294316306710243,
0.026185031980276108,
-0.038846537470817566,
-0.02034470997750759,
0.007609609514474869,
0.019414609298110008,
-0.07123129069805145,
-0.008121540769934654,
0.0022553964518010616,
-0.009455309249460697,
0.020726187154650688,
-0.032405246049165726,
0.0015855025267228484,
0.0375787727534771,
-0.04022064805030823,
-0.016677508130669594,
-0.019907625392079353,
0.04027993604540825,
-0.024007605388760567,
-0.020837845280766487,
0.022667940706014633,
0.014030301943421364,
0.012619595974683762,
0.005780682899057865,
-0.017270002514123917,
0.016720229759812355,
-0.021032223477959633,
-0.02301303669810295,
-0.015879707410931587,
0.007853270508348942,
-0.036885201930999756,
-0.025235407054424286,
0.028478367254137993,
-0.01586228236556053,
0.003505186876282096,
-0.024680105969309807,
-0.024062350392341614,
0.027328623458743095,
-0.011623406782746315,
0.02346254512667656,
0.011686286889016628,
0.06567703187465668,
0.027977658435702324,
0.010106530040502548,
-0.033711425960063934,
-0.02843504026532173,
0.03592175245285034,
0.010346107184886932,
-0.031264178454875946,
-0.00531828822568059,
0.02219364605844021,
-0.030125156044960022,
0.0012077061692252755,
0.04232185706496239,
-0.07412633299827576,
-0.00017135741654783487,
0.03180117532610893,
-0.0335225835442543,
0.024127865210175514,
0.0037287103477865458,
0.004160383250564337,
-0.016416238620877266,
-0.006380577106028795,
0.0369860865175724,
-0.032431770116090775,
-0.023383019492030144,
0.014524152502417564,
0.02818634733557701,
-0.018095295876264572,
-0.023848120123147964,
-0.017071155831217766,
-0.04357413202524185,
-0.0357968807220459,
0.012509468011558056,
-0.05839642137289047,
-0.0066236695274710655,
0.017852116376161575,
-0.052211370319128036,
-0.015590479597449303,
0.05729047954082489,
-0.014103703200817108,
0.04553310200572014,
0.025633174926042557,
-0.018546881154179573,
-0.014042884111404419,
-0.05980728566646576,
0.058941397815942764,
0.005018545780330896,
-0.04611857607960701,
-0.04552292451262474,
-0.011019707657396793,
0.008587097749114037,
0.013094890862703323,
0.0699358657002449,
-0.004085656721144915,
0.0022771419025957584,
0.014471441507339478,
0.021517664194107056,
0.047165852040052414,
-0.03498030826449394,
0.0262541975826025,
0.015699533745646477,
-0.014982981607317924,
0.03770074248313904,
0.004351945128291845,
0.021107546985149384,
0.026374807581305504,
0.03768955543637276,
-0.028600238263607025,
0.017994379624724388,
0.03353936970233917,
0.008250598795711994,
-0.00660278182476759,
-0.0032019559293985367,
-0.02329949662089348,
0.10234566032886505,
-0.032706089317798615,
-0.01939724199473858,
0.031617648899555206,
-0.02669134922325611,
-0.0614861324429512,
0.04017199948430061,
-0.02250807359814644,
0.0017500699032098055,
-0.014870556071400642,
-0.05223098397254944,
0.03834160044789314,
-0.04650968313217163,
-0.00009786584269022569,
0.008190358988940716,
-0.04441288486123085,
-0.015298997052013874,
0.059416264295578,
0.02042294107377529,
0.01258151326328516,
-0.05240410566329956,
0.04557197168469429,
-0.015017526224255562,
-0.001499008503742516,
-0.03133225440979004,
-0.004209460690617561,
0.043171580880880356,
0.04802510514855385,
-0.02180854231119156,
0.07497277110815048,
0.02647346444427967,
0.023497609421610832,
0.004114837385714054,
-0.00399055564776063,
-0.01599232479929924,
-0.0553041473031044,
0.032147977501153946,
0.016388799995183945,
0.012087644077837467,
0.01160463783890009,
-0.03644083812832832,
0.04260078817605972,
-0.009177479892969131,
-0.006525419652462006,
-0.04144538938999176,
0.001542962621897459,
0.01746034249663353,
0.020635731518268585,
-0.027126599103212357,
-0.0014401200460270047,
0.029391873627901077,
-0.028697017580270767,
-0.006844135466963053,
-0.007426307536661625,
-0.009900505654513836,
-0.01888599619269371,
0.0715041309595108,
0.006768620107322931,
0.03289350867271423,
-0.017764423042535782,
-0.03733418881893158,
-0.03008105419576168,
-0.041909169405698776,
0.056185282766819,
0.05422711744904518,
0.0034637697972357273,
-0.023850174620747566,
-0.04184070602059364,
-0.01937296614050865,
0.0677972212433815,
-0.04888260364532471,
-0.04078558087348938,
0.04086977243423462,
-0.015434924513101578,
0.024453982710838318,
-0.057061199098825455
] |
<p>Frequently I see the expression
$$F = \frac{dp}{dt} = \frac{d}{dt}(mv) = \frac{dm}{dt}v + ma,$$
which can be applied to variable mass systems.</p>
<p>But I'm wondering if this derivation is correct, because the second law of Newton is formulated for point masses. </p>
<p>Furthermore if i change the inertial frame of reference, only $v$ on the right side of the formula $F = \frac{dm}{dt}v+ma$ will change, meaning that $F$ would be dependent of the frame of reference, which (according to me) can't be true. </p>
<p>I realize there exists a formula for varying mass systems, that looks quite familiar to this one, but isn't exactly the same, because the $v$ on the right side is there the relative velocity of mass expulsed/accreted. The derivation of that formula is also rather different from this one. </p>
<p>So my question is: is this formula, that I frequently encounter in syllabi and books, correct? Where lies my mistake. </p>
| 8,317 |
[
0.010414197109639645,
-0.017395105212926865,
-0.003606814658269286,
-0.009991701692342758,
0.05995248630642891,
-0.02573820762336254,
-0.021999547258019447,
-0.0049730334430933,
0.009982729330658913,
-0.006238497793674469,
-0.0018972805701196194,
0.045058105140924454,
0.07905801385641098,
0.005826604086905718,
0.02295137383043766,
0.014929918572306633,
-0.01625707931816578,
0.009632525965571404,
0.009938660077750683,
-0.02769983559846878,
-0.012785838916897774,
0.04165935516357422,
0.03786781057715416,
-0.016889555379748344,
-0.013635619543492794,
0.041440900415182114,
-0.006233407184481621,
-0.030340464785695076,
-0.02200326696038246,
0.05231499299407005,
0.0010547852143645287,
0.02066219411790371,
-0.013905578292906284,
0.022080816328525543,
0.015666648745536804,
0.050842247903347015,
-0.0290790144354105,
-0.03924413025379181,
0.018659798428416252,
0.06569702923297882,
-0.05288665369153023,
-0.007708609104156494,
-0.021825993433594704,
0.06033993139863014,
-0.029788771644234657,
0.048536576330661774,
0.031064778566360474,
0.006801829673349857,
0.048727940768003464,
-0.050734441727399826,
0.09748540818691254,
0.00940400455147028,
0.07456006109714508,
0.04065558686852455,
-0.02928510122001171,
0.009439521469175816,
0.06443969160318375,
0.059190619736909866,
-0.007166848052293062,
-0.03738373517990112,
-0.026614179834723473,
-0.04052441939711571,
-0.013982857577502728,
-0.015392916277050972,
-0.01577484793961048,
0.021876594051718712,
-0.01885920949280262,
-0.002021965105086565,
0.029310263693332672,
-0.002685073297470808,
0.03735136240720749,
0.012674027122557163,
0.025308193638920784,
-0.02128818817436695,
-0.017711849883198738,
-0.03620366007089615,
0.04563922807574272,
0.0035137252416461706,
0.012428252957761288,
0.03847520798444748,
0.0007103498792275786,
0.018330905586481094,
0.05434386059641838,
0.03383605554699898,
0.016750432550907135,
-0.04038091003894806,
0.03606995567679405,
0.01003081165254116,
0.03739215433597565,
0.046211615204811096,
-0.007063610013574362,
0.022217756137251854,
0.0026987188030034304,
-0.02504422701895237,
-0.0070350938476622105,
0.01734868995845318,
-0.004802270792424679,
0.014068398624658585,
-0.0005573392263613641,
-0.027219731360673904,
-0.007502482272684574,
-0.0077767884358763695,
0.005416750442236662,
0.07286398857831955,
0.008183086290955544,
-0.053059715777635574,
-0.038971975445747375,
0.005879451520740986,
-0.03780197352170944,
-0.02607322856783867,
-0.05177723988890648,
0.026093756780028343,
0.00357808661647141,
-0.007388655561953783,
0.019954029470682144,
-0.005209181923419237,
-0.005165348295122385,
0.004944831132888794,
0.04959793761372566,
0.05862649530172348,
0.04737501218914986,
-0.03165912628173828,
0.014559032395482063,
-0.036860011518001556,
-0.034665923565626144,
0.018311632797122,
0.013056132942438126,
0.019723139703273773,
0.002724897349253297,
-0.011867816559970379,
0.027824480086565018,
-0.030189016833901405,
-0.005727700423449278,
0.015685047954320908,
-0.006716347765177488,
0.004572777543216944,
-0.05947566032409668,
-0.06333228200674057,
0.02893499657511711,
-0.006428624968975782,
0.0036805893760174513,
-0.06497468054294586,
0.008306843228638172,
0.026735534891486168,
0.04239717498421669,
0.026276027783751488,
-0.03149688243865967,
0.0033519866410642862,
0.07485809922218323,
-0.013843915425240993,
-0.025573009625077248,
-0.045030973851680756,
-0.0051670134998857975,
-0.06383916735649109,
-0.0020077256485819817,
-0.0812474861741066,
0.02902997098863125,
0.04167350381612778,
0.024526318535208702,
0.00797113124281168,
0.04018992558121681,
-0.016775304451584816,
-0.015339000150561333,
0.025631800293922424,
0.017565952613949776,
-0.03648555651307106,
0.06365571171045303,
0.011943158693611622,
0.006094491109251976,
0.02418934740126133,
0.0557953342795372,
0.046513985842466354,
-0.003214126219972968,
0.0434868261218071,
0.02699737250804901,
-0.04842017963528633,
-0.050241678953170776,
-0.01612124778330326,
0.007561763282865286,
0.005025151651352644,
-0.04474811628460884,
-0.05238195136189461,
-0.03752139210700989,
-0.006794294808059931,
0.002097246004268527,
0.052329570055007935,
0.007213940843939781,
0.055781468749046326,
-0.008455968461930752,
-0.046196404844522476,
0.01325767021626234,
-0.0655202567577362,
0.03301449120044708,
-0.06275782734155655,
-0.012508478946983814,
0.015001071617007256,
0.012180749326944351,
0.011766064912080765,
-0.02448219060897827,
0.0027570114471018314,
0.03342873603105545,
0.011669379658997059,
0.00040022091707214713,
-0.02433251403272152,
0.03161932900547981,
0.033955708146095276,
0.008898163214325905,
0.05171351134777069,
-0.0004707154876086861,
-0.024775957688689232,
-0.030885105952620506,
-0.00017713448323775083,
-0.029913758859038353,
0.05152786150574684,
-0.008051520213484764,
-0.005046259146183729,
0.002230100566521287,
-0.0077185677364468575,
0.0030566188506782055,
0.04409186169505119,
-0.030285824090242386,
0.07146172970533371,
0.08088275790214539,
0.01478451956063509,
0.001995527883991599,
0.05847489461302757,
0.0202485341578722,
-4.0405844003998936e-8,
-0.02471729926764965,
-0.06832727044820786,
-0.03650766983628273,
-0.015601410530507565,
0.005026356782764196,
0.01364110317081213,
-0.0228519719094038,
0.041013628244400024,
0.05015100911259651,
0.01819617673754692,
0.028336364775896072,
0.008081612177193165,
-0.0009965978097170591,
-0.06011112406849861,
0.039449941366910934,
0.015782788395881653,
0.010723443701863289,
0.018973249942064285,
0.034710630774497986,
0.03793872892856598,
-0.016773778945207596,
-0.005052260588854551,
0.0012289512669667602,
0.024889713153243065,
0.004274339880794287,
0.003205397864803672,
0.014806400053203106,
-0.04594646766781807,
0.040711916983127594,
-0.01927839405834675,
0.033023301512002945,
0.07956007122993469,
-0.007493197917938232,
-0.022103330120444298,
-0.026875905692577362,
0.0157148614525795,
0.00531671242788434,
-0.0009958274895325303,
-0.024771209806203842,
-0.02758370153605938,
0.009057072922587395,
-0.0648343563079834,
0.02550044097006321,
-0.014321708120405674,
-0.03602450340986252,
-0.004983443766832352,
-0.025367895141243935,
-0.026112545281648636,
0.037690479308366776,
0.023106569424271584,
-0.018632272258400917,
0.027065714821219444,
-0.009935092180967331,
-0.026443000882864,
-0.046037301421165466,
0.006690522655844688,
-0.03555340692400932,
0.01602175086736679,
-0.03738304227590561,
-0.06823066622018814,
0.027635060250759125,
-0.00986949261277914,
0.010152499191462994,
0.0010859431931748986,
-0.015848824754357338,
-0.0786106139421463,
-0.02152162231504917,
-0.025661570951342583,
-0.03411712124943733,
-0.029507339000701904,
-0.01671014167368412,
0.03635452687740326,
0.011639353819191456,
-0.024049261584877968,
-0.015319566242396832,
-0.0685507282614708,
-0.06482592970132828,
-0.024495696648955345,
0.012241479009389877,
0.04570590704679489,
-0.03535224124789238,
0.008948162198066711,
0.03737461566925049,
-0.036132585257291794,
0.0033750368747860193,
-0.034386515617370605,
-0.05418531596660614,
0.0318300686776638,
0.01816854439675808,
0.06367623805999756,
0.0314769446849823,
-0.049369629472494125,
0.08002473413944244,
0.03729658201336861,
-0.0019100962672382593,
0.0033909231424331665,
0.025091663002967834,
0.03392987698316574,
-0.003485198365524411,
-0.0136153819039464,
0.028735218569636345,
-0.02245449647307396,
-0.0038080334197729826,
0.02310965023934841,
-0.016559964045882225,
0.04187804460525513,
0.0006501405732706189,
0.008559439331293106,
-0.018670840188860893,
0.01569448597729206,
-0.00538357300683856,
0.03806304931640625,
0.007199432700872421,
-0.004284930415451527,
0.00032875360921025276,
-0.003962480463087559,
0.05575519800186157,
-0.0331386998295784,
-0.04998107627034187,
0.04529166594147682,
-0.009547716937959194,
-0.031111638993024826,
-0.01720210537314415,
0.04208245873451233,
0.007354757282882929,
0.018099099397659302,
0.021159326657652855,
0.00930432416498661,
0.029594939202070236,
-0.030953535810112953,
0.009901716373860836,
0.03129385784268379,
0.00844275951385498,
-0.013885296881198883,
-0.03532169759273529,
0.004456332419067621,
0.00829964131116867,
0.013784455135464668,
-0.00468324264511466,
-0.01502635981887579,
0.04165546968579292,
0.00552821159362793,
0.03809216246008873,
-0.0056830462999641895,
-0.02055036649107933,
0.03284907341003418,
-0.06777730584144592,
0.015971781685948372,
0.019801441580057144,
-0.004847773816436529,
-0.006363700143992901,
0.0387985035777092,
0.029143551364541054,
0.01945919543504715,
0.014061655849218369,
0.004891022574156523,
-0.06675885617733002,
0.025328854098916054,
-0.060030266642570496,
-0.026979094371199608,
0.00016802255413495004,
0.006795472931116819,
0.010394127108156681,
-0.019921159371733665,
-0.02834423817694187,
-0.005711750127375126,
-0.021062728017568588,
-0.06236977502703667,
0.0015221640933305025,
-0.03666022792458534,
-0.054643504321575165,
-0.03290589898824692,
0.027191396802663803,
0.045297928154468536,
-0.046677365899086,
0.025634044781327248,
0.035002872347831726,
-0.028663083910942078,
-0.012705899775028229,
-0.03469541296362877,
-0.024281350895762444,
0.04855841025710106,
0.006811629049479961,
0.03471774980425835,
0.022085359320044518,
-0.0012407740578055382,
0.03265479579567909,
-0.004743923898786306,
0.0259761493653059,
0.007502371445298195,
-0.0563204325735569,
-0.02123960293829441,
-0.05208458751440048,
0.0019031187985092402,
0.00777340866625309,
0.03828791528940201,
0.006296874489635229,
-0.013208955526351929,
0.05617920681834221,
0.008456177078187466,
-0.0047976612113416195,
0.041256703436374664,
0.04162069037556648,
0.00741968210786581,
0.003586118808016181,
-0.07075832039117813,
0.036963921040296555,
-0.031140029430389404,
-0.01077315118163824,
0.01974332518875599,
-0.006861407775431871,
-0.03507797047495842,
0.0019506108947098255,
-0.013805851340293884,
0.007360562682151794,
0.0010922844521701336,
0.010657870210707188,
-0.059188950806856155,
0.02837652899324894,
0.0020139538682997227,
-0.004593126941472292,
-0.0009743953705765307,
0.035117149353027344,
0.03135009482502937,
-0.0019684291910380125,
-0.010457796975970268,
-0.08175607770681381,
0.007904157973825932,
0.009185370057821274,
0.030818263068795204,
-0.02295883186161518,
0.01078708004206419,
-0.05192140117287636,
-0.03931877389550209,
0.055636387318372726,
-0.013901099562644958,
0.03790116310119629,
0.01230317261070013,
0.00022161361994221807,
0.007636355236172676,
-0.026847049593925476,
-0.02679987996816635,
0.001232176087796688,
-0.020755425095558167,
-0.006390923168510199,
-0.017114803194999695,
0.008532636798918247,
-0.01595059037208557,
-0.01607961393892765,
0.019208652898669243,
0.049455441534519196,
0.03762505203485489,
-0.06277112662792206,
-0.01611466519534588,
0.007340929005295038,
-0.023672938346862793,
-0.044954799115657806,
-0.037939827889204025,
-0.0031118018086999655,
0.018668433651328087,
-0.004015604965388775,
-0.040244098752737045,
-0.0678040161728859,
0.023648537695407867,
-0.024625083431601524,
0.014174247160553932,
0.02214420773088932,
-0.03380094841122627,
0.0005235127173364162,
0.025408977642655373,
-0.0321308858692646,
0.051461026072502136,
0.06183251738548279,
-0.01713973842561245,
-0.015692606568336487,
0.009215216152369976,
0.03595733642578125,
-0.04376459866762161,
-0.05105540156364441,
-0.039946943521499634,
0.014861471951007843,
-0.04317064583301544,
0.03843217343091965,
0.012709471397101879,
0.018122004345059395,
-0.005919595714658499,
-0.02126190811395645,
0.020242605358362198,
0.04924168437719345,
0.0403660424053669,
0.0300737451761961,
-0.0008801597869023681,
0.03241404891014099,
0.004057299345731735,
-0.023270247504115105,
0.005883644334971905,
0.000978057156316936,
0.002313903532922268,
0.0289011150598526,
-0.008174325339496136,
0.016307896003127098,
-0.02170129306614399,
-0.0035718942526727915,
0.03239705041050911,
-0.03874003514647484,
0.004087476991117001,
0.0025420752353966236,
-0.00649620033800602,
0.02909020520746708,
-0.04932700842618942,
-0.06679317355155945,
-0.0013526121620088816,
0.0012469387147575617,
0.005378709174692631,
-0.06307749450206757,
0.0032532319892197847,
-0.010748961940407753,
0.025716489180922508,
-0.06670783460140228,
-0.036493200808763504,
0.029769567772746086,
-0.051900554448366165,
-0.010817093774676323,
-0.026706600561738014,
0.036802537739276886,
-0.0384499654173851,
-0.03953544795513153,
-0.01836652122437954,
0.07735245674848557,
-0.019958000630140305,
-0.018519936129450798,
-0.002055469201877713,
0.012176480144262314,
0.040677621960639954,
-0.02477186731994152,
-0.01884135603904724,
0.002453942084684968,
0.00014647882198914886,
0.007468027528375387,
0.023190654814243317,
0.06437787413597107,
-0.013717765919864178,
-0.008745995350182056,
-0.04384477064013481,
-0.009129881858825684,
0.04566020891070366,
-0.04305412247776985,
-0.006777695380151272,
0.08578004688024521,
0.003928865771740675,
0.010546470060944557,
-0.0005208671791478992,
0.035692911595106125,
-0.029224587604403496,
0.0020499243400990963,
0.028354031965136528,
-0.009516413323581219,
0.01185990683734417,
-0.013062751851975918,
0.020314766094088554,
-0.03085196577012539,
0.02463272586464882,
0.01086804922670126,
0.03582796826958656,
-0.031823232769966125,
0.0031279120594263077,
0.0032213672529906034,
-0.002484611002728343,
0.024219168350100517,
0.004322769120335579,
-0.014167370274662971,
0.012501498684287071,
-0.003418886801227927,
-0.058076877146959305,
0.008834511041641235,
-0.06566209346055984,
0.04001818969845772,
0.08257190883159637,
-0.00438702292740345,
0.0255674310028553,
-0.0052603306248784065,
0.04397575929760933,
0.033558160066604614,
-0.029669303447008133,
-0.02458215318620205,
-0.023825278505682945,
-0.0274447500705719,
0.04678136110305786,
-0.04513442516326904,
-0.010971269570291042,
0.022287804633378983,
0.05043038725852966,
0.004537711851298809,
0.00009242232044925913,
0.012412091717123985,
-0.013066602870821953,
-0.005414256360381842,
0.01572650671005249,
-0.02672511339187622,
0.03459876775741577,
-0.019849035888910294,
0.018673745915293694,
-0.006973105948418379,
-0.012108678929507732,
0.061432402580976486,
0.0037020579911768436,
0.023152444511651993,
-0.054649077355861664,
-0.01856902800500393,
-0.033043380826711655,
0.034258969128131866,
0.03679715842008591,
0.030155006796121597,
0.004447766114026308,
0.03656337037682533,
0.07318268716335297,
0.027002518996596336,
0.008049238473176956,
-0.013171453028917313,
-0.045441191643476486,
-0.029133901000022888,
-0.027485990896821022,
-0.051152803003787994,
0.02800394594669342,
-0.027851708233356476,
-0.025688158348202705,
0.0025728459004312754,
-0.027668219059705734,
0.015492696315050125,
0.03913659229874611,
0.04279956966638565,
-0.015249734744429588,
0.10016035288572311,
-0.033344946801662445,
-0.025836901739239693,
-0.022142967209219933,
0.006234779953956604,
0.11124412715435028,
0.016142072156071663,
0.03517715260386467,
-0.018229680135846138,
0.024735555052757263,
-0.040721695870161057,
-0.002931024879217148,
-0.02235604263842106,
0.020160315558314323,
0.0014346702955663204,
-0.012252479791641235,
-0.001313579617999494,
0.04187846928834915,
0.009585412219166756,
-0.02029121294617653,
0.039393894374370575,
-0.02307000942528248,
-0.01601751334965229,
0.022643914446234703,
-0.01107078418135643,
0.011524503119289875,
0.01562686450779438,
0.006925480905920267,
0.020680474117398262,
-0.004648780915886164,
0.03343336656689644,
-0.0069365715608000755,
-0.010191465727984905,
-0.026712942868471146,
0.010740266181528568,
-0.05726030468940735,
-0.008861444890499115,
0.03086346574127674,
-0.012015166692435741,
-0.02218639850616455,
0.0027693668380379677,
-0.011466448195278645,
-0.0198525320738554,
0.0448845736682415,
0.02881605364382267,
0.0014679275918751955,
0.026349786669015884,
0.04641719534993172,
-0.015297655016183853,
-0.04439729452133179,
0.010041582398116589,
-0.036776818335056305,
0.018015313893556595,
0.0007199108949862421,
0.030953846871852875,
0.024672547355294228,
-0.02062024362385273,
0.002334032906219363,
-0.07630668580532074,
0.009882228448987007,
0.011223498731851578,
0.014462743885815144,
-0.009593019261956215,
0.0006803920841775835,
-0.03521749749779701,
0.029225267469882965,
0.021959898993372917,
0.01386964600533247,
0.0065919868648052216,
0.027287660166621208,
-0.00468107033520937,
0.02044343762099743,
0.05908631905913353,
-0.026193194091320038,
-0.032623499631881714,
-0.02120659500360489,
-0.007325991056859493,
-0.05097659304738045,
-0.027301661670207977,
0.02545878104865551,
0.03400791808962822,
0.0210106298327446,
0.00019616946519818157,
0.014355451799929142,
-0.019448723644018173,
-0.08647889643907547,
0.024246694520115852,
0.017628202214837074,
0.009064964018762112,
-0.022639542818069458,
0.032587066292762756,
-0.006901168264448643,
0.022321468219161034,
-0.038794901221990585,
0.006084644701331854,
-0.01903216913342476,
0.02081303857266903,
0.0029075739439576864,
-0.0397481806576252,
-0.00566538330167532,
0.0000608033369644545,
0.0011121786665171385,
-0.0174560584127903,
-0.03169791027903557,
-0.000720182724762708,
0.038084521889686584,
0.0065657831728458405,
-0.03472642973065376,
0.022563138976693153,
-0.007155522704124451,
0.017172295600175858,
0.01735088601708412,
0.015666868537664413,
0.018884548917412758,
0.012498215772211552,
-0.009193584322929382,
-0.038522880524396896,
0.011267774738371372,
-0.05936824902892113,
-0.009004066698253155,
-0.0532459020614624,
0.03348201513290405,
-0.03812025859951973,
0.02700911834836006,
-0.02408423274755478,
0.012813746929168701,
-0.008044097572565079,
-0.009796051308512688,
-0.02600049041211605,
0.015529747121036053,
-0.01411441806703806,
-0.00507832458242774,
-0.036949820816516876,
0.04337375983595848,
-0.04225867614150047,
-0.01955309696495533,
0.022855903953313828,
0.013106076046824455,
-0.014802895486354828,
-0.027124857529997826,
0.028360536321997643,
-0.03541150689125061,
0.06003500893712044,
-0.028025850653648376,
-0.03248792514204979,
0.015290592797100544,
-0.0038661472499370575,
-0.027045220136642456,
0.03517364338040352,
0.012958664447069168,
0.03435526788234711,
0.010897349566221237,
-0.01840759441256523,
0.008100424893200397,
0.06953126937150955,
-0.03224625065922737,
0.009019311517477036,
0.009092873893678188,
-0.03910617530345917,
-0.0008777628536336124,
-0.00340076582506299,
0.017402123659849167,
-0.008869530633091927,
-0.013593314215540886,
0.02701571211218834,
0.014450681395828724,
-0.01699366793036461,
0.013994798995554447,
0.008619447238743305,
-0.004263286013156176,
0.007456392981112003,
0.015992341563105583,
0.03550964221358299,
0.0313640795648098,
0.03135869279503822,
-0.006385015323758125,
-0.00459576491266489,
0.020185818895697594,
0.014858080074191093,
-0.10827261209487915,
-0.026347145438194275,
-0.01059060450643301,
0.03628731518983841,
0.04461311176419258,
-0.0302156750112772,
-0.022676941007375717,
0.016835931688547134,
-0.04747324436903,
-0.04183873161673546,
-0.06080866605043411,
-0.010693144053220749,
0.0047177523374557495,
-0.016772761940956116,
0.014718873426318169,
0.050375889986753464,
0.030400119721889496,
0.005537736229598522,
-0.0034506407100707293,
-0.0009184714872390032,
-0.011873754672706127,
-0.02288537472486496,
0.01569601520895958,
0.025639789178967476,
0.02183752879500389,
-0.012295925058424473,
0.0408683642745018,
0.017330152913928032,
-0.06694893538951874,
0.060561541467905045,
0.00944528914988041,
0.006521509028971195,
-0.025398559868335724,
0.042606815695762634,
-0.014258502051234245,
0.03174007311463356,
0.012489255517721176,
-0.012501523829996586,
-0.02387133426964283,
-0.014211528934538364,
0.0182122141122818,
0.019365500658750534,
-0.04162485525012016,
-0.01868695765733719,
0.021310044452548027,
-0.047316618263721466,
-0.04303388297557831,
-0.01211563404649496,
-0.02366645261645317,
-0.017389606684446335,
-0.014187730848789215,
0.0039567407220602036,
0.005825518164783716,
-0.03014683537185192,
0.02688777819275856,
-0.04760090634226799,
0.016499949619174004,
0.03204768896102905,
-0.028937017545104027,
0.035118039697408676,
0.009840845130383968,
0.04636460542678833,
-0.01481952890753746,
0.024854375049471855,
0.009151325561106205,
-0.01922428235411644,
-0.059177596122026443,
-0.011875319294631481,
0.0017174966633319855,
-0.00621278490871191,
-0.03643916919827461,
-0.054177746176719666,
-0.019939200952649117,
0.05865549296140671,
0.006402676925063133,
0.05053642764687538,
-0.016840482130646706,
-0.011052357964217663,
-0.007998928427696228,
-0.046849120408296585,
0.029402481392025948,
0.008773046545684338,
-0.05352848023176193,
-0.039097078144550323,
-0.01849740371108055,
-0.002434468362480402,
0.0005843901890330017,
0.055249642580747604,
-0.009846367873251438,
-0.013088364154100418,
0.030251912772655487,
0.017291922122240067,
-0.021818559616804123,
-0.027194932103157043,
0.003274553921073675,
-0.0061414893716573715,
-0.020145226269960403,
0.04675843194127083,
0.008595656603574753,
-0.010572230443358421,
-0.004802871961146593,
-0.0013064498780295253,
-0.02355107292532921,
0.04213951900601387,
0.04332732409238815,
-0.034051187336444855,
0.03301304951310158,
0.041730668395757675,
-0.019002653658390045,
0.047508325427770615,
-0.01429555844515562,
0.014300666749477386,
0.025828029960393906,
-0.024608679115772247,
-0.06609313189983368,
-0.011219716630876064,
-0.021630026400089264,
-0.022409522905945778,
-0.03066324256360531,
0.011668235994875431,
-0.0069286879152059555,
-0.028031503781676292,
0.0067368727177381516,
0.0903305783867836,
-0.05374225601553917,
-0.016307681798934937,
0.026488693431019783,
0.024395301938056946,
0.05973711609840393,
0.0216752290725708,
0.019359905272722244,
0.03131396323442459,
-0.019085031002759933,
0.007995646446943283,
0.004297193139791489,
0.03981560841202736,
0.00010278457921231166,
-0.00841578934341669,
0.07349149137735367,
-0.011647088453173637,
-0.002931607887148857,
0.0015356987714767456,
0.04347690939903259,
-0.025903567671775818,
-0.016922254115343094,
-0.025587907060980797,
-0.005338987335562706,
-0.008860071189701557,
0.04779326915740967,
-0.03197074681520462,
0.05902386084198952,
0.007268229965120554,
0.010653545148670673,
-0.02204878255724907,
0.01953245885670185,
-0.03136386349797249,
0.017289215698838234,
0.006316143088042736,
0.04200734198093414,
-0.007426018826663494,
-0.0020898280199617147,
0.006273770704865456,
-0.04255720227956772,
-0.00316437054425478,
-0.019955024123191833,
-0.024921972304582596,
0.004722692538052797,
0.018467778339982033,
-0.027300141751766205,
0.009384913370013237,
-0.054463643580675125,
-0.03281387686729431,
0.023123132064938545,
0.03286174684762955,
0.0546158030629158,
-0.01690617762506008,
0.004765660502016544,
-0.01565566286444664,
0.04012744128704071,
-0.08753570914268494,
-0.03119577094912529,
-0.024790514260530472,
0.01986999809741974,
-0.001558174379169941,
-0.017893802374601364
] |
<p>I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it there?</p>
<p>I undertand all the advantages that came <em>after</em>
$$\vec v = \vec\omega\times\vec r$$
$$\vec a = \vec\alpha\times\vec r + \vec\omega\times\vec v$$</p>
<p>but I can't see what's before.</p>
<p>PS. I know there is another question opened: <a href="http://physics.stackexchange.com/questions/69345/direction-of-angular-velocity">Direction of angular velocity</a> but I don't understand the answers given there (it's stated that angular velocity <em>points in every direction of the circumference's plane</em>!?) and I can't comment yet so please don't close this one. Thank you.</p>
| 8,318 |
[
-0.03115513175725937,
-0.0038928850553929806,
-0.005513549782335758,
-0.020961659029126167,
0.011512073688209057,
-0.009878319688141346,
-0.02349533885717392,
-0.015885230153799057,
-0.02195359580218792,
0.012422536499798298,
-0.00825019646435976,
0.05074680596590042,
0.08444714546203613,
0.02431502193212509,
0.02577059343457222,
-0.00004654274016502313,
0.00250324048101902,
-0.02818882092833519,
-0.010933035984635353,
-0.052403174340724945,
-0.01151210069656372,
0.004970707464963198,
-0.028593014925718307,
0.015943223610520363,
0.01301638875156641,
0.03291269391775131,
0.0004530767328105867,
-0.011442846618592739,
0.013215441256761551,
0.04100322723388672,
-0.0269665215164423,
0.0026869962457567453,
0.027541140094399452,
0.01702926866710186,
0.0303361676633358,
-0.002854919759556651,
-0.03389524295926094,
0.017809733748435974,
-0.01638445444405079,
0.031464528292417526,
-0.029965940862894058,
0.01566344127058983,
-0.02835833467543125,
0.053539860993623734,
-0.004114675801247358,
0.04570687562227249,
-0.02166842669248581,
0.009725766256451607,
0.0607525072991848,
-0.057330790907144547,
0.03511105850338936,
-0.02099444344639778,
-0.003672417253255844,
0.007196960039436817,
0.0182801540941,
0.009745797142386436,
0.08509860932826996,
0.03938872367143631,
-0.014073967933654785,
-0.018860861659049988,
0.006666218861937523,
-0.0083275455981493,
-0.00981946475803852,
0.005844253581017256,
0.001554566086269915,
-0.0006272498285397887,
0.043342649936676025,
0.007790768053382635,
0.01641479693353176,
-0.028857313096523285,
-0.004769230727106333,
0.018626363947987556,
0.012462510727345943,
-0.04026973992586136,
0.0018006757600232959,
-0.03832363709807396,
0.024919293820858,
0.0005023062694817781,
0.030408864840865135,
0.01826597936451435,
-0.02124158851802349,
0.009473494254052639,
0.07388853281736374,
0.029283402487635612,
-0.004184877034276724,
0.004272863734513521,
0.05747656524181366,
0.008269974030554295,
0.0022291250061243773,
0.027776453644037247,
0.004319795407354832,
-0.005133943632245064,
0.03486059978604317,
0.011095939204096794,
0.0023584640584886074,
0.009663989767432213,
-0.0006193455774337053,
0.0383959524333477,
0.0365598127245903,
-0.0032516687642782927,
0.0035595805384218693,
-0.05313696339726448,
0.014029799029231071,
0.07867569476366043,
0.0032106139697134495,
-0.02301834337413311,
-0.04187976196408272,
0.024817828088998795,
-0.006674075499176979,
-0.023472273722290993,
-0.06508864462375641,
0.039292264729738235,
-0.03890183940529823,
0.019046980887651443,
0.01281429547816515,
-0.015538672916591167,
0.02437244914472103,
0.022214747965335846,
0.06571754813194275,
0.03286602348089218,
0.05930323153734207,
-0.02348916418850422,
-0.019060123711824417,
-0.044626910239458084,
-0.05552173778414726,
0.03114810585975647,
0.025291645899415016,
-0.015127623453736305,
-0.020634135231375694,
0.0000455873814644292,
0.01574537716805935,
-0.013345017097890377,
0.0030275662429630756,
-0.015139020048081875,
0.007265453226864338,
-0.005906073842197657,
-0.10540501773357391,
-0.09321599453687668,
0.08094950020313263,
0.030580973252654076,
-0.036684464663267136,
-0.07133233547210693,
-0.0036083294544368982,
0.021261420100927353,
0.08001973479986191,
-0.03798656538128853,
-0.0211221594363451,
0.018237143754959106,
0.04821774363517761,
0.013231405057013035,
-0.0007950228755362332,
-0.0191670972853899,
-0.018936900421977043,
-0.039152756333351135,
-0.029480233788490295,
-0.056801579892635345,
0.028531799092888832,
0.004014521837234497,
0.01764979586005211,
-0.034456342458724976,
0.08017738163471222,
-0.049288198351860046,
0.033604901283979416,
0.008601636625826359,
0.005898232571780682,
-0.031851693987846375,
0.08860194683074951,
0.04719715937972069,
-0.0033517139963805676,
0.028924020007252693,
-0.02336231991648674,
0.023830918595194817,
-0.008379699662327766,
-0.001009394763968885,
0.07782106846570969,
-0.021961672231554985,
-0.01370823010802269,
-0.029339320957660675,
0.0006111323600634933,
0.001418344210833311,
-0.017430346459150314,
-0.05729063227772713,
0.00551902549341321,
0.01370264496654272,
0.003827358828857541,
0.0709681361913681,
-0.019697602838277817,
0.02115752547979355,
-0.020576735958456993,
-0.04647974297404289,
0.016903288662433624,
-0.036637187004089355,
0.031121710315346718,
-0.004681321792304516,
-0.03449207544326782,
0.008639655075967312,
0.016862640157341957,
-0.019717009738087654,
-0.015273848548531532,
-0.0014591621002182364,
0.01937103271484375,
0.05236658826470375,
0.02426268346607685,
0.010678542777895927,
0.02823653258383274,
0.029812920838594437,
0.017972053959965706,
-0.03722758963704109,
-0.020710429176688194,
-0.015995102003216743,
-0.017279960215091705,
0.003012482775375247,
0.02206050604581833,
0.009487279690802097,
0.03836642950773239,
-0.018195979297161102,
-0.01435971911996603,
0.03703278303146362,
-0.024219825863838196,
0.0492602176964283,
-0.043008431792259216,
0.08222298324108124,
0.06520357728004456,
-0.0016665405128151178,
0.03351740539073944,
0.0623970590531826,
0.005385282915085554,
0.017410770058631897,
0.04008631780743599,
-0.026304902508854866,
-0.06902660429477692,
0.0010950204450637102,
0.03090469166636467,
0.011775962077081203,
-0.0412343293428421,
-0.007873060181736946,
0.021895738318562508,
0.036630697548389435,
-0.016649439930915833,
-0.02627624198794365,
-0.02090919017791748,
-0.05013525113463402,
-0.022138165310025215,
0.01980067603290081,
-0.006215142086148262,
0.0001680074055911973,
0.013334846124053001,
0.0064711738377809525,
0.01645013317465782,
0.02730781026184559,
-0.012644138187170029,
0.05035296082496643,
0.0159932691603899,
0.006416060496121645,
0.03549221530556679,
-0.01041201502084732,
0.03447839990258217,
-0.02939063124358654,
0.025562182068824768,
0.05160677433013916,
0.017098119482398033,
0.006245737429708242,
-0.030576322227716446,
-0.0071109808050096035,
0.010923254303634167,
0.006181736011058092,
-0.015220360830426216,
-0.015109030529856682,
0.025331808254122734,
-0.025795839726924896,
-0.01625438779592514,
-0.02247690223157406,
-0.01646825671195984,
0.001049016136676073,
0.00294101401232183,
-0.0018092921236529946,
0.0019395375857129693,
0.024692881852388382,
-0.031926557421684265,
-0.012075473554432392,
-0.026245413348078728,
-0.019010653719305992,
-0.031022751703858376,
0.011321269907057285,
-0.03913373127579689,
0.019343458116054535,
-0.032587774097919464,
-0.02173595502972603,
0.03698626533150673,
-0.010758105665445328,
-0.025130175054073334,
0.007521682418882847,
0.027043169364333153,
-0.05498134717345238,
-0.03515837714076042,
-0.007174543105065823,
0.035377420485019684,
-0.05735371261835098,
-0.024325888603925705,
0.05102049559354782,
-0.031598642468452454,
-0.03174988552927971,
0.03370237350463867,
-0.04016659036278725,
-0.024575646966695786,
0.006451689638197422,
-0.003655158681795001,
0.019905179738998413,
-0.015832146629691124,
-0.03642444685101509,
0.030139809474349022,
-0.004792311694473028,
-0.00028130027931183577,
-0.02912004478275776,
-0.035512711852788925,
-0.024666400626301765,
-0.014975624158978462,
0.043652601540088654,
-0.018419617787003517,
-0.001797833596356213,
0.08011077344417572,
0.02122431807219982,
-0.05270935967564583,
-0.027061421424150467,
-0.006430486682802439,
-0.013080600649118423,
-0.052327726036310196,
-0.003955367021262646,
0.04347825050354004,
-0.015342089347541332,
0.0035522496327757835,
0.012183214537799358,
0.025076288729906082,
0.013417758047580719,
0.025584876537322998,
-0.009745930321514606,
-0.006177493836730719,
0.02648220583796501,
-0.02192051149904728,
0.06987206637859344,
0.011664985679090023,
-0.017042003571987152,
-0.023993872106075287,
-0.012955446727573872,
0.03643357753753662,
0.04300735890865326,
-0.07277001440525055,
0.006746345665305853,
-0.0005994452512823045,
-0.002181966556236148,
0.013548989780247211,
0.0317239984869957,
0.007780809421092272,
0.02053052932024002,
-0.011588224209845066,
0.008241245523095131,
0.059837985783815384,
-0.020635360851883888,
0.007724064867943525,
0.011433136649429798,
-0.0002617564459796995,
-0.022787731140851974,
-0.0017329473048448563,
-0.031267520040273666,
0.01391302328556776,
0.021353093907237053,
-0.010347506031394005,
-0.014788255095481873,
0.02934897318482399,
0.05202542617917061,
-0.012524483725428581,
0.00023541295377071947,
-0.06466344743967056,
-0.01924658939242363,
-0.05102887749671936,
0.011048618704080582,
-0.014214198105037212,
0.04641830548644066,
0.00980419758707285,
0.0781710296869278,
0.030943255871534348,
0.0187179334461689,
-0.0171397402882576,
0.007055609952658415,
-0.06651023775339127,
-0.0074828993529081345,
-0.046906210482120514,
-0.01618298329412937,
-0.026804665103554726,
-0.02585868537425995,
-0.018733523786067963,
-0.017906947061419487,
-0.030130349099636078,
0.006594227161258459,
-0.034904949367046356,
-0.05556796118617058,
-0.0006528309313580394,
-0.03172558918595314,
-0.050392039120197296,
-0.03180414438247681,
0.04628394544124603,
0.04355492442846298,
-0.021931534633040428,
0.057347800582647324,
0.05228079855442047,
-0.03717435523867607,
-0.005819358862936497,
0.002897422295063734,
0.000759977730922401,
-0.008777562528848648,
0.027292760089039803,
-0.0013084675883874297,
-0.011661258526146412,
-0.005471269134432077,
0.004164605401456356,
0.02227787859737873,
0.03205671161413193,
0.01131001953035593,
-0.027135882526636124,
-0.005545404739677906,
-0.03728550300002098,
0.006281272042542696,
-0.04576713591814041,
0.058269958943128586,
-0.008378114551305771,
0.009389190934598446,
0.04955289512872696,
-0.016905469819903374,
-0.003722574794664979,
0.009227976202964783,
0.025807488709688187,
-0.0062408423982560635,
-0.025773631408810616,
-0.06706765294075012,
-0.020632654428482056,
-0.009077438153326511,
0.006735944654792547,
-0.008224989287555218,
-0.013913321308791637,
-0.01844954304397106,
-0.03223002701997757,
-0.00787520594894886,
-0.008987120352685452,
0.014901765622198582,
0.04073306918144226,
-0.03408059850335121,
-0.0039002227131277323,
-0.027046890929341316,
-0.004555907566100359,
-0.009684900753200054,
0.015389707870781422,
0.06826116144657135,
0.030794374644756317,
0.003867810359224677,
-0.03663461282849312,
-0.0253042783588171,
0.024518894031643867,
0.04195872321724892,
-0.02879262901842594,
-0.02008446864783764,
-0.05647715926170349,
-0.04564264789223671,
0.04942319542169571,
-0.05366368964314461,
0.04679690673947334,
-0.0630682036280632,
-0.0011494798818603158,
-0.052909452468156815,
-0.048933811485767365,
-0.015398470684885979,
0.006735595874488354,
-0.012181442230939865,
0.000755357788875699,
-0.015152506530284882,
0.012569545768201351,
-0.03248779848217964,
-0.00679363589733839,
0.06124625727534294,
0.03641073778271675,
0.022058969363570213,
-0.019496897235512733,
0.0007471177377738059,
0.004670711234211922,
-0.02092231810092926,
-0.0514681339263916,
0.0030033241491764784,
0.008749442175030708,
-0.009809749200940132,
0.003060809103772044,
-0.041379138827323914,
-0.04361693188548088,
0.023432865738868713,
0.0012435666285455227,
0.005697960965335369,
0.006962251383811235,
-0.026369856670498848,
0.04694749414920807,
0.05302305147051811,
-0.019188793376088142,
0.018435925245285034,
0.0577852800488472,
-0.019410107284784317,
-0.014569761231541634,
0.006424791179597378,
0.010178676806390285,
0.011130820959806442,
-0.030538974329829216,
-0.01439778134226799,
0.016188522800803185,
-0.03920503705739975,
0.04396158829331398,
0.011431130580604076,
0.0057235537096858025,
-0.036661095917224884,
-0.06798005104064941,
-0.021900799125432968,
0.03106406331062317,
-0.00016383723414037377,
-0.010970859788358212,
0.03202788159251213,
0.009795768186450005,
0.03696233779191971,
-0.0067672464065253735,
0.035263851284980774,
-0.02522893063724041,
0.03807718679308891,
0.06625408679246902,
0.022675804793834686,
-0.008286509662866592,
-0.006530412007123232,
-0.023199988529086113,
0.0003055081469938159,
-0.06629616022109985,
0.03872308135032654,
-0.011435971595346928,
-0.00587132154032588,
0.034770216792821884,
-0.0981241911649704,
-0.05426221340894699,
-0.0009407911566086113,
-0.005007079336792231,
0.012357335537672043,
-0.059288810938596725,
0.018612630665302277,
0.0038576419465243816,
0.021479785442352295,
-0.04899461567401886,
-0.012758027762174606,
-0.008270404301583767,
-0.005293090827763081,
-0.019481275230646133,
0.0005810983129777014,
0.000024988428776850924,
-0.018879376351833344,
-0.024580804631114006,
-0.01640392653644085,
0.024083251133561134,
-0.012312212027609348,
-0.012147818692028522,
0.01448542345315218,
-0.009328936226665974,
0.07092133164405823,
-0.006580778397619724,
-0.019844383001327515,
0.02241932600736618,
0.01451452262699604,
0.02747463807463646,
0.023789390921592712,
0.0724945068359375,
-0.0279450211673975,
-0.029966404661536217,
0.007888665422797203,
0.0035237593110650778,
0.03517380356788635,
0.024811672046780586,
-0.0003040576120838523,
0.020789388567209244,
-0.009705650620162487,
-0.03461287543177605,
-0.058856431394815445,
0.02498011104762554,
0.00995569583028555,
-0.0057821981608867645,
0.0010667083552107215,
0.020278088748455048,
-0.019145166501402855,
-0.03746337071061134,
0.008085528388619423,
0.004344161134213209,
0.021337810903787613,
-0.00958295539021492,
0.04298103228211403,
-0.06501118838787079,
0.01092454046010971,
-0.01563190668821335,
-0.0011562086874619126,
0.02615748718380928,
0.01262721512466669,
-0.046363696455955505,
0.025605730712413788,
0.005101424641907215,
-0.03971492499113083,
-0.028905101120471954,
-0.017380783334374428,
0.06413484364748001,
0.08048006892204285,
-0.015994077548384666,
0.04959404841065407,
0.02191367745399475,
0.009311873465776443,
-0.0054500107653439045,
0.008265141397714615,
-0.009898173622786999,
-0.039314623922109604,
0.012058704160153866,
0.01562521979212761,
-0.026820745319128036,
0.001514208852313459,
0.011969382874667645,
0.0646369606256485,
0.01365627720952034,
-0.050207819789648056,
0.03776147961616516,
0.03460674732923508,
0.027805577963590622,
0.00643491093069315,
-0.01783025451004505,
0.04422147199511528,
-0.030455097556114197,
0.0414835624396801,
0.00450728228315711,
-0.03979295492172241,
0.03919947147369385,
-0.006513336207717657,
-0.0004983663093298674,
-0.06576836854219437,
0.026317089796066284,
-0.010084773413836956,
-0.020253553986549377,
0.008150969631969929,
0.012482333928346634,
-0.0649983137845993,
0.0033808094449341297,
0.052323129028081894,
-0.0032775853760540485,
-0.0006610259297303855,
-0.01689654029905796,
-0.04881134629249573,
-0.027019882574677467,
-0.034150656312704086,
-0.05218767747282982,
0.0412469319999218,
-0.011074558831751347,
-0.060633428394794464,
0.019486399367451668,
-0.05304265767335892,
0.011231742799282074,
0.011716252192854881,
0.019666261970996857,
0.016380172222852707,
0.08846306800842285,
-0.004537743516266346,
0.011315863579511642,
-0.03463512659072876,
-0.0179130882024765,
0.10346066951751709,
0.0305176991969347,
-0.007283790502697229,
-0.04020203277468681,
0.0462593249976635,
-0.009302080608904362,
0.016762197017669678,
-0.024579903110861778,
0.006942991632968187,
-0.029701929539442062,
0.02844351716339588,
0.027816567569971085,
0.03823063150048256,
0.032199446111917496,
0.01727944053709507,
0.002178770722821355,
-0.06549112498760223,
-0.02611684240400791,
0.0011753520229831338,
-0.026870442554354668,
0.00721753342077136,
0.022657543420791626,
-0.018454328179359436,
0.006312505342066288,
-0.02084234356880188,
-0.02868403121829033,
-0.025907844305038452,
-0.026629827916622162,
0.016248460859060287,
-0.024557171389460564,
-0.0464644692838192,
0.012808868661522865,
0.015341108664870262,
-0.042874205857515335,
-0.04211398959159851,
0.02421422488987446,
0.005996059160679579,
-0.03072386607527733,
0.046751778572797775,
0.025808708742260933,
-0.006435983348637819,
-0.0028857372235506773,
0.014171870425343513,
0.01767110638320446,
-0.026428204029798508,
0.0019272713689133525,
-0.02843347191810608,
0.05199946090579033,
-0.04232614114880562,
0.023297714069485664,
-0.0023274312261492014,
0.012694683857262135,
-0.005776053294539452,
-0.06486321240663528,
-0.010744419880211353,
0.006396320648491383,
0.04866062104701996,
-0.006781077943742275,
-0.017783386632800102,
0.00025263879797421396,
0.016967512667179108,
-0.009327232837677002,
0.018222836777567863,
-0.014017964713275433,
-0.014052961952984333,
-0.03824746236205101,
0.0025085594970732927,
0.03228030353784561,
-0.016547469422221184,
-0.011916253715753555,
0.006915226578712463,
0.01717006042599678,
-0.07666871696710587,
0.020656228065490723,
0.0203672107309103,
0.015548162162303925,
0.016853712499141693,
-0.007443864829838276,
-0.004115920048207045,
-0.017203902825713158,
-0.03237894922494888,
-0.01620379090309143,
-0.014075048267841339,
-0.016528407111763954,
-0.03655673936009407,
-0.016027379781007767,
0.014249385334551334,
0.039494361728429794,
-0.016445467248558998,
-0.008147409185767174,
-0.015207771211862564,
0.0528654120862484,
0.02098442241549492,
0.0025671750772744417,
-0.07678809762001038,
0.04288819059729576,
-0.032446738332509995,
0.04134669899940491,
0.0028449934907257557,
0.023477910086512566,
0.029424497857689857,
0.0021367385052144527,
0.03230958804488182,
0.028298715129494667,
-0.03691044822335243,
-0.02740440145134926,
0.036666907370090485,
-0.05197881534695625,
0.013621431775391102,
0.02939564175903797,
-0.017248431220650673,
-0.05155966803431511,
0.01024266891181469,
-0.029033666476607323,
-0.010973691008985043,
-0.0013994983164593577,
0.021601812914013863,
-0.013427766039967537,
0.026035213842988014,
-0.05763519927859306,
0.020232267677783966,
-0.03732618689537048,
0.014474637806415558,
-0.03429366275668144,
0.01939222775399685,
0.011483043432235718,
-0.02520405687391758,
-0.03134167194366455,
0.05181381106376648,
-0.002802246017381549,
-0.011415569111704826,
-0.030583195388317108,
0.023626355454325676,
-0.005669125355780125,
0.011377764865756035,
0.006462969351559877,
0.008802222087979317,
0.05122167617082596,
-0.02405441738665104,
-0.016401780769228935,
0.0373929999768734,
-0.0043695829808712006,
-0.043770335614681244,
0.034577321261167526,
0.016440993174910545,
0.011439579539000988,
0.009035477414727211,
0.0022280721459537745,
0.013909084722399712,
0.0333116315305233,
-0.0029469619039446115,
-0.009970071725547314,
0.009627440944314003,
-0.03971865773200989,
0.04367446526885033,
-0.015421630814671516,
-0.005710544064640999,
-0.02725515328347683,
0.005166151560842991,
0.026745367795228958,
0.0449400469660759,
-0.007484894245862961,
-0.006118531804531813,
0.01187939289957285,
0.03292421996593475,
-0.0096210902556777,
0.02756921574473381,
0.01702771708369255,
0.027589866891503334,
0.012666992843151093,
-0.06557244062423706,
0.043393589556217194,
0.05431413650512695,
0.0029394386801868677,
-0.07011386007070541,
-0.007102631032466888,
0.0132584935054183,
0.014291631989181042,
0.03050675429403782,
-0.06837061047554016,
0.014835560694336891,
0.04699421674013138,
-0.10915817320346832,
0.04652199149131775,
-0.03090411238372326,
-0.012935377657413483,
-0.05058947950601578,
-0.014361868612468243,
-0.01414090022444725,
0.0712691992521286,
-0.004732382018119097,
0.006492134649306536,
0.03223169967532158,
0.008134441450238228,
-0.017904823645949364,
-0.06209312006831169,
-0.004707374610006809,
0.08057360351085663,
0.0013385879574343562,
0.014666271395981312,
0.05753771960735321,
0.018768740817904472,
-0.021837420761585236,
0.030845286324620247,
-0.03310523182153702,
0.007868558168411255,
-0.004473528359085321,
-0.0022045723162591457,
-0.014916441403329372,
0.03621116280555725,
0.015279121696949005,
0.01449452806264162,
-0.055084485560655594,
0.009177081286907196,
0.03724925220012665,
0.017393656075000763,
0.01881103403866291,
0.008844130672514439,
0.029508080333471298,
-0.007485165260732174,
-0.0013633851194754243,
0.011167643591761589,
-0.005672196391969919,
-0.007084941957145929,
0.01186372060328722,
0.014735867269337177,
0.007576271891593933,
-0.03301641717553139,
-0.018019849434494972,
-0.032096605747938156,
0.01657133549451828,
0.008998646400868893,
0.0026753125712275505,
0.01604529470205307,
-0.02207014709711075,
0.007877448573708534,
-0.04107721149921417,
0.012254542671144009,
-0.0034679651726037264,
0.011869900859892368,
-0.057166166603565216,
0.0011786601971834898,
-0.016696877777576447,
-0.0268254391849041,
0.013004051521420479,
0.009098835289478302,
-0.015316602773964405,
0.009275663644075394,
0.047160807996988297,
0.008201807737350464,
-0.004475552123039961,
-0.0020641430746763945,
-0.01193238515406847,
-0.07211008667945862,
0.062053125351667404,
0.021942462772130966,
-0.03663698211312294,
-0.025569239631295204,
-0.04190966859459877,
0.003213884774595499,
0.023584792390465736,
0.059273380786180496,
-0.003811368253082037,
-0.014040491543710232,
0.018818557262420654,
-0.01347543764859438,
0.015034878626465797,
-0.019296612590551376,
0.023412831127643585,
-0.013839267194271088,
-0.004262065980583429,
0.014395228587090969,
-0.02578297257423401,
-0.03375856205821037,
0.014746651984751225,
0.0243103988468647,
-0.006161781959235668,
0.051240239292383194,
-0.03339052200317383,
-0.01639147289097309,
0.0050176894292235374,
0.01115671917796135,
-0.0015805615112185478,
0.08607099205255508,
0.05184352770447731,
0.0014539114199578762,
0.036919765174388885,
-0.017624342814087868,
-0.019021041691303253,
0.009638410992920399,
-0.04895814508199692,
-0.052818771451711655,
-0.02855503372848034,
0.008750218898057938,
0.05727148428559303,
-0.06599155813455582,
-0.003492901800200343,
0.052127741277217865,
-0.05255249887704849,
-0.03343728929758072,
0.033944789320230484,
0.023341462016105652,
0.054468873888254166,
0.004391826689243317,
0.02092309482395649,
0.018916895613074303,
-0.05495527386665344,
-0.031607285141944885,
0.005212188232690096,
0.038888659328222275,
0.010336928069591522,
0.012421953491866589,
0.04270344600081444,
0.01074357982724905,
0.03654363378882408,
-0.03771035745739937,
0.04799347370862961,
-0.017040370032191277,
0.012364733032882214,
0.004617027938365936,
-0.03226751834154129,
0.011715443804860115,
0.03226572275161743,
-0.013475071638822556,
0.09227319061756134,
-0.012606502510607243,
0.01960158906877041,
0.023385850712656975,
-0.009350989945232868,
-0.02988276444375515,
-0.015952320769429207,
0.0265911053866148,
0.009599928744137287,
-0.021271219477057457,
-0.007292978931218386,
0.015198316425085068,
-0.02120775543153286,
0.05602734535932541,
-0.001781552447937429,
0.017863230779767036,
0.021389400586485863,
-0.013304085470736027,
-0.013356038369238377,
-0.014591575600206852,
0.010125655680894852,
-0.009807177819311619,
0.029424861073493958,
0.04499354213476181,
0.024815283715724945,
0.015765173360705376,
-0.003174067009240389,
0.0013217232190072536,
0.03557148948311806,
-0.04092572256922722,
-0.014423039741814137,
-0.03544885665178299,
0.06173042207956314,
0.036394838243722916,
0.007432935293763876
] |
<p>Suppose we have the following Slater determinant:
\begin{equation}
| \Psi \rangle = \prod \limits_{i,i'} a^+_{i\alpha} a^+_{i'\beta} | \rangle
\end{equation}
where $a^+_{i\alpha}$ creates an electron in state $i$ with spin $\alpha$ and, in general, $i \neq i'$. I want to evaluate $\langle \Psi | S^2 | \Psi \rangle$ using second quantization. We can express the $S^2$ operator as
\begin{equation}
S^2 = S_- S_+ + S_z (S_z +1)
\end{equation}
with
\begin{equation}
S_- = \sum_p a^+_{p\beta} a_{p \alpha} \hspace{1.5cm}
S_+ = \sum_p a^+_{p\alpha} a_{p \beta}.
\end{equation}
Since $|\Psi \rangle$ is an eigenfunction of $S_z$, evaluating $\langle \Psi | S_z | \Psi \rangle$ terms becomes trivial and the problem reduces to the evaluation of $\langle \Psi | S_- S_+ | \Psi \rangle$. In the standard restricted Hartree-Fock method, $i = i'$ and it is easy to show that $\langle \Psi | S_- S_+ | \Psi \rangle = 0$ using the canonical anticommutation relations. When $i \neq i'$ (unrestricted Hartree-Fock) we must have that $\langle \Psi | S_- S_+ | \Psi \rangle = N_\beta - \text{Tr}(PQ)$ (this I verified in books) where $N_\beta$ is the number of $\beta$ electrons and $P_{ij} = \langle \Psi | a^+_{j\alpha} a_{i\alpha} | \Psi \rangle$ and $Q_{ij} = \langle \Psi | a^+_{j\beta} a_{i\beta} | \Psi \rangle$.</p>
<p>My question is then, specifically, how do we obtain $\langle \Psi | S_- S_+ | \Psi \rangle = N_\beta - \text{Tr}(PQ)$ using the anticommutation relations of second quantization? If I try to use these anticommutation relations just in the way they are written in textbooks I do not get the right answer. Clearly, I am getting something wrong or some special consideration needs to be taken into account when $i \neq i'$. If someone can show me how to correctly use second quantization to get the right answer here, I would appreciate it a lot. </p>
| 8,319 |
[
0.00479851383715868,
0.0012606994714587927,
-0.0010772052919492126,
-0.030711300671100616,
0.03555569425225258,
-0.031465210020542145,
-0.06892402470111847,
-0.042638134211301804,
0.007588788401335478,
-0.06415906548500061,
0.07158930599689484,
-0.0010605801362544298,
0.06163917854428291,
0.0031504658982157707,
0.020625410601496696,
-0.0006723090191371739,
-0.024681782349944115,
-0.03296571224927902,
-0.01507240254431963,
-0.0030619860626757145,
0.011828824877738953,
0.018515421077609062,
-0.005289295222610235,
0.0019043614156544209,
-0.018113188445568085,
0.03883044794201851,
0.00454822788015008,
0.000535799830686301,
0.011016994714736938,
0.06903590261936188,
0.0225524939596653,
-0.03494121506810188,
0.0788513645529747,
0.022239800542593002,
0.012322938069701195,
-0.018442749977111816,
-0.030510680750012398,
-0.033319372683763504,
-0.0012659920612350106,
0.010491817258298397,
-0.03542822226881981,
-0.01965612731873989,
-0.02751355804502964,
0.007795203942805529,
-0.0034798101987689734,
0.013703154399991035,
-0.013071524910628796,
-0.008127418346703053,
0.01607254333794117,
-0.030011523514986038,
0.07825469225645065,
0.018757570534944534,
0.01563352346420288,
-0.012736450880765915,
-0.04449417442083359,
-0.03632239252328873,
0.0594659224152565,
0.03875752538442612,
0.0362846665084362,
-0.0540371797978878,
-0.041997428983449936,
-0.054727308452129364,
-0.01087768655270338,
0.007757708430290222,
-0.01926896907389164,
-0.004376824479550123,
0.0161397997289896,
0.002982114441692829,
0.017786147072911263,
-0.02259966731071472,
0.02180311642587185,
-0.010056956671178341,
0.015847573056817055,
-0.030643319711089134,
0.011497155763208866,
-0.0001470703718950972,
0.020752709358930588,
0.009472082369029522,
-0.004856957588344812,
0.012241148389875889,
0.017283964902162552,
0.015479992143809795,
0.01344117522239685,
0.020941616967320442,
-0.0012459881836548448,
-0.03266660496592522,
0.05684099346399307,
0.003403973300009966,
0.018382031470537186,
0.051647938787937164,
0.012283019721508026,
0.030590878799557686,
0.050804343074560165,
-0.02137874625623226,
0.0027850798796862364,
0.024750957265496254,
0.0028795760590583086,
0.05435224249958992,
-0.007616175804287195,
-0.01867026463150978,
-0.011969179846346378,
-0.0720130205154419,
0.005470878444612026,
0.09994406998157501,
-0.008663459680974483,
0.007029321044683456,
-0.02796177752315998,
0.015669597312808037,
0.006449544336646795,
-0.05661384016275406,
-0.027351796627044678,
0.02338360995054245,
-0.009591548703610897,
0.009317097254097462,
0.0077537610195577145,
-0.034946147352457047,
-0.024137839674949646,
-0.00587808433920145,
0.03270076960325241,
0.06221199780702591,
0.006373366340994835,
-0.02440059557557106,
-0.01665477454662323,
-0.03460809215903282,
-0.027123676612973213,
0.027275919914245605,
0.04838094487786293,
-0.021877789869904518,
-0.03549772500991821,
-0.03109065629541874,
0.046154506504535675,
-0.01367377582937479,
0.022875173017382622,
-0.0015875252429395914,
0.007638229057192802,
-0.024610495194792747,
-0.11445436626672745,
-0.04470604285597801,
0.035874418914318085,
-0.02001810446381569,
0.01363296341150999,
-0.05836931988596916,
-0.0013445758959278464,
0.03133188560605049,
0.11905602365732193,
0.020383302122354507,
0.014958013780415058,
-0.0037925743963569403,
0.024880141019821167,
0.05533340945839882,
-0.0025544820819050074,
-0.006651825271546841,
-0.012174006551504135,
-0.03439369797706604,
-0.007959212176501751,
-0.02952355146408081,
0.042228952050209045,
-0.008892308920621872,
0.0031466223299503326,
0.0031361624132841825,
0.0877947062253952,
-0.012901457026600838,
-0.0017035789787769318,
0.04437047988176346,
-0.009347978048026562,
-0.03884609788656235,
0.060196757316589355,
0.027857644483447075,
0.019400442019104958,
0.030998975038528442,
-0.04130631685256958,
-0.021649537608027458,
-0.02766961045563221,
0.03495139256119728,
0.04023737832903862,
-0.05701339617371559,
-0.03039894811809063,
-0.03336884081363678,
0.010720815509557724,
-0.011250568553805351,
-0.023220635950565338,
-0.009406873025000095,
-0.0157639030367136,
0.038506440818309784,
0.04525556042790413,
0.0249544195830822,
0.003695903578773141,
-0.011809347197413445,
0.0026858660858124495,
-0.049531470984220505,
0.011562309227883816,
-0.06443876028060913,
0.027278028428554535,
0.01020735315978527,
-0.03450147435069084,
0.07624207437038422,
-0.006812647450715303,
0.010158253833651543,
0.03143659979104996,
-0.03375181928277016,
-0.02991560474038124,
0.03145498037338257,
0.011429354548454285,
-0.0060164048336446285,
0.0341288186609745,
0.03650336340069771,
0.04462160915136337,
0.02950345166027546,
0.04117029905319214,
-0.014359592460095882,
-0.06456203013658524,
-0.013895716518163681,
0.01855381764471531,
0.05691652372479439,
0.04157022014260292,
-0.015007012523710728,
-0.004603981040418148,
-0.0414959192276001,
-0.03219514712691307,
0.013563827611505985,
-0.0362640842795372,
0.039572570472955704,
0.03387656435370445,
0.013863017782568932,
-0.0011419991496950388,
0.03163570165634155,
-0.00922998134046793,
0.04525904357433319,
0.023802567273378372,
-0.02264850214123726,
-0.005782841704785824,
-0.005408706143498421,
0.036231763660907745,
0.06161569058895111,
-0.05948507413268089,
-0.009775400161743164,
-0.018195074051618576,
0.017192212864756584,
0.03602975606918335,
0.0032307482324540615,
-0.03136533126235008,
-0.029602864757180214,
0.0075566526502370834,
0.0023013493046164513,
-0.014727752655744553,
-0.0002478304086253047,
0.01957903616130352,
-0.01165296882390976,
0.019963592290878296,
0.021435681730508804,
-0.03659205511212349,
-0.0018820069963112473,
-0.0500827431678772,
-0.011270356364548206,
0.01697785034775734,
-0.04660894721746445,
0.029343625530600548,
0.0212211012840271,
0.016429070383310318,
0.031722553074359894,
-0.03269988298416138,
0.004475417081266642,
-0.014951926656067371,
-0.01002582162618637,
0.047362904995679855,
-0.05492353066802025,
-0.028288645669817924,
0.0014785631792619824,
0.000058378773246658966,
-0.062156300991773605,
-0.015038308687508106,
-0.017153222113847733,
-0.022882889956235886,
-0.018705496564507484,
-0.015407387167215347,
0.0335938036441803,
0.001985593233257532,
0.009559083729982376,
-0.015957344323396683,
-0.019813816994428635,
-0.011162006296217442,
0.02197357453405857,
0.05197139084339142,
0.03834262117743492,
-0.05432344973087311,
-0.004840670619159937,
-0.06807702034711838,
-0.015584908425807953,
0.052450742572546005,
-0.0198648814111948,
-0.0037032803520560265,
-0.005135300103574991,
0.014468135312199593,
-0.033426683396101,
-0.019187457859516144,
-0.02674800157546997,
-0.013559791259467602,
-0.07771729677915573,
0.014786182902753353,
0.042539626359939575,
-0.011994315311312675,
-0.041082680225372314,
0.011299261823296547,
-0.021855229511857033,
-0.055076200515031815,
0.010718587785959244,
-0.026748284697532654,
0.03644438087940216,
-0.04460671544075012,
0.027271071448922157,
0.03535060957074165,
-0.02491690404713154,
0.008844282478094101,
-0.08256117254495621,
-0.006844640243798494,
-0.0031317262910306454,
0.008355365134775639,
0.031612902879714966,
0.014473922550678253,
-0.039624862372875214,
0.09765452146530151,
0.04738862067461014,
0.0036388877779245377,
-0.0006392064387910068,
0.015173510648310184,
0.005163904279470444,
-0.0027922417502850294,
0.011265481822192669,
0.04196278005838394,
0.000905997643712908,
0.04497143626213074,
-0.019833557307720184,
0.03796613588929176,
0.06366800516843796,
0.008039421401917934,
-0.005999475717544556,
0.05121107026934624,
0.003588556544855237,
0.02054518461227417,
0.05747747793793678,
-0.04877011850476265,
-0.03150095418095589,
-0.01402811799198389,
0.025534169748425484,
0.009535019285976887,
0.004157820250838995,
-0.05661095306277275,
0.0362517349421978,
-0.015071921981871128,
0.008499869145452976,
-0.009001202881336212,
0.07103809714317322,
-0.0031681181862950325,
-0.038205742835998535,
0.02114051580429077,
0.0014233114197850227,
-0.00036832407931797206,
-0.020304113626480103,
0.021319732069969177,
0.04363808408379555,
-0.0028904976788908243,
-0.027200551703572273,
-0.001759454607963562,
0.008756891824305058,
-0.047137074172496796,
0.021327627822756767,
-0.046920571476221085,
-0.056705594062805176,
0.005707084201276302,
0.006896485574543476,
0.02795500122010708,
-0.039637330919504166,
-0.044118646532297134,
-0.019420836120843887,
-0.035427503287792206,
0.009449310600757599,
-0.021895715966820717,
0.04923680052161217,
0.0012219524942338467,
0.017352573573589325,
0.03126586973667145,
-0.0028890911489725113,
-0.020929429680109024,
-0.0224464014172554,
-0.03751764073967934,
0.004915724042803049,
0.004914193879812956,
-0.0006853227969259024,
0.006595068611204624,
0.009950886480510235,
0.020316291600465775,
-0.02555045858025551,
-0.02070027031004429,
-0.038139283657073975,
-0.01348805334419012,
-0.025703437626361847,
0.00806680228561163,
-0.03883352503180504,
-0.00637340871617198,
-0.01757071539759636,
0.051948431879282,
0.01688835769891739,
-0.002980470424517989,
0.006775240413844585,
0.044028785079717636,
-0.05737253278493881,
0.026843776926398277,
-0.048939406871795654,
0.012174722738564014,
0.03135790675878525,
-0.0059167202562093735,
0.05686872452497482,
0.04364578053355217,
-0.024518297985196114,
-0.03593052551150322,
-0.025935910642147064,
0.06400898098945618,
0.023780005052685738,
-0.01095875445753336,
0.02874007448554039,
-0.035433974117040634,
-0.019381865859031677,
0.016925960779190063,
0.0649360790848732,
-0.012846551835536957,
0.03470481187105179,
0.013609473593533039,
-0.01659276895225048,
0.0010453182039782405,
0.04082208499312401,
0.04459697753190994,
0.004997922107577324,
0.004802399780601263,
-0.035146087408065796,
-0.022058725357055664,
0.0071288105100393295,
0.0004612916964106262,
-0.013419697061181068,
-0.014520841650664806,
-0.005556891206651926,
-0.019040271639823914,
0.015684589743614197,
-0.002594121964648366,
-0.02014200948178768,
0.008980031125247478,
0.03486577048897743,
0.0027585537172853947,
0.030498331412672997,
0.0010047206887975335,
0.010899074375629425,
-0.00857424084097147,
0.015939312055706978,
0.00584372878074646,
0.03867058828473091,
-0.019531184807419777,
-0.03628632053732872,
0.01756403222680092,
0.03488769754767418,
0.013701784424483776,
0.023621397092938423,
-0.023256756365299225,
-0.038893844932317734,
0.030821198597550392,
-0.0032661252189427614,
0.029893789440393448,
0.01587149314582348,
-0.0027286845725029707,
-0.015628280118107796,
-0.05110699683427811,
-0.023392345756292343,
0.05718893185257912,
0.0020134104415774345,
-0.03620303422212601,
-0.03030082955956459,
0.0011905980063602328,
-0.0442151203751564,
0.0044847941026091576,
0.014058684930205345,
0.049453530460596085,
0.016774224117398262,
0.006102674640715122,
0.021065928041934967,
0.05662287399172783,
-0.04666915908455849,
-0.06978444755077362,
0.010587682016193867,
0.009018410928547382,
-0.0344475694000721,
0.011356618255376816,
-0.040039196610450745,
-0.0602596178650856,
0.016293130815029144,
-0.0047838082537055016,
-0.0033184841740876436,
0.017705289646983147,
-0.024128682911396027,
0.07129330188035965,
0.034541867673397064,
0.0015789726749062538,
0.06397368013858795,
0.0483398362994194,
-0.05321335047483444,
0.01691349223256111,
-0.05218634381890297,
-0.004433625843375921,
-0.014025350101292133,
-0.014163649640977383,
-0.030515223741531372,
0.032539453357458115,
0.01602533645927906,
0.0321819931268692,
-0.030359309166669846,
0.006036784034222364,
-0.005010171327739954,
-0.03199309855699539,
-0.004861398600041866,
0.025854988023638725,
-0.0446896106004715,
0.0069382069632411,
-0.021661367267370224,
0.016388533636927605,
0.02533838152885437,
-0.029329746961593628,
0.009887085296213627,
-0.01679046079516411,
0.007344651967287064,
-0.013113007880747318,
-0.041489433497190475,
0.044359106570482254,
-0.012534054927527905,
0.009999574162065983,
-0.0061379289254546165,
-0.029387442395091057,
0.06321439892053604,
0.02245161309838295,
-0.0058925217017531395,
-0.020687494426965714,
-0.03706948459148407,
-0.045039884746074677,
0.058194465935230255,
-0.033399201929569244,
-0.00443518441170454,
-0.02335304766893387,
-0.023573778569698334,
0.02160506509244442,
0.015698054805397987,
-0.07085974514484406,
-0.014500112272799015,
0.01256217435002327,
0.006946033798158169,
-0.013408350758254528,
-0.00452648289501667,
-0.0035231688525527716,
-0.0019536621402949095,
-0.04092508181929588,
0.0001862252247519791,
0.02270086295902729,
-0.03663654625415802,
0.002647602465003729,
0.0434814877808094,
0.02110464498400688,
0.015361729077994823,
-0.03932230919599533,
0.010275686159729958,
-0.005869146902114153,
-0.0459187887609005,
0.038711123168468475,
0.03504796326160431,
0.0007631701300852001,
-0.002989141270518303,
-0.061940792948007584,
-0.025048376992344856,
-0.0019479735055938363,
-0.005615684669464827,
-0.01936313323676586,
-0.019219662994146347,
0.0075015234760940075,
0.00919201411306858,
0.03215275704860687,
-0.007361402735114098,
-0.030775832012295723,
0.014209422282874584,
0.047956619411706924,
0.02284841611981392,
-0.025082729756832123,
-0.042575761675834656,
-0.003413347527384758,
-0.00812646746635437,
0.010394290089607239,
-0.04156439006328583,
0.013830969110131264,
0.060789551585912704,
-0.008062676526606083,
0.031739965081214905,
0.03453357145190239,
-0.003935367334634066,
0.0040275841020047665,
0.01504683680832386,
0.04266943782567978,
0.024451984092593193,
-0.021604403853416443,
-0.021786382421851158,
-0.008624305948615074,
-0.05987926945090294,
0.055272649973630905,
0.0506170392036438,
0.020212475210428238,
0.009258255362510681,
0.013006453402340412,
0.017404068261384964,
-0.02311513014137745,
-0.0435798317193985,
-0.031061304733157158,
0.05509965866804123,
0.01478467509150505,
0.0296621210873127,
-0.022824909538030624,
0.011225459165871143,
0.06229398399591446,
0.031030969694256783,
-0.07742856442928314,
0.010207473300397396,
0.006500582210719585,
0.024302184581756592,
0.0028191781602799892,
-0.01806875318288803,
-0.05860571935772896,
0.04452454671263695,
-0.028087612241506577,
0.022872360423207283,
-0.028634121641516685,
-0.045446548610925674,
0.027345405891537666,
-0.025115126743912697,
0.011067057028412819,
-0.034664105623960495,
-0.034108761698007584,
-0.035551752895116806,
0.019841069355607033,
0.02647823467850685,
-0.01553246472030878,
0.056002113968133926,
0.033448364585638046,
0.019804559648036957,
0.003198363585397601,
0.04168756306171417,
-0.01845627836883068,
-0.02607933059334755,
0.01368068065494299,
-0.04783016815781593,
-0.05180317908525467,
0.02477741613984108,
-0.010194443166255951,
-0.011415282264351845,
-0.02636074088513851,
0.013943188823759556,
0.057533148676157,
0.045572154223918915,
0.01485469564795494,
-0.0055601587519049644,
0.03774882107973099,
-0.007622967008501291,
0.00849495455622673,
0.034672025591135025,
0.006275712046772242,
0.13873033225536346,
0.03385685756802559,
0.02893075719475746,
-0.05597624182701111,
-0.01552227046340704,
0.007733780425041914,
0.006433045491576195,
-0.009591164998710155,
0.03901892527937889,
-0.055865127593278885,
-0.024417513981461525,
-0.02031649462878704,
0.050986286252737045,
-0.013948654755949974,
0.012302998453378677,
0.0490330308675766,
-0.07217460870742798,
-0.02134779654443264,
-0.012289994396269321,
0.03431696444749832,
-0.003053509397432208,
0.010283216834068298,
-0.04332020506262779,
-0.002939448459073901,
-0.04860513657331467,
0.013232294470071793,
-0.04837441071867943,
0.0055435714311897755,
0.006567707750946283,
-0.026120811700820923,
-0.06394483149051666,
0.02938859537243843,
0.0029189966153353453,
-0.003714792663231492,
-0.007359357550740242,
0.02315857633948326,
0.017638102173805237,
-0.023522332310676575,
0.0075044771656394005,
0.019254542887210846,
0.000901397259440273,
0.005083306692540646,
0.02290731482207775,
0.021723829209804535,
-0.026947245001792908,
-0.008259961381554604,
0.005579171236604452,
0.08942340314388275,
-0.05605623126029968,
-0.030154461041092873,
-0.007116527296602726,
-0.03950541093945503,
0.008917358703911304,
-0.01944980025291443,
0.012476447969675064,
-0.010485275648534298,
0.0235525444149971,
0.00422944501042366,
0.015194468200206757,
-0.013483736664056778,
0.03682507202029228,
0.01569852977991104,
0.008820733055472374,
-0.0045656245201826096,
-0.03343085199594498,
-0.0012933665420860052,
-0.0003023056488018483,
0.014074425213038921,
0.038136713206768036,
-0.008758331649005413,
-0.02919190004467964,
-0.0075356741435825825,
-0.02288300171494484,
-0.08439905196428299,
0.02996126562356949,
0.020895348861813545,
0.07519800215959549,
0.0025333191733807325,
-0.007172366138547659,
-0.043738096952438354,
-0.07569057494401932,
-0.0036541081499308348,
-0.016840102151036263,
-0.004141113720834255,
0.018789105117321014,
-0.005996578838676214,
0.0319514274597168,
0.07167866080999374,
-0.0641668364405632,
0.005777140613645315,
0.033346988260746,
0.036556851118803024,
0.02672405168414116,
-0.044350482523441315,
-0.022952046245336533,
-0.005621806718409061,
0.004145296290516853,
0.010099907405674458,
-0.023000624030828476,
-0.02436603046953678,
0.026712557300925255,
0.008971902541816235,
-0.011971230618655682,
0.04382194206118584,
-0.018779557198286057,
-0.017875250428915024,
0.007893954403698444,
0.0046951137483119965,
0.0013100559590384364,
0.022585710510611534,
0.0238922331482172,
-0.02475891448557377,
0.018892696127295494,
0.005200427491217852,
-0.016822591423988342,
0.026201194152235985,
-0.012468542903661728,
-0.023694442585110664,
-0.027111463248729706,
0.014968971721827984,
-0.013459826819598675,
-0.01965472847223282,
-0.00994055438786745,
0.005715677049010992,
0.052783165127038956,
-0.04010501503944397,
0.004719246178865433,
-0.030124204233288765,
0.02460934966802597,
0.03210014849901199,
-0.007674019318073988,
0.03371636942028999,
0.0496562197804451,
-0.007444149814546108,
-0.050693511962890625,
0.007269646506756544,
0.0013077273033559322,
0.017449675127863884,
-0.0021788710728287697,
0.00032057988573797047,
-0.002813366474583745,
-0.03980501741170883,
-0.024915695190429688,
0.053261470049619675,
-0.01608656719326973,
0.0510873980820179,
0.06347817182540894,
0.00797670055180788,
-0.026360610499978065,
0.03660760447382927,
-0.03778572753071785,
-0.041966699063777924,
-0.013754596002399921,
-0.01521929632872343,
0.0019359355792403221,
-0.010807608254253864,
0.0015741848619654775,
-0.010111469775438309,
-0.013056797906756401,
0.004897882230579853,
0.030863815918564796,
-0.05927769094705582,
-0.004047855734825134,
-0.001984811620786786,
0.022201688960194588,
0.06070367619395256,
0.07687431573867798,
-0.02159014903008938,
-0.001431031385436654,
0.044628482311964035,
0.0034342827275395393,
0.0611477792263031,
0.013460224494338036,
0.004261115565896034,
-0.08784736692905426,
0.006080175284296274,
-0.006088555790483952,
0.005458049941807985,
0.0494643896818161,
-0.021065624430775642,
0.03547673672437668,
0.020032184198498726,
-0.06562908738851547,
0.005402328446507454,
-0.04486235976219177,
0.0036720114294439554,
-0.005590990651398897,
-0.02183241955935955,
-0.053744927048683167,
0.02525612711906433,
0.0048604244366288185,
0.06811357289552689,
0.03262294828891754,
-0.0074876900762319565,
-0.016908351331949234,
-0.03979998454451561,
-0.017191588878631592,
0.014229622669517994,
-0.0028782759327441454,
-0.02871774695813656,
0.05369601398706436,
-0.03133217617869377,
-0.016862094402313232,
-0.003160906722769141,
0.007537207566201687,
-0.0024834407959133387,
-0.025824522599577904,
0.07809261232614517,
0.012903779745101929,
0.044460393488407135,
0.012728695757687092,
-0.02017270028591156,
-0.004495420027524233,
0.005915422458201647,
0.017832472920417786,
0.006223420612514019,
-0.031556617468595505,
0.009091943502426147,
-0.035111188888549805,
-0.0354246124625206,
-0.06836245208978653,
0.024145951494574547,
0.0027521352749317884,
-0.01864289678633213,
-0.013033128343522549,
0.01671534590423107,
-0.007413254119455814,
-0.004834635183215141,
0.0009003787999972701,
-0.02662389911711216,
0.01711912453174591,
0.006623763591051102,
0.02835320495069027,
-0.0021237810142338276,
0.024690644815564156,
-0.0348365418612957,
-0.048930201679468155,
0.03761309012770653,
0.015454955399036407,
-0.029831601306796074,
-0.033774834126234055,
-0.045326534658670425,
0.009574650786817074,
0.031142033636569977,
0.0229374747723341,
-0.011414398439228535,
-0.03736488148570061,
0.02661479450762272,
-0.02900931052863598,
0.021054090932011604,
-0.017762431874871254,
-0.02198292501270771,
0.012101857922971249,
-0.06327862292528152,
0.01974685862660408,
0.03929155319929123,
-0.02369483932852745,
0.008326082490384579,
-0.005443224683403969,
0.01828504167497158,
0.00971380528062582,
0.04577339440584183,
-0.007735750172287226,
-0.014172432944178581,
-0.00628453167155385,
-0.008716494776308537,
0.013147235848009586,
-0.015892600640654564,
0.016253985464572906,
0.004214661195874214,
-0.018039360642433167,
-0.00965648889541626,
0.00001555312701384537,
-0.026873450726270676,
0.02198907360434532,
0.018146075308322906,
0.014861672185361385,
-0.013034291565418243,
0.0033083257731050253,
-0.037354156374931335,
0.06964161992073059,
0.0023760301992297173,
-0.020364761352539062,
0.05490903556346893,
0.018471159040927887,
0.00816225353628397,
0.020996060222387314,
-0.026935569941997528,
-0.05168505385518074,
-0.009311552159488201,
0.010527177713811398,
-0.013310697861015797,
-0.01808902993798256,
0.00031023230985738337,
0.005625269375741482,
-0.02024932950735092,
0.010550331324338913,
0.03838188573718071,
-0.0011740010231733322,
-0.024353357031941414,
0.053845688700675964,
-0.0030280116479843855,
0.01003878004848957,
0.02846553735435009,
0.021556252613663673,
0.02302325703203678,
-0.00431718910112977,
0.02293064445257187,
0.01850759983062744,
-0.007463093381375074,
0.006382848601788282,
-0.0019206677097827196,
0.02589564397931099,
0.0018155011348426342,
0.006689819507300854,
0.021233027800917625,
0.014246941544115543,
-0.027616634964942932,
0.003454293590039015,
0.05335736274719238,
-0.02188478596508503,
0.04137042537331581,
0.007543480955064297,
-0.04588475450873375,
0.08862993121147156,
-0.00009748579759616405,
0.02651359885931015,
-0.04617149382829666,
0.017489509657025337,
-0.00557716516777873,
0.007048401050269604,
0.022516552358865738,
0.06145407259464264,
-0.0390620157122612,
-0.028984542936086655,
-0.027247991412878036,
-0.00577900093048811,
0.006930495612323284,
-0.03668718785047531,
0.011275536380708218,
0.04063287749886513,
-0.016952969133853912,
-0.019292915239930153,
-0.023883288726210594,
-0.010120289400219917,
-0.03472553938627243,
0.005773790646344423,
0.03791147843003273,
0.02461049146950245,
0.020769082009792328,
0.0009819484548643231,
-0.004823888186365366,
0.02791989967226982,
0.013593807816505432,
-0.02588045969605446,
0.00823428574949503,
-0.004405135288834572,
-0.06641571968793869,
0.015856916084885597
] |
<p>I recently had to solve the following problem:</p>
<blockquote>
<p><em>A force $F=10\hat x- 8\hat y$ is applied to an object that is constrained to travel towards increasing values of x along the path defined by $y=x^2$ and $z=0$. Find the component of $F$ that is tangent to this path at the point $(2,4,0)$.</em></p>
</blockquote>
<p>Attempt: I used Pythagorean's theorem to $ F=12.81 N$ since the $x$ and $y$ components are given. I just wasn't sure if this is what the questions is asking for, or is there something else I have do do?</p>
<p><strong>Edit.</strong> More generally, suppose that one is given a curve and a force field on the plane. How would one go about computing the component of such a force field in the direction tangent to the curve at a given point?</p>
| 8,320 |
[
0.018532712012529373,
0.004624375142157078,
-0.008921908214688301,
0.0006340763648040593,
0.026938971132040024,
-0.020883118733763695,
-0.015449411235749722,
-0.017786378040909767,
-0.0016896163579076529,
-0.0327564962208271,
0.0042153517715632915,
0.055847831070423126,
0.06146971136331558,
0.03779534250497818,
-0.009660677053034306,
-0.01944778859615326,
-0.05719396099448204,
-0.0006732819601893425,
0.02120467647910118,
-0.050008006393909454,
0.0007286108448170125,
-0.006527100224047899,
-0.004136727191507816,
-0.004110308829694986,
-0.011942235752940178,
0.021611593663692474,
0.021753180772066116,
-0.012766970321536064,
0.005979699548333883,
0.03625272959470749,
-0.005683033261448145,
-0.04432016983628273,
0.03251635283231735,
0.04568837955594063,
0.03179902210831642,
0.0016568225109949708,
-0.05131600797176361,
-0.024883968755602837,
-0.03929479792714119,
0.035111505538225174,
-0.032961029559373856,
-0.036611057817935944,
-0.005177140235900879,
0.03652007132768631,
-0.01685166172683239,
0.0372251495718956,
0.01619013585150242,
-0.007341783028095961,
0.07902776449918747,
-0.050600696355104446,
0.07879072427749634,
0.012588156387209892,
0.021152876317501068,
-0.0058148885145783424,
-0.029069121927022934,
-0.05593154951930046,
0.021989570930600166,
0.05468353256583214,
0.008392775431275368,
-0.017852678894996643,
-0.010104209184646606,
-0.04267827793955803,
-0.04325173795223236,
-0.02272249199450016,
-0.03478293865919113,
0.006788081489503384,
-0.0005582699668593705,
-0.0394885316491127,
-0.012298526242375374,
-0.028341297060251236,
0.008832565508782864,
0.0287267304956913,
0.02705155499279499,
-0.019723515957593918,
-0.03064173460006714,
-0.010535243898630142,
0.013522847555577755,
0.033527620136737823,
0.013363092206418514,
-0.010299064218997955,
-0.002084022853523493,
-0.004193501081317663,
0.040903862565755844,
0.05134228244423866,
0.019472114741802216,
-0.0008953612414188683,
0.04962129145860672,
-0.017441654577851295,
0.016449326649308205,
0.010870176367461681,
0.02515340968966484,
0.016539257019758224,
0.012922998517751694,
0.0028255488723516464,
-0.023732583969831467,
0.016682416200637817,
-0.018342293798923492,
0.00013527314877137542,
0.032258350402116776,
0.009764749556779861,
0.0021616374142467976,
-0.0656295120716095,
-0.004987787455320358,
0.0731269046664238,
0.023124579340219498,
0.0379551462829113,
-0.003784618340432644,
-0.010934075340628624,
-0.021972447633743286,
0.00591515377163887,
-0.04982515051960945,
-0.00011578036355786026,
0.010686188004910946,
-0.028910614550113678,
0.021810712292790413,
-0.0026671814266592264,
-0.009115668945014477,
0.01173072773963213,
0.036632902920246124,
0.023629076778888702,
0.03867214545607567,
-0.04038268327713013,
-0.0010691038332879543,
-0.02466648817062378,
-0.04149812459945679,
-0.007329773157835007,
0.037264175713062286,
-0.03180356323719025,
-0.00267426623031497,
-0.004254629835486412,
0.028723757714033127,
-0.01214104425162077,
0.0018184815999120474,
0.04919450730085373,
0.00804270338267088,
0.023370178416371346,
-0.07906417548656464,
-0.12284848839044571,
0.05491335690021515,
0.012177181430161,
0.016965800896286964,
-0.08115468919277191,
0.026479827240109444,
0.061335720121860504,
0.06160476431250572,
0.0007367436774075031,
0.00046952374395914376,
0.0007252902141772211,
0.058643024414777756,
-0.00466891098767519,
0.01901024766266346,
-0.0019823238253593445,
-0.04047657921910286,
-0.04562787711620331,
-0.030202243477106094,
-0.05196399986743927,
0.04439910128712654,
0.017908485606312752,
0.015745723620057106,
-0.05742688477039337,
0.06938084214925766,
-0.02350274659693241,
0.010091070085763931,
0.0264259185642004,
-0.007179233245551586,
0.004347770009189844,
0.06795002520084381,
0.025135736912488937,
0.02406107448041439,
0.02827523648738861,
0.0023768581449985504,
0.04139849171042442,
-0.002799190580844879,
0.03371978923678398,
0.07180190086364746,
-0.04162212833762169,
-0.04248714819550514,
0.0025824515614658594,
-0.014282174408435822,
-0.008091595023870468,
-0.019863681867718697,
-0.04430799558758736,
-0.02045154944062233,
0.005896522663533688,
0.0007522369269281626,
0.04763250797986984,
0.012546767480671406,
-0.01587781123816967,
0.002292833523824811,
-0.03840749338269234,
-0.006609943229705095,
-0.0684775784611702,
0.0074677858501672745,
-0.025081217288970947,
-0.043312255293130875,
0.012705891393125057,
0.007514568977057934,
0.016033191233873367,
-0.035765379667282104,
0.003678897861391306,
-0.029121315106749535,
0.008665535598993301,
0.05614372715353966,
-0.025181088596582413,
0.00929636973887682,
0.01398357842117548,
0.014655894599854946,
0.015534176491200924,
0.04620121046900749,
-0.06593114882707596,
0.0090057123452425,
-0.01087135262787342,
-0.005426004528999329,
0.012589897029101849,
0.01857621967792511,
0.01692069321870804,
-0.00935144629329443,
-0.025218667462468147,
-0.026258476078510284,
0.07001969963312149,
-0.04550139605998993,
0.05090538039803505,
0.07450835406780243,
0.02935103327035904,
0.003625281387940049,
0.026697734370827675,
0.027248213067650795,
0.05027122423052788,
-0.01056357566267252,
-0.008172632195055485,
-0.014229977503418922,
-0.019110165536403656,
0.04105459898710251,
0.023657049983739853,
-0.07960712164640427,
-0.017950428649783134,
0.10334424674510956,
-0.00442299572750926,
0.03837571293115616,
0.022725552320480347,
-0.008825069293379784,
-0.02724594622850418,
0.017076857388019562,
0.04229491949081421,
0.025177763774991035,
0.014470389112830162,
0.028515271842479706,
0.026938937604427338,
0.02882307395339012,
0.05549012869596481,
-0.025691170245409012,
-0.0066368961706757545,
-0.031126316636800766,
0.046922966837882996,
0.019778961315751076,
-0.012675314210355282,
0.04615812376141548,
0.007329505868256092,
0.022907277569174767,
0.01538193691521883,
0.02195432223379612,
-0.015593822114169598,
-0.03886457905173302,
0.009643885307013988,
0.02863418497145176,
-0.016742631793022156,
-0.027971835806965828,
-0.015074608847498894,
0.041773438453674316,
-0.02404886856675148,
0.003337039379402995,
-0.013631029054522514,
-0.01516915112733841,
0.00674815196543932,
-0.01094022486358881,
0.05082236975431442,
0.022130372002720833,
0.022267945110797882,
0.021834218874573708,
-0.007369546685367823,
-0.021207183599472046,
-0.024132611230015755,
-0.014781861566007137,
0.021721472963690758,
-0.06620829552412033,
-0.04038036987185478,
-0.026293037459254265,
-0.03166992962360382,
0.05014133080840111,
0.022707482799887657,
0.010388973169028759,
0.02544255554676056,
0.012261799536645412,
-0.03433913365006447,
-0.0002767948608379811,
-0.04516442492604256,
-0.0029963047709316015,
-0.09108985215425491,
0.01810266636312008,
0.038256097584962845,
0.024327319115400314,
0.009542159736156464,
0.04167114943265915,
-0.019375763833522797,
-0.0254496019333601,
-0.020441407337784767,
-0.00703875906765461,
0.02480669692158699,
0.009587394073605537,
0.0059836613945662975,
-0.005955320782959461,
0.008250059559941292,
0.028966166079044342,
-0.03586267679929733,
-0.04244232922792435,
-0.02402111515402794,
0.007337884046137333,
0.05034800246357918,
0.025426937267184258,
-0.007763315923511982,
0.08538785576820374,
0.02570038102567196,
-0.05471033602952957,
-0.014076584950089455,
-0.005025958176702261,
0.0038036645855754614,
-0.03867800161242485,
-0.023148586973547935,
0.04298769310116768,
-0.01263396069407463,
-0.03898310661315918,
-0.04368500038981438,
-0.004046862944960594,
0.07091467827558517,
0.0014117053942754865,
0.035653576254844666,
0.024173380807042122,
0.04110487923026085,
-0.0293123722076416,
0.07179421186447144,
0.04618825390934944,
-0.04067118838429451,
0.020163819193840027,
0.010029609315097332,
0.02133224345743656,
0.026420958340168,
-0.021798916161060333,
0.028420601040124893,
0.011974649503827095,
0.005790098570287228,
0.0193647313863039,
0.01767595484852791,
0.008503985591232777,
-0.04130992665886879,
-0.010074326768517494,
0.03022054396569729,
0.032321322709321976,
-0.02692352421581745,
-0.018552999943494797,
0.06929829716682434,
-0.0032692686654627323,
-0.054498687386512756,
0.01148379035294056,
-0.01917004957795143,
-0.0004135366471018642,
0.08140319585800171,
-0.022010691463947296,
-0.017493363469839096,
0.01504380814731121,
0.016249602660536766,
0.0038205080199986696,
0.021181151270866394,
-0.02414821647107601,
0.03676937147974968,
-0.0258121769875288,
-0.012369180098176003,
0.02454451471567154,
0.021177534013986588,
-0.02223857119679451,
0.01008874922990799,
-0.026318702846765518,
0.02711709402501583,
0.051571041345596313,
0.0487910695374012,
-0.12468461692333221,
0.03751903772354126,
-0.022578977048397064,
-0.038099709898233414,
0.004761852324008942,
-0.01864440366625786,
-0.008429869078099728,
-0.001074281521141529,
0.015265003778040409,
0.008697469718754292,
0.0006266107666306198,
-0.03308677673339844,
0.025617675855755806,
-0.035982366651296616,
-0.015562132932245731,
-0.026281146332621574,
0.03001301735639572,
0.059396546334028244,
-0.0665225014090538,
0.005720291752368212,
0.028113480657339096,
-0.055778488516807556,
0.010175196453928947,
-0.007456728257238865,
-0.0029057152569293976,
0.008909555152058601,
0.014867231249809265,
-0.027779486030340195,
0.041605498641729355,
0.013867239467799664,
-0.002986356383189559,
-0.03433395177125931,
0.07669448107481003,
-0.009559504687786102,
0.01745893806219101,
-0.03327856585383415,
-0.03727443516254425,
-0.012612677179276943,
-0.0062275356613099575,
0.08266892284154892,
-0.0050330148078501225,
0.0025174859911203384,
0.03144053742289543,
0.005947684869170189,
0.006416686344891787,
0.03981795907020569,
0.023755284026265144,
0.0279849860817194,
-0.016503741964697838,
-0.04380878061056137,
0.04798606038093567,
-0.05168895423412323,
0.023003989830613136,
0.0068993763998150826,
-0.01184919010847807,
-0.030170323327183723,
0.002292661229148507,
0.035149019211530685,
0.029011840000748634,
-0.007663180585950613,
0.04274381324648857,
-0.03981913626194,
0.043878138065338135,
-0.011899663135409355,
-0.025332259014248848,
0.04350477084517479,
0.02778400294482708,
0.041122712194919586,
-0.0008137380937114358,
-0.029689179733395576,
-0.05690651386976242,
0.02386547066271305,
0.053361352533102036,
0.03856100142002106,
-0.04557335376739502,
0.016110975295305252,
-0.04910498112440109,
-0.037328869104385376,
0.061720047146081924,
-0.011169485747814178,
0.036904219537973404,
-0.038458310067653656,
0.013372325338423252,
-0.013502631336450577,
-0.01773560605943203,
-0.0554838702082634,
0.007785503286868334,
-0.031948406249284744,
0.006787777878344059,
-0.006306142080575228,
-0.006561989895999432,
-0.0034984333906322718,
-0.011723203584551811,
0.02431536838412285,
0.05532664805650711,
0.038386959582567215,
-0.021855413913726807,
-0.0044153062626719475,
-0.012696238234639168,
-0.04117284342646599,
-0.05386758968234062,
-0.012695085257291794,
0.015054436400532722,
-0.031796038150787354,
0.004821406211704016,
-0.022954631596803665,
-0.015054155141115189,
0.032451823353767395,
-0.04118487611413002,
0.030985591933131218,
0.04149691388010979,
-0.002202152507379651,
0.05723930522799492,
0.08639489114284515,
-0.0016260675620287657,
0.031785063445568085,
0.04638408496975899,
-0.016450578346848488,
-0.015572093427181244,
-0.009540785104036331,
0.0074537526816129684,
0.006110585760325193,
-0.023435980081558228,
-0.018606599420309067,
0.0003658334899228066,
-0.016781970858573914,
0.0586809404194355,
-0.01797943376004696,
0.041772324591875076,
-0.03453701734542847,
-0.018353376537561417,
0.010387531481683254,
0.028290845453739166,
-0.008851269260048866,
-0.000035063858376815915,
0.003654099302366376,
0.029686151072382927,
0.012664451263844967,
-0.01579277589917183,
-0.005861970130354166,
-0.007060777395963669,
0.009527632966637611,
0.024921566247940063,
-0.013455994427204132,
-0.0005354154855012894,
-0.05372193455696106,
0.0006191868451423943,
0.003589024767279625,
-0.051301922649145126,
0.030224459245800972,
-0.01817239075899124,
-0.010020089335739613,
0.010298465378582478,
-0.018545793369412422,
-0.0341578871011734,
0.02010374329984188,
0.017224492505192757,
0.04327252507209778,
-0.0502149872481823,
0.022281894460320473,
-0.00275454786606133,
0.023878712207078934,
-0.029817048460245132,
-0.04065137356519699,
-0.0042394050396978855,
0.004633700009435415,
0.006296444684267044,
-0.022068016231060028,
-0.02860446460545063,
-0.026880180463194847,
-0.017966078594326973,
-0.004606880247592926,
0.067299984395504,
-0.028389262035489082,
-0.01329236850142479,
0.030715830624103546,
0.021114856004714966,
0.01703985035419464,
0.009470573626458645,
-0.012483768165111542,
-0.00011767733667511493,
-0.010769405402243137,
0.007459661923348904,
-0.004262054339051247,
-0.007073413580656052,
-0.026332488283514977,
0.00949522852897644,
0.018482863903045654,
-0.002660271478816867,
0.0390925407409668,
-0.0065778400748968124,
0.023828765377402306,
0.024340661242604256,
0.011362725868821144,
-0.034027159214019775,
-0.02800816111266613,
-0.008258040063083172,
-0.057155169546604156,
0.015211074613034725,
-0.017627667635679245,
0.022133946418762207,
-0.03592441976070404,
-0.009788185358047485,
-0.020910777151584625,
0.025860562920570374,
0.006559834349900484,
-0.002663626801222563,
0.04270629584789276,
-0.038509491831064224,
-0.007872872985899448,
0.0018978819716721773,
-0.001038444577716291,
0.028095731511712074,
0.04124467447400093,
-0.008893119171261787,
-0.003005602629855275,
-0.0014660530723631382,
-0.03410063683986664,
-0.00940608885139227,
-0.01576167345046997,
0.012952933087944984,
0.07477421313524246,
-0.03433426097035408,
0.04709635302424431,
0.024920785799622536,
-0.004152292851358652,
0.004172200802713633,
-0.0032665475737303495,
-0.008996675722301006,
-0.0025611831806600094,
0.026136454194784164,
0.06520991027355194,
-0.009636471047997475,
0.026507649570703506,
0.042366206645965576,
-0.0046996367163956165,
0.010820116847753525,
-0.014825337566435337,
0.030048677697777748,
0.030860789120197296,
0.038174107670784,
-0.027723761275410652,
-0.030721144750714302,
-0.005722838919609785,
-0.026615062728524208,
0.01560275163501501,
-0.01965995877981186,
-0.016787828877568245,
0.03065827488899231,
0.018041390925645828,
0.013937804847955704,
-0.04355572164058685,
-0.019607938826084137,
0.018493300303816795,
-0.015341692604124546,
0.003794853575527668,
0.0006683104438707232,
0.004577786196023226,
0.038091227412223816,
0.03874609246850014,
-0.016560569405555725,
0.05251706391572952,
-0.006415781565010548,
-0.014299817383289337,
-0.01640247367322445,
-0.021768083795905113,
-0.041445039212703705,
0.0004718105774372816,
0.009236041456460953,
-0.027950795367360115,
0.039383113384246826,
-0.03992215916514397,
0.016345543786883354,
0.007079656235873699,
0.04639991372823715,
-0.02057836949825287,
0.09193015843629837,
-0.010408192873001099,
-0.00922379456460476,
-0.028451556339859962,
0.030402496457099915,
0.11819332093000412,
0.04483278840780258,
-0.0009701837552711368,
-0.01098831370472908,
-0.01691533252596855,
-0.051240742206573486,
-0.0459284707903862,
-0.05687957629561424,
0.01666831038892269,
0.03963984549045563,
-0.038175877183675766,
0.024815429002046585,
0.03458838909864426,
-0.002228819765150547,
0.003534318646416068,
0.055069226771593094,
-0.03416408970952034,
-0.01328510046005249,
-0.02794140763580799,
0.005326372105628252,
-0.01620624028146267,
0.0014008322032168508,
-0.0058219521306455135,
0.014392958022654057,
-0.06529578566551208,
-0.04471878334879875,
-0.04967055097222328,
-0.038874223828315735,
-0.021696265786886215,
-0.0162410456687212,
-0.08277150988578796,
0.021512949839234352,
0.04337982460856438,
-0.06093992292881012,
-0.027930323034524918,
0.029366275295615196,
0.02081102319061756,
0.008071604184806347,
0.009456079453229904,
0.04266785457730293,
0.01033842470496893,
-0.0003329741593915969,
0.012263083830475807,
0.017183225601911545,
-0.008282991126179695,
0.023781584575772285,
-0.027505965903401375,
0.02822958491742611,
-0.00649366294965148,
-0.003328567836433649,
0.0248253270983696,
0.005322744604200125,
0.011981124989688396,
-0.06486442685127258,
-0.01860721781849861,
0.007010366767644882,
0.021218949928879738,
-0.011501960456371307,
-0.02551509439945221,
0.02997785061597824,
-0.01176172774285078,
0.03673466295003891,
-0.03580590337514877,
0.016385359689593315,
0.011541919782757759,
0.027770182117819786,
-0.001854347181506455,
0.009971313178539276,
-0.03127225488424301,
-0.05844637379050255,
0.02257024496793747,
-0.03127172589302063,
-0.02106395922601223,
0.0015386537415906787,
0.006795812863856554,
0.008940622210502625,
-0.011830905452370644,
-0.007416414096951485,
-0.00810118205845356,
-0.03098057210445404,
0.004792681895196438,
0.0009138673776760697,
-0.025761540979146957,
-0.0038291190285235643,
0.02380352094769478,
-0.024338429793715477,
0.00043238079524599016,
0.03073681890964508,
-0.017857003957033157,
-0.016916360706090927,
-0.015980370342731476,
0.024563491344451904,
0.027851160615682602,
-0.022552547976374626,
-0.05063044652342796,
0.009879343211650848,
-0.013256165198981762,
0.03327677771449089,
-0.006331877317279577,
0.03902093693614006,
0.03463887423276901,
0.0193935614079237,
-0.014045997522771358,
0.009568127803504467,
-0.03376331180334091,
0.04627908766269684,
0.04195992276072502,
-0.04619865119457245,
0.020915530622005463,
0.01191883347928524,
-0.007256734184920788,
-0.08944975584745407,
0.00013714718807023019,
-0.03321351855993271,
0.0038346240762621164,
-0.005501270294189453,
0.0050073228776454926,
-0.009210639633238316,
0.002607587492093444,
-0.01125479768961668,
-0.00741607416421175,
-0.007321112789213657,
0.013790645636618137,
-0.024027105420827866,
-0.02250831387937069,
0.022597676143050194,
0.012917724438011646,
-0.011077805422246456,
0.03235728666186333,
-0.018918562680482864,
-0.009390197694301605,
0.019462544471025467,
0.001764053013175726,
0.005273893941193819,
-0.02272884175181389,
-0.0069227744825184345,
0.031193817034363747,
0.03513176366686821,
-0.015967225655913353,
-0.0019004482310265303,
-0.004371974151581526,
-0.04858653247356415,
-0.016071025282144547,
0.0456572026014328,
-0.008882040157914162,
0.02729141339659691,
0.007857833057641983,
0.010721570812165737,
0.015497404150664806,
0.02004530467092991,
-0.00964905135333538,
0.0010639687534421682,
-0.010480333119630814,
-0.04488539695739746,
-0.03843037411570549,
-0.03149975836277008,
-0.02733117900788784,
-0.006703303661197424,
0.0065946136601269245,
0.018877515569329262,
0.009869265370070934,
0.0025853400584310293,
-0.025231827050447464,
0.01127341017127037,
0.028814461082220078,
-0.045570120215415955,
0.008879953995347023,
0.015661943703889847,
0.0858772024512291,
0.0556253120303154,
-0.015658754855394363,
0.005968119483441114,
0.011801548302173615,
-0.01035984605550766,
-0.10200212150812149,
-0.05900745093822479,
-0.0034277234226465225,
0.013059633783996105,
0.054853010922670364,
-0.07032505422830582,
0.011253119446337223,
-0.025092344731092453,
-0.052254050970077515,
0.016281019896268845,
-0.007333019282668829,
-0.0022249678149819374,
-0.00825815461575985,
-0.019264260306954384,
0.024549510329961777,
0.040103524923324585,
-0.011513952165842056,
0.0839976966381073,
0.022524958476424217,
-0.0024362404365092516,
-0.033261675387620926,
-0.027138875797390938,
0.05980329215526581,
0.022882267832756042,
0.02813551388680935,
-0.045333292335271835,
0.05228402093052864,
-0.02403147891163826,
-0.021693160757422447,
-0.001569229643791914,
-0.018670139834284782,
0.019084077328443527,
-0.025783253833651543,
-0.01883392222225666,
0.013025501742959023,
0.04444284737110138,
-0.002278116764500737,
-0.01317041739821434,
-0.021545926108956337,
-0.019725508987903595,
0.007324029691517353,
0.011354825459420681,
-0.0010467387037351727,
-0.016415970399975777,
0.023215901106595993,
0.008796710520982742,
-0.0446496307849884,
0.01681787520647049,
-0.022307218983769417,
0.00741603784263134,
0.02595761977136135,
-0.00583850871771574,
0.019436484202742577,
-0.06077728047966957,
-0.028485089540481567,
-0.028738951310515404,
0.013477996923029423,
0.01507587917149067,
-0.0347016379237175,
0.015214163810014725,
-0.0453212708234787,
-0.00930242519825697,
-0.03539014607667923,
0.003907369915395975,
-0.004242005292326212,
0.016492042690515518,
-0.0716075599193573,
0.01825954020023346,
-0.014565321616828442,
-0.055447548627853394,
0.006607173476368189,
-0.009201801382005215,
-0.023091433569788933,
-0.009469350799918175,
0.004859450738877058,
0.0032725688070058823,
0.0027282102964818478,
0.00833067949861288,
-0.004227295983582735,
-0.07016931474208832,
0.01478573214262724,
0.05651213601231575,
-0.025480911135673523,
0.001379563705995679,
0.0012626128736883402,
-0.020231196656823158,
-0.02032989263534546,
0.06488129496574402,
-0.047122057527303696,
0.034668900072574615,
-0.01839081570506096,
0.0028874899726361036,
0.00053969252621755,
-0.05282790958881378,
0.006330177187919617,
0.004680714104324579,
-0.017788348719477654,
-0.01901628077030182,
0.0045891799964010715,
0.012665930204093456,
-0.03316299989819527,
-0.0053282068111002445,
0.04742691293358803,
0.0271350909024477,
0.0019906742963939905,
-0.028049422428011894,
0.020897313952445984,
-0.014205330051481724,
-0.004436574410647154,
0.045525215566158295,
0.0206950344145298,
-0.002321528270840645,
0.004196200519800186,
-0.03378608822822571,
-0.03587650507688522,
0.011192047968506813,
-0.03659432753920555,
-0.016973016783595085,
-0.0568915456533432,
-0.01702948659658432,
0.06292682886123657,
-0.06822437047958374,
-0.016562949866056442,
0.04421033337712288,
-0.027930742129683495,
0.021964916959404945,
0.03964827209711075,
0.03453429043292999,
0.03810838982462883,
-0.008689804002642632,
0.020436611026525497,
0.011244808323681355,
-0.03668465465307236,
-0.007931030355393887,
-0.03624739497900009,
0.046267662197351456,
-0.014341247268021107,
-0.018836626783013344,
0.04429849982261658,
-0.015601704828441143,
0.012211759574711323,
-0.0024410937912762165,
0.023724237456917763,
-0.020559770986437798,
-0.03384510427713394,
0.035509999841451645,
-0.005596080794930458,
0.005513717420399189,
0.0024281986989080906,
-0.008839193731546402,
0.061209019273519516,
-0.05781326815485954,
0.004982002545148134,
-0.04236963391304016,
0.024922044947743416,
-0.05098769813776016,
0.030319347977638245,
0.0017624759348109365,
0.013116761110723019,
0.010480271652340889,
0.017278939485549927,
-0.0007675280794501305,
-0.028764445334672928,
0.03414814919233322,
0.011505167931318283,
0.012456041760742664,
-0.020041856914758682,
0.02292291633784771,
-0.0018075177213177085,
-0.041485387831926346,
-0.02678619883954525,
-0.041308626532554626,
0.022862903773784637,
0.04655977711081505,
-0.01768431067466736,
-0.03903710097074509,
0.05230220779776573,
-0.013199693523347378,
0.05907275527715683,
-0.061477165669202805,
-0.030941419303417206,
-0.0063998219557106495,
0.030002761632204056,
0.028465397655963898,
-0.016323769465088844
] |
<p>We all know that light travels in straight a line, which can be proved by pinhole imaging as in the picture shown :
<img src="http://i.stack.imgur.com/lNIN3.png" alt="pinhole camera"></p>
<p>But when I'm doing this little experiment with an apple, no matter how I change the distance between the object and the pinhole, an image can never be observed on the cardboard behind. So what's going wrong? Please help!</p>
<p><img src="http://i.stack.imgur.com/Rp92x.jpg" alt="pinhole camera experiment"></p>
| 8,321 |
[
-0.02907295897603035,
-0.03860730677843094,
0.007086701691150665,
-0.04242197424173355,
-0.009759830310940742,
-0.02147502638399601,
-0.023205740377306938,
-0.0018434596713632345,
-0.040593963116407394,
0.053061727434396744,
0.05116674676537514,
0.054720230400562286,
0.04256127402186394,
0.06620262563228607,
0.0048242597840726376,
0.009000323712825775,
-0.01615479215979576,
0.007266136351972818,
-0.020793354138731956,
-0.03407101705670357,
-0.027811171486973763,
0.039370447397232056,
0.008078400045633316,
-0.02622193656861782,
0.02505873702466488,
0.001749308779835701,
0.02763357013463974,
0.012667861767113209,
0.0380975641310215,
0.018415668979287148,
-0.0239277184009552,
-0.0011147866025567055,
-0.014793166890740395,
0.00860966369509697,
0.033510174602270126,
-0.004300029948353767,
0.024051835760474205,
0.009821642190217972,
0.002455832902342081,
0.010852079838514328,
0.00799908209592104,
-0.0004449440457392484,
-0.018237654119729996,
0.0292068924754858,
-0.009262784384191036,
0.010403227992355824,
0.010324099101126194,
-0.027444101870059967,
0.08040893077850342,
-0.04473895952105522,
0.036495961248874664,
-0.052102383226156235,
0.017247933894395828,
0.05862222984433174,
0.03390253335237503,
-0.0020380693022161722,
0.07482803612947464,
0.03825906291604042,
-0.03361063078045845,
-0.012552970089018345,
-0.014992390759289265,
-0.02575940079987049,
-0.03247874230146408,
-0.030264554545283318,
-0.03445562720298767,
-0.0074155693873763084,
-0.025920959189534187,
-0.013965972699224949,
0.013345385901629925,
-0.025874847546219826,
-0.012203291058540344,
0.05490061268210411,
0.05834800377488136,
-0.014147775247693062,
-0.028992904350161552,
-0.025694608688354492,
0.02991669811308384,
0.02984028123319149,
0.07526696473360062,
0.01862887665629387,
0.0002717390307225287,
-0.013117311522364616,
0.016906026750802994,
0.04256279021501541,
0.03215000405907631,
-0.030836747959256172,
0.040006134659051895,
-0.0002580418367870152,
0.004187552724033594,
0.01967713050544262,
0.0049340189434587955,
-0.0034275634679943323,
0.019623922184109688,
0.02641029842197895,
-0.008066338486969471,
0.05688172206282616,
-0.025428976863622665,
0.04074086621403694,
-0.031991492956876755,
-0.0310079175978899,
-0.0025982693769037724,
0.029192982241511345,
0.018386660143733025,
0.08407630771398544,
-0.005096103064715862,
-0.011680744588375092,
-0.02434464357793331,
0.041037775576114655,
0.019010158255696297,
0.029475374147295952,
-0.04184769093990326,
-0.02167690545320511,
0.01386470627039671,
-0.01039115246385336,
0.010840083472430706,
-0.032401420176029205,
0.021852008998394012,
-0.017798595130443573,
0.05340975150465965,
0.061520129442214966,
0.02053261548280716,
-0.037016525864601135,
0.04355931282043457,
-0.03953935578465462,
-0.0786779448390007,
0.029536478221416473,
0.018052920699119568,
-0.03773902356624603,
-0.02131657488644123,
0.02861574850976467,
0.03130398690700531,
-0.022265911102294922,
0.015696538612246513,
-0.03440941497683525,
0.022742507979273796,
0.01001907791942358,
-0.0847482904791832,
-0.0928957611322403,
0.08831409364938736,
0.017650684341788292,
-0.01827353611588478,
-0.07883124053478241,
-0.009355767630040646,
0.053719811141490936,
0.09720173478126526,
-0.02690931223332882,
0.014488648623228073,
0.0011999789858236909,
0.03854265809059143,
-0.005052370484918356,
-0.010257212445139885,
-0.017671803012490273,
0.025883400812745094,
-0.01323077455163002,
0.0359380804002285,
-0.051347412168979645,
0.04873543232679367,
0.03253334015607834,
0.0013185389107093215,
-0.06217968836426735,
0.05252635478973389,
-0.020744146779179573,
-0.004858941305428743,
-0.0022182827815413475,
-0.020273102447390556,
-0.05096016079187393,
0.07535352557897568,
0.03951296955347061,
0.013182749040424824,
0.01951650157570839,
-0.02126285806298256,
0.04851147159934044,
-0.006293322890996933,
-0.01860024966299534,
0.0419781431555748,
-0.016428614035248756,
-0.03320905938744545,
0.029672661796212196,
0.008670919574797153,
0.028538018465042114,
-0.007015399634838104,
-0.037335846573114395,
0.006501496769487858,
0.033200740814208984,
0.01016734167933464,
0.053260043263435364,
-0.035337433218955994,
-0.00269184447824955,
0.012567942030727863,
-0.0746985673904419,
0.0019953434821218252,
-0.025486886501312256,
-0.00840168260037899,
0.021080711856484413,
-0.020699281245470047,
-0.034796349704265594,
-0.02014903724193573,
0.02593083679676056,
-0.017937548458576202,
-0.020397279411554337,
0.004453544970601797,
0.016006356105208397,
0.001033787615597248,
-0.009445789270102978,
0.013818496838212013,
0.06126658618450165,
0.054406676441431046,
-0.026242977008223534,
0.010433466173708439,
-0.017147120088338852,
0.03717225417494774,
-0.0023201426956802607,
-0.012762460857629776,
-0.019909951835870743,
0.019393322989344597,
0.012546048499643803,
0.021493660286068916,
0.011772973462939262,
0.010159692727029324,
0.05241115391254425,
0.0054962304420769215,
0.03785683214664459,
0.03554427996277809,
-0.011524810455739498,
0.03891538828611374,
-0.0018628943944349885,
0.0012257912894710898,
0.04127134010195732,
0.012242852710187435,
-0.01779075711965561,
-0.021950654685497284,
-0.020459894090890884,
0.008536189794540405,
-0.023048406466841698,
-0.05474112555384636,
0.006880249362438917,
0.02873358689248562,
0.008754092268645763,
0.000682325626257807,
0.0614546574652195,
0.0024026972241699696,
-0.021358979865908623,
-0.007851473055779934,
-0.014245775528252125,
0.009454159066081047,
0.040649767965078354,
0.020474540069699287,
-0.009669541381299496,
-0.0042288536205887794,
0.00432561757043004,
-0.019357480108737946,
0.01568491943180561,
-0.011521666310727596,
0.01900208182632923,
-0.015291695483028889,
0.012020382098853588,
-0.014592938125133514,
-0.019268926233053207,
0.013934762217104435,
0.02567942440509796,
0.016985131427645683,
-0.005964984651654959,
-0.051508255302906036,
-0.021628612652420998,
0.012876133434474468,
0.049065690487623215,
-0.0021305265836417675,
0.006871380377560854,
0.03672533482313156,
-0.014264686964452267,
0.040151700377464294,
-0.0332796610891819,
-0.024661989882588387,
-0.039034903049468994,
-0.0020428479183465242,
0.03128958120942116,
0.048230722546577454,
0.019565708935260773,
-0.05072009935975075,
-0.017253896221518517,
-0.022684812545776367,
-0.012828152626752853,
0.028053462505340576,
-0.006407121662050486,
-0.030701695010066032,
0.03223641216754913,
0.01520784292370081,
-0.025724273175001144,
0.023328030481934547,
0.013546031899750233,
-0.003568768734112382,
-0.007856938987970352,
-0.01003486942499876,
0.007920228876173496,
-0.027270356193184853,
-0.006080134771764278,
-0.00017901368846651167,
-0.045834943652153015,
-0.00432712584733963,
0.02872062660753727,
0.006570576690137386,
-0.037818487733602524,
0.04533392935991287,
-0.028599174693226814,
-0.0427590049803257,
0.00637991726398468,
-0.01631556823849678,
0.02805306762456894,
-0.020161118358373642,
0.0054151760414242744,
0.0027866072487086058,
-0.027792131528258324,
0.03643488883972168,
-0.05631487816572189,
-0.04749469459056854,
0.022073734551668167,
0.03961975872516632,
0.03666222468018532,
-0.0007784873596392572,
0.021516326814889908,
0.056778039783239365,
0.007335489150136709,
-0.04126058518886566,
-0.045743416994810104,
-0.010598292574286461,
-0.023834798485040665,
-0.05699322745203972,
-0.013291707262396812,
0.04054572433233261,
-0.03874852508306503,
0.03356868401169777,
-0.03591050207614899,
0.045452918857336044,
0.05438368767499924,
0.010707005858421326,
-0.010094106197357178,
-0.0073365140706300735,
0.020302582532167435,
-0.03728630021214485,
0.039933569729328156,
0.039883870631456375,
-0.04806706681847572,
-0.01946849189698696,
-0.003966139629483223,
0.021997319534420967,
0.031742390245199203,
-0.0758247822523117,
0.037443578243255615,
-0.024363799020648003,
0.015144545584917068,
0.019840415567159653,
-0.016702065244317055,
0.013470235280692577,
0.043159227818250656,
0.00252564181573689,
0.00269731180742383,
0.05420490354299545,
-0.008496655151247978,
0.007299166172742844,
0.0433955080807209,
0.037383534014225006,
-0.016772396862506866,
-0.027627257630228996,
-0.005878016352653503,
-0.021783869713544846,
0.04816931486129761,
0.01159188337624073,
-0.017547233030200005,
0.03981449455022812,
0.02172739803791046,
0.028993573039770126,
0.022912127897143364,
-0.024874558672308922,
0.002563426038250327,
-0.04041328653693199,
0.036448922008275986,
-0.01941453479230404,
0.025809869170188904,
-0.0024935193359851837,
0.04832501336932182,
0.03447362780570984,
0.008996866643428802,
0.03557887300848961,
0.034711819142103195,
-0.11127330362796783,
0.030244875699281693,
-0.0068909418769180775,
-0.05504684895277023,
-0.03881321847438812,
0.0026450813747942448,
-0.013311393558979034,
-0.006324221845716238,
0.018259825184941292,
0.025431044399738312,
0.021885719150304794,
-0.03868861123919487,
-0.024765489622950554,
-0.03508993983268738,
-0.0448814257979393,
-0.02589130401611328,
0.030358143150806427,
0.04736487567424774,
-0.034754663705825806,
0.005114582367241383,
-0.003361172042787075,
-0.0038503557443618774,
-0.0019013428827747703,
-0.036923848092556,
-0.027775637805461884,
0.02046101726591587,
0.05955780670046806,
0.030320879071950912,
-0.014904809184372425,
-0.024983303621411324,
0.02800099365413189,
0.04479653015732765,
0.038393501192331314,
-0.031522683799266815,
-0.021192116662859917,
-0.024808282032608986,
-0.023907598108053207,
-0.041294414550065994,
-0.013323400169610977,
0.05372471734881401,
-0.06005904823541641,
-0.007797416299581528,
0.03410341590642929,
-0.013830970041453838,
-0.031199390068650246,
-0.02290952205657959,
0.019219236448407173,
0.011080102063715458,
-0.027981840074062347,
-0.05522193759679794,
-0.06644747406244278,
-0.011611731722950935,
0.006002272944897413,
0.052315231412649155,
0.012221751734614372,
-0.01393023319542408,
-0.029363026842474937,
0.04180975258350372,
0.015137417241930962,
-0.021152030676603317,
-0.002678471617400646,
-0.05861588940024376,
-0.020305246114730835,
-0.02317357063293457,
0.019686054438352585,
-0.008244819939136505,
0.04442787170410156,
-0.004899414721876383,
0.02463088557124138,
-0.047189872711896896,
-0.07723039388656616,
-0.04795726016163826,
0.009098305366933346,
0.031695038080215454,
-0.0036192256957292557,
0.002642615232616663,
-0.06714455038309097,
-0.01765594258904457,
0.03315393254160881,
-0.0434744693338871,
0.03845483809709549,
-0.027262190356850624,
0.02223251760005951,
-0.00010142854443984106,
-0.015112094581127167,
-0.06971747428178787,
0.030234329402446747,
0.0012565595097839832,
0.01882893405854702,
-0.011376168578863144,
-0.025967799127101898,
0.020586000755429268,
0.010907570831477642,
0.027500569820404053,
0.059650272130966187,
-0.006751821376383305,
0.03187008947134018,
0.04472546651959419,
-0.0038943695835769176,
-0.03351852297782898,
-0.035645175725221634,
0.0416584275662899,
-0.026339460164308548,
-0.02326481230556965,
0.04844368249177933,
0.018429895862936974,
-0.024275315925478935,
0.043681662529706955,
0.001747948001138866,
0.002104218350723386,
-0.01316839549690485,
-0.05839290842413902,
-0.03843215852975845,
0.01375773549079895,
0.004020329099148512,
0.047453541308641434,
0.04411674663424492,
-0.018942078575491905,
-0.006073360331356525,
-0.01179314311593771,
0.049206048250198364,
0.019206147640943527,
-0.011656124144792557,
-0.030526524409651756,
-0.011604467406868935,
-0.03057137317955494,
0.05478681996464729,
0.04967764392495155,
0.007593957241624594,
-0.02280954271554947,
-0.0301962997764349,
0.005092974286526442,
0.03534013777971268,
-0.03258481249213219,
0.01638270728290081,
0.010088617913424969,
0.0007361365132965147,
0.030746769160032272,
-0.024528922513127327,
-0.0053096129558980465,
-0.008923696354031563,
-0.009659606032073498,
0.01106946263462305,
0.01724904589354992,
0.019147606566548347,
-0.04556220397353172,
-0.012141277082264423,
0.008150442503392696,
-0.05165903642773628,
0.05248301848769188,
-0.0030511580407619476,
-0.006445645354688168,
0.022075826302170753,
-0.05697976052761078,
-0.010353480465710163,
0.004375867545604706,
-0.017360132187604904,
0.036092013120651245,
-0.07211678475141525,
0.006348933558911085,
0.005635133944451809,
0.0063402410596609116,
-0.049901075661182404,
-0.04888644441962242,
0.008470721542835236,
0.04600905254483223,
-0.014522266574203968,
-0.0034139009658247232,
-0.018038734793663025,
0.031734611839056015,
-0.017140673473477364,
-0.03205173462629318,
-0.006832115817815065,
-0.028255289420485497,
-0.03719199076294899,
0.007222646847367287,
0.00037420130684040487,
0.050619229674339294,
0.0060758525505661964,
-0.033888086676597595,
-0.0005035889334976673,
-0.011991911567747593,
-0.01791924424469471,
0.021586578339338303,
0.017570611089468002,
-0.021592753008008003,
-0.05591650307178497,
-0.014233666472136974,
0.01170657854527235,
0.007844175212085247,
-0.022884225472807884,
0.024715488776564598,
0.014854463748633862,
0.045296747237443924,
-0.019339056685566902,
-0.002619533333927393,
0.03904504328966141,
0.0508374348282814,
-0.04384339600801468,
-0.025519154965877533,
0.0057000466622412205,
-0.037211768329143524,
-0.05910312011837959,
0.02261529117822647,
0.022363562136888504,
0.008142183534801006,
-0.004026148002594709,
0.05341332405805588,
-0.06244765967130661,
0.002128320513293147,
0.031209679320454597,
-0.011981654912233353,
0.04449806362390518,
0.03668981418013573,
-0.023727325722575188,
-0.005365915596485138,
-0.0021432528737932444,
-0.026763133704662323,
-0.005391005426645279,
-0.02153562754392624,
0.0021249696146696806,
0.10598281025886536,
-0.010195217095315456,
0.04857868701219559,
0.012259060516953468,
-0.012037554755806923,
-0.007400119677186012,
0.013139244168996811,
0.008102196268737316,
-0.0016778875142335892,
0.00974337849766016,
0.025115974247455597,
-0.03619983792304993,
0.004186531528830528,
-0.003809005953371525,
0.04971538856625557,
0.006840698886662722,
0.0019584884867072105,
0.034062452614307404,
0.0010486309183761477,
0.016026534140110016,
-0.00014057705993764102,
-0.012333083897829056,
0.04943311586976051,
-0.020918384194374084,
0.03902550786733627,
-0.015529096126556396,
0.003008822910487652,
0.08240069448947906,
-0.0336235947906971,
0.004785279743373394,
-0.024496305733919144,
-0.06632284820079803,
-0.053511474281549454,
-0.013708948157727718,
0.009067244827747345,
0.011033190414309502,
-0.004705818369984627,
-0.003282729536294937,
-0.014793761074543,
-0.017169324681162834,
0.03110494837164879,
-0.030199343338608742,
-0.07373522967100143,
-0.03382936865091324,
-0.03797461837530136,
-0.032950352877378464,
0.045347169041633606,
0.011127917096018791,
-0.010285754688084126,
0.015247365459799767,
-0.04007066413760185,
0.00629954831674695,
0.04077080637216568,
0.04705464094877243,
0.0076723480597138405,
0.018957721069455147,
-0.0006966753862798214,
0.011756138876080513,
0.002617228776216507,
0.00930391438305378,
0.11260558664798737,
0.03234318271279335,
0.012540963478386402,
-0.053808290511369705,
0.031514447182416916,
-0.057253144681453705,
0.011984665878117085,
-0.0376286655664444,
0.04495168849825859,
-0.029844366014003754,
0.029782092198729515,
0.00803073588758707,
0.02876763977110386,
0.00892305001616478,
-0.0021124014165252447,
0.019997073337435722,
-0.04273135960102081,
-0.012419348582625389,
0.014588732272386551,
0.006904512643814087,
0.01444183848798275,
0.004962666891515255,
0.0004928510752506554,
0.03208328038454056,
-0.04819827526807785,
-0.024016618728637695,
-0.0035004904493689537,
-0.024447206407785416,
0.042144205421209335,
-0.010683689266443253,
-0.029209895059466362,
0.013196933083236217,
0.05098680779337883,
-0.03147071599960327,
-0.06436272710561752,
0.01200810819864273,
0.022229192778468132,
-0.0014909752644598484,
0.01145927794277668,
0.008295225910842419,
0.030286435037851334,
-0.0013038722099736333,
0.027065884321928024,
-0.025432921946048737,
-0.03995637595653534,
-0.020007355138659477,
-0.007817315869033337,
0.040465038269758224,
0.005828755907714367,
-0.02123946137726307,
-0.013915356248617172,
-0.007936796173453331,
-0.01416668388992548,
-0.0801374763250351,
0.009519940242171288,
0.060389913618564606,
-0.018941178917884827,
0.01109436433762312,
-0.014141158200800419,
0.04131530597805977,
-0.012485072948038578,
0.007212732918560505,
0.003910438623279333,
0.045637231320142746,
0.026433713734149933,
-0.028786325827240944,
0.00319913518615067,
0.062068644911050797,
0.011801018379628658,
-0.030234239995479584,
-0.031287502497434616,
-0.0261373370885849,
-0.014718691818416119,
0.016355518251657486,
0.013241306878626347,
0.05638135224580765,
0.005498221144080162,
-0.011836222372949123,
-0.012257582508027554,
0.016398368403315544,
-0.04647423326969147,
-0.008849860168993473,
-0.031871248036623,
-0.004885556176304817,
-0.04106646776199341,
0.012266338802874088,
0.04926252365112305,
0.03689555078744888,
0.003102755406871438,
-0.014426419511437416,
0.004739377647638321,
0.033404089510440826,
0.033171407878398895,
0.008964814245700836,
-0.06368383020162582,
0.0033040246926248074,
-0.007694135420024395,
-0.012605481781065464,
-0.01123557984828949,
0.05140530318021774,
0.03110460378229618,
0.02311512641608715,
-0.0016856837319210172,
-0.009068497456610203,
-0.06222344562411308,
0.03714607656002045,
0.0016205502906814218,
-0.022553568705916405,
0.008300693705677986,
0.003324241144582629,
0.020723743364214897,
-0.01224754098802805,
-0.03671352565288544,
-0.036282576620578766,
-0.01946960762143135,
-0.011454052291810513,
0.04620004817843437,
0.0004472409491427243,
-0.0030938235577195883,
-0.02443762868642807,
0.032194171100854874,
-0.02133496105670929,
-0.008245429955422878,
-0.043409787118434906,
-0.003044216427952051,
0.005270655266940594,
0.03235768899321556,
-0.025039875879883766,
0.06342533230781555,
-0.023112598806619644,
-0.03819417953491211,
0.0016587435966357589,
0.033508069813251495,
0.014913041144609451,
0.01528051309287548,
0.044260188937187195,
0.020968521013855934,
0.008350687101483345,
0.028025340288877487,
-0.05383516103029251,
0.03742576017975807,
-0.014682229608297348,
-0.04078368842601776,
0.006071281619369984,
-0.04709585756063461,
0.03912316635251045,
0.02285395935177803,
-0.003064361633732915,
0.01369630265980959,
0.06260054558515549,
-0.019396144896745682,
-0.028222423046827316,
-0.020551398396492004,
-0.035593967884778976,
0.029887570068240166,
0.013415917754173279,
0.017488980665802956,
-0.06387598812580109,
-0.017167946323752403,
0.03933070972561836,
0.023540567606687546,
0.002862518187612295,
-0.010310095734894276,
-0.026690751314163208,
-0.03948158398270607,
-0.043938588351011276,
0.007491802331060171,
0.016695108264684677,
-0.01439683884382248,
0.02759421616792679,
-0.014696638099849224,
0.05281423404812813,
0.02383062057197094,
0.010087521746754646,
-0.04853905364871025,
0.02352233976125717,
0.013379181735217571,
0.035493504256010056,
0.024207860231399536,
-0.031713128089904785,
0.011813468299806118,
0.032645080238580704,
-0.07929717004299164,
0.00018268699932377785,
-0.023401323705911636,
-0.02316315844655037,
-0.050902556627988815,
0.0035568808671087027,
-0.002219459740445018,
0.021919382736086845,
-0.015567170456051826,
0.03219546750187874,
0.014715757220983505,
0.05185897648334503,
-0.0394599549472332,
-0.03486577048897743,
0.0022795055992901325,
0.046289972960948944,
0.012461058795452118,
0.0033615974243730307,
0.04614054039120674,
0.0010031085694208741,
0.025009730830788612,
-0.014841588214039803,
-0.016298409551382065,
0.03766481578350067,
0.06301102787256241,
0.0026029504369944334,
0.009957748465240002,
0.01977347396314144,
0.014032063074409962,
-0.018191857263445854,
-0.010354024358093739,
-0.009351924993097782,
0.027787374332547188,
0.007965014316141605,
-0.02245785854756832,
-0.012569759041070938,
-0.022686846554279327,
-0.036894895136356354,
-0.03685150295495987,
-0.027227655053138733,
-0.018299803137779236,
0.00019898737082257867,
0.02531614527106285,
0.03808046132326126,
0.04349876940250397,
-0.04995005205273628,
-0.016567114740610123,
-0.07733966410160065,
0.030967021360993385,
0.027728388085961342,
-0.0026715074200183153,
-0.0391077846288681,
-0.028351077809929848,
-0.0003900567244272679,
-0.027420707046985626,
0.0070442198775708675,
0.0009419783018529415,
0.025391900911927223,
-0.04018711298704147,
-0.013321858830749989,
0.0034031651448458433,
0.015867700800299644,
0.03367091715335846,
0.0035095089115202427,
-0.0506785586476326,
-0.005806089378893375,
0.015091056004166603,
0.008055556565523148,
0.02929561398923397,
-0.03936696797609329,
-0.0370415523648262,
-0.09387389570474625,
0.054372478276491165,
-0.014005188830196857,
-0.03424859046936035,
-0.021529242396354675,
-0.0029003338422626257,
-0.032701101154088974,
0.024194080382585526,
0.05617145076394081,
-0.024224422872066498,
-0.008399688638746738,
0.0028911172412335873,
-0.012617765925824642,
0.006694836542010307,
-0.024621909484267235,
0.010268542915582657,
-0.00010094141907757148,
-0.07026974856853485,
-0.00976079422980547,
-0.009104405529797077,
-0.03134668618440628,
0.010348489508032799,
0.015496351756155491,
0.004196490161120892,
0.02411050722002983,
-0.013115135952830315,
-0.03480101004242897,
0.01773383840918541,
-0.020417824387550354,
0.003105169627815485,
0.07548770308494568,
0.005187768954783678,
0.000615757773630321,
0.01822434552013874,
-0.010021869093179703,
-0.04263167083263397,
0.04278360307216644,
-0.038622308522462845,
-0.022545918822288513,
-0.04323782026767731,
0.008729319088160992,
0.040566567331552505,
-0.05090615153312683,
-0.030522160232067108,
0.029644323512911797,
-0.029920199885964394,
-0.04014194756746292,
0.050568412989377975,
-0.008267875760793686,
0.015721935778856277,
-0.015958325937390327,
0.03190869092941284,
0.0177707951515913,
-0.022252164781093597,
-0.009728621691465378,
0.009025515988469124,
-0.022917205467820168,
-0.01598755456507206,
0.027315113693475723,
0.036337316036224365,
0.01349741779267788,
0.013243507593870163,
0.010639584623277187,
0.058767907321453094,
-0.00563396280631423,
0.009476740844547749,
0.007624238263815641,
-0.023386966437101364,
-0.011780795641243458,
0.00981145165860653,
0.0032189288176596165,
0.08370964974164963,
-0.0046189031563699245,
-0.00585301173850894,
-0.012807613238692284,
0.013056308962404728,
-0.01099648792296648,
0.02777257189154625,
0.009252805262804031,
0.0014530038461089134,
0.008194031193852425,
0.014597639441490173,
-0.02751731686294079,
-0.01972472108900547,
0.05091818422079086,
-0.01927931420505047,
-0.026554187759757042,
-0.025798652321100235,
-0.03381449356675148,
0.005334358662366867,
-0.019602876156568527,
-0.00035519973607733846,
-0.007445201743394136,
0.018548421561717987,
0.004800829570740461,
-0.003040535608306527,
-0.018616817891597748,
0.017701609060168266,
-0.008942823857069016,
0.0737195834517479,
-0.0758485496044159,
-0.014256610535085201,
-0.007755042519420385,
0.038456935435533524,
0.020249271765351295,
-0.002105754567310214
] |
<p>Why the absorption cross section in direct dissociation process is wide and structureless while the absorption cross section in the predissociation process is structured and containing lines which are normally Lorentzian in shape?</p>
| 8,322 |
[
-0.020948370918631554,
0.0030345700215548277,
-0.02139749564230442,
-0.004211165942251682,
0.011155175976455212,
0.027918174862861633,
-0.018833806738257408,
-0.03174959868192673,
0.0006761179538443685,
-0.03864748403429985,
0.024191755801439285,
-0.0007961623487062752,
0.0578453503549099,
-0.0008314396254718304,
0.003599091200158,
0.03724374249577522,
-0.007973951287567616,
0.015308087691664696,
0.009374737739562988,
-0.03191426023840904,
0.014655135571956635,
0.00708399573341012,
0.012570044957101345,
-0.01825692132115364,
-0.04107188433408737,
0.038670215755701065,
0.027391323819756508,
0.02955622784793377,
0.02265552431344986,
0.023667406290769577,
-0.0031810395885258913,
-0.015235848724842072,
-0.012635346502065659,
0.027250392362475395,
0.021180951967835426,
0.0038087922148406506,
-0.020068565383553505,
-0.038576509803533554,
-0.022832568734884262,
-0.0012125371722504497,
-0.029519956558942795,
-0.02666025608778,
-0.028388595208525658,
0.06466593593358994,
-0.020910996943712234,
0.013303651474416256,
-0.013974600471556187,
-0.038582198321819305,
0.04506050795316696,
-0.06322753429412842,
0.014492063783109188,
-0.046864110976457596,
0.05069776624441147,
0.0018749387236312032,
-0.009652405045926571,
-0.00586841581389308,
0.04175655543804169,
0.0858892947435379,
-0.004986975342035294,
-0.038567714393138885,
0.005043084733188152,
-0.028806159272789955,
0.013943317346274853,
0.02101936936378479,
-0.042309004813432693,
0.0046274010092020035,
-0.04419989883899689,
-0.044759683310985565,
0.040321849286556244,
0.02496747300028801,
0.015513845719397068,
0.008603702299296856,
0.006708230823278427,
0.02132049947977066,
-0.003958009649068117,
0.001853641588240862,
0.02940613590180874,
0.004401034209877253,
0.06666798889636993,
0.06842929124832153,
0.018006466329097748,
0.01502086129039526,
0.006602226756513119,
-0.014246759936213493,
-0.02858063206076622,
-0.02294122613966465,
0.057774629443883896,
0.005540389101952314,
-0.0072699678130447865,
0.03781183809041977,
0.03927433118224144,
0.04135056212544441,
0.051718395203351974,
0.011345717124640942,
0.01314456108957529,
0.01609557494521141,
-0.006769693922251463,
0.05816894769668579,
0.01800023950636387,
-0.0409335233271122,
-0.01492474414408207,
-0.008770071901381016,
0.03570679947733879,
0.06428629159927368,
0.03454812988638878,
0.0049599893391132355,
-0.06616488844156265,
0.023530736565589905,
-0.029111353680491447,
-0.023474982008337975,
-0.013169331476092339,
0.020933225750923157,
-0.02218378335237503,
0.005214794538915157,
0.016505056992173195,
-0.037025999277830124,
0.03505357727408409,
-0.01578657701611519,
0.07066605240106583,
0.1074921265244484,
0.03176506981253624,
0.0019794758409261703,
0.010139946825802326,
0.004015753045678139,
-0.027813689783215523,
-0.0002992030349560082,
0.026152124628424644,
0.026281123980879784,
0.0036900138948112726,
-0.02322598174214363,
-0.05048064514994621,
-0.035013582557439804,
0.04127953201532364,
0.000805624935310334,
0.007943703792989254,
-0.006720599252730608,
-0.09754316508769989,
-0.03162076696753502,
0.03603418543934822,
-0.002534876111894846,
0.005873183254152536,
-0.06086505576968193,
0.002589031821116805,
0.02967509999871254,
0.06657576560974121,
-0.015139438211917877,
0.0011538690887391567,
0.01858658343553543,
0.027297059074044228,
0.01929357275366783,
-0.020120827481150627,
-0.027191929519176483,
0.014706787653267384,
-0.009707065299153328,
-0.028227172791957855,
-0.06116979941725731,
0.020556531846523285,
0.02740970067679882,
-0.013559862971305847,
0.007607379462569952,
0.027550652623176575,
-0.04082069545984268,
0.006360999774187803,
0.020531337708234787,
0.004148190841078758,
-0.00480278953909874,
0.057944025844335556,
0.03937380760908127,
-0.009889500215649605,
0.011746414005756378,
0.02206472121179104,
0.014483976177871227,
0.003567272098734975,
0.007785120513290167,
0.015564275905489922,
-0.026291290298104286,
0.0008930062758736312,
0.017264703288674355,
0.014667992480099201,
-0.05140910670161247,
-0.0465116985142231,
-0.018842436373233795,
-0.032609935849905014,
0.012590758502483368,
0.015401023440063,
0.07094606757164001,
-0.005862108897417784,
-0.022574499249458313,
-0.010711250826716423,
-0.08283326029777527,
0.010476458817720413,
-0.007545821834355593,
0.026051880791783333,
0.00919440295547247,
-0.04677894338965416,
0.015664588660001755,
-0.006950706709176302,
-0.00624564616009593,
0.0025735197123140097,
-0.03195592761039734,
-0.013872967101633549,
-0.013506793417036533,
0.0017838787753134966,
0.0013209852622821927,
0.05212223157286644,
0.05841172859072685,
0.03230060264468193,
-0.012406935915350914,
0.023215491324663162,
0.004362006671726704,
-0.010431979782879353,
0.024403035640716553,
-0.030238891020417213,
0.015830954536795616,
-0.019441429525613785,
-0.05499284714460373,
-0.00046822073636576533,
-0.007249611429870129,
-0.010427679866552353,
0.04916256666183472,
-0.054425206035375595,
0.08174385875463486,
0.08269757032394409,
-0.002840680070221424,
0.031672991812229156,
0.045926131308078766,
0.020778661593794823,
0.009193100966513157,
0.027389582246541977,
-0.044306907802820206,
-0.036846548318862915,
-0.006764991208910942,
0.04166750982403755,
0.017401305958628654,
-0.06698556244373322,
-0.019214361906051636,
0.009360619820654392,
0.02075129561126232,
0.043117716908454895,
0.032021816819906235,
-0.034959826618433,
-0.03309030458331108,
0.04883330687880516,
0.015254138968884945,
-0.03157764673233032,
-0.0277869813144207,
-0.003177257953211665,
0.02051629312336445,
-0.006433003582060337,
-0.00007816102879587561,
-0.006699040532112122,
0.03462999686598778,
-0.055011339485645294,
-0.059745557606220245,
0.014269490726292133,
-0.0008125283056870103,
0.012974073179066181,
-0.034625642001628876,
0.015988698229193687,
0.000018768618247122504,
-0.01759658008813858,
-0.013744127936661243,
-0.007364328019320965,
-0.009358478710055351,
0.012792159803211689,
-0.01756136119365692,
-0.017254171893000603,
0.016343720257282257,
0.058015115559101105,
-0.07637020200490952,
-0.010243074037134647,
-0.042589329183101654,
-0.010520786046981812,
-0.022808615118265152,
-0.030926896259188652,
0.05947715416550636,
0.023321056738495827,
0.008576267398893833,
-0.04865926131606102,
-0.006470369640737772,
-0.052369993180036545,
-0.024730145931243896,
0.027062665671110153,
-0.003426057519391179,
-0.012097245082259178,
0.057958703488111496,
-0.030555756762623787,
-0.026405181735754013,
0.04831057786941528,
-0.06938497722148895,
-0.0314955897629261,
0.030160684138536453,
-0.013986125588417053,
-0.0654437467455864,
-0.010662488639354706,
0.04428916051983833,
-0.015489248558878899,
0.005794983822852373,
-0.0016241120174527168,
0.04531140625476837,
-0.05057918652892113,
-0.018016841262578964,
0.01743626594543457,
-0.03199220821261406,
-0.059405289590358734,
-0.032589081674814224,
-0.012707077898085117,
0.026901597157120705,
0.0003817480173893273,
0.0609612800180912,
0.029693730175495148,
-0.04605545848608017,
0.01938210427761078,
-0.0330713614821434,
0.026517657563090324,
0.029148157685995102,
0.0033461428247392178,
0.04326821118593216,
-0.029755087569355965,
0.01044698990881443,
-0.004346475936472416,
0.020069386810064316,
-0.01175029668956995,
-0.059554968029260635,
0.015482606366276741,
-0.02868235483765602,
-0.036597516387701035,
-0.0011551373172551394,
0.02389570139348507,
0.0064145722426474094,
0.04670525714755058,
0.017365941777825356,
0.011425837874412537,
0.04479160159826279,
-0.01633274555206299,
-0.025930751115083694,
-0.018468009307980537,
-0.012727050110697746,
0.012403617613017559,
0.0065881963819265366,
0.006251441314816475,
-0.01863694004714489,
0.049028195440769196,
0.01241922378540039,
0.0431954599916935,
0.02098952606320381,
-0.09238020330667496,
0.04236876219511032,
0.004978455603122711,
0.00914521049708128,
0.007922635413706303,
0.03059644065797329,
-0.04528796300292015,
-0.008524470962584019,
0.01474272832274437,
0.02180919423699379,
0.028270531445741653,
-0.05596831440925598,
0.012556669302284718,
0.007510646712034941,
0.02744705229997635,
-0.037421926856040955,
0.017709437757730484,
-0.0251783300191164,
-0.01467475388199091,
0.029862063005566597,
0.026291918009519577,
-0.01713821291923523,
0.03949473053216934,
0.06262984126806259,
0.020596567541360855,
-0.02905486710369587,
-0.020883312448859215,
-0.020306650549173355,
-0.07685069739818573,
-0.04440845921635628,
0.029343705624341965,
0.03463224321603775,
0.023296309635043144,
0.08352620154619217,
0.0006303505506366491,
0.007528240326792002,
-0.013007200323045254,
-0.01235243957489729,
-0.09024301916360855,
0.016052311286330223,
-0.017445942386984825,
0.01149621233344078,
-0.02127537876367569,
0.0071680862456560135,
-0.02013072744011879,
-0.01868533343076706,
-0.007378013804554939,
0.005384538788348436,
-0.015506668016314507,
-0.05017976835370064,
0.05066761374473572,
-0.021673576906323433,
-0.0035854633897542953,
-0.052463579922914505,
0.05701889842748642,
0.02438221126794815,
0.008663338609039783,
0.056978341192007065,
0.009653398767113686,
-0.027705589309334755,
0.013318450190126896,
-0.02918318845331669,
0.027830690145492554,
0.017148317769169807,
-0.0025821831077337265,
0.048674944788217545,
-0.001425494672730565,
-0.015589279122650623,
-0.02260085754096508,
0.009398221038281918,
0.03514878824353218,
0.010035570710897446,
0.004403147380799055,
-0.005446990951895714,
-0.058192603290081024,
-0.012991875410079956,
-0.009543785825371742,
0.061772916465997696,
-0.04740556702017784,
0.01123060379177332,
-0.018639693036675453,
-0.006737463176250458,
0.020375560969114304,
0.03215733543038368,
0.016870293766260147,
0.011606804095208645,
-0.011228489689528942,
-0.04873891919851303,
-0.019368352368474007,
-0.013298663310706615,
-0.01774413511157036,
0.030622586607933044,
-0.007654107641428709,
0.006906250026077032,
0.008989780209958553,
0.05318541079759598,
0.013456051237881184,
-0.032539643347263336,
-0.0072296359576284885,
-0.0004725501930806786,
-0.002584653440862894,
-0.0033181163016706705,
-0.01917017623782158,
-0.021260885521769524,
0.030906371772289276,
0.07242672145366669,
-0.002437329851090908,
0.018287282437086105,
-0.07047396153211594,
-0.013270560652017593,
-0.0100464578717947,
0.03478188440203667,
-0.0047750407829880714,
0.0015112834516912699,
-0.04279715195298195,
-0.017248323187232018,
0.03893019258975983,
-0.02658240497112274,
0.0263541117310524,
-0.041134629398584366,
-0.0009203763329423964,
-0.058790531009435654,
-0.009608596563339233,
-0.03978116810321808,
0.018489688634872437,
0.05211956426501274,
-0.033173009753227234,
-0.045011039823293686,
-0.006081062369048595,
-0.010940050706267357,
0.004322937689721584,
0.017741786316037178,
0.033326342701911926,
0.005199979059398174,
-0.02137383259832859,
-0.0031915048602968454,
0.049620483070611954,
-0.04187695309519768,
-0.064542755484581,
-0.007683638948947191,
0.0319770984351635,
-0.015139740891754627,
0.07401870936155319,
-0.017240356653928757,
-0.07500956207513809,
-0.008366502821445465,
0.003969773184508085,
-0.006298537366092205,
-0.023046262562274933,
-0.0037733062636107206,
0.028330260887742043,
0.013128873892128468,
-0.03583759814500809,
0.05644357204437256,
0.018443185836076736,
-0.013369952328503132,
0.028524328023195267,
-0.04123489186167717,
0.05006573721766472,
-0.015011277981102467,
-0.027690617367625237,
-0.03279842436313629,
0.01663891039788723,
-0.007614500820636749,
0.015664180740714073,
-0.013375134207308292,
-0.06048888340592384,
-0.018574999645352364,
-0.04085530340671539,
0.006022708490490913,
0.04895773530006409,
-0.012258467264473438,
-0.006996886804699898,
-0.0037764960434287786,
0.03288077935576439,
-0.010185310617089272,
-0.002517613349482417,
0.02654900588095188,
0.002741399919614196,
0.008485572412610054,
0.04079523682594299,
0.01052663940936327,
0.020672006532549858,
-0.07907726615667343,
-0.01800636015832424,
0.022134438157081604,
-0.05370844155550003,
0.031368110328912735,
-0.0011646548518911004,
0.011120862327516079,
0.03471023961901665,
-0.06484263390302658,
-0.0139636704698205,
-0.012480756267905235,
-0.033241938799619675,
0.01939553953707218,
-0.033996786922216415,
0.055474843829870224,
-0.0016560022486373782,
-0.021031510084867477,
-0.1041538417339325,
-0.033484216779470444,
0.01801992394030094,
0.01074234489351511,
-0.03594176471233368,
-0.03785949572920799,
-0.02477402798831463,
-0.025121966376900673,
-0.02399551123380661,
-0.012428577989339828,
0.021260825917124748,
-0.03225536644458771,
-0.0009191443677991629,
0.013210570439696312,
0.02861154079437256,
0.04262067377567291,
-0.0294224563986063,
0.018887639045715332,
-0.019164610654115677,
-0.01338648609817028,
0.010544823482632637,
0.012985141947865486,
0.017768846824765205,
-0.00984065793454647,
-0.042779676616191864,
-0.03742959722876549,
-0.0016698037507012486,
0.024766696617007256,
-0.023669229820370674,
0.008921260945498943,
0.02144913375377655,
-0.016898633912205696,
0.022724678739905357,
0.0020156174432486296,
-0.00663783960044384,
-0.04372285306453705,
0.006274086888879538,
0.028332024812698364,
-0.009558686055243015,
-0.014564299955964088,
-0.0429338738322258,
0.02485419064760208,
-0.00020689499797299504,
-0.0002948575420305133,
-0.020662037655711174,
0.050909388810396194,
-0.015255589969456196,
0.00839466042816639,
0.028900645673274994,
-0.022427529096603394,
0.03974289819598198,
-0.0021617007441818714,
0.03713301569223404,
0.05773073807358742,
-0.01682167313992977,
-0.012237844988703728,
-0.04333094134926796,
-0.054735202342271805,
0.024059413000941277,
0.037687335163354874,
0.0017137848772108555,
0.049511972814798355,
-0.025602906942367554,
0.031214987859129906,
-0.04075527563691139,
-0.033091820776462555,
-0.00723795872181654,
-0.00798625685274601,
0.0004850635305047035,
0.07624112814664841,
-0.03703368082642555,
-0.00224774400703609,
0.007069556973874569,
0.046159274876117706,
-0.0020347845274955034,
0.009995700791478157,
0.049262210726737976,
-0.0082381721585989,
-0.0007197090308181942,
0.009915504604578018,
0.02158377319574356,
0.019161632284522057,
0.011829524300992489,
0.019385164603590965,
-0.006113946903496981,
-0.0017166842008009553,
0.01922265812754631,
-0.04483087733387947,
0.005969680845737457,
-0.053702693432569504,
0.010105743072926998,
-0.02566416934132576,
0.01962735317647457,
0.03106597438454628,
0.010055657476186752,
0.004205470904707909,
0.032929327338933945,
0.011951224878430367,
0.009684938937425613,
0.014511133544147015,
0.03246502950787544,
-0.009235037490725517,
-0.014311949722468853,
-0.007230577990412712,
-0.036762818694114685,
0.05233997479081154,
-0.06962620466947556,
-0.03672776743769646,
-0.0005319177871569991,
-0.028630221262574196,
0.040718208998441696,
0.016861863434314728,
0.0032374749425798655,
-0.013396790251135826,
0.025293022394180298,
-0.008670637384057045,
0.017249820753932,
0.026788415387272835,
-0.01987479440867901,
0.11659887433052063,
0.034901365637779236,
0.0022692172788083553,
-0.032197512686252594,
-0.007311110384762287,
0.028619319200515747,
0.019933072850108147,
-0.016176696866750717,
0.028384817764163017,
0.020283907651901245,
0.02333168312907219,
0.0377737432718277,
0.01693323440849781,
0.0009807449532672763,
0.014671241864562035,
-0.005370262544602156,
-0.062594935297966,
-0.023948941379785538,
0.03597647324204445,
0.001045259297825396,
0.015602193772792816,
0.021407486870884895,
-0.0557926669716835,
0.03548336401581764,
0.001465001842007041,
0.04158933833241463,
-0.03528696671128273,
-0.056531041860580444,
0.03199729323387146,
-0.014197221025824547,
-0.055516358464956284,
0.01887841708958149,
0.03172207996249199,
0.006193224340677261,
-0.016937969252467155,
0.02777865342795849,
0.03470149263739586,
-0.042611949145793915,
-0.023532217368483543,
0.031238321214914322,
0.003450174583122134,
0.01127631962299347,
0.030672725290060043,
0.03273969516158104,
-0.032924581319093704,
-0.0010445270454511046,
-0.004263023380190134,
0.011835375800728798,
-0.010575965978205204,
-0.004261787980794907,
0.015199117362499237,
0.01769840344786644,
-0.006647353060543537,
-0.02880808524787426,
-0.025791984051465988,
0.00946720875799656,
0.007559196092188358,
-0.01649913378059864,
-0.01035149022936821,
-0.005610146094113588,
0.02578280307352543,
0.03742550313472748,
0.014130069874227047,
-0.014611667953431606,
0.033976174890995026,
0.037101391702890396,
0.029906470328569412,
0.059027571231126785,
0.014426854439079762,
0.003442406887188554,
-0.027140449732542038,
0.028980862349271774,
-0.019324809312820435,
-0.057296134531497955,
0.030250005424022675,
0.011399222537875175,
0.07872878015041351,
0.01982402801513672,
-0.003906856290996075,
0.010263202711939812,
-0.03820812702178955,
0.04480016976594925,
0.010268627665936947,
-0.03439982607960701,
-0.016815805807709694,
0.02402615360915661,
-0.0054800063371658325,
-0.012235522270202637,
-0.014699806459248066,
0.05202503129839897,
0.002959689125418663,
0.07040972262620926,
0.009706422686576843,
-0.05135633796453476,
-0.04356513172388077,
0.008884510956704617,
-0.008378777652978897,
-0.0009832287905737758,
-0.010606459341943264,
0.03208506479859352,
-0.00046425845357589424,
0.0346846841275692,
-0.004792028572410345,
0.04698237404227257,
-0.043387819081544876,
-0.018259219825267792,
0.01072536688297987,
0.0066179209388792515,
-0.004568495322018862,
-0.000495333515573293,
-0.01581735722720623,
-0.032135844230651855,
0.015040211379528046,
-0.04810095205903053,
-0.005797922145575285,
0.031947650015354156,
0.02319294586777687,
-0.003861031960695982,
0.043843310326337814,
-0.0315692164003849,
0.011788301169872284,
0.0062564159743487835,
-0.018322546035051346,
-0.050845418125391006,
0.006985815241932869,
-0.05476091802120209,
-0.01242856401950121,
0.006995189934968948,
0.006383400410413742,
-0.0008758008480072021,
-0.023834314197301865,
0.006043849978595972,
0.04837004840373993,
-0.004188980907201767,
-0.017788298428058624,
0.045948293060064316,
-0.005042026750743389,
0.014439461752772331,
-0.0033116729464381933,
-0.03935821354389191,
0.015521693974733353,
-0.05147956311702728,
-0.018417755141854286,
-0.007241399958729744,
-0.02080174721777439,
0.046788182109594345,
-0.012850550003349781,
0.021504269912838936,
0.004976025782525539,
0.0569516196846962,
-0.014323154464364052,
-0.019226698204874992,
0.03603312745690346,
-0.05140869319438934,
0.019709130749106407,
0.011302738450467587,
-0.008137055672705173,
-0.011019237339496613,
0.005166702438145876,
0.011958768591284752,
0.0170053131878376,
-0.01587042585015297,
0.03550424799323082,
0.0004428482207003981,
-0.025930097326636314,
0.052888523787260056,
0.038733646273612976,
0.009717967361211777,
0.029430460184812546,
0.04166135936975479,
-0.04638583958148956,
0.005101416725665331,
-0.004335508681833744,
0.009220960550010204,
-0.07830769568681717,
-0.0041033122688531876,
-0.018248258158564568,
0.004833110608160496,
0.03062269650399685,
-0.040063872933387756,
0.021892491728067398,
0.07698129862546921,
-0.042267847806215286,
-0.0011202687164768577,
-0.04808124899864197,
-0.01538525428622961,
-0.011303640902042389,
-0.014819575473666191,
-0.043191421777009964,
0.04061977192759514,
0.03762991353869438,
0.025652535259723663,
0.02342335321009159,
0.0066021825186908245,
-0.004133531358093023,
-0.007631017826497555,
-0.039070069789886475,
-0.0019709875341504812,
-0.039866309612989426,
-0.008903221227228642,
0.07331858575344086,
0.013167462311685085,
-0.016389690339565277,
0.013958655297756195,
-0.00950266420841217,
-0.008231035433709621,
0.017798790708184242,
0.006515106186270714,
0.02552080526947975,
-0.004315376281738281,
0.010992289520800114,
-0.0318886935710907,
0.02786632999777794,
0.016067199409008026,
-0.0009403165895491838,
-0.011605378240346909,
0.029489954933524132,
-0.0090462202206254,
-0.008790504187345505,
-0.03937092050909996,
-0.022915512323379517,
0.02190958708524704,
0.01729418896138668,
-0.03546419367194176,
-0.013798346742987633,
0.040281541645526886,
0.010538960807025433,
-0.06820188462734222,
-0.01714760810136795,
-0.0704473927617073,
-0.02586180903017521,
0.027785474434494972,
0.014983185566961765,
0.005963100120425224,
0.039253003895282745,
-0.04112251475453377,
-0.024638017639517784,
-0.03104277513921261,
-0.008946788497269154,
0.02299664542078972,
-0.011113408021628857,
-0.011566771194338799,
0.0005267079686746001,
-0.011799358762800694,
-0.02011188119649887,
-0.038991328328847885,
-0.05101317912340164,
0.04884073883295059,
0.004839170258492231,
0.06767769157886505,
-0.02056259475648403,
-0.06321283429861069,
-0.006224288139492273,
-0.050499327480793,
0.04317212477326393,
-0.047893162816762924,
-0.05980192869901657,
-0.04095927253365517,
-0.020462188869714737,
-0.021969348192214966,
0.057340528815984726,
0.06107749789953232,
0.02741095796227455,
-0.030701611191034317,
-0.008281737565994263,
0.007621296215802431,
-0.00336366961710155,
-0.04725292697548866,
0.0023958769161254168,
-0.006917246617376804,
-0.01861056499183178,
0.04105093330144882,
-0.008131023496389389,
-0.009029623121023178,
0.07115992903709412,
0.005796205252408981,
0.025372860953211784,
0.015819862484931946,
-0.006883170455694199,
-0.023014217615127563,
0.05142643302679062,
0.010013677179813385,
-0.0023349407128989697,
0.043924879282712936,
-0.007428963668644428,
0.011106629855930805,
0.038045257329940796,
-0.028327513486146927,
-0.030537569895386696,
0.010958864353597164,
-0.014326613396406174,
-0.0036337568890303373,
-0.020085973665118217,
-0.025966716930270195,
0.04496964067220688,
-0.06477127224206924,
0.01750868745148182,
0.024706542491912842,
-0.048387546092271805,
-0.011471220292150974,
0.038944754749536514,
0.008877277374267578,
0.014664463698863983,
0.018131263554096222,
0.028383681550621986,
0.04716772213578224,
0.0025168710853904486,
-0.024643396958708763,
0.03346766531467438,
0.02739550545811653,
0.04607585072517395,
0.035841625183820724,
-0.003979818895459175,
-0.03657915070652962,
0.0017747844103723764,
0.006211618427187204,
0.060587525367736816,
0.0061769867315888405,
0.0019353546667844057,
0.04468626156449318,
0.009290134534239769,
-0.021367499604821205,
-0.030423199757933617,
0.004726826213300228,
0.0960468202829361,
-0.06309705227613449,
0.018197467550635338,
-0.018263405188918114,
-0.020065518096089363,
-0.03866410627961159,
0.014769106172025204,
0.003173364559188485,
0.03622426465153694,
-0.010865694843232632,
-0.0030376273207366467,
-0.029961170628666878,
0.00724043371155858,
0.009450996294617653,
-0.02032174915075302,
0.020599735900759697,
-0.001852370915003121,
-0.031208384782075882,
-0.01850900612771511,
0.004480397794395685,
0.02341558039188385,
-0.026047689840197563,
0.010327644646167755,
0.028636379167437553,
0.032235968858003616,
0.016233090311288834,
0.0004686974280048162,
-0.03829626366496086,
0.024394268169999123,
-0.0595683678984642,
0.0057360101491212845,
-0.012982720509171486,
0.0069992439821362495,
-0.04625927284359932,
0.021622557193040848
] |
<p>Almost every time somebody talks about atoms, at some point they mention something like this:</p>
<blockquote>
<p>If we remove the spaces between the atoms and atomic components, we can fit the solar system in a <a href="http://en.wikipedia.org/wiki/Thimble">thimble</a>.</p>
</blockquote>
<p>Or</p>
<blockquote>
<p>If we remove the spaces between the electrons and the nucleus, we can fit the universe in a baseball.</p>
</blockquote>
<p>I know that <a href="https://en.wikipedia.org/wiki/Geiger-Marsden_experiment#Conclusions">atoms are mostly empty</a>, but I've always thought that those statements are exaggerating.</p>
<p>Can we really fit the solar system in a thimble (if we remove all those spaces)?</p>
| 8,323 |
[
-0.013248180970549583,
-0.04392525926232338,
0.03579813987016678,
-0.013409854844212532,
0.03509586304426193,
0.027920832857489586,
-0.01732509583234787,
-0.02459130622446537,
-0.008692813105881214,
0.008934833109378815,
0.053365785628557205,
0.019243309274315834,
0.00716797960922122,
0.010951042175292969,
-0.0003984289651270956,
0.019685883074998856,
0.02411043643951416,
-0.034224532544612885,
-0.015420399606227875,
-0.042372554540634155,
0.028558073565363884,
-0.01925341784954071,
-0.043690554797649384,
0.01180996187031269,
0.019253883510828018,
0.030776364728808403,
-0.024202121421694756,
-0.03198337182402611,
-0.01322401687502861,
0.0890427902340889,
-0.005899406038224697,
0.007373382803052664,
0.035930778831243515,
-0.013340051285922527,
0.04601660743355751,
-0.01701832003891468,
0.009571894071996212,
-0.04106397181749344,
0.012256860733032227,
0.020748794078826904,
-0.012940331362187862,
-0.0034865669440478086,
-0.0025346996262669563,
0.03721629083156586,
-0.033713601529598236,
0.05750543624162674,
-0.004886894952505827,
-0.0058995820581912994,
0.0329543873667717,
-0.027333006262779236,
0.04796157404780388,
0.015900861471891403,
0.03372381255030632,
0.022058667615056038,
-0.00802757777273655,
-0.03174914792180061,
0.0869484692811966,
0.028115615248680115,
-0.009733911603689194,
-0.048468951135873795,
-0.017342178151011467,
-0.0202458668500185,
0.006208726670593023,
0.01978655904531479,
-0.020447278395295143,
0.052400488406419754,
-0.045679569244384766,
-0.040460363030433655,
0.00736662931740284,
0.006326999515295029,
0.002654091455042362,
-0.0024360916577279568,
0.06945661455392838,
0.00723862461745739,
0.013971350155770779,
-0.015082287602126598,
0.054235417395830154,
-0.022051842883229256,
0.04234473407268524,
0.044643986970186234,
-0.038582947105169296,
-0.010335397906601429,
0.03312259539961815,
0.007105535827577114,
0.03626975044608116,
-0.014825253747403622,
0.050737444311380386,
-0.045239657163619995,
-0.00003725361966644414,
0.023838376626372337,
-0.01593547686934471,
0.01662634313106537,
0.05574733018875122,
0.013020661659538746,
0.00533688860014081,
0.020307952538132668,
0.009916651993989944,
0.052145056426525116,
0.011488826014101505,
0.0012911920202896,
0.02862490713596344,
-0.004360159393399954,
0.02704622410237789,
0.08684564381837845,
0.02225303091108799,
-0.00001061744933394948,
-0.005051627289503813,
0.01821119897067547,
-0.002871491014957428,
0.020365536212921143,
-0.05421345308423042,
0.012942365370690823,
0.026332484558224678,
0.018351923674345016,
0.02419917657971382,
-0.02489151805639267,
-0.004167707171291113,
-0.0016493480652570724,
0.019210070371627808,
0.08407176285982132,
0.01901262067258358,
-0.02347628027200699,
0.00772411935031414,
-0.04778118059039116,
-0.0669705793261528,
0.024519426748156548,
0.01408685278147459,
0.0029034921899437904,
-0.0485113151371479,
0.007466208189725876,
-0.01625341922044754,
0.023667002096772194,
0.04077453538775444,
-0.025283247232437134,
0.038579829037189484,
-0.022727908566594124,
-0.10975528508424759,
-0.04357253387570381,
0.05974959582090378,
0.0163786131888628,
-0.029715264216065407,
-0.05649605393409729,
0.027327507734298706,
-0.003850237000733614,
0.045636843889951706,
0.04499984532594681,
-0.017025336623191833,
-0.05353111773729324,
0.03645552322268486,
-0.004027089104056358,
-0.050993964076042175,
0.010937483981251717,
-0.0012008253252133727,
-0.035813476890325546,
0.01407993771135807,
-0.04903493449091911,
0.05693451687693596,
0.03920901566743851,
0.028218021616339684,
0.008288448676466942,
0.03274901583790779,
-0.02489844709634781,
-0.021745728328824043,
-0.034965939819812775,
-0.021088412031531334,
-0.025512728840112686,
0.05153618007898331,
0.006413436960428953,
-0.01562638394534588,
0.05237405374646187,
0.019733579829335213,
0.01638488657772541,
-0.0007038761978037655,
-0.01586645282804966,
0.003777365665882826,
-0.0601540133357048,
-0.021691109985113144,
-0.030413666740059853,
-0.011049194261431694,
0.00891781598329544,
-0.0395689532160759,
-0.016094157472252846,
0.0027856645174324512,
0.03653340041637421,
0.08008082211017609,
0.06390518695116043,
0.009790734387934208,
-0.009226609952747822,
0.014975225552916527,
-0.019243886694312096,
-0.019954385235905647,
-0.08309204876422882,
0.0036867910530418158,
-0.0027357451617717743,
-0.009771214798092842,
0.022903479635715485,
-0.008629483170807362,
-0.015800386667251587,
0.0022505077067762613,
-0.0046601188369095325,
-0.02055288851261139,
0.037870243191719055,
0.007315030787140131,
0.01417003758251667,
-0.005530371330678463,
0.09355209767818451,
0.035693589597940445,
-0.007337091024965048,
0.0038949328009039164,
-0.021691007539629936,
-0.023926634341478348,
0.004078095778822899,
-0.02299877442419529,
0.03348667174577713,
0.038445230573415756,
0.007006690837442875,
0.0312948115170002,
0.01901586540043354,
-0.007027612999081612,
0.026930024847388268,
-0.0110798804089427,
0.06901058554649353,
-0.03278845548629761,
-0.007419907953590155,
-0.0026356365997344255,
0.04564882069826126,
0.025775518268346786,
0.03191805258393288,
-0.013680613599717617,
-0.020983777940273285,
-0.05732497572898865,
-0.03407702222466469,
0.04720551520586014,
0.0023473240435123444,
-0.02303815819323063,
0.02278791554272175,
0.0014428544091060758,
0.012237364426255226,
-0.0034789026249200106,
-0.02181927114725113,
-0.05390841141343117,
-0.0350068062543869,
-0.021214395761489868,
0.014823630452156067,
0.005104105919599533,
-0.009517738595604897,
-0.018026316538453102,
-0.014349863864481449,
0.03550489619374275,
0.00942597072571516,
0.047577522695064545,
0.0021668251138180494,
0.03613957762718201,
0.011028673499822617,
-0.019456736743450165,
-0.07321277260780334,
0.01950509287416935,
0.00535590760409832,
-0.0015920907026156783,
-0.00896016601473093,
-0.004860556684434414,
-0.014680293388664722,
-0.046877481043338776,
-0.010632218793034554,
-0.03358843922615051,
0.03072943538427353,
0.025509100407361984,
-0.019913146272301674,
0.013588451780378819,
-0.07006599009037018,
-0.02304672636091709,
-0.005135428626090288,
0.005788296926766634,
-0.05751822888851166,
-0.01817627064883709,
0.024176569655537605,
0.025357725098729134,
0.036580026149749756,
-0.04869364947080612,
-0.021986503154039383,
-0.022444037720561028,
-0.0047164796851575375,
0.003651341190561652,
-0.018412422388792038,
-0.003347983816638589,
0.019946396350860596,
-0.005101812072098255,
-0.01608906500041485,
-0.014355657622218132,
-0.02429305762052536,
0.024323785677552223,
0.010366678237915039,
-0.02101163938641548,
-0.04457031935453415,
0.023092444986104965,
-0.05431174486875534,
-0.010512826964259148,
-0.04491450637578964,
0.0023832442238926888,
0.051043570041656494,
-0.00043889920925721526,
-0.06661681830883026,
-0.05644681304693222,
-0.05288790166378021,
-0.03830093890428543,
-0.0324220173060894,
-0.026399049907922745,
0.02685130015015602,
0.0054904683493077755,
0.009133120998740196,
0.010258101858198643,
-0.026306185871362686,
0.009315126575529575,
-0.0713888555765152,
-0.01140652410686016,
0.02890223264694214,
-0.029366733506321907,
0.02343643270432949,
0.032161518931388855,
-0.04835617542266846,
0.10677458345890045,
-0.011943019926548004,
-0.037008460611104965,
0.015432821586728096,
-0.0159837044775486,
0.0013052530121058226,
-0.023777872323989868,
0.037840086966753006,
0.008318747393786907,
0.041784290224313736,
0.02991497330367565,
0.01004222221672535,
0.09638243168592453,
0.005717633757740259,
0.018283726647496223,
0.032544299960136414,
-0.0009282065439037979,
0.003772728145122528,
-0.02843678556382656,
0.05553603172302246,
0.0047651478089392185,
-0.01607019640505314,
0.01322241686284542,
-0.056977204978466034,
0.01400539930909872,
0.02819383144378662,
-0.06623127311468124,
0.048199430108070374,
-0.006159155163913965,
0.024914616718888283,
-0.024104787036776543,
0.028172768652439117,
0.024329597130417824,
-0.015828387811779976,
0.0073152026161551476,
0.03272121399641037,
0.05844197794795036,
0.03314413130283356,
-0.009661020711064339,
0.036758556962013245,
0.03575615957379341,
-0.03322591632604599,
-0.014247332699596882,
-0.0005114210653118789,
0.03299841284751892,
0.00392075115814805,
0.01289664302021265,
-0.03503752872347832,
0.04810849204659462,
0.03496917337179184,
0.01736081764101982,
-0.022405041381716728,
-0.0582408681511879,
-0.016986267641186714,
-0.06891229748725891,
0.007779913023114204,
-0.0036416156217455864,
0.03748710826039314,
0.007918348535895348,
0.01823413372039795,
0.014803650788962841,
0.040990911424160004,
-0.02678694948554039,
-0.014948452822864056,
-0.047095634043216705,
-0.021514667198061943,
-0.029908886179327965,
-0.01880250871181488,
-0.03034367598593235,
-0.008617050014436245,
-0.002351213712245226,
0.004334271419793367,
0.010345145128667355,
-0.029567183926701546,
0.02166006527841091,
-0.030584299936890602,
-0.007435912266373634,
-0.0031409363728016615,
-0.020267540588974953,
0.015294102020561695,
0.02124619111418724,
0.05826280266046524,
-0.0012489859946072102,
0.04599568992853165,
0.004315332509577274,
-0.02123914659023285,
-0.045211680233478546,
-0.008708263747394085,
0.046747561544179916,
-0.0007340973825193942,
0.008215496316552162,
0.04573779180645943,
0.039881154894828796,
0.005868404172360897,
0.00629447540268302,
-0.00044715157127939165,
0.021863875910639763,
-0.04369590803980827,
-0.0046443878673017025,
-0.03812257945537567,
-0.04728454351425171,
-0.020861124619841576,
-0.021816514432430267,
0.05684015154838562,
-0.007876762188971043,
0.053049519658088684,
0.008822212927043438,
0.01775536872446537,
0.02008896879851818,
0.03209167718887329,
0.02672412432730198,
-0.008069188334047794,
0.019365865737199783,
-0.03222750127315521,
-0.0036511302459985018,
-0.05308275297284126,
0.004520489368587732,
0.008237794041633606,
-0.01069768238812685,
-0.001967149553820491,
0.0020851055160164833,
0.019150368869304657,
0.034292351454496384,
-0.03781231492757797,
0.02087874710559845,
-0.03236417472362518,
0.01005831453949213,
-0.054398708045482635,
0.006838224362581968,
0.04021519422531128,
-0.026165420189499855,
0.0034680054523050785,
0.008898811414837837,
-0.020290261134505272,
-0.06879247725009918,
-0.01817571371793747,
0.05004008486866951,
0.0383831188082695,
-0.024932021275162697,
0.019047396257519722,
-0.0702199786901474,
-0.03271893784403801,
0.027102790772914886,
-0.004336936865001917,
0.01227205153554678,
-0.06810656189918518,
0.007266411557793617,
-0.000023017284547677264,
-0.031198248267173767,
0.04974021762609482,
0.0027605502400547266,
-0.028019072487950325,
0.008031104691326618,
-0.03195590153336525,
-0.0025882560294121504,
-0.011834979057312012,
0.033320341259241104,
0.00399251002818346,
0.042654234915971756,
0.006418850272893906,
-0.005505504552274942,
0.004175769165158272,
-0.001474240212701261,
0.003925207071006298,
-0.0719345435500145,
0.02169238217175007,
0.00806322693824768,
-0.031652890145778656,
0.04478400945663452,
-0.007759855594485998,
-0.06261806935071945,
0.04166465625166893,
0.0006234552711248398,
-0.015662042424082756,
-0.005982804577797651,
-0.08076692372560501,
0.054502733051776886,
-0.000849044241476804,
0.0021266844123601913,
0.03758668899536133,
0.048216674476861954,
0.0118228355422616,
0.03497647866606712,
-0.05056343972682953,
0.01823127456009388,
-0.05350184440612793,
0.0027297697961330414,
-0.023099377751350403,
-0.009919305332005024,
-0.031836677342653275,
0.010522057302296162,
-0.015181400813162327,
0.042356304824352264,
0.030326588079333305,
-0.05925660580396652,
0.04208679497241974,
0.031033789739012718,
-0.00625243317335844,
0.03471273556351662,
-0.043337382376194,
0.03712974861264229,
0.009021583013236523,
-0.0336451381444931,
0.0017156789544969797,
0.009354119189083576,
0.01562679372727871,
0.02568012848496437,
-0.009559327736496925,
0.003074883483350277,
-0.021316610276699066,
-0.023151949048042297,
0.013616956770420074,
-0.035658400505781174,
0.05509357899427414,
-0.03678490221500397,
-0.024846414104104042,
-0.016912827268242836,
-0.03682025894522667,
-0.04739935323596001,
0.013224302791059017,
-0.02553607150912285,
0.008633416146039963,
-0.03298884630203247,
0.017208781093358994,
-0.032236360013484955,
-0.0023958724923431873,
-0.09117238223552704,
-0.05455954000353813,
0.009335443377494812,
-0.004723532125353813,
-0.019490955397486687,
-0.02263370156288147,
-0.013852903619408607,
-0.03497462347149849,
-0.0183853842318058,
0.02346658520400524,
0.012502755038440228,
-0.032548077404499054,
-0.027895718812942505,
0.010190019384026527,
-0.007122388109564781,
0.09394032508134842,
0.0313907116651535,
-0.020865870639681816,
-0.008473988622426987,
-0.001058774534612894,
0.013690640218555927,
0.02749648131430149,
0.008571682497859001,
-0.05053067207336426,
-0.0439477264881134,
-0.014036978594958782,
-0.02152387797832489,
0.02262989990413189,
-0.02412591688334942,
-0.00996694527566433,
0.010425564832985401,
-0.011086918413639069,
0.003970727324485779,
-0.011313616298139095,
0.0320468544960022,
-0.004863010253757238,
0.014641010202467442,
0.0050615305081009865,
0.04590349644422531,
-0.011227342300117016,
-0.02519644983112812,
0.024876156821846962,
0.0013698977418243885,
0.013684147037565708,
0.01760595478117466,
0.06293509155511856,
-0.015948301181197166,
-0.013236640021204948,
0.030100813135504723,
-0.013955713249742985,
0.04819970205426216,
-0.02909456379711628,
0.013805395923554897,
-0.0035525031853467226,
0.011337741278111935,
-0.06534121185541153,
-0.03913671523332596,
-0.052583105862140656,
0.014295234344899654,
0.012575369328260422,
-0.027512572705745697,
0.04455249384045601,
0.0068544428795576096,
-0.04107174649834633,
-0.004399043042212725,
-0.05326194688677788,
0.010359239764511585,
0.010214215144515038,
-0.006994702387601137,
0.04115620627999306,
-0.03811398521065712,
-0.00045152055099606514,
0.05830240249633789,
0.03323664888739586,
-0.008151006884872913,
0.011209966614842415,
0.025999505072832108,
0.020323779433965683,
-0.0172570887953043,
-0.042284101247787476,
-0.022279761731624603,
0.013434619642794132,
-0.08445677906274796,
0.039906036108732224,
0.01060902327299118,
-0.010800120420753956,
0.027270298451185226,
0.028881104663014412,
0.029109911993145943,
-0.00620098365470767,
-0.023481667041778564,
-0.041575364768505096,
0.008659323677420616,
0.014397903345525265,
0.005071599502116442,
-0.026952475309371948,
-0.019449083134531975,
0.0029503204859793186,
-0.008827224373817444,
0.027982791885733604,
-0.026538899168372154,
-0.05914583429694176,
-0.02844296023249626,
-0.04791395366191864,
-0.03156612440943718,
0.015663864091038704,
-0.016872623935341835,
-0.026038946583867073,
-0.010159253142774105,
-0.035583075135946274,
0.03530300036072731,
0.04377777874469757,
0.0006715802010148764,
-0.06153840199112892,
0.060734037309885025,
0.0031394646503031254,
0.036527328193187714,
-0.005745171569287777,
0.02147708274424076,
0.15021537244319916,
0.07349249720573425,
0.012790320441126823,
-0.033552613109350204,
0.01170184276998043,
0.02623612806200981,
0.011571940034627914,
-0.0014617849374189973,
-0.014844469726085663,
-0.014412285760045052,
0.027301214635372162,
0.002865132410079241,
0.030534975230693817,
0.013617572374641895,
0.012250562198460102,
0.032197434455156326,
-0.05019449070096016,
-0.03626694157719612,
0.011903361417353153,
0.015987638384103775,
0.0038848668336868286,
-0.014592302963137627,
-0.05032812058925629,
-0.000038372618291759863,
0.009746129624545574,
0.033464428037405014,
-0.013410039246082306,
-0.00048356468323618174,
0.023532193154096603,
0.01928899623453617,
-0.05285647138953209,
0.010997549630701542,
0.009686622768640518,
-0.02049628086388111,
0.012278000824153423,
0.00033378705848008394,
0.021574996411800385,
-0.014746014028787613,
-0.013419536873698235,
0.042735159397125244,
0.03336354345083237,
0.0029681583400815725,
-0.0037295958027243614,
0.011916751973330975,
-0.04761655628681183,
-0.059310492128133774,
-0.021548887714743614,
0.025923728942871094,
-0.04137108474969864,
-0.024096688255667686,
-0.007021715398877859,
0.002048376016318798,
0.004303281661123037,
-0.05870278924703598,
-0.008969391696155071,
0.017608407884836197,
0.0048294588923454285,
-0.002242337679490447,
-0.028441229835152626,
-0.011834460310637951,
0.02104470692574978,
-0.03081410750746727,
0.012538536451756954,
0.001073571969754994,
0.046414490789175034,
-0.0056325276382267475,
0.008248547092080116,
0.025413228198885918,
-0.015625137835741043,
0.010202478617429733,
-0.026965755969285965,
-0.002711325651034713,
-0.06854143738746643,
-0.03650956600904465,
0.02560603991150856,
0.0432218499481678,
0.028324896469712257,
0.014031419530510902,
0.0124731520190835,
0.0005046332953497767,
-0.03897016495466232,
0.05602766573429108,
0.0003779976104851812,
-0.04716360941529274,
-0.00030086396145634353,
-0.03181290999054909,
-0.0022441446781158447,
0.03321138024330139,
-0.02601701021194458,
-0.004308576695621014,
0.03134991228580475,
0.07895231992006302,
-0.0007782094180583954,
-0.04316532611846924,
-0.012829640880227089,
0.008839793503284454,
-0.0369998924434185,
0.006883989553898573,
0.03457195311784744,
0.03653479740023613,
0.024732058867812157,
0.020230812951922417,
0.015356410294771194,
0.02770877815783024,
-0.027784151956439018,
-0.009818675927817822,
0.03787267208099365,
-0.008722839877009392,
-0.030786430463194847,
0.03462682664394379,
-0.0389917753636837,
-0.041835930198431015,
0.02767847292125225,
-0.018598271533846855,
-0.008198251947760582,
0.042111847549676895,
0.02367420122027397,
-0.02134799025952816,
0.027724741026759148,
-0.01820940151810646,
0.009043564088642597,
-0.02723492495715618,
0.004846298601478338,
-0.04787162318825722,
-0.04669281840324402,
0.004942397121340036,
-0.026332391425967216,
0.020387688651680946,
0.008458878844976425,
-0.0047873700968921185,
-0.015337614342570305,
0.075199194252491,
0.020397217944264412,
-0.01938582956790924,
-0.029966171830892563,
-0.014413555152714252,
0.007640765514224768,
0.028351858258247375,
-0.04263773560523987,
0.0026886819396167994,
0.02706277370452881,
-0.044579219073057175,
-0.04504444822669029,
-0.006664371583610773,
-0.03137986361980438,
0.00272620958276093,
0.03981909528374672,
0.000876935722772032,
-0.029444970190525055,
0.05579840764403343,
-0.031202610582113266,
0.008841391652822495,
-0.012960810214281082,
0.02054113708436489,
0.04259409382939339,
-0.029795492067933083,
-0.009298714809119701,
-0.011433686129748821,
-0.026630735024809837,
0.04343925788998604,
-0.01296625379472971,
0.011173916980624199,
0.0015914324903860688,
0.003961114678531885,
-0.012875743210315704,
-0.011090527288615704,
0.011748328804969788,
0.0034949223045259714,
-0.019212689250707626,
0.05663818120956421,
-0.03000694513320923,
0.06159893423318863,
0.0486467182636261,
0.02099279873073101,
-0.0778622254729271,
0.000295356527203694,
-0.00447895796969533,
-0.0006243927055038512,
0.002670512069016695,
-0.028328875079751015,
0.02382771670818329,
0.01743927225470543,
-0.08054006844758987,
0.013026938773691654,
-0.014503516256809235,
0.011997831985354424,
-0.0542360283434391,
-0.023254215717315674,
-0.027804767712950706,
0.028322363272309303,
0.0016825092025101185,
0.050141531974077225,
-0.023495541885495186,
0.023126255720853806,
-0.013384188525378704,
-0.03830725699663162,
-0.026283051818609238,
0.05711876228451729,
-0.01631992869079113,
-0.007903547026216984,
0.08933348953723907,
-0.013173343613743782,
-0.009404882788658142,
-0.006189516745507717,
-0.015059114433825016,
0.03675476461648941,
-0.03459157794713974,
0.008580577559769154,
0.004437300842255354,
0.036895640194416046,
0.020669445395469666,
0.03211279958486557,
-0.004098764155060053,
-0.020166222006082535,
0.006423090118914843,
0.014890914782881737,
0.015559898689389229,
-0.0041204821318387985,
0.06473754346370697,
-0.015630610287189484,
-0.026622943580150604,
0.03645114228129387,
0.004635073710232973,
0.015370272099971771,
-0.00443490082398057,
0.00648666312918067,
0.014100808650255203,
-0.013278359547257423,
-0.030493780970573425,
-0.03730937838554382,
0.017685558646917343,
0.012903854250907898,
0.03164788708090782,
-0.03176744282245636,
0.03253757208585739,
-0.0013646386796608567,
-0.008375242352485657,
-0.0032616767566651106,
0.02182288095355034,
-0.024167068302631378,
-0.009576253592967987,
-0.003803341882303357,
0.02443971298635006,
0.061361562460660934,
0.014756765216588974,
-0.013494536280632019,
-0.059264253824949265,
0.04068145900964737,
0.05436348170042038,
0.04045696184039116,
0.01612231880426407,
-0.024064449593424797,
-0.014237348921597004,
-0.06398213654756546,
0.0351984016597271,
-0.002330264775082469,
0.013763988390564919,
-0.02253824844956398,
-0.0256195105612278,
0.020099584013223648,
0.013535832054913044,
0.06415750831365585,
0.0035803501959890127,
-0.002979790326207876,
-0.017896082252264023,
0.010287377052009106,
0.02239871956408024,
-0.03781481087207794,
0.015009838156402111,
-0.0045180912129580975,
0.005112421233206987,
0.028410129249095917,
-0.04388927295804024,
-0.035435691475868225,
0.004381194710731506,
0.03591590374708176,
-0.004454675130546093,
0.009799834340810776,
0.0064674555324018,
-0.03784656152129173,
0.04305914044380188,
0.022148137912154198,
-0.007386495359241962,
0.046224482357501984,
-0.004397046752274036,
0.02729225531220436,
-0.003946801647543907,
-0.011924704536795616,
-0.03936739265918732,
0.016514604911208153,
-0.03332344442605972,
0.017468292266130447,
-0.03135073184967041,
-0.024592528119683266,
-0.0019159105140715837,
-0.019513994455337524,
0.011297768913209438,
0.05168943852186203,
-0.03928142786026001,
-0.008672347292304039,
0.02501334436237812,
0.018731219694018364,
0.042934905737638474,
-0.027707567438483238,
-0.001153309945948422,
0.03117472305893898,
-0.017492717131972313,
0.015128578059375286,
0.020905274897813797,
0.05753232166171074,
0.018002457916736603,
0.038285914808511734,
0.025986220687627792,
0.014497783035039902,
0.03988071158528328,
0.03492838144302368,
0.02332046441733837,
-0.013933463022112846,
-0.0317901149392128,
-0.004861769732087851,
0.0018623690120875835,
0.005559728480875492,
0.03423677384853363,
-0.014153645373880863,
0.10451458394527435,
-0.020353369414806366,
0.007682402618229389,
0.00023985856387298554,
0.0003036391572095454,
-0.0215305108577013,
0.025663360953330994,
0.01485125720500946,
-0.009124228730797768,
-0.010156311094760895,
-0.02758673205971718,
-0.04032041132450104,
0.03669014200568199,
0.0027422953862696886,
-0.028601590543985367,
-0.01459110714495182,
-0.039474766701459885,
0.004234297666698694,
-0.007495067548006773,
0.008006623946130276,
-0.015607570298016071,
-0.006131077650934458,
0.011629743501543999,
0.0333792120218277,
0.012389012612402439,
-0.012011226266622543,
-0.015297888778150082,
-0.01396183855831623,
0.04912876337766647,
-0.03577284514904022,
-0.004830105230212212,
-0.027716202661395073,
0.035063955932855606,
-0.05757942423224449,
-0.008056117221713066
] |
<p>I am learning the differential form of <a href="http://en.wikipedia.org/wiki/Gauss%27s_law">Gauss Law</a> derived from the divergence theorem.
$${\rm div}~ \vec{E} =\frac{\rho}{\epsilon_0}.$$
So far in my study of math and physics, the word "differential" has been associated with a infinitesimal change in a value (e.g. dv, dr...etc)
I do not really understand what the physical interpretation of the Gauss Law in differential form is. In general, what is the purpose of putting an equation into differential form? </p>
| 8,324 |
[
-0.01314646378159523,
0.014686199836432934,
0.003918250557035208,
-0.013795849867165089,
0.02679693140089512,
0.014792883768677711,
-0.028697902336716652,
0.0025858767330646515,
-0.024125009775161743,
-0.01676511950790882,
0.023251498118042946,
0.005390179809182882,
0.03947949409484863,
-0.020976336672902107,
0.06362581253051758,
0.03767792508006096,
0.013542826287448406,
-0.01794838346540928,
0.002334411721676588,
-0.04484988749027252,
-0.003497844096273184,
0.015956591814756393,
0.014235883951187134,
-0.004524810239672661,
-0.03008592315018177,
0.046539582312107086,
0.016845056787133217,
-0.003624438075348735,
0.031058743596076965,
0.02592317759990692,
-0.010418270714581013,
-0.022369036450982094,
0.011283373460173607,
0.04036352410912514,
0.00833897665143013,
0.02340422198176384,
-0.00416506826877594,
-0.02563128061592579,
-0.035771436989307404,
0.03478565439581871,
-0.03357457369565964,
-0.01971770077943802,
-0.02101278118789196,
0.058648016303777695,
-0.038018256425857544,
0.009793167933821678,
0.04219891503453255,
-0.050465069711208344,
0.0416572168469429,
-0.05789339914917946,
0.07077714800834656,
0.005108010023832321,
0.07305890321731567,
0.030651632696390152,
0.01540360227227211,
0.03686225041747093,
0.06569208204746246,
0.03147748112678528,
-0.023687094449996948,
-0.0777726098895073,
-0.030080078169703484,
-0.034634873270988464,
-0.0007061366341076791,
-0.008993400260806084,
-0.0198837723582983,
0.04415031522512436,
-0.03357212245464325,
-0.031356971710920334,
0.031772103160619736,
-0.021608248353004456,
0.023570025339722633,
0.03831620141863823,
0.017062416300177574,
-0.02148856595158577,
0.01910255290567875,
-0.020215444266796112,
-0.0020629670470952988,
-0.004429683089256287,
0.014483073726296425,
0.0380854606628418,
-0.006319738924503326,
0.004317999817430973,
-0.006418253295123577,
0.03571215644478798,
-0.0006305868155322969,
-0.009253169409930706,
0.06702817976474762,
-0.01608722284436226,
0.0396973118185997,
0.018968338146805763,
-0.023603305220603943,
0.0315028615295887,
0.007508183363825083,
-0.018616365268826485,
-0.019068904221057892,
0.04675346985459328,
0.011091350577771664,
0.0218894574791193,
-0.0012629160191863775,
-0.05806158110499382,
0.006058167200535536,
-0.02682420425117016,
0.0014015400083735585,
0.040922682732343674,
-0.026296798139810562,
-0.027369532734155655,
-0.002490139566361904,
0.031206119805574417,
-0.027537403628230095,
-0.028239425271749496,
-0.02525399811565876,
0.02523071877658367,
-0.008250663988292217,
0.04425419867038727,
0.041185732930898666,
0.004400905687361956,
-0.00013365125050768256,
0.01137689407914877,
0.04450752213597298,
0.07778915017843246,
0.052943941205739975,
-0.05148343741893768,
0.037228476256132126,
-0.009043898433446884,
-0.050419654697179794,
0.040262218564748764,
0.020245730876922607,
0.003321276279166341,
0.00021716197079513222,
0.008610998280346394,
-0.030291913077235222,
-0.0006188837578520179,
-0.026020515710115433,
0.016368260607123375,
0.006119562312960625,
-0.033272579312324524,
-0.06585031002759933,
-0.05597680062055588,
0.025223996490240097,
0.015293835662305355,
-0.027520647272467613,
-0.0866905227303505,
-0.007500826846808195,
0.04036792367696762,
0.0494559071958065,
0.0017215763218700886,
0.005450088530778885,
-0.022156421095132828,
0.014085263013839722,
-0.01982809044420719,
-0.024871928617358208,
-0.030209628865122795,
0.012760467827320099,
-0.030938180163502693,
0.004339779727160931,
-0.05390079692006111,
0.0023762830533087254,
0.0383235439658165,
-0.017411109060049057,
-0.004253581631928682,
0.05742663890123367,
-0.05700939893722534,
-0.02910451963543892,
0.02661800943315029,
-0.017143607139587402,
-0.02507799305021763,
0.10208146274089813,
0.001176105230115354,
0.046120207756757736,
0.059699997305870056,
0.04102851077914238,
0.021103834733366966,
0.005149306729435921,
0.05073406919836998,
0.04851048067212105,
-0.014420105144381523,
-0.02189362794160843,
-0.027870718389749527,
-0.000534643535502255,
-0.011832906864583492,
-0.02762359380722046,
-0.04616329446434975,
-0.003912150394171476,
-0.00003705838025780395,
-0.03174355626106262,
0.032969750463962555,
-0.0058383638970553875,
0.03566206619143486,
-0.008671071380376816,
-0.038939300924539566,
-0.014432660304009914,
-0.052099935710430145,
0.07613453269004822,
-0.010781930759549141,
0.019123533740639687,
0.007524001877754927,
0.029728766530752182,
0.03858642652630806,
-0.06115035340189934,
-0.036381177604198456,
0.007125734817236662,
0.024181365966796875,
0.00725916912779212,
-0.04348820447921753,
0.03168255090713501,
0.020693084225058556,
0.019432464614510536,
0.013883144594728947,
0.035288792103528976,
-0.01841665804386139,
0.0009983363561332226,
-0.011322268284857273,
-0.019022542983293533,
0.03973987698554993,
-0.001639808528125286,
-0.017102794721722603,
-0.006201650016009808,
-0.03008054569363594,
-0.002636795165017247,
0.02253742143511772,
-0.05365833267569542,
0.09253016859292984,
0.06804173439741135,
0.013935395516455173,
-0.00011223907495150343,
0.045470960438251495,
0.0006389578338712454,
-0.006588979624211788,
-0.016656216233968735,
-0.04841134324669838,
-0.017960648983716965,
0.016638750210404396,
0.006512627471238375,
0.05401043966412544,
-0.03286916762590408,
-0.00379103422164917,
0.011366136372089386,
0.04887653887271881,
0.05241924524307251,
0.030286403372883797,
-0.025691375136375427,
-0.01455613411962986,
0.030228616669774055,
-0.011030510067939758,
-0.012891762889921665,
0.006357492879033089,
0.05675022676587105,
0.04114116355776787,
0.03476865962147713,
-0.010481523349881172,
-0.00725639658048749,
0.060728829354047775,
-0.022029412910342216,
0.014924021437764168,
0.02089121751487255,
-0.01911063678562641,
0.013384939171373844,
-0.028305133804678917,
0.0265425406396389,
0.040673479437828064,
-0.041692618280649185,
0.017891347408294678,
-0.0559053011238575,
-0.015652187168598175,
0.03258013725280762,
0.022351618856191635,
-0.02598579414188862,
-0.038679011166095734,
0.0218922421336174,
-0.05948830395936966,
0.01679196208715439,
-0.01021481491625309,
-0.030217671766877174,
-0.03438413515686989,
-0.023843420669436455,
-0.022129807621240616,
0.018169337883591652,
0.010594536550343037,
-0.006448308937251568,
-0.03466873615980148,
-0.01150637585669756,
-0.024135585874319077,
0.004333461169153452,
0.01042547170072794,
-0.0437542200088501,
0.033975038677453995,
-0.014615073800086975,
-0.045196715742349625,
0.057100072503089905,
-0.021474551409482956,
0.035691551864147186,
0.019115915521979332,
0.0007315776310861111,
-0.052928902208805084,
-0.028168901801109314,
-0.014292536303400993,
0.01717401295900345,
-0.008399900048971176,
-0.006362877320498228,
0.050639815628528595,
-0.07027308642864227,
-0.0019694543443620205,
0.03534127026796341,
-0.0610501654446125,
-0.05109904706478119,
-0.03428921476006508,
0.0019511203281581402,
0.002769963350147009,
-0.013096255250275135,
0.05439598113298416,
0.013060635887086391,
-0.06480048596858978,
-0.010955735109746456,
-0.049307648092508316,
-0.06044468283653259,
0.022032586857676506,
0.018400045111775398,
0.03551233932375908,
0.0037977213505655527,
-0.04133600369095802,
0.06976957619190216,
0.038473062217235565,
-0.04285484552383423,
0.004098603967577219,
0.0008457978838123381,
-0.011355123482644558,
-0.013610770925879478,
0.019004078581929207,
0.03776340186595917,
-0.024414438754320145,
-0.013689890503883362,
0.018920617178082466,
0.023269210010766983,
0.013681108132004738,
0.007585550658404827,
-0.033874399960041046,
-0.0006339223473332822,
-0.017357472330331802,
0.019733717665076256,
0.02750789187848568,
0.0440315306186676,
-0.020350974053144455,
0.011644056998193264,
0.019596917554736137,
0.0490027479827404,
0.02722928673028946,
-0.008292526938021183,
0.0674530491232872,
0.03634634241461754,
-0.025843946263194084,
-0.026607535779476166,
0.03379165753722191,
-0.00812714546918869,
-0.00615693349391222,
0.023279745131731033,
-0.00037229800364002585,
0.02503744326531887,
-0.06157275289297104,
0.020034804940223694,
0.016543498262763023,
0.022587725892663002,
-0.023785898461937904,
-0.018871966749429703,
-0.007895433343946934,
-0.02759615145623684,
0.007887168787419796,
-0.002950474852696061,
-0.006560448091477156,
0.048188429325819016,
0.023702310398221016,
0.0074452972039580345,
-0.014052875339984894,
-0.03580330312252045,
0.019611455500125885,
-0.0590028390288353,
-0.010493792593479156,
0.054077062755823135,
0.030161170288920403,
0.002237618202343583,
0.0801202580332756,
0.03705836832523346,
0.016997626051306725,
0.05488554760813713,
-0.03193787857890129,
-0.09370236843824387,
0.0290917307138443,
-0.042958423495292664,
-0.01254208106547594,
-0.020019151270389557,
0.01785295456647873,
0.03686285763978958,
-0.024912849068641663,
-0.003293694695457816,
-0.014106870628893375,
-0.0022478322498500347,
-0.03826933354139328,
-0.012789302505552769,
-0.030803268775343895,
-0.06807506829500198,
-0.0408339686691761,
0.011942459270358086,
0.023360025137662888,
-0.011792488396167755,
-0.008099054917693138,
0.04906053468585014,
-0.003522708313539624,
-0.026997359469532967,
-0.018932774662971497,
-0.03325415402650833,
0.03724106028676033,
0.027889275923371315,
0.06513194739818573,
0.012870866805315018,
-0.005224660970270634,
0.06114546209573746,
0.020574811846017838,
0.0658884346485138,
-0.0015563232591375709,
-0.018938932567834854,
-0.020113229751586914,
-0.057854145765304565,
-0.00046329290489666164,
-0.020189663395285606,
0.032154738903045654,
0.009458623826503754,
0.010897023603320122,
0.028019174933433533,
0.002486461540684104,
-0.0030806022696197033,
0.025430554524064064,
0.052073054015636444,
-0.019006239250302315,
-0.03343914821743965,
-0.03514893352985382,
0.007431935053318739,
-0.050961583852767944,
-0.003625286277383566,
0.025042414665222168,
0.014565824531018734,
-0.02748805843293667,
0.016742294654250145,
-0.00532342167571187,
0.010416867211461067,
-0.009500441141426563,
-0.04505906254053116,
0.011190429329872131,
0.045689571648836136,
0.027207164093852043,
0.009944840334355831,
0.01278845313936472,
0.03853277489542961,
0.04627791419625282,
-0.024102577939629555,
0.023472033441066742,
-0.08184608072042465,
-0.002648427616804838,
0.03655848279595375,
0.03257007896900177,
-0.009458720684051514,
0.018339816480875015,
-0.04733193665742874,
-0.0062556192278862,
0.05148911103606224,
-0.033014796674251556,
0.000702830555383116,
-0.021412761881947517,
-0.027186378836631775,
-0.01604553684592247,
-0.011242418549954891,
-0.007629943545907736,
0.036768727004528046,
0.008229771628975868,
0.010167188942432404,
-0.011867336928844452,
0.00026425483520142734,
-0.025285977870225906,
0.0017233154503628612,
0.010308224707841873,
0.049615707248449326,
-0.013754558749496937,
-0.031168675050139427,
0.010115737095475197,
0.031367845833301544,
0.010217399336397648,
-0.05717921629548073,
0.009388349950313568,
0.010911129415035248,
0.026679547503590584,
0.04811515659093857,
-0.02525622397661209,
-0.03051549755036831,
0.026067610830068588,
0.031122790649533272,
-0.017270220443606377,
0.004228014964610338,
-0.01937609538435936,
0.02672393061220646,
0.02816230244934559,
0.0013796177227050066,
0.03568785637617111,
0.05403130501508713,
0.0010007086675614119,
-0.013233392499387264,
-0.01816594786942005,
0.052296001464128494,
-0.0007576363277621567,
-0.010970234870910645,
-0.055401694029569626,
0.010869991034269333,
-0.056584376841783524,
0.04509095475077629,
-0.00044129634625278413,
0.021487154066562653,
-0.02504897676408291,
-0.030273130163550377,
0.021260667592287064,
0.029432032257318497,
0.00747427623718977,
-0.022897807881236076,
-0.008718766272068024,
0.010428915731608868,
0.013746825978159904,
-0.028631895780563354,
-0.021299922838807106,
0.01389648299664259,
0.00787444319576025,
0.016235768795013428,
-0.0328400619328022,
-0.009571242146193981,
-0.0064856065437197685,
-0.025210890918970108,
0.051675114780664444,
-0.04099716246128082,
0.025339413434267044,
-0.028585711494088173,
-0.025278527289628983,
0.034717705100774765,
-0.06238936260342598,
-0.026648864150047302,
-0.016052354127168655,
-0.002867743605747819,
0.042637672275304794,
-0.05292574688792229,
0.018965061753988266,
-0.020070860162377357,
0.005442146211862564,
-0.06874534487724304,
-0.044674716889858246,
0.03854667767882347,
-0.029350662603974342,
-0.014915163628757,
-0.02048383094370365,
-0.001718929735943675,
-0.045684222131967545,
-0.02697623334825039,
0.013042829930782318,
0.021381253376603127,
0.0037517002783715725,
0.021814284846186638,
0.01625339686870575,
0.0005448739975690842,
0.03863265737891197,
-0.02679913304746151,
-0.012014288455247879,
-0.002066471381112933,
0.005149980541318655,
-0.004359325859695673,
-0.0036922902800142765,
0.07170508801937103,
-0.016087573021650314,
-0.001502317376434803,
-0.00629801582545042,
-0.03139817342162132,
0.025726275518536568,
-0.060673799365758896,
-0.014971480704843998,
0.016532713547348976,
0.01447961013764143,
0.0098474295809865,
-0.017281021922826767,
-0.008424813859164715,
-0.017156559973955154,
0.0157124362885952,
0.02108215168118477,
-0.006654223892837763,
0.011876457370817661,
-0.01993277296423912,
0.025193581357598305,
0.008593370206654072,
0.012337690219283104,
0.017855297774076462,
0.03505192697048187,
-0.039158377796411514,
0.01733005978167057,
0.00950284581631422,
-0.0021321638487279415,
0.023172985762357712,
-0.0009747646981850266,
0.02754484862089157,
0.024311082437634468,
0.016614533960819244,
-0.04360679164528847,
-0.01684526912868023,
-0.054136939346790314,
0.009861418046057224,
0.08188226073980331,
-0.02270401641726494,
0.06517823785543442,
0.00854385457932949,
0.0037502518389374018,
0.019159825518727303,
-0.01769314520061016,
-0.05510595440864563,
-0.004149663262069225,
-0.021457038819789886,
-0.0024901097640395164,
-0.03279813751578331,
0.00008851494203554466,
0.011676828376948833,
0.01710677705705166,
-0.004750670399516821,
0.027242541313171387,
0.023087894544005394,
0.0091434046626091,
-0.00024182687047868967,
0.006346703041344881,
-0.030380845069885254,
0.05302916094660759,
-0.028429895639419556,
0.02304794080555439,
-0.012755551375448704,
-0.000018349674064666033,
0.0635693296790123,
-0.004710937850177288,
-0.00949178822338581,
-0.04075247049331665,
-0.011490597389638424,
-0.04907943680882454,
0.028607098385691643,
0.03733295202255249,
-0.0070043825544416904,
0.01875392161309719,
0.022997302934527397,
0.015333408489823341,
0.01391980517655611,
0.013514651916921139,
0.0037427954375743866,
-0.04520639032125473,
-0.02480926364660263,
-0.0475756898522377,
-0.02477000653743744,
0.05305501073598862,
-0.008974870666861534,
-0.041788045316934586,
-0.03577015921473503,
-0.02685984969139099,
0.025999441742897034,
0.03910591080784798,
-0.029599688947200775,
-0.009326664730906487,
0.07594586163759232,
-0.014280106872320175,
0.014590900391340256,
-0.025892572477459908,
0.006953902076929808,
0.1100078597664833,
0.029447773471474648,
0.013178127817809582,
-0.055273544043302536,
0.01683584414422512,
-0.040946539491415024,
0.009753880091011524,
-0.03761323541402817,
0.023084787651896477,
0.010447831824421883,
0.0201451126486063,
0.01043285708874464,
0.028955712914466858,
0.013649788685142994,
0.003318402450531721,
0.05864766240119934,
-0.01497340202331543,
-0.03910936042666435,
0.014629694633185863,
0.02394178695976734,
-0.02272285893559456,
0.05291058123111725,
-0.04743516817688942,
0.011373586021363735,
-0.04451334476470947,
-0.010934252291917801,
-0.011577427387237549,
-0.02855522744357586,
0.013135864399373531,
0.026369644328951836,
-0.03346274048089981,
0.023226365447044373,
-0.0004561921232379973,
0.0188232883810997,
-0.042260508984327316,
0.027308102697134018,
0.02842836268246174,
-0.01164731290191412,
-0.004499289207160473,
0.01503648329526186,
-0.004634703043848276,
0.02541879564523697,
0.000275849481113255,
0.016220688819885254,
-0.004881438799202442,
-0.014675435610115528,
-0.028391828760504723,
0.05232711881399155,
-0.02586226537823677,
0.021266914904117584,
-0.00011851546150865033,
0.021743154153227806,
0.008243754506111145,
-0.07812163233757019,
-0.06275684386491776,
-0.024788374081254005,
0.03517105057835579,
-0.008603157475590706,
-0.026166129857301712,
0.0025667408481240273,
0.02257939800620079,
-0.005986753851175308,
0.05157129839062691,
0.0014111521886661649,
-0.013565007597208023,
0.023687738925218582,
-0.013633428141474724,
0.05657816678285599,
-0.05348819121718407,
-0.04370049387216568,
-0.02960023283958435,
0.004706431180238724,
-0.019034210592508316,
0.0021375820506364107,
0.017906155437231064,
0.013913826085627079,
-0.030214548110961914,
-0.002503643510863185,
-0.00025779783027246594,
0.004500558599829674,
-0.06488902121782303,
0.05904041603207588,
0.01231192983686924,
0.02780052088201046,
-0.030576147139072418,
-0.015131146647036076,
0.021209022030234337,
0.014779198914766312,
-0.036193881183862686,
0.010317981243133545,
-0.000932000984903425,
-0.0022639622911810875,
0.01468989159911871,
-0.014660839922726154,
-0.018471749499440193,
-0.002014083554968238,
-0.02814188227057457,
-0.011385646648705006,
-0.021990446373820305,
0.04579480364918709,
0.04539516940712929,
0.003443286754190922,
-0.01541944034397602,
0.045315369963645935,
-0.04486532881855965,
0.029940618202090263,
-0.0067918142303824425,
-0.016304338350892067,
0.009360541589558125,
0.0013160581002011895,
-0.01024013664573431,
-0.03257352113723755,
-0.01013670489192009,
-0.03261147066950798,
0.003253460396081209,
-0.037413373589515686,
0.014139960519969463,
-0.01331070251762867,
-0.002504609990864992,
-0.0215704757720232,
0.0121847465634346,
-0.0200431440025568,
-0.020272554829716682,
-0.06960916519165039,
0.029421256855130196,
-0.01051559392362833,
-0.030155407264828682,
0.02354368194937706,
0.0035224673338234425,
-0.00133139593526721,
-0.023967454209923744,
0.026448236778378487,
0.009086841717362404,
0.01558030303567648,
-0.010142804123461246,
0.03194763511419296,
-0.035391729325056076,
0.03548196703195572,
-0.037315744906663895,
-0.034792494028806686,
0.022732259705662727,
-0.036954618990421295,
-0.0363408662378788,
0.0326545350253582,
0.03549749776721001,
0.04188946634531021,
-0.013115541078150272,
0.0004498592752497643,
-0.029992735013365746,
0.044957954436540604,
0.00138268549926579,
0.03839799016714096,
-0.007305575534701347,
-0.07957260310649872,
-0.047128431499004364,
-0.04149354249238968,
0.018612023442983627,
-0.0050201877020299435,
0.0009321779361926019,
0.020924454554915428,
0.023977093398571014,
-0.012849095277488232,
-0.00922977365553379,
0.025044945999979973,
-0.0013206483563408256,
0.0006850832724012434,
0.01688179187476635,
0.006967985071241856,
0.058144599199295044,
0.0575629398226738,
-0.0242531206458807,
0.005927805323153734,
0.012807331047952175,
0.011962699703872204,
-0.08568017929792404,
0.008559368550777435,
0.034575559198856354,
0.007352742832154036,
0.014554089866578579,
-0.05707211792469025,
-0.02308666706085205,
0.005009944085031748,
-0.013633974827826023,
0.026220181956887245,
-0.057294316589832306,
-0.023699311539530754,
0.003567656734958291,
-0.012710188515484333,
0.006117888260632753,
0.056063003838062286,
0.04517258703708649,
0.01644209586083889,
0.029095634818077087,
-0.009716927073895931,
0.007082964759320021,
-0.02061321772634983,
-0.0030232167337089777,
0.05191993713378906,
0.0004902954096905887,
-0.04246395081281662,
0.04779885709285736,
0.008825763128697872,
-0.053750816732645035,
0.0413847453892231,
0.008581682108342648,
0.002958253724500537,
0.02461881935596466,
0.032444048672914505,
0.011878611519932747,
0.044917959719896317,
0.045143790543079376,
0.002114082919433713,
-0.049050599336624146,
0.007136494852602482,
0.037921272218227386,
0.0192974042147398,
0.004105370491743088,
-0.019720010459423065,
0.018793094903230667,
-0.044900327920913696,
-0.04595372825860977,
0.03456313908100128,
-0.020187053829431534,
-0.0025066628586500883,
-0.014751688577234745,
0.01139516569674015,
0.030234552919864655,
-0.021859731525182724,
0.006207920145243406,
-0.04766339436173439,
-0.02095095068216324,
0.020809153094887733,
0.002303621731698513,
-0.0008912454359233379,
0.019368242472410202,
0.012945089489221573,
-0.05417734012007713,
-0.0007756455452181399,
0.008392943069338799,
0.007084579672664404,
-0.0838056206703186,
0.026613721624016762,
-0.015579302795231342,
-0.07476036995649338,
0.008114978671073914,
-0.006214499473571777,
-0.06385906785726547,
0.03166348114609718,
0.02886962704360485,
0.019351186230778694,
-0.027271438390016556,
-0.06661022454500198,
-0.000898363534361124,
-0.08794781565666199,
0.05077975243330002,
-0.0028475879225879908,
-0.06926445662975311,
-0.05427643284201622,
-0.010380435734987259,
-0.013004614971578121,
-0.015324623323976994,
0.06244341656565666,
-0.008225792087614536,
-0.009794970043003559,
0.028440425172448158,
0.03438952565193176,
-0.010492046363651752,
-0.028762150555849075,
-0.005021993070840836,
-0.006098642945289612,
0.003941307310014963,
-0.012007058598101139,
0.014450021088123322,
-0.0068386392667889595,
0.013576829805970192,
-0.0011114849476143718,
-0.001540973549708724,
0.04395958036184311,
-0.01926558092236519,
-0.01822916977107525,
0.026269813999533653,
0.043778494000434875,
-0.04837938770651817,
0.049908384680747986,
-0.0520964153110981,
0.00284232827834785,
0.0035103512927889824,
-0.015228421427309513,
-0.029111193493008614,
-0.002957375254482031,
-0.031216537579894066,
0.0013183719711378217,
-0.012010637670755386,
-0.018394090235233307,
0.048955414444208145,
-0.055712006986141205,
-0.0005722643691115081,
0.08058801293373108,
-0.05598393827676773,
0.001978849759325385,
0.039133958518505096,
0.005828761495649815,
0.04793320968747139,
-0.0008560701971873641,
-0.015877675265073776,
0.019505826756358147,
-0.008796177804470062,
-0.014505531638860703,
0.019636662676930428,
0.04219105467200279,
-0.028468361124396324,
-0.0008397300844080746,
0.050445307046175,
-0.026656022295355797,
-0.0009875380201265216,
0.006000353954732418,
0.012993982993066311,
-0.03403681144118309,
-0.029138639569282532,
-0.013206849806010723,
-0.03873777762055397,
-0.01239010039716959,
0.016223585233092308,
-0.012173324823379517,
0.08372818678617477,
-0.012861578725278378,
0.016498927026987076,
0.02122630551457405,
0.016193697229027748,
-0.02622186951339245,
-0.0076950606890022755,
0.02349241077899933,
0.04542545974254608,
-0.03253072500228882,
0.035438574850559235,
0.013978238217532635,
0.005943839438259602,
0.019934894517064095,
-0.01820354536175728,
0.03174886479973793,
0.017703860998153687,
-0.029901109635829926,
0.014523939229547977,
0.02889876440167427,
-0.041375692933797836,
-0.011137083172798157,
0.021810803562402725,
0.020279036834836006,
0.036100123077631,
0.029456352815032005,
0.010845629498362541,
-0.009714793413877487,
0.04747776687145233,
-0.06513849645853043,
-0.026920102536678314,
-0.022960161790251732,
0.005053061991930008,
-0.012398721650242805,
-0.010004648007452488
] |
<p>This is spawned from a comment at the answer to <a href="http://physics.stackexchange.com/questions/82487/confusion-about-a-lemma-on-the-time-constraint-of-an-adiabatic-evolution-arxiv">one of my previous questions</a>.</p>
<p>Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out whether it is true?</p>
<blockquote>
<p>If the eigenstate of the initial Hamiltonian are superposition of all
possible states we cannot perform the adiabatic evolution with a
diagonal Hamiltonian as the problem Hamiltonian.</p>
</blockquote>
<p>Thanks in advance!</p>
| 8,325 |
[
-0.03627117723226547,
-0.02871347963809967,
0.011654852889478207,
-0.03935500234365463,
0.04907538741827011,
-0.03349032253026962,
-0.03596643730998039,
-0.010783452540636063,
0.006115375552326441,
-0.03196663036942482,
0.028780316933989525,
0.021299442276358604,
0.01611865870654583,
0.03649451583623886,
0.018925266340374947,
0.009793524630367756,
0.000909132300876081,
0.0005300415796227753,
-0.004023356828838587,
0.014139254577457905,
0.041306838393211365,
0.015319526195526123,
0.01361637283116579,
-0.023560507223010063,
-0.0227203369140625,
-0.0007578631630167365,
0.017617417499423027,
0.023278437554836273,
-0.019165674224495888,
0.09691964089870453,
-0.02984636090695858,
-0.028219731524586678,
0.0670240968465805,
0.05381936579942703,
0.023713937029242516,
0.009489022195339203,
-0.01988440752029419,
-0.05243648216128349,
-0.020345423370599747,
-0.011870935559272766,
-0.01121112797409296,
-0.015119851566851139,
0.01656658761203289,
0.03479941189289093,
0.009507648646831512,
0.04651524871587753,
0.0150574566796422,
-0.019258707761764526,
0.028694184496998787,
-0.036354247480630875,
0.07715578377246857,
0.020677881315350533,
0.04285525530576706,
0.011624767445027828,
-0.012350345030426979,
-0.0053806002251803875,
0.054242610931396484,
0.08609770238399506,
-0.01689833775162697,
-0.005356620065867901,
-0.02187417447566986,
-0.03986790031194687,
0.03100956417620182,
-0.009282595477998257,
-0.09056445956230164,
0.014864359050989151,
0.03330709785223007,
-0.0071845268830657005,
0.009170514531433582,
0.014768734574317932,
-0.0019256517989560962,
-0.01299296598881483,
0.016601981595158577,
-0.0017573846271261573,
0.021898994222283363,
-0.007799254264682531,
-0.009667601436376572,
0.031830109655857086,
0.02902044542133808,
0.04094817489385605,
-0.001970993122085929,
0.020769989117980003,
-0.00405461760237813,
0.03288246691226959,
-0.031583696603775024,
0.009405172429978848,
0.07296732068061829,
-0.0071626207791268826,
0.001328995800577104,
0.02010565996170044,
-0.023685289546847343,
0.0040031238459050655,
0.024778103455901146,
-0.011840039864182472,
-0.0008200574666261673,
-0.0058746798895299435,
0.023509012535214424,
0.04642529413104057,
-0.046941399574279785,
-0.05943792313337326,
-0.004340190906077623,
-0.04462419077754021,
0.019592978060245514,
0.056280963122844696,
-0.0014239997835829854,
-0.0013838959857821465,
-0.05291770398616791,
0.042847536504268646,
-0.004622721578925848,
0.009060927666723728,
-0.034103404730558395,
0.012569724582135677,
-0.006854208651930094,
-0.011177008971571922,
-0.04524973779916763,
-0.013423977419734001,
-0.023582061752676964,
-0.008237305097281933,
0.029222000390291214,
0.08755767345428467,
-0.011093557812273502,
-0.024906933307647705,
0.027678724378347397,
-0.021349651739001274,
-0.06966663897037506,
-0.005325018893927336,
0.027293790131807327,
-0.003972569014877081,
-0.026651175692677498,
-0.01358342170715332,
0.01614595577120781,
0.004344169050455093,
-0.012418597005307674,
-0.014784334227442741,
0.022410975769162178,
-0.026113199070096016,
-0.12112044543027878,
-0.07207681983709335,
-0.0017283440101891756,
-0.007426003459841013,
-0.03020981140434742,
-0.06763004511594772,
0.005819861311465502,
0.051060277968645096,
0.06757166981697083,
-0.02062380313873291,
0.025636157020926476,
0.018137700855731964,
-0.005627488251775503,
0.014936057850718498,
-0.029608385637402534,
-0.031873732805252075,
-0.006462524179369211,
-0.037258319556713104,
0.011383967474102974,
-0.06684980541467667,
0.0056828344240784645,
0.019678842276334763,
0.02068612538278103,
-0.01630719006061554,
0.038506731390953064,
0.009692349471151829,
0.015276467427611351,
0.0029172683134675026,
0.03695571422576904,
-0.03213750198483467,
0.10408687591552734,
0.03476259857416153,
0.005127524491399527,
0.011088050901889801,
-0.013849670067429543,
0.03457550331950188,
-0.025347035378217697,
-0.0003113807179033756,
0.051476530730724335,
-0.05434208735823631,
-0.0480351448059082,
-0.01654268614947796,
0.00041715067345649004,
0.038378238677978516,
0.028284309431910515,
-0.02962556667625904,
0.005615946836769581,
-0.011999046429991722,
-0.0015405714511871338,
0.04014274477958679,
0.013066534884274006,
0.02158568799495697,
-0.002013884950429201,
-0.059408560395240784,
0.005736191291362047,
-0.037777721881866455,
0.028884677216410637,
0.02231243997812271,
-0.010088888928294182,
0.022265855222940445,
-0.010875867679715157,
0.013500514440238476,
0.01243392750620842,
-0.05328493192791939,
-0.016644813120365143,
0.0017991465283557773,
0.01091775856912136,
-0.04018377885222435,
0.040998443961143494,
0.0806003138422966,
0.026273157447576523,
-0.018724633380770683,
0.04154787212610245,
-0.005325541365891695,
-0.05901844799518585,
-0.009074211120605469,
0.008727185428142548,
0.04254908487200737,
0.003412418533116579,
0.01904679276049137,
0.007942502386868,
-0.014475508593022823,
-0.016318460926413536,
0.02819620445370674,
-0.033835407346487045,
0.06960342079401016,
0.0223727747797966,
0.001342373201623559,
-0.0005045902798883617,
0.04248164966702461,
0.045050203800201416,
0.0030520688742399216,
-0.008618608117103577,
-0.029768064618110657,
-0.04384855926036835,
0.012297635897994041,
0.016813457012176514,
0.025463365018367767,
-0.06383094936609268,
0.0197904035449028,
0.021109240129590034,
0.039850153028964996,
0.027621254324913025,
0.021168718114495277,
-0.018294241279363632,
0.0025231370236724615,
0.04253261908888817,
0.01333470456302166,
-0.0008857948123477399,
0.02230001986026764,
0.007044606376439333,
-0.009347249753773212,
-0.0017082052072510123,
-0.024704596027731895,
-0.044376492500305176,
0.06384121626615524,
-0.024923453107476234,
-0.01385369524359703,
0.013396023772656918,
-0.02181566134095192,
0.03876147046685219,
-0.0318034403026104,
0.04967307299375534,
0.022288894280791283,
0.03274808079004288,
-0.005577005911618471,
-0.029864661395549774,
-0.00910043716430664,
0.008483407087624073,
-0.01477830857038498,
-0.02968064323067665,
-0.018771355971693993,
0.0216283667832613,
-0.004636796656996012,
0.03232179954648018,
-0.008114639669656754,
-0.011644980870187283,
-0.005660027731209993,
0.021744845435023308,
0.03889000415802002,
-0.014666914008557796,
0.007403004448860884,
-0.03542091324925423,
-0.01006938423961401,
-0.027786176651716232,
-0.011838297359645367,
0.028259363025426865,
0.04965796694159508,
-0.06340552866458893,
0.01714647375047207,
-0.0388830341398716,
-0.04539702832698822,
0.06592405587434769,
-0.001866659615188837,
0.01476823166012764,
0.03462938219308853,
-0.011992325074970722,
-0.03559144213795662,
-0.00047386280493810773,
-0.041512273252010345,
-0.008270653896033764,
-0.08185230940580368,
0.004633354488760233,
0.0454748310148716,
0.019172271713614464,
-0.04059639945626259,
-0.004568171687424183,
0.003936539404094219,
-0.02136010304093361,
0.014182300306856632,
-0.014379728585481644,
0.04541711136698723,
-0.0038731759414076805,
0.035916510969400406,
0.04559514671564102,
-0.029822004958987236,
0.017018236219882965,
-0.0770319327712059,
-0.07785689830780029,
0.015909455716609955,
0.018683357164263725,
0.030685685575008392,
-0.0008707671076990664,
-0.02934730239212513,
0.0695381611585617,
0.041220396757125854,
-0.04247824847698212,
0.0026566521264612675,
-0.006858617067337036,
0.020413631573319435,
-0.036642856895923615,
0.008627653121948242,
0.018336400389671326,
-0.027695925906300545,
0.03415694832801819,
-0.020191669464111328,
0.027791205793619156,
0.02338794246315956,
-0.029139000922441483,
-0.023985709995031357,
0.024341361597180367,
0.041423261165618896,
0.057299211621284485,
0.007894747890532017,
-0.005619646981358528,
-0.014805332757532597,
0.03411928564310074,
-0.04742254316806793,
0.06332799047231674,
-0.003464740701019764,
-0.062444694340229034,
0.057704146951436996,
-0.04301651194691658,
0.01847126893699169,
-0.02452258951961994,
0.06743594259023666,
-0.026470504701137543,
0.010564281605184078,
0.016860758885741234,
0.035358164459466934,
0.03719889745116234,
-0.014488372020423412,
0.03148474916815758,
0.051906783133745193,
-0.01438082940876484,
-0.02734704501926899,
0.002686969703063369,
0.01965935342013836,
-0.041475288569927216,
-0.006463268306106329,
-0.03664331138134003,
-0.05402917042374611,
0.013612530194222927,
0.015372266061604023,
0.0299539715051651,
-0.001218594959937036,
-0.0035359519533813,
-0.008620481006801128,
-0.05309171974658966,
0.025883447378873825,
0.01751759462058544,
0.04538915306329727,
0.026314768940210342,
0.07447785139083862,
0.009512962773442268,
0.01636672206223011,
-0.0018833144567906857,
0.001704370486550033,
-0.07990052551031113,
-0.0020465366542339325,
-0.016907522454857826,
-0.0279491376131773,
0.02944575995206833,
-0.022189375013113022,
-0.0021257828921079636,
-0.021749842911958694,
-0.03197525814175606,
0.0025020157918334007,
0.028701841831207275,
-0.08022480458021164,
0.01283435057848692,
-0.0325639434158802,
0.003096427069976926,
-0.025777321308851242,
-0.008390289731323719,
0.05920629948377609,
-0.014558807015419006,
0.035388585180044174,
0.032913170754909515,
-0.05195826664566994,
-0.019641445949673653,
-0.0358721949160099,
0.06514579057693481,
0.0027618533931672573,
0.042603280395269394,
0.022056642919778824,
0.014418036676943302,
0.021217763423919678,
-0.005026808474212885,
0.005778269376605749,
0.03445543721318245,
0.008702720515429974,
-0.02737494744360447,
0.03106069006025791,
-0.051214396953582764,
0.010938258841633797,
0.02242845483124256,
0.05633114278316498,
0.006649651564657688,
0.02402954176068306,
-0.006569230929017067,
-0.003566635074093938,
-0.004704383201897144,
0.023994887247681618,
0.04896702617406845,
0.0028246587608009577,
-0.007550413720309734,
-0.04913923889398575,
-0.013210676610469818,
-0.012700872495770454,
0.003392408136278391,
-0.0008582218433730304,
-0.00946835707873106,
-0.0075239441357553005,
0.011980411596596241,
-0.007913900539278984,
0.004171139560639858,
0.006460272707045078,
-0.0013945874525234103,
-0.014745711348950863,
0.017699802294373512,
-0.012294839136302471,
0.015540119260549545,
0.032435912638902664,
0.013630402274429798,
0.01675267331302166,
0.001059555565007031,
0.004430780187249184,
-0.04706348478794098,
-0.013868317008018494,
0.0077765523456037045,
0.05153200775384903,
-0.0006670097936876118,
0.019468193873763084,
-0.061479125171899796,
-0.008431436493992805,
0.04317765310406685,
-0.027978096157312393,
0.04403693601489067,
-0.007437414489686489,
-0.022378411144018173,
0.009163430891931057,
-0.07133012264966965,
0.015447931364178658,
0.010301224887371063,
0.017061280086636543,
0.02935611829161644,
0.02177935279905796,
-0.041919708251953125,
-0.017522228881716728,
-0.030346155166625977,
0.05997571349143982,
0.07450801879167557,
-0.01291881687939167,
-0.02385474182665348,
0.010229140520095825,
0.0271901935338974,
-0.051357705146074295,
-0.07862061262130737,
0.0004833861021324992,
-0.0022405069321393967,
-0.023330966010689735,
0.02380254864692688,
-0.08953088521957397,
-0.06727103888988495,
0.05362384021282196,
-0.004082293249666691,
-0.029310675337910652,
-0.00038817187305539846,
-0.029187457635998726,
0.07739334553480148,
0.06897712498903275,
-0.008339389227330685,
0.036901332437992096,
0.045632459223270416,
-0.025356315076351166,
0.005226834677159786,
-0.0162951797246933,
-0.004290821962058544,
-0.0338621623814106,
0.02927619405090809,
-0.05187366157770157,
0.03384528309106827,
-0.004239152185618877,
0.023745549842715263,
-0.014710577204823494,
-0.01633676141500473,
0.01466369442641735,
-0.02833959273993969,
-0.015234122984111309,
0.02648802660405636,
-0.015356682240962982,
-0.024744359776377678,
-0.04586710035800934,
0.035009194165468216,
0.015472065657377243,
-0.009385290555655956,
-0.004553359933197498,
-0.046840328723192215,
0.0025139187928289175,
0.049157775938510895,
-0.01127805095165968,
0.0523991696536541,
-0.02858375944197178,
-0.023724600672721863,
-0.020969083532691002,
-0.07042638957500458,
0.02010277658700943,
-0.022266505286097527,
-0.0026680089067667723,
0.03178846836090088,
-0.049110084772109985,
-0.02491723746061325,
0.02722017653286457,
-0.014332367107272148,
-0.02708241529762745,
-0.01987142488360405,
0.01944780722260475,
0.014295276254415512,
-0.011090096086263657,
-0.06492584943771362,
-0.03578232601284981,
0.009954647161066532,
0.02414274588227272,
-0.026772288605570793,
-0.0392366461455822,
0.022451741620898247,
-0.03728471323847771,
-0.009350345470011234,
-0.0044137537479400635,
0.0292561873793602,
-0.007121686358004808,
0.01237410493195057,
0.040936440229415894,
0.03807215020060539,
0.040791042149066925,
-0.00026015896582975984,
0.01031680591404438,
-0.009802772663533688,
-0.03451243415474892,
0.008067796006798744,
-0.014463601633906364,
0.02936755120754242,
-0.021495472639799118,
0.005458659026771784,
-0.03585882484912872,
-0.006916246842592955,
0.05142773315310478,
0.005794869270175695,
-0.0022429130040109158,
0.024984629824757576,
-0.018138661980628967,
-0.009611357003450394,
-0.007838897407054901,
-0.015866931527853012,
0.0029575235676020384,
-0.000219352325075306,
0.033476173877716064,
0.003220054553821683,
0.027105649933218956,
-0.04083656147122383,
-0.004493620712310076,
-0.019064297899603844,
0.002146882237866521,
0.01426291186362505,
0.10295798629522324,
0.0032625580206513405,
0.00019141419033985585,
0.02130412496626377,
-0.030031034722924232,
0.0011984416050836444,
0.009668359532952309,
0.003426122246310115,
-0.0030210225377231836,
-0.02874087356030941,
-0.04899470880627632,
-0.03631049767136574,
-0.05536862090229988,
0.043686144053936005,
0.043020542711019516,
-0.001423817127943039,
0.02971147559583187,
0.020095232874155045,
0.028578495606780052,
-0.028563518077135086,
-0.026517760008573532,
0.01256043091416359,
0.016464104875922203,
-0.0005752230063080788,
0.043826792389154434,
0.019699618220329285,
-0.004101612139493227,
0.04808051139116287,
0.019207267090678215,
-0.008764844387769699,
0.010843963362276554,
0.04321352764964104,
-0.00017447350546717644,
0.012635346502065659,
0.00823916494846344,
-0.053200166672468185,
-0.0018382011912763119,
-0.020782899111509323,
0.044296830892562866,
-0.0074461717158555984,
-0.029097089543938637,
0.017551880329847336,
0.01596810482442379,
0.016405856236815453,
-0.018417296931147575,
-0.025352928787469864,
-0.005925391800701618,
0.050473228096961975,
-0.029352771118283272,
0.032180897891521454,
0.03607083857059479,
0.020080480724573135,
0.019426055252552032,
0.03289487957954407,
0.036806631833314896,
0.0022354295942932367,
-0.036974914371967316,
-0.0362076610326767,
-0.019082529470324516,
-0.02866312488913536,
0.025954315438866615,
0.014325488358736038,
-0.006230042316019535,
0.010557970032095909,
0.002166976220905781,
-0.016543781384825706,
-0.0027697377372533083,
0.04715656489133835,
-0.021239839494228363,
0.06619453430175781,
0.025771738961338997,
0.029610801488161087,
-0.014356404542922974,
0.0334305614233017,
0.11352008581161499,
0.08741015940904617,
0.05485943332314491,
-0.04561591520905495,
0.032195549458265305,
0.0055684554390609264,
-0.05465276539325714,
-0.006479847244918346,
0.009182021953165531,
-0.007431409787386656,
-0.03071736916899681,
-0.03014855645596981,
0.02931467816233635,
0.01357746496796608,
-0.0036184946075081825,
0.01054403092712164,
-0.0734252780675888,
-0.03230305388569832,
0.023970406502485275,
0.008903907611966133,
-0.02053089067339897,
-0.02483508177101612,
-0.013309195637702942,
-0.01634248159825802,
-0.025934837758541107,
-0.016559341922402382,
-0.0026255568955093622,
-0.023002857342362404,
0.03699289634823799,
0.00024239935737568885,
-0.009002887643873692,
0.011321515776216984,
0.03634312003850937,
-0.026689795777201653,
-0.03687208890914917,
0.002919659949839115,
-0.0008496469235979021,
-0.002344261622056365,
0.0158797986805439,
0.03221524506807327,
0.05655347928404808,
-0.00034353346563875675,
0.007998425513505936,
-0.001155457110144198,
-0.032149430364370346,
-0.0023823126684874296,
-0.026328641921281815,
0.03954571858048439,
-0.034060727804899216,
0.005294411443173885,
0.0029695462435483932,
-0.019046513363718987,
-0.014881594106554985,
-0.07490936666727066,
0.03422127291560173,
-0.011731909587979317,
0.021984975785017014,
0.007185202091932297,
-0.030435265973210335,
-0.04283243417739868,
-0.02271740697324276,
0.00860870536416769,
0.0015739479567855597,
0.008230301551520824,
0.017500819638371468,
-0.0020375398453325033,
-0.01822756975889206,
0.012169050984084606,
0.007522957399487495,
-0.0032851817086338997,
-0.046262480318546295,
-0.02670089341700077,
-0.0444711372256279,
-0.03278198093175888,
0.038007717579603195,
-0.019762583076953888,
0.0468904972076416,
0.013385722413659096,
0.004424722865223885,
-0.03666526451706886,
-0.09172838181257248,
0.005334667395800352,
0.007865005172789097,
-0.0472455658018589,
-0.00235661375336349,
0.008528259582817554,
0.03751731291413307,
0.030503829941153526,
-0.032586462795734406,
0.06477289646863937,
-0.0017884200206026435,
0.02772972732782364,
-0.002934536896646023,
-0.0022883997298777103,
0.0021539689041674137,
-0.02803833782672882,
-0.06292015314102173,
0.02078576758503914,
-0.009935913607478142,
0.0074249994941055775,
0.01798655465245247,
0.008113915100693703,
0.001972013618797064,
0.04313557595014572,
-0.017734764143824577,
0.0020756125450134277,
0.014067022129893303,
-0.007177972700446844,
-0.000940247904509306,
-0.004453038796782494,
0.047854579985141754,
-0.05541319027543068,
-0.021191444247961044,
-0.0400674007833004,
0.0031838719733059406,
0.013639726676046848,
-0.017696289345622063,
-0.03788153454661369,
-0.0013166452990844846,
-0.018665263429284096,
0.003393288003280759,
-0.03631459176540375,
0.011026372201740742,
-0.029254892840981483,
0.04006730392575264,
-0.010054661892354488,
0.01372090820223093,
-0.01053276751190424,
0.032990287989377975,
0.0130862295627594,
-0.01944316364824772,
0.025120865553617477,
0.06180933862924576,
-0.020625367760658264,
-0.002608401468023658,
0.04068659245967865,
0.021328087896108627,
0.0553160086274147,
-0.02779075689613819,
-0.007612618152052164,
-0.0007016886956989765,
-0.058035872876644135,
-0.038104087114334106,
0.020957425236701965,
-0.05648244917392731,
0.015919294208288193,
0.03998291492462158,
-0.015979958698153496,
0.012066184543073177,
0.02479405514895916,
-0.023050252348184586,
-0.0012817287351936102,
0.03124307096004486,
0.005475570913404226,
-0.07217356562614441,
-0.011854711920022964,
-0.025279277935624123,
-0.005079252645373344,
0.01937721110880375,
-0.012499719858169556,
0.010751450434327126,
0.0016589104197919369,
0.005496883299201727,
-0.016483206301927567,
-0.0017131722997874022,
0.014283535070717335,
0.015689924359321594,
-0.03361159563064575,
0.018804337829351425,
0.05362888053059578,
-0.031171167269349098,
0.030302291736006737,
0.010054812766611576,
0.01120229996740818,
-0.09423009306192398,
-0.004690078552812338,
-0.013880232349038124,
-0.015543309971690178,
0.04902445152401924,
-0.06891190260648727,
0.0508333258330822,
0.039639417082071304,
-0.07018288969993591,
0.0339541994035244,
-0.012061045505106449,
0.02973238006234169,
0.005428697913885117,
0.047699376940727234,
-0.04866508021950722,
0.04137078672647476,
0.044028230011463165,
0.03732149302959442,
0.016812341287732124,
0.02433967776596546,
-0.0017461200477555394,
-0.009872674942016602,
-0.01152100320905447,
0.01590151898562908,
-0.019818607717752457,
-0.025153446942567825,
0.04515499994158745,
-0.018101265653967857,
-0.025338586419820786,
-0.004818350542336702,
-0.023364586755633354,
-0.010980580933392048,
-0.0017885718261823058,
0.03292010352015495,
0.02140689454972744,
-0.009335305541753769,
0.0487794354557991,
-0.0015690928557887673,
0.010889253579080105,
0.005391319282352924,
-0.018044939264655113,
0.017481083050370216,
0.00236852397210896,
0.014506714418530464,
0.017689283937215805,
-0.02703375183045864,
-0.06820127367973328,
0.03195829316973686,
-0.004754385445266962,
0.0120196882635355,
0.0035727948416024446,
-0.03334139287471771,
-0.02035599946975708,
-0.017796920612454414,
-0.013516303151845932,
0.002719311974942684,
-0.0032053617760539055,
0.027651580050587654,
0.01277633011341095,
-0.00885692983865738,
-0.0035518757067620754,
-0.03269779309630394,
-0.07138299942016602,
0.03438028693199158,
-0.005405191797763109,
-0.023625891655683517,
-0.07161300629377365,
0.01751958392560482,
-0.011956815607845783,
-0.015138876624405384,
-0.026559287682175636,
-0.057710301131010056,
-0.03220308944582939,
0.01161471102386713,
0.016157420352101326,
0.006504948250949383,
-0.015700316056609154,
-0.02295864373445511,
-0.007536503951996565,
-0.05996963381767273,
0.03514551371335983,
-0.012008436024188995,
0.03037223406136036,
-0.002425082493573427,
-0.010673143900930882,
0.02680346369743347,
-0.0014934549108147621,
0.024775441735982895,
-0.027540314942598343,
-0.00037797068944200873,
0.031130732968449593,
-0.01834956742823124,
0.04332225024700165,
-0.006334082223474979,
0.015171470120549202,
-0.01808023266494274,
-0.018293598666787148,
0.004166007041931152,
-0.008027949370443821,
0.006565672345459461,
-0.001957886852324009,
0.01659461297094822,
0.0019166854908689857,
-0.0015899750869721174,
0.006620246451348066,
-0.00951817724853754,
0.04160868376493454,
-0.009940975345671177,
0.01632927730679512,
0.054857037961483,
-0.003905749646946788,
0.028569038957357407,
0.013644433580338955,
-0.026645595207810402,
-0.03881867602467537,
0.021350178867578506,
-0.05367801710963249,
-0.012517559342086315,
-0.0014968256000429392,
-0.01820513606071472,
-0.004812059458345175,
-0.046499818563461304,
-0.027980182319879532,
0.006321057677268982,
-0.027405133470892906,
-0.024131741374731064,
0.021930240094661713,
-0.013789479620754719,
0.050521135330200195,
-0.005540431011468172,
0.010773319751024246,
0.0015100426971912384,
0.03124021738767624,
-0.0008482200792059302,
0.030321720987558365,
0.014282571151852608,
-0.014425761066377163,
0.05211814120411873,
0.007493571378290653,
-0.021169079467654228,
0.05160125717520714,
0.01082950085401535,
0.03365075960755348,
0.0053745596669614315,
-0.009644139558076859,
0.040271271020174026,
0.016167430207133293,
-0.013797953724861145,
0.014835945330560207,
-0.01774521917104721,
0.06206045672297478,
-0.006923513952642679,
0.04773297905921936,
-0.009772995486855507,
-0.00966890063136816,
-0.047931913286447525,
-0.0073943231254816055,
-0.011486205272376537,
0.05100250616669655,
-0.040405359119176865,
0.012123273685574532,
-0.01835881546139717,
0.02760224975645542,
0.0001546973071526736,
-0.06809678673744202,
-0.006151604000478983,
0.005325539503246546,
-0.006169217173010111,
-0.041439738124608994,
-0.011427375487983227,
-0.019596483558416367,
0.002674602437764406,
0.006788688246160746,
0.03140917420387268,
-0.02542087435722351,
-0.05238685384392738,
0.021125027909874916,
-0.0035532135516405106,
0.06456045806407928,
-0.028924610465765,
-0.03552965819835663,
-0.02224895916879177,
0.017393341287970543,
-0.0341419018805027,
0.019572870805859566
] |
<p>Does Gravity / curved space cause rotation?</p>
<p>Meaning, if a spaceship is heading not directly toward Earth, but slightly off to one side, and when finally being close to the Earth it falls into earth orbit, does the spaceship continue to point in the same directions as it was when approaching the earth, or does it now rotate at a frequency that is equal to its orbital frequency?</p>
<p>I would expect the spaceship to be pointing in the opposite direction after completing one half of an earth orbit.</p>
| 8,326 |
[
-0.03950916603207588,
-0.017446018755435944,
-0.028627024963498116,
-0.005187162198126316,
0.041301436722278595,
0.020796742290258408,
-0.031927961856126785,
0.006015137769281864,
0.0325230211019516,
-0.06897173076868057,
-0.02531159296631813,
0.06934347748756409,
0.015844084322452545,
0.019138868898153305,
0.02135378308594227,
0.0091089503839612,
-0.019694864749908447,
0.026845036074519157,
-0.006370566785335541,
-0.03133419528603554,
0.01642385870218277,
-0.017053185030817986,
-0.00535842077806592,
-0.014755397103726864,
-0.027191301807761192,
0.007605145685374737,
0.06027083843946457,
-0.020400630310177803,
0.04379837214946747,
0.03287658467888832,
0.0018969039665535092,
0.021612495183944702,
0.0020127359312027693,
0.051242128014564514,
0.027841953560709953,
0.021778110414743423,
-0.03473377227783203,
0.004033924546092749,
-0.0055473484098911285,
0.0060770283453166485,
-0.049464914947748184,
-0.013098425231873989,
-0.046869177371263504,
0.09042197465896606,
0.0042005255818367004,
0.01069800928235054,
-0.005365301854908466,
0.007667323108762503,
0.06242934986948967,
-0.0728996992111206,
0.07960092276334763,
-0.03361641988158226,
0.01098568644374609,
-0.003613564418628812,
0.026297390460968018,
0.012644071131944656,
0.07061287760734558,
0.04463668540120125,
-0.026965012773871422,
-0.0312001034617424,
-0.010660471394658089,
-0.029757587239146233,
-0.013007508590817451,
-0.02283315174281597,
-0.023177698254585266,
0.0303197018802166,
-0.013983998447656631,
-0.030569929629564285,
0.03276319429278374,
0.018687473610043526,
0.017341414466500282,
-0.0000712810069671832,
0.002974884118884802,
-0.02555510215461254,
-0.005764591507613659,
-0.05621371790766716,
0.03483983874320984,
0.006931152660399675,
0.0453449971973896,
0.018610334023833275,
-0.011192061938345432,
-0.021246228367090225,
0.021571706980466843,
0.007923702709376812,
0.03125099465250969,
0.028767770156264305,
0.07381680607795715,
-0.0021446687169373035,
0.028253324329853058,
0.0668710470199585,
0.035510774701833725,
0.014927523210644722,
-0.00885722041130066,
-0.031857434660196304,
-0.03073103353381157,
0.051719073206186295,
0.00034599247737787664,
0.05331667885184288,
0.013931060209870338,
-0.02801993489265442,
-0.01021464355289936,
-0.017012452706694603,
0.005295678041875362,
0.04705476760864258,
0.00514324801042676,
-0.012473599053919315,
-0.035913024097681046,
0.02975887805223465,
-0.047062598168849945,
-0.028477918356657028,
-0.013680405914783478,
0.003217738587409258,
-0.01567716710269451,
-0.030269522219896317,
0.032377421855926514,
0.011764493770897388,
-0.0007560730446130037,
-0.02277463860809803,
0.03142073005437851,
0.06073038652539253,
0.05894588679075241,
-0.015771538019180298,
0.02393568865954876,
-0.009755806066095829,
-0.0351603664457798,
-0.017040783539414406,
0.04826607182621956,
-0.009762718342244625,
-0.04082093387842178,
0.01021598931401968,
-0.005792653653770685,
-0.03219439089298248,
-0.0063241315074265,
-0.006135280709713697,
0.028951475396752357,
0.01536156889051199,
-0.10213761031627655,
-0.03817246854305267,
0.034731846302747726,
0.014057960361242294,
0.01750163361430168,
-0.07257361710071564,
0.037927065044641495,
0.012991610914468765,
0.07568518817424774,
0.0024427275639027357,
-0.024005668237805367,
-0.006723172031342983,
0.02955896407365799,
0.018873700872063637,
-0.02383367344737053,
0.018213586881756783,
-0.019052833318710327,
-0.08706694096326828,
-0.027418872341513634,
-0.054065778851509094,
0.0053901514038443565,
0.03386027365922928,
0.02809438295662403,
-0.06576003134250641,
0.0396324023604393,
-0.02321610599756241,
0.004600084852427244,
0.010834169574081898,
0.0015200269408524036,
-0.01750173233449459,
0.08389218896627426,
0.03765096515417099,
-0.041567619889974594,
0.030997218564152718,
0.02720203809440136,
0.023233680054545403,
0.014595841988921165,
0.003063770243898034,
0.05063113197684288,
-0.04748905822634697,
-0.02131798304617405,
-0.01345572154968977,
0.025193732231855392,
-0.0419633649289608,
-0.016536081209778786,
-0.023173203691840172,
-0.004225160460919142,
-0.0013180217938497663,
-0.013534571044147015,
0.049329791218042374,
0.0017244576010853052,
0.013555498793721199,
-0.018624799326062202,
-0.026641597971320152,
0.022794026881456375,
-0.054307177662849426,
0.021918298676609993,
-0.0421781912446022,
-0.023462846875190735,
-0.005009594839066267,
0.03939454257488251,
0.039786048233509064,
-0.054774846881628036,
-0.04163123294711113,
0.008119418285787106,
0.04759008064866066,
-0.020964480936527252,
-0.02946782298386097,
-0.01964639499783516,
0.05818653851747513,
0.0034463347401469946,
-0.00558612123131752,
-0.0008692604606039822,
0.004992758855223656,
-0.04123445972800255,
-0.028387945145368576,
0.010420271195471287,
0.001040323288179934,
-0.028559748083353043,
0.04606606811285019,
0.011053196154534817,
0.022001203149557114,
-0.002647710731253028,
0.029070992022752762,
-0.033993422985076904,
0.08269970118999481,
0.06691271811723709,
-0.013331959024071693,
0.06268331408500671,
0.05670512840151787,
0.02977563627064228,
-0.02189633436501026,
0.0238371342420578,
-0.03044235147535801,
-0.053298719227313995,
0.003786510555073619,
0.016802959144115448,
-0.0041607581079006195,
-0.0011184947798028588,
0.043242305517196655,
0.044267427176237106,
0.04063853248953819,
0.004420521669089794,
0.05107037350535393,
-0.010954966768622398,
-0.022642701864242554,
0.009372211061418056,
-0.003954366315156221,
0.0209217369556427,
-0.02239849977195263,
0.03226238489151001,
0.04110534489154816,
-0.015580529347062111,
0.027567867189645767,
-0.05336602032184601,
0.035923317074775696,
0.024413669481873512,
0.025714734569191933,
0.0012599837500602007,
-0.026504870504140854,
0.03963320329785347,
-0.016459017992019653,
-0.007174485828727484,
0.025133945047855377,
-0.011198008432984352,
-0.012212554924190044,
-0.03859120234847069,
0.003587462240830064,
-0.04061180353164673,
0.01364399679005146,
-0.020471038296818733,
-0.014212749898433685,
0.03544913977384567,
-0.03998831287026405,
0.01437458861619234,
-0.0265757255256176,
0.020759636536240578,
0.0235039833933115,
0.004733563866466284,
-0.00297467946074903,
0.023892544209957123,
0.03885636106133461,
0.007348860614001751,
-0.02385038137435913,
-0.015427876263856888,
-0.04882602021098137,
-0.03943129628896713,
0.023583510890603065,
-0.05476246029138565,
0.06855708360671997,
-0.012632735073566437,
-0.0120221097022295,
0.031059037894010544,
-0.001596993301063776,
0.010213123634457588,
0.04281032830476761,
0.00232815183699131,
-0.06281256675720215,
-0.01299269963055849,
-0.06844694167375565,
0.002294836100190878,
-0.03170067444443703,
0.015456413850188255,
0.03931904584169388,
0.017225690186023712,
-0.014836271293461323,
0.03795123100280762,
-0.06208377331495285,
-0.03269217908382416,
-0.004081507679075003,
0.011121116578578949,
0.02129729650914669,
-0.022994693368673325,
0.010846748948097229,
-0.013112669810652733,
-0.037771787494421005,
-0.010877645574510098,
-0.0323723703622818,
-0.04666253551840782,
0.025154337286949158,
-0.009906780906021595,
0.032626163214445114,
-0.00861409306526184,
-0.008478077128529549,
0.07653862982988358,
0.016387924551963806,
-0.019643880426883698,
-0.05477214604616165,
-0.0031990741845220327,
0.00910400040447712,
-0.013334482908248901,
0.006165431346744299,
0.00655859662219882,
0.002001925138756633,
0.004894275683909655,
0.04564251750707626,
-0.0036195770371705294,
0.011329865083098412,
0.015843501314520836,
0.005737231113016605,
0.025553008541464806,
0.010840896517038345,
0.0051954565569758415,
0.03188255801796913,
0.032447606325149536,
-0.0065435804426670074,
0.010500694625079632,
0.01240209024399519,
0.02829001098871231,
-0.002865774091333151,
-0.046648863703012466,
0.04436829686164856,
-0.017460785806179047,
-0.00846265722066164,
0.016488492488861084,
0.019492849707603455,
-0.017146797850728035,
0.01645786501467228,
0.0037118899635970592,
0.03090512380003929,
0.05919893458485603,
0.01859363727271557,
-0.03003758005797863,
0.027115067467093468,
0.04306116700172424,
-0.013836551457643509,
-0.020677288994193077,
0.010226568207144737,
-0.01802145317196846,
0.05012179911136627,
-0.045420680195093155,
-0.037402696907520294,
0.017871517688035965,
0.04528288543224335,
0.04569365084171295,
0.008659356273710728,
-0.05589291453361511,
0.02456827275454998,
-0.04763810709118843,
-0.007008847780525684,
-0.02975280210375786,
0.042071253061294556,
-0.002922285348176956,
0.03891356289386749,
-0.0014549678890034556,
0.0005857233190909028,
0.005333577748388052,
-0.005707117263227701,
-0.08700402826070786,
0.03883484750986099,
-0.04487227648496628,
-0.021839667111635208,
0.02983674593269825,
0.005569108761847019,
-0.022442959249019623,
-0.05171774700284004,
-0.0049850656650960445,
-0.019798211753368378,
-0.034763384610414505,
-0.03782457858324051,
0.00696940440684557,
-0.015988437458872795,
-0.037894438952207565,
-0.0030220961198210716,
0.03032144531607628,
0.008603394031524658,
-0.03584497794508934,
0.0544004887342453,
0.064181849360466,
-0.031491655856370926,
0.002166392281651497,
0.010171144269406796,
-0.0006623468361794949,
-0.0149655407294631,
0.014716332778334618,
0.01419891882687807,
-0.00948308315128088,
-0.006467739120125771,
-0.009733005426824093,
0.0040450748056173325,
0.029448915272951126,
-0.024150298908352852,
-0.012487825006246567,
-0.02604004740715027,
-0.025881115347146988,
-0.03110031597316265,
-0.008203217759728432,
0.04258883744478226,
-0.0007944412063807249,
0.0023454371839761734,
0.04456552863121033,
0.008670689538121223,
-0.0017015389166772366,
0.051855579018592834,
0.05334681272506714,
0.028199711814522743,
0.0052728233858942986,
-0.006233781110495329,
0.0016505845123901963,
-0.012773276306688786,
-0.01675405353307724,
0.03048500046133995,
-0.029924830421805382,
-0.0445798896253109,
0.0032821553759276867,
-0.015057075768709183,
0.005647057201713324,
-0.002197562251240015,
0.035207368433475494,
-0.017482193186879158,
0.034199271351099014,
-0.006840409245342016,
0.019182298332452774,
-0.0018622854258865118,
0.04384487867355347,
0.07974869012832642,
0.00007068543345667422,
-0.020885957404971123,
-0.08847229927778244,
-0.007469792850315571,
0.04661591723561287,
0.01861293613910675,
0.0030917907133698463,
-0.010906628333032131,
-0.05195639282464981,
-0.03976250812411308,
0.011493422091007233,
-0.004641123116016388,
0.01816856861114502,
-0.03238369897007942,
0.0059687290340662,
-0.0018361437832936645,
-0.03373941406607628,
-0.037255965173244476,
0.005330825690180063,
-0.021020326763391495,
0.009874776005744934,
-0.03228004276752472,
0.007356061600148678,
-0.021333202719688416,
0.023694690316915512,
0.04771144315600395,
0.001951748039573431,
0.005926408339291811,
0.0016897195018827915,
-0.034722719341516495,
0.01958511956036091,
-0.026704439893364906,
-0.06864356994628906,
0.002928865374997258,
0.018033349886536598,
-0.02556653879582882,
0.03150463104248047,
-0.016545264050364494,
-0.046515028923749924,
0.021858707070350647,
-0.007865752093493938,
0.01775306463241577,
-0.015035745687782764,
-0.007726332172751427,
0.017685435712337494,
0.009395577013492584,
0.02047744207084179,
0.017543870955705643,
0.009786599315702915,
-0.005663832649588585,
-0.010711243376135826,
0.0019128728890791535,
0.03277701139450073,
-0.045094236731529236,
-0.03145591542124748,
-0.008812802843749523,
-0.025808995589613914,
-0.0489468015730381,
0.022054994478821754,
0.0193730928003788,
-0.017185812816023827,
0.00436918530613184,
-0.020824454724788666,
-0.03165894374251366,
0.034897275269031525,
0.031163930892944336,
-0.004439865704625845,
0.0015872917138040066,
0.015438973903656006,
-0.012473986484110355,
-0.018012437969446182,
-0.002481222152709961,
0.0017357630422338843,
0.00457353238016367,
0.04383446276187897,
-0.024250438436865807,
-0.0035877011250704527,
-0.014940840192139149,
-0.0029980044346302748,
0.005184944719076157,
-0.05319586023688316,
0.052662428468465805,
-0.023258423432707787,
-0.01492355577647686,
0.05721729248762131,
-0.03880054131150246,
-0.00512592401355505,
0.013313601724803448,
0.003927234560251236,
-0.009332711808383465,
-0.027553200721740723,
0.024621525779366493,
0.026991792023181915,
0.03814782574772835,
-0.07862431555986404,
-0.05190345272421837,
0.02714822255074978,
0.022863321006298065,
-0.027923474088311195,
-0.026287885382771492,
0.0006893750978633761,
-0.052445605397224426,
-0.04587699472904205,
-0.008047940209507942,
0.023747937753796577,
-0.03820525109767914,
0.0028121951036155224,
0.03802219033241272,
-0.002643881132826209,
0.07554943859577179,
-0.009822923690080643,
-0.04210099205374718,
0.019243795424699783,
-0.008277482353150845,
0.003144981572404504,
-0.02536834590137005,
0.0915842279791832,
-0.015633799135684967,
-0.04229104518890381,
-0.03190978616476059,
0.005512061528861523,
0.012431127019226551,
-0.022791922092437744,
-0.0046150172129273415,
0.05342061072587967,
-0.021112818270921707,
0.004636417608708143,
-0.004911432974040508,
0.022849589586257935,
-0.02131113037467003,
0.027385147288441658,
0.008367777802050114,
-0.002003417583182454,
0.002235783264040947,
-0.041098255664110184,
0.015031007118523121,
-0.007739492226392031,
0.0172046460211277,
0.014166985638439655,
0.0609196200966835,
0.00888056680560112,
-0.0224542748183012,
0.0006857970729470253,
0.0015585041837766767,
0.030251746997237206,
-0.022375423461198807,
-0.006176667753607035,
0.008973142132163048,
0.010428173467516899,
-0.03512590751051903,
-0.03484943136572838,
-0.0036821188405156136,
-0.009795567952096462,
0.09377024322748184,
-0.013343999162316322,
0.07534720748662949,
0.01842188462615013,
0.034896139055490494,
-0.02727469988167286,
-0.006076388992369175,
0.009856306947767735,
-0.007962401024997234,
0.0033964726608246565,
0.011513853445649147,
-0.025614729151129723,
0.004933379590511322,
-0.0025982253719121218,
0.05349518731236458,
-0.02738286927342415,
-0.0037720343098044395,
0.05653338506817818,
0.020595688372850418,
0.054236870259046555,
0.017771562561392784,
-0.051512494683265686,
0.020250745117664337,
-0.01904771849513054,
0.10183746367692947,
0.007215528283268213,
-0.018407877534627914,
0.03629859909415245,
0.0421944260597229,
0.022843196988105774,
-0.02565773017704487,
-0.015123185701668262,
-0.04575195536017418,
0.013901003636419773,
0.02581203170120716,
-0.0010125408880412579,
-0.006075228098779917,
0.012714160606265068,
0.02008712664246559,
-0.003783911932259798,
-0.010577901266515255,
0.011420915834605694,
-0.05958978831768036,
-0.022138552740216255,
-0.03043142519891262,
-0.03851846233010292,
0.03243940323591232,
0.04192478954792023,
-0.03309289738535881,
0.023870740085840225,
0.006594786886125803,
0.01244664192199707,
0.033860817551612854,
0.048053938895463943,
-0.04093674197793007,
0.08346282690763474,
-0.028804700821638107,
-0.014603610150516033,
-0.05196738615632057,
0.011359285563230515,
0.11515776813030243,
0.013683527708053589,
-0.023781225085258484,
-0.03407526761293411,
0.006474238820374012,
-0.020639633759856224,
0.01710873655974865,
-0.018802950158715248,
-0.0019391655223444104,
-0.017121572047472,
0.036525797098875046,
0.004904178436845541,
0.05619153752923012,
0.011335344053804874,
-0.03899449110031128,
0.03376265615224838,
-0.03366244211792946,
-0.03306979686021805,
-0.019364366307854652,
0.00018439414270687848,
-0.01009018998593092,
0.034117307513952255,
-0.011932630091905594,
0.02677309885621071,
-0.05163818970322609,
0.0022968321572989225,
-0.043364789336919785,
-0.03142441064119339,
0.0036263195797801018,
0.014696500264108181,
-0.04873387888073921,
0.0259232260286808,
0.01413097232580185,
-0.032487768679857254,
-0.054037466645240784,
0.028453173115849495,
0.007278301753103733,
-0.02238163724541664,
-0.019424788653850555,
0.02699485793709755,
-0.0016736778197810054,
0.014791887253522873,
0.010379879735410213,
0.016199778765439987,
-0.04368757829070091,
0.030109122395515442,
-0.02572697587311268,
0.04973437637090683,
0.0005322574288584292,
0.012074782513082027,
-0.014341696165502071,
0.03080008365213871,
0.013330936431884766,
-0.06771499663591385,
0.0009282442624680698,
-0.014144115149974823,
0.004967737942934036,
-0.0034950808621942997,
-0.04156525433063507,
-0.005418944172561169,
0.030614597722887993,
-0.005347247235476971,
0.01282816007733345,
-0.0029461560770869255,
0.009660103358328342,
0.02188774198293686,
-0.0133026959374547,
0.0691629946231842,
-0.042238250374794006,
-0.025683263316750526,
-0.04211469739675522,
-0.019134964793920517,
-0.052015520632267,
0.020114419981837273,
0.04062431678175926,
0.0227010790258646,
0.02774694375693798,
-0.0040194387547671795,
-0.02865050546824932,
-0.00903021264821291,
-0.05445577949285507,
0.03805607184767723,
-0.01749766804277897,
-0.023103317245841026,
-0.04227614030241966,
0.011248191818594933,
0.06297639012336731,
0.017443759366869926,
-0.013170791789889336,
-0.0015362389385700226,
-0.023917967453598976,
0.009458893910050392,
0.022842030972242355,
0.0113053098320961,
0.0060988785699009895,
0.025610918179154396,
0.0050984458066523075,
0.017017660662531853,
-0.03948958218097687,
0.04454853758215904,
0.04742453247308731,
0.01578114926815033,
-0.004470013082027435,
0.00952980574220419,
-0.019329853355884552,
0.016214927658438683,
0.02811323292553425,
-0.014105281792581081,
-0.021846221759915352,
0.006819140166044235,
0.013216591440141201,
-0.04098256677389145,
-0.019853929057717323,
-0.006643801461905241,
0.007575584575533867,
-0.0198128130286932,
0.03878558799624443,
-0.012777240015566349,
0.07484644651412964,
-0.015325380489230156,
0.03706163540482521,
-0.07162449508905411,
-0.0030827464070171118,
-0.07616113126277924,
0.001074338098987937,
0.02619551308453083,
-0.024357523769140244,
-0.0004967399290762842,
0.035219334065914154,
-0.011984535492956638,
-0.012594204396009445,
0.01729085110127926,
0.010664740577340126,
-0.004669073037803173,
0.04279174655675888,
0.035103730857372284,
-0.04241063818335533,
0.027650007978081703,
-0.02700466848909855,
-0.016460804268717766,
0.021597187966108322,
-0.02472294680774212,
-0.04929901659488678,
0.013119050301611423,
-0.03132372722029686,
0.053784120827913284,
0.005814715288579464,
-0.020190805196762085,
0.011707788333296776,
0.05231614038348198,
0.0014140786370262504,
-0.0035365368239581585,
-0.003421326633542776,
-0.017382614314556122,
-0.005730455741286278,
-0.009978018701076508,
0.017361726611852646,
-0.04962301626801491,
-0.026014462113380432,
0.03163698688149452,
0.032982099801301956,
-0.040448397397994995,
0.021685991436243057,
-0.019694415852427483,
0.006322015542536974,
-0.006874012760818005,
0.011249467730522156,
0.012484482489526272,
0.032157666981220245,
0.017386076971888542,
-0.020142897963523865,
0.018458742648363113,
0.03827811777591705,
0.0024427808821201324,
-0.08982532471418381,
-0.026905303820967674,
0.01475025899708271,
-0.015049224719405174,
0.01951904408633709,
-0.04223671928048134,
-0.03282257169485092,
0.03167511522769928,
-0.07322827726602554,
0.01932123675942421,
-0.023464960977435112,
-0.017081426456570625,
-0.01799989491701126,
-0.015114646404981613,
0.02638884074985981,
0.033170271664857864,
0.04274279251694679,
0.0038011891301721334,
-0.015234692953526974,
0.00376998377032578,
-0.01699545606970787,
-0.0019672170747071505,
0.023315582424402237,
0.018919382244348526,
0.008324967697262764,
0.004652692005038261,
0.046465203166007996,
-0.002935668919235468,
-0.0022966975811868906,
0.04992444068193436,
0.018967067822813988,
0.033407676964998245,
-0.02093852311372757,
-0.006926165893673897,
0.003277604002505541,
0.0017162339063361287,
0.00792321003973484,
-0.027301907539367676,
-0.04286138340830803,
0.01111407857388258,
-0.008533723652362823,
0.024491094052791595,
-0.01833224669098854,
0.000014710652067151386,
0.004914732184261084,
-0.05052020773291588,
-0.001735628698952496,
0.0014427020214498043,
-0.026032498106360435,
0.014174233190715313,
-0.028826003894209862,
-0.00569500308483839,
-0.0169588103890419,
-0.02893475815653801,
0.013586782850325108,
-0.07565467059612274,
0.012752857059240341,
0.013933703303337097,
-0.017059294506907463,
-0.014741690829396248,
0.031649019569158554,
0.018563468009233475,
-0.004270138684660196,
0.0286580640822649,
-0.0398673340678215,
-0.02088836207985878,
-0.05391877517104149,
0.005983772221952677,
-0.0024895628448575735,
-0.025052644312381744,
0.009628022089600563,
-0.05109575018286705,
0.0012347399024292827,
0.07227636128664017,
0.030714141204953194,
0.016611790284514427,
-0.006401710212230682,
-0.0638253390789032,
-0.035637494176626205,
-0.04895228520035744,
0.044825468212366104,
-0.002686653984710574,
-0.048355989158153534,
-0.04930976405739784,
-0.02859134040772915,
-0.00981954950839281,
-0.00029365374939516187,
0.03796409070491791,
-0.006091017741709948,
0.02413659356534481,
0.014043061062693596,
-0.02607796899974346,
0.0006024582544341683,
-0.06734852492809296,
0.02235495112836361,
-0.00221076887100935,
-0.061415039002895355,
-0.0047483062371611595,
-0.020313652232289314,
-0.03702268749475479,
-0.002328971866518259,
-0.010492948815226555,
-0.01679222658276558,
0.06767642498016357,
0.014747136272490025,
-0.03117567114531994,
0.057935163378715515,
0.06298688054084778,
0.037185948342084885,
0.07690882682800293,
-0.0015758494846522808,
0.006035229191184044,
0.030661428347229958,
-0.013403241522610188,
-0.025859883055090904,
0.018123554065823555,
-0.0285477377474308,
-0.011533580720424652,
-0.02140066586434841,
-0.016287963837385178,
0.04953993484377861,
-0.01925722509622574,
-0.001233907649293542,
0.051956746727228165,
-0.05207385495305061,
0.011738596484065056,
0.018473152071237564,
0.0056175668723881245,
0.02075512334704399,
-0.05005485191941261,
-0.022320276126265526,
0.036789670586586,
-0.013476025313138962,
0.003792263101786375,
0.05715547129511833,
0.0212909746915102,
0.015997614711523056,
-0.014823309145867825,
0.023078564554452896,
0.013173798099160194,
-0.0016737249679863453,
-0.01213936135172844,
0.053750522434711456,
-0.05482310801744461,
0.001788384048268199,
0.03320769593119621,
-0.0034658692311495543,
-0.005773906596004963,
0.009406927973031998,
-0.044728949666023254,
0.03613680228590965,
-0.015862228348851204,
0.03473842516541481,
-0.0010448273969814181,
-0.02201530896127224,
-0.021376991644501686,
0.023243915289640427,
0.01420664694160223,
0.038090676069259644,
0.03233949840068817,
-0.03452736511826515,
-0.0035720551386475563,
-0.00033469300251454115,
0.04884444177150726,
-0.015426241792738438,
0.02482449822127819,
-0.027646003291010857,
0.03546997159719467,
-0.005329695530235767,
0.008052952587604523,
-0.04436761885881424,
-0.044513311237096786,
0.043032266199588776,
0.01990954764187336,
0.04261254146695137,
-0.052275098860263824,
0.0131475068628788,
-0.023358076810836792,
0.05122938007116318,
-0.07099486887454987,
-0.03969039022922516,
0.004623674787580967,
0.02275802567601204,
-0.021100113168358803,
0.003803532337769866
] |
<p>I am reading the book "Lecture notes on Electron Correlation and Magnetism" by Patrik Fazekas.</p>
<p>It says, "The ground state (of Heisenberg FM model) is not unique. We have just found that the system has the maximum value of the total spin $S_{tot}= LS$. $S^{z}_{tot} = LS $ state which is maximally polarized in the z-direction. However the Hamiltonian is spin-rotationally invariant , hence turning the total spin in another direction does not change the energy: the ground state must be (2LS+1)-fold degenerate."
where, L is the no. of lattice sites.</p>
<p>I don't understand why the ground state should be (2LS+1)-fold degenerate and not infinitely degenerate. Are we not considering a global rotation symmetry of the system? I understand it in the following way: All the spins in the system have the same quantization axis which is along z-direction. Now, if every spin is rotated by the same angle,it produces a new state but the energy of the system remains unchanged because it depends on the scalar product of spins in the Heisenberg Hamiltonian. Therefore, a global rotation chosen from any of the infinite no. of possible rotations should produce infinitely many possible states and leave the energy of the Hamiltonian invariant (equal to the ground state energy). "</p>
<p>Does the system has a single quantization axis(i.e. same quantization works for each spin)? or Do we need to consider a unique quantization axis for each spin?
What happens to the quantization axis/axes of the system/spins as we consider a different state which has been globally rotated by some angle?
If the quantization axis (z-axis) remains fixed, then the system no longer has the maximum value of $S^z$ in the new state obtained after a global rotation. But, if the quantization axis rotates with the system, then, why are there only, (2LS+1) possible rotations?
In other words, how does L get into the degeneracy?
Thanks</p>
| 8,327 |
[
-0.038102660328149796,
0.013347327709197998,
-0.004779194947332144,
-0.016880091279745102,
0.05520624667406082,
-0.0025260034017264843,
-0.042516712099313736,
-0.05699090659618378,
-0.005288361106067896,
-0.05985881760716438,
-0.007097987458109856,
0.002225338714197278,
0.024963393807411194,
0.03838691487908363,
-0.014071845449507236,
-0.0054315244778990746,
-0.011531547643244267,
-0.03216409683227539,
-0.028754664584994316,
-0.006633028853684664,
0.003538969438523054,
0.05935614928603172,
0.006367453373968601,
-0.014329484663903713,
-0.02762546017765999,
0.02892429195344448,
0.010279418900609016,
0.02842058800160885,
0.05491471290588379,
0.05298983305692673,
0.010622884146869183,
-0.03884473815560341,
0.02055157721042633,
0.04527673125267029,
0.040834829211235046,
-0.02051672339439392,
-0.01893659308552742,
-0.039064921438694,
0.00872096884995699,
0.027095217257738113,
-0.0699131190776825,
-0.007176671642810106,
-0.046808842569589615,
0.03528947755694389,
-0.026722218841314316,
-0.005478904582560062,
-0.026722583919763565,
-0.0019673898350447416,
0.047450631856918335,
-0.057423923164606094,
0.0473402738571167,
0.03178408369421959,
-0.010167359374463558,
0.006268620956689119,
0.036927882581949234,
-0.011248246766626835,
0.047758642584085464,
0.06529560685157776,
-0.004489484243094921,
-0.03133770450949669,
-0.06554406136274338,
-0.05337574705481529,
0.011452038772404194,
-0.012243224307894707,
-0.01708981581032276,
-0.010478592477738857,
0.04454311355948448,
-0.0112524488940835,
0.0561448335647583,
-0.0005685805226676166,
0.001619892194867134,
0.025913920253515244,
0.029216282069683075,
-0.05530662089586258,
0.030960563570261,
-0.027935834601521492,
0.02970304898917675,
-0.0012023078743368387,
-0.00855710357427597,
0.004236860200762749,
-0.023259468376636505,
0.026253655552864075,
0.01332808006554842,
0.02501709945499897,
-0.004762895405292511,
-0.008394639007747173,
0.0626852810382843,
0.032265886664390564,
0.009080156683921814,
0.0800551101565361,
0.007944048382341862,
0.02104710228741169,
0.04588158056139946,
-0.03021448478102684,
-0.0457647405564785,
0.06220050901174545,
0.020939461886882782,
0.05204363539814949,
-0.01057975459843874,
-0.020451800897717476,
0.019235333427786827,
-0.03244105726480484,
-0.016994571313261986,
0.04758504033088684,
0.011552345007658005,
0.014139823615550995,
-0.03321675583720207,
-0.01603117026388645,
-0.024320006370544434,
-0.010081104002892971,
-0.023250754922628403,
0.01295266579836607,
-0.030035607516765594,
-0.01757146790623665,
0.0075850351713597775,
-0.02004879340529442,
-0.010072963312268257,
-0.021522311493754387,
0.03155573830008507,
0.08246229588985443,
0.015236398205161095,
-0.013693086802959442,
0.029613282531499863,
-0.049867063760757446,
-0.06730667501688004,
0.014711770229041576,
0.032611437141895294,
0.006605965085327625,
-0.04570205882191658,
0.02926519513130188,
0.02580958977341652,
-0.024249201640486717,
-0.007564309518784285,
-0.014469810761511326,
0.031252726912498474,
-0.022389953956007957,
-0.1291835904121399,
-0.02255273424088955,
0.03251829370856285,
-0.027622804045677185,
0.017597680911421776,
-0.08256752043962479,
0.004462885204702616,
0.003620279487222433,
0.0886126160621643,
-0.0100110387429595,
0.03726595640182495,
0.009808692149817944,
0.031792931258678436,
0.02843434177339077,
-0.006927118171006441,
-0.024303309619426727,
0.0025416300632059574,
-0.05237558111548424,
-0.004260727670043707,
-0.051860176026821136,
0.0508660152554512,
0.02731180191040039,
0.03602200746536255,
-0.05465986207127571,
0.05112181976437569,
-0.03628437966108322,
0.021825630217790604,
-0.0009885907638818026,
0.010350390337407589,
0.004168977495282888,
0.0755171999335289,
-0.010704001411795616,
0.0408676415681839,
0.0603940412402153,
-0.030743835493922234,
-0.008173953741788864,
-0.007039500866085291,
0.0485171414911747,
0.03095102868974209,
-0.006628795526921749,
-0.01953447423875332,
-0.05825509876012802,
0.034290432929992676,
0.002009589923545718,
-0.020886538550257683,
-0.01542190182954073,
0.0028632013127207756,
0.01462393719702959,
-0.024697566404938698,
0.04793918505311012,
0.008917407132685184,
0.007539133075624704,
-0.03330250084400177,
-0.0615013912320137,
-0.0050004757940769196,
-0.06654056161642075,
0.023426871746778488,
0.00941342581063509,
-0.006641643587499857,
0.049146100878715515,
0.023306546732783318,
0.02508145570755005,
-0.0196576826274395,
-0.06168941408395767,
-0.012810749001801014,
0.041930947452783585,
0.0024865991435945034,
-0.0035026981495320797,
0.038744501769542694,
0.04430665448307991,
0.016027064993977547,
0.026439622044563293,
0.033125799149274826,
-0.007864594459533691,
-0.040444266051054,
0.03660032898187637,
0.0016641659894958138,
0.014087469317018986,
0.01977279968559742,
0.0014842147938907146,
-0.03191307187080383,
0.041263237595558167,
-0.03111243061721325,
0.015177726745605469,
-0.03479267284274101,
0.05681689456105232,
0.04052622243762016,
-0.04245595633983612,
0.023400889709591866,
0.05586428940296173,
-0.008197140879929066,
0.02936157025396824,
-0.009441781789064407,
-0.05285583809018135,
-0.06550716608762741,
-0.01642521284520626,
0.04077750816941261,
0.0374612882733345,
-0.034930866211652756,
-0.0052215964533388615,
0.012864372693002224,
0.038292720913887024,
0.024340251460671425,
0.0032048956491053104,
-0.032009996473789215,
-0.01803821139037609,
0.012204338796436787,
0.00599763635545969,
0.01479582954198122,
0.019020529463887215,
0.035266537219285965,
0.003590633627027273,
0.006308685056865215,
0.029635434970259666,
-0.029139675199985504,
0.04300596937537193,
-0.025218801572918892,
0.0009140957263298333,
-0.002743363380432129,
-0.029725322499871254,
-0.02553052082657814,
0.014803786762058735,
0.04011277109384537,
0.04498911648988724,
-0.0241533275693655,
-0.01960716024041176,
-0.024875415489077568,
-0.03657291829586029,
-0.003992239944636822,
-0.014387463219463825,
-0.04527872055768967,
-0.03393168747425079,
0.012674251571297646,
-0.0016865084180608392,
-0.0006003089365549386,
-0.0019964836537837982,
-0.014610815793275833,
0.0008170038927346468,
0.01845324970781803,
0.06649565696716309,
0.0002000007953029126,
-0.0025489351246505976,
-0.032462816685438156,
-0.03776833787560463,
0.021259887143969536,
-0.01993188075721264,
0.03670449182391167,
0.03851423040032387,
-0.03996794670820236,
-0.013052348978817463,
-0.05528251454234123,
-0.00716177886351943,
0.025179803371429443,
-0.016416354104876518,
0.04599893093109131,
0.012616150081157684,
0.000869707961101085,
-0.04721641167998314,
-0.021168557927012444,
-0.023061664775013924,
0.02474779076874256,
-0.022961938753724098,
-0.0019320929422974586,
0.060665395110845566,
-0.003909578546881676,
-0.036589302122592926,
0.0006524287746287882,
-0.016806313768029213,
-0.02313850261271,
0.012021617032587528,
-0.013101120479404926,
0.055466629564762115,
-0.03435016795992851,
0.03825792670249939,
0.013938571326434612,
-0.04150211438536644,
-0.01061367429792881,
-0.06123705580830574,
-0.019994650036096573,
0.0010761070298030972,
-0.0323169119656086,
0.025012269616127014,
-0.03715581074357033,
-0.0038362424820661545,
0.07540586590766907,
0.018561089411377907,
-0.04124385863542557,
0.009944895282387733,
0.013545116409659386,
0.005789032205939293,
-0.0464298278093338,
0.003219509730115533,
0.016658080741763115,
0.02880396693944931,
0.050343748182058334,
0.00549226813018322,
0.03248613327741623,
0.04962330684065819,
0.0073637827299535275,
0.029184352606534958,
0.025546925142407417,
0.012209410779178143,
0.002625454915687442,
0.021301457658410072,
-0.012663557194173336,
-0.0024912527296692133,
0.008924580179154873,
0.05147665739059448,
-0.0004899440100416541,
0.0014277423033490777,
-0.09241042286157608,
0.08704709261655807,
0.015918146818876266,
0.04459404572844505,
-0.023868199437856674,
0.04324347898364067,
-0.0005082903662696481,
-0.0047565121203660965,
-0.0025007191579788923,
0.02948804572224617,
0.027284899726510048,
-0.01931893080472946,
0.005832265596836805,
0.025861743837594986,
-0.00936686061322689,
-0.03483078256249428,
-0.030975693836808205,
-0.012989126145839691,
0.005939318798482418,
0.03924252837896347,
-0.028210945427417755,
-0.020351026207208633,
0.014988909475505352,
0.04269682988524437,
0.019780131056904793,
-0.0269736610352993,
-0.029975442215800285,
-0.001154624973423779,
-0.05420180410146713,
0.007034255191683769,
-0.001783276442438364,
0.027567388489842415,
0.017456049099564552,
0.0321265310049057,
0.02227677032351494,
0.03834356367588043,
-0.027558978646993637,
0.026938987895846367,
-0.0903032049536705,
0.007331059779971838,
-0.014206458814442158,
0.030482226982712746,
0.01146515179425478,
-0.0284994188696146,
0.015855224803090096,
0.008750231936573982,
-0.021574359387159348,
-0.010268693789839745,
-0.04077653959393501,
-0.05713885277509689,
0.010335237719118595,
-0.05115623027086258,
-0.01967117004096508,
-0.03627688065171242,
0.07615939527750015,
0.015743277966976166,
-0.059936415404081345,
0.00917865615338087,
-0.0005867991130799055,
-0.05100681632757187,
0.032654426991939545,
0.016476860269904137,
0.032552991062402725,
0.03135623782873154,
0.02481904998421669,
0.05232089012861252,
-0.0033713497687131166,
0.01834033615887165,
-0.02858002483844757,
-0.008934242650866508,
0.04435860738158226,
0.017203737050294876,
-0.008165525272488594,
0.007844747975468636,
-0.019249053671956062,
0.0017729421379044652,
-0.015585776418447495,
0.05156723037362099,
0.008723491802811623,
0.016644282266497612,
0.050606220960617065,
0.012927473522722721,
-0.028397539630532265,
0.014619017019867897,
0.046108972281217575,
0.01816713809967041,
-0.0367581844329834,
-0.020316973328590393,
0.00263149943202734,
-0.04650192707777023,
-0.010868868790566921,
0.026099998503923416,
-0.003533396404236555,
-0.0194381233304739,
0.018600676208734512,
0.017232118174433708,
0.0031579553615301847,
-0.027947083115577698,
-0.011996224522590637,
-0.002468298189342022,
0.06249617785215378,
0.02834419347345829,
-0.006142987869679928,
-0.0028208938892930746,
0.0058952998369932175,
0.01940356381237507,
0.029069919139146805,
-0.012570093385875225,
-0.04765482246875763,
-0.008750966750085354,
0.0018776694778352976,
0.021395891904830933,
0.013079436495900154,
0.01345659326761961,
-0.03487531095743179,
-0.015057417564094067,
0.0010693995282053947,
-0.04322867840528488,
0.039005622267723083,
0.016181927174329758,
-0.028337350115180016,
-0.04787735641002655,
-0.020345861092209816,
-0.033608969300985336,
-0.0022769097704440355,
0.02072260156273842,
0.004075027070939541,
0.007646932732313871,
-0.00003881615702994168,
-0.02962459996342659,
-0.003477663965895772,
0.001971825258806348,
0.018420198932290077,
0.019509661942720413,
0.020442631095647812,
-0.0031358455307781696,
0.0388503223657608,
-0.015935635194182396,
-0.09487490355968475,
-0.02066824398934841,
0.003901187563315034,
-0.00636436278000474,
0.058457523584365845,
-0.039742983877658844,
-0.06794404983520508,
-0.0011541984276846051,
0.021378975361585617,
-0.0016715138917788863,
0.016651855781674385,
-0.03611072897911072,
0.061268147081136703,
0.034119945019483566,
-0.015069489367306232,
0.04263798147439957,
0.006438838317990303,
-0.0029066100250929594,
0.011108972132205963,
-0.014766874723136425,
0.03969399258494377,
-0.03371096029877663,
0.020962601527571678,
-0.05489647015929222,
0.04340077191591263,
-0.018233103677630424,
0.029503557831048965,
-0.03475268930196762,
-0.011337325908243656,
-0.028352292254567146,
-0.005277770571410656,
-0.02350076101720333,
0.01895940490067005,
0.010997923091053963,
-0.00999932549893856,
-0.01728150062263012,
0.02950325794517994,
0.008080117404460907,
-0.0358239971101284,
-0.01452308427542448,
-0.02437320351600647,
-0.024537784978747368,
0.030334385111927986,
0.0007070357096381485,
0.02165994420647621,
-0.022185001522302628,
0.019157884642481804,
-0.005723253358155489,
-0.03882947936654091,
0.05484295263886452,
0.028607498854398727,
0.00942932441830635,
0.008507807739078999,
-0.03413797542452812,
-0.03874507173895836,
-0.0043115816079080105,
-0.007146006915718317,
-0.01243158895522356,
-0.004736609291285276,
0.00774195184931159,
0.014812265522778034,
0.009309305809438229,
-0.0838860422372818,
-0.051886580884456635,
-0.0163434948772192,
-0.005168961361050606,
-0.021678978577256203,
0.020321762189269066,
0.014370961114764214,
0.00039776432095095515,
-0.01819201558828354,
-0.010070063173770905,
0.011862174607813358,
-0.03522208705544472,
0.023663286119699478,
0.020794620737433434,
0.06684674322605133,
0.04843362793326378,
-0.005758322775363922,
-0.020988231524825096,
0.016996027901768684,
-0.019960898905992508,
-0.004234573803842068,
-0.00817659217864275,
0.03320169821381569,
-0.008940526284277439,
-0.01853819563984871,
-0.020225169137120247,
0.02466077357530594,
0.04447648301720619,
-0.015437553636729717,
0.0006590047269128263,
-0.028572440147399902,
-0.009994588792324066,
0.030786238610744476,
-0.011621767655014992,
-0.03687867149710655,
-0.00474190479144454,
0.03717642277479172,
0.004074281547218561,
-0.0077687944285571575,
0.012310069985687733,
-0.038808729499578476,
0.017239069566130638,
0.014784497208893299,
0.010814275592565536,
0.03144584223628044,
0.0671825185418129,
0.025694886222481728,
-0.010608777403831482,
0.005960107780992985,
-0.06361597031354904,
0.009747830219566822,
0.0055957394652068615,
0.0286980252712965,
-0.0009773728670552373,
0.010709764435887337,
0.007984999567270279,
-0.039981212466955185,
-0.012230093590915203,
0.044463541358709335,
0.053652092814445496,
0.011397468857467175,
0.024826500564813614,
0.037003204226493835,
0.008250142447650433,
-0.012563679367303848,
-0.03508341312408447,
-0.014604023657739162,
0.013653404079377651,
-0.013620712794363499,
0.06343840807676315,
0.0033416699152439833,
-0.01363876461982727,
0.04601284861564636,
0.05490070953965187,
-0.00031236972426995635,
0.010214638896286488,
0.07793717831373215,
0.0029066859278827906,
0.016219820827245712,
0.023014627397060394,
-0.07291264832019806,
0.05565594881772995,
-0.037326570600271225,
0.03148213401436806,
0.023222891613841057,
-0.0231171827763319,
0.013275152072310448,
-0.006312426179647446,
0.027518203482031822,
-0.051583874970674515,
-0.01681155525147915,
-0.04580813646316528,
0.05814646556973457,
-0.00325874425470829,
0.02282591164112091,
0.0015547866933047771,
0.011973784305155277,
0.000030318960853037424,
0.012946955859661102,
-0.01595573127269745,
-0.00811541173607111,
-0.0538068450987339,
0.0025001836474984884,
-0.04009034112095833,
-0.047529496252536774,
0.030295751988887787,
0.01580795645713806,
-0.039108797907829285,
0.008070244453847408,
-0.03840218856930733,
0.013239921070635319,
-0.01102205365896225,
0.02846476063132286,
0.0016967295669019222,
0.09497730433940887,
-0.008780832402408123,
0.0918503850698471,
0.012728719040751457,
-0.005468311719596386,
0.09867455810308456,
0.06109359860420227,
0.001328178565017879,
-0.08285608142614365,
-0.006410303991287947,
-0.004400820005685091,
0.005580059252679348,
-0.017154289409518242,
0.032616522163152695,
0.004135445691645145,
0.017012309283018112,
-0.017193587496876717,
0.0429605171084404,
-0.01976938173174858,
-0.02785647101700306,
0.05247810110449791,
-0.05696704983711243,
-0.038050439208745956,
-0.020339833572506905,
0.009891974739730358,
0.005296576768159866,
-0.013256179168820381,
-0.03658314049243927,
-0.010860854759812355,
-0.04086053743958473,
0.023134807124733925,
-0.012848906219005585,
-0.038260892033576965,
0.02059793286025524,
-0.0004341343301348388,
-0.017517533153295517,
0.010191566310822964,
0.008879126980900764,
-0.009025536477565765,
-0.0375465527176857,
-0.0034693204797804356,
0.021798355504870415,
0.038168638944625854,
0.048554785549640656,
0.025110742077231407,
-0.011610827408730984,
-0.0014071081532165408,
0.049839913845062256,
0.0016706521855667233,
-0.01762978918850422,
-0.023004164919257164,
-0.01924712210893631,
0.05218750610947609,
-0.0417829230427742,
-0.015048799104988575,
0.0012157729361206293,
-0.014936775900423527,
-0.0074287718161940575,
-0.02164899930357933,
-0.017812497913837433,
-0.015391066670417786,
0.042864181101322174,
-0.009938796050846577,
-0.00020845755352638662,
-0.02516181394457817,
-0.001359261805191636,
0.017433516681194305,
-0.01625980995595455,
-0.029161497950553894,
-0.011946107260882854,
0.02677539363503456,
-0.008287552744150162,
0.043902426958084106,
0.029473867267370224,
-0.01934988424181938,
-0.01946926862001419,
-0.03812729939818382,
-0.040286585688591,
-0.010461286641657352,
0.0021362858824431896,
-0.016091851517558098,
0.048417139798402786,
-0.02206271141767502,
-0.016825584694743156,
-0.014522537589073181,
-0.02561057358980179,
-0.016002429649233818,
0.005210697650909424,
-0.043010395020246506,
-0.0037926642689853907,
0.01175076887011528,
0.00040416972478851676,
0.04165089875459671,
-0.06564542651176453,
0.0397600419819355,
-0.005037327297031879,
0.000736285001039505,
0.01777978055179119,
-0.017026863992214203,
0.010148477740585804,
0.014517967589199543,
-0.050918418914079666,
0.015518278814852238,
-0.04677170515060425,
0.001941814785823226,
0.020799480378627777,
0.013821723870933056,
0.0039406465366482735,
0.04779168590903282,
0.01047731563448906,
0.0055041201412677765,
0.011374510824680328,
-0.014082053676247597,
0.0032042432576417923,
0.04795627295970917,
0.004560839384794235,
-0.053341254591941833,
-0.04766051098704338,
-0.011190692894160748,
-0.008483484387397766,
0.021430332213640213,
0.0015177951427176595,
-0.05225665122270584,
-0.013912104070186615,
-0.026380058377981186,
0.024415260180830956,
-0.04415840283036232,
-0.011770627461373806,
-0.005366015713661909,
0.03742416575551033,
0.022789660841226578,
0.021358439698815346,
0.009402099996805191,
0.028092019259929657,
0.010719012469053268,
-0.03780798614025116,
-0.0038661775179207325,
0.054961517453193665,
-0.043903499841690063,
0.018059881404042244,
0.004857004154473543,
0.006445433013141155,
0.061337120831012726,
-0.009586642496287823,
-0.03931386023759842,
0.010787458159029484,
-0.024145452305674553,
-0.011312766931951046,
0.023795131593942642,
-0.013185696676373482,
0.010607756674289703,
0.036622170358896255,
-0.004225490149110556,
-0.0285382978618145,
0.026278408244252205,
-0.006910830270498991,
-0.0157223679125309,
-0.0130325797945261,
-0.0056610917672514915,
-0.014352201484143734,
-0.01127895712852478,
0.01286043506115675,
-0.010039472952485085,
-0.012944843620061874,
0.04531433805823326,
0.04220983386039734,
-0.02661847323179245,
-0.0016614937921985984,
-0.03315388411283493,
-0.01518015656620264,
0.034932322800159454,
0.05399822071194649,
0.005658969283103943,
0.018842006102204323,
0.05189187452197075,
-0.0057920897379517555,
0.0015763447154313326,
-0.008122383616864681,
-0.010385972447693348,
-0.07329137623310089,
-0.0114876264706254,
-0.012945419177412987,
-0.01637006178498268,
0.03774585574865341,
-0.009513585828244686,
-0.004372708965092897,
0.03448690101504326,
-0.11122405529022217,
0.026178617030382156,
-0.04371923208236694,
0.02337825298309326,
-0.032747238874435425,
-0.018637361004948616,
-0.05114734172821045,
0.04548535868525505,
0.029714806005358696,
0.055840324610471725,
0.036179766058921814,
0.0007934252498671412,
-0.019950196146965027,
0.014995601959526539,
0.0011090098414570093,
0.021828990429639816,
-0.014652459882199764,
-0.016041206195950508,
0.09071049839258194,
-0.011679882183670998,
-0.045069724321365356,
-0.015139171853661537,
-0.05188184604048729,
-0.03166666626930237,
-0.014038612134754658,
0.021650945767760277,
-0.014678901992738247,
0.04863749071955681,
-0.010587330907583237,
-0.00037483370397239923,
-0.013326269574463367,
-0.007251052185893059,
0.03189145028591156,
0.03375107795000076,
-0.00027733517345041037,
0.0010613935301080346,
0.005848141852766275,
-0.05813619866967201,
-0.020321786403656006,
0.0501859188079834,
-0.028014546260237694,
-0.0011839483631774783,
0.012558992020785809,
0.00930699147284031,
0.007836640812456608,
-0.04047379642724991,
0.01583351381123066,
-0.041318129748106,
-0.019294388592243195,
0.014619600959122181,
0.01837172731757164,
0.036810021847486496,
0.020657777786254883,
-0.003860804485157132,
-0.024257976561784744,
0.04823390766978264,
-0.0011012504110112786,
-0.04818176478147507,
-0.04134900122880936,
-0.010323142632842064,
-0.0010005285730585456,
-0.038077980279922485,
-0.007738766260445118,
-0.03633670508861542,
-0.049366146326065063,
0.01539324689656496,
0.002433817833662033,
0.044435594230890274,
-0.033240772783756256,
-0.05637098476290703,
-0.002429056679829955,
-0.057250842452049255,
0.036307256668806076,
-0.023314885795116425,
-0.004244077950716019,
-0.024411864578723907,
-0.021532325074076653,
0.0038087547291070223,
0.00884665735065937,
0.04070081561803818,
0.018498610705137253,
0.016959194093942642,
0.00682873697951436,
-0.00021483229647856206,
0.03533761948347092,
-0.010017449036240578,
0.006970949470996857,
-0.017852574586868286,
0.006392396055161953,
0.020921986550092697,
0.007683573290705681,
-0.04557013884186745,
0.03663847595453262,
0.00665070628747344,
-0.0014463519910350442,
0.02742830291390419,
0.017262060195207596,
-0.022366754710674286,
0.054304394870996475,
-0.026985904201865196,
0.001047688303515315,
0.03970998525619507,
-0.00991194136440754,
0.007794585544615984,
0.049183279275894165,
-0.018506675958633423,
-0.06131332367658615,
0.026445522904396057,
-0.039275120943784714,
-0.0043532452546060085,
-0.016719838604331017,
0.010386397130787373,
0.0577770359814167,
-0.019114285707473755,
0.0355084165930748,
0.041378144174814224,
-0.016791213303804398,
-0.04737481847405434,
0.041720662266016006,
-0.011294976808130741,
0.0392889529466629,
-0.009705819189548492,
0.00034543563378974795,
-0.010732575319707394,
0.022080738097429276,
0.038778383284807205,
0.04459903761744499,
0.03422433137893677,
0.025151938199996948,
0.02132466994225979,
-0.004385226871818304,
-0.01859922893345356,
0.03588622063398361,
0.019929103553295135,
0.037957724183797836,
-0.053156279027462006,
-0.009295841678977013,
0.036887217313051224,
-0.0012750892201438546,
-0.00006472811219282448,
0.01931627467274666,
-0.032016340643167496,
0.0653761774301529,
-0.01345905102789402,
-0.0037974948063492775,
-0.03727199137210846,
-0.011688505299389362,
-0.025650933384895325,
-0.018250951543450356,
0.005723839160054922,
0.05643371865153313,
0.014424417167901993,
-0.00407172879204154,
-0.040609125047922134,
0.019256407395005226,
0.033928725868463516,
-0.03292280063033104,
0.03462851792573929,
0.011736755259335041,
-0.049342285841703415,
-0.019610241055488586,
-0.02871621772646904,
-0.03452423959970474,
-0.03088507056236267,
0.020781608298420906,
-0.002576167229562998,
0.016476789489388466,
-0.009561206214129925,
-0.035401828587055206,
-0.055341292172670364,
0.03998533636331558,
-0.048560287803411484,
-0.032007500529289246,
-0.008636143989861012,
0.002084464533254504,
-0.027514401823282242,
0.018833257257938385
] |
<p>for those that combine Homology group and some form of Kadanoff scheme for coarse graining on a lattice, am I having a good argument when saying this:
(practical thinking now)
1. I obtain the Homology groups for a lattice space, I do some coarse graining on it, everything looks fine
2. I go to the cohomology. Cohomology induces the linking product, I have a new structure involving possible linked chains.
3. I do coarse graining</p>
<p>While keeping the points of the lattice resp. the duals (the links) and coarse graining isn't it possible that I miss the consistency of the linking product?
I mean, coarse graining should destroy the consistency of the linking product so I may end up with some different space (note that linking product may generate spaces not visible by homology alone)</p>
<p>Shouldn't there be some sort of beta function in cohomology that should take care of this?</p>
| 8,328 |
[
0.013171094469726086,
0.05993543565273285,
0.004374721087515354,
-0.04334692284464836,
-0.01583036594092846,
0.03922972455620766,
-0.01176544651389122,
-0.027347005903720856,
-0.01791529916226864,
-0.0351465679705143,
0.023180978372693062,
0.012767515145242214,
0.06356015801429749,
0.022878514602780342,
0.003106706077232957,
-0.003766929032281041,
-0.012722977437078953,
-0.06526847928762436,
-0.010522930882871151,
-0.013694330118596554,
0.003050045110285282,
0.014831826090812683,
0.0012248365674167871,
-0.018814733251929283,
-0.005007523577660322,
-0.017871733754873276,
0.0017136187525466084,
0.0042168074287474155,
0.022353556007146835,
0.03172777593135834,
-0.025554968044161797,
-0.04086998477578163,
0.02722601778805256,
0.02792416140437126,
-0.0068523334339261055,
0.00010152796312468126,
-0.07601811736822128,
-0.023861896246671677,
0.0012434169184416533,
0.03959288448095322,
-0.012643251568078995,
0.019119979813694954,
-0.049398306757211685,
0.08070915937423706,
-0.011144260875880718,
0.03463461250066757,
-0.025732526555657387,
0.005070023238658905,
0.05323201045393944,
-0.030488193035125732,
0.06573111563920975,
0.0147514957934618,
-0.02216348424553871,
0.07199113070964813,
0.020873863250017166,
-0.03622319921851158,
0.04167134314775467,
0.050183262676000595,
-0.010364390909671783,
-0.0008216559654101729,
-0.028412457555532455,
-0.01873239316046238,
0.054745495319366455,
-0.0588846430182457,
0.004049993585795164,
0.014445489272475243,
-0.011952024884521961,
-0.012507285922765732,
0.03304118663072586,
-0.022969957441091537,
-0.011086754500865936,
-0.01664285734295845,
0.021957188844680786,
-0.015630796551704407,
0.033357568085193634,
0.019122833386063576,
-0.025550054386258125,
0.0061186207458376884,
0.031301990151405334,
0.03918582573533058,
-0.045065369457006454,
-0.0100422203540802,
-0.022509025409817696,
0.04827715829014778,
0.023530328646302223,
-0.013791071251034737,
0.027549758553504944,
-0.04621662572026253,
0.009502602741122246,
0.060518886893987656,
-0.008573785424232483,
-0.04878377914428711,
0.06390300393104553,
0.014535891823470592,
-0.014349921606481075,
0.05642138794064522,
0.021610679104924202,
0.002520700916647911,
-0.006353630218654871,
0.019298745319247246,
-0.020148657262325287,
-0.04620857536792755,
0.006528366357088089,
0.07749123126268387,
-0.023030105978250504,
-0.007927059195935726,
-0.006282234564423561,
0.004306388087570667,
-0.029088472947478294,
-0.008557513356208801,
-0.049039892852306366,
-0.013950775377452374,
-0.02581227384507656,
0.017849208787083626,
0.0007906965911388397,
-0.024972816929221153,
0.0009498682338744402,
-0.012314744293689728,
0.028104951605200768,
0.07066338509321213,
0.025597739964723587,
0.015014815144240856,
0.030551178380846977,
-0.03110896795988083,
-0.09515216946601868,
0.009953675791621208,
0.06438811123371124,
-0.019788557663559914,
-0.005629254505038261,
0.03388260677456856,
0.005934441927820444,
-0.01172302383929491,
0.022074313834309578,
0.01655399613082409,
0.009440654888749123,
-0.033794909715652466,
-0.09183114767074585,
-0.024943070486187935,
0.032203059643507004,
0.031780730932950974,
-0.006275487132370472,
-0.09749633818864822,
0.0353962667286396,
0.0008336068131029606,
0.07811366766691208,
0.008278054185211658,
-0.0014800861245021224,
-0.03101062774658203,
0.019888542592525482,
0.016758648678660393,
-0.04282230883836746,
-0.04377990588545799,
-0.035622674971818924,
-0.04835587739944458,
-0.03278714790940285,
-0.03187282010912895,
0.023627696558833122,
0.019947078078985214,
0.039331771433353424,
-0.033409710973501205,
0.05363843962550163,
-0.017974885180592537,
0.026570817455649376,
-0.015322360210120678,
0.003980469424277544,
-0.030049869790673256,
0.060197751969099045,
0.010586405172944069,
0.05072034150362015,
0.015207570046186447,
-0.01600261963903904,
0.005845523439347744,
-0.02994512766599655,
0.040414147078990936,
0.008761388249695301,
-0.01915346272289753,
0.03280358016490936,
0.001378523069433868,
0.04652626812458038,
0.01825479418039322,
-0.03455200418829918,
-0.02276032418012619,
-0.014048763550817966,
-0.027758726850152016,
-0.02552325464785099,
0.026703746989369392,
0.004393818322569132,
-0.02986372448503971,
0.024566207081079483,
-0.034867580980062485,
-0.005394963547587395,
-0.05330213904380798,
-0.04168796166777611,
-0.03445719555020332,
0.012500864453613758,
0.045137159526348114,
-0.0031205869745463133,
-0.003097112290561199,
-0.02797967754304409,
-0.04184853285551071,
-0.03950502723455429,
0.0045191701501607895,
0.006629433482885361,
-0.022611720487475395,
0.041900668293237686,
0.017948992550373077,
0.018351435661315918,
-0.022131090983748436,
0.0438147597014904,
-0.03856392204761505,
-0.008371233940124512,
0.05005917325615883,
-0.015523994341492653,
0.032190952450037,
-0.021584929898381233,
0.016017455607652664,
0.015952689573168755,
0.023685766384005547,
-0.035165902227163315,
0.014306610450148582,
-0.06724056601524353,
0.08965424448251724,
0.07907400280237198,
0.0254710391163826,
-0.011937875300645828,
0.024435823783278465,
-0.002906450303271413,
0.01505845133215189,
-0.011255302466452122,
-0.047456663101911545,
-0.01691790297627449,
0.02324695885181427,
0.09107020497322083,
0.04743696004152298,
-0.0036219446919858456,
0.009632510133087635,
0.011094030924141407,
0.03800371289253235,
-0.008534652180969715,
-0.0006797905080020428,
-0.014486267231404781,
0.020839236676692963,
0.035059694200754166,
-0.01828509010374546,
0.03300542011857033,
0.0081002963706851,
-0.007023039739578962,
0.02747618779540062,
0.0033138450235128403,
0.008790276944637299,
-0.01692255213856697,
0.0040668463334441185,
-0.02227216213941574,
-0.006376390345394611,
0.007744665257632732,
-0.005758462939411402,
0.03014392778277397,
0.010286851786077023,
0.04692595452070236,
-0.003209533402696252,
0.004801439121365547,
0.016910938546061516,
-0.00006080665116314776,
-0.03163154423236847,
0.020964641124010086,
0.0364009253680706,
-0.05477322265505791,
-0.03213611990213394,
0.018668007105588913,
0.016539009287953377,
-0.014419326558709145,
-0.014500468969345093,
-0.0033066323958337307,
-0.024168794974684715,
0.015297387726604939,
-0.00469616474583745,
-0.05095074698328972,
0.03119058534502983,
-0.06027877703309059,
-0.020050719380378723,
0.015845023095607758,
0.026721522212028503,
0.03805067762732506,
0.03986768424510956,
-0.0627487301826477,
-0.014217001385986805,
-0.009372088126838207,
0.013575494289398193,
0.01848074235022068,
-0.012735322117805481,
0.020806536078453064,
-0.02731495350599289,
-0.007604035548865795,
-0.06581399589776993,
-0.03306381404399872,
-0.019113613292574883,
0.005435211583971977,
0.0086507024243474,
-0.021706273779273033,
0.04506096616387367,
0.036412227898836136,
-0.07136062532663345,
0.0019849331583827734,
-0.014817330054938793,
-0.04020155966281891,
0.004031934309750795,
0.0019168037688359618,
-0.015596111305058002,
-0.023327557370066643,
0.015201498754322529,
0.015391848981380463,
-0.02373349852859974,
-0.0011358248302713037,
-0.029356468468904495,
-0.060594115406274796,
0.019133947789669037,
-0.03770512714982033,
0.04540737345814705,
-0.002345435321331024,
-0.0491105318069458,
0.08859913796186447,
0.027972199022769928,
-0.04509194940328598,
0.006831771228462458,
-0.017272934317588806,
-0.02810787223279476,
-0.0030699630733579397,
-0.0065574343316257,
-0.017563819885253906,
0.00511655118316412,
0.011275146156549454,
0.0628613606095314,
0.025125186890363693,
0.07397530227899551,
0.00942039955407381,
-0.00331393675878644,
0.021735569462180138,
0.029698317870497704,
0.016287581995129585,
-0.007985234260559082,
0.02227151207625866,
-0.0034314822405576706,
0.010615261271595955,
-0.014774175360798836,
0.024211503565311432,
-0.0030854428187012672,
-0.049164388328790665,
0.011012080125510693,
0.04909324645996094,
0.02560603991150856,
-0.017450755462050438,
0.04503381624817848,
0.01761964149773121,
-0.02277033030986786,
0.019001508131623268,
0.0010607948061078787,
0.032268356531858444,
-0.01153719425201416,
0.013740554451942444,
0.03330064192414284,
0.05284265801310539,
0.005967091768980026,
-0.012655644677579403,
-0.00370400445535779,
0.0001868515828391537,
0.007247146684676409,
-0.04183096066117287,
-0.0009717561770230532,
0.030276741832494736,
0.027386758476495743,
-0.006710502319037914,
0.005824120715260506,
-0.06462731212377548,
0.015780936926603317,
-0.06142140552401543,
0.007817214354872704,
-0.0018930655205622315,
0.044311653822660446,
-0.00996481068432331,
0.01959269680082798,
-0.0008645033813081682,
-0.010902650654315948,
-0.03721323609352112,
-0.0018857666291296482,
-0.04415014386177063,
-0.008701314218342304,
-0.028906822204589844,
0.012182229198515415,
-0.0010786934290081263,
-0.0019285180605947971,
0.004552521277219057,
-0.01277815643697977,
-0.05137263983488083,
-0.01879514753818512,
0.0048295315355062485,
-0.06001400202512741,
-0.012203997001051903,
-0.04684632644057274,
-0.02447333373129368,
-0.004043070133775473,
0.008248805068433285,
0.0733172595500946,
0.009894452057778835,
0.030354663729667664,
0.013537188991904259,
-0.013227740302681923,
0.021150272339582443,
-0.03415248543024063,
0.045820292085409164,
-0.014620501548051834,
0.011828833259642124,
-0.00866991188377142,
0.04273880645632744,
-0.0077676912769675255,
0.003477690275758505,
-0.00006257878703763708,
0.01112869381904602,
-0.00012358371168375015,
-0.025472167879343033,
0.006036962382495403,
-0.04844459518790245,
-0.027022134512662888,
-0.0038560032844543457,
0.0696495994925499,
-0.0037579527124762535,
-0.004132165107876062,
0.04945509508252144,
0.02781660482287407,
-0.0018980986205860972,
0.02079281210899353,
0.03265617787837982,
0.02256064862012863,
-0.04863015189766884,
-0.04838161543011665,
-0.01337143499404192,
0.014684551395475864,
0.012879966758191586,
0.02263619564473629,
-0.015409382991492748,
0.013549736700952053,
-0.02808479778468609,
0.0019236467778682709,
-0.05636400729417801,
0.0001676416432019323,
0.004584021400660276,
0.00008212133980123326,
0.0035058537032455206,
0.04079016298055649,
-0.0076368870213627815,
0.01801382564008236,
0.010680210776627064,
0.030386880040168762,
0.02211000584065914,
-0.03415326029062271,
-0.06029115244746208,
-0.002281919354572892,
0.048228029161691666,
0.011832544580101967,
-0.013117657974362373,
-0.004119229968637228,
-0.0653647929430008,
-0.04306444153189659,
0.0689108818769455,
0.003934384323656559,
0.04841998964548111,
-0.014810617081820965,
0.015412251465022564,
-0.02533681131899357,
-0.022335661575198174,
-0.004817349836230278,
0.027031920850276947,
0.012913359329104424,
0.051485367119312286,
-0.0031542940996587276,
-0.023892994970083237,
-0.006029745098203421,
0.02944648265838623,
0.02337639592587948,
0.04298069700598717,
0.01450697984546423,
-0.02432144619524479,
-0.008766351267695427,
0.03357096016407013,
-0.006129097193479538,
-0.05849258229136467,
0.028457675129175186,
0.010754845105111599,
-0.01077261008322239,
0.06979244202375412,
0.012603351846337318,
-0.011694252490997314,
0.021287985146045685,
0.01119505986571312,
-0.01785947196185589,
0.012918304651975632,
-0.02970445342361927,
0.05586014315485954,
0.05546557158231735,
0.035742707550525665,
0.04521181061863899,
0.004306841641664505,
-0.029451653361320496,
0.020737355574965477,
-0.047321781516075134,
0.030897554010152817,
-0.03868377208709717,
0.05756166949868202,
-0.02052716165781021,
-0.020746314898133278,
-0.02821427211165428,
0.03126306086778641,
0.00012251095904503018,
0.015632696449756622,
-0.01901288703083992,
-0.02122064307332039,
0.026671327650547028,
0.017757775261998177,
0.00446352269500494,
0.003805202664807439,
0.01724487543106079,
0.021809738129377365,
0.053100232034921646,
0.003052393440157175,
-0.003552556736394763,
0.018743006512522697,
-0.02673707902431488,
0.017152097076177597,
-0.020763449370861053,
-0.007577499374747276,
-0.03124277852475643,
-0.0017407081322744489,
-0.00478130578994751,
-0.014833766967058182,
0.024963678792119026,
0.018783431500196457,
0.01922108605504036,
-0.02545679546892643,
-0.0546729601919651,
0.005404374096542597,
-0.03364384174346924,
-0.04727360978722572,
-0.011992217041552067,
-0.029547901824116707,
0.04324975237250328,
0.009086166508495808,
-0.009731783531606197,
-0.06636540591716766,
-0.05079614743590355,
-0.01718638278543949,
0.03718819469213486,
-0.02631046250462532,
-0.022799396887421608,
0.026724036782979965,
-0.026193436235189438,
-0.006924053188413382,
0.0095067098736763,
0.027525784447789192,
-0.01615176908671856,
0.016174687072634697,
0.03185054659843445,
0.02126367576420307,
0.07350944727659225,
0.029026923701167107,
0.000623342813923955,
-0.001037649461068213,
-0.020487768575549126,
-0.008069219999015331,
-0.008606623858213425,
-0.022634873166680336,
-0.029570385813713074,
0.004982830490916967,
-0.01282587368041277,
-0.001216204254887998,
0.058363039046525955,
-0.05958324298262596,
-0.017470942810177803,
0.02287030592560768,
0.020740922540426254,
0.02831653505563736,
-0.02461215853691101,
-0.007497590500861406,
-0.005262901075184345,
0.02403111755847931,
-0.0029750701505690813,
0.02234397456049919,
-0.008863251656293869,
-0.04547378048300743,
0.03172450512647629,
0.0371890589594841,
-0.007418106775730848,
0.023873502388596535,
0.04592270776629448,
-0.03688018023967743,
-0.0035124425776302814,
0.013223553076386452,
-0.0504927821457386,
0.007731984835118055,
-0.017248699441552162,
0.010601790621876717,
0.02786594070494175,
0.012950153090059757,
-0.055749665945768356,
-0.05142790079116821,
-0.03509485349059105,
-0.010008728131651878,
0.07335306704044342,
-0.03463722765445709,
0.01838018000125885,
-0.02758261002600193,
-0.028905801475048065,
0.010617957450449467,
0.028364505618810654,
-0.03693479672074318,
0.002283642301335931,
-0.020864827558398247,
0.037468601018190384,
-0.043045204132795334,
-0.030669650062918663,
0.018601268529891968,
0.030826861038804054,
-0.02217288501560688,
0.03797518089413643,
0.012924333103001118,
0.005482952110469341,
0.004118083976209164,
-0.01701894961297512,
-0.03466160595417023,
0.07256070524454117,
-0.06343818455934525,
0.03213846683502197,
-0.011760503984987736,
-0.017127666622400284,
0.02796262502670288,
0.05838143825531006,
0.03291533887386322,
-0.020439885556697845,
-0.04174213856458664,
-0.03417738899588585,
0.054621484130620956,
-0.001745350775308907,
0.017371781170368195,
0.028574420139193535,
-0.030535418540239334,
0.0008389227441512048,
-0.007933974266052246,
0.027498403564095497,
-0.029608620330691338,
-0.060322992503643036,
-0.027389932423830032,
-0.03553706780076027,
-0.018730035051703453,
0.033478252589702606,
0.03496144339442253,
-0.03815561532974243,
0.036313608288764954,
-0.007464283145964146,
0.07616577297449112,
0.026855099946260452,
0.029651498422026634,
-0.029836229979991913,
0.04458818957209587,
0.007155157160013914,
0.05151587352156639,
-0.009077745489776134,
0.00381393451243639,
0.13616204261779785,
0.03545644134283066,
0.03580419346690178,
-0.07580513507127762,
0.03416690602898598,
-0.008931373246014118,
0.009355561807751656,
-0.0362323559820652,
0.05169646441936493,
0.003110298188403249,
0.004333551041781902,
0.012517942115664482,
0.08526793867349625,
-0.03688851743936539,
-0.014510572887957096,
0.01592598669230938,
-0.013929628767073154,
-0.013253883458673954,
0.012691996060311794,
-0.0017741295741871,
-0.01545489951968193,
-0.016247233375906944,
-0.005812652874737978,
0.032773472368717194,
0.02237180806696415,
-0.02185714617371559,
-0.013412061147391796,
0.0008290478144772351,
0.010755592957139015,
0.0534990057349205,
-0.02988719753921032,
0.004084052983671427,
-0.012600606307387352,
-0.036724019795656204,
0.0034464511554688215,
-0.02013571932911873,
0.007717407774180174,
0.005925826262682676,
0.02954617701470852,
0.044110286980867386,
-0.017292171716690063,
0.000731356383766979,
-0.02300138771533966,
0.006680267862975597,
-0.01782081089913845,
-0.03264208510518074,
-0.007133716717362404,
0.03238070756196976,
-0.05172185227274895,
0.05976371094584465,
0.005866258405148983,
-0.003497340716421604,
0.060354627668857574,
-0.048694875091314316,
0.004053909331560135,
0.0047526173293590546,
-0.004623753949999809,
-0.013221284374594688,
-0.0017215167172253132,
-0.0029735181014984846,
0.04388280212879181,
0.004433765541762114,
0.0081702945753932,
0.007360574323683977,
-0.03906363248825073,
-0.047950055450201035,
0.030056249350309372,
0.03400419279932976,
0.008617429994046688,
-0.018179768696427345,
-0.060010600835084915,
0.0030018335673958063,
0.005745657719671726,
-0.030113382264971733,
-0.03773429989814758,
0.018943054601550102,
0.04582565650343895,
-0.05983274430036545,
-0.0233186986297369,
0.02127910777926445,
-0.017528090626001358,
-0.010455411858856678,
-0.02547823265194893,
-0.004903423134237528,
-0.041312191635370255,
0.010388043709099293,
0.018008848652243614,
0.04415887966752052,
0.017959553748369217,
0.0011621515732258558,
-0.029038192704319954,
0.05942847579717636,
0.0026079402305185795,
-0.05605625361204147,
0.0322401225566864,
-0.02724175527691841,
-0.04013965278863907,
-0.019635742530226707,
-0.02045566961169243,
0.02500632219016552,
-0.0006012307130731642,
-0.012426367960870266,
0.012823838740587234,
0.05164311081171036,
0.03880804032087326,
0.02882053144276142,
0.03326801210641861,
-0.01475225854665041,
0.00813374575227499,
0.016036584973335266,
-0.013242701068520546,
-0.03663831949234009,
-0.044312335550785065,
0.017882222309708595,
0.016134299337863922,
0.02201305888593197,
0.00455654039978981,
-0.051419466733932495,
-0.02796001359820366,
-0.027249453589320183,
0.0017579098930582404,
-0.051362838596105576,
-0.003405946074053645,
-0.01656889170408249,
0.012711365707218647,
0.012563969008624554,
0.02169208601117134,
0.02082008123397827,
0.0001565889542689547,
-0.029948420822620392,
-0.033656056970357895,
0.030084596946835518,
-0.011106865480542183,
-0.004105078522115946,
-0.044331930577754974,
0.02518116869032383,
0.019416455179452896,
0.02101118676364422,
-0.03214734047651291,
-0.03629711642861366,
-0.014789187349379063,
0.010592278093099594,
-0.04690856486558914,
-0.022350527346134186,
-0.00902567245066166,
-0.009086714126169682,
0.04508250206708908,
-0.021802177652716637,
-0.04546453058719635,
0.04477115347981453,
-0.011178696528077126,
-0.03236845135688782,
-0.008032971061766148,
0.014099124819040298,
0.010167943313717842,
-0.02493532933294773,
-0.0038693302776664495,
-0.012274534441530704,
0.029271995648741722,
0.01246060710400343,
0.0032864718232303858,
0.010630935430526733,
-0.047131508588790894,
-0.020485637709498405,
-0.029687384143471718,
-0.03259249031543732,
-0.016034649685025215,
0.028463395312428474,
-0.018215684220194817,
0.05500524491071701,
-0.017995458096265793,
0.0034625129774212837,
0.03143242374062538,
0.014671562239527702,
-0.08992177248001099,
-0.029221639037132263,
0.022895876318216324,
-0.017279937863349915,
0.04041805863380432,
-0.0208001509308815,
0.0018415047088637948,
0.010631551034748554,
-0.06986741721630096,
0.011600605212152004,
-0.032064639031887054,
-0.0009528989321552217,
-0.058912646025419235,
0.007234690245240927,
-0.03856159746646881,
0.006097469944506884,
0.011985914781689644,
0.061056334525346756,
0.00872484315186739,
0.019308382645249367,
-0.012139144353568554,
0.016282368451356888,
0.009259029291570187,
-0.03286392241716385,
-0.022508451715111732,
-0.025982148945331573,
0.08798478543758392,
-0.02127779647707939,
-0.06859014183282852,
-0.004448531661182642,
0.018521353602409363,
0.002943187253549695,
0.011683131568133831,
-0.017917105928063393,
0.006124898325651884,
0.02132584899663925,
0.05791940912604332,
-0.009084654040634632,
-0.019386786967515945,
0.021425487473607063,
-0.008123788051307201,
-0.001206814544275403,
-0.013548585586249828,
0.02162293717265129,
0.01169201172888279,
-0.03142509609460831,
-0.023082982748746872,
0.021376052871346474,
-0.027586281299591064,
0.004850081168115139,
-0.04009789973497391,
0.026620950549840927,
0.038037605583667755,
-0.006815008819103241,
-0.01959620974957943,
-0.027071069926023483,
-0.005226754117757082,
0.055864762514829636,
0.014802690595388412,
-0.031247831881046295,
0.037289589643478394,
0.001188428490422666,
-0.067376047372818,
-0.00316764903254807,
0.007140368688851595,
-0.00017459416994825006,
-0.031376902014017105,
-0.03244483843445778,
-0.006985251326113939,
-0.0034374170936644077,
0.017905162647366524,
-0.010299157351255417,
-0.005247476510703564,
0.041226133704185486,
-0.016882581636309624,
0.07424310594797134,
-0.003793200245127082,
-0.04913764446973801,
-0.010725446045398712,
-0.015563133172690868,
0.02506127767264843,
-0.03292730823159218,
-0.008850368671119213,
-0.002956836484372616,
0.010217140428721905,
0.0010242629796266556,
0.029002083465456963,
0.05934471637010574,
0.0006480151205323637,
0.01491278875619173,
-0.02695203758776188,
0.024554967880249023,
0.02866329997777939,
-0.0003902457538060844,
0.005297505296766758,
-0.002832840895280242,
0.038701120764017105,
0.03206497058272362,
0.01839088834822178,
-0.04114001989364624,
-0.003855304094031453,
0.03443193808197975,
0.0029575887601822615,
-0.011182437650859356,
-0.014343313872814178,
-0.04281940683722496,
0.05223330855369568,
-0.00360209122300148,
0.0018914388492703438,
0.0641305148601532,
-0.01934989169239998,
0.027180174365639687,
0.03366883844137192,
-0.009173493832349777,
-0.017998896539211273,
0.03166846185922623,
-0.03952299430966377,
-0.025075701996684074,
0.002324208151549101,
0.007496475242078304,
0.043887410312891006,
-0.023802531883120537,
-0.013341296464204788,
0.00019183587573934346,
-0.031118612736463547,
-0.026608247309923172,
0.005582825746387243,
-0.02169846184551716,
0.04865407198667526,
-0.006821902934461832,
-0.012747560627758503,
0.044049251824617386,
0.019898567348718643,
0.040659595280885696,
0.05138259381055832,
0.037536509335041046,
0.012924066744744778,
0.0472329705953598,
0.0178566575050354,
-0.042623136192560196,
0.00883319042623043,
-0.02163507044315338,
0.08387347310781479,
-0.05883483216166496,
-0.009870004840195179,
-0.014156460762023926,
-0.05509407818317413,
0.017942342907190323,
0.00943814218044281,
0.0010390672832727432,
0.07761338353157043,
-0.02551036700606346,
-0.04237979277968407,
-0.013626132160425186,
-0.029600655660033226,
-0.03646470606327057,
0.035753220319747925,
-0.018697500228881836,
0.07102964073419571,
0.00988365150988102,
0.021908678114414215,
-0.020264793187379837,
-0.0005669939564540982,
0.010381405241787434,
-0.0436173677444458,
0.0020838850177824497,
-0.012108337134122849,
0.002110761823132634,
0.014917909167706966,
-0.037204574793577194,
-0.0496668815612793,
-0.042417533695697784,
0.029696820303797722,
0.04287651181221008,
0.042860958725214005,
-0.01564016565680504,
-0.02955859899520874,
-0.03368060290813446,
0.024650555104017258,
-0.043553609400987625,
0.025739924982190132,
-0.013984708115458488,
-0.004717654082924128,
-0.005313545931130648,
0.015734894201159477
] |
<p>I acknowledge that this question is quite trivial. But in the lattice jargon, what does a $N$-sites lattice mean?</p>
<ul>
<li>it's a lattice $N\times N$ or</li>
<li>it's a lattice with $N$ vertices? </li>
<li>another option perhaps.</li>
</ul>
<p>From the context I cannot infer it. I just know that $N$ is quite large, i.e. in the thermodynamic limit $N\to \infty$, one also has $N^2\to\infty$ and $N^{1/2}\to\infty$.</p>
<hr>
<p><em>Edit:</em> The lattice is in 2D.</p>
| 8,329 |
[
-0.0010409229435026646,
-0.010959114879369736,
0.004574847407639027,
-0.04313251003623009,
0.007920029573142529,
0.023769471794366837,
-0.030164076015353203,
-0.01833946444094181,
-0.04248419031500816,
-0.042218632996082306,
0.03259644657373428,
0.02681354060769081,
0.0496169738471508,
0.015049860812723637,
-0.01674473285675049,
0.04032301902770996,
-0.036028072237968445,
-0.004428528714925051,
-0.0073700170032680035,
-0.015908367931842804,
0.05968267098069191,
0.006041755899786949,
-0.01815185509622097,
0.005335498135536909,
-0.02699318341910839,
0.021070344373583794,
0.023146919906139374,
0.003535587340593338,
0.02516406588256359,
0.05497865006327629,
-0.0007920162170194089,
-0.06638126075267792,
0.055678509175777435,
0.03938286751508713,
0.012762577272951603,
-0.013637122698128223,
-0.032562434673309326,
0.0007706084288656712,
0.026832135394215584,
0.035754308104515076,
-0.024470267817378044,
-0.03468983247876167,
0.0038478488568216562,
0.019106963649392128,
-0.020886622369289398,
0.008263545110821724,
0.004807602614164352,
-0.05106543377041817,
0.037068720906972885,
-0.04854819178581238,
0.061933331191539764,
0.017725590616464615,
0.029146883636713028,
0.017969714477658272,
0.034615807235240936,
-0.013699435628950596,
0.05181853473186493,
0.028903348371386528,
-0.008084708824753761,
-0.04043305292725563,
-0.024480970576405525,
-0.008606498129665852,
0.034476883709430695,
-0.021564744412899017,
-0.002667887369170785,
0.008985520340502262,
0.0021241114009171724,
-0.029850510880351067,
-0.005884405225515366,
0.0037660980597138405,
-0.020031843334436417,
0.013159160502254963,
0.058914896100759506,
-0.01567644625902176,
0.011146023869514465,
0.00018063242896459997,
-0.006801072042435408,
0.0068217432126402855,
0.031221313402056694,
0.008654780685901642,
-0.04183093085885048,
0.020843254402279854,
0.02958400920033455,
-0.00888918712735176,
-0.022194284945726395,
-0.031984228640794754,
0.059726033359766006,
0.00877965334802866,
0.009332181885838509,
0.0254837479442358,
0.0021299896761775017,
-0.0017881648382171988,
0.05220387503504753,
-0.0601373054087162,
-0.0418735109269619,
-0.012287621386349201,
0.02405208721756935,
0.016641773283481598,
0.002191860694438219,
-0.03262743353843689,
-0.0256072748452425,
-0.059784118086099625,
0.00034804598544724286,
0.05634307116270065,
-0.012115741148591042,
0.01223225798457861,
-0.05999790132045746,
-0.0024748300202190876,
-0.018601644784212112,
-0.0030635343864560127,
-0.03713766857981682,
0.04699745401740074,
0.009991967119276524,
0.03654715418815613,
-0.012844891287386417,
-0.03683137893676758,
-0.0022753789089620113,
0.008300083689391613,
0.029301274567842484,
0.06693015992641449,
0.024724852293729782,
-0.017202166840434074,
0.039508331567049026,
-0.01917666383087635,
-0.14459344744682312,
0.04752884805202484,
0.03279216215014458,
0.014707467518746853,
-0.024417610839009285,
0.009993942454457283,
0.027581635862588882,
0.022451087832450867,
-0.011766931042075157,
-0.018862059339880943,
0.062291763722896576,
0.021944386884570122,
-0.06811855733394623,
-0.02758825197815895,
0.06005736440420151,
-0.011935185641050339,
-0.01756327413022518,
-0.08203256875276566,
0.03593466058373451,
0.04011563956737518,
0.08111348748207092,
0.011599615216255188,
0.013544166460633278,
-0.004223524127155542,
0.02619370073080063,
-0.017345502972602844,
-0.03812200576066971,
-0.0013342478778213263,
-0.006385414395481348,
-0.047668322920799255,
0.03536120429635048,
-0.022289397194981575,
0.07664483040571213,
0.04565909132361412,
0.028263473883271217,
-0.0025950444396585226,
0.060044147074222565,
-0.012559560127556324,
0.00010902509529842064,
0.03870857134461403,
0.008903072215616703,
-0.010978062637150288,
0.09192975610494614,
-0.01803351379930973,
0.04736621677875519,
0.060146231204271317,
-0.030571015551686287,
0.011998262256383896,
0.015652012079954147,
0.058140430599451065,
0.06662458181381226,
0.029337136074900627,
-0.01261899620294571,
-0.02263215184211731,
0.0007489336421713233,
0.026080584153532982,
-0.050383735448122025,
-0.012271184474229813,
0.039444781839847565,
0.02067851833999157,
-0.010054613463580608,
0.05075645074248314,
-0.016062723472714424,
-0.026549801230430603,
0.007737752981483936,
-0.009429781697690487,
-0.017993422225117683,
-0.07204403728246689,
-0.0015852601500228047,
-0.024249589070677757,
0.0017326993402093649,
0.028966017067432404,
0.025747032836079597,
-0.0332118459045887,
-0.04240143299102783,
-0.020206764340400696,
-0.03450235351920128,
0.02769724652171135,
0.023877210915088654,
-0.015291730873286724,
0.024750033393502235,
0.048507917672395706,
0.04190465807914734,
-0.004232089035212994,
0.03812559321522713,
-0.034959930926561356,
-0.0036913712974637747,
0.004852540325373411,
-0.037239063531160355,
0.05551890656352043,
-0.03620394319295883,
-0.013656954281032085,
0.0039517758414149284,
0.010988886468112469,
-0.010471529327332973,
0.03193357586860657,
-0.029947500675916672,
0.04313582926988602,
0.05202263593673706,
-0.02282276377081871,
-0.023427827283740044,
0.01521853543817997,
0.0017358368495479226,
0.015757698565721512,
-0.03718147054314613,
-0.03041594848036766,
-0.06873233616352081,
-0.02827700786292553,
0.05038245767354965,
0.05767300724983215,
-0.03253895044326782,
0.009703336283564568,
0.013883538544178009,
0.04776190593838692,
0.00655814865604043,
-0.0014502429403364658,
-0.06495925039052963,
-0.011111103929579258,
0.021929696202278137,
-0.007159634493291378,
-0.003758318955078721,
0.021046852692961693,
-0.018855461850762367,
0.03607938438653946,
0.011913378722965717,
-0.007973028346896172,
-0.02182677388191223,
0.04994674026966095,
-0.03202442824840546,
0.013389271683990955,
-0.005618542432785034,
-0.012313290499150753,
-0.002586008282378316,
-0.0011813252931460738,
0.019560709595680237,
0.0022151682060211897,
-0.002629055641591549,
0.03519623354077339,
-0.031171852722764015,
-0.004769929684698582,
0.00012506169150583446,
0.011615712195634842,
-0.04624729976058006,
-0.03277258202433586,
0.035588640719652176,
-0.01808282732963562,
0.008628890849649906,
-0.0020348099060356617,
-0.02460741065442562,
0.022207332774996758,
0.019360121339559555,
0.02443406544625759,
-0.012921894900500774,
0.011489195749163628,
-0.04154661297798157,
-0.0534432977437973,
0.003520614467561245,
-0.04595143347978592,
0.03952280804514885,
0.014024999924004078,
-0.004339982755482197,
0.019740968942642212,
-0.03883873298764229,
-0.03987649828195572,
-0.0035662550944834948,
0.0026129367761313915,
0.018122060224413872,
-0.008497641421854496,
-0.014136056415736675,
-0.046176593750715256,
0.005378918256610632,
-0.02770029939711094,
0.03675895556807518,
-0.009685177356004715,
-0.013780179433524609,
0.042961034923791885,
-0.012944183312356472,
-0.039199721068143845,
-0.024010706692934036,
-0.037709690630435944,
-0.028733767569065094,
-0.02804609015583992,
0.002510763704776764,
0.044990938156843185,
-0.04954378306865692,
0.010981534607708454,
0.01881757564842701,
-0.010310524143278599,
0.019459817558526993,
-0.026919515803456306,
-0.07700570672750473,
-0.013290760107338428,
-0.03211328014731407,
0.039507895708084106,
-0.010985524393618107,
-0.02189592272043228,
0.08167049288749695,
0.01845487393438816,
-0.021335657685995102,
0.022300031036138535,
-0.015142914839088917,
-0.006688239052891731,
-0.06724659353494644,
0.04371911287307739,
0.011737980879843235,
-0.020854048430919647,
0.041399452835321426,
0.020599743351340294,
0.04304748401045799,
0.06326429545879364,
0.010901957750320435,
-0.0009398683323524892,
0.019134867936372757,
0.010233445093035698,
0.014842716977000237,
0.04203358665108681,
-0.010541873052716255,
-0.010203395038843155,
0.0034583976957947016,
-0.020948700606822968,
0.018282044678926468,
0.01327002514153719,
-0.054318614304065704,
0.03938250243663788,
-0.009013372473418713,
0.0025908288080245256,
-0.02030894346535206,
0.04580521583557129,
0.004780219402164221,
-0.00957535207271576,
0.013398278504610062,
0.03439563140273094,
0.05621664598584175,
-0.03254782781004906,
0.01610422506928444,
-0.015238066203892231,
0.047742776572704315,
-0.048759981989860535,
-0.0004756296693813056,
0.025121575221419334,
-0.0056236013770103455,
-0.016370218247175217,
0.013525038957595825,
-0.03740714490413666,
0.007077762857079506,
0.01928112655878067,
0.005993448197841644,
0.01975967548787594,
-0.006602682638913393,
0.015266030095517635,
-0.055451031774282455,
-0.007563860155642033,
-0.02061518467962742,
0.033285826444625854,
-0.0349138118326664,
0.021121373400092125,
-0.0003652114246506244,
0.0005476032383739948,
0.03319358825683594,
0.018498532474040985,
-0.05265634134411812,
-0.03356738016009331,
0.005870273802429438,
0.03167311102151871,
-0.008713867515325546,
-0.019963450729846954,
0.02164790779352188,
0.003741266205906868,
-0.021491501480340958,
0.033499013632535934,
0.00666552921757102,
-0.07392977178096771,
0.010558473877608776,
-0.034309159964323044,
-0.00043895922135561705,
-0.00399826793000102,
0.03727957606315613,
0.04352312535047531,
-0.05345730856060982,
0.010842411778867245,
0.010669215582311153,
-0.0269747544080019,
0.004865310154855251,
0.021398816257715225,
0.004889873322099447,
0.012935800477862358,
-0.0032265479676425457,
0.019578084349632263,
0.041235122829675674,
-0.005355464294552803,
0.010435564443469048,
-0.004180857911705971,
0.0535239540040493,
0.012178933247923851,
-0.0035202743019908667,
-0.003730291733518243,
-0.05092626065015793,
0.020151222124695778,
0.0013904809020459652,
0.05520905926823616,
0.002870772033929825,
0.03236989304423332,
0.07224462926387787,
-0.005280381999909878,
0.0029845607932657003,
0.02754896879196167,
0.026163486763834953,
0.01832251437008381,
-0.0361018180847168,
-0.011896785348653793,
-0.03554306924343109,
-0.015023174695670605,
0.010223754681646824,
0.013635143637657166,
-0.013676553964614868,
-0.026836030185222626,
0.007522662170231342,
0.019389083608984947,
-0.0036305831745266914,
-0.04377831518650055,
-0.003807868342846632,
-0.031081872060894966,
0.0486568883061409,
0.018486585468053818,
-0.020621664822101593,
-0.04865996167063713,
0.0114130275323987,
0.020722683519124985,
0.015372591093182564,
-0.025501221418380737,
-0.07533905655145645,
-0.0009894280228763819,
0.03599683940410614,
0.01977686397731304,
0.008974018506705761,
-0.0022753411903977394,
-0.017955724149942398,
0.0024725256953388453,
0.03557379171252251,
-0.02642059326171875,
0.00553910480812192,
-0.01732347346842289,
-0.031282685697078705,
-0.017341556027531624,
-0.01971028931438923,
0.002259679604321718,
-0.05517731234431267,
0.014910337515175343,
0.03344148024916649,
0.000020718487576232292,
0.011775976978242397,
-0.016450775787234306,
-0.007270383648574352,
0.02277059108018875,
0.03285092115402222,
0.020301533862948418,
0.01852315291762352,
0.018161555752158165,
0.030196165665984154,
-0.012963746674358845,
-0.055060774087905884,
0.03569215536117554,
0.052933041006326675,
-0.015382546931505203,
0.02712012268602848,
-0.0757242813706398,
-0.04671689495444298,
0.024632781744003296,
-0.004491847939789295,
-0.03636280447244644,
0.002197920111939311,
0.005456586368381977,
0.05180909484624863,
0.03211898356676102,
0.011385934427380562,
0.049193862825632095,
0.03372524306178093,
0.008012612350285053,
0.015246931463479996,
-0.03939174860715866,
0.03381004557013512,
-0.04166112095117569,
0.02165188267827034,
-0.040595777332782745,
0.0024652560241520405,
-0.023561231791973114,
0.03207211568951607,
-0.017301252111792564,
0.042420465499162674,
-0.010582308284938335,
-0.06071542948484421,
-0.018383624032139778,
0.0270694587379694,
0.026701532304286957,
0.006867803167551756,
-0.026540515944361687,
0.0017031936440616846,
0.0490957535803318,
-0.026693658903241158,
0.004360431805253029,
-0.016951784491539,
0.02988283894956112,
-0.014915037900209427,
0.01470604632049799,
-0.00007621195982210338,
-0.04168826714158058,
0.02109387144446373,
0.007623899728059769,
-0.04201364144682884,
0.06849750876426697,
-0.02059353142976761,
0.005762724205851555,
-0.01050560548901558,
-0.05180132016539574,
-0.04617739096283913,
-0.014816470444202423,
-0.0018357840599492192,
-0.0109900226816535,
-0.012714062817394733,
0.02331269159913063,
0.0022719448897987604,
0.024977123364806175,
-0.07770741730928421,
-0.034273695200681686,
0.017485236749053,
-0.008425992913544178,
-0.035080987960100174,
-0.020886393263936043,
-0.022385546937584877,
-0.012778759002685547,
-0.025886304676532745,
0.005501599982380867,
0.05600928142666817,
-0.006234797649085522,
-0.0250009223818779,
0.027066148817539215,
0.048058442771434784,
0.06591875851154327,
0.009645486250519753,
-0.025748297572135925,
0.01293561514467001,
0.01974303461611271,
0.00015038691344670951,
-0.02134373039007187,
0.02063293196260929,
-0.03218832612037659,
0.00600638659670949,
-0.027062641456723213,
-0.031817082315683365,
0.038654547184705734,
-0.03288145735859871,
0.01893211342394352,
0.012804453261196613,
0.012690505012869835,
-0.011640834622085094,
-0.017492808401584625,
-0.011264045722782612,
0.004407402127981186,
0.05021810531616211,
-0.010799305513501167,
-0.007576348725706339,
0.02617979608476162,
-0.008000711910426617,
0.009291802532970905,
0.01012479979544878,
0.010136276483535767,
0.02158401347696781,
0.07079759985208511,
-0.012100305408239365,
-0.012271972373127937,
0.015462728217244148,
-0.047589290887117386,
-0.003114605788141489,
0.018283521756529808,
0.006047358736395836,
0.029047507792711258,
0.034698694944381714,
-0.01338755339384079,
-0.05066680908203125,
-0.05813007056713104,
0.0267304927110672,
0.03796821087598801,
-0.03688681870698929,
-0.0013829927193000913,
0.014833266846835613,
-0.00813563633710146,
0.03351477161049843,
-0.02638683095574379,
-0.014079120010137558,
0.04552989825606346,
-0.012147833593189716,
0.05907716602087021,
-0.046500399708747864,
-0.03145970031619072,
0.03651416301727295,
0.016131103038787842,
-0.0008503181743435562,
0.0240797009319067,
0.011744797229766846,
0.002835174323990941,
0.005711914040148258,
-0.009549289010465145,
-0.021537208929657936,
0.06324345618486404,
-0.05282792076468468,
0.002743672812357545,
-0.001185459434054792,
-0.010710551403462887,
0.05285050719976425,
0.0011470010504126549,
0.0255430955439806,
-0.0409415178000927,
0.001694725826382637,
-0.04222221300005913,
0.010016297921538353,
-0.008086842484772205,
0.014985894784331322,
-0.014903688803315163,
-0.00466266181319952,
0.009835934266448021,
0.010947325266897678,
-0.0009884039172902703,
0.011438167653977871,
-0.04150615260004997,
-0.007514328230172396,
-0.01394991111010313,
-0.036468882113695145,
-0.006258619949221611,
0.004720381926745176,
-0.020241213962435722,
-0.002893465803936124,
-0.051310598850250244,
0.00861066672950983,
-0.006712025962769985,
0.054308436810970306,
-0.049044620245695114,
0.06610093265771866,
0.01072020921856165,
0.06113935634493828,
0.011027599684894085,
0.015556572936475277,
0.10534704476594925,
0.08177104592323303,
0.012333323247730732,
-0.0780247375369072,
0.026229331269860268,
0.008069368079304695,
0.021002715453505516,
-0.030929528176784515,
-0.051559943705797195,
0.036826860159635544,
0.0014186936896294355,
0.04060637205839157,
0.05886665731668472,
-0.028047922998666763,
-0.014493945986032486,
0.029978668317198753,
-0.04312322288751602,
-0.025933057069778442,
0.0019054746953770518,
-0.010832738131284714,
-0.011530015617609024,
0.013161255046725273,
-0.047145020216703415,
0.009541231207549572,
0.035542767494916916,
0.024261485785245895,
-0.03527083992958069,
-0.010370343923568726,
0.03928089514374733,
0.05799651890993118,
-0.009290344081819057,
-0.0037123365327715874,
-0.01084507629275322,
-0.03726337477564812,
-0.028291327878832817,
-0.00260918028652668,
-0.011337385512888432,
0.015368377789855003,
0.018860310316085815,
0.061645980924367905,
-0.021410806104540825,
0.004011263605207205,
0.020260121673345566,
0.015284540131688118,
-0.04339586943387985,
-0.037554167211055756,
-0.0010827332735061646,
0.0006035587284713984,
-0.008643431589007378,
0.009584165178239346,
-0.013210237957537174,
0.013295972719788551,
0.03177084028720856,
-0.0005984855815768242,
0.005998979788273573,
0.007023463025689125,
0.04091173782944679,
-0.040326476097106934,
-0.05759581923484802,
-0.021882306784391403,
-0.011339553631842136,
-0.005936827976256609,
0.026400597766041756,
0.0016494236188009381,
-0.019794311374425888,
0.0303004439920187,
0.0028566850814968348,
0.0192953422665596,
0.02802228555083275,
-0.010487533174455166,
-0.01585652120411396,
0.02798325940966606,
-0.03266480565071106,
0.006820137612521648,
-0.03015795163810253,
-0.01703355275094509,
0.05217107757925987,
0.01552270632237196,
-0.036865200847387314,
-0.003650049911811948,
-0.01883741095662117,
-0.005938345566391945,
-0.0299634151160717,
-0.02239551581442356,
-0.008032424375414848,
0.003601746866479516,
-0.02444825880229473,
0.015353305265307426,
-0.010363162495195866,
0.008668722584843636,
-0.005645389668643475,
-0.003913690336048603,
0.044126108288764954,
-0.030502021312713623,
0.008305604569613934,
0.006661438848823309,
-0.052515704184770584,
-0.002734310692176223,
-0.017291028052568436,
0.025805344805121422,
0.033156346529722214,
-0.011120682582259178,
0.015004394575953484,
0.034070342779159546,
-0.0548456571996212,
-0.015238466672599316,
0.017516547814011574,
-0.024257611483335495,
0.033124133944511414,
0.05091329663991928,
-0.012062743306159973,
-0.0066150762140750885,
-0.041781142354011536,
0.00855435710400343,
-0.0012162708444520831,
0.02847236394882202,
0.005335119552910328,
-0.023738998919725418,
-0.03757496550679207,
-0.03635932505130768,
0.014534245245158672,
-0.040960218757390976,
-0.057450491935014725,
-0.06285416334867477,
-0.015735333785414696,
0.05489519238471985,
0.041286490857601166,
0.003848137566819787,
-0.0034819780848920345,
-0.007270187605172396,
-0.053695037961006165,
-0.0019172673346474767,
0.056075405329465866,
-0.02286509983241558,
-0.051309388130903244,
-0.02187901735305786,
0.04225130006670952,
0.042972154915332794,
-0.02919529750943184,
-0.024701282382011414,
0.03067183308303356,
-0.02874637395143509,
-0.038117747753858566,
0.0022109332494437695,
-0.00373871554620564,
0.028892172500491142,
0.026158349588513374,
-0.007384990807622671,
-0.054105550050735474,
0.06616655737161636,
-0.06875050067901611,
-0.00944904237985611,
-0.021319860592484474,
-0.048822589218616486,
-0.01684214547276497,
-0.05411123111844063,
-0.012350820936262608,
0.01547493040561676,
-0.006823376752436161,
0.009359546937048435,
0.028290726244449615,
-0.013469981960952282,
-0.02214731089770794,
-0.0064973607659339905,
-0.0006641020299866796,
0.027726300060749054,
0.012724941596388817,
0.0273845586925745,
0.017840001732110977,
0.061787642538547516,
-0.04389104247093201,
0.011124944314360619,
0.009530453942716122,
-0.015874521806836128,
-0.06634693592786789,
0.0006164339720271528,
0.0413324311375618,
0.0015451476210728288,
0.017176002264022827,
-0.07573087513446808,
-0.0034013246186077595,
0.028666965663433075,
-0.06760182976722717,
0.03638816997408867,
0.021176554262638092,
-0.06385913491249084,
-0.062285248190164566,
-0.005628358572721481,
-0.0519334152340889,
0.022845113649964333,
0.02674856409430504,
0.05803227052092552,
-0.00010327121708542109,
0.023546423763036728,
-0.062438156455755234,
-0.02296523191034794,
0.04648160561919212,
0.03635788336396217,
-0.02174212969839573,
-0.041193243116140366,
0.03994782641530037,
0.0005025918362662196,
-0.03278222307562828,
0.02754027210175991,
-0.02947090193629265,
-0.0013049525441601872,
0.02275172434747219,
0.006364886648952961,
-0.015939995646476746,
0.01367682870477438,
0.03753916546702385,
-0.02092658542096615,
-0.017041213810443878,
0.015063285827636719,
0.02496953494846821,
0.025331731885671616,
-0.0008927410817705095,
0.020243166014552116,
0.02721118927001953,
-0.01758330874145031,
-0.020142842084169388,
0.06636322289705276,
-0.005507474299520254,
0.009680534712970257,
0.0004969895235262811,
-0.023024221882224083,
0.056147705763578415,
-0.035006556659936905,
0.007378637325018644,
-0.04581857845187187,
0.005126336123794317,
0.03051890805363655,
-0.02453497238457203,
-0.005033506080508232,
0.06806200742721558,
0.0017002832610160112,
-0.024967798963189125,
0.004483153577893972,
-0.005667989142239094,
-0.052868686616420746,
-0.08040890097618103,
-0.01825787127017975,
0.015158933587372303,
-0.022909605875611305,
0.0024203157518059015,
-0.016354667022824287,
-0.025784827768802643,
0.035580676048994064,
0.04158004745841026,
0.033641114830970764,
-0.014587664976716042,
-0.04852403327822685,
-0.01572314463555813,
-0.06120271980762482,
0.014568846672773361,
0.009013411588966846,
0.01846916414797306,
-0.05864202231168747,
-0.029302652925252914,
0.0428541861474514,
0.009281905367970467,
0.06847591698169708,
0.04292897507548332,
0.03360237926244736,
-0.010421548038721085,
0.03383519500494003,
0.038372281938791275,
-0.029031356796622276,
-0.0017385251121595502,
-0.007536666933447123,
-0.0023646624758839607,
-0.011311043985188007,
-0.012813909910619259,
-0.03374127298593521,
0.016278091818094254,
0.06145245581865311,
0.0013372903922572732,
-0.009633774869143963,
-0.012525225058197975,
-0.036308396607637405,
0.06020766496658325,
-0.010043418034911156,
0.012577848508954048,
0.049913085997104645,
-0.023340560495853424,
0.0017008375143632293,
0.04722467437386513,
-0.022762615233659744,
-0.01841457188129425,
-0.0028152514714747667,
-0.03204705938696861,
-0.014725837856531143,
-0.001323576900176704,
0.01650429517030716,
0.019917210564017296,
-0.04554528370499611,
-0.02045351266860962,
0.034043170511722565,
-0.0265293400734663,
-0.020217735320329666,
0.0025665052235126495,
0.0005287395906634629,
0.03818648308515549,
-0.02226639911532402,
-0.01798265241086483,
0.02706252783536911,
-0.0030167957302182913,
0.022698912769556046,
0.04469343647360802,
0.04799184948205948,
-0.011499645188450813,
0.016304820775985718,
0.00432092510163784,
-0.043278031051158905,
0.004234945867210627,
-0.007576600648462772,
-0.009859283454716206,
-0.06039271876215935,
-0.020229388028383255,
0.03436165675520897,
-0.034232135862112045,
0.029730504378676414,
0.026122286915779114,
-0.019317325204610825,
0.09344982355833054,
-0.02822529710829258,
0.02722878009080887,
-0.033269211649894714,
0.003949835430830717,
-0.032871440052986145,
-0.022926699370145798,
0.008331635035574436,
0.05517766252160072,
-0.03724600002169609,
-0.013782886788249016,
0.0032499409280717373,
-0.030450647696852684,
0.019606616348028183,
-0.037985894829034805,
0.033200621604919434,
0.013726864010095596,
-0.005888354033231735,
-0.0067127603106200695,
-0.010543255135416985,
-0.008741870522499084,
-0.0022932221181690693,
0.05396471917629242,
0.039097074419260025,
0.023904483765363693,
0.014803491532802582,
0.02399783581495285,
0.00907475221902132,
0.025922225788235664,
-0.04141892120242119,
-0.02699148841202259,
-0.039027947932481766,
0.010903263464570045,
0.029839178547263145,
-0.017577173188328743
] |
<p><img src="http://i.stack.imgur.com/DDuwM.png" alt="Hydrogen atom"></p>
<p>After seeing this photograph and reading this article : <a href="http://io9.com/the-first-image-ever-of-a-hydrogen-atoms-orbital-struc-509684901" rel="nofollow">The First Image Ever of a Hydrogen Atom's Orbital Structure</a></p>
<p>I was really happy to come to know that orbitals have actually been seen now, but it also made me wonder that how was the orbitals illuminated ? I know that when we send light through a colloidal solution its path is illuminated, but how could the experimental physicists who performed this experiment illuminate an atomic orbital. As I understand it is only a probability density rich region of finding the electron. How is it possible to see/detect a probability density wave ?</p>
<p>Addendum : I understand from the article that the nodal structure is inferred from the interference pattern observed, but how does the interference pattern account for nodal structure, also is this an experimental prove of the results of schrodinger wave equations ?</p>
<p>Addendum 2 : after struggling through this paper <a href="http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.110.213001" rel="nofollow">http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.110.213001</a>
I understood most of the experiment, and got stuck here, I understoot the electrons are ionised and then there interference patterns are observed, but how do the interference pattern represent the shapes of atomic orbitals ? Can the expirement be taken as a solid proof for the establishment of shapes of atomic orbitals ?</p>
| 8,330 |
[
-0.07388980686664581,
-0.017276864498853683,
0.035366687923669815,
-0.025215474888682365,
0.04814324900507927,
-0.017381643876433372,
-0.0320139154791832,
-0.05310362949967384,
0.021460067480802536,
-0.02974604070186615,
0.059706296771764755,
0.03137392923235893,
0.02738732099533081,
0.018315011635422707,
0.03166278451681137,
0.006295220460742712,
-0.0005808545392937958,
-0.03986961022019386,
-0.02749369852244854,
-0.01723056472837925,
0.007020634599030018,
-0.014561452902853489,
0.008540108799934387,
-0.009641111828386784,
-0.016437070444226265,
0.02491025999188423,
-0.010931776836514473,
-0.007708420045673847,
0.055765215307474136,
0.04720691591501236,
-0.013610095717012882,
-0.023782504722476006,
0.021772900596261024,
-0.03187033534049988,
0.011511572636663914,
0.003094525309279561,
-0.0016767192864790559,
-0.04909251257777214,
0.024905385449528694,
0.007917367853224277,
0.004860409069806337,
-0.04001550003886223,
-0.02459549903869629,
0.04519709199666977,
-0.03433651477098465,
-0.0012066449271515012,
0.0072850752621889114,
-0.03330501914024353,
0.03765840828418732,
-0.037283699959516525,
0.06303074955940247,
0.010820843279361725,
0.02784925326704979,
0.012563197873532772,
0.004524854011833668,
-0.0019842907786369324,
0.0268874429166317,
0.07568836212158203,
-0.0038567872252315283,
-0.049518365412950516,
-0.017218507826328278,
-0.03513171151280403,
-0.03139137476682663,
-0.006008997559547424,
-0.02315947599709034,
0.04857995733618736,
-0.00030838287784717977,
-0.06339999288320541,
0.04422933980822563,
0.012472094036638737,
0.009693106636404991,
0.01207863911986351,
0.0409470796585083,
0.0032002939842641354,
0.039011914283037186,
-0.007010847795754671,
0.01928318664431572,
-0.025052543729543686,
0.03494452312588692,
0.028937680646777153,
-0.01821676269173622,
0.021831337362527847,
-0.024082237854599953,
0.050602059811353683,
0.015357657335698605,
0.008947440423071384,
0.06026923656463623,
-0.04429539665579796,
0.0159896332770586,
0.011489522643387318,
-0.02596392296254635,
0.05378258228302002,
0.03862946480512619,
0.03868693858385086,
-0.02724764496088028,
0.033463284373283386,
0.003887203987687826,
0.05616440996527672,
0.0024496593978255987,
-0.030241649597883224,
0.02771167643368244,
-0.0300311092287302,
0.007789317052811384,
0.07583155483007431,
0.015524695627391338,
-0.009762361645698547,
-0.024489058181643486,
0.06130385026335716,
-0.01881083846092224,
0.01502369437366724,
0.007656158413738012,
0.04682333022356033,
0.031593240797519684,
0.012075420469045639,
-0.010237217880785465,
0.010019154287874699,
0.005892387591302395,
-0.01499175000935793,
0.036294594407081604,
0.07426644116640091,
-0.027976740151643753,
-0.004396046511828899,
0.0038664911407977343,
-0.06652478128671646,
-0.04391815513372421,
-0.007370983250439167,
0.03341089189052582,
0.04051695764064789,
-0.0013406721409410238,
0.028767134994268417,
0.015955761075019836,
0.0037091104313731194,
0.030873803421854973,
0.014384648762643337,
0.016715263947844505,
0.0054449643939733505,
-0.11950676143169403,
-0.03479438275098801,
0.03978016972541809,
0.016695888713002205,
-0.032619327306747437,
-0.06890415400266647,
0.037409111857414246,
0.04141837731003761,
0.07171556353569031,
-0.03511430323123932,
-0.011559807695448399,
-0.02649136446416378,
0.035009317100048065,
0.023072930052876472,
-0.001992250792682171,
-0.008792047388851643,
0.025967517867684364,
-0.04258828982710838,
-0.007578384596854448,
-0.037957049906253815,
0.021050341427326202,
0.008254269137978554,
0.018810177221894264,
-0.07345078885555267,
0.088215671479702,
-0.00927596352994442,
0.0002383640530752018,
-0.001058480585925281,
-0.015071445144712925,
-0.04032579064369202,
0.08948575705289841,
0.019605830311775208,
0.009634322486817837,
0.041533391922712326,
-0.02207879349589348,
0.0335647389292717,
-0.03328476473689079,
0.015553930774331093,
-0.023629730567336082,
-0.05370258912444115,
0.0019810288213193417,
-0.01957855559885502,
0.026653101667761803,
-0.017293039709329605,
-0.000055915374105097726,
-0.01996796391904354,
-0.0014875021297484636,
0.04425741359591484,
0.01932981237769127,
0.06049071252346039,
-0.006016538944095373,
-0.0429670624434948,
-0.021325912326574326,
-0.05320340022444725,
0.00447090296074748,
-0.05266944319009781,
0.01850901171565056,
0.002313910750672221,
-0.010791071690618992,
0.052466895431280136,
-0.023494970053434372,
0.0012744935229420662,
0.0036527621559798717,
-0.02295082062482834,
-0.01583397388458252,
0.030406715348362923,
-0.004271019250154495,
0.019825682044029236,
0.04601676017045975,
0.05347184091806412,
0.024265814572572708,
-0.0009722239337861538,
0.0027699714992195368,
-0.044468287378549576,
-0.037438854575157166,
-0.0003880796139128506,
0.0017580135026946664,
0.023714542388916016,
0.01414888072758913,
0.009410358034074306,
0.0038158835377544165,
-0.0021066772751510143,
0.004285781178623438,
-0.0032850683201104403,
-0.022223643958568573,
0.029858699068427086,
0.012351744808256626,
0.008500139228999615,
-0.005240335129201412,
0.03220336511731148,
0.008320984430611134,
0.013224702328443527,
0.0669320672750473,
-0.010704807937145233,
-0.07315073907375336,
-0.015852967277169228,
0.06642672419548035,
0.026917124167084694,
-0.02539793588221073,
0.0008577253320254385,
0.011367041617631912,
0.03683026134967804,
0.03716116398572922,
0.01659792847931385,
-0.06029825657606125,
-0.022932512685656548,
0.02469496987760067,
0.03884970396757126,
-0.02925752103328705,
0.009604284539818764,
0.031127672642469406,
0.015435260720551014,
-0.0007746765622869134,
-0.02408476546406746,
-0.05001108720898628,
0.01985328271985054,
-0.04356595128774643,
-0.014503199607133865,
-0.024064965546131134,
-0.03191130608320236,
0.02869803085923195,
-0.021281322464346886,
0.0058705853298306465,
-0.0004956377670168877,
-0.032497528940439224,
0.029071832075715065,
-0.0866890698671341,
-0.010939504019916058,
0.00711857620626688,
0.020905788987874985,
-0.032554399222135544,
-0.02600400149822235,
0.013382078148424625,
-0.028921915218234062,
0.03766763210296631,
-0.02823471464216709,
0.015175064094364643,
-0.018551234155893326,
0.02685621753334999,
0.04303741455078125,
0.028555097058415413,
0.00314593268558383,
-0.051897164434194565,
-0.040613140910863876,
-0.021617449820041656,
-0.0026175626553595066,
0.03657471761107445,
0.04401807859539986,
-0.05284084007143974,
-0.007792036049067974,
-0.051728423684835434,
0.010158953256905079,
0.052721332758665085,
-0.015974432229995728,
0.009908695705235004,
-0.034654680639505386,
-0.024376336485147476,
-0.04277487099170685,
-0.006535790394991636,
-0.019619470462203026,
0.03734903037548065,
-0.013133281841874123,
-0.013552043586969376,
0.039417341351509094,
-0.014167958870530128,
-0.003182515036314726,
0.04964496195316315,
-0.0055694580078125,
-0.013266569934785366,
-0.014440558850765228,
-0.016552293673157692,
0.018874024972319603,
0.01375854853540659,
0.04586831107735634,
0.011285343207418919,
-0.04336298629641533,
-0.006523832678794861,
-0.06789129972457886,
-0.04531325399875641,
0.015514204278588295,
-0.02389582060277462,
0.01446457114070654,
-0.024563971906900406,
-0.019541244953870773,
0.0298941470682621,
0.007600901648402214,
-0.039740391075611115,
-0.0357961542904377,
0.02722497284412384,
-0.024543844163417816,
-0.004198023118078709,
0.036835040897130966,
0.05339880287647247,
0.037325821816921234,
0.013921611942350864,
-0.012164466083049774,
0.06893109530210495,
0.026466932147741318,
0.03996185585856438,
0.0031996353063732386,
0.016174936667084694,
-0.009007527492940426,
-0.021234890446066856,
0.04165319353342056,
0.001923241070471704,
-0.016987653449177742,
-0.005278150085359812,
-0.025239765644073486,
-0.011385099031031132,
0.034505777060985565,
-0.06315713375806808,
0.05057564750313759,
-0.0036403106059879065,
0.009756003506481647,
-0.016731923446059227,
0.023785321041941643,
-0.004049364477396011,
-0.000977675779722631,
0.017750397324562073,
-0.008815103210508823,
0.061187103390693665,
0.021435383707284927,
-0.02670253999531269,
0.05213760584592819,
-0.013850592076778412,
0.009978489950299263,
-0.019439175724983215,
0.026959262788295746,
-0.01463807001709938,
0.04453001916408539,
-0.042913857847452164,
-0.0584348700940609,
0.02155643329024315,
0.015667034313082695,
0.020838184282183647,
-0.034355394542217255,
-0.03549161180853844,
-0.029300631955266,
-0.04101565480232239,
-0.03633400425314903,
-0.020477524027228355,
0.034456782042980194,
0.008528858423233032,
0.07227519154548645,
0.03660612925887108,
0.03322545439004898,
-0.024416688829660416,
-0.01956956833600998,
-0.08435197919607162,
-0.023482410237193108,
-0.016649626195430756,
0.009415125474333763,
-0.031472817063331604,
-0.026567142456769943,
-0.01151686254888773,
-0.029491111636161804,
-0.0049188947305083275,
-0.010330808348953724,
0.011271624825894833,
-0.042524706572294235,
-0.0038926848210394382,
-0.03908046707510948,
-0.04281657934188843,
-0.043302953243255615,
0.03967013955116272,
0.025798846036195755,
0.003897397080436349,
0.046194739639759064,
0.03342577442526817,
-0.040447428822517395,
0.006535457447171211,
-0.020624177530407906,
0.013097431510686874,
-0.004960349295288324,
0.013201178051531315,
0.03721490502357483,
0.024399269372224808,
-0.01582159474492073,
-0.0400170162320137,
0.019082048907876015,
0.056523196399211884,
-0.010672023519873619,
-0.011665920726954937,
-0.004952746443450451,
-0.0075305444188416,
0.013668752275407314,
-0.012035596184432507,
0.034844014793634415,
-0.029222410172224045,
0.04268307611346245,
0.019436903297901154,
-0.020467959344387054,
-0.025021009147167206,
0.059911731630563736,
0.0388408824801445,
0.020616941154003143,
0.0037641345988959074,
-0.059718355536460876,
-0.006371095310896635,
-0.05205642431974411,
0.007270357105880976,
0.04144560918211937,
0.00522674061357975,
-0.00267319125123322,
0.009677182883024216,
0.039412643760442734,
0.022598471492528915,
-0.003379610599949956,
-0.018095465376973152,
-0.074322909116745,
0.009969793260097504,
-0.02012406662106514,
0.02432648278772831,
0.0033205016516149044,
0.01202368550002575,
0.04124681279063225,
-0.0026159684639424086,
-0.031944338232278824,
-0.06315542012453079,
-0.01541539654135704,
0.026267722249031067,
0.03467864543199539,
-0.013044687919318676,
0.03987753763794899,
-0.08249590545892715,
-0.016177702695131302,
0.05011741816997528,
-0.045261483639478683,
0.01877090148627758,
-0.029070217162370682,
-0.03612636402249336,
-0.008040303364396095,
0.0027511687949299812,
-0.014012136496603489,
-0.0005957828834652901,
0.02990330569446087,
0.0052823456935584545,
-0.0262170247733593,
-0.015005943365395069,
-0.02490302547812462,
0.03516272455453873,
-0.007457907777279615,
0.019124090671539307,
0.014060980640351772,
0.020494209602475166,
-0.03127213567495346,
0.01926310732960701,
-0.04609723389148712,
-0.09193986654281616,
0.007128795143216848,
-0.0029655350372195244,
0.011229399591684341,
0.03274877369403839,
-0.070261649787426,
-0.0770292580127716,
0.02206016704440117,
-0.0016152565367519855,
0.009235798381268978,
0.015340160578489304,
-0.051060132682323456,
0.05671190842986107,
0.02134900726377964,
0.004915301222354174,
0.03871961310505867,
0.03387466445565224,
0.023334303870797157,
0.028836002573370934,
-0.02359149418771267,
0.03283921256661415,
-0.011317095719277859,
0.00481595890596509,
-0.034635741263628006,
0.028730638325214386,
-0.005037381313741207,
0.031386665999889374,
0.02561718225479126,
-0.02098901756107807,
0.014138390310108662,
-0.03594785928726196,
0.017822302877902985,
0.02949332632124424,
-0.014086820185184479,
-0.009672755375504494,
-0.033256646245718,
0.028100378811359406,
0.043319109827280045,
-0.036249902099370956,
0.0035782966297119856,
-0.043333519250154495,
0.020233318209648132,
0.004357512108981609,
0.003858629846945405,
0.020114663988351822,
-0.05316627770662308,
0.01334884949028492,
0.03387591987848282,
-0.0666414201259613,
0.04105053097009659,
-0.01585986278951168,
0.010839330963790417,
0.013077011331915855,
-0.03933906555175781,
-0.03436194732785225,
0.02542799524962902,
-0.03372299298644066,
0.0042908345349133015,
0.009421817027032375,
0.02839001640677452,
0.009282320737838745,
-0.00967643316835165,
-0.04789789021015167,
-0.025808073580265045,
0.003510849317535758,
0.013332823291420937,
-0.04913277179002762,
-0.010155587457120419,
0.019412145018577576,
0.018435785546898842,
0.0037427961360663176,
-0.0014322946080937982,
-0.0017870169831439853,
-0.06587852537631989,
-0.028769269585609436,
0.009356030263006687,
0.010200747288763523,
0.05903569608926773,
-0.037603769451379776,
-0.0461268350481987,
0.00967568438500166,
-0.026993973180651665,
-0.01005852222442627,
0.01680293306708336,
0.013653089292347431,
-0.014401648193597794,
-0.06777430325746536,
-0.04914258420467377,
0.00492922542616725,
0.002875101286917925,
-0.013562113977968693,
-0.03568451851606369,
0.011274096556007862,
0.002773234387859702,
-0.016987821087241173,
0.0007955071050673723,
-0.030981170013546944,
-0.007591797970235348,
0.018116330727934837,
0.03824242576956749,
0.006140058394521475,
-0.02047845348715782,
-0.034173328429460526,
0.04677996411919594,
0.008278412744402885,
-0.018936023116111755,
-0.015277525410056114,
0.04459615796804428,
-0.010632844641804695,
-0.005649534519761801,
0.06351538747549057,
0.002974805189296603,
0.014646266587078571,
-0.04953361675143242,
0.0069517414085567,
0.00969525333493948,
0.04001590609550476,
-0.042922865599393845,
-0.038751598447561264,
-0.07799280434846878,
0.017391890287399292,
0.030023977160453796,
0.002834587823599577,
0.0398014672100544,
-0.005850030109286308,
-0.01785404048860073,
-0.03236664831638336,
-0.018247341737151146,
-0.01410898007452488,
0.00454040477052331,
-0.02796892449259758,
0.04795268923044205,
-0.05526572838425636,
0.013616764917969704,
0.03627420589327812,
0.03578832373023033,
0.01012159138917923,
0.0060501545667648315,
0.05268976464867592,
0.01535947434604168,
0.048819392919540405,
-0.009096336551010609,
-0.036215782165527344,
0.03736596554517746,
-0.026563504710793495,
0.04425022006034851,
0.007135913707315922,
-0.011795783415436745,
0.04363945126533508,
0.018268508836627007,
-0.005915775429457426,
-0.019206540659070015,
-0.0007557821809314191,
-0.03497254103422165,
0.0396888293325901,
0.03519453480839729,
-0.008800319395959377,
-0.005361340008676052,
0.01231077965348959,
0.024849053472280502,
0.006522251293063164,
-0.008536922745406628,
-0.015759950503706932,
-0.030098553746938705,
-0.01946316659450531,
-0.029425472021102905,
-0.02996091917157173,
0.0671236515045166,
0.02714439295232296,
-0.014647610485553741,
0.0028244913555681705,
-0.04910445213317871,
0.012832838110625744,
0.034910596907138824,
0.006846756208688021,
-0.037386320531368256,
0.052496571093797684,
-0.04466316103935242,
0.042842403054237366,
0.010349332354962826,
0.009003935381770134,
0.1203264370560646,
0.05492135509848595,
0.027914676815271378,
-0.04962148517370224,
-0.013045416213572025,
-0.0023920724634081125,
0.022367551922798157,
-0.029839014634490013,
0.03398575633764267,
-0.014769423753023148,
0.02382522076368332,
-0.013894772157073021,
0.03698435053229332,
-0.0028265558648854494,
0.05522194132208824,
0.024815157055854797,
-0.04086688160896301,
-0.028903409838676453,
-0.011717645451426506,
-0.020256998017430305,
0.01899363286793232,
0.0035958958324044943,
-0.0648384541273117,
0.028199145570397377,
-0.02613248862326145,
-0.013310296460986137,
-0.025514936074614525,
-0.01670459844172001,
0.041134752333164215,
0.02481413632631302,
-0.04528125748038292,
-0.016804613173007965,
-0.0026007818523794413,
-0.02283628284931183,
-0.025967132300138474,
0.03469889983534813,
0.013247299939393997,
0.021883340552449226,
0.03439195081591606,
0.034970447421073914,
0.007176375016570091,
0.0021117450669407845,
0.00004237699249642901,
0.05536491423845291,
-0.026033224537968636,
-0.007498417980968952,
-0.004413378890603781,
0.05331117659807205,
-0.032017674297094345,
-0.03233487904071808,
-0.014407480135560036,
-0.03161734342575073,
-0.007163580507040024,
-0.05807148665189743,
-0.029629027470946312,
-0.002337534911930561,
0.02312137559056282,
-0.0023549108300358057,
-0.015101914294064045,
-0.02109765075147152,
-0.003929643891751766,
-0.031359411776065826,
0.00985562801361084,
0.015252634882926941,
0.02082238905131817,
-0.014803426340222359,
-0.018030012026429176,
0.06263218820095062,
0.028904804959893227,
-0.010113258846104145,
-0.05233755335211754,
0.0026822935324162245,
-0.030275188386440277,
-0.023256482556462288,
0.03470403328537941,
0.016599969938397408,
0.03380092605948448,
0.009989187121391296,
-0.0038606205489486456,
0.007931544445455074,
-0.05068162456154823,
0.023737501353025436,
0.02102450095117092,
-0.034188829362392426,
-0.005881635472178459,
0.00070796231739223,
0.036684535443782806,
0.0329834446310997,
-0.012377338483929634,
0.04851718619465828,
0.04591274634003639,
-0.007322549354285002,
0.017921732738614082,
-0.06422235071659088,
-0.021760767325758934,
0.02209431491792202,
0.005943134892731905,
-0.013618187978863716,
-0.013734035193920135,
-0.006823909468948841,
0.0025545295793563128,
0.01580294407904148,
0.029905512928962708,
0.036260589957237244,
-0.03060423582792282,
-0.01571282558143139,
-0.01663706637918949,
-0.024600764736533165,
0.005319727119058371,
-0.026041358709335327,
0.050580866634845734,
-0.029814587906003,
-0.013131285086274147,
-0.02727413922548294,
-0.019314125180244446,
0.007068113423883915,
-0.011407747864723206,
-0.021751079708337784,
-0.002049081027507782,
-0.00040720630204305053,
0.028971455991268158,
-0.006797995883971453,
-0.004424892831593752,
-0.035256240516901016,
-0.00207310589030385,
-0.006929163821041584,
-0.009155092760920525,
-0.0277823805809021,
0.05221555754542351,
0.0361940972507,
-0.04582393541932106,
0.028276270255446434,
0.04881322756409645,
0.010968053713440895,
-0.019431350752711296,
0.0009468994103372097,
-0.014747912995517254,
0.045737624168395996,
-0.007958881556987762,
-0.049022749066352844,
0.003718860913068056,
-0.010241000913083553,
-0.03430023044347763,
0.02278878726065159,
-0.006159620359539986,
0.002098152879625559,
0.03128926455974579,
-0.0027014429215341806,
0.016755234450101852,
0.06615715473890305,
-0.02953779697418213,
0.0018139546737074852,
0.037111882120370865,
-0.012541722506284714,
-0.008115299977362156,
0.01571068726480007,
0.02928689308464527,
-0.018339412286877632,
0.006031546276062727,
0.07987502962350845,
0.0087743466719985,
0.0018034803215414286,
-0.00012077971769031137,
-0.005638292990624905,
-0.009887997061014175,
0.007138464599847794,
0.0182248093187809,
0.008671443909406662,
-0.0045413789339363575,
0.04855038970708847,
-0.016554849222302437,
0.0756898820400238,
0.027355913072824478,
0.0366707518696785,
-0.06917615979909897,
0.007485836744308472,
0.00796471256762743,
0.008179470896720886,
0.036635082215070724,
-0.0357498936355114,
0.00006248816498555243,
0.04618183150887489,
-0.06599099189043045,
0.024294083938002586,
-0.0008135814568959177,
-0.0000174685974343447,
-0.02377949468791485,
0.027639564126729965,
-0.05769515782594681,
0.03741774708032608,
-0.003147742012515664,
0.02324836328625679,
0.03247164189815521,
0.04366470128297806,
-0.006996612064540386,
-0.011632580310106277,
-0.009302543476223946,
0.04855217784643173,
0.006247588433325291,
-0.00314206350594759,
0.06825114041566849,
-0.015603134408593178,
-0.04289385303854942,
0.024231288582086563,
0.01660124771296978,
0.016878284513950348,
-0.03349479287862778,
-0.02490164153277874,
-0.018928833305835724,
0.01703915186226368,
0.01870965212583542,
0.010748031549155712,
-0.010448239743709564,
-0.0068003642372787,
0.023888777941465378,
0.006673712283372879,
0.02433190494775772,
-0.019888684153556824,
0.040559519082307816,
-0.010478858835995197,
-0.056235171854496,
0.036742180585861206,
0.0076523637399077415,
-0.0020757601596415043,
0.005143336020410061,
-0.008575350977480412,
0.021422771736979485,
-0.011316493153572083,
0.010731362737715244,
-0.03207441419363022,
0.02022281102836132,
0.01182236336171627,
0.028629329055547714,
0.0003058431902900338,
0.036791883409023285,
-0.032286692410707474,
-0.025126459077000618,
0.028871769085526466,
-0.0032972220797091722,
-0.03280656039714813,
-0.0445844829082489,
0.017773186787962914,
-0.002615836448967457,
0.018266795203089714,
0.038045190274715424,
-0.013250822201371193,
-0.031257856637239456,
0.024405332282185555,
-0.021002652123570442,
0.0011191369267180562,
0.008528011851012707,
-0.03593631833791733,
-0.05577584728598595,
-0.056324515491724014,
0.056717272847890854,
-0.0031278326641768217,
-0.032807014882564545,
-0.02272620238363743,
-0.02263244427740574,
-0.02496151439845562,
0.03536413237452507,
0.03228922560811043,
0.0008056695223785937,
-0.01015207264572382,
-0.015248242765665054,
-0.02933698520064354,
0.022461004555225372,
-0.02621796727180481,
-0.012471003457903862,
-0.025523344054818153,
0.006650538183748722,
0.01687895692884922,
0.003463617991656065,
0.01224391907453537,
0.02623816952109337,
0.0048849256709218025,
0.001966500421985984,
0.016056297346949577,
-0.011397586204111576,
-0.04492262005805969,
0.03271088749170303,
0.02433665841817856,
-0.010913684964179993,
0.09968741238117218,
0.03788241744041443,
0.01243260595947504,
-0.0037169589195400476,
-0.014632320031523705,
-0.037811797112226486,
0.006543220952153206,
-0.04033621773123741,
-0.030102094635367393,
-0.0006071832031011581,
-0.01531785074621439,
0.0297726821154356,
-0.04990869760513306,
0.01599940098822117,
0.03536350280046463,
-0.02453826367855072,
-0.019971052184700966,
0.044178761541843414,
-0.017635909840464592,
-0.011721017770469189,
0.006739276926964521,
0.03156215324997902,
0.039557866752147675,
-0.01264256238937378,
-0.03139296546578407,
0.03896937891840935,
0.0463019534945488,
-0.014426715672016144,
0.03274054080247879,
0.026409711688756943,
0.03159359097480774,
-0.029068391770124435,
0.016370993107557297,
0.026034735143184662,
-0.013761394657194614,
0.015408117324113846,
0.037437744438648224,
-0.04071405157446861,
-0.06163222715258598,
-0.018081944435834885,
-0.0015279354993253946,
0.07769693434238434,
-0.014000877737998962,
-0.005393208470195532,
-0.003910047467797995,
-0.02501511387526989,
-0.059071123600006104,
0.005678332410752773,
0.04237164929509163,
0.02990400418639183,
-0.019868019968271255,
0.009749309159815311,
-0.02847989648580551,
0.014932571910321712,
0.04204832762479782,
-0.053355664014816284,
-0.0056172506883740425,
-0.017875593155622482,
-0.03204803168773651,
0.03702036291360855,
0.0312493946403265,
-0.03362990915775299,
-0.010328558273613453,
0.002023952780291438,
0.011553606949746609,
-0.007167466916143894,
-0.01045394316315651,
-0.017357338219881058,
-0.0327032171189785,
0.0910506546497345,
-0.05544072017073631,
-0.040277909487485886,
-0.01839250512421131,
0.01753193698823452,
-0.038003113120794296,
-0.02641172893345356
] |
<p>I apologise in advance if this question doesn't appeal to the advanced questions being asked in this Physics forum, but I'm a great fan of the Stack Exchange software and would trust the answers provided here to be more correct than that of Yahoo! Answers etc.</p>
<p>A car is travelling with a constant speed of 80km/h and passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80km/h in 10 seconds reaching a constant speed of 100 km/h after a further 5 seconds. At what time will the policeman catch up with the car?</p>
<p>The answer in the back of the book is 32.5 seconds.</p>
<p>The steps/logic I completed/used to solve the equation were:<br>
- If you let x equal each other, the displacement will be the same, and the time can be solved algebraically.</p>
<p>Therefore:<br>
$$x=vt$$
As the car is moving at 80km/h, we want to convert to m/s. 80/3.6 = 22.22m/s<br>
$$x=22.22t$$</p>
<p>As for the policeman, he reaches 22.22m/s in 10 seconds.<br>
$$\begin{aligned}
x &= \frac12 (u+v) t \\
&= \frac12 \times 22.22 \times 10 \\
&= 111.11 \mathrm m
\end{aligned}$$</p>
<p>The policeman progresses to travel a further 5 seconds and increases his speed to 100km/h.<br>
100km/h -> m/s = 100 / 3.6 = 27.78m/s.</p>
<p>$$\begin{aligned}
x &= \frac12 (u+v) t \\
x &= \frac12 \times (22.22 + 27.78) \times 5 \\
x &= \frac12 \times 50 \times 5 \\
x &= 250 / 2 \\
x &= 125 \mathrm m
\end{aligned}$$ </p>
<p>By adding these two distances together we get 236.1m.
So the equation I have is:<br>
$$22.22t = 27.78t - 236.1 $$
Which solves to let t = 42.47s which is really wrong.</p>
| 8,331 |
[
0.012331257574260235,
-0.027788478881120682,
0.004813545849174261,
-0.002421701094135642,
0.0700286403298378,
-0.03862393647432327,
-0.03806845098733902,
-0.023642223328351974,
-0.0014232229441404343,
0.03092440403997898,
0.02453502081334591,
0.0632435753941536,
0.0448279082775116,
0.031665951013565063,
0.025807971134781837,
0.01756203919649124,
0.0012128425296396017,
-0.0166759192943573,
0.010125537402927876,
-0.019589347764849663,
-0.003036807756870985,
-0.028377780690789223,
0.010918025858700275,
0.0005274342838674784,
-0.009003149345517159,
0.009507901035249233,
0.04900582507252693,
-0.0006366772577166557,
-0.018264614045619965,
0.01297721266746521,
-0.005017410032451153,
-0.014277261681854725,
0.026408005505800247,
0.006052831653505564,
0.001256107701919973,
0.05517806485295296,
-0.0173987727612257,
-0.03345159441232681,
-0.009659791365265846,
0.008456513285636902,
-0.00443308288231492,
0.001852728659287095,
0.007983832620084286,
0.03156718239188194,
-0.013340997509658337,
0.06286437064409256,
0.017808079719543457,
-0.014038687571883202,
0.053403254598379135,
-0.011560307815670967,
0.08283349871635437,
0.03426557406783104,
0.009923974983394146,
-0.002979520708322525,
-0.014436105266213417,
-0.004313200246542692,
0.04105670750141144,
0.03876914829015732,
-0.009739330969750881,
-0.010531519539654255,
-0.009706455282866955,
-0.011001618579030037,
-0.03477301448583603,
-0.020538965240120888,
-0.010407098568975925,
0.019107097759842873,
-0.018141284584999084,
0.039595089852809906,
0.029741402715444565,
-0.017360975965857506,
0.00004914838427794166,
0.009998368099331856,
0.025906307622790337,
-0.00924586784094572,
-0.0021718700882047415,
-0.018037710338830948,
0.002649532398208976,
0.026425054296851158,
0.06029851734638214,
0.05129900202155113,
0.011807460337877274,
0.007460781838744879,
0.04181356728076935,
0.05278903245925903,
0.018167724832892418,
-0.028666235506534576,
0.0757545530796051,
0.03469366207718849,
-0.001865364727564156,
0.017408913001418114,
0.0264581385999918,
0.027165262028574944,
0.004285013303160667,
-0.004194528330117464,
0.045807287096977234,
0.057839639484882355,
-0.003794598625972867,
0.008502711541950703,
0.02548937499523163,
-0.034114185720682144,
0.0033286719117313623,
0.00038311388925649226,
0.009177641943097115,
0.031336091458797455,
0.003412562655285001,
-0.026828065514564514,
-0.023825611919164658,
-0.01867513172328472,
0.0005753090954385698,
-0.007369143422693014,
-0.06503769010305405,
-0.013646533712744713,
-0.00020363427756819874,
0.06015516817569733,
-0.03414585068821907,
-0.030041826888918877,
0.015951642766594887,
-0.025305908173322678,
0.07888295501470566,
0.03689579293131828,
0.015284652821719646,
-0.05138426646590233,
-0.0022541803773492575,
-0.02301614172756672,
-0.09186117351055145,
-0.0017616571858525276,
0.034475937485694885,
0.0028742654249072075,
0.004901302512735128,
0.023969370871782303,
0.021471625193953514,
-0.0033890018239617348,
-0.007863052189350128,
0.03145508095622063,
0.027239684015512466,
-0.007325419690459967,
-0.10220088809728622,
-0.07799098640680313,
0.020260697230696678,
0.03854638710618019,
-0.016685793176293373,
-0.08488146960735321,
0.03059672750532627,
0.022092189639806747,
0.06856002658605576,
0.01556187029927969,
-0.015930848196148872,
0.016603412106633186,
-0.008620127104222775,
-0.016248853877186775,
0.002376375487074256,
-0.03312862291932106,
-0.000038622885767836124,
-0.029009999707341194,
0.01426841039210558,
-0.02647603675723076,
-0.03895442932844162,
0.03572743758559227,
0.004899253137409687,
-0.004654469434171915,
0.04347774386405945,
0.036602068692445755,
-0.032691601663827896,
0.017507530748844147,
-0.010441296733915806,
-0.030525416135787964,
0.0447724349796772,
0.0026033378671854734,
-0.003763271030038595,
-0.0065266345627605915,
0.019256824627518654,
0.025701675564050674,
-0.0031749499030411243,
-0.039432454854249954,
0.03088286519050598,
-0.041220031678676605,
0.000987119390629232,
0.00735862273722887,
-0.037518084049224854,
0.02686483785510063,
-0.028113551437854767,
-0.06404372304677963,
-0.029226699844002724,
0.014352763071656227,
0.02806033194065094,
0.03019423596560955,
0.0014141466235741973,
0.05815405026078224,
0.00579429417848587,
-0.023202868178486824,
0.007493522018194199,
-0.04002787172794342,
0.006514436565339565,
0.02711842954158783,
0.02654692903161049,
0.01385465357452631,
-0.04986444488167763,
0.00838962011039257,
-0.018804039806127548,
-0.024552104994654655,
0.0021851530764251947,
0.05116172879934311,
0.013039544224739075,
-0.018837975338101387,
0.010739627294242382,
0.03848835825920105,
0.028719427064061165,
-0.02875472791492939,
0.019348306581377983,
-0.005731834564357996,
0.042894523590803146,
0.0064322431571781635,
-0.026489505544304848,
0.0165749192237854,
-0.031174875795841217,
-0.009363899007439613,
0.005964324343949556,
-0.010395312681794167,
0.04262133315205574,
0.015954408794641495,
-0.035045042634010315,
0.0764397382736206,
0.06498585641384125,
0.006983385421335697,
-0.031848274171352386,
0.0418563112616539,
-0.004088419023901224,
0.03820977732539177,
0.013345456682145596,
-0.053524088114500046,
-0.03210020065307617,
-0.012415596283972263,
0.013636384159326553,
0.02294175513088703,
-0.028747592121362686,
0.01828562654554844,
0.052052389830350876,
0.03938419371843338,
-0.005346870981156826,
0.0080601517111063,
0.011218520812690258,
-0.058380428701639175,
0.006108049303293228,
0.006139019038528204,
0.01277711521834135,
0.00617751432582736,
0.004635298158973455,
0.005534015130251646,
0.001840503653511405,
-0.006116774398833513,
0.02068883553147316,
-0.009302705526351929,
0.014660407789051533,
0.021331114694476128,
-0.010787250474095345,
-0.03326663374900818,
0.03482867032289505,
-0.009825906716287136,
-0.007767326198518276,
0.05838918685913086,
0.03845331817865372,
0.022737011313438416,
-0.04227932542562485,
0.013710440136492252,
-0.00788623746484518,
0.0010491447756066918,
-0.006961840204894543,
-0.014501727186143398,
0.02638225443661213,
-0.04489109665155411,
-0.011695475317537785,
-0.04155576229095459,
0.012773106805980206,
0.021177737042307854,
-0.029029974713921547,
0.03454076871275902,
0.028881167992949486,
0.018112171441316605,
-0.012013818137347698,
0.019676877185702324,
0.003439256688579917,
-0.012763320468366146,
0.003943989053368568,
-0.0073853651992976665,
-0.05990593880414963,
0.0415726974606514,
-0.00030844268621876836,
-0.054336756467819214,
0.05717639997601509,
0.033235788345336914,
0.015167593955993652,
0.03629801422357559,
-0.007283204235136509,
-0.03749258816242218,
-0.006036999635398388,
-0.02110580913722515,
-0.010747191496193409,
-0.056917376816272736,
0.025355879217386246,
0.03741312772035599,
0.009930962696671486,
-0.05299092456698418,
0.024505697190761566,
-0.05736915394663811,
-0.03936201333999634,
-0.05191292241215706,
0.02591535449028015,
0.012954414822161198,
0.013780576176941395,
0.02012174390256405,
-0.01930125057697296,
-0.019124528393149376,
0.017261244356632233,
-0.08158300817012787,
-0.0064900461584329605,
-0.008267374709248543,
0.01616743579506874,
0.0916747897863388,
0.01376365590840578,
-0.019817395135760307,
0.046938154846429825,
-0.0035056699998676777,
-0.00427001528441906,
-0.026914887130260468,
0.0022320265416055918,
0.004929468035697937,
-0.024972112849354744,
-0.03542677313089371,
0.09066260606050491,
-0.02768230438232422,
0.017091689631342888,
0.00012189996050437912,
0.08333376795053482,
0.07054553925991058,
0.00031100731575861573,
-0.004387322813272476,
-0.013793868944048882,
0.008019383996725082,
0.0067373295314610004,
0.03937705606222153,
0.025364000350236893,
-0.029698768630623817,
0.010063528083264828,
-0.01794087514281273,
0.06161561608314514,
0.021111294627189636,
-0.05250721424818039,
0.03208799287676811,
0.009679486975073814,
-0.02198007144033909,
-0.0880613625049591,
0.03196461871266365,
0.013098313473165035,
-0.02823522314429283,
-0.022608619183301926,
-0.006766868755221367,
0.04614511877298355,
-0.028526997193694115,
0.019833149388432503,
0.03334667161107063,
0.047666359692811966,
-0.010835140012204647,
-0.03229092061519623,
-0.01990596018731594,
-0.029262453317642212,
0.04476238042116165,
-0.053304146975278854,
0.0005239169695414603,
0.0482974648475647,
0.026674041524529457,
0.00316148204728961,
0.006713198032230139,
0.000529244658537209,
-0.018259067088365555,
-0.09678180515766144,
-0.04765404388308525,
0.005097590386867523,
0.012216294184327126,
-0.006162605714052916,
0.018054572865366936,
-0.0019426810322329402,
0.012700062245130539,
0.0060395183973014355,
0.02307279035449028,
-0.03556754067540169,
0.022109977900981903,
-0.006557052489370108,
-0.05273732542991638,
0.014373267069458961,
-0.028187032788991928,
0.014563311822712421,
-0.037104733288288116,
0.009068727493286133,
-0.016981879249215126,
-0.018189433962106705,
-0.05943938344717026,
0.025052757933735847,
-0.022248312830924988,
-0.07610208541154861,
-0.014886504039168358,
0.01985866017639637,
0.03351960331201553,
-0.032070159912109375,
0.029185259714722633,
0.019330322742462158,
-0.006045420654118061,
-0.014946185052394867,
-0.008381768129765987,
-0.02185809798538685,
0.03781716153025627,
0.02330826222896576,
-0.0031067952513694763,
0.013768131844699383,
-0.04881194978952408,
0.013231853954494,
0.010739163495600224,
0.04251253977417946,
0.0009464628528803587,
-0.05329146981239319,
-0.06676636636257172,
-0.01807607151567936,
-0.03179746866226196,
-0.021993355825543404,
0.010854831896722317,
-0.015153123065829277,
0.036702919751405716,
0.020578861236572266,
-0.00969089474529028,
0.025961851701140404,
0.06263797730207443,
0.03707537800073624,
0.007704068440943956,
0.0015276027843356133,
-0.023528657853603363,
-0.023615870624780655,
-0.025517301633954048,
0.0060768937692046165,
-0.0011891521280631423,
-0.010052400641143322,
0.01087112445384264,
-0.014483950100839138,
0.05161818489432335,
0.061773281544446945,
-0.010048690252006054,
0.039501771330833435,
-0.0004147919826209545,
-0.009660063311457634,
0.0009267110144719481,
0.0002640155144035816,
0.011805903166532516,
-0.005510488525032997,
0.03862066939473152,
-0.00789205078035593,
-0.03557267412543297,
-0.07487726211547852,
-0.02273332141339779,
0.007018664851784706,
0.08357714116573334,
-0.018441183492541313,
-0.009999390691518784,
-0.04473882541060448,
-0.013775856234133244,
0.023863086476922035,
-0.02552948147058487,
0.02195826731622219,
0.020738758146762848,
-0.020159419625997543,
-0.007790531497448683,
-0.04343786835670471,
-0.04254927858710289,
0.0055929068475961685,
-0.02168072760105133,
0.02106974646449089,
-0.01054899487644434,
-0.01752346195280552,
-0.011994064785540104,
0.039456769824028015,
0.06350624561309814,
0.039897751063108444,
0.0123505974188447,
-0.04922385513782501,
-0.02510995976626873,
0.0062016770243644714,
-0.05004827678203583,
-0.08137144148349762,
0.004360961262136698,
0.000023049737137625925,
0.0007389740785583854,
0.01818007230758667,
-0.007268101442605257,
-0.04414919763803482,
0.03075891174376011,
-0.008456934243440628,
-0.028277728706598282,
0.03756292164325714,
-0.029454559087753296,
0.020391102880239487,
0.04452122002840042,
0.018105145543813705,
0.012625763192772865,
0.013913723640143871,
-0.03155488520860672,
0.0086430748924613,
0.027972634881734848,
-0.0019543266389518976,
-0.034371234476566315,
0.0006410134374164045,
-0.005649477709084749,
-0.003305458929389715,
-0.035609204322099686,
0.03010016866028309,
-0.036188844591379166,
0.012303206138312817,
-0.05831426754593849,
-0.0100263562053442,
-0.005343603435903788,
0.018087388947606087,
-0.01693485863506794,
0.025104304775595665,
-0.027300581336021423,
-0.04713043197989464,
0.01683148182928562,
-0.0359489880502224,
0.00217571877874434,
-0.013103334233164787,
0.0037780613638460636,
0.006433946546167135,
0.01631646417081356,
-0.02666354551911354,
0.0028255628421902657,
0.034112077206373215,
-0.003405442228540778,
-0.027767540886998177,
0.031284693628549576,
-0.024954214692115784,
-0.039727188646793365,
-0.007198262959718704,
-0.020424988120794296,
-0.07101400196552277,
0.020510170608758926,
0.0011786557734012604,
0.006784240715205669,
-0.03162568435072899,
0.04699620231986046,
0.005961553659290075,
0.0033050980418920517,
-0.04881672188639641,
-0.0153661435469985,
0.044477444142103195,
0.009816441684961319,
-0.01821351982653141,
0.011695089749991894,
0.0033801058307290077,
-0.041637733578681946,
-0.04970966652035713,
0.004409683868288994,
0.04279502481222153,
-0.024781422689557076,
0.0026042067911475897,
-0.028449635952711105,
0.013857439160346985,
0.04819793254137039,
-0.006420910358428955,
0.04558464139699936,
-0.005278570111840963,
-0.011044014245271683,
-0.028095731511712074,
-0.0034185796976089478,
0.04241747781634331,
-0.02089458890259266,
-0.020288890227675438,
0.0033241230994462967,
-0.02721206098794937,
0.019058872014284134,
0.011551576666533947,
-0.014089732430875301,
0.027456875890493393,
0.008691968396306038,
-0.02272520400583744,
-0.009815444238483906,
0.005105467513203621,
0.023464789614081383,
0.03402828425168991,
0.002567867049947381,
0.01646505668759346,
-0.03322042152285576,
-0.034873493015766144,
0.024979831650853157,
-0.016277460381388664,
-0.03576954826712608,
-0.045761335641145706,
0.050477299839258194,
-0.03884219005703926,
0.02036993019282818,
0.05207814648747444,
0.016830746084451675,
0.025098290294408798,
-0.011929157190024853,
-0.03808298707008362,
0.019017832353711128,
-0.016777202486991882,
-0.0172935388982296,
-0.011521385051310062,
-0.046271804720163345,
-0.010758744552731514,
0.041615165770053864,
-0.017230095341801643,
0.043039560317993164,
0.009526758454740047,
-0.008323282934725285,
0.03217511251568794,
-0.01925816759467125,
-0.04860617592930794,
0.010588168166577816,
0.02369111031293869,
0.030946968123316765,
-0.023007061332464218,
0.021218786016106606,
0.043730080127716064,
0.030757112428545952,
0.03813005983829498,
-0.048450496047735214,
-0.010526997968554497,
0.005615205504000187,
-0.00954391434788704,
-0.037969741970300674,
-0.030726801604032516,
-0.017102738842368126,
-0.018161403015255928,
0.019171662628650665,
-0.0033785575069487095,
-0.004509555641561747,
0.044304683804512024,
0.03946136683225632,
0.02154158614575863,
-0.055685024708509445,
0.006351210176944733,
-0.06821487843990326,
-0.04535243660211563,
0.0036907652392983437,
0.03291415050625801,
0.010247604921460152,
0.024744583293795586,
0.034803781658411026,
0.0009540477185510099,
0.031260259449481964,
-0.04744666442275047,
-0.05298781767487526,
-0.019139014184474945,
-0.011232031509280205,
-0.006683286279439926,
0.07127226144075394,
0.011686962097883224,
-0.030866943299770355,
0.018930599093437195,
-0.038076143711805344,
0.0314248688519001,
0.00418510939925909,
0.019888844341039658,
-0.029843337833881378,
0.08304569870233536,
-0.03303171321749687,
0.005412767641246319,
-0.023788616061210632,
0.006827794946730137,
0.14310124516487122,
0.02462034486234188,
0.03247472643852234,
-0.001604812452569604,
0.01506719272583723,
-0.023523153737187386,
0.0061394223012030125,
-0.018605343997478485,
0.02606487087905407,
0.014676788821816444,
-0.018557079136371613,
0.013588293455541134,
0.045169129967689514,
0.017036203294992447,
-0.04991050064563751,
0.0500386618077755,
-0.048201948404312134,
-0.0418514721095562,
-0.0028845646884292364,
0.03660189360380173,
-0.0027068869676440954,
0.012073921039700508,
0.015392855741083622,
0.011476527899503708,
-0.06170306354761124,
0.006241053342819214,
-0.05324333533644676,
-0.03044666349887848,
0.052193086594343185,
0.001822825986891985,
-0.06356941163539886,
0.03368020057678223,
0.008320238441228867,
-0.07296594977378845,
-0.039908267557621,
0.024262776598334312,
0.05709725245833397,
-0.012527728453278542,
0.02136160060763359,
0.06478617340326309,
0.006581171881407499,
0.02882974222302437,
-0.02250136435031891,
-0.003979350905865431,
-0.0725182294845581,
0.021870410069823265,
-0.09427254647016525,
0.061686281114816666,
-0.003287373809143901,
0.01666403003036976,
0.0009556699078530073,
0.007359254639595747,
-0.00688203563913703,
-0.044861916452646255,
0.014811906032264233,
0.014645367860794067,
0.013405689038336277,
0.0015352468471974134,
-0.027434026822447777,
-0.04443342611193657,
0.02478243038058281,
0.02085472270846367,
-0.02974204532802105,
0.021727560088038445,
-0.027197662740945816,
-0.0038291749078780413,
0.0001396071893395856,
0.013732438907027245,
-0.013250843621790409,
-0.0037659883964806795,
-0.022620849311351776,
0.013139604590833187,
-0.018243877217173576,
-0.01638101227581501,
-0.004489004611968994,
0.06729543954133987,
-0.0184338316321373,
-0.00307283503934741,
0.007337732706218958,
-0.046863727271556854,
-0.042480677366256714,
0.029756659641861916,
0.0207877978682518,
0.0076723829843103886,
-0.020053677260875702,
-0.016818927600979805,
-0.010802335105836391,
0.037762030959129333,
-0.009838909842073917,
-0.008795266039669514,
0.009252602234482765,
0.05149297043681145,
0.011299941688776016,
-0.013643288053572178,
-0.0007475332822650671,
0.002645615255460143,
-0.03801887482404709,
0.023100953549146652,
-0.007841800339519978,
0.018096208572387695,
0.05080485716462135,
-0.019009454175829887,
0.0066117653623223305,
0.025015056133270264,
0.007356815971434116,
0.01633479632437229,
0.011743811890482903,
-0.04290946573019028,
-0.019069934263825417,
0.0456417091190815,
0.04145447537302971,
-0.0144305769354105,
-0.00434535788372159,
-0.03238576650619507,
0.01589818112552166,
0.03203066438436508,
-0.01573777385056019,
-0.017004666849970818,
0.04113422706723213,
-0.041134074330329895,
0.03607959672808647,
-0.013503619469702244,
0.004848464857786894,
0.004762326832860708,
0.006331458222121,
-0.007396367844194174,
-0.013525811955332756,
-0.05046217143535614,
0.002242430578917265,
-0.016939839348196983,
0.006243676878511906,
0.03167618438601494,
0.020301271229982376,
0.003971659112721682,
-0.04600481688976288,
0.021017614752054214,
0.016954593360424042,
0.013271613046526909,
-0.022437475621700287,
0.01009657233953476,
0.029846714809536934,
-0.005054198205471039,
-0.022205157205462456,
0.012472174130380154,
0.021010832861065865,
0.026979682967066765,
-0.024305088445544243,
-0.006203135475516319,
0.017046429216861725,
0.0940488651394844,
-0.047145310789346695,
0.013202606700360775,
0.02249044179916382,
-0.038052212446928024,
-0.0037292109336704016,
-0.04210207611322403,
-0.008955993689596653,
-0.00941650290042162,
-0.03037295490503311,
0.03397534787654877,
0.0285016018897295,
-0.05256027728319168,
0.040787797421216965,
0.008748969994485378,
0.011088802479207516,
-0.013888976536691189,
0.011541353538632393,
0.014201410114765167,
0.016184678301215172,
0.023668501526117325,
-0.0053581250831484795,
-0.005071807187050581,
-0.01350228488445282,
-0.019759101793169975,
-0.12899959087371826,
0.006228163838386536,
0.032521024346351624,
0.035254623740911484,
0.06310124695301056,
-0.04755914956331253,
-0.01179015263915062,
0.04277998208999634,
-0.05012942850589752,
-0.01011382695287466,
-0.030888373032212257,
-0.01070594135671854,
-0.015695417299866676,
0.010277819819748402,
0.013053667731583118,
0.030470110476017,
0.021464064717292786,
0.05039036273956299,
0.02682250179350376,
0.013379226438701153,
-0.014213276095688343,
-0.05960493162274361,
0.02493622526526451,
0.029520893469452858,
-0.02648235857486725,
0.025354281067848206,
0.053642988204956055,
-0.04124217852950096,
0.01649828441441059,
0.027812376618385315,
-0.0004985775449313223,
0.03282512351870537,
-0.03441297262907028,
-0.0018422934226691723,
-0.0006769841420464218,
0.036271512508392334,
0.04693113639950752,
0.020667150616645813,
0.016926076263189316,
0.01962261088192463,
-0.020442452281713486,
0.04445986822247505,
-0.0005924747092649341,
-0.020518386736512184,
0.05199827998876572,
-0.01395777054131031,
-0.054726794362068176,
0.01083846390247345,
-0.006201523821800947,
-0.0034399942960590124,
0.023475773632526398,
0.023917678743600845,
-0.03800316900014877,
-0.03137823939323425,
-0.023857247084379196,
-0.032316047698259354,
-0.04759800061583519,
0.0036923494189977646,
-0.032435547560453415,
0.022323964163661003,
0.003500340273603797,
-0.040959082543849945,
0.00828494317829609,
-0.032265108078718185,
0.01279408112168312,
-0.0025266308803111315,
-0.022746378555893898,
0.006853254046291113,
0.03474356234073639,
-0.007660487666726112,
0.015921657904982567,
-0.004795858636498451,
-0.002605763264000416,
-0.012447125278413296,
0.05522646754980087,
0.00048549353959970176,
0.014017396606504917,
-0.007487721741199493,
-0.0359085276722908,
-0.05979081243276596,
-0.01042306236922741,
0.01698901690542698,
-0.022155696526169777,
-0.06576162576675415,
-0.06297138333320618,
0.015546797774732113,
-0.0015336157521232963,
0.06305857002735138,
-0.051405951380729675,
-0.01548581849783659,
-0.0025018383748829365,
-0.02541586384177208,
0.033054523169994354,
-0.032791148871183395,
0.012318725697696209,
0.010262049734592438,
0.013972671702504158,
0.019984977319836617,
0.03169774264097214,
-0.003176341997459531,
-0.02330964431166649,
0.027646778151392937,
-0.021229002624750137,
0.003949564415961504,
-0.011520991101861,
-0.022542685270309448,
0.001451767166145146,
0.046475671231746674,
0.006244236137717962,
0.029652003198862076,
0.01346110925078392,
0.02426687441766262,
0.023104270920157433,
-0.03616222366690636,
-0.055536288768053055,
-0.02861308492720127,
-0.04521406814455986,
-0.0211506225168705,
-0.04727590084075928,
-0.02495502680540085,
0.004199874121695757,
-0.05884204059839249,
0.01851002871990204,
0.04096931219100952,
-0.010082277469336987,
-0.022244036197662354,
0.018165696412324905,
0.029291324317455292,
0.020033560693264008,
0.009449120610952377,
0.02224557101726532,
0.000522832793649286,
-0.02562813088297844,
-0.009415748529136181,
-0.02558218128979206,
0.04922781139612198,
-0.0054839011281728745,
0.0031178609933704138,
0.0377492718398571,
0.005390339531004429,
0.062266603112220764,
0.004526681732386351,
0.027253007516264915,
-0.0163496732711792,
-0.0014044585404917598,
-0.0002495477383490652,
-0.011411000043153763,
0.03619313985109329,
0.03836020082235336,
-0.014013197273015976,
0.06459852308034897,
-0.03408901020884514,
0.011440691538155079,
-0.012921088375151157,
0.01688622683286667,
-0.06723155826330185,
-0.002136766444891691,
-0.006353734526783228,
-0.00017564711743034422,
-0.029247945174574852,
-0.018820753321051598,
-0.007255921605974436,
0.031006325036287308,
0.016220897436141968,
-0.029046621173620224,
-0.0025025836657732725,
0.025469953194260597,
-0.016042299568653107,
-0.025633642449975014,
-0.016522349789738655,
0.010491414926946163,
-0.00884877797216177,
0.07100144773721695,
0.03698281571269035,
-0.014905794523656368,
-0.06188074126839638,
0.0011732637649402022,
-0.03116190806031227,
0.06640692800283432,
-0.057030923664569855,
-0.034839726984500885,
-0.03061654418706894,
0.0027024599257856607,
0.042551036924123764,
-0.01453876681625843
] |
<p>I'd like to keep a container of potable water in my car for when I get stuck, but in the winter it gets cold enough for bottled water to freeze.</p>
<p>I can't put salt in it, because then it won't be drinkable anymore (or at least, will make my condition worse if I do drink it), and I can't mix it with alcohol in case I get the car unstuck and have to drive.</p>
<p>What else could be added to water to sufficiently lower its freezing point without making it undrinkable?</p>
<p>(Or to keep it in line with physics rather than chemistry, how do I calculate the amount of pressure the water need to be under to prevent it from freezing at a given temperature, say 15-20<sup>o</sup> F?)</p>
| 8,332 |
[
-0.04501141607761383,
-0.01191300805658102,
-0.04058905318379402,
-0.014712623320519924,
0.03547890484333038,
-0.015524773858487606,
-0.03807102516293526,
-0.02107127197086811,
-0.004593973513692617,
-0.0003113401762675494,
0.0467180572450161,
0.09969643503427505,
-0.009269149042665958,
0.005014041438698769,
0.0038156546652317047,
0.011379212141036987,
0.017226681113243103,
-0.041429515928030014,
0.00749344052746892,
-0.012543130666017532,
-0.021798666566610336,
-0.0111441845074296,
-0.02642401121556759,
0.021620070561766624,
0.02353706769645214,
0.04649771377444267,
0.03576606512069702,
-0.038510531187057495,
0.013301592320203781,
0.00269313738681376,
0.01319324690848589,
-0.08420449495315552,
0.016704415902495384,
0.033152684569358826,
0.035028740763664246,
0.0011002394603565335,
-0.04281041398644447,
-0.01305452175438404,
-0.04458794370293617,
0.01693119667470455,
-0.026638709008693695,
-0.017880240455269814,
-0.004082075320184231,
0.024784047156572342,
-0.017964106053113937,
0.06105154752731323,
0.012212997302412987,
-0.0447174608707428,
0.01127093005925417,
-0.051638878881931305,
0.015442190691828728,
0.0033761942759156227,
0.034361306577920914,
0.040857162326574326,
0.002914238255470991,
0.007661208510398865,
0.07727654278278351,
0.04819483309984207,
-0.018582971766591072,
-0.06138314679265022,
-0.01593310944736004,
-0.020258480682969093,
-0.03007948212325573,
-0.004421943332999945,
-0.005352359265089035,
-0.02989077940583229,
-0.025445055216550827,
-0.003144211834296584,
0.02727244421839714,
-0.0028378982096910477,
0.0038453650195151567,
-0.023773858323693275,
0.023126624524593353,
-0.03913924843072891,
0.0021528638899326324,
-0.04249498248100281,
-0.009784740395843983,
0.02352682501077652,
0.028205130249261856,
0.02451573684811592,
0.008520296774804592,
-0.018858924508094788,
0.019048308953642845,
0.05978526920080185,
0.015616921707987785,
-0.05003318563103676,
0.06373100727796555,
0.008831758052110672,
0.0321415551006794,
0.038195740431547165,
0.022823749110102654,
-0.0008074089419096708,
0.012590199708938599,
0.010575620457530022,
0.009220165200531483,
0.00048738374607637525,
-0.015023947693407536,
0.05833938345313072,
0.016346566379070282,
0.0056903488002717495,
0.009538073092699051,
0.015415978617966175,
-0.00782936904579401,
0.081627257168293,
-0.016815099865198135,
-0.0677691176533699,
-0.02174568548798561,
-0.0033115691039711237,
0.01888054423034191,
0.004011617507785559,
-0.010578294284641743,
-0.006821645889431238,
-0.012480642646551132,
-0.0405564121901989,
-0.016001442447304726,
-0.022695377469062805,
-0.029674923047423363,
-0.013750175014138222,
0.03099970519542694,
0.017613502219319344,
0.06143343821167946,
-0.036852773278951645,
-0.005224644672125578,
-0.03934575989842415,
-0.06296451389789581,
-0.006757015362381935,
-0.025463735684752464,
0.012365213595330715,
-0.02637476846575737,
-0.017018698155879974,
0.020687272772192955,
-0.010454168543219566,
0.034555014222860336,
-0.008149875327944756,
0.05269889906048775,
-0.004582282155752182,
-0.08335541188716888,
-0.05334555357694626,
0.020890628919005394,
0.008013014681637287,
-0.0414852611720562,
-0.057247716933488846,
0.02365121990442276,
-0.029652630910277367,
0.07922948151826859,
-0.005885284394025803,
0.010249072685837746,
-0.010239298455417156,
-0.0007396119763143361,
0.004315028432756662,
-0.004732328932732344,
-0.011053113266825676,
-0.014327013865113258,
-0.01855103112757206,
-0.018238632008433342,
-0.05261332169175148,
0.04420255497097969,
0.042454060167074203,
0.010253564454615116,
0.00003448525967542082,
0.03395507484674454,
-0.04990798979997635,
-0.008938885293900967,
0.0075795697048306465,
-0.04265837371349335,
-0.030050629749894142,
0.008466674014925957,
-0.008324561640620232,
0.017479948699474335,
0.013773985207080841,
0.009887950494885445,
0.04314007982611656,
0.0011456171050667763,
0.009142975322902203,
0.06994004547595978,
-0.015355006791651249,
0.019109006971120834,
-0.03713572397828102,
-0.0004352109390310943,
0.032523371279239655,
-0.04074413701891899,
0.0024457296822220087,
0.011864413507282734,
0.01653437502682209,
0.011206815019249916,
-0.011468866840004921,
0.016067204996943474,
0.011664487421512604,
0.033914681524038315,
-0.03796254098415375,
-0.005221833940595388,
-0.06907787919044495,
0.005540513899177313,
-0.016437416896224022,
0.019807307049632072,
0.04369497299194336,
0.010601048357784748,
0.03078409470617771,
-0.06905223429203033,
-0.016744425520300865,
0.02316267602145672,
0.04420623183250427,
0.031391922384500504,
-0.006012684665620327,
0.0032926492858678102,
0.06427697092294693,
0.07557111233472824,
-0.03136751428246498,
0.01257291343063116,
-0.06371425092220306,
-0.02489885874092579,
-0.03792852908372879,
-0.04625563696026802,
0.0027547378558665514,
-0.0244981087744236,
-0.030819913372397423,
0.049465734511613846,
0.005669323727488518,
0.04277089238166809,
0.019925368949770927,
-0.01603931188583374,
0.10530328750610352,
0.018873456865549088,
-0.005788543727248907,
0.02681768499314785,
0.01816081441938877,
0.015744950622320175,
0.015316572040319443,
0.008882425725460052,
-0.04036065191030502,
-0.021569643169641495,
-0.022511860355734825,
0.041148919612169266,
0.008359788917005062,
-0.041926417499780655,
0.0037583631929010153,
0.0031117035541683435,
0.050625719130039215,
0.03848433494567871,
0.015086796134710312,
-0.01816929504275322,
0.006150763016194105,
0.02095412090420723,
0.026417160406708717,
0.013798704370856285,
0.023570073768496513,
0.0028118069749325514,
0.01918606087565422,
0.016995418816804886,
-0.03876090049743652,
-0.026196356862783432,
0.0036913298536092043,
0.03162064030766487,
0.05038966238498688,
-0.011216084472835064,
-0.02627057023346424,
0.04068562760949135,
-0.0260204765945673,
0.011477064341306686,
0.009206381626427174,
0.011577311903238297,
0.018131069839000702,
-0.026585789397358894,
-0.016758551821112633,
-0.015201518312096596,
0.03932296857237816,
-0.053879957646131516,
0.022955823689699173,
0.032198045402765274,
-0.02729513868689537,
0.02536938339471817,
-0.014512673951685429,
0.008992256596684456,
-0.016496902331709862,
0.037583108991384506,
0.058730944991111755,
-0.0033134152181446552,
0.051147185266017914,
-0.04237641021609306,
0.014428789727389812,
-0.013563813641667366,
-0.017597850412130356,
-0.041122399270534515,
0.005683580879122019,
-0.01625949703156948,
0.005752837285399437,
0.0077993255108594894,
-0.028803221881389618,
0.02552826702594757,
0.011999118141829967,
-0.03605572506785393,
-0.008949614129960537,
0.02811259590089321,
-0.022346824407577515,
-0.022261163219809532,
-0.00200038799084723,
0.015800729393959045,
-0.026623813435435295,
-0.00844177883118391,
0.028608838096261024,
0.008408011868596077,
-0.03142984211444855,
0.0027316592168062925,
-0.08154746145009995,
-0.007218281738460064,
-0.008502710610628128,
-0.01413701195269823,
0.012040826492011547,
-0.025802379474043846,
-0.012454823590815067,
0.016073530539870262,
-0.07292310893535614,
0.005007241386920214,
-0.0495382659137249,
-0.059892117977142334,
0.01607443578541279,
0.016268162056803703,
0.04691591486334801,
-0.005837630946189165,
0.015115147456526756,
0.05921309441328049,
0.0003191986761521548,
-0.0460120253264904,
-0.014501478523015976,
-0.03859556466341019,
-0.03471304476261139,
-0.02586166374385357,
-0.03503066301345825,
0.05743599310517311,
-0.034925416111946106,
0.0087886368855834,
0.0373867005109787,
0.04109606146812439,
0.011754595674574375,
0.04621325060725212,
-0.03742607310414314,
0.016466960310935974,
0.025582464411854744,
0.03352644294500351,
0.0419941321015358,
0.014818073250353336,
-0.010509424842894077,
0.014397266320884228,
-0.024974672123789787,
0.04050285741686821,
0.0710301548242569,
-0.009977016597986221,
0.03181092441082001,
-0.0009258402860723436,
-0.014038941822946072,
-0.05423692986369133,
0.03393751382827759,
-0.024442927911877632,
-0.010489340871572495,
0.03474121540784836,
0.006390849128365517,
0.01484704576432705,
0.013900366611778736,
-0.013933917507529259,
0.019396889954805374,
0.11819533258676529,
-0.05016825720667839,
-0.06849607825279236,
0.009461671113967896,
-0.008335966616868973,
0.016083450987935066,
0.0027888251934200525,
0.006265564821660519,
0.03149968013167381,
0.004341951571404934,
0.03936806321144104,
-0.015557507984340191,
-0.020573126152157784,
0.0038101691752672195,
-0.06804800778627396,
-0.02135510928928852,
-0.01343256700783968,
-0.01102086529135704,
0.010689745657145977,
0.03866632655262947,
-0.00020040110393892974,
0.01949400268495083,
0.04427450895309448,
0.026135409250855446,
-0.05497764050960541,
0.032291870564222336,
-0.030795946717262268,
-0.006733884569257498,
-0.013782487250864506,
-0.01556235272437334,
-0.02030409872531891,
-0.054454296827316284,
-0.007307747378945351,
-0.022968148812651634,
0.017451025545597076,
-0.006796584464609623,
0.009716040454804897,
-0.016222551465034485,
-0.03336739167571068,
-0.00942020583897829,
-0.0057400804944336414,
0.031147297471761703,
-0.046803321689367294,
-0.014242959208786488,
0.005406525451689959,
-0.021787120029330254,
-0.02230677381157875,
0.015617168508470058,
0.027361629530787468,
0.01643315702676773,
0.04048484191298485,
-0.027200346812605858,
0.02609211578965187,
0.0244744960218668,
-0.039094891399145126,
0.015450574457645416,
0.030019326135516167,
-0.009180071763694286,
0.030919961631298065,
-0.03708959370851517,
-0.04356107860803604,
-0.034789372235536575,
0.028672872111201286,
-0.009610787034034729,
-0.046000491827726364,
0.03855329006910324,
0.002622014842927456,
-0.0421055443584919,
-0.04229511693120003,
0.04123843461275101,
0.06333421170711517,
0.018689163029193878,
0.00043193617602810264,
-0.03319314867258072,
-0.03247908130288124,
-0.011934623122215271,
0.008596211671829224,
0.019297383725643158,
0.052470844238996506,
-0.018743708729743958,
0.0003316537768114358,
-0.0036925303284078836,
-0.029762933030724525,
-0.022634008899331093,
-0.0033281631767749786,
0.010801850818097591,
0.015990732237696648,
-0.00381394661962986,
0.020352113991975784,
0.04829100891947746,
0.002113654976710677,
0.006117137614637613,
0.0028257521335035563,
-0.006094909273087978,
-0.09422078728675842,
0.011204841546714306,
0.048779573291540146,
0.04643435403704643,
0.011752356775105,
0.012059217318892479,
-0.08347966521978378,
-0.028324907645583153,
0.058593377470970154,
-0.02960306406021118,
0.012908346951007843,
0.014620854519307613,
-0.014821323566138744,
0.0006725850980728865,
-0.02520558051764965,
0.005938065238296986,
-0.011610537767410278,
-0.02972422167658806,
0.04135124385356903,
-0.000028399424991221167,
-0.022303711622953415,
-0.013767118565738201,
0.017747877165675163,
0.02759489417076111,
0.04803197458386421,
0.00870885606855154,
-0.012737929821014404,
-0.01146885845810175,
-0.01905989646911621,
-0.013454449363052845,
-0.07869697362184525,
-0.02681255154311657,
0.01840810291469097,
0.0004928156267851591,
0.010258850641548634,
-0.0301264189183712,
-0.03239845111966133,
0.06147264689207077,
-0.017556119710206985,
-0.03987196460366249,
0.015984412282705307,
-0.025702890008687973,
0.039555635303258896,
0.015949763357639313,
0.052109815180301666,
0.03434799984097481,
0.029997825622558594,
-0.015802815556526184,
0.01692536100745201,
-0.03379898518323898,
0.0012243458768352866,
-0.0266552921384573,
0.0013206856092438102,
-0.011627508327364922,
0.01130749098956585,
-0.040045641362667084,
0.015247644856572151,
0.0006999541656114161,
0.006538883317261934,
0.020669838413596153,
-0.009813079610466957,
-0.017426196485757828,
-0.0035639244597405195,
0.018698714673519135,
-0.048802655190229416,
0.014948686584830284,
0.029717938974499702,
-0.004950446542352438,
-0.024252496659755707,
0.07223748415708542,
-0.010576646775007248,
0.00193791335914284,
0.012507663108408451,
-0.05958319082856178,
0.013701834715902805,
-0.004411496687680483,
-0.005004975479096174,
0.016461577266454697,
-0.0008881296380423009,
0.056153763085603714,
-0.04323922097682953,
0.0066064572893083096,
0.021312879398465157,
-0.028557106852531433,
-0.0012246245751157403,
0.062256406992673874,
0.005224758759140968,
0.055458914488554,
-0.01038512121886015,
0.0398988351225853,
0.017776837572455406,
0.020148444920778275,
-0.014781872741878033,
-0.04172104224562645,
0.05837482586503029,
0.01053412165492773,
-0.024617863819003105,
-0.05632675439119339,
0.00864587165415287,
-0.011301283724606037,
-0.03280653432011604,
-0.0026681472081691027,
0.0425720252096653,
-0.04232131317257881,
-0.016654586419463158,
0.012801418080925941,
-0.0033819519449025393,
0.06967812776565552,
0.0024526091292500496,
-0.02735183760523796,
0.045716628432273865,
-0.06970982253551483,
-0.005364199634641409,
0.0207756906747818,
-0.0046429261565208435,
-0.03951627016067505,
-0.00923170056194067,
0.0024398055393248796,
0.0002854946069419384,
0.014667388051748276,
0.012801695615053177,
0.01626981794834137,
0.02479083277285099,
0.04259892553091049,
-0.034918468445539474,
-0.050932712852954865,
0.0629829540848732,
0.018334371969103813,
0.00909025501459837,
-0.014299853704869747,
0.0053985207341611385,
-0.04326319321990013,
-0.03714560344815254,
-0.02061772160232067,
-0.007538256235420704,
0.005268093664199114,
-0.01862957514822483,
0.06084710732102394,
0.008361399173736572,
-0.010901739820837975,
0.03062508814036846,
-0.03604771941900253,
0.02462966926395893,
0.07868189364671707,
-0.026341460645198822,
0.009602904319763184,
-0.009239383973181248,
-0.025956278666853905,
-0.07337740808725357,
-0.03164152428507805,
-0.00272990670055151,
0.03166576474905014,
-0.007003598380833864,
0.028438013046979904,
0.06867041438817978,
-0.02291417494416237,
-0.005205042660236359,
-0.00244762166403234,
-0.027168991044163704,
0.07436178624629974,
0.023899070918560028,
0.035740721970796585,
-0.006273095495998859,
-0.005232183262705803,
0.014344548806548119,
0.05893364176154137,
-0.020018836483359337,
0.019805634394288063,
0.04233700782060623,
-0.0015914661344140768,
0.006988108158111572,
-0.08385108411312103,
-0.04013265669345856,
0.024064192548394203,
-0.047739263623952866,
0.03454621508717537,
-0.0006016287952661514,
-0.028306618332862854,
0.042949382215738297,
0.006581146270036697,
0.013840028084814548,
-0.0565669909119606,
-0.01464791502803564,
-0.03071841225028038,
0.004850725643336773,
0.008725534193217754,
-0.05332870036363602,
0.0026004330720752478,
0.02367429807782173,
0.017879456281661987,
0.0161769799888134,
0.006204051896929741,
-0.008900763466954231,
-0.042070869356393814,
0.021452801302075386,
-0.01989312842488289,
-0.04564804211258888,
0.031059300526976585,
0.0304244514554739,
-0.02143002860248089,
-0.015420815907418728,
-0.012253996916115284,
0.003437260165810585,
0.01516510359942913,
0.014895220287144184,
0.009761796332895756,
0.009363682940602303,
-0.008936197496950626,
-0.015645908191800117,
0.006566967349499464,
-0.006562983617186546,
0.10094551742076874,
0.0323050357401371,
0.03821372613310814,
-0.04137389734387398,
0.007742868736386299,
-0.006792014464735985,
0.005169542506337166,
-0.02677462063729763,
-0.015046533197164536,
-0.019758062437176704,
0.038642238825559616,
0.017710233107209206,
0.04815276712179184,
-0.0525125116109848,
0.008740936405956745,
0.05694466829299927,
-0.07517294585704803,
-0.012091449461877346,
0.0022724675945937634,
0.02561592496931553,
-0.019586186856031418,
0.011076939292252064,
0.025819415226578712,
0.0393531508743763,
-0.007361404597759247,
-0.0018781835678964853,
-0.03805098310112953,
-0.021812759339809418,
0.03699706494808197,
0.005589127540588379,
-0.042646076530218124,
0.024134572595357895,
0.009360136464238167,
0.028006410226225853,
-0.04788437485694885,
0.032104555517435074,
0.04805620387196541,
0.015666702762246132,
-0.036536216735839844,
-0.0008147686021402478,
0.030974281951785088,
0.015972085297107697,
0.0070519717410206795,
0.01966007798910141,
-0.023327283561229706,
0.022540265694260597,
-0.02924230508506298,
0.017789611592888832,
-0.010161164216697216,
-0.04566819965839386,
-0.013818704523146152,
-0.006950540468096733,
0.012608205899596214,
-0.04384613782167435,
-0.05104156211018562,
0.0011730543337762356,
0.037713780999183655,
0.01765560358762741,
-0.015060490928590298,
-0.026459436863660812,
0.02081240527331829,
0.009394297376275063,
-0.008288509212434292,
0.03187382593750954,
0.022683823481202126,
-0.050052303820848465,
0.012758870609104633,
-0.012249310500919819,
-0.012532733380794525,
-0.007092802785336971,
-0.051408134400844574,
-0.00596566591411829,
-0.033824849873781204,
-0.011684929952025414,
0.0005094244843348861,
0.021472256630659103,
0.023316560313105583,
-0.0005816827178932726,
0.07517063617706299,
0.010198796167969704,
-0.04658438265323639,
0.04968252405524254,
-0.02625134214758873,
-0.04009781777858734,
-0.019691482186317444,
0.016491923481225967,
-0.012633134610950947,
0.07220274209976196,
-0.012882010079920292,
-0.01168790366500616,
0.033598095178604126,
0.04563752934336662,
0.031305454671382904,
0.011308007873594761,
-0.030807863920927048,
-0.00933064240962267,
-0.05083112046122551,
0.038153357803821564,
0.042636919766664505,
0.05049875006079674,
0.03491393104195595,
-0.017461223527789116,
0.011699269525706768,
-0.007772183045744896,
-0.031742412596940994,
0.009248225018382072,
0.00435705715790391,
-0.01876154914498329,
-0.04945439100265503,
-0.012660909444093704,
-0.015961352735757828,
-0.01377374492585659,
-0.02948332391679287,
-0.0008109619375318289,
-0.003883413039147854,
0.016717692837119102,
0.013806333765387535,
0.001618147362023592,
0.007835929282009602,
0.0005293902941048145,
0.04427195340394974,
-0.042044803500175476,
0.01180760096758604,
-0.04853416606783867,
-0.0042415824718773365,
0.00583305861800909,
-0.012327766045928001,
-0.0373232364654541,
0.009948461316525936,
-0.04174751043319702,
0.009743891656398773,
0.018368976190686226,
0.00360335735604167,
-0.015524781309068203,
-0.04968060180544853,
0.004594579804688692,
0.0017987097380682826,
0.04357525333762169,
-0.07272661477327347,
-0.043531887233257294,
0.04778569936752319,
-0.025973035022616386,
-0.015892473980784416,
-0.013581485487520695,
-0.008567252196371555,
0.03030431643128395,
0.022730711847543716,
-0.004799476359039545,
-0.023069655522704124,
0.08518008887767792,
-0.04798579216003418,
-0.023684145882725716,
-0.005177769344300032,
0.015587911941111088,
0.020510902628302574,
-0.005121038295328617,
-0.005423119757324457,
-0.0349649116396904,
-0.008645476773381233,
0.023993058130145073,
0.05262332782149315,
0.007561087608337402,
0.00213189166970551,
-0.008943225257098675,
-0.009915590286254883,
-0.01665710285305977,
0.026784636080265045,
-0.001439927495084703,
0.004598226398229599,
0.021313603967428207,
-0.010544945485889912,
0.015227572992444038,
0.012174703180789948,
-0.015101244673132896,
-0.09252521395683289,
-0.000544617185369134,
0.03791840374469757,
-0.03218304365873337,
0.053777649998664856,
-0.02380250208079815,
0.026189615949988365,
-0.000809851277153939,
-0.05459175258874893,
-0.002845918759703636,
-0.04866315796971321,
-0.022851023823022842,
-0.041884344071149826,
0.025755779817700386,
-0.003981658723205328,
0.056649982929229736,
-0.009690284729003906,
0.03361120820045471,
0.022181402891874313,
0.005687952507287264,
0.005599633324891329,
-0.041319143027067184,
0.01666325516998768,
0.040983647108078,
0.025348160415887833,
0.013288668356835842,
0.042879268527030945,
-0.04997805133461952,
-0.02042975276708603,
0.005661399103701115,
-0.02364862710237503,
0.043187547475099564,
0.01787785440683365,
-0.0010985782137140632,
-0.04111046716570854,
0.05265001207590103,
0.016961729153990746,
0.03567607328295708,
0.013634718023240566,
0.03100632317364216,
0.022131986916065216,
0.021756840869784355,
0.010436894372105598,
0.02261900156736374,
0.0019255258375778794,
-0.04894670471549034,
-0.05350371077656746,
0.04403451457619667,
-0.03770306706428528,
0.03570348024368286,
0.044700365513563156,
-0.0010931002907454967,
0.005288992542773485,
-0.017773566767573357,
-0.043253518640995026,
-0.01065179705619812,
0.009760482236742973,
0.06349202245473862,
-0.005442161113023758,
-0.005048641934990883,
0.014868619851768017,
-0.026708267629146576,
0.01794523186981678,
-0.010315673425793648,
0.01727202720940113,
-0.060906171798706055,
-0.023403041064739227,
0.010869752615690231,
0.03016471676528454,
0.01258276216685772,
-0.013915485702455044,
-0.006159136071801186,
-0.0007180457469075918,
0.04370610788464546,
0.032627154141664505,
0.015925128012895584,
0.03270702809095383,
-0.023558150976896286,
0.009671653620898724,
-0.05303914472460747,
0.019008997827768326,
-0.01857113465666771,
0.053784869611263275,
-0.020280897617340088,
-0.028086252510547638,
0.0003747876617126167,
0.024518169462680817,
0.08302053809165955,
-0.010187393054366112,
-0.011645819991827011,
-0.0027128788642585278,
-0.022860407829284668,
0.021668050438165665,
-0.07702846080064774,
0.003915650770068169,
0.009291463531553745,
-0.03634258732199669,
0.019515588879585266,
0.014811176806688309,
-0.008562085218727589,
-0.031938567757606506,
0.02902122214436531,
-0.009610230103135109,
-0.0011631970992311835,
0.028187697753310204,
0.0016334365354850888,
0.030634760856628418,
-0.013944205828011036,
-0.024481944739818573,
0.0435495562851429,
-0.009111111983656883,
0.02974250353872776,
0.025615734979510307,
-0.026865508407354355,
-0.023510023951530457,
0.060683321207761765,
-0.025376327335834503,
0.014027062803506851,
-0.008545506745576859,
-0.04304927587509155,
0.029454493895173073,
-0.02517830766737461,
0.039838358759880066,
0.013113687746226788,
-0.033131830394268036,
0.00943383015692234,
0.04221120476722717,
0.05064775049686432,
0.05335480347275734,
0.005991918500512838,
0.0022467952221632004,
-0.0062660640105605125,
-0.0028065484948456287,
-0.0025406682398170233,
0.03011065348982811,
0.07149091362953186,
-0.0053361449390649796,
-0.00591493071988225,
0.030693162232637405,
0.03294281288981438,
0.022547978907823563,
0.040511973202228546,
0.04339788481593132,
-0.023049093782901764,
-0.03307946026325226,
0.011252548545598984,
-0.010684870183467865,
0.03197017312049866,
-0.02507377229630947,
-0.011529573239386082,
0.03287450224161148,
0.00297768646851182,
-0.00784220825880766,
-0.07499144971370697,
0.030555229634046555,
0.0034518102183938026,
0.00649920804426074,
-0.031788378953933716,
0.026826204732060432,
-0.027451442554593086,
0.01696384698152542,
-0.009714752435684204,
0.006169202271848917,
-0.021967876702547073,
-0.022163260728120804,
0.042715057730674744,
-0.029809001833200455,
0.023332366719841957,
-0.042618490755558014,
-0.030512310564517975,
-0.05137764289975166,
-0.015325956046581268,
0.019994907081127167,
0.04003559798002243,
-0.022490384057164192,
0.02439529076218605,
-0.025843480601906776,
-0.005671751219779253,
0.04715540632605553,
-0.04213287681341171,
-0.00500639621168375,
-0.018049731850624084,
0.007591076195240021,
-0.06543929129838943,
-0.023163145408034325
] |
<p>I've heard that turning on faucets to a slight drip will prevent pipes from freezing, but I've never understood why this is the case. Can anyone out there help me to understand? Thanks!</p>
| 8,333 |
[
-0.010206792503595352,
-0.015365123748779297,
-0.017411598935723305,
-0.028795253485441208,
0.03648395463824272,
-0.002229071920737624,
0.002104369457811117,
-0.0017856316408142447,
0.022084342315793037,
0.0007438386091962457,
-0.003634265623986721,
0.07210927456617355,
-0.015436346642673016,
-0.004752260632812977,
0.028700759634375572,
0.0070016272366046906,
-0.0125891687348485,
-0.03501905873417854,
-0.005003518890589476,
-0.011348324827849865,
-0.03743641451001167,
0.02757677435874939,
0.00559877697378397,
0.012717322446405888,
-0.03615447133779526,
0.0091074388474226,
-0.00582408020272851,
-0.01093942578881979,
0.01877628266811371,
-0.011846509762108326,
0.012968522496521473,
-0.025352230295538902,
0.004398074001073837,
0.031979795545339584,
0.01690841279923916,
-0.03277389332652092,
-0.0017915559001266956,
0.008610768243670464,
-0.0004073021118529141,
0.05102420970797539,
-0.03965632617473602,
-0.023618940263986588,
-0.024998892098665237,
0.0065262517891824245,
-0.038273584097623825,
-0.01977120153605938,
0.013366976752877235,
-0.017684342339634895,
0.03964870050549507,
-0.03949575126171112,
-0.005876976530998945,
0.0012014787644147873,
0.033413391560316086,
0.019253449514508247,
0.02218838781118393,
0.03832248970866203,
0.07939425110816956,
0.06161247938871384,
-0.01915392279624939,
-0.05981896445155144,
-0.025977613404393196,
-0.040688201785087585,
-0.05053049325942993,
-0.0022125691175460815,
-0.031001640483736992,
0.01820114254951477,
0.016367079690098763,
-0.058224719017744064,
0.0318518690764904,
0.007737861480563879,
0.0005181687884032726,
-0.020120583474636078,
0.030625060200691223,
-0.03968650475144386,
0.013353070244193077,
-0.010533841326832771,
0.016427116468548775,
-0.019869372248649597,
0.015659255906939507,
0.023979851976037025,
-0.005669965408742428,
0.02777322567999363,
0.05836833268404007,
0.0685473084449768,
-0.007499555591493845,
-0.015209459699690342,
0.08981073647737503,
-0.009646749123930931,
0.06406969577074051,
0.042758289724588394,
-0.015054327435791492,
0.013768915086984634,
0.004044265951961279,
0.029923170804977417,
-0.03244111314415932,
0.006077611353248358,
0.00801592506468296,
0.042464155703783035,
0.0024223248474299908,
-0.004659716971218586,
0.02148081362247467,
0.01725965552031994,
0.007875080220401287,
0.05487418919801712,
-0.02229439653456211,
-0.034856658428907394,
-0.04981379583477974,
0.03353752940893173,
-0.01073212269693613,
-0.00038543588016182184,
-0.016337811946868896,
-0.037548501044511795,
-0.03969372808933258,
-0.03699205443263054,
0.018126316368579865,
-0.006980714853852987,
0.020402561873197556,
-0.033639997243881226,
0.03097674809396267,
0.03617752343416214,
0.005943369586020708,
-0.016723403707146645,
0.006207432597875595,
-0.014730248600244522,
-0.06049172952771187,
0.036235276609659195,
0.0063801598735153675,
-0.021166376769542694,
-0.03627060726284981,
0.012989485636353493,
-0.010428577661514282,
-0.006893105339258909,
0.02356569655239582,
0.018489506095647812,
0.08121949434280396,
-0.012392709963023663,
-0.08524467796087265,
-0.05553290247917175,
0.06903276592493057,
0.02369908057153225,
-0.010114152915775776,
-0.09165234863758087,
-0.012258767150342464,
-0.0038657926488667727,
0.04336385056376457,
-0.03218041732907295,
0.009899194352328777,
0.001460161292925477,
-0.050393957644701004,
0.014643223024904728,
-0.022444095462560654,
-0.024445239454507828,
0.014841009862720966,
-0.025883173570036888,
-0.006040043663233519,
-0.058547988533973694,
0.021505240350961685,
0.04206954687833786,
-0.034544773399829865,
-0.061352260410785675,
-0.015434550121426582,
-0.014636718668043613,
-0.018388712778687477,
0.004727539140731096,
-0.010928594507277012,
-0.06235971674323082,
0.05977124720811844,
-0.006385487969964743,
-0.003764909924939275,
0.03185956925153732,
-0.015050958842039108,
0.030807195231318474,
0.013288610614836216,
0.07258903980255127,
0.017413437366485596,
-0.02241230010986328,
0.017949359491467476,
-0.017871802672743797,
0.01466363389045,
0.023924633860588074,
-0.03635169193148613,
0.0018017217516899109,
0.017863977700471878,
0.019499389454722404,
-0.012741674669086933,
0.021974895149469376,
-0.007631487213075161,
-0.026154566556215286,
0.029062574729323387,
-0.08082673698663712,
-0.02325483225286007,
-0.07401572912931442,
-0.004115593153983355,
-0.02799253724515438,
-0.003517214674502611,
0.005292506888508797,
0.03825315833091736,
0.05514645203948021,
-0.03446290269494057,
-0.015431246720254421,
0.02519790083169937,
-0.005543451756238937,
0.012626033276319504,
-0.0196200180798769,
0.035073328763246536,
0.039509743452072144,
0.05830095335841179,
0.0105555085465312,
0.023302258923649788,
-0.04056239873170853,
-0.028422027826309204,
-0.01387390960007906,
0.022883176803588867,
0.026070594787597656,
-0.04005224257707596,
-0.02794473245739937,
0.04612382873892784,
-0.010463803075253963,
0.024287303909659386,
0.042969197034835815,
-0.03912538290023804,
0.04796494543552399,
0.036528412252664566,
0.003468242706730962,
-0.02658018283545971,
0.00013614812633022666,
0.041113436222076416,
-0.0022365229669958353,
0.007685611955821514,
-0.0297015942633152,
-0.020229026675224304,
-0.0053266542963683605,
0.046371616423130035,
0.010100610554218292,
-0.04167845472693443,
-0.00934408139437437,
0.023002129048109055,
0.05355123430490494,
0.0037086803931742907,
0.018206067383289337,
-0.02286924421787262,
0.014352640137076378,
-0.0009306404390372336,
0.03403010219335556,
0.012950151227414608,
0.030545352026820183,
0.030357742682099342,
0.026920827105641365,
0.047482457011938095,
-0.0394098237156868,
-0.05424290895462036,
0.028709065169095993,
0.006494127679616213,
0.03355298191308975,
0.0241512693464756,
-0.030639585107564926,
0.037899840623140335,
-0.05434054136276245,
0.0051814657635986805,
0.004305178299546242,
0.017329243943095207,
0.024270663037896156,
-0.03892498090863228,
-0.030292073264718056,
0.06028404459357262,
0.008803632110357285,
-0.02101314254105091,
-0.004288484342396259,
0.04149795323610306,
-0.020842764526605606,
0.03189808502793312,
-0.039581432938575745,
-0.022155990824103355,
-0.027064578607678413,
0.021389702335000038,
0.05281224846839905,
-0.005039124749600887,
0.04190438985824585,
-0.02995062619447708,
-0.02601187489926815,
-0.029607966542243958,
-0.02602986991405487,
-0.04231971502304077,
0.014894524589180946,
-0.007985878735780716,
0.0035374918952584267,
0.014990420080721378,
0.023256530985236168,
0.06247927248477936,
-0.009889421053230762,
0.02024911716580391,
-0.00635267561301589,
0.0008415277698077261,
-0.015737760812044144,
-0.026497654616832733,
-0.027348719537258148,
0.0562087818980217,
-0.011151614598929882,
0.014028606005012989,
0.053473956882953644,
-0.014669652096927166,
-0.027605194598436356,
0.024750076234340668,
-0.05913199484348297,
-0.030954675748944283,
0.008771924301981926,
-0.02966340258717537,
-0.0013671789783984423,
-0.002595430938526988,
0.00973614864051342,
0.0072891367599368095,
-0.10035407543182373,
-0.03446773812174797,
0.00004402674312586896,
-0.057403337210416794,
0.03292229399085045,
-0.016150277107954025,
0.017290420830249786,
-0.0021992181427776814,
-0.01211524661630392,
0.03635173663496971,
-0.008270170539617538,
-0.04264555126428604,
-0.0036161914467811584,
-0.03851459175348282,
-0.02738979086279869,
-0.03941095992922783,
-0.006070888601243496,
0.06976772844791412,
-0.0031084034126251936,
0.018651379272341728,
-0.0012571874540299177,
0.059811100363731384,
0.037391357123851776,
0.02014019526541233,
-0.011421182192862034,
-0.022808386012911797,
0.01448262669146061,
-0.0007691974169574678,
-0.02645571529865265,
-0.006658494472503662,
0.0021190138068050146,
-0.026812536641955376,
-0.021351035684347153,
0.028439000248908997,
0.034315358847379684,
-0.01524539478123188,
0.05708572641015053,
-0.03477892279624939,
0.005669130012392998,
-0.06753476709127426,
0.016762828454375267,
-0.030472882091999054,
0.027428582310676575,
-0.00047918950440362096,
0.00694657489657402,
0.029311614111065865,
-0.03393759950995445,
-0.00767738139256835,
0.03837938234210014,
0.036888301372528076,
-0.03397376835346222,
-0.008966056630015373,
0.006400715559720993,
-0.05249413847923279,
0.03371460363268852,
0.022300034761428833,
-0.009822367690503597,
0.06771954894065857,
0.02283991500735283,
0.0344606377184391,
-0.00849898625165224,
-0.04040953516960144,
0.016789624467492104,
-0.060480646789073944,
0.016767676919698715,
0.005284380633383989,
0.028136953711509705,
-0.010736223310232162,
0.07076898962259293,
0.02097221650183201,
0.055582161992788315,
-0.012835566885769367,
-0.005097496788948774,
-0.05563992261886597,
0.01791652850806713,
-0.04369344934821129,
-0.008639325387775898,
-0.016747182235121727,
-0.004612317308783531,
-0.033215925097465515,
-0.05350538343191147,
-0.040215183049440384,
-0.0011848671128973365,
0.043597083538770676,
-0.038963962346315384,
-0.010172947309911251,
0.0034019481390714645,
-0.0064970143139362335,
-0.024486100301146507,
0.00581629341468215,
0.017983337864279747,
-0.05524924769997597,
0.040628645569086075,
0.0009417439578101039,
-0.032243762165308,
-0.015176794491708279,
0.027376748621463776,
0.042422451078891754,
0.046778567135334015,
0.018834339454770088,
0.04321529343724251,
0.0008921764674596488,
-0.020140059292316437,
-0.03292325511574745,
0.04269273206591606,
0.06006774678826332,
-0.027512770146131516,
-0.02076914720237255,
-0.02930152229964733,
-0.03111911751329899,
-0.022826580330729485,
0.03800113499164581,
0.009176216088235378,
-0.04345141723752022,
0.03766298666596413,
-0.012541151605546474,
-0.018057161942124367,
-0.03504406660795212,
0.04500497132539749,
0.06589322537183762,
0.029538070783019066,
-0.026805205270648003,
-0.03852180391550064,
0.002520800568163395,
-0.01710478961467743,
-0.002260714303702116,
0.04729349538683891,
0.03895534947514534,
-0.0561804436147213,
-0.0006786783342249691,
0.015086204744875431,
-0.02307606302201748,
0.005927725695073605,
-0.04143901914358139,
0.03758057951927185,
0.051592595875263214,
-0.00017998884140979499,
0.009144820272922516,
-0.0013685119338333607,
0.0028020874597132206,
0.013013231568038464,
0.005882780067622662,
-0.011452332139015198,
-0.08127341419458389,
-0.028433341532945633,
0.053412482142448425,
0.023561829701066017,
-0.02605547197163105,
0.014982025139033794,
-0.05908728018403053,
-0.0382164791226387,
0.06784230470657349,
-0.03272739052772522,
0.002318836748600006,
-0.031966015696525574,
0.01810901053249836,
-0.030488107353448868,
-0.027131544426083565,
0.028345812112092972,
0.02672461047768593,
-0.020564908161759377,
0.05323479324579239,
0.004913505632430315,
-0.04251028969883919,
-0.03154219314455986,
-0.014560671523213387,
0.004534177947789431,
0.05095667019486427,
-0.02169658988714218,
0.0027073249220848083,
-0.009590400382876396,
0.05386047437787056,
-0.03561688959598541,
-0.06264150887727737,
-0.0029710542876273394,
-0.02889282815158367,
0.010879626497626305,
0.014246825128793716,
-0.016017068177461624,
-0.009793945588171482,
0.04548392817378044,
0.009864415973424911,
-0.02472788468003273,
-0.017092851921916008,
-0.023028133437037468,
0.02669386751949787,
0.03051430732011795,
0.01285422034561634,
0.06442759186029434,
0.040313854813575745,
-0.047946326434612274,
-0.03998401388525963,
-0.003514823503792286,
0.07202070951461792,
-0.048859283328056335,
0.0033267978578805923,
0.0020412923768162727,
0.002187660662457347,
-0.0246561411768198,
0.046001967042684555,
0.0008456271607428789,
0.037034232169389725,
0.03655540198087692,
0.006047206465154886,
0.0018953154794871807,
0.018161460757255554,
0.04307929053902626,
-0.03117329254746437,
0.0064310915768146515,
0.02669082209467888,
0.001943901996128261,
-0.03577764332294464,
0.04477131366729736,
-0.031105706468224525,
-0.008341604843735695,
0.02744048833847046,
-0.015521845780313015,
0.008452420122921467,
-0.01851198822259903,
-0.010957594029605389,
0.010802287608385086,
-0.025145141407847404,
0.023716796189546585,
-0.023074980825185776,
-0.01841498352587223,
0.02992318384349346,
-0.04912746325135231,
0.028411082923412323,
0.04403157904744148,
0.021671559661626816,
0.032391708344221115,
-0.022366534918546677,
0.057280536741018295,
0.006097124889492989,
0.033198557794094086,
-0.022223403677344322,
-0.06533422321081161,
0.023093681782484055,
0.021543895825743675,
-0.010267442092299461,
-0.057383645325899124,
-0.011105640791356564,
-0.009042481891810894,
-0.040762804448604584,
0.016343168914318085,
0.020268678665161133,
-0.024329306557774544,
0.004500641953200102,
0.04555703327059746,
0.004436578135937452,
0.04842568561434746,
0.009654100053012371,
-0.024916360154747963,
0.02475166879594326,
-0.079002246260643,
-0.028144769370555878,
0.0000028881588605145225,
0.05590415000915527,
-0.023996904492378235,
-0.003181174397468567,
0.03229394927620888,
-0.022317303344607353,
0.07195600122213364,
0.0181327722966671,
0.013316317461431026,
0.021653199568390846,
0.033146459609270096,
0.002714234869927168,
-0.030340127646923065,
0.018267996609210968,
0.01807273179292679,
0.04660754278302193,
0.0005867062136530876,
-0.02416856400668621,
-0.02428416535258293,
-0.0023304950445890427,
-0.026155704632401466,
0.007107832003384829,
-0.022089824080467224,
0.05563511326909065,
0.05782884731888771,
-0.03129900246858597,
0.006595700513571501,
0.007871809415519238,
-0.0001500416692579165,
0.026275472715497017,
0.04076552391052246,
0.007366252597421408,
-0.00867601577192545,
0.004665767773985863,
0.01737891510128975,
-0.04795825853943825,
-0.01615738868713379,
-0.01854955218732357,
0.013223961926996708,
-0.017818668857216835,
0.05294099077582359,
0.04355597868561745,
-0.02598598226904869,
-0.0077762482687830925,
-0.003988177049905062,
-0.033257726579904556,
0.033206600695848465,
-0.014387097209692001,
0.0007998039363883436,
-0.012978736311197281,
-0.0230767372995615,
0.018613500520586967,
0.040020786225795746,
-0.0015755073400214314,
0.01815005950629711,
0.025781983509659767,
0.007645993959158659,
-0.007548592984676361,
-0.006793817039579153,
-0.017791107296943665,
0.06090028956532478,
-0.031268831342458725,
0.03229498863220215,
0.012988794595003128,
-0.018951063975691795,
0.03479887545108795,
-0.04307457059621811,
-0.00793711468577385,
-0.0640004426240921,
0.012315385974943638,
-0.009870908223092556,
-0.0014509657630696893,
0.02091876231133938,
-0.031391941010951996,
0.012693451717495918,
0.02069704420864582,
0.03280378878116608,
0.000859866151586175,
0.00888420082628727,
-0.002188831800594926,
-0.05210351198911667,
0.002253446262329817,
0.0047169337049126625,
-0.028250636532902718,
0.013044793158769608,
0.0003222069644834846,
-0.018937963992357254,
-0.022348036989569664,
-0.006752713583409786,
0.0008669124217703938,
-0.014696934260427952,
0.00041131817852146924,
-0.0062255957163870335,
0.05987181514501572,
0.014818394556641579,
0.010358587838709354,
0.021545488387346268,
-0.04242667928338051,
0.11387942731380463,
0.0397690124809742,
0.021761856973171234,
-0.06362050026655197,
0.018655672669410706,
0.009862701408565044,
0.0039034446235746145,
-0.015937568619847298,
-0.005648145452141762,
0.00723798805847764,
0.023434042930603027,
0.05602080747485161,
0.045513980090618134,
0.010992506518959999,
0.045095499604940414,
0.06835802644491196,
-0.0796898901462555,
-0.03644372150301933,
0.008044055663049221,
0.009022310376167297,
0.0005811614682897925,
-0.01743670180439949,
-0.04493505135178566,
0.03441298007965088,
-0.012764805927872658,
-0.0021995871793478727,
0.0034501415211707354,
-0.030249984934926033,
0.05739634111523628,
0.0012934979749843478,
-0.04770757630467415,
0.03882470726966858,
0.042201172560453415,
-0.01823563687503338,
-0.018329720944166183,
-0.004529342986643314,
0.025098197162151337,
-0.01673649437725544,
0.0015319247031584382,
-0.005843207705765963,
0.007526879198849201,
0.012232900597155094,
0.005598109681159258,
0.029149463400244713,
-0.056127529591321945,
0.0159610565751791,
-0.03988981992006302,
-0.019613690674304962,
0.01441148854792118,
-0.0035313281696289778,
-0.00723547488451004,
-0.01249353215098381,
0.02192641608417034,
-0.020407602190971375,
-0.05438997223973274,
-0.013212022371590137,
0.025093769654631615,
-0.0150747736915946,
-0.03440754860639572,
-0.05190935730934143,
0.02561268024146557,
-0.039400748908519745,
0.03586026281118393,
0.00428258441388607,
-0.008195039816200733,
-0.010307303629815578,
-0.002539189299568534,
-0.004919033031910658,
-0.006894613616168499,
0.021531812846660614,
0.0055457004345953465,
0.02692456729710102,
-0.020051661878824234,
-0.02695702575147152,
0.020230408757925034,
0.008714620023965836,
0.028647566214203835,
-0.001173912431113422,
0.017731428146362305,
0.031005414202809334,
-0.07314649969339371,
0.047431014478206635,
-0.014196347445249557,
-0.03199126571416855,
-0.0473615825176239,
0.026669858023524284,
0.011940560303628445,
0.06357043236494064,
-0.003478997154161334,
0.005272462964057922,
-0.014097968116402626,
0.016488268971443176,
0.028920777142047882,
0.008785251528024673,
-0.0400836318731308,
-0.014484010636806488,
-0.0482463613152504,
0.0062280381098389626,
0.022838963195681572,
0.04493652656674385,
0.035167794674634933,
-0.00775716220960021,
0.01555074006319046,
0.002650932176038623,
-0.037291526794433594,
0.0004775028210133314,
0.009083078242838383,
-0.012999995611608028,
-0.04966076463460922,
0.017144637182354927,
-0.024552233517169952,
-0.04920278489589691,
-0.05888530984520912,
0.0026276360731571913,
0.007330764085054398,
0.015006816945970058,
0.017735058441758156,
-0.003698084969073534,
-0.00751403858885169,
-0.008179767057299614,
0.06027907505631447,
-0.026697324588894844,
-0.06119242683053017,
-0.061335738748311996,
-0.022566620260477066,
0.013275937177240849,
0.004356059245765209,
-0.027023915201425552,
-0.007643730845302343,
-0.011385136283934116,
-0.030520502477884293,
-0.0015276914928108454,
0.009333191439509392,
0.010933583602309227,
-0.002352809300646186,
0.03283463045954704,
-0.021068714559078217,
0.06765911728143692,
-0.05326244235038757,
-0.026233144104480743,
0.053014323115348816,
-0.03630358353257179,
-0.048678893595933914,
0.010987420566380024,
-0.016963863745331764,
0.00407032947987318,
0.03007430024445057,
-0.018059033900499344,
0.008169727399945259,
0.07276993989944458,
-0.03087238222360611,
0.018342044204473495,
-0.027791883796453476,
0.020387841388583183,
0.02087329886853695,
0.018756350502371788,
-0.014440019614994526,
-0.05548088997602463,
0.01041325367987156,
0.03588687255978584,
0.04973730072379112,
0.004675344098359346,
-0.015114408917725086,
-0.03626125305891037,
0.03813957795500755,
-0.0422021746635437,
0.016424521803855896,
0.004088506568223238,
0.00909497868269682,
0.016062786802649498,
-0.018764641135931015,
0.03077237494289875,
-0.005764970555901527,
-0.008342881686985493,
-0.07777652889490128,
0.027044223621487617,
-0.021809272468090057,
-0.04461682215332985,
0.014131815172731876,
-0.006861553993076086,
0.013827377930283546,
0.02050285041332245,
-0.06249656155705452,
-0.00289948214776814,
-0.0046936445869505405,
-0.030553661286830902,
-0.04145290330052376,
0.01029963605105877,
0.0051192715764045715,
0.055076923221349716,
0.03459133952856064,
0.010712014511227608,
0.03537546470761299,
-0.00008377825724892318,
-0.003269806271418929,
-0.0026933772023767233,
0.020345259457826614,
0.0566844679415226,
0.002129080006852746,
0.015478968620300293,
0.00018660366185940802,
-0.03125874325633049,
-0.001406891387887299,
0.0004974888288415968,
-0.012565817683935165,
-0.009700803086161613,
0.018153168261051178,
0.030058080330491066,
-0.017121609300374985,
0.03354258090257645,
0.017543472349643707,
0.02387242019176483,
0.022125622257590294,
0.045418448746204376,
0.027851853519678116,
0.025128865614533424,
0.013530719093978405,
-0.005930961575359106,
-0.014166592620313168,
-0.025750108063220978,
-0.040694475173950195,
0.02044185809791088,
-0.05369706451892853,
-0.017847761511802673,
0.04460645094513893,
0.007261091377586126,
0.043238114565610886,
-0.043098319321870804,
0.0015922409947961569,
-0.018665067851543427,
-0.03524281457066536,
0.0389050729572773,
0.033384449779987335,
0.03238120675086975,
0.015700839459896088,
0.015491900034248829,
-0.025845052674412727,
-0.002785599324852228,
0.025155840441584587,
-0.04460693895816803,
-0.036911722272634506,
-0.002129959873855114,
0.00030734320171177387,
0.010981172323226929,
-0.041719574481248856,
-0.03732055425643921,
-0.014808899722993374,
0.023192429915070534,
0.03035847842693329,
0.01616351678967476,
-0.012110169045627117,
-0.04724671691656113,
-0.03697962313890457,
-0.02612224593758583,
0.057240549474954605,
-0.015543843619525433,
0.013744846917688847,
-0.03510688245296478,
-0.00882761087268591,
-0.028341101482510567,
0.019956348463892937,
0.07211311906576157,
-0.004464714787900448,
0.013128873892128468,
0.0028076395392417908,
-0.000192973340745084,
0.03551589325070381,
-0.042372629046440125,
0.008061372675001621,
0.0024887665640562773,
-0.03677127882838249,
-0.000502644688822329,
-0.02474786341190338,
-0.01831129379570484,
-0.005782958120107651,
-0.0021335540805011988,
-0.0072963647544384,
0.054935991764068604,
-0.008163523860275745,
0.01736939512193203,
0.01194850169122219,
0.012823747470974922,
-0.018465884029865265,
0.07091125100851059,
-0.06953521817922592,
0.012985906563699245,
0.01450097281485796,
-0.008054434321820736,
-0.042306337505578995,
0.05695672333240509,
0.008487650193274021,
0.07265730947256088,
-0.007956565357744694,
-0.03719935193657875,
-0.009830002672970295,
-0.027555763721466064,
0.03497691825032234,
-0.02499609813094139,
-0.04708158224821091,
0.01728402078151703,
0.05969899892807007,
-0.0035629000049084425,
0.019581502303481102,
-0.01241475809365511,
0.01728075183928013,
-0.01390927005559206,
0.04467903822660446,
-0.003017673036083579,
0.06174052506685257,
0.0044632889330387115,
-0.007146545685827732,
0.022944452241063118,
0.025922929868102074,
0.015027820132672787,
0.03849828243255615,
0.004750077612698078,
0.05289243906736374,
-0.007099417969584465,
-0.06994911283254623,
0.013942252844572067,
-0.03788132593035698,
-0.01650257408618927,
0.011959555558860302,
-0.023885779082775116,
0.056567102670669556,
-0.040080174803733826,
0.0355239100754261,
-0.02583027258515358,
-0.02152680978178978,
0.02297820709645748,
-0.02398102544248104,
-0.01679491065442562,
0.007444190327078104,
-0.012843769043684006,
0.009989609010517597,
0.0001726613554637879,
-0.003655797801911831,
0.0029040176887065172,
-0.00175669405143708,
0.026647329330444336,
-0.019370390102267265,
0.03935236111283302,
-0.04640941321849823,
0.010789657942950726,
-0.04096008464694023,
-0.037937842309474945,
0.0054069748148322105,
0.0575614832341671,
0.01582379825413227,
0.0131389070302248,
-0.06847892701625824,
-0.0020701957400888205,
0.05746078863739967,
-0.05458981171250343,
-0.023435449227690697,
-0.006814032327383757,
0.010624369606375694,
-0.0026709758676588535,
0.014284874312579632
] |
<p>I've always heard that watering plants if the temperature goes a few degrees below freezing will help prevent them from freezing, but I've never quite understood the physics behind it. Can you guys help me to understand this a bit better? Thanks!</p>
| 8,334 |
[
-0.007547218352556229,
-0.06426551192998886,
-0.05210157111287117,
-0.018579818308353424,
0.007485915441066027,
-0.011936347000300884,
-0.031931303441524506,
-0.005857475101947784,
0.0012652539880946279,
-0.01660146377980709,
0.022321736440062523,
0.048457760363817215,
-0.0024902268778532743,
-0.035972557961940765,
0.02953515201807022,
0.012755988165736198,
0.00317191518843174,
-0.03352237120270729,
0.0027099838480353355,
0.017106927931308746,
-0.0352323055267334,
0.015035177581012249,
-0.0017486013239249587,
0.02249111607670784,
-0.011635759845376015,
0.017641296610236168,
0.021103471517562866,
-0.001920043840073049,
0.019898926839232445,
-0.007549461908638477,
0.025737715885043144,
-0.03333393111824989,
0.004197177477180958,
0.05420820042490959,
0.02438427321612835,
-0.015056598000228405,
-0.02467801794409752,
-0.028880126774311066,
-0.03842935711145401,
0.021135589107871056,
-0.03822077065706253,
-0.02634258382022381,
-0.017887456342577934,
0.004741932265460491,
-0.029562992975115776,
0.007692407816648483,
0.009842236526310444,
-0.019809599965810776,
0.05384381487965584,
-0.03999549150466919,
0.015213190577924252,
0.03315044566988945,
0.02838299050927162,
0.056399039924144745,
0.018624573945999146,
0.028175828978419304,
0.09597936272621155,
0.04429725185036659,
-0.06291073560714722,
-0.06080441176891327,
-0.031544215977191925,
-0.03586447983980179,
-0.029358679428696632,
-0.005651780404150486,
-0.016556106507778168,
0.010979422368109226,
0.012498563155531883,
-0.029039258137345314,
0.04934660345315933,
0.032571159303188324,
0.016294831410050392,
-0.005256918724626303,
0.04407896846532822,
-0.0205055121332407,
0.005279293283820152,
-0.013277223333716393,
0.0063744657672941685,
0.009457350708544254,
0.02569565549492836,
0.021476618945598602,
0.007968846708536148,
0.04114961251616478,
0.002295004902407527,
0.05762846767902374,
-0.0050251600332558155,
-0.028304316103458405,
0.07847270369529724,
-0.003134157508611679,
0.06384474784135818,
0.016604499891400337,
-0.014303482137620449,
0.031175946816802025,
0.005247794091701508,
-0.008910705335438251,
-0.024674898013472557,
0.010756672360002995,
0.005466686096042395,
0.028284519910812378,
-0.004424400627613068,
-0.03282711282372475,
0.01667005755007267,
-0.009947788901627064,
0.003821357386186719,
0.0625411793589592,
-0.02874671295285225,
-0.05890360847115517,
-0.009516329504549503,
0.022312112152576447,
-6.029912356098066e-7,
0.004012011922895908,
-0.03038606606423855,
-0.009401979856193066,
-0.024331428110599518,
-0.0644821897149086,
0.018370244652032852,
-0.049887046217918396,
0.0001838656171457842,
-0.030115822330117226,
0.02875366061925888,
0.047775860875844955,
0.02068491280078888,
-0.02001785673201084,
0.02223111316561699,
0.0035575919318944216,
-0.06350360065698624,
0.027074798941612244,
0.009133484214544296,
-0.00801137089729309,
-0.05245944857597351,
-0.019972698763012886,
-0.013139513321220875,
0.0291117075830698,
-0.0015359437093138695,
-0.02114293910562992,
0.03900977969169617,
-0.025408517569303513,
-0.06949681043624878,
-0.04488454386591911,
0.04667011275887489,
-0.0031647055875509977,
-0.013226442970335484,
-0.08030907064676285,
0.0033885426819324493,
-0.020302826538681984,
0.0790262222290039,
-0.015286511741578579,
0.011480240151286125,
-0.017528438940644264,
-0.019729534164071083,
0.007779059931635857,
0.014474252238869667,
-0.01052751112729311,
0.025101156905293465,
-0.0393056720495224,
-0.0037092792335897684,
-0.04335051402449608,
0.04618268832564354,
0.05346411094069481,
-0.02627030946314335,
-0.03294932469725609,
0.008143970742821693,
-0.03119736909866333,
0.022045621648430824,
0.0037484231870621443,
-0.0261820200830698,
-0.05568033456802368,
0.036716658622026443,
-0.011876439675688744,
-0.007780308835208416,
0.013236088678240776,
0.0128366369754076,
0.056084178388118744,
0.0007023747893981636,
0.061371687799692154,
0.02790503390133381,
-0.017789317294955254,
0.02401721104979515,
-0.016862936317920685,
0.034824252128601074,
0.01587207242846489,
-0.050651293247938156,
0.004567087162286043,
0.025225652381777763,
0.030549202114343643,
-0.03145487606525421,
0.03328621760010719,
-0.008213048800826073,
-0.01862104795873165,
0.008317436091601849,
-0.08475872874259949,
-0.012178785167634487,
-0.0870257094502449,
0.0015620290068909526,
-0.035478200763463974,
0.017476152628660202,
0.014912186190485954,
0.029042869806289673,
0.03644352778792381,
-0.04477380961179733,
-0.022746562957763672,
0.007387340068817139,
0.03304291516542435,
0.006874764338135719,
-0.020204460248351097,
0.02574663981795311,
0.07716376334428787,
0.04612934589385986,
0.015392892993986607,
0.03466278687119484,
-0.037692852318286896,
-0.02211587317287922,
-0.020198354497551918,
-0.015881787985563278,
-0.016660764813423157,
-0.0025056269951164722,
-0.02730949968099594,
0.058702241629362106,
-0.004585113376379013,
0.022842343896627426,
0.03212353587150574,
-0.03260841965675354,
0.09684719145298004,
0.04191188886761665,
0.00519020389765501,
-0.023184429854154587,
0.007578684017062187,
0.02733468823134899,
0.0003624506643973291,
-0.002816456835716963,
-0.034588221460580826,
-0.04143035039305687,
-0.013259789906442165,
0.06667627394199371,
0.03425261378288269,
-0.03697872906923294,
-0.02245224080979824,
0.008934658020734787,
0.05662725865840912,
0.0516914501786232,
0.035874951630830765,
-0.02516639605164528,
0.024984948337078094,
0.01236726250499487,
0.02885068766772747,
0.008318827487528324,
0.006707358174026012,
0.023975959047675133,
0.016308387741446495,
0.02790183387696743,
-0.019879892468452454,
-0.05045132711529732,
0.023067783564329147,
0.03947333246469498,
0.056785862892866135,
0.015108412131667137,
-0.027996787801384926,
0.009389206767082214,
-0.04976153373718262,
-0.010663743130862713,
-0.004783687647432089,
0.0017926072468981147,
0.03384371101856232,
-0.04542415961623192,
-0.014428451657295227,
0.05453622341156006,
0.03128393366932869,
-0.0412873812019825,
-0.010718243196606636,
0.025145841762423515,
-0.01760117895901203,
0.020773516967892647,
-0.0025108777917921543,
-0.0275713000446558,
0.001778201898559928,
0.03370597958564758,
0.060984596610069275,
0.01693262718617916,
0.048459284007549286,
-0.01620388776063919,
-0.03476634621620178,
-0.026287687942385674,
-0.04982650652527809,
-0.010442105121910572,
0.017494257539510727,
0.005863677244633436,
0.019507460296154022,
-0.005430618301033974,
-0.009753044694662094,
0.042694877833127975,
-0.021371006965637207,
0.014259100891649723,
-0.022671597078442574,
0.00009624374069971964,
0.00014877579815220088,
-0.011114883236587048,
-0.01806083507835865,
0.01906726136803627,
-0.014841959811747074,
0.014497105963528156,
0.04439298436045647,
-0.026448365300893784,
-0.008981343358755112,
0.010961216874420643,
-0.082551509141922,
-0.03839396312832832,
-0.004999564960598946,
-0.007140067405998707,
-0.005346142221242189,
-0.01850701868534088,
0.006860926281660795,
-0.006300861481577158,
-0.08079084753990173,
-0.00013487081741914153,
-0.03413695469498634,
-0.08345386385917664,
0.006890756078064442,
0.030862845480442047,
0.021752865985035896,
-0.008371653035283089,
-0.009362283162772655,
0.051302433013916016,
-0.005410798825323582,
-0.05450094863772392,
-0.012664592824876308,
-0.03341932222247124,
-0.0314055010676384,
-0.004127133637666702,
0.011463217437267303,
0.05697197839617729,
-0.010111333802342415,
0.03900569677352905,
0.06308644264936447,
0.008275889791548252,
0.028404172509908676,
0.0230556633323431,
-0.025489749386906624,
-0.02623068355023861,
0.02318723499774933,
0.027507372200489044,
0.0007411870174109936,
-0.02913324162364006,
-0.01940135657787323,
-0.011164936237037182,
-0.014575817622244358,
0.04803239181637764,
0.04765525087714195,
-0.010487301275134087,
0.06889660656452179,
-0.0020538438111543655,
0.016977181658148766,
-0.048661280423402786,
0.04114313796162605,
-0.0316728800535202,
0.035876885056495667,
0.037457097321748734,
0.0011613056994974613,
0.02196601592004299,
0.0008974395459517837,
-0.03142443299293518,
0.01127812173217535,
0.04751352593302727,
-0.06973231583833694,
-0.011490721255540848,
0.004649478476494551,
-0.03541078418493271,
0.030139319598674774,
-0.0015311570605263114,
-0.007426786702126265,
0.04059462994337082,
0.013750883750617504,
0.019798800349235535,
0.009431061334908009,
-0.03774956241250038,
0.010199079290032387,
-0.04132937267422676,
0.002270189579576254,
0.023005928844213486,
0.018831847235560417,
-0.015493763610720634,
0.08230068534612656,
0.0014814664609730244,
0.05779978260397911,
0.034732118248939514,
0.03707512095570564,
-0.05641479417681694,
0.020384809002280235,
-0.04029202461242676,
-0.01436074823141098,
-0.041233472526073456,
0.033098336309194565,
0.0011371428845450282,
-0.01074218936264515,
0.003053396474570036,
-0.011816351674497128,
0.004427018109709024,
-0.03963132202625275,
-0.0062447525560855865,
0.002871382050216198,
-0.029645174741744995,
-0.04157129302620888,
-0.012441013008356094,
0.02900019846856594,
-0.055002644658088684,
0.031290218234062195,
0.059596676379442215,
-0.022237157449126244,
-0.009160585701465607,
0.0044039213098585606,
0.034375615417957306,
0.062328487634658813,
0.009768189862370491,
0.04159702733159065,
0.0010193688794970512,
0.002602300141006708,
-0.002688587876036763,
0.04839586094021797,
0.06493810564279556,
0.016703782603144646,
0.00302231521345675,
-0.027266932651400566,
-0.04509837552905083,
-0.022239748388528824,
0.01801256090402603,
0.010439816862344742,
-0.047249432653188705,
0.016151104122400284,
0.020648622885346413,
-0.0267702117562294,
-0.01667589321732521,
0.03602607548236847,
0.061967480927705765,
0.016546638682484627,
-0.022627482190728188,
-0.03287938982248306,
0.005243902560323477,
-0.05655014514923096,
0.024058818817138672,
0.048081185668706894,
0.007685929536819458,
-0.029787639155983925,
-0.0003970809339080006,
0.039770398288965225,
-0.017473993822932243,
-0.02473059855401516,
0.009242075495421886,
0.004658381454646587,
0.03618812933564186,
-0.01638404093682766,
-0.006753405090421438,
0.002926062559708953,
0.042651865631341934,
0.000866971502546221,
-0.008819731883704662,
-0.027581121772527695,
-0.08347156643867493,
-0.01850002631545067,
0.04194571077823639,
0.009844076819717884,
-0.015623359940946102,
0.014951418153941631,
-0.0841079130768776,
-0.012052825652062893,
0.06822486966848373,
-0.03485661372542381,
0.013687939383089542,
-0.0025177423376590014,
0.010787924751639366,
-0.02050675079226494,
-0.010204298421740532,
0.030088648200035095,
0.008106831461191177,
0.0009119670721702278,
0.030293026939034462,
0.02473589777946472,
-0.04896388575434685,
-0.008265726268291473,
-0.0040383851155638695,
0.01526675745844841,
0.02519400417804718,
0.0035252023953944445,
0.013273265212774277,
-0.01356099545955658,
0.005845530424267054,
-0.04605468735098839,
-0.07796421647071838,
-0.020383814349770546,
0.016689792275428772,
-0.0033901932183653116,
0.03268352150917053,
0.000049933041736949235,
-0.04565764218568802,
0.0623144805431366,
0.027375785633921623,
-0.017155932262539864,
-0.02767045423388481,
-0.021743623539805412,
0.007041154429316521,
0.04725508391857147,
0.012259949930012226,
0.04548421502113342,
0.032634805887937546,
-0.044129982590675354,
-0.027384772896766663,
-0.017915695905685425,
0.048577360808849335,
-0.03393256664276123,
-0.014479676261544228,
-0.023120585829019547,
0.00965728610754013,
-0.02188008278608322,
0.04206821322441101,
-0.029080411419272423,
0.03212745115160942,
0.0030522188171744347,
-0.03741060197353363,
-0.014421072788536549,
-0.0023642960004508495,
0.026118801906704903,
-0.05514834448695183,
0.00860585831105709,
0.02935918979346752,
0.0037210218142718077,
-0.005747373215854168,
0.04960820451378822,
-0.025205319747328758,
0.00009278176730731502,
0.017265494912862778,
-0.015293966047465801,
0.006031121127307415,
-0.009635519236326218,
-0.018607789650559425,
0.02212831750512123,
-0.011827015317976475,
0.03288084641098976,
-0.037932973355054855,
-0.00373635976575315,
0.018313802778720856,
-0.061874017119407654,
-0.0048781647346913815,
0.035611968487501144,
0.017973067238926888,
0.013306953012943268,
-0.03450961410999298,
0.02522427774965763,
0.032246094197034836,
0.02707233652472496,
-0.020871682092547417,
-0.036204658448696136,
0.042321957647800446,
0.013846547342836857,
-0.015461222268640995,
-0.08212599158287048,
-0.012538925744593143,
-0.023315660655498505,
-0.04513067379593849,
0.030460067093372345,
0.04853545501828194,
-0.03311307728290558,
-0.006377224810421467,
0.005850599613040686,
-0.004266349598765373,
0.05133456736803055,
0.016918912529945374,
-0.005409191362559795,
0.016897451132535934,
-0.05794374644756317,
-0.034593723714351654,
0.011236102320253849,
0.06272967159748077,
-0.03048512525856495,
0.03527165576815605,
0.0014366814866662025,
-0.0019644706044346094,
0.05221952497959137,
0.02479962818324566,
-0.0037802858278155327,
0.04238801449537277,
0.05369532108306885,
0.0003611749270930886,
-0.054245494306087494,
0.03543200343847275,
0.014473166316747665,
0.04520198330283165,
-0.004598688334226608,
-0.03148113936185837,
-0.02187502570450306,
-0.03245999664068222,
-0.038241881877183914,
-0.012927929870784283,
0.008437192998826504,
0.012687246315181255,
0.08075212687253952,
-0.05598504841327667,
0.025040440261363983,
0.015969758853316307,
0.007808866910636425,
0.007965276949107647,
0.028335748240351677,
0.0034999034833163023,
-0.002198899397626519,
0.020559614524245262,
-0.007775275036692619,
-0.042681943625211716,
-0.029134560376405716,
-0.008427654393017292,
0.036772891879081726,
-0.017691830173134804,
0.03134849667549133,
0.030116340145468712,
-0.013433502055704594,
-0.02013128623366356,
-0.02955564670264721,
-0.0083296038210392,
0.05634046345949173,
-0.03198894113302231,
0.005319396499544382,
-0.022122275084257126,
0.007522041443735361,
0.03459487110376358,
0.03973023593425751,
-0.014265565201640129,
0.03179973363876343,
0.0413660928606987,
-0.0020491115283221006,
0.007286944892257452,
-0.05145950987935066,
-0.02504214458167553,
0.055072493851184845,
-0.03374774754047394,
0.03077237866818905,
0.010095490142703056,
-0.027214333415031433,
0.04680102691054344,
-0.016694122925400734,
-0.0051390607841312885,
-0.05660305917263031,
-0.007075042929500341,
-0.054917871952056885,
0.01926364004611969,
0.006442808546125889,
-0.013274210505187511,
0.031658586114645004,
0.01534159854054451,
0.014800663106143475,
0.029940111562609673,
0.01555163785815239,
0.0025529128033667803,
-0.04073738306760788,
-0.02029348909854889,
-0.02100517973303795,
-0.029301289469003677,
0.015428056940436363,
0.03787124156951904,
-0.017259914427995682,
-0.0043426090851426125,
-0.01762576773762703,
0.01721516065299511,
-0.00017165292229037732,
0.03529442101716995,
0.0179000124335289,
0.05380099639296532,
0.021777590736746788,
0.01193692721426487,
0.005592754110693932,
-0.0056907739490270615,
0.11127813160419464,
0.03866642341017723,
0.006716700736433268,
-0.06766327470541,
0.008890031836926937,
0.005400101654231548,
-0.010934594087302685,
-0.042504068464040756,
0.00432707741856575,
-0.03540128841996193,
0.03283453732728958,
0.014769142493605614,
0.04307769984006882,
-0.034952715039253235,
-0.008182715624570847,
0.08923288434743881,
-0.046550165861845016,
-0.050363242626190186,
0.008931084536015987,
0.0015148385427892208,
-0.005711876321583986,
-0.013776400126516819,
-0.03421458974480629,
0.019726280122995377,
-0.0033337862696498632,
-0.006234001833945513,
-0.01735500991344452,
-0.03276664391160011,
0.05837686359882355,
0.012517642229795456,
-0.015546584501862526,
0.029690193012356758,
0.022425560280680656,
0.017621511593461037,
-0.07023335248231888,
0.021995965391397476,
0.04313742741942406,
0.0036574520636349916,
0.00537354638800025,
-0.00483002420514822,
0.011439025402069092,
0.01000846829265356,
0.012408928945660591,
0.033238187432289124,
-0.044363126158714294,
-0.0038652580697089434,
-0.06821200251579285,
0.029181551188230515,
0.001103414106182754,
-0.015482037328183651,
0.00047516514314338565,
-0.005593411158770323,
0.01318735908716917,
-0.007181903347373009,
-0.029062340036034584,
0.00020980504632461816,
0.03251715376973152,
-0.029071148484945297,
-0.027988212183117867,
-0.03642001748085022,
0.026533419266343117,
-0.019096532836556435,
0.026414869353175163,
0.020303688943386078,
0.0013666164595633745,
-0.009764798916876316,
-0.009076028130948544,
0.0051531377248466015,
-0.03320363536477089,
-0.015517829917371273,
-0.027405375614762306,
-0.005976016633212566,
-0.004557701293379068,
-0.028898410499095917,
0.002892340999096632,
0.013042084872722626,
0.018718188628554344,
-0.02132224850356579,
-0.015052990056574345,
0.0186842642724514,
-0.06513410806655884,
0.042488548904657364,
-0.007100203540176153,
-0.04192326217889786,
-0.022721489891409874,
0.021157952025532722,
-0.011600903235375881,
0.04839669540524483,
0.0012434904929250479,
0.03443783149123192,
-0.021724166348576546,
0.023078635334968567,
0.030999666079878807,
-0.013634036295115948,
-0.009698114357888699,
-0.016670580953359604,
-0.052408959716558456,
-0.01540623139590025,
0.019800445064902306,
0.051394276320934296,
0.03876644745469093,
-0.0027338843792676926,
0.014609536156058311,
0.011445989832282066,
-0.045837175101041794,
0.025682156905531883,
0.006131718400865793,
-0.024573223665356636,
-0.024618862196803093,
0.03458402678370476,
-0.03449375554919243,
-0.030767999589443207,
-0.04826868325471878,
0.011169394478201866,
-0.009400871582329273,
0.011259491555392742,
0.029001671820878983,
-0.020515691488981247,
-0.016534877941012383,
0.00878570880740881,
0.027663161978125572,
-0.036518488079309464,
-0.03100442700088024,
-0.07565122097730637,
0.002691632602363825,
0.01441589742898941,
-0.03684178739786148,
-0.02139696665108204,
0.0012637891341000795,
-0.0057291314005851746,
-0.030114520341157913,
0.03569609299302101,
0.01455414667725563,
0.0195765420794487,
-0.04809993505477905,
0.04226015508174896,
0.005455926526337862,
0.06993979215621948,
-0.01998060755431652,
-0.01655595377087593,
0.03774786368012428,
-0.06273030489683151,
-0.013316317461431026,
-0.024790802970528603,
-0.020754892379045486,
0.03243374451994896,
0.01205929834395647,
-0.01900005340576172,
-0.004877807572484016,
0.0796658918261528,
-0.03476082161068916,
-0.006572555750608444,
-0.027763981372117996,
-0.014436387456953526,
0.012796866707503796,
0.007960856892168522,
-0.021922603249549866,
-0.07936491817235947,
0.007630617823451757,
0.05463779345154762,
0.049704521894454956,
-0.01265670545399189,
-0.017897501587867737,
0.013747533783316612,
-0.002819300862029195,
-0.025546297430992126,
0.01708788238465786,
-0.014771692454814911,
0.012972523458302021,
0.04620834439992905,
-0.013508561067283154,
0.024501562118530273,
-0.0061720688827335835,
-0.002441160613670945,
-0.05812997743487358,
0.04926712065935135,
-0.000507305667269975,
-0.027521144598722458,
0.030395694077014923,
-0.024148419499397278,
0.0173442792147398,
0.019816366955637932,
-0.035445842891931534,
-0.00808286014944315,
-0.03279678151011467,
-0.03419996052980423,
-0.02721754088997841,
0.02813255973160267,
0.02127109281718731,
0.04847486689686775,
0.012774959206581116,
0.03204731270670891,
0.0123281916603446,
-0.033805228769779205,
-0.003827531822025776,
-0.018420245498418808,
0.01754128560423851,
0.06472539901733398,
-0.021583907306194305,
-0.020846553146839142,
0.0028277502860873938,
-0.02344849333167076,
-0.007103378884494305,
0.0028582694940268993,
-0.014027337543666363,
0.006132562179118395,
0.038896504789590836,
0.033317044377326965,
-0.015995344147086143,
0.035625725984573364,
0.016916237771511078,
0.008348291739821434,
0.003957225009799004,
0.030744189396500587,
0.006904016248881817,
0.01625671237707138,
0.0195615291595459,
0.02136673592031002,
0.019811976701021194,
-0.054041631519794464,
-0.05062716826796532,
0.05463525280356407,
-0.056828100234270096,
0.006064955610781908,
0.03245537728071213,
-0.008955474011600018,
0.04440785571932793,
-0.02559591270983219,
-0.043741628527641296,
-0.011305168271064758,
-0.02316507138311863,
0.05160818248987198,
-0.009423191659152508,
0.025503627955913544,
-0.007147031836211681,
-0.011175199411809444,
-0.032299064099788666,
-0.031035564839839935,
0.025882607325911522,
-0.009432977996766567,
-0.03185216337442398,
-0.018051670864224434,
0.005639195442199707,
0.0010223916033282876,
-0.05190207436680794,
-0.03188265860080719,
-0.04719085991382599,
0.022833289578557014,
0.039040543138980865,
0.041324518620967865,
0.0002455360081512481,
-0.04260510578751564,
-0.01725003868341446,
-0.04806846007704735,
0.04637929052114487,
-0.03217342495918274,
0.02793802320957184,
-0.04690897837281227,
-0.0008815379696898162,
-0.02055862918496132,
-0.011478579603135586,
0.02766377106308937,
-0.013271956704556942,
0.022861843928694725,
0.007301622536033392,
0.0059066773392260075,
0.03797135502099991,
-0.059312351047992706,
0.019162440672516823,
-0.0008393829339183867,
-0.028896722942590714,
0.006426413543522358,
-0.03193093091249466,
-0.014349997974932194,
-0.005704610142856836,
0.00340934912674129,
-0.017222203314304352,
0.04377473518252373,
0.0011022035032510757,
-0.005365723744034767,
0.03065364435315132,
0.003027294296771288,
-0.013649478554725647,
0.049824293702840805,
-0.03339787945151329,
0.009928741492331028,
0.018039986491203308,
-0.026795802637934685,
-0.03251560777425766,
0.05525951087474823,
-0.032923951745033264,
0.04498458653688431,
0.005269493907690048,
-0.054532237350940704,
0.012092066928744316,
-0.042293936014175415,
0.01470984984189272,
-0.0009164359653368592,
-0.05898033455014229,
0.011070101521909237,
0.036112312227487564,
0.01133002433925867,
0.024600038304924965,
0.0010433817515149713,
0.015630749985575676,
0.013692799024283886,
0.018928200006484985,
-0.03612267225980759,
0.04622020944952965,
0.013012387789785862,
0.03514077886939049,
0.036974649876356125,
-0.015972325578331947,
0.019977761432528496,
0.0325850211083889,
0.02175118587911129,
0.03919447958469391,
-0.0262482687830925,
-0.045375559478998184,
0.018442269414663315,
-0.010736226104199886,
0.0339055173099041,
0.004441307857632637,
0.014341927133500576,
0.0722174346446991,
-0.013533237390220165,
0.023909423500299454,
-0.028954721987247467,
-0.009215734899044037,
0.010454651899635792,
-0.011087359860539436,
-0.013431788422167301,
0.017560748383402824,
-0.013260472565889359,
0.011579408310353756,
-0.008195030502974987,
0.03204088285565376,
-0.002336371224373579,
-0.021398581564426422,
0.05175897479057312,
-0.035574771463871,
0.021253462880849838,
-0.014528813771903515,
-0.017634298652410507,
-0.04031567648053169,
-0.01757819391787052,
0.004499299917370081,
0.021351104602217674,
0.03165313974022865,
0.06112218648195267,
-0.041588105261325836,
-0.00834566354751587,
0.05828491970896721,
-0.05260198563337326,
-0.02948829159140587,
-0.02775438502430916,
-0.024105289950966835,
-0.013792630285024643,
0.008276820182800293
] |
<p>This is a second question (in what will probably become a series) in my attempt to understand LQG a little. In the <a href="http://physics.stackexchange.com/questions/2407/give-a-description-of-loop-quantum-gravity-your-grandmother-could-understand">previous question</a> I asked about the general concepts behind LQG to which <strong>space_cadet</strong> provided a very nice answer.</p>
<p>Let me summarize that answer so that I can check that I've understood it properly. In LQG, one works with connections instead of a metric because this greatly simplifies the equations (space_cadet makes an analogy to "taking a square root" of K-G equation to obtain Dirac equation). The connections should determine the geometry of a given 3D manifold which is a space-like slice of our 4D space-time. Then, as is usual in quantizing a system, one proceeds to define "wave-functions" on the configuration space of connections and the space of these functionals on connections should form a Hilbert space. </p>
<hr>
<p><em>Note:</em> I guess there is more than one Hilbert space present, depending on precisely what space of connections we work with. This will probably have to do with enforcing the usual Einstein constraints and also diffeomorphism constraints. But I'll postpone these technicalities to a later question.</p>
<hr>
<p>So that's one picture we have about LQG. But when people actually talk about LQG, one always hears about spin-networks and area and volume operators. So how does these objects connect with the space_cadet's answer? Let's start slowly</p>
<blockquote>
<ol>
<li>What is a spin-network exactly?</li>
<li>What are the main mathematical properties?</li>
</ol>
</blockquote>
<p>Just a reference to the literature will suffice because I realize that the questions (especially the second one) might be quite broad. Although, for once, <a href="http://en.wikipedia.org/wiki/Spin_network" rel="nofollow">wikipedia article</a> does a decent job in hinting at answers of both 1. and 2. but it leaves me greatly dissatisfied. In particular, I have no idea what happens at the vertices. Wikipedia says that they should carry intertwining operators. Intertwinors always work on two representations so presumably there is an intertwinor for every pair of edges joining at the vertex? Also, by Schur's lemma, intertwinors of inequivalent irreps are zero, so that usually this notion would be pretty trivial. As you can see, I am really confused about this, so I'd like to hear</p>
<blockquote>
<p> 3. What is the significance of vertices and intertwinors for spin-networks?</p>
</blockquote>
<p>Okay, having the definitions out of the way, spin-networks should presumably also form a basis of the aforementioned Hilbert space (I am not sure which one Hilbert space it is and what conditions this puts on the spin-networks; if possible, let's postpone this discussion until some later time) so there must be some correspondence between connection functionals and spin-networks.</p>
<blockquote>
<p> 4. How does this correspondence look precisely? If I have some spin-network, how do I obtain a functional on connections from that?</p>
</blockquote>
| 8,335 |
[
0.003689362434670329,
0.0023346298839896917,
0.03348740190267563,
-0.04639450088143349,
0.03736742213368416,
0.0017727594822645187,
-0.038344282656908035,
-0.03721805289387703,
0.042923711240291595,
-0.04103897511959076,
0.04143914580345154,
0.010442682541906834,
0.058333031833171844,
0.028723474591970444,
0.0030972028616815805,
0.006185008212924004,
0.011858257465064526,
-0.022119266912341118,
-0.029514389112591743,
-0.049244996160268784,
0.003959876485168934,
0.042322490364313126,
-0.029374923557043076,
-0.014072665013372898,
-0.012285435572266579,
0.0027791564352810383,
-0.027132708579301834,
-0.01075177825987339,
-0.011403749696910381,
0.05314448103308678,
-0.03702941909432411,
-0.040457114577293396,
-0.0005888959858566523,
-0.0017963896971195936,
0.0007076046313159168,
0.008369244635105133,
-0.018965573981404305,
-0.011608158238232136,
0.03179526329040527,
-0.001965212868526578,
-0.059572767466306686,
-0.0074308994226157665,
-0.042958974838256836,
0.032053325325250626,
-0.019985763356089592,
0.046438224613666534,
0.024228673428297043,
-0.013894543051719666,
0.0629742443561554,
-0.05144958198070526,
0.06526825577020645,
-0.0015498610446229577,
-0.006734343245625496,
0.003308166516944766,
-0.0016341572627425194,
-0.01951507478952408,
0.07433640956878662,
0.06990781426429749,
0.012743166647851467,
-0.039564669132232666,
-0.02704482339322567,
0.003058484522625804,
-0.0028984725940972567,
-0.03356810659170151,
-0.015016421675682068,
0.018758684396743774,
0.05198395997285843,
0.01284169964492321,
0.0028782032895833254,
-0.024671358987689018,
-0.016146155074238777,
0.015738336369395256,
0.0422784686088562,
0.007269465364515781,
0.026978284120559692,
0.007675908040255308,
-0.010454397648572922,
-0.019430620595812798,
0.017962682992219925,
0.00128033512737602,
-0.03731747344136238,
0.022949500009417534,
-0.002698317402973771,
0.01912480778992176,
0.01029024738818407,
-0.00872886087745428,
0.07870457321405411,
-0.004954693838953972,
-0.006372225470840931,
0.037930481135845184,
-0.012753406539559364,
0.01662333682179451,
0.03573377802968025,
-0.011099101975560188,
-0.020546918734908104,
0.02929944545030594,
0.0147455595433712,
0.03389345854520798,
-0.006145019084215164,
-0.009603035636246204,
-0.0005890289903618395,
-0.04577989503741264,
-0.03376423940062523,
0.10194924473762512,
0.013201066292822361,
-0.00831607636064291,
-0.024974681437015533,
0.018252579495310783,
-0.023850686848163605,
-0.016281109303236008,
-0.04386361315846443,
0.04327971115708351,
-0.03678258880972862,
0.0002996432303916663,
-0.014834214933216572,
-0.04401347413659096,
-0.009200488217175007,
-0.008919916115701199,
0.004456083755940199,
0.0794198215007782,
0.01702602580189705,
-0.020769592374563217,
0.00022513591102324426,
-0.00972867663949728,
-0.059827178716659546,
0.010208828374743462,
0.06686586141586304,
-0.022097649052739143,
-0.046064816415309906,
-0.005518158432096243,
-0.002563909627497196,
-0.03086460754275322,
0.009618311189115047,
0.010002956725656986,
0.023952163755893707,
-0.022301381453871727,
-0.10688919574022293,
-0.05585114657878876,
0.0576004832983017,
0.0021545144263654947,
-0.009492626413702965,
-0.06700843572616577,
0.044076357036828995,
-0.014834143221378326,
0.09599674493074417,
-0.015722619369626045,
0.03600403293967247,
0.026903335005044937,
-0.0014787125401198864,
0.012765011750161648,
-0.02165122516453266,
0.02473781630396843,
-0.01824064366519451,
-0.05672633647918701,
0.014258337207138538,
-0.03706953674554825,
0.0351262167096138,
0.04021410644054413,
0.011914147064089775,
-0.009654834866523743,
0.06961709260940552,
-0.005946833174675703,
0.009421149268746376,
0.025814246386289597,
-0.016423329710960388,
-0.022902166470885277,
0.04358749836683273,
-0.0020141801796853542,
0.006485210731625557,
0.018364066258072853,
-0.018349891528487206,
0.01937022991478443,
-0.02207794040441513,
0.03466634824872017,
0.027724584564566612,
-0.010052991099655628,
-0.0006624865927733481,
-0.0015533955302089453,
0.008292082697153091,
-0.033333323895931244,
-0.03907180577516556,
-0.013709845952689648,
-0.041914958506822586,
0.01119865383952856,
-0.006689734756946564,
0.018027998507022858,
0.02122560702264309,
0.002630864968523383,
0.011267409659922123,
-0.024531183764338493,
0.004069814458489418,
-0.05510878190398216,
0.009056837297976017,
-0.0009944987250491977,
-0.013213059864938259,
0.024831034243106842,
-0.017118027433753014,
-0.009184286929666996,
-0.033220577985048294,
-0.03718734532594681,
0.00794427189975977,
0.06591016054153442,
-0.0004365449713077396,
0.01644320972263813,
0.012254243716597557,
0.05646946653723717,
0.025741448625922203,
0.005495901685208082,
0.022739890962839127,
-0.017276152968406677,
0.005661396309733391,
0.030904488638043404,
0.014960268512368202,
0.0333273746073246,
0.01665421389043331,
0.024587199091911316,
-0.026475969702005386,
0.023495668545365334,
-0.015272456221282482,
0.02261381410062313,
-0.055873896926641464,
0.0640445351600647,
0.02824852615594864,
-0.027017654851078987,
0.03732676804065704,
0.07663115113973618,
-0.0016743149608373642,
0.026807593181729317,
0.03709987550973892,
-0.003556719282642007,
-0.06083400174975395,
-0.011376028880476952,
0.037737730890512466,
0.025477616116404533,
-0.028511131182312965,
0.0037654549814760685,
0.01763322949409485,
0.04944129288196564,
-0.019851094111800194,
-0.01244073174893856,
-0.05089297518134117,
-0.02225147932767868,
0.014662211760878563,
-0.03465643897652626,
-0.019590243697166443,
-0.00467249471694231,
0.0007421947666443884,
0.0342097170650959,
0.000028935210139025003,
-0.025563878938555717,
-0.023897387087345123,
0.03714090585708618,
-0.019239122048020363,
0.0006317807710729539,
0.012008505873382092,
-0.017036205157637596,
0.04872391000390053,
-0.00934747513383627,
0.0063675884157419205,
0.02721964567899704,
-0.013095696456730366,
-0.0362057164311409,
-0.06492803245782852,
-0.0372873991727829,
0.011610664427280426,
-0.01959642581641674,
-0.012891995720565319,
-0.007228669710457325,
0.012592229060828686,
-0.029913336038589478,
0.0072289579547941685,
-0.021933747455477715,
-0.01799733191728592,
0.013090472668409348,
0.017230749130249023,
0.029594186693429947,
0.007004675921052694,
0.023681897670030594,
-0.033489108085632324,
-0.029757561162114143,
0.03212719410657883,
-0.0042534926906228065,
0.029793351888656616,
0.03280946984887123,
-0.03475312888622284,
-0.004771627485752106,
-0.0493442639708519,
0.0004047100665047765,
0.021854590624570847,
0.015321292914450169,
0.01755424588918686,
-0.004658822901546955,
-0.029851315543055534,
-0.02931024506688118,
-0.024828728288412094,
-0.05629488080739975,
0.021613463759422302,
-0.026651322841644287,
-0.011681277304887772,
0.07108622044324875,
-0.001981046749278903,
-0.025636428967118263,
-0.01691192202270031,
-0.008306272327899933,
-0.04278317466378212,
-0.007923347875475883,
0.005684664472937584,
-0.004619143437594175,
-0.03145749121904373,
-0.018622735515236855,
0.06325222551822662,
-0.028384344652295113,
-0.0006751829641871154,
-0.06838589906692505,
-0.01736944541335106,
0.0354611836373806,
0.007204963359981775,
0.029554400593042374,
0.02575938031077385,
-0.045698102563619614,
0.07775787264108658,
0.006474039051681757,
-0.04494740813970566,
-0.039103757590055466,
0.022094735875725746,
-0.0050086588598787785,
-0.03640223294496536,
0.031517256051301956,
0.038221631199121475,
0.02107170596718788,
0.022758925333619118,
0.05282023176550865,
0.044150568544864655,
0.01196092925965786,
0.010956074111163616,
0.009248863905668259,
0.016543686389923096,
0.01876828446984291,
-0.005922570358961821,
0.06529974192380905,
0.0406886525452137,
-0.03185722231864929,
0.018018512055277824,
-0.02888324111700058,
-0.017991598695516586,
0.009032243862748146,
-0.071914903819561,
0.05503183230757713,
0.017009885981678963,
-0.012566966935992241,
-0.0006152339046820998,
0.0394274927675724,
-0.027428114786744118,
-0.04330584034323692,
0.009794933721423149,
0.03205147758126259,
0.02156534232199192,
-0.01122649759054184,
-0.01339021511375904,
0.0128214992582798,
0.04751260578632355,
-0.055788908153772354,
-0.006211075931787491,
0.020092075690627098,
-0.031109975650906563,
0.0194963701069355,
-0.037397053092718124,
-0.01387000922113657,
0.006792401894927025,
0.03303102031350136,
-0.021532773971557617,
-0.008266414515674114,
-0.039795540273189545,
-0.01987745240330696,
-0.08615999668836594,
0.013898941688239574,
-0.004028855357319117,
0.04241996258497238,
0.005503092892467976,
0.016901494935154915,
0.0021376055665314198,
0.004490538965910673,
-0.022730011492967606,
0.011508313938975334,
-0.1016773134469986,
0.00509730726480484,
-0.026020141318440437,
-0.03257276490330696,
0.02679571695625782,
0.0018369522877037525,
0.0272611603140831,
-0.016063004732131958,
-0.03194008767604828,
-0.01662849262356758,
0.026011915877461433,
-0.03328530862927437,
0.029773332178592682,
-0.019867289811372757,
-0.007604238111525774,
-0.0015387018211185932,
0.029565606266260147,
0.03790189325809479,
0.005365522112697363,
-0.018148483708500862,
0.05947896093130112,
0.006724756211042404,
-0.005781303625553846,
0.031989701092243195,
0.023175744339823723,
0.01950480043888092,
-0.006179898977279663,
0.006886896211653948,
-0.02326327934861183,
0.013571317307651043,
-0.021232502534985542,
0.027922427281737328,
0.057978998869657516,
0.012122727930545807,
-0.03608386218547821,
0.01642525941133499,
-0.08107523620128632,
-0.018562184646725655,
-0.012105396948754787,
0.06773208826780319,
-0.00016815151320770383,
0.008282561786472797,
0.04050110653042793,
0.003469035727903247,
-0.018549099564552307,
0.004381035920232534,
0.07060030102729797,
0.0018542673205956817,
-0.06208622455596924,
-0.04091467335820198,
0.0005365894176065922,
-0.03107052482664585,
0.0036744773387908936,
0.026796825230121613,
-0.006826622877269983,
-0.04396530240774155,
0.029481789097189903,
0.007493448443710804,
0.035165462642908096,
-0.032458044588565826,
-0.0179241094738245,
0.023172911256551743,
0.0488787405192852,
-0.02913227118551731,
0.012395884841680527,
-0.018292412161827087,
0.03930000215768814,
0.05671363323926926,
0.005214606411755085,
-0.01588885858654976,
-0.06397759169340134,
-0.03629273176193237,
0.037223849445581436,
0.02713114582002163,
0.04074503481388092,
-0.037617798894643784,
-0.07099347561597824,
-0.04654889553785324,
0.033991482108831406,
-0.03218434751033783,
0.026492120698094368,
0.020796051248908043,
-0.004373081959784031,
-0.01987035758793354,
-0.03463898226618767,
-0.0013822853798046708,
0.026468651369214058,
-0.01222729217261076,
-0.003866950049996376,
-0.01554165594279766,
0.042946793138980865,
0.00021417780953925103,
0.022995062172412872,
-0.02110539749264717,
0.043905071914196014,
0.01704726740717888,
0.003860813332721591,
-0.026345232501626015,
0.03593797981739044,
-0.03818473219871521,
-0.09284871071577072,
0.027463102713227272,
0.010174158029258251,
-0.025649288669228554,
0.04636796563863754,
-0.02547844871878624,
-0.02577747032046318,
0.012077647261321545,
-0.007645683828741312,
0.00986805371940136,
0.0542578361928463,
-0.033587634563446045,
0.055237140506505966,
0.05461245775222778,
0.014811433851718903,
0.03687945008277893,
0.014314936473965645,
-0.03690093383193016,
0.02775638923048973,
-0.009376605972647667,
0.03792954608798027,
-0.025632930919528008,
0.01164205651730299,
-0.0016488760011270642,
0.016870444640517235,
-0.05628490820527077,
0.030659116804599762,
-0.05672350898385048,
0.013520471751689911,
-0.006662840023636818,
-0.01612342894077301,
-0.020201141014695168,
0.000416526134358719,
0.008761441335082054,
-0.03612944483757019,
-0.005833457689732313,
0.03466914966702461,
0.03276871517300606,
-0.0356571264564991,
0.005365791264921427,
0.0026790809351950884,
-0.011867438443005085,
0.07431810349225998,
0.0038495799526572227,
-0.008671198971569538,
-0.028166256844997406,
0.010651466436684132,
-0.01085205189883709,
-0.013919373974204063,
0.04017005115747452,
0.019771350547671318,
-0.01756710186600685,
0.023947356268763542,
-0.003689270466566086,
-0.011696401983499527,
-0.03038346953690052,
-0.05532184615731239,
-0.013197675347328186,
-0.019089477136731148,
-0.0013733920641243458,
0.02426988258957863,
-0.008774328045547009,
-0.07218211889266968,
-0.031268976628780365,
0.03893066570162773,
0.01301973219960928,
-0.023113476112484932,
-0.045081499963998795,
0.02109193056821823,
-0.023150818422436714,
-0.018516739830374718,
0.006601094733923674,
0.06356997787952423,
-0.07543238997459412,
0.014381397515535355,
-0.0023429731372743845,
0.04075693339109421,
0.04876222833991051,
0.022750265896320343,
0.0025465679354965687,
0.014994628727436066,
-0.009545809589326382,
0.01954132318496704,
0.0005090640624985099,
0.008405574597418308,
-0.03460116684436798,
-0.04922869801521301,
-0.06456954032182693,
0.01947936974465847,
0.018195809796452522,
-0.046340569853782654,
-0.033676330000162125,
0.02942311204969883,
0.007668867241591215,
-0.004621926229447126,
-0.059551484882831573,
-0.02242828533053398,
-0.031349580734968185,
0.039072949439287186,
-0.03989564627408981,
0.015385097824037075,
-0.0002357993507757783,
-0.0017798501066863537,
0.0178120918571949,
0.007680137176066637,
-0.0007751215598545969,
0.015799593180418015,
0.04751579463481903,
0.020814813673496246,
-0.04222497344017029,
0.020324673503637314,
-0.008844872936606407,
0.01289456058293581,
-0.011067533865571022,
-0.01605813205242157,
-0.0021870331838726997,
0.020927535369992256,
-0.028401385992765427,
-0.03807387501001358,
-0.047312431037425995,
-0.008044609799981117,
0.05720007047057152,
0.02640116959810257,
0.06552398204803467,
0.026292648166418076,
-0.04092039540410042,
-0.010374296456575394,
-0.016286728903651237,
-0.0057731326669454575,
0.031833797693252563,
-0.006576112005859613,
0.030476907268166542,
-0.030566051602363586,
0.008975088596343994,
0.039270952343940735,
0.03522638976573944,
-0.05749216303229332,
-0.04530312120914459,
0.03079763613641262,
-0.009573351591825485,
0.016203630715608597,
-0.029861658811569214,
-0.06995882838964462,
0.04674919694662094,
-0.02225705236196518,
0.04754741117358208,
-0.0033504494931548834,
-0.008850318379700184,
0.027138805016875267,
0.014126108027994633,
0.02744167670607567,
-0.010199228301644325,
-0.04704686626791954,
-0.06490733474493027,
-0.019292443990707397,
0.03453385829925537,
0.017883891239762306,
-0.02348857745528221,
0.007611526176333427,
0.014377141371369362,
-0.005814362317323685,
-0.006791804451495409,
0.0030937392730265856,
-0.04545647278428078,
-0.006591292563825846,
-0.023716963827610016,
-0.04455453157424927,
0.06208375096321106,
0.03427177295088768,
-0.03975892812013626,
0.0021875675301998854,
-0.03866734355688095,
0.0296236090362072,
0.02081872709095478,
0.03372511267662048,
-0.03194104880094528,
0.06619200855493546,
-0.00013755827967543155,
0.004763091914355755,
-0.003190816380083561,
-0.014097333885729313,
0.1288096010684967,
0.04563750699162483,
0.0010623536072671413,
-0.063494473695755,
-0.0182962603867054,
0.009764744900166988,
-0.0004493158485274762,
-0.03445638716220856,
0.03329083323478699,
0.003549492685124278,
0.02491442859172821,
-0.006463163066655397,
0.027819817885756493,
0.0003135899023618549,
-0.006422651931643486,
0.06534851342439651,
-0.06796558201313019,
-0.008081456646323204,
0.015214990824460983,
-0.015955038368701935,
0.0294652096927166,
0.05759875476360321,
-0.03550559654831886,
0.02738427370786667,
-0.013692078180611134,
0.041323695331811905,
-0.040142036974430084,
-0.03513244166970253,
0.0643782988190651,
-0.013989601284265518,
-0.04812638834118843,
0.013434058055281639,
-0.00929117389023304,
0.008030926808714867,
-0.012957455590367317,
0.017478931695222855,
0.029714636504650116,
-0.004361720755696297,
0.03350275754928589,
0.02246168442070484,
-0.004093976691365242,
-0.013663023710250854,
0.013444808311760426,
0.032192766666412354,
-0.03672517463564873,
0.0032289717346429825,
-0.031911589205265045,
0.06498485803604126,
-0.020951908081769943,
-0.010434702970087528,
0.01224040798842907,
-0.010692191310226917,
0.008977970108389854,
-0.049115970730781555,
-0.008829780854284763,
-0.0074235424399375916,
0.06655572354793549,
0.027716590091586113,
0.007214583922177553,
0.001821186044253409,
0.003880756674334407,
-0.01123355794698,
0.02473466470837593,
-0.03539111092686653,
0.024191739037632942,
0.011114576831459999,
-0.026881210505962372,
0.008419059216976166,
-0.00035021945950575173,
-0.006089086178690195,
-0.017190806567668915,
-0.008415471762418747,
-0.00005554572999244556,
-0.01853030174970627,
0.02744179032742977,
0.0492001473903656,
0.048543836921453476,
0.006877551786601543,
-0.000538384891115129,
0.009260619059205055,
-0.05457921698689461,
0.0020797771867364645,
-0.018027957528829575,
-0.03048289567232132,
-0.009533263742923737,
0.021449029445648193,
-0.0042876917868852615,
0.06615317612886429,
-0.011760815046727657,
0.0019662738777697086,
-0.00912706833332777,
0.0008037275983951986,
0.018043074756860733,
-0.0033555931877344847,
-0.009281865321099758,
0.01588093303143978,
-0.024390405043959618,
-0.005804359447211027,
0.0014815658796578646,
0.016404973343014717,
-0.007143183145672083,
0.01721922494471073,
-0.003927005920559168,
0.008320354856550694,
0.018080055713653564,
0.0009460695437155664,
0.03216000646352768,
-0.01601334474980831,
0.022618422284722328,
0.00709571922197938,
0.030607888475060463,
-0.04536446928977966,
-0.03408754989504814,
0.019921816885471344,
-0.028601422905921936,
0.020960679277777672,
0.05092822015285492,
-0.040238022804260254,
-0.005185399204492569,
0.00023657015117350966,
0.029088933020830154,
-0.0029086056165397167,
0.03014983981847763,
-0.05755115672945976,
0.05119241401553154,
-0.016015440225601196,
-0.015319755300879478,
-0.01943632960319519,
0.02413952723145485,
0.034343522042036057,
-0.03423850238323212,
-0.012229204177856445,
0.01838209107518196,
-0.016527758911252022,
-0.004440381191670895,
-0.005885133054107428,
0.024592993780970573,
0.008366360329091549,
0.03242943435907364,
-0.06452339142560959,
-0.006029787473380566,
-0.03443929925560951,
-0.05711476504802704,
0.03553218021988869,
-0.02354421094059944,
0.03441600501537323,
0.06122501939535141,
-0.024911900982260704,
-0.0023474739864468575,
-0.014356314204633236,
-0.01859079860150814,
-0.007670197635889053,
-0.0014091067714616656,
-0.04547038674354553,
0.0005485356086865067,
-0.03550809621810913,
0.021654069423675537,
-0.005362702067941427,
-0.00001933764542627614,
0.006637440528720617,
-0.005334329791367054,
-0.027300648391246796,
-0.013191791251301765,
0.006632773671299219,
-0.013293824158608913,
0.017513332888484,
-0.008349758572876453,
-0.0005870902677997947,
0.020926548168063164,
0.02970350906252861,
-0.030499082058668137,
0.016853613778948784,
0.006837593857198954,
0.027323195710778236,
-0.1067209392786026,
-0.019785569980740547,
0.010998404584825039,
-0.0005900117103010416,
0.07654357701539993,
-0.042970072478055954,
0.02855652943253517,
0.03514433279633522,
-0.08214631676673889,
0.049152154475450516,
-0.015346774831414223,
0.024027766659855843,
-0.01727495901286602,
-0.002884899964556098,
-0.03414832800626755,
0.04262203350663185,
0.011988382786512375,
0.06326020509004593,
-0.004063988104462624,
-0.012449155561625957,
0.003280268283560872,
-0.018822230398654938,
-0.00709106121212244,
-0.0006999662728048861,
0.014550675638020039,
0.002936752513051033,
0.0645190179347992,
-0.02486313320696354,
-0.0218534916639328,
0.03212171792984009,
0.024574240669608116,
0.0019049877300858498,
-0.0187937431037426,
-0.03825176879763603,
0.007618228904902935,
0.03381652012467384,
0.014672037214040756,
-0.0025138144847005606,
-0.010653773322701454,
0.001383405877277255,
0.030567649751901627,
0.019373340532183647,
0.021998586133122444,
0.0013979582581669092,
0.016779713332653046,
-0.0387045219540596,
-0.00470810616388917,
0.03582621365785599,
-0.0036668942775577307,
0.011027340777218342,
-0.004634283483028412,
-0.031233729794621468,
0.028252843767404556,
-0.02894197404384613,
0.00897204875946045,
-0.03328473120927811,
-0.013504023663699627,
0.01349455863237381,
0.0031837366987019777,
-0.0027783566620200872,
0.019300121814012527,
-0.05455610528588295,
0.0047669848427176476,
0.0027304431423544884,
-0.007755683269351721,
-0.0094652334228158,
-0.05301905795931816,
0.0015749813755974174,
-0.011315127834677696,
-0.004438730422407389,
-0.003766393754631281,
-0.021153384819626808,
-0.0025343375746160746,
0.03728003054857254,
0.00563002796843648,
0.008593607693910599,
-0.047427885234355927,
-0.03926633670926094,
-0.0035222982987761497,
-0.08044307678937912,
0.012713666073977947,
0.04109613597393036,
0.015202339738607407,
-0.019273683428764343,
0.012848122976720333,
0.010554547421634197,
0.029077893123030663,
0.06648999452590942,
-0.0029821235220879316,
-0.012525737285614014,
0.020007362589240074,
-0.0018125532660633326,
0.03719043359160423,
-0.01844506338238716,
-0.003883799770846963,
-0.021671652793884277,
0.002386244246736169,
-0.02644162066280842,
0.010308860801160336,
-0.03352061286568642,
-0.018707355484366417,
0.0027887108735740185,
0.013239357620477676,
0.01445553544908762,
0.00662156380712986,
-0.019885599613189697,
0.04941491037607193,
0.022929364815354347,
-0.011187574826180935,
0.03296462818980217,
0.0026245242916047573,
-0.019771410152316093,
0.06731272488832474,
-0.019831521436572075,
-0.04642896354198456,
0.024189788848161697,
-0.00588392186909914,
-0.017857808619737625,
-0.00008525463636033237,
-0.02186908759176731,
0.03923359513282776,
-0.04620460048317909,
-0.023823319002985954,
0.07932402938604355,
0.0009103534976020455,
-0.03814779594540596,
0.06671752780675888,
0.0007049246923997998,
0.0388253815472126,
-0.018507013097405434,
0.013469110243022442,
0.012157242745161057,
0.002614176133647561,
0.01165868155658245,
0.0065205772407352924,
0.054919276386499405,
-0.01295724418014288,
-0.005263999570161104,
0.053831398487091064,
-0.026540428400039673,
0.037642449140548706,
0.026706280186772346,
0.06269755959510803,
-0.04970235005021095,
-0.0009268851717934012,
0.03381017968058586,
-0.013031634502112865,
-0.00035418730112724006,
0.04114488884806633,
-0.04650162532925606,
0.0735878050327301,
-0.03403710201382637,
-0.014017518609762192,
-0.03556576743721962,
0.03124517947435379,
-0.017917830497026443,
0.03696683049201965,
-0.003724663984030485,
0.0738089382648468,
-0.014851338230073452,
0.023198286071419716,
-0.03233668580651283,
-0.029291244223713875,
0.02408010885119438,
-0.04337326064705849,
-0.007182046305388212,
0.03594819828867912,
-0.010193726047873497,
0.017259597778320312,
-0.009164789691567421,
-0.0449974462389946,
-0.015447085723280907,
0.032660260796546936,
0.020570900291204453,
0.010875973850488663,
-0.03660744056105614,
-0.011720332317054272,
-0.049480050802230835,
0.059725571423769,
-0.05582333728671074,
-0.011416670866310596,
-0.0128146568313241,
0.006933650467544794,
-0.016413945704698563,
-0.0056851571425795555
] |
<p>Two magnets with Iron truncated cone or pyramid: Frustrum</p>
<p><strong>How much low inclination can the truncated cone or pyramid: Frustrum be made,
without non homogeneous lines of magnetic field coming out from the sides ?????????</strong>
<img src="http://I.stack.imgur.com/IqOxV.png" alt="Cone_Inclination"></p>
<p>Two magnets with Iron truncated cone and Yoke
<img src="http://I.stack.imgur.com/9Ak7B.png" alt="Two magnets with Iron truncated cone and Yoke"></p>
<p><a href="http://www.kjmagnetics.com/gap.calculator.asp" rel="nofollow">Link_to_Example_1</a></p>
<p>Two magnets with Iron truncated pyramid and Yoke
in a different set up.
<img src="http://I.stack.imgur.com/w9927.jpg" alt="Two magnets with Iron truncated pyramid and Yoke"></p>
<p><a href="http://www.supermagnete.de/eng/faq/How-can-I-create-a-magnetic-field-that-is-as-homogeneous-as-possible" rel="nofollow">Link_to_Example_2</a></p>
<p>Knowing the magnetic flux at the larger base of the truncated cone or Frustrum,
the area of the smaller base will be the one in which you get the
magnetic saturation of the Iron.
But, ... <strong>How much low inclination can the truncated cone or Frustrum be made,
without non homogeneous lines of magnetic field coming out from the sides ?????????</strong>
<img src="http://I.stack.imgur.com/IqOxV.png" alt="Cone_Inclination"></p>
<p>Also in the image of Link_to_Example_2 the gray rectangular number 2 is
a block between the iron pieces to keep the distance between the two parts. It must also be a non ferromagnetic material like brass, wood, stainless steel, etc.
<strong>But what's the best material to hold strong compression and not catch magnetic field
drawing it away from the main gap (number 4) ???</strong></p>
<p>Help please.
Thank you in advance. </p>
| 8,336 |
[
-0.056429386138916016,
0.0010261618299409747,
-0.00009886141197057441,
-0.025438938289880753,
0.060646191239356995,
-0.0006561956251971424,
-0.07181863486766815,
-0.028276823461055756,
0.011473501101136208,
-0.02494262531399727,
0.05600431188941002,
0.02319488674402237,
0.035577185451984406,
0.0005836680065840483,
0.015208974480628967,
-0.01854124665260315,
0.009449495933949947,
0.00695411441847682,
-0.025997869670391083,
-0.018198242411017418,
-0.005595136899501085,
-0.009494652971625328,
0.001464211498387158,
0.02306201122701168,
-0.01657271943986416,
0.010050328448414803,
0.057924091815948486,
0.014852939173579216,
-0.009692821651697159,
0.06690417975187302,
-0.010183189064264297,
-0.029551686719059944,
-0.019264616072177887,
0.02366650104522705,
0.0405738465487957,
-0.009032380767166615,
0.016961924731731415,
0.01430406142026186,
0.014696192927658558,
0.030795278027653694,
0.0016609614249318838,
0.0065364413894712925,
-0.035200390964746475,
0.03801460564136505,
-0.013863103464245796,
0.017502857372164726,
0.010197965428233147,
-0.03437827527523041,
0.031716085970401764,
-0.0533268041908741,
0.03521813824772835,
-0.002292682183906436,
0.05540004000067711,
0.04675906524062157,
0.03378228098154068,
-0.03221232444047928,
0.05527294799685478,
0.06112239509820938,
-0.007613061461597681,
-0.05320503190159798,
0.0034919301979243755,
-0.01721206307411194,
-0.0032290173694491386,
-0.035673193633556366,
-0.010954598896205425,
0.042228732258081436,
-0.0019428484374657273,
0.009775853715837002,
0.04317348822951317,
-0.04694890230894089,
0.03780146688222885,
0.004634578712284565,
0.010922739282250404,
-0.030437851324677467,
0.029945723712444305,
-0.03015006147325039,
0.020548226311802864,
0.012868855148553848,
0.03913222253322601,
0.030845846980810165,
-0.014322558417916298,
0.022691944614052773,
0.04748547077178955,
0.020320547744631767,
0.0343378446996212,
-0.014018213376402855,
0.03504190221428871,
0.020987708121538162,
0.007493994664400816,
0.020457645878195763,
0.02057688497006893,
0.04190381243824959,
0.07617735862731934,
-0.02573881670832634,
-0.0007876744493842125,
0.005489204544574022,
-0.004986086394637823,
0.015397720038890839,
-0.0013039137702435255,
0.0036745532415807247,
0.014309614896774292,
-0.030887426808476448,
-0.035005901008844376,
0.07033538818359375,
0.06551426649093628,
-0.028744695708155632,
0.0019742436707019806,
0.02710297890007496,
-0.05204886943101883,
-0.003162587760016322,
0.03088691271841526,
0.023210600018501282,
-0.0017089531756937504,
-0.03510354831814766,
-0.005720078945159912,
-0.02070085145533085,
0.008813954889774323,
-0.02045677974820137,
0.040321897715330124,
0.07498037815093994,
0.0212666355073452,
0.0033271664287894964,
-0.00888591818511486,
-0.03827942535281181,
-0.10794054716825485,
-0.00016545617836527526,
0.022830912843346596,
0.010515660047531128,
-0.02070145681500435,
0.013974624685943127,
0.003550824709236622,
-0.004655837081372738,
-0.0013592852046713233,
0.010762441903352737,
0.010099593549966812,
-0.01276334747672081,
-0.07293932884931564,
-0.029563596472144127,
0.020617196336388588,
-0.003443564521148801,
0.019037727266550064,
-0.0627049058675766,
-0.027082815766334534,
0.03714562952518463,
0.06980711966753006,
0.03041854500770569,
0.011218637228012085,
-0.0386357419192791,
0.022682521492242813,
-0.016774673014879227,
0.006300370674580336,
-0.004163676872849464,
-0.010429751127958298,
-0.0061050220392644405,
-0.02330295741558075,
-0.06744685769081116,
0.0768527239561081,
0.021535925567150116,
0.007427144795656204,
-0.006398395635187626,
0.03967636823654175,
-0.027705909684300423,
0.03610436990857124,
-0.0051183076575398445,
-0.025887349620461464,
-0.016668958589434624,
0.10410680621862411,
0.0026582947466522455,
0.0007488614646717906,
0.03273404389619827,
-0.039262957870960236,
-0.01898277923464775,
-0.006489274557679892,
0.011276980862021446,
0.06127006933093071,
-0.053808409720659256,
-0.023066755384206772,
-0.014920402318239212,
0.03414725512266159,
0.016999248415231705,
-0.07585407048463821,
-0.020608387887477875,
-0.014956560917198658,
0.035826873034238815,
0.02845892310142517,
0.05734310671687126,
-0.002128478605300188,
-0.027294570580124855,
0.008404570631682873,
-0.048839956521987915,
-0.02751750685274601,
-0.015500906854867935,
-0.004192654509097338,
-0.029561849310994148,
-0.046038854867219925,
0.04004966840147972,
-0.008314663544297218,
0.03389831259846687,
-0.05046836659312248,
-0.03146187961101532,
0.031204916536808014,
0.00778777152299881,
0.022733034566044807,
0.0274003054946661,
0.04984920099377632,
0.05644243210554123,
0.037004731595516205,
-0.017918376252055168,
0.014925035648047924,
-0.029515719041228294,
-0.02799125388264656,
-0.015926608815789223,
-0.01889953576028347,
-0.02414800226688385,
0.04099169000983238,
-0.009215864352881908,
0.0031720802653580904,
0.08181560784578323,
0.0010348381474614143,
-0.011205621063709259,
-0.022915255278348923,
0.10630153119564056,
0.03419650346040726,
-0.004186980426311493,
0.012795021757483482,
0.007983538322150707,
0.037767525762319565,
0.05303094536066055,
-0.013796940445899963,
-0.023729782551527023,
-0.061532218009233475,
0.0015545865753665566,
0.04883874952793121,
0.04404718801379204,
-0.0734228566288948,
0.00896547269076109,
0.014753058552742004,
0.017272884026169777,
0.02031443826854229,
0.0365380197763443,
-0.011852133087813854,
-0.010750629007816315,
-0.005190508905798197,
-0.0007768998621031642,
-0.014214535243809223,
0.02978748455643654,
0.01983663998544216,
0.0027326352428644896,
0.02357424795627594,
-0.007121858187019825,
-0.019541407003998756,
0.041531093418598175,
0.008290630765259266,
-0.04730015620589256,
0.013172687962651253,
-0.01595930941402912,
0.025564556941390038,
0.01126021333038807,
-0.0018801833502948284,
0.026541907340288162,
-0.0005139913409948349,
0.017488915473222733,
-0.0053012012504041195,
0.015028288587927818,
0.000086752996139694,
-0.005968056619167328,
0.0330466590821743,
-0.051789261400699615,
0.02630847878754139,
-0.04369667172431946,
-0.01880132593214512,
-0.013041248545050621,
0.004387184511870146,
-0.044234443455934525,
-0.00543914083391428,
0.0357963852584362,
-0.005812897812575102,
0.02925884537398815,
-0.0235068928450346,
0.004831228870898485,
-0.029143499210476875,
-0.0060005877166986465,
0.02294851653277874,
-0.00430308049544692,
-0.0685306265950203,
0.02308461256325245,
-0.0263456292450428,
-0.0018856307724490762,
0.048391398042440414,
-0.008828949183225632,
-0.016281267628073692,
0.00865945778787136,
0.023398470133543015,
-0.06367109715938568,
-0.05577722564339638,
-0.01657617650926113,
0.012942273169755936,
-0.03394504263997078,
-0.014840427786111832,
0.06908488273620605,
0.027003737166523933,
-0.05727267265319824,
0.03721211105585098,
-0.015407492406666279,
-0.016566365957260132,
-0.003818999510258436,
-0.006090834736824036,
-0.008988399989902973,
-0.021893193945288658,
0.03404456749558449,
0.010322361253201962,
-0.031027132645249367,
0.02072969824075699,
-0.0811031237244606,
-0.019322458654642105,
0.012479821220040321,
-0.05369042232632637,
0.02832883596420288,
-0.020760228857398033,
-0.05636942386627197,
0.0754815861582756,
0.0202507134526968,
-0.017034325748682022,
-0.05182991176843643,
0.0005476431688293815,
-0.021745998412370682,
-0.023268526419997215,
-0.029545040801167488,
0.029873309656977654,
-0.013695256784558296,
-0.018171019852161407,
-0.002861016197130084,
0.022519290447235107,
0.010697521269321442,
0.04828699305653572,
0.02794964797794819,
0.015134374611079693,
0.014439009130001068,
-0.018902653828263283,
0.08783204108476639,
-0.000617003592196852,
0.00006731224857503548,
0.019558889791369438,
-0.0032456933986395597,
0.06986186653375626,
0.014731334522366524,
-0.05816877633333206,
0.00943959504365921,
-0.013301222585141659,
0.016656188294291496,
-0.038856931030750275,
0.02923933044075966,
-0.003970371093600988,
-0.008898730389773846,
-0.017095252871513367,
-0.0006468378123827279,
0.05922572314739227,
-0.024403875693678856,
0.008500728756189346,
0.048980966210365295,
0.0251682847738266,
-0.012836197391152382,
-0.008258555084466934,
-0.0009328521555289626,
-0.009736556559801102,
0.02532520703971386,
-0.04917033016681671,
-0.037767812609672546,
0.015473703853785992,
0.040680255740880966,
0.005563820246607065,
0.0234100092202425,
0.030230868607759476,
-0.0008698281017132103,
-0.07947988063097,
0.020378008484840393,
-0.007202753331512213,
0.04916513338685036,
0.030383994802832603,
0.025730924680829048,
0.014864383265376091,
-0.01725277490913868,
-0.015468376688659191,
-0.017773738130927086,
-0.06536098569631577,
0.018759872764348984,
-0.008276672102510929,
0.0021272192243486643,
0.03981637954711914,
-0.051094237715005875,
-0.00908829178661108,
-0.020222540944814682,
0.002158339135348797,
0.008876773528754711,
0.004958210047334433,
-0.028466565534472466,
0.018765375018119812,
0.008096159435808659,
-0.027607794851064682,
0.0033789565786719322,
0.0712042972445488,
0.03217015042901039,
-0.04643621668219566,
0.023624110966920853,
-0.01717659831047058,
-0.030832968652248383,
0.03708624094724655,
0.001779506797902286,
0.03623268008232117,
0.015639008954167366,
0.042063143104314804,
0.0005645369528792799,
0.02566053345799446,
-0.019363898783922195,
-0.030623598024249077,
0.023131299763917923,
0.06830548495054245,
0.011803876608610153,
0.0024582426995038986,
-0.03238409757614136,
-0.05404677242040634,
-0.03241131827235222,
-0.027506699785590172,
0.06319864094257355,
-0.043514594435691833,
0.027992283925414085,
0.018060140311717987,
-0.0035761056933552027,
0.017657345160841942,
0.014766174368560314,
0.002146527636796236,
0.027984894812107086,
-0.0153457410633564,
-0.049271080642938614,
-0.043131664395332336,
-0.03226316347718239,
0.0029964616987854242,
0.016546178609132767,
-0.006947746966034174,
-0.0467364676296711,
-0.018699901178479195,
0.03954232484102249,
0.024104811251163483,
0.003924666438251734,
0.04884178936481476,
-0.01087411679327488,
0.019785938784480095,
-0.01445816084742546,
-0.008324705995619297,
0.015404565259814262,
-0.012496481649577618,
0.08182485401630402,
0.001232282374985516,
-0.013532011769711971,
-0.06870334595441818,
-0.04261396452784538,
0.030463244765996933,
0.016806095838546753,
-0.002072051865980029,
0.017076881602406502,
-0.0501687228679657,
0.0008763918303884566,
0.04064735770225525,
-0.052717261016368866,
0.050500672310590744,
-0.012598822824656963,
0.04438049718737602,
-0.02059355564415455,
-0.010879010893404484,
-0.030189601704478264,
0.026942843571305275,
-0.02519455924630165,
0.013092435896396637,
-0.02835932932794094,
-0.01919509842991829,
0.017448727041482925,
0.004454539157450199,
0.06508675217628479,
0.03002987802028656,
-0.009030993096530437,
-0.008319403976202011,
0.027707017958164215,
0.004266750067472458,
-0.0003471791569609195,
-0.10610688477754593,
0.028208112344145775,
0.012249290943145752,
-0.037744082510471344,
0.049708977341651917,
0.004766994621604681,
-0.028482619673013687,
0.0413951650261879,
-0.021964402869343758,
-0.01228283066302538,
0.009354228153824806,
-0.05151858925819397,
0.03852083534002304,
0.025814073160290718,
-0.010130180977284908,
0.04965045303106308,
0.011595271527767181,
-0.024728696793317795,
0.01140927616506815,
-0.056438345462083817,
-0.008088483475148678,
-0.04469391703605652,
0.026585455983877182,
-0.012427229434251785,
0.024095332249999046,
-0.022176994010806084,
0.03254104033112526,
-0.008342319168150425,
-0.005064946599304676,
-0.019329668954014778,
-0.019429735839366913,
0.02257271111011505,
0.026228075847029686,
0.016932319849729538,
-0.0050278413109481335,
-0.020581772550940514,
0.002519692061468959,
-0.016228875145316124,
-0.016959376633167267,
0.02214962989091873,
-0.04911612719297409,
0.021821916103363037,
-0.015564198605716228,
-0.030825864523649216,
-0.0021723411045968533,
-0.035535238683223724,
0.003732918528839946,
0.006329074501991272,
-0.018772996962070465,
0.08480817079544067,
-0.009552083909511566,
0.05196826905012131,
0.0018474541138857603,
-0.015417267568409443,
-0.016559679061174393,
0.020615972578525543,
-0.011860636062920094,
0.004342864267528057,
0.006530117243528366,
0.020594531670212746,
0.024222077801823616,
-0.018469255417585373,
-0.019875450059771538,
-0.02068213000893593,
-0.021694496273994446,
-0.010846029967069626,
0.005134774371981621,
-0.00041984161362051964,
-0.027406049892306328,
0.009291529655456543,
-0.03509587049484253,
0.0011784257367253304,
0.020449014380574226,
-0.03898577019572258,
-0.013866584748029709,
0.016714753583073616,
0.0020650543738156557,
0.05686458200216293,
0.031015068292617798,
-0.013354500755667686,
-0.008578608743846416,
-0.037066057324409485,
-0.020398685708642006,
-0.0048273541033267975,
-0.010180991142988205,
-0.028394728899002075,
-0.048867177218198776,
-0.02562747336924076,
0.025822490453720093,
0.03290200233459473,
-0.008043096400797367,
-0.03235183283686638,
0.023134393617510796,
0.0376296192407608,
-0.015766127035021782,
-0.003379418281838298,
0.016913626343011856,
0.007695764768868685,
0.004121531266719103,
-0.050506897270679474,
0.00012610295380000025,
-0.010911225341260433,
-0.03802384436130524,
-0.002983538433909416,
-0.018473858013749123,
-0.0037433926481753588,
-0.004762243013828993,
0.09657369554042816,
-0.03463481739163399,
-0.021022969856858253,
0.011924618855118752,
0.005251734051853418,
0.023558616638183594,
0.0078500434756279,
0.019918346777558327,
0.011618931777775288,
0.009512899443507195,
-0.011098011396825314,
-0.030311232432723045,
-0.034417588263750076,
0.04439406469464302,
0.03626655787229538,
-0.01624099351465702,
0.020257333293557167,
0.031562440097332,
-0.009506149217486382,
-0.03268282115459442,
-0.03821948170661926,
-0.015268823131918907,
-0.03550511971116066,
0.005363914649933577,
0.03379533439874649,
-0.03807833790779114,
-0.013867090456187725,
0.055442553013563156,
0.043894052505493164,
-0.023164238780736923,
-0.0009040255681611598,
-0.018924886360764503,
0.06441009789705276,
0.018105555325746536,
-0.03549867123365402,
-0.05147956311702728,
0.05009298399090767,
0.01176257710903883,
0.05099186301231384,
0.025990698486566544,
-0.0036134403198957443,
0.030190981924533844,
0.02236146293580532,
0.011724798008799553,
-0.03286227211356163,
-0.017714526504278183,
-0.026971839368343353,
0.02714027650654316,
0.04042386636137962,
-0.008150087669491768,
-0.009026753716170788,
0.016604118049144745,
0.0309992004185915,
-0.01813301257789135,
0.026931246742606163,
-0.04592282325029373,
-0.01961476169526577,
-0.03504906967282295,
-0.024365916848182678,
-0.08131151646375656,
0.04048396646976471,
-0.00646089157089591,
-0.04258442670106888,
0.040025755763053894,
-0.022085871547460556,
0.019827699288725853,
0.022287512198090553,
0.005447868257761002,
0.017821503803133965,
0.02675759419798851,
-0.021071750670671463,
0.04874051734805107,
-0.020237915217876434,
-0.004630539566278458,
0.18491315841674805,
0.060787446796894073,
0.004265741910785437,
-0.05601854622364044,
0.01591111347079277,
-0.050981953740119934,
-0.0050317151471972466,
-0.042085014283657074,
0.009522597305476665,
-0.030308140441775322,
-0.0404353141784668,
0.00959740113466978,
0.018836671486496925,
-0.024818001314997673,
-0.005824308376759291,
0.037147294729948044,
-0.0007837413577362895,
0.00997418724000454,
-0.020177973434329033,
0.03700516000390053,
-0.021074526011943817,
-0.018598735332489014,
-0.013081599958240986,
0.016146350651979446,
-0.024587037041783333,
-0.022828523069620132,
-0.006489678751677275,
0.015499814413487911,
0.03642799332737923,
0.03422422707080841,
-0.04952226206660271,
0.03460993990302086,
0.00936297420412302,
-0.019553307443857193,
-0.031246526166796684,
0.03853989019989967,
0.005832115653902292,
-0.03448885306715965,
-0.008108981885015965,
0.0358254499733448,
0.023531146347522736,
0.00036794552579522133,
0.016187747940421104,
0.045985281467437744,
-0.04110633209347725,
0.0172418300062418,
-0.05388204753398895,
0.02840820886194706,
-0.010670469142496586,
-0.02612397074699402,
-0.013893485069274902,
0.054857607930898666,
0.04057920724153519,
-0.03526286780834198,
-0.04588798061013222,
0.009490590542554855,
-0.021603256464004517,
-0.025179818272590637,
0.01820753887295723,
-0.002053448697552085,
0.033875010907649994,
0.04190608114004135,
-0.00005590023647528142,
-0.0022740846034139395,
0.0035065023694187403,
-0.021284207701683044,
-0.013412948697805405,
0.0889071524143219,
0.027176322415471077,
-0.007571949157863855,
-0.06982086598873138,
0.006938633043318987,
-0.015138253569602966,
0.015355038456618786,
-0.006491794716566801,
-0.01542758010327816,
0.023896748200058937,
-0.002884646411985159,
-0.046155672520399094,
0.023112423717975616,
-0.022977160289883614,
0.02114740200340748,
0.009104444645345211,
-0.018823988735675812,
-0.027271287515759468,
-0.03466226905584335,
0.0007872047717683017,
0.018178293481469154,
-0.0014616046100854874,
0.03413492813706398,
0.00971621461212635,
-0.00004087357592652552,
0.007960192859172821,
-0.024300815537571907,
-0.08780189603567123,
-0.0006088642403483391,
-0.050896257162094116,
-0.00723953265696764,
0.017630763351917267,
0.06225834786891937,
0.06368996202945709,
-0.0013647576561197639,
0.010400773957371712,
0.03252329304814339,
-0.03241695091128349,
-0.015737684443593025,
0.0015519330045208335,
-0.02837785705924034,
0.017754852771759033,
0.006228114012628794,
-0.0135413883253932,
-0.04025813564658165,
0.005298189353197813,
0.0026219093706458807,
-0.0019631017930805683,
0.06515447795391083,
0.02296643704175949,
-0.01897052675485611,
-0.03443996235728264,
-0.014230739325284958,
0.04281872883439064,
0.0009569186368025839,
-0.024474550038576126,
-0.004838212393224239,
-0.006577085237950087,
-0.015885716304183006,
0.02226209081709385,
0.007532711606472731,
0.022851526737213135,
-0.017242249101400375,
0.001163702690973878,
0.020026927813887596,
0.014752316288650036,
0.004667970817536116,
-0.04874677211046219,
0.0025379694998264313,
0.05826795473694801,
0.0037912107072770596,
0.00992343295365572,
-0.018483582884073257,
0.008267060853540897,
0.0040871999226510525,
-0.03628239780664444,
-0.00200413865968585,
0.01090212818235159,
0.01739184744656086,
0.014587906189262867,
0.0006757710943929851,
-0.02713196352124214,
0.042847804725170135,
-0.012200374156236649,
-0.024917583912611008,
-0.02048337459564209,
0.016114136204123497,
0.02717326581478119,
-0.014238436706364155,
0.01715158298611641,
0.003408224554732442,
0.010926591232419014,
0.005284870509058237,
0.034162528812885284,
-0.003273243084549904,
-0.0510253980755806,
-0.006917139049619436,
0.008836831897497177,
-0.023105567321181297,
-0.0037285620346665382,
-0.02147848904132843,
0.002929186448454857,
-0.0037272307090461254,
-0.013270811177790165,
-0.01326439157128334,
0.017725825309753418,
0.010693827643990517,
-0.0991465374827385,
-0.015632223337888718,
0.009482327848672867,
-0.014468216337263584,
0.0489153228700161,
-0.021631883457303047,
0.021776024252176285,
0.02245987579226494,
-0.06924369931221008,
0.0042933933436870575,
-0.005795214790850878,
-0.027569595724344254,
-0.02121145837008953,
-0.05007176846265793,
0.007635416463017464,
0.016666626557707787,
-0.01782088167965412,
0.0576077438890934,
0.02964322827756405,
0.015563285909593105,
-0.039434388279914856,
-0.01003690343350172,
-0.023650839924812317,
-0.0011975483503192663,
-0.021245446056127548,
-0.02421911619603634,
0.06113249808549881,
0.01832551136612892,
0.009000342339277267,
0.0010479537304490805,
-0.030499698594212532,
-0.010512067936360836,
0.0069097732193768024,
0.04538460448384285,
0.03165626525878906,
0.021369371563196182,
-0.01352001167833805,
0.0015461567090824246,
-0.007291468791663647,
-0.02589578367769718,
0.013026908971369267,
0.01671467535197735,
-0.012798676267266273,
0.0020935782231390476,
0.043907444924116135,
-0.029932301491498947,
0.009450423531234264,
0.030264416709542274,
-0.07202207297086716,
-0.011363428086042404,
-0.017834490165114403,
0.0007415763102471828,
0.009025819599628448,
-0.01074153371155262,
0.007234277203679085,
-0.011408161371946335,
0.0015178063185885549,
0.014525136910378933,
-0.027087250724434853,
0.0220149178057909,
0.030211320146918297,
-0.031543683260679245,
-0.0006796361412853003,
0.0016702442662790418,
-0.01753668300807476,
-0.02729458548128605,
-0.018380315974354744,
-0.00746689410880208,
0.0011750597041100264,
0.004816541448235512,
0.013931363821029663,
-0.013364728540182114,
-0.04006592556834221,
0.04222051426768303,
0.036426641047000885,
0.013416601344943047,
0.01495586708188057,
-0.006456473842263222,
-0.01431888435035944,
-0.04488785192370415,
0.02566911280155182,
-0.05658619850873947,
-0.06261169910430908,
-0.03137190639972687,
-0.031539447605609894,
0.004012665711343288,
0.014431772753596306,
0.03971906378865242,
0.00761775765568018,
-0.0032992104534059763,
0.015361565165221691,
-0.02662518247961998,
0.014244326390326023,
-0.0527237206697464,
0.03162743151187897,
0.040388837456703186,
-0.007134194485843182,
0.03881359472870827,
-0.016964657232165337,
0.028782274574041367,
0.016789527609944344,
0.03936021029949188,
0.0015215268358588219,
0.001948138582520187,
0.029811635613441467,
-0.045903559774160385,
-0.022986946627497673,
-0.05067538097500801,
-0.03116787038743496,
0.037992216646671295,
-0.0026956622023135424,
-0.00486023211851716,
-0.0224036555737257,
0.0036656507290899754,
-0.04084409028291702,
-0.02226984314620495,
-0.04736577719449997,
0.009631643071770668,
-0.01634439267218113,
-0.05980497971177101,
0.044627346098423004,
-0.06532202661037445,
-0.0038587101735174656,
0.013749667443335056,
-0.04701181501150131,
0.0013625321444123983,
0.06869460642337799,
0.004026089329272509,
0.04375384747982025,
-0.05591685324907303,
0.01228360366076231,
-0.012596013024449348,
-0.04383853077888489,
0.04731123521924019,
-0.0007609897875227034,
-0.009082473814487457,
0.014761955477297306,
-0.026959815993905067,
0.05705275759100914,
0.0056889536790549755,
0.0013898775214329362,
0.0025959108024835587,
0.03990805521607399,
0.002379802754148841,
-0.03020298480987549,
0.011043580248951912,
-0.04529588669538498,
0.03138057887554169,
0.0413985438644886,
0.007481913082301617,
0.06598329544067383,
-0.008973549120128155,
-0.0026616204995661974,
-0.04481789469718933,
-0.002731699263677001,
-0.033309321850538254,
0.035564176738262177,
-0.02366328053176403,
0.035895444452762604,
0.013034915551543236,
-0.012204572558403015,
0.013451065868139267,
-0.0037567385006695986,
0.01061734277755022,
-0.02255566045641899,
0.02771785296499729,
-0.0004082781379111111,
0.004606249742209911,
0.021591344848275185,
-0.00636475533246994,
-0.03248053044080734,
-0.05024026706814766,
0.014911534264683723,
0.010950310155749321,
0.029678691178560257,
-0.004089779686182737,
-0.015729865059256554,
-0.013795440085232258,
0.03392558917403221,
-0.05140094459056854,
-0.023833932355046272,
-0.030312510207295418,
0.019271692261099815,
-0.021451713517308235,
0.0014553621876984835
] |
<p>Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is,</p>
<p>$$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + \frac{e}{c}\hat{A}(\hat{r})\biggr)^2$$</p>
<p>To convert this in a Feynman-path-integral language, I pick say a gauge $\vec{A}=(-\frac{B}{2}y,\frac{B}{2}x)$and then in this gauge $\hat{p}$ and $\hat{A}$ commute and that makes rewriting in the path-integral language much easier. </p>
<p>If I put this through the usual process of "deriving" a Feynman path-integral then I would get the expression, </p>
<p>$$\int \bigl[\mathcal{D}\vec{r}\bigr]\bigl[\mathcal{D}\vec{p}\bigr] \exp\biggl[i \int dt \biggl(\vec{p}\cdot\dot{\vec{r}} - \frac{1}{2m}\Bigl(\vec{p}+\frac{e}{c}\vec{A}\Bigr)^2\biggr)\biggr]$$</p>
<ul>
<li><p>Is it obvious (or true ) that the above expression is independent of the gauge I chose to the calculation? Is there a way to write the system in the path-integral language without explicitly choosing a gauge? (I have worked through calculations in Yang-Mills theory in the Fadeev-Popov gauge which does exactly that in those cases but I can't see a way out here...) </p></li>
<li><p>Can't I have written down the above path-integral without even going through the usual process of finding infinitesimal transition amplitudes and then collecting them together? I mean how often is it safe to say that for a Hamiltonian $H(p,q)$ the path integral representation of the transition amplitude will be $\int [\mathcal{D}p][\mathcal{D}q]e^{i\int dt (p\dot{q}-H(q,p)) }$? </p></li>
</ul>
<p>Now the Heisenberg's equation of motion will tell that,</p>
<p>$$\frac{d\vec{r}}{dt} = \frac{1}{m} \biggl(\vec{p} + \frac{e}{c}\vec{A}\biggr)^2$$</p>
<p>In the Feynman path-integral the position and the momentum vectors are treated to be independent variables and hence it would be wrong to substitute the above expression into the path-integral but outside one can I guess do this substitution and one would get for the action (whatever sits in the exponent),</p>
<p>$$S = \int dt \biggl(\frac{p^2}{2m} - \frac{e^2}{2mc^2}A^2\biggr)$$</p>
<ul>
<li>But the above expression doesn't look right!? The integrand isn't what the Lagrangian should be. right? </li>
</ul>
<p>Now in the derivation of the Feynman-path-integral if one integrates out the momentum for every infinitesimal transition amplitude and then reconstitutes the path-integral then one would get the expression,</p>
<p>$$\int [\mathcal{D}\vec{r}] \exp\biggl[i\int dt \biggl(\frac{m}{2}\dot{\vec{r}}^2 - \frac{e}{c}\dot{\vec{r}}\cdot\vec{A}\biggr)\biggr]$$</p>
<ul>
<li><p>Now what seems to sit in the exponent is what is the "correct" Lagrangian - I would think. Why did the answer differ in the two different ways of looking at it? </p></li>
<li><p>I wonder if given a Hamiltonian its corresponding Lagrangian can be "defined" as whatever pops out in the exponent if that system is put through this Feynman re-writing. In this case keeping to just classical physics I am not sure how to argue that the $\frac{m}{2} \dot{\vec{r}}^2 - \frac{e}{c} \dot{\vec{r}}\cdot\vec{A}$ is the Lagrangian for the system with the Hamiltonian $\frac{1}{2m}\bigl(\vec{p} + \frac{e}{c}\vec{A}(\vec{r})\bigr)^2$ </p></li>
</ul>
<p>I think I have seen examples on curved space-time where the "classical" Lagrangian differs from what pops out in the exponent when the system is path-integrated. </p>
| 8,337 |
[
-0.006127714179456234,
0.02247869223356247,
0.041081201285123825,
-0.04231216013431549,
0.014574256725609303,
0.06304879486560822,
-0.04844280332326889,
-0.04782632365822792,
0.020058169960975647,
-0.015491600148379803,
0.016321949660778046,
0.00489044189453125,
0.0644523948431015,
0.03524003550410271,
0.013642682693898678,
0.020401794463396072,
0.01759229600429535,
0.007700585760176182,
0.01695932261645794,
-0.04728681966662407,
-0.006942845415323973,
0.03799492493271828,
-0.01408374309539795,
-0.012072502635419369,
0.03828098252415657,
0.027495747432112694,
0.005074094049632549,
0.003680946072563529,
-0.010856106877326965,
0.069774329662323,
0.007761036511510611,
-0.008348004892468452,
0.04636542871594429,
0.025518622249364853,
0.016810506582260132,
0.02234319970011711,
-0.0015961861936375499,
-0.03888070583343506,
0.024262065067887306,
-0.014730137772858143,
-0.029933718964457512,
-0.018662475049495697,
-0.01360885426402092,
0.06601829081773758,
0.002280161716043949,
0.02141106128692627,
-0.0012112597469240427,
0.00030140162562020123,
0.04636182263493538,
-0.04810042306780815,
0.0603560134768486,
0.011087066493928432,
0.03785834461450577,
0.015533334575593472,
-0.02226460538804531,
-0.032818522304296494,
0.018850082531571388,
0.06935947388410568,
0.01935943402349949,
-0.0492653027176857,
-0.019975652918219566,
-0.051135823130607605,
0.001578955794684589,
-0.031636614352464676,
0.0025665746070444584,
-0.003555038245394826,
0.045407913625240326,
-0.00593981146812439,
0.011595764197409153,
-0.011534775607287884,
-0.0064949276857078075,
-0.001397391315549612,
0.024783723056316376,
-0.0337655209004879,
0.05455711483955383,
0.010849902406334877,
0.03379162400960922,
0.025358399376273155,
0.01975443586707115,
0.028640858829021454,
-0.01863071508705616,
0.019089801236987114,
0.05229494348168373,
0.017691731452941895,
0.003193367039784789,
0.006904759909957647,
0.05722104012966156,
0.0006436307448893785,
0.015496904961764812,
0.024418465793132782,
-0.02178041636943817,
0.01940637268126011,
0.04101758077740669,
-0.019082268700003624,
0.004685257561504841,
0.018465805798768997,
0.03786502406001091,
0.05888732522726059,
-0.0009135563741438091,
-0.012273700907826424,
-0.03477700799703598,
-0.028053579851984978,
-0.02430245839059353,
0.06823498755693436,
0.02107851952314377,
0.010177799500524998,
-0.003167698159813881,
-0.016994435340166092,
-0.04185047000646591,
-0.022344978526234627,
-0.06501265615224838,
0.044625867158174515,
-0.020879900082945824,
0.0033749013673514128,
-0.026701541617512703,
-0.0413244254887104,
-0.0021555942948907614,
-0.01244991086423397,
0.06163067743182182,
0.06079743802547455,
0.050671231001615524,
-0.03664108365774155,
-0.004871378652751446,
-0.03705724701285362,
-0.04003914073109627,
0.0029922807589173317,
0.04742269963026047,
0.03262070193886757,
-0.014885063283145428,
-0.018923139199614525,
0.03924742713570595,
-0.02136167325079441,
0.011372305452823639,
0.021075457334518433,
0.003385328222066164,
-0.019513780251145363,
-0.08932997286319733,
-0.049327656626701355,
0.04890378937125206,
0.016198957338929176,
-0.027346545830368996,
-0.046623364090919495,
-0.011201709508895874,
0.030650630593299866,
0.07418324053287506,
-0.0021733283065259457,
0.013736858032643795,
0.02358824573457241,
0.01819942332804203,
-0.002310556825250387,
-0.0001480404898757115,
-0.021185871213674545,
-0.010251137427985668,
-0.02767704427242279,
0.00011772409197874367,
-0.03219008073210716,
0.06927450746297836,
0.05397433787584305,
-0.03193623945116997,
0.01968836784362793,
0.07966084778308868,
-0.011645857244729996,
0.01852463372051716,
0.04097997024655342,
0.007159253116697073,
-0.00437115877866745,
0.04602725803852081,
0.01744075119495392,
0.04909726604819298,
0.024581164121627808,
0.014806482009589672,
0.023224692791700363,
-0.011257250793278217,
0.024104496464133263,
0.07500804215669632,
-0.03275825455784798,
-0.04719582945108414,
-0.035106491297483444,
-0.0007458234904333949,
-0.03130960464477539,
-0.017064766958355904,
-0.08003752678632736,
-0.009673606604337692,
0.010631902143359184,
-0.011652683839201927,
0.0105219017714262,
0.02034766599535942,
0.0020431799348443747,
0.004208609461784363,
-0.0603628046810627,
-0.036375001072883606,
-0.051852576434612274,
0.0023250137455761433,
0.0023100932594388723,
-0.04743272066116333,
0.02275928296148777,
-0.002886380534619093,
-0.010712678544223309,
-0.012809164822101593,
-0.0573546402156353,
0.009733238257467747,
0.056083060801029205,
0.004046614747494459,
-0.00831939373165369,
0.010791897773742676,
0.030155207961797714,
0.06377784162759781,
0.003605884499847889,
0.04010232537984848,
-0.048306338489055634,
-0.02477158047258854,
-0.003639020025730133,
-0.011621086858212948,
0.02021740935742855,
0.020409269258379936,
-0.03362555801868439,
0.008386801928281784,
-0.02068544179201126,
-0.05023432895541191,
0.050339169800281525,
-0.017474394291639328,
0.021512553095817566,
0.07498950511217117,
0.006263707764446735,
-0.005961929447948933,
0.04049158841371536,
-0.013355594128370285,
0.04451020061969757,
-0.014857001602649689,
-0.0032419634517282248,
-0.01226481981575489,
-0.020579272881150246,
0.039631299674510956,
0.02210698463022709,
-0.04219107702374458,
0.0018962653120979667,
0.039293646812438965,
0.029537640511989594,
0.0325530469417572,
0.03725361078977585,
-0.03903186693787575,
-0.03325071930885315,
-0.0011894566705450416,
0.007365742232650518,
-0.027777716517448425,
-0.013320283964276314,
0.020464342087507248,
-0.0291421078145504,
0.0020790817216038704,
0.009302753023803234,
-0.046010345220565796,
0.03280332311987877,
-0.028425680473446846,
0.00359451025724411,
0.03146831691265106,
-0.030855905264616013,
0.05852803960442543,
-0.006272606551647186,
0.08091253787279129,
0.030224766582250595,
-0.019193751737475395,
-0.008299003355205059,
-0.046012286096811295,
-0.034604448825120926,
-0.006758474744856358,
-0.0018519454170018435,
-0.02040780521929264,
-0.03848612681031227,
0.0232405848801136,
-0.013320286758244038,
0.010392508469522,
-0.011750024743378162,
-0.03460114076733589,
-0.024232087656855583,
-0.004882940091192722,
-0.007409329991787672,
0.025739571079611778,
0.013471083715558052,
-0.023754755035042763,
-0.0096064992249012,
0.035857606679201126,
-0.006588587071746588,
0.029936842620372772,
0.044582121074199677,
-0.00945715606212616,
-0.0031473280396312475,
-0.061788126826286316,
-0.019556643441319466,
0.0443861186504364,
-0.01951015368103981,
0.007008610293269157,
-0.004379838239401579,
0.016184158623218536,
-0.05866749584674835,
-0.01274486817419529,
0.004521217197179794,
0.0032735688146203756,
-0.03371324762701988,
-0.022954313084483147,
0.027096601203083992,
0.013604413717985153,
-0.06760551780462265,
0.00846954621374607,
-0.01625346951186657,
-0.02027140185236931,
0.012772442772984505,
-0.014321284368634224,
-0.004252904560416937,
-0.029498737305402756,
0.01852588914334774,
0.010348215699195862,
-0.03314722701907158,
0.013920184224843979,
-0.0677594318985939,
-0.01586337201297283,
0.009058641269803047,
0.01498283352702856,
-0.003547211643308401,
-0.009218472987413406,
-0.051329050213098526,
0.10987090319395065,
0.024651343002915382,
-0.06938662379980087,
-0.00708281435072422,
0.005108480807393789,
0.01806766539812088,
-0.010554783046245575,
0.017608508467674255,
0.019895615056157112,
-0.010832277126610279,
0.0062301279976964,
0.03427718207240105,
0.018209446221590042,
0.010169301182031631,
0.006059880834072828,
0.026007015258073807,
0.035043131560087204,
-0.01999814808368683,
0.023470086976885796,
0.03671261668205261,
0.007182131987065077,
-0.009292475879192352,
-0.01356112863868475,
-0.00016820536984596401,
-0.008790813386440277,
0.055637579411268234,
-0.04820491373538971,
0.06638125330209732,
0.008824445307254791,
0.024929042905569077,
-0.030604837462306023,
0.018472330644726753,
0.00043083832133561373,
-0.04330319166183472,
0.002205889206379652,
0.01695384830236435,
0.017292963340878487,
-0.014130940660834312,
0.005356790032237768,
0.015327425673604012,
0.029040763154625893,
-0.019734254106879234,
-0.02078431099653244,
0.014224538579583168,
-0.030062248930335045,
0.016165716573596,
-0.03629793971776962,
-0.032437097281217575,
0.055800411850214005,
0.056502584367990494,
-0.01668192632496357,
-0.004043142311275005,
-0.028445564210414886,
-0.004886588081717491,
-0.058876652270555496,
0.017527256160974503,
-0.012109818868339062,
0.041304368525743484,
0.019590603187680244,
0.03943723812699318,
-0.0029245037585496902,
0.00462777353823185,
0.02202891744673252,
-0.006297735963016748,
-0.10338027030229568,
0.015235035680234432,
-0.029256319627165794,
-0.018009327352046967,
-0.02166367881000042,
-0.0640554130077362,
0.022121628746390343,
-0.015420679934322834,
-0.04534688964486122,
-0.024968113750219345,
-0.009098073467612267,
-0.014188489876687527,
0.033396001905202866,
-0.024865800514817238,
-0.04083855822682381,
-0.042241912335157394,
0.04322173073887825,
0.05007017403841019,
-0.03141995519399643,
0.01561215054243803,
0.0462845154106617,
-0.020252864807844162,
-0.034183990210294724,
-0.038749199360609055,
0.006506322883069515,
0.03785768896341324,
0.015417728573083878,
0.014695411548018456,
0.02839360386133194,
0.0062069762498140335,
-0.008226538076996803,
0.02538478374481201,
0.05053582042455673,
0.005307079292833805,
-0.021157652139663696,
0.014234472066164017,
-0.045500755310058594,
0.00030895150848664343,
0.00210602767765522,
0.08054659515619278,
-0.008323753252625465,
-0.022143742069602013,
0.0368441604077816,
0.008768976666033268,
0.00015694780449848622,
0.025330185890197754,
0.021546436473727226,
0.014371260069310665,
-0.006567724514752626,
-0.06568639725446701,
0.025972416624426842,
-0.0060655660927295685,
-0.01076721865683794,
-0.020383886992931366,
-0.01412354875355959,
-0.0037439584266394377,
0.0003215847536921501,
0.026797562837600708,
0.04398253560066223,
0.009865502826869488,
0.003779147518798709,
0.01916820928454399,
0.004873724654316902,
0.0313371866941452,
0.006577936466783285,
0.010031490586698055,
0.051690369844436646,
0.010706438682973385,
-0.014994476921856403,
0.01064392738044262,
-0.04980302229523659,
-0.01688169501721859,
0.03580139949917793,
0.08141284435987473,
0.00332630705088377,
-0.021677089855074883,
-0.035203054547309875,
-0.00013798272993881255,
0.05831364169716835,
0.01344581600278616,
-0.018364083021879196,
-0.042796388268470764,
-0.018838463351130486,
-0.027376625686883926,
-0.03500958904623985,
-0.05963741987943649,
0.013815633952617645,
-0.015986992046236992,
0.0015245963586494327,
-0.05410490557551384,
0.009128864854574203,
0.0013472845312207937,
0.027052663266658783,
-0.010228528641164303,
0.025252070277929306,
0.0280467439442873,
-0.003207618370652199,
-0.005000153090804815,
0.020548252388834953,
-0.01375598181039095,
-0.09427497535943985,
0.0009918126743286848,
0.04003870114684105,
0.039657313376665115,
0.04631108045578003,
0.000955127296037972,
-0.049500834196805954,
0.011657042428851128,
-0.005232436116784811,
0.03725271299481392,
0.03530413284897804,
-0.05383921414613724,
0.06732384115457535,
0.021611446514725685,
-0.011471236124634743,
0.05403881520032883,
0.02091914974153042,
-0.008591460064053535,
-0.031767453998327255,
-0.010303732939064503,
0.024036383256316185,
-0.012555524706840515,
0.0009736957727000117,
-0.045845866203308105,
-0.013952406123280525,
-0.02053411863744259,
0.032331936061382294,
-0.02691005915403366,
-0.001354748965241015,
-0.022410908713936806,
-0.03326111286878586,
-0.014089672826230526,
0.015125371515750885,
-0.0029239216819405556,
-0.05845530703663826,
-0.020161079242825508,
0.02582898736000061,
0.01781393401324749,
-0.007870210334658623,
0.015382351353764534,
-0.027774648740887642,
0.005934723187237978,
0.02012884058058262,
0.0034316363744437695,
-0.004088708199560642,
-0.0021684779785573483,
0.008691718801856041,
0.00915579590946436,
-0.06136636435985565,
0.030808763578534126,
0.007085062563419342,
-0.023241844028234482,
0.013926196843385696,
-0.01616460084915161,
-0.06728295236825943,
0.0022345660254359245,
0.012404917739331722,
0.005538553465157747,
-0.03784039989113808,
-0.012825525365769863,
-0.01886686682701111,
-0.004383490886539221,
-0.03409959375858307,
-0.032498426735401154,
-0.012034918181598186,
-0.030318068340420723,
-0.020395759493112564,
-0.00024081813171505928,
-0.005598905496299267,
-0.0019397824071347713,
-0.011727443896234035,
-0.0001666789030423388,
0.021349936723709106,
-0.032682955265045166,
0.007545970380306244,
-0.007832682691514492,
0.059275347739458084,
0.02039330080151558,
-0.017288459464907646,
-0.008599169552326202,
0.005463828798383474,
-0.04059765487909317,
0.01779588870704174,
0.00050183484563604,
0.03414516896009445,
0.0014115433441475034,
-0.042232006788253784,
-0.002047777408733964,
-0.03316149860620499,
0.007781934458762407,
-0.004021953791379929,
-0.014144853688776493,
0.03960122540593147,
0.020278578624129295,
-0.027111241593956947,
0.01675603911280632,
-0.009182136505842209,
0.014772078953683376,
-0.004157773684710264,
0.01966284029185772,
0.0005304613732732832,
-0.022655706852674484,
-0.009497852064669132,
0.02083807811141014,
-0.017673032358288765,
0.004619068931788206,
-0.011569580994546413,
0.011557179503142834,
0.0002025351277552545,
-0.008445528335869312,
0.02417084015905857,
-0.04448770731687546,
-0.01741400733590126,
-0.03552618995308876,
0.0016482275677844882,
0.01990695483982563,
-0.021604260429739952,
-0.038686878979206085,
-0.02978905476629734,
-0.05755479633808136,
0.01052174437791109,
0.057864829897880554,
-0.0004032862198073417,
0.006298013497143984,
-0.015532749705016613,
0.010689904913306236,
-0.013555184006690979,
-0.0036417029332369566,
-0.04539503529667854,
-0.00964030995965004,
-0.004466539714485407,
0.04135531932115555,
-0.031125647947192192,
0.00545648904517293,
0.020223375409841537,
0.06368348747491837,
-0.039119038730859756,
-0.004553769715130329,
0.009947873651981354,
0.015753036364912987,
0.002158262301236391,
-0.007377146743237972,
-0.044964127242565155,
0.0545264296233654,
-0.03204331547021866,
-0.004256279673427343,
-0.012048796750605106,
-0.017924204468727112,
0.047432176768779755,
0.02573256567120552,
-0.038130346685647964,
-0.012715090066194534,
0.009270168840885162,
-0.029685204848647118,
0.03401287645101547,
0.04321032389998436,
-0.00635848892852664,
0.002883271547034383,
0.02694167010486126,
0.04242218658328056,
-0.05012812465429306,
0.026079004630446434,
-0.0007191516342572868,
-0.034403298050165176,
-0.00016516591131221503,
-0.06519685685634613,
-0.06767717003822327,
0.06071925535798073,
-0.015722693875432014,
0.00989267323166132,
-0.009657029993832111,
-0.017906250432133675,
0.0357416570186615,
0.015269885770976543,
0.04353572428226471,
-0.00906455609947443,
0.03463618457317352,
-0.02590601146221161,
0.011647804640233517,
-0.030858376994729042,
-0.011335497722029686,
0.13062037527561188,
0.048316486179828644,
-0.005744210444390774,
-0.0640602856874466,
-0.005311852786689997,
-0.02730085887014866,
0.049499981105327606,
-0.051888853311538696,
0.02442348003387451,
-0.019036687910556793,
-0.04222423955798149,
0.018875330686569214,
0.07411038875579834,
-0.018768033012747765,
-0.004780531860888004,
0.06564009189605713,
-0.04399842396378517,
-0.04075581580400467,
0.00938091054558754,
0.03772791102528572,
-0.03532044589519501,
0.00034266398870386183,
-0.028790578246116638,
-0.001253050984814763,
-0.029688837006688118,
0.06061367318034172,
-0.02920527756214142,
-0.022320931777358055,
0.027790816500782967,
0.005566289648413658,
-0.0583203099668026,
-0.005344392731785774,
0.003699318738654256,
0.013837872073054314,
-0.015579499304294586,
-0.02650689147412777,
0.03750722110271454,
-0.007677988614886999,
0.029157370328903198,
0.03254254534840584,
0.028318384662270546,
-0.0016311497893184423,
-0.009535941295325756,
0.010385510511696339,
-0.0357118658721447,
-0.03003981150686741,
-0.006350951734930277,
0.07136375457048416,
0.003831605426967144,
-0.0018664656672626734,
0.004641542676836252,
0.0009731951868161559,
0.025244001299142838,
-0.04027498513460159,
0.025310544297099113,
-0.015932338312268257,
0.03411491960287094,
-0.0224995668977499,
0.022201163694262505,
-0.0033962023444473743,
0.031153321266174316,
0.00785733014345169,
-0.005415031220763922,
-0.02612091228365898,
-0.027390403673052788,
-0.005117816850543022,
0.0017646540654823184,
0.022409915924072266,
0.025944747030735016,
-0.031050147488713264,
-0.014089331962168217,
-0.014563063159584999,
-0.019994188100099564,
-0.021288616582751274,
0.016888882964849472,
0.010213937610387802,
0.04804985597729683,
-0.0012501110322773457,
-0.012534866109490395,
-0.05008013918995857,
-0.05586981400847435,
0.004522825591266155,
0.0005102634895592928,
0.004596375860273838,
0.008022616617381573,
0.004609220661222935,
0.0009311321191489697,
0.03614954277873039,
0.04657566547393799,
-0.0030342473182827234,
0.01890949159860611,
0.033001210540533066,
0.010571861639618874,
-0.02546430565416813,
-0.037483517080545425,
0.0067003932781517506,
-0.032618582248687744,
0.00843588076531887,
0.00423985393717885,
-0.014837558381259441,
-0.01846139132976532,
0.006350219249725342,
-0.03153090924024582,
0.05538506060838699,
-0.0004923025262542069,
-0.007450678385794163,
0.02376515418291092,
-0.02556600794196129,
0.02692755125463009,
0.015268166549503803,
0.04170442372560501,
-0.021042684093117714,
0.002245941897854209,
-0.012996012344956398,
-0.006086790002882481,
-0.04018072783946991,
0.016632117331027985,
-0.03615524619817734,
-0.003734418423846364,
-0.010353973135352135,
0.006307827774435282,
0.0013859295286238194,
0.02483251504600048,
-0.04621275141835213,
0.019511613994836807,
-0.030840128660202026,
-0.005826329812407494,
-0.003577684983611107,
0.04371962696313858,
-0.026826584711670876,
-0.022732259705662727,
0.0222698412835598,
0.05750841647386551,
-0.04157896712422371,
-0.01095259003341198,
0.0038307958748191595,
-0.006734998431056738,
0.016596123576164246,
-0.0019109562272205949,
-0.03620181977748871,
0.022471202537417412,
-0.010882474482059479,
-0.04148354381322861,
0.01930769346654415,
0.055394601076841354,
0.03371993452310562,
0.04516627639532089,
-0.0390472374856472,
-0.04219503328204155,
0.05801861360669136,
0.009623866528272629,
-0.0021239626221358776,
-0.008144699037075043,
-0.07464394718408585,
-0.03199020028114319,
-0.019856208935379982,
0.01892470195889473,
0.007351005915552378,
0.02283191680908203,
-0.001220601610839367,
-0.01128897350281477,
-0.023851418867707253,
0.01139430608600378,
0.009706957265734673,
0.01568244770169258,
0.032489895820617676,
0.012097380124032497,
-0.018463019281625748,
0.007051124237477779,
0.04133293405175209,
-0.012595384381711483,
0.014366259798407555,
0.03782959654927254,
0.003982746973633766,
-0.10087531805038452,
-0.02017512544989586,
0.022830363363027573,
0.048898883163928986,
0.05420228838920593,
-0.0653897151350975,
-0.015189717523753643,
0.0195926483720541,
-0.07540071755647659,
0.017745912075042725,
-0.004407464060932398,
0.021998761221766472,
-0.020169036462903023,
-0.013006901368498802,
-0.03054022043943405,
0.06530459225177765,
0.05299883708357811,
0.039867501705884933,
0.007358830887824297,
-0.007638723589479923,
-0.012966461479663849,
-0.03598655015230179,
-0.04579813405871391,
0.015810683369636536,
0.0009646406397223473,
-0.045905109494924545,
0.0715194046497345,
-0.036434829235076904,
-0.010617450810968876,
-0.0002045596920652315,
0.019146600738167763,
0.02663949877023697,
-0.04025234654545784,
0.02817046456038952,
0.06330212205648422,
0.010427623055875301,
0.014840403571724892,
-0.020867852494120598,
-0.025546969845891,
-0.042745135724544525,
0.02914479561150074,
0.01454046182334423,
-0.025578737258911133,
-0.007039284333586693,
-0.02735222317278385,
-0.025661153718829155,
-0.06314560025930405,
0.0385885089635849,
-0.011802274733781815,
-0.02353847026824951,
-0.001724969013594091,
0.010303033515810966,
-0.0013532991288229823,
0.010668920353055,
0.012003613635897636,
-0.047791436314582825,
0.031971607357263565,
0.01906183548271656,
-0.018314113840460777,
-0.015240670181810856,
0.016260402277112007,
-0.004430979490280151,
-0.027098398655653,
0.063639797270298,
0.018226327374577522,
-0.017995037138462067,
-0.051718924194574356,
-0.025945913046598434,
-0.030080359429121017,
-0.004527576267719269,
0.028124641627073288,
-0.0329250730574131,
-0.05336148664355278,
-0.022438745945692062,
-0.01293557696044445,
0.025115253403782845,
-0.04417331516742706,
-0.013691224157810211,
0.020062657073140144,
-0.040681011974811554,
0.03430645167827606,
0.042846567928791046,
-0.021352950483560562,
-0.02032787725329399,
-0.030884364619851112,
0.022786611691117287,
0.009212899953126907,
0.06640338897705078,
-0.006871616002172232,
-0.005210191011428833,
0.02435036189854145,
0.023567771539092064,
0.013543444685637951,
-0.07203071564435959,
-0.02654838189482689,
0.0032520354725420475,
0.015184660442173481,
0.026502326130867004,
0.0012993414420634508,
-0.004815823398530483,
0.08162802457809448,
0.04848209023475647,
0.01315796934068203,
0.03126326575875282,
0.014637693762779236,
-0.06897002458572388,
0.05830256640911102,
-0.016892030835151672,
-0.024269292131066322,
0.07272996008396149,
0.017432698979973793,
0.003920950461179018,
0.03001539595425129,
-0.05850587412714958,
-0.03127860277891159,
-0.0216903667896986,
-0.06049613654613495,
-0.050941694527864456,
-0.01569640263915062,
-0.028325479477643967,
-0.0023335616569966078,
-0.03552636131644249,
0.032799772918224335,
0.03467930853366852,
-0.019535863772034645,
-0.017957592383027077,
0.06053261086344719,
-0.0002521712158340961,
0.04630042612552643,
0.05328817293047905,
0.03778821974992752,
0.03818397969007492,
-0.004614520352333784,
0.020516565069556236,
0.006890194956213236,
0.04774005711078644,
-0.014440118335187435,
0.027935359627008438,
0.04201691970229149,
0.004119120538234711,
-0.002344831358641386,
0.03612454980611801,
0.014333941042423248,
-0.04655344784259796,
-0.0035006459802389145,
0.0440758615732193,
-0.022768059745430946,
0.014280346222221851,
0.024403797462582588,
-0.038948725908994675,
0.07785134762525558,
-0.017134269699454308,
0.007185817696154118,
0.007415340282022953,
0.03485502675175667,
-0.015496717765927315,
0.023930059745907784,
-0.0016957990592345595,
0.0518735907971859,
0.0019832777325063944,
-0.02180245704948902,
-0.04159403592348099,
0.006601696368306875,
-0.00011556075332919136,
-0.04635278508067131,
0.014278782531619072,
0.031770970672369,
-0.02129310555756092,
0.009500738233327866,
-0.020642690360546112,
0.00334524130448699,
-0.0461004301905632,
-0.01731930673122406,
0.005543988198041916,
0.020239412784576416,
-0.002439882606267929,
0.0024845676962286234,
-0.025115501135587692,
0.05004703253507614,
-0.05273471772670746,
-0.016942685469985008,
-0.020494451746344566,
0.028010696172714233,
-0.02834787778556347,
0.009133648127317429
] |
<p>This is a common point of argument on internet forums. I think it is fairly well established theoretically that there is a very small amount of mass converted to energy in an exothermic chemical reaction. Has this ever been observed experimentally? </p>
<p>If not, how far off is our current experimental state of the art from being able to detect this change? Is it something that could conceivably be accomplished in the next few decades, or are we unlikely ever to be able to observe it?</p>
| 8,338 |
[
-0.04659130424261093,
-0.013707068748772144,
-0.021811816841363907,
-0.03608972951769829,
0.04992074519395828,
0.006469883490353823,
-0.07127854228019714,
-0.03743571788072586,
0.011911510489881039,
-0.03388526663184166,
-0.004678299650549889,
0.03438016399741173,
0.029733633622527122,
0.002517926972359419,
-0.005388900171965361,
0.03048063814640045,
-0.0015015627723187208,
-0.018299054354429245,
0.013122220523655415,
-0.014903780072927475,
-0.016956310719251633,
-0.008182810619473457,
0.011530854739248753,
-0.021545475348830223,
-0.013795292004942894,
0.013480294495821,
0.0012406344758346677,
-0.015235073864459991,
0.019263556227087975,
0.04552647843956947,
0.012189483270049095,
-0.003712886944413185,
-0.019439060240983963,
0.018284602090716362,
0.02630477398633957,
0.022505637258291245,
0.012876138091087341,
-0.04772629216313362,
0.01958688162267208,
0.01978415623307228,
0.009550942108035088,
-0.007816530764102936,
0.015936387702822685,
0.02877301536500454,
-0.021555539220571518,
0.011099744588136673,
-0.03597884252667427,
-0.016192976385354996,
0.05312004312872887,
-0.08900433033704758,
0.06374133378267288,
0.0038700667209923267,
0.012407500296831131,
0.006848510820418596,
-0.01376261468976736,
0.02391613833606243,
0.04770561307668686,
0.045502133667469025,
-0.038066327571868896,
-0.014900866895914078,
-0.021428974345326424,
-0.006344040390104055,
-0.007627326529473066,
0.0023951015900820494,
-0.05080690607428551,
0.013764280825853348,
-0.012063398025929928,
-0.03384806215763092,
0.06057646498084068,
0.0014122299617156386,
-0.009066318161785603,
0.01687653735280037,
0.03861859068274498,
0.0540696419775486,
0.0036936532706022263,
-0.012527947314083576,
0.04700504243373871,
-0.038482148200273514,
0.047079868614673615,
0.08657198399305344,
-0.02604188211262226,
-0.0033612295519560575,
0.047773901373147964,
0.06705038249492645,
0.018352676182985306,
0.017353836447000504,
0.056085459887981415,
-0.02913108468055725,
0.028650829568505287,
0.05215355381369591,
-0.006126337219029665,
0.0015831802738830447,
-0.005716291721910238,
-0.0065534599125385284,
0.006917939055711031,
0.03352413326501846,
0.01921488530933857,
0.06663352251052856,
0.02213546633720398,
-0.02688695304095745,
0.03308463096618652,
0.01950075849890709,
0.05299089103937149,
0.05468079820275307,
0.021666036918759346,
-0.029135100543498993,
-0.036599524319171906,
-0.010343052446842194,
-0.0061713289469480515,
0.02182200737297535,
-0.06865475326776505,
0.0006447379128076136,
0.021619927138090134,
-0.009905517101287842,
0.016156138852238655,
-0.014087733812630177,
0.024030864238739014,
-0.03443865850567818,
0.05728171765804291,
0.04121050238609314,
0.04530448839068413,
-0.015320653095841408,
0.005341766867786646,
-0.01919289492070675,
-0.039926595985889435,
0.02284734696149826,
0.0022144950926303864,
-0.0020618499256670475,
-0.006322159431874752,
0.036486439406871796,
-0.0071882870979607105,
-0.005917786154896021,
0.01897345669567585,
-0.020996734499931335,
0.02522493712604046,
-0.01944953203201294,
-0.05706280097365379,
-0.055606450885534286,
0.06194392219185829,
-0.007874981500208378,
-0.03760271146893501,
-0.06718908250331879,
-0.036826200783252716,
0.049926433712244034,
0.026927165687084198,
0.02319711446762085,
-0.02274026721715927,
-0.04809942469000816,
0.05692568048834801,
0.00803319737315178,
-0.011305121704936028,
-0.021187569946050644,
0.03697676211595535,
-0.03994159400463104,
0.01266778539866209,
-0.021172236651182175,
0.020933732390403748,
0.0607328787446022,
-0.013271895237267017,
0.0002557582629378885,
0.037463586777448654,
-0.016028515994548798,
-0.0177669208496809,
0.015638751909136772,
0.0075792004354298115,
-0.008354182355105877,
0.10265081375837326,
0.026155108585953712,
-0.014886305667459965,
-0.019465699791908264,
0.05865873396396637,
0.01967025361955166,
0.04086509719491005,
0.011008447036147118,
0.022606782615184784,
-0.037658341228961945,
-0.021547546610236168,
-0.04690663516521454,
0.02297600917518139,
0.017545513808727264,
-0.016727138310670853,
-0.014005365781486034,
-0.006276627536863089,
-0.009763895533978939,
0.03400766849517822,
0.0500827394425869,
-0.028611740097403526,
-0.03600405529141426,
0.04342196509242058,
-0.051858361810445786,
-0.02245492860674858,
-0.058102574199438095,
0.00920557789504528,
-0.0038917928468436003,
-0.0011694820132106543,
0.014435614459216595,
0.016291266307234764,
0.0203957948833704,
-0.07544296979904175,
-0.033906105905771255,
0.03871012479066849,
0.022481732070446014,
-0.012490230612456799,
0.01613437570631504,
0.007104531861841679,
0.03586669638752937,
0.01763680949807167,
-0.02318219095468521,
-0.015320365317165852,
-0.03346594050526619,
-0.034383829683065414,
-0.011274286545813084,
-0.025275535881519318,
-0.010026363655924797,
0.0038195259403437376,
-0.005399701185524464,
0.00656728632748127,
-0.014222661033272743,
-0.010783982463181019,
0.04842587187886238,
-0.010005928575992584,
0.08852659910917282,
0.012272628024220467,
0.02628188394010067,
-0.0022570539731532335,
0.03297670558094978,
0.04932522401213646,
0.007213555742055178,
-0.009418196976184845,
-0.04370599985122681,
-0.07660365849733353,
-0.039981160312891006,
0.017656059935688972,
0.025765011087059975,
-0.0449020154774189,
0.028286319226026535,
0.02844199910759926,
0.029394909739494324,
0.019477354362607002,
-0.0008709339890629053,
-0.014234468340873718,
-0.0042083957232534885,
0.018834847956895828,
0.022991403937339783,
0.001930076745338738,
0.007791050709784031,
0.03149913251399994,
0.017861749976873398,
0.006446291226893663,
-0.0005641829920932651,
0.00882255844771862,
0.004396280739456415,
-0.0011754916049540043,
0.0024304946418851614,
-0.026035219430923462,
-0.02384408935904503,
0.010636653751134872,
-0.005873479414731264,
0.006802449934184551,
-0.011974748224020004,
0.00810699351131916,
0.03373565524816513,
-0.03645062446594238,
0.0046306634321808815,
-0.024122459813952446,
0.014828593470156193,
-0.0028970581479370594,
0.041516512632369995,
0.026191335171461105,
-0.046734537929296494,
0.019717339426279068,
-0.017135996371507645,
0.008510802872478962,
-0.010148967616260052,
0.014254924841225147,
0.017173411324620247,
-0.020134352147579193,
0.015241133980453014,
-0.057804010808467865,
-0.049056608229875565,
-0.017877517268061638,
-0.05491669848561287,
0.01345920655876398,
0.005794732831418514,
-0.026883097365498543,
0.01638110913336277,
-0.040811214596033096,
-0.03232521191239357,
0.02820325642824173,
-0.026866355910897255,
-0.000480205548228696,
0.03749625384807587,
0.0008973158546723425,
-0.0697377398610115,
0.000031795756513020024,
0.015721751376986504,
-0.03919375315308571,
-0.020304637029767036,
0.030745457857847214,
0.006622039247304201,
-0.030450239777565002,
-0.043528344482183456,
0.023685872554779053,
0.01000280026346445,
0.0056595467031002045,
-0.02341657131910324,
-0.012393821962177753,
0.004654208198189735,
-0.0022464629728347063,
0.061239659786224365,
0.04841810092329979,
-0.008663090877234936,
-0.01305895484983921,
-0.05410337448120117,
-0.030519552528858185,
0.028716817498207092,
-0.026256287470459938,
0.06230337172746658,
-0.010133682750165462,
-0.032582446932792664,
0.051442742347717285,
-0.004726039245724678,
-0.03216908127069473,
-0.015303485095500946,
0.003430090146139264,
0.018387025222182274,
0.015396772883832455,
-0.01376498956233263,
-0.008967210538685322,
0.01309999916702509,
0.02675074152648449,
-0.006629135459661484,
0.014929489232599735,
-0.00361769855953753,
0.010461079888045788,
-0.01659240387380123,
0.023669414222240448,
0.007570971734821796,
0.04232683405280113,
0.018328983336687088,
0.023874875158071518,
-0.023889241740107536,
0.03504427149891853,
0.015192238613963127,
0.03665320202708244,
0.012032827362418175,
-0.06835534423589706,
0.06763538718223572,
0.04525122418999672,
-0.007698834873735905,
-0.0167998094111681,
0.03661198168992996,
-0.03832472860813141,
0.008099555969238281,
0.010562057606875896,
0.04906089976429939,
0.07270880043506622,
0.0380026176571846,
-0.012220560573041439,
0.007351880427449942,
0.04571384936571121,
-0.026328841224312782,
-0.03478274121880531,
0.009925692342221737,
-0.03119051083922386,
0.007599717006087303,
0.008288389071822166,
-0.028839122503995895,
0.0480937622487545,
0.02838834933936596,
0.030873265117406845,
0.007330127526074648,
0.02748871222138405,
0.00897123385220766,
-0.045237790793180466,
-0.02868065983057022,
0.011588444001972675,
0.03480350971221924,
0.013927905820310116,
0.0694078728556633,
0.013809525407850742,
0.023293081670999527,
-0.003131269244477153,
-0.046577051281929016,
-0.10004960000514984,
0.0042867157608270645,
-0.04859396815299988,
-0.007141336798667908,
0.003855309681966901,
-0.007835421711206436,
-0.003063097596168518,
-0.0014880737289786339,
-0.029314033687114716,
-0.012061113491654396,
0.03580157458782196,
-0.06740079820156097,
-0.0163749810308218,
-0.039417292922735214,
-0.019709667190909386,
-0.002486633136868477,
0.024641724303364754,
0.05821184813976288,
-0.003332517109811306,
-0.018601762130856514,
0.005361206829547882,
-0.04199126362800598,
0.005684013944119215,
-0.055820025503635406,
0.011939113028347492,
-0.007854104973375797,
0.07246097922325134,
0.020801838487386703,
0.016899826005101204,
-0.03787369653582573,
0.04610554501414299,
0.02901884727180004,
0.022499602288007736,
-0.02881486527621746,
-0.021161459386348724,
-0.026640387251973152,
-0.04732980951666832,
-0.031191224232316017,
0.037573959678411484,
0.01127556711435318,
-0.002866871654987335,
0.03973512724041939,
-0.033962637186050415,
0.016302818432450294,
-0.015504331327974796,
0.04587830975651741,
0.05613362416625023,
0.004722519312053919,
0.005327984225004911,
-0.06142884120345116,
-0.002917312551289797,
-0.025044091045856476,
-0.01723152957856655,
0.03373970091342926,
-0.012829182669520378,
0.02668938599526882,
-0.026553800329566002,
0.000707058294210583,
0.053176090121269226,
-0.001467650174163282,
-0.010412579402327538,
-0.04117642343044281,
0.02330518700182438,
-0.008016439154744148,
0.0007117246859706938,
0.004802642855793238,
0.011378129944205284,
0.0530690960586071,
-0.027873316779732704,
0.006827463395893574,
-0.03979523107409477,
0.020190976560115814,
0.024756330996751785,
0.07220826297998428,
-0.04509613290429115,
0.0342227928340435,
-0.029399095103144646,
0.003994951024651527,
0.032554518431425095,
-0.0181680079549551,
0.015153981745243073,
-0.0372500978410244,
0.029203349724411964,
-0.008301695808768272,
-0.012115524150431156,
0.02614513412117958,
0.006994657218456268,
0.003594024572521448,
-0.03496251627802849,
-0.028364144265651703,
-0.03317023441195488,
0.025957461446523666,
0.016903026029467583,
0.032301533967256546,
0.025882933288812637,
0.00467827869579196,
-0.023113025352358818,
0.0026116054505109787,
0.00012174285075161606,
-0.033612534403800964,
-0.08375904709100723,
-0.019363654777407646,
-0.029392417520284653,
-0.025295333936810493,
0.026343006640672684,
-0.04034813493490219,
-0.08102504909038544,
0.017879268154501915,
0.012586567550897598,
-0.042593810707330704,
-0.03100365400314331,
-0.025236068293452263,
0.02885925956070423,
0.048153091222047806,
-0.011927121318876743,
0.04084667190909386,
0.05352027714252472,
0.0016258382238447666,
0.026906738057732582,
0.0014167133485898376,
0.02281104400753975,
-0.019423509016633034,
0.007270670961588621,
-0.03186380863189697,
0.02025327831506729,
-0.006939101032912731,
0.006820958107709885,
0.01849518157541752,
0.0013115738984197378,
-0.011571777053177357,
-0.024976657703518867,
0.01226959191262722,
0.025933310389518738,
0.008785231970250607,
-0.013833395205438137,
-0.0011372521985322237,
0.0438615120947361,
-0.036070816218853,
-0.012726596556603909,
-0.003575080307200551,
0.018049022182822227,
0.003556634997949004,
-0.011974222026765347,
-0.02368260733783245,
-0.005363510921597481,
-0.037078484892845154,
-0.0044616335071623325,
0.03348352760076523,
-0.031285129487514496,
0.05507712811231613,
-0.014523430727422237,
-0.012801084667444229,
0.027596181258559227,
-0.06205456703901291,
-0.012078284285962582,
0.004683854524046183,
0.02968929149210453,
-0.005778100341558456,
-0.03992418944835663,
0.03215816244482994,
-0.02552691288292408,
0.0019768953789025545,
-0.04116852208971977,
-0.061198890209198,
0.03427983820438385,
0.0007042661309242249,
-0.00834343396127224,
-0.036114901304244995,
-0.033328186720609665,
-0.025579864159226418,
-0.0012727417051792145,
0.00816263910382986,
0.02742103300988674,
-0.027869120240211487,
-0.0012858769623562694,
0.01799703761935234,
-0.003399946028366685,
0.0515296533703804,
-0.020738044753670692,
-0.0524040125310421,
0.03527190908789635,
-0.0021771173924207687,
-0.030154982581734657,
0.017315996810793877,
0.03840646147727966,
-0.015813637524843216,
-0.007782068569213152,
-0.021101802587509155,
-0.03919636830687523,
0.030275659635663033,
-0.034227050840854645,
-0.018867818638682365,
0.04413512349128723,
0.0010560480877757072,
0.04052212834358215,
-0.018480127677321434,
0.025262048467993736,
-0.018544191494584084,
0.029474176466464996,
0.016232531517744064,
-0.00884929858148098,
0.027523433789610863,
0.0007371838437393308,
0.03671041503548622,
0.030531039461493492,
-0.0009703767718747258,
-0.02552461437880993,
0.03519470989704132,
0.011688166297972202,
0.00040387161425314844,
-0.003909156192094088,
-0.028987105935811996,
0.028538310900330544,
-0.02525039203464985,
0.019154604524374008,
-0.02059866487979889,
-0.015427266247570515,
-0.05605249106884003,
-0.055772606283426285,
-0.041908182203769684,
0.0012684626271948218,
0.03782143443822861,
-0.018138311803340912,
0.040107958018779755,
-0.004593480844050646,
0.0015682517550885677,
0.006004514172673225,
-0.031211338937282562,
-0.01984013430774212,
0.009604142978787422,
-0.012285838834941387,
0.005512919742614031,
-0.018529577180743217,
0.016660666093230247,
0.06312558054924011,
0.04252603277564049,
-0.015332604758441448,
0.043914545327425,
0.047187767922878265,
-0.017996320500969887,
0.06724031269550323,
-0.05218393728137016,
-0.05065942928195,
0.025526633486151695,
-0.03743802756071091,
0.05701355263590813,
-0.025264833122491837,
0.007454374339431524,
0.03875398635864258,
0.020703569054603577,
0.008873162791132927,
-0.03896159678697586,
-0.006448137108236551,
-0.04145963117480278,
0.00922284834086895,
-0.025305917486548424,
-0.005862964782863855,
0.0008391881710849702,
-0.0158158577978611,
0.021479647606611252,
-0.0024110903032124043,
-0.012560452334582806,
0.016201814636588097,
-0.07204850763082504,
-0.02332843281328678,
0.007301153149455786,
-0.04621931537985802,
0.03282696381211281,
-0.019152667373418808,
-0.04586787894368172,
0.012629881501197815,
-0.0013554305769503117,
0.012939250096678734,
0.018708253279328346,
0.03927081078290939,
-0.02097140997648239,
0.043081142008304596,
-0.029252465814352036,
0.04260041192173958,
-0.0003723515255842358,
0.057261109352111816,
0.13042470812797546,
0.03972689434885979,
-0.016292698681354523,
-0.02074521593749523,
0.005585851613432169,
-0.05630169436335564,
0.011235530488193035,
-0.00408331211656332,
-0.0027688865084201097,
-0.006029894575476646,
0.023347895592451096,
-0.000658799079246819,
0.08376587182283401,
-0.025774355977773666,
-0.010731547139585018,
0.009031384252011776,
-0.0020107056479901075,
-0.01960633508861065,
0.02960345894098282,
-0.007027570623904467,
-0.02115272730588913,
0.0008008030708879232,
-0.008947848342359066,
0.0013648904860019684,
-0.02827441319823265,
-0.02439853549003601,
0.007878078147768974,
-0.019888466224074364,
0.019575506448745728,
0.014130974188446999,
-0.07633467763662338,
-0.0005896166549064219,
0.03162635117769241,
-0.017015105113387108,
-0.02040778659284115,
0.023746998980641365,
0.00824004877358675,
0.020354511216282845,
-0.0046268948353827,
0.042921628803014755,
0.043451257050037384,
-0.0021521151065826416,
0.0002482729614712298,
0.017147444188594818,
-0.023951388895511627,
-0.028879662975668907,
-0.009821271523833275,
0.02666608616709709,
-0.02431395836174488,
0.010639070533216,
-0.021276915445923805,
-0.05217145383358002,
0.008769326843321323,
-0.025385119020938873,
-0.04579051584005356,
0.026419032365083694,
0.04295282065868378,
-0.0007772496319375932,
-0.015611623413860798,
-0.03564949333667755,
0.04214243218302727,
-0.01166506391018629,
-0.006106812506914139,
0.03751557320356369,
-0.010908948257565498,
-0.014808113686740398,
-0.0025442466139793396,
0.03940296545624733,
0.01151778269559145,
-0.03281707689166069,
-0.015809420496225357,
-0.012689882889389992,
-0.029737167060375214,
-0.047162123024463654,
-0.03854364901781082,
0.015936309471726418,
0.036389756947755814,
0.031094064936041832,
-0.0009043326135724783,
-0.004487678874284029,
-0.04600906744599342,
0.0052119591273367405,
0.014276326633989811,
0.017447052523493767,
-0.04560486599802971,
0.01766119711101055,
0.009157516993582249,
0.030210435390472412,
-0.06010029464960098,
-0.008367395028471947,
0.004410683177411556,
0.015232081525027752,
0.007347769103944302,
-0.029784994199872017,
-0.028366608545184135,
0.054943639785051346,
-0.011474059894680977,
0.001101591158658266,
-0.009991489350795746,
0.04575518146157265,
0.010115398094058037,
-0.04144557937979698,
0.0026422732044011354,
0.004543505609035492,
-0.0014534390065819025,
0.02206932008266449,
0.0305816400796175,
-0.002151885535567999,
-0.017764218151569366,
-0.019926616922020912,
0.011237011291086674,
-0.011270083487033844,
-0.035200100392103195,
-0.0631508082151413,
0.03918646275997162,
-0.03925026208162308,
0.04862262308597565,
0.008596704341471195,
0.03668501600623131,
-0.03291082754731178,
0.06721010059118271,
-0.05908391624689102,
-0.03802795708179474,
-0.03975728899240494,
-0.02425379678606987,
0.025878168642520905,
0.007226535584777594,
-0.015580573119223118,
0.053850382566452026,
0.00002377585587964859,
-0.022376855835318565,
0.015414285473525524,
0.02102026157081127,
-0.029642626643180847,
-0.04502873495221138,
0.008197213523089886,
0.013124678283929825,
0.03570770472288132,
-0.049901071935892105,
-0.04354894906282425,
0.050766780972480774,
-0.03893759846687317,
-0.03239819034934044,
0.030868766829371452,
-0.05951741710305214,
0.006889211945235729,
0.03142232447862625,
-0.025731241330504417,
-0.01047841738909483,
0.05061864107847214,
-0.00013910116103943437,
-0.008000795729458332,
0.021644219756126404,
-0.013517887331545353,
-0.03668827563524246,
0.0225552748888731,
0.03005872294306755,
-0.05730511248111725,
-0.011818303726613522,
0.05879910662770271,
0.0006752812187187374,
-0.006748283747583628,
0.015858959406614304,
-0.0021739727817475796,
-0.02014731802046299,
0.0059799435548484325,
0.048287276178598404,
0.006411498878151178,
0.030033845454454422,
0.05959104001522064,
-0.049307554960250854,
0.025802088901400566,
-0.008610506542026997,
-0.009192775934934616,
-0.08948075771331787,
-0.03529087454080582,
0.0043260399252176285,
-0.0068529327400028706,
0.011865676380693913,
-0.028522484004497528,
0.02920028194785118,
0.021774671971797943,
-0.11106716841459274,
-0.01973726972937584,
-0.04182334244251251,
-0.04341756924986839,
-0.014703798107802868,
-0.03978605568408966,
-0.021534500643610954,
0.031895097345113754,
0.003588098334148526,
0.06728698313236237,
0.0026211687363684177,
0.047485336661338806,
-0.010247516445815563,
0.01700134389102459,
0.0007054134621284902,
0.02125033177435398,
-0.002566355047747493,
-0.04496302083134651,
0.06222950294613838,
-0.039033275097608566,
-0.002250516088679433,
0.026104453951120377,
-0.004453809000551701,
0.028717588633298874,
-0.017438407987356186,
0.013755890540778637,
0.004896821454167366,
0.040063824504613876,
0.016742359846830368,
-0.009293136186897755,
-0.011389942839741707,
0.05695630982518196,
-0.00590568408370018,
0.03268193081021309,
-0.026844115927815437,
-0.011279327794909477,
0.0016414226265624166,
-0.021237241104245186,
-0.008628536947071552,
-0.001168194692581892,
-0.04883025959134102,
-0.020942984148859978,
0.01066563930362463,
0.02620965801179409,
-0.010676715523004532,
-0.03095385618507862,
-0.0028568534180521965,
-0.028254035860300064,
-0.03131496161222458,
0.02338961511850357,
0.00684398366138339,
0.004911475814878941,
0.011183978989720345,
0.0000990890184766613,
0.03354490175843239,
0.011198670603334904,
-0.007916376926004887,
-0.028068825602531433,
-0.048852525651454926,
-0.030274003744125366,
0.01833297871053219,
-0.001514670206233859,
0.004005197435617447,
-0.045283298939466476,
-0.032875753939151764,
0.08245836198329926,
0.004646046552807093,
0.047350361943244934,
-0.015909690409898758,
-0.05452815070748329,
-0.005797537975013256,
-0.06494736671447754,
0.015773292630910873,
-0.00020302885968703777,
0.04171762987971306,
-0.019015712663531303,
-0.04097428545355797,
0.031004980206489563,
-0.04393165186047554,
0.03570011258125305,
-0.00546348188072443,
-0.018824875354766846,
0.012989961542189121,
-0.024536656215786934,
-0.0062681226991117,
-0.03265326842665672,
0.0024105424527078867,
-0.04693478345870972,
-0.010893292725086212,
0.0017529560718685389,
-0.034701842814683914,
-0.012865864671766758,
-0.011734187602996826,
0.05983860418200493,
-0.02454107254743576,
-0.03574565425515175,
-0.02346344105899334,
-0.0007781763561069965,
0.0994473323225975,
0.029675545170903206,
-0.011523985303938389,
0.057105083018541336,
0.013474629260599613,
0.059744544327259064,
0.0017610258655622602,
0.0016585922567173839,
-0.04433421045541763,
0.0400073416531086,
-0.028309082612395287,
0.020513901486992836,
-0.012560528703033924,
-0.014266839250922203,
-0.01684049516916275,
-0.021637987345457077,
0.0553177148103714,
0.032179925590753555,
-0.03601037710905075,
-0.004585922695696354,
0.03741433471441269,
0.016103945672512054,
0.0503549762070179,
0.019620027393102646,
0.03549131751060486,
-0.0067016794346272945,
0.030405612662434578,
0.0031997316982597113,
0.03862202540040016,
0.044418904930353165,
0.0050619905814528465,
0.030860720202326775,
-0.0005889397580176592,
-0.07613545656204224,
-0.03063203953206539,
0.03835872560739517,
0.011015260592103004,
-0.0033030316699296236,
-0.049016427248716354,
0.01722111739218235,
-0.03002227656543255,
0.02025982365012169,
0.029311038553714752,
-0.016248364001512527,
0.08430309593677521,
0.03906404227018356,
0.0027667093090713024,
-0.013936053961515427,
0.0292090754956007,
-0.0015351086622104049,
-0.007881606929004192,
-0.006791284307837486,
0.03171266242861748,
-0.003247086890041828,
0.031631067395210266,
0.01933828927576542,
0.03592658415436745,
0.012137568555772305,
-0.019991030916571617,
0.022516852244734764,
-0.01663714274764061,
-0.008190140128135681,
-0.022838151082396507,
-0.020756928250193596,
-0.028297701850533485,
-0.014867059886455536,
0.03820183128118515,
0.0443219430744648,
0.021407773718237877,
0.017063524574041367,
-0.03298330679535866,
0.009393139742314816,
0.042517900466918945,
-0.030069593340158463,
0.014898387715220451,
-0.03063151240348816,
0.02233654260635376,
-0.03041563741862774,
-0.034551046788692474
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.