question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>I'm guessing that, this would be someone in a rocket or something... When they hit their top speed, at what fraction of $c$ are they traveling?</p>
| 7,592 |
[
0.0023815506137907505,
-0.044547755271196365,
-0.015619750134646893,
0.0074336957186460495,
0.045517828315496445,
-0.0019727128092199564,
-0.02895304560661316,
0.009609025903046131,
-0.005948708392679691,
-0.034024208784103394,
0.02373507246375084,
0.07486869394779205,
0.06245361641049385,
0.033257681876420975,
0.017496773973107338,
-0.01631247065961361,
-0.04653787240386009,
0.02631169930100441,
-0.0016251871129497886,
-0.026967937126755714,
0.052442315965890884,
-0.008405635133385658,
0.013357091695070267,
-0.013416080735623837,
-0.0511942096054554,
0.015428101643919945,
0.0247413981705904,
-0.007378310430794954,
0.033436961472034454,
0.02682655118405819,
-0.029326114803552628,
-0.004241460468620062,
0.042902279645204544,
0.015381481498479843,
0.024729249998927116,
0.004314386285841465,
-0.0691630095243454,
0.015894735231995583,
-0.034643642604351044,
0.04055486246943474,
-0.041784707456827164,
-0.04367915168404579,
0.02869388833642006,
0.047823257744312286,
0.002089935354888439,
0.020271658897399902,
0.015128050930798054,
-0.049639131873846054,
0.07547930628061295,
-0.05008363351225853,
0.0765385776758194,
-0.010330848395824432,
0.025718804448843002,
-0.01861167512834072,
0.01725791208446026,
0.017709312960505486,
0.09944771975278854,
0.07471031695604324,
-0.009681900031864643,
-0.029593344777822495,
0.011725409887731075,
-0.027446221560239792,
0.005514245945960283,
-0.0003752276243176311,
-0.014745677821338177,
0.031034333631396294,
-0.0572410486638546,
-0.024560343474149704,
0.03318782150745392,
0.006432786583900452,
-0.00468460051342845,
0.029645219445228577,
0.025941889733076096,
-0.026453347876667976,
0.04083780199289322,
-0.012450385838747025,
0.048133380711078644,
0.029623759910464287,
0.05637377128005028,
0.04244501143693924,
-0.03882105275988579,
-0.003228551708161831,
0.022055305540561676,
0.04205150529742241,
-0.027745895087718964,
0.007871828973293304,
0.044049542397260666,
-0.0029205421451479197,
0.018035737797617912,
0.03780723363161087,
-0.012801826931536198,
-0.025053998455405235,
0.005272386595606804,
-0.014829094521701336,
-0.018422136083245277,
0.01787373423576355,
0.0030614424031227827,
0.042215071618556976,
0.005498982034623623,
-0.048265766352415085,
0.004262697417289019,
-0.004632287193089724,
-0.009831365197896957,
0.06611442565917969,
0.0065856329165399075,
0.013393493369221687,
-0.04163100942969322,
-0.02343290112912655,
-0.02662734128534794,
-0.01575484126806259,
-0.039839550852775574,
0.009395722299814224,
0.013337352313101292,
0.009419962763786316,
0.006209522020071745,
-0.014562358148396015,
-0.014945492148399353,
-0.047275908291339874,
0.06587507575750351,
0.008656828664243221,
0.04845377057790756,
0.02276666648685932,
0.033498577773571014,
0.035031575709581375,
-0.022141987457871437,
0.031423136591911316,
0.0193185955286026,
-0.004668733570724726,
-0.028043590486049652,
-0.006517224479466677,
-0.04697246104478836,
-0.012616750784218311,
0.03610605373978615,
-0.04056957736611366,
0.0037926568184047937,
-0.021702837198972702,
-0.0772608295083046,
-0.057983361184597015,
0.043704383075237274,
0.0011577184777706861,
-0.020282726734876633,
-0.10099028795957565,
0.019169224426150322,
0.016076257452368736,
0.044965967535972595,
-0.0224449522793293,
0.014727717265486717,
-0.004991441965103149,
0.015826068818569183,
0.0018304825061932206,
-0.00266592507250607,
-0.027245832607150078,
-0.007280787453055382,
-0.056643612682819366,
0.013492727652192116,
-0.032882727682590485,
-0.006496403366327286,
0.04665827378630638,
-0.0029391772113740444,
-0.03480927273631096,
0.034893836826086044,
-0.025545688346028328,
-0.006417316384613514,
-0.011512408964335918,
-0.013601340353488922,
-0.009845806285738945,
0.08054828643798828,
0.07863273471593857,
0.008128986693918705,
0.02721867896616459,
0.011176854372024536,
0.04766322299838066,
-0.020262442529201508,
-0.03839685022830963,
0.08751630038022995,
-0.036573417484760284,
-0.013492031022906303,
-0.00450951186940074,
-0.026848070323467255,
0.008903160691261292,
-0.03937498480081558,
-0.06157712638378143,
0.011797095648944378,
0.01601397432386875,
0.03234019875526428,
0.04622052609920502,
-0.005513187497854233,
-0.015171176753938198,
0.0021237970795482397,
-0.03423424810171127,
-0.029612313956022263,
-0.051618218421936035,
0.006644974462687969,
0.005491132847964764,
0.025022558867931366,
0.009025621227920055,
-0.0006101008621044457,
0.022230319678783417,
-0.03857432305812836,
-0.018898507580161095,
0.025601154193282127,
0.03348551690578461,
0.030577491968870163,
-0.024395305663347244,
0.03576117008924484,
0.0710773840546608,
0.02623097412288189,
0.0032789278775453568,
0.009343224577605724,
0.010526377707719803,
-0.025276636704802513,
-0.01403883658349514,
-0.022114092484116554,
0.038827940821647644,
-0.032926786690950394,
0.0089366864413023,
0.021421372890472412,
0.001583679812029004,
0.021047478541731834,
0.022467782720923424,
0.0072421543300151825,
0.0666363388299942,
0.04358145222067833,
-0.007201703265309334,
-0.008909973315894604,
0.006798077374696732,
-0.011152693070471287,
-0.007585343439131975,
0.005176600068807602,
-0.045741576701402664,
-0.03815217316150665,
0.002808887977153063,
0.032313257455825806,
-0.006120646372437477,
-0.03060866892337799,
-0.026620320975780487,
0.05489277094602585,
0.05273346230387688,
0.05154118686914444,
0.012681031599640846,
-0.02907118946313858,
-0.03659924119710922,
0.017320841550827026,
0.02351023256778717,
-0.022107768803834915,
-0.02429051324725151,
-0.013162488117814064,
0.018176350742578506,
0.012112868018448353,
-0.015050389803946018,
-0.024111252278089523,
0.013225333765149117,
-0.016174282878637314,
0.021910281851887703,
0.0049136606976389885,
-0.022170741111040115,
0.053179677575826645,
-0.03962061554193497,
-0.00004169948442722671,
0.025270259007811546,
0.013000589795410633,
0.020523693412542343,
-0.03283661603927612,
-0.004974641837179661,
0.0033689916599541903,
0.043598681688308716,
-0.008165914565324783,
-0.001984604634344578,
0.037831299006938934,
-0.01669824868440628,
0.03344615548849106,
-0.027802331373095512,
-0.00040095558506436646,
0.012573271058499813,
0.008631953038275242,
0.0414692722260952,
0.02311042696237564,
0.054679062217473984,
-0.019109878689050674,
-0.036156002432107925,
0.010399408638477325,
-0.053237881511449814,
0.0033823461271822453,
0.006057204212993383,
-0.05058157444000244,
0.04123656079173088,
0.0044775730930268764,
-0.05647149309515953,
0.019451389089226723,
0.012531989254057407,
0.014209949411451817,
0.037241801619529724,
-0.018559530377388,
-0.06128043308854103,
-0.0015902050072327256,
-0.020584356039762497,
-0.008479136973619461,
-0.05634681135416031,
0.022141560912132263,
0.07593216747045517,
-0.019000934436917305,
-0.006654657423496246,
0.01799410954117775,
-0.07159925252199173,
-0.029937535524368286,
-0.015651587396860123,
-0.024065697565674782,
-0.0043510389514267445,
-0.042994190007448196,
0.051468029618263245,
0.0012213339796289802,
0.008905000984668732,
-0.0007285702740773559,
-0.0648670345544815,
-0.04114704579114914,
0.03682290017604828,
0.011103334836661816,
0.0375019907951355,
-0.021618355065584183,
-0.03508605808019638,
0.04587702825665474,
0.007154497317969799,
-0.02390272170305252,
-0.047259945422410965,
-0.03614901378750801,
-0.0031613679602742195,
-0.018122473731637,
-0.02218673937022686,
0.038270004093647,
-0.039150163531303406,
-0.019711095839738846,
0.050828464329242706,
0.01758977212011814,
0.021464427933096886,
0.002506725722923875,
0.015145687386393547,
0.01746883988380432,
-0.017185434699058533,
0.05426233634352684,
0.03540649637579918,
-0.0021497239358723164,
-0.015216448344290257,
0.07189355790615082,
-0.015415599569678307,
0.06425662338733673,
0.022533949464559555,
-0.040744390338659286,
0.048078399151563644,
-0.0016679546097293496,
-0.025720026344060898,
0.013394909910857677,
-0.0022361259907484055,
0.03993452340364456,
-0.003900907700881362,
0.010227018967270851,
0.024467390030622482,
-0.0017996281385421753,
-0.01696956157684326,
0.0007178703672252595,
-0.01279310043901205,
0.04424625635147095,
-0.024256732314825058,
-0.066092848777771,
-0.00954304076731205,
-0.02108640968799591,
-0.009250587783753872,
-0.005168246105313301,
-0.062421172857284546,
0.047393109649419785,
0.02294195257127285,
0.009545487351715565,
0.01613512448966503,
-0.0136537104845047,
0.016652971506118774,
-0.08403719216585159,
-0.03083234280347824,
0.02808585949242115,
0.029966043308377266,
-0.014187395572662354,
0.07830161601305008,
0.005349482875317335,
0.031711723655462265,
0.01572434976696968,
0.05179259926080704,
-0.09000612795352936,
0.0012885675532743335,
-0.01839694194495678,
-0.012210975401103497,
0.002819484332576394,
0.001756973098963499,
0.022526733577251434,
-0.03896840289235115,
-0.002715109381824732,
-0.00833461619913578,
-0.0038528519216924906,
-0.026804283261299133,
0.022087935358285904,
0.0025013212580233812,
-0.03574026748538017,
-0.00872637890279293,
0.019846737384796143,
0.023437779396772385,
-0.011845405213534832,
0.01775307208299637,
0.073443204164505,
-0.02575269713997841,
-0.014182773418724537,
-0.0175298061221838,
-0.01321529969573021,
0.016585875302553177,
0.02759629301726818,
-0.005908735562115908,
-0.011947975493967533,
-0.03374378755688667,
0.014876176603138447,
-0.025157107040286064,
0.03789376839995384,
0.000494875421281904,
-0.009741014800965786,
-0.052174948155879974,
-0.04850366711616516,
-0.010479767806828022,
-0.0059575289487838745,
0.015755413100123405,
-0.037579894065856934,
0.018046224489808083,
0.05593378469347954,
0.01487588882446289,
-0.003820283804088831,
0.05254536494612694,
0.05328487604856491,
0.0024034653324633837,
-0.013514380902051926,
-0.022652456536889076,
0.005505387205630541,
-0.025286907330155373,
-0.0017040773527696729,
0.020171483978629112,
-0.002583106979727745,
-0.014871872030198574,
0.01728229783475399,
0.03015277534723282,
0.01051532756537199,
-0.017489831894636154,
0.03603137657046318,
-0.0033547815401107073,
0.02192654274404049,
-0.00830444972962141,
-0.0075194151140749454,
-0.004569567274302244,
0.016475526615977287,
0.033803604543209076,
-0.011794465593993664,
-0.031324200332164764,
-0.060255296528339386,
-0.042556650936603546,
-0.0007911972352303565,
0.03056514263153076,
-0.022025013342499733,
-0.015388025902211666,
-0.058319851756095886,
0.013420268893241882,
0.0759049654006958,
-0.020491404458880424,
0.01316725742071867,
-0.005257907323539257,
-0.0015148769598454237,
0.015156320296227932,
-0.026585886254906654,
-0.02368766814470291,
-0.005395171232521534,
-0.005206315312534571,
-0.02089529298245907,
-0.01974545046687126,
0.028995594009757042,
0.012214520946145058,
-0.01645759306848049,
0.05194537714123726,
0.07207431644201279,
0.033862337470054626,
-0.02980078011751175,
-0.008107755333185196,
0.02169787511229515,
-0.03661897033452988,
-0.06255396455526352,
-0.006109737791121006,
0.0009625034290365875,
0.0008863212424330413,
0.015574222430586815,
-0.023804297670722008,
-0.05635016784071922,
0.02448180690407753,
-0.006266827695071697,
-0.008786002174019814,
-0.014106843620538712,
-0.03828730434179306,
0.05989980697631836,
0.018436718732118607,
-0.017433715984225273,
0.009021054022014141,
0.028047950938344002,
-0.006964965257793665,
-0.030426934361457825,
0.018601438030600548,
0.0349360816180706,
0.01938798278570175,
-0.014416945166885853,
-0.012354391627013683,
-0.017028622329235077,
-0.011052438989281654,
0.026114335283637047,
-0.03734632208943367,
0.004657731391489506,
-0.03325780853629112,
-0.058594681322574615,
-0.014231804758310318,
0.017695367336273193,
0.0303947813808918,
-0.00548060005530715,
-0.003539380617439747,
0.006632677745074034,
0.005850369110703468,
-0.02839585393667221,
0.015879621729254723,
-0.018377136439085007,
0.01670527085661888,
0.02668345719575882,
-0.018696459010243416,
-0.012290127575397491,
-0.051946528255939484,
0.012746065855026245,
-0.00791789498180151,
-0.058061953634023666,
0.042071256786584854,
-0.032805755734443665,
-0.00010311345977243036,
0.00009847823093878105,
-0.018926169723272324,
-0.058379773050546646,
0.03798599913716316,
-0.006120277568697929,
0.022669723257422447,
-0.04990497976541519,
0.03483890742063522,
-0.03418565168976784,
0.03209425136446953,
-0.05234982445836067,
-0.04306884482502937,
0.06797472387552261,
0.02969907969236374,
-0.016200104728341103,
-0.0221481304615736,
0.01618269458413124,
-0.0411645844578743,
-0.04122452810406685,
-0.008406681008636951,
0.040952663868665695,
0.005434168502688408,
-0.019678670912981033,
-0.0007353874389082193,
-0.005445902235805988,
0.06193944811820984,
0.030432110652327538,
-0.033529579639434814,
0.003842207370325923,
-0.0002915309160016477,
-0.04208024591207504,
-0.02027682401239872,
0.055719632655382156,
-0.01988924853503704,
-0.016522014513611794,
-0.006487368140369654,
0.002329250331968069,
0.0035804067738354206,
-0.02989855967462063,
0.00639994814991951,
0.04544210061430931,
0.030797291547060013,
-0.021766433492302895,
0.014782276004552841,
0.03870074450969696,
-0.01528235338628292,
0.04113156720995903,
-0.0027026692405343056,
-0.0071260202676057816,
-0.011412961408495903,
-0.030475515872240067,
0.04405676946043968,
0.031185755506157875,
0.01060500554740429,
-0.025035182014107704,
0.05619562417268753,
-0.02150137349963188,
-0.05427240580320358,
0.006543722935020924,
0.0013656549854204059,
0.007428362965583801,
0.015066209249198437,
-0.03302512690424919,
0.023015238344669342,
-0.010737713426351547,
-0.011976360343396664,
0.0008017894579097629,
-0.04216330498456955,
-0.014976350590586662,
0.048747718334198,
-0.024835482239723206,
0.03758084401488304,
-0.036203403025865555,
0.031770870089530945,
0.036552492529153824,
0.007000315934419632,
-0.04290146008133888,
-0.016983872279524803,
0.0025278658140450716,
0.042420100420713425,
-0.012339106760919094,
-0.02086489647626877,
0.055634573101997375,
0.05097561329603195,
-0.03250465914607048,
0.04050130024552345,
0.01944148726761341,
0.014020033180713654,
0.017455121502280235,
-0.008919978514313698,
-0.029911287128925323,
0.010155410505831242,
0.006705844774842262,
0.05615204945206642,
0.0003763913700822741,
-0.02448367327451706,
0.05357157438993454,
0.0017172895604744554,
0.015539332292973995,
-0.0031329242046922445,
0.0035982253029942513,
-0.023017818108201027,
-0.022033700719475746,
0.00795301329344511,
-0.005926335696130991,
-0.007776310201734304,
-0.00013898384349886328,
0.028067870065569878,
-0.02004922926425934,
0.019186951220035553,
0.004987618420273066,
-0.014613274484872818,
-0.041691817343235016,
-0.022070245817303658,
-0.04119206592440605,
0.032497208565473557,
0.04610482230782509,
-0.022120622918009758,
0.035848431289196014,
0.001788703608326614,
0.005180513486266136,
0.010129044763743877,
0.06309367716312408,
0.012884678319096565,
0.07678225636482239,
0.02095986343920231,
0.01474766992032528,
-0.031077494844794273,
0.0028106390964239836,
0.09170189499855042,
0.07160872220993042,
-0.002923379885032773,
-0.04432942345738411,
-0.00413966691121459,
-0.020624559372663498,
0.016194434836506844,
-0.028269294649362564,
0.0221247598528862,
0.019371764734387398,
0.002142914803698659,
0.050774961709976196,
0.05391770973801613,
-0.03023567423224449,
0.0430305190384388,
0.032250210642814636,
-0.02640032209455967,
-0.018810924142599106,
0.004494048655033112,
0.00028224088600836694,
-0.029033375903964043,
-0.004721629433333874,
-0.009162971749901772,
0.020737381651997566,
-0.04098714888095856,
-0.004526612814515829,
-0.03712242841720581,
-0.04080185666680336,
0.02647433429956436,
-0.01250101812183857,
-0.06350700557231903,
0.029510002583265305,
0.018985344097018242,
-0.02787274867296219,
-0.05451579764485359,
-0.0009636118775233626,
0.00962891336530447,
-0.007990262471139431,
-0.010487663559615612,
0.036899320781230927,
0.005234018433839083,
0.026451248675584793,
0.00009943329496309161,
0.007107441313564777,
-0.026732267811894417,
-0.040925607085227966,
-0.0392015241086483,
0.009084511548280716,
-0.01745435781776905,
-0.0011369383428245783,
-0.008646722882986069,
0.03843649476766586,
-0.020351432263851166,
-0.05209082365036011,
0.010357263498008251,
-0.0021316898055374622,
0.018802879378199577,
-0.012951322831213474,
-0.0182986818253994,
-0.034870605915784836,
-0.020437942817807198,
0.017151739448308945,
-0.009989680722355843,
-0.008336578495800495,
-0.010011325590312481,
0.0034860929008573294,
0.012027815915644169,
0.05022744461894035,
-0.03476237133145332,
-0.026207422837615013,
0.0020577670074999332,
0.0014649105723947287,
-0.04271448776125908,
0.0033781921956688166,
-0.0029316782020032406,
0.007569071836769581,
-0.0036302965600043535,
-0.007478627376258373,
-0.002135265851393342,
-0.006207867059856653,
-0.020029213279485703,
0.027892714366316795,
0.005268202628940344,
-0.006104690954089165,
-0.0350520983338356,
-0.019237695261836052,
0.016282372176647186,
0.04107145220041275,
-0.0316883847117424,
0.02167716808617115,
-0.03707631677389145,
0.0558660514652729,
0.032505981624126434,
-0.009931654669344425,
0.0015842701541259885,
0.01176876574754715,
-0.02935129404067993,
0.04591640830039978,
-0.019625836983323097,
0.066433846950531,
0.022601719945669174,
-0.025943247601389885,
-0.030791884288191795,
-0.02422030083835125,
-0.014576013199985027,
0.028642436489462852,
0.03219379857182503,
-0.05913608893752098,
-0.013670654967427254,
0.010543039999902248,
0.0164051353931427,
-0.01783611625432968,
-0.031922731548547745,
-0.013348864391446114,
0.020176667720079422,
-0.03549833595752716,
0.03766968846321106,
-0.008198904804885387,
0.04381690174341202,
-0.022998102009296417,
-0.012619376182556152,
-0.030129728838801384,
0.023140983656048775,
-0.03896506503224373,
0.030250919982790947,
0.03090260550379753,
0.0022541957441717386,
-0.039553202688694,
0.03865412250161171,
-0.025796204805374146,
0.021189643070101738,
0.011995458044111729,
-0.00029511144384741783,
0.004363420885056257,
-0.021768029779195786,
-0.003680187975987792,
0.02343498356640339,
0.018001670017838478,
-0.04438379034399986,
-0.009609311819076538,
0.059068236500024796,
-0.03721453621983528,
-0.06398345530033112,
0.02310127764940262,
-0.01637883111834526,
0.06352753192186356,
0.004108354449272156,
-0.017494870349764824,
0.03627936914563179,
0.042793091386556625,
-0.028685040771961212,
0.008156683295965195,
0.018630309030413628,
-0.003648434765636921,
-0.007989976555109024,
-0.006515636574476957,
0.043536197394132614,
0.007962933741509914,
-0.013262122869491577,
0.03263584151864052,
0.022517258301377296,
-0.048134926706552505,
0.055854592472314835,
-0.0002792779996525496,
-0.012763245031237602,
-0.0025931105483323336,
0.033306945115327835,
0.0198344849050045,
0.034800756722688675,
0.04804525524377823,
-0.021954737603664398,
-0.006792251951992512,
-0.021564945578575134,
0.02020200900733471,
-0.08968810737133026,
-0.033399906009435654,
-0.025191882625222206,
0.014594381675124168,
0.054286591708660126,
-0.063621386885643,
0.013459732756018639,
0.06205778196454048,
-0.0716949924826622,
0.017819950357079506,
-0.033457182347774506,
-0.01250494085252285,
-0.0494101457297802,
-0.042224813252687454,
-0.0073002539575099945,
0.07322453707456589,
0.02330761030316353,
0.012921490706503391,
0.02975529246032238,
0.013994922861456871,
-0.05049439147114754,
-0.046235837042331696,
0.03251199051737785,
0.019204361364245415,
0.003444850677624345,
-0.011411422863602638,
0.05958542972803116,
-0.007520345970988274,
-0.0038683265447616577,
0.04220518469810486,
0.004076914396136999,
0.028142049908638,
-0.01123896986246109,
0.00020776722521986812,
0.03687058016657829,
0.034359101206064224,
0.018068423494696617,
-0.0013187607983127236,
-0.015780696645379066,
0.009672948159277439,
-0.007085840217769146,
0.02804853394627571,
-0.01752263493835926,
-0.018212664872407913,
0.03770994395017624,
-0.03329392150044441,
-0.04391226917505264,
0.054868679493665695,
-0.008448244072496891,
0.0007301421137526631,
0.012041931040585041,
-0.027788156643509865,
0.011015580967068672,
-0.06621170043945312,
0.013327457942068577,
-0.04329918324947357,
-0.008701599203050137,
0.026738928630948067,
-0.031509753316640854,
-0.009622182697057724,
-0.0045605809427797794,
-0.020452382043004036,
-0.006422973703593016,
0.006499155890196562,
-0.0034107083920389414,
-0.01732659712433815,
-0.049134496599435806,
-0.012072475627064705,
-0.02338002249598503,
-0.0026003101374953985,
-0.017760422080755234,
-0.06318741291761398,
-0.020031731575727463,
0.052848901599645615,
0.038558293133974075,
0.03304149955511093,
-0.002674791729077697,
-0.005340533796697855,
-0.028933802619576454,
-0.07550568878650665,
0.0042372471652925014,
-0.013858907856047153,
0.033907294273376465,
-0.02519470453262329,
-0.03866177052259445,
0.00002990100074384827,
-0.00810559093952179,
0.06417246907949448,
0.013203795999288559,
-0.03075364977121353,
0.032432232052087784,
-0.0075094448402523994,
-0.010192204266786575,
-0.08399977535009384,
0.00025001465110108256,
-0.01694083958864212,
-0.050375137478113174,
-0.03252650052309036,
-0.004595218226313591,
-0.029656626284122467,
-0.01575859636068344,
0.0047349208034574986,
0.04081035405397415,
0.015348250977694988,
-0.014143211767077446,
0.012930541299283504,
0.0334746353328228,
0.034439798444509506,
0.0010911017889156938,
0.06646808236837387,
0.029260138049721718,
0.025424327701330185,
0.046490833163261414,
-0.03426032140851021,
-0.05245104804635048,
0.027900755405426025,
0.0042422148399055,
-0.03157791495323181,
-0.030579587444663048,
-0.014197038486599922,
-0.017447492107748985,
-0.05827868729829788,
0.0338798426091671,
0.03294423222541809,
-0.052461136132478714,
-0.013969588093459606,
0.05972158908843994,
0.03822378069162369,
0.018919378519058228,
0.013337898068130016,
-0.014684613794088364,
0.03939485177397728,
-0.019674479961395264,
-0.03443001210689545,
0.029417602345347404,
0.013734959065914154,
-0.01189136691391468,
0.019374046474695206,
0.017715739086270332,
0.009477200917899609,
0.033056825399398804,
0.006336444057524204,
0.005556095391511917,
-0.0653357207775116,
-0.011981879360973835,
0.0212062057107687,
-0.0593181848526001,
0.03206360712647438,
0.029408300295472145,
-0.01706756465137005,
0.08219663053750992,
-0.013042321428656578,
0.02172747254371643,
0.006258352193981409,
0.004036144819110632,
-0.02669660933315754,
-0.0013686101883649826,
0.013950957916676998,
0.02358134835958481,
-0.04182486981153488,
-0.019385237246751785,
0.004983291961252689,
0.00652847345918417,
0.029841046780347824,
-0.03061286360025406,
0.03763188049197197,
0.003937059082090855,
-0.011366116814315319,
-0.036518026143312454,
-0.03287434205412865,
-0.019428551197052002,
-0.0070779817178845406,
0.007050377316772938,
0.04578761011362076,
-0.0017447079299017787,
0.031707730144262314,
-0.022116202861070633,
0.007593472488224506,
0.046434737741947174,
-0.05977301672101021,
-0.0021897051483392715,
-0.003231727285310626,
0.04660848155617714,
-0.019856834784150124,
-0.028192315250635147
] |
<p>I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM.
Does anybody know whether there is a particularly good reference to start studying SUSY QM from a rigorous mathematical point of view. The reference should cover Spectral analysis and a wide range of all the algebraic properties concerned with the topic. </p>
| 7,593 |
[
0.0075620668940246105,
-0.02182758040726185,
0.004955268930643797,
-0.053435780107975006,
0.01626279391348362,
0.027674030512571335,
-0.004098831210285425,
-0.04386511817574501,
0.01631045527756214,
-0.04791255667805672,
0.02468506619334221,
-0.006095093209296465,
0.026412926614284515,
0.021536514163017273,
0.021030636504292488,
0.0005067706806585193,
-0.004875016864389181,
-0.026707056909799576,
-0.00460785161703825,
-0.002555441576987505,
0.021502742543816566,
0.018649088218808174,
-0.006259591784328222,
-0.0032093266490846872,
-0.015649020671844482,
0.051753804087638855,
-0.01028620358556509,
0.03886904940009117,
0.006314088590443134,
0.05251884087920189,
-0.0279402993619442,
-0.03216687589883804,
-0.0024927561171352863,
0.016120759770274162,
0.018989387899637222,
0.024219611659646034,
-0.011979316361248493,
-0.02282455936074257,
-0.02013837918639183,
-0.011724683456122875,
-0.022947482764720917,
-0.043028656393289566,
-0.030930427834391594,
0.038104068487882614,
-0.028809482231736183,
0.0017683833139017224,
-0.018317867070436478,
-0.02451797015964985,
0.07956062257289886,
-0.0824768915772438,
0.11288277804851532,
0.029192769899964333,
0.04032614454627037,
0.03276352211833,
0.01748126931488514,
0.009717412292957306,
0.04716379567980766,
0.05087690055370331,
0.0034532351419329643,
-0.040004681795835495,
-0.035279009491205215,
-0.061465226113796234,
-0.0027226549573242664,
-0.0526556670665741,
-0.04799500107765198,
0.027017338201403618,
0.009073490276932716,
-0.0044487239792943,
0.03038596548140049,
0.022569067776203156,
-0.01362359058111906,
0.011052080430090427,
0.05014145001769066,
-0.0071088350377976894,
0.008036498911678791,
-0.006003125570714474,
0.0037065662909299135,
-0.02218303643167019,
0.03548501804471016,
0.025057373568415642,
-0.00996373686939478,
0.03388708829879761,
-0.024128539487719536,
0.022962450981140137,
-0.003811783390119672,
-0.024218769744038582,
0.0555841438472271,
0.007733990903943777,
-0.020495666190981865,
0.019654715433716774,
-0.008184333331882954,
0.009242338128387928,
0.025227466598153114,
0.008432657457888126,
-0.03221132606267929,
0.029792889952659607,
0.033710017800331116,
0.05901085585355759,
0.015497949905693531,
-0.04435494914650917,
-0.024504361674189568,
-0.016670487821102142,
0.01720506325364113,
0.08517652750015259,
0.0024775227066129446,
0.0006608681287616491,
-0.0217044185847044,
0.03217260539531708,
-0.030775440856814384,
-0.013549929484724998,
-0.020133856683969498,
-0.011156249791383743,
-0.012469979003071785,
-0.014344194903969765,
-0.011340897530317307,
-0.0007363183540292084,
0.024707959964871407,
-0.027730191126465797,
0.04766253009438515,
0.0989520326256752,
0.06800457090139389,
-0.005596316419541836,
0.012290325947105885,
-0.03108716383576393,
-0.07241850346326828,
-0.001423436333425343,
0.04442653805017471,
0.01778450608253479,
-0.051697053015232086,
0.0234945360571146,
0.017124392092227936,
-0.00046710026799701154,
0.01823774166405201,
-0.04121853783726692,
0.019404619932174683,
-0.017451561987400055,
-0.07613227516412735,
-0.04997514933347702,
0.009855709969997406,
0.004452526569366455,
-0.014891250059008598,
-0.02640160359442234,
0.014673958532512188,
0.03270100802183151,
0.09659693390130997,
-0.012169509194791317,
0.010172161273658276,
-0.003576985327526927,
0.02413725107908249,
0.003428395837545395,
-0.015780553221702576,
-0.05006866529583931,
-0.004864182323217392,
-0.0242153313010931,
-0.006023347843438387,
-0.035038962960243225,
0.009518351405858994,
0.0012972444528713822,
0.02042914368212223,
-0.01279695425182581,
0.08335185050964355,
0.0067473226226866245,
0.002759885275736451,
0.038064245134592056,
-0.003478272119536996,
-0.016641858965158463,
0.05430365726351738,
0.002184423618018627,
-0.006972296629101038,
0.025254303589463234,
0.010146565735340118,
0.020228883251547813,
0.04108124226331711,
0.03997795283794403,
0.024520214647054672,
-0.021785521879792213,
-0.00274105928838253,
0.0010923194931820035,
0.010932963341474533,
-0.014461291022598743,
-0.0363207645714283,
-0.044902291148900986,
0.003798356745392084,
0.05233815312385559,
-0.026466988027095795,
0.011592088267207146,
-0.007152170408517122,
-0.027416419237852097,
0.02490486204624176,
-0.06991434097290039,
-0.011658061295747757,
-0.03152785822749138,
0.00598942069336772,
-0.0127613740041852,
-0.0010958844795823097,
0.060727935284376144,
0.04446530342102051,
0.003025287762284279,
-0.05721559748053551,
-0.027000904083251953,
-0.004320464562624693,
0.036004211753606796,
0.027336150407791138,
-0.004875190556049347,
0.0166388638317585,
0.025394786149263382,
0.013471310958266258,
0.0020239169243723154,
0.045232195407152176,
-0.02547873556613922,
-0.043760593980550766,
-0.003968338016420603,
-0.011828241869807243,
0.029685327783226967,
-0.023728156462311745,
0.023590583354234695,
0.007699099835008383,
-0.03561432659626007,
-0.013070588931441307,
0.06300607323646545,
-0.01603996753692627,
0.03191309794783592,
0.010057749226689339,
0.05632127448916435,
-0.014666595496237278,
0.006020168773829937,
0.005845328327268362,
0.007425682619214058,
0.008173899725079536,
-0.04807933047413826,
-0.03382106125354767,
0.003934772219508886,
0.06926079094409943,
0.036156654357910156,
-0.015176042914390564,
0.00914545077830553,
0.036373935639858246,
0.0504167377948761,
0.04985252395272255,
0.014069043099880219,
-0.051633745431900024,
-0.034339286386966705,
0.018150003626942635,
0.004033767618238926,
0.0023359637707471848,
0.005524797365069389,
-0.003243596525862813,
0.014699799008667469,
-0.008931522257626057,
-0.006530097685754299,
-0.06244182586669922,
0.055297888815402985,
-0.029894934967160225,
-0.01479871105402708,
0.03136710077524185,
-0.04948768392205238,
0.031313709914684296,
-0.05362232029438019,
0.047500867396593094,
0.029716892167925835,
-0.03315507993102074,
0.02628360316157341,
-0.037082280963659286,
-0.04058968275785446,
0.022395117208361626,
-0.021180573850870132,
-0.039836470037698746,
0.0038225073367357254,
0.022265329957008362,
-0.037691447883844376,
-0.00819408893585205,
-0.0062741176225245,
-0.02567889541387558,
-0.026006832718849182,
-0.01639024168252945,
-0.0057994709350168705,
-0.010460985824465752,
0.016841938719153404,
-0.01314705889672041,
-0.023461997509002686,
0.028658639639616013,
-0.006203554105013609,
0.03167724609375,
0.01671203225851059,
-0.04190262779593468,
0.004507547710090876,
-0.07968799024820328,
-0.019628355279564857,
0.0700044333934784,
-0.034065503627061844,
0.015112627297639847,
-0.004868425894528627,
0.012702720239758492,
-0.030286546796560287,
-0.005446579772979021,
0.015130375511944294,
0.02589961513876915,
-0.012004968710243702,
0.004446946084499359,
0.030950717628002167,
-0.02531582862138748,
-0.012704594992101192,
0.005484950728714466,
-0.041508812457323074,
-0.022539017722010612,
-0.02899429202079773,
0.025101007893681526,
0.017489805817604065,
-0.037588246166706085,
0.041873347014188766,
0.02727566659450531,
-0.06540301442146301,
0.045437898486852646,
-0.02761179581284523,
-0.055796168744564056,
0.006432878784835339,
0.011576049961149693,
0.044549811631441116,
0.00643944414332509,
-0.04784836992621422,
0.14100748300552368,
0.025313323363661766,
-0.031495384871959686,
-0.026083700358867645,
0.015747908502817154,
0.0009379418916068971,
0.002579598920419812,
-0.001485855202190578,
0.018137281760573387,
0.0006288930890150368,
0.0126766012981534,
0.04411856830120087,
0.009656005539000034,
0.034540724009275436,
0.007800605613738298,
-0.0620301254093647,
-0.0007556993514299393,
-0.007269884459674358,
0.009362364187836647,
0.001586206373758614,
-0.001819537254050374,
-0.029083818197250366,
0.01212870143353939,
0.011918178759515285,
0.020844100043177605,
-0.024464566260576248,
-0.030117884278297424,
0.028620092198252678,
-0.009392226114869118,
0.007876192219555378,
-0.0016553880413994193,
0.034742988646030426,
-0.012699326500296593,
-0.03294195607304573,
0.005239241756498814,
0.03388037905097008,
-0.007477515377104282,
-0.007339620031416416,
0.024419540539383888,
0.02297602966427803,
0.02055005170404911,
-0.06120919808745384,
-0.024899816140532494,
-0.02037830464541912,
-0.011883617378771305,
0.013040362857282162,
-0.05038144811987877,
-0.04015913978219032,
0.03647458925843239,
0.03469002991914749,
0.03635941818356514,
-0.029222596436738968,
-0.04719891399145126,
0.00033247729879803956,
-0.06517691165208817,
0.0038740907330065966,
0.004126674495637417,
0.04220658168196678,
0.008191052824258804,
0.059529758989810944,
-0.023760085925459862,
0.01143272127956152,
0.011417217552661896,
0.012360429391264915,
-0.08144586533308029,
0.009464344941079617,
-0.06251580268144608,
-0.004511002916842699,
0.000392679387005046,
0.0195632167160511,
0.013503015972673893,
-0.0008716470329090953,
-0.06198742985725403,
-0.04357648640871048,
-0.01676050014793873,
-0.031614985316991806,
0.023138679563999176,
-0.05957738682627678,
-0.02294199727475643,
-0.020252076908946037,
0.014051539823412895,
0.061993032693862915,
-0.059436481446027756,
-0.006728086620569229,
0.0066005755215883255,
-0.04846608638763428,
0.015294297598302364,
-0.01270322222262621,
0.05991735681891441,
-0.002977747702971101,
0.014049937948584557,
0.022002283483743668,
0.050531432032585144,
-0.02202005311846733,
0.014364299364387989,
-0.016542799770832062,
0.054024241864681244,
-0.032442543655633926,
-0.027896447107195854,
0.02302241511642933,
-0.03798319771885872,
-0.011047925800085068,
0.018762605264782906,
0.0579645074903965,
0.006481394171714783,
-0.026620235294103622,
0.04554988443851471,
-0.00044211753993295133,
-0.05915239080786705,
0.024667106568813324,
0.03690832480788231,
-0.012588979676365852,
-0.03975139558315277,
-0.029052505269646645,
-0.007754290476441383,
-0.0284767784178257,
0.0013701023999601603,
0.017880864441394806,
-0.006663267035037279,
-0.03816740959882736,
0.014867614023387432,
0.002134445821866393,
0.008920089341700077,
-0.034109584987163544,
-0.014575155451893806,
0.01956724375486374,
0.007058512419462204,
-0.026444638147950172,
-0.009809001348912716,
0.010034590028226376,
0.041976530104875565,
0.048884276300668716,
-0.018343394622206688,
-0.01056511327624321,
-0.04690496250987053,
0.022185392677783966,
0.06249785050749779,
0.01566939800977707,
0.014221384190022945,
-0.007696259766817093,
-0.0616711750626564,
-0.03273075819015503,
0.07250948250293732,
-0.00761685473844409,
0.023317372426390648,
0.0067645167000591755,
-0.015678297728300095,
-0.008623184636235237,
0.020392678678035736,
0.0048963287845253944,
0.043679893016815186,
0.04370782524347305,
0.025286773219704628,
-0.01912589557468891,
-0.011947670951485634,
-0.0622868686914444,
0.03264357149600983,
0.020305287092924118,
0.04998309910297394,
0.02296987920999527,
0.01317590568214655,
0.012781605124473572,
0.007248425390571356,
-0.019338779151439667,
-0.07677539438009262,
0.015483140014111996,
0.024209365248680115,
-0.0031725929584354162,
0.007328984327614307,
-0.023713506758213043,
-0.053084179759025574,
-0.01124274916946888,
0.019063053652644157,
0.0022588421124964952,
0.0076011428609490395,
-0.029221149161458015,
0.04651765525341034,
0.038637757301330566,
0.020516809076070786,
0.023317519575357437,
0.03749207779765129,
-0.03400369733572006,
-0.012397747486829758,
-0.029471505433321,
0.034792933613061905,
0.004427384585142136,
0.03510913625359535,
-0.05387303978204727,
-0.009782316163182259,
-0.059214819222688675,
0.06048800051212311,
-0.03588530421257019,
-0.011176729574799538,
0.0036322607193142176,
0.0005019482923671603,
-0.018676763400435448,
0.038495440036058426,
-0.003201203653588891,
-0.034238770604133606,
0.0269568283110857,
0.03230580314993858,
0.0008444855338893831,
-0.007831040769815445,
0.02507970482110977,
-0.012791747227311134,
-0.0005218724836595356,
0.014138702303171158,
-0.027999237179756165,
0.02859891578555107,
-0.03635554015636444,
-0.041949715465307236,
0.009675522334873676,
-0.04825599491596222,
0.04040060564875603,
-0.035362523049116135,
0.007353243883699179,
0.016843875870108604,
-0.06293265521526337,
0.002833350095897913,
0.016310786828398705,
-0.027271928265690804,
0.002834967104718089,
-0.03279895335435867,
0.012497015297412872,
0.006819248199462891,
-0.0028957240283489227,
-0.07395853847265244,
-0.045723989605903625,
0.016659848392009735,
-0.0073992102406919,
-0.0282755047082901,
-0.06251280009746552,
0.052420713007450104,
-0.038908667862415314,
0.004860712680965662,
0.024507416412234306,
0.01497139036655426,
-0.04554584249854088,
-0.016078198328614235,
0.016800735145807266,
0.024959543719887733,
0.020724324509501457,
-0.003095699707046151,
-0.0012400213163346052,
-0.0013614209601655602,
0.0011773863807320595,
0.002942063147202134,
0.029971633106470108,
0.030953222885727882,
-0.0000924344130908139,
-0.024173924699425697,
-0.049712155014276505,
-0.007808961905539036,
0.03473595902323723,
-0.037847019731998444,
-0.011852657422423363,
0.04638957232236862,
0.027918409556150436,
0.041231025010347366,
-0.032983943819999695,
-0.00047389414976350963,
-0.005165894515812397,
0.017230628058314323,
-0.034625712782144547,
-0.01622536964714527,
-0.012212765403091908,
-0.035732049494981766,
0.044669292867183685,
-0.01933913491666317,
0.01769569143652916,
0.029797503724694252,
0.037312522530555725,
0.0031042983755469322,
-0.003917109686881304,
0.007473356556147337,
-0.00958996918052435,
-0.04664631187915802,
-0.028508203104138374,
0.020535320043563843,
0.004564695060253143,
0.022134626284241676,
-0.011356404982507229,
-0.06818564236164093,
-0.01031769160181284,
-0.011503846384584904,
0.020150067284703255,
0.0024266450200229883,
0.035072922706604004,
0.0314812995493412,
-0.027590811252593994,
-0.011386777274310589,
0.01574874483048916,
-0.02762719802558422,
0.01830347441136837,
0.0048917243257164955,
0.022009586915373802,
-0.04940151795744896,
0.024523725733160973,
0.0047776056453585625,
0.05901268869638443,
-0.04417029395699501,
0.0361688956618309,
0.02484414353966713,
0.031049225479364395,
0.0811399444937706,
-0.029225757345557213,
-0.029933810234069824,
0.03860421106219292,
-0.02867281250655651,
0.03353385627269745,
0.01717236265540123,
0.002488650381565094,
0.02306777983903885,
0.04737967252731323,
-0.005266821943223476,
0.020659537985920906,
-0.02459089644253254,
-0.04742473363876343,
0.05766499042510986,
0.027188466861844063,
0.028749952092766762,
0.013018780387938023,
0.05795576050877571,
-0.000005799485734314658,
0.014049608260393143,
0.033625103533267975,
0.0376468226313591,
-0.05223190039396286,
-0.042947448790073395,
-0.03977781534194946,
-0.04891479015350342,
0.03163708746433258,
-0.004993429407477379,
-0.00842241570353508,
-0.018826359882950783,
-0.023822180926799774,
0.026379533112049103,
-0.006598056294023991,
0.018194183707237244,
-0.027858449146151543,
0.0418962724506855,
-0.04851425811648369,
0.008144223131239414,
-0.008628779090940952,
0.013623183593153954,
0.09867716580629349,
0.06178811192512512,
0.005504349246621132,
-0.10077408701181412,
0.036313604563474655,
-0.010371165350079536,
0.004931873641908169,
-0.03451474383473396,
0.03722269460558891,
-0.010110219940543175,
-0.009516377002000809,
-0.015252429991960526,
0.04739554226398468,
-0.00415007583796978,
-0.01974942535161972,
0.07655111700296402,
-0.025413913652300835,
-0.02446999028325081,
0.007006515748798847,
0.016705108806490898,
-0.026737624779343605,
0.01631256751716137,
-0.02329232171177864,
0.03400371968746185,
-0.01534536574035883,
-0.00179643789306283,
-0.0752054825425148,
-0.03337038680911064,
0.029646439477801323,
0.005291830748319626,
0.002565059345215559,
-0.002788333687931299,
0.00039156287675723433,
0.0032681156881153584,
-0.0461341068148613,
0.029720347374677658,
0.04071420803666115,
-0.010143284685909748,
0.027451220899820328,
0.017557818442583084,
0.015085356310009956,
0.002141892211511731,
0.009677242487668991,
0.022481225430965424,
-0.03340460732579231,
-0.022853661328554153,
-0.008858073502779007,
0.04346666857600212,
-0.019035324454307556,
-0.015091083012521267,
0.014399806037545204,
0.024858912453055382,
0.029897138476371765,
-0.010784638114273548,
-0.004785670433193445,
0.0016726115718483925,
0.04022734984755516,
-0.08681445568799973,
0.024285156279802322,
0.0017956900410354137,
0.036422524601221085,
-0.027062835171818733,
0.012846242636442184,
0.01354371476918459,
-0.05307088419795036,
-0.017034688964486122,
-0.009185454808175564,
-0.016325367614626884,
-0.013944845646619797,
-0.019975334405899048,
-0.007189467549324036,
-0.01375011820346117,
-0.012167632579803467,
-0.03210201486945152,
0.025792043656110764,
0.016382645815610886,
0.04716941714286804,
-0.004807606339454651,
-0.02328704670071602,
0.009332109242677689,
-0.05786749720573425,
0.02753141149878502,
0.01324470154941082,
-0.006836332380771637,
0.017940448597073555,
-0.0281678494066,
0.03696108236908913,
0.026640169322490692,
-0.02448073774576187,
0.024001773446798325,
-0.015479899011552334,
-0.03525223210453987,
0.03487236052751541,
-0.026190735399723053,
0.017350148409605026,
-0.03247227147221565,
-0.03756791725754738,
0.01984969899058342,
-0.00496195862069726,
0.010833530686795712,
-0.013264388777315617,
0.009618696756660938,
0.02443285472691059,
0.06123659387230873,
-0.027255434542894363,
-0.01956922933459282,
-0.01240494754165411,
-0.06162051111459732,
0.01287562120705843,
0.016626758500933647,
0.036076564341783524,
-0.004962879233062267,
-0.059338152408599854,
-0.007994377054274082,
0.020746886730194092,
0.00011972186621278524,
0.033693842589855194,
-0.06346120685338974,
0.03935676068067551,
0.02260434441268444,
0.012341049499809742,
-0.023404300212860107,
-0.02509515918791294,
-0.03769008815288544,
0.03644052520394325,
0.007646267302334309,
0.002512245671823621,
0.0027823536656796932,
0.0010877866297960281,
0.009651998057961464,
-0.06367410719394684,
0.013832087628543377,
-0.01574140042066574,
-0.029767939820885658,
-0.01868545450270176,
0.0428357757627964,
-0.013012617826461792,
0.05355904996395111,
-0.024261193349957466,
-0.02527690678834915,
-0.009933737106621265,
-0.05287373065948486,
-0.015572831965982914,
0.007252978626638651,
-0.0026857887860387564,
0.003213475225493312,
0.047454942017793655,
-0.01936856284737587,
-0.030842414125800133,
0.01933234930038452,
-0.012237448245286942,
0.006095771677792072,
0.021887585520744324,
0.0014981775311753154,
-0.02195058949291706,
-0.009001996368169785,
-0.0006019666325300932,
-0.011574040167033672,
-0.01787552423775196,
0.026635723188519478,
0.03967108204960823,
-0.006841135211288929,
-0.009281459264457226,
0.001394016551785171,
-0.0074997893534600735,
0.018229855224490166,
0.019064409658312798,
0.009599067270755768,
0.046903789043426514,
0.034666821360588074,
-0.051290467381477356,
0.01128325518220663,
0.0016872629057615995,
0.02028948999941349,
-0.08804119378328323,
0.0046715568751096725,
-0.006193871144205332,
0.015258211642503738,
0.04475710168480873,
-0.0789751410484314,
0.02196967415511608,
0.03850886970758438,
-0.003109684679657221,
0.060232773423194885,
-0.010758919641375542,
-0.015530752018094063,
-0.02632049098610878,
-0.013908817432820797,
-0.010176734998822212,
0.04300336912274361,
0.018171101808547974,
0.00445056427270174,
-0.018184324726462364,
-0.015293450094759464,
0.012188944034278393,
0.0011885348940268159,
-0.055021900683641434,
0.0079331174492836,
-0.004406161606311798,
-0.038943979889154434,
0.059061553329229355,
-0.02327347919344902,
-0.03610154986381531,
0.020823249593377113,
0.00924745760858059,
-0.012135849334299564,
0.013001213781535625,
0.038650281727313995,
-0.011395825073122978,
0.041985832154750824,
0.05172678828239441,
-0.011883932165801525,
-0.003008586587384343,
0.00008482595876557752,
0.010664837434887886,
0.03822248429059982,
-0.007978877052664757,
0.025184903293848038,
0.016698583960533142,
-0.040163975208997726,
-0.05460267886519432,
0.029197534546256065,
0.002825255272909999,
-0.013170447200536728,
0.0058632297441363335,
-0.053899236023426056,
0.006195851601660252,
0.0009488532086834311,
0.03856634721159935,
-0.013263186439871788,
0.025236299261450768,
0.020863769575953484,
0.01037861593067646,
0.005245455075055361,
0.031381215900182724,
-0.024084122851490974,
-0.03670024499297142,
0.018400203436613083,
0.013713333755731583,
0.011432552710175514,
-0.03831760212779045,
0.004815298598259687,
0.012136206962168217,
-0.024372734129428864,
-0.012761463411152363,
-0.04863576963543892,
-0.022763719782233238,
0.01818964257836342,
0.00623241625726223,
0.009715553373098373,
-0.01025373674929142,
-0.0183461531996727,
-0.007066756021231413,
-0.03746436536312103,
0.0587717704474926,
0.0059352051466703415,
0.0015269806608557701,
0.003991553094238043,
0.03181760013103485,
0.03209994360804558,
-0.011247754096984863,
0.02981661632657051,
-0.04420224204659462,
-0.03741007298231125,
0.01626136340200901,
-0.00297798914834857,
0.029767440631985664,
0.016658058390021324,
-0.012381546199321747,
-0.01050227228552103,
-0.030567409470677376,
-0.013754099607467651,
-0.028066640719771385,
0.0010087151313200593,
0.021127648651599884,
0.006697401870042086,
0.0030404950957745314,
-0.0025615200866013765,
-0.00928189605474472,
-0.052648164331912994,
0.06721611320972443,
0.02719537727534771,
-0.012917766347527504,
0.07007871568202972,
-0.024375732988119125,
0.0031220405362546444,
0.018819915130734444,
-0.019967705011367798,
-0.019792839884757996,
0.030291559174656868,
-0.041306670755147934,
0.008206116035580635,
0.011499308981001377,
-0.019911225885152817,
0.04187954589724541,
-0.056983962655067444,
0.02103220485150814,
0.05805804580450058,
-0.048912592232227325,
-0.016397692263126373,
0.05116325244307518,
-0.01331319659948349,
0.002511147642508149,
0.03256236016750336,
-0.0012873985106125474,
0.0652458518743515,
0.017713773995637894,
0.02599218115210533,
0.03867918998003006,
0.03336343541741371,
0.034463249146938324,
0.02638251520693302,
0.017353812232613564,
0.005503587890416384,
0.030493535101413727,
-0.00627256091684103,
0.0204482264816761,
-0.046904999762773514,
0.002812688471749425,
0.03807752579450607,
-0.003294925903901458,
0.013224603608250618,
-0.00047023719525896013,
-0.05468183010816574,
0.1011219322681427,
-0.04727770388126373,
0.03397510573267937,
-0.01709173247218132,
0.024987801909446716,
-0.030357135459780693,
-0.0015731258317828178,
0.018602509051561356,
0.05412847921252251,
-0.03398368880152702,
0.009079599753022194,
-0.03086298145353794,
0.002954669762402773,
0.024330448359251022,
-0.04495140165090561,
0.024003539234399796,
0.008357093669474125,
0.003944148309528828,
0.0020902848336845636,
-0.015237345360219479,
-0.019142664968967438,
-0.019463513046503067,
0.005624561104923487,
0.05080149322748184,
0.002720857970416546,
-0.007878364995121956,
-0.0163691695779562,
-0.03316149860620499,
0.03196956217288971,
-0.0611489936709404,
-0.004510023165494204,
-0.03483070433139801,
-0.009294029325246811,
-0.025598561391234398,
0.010625950060784817
] |
<p>For N non interacting spinless particles in a volume, we have 3N degrees of freedom and we can divide the phase space into 6N dimensional cells of volume h raised to power 3N. </p>
<p>And each cell represents a state of the system. That means the system can be in any of those cells. </p>
<p>How can a cell be visualized? Is it combination of many volumes of the individual particles where the particles might be in? Fixing one particle in its one of the individual states (i.e., in one cell when the system is only one spinless particle) and all the possible combination of the other particles in their cells, does this represent one cell for the N particle system? </p>
| 7,594 |
[
-0.028481164947152138,
-0.0021536063868552446,
-0.01471761241555214,
-0.02786153368651867,
0.03328960761427879,
-0.018421022221446037,
-0.038586825132369995,
-0.00784301571547985,
0.022108642384409904,
-0.04512707144021988,
0.06065303459763527,
0.024518124759197235,
0.043684083968400955,
0.00596365612000227,
-0.014664046466350555,
0.026849661022424698,
-0.005268074572086334,
0.008990446105599403,
-0.03282277286052704,
-0.044024307280778885,
-0.001350683392956853,
0.0446295365691185,
-0.008992243558168411,
-0.023051075637340546,
-0.0015365580329671502,
0.07321164011955261,
0.022127985954284668,
0.0004198978713247925,
0.01372914481908083,
0.04852723702788353,
-0.03424438089132309,
-0.03421510010957718,
0.007998120039701462,
0.03731768950819969,
0.029270922765135765,
-0.018199069425463676,
0.018509795889258385,
-0.009116952307522297,
0.03368314728140831,
-0.0077481516636908054,
-0.053433869034051895,
-0.005410346668213606,
-0.00034221404348500073,
0.03130786865949631,
-0.041118379682302475,
0.02944045700132847,
-0.0057570491917431355,
-0.01606764830648899,
-0.0012743186671286821,
-0.08012509346008301,
0.07265680283308029,
0.015362273901700974,
0.037259675562381744,
0.0007630724576301873,
-0.0017851792508736253,
0.00019093161972705275,
0.01166978757828474,
0.09935423731803894,
0.010051513090729713,
-0.039756178855895996,
-0.014068352058529854,
-0.020707853138446808,
0.006049530114978552,
-0.01648569107055664,
-0.03998672962188721,
0.00832212995737791,
0.014999901875853539,
0.0021677652839571238,
0.015972338616847992,
-0.015986764803528786,
-0.020364349707961082,
0.007412356324493885,
0.06521549820899963,
-0.038506150245666504,
0.015612822026014328,
-0.025159990414977074,
0.04507262259721756,
-0.002099106553941965,
0.04581195488572121,
0.025095239281654358,
-0.01516430638730526,
0.04821373522281647,
-0.04025554656982422,
-0.0010205601574853063,
0.03372378274798393,
-0.024537699297070503,
0.06252200156450272,
-0.028263874351978302,
0.004192111548036337,
0.058133404701948166,
-0.014875145629048347,
0.04778202250599861,
0.05288044363260269,
-0.0015568402595818043,
-0.027129724621772766,
0.0101150032132864,
-0.007996509782969952,
0.02878636308014393,
-0.005494499113410711,
-0.05148385837674141,
-0.03393402323126793,
-0.025109676644206047,
0.0010872597340494394,
0.06712837517261505,
-0.01049434207379818,
0.01275442074984312,
0.019879085943102837,
0.015897180885076523,
-0.03494961932301521,
0.00003621228825068101,
-0.04518493264913559,
0.01730761118233204,
0.030813898891210556,
0.018468722701072693,
0.0013360397424548864,
-0.009985421784222126,
-0.03647870197892189,
-0.011721022427082062,
0.039577800780534744,
0.08081338554620743,
0.05661766976118088,
-0.03834783658385277,
0.030901404097676277,
-0.02751004323363304,
-0.12801103293895721,
0.020418228581547737,
-0.001781224156729877,
0.003552662441506982,
-0.023870697245001793,
0.0021047245245426893,
0.016988074406981468,
0.008417816832661629,
0.012015219777822495,
-0.012361652217805386,
0.02564597874879837,
0.004712849855422974,
-0.10097641497850418,
-0.03330276906490326,
0.0451129712164402,
-0.028232064098119736,
-0.021145371720194817,
-0.025059549137949944,
0.02258460409939289,
0.07810022681951523,
0.08065719902515411,
-0.04617277532815933,
-0.0173103678971529,
0.025581415742635727,
0.051649246364831924,
-0.003470224794000387,
-0.016638698056340218,
0.018557369709014893,
-0.016748398542404175,
-0.040552783757448196,
0.017010841518640518,
-0.03228279575705528,
0.0868544653058052,
0.07180256396532059,
0.030074182897806168,
-0.020671626552939415,
0.03568499535322189,
-0.04518676549196243,
-0.0005222176550887525,
0.015488405711948872,
-0.01424828264862299,
-0.004394089803099632,
0.05076690763235092,
-0.01578674651682377,
0.06330639868974686,
0.027348950505256653,
0.015088880434632301,
0.03524073213338852,
-0.011583651416003704,
0.04579443857073784,
0.035951707512140274,
0.008878585882484913,
0.012697488069534302,
-0.017766382545232773,
-0.014970320276916027,
-0.003962005954235792,
-0.0566587932407856,
-0.03499004244804382,
0.02955625019967556,
0.03154563158750534,
0.03624650835990906,
-0.0053035793825984,
-0.0018866535974666476,
-0.014021802693605423,
-0.016463503241539,
-0.01665852963924408,
-0.037818264216184616,
-0.07308483123779297,
0.03082313947379589,
-0.001474023680202663,
-0.02585737220942974,
0.07189399003982544,
0.01832990162074566,
-0.005028789862990379,
0.0005788638372905552,
-0.020312078297138214,
-0.04099973291158676,
0.034061651676893234,
-0.014493631199002266,
-0.03442319855093956,
0.000888429582118988,
0.07056044042110443,
0.02658110298216343,
0.006375530734658241,
0.02154497802257538,
-0.02207738719880581,
-0.027573317289352417,
-0.031007925048470497,
-0.010533839464187622,
0.026535583660006523,
0.010725649073719978,
0.001375051448121667,
-0.013465995900332928,
0.007026838604360819,
-0.04559897258877754,
0.013146499171853065,
0.005163621157407761,
0.061760637909173965,
0.04471566155552864,
-0.008426329120993614,
0.027767103165388107,
0.0005918210954405367,
-0.011430337093770504,
0.002207407495006919,
0.027293816208839417,
0.011552724987268448,
-0.06295247375965118,
-0.02168259397149086,
0.0104907788336277,
0.04868415743112564,
-0.017505284398794174,
-0.0009513920522294939,
0.0014592836378142238,
0.025300374254584312,
-0.012992994859814644,
-0.002461670897901058,
-0.05903598666191101,
-0.003734118305146694,
0.03522616997361183,
0.005790285766124725,
0.02357589639723301,
-0.00196243729442358,
0.0047083087265491486,
0.011328723281621933,
-0.006102859508246183,
0.013162625022232533,
-0.05294906347990036,
0.027655648067593575,
-0.04920431971549988,
0.0006226440891623497,
0.004369268659502268,
-0.04835294559597969,
-0.008628327399492264,
-0.005968562327325344,
-0.0033892286010086536,
-0.007479291409254074,
-0.02815811149775982,
-0.012286489829421043,
-0.021615948528051376,
-0.02549634501338005,
0.009504766203463078,
0.011610729619860649,
-0.01940046437084675,
-0.01899971067905426,
0.040189940482378006,
-0.03984382376074791,
0.06315150111913681,
-0.03147926554083824,
-0.012448228895664215,
0.011834505945444107,
0.02220735140144825,
0.0399085097014904,
0.004490856546908617,
0.05320024490356445,
-0.04764784127473831,
-0.03352486342191696,
-0.011258007027208805,
-0.016521751880645752,
0.013525235466659069,
0.055814847350120544,
-0.06691265851259232,
0.004616879392415285,
-0.03591253235936165,
-0.05829359218478203,
-0.017368901520967484,
-0.018802588805556297,
-0.0356920100748539,
-0.00006852579099358991,
-0.016096267849206924,
-0.07786426693201065,
-0.007196003571152687,
0.019424429163336754,
0.0341336615383625,
-0.027894994243979454,
0.022753970697522163,
0.02907789871096611,
-0.008744574151933193,
-0.05546937137842178,
-0.011972105130553246,
-0.04093349352478981,
-0.02452150173485279,
0.00022761456784792244,
0.003777627367526293,
0.013296734541654587,
-0.03178567439317703,
0.006080309394747019,
0.047176383435726166,
-0.052029505372047424,
-0.008115742355585098,
-0.06552761048078537,
-0.04135441035032272,
-0.022288722917437553,
-0.030276689678430557,
0.03439915552735329,
-0.011451360769569874,
-0.018543802201747894,
0.04987529665231705,
-0.015959089621901512,
-0.04985181987285614,
0.0007871296838857234,
0.0021677822805941105,
-0.04637652635574341,
-0.04072280600667,
0.06596323847770691,
0.030247041955590248,
-0.004352769814431667,
0.0012159227626398206,
0.0018867081962525845,
0.036844559013843536,
0.04627102613449097,
0.023191720247268677,
-0.02429290860891342,
0.005039475858211517,
-0.0007236383971758187,
-0.010179728269577026,
0.03899510204792023,
0.024181844666600227,
-0.012483387254178524,
0.05297787860035896,
-0.02463146485388279,
0.00988574605435133,
0.03755626454949379,
-0.028380095958709717,
0.05832233652472496,
0.0074782585725188255,
0.04332653433084488,
-0.01585625298321247,
0.02210908755660057,
-0.001577088376507163,
0.011379689909517765,
0.020626744255423546,
0.024772027507424355,
0.055803023278713226,
0.006053477060049772,
-0.03137708082795143,
0.012049787677824497,
0.016884636133909225,
-0.026698924601078033,
-0.024991178885102272,
0.01642642170190811,
0.010384568013250828,
0.01941419020295143,
-0.0157476719468832,
-0.018046511337161064,
0.018740596249699593,
-0.004697937984019518,
0.010053279809653759,
-0.02028198167681694,
0.007750276476144791,
-0.011359701864421368,
-0.035984236747026443,
-0.011838908307254314,
-0.028430886566638947,
-0.007175922859460115,
-0.00011047272710129619,
0.06017669662833214,
-0.023513726890087128,
-0.009936011396348476,
-0.007579737808555365,
-0.027724169194698334,
-0.07161568850278854,
0.00330400001257658,
0.0346178263425827,
0.04089516028761864,
0.02773289382457733,
-0.003826879896223545,
0.04615851864218712,
-0.037861697375774384,
-0.025884471833705902,
0.012213729321956635,
-0.021025748923420906,
-0.043495938181877136,
-0.01954949088394642,
-0.027937939390540123,
-0.014551201835274696,
-0.019678380340337753,
0.02771003171801567,
0.055816274136304855,
-0.00600799173116684,
0.030427807942032814,
0.04705243185162544,
-0.014516654424369335,
0.01302316877990961,
0.024934401735663414,
0.008481532335281372,
0.03689355403184891,
0.006403840146958828,
0.004047498572617769,
0.037108223885297775,
0.023280387744307518,
0.019376246258616447,
-0.0030428592581301928,
0.05073506012558937,
0.02932467684149742,
-0.0003171697608195245,
0.017457108944654465,
-0.04018193483352661,
-0.001233787159435451,
-0.0084952088072896,
0.018717801198363304,
0.022866131737828255,
0.004572669044137001,
0.03216617926955223,
0.027822205796837807,
0.0069511509500443935,
0.03744760528206825,
0.009453645907342434,
0.0017228731885552406,
-0.017180483788251877,
-0.05182676762342453,
-0.023832974955439568,
0.002124553546309471,
0.02288583107292652,
0.03625566139817238,
0.0029768149834126234,
0.007315809838473797,
0.012336374260485172,
0.01666315086185932,
-0.01416695024818182,
-0.04866946116089821,
-0.00046983122592791915,
-0.03207817301154137,
0.011943426914513111,
-0.009221569634974003,
0.02309850975871086,
0.014876492321491241,
0.011918674223124981,
-0.0034250563476234674,
0.04263212904334068,
-0.040781863033771515,
-0.09119343757629395,
-0.0245340745896101,
0.06987877190113068,
-0.00885102991014719,
0.02748980186879635,
-0.003045158227905631,
-0.04206060245633125,
-0.0354449525475502,
0.01874048449099064,
-0.0013222481356933713,
0.0038059833459556103,
-0.0110846608877182,
-0.01901426911354065,
-0.005441027693450451,
-0.027037974447011948,
-0.007214363198727369,
-0.017909551039338112,
0.00659979647025466,
0.01668565161526203,
-0.04465281963348389,
0.04659634083509445,
0.011986183933913708,
0.024460945278406143,
-0.004040344152599573,
0.012043057009577751,
0.019819337874650955,
-0.011845805682241917,
-0.008491537533700466,
0.015987124294042587,
-0.03915498033165932,
-0.07095936685800552,
0.05050472170114517,
0.01930004544556141,
-0.007300676312297583,
0.035930220037698746,
-0.06510694324970245,
-0.07086113840341568,
-0.02884206362068653,
-0.008965281769633293,
0.02252950705587864,
-0.0018180647166445851,
-0.03628908470273018,
0.0983685627579689,
0.003816666081547737,
-0.002219155430793762,
0.03576163202524185,
-0.00390726188197732,
0.02733989618718624,
-0.013694685883820057,
-0.00570533936843276,
0.06481088697910309,
-0.000026330273612984456,
0.027792252600193024,
-0.03955163061618805,
-0.005635811481624842,
0.012382001616060734,
0.0089038647711277,
0.017853807657957077,
0.03291597217321396,
-0.0071588740684092045,
-0.007985697127878666,
-0.036103252321481705,
-0.0003069228259846568,
0.044135089963674545,
-0.020216498523950577,
0.008126848377287388,
0.03486623242497444,
0.035902488976716995,
-0.004693364258855581,
0.010786746628582478,
-0.03148718550801277,
0.017873462289571762,
0.050476498901844025,
-0.00464550219476223,
0.009830554947257042,
-0.05465562269091606,
0.0015916958218440413,
0.03127807006239891,
-0.04971872642636299,
0.06671260297298431,
-0.041952189058065414,
0.01725326105952263,
0.029412753880023956,
-0.06184646859765053,
-0.01976592093706131,
0.005038287490606308,
-0.001139219501055777,
-0.0013744832249358296,
-0.02221243642270565,
-0.010645318776369095,
-0.0055455174297094345,
0.02186311036348343,
-0.07322666794061661,
-0.03151126205921173,
-0.013182969763875008,
0.00662305997684598,
-0.02118837460875511,
-0.04068196192383766,
-0.0009362823329865932,
0.021967576816678047,
-0.03335781395435333,
-0.010307041928172112,
0.04026905819773674,
-0.024267446249723434,
0.009504970163106918,
0.040868815034627914,
0.048874370753765106,
0.07224421203136444,
0.003446791786700487,
-0.02527378313243389,
0.0363263301551342,
-0.015543128363788128,
0.018444959074258804,
-0.012323545292019844,
0.03123137727379799,
-0.00964504387229681,
-0.022365044802427292,
0.008110306225717068,
0.008326797746121883,
0.027995601296424866,
-0.03890932723879814,
-0.017174314707517624,
0.030679134652018547,
-0.007166164927184582,
-0.025402937084436417,
-0.012863261625170708,
-0.03359251841902733,
-0.02689855359494686,
0.019144736230373383,
-0.003969688434153795,
0.013598623685538769,
-0.00628538616001606,
-0.03327592462301254,
0.038852203637361526,
-0.005521830637007952,
-0.02496202476322651,
0.019170038402080536,
0.009842021390795708,
-0.023459013551473618,
-0.036756522953510284,
0.004273463971912861,
-0.011167933233082294,
0.02607758343219757,
-0.02309297025203705,
0.017163902521133423,
-0.006630746182054281,
0.01821296662092209,
-0.025295579805970192,
-0.011410695500671864,
-0.06624627113342285,
0.008774342946708202,
0.05096955969929695,
-0.02876250445842743,
0.01977049931883812,
0.0372413694858551,
-0.003021816723048687,
-0.0031864033080637455,
-0.016279080882668495,
0.014204757288098335,
0.012197194620966911,
0.009130718186497688,
0.026578187942504883,
-0.023148298263549805,
0.003180532017722726,
0.05672793462872505,
0.06511780619621277,
-0.028967928141355515,
0.02714630588889122,
0.03610554337501526,
-0.037590883672237396,
0.04412340745329857,
-0.006177869625389576,
-0.026272116228938103,
0.08904644101858139,
-0.04673084244132042,
0.0504169687628746,
-0.002295109210535884,
-0.014963585883378983,
0.025155983865261078,
0.042708538472652435,
0.006320483051240444,
-0.010977210476994514,
-0.02932080253958702,
-0.033364977687597275,
0.03416374325752258,
-0.0015644087688997388,
0.016163062304258347,
-0.012470318004488945,
-0.009523105807602406,
0.04884510859847069,
-0.0013117792550474405,
-0.020855553448200226,
0.010095130652189255,
-0.044662076979875565,
-0.020055009052157402,
-0.02970733866095543,
-0.024177344515919685,
0.0018329021986573935,
0.011782655492424965,
-0.003028398845344782,
0.018188755959272385,
0.003349418519064784,
0.013420948758721352,
0.00853767804801464,
0.030868541449308395,
-0.003412109101191163,
0.026208987459540367,
0.0006254830514080822,
0.0257911067456007,
-0.014236983843147755,
0.030637409538030624,
0.12036289274692535,
0.029260439798235893,
-0.0004931850708089769,
-0.0506494976580143,
-0.011077575385570526,
-0.01802193932235241,
0.0066217281855642796,
-0.0342961810529232,
0.014721380546689034,
0.01290492806583643,
0.009939705021679401,
-0.044535618275403976,
0.04705965518951416,
-0.023089412599802017,
0.015565825626254082,
0.03716693073511124,
-0.029114609584212303,
-0.05801479518413544,
-0.022963810712099075,
0.0027219897601753473,
0.006297809071838856,
0.00977373868227005,
-0.02995426580309868,
-0.02214544638991356,
0.011839254759252071,
-0.008755971677601337,
-0.02847013995051384,
-0.03046332113444805,
0.033249370753765106,
0.045262522995471954,
-0.015026787295937538,
0.011270156130194664,
-0.013498134911060333,
-0.003931679762899876,
-0.017703864723443985,
0.019693482667207718,
0.013959623873233795,
-0.010789972729980946,
0.026482705026865005,
0.03721349313855171,
-0.010990090668201447,
0.0031132418662309647,
-0.0020016797352582216,
-0.011593530885875225,
-0.021456174552440643,
-0.017529452219605446,
-0.01123154815286398,
0.06199290603399277,
-0.005913874134421349,
-0.053558893501758575,
-0.008857485838234425,
-0.010051079094409943,
0.0066587431356310844,
-0.03611629083752632,
-0.026276500895619392,
0.007784469053149223,
0.057877711951732635,
-0.028707385063171387,
-0.008529569022357464,
-0.020080428570508957,
0.0026564858853816986,
-0.007623443845659494,
0.024592159315943718,
0.0062436931766569614,
0.005956762935966253,
0.014558674767613411,
-0.00844351015985012,
0.02724098227918148,
-0.01679225265979767,
0.03939148038625717,
-0.039626166224479675,
0.007163305301219225,
-0.024712001904845238,
-0.014612440019845963,
0.02370550110936165,
0.02128509245812893,
0.03337009996175766,
0.030953429639339447,
-0.03149951621890068,
0.0201027300208807,
-0.022140447050333023,
-0.003527473658323288,
-0.018012048676609993,
-0.03277050331234932,
0.0027058252599090338,
0.018459219485521317,
0.03613363578915596,
0.029350116848945618,
-0.04137788340449333,
-0.0039348299615085125,
-0.011060073040425777,
0.015077317133545876,
0.048082973808050156,
-0.03490987792611122,
-0.0003107126394752413,
0.01975131593644619,
-0.04229234531521797,
-0.0066237617284059525,
0.00838658306747675,
0.017731670290231705,
0.005456876941025257,
0.014245864935219288,
-0.006628796923905611,
0.07781407982110977,
0.02571852318942547,
-0.015269956551492214,
0.01693006232380867,
-0.024952547624707222,
-0.0013371474342420697,
0.02403412014245987,
0.026803821325302124,
-0.05066228285431862,
-0.023601558059453964,
-0.03369909152388573,
-0.0010135871125385165,
0.018708623945713043,
0.02248714119195938,
-0.021574007347226143,
-0.02267780713737011,
0.00852163601666689,
0.0494096577167511,
0.020713234320282936,
0.027245398610830307,
-0.010278206318616867,
0.013813387602567673,
0.007497143931686878,
0.014185722917318344,
-0.03248758986592293,
0.0017120088450610638,
-0.037173252552747726,
-0.013814224861562252,
0.024921957403421402,
0.018936539068818092,
0.014034582301974297,
-0.05852742865681648,
-0.01911308988928795,
0.010233523324131966,
0.03468209132552147,
-0.03439716994762421,
-0.042880382388830185,
0.02761686034500599,
-0.025269437581300735,
-0.04374624788761139,
-0.015250037424266338,
-0.0070331948809325695,
0.05898181349039078,
0.06003957614302635,
-0.020020781084895134,
-0.03440963476896286,
-0.02655598521232605,
-0.054163120687007904,
-0.010088767856359482,
0.029131239280104637,
-0.0020771233830600977,
-0.02581082656979561,
-0.04010520875453949,
0.005934116430580616,
0.009534471668303013,
-0.012119012884795666,
0.03184889629483223,
0.06588346511125565,
0.007188208866864443,
-0.008167103864252567,
-0.011898248456418514,
-0.011853553354740143,
0.045540060847997665,
0.0016423729248344898,
-0.022017963230609894,
0.0445580780506134,
0.03256111964583397,
-0.01474754512310028,
0.02963278628885746,
0.04002906009554863,
0.008934860117733479,
-0.0950506255030632,
-0.04185539111495018,
0.006568046286702156,
-0.019702123478055,
0.05387883633375168,
-0.008829081431031227,
-0.00863020308315754,
0.044713497161865234,
-0.09305420517921448,
0.0486442930996418,
-0.017245439812541008,
-0.0247846320271492,
-0.034300122410058975,
0.014858148992061615,
-0.0514880008995533,
0.08647382259368896,
0.01679527573287487,
0.008937973529100418,
0.005161728709936142,
-0.01629975251853466,
-0.02941480092704296,
-0.05731798708438873,
-0.010528425686061382,
0.01325927022844553,
-0.003667073789983988,
-0.04492291063070297,
0.0360555574297905,
-0.026005728170275688,
-0.05172820761799812,
-0.003976750187575817,
-0.026511363685131073,
-0.019967593252658844,
-0.013544553890824318,
-0.02537556365132332,
-0.007649820297956467,
0.04087861627340317,
0.011316249147057533,
-0.01330542005598545,
-0.02806679718196392,
0.011327940970659256,
0.037697795778512955,
0.018282592296600342,
-0.005192231852561235,
0.01127705443650484,
0.012979750521481037,
-0.0016176113858819008,
-0.032328635454177856,
0.04458928480744362,
-0.0020181566942483187,
0.018340598791837692,
-0.025373702868819237,
-0.014164243824779987,
0.012074138037860394,
0.010795200243592262,
0.0048035974614322186,
-0.048894815146923065,
0.004260264337062836,
0.0063115619122982025,
0.01485756877809763,
0.0013780889566987753,
0.026186352595686913,
-0.005665344651788473,
-0.029312830418348312,
-0.014946730807423592,
0.032135047018527985,
-0.0436636246740818,
-0.001419723965227604,
-0.005193107761442661,
0.043630026280879974,
-0.0035619160626083612,
0.009896759875118732,
-0.031295597553253174,
-0.04959630221128464,
0.03376180678606033,
0.018236614763736725,
0.04496525228023529,
0.01360806543380022,
-0.06448900699615479,
-0.0393642820417881,
-0.06551520526409149,
0.04015125706791878,
0.02124875783920288,
0.005827578250318766,
-0.03941967710852623,
-0.017989518120884895,
0.004342749714851379,
0.0449780635535717,
0.05472532659769058,
0.033979035913944244,
0.0222341176122427,
-0.005071375053375959,
0.00986892357468605,
0.026428384706377983,
-0.04366510733962059,
-0.012136103585362434,
-0.03543100133538246,
-0.018657585605978966,
-0.016770655289292336,
0.0351148322224617,
-0.000008581290785514284,
0.004406843800097704,
0.03632931783795357,
-0.025609904900193214,
-0.015482011251151562,
-0.009869013912975788,
-0.04542437195777893,
0.05353923141956329,
-0.018671497702598572,
-0.03248836100101471,
0.04048383608460426,
-0.015558665618300438,
0.024155039340257645,
0.02413330040872097,
-0.014615111984312534,
-0.007522408850491047,
0.005589282140135765,
-0.06182034686207771,
-0.06515614688396454,
-0.010464686900377274,
-0.0028526524547487497,
0.043966442346572876,
-0.056272897869348526,
0.041535526514053345,
0.025724435225129128,
-0.051974955946207047,
0.000050810624088626355,
0.0677075907588005,
0.03014436736702919,
0.040078263729810715,
0.022691600024700165,
0.01404390949755907,
0.02303513139486313,
0.008489388972520828,
0.028186094015836716,
0.05812443792819977,
0.05425749346613884,
-0.0035235516261309385,
-0.010489067062735558,
0.04285900667309761,
-0.03396183252334595,
-0.006204765290021896,
0.04427294433116913,
0.03741282597184181,
0.0015560390893369913,
0.016112253069877625,
0.028475170955061913,
-0.027708088979125023,
0.0190417617559433,
-0.021663961932063103,
-0.008482641540467739,
0.11675786972045898,
-0.020875461399555206,
-0.006488174665719271,
-0.012478469870984554,
0.015457794070243835,
-0.024791060015559196,
-0.03435146063566208,
0.0006329191965050995,
0.058182839304208755,
-0.03365509212017059,
-0.04065932705998421,
-0.03030669130384922,
-0.005319749936461449,
0.006739052478224039,
-0.05996232107281685,
0.020058386027812958,
-0.0310976579785347,
0.0014987661270424724,
-0.029303668066859245,
-0.010198256000876427,
-0.03314833343029022,
-0.036379892379045486,
0.020240893587470055,
0.005427655763924122,
0.02187218889594078,
-0.02974902279675007,
-0.01016553770750761,
-0.0378081314265728,
0.02811633236706257,
-0.01784047856926918,
-0.020936692133545876,
-0.027545539662241936,
0.022807985544204712,
-0.02033892460167408,
0.00038023004890419543
] |
<p>Why is the criteria for fusion represented as a triple product nτT instead of the n,τ,T individually? i.e saying the density has to be above this value, temperature above this value? What are the advantage we gain from representing it this way? </p>
| 7,595 |
[
-0.02376582659780979,
0.002515918342396617,
0.006446534767746925,
-0.02834044024348259,
0.035927098244428635,
-0.016221709549427032,
-0.02778616175055504,
-0.005990473087877035,
-0.0163112860172987,
0.02080473303794861,
0.04046644642949104,
-0.02953309193253517,
0.06479043513536453,
0.014400244690477848,
0.004024645779281855,
0.014924020506441593,
0.036478109657764435,
-0.02566714771091938,
-0.018458032980561256,
-0.03546885401010513,
-0.005720131099224091,
0.01157212071120739,
-0.01780019886791706,
0.0051221479661762714,
-0.00011904607526957989,
0.06095799431204796,
0.03444981575012207,
0.016110874712467194,
0.06770384311676025,
0.03958966210484505,
0.007466091774404049,
-0.044774796813726425,
0.04790080711245537,
0.0196299459785223,
0.03898288682103157,
-0.010137657634913921,
-0.007978187873959541,
0.007633601315319538,
-0.022231271490454674,
0.03027273528277874,
-0.05395498871803284,
-0.012569171376526356,
-0.0021424361038953066,
0.02254379913210869,
0.004082206171005964,
0.027829226106405258,
-0.0194393340498209,
-0.014261249452829361,
0.004042772576212883,
-0.02485514245927334,
0.03732491284608841,
0.056336160749197006,
0.007876945659518242,
0.03270989656448364,
-0.010239185765385628,
0.036680761724710464,
0.04434157535433769,
0.060279782861471176,
0.015066164545714855,
-0.044846370816230774,
-0.0437336340546608,
-0.014178600162267685,
-0.0017971714260056615,
0.013219539076089859,
0.005274476483464241,
0.01910828985273838,
0.005364725831896067,
-0.03841656818985939,
-0.0028567740228027105,
0.002183811040595174,
0.007083758246153593,
0.0010425258660688996,
0.009150981903076172,
-0.0475415475666523,
0.014959858730435371,
-0.01624445430934429,
0.023486891761422157,
-0.033691924065351486,
0.06893245130777359,
0.04049525782465935,
0.0017936539370566607,
0.013166551478207111,
0.018327949568629265,
0.026700083166360855,
-0.0003601138014346361,
0.008343800902366638,
0.08759722113609314,
-0.005284569691866636,
0.003440386150032282,
0.019238213077187538,
-0.03676121309399605,
0.0050179907120764256,
0.05607057735323906,
-0.003522647311910987,
-0.035281285643577576,
0.0002686497464310378,
0.0024242510553449392,
0.04720545932650566,
-0.002558422274887562,
-0.012232132256031036,
-0.005670140031725168,
0.010955208912491798,
0.021727463230490685,
0.07863560318946838,
0.010028836317360401,
-0.013674126006662846,
-0.05439778044819832,
-0.04087849706411362,
0.0026423402596265078,
-0.016894031316041946,
-0.030174363404512405,
-0.010489381849765778,
-0.0034566926769912243,
0.026912489905953407,
0.00030118940048851073,
-0.009882091544568539,
0.023991119116544724,
0.0046290201134979725,
0.04244961217045784,
0.05483854562044144,
0.04036177694797516,
-0.022449469193816185,
0.041782647371292114,
0.0007560366066172719,
-0.0843881219625473,
0.024844404309988022,
0.016096550971269608,
0.021748902276158333,
-0.009488904848694801,
0.010100573301315308,
-0.01489010825753212,
-0.03491953760385513,
0.02311222068965435,
-0.00041502367821522057,
0.03752830997109413,
0.009486891329288483,
-0.07176009565591812,
-0.04762270301580429,
0.01863337680697441,
-0.027022669091820717,
-0.05864882469177246,
-0.06517940759658813,
0.01574227213859558,
0.02231220342218876,
0.06210125610232353,
0.00008056302613113075,
-0.035645741969347,
-0.018312331289052963,
0.04721292108297348,
-0.0027808190789073706,
-0.038025565445423126,
-0.04032256081700325,
0.035896673798561096,
-0.04894900694489479,
-0.019930273294448853,
-0.07635649293661118,
0.031106354668736458,
-0.006691476795822382,
-0.003885551355779171,
-0.03512509539723396,
0.07210875302553177,
-0.041879408061504364,
-0.005028096027672291,
0.009305459447205067,
0.045476894825696945,
0.00524937966838479,
0.05789954960346222,
-0.0071505350060760975,
0.010849058628082275,
0.02207755111157894,
0.006812056992202997,
0.02547936886548996,
0.015782451257109642,
0.05032585933804512,
0.018455319106578827,
-0.016746761277318,
0.007241274695843458,
-0.024711819365620613,
-0.00012281644740141928,
-0.0071627297438681126,
-0.018300045281648636,
-0.02140609361231327,
-0.016603311523795128,
0.03663047403097153,
0.025191446766257286,
0.017013389617204666,
-0.03668510541319847,
-0.0077517954632639885,
0.004987863823771477,
-0.03715960681438446,
-0.00754822650924325,
-0.06467258185148239,
0.0016044806689023972,
-0.04921748489141464,
-0.06953967362642288,
0.031434450298547745,
0.03507309406995773,
-0.0017837664345279336,
0.0038217916153371334,
-0.03673475980758667,
-0.03825812041759491,
0.02864842303097248,
0.00785380695015192,
-0.011707106605172157,
0.035564862191677094,
0.04784518480300903,
0.026456039398908615,
0.01604827493429184,
0.007049362640827894,
-0.04863852635025978,
-0.030719133093953133,
0.011426916345953941,
-0.005847307853400707,
0.009505290538072586,
-0.0058084335178136826,
-0.030068891122937202,
-0.02734890952706337,
-0.012249358929693699,
-0.01853521168231964,
0.02704041451215744,
-0.04702198877930641,
0.07460110634565353,
0.04715552553534508,
0.0222873967140913,
0.025020604953169823,
0.07168342918157578,
-0.035522058606147766,
0.03321286663413048,
-0.001148466719314456,
-0.025353746488690376,
-0.04352366924285889,
0.009066036902368069,
0.022174648940563202,
0.07106754183769226,
-0.04363837465643883,
0.03738301619887352,
-0.024945223703980446,
0.0209017526358366,
0.02027938887476921,
0.01714463345706463,
-0.009024851024150848,
-0.04412325099110603,
0.021876150742173195,
0.02048393152654171,
0.01477868389338255,
-0.0003774423385038972,
0.013510012067854404,
0.03046102449297905,
0.012703712098300457,
-0.003562778467312455,
-0.05158679559826851,
0.039473749697208405,
-0.025556787848472595,
-0.018686912953853607,
0.030195672065019608,
0.00667241495102644,
-0.002915031975135207,
-0.03138360753655434,
0.04097878560423851,
0.030099593102931976,
0.0010966600384563208,
0.03567861020565033,
0.00918648298829794,
-0.02669328637421131,
0.041832663118839264,
0.027657803148031235,
0.020058415830135345,
-0.017317205667495728,
0.025639785453677177,
-0.05708463490009308,
-0.0005264836363494396,
-0.019622698426246643,
0.0037544246297329664,
0.018865512683987617,
-0.01593487709760666,
0.03634525090456009,
-0.03858849033713341,
0.020580200478434563,
-0.018194302916526794,
-0.03649760037660599,
-0.03061489574611187,
-0.02071147784590721,
0.0006457020062953234,
0.005665211006999016,
-0.05882667377591133,
0.00557962479069829,
-0.025741729885339737,
-0.04968982934951782,
0.05318593978881836,
-0.04313771799206734,
-0.015453769825398922,
-0.0019473297288641334,
-0.009011594578623772,
-0.05378006771206856,
-0.030259884893894196,
-0.004140773788094521,
-0.006010193843394518,
-0.003988952375948429,
-0.002827283227816224,
0.018345754593610764,
-0.04606124386191368,
-0.06400829553604126,
0.033181123435497284,
-0.04237769916653633,
-0.04302138090133667,
-0.0229539405554533,
0.004382676910609007,
-0.0005257902666926384,
-0.012341932393610477,
0.04240091145038605,
0.07682251930236816,
-0.06500231474637985,
0.0022476266603916883,
-0.04349992051720619,
-0.005186920985579491,
-0.009391509927809238,
-0.010837780311703682,
0.06081930920481682,
0.009235107339918613,
-0.051254961639642715,
0.0648237094283104,
0.018838873133063316,
-0.010157694108784199,
-0.013386424630880356,
0.010221393778920174,
-0.022612931206822395,
-0.013173949904739857,
0.03295968100428581,
0.02487429790198803,
-0.03217285871505737,
0.02876218408346176,
-0.00047475792234763503,
0.027210161089897156,
0.08142469078302383,
0.011606015264987946,
-0.03618394955992699,
0.04998982325196266,
0.0026496259961277246,
-0.002249313984066248,
0.03482081741094589,
-0.00307777663692832,
-0.024107694625854492,
0.016587259247899055,
0.005582219921052456,
0.03236947953701019,
0.0312856025993824,
-0.04006945714354515,
0.02192450687289238,
0.033651553094387054,
-0.004904084838926792,
-0.051398616284132004,
0.00757606653496623,
0.018935799598693848,
-0.03833802416920662,
-0.007460924331098795,
0.07361467182636261,
0.033162545412778854,
-0.03909439221024513,
-0.025828244164586067,
0.038818687200546265,
0.03490149602293968,
-0.015318775549530983,
-0.020947160199284554,
0.010818076319992542,
-0.018178589642047882,
-0.0014508803142234683,
0.009868577122688293,
0.0027064778842031956,
0.04973380267620087,
0.02460203878581524,
0.014698692597448826,
-0.006933015305548906,
0.003282367018982768,
-0.03247617557644844,
-0.08747158944606781,
-0.05254033952951431,
0.002837255597114563,
0.05435514822602272,
0.00918287318199873,
0.06289353221654892,
0.029819080606102943,
0.05615268275141716,
-0.012281173840165138,
-0.003697700100019574,
-0.037147004157304764,
-0.0005633090040646493,
-0.00870987307280302,
-0.004981300327926874,
0.016085349023342133,
-0.05810575559735298,
-0.028709471225738525,
-0.04810796305537224,
-0.036786943674087524,
0.010006085969507694,
0.041017189621925354,
-0.05240907147526741,
-0.007824089378118515,
-0.023279093205928802,
0.003623365191742778,
-0.022957997396588326,
0.06838519871234894,
0.0531059168279171,
-0.005056988913565874,
0.03312394395470619,
0.08235964924097061,
-0.025497743859887123,
0.005319328512996435,
-0.020386964082717896,
0.033418964594602585,
0.02307960018515587,
0.03924860805273056,
0.02449635975062847,
0.017067959532141685,
-0.015492196194827557,
-0.0026666447520256042,
0.05487148091197014,
0.06999392807483673,
0.01943802461028099,
-0.01736113429069519,
-0.01030759233981371,
-0.038528624922037125,
-0.021351952105760574,
0.007122959475964308,
0.030034584924578667,
-0.010289283469319344,
0.024138348177075386,
-0.0062968311831355095,
0.026852507144212723,
0.011943924240767956,
0.012331862933933735,
0.03750380873680115,
0.0013149544829502702,
-0.034299615770578384,
-0.0294477678835392,
-0.03412863612174988,
-0.0027396336663514376,
-0.0009129883255809546,
0.02232271619141102,
0.03198881074786186,
-0.01613977923989296,
-0.0064071426168084145,
0.006633302662521601,
-0.030070750042796135,
-0.07326062768697739,
-0.027081351727247238,
-0.03323454037308693,
0.005277618765830994,
-0.013226805254817009,
-0.0034247206058353186,
0.014855791814625263,
0.029426828026771545,
0.03518114984035492,
0.006707003805786371,
0.018946589902043343,
-0.07516481727361679,
-0.010315549559891224,
0.002333188895136118,
0.054040901362895966,
0.02361583523452282,
-0.0078079430386424065,
-0.0638427883386612,
-0.02349057048559189,
0.06421973556280136,
-0.008535251021385193,
0.0387810654938221,
-0.022498788312077522,
-0.004205536562949419,
-0.002018054947257042,
-0.01812703162431717,
0.03892340511083603,
0.025970136746764183,
0.02382364310324192,
0.012725062668323517,
0.017367949709296227,
0.018237728625535965,
0.019203146919608116,
0.0009431872167624533,
0.009791020303964615,
0.0179313775151968,
0.01225958950817585,
-0.029254239052534103,
-0.015174906700849533,
0.00998847745358944,
-0.03090166486799717,
-0.07157720625400543,
-0.007512961979955435,
-0.009897800162434578,
0.0276299100369215,
0.027968401089310646,
-0.029260216280817986,
-0.05365494638681412,
-0.002676986623555422,
-0.00033882985007949173,
-0.02177394926548004,
0.01721593551337719,
-0.011226297356188297,
0.07866431027650833,
0.0037636645138263702,
0.011726832017302513,
0.05963483452796936,
0.014307735487818718,
-0.009918163530528545,
-0.006416106130927801,
-0.04650063440203667,
0.014850485138595104,
-0.027269048616290092,
0.021595342084765434,
-0.018863966688513756,
-0.005839870776981115,
-0.008768275380134583,
0.004789755214005709,
-0.022174814715981483,
0.0369240939617157,
-0.0016649566823616624,
-0.03242126852273941,
0.0060116746462881565,
0.002594300312921405,
-0.019978417083621025,
-0.021796979010105133,
0.010610364377498627,
0.020492400974035263,
0.03501100093126297,
-0.027528034523129463,
0.024197058752179146,
-0.05095455422997475,
-0.026096034795045853,
-0.010804098099470139,
-0.0031565139070153236,
0.0075000072829425335,
-0.021158931776881218,
-0.01861654408276081,
0.05967489257454872,
-0.00870083924382925,
0.05652986466884613,
-0.021492643281817436,
0.03386193886399269,
0.030209163203835487,
-0.04804587364196777,
-0.014312200248241425,
-0.024576442316174507,
-0.023908698931336403,
0.07750338315963745,
-0.019284367561340332,
0.05930803716182709,
-0.023144753649830818,
0.016669640317559242,
-0.06309463828802109,
-0.024847155436873436,
0.013384280726313591,
-0.004917419049888849,
-0.048757296055555344,
-0.03690533712506294,
0.003833633614704013,
-0.0195915549993515,
-0.03548469766974449,
-0.011303339153528214,
0.08295000344514847,
0.02436324581503868,
-0.053928546607494354,
0.007998527027666569,
0.036998193711042404,
0.04477652162313461,
-0.0026877732016146183,
0.010306778363883495,
0.000010641694643709343,
0.008496156893670559,
0.027508262544870377,
0.013472181744873524,
0.025776661932468414,
-0.01636001467704773,
-0.0270578321069479,
-0.004139778204262257,
-0.008331463672220707,
0.009784320369362831,
-0.005898991134017706,
0.058358609676361084,
0.031269825994968414,
0.007673113606870174,
-0.02115684002637863,
-0.0160933006554842,
-0.005904801189899445,
-0.03982347249984741,
0.027091166004538536,
0.01949840784072876,
0.016753947362303734,
-0.00158033543266356,
-0.017815234139561653,
0.04846995696425438,
0.002813215833157301,
0.014060777612030506,
-0.010189007967710495,
0.04901784658432007,
0.0022721996065229177,
-0.0002742602373473346,
0.025545651093125343,
-0.010295581072568893,
0.02720055542886257,
0.011013511568307877,
-0.032947149127721786,
0.042377129197120667,
-0.03074977733194828,
-0.0394173301756382,
-0.013584201224148273,
-0.030716735869646072,
0.03892839699983597,
0.022355400025844574,
-0.07983427494764328,
0.06401613354682922,
-0.03123706765472889,
-0.028261136263608932,
0.02334771305322647,
-0.03325227275490761,
-0.027813343331217766,
0.021242743358016014,
-0.04110138863325119,
0.038898445665836334,
-0.005395387299358845,
-0.016059180721640587,
0.04575258493423462,
0.03561500832438469,
0.001399688539095223,
0.011515666730701923,
0.036021675914525986,
0.00590352900326252,
-0.02261248044669628,
-0.010658621788024902,
-0.04261114448308945,
0.048013340681791306,
-0.026735110208392143,
-0.005992566235363483,
-0.007392399944365025,
-0.020616669207811356,
0.010907177813351154,
-0.016671309247612953,
-0.0211455337703228,
-0.07847408950328827,
-0.04368174448609352,
-0.013921420089900494,
0.018795711919665337,
0.05468406155705452,
-0.0416741818189621,
0.0343022346496582,
0.0076514920219779015,
0.053541675209999084,
-0.003652130952104926,
-0.04418335482478142,
0.006601153407245874,
-0.024999916553497314,
-0.03465581312775612,
-0.01419246755540371,
-0.05597331374883652,
-0.0020751182455569506,
-0.027037005871534348,
-0.04644320532679558,
0.013941646553575993,
0.010149585083127022,
0.018680419772863388,
0.010983066633343697,
0.025193175300955772,
-0.024343742057681084,
0.07040280848741531,
0.0163472481071949,
0.05105463042855263,
0.0039854287169873714,
0.029124418273568153,
0.13167251646518707,
0.04023987799882889,
0.02990804985165596,
-0.02300848998129368,
0.03180957958102226,
-0.014838959090411663,
-0.0033646521624177694,
-0.028644224628806114,
0.053054824471473694,
0.020444847643375397,
0.014782045036554337,
0.02540692687034607,
0.049900878220796585,
0.030065884813666344,
0.022755127400159836,
0.03771495074033737,
-0.04673875868320465,
-0.03776102885603905,
0.03170629218220711,
0.012194152921438217,
0.005530354101210833,
-0.02586355060338974,
-0.05077867954969406,
-0.021832821890711784,
0.010575731284916401,
0.02819494903087616,
-0.0048921313136816025,
-0.019012806937098503,
0.046397045254707336,
0.016724176704883575,
-0.023857368156313896,
0.003988369833678007,
0.027823571115732193,
0.013580618426203728,
-0.029480475932359695,
0.0028490498661994934,
0.005276800598949194,
-0.021382227540016174,
0.006150045897811651,
0.022165348753333092,
0.013579696416854858,
0.005744210910052061,
-0.04069610685110092,
0.03451988846063614,
-0.013459528796374798,
0.01673453487455845,
0.01888698898255825,
0.006695329677313566,
-0.05169689282774925,
0.0031135869212448597,
-0.013481180183589458,
0.02252095751464367,
0.012255385518074036,
-0.021189255639910698,
-0.035514574497938156,
-0.0261484794318676,
0.021730884909629822,
-0.0032486587297171354,
-0.048376329243183136,
-0.013086948543787003,
0.017306013032794,
0.011465450748801231,
0.03910576179623604,
0.0042571029625833035,
0.00012880116992164403,
0.03841591626405716,
-0.02761886455118656,
0.023791659623384476,
0.022503316402435303,
0.01193267572671175,
-0.04467849060893059,
0.023783350363373756,
-0.05160730332136154,
-0.047043170779943466,
0.006244725547730923,
0.005286623723804951,
0.0305879395455122,
0.015016118064522743,
-0.002250911667943001,
0.005125035531818867,
-0.04908257722854614,
0.029328826814889908,
-0.011932998895645142,
-0.030456500127911568,
-0.024842187762260437,
-0.02378455549478531,
0.006530581042170525,
0.03434237465262413,
-0.03217511624097824,
0.02112698182463646,
-0.004757452756166458,
0.023817278444767,
0.031004291027784348,
-0.0495053194463253,
-0.02108790911734104,
0.02757239155471325,
-0.003994988277554512,
-0.026524195447564125,
-0.03130641579627991,
0.044271692633628845,
0.03622802719473839,
0.03260928764939308,
0.01374801155179739,
0.046915095299482346,
-0.003988065756857395,
-0.01653391867876053,
-0.0025472668930888176,
-0.02199135348200798,
-0.017627160996198654,
-0.0002552713267505169,
-0.006118335295468569,
0.006154798436909914,
-0.011477150954306126,
-0.014134928584098816,
0.0054765501990914345,
0.008179466240108013,
0.020120849832892418,
-0.01907351426780224,
-0.04014158621430397,
-0.004236713983118534,
0.00158509926404804,
0.012014652602374554,
0.026979900896549225,
-0.00858716107904911,
0.036171287298202515,
-0.01431734673678875,
-0.030869798734784126,
-0.030982986092567444,
0.0055006444454193115,
-0.005114687141031027,
-0.0018348078010603786,
0.01578894630074501,
0.007595350034534931,
-0.0001505418331362307,
-0.04712539166212082,
-0.026550600305199623,
0.007465221453458071,
0.040714193135499954,
-0.02657143399119377,
-0.02744731679558754,
0.025265807285904884,
-0.032680075615644455,
-0.03850769251585007,
-0.001681824796833098,
0.014486826956272125,
0.022337384521961212,
0.0074135418981313705,
0.04606698080897331,
-0.039756424725055695,
0.07653672993183136,
-0.06798985600471497,
-0.01177897211164236,
0.018466981127858162,
-0.005584514234215021,
0.02294003590941429,
-0.01392571721225977,
-0.0017174406675621867,
-0.03573348745703697,
0.006009821780025959,
-0.0011105824960395694,
0.02369457669556141,
0.0021759308874607086,
-0.011801148764789104,
-0.014223592355847359,
-0.009542929008603096,
0.04076707363128662,
0.04406289756298065,
0.04239174723625183,
-0.012213081121444702,
0.02142099291086197,
-0.02650645561516285,
-0.022239340469241142,
0.03338797017931938,
0.024875979870557785,
-0.05615973845124245,
-0.04069503769278526,
-0.007313999347388744,
-0.04811227694153786,
0.0490039624273777,
-0.052237238734960556,
0.030450738966464996,
0.00873541459441185,
-0.03851889818906784,
0.01872025616466999,
-0.007026216015219688,
-0.050197552889585495,
-0.044633518904447556,
-0.029486220329999924,
-0.04320194944739342,
0.08897843211889267,
0.0595896914601326,
0.017094817012548447,
0.020269129425287247,
-0.029513325542211533,
-0.005266226828098297,
-0.016197171062231064,
-0.03717470169067383,
0.017850467935204506,
0.0016519572818651795,
-0.03797030821442604,
0.04159269854426384,
0.016750114038586617,
-0.05630394071340561,
0.002031972398981452,
-0.037441033869981766,
-0.020054107531905174,
-0.0059255147352814674,
0.013382183387875557,
-0.017048455774784088,
0.019672712311148643,
0.04279197007417679,
-0.007648560218513012,
-0.024860940873622894,
0.049977872520685196,
0.02199181541800499,
-0.006056897342205048,
-0.032144371420145035,
0.02220059558749199,
0.03708347678184509,
-0.011262698099017143,
-0.074752077460289,
0.03128869831562042,
-0.014038627967238426,
-0.016415419057011604,
0.006729223299771547,
0.01579134538769722,
0.026500150561332703,
-0.04216811805963516,
-0.008479533717036247,
-0.0005369342979975045,
0.008242039009928703,
0.016602156683802605,
0.02002018131315708,
0.011499565094709396,
-0.0034207659773528576,
-0.020042555406689644,
-0.025569569319486618,
-0.018833909183740616,
0.01637008599936962,
-0.03905927389860153,
-0.04133117198944092,
-0.013442235067486763,
0.015217999927699566,
-0.016817236319184303,
-0.00043383543379604816,
-0.003227907232940197,
-0.05347512662410736,
0.03529012203216553,
0.0246446393430233,
0.053884491324424744,
-0.005067628808319569,
-0.07383334636688232,
-0.014478355646133423,
-0.04387666657567024,
0.01597212813794613,
-0.03550584614276886,
-0.013447160832583904,
-0.03802742063999176,
-0.05419035255908966,
-0.04691492021083832,
0.005327716935425997,
0.025405138731002808,
0.03010588511824608,
-0.002995296148583293,
-0.00956149585545063,
-0.012097771279513836,
0.0016691259806975722,
-0.02095109596848488,
0.015065908432006836,
-0.0005175804835744202,
-0.02736864797770977,
-0.012653563171625137,
0.006975894793868065,
0.00021723838290199637,
0.013879689387977123,
0.05056137964129448,
-0.012943345122039318,
0.031044960021972656,
-0.004674047231674194,
-0.005291473586112261,
0.02350516803562641,
0.013590555638074875,
-0.037586528807878494,
0.07011716812849045,
-0.03840361163020134,
-0.002692863577976823,
0.007156808860599995,
-0.010643292218446732,
-0.06405921280384064,
0.028647881001234055,
0.024701600894331932,
-0.03911814093589783,
-0.03857727348804474,
-0.017845304682850838,
0.0017831356963142753,
-0.042547546327114105,
0.014396930113434792,
0.046386152505874634,
-0.033916622400283813,
-0.023775693029165268,
0.03944166749715805,
0.03195829316973686,
0.04227745532989502,
-0.030960841104388237,
0.016324777156114578,
0.006036235950887203,
-0.023877086117863655,
0.0071629006415605545,
0.04045626521110535,
0.039265166968107224,
0.031955916434526443,
0.010649784468114376,
0.00942857563495636,
-0.01905440166592598,
-0.01177813671529293,
0.010948266834020615,
0.02238091453909874,
-0.013090858235955238,
-0.037096500396728516,
0.0666942223906517,
-0.0386483371257782,
0.037461958825588226,
0.009823858737945557,
-0.0017549515468999743,
0.09045717865228653,
-0.03957119584083557,
-0.008083002641797066,
-0.02853010967373848,
0.02919311821460724,
-0.03337695449590683,
-0.0023534027859568596,
0.04565328359603882,
0.06287132948637009,
-0.0487002395093441,
0.01413899939507246,
-0.01725492626428604,
-0.015408453531563282,
0.0462384857237339,
-0.03909989818930626,
0.003119455883279443,
-0.004430919885635376,
-0.02230583131313324,
-0.021894296631217003,
0.023765603080391884,
-0.053958531469106674,
-0.009031773544847965,
0.00035228667547926307,
0.01540157850831747,
0.026602476835250854,
0.027160603553056717,
-0.041982609778642654,
-0.004517437890172005,
0.016063092276453972,
-0.020619414746761322,
-0.059389062225818634,
-0.0387139655649662,
-0.00253670453093946,
-0.008582312613725662,
0.009989272803068161
] |
<p>It strikes me that the recent announcement of data from BICEP2 contains two really Big Deals:</p>
<ul>
<li>the first evidence of gravitational waves</li>
<li>the first evidence of inflation.</li>
</ul>
<p>Is there also a third?</p>
<ul>
<li>the first observation that will require quantum gravity to explain?</li>
</ul>
<p>Will the BICEP2 data, or data from any other experiment, require quantum gravity to explain? (I'm thinking here of other unexplained phenomena, like dark matter, etc )</p>
<p><strong>Update, two days after OP:</strong></p>
<p>Today Lawrence Krauss, Alan Guth, and John Kovac appeared on NPR's Science Friday. Krauss called the event a triple discovery, and a trifecta, providing first direct evidence of all three of these things. Guth said that he agreed. But I understand all the comments and answers; it seems what constitutes "direct evidence" is in the eye of the beholder.</p>
| 7,596 |
[
-0.03358497470617294,
-0.028540784493088722,
-0.005992914084345102,
-0.03222726657986641,
0.046355411410331726,
0.012774406932294369,
0.009071795269846916,
-0.024322889745235443,
-0.0018156807636842132,
-0.0549062117934227,
0.030455075204372406,
0.03686443343758583,
0.037438903003931046,
-0.010895125567913055,
0.01885833777487278,
0.022377289831638336,
0.01678316667675972,
-0.009177307598292828,
0.0039972299709916115,
-0.02899227850139141,
-0.013030868954956532,
0.00705809285864234,
0.005917927250266075,
0.023190833628177643,
0.0017930767498910427,
0.006405015476047993,
0.023524651303887367,
0.03109615109860897,
0.0015147029189392924,
0.04890979453921318,
-0.015151807107031345,
-0.057447582483291626,
-0.037831731140613556,
-0.0036297885235399008,
0.019766172394156456,
0.007800054270774126,
-0.012445631437003613,
-0.0015464391326531768,
0.0031732607167214155,
0.018359635025262833,
-0.04618976637721062,
0.011725472286343575,
-0.029165176674723625,
-0.013790708035230637,
-0.0501876138150692,
0.0005964763113297522,
0.007326872553676367,
0.002092011971399188,
0.04169305041432381,
-0.014398962259292603,
0.04996743053197861,
0.0001487212721258402,
-0.0022912498097866774,
-0.016024518758058548,
-0.015039791353046894,
-0.017781725153326988,
0.07043188065290451,
0.07092192769050598,
0.02265520952641964,
-0.03931330516934395,
-0.0009679804788902402,
0.024246931076049805,
-0.02241574041545391,
0.00661983247846365,
-0.039053235203027725,
0.05685240402817726,
0.00797929149121046,
-0.027379509061574936,
-0.001048198901116848,
-0.01172681339085102,
0.008298019878566265,
0.005609711166471243,
0.07701189070940018,
0.0029886863194406033,
-0.02004084549844265,
0.0008004331029951572,
0.00022839715529698879,
-0.029354924336075783,
0.03860089182853699,
0.0272973645478487,
-0.00952892005443573,
0.002650352194905281,
-0.005894011352211237,
0.08494649082422256,
0.055849842727184296,
0.020508568733930588,
0.07947222143411636,
-0.03308829665184021,
-0.015931876376271248,
0.02806125394999981,
-0.015131188556551933,
-0.018127374351024628,
0.042069025337696075,
-0.00923413410782814,
-0.016842100769281387,
-0.007977873086929321,
-0.00020948391465935856,
0.03997534140944481,
-0.0033792320173233747,
-0.007473134435713291,
0.018291296437382698,
0.0023840826470404863,
-0.008717511780560017,
0.10452796518802643,
0.018534190952777863,
-0.007683564443141222,
-0.004689344204962254,
0.01578606851398945,
-0.05641220510005951,
-0.012248394079506397,
-0.03264934942126274,
0.016228996217250824,
-0.02702718786895275,
0.020412711426615715,
0.005043697543442249,
-0.02264488860964775,
-0.016470732167363167,
0.016598990187048912,
0.03831728175282478,
0.050286564975976944,
0.08534727245569229,
0.003469051094725728,
0.018444115296006203,
-0.04882220923900604,
-0.012377258390188217,
0.041595153510570526,
0.05475538223981857,
-0.04801568388938904,
-0.03185071796178818,
0.02703029289841652,
0.015375714749097824,
0.04330574721097946,
-0.027413224801421165,
-0.020907949656248093,
0.007611841894686222,
-0.02834748663008213,
-0.12099221348762512,
-0.06632108241319656,
0.05216292664408684,
0.014851373620331287,
-0.032635994255542755,
-0.065059594810009,
0.025879938155412674,
0.027490468695759773,
0.06319426745176315,
-0.005187577102333307,
0.009340265765786171,
-0.06309423595666885,
0.019396955147385597,
-0.013539241626858711,
-0.05646421015262604,
-0.02049091085791588,
-0.0014446526765823364,
-0.06899041682481766,
-0.010585079900920391,
-0.04978542774915695,
-0.021381311118602753,
0.019894273951649666,
0.018157044425606728,
-0.028066903352737427,
0.08118700981140137,
0.00233199680224061,
0.00392830790951848,
-0.00976485200226307,
-0.04104037582874298,
0.0007081221556290984,
0.06756187230348587,
0.014341769739985466,
-0.06326276808977127,
0.06706685572862625,
0.023486599326133728,
0.047727108001708984,
0.04529935494065285,
0.02688823826611042,
0.01269901916384697,
-0.053335268050432205,
-0.024224024266004562,
0.0007634913781657815,
0.008093488402664661,
-0.006939588580280542,
-0.015421305783092976,
-0.009387956000864506,
-0.010830284096300602,
-0.018255416303873062,
-0.009179328568279743,
0.036165107041597366,
-0.02843218669295311,
-0.027351856231689453,
0.05920473858714104,
-0.03996134176850319,
-0.0025661138352006674,
-0.029167914763092995,
-0.03508441150188446,
-0.008484887890517712,
-0.02819647081196308,
0.02201158180832863,
0.030681319534778595,
0.016728559508919716,
-0.052801713347435,
-0.039607610553503036,
0.03189074248075485,
0.03202349692583084,
0.018444813787937164,
0.009886466898024082,
0.02649342454969883,
0.04364204779267311,
0.016431448981165886,
-0.017418408766388893,
-0.044503193348646164,
-0.011416865512728691,
-0.002780772978439927,
0.032340358942747116,
-0.011192417703568935,
0.006361276376992464,
-0.03549264743924141,
0.042642299085855484,
0.009466282092034817,
0.009001287631690502,
-0.02626470848917961,
0.03877924010157585,
-0.07498743385076523,
0.0462208092212677,
0.005166180431842804,
-0.022878076881170273,
-0.004713236354291439,
0.02155759185552597,
0.012546109966933727,
0.006568551063537598,
0.007476114667952061,
-0.025342749431729317,
-0.06940694898366928,
-0.02656705304980278,
0.017775991931557655,
0.05995588004589081,
-0.012692127376794815,
0.024055015295743942,
0.018153075128793716,
0.029794618487358093,
-0.035281822085380554,
0.01866348646581173,
-0.0010579308727756143,
-0.0100083127617836,
0.005667340476065874,
0.026178495958447456,
0.006675675045698881,
0.00520349433645606,
0.04958333447575569,
0.03361702710390091,
0.00207925820723176,
-0.013570459559559822,
-0.022004300728440285,
-0.001170654664747417,
-0.01187401544302702,
0.0376741997897625,
-0.002707570092752576,
-0.0311549324542284,
0.03795122355222702,
-0.0360167995095253,
-0.0021374113857746124,
0.021638119593262672,
-0.0019797906279563904,
-0.032268039882183075,
-0.034943610429763794,
-0.010723342187702656,
-0.023930244147777557,
0.025158824399113655,
-0.055022239685058594,
-0.009114858694374561,
0.03989404812455177,
-0.058455176651477814,
-0.004144194070249796,
-0.009730210527777672,
-0.017983803525567055,
-0.01887979544699192,
0.00619718711823225,
-0.020013010129332542,
0.0015786081785336137,
0.012761864811182022,
-0.05970826745033264,
-0.06890405714511871,
0.010977206751704216,
-0.00430282624438405,
-0.0019760082941502333,
0.04727098345756531,
-0.019980086013674736,
0.05132391303777695,
-0.08085279166698456,
0.0022597641218453646,
0.020401455461978912,
-0.014288896694779396,
0.011744093149900436,
0.014872992411255836,
0.01065509207546711,
-0.05059318244457245,
-0.0102531174197793,
-0.014466632157564163,
0.04128693416714668,
-0.045305754989385605,
-0.030462851747870445,
0.04034070298075676,
-0.019197355955839157,
-0.049419473856687546,
-0.023433756083250046,
0.013073761016130447,
-0.005728745833039284,
0.036997344344854355,
0.021523723378777504,
0.013513048179447651,
-0.026978546753525734,
0.04648638889193535,
-0.0061442237347364426,
-0.025584131479263306,
0.019548863172531128,
-0.03366868570446968,
-0.09075988829135895,
0.03767184540629387,
0.00572188850492239,
0.042896807193756104,
-0.058086976408958435,
-0.009129419922828674,
0.02430957742035389,
0.025198785588145256,
-0.00470105791464448,
-0.017437541857361794,
0.02968316525220871,
-0.009771794080734253,
0.00940382108092308,
0.009922889061272144,
-0.021476145833730698,
-0.02327807806432247,
0.05583149567246437,
0.023903220891952515,
0.02335219271481037,
0.008568746969103813,
0.03279449790716171,
-0.014637400396168232,
-0.0029863875824958086,
0.02145233191549778,
0.01492617093026638,
0.02771199680864811,
0.06519202888011932,
-0.021547282114624977,
0.018579356372356415,
-0.015907596796751022,
-0.01559169590473175,
0.0044534471817314625,
-0.004977100528776646,
0.062026020139455795,
0.04317206144332886,
0.021144559606909752,
-0.059939414262771606,
0.01614639349281788,
0.026122193783521652,
-0.022534925490617752,
0.004198894370347261,
-0.0010321136796846986,
0.040543876588344574,
0.003441596869379282,
0.017669174820184708,
0.02611749805510044,
0.04778618365526199,
-0.014488132670521736,
-0.022825872525572777,
-0.017308583483099937,
-0.017253821715712547,
0.009169752709567547,
-0.0016017124289646745,
0.0010901280911639333,
0.019530318677425385,
0.05419838801026344,
0.03953522443771362,
-0.0011417187051847577,
-0.016759062185883522,
-0.028018519282341003,
-0.027515675872564316,
0.0018726657144725323,
0.009593219496309757,
0.010830015875399113,
-0.0003275604685768485,
0.0398898720741272,
-0.003441818291321397,
-0.0084611177444458,
-0.003916630987077951,
-0.01495685987174511,
-0.08523424714803696,
-0.007558326702564955,
-0.04230889305472374,
0.040739722549915314,
0.024410441517829895,
-0.026755239814519882,
-0.003755047917366028,
-0.027882328256964684,
-0.02033638395369053,
-0.02444561943411827,
-0.011421884410083294,
-0.06059280410408974,
0.002414389280602336,
-0.03890388086438179,
-0.047411009669303894,
0.049852125346660614,
-0.0032887866254895926,
0.07223722338676453,
0.0046960460022091866,
0.0061775995418429375,
0.03517518565058708,
-0.022895226255059242,
0.0020052434410899878,
-0.00379618676379323,
0.024443315342068672,
-0.033595580607652664,
0.03887326270341873,
-0.00148451654240489,
0.007998778484761715,
-0.006002647336572409,
0.019219163805246353,
0.047749005258083344,
0.04399723932147026,
-0.01209232583642006,
-0.019467568024992943,
-0.03876401111483574,
-0.03886718302965164,
-0.017887931317090988,
-0.0014368705451488495,
0.06261517107486725,
0.020436275750398636,
0.019853945821523666,
0.04443207383155823,
0.025659825652837753,
-0.0018041386501863599,
0.050887804478406906,
0.05365197733044624,
-0.030777104198932648,
-0.020674197003245354,
-0.04079573228955269,
-0.06963785737752914,
-0.0015975937712937593,
-0.035240378230810165,
0.014274093322455883,
0.021951019763946533,
-0.04331690073013306,
0.02225051261484623,
0.030405603349208832,
-0.012230279855430126,
-0.013836043886840343,
0.0009371344349347055,
0.002734229201450944,
0.03849678114056587,
-0.027267176657915115,
0.006477746181190014,
-0.02951114811003208,
0.048319850116968155,
0.03876708075404167,
-0.003519737860187888,
-0.043004587292671204,
-0.07036573439836502,
0.03425819054245949,
0.032552119344472885,
0.044231560081243515,
-0.00006535810825880617,
0.006194393150508404,
-0.047011420130729675,
-0.017770951613783836,
0.01505073718726635,
-0.03618495166301727,
0.028442183509469032,
-0.01916409283876419,
-0.008506029844284058,
-0.017623716965317726,
-0.0010602398542687297,
-0.0030699505005031824,
0.023394357413053513,
-0.013738622888922691,
-0.026978954672813416,
0.007813837379217148,
0.010403997264802456,
0.004403363447636366,
0.024192815646529198,
0.0011839015642181039,
0.009713506326079369,
0.03081783652305603,
-0.019936148077249527,
0.0010683443397283554,
-0.003317404305562377,
-0.029446518048644066,
-0.10448344051837921,
-0.003346574492752552,
-0.027427824214100838,
-0.04322364181280136,
0.07604403048753738,
-0.02578815631568432,
-0.06085917726159096,
0.008076634258031845,
0.014842701144516468,
-0.018221361562609673,
0.015776975080370903,
-0.020917091518640518,
0.03041214309632778,
0.013365975581109524,
0.03680415451526642,
0.02551678940653801,
0.007823674008250237,
-0.007388990838080645,
0.02675679326057434,
0.0088181272149086,
0.00047196951345540583,
-0.02852383628487587,
0.02488921582698822,
0.0002072829520329833,
0.011313908733427525,
-0.04261964559555054,
0.023507989943027496,
-0.012261321768164635,
-0.012251082807779312,
-0.006190392188727856,
-0.05090384557843208,
-0.019096584990620613,
0.02497982233762741,
-0.010709823109209538,
0.007023356389254332,
-0.058319222182035446,
0.04211937636137009,
-0.027510078623890877,
-0.030221648514270782,
0.010961363092064857,
0.009925318881869316,
-0.02033896930515766,
0.02998964861035347,
-0.010919036343693733,
0.02462378516793251,
-0.007813272066414356,
0.022274544462561607,
0.014924862422049046,
-0.008660491555929184,
0.015236631967127323,
-0.00885152816772461,
-0.0006838144036009908,
0.014649087563157082,
-0.05124356225132942,
-0.028267698362469673,
-0.01604699157178402,
-0.0009228391572833061,
0.01991913840174675,
-0.04080640524625778,
-0.00745368329808116,
0.03787810355424881,
0.0426042266190052,
-0.05863902345299721,
-0.005286675412207842,
0.029935644939541817,
0.0314188189804554,
0.015513000078499317,
-0.007295787334442139,
-0.01989307440817356,
-0.03575153648853302,
-0.017852751538157463,
-0.010814102366566658,
0.042679253965616226,
0.010616215877234936,
-0.026966745033860207,
0.062258169054985046,
0.030489694327116013,
0.049067068845033646,
0.01841059885919094,
-0.028864188119769096,
0.00788560789078474,
0.01889302395284176,
-0.002565424656495452,
0.042072560638189316,
0.028055213391780853,
-0.003994051832705736,
-0.05003438889980316,
-0.06756298989057541,
-0.038878533989191055,
-0.012854558415710926,
-0.055829066783189774,
0.012393482960760593,
0.05253816768527031,
-0.005850527435541153,
0.005906966049224138,
-0.06294134259223938,
0.02337263524532318,
-0.024166429415345192,
0.019110627472400665,
-0.023081474006175995,
-0.00115493917837739,
0.02447829768061638,
-0.03781804442405701,
0.03332614526152611,
-0.011698095127940178,
-0.012574875727295876,
-0.025217672809958458,
0.033203404396772385,
0.016793472692370415,
-0.04121822491288185,
0.012669049203395844,
-0.015360759571194649,
0.004680405370891094,
-0.035230521112680435,
0.018254844471812248,
0.02795867621898651,
-0.00024790805764496326,
-0.04257378354668617,
-0.0004256204701960087,
-0.00016572482127230614,
-0.014055321924388409,
0.05690299719572067,
0.005018303636461496,
0.06013396382331848,
0.010491041466593742,
-0.028078701347112656,
0.012163977138698101,
-0.003996972925961018,
0.01046706736087799,
0.006165347993373871,
0.018637225031852722,
0.01935487799346447,
-0.06107025220990181,
-0.03378424048423767,
0.022951563820242882,
0.03284749761223793,
0.0061979228630661964,
0.00801141932606697,
0.032552313059568405,
0.03817947581410408,
0.028164170682430267,
-0.04883334040641785,
-0.03409520909190178,
0.03278310224413872,
-0.01599600538611412,
0.020492063835263252,
-0.001096693449653685,
-0.042119454592466354,
0.025212792679667473,
0.023960677906870842,
-0.0008383666863664985,
-0.02027880772948265,
-0.05221126228570938,
-0.09301476925611496,
0.015017575584352016,
0.011883102357387543,
0.04952589049935341,
-0.0007065503741614521,
-0.0344189889729023,
0.047399524599313736,
0.04814102128148079,
-0.014179512858390808,
0.01011918019503355,
-0.09767677634954453,
-0.02509324997663498,
0.006623946595937014,
-0.007542119827121496,
0.08578959852457047,
-0.023656224831938744,
-0.041553299874067307,
0.0222382303327322,
0.0019600216764956713,
0.008738790638744831,
0.031561192125082016,
0.011392876505851746,
-0.04555874690413475,
0.058160725980997086,
-0.030386783182621002,
-0.01625330001115799,
-0.01659940369427204,
0.021885491907596588,
0.14055763185024261,
0.04874887689948082,
0.009940763004124165,
-0.041429635137319565,
0.043333496898412704,
0.01661042310297489,
0.026352645829319954,
0.0027854316867887974,
0.010424590669572353,
-0.011130313389003277,
0.01652912236750126,
-0.006765342783182859,
0.056014370173215866,
0.010096825659275055,
-0.014625582844018936,
0.040340978652238846,
-0.020958637818694115,
-0.02355884574353695,
0.026585537940263748,
0.02390628308057785,
0.0432046502828598,
-0.017109420150518417,
-0.03959072381258011,
0.017770245671272278,
-0.03280629217624664,
0.007828173227608204,
0.027423139661550522,
-0.021323537454009056,
0.018652494996786118,
0.01598941907286644,
-0.009852838702499866,
-0.020875299349427223,
-0.0023168721236288548,
0.009256168268620968,
-0.039593908935785294,
0.061116572469472885,
0.01266967412084341,
-0.029625235125422478,
0.07646312564611435,
-0.0005830990266986191,
-0.0011986789759248495,
-0.03780266270041466,
-0.0007752226083539426,
0.024982701987028122,
-0.030778083950281143,
-0.0074342177249491215,
0.002468026475980878,
0.028765540570020676,
-0.03582008555531502,
-0.0028527064714580774,
-0.028363602235913277,
-0.04077484458684921,
0.002029115566983819,
-0.030846625566482544,
-0.028605585917830467,
-0.0003918372676707804,
-0.010078110732138157,
-0.025023171678185463,
-0.029645981267094612,
-0.017774876207113266,
0.023633496835827827,
0.009306838735938072,
0.033282533288002014,
0.00321185146458447,
0.019054943695664406,
-0.0024124961346387863,
0.0017823608359321952,
0.05514420568943024,
0.011266859248280525,
0.007347640581429005,
-0.036416925489902496,
-0.030272578820586205,
-0.08365059643983841,
-0.003837035736069083,
-0.038116324692964554,
-0.0015090900706127286,
0.024761971086263657,
0.015644432976841927,
-0.016706909984350204,
-0.02499467320740223,
-0.0052330382168293,
-0.014176320284605026,
-0.01924045942723751,
0.03284958004951477,
-0.014987807720899582,
0.016191063448786736,
0.006321595050394535,
0.030443498864769936,
-0.034389011561870575,
0.027533862739801407,
0.011003538966178894,
0.03556234762072563,
0.021226704120635986,
-0.04781298339366913,
0.03366054967045784,
0.010555649176239967,
-0.005683916620910168,
0.0028801506850868464,
-0.08531662076711655,
0.02429303713142872,
-0.016098229214549065,
0.028009522706270218,
0.04397443309426308,
-0.007292379625141621,
-0.045093897730112076,
0.0010407164227217436,
0.024544283747673035,
-0.010721023194491863,
0.012724943459033966,
-0.02774246223270893,
0.014009927399456501,
-0.038063377141952515,
-0.03662950545549393,
-0.016022279858589172,
0.013306275010108948,
-0.00038064768887124956,
0.01023666188120842,
-0.05482938140630722,
0.029485497623682022,
0.01168820634484291,
0.033516645431518555,
-0.03989548981189728,
0.003195391735062003,
-0.06612956523895264,
0.00814897008240223,
0.001410776050761342,
-0.0174223892390728,
0.002277624560520053,
0.0387532003223896,
-0.027335990220308304,
-0.02981429360806942,
0.014937488362193108,
0.016218597069382668,
-0.03998991847038269,
-0.005972587503492832,
0.018040932714939117,
-0.01643964648246765,
-0.002001618267968297,
0.03688235208392143,
-0.020618291571736336,
0.0006249310681596398,
-0.036798588931560516,
-0.02498377114534378,
0.05942755192518234,
-0.025174899026751518,
0.015191060490906239,
0.041633084416389465,
-0.020113321021199226,
-0.014178325422108173,
0.028780747205018997,
-0.034846171736717224,
0.006463697180151939,
0.0033014004584401846,
0.0011629046639427543,
-0.014073522761464119,
0.017616087570786476,
0.0028671363834291697,
-0.002615925157442689,
-0.034268949180841446,
0.037665896117687225,
0.016370585188269615,
0.021264949813485146,
0.0021852818317711353,
-0.009688016027212143,
-0.02308065816760063,
-0.007821592502295971,
-0.026857109740376472,
-0.008713148534297943,
0.02398749813437462,
0.033369556069374084,
-0.11117125302553177,
0.03441935032606125,
0.013542125932872295,
0.03131962567567825,
-0.0568401962518692,
-0.0006566981319338083,
0.007799409795552492,
0.0002621894236654043,
0.00835959892719984,
-0.05168667063117027,
0.07051815092563629,
0.0006928651127964258,
-0.016120821237564087,
0.03471434488892555,
-0.041195426136255264,
-0.02932741865515709,
-0.01349874958395958,
0.021228265017271042,
-0.03479625657200813,
0.021942758932709694,
0.03895216062664986,
0.03472932428121567,
0.002697310410439968,
0.032440606504678726,
0.00028738591936416924,
0.00950853992253542,
0.005799123086035252,
0.01878502033650875,
0.008237922564148903,
-0.010482336394488811,
0.1045788899064064,
-0.010863611474633217,
-0.008630913682281971,
0.03727317973971367,
0.002311021089553833,
0.015893811360001564,
-0.025672534480690956,
-0.043930329382419586,
0.013178018853068352,
0.019380399957299232,
0.012009301222860813,
-0.02327403426170349,
-0.001497904653660953,
0.02534029446542263,
0.030387574806809425,
0.06588651239871979,
0.00973250437527895,
-0.015433818101882935,
0.014074637554585934,
-0.016511324793100357,
-0.003893996588885784,
-0.0319695807993412,
0.0017851181328296661,
0.04452001675963402,
0.000994437956251204,
0.03444389998912811,
-0.00919090211391449,
-0.007969224825501442,
-0.0007255279342643917,
-0.07509316504001617,
-0.00998848956078291,
0.026018114760518074,
0.038805700838565826,
-0.034435901790857315,
0.005523107014596462,
-0.020839421078562737,
0.012951801531016827,
-0.008996148593723774,
-0.04032285511493683,
-0.02486620657145977,
-0.07202178984880447,
-0.01912063919007778,
-0.0018634535372257233,
0.03736300393939018,
0.0006853717495687306,
-0.02594945952296257,
-0.013569960370659828,
0.05732879042625427,
-0.011646881699562073,
0.05029863491654396,
-0.013105551712214947,
-0.02063886448740959,
-0.0065360479056835175,
-0.08250926434993744,
0.02359551191329956,
0.04169854149222374,
0.017585203051567078,
-0.0037637948989868164,
-0.023863183334469795,
-0.0008508951868861914,
-0.018983568996191025,
0.03581227734684944,
-0.029029978439211845,
-0.008874436840415001,
0.01134619489312172,
-0.009358244948089123,
-0.016564885154366493,
-0.030734699219465256,
-0.01675146259367466,
-0.022688187658786774,
0.008930927142500877,
0.0020254922565072775,
-0.004824360366910696,
0.018009111285209656,
0.009220419451594353,
0.03150305151939392,
0.011045838706195354,
0.02214680425822735,
-0.003147738054394722,
0.009289400652050972,
0.05692952126264572,
-0.01405616570264101,
-0.004634076729416847,
0.039362650364637375,
-0.017463751137256622,
0.0038798870518803596,
0.01506742648780346,
-0.04259666055440903,
-0.012296441942453384,
0.059675831347703934,
0.02045384794473648,
-0.027532195672392845,
-0.030405614525079727,
0.014008963480591774,
0.014923910610377789,
-0.03923765569925308,
-0.016320738941431046,
0.00129663513507694,
-0.003738590283319354,
0.0011883450206369162,
0.03319019451737404,
0.0026561070699244738,
0.0492837056517601,
0.009542688727378845,
0.00715660210698843,
0.016589786857366562,
0.0015508531359955668,
-0.010905194096267223,
0.009396103210747242,
0.06387358158826828,
0.059441473335027695,
-0.012538356706500053,
0.02498544752597809,
-0.026164637878537178,
-0.0034199405927211046,
0.0282280370593071,
0.051022667437791824,
-0.025579582899808884,
-0.01872210018336773,
0.018814677372574806,
0.012122239917516708,
0.02433313988149166,
-0.020639777183532715,
-0.00021954995463602245,
0.05751414969563484,
0.024403702467679977,
-0.007905946113169193,
0.008273836225271225,
0.011345446109771729,
0.0275383573025465,
0.010496878065168858,
0.010952790267765522,
0.023465655744075775,
0.0006720402743667364,
0.0335020050406456,
-0.02133479155600071,
0.014632323756814003,
0.007908099330961704,
-0.015095734968781471,
0.006445285398513079,
-0.013874690048396587,
-0.007366144564002752,
0.034242406487464905,
-0.009087225422263145,
-0.019904619082808495,
-0.05278858542442322,
0.033056214451789856,
0.035644639283418655,
-0.0283021442592144,
-0.04922455549240112,
-0.021197263151407242,
-0.02237304486334324,
0.060454271733760834,
-0.01729828678071499,
0.003248360240831971,
-0.05537213012576103,
0.047524210065603256,
0.004671939183026552,
-0.02992541715502739
] |
<p>Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d? </p>
| 7,597 |
[
0.044414203613996506,
0.0179048553109169,
0.006913702003657818,
-0.04761846736073494,
-0.0018495689146220684,
0.005665676202625036,
-0.048715293407440186,
-0.026352910324931145,
-0.0000475953784189187,
-0.061894066631793976,
0.06513645499944687,
0.029214635491371155,
0.04444146901369095,
0.03059236891567707,
0.004663668107241392,
0.03717096149921417,
-0.0021920776925981045,
-0.02823435701429844,
-0.031380798667669296,
-0.01741270162165165,
0.04187934845685959,
-0.03863510116934776,
-0.01812395639717579,
0.04696047678589821,
-0.03517625480890274,
0.01242403220385313,
0.024103103205561638,
0.026058074086904526,
0.07214152812957764,
0.025814155116677284,
-0.016819901764392853,
-0.0899992287158966,
0.03907780349254608,
-0.00992020033299923,
0.03548852354288101,
-0.022772300988435745,
-0.020454734563827515,
-0.038867902010679245,
0.0024545337073504925,
0.06786802411079407,
-0.025471225380897522,
-0.022659162059426308,
-0.0029667795170098543,
0.01536573376506567,
-0.008328086696565151,
0.029325664043426514,
0.008585033938288689,
-0.0413946807384491,
0.0691097304224968,
-0.07131731510162354,
0.05866552144289017,
-0.016849124804139137,
0.04212068021297455,
-0.02827172912657261,
0.03451558202505112,
0.028374282643198967,
0.05391784757375717,
0.020108072087168694,
-0.0023897031787782907,
-0.03854101523756981,
0.005159907508641481,
-0.04868186265230179,
0.0327363982796669,
-0.02731214091181755,
-0.033504683524370193,
0.019614242017269135,
0.017996378242969513,
-0.06941819190979004,
0.04742558300495148,
0.05185920000076294,
-0.00964561477303505,
-0.024397503584623337,
0.022228557616472244,
-0.028118900954723358,
0.02299678511917591,
-0.04558805748820305,
-0.01078304834663868,
0.02520936168730259,
0.0023005506955087185,
0.0056768497452139854,
-0.013586267828941345,
0.02041628398001194,
0.014491037465631962,
0.034243255853652954,
-0.033459387719631195,
-0.016855107620358467,
0.045769404619932175,
0.016816237941384315,
-0.01936313882470131,
0.01780497282743454,
0.02050301805138588,
0.00886993482708931,
0.06432494521141052,
0.0023721347097307444,
-0.06464239954948425,
0.02040274068713188,
0.021247154101729393,
0.03797377273440361,
0.000038068672438384965,
-0.021875571459531784,
0.017623964697122574,
-0.010380348190665245,
0.031106719747185707,
0.06720960885286331,
-0.015467053279280663,
0.011308723129332066,
-0.00876232236623764,
-0.024555474519729614,
-0.010697108693420887,
-0.020496467128396034,
-0.02420775778591633,
0.03694033622741699,
-0.009115629829466343,
0.00633525475859642,
0.015109860338270664,
-0.03522682189941406,
0.02784818969666958,
0.019939957186579704,
0.03925621882081032,
0.052923426032066345,
-0.0008680592873133719,
-0.02888917364180088,
0.012402782216668129,
-0.001421581138856709,
-0.10970203578472137,
0.011267479509115219,
0.04828456789255142,
0.005153575912117958,
-0.04447907954454422,
0.03332408145070076,
0.012969703413546085,
-0.01838264986872673,
0.01925421878695488,
-0.015343640930950642,
0.053780172020196915,
-0.02142193727195263,
-0.10861105471849442,
-0.02217445895075798,
0.014792454428970814,
0.013336353935301304,
-0.009068857878446579,
-0.08315231651067734,
0.015123467892408371,
0.022304866462945938,
0.085544653236866,
0.024587541818618774,
0.023127645254135132,
-0.007669640239328146,
-0.008347875438630581,
0.026979733258485794,
-0.007273893803358078,
-0.06233584135770798,
0.013614988885819912,
-0.032665543258190155,
0.006557510234415531,
-0.007280978374183178,
-0.009712930768728256,
0.033839985728263855,
-0.026427235454320908,
0.006209095939993858,
0.019761836156249046,
-0.01593419723212719,
-0.00616334518417716,
0.04230206832289696,
-0.030308203771710396,
-0.045450128614902496,
0.051108840852975845,
-0.0072431378066539764,
0.011295025236904621,
0.06820318847894669,
-0.02433641441166401,
0.023891618475317955,
0.0011384572135284543,
0.04710513353347778,
0.0058122663758695126,
-0.011604804545640945,
-0.03372299298644066,
-0.0074980612844228745,
0.010642151348292828,
-0.01172773726284504,
-0.07759153097867966,
-0.006451180204749107,
0.02795969881117344,
0.03875725343823433,
-0.0055770049802958965,
0.05524447187781334,
-0.018975811079144478,
-0.023120131343603134,
0.012336243875324726,
-0.02113393321633339,
-0.028723038733005524,
-0.028493136167526245,
-0.00800079945474863,
-0.049098290503025055,
-0.025692176073789597,
0.026998354122042656,
0.023546388372778893,
-0.0003014635294675827,
-0.03984159603714943,
-0.02072521299123764,
-0.02401168830692768,
0.03463511914014816,
0.005958137568086386,
-0.013681317679584026,
0.035070616751909256,
0.05752381309866905,
-0.006981291808187962,
-0.015907054767012596,
0.012745048850774765,
-0.023290516808629036,
-0.0027404881548136473,
0.00426769582554698,
-0.01405185367912054,
0.027817394584417343,
0.010126665234565735,
-0.011856910772621632,
0.0013062716461718082,
0.010464404709637165,
-0.021357737481594086,
0.018967900425195694,
-0.005663234740495682,
0.07299637794494629,
0.03552919998764992,
-0.034238364547491074,
0.02409127540886402,
0.01571275107562542,
0.02827763371169567,
0.03975251317024231,
-0.006984087638556957,
-0.017713483422994614,
-0.036476559937000275,
-0.0019690319895744324,
0.0422818548977375,
-0.006745136342942715,
-0.010580654256045818,
-0.011732662096619606,
-0.0019671765621751547,
0.027192963287234306,
0.04700398072600365,
0.024747224524617195,
-0.05073162913322449,
-0.03840632736682892,
0.01929507963359356,
-0.012150908820331097,
-0.022157300263643265,
0.004314813297241926,
0.008865110576152802,
0.03293459862470627,
0.048814792186021805,
0.002515820087864995,
-0.04386954382061958,
0.08368649333715439,
-0.040046267211437225,
-0.014907121658325195,
0.024339277297258377,
-0.05789000168442726,
0.010569579899311066,
-0.03281746432185173,
0.03749991953372955,
0.021367022767663002,
-0.04413008317351341,
0.005336935166269541,
-0.00166880595497787,
-0.037259481847286224,
-0.015877146273851395,
0.014369509182870388,
-0.054943569004535675,
-0.03453105315566063,
0.03209761530160904,
0.0050621856935322285,
0.012112586759030819,
0.0050113145262002945,
0.0026863953098654747,
0.012215339578688145,
-0.0035311507526785135,
0.06506036221981049,
-0.004853296093642712,
0.028093013912439346,
-0.030869731679558754,
-0.028024686500430107,
-0.004245499614626169,
-0.07042931020259857,
0.05365830287337303,
0.014642739668488503,
-0.03189988434314728,
0.03774285316467285,
-0.0511750653386116,
-0.020475097000598907,
0.007883226498961449,
0.013492004945874214,
0.026964811608195305,
-0.0024725247640162706,
-0.017565671354532242,
-0.032282426953315735,
-0.023167084902524948,
-0.01874225214123726,
0.035533733665943146,
-0.01923230290412903,
0.005074643529951572,
0.02133353427052498,
0.00961292628198862,
0.006718792952597141,
-0.020982636138796806,
-0.012501755729317665,
-0.016180725768208504,
-0.00015347468433901668,
-0.025453777983784676,
0.05420716106891632,
-0.00520750880241394,
0.02414867840707302,
0.039460189640522,
-0.0184665285050869,
-0.02561754174530506,
-0.03372636437416077,
-0.047475021332502365,
0.040564149618148804,
-0.0111484844237566,
-0.003540398320183158,
-0.031144848093390465,
-0.019662385806441307,
0.05258942022919655,
-0.002710807602852583,
-0.031875450164079666,
0.002454891102388501,
0.00047070725122466683,
-0.036068301647901535,
-0.05134318768978119,
0.03437104821205139,
0.017717575654387474,
0.017054961994290352,
0.04344674199819565,
0.01322636567056179,
0.05443525314331055,
0.02445836365222931,
0.010418100282549858,
0.004709545057266951,
0.04104213789105415,
0.01346050389111042,
-0.013577086851000786,
0.05027441307902336,
-0.0049390471540391445,
-0.01838492415845394,
0.019703654572367668,
0.00034137399052269757,
0.008311288431286812,
0.00506550632417202,
-0.055311594158411026,
0.03745565563440323,
-0.025990653783082962,
0.01919453777372837,
0.0023666624911129475,
0.05640634149312973,
0.027702797204256058,
-0.01588139683008194,
0.0037855710834264755,
0.02877374365925789,
0.03570356220006943,
0.0010732762748375535,
0.0008619090658612549,
0.03674992918968201,
0.02308662235736847,
-0.040806762874126434,
-0.03137611225247383,
-0.0011703942436724901,
0.021769428625702858,
0.01546704676002264,
-0.04338747262954712,
-0.06289391219615936,
0.030925976112484932,
0.04741501435637474,
0.009566592052578926,
0.010493510402739048,
-0.0412120595574379,
0.017773490399122238,
-0.07649631053209305,
-0.0047462694346904755,
0.022971615195274353,
0.06553901731967926,
-0.017203541472554207,
0.03676896542310715,
0.015346507541835308,
0.032468538731336594,
-0.025738675147294998,
0.01885811984539032,
-0.0562259778380394,
-0.008799475617706776,
-0.015065464191138744,
0.033989861607551575,
0.003869513049721718,
-0.014674565754830837,
0.0005734587321057916,
-0.06209324672818184,
-0.05108011141419411,
-0.014302095398306847,
-0.012996213510632515,
-0.06619323045015335,
0.03363092988729477,
-0.020984768867492676,
0.029448481276631355,
-0.029766418039798737,
0.06914190202951431,
0.015544267371296883,
-0.007556343916803598,
-0.02138526551425457,
0.014446322806179523,
0.0031087729148566723,
-0.000864389177877456,
0.01210325863212347,
-0.010535148903727531,
0.02447379194200039,
0.011384021490812302,
0.07776462286710739,
-0.0032418023329228163,
-0.02318575046956539,
-0.011010952293872833,
0.028561653569340706,
0.06866513937711716,
0.0007773642428219318,
-0.033792831003665924,
0.013544877991080284,
-0.03851683437824249,
0.0060659185983240604,
-0.04184495657682419,
0.04988224431872368,
-0.020679155364632607,
0.01502146851271391,
0.05329233407974243,
-0.00818199198693037,
-0.039456263184547424,
0.03285416588187218,
0.056106481701135635,
0.029711227864027023,
-0.02708808146417141,
-0.04170354828238487,
-0.023762408643960953,
-0.021331630647182465,
-0.016302961856126785,
0.033993352204561234,
-0.014302105642855167,
-0.028980858623981476,
0.03153454512357712,
0.03111967071890831,
-0.023981085047125816,
-0.026087583974003792,
-0.005046671722084284,
-0.03442663699388504,
0.03430340066552162,
0.029329588636755943,
-0.024225613102316856,
-0.02813335508108139,
0.024948934093117714,
-0.02097739651799202,
0.022736597806215286,
0.0008367775590158999,
-0.055340662598609924,
0.01363430917263031,
0.05102013051509857,
0.05662405118346214,
-0.007274460978806019,
-0.007722843904048204,
-0.013938217423856258,
-0.0015447967452928424,
0.01945185847580433,
-0.030778540298342705,
0.028808150440454483,
-0.01241045631468296,
-0.03030279651284218,
-0.022013844922184944,
0.0009869169443845749,
-0.007500276435166597,
-0.0003108039090875536,
-0.01883433572947979,
0.015379470773041248,
-0.00875039678066969,
-0.002708357060328126,
0.011951860971748829,
0.011414132080972195,
0.002519182162359357,
0.004510608967393637,
0.004475846420973539,
0.021515047177672386,
0.005261275917291641,
0.06922804564237595,
0.0003938590525649488,
-0.07776737958192825,
-0.0033413683995604515,
0.008205803111195564,
-0.026481585577130318,
0.02356147952377796,
-0.04587782919406891,
-0.04530259966850281,
0.03449951857328415,
0.015533307567238808,
-0.00793661642819643,
-0.03502223640680313,
-0.03902233764529228,
0.024713575839996338,
0.03725782781839371,
-0.032896168529987335,
0.036637041717767715,
0.05713477358222008,
-0.021347586065530777,
0.013758094049990177,
-0.04250592365860939,
0.05118449404835701,
-0.011877422221004963,
0.035368382930755615,
-0.022506020963191986,
-0.015874002128839493,
-0.03324301913380623,
0.04195722937583923,
-0.034093815833330154,
0.042889565229415894,
-0.0017635877011343837,
-0.038424715399742126,
-0.03497667610645294,
0.0167909674346447,
0.020548267289996147,
-0.018679803237318993,
-0.016757715493440628,
-0.0252974983304739,
-0.0021495954133570194,
0.0024185997899621725,
-0.0105093689635396,
-0.011473712511360645,
-0.009733165614306927,
0.010226696729660034,
0.003743195440620184,
0.02132592163980007,
-0.05378027632832527,
-0.01813252456486225,
0.000411607907153666,
-0.04861323535442352,
0.031109267845749855,
-0.0047859144397079945,
-0.02433459274470806,
-0.010671544820070267,
-0.06426534801721573,
-0.0353461429476738,
0.01659427024424076,
0.004595926497131586,
-0.0040077632293105125,
-0.004874302539974451,
0.034390974789857864,
0.023418143391609192,
0.005984108429402113,
-0.06478023529052734,
-0.0494316928088665,
-0.003688371041789651,
0.001981366891413927,
-0.051939405500888824,
0.014852083288133144,
-0.004228142090141773,
-0.012438273057341576,
-0.01730840653181076,
0.025266915559768677,
0.041518040001392365,
-0.029799431562423706,
-0.011825202032923698,
0.033102795481681824,
-0.031028060242533684,
0.02647325024008751,
0.022068936377763748,
-0.05887361243367195,
-0.017325855791568756,
0.006916071753948927,
0.027751170098781586,
-0.0038955791387706995,
0.049615006893873215,
-0.02465006709098816,
-0.011639242991805077,
-0.04275217652320862,
-0.016151320189237595,
0.06267070770263672,
-0.024175303056836128,
0.0020241737365722656,
-0.015749720856547356,
0.04186197370290756,
0.013879621401429176,
0.000979857286438346,
-0.0036413399502635,
0.021703675389289856,
0.04134656488895416,
0.04077095910906792,
0.017767833545804024,
-0.04435510188341141,
-0.02354319952428341,
-0.01615288481116295,
0.03388866037130356,
0.0069246673956513405,
0.028969869017601013,
0.09218208491802216,
-0.0002976813120767474,
0.0053490158170461655,
0.02487836964428425,
-0.07147890329360962,
-0.020202573388814926,
-0.018818706274032593,
0.03178579360246658,
0.04618251696228981,
0.019844604656100273,
0.0017100522527471185,
-0.03380811959505081,
-0.027324937283992767,
0.0072785415686666965,
0.051994942128658295,
-0.000877100508660078,
0.01997664012014866,
0.03782592713832855,
0.01844005100429058,
0.0026329143438488245,
-0.009586254134774208,
-0.047960568219423294,
0.006304655224084854,
-0.0074892849661409855,
0.046784356236457825,
-0.01774057187139988,
-0.005874267313629389,
0.03130505234003067,
0.05037325993180275,
-0.024375231936573982,
0.037471260875463486,
0.05664435774087906,
0.025683773681521416,
0.0013507292605936527,
0.017517082393169403,
-0.027674920856952667,
0.04173818230628967,
-0.011817778460681438,
0.0380004458129406,
0.007939168252050877,
-0.007263106293976307,
0.06143956258893013,
0.017473677173256874,
0.04088371619582176,
-0.051225244998931885,
-0.011032240465283394,
-0.048740584403276443,
0.01816580444574356,
-0.016413409262895584,
-0.003466303925961256,
-0.03610658273100853,
0.02629234455525875,
0.03548097237944603,
-0.005633735563606024,
0.0214161965996027,
0.018319860100746155,
-0.03560701757669449,
0.015345384366810322,
-0.018080750480294228,
-0.041705407202243805,
0.01911664381623268,
-0.0019004690693691373,
-0.018967704847455025,
0.018185468390583992,
0.007532449439167976,
0.04349680244922638,
-0.014454135671257973,
0.008944717235863209,
-0.04763682931661606,
0.07070911675691605,
0.006294699385762215,
0.046231795102357864,
0.05900828167796135,
0.004989959765225649,
0.1391206979751587,
0.030387192964553833,
-0.01869221217930317,
-0.0691424161195755,
-0.024233223870396614,
-0.01060942467302084,
0.04410563036799431,
0.0016811081441119313,
-0.03231459856033325,
-0.004437778610736132,
0.007455815095454454,
0.024845518171787262,
0.03574732691049576,
0.013771613128483295,
-0.02354421652853489,
0.0002070726186502725,
-0.020165013149380684,
-0.04115134850144386,
0.007046725135296583,
-0.01696198061108589,
-0.002819530665874481,
0.004821871407330036,
-0.053729843348264694,
0.004283239599317312,
0.02066005952656269,
0.029860224574804306,
-0.061987604945898056,
-0.011969526298344135,
0.019607312977313995,
0.01547723077237606,
-0.03546435385942459,
-0.0055743190459907055,
-0.038507964462041855,
0.004908881615847349,
-0.04777112230658531,
0.0015758548397570848,
0.03844984248280525,
0.02144644968211651,
-0.009592912159860134,
0.021257750689983368,
0.011642413213849068,
-0.0059542348608374596,
0.03044535592198372,
0.028048137202858925,
-0.04938977211713791,
-0.006075696554034948,
-0.0013893491122871637,
-0.008900847285985947,
-0.006058311555534601,
0.007405928336083889,
-0.00613587349653244,
-0.004542423877865076,
0.0027957900892943144,
-0.0280729029327631,
-0.01542484201490879,
-0.00938896182924509,
0.027994271367788315,
-0.04190434142947197,
-0.027856260538101196,
-0.03470746800303459,
-0.009434067644178867,
-0.02184603549540043,
0.042481523007154465,
-0.020391585305333138,
-0.018139952793717384,
0.04335173964500427,
0.016369862481951714,
0.04890289902687073,
0.020852793008089066,
-0.019886374473571777,
0.008744502440094948,
0.006260822061449289,
-0.021089358255267143,
0.0033101497683674097,
0.01669776625931263,
-0.021545838564634323,
0.04967586696147919,
-0.029690323397517204,
-0.03133736550807953,
0.0061121308244764805,
-0.03464753180742264,
0.025646869093179703,
-0.03555437922477722,
-0.034573741257190704,
-0.02250264771282673,
0.030788106843829155,
0.021551646292209625,
0.012923509813845158,
-0.001519380952231586,
0.0105513921007514,
-0.010441558435559273,
-0.027032751590013504,
0.004788484890013933,
-0.04750211909413338,
0.02858143113553524,
0.02337389625608921,
-0.022271936759352684,
0.016340594738721848,
-0.027721133083105087,
-0.007651880849152803,
0.04955042898654938,
-0.0075032333843410015,
-0.019186556339263916,
0.03987543657422066,
-0.0363183431327343,
-0.020206524059176445,
0.011260082945227623,
-0.03507710248231888,
0.015392209403216839,
0.004288953263312578,
-0.03928964585065842,
-0.07008004933595657,
-0.0012680814834311604,
-0.027903886511921883,
-0.014193299226462841,
0.011621386744081974,
0.030385958030819893,
-0.030034804716706276,
-0.01374019030481577,
-0.02878362312912941,
0.013759853318333626,
-0.024585971608757973,
-0.006779592949897051,
-0.043213821947574615,
-0.0020793078001588583,
0.03371492400765419,
0.012934340164065361,
-0.02498740889132023,
-0.015721431002020836,
0.05681786686182022,
0.011746019124984741,
0.021763790398836136,
0.05182117223739624,
-0.03247809782624245,
0.0022309895139187574,
0.033767133951187134,
0.00664547411724925,
0.06831858307123184,
-0.009579995647072792,
-0.012431666254997253,
0.007399661932140589,
0.010818269103765488,
-0.03506151959300041,
0.030937695875763893,
-0.03068418614566326,
0.0233398899435997,
0.01950043812394142,
-0.010955850593745708,
-0.030582604929804802,
0.01507998164743185,
-0.028227748349308968,
-0.013318627141416073,
0.010173488408327103,
-0.005295147653669119,
-0.0007045053062029183,
-0.05010341852903366,
-0.04508698359131813,
-0.0007328237406909466,
-0.010967923328280449,
0.028932126238942146,
0.02553298883140087,
-0.039669424295425415,
0.017625069245696068,
-0.009645619429647923,
-0.003729818155989051,
0.0031146318651735783,
0.04560261592268944,
0.0005538769182749093,
0.009646528400480747,
0.017710838466882706,
-0.022742414847016335,
0.05925664305686951,
-0.036325860768556595,
0.002805137075483799,
-0.048477139323949814,
-0.027508242055773735,
0.015704981982707977,
-0.02589980699121952,
0.016598744317889214,
-0.02218487299978733,
0.019874608144164085,
0.06894087046384811,
-0.07992786169052124,
0.039096273481845856,
-0.00004806532888324,
-0.0591975674033165,
-0.03475933149456978,
-0.014326876029372215,
-0.0440450944006443,
0.0549694187939167,
0.015444901771843433,
0.04746612533926964,
0.03999331220984459,
0.002560380147770047,
-0.026702865958213806,
-0.029339134693145752,
-0.033671919256448746,
0.013290753588080406,
-0.009232196025550365,
-0.03523152321577072,
0.0484459213912487,
-0.011339791119098663,
-0.03086945042014122,
0.017661238089203835,
0.004362661391496658,
-0.008079399354755878,
-0.021451281383633614,
0.024065159261226654,
-0.03264664486050606,
0.029057253152132034,
-0.002701766323298216,
-0.032409727573394775,
-0.025184908881783485,
-0.017586344853043556,
0.028114089742302895,
0.04569453373551369,
-0.0035652942024171352,
0.02520579844713211,
-0.02615763247013092,
-0.020589901134371758,
-0.009743274189531803,
0.05566893517971039,
0.013230135664343834,
-0.024520205333828926,
-0.017561350017786026,
0.009901098906993866,
0.019800830632448196,
-0.07783745974302292,
0.004680384416133165,
-0.03131375461816788,
-0.006490551400929689,
0.0007232973002828658,
-0.030678095296025276,
0.0051655275747179985,
0.05934997648000717,
-0.0046090856194496155,
-0.009918434545397758,
0.013526306487619877,
-0.0035609069745987654,
-0.054311949759721756,
-0.04867744818329811,
-0.008180761709809303,
0.03163493052124977,
0.014294011518359184,
-0.010274880565702915,
-0.02707832306623459,
-0.010781307704746723,
0.032383523881435394,
0.032676201313734055,
0.016818886622786522,
-0.030020106583833694,
-0.03412274271249771,
0.009118994697928429,
-0.057976339012384415,
0.024398891255259514,
-0.019120484590530396,
-0.01182080153375864,
-0.03176381066441536,
-0.03045310638844967,
0.01595913991332054,
0.006008072290569544,
0.049684565514326096,
0.049384281039237976,
0.026333218440413475,
-0.031272001564502716,
-0.02097013033926487,
0.02668508142232895,
-0.011811332777142525,
-0.019122373312711716,
-0.05032454431056976,
-0.029985463246703148,
0.006695568561553955,
-0.00176060211379081,
-0.04857015237212181,
0.04165701940655708,
0.03804745897650719,
0.015798024833202362,
0.02627425454556942,
-0.054323967546224594,
-0.0015936529962345958,
0.04849384352564812,
0.03781255707144737,
-0.012035032734274864,
0.03975395858287811,
-0.013536158949136734,
-0.013680090196430683,
0.04111374169588089,
-0.007514150347560644,
-0.031094519421458244,
0.03769884258508682,
-0.012198861688375473,
0.022645441815257072,
0.014751343987882137,
-0.002656861674040556,
0.06515657901763916,
-0.0508120134472847,
-0.016124578192830086,
0.018310299143195152,
-0.03042445331811905,
0.02156502567231655,
0.04423316940665245,
0.005945960059762001,
0.002359997481107712,
-0.011152669787406921,
0.02063036896288395,
0.011796032078564167,
0.0009795124642550945,
0.029588324949145317,
0.04776608198881149,
0.0005841710953973234,
0.02216220088303089,
0.03299172967672348,
0.028237847611308098,
-0.024082979187369347,
0.030204473063349724,
0.03226315975189209,
0.0006215771427378058,
-0.028119249269366264,
0.024476131424307823,
0.029412351548671722,
-0.026406191289424896,
0.040958553552627563,
0.029168520122766495,
-0.03549113869667053,
0.07404611259698868,
-0.042241014540195465,
0.020364968106150627,
-0.03245740011334419,
0.006482607685029507,
-0.021584030240774155,
-0.026837540790438652,
0.004338375758379698,
0.030125044286251068,
-0.018608223646879196,
-0.028292272239923477,
-0.0012010664213448763,
-0.007181176915764809,
0.043402668088674545,
-0.05922732129693031,
0.05489923432469368,
0.0003553046262823045,
-0.002756980014964938,
-0.027442412450909615,
0.011135222390294075,
-0.05211711674928665,
-0.004043111111968756,
0.04346480593085289,
0.023556167259812355,
0.024248216301202774,
0.003879230236634612,
-0.012300831265747547,
-0.01733623817563057,
0.04138987883925438,
-0.0591745600104332,
-0.03946875408291817,
-0.016320712864398956,
0.010023106820881367,
-0.02291300520300865,
-0.0029907869175076485
] |
<p>Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two bodies after a hard sphere collision given $\vec{p}_1$ and $\vec{p}_2$. I have a solution (both for elastic and inelastic collisions), but I wonder whether or not it's correct.</p>
<p>FYI, here are my solutions for elastic, hard-sphere collisions:</p>
<p>$$
\vec{p}_{1f} = \vec{p}_1 + 2\frac{\left(m_1\vec{p}_2 - m_2\vec{p}_1\right)\circ \hat{r}}{m_1 + m_2}\hat{r} \\
\vec{p}_{2f} = \vec{p}_2 - 2\frac{\left(m_1\vec{p}_2 - m_2\vec{p}_1\right)\circ \hat{r}}{m_1 + m_2}\hat{r}
$$</p>
<p>wher $\hat{r}$ is in the direction of the "hard sphere" (i.e. the unit vector connecting the two radii of the spheres). You can see that my formulation trivially conserved momentum--the question is whether or not it conserves energy as well.</p>
| 7,598 |
[
-0.061710648238658905,
0.012372358702123165,
-0.045458052307367325,
-0.020348040387034416,
-0.017814703285694122,
-0.0035083312541246414,
-0.014870337210595608,
0.011265015229582787,
0.023448187857866287,
-0.012231909669935703,
0.018087150529026985,
0.023416725918650627,
0.06606726348400116,
0.027491221204400063,
0.03727579861879349,
-0.026220330968499184,
0.008177965879440308,
-0.012648483738303185,
0.020282112061977386,
-0.03685387969017029,
0.014047443866729736,
-0.016221096739172935,
0.031009074300527573,
-0.028240351006388664,
-0.007201064378023148,
0.048398666083812714,
0.002048057969659567,
-0.04670966789126396,
-0.0035870305728167295,
0.03274684399366379,
-0.0006392230861820281,
-0.0015134926652535796,
0.023045700043439865,
0.018689192831516266,
0.005352525971829891,
0.006498896051198244,
-0.02712852507829666,
-0.03756794333457947,
-0.00470212334766984,
0.022765936329960823,
-0.06255007535219193,
-0.014756539836525917,
-0.02158195897936821,
0.0468984916806221,
-0.008738300763070583,
0.030963288620114326,
0.020572643727064133,
0.010436083190143108,
0.028264885768294334,
-0.07079245150089264,
0.09589280188083649,
0.023599868640303612,
0.06963890790939331,
-0.01389043964445591,
-0.0363897830247879,
-0.02395535446703434,
0.04975638538599014,
0.08397851139307022,
0.029259756207466125,
-0.06297218799591064,
0.01566317491233349,
-0.01925465278327465,
-0.033095311373472214,
0.021111037582159042,
-0.009904671460390091,
0.011895006522536278,
-0.010364275425672531,
-0.014028308913111687,
0.025327043607831,
-0.0030451917555183172,
0.0365896113216877,
0.007452924270182848,
0.04754773899912834,
-0.025996511802077293,
0.02790754847228527,
-0.013034162111580372,
0.049742441624403,
-0.0026723037008196115,
0.012347939424216747,
0.04521634802222252,
0.004667765460908413,
0.005721260327845812,
0.04019126668572426,
0.05166194587945938,
0.0020816221367567778,
0.023279614746570587,
0.048423267900943756,
-0.015672896057367325,
0.007426547352224588,
0.05027482658624649,
0.0044050333090126514,
0.004195809829980135,
0.05636164918541908,
-0.019734038040041924,
-0.012729311361908913,
0.043728385120630264,
-0.010016607120633125,
0.0820309966802597,
-0.039395324885845184,
-0.03560623899102211,
-0.022457130253314972,
-0.025170646607875824,
0.015915963798761368,
0.06929199397563934,
-0.006246868055313826,
-0.040357429534196854,
-0.061130084097385406,
-0.009677817113697529,
-0.020797787234187126,
-0.014427992515265942,
-0.06265546381473541,
0.001431588432751596,
-0.02582775615155697,
-0.02247278392314911,
0.015791162848472595,
-0.0460730716586113,
-0.003742448752745986,
-0.01404122356325388,
0.033725593239068985,
0.07460656762123108,
0.032909292727708817,
-0.01647990010678768,
0.0055056349374353886,
-0.04868270456790924,
-0.06804277747869492,
0.0028667813166975975,
0.03449937328696251,
0.014461931772530079,
-0.04027969762682915,
0.025151701644062996,
0.01742541231215,
-0.030055319890379906,
-0.005471564829349518,
-0.013833717443048954,
0.010533695109188557,
-0.036666564643383026,
-0.05068723112344742,
-0.038850702345371246,
0.056199219077825546,
-0.029933234676718712,
-0.01922336220741272,
-0.10553669184446335,
0.0016867120284587145,
0.023654690012335777,
0.08197373151779175,
-0.0036374833434820175,
0.0008802302763797343,
0.01002467144280672,
0.0820942372083664,
0.002564819762483239,
-0.019534539431333542,
-0.04386879503726959,
0.018501468002796173,
-0.0248691588640213,
-0.017255131155252457,
-0.0784342810511589,
0.019399937242269516,
0.007532609160989523,
0.03927244246006012,
0.022668100893497467,
0.03345818445086479,
-0.02104378305375576,
-0.0012063172180205584,
-0.0023477922659367323,
0.02467007376253605,
-0.0031782309524714947,
0.03103165328502655,
0.011579376645386219,
0.021685408428311348,
0.009104542434215546,
0.020465051755309105,
0.012283560819923878,
-0.0019722753204405308,
0.004254719242453575,
0.037036918103694916,
-0.02671993151307106,
-0.01074146293103695,
-0.02072320692241192,
-0.015032701194286346,
-0.01060236431658268,
-0.031732749193906784,
-0.03718145191669464,
-0.020780591294169426,
-0.035331424325704575,
0.008033093065023422,
0.03592478111386299,
0.026767661795020103,
-0.032086774706840515,
-0.03195762634277344,
-0.001587962731719017,
-0.028444940224289894,
-0.07860815525054932,
0.03661853075027466,
-0.030511917546391487,
-0.018412228673696518,
0.05208553001284599,
0.01728842779994011,
0.028726695105433464,
0.013827966526150703,
-0.049196530133485794,
-0.011639551259577274,
0.003291256492957473,
-0.008177082985639572,
0.0170527845621109,
-0.03829016163945198,
0.04512237384915352,
0.026421643793582916,
-0.009402556344866753,
0.011205986142158508,
0.008375316858291626,
-0.01743386685848236,
-0.009632767178118229,
0.006143583916127682,
0.01801731251180172,
0.026746103540062904,
-0.004145433660596609,
0.013235267251729965,
-0.04707704484462738,
0.01937549002468586,
0.012393583543598652,
-0.03644374758005142,
0.06678001582622528,
0.03968549147248268,
0.016402695327997208,
0.019341858103871346,
0.051029693335294724,
-0.0008512166677974164,
0.011778402142226696,
0.023544276133179665,
-0.03626745194196701,
-0.01881634257733822,
-0.018756501376628876,
0.01045312825590372,
0.08045536279678345,
-0.056619055569171906,
0.026620041579008102,
0.05398919805884361,
0.03465781360864639,
0.026946624740958214,
0.012398166581988335,
-0.008184051141142845,
-0.06669412553310394,
0.03624860197305679,
0.015446994453668594,
-0.012675674632191658,
-0.009413165971636772,
-0.03555877134203911,
0.009541197679936886,
0.027126731351017952,
0.013795757666230202,
-0.02802136354148388,
0.001497549470514059,
0.002428696257993579,
-0.003496449440717697,
0.03047935850918293,
-0.012155728414654732,
0.005485740955919027,
0.020396320149302483,
0.05459928140044212,
0.040886227041482925,
0.01831437461078167,
-0.013116744346916676,
-0.047867413610219955,
-0.00006782753916922957,
-0.0064622992649674416,
0.009262746199965477,
0.024676216766238213,
0.004856274928897619,
0.003134056692942977,
-0.042323555797338486,
-0.00888422504067421,
0.019261201843619347,
-0.02933206595480442,
0.008292797952890396,
0.00018281242228113115,
-0.024645963683724403,
0.01606178842484951,
0.03240122273564339,
-0.01672448217868805,
-0.013854146003723145,
0.0013740425929427147,
-0.0433771088719368,
-0.014082493260502815,
0.011034851893782616,
-0.05440188944339752,
0.0232646893709898,
-0.04267743602395058,
0.012416533194482327,
0.06529036164283752,
-0.003784865839406848,
0.002758821938186884,
0.029274245724081993,
0.010606919415295124,
-0.06124088540673256,
-0.0013253951910883188,
-0.0373680554330349,
0.029477665200829506,
-0.020152315497398376,
0.017930150032043457,
0.06048361584544182,
-0.0022827843204140663,
-0.04638839513063431,
-0.005232258699834347,
-0.01373720820993185,
-0.04845845699310303,
-0.03814973682165146,
-0.008418852463364601,
0.0296309981495142,
-0.0004023166256956756,
0.00656081410124898,
0.04279497638344765,
-0.026268212124705315,
-0.04280398413538933,
-0.041054703295230865,
-0.028366737067699432,
0.05086332559585571,
0.0001150187017628923,
0.03813043609261513,
-0.006402311846613884,
-0.025764236226677895,
0.05987334996461868,
0.0038427631370723248,
-0.01077413372695446,
-0.007220039609819651,
-0.0024467071052640676,
-0.016070129349827766,
-0.03095070645213127,
0.0006777132512070239,
0.025269348174333572,
-0.002653943607583642,
0.008165501058101654,
0.02786019816994667,
-0.021234901621937752,
0.026861870661377907,
0.00006337555532809347,
0.0073796710930764675,
0.02729821763932705,
0.03013487718999386,
-0.017065387219190598,
0.028250765055418015,
0.0038116301875561476,
-0.001104938448406756,
0.011109508574008942,
-0.0043659270741045475,
0.04139651358127594,
0.024779340252280235,
-0.08193659037351608,
0.009863090701401234,
-0.01072408352047205,
0.009194145910441875,
-0.011730421334505081,
0.0027181736659258604,
0.014300059527158737,
-0.022243492305278778,
-0.003476470010355115,
0.04734867066144943,
0.052083875983953476,
-0.04483902081847191,
0.029047340154647827,
0.04650773108005524,
0.05042733624577522,
0.011026203632354736,
-0.0370563380420208,
0.010008840821683407,
0.012561104260385036,
0.02674436941742897,
-0.024096138775348663,
-0.020105045288801193,
0.05267715826630592,
0.005283441860228777,
0.04101613536477089,
0.0045912242494523525,
-0.05620911717414856,
0.015855761244893074,
-0.07205390930175781,
0.026424510404467583,
-0.049103450030088425,
0.009047668427228928,
0.010968686081469059,
0.07949675619602203,
0.034117989242076874,
0.01772371307015419,
0.008845900185406208,
0.005313058849424124,
-0.0733073279261589,
0.018389714881777763,
-0.003934355452656746,
-0.021404115483164787,
-0.0035608718171715736,
-0.02478579804301262,
-0.033456478267908096,
-0.02014726586639881,
0.009672331623733044,
0.030583040788769722,
-0.007361530791968107,
-0.04798915982246399,
0.025585927069187164,
-0.06155163794755936,
-0.09284691512584686,
0.025646720081567764,
0.047445815056562424,
0.05398730933666229,
-0.01673676259815693,
0.06677499413490295,
0.06164323911070824,
-0.028723346069455147,
0.008002632297575474,
-0.04766245558857918,
0.007956639863550663,
0.008150313049554825,
0.002918550046160817,
0.003270382760092616,
0.04335848614573479,
0.02166556939482689,
0.010609573684632778,
0.006336251273751259,
0.035424333065748215,
-0.002046104520559311,
-0.011054723523557186,
-0.03995401784777641,
-0.060348089784383774,
-0.01474034134298563,
-0.0027263674419373274,
0.03335197642445564,
-0.009886634536087513,
-0.0024507457856088877,
0.033148620277643204,
0.01776767335832119,
-0.024745842441916466,
0.041098080575466156,
0.05342691391706467,
0.03289720043540001,
-0.018239865079522133,
-0.06310921907424927,
0.004232021514326334,
-0.005185309797525406,
-0.013958055526018143,
0.022840218618512154,
-0.014077347703278065,
-0.03286361321806908,
-0.01157597079873085,
0.02726125530898571,
0.021588081493973732,
-0.00991959497332573,
0.004151604138314724,
-0.037446144968271255,
0.00031940446933731437,
-0.023856092244386673,
-0.005741498898714781,
0.005650569684803486,
0.03879590332508087,
0.022344019263982773,
0.030672233551740646,
0.015589863993227482,
-0.04729731008410454,
0.0034797457046806812,
0.011954333633184433,
0.060926005244255066,
0.002013112884014845,
0.014951895922422409,
-0.034359224140644073,
-0.018520502373576164,
0.03865569457411766,
-0.0390021950006485,
0.01589488610625267,
-0.00024305976694449782,
-0.007431467529386282,
-0.010099194012582302,
0.0033122135791927576,
-0.08202258497476578,
0.004165899008512497,
-0.03089004196226597,
-0.019651638343930244,
-0.010664857923984528,
-0.03756556659936905,
-0.027757756412029266,
0.012551648542284966,
0.03427477926015854,
0.0370631143450737,
0.010542192496359348,
-0.014650210738182068,
-0.018144089728593826,
-0.0033672417048364878,
-0.008547293022274971,
-0.07171192020177841,
-0.012041110545396805,
-0.004466670099645853,
-0.04002850502729416,
0.07395489513874054,
-0.04437732324004173,
-0.049936648458242416,
0.044021397829055786,
0.010335667058825493,
0.016674796119332314,
0.02370937541127205,
-0.02171374298632145,
0.08443249017000198,
0.02296004816889763,
-0.03295779228210449,
0.03855035826563835,
0.00937094446271658,
-0.03755664825439453,
-0.04402121528983116,
-0.026732731610536575,
0.027050750330090523,
-0.01049572043120861,
-0.0003716417704708874,
-0.04084998369216919,
0.012296316213905811,
-0.03012886643409729,
0.027749821543693542,
0.02152024582028389,
0.01904226839542389,
-0.012441128492355347,
-0.020464567467570305,
-0.006477438844740391,
0.022128408774733543,
0.008691706694662571,
-0.007466965354979038,
0.01706911250948906,
0.011455625295639038,
0.01882311888039112,
0.0033925711177289486,
0.006119398400187492,
0.0013335385592654347,
-0.008392740041017532,
0.04563288763165474,
-0.029510168358683586,
0.050676655024290085,
-0.028908543288707733,
-0.011762849986553192,
-0.006902166176587343,
-0.03754068538546562,
0.0418851412832737,
0.0070284451358020306,
0.02354748360812664,
0.02954094484448433,
-0.03250804916024208,
-0.0016184706473723054,
0.015981405973434448,
0.002894078614190221,
0.011220487765967846,
-0.05555570125579834,
0.014014498330652714,
0.011538185179233551,
0.02276121824979782,
-0.05264204367995262,
-0.02677113004028797,
0.004328371025621891,
0.02173195406794548,
-0.015554573386907578,
-0.023422837257385254,
-0.0106149697676301,
-0.010544619522988796,
-0.039541859179735184,
0.012694512493908405,
0.035231150686740875,
-0.049499187618494034,
-0.0061591798439621925,
0.055935218930244446,
0.029362760484218597,
0.02947453036904335,
0.007411870639771223,
0.019924649968743324,
-0.007899008691310883,
0.016289716586470604,
-0.009952627122402191,
0.017236407846212387,
0.05362755060195923,
-0.01713368110358715,
-0.03157088905572891,
-0.006855951622128487,
-0.0189870186150074,
0.042688895016908646,
-0.017824169248342514,
0.014046397991478443,
0.037974242120981216,
-0.020935332402586937,
0.014270015992224216,
0.009448528289794922,
0.004835719708353281,
-0.04047005996108055,
0.04182755574584007,
-0.02331416867673397,
-0.030960220843553543,
-0.010525273159146309,
-0.024737803265452385,
0.024196553975343704,
-0.018320638686418533,
0.03186729922890663,
-0.016680048778653145,
0.05836205929517746,
-0.011929651722311974,
0.024413738399744034,
0.012101870961487293,
-0.00575428269803524,
0.041014473885297775,
-0.02332482300698757,
-0.05667419359087944,
-0.00012075745326001197,
0.008863041177392006,
-0.009577682241797447,
-0.058038823306560516,
-0.03025873936712742,
0.03581078723073006,
0.07479745894670486,
-0.023966170847415924,
0.021533289924263954,
0.025203855708241463,
0.03163899853825569,
-0.0321069061756134,
-0.03267918527126312,
0.013431035913527012,
0.001922636292874813,
-0.003878310089930892,
0.051719311624765396,
-0.014726979658007622,
0.017618786543607712,
0.03707099333405495,
0.03395552188158035,
-0.014954989776015282,
-0.005808067042380571,
0.01417460385710001,
0.002503818366676569,
0.010880731046199799,
-0.01170993223786354,
-0.007970097474753857,
0.04606499895453453,
-0.026014409959316254,
0.018441038206219673,
-0.0026348624378442764,
-0.04221818596124649,
0.06155640259385109,
0.025237224996089935,
0.015449333935976028,
-0.009819939732551575,
-0.0026161805726587772,
-0.0034215054474771023,
0.018306119367480278,
-0.014575762674212456,
-0.02324387989938259,
-0.027836110442876816,
-0.0026453209575265646,
0.03294255957007408,
0.007164898794144392,
0.005916389636695385,
-0.04135659709572792,
-0.04151269420981407,
-0.013474398292601109,
-0.04164915159344673,
-0.025047076866030693,
0.02682020142674446,
0.020328208804130554,
0.007973025552928448,
0.038109421730041504,
-0.018951155245304108,
0.01465259026736021,
-0.0022971807047724724,
-0.0034889760427176952,
-0.017513340339064598,
0.07598226517438889,
-0.004218119662255049,
-0.000014501942132483236,
-0.031224742531776428,
-0.001283438061363995,
0.1214459016919136,
0.05155399069190025,
0.02134878747165203,
-0.03971577063202858,
0.014995208010077477,
-0.020298466086387634,
-0.00847106333822012,
-0.027304669842123985,
0.0032762258779257536,
-0.010608739219605923,
-0.008150104433298111,
0.0008708644891157746,
0.07797737419605255,
0.012867200188338757,
-0.0315091647207737,
0.03724509850144386,
-0.04197769984602928,
-0.023348644375801086,
-0.01920253038406372,
0.016172662377357483,
-0.03352798521518707,
0.001590617815963924,
0.005742643494158983,
0.025173859670758247,
-0.03462455794215202,
-0.011928926222026348,
-0.027180258184671402,
-0.019125917926430702,
0.018425941467285156,
0.017682544887065887,
-0.01127584744244814,
0.027611935511231422,
-0.019715042784810066,
-0.021313665434718132,
0.0028603202663362026,
0.014710566028952599,
0.008634676225483418,
-0.03156676143407822,
0.026301514357328415,
-0.005461054388433695,
-0.0007728879572823644,
0.02754921466112137,
0.0384141243994236,
0.012446202337741852,
-0.04792991653084755,
0.004289248958230019,
-0.03642526641488075,
0.09671233594417572,
-0.02859274484217167,
0.016272282227873802,
-0.001759159262292087,
-0.03739580884575844,
0.02359098382294178,
-0.06937102973461151,
-0.0016984872054308653,
-0.01645587757229805,
0.03667103126645088,
-0.01278372760862112,
0.03818819671869278,
-0.04119584336876869,
0.00024965277407318354,
0.024538209661841393,
0.011143519543111324,
-0.03368593007326126,
-0.01854965090751648,
-0.011982354335486889,
-0.004383551888167858,
0.07805928587913513,
-0.0201179850846529,
0.0014444880653172731,
-0.059592243283987045,
0.003652130253612995,
-0.04113791510462761,
-0.026168273761868477,
0.010057874955236912,
0.03041328862309456,
0.03332706168293953,
0.008401172235608101,
-0.002188203390687704,
-0.03964073210954666,
-0.07985669374465942,
0.04240714758634567,
-0.02012317068874836,
-0.03416186571121216,
-0.04558698832988739,
-0.0075424592941999435,
-0.0022858786396682262,
0.044957440346479416,
-0.02006491832435131,
0.019640663638710976,
0.00015025165339466184,
0.06048310175538063,
0.007558588869869709,
-0.009528503753244877,
-0.04790070280432701,
0.022867858409881592,
-0.021853093057870865,
0.027375055477023125,
-0.00006485547055490315,
0.01470269076526165,
0.0014029494486749172,
0.002009679563343525,
0.022928107529878616,
0.01932498626410961,
-0.00909170601516962,
0.012909820303320885,
0.00862994883209467,
-0.03510881960391998,
-0.013123173266649246,
0.009862626902759075,
0.020910529419779778,
-0.018007908016443253,
0.011141384951770306,
-0.04598211497068405,
0.0008729474502615631,
-0.020729482173919678,
0.01622367464005947,
-0.05322575569152832,
0.018480820581316948,
-0.06426271796226501,
0.019124792888760567,
-0.04142754524946213,
0.03110419027507305,
-0.027946991845965385,
0.000450647174147889,
0.012862470000982285,
-0.0038833622820675373,
-0.01565374992787838,
0.04902147874236107,
-0.057138506323099136,
0.018152888864278793,
0.03513966128230095,
0.01739313080906868,
-0.0055562471970915794,
0.003982969094067812,
0.004246163181960583,
0.015488555654883385,
0.03992261737585068,
-0.035930830985307693,
-0.02664424479007721,
0.06156672164797783,
-0.012572054751217365,
-0.07222489267587662,
0.015565391629934311,
0.027334563434123993,
0.034333035349845886,
0.02757498249411583,
-0.01766856200993061,
-0.023685693740844727,
0.10779944062232971,
-0.013656663708388805,
-0.009928065352141857,
-0.0023374545853585005,
-0.05744944512844086,
-0.0059641399420797825,
-0.026238560676574707,
0.037012554705142975,
-0.02184915728867054,
0.009463383816182613,
0.04210282862186432,
0.011566710658371449,
-0.014563731849193573,
-0.00234214891679585,
-0.030357345938682556,
0.030174287036061287,
0.022410986945033073,
0.003729758784174919,
0.005615584552288055,
0.0174160897731781,
0.058375485241413116,
-0.026498893275856972,
-0.010452858172357082,
0.045213695615530014,
-0.022433258593082428,
-0.06579184532165527,
-0.014604680240154266,
-0.007908039726316929,
0.019186150282621384,
0.03652215749025345,
-0.0932500883936882,
0.025769753381609917,
0.014707316644489765,
-0.0807165652513504,
0.04581515118479729,
-0.0757424607872963,
-0.0005819525104016066,
-0.028820697218179703,
0.00430687889456749,
-0.017074117437005043,
0.02180708944797516,
0.007695182226598263,
0.050041090697050095,
0.042989715933799744,
0.02175239473581314,
-0.008898635394871235,
-0.013789481483399868,
-0.016680506989359856,
0.005783571861684322,
0.0016694363439455628,
-0.0021349138114601374,
0.09875497967004776,
-0.021382492035627365,
-0.03957539424300194,
0.011064312420785427,
-0.015884192660450935,
0.0196616780012846,
-0.015431081876158714,
0.015993570908904076,
-0.013148769736289978,
0.014923029579222202,
0.005149922799319029,
-0.006514324340969324,
0.021330706775188446,
0.003822714788839221,
0.023858798667788506,
-0.004848686046898365,
-0.022018736228346825,
0.006351449526846409,
0.00768233509734273,
-0.05126194655895233,
-0.004304652102291584,
0.023860884830355644,
-0.005558488890528679,
-0.021096276119351387,
-0.004247616045176983,
0.007797928526997566,
0.04880435764789581,
-0.01481324341148138,
0.028439050540328026,
-0.05969682335853577,
-0.008150371722877026,
0.001522001693956554,
0.007598450873047113,
-0.006898768246173859,
0.033974338322877884,
-0.011532055214047432,
-0.022636253386735916,
-0.007093365304172039,
-0.005668993107974529,
-0.025605030357837677,
-0.06547475606203079,
-0.0070521775633096695,
0.02303469367325306,
-0.006674867123365402,
-0.039563558995723724,
-0.034694854170084,
-0.016636062413454056,
0.026858627796173096,
0.017035305500030518,
0.035047270357608795,
0.010470695793628693,
-0.044971272349357605,
-0.009087638929486275,
-0.06712666898965836,
-0.0021646092645823956,
0.0204016100615263,
-0.015608783811330795,
-0.017066380009055138,
-0.017799893394112587,
0.006473965477198362,
0.0073951794765889645,
0.05223899334669113,
-0.009327366948127747,
-0.01632336899638176,
0.010059851221740246,
-0.02472628280520439,
0.013448347337543964,
-0.04454973340034485,
-0.022965077310800552,
-0.0377991646528244,
0.02890327386558056,
0.005531114526093006,
-0.0017546359449625015,
-0.0002818017383106053,
-0.00008786356193013489,
-0.01524271722882986,
-0.03271685913205147,
0.008107829838991165,
0.01989894174039364,
-0.06305422633886337,
0.01748824305832386,
-0.026219764724373817,
0.0029784042853862047,
0.07980795204639435,
-0.006735180504620075,
0.010105272755026817,
0.021880850195884705,
-0.0446820966899395,
-0.042223066091537476,
0.021968699991703033,
-0.0579742006957531,
-0.04606335982680321,
-0.014599503949284554,
0.0057265604846179485,
0.0482938177883625,
-0.04723638668656349,
-0.00654633529484272,
0.035293594002723694,
-0.01990164816379547,
-0.0365324430167675,
0.018682241439819336,
0.02472594939172268,
0.03763163462281227,
0.025925632566213608,
0.04362759366631508,
0.013671047985553741,
-0.054221078753471375,
-0.002692394657060504,
0.02726103365421295,
0.03842746838927269,
0.0035403440706431866,
0.007395637687295675,
0.008254793472588062,
-0.04390949010848999,
-0.0036234299186617136,
0.014870251528918743,
0.024769235402345657,
-0.017805343493819237,
-0.02513636089861393,
0.03424840793013573,
0.0025421606842428446,
0.026213238015770912,
-0.0058189136907458305,
-0.018503308296203613,
0.044994987547397614,
0.018483152613043785,
0.0006651020376011729,
-0.029526975005865097,
0.03153039142489433,
0.007932975888252258,
0.016859808936715126,
-0.020465321838855743,
0.031877551227808,
0.0044470843859016895,
-0.019488178193569183,
-0.04081326350569725,
-0.010957576334476471,
0.022936921566724777,
-0.014962765388190746,
-0.0032364327926188707,
-0.00010219983232673258,
0.027567846700549126,
-0.005352320149540901,
-0.005128172691911459,
0.008461618795990944,
-0.013230269774794579,
0.022115349769592285,
0.04618310183286667,
0.036950938403606415,
-0.04744143784046173,
0.033074818551540375,
-0.007798639126121998,
0.06544852256774902,
-0.05126297101378441,
-0.009635970927774906,
-0.004024679772555828,
0.029662344604730606,
0.014062752947211266,
0.00932459719479084
] |
<p>Being a grad student in math, and a rather pedantic one indeed, I was unable to accept many of the things taught to me in undergrad physics courses. I am now trying to learn the applications of geometry to string theory and the applications of probability theory, my main field, to statistical physics. Are there other prominent interfaces between abstract math and theoretical physics? </p>
<p>Where can I find these topics explored in a way that would be accepted by a mathematician? (I.e. every object mentioned is a legitimate object or logical statement in ZFC, and every nontrivial claim is proven, no use of unproven conjectures for anything but motivation, and wherever necessary to actually talk about physics of the real world, assumptions that link mathematical ideas (which are merely logical symbols and sets) to what they intend to model are stated in logically precise ways.)</p>
<p>In other words I am looking for a "Bourbaki" approach to physics, and wouldn't mind if the book started even as pedantically as to say, for instance, what a physical unit represents in set theory.</p>
| 185 |
[
0.0015006496105343103,
-0.04327670484781265,
0.018161969259381294,
-0.057300686836242676,
-0.009466597810387611,
0.02385219931602478,
0.01777767576277256,
-0.019026348367333412,
-0.013735965825617313,
-0.00571126164868474,
0.05725343897938728,
0.017114093527197838,
0.0372750498354435,
0.030181806534528732,
0.02540535293519497,
0.00044833659194409847,
-0.007965109311044216,
-0.02974417246878147,
-0.033629536628723145,
-0.03553194925189018,
0.04466238245368004,
0.010252807289361954,
0.013519464060664177,
0.01072020921856165,
-0.027555150911211967,
0.031561486423015594,
-0.008447873406112194,
0.010271161794662476,
0.014072222635149956,
0.0376749150454998,
-0.018945055082440376,
-0.042907796800136566,
0.013950292952358723,
0.032382406294345856,
0.028995025902986526,
0.02655620500445366,
0.0014258261071518064,
-0.0114854471758008,
0.017361940816044807,
-0.04118446260690689,
-0.026914522051811218,
-0.03800756856799126,
-0.014565180987119675,
0.025229420512914658,
-0.015504837967455387,
0.0225624181330204,
-0.025191180408000946,
-0.012878418900072575,
0.07028132677078247,
-0.06576430052518845,
0.05785786733031273,
0.016146432608366013,
0.031203359365463257,
0.059688858687877655,
0.022810479626059532,
0.00019331989460624754,
0.07963584363460541,
0.07008614391088486,
-0.008983698673546314,
-0.05370989069342613,
-0.015033095143735409,
-0.023643385618925095,
-0.004822746850550175,
-0.014136460609734058,
-0.06366250663995743,
0.017990263178944588,
-0.0019970571156591177,
-0.03765273094177246,
0.0457204133272171,
0.012992162257432938,
-0.03625844791531563,
0.042462173849344254,
0.03609307482838631,
0.021003153175115585,
0.015454363077878952,
0.009639544412493706,
-0.009325833059847355,
-0.03170185908675194,
0.030171414837241173,
0.03176440671086311,
-0.015660177916288376,
-0.003904501674696803,
-0.004207896534353495,
0.040262866765260696,
0.010304667986929417,
-0.019343756139278412,
0.05100655555725098,
-0.032850198447704315,
-0.05029096454381943,
0.026866013184189796,
-0.028833461925387383,
-0.026495065540075302,
0.025551745668053627,
-0.006529371719807386,
-0.055712975561618805,
0.02786688320338726,
-0.013408401049673557,
0.05045409873127937,
0.010559520684182644,
-0.010273873805999756,
0.013217882253229618,
-0.02746289223432541,
0.026411989703774452,
0.07076506316661835,
-0.006011165212839842,
-0.025379084050655365,
-0.005477785598486662,
0.009897568263113499,
0.00991569459438324,
-0.006201020907610655,
-0.004389535635709763,
0.05191894993185997,
-0.0037677388172596693,
0.021864542737603188,
0.018061963841319084,
-0.023118119686841965,
-0.01805032603442669,
-0.025202348828315735,
0.045441579073667526,
0.0674736425280571,
0.055927570909261703,
-0.0018400652334094048,
0.049781277775764465,
-0.046036284416913986,
-0.10169506072998047,
0.0006802478455938399,
0.055789604783058167,
-0.03284468129277229,
-0.04682805761694908,
0.020599188283085823,
0.004882680717855692,
0.010634347796440125,
0.017769651487469673,
0.027784962207078934,
0.033720243722200394,
-0.012182195670902729,
-0.07165317982435226,
-0.0477420873939991,
0.03325608745217323,
0.009117396548390388,
-0.028402160853147507,
-0.06144765391945839,
0.02232687920331955,
0.03568951413035393,
0.056738242506980896,
-0.0065224431455135345,
0.003877424169331789,
-0.0029912241734564304,
0.018010633066296577,
0.011756978929042816,
-0.017516257241368294,
-0.034747909754514694,
-0.007848993875086308,
-0.0401417538523674,
0.011767358519136906,
-0.05992455035448074,
0.01656418852508068,
0.024758918210864067,
0.01997561752796173,
-0.030322330072522163,
0.09238690137863159,
-0.038481127470731735,
-0.008879497647285461,
0.020417356863617897,
-0.013310007750988007,
0.012877494096755981,
0.061996832489967346,
-0.010925975628197193,
0.003371040103957057,
0.034458227455616,
0.004486226476728916,
0.01008160226047039,
0.03850401192903519,
0.023334350436925888,
0.05044708028435707,
-0.029654983431100845,
-0.005665387026965618,
0.045686013996601105,
-0.019164351746439934,
0.0007955948240123689,
-0.01879977062344551,
0.00008633431571070105,
-0.055640120059251785,
0.00030671924469061196,
-0.030237507075071335,
0.006941298022866249,
0.030453616753220558,
-0.03066358156502247,
0.02408675104379654,
-0.025763636454939842,
0.0009582836064510047,
-0.05626921355724335,
-0.005140884779393673,
-0.036189060658216476,
0.004395463969558477,
0.03655485436320305,
0.016265714541077614,
-0.0006623977678827941,
-0.0671137124300003,
-0.03557200729846954,
0.005623937584459782,
0.01838432252407074,
0.010781996883451939,
0.013899875804781914,
-0.018974078819155693,
0.004211137071251869,
0.029682889580726624,
-0.032302502542734146,
-0.025282232090830803,
-0.014676186256110668,
-0.04148790240287781,
0.008006497286260128,
-0.03077012486755848,
0.012469245120882988,
0.020764287561178207,
0.0005322393262758851,
0.03842274844646454,
-0.00935584120452404,
-0.001222469611093402,
0.044699616730213165,
-0.030172856524586678,
0.03793040290474892,
0.0202528927475214,
0.01244917418807745,
-0.008132914081215858,
0.061554599553346634,
0.033596720546483994,
0.003927432466298342,
0.017330197617411613,
0.005043383687734604,
-0.010207585990428925,
0.0023616524413228035,
0.05570979788899422,
0.035652510821819305,
-0.019267739728093147,
0.03612310811877251,
0.004111693240702152,
0.05400257930159569,
0.015368685126304626,
0.03179875761270523,
-0.06924548745155334,
-0.026909049600362778,
0.03307164087891579,
-0.04321485012769699,
0.02590138651430607,
0.00449818791821599,
0.006327277980744839,
0.026990855112671852,
-0.02234351448714733,
-0.018094560131430626,
-0.02456427365541458,
0.018741175532341003,
-0.007605917286127806,
0.023831982165575027,
-0.0005117997643537819,
-0.05219598859548569,
0.03690679743885994,
0.013444065116345882,
0.01196495071053505,
-0.015973346307873726,
-0.0029751828406006098,
-0.011404060758650303,
-0.03933154419064522,
-0.029951881617307663,
-0.00444650836288929,
0.014403535053133965,
-0.01328109111636877,
-0.044639166444540024,
0.034620143473148346,
-0.024597369134426117,
-0.017476702108979225,
0.007156464271247387,
-0.0008825308759696782,
-0.015367699787020683,
-0.009601394645869732,
0.007486951071768999,
0.004404167179018259,
0.029029423370957375,
-0.03297467529773712,
-0.01014353334903717,
0.005641318392008543,
-0.04009348899126053,
0.045765094459056854,
0.009085672907531261,
-0.06321200728416443,
0.016946416348218918,
-0.043442923575639725,
-0.05178030580282211,
0.03636128827929497,
-0.027409657835960388,
0.041504163295030594,
0.0005296111921779811,
0.018615281209349632,
-0.026939695701003075,
0.0028255663346499205,
-0.011265674605965614,
-0.003182327141985297,
-0.03679836913943291,
-0.013686488382518291,
0.013573169708251953,
-0.0014950314071029425,
-0.02971273846924305,
0.010828293859958649,
-0.07704833894968033,
-0.06001417711377144,
-0.05032278969883919,
-0.016719045117497444,
0.01272391527891159,
-0.02377212606370449,
0.014392713084816933,
0.03419119119644165,
-0.05803330987691879,
-0.002293005120009184,
-0.06940878927707672,
-0.06157722696661949,
-0.006506150588393211,
-0.01045441534370184,
0.02883961983025074,
0.019787153229117393,
-0.02280309796333313,
0.08996278047561646,
0.014759515412151814,
-0.03191644698381424,
0.0008373476448468864,
0.0023543741554021835,
-0.004742376506328583,
-0.012570121325552464,
0.03177653253078461,
0.01853165216743946,
-0.0016439000610262156,
0.026979373767971992,
0.035266123712062836,
0.017082931473851204,
0.015883665531873703,
0.026510627940297127,
-0.016191670671105385,
-0.00858609564602375,
-0.021105052903294563,
0.019838428124785423,
0.05513397604227066,
0.01676272414624691,
-0.06421232968568802,
0.03254597261548042,
-0.0007476531318388879,
-0.013731040060520172,
0.046915460377931595,
-0.03744428977370262,
0.057391878217458725,
0.00812004879117012,
0.008560330606997013,
-0.016323301941156387,
0.03905751183629036,
0.00124604522716254,
-0.057253558188676834,
0.021142249926924706,
0.031207308173179626,
0.013128125108778477,
0.0011771090794354677,
0.013400022871792316,
0.031113574281334877,
0.04366980865597725,
-0.03906913846731186,
-0.01771872490644455,
0.0019262280547991395,
0.022723890841007233,
0.03586412966251373,
-0.014518852345645428,
0.0038101812824606895,
0.07308594137430191,
0.03828437626361847,
0.017076514661312103,
-0.0031179904472082853,
-0.017351249232888222,
0.01703229919075966,
-0.07387794554233551,
-0.009084919467568398,
-0.017779139801859856,
0.035634879022836685,
-0.00908124540001154,
0.0500921905040741,
-0.027894800528883934,
-0.009252266027033329,
0.017953116446733475,
0.018400203436613083,
-0.11451976001262665,
-0.005268734414130449,
-0.03402703255414963,
-0.0117653151974082,
-0.005200877320021391,
0.014486391097307205,
-0.014300229027867317,
-0.0030438390094786882,
-0.06116337329149246,
-0.02641700766980648,
0.01505804993212223,
-0.05306627228856087,
-0.003909773658961058,
-0.07718628644943237,
-0.08698328584432602,
0.011727706529200077,
0.0078003862872719765,
0.058897700160741806,
-0.06539515405893326,
0.022612331435084343,
-0.0008998297853395343,
-0.023842239752411842,
-0.047962479293346405,
-0.005085412412881851,
0.04978807643055916,
0.013909993693232536,
0.03664062172174454,
0.036068353801965714,
0.0425996333360672,
-0.015308160334825516,
0.052101679146289825,
0.01628568209707737,
0.07758380472660065,
-0.0348847359418869,
-0.020553674548864365,
0.0032072127796709538,
-0.05418546497821808,
-0.043480996042490005,
-0.016045741736888885,
0.055627062916755676,
0.013130768202245235,
-0.014690584503114223,
0.056812647730112076,
0.007236157078295946,
-0.04802544414997101,
0.022558828815817833,
0.017805589362978935,
-0.024894578382372856,
-0.037632107734680176,
-0.0001402947964379564,
-0.03389981761574745,
-0.03514061123132706,
-0.0006096855504438281,
0.006013168953359127,
0.02307933196425438,
0.00830851960927248,
0.024728933349251747,
0.018244998529553413,
0.016577741131186485,
-0.02522418275475502,
0.005812092684209347,
0.0025924600195139647,
-0.007974827662110329,
0.003299753414466977,
-0.036951255053281784,
0.006704223342239857,
0.037914473563432693,
0.03769928216934204,
0.015370303764939308,
0.0037196537014096975,
-0.06027335673570633,
0.025955496355891228,
0.06561069935560226,
0.01315388549119234,
0.03332850709557533,
-0.009035748429596424,
-0.04464089870452881,
-0.04468138515949249,
0.08720427006483078,
-0.014713936485350132,
0.020684314891695976,
-0.01987830363214016,
-0.013888145796954632,
-0.024828635156154633,
-0.03704146295785904,
0.004208455793559551,
-0.013103964738547802,
0.003419068641960621,
0.03575005382299423,
-0.00543210469186306,
0.002475814428180456,
-0.04355250298976898,
0.041819434612989426,
0.043545663356781006,
0.005411983467638493,
0.008998805657029152,
0.0056508127599954605,
-0.0022756578400731087,
0.01229807361960411,
-0.00929997768253088,
-0.05525793507695198,
-0.004430723842233419,
-0.000618861464317888,
-0.0033351851161569357,
0.027766788378357887,
-0.0252335537225008,
-0.03108755312860012,
0.014028572477400303,
-0.023354535922408104,
-0.009775172919034958,
-0.010599253699183464,
-0.036192864179611206,
0.0305708609521389,
0.019141288474202156,
0.051042404025793076,
0.015731511637568474,
-0.0025444726925343275,
-0.018407823517918587,
-0.020800655707716942,
-0.027541054412722588,
0.031088171526789665,
-0.0006409759516827762,
0.029595423489809036,
-0.02255948632955551,
-0.011716920882463455,
-0.05391627550125122,
0.04451765492558479,
-0.0017183497548103333,
-0.03074871562421322,
-0.031059186905622482,
-0.044851310551166534,
-0.02515638805925846,
0.007895804941654205,
0.004351194016635418,
0.00905527826398611,
-0.015014919452369213,
0.027931446209549904,
0.026659686118364334,
-0.016659503802657127,
0.026946458965539932,
0.02148696966469288,
-0.014075207524001598,
-0.007008343935012817,
-0.015661155804991722,
0.060673825442790985,
-0.023998534306883812,
-0.02226046659052372,
0.003531119553372264,
-0.03427266329526901,
0.025223318487405777,
-0.037675436586141586,
0.02520127221941948,
0.04001261293888092,
-0.06214917451143265,
-0.03814224153757095,
-0.0027339980006217957,
0.01923668570816517,
0.0009419903508387506,
-0.05674433708190918,
-0.005208100192248821,
-0.008488770574331284,
0.007479529362171888,
-0.041235096752643585,
-0.05025367811322212,
0.003697995562106371,
-0.0059255934320390224,
-0.04178384318947792,
-0.047103703022003174,
0.05847072973847389,
-0.020540783181786537,
-0.021761851385235786,
0.022271133959293365,
0.033076100051403046,
-0.03201302886009216,
-0.03751043975353241,
0.01596539467573166,
0.03156203776597977,
0.03433584049344063,
-0.022067470476031303,
0.0036445127334445715,
0.006903170142322779,
0.006055203266441822,
0.02686997689306736,
0.01846909336745739,
0.03848279267549515,
-0.00940044317394495,
-0.015798766165971756,
-0.009432598948478699,
-0.002847213065251708,
-0.0028546766843646765,
-0.03321153298020363,
0.022678494453430176,
0.04027380794286728,
0.004528813995420933,
-0.009362122975289822,
-0.004721405915915966,
-0.01231747679412365,
0.0011919173412024975,
0.017381254583597183,
-0.022266950458288193,
-0.004174654837697744,
0.011750910431146622,
-0.007562600541859865,
0.05639423802495003,
0.004519517067819834,
0.0031638776417821646,
0.011798967607319355,
0.04031126946210861,
0.041887711733579636,
-0.004839429631829262,
0.023584019392728806,
0.005426596850156784,
0.015014810487627983,
-0.03637588396668434,
-0.009009049274027348,
-0.02324785478413105,
0.01058470644056797,
-0.013676034286618233,
-0.053772952407598495,
-0.019834985956549644,
-0.008298378437757492,
0.04857155308127403,
0.009083916433155537,
0.07021567970514297,
0.03810688480734825,
-0.022940536960959435,
0.0018934314139187336,
0.014965347945690155,
-0.025280509144067764,
-0.0038993137422949076,
0.011741713620722294,
0.03213352710008621,
-0.05564676970243454,
0.010908705182373524,
0.0212757159024477,
0.008546357043087482,
-0.02056724950671196,
-0.001872490392997861,
0.0377701036632061,
0.027076655998826027,
0.058529067784547806,
-0.03942210599780083,
-0.019061997532844543,
0.05211861431598663,
-0.0598737895488739,
0.04813171178102493,
0.019649244844913483,
-0.012261607684195042,
0.02643367275595665,
0.03120247647166252,
-0.011491388082504272,
0.0030057616531848907,
-0.015417622402310371,
-0.02465023286640644,
0.02387872152030468,
-0.000964373059105128,
0.02923031896352768,
0.008603627793490887,
-0.014838989824056625,
0.019993413239717484,
-0.021996548399329185,
-0.0029611766804009676,
-0.00781581737101078,
-0.06555711477994919,
-0.01121921744197607,
-0.046125710010528564,
-0.05402302369475365,
0.026081694290041924,
0.010281221009790897,
-0.024770470336079597,
-0.029374370351433754,
-0.043012361973524094,
0.03902710601687431,
-0.000653473602142185,
0.015767846256494522,
-0.028641289100050926,
0.03413941711187363,
-0.02050136774778366,
-0.0024735000915825367,
-0.02810823731124401,
-0.013416184112429619,
0.11421872675418854,
0.005188681185245514,
0.014827724546194077,
-0.07362551242113113,
0.03238100931048393,
-0.01858152635395527,
0.04929446429014206,
-0.055263176560401917,
0.016039332374930382,
0.020675767213106155,
0.03748702257871628,
-0.01113393809646368,
0.05044962465763092,
0.030466707423329353,
-0.018514780327677727,
0.052366867661476135,
-0.06462237983942032,
-0.027296356856822968,
0.01224864087998867,
-0.00007982350507518277,
0.003729736665263772,
0.019478341564536095,
-0.05490247532725334,
0.0007903443765826523,
-0.011986016295850277,
0.011840051040053368,
-0.03288029879331589,
-0.05388113483786583,
0.02336161583662033,
0.026541613042354584,
-0.040298230946063995,
0.022790445014834404,
0.013906288892030716,
-0.028590938076376915,
-0.00444861501455307,
0.01871664635837078,
0.023695504292845726,
-0.028210187330842018,
0.04188552871346474,
0.034952741116285324,
0.030240675434470177,
0.00786938238888979,
0.0159987173974514,
-0.008286962285637856,
-0.05452338978648186,
-0.009952756576240063,
-0.031102612614631653,
0.04199688881635666,
-0.04137864336371422,
-0.005643330980092287,
-0.008508438244462013,
-0.004541519097983837,
0.021650776267051697,
-0.050292007625103,
-0.02259422279894352,
-0.0004615369834937155,
0.028806235641241074,
-0.03526076674461365,
0.0049269297160208225,
-0.029811352491378784,
0.021360892802476883,
-0.016227340325713158,
0.0187956765294075,
0.010362506844103336,
-0.0302896685898304,
-0.004950512666255236,
-0.012821413576602936,
0.008534839376807213,
-0.041611894965171814,
-0.009723198600113392,
-0.03378121927380562,
0.01846519112586975,
-0.04462006688117981,
-0.014953050762414932,
0.004675779026001692,
0.04267474263906479,
0.022463632747530937,
-0.012024377472698689,
0.011671853251755238,
0.01134614460170269,
-0.025376465171575546,
0.03796792030334473,
-0.03198112174868584,
-0.02360944263637066,
-0.01694287545979023,
-0.024310089647769928,
0.03796069324016571,
0.02980256825685501,
-0.010520732030272484,
-0.03322174772620201,
-0.01008315198123455,
0.019722219556570053,
0.057440150529146194,
-0.011475850827991962,
-0.013318744488060474,
-0.032573070377111435,
-0.0008984876913018525,
0.03211659938097,
0.02221005968749523,
0.04653147980570793,
0.04418347030878067,
0.014861499890685081,
0.009737132117152214,
0.06839883327484131,
0.006294642109423876,
0.0027538291178643703,
0.013501542620360851,
-0.044901713728904724,
0.014001352712512016,
0.06188175082206726,
0.03518041595816612,
-0.027514679357409477,
-0.016282828524708748,
-0.005739736370742321,
-0.005808341316878796,
0.001657144632190466,
0.009565244428813457,
-0.04241740703582764,
0.024274704977869987,
0.004699230659753084,
0.015074944123625755,
-0.0045445687137544155,
0.019028175622224808,
-0.06921456754207611,
-0.015779919922351837,
0.00769956735894084,
0.022654594853520393,
-0.0057047582231462,
0.06660590320825577,
-0.051977451890707016,
-0.04016955941915512,
0.06621129810810089,
-0.02528323046863079,
0.005387577228248119,
-0.0013522858498618007,
0.00944597739726305,
-0.0038148665335029364,
0.020520463585853577,
-0.036702726036310196,
0.008591897785663605,
0.00819419976323843,
-0.00008081727719400078,
-0.010158119723200798,
0.004870098549872637,
-0.03364310413599014,
-0.018903300166130066,
0.007952316664159298,
-0.011649456806480885,
-0.06365764141082764,
0.01908210851252079,
0.02052086964249611,
0.0011096772504970431,
-0.010993794538080692,
-0.027485214173793793,
-0.00232989271171391,
0.002401583595201373,
0.016157543286681175,
-0.009232607670128345,
-0.020229637622833252,
-0.02937508374452591,
0.061493273824453354,
0.02082056738436222,
-0.017261680215597153,
-0.01962346024811268,
0.001756279612891376,
0.01248957123607397,
-0.003227098612114787,
-0.010294957086443901,
0.022055314853787422,
0.04274430498480797,
-0.05698803812265396,
0.047471046447753906,
0.033370815217494965,
-0.007227870635688305,
-0.08753283321857452,
-0.00046110383118502796,
0.02824740670621395,
0.02348489873111248,
0.01682082563638687,
-0.03441261500120163,
0.04202579706907272,
-0.005013144575059414,
-0.06637143343687057,
0.029902180656790733,
-0.03357511758804321,
-0.044490065425634384,
-0.015851540490984917,
-0.020310256630182266,
-0.045028407126665115,
0.04059293493628502,
0.006763981189578772,
0.0472346656024456,
0.009787683375179768,
0.02523145079612732,
-0.013793372549116611,
-0.027869606390595436,
-0.028111891821026802,
0.010256366804242134,
-0.008184763602912426,
0.002255556406453252,
0.051858384162187576,
-0.012994986027479172,
-0.05144742876291275,
0.015727289021015167,
0.018696287646889687,
-0.018216321244835854,
-0.02294057048857212,
-0.010792843997478485,
0.031722743064165115,
0.06160258874297142,
0.018775641918182373,
-0.013033842667937279,
0.0027506689075380564,
0.012033041566610336,
0.023916378617286682,
0.02472526766359806,
-0.021394727751612663,
-0.016452066600322723,
0.0020047572907060385,
-0.03577083349227905,
-0.028284234926104546,
0.0323432981967926,
0.020765475928783417,
-0.006188206374645233,
0.009861410595476627,
0.025706198066473007,
0.007736718747764826,
-0.012657039798796177,
0.0013868819223716855,
-0.04070361331105232,
0.007600110024213791,
0.03586280345916748,
0.027126330882310867,
0.04241316020488739,
0.010501851327717304,
-0.011992092244327068,
-0.005974656902253628,
0.00953979417681694,
0.027597125619649887,
0.01554447878152132,
-0.05151696503162384,
-0.021750163286924362,
0.021116457879543304,
0.0041829440742731094,
0.015494026243686676,
-0.0347541868686676,
-0.022942321375012398,
0.005565742962062359,
0.00343976984731853,
0.03320017829537392,
0.00530083104968071,
-0.007134259212762117,
-0.005160335451364517,
-0.059990525245666504,
0.04553584009408951,
-0.008577318862080574,
0.043631888926029205,
-0.012607795186340809,
0.02102063037455082,
0.011647581122815609,
0.005868368782103062,
0.014077119529247284,
-0.0069615901447832584,
-0.015152962878346443,
0.016869235783815384,
-0.02304658107459545,
0.03946647793054581,
-0.021184954792261124,
0.011852986179292202,
-0.037371281534433365,
-0.04499496519565582,
-0.012622479349374771,
-0.0007955573964864016,
-0.004402305465191603,
0.012657349929213524,
0.04745619744062424,
-0.0018536625429987907,
0.0030646242666989565,
-0.022300250828266144,
-0.058185726404190063,
0.05570007488131523,
0.006678794976323843,
-0.015183383598923683,
0.061849478632211685,
-0.02619091235101223,
0.015585032291710377,
0.03231022134423256,
-0.018385497853159904,
0.010964304208755493,
0.0522848479449749,
-0.04897448047995567,
-0.012555800378322601,
-0.03808576613664627,
0.044959865510463715,
0.014559912495315075,
-0.032628245651721954,
0.007800897117704153,
0.020273376256227493,
0.007103324867784977,
-0.01496683806180954,
0.07030845433473587,
0.013723245821893215,
0.030929455533623695,
0.008629824034869671,
-0.030003156512975693,
0.024884186685085297,
-0.0417599119246006,
0.016547009348869324,
0.030300138518214226,
0.053080253303050995,
0.0020686916541308165,
0.01929645799100399,
0.041024357080459595,
0.0009862349834293127,
0.05558213219046593,
0.018779149278998375,
0.0360889658331871,
-0.03572358191013336,
0.013567269779741764,
0.0126698799431324,
-0.022663569077849388,
0.05277368053793907,
0.017191147431731224,
-0.03442991524934769,
0.09666251391172409,
-0.03946235775947571,
-0.016108404844999313,
-0.0039252713322639465,
0.002352324780076742,
-0.012932351790368557,
-0.02220241166651249,
0.02831995114684105,
0.03790630027651787,
-0.03618168085813522,
0.032175760716199875,
-0.046529196202754974,
0.03360585868358612,
-0.0020611330401152372,
-0.03898657485842705,
0.005764409434050322,
-0.011170816607773304,
-0.008709750138223171,
0.04013753682374954,
0.0033904241863638163,
-0.01603499799966812,
-0.00004960728620062582,
0.05526621267199516,
0.0861164927482605,
-0.004349803552031517,
-0.050175707787275314,
0.0037944966461509466,
-0.04394397884607315,
0.05460266023874283,
-0.061968665570020676,
0.023422643542289734,
-0.029676444828510284,
-0.000296868005534634,
-0.04123982787132263,
0.00035911297891288996
] |
<p>I am reading the first few pages of Nakahara and refreshing my memory on physics I learned a while ago as a physics math undergrad. Nakahara defines a field $F$ to be conservative if it's the gradient of some potential $V(x)$. (standard) Then he defines the total energy as $1/2mv^2+V(x)$. He then states that $E$ is "often" the kinetic+potential energy, hence deserving the name "total energy." I was taught that kinetic is defined as $1/2mv^2$. So what does he mean here?</p>
<p><strong>Addum:</strong> The exact quote of Ref. 1 is: </p>
<blockquote>
<p><em>The function $E$, which is often the sum of the kinetic energy and the potential energy, is called the <strong>energy</strong>.</em></p>
</blockquote>
<p>References:</p>
<ol>
<li>M. Nakahara, <em>Geometry, Topology & Physics,</em> 2nd edition, 2003, Section 1.1.1.</li>
</ol>
| 7,599 |
[
-0.02352534607052803,
-0.018218139186501503,
0.04954468831419945,
-0.017058007419109344,
0.03596840798854828,
0.041602298617362976,
0.01560086291283369,
-0.01650628261268139,
-0.004507359117269516,
-0.04160409793257713,
0.04361256584525108,
0.01885182037949562,
0.09146172553300858,
0.0010326923802495003,
0.03654932230710983,
0.013594475574791431,
-0.01801067590713501,
-0.006065873894840479,
-0.012637182138860226,
-0.04066315293312073,
-0.01243913359940052,
-0.008550511673092842,
0.011963357217609882,
0.0278556440025568,
-0.01606171578168869,
0.03728640824556351,
0.004681331571191549,
0.0028134577441960573,
-0.0066193570382893085,
0.052939899265766144,
-0.026183122768998146,
-0.057267457246780396,
-0.001736339763738215,
-0.010646628215909004,
-0.006180030759423971,
-0.00667486572638154,
-0.04117777571082115,
-0.02471284009516239,
-0.00024063342425506562,
0.04350657016038895,
-0.04853234812617302,
-0.020607560873031616,
-0.022816915065050125,
0.02969064563512802,
-0.07265402376651764,
0.01210334338247776,
-0.0018576409202069044,
-0.019133739173412323,
0.05232825130224228,
-0.04530283436179161,
0.05541567876935005,
-0.002084001200273633,
0.0567837730050087,
0.037513550370931625,
-0.026349907740950584,
0.023475587368011475,
0.04999380558729172,
0.03844993934035301,
-0.013743395917117596,
-0.07182706892490387,
-0.02157878689467907,
-0.04143885523080826,
-0.003173134056851268,
-0.033580172806978226,
-0.004960774909704924,
0.05714714527130127,
0.017593957483768463,
-0.02018747851252556,
0.045662786811590195,
-0.0022682547569274902,
-0.005443588364869356,
0.03153174743056297,
0.008098886348307133,
-0.0358562245965004,
0.0018743964610621333,
0.035683780908584595,
-0.005396893247961998,
0.012354285456240177,
0.036739639937877655,
0.02186383679509163,
-0.028446611016988754,
-0.008843587711453438,
0.04652121290564537,
0.04799310490489006,
-0.018629247322678566,
0.01454369816929102,
0.06486891955137253,
-0.0029418314807116985,
0.02288965694606304,
-0.005579840857535601,
-0.004527938552200794,
0.007793217897415161,
-0.002049804199486971,
-0.02550038881599903,
-0.04815173149108887,
0.03650915250182152,
-0.00006800558912800625,
0.033334001898765564,
-0.016757400706410408,
-0.016124272719025612,
0.0012061098823323846,
-0.004135340917855501,
0.013977193273603916,
0.030310794711112976,
0.010874073021113873,
-0.04820530116558075,
-0.05998285114765167,
0.012926114723086357,
-0.033261872828006744,
0.010939081199467182,
-0.04466524347662926,
-0.004302461631596088,
-0.0013708022888749838,
-0.011633433401584625,
-0.013299509882926941,
-0.018740806728601456,
0.0021871093194931746,
0.003093395382165909,
0.020322144031524658,
0.03491539880633354,
0.07488526403903961,
-0.04674084857106209,
0.03308366611599922,
-0.03943037614226341,
-0.1044846624135971,
0.036274153739213943,
0.08260318636894226,
0.0027919511776417494,
-0.06151009351015091,
0.020904170349240303,
0.005791733972728252,
0.012077957391738892,
-0.025655442848801613,
0.04552239924669266,
0.04296223819255829,
-0.035808414220809937,
-0.0805424302816391,
-0.07277914881706238,
0.036349501460790634,
-0.003684055292978883,
-0.044350430369377136,
-0.08858697861433029,
-0.035106170922517776,
0.0597771517932415,
0.053354956209659576,
-0.01589609682559967,
0.01960950717329979,
-0.021683694794774055,
-0.007936556823551655,
0.011799545958638191,
-0.05400356277823448,
-0.05561338737607002,
0.012069407850503922,
-0.025854060426354408,
-0.02321280725300312,
-0.04285667464137077,
-0.030658258125185966,
0.007610820699483156,
0.004621571395546198,
-0.008299178443849087,
0.08438058942556381,
-0.04486927390098572,
-0.0247432142496109,
0.02008267492055893,
-0.022855861112475395,
-0.03042561747133732,
0.07880894839763641,
0.04096353426575661,
0.030004272237420082,
0.032633934170007706,
0.0009905252372846007,
0.04769936576485634,
0.027470054104924202,
0.05041835084557533,
0.05630265548825264,
-0.019049590453505516,
0.008158267475664616,
-0.016266852617263794,
-0.015396889299154282,
0.004510079976171255,
-0.05130675435066223,
-0.057029008865356445,
0.017048850655555725,
0.015152109786868095,
-0.03667913004755974,
0.07552540302276611,
-0.004970243666321039,
-0.03046674095094204,
-0.004999128635972738,
-0.006012722849845886,
-0.038817111402750015,
-0.06093626841902733,
0.03515243157744408,
-0.00005133881131769158,
0.0022620379459112883,
0.030465861782431602,
-0.01914205588400364,
0.004292126279324293,
-0.034177809953689575,
-0.011030192486941814,
0.009532363153994083,
0.019162949174642563,
0.011683189310133457,
0.004275097046047449,
-0.003999054431915283,
0.028316067531704903,
0.010019134730100632,
0.04911332577466965,
0.01591395027935505,
-0.007389361970126629,
-0.05095125362277031,
0.02156207524240017,
-0.04846404492855072,
0.05544012784957886,
-0.0029933827463537455,
-0.0307166650891304,
-0.009821632876992226,
-0.009481286630034447,
-0.0031897341832518578,
0.004395314026623964,
-0.06084192544221878,
0.04981515184044838,
0.043819744139909744,
0.011455953121185303,
-0.030640626326203346,
0.07101849466562271,
-0.006930621340870857,
0.011508956551551819,
-0.02575860545039177,
-0.005422487854957581,
0.003096509026363492,
0.02038668654859066,
0.03633582964539528,
0.022960379719734192,
-0.0443539135158062,
-0.02284938097000122,
0.030368832871317863,
-0.002177004935219884,
0.02915327250957489,
-0.004417716059833765,
-0.008342638611793518,
-0.04272103309631348,
0.04105111584067345,
0.006420973222702742,
-0.0030612354166805744,
-0.014663193374872208,
0.01842276193201542,
0.04101332649588585,
0.017510147765278816,
0.0233911219984293,
-0.014036145992577076,
0.030153773725032806,
-0.0012084858026355505,
-0.0020504589192569256,
0.010280678048729897,
-0.02229449525475502,
0.0438058115541935,
-0.04312139376997948,
0.0878797248005867,
0.04321965202689171,
-0.014638351276516914,
-0.01715766452252865,
-0.05203332379460335,
-0.021202201023697853,
0.010022786445915699,
0.01470169611275196,
-0.018634848296642303,
0.0104743717238307,
0.02009366638958454,
-0.005745165515691042,
-0.006728725973516703,
0.010665041394531727,
-0.021451909095048904,
-0.0130271315574646,
-0.02547028288245201,
0.030622566118836403,
-0.01274084858596325,
0.008640224114060402,
-0.032922036945819855,
-0.02313462272286415,
-0.02397884987294674,
-0.025885604321956635,
-0.014999053440988064,
0.029790649190545082,
-0.03920701518654823,
-0.006678130943328142,
-0.05032363906502724,
-0.022175408899784088,
0.057740096002817154,
-0.014885295182466507,
-0.006745585240423679,
0.026387572288513184,
-0.012975679710507393,
-0.06286469101905823,
-0.03761604428291321,
-0.0054776412434875965,
0.012396196834743023,
0.011423561722040176,
-0.019778776913881302,
0.05134045332670212,
-0.0413237102329731,
-0.030731435865163803,
0.016180269420146942,
-0.028628775849938393,
-0.0423283688724041,
-0.024514229968190193,
-0.016246387735009193,
0.02767084538936615,
-0.017731545493006706,
0.029987318441271782,
0.0184896532446146,
-0.03801175206899643,
-0.022035447880625725,
-0.05358283966779709,
-0.044572342187166214,
0.008331160061061382,
-0.016157004982233047,
0.03963073343038559,
0.0016163421096280217,
-0.06267105787992477,
0.080340676009655,
0.04617605730891228,
-0.03683529794216156,
-0.02605406939983368,
-0.0008006328716874123,
-0.0041612558998167515,
-0.03235951066017151,
-0.0025526415556669235,
-0.006288595963269472,
0.002320478204637766,
0.026519428938627243,
-0.010035487823188305,
0.05132784694433212,
0.03636198863387108,
-0.009891453199088573,
-0.030189385637640953,
0.00842979270964861,
-0.011199422180652618,
0.00868312455713749,
0.03725043311715126,
0.029608868062496185,
-0.02255656197667122,
0.008050665259361267,
0.005903830751776695,
0.05474784970283508,
0.017426880076527596,
-0.0371638759970665,
0.10087567567825317,
0.003116931766271591,
-0.016387423500418663,
-0.06615544855594635,
0.059298768639564514,
0.016763487830758095,
-0.03842736408114433,
0.012436301447451115,
0.022785475477576256,
0.005964794661849737,
-0.02310754545032978,
0.02104019746184349,
0.008473426103591919,
0.06846430897712708,
-0.040880732238292694,
-0.02848774380981922,
-0.02330809086561203,
0.033830463886260986,
0.019246451556682587,
0.00374715612269938,
-0.004129211883991957,
0.03036237321794033,
0.026027290150523186,
0.013030325062572956,
0.01998080685734749,
-0.0349537618458271,
0.019209906458854675,
-0.037382904440164566,
-0.014566882513463497,
0.020512226969003677,
0.02415771223604679,
-0.023578807711601257,
0.0671692043542862,
0.012505684047937393,
0.02686355821788311,
0.060612235218286514,
-0.0049668108113110065,
-0.0674530565738678,
-0.0018845486920326948,
-0.02110104076564312,
-0.039138395339250565,
0.006648457609117031,
0.01538076438009739,
0.002578696934506297,
-0.027057312428951263,
-0.03113245964050293,
-0.028845811262726784,
-0.013348458334803581,
-0.045934829860925674,
0.0027495340909808874,
-0.04885074868798256,
-0.040165144950151443,
-0.0017824707319959998,
0.02563324384391308,
0.07491684705018997,
-0.06313877552747726,
-0.00548821035772562,
0.06898213177919388,
-0.034889236092567444,
0.007286373525857925,
-0.002110835863277316,
-0.03329150751233101,
0.012205978855490685,
0.012325138784945011,
0.00378839741460979,
0.03109409101307392,
-0.0018056895351037383,
0.03089544177055359,
0.013149697333574295,
0.08274240791797638,
0.01641351915895939,
-0.03205924108624458,
-0.000872594362590462,
-0.04186486825346947,
0.00788519810885191,
-0.00501937884837389,
0.03018685057759285,
0.009187397547066212,
0.011845306493341923,
0.031660471111536026,
0.04444729909300804,
-0.033128686249256134,
0.06192433461546898,
0.04278332367539406,
-0.00315638305619359,
-0.028247013688087463,
-0.06057751551270485,
0.010674303397536278,
-0.02577533945441246,
-0.04584280028939247,
-0.011142215691506863,
0.00403555016964674,
-0.004493059124797583,
0.010167879983782768,
0.01924773119390011,
-0.01212140079587698,
-0.048802148550748825,
-0.015291333198547363,
-0.015383215621113777,
-0.004412587266415358,
-0.025923119857907295,
-0.031852301210165024,
0.0005480629624798894,
0.02684764564037323,
0.05168364569544792,
-0.030135950073599815,
0.016309404745697975,
-0.06628644466400146,
-0.025648919865489006,
0.04549115523695946,
0.02428564801812172,
0.0006175610469654202,
-0.020702213048934937,
-0.019506946206092834,
-0.032592661678791046,
0.02806798368692398,
-0.011779007501900196,
0.029499787837266922,
-0.0065718358382582664,
0.011975402943789959,
0.007937850430607796,
-0.04832344874739647,
-0.014453139156103134,
0.044604912400245667,
0.0028151627629995346,
0.030880393460392952,
-0.01175216306000948,
0.004521180409938097,
-0.024001862853765488,
-0.0032143662683665752,
-0.016896288841962814,
0.04939110204577446,
-0.005573061294853687,
-0.03556330129504204,
0.008028640411794186,
0.016178840771317482,
-0.010374150238931179,
-0.07750692963600159,
-0.04191796854138374,
0.010191264562308788,
-0.014368257485330105,
0.007796897552907467,
-0.059889450669288635,
-0.021335434168577194,
0.04860692843794823,
0.009318959899246693,
0.008050941862165928,
0.02356312982738018,
-0.029557600617408752,
0.06991374492645264,
0.05229213088750839,
0.019960174337029457,
0.022643085569143295,
0.002654706360772252,
-0.0220104418694973,
0.0113733084872365,
-0.020247910171747208,
0.025684742256999016,
-0.01019064150750637,
0.008620284497737885,
-0.048784367740154266,
-0.018488053232431412,
-0.05921166017651558,
0.03982827812433243,
-0.008342129178345203,
0.010430840775370598,
-0.013206821866333485,
-0.029122214764356613,
-0.0011200529988855124,
0.015575406141579151,
0.046513259410858154,
-0.006800456903874874,
0.0012502147583290935,
0.05233728885650635,
-0.005337610375136137,
-0.013386877253651619,
-0.002708071144297719,
0.022028597071766853,
0.001153594464994967,
0.017436373978853226,
0.0027930026408284903,
0.023177076131105423,
-0.04055539146065712,
-0.018082210794091225,
0.014622827991843224,
-0.011634904891252518,
0.02867109701037407,
-0.021540194749832153,
-0.017612965777516365,
-0.003482531290501356,
-0.04894793778657913,
-0.06536798924207687,
0.00532117672264576,
-0.012702667154371738,
-0.02035335637629032,
-0.030574582517147064,
0.0257450882345438,
0.035794924944639206,
0.031328801065683365,
-0.0383061021566391,
-0.015160249546170235,
-0.017234859988093376,
-0.009960256516933441,
-0.010843348689377308,
-0.02321326546370983,
0.016741789877414703,
-0.023919813334941864,
-0.026147136464715004,
0.029609454795718193,
0.03241104260087013,
0.014272156171500683,
-0.00802412535995245,
0.013738571666181087,
0.021585673093795776,
-0.0006595266750082374,
-0.00051881093531847,
0.004579680506139994,
0.022414864972233772,
0.0012595800217241049,
-0.027141250669956207,
-0.013355618342757225,
0.05528446286916733,
-0.006939366459846497,
0.016315946355462074,
-0.014850158244371414,
-0.033522337675094604,
0.036106713116168976,
-0.028127165511250496,
0.014332938939332962,
0.07064368575811386,
0.009056098759174347,
-0.01455637812614441,
0.017849713563919067,
0.023493295535445213,
-0.014686904847621918,
0.04589380323886871,
0.0022278556134551764,
0.014634118415415287,
0.008334875106811523,
-0.010311209596693516,
0.02577025629580021,
0.013243039138615131,
0.007450738921761513,
-0.010668675415217876,
0.047128185629844666,
-0.013915837742388248,
0.0007920057978481054,
-0.009969149716198444,
0.005531707778573036,
0.023525722324848175,
-0.014777793549001217,
0.00945538841187954,
0.00642688712105155,
0.01720714010298252,
0.002346673747524619,
-0.025610066950321198,
-0.013911338523030281,
0.01696985773742199,
0.07054063677787781,
-0.05176649987697601,
0.037342678755521774,
-0.012170564383268356,
-0.018340695649385452,
0.024139944463968277,
-0.026353154331445694,
-0.020269732922315598,
-0.02118188701570034,
0.03136090561747551,
0.002063500229269266,
-0.009437845088541508,
0.0021372258197516203,
0.022817475721240044,
0.036972228437662125,
-0.06082034483551979,
-0.007096403278410435,
0.0048020873218774796,
0.038015563040971756,
0.018594790250062943,
-0.021612226963043213,
-0.06213965266942978,
0.0482102669775486,
-0.0034531240817159414,
0.02686900645494461,
-0.02585345320403576,
-0.028946857899427414,
0.03300498425960541,
0.018221070989966393,
0.010922038927674294,
-0.04123973846435547,
-0.007278773467987776,
-0.026686783879995346,
0.03188280761241913,
0.024696985259652138,
-0.004393334034830332,
-0.009761047549545765,
0.0087041687220335,
0.016765357926487923,
0.022814849391579628,
0.008151214569807053,
-0.021065445616841316,
-0.0690421611070633,
-0.032521605491638184,
-0.026860106736421585,
-0.015832845121622086,
-0.0007897003670223057,
0.0036612139083445072,
-0.0622793510556221,
0.024475617334246635,
0.005502323620021343,
0.028955360874533653,
0.0219517070800066,
-0.010692059993743896,
0.006123762112110853,
0.06793732196092606,
0.011503447778522968,
0.027377547696232796,
-0.03677226975560188,
0.0032654355745762587,
0.1262664496898651,
0.08503478020429611,
0.018108949065208435,
-0.06186908856034279,
-0.0004938959027640522,
-0.04276988282799721,
-0.007291016168892384,
-0.002614287193864584,
0.009606105275452137,
-0.0025622209068387747,
0.02865578606724739,
0.011145214550197124,
0.05863364040851593,
-0.004538760520517826,
-0.019043078646063805,
0.04681005701422691,
-0.026591693982481956,
-0.06161120533943176,
0.015959015116095543,
0.009756267070770264,
-0.017372170463204384,
0.0006556144799105823,
-0.026664206758141518,
-0.0036265142261981964,
0.0013651513727381825,
0.020670810714364052,
0.004347560461610556,
-0.057839516550302505,
0.02354642003774643,
0.0283780749887228,
-0.021316170692443848,
0.008469165302813053,
0.008144265972077847,
0.00028980066417716444,
-0.03169388324022293,
0.014094462618231773,
0.043794937431812286,
0.003933953121304512,
0.009195455349981785,
0.031031712889671326,
0.01614553853869438,
0.012608382850885391,
0.011007983237504959,
0.036126650869846344,
0.007870241068303585,
-0.015131163410842419,
-0.045185256749391556,
0.047840625047683716,
-0.0095674442127347,
0.04625891149044037,
-0.014366822317242622,
-0.004090052098035812,
0.0023035474587231874,
-0.008631904609501362,
-0.008240419439971447,
-0.016627540811896324,
0.045210618525743484,
-0.006339259911328554,
-0.0036780540831387043,
-0.041443146765232086,
0.014994614757597446,
-0.01343478262424469,
0.004103810526430607,
0.002082872437313199,
-0.03808372840285301,
0.04452923312783241,
-0.001404996495693922,
0.02297770231962204,
-0.005080107599496841,
-0.02885039709508419,
-0.0018115534912794828,
-0.01900690421462059,
-0.04023423790931702,
-0.0021657210309058428,
-0.010993576608598232,
0.01788555458188057,
0.04010044038295746,
-0.022265248000621796,
0.017523137852549553,
0.002588690957054496,
-0.07610190659761429,
0.051711928099393845,
-0.012258395552635193,
-0.011115211062133312,
-0.031653787940740585,
0.0030089865904301405,
-0.03113565221428871,
0.051202546805143356,
-0.016283486038446426,
-0.0007034944137558341,
-0.0066241114400327206,
0.005358847789466381,
0.0267262514680624,
-0.03131040558218956,
-0.052828989923000336,
-0.016941538080573082,
-0.026782190427184105,
-0.0009300360106863081,
0.0032530869357287884,
-0.007899139076471329,
0.0015878855483606458,
0.03649831935763359,
-0.010386033914983273,
0.01775093749165535,
0.0021013212390244007,
0.002889384049922228,
0.0169841218739748,
-0.011031685397028923,
0.004453908186405897,
0.02101723663508892,
-0.006600516382604837,
-0.025763968005776405,
0.006799463182687759,
0.012580675072968006,
0.027340637519955635,
-0.0006982078193686903,
0.03786453977227211,
-0.04285566136240959,
0.035832371562719345,
-0.013987993821501732,
0.02818690612912178,
-0.039506200700998306,
-0.038912367075681686,
-0.023528259247541428,
0.06491366028785706,
0.02084863930940628,
0.0007461000350303948,
0.00958181731402874,
0.03201588615775108,
-0.006490133237093687,
-0.005050278268754482,
0.024515241384506226,
0.0015222254442051053,
-0.0017475703498348594,
-0.010824907571077347,
0.03716778755187988,
-0.03214055299758911,
0.0524597130715847,
-0.012273347936570644,
-0.01890394650399685,
0.03685728833079338,
-0.02669331058859825,
-0.06532689929008484,
0.0007905720849521458,
0.02150922454893589,
0.00483075063675642,
0.031156934797763824,
-0.0033565214835107327,
-0.04292876273393631,
0.025252260267734528,
-0.030012477189302444,
-0.010858307592570782,
0.01487766019999981,
-0.06192110478878021,
-0.013088689185678959,
-0.07414087653160095,
0.023760700598359108,
0.017718803137540817,
0.01929459162056446,
0.01595952734351158,
-0.004471370950341225,
-0.04050704091787338,
-0.05066603794693947,
0.00209324574097991,
0.011693408712744713,
-0.023826071992516518,
-0.002549203112721443,
0.017024459317326546,
0.03905178979039192,
0.06047457829117775,
-0.05234842374920845,
-0.017171509563922882,
-0.010151062160730362,
-0.02171526663005352,
-0.08055827766656876,
-0.024634020403027534,
0.005378635134547949,
-0.009426292963325977,
0.040157366544008255,
-0.06582628935575485,
0.031987473368644714,
0.017966914921998978,
-0.07557839155197144,
-0.003981129731982946,
-0.010626032017171383,
0.0013586597051471472,
-0.02793363854289055,
-0.013494632206857204,
-0.008115055039525032,
0.03221188858151436,
0.017475947737693787,
0.04925980418920517,
-0.00539232324808836,
-0.000009493722245679237,
0.013777936808764935,
-0.009775047190487385,
-0.014969020150601864,
0.022915750741958618,
-0.006157238502055407,
-0.03201040253043175,
0.07596423476934433,
0.02843543514609337,
-0.043523866683244705,
0.05221576243638992,
-0.04096680507063866,
-0.02406190149486065,
0.010319490917026997,
0.023102829232811928,
-0.005504001397639513,
0.02593878097832203,
0.026895392686128616,
0.006261596456170082,
-0.003482379950582981,
0.00806196965277195,
0.02278447523713112,
0.031148601323366165,
0.0015841724816709757,
0.026383962482213974,
0.014769683592021465,
-0.017032310366630554,
-0.04135846346616745,
0.04345555976033211,
-0.014055843465030193,
-0.02386295422911644,
0.030131898820400238,
0.02781987562775612,
0.01708795875310898,
-0.014993100427091122,
0.029873933643102646,
-0.012023113667964935,
-0.0134512884542346,
0.05071187764406204,
-0.04615040123462677,
0.023279378190636635,
0.029595019295811653,
0.014408252201974392,
-0.01902550831437111,
0.0264991857111454,
0.04412907361984253,
-0.01764732412993908,
-0.06585580855607986,
0.030020983889698982,
0.023737147450447083,
-0.022458693012595177,
-0.013930880464613438,
-0.05661763623356819,
-0.04078693315386772,
0.00567722599953413,
0.029087333008646965,
0.03490491211414337,
-0.002659090328961611,
-0.035919032990932465,
0.0030789801385253668,
-0.05867113173007965,
0.02160818874835968,
0.03860272094607353,
-0.016720132902264595,
-0.00664876913651824,
0.0041417935863137245,
-0.0009230705909430981,
-0.010314906015992165,
0.04018300399184227,
-0.01939200796186924,
-0.03192134201526642,
0.0197797529399395,
-0.0023124509025365114,
0.03165096044540405,
-0.031092917546629906,
-0.012574943713843822,
0.0018314184853807092,
0.0036008425522595644,
0.02132095955312252,
0.02528085559606552,
-0.007034617941826582,
0.01669236086308956,
0.029383307322859764,
-0.006231633946299553,
0.022030334919691086,
-0.028994081541895866,
0.002991839312016964,
0.046338632702827454,
-0.0020317526068538427,
-0.024346185848116875,
0.06677912175655365,
-0.03325991705060005,
0.02091088332235813,
0.022871188819408417,
-0.026000482961535454,
-0.0218967255204916,
0.03257553651928902,
-0.03797770291566849,
-0.025141598656773567,
-0.005868605338037014,
-0.017187325283885002,
0.05426210165023804,
-0.03940833359956741,
-0.06379466503858566,
0.06218057498335838,
-0.044593244791030884,
-0.010989212431013584,
0.05137551575899124,
0.05161678045988083,
0.018541546538472176,
0.048958081752061844,
-0.0080086225643754,
0.010277695953845978,
0.0006454632966779172,
0.005533047951757908,
0.048502031713724136,
0.06337100267410278,
0.02173066884279251,
-0.0012646439718082547,
0.02452387474477291,
-0.012374620884656906,
0.0037997241597622633,
0.01905335672199726,
0.03957356885075569,
-0.05950857698917389,
-0.01899648644030094,
-0.01609884575009346,
0.03040899895131588,
-0.009076316840946674,
-0.009186645969748497,
-0.028759784996509552,
0.07192850112915039,
-0.02108081430196762,
0.0045502702705562115,
-0.024598874151706696,
0.01413082517683506,
-0.036260075867176056,
0.009492386132478714,
0.019454604014754295,
0.026594826951622963,
0.00782498437911272,
0.0202488973736763,
-0.032071132212877274,
0.009897975251078606,
-0.0022415081039071083,
-0.02001998759806156,
0.004809089936316013,
0.05097004398703575,
-0.009754526428878307,
0.008329388685524464,
0.01604628376662731,
0.006818752270191908,
-0.02927984483540058,
0.004164798650890589,
0.04864943027496338,
0.033372774720191956,
-0.012673388235270977,
-0.010473322123289108,
-0.010368544608354568,
0.051812730729579926,
-0.0496094636619091,
0.025606561452150345,
-0.032878246158361435,
-0.0019736704416573048,
-0.014302460476756096,
0.02353529818356037
] |
<p>From Griffith's <em>Introduction to Electrodynamics</em></p>
<blockquote>
<p>The principle of superposition may seem obvious to you, but it did not have to be so simple: if the electromagnetic force were proportional to the <em>square</em> of the total source charge, for instance, the principle of superposition would not hold, since $\left(q_1+q_2\right)^2\ne q_1^2 + q_2^2$ (there would be cross terms to consider). Superposition is not a logical necessity, but an experimental fact.</p>
</blockquote>
<p>I am confused as to why it is important that electromagnetic force must depend linearly on charge for the superposition principle to hold. Suppose it <em>was</em> the case that electromagnetic force depended on the square of charge. Then, defining, a new quantity "squarecharge" $k = q^2$, electromagnetic force would depend linearly on "squarecharge", and therefore does superposition not hold?</p>
<p>Put another way, every object with charge $q$ has an associated quantity $m = q^{1/3}$. Suppose that $m$ is more naturally measured than $q$, therefore it is used in place of $q$ in all formulas. Then, even though electromagnetic forces are proportional to the cube of $m$, superposition still holds.</p>
| 7,600 |
[
-0.031292371451854706,
0.03920019045472145,
0.02680063433945179,
-0.04549683257937431,
0.01794339343905449,
0.015413411892950535,
-0.024191051721572876,
-0.007941649295389652,
-0.0023077246733009815,
-0.009541632607579231,
0.03207382932305336,
-0.018330728635191917,
0.08323367685079575,
-0.009201649576425552,
0.014058627188205719,
0.01370785292237997,
0.014479158446192741,
-0.025517331436276436,
-0.02018040046095848,
-0.021076086908578873,
-0.016184084117412567,
0.04674624279141426,
0.017179390415549278,
0.018881645053625107,
-0.011082425713539124,
0.05425749346613884,
0.025063106790184975,
-0.029989048838615417,
0.05186251923441887,
0.052337825298309326,
0.004665551707148552,
-0.02746807225048542,
0.012704811058938503,
0.031973946839571,
0.005824180785566568,
-0.005966449622064829,
-0.009736191481351852,
-0.036929525434970856,
0.009773044846951962,
0.013958803378045559,
-0.029736490920186043,
-0.01877804659307003,
-0.0022609438747167587,
0.026933370158076286,
-0.02302912063896656,
0.02363544888794422,
0.0170428529381752,
-0.034623321145772934,
0.03414514660835266,
-0.05960734188556671,
0.029383046552538872,
0.03532673418521881,
0.0578712560236454,
0.042004186660051346,
-0.023458033800125122,
-0.021481700241565704,
0.074518583714962,
0.06155181676149368,
0.0011021271347999573,
-0.04278554022312164,
-0.036223769187927246,
-0.036762040108442307,
-0.003476049518212676,
-0.044675637036561966,
-0.017928458750247955,
0.05795322731137276,
0.018689047545194626,
0.031586628407239914,
0.011405876837670803,
-0.04795042425394058,
0.02688433788716793,
0.025717223063111305,
0.01670733280479908,
-0.008982357569038868,
-0.023749511688947678,
-0.027758365496993065,
0.0007714770617894828,
0.005209877155721188,
0.04809881001710892,
0.017203496769070625,
-0.027800796553492546,
0.04006335511803627,
0.03795593976974487,
0.041909098625183105,
0.017766747623682022,
-0.02420024573802948,
0.04699108377099037,
-0.005305268801748753,
0.00602858979254961,
0.01576400175690651,
-0.013311565853655338,
0.045935992151498795,
0.02863154001533985,
-0.03158039599657059,
-0.0020881567616015673,
0.043172866106033325,
-0.00386052206158638,
0.027515022084116936,
0.00785479974001646,
-0.036375340074300766,
0.021270206198096275,
-0.021079910919070244,
0.026355063542723656,
0.07315728068351746,
0.008764160796999931,
-0.03754352033138275,
-0.005163777619600296,
0.038645196706056595,
-0.019750433042645454,
-0.041885267943143845,
0.00681969104334712,
0.01495340932160616,
-0.003108353354036808,
0.0332515612244606,
-0.01105957105755806,
-0.006287997588515282,
0.008628799580037594,
-0.0002842389512807131,
0.0938396230340004,
0.05906256288290024,
0.029185352846980095,
-0.036159466952085495,
-0.022353092208504677,
-0.02542026899755001,
-0.0632600262761116,
0.0008750908309593797,
-0.0036218531895428896,
-0.017464779317378998,
-0.026540540158748627,
0.005666617304086685,
0.05928148329257965,
-0.02212074026465416,
-0.0303223617374897,
0.016678689047694206,
0.017755966633558273,
-0.008227723650634289,
-0.10620836913585663,
-0.05455055460333824,
0.04251778870820999,
-0.010494704358279705,
-0.019928500056266785,
-0.05646054074168205,
-0.00017593748634681106,
0.044738490134477615,
0.0832938551902771,
-0.0021222832147032022,
-0.006944375578314066,
-0.002757407259196043,
0.040664248168468475,
-0.003646878059953451,
-0.015905270352959633,
-0.04196104407310486,
0.020541667938232422,
-0.03806468844413757,
-0.029780665412545204,
-0.07368290424346924,
0.04421839490532875,
0.015373061411082745,
0.029737982898950577,
0.006911566015332937,
0.0736130028963089,
-0.034841716289520264,
-0.004001502878963947,
0.0420905277132988,
-0.002500133356079459,
-0.04464282467961311,
0.05928533896803856,
0.022667810320854187,
0.02072576992213726,
0.02180308662354946,
0.017319409176707268,
0.02078915201127529,
0.022043930366635323,
0.010217061266303062,
0.02831176482141018,
-0.036837369203567505,
0.00673752510920167,
-0.017809990793466568,
0.017484985291957855,
0.006875856779515743,
-0.04613988846540451,
-0.044887054711580276,
0.018958641216158867,
0.02191110886633396,
0.011322499252855778,
0.05544985458254814,
-0.03882705792784691,
0.008730161003768444,
-0.010866696946322918,
-0.04417407885193825,
-0.05008649080991745,
-0.040336549282073975,
0.0465216226875782,
0.006102240178734064,
-0.025270530954003334,
0.025097070261836052,
-0.008740702643990517,
-0.013652375899255276,
-0.02504625916481018,
-0.034221842885017395,
0.045685309916734695,
0.05696137621998787,
-0.004050431307405233,
-0.023404570296406746,
0.04076797887682915,
0.03972441330552101,
0.05239156633615494,
0.011065804399549961,
-0.007795669138431549,
0.010277993977069855,
-0.032873548567295074,
0.05241239070892334,
-0.02812470868229866,
0.01813572831451893,
0.0009076290298253298,
0.0006970189278945327,
-0.007215948309749365,
-0.007786507718265057,
-0.026570411399006844,
0.055573370307683945,
-0.03283927962183952,
0.06797771900892258,
0.0337650403380394,
-0.019877823069691658,
-0.002672039670869708,
0.055204108357429504,
0.011802555993199348,
0.010244783945381641,
0.023211756721138954,
-0.018827417865395546,
-0.04912986233830452,
0.01285568531602621,
0.008508598431944847,
0.042054422199726105,
-0.027016503736376762,
0.04182082787156105,
0.0033123388420790434,
0.048021599650382996,
0.01855417713522911,
0.0053273835219442844,
0.01465815119445324,
-0.04020461067557335,
-0.007877926342189312,
-0.01007589977234602,
0.006258726119995117,
0.011327436193823814,
-0.0026435123290866613,
0.013110950589179993,
0.0017947101732715964,
0.003191649680957198,
0.0038355824071913958,
0.011472686193883419,
-0.02744608372449875,
0.022739265114068985,
0.009683928452432156,
-0.039792757481336594,
0.03008524887263775,
-0.04174342378973961,
0.03263821080327034,
0.017842739820480347,
-0.039254914969205856,
0.012457811273634434,
-0.040618427097797394,
-0.021259676665067673,
-0.008140774443745613,
-0.02894444204866886,
-0.04396508261561394,
-0.0026025024708360434,
0.01699177920818329,
-0.036998409777879715,
-0.015501498244702816,
-0.007256949786096811,
-0.02414359524846077,
-0.03816623613238335,
-0.005560948513448238,
0.022973500192165375,
0.0026514134369790554,
0.06563226878643036,
-0.04340450093150139,
-0.034474268555641174,
-0.02132367342710495,
-0.039758335798978806,
-0.010695580393075943,
0.019927604123950005,
-0.01755131036043167,
-0.036261942237615585,
-0.0802135318517685,
-0.015553029254078865,
0.06638200581073761,
-0.005172189325094223,
-0.005657284986227751,
0.022072162479162216,
0.00045833614422008395,
-0.03040076419711113,
-0.028959477320313454,
-0.0294960904866457,
-0.015035691671073437,
-0.017122359946370125,
-0.016132166609168053,
0.048777468502521515,
-0.01930272951722145,
-0.040576159954071045,
0.022703517228364944,
-0.036048952490091324,
-0.04064419865608215,
0.009952442720532417,
-0.031141698360443115,
0.005431214813143015,
-0.05362621322274208,
0.02410530112683773,
0.01607411727309227,
-0.06539177894592285,
-0.03664366155862808,
-0.036350857466459274,
-0.07740555703639984,
0.016300296410918236,
-0.0006114677526056767,
0.05752477049827576,
0.015307518653571606,
-0.069212906062603,
0.07793762534856796,
0.012717184610664845,
-0.020069675520062447,
-0.004080795682966709,
-0.022485598921775818,
0.006075222510844469,
-0.01858733594417572,
-0.015111755579710007,
0.020608635619282722,
-0.0006033749086782336,
-0.00027397327357903123,
-0.002726588398218155,
0.021083857864141464,
-0.002431360771879554,
0.0022939585614949465,
-0.009076097048819065,
-0.005011921748518944,
0.023378757759928703,
-0.0222096536308527,
0.04900215193629265,
0.02660607174038887,
-0.026224125176668167,
-0.015015751123428345,
0.019962435588240623,
0.028335770592093468,
0.014745166525244713,
-0.01681986078619957,
0.03442543372511864,
-0.033339809626340866,
0.018833057954907417,
-0.011050431057810783,
0.05558178573846817,
-0.02218952588737011,
-0.02428075298666954,
0.021358048543334007,
0.02348357066512108,
-0.020714888349175453,
-0.056809812784194946,
-0.01478780247271061,
0.037717320024967194,
0.05429081246256828,
-0.05447470769286156,
-0.03757816553115845,
0.016177281737327576,
0.0017656992422416806,
0.029944008216261864,
-0.012987527064979076,
-0.0042691598646342754,
0.034274835139513016,
0.023043494671583176,
0.014806784689426422,
-0.005216928198933601,
-0.021490542218089104,
-0.012734916061162949,
-0.04435346648097038,
-0.015959348529577255,
0.024067450314760208,
0.047708556056022644,
0.008780593052506447,
0.0639440193772316,
0.02966197580099106,
0.0054610855877399445,
0.02970222383737564,
0.012100701220333576,
-0.07741037756204605,
-0.004329477436840534,
-0.027550632134079933,
-0.039999302476644516,
-0.012520083226263523,
-0.029836509376764297,
-0.0415765643119812,
-0.0134843485429883,
-0.04019656777381897,
-0.008053312078118324,
-0.004881016444414854,
-0.0346430204808712,
0.045053012669086456,
-0.04108868166804314,
-0.03448076546192169,
-0.02107502520084381,
0.0073487041518092155,
0.03214138373732567,
-0.05052328482270241,
-0.027077211067080498,
0.02855340950191021,
-0.057571928948163986,
-0.0017510972684249282,
-0.010241364128887653,
0.013111132197082043,
0.039672113955020905,
0.015977485105395317,
0.022537382319569588,
-0.022240012884140015,
-0.020074093714356422,
0.013775491155683994,
0.03645213320851326,
0.054683391004800797,
0.004582483321428299,
-0.0296340249478817,
-0.023289958015084267,
-0.009663845412433147,
-0.027636079117655754,
-0.007081275340169668,
0.08379939943552017,
0.03002881444990635,
-0.004217211157083511,
0.025469914078712463,
0.008141330443322659,
0.020732782781124115,
0.06024834141135216,
0.029723983258008957,
0.006318334490060806,
-0.0327947698533535,
-0.06228186935186386,
0.032763026654720306,
-0.042154379189014435,
-0.036691971123218536,
0.020931052044034004,
-0.011294694617390633,
0.01296172197908163,
-0.03141048178076744,
-0.002383529907092452,
0.017634766176342964,
-0.010898607783019543,
0.042459942400455475,
0.01090517733246088,
-0.00898793712258339,
0.0020803960505872965,
0.006498447619378567,
0.03162333741784096,
0.04068279266357422,
0.04060634598135948,
0.0026431495789438486,
-0.03307681903243065,
-0.06716150790452957,
0.021096760407090187,
0.013891030102968216,
0.03763919696211815,
-0.02202758565545082,
-0.01221061497926712,
-0.045514337718486786,
-0.009856890887022018,
0.0324404202401638,
-0.024788718670606613,
0.030896255746483803,
-0.03614092245697975,
0.005881877150386572,
-0.03944694995880127,
-0.039733633399009705,
-0.043667279183864594,
0.00917479582130909,
0.015521201305091381,
0.021867677569389343,
-0.005495843477547169,
0.016728481277823448,
0.027295269072055817,
0.028467517346143723,
0.07543303817510605,
0.07092287391424179,
0.006688613444566727,
0.0016286182217299938,
-0.02258440852165222,
0.00935960840433836,
-0.04822587966918945,
-0.057876020669937134,
0.03359564021229744,
-0.03475756198167801,
-0.010810616426169872,
0.006909566931426525,
-0.022787464782595634,
-0.049661166965961456,
-0.006403991021215916,
-0.006683829240500927,
-0.03137867525219917,
-0.00002840785964508541,
-0.028325891122221947,
0.03357734903693199,
0.03650420159101486,
0.021047478541731834,
0.03729734569787979,
0.027762901037931442,
-0.031084610149264336,
-0.038476429879665375,
-0.011689020320773125,
0.01599104143679142,
0.00018641204223968089,
0.0018885467434301972,
-0.03309391438961029,
0.029715461656451225,
-0.05334573984146118,
0.03785872459411621,
-0.012617424130439758,
-0.007019922602921724,
-0.0402616411447525,
-0.018578290939331055,
0.001348966034129262,
0.01256618369370699,
-0.01687779650092125,
0.016759151592850685,
-0.017323609441518784,
0.04175335541367531,
0.0003883884637616575,
0.02478806860744953,
0.011083770543336868,
0.006735741160809994,
0.022857632488012314,
0.024728810414671898,
-0.008735356852412224,
0.009171763435006142,
-0.02174227684736252,
0.012882156297564507,
-0.0063880137167871,
-0.03171543404459953,
0.03471485897898674,
-0.0077987597323954105,
-0.0223664790391922,
-0.0013561471132561564,
-0.08583151549100876,
-0.05047198012471199,
0.01902168057858944,
0.007058458868414164,
0.02799866907298565,
-0.05646514520049095,
0.02340386062860489,
0.05072202533483505,
0.025568481534719467,
-0.044876113533973694,
-0.05546459183096886,
-0.02813810296356678,
0.024371182546019554,
0.043197743594646454,
0.010368508286774158,
0.014372465200722218,
-0.030323978513479233,
-0.01832725666463375,
0.002439557109028101,
0.06922242790460587,
-0.02420637011528015,
-0.007199379149824381,
0.01674296148121357,
0.0011049414752051234,
0.02653638646006584,
-0.024966944009065628,
-0.008137580007314682,
0.006324103567749262,
0.010828234255313873,
0.02919960580766201,
-0.003430483862757683,
0.056140776723623276,
-0.0003191518771927804,
-0.044168587774038315,
0.004498772323131561,
-0.007753347046673298,
0.04851968586444855,
-0.03397779166698456,
-0.03967314958572388,
0.0303861852735281,
0.03141970559954643,
-0.015532624907791615,
-0.020425323396921158,
0.0055878800339996815,
0.03272649273276329,
0.01766286790370941,
-0.006349967326968908,
0.023799216374754906,
-0.039491407573223114,
-0.049350131303071976,
0.02515425905585289,
-0.004099052399396896,
-0.007778706960380077,
-0.013972925022244453,
0.08099043369293213,
0.003319665789604187,
-0.000721483607776463,
0.03162478655576706,
-0.013521059416234493,
0.011687308549880981,
0.029441097751259804,
0.006785299628973007,
0.012881984002888203,
-0.008850766345858574,
0.021114686504006386,
0.0014458458172157407,
-0.011304274201393127,
0.04935796186327934,
0.09948872774839401,
-0.038570303469896317,
0.06875385344028473,
0.023408621549606323,
-0.006842521950602531,
-0.011081556789577007,
-0.03140651807188988,
0.018001064658164978,
-0.010689697228372097,
-0.01688246615231037,
0.028663264587521553,
-0.03659505397081375,
0.012005060911178589,
0.02818560227751732,
0.0518307127058506,
-0.01747734844684601,
-0.016957798972725868,
0.03324666991829872,
0.0574234277009964,
0.03178836405277252,
-0.02017729915678501,
-0.04082665219902992,
0.051595430821180344,
-0.036161795258522034,
-0.009306509047746658,
0.008378477767109871,
-0.025292277336120605,
0.02517859824001789,
-0.003006669459864497,
-0.009267923422157764,
-0.02714749425649643,
-0.018479011952877045,
-0.012031328864395618,
0.0078888526186347,
0.0069382889196276665,
0.019062291830778122,
0.012223928235471249,
-0.0015537081053480506,
0.044055692851543427,
0.007970957085490227,
0.021345874294638634,
0.00007659780385438353,
-0.07990236580371857,
-0.05726683512330055,
-0.04301805421710014,
-0.007039990276098251,
0.044550780206918716,
-0.018030056729912758,
-0.028270114213228226,
-0.0045152697712183,
-0.017697805538773537,
0.06419940292835236,
0.0385625921189785,
-0.00466530816629529,
-0.03865806758403778,
0.03357947617769241,
-0.032567061483860016,
-0.0005286657251417637,
-0.026359334588050842,
0.009074843488633633,
0.12665405869483948,
0.03059380128979683,
0.009927947074174881,
-0.03603459522128105,
0.03443855047225952,
0.004786999896168709,
-0.038426343351602554,
-0.01969734951853752,
0.002775866538286209,
-0.03579803183674812,
-0.0015830063493922353,
0.009030437096953392,
0.024096190929412842,
0.03243498131632805,
-0.025923151522874832,
0.04655195772647858,
-0.04107632860541344,
-0.019706472754478455,
0.009407557547092438,
0.0172087661921978,
-0.018620356917381287,
0.03613860905170441,
-0.026181593537330627,
0.029460066929459572,
-0.02982315979897976,
-0.007531662471592426,
0.014709078706800938,
-0.00790849793702364,
0.014712551608681679,
0.0386410690844059,
-0.04313969612121582,
0.018594184890389442,
0.01782274805009365,
-0.03539491444826126,
-0.0680975615978241,
0.045996811240911484,
0.028076641261577606,
-0.01861647516489029,
0.009603215381503105,
-0.018570244312286377,
0.0328802689909935,
-0.007654767483472824,
0.037175942212343216,
0.03946034237742424,
-0.04785729944705963,
0.023676659911870956,
-0.044075995683670044,
0.03778298199176788,
-0.030886687338352203,
-0.000973649846855551,
0.004221306648105383,
-0.01550966314971447,
-0.017896413803100586,
-0.06258345395326614,
-0.013875320553779602,
-0.01025047991424799,
0.042353224009275436,
-0.008249474689364433,
-0.014306429773569107,
0.02284039370715618,
0.02910713292658329,
-0.019078796729445457,
0.006442896090447903,
0.007463534362614155,
0.006311628036201,
-0.0013001755578443408,
0.029339144006371498,
0.0036289608106017113,
-0.006245219148695469,
-0.011587852612137794,
-0.04111356660723686,
-0.041247814893722534,
-0.04998883605003357,
-0.004539337940514088,
0.021087396889925003,
0.040039706975221634,
0.02692134864628315,
-0.014171617105603218,
0.01586511917412281,
-0.04660879075527191,
-0.07748395204544067,
-0.0012025187024846673,
0.0020530824549496174,
-0.01747015491127968,
-0.020128874108195305,
-0.020245319232344627,
0.02407141588628292,
0.0306015033274889,
-0.012654336169362068,
-0.010274527594447136,
0.03130429610610008,
0.02702111192047596,
-0.005405713338404894,
-0.0039351936429739,
-0.0197585541754961,
0.017681114375591278,
-0.0075233690440654755,
0.00242991023696959,
-0.02956307865679264,
0.0017126095481216908,
0.017199495807290077,
0.027738338336348534,
-0.02451559156179428,
0.06529425829648972,
0.009653293527662754,
0.027935750782489777,
0.01811080425977707,
0.014007532969117165,
0.011251874268054962,
0.05281330645084381,
0.03028981387615204,
-0.015211740508675575,
-0.025761311873793602,
-0.02621370367705822,
0.008589066565036774,
0.011893684044480324,
0.008825010620057583,
-0.022310398519039154,
-0.042648591101169586,
0.004772834945470095,
-0.002378898672759533,
-0.010397880338132381,
-0.02329687774181366,
-0.03999441862106323,
-0.0033019590191543102,
-0.01909138821065426,
-0.028904559090733528,
0.00018040639406535774,
0.018333539366722107,
-0.022105233743786812,
-0.005179147701710463,
0.017876701429486275,
0.025725776329636574,
-0.02373524010181427,
-0.02672763355076313,
-0.005129541736096144,
-0.006100015249103308,
0.056934043765068054,
-0.027691803872585297,
-0.008101994171738625,
0.03116675280034542,
-0.025873787701129913,
-0.02550201676785946,
0.020912719890475273,
-0.0267794206738472,
0.0011040129465982318,
0.07035701721906662,
0.019250893965363503,
0.011027874425053596,
0.036960046738386154,
-0.03260871022939682,
0.040493737906217575,
-0.007877673022449017,
-0.04034406691789627,
-0.01618986204266548,
-0.03617914021015167,
-0.009559033438563347,
0.0007408551755361259,
0.012982730753719807,
0.028935495764017105,
0.0473693311214447,
0.018051261082291603,
0.0034253536723554134,
0.031177926808595657,
0.013186370022594929,
-0.029526237398386,
0.05371107533574104,
0.011676141060888767,
0.007987892255187035,
0.02615926042199135,
-0.05798365920782089,
0.021885108202695847,
0.004179198294878006,
-0.02249945141375065,
-0.0971321165561676,
-0.027851799502968788,
0.021818894892930984,
0.022762225940823555,
0.05908574163913727,
-0.049954380840063095,
-0.002120775869116187,
0.0383293554186821,
-0.0737910270690918,
0.017326967790722847,
-0.006011461839079857,
-0.029998473823070526,
0.011577490717172623,
-0.005796530749648809,
0.02308829128742218,
0.030727455392479897,
0.01363321766257286,
0.030553530901670456,
0.010857940651476383,
0.01743520237505436,
0.019073013216257095,
-0.024105466902256012,
-0.05192335695028305,
0.012064311653375626,
-0.017315153032541275,
0.003078693524003029,
0.05435365065932274,
0.018124958500266075,
0.010665417648851871,
0.059330444782972336,
-0.02505909837782383,
-0.016457868739962578,
0.023404940962791443,
0.036398377269506454,
-0.013536045327782631,
0.026106825098395348,
0.008176177740097046,
-0.013371500186622143,
0.004436568357050419,
0.02012578956782818,
0.06684572994709015,
0.03355630859732628,
0.0009494475089013577,
-0.012676678597927094,
0.022792572155594826,
-0.014258458279073238,
-0.047687456011772156,
-0.007111829239875078,
-0.03035111166536808,
-0.01775169000029564,
0.01959647424519062,
0.07636433094739914,
-0.01703755557537079,
0.0053209881298244,
0.00016564957331866026,
-0.048243701457977295,
-0.013497724197804928,
0.04469990357756615,
0.02388375997543335,
-0.0045427484437823296,
-0.003538127988576889,
-0.02705513872206211,
-0.03162689134478569,
0.02143268845975399,
0.015421855263411999,
0.007546059787273407,
-0.06538283079862595,
-0.00756665226072073,
-0.0016090029384940863,
-0.010368932038545609,
0.015557334758341312,
-0.042873576283454895,
-0.0672406554222107,
0.05102283135056496,
0.014128345996141434,
0.0035783485509455204,
-0.024625713005661964,
-0.018257899209856987,
0.0011754677398130298,
-0.08404842764139175,
0.04990188032388687,
0.018522026017308235,
-0.039170801639556885,
-0.02624976448714733,
-0.020610809326171875,
-0.017062945291399956,
-0.025804884731769562,
0.05857259780168533,
-0.004177716560661793,
-0.004627905786037445,
0.019041098654270172,
-0.004264552146196365,
0.011499813757836819,
-0.025363821536302567,
-0.026365898549556732,
0.014033657498657703,
-0.010878726840019226,
-0.03361579403281212,
0.014227231033146381,
-0.005809018854051828,
0.0009532389813102782,
-0.01662268303334713,
0.002649668836966157,
0.03933876007795334,
-0.016343601047992706,
-0.01289736945182085,
0.04644790664315224,
0.015827154740691185,
-0.021661974489688873,
0.032881200313568115,
-0.03694082796573639,
0.04073568060994148,
0.0013717117253690958,
-0.03495115414261818,
-0.05265842005610466,
0.0019040853949263692,
-0.023832637816667557,
0.01191137358546257,
-0.006733633577823639,
-0.02023918181657791,
0.02804216742515564,
-0.03263916075229645,
-0.030565856024622917,
0.04951535165309906,
-0.0486828051507473,
-0.024970900267362595,
0.07163593918085098,
-0.014664139598608017,
0.021391164511442184,
0.01951749064028263,
0.002968503162264824,
0.021196486428380013,
-0.01868688501417637,
0.008965964429080486,
0.013593794777989388,
0.016926761716604233,
0.01394671481102705,
0.015858307480812073,
0.09616188704967499,
0.01758141629397869,
-0.002223850693553686,
0.0017818165943026543,
0.017057958990335464,
-0.016010316088795662,
-0.031358782202005386,
0.01478319987654686,
-0.01911727525293827,
0.04099896177649498,
-0.022624896839261055,
-0.002614692784845829,
0.08320693671703339,
-0.023531874641776085,
0.032527800649404526,
-0.027805645018815994,
0.019194288179278374,
0.0011672088876366615,
-0.013775939121842384,
-0.020369525998830795,
0.06526904553174973,
-0.02560962550342083,
-0.027908068150281906,
-0.0281797144562006,
-0.014766202308237553,
0.03670115023851395,
-0.008928303606808186,
0.019004741683602333,
-0.021606341004371643,
0.008598252199590206,
-0.027683690190315247,
-0.0043699732050299644,
-0.01595926098525524,
-0.03218584880232811,
0.02595420926809311,
0.0034484073985368013,
0.03984769806265831,
-0.00038373758434318006,
0.0045724473893642426,
-0.0474642775952816,
0.015212306752800941,
-0.040826015174388885,
-0.03933955356478691,
-0.015925314277410507,
0.017877845093607903,
0.010097827762365341,
-0.0018832364585250616
] |
<p>I know it does not because it emerges out of denser medium at 300,000 KM per second, but according to E=MC square and given that speed of light decreases inside denser medium with refractive index greater than 1, does not it suggest that energy of light inside denser medium is less?</p>
| 7,601 |
[
-0.06614520400762558,
-0.021660247817635536,
-0.002809383673593402,
-0.017287887632846832,
0.04156126454472542,
0.04534532502293587,
-0.06126691773533821,
-0.051597919315099716,
-0.036316145211458206,
-0.043628156185150146,
0.014253443107008934,
0.027329478412866592,
0.06427893042564392,
0.02001368999481201,
0.01998915523290634,
0.026413245126605034,
0.00403154781088233,
0.018006887286901474,
-0.004574066959321499,
-0.05240575596690178,
-0.029804423451423645,
0.01611233502626419,
0.01874961517751217,
0.0028529115952551365,
-0.05119018629193306,
0.038626622408628464,
0.00971535500138998,
0.007720845751464367,
0.028748296201229095,
0.04965633898973465,
-0.0009157361928373575,
-0.001569160376675427,
0.02927270159125328,
0.04943221062421799,
0.004435249138623476,
0.015158288180828094,
-0.03253059834241867,
-0.0021838098764419556,
0.002867999719455838,
0.008107046596705914,
0.03764241188764572,
-0.012178746983408928,
0.0009599539334885776,
0.06481028348207474,
-0.01578373648226261,
0.01016878243535757,
0.02997608110308647,
-0.03312552720308304,
0.04521039128303528,
-0.06463967263698578,
0.04923568665981293,
-0.02365032210946083,
0.021199889481067657,
0.018502434715628624,
-0.026140926405787468,
-0.007967183366417885,
0.09003077447414398,
0.07242893427610397,
-0.0076757981441915035,
-0.030244646593928337,
0.003255018964409828,
0.002399883233010769,
-0.006499875336885452,
0.0006171261193230748,
-0.005216118413954973,
0.005046179983764887,
-0.02578425221145153,
-0.020354686304926872,
0.03666076436638832,
0.020547226071357727,
0.000003962526079703821,
0.004650048445910215,
0.0256662555038929,
0.007397869136184454,
0.015106280334293842,
-0.028224674984812737,
0.022437816485762596,
0.01219707727432251,
0.055309511721134186,
0.051334794610738754,
-0.018440835177898407,
-0.01276321616023779,
0.02741887792944908,
0.045515161007642746,
0.02079971879720688,
0.03037620335817337,
0.06568817049264908,
-0.011588510125875473,
-0.00811986718326807,
0.03315304219722748,
-0.02908400073647499,
-0.012206624262034893,
0.00862520094960928,
0.0004318256687838584,
0.0016529278364032507,
0.00951874814927578,
-0.02634080871939659,
0.055383265018463135,
0.019916987046599388,
-0.04040369763970375,
-0.00258517824113369,
0.0044181994162499905,
0.052311547100543976,
0.06718842685222626,
0.02160712704062462,
-0.0323384664952755,
-0.0854482650756836,
0.020675061270594597,
-0.0389605350792408,
-0.005068728234618902,
-0.010178998112678528,
0.007732025813311338,
-0.009784052148461342,
-0.012996373698115349,
0.023533891886472702,
-0.05415597930550575,
0.028976110741496086,
0.0121648283675313,
0.07513533532619476,
0.08288471400737762,
0.025854481384158134,
-0.025430355221033096,
0.015357238240540028,
-0.020199870690703392,
-0.06351151317358017,
0.054838165640830994,
0.031223200261592865,
-0.025026194751262665,
-0.028612222522497177,
0.027976416051387787,
-0.03353044390678406,
-0.016363294795155525,
-0.0028993249870836735,
-0.03310889005661011,
0.03074765019118786,
-0.00047287638881243765,
-0.09084071964025497,
-0.057650670409202576,
0.046959277242422104,
-0.013202009722590446,
-0.014605237171053886,
-0.07649321854114532,
0.021622372791171074,
0.01425067987293005,
0.09367594867944717,
-0.0048197489231824875,
0.03553714603185654,
-0.03373951092362404,
0.04521552845835686,
-0.008607602678239346,
-0.030291788280010223,
-0.03481235355138779,
0.016556788235902786,
-0.05259142071008682,
0.014379824511706829,
-0.09599719196557999,
-0.001893484266474843,
0.02654632367193699,
-0.027304422110319138,
-0.01260150782763958,
0.0712088868021965,
-0.0575532391667366,
0.02338285557925701,
0.011495377868413925,
-0.000042419531382620335,
-0.023578966036438942,
0.10452074557542801,
0.022475866600871086,
0.03431034833192825,
0.004517670720815659,
0.018504351377487183,
0.01824057660996914,
-0.01420122291892767,
0.011737667955458164,
0.042454950511455536,
-0.031808096915483475,
-0.02100687474012375,
-0.018613748252391815,
0.033652838319540024,
0.018855201080441475,
-0.02952837385237217,
-0.056378141045570374,
0.005449430085718632,
-0.023845698684453964,
-0.004132901318371296,
0.057280246168375015,
-0.0184688288718462,
-0.01128061581403017,
-0.01866152510046959,
-0.04376767948269844,
-0.01664520427584648,
-0.013667167164385319,
0.018939388915896416,
0.06464087218046188,
0.004018837586045265,
-0.0051661645993590355,
-0.00986047089099884,
0.028489975258708,
-0.017654893919825554,
0.0002943102444987744,
-0.0276565533131361,
0.02107631228864193,
-0.007833467796444893,
-0.02048306167125702,
0.027366340160369873,
0.023103931918740273,
0.03316059336066246,
-0.0040275948122143745,
-0.013561087660491467,
0.005099799018353224,
-0.04756845161318779,
0.02521008811891079,
0.004951881244778633,
0.003864265512675047,
0.002559546148404479,
-0.017052799463272095,
0.025270255282521248,
0.03491311892867088,
-0.0001393529964843765,
0.02566465735435486,
-0.01579238288104534,
0.05472999066114426,
0.030102377757430077,
0.028482593595981598,
-0.004002630710601807,
0.028572550043463707,
-0.00161740614566952,
-0.004542213398963213,
-0.0037118406035006046,
-0.01202442217618227,
-0.01276091393083334,
-0.009619705379009247,
0.0359729528427124,
-0.023024169728159904,
-0.07549218833446503,
0.019276300445199013,
0.04181750863790512,
0.020445754751563072,
0.04030902311205864,
0.038941774517297745,
-0.028685996308922768,
-0.07365989685058594,
0.0186239555478096,
0.03655298426747322,
0.000975417613517493,
0.002440743613988161,
0.029003651812672615,
-0.0060960277915000916,
-0.008497575297951698,
-0.03205622360110283,
0.0234125517308712,
-0.012653215788304806,
0.00646372651681304,
-0.008350259624421597,
-0.0016627260483801365,
-0.031052177771925926,
-0.004099925514310598,
-0.02922039106488228,
0.013320832513272762,
0.010242833755910397,
-0.004337608814239502,
0.043681975454092026,
-0.05638383701443672,
-0.014455953612923622,
0.03582931309938431,
0.019550520926713943,
-0.01527644507586956,
0.003584829391911626,
0.04248269647359848,
-0.06505943089723587,
0.02125518210232258,
-0.010183676145970821,
-0.001389803714118898,
-0.05716283991932869,
-0.013812670484185219,
0.009706650860607624,
-0.011704644188284874,
0.005119593348354101,
-0.04366841912269592,
-0.030649637803435326,
-0.002503756433725357,
-0.04053037613630295,
-0.023642979562282562,
-0.018064916133880615,
-0.025983108207583427,
0.0390874519944191,
-0.0059923394583165646,
-0.05592183768749237,
0.023153435438871384,
-0.01491524837911129,
0.006733734626322985,
0.033975351601839066,
0.00031298381509259343,
-0.05489133298397064,
0.007565173786133528,
-0.02330205589532852,
-0.02094457857310772,
-0.010694464668631554,
-0.028360659256577492,
0.05299143120646477,
-0.03955082595348358,
-0.04139747470617294,
-0.015785548835992813,
-0.032593391835689545,
-0.03822578489780426,
-0.03026822954416275,
-0.01520365197211504,
0.023025818169116974,
-0.030412564054131508,
0.040143031626939774,
0.009224520064890385,
-0.03414861485362053,
0.016634240746498108,
-0.04176389425992966,
-0.048533886671066284,
0.05425842106342316,
0.00020081967522855848,
0.06223593279719353,
-0.028270283713936806,
-0.05000532791018486,
0.023504238575696945,
0.07422953844070435,
-0.014772379770874977,
-0.01942365989089012,
-0.003053575288504362,
0.017705712467432022,
-0.025949031114578247,
0.008561765775084496,
0.016134018078446388,
0.013762268237769604,
0.013621860183775425,
0.0225882176309824,
0.04842013865709305,
0.022746600210666656,
0.005469476338475943,
-0.014822198078036308,
0.01889672875404358,
-0.023503027856349945,
0.00802500918507576,
0.05086873844265938,
0.031698353588581085,
-0.056986335664987564,
0.03549714758992195,
-0.004260670859366655,
0.06351486593484879,
0.004317617509514093,
-0.028716936707496643,
0.06428937613964081,
0.007406170479953289,
0.03963269293308258,
-0.007716365158557892,
0.05034417659044266,
0.022595005109906197,
0.03314288705587387,
0.012819916009902954,
0.005081535782665014,
0.03477194532752037,
0.005113492254167795,
-0.014779181219637394,
-0.005871723871678114,
0.006791213992983103,
0.00014287815429270267,
-0.037097036838531494,
-0.005693553481251001,
-0.03607020154595375,
0.03208146616816521,
-0.024250568822026253,
-0.03073248825967312,
0.06801072508096695,
0.022899582982063293,
0.018878327682614326,
-0.0146170724183321,
-0.03727466240525246,
0.003296256996691227,
-0.018653504550457,
-0.01110887248069048,
0.006564669776707888,
0.034922078251838684,
0.025714769959449768,
0.060041312128305435,
0.03423057496547699,
0.029789380729198456,
0.02496819943189621,
0.012035658583045006,
-0.07807281613349915,
-0.0232512429356575,
-0.05337110906839371,
-0.042965080589056015,
-0.021961314603686333,
-0.0171958114951849,
-0.05390969291329384,
-0.014831658452749252,
-0.006435599643737078,
-0.005325850564986467,
-0.0022711954079568386,
-0.06801249831914902,
-0.0039174677804112434,
-0.03784450143575668,
-0.031358007341623306,
-0.0335637591779232,
0.0433853343129158,
0.027989858761429787,
0.026994451880455017,
0.013446497730910778,
0.04426753148436546,
-0.041515570133924484,
-0.0009385602897964418,
0.020623117685317993,
0.005682963877916336,
-0.0005606810445897281,
0.009384975768625736,
0.031424105167388916,
-0.01223059929907322,
-0.026814963668584824,
0.030323451384902,
0.05378319323062897,
0.020966019481420517,
-0.004202354699373245,
-0.013177539221942425,
-0.033703308552503586,
0.009206998161971569,
-0.04049474373459816,
-0.0015569429378956556,
0.04733624309301376,
-0.03265571966767311,
-0.0006482115713879466,
0.014050887897610664,
0.003064096439629793,
0.001196448807604611,
0.03073047287762165,
0.019908737391233444,
-0.017611131072044373,
-0.02024185098707676,
-0.056712958961725235,
-0.006669926922768354,
-0.044601306319236755,
-0.04385734722018242,
0.013043545186519623,
0.0020989314652979374,
-0.028739623725414276,
-0.004191630519926548,
0.0027181997429579496,
0.01947467401623726,
-0.0016023569041863084,
-0.014046363532543182,
-0.01350050326436758,
-0.01393046136945486,
-0.010144948959350586,
-0.006802969612181187,
0.012332597747445107,
0.038842540234327316,
0.014194696210324764,
-0.024276012554764748,
0.013266125693917274,
-0.06760554760694504,
-0.021049920469522476,
0.014311017468571663,
0.04347757622599602,
-0.005841624457389116,
0.010017209686338902,
-0.0681094080209732,
-0.0005131819052621722,
0.017090018838644028,
-0.04948211461305618,
0.020980283617973328,
0.0024520275183022022,
0.0017341946950182319,
-0.004577377811074257,
-0.012855513952672482,
-0.00826021283864975,
0.03497327119112015,
0.015372518450021744,
0.013597503304481506,
-0.0013231231132522225,
0.030744237825274467,
-0.0020247206557542086,
-0.008690482936799526,
0.011113631539046764,
0.049776263535022736,
0.011317845433950424,
-0.010104905813932419,
-0.020963599905371666,
0.024400494992733,
-0.014310400933027267,
-0.05585116893053055,
-0.01151012908667326,
-0.012875283136963844,
-0.016451796516776085,
0.033398982137441635,
-0.0363243892788887,
-0.04400264099240303,
0.04322930797934532,
0.024870740249753,
-0.03255932405591011,
-0.008300690911710262,
-0.055775951594114304,
0.028662653639912605,
-0.03277908265590668,
-0.01935291662812233,
0.01751314103603363,
0.055624376982450485,
-0.010742757469415665,
-0.002433585003018379,
-0.019566284492611885,
0.056440651416778564,
-0.06666846573352814,
-0.009307077154517174,
0.022342262789607048,
0.008335625752806664,
-0.026508042588829994,
0.04903019219636917,
-0.035929225385189056,
0.03170938044786453,
0.006444551981985569,
-0.020486872643232346,
-0.02749958634376526,
0.02998611517250538,
0.0036665392108261585,
0.0086543969810009,
-0.045931048691272736,
0.0006212638691067696,
-0.001092909020371735,
-0.023996956646442413,
0.02323099970817566,
0.0001840147451730445,
-0.006732044741511345,
0.05864594876766205,
0.028948215767741203,
0.04168432950973511,
-0.015172230079770088,
-0.011031236499547958,
0.01665758527815342,
-0.037799037992954254,
0.036641206592321396,
-0.012355508282780647,
0.014705483801662922,
0.014362993650138378,
-0.05659015476703644,
-0.005005931947380304,
-0.020047307014465332,
-0.010012457147240639,
0.02020583488047123,
-0.0573456808924675,
0.010174314491450787,
0.00008541849092580378,
0.0027597094886004925,
-0.08800617605447769,
-0.038761936128139496,
-0.009556550532579422,
0.023653903976082802,
-0.004791100975126028,
-0.013900048099458218,
0.008721268735826015,
-0.03751781955361366,
-0.024154167622327805,
-0.02031867206096649,
0.005953694693744183,
0.007835068739950657,
-0.015120964497327805,
-0.010679119266569614,
-0.015177411027252674,
0.03343568742275238,
-0.005585983395576477,
-0.018609868362545967,
0.018198354169726372,
0.0019530677236616611,
-0.017882509157061577,
-0.006377238780260086,
0.07880296558141708,
-0.003597622737288475,
-0.024578923359513283,
-0.016576426103711128,
-0.0177882369607687,
0.006656719371676445,
0.0006001575966365635,
0.02855641022324562,
0.05840672552585602,
-0.004394496791064739,
0.006339340936392546,
-0.026537885889410973,
0.02609049715101719,
-0.004336441867053509,
0.029136890545487404,
0.02593880146741867,
-0.03850933909416199,
-0.05857514962553978,
-0.041426174342632294,
0.009963160380721092,
-0.008651338517665863,
0.036417558789253235,
-0.029115211218595505,
0.10355167835950851,
0.012968098744750023,
-0.010724793188273907,
-0.005839006509631872,
0.0009102069307118654,
-0.02860422618687153,
-0.007400469854474068,
-0.011734302155673504,
0.01781608536839485,
0.03422066941857338,
0.010495399124920368,
-0.025090180337429047,
0.0015132083790376782,
0.00579494796693325,
0.0645667240023613,
-0.018273741006851196,
0.051466748118400574,
-0.035292647778987885,
-0.016315557062625885,
0.01788884587585926,
-0.0149474972859025,
0.001860601594671607,
0.002394811948761344,
-0.0020483683329075575,
0.019284391775727272,
-0.00042532404768280685,
0.0015453564701601863,
0.037001833319664,
0.07271462678909302,
-0.02724754624068737,
0.05476158484816551,
0.0487639419734478,
0.03463993966579437,
0.01568153314292431,
0.01088913343846798,
-0.048972997814416885,
0.0315232053399086,
-0.03128940239548683,
0.036323029547929764,
-0.002306757727637887,
0.006221772637218237,
0.03902047127485275,
0.002571587450802326,
0.003503878600895405,
-0.039363134652376175,
-0.03525036945939064,
-0.03193880245089531,
0.01078872848302126,
0.009185335598886013,
0.011319134384393692,
-0.021186571568250656,
0.010599733330309391,
-0.01997881568968296,
0.05531218275427818,
0.01992756500840187,
0.007386784069240093,
-0.055035512894392014,
-0.04083099216222763,
-0.0331043042242527,
-0.03044583648443222,
0.017693674191832542,
0.006698209792375565,
-0.038088396191596985,
0.0006891554221510887,
-0.036202892661094666,
0.017849944531917572,
0.030346406623721123,
0.01817082241177559,
0.023860014975070953,
0.04810921847820282,
0.012006803415715694,
0.03356509283185005,
0.006773138418793678,
-0.00373923615552485,
0.09007071703672409,
0.06295861303806305,
0.0039756339974701405,
-0.06971362978219986,
0.018033772706985474,
-0.04374212399125099,
0.04648659750819206,
-0.04859161749482155,
0.023610981181263924,
-0.03346172720193863,
0.03970600292086601,
0.02989768609404564,
0.052835170179605484,
-0.0033851589541882277,
-0.018172932788729668,
-0.012370957061648369,
-0.03740912303328514,
-0.034343671053647995,
0.020296024158596992,
0.0521429181098938,
-0.008363657630980015,
0.001689690281637013,
-0.02470851130783558,
0.0029697392601519823,
-0.03830726444721222,
-0.0127830496057868,
-0.025394003838300705,
-0.029181914404034615,
0.034266192466020584,
-0.023462919518351555,
-0.06113533303141594,
-0.04010198265314102,
0.029216531664133072,
-0.023669565096497536,
-0.034941647201776505,
0.0030539161525666714,
0.03366844356060028,
0.0052553522400557995,
-0.01019938476383686,
0.027275878936052322,
0.02292720042169094,
0.025270191952586174,
0.006627711001783609,
0.01882794126868248,
-0.043600037693977356,
0.024144310504198074,
-0.01877840794622898,
0.05883857607841492,
-0.004179815296083689,
0.007156827952712774,
0.021608388051390648,
0.006345571484416723,
-0.011795025318861008,
-0.07881522923707962,
0.0061990139074623585,
-0.014402217231690884,
-0.014904211275279522,
0.014449632726609707,
-0.03793221712112427,
-0.038009434938430786,
-0.016647547483444214,
0.008110829629004002,
0.005662850104272366,
-0.031489208340644836,
0.004679740406572819,
0.0002611606614664197,
0.011726677417755127,
0.006439157761633396,
-0.0554019957780838,
-0.049322038888931274,
-0.03512204438447952,
0.008264685049653053,
-0.05445490777492523,
-0.019254673272371292,
0.009408465586602688,
0.019688963890075684,
0.03397069498896599,
0.009815222583711147,
-0.016038434579968452,
-0.023555690422654152,
-0.08289928734302521,
0.03212622553110123,
-0.024135297164320946,
-0.010822772048413754,
-0.04152359440922737,
0.038044366985559464,
0.03213512897491455,
0.03016139194369316,
-0.009927981533110142,
0.0065339053981006145,
-0.02098977379500866,
0.054282043129205704,
0.004157536197453737,
-0.009550855495035648,
-0.02644399181008339,
-0.01855994574725628,
-0.01190311461687088,
0.011905476450920105,
-0.0005472348420880735,
0.002357345772907138,
0.02128591015934944,
0.006084777880460024,
0.013663689605891705,
0.01978403888642788,
-0.014277560636401176,
0.015800585970282555,
-0.013534201309084892,
-0.030201174318790436,
0.009190586395561695,
0.01811392977833748,
0.000028423693947843276,
0.01888859085738659,
-0.044532597064971924,
-0.030273588374257088,
0.0138913718983531,
-0.013614270836114883,
0.004306826740503311,
-0.01904154382646084,
0.0023338370956480503,
-0.012336726300418377,
0.027278533205389977,
-0.06082732230424881,
-0.021571798250079155,
-0.028839867562055588,
0.017537828534841537,
0.011317430064082146,
-0.021900029852986336,
-0.015772253274917603,
0.04816299304366112,
-0.019270852208137512,
0.0002900414983741939,
0.02301660180091858,
0.021664489060640335,
0.0006543059134855866,
0.0023153917863965034,
0.03729721158742905,
-0.0007213249336928129,
0.07050386816263199,
-0.020093949511647224,
-0.02435416541993618,
0.022092565894126892,
-0.053486213088035583,
-0.03746064379811287,
0.04131961241364479,
-0.00034125387901440263,
0.008832390420138836,
0.021076949313282967,
0.02411358430981636,
-0.02987579256296158,
0.08352577686309814,
0.009350006468594074,
-0.012155448086559772,
0.029884042218327522,
-0.049537159502506256,
0.03374674543738365,
-0.007737525273114443,
-0.007762141525745392,
0.000025004665076266974,
-0.013776020146906376,
0.04949444159865379,
0.024463867768645287,
-0.011422133073210716,
-0.009180130437016487,
0.005694081075489521,
-0.019702406600117683,
-0.006908513605594635,
0.03365295007824898,
-0.018180975690484047,
0.02866710163652897,
0.057543836534023285,
-0.03733039274811745,
0.04837775602936745,
0.04609835892915726,
-0.016689790412783623,
-0.11554337292909622,
-0.02128148078918457,
-0.01943349651992321,
0.03936449810862541,
0.027095824480056763,
-0.053294587880373,
0.07095498591661453,
0.02440391667187214,
-0.08867132663726807,
-0.007794510573148727,
-0.01956643909215927,
0.0014051038306206465,
-0.03400900959968567,
0.002598737133666873,
-0.014596459455788136,
0.046448707580566406,
0.037981923669576645,
0.013041011989116669,
0.04583120346069336,
0.022672563791275024,
-0.022025365382432938,
-0.0035738078877329826,
-0.006306988652795553,
0.05126089230179787,
-0.00447965320199728,
0.014701380394399166,
0.05522419512271881,
-0.00971157755702734,
-0.005106316413730383,
0.02709098905324936,
-0.011664008721709251,
0.01582038588821888,
0.030649051070213318,
-0.0014783788938075304,
0.005164422560483217,
0.008772904053330421,
0.026573508977890015,
-0.006999220699071884,
-0.01605517417192459,
0.039343416690826416,
0.016243314370512962,
-0.011545052751898766,
-0.018178418278694153,
-0.03145817667245865,
0.03035091608762741,
-0.061918988823890686,
-0.008295154199004173,
0.04098223149776459,
0.0019964773673564196,
0.01931270770728588,
-0.01650402694940567,
0.00034251835313625634,
0.023806467652320862,
0.003039602655917406,
0.00907187256962061,
-0.08843421190977097,
-0.03205451741814613,
0.033817749470472336,
0.021559860557317734,
-0.04590902104973793,
0.005556826014071703,
0.008706028573215008,
-0.041327983140945435,
0.007117731496691704,
-0.0012325919233262539,
-0.004582083784043789,
-0.0372258685529232,
0.0001733030949253589,
-0.009344910271465778,
-0.010210120119154453,
0.019212540239095688,
-0.04443599283695221,
-0.051318224519491196,
0.028632575646042824,
0.03397056460380554,
0.008813434280455112,
0.030301174148917198,
-0.007836783304810524,
-0.03547833487391472,
-0.08221472799777985,
0.041424915194511414,
-0.04740004613995552,
-0.021065931767225266,
-0.031334951519966125,
0.017138689756393433,
-0.0476565957069397,
0.01985146477818489,
0.041218351572752,
0.003830923466011882,
-0.02612561360001564,
0.017751913517713547,
0.027438294142484665,
-0.00013372239482123405,
-0.04452555999159813,
-0.005010311026126146,
0.012773536145687103,
-0.027655277401208878,
-0.013801246881484985,
0.009114712476730347,
-0.019069146364927292,
0.0021825116127729416,
0.012730948626995087,
0.008369389921426773,
0.019259341061115265,
-0.01261268649250269,
0.004008632153272629,
0.031121792271733284,
0.0002851073513738811,
-0.0019885024521499872,
0.06452296674251556,
-0.02349316142499447,
0.016924690455198288,
0.048425089567899704,
-0.0028955163434147835,
-0.017219319939613342,
0.02114640176296234,
-0.035408005118370056,
0.01985492743551731,
0.035198431462049484,
0.020342392846941948,
0.023677313700318336,
-0.031903836876153946,
0.020125851035118103,
0.0074632419273257256,
-0.03321443498134613,
-0.011532220058143139,
0.03843679279088974,
0.005668648984283209,
0.04359911382198334,
-0.01619027554988861,
0.03697308525443077,
0.0043716891668736935,
0.012707327492535114,
-0.033399730920791626,
0.06440473347902298,
-0.014736292883753777,
-0.008891037665307522,
0.04558168724179268,
0.016674384474754333,
-0.002261892892420292,
0.006831830367445946,
0.002307386137545109,
0.014996614307165146,
-0.03862406313419342,
-0.029232189059257507,
0.01800132542848587,
-0.025886170566082,
0.014882958494126797,
0.03180660679936409,
-0.01861305721104145,
0.05663355812430382,
0.005578272510319948,
0.03111620619893074,
-0.0017947745509445667,
-0.02004104293882847,
-0.04827982187271118,
0.03025531768798828,
0.05569372698664665,
0.03097725845873356,
0.011682679876685143,
-0.005458578933030367,
0.0035951780155301094,
-0.01005169004201889,
0.019327539950609207,
-0.05804478004574776,
-0.015307262539863586,
-0.03362847864627838,
-0.01465253159403801,
-0.015463856048882008,
0.03168188035488129,
0.02500247023999691,
-0.02212272398173809,
-0.016196338459849358,
0.006709689274430275,
0.02827838622033596,
0.0063375686295330524,
-0.0001868313702289015,
0.012079617008566856,
0.0789080411195755,
-0.02100243978202343,
0.018245814368128777,
0.001294660265557468,
0.02593095414340496,
-0.019622787833213806,
-0.00405103387311101
] |
<p>According to Landau's symmetry breaking theory, there is a symmetry breaking when phase transition occurs. </p>
<ol>
<li><p>What is the symmetry breaking of superfluid-Mott insulator transition in <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Hubbard_model" rel="nofollow">Bose-Hubbard model</a>? </p></li>
<li><p>Why metallic state to <a href="http://en.wikipedia.org/wiki/Mott_insulator" rel="nofollow">Mott insulator</a> state transition in <a href="http://www.google.com/search?q=Fermi+Hubbard+model" rel="nofollow">Fermi-Hubbard model</a> is not a phase transition, but a crossover.</p></li>
</ol>
| 7,602 |
[
-0.05342277139425278,
-0.025453979149460793,
0.01581513322889805,
-0.04689149558544159,
0.01645251363515854,
0.004912360571324825,
-0.046811699867248535,
-0.019821036607027054,
0.02221100404858589,
-0.04903729259967804,
0.05855215713381767,
-0.0008463873527944088,
0.0022217018995434046,
0.06188628450036049,
0.008086654357612133,
0.05840226635336876,
0.03049471415579319,
-0.028531638905405998,
-0.024222878739237785,
0.02747408114373684,
-0.026774270460009575,
0.052828915417194366,
-0.029915103688836098,
0.00008431985770585015,
-0.05891602858901024,
0.012833737768232822,
0.008345916867256165,
0.0340101458132267,
0.04345105215907097,
0.03416718170046806,
-0.033280808478593826,
-0.00910119153559208,
0.024031000211834908,
-0.013001907616853714,
0.009577692486345768,
0.014510457403957844,
-0.004596755374222994,
-0.037510715425014496,
0.026575051248073578,
-0.012131813913583755,
-0.007015800569206476,
0.03395954892039299,
-0.027383092790842056,
0.05185915157198906,
0.0040994323790073395,
-0.012773798778653145,
0.0067342245019972324,
-0.01807353086769581,
0.024048160761594772,
-0.06044843792915344,
0.03475368767976761,
-0.021612320095300674,
0.016632135957479477,
-0.019232161343097687,
0.010621490888297558,
0.004491189029067755,
0.03073039837181568,
0.09407588839530945,
0.010310627520084381,
-0.08186505734920502,
-0.008393301628530025,
-0.022032657638192177,
0.006497953552752733,
-0.027644725516438484,
-0.052255865186452866,
0.07453081011772156,
0.01322926115244627,
-0.025962665677070618,
0.0021601361222565174,
0.031543176621198654,
-0.02598137967288494,
0.0036221295595169067,
0.006432949099689722,
-0.006935177370905876,
0.04465324059128761,
-0.046360332518815994,
-0.0028220629319548607,
0.005176371429115534,
0.017233440652489662,
0.05250057950615883,
0.005243950989097357,
0.031852636486291885,
0.012839386239647865,
0.03599293529987335,
-0.0044040922075510025,
0.019478285685181618,
0.07169222831726074,
-0.013830697163939476,
0.0017999657429754734,
0.06602694094181061,
-0.0035049081780016422,
0.006659285165369511,
0.0264266524463892,
-0.027650563046336174,
-0.03433333337306976,
0.02304955944418907,
0.013433893211185932,
0.04551413655281067,
-0.023147979751229286,
-0.01196322962641716,
-0.0028224342968314886,
-0.010233653709292412,
0.03443024307489395,
0.06638304889202118,
-0.028635216876864433,
-0.006641396787017584,
-0.011769875884056091,
0.017213718965649605,
-0.03486045449972153,
-0.0257754884660244,
-0.0325586199760437,
-0.006117984652519226,
-0.00264921085909009,
-0.005125458352267742,
-0.03341293707489967,
-0.01370740681886673,
-0.020845161750912666,
-0.03386319428682327,
0.05200312286615372,
0.08566383272409439,
0.007759599015116692,
0.002832953818142414,
-0.01216980628669262,
-0.026080545037984848,
-0.09631484001874924,
0.00877625122666359,
0.028662515804171562,
-0.006248765625059605,
-0.026745382696390152,
0.030644968152046204,
-0.02653471753001213,
-0.0013327475171536207,
0.00008985824388219044,
-0.03274796903133392,
0.048985805362463,
-0.03505460545420647,
-0.10964228957891464,
-0.04329061880707741,
0.037501104176044464,
-0.008945349603891373,
-0.00577509356662631,
-0.05465737357735634,
0.052033599466085434,
0.013129121623933315,
0.08305846899747849,
-0.006960620172321796,
0.043873269110918045,
-0.005849902983754873,
0.021523769944906235,
0.014274239540100098,
0.020415250211954117,
-0.013750148937106133,
0.03697465732693672,
-0.012612727470695972,
0.002971309470012784,
-0.08971188962459564,
0.004733202047646046,
0.030381377786397934,
-0.009074074216187,
0.010006573982536793,
0.034096814692020416,
-0.011306668631732464,
0.0043093422427773476,
-0.012219863943755627,
0.007357334718108177,
-0.005554269067943096,
0.10539370030164719,
-0.04091520234942436,
0.029626520350575447,
0.060451384633779526,
-0.033768221735954285,
-0.010497340932488441,
-0.008924387395381927,
0.03446680307388306,
0.026463281363248825,
-0.02613266184926033,
-0.009860794059932232,
-0.030284691601991653,
-0.012401323765516281,
-0.01710890233516693,
-0.06071047857403755,
-0.019762979820370674,
-0.008142223581671715,
-0.016563227400183678,
-0.010669950395822525,
0.007481211796402931,
0.013393031433224678,
0.009483523666858673,
0.016144143417477608,
-0.0711372047662735,
-0.041592150926589966,
-0.06621899455785751,
0.004791655112057924,
-0.019617633894085884,
-0.028695890679955482,
0.02482360042631626,
0.02854854427278042,
0.03018660470843315,
-0.03435017913579941,
-0.03848756104707718,
-0.03086911141872406,
0.016955379396677017,
0.011094536632299423,
0.010506922379136086,
0.03722788766026497,
0.048816002905368805,
0.028572600334882736,
-0.04295537620782852,
0.027330122888088226,
-0.026489850133657455,
-0.0114689189940691,
0.020958498120307922,
-0.0005608052597381175,
0.02203259989619255,
-0.007311958819627762,
-0.01995224505662918,
0.000016949812561506405,
0.02173018641769886,
-0.020663022994995117,
0.020718125626444817,
-0.023923933506011963,
0.07844796776771545,
0.03298269212245941,
0.002252056961879134,
0.03623422980308533,
0.016570134088397026,
0.015004881657660007,
0.0376412570476532,
-0.010206244885921478,
-0.0003205573302693665,
-0.08351573348045349,
-0.023788131773471832,
0.0249570794403553,
0.01633754000067711,
-0.02976568043231964,
0.049279093742370605,
0.012199005112051964,
0.020487964153289795,
0.0356113575398922,
-0.00740071851760149,
-0.07084663212299347,
-0.0008064149878919125,
0.023848311975598335,
0.022578004747629166,
0.0273167435079813,
0.012814940884709358,
0.04274410009384155,
-0.009971006773412228,
0.008867770433425903,
-0.04136320576071739,
-0.0501401387155056,
0.025046875700354576,
0.05599483475089073,
-0.022763440385460854,
-0.001873468398116529,
-0.05670353025197983,
0.020436279475688934,
0.0021041203290224075,
0.025330567732453346,
0.06159845367074013,
0.008893599733710289,
0.02131721004843712,
-0.04425438493490219,
-0.007401989307254553,
-0.02115023508667946,
-0.00315664685331285,
-0.019533129408955574,
-0.05407009273767471,
0.005369591526687145,
-0.004457715433090925,
-0.030346130952239037,
-0.02470475621521473,
-0.003029231447726488,
-0.04834672063589096,
0.005325975827872753,
-0.003514352720230818,
-0.007470004726201296,
0.013827165588736534,
-0.04849189892411232,
-0.006901188753545284,
0.024285973981022835,
-0.024180155247449875,
0.015461273491382599,
0.017841599881649017,
-0.04884614795446396,
0.04334921017289162,
-0.02392025664448738,
-0.0089499456807971,
0.013914937153458595,
0.0195204745978117,
0.06559420377016068,
-0.007699375972151756,
-0.009579352103173733,
-0.03419484943151474,
-0.021949343383312225,
0.005060216411948204,
0.030037758871912956,
-0.021330861374735832,
0.010637948289513588,
0.007295398041605949,
-0.00817671325057745,
-0.05473698675632477,
0.01589837670326233,
-0.024004178121685982,
-0.04707201570272446,
-0.019877061247825623,
0.011427106335759163,
-0.0020208139903843403,
-0.002259673550724983,
0.024867461994290352,
0.015826085582375526,
-0.028089813888072968,
-0.0013491242425516248,
-0.05915449187159538,
-0.01638827659189701,
0.017560094594955444,
-0.004831792786717415,
0.04063143953680992,
-0.0269763246178627,
-0.06091231107711792,
0.02047649957239628,
0.02680552750825882,
-0.010371428914368153,
-0.020004400983452797,
0.011852734722197056,
-0.013410038314759731,
-0.020306149497628212,
0.03996111825108528,
0.052339810878038406,
0.003898765193298459,
0.01795625500380993,
0.03902752697467804,
0.07686906307935715,
-0.005840476136654615,
0.031048286706209183,
-0.03856967017054558,
-0.01715254783630371,
0.01663065142929554,
-0.0027017327956855297,
0.032322779297828674,
-0.0295049250125885,
-0.009408262558281422,
0.016778167337179184,
-0.03128015622496605,
0.020303471013903618,
0.04754921421408653,
-0.052047595381736755,
0.054936449974775314,
-0.018824104219675064,
0.010854808613657951,
-0.04318884387612343,
0.021109141409397125,
0.026884008198976517,
-0.030627166852355003,
-0.012092835269868374,
0.02477394975721836,
0.022324543446302414,
-0.012169689871370792,
-0.0018051599618047476,
0.023581329733133316,
0.0003550902474671602,
-0.03799159824848175,
-0.010697951540350914,
-0.013833784498274326,
-0.006685587577521801,
0.02414839155972004,
-0.03822898864746094,
0.00034725197474472225,
0.04063176363706589,
0.059717483818531036,
0.04439551755785942,
-0.02115192636847496,
-0.03494822978973389,
-0.04392410069704056,
-0.03658834844827652,
0.03959621116518974,
-0.0005681386101059616,
0.08953742682933807,
0.002348619978874922,
0.0533759668469429,
0.05613989755511284,
0.026098864153027534,
-0.004065323155373335,
-0.03867170214653015,
-0.12355652451515198,
0.015197645872831345,
-0.008993844501674175,
-0.013296208344399929,
0.02767818048596382,
-0.014807494357228279,
0.006968626286834478,
-0.020157769322395325,
-0.013386944308876991,
-0.04424377158284187,
0.0027329609729349613,
-0.05203815549612045,
0.02041393704712391,
-0.03452828526496887,
-0.05800608918070793,
0.005229010712355375,
0.01820260100066662,
0.04155455157160759,
-0.06803800910711288,
0.043686553835868835,
0.018083319067955017,
-0.008128158748149872,
-0.006389978341758251,
0.0003851351502817124,
0.02111075632274151,
0.04124930873513222,
0.05362490564584732,
0.008451639674603939,
0.006291352212429047,
-0.030042029917240143,
0.00873524695634842,
0.026477543637156487,
0.046891164034605026,
0.012399622239172459,
0.0295293927192688,
-0.03545009717345238,
-0.05168011039495468,
-0.01981589011847973,
-0.016901057213544846,
0.03960893303155899,
0.003278926247730851,
0.008345172740519047,
0.010875703766942024,
0.020894257351756096,
-0.04932771250605583,
0.03725501522421837,
0.04706800356507301,
-0.01741689071059227,
0.0062840781174600124,
-0.01304020918905735,
-0.057472873479127884,
-0.02289775013923645,
-0.027382446452975273,
0.017520394176244736,
0.00452440558001399,
-0.04301821067929268,
0.037921637296676636,
0.030499350279569626,
0.03592997416853905,
-0.03813675045967102,
-0.03177189081907272,
0.03141200914978981,
0.03158095106482506,
0.004472739063203335,
0.006765910889953375,
-0.018070951104164124,
0.030456682667136192,
0.040667574852705,
-0.005791683681309223,
0.0032613244839012623,
-0.06664684414863586,
0.0168469175696373,
0.036939624696969986,
0.020335569977760315,
-0.006177839823067188,
-0.0064170039258897305,
-0.0331144779920578,
-0.02164328098297119,
0.019645987078547478,
-0.004057145677506924,
0.04671946540474892,
-0.027165520936250687,
-0.009327970445156097,
-0.03735961392521858,
-0.03465351089835167,
0.0178608987480402,
0.0191615242511034,
-0.0060463882982730865,
0.03459300100803375,
-0.042418502271175385,
-0.007925206795334816,
-0.0032790449913591146,
-0.00479996157810092,
-0.0019152775639668107,
0.025650065392255783,
-0.01674809865653515,
0.02651781402528286,
0.028795091435313225,
0.02615099772810936,
-0.0652623176574707,
-0.10726992785930634,
0.009723689407110214,
-0.010190312750637531,
-0.020775262266397476,
0.005770210642367601,
-0.027276961132884026,
-0.052745379507541656,
0.02206520177423954,
0.03835807740688324,
0.008945432491600513,
-0.005451673176139593,
-0.0274030864238739,
0.05708378553390503,
0.02033335156738758,
0.006525842472910881,
0.05378488078713417,
0.01926041767001152,
-0.006871822755783796,
-0.0162191241979599,
-0.01934594102203846,
0.03918410465121269,
0.0037740543484687805,
0.010088329203426838,
-0.02815213054418564,
0.022511351853609085,
-0.04870164766907692,
0.06296317279338837,
-0.03573530912399292,
-0.0013090202119201422,
-0.01871882937848568,
0.010377834551036358,
0.016922300681471825,
-0.00023831323778722435,
0.02215283364057541,
-0.01673007756471634,
0.010952633805572987,
0.018164487555623055,
0.012858082540333271,
-0.018205631524324417,
0.03314566984772682,
-0.014033561572432518,
-0.014008371159434319,
0.022587528452277184,
0.010357888415455818,
0.03416893258690834,
-0.058312129229307175,
-0.04199653118848801,
-0.007916891947388649,
-0.04421049728989601,
0.010452315211296082,
-0.010554214008152485,
0.0031514796428382397,
0.010701396502554417,
-0.02930881828069687,
-0.0023498027585446835,
0.02465619333088398,
0.000047685021854704246,
-0.035022810101509094,
-0.018979696556925774,
0.047005608677864075,
0.027246538549661636,
-0.00405087461695075,
-0.07886505126953125,
-0.07250016182661057,
0.02573336847126484,
-0.003598392941057682,
-0.037225596606731415,
0.007763485889881849,
-0.01452512014657259,
-0.02552485279738903,
-0.039946433156728745,
0.01624714396893978,
-0.018343785777688026,
-0.04818330705165863,
-0.023514050990343094,
0.03450022265315056,
0.002026030095294118,
0.05242234840989113,
0.04079814255237579,
-0.05371113121509552,
-0.03891526162624359,
-0.027884798124432564,
0.015506927855312824,
0.0001747002825140953,
0.050396379083395004,
-0.00786526594310999,
-0.04160453379154205,
-0.0003468437644187361,
0.0034098816104233265,
0.04108579084277153,
0.01398010365664959,
0.008090207353234291,
0.009093343280255795,
-0.0014564016601070762,
-0.02917906641960144,
-0.053152985870838165,
0.0045125181786715984,
0.018598118796944618,
0.02526303380727768,
0.002340929117053747,
-0.0045897881500422955,
-0.022624656558036804,
-0.025866452604532242,
0.039110276848077774,
0.0020619407296180725,
0.003912406973540783,
0.005419665016233921,
0.07044575363397598,
0.009764863178133965,
-0.02304164506494999,
0.026040425524115562,
-0.04452235996723175,
0.01785963959991932,
0.004571398254483938,
-0.016067737713456154,
0.010945756919682026,
0.0413963757455349,
-0.011298364028334618,
-0.05485481023788452,
-0.03217365965247154,
-0.004865346476435661,
0.03155975416302681,
-0.0060571953654289246,
0.03491417318582535,
0.04623335227370262,
-0.030433151870965958,
0.0034128630068153143,
-0.05621439963579178,
0.010448366403579712,
0.014804380014538765,
-0.001929884310811758,
0.042163848876953125,
-0.01393677294254303,
-0.004545370116829872,
0.04330923780798912,
0.06272199004888535,
-0.013815016485750675,
0.0375894159078598,
0.08419044315814972,
-0.005889588501304388,
0.028709035366773605,
-0.009930030442774296,
-0.022910235449671745,
0.08601221442222595,
-0.05158524960279465,
0.0516996793448925,
0.017406437546014786,
0.0432625487446785,
0.025822538882493973,
0.0007365135825239122,
0.01080302707850933,
-0.013316967524588108,
-0.006937514990568161,
-0.06168638914823532,
0.048000093549489975,
-0.01778382435441017,
0.00012136733857914805,
0.021502558141946793,
0.028344331309199333,
0.010033687576651573,
0.008693578653037548,
-0.010157396085560322,
-0.007319302763789892,
-0.06328333169221878,
-0.0036670956760644913,
-0.0026791030541062355,
-0.015644337981939316,
0.009142757393419743,
-0.010848499834537506,
0.007774727884680033,
0.017523080110549927,
-0.04321112483739853,
-0.0006933911936357617,
-0.0014499608660116792,
0.035619739443063736,
-0.015051718801259995,
0.05158811807632446,
-0.0182783380150795,
0.0291700791567564,
-0.003919058945029974,
0.016330569982528687,
0.1370660662651062,
0.043516866862773895,
0.014127765782177448,
-0.07819776982069016,
0.028537113219499588,
0.03015068732202053,
0.03297112137079239,
-0.017110297456383705,
-0.03014623187482357,
0.00030324194813147187,
0.027377717196941376,
-0.003940050955861807,
0.04919179901480675,
0.016869859769940376,
-0.016980009153485298,
-0.0038614014629274607,
-0.055088844150304794,
-0.06037331745028496,
-0.016746746376156807,
0.010184595361351967,
-0.03843947499990463,
0.018819032236933708,
-0.027315180748701096,
-0.015065588988363743,
-0.0019635262433439493,
0.017069753259420395,
-0.03340300917625427,
-0.04454171657562256,
0.05179189518094063,
0.023538857698440552,
-0.015492205508053303,
0.019527161493897438,
0.025389734655618668,
0.009610424749553204,
-0.028638871386647224,
-0.00766583951190114,
-0.0036827849689871073,
0.0013239028630778193,
0.017938390374183655,
0.0555301196873188,
-0.01575874350965023,
-0.032921697944402695,
0.006709872744977474,
0.009421676397323608,
-0.06399096548557281,
0.007686528377234936,
-0.03326721116900444,
0.031737715005874634,
-0.02222251705825329,
-0.001315311761572957,
0.01478295773267746,
-0.012703151442110538,
0.015023003332316875,
0.0028133040759712458,
-0.03034171089529991,
-0.020101744681596756,
0.03115159645676613,
-0.013518009334802628,
-0.02756967581808567,
-0.05123545974493027,
-0.010976632125675678,
-0.007730426732450724,
-0.005863360594958067,
-0.000490425678435713,
0.00913868099451065,
0.02262195385992527,
0.015110938809812069,
0.024278907105326653,
-0.007590003311634064,
0.019638586789369583,
-0.029851572588086128,
0.021478427574038506,
-0.03703310340642929,
0.018311794847249985,
0.008487570099532604,
0.02841680496931076,
0.038637906312942505,
0.01850915513932705,
-0.0025333580560982227,
0.014914204366505146,
-0.03479795902967453,
0.0077328854240477085,
0.021831301972270012,
-0.008821643888950348,
-0.029758786782622337,
-0.0020563588477671146,
0.015317683108150959,
0.016670165583491325,
-0.021081870421767235,
0.019615178927779198,
0.030422372743487358,
0.01909385621547699,
0.0227802861481905,
-0.01499299705028534,
-0.01580335572361946,
0.010745873674750328,
-0.02400372177362442,
0.011678087525069714,
-0.041536301374435425,
0.036477230489254,
0.038232091814279556,
-0.02239895798265934,
-0.008136111311614513,
0.03940925374627113,
-0.019978854805231094,
-0.03890985995531082,
0.059333380311727524,
-0.011794712394475937,
0.020814107730984688,
0.028047895058989525,
-0.003550359047949314,
0.010960440151393414,
-0.04342784360051155,
-0.00006918168219272047,
-0.007793605327606201,
-0.006484454032033682,
-0.013334264047443867,
-0.040025416761636734,
0.03143168240785599,
-0.01901249960064888,
0.014753244817256927,
-0.061257898807525635,
-0.007110315840691328,
-0.014796349219977856,
0.01469453889876604,
0.02535848319530487,
0.014279218390583992,
-0.006529349833726883,
0.038175683468580246,
-0.01658056676387787,
0.02549111843109131,
0.027616648003458977,
0.053097985684871674,
0.005304712802171707,
-0.003955801948904991,
0.028770890086889267,
0.02752752974629402,
0.034998245537281036,
-0.017024047672748566,
0.009545509703457355,
0.0644523948431015,
-0.05428473651409149,
-0.042893894016742706,
0.031834814697504044,
-0.0035317197907716036,
0.007487138267606497,
-0.023173797875642776,
0.00428588455542922,
-0.010637729428708553,
0.04765436798334122,
-0.018354924395680428,
0.008488795720040798,
-0.025639500468969345,
-0.022959180176258087,
0.014809605665504932,
-0.015953438356518745,
0.011314839124679565,
-0.027951696887612343,
-0.035671934485435486,
0.028095202520489693,
0.0774635598063469,
0.002038772916421294,
-0.006434100214391947,
-0.020312175154685974,
-0.014082958921790123,
0.020307430997490883,
0.02076621726155281,
0.000927484652493149,
0.012565926648676395,
0.05875450745224953,
0.008178136311471462,
0.05014822632074356,
-0.009199859574437141,
-0.0014042351394891739,
-0.0911388099193573,
-0.01868833415210247,
0.0087285740301013,
0.00003341716728755273,
0.02409244142472744,
-0.05900217592716217,
0.05194723233580589,
0.026226207613945007,
-0.047128766775131226,
0.018199099227786064,
-0.03802115097641945,
-0.020084964111447334,
-0.01074517983943224,
-0.01227240078151226,
-0.05069451406598091,
0.07132744789123535,
0.0445454902946949,
0.014183513820171356,
0.04548344388604164,
0.025943875312805176,
-0.02138489857316017,
-0.01656929776072502,
-0.01326383650302887,
0.027944596484303474,
-0.008983428589999676,
-0.03246025741100311,
0.04495194926857948,
0.007476403843611479,
-0.04417235776782036,
0.005123137030750513,
0.006526312790811062,
-0.014120547100901604,
0.012203511781990528,
-0.0077996752224862576,
-0.015403361059725285,
0.016835184767842293,
-0.00960434041917324,
0.006021829321980476,
-0.018706319853663445,
-0.008683713153004646,
0.004785026889294386,
0.031994178891181946,
0.0166973527520895,
-0.01807481050491333,
0.004320257343351841,
-0.017854344099760056,
0.013175553642213345,
0.04595136642456055,
-0.032206837087869644,
-0.003645883407443762,
0.00975707545876503,
-0.0004017304163426161,
-0.0043213944882154465,
-0.04051155224442482,
0.0036064444575458765,
-0.02920563332736492,
-0.05039972439408302,
-0.014062018133699894,
0.0247484277933836,
-0.017856189981102943,
0.004587521776556969,
-0.0008880998357199132,
-0.025179356336593628,
0.046982597559690475,
-0.009464445523917675,
-0.017240984365344048,
-0.021761933341622353,
-0.009384609758853912,
-0.010578513145446777,
0.01856844499707222,
0.005823556333780289,
-0.02515261434018612,
-0.032791778445243835,
0.01851721480488777,
-0.0040331268683075905,
0.013934061862528324,
-0.04796610027551651,
-0.055499982088804245,
-0.023231491446495056,
-0.05380411073565483,
0.029767032712697983,
-0.018028518185019493,
0.0018341849790886045,
-0.030137887224555016,
0.0008227304206229746,
-0.019204745069146156,
0.043870821595191956,
0.018954942002892494,
0.01783210225403309,
-0.000341576844220981,
-0.007412707433104515,
-0.005224748980253935,
0.03879828006029129,
-0.018179044127464294,
0.008936397731304169,
-0.007961872033774853,
0.00012647220864892006,
0.0069106160663068295,
0.014308972284197807,
-0.0034597371704876423,
0.021929359063506126,
0.03538016974925995,
-0.00867948867380619,
0.02259485423564911,
0.04325953498482704,
-0.049379535019397736,
0.0051186480559408665,
0.019381675869226456,
-0.012223665602505207,
0.060865577310323715,
-0.05608825385570526,
0.028513090685009956,
0.005948823411017656,
0.006004441995173693,
-0.00861315242946148,
0.03643764555454254,
-0.03094102256000042,
-0.022622428834438324,
-0.011406845413148403,
-0.013464738614857197,
0.01485089398920536,
-0.01114724576473236,
0.038366395980119705,
0.014105171896517277,
-0.012347868643701077,
-0.028209134936332703,
0.03185360133647919,
-0.004563558846712112,
0.04772038012742996,
-0.03120615892112255,
-0.0090624475851655,
-0.005261323880404234,
0.0013431150000542402,
0.02546032704412937,
0.05401451140642166,
0.012675857171416283,
0.02518940344452858,
0.01722518727183342,
0.02011338248848915,
-0.019660480320453644,
0.03220662102103233,
0.02846451848745346,
-0.006876187864691019,
-0.031996358186006546,
0.017534779384732246,
0.06289909034967422,
-0.02130575105547905,
0.01848144456744194,
0.0239225123077631,
-0.041734445840120316,
0.08797955513000488,
-0.00731566222384572,
0.0109739163890481,
-0.015674535185098648,
0.011119012720882893,
-0.03391711413860321,
-0.04932678863406181,
-0.012751379981637001,
0.044781386852264404,
0.008927077054977417,
-0.0037196590565145016,
-0.032036811113357544,
0.023653695359826088,
0.045705050230026245,
-0.05527947098016739,
0.0048180995509028435,
-0.01885763183236122,
-0.01828422211110592,
-0.010686407797038555,
0.015292712487280369,
-0.02052048034965992,
-0.0008410031441599131,
0.049916353076696396,
0.021742897108197212,
-0.0028475867584347725,
-0.007263856008648872,
-0.009960093535482883,
-0.021619295701384544,
0.03329005464911461,
-0.03535940498113632,
-0.006114316172897816,
-0.019974898546934128,
-0.009200298227369785,
-0.04734886810183525,
-0.03265891596674919
] |
<p>As you know, impedance is defined as a complex number.</p>
<p>Ideal capacitors:
$$
\frac {1} {j \omega C} \hspace{0.5 pc} \mathrm{or} \hspace{0.5 pc} \frac {1} {sC}
$$</p>
<p>Ideal inductors:
$$
j \omega L \hspace{0.5 pc} \mathrm{or} \hspace{0.5 pc} sL
$$</p>
<p>I know that the reason why they 'invented' the concept of impedance is because it makes it easy to work with circuits in the frequency domain (or complex frequency domain).</p>
<p>However, since in real-life circuits both voltages and currents are real numbers, I'm wondering if there is any actual physical meaning behind the imaginary component of impedance.</p>
| 7,603 |
[
0.006793915294110775,
0.0073002055287361145,
-0.01410273090004921,
-0.03208048641681671,
0.05579986423254013,
0.025086862966418266,
-0.02874794788658619,
0.015056813135743141,
0.01286319363862276,
-0.01760285533964634,
0.01609685644507408,
0.07525957375764847,
0.05272943153977394,
-0.01310882531106472,
-0.01351623609662056,
0.00880045723170042,
-0.041036687791347504,
0.01764496974647045,
-0.026727570220828056,
-0.020253093913197517,
0.02577350288629532,
0.016065536066889763,
0.05742186680436134,
0.03242648392915726,
-0.00012944050831720233,
0.03603016585111618,
0.0008635281701572239,
0.003240149701014161,
0.03679490461945534,
0.0157137680798769,
0.009688304737210274,
-0.014482137747108936,
-0.00494407070800662,
0.004485474433749914,
0.03431079164147377,
-0.0023693451657891273,
-0.02210160158574581,
-0.033332787454128265,
-0.004959530662745237,
0.05103842169046402,
-0.02421184442937374,
-0.0008822256932035089,
-0.01181722804903984,
0.013500177301466465,
0.006511150859296322,
0.004676200449466705,
-0.01342845056205988,
-0.025512125343084335,
0.026758242398500443,
-0.08373665809631348,
0.05328531935811043,
-0.015757771208882332,
0.0342739038169384,
0.030870210379362106,
0.005712117068469524,
0.008671507239341736,
0.07480276376008987,
0.05820317566394806,
-0.03871706873178482,
-0.06854835897684097,
0.022236894816160202,
-0.00928115751594305,
-0.004991582129150629,
-0.00944780558347702,
-0.0011575185926631093,
0.042804691940546036,
0.012681454420089722,
-0.03524421155452728,
0.029389534145593643,
0.016947166994214058,
0.018919162452220917,
0.025067802518606186,
0.005870831664651632,
-0.04117491841316223,
0.027333742007613182,
-0.044067274779081345,
-0.008145423606038094,
0.0009776430670171976,
0.030306152999401093,
0.01209217682480812,
-0.024055249989032745,
0.0017186690820381045,
0.012463909573853016,
0.024619154632091522,
-0.004696296062320471,
-0.001334254047833383,
0.0726751759648323,
-0.015936076641082764,
0.03000432252883911,
-0.0050883824005723,
0.012215168215334415,
0.029419252648949623,
0.024647507816553116,
-0.020045682787895203,
-0.0011269834358245134,
0.030558744445443153,
-0.005638027098029852,
0.031008949503302574,
0.0052549466490745544,
-0.030666518956422806,
0.02855093404650688,
-0.01103739719837904,
0.01723831333220005,
0.04917099326848984,
0.006044994108378887,
-0.04044407978653908,
-0.030429691076278687,
0.024866797029972076,
0.01320637110620737,
-0.04370110481977463,
-0.024031879380345345,
0.022619398310780525,
0.024476036429405212,
0.036724623292684555,
0.025251075625419617,
-0.03744599595665932,
0.024718262255191803,
-0.017152322456240654,
0.03555484116077423,
0.04435073584318161,
0.023599447682499886,
-0.03457305580377579,
0.020781023427844048,
0.005994049366563559,
-0.07028760761022568,
0.037489548325538635,
-0.0192575603723526,
0.0267174132168293,
-0.02580813691020012,
0.0077881477773189545,
0.006958352867513895,
0.0021568506490439177,
0.009900534525513649,
0.018366118893027306,
0.05509570240974426,
-0.032946668565273285,
-0.09003736823797226,
-0.0611841045320034,
-0.000030197992600733414,
-0.05192146450281143,
-0.014839907176792622,
-0.09696657955646515,
0.012587315402925014,
0.01392250694334507,
0.06426990777254105,
0.02254674583673477,
-0.013020982965826988,
-0.01717773638665676,
0.021061116829514503,
0.034101735800504684,
-0.0064917514100670815,
-0.06776616722345352,
-0.028163818642497063,
-0.028544001281261444,
0.037798020988702774,
-0.02549373172223568,
0.005607699975371361,
0.04422710835933685,
-0.011128588579595089,
-0.04888828843832016,
0.03233690187335014,
-0.04216662794351578,
-0.014455629512667656,
0.038415051996707916,
-0.04511547088623047,
-0.03142472729086876,
0.07950706034898758,
0.015366998501121998,
0.011060536839067936,
0.04918192699551582,
0.0035100476816296577,
0.037620365619659424,
0.03852288797497749,
0.027239615097641945,
0.03155159950256348,
-0.06268935650587082,
-0.03209155052900314,
-0.004610330797731876,
0.04020888730883598,
-0.0030250686686486006,
-0.05332441255450249,
-0.04756738618016243,
0.028845161199569702,
0.020442770794034004,
0.004516633227467537,
0.06091613322496414,
-0.021658919751644135,
-0.02260928973555565,
0.045998942106962204,
-0.03796617314219475,
-0.03305474668741226,
-0.02919929102063179,
0.03476210683584213,
0.02238239161670208,
-0.04724789783358574,
0.00828228797763586,
0.034649450331926346,
0.017773054540157318,
-0.027448508888483047,
-0.005364571698009968,
-0.012969770468771458,
0.011278926394879818,
0.0415496863424778,
-0.024810954928398132,
0.05094698444008827,
0.03522379696369171,
0.005843266379088163,
-0.03336547315120697,
0.03594861552119255,
-0.025953149423003197,
-0.0411875955760479,
0.014020530506968498,
-0.03964326158165932,
0.05017693713307381,
0.018928801640868187,
-0.0041810316033661366,
-0.011234146542847157,
-0.04562292620539665,
0.011645936407148838,
0.054609961807727814,
0.007306485902518034,
0.08284066617488861,
0.04698853939771652,
0.007938171736896038,
-0.009699511341750622,
0.06796848028898239,
-0.0051102773286402225,
0.004657800775021315,
-0.00974583812057972,
-0.020792046561837196,
-0.05505121871829033,
0.00023877261264715344,
0.08230724930763245,
0.06139492616057396,
-0.047544822096824646,
0.0033448170870542526,
0.02563941292464733,
0.03293265029788017,
0.06242063269019127,
0.017412766814231873,
-0.027804581448435783,
-0.02072480507194996,
-0.00020945425785612315,
0.001207333873026073,
0.017276020720601082,
0.009340609423816204,
0.006582537200301886,
0.019396942108869553,
0.0360342338681221,
-0.0232743788510561,
-0.0025472219567745924,
0.03993288800120354,
0.0018382417038083076,
0.007530726492404938,
0.02810904197394848,
-0.00880370382219553,
0.021946953609585762,
-0.05114590376615524,
-0.0010701945284381509,
0.01526271179318428,
-0.0447087399661541,
0.005096567329019308,
-0.012995964847505093,
0.009377297013998032,
-0.005794190801680088,
-0.016195695847272873,
-0.037986449897289276,
-0.025975240394473076,
0.016723453998565674,
-0.0286579467356205,
0.015593341551721096,
0.0012036665575578809,
0.017897954210639,
-0.014222189784049988,
-0.01375043485313654,
0.02510208450257778,
0.012199482880532742,
0.048869531601667404,
-0.029009679332375526,
-0.035200271755456924,
-0.005871061701327562,
-0.044446393847465515,
0.004815234802663326,
0.034813303500413895,
-0.010401270352303982,
0.00795729923993349,
-0.01730598695576191,
-0.03098599798977375,
0.027735678479075432,
0.012643696740269661,
-0.004046820104122162,
-0.02108040452003479,
-0.043519001454114914,
-0.06495075672864914,
-0.03615063428878784,
-0.014535266906023026,
0.0622296966612339,
0.0023159233387559652,
-0.009991273283958435,
0.04993131011724472,
-0.031183240935206413,
0.005808428395539522,
-0.001452546683140099,
-0.009583964012563229,
-0.041186679154634476,
0.0013700013514608145,
-0.04283658787608147,
0.019699418917298317,
-0.03576963022351265,
-0.000052837986004306003,
0.018664918839931488,
-0.04929153993725777,
-0.016962289810180664,
-0.020834853872656822,
-0.08045878261327744,
0.015169553458690643,
-0.01516517624258995,
0.025281567126512527,
0.02986695058643818,
-0.036257553845644,
0.09748657792806625,
0.009714026004076004,
-0.034692417830228806,
-0.026703687384724617,
-0.04046708717942238,
-0.014217549934983253,
-0.033194612711668015,
0.015580613166093826,
0.040256813168525696,
-0.00612203124910593,
0.02009519375860691,
0.04217243567109108,
0.01922854222357273,
0.017325477674603462,
0.024181338027119637,
0.025985518470406532,
0.0018384266877546906,
-0.02890733815729618,
-0.025798019021749496,
0.04259267821907997,
0.005460790358483791,
-0.029081828892230988,
0.035311464220285416,
-0.013072540983557701,
0.02071049064397812,
0.011967821978032589,
0.009777032770216465,
0.010670077987015247,
-0.03696468099951744,
0.031896211206912994,
-0.033571332693099976,
0.02688281610608101,
-0.003479355713352561,
0.010266593657433987,
-0.018955307081341743,
0.043215811252593994,
0.026168258860707283,
-0.02796167880296707,
0.010011773556470871,
0.023373514413833618,
-0.015782810747623444,
-0.032831043004989624,
0.015940101817250252,
0.00905272364616394,
-0.011874940246343613,
0.02248985320329666,
-0.001080620102584362,
-0.03148168325424194,
0.0374167300760746,
0.012022445909678936,
-0.02018909342586994,
-0.015637218952178955,
-0.04714532941579819,
-0.000807210395578295,
-0.03953135386109352,
-0.02329130470752716,
-0.0024043433368206024,
0.03884893283247948,
-0.0007087941630743444,
0.04657433182001114,
0.0017962843412533402,
-0.005501870531588793,
0.00014466914581134915,
-0.024757057428359985,
-0.08033394068479538,
-0.003063328331336379,
-0.0418863371014595,
-0.00010419187310617417,
-0.027547452598810196,
0.00955048855394125,
0.026667078956961632,
-0.032681941986083984,
-0.03785650432109833,
-0.024484246969223022,
-0.012507433071732521,
-0.04422383010387421,
0.019892040640115738,
0.014993916265666485,
-0.007289580535143614,
-0.04131953790783882,
0.014831991866230965,
0.003989937249571085,
-0.023270579054951668,
-0.023496093228459358,
0.027773991227149963,
-0.03360702469944954,
-0.005021141842007637,
-0.01918140798807144,
-0.03004547953605652,
0.02605714462697506,
0.010959763079881668,
0.049856461584568024,
0.029633112251758575,
-0.0133506553247571,
0.03160832077264786,
-0.004433352034538984,
0.058815933763980865,
0.03710874170064926,
-0.04264625534415245,
-0.027434125542640686,
-0.08476066589355469,
-0.012588417157530785,
-0.01560967043042183,
0.04150855168700218,
-0.0013609313173219562,
0.001506550470367074,
0.04724068567156792,
-0.009748030453920364,
0.01023021712899208,
0.022661719471216202,
0.029365895316004753,
0.040769755840301514,
-0.027951978147029877,
-0.046300217509269714,
-0.028501275926828384,
-0.024758411571383476,
0.0024440630804747343,
0.03513247147202492,
-0.008904180489480495,
-0.009558383375406265,
-0.005878531374037266,
0.034500788897275925,
-0.012434011325240135,
0.02742382325232029,
0.01865808665752411,
0.02195870503783226,
0.021771907806396484,
0.01987682655453682,
-0.0022672859486192465,
-0.027909109368920326,
0.031035248190164566,
0.07474768906831741,
0.03406806290149689,
-0.022182300686836243,
-0.07730548828840256,
0.00674024410545826,
0.03547516092658043,
0.028687523677945137,
-0.028846772387623787,
-0.020566025748848915,
-0.017047548666596413,
-0.00914906244724989,
0.05021800473332405,
-0.03607971593737602,
0.03296135738492012,
-0.03122742474079132,
-0.014160305261611938,
-0.027440186589956284,
-0.015658877789974213,
0.02099359594285488,
0.04752375930547714,
0.02391744591295719,
0.020184028893709183,
-0.0655534639954567,
-0.03239480406045914,
-0.020198678597807884,
0.03961379826068878,
0.02528923749923706,
0.063178651034832,
-0.013030926696956158,
0.023586830124258995,
0.015481560491025448,
0.07289605587720871,
0.00702174985781312,
-0.06413286179304123,
0.010227429680526257,
0.0022878670133650303,
0.024018336087465286,
0.02212720923125744,
-0.02379007264971733,
-0.044247303158044815,
-0.00980614684522152,
0.03987300023436546,
0.018765611574053764,
-0.0006895358674228191,
0.026138022541999817,
0.03825494647026062,
0.010986785404384136,
-0.0026860034558922052,
0.021628670394420624,
0.007871842943131924,
-0.030526185408234596,
-0.02087564207613468,
-0.032318465411663055,
0.03161954879760742,
-0.03331609442830086,
-0.01586076430976391,
-0.01903485134243965,
0.024600952863693237,
-0.02929878793656826,
0.07633467018604279,
0.015050358138978481,
0.02624971605837345,
-0.03465699777007103,
-0.025410208851099014,
-0.015346175990998745,
0.01162194088101387,
-0.015983713790774345,
-0.016095170751214027,
-0.005017627961933613,
0.05378453806042671,
0.02194567583501339,
-0.012735577300190926,
0.0008959978586062789,
0.0005991008947603405,
0.02886688895523548,
0.032931555062532425,
-0.0013698992552235723,
0.012229235842823982,
-0.031094664707779884,
-0.025859292596578598,
0.034371647983789444,
-0.003942595329135656,
0.031056702136993408,
-0.03892398253083229,
-0.022695615887641907,
-0.005208047106862068,
-0.06473499536514282,
-0.03325285762548447,
0.011615787632763386,
0.00010489307896932587,
0.03500300273299217,
-0.053197044879198074,
0.016204223036766052,
-0.0039012045599520206,
0.030086006969213486,
-0.052518751472234726,
-0.07110657542943954,
0.014070256613194942,
0.0145260626450181,
-0.004020054358989,
0.0014779366319999099,
-0.028622079640626907,
0.022934813052415848,
-0.02984965406358242,
0.04847344011068344,
0.05160166323184967,
-0.021284034475684166,
-0.03471045196056366,
-0.004654949065297842,
-0.012715497985482216,
0.05368279665708542,
0.02133490890264511,
0.0119667062535882,
0.031960733234882355,
-0.03810327500104904,
0.016184911131858826,
0.00653935968875885,
0.06327387690544128,
-0.022513054311275482,
-0.0140279121696949,
-0.005958995316177607,
-0.01593955233693123,
0.044214412569999695,
0.015241016633808613,
-0.014960561878979206,
0.003611175576224923,
0.0028129369020462036,
-0.01646093651652336,
-0.009525920264422894,
0.03451090306043625,
0.0006165747181512415,
-0.0011435209307819605,
0.031911205500364304,
0.007496626116335392,
-0.0815712958574295,
-0.026164527982473373,
0.008505110628902912,
0.016308991238474846,
0.005826784763485193,
-0.03515872359275818,
0.04312329366803169,
-0.021556908264756203,
-0.022515391930937767,
0.016827495768666267,
-0.0133567675948143,
0.026935795322060585,
0.015333534218370914,
0.015668660402297974,
0.0016861443873494864,
0.03415526822209358,
-0.04309292882680893,
-0.05954775586724281,
-0.065301813185215,
-0.000800377456471324,
0.03813285380601883,
-0.01981779932975769,
0.0698893815279007,
0.026225319132208824,
-0.045206863433122635,
-0.017980027943849564,
0.0006729582673870027,
-0.020179852843284607,
0.0249972902238369,
-0.0075834994204342365,
0.01985207200050354,
-0.0420987568795681,
-0.008481701835989952,
0.02861841395497322,
0.03361041098833084,
-0.008419724181294441,
0.01313274260610342,
0.014291469939053059,
0.059507984668016434,
0.006381831597536802,
-0.002157169161364436,
-0.03568791225552559,
0.03159353509545326,
-0.02688182331621647,
0.03775911033153534,
0.014250216074287891,
-0.03598109632730484,
0.03465697914361954,
0.00003934337291866541,
-0.0018143960041925311,
-0.03030104748904705,
0.00750403106212616,
-0.027108315378427505,
0.0057615661062300205,
0.05037136375904083,
-0.010655264370143414,
-0.01413700170814991,
-0.011849965900182724,
0.02981661818921566,
-0.009860539808869362,
0.05885571241378784,
0.015440613962709904,
-0.05586637556552887,
-0.017315907403826714,
-0.01909470744431019,
-0.04019530862569809,
0.005009690299630165,
0.007080300711095333,
-0.019610371440649033,
0.03768720477819443,
-0.03278312087059021,
0.0179391261190176,
0.0036223912611603737,
0.03559806942939758,
-0.03594155237078667,
0.08305332809686661,
-0.018390262499451637,
0.006369574926793575,
-0.011740014888346195,
-0.0052277809008955956,
0.10541625320911407,
0.05208002030849457,
-0.014158986508846283,
-0.06834953278303146,
0.0124227125197649,
-0.028852803632616997,
0.022165648639202118,
-0.0244449395686388,
0.014733328483998775,
-0.017172254621982574,
0.014018296264111996,
0.04421302676200867,
0.03482574224472046,
0.01170103345066309,
0.023277143016457558,
0.023278595879673958,
-0.039011795073747635,
-0.02100970223546028,
-0.0011633409885689616,
0.03453094884753227,
-0.02256971225142479,
0.0038850975688546896,
-0.039417997002601624,
0.014854641631245613,
-0.028129981830716133,
-0.0024014355149120092,
-0.030207931995391846,
-0.021783586591482162,
0.04738044738769531,
-0.0010828442173078656,
-0.04800336807966232,
0.03269016742706299,
0.016944805160164833,
-0.007926407270133495,
-0.020455854013562202,
0.032467104494571686,
0.022023482248187065,
0.0015977966831997037,
-0.013881219550967216,
0.03148164227604866,
0.026618629693984985,
-0.04652528464794159,
0.01662999391555786,
0.010924077592790127,
-0.06504472345113754,
-0.024194438010454178,
-0.034299276769161224,
0.005173420533537865,
0.0016213010530918837,
0.004455168731510639,
-0.02276444435119629,
0.005486683454364538,
0.012296146713197231,
-0.061631929129362106,
-0.04678390920162201,
-0.01143093965947628,
0.02473434992134571,
-0.010214310139417648,
-0.006468469742685556,
-0.016292575746774673,
-0.00040726567385718226,
-0.00481758639216423,
0.0410287007689476,
0.004751388914883137,
-0.03661090135574341,
0.010190592147409916,
0.011852681636810303,
0.013054369017481804,
-0.011424344033002853,
-0.022074032574892044,
-0.004848909098654985,
-0.01340271532535553,
-0.03200023993849754,
-0.04399225115776062,
-0.006210144609212875,
0.009816711768507957,
0.03809195011854172,
-0.03154142573475838,
-0.012925910763442516,
-0.011968891136348248,
-0.06099630147218704,
0.01764746755361557,
0.013017283752560616,
-0.015687139704823494,
-0.04195984825491905,
-0.026181668043136597,
0.034162238240242004,
0.03933928906917572,
-0.036419909447431564,
-0.011913236230611801,
-0.010768155567348003,
-0.004025382921099663,
-0.009528983384370804,
-0.002834575017914176,
-0.014964238740503788,
0.04093588888645172,
-0.04748012498021126,
0.049178145825862885,
0.03182836249470711,
0.03445439413189888,
0.023075630888342857,
0.007858349941670895,
-0.010468719527125359,
0.046628572046756744,
-0.023934345692396164,
0.0053407116793096066,
0.021521296352148056,
-0.04654249921441078,
0.03307564556598663,
-0.009504650719463825,
0.04218237102031708,
-0.018383203074336052,
-0.02285771444439888,
-0.03003908507525921,
-0.0038541615940630436,
-0.00739173823967576,
0.06122273579239845,
-0.019236432388424873,
-0.008434250950813293,
-0.03239523991942406,
0.012983348220586777,
-0.0611661821603775,
-0.02372942678630352,
-0.05925963073968887,
-0.0032760845497250557,
0.026424052193760872,
-0.0032599149271845818,
0.006471112370491028,
-0.016155634075403214,
-0.017768116667866707,
-0.0037658056244254112,
0.037596847862005234,
0.014270246028900146,
-0.03063659742474556,
-0.009741718880832195,
0.004685425199568272,
0.003142968285828829,
0.01850980892777443,
-0.07590777426958084,
-0.02430526353418827,
0.046003520488739014,
-0.025036398321390152,
-0.058170098811388016,
0.0348033607006073,
-0.021396102383732796,
-0.0008795903413556516,
0.04149039462208748,
-0.012418369762599468,
-0.03275435417890549,
0.045523226261138916,
-0.01785479485988617,
0.0082799531519413,
-0.043810777366161346,
0.010949390009045601,
-0.029912618920207024,
0.00006607641989830881,
-0.011531609110534191,
-0.0071869189850986,
0.023381827399134636,
0.007624919526278973,
0.03888079896569252,
0.00034560661879368126,
-0.009807239286601543,
0.02169778198003769,
0.02643211930990219,
-0.01039334386587143,
0.0264288280159235,
0.01207725703716278,
0.029777660965919495,
0.004385549109429121,
-0.046377550810575485,
0.007433844730257988,
0.015865741297602654,
0.0014592621009796858,
-0.07798317819833755,
0.004746070597320795,
-0.0009242314845323563,
0.005525076761841774,
0.008930782787501812,
-0.017733654007315636,
0.004890962038189173,
-0.00003131280027446337,
-0.07052453607320786,
-0.017065437510609627,
-0.05482892692089081,
-0.04449174180626869,
-0.03268594294786453,
-0.038943178951740265,
-0.011641018092632294,
0.018812311813235283,
0.02983982488512993,
-0.0008705438813194633,
0.011555852368474007,
-0.042455412447452545,
0.0165094044059515,
0.00824669934809208,
-0.023787755519151688,
0.045292772352695465,
-0.03892557695508003,
0.011386316269636154,
0.038041889667510986,
-0.01246775221079588,
0.00043214706238359213,
0.025002988055348396,
-0.0101850014179945,
0.014348671771585941,
0.017473289743065834,
0.05307832360267639,
0.00926151592284441,
0.06255047023296356,
0.028990427032113075,
-0.03780405968427658,
-0.053663238883018494,
0.017285985872149467,
0.05407565459609032,
0.025238575413823128,
0.02186991460621357,
0.006918177008628845,
-0.005986154079437256,
-0.020111333578824997,
0.013897332362830639,
0.0010228659957647324,
-0.022554272785782814,
-0.03152371942996979,
0.0031815513502806425,
-0.002032593358308077,
0.0032812103163450956,
-0.03655444085597992,
0.06446488201618195,
-0.020122068002820015,
-0.02761230804026127,
0.03806179389357567,
-0.007633216213434935,
0.01195861678570509,
-0.03206445649266243,
0.02416149340569973,
-0.03631477802991867,
0.05503665655851364,
0.0586668998003006,
-0.017792224884033203,
-0.08878553658723831,
-0.035803720355033875,
0.019467735663056374,
-0.006691945716738701,
0.03816339373588562,
-0.03565135970711708,
-0.02403457649052143,
0.03571018949151039,
0.020746424794197083,
0.029407786205410957,
0.011543522588908672,
-0.07857102155685425,
-0.04203895106911659,
-0.041317421942949295,
0.07279200851917267,
-0.0015705605037510395,
-0.01035788469016552,
-0.042259592562913895,
-0.012230941094458103,
-0.004320438951253891,
0.02871948853135109,
0.07617225497961044,
0.003012931440025568,
-0.020333847030997276,
-0.02896406501531601,
0.0189496036618948,
0.027784379199147224,
-0.06738527864217758,
-0.0007328088395297527,
0.011537815444171429,
-0.029640810564160347,
-0.000512863858602941,
-0.007133999839425087,
-0.009296193718910217,
0.011725402437150478,
0.0204248558729887,
0.02230192720890045,
0.017992863431572914,
-0.0333445742726326,
-0.02813439443707466,
0.03787089139223099,
0.04047244042158127,
-0.018476242199540138,
0.07543075829744339,
0.019487295299768448,
0.005095279309898615,
-0.008223663084208965,
-0.02634703926742077,
-0.022261325269937515,
0.025451499968767166,
0.01130989845842123,
0.019536413252353668,
-0.010673128068447113,
0.016486328095197678,
0.022035714238882065,
-0.05787186697125435,
-0.013982466422021389,
0.032878078520298004,
-0.05112173408269882,
-0.020498184487223625,
0.04673159494996071,
-0.009425245225429535,
0.026159102097153664,
0.02957894094288349,
0.005982835777103901,
0.008778899908065796,
-0.018398242071270943,
-0.005364707205444574,
0.042132798582315445,
0.02410954236984253,
-0.012503490783274174,
0.007709641940891743,
0.05365268141031265,
0.009523667395114899,
0.018066123127937317,
0.01458956953138113,
0.027437971904873848,
-0.048100292682647705,
-0.014164441265165806,
0.019195394590497017,
-0.05148743465542793,
0.03522777929902077,
0.04154875501990318,
0.0011398971546441317,
0.08929064124822617,
-0.027673009783029556,
-0.007074275519698858,
0.00258317100815475,
-0.017038429155945778,
-0.013882707804441452,
-0.01696636527776718,
0.02274845540523529,
0.03514232486486435,
-0.018200384452939034,
-0.01931796781718731,
0.003136394079774618,
-0.04047837108373642,
0.04066457226872444,
-0.07732319086790085,
0.009507646784186363,
0.014699691906571388,
0.03176351264119148,
-0.03294837102293968,
-0.004264725372195244,
-0.019859520718455315,
-0.01766532100737095,
0.019839845597743988,
0.04759082570672035,
0.0325927659869194,
0.01874079927802086,
-0.03189200907945633,
0.013425398617982864,
0.037903331220149994,
-0.08165266364812851,
0.027519019320607185,
0.0012815974187105894,
0.026856062933802605,
0.021966872736811638,
-0.010780753567814827
] |
<p>How has CMBR temperature dropped as function of time? A graph would be nice, but I'd be happy with times (age of universe) when it cooled enough to not be visible to human eye, became room temperature equivalent, or reached some interesting temperatures regarding matter in the universe.</p>
<p>If there is a nice formula giving the temperature as function of time, that would be great too.</p>
| 7,604 |
[
0.016341233626008034,
-0.0586504228413105,
0.006634370889514685,
-0.023992551490664482,
0.052238933742046356,
0.022845732048153877,
-0.018843241035938263,
-0.005970099475234747,
-0.01617777906358242,
-0.05603979900479317,
0.015408076345920563,
0.059654351323843,
0.02441544085741043,
0.02399013750255108,
0.0016777350101619959,
-0.03741484507918358,
0.003998122178018093,
-0.014564716257154942,
-0.0016734660603106022,
-0.019314883276820183,
0.04282714053988457,
0.019772935658693314,
0.026936879381537437,
0.038870058953762054,
-0.031195061281323433,
0.03334284573793411,
0.011334790848195553,
-0.018714049831032753,
-0.007270657457411289,
0.06681648641824722,
-0.03555908799171448,
-0.05960676074028015,
0.007144940085709095,
0.01080237701535225,
0.048298224806785583,
-0.015582282096147537,
-0.011048343032598495,
-0.059004418551921844,
-0.03719340264797211,
0.030533110722899437,
-0.0223816130310297,
-0.023891031742095947,
-0.023953724652528763,
0.05178738757967949,
-0.03815416619181633,
-0.018170790746808052,
0.009045322425663471,
0.013561888597905636,
0.06756081432104111,
-0.04743196442723274,
0.06579165905714035,
-0.030467253178358078,
0.0354967936873436,
-0.0023834514431655407,
-0.044909361749887466,
-0.0017871238524094224,
0.06998100131750107,
0.043752700090408325,
-0.008889281190931797,
-0.027742071077227592,
-0.0325186513364315,
0.008807864971458912,
0.006959218997508287,
0.03791603818535805,
-0.01660081185400486,
0.015583795495331287,
0.013816406019032001,
-0.005155866965651512,
0.020331013947725296,
-0.005450212396681309,
-0.004434038884937763,
-0.014859369024634361,
0.017247291281819344,
0.018194658681750298,
0.004924265202134848,
-0.020296039059758186,
0.027642548084259033,
0.022527815774083138,
0.02214922569692135,
0.05215272307395935,
-0.030382197350263596,
0.0060883150435984135,
0.030151914805173874,
0.0032891493756324053,
-0.02036072127521038,
0.004992614034563303,
0.09366844594478607,
-0.015363872051239014,
0.004419025965034962,
0.0619877390563488,
-0.00023913726909086108,
0.04017287492752075,
0.03456274792551994,
-0.007768049370497465,
-0.042079076170921326,
-0.006245996803045273,
-0.0149006936699152,
0.06143880635499954,
-0.010509006679058075,
-0.048453304916620255,
0.045504387468099594,
-0.016162073239684105,
0.00586620531976223,
0.05486410856246948,
0.004007985815405846,
-0.005921568255871534,
-0.022788366302847862,
-0.02076656185090542,
-0.023574428632855415,
-0.04293103143572807,
-0.07629721611738205,
-0.019198179244995117,
0.00023309678363148123,
-0.02349260449409485,
0.012622985988855362,
-0.053743112832307816,
0.01730385236442089,
-0.02902422472834587,
0.05982520431280136,
0.018308915197849274,
0.02616521157324314,
0.003916196059435606,
0.013602915219962597,
-0.016421407461166382,
-0.051382362842559814,
0.010694420896470547,
0.03659430891275406,
-0.012753947637975216,
-0.02093476988375187,
0.02472171187400818,
-0.04732624813914299,
-0.022351456806063652,
0.022801311686635017,
-0.07439758628606796,
-0.0048220474272966385,
-0.007881831377744675,
-0.0784735158085823,
-0.06121531128883362,
0.04042600840330124,
0.007632519584149122,
-0.023758573457598686,
-0.044977325946092606,
0.03579822927713394,
0.03344455733895302,
0.0403670109808445,
0.021233730018138885,
0.008783889934420586,
-0.03475320339202881,
0.03286338597536087,
-0.012295172549784184,
-0.03354472294449806,
-0.017634673044085503,
0.03286200389266014,
-0.01926269941031933,
-0.027180375531315804,
-0.07509082555770874,
0.020804228261113167,
0.05003870651125908,
0.004331161268055439,
-0.013707985170185566,
0.05815567448735237,
-0.04293987154960632,
-0.016531456261873245,
-0.016201898455619812,
-0.01648893393576145,
-0.044234875589609146,
0.10300459712743759,
0.030778666958212852,
-0.0175057053565979,
-0.020305173471570015,
0.05077951028943062,
0.025335172191262245,
0.03915022313594818,
0.015346406027674675,
0.04345723241567612,
-0.017295846715569496,
0.0014238134026527405,
0.0213950052857399,
-0.05900263041257858,
0.02362377941608429,
-0.06357972323894501,
-0.014290377497673035,
0.003908638842403889,
-0.02686455473303795,
0.018870489671826363,
0.04986518621444702,
-0.011911144480109215,
-0.00938511174172163,
0.011868084780871868,
-0.053998641669750214,
-0.003501282539218664,
-0.08555346727371216,
-0.06289257109165192,
0.019352108240127563,
0.0011539554689079523,
-0.028250854462385178,
0.007831146009266376,
0.02810424007475376,
-0.02162065915763378,
-0.038001786917448044,
0.04386650025844574,
0.00807750690728426,
0.014678179286420345,
-0.005772911477833986,
0.008002061396837234,
0.020612496882677078,
0.05791448801755905,
0.012729204259812832,
-0.026778243482112885,
-0.04606122151017189,
-0.025992300361394882,
-0.030406488105654716,
-0.007864857092499733,
0.01834217458963394,
-0.03482316434383392,
0.0038501557428389788,
-0.010104276239871979,
0.006022535264492035,
0.00434104073792696,
-0.00010780664888443425,
0.0020965547300875187,
0.04743543639779091,
-0.006549262907356024,
0.04585352540016174,
-0.016348235309123993,
0.03778926655650139,
0.022410618141293526,
-0.013583249412477016,
-0.0244621429592371,
-0.03206096217036247,
-0.03172532469034195,
-0.009444000199437141,
0.0158386193215847,
0.026744728907942772,
-0.022993428632616997,
0.02856665849685669,
0.004991647321730852,
0.05122903734445572,
0.03448256477713585,
-0.019417747855186462,
-0.01745295338332653,
-0.02885798178613186,
0.017059050500392914,
-0.018682407215237617,
0.021623337641358376,
-0.020249715074896812,
0.007838157936930656,
0.03674151375889778,
0.03660476580262184,
0.001210124813951552,
-0.011503615416586399,
0.00628643948584795,
0.004351269453763962,
-0.01482498086988926,
0.006156343501061201,
-0.034631792455911636,
0.04382210969924927,
-0.05068040266633034,
-0.029946180060505867,
0.02753675915300846,
0.03167098015546799,
0.04252788797020912,
-0.016724083572626114,
-0.04322996735572815,
0.0020143736619502306,
0.006140700541436672,
-0.02039966732263565,
-0.006956536788493395,
0.030167803168296814,
-0.00654817558825016,
0.034991249442100525,
-0.018335923552513123,
0.007972415536642075,
-0.04144902154803276,
-0.021908141672611237,
-0.026691483333706856,
0.012648328207433224,
0.013160142116248608,
-0.02292509935796261,
-0.03324496001005173,
0.009480657987296581,
-0.004152223933488131,
0.036705177277326584,
-0.004780635703355074,
-0.01742529310286045,
0.016666695475578308,
0.008000965230166912,
0.0049361577257514,
0.03102967143058777,
-0.014062374830245972,
-0.01174101885408163,
0.031550321727991104,
-0.003063845681026578,
-0.07722486555576324,
-0.02829984575510025,
-0.009118430316448212,
0.01620897464454174,
-0.04485858976840973,
0.015134952962398529,
0.05644020065665245,
-0.0234829131513834,
-0.024159710854291916,
-0.01308179646730423,
-0.02298581786453724,
-0.02516995556652546,
-0.024996057152748108,
-0.006346256006509066,
-0.01975407265126705,
-0.031904514878988266,
0.05279362201690674,
0.03949708491563797,
-0.01115492545068264,
-0.004094019532203674,
-0.039350491017103195,
-0.05511121451854706,
0.04810764640569687,
-0.03473303094506264,
0.0423959344625473,
-0.049242883920669556,
0.010991229675710201,
0.031310323625802994,
0.03747425600886345,
-0.011704710312187672,
-0.0188160203397274,
0.01824604906141758,
-0.0024700795765966177,
-0.02877994067966938,
-0.014796980656683445,
-0.00012856449757236987,
-0.00829377118498087,
0.006744609214365482,
0.025526992976665497,
0.05580061674118042,
0.06020260229706764,
0.013297258876264095,
-0.007946799509227276,
0.003943406045436859,
-0.03595637157559395,
0.028330231085419655,
0.01716797985136509,
0.03051752783358097,
-0.01839677058160305,
0.04101799055933952,
0.011539817787706852,
0.05192205682396889,
0.016023743897676468,
-0.057585861533880234,
0.03353434428572655,
-0.010757047683000565,
-0.010587399825453758,
-0.01745852641761303,
0.020796537399291992,
-0.027591152116656303,
0.026598747819662094,
-0.0017129088519141078,
0.028375014662742615,
0.03212872892618179,
0.016359204426407814,
-0.008683033287525177,
0.014225906692445278,
0.0454443022608757,
0.00577070377767086,
-0.02545572631061077,
0.01741790398955345,
-0.02237839810550213,
0.035621847957372665,
-0.011671231128275394,
0.01783430017530918,
0.04980812221765518,
0.014879588969051838,
0.035917188972234726,
0.02439364232122898,
-0.04432360827922821,
-0.011223750188946724,
-0.035263027995824814,
-0.03798498958349228,
0.004550219513475895,
0.06161165237426758,
0.01894628070294857,
0.027414584532380104,
0.023015782237052917,
0.005017291754484177,
0.03008795529603958,
-0.005383076146245003,
-0.057390134781599045,
0.033879172056913376,
-0.06674276292324066,
-0.001255639479495585,
0.0003683537943288684,
0.031291402876377106,
-0.005713174119591713,
0.017462681978940964,
0.010656384751200676,
-0.007231319323182106,
0.011838242411613464,
-0.015964802354574203,
0.010860776528716087,
-0.04923384636640549,
-0.03555534780025482,
-0.037061337381601334,
0.00023035870981402695,
0.08840648084878922,
-0.022958064451813698,
0.016866492107510567,
0.03276637941598892,
0.005054464563727379,
0.0033792362082749605,
-0.030880678445100784,
-0.004245362710207701,
0.014666205272078514,
0.01339191384613514,
0.0009446683689020574,
0.00019986741244792938,
-0.05261985957622528,
0.028218818828463554,
0.043905191123485565,
0.013838911429047585,
0.003308610524982214,
-0.013850384391844273,
-0.0058803558349609375,
-0.0625246986746788,
-0.006040921434760094,
0.035868119448423386,
-0.008274922147393227,
0.0025256124790757895,
0.01046984177082777,
0.014465143904089928,
0.0034091121051460505,
0.009788782335817814,
0.028080442920327187,
0.039694637060165405,
-0.03606037795543671,
0.0036573323886841536,
0.011032206006348133,
-0.03240456432104111,
-0.011212322860956192,
-0.024839041754603386,
0.022417977452278137,
0.02734566107392311,
0.0016739539569243789,
-0.009744592010974884,
0.010153797455132008,
0.024217408150434494,
0.005520906299352646,
-0.01927005499601364,
0.013246515765786171,
0.02634596824645996,
0.0017368801636621356,
0.012676537036895752,
0.02578028105199337,
0.03518480062484741,
0.06523827463388443,
0.007024053949862719,
0.015460927970707417,
-0.05887265130877495,
-0.022650476545095444,
0.021293889731168747,
0.019447019323706627,
0.02989206090569496,
-0.04131511226296425,
-0.09372048079967499,
-0.020162776112556458,
0.054382454603910446,
-0.013043181039392948,
0.02699858695268631,
-0.005535788368433714,
0.0062917908653616905,
-0.0497233085334301,
-0.0246955007314682,
0.025772597640752792,
0.03981076925992966,
0.027265118435025215,
-0.004500821698457003,
-0.019235290586948395,
-0.017383569851517677,
-0.0070981779135763645,
-0.011673490516841412,
0.023676114156842232,
0.06199507415294647,
0.00837516225874424,
0.017421461641788483,
-0.00023956397490110248,
-0.012665803544223309,
-0.04218944534659386,
-0.07135868817567825,
-0.005577208008617163,
-0.017805175855755806,
0.01701788604259491,
0.03746132180094719,
-0.00791000947356224,
-0.003671894082799554,
0.05378907918930054,
0.026292534545063972,
-0.04636145010590553,
-0.00929228588938713,
-0.07588368654251099,
0.0641174241900444,
0.005522061605006456,
-0.02002893015742302,
0.08052526414394379,
0.037671104073524475,
0.023858604952692986,
0.017399519681930542,
-0.014857434667646885,
0.03605808690190315,
-0.017384784296154976,
0.017823660746216774,
-0.007695577573031187,
-0.0136930076405406,
-0.051522258669137955,
0.029543990269303322,
-0.040487658232450485,
-0.00617188261821866,
-0.02482668124139309,
-0.022777670994400978,
0.0282907597720623,
0.007514050230383873,
0.005261546932160854,
0.011880279518663883,
0.06349460780620575,
0.004373364150524139,
-0.011378657072782516,
-0.020308908075094223,
0.05963446944952011,
-0.02816520817577839,
-0.009048267267644405,
0.021332623437047005,
-0.04374649003148079,
0.028651969507336617,
0.0035380811896175146,
0.004940370563417673,
-0.012939848937094212,
-0.00037346011959016323,
0.05154198780655861,
0.005569422151893377,
0.0065642609260976315,
0.03664088994264603,
-0.03871060535311699,
-0.01593356765806675,
0.005018445663154125,
0.000926631095353514,
0.01838471181690693,
-0.07165010273456573,
-0.029478246346116066,
-0.015144689939916134,
0.01955091953277588,
-0.10197916626930237,
-0.0434066504240036,
0.049264322966337204,
0.0495554618537426,
-0.03662138432264328,
-0.007552438881248236,
0.006619289983063936,
-0.03378928452730179,
-0.043039754033088684,
0.00319346459582448,
0.06811486184597015,
-0.007928263396024704,
0.0038530617021024227,
-0.0162773709744215,
0.006772098131477833,
0.028770877048373222,
0.0011604911414906383,
-0.001697778468951583,
0.015319771133363247,
-0.00916491448879242,
-0.03315834328532219,
0.0020954585634171963,
0.0655522495508194,
-0.015435130335390568,
-0.022247912362217903,
-0.025797879323363304,
0.006438151001930237,
0.025266174226999283,
-0.013728045858442783,
-0.037640538066625595,
0.039963625371456146,
0.014370759949088097,
0.005728318355977535,
-0.002972371643409133,
0.0246034674346447,
0.01795109175145626,
0.04016263410449028,
-0.031084923073649406,
-0.024180183187127113,
0.012549747712910175,
-0.06969965994358063,
-0.004915495403110981,
-0.02177591063082218,
0.03731376677751541,
0.005940428469330072,
0.057659812271595,
0.012327583506703377,
-0.048130203038454056,
0.015493164770305157,
-0.022515587508678436,
-0.001593922614119947,
0.004577405750751495,
-0.01896560750901699,
-0.00965087115764618,
-0.010352205485105515,
-0.019635332748293877,
-0.032657790929079056,
-0.0055550276301801205,
-0.026773391291499138,
0.0459858775138855,
-0.009075618349015713,
0.032653678208589554,
0.021560195833444595,
-0.030618812888860703,
-0.03580985218286514,
-0.02144782803952694,
-0.032605744898319244,
0.03280351310968399,
-0.009719052352011204,
0.008387592621147633,
-0.01878330670297146,
0.013395841233432293,
0.027464011684060097,
0.0449829027056694,
-0.0020244817715138197,
0.05801250785589218,
0.03706774115562439,
0.009128435514867306,
0.033447809517383575,
-0.06053876504302025,
-0.04916093125939369,
0.04986897110939026,
0.003090332495048642,
0.03839784860610962,
0.024595830589532852,
-0.012822791002690792,
0.04581529274582863,
-0.014720750041306019,
-0.021566206589341164,
-0.06749960780143738,
-0.01959173008799553,
-0.03715460002422333,
-0.028755279257893562,
0.07088743150234222,
-0.00010885664232773706,
0.015060796402394772,
0.01514859776943922,
0.005606511607766151,
-0.021043462678790092,
0.01049704197794199,
0.0034133472945541143,
-0.012023982591927052,
0.0008730386034585536,
-0.0023378957994282246,
-0.05626193434000015,
0.02609950676560402,
-0.022337201982736588,
-0.034279875457286835,
-0.008049588650465012,
0.0016343839233741164,
0.0060318708419799805,
0.014232911169528961,
-0.002938417252153158,
-0.008569539524614811,
0.04823802411556244,
-0.002195310313254595,
-0.009992462582886219,
-0.01089967880398035,
0.0008455015486106277,
0.11850173026323318,
0.05083600431680679,
0.011964705772697926,
-0.06812082976102829,
0.04258258640766144,
0.006966012064367533,
0.023581158369779587,
-0.07798773050308228,
-0.006550370715558529,
-0.021023912355303764,
0.031667664647102356,
0.056431982666254044,
0.04518643021583557,
0.015890251845121384,
-0.004159339237958193,
0.011967978440225124,
-0.007005081046372652,
-0.019350286573171616,
0.01266094297170639,
0.04184654727578163,
-0.003934898879379034,
0.008510160259902477,
-0.07796144485473633,
0.016968371346592903,
-0.006432068068534136,
0.02554323896765709,
-0.020380759611725807,
-0.049527041614055634,
0.02535964921116829,
-0.026573771610856056,
-0.03970194235444069,
0.013250906951725483,
0.02721807174384594,
-0.007518564350903034,
-0.012731299735605717,
0.015341592021286488,
0.06555946171283722,
-0.0014919583918526769,
0.007502226624637842,
0.03707702085375786,
0.045032769441604614,
0.0012688370188698173,
-0.024976838380098343,
0.004081401973962784,
-0.004890610929578543,
-0.03896407410502434,
-0.02190246991813183,
0.0444156676530838,
-0.03354461118578911,
-0.013401188887655735,
0.004855751525610685,
0.006601215340197086,
-0.02167689986526966,
-0.02023031935095787,
0.0036369964946061373,
0.020747855305671692,
0.018352018669247627,
-0.016729239374399185,
-0.0025557808112353086,
-0.01589638739824295,
0.047337912023067474,
-0.0029113837517797947,
0.010378848761320114,
-0.01057101134210825,
0.003383476519957185,
-0.02193463034927845,
-0.043009936809539795,
0.002311386400833726,
-0.017388926818966866,
-0.011867254972457886,
0.0029289184603840113,
0.004844252951443195,
-0.040904607623815536,
-0.0316624790430069,
-0.002920914674177766,
0.006194878835231066,
0.017022518441081047,
-0.008475366048514843,
-0.013110494241118431,
-0.015428967773914337,
-0.06319089978933334,
0.0308739822357893,
0.002367599168792367,
0.0054923901334404945,
-0.05379771068692207,
-0.010528812184929848,
0.0018037526169791818,
0.019176140427589417,
0.0033476136159151793,
0.008150294423103333,
-0.00932710338383913,
0.02931874431669712,
0.02148372121155262,
-0.03209161013364792,
-0.006263568997383118,
0.044087640941143036,
-0.023882059380412102,
-0.02509291097521782,
-0.03511164337396622,
0.09063507616519928,
-0.024836000055074692,
-0.008899133652448654,
0.026694616302847862,
0.007267084904015064,
-0.015259058214724064,
0.003263981780037284,
0.03855258226394653,
-0.04651128128170967,
-0.009787207469344139,
-0.02547391876578331,
0.016111109405755997,
-0.0007569431909359992,
-0.031728293746709824,
-0.026422599330544472,
0.004842797759920359,
0.032695524394512177,
-0.0021230154670774937,
-0.036342862993478775,
0.028817834332585335,
-0.017599772661924362,
-0.00029244949109852314,
-0.050378940999507904,
0.02659076265990734,
-0.044758450239896774,
-0.03516562655568123,
-0.005256555508822203,
0.00009305860294261947,
0.023883016780018806,
0.05421791225671768,
-0.04000478982925415,
0.010614486411213875,
0.011531348340213299,
0.035308416932821274,
0.01838957518339157,
-0.01815171353518963,
-0.0010305691976100206,
0.05695435777306557,
0.03526079282164574,
-0.011881290003657341,
-0.0321371890604496,
0.008815476670861244,
-0.0388367585837841,
-0.060961656272411346,
0.009931092150509357,
0.023249350488185883,
-0.0013290693750604987,
-0.021387437358498573,
-0.014292679727077484,
-0.027098100632429123,
0.06008540466427803,
-0.020264530554413795,
-0.004716621246188879,
-0.009453450329601765,
-0.0026661078445613384,
0.06626291573047638,
0.019166991114616394,
0.0071419463492929935,
-0.004376711789518595,
0.009373151697218418,
0.04407490789890289,
-0.004431704059243202,
-0.020592305809259415,
-0.0026301287580281496,
-0.03984309732913971,
-0.041722621768713,
0.004620864521712065,
0.027903318405151367,
0.04097568988800049,
0.059664662927389145,
0.047279443591833115,
-0.06715407222509384,
0.02824113704264164,
0.05351395159959793,
-0.025276271626353264,
-0.0766889899969101,
-0.003664139425382018,
-0.012837901711463928,
0.0019048851681873202,
0.04590722545981407,
-0.0514204241335392,
0.06190430745482445,
0.02996613085269928,
-0.061622001230716705,
0.025790374726057053,
-0.032527290284633636,
-0.022337118163704872,
-0.00986519642174244,
-0.03313801437616348,
-0.012438016012310982,
0.08402587473392487,
0.06718720495700836,
0.04452405124902725,
0.0499962717294693,
0.032345835119485855,
-0.01895039714872837,
-0.03689805790781975,
-0.022474559023976326,
0.029443472623825073,
0.008379904553294182,
-0.019057229161262512,
0.005622070282697678,
-0.003727993229404092,
0.020208675414323807,
0.05060294270515442,
-0.023942722007632256,
-0.0002517988032195717,
-0.015857918187975883,
0.02712264284491539,
0.009520425461232662,
0.011528071947395802,
0.030169157311320305,
-0.034479402005672455,
-0.020546691492199898,
0.0460723415017128,
-0.00538982730358839,
0.012062500230967999,
0.03546663373708725,
0.03822275996208191,
0.024555379524827003,
-0.0682462677359581,
-0.014890608377754688,
0.0012727065477520227,
-0.002812572754919529,
-0.009884133003652096,
0.010342289693653584,
-0.02604682184755802,
0.025552112609148026,
-0.01852615922689438,
0.011539801955223083,
-0.04336380586028099,
-0.002164544304832816,
0.04364051669836044,
0.025904659181833267,
-0.009092266671359539,
-0.019256621599197388,
-0.023533226922154427,
-0.02328862063586712,
-0.01543309073895216,
0.008173917420208454,
0.0005362259107641876,
-0.0177492443472147,
-0.01270125713199377,
-0.022997193038463593,
-0.002700637560337782,
-0.01801276206970215,
-0.026291992515325546,
-0.07755608856678009,
0.0347200408577919,
0.028497569262981415,
-0.0007800469757057726,
-0.010101552121341228,
-0.0078435642644763,
-0.010507182218134403,
-0.05399291217327118,
-0.008167377673089504,
-0.004554725717753172,
0.014856692403554916,
-0.02796775847673416,
0.0014208208303898573,
-0.03026735782623291,
-0.0021050504874438047,
0.07946933060884476,
0.0033977613784372807,
-0.013393772765994072,
-0.02287258952856064,
0.01952439360320568,
0.016461269930005074,
-0.06098204106092453,
0.038525283336639404,
0.014909017831087112,
-0.015546453185379505,
-0.023420779034495354,
-0.02980007231235504,
-0.00512259267270565,
0.00010311851656297222,
0.01981435716152191,
0.027372438460588455,
0.01457560621201992,
0.020497778430581093,
0.0007383833290077746,
0.04008742421865463,
0.018469281494617462,
-0.05062029883265495,
0.08866985142230988,
0.014535306952893734,
-0.009971173480153084,
0.03342247009277344,
0.013188822194933891,
-0.031205343082547188,
0.018431808799505234,
-0.001121013192459941,
0.0006599752814508975,
0.019315926358103752,
-0.01535110268741846,
-0.024322085082530975,
-0.04254240170121193,
0.013039638288319111,
0.035544056445360184,
-0.05431900545954704,
0.0007535571930930018,
0.03095129318535328,
-0.007111044600605965,
0.040221985429525375,
-0.0038307406939566135,
-0.02015753462910652,
-0.008994919247925282,
0.015437987633049488,
0.010377743281424046,
0.027890954166650772,
0.0441306009888649,
0.026091163977980614,
0.04504421725869179,
0.0013923693913966417,
-0.022429775446653366,
0.0004769221995957196,
0.0051333848387002945,
0.015354746021330357,
-0.013147257268428802,
-0.0300309881567955,
0.00951017439365387,
-0.03655062988400459,
0.013034017756581306,
0.023197509348392487,
-0.007004000246524811,
0.07398714870214462,
-0.005174741614609957,
0.010183993726968765,
0.004199175629764795,
-0.028341516852378845,
-0.04396561160683632,
0.032874684780836105,
0.016857553273439407,
0.017791861668229103,
-0.03554312884807587,
-0.030263464897871017,
0.00978057086467743,
0.029091913253068924,
0.03075539320707321,
-0.030533283948898315,
0.010189980268478394,
-0.016413547098636627,
-0.03418118879199028,
-0.00809603463858366,
0.03746065869927406,
-0.019861683249473572,
-0.03146034851670265,
0.0065085976384580135,
0.02520739659667015,
0.05628180876374245,
0.02234976552426815,
-0.006360197439789772,
-0.01879272796213627,
0.038070786744356155,
-0.07114764302968979,
-0.030953729525208473,
-0.047030720859766006,
0.05878792330622673,
-0.04428679868578911,
-0.0027859352994710207
] |
<p>I know G.R. change our vision of space and time as a unique surface than can bend.
We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can we measure the <a href="http://en.wikipedia.org/wiki/Curvature">curvature</a> of the space-time for calculate, as an example, the position of a star? </p>
| 7,605 |
[
-0.01408944372087717,
0.006947223097085953,
0.01231202483177185,
-0.026586852967739105,
0.06223111227154732,
0.007685812655836344,
-0.07939735800027847,
-0.02731134183704853,
-0.007158847525715828,
-0.020221011713147163,
0.021200276911258698,
0.0019410578534007072,
0.019046278670430183,
0.04448136314749718,
0.04411599785089493,
0.008602122776210308,
-0.007367455866187811,
0.012323467992246151,
-0.017941826954483986,
-0.06983911991119385,
0.048883356153964996,
-0.012973645702004433,
-0.016343997791409492,
-0.007603696547448635,
-0.020471101626753807,
0.010973750613629818,
0.03366202488541603,
-0.027590395882725716,
0.003398869652301073,
0.07484640926122665,
-0.02707025222480297,
0.004865837283432484,
0.0065181925892829895,
0.04579344391822815,
0.03273438662290573,
-0.030565623193979263,
-0.03910037875175476,
0.008007881231606007,
-0.03781343623995781,
0.03291287645697594,
-0.035934869199991226,
-0.03474044427275658,
-0.0170906912535429,
0.05225355923175812,
-0.035203613340854645,
-0.004741779528558254,
-0.015610580332577229,
-0.01351164747029543,
0.07189592719078064,
-0.04564888775348663,
0.0362607017159462,
0.003024312434718013,
0.0022722806315869093,
-0.01884186454117298,
-0.03176850080490112,
0.04365357384085655,
0.08153936266899109,
0.04309244826436043,
-0.02984173595905304,
-0.050256576389074326,
-0.01934819668531418,
-0.007654787972569466,
0.0002699274045880884,
-0.041661880910396576,
-0.013387655839323997,
0.0010299436980858445,
-0.031056785956025124,
-0.0026942912954837084,
0.026954203844070435,
-0.01267464179545641,
-0.019062180072069168,
0.02391604706645012,
-0.0022163004614412785,
0.024480734020471573,
0.0052863555029034615,
-0.0627426952123642,
0.004517958499491215,
-0.016182927414774895,
0.06259267777204514,
0.005728282034397125,
0.00032175928936339915,
0.010286549106240273,
0.05373334139585495,
0.06020959094166756,
0.010311136022210121,
-0.01829148828983307,
0.06381051987409592,
0.005132892169058323,
0.020126866176724434,
0.03463796526193619,
0.004792873747646809,
-0.011584811843931675,
0.04485524445772171,
-0.015623319894075394,
-0.04383476451039314,
0.03690560162067413,
-0.018067285418510437,
0.04568042233586311,
-0.008228247985243797,
-0.02689756080508232,
0.020145736634731293,
0.004943745210766792,
0.01329461857676506,
0.08457724750041962,
0.00470345513895154,
-0.00811037141829729,
-0.018076356500387192,
0.014826413244009018,
0.006982713472098112,
-0.014506523497402668,
-0.0426093190908432,
-0.0003076601424254477,
0.019053427502512932,
-0.026545148342847824,
0.06533942371606827,
-0.010474888607859612,
-0.006495315115898848,
-0.0037389120552688837,
0.07176737487316132,
0.07446497678756714,
0.0335741750895977,
-0.04885716736316681,
-0.0015177458990365267,
-0.01976224035024643,
-0.06921015679836273,
0.04698504880070686,
0.06211421638727188,
-0.029060058295726776,
-0.010469324886798859,
0.013353564776480198,
0.008846351876854897,
0.0033009920734912157,
0.012109016068279743,
0.011550027877092361,
0.027923237532377243,
0.008024652488529682,
-0.13071665167808533,
-0.02651873603463173,
0.03393791243433952,
0.02974538318812847,
-0.011513355188071728,
-0.019152173772454262,
0.03901030123233795,
-0.005130705889314413,
0.07699613273143768,
0.02165209874510765,
0.0262183528393507,
0.012353477999567986,
0.04660462215542793,
-0.026651103049516678,
-0.05070505291223526,
-0.02241664007306099,
0.009345237165689468,
-0.054408375173807144,
-0.002249573590233922,
-0.058679889887571335,
-0.006180045194923878,
0.02209452912211418,
-0.00621170736849308,
-0.06371065229177475,
0.07162006199359894,
-0.008062093518674374,
0.006177367176860571,
0.0038820442277938128,
-0.02017338201403618,
-0.019787462428212166,
0.071025550365448,
0.0023207669146358967,
-0.02924908511340618,
0.02823433093726635,
-0.011998499743640423,
0.037584658712148666,
0.01711958274245262,
0.014552591368556023,
0.03950648754835129,
-0.040890179574489594,
-0.00871554296463728,
0.004002771805971861,
-0.018012870103120804,
0.004130060784518719,
-0.023338686674833298,
-0.036723218858242035,
0.033155422657728195,
-0.01707279123365879,
0.013562541455030441,
0.03510116785764694,
-0.007685297168791294,
0.02004222758114338,
-0.015169489197432995,
-0.023892248049378395,
0.01995784416794777,
-0.07981432229280472,
-0.006788977887481451,
-0.006604520138353109,
-0.032982632517814636,
-0.021749012172222137,
0.029755253344774246,
0.023137519136071205,
-0.030304666608572006,
-0.05467119812965393,
-0.003034421941265464,
0.058047838509082794,
-0.008868720382452011,
-0.007850195281207561,
-0.0074264067225158215,
0.06509391963481903,
0.0330016203224659,
-0.022496849298477173,
0.005350322462618351,
-0.007041407283395529,
-0.002107611857354641,
0.04635138064622879,
0.008897935040295124,
0.02926800772547722,
0.008225150406360626,
-0.014638753607869148,
0.010057426989078522,
0.020294513553380966,
-0.005000577308237553,
0.041274238377809525,
-0.04081311076879501,
0.07958303391933441,
0.043009888380765915,
0.008527097292244434,
0.032672349363565445,
0.029409542679786682,
0.010527887381613255,
0.03170381113886833,
0.007934761233627796,
-0.001970618264749646,
-0.04398213326931,
-0.018098294734954834,
0.030164601281285286,
0.017070796340703964,
-0.020576249808073044,
0.0038998976815491915,
0.051942575722932816,
0.026366259902715683,
-0.0006162096397019923,
0.010266399942338467,
-0.026998324319720268,
-0.049073122441768646,
-0.026422476395964622,
-0.00506292749196291,
0.007324593607336283,
-0.004694462288171053,
0.019064679741859436,
0.0569198802113533,
0.022210855036973953,
-0.01006956398487091,
-0.012926426716148853,
0.03178926557302475,
-0.01955481246113777,
0.02759009599685669,
0.030067583546042442,
-0.0058900718577206135,
0.04194584861397743,
-0.023912029340863228,
-0.0014047734439373016,
0.0318111851811409,
-0.026248697191476822,
0.015804093331098557,
-0.029367413371801376,
-0.01397346705198288,
0.007236858829855919,
0.04683999344706535,
-0.03708501160144806,
-0.026763053610920906,
0.023963216692209244,
-0.03254538029432297,
0.009093021973967552,
-0.01236751303076744,
-0.005325704347342253,
-0.045100126415491104,
-0.00881030224263668,
0.02810787782073021,
0.005942508112639189,
0.0021385475993156433,
0.00218853447586298,
-0.04317060485482216,
0.019050274044275284,
-0.042469970881938934,
-0.03137592971324921,
0.006637982092797756,
-0.05639228597283363,
0.03881416469812393,
-0.008453527465462685,
-0.01884603686630726,
0.0029148473404347897,
-0.015372774563729763,
0.024371113628149033,
-0.000950316374655813,
0.03135831654071808,
-0.04216214641928673,
0.00022783390886615962,
-0.029690511524677277,
0.02255728654563427,
-0.03132396563887596,
0.0050179604440927505,
0.0300835520029068,
-0.010734053328633308,
-0.04093603789806366,
0.010412651114165783,
-0.06079690158367157,
-0.0377708300948143,
-0.045092638581991196,
-0.01542102824896574,
0.004414686933159828,
-0.023133907467126846,
0.02186589129269123,
0.04333096370100975,
-0.019176192581653595,
-0.036062199622392654,
-0.03910614922642708,
-0.04409148916602135,
0.05257275700569153,
0.0017853841418400407,
0.02504494972527027,
-0.03036576323211193,
-0.008251973427832127,
0.06396796554327011,
0.016949333250522614,
-0.043002981692552567,
-0.059044692665338516,
0.004672458861023188,
0.010888694785535336,
0.009777740575373173,
0.01779073290526867,
0.017185896635055542,
0.014036710374057293,
0.02729472890496254,
0.028162412345409393,
0.00956637691706419,
0.01998061127960682,
0.031168168410658836,
-0.027858316898345947,
-0.039721716195344925,
-0.009332669898867607,
0.007544226013123989,
0.049292419105768204,
0.021644985303282738,
-0.028361821547150612,
-0.004932032898068428,
-0.0022235875949263573,
0.02228611335158348,
0.0005532832001335919,
-0.012840080074965954,
0.014037440530955791,
0.00028544035740196705,
0.006056977901607752,
0.0014629047363996506,
-0.024960190057754517,
-0.014818609692156315,
0.015545308589935303,
0.02500605396926403,
0.023955542594194412,
0.060816261917352676,
0.01316055003553629,
-0.019120030105113983,
0.018389400094747543,
0.028505584225058556,
-0.02821294777095318,
-0.02885829657316208,
-0.012430432252585888,
-0.020897353067994118,
0.054558273404836655,
-0.01861700788140297,
-0.019636262208223343,
0.059286344796419144,
0.07504595071077347,
0.003705461509525776,
-0.012813613750040531,
-0.02401493676006794,
-0.02672911249101162,
-0.07112809270620346,
-0.014823837205767632,
0.025622356683015823,
0.06539308279752731,
0.014743362553417683,
0.032418470829725266,
0.05081765353679657,
0.03452149033546448,
0.03703176602721214,
-0.022624867036938667,
-0.09086716920137405,
0.016566302627325058,
-0.026400592178106308,
-0.026717660948634148,
-0.005845244973897934,
-0.016335908323526382,
0.005247861612588167,
-0.0354032963514328,
0.008250860497355461,
-0.02031237818300724,
-0.027526486665010452,
-0.0616770014166832,
0.00956029538065195,
-0.006893370300531387,
-0.04556925594806671,
-0.018448442220687866,
0.04468611627817154,
0.0352582149207592,
-0.018779080361127853,
0.0020962562412023544,
0.025117654353380203,
0.0007228701724670827,
-0.030490243807435036,
0.0008918847888708115,
-0.006811091210693121,
0.00670367106795311,
0.03875935822725296,
0.016183704137802124,
0.020754914730787277,
-0.025870362296700478,
0.023773768916726112,
0.02485944703221321,
0.0495249442756176,
-0.0030595227144658566,
-0.025503717362880707,
-0.010163298808038235,
-0.03268314152956009,
-0.004309089854359627,
-0.036308158189058304,
0.07015665620565414,
-0.028264565393328667,
-0.003477120539173484,
0.015231337398290634,
0.016688035801053047,
-0.024933086708188057,
0.020994678139686584,
0.046884335577487946,
-0.006319404114037752,
-0.02992607280611992,
-0.03952925652265549,
-0.0307073462754488,
-0.02733786217868328,
-0.024755455553531647,
0.01740434020757675,
0.004381412640213966,
-0.03826364129781723,
-0.01958824135363102,
0.03696516901254654,
0.024144301190972328,
-0.03326428309082985,
-0.015290811657905579,
0.02619699016213417,
0.005352615844458342,
-0.01045431662350893,
0.01866701804101467,
-0.0021624742075800896,
0.0545327253639698,
0.06007802113890648,
-0.028953975066542625,
-0.027246031910181046,
-0.08145732432603836,
0.014745776541531086,
0.04760546237230301,
0.017138516530394554,
-0.0037930195685476065,
-0.04380359500646591,
-0.046523936092853546,
0.009783252142369747,
0.04715485870838165,
-0.010968969203531742,
0.005413890350610018,
-0.015532043762505054,
-0.01421010959893465,
-0.008115445263683796,
0.026953214779496193,
-0.010886205360293388,
0.053813450038433075,
-0.004291237331926823,
-0.0074038514867424965,
-0.0137382373213768,
0.044464003294706345,
-0.002915289718657732,
-0.005241610109806061,
0.004084627144038677,
0.06459897756576538,
0.05078496038913727,
0.023826900869607925,
0.027802225202322006,
0.02292918600142002,
-0.0546601302921772,
-0.05373739078640938,
0.0049638161435723305,
0.030724603682756424,
-0.022763794288039207,
0.05036541819572449,
-0.0024316548369824886,
-0.03314150124788284,
0.03271378204226494,
0.0016277777031064034,
0.017754819244146347,
-0.005551225505769253,
-0.008393903262913227,
0.00844375416636467,
0.04379356652498245,
0.0006451861117966473,
0.06120286136865616,
0.026151509955525398,
-0.009638174436986446,
-0.02135446108877659,
0.023236824199557304,
0.002250144025310874,
-0.03470313549041748,
-0.026882896199822426,
-0.0007512939628213644,
-0.0024173224810510874,
-0.05984404683113098,
0.026126816868782043,
0.01613006740808487,
-0.014620138332247734,
0.0024493159726262093,
-0.034971702843904495,
-0.018272627145051956,
0.013281036168336868,
0.034147556871175766,
-0.006078165955841541,
0.02384970523416996,
0.015555305406451225,
0.02432505413889885,
-0.01331208273768425,
-0.002580501139163971,
0.03586722910404205,
-0.03138314560055733,
0.026613732799887657,
0.0113676181063056,
0.012222755700349808,
0.001354431500658393,
-0.022529613226652145,
0.040858909487724304,
-0.03458428755402565,
0.06173625960946083,
-0.022750625386834145,
0.024616487324237823,
0.047736942768096924,
-0.04121994599699974,
-0.032508715987205505,
-0.010299001820385456,
-0.025018863379955292,
-0.0082542197778821,
-0.0510224923491478,
-0.018618809059262276,
0.019106997177004814,
0.015798039734363556,
-0.09390519559383392,
-0.01552936714142561,
0.04169598966836929,
-0.0007501841173507273,
-0.01559546310454607,
0.005816010758280754,
0.045624010264873505,
-0.04290325939655304,
0.009474333375692368,
-0.024300267919898033,
0.013158165849745274,
0.0021583421621471643,
-0.002497041132301092,
-0.0072567942552268505,
0.01848902739584446,
0.06785021722316742,
-0.001394549268297851,
-0.02661341056227684,
0.01845771260559559,
0.005147489253431559,
0.011451918631792068,
0.01477000955492258,
0.02820293977856636,
-0.03017011284828186,
-0.025512002408504486,
-0.029141895473003387,
0.005531536415219307,
0.0021905500907450914,
-0.019158288836479187,
0.02378018945455551,
0.009902664460241795,
0.0011844501132145524,
-0.03281646594405174,
-0.03813299164175987,
0.015538006089627743,
-0.030047891661524773,
-0.02146597020328045,
-0.043734095990657806,
0.01758098043501377,
-0.001974375220015645,
-0.026846641674637794,
0.05061737447977066,
-0.0013413232518360019,
-0.012462922371923923,
-0.025625355541706085,
0.05494771525263786,
0.01145800482481718,
-0.0516529306769371,
0.03352317214012146,
-0.014268577098846436,
0.007991752587258816,
-0.008634572848677635,
0.0210099034011364,
0.03151709586381912,
0.00032704047043807805,
-0.022682033479213715,
-0.025519341230392456,
0.016378777101635933,
0.01813536323606968,
0.05915885046124458,
0.005733191501349211,
0.10522326081991196,
0.024554481729865074,
-0.011485019698739052,
-0.03512571007013321,
-0.008406567387282848,
0.004674065858125687,
0.0037623457610607147,
0.0007698560948483646,
0.046249404549598694,
-0.002727486426010728,
-0.008818020112812519,
-0.003227200359106064,
0.007164169102907181,
-0.04544123634696007,
0.01910262554883957,
0.013401745818555355,
0.06417178362607956,
0.02609444037079811,
-0.015055886469781399,
-0.030007412657141685,
0.04343464598059654,
0.0004925646353513002,
0.03730418533086777,
0.010197189636528492,
0.0168604776263237,
0.009994154796004295,
0.01580858789384365,
0.03316953405737877,
-0.013091006316244602,
-0.03563689813017845,
-0.05818662792444229,
-0.01004733145236969,
0.01631457544863224,
-0.032464127987623215,
-0.0017200660659000278,
0.03471631929278374,
0.023824604228138924,
-0.00024818492238409817,
0.03402605652809143,
-0.009133685380220413,
-0.08024752885103226,
-0.008144227787852287,
-0.05425930768251419,
-0.04375724866986275,
0.059814680367708206,
0.02968299202620983,
-0.05416329205036163,
0.010070602409541607,
0.010975013487040997,
0.013437415473163128,
0.025985214859247208,
0.016701269894838333,
-0.040650710463523865,
0.07404237240552902,
-0.015450106002390385,
0.03572056442499161,
-0.0025760612916201353,
-0.009513447061181068,
0.10625757277011871,
0.042037587612867355,
-0.009430122561752796,
-0.05482640862464905,
-0.0032797236926853657,
-0.017441898584365845,
0.01820559985935688,
-0.03950434550642967,
0.023572996258735657,
-0.015303784050047398,
-0.00037746253656223416,
-0.005921874660998583,
0.04310307651758194,
0.005145321134477854,
-0.034255217760801315,
0.058976732194423676,
-0.027801619842648506,
-0.007171375676989555,
0.019467484205961227,
0.019314005970954895,
0.004222537390887737,
0.03721946105360985,
-0.028437728062272072,
0.05026449263095856,
-0.03267365321516991,
0.004785310011357069,
-0.03730103000998497,
-0.035124365240335464,
-0.013933581300079823,
0.011189608834683895,
-0.06875542551279068,
0.025665489956736565,
0.040027376264333725,
-0.031209146603941917,
-0.050722766667604446,
-0.030249103903770447,
0.02355215512216091,
-0.017691370099782944,
-0.0012669709976762533,
0.016380198299884796,
-0.03275984898209572,
-0.0076653012074530125,
-0.022927431389689445,
0.03889928013086319,
-0.015270596370100975,
-0.03801737353205681,
-0.03636256605386734,
0.059202879667282104,
-0.03553726524114609,
-0.013574127107858658,
0.007478431332856417,
-0.0050422209315001965,
0.0026736329309642315,
-0.058431174606084824,
0.003630826249718666,
-0.008390087634325027,
0.01801455393433571,
-0.017169728875160217,
-0.04665113985538483,
0.005793311633169651,
0.021527890115976334,
-0.020791998133063316,
0.041830964386463165,
-0.043979544192552567,
0.02352619171142578,
0.01396144088357687,
-0.017827413976192474,
0.03927475959062576,
-0.029466573148965836,
-0.029446255415678024,
-0.056551989167928696,
-0.02114243432879448,
-0.031030183658003807,
0.013168011792004108,
0.012012863531708717,
0.022308671846985817,
-0.02457726001739502,
0.009214983321726322,
0.02716854400932789,
0.01782693713903427,
-0.011751040816307068,
0.026067497208714485,
-0.048169929534196854,
-0.037517014890909195,
-0.04752735421061516,
0.0020596333779394627,
0.07367490977048874,
0.03484635427594185,
0.004211672116070986,
-0.0007046968094073236,
-0.007581993006169796,
-0.0159769207239151,
0.017491428181529045,
-0.01189297903329134,
0.015611440874636173,
0.012004726566374302,
-0.01781582087278366,
0.018159719184041023,
-0.039852093905210495,
0.004760633688420057,
0.0430276021361351,
-0.030141497030854225,
0.0016309821512550116,
0.031219178810715675,
-0.02531519904732704,
-0.0002278761676279828,
-0.01197715476155281,
-0.012979436665773392,
0.01895996369421482,
-0.04264479875564575,
-0.01594993844628334,
-0.0455862395465374,
-0.007836459204554558,
-0.05689731240272522,
-0.01629781164228916,
-0.004500866401940584,
0.003660376649349928,
0.01625775918364525,
0.08120876550674438,
-0.019971758127212524,
0.007595295086503029,
-0.04900480434298515,
0.027121171355247498,
-0.031930822879076004,
0.00845719687640667,
-0.007005739491432905,
-0.012063923291862011,
-0.004200590308755636,
0.017332181334495544,
-0.01854100450873375,
-0.029603730887174606,
0.001171007053926587,
0.01364868599921465,
-0.02018178068101406,
0.026083290576934814,
0.05048821493983269,
0.0031891039106994867,
0.07140888273715973,
0.001211529946886003,
-0.008084692992269993,
-0.00212035421282053,
-0.0742390975356102,
-0.07470786571502686,
0.03452621027827263,
-0.021092943847179413,
0.016063254326581955,
0.019552873447537422,
-0.018795151263475418,
0.015086572617292404,
0.0178283229470253,
-0.005230898968875408,
0.0006383407744579017,
-0.007480936590582132,
-0.02540333941578865,
-0.0017907675355672836,
-0.0022093395236879587,
0.04452851414680481,
-0.032903943210840225,
-0.02730860747396946,
0.0008314429433085024,
0.007422397844493389,
-0.010295098647475243,
0.019773118197917938,
0.01913163810968399,
-0.0302489772439003,
0.0008996175602078438,
0.01448537316173315,
-0.039647284895181656,
0.054529715329408646,
0.05141964554786682,
-0.045950133353471756,
0.009177599102258682,
0.03912418708205223,
0.01889367401599884,
-0.08033435791730881,
0.0056540523655712605,
-0.011720167472958565,
-0.021486258134245872,
0.040933556854724884,
-0.05461489036679268,
0.01562543958425522,
0.023183904588222504,
-0.06169808283448219,
0.068653903901577,
-0.014913428574800491,
-0.00534519599750638,
-0.007909685373306274,
-0.0015713237226009369,
-0.0004972401075065136,
0.0772050991654396,
0.04487856850028038,
0.02864280715584755,
0.0072349668480455875,
0.01161227747797966,
0.01088564284145832,
-0.008915755897760391,
0.0009059089934453368,
0.006278629880398512,
0.00048628231161274016,
-0.031193967908620834,
0.06813526153564453,
-0.014420990832149982,
-0.013180075213313103,
0.008417168632149696,
-0.0029592132195830345,
0.058857511729002,
-0.03043992817401886,
-0.008714963681995869,
-0.001064592506736517,
0.014932900667190552,
0.01206127367913723,
-0.0257292240858078,
-0.045223455876111984,
0.012471776455640793,
-0.015290428884327412,
0.004846874158829451,
0.027293875813484192,
0.018313877284526825,
0.010869295336306095,
-0.020412985235452652,
-0.027383528649806976,
0.012301375158131123,
-0.02846885286271572,
0.002912957686930895,
0.008473987691104412,
0.03974979743361473,
-0.020027905702590942,
-0.032720308750867844,
-0.01677119731903076,
-0.04682329669594765,
0.019870394840836525,
0.010556290857493877,
-0.0034577008336782455,
-0.01657276228070259,
0.025998258963227272,
-0.006189171224832535,
-0.015250897035002708,
0.028712239116430283,
-0.03493354842066765,
-0.020389383658766747,
-0.05459470674395561,
0.011032198555767536,
0.011006990447640419,
-0.019111016765236855,
0.012505018152296543,
-0.005888486746698618,
-0.02238895557820797,
0.0295685064047575,
0.03440691530704498,
-0.006026074290275574,
-0.02199368365108967,
-0.01022712979465723,
-0.004216327797621489,
-0.051721520721912384,
0.018488263711333275,
0.0036556320264935493,
-0.011492753401398659,
-0.02527143619954586,
-0.00744216563180089,
-0.0020569022744894028,
-0.01430219691246748,
0.05097451061010361,
-0.03271854668855667,
-0.01476031169295311,
0.03531511127948761,
0.016800204291939735,
0.006054334808140993,
-0.045137643814086914,
-0.009852065704762936,
-0.008541208691895008,
-0.05377530679106712,
-0.01180619839578867,
-0.015022838488221169,
-0.005841884762048721,
-0.011624637059867382,
-0.0012573774438351393,
-0.013324616476893425,
0.05974695831537247,
0.005131800193339586,
-0.027196137234568596,
0.03480065241456032,
0.016424056142568588,
-0.002027111127972603,
0.036190349608659744,
0.020628370344638824,
-0.011134226806461811,
0.03454297408461571,
-0.018612012267112732,
-0.009563376195728779,
0.020415447652339935,
-0.006251955404877663,
-0.042030949145555496,
-0.021226219832897186,
-0.02228301577270031,
-0.004165101796388626,
-0.02099805325269699,
-0.02547665871679783,
0.05842353031039238,
-0.03952610492706299,
0.016686955466866493,
0.056534964591264725,
-0.035948045551776886,
0.019218431785702705,
-0.03523518517613411,
-0.0014254482230171561,
0.02405044063925743,
0.0017453922191634774,
-0.015820879489183426,
0.050455059856176376,
0.044608525931835175,
0.014273588545620441,
0.01027720607817173,
0.04297870025038719,
0.007377144880592823,
0.024339815601706505,
0.012811526656150818,
0.05876511335372925,
-0.0417463481426239,
0.029505502432584763,
0.02005109377205372,
-0.010207504965364933,
-0.004403409082442522,
0.010396398603916168,
-0.029596848413348198,
0.07014138251543045,
-0.0286958497017622,
-0.036374904215335846,
-0.023516692221164703,
-0.02534121461212635,
-0.03693561255931854,
0.015489538200199604,
0.008737633004784584,
0.04751604050397873,
0.04821978136897087,
-0.00634492514654994,
0.004019958898425102,
0.01957608386874199,
0.02592606469988823,
0.02410637028515339,
0.031052567064762115,
-0.02643398754298687,
0.007187787909060717,
0.011384442448616028,
0.017792275175452232,
-0.02958899736404419,
-0.030015598982572556,
0.0483970008790493,
0.016399608924984932,
0.05888144299387932,
0.0033231067936867476,
0.020559988915920258,
-0.0556451641023159,
0.04273100942373276,
-0.10868657380342484,
-0.04319014772772789,
-0.028319168835878372,
0.024376317858695984,
-0.034353870898485184,
-0.014631684869527817
] |
<p>In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity of the particles. However no such velocity can exceed that of light. Is there therefore an absolute upper bound to temperature as well as an absolute zero?</p>
| 7,606 |
[
-0.015201066620647907,
-0.049520980566740036,
-0.007293978240340948,
-0.04965382069349289,
0.04986879229545593,
-0.0005277756717987359,
-0.045722559094429016,
-0.003946368116885424,
-0.0336451418697834,
-0.010100290179252625,
0.04434735327959061,
0.055624496191740036,
0.049003783613443375,
0.010346255265176296,
0.016079116612672806,
-0.007318550255149603,
-0.02017050050199032,
-0.0070184096693992615,
-0.011581705883145332,
-0.01749090664088726,
0.006758530158549547,
0.03480725735425949,
0.048757247626781464,
0.005381395108997822,
-0.009654863737523556,
0.022046919912099838,
0.031204121187329292,
0.022748230025172234,
0.001170725328847766,
0.012143658474087715,
0.00009794833022169769,
-0.00008049709867918864,
0.00666354363784194,
0.02214295230805874,
0.05464784428477287,
0.007240204606205225,
-0.014007506892085075,
-0.011712347157299519,
-0.012702817097306252,
-0.002313352655619383,
-0.06357286125421524,
-0.0264038797467947,
-0.01270009484142065,
-0.003260653465986252,
-0.025669023394584656,
-0.019921597093343735,
0.03369593992829323,
-0.011148244142532349,
0.039847444742918015,
-0.06553767621517181,
0.05320609733462334,
-0.016968445852398872,
0.032936159521341324,
0.004423572216182947,
0.01420485507696867,
0.0019033048301935196,
0.06948080658912659,
0.07764856517314911,
-0.023263074457645416,
-0.04198457673192024,
-0.009969513863325119,
0.012140624225139618,
0.02274486795067787,
-0.01167372614145279,
-0.019105838611721992,
0.010297905653715134,
-0.0033423227723687887,
-0.03385518118739128,
0.029331844300031662,
0.0387297086417675,
-0.02513141557574272,
-0.002425919286906719,
0.0487675666809082,
0.0296272411942482,
0.029469700530171394,
-0.032569363713264465,
-0.0035526915453374386,
0.0012854003580287099,
0.01704251952469349,
0.06681070476770401,
-0.0013653667410835624,
0.00797293707728386,
0.027208708226680756,
0.031794920563697815,
-0.0006278608343563974,
-0.004095811862498522,
0.05782679095864296,
-0.030360588803887367,
0.012597773224115372,
0.0660618469119072,
-0.020953720435500145,
0.024976199492812157,
0.00614848081022501,
0.025628067553043365,
-0.030127672478556633,
0.0037672286853194237,
0.0069905542768538,
0.028902078047394753,
-0.008506408892571926,
-0.0036991387605667114,
-0.013064336031675339,
0.0005284579237923026,
0.03635537624359131,
0.05663782358169556,
-0.0028220072854310274,
-0.046906329691410065,
-0.03391698747873306,
-0.028917549178004265,
-0.012969082221388817,
-0.0013613831251859665,
-0.03854294493794441,
-0.003196555422618985,
0.023935047909617424,
0.01976519636809826,
0.0061746700666844845,
-0.006606775335967541,
0.014964898116886616,
-0.05314302444458008,
0.06160355731844902,
0.04037020355463028,
0.03983434662222862,
-0.025309447199106216,
-0.0004561524256132543,
-0.007728915195912123,
-0.052390314638614655,
0.008628156036138535,
0.01694890484213829,
-0.0004763276665471494,
-0.030581193044781685,
-0.0029870737344026566,
0.0001161708714789711,
0.012911418452858925,
0.00033800711389631033,
-0.03823921084403992,
0.03424377739429474,
-0.038035858422517776,
-0.07106009125709534,
-0.06495635211467743,
0.05275138467550278,
-0.011460112407803535,
-0.03076704777777195,
-0.05560436472296715,
-0.009446593001484871,
0.031286466866731644,
0.050117626786231995,
0.009004275314509869,
0.021280916407704353,
-0.043494660407304764,
0.04161816090345383,
0.007991008460521698,
0.0031903618946671486,
-0.031573861837387085,
0.011153166182339191,
-0.0293170977383852,
0.02259482443332672,
-0.08146741986274719,
0.04108564555644989,
0.044652581214904785,
-0.015169354155659676,
-0.002466714708134532,
0.012319509871304035,
-0.07418421655893326,
0.023736802861094475,
0.011965606361627579,
0.02105156145989895,
-0.018235202878713608,
0.0910462886095047,
0.029832523316144943,
-0.007117534056305885,
-0.009270306676626205,
0.02927282266318798,
0.017980827018618584,
0.012497910298407078,
0.022635268047451973,
0.03724629431962967,
-0.008478649891912937,
-0.010016188956797123,
-0.008205211721360683,
0.00686954939737916,
0.04722842201590538,
-0.042531441897153854,
-0.010121173225343227,
0.017124980688095093,
0.020373376086354256,
-0.01029453705996275,
0.027072031050920486,
-0.020753927528858185,
0.016271771863102913,
0.02505464106798172,
-0.03950197994709015,
-0.0009392554056830704,
-0.07538948208093643,
0.004623504355549812,
0.05211775004863739,
0.0012393540237098932,
0.03267200291156769,
0.03543836623430252,
0.021900972351431847,
-0.047727134078741074,
-0.019308827817440033,
-0.0004995614872314036,
0.02881912887096405,
0.0014449127484112978,
-0.01944376900792122,
0.04013120010495186,
0.07480653375387192,
0.06130671128630638,
-0.017204994335770607,
-0.0009121397160924971,
-0.0072721089236438274,
-0.08959979563951492,
0.001501549151726067,
-0.027355071157217026,
0.020665014162659645,
0.02603747695684433,
0.00920826941728592,
0.03420621156692505,
-0.0007216265657916665,
-0.026988480240106583,
0.007252473849803209,
-0.012722603976726532,
0.04586309939622879,
0.016705507412552834,
0.0077894702553749084,
-0.012855201959609985,
0.05577725172042847,
0.02182621695101261,
-0.02520359493792057,
-0.008822837844491005,
-0.019130272790789604,
-0.02577614225447178,
-0.005093334708362818,
0.044270485639572144,
0.06100711226463318,
-0.06197793781757355,
0.0036961594596505165,
0.03968639299273491,
0.044297438114881516,
0.04200674965977669,
0.030691565945744514,
-0.025442279875278473,
-0.03178859129548073,
0.012609506025910378,
0.004632677882909775,
0.03680230304598808,
0.028077393770217896,
0.03534374386072159,
0.014928288757801056,
0.019010700285434723,
-0.0034621262457221746,
-0.038520410656929016,
0.0031890058889985085,
0.01845226250588894,
0.007203713059425354,
0.016215184703469276,
-0.04883255064487457,
0.013552624732255936,
-0.03996187821030617,
0.0332968533039093,
0.00824995618313551,
0.008384903892874718,
0.023331696167588234,
-0.011510917916893959,
-0.014583772979676723,
0.0011161022121086717,
0.0007912942674010992,
-0.0168139785528183,
-0.0009783545974642038,
0.027153190225362778,
-0.05825087055563927,
0.01077945251017809,
-0.032277900725603104,
0.005965552292764187,
-0.03804784640669823,
-0.00628255307674408,
0.03945091739296913,
0.0012011711951345205,
0.0378897599875927,
-0.03463127836585045,
-0.03623412549495697,
-0.0037838981952518225,
-0.04436349496245384,
-0.0012150174006819725,
0.045433755964040756,
-0.033325426280498505,
0.028869345784187317,
-0.026837924495339394,
-0.07811161130666733,
0.024912996217608452,
-0.04998849332332611,
0.018878154456615448,
0.06654887646436691,
-0.02830338478088379,
-0.048383928835392,
-0.004611418582499027,
0.002601892687380314,
-0.038014501333236694,
-0.04273685812950134,
0.026470717042684555,
0.017332442104816437,
-0.0502922423183918,
-0.0626620501279831,
0.0037772038485854864,
-0.052658479660749435,
-0.05883556604385376,
-0.06031765416264534,
0.005646811332553625,
0.015029249712824821,
0.000050103866669815034,
0.03555256873369217,
0.07551733404397964,
-0.04654280096292496,
0.0015472974628210068,
-0.04633796960115433,
-0.04690792039036751,
0.04001537337899208,
-0.01646234653890133,
0.05665168911218643,
-0.008885064162313938,
0.021962041035294533,
0.06812799721956253,
0.048719678074121475,
-0.012992892414331436,
-0.03359701484441757,
-0.012215271592140198,
-0.022668808698654175,
0.006167996674776077,
0.019918739795684814,
0.020513493567705154,
-0.027526596561074257,
0.00796827394515276,
0.03120291978120804,
0.01885550282895565,
0.008846312761306763,
-0.003420440014451742,
-0.01553476881235838,
0.007065890822559595,
-0.0020445568952709436,
0.010831758379936218,
0.03665497899055481,
0.02736656926572323,
-0.006146869156509638,
0.03154534101486206,
0.021699048578739166,
0.07976939529180527,
0.026024656370282173,
-0.03622124344110489,
0.06881154328584671,
0.00491474149748683,
0.03941801190376282,
-0.026456285268068314,
0.049537476152181625,
0.016804229468107224,
0.018339231610298157,
-0.007315859664231539,
0.023927433416247368,
-0.0062388889491558075,
0.015639042481780052,
-0.003935537301003933,
0.027981892228126526,
0.04807161167263985,
-0.01200910098850727,
-0.00810996163636446,
0.01917722076177597,
-0.014829636551439762,
0.015342243015766144,
-0.01909908838570118,
-0.012614409439265728,
0.021964984014630318,
0.022027231752872467,
0.0387563556432724,
0.019819311797618866,
-0.028635254129767418,
0.001988399075344205,
-0.042051736265420914,
-0.01761307194828987,
-0.0175732783973217,
0.02876538224518299,
0.010633750818669796,
0.029530972242355347,
0.00027985312044620514,
0.04021250829100609,
0.03106113336980343,
0.005666279699653387,
-0.0916096493601799,
-0.010865089483559132,
-0.0632103905081749,
-0.022646507248282433,
-0.028719322755932808,
0.003921358846127987,
-0.0046159736812114716,
-0.041990287601947784,
-0.009240979328751564,
-0.017536021769046783,
0.012522445060312748,
-0.061093322932720184,
-0.01437138207256794,
-0.07268501818180084,
-0.020310277119278908,
-0.0028683021664619446,
-0.008207293227314949,
0.029017414897680283,
-0.03748635947704315,
0.03622503951191902,
0.04567766562104225,
-0.04627479985356331,
0.018406447023153305,
-0.0230825487524271,
0.018059594556689262,
0.03418194130063057,
0.03351157158613205,
0.06487681716680527,
0.006211662199348211,
-0.023650769144296646,
0.009137454442679882,
0.016162151470780373,
0.02542066015303135,
0.007639874704182148,
-0.008214143104851246,
-0.017527978867292404,
-0.011720370501279831,
-0.021430231630802155,
0.007689997088164091,
0.02442939765751362,
-0.026950767263770103,
0.015761634334921837,
0.027530869469046593,
-0.0030169901438057423,
-0.01358244102448225,
0.03555656969547272,
0.03678810968995094,
-0.0011611137306317687,
0.009702606126666069,
-0.01931305229663849,
-0.006813673302531242,
-0.024888258427381516,
0.02507348358631134,
0.049401868134737015,
0.0002891759213525802,
-0.005708417389541864,
0.003111043944954872,
-0.015751397237181664,
0.021853040903806686,
-0.027172114700078964,
-0.034563008695840836,
-0.008146666921675205,
0.026511631906032562,
-0.012011946178972721,
-0.01611221395432949,
-0.027116969227790833,
0.001406593364663422,
-0.0012765247374773026,
-0.014502130448818207,
-0.030778907239437103,
-0.05804278701543808,
0.001781382248736918,
0.029129747301340103,
0.04220190644264221,
0.007265308406203985,
0.03654847666621208,
-0.029569357633590698,
0.009412415325641632,
0.046246226876974106,
-0.015448887832462788,
0.010014881379902363,
-0.01361361425369978,
-0.029496565461158752,
-0.010087546892464161,
-0.04496206343173981,
0.025555435568094254,
0.028058309108018875,
0.031769685447216034,
-0.025228973478078842,
0.004274394828826189,
0.014546392485499382,
-0.024188026785850525,
0.030807001516222954,
0.019230356439948082,
0.04283319041132927,
-0.0032217411790043116,
-0.0012556335423141718,
0.019357064738869667,
-0.019812127575278282,
-0.027366677299141884,
-0.07923504710197449,
-0.027774354442954063,
0.019787339493632317,
-0.016363201662898064,
0.02555055171251297,
-0.05109608918428421,
-0.010325678624212742,
0.021715642884373665,
-0.022468099370598793,
-0.04938686266541481,
0.016324402764439583,
-0.017513368278741837,
0.02985553815960884,
0.00693021435290575,
-0.02275085635483265,
0.03216005116701126,
0.0033572372049093246,
0.02006492391228676,
-0.0071214335039258,
-0.015690023079514503,
0.052094966173172,
-0.02149905264377594,
-0.01777561940252781,
-0.04664960503578186,
-0.02833373099565506,
-0.013737639412283897,
0.05207791551947594,
-0.01688597910106182,
-0.01220805011689663,
0.022477978840470314,
-0.03582775592803955,
-0.01950203999876976,
0.010891794227063656,
0.016413738951086998,
-0.024143891409039497,
-0.040446557104587555,
0.023178275674581528,
-0.03752071037888527,
-0.04266303777694702,
0.02506173960864544,
0.016059426590800285,
-0.00040232716128230095,
0.030146872624754906,
-0.00504680909216404,
0.048035480082035065,
-0.03671746328473091,
-0.0005174650577828288,
-0.00940136518329382,
-0.030269548296928406,
0.04058164358139038,
-0.019477618858218193,
0.010630043223500252,
0.03218008950352669,
-0.02637415938079357,
-0.030034519731998444,
0.014252378605306149,
-0.012096350081264973,
0.02530139684677124,
-0.05058016628026962,
0.039199527353048325,
0.006483054254204035,
0.018691670149564743,
-0.06960800290107727,
-0.028078900650143623,
0.008159289136528969,
0.0249419454485178,
-0.012731586582958698,
-0.05004546418786049,
-0.006888074334710836,
-0.0502193458378315,
0.0034520523622632027,
-0.0018977386644110084,
0.050161633640527725,
0.0415336973965168,
-0.018957795575261116,
-0.016479728743433952,
0.008471212349832058,
0.03504670783877373,
-0.008800608105957508,
-0.053012702614068985,
0.03968850150704384,
0.019503429532051086,
-0.006166255101561546,
0.03464377298951149,
0.06521033495664597,
-0.025859639048576355,
-0.0397937037050724,
0.00009427411714568734,
-0.012854666449129581,
0.005068902391940355,
0.00806690938770771,
-0.012810974381864071,
0.06862472742795944,
0.03827023133635521,
-0.007439061067998409,
-0.019521430134773254,
0.03341181203722954,
-0.0008540683193132281,
0.025550875812768936,
0.006027472671121359,
-0.02305738441646099,
0.02090531215071678,
-0.05717993155121803,
0.010947448201477528,
0.01876518689095974,
-0.0007805430795997381,
-0.005562322214245796,
0.04550516977906227,
0.018288541585206985,
-0.01814291439950466,
-0.010684972628951073,
0.001056108856573701,
0.006402178201824427,
-0.010532315820455551,
-0.010771599598228931,
-0.02215125411748886,
-0.01413764152675867,
-0.030787141993641853,
-0.042910732328891754,
-0.025714285671710968,
-0.028623512014746666,
0.032534416764974594,
-0.03814198449254036,
0.048940885812044144,
-0.023272274062037468,
-0.023457353934645653,
-0.00615406921133399,
-0.04090333729982376,
-0.008219461888074875,
0.03705093264579773,
0.009598101489245892,
0.02091480791568756,
-0.022859418764710426,
-0.006572480779141188,
0.06151251122355461,
0.05731567367911339,
-0.011026912368834019,
0.02517024055123329,
0.01374625414609909,
0.014317430555820465,
-0.011146079748868942,
-0.03948212414979935,
-0.012981954030692577,
0.04361346736550331,
-0.056729141622781754,
0.05980544909834862,
-0.012818203307688236,
-0.009495277889072895,
-0.000596371537540108,
-0.01524911168962717,
0.02380412630736828,
-0.04457095265388489,
-0.026774777099490166,
-0.007902476005256176,
0.03964420035481453,
0.012884633615612984,
0.03099568374454975,
0.02925160527229309,
-0.021181242540478706,
0.012330965138971806,
0.04144423082470894,
0.010502819903194904,
0.007671872153878212,
-0.06442448496818542,
-0.036340247839689255,
-0.024051250889897346,
-0.06976403295993805,
0.023112334311008453,
0.0067916749976575375,
-0.036587633192539215,
0.009934861212968826,
-0.020670635625720024,
-0.004495760425925255,
-0.0014532239874824882,
0.03020544908940792,
0.039795201271772385,
0.023303568363189697,
0.028276769444346428,
0.019760018214583397,
0.0007653689826838672,
0.02758239023387432,
0.11071734875440598,
0.042796261608600616,
0.012293864972889423,
-0.0437825545668602,
0.03066873922944069,
-0.03639112785458565,
-0.007514307741075754,
-0.058103326708078384,
0.02472284808754921,
-0.023857481777668,
0.023587794974446297,
0.005030868574976921,
0.058158840984106064,
-0.02035592868924141,
-0.027948757633566856,
0.028195420280098915,
-0.058560289442539215,
-0.005297831725329161,
0.014496623538434505,
0.04559174180030823,
-0.003076038556173444,
0.05329388380050659,
-0.03165135160088539,
0.00635085953399539,
-0.0298419501632452,
0.0056050862185657024,
-0.008829650469124317,
-0.026250528171658516,
0.007464237976819277,
-0.03249835968017578,
-0.04143207520246506,
-0.004891632124781609,
0.06149299815297127,
-0.03927993029356003,
-0.06556655466556549,
-0.022339865565299988,
0.027700675651431084,
0.0074313972145318985,
0.002727887127548456,
0.015137918293476105,
0.0010215725051239133,
0.029399296268820763,
0.03725367411971092,
0.002165536629036069,
-0.01738276705145836,
-0.03018195368349552,
0.010908837430179119,
0.018668977543711662,
-0.017713816836476326,
0.03640689328312874,
0.03844929113984108,
-0.027369549497961998,
-0.00620499299839139,
-0.0320848748087883,
0.0009200633503496647,
-0.006152708549052477,
0.0744747593998909,
-0.017787842079997063,
-0.009477226063609123,
-0.038446392863988876,
0.03546731919050217,
0.01654045656323433,
0.019884957000613213,
-0.007002988830208778,
-0.015423666685819626,
0.017310025170445442,
-0.00550704263150692,
0.05064424127340317,
-0.03260403871536255,
-0.023168621584773064,
0.002417029347270727,
-0.017840124666690826,
-0.04338880255818367,
-0.034264035522937775,
0.005747797433286905,
-0.012849287129938602,
0.017234113067388535,
0.020862922072410583,
-0.00021605772781185806,
-0.030908837914466858,
-0.05376763641834259,
-0.03192739561200142,
-0.0427926667034626,
-0.04722950980067253,
0.027260784059762955,
-0.011751977726817131,
0.03879653289914131,
0.056855425238609314,
-0.06546995043754578,
-0.009798086248338223,
0.0030386648140847683,
0.06080268695950508,
0.05144766718149185,
-0.016127970069646835,
0.030690157786011696,
0.003707582363858819,
-0.06048194319009781,
0.023017719388008118,
0.03113974817097187,
0.051491472870111465,
0.02353578805923462,
-0.007267809007316828,
-0.0139651820063591,
0.024762099608778954,
-0.0013705282472074032,
-0.014526394195854664,
0.04193573445081711,
-0.014200259000062943,
-0.012053963728249073,
0.04450469836592674,
-0.00585820060223341,
-0.03436772897839546,
-0.07495041936635971,
-0.059162162244319916,
0.00920187495648861,
-0.021765753626823425,
0.004709760192781687,
-0.006363730411976576,
0.009832539595663548,
0.002663314575329423,
-0.0071555813774466515,
-0.0506918728351593,
-0.006957544945180416,
-0.025200219824910164,
0.009064801037311554,
0.011717879213392735,
-0.021938951686024666,
-0.03135959431529045,
0.03238633647561073,
-0.016930535435676575,
-0.010160153731703758,
0.015207497403025627,
0.04902111366391182,
0.0259407889097929,
-0.03497466817498207,
-0.007610619533807039,
-0.015055007301270962,
0.08725307881832123,
-0.03696668893098831,
-0.04711319878697395,
0.03166109696030617,
-0.04386627674102783,
-0.05128078535199165,
0.02218371257185936,
-0.031551677733659744,
0.004616251680999994,
0.02770412340760231,
-0.000673227128572762,
-0.02457933872938156,
0.046519290655851364,
-0.014227359555661678,
-0.018341826274991035,
-0.009644461795687675,
-0.03087872825562954,
-0.028186053037643433,
-0.0024109194055199623,
0.021084962412714958,
-0.007074656896293163,
-0.03464042395353317,
0.03667920082807541,
0.03177551180124283,
-0.025370271876454353,
0.008576106280088425,
0.007488415576517582,
-0.04388218745589256,
0.001966459909453988,
0.03247571736574173,
0.007298381067812443,
0.04688870161771774,
0.033684223890304565,
-0.03686179965734482,
0.052481167018413544,
0.029534336179494858,
0.03336840122938156,
-0.12801675498485565,
0.012030056677758694,
0.012413380667567253,
-0.0011305027874186635,
0.006248687859624624,
-0.038362640887498856,
0.044260233640670776,
0.023576298728585243,
-0.06255830079317093,
0.005028652027249336,
-0.01577058434486389,
-0.003919961862266064,
-0.05269741266965866,
-0.005090097896754742,
-0.020900826901197433,
0.04482744634151459,
0.014567829668521881,
0.03664471209049225,
0.018020397052168846,
0.03513572737574577,
-0.015824710950255394,
-0.05566275492310524,
-0.012518360279500484,
0.046411968767642975,
-0.02393430285155773,
-0.007849535904824734,
0.05405959114432335,
-0.01798756793141365,
-0.008616515435278416,
0.010540241375565529,
-0.023260924965143204,
0.01731935702264309,
0.0042519718408584595,
0.016589097678661346,
-0.0001250542263733223,
0.036691609770059586,
0.01855137199163437,
0.0006562026683241129,
-0.018791573122143745,
0.013986274600028992,
0.0019180710660293698,
0.015867209061980247,
-0.04214812070131302,
-0.002074239542707801,
0.013536259531974792,
-0.0610070526599884,
-0.0420798659324646,
0.03348715230822563,
-0.01791660487651825,
-0.03934920206665993,
0.037118732929229736,
0.040141984820365906,
-0.00850867759436369,
-0.044454511255025864,
0.004495335277169943,
-0.009850851260125637,
-0.02940673753619194,
0.018315115943551064,
0.025626523420214653,
-0.018157178536057472,
-0.036196019500494,
0.006958651356399059,
-0.020587870851159096,
0.012552168220281601,
0.014764503575861454,
-0.012570103630423546,
-0.061462994664907455,
-0.013267732225358486,
-0.0040113613940775394,
-0.007611189968883991,
-0.018562480807304382,
-0.05327508971095085,
-0.029591098427772522,
0.024537384510040283,
0.0050501334480941296,
0.05361441522836685,
-0.03632201999425888,
-0.005025808699429035,
-0.015622871927917004,
-0.060705479234457016,
-0.004367352928966284,
-0.03684617578983307,
0.07361142337322235,
-0.04156779497861862,
-0.007110686507076025,
0.010066819377243519,
-0.013159283436834812,
0.06681198626756668,
0.014486163854598999,
-0.019457247108221054,
0.026351654902100563,
0.007306372746825218,
0.0075998008251190186,
-0.004090158734470606,
0.004885517526417971,
-0.03582771122455597,
-0.037735503166913986,
-0.014329539611935616,
-0.02390938252210617,
-0.025692827999591827,
0.015191697515547276,
0.02053755708038807,
-0.017030004411935806,
0.027146410197019577,
0.01277353148907423,
-0.01728091575205326,
0.08286233246326447,
0.03145040571689606,
-0.020701618865132332,
0.06365060806274414,
-0.03194325417280197,
0.024112634360790253,
0.04753830283880234,
0.00022940589406061918,
-0.05231545865535736,
0.04031073674559593,
0.0043527656234800816,
-0.046596501022577286,
0.000017557418686919846,
0.03106357716023922,
0.003714301623404026,
-0.0373571515083313,
0.026072591543197632,
0.05580173060297966,
-0.03522244095802307,
0.002126284409314394,
0.02675548568367958,
0.005737164057791233,
0.05784226208925247,
-0.022210175171494484,
0.024292174726724625,
0.01920667290687561,
-0.0000848980198497884,
-0.0020660560112446547,
0.055144019424915314,
0.03398232161998749,
0.0020129899494349957,
0.04640853404998779,
0.033838532865047455,
-0.009147492237389088,
-0.001223795348778367,
0.011444478295743465,
0.00852865632623434,
-0.004237313289195299,
-0.020613061264157295,
0.01645039953291416,
-0.017595674842596054,
0.037761885672807693,
0.019186634570360184,
0.020934587344527245,
0.0738377794623375,
-0.023620709776878357,
-0.0011549977352842689,
-0.026660706847906113,
0.012074503116309643,
-0.01409988384693861,
-0.003026236081495881,
0.00028643550467677414,
0.010898956097662449,
-0.02038223296403885,
0.0005542076542042196,
-0.028057323768734932,
0.022891707718372345,
0.0010164706036448479,
-0.053791943937540054,
0.005272579845041037,
0.0009666965925134718,
-0.016641395166516304,
-0.035576339811086655,
-0.01001324225217104,
-0.027333324775099754,
0.021015960723161697,
0.012847082689404488,
0.03364870697259903,
0.016572950407862663,
0.0507328137755394,
0.004947938024997711,
0.010496427305042744,
0.037095971405506134,
-0.05513150617480278,
-0.0039180563762784,
-0.043181512504816055,
0.03271734341979027,
-0.042447611689567566,
-0.02259834110736847
] |
<p>Is photosynthesis more efficient than solar panels? If so, by how much?</p>
| 7,607 |
[
-0.02699107676744461,
-0.03839552029967308,
-0.022575587034225464,
0.003787281922996044,
0.010142031125724316,
0.0013817782746627927,
-0.022483890876173973,
-0.051002614200115204,
0.000866473070345819,
-0.025474386289715767,
0.040724415332078934,
0.040351614356040955,
-0.0008081229170784354,
0.013911102898418903,
0.0014582312433049083,
-0.00699982326477766,
-0.02340930514037609,
0.012975412420928478,
0.0012398920953273773,
0.013689111918210983,
-0.03766494244337082,
0.01560662966221571,
0.02184828743338585,
0.03082285076379776,
-0.004464445635676384,
0.02745535410940647,
0.04317288473248482,
0.01296785194426775,
-0.019072173163294792,
0.0715131014585495,
0.001562149845995009,
-0.024797707796096802,
0.025480130687355995,
0.0640648603439331,
0.020201684907078743,
-0.029120534658432007,
-0.009399057365953922,
-0.063712939620018,
-0.022211190313100815,
0.021488217636942863,
0.008330457843840122,
0.0019131633453071117,
0.011897904798388481,
-0.019753891974687576,
-0.001611305633559823,
0.02433359995484352,
-0.020474012941122055,
-0.02732120268046856,
0.027036424726247787,
-0.07873774319887161,
0.04561064392328262,
-0.011496881023049355,
0.032970454543828964,
0.021782491356134415,
0.0011229822412133217,
0.005364014767110348,
0.07601280510425568,
0.06290952116250992,
-0.006414331030100584,
-0.03875533118844032,
-0.014012028463184834,
0.004674780648201704,
0.007011356297880411,
-0.03166842460632324,
-0.06537576019763947,
0.012687954120337963,
-0.02179495431482792,
-0.03174898028373718,
0.05790536478161812,
0.026280827820301056,
0.0023419144563376904,
0.01791595295071602,
0.03462893143296242,
0.0028776638209819794,
-0.020809223875403404,
-0.02723100781440735,
-0.006650510709732771,
0.016817158088088036,
0.04366569593548775,
0.04352866858243942,
0.007181060966104269,
0.041484903544187546,
0.01193900965154171,
0.0443008653819561,
0.03268065303564072,
-0.0028436107095330954,
0.05877983942627907,
-0.023781560361385345,
0.03977593407034874,
-0.006214576307684183,
0.01949545182287693,
0.023600704967975616,
0.04777185618877411,
-0.0024755115155130625,
0.0021335831843316555,
0.019638750702142715,
-0.02556423470377922,
0.0236218199133873,
0.02889852412045002,
-0.02114248275756836,
0.018656261265277863,
-0.021312307566404343,
0.02473387122154236,
0.0759926289319992,
0.03721236437559128,
-0.048809975385665894,
-0.034574851393699646,
0.017536520957946777,
0.019787397235631943,
0.0035684641916304827,
-0.040046487003564835,
0.001986992545425892,
0.010411171242594719,
-0.011142168194055557,
0.06563220918178558,
-0.033786334097385406,
0.0012032734230160713,
-0.019604068249464035,
0.06895650178194046,
0.07434497028589249,
0.02890760637819767,
-0.006369332782924175,
0.03394186124205589,
-0.01937396079301834,
-0.013945628888905048,
0.032561998814344406,
0.0018160255858674645,
-0.012688090093433857,
-0.057093750685453415,
0.01244595181196928,
-0.019839800894260406,
-0.009240983985364437,
-0.010285829193890095,
-0.04392591863870621,
0.03246352821588516,
0.00523636257275939,
-0.06434296071529388,
-0.02932131476700306,
0.03984206169843674,
0.007810807786881924,
0.014265152625739574,
-0.0471879281103611,
0.003383641131222248,
-0.008266167715191841,
0.06821336597204208,
-0.004999115131795406,
0.0063046785071492195,
0.011292627081274986,
0.05272698774933815,
-0.023198744282126427,
-0.012867383658885956,
0.008955377154052258,
0.0351969413459301,
-0.022647932171821594,
0.03404943272471428,
-0.05659506097435951,
0.023664366453886032,
0.05263927951455116,
0.0020535956136882305,
-0.003323047189041972,
0.035489521920681,
-0.025901686400175095,
-0.010563145391643047,
0.009445969015359879,
-0.022743692621588707,
-0.03092828020453453,
0.051854170858860016,
0.017030343413352966,
0.04375273361802101,
0.011057499796152115,
-0.007621111813932657,
0.0005253136623650789,
0.03501076623797417,
0.02249455451965332,
0.030613504350185394,
-0.014182685874402523,
-0.010959083214402199,
-0.015972662717103958,
0.03923391178250313,
0.031138816848397255,
-0.06253764778375626,
-0.004022201057523489,
0.00038959828088991344,
0.016701946035027504,
0.03947427123785019,
0.06903505325317383,
-0.02371870167553425,
-0.039185911417007446,
-0.02555062249302864,
-0.037346579134464264,
-0.011454536579549313,
-0.05668402463197708,
-0.015963980928063393,
0.022757025435566902,
0.012111143209040165,
-0.00426056794822216,
0.02761823870241642,
0.02502375654876232,
-0.028312046080827713,
-0.007508421316742897,
-0.01284254714846611,
0.0672246441245079,
0.011882392689585686,
0.005030679050832987,
0.009643063880503178,
0.07993311434984207,
0.06033666431903839,
-0.006162372883409262,
0.00970342569053173,
-0.004099132958799601,
-0.03586152195930481,
0.007188909221440554,
-0.05235457047820091,
0.010622245259582996,
0.011686071753501892,
-0.032430872321128845,
0.03961794450879097,
0.0039200144819915295,
-0.024956781417131424,
0.037132542580366135,
0.0019077410688623786,
0.06581083685159683,
0.027808591723442078,
0.02367454022169113,
0.03463597595691681,
-0.017236066982150078,
-0.016831615939736366,
0.0012807799503207207,
-0.0433521531522274,
-0.01840849779546261,
-0.04198548570275307,
0.014668493531644344,
0.07085976004600525,
0.033542390912771225,
-0.0389498695731163,
0.02056492492556572,
0.023266814649105072,
0.01888483576476574,
0.03494540974497795,
0.025017226114869118,
-0.03795038163661957,
-0.005554860457777977,
0.04836149886250496,
0.02929779328405857,
-0.005731047596782446,
0.020383404567837715,
0.035905055701732635,
-0.006822224706411362,
0.015318824909627438,
-0.008558272384107113,
-0.039892517030239105,
0.03165889158844948,
0.007585106883198023,
0.021355489268898964,
0.02809353731572628,
-0.04022199660539627,
-0.000018481139704817906,
-0.05688765272498131,
-0.033586323261260986,
-0.01179509051144123,
-0.005204123444855213,
0.02122725360095501,
-0.010705629363656044,
-0.03751686215400696,
-0.0004448586259968579,
0.010060153901576996,
-0.009806559421122074,
0.007684626150876284,
0.04929892718791962,
-0.022173112258315086,
0.06338514387607574,
-0.023645706474781036,
-0.0018002268625423312,
-0.01163527462631464,
-0.04052698612213135,
0.016661981120705605,
-0.02597167156636715,
0.02118818275630474,
-0.027187563478946686,
-0.005829505622386932,
0.011922911740839481,
-0.04652951657772064,
0.008547510951757431,
-0.013670403510332108,
-0.015814688056707382,
0.000759197399020195,
-0.015903042629361153,
-0.04166190326213837,
0.026327023282647133,
-0.01632341928780079,
-0.007021673023700714,
0.01056007668375969,
0.012825185433030128,
-0.05092010274529457,
0.03538547083735466,
-0.008528772741556168,
0.008401633240282536,
-0.001288140774704516,
-0.02587137743830681,
0.013732031919062138,
-0.024782486259937286,
-0.031620025634765625,
0.008065887726843357,
-0.03485582023859024,
-0.018430938944220543,
0.004709941800683737,
0.0009899858850985765,
-0.0036072940565645695,
-0.04513993114233017,
0.01949511468410492,
0.01948484778404236,
-0.07806156575679779,
0.006445255130529404,
-0.06243394315242767,
-0.05303122475743294,
0.00838799960911274,
-0.029892249032855034,
0.022956209257245064,
-0.013383404351770878,
-0.05201765149831772,
0.03583471104502678,
0.037611912935972214,
-0.0025132521986961365,
0.001985461451113224,
-0.036179084330797195,
-0.01919889636337757,
0.013513756915926933,
0.0001932314335135743,
0.026167966425418854,
0.024044793099164963,
0.019174814224243164,
-0.012942866422235966,
0.011085176840424538,
0.021503815427422523,
0.01750817336142063,
-0.030976133421063423,
-0.010152977891266346,
-0.01979193091392517,
0.02076025865972042,
0.028076136484742165,
0.004530712030827999,
-0.042639896273612976,
0.02956622652709484,
0.0007666866877116263,
0.015224653296172619,
0.003329237923026085,
-0.03901859372854233,
0.0666424036026001,
-0.000707301136571914,
0.043774910271167755,
-0.07031797617673874,
0.026020580902695656,
0.029860462993383408,
0.03172025829553604,
0.02274876832962036,
0.008675580844283104,
0.05539730191230774,
0.018273567780852318,
-0.008587517775595188,
0.012272169813513756,
0.05920698121190071,
-0.01808737777173519,
-0.04722067341208458,
0.00256750313565135,
-0.019605565816164017,
-0.0009556429577060044,
0.013171574100852013,
-0.030492287129163742,
0.059338588267564774,
0.032941848039627075,
0.02528369054198265,
-0.002629387192428112,
-0.025131983682513237,
0.0065106796100735664,
-0.08114179968833923,
-0.0173150897026062,
-0.02427062764763832,
0.037186332046985626,
-0.007213611621409655,
0.04122673347592354,
-0.032706327736377716,
-0.014088490046560764,
0.021490108221769333,
-0.013727471232414246,
-0.022914079949259758,
0.011606773361563683,
-0.008869954384863377,
-0.00005352255539037287,
-0.004737525247037411,
-0.012051915749907494,
-0.006852930411696434,
-0.040810298174619675,
-0.012202369049191475,
-0.04180802032351494,
-0.005152649246156216,
-0.023151542991399765,
0.005341304466128349,
-0.015581676736474037,
-0.03667276352643967,
-0.010481519624590874,
-0.017275767400860786,
-0.0010593539336696267,
-0.03196628391742706,
0.0378243513405323,
0.04560204595327377,
-0.059295833110809326,
0.013237465173006058,
0.019327588379383087,
0.019076460972428322,
-0.009395483881235123,
0.013186609372496605,
0.05293334275484085,
0.0012330851750448346,
-0.004350367002189159,
-0.011314651928842068,
0.015813613310456276,
0.01151919737458229,
-0.010562555864453316,
0.002976858289912343,
-0.029400326311588287,
-0.02705181948840618,
-0.02881476655602455,
0.010753088630735874,
-0.003020155243575573,
-0.019661594182252884,
0.0044206492602825165,
0.012488499283790588,
-0.015635985881090164,
-0.018204104155302048,
0.04966985434293747,
0.023301083594560623,
-0.0201261006295681,
-0.025090385228395462,
-0.06618425250053406,
-0.03228606656193733,
-0.03761228546500206,
0.0029911776073276997,
0.05182139202952385,
0.0009535465505905449,
-0.023446639999747276,
-0.003568114945665002,
0.020360631868243217,
-0.0172793660312891,
-0.02571447379887104,
0.03571406379342079,
-0.0055353837087750435,
0.02001611329615116,
0.01700587198138237,
-0.018108336254954338,
-0.009969626553356647,
0.03896414861083031,
0.02005639672279358,
0.022257879376411438,
-0.0005766990361735225,
-0.06359238922595978,
0.002322629326954484,
0.03710760921239853,
0.033814817667007446,
-0.06546249240636826,
0.0019167137797921896,
-0.04823210462927818,
-0.01833498850464821,
0.017807116732001305,
-0.02860809490084648,
0.027265584096312523,
-0.032391224056482315,
-0.007026625331491232,
-0.03521692380309105,
-0.004720947705209255,
-0.012258005328476429,
0.0015026256442070007,
-0.004072718322277069,
0.031034156680107117,
0.0016427206574007869,
-0.02338704653084278,
-0.01463261991739273,
0.03238128498196602,
0.0353417694568634,
0.0645022839307785,
-0.01192465703934431,
0.0006230692961253226,
0.005484634079039097,
0.026831546798348427,
-0.03561094030737877,
-0.07200109958648682,
0.017413830384612083,
-0.004734487738460302,
-0.031415387988090515,
0.026674088090658188,
-0.014987551607191563,
-0.06545297056436539,
0.05220566317439079,
0.0009930741507560015,
-0.018955696374177933,
-0.04975062608718872,
-0.0582101009786129,
0.000976205337792635,
0.033535175025463104,
0.01798638328909874,
0.06068113073706627,
0.08160028606653214,
-0.08442694693803787,
0.022711245343089104,
-0.05146957188844681,
0.046192917972803116,
-0.046513427048921585,
-0.031163770705461502,
0.004391292110085487,
-0.04160825163125992,
0.0032588839530944824,
-0.005266467109322548,
0.006326031871140003,
0.03871084004640579,
-0.014346064068377018,
-0.05680670216679573,
-0.01092209480702877,
-0.000529929471667856,
0.00044234495726414025,
-0.018654726445674896,
-0.03694695234298706,
0.03503201901912689,
0.01901928149163723,
-0.027442041784524918,
0.019018294289708138,
0.010464942082762718,
-0.014046990312635899,
-0.012049293145537376,
-0.0023918829392641783,
-0.006655062083154917,
-0.05816037207841873,
0.007511169649660587,
0.005906326696276665,
0.005046461708843708,
0.07142772525548935,
-0.005542209837585688,
0.010264692828059196,
0.005502753891050816,
-0.09521711617708206,
-0.0409766286611557,
0.03691500052809715,
-0.014616737142205238,
0.022645700722932816,
-0.05280492082238197,
0.038351595401763916,
-0.005394298583269119,
-0.014853520318865776,
-0.07105617970228195,
-0.01834852248430252,
0.0074799545109272,
0.04530005902051926,
0.005579834803938866,
-0.051980987191200256,
-0.0042252433486282825,
-0.010022302158176899,
-0.019988181069493294,
-0.007965958677232265,
0.03160099312663078,
-0.0547696053981781,
-0.010037059895694256,
-0.03092995285987854,
-0.019748948514461517,
0.08095379173755646,
-0.04338774085044861,
-0.003617854556068778,
-0.0038354338612407446,
-0.05286407470703125,
-0.01440308429300785,
-0.05490962788462639,
0.02280009724199772,
-0.019312558695673943,
-0.004719316028058529,
-0.011716997250914574,
-0.01895519159734249,
0.02361699566245079,
-0.020758092403411865,
-0.008798488415777683,
0.0789269357919693,
0.01726732961833477,
-0.020708825439214706,
0.005496059078723192,
0.06205188110470772,
-0.018698254600167274,
0.038779716938734055,
-0.002675415016710758,
-0.012665100395679474,
-0.0014476192882284522,
-0.037111081182956696,
0.020522067323327065,
-0.015138287097215652,
-0.01979895867407322,
-0.003192452946677804,
0.09208188951015472,
-0.022359365597367287,
-0.003410925157368183,
0.02274089865386486,
-0.02417473867535591,
0.024453626945614815,
-0.016082074493169785,
0.026924019679427147,
-0.01988835260272026,
-0.008172149769961834,
-0.030412612482905388,
-0.02955365926027298,
-0.020923614501953125,
-0.032249804586172104,
0.03515499830245972,
0.003931745886802673,
0.03213856741786003,
-0.004763582721352577,
0.00731104938313365,
0.029943028464913368,
-0.051072556525468826,
0.008104185573756695,
0.01954050175845623,
-0.01936599425971508,
0.03753013536334038,
0.0038604505825787783,
0.00979079119861126,
0.0681115910410881,
0.02754572592675686,
-0.008373798802495003,
0.05347193032503128,
0.020933235064148903,
0.0010486897081136703,
0.02727035991847515,
-0.048427823930978775,
-0.07135380804538727,
0.009914625436067581,
-0.0844692587852478,
0.006345083471387625,
-0.03271937370300293,
-0.06167520582675934,
0.07967302203178406,
-0.013250421732664108,
-0.016659749671816826,
-0.024609399959445,
-0.0022992785088717937,
-0.04562988877296448,
0.0026685274206101894,
-0.002163334283977747,
0.017571507021784782,
-0.001703571411781013,
0.008460702374577522,
0.019868504256010056,
0.006999422330409288,
-0.001532891532406211,
0.003060159971937537,
-0.0856422558426857,
-0.036118388175964355,
-0.00204420555382967,
-0.03831777349114418,
0.03364725410938263,
0.022476866841316223,
-0.04986374452710152,
0.014109744690358639,
-0.016034921631217003,
0.004349344410002232,
-0.011464469134807587,
0.06688998639583588,
-0.009670493192970753,
0.020662058144807816,
-0.025516411289572716,
0.02949761040508747,
-0.020057152956724167,
0.0060057006776332855,
0.10845689475536346,
0.03133494406938553,
0.010226450860500336,
-0.054875586181879044,
0.05545945093035698,
-0.03361130133271217,
0.023220665752887726,
-0.009981860406696796,
-0.002352573676034808,
-0.0013551629381254315,
0.009222518652677536,
-0.021065376698970795,
0.028348656371235847,
-0.007378125563263893,
-0.0160637479275465,
0.04816874489188194,
-0.0022678212262690067,
-0.020743563771247864,
0.06233934685587883,
0.02613312005996704,
-0.013401036150753498,
0.009799591265618801,
-0.055389806628227234,
-0.015048393048346043,
-0.049032796174287796,
-0.024181541055440903,
-0.024818329140543938,
-0.04152628034353256,
0.03674366697669029,
-0.01030146237462759,
-0.01592390052974224,
-0.026334822177886963,
-0.012130890972912312,
0.009514638222754002,
-0.054090581834316254,
0.02197444997727871,
0.034366674721241,
0.007713955361396074,
0.0027979498263448477,
0.027657190337777138,
0.014378909021615982,
0.018957527354359627,
0.03767848014831543,
0.02504865825176239,
-0.06265725195407867,
0.012750987894833088,
-0.021275248378515244,
0.00985633209347725,
0.009745241142809391,
0.03175656497478485,
0.005011214874684811,
0.0057666306383907795,
-0.023692971095442772,
-0.021624501794576645,
-0.00819151196628809,
0.004922779742628336,
0.011613588780164719,
-0.009704776108264923,
-0.05187394469976425,
-0.0226808562874794,
0.017832202836871147,
-0.024822114035487175,
0.04853048175573349,
0.020158492028713226,
0.006240218877792358,
0.018703650683164597,
0.024126065894961357,
0.016823362559080124,
-0.018200477585196495,
-0.022533612325787544,
-0.02932737022638321,
-0.008478928357362747,
-0.028596796095371246,
-0.053824566304683685,
0.03560015931725502,
0.03744092211127281,
0.02517533488571644,
0.028172263875603676,
-0.0237442497164011,
0.014424136839807034,
-0.08033653348684311,
0.05004004389047623,
-0.021708136424422264,
-0.008763734251260757,
-0.04203084483742714,
0.014412443153560162,
0.06573241204023361,
0.01674928516149521,
0.00004123123289900832,
0.04845282435417175,
-0.03394204005599022,
0.020479252561926842,
0.02448289841413498,
-0.053200799971818924,
-0.013292931020259857,
-0.0033247906249016523,
-0.00945248082280159,
-0.027948133647441864,
-0.012765024788677692,
0.024848751723766327,
0.02201482653617859,
0.006897666025906801,
-0.03150572255253792,
-0.0089229391887784,
-0.035170383751392365,
0.02399209327995777,
0.008680908009409904,
-0.007372390478849411,
-0.031142113730311394,
0.01592247560620308,
0.04160289838910103,
-0.008863360621035099,
-0.01184143591672182,
-0.03359035775065422,
-0.002870772732421756,
0.009246189147233963,
-0.005482506938278675,
-0.018824821338057518,
0.008351537398993969,
-0.025335220620036125,
0.026196785271167755,
-0.045979369431734085,
-0.03655535355210304,
-0.06441936641931534,
0.0013038254110142589,
0.02146594040095806,
-0.00972265750169754,
-0.0014377455227077007,
0.013457361608743668,
-0.0013112345477566123,
0.02256922796368599,
0.08079364895820618,
0.004421365447342396,
0.014219862408936024,
0.0008302853675559163,
0.0531785674393177,
-0.016722699627280235,
0.056361325085163116,
-0.04522505775094032,
-0.025562476366758347,
0.06386016309261322,
-0.04106743633747101,
-0.03226727247238159,
-0.015538668259978294,
-0.03953995183110237,
0.04954402521252632,
0.02834257483482361,
-0.02544299140572548,
-0.022721996530890465,
0.04177777096629143,
-0.01706012710928917,
-0.006670307833701372,
-0.009244742803275585,
-0.011125088669359684,
-0.0072428579442203045,
0.03545442968606949,
0.00023010108270682395,
-0.04732929542660713,
-0.024783680215477943,
0.04046507552266121,
0.021031755954027176,
-0.007548217196017504,
0.019566353410482407,
-0.012486934661865234,
-0.03875903785228729,
0.0037595408502966166,
0.03205564245581627,
-0.016818149015307426,
0.0003674417093861848,
0.036816418170928955,
-0.007022797595709562,
0.031247522681951523,
0.018842438235878944,
-0.013980885036289692,
-0.05833275988698006,
0.011614102870225906,
-0.011087169870734215,
0.018923578783869743,
-0.002245743293315172,
-0.019724877551198006,
0.041832879185676575,
0.028559844940900803,
-0.07921954989433289,
0.019264107570052147,
0.016332212835550308,
-0.010463433340191841,
-0.04032416269183159,
0.033561188727617264,
-0.02575857937335968,
0.034680064767599106,
0.012121384032070637,
0.04597682133316994,
-0.017038634046912193,
0.046345725655555725,
0.011685372330248356,
-0.02122855931520462,
-0.005827811546623707,
0.03153977543115616,
-0.019932173192501068,
-0.016273928806185722,
0.026482602581381798,
-0.00823642872273922,
-0.02434551529586315,
-0.0015962510369718075,
0.005716689396649599,
0.05888805538415909,
-0.00046073802514001727,
0.02597425878047943,
-0.0007964368560351431,
0.042632654309272766,
0.03569074347615242,
-0.028127506375312805,
-0.058868713676929474,
0.015896739438176155,
0.0010743695311248302,
0.007672758772969246,
0.007695304229855537,
0.035643529146909714,
0.020861748605966568,
0.013831580989062786,
-0.01849697157740593,
0.024812959134578705,
-0.0029353941790759563,
-0.013383481651544571,
0.028560088947415352,
0.024055177345871925,
0.023446956649422646,
0.015008443966507912,
-0.024783113971352577,
-0.06542668491601944,
0.017017314210534096,
0.00344001199118793,
-0.035027503967285156,
0.015708204358816147,
0.000060013262555003166,
0.047815512865781784,
0.013726659119129181,
-0.0004310564836487174,
-0.0004947547568008304,
0.0006388422334566712,
-0.04076884314417839,
0.004837574902921915,
0.02505149319767952,
-0.011168609373271465,
-0.011345050297677517,
-0.02141513302922249,
-0.04701017960906029,
0.05215558782219887,
0.016225239261984825,
0.04614841938018799,
0.03294749930500984,
-0.02358313277363777,
-0.015576702542603016,
-0.05501343309879303,
0.060110438615083694,
-0.011017318814992905,
0.009133505634963512,
-0.037480857223272324,
-0.03646136075258255,
-0.041630279272794724,
0.010033990256488323,
0.04982053115963936,
-0.01324340421706438,
-0.022902026772499084,
0.007579513359814882,
0.003278546268120408,
0.04605559632182121,
-0.06056671217083931,
0.05432116985321045,
0.01056324690580368,
-0.03742855414748192,
-0.00205250340513885,
-0.04636739194393158,
-0.010270639322698116,
0.01308874599635601,
0.05259174481034279,
-0.007311488501727581,
0.0179666206240654,
0.007253542542457581,
0.013059008866548538,
0.06447019428014755,
0.02005261927843094,
0.015757784247398376,
0.08757728338241577,
-0.024783020839095116,
0.0394662581384182,
0.02795160934329033,
-0.00894219521433115,
-0.04914747178554535,
-0.001648270059376955,
-0.04857556149363518,
0.012131339870393276,
0.029425857588648796,
-0.009469089098274708,
0.02875177003443241,
-0.06248202919960022,
-0.01766132190823555,
0.01437368243932724,
-0.03593346104025841,
-0.0014710862888023257,
0.021754520013928413,
0.0011436414206400514,
0.03175986558198929,
-0.02941090799868107,
0.05156300961971283,
0.0029899284709244967,
0.02834705077111721,
-0.03763202205300331,
0.037074144929647446,
0.0353059358894825,
0.0077078635804355145,
0.054873980581760406,
0.014445954002439976,
0.015880655497312546,
0.019758831709623337,
0.026943819597363472,
0.0073823449201881886,
-0.028426211327314377,
-0.04312710091471672,
0.025758318603038788,
0.026613198220729828,
0.010163949802517891,
0.028092194348573685,
0.01991243287920952,
0.09320846945047379,
-0.03319620341062546,
-0.011319939978420734,
-0.01412250567227602,
-0.029072346165776253,
-0.007058119401335716,
-0.002196355490013957,
0.011854734271764755,
0.031050190329551697,
-0.006724144797772169,
-0.009815133176743984,
-0.025966288521885872,
0.049585819244384766,
0.027495158836245537,
-0.047623276710510254,
0.04140380397439003,
-0.00786382332444191,
-0.018639609217643738,
-0.024846060201525688,
0.03869510442018509,
0.006847763434052467,
-0.033277709037065506,
0.00856715440750122,
0.030792465433478355,
0.000020871966626145877,
0.03932955861091614,
-0.029626812785863876,
0.023657698184251785,
0.04566655680537224,
-0.0518149808049202,
-0.011909157037734985,
-0.011834828183054924,
-0.01727020926773548,
-0.030370166525244713,
-0.02701117843389511
] |
<p>Is it correct that for a motion in a <a href="http://en.wikipedia.org/wiki/Central_force" rel="nofollow">central force</a> field, e.g. a gravitational field, the absolute value of the total angular momentum of the particle and the component of the perpendicular to the plane of motion are conserved, but the other components of the angular momentum in general not?</p>
| 7,608 |
[
-0.04079360514879227,
-0.012405824847519398,
-0.04386395215988159,
-0.0036137106362730265,
0.0702267587184906,
0.019245918840169907,
-0.04298180714249611,
-0.015382378362119198,
-0.009488684125244617,
-0.07467304915189743,
-0.01890518330037594,
0.03461217135190964,
0.05643538013100624,
0.022033726796507835,
0.0303206704556942,
-0.020675482228398323,
-0.019511112943291664,
0.019261255860328674,
-0.0005724190268665552,
-0.036749694496393204,
-0.030854320153594017,
0.02818160131573677,
0.007356938440352678,
-0.003156837075948715,
0.0044081974774599075,
0.03832840174436569,
0.015080808661878109,
-0.0002421579702058807,
0.021395636722445488,
0.0733162984251976,
-0.0135490158572793,
0.002690651686862111,
-0.026071902364492416,
0.028422681614756584,
0.014724228531122208,
0.013791489414870739,
-0.02711011841893196,
-0.012936064973473549,
-0.024978861212730408,
0.026264403015375137,
-0.052129387855529785,
-0.017747700214385986,
-0.03055463917553425,
0.10460209846496582,
-0.035482220351696014,
0.014999140053987503,
-0.00559615483507514,
0.03624572977423668,
0.04715689644217491,
-0.04140869155526161,
0.07766294479370117,
0.012121484614908695,
0.0341387540102005,
0.010847259312868118,
-0.010594711638987064,
-0.012467277236282825,
0.0520765483379364,
0.0431792251765728,
-0.011191105470061302,
-0.043919071555137634,
0.002962214406579733,
0.0011500234249979258,
0.0005133294616825879,
-0.022633139044046402,
-0.015220720320940018,
0.0331280417740345,
0.0226154625415802,
-0.01590844988822937,
0.038043294101953506,
0.015503290109336376,
0.000043225321860518306,
0.005262262653559446,
0.014268654398620129,
-0.02888326533138752,
-0.019533634185791016,
-0.024602409452199936,
0.04053282365202904,
0.02081221155822277,
0.015397337265312672,
0.020001741126179695,
0.015104501508176327,
-0.007877946831285954,
0.029770947992801666,
0.04327928647398949,
0.025346791371703148,
0.04028211534023285,
0.06342111527919769,
-0.0047667501494288445,
0.019811896607279778,
0.042611535638570786,
0.011723360978066921,
0.01743590459227562,
0.0037709467578679323,
-0.01798672042787075,
-0.04991716146469116,
0.02072843350470066,
0.0021026853937655687,
0.04689402133226395,
-0.005634829867631197,
-0.002776768524199724,
0.0037801587022840977,
0.0012339444365352392,
0.009271054528653622,
0.04812948405742645,
-0.00924519170075655,
-0.011825496330857277,
-0.037831004709005356,
-0.004656617529690266,
-0.026955170556902885,
-0.03183409571647644,
-0.06951221823692322,
0.008061598055064678,
-0.034340959042310715,
-0.015839096158742905,
0.026213038712739944,
-0.021090758964419365,
-0.009492440149188042,
0.0019651874899864197,
0.05827881768345833,
0.0502585843205452,
0.06348176300525665,
-0.03917054459452629,
-0.008814012631773949,
-0.027529418468475342,
-0.04789602383971214,
0.004751038737595081,
0.01239517331123352,
0.034374434500932693,
-0.03761225566267967,
0.004572645295411348,
0.02913479134440422,
-0.016934365034103394,
-0.010978330858051777,
-0.0064033265225589275,
0.011755469255149364,
0.005134683568030596,
-0.1130727007985115,
-0.07624167948961258,
0.04542771726846695,
-0.03515681251883507,
-0.005944016855210066,
-0.08438324928283691,
-0.004305381327867508,
0.016541821882128716,
0.05245182663202286,
-0.00913415290415287,
-0.010864105075597763,
-0.003342234995216131,
0.03051760047674179,
0.00929867010563612,
0.008609701879322529,
-0.027201585471630096,
0.03022828884422779,
-0.07273910194635391,
-0.0399298220872879,
-0.09712060540914536,
-0.00455824751406908,
0.021259017288684845,
0.03042483702301979,
-0.014680985361337662,
0.030504019930958748,
-0.01475172583013773,
0.05072658509016037,
0.003150476375594735,
0.010613017715513706,
-0.02810550667345524,
0.05376741290092468,
0.03210441768169403,
-0.014224904589354992,
0.024442970752716064,
0.04491846635937691,
0.028306467458605766,
-0.03521032631397247,
0.008330509066581726,
0.08195045590400696,
-0.03591127693653107,
-0.0019184103002771735,
-0.018704818561673164,
0.02679002843797207,
-0.008051840588450432,
-0.06040773168206215,
-0.03964082896709442,
-0.02568919211626053,
0.03025544062256813,
-0.037698302417993546,
0.0769072026014328,
-0.0027871252968907356,
-0.000747255573514849,
-0.0017775841988623142,
-0.012403316795825958,
0.02572971023619175,
-0.05057385191321373,
0.05031164735555649,
-0.009231609292328358,
-0.025317776948213577,
0.025739168748259544,
0.023837372660636902,
0.05342859774827957,
-0.042383745312690735,
-0.03438220173120499,
0.002520639216527343,
0.035755403339862823,
-0.02380487136542797,
-0.020603623241186142,
0.016937104985117912,
0.03839142993092537,
0.03656531125307083,
0.026160428300499916,
0.01571003533899784,
0.012582979165017605,
-0.029338814318180084,
-0.0026288162916898727,
-0.020732158794999123,
0.02270733192563057,
0.053458668291568756,
-0.02402965910732746,
0.012734738178551197,
0.028511101379990578,
0.018755456432700157,
0.04790192469954491,
-0.028753643855452538,
0.07667425274848938,
0.03613975644111633,
-0.013175294734537601,
0.014434905722737312,
0.07645327597856522,
0.016903206706047058,
0.005152490921318531,
-0.008388234302401543,
-0.01714383251965046,
-0.024329019710421562,
-0.015598060563206673,
0.04013574495911598,
0.01686267927289009,
-0.060528382658958435,
0.006214048247784376,
0.03126712515950203,
0.03199164196848869,
0.02832280844449997,
0.003123493632301688,
0.016037994995713234,
-0.08859732747077942,
-0.014594103209674358,
0.02367456816136837,
-0.00758390175178647,
0.017071431502699852,
0.016705328598618507,
-0.006456481758505106,
0.025068525224924088,
0.017259985208511353,
-0.02366868406534195,
0.04094323515892029,
-0.011204506270587444,
0.02024814300239086,
0.027527062222361565,
-0.04289914667606354,
0.03405792638659477,
-0.00736127607524395,
0.07101093977689743,
0.017108149826526642,
0.0007449603290297091,
-0.021692931652069092,
-0.013401291333138943,
-0.00861723069101572,
0.015747906640172005,
0.009064159356057644,
-0.02861502394080162,
-0.006807147525250912,
0.002519235946238041,
-0.014919020235538483,
-0.023285701870918274,
-0.03834668919444084,
-0.01994202472269535,
-0.011990716680884361,
-0.014357568696141243,
0.03983299806714058,
0.0009627448744140565,
0.03421774506568909,
-0.023490503430366516,
-0.028724772855639458,
-0.0144925806671381,
-0.034621454775333405,
-0.03780490905046463,
0.04382574185729027,
-0.053290270268917084,
0.03205163776874542,
-0.059525828808546066,
-0.017744164913892746,
0.017259787768125534,
-0.026581374928355217,
0.023440903052687645,
0.025981653481721878,
-0.024299360811710358,
-0.076451376080513,
0.018322637304663658,
-0.03771662712097168,
-0.022858504205942154,
-0.041738010942935944,
-0.02007882483303547,
0.044598255306482315,
-0.02081468515098095,
0.011697174981236458,
0.011682447046041489,
-0.030735835433006287,
-0.07382714748382568,
-0.0027354059275239706,
0.016558630391955376,
0.020825371146202087,
-0.0018746047280728817,
0.009034491144120693,
0.03204282745718956,
-0.041503094136714935,
-0.018068308010697365,
-0.03364168852567673,
-0.029502911493182182,
0.015233361162245274,
-0.013030525296926498,
0.03159628435969353,
-0.023712189868092537,
-0.024508550763130188,
0.11173353344202042,
0.050820618867874146,
-0.059305403381586075,
-0.00451922370120883,
0.0021543814800679684,
-0.004126300103962421,
-0.02348916418850422,
0.00836893729865551,
0.004892519675195217,
-0.039003994315862656,
0.02781630866229534,
0.007026543375104666,
0.0045239003375172615,
0.0007261077989824116,
0.009647112339735031,
-0.027173077687621117,
0.007563569582998753,
0.02275688759982586,
0.003482436528429389,
0.06367599964141846,
0.0203024223446846,
0.004187979735434055,
-0.004314980003982782,
0.02525179646909237,
0.05647200345993042,
-0.0015246478142216802,
-0.053809281438589096,
0.07964638620615005,
-0.024540523067116737,
0.030963856726884842,
0.00006165608647279441,
0.06363648176193237,
0.011439569294452667,
0.016803177073597908,
0.014997346326708794,
0.005417350213974714,
0.03799452260136604,
-0.005053631495684385,
0.01901521533727646,
0.03756452724337578,
0.01954975537955761,
-0.010753162205219269,
-0.0037915981374680996,
0.00983968935906887,
0.006118967663496733,
0.038044240325689316,
-0.04165354371070862,
-0.04252026602625847,
0.003910883329808712,
0.03736858069896698,
0.02085247077047825,
0.023064199835062027,
-0.0719330832362175,
0.005622345954179764,
-0.06545642763376236,
0.048763103783130646,
0.003421800909563899,
0.009070922620594501,
0.016091862693428993,
0.05523112788796425,
0.021151985973119736,
0.00670907087624073,
0.0024663079530000687,
0.013732017017900944,
-0.07135872542858124,
0.03396238014101982,
-0.028504831716418266,
-0.012510555796325207,
-0.02012247033417225,
-0.03191220387816429,
0.013471013866364956,
-0.010610997676849365,
-0.010342687368392944,
-0.018260132521390915,
-0.026907052844762802,
-0.04292391240596771,
-0.007289857603609562,
-0.04004524275660515,
-0.03381114453077316,
-0.01622147299349308,
0.04486248269677162,
0.06097102537751198,
-0.048646796494722366,
0.037614934146404266,
0.04712098464369774,
-0.06193239986896515,
0.010520772077143192,
-0.016627443954348564,
-0.004734729882329702,
0.015217237174510956,
0.0201119352132082,
0.03631897270679474,
0.01582525297999382,
-0.0017961438279598951,
-0.002168318722397089,
0.009342296048998833,
0.03672245889902115,
0.01311860978603363,
-0.01436848845332861,
-0.019321082159876823,
-0.05935269221663475,
-0.006323949433863163,
0.007977397181093693,
0.03459784388542175,
0.01000390388071537,
-0.019766682758927345,
0.057019755244255066,
0.03942952677607536,
-0.0175089742988348,
0.030623450875282288,
0.02998974360525608,
0.03490929305553436,
0.017791450023651123,
-0.06333394348621368,
0.014141328632831573,
-0.017130330204963684,
-0.03137076273560524,
0.02378067560493946,
-0.038557421416044235,
-0.07075952738523483,
-0.013255389407277107,
0.0035688907373696566,
0.02301287278532982,
-0.009086903184652328,
0.035018883645534515,
-0.036913856863975525,
0.010873553343117237,
-0.01563897356390953,
0.004330669064074755,
0.003604533616453409,
0.02412751130759716,
0.03417182341217995,
0.017241667956113815,
-0.0033866597805172205,
-0.031564608216285706,
-0.002734292531386018,
0.03162287548184395,
0.042575228959321976,
-0.01638144440948963,
0.0009249945287592709,
-0.021421438083052635,
-0.034678854048252106,
0.043625008314847946,
-0.012358580715954304,
0.060403622686862946,
-0.0006080373423174024,
-0.006903592962771654,
0.013331137597560883,
-0.04721662774682045,
-0.026483379304409027,
0.019531741738319397,
-0.029453370720148087,
-0.023815808817744255,
-0.04073632135987282,
0.02206259034574032,
-0.02032470516860485,
0.0013806602219119668,
0.011844761669635773,
0.02384343557059765,
0.03908662497997284,
-0.00866373348981142,
-0.007271946873515844,
0.012144027277827263,
-0.020129483193159103,
-0.08120890706777573,
-0.018118243664503098,
0.02767086587846279,
-0.0065141660161316395,
0.026135556399822235,
-0.0413520485162735,
-0.04775447025895119,
0.0020209900103509426,
0.008271404542028904,
0.012204905040562153,
0.028890226036310196,
-0.018959568813443184,
0.038650814443826675,
0.05131470039486885,
-0.04034813120961189,
0.056182049214839935,
0.024004559963941574,
0.005132127087563276,
-0.04095059260725975,
-0.021154794842004776,
0.021243108436465263,
-0.01376158744096756,
-0.007284965831786394,
-0.051093243062496185,
0.017626333981752396,
0.00150434416718781,
0.037257418036460876,
-0.0011187022319063544,
0.009003794752061367,
-0.02299327775835991,
-0.025492724031209946,
-0.01740119233727455,
0.01438911072909832,
-0.0006441274890676141,
-0.019349534064531326,
-0.004907552618533373,
0.005771392025053501,
-0.0023940415121614933,
-0.0052397409453988075,
-0.008714355528354645,
-0.018995501101017,
-0.004460008814930916,
0.0321507565677166,
0.0039239199832081795,
0.0009523280896246433,
-0.015365371480584145,
-0.038108982145786285,
-0.01547093316912651,
-0.05893206596374512,
0.008457054384052753,
-0.020952925086021423,
-0.02630596049129963,
0.03301938623189926,
-0.05280419439077377,
-0.05884560942649841,
0.021337859332561493,
-0.008635329082608223,
0.026961009949445724,
-0.05489692836999893,
0.016342591494321823,
0.021306535229086876,
0.04260442033410072,
-0.06026332825422287,
-0.03052898496389389,
0.017477013170719147,
0.003891285276040435,
-0.0002540540008340031,
-0.012300634756684303,
-0.027665501460433006,
-0.020423414185643196,
-0.032581012696027756,
-0.008009364828467369,
0.03552756458520889,
-0.03716692700982094,
-0.006462537683546543,
0.01744171418249607,
-0.008067773655056953,
0.06656323373317719,
0.013876624405384064,
-0.015535085462033749,
0.014410866424441338,
0.008622446097433567,
-0.0021758065558969975,
0.01195771899074316,
0.07553046941757202,
-0.025584587827324867,
-0.02894560806453228,
0.014103095047175884,
-0.007636214140802622,
0.014930050820112228,
0.029371686279773712,
0.006011701188981533,
0.05730191990733147,
0.0015527247451245785,
-0.003935286775231361,
-0.002566237933933735,
0.024937933310866356,
-0.0073612285777926445,
0.018223747611045837,
0.02108674682676792,
-0.001466722460463643,
-0.008045232854783535,
-0.04500477388501167,
0.0025795651599764824,
0.009153567254543304,
0.012678530067205429,
-0.0031507581006735563,
0.05373009666800499,
0.01432928815484047,
-0.009907471016049385,
-0.006283917929977179,
-0.01944909058511257,
0.0194557998329401,
-0.02102407068014145,
0.015460968017578125,
0.0018759180093184114,
0.025244999676942825,
-0.01517284195870161,
-0.0058777667582035065,
0.002978753997012973,
0.008418071083724499,
0.056987207382917404,
-0.02519497461616993,
0.051771752536296844,
0.03019583411514759,
0.027137866243720055,
-0.027461044490337372,
-0.04385117068886757,
0.01439820509403944,
0.012561829760670662,
0.020489227026700974,
0.02945789322257042,
-0.010918688029050827,
0.01221416424959898,
0.015882903710007668,
0.053230807185173035,
-0.0291304849088192,
0.004992610774934292,
0.023309040814638138,
0.004589371848851442,
-0.006654784549027681,
0.02885398082435131,
-0.06277599185705185,
0.003272350411862135,
-0.0094600236043334,
0.06831701099872589,
-0.0013889640104025602,
-0.04858006164431572,
0.031158827245235443,
-0.005678167566657066,
0.04499498009681702,
-0.00922755803912878,
-0.03120230697095394,
0.0019741852302104235,
0.03628571704030037,
-0.03823181986808777,
0.012331032194197178,
-0.047672152519226074,
-0.004792674910277128,
0.07285749167203903,
0.021808002144098282,
-0.006181822158396244,
-0.008600760251283646,
-0.04208134114742279,
-0.024416323751211166,
-0.038560785353183746,
-0.03592785820364952,
0.02908405289053917,
-0.012258805334568024,
-0.01615373231470585,
0.017861763015389442,
-0.0064470404759049416,
-0.0008433905313722789,
0.020082689821720123,
0.018742624670267105,
-0.02269880287349224,
0.03142023831605911,
0.015486371703445911,
0.012766472063958645,
-0.015604725107550621,
-0.005724893417209387,
0.11722976714372635,
0.04180826246738434,
0.007414893712848425,
-0.04180631414055824,
0.019824696704745293,
-0.041683487594127655,
0.01617167890071869,
-0.03914380073547363,
0.008880382403731346,
-0.025204060599207878,
-0.006373672280460596,
0.02374829351902008,
0.045814841985702515,
-0.02135843224823475,
-0.043245065957307816,
0.06546926498413086,
-0.0212008748203516,
-0.032074104994535446,
-0.015579817816615105,
0.03230983018875122,
-0.027793601155281067,
0.006308185867965221,
-0.034520119428634644,
0.037812236696481705,
-0.03833342716097832,
-0.005920470226556063,
-0.01362792681902647,
-0.04098961502313614,
-0.01233084686100483,
-0.025397220626473427,
-0.03037198632955551,
0.012907165102660656,
0.013624390587210655,
-0.015739304944872856,
-0.07360662519931793,
-0.002729579573497176,
0.026780743151903152,
0.0008602880989201367,
0.03331936523318291,
0.029326383024454117,
-0.01936843991279602,
0.0161298718303442,
0.037178486585617065,
0.00030904498999007046,
-0.06937848031520844,
0.00805220939218998,
-0.027767479419708252,
0.044514793902635574,
-0.0008931399788707495,
0.05594273656606674,
0.025387121364474297,
-0.049072302877902985,
0.008987088687717915,
-0.05597076937556267,
0.009483987465500832,
-0.00950395967811346,
0.012280863709747791,
0.015251562930643559,
0.0048447903245687485,
-0.027969228103756905,
-0.0007761120796203613,
0.02013653703033924,
-0.005321580916643143,
-0.01276278868317604,
-0.0016607431462034583,
0.019317327067255974,
-0.005390822887420654,
0.02426782064139843,
-0.020875120535492897,
-0.022995632141828537,
-0.030538419261574745,
-0.019136324524879456,
-0.04960288479924202,
0.013599801808595657,
0.02361352927982807,
0.012623930349946022,
0.011416640132665634,
-0.0017410552827641368,
0.00041544492705725133,
0.005635169334709644,
-0.06541462987661362,
0.01548550371080637,
-0.017518164590001106,
-0.025767823681235313,
-0.005858805496245623,
0.01255218405276537,
0.025866681709885597,
0.08161339908838272,
-0.03235197812318802,
0.008123918436467648,
-0.0051072267815470695,
0.03541189432144165,
0.01922726444900036,
-0.015535046346485615,
-0.020662087947130203,
0.012881471775472164,
-0.053612492978572845,
-0.030646657571196556,
-0.015675289556384087,
-0.004606579430401325,
0.038134828209877014,
0.029085280373692513,
0.009367304854094982,
0.03171023353934288,
0.0006546073709614575,
0.015139889903366566,
0.03948105126619339,
-0.021697457879781723,
0.012864391319453716,
0.04623815044760704,
-0.0060773445293307304,
-0.07537396252155304,
-0.016944939270615578,
-0.016031481325626373,
0.004418015945702791,
0.003198451129719615,
0.03378135710954666,
-0.03196803852915764,
-0.003595969406887889,
-0.024702880531549454,
0.04287517070770264,
-0.04702580347657204,
0.023568592965602875,
-0.0545385368168354,
0.026306895539164543,
0.010350385680794716,
-0.03149264305830002,
-0.03420894220471382,
0.043186429888010025,
0.020587703213095665,
0.006390271242707968,
0.03129415214061737,
0.005311738234013319,
-0.015708724036812782,
-0.031786516308784485,
0.02897043712437153,
0.025812169536948204,
0.09351902455091476,
0.0035692225210368633,
-0.02147151343524456,
0.047425348311662674,
-0.044389910995960236,
-0.04323471337556839,
0.04070967808365822,
-0.030130965635180473,
-0.007621810771524906,
0.01863090693950653,
-0.012658669613301754,
0.029883071780204773,
0.033301349729299545,
0.008749334141612053,
0.0044488501735031605,
0.01658755913376808,
-0.026450246572494507,
0.011820350773632526,
-0.015270342119038105,
0.02211608737707138,
-0.000602836487814784,
-0.015634316951036453,
0.033138152211904526,
0.03391623869538307,
-0.023205524310469627,
0.007966904900968075,
-0.020856689661741257,
0.009508457034826279,
-0.0064492435194551945,
0.043156225234270096,
0.011417441070079803,
0.011507729068398476,
0.03156070411205292,
-0.0603037029504776,
0.02093900740146637,
0.027373993769288063,
0.015874451026320457,
-0.08905672281980515,
-0.03043859638273716,
-0.020527644082903862,
0.0222236979752779,
0.005416984669864178,
-0.05481673404574394,
0.0030832746997475624,
0.026402616873383522,
-0.07681751251220703,
0.002237162785604596,
-0.043213702738285065,
-0.019853761419653893,
-0.03886781632900238,
-0.005121093243360519,
0.00672605587169528,
0.04364493489265442,
-0.020167158916592598,
0.049641162157058716,
0.006093201227486134,
-0.012383419089019299,
-0.0015334784984588623,
-0.018106980249285698,
-0.008689099922776222,
0.027027927339076996,
-0.01354260928928852,
-0.010615338571369648,
0.06434041261672974,
-0.010501543991267681,
-0.052901629358530045,
0.02753029577434063,
-0.030186692252755165,
-0.0036890897899866104,
-0.03501947224140167,
0.009409770369529724,
0.009165213443338871,
0.01574956253170967,
0.0035174170043319464,
-0.015469484962522984,
-0.0028358614072203636,
0.01643012836575508,
0.013272164389491081,
0.019239677116274834,
-0.02416079491376877,
-0.006120326928794384,
0.02910567820072174,
-0.06761573255062103,
-0.0566064715385437,
0.009743204340338707,
-0.018111087381839752,
0.02332623489201069,
-0.024392535910010338,
0.02448686584830284,
-0.02285231091082096,
-0.02499270625412464,
0.016091011464595795,
-0.06259123980998993,
0.022362839430570602,
0.022377975285053253,
-0.04598039388656616,
-0.024483025074005127,
0.0010481961071491241,
0.05796206369996071,
-0.015863917768001556,
0.02685222215950489,
-0.006806621327996254,
-0.008275816217064857,
-0.047346312552690506,
-0.007456226274371147,
0.01623951829969883,
-0.008995077572762966,
-0.023134609684348106,
-0.0518435463309288,
-0.011713574640452862,
0.012297670356929302,
0.020032860338687897,
0.02769356407225132,
-0.03483469784259796,
-0.021635238081216812,
-0.02105867862701416,
-0.07042379677295685,
0.01954580843448639,
0.015031775459647179,
-0.02121783047914505,
-0.01677972637116909,
-0.015026397071778774,
-0.012298514135181904,
-0.005745904054492712,
0.021296974271535873,
-0.018942201510071754,
-0.007679041940718889,
0.056098952889442444,
0.0008501019910909235,
0.011245377361774445,
-0.05305709317326546,
0.018610280007123947,
-0.02248983457684517,
-0.029107850044965744,
0.010549230501055717,
-0.023233775049448013,
-0.03645791858434677,
0.00856303982436657,
0.028083210811018944,
-0.009186157956719398,
0.030778024345636368,
-0.0025801376905292273,
-0.012264830060303211,
0.06434083729982376,
-0.0063401381485164165,
-0.005611649248749018,
0.09181974828243256,
0.0026030237786471844,
0.010579679161310196,
0.05860966816544533,
-0.03652258217334747,
-0.027448635548353195,
0.010362768545746803,
-0.03778262436389923,
-0.015670936554670334,
-0.02094956673681736,
0.010716528631746769,
0.07223272323608398,
-0.039135903120040894,
-0.01399714034050703,
0.06437299400568008,
-0.02915269136428833,
-0.023907827213406563,
0.012952492572367191,
0.01902785152196884,
0.05269921198487282,
0.012194876559078693,
0.05546905845403671,
0.03415719419717789,
-0.01530215609818697,
0.0022755188401788473,
0.04059527814388275,
0.043126679956912994,
0.01606687530875206,
-0.010648109018802643,
0.0258635263890028,
-0.030618852004408836,
0.013953014276921749,
0.007630340289324522,
0.02645707316696644,
-0.012324257753789425,
-0.0037078026216477156,
0.02427194081246853,
-0.02742134779691696,
0.02384413592517376,
0.0031800693832337856,
-0.023553133010864258,
0.056440383195877075,
-0.03184125944972038,
0.0009389845072291791,
-0.020566632971167564,
0.017865680158138275,
-0.02850838005542755,
0.028131594881415367,
0.02278938889503479,
0.039649393409490585,
0.0004256008833181113,
-0.04291922599077225,
-0.01716691255569458,
-0.003992857877165079,
-0.00022292169160209596,
-0.020829536020755768,
0.021946093067526817,
-0.006555718835443258,
0.02257077395915985,
-0.01531135942786932,
-0.03041478991508484,
-0.03668135404586792,
-0.02900695987045765,
0.002304562833160162,
0.031499531120061874,
0.041192371398210526,
-0.011841162107884884,
0.030654627829790115,
-0.027921706438064575,
0.03162847459316254,
-0.047543928027153015,
-0.01870533637702465,
-0.007166497875005007,
0.043651383370161057,
0.018349720165133476,
0.0003567175881471485
] |
<p>I understand the reason that bicycle pedals are oppositely threaded on either side. What I don't understand is why it works because I'm missing something.</p>
<p>Take the right pedal for example. It's threads are right-handed, so it would be tightened by turning it clockwise (if the pedal were in between you and the bike). Now imagining this from the same perspective, a person pedaling makes the right pedal constantly turn counter-clockwise, relative to the crank. If there's any friction between the pedal and the bolt attaching it to the crank, I would imagine that it would create a force that would try to turn the bolt counter-clockwise along with the pedal.</p>
<p>This is the opposite of what happens, and I've seen the bolts unthread after pedaling backwards a lot myself. What am I missing?</p>
| 7,609 |
[
-0.03403199464082718,
-0.012031087651848793,
0.026467135176062584,
0.005605011247098446,
0.009596643038094044,
-0.01576218754053116,
-0.005409494042396545,
0.027507135644555092,
0.0003595641173887998,
0.017815403640270233,
0.020533321425318718,
0.0556810200214386,
0.021493567153811455,
0.03525516390800476,
0.015613588504493237,
-0.013552641496062279,
0.029899343848228455,
-0.05732061341404915,
0.0010006612865254283,
-0.02030612714588642,
-0.029829218983650208,
-0.016139620915055275,
0.001540933270007372,
0.019058171659708023,
-0.032805074006319046,
-0.004904778674244881,
0.04371907189488411,
-0.014934496022760868,
0.03905070945620537,
0.02357969805598259,
-0.03297756612300873,
-0.03027402050793171,
-0.019201314076781273,
0.002479687100276351,
0.03230726346373558,
0.016316482797265053,
-0.05426618829369545,
-0.0399775393307209,
-0.017962053418159485,
0.0268903449177742,
0.00902264378964901,
0.0003535102296154946,
-0.06830783933401108,
0.044365283101797104,
-0.04902752488851547,
0.04700378328561783,
-0.005788091104477644,
0.00839250534772873,
0.0752331092953682,
-0.035466212779283524,
0.0486510805785656,
-0.011484774760901928,
0.0390029102563858,
0.0453660823404789,
0.010504304431378841,
0.015020685270428658,
0.0802895650267601,
0.038311634212732315,
-0.009534025564789772,
-0.05269502475857735,
-0.0235446784645319,
0.004682688042521477,
-0.025485461577773094,
-0.00890101958066225,
-0.02518361061811447,
0.02702520415186882,
-0.0019507941324263811,
-0.020869605243206024,
0.05887790769338608,
0.0006592546124011278,
0.03667512908577919,
-0.00841059535741806,
0.0425138920545578,
-0.01072575245052576,
-0.028850499540567398,
-0.06796462833881378,
0.01164710707962513,
0.007931347005069256,
0.028813593089580536,
0.04050261154770851,
-0.004518507048487663,
0.0006389671470969915,
0.01232877653092146,
0.051639068871736526,
0.015028317458927631,
-0.04249949753284454,
0.06299427151679993,
-0.0040885889902710915,
0.016035854816436768,
0.04364503547549248,
0.02071632444858551,
0.007246134802699089,
-0.021988319233059883,
0.026713499799370766,
-0.006187721621245146,
0.0671975165605545,
-0.003388442797586322,
0.031325921416282654,
-0.0010260968701913953,
0.00589167233556509,
-0.0025988388806581497,
-0.0014191488735377789,
-0.024755539372563362,
0.02609780617058277,
0.01025118213146925,
-0.036672890186309814,
-0.0006358579848892987,
0.0546824112534523,
-0.015276740305125713,
-0.005085006356239319,
-0.05291600152850151,
-0.02898874320089817,
-0.009396305307745934,
-0.009766173548996449,
0.03696545213460922,
0.001266594510525465,
-0.0250131506472826,
-0.0018388283206149936,
0.01417841762304306,
0.03797561302781105,
-0.02002294547855854,
-0.022444315254688263,
-0.003825192106887698,
-0.0483601838350296,
-0.014952480792999268,
-0.0007517237099818885,
0.04997936636209488,
-0.04198810085654259,
0.021041542291641235,
0.019163642078638077,
0.018498335033655167,
-0.052377745509147644,
-0.010852965526282787,
0.016596227884292603,
0.04764567315578461,
-0.005132907070219517,
-0.11487265676259995,
-0.07295046001672745,
0.05474747344851494,
0.024350322782993317,
-0.015517753548920155,
-0.06782973557710648,
0.005137567408382893,
0.02345942333340645,
0.04202910140156746,
-0.027672918513417244,
0.02373296581208706,
0.00802101381123066,
-0.004767334554344416,
0.0402085967361927,
0.01624174416065216,
-0.04347042366862297,
-0.012588201090693474,
-0.030468065291643143,
-0.018735144287347794,
-0.05386810749769211,
0.04256603121757507,
-0.005280341953039169,
-0.002375930082052946,
-0.0690072700381279,
0.028135007247328758,
0.006681487895548344,
-0.004006394185125828,
0.020572604611516,
-0.04686594009399414,
-0.04135943949222565,
0.07355181127786636,
0.012234180234372616,
-0.056821659207344055,
0.032128509134054184,
0.009490425698459148,
0.008654008619487286,
-0.006572189275175333,
0.015494291670620441,
0.004689421970397234,
-0.05408965051174164,
-0.031765516847372055,
-0.02145075984299183,
0.011187804862856865,
-0.023895373567938805,
-0.03024590015411377,
-0.029421735554933548,
0.012987115420401096,
0.0031806672923266888,
0.028536029160022736,
0.017346404492855072,
0.02050485648214817,
-0.002441193675622344,
0.000595075311139226,
-0.04053424298763275,
0.0072025116533041,
-0.038985297083854675,
0.040748756378889084,
0.0016223720740526915,
-0.02421209216117859,
0.0025296600069850683,
-0.003651292761787772,
0.052950192242860794,
-0.045923762023448944,
0.007869921624660492,
0.0044815028086304665,
0.03336698189377785,
-0.01445841882377863,
0.018963461741805077,
-0.0175092164427042,
0.051216863095760345,
0.07169540971517563,
0.0003386651223991066,
0.05128451809287071,
-0.023166919127106667,
-0.0249087642878294,
0.029049256816506386,
-0.047979265451431274,
0.0019296790705993772,
-0.0020810153800994158,
-0.02667267806828022,
0.028299231082201004,
-0.022970354184508324,
0.01678086444735527,
0.023544661700725555,
0.008291066624224186,
0.0524628572165966,
0.03479833900928497,
-0.039513520896434784,
-0.007068718317896128,
0.03454975411295891,
0.001823159633204341,
0.017668437212705612,
0.016080493107438087,
-0.018287500366568565,
-0.05969150736927986,
0.009510376490652561,
0.019788678735494614,
0.006999638397246599,
-0.030354535207152367,
0.013254109770059586,
0.02406022511422634,
0.06164815276861191,
-0.03829030692577362,
0.02283664420247078,
-0.007200475316494703,
-0.02266830950975418,
0.021255623549222946,
0.03337730094790459,
0.028145264834165573,
0.005609175655990839,
0.04814271628856659,
0.006959949154406786,
0.006819185335189104,
-0.016620688140392303,
-0.04548586905002594,
0.071134053170681,
0.01688072830438614,
0.017853057011961937,
0.03115544654428959,
-0.06268326193094254,
0.052661798894405365,
-0.012794656679034233,
0.01315261423587799,
0.02777172438800335,
0.01785932667553425,
0.01621050015091896,
0.0001244198065251112,
0.0052877250127494335,
0.007030208595097065,
0.02776492014527321,
-0.023685330525040627,
-0.04562174901366234,
0.019377686083316803,
-0.0176878459751606,
0.007918520830571651,
-0.02998238243162632,
0.0034439112059772015,
-0.006028566975146532,
-0.029435593634843826,
0.025271421298384666,
0.059730738401412964,
0.0178544744849205,
-0.02018967643380165,
-0.048973072320222855,
-0.020067591220140457,
-0.03566260635852814,
0.01940123178064823,
0.003970819991081953,
-0.04987170547246933,
0.02716050297021866,
-0.004921696148812771,
-0.017825981602072716,
0.02231697365641594,
-0.001072452636435628,
0.022126374766230583,
0.0050798021256923676,
-0.02116951160132885,
-0.03283818066120148,
-0.021738583222031593,
-0.017894761636853218,
-0.021661335602402687,
-0.015192399732768536,
-0.005581766366958618,
0.07442387193441391,
-0.012931528501212597,
-0.033104948699474335,
0.005796570796519518,
-0.03647346422076225,
-0.0167357437312603,
0.03514094650745392,
-0.036450907588005066,
0.035529568791389465,
0.016420256346464157,
-0.0001304325123783201,
0.0183875635266304,
-0.08208110928535461,
-0.00933237373828888,
-0.06663993746042252,
-0.026067478582262993,
0.0018355966312810779,
0.007308016065508127,
0.034988466650247574,
0.009866341948509216,
0.002307896502315998,
0.055794160813093185,
0.011686625890433788,
-0.04777984693646431,
0.0012192745925858617,
-0.01093992404639721,
-0.03792070969939232,
-0.04228442907333374,
0.026498116552829742,
0.047164034098386765,
0.021593935787677765,
0.03037317655980587,
0.02294863946735859,
0.054328981786966324,
0.0367157943546772,
-0.0019440572941675782,
-0.010919282212853432,
0.011434980668127537,
0.0035768887028098106,
-0.0037695083301514387,
-0.006005081348121166,
0.005353124812245369,
-0.024047888815402985,
0.016594266518950462,
-0.0010685716988518834,
-0.005444373469799757,
-0.0019961462821811438,
-0.04904298484325409,
0.051247600466012955,
0.026498539373278618,
0.01705973967909813,
-0.050168152898550034,
0.030738690868020058,
-0.008956748992204666,
-0.034684840589761734,
-0.022911865264177322,
0.034095652401447296,
0.08059929311275482,
-0.03313670679926872,
0.010718180797994137,
0.02801034040749073,
0.026794245466589928,
0.006613704841583967,
-0.0683058351278305,
0.01106700673699379,
0.004027682356536388,
0.009477437473833561,
-0.034718647599220276,
-0.003106816438958049,
0.03197237849235535,
-0.003949487581849098,
0.026662448421120644,
0.02601481042802334,
-0.06513051688671112,
-0.007989218458533287,
-0.08255819976329803,
-0.011614507995545864,
0.020541079342365265,
0.04458611458539963,
-0.013022508472204208,
0.034486427903175354,
0.028544293716549873,
0.05067746713757515,
-0.02820049785077572,
-0.01333808433264494,
-0.10091917216777802,
0.05056069418787956,
-0.029732588678598404,
-0.028822124004364014,
-0.020171640440821648,
0.00215707253664732,
-0.0012389515759423375,
-0.023032214492559433,
-0.03503250703215599,
0.007336643058806658,
-0.0005160181317478418,
-0.05959590896964073,
-0.007645431440323591,
-0.015331543050706387,
-0.05338330939412117,
-0.008717495948076248,
-0.005249100737273693,
0.0417025089263916,
-0.041188500821590424,
0.05270122364163399,
0.02423546276986599,
-0.014432900585234165,
-0.03381999209523201,
-0.0359705351293087,
0.015419244766235352,
0.018753008916974068,
0.006618066690862179,
0.013109766878187656,
0.014678205363452435,
0.015866994857788086,
-0.020499279722571373,
0.03071601130068302,
0.025461824610829353,
0.06656859070062637,
0.023650437593460083,
-0.028333866968750954,
-0.034303970634937286,
-0.017671838402748108,
0.03272920101881027,
0.031086094677448273,
-0.018067898228764534,
0.03699183836579323,
0.05323620140552521,
0.009502234868705273,
-0.021920425817370415,
0.0038689339999109507,
0.02068954147398472,
0.023028463125228882,
-0.04092300310730934,
-0.05353216081857681,
-0.009004345163702965,
-0.023219045251607895,
-0.008482345379889011,
-0.006593386642634869,
-0.0038574000354856253,
-0.02181684412062168,
0.004274994600564241,
0.01484469324350357,
-0.003587418468669057,
0.024407392367720604,
0.03380797058343887,
-0.060724738985300064,
0.08942411839962006,
0.027503788471221924,
0.03180243447422981,
0.017832400277256966,
-0.005389085505157709,
0.07176738232374191,
0.007341099437326193,
-0.034796737134456635,
-0.05053132772445679,
-0.016232596710324287,
0.0422474667429924,
0.03830888122320175,
-0.058511994779109955,
0.0007121247472241521,
-0.013422234915196896,
-0.030879514291882515,
0.03346658870577812,
-0.03182992711663246,
0.025937706232070923,
-0.017957955598831177,
0.005080776754766703,
-0.027446478605270386,
-0.019022762775421143,
-0.049874160438776016,
-0.0006200456409715116,
-0.017397060990333557,
-0.010182974860072136,
-0.020392155274748802,
-0.015139207243919373,
-0.06485285609960556,
0.011877544224262238,
0.0630781501531601,
0.03337550163269043,
-0.016697712242603302,
0.012135319411754608,
-0.004598463419824839,
0.038833264261484146,
-0.023768838495016098,
-0.10617662966251373,
-0.014492306858301163,
0.0070314593613147736,
0.007063478697091341,
0.020731739699840546,
-0.04902070015668869,
-0.0429370291531086,
-0.017807064577937126,
-0.019793884828686714,
-0.015676502138376236,
0.018212176859378815,
-0.00009988490637624636,
0.0021782051771879196,
0.03069627285003662,
0.0007578825461678207,
0.048204097896814346,
0.026529202237725258,
-0.020542636513710022,
-0.02073182910680771,
-0.011280140839517117,
-0.025705475360155106,
0.0024640171322971582,
0.055677611380815506,
-0.016186026856303215,
0.01676327735185623,
-0.04123860225081444,
0.0356639139354229,
-0.016094814985990524,
0.020648036152124405,
0.017054332420229912,
-0.030181366950273514,
-0.032343145459890366,
0.01216355711221695,
0.02157537266612053,
0.008212043903768063,
0.0051605370827019215,
-0.01976330764591694,
-0.017595965415239334,
-0.02087346650660038,
0.013376968912780285,
-0.019475057721138,
-0.012607276439666748,
0.02792392484843731,
-0.029557200148701668,
-0.014247067272663116,
-0.0029985355213284492,
-0.007727819494903088,
-0.007034495007246733,
0.0015496629057452083,
0.013941684737801552,
0.014471443369984627,
-0.007028753403574228,
0.020748429000377655,
-0.001421527354978025,
-0.02087361365556717,
0.026990201324224472,
-0.045757923275232315,
0.001760162995196879,
-0.025111770257353783,
0.05192740261554718,
0.019231434911489487,
-0.016391782090067863,
-0.032985687255859375,
-0.04587538167834282,
0.08193986117839813,
-0.04338860884308815,
-0.00478171743452549,
-0.032051749527454376,
0.008796429261565208,
-0.0020441703964024782,
-0.03452106937766075,
0.0063632456585764885,
0.04713482782244682,
-0.0734693631529808,
0.026096155866980553,
0.04403150826692581,
-0.02490370348095894,
0.03939526900649071,
-0.02224842645227909,
-0.029702406376600266,
-0.020024925470352173,
-0.04291704669594765,
-0.030459361150860786,
-0.012667427770793438,
0.019323503598570824,
-0.011365986429154873,
-0.030847100540995598,
0.0171040166169405,
0.010941910557448864,
0.04642510414123535,
-0.018386267125606537,
-0.02749655768275261,
0.027315735816955566,
0.026789411902427673,
-0.009456180967390537,
-0.03651823103427887,
0.021832294762134552,
0.03721291199326515,
0.03124258480966091,
0.014519806951284409,
-0.0035086595453321934,
-0.016979839652776718,
-0.05532313138246536,
-0.003469303948804736,
0.060842256993055344,
-0.008762895129621029,
-0.004971484187990427,
0.03421991690993309,
-0.023844417184591293,
0.022150930017232895,
0.03048219159245491,
-0.05350414291024208,
0.07190752029418945,
0.0004664224397856742,
0.011884069070219994,
-0.00024378550006076694,
-0.023764461278915405,
-0.024425039067864418,
-0.034999437630176544,
-0.013635078445076942,
-0.018979303538799286,
0.04279245063662529,
-0.027832234278321266,
0.05025479570031166,
0.03617927059531212,
0.0012653568992391229,
0.0017943624407052994,
0.026304680854082108,
-0.010250560007989407,
0.007368393708020449,
0.007626835256814957,
0.004305580165237188,
-0.02070879004895687,
0.008878997527062893,
0.06383385509252548,
0.03593028336763382,
-0.020823711529374123,
-0.027460750192403793,
0.028845392167568207,
0.01849544793367386,
-0.022124089300632477,
0.048229992389678955,
-0.0423530749976635,
0.011839056387543678,
-0.02707488089799881,
0.045292243361473083,
0.009581713005900383,
-0.028550846502184868,
0.0672672763466835,
-0.0035652825608849525,
0.0239570252597332,
-0.01879970170557499,
-0.010328053496778011,
-0.0369427353143692,
0.0004379479505587369,
-0.0010078944033011794,
0.03145803511142731,
-0.027687810361385345,
-0.0012227768311277032,
0.04779946058988571,
0.03002329356968403,
0.0065568736754357815,
-0.0348934642970562,
-0.021044068038463593,
-0.015293912030756474,
-0.005997610744088888,
-0.006930805277079344,
0.05739710107445717,
0.003386613680049777,
-0.03215353935956955,
0.029495587572455406,
-0.015132448635995388,
0.016741106286644936,
0.022839738056063652,
0.035695187747478485,
-0.0034694571513682604,
0.06421805918216705,
0.0019432423869147897,
0.012439466081559658,
-0.026441704481840134,
-0.018520314246416092,
0.11753396689891815,
0.013986029662191868,
0.026538193225860596,
-0.0503142811357975,
-0.01675245352089405,
-0.033561550080776215,
-0.014994505792856216,
0.006274334155023098,
0.024645596742630005,
0.0075496467761695385,
0.06826983392238617,
0.06414705514907837,
0.03201185539364815,
-0.00858832336962223,
-0.00572100467979908,
0.04675110802054405,
-0.010754969902336597,
-0.028574615716934204,
0.0007257671095430851,
-0.0199362114071846,
-0.0025033920537680387,
-0.009661193005740643,
-0.049133311957120895,
0.016366252675652504,
-0.01667175628244877,
-0.021696509793400764,
-0.03814469277858734,
-0.059922557324171066,
0.012835171073675156,
-0.0014473741175606847,
-0.03872266411781311,
0.004403334576636553,
0.015334038995206356,
-0.03714735805988312,
-0.020047057420015335,
0.04295334964990616,
0.042404595762491226,
-0.004537705332040787,
0.04776742681860924,
0.0034962946083396673,
0.0016339374706149101,
0.018709206953644753,
0.042152661830186844,
-0.01875186152756214,
-0.04718215763568878,
0.0016582629177719355,
-0.021622681990265846,
0.0018756651552394032,
-0.016086580231785774,
0.017261045053601265,
0.012396721169352531,
-0.028094938024878502,
-0.00007340251613641158,
-0.04004485160112381,
0.004920293111354113,
-0.010003367438912392,
0.010394223034381866,
0.0032454614993184805,
0.006734326481819153,
-0.029957283288240433,
0.008089211769402027,
-0.036069609224796295,
0.021878018975257874,
0.0019045211374759674,
-0.0089303283020854,
-0.00791515689343214,
-0.001546876854263246,
0.042293306440114975,
-0.02519000507891178,
-0.02047622762620449,
-0.02688697539269924,
0.012400021776556969,
-0.03506239131093025,
0.012960519641637802,
0.022734636440873146,
0.012774997390806675,
0.05095450580120087,
-0.007224250119179487,
-0.04189006984233856,
-0.03470586985349655,
-0.03184833005070686,
0.040388479828834534,
-0.0007415229338221252,
-0.016592521220445633,
-0.013643353246152401,
0.018811466172337532,
0.042500365525484085,
0.022582735866308212,
-0.025831906124949455,
0.019658023491501808,
-0.00045060337288305163,
-0.008374659344553947,
0.0018319257069379091,
-0.009603135287761688,
-0.04082535579800606,
0.01590931974351406,
-0.021880676969885826,
-0.011598272249102592,
0.0022067856043577194,
0.02130054496228695,
0.032627735286951065,
0.019992312416434288,
0.010502001270651817,
0.01935298927128315,
0.0042430036701262,
0.01161043718457222,
0.0474543459713459,
0.0018082648748531938,
-0.01802419126033783,
0.019088225439190865,
-0.001596273621544242,
-0.0724899023771286,
-0.019017526879906654,
0.006377036217600107,
-0.01907510496675968,
0.009974888525903225,
0.01734148897230625,
-0.01575450412929058,
-0.002669265726581216,
-0.03247634693980217,
0.031133828684687614,
-0.031040996313095093,
-0.000060284008213784546,
-0.0812457948923111,
-0.021051522344350815,
0.014579905197024345,
0.03308814391493797,
-0.029026225209236145,
0.030956126749515533,
0.031118638813495636,
0.002736985683441162,
0.005382209084928036,
0.017202606424689293,
0.012726370245218277,
0.019714584574103355,
0.014831339940428734,
0.021831262856721878,
0.03849991783499718,
-0.042193662375211716,
-0.036440253257751465,
0.0572202242910862,
-0.04168272018432617,
-0.04510387033224106,
0.004140263423323631,
-0.019161595031619072,
-0.018389303237199783,
0.001581754651851952,
-0.03535410761833191,
0.004259498789906502,
0.04739198833703995,
-0.02528233267366886,
-0.013152452185750008,
0.00804188847541809,
0.02573467791080475,
-0.0221317857503891,
0.0015392847126349807,
-0.01672370173037052,
-0.055724047124385834,
0.001987091265618801,
0.02976580522954464,
0.0438992939889431,
0.017979832366108894,
0.001642617047764361,
0.009400758892297745,
0.01744093932211399,
0.017663201317191124,
0.011519734747707844,
-0.012437050230801105,
0.007064823992550373,
0.031408410519361496,
-0.03236301615834236,
0.04179748147726059,
-0.03137439116835594,
0.008715745992958546,
-0.1069990023970604,
0.015342239290475845,
-0.013547375798225403,
-0.046979017555713654,
-0.002807010430842638,
-0.022408049553632736,
-0.025592686608433723,
-0.019692733883857727,
-0.03206515684723854,
0.004149498883634806,
-0.0034654734190553427,
-0.07438794523477554,
-0.03329859673976898,
0.030027255415916443,
-0.016344144940376282,
0.0599607452750206,
0.03389199450612068,
0.058950137346982956,
0.013398997485637665,
-0.011636558920145035,
-0.05237562581896782,
-0.0019516779575496912,
0.011969132348895073,
0.017807023599743843,
-0.04351598769426346,
-0.0035815872251987457,
0.07188086956739426,
-0.008729537017643452,
-0.020038511604070663,
0.022914528846740723,
-0.021794959902763367,
-0.003934740088880062,
-0.016661429777741432,
0.03909597918391228,
-0.010386340320110321,
0.022350862622261047,
-0.0012040233705192804,
-0.039402078837156296,
-0.025745438411831856,
0.025357894599437714,
0.030970348045229912,
-0.010770255699753761,
-0.008035817183554173,
0.05386519432067871,
0.008123861625790596,
-0.0446820966899395,
0.008072305470705032,
0.03522280976176262,
-0.04787308722734451,
0.010355004109442234,
0.008888395503163338,
0.02740417793393135,
0.010157190263271332,
-0.03151930496096611,
-0.032567888498306274,
0.0016502125654369593,
-0.029895484447479248,
0.020050156861543655,
0.003364087548106909,
0.029362697154283524,
0.06588471680879593,
-0.010180847719311714,
0.0024136491119861603,
0.006020950153470039,
-0.011163894087076187,
-0.024605421349406242,
-0.06625634431838989,
0.016676662489771843,
0.019932420924305916,
-0.023338325321674347,
0.02295159362256527,
-0.049998439848423004,
0.025338677689433098,
0.07527460157871246,
0.031165601685643196,
0.011994820088148117,
0.043745629489421844,
-0.042105551809072495,
-0.002206662204116583,
-0.0552256777882576,
0.03397275134921074,
0.0003879524301737547,
-0.03148785978555679,
-0.038334090262651443,
-0.018304143100976944,
0.0030644689686596394,
-0.0008362131775356829,
0.07174891233444214,
-0.005691719241440296,
-0.0084712328389287,
0.04199047014117241,
0.0015354041242972016,
0.02985638752579689,
-0.031174561008810997,
0.010309861041605473,
-0.020633120089769363,
-0.0032598564866930246,
0.016282787546515465,
-0.025266896933317184,
-0.06115712225437164,
-0.004059224389493465,
0.00875932164490223,
-0.023648355156183243,
0.03293497487902641,
0.00844047125428915,
-0.018402675166726112,
0.03372031822800636,
0.00478409044444561,
-0.00010428492532810196,
0.07676338404417038,
0.033469777554273605,
0.03495412319898605,
0.018518570810556412,
-0.022720616310834885,
-0.054773520678281784,
0.05636495724320412,
0.001404722803272307,
0.003347803372889757,
0.005560307763516903,
-0.02634674683213234,
0.06223002076148987,
-0.03470493108034134,
0.0008475446957163513,
0.030630331486463547,
-0.03940995782613754,
0.021896999329328537,
0.004599057603627443,
0.020777681842446327,
0.005530679598450661,
-0.03733203187584877,
0.014225459657609463,
0.04791951924562454,
-0.008031269535422325,
0.017805971205234528,
0.019405655562877655,
-0.00449314946308732,
-0.001737818238325417,
0.00028618521173484623,
0.06285570561885834,
-0.010740990750491619,
0.07211273163557053,
0.0025787039194256067,
0.01866423524916172,
-0.03134175017476082,
-0.028649112209677696,
0.018689876422286034,
-0.05137470364570618,
0.003467793110758066,
0.038664355874061584,
-0.012698066420853138,
0.04976191371679306,
-0.03540115803480148,
0.041392698884010315,
0.025262778624892235,
0.039446525275707245,
0.021596642211079597,
-0.025856763124465942,
-0.015234649181365967,
0.005920719355344772,
0.0015585763612762094,
-0.012380525469779968,
0.044338710606098175,
-0.002735744696110487,
0.03933631256222725,
-0.004096789751201868,
0.029172740876674652,
-0.017135590314865112,
0.0037165721878409386,
-0.0012716661440208554,
0.030007991939783096,
-0.06152257323265076,
-0.06242469325661659,
0.07234269380569458,
0.014519767835736275,
0.012328291311860085,
0.01028099562972784,
-0.029242753982543945,
-0.011764990165829659,
0.05258330702781677,
-0.07360346615314484,
-0.03294425457715988,
-0.007881734520196915,
0.01020524837076664,
-0.007906930521130562,
-0.025549035519361496
] |
<p>Here is a video of a GoPro falling from a plane: <a href="http://www.youtube.com/watch?v=QrxPuk0JefA" rel="nofollow">http://www.youtube.com/watch?v=QrxPuk0JefA</a></p>
<p>Any idea what is happening when the image "stabilizes" around 0:35? I think it is because the camera's tangential velocity approaches the speed of the GoPro's rolling shutter.</p>
<p>Follow-up question: </p>
<ul>
<li>Why is the image skewed with the left side skewed "up" and the right side skewed "down?"</li>
</ul>
<p>A challenge: </p>
<ul>
<li>Find the axis of rotation (with supporting diagram and explanation of how it was computed).</li>
</ul>
| 7,610 |
[
-0.049673184752464294,
-0.03993883356451988,
-0.005684698931872845,
0.008506771177053452,
0.03711111471056938,
-0.027498601004481316,
-0.0742022842168808,
-0.0077988868579268456,
-0.029057258740067482,
-0.07020311802625656,
0.001475648838095367,
0.039900749921798706,
0.005236944183707237,
0.05541679263114929,
0.01542303990572691,
-0.00014387612463906407,
-0.0030428811442106962,
-0.03282119706273079,
-0.01747923530638218,
-0.02129916101694107,
-0.03918459266424179,
0.028552433475852013,
0.014240375719964504,
0.018903397023677826,
-0.03730347380042076,
0.016361569985747337,
0.03432861343026161,
-0.088062584400177,
0.011867241002619267,
0.03084087371826172,
-0.027439454570412636,
0.012865392491221428,
-0.014470111578702927,
-0.015305746346712112,
0.026706108823418617,
0.017054293304681778,
-0.032131124287843704,
-0.004219743888825178,
-0.025437548756599426,
0.02024671621620655,
0.009480911307036877,
0.049090299755334854,
-0.01715749315917492,
0.004640854895114899,
-0.025014609098434448,
0.02361796237528324,
-0.022432822734117508,
-0.0006798870745114982,
0.0641925260424614,
-0.03928366303443909,
0.07896320521831512,
-0.024562062695622444,
0.011143282055854797,
0.02461737021803856,
0.02969556860625744,
-0.006507295649498701,
0.06621325761079788,
0.03469225764274597,
-0.029789747670292854,
-0.029586026445031166,
-0.004315400496125221,
-0.07220238447189331,
-0.03199204429984093,
0.028961384668946266,
0.017486223950982094,
0.013356983661651611,
0.014213834889233112,
-0.024674445390701294,
0.04861653596162796,
0.00874845776706934,
-0.030427731573581696,
-0.0027542077004909515,
0.011618979275226593,
-0.024638693779706955,
0.0295305997133255,
-0.03223221004009247,
-0.00000828229258331703,
0.034333791583776474,
0.01784164272248745,
0.02133069559931755,
0.03177184239029884,
0.008480444550514221,
-0.006631269585341215,
-0.003045439487323165,
0.05364013463258743,
-0.020525749772787094,
0.09549769759178162,
0.048098351806402206,
0.008672432042658329,
0.02373347617685795,
0.037272483110427856,
-0.01371309719979763,
-0.013511407189071178,
-0.009711336344480515,
-0.04193390533328056,
0.03862869739532471,
0.001072474056854844,
0.032704584300518036,
0.02197772078216076,
-0.013097486458718777,
0.01384088583290577,
-0.028576137498021126,
-0.020757373422384262,
0.0722290426492691,
0.0008997407276183367,
0.03187272697687149,
-0.011467769742012024,
0.012039151042699814,
-0.0244827289134264,
0.008609689772129059,
-0.06590507179498672,
-0.01449689082801342,
-0.006549498066306114,
-0.015228759497404099,
-0.009531707502901554,
-0.0009426949545741081,
-0.016046419739723206,
-0.011567543260753155,
0.04387395456433296,
0.00859690923243761,
0.041886989027261734,
-0.03364423289895058,
0.008976939134299755,
-0.0377962589263916,
-0.06373445689678192,
0.03328390419483185,
0.02879447489976883,
-0.032971736043691635,
-0.0420244000852108,
0.024645455181598663,
0.029180854558944702,
0.0007919500349089503,
-0.01511039026081562,
-0.0038836931344121695,
0.0036869007162749767,
0.006422640755772591,
-0.10942722856998444,
-0.04662475362420082,
0.0555848553776741,
0.043966587632894516,
-0.026064882054924965,
-0.09524083137512207,
-0.04604171961545944,
0.05378428474068642,
0.07296009361743927,
-0.033333297818899155,
0.019455131143331528,
-0.0004406040534377098,
-0.03661179542541504,
-0.029889073222875595,
0.029867097735404968,
-0.006004747003316879,
0.017371509224176407,
-0.025725098326802254,
-0.03638526424765587,
-0.051070909947156906,
0.006865913514047861,
0.03394977003335953,
0.011674739420413971,
-0.04885631054639816,
0.004866934381425381,
0.0013314156094565988,
-0.006948468275368214,
0.0013279459672048688,
-0.050561483949422836,
-0.036934852600097656,
0.059533700346946716,
0.04397464543581009,
0.005127446260303259,
0.014313332736492157,
-0.03395664691925049,
0.07280415296554565,
-0.02120220474898815,
-0.023092228919267654,
0.06446951627731323,
-0.015948327258229256,
-0.019421031698584557,
-0.039451368153095245,
-0.023294489830732346,
-0.01083247922360897,
-0.001537223462946713,
-0.04323390871286392,
-0.0262617114931345,
0.01657457835972309,
0.03055180236697197,
0.03830699995160103,
0.00818757712841034,
0.010180443525314331,
-0.014367498457431793,
-0.03561629354953766,
-0.0012823814759030938,
-0.008823241107165813,
0.013535797595977783,
-0.014068801887333393,
-0.027113793417811394,
-0.005568460561335087,
0.018776612356305122,
0.029667112976312637,
-0.011697616428136826,
-0.010628102347254753,
0.002446334343403578,
0.022777210921049118,
0.01766117289662361,
0.03674723207950592,
-0.005639365874230862,
0.06006622686982155,
0.016480760648846626,
-0.0010363110341131687,
0.0009871028596535325,
-0.007724495138972998,
0.01568491943180561,
-0.0537802018225193,
0.007837588898837566,
-0.011258051730692387,
-0.01845204271376133,
0.015136395581066608,
0.027897687628865242,
0.023150844499468803,
0.009298563934862614,
-0.01664343662559986,
-0.0252639539539814,
0.058948781341314316,
0.06260288506746292,
-0.008173158392310143,
0.035838063806295395,
0.022372299805283546,
0.015385190956294537,
0.024286510422825813,
-0.013218743726611137,
-0.0006010051583871245,
-0.03398266062140465,
-0.02974032051861286,
0.020885152742266655,
0.015243709087371826,
-0.04552780091762543,
0.011959641240537167,
0.04724140465259552,
0.06376666575670242,
0.017252599820494652,
0.0013483199290931225,
0.0056810323148965836,
-0.03509450703859329,
0.01575067825615406,
-0.017073825001716614,
0.0066870953887701035,
0.03916950151324272,
0.029167892411351204,
-0.02685454860329628,
0.003625270212069154,
-0.014207408763468266,
-0.04345005378127098,
0.0010512742446735501,
0.013754764571785927,
0.024995896965265274,
-0.0051264408975839615,
-0.01303260400891304,
0.016664599999785423,
-0.00018802864360623062,
-0.013875356875360012,
0.030885031446814537,
0.01448039524257183,
-0.023987481370568275,
-0.040329739451408386,
0.008015993982553482,
0.0022020412143319845,
0.031395383179187775,
-0.00994926504790783,
-0.00781001104041934,
0.034198809415102005,
-0.026379035785794258,
0.008933313190937042,
-0.020053347572684288,
-0.022647716104984283,
0.024221565574407578,
-0.024124372750520706,
0.028915192931890488,
0.04565948247909546,
0.03773805499076843,
-0.025118442252278328,
0.017203081399202347,
-0.00193448003847152,
-0.0076574841514229774,
-0.003229159861803055,
0.036456260830163956,
-0.05211842060089111,
0.044941917061805725,
0.021251779049634933,
0.014891632832586765,
0.0351809523999691,
0.026515593752264977,
-0.006267740856856108,
0.002234414918348193,
0.010903749614953995,
-0.04564991965889931,
0.005144152790307999,
-0.0146864652633667,
0.0017990920459851623,
-0.047283634543418884,
0.028306199237704277,
0.028130734339356422,
0.017632896080613136,
-0.031405627727508545,
0.055804893374443054,
-0.0367620550096035,
-0.03653847798705101,
-0.005059629213064909,
0.01745600998401642,
0.019368357956409454,
-0.01844659633934498,
0.009846609085798264,
-0.024086199700832367,
0.03407157212495804,
0.0036936094984412193,
-0.06492328643798828,
-0.023284615948796272,
-0.011536593548953533,
-0.014999102801084518,
0.0469801165163517,
0.013993978500366211,
0.004819415509700775,
0.08267350494861603,
0.03799872100353241,
-0.027253732085227966,
-0.04744561389088631,
-0.011543496511876583,
-0.021125825121998787,
-0.05070929601788521,
0.019988758489489555,
-0.02029280737042427,
-0.005892691668123007,
0.04889478161931038,
-0.015711011365056038,
-0.0067435503005981445,
0.0774441659450531,
0.003459231462329626,
0.010625009424984455,
0.0018342267721891403,
-0.004501795396208763,
-0.011003424413502216,
0.04720829799771309,
0.05261879414319992,
0.011054952628910542,
0.018124215304851532,
-0.0006986692314967513,
0.07620266824960709,
0.015354200266301632,
-0.04312847554683685,
0.046189118176698685,
-0.0040942104533314705,
-0.027440978214144707,
-0.005107974633574486,
0.05154159292578697,
-0.023144816979765892,
0.006876004859805107,
0.001867238199338317,
0.020867494866251945,
0.11075835675001144,
0.021455315873026848,
0.029918361455202103,
0.011609257198870182,
0.055174265056848526,
-0.022694386541843414,
-0.03669426590204239,
-0.023415567353367805,
-0.012826940044760704,
0.03739679604768753,
-0.04515477642416954,
-0.0034600794315338135,
0.05791138857603073,
-0.013494991697371006,
0.03516857326030731,
0.002020489191636443,
-0.023659363389015198,
-0.00044308797805570066,
-0.04930827394127846,
0.013879869133234024,
0.013466701842844486,
0.020686231553554535,
0.015670878812670708,
0.03066346049308777,
0.019585449248552322,
0.03316226974129677,
-0.00579921156167984,
0.010664941743016243,
-0.08183087408542633,
0.018047165125608444,
-0.002396581694483757,
-0.012285880744457245,
0.010926338844001293,
-0.01075582392513752,
0.028401033952832222,
0.005875521805137396,
-0.013993114233016968,
-0.02830658107995987,
0.013948834501206875,
-0.007568577770143747,
0.003555516479536891,
-0.01119508221745491,
-0.026761578395962715,
0.0019243385177105665,
0.03361982852220535,
0.057077229022979736,
-0.01856890693306923,
0.030474849045276642,
0.030417999252676964,
0.03297547623515129,
0.001080544083379209,
0.002159521682187915,
0.012352874502539635,
-0.013913274742662907,
0.02481061778962612,
-0.04126468673348427,
0.010395700111985207,
0.032132264226675034,
0.006142560858279467,
0.04308163747191429,
0.03740008547902107,
-0.004606818780303001,
-0.02468479610979557,
-0.034775059670209885,
-0.046853967010974884,
-0.07268853485584259,
-0.02346217632293701,
0.02096478082239628,
-0.014937594532966614,
-0.01228242926299572,
0.0070000942796468735,
0.009612010791897774,
-0.019106850028038025,
0.030569756403565407,
0.06094731017947197,
0.01525407936424017,
0.03288153186440468,
-0.04526922479271889,
-0.061745867133140564,
-0.00887536071240902,
-0.0028164286632090807,
0.005468859802931547,
0.006559661123901606,
-0.010328205302357674,
-0.0010941296350210905,
0.06711144745349884,
-0.0054281726479530334,
-0.01878027245402336,
0.039889976382255554,
-0.0202834140509367,
0.01033639907836914,
0.00042890795157290995,
-0.0013733361847698689,
-0.02040993422269821,
0.06062889099121094,
0.08148537576198578,
0.019172104075551033,
-0.020098697394132614,
-0.06525743007659912,
-0.041956398636102676,
0.028159964829683304,
0.032646842300891876,
0.0045056757517158985,
0.0007041539647616446,
-0.07369300723075867,
-0.0015064742183312774,
0.010728971101343632,
-0.024428943172097206,
0.0434664748609066,
-0.012767352163791656,
0.0272023044526577,
0.00975057389587164,
-0.037241216748952866,
-0.006675762124359608,
-0.019077226519584656,
-0.02549520693719387,
0.03563949838280678,
-0.031137552112340927,
-0.027504868805408478,
-0.009138672612607479,
0.02046797052025795,
0.03265359625220299,
0.04863205924630165,
0.017758827656507492,
-0.014817938208580017,
0.00792045146226883,
0.002203767653554678,
-0.05123470351099968,
-0.06253699958324432,
0.012428226880729198,
-0.005249183624982834,
-0.014696478843688965,
0.01328868418931961,
-0.01096914242953062,
-0.021154340356588364,
0.04010787978768349,
-0.008670642971992493,
-0.015288463793694973,
-0.0016750823706388474,
-0.04964857175946236,
-0.03198713809251785,
0.03855438157916069,
-0.01245032250881195,
0.010631823912262917,
0.031347934156656265,
-0.020831212401390076,
-0.01046814676374197,
-0.02199144847691059,
0.010935887694358826,
-0.029748590663075447,
-0.027393002063035965,
-0.0033725881949067116,
-0.000519154011271894,
-0.03583282232284546,
0.02215067856013775,
0.02854315936565399,
0.042920585721731186,
0.007868162356317043,
-0.028551390394568443,
-0.009239854291081429,
0.0032920411322265863,
0.020674174651503563,
-0.019688216969370842,
0.01676752045750618,
0.007913284003734589,
-0.003456034930422902,
0.013467349112033844,
0.040621835738420486,
-0.020456664264202118,
0.0059746946208179,
0.028946010395884514,
-0.0014176716795191169,
-0.016045918688178062,
-0.06151103973388672,
-0.02179741859436035,
-0.024602951481938362,
-0.03724253177642822,
0.054242443293333054,
-0.010432693175971508,
0.0178987979888916,
0.061897359788417816,
-0.019135871902108192,
-0.0165398009121418,
0.008099202066659927,
-0.02314150333404541,
0.01672646962106228,
-0.04605132341384888,
-0.021141862496733665,
0.04616696387529373,
0.0321296826004982,
-0.026578709483146667,
-0.026965230703353882,
0.042408838868141174,
-0.021361274644732475,
-0.020576177164912224,
-0.00991362240165472,
0.015018871054053307,
0.008174137212336063,
-0.04164709895849228,
0.01972409524023533,
0.004616147838532925,
-0.01071604061871767,
-0.007078271359205246,
0.010819945484399796,
0.0030842607375234365,
0.06532120704650879,
-0.04767211899161339,
0.00009534118726151064,
0.042094048112630844,
-0.01908699795603752,
-0.0391572043299675,
-0.0068829855881631374,
0.06075819954276085,
-0.024333663284778595,
-0.0213927049189806,
-0.00752849318087101,
-0.01909809373319149,
0.015396321192383766,
0.00020307934028096497,
0.027046920731663704,
-0.007885987870395184,
-0.003896955866366625,
0.028774330392479897,
-0.04780435934662819,
0.022197894752025604,
0.03459088131785393,
-0.0021490061189979315,
0.007405693177133799,
0.020500127226114273,
-0.019944824278354645,
-0.0713760107755661,
0.04892497882246971,
-0.00015661994984839112,
0.03230452165007591,
0.009083929471671581,
0.0781068280339241,
-0.02817988023161888,
-0.027401743456721306,
0.03405686840415001,
-0.008564284071326256,
0.0470065139234066,
0.012650955468416214,
0.00037686902214773,
0.05441630259156227,
0.0073384931311011314,
-0.03763232380151749,
-0.027505794540047646,
-0.030623994767665863,
0.004927593283355236,
0.06003666669130325,
-0.009566927328705788,
0.05246211215853691,
0.015324423089623451,
-0.009021719917654991,
0.007939307950437069,
-0.0055589317344129086,
0.008047642186284065,
-0.010661453939974308,
0.00609730975702405,
0.003911669831722975,
-0.032170992344617844,
0.01669236645102501,
-0.015667501837015152,
0.051577989012002945,
0.028236225247383118,
0.009874972514808178,
0.03973526507616043,
0.005329945590347052,
0.0456131249666214,
-0.037864793092012405,
-0.050614554435014725,
0.03100176341831684,
-0.008795583620667458,
0.08752282708883286,
-0.02311358042061329,
-0.022703615948557854,
0.06463220715522766,
0.013545130379498005,
-0.011952287517488003,
-0.07836495339870453,
-0.004481805954128504,
-0.08565310388803482,
0.01270400732755661,
-0.03214074298739433,
-0.012064381502568722,
-0.024440713226795197,
0.007271645590662956,
0.0688965916633606,
0.01851082220673561,
0.02215348184108734,
-0.027091894298791885,
-0.029711224138736725,
-0.022000065073370934,
0.016161885112524033,
-0.0464385524392128,
0.032746121287345886,
0.006881081499159336,
0.051999256014823914,
0.008442931808531284,
-0.017374346032738686,
-0.03561103343963623,
0.013968560844659805,
0.036693915724754333,
-0.03636014834046364,
0.024931669235229492,
0.0029553272761404514,
0.03647365793585777,
-0.03357402980327606,
-0.011441019363701344,
0.12628455460071564,
0.04916509613394737,
-0.02096681483089924,
-0.017587048932909966,
-0.008145415224134922,
0.0009184796363115311,
0.03226276487112045,
-0.03084501251578331,
-0.011281440034508705,
0.009409206919372082,
-0.0014160472201183438,
0.030641447752714157,
-0.004497638903558254,
0.014416949823498726,
-0.021534601226449013,
-0.02892211824655533,
-0.03648721054196358,
-0.002358378143981099,
-0.03450899198651314,
0.014340987429022789,
-0.02564716339111328,
0.02121683582663536,
-0.06062009558081627,
0.031091146171092987,
-0.038082897663116455,
-0.03933851048350334,
0.009023632854223251,
-0.0720944032073021,
0.027686377987265587,
-0.004431320354342461,
-0.012945743277668953,
0.026241552084684372,
0.0040863147005438805,
-0.0342414453625679,
-0.00999067910015583,
0.026797287166118622,
-0.010542894713580608,
-0.02153642475605011,
0.0038940960075706244,
-0.012689502909779549,
-0.02165452390909195,
0.011058825068175793,
-0.010152398608624935,
-0.01948760263621807,
-0.03086121752858162,
-0.0017112013883888721,
-0.04270016774535179,
0.03356287255883217,
-0.035033974796533585,
0.02019791305065155,
-0.037864070385694504,
-0.016088973730802536,
-0.002504051895812154,
-0.07719729840755463,
-0.006050650030374527,
0.04229067265987396,
0.011173454113304615,
0.0015550671378150582,
-0.04574594646692276,
0.00596354017034173,
0.029259074479341507,
0.05438952147960663,
0.0031017677392810583,
0.003965861164033413,
0.009593304246664047,
-0.019183620810508728,
-0.0418829470872879,
0.057007890194654465,
-0.023273957893252373,
-0.007628681603819132,
-0.004744640551507473,
-0.0020709510426968336,
-0.00650175241753459,
-0.011431124061346054,
0.02012929692864418,
-0.0072966828010976315,
0.012452350929379463,
0.036325614899396896,
-0.0003089930396527052,
-0.0158754400908947,
-0.03887598589062691,
0.05517806485295296,
-0.03826943412423134,
-0.02456183359026909,
-0.08164671808481216,
-0.03819271922111511,
0.04189801588654518,
0.009468074887990952,
-0.030516887083649635,
0.026610475033521652,
-0.04667209833860397,
0.03188131004571915,
0.001248470158316195,
0.0010320424335077405,
-0.04500585049390793,
0.05454784631729126,
-0.012813401408493519,
-0.019740307703614235,
-0.03006342425942421,
0.07114376872777939,
0.02776000276207924,
-0.0076045324094593525,
0.0165270809084177,
0.02159067988395691,
-0.024220572784543037,
-0.006546214688569307,
0.021741939708590508,
-0.004441334865987301,
-0.0020396297331899405,
0.0017203622264787555,
0.004013105761259794,
-0.036386050283908844,
0.024911053478717804,
-0.007251323666423559,
-0.05708175152540207,
-0.03076905757188797,
0.043035317212343216,
0.028343284502625465,
0.015638507902622223,
-0.05822993814945221,
0.0709022581577301,
0.001023803255520761,
0.006923619657754898,
-0.04180056229233742,
-0.006791496183723211,
0.0004674328083638102,
-0.015480089001357555,
-0.022491998970508575,
0.009461291134357452,
0.0477469302713871,
-0.005727848038077354,
0.004454204346984625,
-0.001844893442466855,
0.020958177745342255,
0.000051125774916727096,
0.019074957817792892,
-0.006262465845793486,
0.0013983198441565037,
0.0002939152764156461,
-0.012444502674043179,
0.06666508316993713,
-0.007950053550302982,
-0.02934081479907036,
0.030018234625458717,
0.030934447422623634,
0.01560287456959486,
0.008144490420818329,
-0.05268006771802902,
0.03351590782403946,
0.032537080347537994,
0.0054842643439769745,
-0.023111840710043907,
-0.014979966916143894,
-0.033145464956760406,
-0.007808583788573742,
-0.017277657985687256,
0.0047730011865496635,
-0.0503695048391819,
0.0034763759467750788,
0.01869109272956848,
0.017629772424697876,
-0.051167551428079605,
-0.0035633398219943047,
0.036325469613075256,
-0.034705761820077896,
0.0006417515687644482,
-0.003647776087746024,
0.0485566109418869,
0.038662832230329514,
-0.0055218953639268875,
0.0030732578597962856,
0.027988633140921593,
0.004843881353735924,
-0.0014074844075366855,
-0.0808425098657608,
-0.016204532235860825,
0.03900803625583649,
-0.002052033320069313,
0.006505042780190706,
-0.06627530604600906,
-0.018497934564948082,
0.054810699075460434,
-0.09446638077497482,
0.0022316938266158104,
-0.04032882675528526,
-0.047293905168771744,
-0.052993953227996826,
0.0011783468071371317,
0.020147083327174187,
0.03866320848464966,
-0.02030077949166298,
0.030189160257577896,
0.037693802267313004,
0.007724305149167776,
-0.03867735341191292,
-0.04606243222951889,
0.014143291860818863,
0.003360122675076127,
0.004475558642297983,
-0.001842614496126771,
0.04622568190097809,
-0.009337001480162144,
0.023740341886878014,
0.0025762657169252634,
-0.02015320397913456,
0.016145989298820496,
-0.02310686931014061,
0.039781440049409866,
0.006857599131762981,
0.019134853035211563,
0.003442330053076148,
0.005280069075524807,
-0.011690597049891949,
-0.018171271309256554,
0.04892578721046448,
0.053560636937618256,
0.014462761580944061,
0.008605283685028553,
-0.011070922017097473,
-0.05339236184954643,
-0.013443171977996826,
0.045990150421857834,
-0.02200406789779663,
-0.004134790040552616,
-0.02127004787325859,
0.007488882169127464,
0.0007915504975244403,
-0.05740515515208244,
0.021980801597237587,
-0.03486229106783867,
0.009386221878230572,
0.03463846817612648,
-0.022855162620544434,
-0.017585070803761482,
0.021935639902949333,
-0.00158680381719023,
-0.004858712200075388,
-0.0038358368910849094,
-0.01082991436123848,
-0.01886480674147606,
-0.024912899360060692,
-0.002949572168290615,
0.019864341244101524,
-0.01984814554452896,
0.01580175943672657,
-0.03899535536766052,
-0.0036744368262588978,
0.05614449828863144,
0.03648986667394638,
0.03155095502734184,
0.02482645958662033,
-0.016075925901532173,
-0.0398881770670414,
-0.09830179810523987,
0.04184738174080849,
0.03204445168375969,
-0.031143637374043465,
-0.023361284285783768,
-0.028254467993974686,
-0.004006925970315933,
0.01272604987025261,
0.04741910472512245,
0.021090269088745117,
-0.0016877776943147182,
0.022486357018351555,
-0.016200195997953415,
0.015705732628703117,
-0.02450861595571041,
-0.013030975125730038,
-0.006242088042199612,
-0.014442122541368008,
0.008578442968428135,
-0.00135447783395648,
-0.032094091176986694,
0.004253332503139973,
0.01609250344336033,
-0.022650644183158875,
0.036195822060108185,
-0.02936674654483795,
-0.011122298426926136,
0.007229298818856478,
-0.0070267668925225735,
-0.0038361765909940004,
0.08738984167575836,
0.03910382464528084,
-0.023488353937864304,
0.00540960393846035,
-0.02577059529721737,
-0.050376031547784805,
0.007183372974395752,
-0.03358518332242966,
-0.044736914336681366,
-0.022901004180312157,
-0.012754957191646099,
0.03670957684516907,
-0.05877842754125595,
0.021967146545648575,
0.007918702438473701,
-0.05577848479151726,
-0.035857170820236206,
0.03550197556614876,
0.028341034427285194,
0.016356823965907097,
-0.020970748737454414,
0.04332903027534485,
0.024916278198361397,
-0.06323710083961487,
0.015225975774228573,
0.03097997047007084,
0.0033392347395420074,
0.005398020148277283,
-0.006304382812231779,
0.004611677024513483,
0.030946332961320877,
0.03179966285824776,
0.017149271443486214,
0.025309009477496147,
0.002847652416676283,
0.0020659267902374268,
0.005775404628366232,
-0.007275901734828949,
-0.023008108139038086,
0.01896725781261921,
-0.026762261986732483,
0.02200740948319435,
-0.008258413523435593,
-0.0025350642390549183,
-0.025969427078962326,
0.042063094675540924,
-0.021361397579312325,
0.018311724066734314,
0.03173932433128357,
0.060994260013103485,
0.005151272285729647,
-0.02870960719883442,
0.012875561602413654,
0.011598181910812855,
-0.035144299268722534,
-0.01953067258000374,
0.05253605544567108,
0.0034495473373681307,
0.017396729439496994,
0.025547241792082787,
-0.01330658607184887,
-0.02878439985215664,
-0.024300754070281982,
-0.003286476479843259,
0.004936415236443281,
-0.0032519116066396236,
0.0006246795528568327,
-0.03620642423629761,
-0.02957569621503353,
0.0599505640566349,
-0.045635778456926346,
-0.010588596574962139,
0.014605133794248104,
0.06594140827655792,
0.027140920981764793,
0.019524306058883667
] |
<p>Here and on many other forums and blogs people ask the question <a href="http://physics.stackexchange.com/questions/6438/what-if-the-lhc-doesnt-see-susy">"What if LHC does not find SUSY?"</a>. I would like to ask the opposite. What if it finds it? What would the implications be? Is it going to just confirm something understood and expected or is it gong to bring something new? Will there be implications for string theory? String theorists will take it as a good sign, but by itself it is not a confirmation of string theory. </p>
<p>I do realize this is more that one question, but they are on the same topic.</p>
<p>p.s If this question is not suitable for this site, please delete/close </p>
| 7,611 |
[
-0.022867802530527115,
-0.0036104090977460146,
0.01394682563841343,
-0.027144713327288628,
-0.022486841306090355,
0.04390779510140419,
0.008720885030925274,
-0.04706070199608803,
0.01795114018023014,
-0.012909093871712685,
0.03445509076118469,
0.023263387382030487,
0.05116064101457596,
0.02275133691728115,
-0.01164988148957491,
0.01696506328880787,
-0.03153563663363457,
-0.009661921299993992,
-0.0057186465710401535,
-0.006828804034739733,
0.03271301090717316,
0.014630899764597416,
-0.00660990783944726,
0.040674179792404175,
-0.021080100908875465,
0.007380153052508831,
0.008022144436836243,
0.010259013622999191,
0.02510077692568302,
0.048692893236875534,
-0.030926275998353958,
-0.017639312893152237,
0.013718578964471817,
0.020886093378067017,
0.026634197682142258,
0.016804637387394905,
0.01605108007788658,
-0.005672965664416552,
-0.0009695135522633791,
0.010777734220027924,
0.018078923225402832,
-0.00993796344846487,
0.020835667848587036,
0.06359618902206421,
-0.025730228051543236,
-0.0021385452710092068,
-0.026290450245141983,
-0.009388917125761509,
0.07295147329568863,
-0.0750553235411644,
0.05165368691086769,
-0.013242188841104507,
-0.025415994226932526,
-0.006685215514153242,
0.008667197078466415,
-0.016614917665719986,
0.06365995109081268,
0.0672125443816185,
0.011462682858109474,
-0.045921243727207184,
-0.06206750497221947,
-0.021399706602096558,
0.01655726134777069,
0.006566493771970272,
-0.06858912855386734,
0.0298122800886631,
-0.010259319096803665,
0.0027573667466640472,
0.026347773149609566,
0.035190895199775696,
-0.0013812273973599076,
0.029995791614055634,
0.025556745007634163,
0.009997148998081684,
0.03453535959124565,
-0.011689226143062115,
0.0010397451696917415,
0.0035637482069432735,
0.0007334872498176992,
0.052629504352808,
-0.036268021911382675,
-0.003017486771568656,
-0.015216236002743244,
0.04629414156079292,
0.0331275537610054,
-0.0094569381326437,
0.05506734922528267,
-0.03270220756530762,
-0.05020982399582863,
0.021894527599215508,
-0.00787933636456728,
-0.03158020228147507,
0.04810110852122307,
-0.00904301181435585,
-0.004012692254036665,
0.0028286860324442387,
0.0027469086926430464,
0.05627652630209923,
0.001452391385100782,
-0.028180256485939026,
0.008431736379861832,
-0.009922215715050697,
0.026539945974946022,
0.049769461154937744,
-0.02096022106707096,
-0.009600488469004631,
-0.0265799667686224,
0.027298929169774055,
-0.03917801007628441,
-0.03244255855679512,
-0.017153391614556313,
-0.0070035518147051334,
0.014915128238499165,
-0.005827364511787891,
0.020685777068138123,
-0.04367366060614586,
0.004316830076277256,
-0.02343188226222992,
0.06765449792146683,
0.06511187553405762,
0.05718773975968361,
-0.007625001948326826,
0.006984066218137741,
0.018508708104491234,
-0.03827963024377823,
-0.019668541848659515,
0.050471607595682144,
0.001839753589592874,
-0.00891333632171154,
0.042505040764808655,
-0.03575785085558891,
-0.008197763003408909,
-0.001276040798984468,
-0.012102918699383736,
0.0736362412571907,
-0.002274563303217292,
-0.07936431467533112,
-0.06951948255300522,
0.06154808774590492,
0.03055400773882866,
-0.05972081422805786,
-0.04033501446247101,
-0.038448937237262726,
0.02462822012603283,
0.07273884862661362,
-0.025558894500136375,
-0.021572008728981018,
0.02665259875357151,
0.03953427076339722,
0.008924998342990875,
-0.010806551203131676,
-0.004935050383210182,
-0.014625762589275837,
-0.03533270210027695,
-0.02098572440445423,
-0.04887695983052254,
-0.02246847189962864,
0.005350969731807709,
-0.014730457216501236,
-0.028939733281731606,
0.04477255418896675,
0.024327091872692108,
0.028501715511083603,
0.008526728488504887,
-0.015415913425385952,
-0.0023200083523988724,
0.0960424393415451,
0.007786792237311602,
-0.02646905556321144,
0.02461632341146469,
-0.002520028967410326,
-0.0020351808052510023,
0.011092576198279858,
0.0054011535830795765,
0.020520027726888657,
-0.021078893914818764,
-0.029102489352226257,
0.013756309635937214,
0.059749312698841095,
-0.04753103479743004,
-0.031336262822151184,
-0.024552060291171074,
-0.025771191343665123,
0.022256646305322647,
-0.0008895929204300046,
0.03691155090928078,
-0.034415315836668015,
-0.023988474160432816,
0.03846229985356331,
-0.060494400560855865,
-0.03733951225876808,
-0.06163002550601959,
-0.048909351229667664,
0.0034311264753341675,
0.0031635987106710672,
0.02665584906935692,
0.022454075515270233,
0.0020182053558528423,
-0.052176836878061295,
0.024422425776720047,
0.01821751333773136,
0.02282777614891529,
0.036818332970142365,
-0.0020370716229081154,
-0.007167865987867117,
0.012036574073135853,
0.050877898931503296,
-0.03105158731341362,
0.005060989875346422,
-0.03696858510375023,
-0.05191775783896446,
0.023965779691934586,
0.01009217370301485,
-0.007144584320485592,
-0.006510205566883087,
0.022045094519853592,
0.013656502589583397,
-0.01677752286195755,
-0.032073717564344406,
0.03945915773510933,
-0.007304642349481583,
0.0717272236943245,
0.02997635491192341,
0.02095005474984646,
0.02305815927684307,
0.014706478454172611,
-0.010470588691532612,
0.01512516476213932,
-0.0522417277097702,
-0.047575514763593674,
-0.05631576105952263,
-0.0066895876079797745,
0.036267515271902084,
0.021595638245344162,
-0.03273187577724457,
0.027741357684135437,
0.0184963196516037,
0.0007247343310154974,
0.01361328549683094,
0.022604575380682945,
-0.039579156786203384,
-0.032529257237911224,
0.00517901498824358,
0.04080495238304138,
-0.012939948588609695,
0.011227769777178764,
0.016358252614736557,
0.03363880142569542,
0.02076728269457817,
0.020851798355579376,
-0.03669280931353569,
0.08058343827724457,
0.0132028479129076,
0.012734569609165192,
0.014946986921131611,
-0.027865391224622726,
0.04310046136379242,
-0.008671841584146023,
0.03959779441356659,
0.02106204256415367,
-0.0014291808474808931,
-0.006003853864967823,
-0.0043566529639065266,
-0.02241586707532406,
-0.011998684145510197,
0.04560230299830437,
-0.04720611497759819,
-0.054051995277404785,
0.018798556178808212,
-0.058754175901412964,
-0.003167431801557541,
0.021267691627144814,
-0.009579312987625599,
-0.0012180765625089407,
-0.0039211115799844265,
-0.03592991828918457,
0.0036626290529966354,
0.033675894141197205,
-0.03698039799928665,
-0.02648421749472618,
0.015283232554793358,
-0.033128898590803146,
-0.0012137468438595533,
0.039826009422540665,
-0.032912228256464005,
-0.02119852602481842,
-0.03805945813655853,
-0.03351638466119766,
0.001736100995913148,
-0.023679157719016075,
0.010832751169800758,
0.0165398009121418,
-0.007093171589076519,
-0.02789502963423729,
-0.010197740979492664,
-0.028578849509358406,
0.03795032203197479,
-0.033805862069129944,
-0.0033854360226541758,
0.03665967658162117,
0.031173469498753548,
-0.024302298203110695,
-0.025329332798719406,
-0.020580651238560677,
-0.0373920276761055,
0.008479195646941662,
-0.007298680488020182,
0.02997465245425701,
-0.046951718628406525,
0.05629283934831619,
0.0040146224200725555,
-0.06332343071699142,
0.028581948950886726,
-0.049252793192863464,
-0.048944130539894104,
0.035499319434165955,
0.006320291664451361,
0.03176772966980934,
-0.011927861720323563,
-0.03225098177790642,
0.0976676195859909,
0.019203118979930878,
-0.037763647735118866,
-0.037343718111515045,
-0.030851071700453758,
0.004183322191238403,
-0.049210913479328156,
-0.006487889215350151,
-0.008218218572437763,
0.004739721771329641,
0.0036625773645937443,
0.04006900638341904,
0.04228924959897995,
0.0010333603713661432,
0.0329824760556221,
-0.04657302796840668,
-0.04339178651571274,
0.001610984792932868,
0.0053809587843716145,
0.019874805584549904,
0.010605468414723873,
-0.007436499465256929,
0.001464980305172503,
-0.00209284876473248,
0.02902386710047722,
0.009741092100739479,
-0.0037272998597472906,
0.06965558230876923,
-0.0014507038285955787,
0.002808269811794162,
-0.007753700949251652,
0.02192535623908043,
-0.0028536254540085793,
-0.01230164710432291,
-0.036185573786497116,
-0.00610321806743741,
0.04774276912212372,
0.010497774928808212,
-0.005060142371803522,
0.011600829660892487,
0.03365244343876839,
-0.03736790269613266,
-0.03621835634112358,
-0.012180224992334843,
-0.010368149727582932,
0.011032967828214169,
-0.015569708310067654,
-0.052479106932878494,
0.041146304458379745,
0.06937317550182343,
0.018087835982441902,
-0.042536411434412,
-0.03427668660879135,
-0.011318912729620934,
-0.025548802688717842,
0.0016817896394059062,
0.025106338784098625,
0.03351746127009392,
-0.0010397292207926512,
0.026664774864912033,
0.06168406456708908,
0.0021858313120901585,
-0.01104785967618227,
0.031595610082149506,
-0.09658180922269821,
0.024747885763645172,
-0.056327179074287415,
-0.0007479224586859345,
-0.0010269965277984738,
-0.015881121158599854,
-0.007743121590465307,
-0.009014417417347431,
-0.018681254237890244,
-0.0012546568177640438,
0.018826134502887726,
-0.049424510449171066,
-0.005553131457418203,
-0.02963213436305523,
-0.014106174930930138,
-0.014155538752675056,
0.040625959634780884,
0.04990251362323761,
-0.0027744099497795105,
0.007741058245301247,
-0.02171805128455162,
-0.028727147728204727,
-0.044030699878931046,
-0.005480542778968811,
0.03601350262761116,
-0.010700996033847332,
0.04576992243528366,
0.0397329218685627,
0.02420823648571968,
-0.07205570489168167,
0.0380849726498127,
0.03373345732688904,
0.05737196281552315,
0.006239430978894234,
0.03410087898373604,
0.006333185825496912,
-0.03835100680589676,
-0.021355604752898216,
-0.016070576384663582,
0.047449201345443726,
-0.007731208577752113,
-0.03393802046775818,
0.06920460611581802,
-0.00793458241969347,
-0.014307917095720768,
0.05725225806236267,
0.06707921624183655,
-0.0015569580718874931,
-0.053633153438568115,
-0.02252640575170517,
-0.002981016179546714,
-0.029912324622273445,
-0.022101663053035736,
0.001984745729714632,
0.005761352367699146,
-0.02005983144044876,
-0.01890314184129238,
-0.013364442624151707,
0.03468108922243118,
-0.062459804117679596,
-0.004626124631613493,
-0.0278923436999321,
0.017213622108101845,
-0.011896617710590363,
-0.0066854446195065975,
0.009487493894994259,
0.027362866327166557,
0.00996742956340313,
-0.017184527590870857,
0.004083053674548864,
-0.08916230499744415,
0.002256537787616253,
0.06291303038597107,
0.05594504997134209,
-0.013317075558006763,
-0.046341314911842346,
-0.04355257377028465,
0.02000344730913639,
0.08335954695940018,
-0.05127429962158203,
0.03416065126657486,
-0.020408034324645996,
0.018729571253061295,
-0.005493937525898218,
0.021198848262429237,
-0.009404314681887627,
0.025181826204061508,
-0.014286236837506294,
0.02049408107995987,
-0.015438573434948921,
-0.00689035514369607,
-0.019513128325343132,
-0.013686602003872395,
0.027543291449546814,
0.046034958213567734,
-0.013894760049879551,
0.03946920484304428,
-0.028725404292345047,
0.010613184422254562,
-0.0027252822183072567,
-0.09490242600440979,
0.03608248755335808,
0.01657848432660103,
-0.05255512520670891,
0.03319980576634407,
-0.01837526448071003,
-0.047246284782886505,
0.012979022227227688,
0.02271026186645031,
-0.01607045717537403,
-0.002263230737298727,
-0.0597851425409317,
0.02590733766555786,
0.060885511338710785,
0.011587661691009998,
-0.00037190926377661526,
0.04473622143268585,
0.0008223088225349784,
0.003292733570560813,
-0.03302115574479103,
0.018231511116027832,
-0.0234676580876112,
0.008546609431505203,
-0.026860691606998444,
0.013905818574130535,
-0.06148279085755348,
0.07060065120458603,
-0.006890567950904369,
0.013333754613995552,
0.017694685608148575,
-0.022159487009048462,
-0.024080665782094002,
0.016879260540008545,
0.02117924392223358,
0.00801883079111576,
0.007007351145148277,
0.015717264264822006,
-0.016993869096040726,
-0.02325311303138733,
0.0063700624741613865,
-0.024148568511009216,
-0.012050143443048,
0.03574441000819206,
0.004541154485195875,
0.03555161505937576,
0.013677028939127922,
-0.014636661857366562,
0.05211808159947395,
-0.05835780128836632,
0.026976345106959343,
-0.026131972670555115,
0.01776672527194023,
0.020610343664884567,
-0.04265463352203369,
0.010281472466886044,
0.031078020110726357,
0.0009731280151754618,
0.0011682918993756175,
-0.04818805307149887,
0.04715191572904587,
-0.014392438344657421,
-0.014817534014582634,
-0.09262920171022415,
-0.021025553345680237,
0.011386831291019917,
-0.001890478772111237,
-0.002215629443526268,
-0.009848438203334808,
-0.029492758214473724,
-0.050621431320905685,
0.00034652676549740136,
-0.03254115954041481,
0.02888018637895584,
-0.03935933858156204,
-0.02236677147448063,
0.024700544774532318,
0.008571994490921497,
0.05241869390010834,
-0.007185336202383041,
-0.006726168096065521,
-0.01939581334590912,
-0.010067874565720558,
0.008138690143823624,
-0.00551455607637763,
0.03337225690484047,
-0.025480933487415314,
-0.053580280393362045,
-0.018279118463397026,
-0.03046160563826561,
0.04921242594718933,
-0.033699166029691696,
-0.0144368140026927,
0.027200480923056602,
0.011804812587797642,
0.04372449219226837,
-0.0246467012912035,
0.033867478370666504,
-0.002501360373571515,
0.00797712616622448,
-0.011696764267981052,
0.006764470599591732,
0.015840912237763405,
-0.009419931098818779,
-0.0019927609246224165,
0.025083770975470543,
-0.00288050202652812,
0.018206989392638206,
0.03951796516776085,
-0.011723374016582966,
-0.016263745725154877,
-0.004665695130825043,
-0.031099626794457436,
0.014233533293008804,
-0.007289646193385124,
0.02322889305651188,
0.004099701996892691,
0.005457959603518248,
0.009334930218756199,
-0.05574079230427742,
0.008504536934196949,
-0.024777179583907127,
0.05159243568778038,
-0.017688695341348648,
0.06006419658660889,
0.004659425001591444,
-0.029775964096188545,
0.00891861692070961,
-0.010608894750475883,
0.023722106590867043,
-0.0026064023841172457,
0.030285220593214035,
0.0035450474824756384,
-0.015858910977840424,
0.012522284872829914,
0.016621612012386322,
0.04179466515779495,
0.014863497577607632,
0.016816770657896996,
0.06712667644023895,
0.06416286528110504,
0.08523596823215485,
-0.02303382381796837,
-0.04475867748260498,
0.012838941067457199,
-0.057847052812576294,
0.018009699881076813,
0.019313879311084747,
-0.026115519925951958,
0.021666131913661957,
0.010080345906317234,
-0.01936069130897522,
0.012840264476835728,
-0.013329694047570229,
-0.05321431905031204,
0.02030090056359768,
0.026165124028921127,
0.02180587127804756,
0.018861252814531326,
0.023272400721907616,
-0.0019307476468384266,
0.028933752328157425,
0.01609678938984871,
0.014042857103049755,
-0.08225338906049728,
-0.04351527988910675,
-0.05146075040102005,
-0.016146477311849594,
0.04897330328822136,
0.03270819038152695,
0.02158552035689354,
0.03142824396491051,
-0.02567409910261631,
0.007014336530119181,
0.007305304519832134,
0.05511363595724106,
-0.028718851506710052,
0.04960547760128975,
-0.038232047110795975,
0.06297190487384796,
-0.04534395411610603,
0.03223064914345741,
0.10244505107402802,
0.05321778357028961,
0.029091088101267815,
-0.0812649056315422,
0.040217187255620956,
-0.01609055884182453,
-0.023794282227754593,
-0.009116428904235363,
0.024855641648173332,
0.00611777463927865,
-0.02738281711935997,
-0.006756844464689493,
0.0427209734916687,
0.02303648367524147,
-0.01471633929759264,
0.06705296784639359,
-0.031050104647874832,
-0.031089790165424347,
0.012475885450839996,
0.03565571457147598,
-0.01945575512945652,
-0.010363125242292881,
-0.008112195879220963,
0.0401151180267334,
-0.01215902529656887,
0.015970714390277863,
-0.01170418318361044,
-0.053419921547174454,
-0.014094016514718533,
0.0006951700197532773,
-0.028770774602890015,
-0.01465128269046545,
0.01888258010149002,
-0.010436004027724266,
-0.0684642344713211,
-0.007755044382065535,
0.02395443245768547,
0.019441645592451096,
0.022274082526564598,
0.0460067056119442,
0.03389794006943703,
0.0008986549219116569,
0.02411571331322193,
0.04078337550163269,
-0.02841763198375702,
-0.003993981517851353,
0.00999742466956377,
0.0333215557038784,
0.00794934295117855,
-0.029244299978017807,
-0.023734789341688156,
0.011781378649175167,
0.019617700949311256,
0.0029638076666742563,
-0.017313852906227112,
-0.010930697433650494,
0.01030980795621872,
-0.03316478431224823,
-0.00038490135921165347,
0.026899239048361778,
0.033426303416490555,
0.001003685756586492,
0.017968179658055305,
0.003942792769521475,
0.007954904809594154,
0.017820587381720543,
0.019208796322345734,
0.024903131648898125,
0.03448931872844696,
-0.002835166407749057,
-0.017397914081811905,
0.009703122079372406,
-0.06828946620225906,
0.01591956801712513,
0.019078802317380905,
0.025572165846824646,
0.05714607238769531,
0.009425163269042969,
-0.006659378297626972,
-0.03160395100712776,
-0.030494246631860733,
0.0382825993001461,
-0.0009358482784591615,
-0.006565913558006287,
-0.029218826442956924,
-0.0002856865175999701,
0.025396043434739113,
0.014113563112914562,
-0.040181465446949005,
-0.01252798456698656,
0.008160772733390331,
0.06372708082199097,
-0.004787853453308344,
-0.044310472905635834,
-0.0348159484565258,
0.002007237868383527,
-0.04429744929075241,
0.02102610468864441,
-0.008224480785429478,
0.014725666493177414,
-0.005528450943529606,
0.0359964594244957,
0.01513912808150053,
0.05347777530550957,
-0.031075144186615944,
-0.02102184295654297,
0.02161557227373123,
-0.02741483971476555,
-0.0019685945007950068,
0.0307566337287426,
0.04288230091333389,
0.012278757058084011,
-0.030120549723505974,
0.011607066728174686,
-0.038213811814785004,
0.048020824790000916,
0.017483612522482872,
-0.0633462592959404,
0.021782072260975838,
-0.005474867764860392,
0.0032354749273508787,
-0.029327789321541786,
-0.018337402492761612,
-0.06800352036952972,
-0.004471492022275925,
0.02760224975645542,
-0.017525501549243927,
0.005866493098437786,
0.023809900507330894,
-0.04051189869642258,
-0.03973913937807083,
-0.02631843462586403,
0.00824559386819601,
-0.047356534749269485,
0.012444766238331795,
-0.010530957952141762,
0.00929966475814581,
0.031456347554922104,
-0.013284120708703995,
-0.0018627248937264085,
0.05415528640151024,
-0.0348144955933094,
-0.029408380389213562,
0.04473583772778511,
-0.0026968696620315313,
0.02501971647143364,
0.04318453371524811,
-0.00743080023676157,
-0.04021822661161423,
0.028904568403959274,
-0.026941142976284027,
0.035264335572719574,
0.009760809130966663,
-0.0020542636048048735,
-0.017304470762610435,
0.007690172642469406,
-0.02977205254137516,
0.03443418815732002,
-0.020455768331885338,
0.002649292815476656,
0.051706526428461075,
0.020189838483929634,
0.0002906950539909303,
-0.02963436208665371,
-0.022714484483003616,
-0.019423946738243103,
-0.04136064276099205,
-0.02211112156510353,
-0.037492912262678146,
0.038338448852300644,
-0.05453674867749214,
-0.008989894762635231,
-0.00007162552356021479,
0.007571570109575987,
-0.09525845944881439,
0.0050184824503958225,
0.0038294659461826086,
0.009726162999868393,
0.03288024663925171,
-0.03684687241911888,
0.03565472364425659,
0.04314003512263298,
-0.030613241717219353,
0.019138628616929054,
-0.00013599175144918263,
-0.0463549979031086,
-0.045847199857234955,
-0.0030265459790825844,
-0.008425042033195496,
0.05514156445860863,
0.022443614900112152,
0.04180218651890755,
-0.009524091146886349,
0.004005155060440302,
-0.0035655610263347626,
-0.02331848442554474,
-0.0333511047065258,
0.03194500505924225,
0.01478592585772276,
-0.0237773098051548,
0.06353993713855743,
-0.008570206351578236,
-0.03587203100323677,
0.012382878921926022,
0.023254146799445152,
-0.02146868407726288,
0.021473880857229233,
0.009833084419369698,
-0.02009015902876854,
0.042355891317129135,
0.05274795740842819,
-0.027500327676534653,
-0.01097869873046875,
0.015890996903181076,
0.004512641578912735,
0.05507345870137215,
-0.008994342759251595,
0.013477972708642483,
-0.021206999197602272,
-0.00041211486677639186,
-0.02938205562531948,
0.030077774077653885,
-0.05420197546482086,
0.011650169268250465,
-0.011997884139418602,
-0.006328200921416283,
0.01847359724342823,
-0.035982128232717514,
-0.0253155417740345,
-0.030535269528627396,
0.033543284982442856,
0.030055087059736252,
0.030510928481817245,
-0.019955119118094444,
0.019253412261605263,
-0.036276042461395264,
-0.04577852040529251,
-0.0032509425655007362,
-0.010036910884082317,
-0.023052530363202095,
-0.03130371868610382,
-0.03187909349799156,
-0.04929804801940918,
0.03758988529443741,
0.013408901169896126,
-0.040704868733882904,
-0.020751647651195526,
0.05551743507385254,
0.008382530882954597,
0.04468787461519241,
-0.0009626647806726396,
-0.04266167804598808,
-0.0093868812546134,
-0.05083079636096954,
0.035464808344841,
0.005743876565247774,
0.00202724221162498,
-0.01677984930574894,
-0.010506951250135899,
-0.0067041474394500256,
0.0026039867661893368,
0.016095036640763283,
-0.026333171874284744,
0.002150118350982666,
0.03518455848097801,
0.01241984311491251,
-0.016197357326745987,
-0.016495628282427788,
0.009236837737262249,
0.013098986819386482,
-0.029198242351412773,
-0.012114988639950752,
-0.029557062312960625,
0.004624680150300264,
0.009196094237267971,
0.0678672343492508,
0.004564760252833366,
0.006629474461078644,
-0.028578463941812515,
-0.012478513643145561,
0.07153194397687912,
0.0032742370385676622,
0.00731480959802866,
0.05450025200843811,
0.007794611155986786,
0.030838247388601303,
-0.016702942550182343,
0.015213816426694393,
0.0035021768417209387,
0.04543934762477875,
-0.05346818268299103,
0.003114058868959546,
-0.011503071524202824,
0.0028789087664335966,
0.026714615523815155,
-0.050497617572546005,
-0.0008574930834583938,
0.03925333544611931,
-0.030490262433886528,
-0.04708869382739067,
0.042077530175447464,
0.003838494885712862,
0.029679661616683006,
-0.0023402885999530554,
-0.024365637451410294,
0.05304550752043724,
-0.026963787153363228,
-0.001163053559139371,
0.006261769682168961,
-0.009636547416448593,
0.00718229915946722,
0.00941383931785822,
0.032113440334796906,
0.008051327429711819,
0.0026208769995719194,
-0.01262402068823576,
0.04742884635925293,
-0.024013236165046692,
-0.01932472176849842,
0.021895434707403183,
0.001665587304159999,
0.03842863440513611,
0.012908813543617725,
-0.01649084873497486,
0.11063943058252335,
-0.01992621086537838,
0.03126802295446396,
-0.013100524432957172,
-0.006127841304987669,
0.02130565047264099,
0.0036295170430094004,
-0.0041905054822564125,
0.017779763787984848,
0.0014092717319726944,
-0.0004291727382224053,
0.021776115521788597,
0.0220154020935297,
0.02874383144080639,
-0.053146690130233765,
-0.027240391820669174,
-0.04235902428627014,
-0.006842436268925667,
-0.013856884092092514,
-0.031817566603422165,
-0.03477068990468979,
-0.03062991425395012,
0.011476447805762291,
0.022845879197120667,
0.007096331566572189,
-0.020519845187664032,
-0.03706585615873337,
-0.03681667149066925,
0.014341483823955059,
-0.00698099797591567,
-0.011173340491950512,
-0.04168947786092758,
0.02313445508480072,
-0.040450360625982285,
-0.031019961461424828
] |
<p>In optics it is widely mentioned real images are projectable onto screens whereas virtual ones can only be seen by a person. Isn't that contradictory? I mean in order to see the virtual image it has to be <em>projected</em> onto the retina (ultimately acting as a screen). </p>
<p>So, why can you see <a href="http://en.wikipedia.org/wiki/Virtual_image">virtual images</a> in the first place?</p>
| 209 |
[
-0.04365190118551254,
-0.04801373556256294,
-0.002185754245147109,
-0.04146097972989082,
0.01171162724494934,
0.018020041286945343,
-0.03551096096634865,
0.02305215410888195,
-0.004089418798685074,
0.008093439973890781,
0.04179469123482704,
0.04041542112827301,
0.037019290030002594,
0.022286752238869667,
-0.03175768628716469,
0.012336133979260921,
-0.014895168133080006,
-0.014209688641130924,
-0.028502460569143295,
-0.011953870765864849,
-0.027867333963513374,
0.056867096573114395,
0.008331510238349438,
0.007473562378436327,
-0.013564868830144405,
0.009279629215598106,
0.023054007440805435,
0.010939518921077251,
0.047155894339084625,
0.05764470249414444,
-0.005340560805052519,
0.014345328323543072,
-0.021017728373408318,
-0.001053372398018837,
-0.012082826346158981,
-0.017788885161280632,
-0.0644042119383812,
0.009823701344430447,
0.01835508458316326,
-0.018100792542099953,
0.03257357329130173,
0.02641134150326252,
0.017612647265195847,
0.09795533120632172,
0.0038424101658165455,
0.001293072011321783,
-0.035814069211483,
-0.01697387918829918,
0.02032904140651226,
-0.043629568070173264,
0.05822226032614708,
-0.03380277007818222,
0.028912357985973358,
0.024984857067465782,
0.008036879822611809,
0.03674374148249626,
0.06678187102079391,
0.10195685178041458,
-0.04753527045249939,
-0.04097069799900055,
-0.0014362720539793372,
0.009962300769984722,
-0.022765539586544037,
-0.03235301002860069,
-0.028872719034552574,
0.028994429856538773,
0.02167765609920025,
-0.01648741401731968,
0.038074128329753876,
0.011226987466216087,
-0.02613612450659275,
0.017175644636154175,
0.043232690542936325,
-0.022183077409863472,
0.005158496554940939,
-0.007588733918964863,
0.03279504179954529,
0.0044755176641047,
0.04223724454641342,
0.018057918176054955,
0.0068473052233457565,
0.025526171550154686,
0.010834930464625359,
0.04593426734209061,
0.030191443860530853,
-0.01564851962029934,
0.07781707495450974,
0.0017977145034819841,
0.016576535999774933,
0.03134095296263695,
-0.007932924665510654,
-0.00824730284512043,
0.05503632873296738,
-0.02914491295814514,
-0.029844554141163826,
0.00915477704256773,
-0.011486176401376724,
0.05844052881002426,
0.044018108397722244,
-0.058644626289606094,
-0.008100626058876514,
0.004301500506699085,
0.025895092636346817,
0.043194931000471115,
-0.01483925525099039,
-0.04230574890971184,
-0.021476101130247116,
0.05072413384914398,
0.013849630951881409,
0.020226571708917618,
-0.036102648824453354,
0.02521057426929474,
0.01047833263874054,
0.04639092832803726,
0.035970449447631836,
-0.02272667922079563,
0.030239595100283623,
0.0005315598100423813,
0.06765919178724289,
0.05711362138390541,
0.0220735352486372,
-0.03448987752199173,
0.019763173535466194,
-0.013931414112448692,
-0.06851722300052643,
0.04210298880934715,
0.03605589270591736,
-0.006215203553438187,
-0.02224220708012581,
0.005765940062701702,
0.012330322526395321,
0.005323923658579588,
0.05881251394748688,
0.0004820484318770468,
0.03371425345540047,
-0.017851639539003372,
-0.10946813970804214,
-0.03769897297024727,
0.02003522403538227,
-0.014373598620295525,
-0.015948794782161713,
-0.0681237280368805,
0.039200011640787125,
0.05958785116672516,
0.07372742891311646,
-0.011426679790019989,
0.0018181975465267897,
-0.011266308836638927,
0.03241259232163429,
-0.016117600724101067,
-0.016754448413848877,
-0.0027378194499760866,
0.004210214130580425,
-0.01853715069591999,
0.009262794628739357,
-0.06539754569530487,
0.01265669520944357,
0.05120792239904404,
0.00018489321519155055,
-0.06119203940033913,
0.05370793119072914,
-0.023536860942840576,
-0.003912278916686773,
-0.008830186910927296,
-0.02623453363776207,
-0.038784727454185486,
0.06874798983335495,
-0.003652381943538785,
0.02922089584171772,
0.05113493651151657,
-0.021480102092027664,
0.06284752488136292,
-0.0037932114209979773,
0.02018336020410061,
0.011757338419556618,
-0.004769333638250828,
-0.021477796137332916,
0.00481135630980134,
0.03316499665379524,
-0.002835388295352459,
-0.036680564284324646,
-0.04702597111463547,
0.017333097755908966,
0.04513102024793625,
0.0162525475025177,
0.026195600628852844,
-0.010323978960514069,
0.0008929065079428256,
-0.004731899127364159,
-0.04409297555685043,
-0.03725874796509743,
-0.0594097301363945,
0.029192762449383736,
0.02272438071668148,
0.024905523285269737,
-0.0025200818199664354,
0.0030954163521528244,
-0.004669925197958946,
0.005445788614451885,
-0.002544648014008999,
-0.026609523221850395,
0.011854315176606178,
0.029313262552022934,
-0.008801986463367939,
0.026712337508797646,
0.04799859970808029,
0.03520499914884567,
-0.0032207630574703217,
0.01844637654721737,
-0.01535309012979269,
-0.044686924666166306,
0.021331433206796646,
-0.016106635332107544,
0.05631090700626373,
0.0094867879524827,
-0.022866062819957733,
-0.027089601382613182,
0.06329331547021866,
-0.0367240384221077,
0.043119583278894424,
-0.002355170901864767,
0.06030336394906044,
0.037936314940452576,
0.009210903197526932,
-0.011472157202661037,
0.01601949892938137,
0.010829971171915531,
-0.0198250412940979,
0.00862401258200407,
-0.022442921996116638,
-0.0512886680662632,
-0.020591963082551956,
0.052157215774059296,
0.043330077081918716,
-0.01823979802429676,
0.04994778335094452,
0.0019377258140593767,
0.04859625920653343,
0.02960883267223835,
0.0438602976500988,
-0.03424960747361183,
-0.0215025395154953,
-0.012452217750251293,
-0.0009869557106867433,
0.031070033088326454,
0.04913579300045967,
-0.002687259577214718,
0.014951225370168686,
-0.007357811089605093,
-0.032728325575590134,
-0.004751131869852543,
0.06190439686179161,
-0.034625884145498276,
0.02159877121448517,
-0.011855008080601692,
-0.015854645520448685,
0.0103862090036273,
-0.020428869873285294,
-0.014177444390952587,
-0.017967114225029945,
-0.012819573283195496,
-0.03706669062376022,
-0.058547575026750565,
-0.02158167213201523,
0.04609080031514168,
0.035882219672203064,
-0.05655408650636673,
0.013146651908755302,
0.02900807373225689,
-0.027183115482330322,
0.012093535624444485,
-0.028577979654073715,
0.0007304997416213155,
-0.03519904986023903,
0.013415117748081684,
-0.010488632135093212,
-0.00033438741229474545,
0.045549772679805756,
-0.002526265801861882,
-0.060907673090696335,
-0.025431305170059204,
-0.05131981149315834,
-0.00445360504090786,
-0.0038349463138729334,
-0.01835446245968342,
0.024517124518752098,
-0.009827503934502602,
-0.04531035199761391,
0.013314603827893734,
-0.017269082367420197,
0.00795532576739788,
-0.0165423434227705,
-0.025988224893808365,
-0.05572357773780823,
-0.01327391155064106,
-0.016266856342554092,
0.013712579384446144,
0.016658533364534378,
-0.017048556357622147,
0.01471541728824377,
-0.006078906357288361,
-0.04554254189133644,
0.008878598921000957,
-0.0196648258715868,
-0.08760613203048706,
0.02731168270111084,
0.01920303888618946,
0.019360879436135292,
-0.059576865285634995,
0.007553006988018751,
-0.0031219765078276396,
-0.04783599078655243,
0.035354819148778915,
-0.029131732881069183,
-0.07018845528364182,
0.043578166514635086,
0.013839822262525558,
0.03595704957842827,
-0.041459307074546814,
-0.009313306771218777,
0.06159196421504021,
0.007889957167208195,
-0.016017043963074684,
-0.019603092223405838,
-0.01051276084035635,
0.0012053881073370576,
-0.01975374110043049,
0.004883236717432737,
0.019036119803786278,
-0.01778983511030674,
0.07352370023727417,
0.014276718720793724,
-0.019008776172995567,
0.04367778077721596,
0.030586382374167442,
-0.03363148123025894,
-0.044543907046318054,
-0.0043376958929002285,
-0.03443380817770958,
0.03455800563097,
0.02216460555791855,
-0.048796396702528,
0.010137517005205154,
-0.023823998868465424,
0.031246555969119072,
-0.012392817996442318,
-0.0285529512912035,
0.04968930780887604,
-0.023118361830711365,
0.042061805725097656,
-0.017399033531546593,
0.032960906624794006,
0.014428860507905483,
0.018005061894655228,
-0.03645562008023262,
0.0319308303296566,
0.03504200279712677,
-0.04503418877720833,
-0.026813477277755737,
0.024232491850852966,
0.016980046406388283,
-0.03346432372927666,
-0.012013777159154415,
0.002608626615256071,
0.01150560099631548,
0.020435480400919914,
-0.012215899303555489,
-0.003780459286645055,
0.0672958642244339,
0.03420790657401085,
0.010354818776249886,
0.005086916033178568,
-0.008425666950643063,
-0.05774010345339775,
-0.04289853572845459,
0.019386790692806244,
-0.007700652349740267,
0.02215142361819744,
0.01756216026842594,
0.014273240230977535,
0.033750809729099274,
0.027212858200073242,
-0.03692936897277832,
0.009043087251484394,
-0.054992396384477615,
-0.004020508844405413,
0.006504839286208153,
0.006782068870961666,
-0.045071013271808624,
-0.01270123291760683,
-0.004288994707167149,
-0.03370757773518562,
-0.04043664410710335,
-0.03450237959623337,
-0.007156199309974909,
-0.03408261016011238,
-0.021181924268603325,
-0.007539958227425814,
-0.02326313406229019,
-0.02196943387389183,
0.0003694471961352974,
-0.018525665625929832,
-0.008312737569212914,
0.03260074928402901,
0.04586760699748993,
-0.05673590302467346,
0.01927240751683712,
-0.008184530772268772,
-0.0102420374751091,
0.008856061846017838,
0.022687027230858803,
0.04712560400366783,
0.0325063057243824,
-0.04391477257013321,
-0.002460120478644967,
-0.014873767271637917,
0.040768638253211975,
0.0012471993686631322,
0.006908623035997152,
-0.011852666735649109,
-0.05460203066468239,
-0.02932819165289402,
-0.013482985086739063,
0.035045117139816284,
-0.014300351031124592,
-0.015705270692706108,
0.03135807812213898,
-0.020342538133263588,
0.008905136026442051,
0.02190655842423439,
0.009555310010910034,
-0.001051135128363967,
-0.00985016394406557,
-0.045664962381124496,
-0.023541774600744247,
-0.02799202874302864,
-0.011179918423295021,
0.07054167240858078,
0.025312302634119987,
0.017156146466732025,
-0.012399145402014256,
0.014837121590971947,
-0.017394397407770157,
-0.02752923034131527,
0.03641074523329735,
-0.011954090557992458,
-0.06506161391735077,
-0.004015619866549969,
0.02592531405389309,
0.016399618238210678,
0.04393989220261574,
0.035097621381282806,
-0.0014820211799815297,
-0.05417994037270546,
-0.08036746829748154,
0.0033912325743585825,
0.05949223041534424,
0.03469965606927872,
0.013875683769583702,
-0.027582833543419838,
-0.042450156062841415,
-0.0338096059858799,
0.010063142515718937,
-0.027606436982750893,
0.020683107897639275,
-0.038193229585886,
0.017821207642555237,
-0.012604999355971813,
0.007005102466791868,
0.0227919090539217,
0.0038676669355481863,
-0.0050186761654913425,
0.009433425962924957,
-0.04663468897342682,
0.007958886213600636,
-0.012549670413136482,
0.0016775570111349225,
0.02601585164666176,
0.057816676795482635,
0.011124971322715282,
0.01153312623500824,
0.01000627689063549,
0.03059270791709423,
-0.06382351368665695,
-0.01769719459116459,
0.03689275309443474,
0.029132651165127754,
-0.005072928965091705,
0.04337599501013756,
-0.012945352122187614,
-0.03084973245859146,
0.014331582002341747,
0.004756154026836157,
0.009557751938700676,
0.0073872036300599575,
-0.016132351011037827,
0.01752558909356594,
0.0160409864038229,
0.004296749364584684,
0.04202968627214432,
0.04400872439146042,
0.0024001921992748976,
-0.011678093113005161,
-0.021445374935865402,
0.03000415302813053,
-0.03615636005997658,
0.002339056460186839,
-0.0055162678472697735,
0.016187462955713272,
-0.013502228073775768,
0.04355411231517792,
0.015032484196126461,
0.006374277174472809,
-0.020752444863319397,
-0.03506321832537651,
-0.027296075597405434,
0.013792218640446663,
0.016922499984502792,
0.006219985894858837,
-0.011605076491832733,
-0.009361829608678818,
0.01842649094760418,
0.00222630612552166,
0.005048783496022224,
0.008094623684883118,
-0.0048080808483064175,
0.04767487943172455,
0.031104832887649536,
0.0028944481164216995,
-0.030733101069927216,
-0.0006199590279720724,
0.011563715524971485,
-0.027295099571347237,
0.04830324277281761,
0.0015221486100926995,
0.020692547783255577,
0.03346585854887962,
-0.08952486515045166,
-0.012203794904053211,
-0.015767233446240425,
-0.03735089674592018,
0.03204544261097908,
-0.03290886431932449,
0.024719152599573135,
0.04121916741132736,
0.011745133437216282,
-0.04543936997652054,
-0.040179744362831116,
0.012854939326643944,
0.030550234019756317,
-0.0159690473228693,
0.022725936025381088,
0.016294337809085846,
0.006194428540766239,
-0.025162145495414734,
-0.009300406090915203,
-0.018008079379796982,
0.011625773273408413,
-0.011050687171518803,
0.010774903930723667,
0.00004171258115093224,
0.0589001439511776,
-0.009157402440905571,
-0.037188515067100525,
-0.013806089758872986,
-0.012036050669848919,
0.005599725525826216,
0.0060399495996534824,
0.03205866366624832,
-0.024244319647550583,
-0.004771522246301174,
-0.0046633463352918625,
-0.008359037339687347,
0.03622755408287048,
0.003828017506748438,
0.03927600756287575,
-0.004468474071472883,
-0.004202139563858509,
-0.007079289760440588,
-0.04366700351238251,
0.021343618631362915,
-0.005063717253506184,
0.009883003309369087,
-0.0013518306659534574,
-0.0013951420551165938,
-0.002110191388055682,
-0.019930537790060043,
0.044252198189496994,
0.013469778932631016,
0.026000764220952988,
0.005285582970827818,
0.04001487419009209,
-0.04161586984992027,
0.039573099464178085,
0.015192127786576748,
-0.04371855407953262,
0.0242674071341753,
-0.0055511752143502235,
0.01043916679918766,
0.012247174978256226,
0.0553743913769722,
-0.03837137296795845,
-0.01015270035713911,
-0.02334187924861908,
0.022159770131111145,
0.06651978194713593,
-0.015034974552690983,
0.08048740029335022,
-0.026417987421154976,
-0.02842066064476967,
-0.007256335578858852,
-0.0013822197215631604,
0.0023112294729799032,
0.011137377470731735,
-0.004012047313153744,
0.023881804198026657,
-0.0402432419359684,
0.016400974243879318,
-0.028890419751405716,
0.03873388469219208,
0.04150965437293053,
0.03348251432180405,
0.02777128666639328,
0.027725329622626305,
-0.0011864003026857972,
-0.034168779850006104,
-0.04595578461885452,
0.03205413743853569,
-0.05149981379508972,
0.018853548914194107,
0.008515970781445503,
0.010841308161616325,
0.04419465363025665,
-0.07306787371635437,
0.01863721013069153,
-0.06136751547455788,
-0.039909474551677704,
-0.024745039641857147,
-0.022506587207317352,
-0.02775539644062519,
0.04075774922966957,
-0.015500577166676521,
-0.06530311703681946,
0.01587621122598648,
-0.0026452767197042704,
0.028887886554002762,
-0.021406255662441254,
-0.09022527188062668,
-0.09782444685697556,
-0.0502958819270134,
-0.01127203181385994,
0.042178183794021606,
0.03889690712094307,
-0.043832775205373764,
-0.010982618667185307,
-0.04852697625756264,
0.01491195522248745,
0.011991932056844234,
0.05490195006132126,
-0.04070355370640755,
0.018561560660600662,
-0.01221445295959711,
0.04987943172454834,
0.003932070452719927,
0.01930282451212406,
0.0918145701289177,
0.020241698250174522,
0.01285153441131115,
-0.056302428245544434,
0.013237472623586655,
-0.04639943689107895,
0.03027353063225746,
-0.01533294003456831,
0.05238913744688034,
-0.015888670459389687,
0.015139528550207615,
0.02543279342353344,
0.034631773829460144,
0.045896563678979874,
0.016497446224093437,
0.01162638794630766,
-0.03931192308664322,
-0.044443823397159576,
-0.0029845337849110365,
-0.0020858368370682,
-0.02248433604836464,
0.019717322662472725,
-0.06663764268159866,
0.025560395792126656,
-0.003349369391798973,
-0.022160330787301064,
0.010224285535514355,
-0.026352304965257645,
0.04004175215959549,
0.02010863646864891,
-0.03284728527069092,
-0.009638111107051373,
0.01806667074561119,
-0.02708163671195507,
-0.02657577209174633,
-0.014441261999309063,
0.0008235306013375521,
-0.024425990879535675,
0.02891993522644043,
0.03356877714395523,
0.00241460301913321,
-0.020876215770840645,
-0.014381765387952328,
0.01390819437801838,
-0.039807867258787155,
-0.00622339965775609,
-0.01585366763174534,
0.011006002314388752,
-0.017586885020136833,
0.017265433445572853,
0.001959553686901927,
-0.052894141525030136,
-0.011205649934709072,
-0.056840963661670685,
-0.03875933960080147,
0.012951655313372612,
-0.028903894126415253,
0.00700807198882103,
-0.03330575302243233,
-0.0420958511531353,
0.04623092710971832,
-0.011943542398512363,
0.025350747630000114,
0.007051588036119938,
0.014446540735661983,
0.004199287388473749,
-0.031226756051182747,
0.02171850949525833,
-0.008176262490451336,
-0.007372878957539797,
-0.012395886704325676,
-0.0015460526337847114,
-0.016435988247394562,
-0.025371314957737923,
-0.006760828197002411,
0.02662946842610836,
0.03708561882376671,
0.022331608459353447,
-0.015103639103472233,
-0.017939141020178795,
-0.02105218544602394,
0.008288972079753876,
-0.035008639097213745,
-0.058217279613018036,
-0.024257555603981018,
0.0253159012645483,
0.06188654154539108,
0.022758565843105316,
0.012090886011719704,
0.019136708229780197,
0.011909357272088528,
-0.006850941572338343,
0.028439955785870552,
-0.05303788185119629,
-0.049525197595357895,
0.03478424623608589,
-0.008850025944411755,
-0.024694040417671204,
-0.01796697825193405,
0.02122708596289158,
0.02256203256547451,
0.0026887960266321898,
0.027343912050127983,
0.032275162637233734,
-0.02609185501933098,
0.010713606141507626,
0.0027212509885430336,
-0.0009783973218873143,
0.009081751108169556,
-0.0017334318254143,
0.007253624498844147,
-0.022040480747818947,
-0.03090813010931015,
-0.03815128654241562,
-0.004721358884125948,
0.0136470478028059,
0.002499862341210246,
0.04000120982527733,
0.0014219151344150305,
-0.012199604883790016,
0.0375053696334362,
-0.031442973762750626,
-0.05255312845110893,
-0.03675214201211929,
0.027546728029847145,
0.02024129405617714,
-0.025806793943047523,
-0.034336261451244354,
0.012251594103872776,
-0.013783288188278675,
-0.009389225393533707,
0.006526308134198189,
0.010668797418475151,
-0.03119087964296341,
0.02245914563536644,
0.0021311433520168066,
0.0022082128562033176,
0.02788163349032402,
-0.0010204610880464315,
-0.04405741021037102,
0.04108067601919174,
-0.016876960173249245,
-0.03389211744070053,
-0.00010527943959459662,
-0.014907099306583405,
0.02595224417746067,
0.04705589637160301,
0.00403973925858736,
-0.019135598093271255,
0.07596533745527267,
-0.006343024782836437,
-0.002587641356512904,
0.008658559061586857,
-0.008509180508553982,
-0.001206715707667172,
0.014269011095166206,
-0.0006296150968410075,
-0.033701129257678986,
-0.009848587214946747,
0.029871134087443352,
-0.0009112164843827486,
0.02714529260993004,
-0.005399933084845543,
0.001413983991369605,
0.01755870319902897,
0.00647368049249053,
0.003992416430264711,
0.004286652430891991,
0.026203623041510582,
0.013676024973392487,
-0.03166184574365616,
0.05595304071903229,
0.02926970273256302,
-0.023293068632483482,
-0.09442713856697083,
0.010693810880184174,
-0.0004464224330149591,
0.0007733409875072539,
0.024130403995513916,
-0.037927404046058655,
0.007790206465870142,
0.025966044515371323,
-0.10620085895061493,
-0.0042995307594537735,
-0.0030372319743037224,
-0.06388956308364868,
-0.05243698135018349,
0.027817608788609505,
0.006438846234232187,
0.03124629147350788,
0.016714779660105705,
0.024742435663938522,
0.009819881990551949,
-0.016504036262631416,
-0.018711863085627556,
0.009506226517260075,
-0.015020483173429966,
0.03996464982628822,
-0.041998766362667084,
-0.000481471826788038,
0.11226244270801544,
-0.021126454696059227,
-0.044185396283864975,
0.01823946088552475,
0.01644313894212246,
0.01559157483279705,
0.026103634387254715,
0.007498790509998798,
0.028830939903855324,
0.0331561453640461,
0.02935275435447693,
-0.003585842903703451,
-0.03628471493721008,
0.011009409092366695,
0.02114245854318142,
0.04345414787530899,
0.01817888580262661,
-0.009680576622486115,
0.014880243688821793,
-0.003606497310101986,
-0.025989387184381485,
-0.008989347144961357,
0.008996150456368923,
-0.052093345671892166,
-0.012675337493419647,
0.01631724089384079,
0.028053009882569313,
-0.024894315749406815,
0.021289583295583725,
-0.0708921030163765,
-0.002109121298417449,
0.01545459683984518,
-0.02078775130212307,
-0.00748863210901618,
0.013318298384547234,
-0.011565134860575199,
-0.06185910478234291,
0.027885470539331436,
-0.007366210222244263,
-0.0033244641963392496,
-0.02530885674059391,
0.003845993662253022,
0.03708653897047043,
-0.00375227234326303,
0.03919307887554169,
-0.015910791233181953,
-0.010655738413333893,
0.02695687860250473,
0.023206086829304695,
0.011735635809600353,
0.02384275197982788,
-0.04936853051185608,
-0.058839041739702225,
-0.04127819836139679,
0.048925790935754776,
-0.017035845667123795,
-0.01626981608569622,
-0.039378538727760315,
-0.013237041421234608,
-0.024309223517775536,
0.031643882393836975,
0.05443566292524338,
-0.015322069637477398,
-0.009645317681133747,
-0.0035759974271059036,
0.0018943167524412274,
0.003453317563980818,
-0.06931706517934799,
-0.009586301632225513,
0.0014902281109243631,
-0.04373568296432495,
0.016356803476810455,
-0.01822151616215706,
-0.035628028213977814,
0.032262418419122696,
0.04403860494494438,
-0.014413537457585335,
0.03585592657327652,
0.007459254469722509,
-0.01767911948263645,
0.031048482283949852,
0.034329481422901154,
-0.0026259988080710173,
0.07151655107736588,
-0.02079787477850914,
0.00024204117653425783,
-0.01837124302983284,
0.015383938327431679,
0.00042279402259737253,
0.008932377211749554,
-0.03982459753751755,
0.011681154370307922,
-0.001859560376033187,
-0.040557704865932465,
0.008712082169950008,
-0.043588295578956604,
-0.004982977174222469,
0.014116158708930016,
-0.013365257531404495,
-0.012743025086820126,
0.07003791630268097,
0.016896676272153854,
0.001995865721255541,
-0.010444648563861847,
0.0641394630074501,
-0.014643149450421333,
-0.046564023941755295,
-0.008701949380338192,
0.04221409559249878,
-0.001642530900426209,
-0.012087437324225903,
0.042423468083143234,
0.07160410284996033,
0.015561619773507118,
0.04721364378929138,
-0.034760214388370514,
0.08474163711071014,
-0.040023256093263626,
-0.0356854572892189,
-0.04437403753399849,
-0.0036641075275838375,
-0.012148095294833183,
0.030474312603473663,
0.0019004385685548186,
0.10278525203466415,
-0.037059485912323,
0.020298967137932777,
-0.000805443269200623,
0.018533626571297646,
-0.0455455407500267,
-0.009429764933884144,
0.03060782514512539,
-0.0033909764606505632,
-0.028284115716814995,
-0.023476075381040573,
-0.0049178884364664555,
-0.005033512599766254,
0.03358277678489685,
-0.002412680070847273,
0.023521052673459053,
-0.013604526408016682,
-0.03556022047996521,
0.015858957543969154,
-0.004143854603171349,
0.008708641864359379,
0.029697932302951813,
0.02364511787891388,
0.02295561507344246,
-0.014581314288079739,
0.00024582160403952,
-0.008624277077615261,
-0.04425996541976929,
0.02308652177453041,
-0.09667176753282547,
0.02426973544061184,
0.0097678042948246,
0.027201231569051743,
0.026181910187005997,
-0.023997100070118904
] |
<p>Together with colleagues we got this question. Imagine to take small mirrors, the size for example of a dentist mirror, and stick them to a wooden frame with a parabolic shape. Each mirror is flat, and once set of the frame it can be aligned properly with screws so that it redirects its reflection towards the focus of the parabola. All the parabolic surface is covered with these small mirrors.</p>
<p>Now, if you build a Newtonian telescope out of this system, would you get a decent telescope? I expect it to be affected by various aberrations, but would it work ? </p>
| 7,612 |
[
-0.02079867571592331,
-0.025868399068713188,
-0.008521311916410923,
-0.028224481269717216,
0.08922979980707169,
0.030606193467974663,
-0.021197760477662086,
-0.008410757407546043,
-0.019779367372393608,
-0.010057592764496803,
0.02322377823293209,
0.05099271610379219,
0.03602791950106621,
0.010692432522773743,
-0.02889205701649189,
-0.0020114616490900517,
-0.013847630470991135,
-0.0076299007050693035,
-0.01493204664438963,
-0.041316818445920944,
0.00649998476728797,
0.05013097822666168,
0.03989798575639725,
-0.020830338820815086,
-0.019589494913816452,
0.001453891396522522,
0.024501560255885124,
-0.05319909751415253,
-0.009953048080205917,
0.04012112691998482,
0.004935231525450945,
0.029620405286550522,
0.006679943297058344,
0.046869080513715744,
0.025909358635544777,
0.013182959519326687,
-0.04914332181215286,
-0.04643099755048752,
0.010233856737613678,
0.022413311526179314,
-0.026104474440217018,
-0.03274565190076828,
0.004102977924048901,
0.026734312996268272,
-0.0038177259266376495,
-0.00811766367405653,
-0.01697559282183647,
-0.03784153237938881,
0.06878301501274109,
-0.054349981248378754,
0.03586139157414436,
0.017568672075867653,
0.006211783271282911,
0.04519834369421005,
-0.0050109755247831345,
-0.023427441716194153,
0.03810984268784523,
0.04584447667002678,
-0.03945309296250343,
-0.039925720542669296,
-0.01757318153977394,
0.005305545404553413,
0.020940663293004036,
-0.0009390159975737333,
-0.005478264763951302,
0.014155295677483082,
-0.05275849997997284,
-0.026569891721010208,
0.0247998908162117,
0.004498048685491085,
0.006639301776885986,
0.0020303099881857634,
0.03941575810313225,
0.008929942734539509,
-0.02684001810848713,
-0.0028816908597946167,
0.030487796291708946,
-0.014354517683386803,
0.04010481387376785,
0.005437701009213924,
-0.006113831419497728,
-0.006303312256932259,
0.0031544144731014967,
0.0773347020149231,
0.026240304112434387,
0.010269830003380775,
0.045846834778785706,
-0.04252176359295845,
0.02184329368174076,
0.003838031552731991,
0.021064147353172302,
0.012237283401191235,
0.03727484121918678,
0.007850810885429382,
0.008341516368091106,
0.011932345107197762,
-0.024016818031668663,
0.039309535175561905,
0.01749633252620697,
-0.016134999692440033,
-0.016590353101491928,
0.010034921579062939,
-0.03668176382780075,
0.05196204409003258,
0.023583028465509415,
-0.04300494119524956,
-0.001029613777063787,
-0.003187814261764288,
-0.022023333236575127,
0.0010010011028498411,
-0.023774627596139908,
0.009781098924577236,
0.006546987686306238,
0.00447225384414196,
0.047145262360572815,
-0.027681542560458183,
0.0336255319416523,
-0.03048691712319851,
0.04816912114620209,
0.0812712237238884,
0.04288512095808983,
-0.0010041875066235662,
0.0429653525352478,
-0.05365091562271118,
-0.074565589427948,
0.01799417845904827,
0.010135501623153687,
-0.015365861356258392,
-0.04014941304922104,
-0.03240913897752762,
0.03893142566084862,
-0.010896495543420315,
-0.008972535841166973,
0.0004840647161472589,
0.023454517126083374,
-0.005340352188795805,
-0.06453166902065277,
-0.07158201187849045,
0.01573384739458561,
0.01739206351339817,
-0.005290316883474588,
-0.051126014441251755,
0.028238410130143166,
0.045514415949583054,
0.08223730325698853,
-0.011994380503892899,
-0.0010570615995675325,
0.017342090606689453,
0.08203885704278946,
-0.021785886958241463,
-0.03571758419275284,
0.0003027584752999246,
-0.012361603789031506,
-0.04795518517494202,
-0.0016275708330795169,
-0.12461180984973907,
0.04278082773089409,
0.01565350778400898,
0.045100875198841095,
-0.055239640176296234,
0.024311117827892303,
-0.02129223570227623,
0.04626351594924927,
-0.0013771697413176298,
-0.019838711246848106,
0.012001975439488888,
0.0670316144824028,
0.020831787958741188,
0.00039708593976683915,
0.020131811499595642,
-0.004411752335727215,
0.011605863459408283,
0.028650181367993355,
-0.02842492237687111,
0.008879336528480053,
-0.06525644659996033,
-0.0037640556693077087,
0.00593411223962903,
0.03793703764677048,
0.013109870254993439,
-0.019750164821743965,
0.010931618511676788,
-0.037455473095178604,
0.02529270015656948,
0.019802743569016457,
0.07765235751867294,
0.008123847655951977,
0.004611311014741659,
0.013507264666259289,
-0.02325844019651413,
0.005857166368514299,
-0.00930110365152359,
0.01836518570780754,
-0.022306280210614204,
-0.01953224465250969,
-0.00269871624186635,
-0.009170633740723133,
-0.0179933849722147,
0.0007145435665734112,
-0.005888172425329685,
-0.012231639586389065,
0.004622726235538721,
0.006493864115327597,
0.039605122059583664,
0.028323592618107796,
0.057704780250787735,
0.04163367301225662,
-0.02026875875890255,
0.014819080010056496,
0.0036999634467065334,
-0.040667928755283356,
0.0006845251191407442,
-0.039471935480833054,
0.0468459390103817,
-0.00781405158340931,
0.022025814279913902,
-0.006778209004551172,
0.024006711319088936,
0.025680752471089363,
0.04851400479674339,
-0.03356742858886719,
0.06076302006840706,
0.03495310619473457,
-0.02449970878660679,
0.028022905811667442,
0.015068459324538708,
0.014028740115463734,
0.02179904468357563,
0.020977512001991272,
-0.014516751281917095,
-0.062075454741716385,
0.0009279249934479594,
0.025788193568587303,
0.03814549744129181,
-0.04414454847574234,
0.032641492784023285,
0.054199978709220886,
0.027186749503016472,
0.022454898804426193,
-0.009060944430530071,
0.005548045504838228,
-0.005481126252561808,
0.015614948235452175,
0.00124301144387573,
0.048399630934000015,
0.04115814343094826,
-0.023576432839035988,
0.016669616103172302,
0.019534051418304443,
-0.032205261290073395,
0.0203365720808506,
0.036577921360731125,
-0.001632609055377543,
0.03545614704489708,
0.0025159036740660667,
-0.010657444596290588,
0.03962438553571701,
0.0002920893603004515,
0.01853151060640812,
0.03705025464296341,
-0.014626684598624706,
-0.004382760263979435,
-0.07312074303627014,
0.01641124300658703,
-0.021272242069244385,
-0.005770520772784948,
-0.018632344901561737,
-0.0625615194439888,
0.031047318130731583,
-0.04340960457921028,
0.0011857186909765005,
-0.02703751064836979,
-0.004700992256402969,
-0.01571962796151638,
0.019268948584794998,
-0.013908174820244312,
0.011356900446116924,
0.0330834724009037,
-0.018875187262892723,
-0.055631693452596664,
0.0017016360070556402,
0.0004236527602188289,
-0.00992580596357584,
0.024983443319797516,
-0.08648861944675446,
0.03089710883796215,
-0.0034100469201803207,
-0.02413344383239746,
0.06369013339281082,
0.0044748131185770035,
0.016683069989085197,
0.010273575782775879,
-0.04072006419301033,
0.0059808590449392796,
-0.009949693456292152,
-0.019109925255179405,
-0.04006071761250496,
-0.038147419691085815,
0.006954228039830923,
0.007670481689274311,
0.030712047591805458,
-0.017061013728380203,
-0.014816762879490852,
-0.056993380188941956,
-0.055093344300985336,
0.01034584827721119,
0.0036856902297586203,
0.00527563551440835,
-0.03831266239285469,
0.03967978432774544,
0.0280867051333189,
-0.028262842446565628,
0.025401581078767776,
-0.06431619077920914,
-0.05979306995868683,
0.021134953945875168,
-0.0029294160194694996,
0.04874669015407562,
0.011822700500488281,
0.0014142319560050964,
0.06996874511241913,
0.02380330115556717,
-0.048773471266031265,
-0.03523976355791092,
0.017092349007725716,
0.020994195714592934,
-0.06876691430807114,
0.017187681049108505,
0.029998768121004105,
-0.00336242257617414,
0.027353297919034958,
-0.0036302681546658278,
-0.021359946578741074,
0.005106074269860983,
0.043972376734018326,
0.021712133660912514,
-0.04121009260416031,
0.005521000828593969,
-0.031487226486206055,
0.00837752129882574,
0.06875726580619812,
-0.014674071222543716,
0.020251348614692688,
-0.008766750805079937,
0.03831694647669792,
0.01646638661623001,
-0.060927826911211014,
0.027646077796816826,
0.016878508031368256,
-0.014571448788046837,
0.004805303644388914,
0.02892897091805935,
0.006997968535870314,
0.034461308270692825,
0.0018645937088876963,
0.026868024840950966,
0.04616672918200493,
0.011410999111831188,
0.021341290324926376,
0.023749975487589836,
0.04600166156888008,
0.019346270710229874,
-0.0028512568678706884,
-0.009915845468640327,
0.008168976753950119,
-0.012123746797442436,
-0.017566552385687828,
-0.04097483679652214,
0.05345664545893669,
0.02315312810242176,
0.023809440433979034,
0.00306601426564157,
0.020383557304739952,
0.02767571248114109,
-0.03361259400844574,
0.01621738076210022,
-0.012293752282857895,
0.010459165088832378,
0.003137590130791068,
0.008283895440399647,
0.006275438237935305,
0.017385398969054222,
0.007119852118194103,
-0.007660865318030119,
-0.04858212545514107,
0.019655738025903702,
-0.050825417041778564,
-0.01665949448943138,
-0.020811108872294426,
0.016094906255602837,
-0.014284085482358932,
-0.007582797668874264,
0.0038118206430226564,
-0.015038078650832176,
0.018958717584609985,
-0.020891068503260612,
0.00289979693479836,
-0.010149666108191013,
-0.04933510720729828,
-0.011591603979468346,
0.04878319799900055,
0.04447120428085327,
-0.019895164296030998,
0.04593523219227791,
-0.017736123874783516,
-0.0238688662648201,
0.012954520992934704,
-0.0002447195292916149,
0.03802981227636337,
-0.010578403249382973,
0.03923182934522629,
0.013306098990142345,
0.06570836901664734,
-0.01783190295100212,
0.04390936717391014,
0.029981855303049088,
0.021525952965021133,
-0.0022900463081896305,
-0.009209579788148403,
0.0020062183029949665,
-0.04057573527097702,
-0.020659824833273888,
0.0038025344256311655,
0.03000916726887226,
-0.05157718434929848,
-0.015105286613106728,
0.00847048033028841,
-0.03723282739520073,
-0.02196885645389557,
-0.008109990507364273,
0.013653837144374847,
0.001920025679282844,
-0.0021274748723953962,
-0.040549442172050476,
-0.012514839880168438,
-0.012808742001652718,
0.012544253841042519,
0.05263610929250717,
0.03477173671126366,
-0.05015053600072861,
-0.04120347276329994,
0.02838229015469551,
-0.014147705398499966,
-0.03793251886963844,
0.04256695881485939,
-0.03817597031593323,
0.006893168669193983,
0.005169406067579985,
0.02285049855709076,
0.016358323395252228,
0.047261688858270645,
0.02577424794435501,
-0.004511497914791107,
-0.03476931154727936,
-0.09030768275260925,
0.01667140983045101,
0.01108533889055252,
0.025204474106431007,
-0.018067602068185806,
-0.0026978780515491962,
-0.03929033502936363,
-0.054069358855485916,
0.05136687308549881,
-0.04261202737689018,
0.05194869264960289,
-0.021237527951598167,
0.03691953420639038,
-0.018129555508494377,
-0.012922005727887154,
-0.020742708817124367,
0.006567349657416344,
-0.028082260861992836,
-0.010984119959175587,
-0.004808205179870129,
0.003492430318146944,
0.005550365429371595,
-0.01536427903920412,
0.0461115762591362,
0.02316286787390709,
0.034749340265989304,
-0.023947710171341896,
0.014741364866495132,
0.015028080902993679,
0.0030461852438747883,
-0.05368873104453087,
0.008532190695405006,
0.005988640710711479,
-0.072427898645401,
0.02141874097287655,
-0.06757315248250961,
-0.01563025638461113,
0.02777835726737976,
-0.01246880367398262,
-0.024310804903507233,
0.03694082424044609,
-0.03071499988436699,
-0.013776051811873913,
0.03935650736093521,
0.00829759705811739,
0.052382469177246094,
0.023652564734220505,
-0.05413215979933739,
0.0006141183548606932,
-0.004928250331431627,
0.005173657089471817,
-0.040992818772792816,
-0.004919613711535931,
-0.02180275321006775,
0.012569272890686989,
-0.03014528378844261,
0.03451986610889435,
0.030895181000232697,
0.04554298520088196,
0.018964912742376328,
-0.007372234482318163,
-0.019688155502080917,
0.02508600801229477,
-0.010172978974878788,
-0.004618397448211908,
-0.01840899884700775,
0.027131028473377228,
0.07533089816570282,
-0.010673386044800282,
0.022675851359963417,
-0.014405605383217335,
0.052243027836084366,
0.014404287561774254,
0.02108859270811081,
0.007521351333707571,
-0.030728520825505257,
-0.0026155158411711454,
-0.002525108866393566,
-0.056434791535139084,
0.03494994714856148,
-0.01606304571032524,
0.04968010261654854,
0.05828969553112984,
-0.044415924698114395,
-0.023759739473462105,
-0.00024160677276086062,
-0.033833444118499756,
0.02575097605586052,
-0.0397440530359745,
0.0016674251528456807,
-0.023281116038560867,
-0.0060059260576963425,
-0.04770855978131294,
-0.004830610938370228,
0.009726712480187416,
0.017686761915683746,
0.024979395791888237,
0.028645452111959457,
-0.009417013265192509,
-0.031579937785863876,
-0.01963290013372898,
0.008277563378214836,
0.04714315012097359,
-0.05834655463695526,
-0.014761099591851234,
-0.007001442369073629,
0.00136186636518687,
0.04642648622393608,
-0.017367908731102943,
-0.01136139128357172,
-0.0029374754521995783,
-0.029022950679063797,
-0.03439241275191307,
-0.024314958602190018,
0.05035088583827019,
-0.00994821172207594,
-0.06051553040742874,
-0.061495233327150345,
0.01760532148182392,
0.018631044775247574,
-0.017699098214507103,
0.008231604471802711,
0.042779650539159775,
0.0054655857384204865,
-0.02147224359214306,
0.017863687127828598,
-0.0005480503896251321,
-0.009772412478923798,
0.002545165130868554,
-0.009008163586258888,
0.0069402726367115974,
0.02505599707365036,
-0.06175706908106804,
0.04843003675341606,
-0.001556619070470333,
-0.039012450724840164,
-0.018129533156752586,
0.059009451419115067,
-0.02298274263739586,
-0.009972726926207542,
0.023142317309975624,
0.002746967598795891,
0.015500853769481182,
0.020128723233938217,
0.01465697679668665,
-0.0000032438042580906767,
0.032817453145980835,
0.0144329983741045,
-0.04071782901883125,
-0.02274099364876747,
-0.024589836597442627,
0.09845054894685745,
-0.00286387768574059,
0.018129320815205574,
0.002242114394903183,
-0.01061734277755022,
-0.041862744837999344,
-0.014663652516901493,
-0.01738123968243599,
-0.0011248454684391618,
-0.010559458285570145,
0.06179293245077133,
-0.01536613143980503,
-0.008269996382296085,
0.03055928274989128,
0.05177614837884903,
0.033001117408275604,
0.030052432790398598,
0.0730239525437355,
0.03677252307534218,
0.002557795261964202,
-0.007274337578564882,
-0.0028821055311709642,
0.02386081963777542,
-0.062299493700265884,
0.024163419380784035,
-0.02278733067214489,
0.0027684078086167574,
0.0004937092890031636,
0.022803688421845436,
0.039024073630571365,
-0.0578109472990036,
-0.02390916459262371,
-0.04883391037583351,
0.023538922891020775,
0.024175133556127548,
0.005092631094157696,
-0.023964716121554375,
0.027244072407484055,
0.012821673415601254,
0.028719237074255943,
0.07404763996601105,
-0.038110096007585526,
-0.07981531322002411,
-0.055284373462200165,
-0.04206228628754616,
-0.02258969470858574,
0.03384006395936012,
-0.004965807776898146,
-0.0015509892255067825,
-0.011629949323832989,
-0.032782234251499176,
-0.01400434598326683,
0.009737777523696423,
0.06485632061958313,
-0.05496784672141075,
0.01820000819861889,
-0.046294476836919785,
0.053374212235212326,
0.003945681266486645,
0.003718323539942503,
0.12099789828062057,
0.024660160765051842,
0.009890003129839897,
-0.032229918986558914,
0.037025075405836105,
-0.04560048133134842,
-0.013113085180521011,
-0.00990759115666151,
0.044012587517499924,
0.006353589240461588,
0.010704048909246922,
7.153114438551711e-7,
0.016473393887281418,
-0.0016112675657495856,
-0.028259508311748505,
0.03845164179801941,
-0.05343610420823097,
-0.00869465060532093,
0.020153097808361053,
-0.0005342166405171156,
0.0009870105423033237,
0.05825183540582657,
-0.01716132089495659,
0.00450776144862175,
-0.04533427581191063,
0.025194013491272926,
-0.010647804476320744,
-0.03481617569923401,
-0.010889539495110512,
-0.005808147136121988,
-0.022143306210637093,
0.018017156049609184,
-0.005353893153369427,
-0.06936299800872803,
-0.03242747485637665,
0.013445554301142693,
0.01532045193016529,
-0.01924017071723938,
0.02978498861193657,
0.06201436370611191,
-0.0004959275829605758,
0.001093916711397469,
0.018112894147634506,
-0.00920496229082346,
-0.05594842508435249,
-0.006153744179755449,
-0.026889443397521973,
0.007243666797876358,
0.014026432298123837,
0.022376008331775665,
-0.03373636677861214,
-0.017586542293429375,
0.013470555655658245,
-0.06916039437055588,
0.019380509853363037,
0.020820805802941322,
-0.01257361564785242,
-0.01816955767571926,
-0.05684993788599968,
0.02953152172267437,
0.018249809741973877,
0.023984270170331,
-0.0141356335952878,
0.019680682569742203,
-0.014100166969001293,
0.00032781990012153983,
0.030859386548399925,
0.05754566192626953,
0.01156700775027275,
-0.03850973770022392,
-0.06049995869398117,
-0.027452174574136734,
-0.037512391805648804,
0.027090156450867653,
0.015122597105801105,
0.032195642590522766,
-0.00046087216469459236,
-0.000754041422624141,
0.0070059634745121,
-0.02545846439898014,
-0.040818966925144196,
0.04888124018907547,
-0.03333645686507225,
-0.0029363203793764114,
-0.008447032421827316,
0.0017947027226909995,
0.04484175145626068,
0.041559185832738876,
-0.016497014090418816,
-0.03598366305232048,
0.018121691420674324,
0.015534808859229088,
0.002294579055160284,
-0.016821004450321198,
-0.021816091611981392,
-0.003485423978418112,
-0.03044731914997101,
-0.021486392244696617,
-0.007377677597105503,
0.047652654349803925,
0.029311858117580414,
0.006721772253513336,
-0.013138668611645699,
0.03304792568087578,
-0.0398569293320179,
0.02961364947259426,
0.026843592524528503,
-0.05064189061522484,
-0.017717866227030754,
0.004182123579084873,
0.03145992010831833,
-0.06985923647880554,
-0.021338488906621933,
-0.04419398307800293,
-0.01418772991746664,
0.025180276483297348,
0.018128493800759315,
-0.0006804069853387773,
0.01601891592144966,
-0.007200479507446289,
0.019800709560513496,
-0.04709112271666527,
0.03503348305821419,
-0.011686068028211594,
0.026439454406499863,
-0.0017320603365078568,
0.012532803229987621,
-0.0062219565734267235,
0.03159147500991821,
-0.003557502292096615,
-0.07965884357690811,
0.006849911529570818,
0.032042570412158966,
-0.029228487983345985,
0.00521441362798214,
-0.0045695132575929165,
0.014938117936253548,
0.012980246916413307,
-0.04325036704540253,
-0.014669135212898254,
0.015781642869114876,
-0.030657880008220673,
-0.035708505660295486,
0.032813478261232376,
-0.008136732503771782,
0.026621611788868904,
-0.010730979964137077,
-0.04809904471039772,
-0.007632122840732336,
0.05369047075510025,
-0.009790516458451748,
-0.024959852918982506,
0.012189749628305435,
-0.010687088593840599,
0.015902958810329437,
-0.016789881512522697,
0.039883457124233246,
-0.02939777635037899,
0.004559362772852182,
0.0675419270992279,
0.028644580394029617,
0.0019827974028885365,
0.007511017844080925,
0.006567106582224369,
-0.01999150775372982,
-0.06918144226074219,
-0.023376505821943283,
-0.0015347037697210908,
0.004286743700504303,
-0.002285846509039402,
-0.05118807032704353,
0.05520166456699371,
0.03424299508333206,
0.01662207953631878,
-0.09292543679475784,
-0.012799517251551151,
-0.0014712548581883311,
-0.005113630089908838,
0.027525769546628,
-0.08144383132457733,
-0.015792960301041603,
0.020697612315416336,
-0.07125969976186752,
0.012909152545034885,
-0.02169746905565262,
-0.053102243691682816,
-0.039972689002752304,
0.020486930385231972,
-0.02578571066260338,
0.05724716559052467,
0.0275310967117548,
0.025771649554371834,
0.023672781884670258,
-0.0050268699415028095,
-0.0307453740388155,
0.03131876885890961,
0.02605162002146244,
-0.004289231728762388,
-0.038268476724624634,
0.019191410392522812,
0.08083797991275787,
-0.03411811590194702,
-0.04199053347110748,
0.040729910135269165,
0.007514236960560083,
0.0011066850274801254,
-0.04819171130657196,
-0.002757513662800193,
0.014642554335296154,
0.01982303522527218,
0.01178805623203516,
0.021616680547595024,
-0.012491951696574688,
-0.0073549156077206135,
0.02074052393436432,
0.007135201711207628,
-0.004177648574113846,
0.013824407942593098,
0.022203629836440086,
-0.037760067731142044,
-0.02735581062734127,
-0.012750341556966305,
0.01219649612903595,
0.0034114262089133263,
-0.020478738471865654,
0.03564475104212761,
0.02102051116526127,
-0.03457999601960182,
-0.004204477649182081,
-0.059391088783741,
0.0345400907099247,
0.010436855256557465,
0.009491173550486565,
0.02068064548075199,
0.026145819574594498,
-0.0400557816028595,
-0.028748489916324615,
-0.01563362218439579,
0.0034405547194182873,
-0.024019936099648476,
-0.05181889608502388,
-0.00896233320236206,
0.0009274634649045765,
-0.008987311273813248,
0.017821550369262695,
-0.04429479315876961,
-0.0054676588624715805,
0.06775446236133575,
0.006468066945672035,
0.027709366753697395,
0.03466646000742912,
-0.047430619597435,
-0.03218448534607887,
-0.06334274262189865,
0.012389962561428547,
-0.02395903505384922,
-0.009587067179381847,
-0.00427803210914135,
0.0020977759268134832,
0.010309409350156784,
0.006286648102104664,
-0.0024380639661103487,
-0.03281264007091522,
0.014759951271116734,
-0.019445933401584625,
-0.018596690148115158,
0.007698641158640385,
-0.060259606689214706,
0.030203912407159805,
0.001426199683919549,
-0.03301004692912102,
-0.016770921647548676,
-0.03755303844809532,
0.004924512468278408,
-0.012600605376064777,
0.03138423711061478,
-0.01863536424934864,
0.024288494139909744,
0.02324405312538147,
-0.03799571469426155,
0.04354436323046684,
-0.006326382048428059,
-0.028375163674354553,
0.06868923455476761,
0.03451501950621605,
0.01583891548216343,
-0.0034002866595983505,
-0.022616935893893242,
-0.03919929265975952,
0.01378068421036005,
-0.062349796295166016,
0.02344927377998829,
-0.05532089248299599,
-0.027136124670505524,
0.025893528014421463,
-0.02777933143079281,
0.01543292123824358,
0.033151354640722275,
-0.02347162365913391,
-0.005780783947557211,
0.04115895554423332,
-0.0163717083632946,
0.003994361497461796,
-0.029129790142178535,
0.030628997832536697,
0.030573563650250435,
-0.01592196524143219,
-0.0153112867847085,
0.04041197523474693,
0.010468566790223122,
-0.0053621078841388226,
0.005454039666801691,
0.03941358998417854,
-0.036939751356840134,
0.03638560324907303,
-0.009518795646727085,
0.01904165744781494,
-0.015472518280148506,
0.013033452443778515,
0.034391701221466064,
0.051691934466362,
0.002995995804667473,
0.023274965584278107,
0.01206200011074543,
0.08589048683643341,
-0.00469981599599123,
-0.011802852153778076,
-0.037014108151197433,
-0.007685610558837652,
-0.050382453948259354,
0.02407045103609562,
0.05406763032078743,
0.016652638092637062,
0.0031874426640570164,
-0.025828003883361816,
-0.013249373994767666,
0.006953786127269268,
0.045400481671094894,
-0.05176743119955063,
-0.00014606813783757389,
-0.017877895385026932,
0.009239031933248043,
0.02605932392179966,
0.01800292544066906,
-0.014276242814958096,
-0.0380704291164875,
0.005205526016652584,
0.0252592284232378,
0.005748688708990812,
0.004172917455434799,
-0.017304478213191032,
-0.0040292274206876755,
0.029425358399748802,
-0.07009494304656982,
-0.0043661948293447495,
0.006803078576922417,
0.0176092516630888,
0.024996554479002953,
-0.0022731611970812082
] |
<p>I have a graph that i drew and i got all the point and a question came up that what is SI Unit for intercept of a graph.</p>
<p>I have no idea what the answer is. (I'm a total newbie in Physics)</p>
| 7,613 |
[
-0.03496452793478966,
0.01423141360282898,
-0.03498256951570511,
-0.009332865476608276,
0.04491066932678223,
0.0422382615506649,
-0.032618168741464615,
-0.006016416009515524,
0.005775547586381435,
-0.03071625344455242,
0.07793626189231873,
0.01807909458875656,
0.06479579210281372,
0.04107769951224327,
-0.0021224981173872948,
0.026244232431054115,
-0.03768964856863022,
0.017543530091643333,
-0.010160989128053188,
-0.04071569815278053,
0.005853950046002865,
-0.019307352602481842,
-0.0015160979237407446,
0.05010915920138359,
-0.03653741255402565,
0.061406176537275314,
0.01981028914451599,
-0.017280438914895058,
0.022888537496328354,
0.004714561626315117,
-0.02996033988893032,
-0.018664227798581123,
0.050549641251564026,
0.02516353689134121,
0.04188127443194389,
0.007013597059994936,
0.007953396998345852,
-0.03527901694178581,
-0.0412679985165596,
0.026615556329488754,
-0.015844427049160004,
0.003892242908477783,
0.02277839183807373,
0.014800529927015305,
-0.040709998458623886,
0.01526719518005848,
-0.005851810798048973,
-0.04600004479289055,
0.06006350740790367,
-0.06473036855459213,
0.07695632427930832,
-0.007885327562689781,
0.059285517781972885,
0.011962281540036201,
-0.023844119161367416,
0.008375651203095913,
0.10235372930765152,
0.023273738101124763,
-0.0016535891918465495,
-0.04651465639472008,
0.001740179257467389,
-0.02891349047422409,
-0.006017167121171951,
-0.029229536652565002,
-0.03135964274406433,
0.014871717430651188,
-0.003449981566518545,
-0.027188917621970177,
0.05049852281808853,
0.017497846856713295,
-0.026500415056943893,
0.011784289963543415,
0.04456491768360138,
-0.03157420828938484,
0.018988972529768944,
-0.06266642361879349,
0.028425857424736023,
0.030692631378769875,
0.055524203926324844,
0.031166192144155502,
-0.021435804665088654,
0.05320154130458832,
0.044993169605731964,
0.01844630017876625,
-0.017670821398496628,
-0.004295149352401495,
0.08217916637659073,
0.010581676848232746,
0.013069063425064087,
0.014123690314590931,
-0.01442102249711752,
0.03324596583843231,
0.030662108212709427,
-0.009907313622534275,
-0.006860090885311365,
0.02440355345606804,
0.01039635669440031,
0.03869301453232765,
0.05076417326927185,
-0.017634423449635506,
0.03420524671673775,
-0.02796167880296707,
0.016955755650997162,
0.0793488398194313,
0.015273921191692352,
-0.00994131900370121,
-0.02455703169107437,
0.002223422983661294,
-0.0247789416462183,
-0.004706351086497307,
-0.025526726618409157,
0.006052305456250906,
0.0008388658170588315,
0.010282803326845169,
0.03463960066437721,
-0.02079242281615734,
-0.010797920636832714,
0.0016131375450640917,
0.04838856682181358,
0.018829748034477234,
0.022683046758174896,
-0.03579938784241676,
0.028322748839855194,
0.016898715868592262,
-0.07952172309160233,
0.01863391138613224,
-0.00040708729648031294,
0.022902529686689377,
-0.020983630791306496,
0.03381515294313431,
0.013972257263958454,
-0.025437723845243454,
0.018328871577978134,
-0.024180881679058075,
0.05074351653456688,
-0.031140154227614403,
-0.06707826256752014,
-0.07585188746452332,
0.006673444528132677,
0.016793007031083107,
-0.03556344285607338,
-0.0929919108748436,
-0.020623812451958656,
0.022785723209381104,
0.04894031956791878,
0.005592728964984417,
0.010137499310076237,
-0.0012357094092294574,
-0.011740286834537983,
-0.004675506614148617,
-0.00193269201554358,
-0.0383649542927742,
-0.003379239933565259,
-0.06911297142505646,
0.04761696606874466,
-0.018800122663378716,
0.012115460820496082,
0.0315779373049736,
-0.0405597910284996,
-0.007956295274198055,
0.03503941372036934,
-0.016996968537569046,
0.0027523653116077185,
0.04110029712319374,
-0.03711642324924469,
-0.047772787511348724,
0.08344694972038269,
0.0032361296471208334,
0.005447011440992355,
0.029736407101154327,
0.00961809977889061,
-0.0032644416205585003,
0.010020559653639793,
0.03795444965362549,
0.0518813356757164,
0.00742823863402009,
-0.04388292878866196,
-0.03459592163562775,
-0.013835654594004154,
0.013216742314398289,
-0.03488776832818985,
-0.06580918282270432,
0.007944594137370586,
0.01616501994431019,
0.00885279942303896,
0.04058649018406868,
-0.009563748724758625,
-0.004349683411419392,
0.018534574657678604,
-0.013419628143310547,
-0.03295645862817764,
-0.0446137860417366,
0.021410219371318817,
0.01406178716570139,
-0.005776391364634037,
0.001449307077564299,
0.01627884991466999,
-0.006751485634595156,
-0.027213629335165024,
-0.062271639704704285,
-0.0037290260661393404,
0.023131102323532104,
0.0076706185936927795,
-0.014103435911238194,
-0.01583792455494404,
0.05727217346429825,
0.047219160944223404,
-0.013120418414473534,
0.012741927057504654,
-0.01585274562239647,
0.007091268431395292,
0.011863043531775475,
-0.026733852922916412,
0.012096244841814041,
0.0005255278083495796,
-0.023737028241157532,
0.006236673332750797,
-0.0017031010938808322,
-0.011147917248308659,
0.05095304921269417,
-0.006801967043429613,
0.06607022136449814,
0.023430993780493736,
0.014450021088123322,
-0.028018198907375336,
0.025601891800761223,
-0.007723583839833736,
0.030624674633145332,
-0.01017200481146574,
-0.03912776708602905,
-0.049893610179424286,
-0.039896994829177856,
-0.007161907386034727,
0.013305352069437504,
-0.0006584626389667392,
-0.01814919523894787,
0.01805901899933815,
0.039577141404151917,
0.03303331509232521,
0.009105948731303215,
-0.054067280143499374,
-0.038722723722457886,
-0.0225189421325922,
0.012598637491464615,
0.003151282435283065,
0.03738492354750633,
0.018813783302903175,
0.029275361448526382,
0.02268037386238575,
-0.006816790904849768,
-0.009824629873037338,
0.025579705834388733,
-0.025072980672121048,
-0.0034592202864587307,
0.028929024934768677,
-0.03331272676587105,
0.04349060729146004,
-0.02369735762476921,
0.033076122403144836,
0.03654225170612335,
-0.014267213642597198,
-0.008420905098319054,
-0.011762762442231178,
0.0302131325006485,
-0.010491141118109226,
-0.00839310884475708,
-0.0006414250237867236,
-0.03871992230415344,
0.03231891617178917,
-0.038417741656303406,
0.03369050845503807,
0.01562976837158203,
0.013182207010686398,
-0.03319399803876877,
-0.003739437321200967,
0.020612163469195366,
0.024921702221035957,
0.02777421660721302,
-0.03909919410943985,
-0.053050361573696136,
0.028497522696852684,
-0.04794008657336235,
0.026408543810248375,
-0.00024857360403984785,
-0.0073877424001693726,
0.022752055898308754,
-0.05401146411895752,
-0.028802767395973206,
0.0024203332141041756,
-0.020298173651099205,
0.012753922492265701,
0.03601113334298134,
-0.004075706470757723,
-0.05581023916602135,
-0.014846444129943848,
-0.030189860612154007,
0.03727860003709793,
-0.017135346308350563,
-0.0019414337584748864,
0.01677638478577137,
-0.0024024168960750103,
-0.006472444161772728,
0.015499106608331203,
-0.04244581237435341,
-0.0035946699790656567,
-0.032343994826078415,
-0.023569053038954735,
0.02428896725177765,
0.011185464449226856,
-0.005620598327368498,
0.048239320516586304,
-0.025568712502717972,
0.003134838305413723,
-0.08732135593891144,
-0.06166901811957359,
0.0128576485440135,
0.016793260350823402,
0.03215203434228897,
0.009362837299704552,
-0.014913702383637428,
0.0459180511534214,
0.007171432487666607,
-0.02601504698395729,
-0.005148713476955891,
-0.020668936893343925,
-0.008100817911326885,
-0.04402932897210121,
0.059616830199956894,
0.01332439761608839,
0.035357940942049026,
-0.0001616637164261192,
0.0010756124975159764,
0.05538501963019371,
0.03182244300842285,
0.003372499719262123,
0.022101905196905136,
0.0015371964545920491,
-0.04556502029299736,
0.0053787813521921635,
0.04957319423556328,
0.02415613643825054,
-0.005942056886851788,
0.024455580860376358,
-0.00892296340316534,
0.02462625503540039,
0.022581346333026886,
0.009275093674659729,
0.03825688734650612,
-0.022727947682142258,
0.023280879482626915,
-0.045800965279340744,
0.020381683483719826,
0.009699394926428795,
-0.008040908724069595,
-0.0017623694147914648,
0.028303129598498344,
0.01808878220617771,
-0.024679262191057205,
-0.007982566952705383,
0.049847718328237534,
0.006944955326616764,
-0.024752657860517502,
-0.0062670717015862465,
-0.011681470088660717,
0.02615847811102867,
-0.015783296898007393,
-0.024482982233166695,
-0.008907456882297993,
0.048895638436079025,
0.02048518694937229,
-0.007372647523880005,
0.0177773367613554,
-0.02851005084812641,
-0.0020897809881716967,
-0.03469076752662659,
-0.032587774097919464,
0.028250806033611298,
0.05028124898672104,
0.0006419730489142239,
0.06459542363882065,
0.00047355573042295873,
0.0320880301296711,
0.007571815978735685,
-0.010365729220211506,
-0.056833285838365555,
0.013109717518091202,
-0.052009329199790955,
-0.04267466813325882,
0.008265840820968151,
-0.014863531105220318,
-0.006797014269977808,
-0.03096270188689232,
-0.007518521510064602,
0.016444342210888863,
-0.002861140063032508,
-0.0036681639030575752,
0.03623752295970917,
-0.003552224487066269,
-0.004112559370696545,
-0.024384118616580963,
0.014818570576608181,
0.0394611656665802,
-0.011891154572367668,
0.017416566610336304,
0.055325090885162354,
-0.0014913043705746531,
-0.044202521443367004,
0.013714904896914959,
0.014068023301661015,
0.04058121144771576,
0.03759992867708206,
0.029394876211881638,
-0.040594588965177536,
-0.016598327085375786,
-0.01612410880625248,
0.02488241344690323,
0.0265874732285738,
0.02832592837512493,
-0.012652719393372536,
-0.03024095483124256,
-0.0729348212480545,
-0.018918009474873543,
-0.028198134154081345,
0.05262811854481697,
-0.03960934653878212,
0.0014687984948977828,
0.003635752247646451,
0.02411593496799469,
-0.036511749029159546,
0.07382508367300034,
0.09056921303272247,
0.03487418219447136,
-0.023078180849552155,
-0.037706103175878525,
-0.02242833375930786,
-0.04077659174799919,
-0.001809091423638165,
0.004637198057025671,
0.006224582437425852,
-0.04395114257931709,
-0.002043636981397867,
0.049694351851940155,
0.006397206336259842,
-0.009595833718776703,
0.017483489587903023,
-0.005521910730749369,
0.03370613604784012,
0.014379715546965599,
-0.014106657356023788,
-0.011007747612893581,
0.06024964153766632,
0.011974056251347065,
-0.0025869475211948156,
-0.012842581607401371,
-0.09136714786291122,
0.0012512608664110303,
0.007027078419923782,
0.03536292910575867,
-0.046762872487306595,
-0.019184017553925514,
-0.04044952243566513,
0.03558892384171486,
0.041504815220832825,
-0.02420101873576641,
0.02328881062567234,
-0.03038865700364113,
0.033436790108680725,
-0.015046742744743824,
-0.0359417200088501,
-0.0555468425154686,
0.05122806876897812,
0.025211375206708908,
0.008539057336747646,
-0.018701734021306038,
0.0004513722669798881,
-0.017609478905797005,
0.00969847571104765,
0.010660412721335888,
0.0447268933057785,
0.01626315712928772,
-0.01642727479338646,
0.031459830701351166,
0.05307906121015549,
-0.023857858031988144,
-0.08310423046350479,
0.033581361174583435,
-0.019312871620059013,
-0.010487617924809456,
0.023271342739462852,
-0.012637000530958176,
-0.004710049834102392,
0.02018161304295063,
-0.0077311391942203045,
-0.009153368882834911,
-0.0031743815634399652,
-0.04566793516278267,
0.061882950365543365,
0.06698856502771378,
0.024054966866970062,
0.017923031002283096,
0.027749042958021164,
-0.018391665071249008,
-0.01321773324161768,
-0.046395786106586456,
0.045854076743125916,
-0.008739299140870571,
-0.03680981323122978,
-0.0007259699632413685,
0.00798860751092434,
-0.047317855060100555,
0.02718852460384369,
-0.020092273131012917,
0.053951334208250046,
-0.01957833394408226,
-0.06389186531305313,
-0.0018684390233829618,
0.01485526841133833,
-0.01236953679472208,
0.024114355444908142,
0.04422147944569588,
0.025949571281671524,
0.020525911822915077,
-0.039893511682748795,
0.0020623733289539814,
0.022298311814665794,
0.0023161352146416903,
0.02248639054596424,
0.016631413251161575,
-0.014907067641615868,
-0.020877834409475327,
-0.03539717569947243,
-0.01573445275425911,
-0.05016263946890831,
0.03529899939894676,
-0.04100767523050308,
0.007351770531386137,
0.004286233801394701,
-0.04151970520615578,
-0.05668846145272255,
0.010620605200529099,
0.00847428198903799,
0.026699284091591835,
-0.07162022590637207,
0.04556955024600029,
-0.03971124812960625,
0.010741019621491432,
-0.05566336587071419,
-0.0741342231631279,
0.0006091053364798427,
-0.03585918992757797,
-0.026730049401521683,
0.022666513919830322,
0.003114785999059677,
0.00360228237695992,
-0.031557418406009674,
0.013028019107878208,
0.0193945299834013,
-0.035340141505002975,
-0.037166398018598557,
-0.014887530356645584,
-0.01935235969722271,
0.044013433158397675,
0.005653103813529015,
-0.016580812633037567,
0.001826013089157641,
-0.029035557061433792,
-0.010148531757295132,
0.021038802340626717,
0.07654159516096115,
-0.018548086285591125,
-0.01007954403758049,
0.009373259730637074,
-0.03516976535320282,
0.004385614302009344,
0.01736578531563282,
0.021639477461576462,
0.027269234880805016,
0.0063261594623327255,
-0.029430817812681198,
0.017987485975027084,
0.03010237216949463,
0.011018306016921997,
0.003760328982025385,
-0.0081176171079278,
0.004387817345559597,
-0.024236256256699562,
-0.006254137959331274,
0.020238257944583893,
0.030467288568615913,
0.011288491077721119,
0.0011410416336730123,
0.04728468880057335,
0.004989139270037413,
0.008018577471375465,
0.011254456825554371,
0.0028304834850132465,
0.009568430483341217,
-0.019722824916243553,
-0.007887238636612892,
-0.0005475404905155301,
-0.01921961084008217,
-0.05826805904507637,
-0.02460312657058239,
-0.011627868749201298,
0.026117006316781044,
0.03231557831168175,
-0.009318524040281773,
0.03487195447087288,
0.007780483458191156,
-0.009302248246967793,
0.03352481499314308,
-0.021647479385137558,
-0.0011698664166033268,
-0.00863740872591734,
0.007573976647108793,
0.012993976473808289,
-0.009891858324408531,
-0.014535701833665371,
0.018641730770468712,
0.04551592096686363,
-0.003048448823392391,
0.016018923372030258,
-0.015670401975512505,
0.01627298630774021,
0.008123097941279411,
-0.01355444360524416,
-0.059892065823078156,
0.03706518933176994,
-0.012960243970155716,
0.03422365337610245,
-0.010871266946196556,
-0.048239391297101974,
0.046767208725214005,
0.00896093063056469,
0.015965715050697327,
-0.04192991182208061,
-0.0018863184377551079,
-0.02572236768901348,
-0.03174271807074547,
0.03836370259523392,
-0.026656050235033035,
-0.04415115714073181,
0.00403225002810359,
0.014756706543266773,
-0.022585410624742508,
0.04222091659903526,
-0.006301685702055693,
-0.07831965386867523,
-0.029428930953145027,
-0.04497392475605011,
-0.02389920875430107,
0.03441864624619484,
0.004648427478969097,
-0.04548466578125954,
0.03382308408617973,
-0.03226102143526077,
-0.0011669457890093327,
-0.0026071015745401382,
0.04505130276083946,
0.005411810707300901,
0.06398534029722214,
-0.005404640920460224,
0.00197777571156621,
-0.015436521731317043,
-0.00465753860771656,
0.1017155572772026,
0.07384826242923737,
0.010305508971214294,
-0.03328124061226845,
0.032259076833724976,
-0.037236299365758896,
0.008218837901949883,
-0.03487001359462738,
0.017135871574282646,
-0.025512779131531715,
0.0013926507672294974,
0.04692218080163002,
0.00372672569938004,
-0.0026045769918709993,
0.009577281773090363,
0.056607190519571304,
-0.040172744542360306,
-0.04666788876056671,
0.0011799887288361788,
0.019090062007308006,
-0.021409358829259872,
0.020397445186972618,
-0.03702897951006889,
0.010106142610311508,
-0.05562983453273773,
-0.01106806006282568,
-0.01701805181801319,
-0.012388386763632298,
0.06004605442285538,
0.023798547685146332,
-0.03624074161052704,
0.020655915141105652,
0.029844703152775764,
-0.02538173459470272,
-0.05811227485537529,
-0.005620618816465139,
0.035289306193590164,
0.018431123346090317,
0.012341450899839401,
0.024098176509141922,
-0.009579548612236977,
0.00791820790618658,
0.005374021828174591,
-0.043791063129901886,
-0.041356161236763,
-0.0392008051276207,
0.0021110072266310453,
0.0278778113424778,
0.023492878302931786,
0.022044643759727478,
-0.002031918615102768,
0.05647694319486618,
0.015895560383796692,
-0.019802076742053032,
-0.023469995707273483,
-0.029933907091617584,
0.04620945453643799,
-0.026370098814368248,
-0.022295484319329262,
-0.01443856954574585,
0.024243606254458427,
-0.013788672164082527,
0.02940056100487709,
0.006962591782212257,
-0.00846583116799593,
0.0027463382575660944,
-0.03490421548485756,
0.026515362784266472,
-0.0003133714199066162,
-0.03400271013379097,
0.05831114202737808,
-0.014509492553770542,
-0.042279813438653946,
-0.046005189418792725,
-0.010329356417059898,
0.06011613830924034,
0.020843759179115295,
-0.006168527062982321,
0.0020123024005442858,
-0.03841591253876686,
-0.032181043177843094,
0.031149590387940407,
-0.025814205408096313,
0.000645371968857944,
-0.04090183973312378,
0.013559925369918346,
0.06309524178504944,
0.04115328565239906,
-0.01789008639752865,
0.019385281950235367,
-0.019948141649365425,
0.010405683889985085,
0.04851358011364937,
-0.018000172451138496,
-0.03762850537896156,
0.02586248144507408,
-0.014632273465394974,
0.029010208323597908,
0.014099078252911568,
0.06555736064910889,
0.0375622995197773,
0.011214153841137886,
0.01783304661512375,
0.01526536326855421,
-0.0022467882372438908,
0.006377530284225941,
0.007146135438233614,
-0.0732286274433136,
0.04870617762207985,
0.005281148944050074,
-0.012516496703028679,
-0.01912693679332733,
-0.03860341012477875,
0.0033590488601475954,
0.0346825085580349,
-0.03760221228003502,
0.03802582249045372,
-0.038405586034059525,
0.041317690163850784,
-0.01566779427230358,
-0.014082327485084534,
-0.011849992908537388,
-0.0038783252239227295,
-0.05836983397603035,
-0.01374034583568573,
0.027851203456521034,
-0.01942835934460163,
-0.02566550485789776,
0.038337692618370056,
-0.006718190386891365,
0.0010532541200518608,
0.014542349614202976,
0.020883765071630478,
-0.0022603583056479692,
-0.029185989871621132,
-0.008369643241167068,
0.02392597869038582,
0.06560441851615906,
-0.0388125516474247,
-0.013724981807172298,
0.06296976655721664,
-0.032867271453142166,
-0.02897505834698677,
0.04724518582224846,
-0.013932800851762295,
0.012656670063734055,
0.020494498312473297,
0.005686214659363031,
-0.007298820652067661,
0.016560031101107597,
-0.019598189741373062,
-0.004046686924993992,
-0.013798284344375134,
-0.047315798699855804,
0.0006421108264476061,
-0.018563902005553246,
-0.03286137804389,
-0.008870410732924938,
0.048038776963949203,
0.014727978967130184,
-0.011979429982602596,
-0.015582437627017498,
0.017658870667219162,
-0.02262815088033676,
0.0146794393658638,
-0.016896478831768036,
0.028299694880843163,
-0.022942835465073586,
0.04131437465548515,
0.016630293801426888,
-0.04278379678726196,
0.02434305101633072,
0.0181023720651865,
0.0155022656545043,
-0.07704000174999237,
-0.002447183011099696,
-0.006982068531215191,
0.046873532235622406,
0.04489237442612648,
-0.05146535858511925,
-0.014005370438098907,
0.05330188572406769,
-0.05361693352460861,
0.0014152040239423513,
-0.019161483272910118,
-0.03614649921655655,
-0.03348471596837044,
-0.015617464669048786,
0.015414995141327381,
0.011118395254015923,
0.04303522780537605,
0.03160617873072624,
0.0449250303208828,
-0.006728068459779024,
0.0006892222445458174,
-0.02841232344508171,
0.01689114235341549,
0.018996695056557655,
-0.00041495103505440056,
-0.035032033920288086,
0.024936866015195847,
-0.03257424384355545,
-0.009970271959900856,
0.020013736560940742,
-0.01811796985566616,
0.00887715257704258,
0.021169964224100113,
-0.005022048484534025,
0.01705772615969181,
0.04443955048918724,
0.01012809295207262,
-0.018548617139458656,
-0.028653260320425034,
0.00903105828911066,
0.0004779794253408909,
0.07261580973863602,
0.0057975961826741695,
-0.002357857534661889,
-0.022540591657161713,
-0.07713381201028824,
-0.0383540540933609,
0.012387889437377453,
-0.006481899879872799,
-0.03238895162940025,
-0.0034014752600342035,
-0.018771303817629814,
0.03190106526017189,
-0.03704095259308815,
-0.024370254948735237,
-0.025700189173221588,
-0.018039580434560776,
0.03820737823843956,
-0.031540047377347946,
-0.0063819000497460365,
-0.022954076528549194,
0.02054985985159874,
-0.0204192865639925,
0.057414207607507706,
0.000992999761365354,
-0.0371510274708271,
-0.06410449743270874,
0.0014030563179403543,
0.01854378916323185,
-0.03892003372311592,
0.008915122598409653,
-0.011467832140624523,
-0.026008540764451027,
0.05006467550992966,
0.017933333292603493,
-0.030850417912006378,
0.01204514317214489,
-0.054626572877168655,
-0.02133185975253582,
-0.06467241793870926,
0.0502341166138649,
0.018387015908956528,
-0.004116245079785585,
-0.03231647610664368,
-0.009488269686698914,
-0.021225452423095703,
-0.0037422736641019583,
0.02639048732817173,
0.021917954087257385,
-0.03512604907155037,
-0.0007527898997068405,
0.008520846255123615,
0.038173943758010864,
-0.04048485308885574,
-0.006323571782559156,
0.028932789340615273,
-0.026851262897253036,
-0.007475708145648241,
0.012562505900859833,
0.0032441287767142057,
0.0019466605735942721,
0.018263595178723335,
0.013363718055188656,
0.016758034005761147,
-0.034647777676582336,
-0.07081107795238495,
0.0018223128281533718,
0.04410238936543465,
-0.00828816182911396,
0.07626301795244217,
0.025356408208608627,
-0.004682198632508516,
0.06311849504709244,
-0.006021114066243172,
-0.04825487360358238,
0.024236779659986496,
-0.016724471002817154,
0.016139063984155655,
-0.015428594313561916,
-0.015081851743161678,
0.002092399401590228,
-0.06013287976384163,
0.002518555847927928,
0.04802710935473442,
-0.011668113060295582,
-0.022369027137756348,
0.03025733307003975,
0.025086265057325363,
0.018359316512942314,
0.01508772186934948,
0.029017137363553047,
0.030418209731578827,
-0.007533852476626635,
0.026939254254102707,
0.02832617238163948,
-0.00013020516780670732,
-0.022901881486177444,
0.005327338818460703,
0.04676889255642891,
0.013753881677985191,
0.030176110565662384,
0.017217976972460747,
0.03846946731209755,
-0.0023548812605440617,
-0.0010917169274762273,
-0.0012890063226222992,
-0.03612952306866646,
0.054098449647426605,
0.04780667647719383,
-0.025785809382796288,
0.062286168336868286,
-0.055265795439481735,
0.023213200271129608,
-0.011563844978809357,
0.01206509955227375,
-0.06529323756694794,
-0.019854817539453506,
0.04336386173963547,
0.03630972281098366,
-0.04960942268371582,
-0.045067280530929565,
-0.014826150611042976,
-0.007261074148118496,
0.031061334535479546,
-0.08771027624607086,
0.05079001188278198,
0.012159755453467369,
-0.005265770014375448,
-0.06658267974853516,
-0.005016437266021967,
-0.0074323625303804874,
-0.03755106404423714,
0.0343170166015625,
0.029319485649466515,
-0.011634121648967266,
0.0319192074239254,
-0.009961300529539585,
-0.007855267263948917,
0.03487969562411308,
-0.06020531430840492,
-0.01603797823190689,
-0.026956187561154366,
0.06013478338718414,
0.0012162479106336832,
-0.016259662806987762
] |
<p>I've heard from a physics professor that there's no stationary platform to observe and analyze a body in motion.Why did he mention that? Is it because even seemingly stationary objects like a parked car on a road moves along with the earth's rotation? </p>
<p>As per my intuition there is a stationary platform.If you or your car is at rest then that becomes a stationary platform and you can study the kinematics of other objects.Am i right??</p>
<p>Also what is a frame of reference? Which one is intertial and non inertial?</p>
<p>(I might have not framed the question correctly.appologize for that)</p>
| 7,614 |
[
0.02429746463894844,
-0.03613650053739548,
-0.025369174778461456,
-0.018865132704377174,
0.0618286095559597,
-0.002248452277854085,
-0.013983478769659996,
-0.026249896734952927,
-0.030664075165987015,
-0.014291882514953613,
0.005979942157864571,
0.04997863620519638,
0.028392616659402847,
-0.004929516930133104,
0.03723394125699997,
0.015951309353113174,
0.0020607265178114176,
-0.012388147413730621,
-0.02409571409225464,
-0.030581409111618996,
-0.0030772476457059383,
-0.008091921918094158,
0.06585003435611725,
-0.012914641760289669,
-0.026180552318692207,
0.0020417391788214445,
0.003576788818463683,
-0.008815670385956764,
0.024262666702270508,
0.045141540467739105,
-0.028662046417593956,
-0.01953907497227192,
-0.03390256315469742,
0.031816232949495316,
0.01377309113740921,
-0.005581312347203493,
-0.022746941074728966,
-0.029897989705204964,
0.017469126731157303,
0.025092285126447678,
-0.04739398509263992,
-0.002798998961225152,
-0.0073894620873034,
0.10455410182476044,
-0.05185092240571976,
0.02211630344390869,
0.03432691469788551,
-0.005765499081462622,
0.06471920758485794,
-0.048807498067617416,
0.05762052908539772,
-0.037511542439460754,
0.011810527183115482,
0.008341234177350998,
0.006921463645994663,
0.01832687109708786,
0.08390901237726212,
0.03496110439300537,
-0.05622664466500282,
-0.045133866369724274,
-0.03512665256857872,
-0.004513448569923639,
-0.010181880556046963,
-0.027977358549833298,
-0.0014166499022394419,
0.016557080671191216,
-0.03987429663538933,
-0.00017536227824166417,
0.04356227442622185,
0.008167039602994919,
-0.006574251689016819,
0.004358154721558094,
0.03910917043685913,
-0.026863517239689827,
-0.0137711800634861,
-0.06650905311107635,
0.04601026698946953,
-0.014847812242805958,
0.0106040108948946,
0.042010050266981125,
0.015784215182065964,
-0.014321446418762207,
0.017260389402508736,
0.02062627673149109,
0.03379902243614197,
-0.04244879633188248,
0.04731239005923271,
0.0005855181952938437,
0.02474699169397354,
0.0383412204682827,
0.005376690067350864,
-0.014667928218841553,
0.012999997474253178,
-0.005971429403871298,
-0.026563545688986778,
0.032055459916591644,
-0.011287851259112358,
0.04971608519554138,
0.031765472143888474,
-0.04237517714500427,
0.015745015814900398,
-0.013413599692285061,
0.026912881061434746,
0.06951084733009338,
0.021632052958011627,
-0.0010826324578374624,
-0.01808091253042221,
0.021359408274292946,
0.01351366750895977,
0.0015175029402598739,
-0.028485670685768127,
0.017930231988430023,
0.01037284079939127,
0.02392948977649212,
0.018003525212407112,
0.0019362806342542171,
0.004268532153218985,
-0.0030094520188868046,
0.0509156808257103,
0.039739470928907394,
0.0324162021279335,
-0.027991866692900658,
-0.007615240756422281,
-0.021940533071756363,
-0.08825258165597916,
0.030409283936023712,
0.012239399366080761,
0.002626438159495592,
0.004332186188548803,
0.012203337624669075,
0.02996072918176651,
0.016792144626379013,
-0.01595531776547432,
0.02212442457675934,
0.04424777254462242,
-0.023596053943037987,
-0.11049944162368774,
-0.06116520240902901,
0.0675857663154602,
0.023314863443374634,
-0.011391431093215942,
-0.08422785997390747,
0.020536251366138458,
0.005401680711656809,
0.06506051868200302,
-0.014223143458366394,
0.008603489026427269,
0.022845908999443054,
0.022218860685825348,
-0.026222074404358864,
-0.018599335104227066,
-0.007696379907429218,
-0.0178717989474535,
-0.03605223447084427,
0.009374094195663929,
-0.06295370310544968,
0.029929136857390404,
0.02505822293460369,
0.024912379682064056,
-0.034483399242162704,
0.04534159228205681,
-0.017887769266963005,
-0.0032710351515561342,
0.013731137849390507,
-0.012003199197351933,
-0.02853776328265667,
0.06577984988689423,
-0.01200751680880785,
0.013547572307288647,
0.03000788390636444,
0.04328039288520813,
0.06476633995771408,
-0.014702857472002506,
0.01860523223876953,
0.041761450469493866,
-0.03341592103242874,
-0.049749597907066345,
0.005767175927758217,
-0.010868433862924576,
-0.011019584722816944,
-0.04962293058633804,
-0.028774652630090714,
0.02722594514489174,
-0.0033134575933218002,
-0.02380479872226715,
0.07369683682918549,
0.001254894188605249,
0.028752032667398453,
-0.017282573506236076,
-0.031246235594153404,
0.022193554788827896,
-0.06666895002126694,
0.02933388575911522,
-0.013625522144138813,
0.010713042691349983,
0.02624986506998539,
0.05182430148124695,
0.025345182046294212,
-0.04457900673151016,
-0.011485693044960499,
-0.023251179605722427,
0.036442842334508896,
0.00475401571020484,
-0.02209954708814621,
0.0011154880048707128,
0.03904489055275917,
0.026352649554610252,
0.02948749251663685,
-0.0067764571867883205,
0.001954275881871581,
-0.024592993780970573,
0.009085866622626781,
-0.02288004942238331,
0.01707930862903595,
0.011274563148617744,
-0.0027589851524680853,
-0.014700660482048988,
-0.0004289114731363952,
-0.02613234706223011,
0.05232866108417511,
-0.015521961264312267,
0.0837302878499031,
0.017713036388158798,
-0.025765078142285347,
0.008382358588278294,
0.027361726388335228,
0.005431788973510265,
-0.025493882596492767,
0.014530814252793789,
-0.018647504970431328,
-0.04625510051846504,
-0.02060525305569172,
0.011959117837250233,
0.02937910705804825,
-0.05653344839811325,
0.014443648979067802,
0.04768054559826851,
0.049602895975112915,
0.020766638219356537,
0.0016257043462246656,
-0.020076939836144447,
-0.05073220655322075,
0.014666846953332424,
-0.01535975281149149,
0.011491133831441402,
0.038689494132995605,
0.036462124437093735,
0.024081068113446236,
0.012004324235022068,
0.010302253067493439,
-0.022741783410310745,
0.04270528629422188,
0.009983264841139317,
0.002941430313512683,
0.009386172518134117,
-0.016715645790100098,
0.016600914299488068,
-0.006292836740612984,
0.016523249447345734,
0.0010098208440467715,
-0.00036332817398943007,
-0.02210303395986557,
-0.024545231834053993,
-0.009932889603078365,
-0.0118406992405653,
-0.00792010873556137,
-0.05633504316210747,
-0.00646705599501729,
0.04201308265328407,
-0.06960123777389526,
0.026583023369312286,
-0.04021910950541496,
-0.017907610163092613,
-0.00023821937793400139,
0.019605087116360664,
0.039226483553647995,
0.015586904250085354,
0.038146328181028366,
-0.02115868404507637,
-0.012949970550835133,
-0.04406348243355751,
-0.04525485634803772,
-0.01353023573756218,
0.006755922455340624,
-0.05193202197551727,
0.029850637540221214,
-0.025568628683686256,
-0.03074946254491806,
0.015424770303070545,
-0.01172707974910736,
0.013116724789142609,
0.041291456669569016,
-0.016529379412531853,
-0.06152462586760521,
-0.0063276151195168495,
-0.0033093320671468973,
0.00020199557184241712,
-0.03358425199985504,
-0.01203834731131792,
0.03346536308526993,
-0.009938648901879787,
-0.002295569283887744,
0.0018081854796037078,
-0.07175735384225845,
-0.04424060136079788,
0.0009467501076869667,
-0.0004066597030032426,
0.05450744181871414,
-0.03359654173254967,
-0.0005324185476638377,
0.006327715236693621,
-0.036768391728401184,
0.02016804926097393,
-0.010128983296453953,
-0.07118726521730423,
0.007984711788594723,
0.013596554286777973,
0.03637019172310829,
-0.0027212356217205524,
0.009266219101846218,
0.07236290723085403,
0.01369138527661562,
-0.03907018154859543,
-0.035129059106111526,
0.010942011140286922,
-0.027887869626283646,
-0.03183269500732422,
-0.0035105845890939236,
0.01029972080141306,
-0.026494331657886505,
0.01004831399768591,
0.03895680978894234,
-0.015972841531038284,
0.02519669383764267,
0.03019327111542225,
0.006472223903983831,
-0.03074333816766739,
-0.016573451459407806,
0.0197102352976799,
0.025836672633886337,
0.013941986486315727,
-0.05831917002797127,
0.0026292717084288597,
-0.021217238157987595,
0.037898510694503784,
0.01858333870768547,
-0.03660472109913826,
0.048726290464401245,
-0.0006299944943748415,
0.000563210342079401,
-0.029314279556274414,
0.023157110437750816,
0.0005016517825424671,
0.032081760466098785,
-0.03462823107838631,
0.008551981300115585,
0.04281528666615486,
-0.004694778006523848,
0.0037506490480154753,
0.03002094104886055,
0.011974710039794445,
-0.06041527912020683,
-0.028561444953083992,
-0.013822315260767937,
-0.0015584793873131275,
-0.002877592109143734,
-0.006074158009141684,
-0.058288540691137314,
0.0238722562789917,
0.03631388768553734,
-0.006061336025595665,
0.016957666724920273,
-0.03181503340601921,
-0.01373214926570654,
-0.056405019015073776,
0.00458527309820056,
0.020332258194684982,
0.00928514450788498,
0.004086783155798912,
0.01026082318276167,
-0.003971345257014036,
0.010853376239538193,
0.029935305938124657,
-0.007797053549438715,
-0.042573388665914536,
0.05494004115462303,
-0.052858561277389526,
-0.014108594506978989,
-0.020473282784223557,
0.006977852433919907,
0.011756716296076775,
-0.023770250380039215,
-0.0057989973574876785,
0.0005419510416686535,
-0.002953119808807969,
-0.05645158141851425,
-0.006695014890283346,
-0.021438293159008026,
-0.057711582630872726,
-0.011757655069231987,
0.017190031707286835,
0.05666818469762802,
-0.02117089554667473,
0.01647755689918995,
0.007205040659755468,
-0.012613154016435146,
-0.018702400848269463,
0.017199337482452393,
-0.0298969317227602,
-0.003010412212461233,
0.009649893268942833,
0.02288268692791462,
0.02330402471125126,
0.004303238820284605,
0.02971016801893711,
-0.014505712315440178,
0.04143676534295082,
-0.007491454016417265,
-0.02229311130940914,
-0.027844013646245003,
-0.041816048324108124,
-0.0005885525606572628,
-0.01613171584904194,
0.03488446772098541,
-0.013203360140323639,
-0.018164468929171562,
0.02695358172059059,
0.005456399638205767,
-0.011309633031487465,
0.027097269892692566,
0.04342369735240936,
0.022546080872416496,
0.0070696319453418255,
-0.07520023733377457,
-0.030419396236538887,
-0.0341905876994133,
0.004767739679664373,
0.0401405468583107,
0.013268871232867241,
-0.015436754561960697,
0.00923172291368246,
0.012258126400411129,
0.014417476020753384,
0.018629517406225204,
0.004789786413311958,
-0.0496646873652935,
0.029220303520560265,
0.014196548610925674,
-0.00720366183668375,
-0.016241254284977913,
0.04153654724359512,
0.06282764673233032,
0.01785881817340851,
-0.01623600535094738,
-0.09145466238260269,
0.019903715699911118,
0.031348783522844315,
-0.009334344416856766,
-0.015896372497081757,
-0.01239042542874813,
-0.04256216064095497,
0.008112452924251556,
0.05616392940282822,
-0.029302382841706276,
0.029013410210609436,
-0.029192792251706123,
-0.009287155233323574,
-0.01968870684504509,
-0.022831067442893982,
-0.012966813519597054,
-0.05821554362773895,
-0.04158778488636017,
0.009365924634039402,
-0.02970804274082184,
-0.015101112425327301,
-0.03126438334584236,
0.02531948871910572,
-0.006532657891511917,
0.01703662797808647,
0.04528064280748367,
0.03233764320611954,
0.0024721412919461727,
0.03673482686281204,
-0.016856705769896507,
-0.06737424433231354,
-0.014811723493039608,
0.02883037179708481,
-0.02377619408071041,
0.03965097665786743,
-0.03471323847770691,
-0.03255743533372879,
-0.0047455583699047565,
0.007041435223072767,
-0.029735246673226357,
0.020817982032895088,
-0.067576564848423,
-0.006393420975655317,
0.00211259163916111,
0.016545254737138748,
0.03451794385910034,
0.016054930165410042,
0.007496126461774111,
-0.013333761133253574,
0.011480817571282387,
0.039750147610902786,
-0.04022139683365822,
-0.025706134736537933,
-0.018612178042531013,
-0.003655858337879181,
-0.0561460480093956,
0.04284096136689186,
-0.005727925803512335,
0.010715094394981861,
0.004930485505610704,
-0.021491192281246185,
-0.03239313140511513,
0.05878116935491562,
0.03491399437189102,
-0.005761124659329653,
-0.03284154087305069,
0.011221198365092278,
-0.028252827003598213,
-0.03653303161263466,
-0.013278394937515259,
0.0023562980350106955,
-0.011467435397207737,
0.02808285504579544,
0.01568697951734066,
0.02557440847158432,
-0.05401494354009628,
-0.02611059509217739,
0.014286426827311516,
-0.03269585594534874,
0.03282001242041588,
0.0003366644377820194,
0.016920313239097595,
0.03916504234075546,
-0.0984296128153801,
-0.052345260977745056,
0.01110393088310957,
-0.01783186011016369,
0.012402811087667942,
-0.058184485882520676,
0.025757040828466415,
0.02353423461318016,
0.01832047663629055,
-0.07679396867752075,
-0.06415366381406784,
0.015169628895819187,
-0.0028322702273726463,
0.0021502284798771143,
-0.033679328858852386,
0.032463040202856064,
-0.0027522461023181677,
-0.042003657668828964,
-0.015441911295056343,
0.03371034562587738,
-0.01432077493518591,
-0.026685141026973724,
0.020515166223049164,
-0.014965697191655636,
0.034042827785015106,
-0.03714983910322189,
-0.02177364192903042,
0.009685097262263298,
-0.009285048581659794,
-0.006893647834658623,
-0.03761902451515198,
0.058479323983192444,
-0.0060639213770627975,
-0.0029062849935144186,
-0.02202032320201397,
-0.00981978140771389,
0.011659534648060799,
0.009521392174065113,
0.028897849842905998,
0.05108516290783882,
-0.002335561206564307,
-0.006448620930314064,
-0.03102410025894642,
0.02810685709118843,
0.0011239481391385198,
-0.0040598479099571705,
-0.014552971348166466,
0.02103699930012226,
0.0112893832847476,
-0.05674103647470474,
0.023176010698080063,
-0.03402963653206825,
0.014307231642305851,
0.015358109958469868,
0.02025867998600006,
-0.006110601592808962,
0.029271617531776428,
0.027437269687652588,
0.008516883477568626,
0.027613630518317223,
0.0031831974629312754,
0.006380443461239338,
-0.0013297906843945384,
0.010448160581290722,
-0.007805646862834692,
-0.018334249034523964,
-0.0023030759766697884,
-0.004325125366449356,
0.04352101311087608,
-0.00534438481554389,
0.06751760840415955,
0.0668833926320076,
0.02848590910434723,
0.014332777820527554,
0.01003250852227211,
0.012352041900157928,
0.015256245620548725,
0.0065823025070130825,
0.04337920621037483,
-0.03685389459133148,
-0.0011615605326369405,
0.03746534138917923,
0.06204141303896904,
0.005728938616812229,
0.01680067740380764,
0.01610546186566353,
0.010218375362455845,
0.022757260128855705,
0.03708009421825409,
-0.017805466428399086,
0.003982470836490393,
-0.006081975065171719,
0.047193195670843124,
-0.0031073358841240406,
-0.028731202706694603,
0.03996608778834343,
0.0032294848933815956,
0.05730124190449715,
-0.04909706488251686,
0.00258747860789299,
-0.05979422107338905,
0.021258268505334854,
-0.02837483212351799,
0.032723475247621536,
-0.04772073030471802,
0.0044080582447350025,
0.023445798084139824,
-0.007357732392847538,
0.013362652622163296,
-0.018440360203385353,
-0.0731169655919075,
-0.0718793198466301,
-0.045741498470306396,
-0.019219771027565002,
0.06113212928175926,
0.006433369126170874,
-0.01189059391617775,
-0.0007838090532459319,
-0.01577022485435009,
0.013938016258180141,
-0.0008944389410316944,
0.06795796751976013,
-0.0394117534160614,
0.07896595448255539,
-0.022846441715955734,
0.009075074456632137,
-0.006064121145755053,
0.0373840294778347,
0.08447469770908356,
0.0232350192964077,
0.008263996802270412,
-0.04961591586470604,
0.009496484883129597,
-0.0060979099944233894,
0.02364729717373848,
-0.03644624724984169,
0.04742143303155899,
0.01132641639560461,
0.028877127915620804,
0.019674494862556458,
0.017754871398210526,
0.011785450391471386,
-0.022549843415617943,
0.06869275122880936,
-0.0440814346075058,
-0.015583069995045662,
-0.01666698046028614,
0.021250398829579353,
-0.005985506344586611,
0.007898076437413692,
-0.008438456803560257,
0.05078984051942825,
-0.01061844639480114,
-0.03068050742149353,
-0.005076527129858732,
-0.05381559208035469,
0.005449481774121523,
0.010649419389665127,
-0.045316774398088455,
-0.006045214366167784,
0.00667148269712925,
-0.009349132888019085,
-0.037799615412950516,
0.026116423308849335,
0.010604262351989746,
-0.008606326766312122,
0.024137679487466812,
0.024618327617645264,
-0.002558260690420866,
0.0025043801870197058,
-0.014068909920752048,
-0.02364976890385151,
-0.005064900033175945,
0.014423288404941559,
-0.04865419864654541,
0.0516427718102932,
-0.020345158874988556,
-0.005087021738290787,
-0.042532727122306824,
-0.01110426802188158,
-0.00030362841789610684,
-0.06941725313663483,
-0.023110777139663696,
-0.004601871594786644,
0.018284544348716736,
-0.005278823897242546,
-0.02686431258916855,
-0.048269122838974,
0.005188004579395056,
0.0025302788708359003,
0.0006215603789314628,
0.027994003146886826,
0.03061777725815773,
0.013166205026209354,
0.008070441894233227,
0.04072814807295799,
-0.03403601795434952,
-0.009457552805542946,
-0.014765390194952488,
-0.03241722658276558,
-0.020071974024176598,
0.005609346553683281,
0.03582706302404404,
0.016719063743948936,
0.004462500102818012,
-0.019334210082888603,
0.0044961124658584595,
-0.02496323548257351,
-0.025226116180419922,
0.01974470540881157,
-0.049295008182525635,
-0.02830042876303196,
0.029630282893776894,
-0.0001404193608323112,
0.038376666605472565,
0.0450347401201725,
-0.01842336356639862,
0.005864832084625959,
0.023678865283727646,
0.0005193196702748537,
0.027877550572156906,
-0.02375485934317112,
0.0009774331701919436,
0.04063838720321655,
-0.004894547630101442,
0.02685238979756832,
-0.06767044961452484,
0.016704516485333443,
0.05770590901374817,
-0.017550153657794,
-0.0020037665963172913,
0.02928558923304081,
-0.04634890705347061,
0.015515881590545177,
0.03078092820942402,
-0.015499969944357872,
-0.01103739533573389,
0.028168462216854095,
0.020056989043951035,
-0.04864417389035225,
-0.02133580669760704,
-0.020595647394657135,
0.0029409087728708982,
-0.010383508168160915,
0.02106601558625698,
-0.015952350571751595,
0.03476501628756523,
-0.003729452844709158,
0.04578317329287529,
-0.03035038150846958,
0.034489672631025314,
-0.05631663650274277,
0.02478737197816372,
0.04079749435186386,
0.00002772721381916199,
-0.023889465257525444,
-0.009402803145349026,
-0.02055949717760086,
-0.037678249180316925,
0.015479465946555138,
0.024943608790636063,
-0.03793913498520851,
-0.00459705013781786,
0.02993861958384514,
-0.002135962713509798,
0.034168001264333725,
-0.03181188926100731,
-0.002914820099249482,
0.04380365461111069,
-0.05667833983898163,
-0.026280289515852928,
0.04722217842936516,
-0.018626656383275986,
0.012354891747236252,
0.03515997529029846,
-0.034531090408563614,
0.007160651031881571,
0.0406058169901371,
-0.013932166621088982,
-0.007917867042124271,
0.00845238845795393,
0.0065891556441783905,
-0.039084505289793015,
-0.03946289047598839,
0.025814207270741463,
-0.031871501356363297,
-0.06286341696977615,
0.06879688799381256,
0.049514852464199066,
-0.002617575228214264,
0.010265549644827843,
-0.008245453238487244,
0.0030165722128003836,
-0.0059874472208321095,
0.012397034093737602,
0.0027616319712251425,
0.05896737799048424,
0.0533241331577301,
-0.06572206318378448,
0.02467403933405876,
0.012469768524169922,
0.023781703785061836,
-0.08658376336097717,
0.008334541693329811,
0.00267411838285625,
-0.0005250899121165276,
0.05461181700229645,
-0.026848888024687767,
-0.025108542293310165,
0.07021813839673996,
-0.09269767254590988,
-0.01258599478751421,
0.009059612639248371,
-0.06359919160604477,
-0.014785850420594215,
0.004748436622321606,
0.015182777307927608,
0.043767768889665604,
0.009199047461152077,
0.014510147273540497,
-0.001961513888090849,
0.0104764923453331,
-0.015552400611341,
-0.03424230217933655,
-0.01162798423320055,
0.05145174264907837,
-0.01789269596338272,
0.02462122030556202,
0.11272977292537689,
-0.0275057815015316,
-0.031591203063726425,
0.026085006073117256,
-0.001049392274580896,
0.0456688366830349,
-0.018870579078793526,
-0.006890241988003254,
-0.036059219390153885,
-0.0053428346291184425,
0.024504559114575386,
-0.02439996786415577,
-0.015376145020127296,
0.03967032954096794,
0.03380589559674263,
0.052647821605205536,
0.04520097002387047,
-0.0035633796360343695,
0.0045094736851751804,
-0.04052741080522537,
-0.02734454534947872,
-0.011366036720573902,
-0.0007442207424901426,
-0.004646829795092344,
0.03728828951716423,
0.029185466468334198,
0.009536641649901867,
-0.011766336858272552,
-0.03633547201752663,
-0.056650564074516296,
0.01494763046503067,
-0.010593137703835964,
-0.010953744873404503,
0.0028315926901996136,
0.006071761716157198,
-0.022911762818694115,
-0.009388480335474014,
0.023558054119348526,
0.008924729190766811,
-0.03666466102004051,
-0.08071086555719376,
-0.010312747210264206,
0.050240207463502884,
-0.05240844562649727,
-0.022406036034226418,
-0.02539350651204586,
-0.015451861545443535,
0.015237930230796337,
0.03181389719247818,
0.025533366948366165,
0.022501735016703606,
-0.005245862063020468,
-0.019399430602788925,
-0.08303146809339523,
0.05360870063304901,
0.01756730116903782,
-0.004309718497097492,
-0.06456886231899261,
-0.019608857110142708,
-0.02336243726313114,
0.01854551210999489,
0.032081302255392075,
-0.020885145291686058,
0.014764399267733097,
0.01205768994987011,
-0.027733448892831802,
-0.013271826319396496,
-0.02122962847352028,
0.016427230089902878,
-0.005691433325409889,
-0.05972224473953247,
0.021997353062033653,
-0.022195592522621155,
-0.024593418464064598,
0.0028841544408351183,
0.019152652472257614,
0.00005259253885014914,
0.08072524517774582,
-0.007835911586880684,
-0.0394589938223362,
0.041256409138441086,
0.020725198090076447,
-0.01755981147289276,
0.038075659424066544,
0.01069778110831976,
0.031956564635038376,
0.040118999779224396,
-0.040058884769678116,
-0.011208880692720413,
0.027325693517923355,
-0.0235586054623127,
0.01405965257436037,
-0.013266745954751968,
0.010378912091255188,
-0.003032033098861575,
-0.036100491881370544,
0.001970733981579542,
0.04700615629553795,
-0.002643924904987216,
-0.007221536245197058,
0.03551284968852997,
0.054402124136686325,
0.009465904906392097,
0.012047656811773777,
0.03632308170199394,
0.027285337448120117,
-0.0015944597544148564,
0.023362940177321434,
0.03101016767323017,
0.039544228464365005,
-0.010339418426156044,
0.00618903199210763,
0.056954316794872284,
0.0014887150609865785,
0.04553723707795143,
-0.013907715678215027,
0.06984537839889526,
-0.023734595626592636,
0.0022643639240413904,
-0.06587540358304977,
-0.001790201524272561,
0.046993985772132874,
0.022710124030709267,
-0.017758630216121674,
0.07042110711336136,
-0.03633595630526543,
-0.011815248057246208,
0.009597095660865307,
0.017324641346931458,
-0.012269222177565098,
0.005738074891269207,
0.017467333003878593,
0.06038183718919754,
-0.0022930875420570374,
-0.010726161301136017,
-0.020091239362955093,
-0.004084444139152765,
0.052485186606645584,
-0.015015197917819023,
0.013216152787208557,
-0.013526814058423042,
0.018155209720134735,
0.0007395421853289008,
0.018196264281868935,
0.000005255148607830051,
0.0026073975022882223,
0.023813286796212196,
0.038248658180236816,
0.012338903732597828,
-0.01632651314139366,
-0.004299335181713104,
-0.027271714061498642,
0.05180441960692406,
-0.09184739738702774,
-0.017770055681467056,
-0.019403692334890366,
0.02935699187219143,
-0.014244155026972294,
0.02999962866306305
] |
<p>Assume that the air pressure and the amount of water in the air stay constant. How can I figure out how much a change in temperature affects the relative humidity?</p>
| 7,615 |
[
-0.0018866572063416243,
-0.011240457184612751,
-0.011203338392078876,
0.008272084407508373,
0.04872673749923706,
-0.004313202574849129,
-0.02820926532149315,
-0.019650960341095924,
-0.012679655104875565,
-0.008633522316813469,
0.04125417768955231,
0.06718642264604568,
0.022843338549137115,
-0.00018740369705483317,
-0.00956715177744627,
-0.005090710241347551,
-0.016783634200692177,
-0.03320346027612686,
0.003796424949541688,
0.01697872020304203,
-0.02270515263080597,
0.017110977321863174,
-0.006585853639990091,
0.008701708167791367,
-0.030798500403761864,
0.03931000083684921,
0.034856658428907394,
-0.012558498419821262,
0.051140714436769485,
0.034908294677734375,
-0.039506711065769196,
-0.03575405478477478,
0.035066843032836914,
0.04592079669237137,
0.024042408913373947,
-0.0091526685282588,
-0.024868935346603394,
-0.0160489734262228,
-0.05432635918259621,
0.02838313765823841,
-0.03701860457658768,
-0.018034406006336212,
-0.01932503469288349,
-0.008693885989487171,
-0.03896024078130722,
0.04371018335223198,
0.03238610178232193,
0.003068993566557765,
0.04786757752299309,
-0.05933729559183121,
0.06280767917633057,
0.01815282739698887,
0.060307327657938004,
0.0683913305401802,
-0.03533797711133957,
0.02333011105656624,
0.06513644009828568,
0.0608389675617218,
-0.03434618562459946,
-0.020867953076958656,
-0.03523297235369682,
-0.03173862025141716,
-0.008985851891338825,
-0.03225267678499222,
-0.03343218192458153,
-0.007059451658278704,
-0.014964819885790348,
-0.011919441632926464,
0.030813660472631454,
-0.0017008897848427296,
0.006791727617383003,
-0.007750390097498894,
0.016288286074995995,
-0.022829417139291763,
-0.002960929414257407,
-0.02807854302227497,
-0.0018835102673619986,
0.07809588313102722,
0.03346802666783333,
0.05070113763213158,
-0.011858177371323109,
0.03581243380904198,
0.02128775417804718,
0.02769910730421543,
0.03014293499290943,
-0.05615032836794853,
0.07425642013549805,
0.0054665012285113335,
-0.005540485493838787,
0.041038066148757935,
0.010165167972445488,
-0.006063601467758417,
-0.006231068167835474,
-0.0012326198630034924,
0.0019758925773203373,
0.007653491105884314,
-0.027304958552122116,
0.02993031218647957,
-0.0097216060385108,
-0.016874056309461594,
0.02358063869178295,
-0.020269105210900307,
0.04238620400428772,
0.05499282106757164,
-0.02558867074549198,
-0.048768118023872375,
-0.016229374334216118,
-0.01071885321289301,
0.01989080011844635,
-0.00514494301751256,
-0.031250033527612686,
0.006392091978341341,
-0.03324102237820625,
-0.060500193387269974,
0.03346414864063263,
-0.019565848633646965,
0.02538013830780983,
-0.020446117967367172,
0.057722777128219604,
0.05164118856191635,
0.06421410292387009,
-0.023433301597833633,
0.01562502421438694,
-0.0026393267326056957,
-0.058159396052360535,
0.040608033537864685,
-0.010899106971919537,
-0.016818998381495476,
-0.03791620954871178,
0.016162218526005745,
-0.016631821170449257,
-0.011136244051158428,
0.017495231702923775,
-0.023354612290859222,
0.016103124246001244,
-0.014461698941886425,
-0.09824111312627792,
-0.04899035766720772,
0.0246465802192688,
-0.010069899260997772,
-0.018650969490408897,
-0.06883058696985245,
0.04386385157704353,
0.018318841233849525,
0.05032959580421448,
0.009926845319569111,
0.027186164632439613,
-0.012468462809920311,
0.008877324871718884,
0.026736343279480934,
-0.008915341459214687,
-0.012014604173600674,
0.03891869634389877,
-0.03541194275021553,
-0.02065400779247284,
-0.04866372421383858,
0.0036731287837028503,
0.076195128262043,
-0.015254532918334007,
-0.0025548352859914303,
0.06153589114546776,
0.009820733219385147,
-0.017041241750121117,
-0.015046685934066772,
0.0010900923516601324,
-0.06435412913560867,
0.05103185772895813,
-0.03079811856150627,
-0.006192054133862257,
-0.01779392547905445,
0.02434537746012211,
0.024036714807152748,
-0.04442541301250458,
0.022215159609913826,
0.08238272368907928,
0.014590330421924591,
0.013315333053469658,
-0.03370004892349243,
0.009786638431251049,
0.021222513169050217,
-0.030250750482082367,
-0.007129492703825235,
0.027212589979171753,
0.01391000859439373,
0.01071113720536232,
0.024635139852762222,
-0.013105019927024841,
-0.022796595469117165,
-0.007391396444290876,
-0.07767723500728607,
-0.024976840242743492,
-0.08769041299819946,
0.025539793074131012,
-0.001592913642525673,
0.01615777425467968,
0.015266947448253632,
0.040647245943546295,
0.02655976638197899,
-0.027407752349972725,
-0.05546564236283302,
-0.00500693591311574,
-0.007573337759822607,
0.015936773270368576,
-0.04915207251906395,
0.019459841772913933,
0.03753579407930374,
0.07220891863107681,
0.000846395269036293,
0.03611430898308754,
-0.07197561115026474,
-0.04308578744530678,
0.0030943513847887516,
-0.04213419184088707,
-0.009892946109175682,
0.002597201382741332,
-0.02362208254635334,
-0.009461532346904278,
-0.002849093172699213,
0.00335570122115314,
-0.009104709140956402,
-0.007306521292775869,
0.06694338470697403,
0.056655582040548325,
0.016924981027841568,
0.01745849847793579,
0.01572522334754467,
0.03610535338521004,
-0.0041798981837928295,
-0.010910321027040482,
-0.03539462387561798,
-0.03250215947628021,
-0.026775045320391655,
-0.0024101489689201117,
0.04040396586060524,
-0.03795722499489784,
0.024461086839437485,
0.02157728187739849,
0.0516667403280735,
0.04380890727043152,
0.030911670997738838,
0.025259198620915413,
-0.023670265451073647,
-0.002637450583279133,
0.0004578430962283164,
0.020969141274690628,
0.01977664604783058,
0.026331253349781036,
0.059706371277570724,
0.04312813654541969,
-0.0018398633692413568,
-0.01447755191475153,
0.046873390674591064,
0.011681288480758667,
0.057796660810709,
-0.0024776323698461056,
-0.04460545629262924,
0.006010723300278187,
-0.03770388290286064,
-0.007312844041734934,
0.007184413727372885,
0.010650889948010445,
0.03708595037460327,
-0.004876592196524143,
-0.0376809760928154,
0.01659500040113926,
-0.007432097103446722,
-0.02467307820916176,
0.014159238897264004,
0.04017527028918266,
-0.05627458170056343,
0.03423214703798294,
-0.02910289354622364,
0.02264203317463398,
-0.022794079035520554,
0.006950906943529844,
0.055391281843185425,
0.013066775165498257,
0.022523047402501106,
-0.003668302670121193,
-0.0544569157063961,
-0.011287398636341095,
-0.028708061203360558,
-0.037423085421323776,
-0.0014357661129906774,
-0.03099811263382435,
0.008420743979513645,
0.0044511351734399796,
-0.018954318016767502,
0.013699247501790524,
-0.022239629179239273,
-0.03172580897808075,
0.0318482480943203,
0.001253066468052566,
-0.0438925065100193,
0.0076837679371237755,
-0.04762518033385277,
-0.0074449642561376095,
-0.03266536444425583,
-0.006920983083546162,
0.022807985544204712,
-0.032625213265419006,
-0.000418921175878495,
0.030468137934803963,
-0.029937556013464928,
-0.027953485026955605,
-0.021861014887690544,
-0.022445471957325935,
0.014683393761515617,
-0.023378664627671242,
-0.0184247475117445,
0.041697245091199875,
-0.048259951174259186,
-0.016369637101888657,
-0.04123949632048607,
-0.08740825206041336,
0.0218143779784441,
0.03332788497209549,
0.06617426127195358,
-0.000073001574492082,
-0.026585061103105545,
0.054107002913951874,
-0.004766139201819897,
-0.04285050556063652,
0.008543085306882858,
-0.0011306233936920762,
-0.04306597262620926,
-0.008909938856959343,
-0.008910348638892174,
0.029087578877806664,
-0.02067471668124199,
-0.00019868074741680175,
0.07318176329135895,
-0.00908287987112999,
0.04792489483952522,
0.02401350811123848,
0.008524772711098194,
-0.030038107186555862,
0.03250711411237717,
0.012734008952975273,
0.04175497591495514,
-0.0205066055059433,
0.034157223999500275,
-0.02211889624595642,
-0.000441421230789274,
0.04411744326353073,
0.02644219622015953,
-0.018929194658994675,
0.044317103922367096,
-0.005077482666820288,
0.012138315476477146,
-0.0632040873169899,
0.09826871007680893,
-0.012110619805753231,
0.021678775548934937,
0.015759963542222977,
-0.012821130454540253,
0.03536165505647659,
0.0004000002518296242,
-0.03164516016840935,
0.09075421839952469,
0.07376441359519958,
-0.03330544754862785,
-0.021688053384423256,
0.029905138537287712,
-0.019684385508298874,
0.013816315680742264,
-0.03349785879254341,
-0.031494010239839554,
0.03134789690375328,
-0.010057724080979824,
0.020000465214252472,
0.008595279417932034,
-0.04978248104453087,
0.006334783975034952,
-0.0345403328537941,
-0.00955489743500948,
0.013942508026957512,
0.05009434372186661,
-0.014691074378788471,
0.07365526258945465,
0.0059957257471978664,
0.021815063431859016,
0.03782595321536064,
-0.017269544303417206,
-0.0366998165845871,
0.0621626116335392,
-0.02864225208759308,
-0.002779104048386216,
0.01161178294569254,
0.005482664797455072,
0.034575771540403366,
-0.0260989461094141,
-0.002540679182857275,
-0.0028341261204332113,
0.0037953222636133432,
-0.021578654646873474,
-0.008741354569792747,
-0.02298291213810444,
-0.01680118963122368,
-0.02606704831123352,
0.03461500257253647,
0.0344720259308815,
-0.016509320586919785,
0.06709684431552887,
0.06531011313199997,
-0.02283329889178276,
-0.017814094200730324,
-0.03126194328069687,
0.01695961132645607,
0.016393741592764854,
0.04594966396689415,
0.02280241996049881,
-0.0009945539059117436,
-0.0028631531167775393,
0.003217938356101513,
-0.019858071580529213,
0.018355131149291992,
0.010317963548004627,
0.016033943742513657,
-0.010231781750917435,
-0.030991336330771446,
-0.018712446093559265,
0.014744243584573269,
0.014284217730164528,
-0.042338766157627106,
0.014432299882173538,
0.03215663507580757,
-0.016437141224741936,
-0.05354604497551918,
0.041344862431287766,
0.03845204412937164,
0.011427619494497776,
0.026248393580317497,
-0.02337239310145378,
0.0051550730131566525,
-0.03002692200243473,
0.021856307983398438,
0.030009625479578972,
0.004632859956473112,
-0.02494596317410469,
-0.013430907391011715,
0.02160612866282463,
0.0007857701857574284,
-0.007081617135554552,
0.006501480005681515,
0.011784443631768227,
0.029212070629000664,
0.0061721839010715485,
-0.045878682285547256,
0.016283191740512848,
0.038451846688985825,
-0.008064680732786655,
-0.01639537513256073,
-0.021599644795060158,
-0.0797639936208725,
-0.013733578845858574,
0.03449758514761925,
0.02897712029516697,
-0.03521690517663956,
-0.007159097585827112,
-0.042360685765743256,
-0.01566728577017784,
0.08632916212081909,
-0.016641991212964058,
0.01957801915705204,
-0.0006078230799175799,
0.020903443917632103,
-0.003111504949629307,
-0.023654120042920113,
-0.018775589764118195,
0.011332747526466846,
-0.015202244743704796,
0.012278732843697071,
-0.003060407005250454,
-0.021625956520438194,
-0.022541383281350136,
0.02752084843814373,
0.04987422749400139,
0.053697369992733,
0.028306515887379646,
0.009818453341722488,
-0.01937728188931942,
-0.006139344070106745,
-0.036366526037454605,
-0.05381614342331886,
0.01828118786215782,
-0.002220607828348875,
-0.003224823158234358,
0.022928515449166298,
-0.0041618384420871735,
-0.009958077222108841,
0.031056849285960197,
-0.024169573560357094,
-0.03960837796330452,
0.002383972518146038,
-0.026622336357831955,
0.030049754306674004,
0.02083555981516838,
0.009235216304659843,
0.03758987784385681,
0.007692409213632345,
0.003265910781919956,
0.014865299686789513,
-0.017206283286213875,
0.03286843001842499,
-0.036269351840019226,
-0.017638565972447395,
-0.008886718191206455,
-0.011091251857578754,
-0.0250132754445076,
0.03728630021214485,
-0.010094189085066319,
0.030837610363960266,
0.006736056413501501,
-0.032751549035310745,
-0.023251717910170555,
-0.012675798498094082,
0.0022013355046510696,
-0.006182589568197727,
0.028318829834461212,
0.02608710527420044,
0.00830120500177145,
-0.027116455137729645,
0.014268177561461926,
-0.011289198882877827,
0.019092494621872902,
-0.0069631184451282024,
-0.03253887966275215,
0.04319547116756439,
-0.03995063155889511,
-0.018829800188541412,
0.006044725421816111,
-0.04049055650830269,
0.023601271212100983,
-0.03434096649289131,
-0.00703387800604105,
0.025768505409359932,
-0.04947908595204353,
-0.02145271748304367,
0.03430650383234024,
0.02604479342699051,
0.04395301267504692,
-0.03293959051370621,
0.021921150386333466,
0.037092968821525574,
-0.007149779237806797,
-0.055799081921577454,
-0.033376339823007584,
0.03211415931582451,
0.01752546988427639,
0.005350498482584953,
-0.09647570550441742,
-0.005748711992055178,
-0.04872148856520653,
-0.01880977489054203,
-0.017432447522878647,
0.0174461267888546,
-0.009774395264685154,
-0.003321019932627678,
-0.005388997495174408,
-0.005397184286266565,
0.06793753802776337,
-0.016199883073568344,
0.012418924830853939,
0.00026966320001520216,
-0.04130580276250839,
-0.03626827150583267,
0.0034079246688634157,
0.011412756517529488,
-0.030538689345121384,
-0.009681950323283672,
0.023138873279094696,
-0.02104414626955986,
0.04876745864748955,
-0.019342441111803055,
0.002840051194652915,
0.0117898378521204,
0.04164877533912659,
-0.010247320868074894,
-0.007297964300960302,
0.013375748880207539,
-0.005007739644497633,
0.04040047898888588,
-0.020277295261621475,
-0.010070917196571827,
-0.02967854216694832,
-0.023918937891721725,
-0.05222942307591438,
0.004073117859661579,
-0.03353404253721237,
0.009082301519811153,
0.08999671787023544,
-0.005736531224101782,
0.0015930604422464967,
0.022401239722967148,
-0.02466898411512375,
0.01100242044776678,
0.01942070946097374,
-0.023535212501883507,
-0.006622775457799435,
0.00971396267414093,
-0.02884913980960846,
-0.026140280067920685,
-0.04212886840105057,
-0.022743675857782364,
0.0845174789428711,
0.006824882235378027,
0.0826113298535347,
0.05660185590386391,
0.014589407481253147,
0.01904849335551262,
0.0004874267615377903,
-0.009329880587756634,
0.020725049078464508,
-0.019826127216219902,
0.016742244362831116,
0.002534514991566539,
0.025576915591955185,
0.001073746825568378,
0.017676882445812225,
0.006105601787567139,
0.034599918872117996,
0.01657424494624138,
0.027744868770241737,
0.024032730609178543,
-0.05434251204133034,
-0.057341743260622025,
0.034319061785936356,
-0.04227285459637642,
0.016707785427570343,
-0.01178738009184599,
-0.0031187969725579023,
0.045916084200143814,
-0.0017632355447858572,
-0.003615441033616662,
-0.032658178359270096,
-0.04489848390221596,
-0.026456180959939957,
-0.008038709871470928,
0.014386316761374474,
0.03137992322444916,
0.019772622734308243,
0.05929070711135864,
0.03822643682360649,
-0.01565220206975937,
0.0020609789062291384,
-0.010179641656577587,
-0.024744072929024696,
0.0028589365538209677,
-0.022064274176955223,
-0.030486544594168663,
0.017551109194755554,
0.013400218449532986,
-0.04656238481402397,
0.032391540706157684,
0.01607617735862732,
0.00536229507997632,
0.025006821379065514,
0.007453467231243849,
0.023508304730057716,
0.0468682199716568,
0.015677716583013535,
-0.007006851956248283,
0.004916556179523468,
0.023664291948080063,
0.10631539672613144,
0.045903053134679794,
0.010560845956206322,
-0.05101773887872696,
0.008407770656049252,
0.0016691262135282159,
-0.02586730197072029,
-0.04630352184176445,
0.02688642032444477,
-0.024022528901696205,
0.05048602819442749,
0.03855828195810318,
0.04447140544652939,
-0.03508968651294708,
0.002998603042215109,
0.07571110129356384,
-0.03994316980242729,
-0.010622440837323666,
-0.010289058089256287,
-0.006667740643024445,
-0.02482656016945839,
0.01129246037453413,
-0.015153881162405014,
0.03147843852639198,
-0.04294392839074135,
-0.015597443096339703,
-0.04748259857296944,
-0.02874097041785717,
0.00361516117118299,
-0.030555037781596184,
-0.04585257172584534,
0.035130612552165985,
0.021280696615576744,
0.015951689332723618,
-0.08579625934362411,
0.027140192687511444,
0.03795470669865608,
-0.029195573180913925,
-0.013763003051280975,
0.02006511390209198,
0.023666933178901672,
-0.012452134862542152,
-0.006585551425814629,
0.027291394770145416,
-0.03921716287732124,
-0.011173820123076439,
-0.033749520778656006,
0.011832660995423794,
0.02453300543129444,
0.006543461233377457,
0.015716638416051865,
0.024687958881258965,
-0.045167069882154465,
-0.03433717042207718,
-0.025225935503840446,
0.03818189725279808,
0.061976734548807144,
-0.028368493542075157,
-0.03916102647781372,
-0.021930767223238945,
0.018026819452643394,
-0.024131808429956436,
0.026912136003375053,
0.021885471418499947,
-0.01827417127788067,
-0.0199582539498806,
0.003192383795976639,
0.0248509980738163,
-0.04276791214942932,
-0.030471285805106163,
-0.04009296000003815,
-0.024958638474345207,
0.005234639160335064,
-0.026719830930233,
-0.022164130583405495,
-0.016671080142259598,
0.05493982136249542,
0.014598564244806767,
0.009418991394340992,
0.003792654490098357,
-0.07830904424190521,
-0.0004060408682562411,
-0.004507837817072868,
-0.00023729962413199246,
-0.02022579126060009,
0.006912454962730408,
0.013412809930741787,
0.05200568586587906,
0.013328442350029945,
-0.005067422054708004,
0.006679993588477373,
0.03653624281287193,
0.06992868334054947,
-0.052488889545202255,
-0.0010532564483582973,
-0.010679258964955807,
-0.05117107555270195,
0.005745700094848871,
0.006917749531567097,
0.0832933783531189,
0.04984460771083832,
0.02130783535540104,
0.0018255828181281686,
0.018760161474347115,
-0.036113712936639786,
0.017212839797139168,
-0.004086719360202551,
-0.036037929356098175,
-0.007394453976303339,
0.00981030985713005,
-0.022598132491111755,
-0.049768175929784775,
-0.006719974335283041,
-0.02032408118247986,
-0.007163746282458305,
-0.015936212614178658,
-0.010176575742661953,
0.01595376431941986,
0.024976888671517372,
0.007814041338860989,
0.03499025106430054,
-0.019347939640283585,
-0.018914522603154182,
-0.07121096551418304,
-0.03430629149079323,
0.030901489779353142,
0.007380800321698189,
0.00987823773175478,
0.005974780302494764,
-0.039407286792993546,
-0.009678993374109268,
0.06213700398802757,
0.002982894191518426,
0.04519737511873245,
-0.017161181196570396,
0.018985018134117126,
0.008346389047801495,
0.06798277050256729,
-0.028872329741716385,
-0.04537051543593407,
0.049922168254852295,
-0.027522243559360504,
-0.0068778907880187035,
0.021655261516571045,
0.005677415058016777,
0.046934641897678375,
0.030285781249403954,
-0.052703965455293655,
-0.006427993066608906,
0.02354622073471546,
-0.019153330475091934,
-0.0019389664521440864,
-0.0020135468803346157,
-0.006331287790089846,
0.0017492191400378942,
-0.013172163628041744,
-0.020576011389493942,
-0.02478506788611412,
-0.023172276094555855,
0.03956276550889015,
0.043010324239730835,
0.0014368620468303561,
-0.012719238176941872,
0.008756815455853939,
-0.02050534449517727,
-0.00029843481024727225,
0.00611400930210948,
0.002616364508867264,
0.040527936071157455,
0.024967603385448456,
-0.03795701265335083,
0.0041456930339336395,
0.00671088183298707,
0.008371269330382347,
-0.09832599014043808,
0.009823034517467022,
0.010577533394098282,
0.0004439550975803286,
0.04766951873898506,
-0.033121805638074875,
0.019283900037407875,
0.046382684260606766,
-0.03254380077123642,
-0.03720821440219879,
-0.022405454888939857,
0.00896066427230835,
-0.03266759216785431,
0.025995273143053055,
-0.01707509160041809,
0.03217344358563423,
0.025242196395993233,
0.03898604214191437,
0.02141762338578701,
0.005628037266433239,
0.017827870324254036,
-0.052553314715623856,
0.011429818347096443,
0.008345318026840687,
0.017852207645773888,
-0.05808143690228462,
0.00019879180763382465,
-0.006917069666087627,
-0.001082278904505074,
0.007994801737368107,
-0.05566706135869026,
-0.002017328515648842,
-0.025597071275115013,
0.017968356609344482,
-0.004243254195898771,
0.05589074268937111,
0.005400087218731642,
-0.0029131006449460983,
-0.008756645023822784,
0.00415386538952589,
0.008081710897386074,
0.008713407441973686,
-0.002987378276884556,
0.005839249584823847,
0.014062736183404922,
-0.0326719805598259,
-0.049289263784885406,
0.010419373400509357,
-0.028780244290828705,
-0.01900934986770153,
0.031303294003009796,
-0.023093417286872864,
0.006172324996441603,
-0.04263338819146156,
-0.05377323180437088,
-0.005692594218999147,
0.00033761965460143983,
0.052306775003671646,
0.003579891985282302,
-0.0375971794128418,
-0.018921030685305595,
0.021507667377591133,
-0.02670028619468212,
0.02107679843902588,
0.020063679665327072,
-0.013422307558357716,
-0.06020662561058998,
-0.0370650440454483,
0.007248454261571169,
-0.002335859229788184,
-0.032304566353559494,
-0.03164057433605194,
-0.04498739540576935,
0.01708962954580784,
0.0013293495867401361,
-0.018977753818035126,
-0.012273309752345085,
-0.03580661863088608,
0.005920097231864929,
-0.04833902791142464,
0.039388999342918396,
-0.001225622952915728,
-0.019974360242486,
-0.030497148633003235,
-0.003723759204149246,
-0.030048415064811707,
0.02801923081278801,
0.05789338797330856,
0.03218161687254906,
-0.0030753808096051216,
-0.020249443128705025,
0.024196583777666092,
0.01918199472129345,
-0.039796773344278336,
0.0073786224238574505,
0.0005647170473821461,
-0.03871224820613861,
0.025367330759763718,
-0.03539849445223808,
0.01199924387037754,
-0.002541585825383663,
0.014733475632965565,
-0.010184760205447674,
0.015563929453492165,
0.018782658502459526,
-0.005495371762663126,
0.04620577022433281,
0.02557217888534069,
-0.030855242162942886,
0.054441165179014206,
-0.015298738144338131,
0.01574661210179329,
0.02684173174202442,
-0.013791450299322605,
-0.0587245337665081,
0.02708706632256508,
-0.029622500762343407,
0.01593647710978985,
0.021515242755413055,
-0.013537437655031681,
0.012763402424752712,
-0.05906333774328232,
-0.006201537325978279,
0.013874256052076817,
-0.0544113889336586,
0.010422940365970135,
0.024834243580698967,
0.01731550320982933,
0.015041627921164036,
-0.007414571940898895,
0.03874542564153671,
0.04633639007806778,
0.0004800862225238234,
-0.018459921702742577,
0.05240572243928909,
0.05795836076140404,
-0.016764501109719276,
0.01775091141462326,
0.028494324535131454,
-0.009821177460253239,
0.01431141048669815,
0.021510181948542595,
0.03186158463358879,
-0.03550499677658081,
-0.05096810311079025,
0.013840090483427048,
-0.030653582885861397,
-0.005103432107716799,
0.02657207101583481,
-0.0017339648911729455,
0.030573993921279907,
-0.002881646156311035,
-0.01847831718623638,
-0.048209115862846375,
0.029225416481494904,
-0.03595057502388954,
0.03954572603106499,
0.032681114971637726,
0.03925808146595955,
0.015065893530845642,
0.012260226532816887,
0.026920348405838013,
0.0016108069103211164,
-0.02482220157980919,
-0.03522782772779465,
0.038939524441957474,
-0.0074982549995183945,
-0.007619860582053661,
-0.0511721670627594,
0.003726121038198471,
-0.042669158428907394,
-0.012743694707751274,
0.03673277050256729,
0.023312004283070564,
0.03752446174621582,
0.05294923484325409,
-0.012788990512490273,
-0.02691113017499447,
0.04243304207921028,
-0.06502776592969894,
-0.05731544643640518,
-0.03626574948430061,
0.004784927703440189,
-0.019715329632163048,
-0.04838353022933006
] |
<p>Consider a charge distribution $ρ_1(r)$ and the potential $φ_1(r)$ due to it. Consider another charge distribution $ρ_2(r)$ and $φ_2(r)$ due to it. Both distributions have finite extent, but are otherwise arbitrary and need not have anything to do with each other. Show that the $$∫ρ_1(r) φ_2(r) dv = ∫ρ_2(r) φ_1(r) \; dv$$ where the integrals are taken over all space. Solve this in two different ways as follows.</p>
<p>a) Consider the two collections of charges to be rigid objects that can be moved around. Start with them initially located very far apart, and then bring them together. How much work does this require. Imagine moving collection 1 toward collection 2, and then the other way around.</p>
<p>b) Consider the integral of $∫E_1 E_2 \; dv$ over all space, where $E_1$ and $E_2$ are electric fields due to the two distributions. By using the vector identity $∇ \cdot (E_1φ_2) = (∇ \cdot E_1)φ_2 + E_1 \cdot ∇φ_2$ (and similarly with the $1$'s and $2$'s switched), rewrite the integral $∫E_1 E_2 \; dv$ in two different ways.</p>
<p>This is a homework question, and I have no idea where to start. If someone could show me how to set this equation up to solve, then I would deeply be thankful. </p>
| 7,616 |
[
-0.028867121785879135,
0.05186872184276581,
-0.00013386571663431823,
0.013665578328073025,
0.022477058693766594,
-0.010488933883607388,
-0.00288787973113358,
-0.02252562716603279,
0.002773755230009556,
0.001737495418637991,
0.025434691458940506,
-0.0012274134205654263,
0.059746988117694855,
0.018751028925180435,
0.04249114915728569,
-0.021485455334186554,
0.009886307641863823,
-0.018159998580813408,
0.038233984261751175,
-0.02312028780579567,
-0.014280465431511402,
0.001567378407344222,
0.0411207377910614,
-0.022229719907045364,
-0.04319991171360016,
0.025618456304073334,
0.006637463346123695,
-0.030083930119872093,
-0.007546234875917435,
0.04951412230730057,
-0.009391739964485168,
-0.03890116512775421,
0.0072469562292099,
0.02507479302585125,
0.0016177755314856768,
-0.0011526835151016712,
-0.06663598120212555,
-0.022511707618832588,
-0.0036065741442143917,
0.012711109593510628,
-0.0431545116007328,
-0.005793075542896986,
0.0029480457305908203,
0.03422868996858597,
0.007001842372119427,
0.009514588862657547,
-0.02337603084743023,
-0.00003490843664621934,
0.05478952080011368,
-0.07457112520933151,
0.08272212743759155,
0.021455325186252594,
0.054120976477861404,
0.01701495423913002,
-0.004095342010259628,
0.00038547266740351915,
0.04249302297830582,
0.08009319007396698,
0.007497428450733423,
-0.04946489259600639,
-0.059652410447597504,
-0.00831998884677887,
-0.03505382686853409,
-0.03956640139222145,
-0.02753382921218872,
0.023332547396421432,
-0.007145299110561609,
-0.0001591337932040915,
0.02190699800848961,
-0.007086466532200575,
0.028240585699677467,
0.04287400841712952,
0.018129747360944748,
-0.03208192437887192,
0.05061228200793266,
0.01948230341076851,
0.032381534576416016,
0.01704396679997444,
0.007737157866358757,
0.027384961023926735,
-0.04022952914237976,
0.012003188952803612,
0.07179751992225647,
0.06628259271383286,
0.014601405709981918,
-0.0438711978495121,
0.05959916114807129,
0.0159566979855299,
0.015403560362756252,
-0.02209741435945034,
-0.006075832527130842,
0.007030855864286423,
0.04190940409898758,
0.024588366970419884,
-0.01941606216132641,
0.043672677129507065,
0.007660298142582178,
0.05399797856807709,
-0.013545713387429714,
-0.04400230571627617,
-0.01558464765548706,
-0.0069641899317502975,
0.037390440702438354,
0.08279900997877121,
0.009850259870290756,
-0.029055260121822357,
-0.01908186823129654,
0.003912836313247681,
-0.011531471274793148,
0.025227319449186325,
-0.02792133018374443,
0.055899787694215775,
-0.0004147056897636503,
0.007777458522468805,
0.010192321613430977,
-0.0018125856295228004,
-0.01486842893064022,
-0.012153444811701775,
0.05285540595650673,
0.07176107168197632,
0.07247482985258102,
-0.037155602127313614,
0.032890044152736664,
-0.038294799625873566,
-0.05956890434026718,
0.023291004821658134,
0.031041551381349564,
-0.018027929589152336,
-0.03625880926847458,
0.03350415825843811,
-0.013736640103161335,
-0.010410849936306477,
-0.037655267864465714,
0.008080155588686466,
0.0034199408255517483,
-0.018047954887151718,
-0.08739852905273438,
-0.03005223348736763,
-0.002839934779331088,
-0.007183947134763002,
0.003265120554715395,
-0.07003548741340637,
0.0017513720085844398,
0.01166385319083929,
0.06342069804668427,
-0.007195856887847185,
-0.03248708322644234,
0.0009886046173051,
0.05739660561084747,
0.00008995544339995831,
-0.01454097405076027,
0.0007304393802769482,
-0.011725688353180885,
-0.018125923350453377,
-0.00907580740749836,
-0.0884745866060257,
0.040652282536029816,
0.03663473203778267,
-0.007131293881684542,
-0.03142398223280907,
0.06727006286382675,
0.01256667822599411,
0.0067166611552238464,
-0.0018607242964208126,
-0.0060767848044633865,
-0.016031481325626373,
0.055911462754011154,
0.014798508025705814,
0.028956221416592598,
0.052731953561306,
0.005269065964967012,
0.028859183192253113,
-0.016638703644275665,
0.025457486510276794,
0.05024385079741478,
-0.045907843858003616,
-0.007919201627373695,
-0.030775392428040504,
-0.010360917076468468,
0.01621275581419468,
0.0010261419229209423,
-0.03213319554924965,
-0.008846593089401722,
-0.018495244905352592,
0.016259076073765755,
0.04291186481714249,
-0.005421760492026806,
-0.007872693240642548,
-0.05203477293252945,
0.010252086445689201,
-0.033058226108551025,
-0.06745322048664093,
0.028758922591805458,
-0.016361679881811142,
-0.0427369698882103,
0.04953314736485481,
-0.0170883871614933,
0.028625132516026497,
-0.02396981231868267,
-0.05140241980552673,
-0.00446113757789135,
0.03256964311003685,
-0.013943495228886604,
-0.009947563521564007,
0.0024384178686887026,
0.04471597075462341,
0.05936083942651749,
0.02729174494743347,
0.04684823006391525,
-0.027224546298384666,
0.002462842036038637,
0.011229884810745716,
-0.021064242348074913,
0.03975403308868408,
0.017930012196302414,
0.0077472832053899765,
0.01448663417249918,
0.014141322113573551,
0.017921103164553642,
0.016161112114787102,
-0.0263363067060709,
0.04729115590453148,
0.06468355655670166,
0.007036071736365557,
-0.030390845611691475,
0.04199986159801483,
-0.0069073825143277645,
0.009626542218029499,
0.008325889706611633,
-0.04781613126397133,
-0.033202338963747025,
0.010747686959803104,
0.04221159592270851,
0.017466461285948753,
-0.008639802224934101,
0.0048179347068071365,
0.0390445776283741,
0.012444180436432362,
0.0078576123341918,
-0.008955845609307289,
-0.05270027369260788,
-0.02540896274149418,
0.05445486307144165,
0.03658057749271393,
0.002686385763809085,
-0.018351905047893524,
0.01157074049115181,
-0.017657335847616196,
0.015087656676769257,
0.015524609014391899,
-0.019942572340369225,
0.05277392268180847,
0.006507429759949446,
0.029194246977567673,
0.028850890696048737,
0.004640128463506699,
0.04871191829442978,
-0.0016119935316964984,
0.046924419701099396,
0.044514596462249756,
-0.043779220432043076,
-0.0021733080502599478,
-0.0139003312215209,
0.020402224734425545,
0.027597563341259956,
-0.03150540590286255,
0.023329749703407288,
-0.019654665142297745,
0.01930058002471924,
-0.03937150165438652,
-0.00663305539637804,
0.013801323249936104,
-0.02051011100411415,
-0.007786671631038189,
-0.02010907419025898,
-0.0007964572869241238,
0.014457772485911846,
0.012028510682284832,
-0.0163546372205019,
-0.014687323942780495,
0.017047932371497154,
-0.009607383981347084,
0.03922874480485916,
0.021108489483594894,
-0.054457638412714005,
0.014600582420825958,
-0.039341699331998825,
-0.03740526735782623,
0.061684489250183105,
0.00287725985981524,
0.007190684787929058,
0.021639680489897728,
0.021085185930132866,
-0.04053850844502449,
0.013173428364098072,
0.0054257833398878574,
0.04970663785934448,
-0.029443468898534775,
-0.009694648906588554,
0.034451693296432495,
-0.01458340510725975,
-0.04260040074586868,
0.012427751906216145,
-0.03967982530593872,
-0.05005975067615509,
-0.02271881327033043,
-0.016198530793190002,
0.03719354420900345,
-0.009797902777791023,
0.014077067375183105,
-0.01622587814927101,
-0.02173306979238987,
-0.039125263690948486,
-0.06847954541444778,
-0.03620282560586929,
0.013771936297416687,
-0.0208352692425251,
0.014747874811291695,
-0.031427666544914246,
-0.06414680182933807,
0.03726358711719513,
0.029688434675335884,
-0.04597538337111473,
0.025946538895368576,
-0.01590576581656933,
-0.03154304251074791,
-0.0028276138473302126,
-0.002581169828772545,
0.030732640996575356,
-0.024203410372138023,
-0.0011183223687112331,
0.03987901285290718,
0.04076134040951729,
0.03281831741333008,
-0.02027023397386074,
-0.0212785042822361,
0.03290117532014847,
0.03523753210902214,
0.0033471400383859873,
0.027754012495279312,
-0.01469424832612276,
-0.002167492639273405,
0.01657784730195999,
-0.0017722906777635217,
-0.01008864026516676,
0.031866271048784256,
-0.03432908654212952,
0.029539313167333603,
-0.007309097796678543,
0.01792527362704277,
-0.012337039224803448,
0.02665548212826252,
0.032856836915016174,
-0.05301273986697197,
0.004713729023933411,
0.047972023487091064,
0.03849975764751434,
-0.06964873522520065,
-0.012132487259805202,
0.013654133304953575,
0.0729510560631752,
-0.012387902475893497,
-0.0741022601723671,
-0.01863623410463333,
0.015008244663476944,
0.025048427283763885,
-0.026804985478520393,
-0.05404968187212944,
0.019755780696868896,
0.00904498528689146,
0.02504645101726055,
0.003395783482119441,
-0.02121506817638874,
0.009004744701087475,
-0.0765271931886673,
0.003855266608297825,
-0.014624887146055698,
0.07788155972957611,
0.009294616058468819,
0.03550625964999199,
0.019805023446679115,
0.009202435612678528,
0.00014258490409702063,
0.026770617812871933,
-0.0968581959605217,
0.062144685536623,
0.024895837530493736,
-0.0025228275917470455,
-0.03623278811573982,
-0.007159686181694269,
0.004185905680060387,
-0.020202385261654854,
-0.018512990325689316,
-0.026875553652644157,
-0.029170136898756027,
-0.0651530921459198,
0.006757810246199369,
-0.03775401785969734,
-0.02395821548998356,
-0.02865610085427761,
0.05751122534275055,
0.014744608663022518,
-0.03860880807042122,
0.03239266201853752,
0.041599076241254807,
-0.03557279706001282,
0.018421011045575142,
-0.03583506494760513,
-0.012379728257656097,
-0.002945746062323451,
0.024898052215576172,
0.004329213872551918,
0.029767967760562897,
0.04505796730518341,
-0.011229779571294785,
-0.007604600861668587,
0.04533350095152855,
0.005659115966409445,
-0.03318614140152931,
-0.03770296648144722,
-0.04181588068604469,
-0.01711338944733143,
-0.033865299075841904,
0.07443060725927353,
-0.015239289961755276,
0.002575774909928441,
0.021934352815151215,
0.017287330701947212,
-0.008660746738314629,
0.01967502385377884,
0.05747256055474281,
0.021663250401616096,
-0.05178099870681763,
-0.05712584778666496,
-0.013038829900324345,
-0.0380103662610054,
-0.005918067879974842,
0.05183086916804314,
-0.030620817095041275,
-0.009772589430212975,
0.006386408116668463,
0.01655605435371399,
0.02129233442246914,
0.004396643023937941,
0.014344125986099243,
0.010861914604902267,
-0.02354075387120247,
0.01578340120613575,
-0.02497628703713417,
0.0185678843408823,
0.008979330770671368,
0.047679632902145386,
-0.02094305492937565,
-0.008940914645791054,
-0.08379621058702469,
0.001789140049368143,
0.012486652471125126,
-0.00527554377913475,
-0.010619868524372578,
0.02272072061896324,
-0.013792933896183968,
0.0020392080768942833,
0.031075650826096535,
-0.049355730414390564,
0.021415524184703827,
-0.0063988324254751205,
-0.02050361968576908,
-0.019361231476068497,
-0.037076517939567566,
-0.07120583206415176,
0.023608682677149773,
-0.009322033263742924,
0.026541249826550484,
-0.022160831838846207,
0.012575731612741947,
-0.007034888956695795,
0.008135947398841381,
0.03354168310761452,
0.07887674868106842,
-0.001187004498206079,
0.0037657180801033974,
-0.003682352602481842,
0.021797150373458862,
0.013052480295300484,
-0.054477375000715256,
0.03544123098254204,
-0.009984839707612991,
-0.0025335620157420635,
0.047170210629701614,
-0.042781367897987366,
-0.04189356416463852,
0.06076018884778023,
-0.00016990657604765147,
0.01893114298582077,
-0.004250365775078535,
-0.015274968929588795,
0.05378889665007591,
0.07246258854866028,
0.043490875512361526,
0.05480499565601349,
0.005954854190349579,
-0.017352845519781113,
0.015769891440868378,
-0.009984791278839111,
0.030342012643814087,
0.005817573517560959,
-0.026439597830176353,
-0.0037693229969590902,
0.0310958381742239,
-0.025359340012073517,
0.07145559787750244,
-0.00048826850252225995,
0.018556056544184685,
-0.021314308047294617,
-0.011202064342796803,
-0.011075452901422977,
0.01882953755557537,
-0.018427379429340363,
-0.024446945637464523,
-0.010670503601431847,
0.03494293615221977,
0.04644744098186493,
-0.004555196966975927,
-0.012230881489813328,
-0.003009712090715766,
-0.021764997392892838,
-0.0021877079270780087,
-0.02500395104289055,
0.024714021012187004,
-0.02061290852725506,
-0.0018744844710454345,
-0.008272461593151093,
-0.04454822465777397,
0.02948170341551304,
0.008826355449855328,
0.013917403295636177,
0.03506096079945564,
-0.05873579531908035,
-0.0527232401072979,
0.02358565293252468,
0.006892674136906862,
0.008572285994887352,
-0.05295424908399582,
0.014460986480116844,
0.016330549493432045,
0.010538541711866856,
-0.056221358478069305,
-0.03704335540533066,
0.013698314316570759,
0.025009242817759514,
0.004316260572522879,
-0.04366779699921608,
0.010352996177971363,
-0.004055251367390156,
-0.039332255721092224,
0.00437565241008997,
0.04284455254673958,
-0.03608638420701027,
-0.0012876334367319942,
0.024382350966334343,
0.019654054194688797,
0.027906646952033043,
-0.006227786652743816,
0.03155750781297684,
0.020158102735877037,
-0.04298606887459755,
-0.015513470396399498,
0.009990009479224682,
0.04990135878324509,
-0.016115693375468254,
-0.044657111167907715,
-0.014451568014919758,
-0.0033765225671231747,
0.032301608473062515,
-0.03611740842461586,
-0.031060034409165382,
0.01741722971200943,
0.018435465171933174,
0.0052513484843075275,
-0.010124470107257366,
-0.00022787413035985082,
0.01916159875690937,
0.028771059587597847,
-0.010132853873074055,
0.025645820423960686,
-0.05804158374667168,
-0.022915316745638847,
-0.002095357049256563,
0.008469553664326668,
0.006446700543165207,
0.008331671357154846,
0.06977333128452301,
-0.03857775777578354,
0.001086485804989934,
0.060397226363420486,
0.04391450434923172,
0.040469031780958176,
-0.04085696116089821,
-0.010657032951712608,
0.030861178413033485,
0.00310993823222816,
-0.017862370237708092,
0.004276038147509098,
-0.03946436196565628,
0.009098575450479984,
0.06278111785650253,
-0.03838683292269707,
0.04426991194486618,
0.03200380504131317,
0.000635914271697402,
-0.01186174526810646,
-0.004755476024001837,
-0.027784915640950203,
-0.000513054896146059,
0.013366605155169964,
0.006033151876181364,
-0.0549066886305809,
0.016209866851568222,
0.040048643946647644,
0.023647630587220192,
-0.035818662494421005,
-0.018478989601135254,
0.012661321088671684,
0.04391954094171524,
0.012725495733320713,
-0.02686915174126625,
-0.0256943441927433,
0.062218084931373596,
-0.017297828570008278,
0.03222394362092018,
0.012473201379179955,
-0.021841296926140785,
0.0804808959364891,
0.01307054702192545,
-0.010967970825731754,
-0.020078156143426895,
-0.031042685732245445,
-0.04413044825196266,
0.009731970727443695,
0.022490980103611946,
0.011514374986290932,
0.006149037275463343,
-0.0022121532820165157,
0.019660407677292824,
-0.02059456892311573,
0.013475382700562477,
0.0006833945517428219,
-0.05884821340441704,
-0.01547826174646616,
-0.04301217198371887,
-0.05454973503947258,
0.048673734068870544,
-0.007455575745552778,
-0.006027312949299812,
0.017040347680449486,
-0.016222963109612465,
0.02893373742699623,
0.05530257523059845,
0.007169623859226704,
-0.023427410051226616,
0.09802710264921188,
-0.016520032659173012,
0.04814024642109871,
-0.036347270011901855,
-0.019631903618574142,
0.0845070481300354,
0.016841024160385132,
0.04111610725522041,
-0.04056694731116295,
0.0021941878367215395,
-0.032722894102334976,
0.004398255608975887,
-0.03890998661518097,
0.020687025040388107,
-0.025969795882701874,
0.018795255571603775,
-0.006223771255463362,
0.07100804895162582,
0.026650555431842804,
0.015991726890206337,
0.0302224513143301,
-0.028808273375034332,
-0.03468921408057213,
0.008107167668640614,
0.017145363613963127,
-0.026338113471865654,
-0.0011192609090358019,
-0.054959580302238464,
0.007532528601586819,
-0.06337534636259079,
0.02028639428317547,
-0.05069306865334511,
-0.021760499104857445,
0.016520913690328598,
0.010104178451001644,
-0.02882957272231579,
0.025292951613664627,
-0.009522358886897564,
-0.03358832374215126,
-0.0007469010888598859,
0.029494954273104668,
0.04026120901107788,
-0.03205752372741699,
0.019301708787679672,
0.04321698099374771,
0.023177647963166237,
0.018638890236616135,
0.02061009593307972,
0.03154651075601578,
-0.06131104379892349,
-0.026703113690018654,
-0.050444673746824265,
0.061147160828113556,
-0.04476664587855339,
0.018394431099295616,
0.021374864503741264,
-0.0018804707797244191,
-0.01592767983675003,
-0.038291752338409424,
-0.05292912572622299,
-0.021649140864610672,
-0.00023537578817922622,
0.015784267336130142,
0.011884016916155815,
-0.046900805085897446,
0.03637593612074852,
0.012831215746700764,
0.010633221827447414,
-0.02803940139710903,
0.002774580614641309,
-0.032451704144477844,
0.03196636587381363,
0.07977964729070663,
-0.014822982251644135,
-0.02382989041507244,
-0.04922560602426529,
-0.021452268585562706,
-0.005559383891522884,
0.02825484424829483,
-0.017683936282992363,
0.025737226009368896,
0.027140460908412933,
-0.042953986674547195,
-0.02571200020611286,
-0.01158673595637083,
-0.06429240852594376,
-0.013272883370518684,
0.0214310884475708,
-0.013527692295610905,
-0.031633567065000534,
0.0060069626197218895,
0.013287519104778767,
0.019402606412768364,
0.030861858278512955,
0.0007547296700067818,
0.027606913819909096,
0.05284208804368973,
0.005334056913852692,
-0.031846486032009125,
-0.023901352658867836,
-0.051541462540626526,
-0.014465734362602234,
-0.006109311245381832,
-0.005078943446278572,
0.007246223744004965,
-0.007077214773744345,
0.009518792852759361,
0.015224277041852474,
0.021725159138441086,
-0.036985766142606735,
0.016639795154333115,
0.015298554673790932,
-0.007947893813252449,
-0.01922093704342842,
0.01611867919564247,
-0.016209380701184273,
-0.04358542710542679,
-0.005065930541604757,
0.002719227224588394,
0.002638421254232526,
0.01164952851831913,
-0.0013064307859167457,
-0.03919219598174095,
-0.03327720984816551,
-0.03965703397989273,
0.03880736231803894,
-0.0356314517557621,
0.023072367534041405,
-0.012576613575220108,
0.0028318266849964857,
-0.01152325514703989,
0.03842078521847725,
-0.012495582923293114,
0.04377776011824608,
-0.04817204922437668,
-0.032037414610385895,
0.002504190430045128,
-0.00431339256465435,
-0.004164393991231918,
-0.007789532653987408,
-0.010782178491353989,
0.0013530234573408961,
0.023716898635029793,
-0.014631720259785652,
-0.013684292323887348,
0.03491087630391121,
-0.018396060913801193,
-0.015600915998220444,
-0.017312660813331604,
0.019372649490833282,
0.04157823324203491,
0.013706323690712452,
-0.02603207714855671,
-0.017578236758708954,
0.07517943531274796,
-0.0072523667477071285,
-0.0011994767701253295,
0.00011876581265823916,
-0.0515110120177269,
-0.025675706565380096,
-0.03533841297030449,
0.009201347827911377,
-0.006646737456321716,
0.024585185572504997,
0.034345291554927826,
-0.0077192471362650394,
-0.01353949960321188,
-0.03270455822348595,
0.033697426319122314,
0.02163592539727688,
0.02577415108680725,
0.020658882334828377,
-0.010757874697446823,
0.0380440279841423,
0.08090303838253021,
-0.01735074445605278,
-0.0036051806528121233,
0.01173897460103035,
-0.016793537884950638,
-0.06653261184692383,
-0.019924724474549294,
0.0025629792362451553,
-0.038855280727148056,
0.02263440005481243,
-0.06098616123199463,
-0.00496980594471097,
0.03757347911596298,
-0.09113185852766037,
0.015703177079558372,
-0.042668525129556656,
-0.005773863289505243,
-0.025812888517975807,
-0.023166941478848457,
-0.02632681280374527,
0.02764309197664261,
0.022236144170165062,
0.046522241085767746,
0.02765302173793316,
0.013685628771781921,
0.007277888711541891,
-0.027521638199687004,
-0.02521667629480362,
0.027302861213684082,
0.0180817861109972,
-0.02534114196896553,
0.06299526244401932,
-0.01518444623798132,
-0.002017917111515999,
0.020213814452290535,
-0.012252415530383587,
-0.03138245642185211,
-0.00754349073395133,
0.012907171621918678,
0.02842613495886326,
0.028109339997172356,
-0.03334428369998932,
0.007784924935549498,
-0.013110226951539516,
0.006128364242613316,
0.02225438319146633,
-0.01743125356733799,
-0.02643945813179016,
-0.003684645751491189,
0.0244551133364439,
-0.01130602601915598,
-0.013015354983508587,
0.05073565989732742,
-0.016270790249109268,
-0.017899781465530396,
0.007214594166725874,
-0.01931820623576641,
0.02141091600060463,
-0.017607003450393677,
0.004056943114846945,
-0.032039348036050797,
-0.008957326412200928,
0.012735564261674881,
0.00004772057945956476,
-0.0009746660944074392,
0.03902897611260414,
-0.04077553376555443,
-0.02203204296529293,
0.005807861220091581,
0.018080517649650574,
-0.01593419909477234,
-0.07363007962703705,
0.01879790611565113,
0.013392680324614048,
0.01315233949571848,
0.009727316908538342,
-0.03625660017132759,
-0.05719107389450073,
0.015996122732758522,
0.019398469477891922,
0.02161416783928871,
0.0015792850172147155,
-0.00846547819674015,
-0.01598050445318222,
-0.05932902172207832,
0.02732151746749878,
0.033485569059848785,
-0.03097151219844818,
-0.016168169677257538,
-0.021305706351995468,
-0.0461309440433979,
0.04338974505662918,
0.07489168643951416,
-0.002648048335686326,
-0.05725669860839844,
-0.012790156528353691,
0.005554939620196819,
0.042251523584127426,
-0.07271715998649597,
-0.0044620456174016,
0.007136564236134291,
-0.006184502504765987,
0.04228149354457855,
0.02110891416668892,
-0.011822475120425224,
0.017941150814294815,
-0.03075423277914524,
-0.008233064785599709,
0.001701127621345222,
-0.007344559766352177,
-0.06666966527700424,
-0.035915736109018326,
-0.033465318381786346,
0.010422546416521072,
0.0338398702442646,
-0.035571400076150894,
0.032281771302223206,
-0.02746543660759926,
-0.02352900803089142,
-0.0034169016871601343,
0.007009789813309908,
-0.07260271161794662,
0.014614460989832878,
-0.017756711691617966,
-0.01771608553826809,
0.04525746777653694,
-0.046308573335409164,
-0.004853041376918554,
0.03217853978276253,
-0.019679754972457886,
-0.021298756822943687,
0.026516268029808998,
0.027704067528247833,
0.011850031092762947,
0.008689269423484802,
0.02970917336642742,
0.0003898437134921551,
0.009067313745617867,
0.0006039887084625661,
0.014154750853776932,
0.03838883340358734,
-0.013340603560209274,
0.01928205043077469,
0.060510989278554916,
-0.017383793368935585,
0.005625693593174219,
0.009907697327435017,
0.036627043038606644,
-0.011026754975318909,
-0.011065411381423473,
0.02528492361307144,
-0.011972187086939812,
-0.048124607652425766,
0.0204944871366024,
-0.01533520221710205,
0.057764120399951935,
-0.02264770306646824,
0.030869971960783005,
-0.004755473230034113,
-0.015246245078742504,
-0.005763922818005085,
0.02055640146136284,
0.02221250906586647,
0.05105846747756004,
0.0008362680673599243,
-0.0009711422608233988,
-0.0456860288977623,
0.012758884578943253,
0.013529988005757332,
0.010772901587188244,
0.039165765047073364,
-0.0090107973664999,
-0.022277090698480606,
-0.021000517532229424,
0.014440511353313923,
0.007135983556509018,
-0.0378839485347271,
-0.016646036878228188,
0.05899237468838692,
0.05423595756292343,
-0.00813831202685833,
-0.02247178740799427,
-0.024478627368807793,
0.05581264942884445,
-0.05075244978070259,
-0.03729136288166046,
-0.00801368523389101,
-0.005050002597272396,
-0.0005734189180657268,
0.012593281455338001
] |
<p>This might be little of the track but my question is more on possibility of application of principle of center of mass.<br><p>
The probability of a vehicle overturning depends more on the level of center of mass of the body above the ground, the higher it is and smaller is the base to support it, the easier it is to tumble it.<br>
In case of vehicles on the road, how much is the possibility that lives can be saved to some extent if the driver or some intelligent system in car can let go the tires to bring the center of the mass of body closer to the ground and preventing it from deviating in the traffic to a great extent.<br>
I can fully understand the momentum of the body but it might be helpful in preventing it from crossing over the divider to the other side of the road.<br>
This question is amateur but seeing these horrific videos of road accident, this thought came to me. </p>
| 7,617 |
[
-0.01191161572933197,
-0.035598695278167725,
0.007250089664012194,
-0.014604889787733555,
0.035379257053136826,
-0.0017508729360997677,
-0.028909832239151,
-0.03366956487298012,
0.0039892238564789295,
-0.017745673656463623,
-0.025605089962482452,
0.05401995778083801,
0.015778645873069763,
0.04856477677822113,
0.022060617804527283,
0.010686219669878483,
0.014364230446517467,
-0.02644258923828602,
-0.009220000356435776,
-0.039615947753190994,
-0.019632257521152496,
-0.034698083996772766,
0.008081563748419285,
0.033807989209890366,
-0.04426073655486107,
0.022036584094166756,
0.018466178327798843,
-0.020912304520606995,
-0.001955460524186492,
0.035167939960956573,
-0.01546021644026041,
-0.031657665967941284,
0.00005343623706721701,
-0.0005856941570527852,
0.02212987095117569,
-0.0034839843865484,
-0.039879776537418365,
-0.005231074057519436,
-0.020183857530355453,
-0.00214498583227396,
-0.035731881856918335,
-0.017030054703354836,
0.0025890290271490812,
0.07560335844755173,
-0.02541745826601982,
0.051436346024274826,
0.005020790733397007,
-0.026293734088540077,
0.022703513503074646,
-0.07844681292772293,
0.057561568915843964,
-0.003856470575556159,
0.02340063452720642,
0.03234687075018883,
0.02456471510231495,
-0.015229981392621994,
0.03247236832976341,
0.0633457824587822,
0.0001261281140614301,
-0.020448407158255577,
-0.025420134887099266,
0.01140737347304821,
-0.010313890874385834,
-0.021854447200894356,
-0.0357910618185997,
-0.008286705240607262,
-0.0359157919883728,
-0.017425410449504852,
0.01647072657942772,
0.03159810230135918,
-0.020180420950055122,
0.010261418297886848,
0.01046024076640606,
0.046839259564876556,
0.06693537533283234,
-0.02980385534465313,
0.019795266911387444,
0.00038656979450024664,
0.016343556344509125,
0.023131301626563072,
0.03547916188836098,
-0.023900700733065605,
0.058693964034318924,
0.04666314274072647,
0.01998100057244301,
-0.028305791318416595,
0.08232122659683228,
0.0025654316414147615,
0.03719821572303772,
0.034844622015953064,
-0.0033013182692229748,
-0.016016431152820587,
0.020478148013353348,
-0.008314182050526142,
-0.029163239523768425,
0.024995995685458183,
0.017740299925208092,
0.04560277983546257,
0.022087424993515015,
0.010736634023487568,
0.019508635625243187,
0.033552080392837524,
0.020208407193422318,
0.06138639152050018,
0.01739060878753662,
-0.02044401317834854,
-0.02650926075875759,
-0.018340250477194786,
-0.0002566410112194717,
-0.005481324158608913,
-0.0499567836523056,
0.000886834692209959,
0.007932127453386784,
0.0016974307363852859,
0.02872760221362114,
-0.0038836642634123564,
-0.0009883121820166707,
-0.030784420669078827,
0.047592997550964355,
0.01958754099905491,
0.047646161168813705,
-0.008480793796479702,
-0.012620092369616032,
-0.06060169264674187,
-0.016778716817498207,
0.02709623984992504,
0.03046787530183792,
0.021185318008065224,
-0.024493446573615074,
0.003595160786062479,
0.038939639925956726,
-0.01163571048527956,
0.0027858917601406574,
0.021785970777273178,
0.04637876898050308,
0.002065081615000963,
-0.09177495539188385,
-0.02130822278559208,
0.05482837185263634,
0.008503558114171028,
-0.020872652530670166,
-0.06654784828424454,
-0.0007186817238107324,
0.011983327567577362,
0.05585991218686104,
-0.003945378120988607,
0.024110490456223488,
0.03525969758629799,
0.00927573349326849,
0.007656141184270382,
0.03274005278944969,
-0.03979716822504997,
-0.04110827296972275,
-0.02404331974685192,
0.0008199780713766813,
-0.07698747515678406,
0.030313776805996895,
0.018556637689471245,
-0.013538327068090439,
-0.03267459571361542,
-0.023664256557822227,
-0.00730509590357542,
-0.008213534951210022,
0.00000896553410711931,
-0.04699960723519325,
-0.036299869418144226,
0.028900671750307083,
0.01089366152882576,
-0.0048346612602472305,
0.01150071993470192,
0.06556373089551926,
0.049257125705480576,
0.011002142913639545,
0.0060129291377961636,
0.02140374854207039,
-0.02240627072751522,
-0.01793750934302807,
-0.028674408793449402,
-0.0056776851415634155,
-0.04679536446928978,
-0.043221693485975266,
-0.037231337279081345,
0.03930431604385376,
0.03736862912774086,
0.02167188748717308,
0.028547855094075203,
-0.006132349371910095,
0.03890841454267502,
0.044155556708574295,
0.004860625136643648,
-0.00542272487655282,
-0.029806027188897133,
0.030164718627929688,
-0.03773245960474014,
-0.003793318523094058,
-0.030705537647008896,
-0.008121826685965061,
0.02178254909813404,
-0.05266318470239639,
0.016131756827235222,
-0.017035959288477898,
0.05378187447786331,
0.01578633300960064,
-0.01676728017628193,
-0.010073608718812466,
0.046625860035419464,
-0.00573786161839962,
-0.01599055342376232,
0.028562000021338463,
-0.008923857472836971,
-0.0478709414601326,
-0.009158296510577202,
-0.04388771951198578,
0.021266896277666092,
0.007347973994910717,
0.0014723243657499552,
0.04776015505194664,
-0.02115643583238125,
0.003336049383506179,
0.019057419151067734,
-0.02811020240187645,
0.12678387761116028,
0.056571636348962784,
0.05131339281797409,
0.028117099776864052,
0.036599647253751755,
0.020777063444256783,
-0.018091564998030663,
0.0049633728340268135,
-0.019124209880828857,
-0.0694439485669136,
-0.008816356770694256,
-0.00887995958328247,
0.02390790544450283,
-0.03543631359934807,
-0.002412572968751192,
0.044451069086790085,
0.017285550013184547,
0.027156107127666473,
0.0050794766284525394,
0.00407867506146431,
-0.018016662448644638,
0.02087492309510708,
0.011512151919305325,
0.006463282275944948,
-0.029303237795829773,
-0.029552843421697617,
-0.0008812563610263169,
-0.00830629002302885,
-0.05278078094124794,
-0.00003763126733247191,
-0.016022689640522003,
0.04000793397426605,
0.025395700708031654,
-0.00897115096449852,
0.003775401972234249,
0.022442489862442017,
-0.00014477554941549897,
0.01708025485277176,
0.03256181254982948,
0.026370622217655182,
0.006035391241312027,
-0.04269709065556526,
-0.03649921715259552,
0.03073429875075817,
0.06280576437711716,
-0.05383508279919624,
0.012458265759050846,
0.0483403354883194,
-0.047520119696855545,
-0.020737651735544205,
0.012928478419780731,
0.0047456929460167885,
-0.01276607159525156,
0.011939158663153648,
0.06800474971532822,
-0.036045659333467484,
0.032259561121463776,
-0.056045301258563995,
0.009049157612025738,
-0.0177981685847044,
0.010201947763562202,
-0.024035321548581123,
0.01731821894645691,
-0.07131128758192062,
0.019784752279520035,
-0.023940810933709145,
-0.015929054468870163,
0.041861485689878464,
0.01304837130010128,
-0.0029667606577277184,
0.008666210807859898,
0.019402537494897842,
-0.061524178832769394,
-0.03402266651391983,
-0.024845676496624947,
-0.008656295016407967,
-0.04070662707090378,
-0.023526150733232498,
0.028596388176083565,
0.004266532137989998,
-0.03972819820046425,
0.018722640350461006,
-0.02265157364308834,
-0.04630682244896889,
-0.026822248473763466,
0.029529908671975136,
0.009714526124298573,
0.0026984980795532465,
0.027509840205311775,
0.019055403769016266,
-0.0018539190059527755,
-0.002541935769841075,
-0.03654235973954201,
-0.05223320052027702,
0.020427990704774857,
-0.013605035841464996,
0.05084508657455444,
0.008425666950643063,
0.0059264651499688625,
0.07348258793354034,
0.015109061263501644,
-0.053376827389001846,
-0.008948276750743389,
-0.015333421528339386,
-0.014958403073251247,
0.004414141643792391,
-0.006300177425146103,
0.0646895319223404,
0.003157408908009529,
0.019668014720082283,
0.05511695519089699,
0.005296413321048021,
0.018300028517842293,
0.009604002349078655,
-0.024770207703113556,
-0.030971361324191093,
-0.02110154926776886,
-0.007603480946272612,
0.04565771669149399,
0.023012058809399605,
0.005611366126686335,
-0.0025312930811196566,
-0.018590956926345825,
0.05813238024711609,
-0.005650568287819624,
-0.04541951045393944,
0.03663049638271332,
0.015650639310479164,
-0.010967293754220009,
0.026610618457198143,
0.028301473706960678,
0.018656373023986816,
0.0053146095015108585,
-0.01987762749195099,
0.025561971589922905,
0.05652780458331108,
-0.01551729068160057,
0.016167722642421722,
0.00034907954977825284,
0.06125042960047722,
-0.05871732160449028,
-0.05835456773638725,
-0.00026821185019798577,
0.024659181013703346,
-0.011325337924063206,
-0.03780224919319153,
-0.00885564461350441,
0.008350672200322151,
0.06466300785541534,
0.017212938517332077,
0.04343019798398018,
-0.028164092451334,
-0.007871449925005436,
-0.079391248524189,
-0.04019361361861229,
-0.01923484541475773,
0.04042110592126846,
0.008024805225431919,
-0.0028298436664044857,
0.0485382042825222,
0.012488086707890034,
0.016194665804505348,
-0.004385750275105238,
-0.057309191673994064,
0.016118895262479782,
-0.030478481203317642,
-0.012374784797430038,
-0.013863648287951946,
-0.019896989688277245,
0.02231821045279503,
-0.0569637306034565,
-0.0184811782091856,
-0.05761164054274559,
0.012479285709559917,
-0.0471494197845459,
0.00997226219624281,
-0.046478234231472015,
-0.03666728734970093,
0.005771004594862461,
0.022267304360866547,
0.041767604649066925,
-0.0050665233284235,
-0.006633910816162825,
0.014523481950163841,
-0.04027076065540314,
-0.04201557859778404,
-0.041392289102077484,
-0.007484023459255695,
-0.0294322706758976,
0.038011398166418076,
0.019023409113287926,
0.0037550285924226046,
-0.04572943598031998,
0.015100021846592426,
0.012116437777876854,
0.018641071394085884,
0.0009826052701100707,
-0.003558605909347534,
-0.02543097361922264,
-0.03764589503407478,
-0.017083318904042244,
0.0028043410275131464,
0.0027345693670213223,
-0.046903759241104126,
-0.012640556320548058,
0.04019240289926529,
0.008455692790448666,
-0.06337243318557739,
0.03934783861041069,
0.06361853331327438,
0.036911334842443466,
0.019578440114855766,
-0.10627493262290955,
-0.029658900573849678,
0.012189836241304874,
-0.01263448502868414,
0.02291763387620449,
-0.01104965340346098,
-0.023763086646795273,
0.01211308129131794,
0.04677977412939072,
0.032603781670331955,
-0.016774097457528114,
0.022325538098812103,
-0.03866966441273689,
0.047384146600961685,
-0.01600148342549801,
-0.012282135896384716,
-0.005682813469320536,
0.037534572184085846,
0.05761146917939186,
0.027430929243564606,
0.016996407881379128,
-0.04809592664241791,
-0.022541124373674393,
0.019130976870656013,
0.026928553357720375,
-0.023445580154657364,
0.0061319186352193356,
-0.03538288176059723,
-0.03103097714483738,
0.054637420922517776,
-0.0046614669263362885,
0.026317451149225235,
-0.05030595883727074,
-0.010423779487609863,
-0.020720237866044044,
-0.015191040933132172,
-0.02987240068614483,
-0.013071726076304913,
-0.010922536253929138,
0.012175080366432667,
0.0014275945723056793,
-0.011494257487356663,
-0.011125464923679829,
0.01847466640174389,
0.005394366569817066,
0.021075932309031487,
0.030292551964521408,
-0.005583771504461765,
-0.041809167712926865,
0.05581728368997574,
-0.0609949566423893,
-0.06868132948875427,
-0.020627014338970184,
0.01617540791630745,
-0.005733321886509657,
0.018227674067020416,
-0.023435449227690697,
-0.010680661536753178,
0.025630947202444077,
0.007656528614461422,
-0.020532453432679176,
0.008654533885419369,
-0.004521468188613653,
0.014520972967147827,
0.050420667976140976,
0.0019541855435818434,
-0.002711466746404767,
0.019681338220834732,
0.004963611718267202,
0.008846970275044441,
0.01722847856581211,
0.0131069989874959,
0.03601474687457085,
0.006159439217299223,
-0.0014861479867249727,
-0.0016092166770249605,
-0.0491824746131897,
0.012375460006296635,
0.010671878233551979,
0.07695505023002625,
-0.04034564644098282,
-0.026071028783917427,
-0.05146598443388939,
0.02393965795636177,
-0.0004744498000945896,
-0.026632046326994896,
-0.0077417572028934956,
0.023735055699944496,
0.0004546720301732421,
-0.01399244088679552,
0.024536479264497757,
-0.03478498011827469,
0.029654577374458313,
0.01883656717836857,
-0.032840993255376816,
-0.006553725339472294,
-0.03768923133611679,
-0.03770650923252106,
0.009715220890939236,
-0.04533836618065834,
0.06310087442398071,
0.0071463813073933125,
0.0170834232121706,
0.06288925558328629,
-0.02052261494100094,
-0.029919877648353577,
0.02505246177315712,
-0.025747837498784065,
0.024631142616271973,
-0.050781525671482086,
0.0005423632101155818,
0.029558628797531128,
0.011167807504534721,
-0.03958476334810257,
-0.03497762233018875,
0.07996934652328491,
0.013223335146903992,
-0.0035453953314572573,
-0.0609968863427639,
-0.01678723283112049,
-0.0015466798795387149,
-0.061024751514196396,
-0.01424234826117754,
0.028398800641298294,
-0.004898018669337034,
0.02927791140973568,
0.0011433707550168037,
-0.03801672160625458,
0.03935369849205017,
0.0012448447523638606,
-0.0050079477950930595,
0.03476344421505928,
-0.02081947959959507,
-0.016476666554808617,
0.000015856654499657452,
0.05292380228638649,
-0.0233094971626997,
-0.02957208640873432,
-0.012116700410842896,
-0.011020598001778126,
0.033860012888908386,
0.006415143143385649,
0.00258971331641078,
0.011881990358233452,
0.030689125880599022,
-0.013037115335464478,
-0.000022260734112933278,
0.005300004035234451,
0.027020175009965897,
0.018245920538902283,
0.030900107696652412,
0.015561750158667564,
0.01990877091884613,
-0.08483684808015823,
0.00013944609963800758,
-0.026443254202604294,
-0.0031118521001189947,
-0.02878119982779026,
0.028607122600078583,
0.003756297053769231,
-0.0014167920453473926,
-0.00928394217044115,
-0.019256316125392914,
0.06472081691026688,
-0.02172226645052433,
0.0033699069172143936,
0.013565531931817532,
0.024728933349251747,
0.013642136938869953,
-0.037683162838220596,
-0.008907829411327839,
0.011453673243522644,
-0.004634049721062183,
-0.045979488641023636,
0.012296323664486408,
0.03127496689558029,
0.033511124551296234,
-0.020235352218151093,
0.009278976358473301,
0.00930433627218008,
0.002391230780631304,
-0.0033789905719459057,
0.010413262993097305,
-0.022174246609210968,
0.008232053369283676,
0.02208211086690426,
0.0364278107881546,
-0.0349707193672657,
0.01854250766336918,
0.04222407937049866,
0.022067224606871605,
0.025591155514121056,
-0.031039712950587273,
-0.004338392056524754,
0.016329461708664894,
-0.014286531135439873,
0.01719008944928646,
-0.03062414936721325,
-0.0015724364202469587,
0.028148725628852844,
-0.01186536718159914,
0.026597632095217705,
-0.022691428661346436,
-0.007910121232271194,
-0.025928065180778503,
0.034444574266672134,
0.007334037683904171,
-0.050755955278873444,
-0.021885719150304794,
-0.006311445031315088,
0.03336600959300995,
0.0025508934631943703,
0.0007584881968796253,
-0.048610787838697433,
-0.032370951026678085,
-0.053047195076942444,
-0.021557606756687164,
-0.06322060525417328,
0.04180080443620682,
0.03367031365633011,
0.0055933003313839436,
0.05701606348156929,
-0.016423095017671585,
0.03587685525417328,
-0.009222598746418953,
0.04633575305342674,
-0.025367606431245804,
0.06641920655965805,
0.027029206976294518,
0.007973887026309967,
0.02983539178967476,
-0.0031137759797275066,
0.13559292256832123,
0.040835894644260406,
0.0028924227226525545,
-0.0116876857355237,
-0.008339481428265572,
0.0006179999327287078,
0.02052885666489601,
-0.02748456969857216,
0.004803952760994434,
0.059252042323350906,
0.021066533401608467,
0.020052209496498108,
0.0029348237439990044,
0.008355689235031605,
-0.04677301272749901,
0.04310162365436554,
-0.025284966453909874,
-0.020946063101291656,
-0.02431483194231987,
0.0158709604293108,
-0.035125043243169785,
-0.031082559376955032,
-0.0209172535687685,
-0.00032311852555722,
0.013647761195898056,
0.009594546630978584,
-0.0479910783469677,
-0.02042251080274582,
-0.007206283509731293,
-0.02578374557197094,
-0.027973338961601257,
-0.011003641411662102,
0.01294901967048645,
-0.051222484558820724,
-0.015029245056211948,
0.015065385028719902,
0.017742818221449852,
-0.002276778919622302,
-0.002035300014540553,
0.022456957027316093,
0.02423476241528988,
0.023979557678103447,
0.020378366112709045,
-0.0008465484133921564,
-0.05797332525253296,
-0.008381503634154797,
-0.07634436339139938,
0.02413526177406311,
0.004532736726105213,
0.04687952622771263,
0.017165161669254303,
-0.018109675496816635,
0.04247575253248215,
-0.007428331766277552,
-0.029285993427038193,
0.006720393430441618,
0.005583309102803469,
0.0062906742095947266,
-0.049853499978780746,
0.0010637178784236312,
0.029870621860027313,
0.012133845128118992,
-0.026138456538319588,
0.004359519109129906,
-0.03925368934869766,
-0.05596458911895752,
0.015266435220837593,
0.09082222729921341,
-0.013481208123266697,
-0.004781472962349653,
-0.07583296298980713,
-0.00841332133859396,
-0.01990557089447975,
-0.006125928834080696,
-0.013705614022910595,
0.0023250652011483908,
-0.03795383498072624,
0.006267718970775604,
0.01609737239778042,
-0.01385485753417015,
-0.0007083696546033025,
0.015271084383130074,
-0.01145796850323677,
-0.0010795636335387826,
-0.018550286069512367,
-0.020223744213581085,
0.018552439287304878,
0.01124817319214344,
-0.060469552874565125,
-0.01132349856197834,
0.013012448325753212,
0.02483355440199375,
-0.036361731588840485,
0.005126466974616051,
-0.01445742230862379,
-0.014815346337854862,
-0.03715626522898674,
0.06903958320617676,
0.008622009307146072,
0.054326027631759644,
-0.008796959184110165,
-0.037419769912958145,
-0.0009982375195249915,
0.02258269116282463,
0.020059119910001755,
0.03941803798079491,
0.027808254584670067,
-0.04788622260093689,
-0.05209989473223686,
0.016610169783234596,
0.031513720750808716,
-0.026018232107162476,
-0.0066750734113156796,
-0.019505267962813377,
-0.03417135775089264,
-0.01811039075255394,
0.005588260479271412,
-0.008409464731812477,
0.024135837331414223,
-0.02273494377732277,
-0.00028328748885542154,
-0.011508331634104252,
0.04227611422538757,
-0.044573236256837845,
0.011098596267402172,
-0.02180665358901024,
-0.039557844400405884,
-0.02804841473698616,
0.05085831135511398,
0.028375089168548584,
0.02518041990697384,
-0.030886055901646614,
-0.001150243915617466,
-0.02709808759391308,
-0.016235195100307465,
0.011490516364574432,
0.042851753532886505,
0.07435707002878189,
-0.032864153385162354,
-0.004552002996206284,
0.07768602669239044,
-0.04429927468299866,
-0.03782764449715614,
0.03128090873360634,
0.00009095539280679077,
0.025454383343458176,
-0.014347354881465435,
0.00036707374965772033,
0.005263287574052811,
0.06008906289935112,
-0.0016305880853906274,
-0.007364897057414055,
0.019208084791898727,
0.008035180158913136,
-0.02900826744735241,
0.007869797758758068,
0.026216059923171997,
-0.029133861884474754,
-0.05767646059393883,
-0.015278981067240238,
0.038872890174388885,
-0.052486155182123184,
0.041285160928964615,
0.034913331270217896,
-0.0214742012321949,
0.014326997101306915,
-0.008745402097702026,
0.0493985116481781,
0.03886624798178673,
0.04601593688130379,
-0.02922375500202179,
-0.009642533957958221,
0.005372082814574242,
0.016658537089824677,
-0.06813731789588928,
-0.052214886993169785,
0.04088323563337326,
-0.012575256638228893,
0.06202864646911621,
-0.04083840548992157,
0.0016827477375045419,
0.01706991158425808,
-0.07592890411615372,
0.0071870312094688416,
-0.03158390894532204,
-0.03893972933292389,
-0.0602971576154232,
0.019668417051434517,
-0.002613135613501072,
0.074133962392807,
0.0031133710872381926,
0.007270763162523508,
0.03547802194952965,
0.015188818797469139,
-0.02931373566389084,
-0.010320611298084259,
0.017163317650556564,
0.04005609080195427,
-0.011377330869436264,
0.007981248199939728,
0.104655921459198,
-0.05451957881450653,
-0.039267588406801224,
0.025548798963427544,
-0.00566790672019124,
0.0075350538827478886,
-0.011376517824828625,
-0.0022531526628881693,
-0.004121828358620405,
0.006012702826410532,
-0.0026042484678328037,
-0.002278360305353999,
0.005503436550498009,
0.03523338586091995,
-0.011657832190394402,
-0.019044235348701477,
-0.02114962227642536,
0.018252704292535782,
0.025829637423157692,
-0.04199463874101639,
0.004362489562481642,
-0.0012774106580764055,
-0.009241165593266487,
-0.012889961712062359,
-0.027864720672369003,
0.04382890462875366,
-0.014146451838314533,
-0.04698700085282326,
0.030305415391921997,
-0.03738034889101982,
-0.006065603345632553,
0.01279938779771328,
0.009529395028948784,
0.02841714210808277,
0.030073115602135658,
-0.010553899221122265,
-0.02934916317462921,
-0.010715159587562084,
0.0005837603821419179,
-0.06003040820360184,
-0.03537706285715103,
0.03348777815699577,
-0.014369992539286613,
0.018891023471951485,
-0.011067639105021954,
-0.04875004291534424,
-0.004453250207006931,
0.02923552878201008,
0.03791176155209541,
0.05779712647199631,
0.03193070366978645,
-0.027514811605215073,
-0.0009682700620032847,
-0.0735718309879303,
0.006767836399376392,
-0.013617129996418953,
0.004422027617692947,
-0.004551200661808252,
-0.017357833683490753,
-0.014081550762057304,
-0.03130644932389259,
0.03301282227039337,
0.014538424089550972,
-0.004473010078072548,
0.006186823360621929,
-0.02095150202512741,
-0.004731933586299419,
0.0013161096721887589,
-0.025159625336527824,
0.0027863176073879004,
-0.014490492641925812,
-0.00272752670571208,
0.00853514764457941,
0.013089991174638271,
-0.010833177715539932,
0.015261184424161911,
-0.0006167132523842156,
0.03970243036746979,
0.019805273041129112,
-0.05036064237356186,
-0.0013025299413129687,
0.027000313624739647,
0.01896832510828972,
0.08414630591869354,
-0.008249668404459953,
0.007895532995462418,
0.008450224064290524,
-0.05717000365257263,
-0.028372758999466896,
0.032600272446870804,
-0.04750530421733856,
0.011129054240882397,
-0.03093276545405388,
-0.04086940735578537,
0.030181854963302612,
-0.04855206981301308,
-0.002837385283783078,
0.041877392679452896,
-0.05448077246546745,
0.015977388247847557,
0.016498053446412086,
0.061001092195510864,
0.05166851356625557,
0.009500679560005665,
0.036382611840963364,
0.010739642195403576,
-0.023444268852472305,
-0.030920514836907387,
0.0434107705950737,
0.018279587849974632,
-0.0020906799472868443,
0.00023684957704972476,
0.046386636793613434,
0.022457310929894447,
0.06028692424297333,
-0.009336334653198719,
0.011676209047436714,
-0.0010470256675034761,
-0.016877423971891403,
-0.0055853757075965405,
-0.006695440970361233,
0.01767781749367714,
0.017678754404187202,
0.018520144745707512,
0.07215069979429245,
0.028198981657624245,
-0.018221333622932434,
-0.015836484730243683,
-0.013415870256721973,
-0.030054273083806038,
0.014526189304888248,
0.007121886592358351,
-0.014948652125895023,
-0.007454396225512028,
-0.05002062767744064,
0.014614448882639408,
0.008342674002051353,
0.00920520257204771,
0.007331246044486761,
0.05797974392771721,
-0.015757719054818153,
0.005094751715660095,
0.03373866155743599,
-0.04159894585609436,
-0.028699874877929688,
-0.02434680238366127,
0.06447630375623703,
0.04913746938109398,
0.03297395259141922,
0.026178140193223953,
-0.013541417196393013,
0.000240855646552518,
0.03633037582039833,
-0.037351176142692566,
-0.03788374736905098,
-0.03147517144680023,
0.05566280335187912,
-0.02854389324784279,
-0.005842484533786774
] |
<p>It is well known that a <a href="http://en.wikipedia.org/wiki/SQUID" rel="nofollow">SQUID</a> can detect an extremely small magnetic flux.</p>
<p>What if the flux is time-dependent? E.g. a slow varying sinusoidal magnetic flux</p>
<p>$$\Phi=\Phi_0\sin(\omega t).$$</p>
<p>Can I still perform a real time measurement of the slow varying flux considering the induced EMF?</p>
<p>By "slow" I mean $\omega$ is smaller than Josephson frequency (AC Josephson effect due to the EMF).</p>
| 7,618 |
[
0.0269215889275074,
-0.042981553822755814,
-0.02785128355026245,
-0.03753028064966202,
0.04868410527706146,
0.004885670263320208,
-0.05229197442531586,
-0.034731633961200714,
0.026181960478425026,
-0.00892823375761509,
0.04281576722860336,
0.04322851076722145,
0.04204268380999565,
0.018205808475613594,
-0.0025281545240432024,
-0.003903242526575923,
-0.03349888697266579,
0.019077571108937263,
-0.01269912626594305,
-0.03164103254675865,
0.019149277359247208,
0.06326743215322495,
0.01659679412841797,
0.010160227306187153,
-0.015579098835587502,
0.018325142562389374,
0.007339464034885168,
0.038512252271175385,
0.014558103866875172,
0.05196092650294304,
-0.0122373066842556,
-0.05191472917795181,
0.00295728980563581,
0.023041291162371635,
0.013234889134764671,
-0.025464419275522232,
-0.07729414105415344,
-0.0630694255232811,
-0.0017006754642352462,
0.01473222766071558,
-0.03153103590011597,
0.0064957961440086365,
0.026084939017891884,
0.05798137187957764,
-0.0017030418384820223,
-0.025215180590748787,
-0.0011352128349244595,
-0.0007707069162279367,
0.011934436857700348,
-0.059805482625961304,
0.05203086882829666,
-0.021090067923069,
0.03191092610359192,
-0.027228252962231636,
0.0001440605556126684,
-0.019536413252353668,
0.06498384475708008,
0.05733570456504822,
-0.050219662487506866,
-0.03600497171282768,
-0.01320955716073513,
-0.03439708426594734,
0.03134683519601822,
-0.049330852925777435,
-0.04191402718424797,
0.022373806685209274,
-0.02096070535480976,
-0.01321730762720108,
0.020113978534936905,
-0.019191188737750053,
0.02047317661345005,
-0.003820825135335326,
-0.0144433518871665,
0.035173580050468445,
-0.007873106747865677,
-0.0402999110519886,
-0.010820506140589714,
0.03730535879731178,
0.022645996883511543,
0.06337212771177292,
-0.02828354761004448,
-0.011319959536194801,
0.02648855745792389,
0.04346705973148346,
0.02571282908320427,
0.005816440097987652,
0.03697790950536728,
-0.030468977987766266,
0.012360083870589733,
0.018618831411004066,
-0.005837535951286554,
0.03376065939664841,
0.0048914020881056786,
-0.04235103726387024,
-0.01319354958832264,
-0.02745033986866474,
0.0003342046111356467,
0.024212157353758812,
0.002985724713653326,
-0.017773590981960297,
0.03584573045372963,
-0.01462839636951685,
0.03533392399549484,
0.06547895818948746,
-0.017168311402201653,
-0.011814789846539497,
-0.0012572467094287276,
0.0013348330976441503,
-0.02026655338704586,
-0.02141549624502659,
-0.030568720772862434,
-0.00526032317429781,
0.008974875323474407,
0.022465096786618233,
0.050125181674957275,
-0.03205292671918869,
-0.00006219160422915593,
-0.04918668419122696,
0.039959974586963654,
0.07220157235860825,
0.04654131457209587,
-0.059570152312517166,
0.013642209582030773,
-0.0033849116880446672,
-0.06148248165845871,
0.03443495184183121,
0.016109272837638855,
0.011181177571415901,
-0.018938245251774788,
0.013378686271607876,
-0.011369532905519009,
-0.009893922135233879,
0.02231442742049694,
-0.015094862319529057,
0.06012653559446335,
-0.0076356492936611176,
-0.11454117298126221,
-0.04765629395842552,
0.02611972764134407,
-0.020587271079421043,
0.013798804953694344,
-0.10626144707202911,
0.01964014768600464,
0.043536242097616196,
0.04194820299744606,
0.008707222528755665,
-0.00553938141092658,
0.0036059000995010138,
0.038705237209796906,
0.0140959732234478,
-0.00183209334500134,
-0.01564321294426918,
-0.004325810354202986,
-0.020132018253207207,
-0.016871634870767593,
-0.046902045607566833,
0.04207131639122963,
0.002367667155340314,
-0.0029915652703493834,
-0.02202477678656578,
0.09272495657205582,
0.0016004008939489722,
0.01613437384366989,
0.030457688495516777,
-0.02494167909026146,
-0.04047582671046257,
0.1377447247505188,
-0.011574088595807552,
0.014355861581861973,
0.011828950606286526,
-0.010111148469150066,
-0.012543609365820885,
0.002081063110381365,
0.004001133143901825,
0.04150199890136719,
-0.03288355842232704,
-0.035192836076021194,
0.0005801221705041826,
0.026716824620962143,
0.0006607083487324417,
-0.03235642611980438,
-0.018048681318759918,
-0.023244692012667656,
0.023227890953421593,
0.013554820790886879,
0.039107974618673325,
-0.018736297264695168,
-0.01588289439678192,
-0.0005985919269733131,
-0.08266574144363403,
-0.02140754647552967,
-0.0175810344517231,
0.035820260643959045,
0.006885588634759188,
-0.011121039278805256,
0.04852141812443733,
0.010063639841973782,
0.006869668606668711,
-0.048225078731775284,
-0.05581795424222946,
-0.0056150369346141815,
-0.004303228110074997,
0.00724228797480464,
-0.03620533272624016,
0.01725495606660843,
-0.01886001043021679,
0.003507950808852911,
0.0009130163234658539,
0.011363046243786812,
-0.03486224263906479,
-0.06753385812044144,
0.009896349161863327,
-0.03009795770049095,
0.0374024324119091,
0.051580820232629776,
0.0018539627781137824,
0.012446404434740543,
-0.019002312794327736,
-0.014075147919356823,
0.01053700316697359,
0.002391085959970951,
0.06498698890209198,
0.04149032384157181,
0.010592162609100342,
0.023679768666625023,
0.006880979984998703,
0.04876547306776047,
-0.014053907245397568,
-0.013032575137913227,
-0.0481475368142128,
-0.07476719468832016,
-0.017175283282995224,
0.02974984236061573,
0.03764220327138901,
-0.03760834410786629,
0.03424398973584175,
0.03986300155520439,
0.009216252714395523,
0.043528810143470764,
-0.02255656011402607,
-0.003297795308753848,
-0.04058825969696045,
-0.01283701229840517,
0.026370933279395103,
-0.02807014063000679,
0.037997860461473465,
0.04787832126021385,
0.02171965502202511,
0.02247544191777706,
-0.009718483313918114,
0.0008916736696846783,
0.03484183922410011,
-0.01629464142024517,
-0.0017396542243659496,
0.004519494250416756,
-0.04447643831372261,
0.01002154964953661,
-0.020109619945287704,
0.054020337760448456,
0.0223966296762228,
-0.010360668413341045,
0.01985442265868187,
0.013981231488287449,
-0.02622688189148903,
0.022413423284888268,
-0.03806331753730774,
-0.02608494646847248,
-0.057254523038864136,
0.017213040962815285,
-0.04286598786711693,
0.0021865013986825943,
-0.019577905535697937,
0.03360796347260475,
-0.03917914628982544,
-0.011126808822154999,
0.00981186330318451,
-0.015705496072769165,
0.03644943982362747,
-0.032646294683218,
-0.036290787160396576,
0.004549706354737282,
-0.03366776928305626,
0.03250875324010849,
0.04822390899062157,
-0.05181661620736122,
0.014347006566822529,
0.01126166246831417,
-0.019117336720228195,
0.03518122807145119,
-0.024964092299342155,
0.015471500344574451,
0.009717283770442009,
0.0009527684887871146,
-0.07589773833751678,
0.0020737468730658293,
0.0033110673539340496,
-0.002184186829254031,
-0.024014659225940704,
0.011107885278761387,
0.04779425263404846,
-0.011838051490485668,
-0.015923187136650085,
0.003229303751140833,
-0.039991457015275955,
-0.03753255307674408,
0.014623125083744526,
-0.007080297917127609,
-0.02548195980489254,
-0.02025693841278553,
0.023726919665932655,
0.03789475932717323,
-0.06337305158376694,
-0.015013710595667362,
-0.030008217319846153,
-0.05997888743877411,
0.02853463590145111,
-0.025352926924824715,
0.03708275780081749,
-0.006471820175647736,
-0.07161694020032883,
0.05850851535797119,
0.036434050649404526,
-0.04763242229819298,
-0.0005712143029086292,
-0.027462277561426163,
-0.021948421373963356,
-0.08065471053123474,
-0.018600359559059143,
0.03430291265249252,
-0.03633444011211395,
0.008444806560873985,
0.017119595780968666,
0.005666396580636501,
0.025071023032069206,
0.07333534955978394,
-0.009901972487568855,
0.007440594956278801,
-0.012799134477972984,
0.02033822238445282,
0.06707791984081268,
0.01991908811032772,
-0.011624012142419815,
-0.006413675844669342,
-0.01736137643456459,
0.054011810570955276,
0.00117266527377069,
-0.0031472938135266304,
0.03952540457248688,
-0.03153827041387558,
0.01084933616220951,
-0.018659763038158417,
0.04196934401988983,
-0.003678401932120323,
0.023518890142440796,
-0.027956044301390648,
0.034796055406332016,
0.01791083626449108,
-0.008391209878027439,
0.0011112577049061656,
0.04522010684013367,
-0.005144581198692322,
0.013831530697643757,
-0.04025188833475113,
-0.04236100986599922,
-0.011127417907118797,
0.07242926955223083,
-0.07120764255523682,
-0.0432005301117897,
0.023002536967396736,
0.033182546496391296,
0.04261703044176102,
-0.031562719494104385,
0.02304311841726303,
-0.05791676416993141,
-0.05186133459210396,
-0.0201080534607172,
-0.003252022434026003,
0.05293906480073929,
0.0492350310087204,
0.02979586273431778,
0.019690027460455894,
-0.029401609674096107,
-0.027399923652410507,
-0.017395786941051483,
-0.10053911060094833,
0.028112830594182014,
-0.03921554982662201,
-0.012622815556824207,
0.004394044633954763,
-0.013913311064243317,
0.007001978810876608,
-0.01910368725657463,
0.015104392543435097,
-0.028014035895466805,
-0.004069870337843895,
-0.05455905944108963,
-0.021740365773439407,
0.004919377155601978,
-0.01606295444071293,
-0.032838836312294006,
0.033445749431848526,
0.019596107304096222,
-0.043558139353990555,
0.013232219964265823,
0.02666606940329075,
-0.03955990448594093,
0.01256394200026989,
-0.008127909153699875,
-0.00012982926273252815,
-0.014544072560966015,
0.05138828605413437,
0.01898626983165741,
-0.004335603676736355,
-0.05936657264828682,
0.04254036024212837,
-0.0028762121219187975,
0.04903392121195793,
0.0010555338812991977,
0.02725004404783249,
-0.036898933351039886,
-0.03838298097252846,
0.0008087954483926296,
0.017964309081435204,
0.0860092043876648,
0.012678994797170162,
-0.02818555012345314,
0.006238414440304041,
-0.011239801533520222,
-0.019070038571953773,
0.0228106752038002,
0.05637315288186073,
-0.016682347282767296,
0.010222885757684708,
-0.0631769672036171,
-0.02342809922993183,
-0.024953262880444527,
-0.02077929675579071,
-0.012035606428980827,
0.01443477813154459,
-0.006898972671478987,
0.0039023254066705704,
0.010996303521096706,
0.03092372976243496,
0.028752632439136505,
-0.020314039662480354,
0.028233565390110016,
0.0007588468142785132,
0.0258418507874012,
0.020570220425724983,
0.04478573426604271,
0.038257576525211334,
0.05551982298493385,
-0.006052468903362751,
-0.014048432931303978,
-0.11903487145900726,
-0.023557337000966072,
0.027365295216441154,
0.02176421694457531,
0.011036070995032787,
-0.01847964897751808,
-0.05250696837902069,
-0.03128952905535698,
0.05769877880811691,
-0.007209694478660822,
0.06544728577136993,
0.003179130144417286,
-0.024218177422881126,
-0.04056932404637337,
-0.0013037723256275058,
0.004492855165153742,
0.04747142270207405,
0.0019025483634322882,
0.002536285435780883,
-0.029321370646357536,
0.0009780845139175653,
0.01187940500676632,
0.003521473379805684,
0.03640091046690941,
0.04074093699455261,
-0.004532489459961653,
-0.0056960489600896835,
0.007629991043359041,
0.01368728093802929,
-0.023789141327142715,
-0.055562179535627365,
0.036979325115680695,
0.009637009352445602,
-0.01017323974519968,
0.01328608114272356,
0.003370450111106038,
-0.057992324233055115,
0.02182462438941002,
0.010052685625851154,
0.0005057828384451568,
-0.004439531359821558,
-0.01267090905457735,
0.06996192783117294,
0.0044743213802576065,
0.007676903158426285,
0.05420822650194168,
0.037328172475099564,
0.010685129091143608,
0.018003730103373528,
0.021540965884923935,
0.05525585636496544,
-0.04291652888059616,
0.039931051433086395,
0.024962127208709717,
0.040628258138895035,
-0.034377191215753555,
0.07263229787349701,
-0.03293805196881294,
0.013262310065329075,
-0.003219046164304018,
0.0050706458278000355,
-0.0030883958097547293,
0.007735616993159056,
0.0039180428721010685,
-0.030411148443818092,
0.005689919926226139,
0.006594638340175152,
-0.01047942042350769,
-0.04549716040492058,
0.011604112572968006,
-0.015281347557902336,
0.020096343010663986,
0.014534946531057358,
-0.00043218766222707927,
0.04693365842103958,
-0.011154486797749996,
-0.02725592814385891,
0.017713148146867752,
-0.06027389317750931,
0.039012063294649124,
-0.018581507727503777,
0.023531749844551086,
-0.012691039592027664,
-0.045049507170915604,
0.012598034925758839,
0.04605700448155403,
-0.010406027548015118,
0.010587687604129314,
-0.03805645555257797,
0.04499739035964012,
0.028908248990774155,
0.009985881857573986,
-0.0515010729432106,
-0.07146093249320984,
0.003975007217377424,
0.02145824395120144,
0.024426981806755066,
-0.006218646187335253,
-0.024532558396458626,
-0.016501164063811302,
0.015749670565128326,
-0.01120764296501875,
0.03934212028980255,
-0.035791341215372086,
-0.008077051490545273,
0.02840178832411766,
0.016973592340946198,
0.0659947395324707,
0.004198289941996336,
-0.031956106424331665,
0.021128429099917412,
-0.04988774657249451,
-0.024652449414134026,
-0.008362868800759315,
0.021167485043406487,
-0.03294527903199196,
-0.027507653459906578,
0.0020307262893766165,
-0.024107102304697037,
0.036574605852365494,
0.01435568742454052,
-0.015166479162871838,
0.0428529717028141,
0.0015781647525727749,
0.009005407802760601,
-0.014852376654744148,
0.02207442931830883,
0.029770392924547195,
0.018522851169109344,
-0.009454868733882904,
-0.044440608471632004,
-0.04116034507751465,
-0.027955492958426476,
0.029760969802737236,
0.016850633546710014,
-0.02496909163892269,
-0.00026625656755641103,
0.04111630097031593,
-0.020975440740585327,
-0.024492856115102768,
0.023334641009569168,
0.003365694312378764,
-0.007801412604749203,
0.0017700149910524487,
0.013181200250983238,
0.012315702624619007,
-0.0033500005956739187,
-0.041742853820323944,
-0.04242558032274246,
-0.020906737074255943,
-0.04880686104297638,
0.05224659666419029,
-0.0005434663034975529,
0.049758002161979675,
-0.011344905942678452,
-0.015186445787549019,
-0.005010769236832857,
-0.02114361897110939,
-0.025814475491642952,
-0.00887254811823368,
-0.027507103979587555,
0.008050216361880302,
0.014801929704844952,
0.014828264713287354,
0.003247668035328388,
0.006840863265097141,
-0.006778841372579336,
0.020254775881767273,
0.02313617616891861,
0.10591018944978714,
0.06349176913499832,
-0.006285902112722397,
-0.04295899346470833,
0.019419822841882706,
-0.053072597831487656,
0.05846361815929413,
-0.026981409639120102,
-0.021993154659867287,
0.037329934537410736,
0.007282599341124296,
0.030804937705397606,
-0.04174036160111427,
0.01918371580541134,
-0.026258835569024086,
0.01627523824572563,
0.009042196907103062,
-0.012363367713987827,
0.014956611208617687,
0.024741997942328453,
0.027338678017258644,
0.0012865610187873244,
0.010328897275030613,
0.012720337137579918,
-0.0941101610660553,
-0.01427111029624939,
-0.016215048730373383,
-0.027764635160565376,
0.062195926904678345,
-0.028520023450255394,
-0.032767023891210556,
0.02856319770216942,
0.0057155475951731205,
0.0814594253897667,
0.032308757305145264,
0.03445475548505783,
-0.034601401537656784,
0.0574645921587944,
-0.03157701715826988,
0.030897872522473335,
-0.021639330312609673,
0.012452098540961742,
0.08459508419036865,
0.06331770867109299,
0.009723342955112457,
-0.045069288462400436,
0.018305983394384384,
-0.07248152047395706,
0.028537264093756676,
-0.025195997208356857,
-0.004345903638750315,
-0.03943932428956032,
-0.018627524375915527,
-0.010417415760457516,
0.020794300362467766,
0.013952097855508327,
-0.005033102817833424,
0.042570460587739944,
-0.022828437387943268,
-0.008856071159243584,
-0.030600469559431076,
0.03989041596651077,
0.006876773200929165,
0.011144913733005524,
-0.02089860290288925,
0.04104969650506973,
-0.029936859384179115,
-0.01948040910065174,
-0.0010521840304136276,
-0.041356343775987625,
0.003364147851243615,
-0.021322397515177727,
-0.05561916530132294,
0.02640843391418457,
0.023684345185756683,
-0.010641583241522312,
-0.023558683693408966,
0.018933981657028198,
0.007724794093519449,
0.012018375098705292,
0.024343444034457207,
0.06201866269111633,
0.03708835691213608,
-0.030878650024533272,
0.029353516176342964,
0.025690540671348572,
-0.04088560864329338,
0.002258565276861191,
-0.03752558305859566,
0.03866826370358467,
-0.00870500784367323,
0.016200460493564606,
-0.010662057437002659,
0.00952546764165163,
0.0216065663844347,
-0.01770702376961708,
-0.07452147454023361,
0.010394830256700516,
-0.0032223050948232412,
-0.03267775475978851,
0.007487255614250898,
-0.034428246319293976,
0.03235418349504471,
0.00713592953979969,
0.009334827773272991,
0.01628165692090988,
0.01834707148373127,
0.011139334179461002,
0.015223522670567036,
0.014878001064062119,
-0.004127637017518282,
-0.017077140510082245,
0.00030049250926822424,
0.018768632784485817,
-0.027757080271840096,
0.035058025270700455,
0.036941878497600555,
-0.005772884469479322,
0.01220020093023777,
-0.0010554165346547961,
-0.04453412815928459,
-0.0037793393712490797,
-0.05561086907982826,
0.03962358087301254,
0.0017431601881980896,
-0.015499701723456383,
-0.010518980212509632,
0.007030791603028774,
0.035323258489370346,
0.05612800642848015,
-0.009701193310320377,
0.000027061911168857478,
0.004650185815989971,
0.020044391974806786,
0.06489213556051254,
-0.016167907044291496,
-0.059261467307806015,
-0.007798489648848772,
-0.00965131539851427,
0.014469422399997711,
-0.003514588112011552,
0.043033212423324585,
0.04402399808168411,
-0.003563595935702324,
0.0016605877317488194,
0.02239995263516903,
-0.017845751717686653,
0.0004173046618234366,
0.01713019795715809,
-0.025448447093367577,
-0.006841119844466448,
-0.023227347061038017,
0.01909591443836689,
-0.0002231475809821859,
-0.037261757999658585,
-0.035468343645334244,
0.02808622643351555,
0.0035126691218465567,
0.00022068285034038126,
-0.021743103861808777,
-0.0030136045534163713,
-0.00443038996309042,
-0.003066220786422491,
-0.03440253064036369,
0.012361368164420128,
-0.0015959469601511955,
-0.028892971575260162,
-0.023650430142879486,
0.017271732911467552,
0.010232750326395035,
0.03127610310912132,
-0.042957957834005356,
0.004127561114728451,
0.011537895537912846,
-0.013307740911841393,
-0.007150597870349884,
0.014117448590695858,
0.026199810206890106,
0.02231680043041706,
0.02732999064028263,
-0.038773711770772934,
-0.01996500790119171,
0.03870755806565285,
-0.041571494191884995,
0.011646789498627186,
0.06870347261428833,
0.01903328113257885,
0.016545370221138,
0.04450167343020439,
-0.011311431415379047,
-0.01287342980504036,
0.007012868765741587,
0.003937177825719118,
0.01260044053196907,
0.01370841171592474,
-0.005921534728258848,
-0.024827420711517334,
-0.02164176106452942,
-0.002378033474087715,
0.0009466110495850444,
-0.004242005757987499,
0.00856776349246502,
0.05397649481892586,
0.031009195372462273,
-0.004553094040602446,
-0.02705918811261654,
0.06851502507925034,
-0.019266311079263687,
0.04747425392270088,
-0.0018819643883034587,
0.022098863497376442,
0.048919446766376495,
-0.016726654022932053,
-0.0009159580222330987,
0.019324148073792458,
0.013276388868689537,
-0.08558297157287598,
-0.017095303162932396,
0.008432506583631039,
0.016863983124494553,
0.03835282474756241,
-0.056614506989717484,
0.027095841243863106,
0.0437164269387722,
-0.04717244952917099,
0.018163837492465973,
-0.05109588801860809,
-0.017785819247364998,
-0.030462419614195824,
-0.012487531639635563,
0.011101101525127888,
0.017252353951334953,
0.0319613441824913,
0.016439665108919144,
0.023048076778650284,
0.017466628924012184,
0.038381390273571014,
-0.007698030676692724,
-0.01869795098900795,
0.016839848831295967,
0.029194727540016174,
-0.03494156524538994,
0.048085860908031464,
-0.04894183576107025,
-0.013727094978094101,
0.022268716245889664,
-0.02705780230462551,
0.01652456820011139,
-0.00457767304033041,
0.03074798174202442,
0.006215425208210945,
0.018130149692296982,
-0.019157564267516136,
-0.013755641877651215,
-0.004113003145903349,
0.022708671167492867,
-0.005145183764398098,
0.020621154457330704,
-0.005724360700696707,
-0.0218088049441576,
0.011520023457705975,
-0.027043210342526436,
0.00010213996574748307,
0.012210388667881489,
-0.009250248782336712,
0.0016419840976595879,
-0.009184099733829498,
-0.012690972536802292,
0.004119414370507002,
-0.004623993765562773,
-0.008556067943572998,
-0.04698297753930092,
-0.019366493448615074,
0.028964709490537643,
0.017689527943730354,
-0.0054972511716187,
-0.0170099176466465,
-0.014187663793563843,
-0.029113782569766045,
0.06503639370203018,
0.024778809398412704,
-0.006405756343156099,
-0.06226959452033043,
-0.04058797284960747,
0.008561338298022747,
0.0035259246360510588,
0.017819764092564583,
-0.02186531387269497,
-0.002838070271536708,
0.024794191122055054,
-0.005280765704810619,
0.0033149796072393656,
0.021931232884526253,
-0.03272087872028351,
-0.013469337485730648,
-0.03660328686237335,
0.032595548778772354,
-0.001507253386080265,
-0.0024243160150945187,
-0.0052410620264709,
-0.04037337377667427,
-0.02932143770158291,
-0.002235405845567584,
0.05928130820393562,
-0.007274386007338762,
-0.006053448189049959,
0.031129829585552216,
-0.026465972885489464,
0.013509957119822502,
-0.03719064220786095,
0.018602484837174416,
-0.028175704181194305,
-0.013280937448143959,
0.02949676662683487,
-0.022304540500044823,
-0.02767423540353775,
0.012881101109087467,
0.017086045816540718,
0.05219587683677673,
0.002418523421511054,
-0.018394386395812035,
-0.018716098740696907,
0.03424788638949394,
-0.007660542149096727,
0.019754808396100998,
0.004763054195791483,
-0.02976609393954277,
0.03811682015657425,
-0.022167742252349854,
0.006988906301558018,
-0.06898397207260132,
-0.011650629341602325,
-0.034447506070137024,
0.006718326359987259,
-0.02161605842411518,
0.014847418293356895,
0.01660764403641224,
-0.0362684428691864,
-0.02646831050515175,
0.005383234471082687,
-0.016067713499069214,
0.015296585857868195,
0.05219479277729988,
-0.01417308859527111,
0.031199537217617035,
-0.03095526248216629,
0.01627318747341633,
0.024139903485774994,
0.023991698399186134,
0.009179112501442432,
0.05386311560869217,
-0.007641793228685856,
-0.05379118397831917,
0.036706242710351944,
0.005863415542989969,
0.015087340027093887,
0.019477352499961853,
0.008548742160201073,
0.024209262803196907,
-0.021667785942554474,
-0.03172900155186653,
0.022481491789221764,
-0.02220502495765686,
-0.011994093656539917,
0.028436914086341858,
-0.01077655702829361,
0.06798861175775528,
-0.009181329980492592,
-0.00326123321428895,
-0.017141954973340034,
0.000947693653870374,
-0.00423102593049407,
0.023222588002681732,
0.030225204303860664,
0.038033775985240936,
-0.03948981687426567,
-0.005342274438589811,
-0.008245632983744144,
-0.008645175024867058,
0.024942712858319283,
-0.08099988847970963,
0.02314651384949684,
-0.0007853268180042505,
0.011576472781598568,
0.008438441902399063,
-0.04062219709157944,
-0.02822614461183548,
-0.03288288414478302,
0.021614260971546173,
0.038528669625520706,
0.03375087305903435,
-0.042950667440891266,
-0.007106794510036707,
-0.012491308152675629,
0.0451141782104969,
-0.06270253658294678,
0.02649594098329544,
-0.001535867340862751,
0.021759942173957825,
0.01192188635468483,
0.008076317608356476
] |
<p>We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these problems. </p>
<p>So, the question is, if there is a solution that is allowed by Klein-Gordon, but not by Dirac, can this solution be considered valid?</p>
<p>Also, can Dirac equation be used for spin-0 particles? </p>
| 7,619 |
[
-0.008384231477975845,
-0.0042248195968568325,
0.009190461598336697,
-0.04945312812924385,
0.0267673060297966,
0.004335909616202116,
-0.06476327776908875,
-0.015454107895493507,
0.022972024977207184,
-0.036756426095962524,
0.020484182983636856,
0.017367424443364143,
0.028174901381134987,
0.0010397261939942837,
0.04146107658743858,
0.03636934608221054,
-0.029235977679491043,
-0.006224354729056358,
-0.006153632886707783,
-0.01222325675189495,
0.02166632004082203,
0.037836357951164246,
0.028481468558311462,
0.02094740979373455,
-0.01606423780322075,
-0.006667511072009802,
0.0033174550626426935,
0.025663964450359344,
0.01453380472958088,
0.03179383650422096,
-0.02382209524512291,
-0.015695810317993164,
0.01689479872584343,
0.046080172061920166,
0.03556118533015251,
0.007995852269232273,
-0.029109278693795204,
-0.03983820602297783,
-0.012199779972434044,
-0.007291335146874189,
0.01492332573980093,
-0.047053758054971695,
-0.004612091928720474,
0.03645133599638939,
-0.007373266853392124,
0.0629768967628479,
0.02347548119723797,
-0.04808146134018898,
0.0721217542886734,
-0.04854085296392441,
0.05079559609293938,
0.017096472904086113,
0.020370880141854286,
-0.022385455667972565,
-0.010727142915129662,
-0.022340526804327965,
0.05644802376627922,
0.08666858822107315,
-0.016163287684321404,
-0.007419771049171686,
-0.03127351403236389,
-0.0012944801710546017,
0.01721392758190632,
-0.017785904929041862,
-0.027556391432881355,
0.02410823665559292,
0.029506143182516098,
-0.014061504043638706,
-0.002647275337949395,
-0.02298867329955101,
0.03131505101919174,
0.010218683630228043,
0.03494364768266678,
-0.016114989295601845,
0.04302092269062996,
-0.04374738410115242,
-0.00562030216678977,
0.004590747412294149,
0.009895087219774723,
0.01481265015900135,
0.012506474740803242,
0.03452896326780319,
0.010312624275684357,
0.005790922325104475,
-0.004575191996991634,
-0.02772960066795349,
0.05766364932060242,
0.024930641055107117,
0.011756609193980694,
0.023765774443745613,
-0.0027589970268309116,
0.01383319403976202,
0.049049586057662964,
0.007322934456169605,
-0.012952134013175964,
0.040154844522476196,
0.005438327323645353,
0.039095401763916016,
0.0016329808859154582,
-0.0207914300262928,
0.024039695039391518,
-0.028833802789449692,
0.01895371451973915,
0.07678857445716858,
0.006686680484563112,
-0.0021122233010828495,
-0.045181408524513245,
0.020544756203889847,
-0.00638739624992013,
-0.004277403466403484,
-0.013314059935510159,
0.030654333531856537,
-0.015212923288345337,
-0.018316034227609634,
0.0033541126176714897,
-0.03786611929535866,
-0.0050394306890666485,
-0.03862665593624115,
0.06892513483762741,
0.07841040194034576,
0.006950969807803631,
-0.010029261000454426,
0.006710356567054987,
-0.010998568497598171,
-0.0623660683631897,
-0.019278766587376595,
0.03356515243649483,
-0.008211705833673477,
-0.02843424305319786,
0.015287249349057674,
-0.009117948822677135,
-0.02086392417550087,
-0.0016839514719322324,
0.02241489849984646,
0.020187541842460632,
-0.05927474424242973,
-0.08610910922288895,
-0.0567239448428154,
-0.00885725300759077,
-0.0014047309523448348,
-0.022063734009861946,
-0.04060988128185272,
0.004708557855337858,
0.005045687779784203,
0.11249576508998871,
-0.0022349802311509848,
0.030202070251107216,
0.04591310769319534,
0.024402640759944916,
-0.023258820176124573,
-0.022477636113762856,
-0.004898731596767902,
0.002513717394322157,
-0.02900630049407482,
0.010679963044822216,
-0.05364229902625084,
-0.011159112676978111,
0.010574448853731155,
0.0008676483412273228,
-0.009766939096152782,
0.03676052764058113,
-0.014722973108291626,
0.020799003541469574,
0.034430213272571564,
-0.012390874326229095,
-0.0401633083820343,
0.07360883057117462,
0.011449998244643211,
0.012548279017210007,
0.062463562935590744,
0.007355384528636932,
0.04434552416205406,
0.009380481205880642,
0.02322545275092125,
-0.005402011331170797,
-0.020715786144137383,
-0.06418740749359131,
-0.0013843710767105222,
0.03725377470254898,
-0.009865032508969307,
-0.04807649925351143,
0.0005944634904153645,
-0.011615422554314137,
0.027535369619727135,
0.0033775789197534323,
0.024076437577605247,
0.008991998620331287,
0.02401653677225113,
-0.0011550604831427336,
-0.05668734014034271,
0.015466057695448399,
-0.06376728415489197,
0.02588880993425846,
-0.004846997559070587,
0.01801130920648575,
0.04075666144490242,
0.019312752410769463,
0.002697192132472992,
-0.056061532348394394,
-0.016185270622372627,
-0.003399408422410488,
0.06590278446674347,
-0.030576642602682114,
0.00039992175879888237,
0.018174100667238235,
0.06712906062602997,
0.03681330010294914,
-0.011885009706020355,
0.023873185738921165,
0.02316839061677456,
-0.05170455947518349,
-0.016831811517477036,
0.022926706820726395,
0.0371626541018486,
0.030470695346593857,
-0.010962397791445255,
0.012188178487122059,
-0.009860810823738575,
-0.03569083288311958,
0.04945973679423332,
-0.010227876715362072,
0.0673866719007492,
0.015850424766540527,
-0.009200118482112885,
0.008621428161859512,
0.025313837453722954,
0.0352000817656517,
0.006609241012483835,
0.01562096644192934,
-0.04795863851904869,
-0.05307241156697273,
0.002153929555788636,
0.05922941863536835,
0.055264249444007874,
-0.06912828236818314,
0.014131373725831509,
0.02365913800895214,
0.006451176945120096,
0.01098314207047224,
0.012219519354403019,
-0.043452683836221695,
-0.04753701388835907,
0.038862425833940506,
-0.017963726073503494,
-0.0038406113162636757,
0.023440903052687645,
0.018490280956029892,
-0.014919702894985676,
-0.0011392380110919476,
-0.025954727083444595,
-0.039374008774757385,
0.030418669804930687,
-0.03324611857533455,
-0.01635095477104187,
0.022463900968432426,
-0.051442284137010574,
0.029454754665493965,
-0.017590155825018883,
0.04489177465438843,
0.03126760199666023,
-0.027647802606225014,
-0.020370976999402046,
-0.011052355170249939,
-0.0332396999001503,
0.012406720779836178,
-0.018689120188355446,
-0.014466885477304459,
-0.02860420197248459,
0.009949935600161552,
-0.03633332997560501,
-0.015261020511388779,
-0.025728615000844002,
-0.020193925127387047,
-0.013186762109398842,
-0.011478926986455917,
0.06177647411823273,
0.026329999789595604,
0.023174112662672997,
-0.014135130681097507,
-0.010170387104153633,
0.006019847467541695,
-0.040523648262023926,
-0.005450566299259663,
0.04825710505247116,
-0.04837123677134514,
0.0387875959277153,
-0.060839444398880005,
-0.039160456508398056,
0.022422829642891884,
0.004397429060190916,
0.06629732996225357,
0.035878993570804596,
-0.028467534109950066,
-0.033721085637807846,
0.009611019864678383,
-0.024428078904747963,
0.019477225840091705,
-0.038426388055086136,
0.022413909435272217,
0.04612552747130394,
0.0024326792918145657,
-0.0053008669055998325,
0.004419701639562845,
-0.0016219569370150566,
-0.0639905259013176,
0.008688606321811676,
0.007069601211696863,
0.04918717220425606,
-0.02858991175889969,
0.048375751823186874,
0.020763222128152847,
-0.07247643172740936,
0.0023943004198372364,
-0.06464782357215881,
-0.042697690427303314,
0.01843987964093685,
-0.028467649593949318,
0.0036541291046887636,
0.008206228725612164,
-0.032891783863306046,
0.07988382130861282,
0.016608858481049538,
0.0012801273260265589,
-0.0006334150675684214,
-0.018965894356369972,
0.000912779476493597,
-0.006575659848749638,
-0.0016992395976558328,
0.022891398519277573,
0.012844273820519447,
0.0010491135763004422,
0.0215944591909647,
0.02667512558400631,
0.0007190547185018659,
0.0009990044636651874,
-0.042233727872371674,
-0.011677819304168224,
0.026871003210544586,
0.003296846291050315,
0.05594984441995621,
-0.0005054967477917671,
-0.02138354629278183,
0.013334624469280243,
0.0035742251202464104,
0.044500187039375305,
0.006598528940230608,
-0.027176929637789726,
0.02698582224547863,
0.00566444406285882,
0.03652205318212509,
0.0025536825414747,
0.040217719972133636,
-0.0012468509376049042,
-0.004562359303236008,
0.022413989529013634,
0.01740678958594799,
0.029764272272586823,
-0.018508411943912506,
-0.0003571534180082381,
0.035734694451093674,
0.04833023250102997,
-0.042893245816230774,
-0.023341186344623566,
-0.016397666186094284,
-0.01176443975418806,
0.05350983142852783,
-0.020674947649240494,
-0.0014101688284426928,
0.03988540917634964,
0.017632117494940758,
0.03916224464774132,
-0.0187472403049469,
-0.008662120439112186,
0.00423929188400507,
-0.07966126501560211,
0.028706107288599014,
-0.02135344408452511,
0.04836847633123398,
0.013337590731680393,
0.020967265591025352,
0.04986909031867981,
0.010202626697719097,
0.03287259116768837,
0.0073559177108109,
-0.07821621745824814,
-0.01131847221404314,
-0.04136211797595024,
0.004688595421612263,
-0.03667193278670311,
-0.014102861285209656,
-0.021173246204853058,
-0.03216978907585144,
-0.007790058851242065,
-0.024230901151895523,
-0.033956993371248245,
-0.05150986835360527,
0.04445574805140495,
-0.04290500283241272,
-0.02343621477484703,
0.01045219600200653,
0.034182555973529816,
0.015985965728759766,
0.027293343096971512,
-0.021640365943312645,
0.05665113776922226,
-0.037800393998622894,
-0.001902289455756545,
-0.013445672579109669,
0.011771527118980885,
0.010281046852469444,
0.04524191841483116,
0.041511837393045425,
0.044924501329660416,
-0.020935436710715294,
-0.0010700663551688194,
0.03581951558589935,
0.0577857606112957,
-0.010898535139858723,
-0.012447456829249859,
-0.019151052460074425,
-0.06892769038677216,
-0.01917879655957222,
-0.047602493315935135,
0.0689094141125679,
-0.003835841082036495,
0.00019416878058109432,
-0.0026650838553905487,
-0.007463760673999786,
-0.016996530815958977,
0.0018209393601864576,
0.05418766289949417,
0.03017326630651951,
-0.05110776796936989,
-0.022937890142202377,
0.00047933118185028434,
-0.029983043670654297,
-0.03006039187312126,
-0.015997570008039474,
-0.00494688656181097,
-0.0353257916867733,
0.030294988304376602,
0.021235300227999687,
0.036316968500614166,
-0.04955887794494629,
0.01993614062666893,
-0.0060575720854103565,
0.003653815947473049,
-0.011734369210898876,
0.014035264030098915,
-0.027592819184064865,
0.02593049593269825,
0.03489811345934868,
-0.021597489714622498,
-0.00923585519194603,
-0.05603853985667229,
-0.011321606114506721,
0.06256339699029922,
0.017502427101135254,
0.021031919866800308,
-0.019904091954231262,
-0.07823999971151352,
0.01041090302169323,
0.06555361300706863,
-0.04577309265732765,
0.01304975152015686,
-0.025364117696881294,
-0.02994023635983467,
0.000737505906727165,
-0.015077687799930573,
-0.013180959969758987,
0.02882947213947773,
-0.025799289345741272,
-0.030177125707268715,
-0.03201834112405777,
0.018780745565891266,
-0.001598327187821269,
0.010573350824415684,
0.010525518096983433,
0.0707668736577034,
0.008655850775539875,
0.02106011100113392,
-0.0002132849913323298,
0.031027397140860558,
-0.020937791094183922,
-0.09764207899570465,
-0.027018211781978607,
0.03534562885761261,
-0.023597391322255135,
0.05936575308442116,
-0.03638553246855736,
-0.04769090563058853,
0.015779979526996613,
-0.023030048236250877,
-0.005869201384484768,
0.011268183588981628,
-0.07082260400056839,
0.04452148824930191,
0.03226500749588013,
-0.016632340848445892,
0.030921325087547302,
0.03965596482157707,
-0.0038826270028948784,
-0.05360792204737663,
-0.025810617953538895,
0.017156852409243584,
-0.03660328686237335,
-0.0005769545678049326,
-0.008032804355025291,
0.007351376581937075,
-0.026124823838472366,
0.03919905796647072,
-0.006414174102246761,
0.009174088016152382,
0.03665846213698387,
-0.023780498653650284,
-0.029372800141572952,
0.01613558456301689,
-0.007035877555608749,
-0.004370140377432108,
-0.03373086825013161,
-0.016110943630337715,
0.0038822025526314974,
-0.02874222956597805,
-0.0036526925396174192,
-0.0016930478159338236,
-0.03912268951535225,
0.06204919144511223,
-0.01434620376676321,
0.03398638218641281,
0.0009652684675529599,
-0.0016150751616805792,
0.012813057750463486,
-0.05154966190457344,
0.03246056288480759,
0.0019198724767193198,
-0.02548680268228054,
0.035849105566740036,
-0.03953845053911209,
-0.001602913485839963,
0.018975911661982536,
-0.004454479087144136,
-0.008216509595513344,
-0.03019225224852562,
0.007317415904253721,
0.062150102108716965,
-0.018945131450891495,
-0.09450279176235199,
-0.04328306391835213,
-0.0003018053830601275,
-0.012824536301195621,
0.015184407122433186,
-0.02300243079662323,
-0.0025475758593529463,
0.00020304127247072756,
-0.016320498660206795,
0.017096010968089104,
0.0523245669901371,
-0.01843375526368618,
-0.03462203964591026,
-0.023453330621123314,
0.01569179631769657,
0.02491278201341629,
-0.014018522575497627,
-0.015537276864051819,
0.012846660800278187,
-0.021840441972017288,
0.03991634026169777,
0.01652316004037857,
0.05795833840966225,
0.0006215378525666893,
-0.07043690979480743,
-0.03193559870123863,
0.0039197588339447975,
0.016997991129755974,
-0.005253970623016357,
-0.021956538781523705,
0.07017514854669571,
0.01983647234737873,
-0.003493674099445343,
-0.04319363459944725,
0.005031188018620014,
-0.013966322876513004,
0.005519611295312643,
0.02164146676659584,
0.002243347931653261,
-0.07493621855974197,
-0.047557901591062546,
0.034513432532548904,
-0.03951909393072128,
-0.008268982172012329,
0.0188805740326643,
0.061187952756881714,
0.018547644838690758,
-0.0011842749081552029,
0.013514230027794838,
-0.013215829618275166,
0.024388516321778297,
-0.02146870270371437,
0.008537041023373604,
0.014773000031709671,
0.026382023468613625,
-0.03617376089096069,
-0.02949666790664196,
0.0024420195259153843,
0.019874002784490585,
0.04613400250673294,
0.012696212157607079,
0.02319166250526905,
0.02000369317829609,
0.013954197987914085,
-0.03374748304486275,
-0.001121327979490161,
-0.0061013419181108475,
0.019155588001012802,
-0.0007466165698133409,
0.047298748046159744,
-0.004581731278449297,
-0.0043683466501533985,
0.048121482133865356,
0.06625407934188843,
0.017012037336826324,
-0.0068579623475670815,
0.02609899267554283,
0.022462718188762665,
-0.006031970027834177,
0.008098890073597431,
-0.07056409120559692,
0.040241826325654984,
-0.008410223759710789,
0.03128599748015404,
0.01468532346189022,
-0.04644972085952759,
0.03540544584393501,
0.0049084024503827095,
0.04002821072936058,
-0.005333814769983292,
-0.015047444961965084,
-0.030029624700546265,
0.025844145566225052,
0.005080588161945343,
-0.0005879184463992715,
0.011599206365644932,
0.027971554547548294,
0.021405145525932312,
0.040901068598032,
0.029272163286805153,
0.002671195659786463,
-0.07794283330440521,
-0.0004028624971397221,
-0.07659519463777542,
-0.06166646629571915,
0.03424588590860367,
0.00031700002728030086,
0.019517973065376282,
-0.026868293061852455,
-0.032207440584897995,
0.02009768784046173,
-0.009728990495204926,
0.05636989697813988,
-0.03449111059308052,
0.03253665193915367,
-0.01946117728948593,
0.012584712356328964,
-0.014675093814730644,
0.01852639764547348,
0.10046812146902084,
0.028785714879631996,
0.010060661472380161,
-0.05523580312728882,
-0.0022272728383541107,
-0.04239846393465996,
-0.01729414239525795,
-0.026120755821466446,
0.04771222546696663,
-0.00016919366316869855,
-0.03013307973742485,
0.005792731884866953,
0.02388901822268963,
0.01144190039485693,
-0.0015728557482361794,
0.08141989260911942,
-0.048302870243787766,
-0.05730064585804939,
-0.0012939462903887033,
0.01986582763493061,
0.028917700052261353,
0.01157655380666256,
-0.0056149582378566265,
0.0025825458578765392,
-0.01690356247127056,
0.00808306597173214,
-0.020922381430864334,
-0.008549755439162254,
0.027247948572039604,
-0.0061711277812719345,
-0.05201113596558571,
-0.009856349788606167,
-0.007366286125034094,
-0.014368133619427681,
-0.04426110163331032,
-0.0017143364530056715,
0.02958519198000431,
-0.007723224814981222,
0.03661216422915459,
0.015167039819061756,
0.005394759587943554,
-0.010391678661108017,
-0.002923422958701849,
0.020107993856072426,
-0.0539785698056221,
0.02531357668340206,
-0.020645402371883392,
0.03181383013725281,
-0.03483496233820915,
-0.02727143093943596,
0.030488979071378708,
-0.0024760495871305466,
0.02643803134560585,
-0.0573912113904953,
-0.021987680345773697,
-0.012873628176748753,
0.010976006276905537,
0.018983574584126472,
-0.022474296391010284,
-0.023148169741034508,
0.03838915377855301,
-0.010557242669165134,
0.02594798430800438,
-0.006960917729884386,
-0.02617902122437954,
0.015741847455501556,
-0.0021594481077045202,
0.03908999264240265,
-0.01786247082054615,
-0.010359048843383789,
-0.00039376976201310754,
-0.025287233293056488,
-0.020709026604890823,
-0.022675933316349983,
0.05464978143572807,
0.04606902599334717,
0.025898076593875885,
0.005096087697893381,
0.013741796836256981,
-0.008636673912405968,
-0.063188336789608,
0.01245660800486803,
-0.048377446830272675,
-0.015696601942181587,
-0.007215495686978102,
0.018656158819794655,
0.03656090423464775,
0.06956598162651062,
-0.06437762826681137,
-0.005938362330198288,
-0.020783092826604843,
-0.006659355014562607,
0.0025012753903865814,
-0.021477431058883667,
-0.012112997472286224,
0.012279799208045006,
-0.05653693899512291,
0.03049524873495102,
-0.03903155401349068,
0.0007783057517372072,
0.033373188227415085,
0.01566344127058983,
-0.017813758924603462,
0.03811616823077202,
-0.02061193808913231,
0.0028219169471412897,
0.008556261658668518,
-0.017020631581544876,
-0.005569908302277327,
0.006910486146807671,
0.03662905842065811,
-0.03563845530152321,
-0.02714839205145836,
-0.05742528289556503,
-0.0060756150633096695,
0.02233961969614029,
0.03221067786216736,
-0.02268233336508274,
-0.002238843124359846,
-0.01437239721417427,
-0.012424545362591743,
-0.05416770279407501,
0.0005156311090104282,
-0.048838019371032715,
0.01566508784890175,
-0.021008241921663284,
-0.023403340950608253,
-0.025396134704351425,
0.03558138757944107,
0.005775158293545246,
-0.016656463965773582,
0.013829642906785011,
0.03154624626040459,
-0.05748748779296875,
0.008338676765561104,
0.026472512632608414,
0.013578846119344234,
0.041296668350696564,
0.005544197279959917,
-0.016012869775295258,
0.014751614071428776,
-0.04254043102264404,
-0.0221543051302433,
0.02420811727643013,
-0.026878835633397102,
-0.008136464282870293,
0.030355967581272125,
-0.005001530982553959,
0.007475712802261114,
0.04738082364201546,
-0.010114062577486038,
-0.017163686454296112,
0.01344791054725647,
-0.05012926459312439,
-0.018981626257300377,
-0.008763054385781288,
-0.0027396150398999453,
0.0017595399403944612,
-0.02693319506943226,
0.02189425751566887,
0.020442655310034752,
-0.024740420281887054,
-0.0003602265496738255,
0.01354353129863739,
0.005148035008460283,
0.010785427875816822,
0.04989682137966156,
-0.02660163678228855,
-0.009775711223483086,
0.05658218264579773,
-0.053218092769384384,
0.021313447505235672,
0.04695369675755501,
0.01918686367571354,
-0.08201513439416885,
0.022624414414167404,
0.03337525576353073,
-0.0025683322455734015,
0.04913555830717087,
0.0006408651825040579,
0.03713075444102287,
0.009877967648208141,
-0.056676577776670456,
0.05373658612370491,
-0.022085806354880333,
-0.018066370859742165,
-0.006762860342860222,
0.010502656921744347,
-0.02342941425740719,
0.08343703299760818,
0.030271079391241074,
0.05135749280452728,
0.030124450102448463,
0.011088691651821136,
-0.00432022288441658,
-0.04148884117603302,
-0.020523425191640854,
0.0004036892205476761,
-0.01943042501807213,
-0.01993524469435215,
0.06205194070935249,
-0.04229746013879776,
-0.0318344421684742,
0.0006409540073946118,
0.03842708095908165,
-0.025445247069001198,
-0.01741463504731655,
0.019281407818198204,
0.007840625941753387,
0.022838987410068512,
0.03195396438241005,
-0.0028596988413482904,
-0.00819926243275404,
0.004060131032019854,
0.012544183991849422,
0.024532947689294815,
-0.0051176296547055244,
0.005382235161960125,
-0.035078953951597214,
-0.03743143379688263,
-0.027706047520041466,
0.04040898382663727,
-0.004421611782163382,
-0.038869671523571014,
-0.02748829498887062,
0.007229887880384922,
-0.004085271619260311,
0.006470298394560814,
0.0004552332975436002,
-0.05112001299858093,
-0.009097020141780376,
0.0065077487379312515,
-0.015298129059374332,
-0.002444606274366379,
0.04219520092010498,
-0.043531566858291626,
-0.016436953097581863,
0.030003622174263,
0.010220042429864407,
-0.0026476553175598383,
-0.03129158914089203,
0.02432626485824585,
0.010042688809335232,
0.02270318754017353,
-0.008341187611222267,
-0.033736035227775574,
-0.024091731756925583,
0.03323623910546303,
-0.0069979275576770306,
0.006806505843997002,
-0.018804410472512245,
-0.027753261849284172,
-0.0237568486481905,
-0.04490911215543747,
0.04308660700917244,
0.0038488733116537333,
0.03178103640675545,
0.00011987170728389174,
-0.029483040794730186,
-0.012300477363169193,
0.009485287591814995,
0.05249447375535965,
-0.01500757411122322,
-0.022748064249753952,
0.033867258578538895,
0.002113479422405362,
-0.027290765196084976,
-0.011836123652756214,
-0.008214890025556087,
-0.014573382213711739,
-0.035684697329998016,
-0.011040054261684418,
0.01654716022312641,
-0.024997062981128693,
0.028561508283019066,
-0.007036873605102301,
0.021359091624617577,
0.010751093737781048,
0.005560943856835365,
-0.06152400001883507,
0.0534353107213974,
0.04707498848438263,
-0.030285339802503586,
0.059320125728845596,
-0.03130239248275757,
0.02025018073618412,
0.025050373747944832,
-0.024008236825466156,
-0.0033258856274187565,
0.006660839542746544,
-0.04313667118549347,
-0.035882268100976944,
-0.039246153086423874,
-0.025708958506584167,
0.025333954021334648,
-0.04556016996502876,
0.0005150634096935391,
0.06630069762468338,
-0.022788899019360542,
0.016228171065449715,
0.0491320863366127,
0.01782313920557499,
0.07560599595308304,
-0.007477140519768,
-0.03785308450460434,
0.042744699865579605,
0.00389552628621459,
0.0029213079251348972,
0.040690355002880096,
-0.020682763308286667,
-0.004077968653291464,
0.0013723640004172921,
0.023589108139276505,
0.012918400578200817,
-0.0018146777292713523,
0.051244575530290604,
0.05954635515809059,
-0.019499871879816055,
0.006711201276630163,
0.06295694410800934,
-0.013664924539625645,
0.04925276339054108,
0.006589036900550127,
-0.04424654319882393,
0.08959554880857468,
-0.01865529827773571,
0.034030359238386154,
-0.04602278769016266,
0.021897006779909134,
0.0017785757081583142,
0.021675894036889076,
-0.00990254245698452,
0.040260493755340576,
0.006062667816877365,
-0.03818615525960922,
-0.003850012319162488,
0.03530842065811157,
0.024928366765379906,
-0.06087573617696762,
-0.02662491425871849,
-0.018669234588742256,
-0.002061475533992052,
-0.030937422066926956,
-0.02050025947391987,
-0.00045837799552828074,
0.02461683191359043,
0.025684848427772522,
0.026781121268868446,
0.014751792885363102,
-0.019202115014195442,
0.0008535319939255714,
-0.04832132160663605,
0.0053162239491939545,
-0.05615963786840439,
-0.018990974873304367,
-0.0009689486469142139,
0.019108150154352188,
-0.07048583030700684,
-0.01332256942987442
] |
<p>Every wavefunction of a form $\Psi(x)$ can be described as a superposition of multiple free particle solutions.
We can see the following Fourier transform:
$$ \psi(x) = \int e^{ik\cdot x} \psi(k) dk $$</p>
<p>We can make it time dependent by replacing $e^{ik\cdot x}$ with $e^{ik\cdot x - i E_k t}$ where $E_k = \sqrt{k^2 + m^2}$. The result gives the positive energy time evolution of any initial wavefunction data. </p>
<p>The question is,</p>
<p>A. This may violate locality, as $E_k$ can be set as we want to, as $k$ can be set as we want to. Is this correct?</p>
<p>B. Why is this related to requiring a multi-particle theory to fix formalism in Klein-Gordon equation? (Context: <a href="http://physics.stackexchange.com/q/39323/2451">Complete set and Klein-Gordon equation</a>) </p>
<p>C. How is adding negative energy preserve locality? </p>
| 7,620 |
[
-0.012805168516933918,
-0.02512824349105358,
0.025432545691728592,
-0.03413337469100952,
0.043331343680620193,
-0.010577073320746422,
-0.053869228810071945,
-0.04145323485136032,
0.009556598030030727,
-0.024084437638521194,
0.04562252014875412,
0.01616852730512619,
0.01814410276710987,
-0.003449286101385951,
-0.00813335832208395,
0.017141137272119522,
-0.009424041025340557,
-0.046804677695035934,
-0.0324990339577198,
-0.03240720555186272,
0.013021818362176418,
0.04084986820816994,
0.022563010454177856,
0.007573194336146116,
-0.02813059650361538,
0.04160166159272194,
0.03191434592008591,
0.01116133201867342,
0.02071254700422287,
0.06955884397029877,
-0.029109232127666473,
-0.018744230270385742,
0.004042947199195623,
0.025155585259199142,
-0.016549406573176384,
-0.014437006786465645,
-0.06192021816968918,
-0.03233050927519798,
0.03958779573440552,
0.005865408573299646,
-0.051414571702480316,
-0.030768008902668953,
-0.005076846107840538,
0.04173913970589638,
-0.010973487980663776,
0.03110254555940628,
0.02037777006626129,
-0.01540728285908699,
0.045471709221601486,
-0.012276189401745796,
0.03809373080730438,
-0.005106342025101185,
0.019802477210760117,
0.009546224027872086,
-0.026709329336881638,
0.005924512632191181,
0.05130733922123909,
0.10862817615270615,
0.008684017695486546,
-0.06377231329679489,
-0.03319169953465462,
-0.013076314702630043,
0.03301727771759033,
-0.0018599404720589519,
-0.01677481085062027,
0.0012491131201386452,
0.025382809340953827,
0.010915598832070827,
-0.029341554269194603,
-0.047174643725156784,
0.022504746913909912,
0.0030506299808621407,
0.026074044406414032,
-0.036861352622509,
0.018454808741807938,
0.024050837382674217,
0.016516733914613724,
0.03757705166935921,
0.020610351115465164,
0.03766985982656479,
-0.011647914536297321,
-0.012652267701923847,
0.04946140944957733,
0.024547336623072624,
0.014362902380526066,
-0.012430152855813503,
0.07341661304235458,
0.04175134375691414,
0.01688089407980442,
0.015778101980686188,
0.01382459606975317,
0.012636123225092888,
0.06041225045919418,
-0.019468486309051514,
-0.021761454641819,
0.03556051105260849,
-0.0009285788401030004,
0.05694175511598587,
-0.0019978792406618595,
-0.021469008177518845,
-0.005261262413114309,
-0.06086440756917,
0.019623886793851852,
0.06487292051315308,
-0.006068733986467123,
-0.017415348440408707,
-0.058604251593351364,
0.02345542423427105,
-0.033123962581157684,
-0.012545466423034668,
-0.0020962366834282875,
-0.0014871450839564204,
-0.011888575740158558,
-0.001413244055584073,
0.005165208596736193,
0.011532147414982319,
-0.009242170490324497,
-0.0053597260266542435,
0.06178678572177887,
0.07025591284036636,
0.026966430246829987,
-0.02897193655371666,
0.02072663977742195,
-0.02449013665318489,
-0.09626223146915436,
0.0023441941011697054,
0.02196899801492691,
0.006827703211456537,
-0.03266482427716255,
0.005961745977401733,
0.029050027951598167,
-0.011563027277588844,
0.028668109327554703,
0.0033554479014128447,
0.02295723184943199,
-0.010457457043230534,
-0.14754462242126465,
-0.0664445087313652,
0.015431884676218033,
-0.006709794048219919,
-0.009706052951514721,
-0.063653863966465,
-0.011785319074988365,
0.018480509519577026,
0.09750693291425705,
-0.03766920790076256,
-0.050341714173555374,
-0.0011470902245491743,
0.028009258210659027,
0.01130993478000164,
-0.010859064757823944,
-0.023664362728595734,
-0.016317203640937805,
-0.010960767045617104,
-0.028107600286602974,
-0.07074723392724991,
0.016684090718626976,
0.0334073007106781,
0.021061699837446213,
0.006640653125941753,
0.08597477525472641,
-0.00576326809823513,
0.017231814563274384,
0.016918698325753212,
-0.0019415224669501185,
-0.03743495047092438,
0.06765434890985489,
0.041822560131549835,
0.006175891496241093,
0.0061681512743234634,
0.014851455576717854,
0.010203111916780472,
-0.037541404366493225,
0.017005793750286102,
0.0012149126268923283,
-0.029486000537872314,
-0.01020536944270134,
-0.03723294287919998,
-0.00361460680142045,
-0.006986362859606743,
-0.021340858191251755,
-0.033633310347795486,
-0.02645421400666237,
-0.00018588014063425362,
0.009119417518377304,
0.03535199537873268,
-0.0076509094797074795,
0.03695274889469147,
-0.01713186502456665,
-0.057628024369478226,
-0.011972233653068542,
-0.063628189265728,
0.055943578481674194,
0.018502186983823776,
-0.017488455399870872,
0.04487963020801544,
-0.034171029925346375,
0.012489487417042255,
-0.023713767528533936,
-0.04403703659772873,
0.004689726512879133,
0.041005175560712814,
-0.02822176367044449,
-0.018474845215678215,
0.03402300179004669,
0.061951275914907455,
0.01734318397939205,
-0.0026386119425296783,
0.002095393603667617,
0.020831262692809105,
-0.04635615646839142,
0.012549076229333878,
0.009457770735025406,
0.029428986832499504,
-0.016993241384625435,
-0.030074430629611015,
-0.029739094898104668,
0.03464056923985481,
-0.01796204410493374,
0.0003176706959493458,
-0.053172849118709564,
0.030179431661963463,
0.05177883431315422,
-0.005539073143154383,
0.022683920338749886,
0.04015973210334778,
0.003762794891372323,
0.038072433322668076,
0.016763944178819656,
-0.062411271035671234,
-0.06189605966210365,
-0.020741896703839302,
-0.0011101200943812728,
0.05501191318035126,
-0.031097177416086197,
0.046182405203580856,
0.018170813098549843,
0.03167206048965454,
-0.0034079020842909813,
-0.007654648739844561,
0.005755903664976358,
-0.036795273423194885,
0.009032081812620163,
0.012821990065276623,
-0.0007970405858941376,
0.00023214159591589123,
0.014522532001137733,
-0.022690435871481895,
0.007844613865017891,
-0.011238692328333855,
-0.003424650989472866,
-0.00949277076870203,
-0.01936963200569153,
-0.009621484205126762,
-0.004088105168193579,
-0.023167185485363007,
0.014754652045667171,
-0.002129561034962535,
0.04298003390431404,
0.041623178869485855,
-0.01588364504277706,
0.0026154164224863052,
-0.030527055263519287,
-0.057641949504613876,
0.00494296383112669,
0.019369451329112053,
-0.00023366535606328398,
-0.03204638883471489,
-0.003811894217506051,
-0.03971734270453453,
-0.03183294087648392,
0.008338456973433495,
-0.007826480083167553,
-0.006127862259745598,
0.022437462583184242,
0.058321915566921234,
0.009404071606695652,
0.041566554456949234,
-0.057919181883335114,
-0.0378250889480114,
0.0021937391720712185,
-0.02217238023877144,
0.018003474920988083,
0.018538115546107292,
-0.033515240997076035,
0.012689465656876564,
-0.06891810894012451,
-0.012527821585536003,
0.0531582348048687,
-0.010096688754856586,
0.02718442492187023,
0.012678734958171844,
0.011829450726509094,
-0.04663461446762085,
-0.032900772988796234,
-0.02303355745971203,
0.019858991727232933,
-0.04856570065021515,
0.005373591091483831,
0.05606380105018616,
0.006605030503123999,
-0.044661518186330795,
0.01809706538915634,
-0.012628372758626938,
-0.044473715126514435,
-0.004400929436087608,
-0.028977587819099426,
0.0726107656955719,
-0.01612098328769207,
0.006677190773189068,
0.017978522926568985,
-0.035702504217624664,
0.015210880897939205,
-0.04358633980154991,
-0.0863511934876442,
0.038573745638132095,
-0.0019052323186770082,
0.03304263576865196,
-0.011194853112101555,
-0.02782861329615116,
0.05046601966023445,
0.02295312099158764,
-0.00453720148652792,
0.0017485527787357569,
0.002320194384083152,
0.007237326353788376,
-0.02513875626027584,
-0.010243766009807587,
0.005963340401649475,
-0.004040215164422989,
0.07319389283657074,
0.009143724106252193,
0.06266850233078003,
0.04715191200375557,
0.0019620282109826803,
-0.03896024823188782,
-0.003696186700835824,
0.019645586609840393,
-0.0010696335230022669,
0.04444585368037224,
-0.004031925927847624,
-0.00348305725492537,
0.001974028069525957,
-0.027534302324056625,
0.00023579978733323514,
0.017626382410526276,
-0.023666711524128914,
0.04721837863326073,
-0.005704579409211874,
-0.01983775570988655,
-0.030714448541402817,
0.054964132606983185,
-0.014171616174280643,
-0.02165812812745571,
0.001449474599212408,
-0.012149914167821407,
0.03786560520529747,
-0.020542392507195473,
0.007727379910647869,
-0.0015396146336570382,
0.01070199254900217,
-0.003521886421367526,
-0.02526705525815487,
-0.01226463820785284,
0.036294881254434586,
0.029348133131861687,
-0.02858000621199608,
-0.03840513154864311,
0.008787306025624275,
0.026171622797846794,
0.030662937089800835,
-0.014143779873847961,
-0.03286617994308472,
0.003286185674369335,
-0.05159378424286842,
-0.008710213005542755,
0.0013065917883068323,
0.0462416373193264,
0.019115688279271126,
0.05502980202436447,
0.036751385778188705,
0.0056887660175561905,
-0.012819110415875912,
0.00648071151226759,
-0.051430217921733856,
-0.002280403161421418,
-0.0205962136387825,
0.0084989657625556,
0.0029928970616310835,
-0.01995709538459778,
0.00608392059803009,
-0.04064716398715973,
-0.023230651393532753,
0.02519652433693409,
-0.008559825830161572,
-0.060757074505090714,
0.0038650850765407085,
-0.04395125061273575,
-0.03243939206004143,
-0.03959227353334427,
0.04504258558154106,
0.04072105139493942,
-0.024432320147752762,
-0.005262318998575211,
0.041555725038051605,
-0.04614432156085968,
-0.007239648140966892,
-0.01790536940097809,
0.02197633869946003,
0.03336847200989723,
0.040623366832733154,
0.05013367161154747,
0.029270227998495102,
-0.005303842481225729,
0.0013256799429655075,
0.028740357607603073,
0.06532842665910721,
0.013728009536862373,
-0.051123276352882385,
0.02710883691906929,
-0.021159157156944275,
-0.005168866831809282,
0.0024088111240416765,
0.06644368916749954,
0.009605676867067814,
0.02152460813522339,
0.0038102862890809774,
0.027867211028933525,
0.005986344069242477,
0.028881028294563293,
0.03367104381322861,
-0.05309154838323593,
-0.0030445025768131018,
-0.02411738783121109,
0.009299513883888721,
0.012338286265730858,
-0.007684823125600815,
0.004231385886669159,
0.01710350625216961,
-0.004543649032711983,
0.026117874309420586,
-0.0003655845357570797,
-0.007358179427683353,
-0.03860977292060852,
-0.0016025217482820153,
-0.00878741405904293,
-0.024578757584095,
-0.018537377938628197,
0.027117859572172165,
0.028246281668543816,
0.012278497219085693,
0.0432891845703125,
-0.014730213209986687,
0.016070641577243805,
-0.05556082725524902,
-0.030145982280373573,
0.049007341265678406,
0.04051710665225983,
0.021067827939987183,
0.0018978489097207785,
-0.06069901958107948,
-0.029824718832969666,
0.006136046722531319,
-0.02336282841861248,
0.03663654625415802,
0.021847769618034363,
-0.00445216242223978,
-0.028907202184200287,
-0.0915384516119957,
-0.020126836374402046,
0.02458803914487362,
0.001110267243348062,
0.021654831245541573,
-0.01776103302836418,
-0.019536525011062622,
-0.011267781257629395,
0.03081570751965046,
0.010525430552661419,
0.0632157176733017,
-0.003237913129851222,
-0.021107543259859085,
-0.02099987305700779,
0.006393450312316418,
-0.019188961014151573,
-0.09361273795366287,
0.01743737980723381,
-0.011245302855968475,
-0.013627544976770878,
0.06073116883635521,
-0.040001410990953445,
-0.05696908384561539,
-0.003059803042560816,
0.015355001203715801,
-0.025350041687488556,
0.014736930839717388,
-0.07852257788181305,
0.07265578210353851,
0.02828681655228138,
0.031425245106220245,
0.05214725062251091,
0.024974452331662178,
-0.019202107563614845,
0.0023090403992682695,
-0.006190956570208073,
0.019723789766430855,
-0.03988450765609741,
0.0757017582654953,
-0.043135467916727066,
-0.004214618820697069,
-0.02733543887734413,
0.03820691630244255,
0.0030348317231982946,
-0.0338485985994339,
-0.011181660927832127,
0.005208287388086319,
-0.0030888551846146584,
0.020645981654524803,
-0.022331949323415756,
0.018704328685998917,
-0.022132890298962593,
-0.00883078295737505,
-0.00004436003655428067,
-0.026203634217381477,
0.0067213610745966434,
-0.006232553627341986,
-0.02566198632121086,
0.029187390580773354,
0.011320184916257858,
0.032490324229002,
-0.028490310534834862,
-0.033257856965065,
0.017111415043473244,
-0.03635157644748688,
0.004397644195705652,
0.020703934133052826,
-0.008838438428938389,
0.021064393222332,
-0.045291196554899216,
-0.013626189902424812,
0.011144977062940598,
0.0034320689737796783,
-0.005836519878357649,
-0.027353720739483833,
0.014248705469071865,
0.05037891864776611,
0.031313423067331314,
-0.09999159723520279,
-0.01953285001218319,
-0.019902534782886505,
-0.012875325046479702,
0.0003314850036986172,
-0.012421679683029652,
0.000693393056280911,
-0.06496165692806244,
0.007930493913590908,
-0.012858608737587929,
0.04819002002477646,
-0.025385398417711258,
-0.023062216117978096,
0.015064837411046028,
0.016890333965420723,
0.027430381625890732,
-0.005596441682428122,
-0.016272589564323425,
0.038640253245830536,
-0.01937144249677658,
-0.01596248894929886,
0.023924976587295532,
0.04609544202685356,
-0.00971533078700304,
-0.017971200868487358,
-0.008665692061185837,
-0.002481372794136405,
0.00868317112326622,
0.017365455627441406,
-0.05273463949561119,
0.02790786884725094,
0.0015765568241477013,
0.012621563859283924,
0.0025948709808290005,
-0.0016514237504452467,
-0.0005436046631075442,
0.04103600233793259,
0.03345470502972603,
-0.0002320478088222444,
-0.0022343583405017853,
-0.04282384738326073,
0.009989115409553051,
-0.0021006015595048666,
-0.03311523422598839,
0.02930702269077301,
0.03358738124370575,
-0.02807505987584591,
0.03394623100757599,
0.03988140821456909,
-0.01846173405647278,
0.022341357544064522,
-0.03411693498492241,
-0.007616204675287008,
0.013086185790598392,
0.003816866083070636,
-0.010987067595124245,
-0.02475862391293049,
-0.03350161761045456,
0.025416174903512,
0.030310126021504402,
-0.018467795103788376,
0.04605170711874962,
0.0017687795916572213,
-0.005558936391025782,
-0.021427100524306297,
-0.03087441436946392,
0.023741016164422035,
-0.004384428728371859,
-0.03613486886024475,
0.016392473131418228,
-0.04109205678105354,
-0.016390731558203697,
0.03751082345843315,
0.056353311985731125,
-0.028163304552435875,
-0.000302590400679037,
0.012817559763789177,
0.01837177760899067,
0.0019856372382491827,
-0.02829395979642868,
-0.07259049266576767,
0.036561064422130585,
-0.027663804590702057,
0.022836729884147644,
0.011801882646977901,
0.00500431377440691,
-0.000272922043222934,
0.05907813459634781,
0.03627254068851471,
-0.04816996306180954,
0.015562544576823711,
-0.038427773863077164,
0.004533341154456139,
0.005364452954381704,
0.012209873646497726,
0.005549616180360317,
0.005653310101479292,
0.02244880050420761,
0.0394228957593441,
-0.008995032869279385,
0.0004995398921892047,
-0.05961111560463905,
-0.007512790150940418,
-0.042311687022447586,
-0.04689280316233635,
-0.0006590642151422799,
-0.016498945653438568,
-0.01088804192841053,
0.02829638123512268,
-0.020180076360702515,
0.026049302890896797,
0.010046246461570263,
-0.0041751437820494175,
-0.011319635435938835,
0.07356049120426178,
-0.0013443424832075834,
0.009308993816375732,
0.006982504855841398,
0.014624763280153275,
0.12230929732322693,
0.07597662508487701,
0.01925976760685444,
-0.06025203689932823,
0.004187749698758125,
-0.005209028720855713,
-0.005604674108326435,
-0.043216925114393234,
0.001473323442041874,
-0.008690625429153442,
-0.019844062626361847,
-0.00956806167960167,
0.045178063213825226,
0.035780169069767,
0.0019457762828096747,
0.02722020447254181,
-0.06176624074578285,
-0.06918174028396606,
-0.011369253508746624,
-0.011295015923678875,
0.011947182938456535,
0.016589853912591934,
-0.007615784183144569,
0.00861374195665121,
-0.03612009435892105,
0.013127816841006279,
-0.00470041623339057,
-0.025384465232491493,
0.03699485957622528,
0.03883625194430351,
-0.038660354912281036,
0.0025845610070973635,
-0.006619120016694069,
-0.004837295971810818,
-0.041343774646520615,
0.008510081097483635,
0.03966594859957695,
-0.034360289573669434,
0.035460494458675385,
0.024439478293061256,
-0.022942353039979935,
-0.015636997297406197,
0.006510272156447172,
0.010221357457339764,
-0.04114755988121033,
-0.007073808927088976,
-0.02535894513130188,
0.07031627744436264,
-0.01570814661681652,
-0.019863419234752655,
0.014451940543949604,
-0.014246244914829731,
-0.007312942296266556,
-0.07383416593074799,
-0.02646406553685665,
0.004527444019913673,
0.04558359831571579,
-0.016507701948285103,
0.006211241707205772,
-0.02257898636162281,
0.03433024510741234,
-0.000345756794558838,
-0.005033242981880903,
0.001229963731020689,
-0.004739896394312382,
-0.010650962591171265,
-0.010383514687418938,
0.0037297653034329414,
0.017501484602689743,
0.01765931025147438,
-0.051537852734327316,
0.003941416274756193,
-0.04832722991704941,
-0.017634013667702675,
0.059490058571100235,
0.025346040725708008,
0.05981344357132912,
-0.020403914153575897,
0.02848888747394085,
-0.036655157804489136,
-0.06356625258922577,
0.02000405266880989,
-0.01482429914176464,
-0.023679079487919807,
-0.0011698378948494792,
0.018251631408929825,
0.005789890419691801,
0.06534693390130997,
-0.03703371062874794,
0.0027341749519109726,
-0.029075438156723976,
0.02104485034942627,
0.01613788679242134,
-0.03225758671760559,
-0.020882952958345413,
-0.013865849003195763,
-0.033900655806064606,
0.012880682945251465,
-0.03769918903708458,
0.0024305994156748056,
-0.02617090754210949,
-0.010126919485628605,
0.030144738033413887,
0.0586719773709774,
-0.0036245002411305904,
-0.013142583891749382,
0.024865396320819855,
-0.018519675359129906,
0.019635546952486038,
0.03161025419831276,
0.030254894867539406,
-0.006570013705641031,
-0.03864239901304245,
-0.005735525395721197,
0.005912615451961756,
0.04632626473903656,
0.0003163508663419634,
-0.017463985830545425,
0.020678190514445305,
-0.004366430453956127,
0.013162166811525822,
-0.01739991083741188,
0.002840888686478138,
-0.030232256278395653,
0.03249640390276909,
-0.03500184044241905,
-0.03896928206086159,
0.028491031378507614,
0.02211705595254898,
-0.028487609699368477,
-0.02534506283700466,
0.02419290319085121,
0.06311876326799393,
-0.034997228533029556,
0.001797549077309668,
0.03188345581293106,
0.013659290038049221,
0.04881111904978752,
0.0066417427733540535,
-0.02103230729699135,
0.021121740341186523,
-0.039543088525533676,
-0.0073227062821388245,
0.013630245812237263,
0.0021643126383423805,
-0.005349015351384878,
0.014940736815333366,
0.029730290174484253,
-0.03973173722624779,
0.03956272453069687,
-0.013897525146603584,
-0.009324946440756321,
0.04569757729768753,
-0.04455127567052841,
-0.0033619266469031572,
0.0031911861151456833,
-0.0010187834268435836,
-0.0023015900515019894,
-0.0019283391302451491,
0.06665495783090591,
0.031208237633109093,
0.006299647968262434,
-0.006294803228229284,
0.0007809337694197893,
-0.038173627108335495,
0.059012819081544876,
0.039664119482040405,
-0.009442582726478577,
0.01920410990715027,
0.016422823071479797,
-0.03165838494896889,
0.02409396506845951,
0.0066092354245483875,
-0.018210411071777344,
-0.0734248086810112,
0.014704806730151176,
0.01222193706780672,
0.010450880043208599,
0.04854191839694977,
-0.027762295678257942,
0.004252320621162653,
0.0193185992538929,
-0.058319415897130966,
0.08034437894821167,
0.0026934780180454254,
0.00403699791058898,
-0.015166929922997952,
0.012573680840432644,
-0.03982764855027199,
0.025887606665492058,
0.04400600492954254,
0.058253489434719086,
0.023766430094838142,
0.03471367806196213,
-0.005499264225363731,
-0.018860839307308197,
-0.0044142273254692554,
0.01001766324043274,
-0.0016990326112136245,
-0.021717188879847527,
0.051895614713430405,
-0.024413255974650383,
-0.03901677206158638,
0.03210706636309624,
-0.017861805856227875,
-0.0363311693072319,
-0.021028846502304077,
0.03390689566731453,
0.015118860639631748,
0.018604954704642296,
0.04333025589585304,
0.0017609980423003435,
0.023856492713093758,
0.023097697645425797,
0.007110124453902245,
0.009787486866116524,
0.018667198717594147,
0.006551255006343126,
-0.020702699199318886,
-0.04716833308339119,
-0.009366726502776146,
0.05307919904589653,
0.01183311641216278,
-0.024140292778611183,
-0.013423814438283443,
-0.012968659400939941,
0.011787546798586845,
0.010657167993485928,
-0.013543538749217987,
-0.010054402984678745,
-0.019779354333877563,
0.051678430289030075,
0.02084367722272873,
-0.01877855509519577,
-0.006123263388872147,
-0.014338729903101921,
-0.051090653985738754,
0.05525127425789833,
-0.015722712501883507,
0.01851450465619564,
-0.03943794593214989,
-0.023595865815877914,
-0.01558487769216299,
0.030517589300870895,
-0.032952532172203064,
-0.039967771619558334,
-0.022097140550613403,
0.013355113565921783,
-0.02028122916817665,
0.04507056251168251,
-0.04290468618273735,
-0.005476468242704868,
-0.029766907915472984,
-0.06852380931377411,
0.031081929802894592,
0.002374633913859725,
0.02967960573732853,
-0.03812237083911896,
-0.0013923877850174904,
-0.0022153393365442753,
0.010838148184120655,
0.05087476596236229,
-0.013798083178699017,
-0.023846197873353958,
0.010650837793946266,
-0.0309417936950922,
0.019682349637150764,
-0.009633269160985947,
0.023139934986829758,
-0.00288232509046793,
-0.032006461173295975,
0.01841118186712265,
-0.01232802402228117,
-0.035427313297986984,
0.0443112887442112,
0.02034609206020832,
-0.0029067215509712696,
0.024863261729478836,
0.0021392321214079857,
-0.04604872316122055,
0.05600056052207947,
0.008202395401895046,
-0.0028982001822441816,
0.07056489586830139,
0.009265568107366562,
0.056124161928892136,
0.02650861069560051,
-0.017836391925811768,
-0.01644035242497921,
-0.015117301605641842,
-0.05966951325535774,
-0.021930821239948273,
0.0021591847762465477,
-0.015990911051630974,
0.011561190709471703,
-0.024008600041270256,
-0.023104235529899597,
0.047574255615472794,
-0.04881097748875618,
-0.020782776176929474,
0.08986450731754303,
0.03573763743042946,
0.038115113973617554,
0.01935315877199173,
-0.013469882309436798,
-0.0126106021925807,
0.016489824280142784,
0.013592099770903587,
0.04266953840851784,
0.003757669823244214,
-0.021748293191194534,
0.02486097253859043,
0.025865470990538597,
0.0025369739159941673,
-0.008001992478966713,
-0.028836116194725037,
0.05578618124127388,
-0.040120817720890045,
0.00740200886502862,
0.04174533486366272,
-0.010102838277816772,
-0.008184104226529598,
0.028510604053735733,
-0.014680503867566586,
0.06992360204458237,
-0.003321669064462185,
0.010882078669965267,
-0.03397494927048683,
-0.012217441573739052,
-0.011228221468627453,
0.02153819613158703,
0.03745191544294357,
0.06264234334230423,
0.01834903471171856,
-0.014614555053412914,
-0.02945343218743801,
-0.017528042197227478,
0.03954169899225235,
-0.09624357521533966,
-0.013155778869986534,
0.00045887299347668886,
-0.024920348078012466,
0.011249574832618237,
-0.007483767811208963,
0.005829625762999058,
-0.038638025522232056,
0.015122811309993267,
0.040744882076978683,
0.04047376662492752,
-0.03445695340633392,
0.0063865515403449535,
-0.02428395301103592,
0.0407719761133194,
-0.0419783852994442,
0.017285402864217758,
-0.04205520451068878,
-0.006232548039406538,
-0.005123593378812075,
0.004128058906644583
] |
<p>During a transition of a molecule from one state to another, it pass through a transition state. This transition state, mathematically speaking, is a saddle point. That means, the second derivative along all the coordinates, except one, is greater than zero. I have two questions: </p>
<p>1) Is it possible for a molecule to have a transition state at a maximum if there is no saddle point on the potential energy surface?</p>
<p>2) In the case of a diatomic molecule, there is no saddle point on the potential energy surface. So the transition state should be at a maximum right?</p>
| 7,621 |
[
-0.0461287796497345,
-0.015021439641714096,
0.000873446580953896,
0.013667034916579723,
0.0403544045984745,
0.019188478589057922,
-0.03805604204535484,
-0.03800053521990776,
0.0004839845350943506,
-0.055098552256822586,
0.034013666212558746,
0.014354093000292778,
0.003383929142728448,
0.026689019054174423,
0.03157421573996544,
0.015130046755075455,
-0.0019410818349570036,
-0.02132386341691017,
-0.01090220082551241,
0.002997191622853279,
-0.026570556685328484,
0.02003614790737629,
0.02293386682868004,
-0.02109738625586033,
-0.029675718396902084,
-0.01496073603630066,
0.02623085491359234,
0.006099585443735123,
0.008219541050493717,
0.045207612216472626,
-0.03668538108468056,
-0.03819585219025612,
0.02086912840604782,
0.016262633726000786,
0.035744018852710724,
0.013920399360358715,
-0.036004383116960526,
-0.009999901987612247,
-0.026563305407762527,
0.0070998165756464005,
-0.016371095553040504,
-0.021735861897468567,
0.009497246704995632,
0.0537981241941452,
-0.033591993153095245,
0.013507889583706856,
0.0044769709929823875,
-0.03861868754029274,
0.056992292404174805,
-0.057391099631786346,
0.059530436992645264,
-0.002651889342814684,
0.0261387936770916,
0.005491374991834164,
-0.015998845919966698,
-0.002596020232886076,
0.052935607731342316,
0.10519487410783768,
-0.040729228407144547,
-0.04516194388270378,
-0.019717128947377205,
-0.04620065167546272,
0.01913786120712757,
0.021262601017951965,
-0.054706212133169174,
0.050328291952610016,
-0.014900727197527885,
-0.027535701170563698,
0.02179928682744503,
0.03707651048898697,
-0.018314151093363762,
0.007731058169156313,
0.025790834799408913,
-0.019883539527654648,
0.0342012494802475,
-0.03762756288051605,
0.06282881647348404,
-0.0024821634870022535,
0.07222786545753479,
0.04969196021556854,
0.007619292009621859,
0.04022477939724922,
0.009611254557967186,
0.033797428011894226,
0.005851468071341515,
0.012628634460270405,
0.07783249020576477,
0.0006621891516260803,
0.03711096569895744,
0.059352509677410126,
0.0012992465635761619,
0.00089227658463642,
0.02916037105023861,
0.003290321910753846,
-0.006108769681304693,
0.002936981851235032,
-0.004842268768697977,
0.070329949259758,
-0.022337617352604866,
-0.010240026749670506,
0.006495541427284479,
-0.013964416459202766,
0.02456039749085903,
0.056408755481243134,
0.022534260526299477,
0.011901367455720901,
-0.044400181621313095,
0.006746544968336821,
0.016787102445960045,
0.012995678000152111,
-0.06035681068897247,
0.0076851146295666695,
-0.003352544503286481,
-0.004203179385513067,
-0.0027763941325247288,
-0.020531706511974335,
-0.03142255172133446,
-0.040178850293159485,
0.00921841710805893,
0.05170106887817383,
0.028987066820263863,
-0.039177313446998596,
-0.0009117858717218041,
0.01813543029129505,
-0.06038907170295715,
0.005801187828183174,
0.011478690430521965,
0.029359102249145508,
-0.026431739330291748,
-0.00486629456281662,
-0.004632425960153341,
0.006031259428709745,
0.02487969771027565,
-0.004174643196165562,
0.03076186403632164,
-0.01900394633412361,
-0.09283551573753357,
-0.06448128074407578,
-0.006000983528792858,
-0.01736420951783657,
-0.011392896063625813,
-0.09183600544929504,
-0.004769441671669483,
0.0402144193649292,
0.06435362994670868,
-0.0157635435461998,
-0.024528739973902702,
0.0011213271645829082,
0.03181947395205498,
-0.017645280808210373,
-0.00359551003202796,
-0.03218177333474159,
0.013085709884762764,
-0.07161083072423935,
-0.00016461475752294064,
-0.05911361426115036,
0.0361366905272007,
0.026322675868868828,
0.0007226171437650919,
-0.0023598612751811743,
0.06429890543222427,
-0.040462981909513474,
-0.0022873699199408293,
-0.0035320378374308348,
0.024244705215096474,
0.011351034045219421,
0.06465970724821091,
0.04609919339418411,
0.021088168025016785,
0.013593808747828007,
0.03166831657290459,
0.04225512221455574,
-0.03654441609978676,
0.02461368776857853,
0.06196225434541702,
-0.038917697966098785,
-0.03807167708873749,
-0.06013762578368187,
0.023059798404574394,
0.01182671170681715,
-0.03902004286646843,
-0.02755313739180565,
-0.0011788667179644108,
0.03024202398955822,
-0.010085155256092548,
0.03708413615822792,
-0.0048773037269711494,
0.039694949984550476,
-0.008750182576477528,
-0.05347425863146782,
-0.027122745290398598,
-0.03150507062673569,
0.03243088349699974,
-0.007973630912601948,
-0.018176022917032242,
0.004028618801385164,
0.04387584701180458,
0.01135704293847084,
-0.052002206444740295,
-0.024142827838659286,
-0.03756256029009819,
0.021353704854846,
0.010526630096137524,
-0.004875870421528816,
0.04447707161307335,
0.06775566190481186,
0.032541219145059586,
-0.00653429888188839,
0.03340460732579231,
-0.04122062027454376,
-0.01695478893816471,
0.022246675565838814,
0.000012784831596945878,
0.021796487271785736,
0.020596100017428398,
0.008929300121963024,
-0.02158367447555065,
-0.00041925336699932814,
-0.018957877531647682,
0.019529247656464577,
-0.060248397290706635,
0.06501364707946777,
0.044323451817035675,
-0.0013438280439004302,
0.0046652210876345634,
0.03089922107756138,
0.013607135973870754,
-0.009981131181120872,
0.0184222050011158,
-0.01948680728673935,
-0.04207644984126091,
0.02399263344705105,
0.05570124089717865,
0.006951609626412392,
-0.08756706863641739,
-0.005387286189943552,
0.045010775327682495,
0.015124103054404259,
0.01972562074661255,
0.019635936245322227,
-0.01707891933619976,
0.0040051257237792015,
0.013141505420207977,
0.03145141527056694,
0.024604571983218193,
0.05255083367228508,
0.0337565615773201,
0.003530736081302166,
0.04150046408176422,
-0.03324127569794655,
-0.012174403294920921,
0.048819802701473236,
0.01137417834252119,
-0.024354659020900726,
0.00513213686645031,
-0.021957527846097946,
0.050246987491846085,
-0.03385172411799431,
0.02238311991095543,
0.01919880136847496,
-0.023694029077887535,
0.006928370799869299,
-0.004219072870910168,
-0.002676777308806777,
0.027718549594283104,
0.018643414601683617,
-0.04689344763755798,
-0.00911534484475851,
0.04118787869811058,
-0.0463295504450798,
0.022438757121562958,
-0.022075433284044266,
-0.00927265826612711,
-0.009618887677788734,
-0.03136495500802994,
0.0327613465487957,
0.02324596606194973,
0.026219815015792847,
-0.010637437924742699,
-0.04027041420340538,
-0.011146648786962032,
-0.05327280983328819,
-0.004200047347694635,
0.03593539446592331,
-0.03614967688918114,
0.006803739350289106,
-0.0466613695025444,
-0.028310580179095268,
0.049754299223423004,
-0.016697866842150688,
0.013661126606166363,
0.027556050568819046,
-0.02002812922000885,
-0.051679953932762146,
-0.030583864077925682,
-0.02396150678396225,
0.009427456185221672,
-0.023314759135246277,
0.0016461672494187951,
0.05124837905168533,
-0.033361829817295074,
-0.03727469593286514,
0.03192046657204628,
-0.024309298023581505,
-0.03361018747091293,
-0.02773863449692726,
-0.0013598488876596093,
0.01855645328760147,
0.017646992579102516,
0.02367204986512661,
0.009239297360181808,
-0.04167386516928673,
0.039164457470178604,
-0.03820641711354256,
-0.029943061992526054,
0.02347710356116295,
-0.006335047539323568,
0.03414129465818405,
0.00037417825660668314,
-0.018777936697006226,
0.06496527045965195,
0.017595412209630013,
-0.05431189015507698,
-0.0006532762781716883,
-0.019038813188672066,
-0.031906843185424805,
-0.018218036741018295,
0.01899375021457672,
0.007038893178105354,
0.007107520941644907,
0.014642958529293537,
0.015789849683642387,
0.05469971150159836,
0.026997823268175125,
-0.02176847867667675,
-0.012260879389941692,
0.005233305040746927,
0.014685163274407387,
0.00914984755218029,
0.025492146611213684,
0.011423650197684765,
-0.017014814540743828,
0.060044847428798676,
-0.02460549585521221,
0.04049994796514511,
0.018851153552532196,
-0.04102303087711334,
0.0665307566523552,
-0.01458002533763647,
0.03602324053645134,
-0.02812669239938259,
0.017641732469201088,
0.0069798133336007595,
-0.009361840784549713,
0.01295262947678566,
0.02863347716629505,
0.048297978937625885,
0.0016497449250891805,
-0.014521029777824879,
0.02297304756939411,
0.004353374242782593,
0.013503124006092548,
-0.010200866498053074,
0.0211181677877903,
-0.031386010348796844,
0.010564468801021576,
0.0025226420257240534,
-0.040794678032398224,
0.054513685405254364,
0.036203544586896896,
0.028577424585819244,
0.018203988671302795,
-0.043988410383462906,
0.013515106402337551,
-0.075468510389328,
0.013896796852350235,
0.02729872800409794,
0.04205064848065376,
-0.021884940564632416,
0.055559296160936356,
-0.0011529510375112295,
0.04741854593157768,
0.03657400980591774,
-0.003395769512280822,
-0.10050422698259354,
0.03472341597080231,
-0.016301032155752182,
-0.026136569678783417,
-0.005890038795769215,
-0.030135424807667732,
-0.011402726173400879,
-0.04145543649792671,
-0.010248071514070034,
-0.012255384586751461,
-0.003417733358219266,
-0.05463710054755211,
0.0025394500698894262,
-0.04661864787340164,
-0.018704872578382492,
-0.036679767072200775,
0.03615308180451393,
0.042288824915885925,
-0.029037240892648697,
0.036072034388780594,
0.052365195006132126,
-0.03635361045598984,
-0.002381958533078432,
-0.02112555131316185,
0.0325358547270298,
0.01670129969716072,
0.05956408381462097,
0.002922310493886471,
-0.007945136167109013,
0.025835376232862473,
-0.01631307601928711,
-0.0004628335009329021,
0.05795169249176979,
0.02925054542720318,
-0.010124631226062775,
-0.01938294805586338,
-0.02720753289759159,
0.01206873171031475,
0.00345046678557992,
0.030260978266596794,
-0.01565880887210369,
0.007060951087623835,
-0.022753460332751274,
0.01243424043059349,
-0.028452875092625618,
0.04655739665031433,
0.022336365655064583,
0.01318096648901701,
-0.003479741048067808,
-0.07218874990940094,
-0.01406360138207674,
-0.0253700353205204,
0.011567370966076851,
0.002741973614320159,
-0.018398074433207512,
-0.04496577009558678,
0.00856093131005764,
0.004688807763159275,
0.0360121950507164,
-0.02467990852892399,
-0.020457753911614418,
-0.0029630837962031364,
0.06114448979496956,
0.0008813643944449723,
-0.004324872046709061,
0.03454943001270294,
-0.03207264468073845,
0.04513225704431534,
-0.018039705231785774,
0.0035654683597385883,
-0.09183499962091446,
-0.03764735534787178,
0.030074307695031166,
0.036472950130701065,
-0.012599230743944645,
0.005389636382460594,
-0.03316214308142662,
0.027465373277664185,
0.05488482862710953,
-0.01915566995739937,
0.030502356588840485,
-0.024821683764457703,
-0.01882849633693695,
-0.01047707162797451,
-0.03585100173950195,
-0.009673802182078362,
-0.006234683096408844,
0.03199579939246178,
-0.013202520087361336,
-0.011444964446127415,
0.017514009028673172,
-0.016652589663863182,
0.006823554635047913,
0.013042634353041649,
0.09004668891429901,
0.010779911652207375,
-0.030382754281163216,
0.028100015595555305,
0.014581591822206974,
-0.0032335713040083647,
-0.07082213461399078,
0.016692010685801506,
0.015336969867348671,
0.0048982431180775166,
0.050871655344963074,
-0.04688163846731186,
-0.0664360374212265,
0.04577266424894333,
-0.016693124547600746,
-0.028509870171546936,
-0.005999411456286907,
0.010466859675943851,
0.050845857709646225,
0.07934161275625229,
-0.019849039614200592,
0.055317457765340805,
0.06091037392616272,
-0.004493714310228825,
-0.0013674964429810643,
-0.006740739569067955,
0.04038754850625992,
-0.008128882385790348,
0.0052950442768633366,
-0.06239032372832298,
-0.02109571360051632,
-0.0151078375056386,
0.0008093927754089236,
0.004288725089281797,
0.02605060487985611,
-0.024840617552399635,
-0.010470852255821228,
-0.0032055231276899576,
0.04590797796845436,
0.008236904628574848,
-0.021523816511034966,
-0.03549009934067726,
0.025067070499062538,
-0.018349042162299156,
-0.020233137533068657,
0.007765519432723522,
-0.00973929837346077,
-0.004484955221414566,
0.04796314612030983,
-0.026529861614108086,
0.02973989024758339,
-0.055388279259204865,
-0.029171112924814224,
-0.016820278018712997,
-0.09770232439041138,
0.039182938635349274,
-0.04430736228823662,
-0.021225353702902794,
0.01332270260900259,
-0.03825267404317856,
-0.029568077996373177,
0.04274088889360428,
-0.0040263948030769825,
-0.0066841463558375835,
-0.045291971415281296,
0.05252457410097122,
-0.017760103568434715,
0.021839888766407967,
-0.06382149457931519,
-0.03944026306271553,
0.054056908935308456,
0.037787552922964096,
-0.0418240986764431,
0.002114861039444804,
-0.014647816307842731,
-0.008678719401359558,
-0.010937216691672802,
0.013095047324895859,
0.025263750925660133,
-0.0006233299500308931,
-0.04190859943628311,
0.05947667360305786,
0.005411047954112291,
0.048476580530405045,
-0.001925138640217483,
-0.01985306292772293,
0.024241866543889046,
-0.01732259802520275,
-0.025250734761357307,
-0.048413462936878204,
0.05369461700320244,
-0.014748690649867058,
-0.026416731998324394,
-0.014757904224097729,
0.010748784057796001,
0.04883821681141853,
-0.0021696242038160563,
-0.019083114340901375,
0.03229239583015442,
-0.0032946353312581778,
0.010591119527816772,
-0.04595706984400749,
-0.006865323055535555,
-0.05798107013106346,
-0.004912802018225193,
0.01499688159674406,
0.01003818679600954,
0.0167145486921072,
-0.06246310472488403,
0.0022780606523156166,
0.021098313853144646,
0.03528282046318054,
-0.0027728567365556955,
0.08143951743841171,
0.008395446464419365,
0.017782026901841164,
-0.0026916000060737133,
-0.04129479452967644,
0.003955269232392311,
0.026977287605404854,
0.007712338585406542,
0.024900322780013084,
0.006238317582756281,
-0.04072247073054314,
-0.009054809808731079,
-0.04290783405303955,
0.02669553831219673,
0.01693846471607685,
-0.02038436010479927,
-0.009945260360836983,
-0.006486526690423489,
0.03651110827922821,
0.005609044339507818,
-0.03899542987346649,
-0.01596585288643837,
-0.010623476468026638,
-0.01395274419337511,
0.056477710604667664,
-0.0002531263162381947,
0.02427101507782936,
0.0546480193734169,
0.042221616953611374,
-0.024944685399532318,
0.060418806970119476,
0.022165674716234207,
0.0008707004017196596,
0.02245982363820076,
0.004826389253139496,
-0.029255323112010956,
0.04454459995031357,
-0.016319839283823967,
0.04545611888170242,
0.0005725547089241445,
-0.026629194617271423,
0.025440752506256104,
-0.01235237903892994,
0.04936626926064491,
-0.021652953699231148,
-0.0011879072990268469,
-0.023860938847064972,
0.06845396012067795,
-0.022913001477718353,
-0.001301691634580493,
0.01147541031241417,
0.024254651740193367,
0.022290151566267014,
0.00836277101188898,
0.005627255886793137,
-0.018862169235944748,
-0.03626308962702751,
-0.03077346831560135,
-0.016349144279956818,
-0.05683056265115738,
0.030265193432569504,
-0.004206249490380287,
-0.03678956627845764,
0.03699956834316254,
-0.007751302793622017,
0.008976628072559834,
-0.027074186131358147,
0.05502905324101448,
0.023105036467313766,
0.07660824805498123,
0.021228002384305,
0.047122009098529816,
0.0010855237487703562,
0.012407509610056877,
0.10164544731378555,
0.06112053617835045,
-0.0028098104521632195,
-0.03129728510975838,
0.015967708081007004,
-0.007907181046903133,
0.0017898050136864185,
-0.013950038701295853,
0.005676092114299536,
-0.011494714766740799,
0.0049202702939510345,
-0.008645093068480492,
0.03241408243775368,
-0.03305226191878319,
0.03558294475078583,
0.03733692318201065,
-0.04658159613609314,
-0.03457820042967796,
0.00809730775654316,
0.03356126695871353,
-0.015438714995980263,
-0.009063538163900375,
-0.019063668325543404,
0.025518085807561874,
-0.02170495316386223,
0.012560737319290638,
-0.027846019715070724,
-0.041271600872278214,
0.027122631669044495,
0.010612520389258862,
-0.018860474228858948,
-0.003180233994498849,
0.0056402734480798244,
0.0116779375821352,
-0.03522011265158653,
0.029769698157906532,
0.0013789370423182845,
-0.001431128359399736,
0.0002940916165243834,
0.062316086143255234,
0.01403765007853508,
0.009304924868047237,
0.023627910763025284,
0.003906289115548134,
-0.03429929539561272,
-0.007524136919528246,
-0.03598294034600258,
-0.005860332865267992,
-0.0331210233271122,
-0.014828217215836048,
-0.01609245128929615,
0.008109774440526962,
0.015981724485754967,
-0.03828825056552887,
-0.03817566856741905,
-0.03240470588207245,
0.04489315673708916,
-0.010231858119368553,
-0.010998111218214035,
-0.05590205267071724,
0.007380976341664791,
0.005518597085028887,
-0.017001615837216377,
-0.016031676903367043,
0.0014652445679530501,
0.015672190114855766,
-0.004834366962313652,
0.059091273695230484,
-0.024587195366621017,
-0.009152136743068695,
0.01994907110929489,
0.006619655527174473,
-0.02943878248333931,
-0.04452380910515785,
0.038406502455472946,
-0.0037926624063402414,
0.03313542157411575,
0.01856522262096405,
0.003886125050485134,
-0.012328998185694218,
-0.06457454711198807,
0.007393567822873592,
0.003279372351244092,
-0.023450106382369995,
-0.0166378915309906,
0.023985007777810097,
0.024779530242085457,
0.02291964367032051,
-0.03400838375091553,
0.03713343292474747,
0.009986155666410923,
0.008254836313426495,
0.01062852144241333,
-0.020801648497581482,
-0.027309661731123924,
-0.010148468427360058,
-0.018058260902762413,
0.019971325993537903,
-0.030863529071211815,
0.07127750664949417,
-0.00019133712339680642,
0.00198539299890399,
-0.001381574897095561,
0.0027770460583269596,
-0.02793852984905243,
0.01176624745130539,
0.02454773522913456,
-0.012395068071782589,
-0.0187767893075943,
0.00044143362902104855,
0.025539668276906013,
-0.014090078882873058,
-0.049704376608133316,
-0.02278096042573452,
-0.009942193515598774,
0.000899365870282054,
0.016592279076576233,
-0.0017831939039751887,
0.014309179969131947,
-0.009449967183172703,
-0.0103987455368042,
-0.04730086401104927,
-0.01871570013463497,
-0.054436035454273224,
0.03391939029097557,
0.037505920976400375,
0.0016261939890682697,
-0.0010808998486027122,
-0.007578178774565458,
-0.020358281210064888,
-0.015599080361425877,
0.020875586196780205,
0.05553038418292999,
-0.014784744009375572,
-0.007397957146167755,
0.01417007576674223,
0.015078172087669373,
0.04991672933101654,
-0.034930404275655746,
-0.0012088638031855226,
0.033509157598018646,
-0.05541476979851723,
-0.02056867443025112,
0.0017159698763862252,
-0.017018819227814674,
0.019056152552366257,
-0.0005660437745973468,
0.007063946686685085,
-0.01663166657090187,
0.0450846292078495,
-0.005163924768567085,
0.016579391434788704,
0.018233468756079674,
-0.041427481919527054,
-0.03961223363876343,
-0.001640629954636097,
0.007676041219383478,
-0.022441348060965538,
-0.006224225275218487,
0.025995545089244843,
0.016075139865279198,
0.0058318632654845715,
-0.014506131410598755,
0.004631470888853073,
-0.03432942181825638,
0.024607274681329727,
0.009878785349428654,
0.0114997373893857,
0.039947010576725006,
0.044685911387205124,
-0.0333254411816597,
0.02953510917723179,
0.02155088447034359,
0.00876899715512991,
-0.08739262074232101,
-0.012480834499001503,
-0.005210505798459053,
-0.06750155985355377,
0.010295667685568333,
-0.023159733042120934,
0.02554628625512123,
0.04457363113760948,
-0.05080015957355499,
-0.006131515372544527,
0.0006310201715677977,
-0.01887516863644123,
-0.029794378206133842,
-0.021626072004437447,
-0.04095565900206566,
0.06160867586731911,
0.04358767718076706,
0.043248482048511505,
0.006856271997094154,
0.018565325066447258,
-0.010567585937678814,
-0.03277348726987839,
-0.010647589340806007,
0.021214744076132774,
-0.03742513805627823,
-0.049380458891391754,
0.06382670253515244,
-0.01854189671576023,
-0.03781149163842201,
0.007972106337547302,
-0.03411460667848587,
0.011654750443994999,
0.012222809717059135,
-0.047616809606552124,
-0.0028345149476081133,
-0.003301425836980343,
0.035922255367040634,
0.007135377265512943,
-0.03592482581734657,
0.040651336312294006,
-0.002890420611947775,
0.01387979555875063,
-0.03433794900774956,
-0.00950078759342432,
0.00928082037717104,
-0.032718971371650696,
-0.06518297642469406,
0.03082498535513878,
-0.020191030576825142,
-0.02673719823360443,
0.010155156254768372,
0.023222874850034714,
-0.004315198864787817,
-0.020072586834430695,
-0.02494276873767376,
-0.024465681985020638,
-0.046661198139190674,
0.02504715695977211,
0.04441091790795326,
-0.014676840044558048,
0.024742431938648224,
-0.025355177000164986,
-0.03588759899139404,
0.04662624001502991,
0.009091382846236229,
-0.03249962627887726,
-0.06807281821966171,
0.014975708909332752,
0.0007069989223964512,
-0.04753749445080757,
-0.026833444833755493,
-0.0030699786730110645,
-0.04638203978538513,
0.03413325175642967,
0.024909453466534615,
0.0023427442647516727,
-0.008994538336992264,
-0.044914793223142624,
-0.040447548031806946,
-0.08828328549861908,
0.03652124106884003,
-0.015941176563501358,
0.013909759931266308,
-0.0301793422549963,
-0.011412499472498894,
0.004993857350200415,
-0.02327055111527443,
0.04676065221428871,
-0.019869530573487282,
-0.004094196017831564,
0.014395307749509811,
0.00766501110047102,
0.030379556119441986,
-0.036519650369882584,
-0.0031933062709867954,
0.017519790679216385,
-0.023139968514442444,
0.000397431111196056,
-0.01851736195385456,
-0.009754449129104614,
0.028337489813566208,
0.01271043810993433,
0.007827315479516983,
0.06527046114206314,
0.020853759720921516,
0.009423418901860714,
0.035576410591602325,
-0.0012839260743930936,
-0.007491630036383867,
0.05880088731646538,
-0.03295910730957985,
0.013077348470687866,
0.01980992965400219,
-0.04882432147860527,
-0.053944144397974014,
0.011077962815761566,
-0.04495539888739586,
-0.012494828552007675,
-0.06458631157875061,
-0.041581541299819946,
-0.029189860448241234,
-0.032786186784505844,
0.026625972241163254,
0.03790063410997391,
-0.02701805718243122,
-0.009308229200541973,
0.05892607942223549,
-0.015600317157804966,
0.05950264632701874,
-0.011854053474962711,
0.006681122351437807,
0.029463214799761772,
0.020868482068181038,
0.01995883323252201,
0.036878686398267746,
0.041215263307094574,
0.0035421254578977823,
0.028063489124178886,
-0.010577091947197914,
-0.03299695998430252,
0.01325337216258049,
0.05581871420145035,
-0.01513390801846981,
-0.01606019027531147,
-0.03949494659900665,
0.04547629505395889,
0.013001149520277977,
0.007454367820173502,
-0.010591724887490273,
-0.010426443070173264,
0.053372595459222794,
-0.00514656025916338,
-0.0006959060556255281,
-0.02217644453048706,
0.02711375802755356,
-0.031081868335604668,
-0.017650730907917023,
0.003595784306526184,
0.04766196012496948,
-0.020274868234992027,
0.008148113265633583,
-0.013392855413258076,
0.037124376744031906,
0.025041142478585243,
-0.022427497431635857,
0.04709383472800255,
-0.02749539166688919,
-0.004528192337602377,
-0.04349413514137268,
0.02270808443427086,
-0.011238940991461277,
-0.01627386175096035,
0.027426602318882942,
0.020635847002267838,
0.01087232120335102,
0.014712084084749222,
5.3166684210737e-7,
-0.009561953134834766,
0.03570624068379402,
-0.028180871158838272,
-0.011201141402125359,
-0.012629227712750435,
0.0038469990249723196,
-0.03210488706827164,
-0.030150586739182472
] |
<p>I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically? </p>
| 7,622 |
[
-0.05909636989235878,
-0.03233175724744797,
-0.022015394642949104,
0.004538207780569792,
0.04577263444662094,
-0.01988818868994713,
-0.03171871230006218,
0.015819203108549118,
-0.029772669076919556,
-0.0060699633322656155,
0.03059348464012146,
0.04175928607583046,
0.03129887580871582,
0.001871586893685162,
0.03746996819972992,
0.01184599194675684,
-0.019815921783447266,
0.016940545290708542,
0.003955187741667032,
-0.012375283055007458,
-0.0034657877404242754,
-0.0008596197585575283,
-0.004739667754620314,
-0.03133496269583702,
-0.008048541843891144,
0.0184330977499485,
0.04593636840581894,
-0.014476693235337734,
0.02128128707408905,
0.06443518400192261,
0.017308015376329422,
-0.02557298168540001,
0.03152254596352577,
0.028343861922621727,
0.03992201387882233,
0.026393234729766846,
-0.030928710475564003,
-0.005018696188926697,
-0.027670908719301224,
0.035594042390584946,
-0.02458718977868557,
-0.030658172443509102,
0.007774283178150654,
0.07066917419433594,
-0.013119705952703953,
0.02912188693881035,
-0.012609315104782581,
0.018222307786345482,
0.05739662051200867,
-0.09233827888965607,
0.06474906206130981,
0.00603833980858326,
0.027253154665231705,
0.026909764856100082,
0.018859267234802246,
0.02025246061384678,
0.05194869637489319,
0.03383290022611618,
-0.024073807522654533,
-0.053959205746650696,
0.01609138585627079,
-0.01957128942012787,
0.006771070417016745,
0.003736336948350072,
-0.01818215847015381,
-0.014795592986047268,
-0.012621351517736912,
-0.02408570609986782,
0.01993374526500702,
-0.03264927864074707,
-0.027223600074648857,
0.006390529219061136,
0.055281464010477066,
-0.03519789129495621,
-0.017320042476058006,
-0.013850782997906208,
0.0185331329703331,
-0.012123731896281242,
0.058710627257823944,
-0.01689666509628296,
-0.021709421649575233,
0.01712317205965519,
0.02921335957944393,
0.01917574368417263,
0.012698627077043056,
0.021087665110826492,
0.06815608590841293,
-0.03320307284593582,
0.03231841325759888,
0.056252703070640564,
0.0016566956182941794,
0.016781773418188095,
0.012768365442752838,
0.004356276709586382,
-0.013509230688214302,
0.020868780091404915,
-0.008483951911330223,
-0.0011876248754560947,
0.0319833867251873,
-0.03426732122898102,
0.0038430015556514263,
-0.03146221116185188,
-0.03308039903640747,
0.0746380016207695,
0.008517151698470116,
-0.00957864336669445,
-0.045160721987485886,
0.029938703402876854,
-0.0008924031280912459,
0.02101154811680317,
-0.03211941570043564,
-0.02489917166531086,
0.013432755134999752,
-0.009869459085166454,
-0.0028836301062256098,
-0.017788736149668694,
-0.007016156334429979,
-0.04413164407014847,
0.014203760772943497,
0.08590859174728394,
0.05086676403880119,
-0.019232936203479767,
0.02955765090882778,
-0.0397990345954895,
-0.03141507878899574,
0.041737329214811325,
0.009864657185971737,
-0.00007831622497178614,
-0.0455624982714653,
0.009983500465750694,
0.02062881551682949,
-0.007636759430170059,
-0.007354788016527891,
0.030531052500009537,
0.021546637639403343,
-0.025003831833600998,
-0.08281765133142471,
-0.04524264112114906,
0.05576227232813835,
-0.03636568412184715,
-0.03797721862792969,
-0.05133705213665962,
0.012228607200086117,
0.0432065911591053,
0.07664483040571213,
-0.04373681917786598,
-0.0018640230409801006,
0.0062405746430158615,
0.08534226566553116,
-0.02536657452583313,
-0.01238240022212267,
-0.002233479404821992,
0.00022229460591915995,
-0.04035232961177826,
0.007085699122399092,
-0.080062635242939,
0.008280747570097446,
-0.006449396722018719,
0.030500542372465134,
-0.052192602306604385,
0.0463784784078598,
-0.05531115084886551,
0.002971440553665161,
0.012816241011023521,
-0.0041202702559530735,
-0.024522362276911736,
0.07573695480823517,
0.009234968572854996,
-0.03263857215642929,
0.022735491394996643,
-0.016335083171725273,
0.05134234577417374,
0.0006734399357810616,
0.018839236348867416,
0.03736530989408493,
-0.04994526132941246,
-0.020778553560376167,
0.01479246374219656,
0.027988223358988762,
0.01679377071559429,
-0.02675558812916279,
-0.025051284581422806,
-0.00920735951513052,
0.012992084957659245,
0.00521154934540391,
0.06151457875967026,
-0.02210857905447483,
-0.00954998005181551,
0.008461426012217999,
-0.07056620717048645,
0.03997469320893288,
-0.03342697396874428,
0.040028396993875504,
-0.02795172855257988,
-0.022635290399193764,
0.01553274504840374,
0.024606211110949516,
0.027784274891018867,
-0.0070412615314126015,
-0.008931290358304977,
-0.012544079683721066,
0.034968599677085876,
0.017770621925592422,
-0.03615773469209671,
0.01364821009337902,
0.0328223817050457,
0.020212456583976746,
-0.012818246148526669,
0.018233614042401314,
-0.0026483298279345036,
-0.023137370124459267,
-0.016811402514576912,
-0.02160745859146118,
0.009143784642219543,
-0.03790486976504326,
-0.040489211678504944,
0.01489716861397028,
0.03534548729658127,
0.025470955297350883,
0.02914702333509922,
-0.05136820301413536,
0.05375068262219429,
0.05141858011484146,
0.007173831574618816,
0.01698383130133152,
0.018181681632995605,
0.02806135080754757,
0.007274378556758165,
0.02828580141067505,
-0.04295174032449722,
-0.031918805092573166,
-0.011403318494558334,
0.03285844996571541,
0.04162614792585373,
-0.02998104877769947,
-0.003700250992551446,
0.03691055253148079,
0.04383021220564842,
0.014415735378861427,
0.009502843953669071,
-0.0023411789443343878,
-0.008155014365911484,
0.017617302015423775,
0.011492828838527203,
0.024958766996860504,
0.031072445213794708,
0.012867659330368042,
0.009717767126858234,
0.015805695205926895,
0.0036302616354078054,
-0.06698720902204514,
-0.008428988046944141,
0.004060055129230022,
0.0073231980204582214,
0.014657302759587765,
-0.0024707806296646595,
0.03544594720005989,
-0.041065800935029984,
-0.004668154288083315,
0.02811587229371071,
-0.0010555676417425275,
0.03136594593524933,
-0.038676243275403976,
0.024301806464791298,
0.005558778531849384,
-0.009599643759429455,
-0.02665584534406662,
-0.018219223245978355,
0.043467022478580475,
-0.04125479236245155,
-0.01744748093187809,
-0.01235959678888321,
-0.003998043946921825,
0.026200730353593826,
0.010160381905734539,
0.006982898339629173,
0.002995697781443596,
-0.014476961456239223,
0.004817289765924215,
-0.014377441257238388,
0.022060222923755646,
0.00003477996870060451,
-0.006609470117837191,
-0.004136517643928528,
-0.07051901519298553,
0.03297661244869232,
-0.029358262196183205,
0.011095262132585049,
0.07100900262594223,
-0.025712132453918457,
0.005187039263546467,
-0.020497959107160568,
-0.007741523440927267,
-0.040337733924388885,
-0.019152147695422173,
-0.027196133509278297,
0.01776832528412342,
-0.039559271186590195,
0.045442286878824234,
0.027777019888162613,
-0.014240380376577377,
-0.06536684185266495,
0.04048809036612511,
-0.03369168937206268,
-0.0391053780913353,
-0.014315327629446983,
-0.004896055907011032,
0.06543635576963425,
-0.028405310586094856,
0.007669676560908556,
0.004383973311632872,
-0.02828962728381157,
-0.0035597598180174828,
-0.02897259220480919,
-0.027002748101949692,
-0.0028209236916154623,
-0.029250040650367737,
0.07445987313985825,
0.032922159880399704,
-0.031151089817285538,
0.0618714764714241,
-0.0136514101177454,
-0.07988227903842926,
-0.0352032370865345,
0.025965984910726547,
0.0011368610430508852,
-0.07109373807907104,
0.04608488455414772,
0.04121642932295799,
-0.01765824668109417,
0.027915889397263527,
0.00642165495082736,
0.012297289445996284,
0.04460320621728897,
0.0030088734347373247,
-0.0027969868388026953,
0.02172006480395794,
0.005681782029569149,
0.010851822793483734,
-0.010309404693543911,
0.010771751403808594,
-0.018550727516412735,
0.027600649744272232,
0.015435576438903809,
0.03909548372030258,
0.022924713790416718,
-0.048554159700870514,
0.059012431651353836,
0.0006091410759836435,
0.0006568050011992455,
0.005286052823066711,
0.030445681884884834,
-0.03751983121037483,
-0.0011679939925670624,
0.017043158411979675,
0.0299055278301239,
0.03280388563871384,
-0.03256513923406601,
0.021028025075793266,
0.0368901863694191,
0.02988255023956299,
-0.029055533930659294,
-0.024752158671617508,
-0.011341688223183155,
-0.019497398287057877,
0.035833366215229034,
-0.02679244987666607,
-0.02941453643143177,
0.053375352174043655,
0.021270906552672386,
-0.00828720536082983,
-0.010141825303435326,
-0.007834570482373238,
0.01848161406815052,
-0.06554826349020004,
-0.022725120186805725,
-0.005772181320935488,
0.03452364727854729,
-0.013859456405043602,
0.07641900330781937,
0.0006088070222176611,
0.016621340066194534,
0.013236917555332184,
0.006969594396650791,
-0.08893489837646484,
0.011770233511924744,
-0.007014547009021044,
0.0250138770788908,
-0.012972570955753326,
-0.0003442412125878036,
0.0037427679635584354,
-0.03385140746831894,
-0.031661637127399445,
-0.02255159243941307,
-0.0033728559501469135,
-0.06267993152141571,
0.023440644145011902,
0.005850008688867092,
-0.035283640027046204,
-0.033236030489206314,
0.03373664617538452,
0.02312268503010273,
-0.019392291083931923,
0.07727153599262238,
0.04231993854045868,
-0.014821924269199371,
0.046414975076913834,
-0.013602565973997116,
0.018903881311416626,
0.016216089949011803,
0.030884407460689545,
0.02737255208194256,
0.005456293001770973,
0.005642575211822987,
-0.006875940132886171,
-0.004692915827035904,
0.013996778056025505,
-0.023731844499707222,
0.006715450901538134,
-0.033811572939157486,
-0.025371141731739044,
0.014591913670301437,
0.01458378043025732,
0.03385801240801811,
0.00613643042743206,
0.020624717697501183,
0.013502362184226513,
-0.022342072799801826,
-0.023974070325493813,
0.015459011308848858,
0.033993665128946304,
0.019164860248565674,
-0.03970072790980339,
-0.06261928379535675,
-0.012183278799057007,
-0.0458151213824749,
-0.011767188087105751,
-0.004526687320321798,
-0.006695159245282412,
-0.03612310811877251,
-0.0018428526818752289,
0.028093991801142693,
-0.017856432124972343,
-0.015041650272905827,
-0.02846148982644081,
0.003996540326625109,
0.03158567473292351,
-0.025559911504387856,
0.023076746612787247,
0.003949643112719059,
0.057774242013692856,
0.04735959321260452,
-0.004712584428489208,
-0.033101823180913925,
-0.061017535626888275,
-0.027776947245001793,
0.024511422961950302,
0.029412370175123215,
-0.005358072463423014,
0.020285271108150482,
-0.04315407946705818,
-0.05913369730114937,
0.08765624463558197,
-0.019731078296899796,
-0.0009048593346960843,
-0.028393615037202835,
-0.010909494943916798,
0.012677866034209728,
-0.03323924168944359,
-0.011572017334401608,
0.01852289028465748,
-0.023066727444529533,
0.0060199107974767685,
-0.006486137863248587,
0.011324407532811165,
-0.017766376957297325,
0.008082150481641293,
0.023047329857945442,
0.023838086053729057,
0.03334889933466911,
-0.013334754854440689,
0.0012606140226125717,
0.048446428030729294,
-0.026748910546302795,
-0.04907066375017166,
0.000249457370955497,
-0.005464987829327583,
0.0008462985861115158,
-0.00039166660280898213,
-0.038149621337652206,
-0.05816667899489403,
-0.013122362084686756,
0.02103494666516781,
-0.01928362064063549,
0.031464677304029465,
-0.038966402411460876,
0.0175090953707695,
0.001328861340880394,
0.03314840793609619,
0.005519398488104343,
0.04982021450996399,
-0.022976277396082878,
-0.06924566626548767,
-0.02646285854279995,
0.029919132590293884,
-0.030649268999695778,
-0.040871281176805496,
-0.036089081317186356,
0.027348699048161507,
-0.043615736067295074,
0.020580386742949486,
0.026041315868496895,
-0.010359631851315498,
0.025288980454206467,
-0.01475577987730503,
-0.0019516423344612122,
0.03007536754012108,
0.03865477442741394,
-0.03790036216378212,
0.003560359124094248,
0.023256367072463036,
0.059092141687870026,
-0.03214924782514572,
0.028912363573908806,
-0.01185885351151228,
0.011864613741636276,
0.023981919512152672,
-0.003832706017419696,
0.00808178260922432,
-0.019200723618268967,
-0.015213362872600555,
-0.0073602404445409775,
-0.023394960910081863,
0.043783582746982574,
-0.03156091272830963,
0.011905509047210217,
0.04535708948969841,
-0.06326474994421005,
0.00576604763045907,
0.030096184462308884,
-0.018954996019601822,
0.0044961660169065,
-0.055450838059186935,
0.015145905315876007,
0.013265488669276237,
-0.001398109714500606,
-0.06371946632862091,
-0.03500973805785179,
0.04035932570695877,
-0.004552188795059919,
-0.039301540702581406,
-0.02467152290046215,
-0.009490208700299263,
-0.03732699155807495,
-0.05177496373653412,
-0.005006313789635897,
0.020838864147663116,
-0.037622567266225815,
-0.019748587161302567,
0.019710635766386986,
0.009054153226315975,
0.0631091296672821,
-0.02540266327559948,
-0.017746055498719215,
0.021191367879509926,
-0.016866711899638176,
-0.014380278997123241,
-0.01519075408577919,
0.05878851190209389,
-0.010091133415699005,
-0.006723587866872549,
-0.006831324193626642,
-0.031281728297472,
0.015794744715094566,
-0.00036777547211386263,
0.029878737404942513,
0.016811233013868332,
-0.012623370625078678,
-0.0021381538826972246,
-0.019227223470807076,
-0.0035121103283017874,
-0.0026537112426012754,
0.034398749470710754,
-0.0009840737329795957,
-0.01414143294095993,
-0.01025905180722475,
-0.021043935790657997,
0.04247291758656502,
-0.008491850458085537,
-0.06285755336284637,
0.004285163711756468,
0.062098968774080276,
-0.02006293646991253,
-0.00285484385676682,
0.0016512428410351276,
-0.00458429055288434,
-0.00822365377098322,
0.040394850075244904,
-0.02146437205374241,
-0.005210222210735083,
0.02793554961681366,
-0.039076417684555054,
-0.030018212273716927,
-0.026074914261698723,
0.013503755442798138,
0.09459666907787323,
-0.014673411846160889,
0.03418871760368347,
0.008719229139387608,
0.008694900199770927,
-0.0015148171223700047,
0.03779035061597824,
-0.01312885619699955,
0.0005863775731995702,
-0.022739574313163757,
0.09312813729047775,
-0.03765011951327324,
0.009936193935573101,
-0.008969013579189777,
0.037691906094551086,
-0.016904274001717567,
0.022375348955392838,
0.02317323163151741,
-0.008785944432020187,
0.03308039531111717,
0.05845332518219948,
-0.02595871314406395,
0.03414633497595787,
-0.018957823514938354,
0.04921884462237358,
0.012194239534437656,
-0.006343276239931583,
0.018461883068084717,
0.01222726795822382,
0.007585716899484396,
-0.029075106605887413,
0.014426502399146557,
-0.03861090913414955,
0.02309689112007618,
0.03174649924039841,
0.011496903374791145,
-0.0036612532567232847,
0.025607168674468994,
0.028203461319208145,
-0.0036310292780399323,
-0.014774985611438751,
-0.02030978910624981,
-0.02598198503255844,
-0.0023529715836048126,
-0.03030846267938614,
-0.04707775637507439,
0.030630527064204216,
0.021465927362442017,
-0.023705359548330307,
-0.009850025177001953,
-0.0021548389922827482,
-0.01780504174530506,
0.03361928462982178,
0.029632503166794777,
-0.0028030239045619965,
0.07150125503540039,
-0.023600392043590546,
0.023108769208192825,
-0.0499916635453701,
0.00950612872838974,
0.1122676283121109,
0.023224173113703728,
0.02569873072206974,
-0.0644034668803215,
0.029024478048086166,
-0.031633492559194565,
-0.005732257384806871,
-0.029387686401605606,
0.062981978058815,
-0.02300039306282997,
0.02781728096306324,
-0.0011904535349458456,
0.07439050823450089,
-0.015612472780048847,
0.01174534484744072,
0.06779763847589493,
-0.05422312766313553,
-0.011392271146178246,
0.0005437330692075193,
-0.016821611672639847,
-0.03209860995411873,
0.03295115754008293,
-0.045676350593566895,
0.037620384246110916,
-0.03982669487595558,
-0.022823024541139603,
-0.04205752909183502,
-0.049100734293460846,
0.04006214067339897,
-0.00815983209758997,
-0.05849986895918846,
0.05028910934925079,
0.0023577448446303606,
0.0009479527943767607,
-0.05807467922568321,
0.016048787161707878,
0.006464602891355753,
-0.01912701316177845,
0.02338155172765255,
-0.0012106404174119234,
0.041890259832143784,
0.0008716635056771338,
-0.012041478417813778,
0.027067268267273903,
-0.018676580861210823,
-0.0018425175221636891,
-0.04275687411427498,
0.022757595404982567,
-0.006582051981240511,
0.000129260792164132,
-0.009909029118716717,
-0.012834477238357067,
0.010879051871597767,
-0.06641901284456253,
-0.02390201948583126,
-0.008920127525925636,
0.020342037081718445,
0.019177228212356567,
-0.03289185091853142,
-0.02356863208115101,
-0.007401470560580492,
-0.006722643971443176,
0.011060452088713646,
-0.019612079486250877,
0.003801217069849372,
0.02311849221587181,
0.024949103593826294,
0.06137421354651451,
-0.015249354764819145,
-0.02948966808617115,
-0.02709849551320076,
0.0041974252089858055,
-0.0508870929479599,
0.0024774407502263784,
0.02869502827525139,
-0.0028791276272386312,
0.0010257461108267307,
0.033730730414390564,
-0.01786191388964653,
0.04651390388607979,
-0.06133503094315529,
0.04726269468665123,
0.0013607606524601579,
-0.008794991299510002,
-0.00834670104086399,
0.0034335367381572723,
0.02844788320362568,
0.04980318993330002,
-0.008608018048107624,
0.007251518312841654,
-0.007972978986799717,
0.015697089955210686,
-0.0021146642975509167,
-0.015232754871249199,
-0.031132182106375694,
0.004183261189609766,
-0.03206201642751694,
-0.025139765813946724,
-0.02556600794196129,
0.04593083634972572,
0.06488310545682907,
0.047064054757356644,
-0.013786683790385723,
-0.005230836104601622,
-0.04726023226976395,
-0.0020166411995887756,
-0.0035327367950230837,
-0.03730108216404915,
-0.02399628423154354,
0.004509119316935539,
-0.013196498155593872,
-0.06063518673181534,
-0.033623579889535904,
-0.028235699981451035,
0.019918983802199364,
0.004677192308008671,
0.047470927238464355,
-0.003820569720119238,
0.001639098976738751,
0.002151607535779476,
0.026998845860362053,
-0.04188696667551994,
0.00717295054346323,
-0.05422838777303696,
0.00048019824316725135,
0.005473601631820202,
-0.0005752649158239365,
-0.010502258315682411,
0.02551567554473877,
-0.012241963297128677,
-0.0028137071058154106,
0.022691940888762474,
0.014906576834619045,
0.022939104586839676,
0.030793139711022377,
0.04745987430214882,
-0.010884422808885574,
0.028417598456144333,
-0.052021946758031845,
-0.072665736079216,
0.04452329874038696,
-0.03318887948989868,
-0.03943246603012085,
-0.017375724390149117,
-0.025422925129532814,
0.0024521604645997286,
0.012112446129322052,
-0.0040894318372011185,
0.002630044473335147,
0.034165337681770325,
0.012800090946257114,
0.016410773620009422,
-0.021568330004811287,
-0.025687338784337044,
0.005179756321012974,
-0.020917005836963654,
0.02602957934141159,
-0.032787006348371506,
-0.0032407506369054317,
0.05166661739349365,
0.05437275767326355,
0.0010099412174895406,
-0.013375564478337765,
0.028737597167491913,
0.004023648798465729,
0.027963632717728615,
0.020214879885315895,
0.016933586448431015,
0.022668421268463135,
0.02171606570482254,
-0.022258475422859192,
0.03969905525445938,
0.006223927717655897,
-0.0011738943867385387,
-0.11531105637550354,
0.007747930474579334,
0.02862194925546646,
-0.02291337214410305,
0.020041653886437416,
-0.05586123466491699,
-0.02058522403240204,
0.030705558136105537,
-0.07370919734239578,
-0.009579051285982132,
-0.05020030215382576,
0.005384370684623718,
-0.027531234547495842,
-0.006851883139461279,
-0.0184255950152874,
0.05622541904449463,
0.05355110764503479,
0.008665098808705807,
0.04212521016597748,
0.01694629155099392,
-0.03478245809674263,
-0.014966413378715515,
-0.0026728748343884945,
0.026041265577077866,
-0.030769363045692444,
-0.0058277747593820095,
0.05355590954422951,
0.015715589746832848,
-0.04249623417854309,
0.009291994385421276,
-0.02777370624244213,
-0.0018498302670195699,
-0.020577672868967056,
-0.0037237938959151506,
-0.02635432779788971,
0.009996965527534485,
0.014056254178285599,
0.0017559857806190848,
-0.02017349936068058,
0.018408838659524918,
0.044453684240579605,
0.017304865643382072,
-0.01908443681895733,
-0.01004913728684187,
0.01806660182774067,
-0.03722511604428291,
-0.015233894810080528,
0.04138273000717163,
-0.03901270404458046,
0.0012550315586850047,
-0.01218848954886198,
-0.007428695913404226,
0.001883370103314519,
-0.029507288709282875,
0.0370577909052372,
-0.03204682469367981,
0.0425330325961113,
-0.008606796152889729,
0.03854765370488167,
-0.009904266335070133,
0.04912857711315155,
0.031203512102365494,
-0.06781318038702011,
-0.004117400851100683,
0.0033627431839704514,
0.002122321864590049,
-0.055991265922784805,
0.010028012096881866,
-0.017268748953938484,
-0.02979206293821335,
-0.009176266379654408,
-0.06694544851779938,
-0.014895305037498474,
0.027100108563899994,
0.05350491404533386,
0.019803039729595184,
0.03136803209781647,
-0.01908748224377632,
-0.032209645956754684,
-0.06912434101104736,
0.030697427690029144,
-0.025232087820768356,
-0.008523457683622837,
-0.028768032789230347,
-0.028426866978406906,
-0.028320077806711197,
0.021985752508044243,
0.05531030520796776,
0.0007878598407842219,
0.010687212459743023,
-0.012670213356614113,
-0.0007836309960111976,
0.0020013516768813133,
-0.02188701368868351,
-0.019270507618784904,
-0.021735049784183502,
-0.04713927581906319,
0.04712119325995445,
-0.03650436922907829,
0.006267055869102478,
-0.017913326621055603,
0.02198382467031479,
0.0066169677302241325,
0.04063741862773895,
0.010639388114213943,
-0.04267497733235359,
0.024093423038721085,
0.025174923241138458,
-0.042316287755966187,
0.0890742614865303,
0.006700817029923201,
-0.006342909298837185,
0.011375200934708118,
-0.030133236199617386,
-0.036183569580316544,
0.03404820337891579,
-0.04779186099767685,
-0.005584664177149534,
-0.023768508806824684,
-0.024406136944890022,
0.04174494370818138,
-0.028025373816490173,
0.019086245447397232,
0.06156136468052864,
-0.042690880596637726,
-0.02044590562582016,
0.04354187101125717,
0.016192235052585602,
0.009477159939706326,
-0.010908164083957672,
0.019975584000349045,
0.02282833866775036,
0.007558642420917749,
0.022134706377983093,
0.05454251542687416,
0.040460359305143356,
0.035703595727682114,
-0.02877102792263031,
0.015817025676369667,
-0.023941650986671448,
0.025205068290233612,
0.012022418901324272,
-0.008333422243595123,
-0.008461715653538704,
-0.024379583075642586,
0.012221334502100945,
-0.052134670317173004,
0.002152091357856989,
0.0097480658441782,
-0.0005720689659938216,
0.08694950491189957,
-0.01575113832950592,
0.0067542544566094875,
-0.01716918684542179,
0.01874273084104061,
-0.0369170643389225,
0.004890065640211105,
0.055180780589580536,
0.025615287944674492,
0.008642667904496193,
0.0042667570523917675,
0.014952996745705605,
-0.0029524306301027536,
0.03390089422464371,
0.006258683744817972,
0.014357739128172398,
-0.01652066595852375,
-0.004140340723097324,
-0.018764333799481392,
-0.025313356891274452,
-0.019957948476076126,
-0.03247641399502754,
0.018155647441744804,
0.033433206379413605,
0.029210995882749557,
0.026537202298641205,
-0.01855805329978466,
-0.02536584436893463,
0.0837332159280777,
-0.10198046267032623,
-0.02791152521967888,
0.029482334852218628,
0.027474407106637955,
0.01216347049921751,
-0.01741897314786911
] |
<p>In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it muonic atoms, some sort of muonic lattice, etc.?</p>
<p>Granted, the energetic benefit of the neutron $\beta$ decay is only about 0.08% of its rest mass, while the muon is roughly 200 times as massive as the electron, thus having much more to gain from decaying - making this proposition seem somewhat unlikely. </p>
| 7,623 |
[
-0.04450538754463196,
-0.015191891230642796,
0.013645452447235584,
-0.07019098103046417,
0.00947253592312336,
0.07590720802545547,
-0.047192249447107315,
-0.047861505299806595,
0.0211615189909935,
-0.05450926721096039,
0.04303174838423729,
0.036854881793260574,
0.05055715888738632,
0.01064134482294321,
-0.033498380333185196,
0.03760456666350365,
0.0019016683800145984,
-0.04276745393872261,
-0.03840196877717972,
-0.03319625183939934,
0.016721701249480247,
0.009691216982901096,
-0.0286002978682518,
0.024280589073896408,
-0.037711918354034424,
0.047037988901138306,
0.023436738178133965,
-0.03419259563088417,
0.027854787185788155,
0.07150420546531677,
-0.00984982494264841,
-0.04602154344320297,
0.06338757276535034,
-0.011869761161506176,
0.03085498698055744,
-0.011105438694357872,
-0.0174892358481884,
-0.019974272698163986,
-0.0337023101747036,
0.031667787581682205,
-0.010226279497146606,
-0.04665328189730644,
-0.029491672292351723,
0.02059239335358143,
-0.049894388765096664,
-0.01860152557492256,
0.012709163129329681,
-0.011179919354617596,
0.07471563667058945,
-0.019124673679471016,
0.030984820798039436,
0.009972008876502514,
0.0126471733674407,
0.015144629403948784,
-0.007943361066281796,
-0.029896670952439308,
0.07981132715940475,
0.07174637168645859,
0.0009293833863921463,
-0.059337958693504333,
-0.0148438336327672,
-0.037901315838098526,
-0.003634636290371418,
0.02264019101858139,
0.00477646803483367,
0.020456643775105476,
-0.016742706298828125,
-0.013991514220833778,
0.04692426323890686,
-0.0036530857905745506,
0.00565256318077445,
-0.0009374824585393071,
0.0019475758308544755,
0.014954444020986557,
-0.003552630078047514,
-0.00532644335180521,
-0.001061894465237856,
0.0021470144856721163,
0.027838390320539474,
0.06487271934747696,
-0.015551554970443249,
-0.0007056370377540588,
0.062078479677438736,
0.03018307313323021,
-0.016339147463440895,
-0.018930938094854355,
0.07578671723604202,
-0.03876606002449989,
0.010373808443546295,
0.0723656713962555,
0.036938346922397614,
-0.009899849072098732,
0.048370279371738434,
0.015575052239000797,
-0.04894055426120758,
-0.008039728738367558,
0.00881008617579937,
0.06943550705909729,
0.021957870572805405,
0.0009273363393731415,
0.026236478239297867,
-0.012594323605298996,
0.00339838326908648,
0.06761649250984192,
0.035396259278059006,
-0.00010956814367091283,
-0.014238218776881695,
-0.002282720524817705,
-0.0143478624522686,
0.00469853263348341,
-0.04366942495107651,
0.0002499208494555205,
-0.04050397872924805,
0.0057604373432695866,
0.028409982100129128,
-0.028335317969322205,
-0.004138967487961054,
-0.03087294101715088,
0.0535079762339592,
0.0579661950469017,
0.028092171996831894,
0.0003397101245354861,
0.011827999725937843,
-0.03994988277554512,
-0.09657855331897736,
0.0041569555178284645,
0.035157036036252975,
0.033307138830423355,
-0.06932608783245087,
0.013570291921496391,
0.034184779971838,
-0.013717247173190117,
0.02927710860967636,
-0.004778526723384857,
0.031802888959646225,
-0.018057825043797493,
-0.0762973204255104,
-0.024096284061670303,
0.06175031140446663,
0.0034178306814283133,
-0.04443119838833809,
-0.05654985085129738,
-0.0041525401175022125,
0.026467252522706985,
0.08881349116563797,
0.011443882249295712,
-0.018003901466727257,
0.0035477380733937025,
0.004827415570616722,
0.0028002711478620768,
0.007657533511519432,
-0.025330279022455215,
-0.0064165834337472916,
-0.05343787372112274,
0.0036575046833604574,
-0.05204560607671738,
0.05091337859630585,
0.0029475558549165726,
0.011159958317875862,
0.004430175758898258,
0.050208091735839844,
-0.028094038367271423,
0.022663885727524757,
-0.045406557619571686,
-0.028770141303539276,
-0.03318363055586815,
0.032295070588588715,
0.014242197386920452,
-0.014474245719611645,
0.01863710954785347,
0.0010279909474775195,
0.007577202282845974,
0.006650211755186319,
0.013828127644956112,
0.045391473919153214,
-0.056284643709659576,
-0.02626085840165615,
-0.0342128612101078,
-0.025416076183319092,
-0.009399699978530407,
-0.03721385449171066,
-0.0064544519409537315,
-0.039883363991975784,
0.0032882795203477144,
0.002467347541823983,
0.04985535144805908,
-0.010533840395510197,
0.0011988020269200206,
0.020255079492926598,
-0.0638294592499733,
-0.011177530512213707,
-0.10715904086828232,
0.002930163173004985,
0.024966605007648468,
0.0060832747258245945,
-0.007154649589210749,
0.004200924187898636,
-0.012779287993907928,
-0.012319976463913918,
-0.020919864997267723,
-0.030156632885336876,
0.022815058007836342,
-0.009839188307523727,
-0.007729102857410908,
0.041000183671712875,
0.0278805922716856,
0.0192263126373291,
-0.010342755354940891,
0.03422826528549194,
-0.012188492342829704,
-0.0517265759408474,
-0.028660448268055916,
-0.013958550989627838,
0.022887900471687317,
0.02105613425374031,
0.007770367432385683,
0.01950431801378727,
-0.04324113205075264,
0.0027181210462003946,
0.02322857454419136,
-0.01942935399711132,
0.051706209778785706,
0.0169712845236063,
-0.0016676922095939517,
0.022068925201892853,
0.02521161548793316,
0.045087020844221115,
-0.005441481713205576,
-0.00688035087659955,
-0.05749891698360443,
-0.05667910724878311,
-0.003314276458695531,
0.015742361545562744,
0.04766455292701721,
-0.043664902448654175,
0.04115484282374382,
-0.03478509932756424,
0.06816611438989639,
0.00896679237484932,
0.024889029562473297,
-0.033137958496809006,
-0.03999815881252289,
0.0338902585208416,
0.0107819102704525,
0.003939877729862928,
0.014722686260938644,
-0.014991837553679943,
0.013117613270878792,
-0.05633433908224106,
-0.050423696637153625,
0.03145575895905495,
0.01996663212776184,
0.002851155586540699,
-0.04187599569559097,
-0.018664084374904633,
-0.06732892990112305,
0.01688111200928688,
-0.04045191779732704,
0.016872426494956017,
0.013652423396706581,
0.007523061241954565,
0.020506884902715683,
-0.041260577738285065,
-0.043681930750608444,
-0.0017441725358366966,
0.03759929910302162,
-0.01638500764966011,
-0.023995473980903625,
0.03639086335897446,
-0.00685153529047966,
0.003989573568105698,
0.0017033937619999051,
0.008198527619242668,
0.02677137963473797,
-0.006325517315417528,
0.0047968290746212006,
0.018464379012584686,
0.003138588508591056,
-0.023028718307614326,
-0.027456799522042274,
0.045302778482437134,
-0.04354191571474075,
-0.008764836937189102,
0.02953784354031086,
-0.03749055042862892,
-0.005597746465355158,
-0.0007651761989109218,
-0.033750269562006,
0.010420317761600018,
0.012861670926213264,
0.004803563933819532,
0.007235430181026459,
-0.01128196157515049,
-0.08989179134368896,
-0.031057769432663918,
-0.017893435433506966,
-0.03206383436918259,
-0.02828320302069187,
0.040673691779375076,
0.05480720475316048,
0.011092469096183777,
-0.041433434933423996,
0.0017055427888408303,
-0.05439106747508049,
-0.002482543233782053,
-0.00167708785738796,
-0.009362723678350449,
0.017742842435836792,
0.00013538001803681254,
0.03728298842906952,
0.05905408412218094,
-0.004700089804828167,
0.00765545479953289,
-0.043236974626779556,
-0.03952111303806305,
0.0007243386935442686,
-0.0502287819981575,
0.025666287168860435,
0.027997270226478577,
-0.0023998229298740625,
0.10798074305057526,
0.025201324373483658,
-0.045919500291347504,
0.0145059609785676,
-0.02722001262009144,
-0.01229642704129219,
-0.0705355629324913,
0.001288405735976994,
0.005404909607023001,
0.01449100486934185,
-0.031987689435482025,
0.04340129345655441,
0.024747706949710846,
0.005485899746417999,
0.01613500900566578,
-0.013796024024486542,
-0.00926024280488491,
-0.006294187158346176,
0.011395578272640705,
0.02878759056329727,
0.0007203706772997975,
0.02139035053551197,
0.012929991818964481,
0.016823802143335342,
0.0527876615524292,
-0.0030694380402565002,
-0.0554976686835289,
0.061092160642147064,
0.012936788611114025,
0.02404480054974556,
-0.0337887667119503,
0.05521741881966591,
-0.02000652253627777,
-0.015847761183977127,
0.004317370243370533,
-0.002372153103351593,
0.048854563385248184,
-0.004859359003603458,
-0.003258638782426715,
-0.014119020663201809,
0.040343400090932846,
0.012610139325261116,
-0.020038912072777748,
-0.02876921184360981,
0.004447272513061762,
-0.025912974029779434,
-0.020547030493617058,
-0.005511528812348843,
0.01790209300816059,
0.003538655349984765,
0.03812668099999428,
0.01599411852657795,
-0.046552013605833054,
-0.027021529152989388,
-0.06446381658315659,
-0.02349701151251793,
-0.012970390729606152,
0.050280097872018814,
0.027366412803530693,
0.0329202301800251,
0.01855642721056938,
-0.007334138732403517,
-0.020084448158740997,
-0.05463195964694023,
-0.10692379623651505,
0.011870072223246098,
-0.043900277465581894,
0.006681567989289761,
-0.019704533740878105,
-0.016891000792384148,
-0.023782754316926003,
0.009533409029245377,
-0.059487950056791306,
-0.020834406837821007,
-0.0008378697675652802,
-0.0615566223859787,
0.035310495644807816,
-0.06818170100450516,
-0.03481978178024292,
-0.0310521200299263,
0.03863098844885826,
0.049258291721343994,
-0.012650784105062485,
-0.020879339426755905,
-0.04696217179298401,
-0.04062926024198532,
0.017372222617268562,
-0.01990857720375061,
0.04462991654872894,
0.001889370265416801,
0.0143703268840909,
0.009463883005082607,
0.041390180587768555,
-0.023509569466114044,
-0.016568981111049652,
0.04708172380924225,
0.03371240943670273,
-0.0033363618422299623,
-0.006075036246329546,
-0.027122775092720985,
-0.05082380399107933,
-0.03388175740838051,
0.04660702124238014,
0.03194761648774147,
-0.0004650690243579447,
0.0011332390131428838,
0.012661449611186981,
-0.017954394221305847,
-0.025010647252202034,
0.06523953378200531,
0.04402368888258934,
0.021031402051448822,
-0.04444892331957817,
-0.04503008723258972,
0.016767675057053566,
-0.005758615676313639,
0.002006091410294175,
-0.022177904844284058,
-0.00873738806694746,
-0.01735839433968067,
0.019140012562274933,
0.009885085746645927,
-0.0014394124737009406,
-0.008340763859450817,
0.007438977714627981,
0.01046706922352314,
0.011687954887747765,
-0.009381686337292194,
0.01672418974339962,
0.01940971426665783,
0.0320095419883728,
0.038375988602638245,
0.0422704741358757,
0.010182250291109085,
-0.07630956918001175,
0.00795290432870388,
0.03370905667543411,
0.06470776349306107,
0.015039406716823578,
-0.03447966277599335,
-0.08140471577644348,
-0.0014651613309979439,
0.05224597454071045,
-0.011360203847289085,
0.01858176663517952,
0.002494147280231118,
0.01953756809234619,
-0.007510614115744829,
-0.03304480016231537,
0.03384769707918167,
0.015851091593503952,
-0.0077986279502511024,
0.020939309149980545,
-0.0455632321536541,
-0.005429606419056654,
-0.000370591355022043,
0.05100056156516075,
0.026335274800658226,
0.06667717546224594,
0.015256290324032307,
0.029041200876235962,
0.020455284044146538,
-0.002637344179674983,
0.012046021409332752,
-0.09343677759170532,
-0.0022362624295055866,
0.012086575850844383,
-0.007555021904408932,
0.0044637578539550304,
-0.028863808140158653,
-0.0729178935289383,
0.01806561090052128,
-0.006823685951530933,
-0.02271963842213154,
0.0038094832561910152,
-0.03028062731027603,
0.039212677627801895,
0.015379239805042744,
0.02285424806177616,
0.03874187171459198,
0.05657772347331047,
0.006936386227607727,
0.01851704530417919,
-0.0345885306596756,
0.016759809106588364,
-0.04517436400055885,
0.058633722364902496,
-0.013168752193450928,
0.011088692583143711,
-0.010601826943457127,
0.04226364567875862,
0.008863642811775208,
0.015313235111534595,
0.034238673746585846,
-0.019693249836564064,
-0.04053492471575737,
0.018040990456938744,
-0.019368210807442665,
-0.04667849838733673,
-0.001666567986831069,
-0.009621486999094486,
-0.02213754504919052,
-0.020268922671675682,
0.04537782073020935,
-0.03430818021297455,
0.02396068535745144,
0.03798574209213257,
-0.041966427117586136,
-0.0017089077737182379,
-0.041008222848176956,
-0.025017550215125084,
0.011501387692987919,
-0.04210381209850311,
0.07843707501888275,
-0.00924635212868452,
0.0021938318386673927,
0.015888676047325134,
-0.047998636960983276,
-0.006504336837679148,
0.03506963327527046,
-0.013412724249064922,
-0.013166005723178387,
-0.013943172059953213,
0.035689130425453186,
0.020060360431671143,
-0.02928909845650196,
-0.09908442944288254,
-0.001632793340831995,
0.015130053274333477,
0.014060746878385544,
-0.011685751378536224,
-0.03626729175448418,
-0.004746740683913231,
-0.04225718602538109,
-0.01931503228843212,
0.019926754757761955,
-0.00848473235964775,
-0.06325802952051163,
0.017179183661937714,
0.009858079254627228,
0.0333995558321476,
0.05804300308227539,
0.018264329060912132,
-0.037716880440711975,
0.000797223940026015,
-0.014454890042543411,
0.003096042899414897,
-0.013983340933918953,
0.03767278045415878,
-0.015690919011831284,
-0.04379449039697647,
0.017192400991916656,
-0.003488125978037715,
0.0567208006978035,
0.018692882731556892,
-0.02388583868741989,
0.06785613298416138,
0.0010642587440088391,
0.015558324754238129,
-0.0020380306523293257,
0.018208544701337814,
0.029036546126008034,
0.05677954480051994,
0.015748605132102966,
0.016324497759342194,
0.00009838466212386265,
-0.026541810482740402,
0.053013771772384644,
0.029025478288531303,
0.01973680965602398,
0.022593699395656586,
0.07095811516046524,
-0.02628970891237259,
-0.020771902054548264,
0.005974683910608292,
-0.0038406369276344776,
0.03563600033521652,
-0.021357882767915726,
0.015245911665260792,
0.005565924569964409,
0.017848731949925423,
-0.03877602145075798,
-0.037054624408483505,
-0.011333471164107323,
-0.019340796396136284,
0.03401082754135132,
-0.03710227459669113,
-0.013451715931296349,
0.0016749214846640825,
-0.02446061372756958,
-0.012707570567727089,
-0.02253858558833599,
-0.025890447199344635,
0.023568695411086082,
-0.03557555377483368,
0.019793065264821053,
-0.024062125012278557,
0.0031811955850571394,
0.0027976706624031067,
0.051384955644607544,
-0.015189270488917828,
0.030318034812808037,
0.018556764349341393,
0.053909771144390106,
-0.015500294044613838,
-0.02547205239534378,
-0.047353003174066544,
0.039777033030986786,
-0.04107419401407242,
0.02441907487809658,
-0.00037985696690157056,
0.011051574721932411,
-0.004193742293864489,
0.024605905637145042,
0.0493042953312397,
-0.009705891832709312,
0.0029522560071200132,
-0.03530032932758331,
0.08135590702295303,
0.00026853062445297837,
-0.015035108663141727,
-0.02002587355673313,
-0.004177278373390436,
0.05071894824504852,
0.004338920582085848,
-0.00423243036493659,
0.009034957736730576,
-0.04511941596865654,
0.0035956413485109806,
-0.03422141447663307,
-0.014137672260403633,
0.03258748725056648,
-0.027657611295580864,
-0.023025717586278915,
-0.003814930096268654,
0.024266915395855904,
0.01632637158036232,
-0.01992768794298172,
0.024324988946318626,
-0.05329049378633499,
0.031177693977952003,
-0.042785026133060455,
0.016689838841557503,
-0.01852511055767536,
-0.01914481818675995,
0.12594987452030182,
0.0355231948196888,
-0.00559200206771493,
-0.024912096560001373,
0.011560342274606228,
-0.04710869863629341,
0.035821862518787384,
-0.014954561367630959,
-0.0017192712984979153,
0.01516776904463768,
-0.01991806924343109,
-0.01942080818116665,
0.0702957734465599,
0.009473315440118313,
0.016765790060162544,
0.026796389371156693,
-0.030975785106420517,
-0.01408090628683567,
-0.02425059676170349,
0.01822199486196041,
0.0006483416073024273,
0.01640332117676735,
-0.05302928760647774,
0.06072273850440979,
0.0022481270134449005,
-0.014772163704037666,
-0.03857050836086273,
0.0075743477791547775,
0.02741265296936035,
-0.004202626179903746,
-0.03465399518609047,
-0.027788929641246796,
-0.038904592394828796,
0.005616169888526201,
-0.010252738371491432,
0.010359620675444603,
0.025618629530072212,
-0.016498196870088577,
0.04021340236067772,
0.04707708954811096,
0.049067288637161255,
0.004183097276836634,
-0.024638667702674866,
0.006960580591112375,
-0.05543822795152664,
-0.007928835228085518,
-0.026094576343894005,
0.04288700595498085,
-0.032954517751932144,
0.011757261119782925,
0.043810274451971054,
-0.0036284930538386106,
0.030580593273043633,
-0.009049588814377785,
-0.006040182895958424,
-0.023667728528380394,
-0.030186209827661514,
-0.015948347747325897,
0.002766487654298544,
-0.005085173062980175,
0.04050440341234207,
-0.0065915873274207115,
0.0017993621295318007,
0.0010849901009351015,
0.014143995940685272,
-0.028187057003378868,
-0.004294631537050009,
0.03703274950385094,
-0.03379364311695099,
-0.003811997128650546,
-0.045630842447280884,
-0.00976851861923933,
-0.010593068785965443,
0.007041478529572487,
0.008335743099451065,
0.028405385091900826,
0.015272037126123905,
0.03510339558124542,
0.040348827838897705,
-0.0008553555817343295,
-0.0427514873445034,
0.09193053841590881,
0.0018255728064104915,
-0.014809065498411655,
-0.0023762378841638565,
-0.023770831525325775,
0.007477687206119299,
0.02979401685297489,
-0.047959405928850174,
0.021265333518385887,
-0.011192447505891323,
0.011680945754051208,
-0.006978337187319994,
-0.05235163867473602,
0.010539482347667217,
0.013355388306081295,
-0.04164642095565796,
0.02344200201332569,
-0.009065130725502968,
0.018265321850776672,
0.0067333318293094635,
0.02772454544901848,
0.014569683000445366,
0.050683751702308655,
-0.009999615140259266,
0.001067217905074358,
0.029125170782208443,
-0.04742760956287384,
-0.0009508376242592931,
0.009867331944406033,
0.016279311850667,
-0.013241561129689217,
-0.03577684238553047,
-0.014372408390045166,
-0.0035600524861365557,
0.03256027773022652,
0.02198067121207714,
0.014301911927759647,
0.018417363986372948,
-0.013979124836623669,
0.01905948482453823,
-0.023592133074998856,
0.006209234707057476,
-0.022563843056559563,
-0.036002907902002335,
-0.002686695195734501,
-0.021406538784503937,
0.0012614673469215631,
0.0291819479316473,
-0.028847914189100266,
-0.01728612557053566,
0.01378919929265976,
0.00350784114561975,
-0.03585251048207283,
0.026840128004550934,
0.007978788577020168,
-0.010795483365654945,
0.017518915235996246,
-0.0289898868650198,
-0.015412971377372742,
0.017849763855338097,
-0.013623933307826519,
-0.01907564327120781,
0.0034657863434404135,
-0.015059640631079674,
0.01850849762558937,
0.009897671639919281,
-0.041187819093465805,
-0.016131708398461342,
0.050271324813365936,
-0.034483883529901505,
-0.0028552457224577665,
0.046224288642406464,
-0.005785032175481319,
-0.014311226084828377,
-0.00844329223036766,
-0.007250774651765823,
0.00005036332368035801,
0.0026025110855698586,
0.03876098617911339,
0.01216189470142126,
-0.013741561211645603,
-0.03623165562748909,
-0.046468913555145264,
-0.025896543636918068,
0.0033774953335523605,
-0.016951365396380424,
0.048751186579465866,
0.0038791168481111526,
0.011499114334583282,
-0.02052309736609459,
0.018729982897639275,
0.009347721002995968,
-0.004236438311636448,
-0.09899871051311493,
-0.025013945996761322,
0.027286158874630928,
0.00872716773301363,
0.024769792333245277,
-0.04151907190680504,
0.031996071338653564,
0.014799483120441437,
-0.0674341693520546,
-0.03145703673362732,
-0.03926960751414299,
-0.021927161142230034,
-0.053855203092098236,
-0.030434835702180862,
-0.028104856610298157,
0.031589627265930176,
-0.0038869455456733704,
0.05460452288389206,
0.00709851598367095,
0.05151038616895676,
-0.03204468637704849,
-0.024911051616072655,
-0.010779645293951035,
-0.0026362247299402952,
0.007389357313513756,
0.023919740691781044,
0.09167486429214478,
-0.02446679398417473,
-0.024699287489056587,
0.03221362084150314,
0.028757605701684952,
0.023571381345391273,
-0.020523851737380028,
0.028940245509147644,
0.0006457039853557944,
0.03226194903254509,
0.0010764767648652196,
-0.01126185990869999,
0.004639005754143,
-0.013400858268141747,
0.045964524149894714,
0.016194026917219162,
0.008354254998266697,
-0.001603366108611226,
0.014744371175765991,
-0.003251299960538745,
-0.012105418369174004,
0.016837045550346375,
-0.015922220423817635,
-0.012866062112152576,
-0.029841190204024315,
-0.0005635105771943927,
0.03440343961119652,
0.006394769996404648,
-0.018387246876955032,
-0.004383455496281385,
0.01665778085589409,
0.027416862547397614,
0.03927702456712723,
0.014576414600014687,
0.03344077989459038,
-0.004898874554783106,
-0.00842804741114378,
0.010969007387757301,
0.032230447977781296,
-0.017027467489242554,
-0.009277132339775562,
-0.009482508525252342,
0.021854814141988754,
0.03026188537478447,
-0.03376643359661102,
-0.028421558439731598,
-0.02894732728600502,
0.026200901716947556,
0.031554706394672394,
0.05115216225385666,
-0.009213746525347233,
-0.0165804922580719,
-0.01608479581773281,
-0.02555200271308422,
0.021214332431554794,
-0.020163631066679955,
0.03694891557097435,
-0.016185401007533073,
-0.010044285096228123,
0.012022740207612514,
0.004610985983163118,
0.06548042595386505,
0.003784387605264783,
0.008982791565358639,
0.020530063658952713,
-0.03568946570158005,
0.0011549504706636071,
-0.0009691243758425117,
-0.014959736727178097,
-0.01122833602130413,
-0.027760669589042664,
-0.015026220120489597,
-0.018802139908075333,
-0.028764555230736732,
0.04569300636649132,
0.02610097825527191,
0.012595831416547298,
-0.049725260585546494,
0.0033380098175257444,
0.012551619671285152,
0.05139834061264992,
0.004410216119140387,
-0.026956835761666298,
0.06374015659093857,
0.016957946121692657,
0.016144702211022377,
0.015420946292579174,
-0.03880319371819496,
-0.028615877032279968,
0.031834423542022705,
-0.04662005230784416,
0.02634400874376297,
-0.010027971118688583,
-0.0417381152510643,
0.006566822528839111,
-0.03721584379673004,
0.031238559633493423,
0.030366526916623116,
-0.04741959273815155,
0.0030759687069803476,
0.045956727117300034,
0.027868300676345825,
0.06915803253650665,
0.0013885560911148787,
-0.00406417204067111,
0.03286387398838997,
0.045275621116161346,
-0.001952959457412362,
0.06504666060209274,
0.0006733713671565056,
-0.026090601459145546,
0.03881091997027397,
-0.012205639854073524,
0.0066204918548464775,
-0.005422983784228563,
0.014414655975997448,
0.01661829836666584,
0.0010086357360705733,
-0.00595651613548398,
0.013502844609320164,
-0.00476180762052536,
-0.012065691873431206,
-0.022174028679728508,
-0.027379756793379784,
0.05634472519159317,
-0.027438171207904816,
0.013452991843223572,
0.006685882806777954,
0.0021832254715263844,
-0.000516388681717217,
0.054252710193395615,
0.012822464108467102,
0.04508812725543976,
0.01672946847975254,
0.003391445381566882,
0.0041209333576262,
0.026459893211722374,
0.020267892628908157,
-0.019762523472309113,
0.014970967546105385,
-0.015755992382764816,
0.035600446164608,
-0.004975590389221907,
0.003660519141703844,
-0.04329869896173477,
-0.01329603511840105,
0.029168324545025826,
0.009869227185845375,
0.0006446294719353318,
0.011699536815285683,
-0.026772256940603256,
-0.007475375197827816,
0.04893684759736061,
0.0007587654981762171,
0.003364736679941416,
-0.047692302614450455,
0.026692049577832222,
-0.03694824501872063,
0.003976529464125633
] |
<p>Just a quick question: In high energy experiments, the fundamental forces are thought to merge into a single force. My question is, in very low energy experiments (very low), do the forces we know about split up even more/is this possible or likely?</p>
<p>Thanks</p>
| 7,624 |
[
-0.015389186330139637,
0.014243905432522297,
-0.022147292271256447,
-0.025528021156787872,
0.03424635902047157,
0.01659392938017845,
-0.02726440690457821,
-0.03852920979261398,
-0.010571911931037903,
-0.04519856721162796,
0.0028216568753123283,
0.027042793110013008,
0.022184642031788826,
-0.02546950802206993,
0.0010012732818722725,
0.011098794639110565,
0.014621201902627945,
0.009368172846734524,
0.023828933015465736,
-0.007117428816854954,
0.002110340865328908,
0.002595453290268779,
0.006356630474328995,
0.023822519928216934,
-0.021341465413570404,
0.032377734780311584,
0.036806266754865646,
-0.02658863738179207,
0.021543845534324646,
0.05350980907678604,
0.01948339119553566,
-0.0319029800593853,
-0.004447817802429199,
0.0512334406375885,
0.039784230291843414,
-0.02091248147189617,
-0.003289711894467473,
-0.05195141211152077,
-0.03142194077372551,
0.029466820880770683,
-0.056114938110113144,
-0.004824620205909014,
-0.06154504045844078,
0.04904454946517944,
-0.05731634795665741,
-0.008463403210043907,
0.01937044970691204,
-0.03857932239770889,
0.06334422528743744,
-0.05365194007754326,
0.030003035441040993,
0.014585684984922409,
0.05924966558814049,
0.03228229656815529,
0.0037883869372308254,
-0.019374238327145576,
0.07206789404153824,
0.06451919674873352,
-0.007429866585880518,
-0.046991098672151566,
-0.037799082696437836,
-0.0253695510327816,
-0.012326640076935291,
-0.0009911757661029696,
-0.029012281447649002,
0.06677620857954025,
-0.035587821155786514,
-0.037744808942079544,
0.0037421686574816704,
0.0026318146847188473,
0.009357115253806114,
0.020024916157126427,
0.05663483217358589,
-0.0028956823516637087,
0.017107786610722542,
-0.009022383019328117,
0.031374674290418625,
0.0029747060034424067,
0.0300655085593462,
0.06719616055488586,
-0.06436773389577866,
-0.0071649206802248955,
0.03944512829184532,
0.03303655609488487,
0.017323365435004234,
-0.014228526502847672,
0.06337958574295044,
-0.06109797582030296,
-0.03421270102262497,
0.018914062529802322,
-0.027087800204753876,
-0.002861947054043412,
0.03878873214125633,
-0.0009902814636006951,
-0.024610403925180435,
0.05355605483055115,
0.01971779763698578,
0.05048609897494316,
0.012080341577529907,
-0.005107126664370298,
0.04525347426533699,
0.011152641847729683,
0.026570232585072517,
0.07861411571502686,
0.03101629577577114,
-0.03918271139264107,
-0.04382922500371933,
-0.010884814895689487,
-0.02663644216954708,
0.01072982233017683,
-0.002034159144386649,
-0.02336719259619713,
-0.00011497249215608463,
-0.004935725126415491,
0.005083216354250908,
-0.03214799612760544,
0.009876132011413574,
-0.035670723766088486,
0.10815306007862091,
0.07684726268053055,
0.059095099568367004,
-0.04630075767636299,
0.029534589499235153,
-0.028779523447155952,
-0.026588482782244682,
-0.007983151823282242,
0.03301601484417915,
-0.012078986503183842,
-0.024528253823518753,
0.033241499215364456,
0.0025741937570273876,
-0.0028439851012080908,
-0.021141234785318375,
-0.016449222341179848,
0.030575094744563103,
-0.011732078157365322,
-0.09608496725559235,
-0.05338618904352188,
0.03256484493613243,
-0.05923757329583168,
-0.03313715383410454,
-0.0852024033665657,
-0.010421731509268284,
0.003966822754591703,
0.06884369999170303,
0.006752324290573597,
0.0033597564324736595,
-0.0069428677670657635,
0.0335247777402401,
-0.0019439186435192823,
-0.0013068849220871925,
0.0064388723112642765,
-0.010293731465935707,
-0.022644462063908577,
-0.009675148874521255,
-0.09343323856592178,
-0.00018186446686740965,
0.040664512664079666,
-0.008296901360154152,
0.0014744480140507221,
0.018293999135494232,
-0.02423330768942833,
0.045272961258888245,
-0.0030333222821354866,
0.037558071315288544,
-0.033400002866983414,
0.09018232673406601,
-0.006912524346262217,
-0.008464643731713295,
0.048072222620248795,
-0.007777804043143988,
-0.00035014873719774187,
0.019333336502313614,
0.021955495700240135,
0.02557005174458027,
-0.017282061278820038,
-0.0030906337779015303,
-0.021343674510717392,
0.00737577211111784,
-0.027144035324454308,
-0.04723328724503517,
-0.012150218710303307,
-0.002776648849248886,
0.009349964559078217,
-0.0011401558294892311,
0.059589970856904984,
-0.005515396129339933,
-0.02487124875187874,
-0.009664849378168583,
-0.036941349506378174,
-0.036208443343639374,
-0.03566623851656914,
-0.010661079548299313,
-0.002193407155573368,
-0.013505876064300537,
0.01736055687069893,
0.03686555474996567,
0.04777071252465248,
-0.04478386044502258,
-0.03960742428898811,
-0.025976717472076416,
0.024679560214281082,
-0.024944016709923744,
-0.02245623990893364,
0.055546246469020844,
0.0313599556684494,
0.016970599070191383,
0.0033667883835732937,
0.04613577947020531,
0.02083783783018589,
-0.05025312304496765,
0.03702941909432411,
-0.026942826807498932,
0.0462680421769619,
0.03275556489825249,
-0.005916727241128683,
0.008428449742496014,
-0.021747717633843422,
0.006511945743113756,
0.03322010859847069,
-0.009542985819280148,
0.09846911579370499,
0.006033905316144228,
0.012673642486333847,
-0.01415157224982977,
0.04924364760518074,
0.04558537155389786,
0.004028858616948128,
-0.017633408308029175,
0.011423218064010143,
-0.0855615884065628,
-0.02494089864194393,
0.04663568362593651,
0.02257314883172512,
-0.035928692668676376,
0.028770575299859047,
0.04740254953503609,
0.020715905353426933,
0.008934746496379375,
0.02163689024746418,
-0.01247162465006113,
-0.03797832876443863,
0.010935385711491108,
0.04273758456110954,
0.009000965394079685,
0.018071765080094337,
0.01268339715898037,
0.028903217986226082,
0.01935354433953762,
0.021878724917769432,
0.011188598349690437,
0.010094412602484226,
-0.0016838796436786652,
0.011396466754376888,
-0.003391362028196454,
-0.041660893708467484,
0.02542291022837162,
-0.00007078753696987405,
0.0711696594953537,
-0.004738055635243654,
0.010371515527367592,
-0.042114678770303726,
-0.025755837559700012,
-0.015988346189260483,
0.03231552615761757,
0.004203219432383776,
-0.019471103325486183,
0.0036266357637941837,
0.024625176563858986,
-0.03355863317847252,
-0.0038558170199394226,
-0.009356535039842129,
0.020050380378961563,
-0.015025164000689983,
0.0030587418004870415,
0.013380341231822968,
-0.025553416460752487,
0.061210907995700836,
-0.04339638352394104,
-0.025521278381347656,
-0.011065514758229256,
-0.0622442401945591,
0.03718087822198868,
-0.001579547068104148,
-0.021443402394652367,
0.036186084151268005,
-0.022832943126559258,
-0.020932823419570923,
0.03127949684858322,
-0.031192272901535034,
0.029880790039896965,
0.029714029282331467,
-0.03394446521997452,
-0.05856088176369667,
-0.015887482091784477,
-0.02029847539961338,
0.006409476511180401,
-0.008341056294739246,
0.0008374719764105976,
0.031778257340192795,
-0.0019259200198575854,
-0.02186346985399723,
0.004464627709239721,
-0.014476313255727291,
-0.06099469214677811,
-0.03092040680348873,
0.024876639246940613,
0.004657318815588951,
-0.0069303507916629314,
0.02817474864423275,
0.042243022471666336,
-0.053894948214292526,
-0.0039768037386238575,
-0.045304879546165466,
-0.03125857561826706,
0.025077316910028458,
0.006650286260992289,
0.028709454461932182,
-0.01071141380816698,
-0.030368996784090996,
0.07493571192026138,
0.006306461989879608,
-0.0301540344953537,
0.006309463642537594,
-0.006317229941487312,
-0.0239272378385067,
0.0026956843212246895,
0.024268681183457375,
-0.006179110147058964,
0.007869021035730839,
0.024791035801172256,
0.031992990523576736,
0.05393581464886665,
-0.009767585434019566,
0.03419240564107895,
-0.02653847075998783,
-0.0037564029917120934,
0.020494917407631874,
-0.01872154511511326,
0.032956164330244064,
0.01575642265379429,
-0.04788980260491371,
-0.010052908211946487,
-0.003268298227339983,
0.06122153624892235,
0.007712640333920717,
-0.051330357789993286,
0.05704638734459877,
0.016061054542660713,
0.015081069432199001,
-0.012155434116721153,
0.00586940161883831,
0.006963391322642565,
0.005434627179056406,
0.0014479318633675575,
0.02930431440472603,
0.07771019637584686,
-0.008780810981988907,
0.019674597308039665,
0.03142741322517395,
0.023777464404702187,
-0.03444903343915939,
-0.02508697286248207,
-0.01965617761015892,
0.0021455048117786646,
0.01902080327272415,
0.005070058163255453,
-0.015979887917637825,
0.01736738160252571,
0.02358650416135788,
0.04313463717699051,
0.017451046034693718,
-0.0022318861447274685,
0.016946442425251007,
-0.055404845625162125,
-0.018283139914274216,
-0.0008862922550179064,
0.02047429047524929,
0.008326237089931965,
0.05591242387890816,
0.030525008216500282,
0.026208795607089996,
-0.01780598983168602,
-0.01611628755927086,
-0.10758546739816666,
0.015933768823742867,
-0.04339873045682907,
-0.0007094041793607175,
-0.01335794199258089,
0.0047911289148032665,
-0.010728498920798302,
-0.009675618261098862,
-0.009380875155329704,
-0.036958832293748856,
0.0011116302339360118,
-0.033833134919404984,
-0.001443072920665145,
-0.036185264587402344,
-0.0024719065986573696,
-0.01788620464503765,
0.0211709663271904,
0.031669098883867264,
0.0024454169906675816,
-0.004534970037639141,
-0.011904891580343246,
-0.03402846306562424,
-0.020884361118078232,
-0.012256907299160957,
0.02694171853363514,
0.009715868160128593,
0.02812821790575981,
0.025564957410097122,
0.05485592782497406,
-0.015467563644051552,
-0.006577642634510994,
0.02301504835486412,
0.05584093928337097,
-0.008189563639461994,
-0.01850390061736107,
0.023503685370087624,
-0.061222709715366364,
-0.03402506932616234,
0.0026158869732171297,
0.04944227635860443,
-0.020719783380627632,
0.009419932030141354,
-0.00041723009780980647,
0.017844371497631073,
-0.031752362847328186,
0.060318127274513245,
0.05933809652924538,
-0.023672157898545265,
-0.04475877061486244,
-0.04812691733241081,
0.008443199098110199,
-0.02077118493616581,
-0.004242820665240288,
0.013458657078444958,
-0.033765651285648346,
-0.04561670497059822,
-0.002871376695111394,
0.025124693289399147,
0.045655157417058945,
-0.05050825700163841,
0.016500303521752357,
-0.02216932363808155,
0.012744085863232613,
-0.01740599423646927,
-0.026481835171580315,
0.015411381609737873,
0.027880234643816948,
0.0363762192428112,
0.029324140399694443,
0.0016073735896497965,
-0.06697533279657364,
0.030880702659487724,
0.02327718771994114,
0.024567993357777596,
-0.0069001722149550915,
0.0030589525122195482,
-0.022987496107816696,
-0.05689353495836258,
0.06602877378463745,
-0.010123453103005886,
0.01566399447619915,
-0.01356856431812048,
0.018386293202638626,
-0.006048223469406366,
-0.029919220134615898,
-0.027895551174879074,
0.009592624381184578,
0.006983831990510225,
-0.008774867281317711,
-0.028535062447190285,
-0.009010923095047474,
0.003500171471387148,
0.05323032662272453,
0.04603820666670799,
0.041242633014917374,
0.03415575996041298,
0.01714262366294861,
-0.030960511416196823,
-0.003821146208792925,
-0.02760138548910618,
-0.08017916977405548,
0.028819425031542778,
0.02379569597542286,
-0.01969148963689804,
0.05188241973519325,
-0.033516108989715576,
-0.05026085302233696,
0.011083872988820076,
0.014138385653495789,
0.03509092330932617,
-0.021451087668538094,
-0.053017329424619675,
0.020548472180962563,
0.04927931725978851,
0.008071537129580975,
0.0386291965842247,
0.005203717853873968,
-0.022282306104898453,
0.016273003071546555,
-0.009906881488859653,
0.03596258535981178,
-0.02740333043038845,
0.0069962153211236,
-0.03819001093506813,
0.02512875199317932,
-0.011345107108354568,
0.04435061663389206,
-0.0220956988632679,
0.04857837036252022,
-0.0038855255115777254,
-0.06313852965831757,
-0.009896593168377876,
0.024014806374907494,
0.007847190834581852,
-0.02132001332938671,
0.037877727299928665,
0.008777908980846405,
-0.007374174427241087,
-0.0022275582887232304,
-0.01661836914718151,
0.01899588666856289,
-0.007043891120702028,
-0.002534375060349703,
-0.004853938240557909,
0.002924953354522586,
-0.028304709121584892,
-0.03266559913754463,
0.04174329712986946,
-0.04044129699468613,
0.038445133715867996,
-0.02712038718163967,
-0.006116599775850773,
0.0044298176653683186,
-0.04270254448056221,
-0.020107373595237732,
0.008764363825321198,
-0.021766966208815575,
0.03960761800408363,
-0.030271753668785095,
0.04867061972618103,
0.0003769796749111265,
-0.019574379548430443,
-0.06344422698020935,
-0.044972095638513565,
0.014141248539090157,
0.02390335686504841,
0.028900617733597755,
0.00011912063200725242,
-0.019910074770450592,
-0.04160677269101143,
0.001669066259637475,
-0.030038924887776375,
0.06996338814496994,
-0.03484655171632767,
0.009670165367424488,
0.0018274100730195642,
-0.011103659868240356,
0.025589654222130775,
0.02018306963145733,
-0.029539838433265686,
-0.00823699776083231,
0.008855018764734268,
-0.0014429690781980753,
-0.003566387575119734,
0.053510963916778564,
-0.038773227483034134,
-0.016150960698723793,
0.02169744111597538,
-0.014516518451273441,
0.03799455985426903,
-0.05390530824661255,
0.02837260439991951,
0.04766432195901871,
-0.0011407232377678156,
0.05253871902823448,
-0.008874493651092052,
0.050630126148462296,
-0.007744327187538147,
0.006745527498424053,
0.006598264444619417,
0.005106792785227299,
-0.027833376079797745,
-0.05063996464014053,
0.009036717936396599,
-0.006728131324052811,
0.0012690020957961679,
-0.004984491039067507,
0.031885042786598206,
0.025463875383138657,
-0.038339823484420776,
0.01964552141726017,
-0.013390135951340199,
0.0007912142900750041,
0.008161772042512894,
0.008911153301596642,
0.016050703823566437,
0.055386900901794434,
-0.00055499846348539,
-0.02710696868598461,
0.0008693702984601259,
-0.00048547639744356275,
0.04843371734023094,
-0.026290128007531166,
0.021664531901478767,
0.019929295405745506,
-0.02043447457253933,
-0.010444540530443192,
-0.036307137459516525,
0.010506615042686462,
0.008341660723090172,
0.009267757646739483,
0.024254268035292625,
-0.046978652477264404,
0.008701186627149582,
-0.00012938938743900508,
0.04198785871267319,
-0.0022950763814151287,
0.013117345981299877,
0.021122990176081657,
0.03789496421813965,
0.020180046558380127,
-0.03847721219062805,
-0.051929131150245667,
0.021768631413578987,
-0.043164342641830444,
0.0491204671561718,
-0.0036950858775526285,
-0.00914386473596096,
-0.006467059720307589,
0.0321485698223114,
0.008996166288852692,
-0.041708528995513916,
-0.018050245940685272,
-0.017357351258397102,
0.045741673558950424,
-0.0102990148589015,
0.007451789453625679,
-0.03031587414443493,
-0.009298425167798996,
0.00852062739431858,
0.04978463053703308,
0.012598061934113503,
0.019761621952056885,
-0.0541156642138958,
-0.058731645345687866,
-0.042686935514211655,
-0.024232536554336548,
0.015793249011039734,
-0.037619467824697495,
-0.024407394230365753,
0.025238648056983948,
-0.026819264516234398,
0.040845200419425964,
-0.009192606434226036,
0.03229086101055145,
-0.03216203302145004,
0.019112756475806236,
0.018102126196026802,
0.05145401880145073,
-0.013763944618403912,
0.02065970003604889,
0.12548388540744781,
0.05451047047972679,
0.012741973623633385,
-0.030678769573569298,
0.032202158123254776,
-0.04264526441693306,
0.00462133064866066,
-0.023897221311926842,
0.015990378335118294,
-0.009488153271377087,
0.011987907811999321,
0.005927019286900759,
0.0941275805234909,
-0.0038134308997541666,
-0.025046957656741142,
0.08168156445026398,
-0.03460205718874931,
-0.017452850937843323,
-0.008878011256456375,
0.04679255560040474,
-0.01800858974456787,
-0.007578151300549507,
-0.008503402583301067,
0.03938467800617218,
-0.01037322822958231,
-0.00044578086817637086,
-0.0019884470384567976,
-0.012539654038846493,
0.02185460366308689,
0.006541190203279257,
-0.04093131050467491,
0.012208894826471806,
-0.0002671226975508034,
-0.025588039308786392,
-0.010217334143817425,
0.03490859642624855,
0.03460126370191574,
-0.02701510675251484,
0.006031401921063662,
0.009393762797117233,
0.011897911317646503,
0.015784773975610733,
-0.015864728018641472,
-0.012782017700374126,
-0.011632543057203293,
-0.04793731868267059,
0.00007764026668155566,
0.05866115540266037,
-0.028928643092513084,
-0.00901039782911539,
-0.019157476723194122,
-0.0007712572696618736,
0.0007241066196002066,
-0.02005135267972946,
-0.04470875486731529,
-0.011962872929871082,
0.00856646429747343,
-0.02863611839711666,
-0.023905165493488312,
-0.0283710565418005,
0.04508506879210472,
-0.01291832234710455,
0.003034734632819891,
-0.012987633235752583,
0.022473691031336784,
-0.022870946675539017,
0.025797387585043907,
0.037907056510448456,
-0.02645805850625038,
-0.03801918402314186,
-0.02026492729783058,
-0.019785288721323013,
-0.03960546851158142,
-0.0386357307434082,
-0.007684170734137297,
0.050441473722457886,
0.01841558702290058,
-0.011188327334821224,
-0.013217544183135033,
-0.04546282812952995,
0.0020397042389959097,
0.04380600526928902,
-0.02685737982392311,
-0.043079692870378494,
0.03274649381637573,
-0.020398888736963272,
-0.010922105982899666,
0.02012026682496071,
-0.05128242075443268,
0.004314797930419445,
-0.025867560878396034,
0.028270049020648003,
0.03572768345475197,
-0.026632869616150856,
-0.03860514983534813,
0.012072010897099972,
-0.043316151946783066,
0.005827987566590309,
-0.02849339134991169,
0.007457950618118048,
0.012385733425617218,
-0.03323664143681526,
0.03486010059714317,
0.014239584095776081,
-0.004217851907014847,
0.014751779846847057,
0.04163360968232155,
-0.036030013114213943,
0.012841681949794292,
0.015581335872411728,
-0.010977067053318024,
-0.014758984558284283,
-0.02121329866349697,
-0.03292761743068695,
0.02852863073348999,
0.01730750873684883,
0.04816534370183945,
-0.01221804041415453,
0.01718045026063919,
-0.038174401968717575,
0.027127020061016083,
-0.0022385900374501944,
-0.011979369446635246,
-0.05417352914810181,
-0.014121662825345993,
-0.013024205341935158,
-0.0406317338347435,
-0.015679771080613136,
0.050548143684864044,
-0.008055845275521278,
-0.036188069730997086,
0.05020308122038841,
0.0314737930893898,
-0.02862953022122383,
-0.025758396834135056,
0.04328879341483116,
-0.026729891076683998,
0.010617980733513832,
0.02847978100180626,
-0.04964689910411835,
0.052042242139577866,
-0.05878414958715439,
-0.08137384802103043,
0.0405215360224247,
-0.009156458079814911,
0.020386606454849243,
0.050928544253110886,
-0.01603521592915058,
-0.02150225266814232,
0.08570201694965363,
-0.03092709369957447,
-0.03445325791835785,
0.0037859741132706404,
0.023157289251685143,
-0.009874993935227394,
-0.006050306838005781,
0.02138994075357914,
-0.025297660380601883,
-0.012315177358686924,
0.02631884627044201,
-0.003629367332905531,
0.020020892843604088,
-0.01948561519384384,
-0.0027840817347168922,
-0.01801108382642269,
0.04443346709012985,
0.009943675249814987,
-0.006807501427829266,
0.007385812234133482,
0.08223859965801239,
-0.038280121982097626,
0.012024353258311749,
0.01946263015270233,
0.007095544133335352,
-0.09723157435655594,
-0.05272882804274559,
-0.029791155830025673,
0.002622107742354274,
0.0047188494354486465,
-0.05704869329929352,
0.0252202320843935,
0.0464211106300354,
-0.0601290687918663,
0.012701185420155525,
-0.04063625633716583,
-0.0007575380732305348,
-0.012203597463667393,
-0.024027535691857338,
-0.017005618661642075,
0.02459581196308136,
-0.000582394131924957,
0.06461340188980103,
0.02096863090991974,
-0.007335089612752199,
-0.0161870326846838,
0.003887736238539219,
-0.037116460502147675,
-0.002395582851022482,
0.002410023007541895,
-0.007340188138186932,
0.08020035922527313,
-0.014528986997902393,
-0.044105157256126404,
0.027465075254440308,
-0.013189350254833698,
0.006778164766728878,
-0.023632392287254333,
-0.010366344824433327,
0.004543590359389782,
0.017657291144132614,
-0.02459407038986683,
-0.01065538078546524,
0.029122766107320786,
0.04698491841554642,
-0.013466836884617805,
0.03348824754357338,
0.018534911796450615,
0.024500060826539993,
0.021412964910268784,
-0.0326380729675293,
-0.03630124777555466,
0.024302659556269646,
0.01912611350417137,
0.021359343081712723,
-0.008483787067234516,
-0.0015036582481116056,
0.03909172862768173,
-0.030862770974636078,
-0.005586843937635422,
-0.040725335478782654,
-0.01884005032479763,
0.03352319449186325,
0.02939211018383503,
0.01073168683797121,
0.032821036875247955,
-0.00037128321127966046,
-0.007298610173165798,
0.00034670173772610724,
0.009353075176477432,
0.005139585584402084,
-0.06816444545984268,
-0.019292140379548073,
0.023154906928539276,
0.00796845555305481,
-0.006233925931155682,
-0.06876116991043091,
-0.03608446940779686,
0.026797298341989517,
0.018243812024593353,
0.05214350298047066,
-0.023670470342040062,
-0.055681511759757996,
-0.014865347184240818,
-0.07267134636640549,
0.0066627576015889645,
-0.004177887458354235,
0.045016441494226456,
-0.05211639776825905,
-0.00808687973767519,
-0.022866571322083473,
-0.027395911514759064,
0.0027968757785856724,
0.008271474391222,
0.01905106008052826,
0.005655491724610329,
-0.005834541749209166,
0.006432462949305773,
-0.032178089022636414,
0.007570208515971899,
-0.039291709661483765,
-0.0036206813529133797,
-0.0183575376868248,
-0.042142923921346664,
0.01282184012234211,
0.0074501498602330685,
0.01968551240861416,
-0.036158159375190735,
-0.0122514758259058,
-0.040286917239427567,
-0.016996847465634346,
0.060363855212926865,
-0.011975382454693317,
-0.00905612949281931,
0.036317985504865646,
-0.03209897503256798,
0.04083285853266716,
0.007467289455235004,
-0.03481854870915413,
-0.010415715165436268,
0.01373873557895422,
-0.04188438877463341,
0.010250317864120007,
-0.0056145889684557915,
-0.0001669841876719147,
0.01632886752486229,
-0.013834556564688683,
0.009540332481265068,
0.02726616896688938,
-0.02182953432202339,
0.030756419524550438,
0.042504459619522095,
0.026698525995016098,
0.021451732143759727,
0.012186059728264809,
0.002783408621326089,
0.04936334863305092,
0.012422685511410236,
-0.0007976724882610142,
0.0528968945145607,
0.021846342831850052,
0.0034461633767932653,
-0.00862156879156828,
0.017044594511389732,
0.016971400007605553,
0.0011122977593913674,
0.0027932897210121155,
0.037498634308576584,
-0.023601243272423744,
-0.008285601623356342,
0.00999525934457779,
-0.018914656713604927,
0.010439827106893063,
0.0021663655061274767,
-0.013100489974021912,
0.06769442558288574,
-0.038917798548936844,
0.010014500468969345,
-0.00911877304315567,
0.02202998474240303,
0.005837005563080311,
0.03951827436685562,
-0.007142586633563042,
0.06950771063566208,
-0.006019786931574345,
-0.02355608344078064,
-0.05035901069641113,
0.02893352508544922,
0.015011899173259735,
-0.021286604925990105,
0.008272431790828705,
-0.019581494852900505,
0.020841607823967934,
-0.008495710790157318,
0.022492805495858192,
-0.041037097573280334,
-0.052996616810560226,
0.010189641267061234,
0.030326636508107185,
0.023113135248422623,
-0.03299517557024956,
-0.03188616409897804,
-0.020436085760593414,
0.033203959465026855,
0.0015202350914478302,
-0.001927321427501738,
-0.040990836918354034,
0.04334168881177902,
-0.03168761357665062,
0.02208588272333145
] |
<p>Hi all what is the definition of pressure derivative of <a href="http://en.wikipedia.org/wiki/Bulk_modulus" rel="nofollow">bulk modulus</a> if it is a pressure derivative of bulk modulus at zero pressure. if the pressure is zero how it is derivative by pressure? </p>
| 7,625 |
[
0.019864125177264214,
0.014927172102034092,
0.007794822566211224,
0.004074377007782459,
0.04182571545243263,
-0.0021601824555546045,
-0.0445239283144474,
-0.0173769723623991,
0.006989817600697279,
-0.03264254331588745,
0.00862262211740017,
0.010684432461857796,
0.05786211043596268,
-0.011640254408121109,
0.0046576946042478085,
0.018121445551514626,
-0.015422634780406952,
0.02987411618232727,
0.013305912725627422,
-0.020971206948161125,
0.013058067299425602,
-0.00381942605599761,
0.006902517285197973,
0.04427378997206688,
0.006237194407731295,
0.036140184849500656,
0.01955399103462696,
0.016069963574409485,
0.028887314721941948,
0.053581539541482925,
0.004183542914688587,
-0.060265492647886276,
-0.004346516914665699,
0.0156333576887846,
0.014722231775522232,
0.010174262337386608,
-0.0493638813495636,
-0.00027508632047101855,
-0.049113642424345016,
0.026402778923511505,
-0.02401476912200451,
-0.025439422577619553,
0.03256933018565178,
0.015598966740071774,
-0.012336269952356815,
0.01205394696444273,
0.05798988789319992,
-0.028008149936795235,
0.03704462945461273,
-0.0570223331451416,
0.02993374690413475,
-0.00580188212916255,
0.04500153660774231,
0.027565650641918182,
-0.021706722676753998,
-0.01669483445584774,
0.050627224147319794,
0.09824661165475845,
-0.04690224304795265,
-0.0905507504940033,
0.0199365746229887,
0.010791084729135036,
0.014650247059762478,
-0.036020465195178986,
-0.017723001539707184,
0.031715475022792816,
-0.0031067123636603355,
0.00005701647387468256,
0.02107587829232216,
0.000441008189227432,
-0.010170836001634598,
-0.00006990633846726269,
0.016918258741497993,
-0.045944154262542725,
0.0047849747352302074,
-0.03572733700275421,
-0.020662523806095123,
0.005669465288519859,
0.024965034797787666,
0.04833194985985756,
-0.01341353077441454,
0.0394611582159996,
0.018640387803316116,
0.02318102866411209,
-0.007795942481607199,
-0.02876976504921913,
0.097065269947052,
-0.01166466809809208,
0.019655251875519753,
0.0016781830927357078,
0.0034767217002809048,
-0.013804483227431774,
0.016938328742980957,
-0.016252171248197556,
0.01750161312520504,
-0.0024661507923156023,
-0.00482708215713501,
0.05158408731222153,
-0.008511241525411606,
-0.03793773800134659,
0.03402352333068848,
-0.03653758019208908,
0.03999759256839752,
0.07409192621707916,
0.0043840897269546986,
0.002485930221155286,
-0.039336755871772766,
0.0013806847855448723,
0.004793480504304171,
-0.028881190344691277,
-0.007991204038262367,
0.014680489897727966,
-0.01259253267198801,
-0.04491756856441498,
-0.024584587663412094,
-0.02814510650932789,
0.016737187281250954,
-0.014226069673895836,
0.017504272982478142,
0.03260695934295654,
0.050690483301877975,
-0.03973744437098503,
0.020258916541934013,
-0.0006346006994135678,
-0.09213989973068237,
0.03470148518681526,
0.021205000579357147,
-0.015758607536554337,
-0.041116081178188324,
0.003597926814109087,
-0.007486992049962282,
-0.024556970223784447,
0.022811200469732285,
0.035628896206617355,
0.015423261560499668,
-0.010202343575656414,
-0.0924667939543724,
-0.038809020072221756,
0.02766459248960018,
-0.0034161494113504887,
-0.03334644436836243,
-0.05996745079755783,
0.023700838908553123,
0.01777781918644905,
0.05701984465122223,
0.02303960919380188,
0.030399998649954796,
-0.005211465526372194,
0.0208040289580822,
0.009130622260272503,
0.003465912537649274,
-0.0404522530734539,
0.0008672170806676149,
-0.05462409555912018,
0.007586352992802858,
-0.0862472876906395,
0.0026533796917647123,
0.02687954716384411,
-0.03390716388821602,
-0.024768546223640442,
0.06628061830997467,
-0.0370953306555748,
-0.009991820901632309,
0.005448118317872286,
-0.015161032788455486,
-0.04833689704537392,
0.04411645606160164,
0.01434906292706728,
0.021503988653421402,
0.014269675128161907,
0.03189327195286751,
0.011175163090229034,
-0.004006147850304842,
0.04572276398539543,
0.042528185993433,
-0.022320184856653214,
-0.006117699667811394,
-0.05062583088874817,
0.02856999635696411,
-0.013156305067241192,
-0.0499398298561573,
-0.011405871249735355,
0.02287895232439041,
0.026639532297849655,
-0.005980538669973612,
-0.0070854113437235355,
0.02014612779021263,
-0.011582770384848118,
0.025321053341031075,
-0.054148200899362564,
0.00862977560609579,
-0.08019930124282837,
0.040484488010406494,
-0.031278062611818314,
-0.0062956553883850574,
-0.004673597402870655,
0.019881173968315125,
-0.015801824629306793,
-0.04086380824446678,
0.009205572307109833,
0.023742789402604103,
-0.005849200766533613,
0.005361662711948156,
-0.03895003721117973,
0.019159454852342606,
0.019106367602944374,
0.029069263488054276,
0.008425326086580753,
0.00879254937171936,
-0.018860790878534317,
-0.029062824323773384,
0.06532525271177292,
-0.012454786337912083,
0.020636582747101784,
-0.04812714084982872,
-0.0014474511845037341,
0.024838684126734734,
-0.009861757978796959,
-0.022040456533432007,
0.018705446273088455,
-0.05162270367145538,
0.07121510058641434,
0.07250621914863586,
0.031051522120833397,
0.002125753788277507,
-0.00048187808715738356,
-0.01043054647743702,
0.024230601266026497,
-0.013490218669176102,
0.001998310908675194,
-0.04549849033355713,
-0.013914398849010468,
0.011038513854146004,
0.03682657703757286,
-0.013268738985061646,
-0.005157435778528452,
0.020099282264709473,
0.0018463671440258622,
0.07229955494403839,
0.024532470852136612,
0.006957264617085457,
-0.027389181777834892,
0.034385908395051956,
0.01906907744705677,
0.021191272884607315,
0.05215366184711456,
0.009041592478752136,
0.039754848927259445,
0.08491967618465424,
-0.02191893942654133,
-0.010547126643359661,
0.061663590371608734,
0.020336143672466278,
-0.013584363274276257,
0.017677107825875282,
-0.015796130523085594,
0.030196024104952812,
-0.020909413695335388,
0.0164527278393507,
0.03103548102080822,
-0.010884350165724754,
0.02163245715200901,
-0.03302294760942459,
-0.008280159905552864,
0.04113279655575752,
0.013365707360208035,
-0.04188350960612297,
-0.05867268517613411,
0.013386119157075882,
-0.01874413527548313,
-0.033527687191963196,
-0.006093799136579037,
0.0018124793423339725,
-0.02922854572534561,
-0.02575218677520752,
0.0531817264854908,
0.014471017755568027,
0.048094868659973145,
-0.0014424917753785849,
-0.025905093178153038,
0.012665420770645142,
-0.052891723811626434,
0.0008506380254402757,
-0.039766404777765274,
-0.027388541027903557,
0.028017424046993256,
-0.006894728634506464,
-0.056726474314928055,
0.0336022824048996,
-0.011836167424917221,
0.010179395787417889,
0.012129965238273144,
-0.04115558788180351,
-0.0389147587120533,
-0.01756817102432251,
-0.007133485283702612,
0.007529265712946653,
-0.03526047617197037,
0.0013393450062721968,
0.02751527726650238,
-0.0013804894406348467,
-0.005447207018733025,
0.002856210572645068,
-0.02229328453540802,
-0.02165011502802372,
-0.021822871640324593,
-0.007252891082316637,
0.02568230777978897,
-0.042242709547281265,
0.04712001979351044,
0.040804896503686905,
-0.039503950625658035,
0.012429631315171719,
-0.0011348756961524487,
-0.04074295237660408,
0.019851166754961014,
-0.02347896620631218,
0.02060532383620739,
0.0012795808725059032,
-0.07064761221408844,
0.08828336000442505,
0.009164642542600632,
-0.031466592103242874,
0.005866215564310551,
-0.015104591846466064,
0.010825486853718758,
-0.049479350447654724,
0.018801236525177956,
0.029565131291747093,
0.01825600489974022,
-0.026674291118979454,
0.051076266914606094,
0.04039202257990837,
0.054181210696697235,
0.022726736962795258,
-0.013153130188584328,
-0.021713193506002426,
0.015866002067923546,
-0.011462158523499966,
0.029139725491404533,
0.010578635148704052,
-0.009597612544894218,
0.025440678000450134,
-0.017527131363749504,
0.06428291648626328,
0.038819678127765656,
-0.03154598921537399,
0.015667587518692017,
0.02760462649166584,
-0.004177440889179707,
-0.027493789792060852,
0.03216037154197693,
0.0015054891118779778,
-0.029863374307751656,
0.007674701977521181,
-0.007898901589214802,
0.008447876200079918,
-0.01913422718644142,
-0.021080633625388145,
0.019252663478255272,
0.014673799276351929,
-0.021568886935710907,
-0.019948530942201614,
0.00443359836935997,
-0.02873264253139496,
0.03975226357579231,
-0.02080943062901497,
-0.008500343188643456,
0.046195801347494125,
0.024057641625404358,
0.018567098304629326,
-0.03225129097700119,
-0.05574474483728409,
0.002879462670534849,
-0.07379746437072754,
0.009094536304473877,
0.03739304840564728,
0.06885705888271332,
-0.0036649785470217466,
0.07985249906778336,
0.015019341371953487,
0.038687966763973236,
0.04500799626111984,
0.016453728079795837,
-0.08953781425952911,
0.013273407705128193,
-0.03336857259273529,
-0.046111106872558594,
0.011635933071374893,
-0.00018064759206026793,
-0.005917586851865053,
-0.025743534788489342,
-0.04509609937667847,
-0.026867108419537544,
0.003298367140814662,
-0.07891397178173065,
0.006122880149632692,
-0.01749213971197605,
-0.009563765488564968,
-0.004237192217260599,
0.02562505379319191,
0.022513991221785545,
0.025921814143657684,
0.04885336384177208,
0.048430752009153366,
0.012960396707057953,
-0.010829041711986065,
-0.013309724628925323,
-0.014158765785396099,
0.01865990459918976,
0.04080867022275925,
0.020824812352657318,
0.014274525456130505,
0.0003984830400440842,
0.017322681844234467,
0.0022856525611132383,
0.07593797147274017,
0.013093266636133194,
0.002147677354514599,
-0.017251793295145035,
-0.032298315316438675,
0.007902482524514198,
-0.0021230452693998814,
0.025690989568829536,
0.0011022010585293174,
0.016628220677375793,
0.009807420894503593,
-0.025142846629023552,
0.0038071642629802227,
0.05484287813305855,
0.07206960022449493,
0.02826482243835926,
-0.04208741337060928,
-0.06792011111974716,
-0.0014624608447775245,
-0.04573056101799011,
-0.007733951788395643,
0.012215224094688892,
0.014145183376967907,
-0.023968130350112915,
0.010632998310029507,
-0.023481111973524094,
0.026935910806059837,
-0.0030642172787338495,
-0.02219439297914505,
0.028562355786561966,
0.018293775618076324,
-0.03909562900662422,
-0.027784498408436775,
0.022635826840996742,
0.055579040199518204,
0.04480684921145439,
-0.012940092012286186,
0.0032381098717451096,
-0.09806407988071442,
0.01579630747437477,
0.006465662270784378,
0.05074578896164894,
-0.019642561674118042,
-0.009209995158016682,
-0.02787788212299347,
-0.026064619421958923,
0.03450214862823486,
-0.021374568343162537,
0.0003429922799114138,
-0.013215928338468075,
0.03957328572869301,
-0.0025789157953113317,
0.030103085562586784,
-0.000944123137742281,
0.028065701946616173,
-0.03141789883375168,
-0.021647708490490913,
0.004085392691195011,
0.01916361041367054,
-0.0217315424233675,
-0.006039367523044348,
-0.012412606738507748,
0.056701160967350006,
-0.00383342825807631,
-0.014052148908376694,
-0.025949591770768166,
0.017289504408836365,
-0.038664963096380234,
-0.057038258761167526,
0.020985309034585953,
-0.0127974022179842,
-0.0013008909299969673,
0.011477863416075706,
-0.0043492973782122135,
-0.05949626863002777,
0.05772307887673378,
0.007290884852409363,
-0.037738505750894547,
0.01184065267443657,
-0.0071464781649410725,
0.028693854808807373,
0.012852339074015617,
-0.03783788904547691,
0.040164653211832047,
0.06295567005872726,
-0.015518349595367908,
-0.014377187937498093,
-0.02979504130780697,
0.040233220905065536,
-0.05547918751835823,
-0.014641701243817806,
-0.04164660722017288,
0.024646613746881485,
-0.049861013889312744,
0.025367451831698418,
0.0012895086547359824,
0.022378765046596527,
-0.020180895924568176,
-0.047000184655189514,
-0.011547574773430824,
0.035201460123062134,
0.017327308654785156,
0.0028585302643477917,
-0.014843173325061798,
0.025025896728038788,
0.009019281715154648,
-0.015457361936569214,
0.006014395970851183,
0.03834839537739754,
0.01859966479241848,
0.011300408281385899,
-0.005364360753446817,
0.04592078924179077,
0.019369356334209442,
-0.015369215048849583,
0.038471769541502,
-0.03581580892205238,
0.06519756466150284,
0.009241494350135326,
0.018096888437867165,
0.018131326884031296,
-0.055305201560258865,
-0.020708076655864716,
-0.0041529107838869095,
-0.013640069402754307,
0.03405237942934036,
-0.0796116441488266,
0.04401692748069763,
0.03593629598617554,
0.016444005072116852,
-0.06777962297201157,
-0.07617894560098648,
0.04325887933373451,
0.011280450969934464,
-0.023433564230799675,
-0.01079581305384636,
0.025198744609951973,
-0.020000798627734184,
-0.025524206459522247,
0.01314601395279169,
0.045821283012628555,
-0.00460883928462863,
-0.01752195693552494,
0.03252362459897995,
0.009198881685733795,
0.044203609228134155,
0.024373508989810944,
-0.032604459673166275,
-0.006446578539907932,
0.006178413983434439,
-0.006673481781035662,
-0.003291804576292634,
0.037104252725839615,
-0.03625418245792389,
0.020618749782443047,
-0.011718797497451305,
-0.040718916803598404,
0.021194830536842346,
-0.012152206152677536,
0.02589481510221958,
-0.03393048048019409,
0.03535277023911476,
-0.03010028600692749,
-0.03427128866314888,
-0.005416128318756819,
-0.029483547434210777,
0.017134783789515495,
-0.00008312855061376467,
-0.017142582684755325,
-0.007918945513665676,
-0.05493335425853729,
0.00248770322650671,
0.01121539156883955,
-0.002740563591942191,
0.004417938180267811,
0.08305361121892929,
0.007526443339884281,
0.000717144226655364,
0.0002456053625792265,
-0.052070252597332,
0.002819973975419998,
0.04479104280471802,
-0.007150887046009302,
0.04646029323339462,
-0.013219304382801056,
-0.030972948297858238,
0.0065969442948699,
-0.06638634204864502,
0.0013747403863817453,
0.08143206685781479,
-0.034177254885435104,
0.025318073108792305,
0.004880971275269985,
-0.009800371713936329,
-0.011481277644634247,
-0.005480676889419556,
-0.010684310458600521,
0.00437098927795887,
-0.018123118206858635,
0.05469108000397682,
-0.01987912505865097,
-0.01833272911608219,
0.020931214094161987,
0.017425108700990677,
-0.03427501395344734,
0.022362062707543373,
0.009797739796340466,
0.03559427708387375,
-0.006971418857574463,
-0.032685983926057816,
-0.02291349321603775,
0.01725776307284832,
0.025026904419064522,
0.017566172406077385,
0.008873658254742622,
-0.034826405346393585,
0.013006269931793213,
0.001295336987823248,
0.021026264876127243,
-0.04645605385303497,
-0.01232730969786644,
-0.016631823033094406,
0.017996471375226974,
0.036281730979681015,
-0.005233462899923325,
0.045694492757320404,
0.02081734873354435,
-0.010288402438163757,
0.02815677411854267,
0.04857780784368515,
-0.005958635360002518,
-0.04180644825100899,
-0.0016587423160672188,
-0.01736389845609665,
-0.046117350459098816,
0.00601198710501194,
0.007084886077791452,
-0.059376563876867294,
0.032073281705379486,
-0.002536236774176359,
0.04964427649974823,
0.04954551160335541,
-0.009516298770904541,
0.019085830077528954,
0.08873383700847626,
-0.0010612559271976352,
0.019275538623332977,
0.011005847714841366,
-0.0003724679409060627,
0.10854118317365646,
0.03319575637578964,
0.03738877549767494,
-0.0482625737786293,
-0.02022104151546955,
-0.006864369381219149,
-0.0013147458666935563,
-0.045718371868133545,
0.030900863930583,
-0.008282884024083614,
0.014442399144172668,
0.03312438726425171,
0.0475122295320034,
-0.013290118426084518,
0.0039405738934874535,
0.04411860927939415,
-0.02076057158410549,
-0.03454800695180893,
-0.04261934757232666,
0.01396806351840496,
-0.030765246599912643,
0.020349040627479553,
-0.04179373383522034,
0.022050928324460983,
0.029304489493370056,
0.009749495424330235,
-0.05992080271244049,
-0.03873712942004204,
0.021702956408262253,
-0.02702156826853752,
-0.019482871517539024,
0.004348962102085352,
-0.01760861650109291,
-0.00652175722643733,
-0.06497669965028763,
0.03510567918419838,
0.0019463476492092013,
-0.019501762464642525,
-0.012085335329174995,
0.037011537700891495,
0.009089607745409012,
-0.030062010511755943,
0.00995622668415308,
0.009610217995941639,
-0.036570459604263306,
0.02715185470879078,
-0.033249713480472565,
0.022632380947470665,
-0.0048482054844498634,
-0.01594455912709236,
0.0008567924960516393,
0.005546749569475651,
-0.040144313126802444,
-0.05263006314635277,
-0.05165627971291542,
-0.016338897868990898,
0.0259027611464262,
-0.02486511319875717,
-0.0402810163795948,
-0.0010552299208939075,
0.0036730647552758455,
0.0008277862798422575,
0.04015562683343887,
-0.0392850823700428,
-0.009611629880964756,
0.005687427241355181,
0.029254358261823654,
0.03673345595598221,
-0.06445566564798355,
-0.009288433007895947,
0.001390442019328475,
0.01515665277838707,
-0.05195567384362221,
-0.013661645352840424,
0.005786492023617029,
-0.0055877529084682465,
0.019743897020816803,
-0.02543557621538639,
0.014733939431607723,
-0.014251451008021832,
-0.03780010715126991,
0.05265655368566513,
-0.052868232131004333,
0.006212062202394009,
-0.02210971899330616,
0.013078336603939533,
0.01860104314982891,
0.05783740058541298,
-0.003955251071602106,
0.012975645251572132,
0.009252085350453854,
0.00699408957734704,
0.03791475668549538,
-0.03307193145155907,
-0.02972528524696827,
0.032376714050769806,
-0.034238334745168686,
0.01936379261314869,
0.033124662935733795,
0.02870750054717064,
0.0470738410949707,
0.010689760558307171,
-0.04332857206463814,
0.01649506576359272,
-0.02468200959265232,
0.024654757231473923,
-0.0022952149156481028,
-0.013855664990842342,
0.01283058151602745,
0.033638086169958115,
0.019144941121339798,
-0.041541937738657,
-0.013062434270977974,
-0.02944701910018921,
0.0011045048013329506,
0.014001999981701374,
-0.005521188024431467,
-0.023869650438427925,
0.007710705511271954,
-0.022190162912011147,
0.006236577406525612,
-0.030023053288459778,
-0.003984389360994101,
-0.04168286919593811,
-0.0019389711087569594,
0.05451694130897522,
0.005471996031701565,
-0.016083527356386185,
0.018086949363350868,
-0.0562627948820591,
-0.016391389071941376,
0.024487538263201714,
0.014113296754658222,
0.022867318242788315,
0.004647246096283197,
0.0688348114490509,
-0.018931904807686806,
0.033517006784677505,
0.001763703883625567,
-0.013864366337656975,
0.02438325062394142,
-0.025870855897665024,
-0.06953396648168564,
0.02097873017191887,
0.03343808278441429,
0.03548695147037506,
-0.01040948648005724,
-0.012794142588973045,
-0.033786505460739136,
0.05207943171262741,
-0.025510555133223534,
0.02355465665459633,
-0.026240486651659012,
-0.026469705626368523,
-0.03343473747372627,
0.00003143071080558002,
-0.007312676403671503,
-0.01963009685277939,
-0.009511218406260014,
0.03345740959048271,
0.026412636041641235,
-0.012981414794921875,
-0.02294224128127098,
0.049393098801374435,
0.009186869487166405,
-0.00277237081900239,
0.020650455728173256,
0.02340497449040413,
-0.000319074431899935,
0.027729149907827377,
0.003610868938267231,
0.026507684960961342,
0.0011335378512740135,
0.026242680847644806,
-0.10052809864282608,
-0.021181246265769005,
-0.02111237868666649,
0.006695451680570841,
0.03765863552689552,
-0.03869636729359627,
0.019788851961493492,
-0.0005054382490925491,
-0.015382086858153343,
-0.01130423229187727,
-0.03699776157736778,
-0.03447391837835312,
0.018431611359119415,
-0.0037087902892380953,
0.015861639752984047,
0.07402937859296799,
0.04148285835981369,
0.01872727833688259,
0.012612353079020977,
0.018080884590744972,
-0.020255500450730324,
0.04502587765455246,
-0.016377979889512062,
0.02707698382437229,
0.012006915174424648,
-0.02662201039493084,
0.07070925831794739,
0.0041642324067652225,
-0.031936608254909515,
0.022929687052965164,
-0.021998852491378784,
0.005135236773639917,
0.014493858441710472,
0.022742796689271927,
0.0109795480966568,
0.03730928897857666,
0.01698288880288601,
-0.01806429773569107,
-0.04950787127017975,
0.04549131542444229,
-0.01637527532875538,
0.0340421125292778,
-0.04243887960910797,
-0.002255462110042572,
-0.0041983346454799175,
-0.024801868945360184,
-0.011126259341835976,
0.015296774916350842,
-0.0332895964384079,
-0.025392234325408936,
-0.01695445366203785,
-0.018759431317448616,
-0.008916723541915417,
-0.013992317952215672,
0.023980360478162766,
-0.03305120766162872,
-0.009608272463083267,
0.026071079075336456,
-0.0067072538658976555,
-0.06785871088504791,
0.04165879637002945,
0.01566431112587452,
-0.05916750803589821,
0.026571908965706825,
-0.005466276779770851,
-0.0577702634036541,
-0.057464174926280975,
-0.004993434529751539,
-0.011096520349383354,
-0.038291797041893005,
-0.01749598979949951,
-0.014660825952887535,
-0.010426283814013004,
0.035151079297065735,
0.0351787805557251,
0.009375370107591152,
-0.009625745005905628,
-0.031674932688474655,
0.002262597670778632,
-0.07281804084777832,
0.053724367171525955,
-0.027706947177648544,
-0.025098320096731186,
-0.034007929265499115,
-0.004326812457293272,
-0.02367781288921833,
0.011767551302909851,
0.0596049427986145,
-0.00012132720439694822,
0.004270995035767555,
-0.017798196524381638,
0.00915242824703455,
0.006077216472476721,
-0.021121971309185028,
-0.030695263296365738,
0.03209404647350311,
-0.04886205494403839,
0.006435442250221968,
0.007175746373832226,
-0.006212703883647919,
0.041631683707237244,
0.03597283735871315,
-0.001348475692793727,
0.02049410529434681,
0.0004690874775405973,
-0.03996242582798004,
0.0464460663497448,
0.025500375777482986,
-0.013863441534340382,
0.09461659938097,
-0.053109560161828995,
0.0016150653827935457,
0.006235301494598389,
-0.005158723797649145,
-0.07217302918434143,
0.007258098106831312,
-0.02926562912762165,
0.006846418138593435,
-0.01721024513244629,
-0.005974924191832542,
0.004872097168117762,
-0.06392260640859604,
-0.009657575748860836,
0.02751868963241577,
-0.05717853084206581,
0.02340490184724331,
0.06714379787445068,
0.007549465633928776,
0.0312909334897995,
-0.005123613402247429,
-0.001962115755304694,
-0.017034655436873436,
-0.028503844514489174,
0.005108692217618227,
0.021322228014469147,
0.033360280096530914,
-0.00693480996415019,
-0.0008073985227383673,
0.024237925186753273,
-0.02389342524111271,
0.013715610839426517,
0.011644408106803894,
0.008694523945450783,
-0.06022312119603157,
-0.042820438742637634,
0.0030195412691682577,
-0.02854454331099987,
0.008368093520402908,
0.03802730515599251,
-0.015233912505209446,
0.09027838706970215,
0.0064405458979308605,
0.012833870016038418,
-0.005917851347476244,
0.014507963322103024,
-0.019872769713401794,
-0.014402409084141254,
0.0130222262814641,
0.0053764209151268005,
-0.012965341098606586,
-0.014077410101890564,
0.0064314561896026134,
-0.04157400503754616,
0.028273222967982292,
-0.014758730307221413,
0.011684026569128036,
0.005500099156051874,
-0.015646889805793762,
-0.013090063817799091,
-0.019214898347854614,
-0.0318589061498642,
0.00439432030543685,
0.023807287216186523,
0.011506132781505585,
0.013675223104655743,
0.038314126431941986,
0.0248799379914999,
-0.009515408426523209,
0.07243715226650238,
-0.04958444833755493,
0.017637036740779877,
-0.006057587452232838,
0.009670920670032501,
-0.019171277061104774,
-0.03247573971748352
] |
<p>When a sensor registers electromagnetic radiation, such as that used for the transmission of communication like light or radio waves, does this radiation "abrade" or "erode" the material of the sensor?</p>
<p>Are there any traces of the received radiation that can be detected, even if only theoretically?</p>
<p>An example from a biological background would be that high energy light (such as that in the UV range) destroys the pigments in the eyes, which is why animals that live longer than a few years cannot see in the UV range. Maybe something similar happens with man made sensors for different wavelengths of electromagnetic radiation.</p>
| 7,626 |
[
0.005125893745571375,
-0.05158929526805878,
0.0346466563642025,
-0.04393405094742775,
0.01478540152311325,
0.03469683229923248,
-0.030965207144618034,
-0.013343855738639832,
0.011053010821342468,
-0.03098900243639946,
0.03021308220922947,
0.03210662677884102,
0.04744460806250572,
0.013556262478232384,
0.0028965272940695286,
-0.013102714903652668,
-0.0002853123296517879,
-0.016246045008301735,
-0.020298006013035774,
-0.06730745732784271,
-0.013731666840612888,
-0.01299941074103117,
0.018137289211153984,
-0.00720113143324852,
-0.0621333085000515,
0.0015460572903975844,
0.034545425325632095,
-0.019113102927803993,
0.030739227309823036,
0.027291622012853622,
-0.01124325767159462,
0.0013048795517534018,
-0.005850124638527632,
0.0027988606598228216,
0.02359144203364849,
-0.03268536925315857,
-0.049518194049596786,
-0.05220355466008186,
-0.014068838208913803,
0.012260369956493378,
-0.00633600540459156,
0.009031328372657299,
0.005286762956529856,
0.03873312845826149,
-0.01796095445752144,
-0.04147261753678322,
-0.019819226115942,
-0.009565816260874271,
0.004194396547973156,
-0.06301102042198181,
0.03395044803619385,
-0.028728917241096497,
0.02678329311311245,
-0.009130679070949554,
-0.009692531079053879,
0.011368581093847752,
0.1032218262553215,
0.0502045601606369,
-0.0013524288078770041,
-0.04328825697302818,
0.020545098930597305,
-0.02280094102025032,
-0.028849557042121887,
-0.030906103551387787,
-0.0489841066300869,
0.012276658788323402,
-0.03207504376769066,
-0.046545032411813736,
0.07016216218471527,
0.058592669665813446,
0.01800714246928692,
0.0264147836714983,
-0.0010633841156959534,
0.024586718529462814,
0.02691051922738552,
-0.03022128716111183,
0.005319138988852501,
0.04159262403845787,
0.05278295278549194,
0.029169006273150444,
-0.01594364270567894,
-0.013639319688081741,
-0.020810460671782494,
0.04264828562736511,
0.006836417596787214,
-0.04923522472381592,
0.0446014441549778,
-0.03117862530052662,
0.0213150754570961,
-0.013299835845828056,
0.021144263446331024,
0.013333228416740894,
0.001223913044668734,
0.022540180012583733,
-0.045806434005498886,
0.016493765637278557,
-0.010362621396780014,
0.0527300126850605,
0.002978126984089613,
-0.026765411719679832,
0.00853230431675911,
0.030506456270813942,
0.04266330227255821,
0.054449789226055145,
-0.02280295267701149,
-0.03180566802620888,
-0.002188068814575672,
-0.010520565323531628,
-0.019495965912938118,
0.007066868711262941,
-0.045005250722169876,
-0.00012596954184118658,
0.012752004899084568,
0.023095199838280678,
0.05044649913907051,
0.004093992058187723,
0.00255661946721375,
-0.029901206493377686,
0.07969515025615692,
0.07577299326658249,
0.003934910986572504,
-0.017142118886113167,
0.007771079894155264,
-0.009488229639828205,
-0.06440889090299606,
0.026868920773267746,
0.018872791901230812,
-0.010219338349997997,
-0.062405407428741455,
0.009631027467548847,
-0.021379174664616585,
-0.005585876759141684,
0.029497552663087845,
-0.050463251769542694,
0.022405855357646942,
0.0015688752755522728,
-0.07613512128591537,
-0.04935016483068466,
0.009100680239498615,
0.01355003658682108,
-0.009776605293154716,
-0.04570528119802475,
0.007415697909891605,
0.034329600632190704,
0.060534849762916565,
0.011387715116143227,
0.0022823286708444357,
-0.02490580640733242,
0.03728815168142319,
-0.032397277653217316,
-0.011346576735377312,
-0.026702554896473885,
0.0060510397888720036,
-0.023085158318281174,
-0.007926682941615582,
-0.04834681376814842,
0.010450568050146103,
0.04593765363097191,
-0.006320357788354158,
-0.04162871837615967,
0.02872762642800808,
-0.011102121323347092,
0.016002876684069633,
0.013122356496751308,
-0.011759953573346138,
-0.03237012401223183,
0.08660805970430374,
0.010099081322550774,
0.0009936284041032195,
-0.01154155284166336,
0.02766529656946659,
0.04793483763933182,
0.00996378343552351,
0.003671437269076705,
0.03983724117279053,
-0.024934282526373863,
-0.019851278513669968,
-0.0035400849301368,
0.038842372596263885,
0.0049131326377391815,
-0.04415431246161461,
-0.024665025994181633,
-0.007272091694176197,
0.024415453895926476,
0.018307309597730637,
0.029860377311706543,
0.007465542294085026,
-0.03644533082842827,
0.04364164173603058,
-0.04159767925739288,
0.02009284868836403,
-0.050746627151966095,
0.019963229075074196,
-0.006260894704610109,
-0.02841201424598694,
0.01342848688364029,
-0.026643013581633568,
0.00795510783791542,
-0.04827520251274109,
-0.04598432034254074,
0.011853896081447601,
-0.0074998424388468266,
0.0032678539864718914,
-0.03101876564323902,
-0.026685159653425217,
0.060696765780448914,
-0.003977701533585787,
0.03529456630349159,
0.027121203020215034,
-0.01853330060839653,
-0.02772034890949726,
0.02103455364704132,
-0.029968837276101112,
0.012702535837888718,
0.007418828550726175,
0.008503089658915997,
0.000895140110515058,
-0.015120484866201878,
0.012020010501146317,
0.017979610711336136,
-0.01450949814170599,
0.04397339001297951,
0.03027600795030594,
0.00014551095955539495,
-0.006915703881531954,
0.016140444204211235,
0.006067825015634298,
-0.03616582229733467,
-0.028373626992106438,
-0.026256220415234566,
-0.07889462262392044,
-0.008198046125471592,
0.03216656297445297,
0.014356383122503757,
-0.05232136324048042,
0.030881930142641068,
0.0015139303868636489,
0.046306461095809937,
-0.0016213636845350266,
0.011990809813141823,
0.0012666854308918118,
-0.01678691804409027,
0.027761587873101234,
0.02643088810145855,
0.001859681447967887,
0.015540879219770432,
0.012679110281169415,
-0.001983094494789839,
0.034318841993808746,
-0.005601541139185429,
0.031273648142814636,
0.013968340121209621,
-0.010081831365823746,
0.05744701996445656,
-0.024975083768367767,
-0.01813909225165844,
-0.0034822444431483746,
-0.0033566816709935665,
-0.000513956299982965,
-0.015308829955756664,
-0.025417722761631012,
-0.008835059590637684,
0.006110121961683035,
0.00287579745054245,
-0.025409581139683723,
-0.01799989491701126,
-0.019261907786130905,
-0.010873575694859028,
0.04147802293300629,
-0.05026305094361305,
0.02236616425216198,
-0.006065261084586382,
0.01263731811195612,
0.0005925673758611083,
0.00881462823599577,
0.03400922194123268,
-0.026697639375925064,
0.03236280381679535,
-0.05378732085227966,
-0.0601557195186615,
-0.004769383929669857,
-0.0747695118188858,
0.008553066290915012,
0.030190352350473404,
-0.03521082177758217,
-0.0177582036703825,
-0.022176681086421013,
-0.05399749428033829,
0.0387834869325161,
-0.030051469802856445,
0.00890472810715437,
0.017789041623473167,
-0.015386276878416538,
-0.05137454345822334,
-0.014573141001164913,
-0.0035144761204719543,
-0.03484293445944786,
0.0031986196991056204,
-0.0016748309135437012,
0.056928131729364395,
-0.02917860448360443,
-0.010095072910189629,
-0.0014453050680458546,
-0.034665416926145554,
-0.0041800313629209995,
-0.025159021839499474,
-0.0318012572824955,
-0.0017077047377824783,
-0.037508703768253326,
0.002654438139870763,
0.021279122680425644,
-0.052344851195812225,
-0.0020899970550090075,
-0.042701903730630875,
-0.07378494739532471,
0.029471006244421005,
-0.022904612123966217,
0.043661367148160934,
0.007280485704541206,
0.005930759012699127,
0.03945835307240486,
0.04683363810181618,
0.008810346946120262,
0.02159390226006508,
-0.01914818584918976,
-0.009911068715155125,
-0.03145773708820343,
-0.022959666326642036,
0.03090733103454113,
0.022227270528674126,
0.023430747911334038,
-0.007066798396408558,
0.02429061196744442,
0.020882537588477135,
0.013112912885844707,
-0.04338940978050232,
-0.0009047226049005985,
-0.005925506353378296,
-0.0009146666270680726,
0.039763566106557846,
0.05316419154405594,
-0.016422085464000702,
0.04349210858345032,
0.03619278222322464,
0.0347442664206028,
0.039034295827150345,
-0.03059563972055912,
0.012822730466723442,
0.000829059979878366,
0.02851971797645092,
-0.02644319087266922,
0.007577461190521717,
0.009683105163276196,
0.025754213333129883,
-0.01816640794277191,
0.044187940657138824,
0.0520741306245327,
0.008939546532928944,
0.000646545144263655,
-0.0022363238967955112,
0.06820116937160492,
-0.0032928467262536287,
-0.016247183084487915,
0.01032260712236166,
-0.012453611008822918,
0.0008683518972247839,
-0.004541373811662197,
0.003891215892508626,
0.05762132257223129,
0.013330423273146152,
0.02369743399322033,
0.02219735085964203,
-0.02133096382021904,
-0.03709347918629646,
-0.019156280905008316,
-0.05083228275179863,
0.0008812237065285444,
0.052185967564582825,
0.020593935623764992,
0.012113133445382118,
0.013990507461130619,
0.0005388704594224691,
0.036412082612514496,
-0.005009392276406288,
-0.060425929725170135,
-0.013385691680014133,
-0.007117038127034903,
-0.036002036184072495,
-0.004671171307563782,
-0.03460625186562538,
-0.004808857571333647,
-0.03601687029004097,
-0.03874675929546356,
0.005330400541424751,
0.036185845732688904,
-0.07381520420312881,
0.028709247708320618,
-0.012564471922814846,
-0.03835250437259674,
-0.06572351604700089,
0.0356498658657074,
0.020628927275538445,
-0.0038647977635264397,
-0.010245506651699543,
0.022802187129855156,
-0.025308536365628242,
0.016141174361109734,
-0.021296856924891472,
-0.0014915285864844918,
0.005075282882899046,
0.0573435053229332,
0.04407062008976936,
-0.003128026146441698,
-0.02473723515868187,
0.027929266914725304,
0.009258510544896126,
0.040863193571567535,
0.006719577591866255,
-0.003450538497418165,
-0.037761956453323364,
-0.027745801955461502,
-0.027604106813669205,
-0.006854945328086615,
0.07217191159725189,
-0.02201680652797222,
-0.012326090596616268,
-0.0035568957682698965,
-0.010439127683639526,
-0.028813352808356285,
0.02371993288397789,
0.028556160628795624,
0.013321978971362114,
0.015500743873417377,
0.014563308097422123,
-0.00028185671544633806,
-0.019973644986748695,
-0.003107244148850441,
0.0099724056199193,
0.003375312779098749,
-0.009744992479681969,
-0.015838826075196266,
0.006471783388406038,
0.02238486520946026,
-0.028351327404379845,
0.0033604640047997236,
0.01730978861451149,
0.006237223744392395,
-0.0010794856352731586,
-0.00867222249507904,
0.028757169842720032,
0.05015520378947258,
0.05228857323527336,
0.014048699289560318,
-0.019230540841817856,
-0.11909455060958862,
0.02614438720047474,
0.03076164983212948,
0.03624944016337395,
0.007081649266183376,
-0.017250485718250275,
-0.04607085511088371,
-0.020168796181678772,
0.01653313636779785,
0.01984752155840397,
0.03637378662824631,
-0.005792390555143356,
-0.011360115371644497,
-0.031904906034469604,
-0.004745526239275932,
-0.008063577115535736,
0.018847011029720306,
0.02205575443804264,
0.019033992663025856,
-0.00021828226454090327,
-0.014885246753692627,
0.018104977905750275,
-0.0073987399227917194,
0.03211434930562973,
0.055527154356241226,
0.01983792893588543,
0.008638180792331696,
-0.027004554867744446,
-0.00882420502603054,
-0.029365960508584976,
-0.04860041290521622,
0.032582659274339676,
0.02878989279270172,
-0.01566675305366516,
0.0856090560555458,
0.01772340200841427,
0.003678862936794758,
0.05597483739256859,
0.02358577400445938,
0.004572763107717037,
-0.033422984182834625,
-0.050715625286102295,
0.04472940415143967,
0.026868177577853203,
-0.009581663645803928,
0.060789499431848526,
0.035386476665735245,
-0.010270853526890278,
0.02004893310368061,
0.00340091809630394,
0.050022922456264496,
-0.047481779009103775,
0.011746027506887913,
0.013630270026624203,
0.02324538119137287,
-0.031380489468574524,
0.07830508798360825,
0.03772039711475372,
0.008717863820493221,
-0.01559775322675705,
-0.025800557807087898,
-0.00433745700865984,
-0.01027285773307085,
-0.04702237620949745,
-0.014540179632604122,
-0.031075920909643173,
0.06183963268995285,
-0.06244449317455292,
0.007142779417335987,
0.00400159414857626,
-0.004471869673579931,
-0.021354971453547478,
0.007094859145581722,
0.018620295450091362,
0.029315460473299026,
-0.0649641826748848,
0.03401646763086319,
0.003388867946341634,
0.010263638570904732,
0.05371531471610069,
0.018231023102998734,
-0.012198704294860363,
0.02525550127029419,
-0.02290056087076664,
-0.010844061151146889,
0.03253967687487602,
-0.016801010817289352,
0.042612720280885696,
-0.035488784313201904,
0.054770246148109436,
0.018918653950095177,
0.018124226480722427,
-0.051335420459508896,
-0.02853260189294815,
0.007131320424377918,
0.05469325929880142,
0.01380041241645813,
-0.007448683492839336,
0.025279751047492027,
-0.07045195251703262,
-0.038763515651226044,
-0.005561433266848326,
0.025157617405056953,
-0.06757909804582596,
0.0012691449373960495,
0.0310503076761961,
-0.012817395851016045,
0.06294071674346924,
-0.0058259484358131886,
0.0024115501437336206,
0.04443082958459854,
0.0018821065314114094,
-0.018681898713111877,
-0.03763357549905777,
0.023668436333537102,
-0.023683922365307808,
-0.06026269495487213,
-0.013768229633569717,
-0.023982767015695572,
0.03205271065235138,
-0.03658827766776085,
-0.062000297009944916,
0.03383529931306839,
0.003369673853740096,
0.0027754721231758595,
-0.00505245802924037,
0.03801189735531807,
0.004745492711663246,
0.022291338071227074,
0.028048550710082054,
-0.005594850983470678,
-0.018643174320459366,
-0.030127618461847305,
0.023064950481057167,
0.028854167088866234,
0.01609034091234207,
0.004557427484542131,
0.05762053281068802,
-0.03739338740706444,
-0.007009939756244421,
0.020923536270856857,
-0.01636645384132862,
0.030970022082328796,
-0.03673725575208664,
0.039887215942144394,
-0.0060960822738707066,
-0.0023026338312774897,
-0.027321413159370422,
-0.06016325205564499,
-0.029068473726511,
-0.08050337433815002,
0.06562136113643646,
-0.04389679431915283,
0.03934786468744278,
-0.0049355183728039265,
0.007808729074895382,
0.008330296725034714,
-0.015083122067153454,
-0.031341537833213806,
0.024839218705892563,
-0.03691936284303665,
0.017866501584649086,
0.00627462612465024,
0.0029503426048904657,
0.005590967833995819,
0.002158629009500146,
0.015359996818006039,
0.005688042845577002,
0.009066326543688774,
0.040327657014131546,
0.029070613905787468,
-0.03881343826651573,
-0.04756537079811096,
0.002817540429532528,
-0.07338104397058487,
0.007550244685262442,
0.029479093849658966,
-0.012999934144318104,
0.050435565412044525,
0.01653868705034256,
0.020267052575945854,
-0.026680750772356987,
-0.02993052825331688,
-0.05626784637570381,
0.04160071164369583,
-0.005537504330277443,
0.003483840264379978,
-0.011643413454294205,
-0.002996648894622922,
0.04213422164320946,
-0.005183658096939325,
-0.023482806980609894,
0.02112494595348835,
-0.05940888822078705,
-0.042764682322740555,
-0.04005366191267967,
-0.02231106162071228,
0.06806697696447372,
-0.050926804542541504,
-0.027689289301633835,
0.003634439781308174,
-0.05413903668522835,
0.06364346295595169,
0.010398329235613346,
0.07743962109088898,
-0.019023390486836433,
0.010894833132624626,
-0.01792149432003498,
0.03737479820847511,
-0.0021014204248785973,
0.020396508276462555,
0.11251755058765411,
0.05347854271531105,
0.030081724748015404,
-0.03724786639213562,
0.01196467038244009,
-0.026781398802995682,
0.006704611703753471,
-0.02221093513071537,
-0.0009655003668740392,
-0.024194590747356415,
0.06009722873568535,
0.033591609448194504,
0.007768727373331785,
0.008244560100138187,
-0.0023861676454544067,
-0.007117339875549078,
-0.03009166195988655,
0.009455952793359756,
0.04178953915834427,
0.021402426064014435,
-0.03469426929950714,
0.057790838181972504,
-0.0681956484913826,
-0.0016578997019678354,
-0.04356927052140236,
-0.03771848976612091,
-0.01482484582811594,
0.013392005115747452,
0.017082663252949715,
0.024457771331071854,
-0.040171027183532715,
-0.0198731180280447,
-0.00230628764256835,
-0.007520357146859169,
-0.020382896065711975,
0.03814437612891197,
0.004005850292742252,
0.025147249922156334,
0.01503433845937252,
0.03419945389032364,
0.056297723203897476,
-0.01638932339847088,
0.02070208452641964,
0.018856268376111984,
-0.048459846526384354,
-0.017638057470321655,
0.004760144278407097,
0.028713254258036613,
-0.017945215106010437,
-0.009160027839243412,
-0.015718474984169006,
-0.0026508013252168894,
-0.003659509588032961,
-0.03341410309076309,
-0.04793957993388176,
0.01888110488653183,
0.008981876075267792,
-0.03432144597172737,
-0.012326066382229328,
-0.001967313466593623,
0.04411124810576439,
-0.01860908605158329,
-0.00416418444365263,
0.02798818051815033,
-0.01507013849914074,
-0.017568843439221382,
-0.00422185193747282,
0.04439651966094971,
-0.016682684421539307,
-0.03205421566963196,
-0.052570853382349014,
-0.03972654789686203,
-0.037027593702077866,
-0.00844568945467472,
-0.01623387634754181,
0.03160831332206726,
0.008239162154495716,
0.017113778740167618,
-0.012979124672710896,
-0.01634461246430874,
-0.07354635745286942,
0.055314626544713974,
-0.03454451635479927,
-0.028852026909589767,
-0.03303699567914009,
-0.026758689433336258,
0.07542689144611359,
-0.006450999528169632,
-0.006445963867008686,
-0.026007305830717087,
-0.001989485463127494,
0.05445113778114319,
0.04452410712838173,
-0.014331050217151642,
-0.006604121997952461,
0.027882231399416924,
0.006376831792294979,
0.017894580960273743,
-0.0119947399944067,
0.03613996133208275,
0.037853486835956573,
0.05280241370201111,
0.027327580377459526,
-0.006501892581582069,
-0.02106902003288269,
-0.014345934614539146,
0.011281881481409073,
0.011699192225933075,
-0.009207592345774174,
-0.01657591015100479,
0.026956431567668915,
0.009222157299518585,
-0.04846961051225662,
-0.038800112903118134,
-0.03614666312932968,
-0.014750567264854908,
0.006682988256216049,
0.019423365592956543,
0.039174143224954605,
-0.029362166300415993,
0.014550373889505863,
-0.01451188512146473,
0.01782095804810524,
-0.04976445436477661,
-0.0485459640622139,
0.01594456098973751,
-0.016904635354876518,
0.010295813903212547,
0.0096712252125144,
-0.021130120381712914,
-0.036097485572099686,
0.02304033935070038,
0.04725203663110733,
0.009684799239039421,
0.037954848259687424,
-0.006211703177541494,
-0.01633351854979992,
0.050653163343667984,
-0.0033203514758497477,
-0.005688919685781002,
0.044699035584926605,
-0.036183301359415054,
-0.013129846192896366,
0.04361587390303612,
-0.04368101432919502,
0.02360960654914379,
0.003494258737191558,
0.014250089414417744,
0.021535677835345268,
0.04607477784156799,
0.02976738102734089,
-0.008708306588232517,
-0.010817201808094978,
-0.019202519208192825,
-0.015062347985804081,
0.03593245893716812,
0.06379080563783646,
-0.02085934951901436,
0.0036993850953876972,
0.03352268412709236,
-0.02906346134841442,
0.01852460391819477,
0.025567248463630676,
0.00024393571948166937,
-0.05419543758034706,
-0.015543573535978794,
0.022729605436325073,
-0.0029247598722577095,
-0.00212654797360301,
0.06426502019166946,
-0.01829785481095314,
0.04162045195698738,
0.0012615150772035122,
-0.021527254953980446,
-0.109953373670578,
-0.007722374051809311,
0.035038240253925323,
0.040341950953006744,
-0.004370164126157761,
-0.03692735731601715,
-0.00244779116474092,
0.0457632951438427,
-0.10523868352174759,
-0.01138771791011095,
0.0009096568683162332,
-0.03571669012308121,
-0.045132238417863846,
0.0400010421872139,
-0.04927242547273636,
0.0025126407854259014,
0.04370032623410225,
0.05221531540155411,
0.02591446414589882,
0.05069151893258095,
-0.015477611683309078,
-0.02087455615401268,
-0.03742564097046852,
0.026146236807107925,
-0.0007999986410140991,
-0.022181089967489243,
0.04919334873557091,
-0.019945228472352028,
0.020725397393107414,
0.014866989105939865,
-0.049593307077884674,
0.024482600390911102,
-0.008419068530201912,
-0.011181122623383999,
0.055288758128881454,
0.002400026423856616,
0.001970205456018448,
-0.027930444106459618,
-0.024698100984096527,
0.023399069905281067,
0.009756701067090034,
0.002557971980422735,
-0.031133398413658142,
0.044028960168361664,
-0.014973937533795834,
-0.024421822279691696,
-0.017243005335330963,
0.0083048390224576,
0.0017935753567144275,
-0.02912113070487976,
0.03433806821703911,
0.06809428334236145,
0.038558948785066605,
-0.03367902338504791,
0.011575747281312943,
-0.041077904403209686,
0.0005156161496415734,
-0.007001576945185661,
0.049177136272192,
0.010703920386731625,
-0.018389418721199036,
-0.017821647226810455,
-0.00498129753395915,
0.004723566584289074,
0.02642102725803852,
-0.008159952238202095,
-0.014304854907095432,
0.016528351232409477,
-0.02089996077120304,
0.00041986457654275,
0.013522053137421608,
-0.0029157495591789484,
-0.024973981082439423,
0.03497764840722084,
-0.02410397306084633,
0.012396950274705887,
0.00024929517530836165,
-0.04839402437210083,
-0.029897650703787804,
-0.07078813761472702,
0.026880864053964615,
-0.012903030961751938,
0.021746035665273666,
-0.0635695531964302,
-0.04638785496354103,
-0.02347942627966404,
0.05091870203614235,
0.03502802550792694,
-0.011004297994077206,
-0.026633944362401962,
0.008621448650956154,
-0.01488455943763256,
0.012943953275680542,
-0.04070834815502167,
0.05958635360002518,
-0.01424227561801672,
-0.009331089444458485,
-0.03379451110959053,
0.001302017248235643,
0.0012254987377673388,
0.0029284926131367683,
0.002182902069762349,
0.008890018798410892,
-0.0206584595143795,
-0.02825467474758625,
0.016409551724791527,
0.06620165705680847,
0.01850898191332817,
0.03558028116822243,
0.06762970238924026,
-0.004072573501616716,
0.03120293840765953,
0.021814195439219475,
0.011256290599703789,
-0.05109904333949089,
0.025954123586416245,
-0.023692527785897255,
0.03198077902197838,
-0.011677085421979427,
0.03942815214395523,
0.02908414602279663,
-0.01314137876033783,
-0.001242987927980721,
0.012221368961036205,
-0.025442279875278473,
-0.022611230611801147,
0.044443290680646896,
-0.034228257834911346,
0.019016418606042862,
-0.0022876011207699776,
0.01621047779917717,
0.022061854600906372,
-0.004121704958379269,
-0.03227941319346428,
0.060933053493499756,
-0.00010590569581836462,
-0.023772064596414566,
0.04184305667877197,
0.02185756340622902,
-0.02955803833901882,
-0.009333712048828602,
-0.0013581904349848628,
0.03485875204205513,
-0.021912382915616035,
0.011430138722062111,
0.024804219603538513,
0.03789106383919716,
-0.04597092047333717,
0.02658206783235073,
-0.011252546682953835,
0.0637444406747818,
-0.03103461302816868,
0.005156353116035461,
-0.04976460710167885,
0.003837243188172579,
0.023809215053915977,
0.05224988982081413,
0.03805678337812424,
0.03641370311379433,
0.014080250635743141,
0.013733570463955402,
-0.024128848686814308,
0.0375412218272686,
0.030751079320907593,
-0.059078868478536606,
0.031500086188316345,
-0.014265717007219791,
-0.006178195122629404,
0.010445069521665573,
-0.008769859559834003,
-0.012460554949939251,
-0.033540863543748856,
0.0022053816355764866,
0.019256161525845528,
-0.0023328063543885946,
0.04559636861085892,
-0.015507981181144714,
-0.03236930072307587,
0.00003929315789719112,
-0.04577499255537987,
0.00289728376083076,
-0.02459740824997425,
0.03221550211310387,
-0.019111663103103638,
-0.013094373047351837
] |
<ol>
<li><p>My question is why are we colliding particles in LHC to produce new ones? </p></li>
<li><p>And these particles that they sometimes say live for a fraction of a second, how in space they exists then? </p></li>
<li><p>In space all these particle exist without smashing to each other, why do we need to smash them to produce them?</p></li>
</ol>
| 7,627 |
[
-0.011584289371967316,
-0.023507168516516685,
0.006247640587389469,
-0.06915340572595596,
0.03447156026959419,
0.022103549912571907,
-0.04125406593084335,
-0.052170079201459885,
0.012034757062792778,
-0.021497689187526703,
0.025323446840047836,
0.051928114145994186,
-0.008886061608791351,
0.016541486606001854,
-0.013495029881596565,
0.00764218345284462,
-0.013151395134627819,
-0.026914723217487335,
-0.025901878252625465,
-0.019445665180683136,
0.021320868283510208,
-0.006599296350032091,
0.01758548617362976,
0.012281624600291252,
-0.03437262400984764,
-0.0077639734372496605,
0.014543648809194565,
0.007390061859041452,
-0.0031175168696790934,
0.0728701576590538,
0.005831602029502392,
-0.02579236589372158,
0.026552839204669,
-0.012170486152172089,
0.006653332617133856,
-0.012943550944328308,
0.007350952830165625,
-0.0405668169260025,
0.01469852402806282,
0.019714657217264175,
-0.04242304340004921,
-0.012324386276304722,
-0.017306845635175705,
0.04923096299171448,
-0.03462342917919159,
0.012266630306839943,
0.004213066305965185,
0.014187519438564777,
0.03933601826429367,
-0.08581830561161041,
0.025467373430728912,
-0.014036566019058228,
0.014285002835094929,
0.004273832309991121,
0.012817366048693657,
-0.004037025384604931,
0.07182548940181732,
0.0902794823050499,
0.007815210148692131,
-0.028198691084980965,
-0.016606345772743225,
-0.03277848660945892,
0.028974100947380066,
0.017101062461733818,
-0.006499599665403366,
0.0011027486762031913,
-0.009196621365845203,
0.02160666137933731,
0.010072301141917706,
0.021671656519174576,
0.050251659005880356,
-0.000007803020707797259,
-0.00701105035841465,
0.011170933023095131,
0.051962610334157944,
-0.02600613608956337,
0.03369291499257088,
-0.00448243273422122,
0.026585739105939865,
0.047613710165023804,
-0.00852945540100336,
0.003615641500800848,
0.03828028589487076,
-0.026605520397424698,
-0.016912376508116722,
0.008670821785926819,
0.09567877650260925,
-0.013033668510615826,
-0.0009290141169913113,
0.027009595185518265,
0.0168087687343359,
0.027919771149754524,
0.06415164470672607,
0.021523110568523407,
0.008836043067276478,
0.01640152558684349,
0.01683643087744713,
0.03552541509270668,
-0.01681245118379593,
-0.015517513267695904,
0.01696709915995598,
-0.012558214366436005,
0.01868242211639881,
0.05246778205037117,
-0.019502172246575356,
-0.019166944548487663,
-0.02325921691954136,
-0.007179202977567911,
-0.024435633793473244,
-0.0024993964470922947,
-0.04437042027711868,
0.005572477821260691,
-0.0008261432521976531,
0.037538908421993256,
0.022614765912294388,
-0.0188196562230587,
0.0007998063811101019,
-0.007852538488805294,
0.09705618023872375,
0.07340453565120697,
0.03289784491062164,
-0.012187281623482704,
0.041892554610967636,
-0.00427985331043601,
-0.0713268369436264,
0.008519680239260197,
0.006818360649049282,
0.020673956722021103,
-0.023600570857524872,
0.03226445987820625,
-0.015258114784955978,
0.0050395880825817585,
0.03654918074607849,
-0.0026353688444942236,
0.050439003854990005,
-0.012795020826160908,
-0.11265353858470917,
-0.03292283043265343,
0.09552822262048721,
0.02635546773672104,
-0.042147498577833176,
-0.09825928509235382,
0.024577995762228966,
-0.0043840534053742886,
0.06396500021219254,
-0.01683831959962845,
-0.03480677306652069,
0.01570671796798706,
0.03225988522171974,
0.023177707567811012,
-0.003326136153191328,
-0.010841737501323223,
-0.011309587396681309,
-0.0475010871887207,
0.018466956913471222,
-0.05031539872288704,
0.00725997518748045,
0.06436686217784882,
-0.0130100566893816,
-0.025346921756863594,
0.034777309745550156,
-0.044437725096940994,
0.04105953499674797,
0.03229953348636627,
-0.01134106982499361,
-0.03671707212924957,
0.07314092665910721,
0.03307004272937775,
0.014183485880494118,
0.04894610866904259,
0.013329305686056614,
0.029499975964426994,
0.009500051848590374,
0.00873502530157566,
0.006550130434334278,
-0.04467318579554558,
-0.04326450824737549,
-0.010873816907405853,
0.004154955502599478,
-0.04261200875043869,
-0.04731667786836624,
-0.014237421564757824,
-0.03270875662565231,
0.008611226454377174,
0.005708904471248388,
0.030165458098053932,
0.020467150956392288,
-0.008123788982629776,
-0.0027721410151571035,
-0.0331951379776001,
-0.07497590780258179,
-0.0926474779844284,
-0.011010522022843361,
-0.0006204850506037474,
-0.009493581019341946,
0.009674591943621635,
0.027621721848845482,
-0.01125833299010992,
-0.01183992624282837,
-0.019208986312150955,
-0.003955820109695196,
0.04164706543087959,
0.006277893669903278,
0.0033155945129692554,
-0.015764137730002403,
0.07904910296201706,
0.00910120364278555,
0.004792327061295509,
-0.0121779078617692,
0.019882960245013237,
-0.01338440366089344,
-0.03361162543296814,
-0.025055011734366417,
-0.021197844296693802,
-0.024881822988390923,
0.014387011528015137,
0.053959667682647705,
-0.008278737775981426,
-0.029659884050488472,
0.029357895255088806,
-0.017755011096596718,
0.08820876479148865,
0.046547554433345795,
-0.007489104755222797,
0.01717100851237774,
0.02385031431913376,
0.0031598657369613647,
0.024202175438404083,
0.006603864021599293,
-0.048401184380054474,
-0.05132242292165756,
-0.031066641211509705,
0.019236288964748383,
-0.00849131029099226,
0.008753232657909393,
0.012189589440822601,
0.0011711890110746026,
0.0061481003649532795,
0.0027491708751767874,
0.012374739162623882,
-0.03213546425104141,
-0.02232283540070057,
0.016602549701929092,
0.004542478360235691,
0.0013635491486638784,
0.013884617015719414,
0.006603017449378967,
-0.02192307822406292,
-0.015929147601127625,
-0.037742678076028824,
-0.006138753145933151,
0.02469158172607422,
0.013526429422199726,
0.007279711309820414,
0.01918000541627407,
-0.044232077896595,
0.019303668290376663,
0.012385301291942596,
0.008216452784836292,
-0.014306857250630856,
0.00005302217687130906,
-0.02455112151801586,
-0.045007165521383286,
-0.0020830093417316675,
-0.0162062868475914,
0.018798060715198517,
-0.005027804523706436,
-0.025503315031528473,
0.03362921625375748,
-0.06214029714465141,
0.04106917232275009,
0.030045032501220703,
-0.027922233566641808,
0.0020764830987900496,
-0.021825967356562614,
0.021518127992749214,
0.021178115159273148,
0.048042409121990204,
-0.022689666599035263,
0.009213738143444061,
0.019541749730706215,
-0.029771383851766586,
0.006557101849466562,
0.04260970652103424,
-0.05539056658744812,
0.0416228286921978,
-0.03621313348412514,
-0.03993728384375572,
0.0105103999376297,
-0.010669282637536526,
0.046418167650699615,
0.0367780476808548,
-0.007933300919830799,
-0.05982013791799545,
-0.01211712695658207,
-0.03395545855164528,
0.01622159779071808,
-0.021150022745132446,
0.023271504789590836,
0.03278757259249687,
0.014629499055445194,
-0.061040110886096954,
0.010767001658678055,
-0.05611104890704155,
0.003613965352997184,
-0.035588931292295456,
-0.011597301810979843,
0.0202706977725029,
-0.02808542363345623,
0.006393485236912966,
0.0443512462079525,
-0.028029270470142365,
0.027739690616726875,
-0.047356393188238144,
-0.010899891145527363,
-0.0068616000935435295,
-0.022778159007430077,
0.04154697433114052,
-0.0359991081058979,
-0.02303455024957657,
0.06713700294494629,
0.055152133107185364,
-0.036052096635103226,
-0.02921551652252674,
0.01344808004796505,
-0.03184005618095398,
-0.032428473234176636,
0.030006660148501396,
0.015183315612375736,
-0.03608141466975212,
-0.014909729361534119,
0.02652028389275074,
0.03056885488331318,
-0.003009775886312127,
0.013255089521408081,
-0.019680771976709366,
-0.06001495569944382,
-0.017942655831575394,
-0.017279189079999924,
0.02676505036652088,
0.03412451967597008,
-0.045822933316230774,
0.02860199473798275,
-0.010158303193747997,
0.024885423481464386,
0.034069810062646866,
-0.07241205126047134,
0.04031858220696449,
0.00966129545122385,
-0.01687805913388729,
0.0036054744850844145,
0.026818742975592613,
-0.022822042927145958,
-0.024875489994883537,
0.009930203668773174,
0.00861884281039238,
0.02954563871026039,
-0.018909098580479622,
-0.01179256197065115,
0.0087521867826581,
0.03432043269276619,
-0.05223849415779114,
-0.016428422182798386,
-0.03254600241780281,
-0.0055021122097969055,
-0.0107905063778162,
0.018152685835957527,
-0.027188928797841072,
0.023637641221284866,
0.016301916912198067,
0.02967541664838791,
-0.016156179830431938,
-0.032589852809906006,
-0.04409000650048256,
-0.04663940891623497,
0.020040692761540413,
0.02607661485671997,
0.01767285168170929,
0.019215606153011322,
0.06629648804664612,
0.02090880088508129,
-0.028930045664310455,
-0.0020817997865378857,
-0.03026520274579525,
-0.09959746897220612,
0.0024481688160449266,
-0.05662987753748894,
-0.007460370659828186,
-0.014917387627065182,
-0.017911147326231003,
-0.035114653408527374,
-0.029417386278510094,
-0.027676066383719444,
-0.024257425218820572,
0.014952772296965122,
-0.04273919016122818,
-0.002809348050504923,
-0.044236309826374054,
-0.017868174239993095,
-0.038380660116672516,
0.03703160211443901,
0.055586058646440506,
0.01508314162492752,
0.017864473164081573,
0.04256107658147812,
-0.031143035739660263,
-0.009090038016438484,
0.016929011791944504,
-0.0035954599734395742,
0.03038538061082363,
0.024455729871988297,
-0.00028068156098015606,
-0.003194391494616866,
-0.037536635994911194,
-0.012914976105093956,
0.012347813695669174,
0.02539319358766079,
0.0010853245621547103,
0.016540316864848137,
-0.03178536146879196,
-0.029413839802145958,
-0.014090255834162235,
0.01064800750464201,
0.011631843633949757,
0.020578334107995033,
-0.02328426204621792,
0.03859664127230644,
0.004151885397732258,
-0.012396021746098995,
0.04721354320645332,
0.06208375468850136,
-0.01598052680492401,
-0.008301426656544209,
-0.01717442274093628,
-0.023206155747175217,
-0.01977713219821453,
-0.028871364891529083,
0.02722872979938984,
0.019344201311469078,
-0.022811543196439743,
0.04418759047985077,
0.011558495461940765,
0.007559430785477161,
-0.031074317172169685,
0.00023903715191408992,
-0.025924917310476303,
-0.045109014958143234,
-0.04577239230275154,
-0.014665650203824043,
-0.008157708682119846,
0.0581233985722065,
-0.0012847440084442496,
-0.0006245654076337814,
-0.006731572560966015,
-0.07557085901498795,
-0.00236130366101861,
0.016236810013651848,
0.03407762572169304,
-0.0020957733504474163,
-0.012136486358940601,
-0.03879760578274727,
-0.011794446036219597,
0.04211742430925369,
-0.07132360339164734,
0.00045463722199201584,
-0.001835809787735343,
0.028881696984171867,
-0.03009902685880661,
-0.005980516318231821,
0.017163660377264023,
0.0501890666782856,
-0.014910399913787842,
0.02304817922413349,
-0.030540138483047485,
-0.019426211714744568,
-0.030342968180775642,
0.04347894340753555,
0.007523173466324806,
0.04617740213871002,
0.011672783643007278,
0.02850220911204815,
-0.012321325950324535,
-0.0020022159442305565,
-0.030124079436063766,
-0.07003961503505707,
0.01595710776746273,
-0.013872220180928707,
-0.00979403406381607,
0.0342864952981472,
-0.03164678066968918,
-0.05544054135680199,
0.0022356549743562937,
0.027501314878463745,
0.023231392726302147,
-0.02807498723268509,
-0.07718030363321304,
0.01182143297046423,
0.0527024120092392,
0.020129011943936348,
0.033427488058805466,
-0.0005390960141085088,
-0.058469563722610474,
0.007129641715437174,
-0.03011796437203884,
0.05894256383180618,
-0.007747690659016371,
-0.0010536893969401717,
-0.024829398840665817,
0.009192904457449913,
-0.02356102503836155,
0.050393737852573395,
-0.024345485493540764,
0.006063349545001984,
0.0010612595360726118,
-0.05485553294420242,
-0.018202397972345352,
0.032518308609724045,
0.022555271163582802,
-0.012667074799537659,
-0.02503637596964836,
0.02485327422618866,
0.01700586825609207,
-0.01178787276148796,
0.011115467175841331,
-0.002368985442444682,
-0.010389941744506359,
-0.009337606839835644,
-0.01108495146036148,
-0.0009745136485435069,
-0.052999239414930344,
-0.019820138812065125,
0.04615109786391258,
-0.03138492628931999,
0.02328922227025032,
0.01376359909772873,
-0.0026912735775113106,
0.03634857386350632,
-0.06032417714595795,
-0.05738474428653717,
-0.014054127968847752,
-0.021749967709183693,
0.038753580302000046,
-0.057411257177591324,
0.041047610342502594,
-0.015291734598577023,
0.02093001827597618,
-0.07105214148759842,
-0.04015437886118889,
0.01765373721718788,
-0.03681991994380951,
-0.003504888154566288,
-0.03289729356765747,
0.00029131886549293995,
-0.017557960003614426,
-0.034743327647447586,
-0.012109868228435516,
0.04659118130803108,
-0.039476536214351654,
-0.0065754977986216545,
-0.005505084991455078,
0.04663272947072983,
0.024711012840270996,
0.01759341172873974,
-0.010005410760641098,
-0.01580364629626274,
0.03311731293797493,
0.023671256378293037,
-0.020362718030810356,
0.06282481551170349,
-0.01854802295565605,
-0.05776158720254898,
-0.004776737652719021,
-0.013522211462259293,
0.0021980120800435543,
-0.044608574360609055,
0.029952313750982285,
0.049552518874406815,
0.01797260157763958,
0.016284754499793053,
0.010469199158251286,
0.046700846403837204,
-0.002100694691762328,
0.006308700889348984,
0.005163898691534996,
0.021654102951288223,
0.013118754141032696,
-0.008994065225124359,
0.0265838410705328,
-0.02734784036874771,
0.05494150519371033,
0.026044128462672234,
-0.00857849232852459,
-0.018467284739017487,
-0.017255472019314766,
0.01577180065214634,
-0.03150125592947006,
0.02534191869199276,
-0.044578757137060165,
-0.012204177677631378,
0.015896063297986984,
-0.024579517543315887,
-0.028397900983691216,
-0.008222087286412716,
-0.03274233266711235,
-0.0008861527894623578,
0.031952083110809326,
-0.02376573532819748,
0.051281221210956573,
-0.017027871683239937,
0.017280373722314835,
-0.012290118262171745,
-0.025542957708239555,
0.02016192302107811,
0.009809992276132107,
0.003276257077232003,
0.00028852655668742955,
-0.012533744797110558,
-0.018200743943452835,
0.049565091729164124,
0.04644056409597397,
-0.03642423078417778,
-0.01412439439445734,
0.04573982581496239,
0.0039869858883321285,
-0.004336681216955185,
-0.01649804413318634,
-0.028420455753803253,
0.05344878509640694,
-0.01851559802889824,
0.00425367709249258,
0.02803126536309719,
0.002955158706754446,
0.0318094901740551,
-0.005031901877373457,
0.004851443227380514,
-0.020837612450122833,
0.02714042365550995,
-0.08894604444503784,
0.012150983326137066,
0.027387697249650955,
-0.04121385142207146,
0.012692201882600784,
0.023577937856316566,
0.018392289057374,
0.025060312822461128,
-0.02303597517311573,
0.03306403011083603,
-0.05807099863886833,
-0.02811450883746147,
-0.034550946205854416,
-0.01085554901510477,
0.019548160955309868,
-0.012134863995015621,
-0.001362441573292017,
0.008402107283473015,
-0.01870802231132984,
0.008000772446393967,
-0.006715343799442053,
0.04288821294903755,
-0.021624308079481125,
0.04284738004207611,
0.0209515318274498,
0.030785636976361275,
-0.06265586614608765,
0.03564220666885376,
0.12288651615381241,
0.024847589433193207,
-0.009560570120811462,
-0.03299484774470329,
0.028213758021593094,
-0.008066501468420029,
0.019518988206982613,
0.011267432942986488,
0.019380556419491768,
0.03706592693924904,
0.019673969596624374,
0.0004931113799102604,
0.031035972759127617,
-0.002155771479010582,
0.010881694033741951,
0.04570740833878517,
-0.04301569610834122,
-0.060795653611421585,
-0.004007570445537567,
0.016874942928552628,
0.0006140442565083504,
-0.001116533181630075,
-0.027675241231918335,
0.04376008361577988,
-0.008427183143794537,
-0.008406981825828552,
-0.01035144180059433,
-0.041012659668922424,
0.008813722990453243,
-0.01082652248442173,
-0.03240717574954033,
0.022044602781534195,
0.015963654965162277,
-0.023316560313105583,
-0.005611801519989967,
0.012432150542736053,
0.003906290978193283,
-0.006626649294048548,
0.026013027876615524,
0.015768544748425484,
0.03040122240781784,
-0.004057460464537144,
-0.01435065921396017,
0.022208688780665398,
-0.036466874182224274,
-0.02783389575779438,
-0.02420012280344963,
0.0506485290825367,
-0.024000804871320724,
0.009916053153574467,
-0.006373454350978136,
0.042687010020017624,
-0.0002411952445982024,
-0.02451566979289055,
-0.016719037666916847,
0.023412298411130905,
0.02388565056025982,
-0.008897088468074799,
0.0043146610260009766,
-0.051477305591106415,
-0.0036513719242066145,
-0.03701484203338623,
0.03200575336813927,
-0.016968801617622375,
0.04553454741835594,
0.03215326368808746,
-0.004463278688490391,
0.023879745975136757,
-0.014216572977602482,
0.024696042761206627,
-0.0596216656267643,
-0.0004758957657031715,
-0.06739926338195801,
-0.00023800303461030126,
0.02738695964217186,
0.041642799973487854,
0.028616441413760185,
0.005315291229635477,
-0.023872600868344307,
-0.038933683186769485,
-0.0040976437740027905,
0.05427701771259308,
0.011576597578823566,
-0.041962556540966034,
-0.026576749980449677,
0.013929774053394794,
0.024360496550798416,
0.0480535589158535,
-0.0345631018280983,
0.00834703166037798,
-0.0241981390863657,
0.054952144622802734,
0.015199937857687473,
-0.0267415102571249,
-0.026476116850972176,
0.01659742370247841,
-0.0024247521068900824,
0.003833025461062789,
-0.015399785712361336,
0.019520007073879242,
0.007592551875859499,
-0.003883745288476348,
0.04906556010246277,
0.03852738067507744,
-0.020094405859708786,
-0.00875511858612299,
0.04108155891299248,
-0.028458602726459503,
0.015864957123994827,
0.014843359589576721,
0.03955960273742676,
-0.012100878171622753,
0.006443322170525789,
0.02457687258720398,
-0.006711182650178671,
-0.0009909161599352956,
0.019985737279057503,
-0.018333198502659798,
0.0033427109010517597,
-0.011840627528727055,
0.04264521598815918,
-0.03315932676196098,
0.015575618483126163,
-0.05054840072989464,
0.0363822877407074,
-0.015652403235435486,
-0.03447916731238365,
-0.039142414927482605,
0.04762757942080498,
-0.015748504549264908,
-0.01316161546856165,
0.001659928821027279,
0.0031489047687500715,
-0.03977891802787781,
0.0025185132399201393,
0.04754357039928436,
-0.0053762467578053474,
0.013350851833820343,
-0.0038732036482542753,
-0.03512755408883095,
0.01669645495712757,
-0.031137607991695404,
-0.09446790814399719,
0.02057378925383091,
-0.00950638111680746,
0.014121690765023232,
0.05359644070267677,
-0.04037763923406601,
-0.02771083638072014,
0.05620870739221573,
-0.01675981841981411,
-0.018098894506692886,
-0.023265227675437927,
0.0018618319882079959,
-0.022570282220840454,
0.014117099344730377,
0.010482226498425007,
-0.011168052442371845,
-0.015462293289601803,
0.05304860323667526,
0.015127170830965042,
0.0038195508532226086,
0.03701281547546387,
-0.05028460547327995,
0.007656513247638941,
0.03913639485836029,
-0.006187655963003635,
0.011190378107130527,
-0.015745284035801888,
0.04427873715758324,
-0.008243455551564693,
0.023797037079930305,
0.009544390253722668,
-0.013591640628874302,
-0.1081286370754242,
0.0024187969975173473,
-0.010466838255524635,
-0.002996370429173112,
0.06184736266732216,
-0.013823240995407104,
0.009446825832128525,
0.059541940689086914,
-0.07176505029201508,
0.009869161061942577,
-0.020773258060216904,
-0.01844935119152069,
-0.04948196932673454,
0.001494689960964024,
-0.021446337923407555,
0.07384432107210159,
0.017457779496908188,
0.05564021319150925,
0.004353460390120745,
0.008616216480731964,
-0.004532390274107456,
-0.022274820134043694,
-0.01898200809955597,
0.02590702287852764,
0.008291635662317276,
0.017651928588747978,
0.10803873836994171,
-0.007256519980728626,
-0.012433233670890331,
0.02779635787010193,
0.007101947907358408,
-0.024951867759227753,
-0.004530196078121662,
0.013985940255224705,
0.03407607227563858,
0.03555763512849808,
0.006398530676960945,
0.004950778558850288,
0.03599895164370537,
-0.002190178260207176,
0.010401658713817596,
0.005618218798190355,
0.039043933153152466,
0.015119412913918495,
0.018074514344334602,
-0.015882616862654686,
-0.00484360009431839,
-0.0022274479269981384,
-0.002599175553768873,
-0.004618670791387558,
0.01940879225730896,
0.05161331966519356,
-0.0018721433589234948,
-0.014238306321203709,
-0.01252378523349762,
-0.012048316188156605,
0.021817520260810852,
-0.0037115521263331175,
0.008942636661231518,
-0.02711382508277893,
0.024711083620786667,
-0.03314949572086334,
0.036859478801488876,
0.009133300743997097,
0.028272360563278198,
-0.024532418698072433,
-0.005040383897721767,
-0.03431016951799393,
0.026286037638783455,
0.06524583697319031,
0.01087240781635046,
-0.017321646213531494,
-0.0451677106320858,
0.04364169389009476,
-0.025741586461663246,
0.049923282116651535,
-0.026566626504063606,
-0.0191885344684124,
-0.022221600636839867,
-0.03500504791736603,
0.023650290444493294,
0.03089672513306141,
-0.0016821190947666764,
-0.06928947567939758,
-0.07341104000806808,
-0.0019187431316822767,
0.036829873919487,
0.028871499001979828,
0.027852578088641167,
0.030237995088100433,
0.04015536978840828,
0.015276872552931309,
0.02523164078593254,
-0.02568195015192032,
0.022155217826366425,
0.02171950973570347,
-0.004666027147322893,
0.0008910575998015702,
0.016499219462275505,
-0.016030222177505493,
0.04712998867034912,
0.04600943997502327,
-0.029986882582306862,
0.021448887884616852,
0.017027074471116066,
-0.05334528163075447,
0.03549541160464287,
-0.028530048206448555,
-0.010404534637928009,
0.05215582624077797,
-0.02354072593152523,
0.03899495676159859,
0.010349969379603863,
0.007014288101345301,
-0.013202022761106491,
-0.014117035083472729,
-0.04922279715538025,
0.0015268148854374886,
-0.014154334552586079,
-0.01962237060070038,
0.008198610506951809,
-0.032365813851356506,
-0.0053870719857513905,
0.04558514431118965,
-0.03659029304981232,
-0.011632456444203854,
0.056791458278894424,
0.03422924131155014,
0.04917529597878456,
0.03890888765454292,
0.022191304713487625,
-0.002620411105453968,
0.007461801636964083,
-0.026514770463109016,
0.04396364092826843,
0.006782422307878733,
-0.02087051048874855,
0.011159546673297882,
0.01743539609014988,
0.02913532219827175,
0.018053889274597168,
0.024261754006147385,
0.06660152971744537,
-0.012925858609378338,
-0.026530807837843895,
-0.0022970507852733135,
-0.03128964453935623,
0.02040463499724865,
0.03633059561252594,
-0.006568162236362696,
0.100748710334301,
-0.010410236194729805,
0.0006121974438428879,
-0.006101686041802168,
-0.011925866827368736,
-0.0216522216796875,
0.015793902799487114,
-0.01606397144496441,
0.05033322423696518,
0.001396921114064753,
-0.028177591040730476,
-0.021913308650255203,
0.06259529292583466,
0.023303082212805748,
-0.04512152075767517,
0.014319141395390034,
0.00989177729934454,
0.0025609340518712997,
-0.027083687484264374,
-0.007095078472048044,
-0.012168056331574917,
-0.037022218108177185,
0.041334766894578934,
0.014395306818187237,
-0.0324973501265049,
0.004849183838814497,
-0.05464937910437584,
-0.07157181948423386,
0.014003952965140343,
0.0018294628243893385,
-0.029568839818239212,
-0.008546710014343262,
0.02123432233929634,
-0.06314841657876968,
0.015495391562581062
] |
<p>I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. </p>
<p>So how to calculate it? In which book can I find the answer?</p>
| 7,628 |
[
0.005287604872137308,
-0.001574467052705586,
0.02921511046588421,
-0.03438582643866539,
0.000955188472289592,
0.026848115026950836,
-0.0345095656812191,
-0.04919689893722534,
-0.01925022341310978,
-0.03553067892789841,
0.04222748428583145,
0.0382041409611702,
0.05218297615647316,
0.028022924438118935,
0.00015109289961401373,
-0.028471825644373894,
-0.01747274398803711,
-0.004559921566396952,
-0.01646590419113636,
-0.04205665364861488,
0.023554662242531776,
0.022827425971627235,
-0.006788224447518587,
-0.027827387675642967,
0.005788057576864958,
0.014065511524677277,
0.03367353230714798,
-0.004527371376752853,
0.027314849197864532,
0.07543183118104935,
-0.03672269359230995,
-0.04098517447710037,
0.00718671502545476,
0.022565146908164024,
0.005657922476530075,
0.029608719050884247,
-0.04603634402155876,
-0.018297795206308365,
-0.01781044714152813,
0.014999579638242722,
-0.040496211498975754,
-0.02015850320458412,
-0.0215394739061594,
0.05432908236980438,
-0.004936438053846359,
0.026163270696997643,
0.027556993067264557,
-0.0034397428389638662,
0.050196949392557144,
-0.06969380378723145,
0.07263310998678207,
0.031624168157577515,
0.02842349372804165,
-0.028413312509655952,
-0.028839487582445145,
0.008649108931422234,
0.06305141746997833,
0.06732342392206192,
-0.016423573717474937,
-0.058812402188777924,
-0.060710735619068146,
-0.031500544399023056,
-0.008160097524523735,
-0.04712434858083725,
-0.003885693848133087,
0.043751515448093414,
-0.005671380087733269,
-0.017712440341711044,
0.02110832929611206,
-0.009443358518183231,
0.00018309344886802137,
0.002866446739062667,
0.03531370684504509,
-0.004102814942598343,
0.007163508329540491,
-0.013895584270358086,
0.030354037880897522,
-0.016245277598500252,
0.026637805625796318,
0.018652740865945816,
-0.02310311049222946,
0.043316569179296494,
0.04870137199759483,
0.016192620620131493,
0.012916951440274715,
-0.009052074514329433,
0.058807674795389175,
0.0339970737695694,
-0.005243542604148388,
0.03580892086029053,
-0.05020573362708092,
-0.023066580295562744,
0.03625309839844704,
-0.011106125079095364,
-0.024335088208317757,
0.027185706421732903,
0.0011137576075270772,
0.04162168875336647,
-0.005754297599196434,
-0.030477376654744148,
-0.01463301107287407,
-0.01225226279348135,
-0.0024812882766127586,
0.09333165735006332,
0.005757378879934549,
-0.01647932268679142,
-0.006237856578081846,
-0.009503834880888462,
-0.01571045070886612,
-0.007818608544766903,
-0.03400802239775658,
0.011716475710272789,
-0.014618556946516037,
-0.012615513987839222,
0.017542501911520958,
-0.012064113281667233,
0.01788509264588356,
-0.003320696298032999,
0.04912910610437393,
0.044409044086933136,
0.04871883988380432,
0.011985274963080883,
0.016611294820904732,
-0.02878774330019951,
-0.01802341267466545,
0.012314409017562866,
0.0413554310798645,
-0.018675843253731728,
-0.024505870416760445,
0.019763700664043427,
0.03292263299226761,
-0.0034824807662516832,
0.007614894770085812,
0.043701428920030594,
0.014506615698337555,
-0.020625652745366096,
-0.05198895186185837,
-0.08526909351348877,
0.03740309178829193,
-0.003948771860450506,
-0.004238960333168507,
-0.044103097170591354,
0.011157534085214138,
0.02766181342303753,
0.07994424551725388,
0.029657578095793724,
0.001008055405691266,
-0.013474475592374802,
0.05246727168560028,
0.006402235943824053,
-0.02675444260239601,
-0.01577986590564251,
-0.015974294394254684,
-0.02146819792687893,
-0.01841750182211399,
-0.049943339079618454,
0.021974222734570503,
0.023100875318050385,
-0.014394860714673996,
-0.034618958830833435,
0.1046755313873291,
-0.018012760207057,
-0.0175824835896492,
0.01642327383160591,
-0.019299250096082687,
-0.03706580027937889,
0.05861230567097664,
0.0197921060025692,
-0.02667197585105896,
0.026806093752384186,
-0.020901115611195564,
0.025729183107614517,
-0.008389946073293686,
0.01388282235711813,
0.01022656075656414,
-0.025980763137340546,
-0.03354375809431076,
-0.015576816163957119,
0.03061608225107193,
0.005133383441716433,
0.010278376750648022,
-0.028384221717715263,
0.001677884953096509,
0.020420845597982407,
-0.01952550932765007,
0.015526105649769306,
-0.010182608850300312,
0.011501655913889408,
-0.013608196750283241,
-0.003808354726061225,
0.01425879541784525,
-0.06263643503189087,
-0.006403939798474312,
0.012647927738726139,
0.02020539902150631,
0.012763632461428642,
0.028562886640429497,
0.01509128324687481,
-0.035934191197156906,
-0.05568423867225647,
0.0018336869543418288,
0.03108925372362137,
0.001519087585620582,
-0.005954358261078596,
0.015224200673401356,
0.04647309333086014,
0.0424637496471405,
0.028471779078245163,
0.029671762138605118,
-0.03257991746068001,
-0.009065814316272736,
0.03127022460103035,
-0.012073603458702564,
0.04257046431303024,
-0.04435788467526436,
0.024312831461429596,
-0.022762790322303772,
0.0247750636190176,
0.027336206287145615,
0.0100719528272748,
-0.04731056094169617,
0.05563918128609657,
0.0771072655916214,
0.021152233704924583,
0.009496319107711315,
0.016044462099671364,
-0.009893524460494518,
0.02703040838241577,
-0.00115709169767797,
-0.01219259761273861,
-0.023903483524918556,
-0.033893078565597534,
0.03812067583203316,
0.03240150585770607,
-0.02208840474486351,
-0.04123467206954956,
0.06486912071704865,
0.028076715767383575,
0.004261476919054985,
0.022905021905899048,
-0.021964065730571747,
-0.025838427245616913,
0.021209627389907837,
-0.010516658425331116,
0.0047483122907578945,
0.013250736519694328,
0.0429946593940258,
0.02755361795425415,
-0.026005998253822327,
-0.005485127214342356,
-0.054175857454538345,
0.030688749626278877,
0.0004946077824570239,
-0.012655692175030708,
-0.009868139401078224,
-0.007619393989443779,
0.05881655216217041,
-0.02581777796149254,
0.012242143973708153,
0.03008233569562435,
-0.016642356291413307,
-0.022517623379826546,
-0.015048849396407604,
-0.00847215112298727,
0.013104361481964588,
-0.005561775527894497,
-0.010642735287547112,
-0.026388922706246376,
0.027839181944727898,
-0.06536845117807388,
0.010997404344379902,
-0.002398971002548933,
-0.012483442202210426,
-0.001517586992122233,
-0.0015562272164970636,
0.009688498452305794,
0.021823294460773468,
0.0447879321873188,
-0.006059702951461077,
-0.03157191723585129,
0.022385554388165474,
-0.01604580134153366,
0.0028882543556392193,
0.017760366201400757,
-0.05998733639717102,
0.03190809488296509,
-0.051128704100847244,
-0.016058066859841347,
0.034946639090776443,
-0.012483318336308002,
0.016111185774207115,
-0.0007467055693268776,
-0.026885688304901123,
-0.02726822718977928,
-0.007009564433246851,
-0.02008342370390892,
-0.00364865455776453,
-0.06531471759080887,
0.03207717463374138,
0.024934466928243637,
0.0030438299290835857,
-0.01586955040693283,
0.003241736674681306,
-0.02958827279508114,
-0.024564066901803017,
-0.012982144020497799,
0.0051339492201805115,
0.011340525932610035,
-0.049074266105890274,
0.005085735581815243,
-0.013201841153204441,
-0.02897052839398384,
0.022684892639517784,
-0.05554915964603424,
-0.023634048178792,
0.01301916316151619,
-0.006683461833745241,
0.030275551602244377,
0.0000217972592508886,
-0.04791031777858734,
0.08364284038543701,
0.03148721531033516,
-0.005017775110900402,
-0.00626639649271965,
-0.0016931521240621805,
0.02839684672653675,
0.005061091389507055,
0.030104171484708786,
0.01226622425019741,
-0.01634865440428257,
0.011956848204135895,
0.023875467479228973,
-0.0002819308720063418,
0.07665879279375076,
0.01088222861289978,
0.00548054464161396,
0.0006648353300988674,
0.002794754458591342,
0.01190965622663498,
0.031580325216054916,
0.021787084639072418,
-0.03424016758799553,
0.03077832981944084,
-0.008024835959076881,
-0.0015649169217795134,
-0.016901982948184013,
-0.01812216080725193,
0.024490859359502792,
0.007272576447576284,
-0.01436929777264595,
-0.014168745838105679,
0.046601686626672745,
0.004501946270465851,
-0.026158075779676437,
0.04008816182613373,
-0.005168228410184383,
0.03845058009028435,
-0.009878968819975853,
0.01642051711678505,
0.027836713939905167,
0.04521302506327629,
-0.03778798133134842,
-0.04902007058262825,
0.008228412829339504,
0.014946051873266697,
0.0287530068308115,
-0.015946639701724052,
-0.022671181708574295,
0.03146840259432793,
0.03901870921254158,
0.005378389731049538,
0.019171839579939842,
-0.038371868431568146,
0.002873620018362999,
-0.043310798704624176,
-0.011371063068509102,
0.006087753921747208,
0.03667944297194481,
0.011054245755076408,
0.026965083554387093,
0.02683512680232525,
0.03671472892165184,
0.015162318013608456,
-0.023731563240289688,
-0.10481557250022888,
0.009318121708929539,
-0.06124596670269966,
0.002377426251769066,
0.006222814787179232,
0.009862388484179974,
0.008200214244425297,
0.003548380685970187,
-0.058927979320287704,
-0.01749453693628311,
-0.01081047859042883,
-0.040773287415504456,
0.03793613612651825,
-0.015527786687016487,
-0.0405832976102829,
-0.012188183143734932,
0.06683970987796783,
0.04411282762885094,
-0.04745829105377197,
-0.03538535535335541,
0.05464216321706772,
-0.05008247494697571,
0.003572622546926141,
0.004435929004102945,
0.031527068465948105,
0.0050569986924529076,
0.03957732394337654,
0.01824919693171978,
0.04141025245189667,
-0.028606688603758812,
-0.000010758642019936815,
0.01787070743739605,
0.06378234922885895,
0.021623864769935608,
-0.06442976742982864,
-0.030583029612898827,
-0.029574574902653694,
-0.008963181637227535,
-0.020190320909023285,
0.07673020660877228,
-0.008595000952482224,
0.015563695691525936,
0.045754991471767426,
0.035435859113931656,
-0.030714072287082672,
0.04021408036351204,
0.07852990925312042,
0.0041227987967431545,
-0.021497678011655807,
-0.009004230611026287,
-0.03882019966840744,
-0.017195168882608414,
0.008023268543183804,
0.003337207017466426,
-0.03981668874621391,
-0.07286982983350754,
0.008178052492439747,
0.0009975918801501393,
0.007971339859068394,
-0.05052007734775543,
-0.052334994077682495,
-0.003303150413557887,
0.017729533836245537,
0.005021972581744194,
-0.01474436093121767,
0.0021218247711658478,
0.06174513325095177,
0.046667248010635376,
0.023421870544552803,
-0.011979999020695686,
-0.03871694579720497,
-0.011099540628492832,
0.014378872700035572,
0.010988240130245686,
0.03515905514359474,
-0.02396245487034321,
-0.028190212324261665,
-0.019818106666207314,
0.057526107877492905,
-0.02551352046430111,
0.011300196871161461,
0.012299525551497936,
0.0027571951504796743,
-0.006398916710168123,
0.002803044393658638,
-0.03713846951723099,
0.0185399167239666,
-0.03876078501343727,
-0.011821805499494076,
-0.061529744416475296,
0.011358533054590225,
-0.0254908986389637,
0.026757990941405296,
0.02628922089934349,
0.07618628442287445,
0.022782310843467712,
0.011954041197896004,
0.00027107936330139637,
0.019902333617210388,
-0.06188858300447464,
-0.04742276668548584,
-0.03557218983769417,
0.0077615343034267426,
-0.018338562920689583,
0.0384640097618103,
-0.02439148537814617,
-0.039362918585538864,
0.024553660303354263,
0.009090487845242023,
0.004191395826637745,
0.030750548467040062,
-0.05121007189154625,
-0.012469747103750706,
0.02386833168566227,
0.008077745325863361,
0.07067835330963135,
-0.00426409812644124,
-0.03863659128546715,
-0.0026370773557573557,
-0.03192242607474327,
0.043359603732824326,
-0.013953489251434803,
-0.00703539839014411,
0.0026958570815622807,
-0.01965472660958767,
-0.0691947266459465,
0.012743744067847729,
-0.013586428016424179,
0.009802021086215973,
-0.00006296622450463474,
-0.010827702470123768,
-0.015548093244433403,
0.03455729782581329,
0.003881253534927964,
0.025511857122182846,
0.02591499127447605,
0.0312691330909729,
0.03471937030553818,
-0.013162780553102493,
0.025446638464927673,
-0.014195500873029232,
-0.015685755759477615,
-0.01284474041312933,
-0.012587453238666058,
0.036639776080846786,
-0.0425790511071682,
-0.02738366276025772,
0.016178781166672707,
-0.0432736799120903,
0.057095471769571304,
-0.027498111128807068,
-0.03701348230242729,
0.015132585540413857,
-0.054706573486328125,
-0.07610096782445908,
0.017426205798983574,
0.04072999581694603,
0.04900549352169037,
-0.03449277952313423,
-0.00912482850253582,
0.044421497732400894,
0.013748073019087315,
-0.06251586228609085,
-0.016143349930644035,
0.04435037821531296,
-0.018805956467986107,
-0.023981450125575066,
-0.03254074603319168,
0.0451711043715477,
-0.03796352073550224,
-0.0003475870762486011,
-0.009457229636609554,
0.04061392322182655,
-0.01020244974642992,
-0.018188616260886192,
-0.004383950028568506,
0.00906692910939455,
0.024325594305992126,
0.022806989029049873,
-0.040385160595178604,
0.03350304439663887,
0.024525800719857216,
-0.02722054161131382,
-0.006674998439848423,
0.05043667554855347,
-0.022974325343966484,
-0.032916147261857986,
-0.027510525658726692,
-0.002433938439935446,
-0.017630215734243393,
-0.03059481829404831,
0.008111132308840752,
0.0447220578789711,
0.0632447823882103,
-0.026601221412420273,
-0.018591415137052536,
-0.01308125164359808,
-0.019708342850208282,
0.02173956297338009,
-0.033221133053302765,
-0.026819366961717606,
-0.030392421409487724,
-0.014351294375956059,
0.027620181441307068,
-0.0018257256597280502,
-0.0023867858108133078,
0.00968649610877037,
0.04252588003873825,
0.008395731449127197,
-0.05069706216454506,
0.031250812113285065,
-0.01417513657361269,
-0.029255835339426994,
0.033310241997241974,
0.01076350174844265,
0.03930472582578659,
0.0073338961228728294,
-0.035224102437496185,
-0.03263847902417183,
-0.03446842357516289,
0.012052814476191998,
0.07524089515209198,
-0.019324492663145065,
0.04790377616882324,
0.04249181970953941,
0.02245502360165119,
0.00040097875171341,
-0.002577299252152443,
-0.04067118093371391,
0.00811716541647911,
0.027613123878836632,
0.018961157649755478,
-0.0407913476228714,
-0.01989794708788395,
0.010946131311357021,
0.026721538975834846,
-0.05360030010342598,
0.022830773144960403,
-0.018847502768039703,
0.01891626976430416,
0.013710139319300652,
-0.01753619685769081,
-0.038324471563100815,
0.037500571459531784,
0.009369689039885998,
0.03519725799560547,
-0.00931877363473177,
-0.005057396367192268,
0.020396528765559196,
0.011526862159371376,
0.031688619405031204,
0.003052585991099477,
-0.04632015898823738,
-0.05611472204327583,
0.004337351303547621,
0.04823262244462967,
0.004553865175694227,
0.0026966407895088196,
0.06733974814414978,
0.028054121881723404,
-0.023675523698329926,
0.038775328546762466,
0.0200081504881382,
-0.06752455234527588,
-0.007723342161625624,
-0.04480681195855141,
-0.07467662543058395,
0.03779987618327141,
0.014616797678172588,
-0.034063152968883514,
0.034961115568876266,
-0.018362747505307198,
0.007997408509254456,
0.03439759090542793,
0.05035170540213585,
-0.022710660472512245,
0.11933758109807968,
-0.03950541839003563,
0.0026535727083683014,
-0.013406625017523766,
-0.017493588849902153,
0.11700230091810226,
0.047217268496751785,
0.006459655240178108,
-0.11698326468467712,
0.010916712693870068,
-0.022006217390298843,
0.010344848036766052,
-0.0423012338578701,
0.027929356321692467,
-0.028245504945516586,
-0.011162172071635723,
0.022106165066361427,
0.050746504217386246,
-0.009913885965943336,
-0.051128607243299484,
0.054930511862039566,
-0.03035796247422695,
-0.059597525745630264,
0.001431741053238511,
0.04191422089934349,
-0.002830162178725004,
0.01066102460026741,
-0.01173789519816637,
0.013261573389172554,
-0.013667958788573742,
0.03537401929497719,
-0.056355200707912445,
-0.030848676338791847,
0.016062384471297264,
-0.024949369952082634,
-0.051504455506801605,
-0.002089771442115307,
-0.004661445040255785,
-0.006670382805168629,
-0.023463573306798935,
0.024506038054823875,
0.022557156160473824,
0.022742467001080513,
0.017005521804094315,
0.03709984943270683,
-0.004326985217630863,
0.03493786230683327,
0.010355482809245586,
0.020131541416049004,
-0.03195837885141373,
-0.006373778451234102,
-0.012856191024184227,
0.05613510310649872,
-0.03673992305994034,
-0.02131679467856884,
0.030993347987532616,
0.0032726761419326067,
-0.007284837309271097,
-0.023964451625943184,
-0.00023356711608357728,
0.0015725379344075918,
0.009138621389865875,
0.0034828390926122665,
-0.011160331778228283,
-0.020016217604279518,
0.05587616190314293,
-0.027577372267842293,
0.0031139403581619263,
-0.011749403551220894,
0.008232793770730495,
0.022625641897320747,
0.00442701019346714,
0.0395333394408226,
-0.005918748211115599,
-0.04073037952184677,
-0.03569500893354416,
-0.02378728613257408,
-0.020047204568982124,
-0.023906484246253967,
-0.008262349292635918,
0.007195033133029938,
0.02260023169219494,
-0.005215771030634642,
0.00026594806695356965,
-0.009307953529059887,
-0.038269493728876114,
0.03328709676861763,
-0.030289748683571815,
0.012718802317976952,
-0.0104308957234025,
0.004301710985600948,
0.005060053430497646,
0.04324636608362198,
0.004587722476571798,
-0.028508463874459267,
-0.0062849260866642,
-0.01576501689851284,
0.0326395109295845,
-0.034372251480817795,
-0.0025985557585954666,
-0.010688609443604946,
-0.014241957105696201,
-0.055601853877305984,
-0.03987112268805504,
0.014452685602009296,
0.02211896702647209,
0.005030580796301365,
-0.0013627547305077314,
0.00573268486186862,
-0.035238467156887054,
-0.014489486813545227,
0.006925002671778202,
-0.00760416965931654,
-0.0008619757136330009,
0.03237480670213699,
-0.002095639705657959,
-0.04724365100264549,
-0.003078204346820712,
0.019833603873848915,
-0.008093145675957203,
0.024038050323724747,
0.06274629384279251,
-0.04997430369257927,
0.01710290089249611,
0.007858376950025558,
-0.014787038788199425,
-0.04681169614195824,
0.0383947528898716,
-0.01419635396450758,
0.044907670468091965,
-0.03157416358590126,
-0.02451453171670437,
-0.010438576340675354,
0.029654741287231445,
-0.010561585426330566,
-0.010884217917919159,
0.0008635758422315121,
0.009811361320316792,
-0.026875607669353485,
0.019262084737420082,
0.04424978420138359,
-0.028996484354138374,
0.04683452472090721,
0.031132245436310768,
-0.011435589753091335,
0.015873700380325317,
-0.06948284804821014,
-0.02675437368452549,
0.04020880162715912,
-0.011377757415175438,
0.05401095375418663,
0.013643012382090092,
-0.024881552904844284,
-0.02264527603983879,
0.053585611283779144,
-0.009737092070281506,
-0.03670402616262436,
-0.007306527346372604,
-0.021758422255516052,
-0.014370770193636417,
-0.007104635704308748,
-0.0033633385319262743,
-0.006961938925087452,
0.01515594869852066,
0.026654431596398354,
0.008712992072105408,
-0.030003465712070465,
0.014794502407312393,
0.003095140215009451,
-0.006064733490347862,
-0.006648993119597435,
0.036704208701848984,
-0.024177242070436478,
0.005346142221242189,
0.06876674294471741,
-0.008370205760002136,
0.006401411723345518,
0.008477842435240746,
0.0028592373710125685,
-0.09325124323368073,
-0.02347719483077526,
-0.019218549132347107,
-0.013432439416646957,
0.08731971681118011,
-0.034224919974803925,
0.013285658322274685,
0.007661243434995413,
-0.02520613558590412,
0.04673105478286743,
-0.00846115406602621,
-0.028311148285865784,
-0.017796985805034637,
-0.028482427820563316,
-0.014756542630493641,
0.0668204203248024,
0.03420398011803627,
0.03906674310564995,
-0.0021027724724262953,
-0.022939899936318398,
-0.009861761704087257,
-0.06686480343341827,
-0.0013334931572899222,
0.014298916794359684,
-0.026850547641515732,
-0.02726457267999649,
0.039041630923748016,
0.010698162019252777,
-0.02716509811580181,
0.037214167416095734,
-0.03918332979083061,
-0.01905093714594841,
-0.041938140988349915,
0.006257505156099796,
0.0031525548547506332,
0.0640074834227562,
0.027612730860710144,
-0.005303323734551668,
-0.00743062561377883,
-0.015166493132710457,
0.01031770184636116,
-0.00455129612237215,
-0.03349274769425392,
0.033886879682540894,
0.009126645512878895,
-0.03222346678376198,
-0.032082200050354004,
0.045739419758319855,
-0.001692511374130845,
-0.018477967008948326,
-0.010549461469054222,
-0.02706821635365486,
0.01734602451324463,
-0.03641526773571968,
0.009316361509263515,
-0.04533153027296066,
0.02936430834233761,
0.028117209672927856,
-0.004891326650977135,
0.002871013944968581,
0.01679742895066738,
-0.008087175898253918,
-0.02228531800210476,
0.027284154668450356,
0.02632969431579113,
0.005710199009627104,
-0.06127744913101196,
0.001191609539091587,
0.03830965608358383,
0.020199283957481384,
0.017459915950894356,
-0.06951506435871124,
-0.006745293270796537,
-0.0027884538285434246,
0.00427054800093174,
0.007461649365723133,
-0.01872575469315052,
-0.009016433730721474,
0.031054502353072166,
-0.07884959876537323,
0.03063547983765602,
0.04488601163029671,
-0.015075348317623138,
-0.009200341068208218,
-0.01086202822625637,
0.005593692883849144,
-0.004354524426162243,
0.023747151717543602,
-0.025226527824997902,
-0.031107136979699135,
-0.026120617985725403,
-0.0009583798819221556,
0.0036688675172626972,
-0.017857884988188744,
-0.01412979792803526,
-0.0022626810241490602,
-0.03999265283346176,
0.004198259208351374,
0.0214263703674078,
-0.005714867729693651,
0.03686877340078354,
0.015228145755827427,
0.0020033258479088545,
0.036919184029102325,
-0.012450563721358776,
-0.049243081361055374,
0.0360875278711319,
0.0286578256636858,
0.02514924854040146,
0.06119433045387268,
-0.0214364156126976,
0.009213951416313648,
0.0475706048309803,
-0.01858925260603428,
-0.014761604368686676,
0.004626750480383635,
-0.029554950073361397,
-0.03900739550590515,
-0.012118900194764137,
0.009230125695466995,
-0.004202932585030794,
-0.056011319160461426,
-0.00037097797030583024,
0.06630115956068039,
-0.010582341812551022,
-0.018014222383499146,
0.054552242159843445,
0.02350187674164772,
0.05837073177099228,
0.022140927612781525,
-0.04554012790322304,
0.025089791044592857,
-0.013024158775806427,
0.012466086074709892,
0.0004586606228258461,
0.030852651223540306,
0.03514622524380684,
0.01704806089401245,
0.024138374254107475,
-0.006354921031743288,
0.0008955364464782178,
0.0219494067132473,
0.01724315620958805,
-0.04071938246488571,
-0.0007957218331284821,
0.0348653607070446,
-0.020793307572603226,
0.040932729840278625,
0.018813481554389,
-0.049655575305223465,
0.08056185394525528,
-0.020303383469581604,
0.0054860361851751804,
-0.039666276425123215,
-0.0043696253560483456,
-0.03938865661621094,
0.016312744468450546,
0.03496500849723816,
0.0980432853102684,
0.007456487510353327,
0.007463712245225906,
-0.004174773581326008,
-0.008918214589357376,
0.006515271030366421,
-0.04098360240459442,
0.031469348818063736,
0.017709311097860336,
0.000893250631634146,
-0.023067260161042213,
-0.025500452145934105,
-0.03470705449581146,
-0.013995818793773651,
0.023407110944390297,
0.011637122370302677,
0.0063973842188715935,
-0.01564227230846882,
0.02804482728242874,
-0.04319798946380615,
0.05417446047067642,
-0.06929374486207962,
-0.015084466896951199,
-0.03196679428219795,
0.009504979476332664,
-0.04209019988775253,
-0.0019129678839817643
] |
<p>I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me understand better how to do so, and I was hoping that one of you might help me out. I'll first describe exactly what I want to express, so that it's a little more clear what I mean. Note that this is not a homework question or something, it has to do with an experiment that I came up with, so chances are that it might be somewhat impossible to actually write it out the way I want to.</p>
<p>I have a system that lives on the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a>, like this one, but with $\left|\uparrow\right>$ instead of $\left|0\right>$ and $\left|\downarrow\right>$ instead of $\left|1\right>$</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Bloch_Sphere.svg/256px-Bloch_Sphere.svg.png" alt="Bloch Sphere"></p>
<p>Now, initially I am able to fully initialize something, say a spin, into 1 state, being $\left|0\right>$. Then, I rotate the state by pi/2 around the x-axis, and I wait a time t. In this time t, some more complex stuff happens. Depending on the state of a second spin, stuff will happen. This second spin can be in either of three states, $\left|-1\right>$, $\left|0\right>$ and $\left|1\right>$.</p>
<p>Now, during this time $t$, the state of the first spin will precess about the Bloch sphere depending on the state of the second spin. If the second spin is in state $\left|-1\right>$ the first state will rotate around the z-axis clock wise, if the second spin is in state $\left|0\right>$ the first spin will not change, and if the second spin is in state $\left|1\right>$ the first spin will rotate about the $z$-axis counterclockwise. </p>
<p>So, after this time $t$, I will rotate the first spin again, but this time by $\pi/2$ around the $y$-axis. This means that if I choose t such that it is exactly a quarter of the period in which the spin makes a full circle, the two spin states will be entangled. I can use this to establish what the second spin state is by reading out the first spin state:</p>
<p>If $\left|-1\right>$, then I will readout $\left|\uparrow\right>$ with $P=0$, if $\left|0\right>$, then I will readout $\left|\uparrow\right>$ with $P=0.5$, and if $\left|1\right>$, then I will readout $\left|\uparrow\right>$ with $P=1$.</p>
<p>I understand that this probably might be a little confusing, which is of course also the primary reason why I would just want to write this in nice, clean bra-ket notation. If there's anything in particular that's not clear, please let me know. And if someone could help me get started (possibly by pointing me to a similar example) I'd be very grateful.</p>
<p><strong>Edit:</strong>
Alright, I've done a little bit of reading on what I could find, and this is how far I get now</p>
<p>Initially:
$\left|\psi\right>$ = $\left|\psi_1\right> \otimes \left|\psi_2\right> = \left|\uparrow\right> \otimes \frac{1}{\sqrt{3}}\left( \left|-1\right> + \left|0\right>+ \left|1\right> \right)$ </p>
<p>Rotate first spin by $\pi /2$ around x-axis</p>
<p>$\left|\psi\right>$ = $R_x (\frac{\pi}{2}) \left|\psi_1\right> \otimes \left|\psi_2\right> = \frac{1}{\sqrt{2}} \left( \left|\uparrow\right> -i \left|\downarrow\right> \right) \otimes \frac{1}{\sqrt{3}}\left( \left|-1\right> + \left|0\right>+ \left|1\right> \right)$ </p>
<p>But here I get stuck again, as it is here that the rotation conditional on the second spin has to happen, and that I don't know how to do.</p>
| 7,629 |
[
-0.009426075965166092,
-0.0021968099754303694,
-0.008672327734529972,
-0.02350287325680256,
0.014665409922599792,
-0.044004589319229126,
-0.056354112923145294,
-0.014932479709386826,
0.0034063237253576517,
-0.04292694479227066,
0.040924105793237686,
0.048613741993904114,
0.03516646847128868,
0.0591067373752594,
0.013263856992125511,
0.02536403387784958,
0.003583105280995369,
-0.019705651327967644,
-0.04364021494984627,
-0.03139416500926018,
0.030354706570506096,
0.01043712254613638,
0.0036045436281710863,
0.013137269765138626,
-0.01000355463474989,
0.018196256831288338,
0.0066413190215826035,
-0.01892920956015587,
0.017076587304472923,
0.061004411429166794,
-0.02828563190996647,
-0.036407701671123505,
0.0011410204460844398,
0.012325849384069443,
-0.012427788227796555,
-0.01784268394112587,
-0.017281942069530487,
-0.01826520264148712,
0.01188560388982296,
0.0014928324380889535,
-0.04959942400455475,
-0.009495394304394722,
-0.050698813050985336,
0.03289303183555603,
0.0021622369531542063,
-0.03309651464223862,
-0.02030189149081707,
0.011740291491150856,
0.04120589792728424,
-0.047622472047805786,
0.07202107459306717,
-0.009188195690512657,
0.016596276313066483,
0.0000020874344954791013,
0.020514607429504395,
-0.013421879149973392,
0.060730837285518646,
0.05432123690843582,
0.025029055774211884,
-0.019861066713929176,
-0.031124578788876534,
-0.0036672460846602917,
-0.015847282484173775,
-0.03470039740204811,
-0.017348872497677803,
-0.010689813643693924,
0.030073488131165504,
-0.002719330135732889,
0.05486147850751877,
-0.03312668576836586,
0.005506881047040224,
-0.02548259124159813,
0.04212856665253639,
-0.03840179741382599,
0.015767034143209457,
-0.01647414080798626,
-0.009261268191039562,
-0.01637124828994274,
0.03191778063774109,
0.026255624368786812,
-0.0019532328005880117,
0.0069184270687401295,
0.02751838229596615,
0.011764276772737503,
0.00429896404966712,
-0.008207670412957668,
0.06896188855171204,
-0.0025050295516848564,
0.013930822722613811,
0.03559194132685661,
-0.00038610317278653383,
0.01935547962784767,
0.048176832497119904,
-0.01575850509107113,
-0.00625937944278121,
0.011782358400523663,
0.006139586679637432,
0.049490995705127716,
0.007806145120412111,
-0.02572077512741089,
-0.01564622111618519,
-0.0331319235265255,
-0.005296844989061356,
0.08350132405757904,
-0.0005984833696857095,
0.04657074064016342,
0.004676471464335918,
-0.00814781617373228,
-0.008541326969861984,
-0.03605235368013382,
-0.04248039051890373,
0.03783724084496498,
-0.03727737069129944,
0.003555431729182601,
-0.03258723020553589,
-0.05269881710410118,
-0.02194744348526001,
-0.026152921840548515,
0.040819138288497925,
0.06492539495229721,
0.047888245433568954,
-0.03864655643701553,
0.005524905864149332,
-0.07320035994052887,
-0.07192914187908173,
0.01168292947113514,
0.05077337473630905,
-0.0036385823041200638,
-0.04319046065211296,
0.018126284703612328,
0.0010889589320868254,
0.014311186969280243,
0.009651134721934795,
-0.021392233669757843,
0.01123551744967699,
-0.03500783443450928,
-0.11684736609458923,
-0.06539234519004822,
0.0220051072537899,
-0.004686058033257723,
-0.027779875323176384,
-0.06880561262369156,
0.01296495646238327,
0.05309255048632622,
0.0722225159406662,
-0.008288235403597355,
-0.024797379970550537,
0.022089503705501556,
0.05105495825409889,
0.027220414951443672,
-0.02385525219142437,
0.004971160087734461,
-0.015446996316313744,
-0.023780912160873413,
0.001666068215854466,
-0.01017836481332779,
0.02678188867866993,
0.04244218394160271,
-0.026454107835888863,
-0.006148896645754576,
0.037531886249780655,
0.005754678975790739,
0.018909648060798645,
0.030978957191109657,
-0.03177899867296219,
-0.046063657850027084,
0.07909224927425385,
0.005576655734330416,
0.00010968476999551058,
0.049138884991407394,
-0.03338521718978882,
0.02163243666291237,
-0.015190038830041885,
0.011808543466031551,
0.03291770815849304,
-0.0003760879335459322,
0.016736311838030815,
0.019340040162205696,
0.001519018318504095,
-0.02039603516459465,
-0.007710212375968695,
-0.01200935710221529,
0.004645772743970156,
0.02498294785618782,
-0.005948970094323158,
0.03286187723278999,
0.011892428621649742,
-0.004665898159146309,
-0.012048404663801193,
-0.06230573356151581,
-0.03021857887506485,
-0.02734401449561119,
-0.004926992114633322,
-0.0022963620722293854,
-0.04551389440894127,
0.036189500242471695,
-0.0021455814130604267,
0.028503652662038803,
0.006917646154761314,
-0.0674651637673378,
-0.028298256918787956,
0.014068664982914925,
0.013255273923277855,
-0.015871889889240265,
0.014781582169234753,
0.10800974071025848,
0.017755119130015373,
0.00477072037756443,
0.005852951668202877,
-0.012752116657793522,
0.03713854402303696,
-0.045734334737062454,
0.03948041796684265,
0.02783038839697838,
0.017302559688687325,
0.012003562413156033,
0.02511300891637802,
0.02512560971081257,
-0.022861363366246223,
-0.018494563177227974,
-0.05466950312256813,
0.05974211543798447,
0.03165674954652786,
-0.007367224898189306,
-0.004210769664496183,
0.023790208622813225,
0.040785521268844604,
0.018839694559574127,
0.018381226807832718,
-0.04953039065003395,
-0.02770155481994152,
0.019557714462280273,
0.02667681686580181,
0.04310983791947365,
-0.029546396806836128,
0.0187127273529768,
-0.007658167276531458,
0.012606040574610233,
0.02231653966009617,
0.015949638560414314,
0.0017267009243369102,
-0.011974048800766468,
0.013313927687704563,
-0.021866559982299805,
-0.00886851642280817,
-0.007455949205905199,
0.037053730338811874,
-0.014053510501980782,
0.03490332514047623,
0.022760028019547462,
-0.04531315714120865,
0.004300357308238745,
-0.04656451195478439,
-0.0230289027094841,
0.009476632811129093,
-0.025987153872847557,
0.024932704865932465,
0.00555522320792079,
-0.0027661616913974285,
0.01853485405445099,
-0.01839112862944603,
0.019799519330263138,
-0.037338435649871826,
-0.022734936326742172,
-0.015254105441272259,
0.00150960439350456,
-0.009120735339820385,
-0.022657359018921852,
0.020302049815654755,
-0.02529248036444187,
0.01839505508542061,
0.0350525826215744,
-0.008036680519580841,
0.006632364820688963,
-0.009343618527054787,
0.025575261563062668,
0.01887604594230652,
-0.017570922151207924,
-0.056193090975284576,
-0.0008336409227922559,
0.02107297070324421,
0.02628502994775772,
0.048530615866184235,
0.039952173829078674,
-0.05981013551354408,
0.035918671637773514,
-0.049539338797330856,
-0.006980088073760271,
0.017338203266263008,
-0.006709115579724312,
-0.037789445370435715,
-0.0075094858184456825,
0.03527874872088432,
-0.082707978785038,
-0.011161522008478642,
-0.021059101447463036,
-0.019735965877771378,
-0.04471919685602188,
0.007435660343617201,
0.06343398988246918,
-0.004947736859321594,
-0.051556412130594254,
0.016198305413126945,
-0.03956740349531174,
-0.05964887514710426,
-0.019367815926671028,
-0.0011295285075902939,
0.014933427795767784,
-0.033514976501464844,
0.007892340421676636,
-0.021297311410307884,
-0.015058391727507114,
0.0007986302371136844,
-0.052546750754117966,
-0.025967471301555634,
0.018506454303860664,
-0.004782424308359623,
0.02926359511911869,
-0.013551692478358746,
-0.01125605870038271,
0.10155848413705826,
0.007429799996316433,
-0.040394727140665054,
-0.02664661593735218,
0.003119684988632798,
-0.021910058334469795,
-0.04028179496526718,
-0.021003853529691696,
0.040669508278369904,
-0.013357292860746384,
-0.004660439677536488,
0.005457536317408085,
0.02303488738834858,
0.031932711601257324,
0.021442348137497902,
-0.014337289147078991,
0.036712463945150375,
-0.017361432313919067,
-0.029194112867116928,
0.03961065411567688,
0.018488900735974312,
0.027725528925657272,
-0.006922460161149502,
-0.011470251716673374,
-0.007134715095162392,
0.004419755656272173,
-0.03898981958627701,
0.05327128246426582,
0.0003492020186968148,
-0.003714571939781308,
-0.0028963531367480755,
0.05920957401394844,
-0.030986042693257332,
-0.04255634546279907,
-0.022129138931632042,
0.03892064467072487,
0.033761389553546906,
0.003802254796028137,
-0.0037821787409484386,
0.05233723297715187,
0.027960726991295815,
-0.03185075893998146,
0.002155377296730876,
-0.01832645572721958,
-0.020793385803699493,
0.06496763229370117,
-0.04355267807841301,
-0.01757954992353916,
0.014402201399207115,
0.047364503145217896,
0.03987467288970947,
-0.002282828325405717,
-0.015022139064967632,
-0.015058516524732113,
-0.04099060967564583,
0.007629087194800377,
0.0068490710109472275,
0.034891340881586075,
0.013916169293224812,
0.05838198587298393,
0.01112422626465559,
-0.0023450038861483335,
-0.027321023866534233,
-0.02492232620716095,
-0.062127579003572464,
0.014569812454283237,
0.021650562062859535,
0.005579357501119375,
-0.003530845744535327,
-0.01567995920777321,
0.03550228849053383,
-0.03957691043615341,
-0.045203592628240585,
-0.03913451358675957,
-0.013083691708743572,
-0.056173864752054214,
0.01869744062423706,
-0.03580378368496895,
0.006704295985400677,
-0.042160216718912125,
0.05994625762104988,
0.081693135201931,
0.017152532935142517,
0.035845473408699036,
0.03349609673023224,
-0.03306495025753975,
0.066127710044384,
-0.006484631448984146,
0.010040448047220707,
0.036532096564769745,
0.007192802149802446,
0.04944054037332535,
0.031135717406868935,
0.026768608018755913,
-0.030567288398742676,
-0.002214351436123252,
0.035795897245407104,
0.02342807874083519,
-0.03413918614387512,
0.042830344289541245,
-0.04344717413187027,
0.00644746795296669,
-0.0316191241145134,
0.0736207440495491,
-0.03941312059760094,
0.0467006079852581,
-0.006128157954663038,
-0.039433494210243225,
-0.01679806411266327,
0.03442082554101944,
0.03220710530877113,
-0.002729065716266632,
-0.01583772338926792,
-0.0647866427898407,
-0.05195530876517296,
-0.0021672360599040985,
0.015132073312997818,
0.008058512583374977,
-0.018274782225489616,
-0.040772512555122375,
-0.013543118722736835,
-0.0011805732501670718,
-0.00012618517212104052,
-0.0004442400240805,
-0.008888567797839642,
-0.012375902384519577,
0.00008660367893753573,
0.03011234849691391,
0.0022602821700274944,
0.029565107077360153,
0.03597385063767433,
0.023680048063397408,
-0.0038177960086613894,
0.01665857434272766,
-0.06939815729856491,
-0.056225329637527466,
0.015454087406396866,
0.01572231948375702,
0.04967011138796806,
0.019185131415724754,
-0.04944879934191704,
-0.05028385668992996,
0.040367309004068375,
-0.0513274110853672,
0.08294501155614853,
-0.017566869035363197,
0.006100748665630817,
-0.007148647215217352,
-0.05973820388317108,
-0.03483108431100845,
0.013354701921343803,
-0.02900306135416031,
0.020013906061649323,
-0.01033657044172287,
0.007436451502144337,
0.013580827042460442,
0.00328639498911798,
-0.01193250622600317,
0.014655319973826408,
-0.01530524343252182,
0.0050086709670722485,
0.03227817639708519,
0.007556629832834005,
-0.026480471715331078,
-0.08732161670923233,
0.020531749352812767,
0.004631608258932829,
-0.010298670269548893,
0.053469471633434296,
-0.03163360059261322,
-0.04666181281208992,
0.013504496775567532,
-0.006035136990249157,
0.0032326537184417248,
0.04446442425251007,
-0.03735162690281868,
0.041718557476997375,
0.026060687378048897,
0.002256272127851844,
0.02981620468199253,
0.0313718281686306,
0.02255270630121231,
-0.002200054470449686,
-0.020029425621032715,
0.030789624899625778,
0.01131687592715025,
0.021796464920043945,
-0.024878624826669693,
0.02070188708603382,
-0.003064120654016733,
0.0688202828168869,
-0.02667064405977726,
0.028595656156539917,
0.0024692523293197155,
-0.007265040185302496,
0.01812259666621685,
0.0070972018875181675,
-0.013732044026255608,
-0.005183392204344273,
-0.04158911854028702,
-0.007975037209689617,
-0.006388049107044935,
-0.008239462971687317,
-0.005287526175379753,
-0.026219304651021957,
0.02723243460059166,
0.03232366219162941,
-0.047654084861278534,
0.040464140474796295,
-0.048251088708639145,
-0.006451158784329891,
-0.04983207955956459,
-0.08119027316570282,
0.0690666139125824,
-0.00693534268066287,
-0.0005235493299551308,
0.0210880134254694,
-0.05358221009373665,
-0.02213194966316223,
0.030347323045134544,
0.001788017456419766,
-0.01066178735345602,
-0.03676914423704147,
-0.006404198706150055,
0.03953569009900093,
0.013269534334540367,
-0.04679672792553902,
-0.04387928918004036,
0.05303127318620682,
0.0027685256209224463,
-0.013247883878648281,
-0.025048164650797844,
0.029833747074007988,
0.015551789663732052,
-0.03428279235959053,
-0.026292722672224045,
0.02087307721376419,
-0.004931087139993906,
0.025735486298799515,
0.014143884181976318,
0.033374667167663574,
0.03262454271316528,
-0.029403388500213623,
-0.03144808113574982,
-0.003209460759535432,
-0.006103049498051405,
-0.01716453954577446,
0.018914993852376938,
-0.0027424199506640434,
-0.01637961156666279,
-0.034139811992645264,
-0.011161147616803646,
0.02762366086244583,
0.035578906536102295,
-0.011093445122241974,
-0.007419490721076727,
0.00892684143036604,
0.004144513513892889,
0.032977934926748276,
-0.05008812993764877,
-0.03413872420787811,
0.013655525632202625,
-0.00612181331962347,
-0.0018689638236537576,
-0.01793854311108589,
-0.0094910291954875,
-0.05755451321601868,
0.010164265520870686,
0.00040754539077170193,
0.00975428894162178,
0.00737853953614831,
0.05499299615621567,
0.026228735223412514,
-0.011435067281126976,
0.0007093080203048885,
0.03660993650555611,
-0.007661832496523857,
-0.00003751600161194801,
-0.015378951095044613,
0.045052092522382736,
0.011862549930810928,
-0.03190932050347328,
0.00018201553029939532,
-0.03387412056326866,
-0.00563247874379158,
0.08032243698835373,
0.024136796593666077,
0.061941590160131454,
0.00922434963285923,
-0.0011399645591154695,
-0.029694875702261925,
0.0024530987720936537,
-0.020524458959698677,
0.0018618542235344648,
0.025865929201245308,
0.028250258415937424,
-0.03629693016409874,
0.027237210422754288,
0.013219582848250866,
0.040131453424692154,
-0.03445517644286156,
0.028413811698555946,
0.02974691055715084,
-0.03472420573234558,
0.024960584938526154,
-0.0456535778939724,
-0.040803372859954834,
0.03214183449745178,
-0.03656243160367012,
0.06243074685335159,
0.0016389620723202825,
-0.03292408213019371,
0.05454143136739731,
0.029136326164007187,
0.019591091200709343,
-0.07352717220783234,
-0.019731339067220688,
-0.0674205794930458,
0.009818482212722301,
0.00438869372010231,
-0.03808728978037834,
0.01471385546028614,
-0.017934193834662437,
0.036461666226387024,
-0.0012694464530795813,
0.014926251024007797,
-0.02103818580508232,
-0.029855217784643173,
0.014875497668981552,
-0.05298593267798424,
-0.06316352635622025,
0.10018908232450485,
0.010749239474534988,
0.029240835458040237,
0.029912810772657394,
-0.01893821731209755,
0.04027828946709633,
0.0014399837236851454,
0.025152821093797684,
-0.016547687351703644,
0.06345318257808685,
0.0038444011006504297,
0.03780323639512062,
-0.00004397111479192972,
-0.0069365594536066055,
0.131325364112854,
0.06994932889938354,
-0.017777564004063606,
-0.0659041777253151,
0.00865931250154972,
-0.008088233880698681,
0.03080509416759014,
-0.01644160784780979,
-0.013459987938404083,
-0.02317454293370247,
-0.023747596889734268,
-0.03393854573369026,
0.058523908257484436,
-0.007858699187636375,
-0.005369118414819241,
0.02572915516793728,
-0.04490211606025696,
-0.010478110983967781,
-0.014442412182688713,
0.04041380435228348,
-0.011305056512355804,
0.02242710441350937,
-0.03272993117570877,
0.03946319967508316,
-0.045520368963479996,
-0.0032754740677773952,
-0.023045910522341728,
-0.01093628816306591,
0.029701314866542816,
0.0016756601398810744,
-0.004925457760691643,
0.02867947891354561,
-0.033732399344444275,
-0.0434405691921711,
-0.05345974117517471,
0.007855013944208622,
0.03197067975997925,
-0.023543523624539375,
0.015221319161355495,
0.026339935138821602,
-0.003719623200595379,
0.020691566169261932,
0.01658710278570652,
-0.024814490228891373,
-0.0640517920255661,
-0.0017542049754410982,
-0.04362267255783081,
0.04862383380532265,
-0.015604516491293907,
-0.007701694034039974,
-0.043457064777612686,
-0.015455605462193489,
0.013395742513239384,
-0.0318203866481781,
-0.015612833201885223,
-0.0022094992455095053,
0.041970379650592804,
-0.017272887751460075,
0.0012731999158859253,
0.008586416952311993,
0.021526413038372993,
0.03801008686423302,
0.02899102121591568,
-0.01619182527065277,
-0.005270128604024649,
0.0005638495204038918,
-0.0024648872204124928,
0.054599594324827194,
0.022033581510186195,
0.010837776586413383,
-0.009142248891294003,
-0.0012478240532800555,
-0.02857336215674877,
-0.008250015787780285,
0.048930030316114426,
-0.014410511590540409,
0.03279717266559601,
0.00985205452889204,
-0.033182911574840546,
-0.005917356349527836,
-0.027065390720963478,
-0.004012503195554018,
-0.015891674906015396,
-0.03331423178315163,
0.011378963477909565,
0.029647639021277428,
0.030417082831263542,
0.05671565607190132,
-0.025051914155483246,
-0.010733798146247864,
0.03868173062801361,
0.04031741991639137,
0.052054207772016525,
-0.018217559903860092,
-0.011001971550285816,
0.028827577829360962,
-0.020478351041674614,
-0.0031627966091036797,
-0.04809417575597763,
0.013895636424422264,
0.025572020560503006,
-0.017131144180893898,
0.025627512484788895,
0.04900861158967018,
-0.0037017471622675657,
-0.014056777581572533,
-0.027573376893997192,
-0.042363766580820084,
0.011085749603807926,
0.01946697197854519,
-0.00810814369469881,
-0.050684284418821335,
-0.015191166661679745,
0.030117174610495567,
-0.013785621151328087,
-0.004611846059560776,
0.02417946606874466,
-0.028391480445861816,
0.023186828941106796,
-0.003306611208245158,
0.015905659645795822,
0.0065304432064294815,
0.0028355836402624846,
-0.005041687749326229,
0.03521699830889702,
-0.027139639481902122,
0.016001004725694656,
-0.024374477565288544,
0.05554334074258804,
0.02789079211652279,
-0.016691040247678757,
0.053823716938495636,
0.030972404405474663,
-0.006496389862149954,
-0.016932975500822067,
0.03140115737915039,
-0.003512851195409894,
0.019810480996966362,
0.01068523433059454,
-0.03281586244702339,
-0.00038220291025936604,
-0.041020140051841736,
0.006669757422059774,
0.043242719024419785,
0.03149624541401863,
0.020207399502396584,
0.043641168624162674,
-0.007739595137536526,
-0.005829208064824343,
0.027684584259986877,
-0.026674650609493256,
-0.0071115088649094105,
0.017635412514209747,
-0.021397758275270462,
-0.00646946532651782,
-0.024868465960025787,
0.023907054215669632,
0.010801148600876331,
-0.014211023226380348,
0.018181296065449715,
-0.011457172222435474,
-0.0448465459048748,
0.0041593764908611774,
-0.041896406561136246,
0.019775452092289925,
0.0047888015396893024,
-0.0011466051219031215,
-0.02020954340696335,
0.043008044362068176,
0.0337195061147213,
-0.05034990608692169,
0.03361305966973305,
0.016268083825707436,
-0.023527247831225395,
-0.09311507642269135,
-0.009058668278157711,
0.025096310302615166,
0.003044931450858712,
0.06256503611803055,
-0.027812518179416656,
0.019380567595362663,
0.049791399389505386,
-0.06297304481267929,
0.029996728524565697,
-0.020788732916116714,
0.02481021359562874,
0.00395507737994194,
-0.030599813908338547,
-0.03829709440469742,
0.033601291477680206,
0.009755892679095268,
0.04417050629854202,
0.033548712730407715,
0.01890474371612072,
-0.027223944664001465,
-0.044356364756822586,
0.020735319703817368,
0.016986455768346786,
0.016813840717077255,
-0.02136848121881485,
0.05846821144223213,
-0.013303822837769985,
-0.017735498026013374,
-0.002524597104638815,
-0.006719875615090132,
0.00427941232919693,
-0.030650457367300987,
0.01204642467200756,
0.003993954975157976,
0.03666166961193085,
-0.013525356538593769,
-0.007214928045868874,
0.002720216754823923,
0.0005298624746501446,
0.05080094933509827,
-0.006522172596305609,
-0.028474396094679832,
-0.007395599503070116,
0.0027353547047823668,
-0.028657864779233932,
0.0006781036499887705,
0.04166596382856369,
-0.012084689922630787,
0.0001487627305323258,
0.010501222684979439,
0.0038950538728386164,
-0.020742494612932205,
-0.0314941331744194,
-0.011963995173573494,
-0.014746157452464104,
0.014368628151714802,
0.0188776645809412,
-0.00031118374317884445,
0.003442240646108985,
0.006752470042556524,
-0.048809394240379333,
-0.052147962152957916,
0.028245365247130394,
-0.018788181245326996,
-0.035529233515262604,
-0.02654585801064968,
-0.05616220086812973,
0.022696472704410553,
-0.0071946983225643635,
-0.016319256275892258,
-0.009670759551227093,
-0.020225413143634796,
0.03986163064837456,
0.0033955173566937447,
0.02662939950823784,
-0.021679416298866272,
-0.05040408670902252,
-0.04262915253639221,
-0.08010370284318924,
0.008730175904929638,
0.022168705239892006,
-0.009452874772250652,
-0.036011166870594025,
-0.010947391390800476,
-0.002668794710189104,
-0.00543801486492157,
0.058215510100126266,
0.003008646657690406,
-0.028512857854366302,
0.013465027324855328,
0.003579943673685193,
0.06791143864393234,
-0.033342551440000534,
0.03158866614103317,
-0.023030826821923256,
-0.0020739410538226366,
0.04890210181474686,
0.004847664851695299,
-0.03759229928255081,
0.035699084401130676,
0.022414816543459892,
0.012594546191394329,
-0.03414821997284889,
-0.004364671651273966,
-0.021432088688015938,
0.049574244767427444,
-0.0003191919531673193,
-0.00974410492926836,
0.05042356997728348,
0.011880768463015556,
-0.015669861808419228,
0.047314923256635666,
-0.01716879941523075,
-0.05912768840789795,
0.0036553540267050266,
-0.024537596851587296,
-0.02517709694802761,
-0.02464846521615982,
-0.0380161814391613,
0.05106475576758385,
-0.02996506169438362,
-0.006042329594492912,
0.010936726815998554,
-0.04332857206463814,
0.011991803534328938,
0.050069570541381836,
-0.024464037269353867,
0.06468212604522705,
-0.01400852669030428,
0.04415223374962807,
-0.024808647111058235,
0.011872134171426296,
0.013523629866540432,
0.04001450911164284,
0.01995091885328293,
-0.0035609423648566008,
0.034160736948251724,
0.019378365948796272,
-0.024971213191747665,
-0.02098727598786354,
0.03967034071683884,
0.05239083617925644,
-0.015749722719192505,
-0.007052176631987095,
0.03283386677503586,
-0.00004717697447631508,
-0.03547035902738571,
0.005597330164164305,
-0.011884583160281181,
0.06685187667608261,
-0.015347039327025414,
0.009545134380459785,
-0.02765546552836895,
0.026544159278273582,
-0.007552662398666143,
0.05468111112713814,
0.020129255950450897,
0.04481389373540878,
-0.028981536626815796,
-0.011039880104362965,
-0.05637989938259125,
-0.003456264268606901,
-0.012883977964520454,
-0.0028092972934246063,
0.010607204400002956,
0.028688013553619385,
0.017788482829928398,
0.0317036397755146,
-0.019031770527362823,
-0.03399698808789253,
-0.04870090261101723,
0.024832695722579956,
0.00031788175692781806,
0.018512757495045662,
-0.02502673864364624,
0.012399496510624886,
-0.027593711391091347,
0.022539252415299416,
-0.03967555984854698,
-0.025986721739172935,
-0.00269321515224874,
0.013598527759313583,
0.0014667198993265629,
0.03304433077573776
] |
<p>I have come to know the electrostatic potential energy in vacuum is given by
$${\frac{1}{2}} \epsilon_0\int d^3x {E^2} $$ and this energy is due to the mutual electrostatic coulomb potential energy.</p>
<p>So only a single point charge in space also contributes to some electrostatic potential energy according to $${\frac{1}{2}} \epsilon_0 \int d^3x {E^2} $$ as due to a single point charge also we have electric field at every point in space. </p>
<p>Now I am not getting it physically why should there be any Coulomb energy in this case as there is no another charge to provide the electrostatic coulomb potential energy?</p>
| 7,630 |
[
-0.026029353961348534,
0.010732980445027351,
0.023552659898996353,
-0.013385087251663208,
0.02283789962530136,
0.011393377557396889,
-0.01864304021000862,
-0.040449175983667374,
-0.0048103635199368,
-0.03889351710677147,
0.01826605200767517,
0.022855857387185097,
0.07008088380098343,
0.02197963558137417,
0.008972126059234142,
0.009044981561601162,
-0.01137993298470974,
-0.015492433682084084,
-0.013369271531701088,
-0.046114906668663025,
-0.040524568408727646,
0.03186602145433426,
0.01753268577158451,
0.010386486537754536,
-0.0029264038894325495,
0.008296729996800423,
0.045913223177194595,
-0.011466240510344505,
0.02890906296670437,
0.05500127747654915,
-0.012253074906766415,
-0.055674050003290176,
0.0015334661584347486,
0.027184326201677322,
0.016481351107358932,
-0.004614296369254589,
-0.030403386801481247,
-0.03144388273358345,
-0.02056737057864666,
0.04136393219232559,
-0.0295791607350111,
-0.019412484019994736,
-0.014492644928395748,
0.034277331084012985,
-0.032446734607219696,
0.015280986204743385,
0.02516981028020382,
-0.020023919641971588,
0.05805835872888565,
-0.06507682055234909,
0.03691748529672623,
0.004258373286575079,
0.06356780230998993,
0.008893621154129505,
-0.0003939760790672153,
-0.015158369205892086,
0.06685972213745117,
0.07363471388816833,
0.009354461915791035,
-0.017222683876752853,
-0.05229366198182106,
-0.004116292577236891,
0.016199888661503792,
-0.031011126935482025,
0.001518539502285421,
0.04749476537108421,
-0.0011385813122615218,
0.00328548951074481,
0.013661003671586514,
0.004466074053198099,
0.037746280431747437,
0.0289278756827116,
-0.005634653847664595,
-0.03010556660592556,
0.011930546723306179,
-0.012413294985890388,
0.016560224816203117,
-0.015443024225533009,
0.040637023746967316,
0.044948551803827286,
-0.024694865569472313,
0.005160386208444834,
0.04042360931634903,
0.03113073669373989,
0.01659121923148632,
-0.007699098903685808,
0.04105847328901291,
0.0023639495484530926,
-0.023243281990289688,
0.018223239108920097,
-0.004791191779077053,
0.016032030805945396,
0.01938474178314209,
-0.006301551591604948,
-0.025959186255931854,
0.04498370364308357,
-0.021011771634221077,
0.02081744559109211,
-0.011960001662373543,
-0.009399011731147766,
0.012276888824999332,
0.0134578300639987,
0.02558160573244095,
0.08876175433397293,
0.006761276163160801,
-0.03659125417470932,
-0.04270325228571892,
0.028838828206062317,
0.00389711931347847,
0.0022464697249233723,
-0.0416632816195488,
0.026024747639894485,
0.0149539178237319,
0.015363659709692001,
0.017099494114518166,
-0.00005590842556557618,
0.04855021461844444,
-0.0070073907263576984,
0.04398011788725853,
0.060504235327243805,
0.030193688347935677,
-0.028710342943668365,
0.03430449217557907,
-0.03346676751971245,
-0.06392934918403625,
0.008696277625858784,
0.03569285571575165,
0.014932571910321712,
-0.021930279210209846,
0.0033097437117248774,
-0.003001089906319976,
0.004703030921518803,
-0.0034227955620735884,
0.03773064166307449,
0.057695213705301285,
-0.028866931796073914,
-0.10730286687612534,
-0.01919672265648842,
-0.0013927870895713568,
-0.0222726222127676,
0.005790679715573788,
-0.06030944362282753,
-0.016089079901576042,
-0.0075178914703428745,
0.06821839511394501,
0.001043032156303525,
-0.02983172982931137,
-0.009873181581497192,
0.03419666737318039,
0.04208884760737419,
-0.041217438876628876,
-0.017692608758807182,
-0.015026121400296688,
-0.03667135536670685,
-0.018089842051267624,
-0.0584469772875309,
0.030886251479387283,
0.02255437895655632,
0.008375702425837517,
-0.014329934492707253,
0.05667813494801521,
-0.024587536230683327,
0.008624139241874218,
-0.0029299440793693066,
0.0038192144129425287,
-0.038523007184267044,
0.06928108632564545,
0.040574632585048676,
0.02111857198178768,
0.061118509620428085,
0.01276401150971651,
0.0485089048743248,
0.017916137352585793,
0.03533235564827919,
0.0544426292181015,
-0.06808443367481232,
-0.0373787097632885,
-0.04571535065770149,
0.028570236638188362,
-0.0066902427934110165,
-0.05756421387195587,
-0.05557830631732941,
0.019050685688853264,
0.005608080420643091,
-0.0108270775526762,
0.04661650210618973,
-0.016536694020032883,
-0.00962575152516365,
-0.029005268588662148,
-0.028327731415629387,
-0.010875403881072998,
-0.06586519628763199,
0.03292526304721832,
0.01825355924665928,
-0.008802516385912895,
0.026513326913118362,
0.012698093429207802,
0.010871665552258492,
-0.05351566895842552,
-0.01623259298503399,
-0.0301777645945549,
0.05635492876172066,
-0.018235109746456146,
-0.019810287281870842,
0.05244342237710953,
0.024949796497821808,
0.016517410054802895,
0.02529570832848549,
-0.008017887361347675,
0.019194122403860092,
-0.027373243123292923,
0.01414475217461586,
-0.07695108652114868,
0.05082441866397858,
0.004786072298884392,
0.015808727592229843,
0.0011294599389657378,
0.02158191055059433,
-0.019923176616430283,
0.03929273411631584,
-0.020602576434612274,
0.07687471807003021,
0.06375715136528015,
0.007060110103338957,
-0.023533999919891357,
0.04379681870341301,
-0.01139751449227333,
0.011447815224528313,
0.000822376343421638,
-0.04621407017111778,
-0.045392248779535294,
0.016060924157500267,
0.06460767239332199,
0.019312577322125435,
-0.03786167502403259,
-0.009109368547797203,
0.0193439032882452,
0.02211158722639084,
0.034671444445848465,
0.0267472006380558,
-0.010539394803345203,
-0.0025150980800390244,
0.04921113699674606,
0.02675885334610939,
0.006998302415013313,
0.0017429899889975786,
0.03283488005399704,
0.019815264269709587,
-0.002397760283201933,
-0.020776966586709023,
-0.005093492567539215,
0.05798421800136566,
-0.025115590542554855,
0.038660403341054916,
0.003877924056723714,
0.007295364513993263,
0.017445022240281105,
-0.03349072113633156,
0.07744079828262329,
0.00778290256857872,
-0.021844541653990746,
-0.01209003571420908,
-0.04476108402013779,
-0.036291126161813736,
0.030964205041527748,
0.03302070498466492,
-0.0166696198284626,
-0.02651534415781498,
0.0021268753334879875,
-0.05028929561376572,
0.024777524173259735,
0.022858187556266785,
-0.005262135993689299,
-0.017565511167049408,
-0.016236627474427223,
0.018094033002853394,
-0.00068154267501086,
0.020611818879842758,
-0.03325566276907921,
0.012239370495080948,
-0.025441410019993782,
-0.026871372014284134,
-0.023569203913211823,
0.026695063337683678,
-0.03688444569706917,
-0.01719553768634796,
-0.016662027686834335,
-0.012729768641293049,
0.0769844725728035,
0.007114091422408819,
0.019782522693276405,
0.004654433112591505,
-0.023986658081412315,
-0.05264966934919357,
0.0068952846340835094,
-0.03784568980336189,
0.04489113762974739,
-0.023881206288933754,
-0.017899682745337486,
0.0324825756251812,
-0.003108040662482381,
-0.04535769298672676,
0.04535377770662308,
-0.0455993115901947,
-0.04911985248327255,
-0.010164027102291584,
-0.017658822238445282,
0.026424609124660492,
-0.045422036200761795,
0.029206039384007454,
0.011956235393881798,
-0.0486365407705307,
-0.021237604320049286,
-0.044564202427864075,
-0.0306321419775486,
0.015488864853978157,
-0.007101633120328188,
0.012499556876718998,
-0.04798056185245514,
-0.06766897439956665,
0.04654726758599281,
0.027123603969812393,
-0.02918732352554798,
0.001313721644692123,
-0.015782508999109268,
-0.033933792263269424,
0.029766792431473732,
-0.005899728275835514,
0.010722297243773937,
-0.0017422635573893785,
0.01145047228783369,
-0.004659975413233042,
0.0625193789601326,
0.008764727972447872,
0.004771532956510782,
-0.019487150013446808,
-0.005585735663771629,
-0.004074337426573038,
0.00472178403288126,
0.056524042040109634,
-0.00008058396633714437,
-0.027601255103945732,
-0.034721460193395615,
0.013386178761720657,
0.020505066961050034,
0.020776474848389626,
-0.039332881569862366,
0.04953581839799881,
-0.026587624102830887,
0.03311634436249733,
-0.05304717272520065,
0.009536092169582844,
0.02760484628379345,
-0.030478527769446373,
0.016598829999566078,
0.016751017421483994,
0.05244595929980278,
-0.01609872654080391,
-0.007588792592287064,
0.025667792186141014,
0.04388126730918884,
-0.03851284459233284,
-0.039265263825654984,
0.0022075672168284655,
0.019798414781689644,
0.0065015158616006374,
0.004304854664951563,
-0.012331336736679077,
0.028495650738477707,
0.05570058152079582,
0.029524926096200943,
-0.0024444719310849905,
-0.0427376851439476,
0.01816057600080967,
-0.04642760008573532,
-0.005213833414018154,
0.021617282181978226,
0.055831845849752426,
0.0013659996911883354,
0.04989016801118851,
0.025992119684815407,
-0.004208635538816452,
0.02177273854613304,
0.012457824312150478,
-0.07004167139530182,
0.014326656237244606,
-0.03206207603216171,
-0.011369018815457821,
-0.02522798627614975,
-0.02252156473696232,
-0.0355314165353775,
-0.023036472499370575,
-0.029030654579401016,
-0.01464929524809122,
0.005605470389127731,
-0.053615178912878036,
-0.003553343005478382,
-0.04038986936211586,
-0.014833900146186352,
-0.025366248562932014,
0.07453940808773041,
0.028809387236833572,
-0.05536903068423271,
-0.03766373544931412,
0.0406680628657341,
-0.03128272294998169,
-0.030878297984600067,
-0.01705310307443142,
-0.012586768716573715,
0.017657088115811348,
-0.005046055652201176,
0.004923604428768158,
0.0027044133748859167,
0.022568264976143837,
-0.023569535464048386,
0.00483194924890995,
0.046881239861249924,
0.00979230273514986,
-0.021455153822898865,
-0.01850573904812336,
-0.03438463807106018,
0.005649308208376169,
-0.01261888351291418,
0.042267780750989914,
-0.00455457204952836,
0.03309570252895355,
0.027735833078622818,
0.01385012362152338,
-0.012089603580534458,
0.06359733641147614,
0.060567837208509445,
0.01527367252856493,
-0.036985136568546295,
-0.0485134981572628,
0.0038648161571472883,
-0.04277300834655762,
-0.01646258495748043,
0.02761968784034252,
-0.025110144168138504,
-0.043809060007333755,
0.006184838712215424,
0.001003336627036333,
-0.005515772383660078,
-0.01057388074696064,
-0.00761343352496624,
0.01617465727031231,
0.03791679069399834,
-0.009723151102662086,
-0.023884424939751625,
0.0317574180662632,
-0.031978681683540344,
0.025397170335054398,
-0.005178116261959076,
-0.002410751534625888,
-0.06483679264783859,
-0.019602281972765923,
0.04055953398346901,
0.016164356842637062,
-0.003924427554011345,
-0.012095383368432522,
-0.05917224660515785,
0.012701342813670635,
0.034575074911117554,
-0.04265868663787842,
-0.006023673340678215,
0.001639557653106749,
0.026843512430787086,
-0.03447796776890755,
-0.0436459444463253,
-0.04182840511202812,
0.01694214716553688,
-0.009976516477763653,
0.026823608204722404,
-0.02802516706287861,
0.02172498032450676,
-0.004824972711503506,
0.0554446205496788,
0.037848010659217834,
0.08537199348211288,
0.03905286639928818,
0.025396481156349182,
-0.008626648224890232,
0.014757274650037289,
0.012975594028830528,
-0.08439932018518448,
-0.010014684870839119,
-0.017920996993780136,
0.004079105798155069,
0.03021809831261635,
-0.033297520130872726,
-0.03458437696099281,
0.04094770550727844,
0.005857272073626518,
0.021560052409768105,
-0.001642568618990481,
-0.032337456941604614,
0.03417455032467842,
0.03742453083395958,
0.019098829478025436,
0.04127876088023186,
0.005421563051640987,
-0.05559568479657173,
-0.0008717246237210929,
-0.035001832991838455,
0.020654423162341118,
-0.01865275576710701,
-0.01731153018772602,
-0.04419369250535965,
0.04582783207297325,
-0.03485551103949547,
0.030406752601265907,
-0.03245596960186958,
-0.008161484263837337,
-0.033868011087179184,
-0.025648033246397972,
-0.027649609372019768,
0.018360869958996773,
0.024070218205451965,
0.02380269393324852,
-0.03458617627620697,
0.029311785474419594,
0.02547878958284855,
-0.0046722195111215115,
-0.018006933853030205,
0.019619345664978027,
-0.03831600397825241,
0.015542237088084221,
0.014270254410803318,
-0.018266163766384125,
0.001682772533968091,
-0.012563052587211132,
0.02513105981051922,
-0.06306634843349457,
0.021977361291646957,
-0.025924518704414368,
-0.006050047930330038,
0.0201454795897007,
-0.09202439337968826,
-0.0623839870095253,
0.005992786027491093,
0.011915656737983227,
0.03864242136478424,
-0.027816927060484886,
0.01123840268701315,
0.023116549476981163,
0.019865166395902634,
-0.0637172982096672,
-0.05018630251288414,
0.029719019308686256,
-0.010027353651821613,
-0.00028083560755476356,
-0.031195638701319695,
-0.00831597764045,
-0.03064321167767048,
-0.01807943359017372,
0.04312066361308098,
0.029335204511880875,
-0.019478019326925278,
-0.005415650084614754,
0.004555046558380127,
0.04342973232269287,
0.012610985897481441,
0.008040590211749077,
0.00654691644012928,
0.04790491983294487,
0.008574695326387882,
0.016524942591786385,
-0.010404352098703384,
0.058988820761442184,
0.004151942674070597,
-0.02976522222161293,
-0.0238119438290596,
-0.018267381936311722,
0.033173490315675735,
-0.05164571478962898,
-0.026482893154025078,
0.03501633554697037,
0.030127452686429024,
-0.03741537034511566,
-0.009861025959253311,
0.02574015036225319,
0.003971918486058712,
0.027371788397431374,
0.001913221087306738,
0.02118200995028019,
-0.05125851556658745,
-0.02119699865579605,
0.02045612595975399,
0.0000034671265893848613,
0.015318167395889759,
-0.01574970968067646,
0.035586003214120865,
0.003563510486856103,
-0.0072026909328997135,
0.03167528659105301,
-0.01664024405181408,
-0.008796051144599915,
-0.0349358469247818,
-0.005748468451201916,
0.0233769454061985,
0.021816028282046318,
-0.016329627484083176,
0.004642981104552746,
-0.021498437970876694,
0.031374912708997726,
0.056717269122600555,
-0.02005106210708618,
0.034805141389369965,
0.0253450945019722,
0.014053083956241608,
0.0013277370017021894,
-0.011220182292163372,
-0.02248162403702736,
0.0014132867800071836,
-0.001763347303494811,
0.0014657818246632814,
-0.041273489594459534,
-0.0030067896004766226,
0.030190614983439445,
0.06333450973033905,
-0.03340151906013489,
0.007720602210611105,
0.015972699970006943,
0.013732373714447021,
0.0014380645006895065,
-0.00046442507300525904,
-0.045935675501823425,
0.06218681484460831,
-0.015153245069086552,
0.01600385084748268,
0.04670262336730957,
-0.04209771379828453,
0.04778105765581131,
-0.00982588529586792,
-0.007145632058382034,
-0.03708261623978615,
-0.029392287135124207,
-0.038110002875328064,
0.05111867934465408,
0.005042284727096558,
-0.00020397549087647349,
0.012193153612315655,
0.017617223784327507,
0.006616477854549885,
0.007292497903108597,
-0.019356798380613327,
0.024860965088009834,
-0.08496847748756409,
-0.02211488038301468,
-0.03329530358314514,
-0.034002598375082016,
0.019600091502070427,
-0.0009571718401275575,
-0.055035799741744995,
0.021034393459558487,
-0.020322179421782494,
0.07048304378986359,
0.0009060432203114033,
0.006246880162507296,
-0.030874239280819893,
0.08129338920116425,
0.0026255641132593155,
0.026089197024703026,
-0.02945108711719513,
0.011267758905887604,
0.12564334273338318,
0.05315493419766426,
0.012383097782731056,
-0.052940092980861664,
-0.005760336760431528,
-0.0206587053835392,
0.014523223042488098,
-0.04387396201491356,
0.050786495208740234,
-0.027850482612848282,
0.029767272993922234,
-0.014311435632407665,
0.03197572007775307,
0.0035289470106363297,
0.0037562143988907337,
0.03691793605685234,
-0.04658268764615059,
-0.0680273026227951,
0.017618006095290184,
0.040524158626794815,
0.006942503619939089,
-0.004603369161486626,
-0.011263265274465084,
0.03483232483267784,
-0.042840275913476944,
0.024640047922730446,
-0.03560617193579674,
-0.037281204015016556,
0.007940485142171383,
0.0035372236743569374,
-0.05843648314476013,
-0.011423328891396523,
-0.008507108315825462,
-0.01649872399866581,
-0.043412402272224426,
0.025710418820381165,
0.03231038153171539,
-0.006738151423633099,
0.023475296795368195,
0.008330236189067364,
-0.005772567354142666,
0.022725172340869904,
0.019785422831773758,
0.023360490798950195,
-0.0228147991001606,
-0.0029271182138472795,
-0.021985860541462898,
0.07524429261684418,
-0.039227355271577835,
0.0004946389235556126,
-0.013943467289209366,
0.032019488513469696,
-0.004041632171720266,
-0.027757178992033005,
-0.03917936608195305,
-0.044426411390304565,
0.03542246297001839,
0.005777079612016678,
-0.01835198514163494,
-0.03139599785208702,
0.020803609862923622,
-0.02654181607067585,
0.03246960788965225,
-0.041110772639513016,
-0.023870382457971573,
0.017539314925670624,
0.01532471738755703,
0.05447624623775482,
-0.0031133273150771856,
-0.007695554289966822,
0.01770230568945408,
-0.049806226044893265,
-0.02275613695383072,
-0.04086226969957352,
0.0029700433369725943,
0.029163820669054985,
0.037990767508745193,
-0.007503264583647251,
0.030213696882128716,
0.004130771849304438,
-0.07471983879804611,
0.02568936161696911,
-0.00453063054010272,
0.0023067928850650787,
-0.013162977062165737,
0.022451071068644524,
0.01154167391359806,
0.07370197027921677,
-0.018695781007409096,
-0.01127272006124258,
-0.0003947748336941004,
0.011603940278291702,
0.004443127196282148,
-0.013166902586817741,
-0.0113271065056324,
0.0028093645814806223,
-0.02435143291950226,
0.02394060045480728,
-0.034027740359306335,
-0.017109358683228493,
-0.017820188775658607,
0.03550367057323456,
0.01714206300675869,
0.04677653685212135,
-0.030677009373903275,
-0.0007351069361902773,
0.013892794959247112,
0.011740363202989101,
0.009235636331140995,
0.023375701159238815,
0.00015434605302289128,
-0.03036634437739849,
-0.005366999190300703,
0.017421672120690346,
0.013595830649137497,
-0.007030966226011515,
0.015468306839466095,
-0.04051037132740021,
-0.01795141212642193,
-0.017838748171925545,
-0.0053967442363500595,
-0.053745727986097336,
-0.0270050261169672,
-0.04935208335518837,
0.05031320080161095,
0.004886116832494736,
-0.010708748362958431,
-0.02780783921480179,
0.014938760548830032,
-0.04313056170940399,
-0.009335692971944809,
0.023945897817611694,
0.015144947916269302,
-0.04868033155798912,
0.0015921836020424962,
0.04402056708931923,
-0.023950310423970222,
0.04069744050502777,
-0.01821279153227806,
-0.01525160763412714,
0.021705234423279762,
-0.03544548898935318,
-0.07805047929286957,
0.007791419979184866,
0.01224906463176012,
0.026505811139941216,
0.029976176097989082,
0.0031427545472979546,
-0.03717052564024925,
0.06709611415863037,
-0.024874817579984665,
0.015028659254312515,
0.010531026870012283,
-0.01149752363562584,
0.015290973708033562,
-0.013234206475317478,
-0.013167507946491241,
-0.0257564764469862,
0.017269102856516838,
0.03850632160902023,
0.0005081413546577096,
-0.016527114436030388,
-0.013275387696921825,
0.044141534715890884,
-0.042752571403980255,
0.003576055634766817,
0.04099443554878235,
0.025919562205672264,
-0.005906084086745977,
0.06033432483673096,
-0.040455594658851624,
0.025124918669462204,
0.0334073044359684,
-0.00331358821131289,
-0.08220136910676956,
-0.01711723580956459,
-0.004112205933779478,
0.0030269070994108915,
0.021120823919773102,
-0.017843658104538918,
-0.006723035126924515,
0.0248755794018507,
-0.07722175866365433,
0.03225865960121155,
-0.0012144488282501698,
0.0023020675871521235,
-0.015582398511469364,
-0.040257081389427185,
-0.03638974577188492,
0.03776821494102478,
0.03217413276433945,
0.03711755573749542,
0.029230842366814613,
0.00601477175951004,
-0.00043441951856948435,
-0.041405029594898224,
-0.054055895656347275,
0.034157998859882355,
-0.013981959782540798,
0.005074460059404373,
0.08424361050128937,
-0.01110739354044199,
-0.006638749968260527,
-0.0034054142888635397,
-0.0023739393800497055,
-0.04084397852420807,
-0.004611608572304249,
0.024831604212522507,
-0.007677372545003891,
0.05451161414384842,
0.032307181507349014,
-0.005334046203643084,
-0.02105884440243244,
0.002097414806485176,
0.03549260273575783,
0.0036352952010929585,
0.014617259614169598,
0.005105883348733187,
0.03775537386536598,
-0.015681838616728783,
-0.04339611157774925,
0.03217596933245659,
0.0047493609599769115,
-0.024251369759440422,
0.01508933212608099,
0.04862275347113609,
0.00568847032263875,
-0.03056229278445244,
-0.020940357819199562,
-0.05232754722237587,
-0.02799217216670513,
0.04634096473455429,
0.0036260245833545923,
0.008164001628756523,
-0.0004047997354064137,
0.013512810692191124,
-0.025691760703921318,
0.0320710651576519,
0.034021489322185516,
-0.007743466179817915,
-0.07494708150625229,
-0.0003339974791742861,
0.006035900674760342,
-0.01552011538296938,
-0.011103830300271511,
-0.036514170467853546,
-0.0529598630964756,
0.03164350241422653,
0.01706068404018879,
0.011922691948711872,
-0.024410806596279144,
-0.03308102861046791,
-0.030503971502184868,
-0.037492766976356506,
0.033486202359199524,
-0.013998554088175297,
-0.04753613471984863,
-0.025407569482922554,
-0.04625895619392395,
0.002986589912325144,
0.013249936513602734,
0.023006875067949295,
-0.01986640691757202,
-0.020098496228456497,
0.026467004790902138,
0.0005240587051957846,
0.03473822399973869,
-0.04170455038547516,
0.009929449297487736,
0.03765946999192238,
-0.026341944932937622,
0.022012783214449883,
-0.005024369806051254,
0.007999864406883717,
0.032297566533088684,
0.021204961463809013,
-0.03772879019379616,
0.023914137855172157,
-0.04337894171476364,
-0.003151685930788517,
0.026592407375574112,
0.009165712632238865,
-0.019731367006897926,
0.06798842549324036,
-0.037209998816251755,
0.027463799342513084,
-0.012913314625620842,
-0.007613137364387512,
0.014406702481210232,
0.004327124450355768,
-0.017518842592835426,
-0.011670874431729317,
-0.03592531010508537,
-0.010618635453283787,
0.033974602818489075,
-0.05599142983555794,
-0.018150189891457558,
0.07164740562438965,
-0.032981112599372864,
-0.020167550072073936,
0.06546744704246521,
-0.00830280501395464,
0.024010304361581802,
0.044148191809654236,
0.017598893493413925,
0.022686557844281197,
0.0174237210303545,
0.008791029453277588,
0.02409461885690689,
0.03187026455998421,
-0.010263235308229923,
0.006760512478649616,
0.04564031586050987,
0.0362960584461689,
0.001705148839391768,
0.01888643018901348,
0.022463232278823853,
-0.05243751034140587,
-0.02895379066467285,
-0.00395891722291708,
0.0001151982432929799,
0.041837625205516815,
0.004440375603735447,
-0.024323543533682823,
0.08623437583446503,
-0.031820148229599,
0.010225990787148476,
0.004981278441846371,
-0.011376060545444489,
-0.006013099569827318,
0.018518149852752686,
0.003743463661521673,
0.05682669207453728,
0.006246572360396385,
-0.016703514382243156,
-0.01491119246929884,
0.025361385196447372,
0.0008934661746025085,
-0.03917735069990158,
0.0069231255911290646,
0.008195862174034119,
-0.007886683568358421,
-0.033695634454488754,
0.012411445379257202,
-0.007779643405228853,
-0.024521082639694214,
0.02139115519821644,
0.03336699679493904,
0.03893793374300003,
0.011255079880356789,
-0.009387698024511337,
-0.02745332010090351,
0.06421071290969849,
-0.06638453900814056,
-0.016948679462075233,
-0.0032336951699107885,
-0.006699482910335064,
-0.02208968624472618,
0.010492207482457161
] |
<p>What are the results of fusing an electron neutrino and a muon neutrino? If you have an answer, then why? I looked this up and searched for stuff on Google, Wikipedia and a few other sites, but all the results say are stuff on nuclear fusion and neutrinos.</p>
<p><b> BONUS QUESTION: </b>
<br>
What happens if you put another muon neutrino into the mix?</p>
| 7,631 |
[
-0.005522259511053562,
-0.029681269079446793,
-0.0054066237062215805,
-0.041811615228652954,
0.01384148932993412,
0.049230121076107025,
-0.03339244797825813,
-0.05291718989610672,
0.017335107550024986,
-0.0004131857131142169,
0.048645664006471634,
0.03976448252797127,
0.0422697588801384,
-0.028151599690318108,
-0.0012135036522522569,
0.026776902377605438,
0.002055536722764373,
-0.01193142682313919,
-0.007848501205444336,
-0.013072982430458069,
-0.013843338005244732,
-0.0030669078696519136,
-0.0033412515185773373,
0.003092403057962656,
-0.020881980657577515,
0.03067762404680252,
0.03175286203622818,
0.014845780096948147,
0.04588188976049423,
0.06034160405397415,
0.02631545253098011,
-0.07606054097414017,
0.03085271269083023,
0.025528116151690483,
0.012662870809435844,
-0.013796895742416382,
-0.005876082926988602,
-0.02680470049381256,
-0.02322288043797016,
0.016443708911538124,
-0.011305871419608593,
-0.046248458325862885,
-0.02204621024429798,
0.013038977980613708,
-0.03988078981637955,
0.00960314180701971,
-0.00025274240761063993,
-0.009287034161388874,
0.05223768204450607,
-0.05330703407526016,
0.023148341104388237,
0.04282978177070618,
0.015549162402749062,
0.018831579014658928,
0.012294155545532703,
0.027382705360651016,
0.08565546572208405,
0.05839760974049568,
0.006789319217205048,
-0.06507027894258499,
-0.003860964672639966,
-0.04884524270892143,
0.0060820202343165874,
0.018163179978728294,
-0.03494125232100487,
0.08375982940196991,
-0.032578546553850174,
-0.0018477538833394647,
-0.000008489635547448415,
0.003568947082385421,
0.02480924129486084,
0.0011443664552643895,
0.0020095512736588717,
0.0017098111566156149,
0.019869742915034294,
-0.02912868931889534,
0.02653161995112896,
-0.008015101775527,
0.039807870984077454,
0.07599876821041107,
-0.045812688767910004,
0.03607236221432686,
0.040543049573898315,
0.008454042486846447,
0.000737371388822794,
-0.009463568218052387,
0.09354414790868759,
0.0070984866470098495,
-0.016592983156442642,
0.03312816843390465,
0.006042533088475466,
0.006079669110476971,
0.015495146624743938,
0.0036141599994152784,
-0.021116074174642563,
0.030845746397972107,
0.016202764585614204,
0.056420017033815384,
0.01770506426692009,
-0.04336889460682869,
0.021107155829668045,
0.03405647352337837,
0.02061603218317032,
0.0628587082028389,
0.010952933691442013,
-0.04282531142234802,
-0.013377820141613483,
0.002713944297283888,
-0.026483798399567604,
-0.012935066595673561,
-0.003009853418916464,
-0.006325583439320326,
-0.023175466805696487,
0.0010768526699393988,
0.03316975012421608,
-0.04192616045475006,
0.023874439299106598,
-0.016057876870036125,
0.07073069363832474,
0.05979752168059349,
0.03596286103129387,
-0.020305229350924492,
0.008726627565920353,
-0.03082066774368286,
-0.051577627658843994,
-0.02058311738073826,
0.012732789851725101,
0.026117505505681038,
-0.031918905675411224,
0.033860720694065094,
-0.028986798599362373,
-0.02225031517446041,
-0.002822574693709612,
-0.018299613147974014,
0.02292046509683132,
-0.009934984147548676,
-0.08164761960506439,
-0.07497333735227585,
0.0715462937951088,
-0.04916317015886307,
-0.0513392798602581,
-0.07113280892372131,
0.0032665394246578217,
0.0013850844698026776,
0.08907365053892136,
0.022483211010694504,
-0.01856350712478161,
-0.010736295953392982,
0.04271715506911278,
0.03484911099076271,
0.0007994699408300221,
-0.03507094085216522,
0.004154758527874947,
-0.04040652513504028,
0.000023699270968791097,
-0.03639909625053406,
-0.008522920310497284,
0.020653607323765755,
-0.013892825692892075,
-0.024566512554883957,
0.09231125563383102,
0.003461203770712018,
0.035350751131772995,
0.003566515166312456,
-0.018967632204294205,
-0.013655600138008595,
0.07787628471851349,
0.03795809671282768,
-0.026587417349219322,
0.054101746529340744,
-0.034713391214609146,
0.04574467986822128,
0.01779641956090927,
0.02460942231118679,
0.017076583579182625,
-0.04544173181056976,
-0.03700277581810951,
-0.04057462513446808,
0.010472490452229977,
-0.02432326041162014,
-0.016096927225589752,
-0.020445721223950386,
-0.02589958906173706,
0.008079149760305882,
0.021047484129667282,
0.056091632694005966,
-0.023533541709184647,
-0.025137420743703842,
0.00002728356048464775,
-0.05868089571595192,
-0.032526928931474686,
-0.08173662424087524,
-0.011590365320444107,
-0.012779980897903442,
-0.029281962662935257,
0.01076696440577507,
0.02037007175385952,
0.0188252255320549,
-0.036388181149959564,
-0.04465833678841591,
-0.02437889762222767,
0.03865688666701317,
-0.02055451273918152,
0.029766762629151344,
0.013990329578518867,
0.06405521929264069,
0.02180970273911953,
-0.050097666680812836,
0.007359667215496302,
-0.012982825748622417,
-0.03144292160868645,
-0.0022383974865078926,
-0.007289046887308359,
0.0038916992489248514,
-0.0016058140899986029,
0.0008491796324960887,
0.005804358050227165,
-0.01307850144803524,
0.008168787695467472,
0.00978287123143673,
-0.004343552514910698,
0.1030144989490509,
0.0017327758250758052,
-0.00429597357288003,
0.03601408749818802,
0.03344123810529709,
0.049003131687641144,
0.032478682696819305,
0.006839196663349867,
-0.007272530347108841,
-0.046243246644735336,
0.01364867016673088,
0.02866966277360916,
0.018343599513173103,
-0.0434880331158638,
0.03387339040637016,
-0.040393929928541183,
0.030128445476293564,
-0.014101041480898857,
0.03972037136554718,
-0.033920977264642715,
-0.02846631035208702,
-0.016824765130877495,
0.016022663563489914,
-0.017357591539621353,
0.02304663136601448,
0.008627728559076786,
0.00971013493835926,
0.0020590885542333126,
-0.02272903174161911,
-0.052330560982227325,
0.055396415293216705,
-0.019394775852560997,
-0.019580131396651268,
-0.012104841880500317,
-0.03927973657846451,
-0.004093524534255266,
-0.0488206185400486,
0.018233034759759903,
-0.011529931798577309,
-0.008908340707421303,
0.0058760386891663074,
-0.007670069113373756,
-0.003611728549003601,
0.00891568697988987,
0.013967728242278099,
0.02405165508389473,
0.008516683243215084,
0.018554700538516045,
-0.053641177713871,
0.01652647741138935,
0.006982291582971811,
0.019016943871974945,
0.0011707773664966226,
0.014072834514081478,
0.008284256793558598,
-0.011851360090076923,
0.026690764352679253,
-0.03243755176663399,
-0.067927785217762,
-0.00413782661780715,
-0.06695719063282013,
-0.007012064568698406,
0.03292852267622948,
-0.06344867497682571,
0.04378625005483627,
-0.056448403745889664,
-0.02941049449145794,
0.02669891156256199,
0.012925992719829082,
0.02024247497320175,
0.018637392669916153,
-0.012018216773867607,
-0.06637260317802429,
-0.041045237332582474,
-0.03554333373904228,
-0.014537987299263477,
0.000009702254828880541,
0.018214300274848938,
0.045557644218206406,
-0.012094387784600258,
-0.03346490487456322,
-0.010848780162632465,
-0.03189712390303612,
-0.03388092666864395,
-0.0041188569739460945,
-0.004201127216219902,
0.04197324067354202,
-0.043672267347574234,
0.01137569360435009,
0.028271926566958427,
-0.07027328759431839,
0.02532871626317501,
-0.028528183698654175,
-0.019576426595449448,
0.017422763630747795,
-0.017999175935983658,
0.009535727091133595,
0.0077229333110153675,
-0.045956749469041824,
0.035550009459257126,
-0.009916884824633598,
-0.02560453861951828,
-0.016036756336688995,
0.022454220801591873,
-0.005039561074227095,
-0.03940311446785927,
0.028425639495253563,
0.03208697587251663,
0.011057293973863125,
0.011987554840743542,
0.03529771417379379,
0.03805692493915558,
0.007475425023585558,
0.03621680289506912,
-0.02420627698302269,
-0.02555975317955017,
0.019973618909716606,
-0.0023809627164155245,
0.0308382511138916,
0.003670152509585023,
-0.015082618221640587,
0.03321316838264465,
0.017481330782175064,
0.0454997643828392,
0.020763156935572624,
-0.01997285708785057,
0.04440239071846008,
0.02343304455280304,
-0.014623498544096947,
-0.04824838787317276,
0.04007415845990181,
0.005900162737816572,
0.00890329573303461,
0.004900703206658363,
0.0047525386326014996,
0.05037098377943039,
-0.0312434583902359,
0.0023501731920987368,
0.0132890110835433,
0.027973182499408722,
-0.02851974591612816,
-0.039013080298900604,
-0.024954475462436676,
0.007685581687837839,
-0.003247765591368079,
0.01647959090769291,
0.011139356531202793,
0.04383179545402527,
0.029710713773965836,
0.013753481209278107,
-0.021051542833447456,
-0.026420805603265762,
-0.04203109070658684,
-0.07124102860689163,
-0.00994876865297556,
0.00438228202983737,
0.020437320694327354,
0.0030214316211640835,
0.06304246932268143,
0.011667966842651367,
-0.007672689389437437,
-0.0007607120787724853,
-0.02206752821803093,
-0.06457893550395966,
0.04852169752120972,
-0.019563788548111916,
-0.01641557738184929,
-0.017014844343066216,
-0.01850283145904541,
-0.030574368312954903,
0.00028222441324032843,
-0.0275478046387434,
-0.03004639782011509,
-0.028880486264824867,
-0.03808654099702835,
0.01712244376540184,
-0.03818778321146965,
-0.04096872732043266,
-0.01965337060391903,
0.05857941880822182,
0.033996570855379105,
-0.0025016353465616703,
0.0007083936361595988,
0.008037962019443512,
-0.043615974485874176,
-0.0037185661494731903,
-0.0011588884517550468,
0.023013895377516747,
0.0006221323856152594,
0.026277819648385048,
0.03597613424062729,
0.028576428070664406,
-0.023631688207387924,
0.029269350692629814,
0.03669773414731026,
0.06090404465794563,
0.017268680036067963,
0.008026083000004292,
-0.028844401240348816,
-0.04079056903719902,
-0.020077478140592575,
0.005697021726518869,
0.0416523702442646,
-0.02080472745001316,
0.01801636442542076,
0.03356195613741875,
0.01768738217651844,
-0.0070302910171449184,
0.06043717637658119,
0.06099722534418106,
-0.005405524745583534,
-0.026601048186421394,
-0.025167616084218025,
-0.015073933638632298,
0.00425957003608346,
0.01983109675347805,
0.008412162773311138,
-0.00852377712726593,
-0.02866366133093834,
-0.03202604502439499,
0.003680318593978882,
0.010191431269049644,
-0.03629116341471672,
-0.008965576998889446,
-0.0012755190255120397,
0.0024593614507466555,
-0.013767953962087631,
0.0028977866750210524,
-0.02407272532582283,
0.05114109069108963,
0.04088037461042404,
-0.013802235946059227,
-0.012145048938691616,
-0.05707350745797157,
0.027935916557908058,
0.06629914045333862,
0.06594301760196686,
-0.016810480505228043,
-0.04472209885716438,
-0.07419399917125702,
0.006771238520741463,
0.028454283252358437,
-0.04393524304032326,
0.021527063101530075,
-0.007843839935958385,
0.02376440539956093,
-0.030580833554267883,
-0.01694103330373764,
0.017614062875509262,
0.034213338047266006,
0.02467677928507328,
0.029696930199861526,
-0.03909705579280853,
-0.0031010094098746777,
-0.017688734456896782,
0.01414579525589943,
0.07624039053916931,
0.052531760185956955,
0.015408573672175407,
0.00430214824154973,
0.019843073561787605,
0.01642625592648983,
0.012236073613166809,
-0.10809469223022461,
0.023265548050403595,
0.009913070127367973,
-0.030776847153902054,
0.05659264698624611,
-0.05637477710843086,
-0.050257712602615356,
0.011973797343671322,
0.012545307166874409,
-0.0077912877313792706,
-0.02362794615328312,
-0.055702682584524155,
0.03441866859793663,
0.046760644763708115,
0.007705135736614466,
0.045965876430273056,
0.0004469300911296159,
-0.022478289902210236,
0.016996173188090324,
-0.03738545998930931,
0.022068390622735023,
-0.05254865437746048,
0.01796426624059677,
0.015500220470130444,
0.009623836725950241,
-0.04047912731766701,
0.04058149829506874,
0.008063186891376972,
0.03972587734460831,
0.00014399814244825393,
-0.042485978454351425,
-0.045235663652420044,
0.014713088981807232,
-0.010622475296258926,
-0.0015594161814078689,
0.00033819107920862734,
-0.016219064593315125,
0.022292565554380417,
-0.03092566318809986,
0.03466586396098137,
-0.01206229068338871,
0.003425072180107236,
-0.009600800462067127,
-0.02028866484761238,
0.02508261241018772,
-0.001349913072772324,
-0.008197218179702759,
0.05342123657464981,
-0.03171810507774353,
0.0033012947533279657,
-0.019436540082097054,
-0.0002894240606110543,
0.04303682595491409,
-0.0547594279050827,
-0.03965531662106514,
0.009318453259766102,
-0.010528761893510818,
0.04047152027487755,
-0.025436483323574066,
0.03494090959429741,
0.011475073173642159,
0.021224245429039,
-0.06719567626714706,
-0.04654853790998459,
0.029896419495344162,
-0.00583705585449934,
0.0028319198172539473,
-0.023519078269600868,
-0.015322761610150337,
-0.05119580030441284,
-0.035522136837244034,
-0.004531425423920155,
0.06485036760568619,
-0.05245329812169075,
-0.027834603562951088,
-0.004885366186499596,
0.004478125832974911,
0.06905089318752289,
0.02911185659468174,
-0.0031344310846179724,
0.01379428617656231,
-0.02393285557627678,
0.0037423199974000454,
0.019094811752438545,
0.032829318195581436,
0.004686309024691582,
-0.06924562156200409,
0.017322471365332603,
-0.028864232823252678,
0.035512104630470276,
-0.006379032041877508,
0.023259667679667473,
0.06221381947398186,
0.03960913047194481,
0.0022463274654000998,
-0.005324918776750565,
0.025035785511136055,
-0.031293388456106186,
0.023472651839256287,
0.009727799333631992,
0.018982548266649246,
-0.01762206293642521,
-0.044982410967350006,
0.04121196269989014,
0.0016431191470474005,
0.022707056254148483,
0.002542857313528657,
0.03911741450428963,
-0.00960602331906557,
-0.028325162827968597,
0.00975111685693264,
-0.030247261747717857,
0.038649044930934906,
-0.005972146987915039,
0.02080773189663887,
0.0329987034201622,
0.021925142034888268,
-0.03899015858769417,
-0.017282692715525627,
-0.03748106583952904,
-0.009276133961975574,
0.047055650502443314,
-0.06867161393165588,
0.022237086668610573,
-0.004732426255941391,
-0.0076079233549535275,
-0.012417040765285492,
-0.030488304793834686,
0.0055976686999201775,
0.02551981806755066,
-0.012757563963532448,
0.01011692639440298,
0.00764098484069109,
-0.002080388367176056,
0.018922561779618263,
0.06144072115421295,
0.03205791860818863,
-0.005429510027170181,
0.052095118910074234,
0.053163640201091766,
-0.015410220250487328,
0.008691373281180859,
-0.0561278872191906,
0.018227174878120422,
-0.03361612930893898,
-0.0008830970036797225,
0.012874831445515156,
-0.015583092346787453,
0.022246140986680984,
-0.013334883376955986,
0.016822069883346558,
0.012207080610096455,
-0.011653636582195759,
-0.024586057290434837,
0.014353717677295208,
0.011275422759354115,
-0.019317710772156715,
0.0077093131840229034,
0.037334978580474854,
0.049466706812381744,
0.00804897490888834,
-0.004963323939591646,
-0.033668749034404755,
-0.0825737863779068,
-0.03693070262670517,
-0.009682990610599518,
-0.0264936164021492,
0.012023852206766605,
-0.02566060610115528,
-0.021290728822350502,
0.010770794935524464,
-0.0047037419863045216,
-0.0006234199390746653,
-0.00009189057891489938,
0.03479844331741333,
-0.04755425453186035,
0.03742580860853195,
-0.020600931718945503,
0.029351867735385895,
-0.004924447741359472,
-0.005138839595019817,
0.09975285828113556,
0.017653364688158035,
0.024656692519783974,
-0.05390695855021477,
0.03640998899936676,
-0.03326623886823654,
0.013516884297132492,
-0.01451967190951109,
0.003316898364573717,
0.022307751700282097,
0.04979874566197395,
0.013127117417752743,
0.05739531293511391,
0.0383547879755497,
-0.008321289904415607,
0.020930659025907516,
-0.026062745600938797,
-0.05572040006518364,
0.0036848215386271477,
0.01004651840776205,
-0.006548488512635231,
-0.010085254907608032,
-0.05785439535975456,
-0.001457174657844007,
-0.029960447922348976,
0.006840840447694063,
-0.03467927500605583,
-0.0023860486689954996,
0.057964492589235306,
-0.007408713456243277,
-0.04087844118475914,
-0.010761121287941933,
-0.007240484934300184,
-0.01693260483443737,
-0.005595513619482517,
0.02824295312166214,
0.025190135464072227,
-0.02344009093940258,
0.031815193593502045,
0.015411065891385078,
0.06134862080216408,
-0.003994031809270382,
-0.008440671488642693,
0.03721427917480469,
-0.08290878683328629,
0.001493492047302425,
0.01564909517765045,
0.047367893159389496,
0.014143048785626888,
-0.027462929487228394,
-0.016948143020272255,
0.031632810831069946,
0.007749781012535095,
-0.007436301559209824,
-0.015760039910674095,
-0.012993184849619865,
0.013105862773954868,
-0.015409013256430626,
0.001105195377022028,
-0.02939557284116745,
0.059663932770490646,
-0.03541778028011322,
0.02350943349301815,
-0.002710886299610138,
0.019004790112376213,
-0.02161518856883049,
-0.0147108668461442,
-0.012403995729982853,
0.008582193404436111,
-0.036259546875953674,
-0.041921645402908325,
0.0038199510890990496,
-0.03548828139901161,
-0.006250226870179176,
0.02998635172843933,
0.022298092022538185,
0.04163128137588501,
0.009395718574523926,
0.007530478294938803,
-0.006565692834556103,
-0.052373193204402924,
0.08200909197330475,
0.0030134115368127823,
-0.014222513884305954,
-0.004154716618359089,
-0.024584295228123665,
0.019815118983387947,
0.03673921152949333,
-0.030933652073144913,
0.007070394232869148,
-0.022485971450805664,
-0.010884308256208897,
0.02197214588522911,
-0.02870122529566288,
-0.01008014939725399,
0.019299698993563652,
-0.029904304072260857,
-0.025561654940247536,
-0.08452670276165009,
0.030409572646021843,
0.034284088760614395,
0.01623472385108471,
0.036779262125492096,
0.0004154304333496839,
-0.011639886535704136,
-0.022248366847634315,
0.016819989308714867,
-0.013740862719714642,
-0.009972917847335339,
-0.008207590319216251,
0.026046056300401688,
0.01283117476850748,
0.006952990777790546,
-0.01216099038720131,
0.008061929605901241,
0.024823477491736412,
0.02339966595172882,
-0.009019573219120502,
0.0314980074763298,
-0.042007360607385635,
0.04582592099905014,
0.011335751041769981,
0.0032871265430003405,
-0.04131104052066803,
0.005773188080638647,
0.0027509555220603943,
-0.05195967108011246,
-0.0028762423899024725,
0.005939770024269819,
0.011339160613715649,
-0.007477718871086836,
0.01048899907618761,
0.040396444499492645,
-0.021295342594385147,
0.0043818093836307526,
0.017548875883221626,
-0.011059321463108063,
0.0026319969911128283,
-0.009169827215373516,
-0.021712027490139008,
0.07674980163574219,
-0.0408351868391037,
-0.04880741983652115,
0.03096115216612816,
-0.01917736977338791,
0.03370415419340134,
0.025413276627659798,
-0.03050263784825802,
-0.015130789950489998,
0.1041548028588295,
-0.0350307859480381,
-0.02780059538781643,
0.014365567825734615,
-0.028281565755605698,
-0.018120132386684418,
0.008054451085627079,
-0.023180963471531868,
-0.01878000609576702,
-0.008801786229014397,
0.054662156850099564,
0.022664478048682213,
-0.015205493196845055,
0.007453403901308775,
-0.043500110507011414,
-0.01315005961805582,
0.049559563398361206,
0.01861002668738365,
0.009835097938776016,
-0.011211616918444633,
0.04517548531293869,
0.004009935539215803,
0.02272995002567768,
0.0017452137544751167,
-0.015638846904039383,
-0.0860428735613823,
-0.04204997047781944,
-0.00025026570074260235,
-0.01452098973095417,
0.04108021408319473,
-0.03514055535197258,
0.0324133038520813,
0.0419536791741848,
-0.04741701856255531,
-0.031452108174562454,
-0.024461649358272552,
-0.04829375818371773,
-0.02642655372619629,
-0.022884396836161613,
-0.011219148524105549,
0.04360942170023918,
0.028735248371958733,
0.06001383811235428,
-0.0014265108620747924,
-0.012206249870359898,
-0.004297425504773855,
-0.006859147921204567,
-0.031253185123205185,
0.021480010822415352,
0.010600446723401546,
-0.003866049228236079,
0.0686771497130394,
-0.020862985402345657,
-0.022526100277900696,
0.016956936568021774,
-0.004634427838027477,
-0.0059178490191698074,
-0.0026927513536065817,
0.004004367161542177,
0.008597806096076965,
0.012812310829758644,
0.013058378361165524,
-0.004336210899055004,
-0.006698319222778082,
0.043120354413986206,
0.041135210543870926,
0.02133828029036522,
-0.02435268834233284,
0.01375180296599865,
0.024137957021594048,
-0.013076218776404858,
-0.016389263793826103,
0.03442487120628357,
-0.014868066646158695,
-0.04486497491598129,
0.004878370091319084,
-0.0013731379294767976,
0.04772651568055153,
-0.026816004887223244,
-0.012232583947479725,
0.008299946784973145,
0.005042504984885454,
0.026234040036797523,
0.04305749014019966,
0.03051970712840557,
0.034889087080955505,
-0.0023049581795930862,
0.00524479802697897,
-0.013701563701033592,
0.017550569027662277,
-0.0107200238853693,
-0.014211129397153854,
-0.0023723989725112915,
0.032718196511268616,
0.012939666397869587,
0.01868096925318241,
-0.039753567427396774,
-0.04064379632472992,
0.022828448563814163,
-0.0033331902232021093,
0.04184219241142273,
-0.0003989459073636681,
-0.06987134367227554,
-0.00952367763966322,
-0.023452313616871834,
0.0020005989354103804,
-0.012901375070214272,
0.02910144254565239,
-0.04792792722582817,
-0.020093321800231934,
-0.005933248437941074,
0.02737804688513279,
0.03807863965630531,
0.001731823431327939,
-0.007111805956810713,
0.00403141975402832,
-0.007107721175998449,
0.027293860912322998,
-0.06147528067231178,
0.004276422318071127,
-0.006696862634271383,
-0.018643246963620186,
-0.017756083980202675,
0.0018478884594514966,
-0.01381042879074812,
0.025914616882801056,
0.051860492676496506,
-0.019501496106386185,
0.0009635307942517102,
-0.007669075857847929,
0.005703777074813843,
0.05990087613463402,
0.021224141120910645,
-0.011442276649177074,
0.07398616522550583,
-0.030970493331551552,
-0.001157855149358511,
0.006796502973884344,
-0.04123301059007645,
-0.018674325197935104,
0.019901776686310768,
-0.009747968055307865,
0.02438543736934662,
-0.021350577473640442,
-0.013351640664041042,
0.04953116551041603,
-0.04200427979230881,
0.01420557126402855,
0.028259335085749626,
-0.05107974633574486,
-0.03406394273042679,
0.06073637306690216,
0.022645199671387672,
0.04097743332386017,
0.0038327311631292105,
0.003432775381952524,
-0.0005429698503576219,
0.0036068132612854242,
-0.0025086512323468924,
0.04720258712768555,
0.012254728004336357,
0.01444457471370697,
-0.004205271601676941,
-0.00830148160457611,
0.014925207011401653,
0.01325000636279583,
-0.026741009205579758,
0.04135673865675926,
-0.01998615451157093,
-0.03758662939071655,
0.02200416475534439,
-0.01787281222641468,
0.03206925839185715,
0.006582573521882296,
-0.037438854575157166,
0.07829650491476059,
-0.06782419234514236,
0.03303571045398712,
0.003675847314298153,
-0.005879801232367754,
-0.014420771040022373,
0.025744589045643806,
0.0049856179393827915,
0.05461924895644188,
0.012218186631798744,
0.01156366616487503,
-0.007837564684450626,
0.022385118529200554,
0.04674582928419113,
-0.07826529443264008,
0.008070485666394234,
-0.0006503494223579764,
-0.0011087222956120968,
-0.045825134962797165,
-0.010158201679587364,
-0.01651146076619625,
-0.042227987200021744,
0.014807607047259808,
0.020383423194289207,
-0.029208006337285042,
-0.016493378207087517,
-0.05368971824645996,
-0.030794598162174225,
0.016513269394636154,
-0.003976314794272184,
-0.02403370663523674,
-0.04109552875161171,
0.014894145540893078,
-0.03173813596367836,
0.011136709712445736
] |
<p>When an coil rotor is moving around a magnetic field there is -V induced to resist the input V.</p>
<p>Let's take an example, a 12 V DC motor induces -10V, and the actual running voltage is 2V.</p>
<p>If there we're no -V in the process, the motor would preform a lot better?
What is the advantages and disadvantages of counter EMF? Is it wasting energy?</p>
<p>I understand the concept, but I can not fathom how initially, the motor runs at 12V then drops to 2V(actual) and still preforms the same?
Are all current motors today lose 70%+ of their input voltage due to counter EMF?</p>
| 7,632 |
[
-0.013915589079260826,
0.008809246122837067,
-0.010156236588954926,
-0.01817084662616253,
0.0313052237033844,
0.02182784676551819,
-0.014584284275770187,
-0.010348017327487469,
0.027005881071090698,
-0.03955146297812462,
0.0010189629392698407,
0.0660102367401123,
0.0317671112716198,
-0.0038456516340374947,
0.04081518203020096,
-0.014462917111814022,
0.013336006551980972,
-0.028101863339543343,
0.011482511647045612,
-0.009748057462275028,
-0.019223561510443687,
-0.0043933033011853695,
0.03964387997984886,
0.021657120436429977,
-0.0360342338681221,
0.020851463079452515,
0.03507966920733452,
-0.014347097836434841,
0.02358699031174183,
0.035041242837905884,
-0.013109538704156876,
-0.018127350136637688,
-0.013741947710514069,
0.040091365575790405,
0.02391124702990055,
0.01616048812866211,
0.0025708621833473444,
-0.07229742407798767,
-0.018027255311608315,
0.045582305639982224,
-0.03309505805373192,
0.0424155592918396,
0.006558986380696297,
0.06878460198640823,
0.010614675469696522,
-0.014476491138339043,
-0.011635340750217438,
0.010978646576404572,
0.04087340086698532,
-0.08360612392425537,
0.02414177544414997,
-0.029779551550745964,
0.012203867547214031,
0.014530704356729984,
0.012792181223630905,
0.020472194999456406,
0.0946623831987381,
0.04761944338679314,
0.009563499130308628,
-0.018659304827451706,
0.00879630632698536,
-0.01683749631047249,
-0.03508011996746063,
-0.030492493882775307,
-0.008934155106544495,
0.04468459635972977,
0.029642848297953606,
0.007525545544922352,
0.06543022394180298,
-0.015861790627241135,
0.05773597210645676,
-0.008222985081374645,
0.0070722270756959915,
-0.005537572782486677,
0.013434591703116894,
-0.03020142950117588,
0.03561832755804062,
0.031570129096508026,
0.0036577139981091022,
0.05468612536787987,
-0.05861705169081688,
-0.016130851581692696,
0.014117973856627941,
0.0749005600810051,
-0.029396556317806244,
-0.015094868838787079,
0.01927175559103489,
-0.01954934373497963,
0.048066236078739166,
0.01381558459252119,
0.010392526164650917,
0.0362074039876461,
0.038995224982500076,
-0.03125564754009247,
-0.03203389421105385,
0.03368460014462471,
-0.00882883369922638,
0.03821852430701256,
0.02227194793522358,
-0.01572209782898426,
-0.02632404863834381,
0.024483272805809975,
0.028467364609241486,
0.05935843288898468,
-0.009656481444835663,
-0.011744983494281769,
-0.017340298742055893,
0.001497593941166997,
-0.049464158713817596,
0.020445410162210464,
-0.05955449491739273,
-0.013069266453385353,
0.02671971544623375,
-0.028464559465646744,
0.025737283751368523,
-0.02341131493449211,
-0.0027433251962065697,
-0.002558184787631035,
0.028233245015144348,
0.042139071971178055,
0.013506603427231312,
0.0006383952568285167,
0.03645744174718857,
-0.00939594954252243,
-0.041930191218853,
-0.018655486404895782,
0.02888421341776848,
0.0067672948352992535,
-0.02533489651978016,
0.0213128961622715,
0.0017301032785326242,
-0.0382990688085556,
0.02109992876648903,
0.02699771709740162,
0.06102216616272926,
0.0003178772167302668,
-0.08168469369411469,
-0.08323149383068085,
0.034439753741025925,
-0.04286171868443489,
-0.009575619362294674,
-0.07530692964792252,
0.02612294815480709,
0.028954949229955673,
0.06838567554950714,
0.01827647164463997,
-0.04019007831811905,
-0.01762988604605198,
0.016413694247603416,
-0.0016606745775789022,
0.03211004287004471,
-0.04517276957631111,
-0.014936328865587711,
-0.009666683152318,
-0.02619769051671028,
-0.03384013846516609,
0.04526568204164505,
0.01987338252365589,
-0.004705806728452444,
-0.0005211978568695486,
0.02685352973639965,
-0.02771260030567646,
-0.014148850925266743,
0.02515392191708088,
-0.02328941412270069,
-0.035453829914331436,
0.07345467805862427,
0.012681649066507816,
0.022019369527697563,
0.024149684235453606,
0.026868600398302078,
0.034265175461769104,
0.017655981704592705,
0.01957068033516407,
0.04382747784256935,
-0.0338335782289505,
-0.0319526381790638,
-0.017978211864829063,
0.058093104511499405,
-0.0326034277677536,
-0.0328519307076931,
-0.05427025258541107,
0.010586047545075417,
0.027155058458447456,
0.010714308358728886,
0.026898609474301338,
-0.012114259414374828,
-0.0003571325505618006,
0.06885064393281937,
-0.03987633436918259,
-0.04340749979019165,
-0.056426603347063065,
0.043163951486349106,
-0.0010245096636936069,
-0.02765168622136116,
0.0357951745390892,
0.02684308961033821,
0.023145144805312157,
-0.01840951479971409,
-0.03868194296956062,
0.005678921472281218,
0.007053433917462826,
0.0022018069867044687,
0.004369393922388554,
0.011639051139354706,
0.006481992546468973,
0.04908154532313347,
-0.018386784940958023,
0.058245230466127396,
-0.0377703458070755,
-0.06454338133335114,
-0.02391080930829048,
-0.027583599090576172,
-0.002719127107411623,
0.036938104778528214,
-0.01757223904132843,
0.04548591002821922,
0.004918897524476051,
-0.018755171447992325,
0.015730999410152435,
-0.04166961833834648,
0.07759854942560196,
0.07829173654317856,
0.008927740156650543,
0.001594266970641911,
0.04648810625076294,
-0.009568034671247005,
0.014629621990025043,
-0.03705776855349541,
-0.042459141463041306,
-0.03914639726281166,
-0.012596221640706062,
0.05820542946457863,
0.03420918434858322,
-0.032775942236185074,
0.02548753283917904,
0.05045589432120323,
0.012494903057813644,
0.025731943547725677,
0.024687930941581726,
-0.026686565950512886,
-0.03311322256922722,
0.03334956243634224,
0.025089900940656662,
0.007261388469487429,
0.022799279540777206,
0.017828356474637985,
0.038361407816410065,
-0.01629033125936985,
0.03704140707850456,
-0.04030872508883476,
0.05312570929527283,
0.0036243884824216366,
0.01081215962767601,
-0.0013372910907492042,
-0.03211984038352966,
0.020731819793581963,
-0.030383802950382233,
0.021197468042373657,
0.0035237553529441357,
-0.008100556209683418,
0.035825472325086594,
-0.02917405031621456,
-0.04392264410853386,
-0.014248786494135857,
-0.02031785622239113,
-0.01040518470108509,
-0.02895054966211319,
0.019600629806518555,
-0.029208704829216003,
0.001343994284979999,
-0.023485790938138962,
0.0060710180550813675,
-0.04903165251016617,
0.023820893839001656,
0.016918638721108437,
-0.04746275395154953,
0.021643908694386482,
-0.033017080277204514,
-0.005655874963849783,
-0.03463394567370415,
-0.017291562631726265,
0.020833980292081833,
0.030432581901550293,
-0.033850762993097305,
-0.0022259976249188185,
-0.01540634036064148,
-0.020615624263882637,
0.07440440356731415,
-0.001395747414790094,
-0.011477017775177956,
-0.0006965231150388718,
0.03474904224276543,
-0.06254737079143524,
0.0037935615982860327,
0.0020071654580533504,
-0.015101552940905094,
0.020821664482355118,
-0.03650325536727905,
0.06868965923786163,
-0.023231064900755882,
-0.02321663312613964,
0.019229603931307793,
-0.09230396896600723,
-0.04006445035338402,
0.004438442178070545,
-0.04087822511792183,
0.08351751416921616,
-0.061761852353811264,
0.03499329462647438,
0.026585090905427933,
-0.030929740518331528,
0.003959315363317728,
-0.04860321432352066,
-0.020289817824959755,
-0.02031783200800419,
-0.005174539051949978,
0.05078491196036339,
0.0000323820422636345,
-0.044983819127082825,
0.07694166153669357,
0.03476092964410782,
-0.0337132029235363,
-0.007007065694779158,
-0.0314037948846817,
0.008811518549919128,
-0.06673955172300339,
-0.013370286673307419,
0.0560622476041317,
-0.03411766141653061,
0.0024883863516151905,
0.0029065338894724846,
-0.013596754521131516,
0.028347700834274292,
0.002471903106197715,
-0.025122571736574173,
0.010157822631299496,
-0.01801382005214691,
-0.020684843882918358,
0.06659959256649017,
-0.00432481337338686,
-0.0065737213008105755,
0.025130020454525948,
0.0032935766503214836,
0.05242590233683586,
-0.013305424712598324,
-0.0012420362327247858,
0.062569759786129,
-0.05127175152301788,
0.05763194337487221,
-0.03128717094659805,
0.036046117544174194,
-0.027100220322608948,
0.012028515338897705,
0.0032201381400227547,
0.0005222869222052395,
0.03723083809018135,
-0.0348537415266037,
-0.004815252032130957,
0.0017404895043000579,
0.02299658954143524,
-0.008892146870493889,
-0.01218455471098423,
-0.02230335772037506,
-0.016434062272310257,
-0.005962868686765432,
-0.011104551143944263,
0.006899076979607344,
0.055903781205415726,
0.06102496013045311,
0.015233236365020275,
0.017352841794490814,
-0.015282871201634407,
-0.007348923943936825,
-0.046333298087120056,
-0.03706754371523857,
-0.004595844075083733,
0.03183560445904732,
0.013091660104691982,
0.044473934918642044,
0.005534352269023657,
-0.012640771456062794,
0.019526442512869835,
-0.02806192822754383,
-0.11295506358146667,
0.014524479396641254,
-0.039899419993162155,
0.007421933114528656,
-0.0067973327822983265,
-0.007387862540781498,
0.029376456514000893,
-0.008014997467398643,
-0.02965046651661396,
-0.025814302265644073,
-0.002362800994887948,
-0.05421747639775276,
0.01858990266919136,
-0.0008054763893596828,
-0.0007340222364291549,
-0.05392872914671898,
0.016385899856686592,
0.028348447754979134,
-0.04436199739575386,
-0.003100144909694791,
-0.0001605750439921394,
-0.06172405928373337,
0.011890336871147156,
-0.0191442109644413,
0.0028624660335481167,
-0.013412434607744217,
0.022926462814211845,
0.03496072441339493,
0.019648568704724312,
-0.05852449685335159,
0.01281225960701704,
0.01896052435040474,
0.03635084629058838,
0.05346665158867836,
-0.02079256996512413,
-0.0007239359547384083,
-0.06890209019184113,
-0.04093071073293686,
-0.003446632530540228,
0.04205308109521866,
0.029283935204148293,
0.0011515308870002627,
-0.014111896976828575,
0.020675895735621452,
0.0032105576246976852,
0.021421847864985466,
0.04240124672651291,
-0.005932304076850414,
0.016267813742160797,
-0.08429133147001266,
-0.046582747250795364,
-0.008163942024111748,
-0.029619522392749786,
0.038838788866996765,
-0.002034079283475876,
-0.0019876223523169756,
-0.003802048973739147,
0.037707023322582245,
0.019220275804400444,
0.012144748121500015,
0.017042767256498337,
-0.002258091699331999,
0.01831638067960739,
0.008881589397788048,
0.029624780640006065,
0.030630147084593773,
0.024217020720243454,
0.07154955714941025,
0.003822297090664506,
-0.04154890030622482,
-0.10145388543605804,
-0.022838817909359932,
0.06231417879462242,
0.04298766329884529,
-0.01985698565840721,
-0.009314837865531445,
-0.020788179710507393,
-0.03890279307961464,
0.07112126052379608,
-0.07932672649621964,
0.028628312051296234,
-0.042132001370191574,
-0.029581496492028236,
-0.024998214095830917,
-0.05839775875210762,
-0.003986515570431948,
0.019144147634506226,
0.0005333729786798358,
0.0460488498210907,
0.0012369254836812615,
-0.02199472300708294,
-0.010840407572686672,
-0.02348301373422146,
-0.001682070316746831,
0.0690314918756485,
-0.025059109553694725,
-0.0034068753011524677,
0.0021368765737861395,
0.026613987982273102,
-0.022708486765623093,
-0.0686315968632698,
-0.006975223310291767,
-0.03016592003405094,
0.012993923388421535,
0.018700001761317253,
-0.02072766423225403,
-0.03847130388021469,
0.01576784811913967,
0.0028231232427060604,
0.025657936930656433,
0.000779617577791214,
-0.0563686229288578,
0.01884200982749462,
0.01743972860276699,
-0.01598530448973179,
0.07407673448324203,
-0.023773739114403725,
-0.031145861372351646,
0.021449018269777298,
0.014934343285858631,
0.021775275468826294,
-0.008589412085711956,
0.019878719002008438,
-0.03260776400566101,
0.01739284209907055,
-0.0013749176869168878,
0.08121953159570694,
-0.03196197375655174,
0.02155960537493229,
-0.022691702470183372,
0.010088063776493073,
0.00031488604145124555,
0.005178437568247318,
-0.0030244258232414722,
-0.0456809364259243,
0.02808338589966297,
0.010982350446283817,
-0.011965814046561718,
0.001114344922825694,
0.0345446802675724,
-0.006916275713592768,
-0.0027984592597931623,
0.008453711867332458,
-0.020521560683846474,
-0.009089497849345207,
-0.046578649431467056,
-0.015831682831048965,
0.027492260560393333,
-0.05996117740869522,
0.03654709458351135,
-0.018067343160510063,
-0.04186149686574936,
0.009441333822906017,
-0.023274004459381104,
-0.012244034558534622,
0.038912273943424225,
-0.03625306487083435,
0.02232617326080799,
-0.04141268879175186,
0.030581548810005188,
0.01726151816546917,
-0.013820545747876167,
-0.051226552575826645,
-0.06294874846935272,
0.012131113559007645,
-0.005768416915088892,
0.013040984980762005,
-0.012176785618066788,
-0.050535641610622406,
0.0006498469738289714,
-0.03769807890057564,
0.03504595905542374,
0.039675623178482056,
-0.02973172813653946,
0.03403044119477272,
0.044244688004255295,
0.03708728402853012,
0.02928905375301838,
0.0025032036937773228,
-0.05940533056855202,
0.02987680211663246,
-0.0518551766872406,
-0.054639704525470734,
-0.02780134417116642,
0.020752262324094772,
-0.02382744662463665,
-0.006930955220013857,
0.01214319746941328,
-0.014696083031594753,
0.015739768743515015,
-0.003363374387845397,
-0.003661918919533491,
0.03504703566431999,
-0.01852453127503395,
0.010300029069185257,
-0.03521544113755226,
-0.0011674616253003478,
0.002931178081780672,
0.03336002677679062,
0.026903880760073662,
-0.008609051816165447,
-0.049772050231695175,
-0.018896764144301414,
0.06631999462842941,
0.030163530260324478,
-0.009698032401502132,
-0.018232379108667374,
0.03753099590539932,
-0.07076947391033173,
0.028728069737553596,
0.008593977428972721,
-0.016759885475039482,
0.008993908762931824,
-0.012029686011373997,
0.04559020698070526,
0.02048509195446968,
0.0074688768945634365,
-0.0383821576833725,
-0.011155174113810062,
-0.01610528491437435,
0.004460345953702927,
0.04623378813266754,
-0.012175082229077816,
0.06739203631877899,
-0.012095515616238117,
0.0002952883078251034,
-0.004642251413315535,
-0.03305819630622864,
-0.032212089747190475,
-0.007296633906662464,
-0.040061336010694504,
0.019300874322652817,
0.012496168725192547,
-0.002153135370463133,
0.02519148588180542,
0.01911749690771103,
-0.012866667471826077,
0.015746857970952988,
0.04445163160562515,
0.03541284427046776,
0.042903024703264236,
0.010199761018157005,
-0.02836226299405098,
0.031220605596899986,
-0.029570234939455986,
0.03782576322555542,
-0.01191108487546444,
-0.0006184267112985253,
0.06417692452669144,
-0.007604914251714945,
0.019217614084482193,
-0.07946507632732391,
-0.020680788904428482,
-0.0232639629393816,
0.025844596326351166,
-0.004392449744045734,
-0.036136142909526825,
0.006108887959271669,
0.04176294058561325,
0.023050839081406593,
-0.015529440715909004,
-0.003119603032246232,
-0.00943738128989935,
-0.08793240040540695,
0.009079994633793831,
-0.02815067768096924,
-0.002276115585118532,
0.03551758825778961,
-0.024907927960157394,
0.016137341037392616,
0.01819438673555851,
-0.007811186369508505,
0.03637896105647087,
-0.007417923770844936,
0.01273777149617672,
-0.05853516608476639,
0.0527409166097641,
0.0073762740939855576,
0.0659034326672554,
-0.025181302800774574,
0.01872665248811245,
0.11781348288059235,
0.03564475104212761,
0.0032160310074687004,
-0.04441092535853386,
-0.018878329545259476,
-0.010486829094588757,
0.015240187756717205,
-0.018611686304211617,
0.0327238105237484,
-0.004297207575291395,
-0.0284705962985754,
0.020076848566532135,
0.002686697756871581,
0.023395398631691933,
-0.014464528299868107,
0.03412734717130661,
0.0022965825628489256,
-0.044226501137018204,
-0.014732375741004944,
0.030025659129023552,
-0.017153237015008926,
-0.0024573607370257378,
-0.024620505049824715,
0.01705452799797058,
-0.029662705957889557,
0.00841102097183466,
-0.001197062199935317,
-0.06364407390356064,
0.02391701191663742,
0.015024139545857906,
0.001634089509025216,
0.013799821957945824,
0.003444832284003496,
-0.00603274954482913,
-0.026511074975132942,
0.008761165663599968,
0.022046945989131927,
0.04147500544786453,
-0.014397955499589443,
0.042664527893066406,
0.03369565308094025,
-0.009887187741696835,
-0.012992559932172298,
0.011641609482467175,
-0.06692156195640564,
0.05061303824186325,
-0.04530077427625656,
0.04442266747355461,
0.0015500948065891862,
0.04103473201394081,
0.007525337394326925,
0.02073723077774048,
0.01086196769028902,
-0.027605194598436356,
-0.04681077226996422,
-0.003570569446310401,
0.014378096908330917,
-0.014620766043663025,
-0.044615671038627625,
-0.021541165187954903,
0.04119851812720299,
-0.0032258806750178337,
-0.0013708493206650019,
0.014838702976703644,
0.0074788355268538,
0.015592463314533234,
-0.006804587319493294,
0.02861042693257332,
-0.004832542035728693,
-0.025411726906895638,
-0.016730627045035362,
0.014627148397266865,
-0.013620372861623764,
-0.001894483924843371,
-0.009195965714752674,
0.022115059196949005,
0.009674745611846447,
-0.012130357325077057,
-0.01816977933049202,
-0.0017335755983367562,
-0.061938200145959854,
0.03402112424373627,
0.029014604166150093,
-0.000531266734469682,
0.002014641184359789,
0.0032172317150980234,
0.010057633742690086,
0.007616609800606966,
-0.025696726515889168,
0.020253857597708702,
-0.00520027382299304,
0.06235603243112564,
-0.004242014605551958,
0.008217056281864643,
-0.053362276405096054,
0.0008430372690781951,
-0.041077759116888046,
0.010232441127300262,
-0.009416929446160793,
0.04844321683049202,
0.022275904193520546,
-0.0010889570694416761,
0.025807131081819534,
0.016629690304398537,
-0.0015615449519827962,
-0.020588435232639313,
0.011827012524008751,
-0.03328244760632515,
-0.006306379102170467,
-0.009614397771656513,
-0.009485543705523014,
-0.015574091114103794,
-0.028142262250185013,
0.00495500210672617,
-0.013760972768068314,
-0.016061272472143173,
0.009989112615585327,
-0.01693876087665558,
-0.020397551357746124,
-0.04615011811256409,
0.054005350917577744,
-0.05269839987158775,
0.0010698615806177258,
-0.04311184585094452,
0.016655562445521355,
-0.00211068126372993,
0.0045110867358744144,
0.023686107248067856,
0.01392651442438364,
0.006824469659477472,
0.031582336872816086,
-0.0034824770409613848,
0.03195318579673767,
0.008874519728124142,
0.02941458858549595,
0.039765793830156326,
0.008860044181346893,
0.050903305411338806,
-0.02580730803310871,
-0.04998868331313133,
0.06543071568012238,
-0.015432748012244701,
-0.03896864503622055,
0.02504967525601387,
0.014158644713461399,
0.004341466818004847,
0.01285069901496172,
-0.008082730695605278,
0.007550894282758236,
0.01242718007415533,
0.013232364319264889,
0.011340591125190258,
0.022871743887662888,
-0.027871236205101013,
-0.0035701263695955276,
0.013137418776750565,
0.02033820189535618,
-0.020081590861082077,
-0.0000524013776157517,
0.011500455439090729,
0.033229779452085495,
-0.01638106256723404,
-0.03029581904411316,
-0.0019331079674884677,
0.028391635045409203,
-0.0057191490195691586,
0.006505998317152262,
0.011831025592982769,
0.007579753175377846,
-0.023553883656859398,
-0.008341090753674507,
0.002170129679143429,
-0.03522788733243942,
-0.04597768932580948,
-0.05893370881676674,
-0.005528297740966082,
-0.011199434287846088,
0.014901351183652878,
0.00008761178469285369,
-0.026760932058095932,
-0.0031191345769912004,
0.00045783829409629107,
-0.08414266258478165,
0.012895433232188225,
-0.004585448186844587,
-0.04946933314204216,
-0.01146495807915926,
-0.018011804670095444,
-0.017379209399223328,
0.024713270366191864,
-0.012828654609620571,
0.014842352829873562,
0.01518481969833374,
-0.009501131251454353,
-0.0016861781477928162,
-0.0428946353495121,
-0.009217821061611176,
0.0056786383502185345,
-0.04045203700661659,
0.01682877354323864,
0.045876309275627136,
0.007622790057212114,
-0.020282292738556862,
0.03733743727207184,
-0.021234164014458656,
0.010395396500825882,
-0.019120126962661743,
0.03069842793047428,
-0.00857267715036869,
0.03800034895539284,
0.01751197874546051,
-0.01272672601044178,
-0.011292317882180214,
-0.012156535871326923,
0.010651358403265476,
0.013829286210238934,
-0.0022714431397616863,
0.05995776876807213,
0.02736138552427292,
-0.0010831364197656512,
0.014964479953050613,
0.015069550834596157,
-0.045512232929468155,
-0.013695034198462963,
0.0004323984612710774,
0.03372008726000786,
0.03056318499147892,
-0.012943783774971962,
0.016047028824687004,
-0.045810259878635406,
-0.0360029973089695,
0.01206610444933176,
-0.0003884857287630439,
0.004192881286144257,
0.00786203145980835,
-0.009149736724793911,
-0.001777605270035565,
0.039562150835990906,
0.017815930768847466,
0.022522179409861565,
-0.016070937737822533,
0.011385680176317692,
0.02919812873005867,
0.003742422442883253,
-0.02840724214911461,
-0.026862476021051407,
-0.03482992947101593,
0.02999553084373474,
0.01011489238590002,
0.03296056389808655,
0.000725016463547945,
-0.05128157511353493,
-0.006911312695592642,
-0.03504045680165291,
0.036645837128162384,
-0.00796908512711525,
-0.027929343283176422,
-0.017363622784614563,
-0.03584986552596092,
0.015005658380687237,
-0.01003844104707241,
0.025615278631448746,
0.024895569309592247,
-0.018172545358538628,
0.031240304931998253,
0.008412822149693966,
0.033498164266347885,
-0.057258181273937225,
0.029371686279773712,
-0.012640138156712055,
-0.02152405120432377,
0.034807246178388596,
-0.004201709758490324,
-0.024819204583764076,
0.031526852399110794,
0.03748790919780731,
0.02121449075639248,
-0.019622577354311943,
-0.03742341324687004,
-0.03188905492424965,
0.03657782822847366,
0.03992642089724541,
0.0387299582362175,
0.05930529907345772,
-0.03722130134701729,
0.04856594651937485,
-0.03253455460071564,
0.0010787469800561666,
-0.04486092925071716,
0.010555357672274113,
-0.029822103679180145,
0.006955394987016916,
-0.032023586332798004,
-0.0035830489359796047,
0.06497400999069214,
-0.007115000858902931,
-0.014379418455064297,
0.02700124867260456,
-0.01911943592131138,
0.0014618930872529745,
0.04186755046248436,
0.010009577497839928,
0.01574474573135376,
0.012121298350393772,
0.04201320931315422,
-0.03130899742245674,
0.021946029737591743,
-0.03588887304067612,
0.031094152480363846,
0.007020705845206976,
-0.030618812888860703,
-0.03035791963338852,
0.05882153660058975,
-0.03378457576036453,
0.022069303318858147,
0.015091665089130402,
0.02649003267288208,
-0.038795534521341324,
-0.027430767193436623,
0.0135895274579525,
-0.005708775483071804,
0.017939915880560875,
0.018491646274924278,
-0.012315398082137108,
0.07219725847244263,
-0.052091602236032486,
0.003216054290533066,
-0.026728389784693718,
-0.011422590352594852,
-0.007946189492940903,
-0.010405801236629486,
-0.008723786100745201,
0.07115381211042404,
0.0035891286097466946,
-0.002961794612929225,
-0.008668212220072746,
-0.006926358211785555,
0.05999504029750824,
0.009088813327252865,
0.04281559959053993,
0.0012456466211006045,
-0.046242307871580124,
-0.0007931571453809738,
-0.01626812480390072,
-0.05492645874619484,
-0.060187581926584244,
-0.01688482239842415,
0.06206643953919411,
0.021922403946518898,
-0.010997846722602844,
-0.04316091537475586,
0.004769761580973864,
-0.01979764550924301,
-0.01675279811024666,
0.0034004084300249815,
-0.02423355169594288,
0.007391177583485842,
0.046307675540447235,
-0.0032704295590519905
] |
<p>The question relates to <a href="http://physics.stackexchange.com/questions/53148/in-qft-why-does-a-vanishing-commutator-ensure-causality">this post</a>.</p>
<p>As shown in Peskin and Schroeder's introduction to quantum field theory p. 28.,</p>
<p>$$[\phi(x),\phi(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$,</p>
<p>which implies the measurements between two spacelike places do not affect each other. However, in the EPR paradox, even two experiments are spacelike separated, once experimentalist $A$ obtained $+$ result of $S_z$, $B$ has to obtain $-$.</p>
<p>Though at this stage of EPR, no information is delivered. It still seems to me, actually, that the two measurements affect each other. Is there any further reasoning to reconcile this inconsistency?</p>
| 7,633 |
[
0.016840917989611626,
-0.0009427714976482093,
-0.010414707474410534,
-0.01806207373738289,
0.020617056638002396,
-0.0024211902637034655,
-0.03835909068584442,
-0.04135626181960106,
0.010865626856684685,
-0.0023860621731728315,
0.016082769259810448,
0.006346557755023241,
0.05393187701702118,
0.02619011141359806,
-0.017392205074429512,
-0.006431295536458492,
-0.03833583742380142,
-0.004657489247620106,
0.010841857641935349,
-0.038102611899375916,
-0.012157653458416462,
0.05583522096276283,
0.018591556698083878,
0.024600457400083542,
-0.02877863496541977,
-0.017275292426347733,
-0.000010678129001462366,
0.0034186418633908033,
0.0004379519377835095,
0.06896714121103287,
-0.03712036833167076,
-0.026398465037345886,
-0.024657512083649635,
0.05946679040789604,
0.007248423993587494,
-0.022122571244835854,
-0.0025157120544463396,
-0.032450366765260696,
-0.0035246594343334436,
-0.0006093692500144243,
-0.021439606323838234,
-0.024597298353910446,
-0.009190141223371029,
0.07665782421827316,
-0.01741056889295578,
-0.009226745925843716,
-0.005200001411139965,
0.013617856428027153,
0.06417083740234375,
-0.03955141454935074,
0.038273345679044724,
0.01747950166463852,
0.005458952859044075,
0.02510589361190796,
0.0004538033972494304,
-0.000023577496904181316,
0.07814352214336395,
0.04140545427799225,
0.005250674206763506,
-0.0356002114713192,
-0.046043600887060165,
-0.021348850801587105,
-0.022864587604999542,
-0.032175347208976746,
-0.02839575707912445,
-0.015269811265170574,
0.025507327169179916,
0.012808406725525856,
0.02568899653851986,
-0.03729525953531265,
0.0033098876010626554,
0.03813410550355911,
0.027271363884210587,
-0.017339060083031654,
0.04270622134208679,
-0.0015682581579312682,
0.015315922908484936,
0.035142380744218826,
0.03535882756114006,
0.024234233424067497,
-0.0328221395611763,
-0.009432518854737282,
0.04975452274084091,
0.008237532339990139,
0.024292735382914543,
-0.021040013059973717,
0.04178823530673981,
-0.010510643944144249,
-0.01290661096572876,
0.024866271764039993,
-0.02088146097958088,
-0.01943441666662693,
0.03043178841471672,
-0.02939048781991005,
-0.014033205807209015,
0.057988040149211884,
-0.001650310354307294,
0.044437676668167114,
-0.00955270603299141,
-0.0370861180126667,
-0.021212026476860046,
-0.01569432206451893,
0.035132233053445816,
0.05532343313097954,
-0.005573259200900793,
0.005561348516494036,
-0.02774093672633171,
0.05571112781763077,
-0.0071031139232218266,
-0.03294840455055237,
-0.03156138211488724,
0.010937661863863468,
-0.021718885749578476,
0.001205520355142653,
0.009518144652247429,
-0.050837043672800064,
0.000932695169467479,
-0.015856817364692688,
0.035752348601818085,
0.06668466329574585,
0.04251037910580635,
-0.04857060685753822,
-0.025072939693927765,
-0.03585032746195793,
-0.045265763998031616,
0.005346071906387806,
0.04881954565644264,
-0.011669237166643143,
-0.01731884852051735,
0.038685254752635956,
0.04568607732653618,
0.012336643412709236,
0.0063017201609909534,
-0.009942751377820969,
0.014585481025278568,
0.03382493183016777,
-0.12112241983413696,
-0.03987056016921997,
0.04820855334401131,
-0.01371520571410656,
-0.0017983702709898353,
-0.06279729306697845,
-0.017023051157593727,
0.03145673871040344,
0.09544652700424194,
-0.015618120320141315,
-0.013009464368224144,
0.008172895759344101,
0.06227213889360428,
0.027857434004545212,
-0.0010672385105863214,
-0.011569272726774216,
-0.024741698056459427,
-0.07025445252656937,
-0.038163747638463974,
-0.03012911230325699,
0.032454848289489746,
0.06748348474502563,
0.0002186593337683007,
-0.0020438595674932003,
0.06835873425006866,
-0.015775203704833984,
0.0165469441562891,
0.006125313695520163,
0.006177831441164017,
-0.03647676855325699,
0.08798817545175552,
0.0295326579362154,
-0.0010787725914269686,
0.036456599831581116,
0.007346392143517733,
0.014227033592760563,
0.007175925187766552,
0.049074143171310425,
0.003755538258701563,
-0.032509393990039825,
-0.050883177667856216,
-0.0013802340254187584,
0.011126943863928318,
-0.04032714664936066,
-0.07584091275930405,
-0.025041135028004646,
-0.05030445381999016,
0.02316817082464695,
0.00781951192766428,
0.04383853077888489,
-0.02912704460322857,
0.01894696243107319,
0.025465747341513634,
-0.040891267359256744,
-0.03456518426537514,
-0.073638416826725,
0.0025862022303044796,
0.03560933843255043,
-0.057310763746500015,
0.05614279955625534,
-0.00710199074819684,
0.03139552101492882,
-0.023582732304930687,
-0.043352220207452774,
0.0073900832794606686,
0.030930716544389725,
0.00962688960134983,
0.012938753701746464,
0.004344089888036251,
0.03940535709261894,
0.0847979411482811,
0.021033694967627525,
0.025117475539445877,
-0.02472975105047226,
-0.05070401355624199,
0.027123885229229927,
0.014905771240592003,
-0.0053222342394292355,
-0.004248500801622868,
-0.008833141066133976,
0.024257849901914597,
0.01064888946712017,
-0.02326677180826664,
0.015534618869423866,
-0.044371347874403,
0.04415784031152725,
0.04091043397784233,
-0.014307212084531784,
-0.010346822440624237,
0.044767819344997406,
0.03533092513680458,
0.01571221649646759,
-0.01450344454497099,
-0.0634741261601448,
-0.030503902584314346,
-0.004921168088912964,
0.014146949164569378,
0.04205483943223953,
-0.02555195428431034,
0.0399407297372818,
0.00006604708323720843,
0.03356233239173889,
-0.0007790383533574641,
0.03583141416311264,
-0.002876645652577281,
-0.03020862117409706,
-0.001969157252460718,
0.008840370923280716,
0.010309276171028614,
0.005924327298998833,
0.012170189991593361,
-0.030224565416574478,
0.01656939648091793,
0.013856900855898857,
-0.01970410905778408,
0.006136993877589703,
-0.03677600622177124,
0.01920272968709469,
0.018239617347717285,
-0.001578845432959497,
0.003959625959396362,
0.03232983872294426,
0.04049251601099968,
0.007930319756269455,
-0.010133195668458939,
-0.005074578803032637,
-0.03404007479548454,
-0.010459113866090775,
0.05692439153790474,
-0.0009098975569941103,
-0.04554827883839607,
-0.00417212164029479,
0.007535083219408989,
-0.050817184150218964,
-0.008395003154873848,
-0.02720388025045395,
-0.003966654185205698,
0.01854802668094635,
0.0233475249260664,
0.04619860649108887,
0.01569344289600849,
0.04343076050281525,
-0.04855652153491974,
-0.0172969289124012,
-0.0069703771732747555,
-0.023581035435199738,
0.03941424563527107,
0.006510401144623756,
-0.052436068654060364,
0.007607961073517799,
-0.05676001310348511,
-0.021184580400586128,
0.02518611215054989,
-0.01997305080294609,
0.04228035360574722,
-0.011097979731857777,
-0.001500534126535058,
-0.0422787182033062,
-0.029392410069704056,
-0.03814937174320221,
0.019362296909093857,
-0.019191954284906387,
-0.038479071110486984,
0.051777325570583344,
-0.0172475203871727,
-0.05224258825182915,
0.018883919343352318,
-0.014670183882117271,
-0.030444083735346794,
0.018581021577119827,
-0.049492377787828445,
0.028160247951745987,
-0.05269496142864227,
-0.002482027979567647,
0.017701828852295876,
-0.022155283018946648,
-0.04688475281000137,
-0.0421413853764534,
-0.05934617295861244,
0.04104020074009895,
-0.012400840409100056,
0.013355636037886143,
-0.039682164788246155,
0.008727377280592918,
0.037907231599092484,
-0.00451586302369833,
0.007282510865479708,
-0.00021257225307635963,
0.016950704157352448,
-0.005549952387809753,
-0.016354888677597046,
-0.01392635703086853,
0.035566698759794235,
0.013063065707683563,
0.08468680828809738,
0.025050241500139236,
0.020900165662169456,
0.019789015874266624,
0.009254537522792816,
-0.023363150656223297,
0.00880589708685875,
0.02342216856777668,
0.004000323358923197,
0.047120679169893265,
0.016377456486225128,
-0.026000890880823135,
-0.04481114074587822,
0.01722332462668419,
0.0037881145253777504,
-0.031774234026670456,
-0.05570373311638832,
0.04197802394628525,
0.00027832313207909465,
0.04379802942276001,
-0.0037266667932271957,
0.0009453821112401783,
0.014223297126591206,
-0.036861736327409744,
-0.02781730890274048,
-0.02683081105351448,
0.028279323130846024,
-0.010133779607713223,
0.013032153248786926,
0.06394635885953903,
0.005600959528237581,
-0.04178744927048683,
-0.03471670299768448,
-0.004429845605045557,
-0.032139722257852554,
0.031863439828157425,
0.022560466080904007,
-0.05582518130540848,
0.022953463718295097,
0.026142358779907227,
0.013452193699777126,
-0.01615583896636963,
-0.03391045331954956,
-0.02080986648797989,
-0.05420142412185669,
0.01764112524688244,
0.004098068457096815,
0.020932460203766823,
0.01847255602478981,
0.021078389137983322,
0.017222465947270393,
-0.007334616035223007,
-0.033551331609487534,
-0.0018547929357737303,
-0.07991700619459152,
-0.013175874948501587,
-0.048548370599746704,
-0.02786732278764248,
-0.01569937728345394,
-0.026747940108180046,
0.027565382421016693,
-0.002420412842184305,
0.029550455510616302,
-0.011203724890947342,
-0.004611165728420019,
-0.08629149198532104,
-0.005216552410274744,
-0.03727882727980614,
-0.020342864096164703,
-0.040328413248062134,
0.0007826585206203163,
0.04239925742149353,
-0.007985799573361874,
0.015689242631196976,
0.013274366036057472,
-0.06438873708248138,
-0.012272738851606846,
-0.029316868633031845,
0.02143990993499756,
0.004829936195164919,
0.027969980612397194,
0.014681312255561352,
0.009045123122632504,
-0.0011029819725081325,
-0.0011585952015593648,
0.02707434631884098,
0.042088910937309265,
-0.008474744856357574,
-0.0395737960934639,
-0.03313517943024635,
-0.015019516460597515,
-0.012688815593719482,
-0.015438991598784924,
0.08906862884759903,
0.011499746702611446,
0.012337138876318932,
0.04158831015229225,
0.006085604429244995,
0.007430052384734154,
0.002794612431898713,
0.047131553292274475,
-0.007895001210272312,
-0.009488308802247047,
-0.026730794459581375,
0.003723764792084694,
-0.020114121958613396,
-0.012407869100570679,
0.006352744065225124,
0.00038759104791097343,
-0.014053547754883766,
-0.028559450060129166,
0.008153682574629784,
0.05826118215918541,
-0.0027209878899157047,
0.02248280681669712,
0.03137696906924248,
-0.005785826593637466,
0.004171454813331366,
0.016077643260359764,
0.005576677154749632,
0.029617970809340477,
0.023272870108485222,
0.024128131568431854,
-0.016121309250593185,
-0.038505759090185165,
-0.028166530653834343,
0.031489886343479156,
0.055298686027526855,
-0.005198221653699875,
-0.0010218211682513356,
-0.03535086289048195,
-0.024190044030547142,
0.056986816227436066,
-0.021634209901094437,
0.034787826240062714,
-0.010648705996572971,
-0.008358659222722054,
-0.03365028277039528,
-0.03876521438360214,
-0.027943529188632965,
0.042726144194602966,
0.0085823442786932,
0.015947043895721436,
0.006266450509428978,
-0.03255875036120415,
-0.004458483774214983,
-0.013026164844632149,
0.003746933536604047,
0.05795873701572418,
0.007863500155508518,
0.03864048793911934,
-0.002949455985799432,
0.01800219528377056,
0.0060276915319263935,
-0.09660741686820984,
0.031792834401130676,
0.007529635913670063,
-0.030221570283174515,
0.05613246187567711,
0.008154559880495071,
-0.04614870622754097,
0.025437744334340096,
0.007893471047282219,
-0.01526294182986021,
0.031783878803253174,
-0.02923613041639328,
0.08370448648929596,
0.022329337894916534,
0.0127840805798769,
0.06103035807609558,
-0.0010246273595839739,
-0.012375888414680958,
-0.03382139280438423,
0.006228107959032059,
0.05171656981110573,
-0.0007767626084387302,
0.01884743757545948,
-0.021520324051380157,
-0.008900719694793224,
-0.02505919337272644,
0.07069004327058792,
-0.022233804687857628,
0.013311157003045082,
-0.007330456282943487,
-0.019087711349129677,
-0.02527162805199623,
0.011110661551356316,
-0.03894471004605293,
0.011842561885714531,
-0.040010228753089905,
-0.003241993021219969,
0.01086004264652729,
-0.05317588150501251,
-0.015521018765866756,
0.009040125645697117,
0.009262336418032646,
0.01884440705180168,
-0.0284291822463274,
0.02784457616508007,
0.011902431026101112,
-0.009839664213359356,
-0.0072005316615104675,
-0.02175142429769039,
0.011327090673148632,
-0.001486202934756875,
-0.02659734897315502,
-0.0007294537499547005,
-0.01333611086010933,
-0.06236841902136803,
0.0006436646217480302,
-0.006173701491206884,
-0.01727893389761448,
-0.07943248748779297,
-0.0014883450930938125,
0.02251989021897316,
0.023122044280171394,
-0.09303635358810425,
-0.04622208699584007,
-0.0022784792818129063,
0.007512025069445372,
0.01884552463889122,
-0.008900837041437626,
0.0030500683933496475,
-0.028470918536186218,
-0.029824497178196907,
-0.042131539434194565,
0.03440722078084946,
-0.033666402101516724,
-0.010224850848317146,
-0.013397399336099625,
0.015760298818349838,
0.0168110691010952,
-0.042556282132864,
-0.010688243433833122,
0.034085310995578766,
-0.019708001986145973,
-0.020822705700993538,
0.020923426374793053,
0.04488197714090347,
-0.01963043585419655,
-0.05544160678982735,
-0.005905613768845797,
-0.006779391784220934,
0.01312309317290783,
-0.028559496626257896,
-0.0002806735865306109,
0.025090334936976433,
0.007315530441701412,
0.040868911892175674,
0.007395276799798012,
0.004865687806159258,
0.013283353298902512,
0.017293622717261314,
0.008083190768957138,
-0.01888747699558735,
-0.013139257207512856,
-0.03437243029475212,
0.01843809336423874,
0.01646028459072113,
-0.039325978606939316,
-0.0013165108393877745,
0.0647074356675148,
0.01075560413300991,
-0.008943847380578518,
0.0030191552359610796,
0.003951636143028736,
-0.015596124343574047,
-0.0058922432363033295,
0.027630679309368134,
0.011583087034523487,
-0.0172044038772583,
-0.02272786572575569,
-0.0017994935624301434,
-0.020549410954117775,
0.016305018216371536,
0.0762113630771637,
0.02584117092192173,
0.04364411160349846,
0.015007729642093182,
-0.030087484046816826,
-0.023214494809508324,
0.002742777345702052,
0.008455623872578144,
0.018090199679136276,
-0.003747948445379734,
0.020880041643977165,
-0.04041953757405281,
0.008428393863141537,
0.028101598843932152,
0.026285119354724884,
-0.026229387149214745,
-0.011245759204030037,
0.021490680053830147,
0.048537254333496094,
0.03122955746948719,
-0.027906974777579308,
-0.05802454054355621,
0.035679250955581665,
-0.033231884241104126,
0.03618944436311722,
0.0055197784677147865,
-0.007201840169727802,
0.02790062502026558,
0.024000633507966995,
-0.022966526448726654,
-0.03320494294166565,
-0.023327842354774475,
-0.07567169517278671,
-0.03236902505159378,
0.012346155941486359,
0.019202111288905144,
0.006292762700468302,
-0.025230810046195984,
0.019441045820713043,
0.016749240458011627,
0.01723531074821949,
0.003295457223430276,
-0.07083101570606232,
-0.011370876803994179,
-0.03784707188606262,
-0.004080248065292835,
0.09284931421279907,
-0.004481964278966188,
-0.03504841774702072,
0.005537423305213451,
-0.06583118438720703,
0.045865654945373535,
0.01544483844190836,
0.03351972997188568,
-0.0560595728456974,
0.03495442494750023,
0.008925219997763634,
0.01959243044257164,
-0.026465903967618942,
0.024859100580215454,
0.09118086099624634,
0.06907695531845093,
0.02780199982225895,
-0.0682184025645256,
0.015101880766451359,
0.02636968158185482,
0.003953218925744295,
-0.019292855635285378,
0.05876868590712547,
0.01225586049258709,
-0.0203007273375988,
-0.0009065883350558579,
0.06188897043466568,
0.03131870925426483,
-0.02876458503305912,
0.02525731734931469,
-0.061809640377759933,
-0.020175226032733917,
-0.011490867473185062,
0.024916356429457664,
0.004888562951236963,
-0.034156620502471924,
-0.017767494544386864,
0.021953046321868896,
-0.04370379447937012,
0.02600475586950779,
-0.03416811674833298,
-0.005109076853841543,
-0.004157732240855694,
0.009854194708168507,
-0.0014289825921878219,
0.010809692554175854,
0.013297267258167267,
-0.003241572994738817,
-0.05235108360648155,
0.0031740039121359587,
0.02524520456790924,
0.008687516674399376,
0.03921230509877205,
0.029690846800804138,
-0.008398803882300854,
0.0015927798813208938,
0.004476084839552641,
0.019857507199048996,
-0.058373432606458664,
-0.011138674803078175,
0.008082404732704163,
0.07838144153356552,
0.004276713356375694,
-0.0018861346179619431,
-0.006448950618505478,
-0.041602522134780884,
0.0015743045369163156,
-0.012988963164389133,
-0.048155080527067184,
0.003840178484097123,
0.006658714730292559,
-0.017558438703417778,
0.03686969727277756,
0.012997854501008987,
0.051352404057979584,
-0.030531814321875572,
-0.001261199708096683,
0.007306152489036322,
-0.019792720675468445,
0.0038865511305630207,
0.01942463591694832,
0.03226194530725479,
0.044044993817806244,
0.018875371664762497,
-0.024987874552607536,
-0.039374466985464096,
-0.03555253520607948,
0.004513712599873543,
0.021490272134542465,
0.03037414886057377,
0.042878154665231705,
-0.010716930963099003,
-0.005319548305124044,
-0.006540836300700903,
-0.054226212203502655,
0.008438668213784695,
-0.028641439974308014,
-0.023869499564170837,
-0.019279439002275467,
-0.007161459419876337,
0.03856602683663368,
0.03321292996406555,
0.0012223691446706653,
-0.02366119995713234,
0.002910902723670006,
0.06298638880252838,
0.005638173781335354,
-0.0056353467516601086,
-0.0035186728928238153,
-0.017440009862184525,
-0.037323642522096634,
0.0011294374708086252,
-0.018178081139922142,
0.007130792364478111,
-0.000552206882275641,
0.05365372821688652,
0.025706754997372627,
0.024752363562583923,
-0.03873046487569809,
-0.007055971305817366,
0.0170039813965559,
-0.028152523562312126,
0.011281291954219341,
0.023618575185537338,
0.018220072612166405,
-0.029877973720431328,
-0.044568803161382675,
0.02058800682425499,
0.00045689326361753047,
0.024015959352254868,
-0.0003239140205550939,
-0.03073699027299881,
-0.041783854365348816,
0.014583146199584007,
0.030465291813015938,
-0.00798055063933134,
0.011327167972922325,
-0.06856963783502579,
0.040406063199043274,
-0.016906315460801125,
0.0069870781153440475,
0.007343661971390247,
0.05778632313013077,
-0.023661604151129723,
-0.009296095930039883,
-0.014213982969522476,
0.021463729441165924,
-0.020539691671729088,
0.00786951556801796,
0.02472541667521,
0.02069064974784851,
0.0213951263576746,
0.016592487692832947,
-0.05011822655797005,
0.009313586167991161,
-0.05367020145058632,
-0.017425473779439926,
0.06696566194295883,
0.019620636478066444,
-0.0007053219014778733,
0.04454518109560013,
0.0023927742149680853,
-0.014154785312712193,
0.043605249375104904,
-0.008791280910372734,
0.0007174398633651435,
0.014614179730415344,
-0.04756101965904236,
-0.021879032254219055,
0.0038558177184313536,
0.04106994345784187,
0.0028361177537590265,
-0.010498067364096642,
0.022946849465370178,
0.03262421861290932,
-0.008681044913828373,
0.011128646321594715,
-0.00007685960008529946,
0.020753776654601097,
0.0022014316637068987,
0.01726670190691948,
-0.02765582501888275,
0.01130698248744011,
0.07464951276779175,
-0.025176942348480225,
0.006858500652015209,
0.02993496134877205,
0.03215445950627327,
-0.09643097221851349,
-0.02284134365618229,
0.019343649968504906,
0.052334755659103394,
0.020344486460089684,
-0.02505773864686489,
0.023448890075087547,
0.020698903128504753,
-0.08188100904226303,
0.02508906088769436,
0.012825531885027885,
-0.014277158305048943,
-0.03717983514070511,
-0.007582899648696184,
-0.03275139629840851,
0.02848155051469803,
0.057635266333818436,
0.039580389857292175,
-0.014675586484372616,
0.040550220757722855,
-0.030442481860518456,
-0.021673204377293587,
-0.06994316726922989,
-0.001298606744967401,
-0.001625956385396421,
-0.006693786475807428,
0.0758436769247055,
0.0010848151287063956,
-0.009361783042550087,
0.013437929563224316,
0.006802750751376152,
-0.030081091448664665,
-0.026948628947138786,
0.038576286286115646,
0.04304217919707298,
0.002126316074281931,
0.03728995844721794,
0.01814892143011093,
-0.010399891063570976,
-0.029729053378105164,
0.03555390238761902,
0.04164428636431694,
-0.02123812772333622,
-0.04013415426015854,
-0.004817028064280748,
-0.02053547278046608,
0.010009252466261387,
0.011404135264456272,
-0.015264005400240421,
-0.01911318674683571,
0.01431992370635271,
0.033858463168144226,
0.013911372981965542,
-0.005658566951751709,
0.004288928583264351,
-0.041641850024461746,
-0.04618373140692711,
0.030236443504691124,
0.011922583915293217,
-0.045126188546419144,
0.02142426185309887,
-0.052908726036548615,
-0.04851456731557846,
0.04189981147646904,
-0.013961110264062881,
0.020275618880987167,
-0.04323429614305496,
-0.03220367804169655,
-0.0052091460675001144,
-0.013723859563469887,
0.04294489696621895,
-0.05168521776795387,
-0.04821603745222092,
-0.0024259730707854033,
0.006400495767593384,
0.04713878408074379,
-0.029198486357927322,
-0.006001261994242668,
-0.022393839433789253,
-0.09280667454004288,
0.010000939480960369,
0.017869116738438606,
0.015240510925650597,
-0.041140954941511154,
-0.010948751121759415,
-0.010879307985305786,
0.014506030827760696,
0.040563419461250305,
-0.001058046706020832,
-0.029731331393122673,
0.03598954156041145,
0.019876990467309952,
0.03636819124221802,
-0.032658156007528305,
0.017402511090040207,
0.016429288312792778,
-0.012730378657579422,
0.002749842591583729,
-0.03750750049948692,
-0.0030115351546555758,
0.02086445689201355,
0.015853215008974075,
0.003151594428345561,
0.012987645342946053,
0.018832458183169365,
-0.04166719317436218,
0.061559878289699554,
-0.012636687606573105,
0.029104379937052727,
0.047808803617954254,
0.02189590409398079,
0.05004807189106941,
0.03755728900432587,
-0.006547139026224613,
-0.03674231842160225,
0.03803323954343796,
-0.028087498620152473,
0.005568970460444689,
0.03485790267586708,
0.024570835754275322,
0.008519577793776989,
-0.05057240650057793,
-0.01189104188233614,
0.0667702853679657,
-0.048559147864580154,
-0.012368961237370968,
0.06777720153331757,
-0.011802897788584232,
0.0035781250335276127,
0.02237105555832386,
-0.0027308505959808826,
0.031098732724785805,
0.02745579183101654,
0.03738556429743767,
0.0367046520113945,
0.01710766740143299,
0.014245697297155857,
-0.016337646171450615,
0.033451635390520096,
-0.01601838693022728,
0.0439545102417469,
0.009953959845006466,
0.0181865394115448,
-0.04806055873632431,
-0.00584051851183176,
0.016594914719462395,
-0.0025282909628003836,
0.010959119535982609,
0.020122984424233437,
-0.03053777478635311,
0.053966622799634933,
-0.020653752610087395,
0.01395644061267376,
-0.02726282924413681,
0.01887284405529499,
0.009725918062031269,
0.02076033316552639,
0.04024824500083923,
0.0392891950905323,
-0.010991046205163002,
-0.007133394945412874,
-0.04104060307145119,
-0.017699506133794785,
-0.004690139554440975,
-0.03938554972410202,
-0.007207135669887066,
-0.012768354266881943,
-0.03406308963894844,
0.026813849806785583,
-0.04469660297036171,
-0.01317557506263256,
-0.03355194628238678,
0.014926942065358162,
0.06604868173599243,
0.015447619371116161,
-0.038696400821208954,
0.019048865884542465,
-0.029779015108942986,
0.043164607137441635,
-0.04982712119817734,
-0.009177557192742825,
0.03481708839535713,
0.036916233599185944,
-0.026525473222136497,
-0.0020242566242814064
] |
<p>If something crossed the horizon of the observable Universe, does this mean that all information about it is lost forever? If yes (or no), how this fits with the information-cannot-be-lost law? </p>
<p>Also, does it mean that the energy of our observable Universe is constantly decreasing? If yes, what are the consequences of that?</p>
| 7,634 |
[
-0.018725702539086342,
-0.07088848948478699,
0.019347921013832092,
-0.0332074910402298,
0.04522847384214401,
0.022398946806788445,
-0.05290994048118591,
0.009430382400751114,
-0.018905218690633774,
-0.04598759487271309,
-0.03161173313856125,
0.02098182775080204,
0.013662949204444885,
0.017624249681830406,
0.010371262207627296,
0.005493393633514643,
-0.017028341069817543,
0.008181741461157799,
-0.041421763598918915,
-0.04247201234102249,
-0.001791234128177166,
0.03670496121048927,
0.016276853159070015,
-0.0009586747037246823,
-0.06341883540153503,
0.02685374766588211,
0.01625787280499935,
0.008159122429788113,
0.03254498541355133,
0.03667951002717018,
0.006105109583586454,
-0.016321925446391106,
-0.014116612263023853,
0.058008331805467606,
0.007390407845377922,
-0.03029710240662098,
-0.03378429636359215,
-0.043192438781261444,
-0.036374084651470184,
-0.01077245268970728,
-0.028606418520212173,
-0.027162054553627968,
-0.019172528758645058,
0.09046737849712372,
-0.03982378914952278,
-0.02984941005706787,
-0.01719311997294426,
0.023726318031549454,
0.009927152656018734,
-0.009259697049856186,
0.03213280439376831,
-0.039316266775131226,
0.007103333715349436,
0.014227728359401226,
-0.0014896318316459656,
0.01900281198322773,
0.09592331945896149,
0.06545790284872055,
-0.015948699787259102,
-0.054811544716358185,
-0.05367496982216835,
0.002865463960915804,
0.008160012774169445,
0.0018440370913594961,
0.00080726487794891,
0.0639301985502243,
-0.0066014910116791725,
-0.03188801929354668,
0.03983103111386299,
0.0066800955682992935,
-0.00522508192807436,
0.04120120033621788,
0.01214213389903307,
0.01577417179942131,
0.04938598349690437,
-0.030900541692972183,
0.015067927539348602,
-0.009062720462679863,
0.021748464554548264,
0.09223096072673798,
0.02238393947482109,
-0.012879783287644386,
0.05945775285363197,
0.037408724427223206,
0.023242149502038956,
0.031160762533545494,
0.06877802312374115,
-0.0002489775069989264,
0.04131711646914482,
0.055002808570861816,
-0.0093331104144454,
-0.009818586520850658,
0.0012153120478615165,
-0.038189150393009186,
-0.06570887565612793,
0.039792198687791824,
-0.014541888609528542,
0.06272463500499725,
-0.026753081008791924,
-0.03439992293715477,
0.024648571386933327,
0.017931180074810982,
-0.006172826513648033,
0.040507763624191284,
0.0025598248466849327,
-0.04817425459623337,
-0.08624331653118134,
0.01821521669626236,
-0.05324622616171837,
-0.041828177869319916,
-0.013769292272627354,
0.01578143611550331,
0.018217379227280617,
0.027394380420446396,
-0.0031902259215712547,
-0.04959215968847275,
0.005121169146150351,
-0.020395608618855476,
0.052795760333538055,
0.05625157058238983,
0.05069425329566002,
-0.012182053178548813,
0.00019733149383682758,
0.005132573656737804,
-0.06085477024316788,
0.03821030259132385,
0.04382672905921936,
-0.018467282876372337,
-0.07376756519079208,
0.0243381280452013,
-0.018349016085267067,
-0.0019733530934900045,
-0.005122884176671505,
-0.016658075153827667,
0.03924962878227234,
-0.013134356588125229,
-0.11833737045526505,
-0.052571721374988556,
0.04113321378827095,
0.008172652684152126,
-0.057962626218795776,
-0.05531854182481766,
0.00010510243737371638,
0.02572266384959221,
0.05366510525345802,
-0.01122500840574503,
-0.030988190323114395,
0.0021759134251624346,
0.018388276919722557,
0.004124480299651623,
-0.03303162753582001,
-0.0185921061784029,
0.0032819488551467657,
-0.022215403616428375,
-0.011495574377477169,
-0.07120785862207413,
-0.005345775280147791,
0.040398918092250824,
-0.0028164645191282034,
-0.06528867036104202,
0.037326134741306305,
-0.015228016301989555,
-0.005835422780364752,
-0.01102703157812357,
-0.02463470585644245,
-0.033426906913518906,
0.09152134507894516,
0.03267887979745865,
0.03465715050697327,
0.03278240188956261,
0.028557350859045982,
0.03944844752550125,
-0.027857892215251923,
0.005083396565169096,
0.027030175551772118,
-0.03709825128316879,
-0.02195011079311371,
-0.031757209450006485,
-0.005987674463540316,
-0.011376645416021347,
-0.0051952083595097065,
-0.04569130390882492,
-0.03446272015571594,
-0.0037424953188747168,
0.024112729355692863,
0.006409319117665291,
-0.0065284185111522675,
0.001324247452430427,
0.012249676510691643,
-0.028836240991950035,
-0.013817832805216312,
-0.06447044014930725,
0.0405798964202404,
0.019401472061872482,
0.005029512103646994,
0.04239467903971672,
0.022043602541089058,
0.026826297864317894,
-0.0539441853761673,
-0.04583169147372246,
0.03340929374098778,
0.034847062081098557,
-0.014025827869772911,
-0.04346068575978279,
0.003045210847631097,
0.036822471767663956,
0.024574147537350655,
0.00009013692033477128,
0.015464016236364841,
-0.007365169003605843,
-0.05093345046043396,
0.0023027241695672274,
0.014552534557878971,
0.03353094682097435,
-0.02450663410127163,
0.03016079030930996,
0.0227824579924345,
0.0074781388975679874,
0.038520194590091705,
0.01276390627026558,
-0.04637153074145317,
0.06851966679096222,
0.0389697439968586,
-0.004102401901036501,
-0.018928751349449158,
0.025508897379040718,
0.0002910649054683745,
0.011390678584575653,
-0.024775922298431396,
-0.012203694321215153,
-0.054526567459106445,
0.0022236465010792017,
0.01315942034125328,
0.02044208161532879,
-0.02141791395843029,
0.019007671624422073,
0.04498939961194992,
0.023130647838115692,
0.009536806493997574,
0.015716340392827988,
0.0004992996691726148,
-0.030263720080256462,
-0.012613563798367977,
-0.0035191888455301523,
0.012400013394653797,
0.050548020750284195,
0.01839163899421692,
-0.022693857550621033,
-0.014562801457941532,
-0.008963602595031261,
0.014194279909133911,
0.04390955716371536,
0.036568015813827515,
0.018199408426880836,
0.007673976477235556,
-0.04904879257082939,
0.023175790905952454,
-0.03124222718179226,
0.021371889859437943,
0.02058027684688568,
0.01902630738914013,
-0.0016287524485960603,
-0.06070467084646225,
0.009619594551622868,
-0.01777387224137783,
0.01742001250386238,
-0.017945267260074615,
0.006300399079918861,
0.02880001626908779,
-0.024615319445729256,
0.007815873250365257,
0.014731951989233494,
-0.007091377396136522,
0.00994102656841278,
-0.008413874544203281,
0.023632682859897614,
-0.01277295034378767,
0.011718030087649822,
-0.054327256977558136,
-0.019722599536180496,
0.014478860422968864,
-0.03769102692604065,
0.0015389382606372237,
0.02927519753575325,
-0.04056485369801521,
0.036546338349580765,
-0.011531616561114788,
-0.04413970932364464,
0.04375482723116875,
-0.018727945163846016,
0.03635574132204056,
0.016140993684530258,
-0.003560479963198304,
-0.02591683715581894,
-0.005500716157257557,
-0.017836758866906166,
0.009374591521918774,
-0.03855409473180771,
0.02278912253677845,
0.06273070722818375,
-0.037543293088674545,
-0.04179355874657631,
-0.009646580554544926,
-0.045593224465847015,
-0.06271526217460632,
0.021400034427642822,
0.0012343204580247402,
-0.0015533671248704195,
-0.014331831596791744,
0.01931682787835598,
0.011469360440969467,
-0.06505502760410309,
-0.009154744446277618,
-0.057509664446115494,
-0.06207238882780075,
0.04720797389745712,
0.002065811539068818,
-0.01944468729197979,
-0.02498926781117916,
-0.007710158359259367,
0.04656967148184776,
0.03102704882621765,
-0.005485788453370333,
-0.023182090371847153,
0.00023979142133612186,
0.026873845607042313,
0.0029207817278802395,
0.0026048612780869007,
-0.019597895443439484,
-0.0029806792736053467,
-0.01788751222193241,
0.028793565928936005,
0.034994471818208694,
0.007677842862904072,
-0.004323320463299751,
-0.03246999531984329,
0.005615796893835068,
-0.013729099184274673,
0.038173574954271317,
0.013276071287691593,
0.022519957274198532,
-0.008833659812808037,
0.0012733119074255228,
0.000059483169025043026,
0.03981935232877731,
0.02732772007584572,
-0.02661796100437641,
0.060791049152612686,
0.009549596346914768,
0.017605191096663475,
-0.013334039598703384,
0.05005998909473419,
-0.016656795516610146,
-0.0011423607356846333,
-0.028675414621829987,
0.006730825640261173,
0.07892664521932602,
0.02009342983365059,
0.006972930394113064,
-0.008179126307368279,
0.019646044820547104,
-0.01539361197501421,
-0.019283441826701164,
-0.04197308048605919,
-0.0004651291237678379,
0.002950904192402959,
0.014584865421056747,
-0.008197246119379997,
0.01480006705969572,
0.03029465302824974,
-0.025569383054971695,
0.016253862529993057,
-0.012902176938951015,
-0.030466387048363686,
-0.04542943462729454,
-0.028549863025546074,
-0.01663769595324993,
0.013127373531460762,
0.06082964688539505,
0.052770569920539856,
0.02351178415119648,
0.0219741053879261,
0.005761945620179176,
0.021449750289320946,
-0.06733591109514236,
-0.013236720114946365,
-0.04998743534088135,
0.004763328470289707,
-0.017042653635144234,
0.01700696349143982,
0.0009361424017697573,
-0.003420360153540969,
0.010455293580889702,
-0.01795564778149128,
-0.001095798797905445,
-0.07860453426837921,
-0.01726362481713295,
-0.026142174378037453,
-0.03784113749861717,
-0.04177312180399895,
0.05623820051550865,
0.05189253017306328,
-0.01083433348685503,
0.05334394797682762,
0.03465116024017334,
-0.013940922915935516,
-0.019285637885332108,
-0.009797054342925549,
-0.03829686716198921,
-0.006384024862200022,
0.00593125494197011,
0.04132624715566635,
-0.01399840135127306,
-0.009327535517513752,
0.0015415134839713573,
0.06021871417760849,
0.02465098351240158,
-0.018904974684119225,
0.0015103372279554605,
-0.021559078246355057,
-0.016528699547052383,
0.014823739416897297,
-0.032045651227235794,
0.04400355741381645,
-0.022361602634191513,
-0.006201716605573893,
0.018907541409134865,
0.004669478163123131,
-0.020805735141038895,
0.015272848308086395,
0.055575691163539886,
-0.006124578882008791,
-0.011464651674032211,
0.023927021771669388,
-0.004625958390533924,
-0.041002847254276276,
-0.008960716426372528,
-0.015354039147496223,
-0.007248795125633478,
-0.04671454057097435,
0.018710482865571976,
-0.011099577881395817,
0.007915914990007877,
-0.030890772119164467,
-0.03299165144562721,
-0.019541241228580475,
-0.00004971770613337867,
0.0025728289037942886,
0.008072283118963242,
0.019664641469717026,
0.04470085725188255,
0.06366968899965286,
0.014161976985633373,
-0.00658061821013689,
-0.07632715255022049,
0.0016856318106874824,
0.04527870565652847,
0.030656088143587112,
0.030414659529924393,
0.002159660682082176,
-0.07955310493707657,
-0.030453914776444435,
0.050511084496974945,
0.005800589919090271,
0.013403107412159443,
-0.006679598707705736,
-0.004499502945691347,
-0.01763775385916233,
-0.03141731023788452,
-0.013676783069968224,
0.0263985563069582,
-0.03520253300666809,
0.046052198857069016,
-0.003934605047106743,
0.056740980595350266,
-0.029067659750580788,
0.013731447979807854,
0.0065549337305128574,
0.06010723486542702,
0.00773994717746973,
-0.005379388574510813,
0.0024860184639692307,
0.00998709723353386,
-0.030491475015878677,
-0.05823054909706116,
0.007832014933228493,
0.007190709467977285,
-0.03469796106219292,
0.04517892748117447,
-0.021674739196896553,
-0.022893700748682022,
0.0329701267182827,
0.03381090611219406,
-0.030126996338367462,
-0.005507010966539383,
-0.05140053853392601,
0.028982145711779594,
0.009855958633124828,
-0.01249392144382,
0.03128129243850708,
0.02576344460248947,
0.017234252765774727,
0.016990195959806442,
-0.004978025332093239,
0.05496034398674965,
-0.027199845761060715,
0.017582284286618233,
-0.015250892378389835,
-0.029472941532731056,
-0.04972691088914871,
0.03472541272640228,
0.019166555255651474,
0.0071963956579566,
0.01664610393345356,
-0.029502520337700844,
-0.03304022550582886,
-0.009171057492494583,
0.02685021236538887,
0.01040936354547739,
-0.023028800264000893,
0.031736329197883606,
-0.026960168033838272,
-0.048475224524736404,
0.01610410399734974,
-0.004154745489358902,
-0.009725026786327362,
0.0402810201048851,
-0.005400222726166248,
0.06268049776554108,
0.0036087692715227604,
-0.033351872116327286,
0.04016595706343651,
-0.016536232084035873,
0.009078831411898136,
-0.013584908097982407,
-0.020977379754185677,
0.03145364299416542,
-0.01946481503546238,
-0.06337614357471466,
0.025029471144080162,
-0.03467618674039841,
0.016518717631697655,
-0.02278849482536316,
0.04221372306346893,
0.0055492534302175045,
0.04480240121483803,
-0.07288829982280731,
-0.012587917037308216,
0.012881957925856113,
0.026173939928412437,
-0.007718288339674473,
0.011846118606626987,
0.03677855804562569,
-0.053169284015893936,
-0.033170074224472046,
-0.033017709851264954,
0.015750247985124588,
-0.010041392408311367,
0.011723664589226246,
-0.015172800980508327,
-0.018356695771217346,
0.041856005787849426,
-0.01084862370043993,
-0.007933984510600567,
0.02497653104364872,
0.0013469778932631016,
-0.01624453067779541,
-0.031123263761401176,
0.054485686123371124,
-0.01424342766404152,
-0.04516037553548813,
-0.01699674502015114,
-0.012056209146976471,
0.015497560612857342,
-0.016050584614276886,
-0.0032658150885254145,
0.035383060574531555,
-0.00022855354472994804,
-0.020062435418367386,
0.0014279262395575643,
0.03029199317097664,
-0.02770865522325039,
0.021938743069767952,
0.002236664993688464,
-0.006693876348435879,
-0.0018473194213584065,
-0.048147208988666534,
0.020604485645890236,
-0.003584188176319003,
0.030509576201438904,
0.01817377284169197,
0.037063486874103546,
-0.008763231337070465,
-0.006271156016737223,
-0.0024764975532889366,
-0.026383517310023308,
-0.00034495917498134077,
-0.007229711394757032,
0.03591696545481682,
-0.014801496639847755,
0.003123235423117876,
-0.04322732612490654,
-0.02704499289393425,
-0.0232432559132576,
-0.024300673976540565,
0.04216141253709793,
-0.00432346947491169,
-0.012334124185144901,
-0.015356703661382198,
0.026682868599891663,
0.014728143811225891,
-0.04778595268726349,
0.002059653867036104,
0.030193796381354332,
0.010114151053130627,
0.0033240607008337975,
-0.0032493951730430126,
-0.004623796325176954,
0.04720683768391609,
0.04490125551819801,
-0.02714656852185726,
0.0019575359765440226,
0.029017025604844093,
0.035844914615154266,
0.03212941065430641,
-0.045456502586603165,
-0.03581883758306503,
0.0242751557379961,
-0.03279898688197136,
0.011287230998277664,
0.007854126393795013,
0.012039712630212307,
0.02882510982453823,
0.023914040997624397,
0.03130874037742615,
-0.02288486808538437,
-0.026956824585795403,
-0.07389847189188004,
0.015408818610012531,
-0.00918770395219326,
0.04292707145214081,
-0.01888551376760006,
-0.007423638366162777,
-0.006292634177953005,
-0.007225262466818094,
1.8425780012876203e-7,
0.010099843144416809,
-0.07837092876434326,
-0.05018138140439987,
-0.03041442483663559,
-0.04798220470547676,
0.04119091480970383,
0.013054130598902702,
0.012313192710280418,
0.00498347170650959,
-0.02440771833062172,
-0.003994759172201157,
0.01628047041594982,
0.07136984914541245,
-0.048796020448207855,
0.04280715808272362,
0.007356086280196905,
0.05550806224346161,
-0.003837536321952939,
0.008749838918447495,
0.10966232419013977,
0.08142081648111343,
0.0025825961492955685,
-0.04271853342652321,
0.03100941888988018,
-0.010494079440832138,
0.025657933205366135,
-0.03514377027750015,
0.04020565375685692,
-0.009969380684196949,
0.02091226354241371,
0.053290002048015594,
0.059564463794231415,
-0.015184475108981133,
-0.020954497158527374,
0.02279689908027649,
-0.04833923280239105,
0.014051074162125587,
0.021767089143395424,
0.04181438311934471,
-0.004307451657950878,
0.010393954813480377,
-0.02636565826833248,
0.011348474770784378,
-0.030100509524345398,
-0.014498031698167324,
0.007397185545414686,
-0.03427291661500931,
-0.00903179869055748,
-0.033521268516778946,
-0.03141417354345322,
0.034525029361248016,
0.016544129699468613,
-0.00428370526060462,
-0.014964461326599121,
0.007631666027009487,
0.05192771181464195,
0.017865892499685287,
0.010796166956424713,
0.057638268917798996,
0.014701789245009422,
0.008498108945786953,
-0.019864985719323158,
0.01453324593603611,
-0.039414677768945694,
-0.021723266690969467,
0.004481643904000521,
0.05479593575000763,
-0.035687513649463654,
0.02742716297507286,
-0.019976262003183365,
-0.03038611263036728,
-0.032583627849817276,
-0.05556352064013481,
-0.04083608463406563,
0.03473557159304619,
-0.006350747775286436,
0.011751255951821804,
-0.02473997138440609,
-0.025600941851735115,
0.014597267843782902,
0.02348668873310089,
0.036203619092702866,
0.0051605296321213245,
0.037159327417612076,
0.010726588778197765,
0.001276115421205759,
0.043073028326034546,
0.003354893298819661,
-0.022561760619282722,
0.0032140021212399006,
-0.006764620542526245,
-0.03481695428490639,
0.01424949336796999,
-0.01468667108565569,
0.01191197894513607,
-0.015313057228922844,
0.002275365637615323,
0.031531017273664474,
-0.014343764632940292,
-0.03657711669802666,
0.03210967406630516,
-0.02998650260269642,
-0.040243811905384064,
-0.04242902249097824,
0.033778995275497437,
0.03232660889625549,
0.03255036100745201,
-0.008112373761832714,
-0.015524071641266346,
0.01635112054646015,
0.0400618240237236,
0.038311801850795746,
-0.0008203099714592099,
0.02087235450744629,
-0.01775401085615158,
-0.03395885229110718,
-0.006943422369658947,
-0.04752171412110329,
0.057605233043432236,
0.029067263007164,
0.028720272704958916,
0.015549479983747005,
0.010494332760572433,
-0.01345997303724289,
0.0215113814920187,
0.04144939407706261,
-0.01999012380838394,
-0.003156811697408557,
0.009912915527820587,
0.041804663836956024,
-0.008441731333732605,
-0.02493751421570778,
-0.013434668071568012,
0.029595831409096718,
-0.02524685114622116,
-0.0016007160302251577,
-0.02682914212346077,
0.037171874195337296,
0.01883743330836296,
0.05753203481435776,
-0.03236647695302963,
0.027646485716104507,
-0.03746480867266655,
0.009052329696714878,
0.011368252336978912,
-0.0327506922185421,
0.01342593040317297,
0.03473773971199989,
-0.016803845763206482,
-0.054969556629657745,
-0.003943153191357851,
0.03254406899213791,
-0.05001608654856682,
0.0016098428750410676,
0.022246450185775757,
-0.008390821516513824,
0.050507139414548874,
0.021922016516327858,
-0.027367331087589264,
0.02449706383049488,
-0.01900765299797058,
-0.029495330527424812,
0.05404616519808769,
-0.0098728584125638,
0.04923254996538162,
0.003418919863179326,
-0.021718714386224747,
-0.00671641668304801,
0.046910129487514496,
-0.008445469662547112,
-0.006790103390812874,
0.021028749644756317,
-0.07037454098463058,
-0.03158390149474144,
0.023279400542378426,
0.05642988532781601,
0.02493717335164547,
-0.021337855607271194,
0.04112009331583977,
0.014553639106452465,
0.006486575584858656,
-0.0036648826207965612,
0.0017542724963277578,
-0.04001446068286896,
0.015551653690636158,
-0.011355835013091564,
-0.0023196220863610506,
0.05795600637793541,
0.05839549005031586,
-0.036810122430324554,
0.040610913187265396,
0.05300169438123703,
-0.006084307096898556,
-0.09750791639089584,
-0.001812581205740571,
0.009106329642236233,
0.026882821694016457,
0.051987577229738235,
-0.04254193976521492,
0.030137550085783005,
0.033464159816503525,
-0.07108898460865021,
0.0324382483959198,
0.007734179496765137,
0.015531172975897789,
-0.02352454885840416,
0.039546746760606766,
-0.017428306862711906,
0.06924110651016235,
0.08182893693447113,
0.029710248112678528,
-0.027037598192691803,
0.03354574739933014,
-0.028350720182061195,
-0.02862977795302868,
-0.023519005626440048,
0.02024422585964203,
-0.04132912680506706,
-0.014964055269956589,
0.08270638436079025,
-0.012898590415716171,
-0.017280858010053635,
0.027825012803077698,
-0.005005193408578634,
0.01722773164510727,
0.0009657031041570008,
0.004354401025921106,
0.06091252341866493,
-0.002192488871514797,
-0.004228524398058653,
-0.022487973794341087,
-0.032697416841983795,
0.04150253161787987,
0.005185986403375864,
-0.013271350413560867,
0.009453636594116688,
-0.005384776741266251,
-0.014464630745351315,
-0.05418037623167038,
-0.010829477570950985,
0.0027942676097154617,
-0.006033266428858042,
-0.003499841084703803,
-0.005445484071969986,
0.0005513150827027857,
0.004376217722892761,
-0.026628779247403145,
0.010978677310049534,
-0.030560925602912903,
-0.049640774726867676,
0.044467657804489136,
0.023542867973446846,
-0.00928462389856577,
-0.013145488686859608,
-0.040688056498765945,
-0.032147154211997986,
0.013322790153324604,
0.000005893591151107103,
0.021552065387368202,
-0.04110891371965408,
0.004224724136292934,
-0.02479768916964531,
-0.01765216700732708,
0.0379655547440052,
-0.03286702185869217,
-0.02066398225724697,
0.017460471019148827,
0.0350169762969017,
0.004327042028307915,
0.006386811379343271,
-0.04425668343901634,
-0.03049255721271038,
-0.0662217065691948,
-0.0034672378096729517,
-0.010676147416234016,
0.031659431755542755,
-0.04925696551799774,
-0.03863140195608139,
0.0111841456964612,
-0.011296460404992104,
0.03889366239309311,
-0.037766557186841965,
-0.0021417238749563694,
0.02100423537194729,
-0.01198401115834713,
0.014969512820243835,
-0.07758060097694397,
0.01868971437215805,
-0.012359497137367725,
-0.0027798921801149845,
-0.019893920049071312,
-0.016057895496487617,
-0.015468112193048,
-0.009336275048553944,
0.02234756387770176,
0.00551385385915637,
0.03028854727745056,
0.007344908080995083,
-0.027704885229468346,
0.02341536618769169,
0.02258926071226597,
-0.017094522714614868,
0.05936957150697708,
-0.005908177234232426,
0.04611223191022873,
0.036348115652799606,
-0.010839071124792099,
-0.0034832488745450974,
0.019214361906051636,
-0.014133406803011894,
-0.010870063677430153,
0.01627315767109394,
0.011076044291257858,
0.004138277843594551,
-0.02149469219148159,
-0.035800863057374954,
0.06228338181972504,
-0.053986806422472,
-0.02238527126610279,
0.05357927083969116,
-0.016828682273626328,
0.06590338051319122,
0.00208628480322659,
-0.021428562700748444,
-0.009287484921514988,
0.012377251870930195,
-0.024777838960289955,
0.062438104301691055,
0.01920352689921856,
-0.02536495216190815,
0.034267693758010864,
0.01576283946633339,
-0.018116701394319534,
-0.013905659317970276,
0.0006463199970312417,
0.06449940800666809,
-0.05315031111240387,
-0.032221920788288116,
-0.007043743506073952,
-0.007605378981679678,
0.0007302282028831542,
0.017052674666047096,
-0.009642788209021091,
0.05513915792107582,
-0.0063811358995735645,
0.028025371953845024,
-0.012301684357225895,
-0.019938534125685692,
-0.05116541311144829,
0.04099065065383911,
-0.005465654190629721,
0.05408868566155434,
0.03582903370261192,
-0.015127576887607574,
-0.0411556214094162,
0.020216690376400948,
0.012174788862466812,
-0.04846859350800514,
-0.001883801305666566,
0.015992851927876472,
-0.016691643744707108,
-0.018242839723825455,
-0.006371017079800367,
-0.022632045671343803,
-0.02870984561741352,
0.03311648219823837,
0.008717712014913559,
0.01587485335767269,
-0.00972544215619564,
-0.019072799012064934,
-0.014975073747336864,
0.03760462626814842,
-0.026631079614162445,
0.01449695136398077,
-0.023885728791356087,
0.03277112916111946,
-0.019272366538643837,
-0.01896936260163784
] |
<p>There is a surprising number of papers seriously discussing the "<a href="http://focus.aps.org/story/v13/st3" rel="nofollow">feigel effect</a>" This has been linked to the <a href="http://peter.mapledesign.co.uk/writings/physics/2005_dissertation_The_Abraham-Minkowski_Controversy.pdf" rel="nofollow">Abraham-Minkowski controversy</a> also <a href="http://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy" rel="nofollow">here</a>. Although there are good discussions picking apart the feigel effect calculations, there does not appear to be a conclusive refutation of the effect under certain experimental circumstances. Much of this is linked to when the Poynting vector vanishes in the vacuum. Is there a legitimate possibility for seeing the Feigel effect? What would that mean about the nature of the poynting vector in physics?</p>
<p><a href="http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-PHY-ARI-041201-Grenoble_Feigel.pdf" rel="nofollow">The Feigel Process: Lorentz invariance, regularization, and experimental feasibility Final Report</a></p>
<p><a href="http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-PHY-ARI-041201-Koln_Feigel.pdf" rel="nofollow">Lorentz-invariant description of the Feigel Process for the Extraction of Momentum from a
vacuum Final Report</a></p>
<p><a href="http://arxiv.org/PS_cache/arxiv/pdf/1008/1008.3656v2.pdf" rel="nofollow">Alternative derivation of the Feigel effect and call for its experimental verification</a></p>
| 7,635 |
[
-0.014169017784297466,
-0.00970982201397419,
0.027149148285388947,
-0.05246591940522194,
0.05400228127837181,
0.01651577465236187,
-0.04701681062579155,
0.007482875604182482,
-0.012554132379591465,
-0.02580665983259678,
-0.00277665164321661,
0.035672228783369064,
0.07983168959617615,
0.01119455136358738,
-0.04151690751314163,
0.017851095646619797,
0.04385511204600334,
0.01243638526648283,
-0.031004322692751884,
-0.028297537937760353,
-0.021423382684588432,
0.03171773627400398,
-0.005014394409954548,
-0.041153036057949066,
-0.03687373176217079,
-0.0038409586995840073,
0.02420669235289097,
0.003411285113543272,
-0.032883767038583755,
0.07497501373291016,
-0.038882460445165634,
0.010203724727034569,
-0.01935369148850441,
-0.03514009714126587,
-0.008163605816662312,
0.009365616366267204,
0.006259700749069452,
-0.031528178602457047,
0.029603609815239906,
0.012106722220778465,
-0.026837756857275963,
0.015146034769713879,
-0.045975957065820694,
0.057694707065820694,
-0.047882720828056335,
0.04139168933033943,
-0.007728304248303175,
-0.010179336182773113,
0.0529511459171772,
-0.022919103503227234,
0.008315176703035831,
0.008952070027589798,
0.03000585362315178,
0.014624914154410362,
-0.014390387572348118,
-0.04427988454699516,
0.03733506053686142,
0.06977304071187973,
0.025698747485876083,
-0.05410684645175934,
0.0042556282132864,
-0.007874970324337482,
-0.015462520532310009,
-0.009650207124650478,
-0.02057972364127636,
0.0446133092045784,
0.009718799963593483,
-0.01478252001106739,
0.014189695939421654,
-0.006461907643824816,
-0.0062386272475123405,
-0.003964877221733332,
0.010602439753711224,
0.0008718070457689464,
0.02105192095041275,
-0.009940867312252522,
0.02506217174232006,
0.009112953208386898,
0.013100867159664631,
0.02579868771135807,
0.008947314694523811,
0.020813213661313057,
0.049899112433195114,
0.0440513901412487,
0.03364713117480278,
-0.019361497834324837,
0.05174665525555611,
-0.0651322454214096,
0.0005212844698689878,
0.07340473681688309,
-0.026973780244588852,
0.006476499140262604,
0.030431421473622322,
0.027573352679610252,
-0.04634217545390129,
0.09438144415616989,
-0.029376698657870293,
0.0371721014380455,
-0.0019170473096892238,
-0.01594192534685135,
-0.026306308805942535,
-0.003613750683143735,
0.0033185784704983234,
0.0778975561261177,
0.0012455221731215715,
-0.019941113889217377,
0.018986444920301437,
0.0189749076962471,
-0.07699517905712128,
-0.028788769617676735,
-0.030002795159816742,
-0.007097890134900808,
-0.004125350620597601,
0.02762465551495552,
0.025479137897491455,
-0.046590305864810944,
-0.0016855696449056268,
-0.03322647139430046,
0.08669841289520264,
0.09323408454656601,
0.017335867509245872,
0.004136667121201754,
-0.04256213456392288,
-0.02211780659854412,
-0.08541189134120941,
0.0012329034507274628,
0.03002413734793663,
-0.01684275083243847,
-0.03657681494951248,
0.019709520041942596,
0.022292286157608032,
-0.0025266772136092186,
0.0033077169209718704,
-0.0018480420112609863,
-0.002481444738805294,
-0.018557753413915634,
-0.10599712282419205,
-0.052147530019283295,
0.045553844422101974,
0.025211181491613388,
0.010426911525428295,
-0.05499348044395447,
-0.005396436899900436,
0.0020539076067507267,
0.0714404433965683,
-0.007994720712304115,
0.013067851774394512,
-0.020228033885359764,
0.08075182884931564,
-0.01154850609600544,
-0.030399298295378685,
-0.01090847048908472,
0.032663725316524506,
-0.0183780025690794,
-0.021837055683135986,
-0.0501532219350338,
0.02060907706618309,
0.03025509975850582,
-0.01742227002978325,
0.004698385018855333,
0.01195117924362421,
-0.0230557881295681,
-0.01582004316151142,
-0.0347311832010746,
0.0026505282148718834,
-0.021938364952802658,
0.034525103867053986,
0.026227237656712532,
-0.017108222469687462,
0.0039829290471971035,
-0.013203773647546768,
0.03450038656592369,
-0.022649426013231277,
-0.009681103751063347,
0.055163830518722534,
-0.018114257603883743,
0.005772474687546492,
0.005693976301699877,
0.011421875096857548,
0.0023969849571585655,
-0.027943266555666924,
0.008160614408552647,
-0.06322840601205826,
-0.006784171797335148,
0.000917652330826968,
0.04597228020429611,
0.019291246309876442,
0.04710496962070465,
-0.007072689477354288,
-0.08074318617582321,
-0.012922817841172218,
-0.06444688141345978,
0.00007814278069417924,
0.024821622297167778,
0.0014222015161067247,
0.04468826577067375,
-0.045530784875154495,
0.007324122823774815,
-0.01730269379913807,
-0.021711142733693123,
-0.0065292660146951675,
0.05294505134224892,
0.03112548403441906,
-0.033358439803123474,
0.02611413039267063,
0.049544136971235275,
0.039945054799318314,
0.006333645433187485,
-0.004072622861713171,
-0.01682821661233902,
-0.04316464811563492,
-0.002636374905705452,
-0.011859042569994926,
0.0013801626628264785,
0.01236017607152462,
0.007177455350756645,
0.03262155503034592,
0.03405929356813431,
-0.02063099853694439,
0.013393537141382694,
-0.02668830379843712,
0.05066372826695442,
0.053398072719573975,
0.012671712785959244,
-0.010503939352929592,
0.050252046436071396,
0.0015919840661808848,
-0.02379373088479042,
-0.014254849404096603,
-0.02650456875562668,
0.009982746094465256,
-0.018435871228575706,
0.02520899474620819,
0.033313099294900894,
-0.025872236117720604,
0.014237797819077969,
-0.002018541796132922,
0.020582132041454315,
-0.0093259047716856,
0.032779280096292496,
0.017005426809191704,
-0.047929417341947556,
0.028005624189972878,
-0.0017203716561198235,
0.00718439556658268,
0.018822677433490753,
0.019170349463820457,
-0.030700046569108963,
0.016771163791418076,
-0.058667633682489395,
-0.004254613537341356,
-0.010170542635023594,
0.0012190024135634303,
-0.03916352987289429,
-0.00493989884853363,
-0.0010852402774617076,
0.04575248435139656,
-0.024511869996786118,
0.02985011599957943,
0.05502842366695404,
0.012868057936429977,
0.017305849120020866,
-0.03154673054814339,
-0.043102338910102844,
-0.018786942586302757,
-0.030106686055660248,
0.019614817574620247,
-0.005529261194169521,
0.03047880157828331,
-0.04439978674054146,
0.027008501812815666,
-0.03758145496249199,
-0.005690811667591333,
-0.05324085056781769,
-0.026295233517885208,
0.0010610963217914104,
0.03186105564236641,
-0.02342105470597744,
-0.01830384135246277,
-0.031928565353155136,
0.01988183706998825,
-0.01801869459450245,
0.0027520754374563694,
0.02705192007124424,
-0.07397858798503876,
0.044109854847192764,
-0.050671618431806564,
-0.046868305653333664,
0.05226605758070946,
-0.004997745156288147,
0.0395616814494133,
0.024080218747258186,
0.00900485459715128,
-0.06935916095972061,
-0.040162280201911926,
-0.03083493560552597,
-0.025836415588855743,
-0.0067964293994009495,
0.007944482378661633,
0.043572090566158295,
-0.009392290376126766,
-0.07757782191038132,
0.027230240404605865,
-0.0046670702286064625,
-0.06443509459495544,
-0.05474228039383888,
-0.02459036558866501,
0.0036191672552376986,
-0.00959437619894743,
0.030825002118945122,
0.004222793970257044,
-0.013597925193607807,
0.00281127798371017,
-0.010129814967513084,
-0.035060059279203415,
-0.00798069778829813,
-0.051580239087343216,
0.03070138208568096,
-0.0029641310684382915,
-0.011289066635072231,
0.06751471757888794,
0.03611563891172409,
-0.011214583180844784,
-0.03447934240102768,
0.0061666942201554775,
0.006525035016238689,
0.0035354779101908207,
-0.0009729581652209163,
0.026545103639364243,
-0.02760498970746994,
0.038952216506004333,
-0.011908546090126038,
0.061446283012628555,
-0.011304116807878017,
0.03689193353056908,
-0.016038864850997925,
0.009526269510388374,
-0.008906705304980278,
-0.001976137049496174,
0.016445700079202652,
0.033548325300216675,
-0.04200432077050209,
0.00407580379396677,
0.023320185020565987,
0.03197897970676422,
0.022871462628245354,
-0.05577509477734566,
0.04879331961274147,
0.039308883249759674,
0.019060147926211357,
-0.025275159627199173,
-0.00587809830904007,
-0.021050844341516495,
-0.021193115040659904,
0.026305900886654854,
-0.02663385309278965,
0.040361467748880386,
-0.016717979684472084,
0.002836960833519697,
0.05397958308458328,
0.054249998182058334,
0.014088514260947704,
-0.007192451972514391,
-0.02342262864112854,
0.007371983956545591,
0.012393811717629433,
-0.03912518918514252,
-0.027234673500061035,
0.045912839472293854,
0.028683243319392204,
0.007201983593404293,
0.018483966588974,
-0.031352099031209946,
-0.000753501255530864,
-0.031753282994031906,
0.0003096263681072742,
-0.00867417361587286,
0.027533939108252525,
0.014943852089345455,
0.022324565798044205,
-0.023393888026475906,
0.012270725332200527,
-0.010347924195230007,
0.008394688367843628,
-0.08926131576299667,
0.010538524016737938,
-0.0021435103844851255,
-0.029043465852737427,
-0.023921797052025795,
-0.006515210494399071,
-0.027914531528949738,
-0.006097467616200447,
0.014531080611050129,
-0.031722087413072586,
-0.0019492823630571365,
-0.0642327144742012,
0.046151675283908844,
-0.005775735713541508,
-0.05937124416232109,
-0.02542239986360073,
-0.006910816300660372,
0.07429471611976624,
-0.022620704025030136,
0.0003655621549114585,
-0.01334819570183754,
-0.08086302131414413,
0.001988739939406514,
-0.006265736185014248,
0.030178600922226906,
0.027274509891867638,
0.018210144713521004,
0.031452618539333344,
0.040409546345472336,
-0.029686488211154938,
0.031875789165496826,
0.037863533943891525,
0.038011062890291214,
-0.004233350977301598,
-0.01438206247985363,
-0.040201399475336075,
-0.002750182757154107,
-0.04433906823396683,
-0.03387307748198509,
0.06033140420913696,
0.000161669566296041,
0.013019278645515442,
-0.0013475687010213733,
0.010800261050462723,
0.017547814175486565,
0.012467652559280396,
-0.0017527183517813683,
0.011453881859779358,
-0.0003128386160824448,
-0.03340381011366844,
-0.014156432822346687,
-0.017064455896615982,
0.008665239438414574,
0.010141047649085522,
0.029144173488020897,
-0.022692294791340828,
0.01691526547074318,
0.018101761117577553,
0.02109856903553009,
-0.01864578202366829,
0.017598111182451248,
0.013132241554558277,
-0.016437385231256485,
-0.013686444610357285,
0.018047885969281197,
0.00542744854465127,
0.018040087074041367,
0.042582813650369644,
0.048200927674770355,
0.03602362424135208,
-0.05154726281762123,
-0.025632157921791077,
0.029599342495203018,
0.02469833567738533,
-0.005176241509616375,
0.0004539781657513231,
-0.03515808284282684,
-0.028689997270703316,
0.012602675706148148,
-0.03136935457587242,
-0.007050856947898865,
-0.01744316890835762,
-0.040299613028764725,
-0.014171542599797249,
-0.022976182401180267,
-0.007791818119585514,
0.007478206418454647,
-0.02512883022427559,
-0.0026639504358172417,
-0.014784632250666618,
-0.013454862870275974,
0.043536409735679626,
0.027670251205563545,
-0.03488340973854065,
0.022324182093143463,
0.0033106729388237,
0.027861399576067924,
-0.027055060490965843,
0.013653457164764404,
-0.04498213529586792,
-0.0395604707300663,
-0.010403627529740334,
0.026263518258929253,
-0.015126589685678482,
0.042704805731773376,
-0.03168432414531708,
-0.04378589987754822,
-0.013489721342921257,
0.012072202749550343,
0.012735351920127869,
0.019862299785017967,
-0.025947729125618935,
0.015000131912529469,
0.031435634940862656,
-0.039920225739479065,
0.02182837948203087,
0.06350323557853699,
-0.03727315738797188,
-0.009238122031092644,
-0.05748661234974861,
0.036085281521081924,
-0.009843802079558372,
0.007777477614581585,
-0.016034500673413277,
0.047692861407995224,
-0.013954189606010914,
0.04261770471930504,
0.01888856291770935,
0.04101749137043953,
-0.013376470655202866,
0.0036795635242015123,
0.04653456434607506,
0.00995952170342207,
-0.004353622440248728,
-0.020357638597488403,
-0.040937550365924835,
0.02231609635055065,
-0.01738619990646839,
0.00649576261639595,
0.01584378443658352,
0.019868629053235054,
0.009552973322570324,
0.014881929382681847,
0.01363668218255043,
-0.019379783421754837,
-0.0019091712310910225,
-0.010390355251729488,
0.06426288187503815,
-0.03472603112459183,
0.049154430627822876,
-0.02943887747824192,
0.017329411581158638,
0.021525980904698372,
0.0014554207446053624,
-0.06255801022052765,
0.024802645668387413,
-0.05021602287888527,
0.036468032747507095,
-0.05463395267724991,
-0.010888776741921902,
0.02947210520505905,
0.0306689515709877,
-0.022716525942087173,
-0.015823129564523697,
0.0382758267223835,
-0.020513160154223442,
-0.055539123713970184,
-0.020802820101380348,
-0.017259793356060982,
-0.008809194900095463,
-0.02785114385187626,
-0.014538160525262356,
0.04950622841715813,
-0.05356203392148018,
-0.017924146726727486,
0.002379865851253271,
-0.006506182719022036,
0.06616988778114319,
-0.025675548240542412,
-0.0185054000467062,
-0.012379887513816357,
0.017783675342798233,
-0.006075679324567318,
0.04177591949701309,
-0.0031648152507841587,
-0.004057823680341244,
-0.010917389765381813,
0.027046283707022667,
0.012770149856805801,
-0.022062083706259727,
0.040457457304000854,
0.020343920215964317,
0.04057096317410469,
0.016372371464967728,
0.021089643239974976,
-0.001222954597324133,
0.020191853865981102,
0.022116178646683693,
0.05383021757006645,
0.009501956403255463,
0.00408162223175168,
-0.01990443840622902,
-0.06106836721301079,
0.03868013620376587,
0.0160174909979105,
-0.007429009769111872,
-0.01917247660458088,
0.04003234952688217,
-0.02099856361746788,
-0.004907278344035149,
0.06092039495706558,
-0.008045936934649944,
-0.027475973591208458,
-0.0368233285844326,
0.02453620545566082,
0.009488433599472046,
-0.018637623637914658,
-0.006084803491830826,
-0.049626339226961136,
-0.05852418765425682,
0.03784327581524849,
0.04193588346242905,
-0.029312120750546455,
0.02834482304751873,
0.011927444487810135,
-0.02389366738498211,
-0.03318344056606293,
-0.032130856066942215,
0.020461497828364372,
0.006928432732820511,
0.007012954447418451,
0.015141752548515797,
-0.05001932010054588,
-0.012269177474081516,
0.03431680426001549,
0.03324535861611366,
-0.021583018824458122,
0.04021280258893967,
0.02501254342496395,
0.020652251318097115,
0.043614208698272705,
-0.036901574581861496,
-0.036020923405885696,
0.04725700616836548,
-0.030176278203725815,
0.028231242671608925,
0.04153140261769295,
0.0003672003513202071,
0.06328730285167694,
0.05660970136523247,
0.012289068661630154,
-0.04108283296227455,
-0.004667710512876511,
-0.030842546373605728,
0.031675226986408234,
0.011583155021071434,
-0.005156367551535368,
-0.0048361183144152164,
-0.0321381613612175,
0.056471262127161026,
0.022083181887865067,
0.020326657220721245,
-0.033537935465574265,
-0.03825913369655609,
-0.02377457357943058,
-0.060610249638557434,
-0.04537782818078995,
0.07818607985973358,
-0.0037144101224839687,
0.01056058332324028,
-0.014213348738849163,
-0.029144132509827614,
0.010242333635687828,
0.03012603521347046,
0.03493693843483925,
-0.026058191433548927,
0.05442633852362633,
-0.05753301829099655,
0.02256264165043831,
-0.0445885993540287,
0.004032330121845007,
0.1436900794506073,
0.021039893850684166,
0.008976736105978489,
-0.026033123955130577,
-0.016243577003479004,
-0.007000526413321495,
0.00044578209053725004,
-0.0167243555188179,
0.018693942576646805,
-0.03571975976228714,
-0.02798391692340374,
0.05916893482208252,
0.020717784762382507,
0.00727107934653759,
-0.024193355813622475,
0.05803027004003525,
-0.03876646235585213,
-0.01809883303940296,
-0.02468254417181015,
0.05076652020215988,
-0.007179215084761381,
0.004189599305391312,
-0.024548938497900963,
0.04116907715797424,
-0.031512245535850525,
-0.020252913236618042,
-0.01026767399162054,
0.013311149552464485,
-0.03514682874083519,
-0.007843796163797379,
-0.015307369641959667,
0.007053678389638662,
0.017689447849988937,
-0.019699087366461754,
-0.015646783635020256,
0.004080376587808132,
0.03094176948070526,
-0.02705838717520237,
0.015893153846263885,
0.03283555433154106,
-0.007850902155041695,
0.016975749284029007,
0.010947258211672306,
0.05294117331504822,
-0.037968117743730545,
0.001264648512005806,
0.0004960883525200188,
0.060777343809604645,
0.01604585349559784,
0.01092616468667984,
-0.01155855879187584,
-0.02780754305422306,
0.05308614671230316,
-0.06040478125214577,
-0.03321806713938713,
-0.011868605390191078,
0.02736051194369793,
0.005851817317306995,
0.01008535549044609,
0.017214059829711914,
0.02163076214492321,
0.02395387925207615,
0.025947201997041702,
-0.015119250863790512,
-0.04526125267148018,
-0.005618346389383078,
0.022152673453092575,
0.07073372602462769,
-0.015069386921823025,
-0.03562144935131073,
-0.035933226346969604,
-0.02089923433959484,
-0.027299586683511734,
-0.004162870347499847,
-0.015985814854502678,
0.031865864992141724,
0.07780200242996216,
-0.027842789888381958,
-0.004201935604214668,
-0.01167329028248787,
-0.044802695512771606,
0.04913781210780144,
-0.04019932448863983,
0.009925255551934242,
-0.006207754369825125,
0.022195760160684586,
0.01995438151061535,
0.03066280670464039,
-0.02369222231209278,
-0.02022607997059822,
0.021487297490239143,
0.010487972758710384,
0.028670534491539,
0.018001265823841095,
-0.04352358356118202,
-0.024239659309387207,
-0.0006000661524012685,
-0.038525160402059555,
-0.029347172006964684,
0.009411340579390526,
0.02411995828151703,
0.01758514903485775,
0.0012859223643317819,
-0.010332562029361725,
-0.005167341325432062,
-0.028770364820957184,
0.03372609615325928,
0.016788525506854057,
-0.012587410397827625,
-0.01627436839044094,
-0.008788404986262321,
-0.02815309539437294,
0.0014754598960280418,
-0.01812083274126053,
-0.009471377357840538,
-0.0015399792464450002,
0.04086453095078468,
-0.024539481848478317,
0.014969383366405964,
-0.0515955314040184,
0.026268238201737404,
-0.011705085635185242,
-0.0018961557652801275,
0.01078372448682785,
-0.024785751476883888,
-0.004599419888108969,
0.004879997577518225,
-0.008711290545761585,
0.03345377370715141,
-0.018276505172252655,
-0.0058365194126963615,
0.005723349284380674,
0.0189516544342041,
0.0016218113014474511,
0.000889533432200551,
0.030565863475203514,
0.027800871059298515,
0.010104475542902946,
0.014301343820989132,
-0.03758051618933678,
0.02671290747821331,
-0.020597713068127632,
-0.055509600788354874,
0.03979390859603882,
-0.01760275661945343,
0.001560131786391139,
0.016770007088780403,
-0.024125197902321815,
-0.028074931353330612,
0.0392472967505455,
-0.0014095226069912314,
0.002467663725838065,
-0.009429344907402992,
-0.024644412100315094,
0.020739048719406128,
-0.012980842031538486,
0.02079988643527031,
-0.011555515229701996,
-0.011563988402485847,
0.02217593416571617,
-0.0011702303308993578,
-0.006134199909865856,
-0.02171764336526394,
0.0016866782680153847,
-0.039845023304224014,
-0.025428446009755135,
0.011844349093735218,
-0.021062837913632393,
0.012477084994316101,
0.06019372493028641,
-0.03173424303531647,
0.012107563205063343,
0.008226124569773674,
0.012854930013418198,
-0.1305953711271286,
0.005999701097607613,
-0.01289383228868246,
0.03376976400613785,
0.037569258362054825,
-0.036330971866846085,
-0.008900047279894352,
0.012827558442950249,
-0.09524855017662048,
0.04121895879507065,
-0.02321350947022438,
-0.008610892109572887,
-0.05807775631546974,
0.0032092744950205088,
-0.030006613582372665,
0.07371219992637634,
0.012655148282647133,
0.023122018203139305,
0.024602625519037247,
0.051652707159519196,
-0.025766655802726746,
-0.014806224964559078,
-0.00023703357146587223,
0.002208451507613063,
-0.0675109326839447,
0.023422282189130783,
0.05254152789711952,
0.0010760356672108173,
-0.029787996783852577,
0.017668962478637695,
0.0061601982451975346,
0.004171348176896572,
-0.021269595250487328,
0.02129492536187172,
0.01507412176579237,
0.02879372052848339,
0.03413451835513115,
-0.019394049420952797,
0.015500843524932861,
0.020452426746487617,
0.012928593903779984,
0.0388064868748188,
-0.002087617991492152,
-0.017908966168761253,
-0.015306406654417515,
-0.05298854783177376,
-0.0007988754659891129,
0.035794857889413834,
-0.009693716652691364,
-0.02733510546386242,
0.01351234782487154,
0.0040134647861123085,
-0.010379483923316002,
0.03683856502175331,
0.008412214927375317,
-0.05427056923508644,
-0.03511612117290497,
0.000509557721670717,
-0.021997781470417976,
0.016289442777633667,
0.029655100777745247,
-0.05520721897482872,
-0.0050934539176523685,
0.04556896537542343,
-0.04451154172420502,
0.04246257618069649,
0.004364596214145422,
-0.02899644337594509,
0.004315506666898727,
0.007058729883283377,
-0.025389118120074272,
-0.04153114929795265,
-0.04641539230942726,
0.013554726727306843,
0.044363219290971756,
0.013223791494965553,
-0.025259528309106827,
0.006302806548774242,
0.016926785930991173,
-0.03808502107858658,
-0.004727928899228573,
-0.01751420646905899,
0.003026472870260477,
-0.02253682352602482,
-0.0010436002630740404,
0.0039405315183103085,
0.03232623636722565,
0.07192454487085342,
-0.02459297515451908,
-0.04420263320207596,
0.047922614961862564,
-0.0462314747273922,
0.007581691723316908,
-0.0214825589209795,
-0.009524797089397907,
-0.003739243373274803,
-0.0019734827801585197,
0.0076409862376749516,
-0.0057457550428807735,
0.003515147138386965,
-0.006434873677790165,
0.033167965710163116,
0.004880362655967474,
0.014426471665501595,
0.019827846437692642,
-0.029065126553177834,
0.053234782069921494,
0.06784383952617645,
0.020247528329491615,
0.059019848704338074,
0.01026043388992548,
0.01905037648975849,
-0.023296473547816277,
-0.03246219456195831,
-0.022418752312660217,
-0.010556493885815144,
-0.025373896583914757,
-0.020499320700764656,
-0.007576242554932833,
-0.003029355313628912,
0.021345794200897217,
-0.039914894849061966,
0.00023181807773653418,
0.0382511131465435,
-0.018470918759703636,
0.008137911558151245,
0.06032025068998337,
-0.008627030998468399,
0.046601079404354095,
-0.028863389045000076,
0.033764246851205826,
0.008267366327345371,
-0.041483182460069656,
0.03207520395517349,
0.05108482018113136,
0.015974270179867744,
0.02393321879208088,
-0.03752416372299194,
0.056481312960386276,
-0.016650907695293427,
0.0366056002676487,
0.04723355546593666,
0.046606700867414474,
-0.03587312996387482,
-0.014719094149768353,
-0.02661527507007122,
-0.00390324997715652,
-0.01138345431536436,
0.042268846184015274,
-0.007723002228885889,
0.08890808373689651,
-0.003689876291900873,
-0.003712048754096031,
-0.005532394628971815,
0.05413281172513962,
0.019625011831521988,
0.022097954526543617,
0.0041302647441625595,
0.03749566152691841,
-0.003761622356250882,
-0.02403157390654087,
-0.06903934478759766,
0.017247963696718216,
-0.010097382590174675,
-0.017230113968253136,
0.007768158335238695,
-0.011446377262473106,
0.024091077968478203,
0.016534103080630302,
-0.004581565037369728,
-0.012657398357987404,
-0.03147492557764053,
0.003814003197476268,
-0.008794653229415417,
0.0062491497956216335,
-0.03255826234817505,
0.03217260539531708,
-0.034915950149297714,
0.05494729429483414,
-0.04310121014714241,
-0.011056048795580864,
-0.006234077271074057,
0.033679086714982986,
-0.04169739410281181,
0.03305875509977341
] |
<p>We learn that the quantum wave function $\Psi$ <a href="http://en.wikipedia.org/wiki/Wave_function_collapse" rel="nofollow">collapses</a> when it interacts with a classic object (measurement). </p>
<p><strong>My question is:</strong><br> Why are there <em>classic</em> objects after all, how did it all start? In a <em>quantum universe</em> (and I understand we live in one) there should only be <em>superposition</em>, how did these <em>classic</em> beings came into existence (which "decohere" the others) in the first place? Is it a statistical necessity like <em>entropy</em> - or doesn't, quite simply, anybody know the answer to that riddle? </p>
| 7,636 |
[
-0.03588555380702019,
-0.012498429976403713,
0.025810634717345238,
-0.032936111092567444,
0.008791442960500717,
0.01616043783724308,
-0.01554210763424635,
-0.025404149666428566,
0.0017354213632643223,
-0.018691346049308777,
0.04665382206439972,
0.038812488317489624,
0.012186622247099876,
0.010269840247929096,
0.019231824204325676,
0.004458735231310129,
0.0224890299141407,
-0.01629236526787281,
-0.029784107580780983,
-0.03190010413527489,
0.005892490968108177,
0.013168683275580406,
0.008806508965790272,
0.006180689670145512,
-0.02028009295463562,
0.039536669850349426,
-0.013670100830495358,
0.017744911834597588,
0.05544257536530495,
0.07057023793458939,
-0.026196911931037903,
-0.04598163440823555,
-0.021497782319784164,
0.023315778002142906,
0.008930332958698273,
-0.04841407388448715,
0.0008409949368797243,
-0.031190820038318634,
0.02304796315729618,
0.01101105660200119,
-0.02648644708096981,
-0.029012594372034073,
-0.011878039687871933,
0.030998695641756058,
-0.056536316871643066,
-0.01068989746272564,
0.007889236323535442,
-0.015248449519276619,
0.04295629262924194,
-0.0454510897397995,
0.04757816344499588,
0.013519118539988995,
0.028506401926279068,
0.009962386451661587,
-0.02085338905453682,
-0.007135341875255108,
0.09010043740272522,
0.029017163440585136,
-0.043967798352241516,
-0.030795352533459663,
-0.024469956755638123,
-0.0054480512626469135,
0.013126459904015064,
-0.002576465019956231,
-0.021231386810541153,
0.04878151789307594,
0.015701057389378548,
0.011411835439503193,
0.028669405728578568,
-0.010753309354186058,
0.011819906532764435,
0.004417475312948227,
0.04618915542960167,
0.016016127541661263,
0.022819222882390022,
0.010920046828687191,
0.027317769825458527,
-0.011887708678841591,
0.04359005391597748,
0.04596570134162903,
0.032377615571022034,
-0.01047950703650713,
0.019332405179739,
0.008955882862210274,
0.037872232496738434,
-0.00674365134909749,
0.07655266672372818,
-0.01904933527112007,
-0.010237487964332104,
0.05685458332300186,
0.014866361394524574,
0.0011694903951138258,
0.06588791310787201,
0.005711352918297052,
-0.03866619989275932,
0.01248891931027174,
0.013341771438717842,
0.06741662323474884,
0.005173989571630955,
-0.0024680898059159517,
0.01711939461529255,
-0.038909800350666046,
0.024425040930509567,
0.05557351931929588,
-0.016505921259522438,
0.006444755010306835,
-0.08293293416500092,
0.04713590815663338,
-0.005407138727605343,
-0.024368325248360634,
-0.029599379748106003,
0.017060164362192154,
0.011888034641742706,
0.025853419676423073,
-0.006500975228846073,
-0.012538980692625046,
-0.0173427052795887,
-0.020372914150357246,
0.07183872163295746,
0.05681858956813812,
0.02055913396179676,
-0.020415667444467545,
-0.024528782814741135,
-0.03617743402719498,
-0.04558369517326355,
0.005997186526656151,
0.01665002852678299,
-0.011773679405450821,
-0.008055000565946102,
0.051943548023700714,
-0.02717345766723156,
-0.020442616194486618,
0.028772098943591118,
0.010542614385485649,
0.006749718450009823,
-0.043321698904037476,
-0.1364368200302124,
-0.046643372625112534,
0.025010846555233,
-0.021022289991378784,
-0.0613270029425621,
-0.05579811707139015,
0.028201159089803696,
0.012742195278406143,
0.08130927383899689,
-0.05518059432506561,
-0.017847970128059387,
0.02290622517466545,
0.019041912630200386,
0.024295847862958908,
-0.0059377108700573444,
-0.032443489879369736,
0.007168496027588844,
-0.048875659704208374,
-0.03799424692988396,
-0.046434223651885986,
0.025962233543395996,
0.03930674493312836,
0.015395061112940311,
-0.004283545073121786,
0.014581272378563881,
-0.016412600874900818,
-0.046659041196107864,
0.019590623676776886,
-0.014377780258655548,
-0.0808030292391777,
0.06992585211992264,
0.015632424503564835,
0.004669808316975832,
0.0535728745162487,
-0.009746217168867588,
0.018674809485673904,
0.014879820868372917,
0.024035796523094177,
-0.02674981951713562,
-0.018623031675815582,
-0.03010977804660797,
-0.009573421441018581,
0.0013360062148422003,
-0.01481460127979517,
-0.023903464898467064,
-0.0122308861464262,
-0.0071543254889547825,
-0.015539518557488918,
0.026203719899058342,
0.05192626640200615,
0.0011619670549407601,
-0.03873516619205475,
-0.01636042818427086,
-0.04198317229747772,
-0.010390058159828186,
-0.08227093517780304,
0.004833855666220188,
0.006936994846910238,
-0.008082418702542782,
0.010060589760541916,
0.004988650791347027,
0.002487081103026867,
0.005377660971134901,
-0.049294613301754,
-0.028611047193408012,
0.00959458202123642,
0.0187449399381876,
-0.006882128771394491,
0.0023533550556749105,
0.06585124135017395,
0.04596201330423355,
-0.017233671620488167,
0.005374422296881676,
-0.014131574891507626,
-0.050911691039800644,
-0.0012102064210921526,
0.011276758275926113,
0.005280728917568922,
-0.03263617306947708,
-0.003969949670135975,
0.03614336997270584,
-0.010238869115710258,
-0.019071776419878006,
0.02340151183307171,
-0.03282315284013748,
0.047822508960962296,
-0.015792135149240494,
-0.0030931567307561636,
-0.02379700168967247,
0.04894061014056206,
0.015528786927461624,
0.025595534592866898,
-0.008577055297791958,
0.002329134149476886,
-0.06398820877075195,
-0.019566521048545837,
0.001447858288884163,
0.05624201521277428,
-0.012336425483226776,
0.02292834408581257,
0.006201206240803003,
0.05227195471525192,
-0.024480432271957397,
-0.029835721477866173,
-0.03558064252138138,
-0.027888860553503036,
-0.03586666285991669,
-0.012442998588085175,
0.0347021259367466,
0.02574082836508751,
0.011055008508265018,
0.018617717549204826,
-0.02886679396033287,
-0.0080060213804245,
-0.019125202670693398,
0.00696207769215107,
0.014099215157330036,
0.037317462265491486,
-0.02067134529352188,
-0.061378467828035355,
0.0006789440521970391,
-0.0028117571491748095,
0.019388597458600998,
-0.012315203435719013,
0.014634114690124989,
-0.015515930019319057,
-0.043790098279714584,
-0.02824043110013008,
-0.02501290664076805,
-0.007999409921467304,
-0.01758859120309353,
0.001133943093009293,
0.03313896805047989,
-0.02097783423960209,
-0.023052718490362167,
0.005466706585139036,
-0.012239163741469383,
-0.009190148673951626,
-0.0065958937630057335,
0.013720300048589706,
-0.016727587208151817,
0.07525604218244553,
-0.06654147058725357,
-0.04835629463195801,
-0.031883418560028076,
0.011767009273171425,
-0.008552095852792263,
0.04768020659685135,
-0.04979908466339111,
0.027574004605412483,
-0.05264623090624809,
-0.024332471191883087,
0.0404508076608181,
0.012033818289637566,
0.036363083869218826,
0.006067271344363689,
-0.031490445137023926,
-0.037518590688705444,
-0.013264787383377552,
-0.04172462970018387,
0.002013910561800003,
-0.061268117278814316,
0.02559138648211956,
0.06154835224151611,
-0.04539630934596062,
-0.049406345933675766,
-0.0238795168697834,
-0.061096373945474625,
-0.07490228116512299,
-0.01919686049222946,
-0.01542804017663002,
0.0042850361205637455,
-0.039522092789411545,
0.006278356071561575,
0.019334210082888603,
-0.030240362510085106,
0.0021517735440284014,
-0.05691494792699814,
-0.06492193788290024,
0.01922536827623844,
-0.011482462286949158,
0.06807554513216019,
0.00292688375338912,
-0.01631329581141472,
0.04804019629955292,
0.00380111881531775,
-0.05579771846532822,
-0.020726334303617477,
0.008152429014444351,
0.032702963799238205,
-0.03115101158618927,
-0.018290923908352852,
0.056992534548044205,
-0.011009667068719864,
0.06728490442037582,
0.005399732850492001,
0.021907567977905273,
-0.017030339688062668,
-0.003912828862667084,
-0.02515863999724388,
0.02497721277177334,
0.012250698171555996,
-0.00924773421138525,
0.04356786236166954,
0.024321500211954117,
-0.0044358838349580765,
-0.003493941156193614,
-0.01153208315372467,
0.011936691589653492,
-0.0035906797274947166,
-0.03419681265950203,
0.061965588480234146,
0.017485061660408974,
0.03727046772837639,
-0.008374619297683239,
0.03813273087143898,
-0.025576256215572357,
-0.017024921253323555,
0.008032161742448807,
0.004539936780929565,
0.04714486002922058,
-0.0068582831881940365,
0.011314832605421543,
0.02581823244690895,
0.014108074828982353,
-0.036349136382341385,
-0.007130803540349007,
-0.001756361685693264,
-0.024198463186621666,
0.019369933754205704,
0.011235799640417099,
-0.020999155938625336,
0.013123959302902222,
0.046618156135082245,
0.03076930157840252,
-0.015124347060918808,
-0.03761347755789757,
-0.011334458366036415,
-0.005541779100894928,
-0.0129490215331316,
0.008325129747390747,
0.03686382621526718,
-0.0005803801468573511,
0.06620314717292786,
0.02005377970635891,
0.016139501705765724,
-0.03110545128583908,
-0.02014671079814434,
-0.09981318563222885,
-0.0008927001617848873,
-0.040632206946611404,
-0.01929991878569126,
0.020876046270132065,
-0.009090036153793335,
0.022676194086670876,
-0.04247087612748146,
-0.032542724162340164,
-0.029803525656461716,
0.017314892262220383,
-0.036987703293561935,
-0.0053693996742367744,
-0.0170313511043787,
-0.03515556454658508,
0.0001825277868192643,
0.010589909739792347,
0.043531760573387146,
0.02157723717391491,
0.013813937082886696,
0.028495052829384804,
-0.054971497505903244,
0.011620907112956047,
-0.010163313709199429,
0.02245250716805458,
0.02413908764719963,
0.0015678834170103073,
0.031763430684804916,
-0.01215112954378128,
-0.02292010188102722,
-0.012266702018678188,
0.004822308663278818,
0.07014822214841843,
-0.010380925610661507,
-0.03406538814306259,
0.022804081439971924,
0.0012200475903227925,
-0.0157639067620039,
0.0012556706788018346,
0.030016643926501274,
-0.002764068776741624,
0.01893659122288227,
0.005304575432091951,
0.013971873559057713,
-0.002731515094637871,
0.067447230219841,
0.045132506638765335,
-0.020259100943803787,
0.00026179870474152267,
-0.01189520861953497,
-0.03380677103996277,
-0.043113600462675095,
0.005565970204770565,
0.006152437999844551,
0.023846544325351715,
0.028934629634022713,
0.0003198038029950112,
-0.0030585594940930605,
0.013676946051418781,
0.01245152112096548,
-0.04210539907217026,
-0.004258745349943638,
0.02641875669360161,
-0.041841622442007065,
-0.005421523004770279,
0.02269352227449417,
0.031271230429410934,
0.01468568667769432,
-0.0038254105020314455,
-0.024621063843369484,
-0.04365745559334755,
-0.02189396135509014,
0.019650692120194435,
0.018071627244353294,
0.027846936136484146,
-0.001966660376638174,
-0.05570834502577782,
-0.052812349051237106,
0.05062064155936241,
-0.01131356693804264,
0.01608338952064514,
0.004927723668515682,
-0.005038043949753046,
-0.023629052564501762,
-0.027028296142816544,
0.02473791129887104,
0.027041640132665634,
-0.0008894369238987565,
0.024654973298311234,
-0.007225280161947012,
-0.007335868664085865,
-0.020879629999399185,
0.019852548837661743,
0.0012018154375255108,
0.030957330018281937,
-0.01541903056204319,
-0.0005267843953333795,
0.0032259798608720303,
0.023735634982585907,
-0.004973093047738075,
-0.0766219049692154,
0.030916817486286163,
-0.04082518070936203,
-0.04162335395812988,
0.03851260617375374,
-0.029392719268798828,
-0.026798347011208534,
-0.01917201653122902,
-0.017217272892594337,
-0.029471663758158684,
0.052639979869127274,
-0.030305981636047363,
0.03866129741072655,
0.023216402158141136,
0.048895176500082016,
0.012990634888410568,
-0.002255425788462162,
-0.013698972761631012,
-0.00784041453152895,
-0.02849220111966133,
0.008916361257433891,
-0.015628455206751823,
0.047968875616788864,
-0.046861711889505386,
0.012567677535116673,
-0.0318867452442646,
0.07347023487091064,
-0.011244148015975952,
0.005494445096701384,
0.0067594414576888084,
-0.0405157096683979,
0.005986655130982399,
-0.02205841988325119,
-0.025315266102552414,
0.005047519225627184,
-0.014757372438907623,
0.015737684443593025,
-0.0012575116707012057,
-0.05745751038193703,
-0.0014178315177559853,
0.0188857764005661,
0.022183356806635857,
0.029841937124729156,
-0.003547263564541936,
0.06048217788338661,
-0.07167133688926697,
-0.0363055020570755,
0.030081264674663544,
-0.0532965324819088,
0.019881291314959526,
0.015165003947913647,
0.008004848845303059,
0.018573297187685966,
-0.038397446274757385,
-0.0468682125210762,
-0.031239813193678856,
-0.01584867760539055,
-0.0047967154532670975,
-0.027638407424092293,
0.014542943798005581,
0.0027678266633301973,
-0.019682126119732857,
-0.0711083933711052,
-0.0036685748491436243,
0.019215045496821404,
0.02391435019671917,
-0.004138872027397156,
-0.016456402838230133,
0.03609192743897438,
-0.0427987314760685,
-0.027711564674973488,
0.008483636192977428,
0.014876975677907467,
-0.00826023519039154,
-0.0027793680783361197,
0.023846376687288284,
0.041434649378061295,
0.024996956810355186,
-0.02742910571396351,
-0.026735486462712288,
0.028851374983787537,
-0.00011572350194910541,
0.01196557842195034,
-0.003801801009103656,
0.03775704279541969,
-0.02667391486465931,
-0.05650614574551582,
0.0033466718159615993,
-0.011052124202251434,
0.02807835303246975,
-0.004195471294224262,
0.004528180230408907,
-0.007813244126737118,
0.004924011882394552,
0.000007030086180748185,
-0.003474050434306264,
0.01834709383547306,
0.015994757413864136,
0.022596653550863266,
-0.012098139151930809,
0.033933479338884354,
-0.009417198598384857,
-0.05864712595939636,
0.05107739940285683,
-0.025177938863635063,
0.01023955550044775,
0.02813960611820221,
0.02408105880022049,
0.013253872282803059,
-0.014420260675251484,
0.005523194093257189,
-0.024718770757317543,
-0.0037102324422448874,
0.026318615302443504,
-0.0007532069575972855,
0.028292395174503326,
0.009254420176148415,
-0.009772755205631256,
0.016436463221907616,
-0.025330351665616035,
0.01941750943660736,
0.036617837846279144,
0.0029083401896059513,
0.05409883335232735,
0.03636762127280235,
-0.027464602142572403,
-0.022043099626898766,
-0.05238627269864082,
-0.00030152464751154184,
0.03248913213610649,
0.020351294428110123,
0.0212875809520483,
-0.030052736401557922,
0.03438664972782135,
0.04458992928266525,
0.030681027099490166,
-0.025554753839969635,
0.029928484931588173,
0.022346563637256622,
0.034454647451639175,
0.0033482355065643787,
-0.032975319772958755,
-0.01404666993767023,
0.038075730204582214,
-0.03771090507507324,
0.0187034010887146,
0.014536135829985142,
0.018649538978934288,
-0.02405593730509281,
0.006478721275925636,
0.03229590505361557,
-0.03918599709868431,
-0.018819961696863174,
-0.03171146661043167,
-0.02279694937169552,
0.0031897309236228466,
0.01592579297721386,
-0.002507616765797138,
0.03696565702557564,
-0.027350816875696182,
0.011896712705492973,
-0.0008178106509149075,
0.024588488042354584,
-0.058516744524240494,
-0.022949298843741417,
-0.026323823258280754,
-0.02510383166372776,
0.043703626841306686,
0.007580197881907225,
-0.011485624127089977,
0.010842681862413883,
-0.05925673246383667,
0.03762746974825859,
0.02629207633435726,
0.018617676571011543,
-0.029478199779987335,
0.036789972335100174,
0.027958080172538757,
0.009484388865530491,
-0.031918805092573166,
0.01928454264998436,
0.12103156745433807,
0.059681229293346405,
0.019439445808529854,
-0.056425683200359344,
-0.001726518152281642,
0.00472119590267539,
0.017983002588152885,
0.015503807924687862,
0.023440098389983177,
0.0005725124501623213,
0.02274283766746521,
0.0025566737167537212,
0.06372404098510742,
0.03933217003941536,
0.006592773832380772,
0.01693856716156006,
-0.0638706237077713,
-0.02834894135594368,
-0.03593739494681358,
0.00041561873513273895,
0.005622867960482836,
0.008337702602148056,
-0.022312618792057037,
0.018824076279997826,
-0.013565436005592346,
-0.024143274873495102,
0.008523089811205864,
-0.03205915167927742,
0.02675238437950611,
-0.0067975278943777084,
0.01984681375324726,
0.04248123615980148,
0.03671431541442871,
-0.03382769599556923,
-0.03122076392173767,
0.0354606956243515,
0.04796773940324783,
-0.011210081167519093,
0.0169506948441267,
0.003308693878352642,
0.023759454488754272,
0.01620594970881939,
0.001870017615146935,
0.0004131767782382667,
-0.030693303793668747,
-0.000055934775446075946,
-0.023379851132631302,
0.06318122893571854,
-0.02993355132639408,
-0.023863855749368668,
-0.03643462806940079,
-0.039090853184461594,
-0.005233722273260355,
-0.02709423005580902,
-0.026205310598015785,
-0.0035759375896304846,
0.026113361120224,
-0.013062961399555206,
-0.042138148099184036,
-0.010089658200740814,
-0.00539749301970005,
-0.024887660518288612,
0.04331774264574051,
-0.03370761126279831,
0.012668991461396217,
0.0007592504844069481,
-0.026133514940738678,
0.005573553033173084,
0.0010442418279126287,
0.01920582540333271,
-0.04174627736210823,
-0.018603026866912842,
-0.07538969814777374,
-0.05345799773931503,
0.037650708109140396,
0.022951951250433922,
0.06175995245575905,
0.034269630908966064,
0.03409290686249733,
-0.04107043892145157,
-0.04906977713108063,
0.00835566595196724,
-0.0437820628285408,
-0.004786279052495956,
-0.00984638836234808,
-0.019387731328606606,
-0.014462822116911411,
0.04826359078288078,
-0.015194809064269066,
-0.015140598639845848,
0.03627689555287361,
0.031573113054037094,
0.010270730592310429,
-0.01737450808286667,
0.015229946002364159,
0.03511993587017059,
-0.002516354201361537,
0.01399700716137886,
-0.06122351065278053,
0.009357304312288761,
-0.001888088881969452,
0.01421693991869688,
0.02675136737525463,
0.029239099472761154,
-0.0012835905654355884,
-0.004292373079806566,
0.0008184444741345942,
-0.03576856106519699,
0.0004419043252710253,
0.046779099851846695,
0.03813557326793671,
-0.0021395059302449226,
-0.03508550301194191,
0.0011863444233313203,
0.030295949429273605,
-0.007925104349851608,
0.03470851853489876,
-0.03682459890842438,
0.008364875800907612,
-0.018030235543847084,
0.056362103670835495,
-0.0069138891994953156,
-0.023006552830338478,
-0.054137855768203735,
0.04741063341498375,
0.012316703796386719,
-0.013307521119713783,
-0.022223947569727898,
0.0262251365929842,
0.005927847698330879,
-0.030986236408352852,
-0.0010549492435529828,
0.039575617760419846,
-0.03842160105705261,
-0.0019152051536366343,
0.017397599294781685,
0.01470722071826458,
0.036101482808589935,
0.005311189219355583,
0.00997970998287201,
0.027613842859864235,
-0.04523909091949463,
-0.043008264154195786,
0.047855619341135025,
0.009633930400013924,
0.011900651268661022,
0.054184917360544205,
-0.005814956501126289,
-0.00535748852416873,
0.027103306725621223,
-0.019344666972756386,
-0.0046434784308075905,
0.006052286829799414,
-0.0281376950442791,
0.004589987453073263,
0.00012350891483947635,
0.012979353778064251,
0.02272995188832283,
-0.030721250921487808,
0.060272153466939926,
0.02496405318379402,
0.01949680782854557,
0.004855351056903601,
0.028959983959794044,
-0.019410500302910805,
0.04404221847653389,
0.005719617009162903,
0.008636546321213245,
0.010695068165659904,
0.028072377666831017,
-0.04936610162258148,
0.06004994362592697,
0.029689937829971313,
-0.0004719959106296301,
-0.08759694546461105,
0.004016486927866936,
-0.0010195731883868575,
0.007479709107428789,
0.03779686242341995,
-0.025199059396982193,
0.002743192482739687,
0.06129710003733635,
-0.06562331318855286,
0.023398341611027718,
-0.008209800347685814,
-0.03360969200730324,
0.0014107086462900043,
0.017553143203258514,
-0.04562663659453392,
0.0597400888800621,
-0.007324662990868092,
0.060448575764894485,
0.02501448430120945,
0.020073918625712395,
-0.004854495171457529,
-0.03840352222323418,
-0.033739157021045685,
0.01326956320554018,
-0.03735722228884697,
0.03170757740736008,
0.0968116745352745,
-0.027674267068505287,
0.01403879001736641,
0.05128972977399826,
0.02024129591882229,
0.015401981770992279,
-0.007966829463839531,
-0.02535826340317726,
0.009883017279207706,
0.02476528473198414,
0.02374858781695366,
0.009173632599413395,
0.01654180884361267,
0.00601167231798172,
0.01656508445739746,
0.027756135910749435,
0.02480255626142025,
-0.027464086189866066,
-0.008082096464931965,
-0.007582793012261391,
-0.03803987428545952,
-0.002019585808739066,
0.00995269138365984,
0.0451878160238266,
0.03163595497608185,
0.06311092525720596,
-0.0035724889021366835,
0.014432832598686218,
-0.007479445543140173,
-0.04496726766228676,
-0.02001761458814144,
0.022951239719986916,
0.027071893215179443,
-0.011319171637296677,
0.04611338675022125,
-0.03856778144836426,
-0.02001461572945118,
0.011546537280082703,
0.0006074213306419551,
0.00045294847222976387,
-0.057496748864650726,
0.0037572465371340513,
-0.002357753925025463,
0.03275011107325554,
0.03582487255334854,
-0.0254953783005476,
-0.057052358984947205,
0.028748933225870132,
-0.008786545135080814,
0.027419427409768105,
-0.04561365395784378,
-0.07617685943841934,
-0.034719932824373245,
-0.09445508569478989,
0.039306387305259705,
0.02787948213517666,
0.043070174753665924,
-0.05702747032046318,
-0.029304521158337593,
-0.017431845888495445,
0.009247401729226112,
0.04549586400389671,
0.0004955099429935217,
0.005710497032850981,
0.027149580419063568,
-0.0018965527415275574,
0.05727991461753845,
-0.024251196533441544,
0.016817590221762657,
0.009160726331174374,
0.007842018269002438,
-0.009942217729985714,
0.007526579778641462,
0.047667600214481354,
0.007259680423885584,
0.012503616511821747,
-0.02970852516591549,
0.04002665728330612,
-0.01856360398232937,
-0.03761247172951698,
0.05690461024641991,
0.003440841566771269,
-0.005404189229011536,
0.0469023659825325,
-0.04900434985756874,
0.07248608767986298,
0.052144233137369156,
-0.0019908305257558823,
-0.01672200672328472,
0.03657572716474533,
0.00863280612975359,
-0.04636864736676216,
0.000478628819109872,
0.02349657192826271,
0.0005908591556362808,
-0.04123292863368988,
-0.03105209767818451,
0.036877211183309555,
-0.018933746963739395,
-0.02959281951189041,
0.0460517592728138,
-0.01244314294308424,
0.08087018132209778,
-0.0015795555664226413,
-0.011562702246010303,
-0.002762921154499054,
0.008239666931331158,
0.007213841192424297,
0.059701837599277496,
0.04762587323784828,
0.01565065048635006,
0.004821366164833307,
0.03524813428521156,
-0.0010449043475091457,
0.019358672201633453,
0.002774409716948867,
0.03514206036925316,
-0.03405525162816048,
-0.020417479798197746,
-0.005715864710509777,
-0.01031323429197073,
0.0029332120902836323,
0.014802370220422745,
-0.01326004695147276,
0.07576082646846771,
-0.01653861068189144,
0.006100529804825783,
-0.038779184222221375,
0.03967507928609848,
-0.03465055301785469,
-0.007919630035758018,
0.004721070174127817,
0.02103029005229473,
-0.037422098219394684,
0.0014262330951169133,
-0.04938458278775215,
0.02581539750099182,
0.046597179025411606,
-0.03262641653418541,
-0.00008551286737201735,
-0.020452842116355896,
-0.028174877166748047,
0.026860402897000313,
-0.010545125231146812,
-0.0036726256366819143,
-0.051160454750061035,
0.042038444429636,
0.041093360632658005,
0.00722825713455677,
-0.038723401725292206,
-0.012587184086441994,
-0.056176867336034775,
0.05283287912607193,
-0.03821122646331787,
0.0005142043228261173,
-0.02485622838139534,
0.062490928918123245,
-0.06265581399202347,
-0.013980254530906677
] |
<p>A <a href="http://prl.aps.org/abstract/PRL/v104/i7/e070401" rel="nofollow">paper</a> was published in 2010 claiming to resolve the <a href="http://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy" rel="nofollow">Abraham-Minkowski controversy</a>. Is this paper viewed as definitive by physicists?</p>
| 7,637 |
[
-0.022386178374290466,
-0.024425547569990158,
0.0021035673562437296,
-0.036098890006542206,
0.07391151040792465,
0.01897573284804821,
-0.04536305367946625,
-0.03416156396269798,
-0.019507383927702904,
-0.02999035082757473,
0.011140629649162292,
0.03017728589475155,
0.06376028805971146,
0.021765833720564842,
-0.0005325992242433131,
0.008770857937633991,
0.018607983365654945,
0.01813393644988537,
-0.014407992362976074,
-0.05622288957238197,
0.008694002404808998,
0.033832501620054245,
-0.003920644987374544,
-0.02744881622493267,
-0.04278964549303055,
-0.007090471684932709,
0.0378861241042614,
-0.001004521269351244,
-0.008855338208377361,
0.029550625011324883,
-0.05137467011809349,
0.008200309239327908,
0.010998150333762169,
0.00044868653640151024,
-0.013748588040471077,
-0.005258956924080849,
-0.0032156063243746758,
-0.05010693520307541,
0.004467696417123079,
0.02507529780268669,
-0.013422581367194653,
0.008440028876066208,
0.001953712198883295,
0.03113498166203499,
-0.049635887145996094,
0.05875665694475174,
0.013703946955502033,
-0.01304502785205841,
0.03378086909651756,
-0.05906317010521889,
0.05871465057134628,
0.005651629529893398,
0.028821175917983055,
0.02033008635044098,
-0.027374863624572754,
-0.004329029005020857,
0.06413283944129944,
0.05723050236701965,
0.024670813232660294,
-0.046439118683338165,
-0.022050784900784492,
-0.012451293878257275,
-0.000748045917134732,
0.01927509531378746,
-0.02239186130464077,
0.031698163598775864,
0.002392549766227603,
-0.006608214695006609,
-0.005884899292141199,
-0.011720423586666584,
-0.006188316270709038,
0.02250196970999241,
0.0636182576417923,
0.0037046505603939295,
0.04560035839676857,
-0.020012974739074707,
0.002779798349365592,
0.023171059787273407,
0.02835475653409958,
0.030817287042737007,
0.0003427688789088279,
0.01696988008916378,
0.02861948497593403,
0.009364823810756207,
0.02149060368537903,
-0.024886375293135643,
0.06596416234970093,
-0.02200351469218731,
-0.0036996169947087765,
0.05219487100839615,
-0.023838188499212265,
0.0344906784594059,
0.03398001566529274,
0.020368823781609535,
-0.025130610913038254,
0.07849375903606415,
-0.007575124502182007,
0.04996444657444954,
-0.040271710604429245,
-0.03586863726377487,
0.028831399977207184,
-0.0037100340705364943,
0.004782378673553467,
0.06728300452232361,
0.0034981677308678627,
-0.033442769199609756,
-0.014330453239381313,
0.04237409681081772,
-0.0590839721262455,
-0.021195752546191216,
-0.04346071556210518,
0.013635083101689816,
-0.014769441448152065,
0.014584618620574474,
0.01974942348897457,
-0.022880250588059425,
0.016983741894364357,
-0.0189425777643919,
0.08381425589323044,
0.06468398123979568,
0.04684014245867729,
-0.01600497215986252,
-0.045338694006204605,
-0.021008498966693878,
-0.07260361313819885,
-0.015615579672157764,
0.03288790583610535,
-0.015039189718663692,
-0.034109994769096375,
0.029915543273091316,
0.007436439394950867,
0.00860530138015747,
0.020539574325084686,
-0.004470898304134607,
0.018984418362379074,
0.008015508763492107,
-0.12342967092990875,
-0.05121666193008423,
0.06577380746603012,
0.02206428349018097,
-0.011383213102817535,
-0.08952436596155167,
0.003763498505577445,
-0.001142548630014062,
0.09000420570373535,
-0.026107698678970337,
0.03270285949110985,
0.008037849329411983,
0.08087151497602463,
-0.031129514798521996,
-0.007633104920387268,
-0.00190472393296659,
0.06274193525314331,
-0.011183295398950577,
-0.034465812146663666,
-0.040412530303001404,
0.006618006154894829,
0.056576717644929886,
-0.013808258809149265,
0.00002705096085264813,
0.04756752774119377,
0.001383881433866918,
-0.021808983758091927,
-0.008153502829372883,
0.002778648631647229,
-0.04220594838261604,
0.06050587818026543,
0.006438259966671467,
-0.014221064746379852,
0.007032518275082111,
-0.011392767541110516,
0.06883656978607178,
-0.014803915284574032,
-0.009248880669474602,
0.02844388782978058,
-0.027376189827919006,
0.011946802958846092,
0.01636958308517933,
0.013791579753160477,
0.030566761270165443,
-0.04127370938658714,
0.010301492176949978,
-0.052884746342897415,
0.019562434405088425,
0.0020661072339862585,
0.08062133938074112,
-0.019578248262405396,
0.05705781280994415,
0.026761434972286224,
-0.0730602964758873,
-0.01687740907073021,
-0.05638230964541435,
-0.0001481594517827034,
0.004637281410396099,
-0.02404283918440342,
0.042451854795217514,
-0.05541328713297844,
-0.0035052699968218803,
-0.03270617499947548,
-0.014862043783068657,
-0.018610868602991104,
0.05391888692975044,
0.021376125514507294,
0.0011811055010184646,
0.036160826683044434,
0.029235320165753365,
0.05094604194164276,
0.001572708715684712,
-0.03719257190823555,
-0.0026707930956035852,
-0.06828837096691132,
0.028710929676890373,
-0.019017204642295837,
0.001921895775012672,
0.05212711915373802,
0.013615421950817108,
0.006856030784547329,
0.024024952203035355,
0.0001395936997141689,
0.04434569552540779,
-0.020678335800766945,
0.054786648601293564,
-0.0005064250435680151,
0.0011811171425506473,
-0.010479641146957874,
0.05435730516910553,
0.0172585342079401,
-0.012039604596793652,
0.028841225430369377,
-0.048864204436540604,
-0.036317769438028336,
-0.04098033159971237,
0.0487523227930069,
0.046911586076021194,
-0.04927676171064377,
0.005447860341519117,
-0.0037239468656480312,
0.047468461096286774,
-0.026502104476094246,
0.029400823637843132,
-0.013880393467843533,
-0.07364198565483093,
0.046371374279260635,
-0.0067725153639912605,
-0.0031814957037568092,
0.04174254089593887,
0.0029864772222936153,
-0.015784746035933495,
0.01365514937788248,
-0.026758333668112755,
-0.006507578771561384,
0.018474115058779716,
-0.03519299253821373,
-0.007691250182688236,
-0.008497468195855618,
-0.0013413472333922982,
0.024663826450705528,
-0.04410749301314354,
0.02316032536327839,
0.03043466992676258,
-0.002253316342830658,
-0.00028548453701660037,
-0.02885160595178604,
-0.009645728394389153,
0.012051851488649845,
-0.002143023768439889,
-0.00476966192945838,
-0.028963768854737282,
0.018156835809350014,
-0.054384905844926834,
0.0021223588846623898,
-0.033283427357673645,
-0.025113865733146667,
0.01840563304722309,
-0.01789652183651924,
0.02021722123026848,
0.02620481513440609,
0.02150578424334526,
-0.023786207661032677,
-0.015523302368819714,
0.009509666822850704,
-0.007585915271192789,
-0.014259864576160908,
0.012594674713909626,
-0.03848422318696976,
0.037214457988739014,
-0.06165054067969322,
-0.02517833188176155,
0.02555045671761036,
-0.04725638031959534,
0.04930362105369568,
0.001363470801152289,
-0.022676941007375717,
-0.04081857204437256,
-0.030269430950284004,
-0.007940038107335567,
-0.012126702815294266,
0.013698541559278965,
-0.0013388411607593298,
0.04247036576271057,
0.01733381673693657,
-0.022986454889178276,
0.001095483428798616,
-0.01714620180428028,
-0.0359220989048481,
0.014063334092497826,
-0.04579022526741028,
0.04534028843045235,
0.0009342738194391131,
0.01737450808286667,
0.027718696743249893,
-0.028737852349877357,
-0.02373981662094593,
-0.0348944328725338,
-0.06274572759866714,
0.03380380570888519,
-0.06236923858523369,
0.03731720522046089,
0.02605653554201126,
-0.036064568907022476,
0.0521833561360836,
0.026322033256292343,
-0.03206592798233032,
0.0058433557860553265,
0.03540084883570671,
0.0076088812202215195,
-0.00007139655645005405,
-0.010201758705079556,
0.033631905913352966,
0.012377358041703701,
0.0452849380671978,
-0.018207775428891182,
-0.011082172393798828,
0.011829804629087448,
0.025729669257998466,
0.0034232474863529205,
-0.01292171236127615,
0.01621849648654461,
0.008241245523095131,
0.020001839846372604,
0.015527540817856789,
-0.009379890747368336,
0.00958054419606924,
0.004930771421641111,
0.03302016854286194,
0.0046033114194869995,
-0.05849086493253708,
0.04530302807688713,
-0.010974249802529812,
0.015893321484327316,
-0.01905643753707409,
0.004404480569064617,
-0.01146127562969923,
-0.014606853947043419,
0.04582533240318298,
0.02706245146691799,
0.013381784781813622,
0.018969349563121796,
0.02349862828850746,
0.020119931548833847,
0.02155371941626072,
0.0039066411554813385,
-0.0008752943249419332,
-0.02259248122572899,
0.001535742892883718,
0.01223734300583601,
-0.04712514206767082,
-0.049860142171382904,
0.04627527669072151,
0.015224160626530647,
0.022043317556381226,
0.0047221677377820015,
-0.03387380391359329,
0.0026452429592609406,
-0.08667176961898804,
0.011682470329105854,
-0.032395705580711365,
0.026359181851148605,
-0.010865628719329834,
0.022401990368962288,
-0.03216612711548805,
-0.022577280178666115,
0.015295389108359814,
0.005103592295199633,
-0.08245769888162613,
-0.02090180478990078,
-0.04731852561235428,
-0.019361859187483788,
-0.024282773956656456,
-0.015692202374339104,
-0.012841896153986454,
0.012635957449674606,
0.01484558917582035,
-0.03936144709587097,
-0.012098336592316628,
-0.07047256082296371,
0.0204765722155571,
-0.02322414331138134,
-0.044587668031454086,
-0.0016847664956003428,
-0.011853272095322609,
0.06384655833244324,
-0.010781907476484776,
0.02148764207959175,
0.00988809671252966,
-0.059545569121837616,
-0.033793140202760696,
-0.011151527985930443,
0.027714531868696213,
-0.0035758300218731165,
0.015520314686000347,
-0.018758410587906837,
0.043155737221241,
-0.009859398938715458,
0.04202042147517204,
0.041658978909254074,
0.04977839067578316,
0.017162533476948738,
-0.03174059838056564,
-0.07060044258832932,
-0.0408012792468071,
-0.00374732818454504,
-0.03461388126015663,
0.032599546015262604,
0.006314155645668507,
-0.031279731541872025,
0.034120816737413406,
0.014771929010748863,
-0.005957797635346651,
0.04890129715204239,
-0.0017592640360817313,
-0.014684027060866356,
0.02438267506659031,
-0.03679604455828667,
-0.021461330354213715,
-0.016434041783213615,
-0.004798587877303362,
0.043363895267248154,
0.020349618047475815,
-0.023130783811211586,
-0.0030210912227630615,
0.05415172874927521,
0.02950884960591793,
-0.04203183948993683,
0.05315156280994415,
0.01507977768778801,
-0.021683648228645325,
-0.01610870473086834,
0.04699040204286575,
0.006728350184857845,
0.043424587696790695,
0.06681552529335022,
0.0324486568570137,
-0.012579805217683315,
-0.057708241045475006,
0.0035476128105074167,
0.02937244437634945,
0.04905658960342407,
-0.025033853948116302,
0.01342751458287239,
-0.0691443607211113,
-0.0037734215147793293,
0.041986946016550064,
-0.029164593666791916,
0.01573188230395317,
-0.005445023998618126,
0.0020847392734140158,
-0.039462458342313766,
0.006824060343205929,
-0.022829188033938408,
-0.001872420427389443,
0.005287317093461752,
-0.0012833375949412584,
-0.028793033212423325,
-0.012399215251207352,
0.024205893278121948,
-0.0012402025749906898,
0.014972074888646603,
0.04593935236334801,
0.010023890063166618,
0.018750527873635292,
-0.005125196184962988,
0.002072554314509034,
-0.05045212805271149,
-0.045914024114608765,
-0.023552391678094864,
-0.010130303911864758,
-0.03189365565776825,
0.006509713362902403,
-0.03342311456799507,
-0.050271209329366684,
0.02591363713145256,
0.0314718522131443,
0.00881213042885065,
0.00347084179520607,
-0.017742453143000603,
0.04033409059047699,
0.043795280158519745,
-0.04599635675549507,
0.014087516814470291,
0.05388456583023071,
-0.004125841893255711,
-0.04276379570364952,
-0.03148800879716873,
0.045544013381004333,
-0.011189079843461514,
0.016541147604584694,
0.0006382705760188401,
0.00986343715339899,
-0.03676356375217438,
0.019020475447177887,
-0.0007983080577105284,
0.042281635105609894,
-0.0266922228038311,
-0.039348602294921875,
0.02309943363070488,
0.022410884499549866,
-0.06877129524946213,
0.008372609503567219,
-0.0414176769554615,
-0.0006743862759321928,
0.016979090869426727,
0.023138444870710373,
0.004362132865935564,
0.018412996083498,
0.03661447390913963,
0.05388154461979866,
0.008474624715745449,
0.05136610195040703,
-0.024352410808205605,
-0.019507644698023796,
0.024438947439193726,
-0.05402034893631935,
0.04902932792901993,
-0.02963707596063614,
-0.04264186695218086,
0.005322628654539585,
-0.05723926052451134,
-0.051771603524684906,
0.040330104529857635,
-0.030952902510762215,
0.04327402263879776,
-0.05450497940182686,
0.009661238640546799,
0.028536861762404442,
0.03718613088130951,
-0.03040221706032753,
-0.019730785861611366,
0.01508717704564333,
0.021934663876891136,
-0.01195346750319004,
-0.037432946264743805,
-0.017936469987034798,
-0.020401356741786003,
-0.022926868870854378,
0.008229002356529236,
0.03513308987021446,
-0.03648560494184494,
-0.03738044947385788,
-0.003781411796808243,
-0.0051615857519209385,
0.05243620276451111,
-0.017115555703639984,
0.0012721418170258403,
0.006472183857113123,
-0.0002445716818328947,
-0.013360582292079926,
0.004287298768758774,
0.04556485265493393,
-0.02071351557970047,
-0.010672667995095253,
-0.0006888123461976647,
0.03267061710357666,
0.007601164281368256,
0.043205369263887405,
-0.009312443435192108,
0.05779726430773735,
-0.0010930112330242991,
0.027199411764740944,
-0.002971724607050419,
0.025941189378499985,
-0.00355847948230803,
0.013467309065163136,
-0.0024180172476917505,
-0.035681307315826416,
-0.025253526866436005,
-0.05372823402285576,
0.04786688834428787,
-0.00564027251675725,
-0.02343202568590641,
-0.015604447573423386,
0.06572194397449493,
-0.017050983384251595,
0.004109288565814495,
0.019936684519052505,
-0.02733774669468403,
0.0002654676791280508,
-0.018742810934782028,
0.03497857600450516,
-0.0037105181254446507,
-0.016303637996315956,
0.007761933375149965,
-0.05437623709440231,
-0.02430059015750885,
0.03350982069969177,
0.029785342514514923,
0.0047994013875722885,
0.01865443028509617,
0.03975580260157585,
-0.025176627561450005,
-0.033897362649440765,
-0.02267477475106716,
0.008291197940707207,
-0.0003379441041033715,
-0.0009828130714595318,
0.0114496611058712,
-0.06905389577150345,
-0.009981299750506878,
0.033160023391246796,
0.040337372571229935,
-0.023939581587910652,
0.010783032514154911,
0.013318766839802265,
0.03480319306254387,
0.007164040580391884,
-0.01272850576788187,
-0.03717746585607529,
0.06340193748474121,
-0.03613975644111633,
0.01870717667043209,
0.001872269669547677,
-0.022052161395549774,
0.02497369423508644,
0.0336020365357399,
0.04472612217068672,
-0.021777553483843803,
-0.01181725412607193,
-0.023104988038539886,
0.010327544994652271,
0.008951310999691486,
0.0020951780024915934,
-0.0028701715636998415,
-0.012381458654999733,
0.05425513535737991,
0.036019228398799896,
0.04103098809719086,
-0.03424213081598282,
-0.046354472637176514,
-0.02143104560673237,
-0.04281852766871452,
-0.03050440363585949,
0.05281267687678337,
-0.02908727154135704,
-0.021228374913334846,
-0.009340651333332062,
-0.030801991000771523,
0.007563629653304815,
0.004922793246805668,
0.04027842357754707,
-0.06921091675758362,
0.05397198349237442,
-0.07912876456975937,
0.021279338747262955,
-0.00768960639834404,
0.009443536400794983,
0.12795786559581757,
0.06053336709737778,
0.01801953837275505,
-0.04262600094079971,
0.05079026147723198,
-0.01915176957845688,
-0.013564425520598888,
-0.03347640857100487,
0.019496990367770195,
-0.03571215271949768,
-0.0318274162709713,
0.003829386318102479,
0.009035457856953144,
0.004431841429322958,
-0.03264736011624336,
0.017482474446296692,
-0.02791895531117916,
-0.058370474725961685,
0.027882825583219528,
0.01714828610420227,
0.021649526432156563,
-0.021947884932160378,
-0.017286844551563263,
0.020883066579699516,
-0.024798976257443428,
-0.029179772362113,
-0.016973204910755157,
0.007213712204247713,
0.0053559900261461735,
0.028837846592068672,
-0.0012215544702485204,
0.006380636710673571,
0.029468907043337822,
0.003661214141175151,
-0.025744371116161346,
-0.01235310547053814,
-0.008324967697262764,
0.013053548522293568,
0.03815799206495285,
0.07595166563987732,
0.028459548950195312,
0.0008031607139855623,
0.016912955790758133,
0.02814333327114582,
-0.08275017142295837,
0.000827098498120904,
-0.03110065497457981,
0.051517304033041,
-0.008721593767404556,
-0.0288091953843832,
0.02422003075480461,
-0.06389512121677399,
-0.010820337571203709,
-0.055429860949516296,
-0.0202771108597517,
0.03977495804429054,
0.012290368787944317,
0.008048702962696552,
0.008281834423542023,
-0.027079792693257332,
0.04386219382286072,
-0.014578381553292274,
0.023451050743460655,
0.005196756683290005,
-0.02067001722753048,
-0.00995542947202921,
0.0167850311845541,
0.02700822800397873,
-0.021647479385137558,
-0.02063189260661602,
-0.049321841448545456,
-0.02268769033253193,
-0.02552272565662861,
-0.03792741149663925,
0.018067507073283195,
0.036575958132743835,
0.04711068794131279,
0.021269377321004868,
0.0015463479794561863,
-0.03551989421248436,
-0.0514722503721714,
0.03611341118812561,
-0.030025595799088478,
-0.027472293004393578,
-0.009894228540360928,
0.017546996474266052,
0.028452591970562935,
0.03627419099211693,
-0.035187382251024246,
-0.004813464358448982,
-0.006236468441784382,
0.015592947602272034,
-0.0026721907779574394,
-0.008463561534881592,
-0.004020921420305967,
-0.04774719849228859,
0.005584708880633116,
0.0031934480648487806,
-0.04138924181461334,
0.019089411944150925,
0.010802938602864742,
0.020719503983855247,
0.04122162237763405,
0.012223809957504272,
0.006713680922985077,
-0.016939125955104828,
0.003827964887022972,
-0.00621436070650816,
0.020976673811674118,
-0.0043566785752773285,
0.040689751505851746,
-0.03859966993331909,
0.005293724127113819,
-0.02850188873708248,
0.014705183915793896,
0.01555592194199562,
0.025968031957745552,
-0.03954531252384186,
-0.008504120633006096,
-0.020566843450069427,
-0.014386928640305996,
-0.02915732003748417,
-0.0029960663523525,
-0.015495359897613525,
-0.029134457930922508,
-0.02502746693789959,
0.03117620013654232,
0.020677687600255013,
0.043230440467596054,
0.005333174951374531,
-0.03132279962301254,
0.05034478008747101,
-0.001698800246231258,
-0.028888612985610962,
0.028752358630299568,
-0.0010626517469063401,
0.03998877480626106,
0.047130193561315536,
-0.02650538831949234,
-0.016538377851247787,
0.009207719936966896,
-0.05557898059487343,
-0.055507250130176544,
0.03914688527584076,
-0.043440382927656174,
-0.018290558829903603,
-0.006686078384518623,
-0.004398179240524769,
0.010381398722529411,
0.051099542528390884,
-0.016169782727956772,
0.01299380138516426,
0.01257734838873148,
0.0008380998624488711,
0.014375096186995506,
0.002207346959039569,
0.012712693773210049,
-0.01098929438740015,
0.001662622089497745,
0.03144829720258713,
0.028924645856022835,
-0.013306668028235435,
-0.01880776137113571,
0.008239004760980606,
-0.024410851299762726,
-0.043937381356954575,
-0.010181432589888573,
0.011512598022818565,
0.03561314567923546,
0.04554157704114914,
-0.03583401069045067,
-0.0019455142319202423,
0.028864121064543724,
-0.0013024610234424472,
-0.08843601495027542,
-0.0038884137757122517,
0.00719953840598464,
0.04172847792506218,
0.021890901029109955,
-0.036949966102838516,
0.013230436481535435,
0.028495818376541138,
-0.059051427990198135,
0.003929118160158396,
-0.03545694798231125,
-0.0430791974067688,
-0.050976939499378204,
-0.006044093053787947,
-0.012606551870703697,
0.06672707200050354,
0.0247125793248415,
0.039775170385837555,
-0.0021862799767404795,
0.020368266850709915,
-0.02718408778309822,
-0.03358539566397667,
0.021406099200248718,
0.0076431818306446075,
-0.03983721137046814,
0.006144266575574875,
0.05880676209926605,
0.00012289712321944535,
-0.05572948977351189,
0.0486132837831974,
0.0015004200395196676,
0.0031249490566551685,
-0.014109387062489986,
-0.003179354825988412,
0.028473908081650734,
0.01596958376467228,
0.029440660029649734,
-0.023962099105119705,
0.01358751766383648,
0.017115715891122818,
0.00680969376116991,
0.02507728710770607,
-0.0018502421444281936,
-0.0017025528941303492,
-0.005968691781163216,
-0.05429269000887871,
-0.01305645052343607,
0.025628631934523582,
-0.009130306541919708,
0.007144613657146692,
-0.029736539348959923,
-0.00737811578437686,
0.003082869341596961,
0.0065897563472390175,
0.028033548966050148,
-0.06033242866396904,
-0.02800269052386284,
0.005480160936713219,
0.0020768598187714815,
-0.014683634974062443,
-0.0027885029558092356,
-0.026077115908265114,
-0.020682448521256447,
0.038522869348526,
-0.03823546692728996,
0.002372817602008581,
-0.019905928522348404,
-0.028515322133898735,
0.031253982335329056,
0.009337218478322029,
-0.0010444524232298136,
-0.06822755187749863,
-0.030764907598495483,
0.012551702558994293,
0.015039834193885326,
0.0027482197619974613,
0.012997567653656006,
-0.02008541114628315,
-0.03136010095477104,
-0.03652465343475342,
0.020527418702840805,
-0.00803746934980154,
0.0041574155911803246,
-0.025703594088554382,
0.0000848867348395288,
-0.017931001260876656,
0.020402776077389717,
0.06096981093287468,
-0.016936883330345154,
-0.01704121008515358,
0.01934172213077545,
-0.04203888401389122,
0.009350020438432693,
-0.028979849070310593,
-0.005935120861977339,
-0.0026568674948066473,
-0.016469212248921394,
-0.02193932980298996,
-0.017488105222582817,
-0.011815417557954788,
-0.0011568868067115545,
0.006495271809399128,
0.004408384673297405,
0.022973112761974335,
0.04796719178557396,
-0.01525879092514515,
0.05617146193981171,
0.0252629816532135,
0.006023269146680832,
0.04794580861926079,
0.016364891082048416,
0.03924889490008354,
0.01140709687024355,
-0.009389074519276619,
-0.04522024840116501,
-0.02622278779745102,
-0.027781156823039055,
-0.023852931335568428,
0.0033798187505453825,
0.00707286549732089,
0.01045533362776041,
-0.005296479910612106,
-0.03658761456608772,
0.043609343469142914,
0.002561155939474702,
-0.046579327434301376,
0.019341638311743736,
-0.008163465186953545,
0.032272979617118835,
-0.004833685699850321,
0.031488820910453796,
0.06087171658873558,
-0.03775643929839134,
-0.027249405160546303,
0.05511971563100815,
0.025637466460466385,
0.017567625269293785,
0.002717517549172044,
0.023503372445702553,
0.014661263674497604,
0.045342687517404556,
0.027736153453588486,
0.05718337744474411,
-0.004468977451324463,
-0.004887801595032215,
0.02122638374567032,
-0.007788859773427248,
-0.007458974607288837,
0.031471990048885345,
-0.02015836350619793,
0.07030416280031204,
-0.006761727388948202,
0.011504522524774075,
0.0030100480653345585,
-0.007177188992500305,
-0.006483143661171198,
0.02225111424922943,
0.02462262474000454,
0.04249155521392822,
0.018870549276471138,
-0.014871873892843723,
-0.045916032046079636,
0.04439321532845497,
0.0021617331076413393,
-0.04060635343194008,
0.005335336085408926,
-0.019201042130589485,
0.03514265641570091,
0.010297652333974838,
-0.003500305349007249,
-0.007347390986979008,
-0.007997740991413593,
0.04169148951768875,
0.03879924863576889,
0.02358551323413849,
-0.05423156917095184,
0.008936780504882336,
-0.03612704202532768,
0.03789416328072548,
-0.05346135050058365,
0.016938012093305588,
0.01029626838862896,
0.06731248646974564,
-0.00158906530123204,
-0.009088966064155102
] |
<p>This was my engineering viva question and I couldn't think of any example, for I am totally convinced that there cannot be drag in a inviscid flow. It also bothers me whether it is possible, a tricky scenario in fluid mechanics or gas dynamics. </p>
| 7,638 |
[
0.0007317185518331826,
-0.01626369170844555,
-0.026800690218806267,
0.008459480479359627,
0.02584206685423851,
-0.018718400970101357,
-0.028270259499549866,
0.007665143348276615,
-0.009748991578817368,
-0.016014404594898224,
0.013027018867433071,
0.039298105984926224,
0.05974781513214111,
0.0015230876160785556,
0.004656070377677679,
0.02870568260550499,
-0.024728059768676758,
0.012181210331618786,
0.028915978968143463,
-0.0034080189652740955,
-0.02276976965367794,
0.00904447678476572,
0.03429625183343887,
-0.009571882896125317,
0.015412749722599983,
-0.03982522711157799,
0.03716156631708145,
-0.003565987106412649,
0.005685591138899326,
0.02343548648059368,
-0.014732773415744305,
0.0035073591861873865,
-0.011414336040616035,
0.0531618669629097,
0.03132662922143936,
0.011990426108241081,
-0.04731110855937004,
0.014681253582239151,
-0.008850978687405586,
0.004437027964740992,
-0.02107921615242958,
-0.04287242144346237,
-0.01988176442682743,
0.04610395431518555,
-0.03672044724225998,
-0.0025376793928444386,
0.0519065298140049,
-0.05111265927553177,
0.0563788041472435,
-0.07204654812812805,
0.05134468525648117,
-0.011808631010353565,
0.062423236668109894,
0.02656085044145584,
0.001794026349671185,
0.0006388628971762955,
0.03698685020208359,
0.06529247760772705,
-0.04028817638754845,
-0.015091328881680965,
0.0001997473300434649,
-0.005697205662727356,
-0.04776456207036972,
0.002561726374551654,
-0.04740920662879944,
-0.01471272949129343,
-0.023245422169566154,
-0.03558781370520592,
0.02908296138048172,
0.024393094703555107,
-0.01386166550219059,
0.016467008739709854,
-0.015271050855517387,
-0.018948093056678772,
0.006703607738018036,
0.008155163377523422,
0.015359554439783096,
-0.02947733923792839,
0.027894003316760063,
0.04365461692214012,
-0.00022473417629953474,
0.0038446392863988876,
0.0483783595263958,
0.018743891268968582,
-0.003036834066733718,
-0.06531037390232086,
0.06553381681442261,
-0.04129772633314133,
-0.006792192347347736,
0.013425960205495358,
0.001454233075492084,
-0.0297976303845644,
0.017560260370373726,
0.017832087352871895,
-0.016080765053629875,
0.010443804785609245,
-0.0162028968334198,
0.050659533590078354,
0.059584710747003555,
-0.03368941321969032,
-0.0008456788491457701,
0.011157488450407982,
0.03985324129462242,
0.07560915499925613,
0.005974309518933296,
-0.007579542230814695,
-0.00322174490429461,
0.03333951160311699,
-0.01125956978648901,
-0.011529100127518177,
-0.03656843304634094,
0.015271876007318497,
0.007244130130857229,
0.006257596425712109,
-0.011165374889969826,
-0.008183389902114868,
0.00007307878695428371,
-0.037468988448381424,
0.04849174618721008,
0.07026588171720505,
0.03889662027359009,
-0.014000176452100277,
0.01283729262650013,
0.011192971840500832,
-0.03631461039185524,
0.03518153727054596,
0.028185127303004265,
-0.020548591390252113,
-0.00650247186422348,
0.0070236846804618835,
-0.013716567307710648,
-0.012226606719195843,
-0.0033781302627176046,
-0.020015716552734375,
0.07073334604501724,
-0.0316150076687336,
-0.07406044006347656,
-0.05809370428323746,
0.040036529302597046,
0.01876291073858738,
-0.02565895952284336,
-0.041225727647542953,
0.02126428298652172,
0.022613372653722763,
0.05658910796046257,
-0.005615329369902611,
-0.0017421385273337364,
-0.013074833899736404,
0.04038015753030777,
-0.037300948053598404,
0.0068047186359763145,
0.004644360858947039,
0.002199969021603465,
-0.06377090513706207,
0.008701805956661701,
-0.0671294778585434,
-0.008891613222658634,
0.03732823207974434,
0.024846695363521576,
-0.03165465220808983,
0.02672647498548031,
-0.02608673833310604,
0.02173537015914917,
0.010889885947108269,
0.022816931828856468,
-0.04786986485123634,
0.08206792175769806,
0.012946698814630508,
-0.0023578698746860027,
0.005465478170663118,
0.04932054504752159,
0.010624943301081657,
-0.006602748762816191,
-0.01946253515779972,
0.06908410042524338,
-0.03851041942834854,
-0.01235379371792078,
-0.02447969652712345,
0.018041526898741722,
0.016956232488155365,
-0.026569729670882225,
-0.05031747370958328,
0.022845139726996422,
-0.005354057066142559,
-0.007707666605710983,
0.04353367164731026,
-0.017905283719301224,
-0.012596112675964832,
0.01670938916504383,
-0.055569086223840714,
0.019572721794247627,
-0.02798897586762905,
0.019358769059181213,
-0.010862447321414948,
-0.011695298366248608,
0.012787319719791412,
0.03283943980932236,
0.0344330295920372,
-0.0786220133304596,
-0.005659799091517925,
-0.020042166113853455,
0.0013759387657046318,
-0.004651398863643408,
-0.00812812801450491,
0.010835278779268265,
0.009274720214307308,
0.010541620664298534,
0.020274583250284195,
0.05222800374031067,
0.01005132868885994,
-0.011315192095935345,
-0.01678452081978321,
-0.03960863873362541,
0.07183310389518738,
-0.014584541320800781,
-0.0039055985398590565,
0.03584324195981026,
-0.0021962455939501524,
-0.0002726990496739745,
0.028746122494339943,
0.0009790476178750396,
0.06452823430299759,
0.03416923061013222,
0.024944385513663292,
-0.018200846388936043,
0.0009498249855823815,
0.006007554475218058,
-0.046405594795942307,
0.03582491725683212,
-0.03453359007835388,
-0.009180894121527672,
0.0009038941934704781,
0.04550248011946678,
0.03592472895979881,
-0.045729395002126694,
0.03190356492996216,
0.04416462779045105,
0.052993543446063995,
0.05864613130688667,
0.05115453526377678,
-0.02070612646639347,
-0.05614946410059929,
0.031458888202905655,
0.044533148407936096,
0.046361349523067474,
0.03111634962260723,
0.0500541552901268,
0.02299700491130352,
0.022456282749772072,
-0.023176467046141624,
-0.030405374243855476,
0.02134394459426403,
0.01728779636323452,
-0.020652614533901215,
0.014513887465000153,
0.006010763347148895,
0.03145859017968178,
-0.039253491908311844,
0.022351866587996483,
-0.0003217370540369302,
0.007996230386197567,
0.014875675551593304,
0.0026803126093000174,
0.023205066099762917,
0.030093567445874214,
0.01625734381377697,
-0.04235788807272911,
-0.005417002830654383,
0.06607404351234436,
-0.022784406319260597,
0.027018513530492783,
-0.03191930800676346,
0.035359714180231094,
-0.03891829028725624,
-0.004205179866403341,
0.025799617171287537,
0.015006650239229202,
0.0651349127292633,
-0.0037284221034497023,
-0.0395815335214138,
-0.01409169565886259,
-0.05070056766271591,
-0.02960187755525112,
0.015201019123196602,
-0.022933658212423325,
0.07124976068735123,
-0.04904741048812866,
-0.029330594465136528,
0.06016484647989273,
-0.046076081693172455,
-0.006902752909809351,
0.04225993528962135,
-0.051201481372117996,
-0.034969694912433624,
-0.0008783774101175368,
-0.06337886303663254,
-0.007884643040597439,
-0.017254967242479324,
0.05593312159180641,
0.06321324408054352,
-0.00015168059326242656,
-0.062184881418943405,
0.024998975917696953,
-0.010144987143576145,
-0.03259902074933052,
-0.036709126085042953,
-0.0038167210295796394,
0.04738559201359749,
-0.05457178130745888,
0.045171864330768585,
0.003272366477176547,
-0.031466156244277954,
0.027244817465543747,
-0.000806596886832267,
-0.029487304389476776,
0.02048100158572197,
-0.0054571968503296375,
0.03714442998170853,
-0.009969892911612988,
-0.037852074950933456,
0.046956490725278854,
-0.005097497720271349,
-0.04992813244462013,
-0.02209371142089367,
-0.035915810614824295,
-0.013768961653113365,
-0.020553359761834145,
-0.01095938216894865,
0.03119208663702011,
-0.021006781607866287,
0.004313845187425613,
0.022659964859485626,
0.045127417892217636,
-0.019029011949896812,
-0.0015807467279955745,
-0.02657540701329708,
-0.000987506122328341,
0.018604667857289314,
0.006145738996565342,
0.05197981745004654,
0.018729697912931442,
-0.05686028301715851,
0.03620964288711548,
-0.016238581389188766,
0.052977532148361206,
0.018519142642617226,
-0.042773403227329254,
0.06662678718566895,
-0.023251406848430634,
0.006973668932914734,
-0.02779938094317913,
0.021502530202269554,
-0.0047564576379954815,
0.03576957806944847,
0.0066587855108082294,
0.048796147108078,
-0.000973435235209763,
-0.03180168941617012,
0.00015389356121886522,
0.033448800444602966,
0.050027310848236084,
-0.020867828279733658,
0.00887886993587017,
-0.0031220426317304373,
-0.00931093655526638,
0.06553741544485092,
0.002899536630138755,
-0.027320481836795807,
0.06495503336191177,
0.02425459399819374,
0.007725163362920284,
0.010930784977972507,
-0.018801361322402954,
0.02929648756980896,
-0.05958596616983414,
-0.017267070710659027,
-0.012628036551177502,
0.023706277832388878,
-0.025319678708910942,
0.028626292943954468,
-0.004207227379083633,
0.06444726884365082,
0.00327934673987329,
-0.021616961807012558,
-0.09894365072250366,
0.021576201543211937,
-0.029333652928471565,
-0.04357755556702614,
-0.028630416840314865,
0.019412990659475327,
0.001335230772383511,
-0.05080572888255119,
-0.032284870743751526,
0.0030824532732367516,
0.01669764332473278,
-0.06416252255439758,
0.020403049886226654,
-0.02577974461019039,
-0.027183253318071365,
0.013689877465367317,
0.028744053095579147,
0.036705996841192245,
-0.023059694096446037,
0.018273286521434784,
0.020073961466550827,
-0.003181894775480032,
-0.02903934195637703,
-0.016599534079432487,
-0.015952318906784058,
0.014543049968779087,
0.01589399203658104,
0.022329552099108696,
0.01950792782008648,
-0.05233902484178543,
0.024168608710169792,
0.00765583012253046,
0.04261714592576027,
-0.021554995328187943,
0.0176240224391222,
-0.015316992998123169,
-0.03885918855667114,
-0.0030636913143098354,
0.0455935113132,
0.027706153690814972,
-0.013939124532043934,
0.018682008609175682,
-0.02018781751394272,
0.017889730632305145,
-0.015779657289385796,
0.04853549599647522,
0.029658200219273567,
0.048440657556056976,
-0.0006108252564445138,
-0.05167189985513687,
0.0021336390636861324,
-0.003918613772839308,
0.009329778142273426,
0.0175246000289917,
0.027075067162513733,
-0.03879612311720848,
-0.010262093506753445,
-0.011310436762869358,
0.015996303409337997,
0.013444333337247372,
0.006113067734986544,
-0.02128407545387745,
0.009090562351047993,
0.006210128776729107,
0.010900230146944523,
0.02624133788049221,
0.009898233227431774,
0.040901996195316315,
0.023673580959439278,
0.00021711227600462735,
-0.10166122019290924,
0.004057489801198244,
0.07354427874088287,
0.00042688834946602583,
-0.010517471469938755,
0.010558507405221462,
-0.007908403873443604,
-0.011921504512429237,
0.068171426653862,
-0.029195766896009445,
0.009707915596663952,
-0.04916821047663689,
-0.000016102439985843375,
0.04385107010602951,
-0.0403292290866375,
0.005567485466599464,
0.008129472844302654,
0.00028296990785747766,
-0.041583433747291565,
-0.029907558113336563,
-0.011874580755829811,
0.00943007506430149,
0.02307978831231594,
0.04166451096534729,
0.0500376895070076,
0.050496987998485565,
-0.006179756484925747,
-0.0276294257491827,
0.023578619584441185,
-0.059252478182315826,
-0.0683751180768013,
0.012147475965321064,
0.04125102236866951,
-0.01584211364388466,
0.02855219505727291,
-0.045738983899354935,
-0.05397222563624382,
0.04552335664629936,
-0.02555973082780838,
-0.023725438863039017,
0.004050527233630419,
-0.017806580290198326,
0.006636110600084066,
0.04177603870630264,
0.016321737319231033,
0.05213363841176033,
0.07739780843257904,
-0.012401553802192211,
-0.03705426678061485,
0.010664032772183418,
0.04764406010508537,
-0.021254904568195343,
-0.04224606975913048,
-0.02345362864434719,
-0.013468308374285698,
-0.004560654517263174,
0.030504517257213593,
0.0002725350495893508,
0.00147918495349586,
0.03795981407165527,
-0.04441158473491669,
-0.02159760519862175,
0.023661645129323006,
0.022508028894662857,
-0.0402560792863369,
-0.009837324731051922,
0.031037652865052223,
-0.02160022035241127,
-0.03740910440683365,
-0.0032275267876684666,
0.042434729635715485,
-0.027196010574698448,
0.03177007660269737,
-0.011086289770901203,
0.004339374136179686,
-0.005600733682513237,
0.010586541146039963,
-0.00176720111630857,
-0.05183238163590431,
0.0651165172457695,
-0.029246428981423378,
0.0037072773557156324,
0.008078997023403645,
-0.05483455955982208,
-0.01636110432446003,
-0.0010324025060981512,
0.04793956130743027,
0.024788377806544304,
-0.04727092385292053,
0.027371058240532875,
-0.0015086685307323933,
-0.010941928252577782,
-0.0505509115755558,
-0.04888623580336571,
0.020514952018857002,
0.05186987668275833,
0.013777829706668854,
-0.036328986287117004,
-0.06963299214839935,
-0.03924357891082764,
-0.05681698024272919,
-0.025351090356707573,
0.027373429387807846,
-0.046116799116134644,
0.008422113955020905,
-0.004579751752316952,
0.006340833846479654,
0.013131826184689999,
-0.008684610016644001,
-0.017172953113913536,
0.01086971815675497,
-0.04904952272772789,
0.011349000036716461,
0.012090394273400307,
0.034465473145246506,
-0.008506461046636105,
0.0014853024622425437,
0.016817763447761536,
-0.03953208774328232,
0.032385047525167465,
-0.017101099714636803,
-0.0012690204894170165,
0.053138475865125656,
-0.0482630617916584,
0.023055529221892357,
0.007846645079553127,
0.03660006448626518,
-0.0420362651348114,
0.028405198827385902,
-0.0011814344907179475,
-0.019292229786515236,
0.0008501951233483851,
-0.07283596694469452,
0.03511834517121315,
0.017760440707206726,
0.020037371665239334,
-0.029094861820340157,
0.03998953476548195,
-0.01919810101389885,
-0.0392477922141552,
0.031195776537060738,
-0.00029434339376166463,
0.022436605766415596,
0.011425899341702461,
-0.006638598162680864,
-0.013797372579574585,
-0.00930627528578043,
-0.021849658340215683,
-0.032745394855737686,
0.013249227777123451,
-0.014422963373363018,
0.06361910700798035,
-0.06034107133746147,
0.0631093680858612,
-0.009593716822564602,
-0.012344473972916603,
0.020969033241271973,
0.01773141697049141,
-0.035955965518951416,
0.014106562361121178,
-0.011396598070859909,
0.042195677757263184,
-0.021254004910588264,
0.005599679425358772,
0.02583957090973854,
0.029337793588638306,
0.003923838026821613,
-0.0009878817945718765,
0.000025281948182964697,
0.01143808476626873,
0.019382672384381294,
0.04904713109135628,
-0.02174603007733822,
0.018315274268388748,
-0.03419049084186554,
0.0681813657283783,
-0.005989579018205404,
-0.01376632135361433,
0.05283166840672493,
-0.024635110050439835,
0.01713797263801098,
-0.04373429715633392,
0.006001145113259554,
-0.016643289476633072,
0.039402853697538376,
-0.012965593487024307,
-0.0024240559432655573,
0.01425315160304308,
-0.026398632675409317,
0.041933976113796234,
-0.014865278266370296,
-0.006321337074041367,
-0.0287859458476305,
-0.05169520154595375,
-0.03877352550625801,
-0.003545525949448347,
0.014405126683413982,
0.030059296637773514,
0.013881407678127289,
-0.02545939013361931,
-0.013323530554771423,
-0.024383753538131714,
-0.005165854003280401,
0.006548314820975065,
0.054533977061510086,
0.022246625274419785,
0.061884135007858276,
-0.004229291807860136,
0.021626142784953117,
-0.04924580082297325,
0.03972812741994858,
0.11558618396520615,
0.030971765518188477,
0.034221988171339035,
-0.05784674361348152,
-0.021032873541116714,
-0.03721323236823082,
-0.0053269765339791775,
-0.03603142499923706,
0.019403211772441864,
0.013044437393546104,
0.0038700313307344913,
0.022029142826795578,
0.08755336701869965,
0.002874827478080988,
0.006429904140532017,
0.024608612060546875,
-0.05193205550312996,
-0.035969652235507965,
-0.01291953306645155,
-0.004865780007094145,
-0.035384636372327805,
0.029874084517359734,
-0.0440472811460495,
0.0666642114520073,
-0.002914744894951582,
0.02145308442413807,
-0.006796518340706825,
-0.042187925428152084,
0.025180501863360405,
0.02121216431260109,
-0.08567903190851212,
-0.029370896518230438,
0.04062468931078911,
-0.011759735643863678,
-0.05966534838080406,
-0.03444350138306618,
0.00030404492281377316,
-0.02372404932975769,
-0.00011928244202863425,
0.032967180013656616,
0.017468880861997604,
0.026313364505767822,
0.006153604481369257,
-0.005611571483314037,
-0.021960383281111717,
-0.03479563072323799,
-0.0113007677718997,
-0.0024557518772780895,
0.005055268760770559,
0.03191410377621651,
-0.013434769585728645,
-0.01787726953625679,
0.002900870982557535,
-0.046667519956827164,
-0.04403942450881004,
-0.05913116782903671,
0.009766899980604649,
0.0017840262735262513,
-0.03891008719801903,
0.03648454323410988,
0.04858991131186485,
0.007487309630960226,
0.0002715929294936359,
0.021222207695245743,
0.00832934956997633,
0.014182559214532375,
-0.00685895187780261,
0.06158308684825897,
-0.0015517985448241234,
-0.021419135853648186,
-0.0067765191197395325,
0.009715905413031578,
-0.027105184271931648,
0.004458711948245764,
-0.005269899033010006,
0.007662434130907059,
0.019029179587960243,
0.009032136760652065,
-0.029229292646050453,
-0.02786894515156746,
-0.014308381825685501,
0.022436898201704025,
0.009598237462341785,
-0.0010403057094663382,
0.01581638678908348,
0.011200767941772938,
0.031265437602996826,
0.023926444351673126,
-0.02007165551185608,
-0.03507402539253235,
-0.022192714735865593,
0.05949586629867554,
0.001693779369816184,
-0.032008931040763855,
-0.06331027299165726,
0.016950281336903572,
-0.03707152232527733,
0.007181207183748484,
0.010468441992998123,
0.02564839832484722,
0.01595059223473072,
-0.011605032719671726,
-0.03651268780231476,
0.03049927018582821,
-0.005542647559195757,
0.020485779270529747,
0.04102436825633049,
-0.02841636911034584,
0.005494742188602686,
0.018637821078300476,
0.026058601215481758,
-0.02730708196759224,
-0.04802309349179268,
-0.030499039217829704,
0.022981885820627213,
-0.015800615772604942,
0.0327051505446434,
-0.0032163793221116066,
0.046663522720336914,
0.0062835062853991985,
0.03353019058704376,
-0.04314348101615906,
-0.00842486135661602,
-0.04906632378697395,
-0.0042503876611590385,
0.00531249912455678,
0.00519120367243886,
-0.017294814810156822,
0.024904128164052963,
-0.08201140910387039,
0.0064645432867109776,
-0.025041159242391586,
0.042026203125715256,
-0.018048787489533424,
-0.01651686429977417,
0.019129447638988495,
0.022733408957719803,
-0.009374282322824001,
-0.008181811310350895,
-0.02289721556007862,
0.0780501514673233,
-0.013753625564277172,
-0.06470858305692673,
0.021255863830447197,
-0.021135114133358,
0.003305799560621381,
0.005146179813891649,
-0.014581548050045967,
-0.032460715621709824,
0.07109305262565613,
0.02926342561841011,
0.002666570944711566,
-0.018595153465867043,
-0.017568137496709824,
-0.04821328818798065,
-0.013719936832785606,
0.028848081827163696,
-0.04526442661881447,
-0.010242938064038754,
0.032607149332761765,
0.03171669691801071,
-0.022027917206287384,
-0.01568276435136795,
0.009995159693062305,
0.007936402224004269,
0.011601864360272884,
0.013760901056230068,
0.0069151162169873714,
0.013315300457179546,
0.041578326374292374,
-0.04999956488609314,
0.034242644906044006,
0.009392446838319302,
-0.0026206441689282656,
-0.12176372110843658,
0.007769924588501453,
0.01544493529945612,
0.014981041662395,
0.018143674358725548,
-0.06768912822008133,
0.012814738787710667,
0.021734114736318588,
-0.06310960650444031,
-0.015310946851968765,
-0.03914903104305267,
0.005397918168455362,
-0.03233100101351738,
-0.010021233931183815,
0.01624944806098938,
0.010772685520350933,
0.02938336879014969,
0.00579812889918685,
-0.03015972301363945,
0.03727265074849129,
-0.0156888198107481,
-0.008792526088654995,
-0.008154378272593021,
0.009800311177968979,
-0.01630515232682228,
0.0040024458430707455,
0.026683764532208443,
0.0021406938321888447,
-0.02046729065477848,
-0.003039329079911113,
0.013313629664480686,
0.023093337193131447,
0.004744622390717268,
-0.015792056918144226,
-0.026648717001080513,
0.006727814208716154,
0.00882378313690424,
0.014018172398209572,
-0.026679642498493195,
0.05012136325240135,
-0.0022682619746774435,
0.002635417738929391,
-0.003081300761550665,
-0.011649440973997116,
0.019203124567866325,
-0.030824508517980576,
-0.025057028979063034,
0.031445205211639404,
-0.03632495924830437,
-0.037408750504255295,
0.012351864948868752,
0.006038253661245108,
0.0364702008664608,
-0.015908746048808098,
0.005725732073187828,
-0.07706451416015625,
-0.01005590334534645,
-0.0006095101125538349,
0.018759706988930702,
0.007143272086977959,
0.016568047925829887,
-0.0027311849407851696,
-0.020189860835671425,
-0.0017127208411693573,
-0.029533758759498596,
-0.0024677824694663286,
-0.031282052397727966,
-0.011691314168274403,
-0.04906320944428444,
-0.023543208837509155,
0.0007862095371820033,
-0.04847567528486252,
0.01861582323908806,
0.047929778695106506,
0.01673560030758381,
0.003857119008898735,
-0.017947789281606674,
-0.00019935808086302131,
-0.0340469665825367,
-0.017992941662669182,
0.019838815554976463,
-0.004275182727724314,
0.02839558757841587,
-0.02099747024476528,
0.016393642872571945,
0.00896284356713295,
0.031500786542892456,
0.01602146588265896,
-0.03876989334821701,
0.012116499245166779,
0.05557037517428398,
-0.01167108304798603,
-0.02185199037194252,
-0.02758699283003807,
-0.006115542724728584,
-0.02034803293645382,
-0.030299102887511253,
-0.0102050406858325,
-0.015307174995541573,
-0.008784893900156021,
-0.010610810481011868,
0.018898189067840576,
0.040653131902217865,
0.047581978142261505,
-0.00517335394397378,
-0.023979714140295982,
0.02217281050980091,
0.05238496884703636,
-0.011820513755083084,
0.015189656987786293,
0.005739122629165649,
0.008795423433184624,
-0.0024752251338213682,
-0.03494439646601677,
-0.02121027000248432,
0.029923956841230392,
-0.03341960906982422,
-0.021109869703650475,
-0.03720618039369583,
-0.016370369121432304,
-0.008224236778914928,
-0.03334278613328934,
0.022219564765691757,
0.03527592867612839,
-0.030027326196432114,
-0.0100683169439435,
0.03017263114452362,
0.025356823578476906,
0.017211927101016045,
-0.029129501432180405,
-0.024417662993073463,
0.014118524268269539,
0.015668150037527084,
-0.017648836597800255,
0.052838534116744995,
0.022003116086125374,
0.0036545125767588615,
0.004413135349750519,
0.029806019738316536,
-0.002675378927960992,
-0.015967411920428276,
0.003936371300369501,
0.0031910231336951256,
-0.008145752362906933,
-0.03845351189374924,
-0.004363473039120436,
-0.022684413939714432,
0.006025674752891064,
-0.01043475978076458,
0.004127015359699726,
0.06967766582965851,
-0.031010936945676804,
0.051359571516513824,
-0.0362946055829525,
0.014224112965166569,
-0.019532080739736557,
0.02605254203081131,
0.026986252516508102,
0.06297093629837036,
-0.005820855963975191,
-0.03808654472231865,
-0.0013439168687909842,
-0.025589361786842346,
0.005319497548043728,
-0.014095154590904713,
0.005758489016443491,
-0.026698941364884377,
0.004387053661048412,
-0.029626235365867615,
0.001421180902980268,
-0.035065967589616776,
-0.019820626825094223,
0.0221093837171793,
0.051253534853458405,
0.005784445907920599,
0.039938803762197495,
-0.022047344595193863,
-0.016909977421164513,
0.07236406207084656,
-0.06477170437574387,
-0.004549745004624128,
-0.002168698702007532,
0.06447724997997284,
-0.044276993721723557,
0.0015171192353591323
] |
<p>How can one make sense of the idea of extremizing a Hamilton-Jacobi equation?</p>
<p>In Schrödinger's paper "Quantisation as a Problem of Proper Values I" (<em>Annalen der Physik</em> (4), vol. 79, 1926, p. 1, available e.g. in <a href="http://einstein.drexel.edu/~bob/Quantum_Papers/Schr_1.pdf" rel="nofollow"><em>Collected papers on wave mechanics</em>, AMS publishing</a>) he begins with the classical time-independent Hamilton-Jacobi equation </p>
<p>$$H(q,\frac{\partial S}{\partial q}) = E$$</p>
<p>and instead of assuming an additive solution for separation of variables he assumes a multiplicative solution thus defining $S = K\ln(\psi)$ to get</p>
<p>$$H(q,\frac{K}{\psi} \frac{\partial \psi}{\partial q}) = E.$$</p>
<p>Instead of solving it he talks about how this last equation "can always be transformed so as to become a quadratic form (of $\psi$ & its first derivatives) equated to zero", neglecting the relativistic variation of mass.</p>
<p>(I'm assuming that transforming this to a quadratic form means a Taylor expansion in powers of $\psi$, though I'm not sure about that).</p>
<p>Then he seeks "a function $\psi$, such that for any arbitrary variation of it the integral of the said quadratic form, taken over the whole of coordinate space (I am aware this formulation is not entirely unambiguous), is stationary, $\psi$ being everywhere real, single-valued, finite, and continuously differentiable up to the second order."</p>
<p>In other words, he basically extremizes</p>
<p>$$I = \iiint\left(\frac{K^2}{2m}\left[\left(\frac{\partial \psi}{\partial x}\right)^2 \ + \ \left(\frac{\partial \psi}{\partial y}\right)^2 \ + \ \left(\frac{\partial \psi}{\partial z}\right)^2\right] + (V - E)\psi^2\right)\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$$ </p>
<p>and ends up with the time independent Schrödinger equation, but the issue is extremizing the Hamilton-Jacobi equation. Where is the justification for this?</p>
<p>I can only find a reference to it <a href="https://www.google.ie/search?q=extremizing%20the%20hamilton-jacobi%20equation&ie=utf-8&oe=utf-8&rls=org.mozilla%3aen-US%3aofficial&client=firefox-a&gws_rd=cr&ei=b8kxUvrZMoiV7AaLooCQDg#psj=1&q=%22variation%20of%20the%20hamilton-jacobi%20equation%22&rls=org.mozilla%3aen-US%3aofficial" rel="nofollow">here</a> (in the ps.gz link), so it does seem to be something more than one person has done, but what is the theory behind this? Does it function as another method of solving Hamilton's equations? If so, why?</p>
| 7,639 |
[
-0.013226783834397793,
0.022511625662446022,
0.04867943003773689,
-0.07329791784286499,
0.06043796241283417,
-0.02741837128996849,
-0.06739600747823715,
-0.03849523141980171,
-0.0027254982851445675,
-0.05166545882821083,
0.03240574523806572,
0.008628484793007374,
0.054671913385391235,
0.0318308100104332,
0.04485062137246132,
0.014379812404513359,
0.010544327087700367,
-0.04600286856293678,
-0.028859781101346016,
-0.028429025784134865,
-0.005830117966979742,
0.018600108101963997,
-0.008819221518933773,
0.0010779786389321089,
-0.022198490798473358,
0.013229487463831902,
-0.015372632071375847,
0.007999726571142673,
-0.010894029401242733,
0.09302569925785065,
-0.005512728355824947,
-0.01580108515918255,
0.013020223006606102,
0.016491394490003586,
0.011456278152763844,
0.03486170247197151,
-0.03152243047952652,
-0.036412313580513,
-0.0068381354212760925,
0.016350235790014267,
-0.03643020614981651,
-0.0032446321565657854,
0.031148992478847504,
0.032095085829496384,
0.0003008109924849123,
0.06508922576904297,
0.029396243393421173,
-0.039050109684467316,
0.021244948729872704,
-0.04679403826594353,
0.0768621563911438,
0.029090162366628647,
0.01716022752225399,
-0.00778186833485961,
0.005426378455013037,
-0.006879068911075592,
0.07881857454776764,
0.04457017406821251,
-0.0029673667158931494,
-0.07787206768989563,
-0.023515230044722557,
0.0015435911482200027,
0.00769795523956418,
0.008748399093747139,
-0.011992628686130047,
-0.005867112427949905,
0.03355962783098221,
-0.0208818931132555,
0.008762327954173088,
-0.029906529933214188,
-0.011753188446164131,
0.005550761241465807,
0.04634978249669075,
-0.011394056491553783,
0.004146231804043055,
-0.002190233441069722,
-0.007820886559784412,
-0.008099679835140705,
0.0019701621495187283,
0.002824612660333514,
-0.013344388455152512,
0.0037841324228793383,
0.02649524435400963,
0.030671853572130203,
-0.013787268660962582,
0.01063952874392271,
0.07959195226430893,
0.016647765412926674,
0.020136291161179543,
0.043918538838624954,
-0.021774936467409134,
0.057728178799152374,
0.035471171140670776,
-0.01551575306802988,
-0.00722879683598876,
0.014988796785473824,
0.026801766827702522,
0.03982110694050789,
-0.012113005854189396,
-0.028941377997398376,
0.03355572372674942,
-0.03740588575601578,
-0.02887195348739624,
0.045030344277620316,
0.025597071275115013,
0.0035953556653112173,
-0.004765568301081657,
0.027220701798796654,
-0.019796540960669518,
-0.021584540605545044,
0.0005383439711295068,
0.03841819241642952,
-0.0011607728665694594,
0.023158099502325058,
-0.014925315976142883,
-0.026115287095308304,
0.0001602414413355291,
-0.017679881304502487,
0.05652054771780968,
0.04268611595034599,
0.033031634986400604,
-0.026058904826641083,
0.02707100845873356,
-0.026131022721529007,
-0.042927343398332596,
-0.005338621791452169,
0.01391756534576416,
0.0287350881844759,
-0.05599784478545189,
-0.006682150065898895,
0.019384730607271194,
-0.006745833903551102,
-0.015834294259548187,
0.030350523069500923,
0.006932714954018593,
-0.048714328557252884,
-0.10604651272296906,
-0.0592193640768528,
0.03595099225640297,
-0.017900506034493446,
0.004385573323816061,
-0.06246107444167137,
0.0006010759971104562,
0.04371373727917671,
0.08208955079317093,
-0.02657867781817913,
-0.022787224501371384,
0.013376126997172832,
0.05328480526804924,
0.012782690115272999,
-0.01443912647664547,
-0.034865256398916245,
-0.005447182338684797,
-0.03073461912572384,
0.02200612984597683,
-0.04876766726374626,
0.001977742649614811,
0.026683716103434563,
-0.007396582514047623,
0.02430829219520092,
0.07542812079191208,
-0.0019825275521725416,
-0.03536803275346756,
0.0394301563501358,
0.006244577467441559,
-0.005876361858099699,
0.047993097454309464,
0.02219231054186821,
0.014621127396821976,
0.031825050711631775,
0.01060323417186737,
0.03832659870386124,
-0.036749329417943954,
0.006203243974596262,
-0.018980829045176506,
-0.06507319211959839,
-0.0027392711490392685,
-0.06715930253267288,
-0.009607727639377117,
0.007424306124448776,
-0.021226918324828148,
-0.03435998409986496,
0.0005844427505508065,
0.012158886529505253,
-0.008125726133584976,
0.02672152779996395,
-0.01018369011580944,
0.03741596266627312,
-0.0068443468771874905,
-0.018552454188466072,
0.01261294074356556,
-0.04563218355178833,
0.03182735666632652,
0.011463981121778488,
0.015198214910924435,
0.03582533821463585,
0.019152918830513954,
-0.0019809301011264324,
-0.01040336862206459,
-0.02028352953493595,
0.032743778079748154,
0.03527780622243881,
0.001968571450561285,
-0.015085828490555286,
0.047550324350595474,
0.076020747423172,
0.009850178845226765,
0.01960868388414383,
0.037566669285297394,
0.014535311609506607,
-0.04581352323293686,
0.01651061698794365,
-0.005220144055783749,
0.053133316338062286,
-0.015037523582577705,
0.0055107478983700275,
-0.015276055783033371,
-0.02775697596371174,
0.013180621899664402,
-0.01890670321881771,
-0.06696262955665588,
0.027095017954707146,
0.02569308690726757,
0.012239855714142323,
-0.008967725560069084,
0.0607234425842762,
0.005478843580931425,
0.04681374505162239,
0.026141300797462463,
-0.016330726444721222,
-0.02941143326461315,
0.007804289925843477,
0.03949035331606865,
0.05224153399467468,
-0.02842807024717331,
-0.02155630849301815,
0.02997155301272869,
0.04333340749144554,
0.04992399364709854,
0.026451576501131058,
-0.05632501840591431,
-0.02743268758058548,
0.022701812908053398,
-0.012839533388614655,
-0.0235849991440773,
0.020367125049233437,
0.035656463354825974,
-0.01647089049220085,
0.024100786074995995,
-0.01752609945833683,
-0.028857050463557243,
0.011415055952966213,
-0.009110062383115292,
0.00781969353556633,
0.045205067843198776,
-0.033551398664712906,
0.02393849939107895,
-0.007540382910519838,
-0.005970400292426348,
0.033321529626846313,
-0.042105600237846375,
0.016971981152892113,
-0.06704139709472656,
0.0009414463420398533,
0.01362151000648737,
-0.03911619633436203,
-0.0059198844246566296,
-0.027381042018532753,
0.01470674853771925,
-0.052078958600759506,
-0.027414824813604355,
-0.042155299335718155,
-0.03545839712023735,
-0.018307512626051903,
-0.02983756549656391,
0.029261842370033264,
0.03131590038537979,
-0.002996844006702304,
-0.020109662786126137,
-0.00018411599739920348,
0.024453911930322647,
-0.020403681322932243,
0.01696438156068325,
0.027677686884999275,
-0.028172852471470833,
0.008552877232432365,
-0.07882125675678253,
-0.02974875643849373,
0.03917815908789635,
-0.0016847377410158515,
0.016510089859366417,
0.034627869725227356,
-0.007475378457456827,
-0.030622148886322975,
-0.017016448080539703,
-0.03643185645341873,
-0.009870053268969059,
0.00019856025755871087,
0.022141918540000916,
0.0637262612581253,
0.019514450803399086,
-0.031542178243398666,
0.0010019430192187428,
-0.02209794707596302,
-0.03368833661079407,
-0.033132802695035934,
-0.027769241482019424,
0.022850772365927696,
-0.035651445388793945,
0.005915015935897827,
0.003082815557718277,
-0.018820764496922493,
-0.03169833496212959,
-0.0914287194609642,
-0.028868021443486214,
0.02625388838350773,
0.01725403219461441,
0.06143574044108391,
0.006711706984788179,
-0.017973247915506363,
0.07596994936466217,
0.017478207126259804,
-0.0025425832718610764,
-0.034223247319459915,
0.02288711629807949,
0.005564176477491856,
-0.009424000047147274,
-0.0006556296139024198,
0.021498242393136024,
0.006430320907384157,
0.023920586332678795,
-0.005227730143815279,
0.01776926778256893,
0.023836160078644753,
-0.011290258727967739,
-0.002393365139141679,
0.029575448483228683,
-0.035838525742292404,
0.03333970904350281,
0.02253745123744011,
0.0302544217556715,
-0.007133562583476305,
0.0005038993549533188,
0.00864753220230341,
0.05224357172846794,
-0.008476895280182362,
-0.03264210745692253,
0.06630450487136841,
0.01958434283733368,
0.010715204291045666,
-0.012371360324323177,
0.03049652650952339,
-0.019560622051358223,
-0.03996053710579872,
-0.026179835200309753,
0.0007681567803956568,
0.012661603279411793,
-0.012089364230632782,
0.0075163147412240505,
0.004580473527312279,
0.03849928826093674,
-0.016508469358086586,
-0.017420850694179535,
0.011506729759275913,
-0.017488740384578705,
0.051415275782346725,
-0.05011717230081558,
-0.05244188755750656,
0.018739543855190277,
0.017629455775022507,
0.0020182745065540075,
-0.037737686187028885,
-0.035251788794994354,
-0.028207983821630478,
-0.03567139059305191,
-0.015368037857115269,
0.020696444436907768,
0.07594937086105347,
0.027778802439570427,
0.07937251031398773,
0.030724508687853813,
0.014315138570964336,
-0.014978190883994102,
0.009762262925505638,
-0.06663487106561661,
0.00689366040751338,
-0.03243379294872284,
0.030255474150180817,
-0.00322100892663002,
-0.007251119241118431,
0.016927797347307205,
-0.0351041741669178,
-0.034465666860342026,
-0.024825366213917732,
-0.004303787834942341,
-0.05638055503368378,
0.0016302745789289474,
-0.04035922884941101,
-0.043823130428791046,
-0.04696124792098999,
0.029934577643871307,
0.036003757268190384,
-0.010811645537614822,
-0.001089051365852356,
0.03401567041873932,
-0.032396622002124786,
0.0026693991385400295,
-0.010718266479671001,
0.005217715632170439,
0.06178008392453194,
0.03686721622943878,
0.018413811922073364,
0.006204313598573208,
-0.022890569642186165,
0.025173746049404144,
0.01736106164753437,
0.07342033088207245,
0.024860061705112457,
-0.049799807369709015,
0.019661888480186462,
-0.02105971798300743,
0.01396499015390873,
-0.003106206189841032,
0.06622302532196045,
-0.004718730691820383,
-0.003293414833024144,
0.011979286558926105,
0.00325657706707716,
-0.008234300650656223,
0.024926625192165375,
0.03949427604675293,
0.003420844441279769,
0.0011663574259728193,
-0.030680445954203606,
0.006627887953072786,
-0.03646927699446678,
0.00783443171530962,
-0.008222624659538269,
0.00875034462660551,
-0.016186311841011047,
-0.0032481530215591192,
0.010369103401899338,
0.016322650015354156,
-0.04274650290608406,
-0.029218873009085655,
0.013670594431459904,
0.004034458193928003,
-0.020239239558577538,
-0.00007219790859380737,
0.010900559835135937,
0.04388825595378876,
0.047084588557481766,
-0.010349810123443604,
0.04018957167863846,
-0.03651265427470207,
-0.022916153073310852,
0.012316115200519562,
0.028452660888433456,
-0.012894322164356709,
0.010397648438811302,
-0.060192327946424484,
-0.02740701101720333,
0.010404612869024277,
-0.03108232282102108,
0.03290658816695213,
0.0028133310843259096,
0.01149184349924326,
-0.021509375423192978,
-0.047622233629226685,
-0.039980459958314896,
0.012839206494390965,
-0.030268318951129913,
0.019060388207435608,
-0.01321016252040863,
0.013434556312859058,
-0.03436984121799469,
0.005428233649581671,
-0.018776308745145798,
0.06088408827781677,
0.013730197213590145,
-0.01901797205209732,
-0.007986754179000854,
-0.00388755789026618,
-0.005223120097070932,
-0.06628189235925674,
-0.012941692024469376,
-0.01033407635986805,
-0.004587107803672552,
0.03664671257138252,
-0.024710364639759064,
-0.07336880266666412,
0.029741983860731125,
0.006709061563014984,
-0.03029567003250122,
0.038033850491046906,
-0.018993286415934563,
0.0500670000910759,
0.02325914241373539,
-0.015906525775790215,
0.03709769621491432,
0.04832407832145691,
-0.018840303644537926,
-0.03136541694402695,
-0.04054279252886772,
0.0018464839085936546,
-0.025074796751141548,
-0.03053697943687439,
-0.07514960318803787,
0.00871464516967535,
-0.02999996393918991,
0.016411077231168747,
-0.007491367869079113,
-0.013976598158478737,
-0.00974196381866932,
-0.008130629546940327,
-0.00506284786388278,
-0.000013674572073796298,
-0.028288571164011955,
-0.033154089003801346,
-0.012106790207326412,
0.03379529342055321,
0.023712074384093285,
-0.020711081102490425,
-0.00007263189036166295,
0.02598065324127674,
0.014895847998559475,
0.06546537578105927,
0.00014864368131384254,
-0.00015660746430512518,
-0.020462747663259506,
-0.005493759177625179,
0.015230509452521801,
-0.025179214775562286,
0.048768166452646255,
-0.0012788540916517377,
-0.012161235325038433,
0.0385584719479084,
-0.023916399106383324,
-0.0398004911839962,
-0.012017820030450821,
-0.019212372601032257,
-0.007863394916057587,
-0.02438589744269848,
-0.024413857609033585,
0.046315036714076996,
-0.0013782529858872294,
-0.0796407088637352,
0.002730682725086808,
0.06778699904680252,
-0.01453141588717699,
-0.011594390496611595,
-0.024020683020353317,
0.011427877470850945,
-0.0189841166138649,
-0.005140703171491623,
0.023164762184023857,
0.06159517914056778,
-0.008437787182629108,
0.01061279233545065,
-0.034741953015327454,
0.05402248725295067,
0.013519134372472763,
-0.0249609537422657,
-0.027139080688357353,
0.01749267615377903,
0.010447963140904903,
0.015190265141427517,
0.0230407752096653,
0.03368544951081276,
0.004570553544908762,
-0.0024816952645778656,
-0.025767263025045395,
-0.031128989532589912,
-0.012723603285849094,
0.012669905088841915,
-0.04356388747692108,
0.0207100510597229,
-0.0009393975487910211,
-0.003285260871052742,
0.006462767720222473,
-0.027194229885935783,
0.028112247586250305,
0.04959182068705559,
0.012294198386371136,
0.00021771497267764062,
0.012993360869586468,
-0.04862203449010849,
0.03524003550410271,
-0.019283372908830643,
-0.013142524287104607,
-0.0006998575991019607,
0.046433448791503906,
-0.020409656688570976,
-0.01595759578049183,
-0.001350877108052373,
-0.01130557619035244,
-0.0023302314803004265,
-0.00017252103134524077,
0.01282565202564001,
0.011117875576019287,
-0.011898285709321499,
0.003461354412138462,
-0.03791859745979309,
-0.06498688459396362,
0.04361429437994957,
0.04539527744054794,
0.03927256539463997,
0.027891632169485092,
0.026253128424286842,
0.020038582384586334,
-0.029299242421984673,
-0.038867972791194916,
-0.023573335260152817,
0.000108116670162417,
-0.012000754475593567,
0.054792679846286774,
-0.04967415705323219,
-0.015170473605394363,
0.048084061592817307,
0.05231717228889465,
-0.04377786070108414,
0.008994060568511486,
0.01931949518620968,
0.03077789396047592,
0.005709528923034668,
-0.018934423103928566,
-0.058129120618104935,
0.035467084497213364,
-0.029376709833741188,
0.0322207547724247,
0.0332769900560379,
-0.018321214243769646,
-0.013326653279364109,
0.04432544484734535,
0.008312078192830086,
-0.04353000223636627,
-0.01712365634739399,
-0.0656927227973938,
0.025907088071107864,
0.014897726476192474,
-0.0101290512830019,
0.03174589201807976,
0.0322052538394928,
-0.0011682285694405437,
0.017977816984057426,
0.01834810897707939,
0.02162950113415718,
-0.009274537675082684,
0.01038992777466774,
-0.05713673308491707,
-0.08223136514425278,
0.06175551936030388,
-0.00035336767905391753,
-0.02590816654264927,
0.011455555446445942,
-0.01402050256729126,
0.013295912183821201,
0.02399490959942341,
-0.000872307107783854,
0.010571437887847424,
0.0727008730173111,
-0.008730278350412846,
0.009974903427064419,
-0.03973843902349472,
0.01916172169148922,
0.13269463181495667,
0.05264221131801605,
0.02255178429186344,
-0.03184445947408676,
0.012502789497375488,
-0.024471253156661987,
0.017247188836336136,
-0.013773571699857712,
0.007611717563122511,
-0.016728926450014114,
-0.01910775527358055,
-0.008390864357352257,
0.04571301490068436,
-0.01891753450036049,
0.008894185535609722,
0.06347955018281937,
-0.06748859584331512,
-0.01839352771639824,
0.0029527777805924416,
0.011991748586297035,
0.01569177210330963,
0.0176820270717144,
-0.013570557348430157,
0.00859113410115242,
-0.03845161944627762,
0.0026974582578986883,
-0.023715637624263763,
-0.035478804260492325,
0.0014137818943709135,
0.005458981730043888,
-0.07510475069284439,
-0.008268523029983044,
0.042088478803634644,
-0.028260856866836548,
-0.006452346220612526,
0.02019985020160675,
0.03604357689619064,
-0.017881425097584724,
0.02206674963235855,
0.03049980290234089,
0.005935418885201216,
-0.021853061392903328,
0.011516109108924866,
-0.0013285171007737517,
-0.03841591626405716,
-0.0011018847580999136,
-0.040575701743364334,
0.04427226260304451,
-0.016912981867790222,
-0.02776503935456276,
-0.021427350118756294,
-0.02743503637611866,
-0.000051015507779084146,
-0.044144634157419205,
-0.02031368389725685,
-0.035047054290771484,
0.013293308205902576,
-0.023334544152021408,
0.001907726051285863,
-0.03244233503937721,
-0.006331409327685833,
0.03086031787097454,
0.0018421130953356624,
0.009708334691822529,
-0.003042995696887374,
-0.014931045472621918,
-0.00910122785717249,
0.004722531884908676,
-0.004813875537365675,
-0.015000543557107449,
-0.007309663575142622,
-0.02598230354487896,
-0.06430216133594513,
-0.03466821834445,
0.0030112206004559994,
0.005591203458607197,
0.06315084546804428,
-0.0006872773519717157,
-0.003234259318560362,
-0.08731208741664886,
-0.08549659699201584,
0.028134005144238472,
-0.0023948049638420343,
0.012176312506198883,
0.021742582321166992,
0.013196120969951153,
-0.00043666744022630155,
0.05656035616993904,
-0.06897922605276108,
0.007161059882491827,
0.02095126174390316,
0.028649089857935905,
0.03255752474069595,
-0.024289913475513458,
-0.013089745305478573,
0.019590003415942192,
-0.022503700107336044,
-0.0006355287041515112,
0.0038375998847186565,
-0.03472031280398369,
0.04633167386054993,
0.030282428488135338,
-0.009590686298906803,
0.03756709396839142,
-0.006030542775988579,
0.012586106546223164,
0.038433149456977844,
-0.014741017483174801,
0.01663348264992237,
0.048031244426965714,
0.08186237514019012,
-0.03310506418347359,
0.014094746671617031,
-0.04129550978541374,
0.014257119037210941,
-0.01305335946381092,
0.021934866905212402,
-0.013388050720095634,
-0.0008266496588476002,
-0.028337927535176277,
0.020783349871635437,
-0.025421787053346634,
-0.006629178766161203,
-0.02981535904109478,
0.0637478455901146,
-0.008193972520530224,
-0.003290774766355753,
-0.034612059593200684,
0.0390016995370388,
0.04554859921336174,
-0.043180324137210846,
0.03163864091038704,
0.0205275546759367,
-0.025845594704151154,
0.002314366865903139,
0.011674711480736732,
0.01733565703034401,
0.015110972337424755,
0.017337704077363014,
-0.02345225401222706,
-0.019139224663376808,
-0.006231142207980156,
-0.0659167617559433,
0.012595560401678085,
0.007599732372909784,
0.00006813390064053237,
0.05344996601343155,
-0.013134189881384373,
-0.026028193533420563,
0.014213966205716133,
0.011913330294191837,
-0.031516168266534805,
0.029069464653730392,
-0.026360811665654182,
0.013724114745855331,
-0.03931020200252533,
0.002577651059255004,
0.01749969646334648,
-0.018109554424881935,
0.03909572213888168,
0.009820085018873215,
-0.02218673564493656,
0.02138051576912403,
0.03193124756217003,
-0.029613181948661804,
0.025569986552000046,
0.039751648902893066,
-0.018944939598441124,
0.03421679884195328,
0.07125984877347946,
-0.048606693744659424,
0.001713470439426601,
0.0029990109615027905,
0.004478399641811848,
-0.09579924494028091,
-0.0188829954713583,
-0.028283335268497467,
0.022983968257904053,
0.06311264634132385,
-0.03763168305158615,
0.003494912525638938,
0.03810450807213783,
-0.053119126707315445,
-0.00617603026330471,
0.003195134224370122,
0.01006761472672224,
0.014704084023833275,
-0.00914548896253109,
-0.047867000102996826,
0.04904244467616081,
0.03314763680100441,
0.04488396644592285,
0.014513975009322166,
0.018562447279691696,
0.0038483303505927324,
-0.010809740051627159,
-0.0151474978774786,
0.03534331172704697,
0.013284493237733841,
0.012757825665175915,
0.07963789999485016,
-0.006954170763492584,
-0.031089283525943756,
0.05186223238706589,
0.014159568585455418,
0.03079528920352459,
-0.06312717497348785,
0.018281694501638412,
0.030575081706047058,
0.03176099434494972,
0.007635520305484533,
0.014931851997971535,
0.006993894465267658,
-0.011098681949079037,
0.011353600770235062,
-0.009576139971613884,
-0.015329157002270222,
-0.012179602868855,
0.016884036362171173,
-0.059409305453300476,
-0.05569424480199814,
0.04716814309358597,
-0.0023740774486213923,
-0.02333831414580345,
-0.01375321764498949,
-0.013147233985364437,
-0.005978436209261417,
0.00039025358273647726,
0.031158244237303734,
-0.017962731420993805,
-0.02427740767598152,
-0.01621534861624241,
-0.023067103698849678,
-0.00003250684676459059,
0.00897085852921009,
-0.02340996079146862,
-0.019326267763972282,
0.02988160029053688,
0.005013905931264162,
-0.02301916293799877,
-0.09480404853820801,
-0.036880817264318466,
-0.030150866135954857,
0.013310384936630726,
-0.012657889164984226,
-0.028597623109817505,
-0.04015938565135002,
-0.001943189650774002,
0.026793034747242928,
0.02747984416782856,
-0.0563371516764164,
-0.029225487262010574,
0.00019362528109923005,
-0.08272328227758408,
0.03514939546585083,
0.032838597893714905,
-0.01594744436442852,
0.007914443500339985,
-0.026881959289312363,
0.013009550981223583,
0.005314369685947895,
0.08267349004745483,
-0.01691472716629505,
-0.03528602421283722,
0.030590718612074852,
-0.020014170557260513,
0.021319128572940826,
-0.029011934995651245,
-0.0329059362411499,
-0.016336552798748016,
-0.012014104053378105,
0.01425543986260891,
0.0011180660221725702,
-0.004753594286739826,
0.026232102885842323,
-0.0033972642850130796,
0.012507213279604912,
0.016518155112862587,
0.011650478467345238,
-0.04268229007720947,
0.05477607250213623,
0.026994643732905388,
-0.048416513949632645,
0.037520959973335266,
-0.000723368430044502,
0.025053273886442184,
0.026672229170799255,
-0.04496162384748459,
-0.07817838340997696,
-0.0050832233391702175,
-0.04913086071610451,
0.0028418416623026133,
0.008880527690052986,
-0.007726411335170269,
0.024365665391087532,
0.001979278400540352,
0.016627229750156403,
0.05106300860643387,
-0.018072089180350304,
-0.02495037019252777,
0.06184659153223038,
0.0060996003448963165,
0.04980501905083656,
0.047187160700559616,
0.0008964836015366018,
0.02038252167403698,
0.015812719240784645,
0.024468466639518738,
0.00842791423201561,
0.034608229994773865,
0.007822310552001,
-0.0061401925049722195,
0.017736313864588737,
-0.0054496400989592075,
0.025615399703383446,
0.010582739487290382,
0.0020504845306277275,
-0.045012880116701126,
-0.018060680478811264,
0.040679920464754105,
0.0004089923168066889,
-0.033249396830797195,
0.025029148906469345,
-0.012980909086763859,
0.07406656444072723,
0.022736869752407074,
0.010376718826591969,
-0.007528736721724272,
0.0068089934065938,
-0.0013906719395890832,
0.00645361328497529,
0.026442142203450203,
0.042365897446870804,
-0.03668439760804176,
-0.03145842254161835,
-0.025985267013311386,
0.014603459276258945,
-0.0015912331873551011,
-0.04823599010705948,
-0.01020909659564495,
0.055171381682157516,
-0.015949590131640434,
-0.006040618754923344,
-0.02491745539009571,
-0.0030914307571947575,
-0.015835154801607132,
0.039896588772535324,
0.039766550064086914,
0.018067272379994392,
-0.0006071336683817208,
0.013668267987668514,
-0.03774045407772064,
0.04854019731283188,
-0.05106023699045181,
0.01136001106351614,
-0.003487330162897706,
-0.03771459683775902,
-0.003401589347049594,
-0.0014934642240405083
] |
<p>The ability to manipulate light spectra (as in mercury lamps, sodium lamps, infra red) is within the ambit of contemporary technology. Stars are said to be unique in the spectrum they emit ; </p>
<p><a href="http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/" rel="nofollow">http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/</a> writes to say</p>
<blockquote>
<p>The best tool we have for studying a star's light is the star's spectrum. A spectrum (the plural is "spectra") of a star is like the star's fingerprint. Just like each person has unique fingerprints, each star has a unique spectrum.</p>
</blockquote>
<p>with my limited understanding of physics, I may have understood wrong!!</p>
<p>Can contemporary technology simulate the spectrum of a star? </p>
| 7,640 |
[
-0.019808150827884674,
-0.0748608186841011,
0.020889945328235626,
-0.019844038411974907,
0.08697684109210968,
-0.01119211595505476,
-0.03244321793317795,
-0.0396764874458313,
0.012777182273566723,
-0.03471270576119423,
0.054444316774606705,
0.027092061936855316,
0.02464473247528076,
0.04797307029366493,
0.013064970262348652,
0.017934923991560936,
0.01860640197992325,
0.010976838879287243,
-0.03808344528079033,
0.010300571098923683,
-0.01715140789747238,
-0.023035602644085884,
-0.017392117530107498,
-0.008934755809605122,
-0.05482092127203941,
0.02183469943702221,
0.03346697613596916,
-0.04144452512264252,
0.01947735622525215,
0.04089214280247688,
-0.03530092537403107,
0.043472807854413986,
0.03413083776831627,
0.07307946681976318,
0.03246239945292473,
0.0014702717307955027,
-0.0480317622423172,
-0.012565748766064644,
0.009834994561970234,
0.02020016685128212,
-0.026115573942661285,
-0.012144705280661583,
-0.019850974902510643,
0.030981287360191345,
-0.012010634876787663,
-0.002747445600107312,
-0.02278427593410015,
-0.006317500025033951,
0.01569044031202793,
-0.014350194483995438,
0.07882728427648544,
-0.03583496809005737,
0.04122917726635933,
0.02378210425376892,
-0.06386356800794601,
0.01735285483300686,
0.07681713253259659,
0.050442010164260864,
-0.011600037105381489,
-0.024774599820375443,
0.0013051574351266026,
0.014414438977837563,
-0.02670413628220558,
-0.008654894307255745,
-0.0595102459192276,
-0.003971862141042948,
0.010218463838100433,
-0.009225389920175076,
0.02183246612548828,
0.005223735235631466,
0.01930457353591919,
0.025792544707655907,
0.026873234659433365,
0.0042699058540165424,
-0.005063882563263178,
-0.04530207812786102,
0.018712814897298813,
0.014809561893343925,
0.05530693009495735,
0.014438515529036522,
0.018057582899928093,
0.02855350263416767,
-0.009742512367665768,
0.008166762068867683,
0.03665245324373245,
-0.010744980536401272,
0.057255275547504425,
-0.026873808354139328,
0.04219624400138855,
0.0039453050121665,
0.003925777971744537,
0.02485666424036026,
0.028428325429558754,
0.009233750402927399,
-0.030074886977672577,
0.012134715914726257,
-0.03581878915429115,
0.03072294034063816,
-0.01883900724351406,
-0.035529252141714096,
0.011717825196683407,
-0.009525000117719173,
0.05138580501079559,
0.046270500868558884,
-0.01193595863878727,
-0.02579219453036785,
0.019048364832997322,
-0.03882899880409241,
0.017978910356760025,
0.012143392115831375,
-0.027913283556699753,
0.004041031934320927,
0.017676562070846558,
-0.006434047129005194,
0.022543635219335556,
-0.02478340081870556,
0.014072294346988201,
-0.0010060346685349941,
0.07398328185081482,
0.07009751349687576,
-0.020715119317173958,
-0.04095282033085823,
0.014085061848163605,
-0.04106945917010307,
-0.039824265986680984,
0.035142287611961365,
-0.0026974109932780266,
0.0086206728592515,
-0.026544805616140366,
-0.012376310303807259,
-0.0265422984957695,
-0.0001963621616596356,
0.007162156980484724,
-0.013563779182732105,
0.006747651845216751,
-0.03955528885126114,
-0.13709433376789093,
-0.035585422068834305,
0.022354597225785255,
0.01989573799073696,
0.002774933585897088,
-0.03618872910737991,
0.00805738940834999,
0.019609680399298668,
0.06683707237243652,
0.023468244820833206,
0.0036202161572873592,
-0.0019515687599778175,
0.05865831300616264,
0.0027493578381836414,
-0.020291311666369438,
-0.0023512186016887426,
0.010805743746459484,
-0.02078906074166298,
-0.020825223997235298,
-0.07770851254463196,
-0.0029111544135957956,
0.020866721868515015,
-0.024590061977505684,
-0.018143704161047935,
0.041568417102098465,
-0.0006016217521391809,
-0.0055230483412742615,
0.009612822905182838,
0.008574516512453556,
-0.04378455504775047,
0.07840041071176529,
0.0018953524995595217,
-0.0034410080406814814,
0.025088924914598465,
-0.02336071990430355,
0.027550889179110527,
-0.01166500709950924,
0.030239123851060867,
0.025105752050876617,
-0.01745268888771534,
0.005409515928477049,
-0.012709088623523712,
0.021447112783789635,
-0.025866936892271042,
-0.05702760070562363,
-0.04188656806945801,
0.021056052297353745,
0.01033062394708395,
0.05013047531247139,
0.059596218168735504,
0.006672321818768978,
-0.012797113507986069,
0.011726437136530876,
-0.03984253481030464,
0.01121472381055355,
-0.051075175404548645,
0.015327049419283867,
-0.0007278184639289975,
-0.033731065690517426,
-0.017523612827062607,
0.0001947948185261339,
0.04663791507482529,
0.007580054923892021,
-0.03290676325559616,
-0.008260643109679222,
0.03287077695131302,
0.06020986661314964,
-0.00018210972484666854,
0.010745768435299397,
0.07966481894254684,
0.042447853833436966,
-0.008725344203412533,
0.01943935826420784,
-0.02199544757604599,
-0.07245507836341858,
0.01223014947026968,
-0.0184708833694458,
0.03507888689637184,
0.029815474525094032,
0.01827661506831646,
0.049845140427351,
-0.024397626519203186,
-0.02401948906481266,
0.05634913221001625,
-0.0007068357663229108,
0.014791668392717838,
-0.0032216645777225494,
0.012723213993012905,
0.02150043286383152,
0.01742001809179783,
-0.0002441477554384619,
0.01675296016037464,
0.0293662678450346,
-0.05535024031996727,
-0.040413036942481995,
0.007045119069516659,
0.023100169375538826,
0.030743665993213654,
-0.04137466102838516,
0.019542360678315163,
0.0343049131333828,
0.05289652198553085,
0.06054516136646271,
0.015189464204013348,
-0.03446483239531517,
-0.002001218032091856,
-0.013537351973354816,
-0.007563105784356594,
0.032119229435920715,
0.021654963493347168,
0.013663094490766525,
0.024383777752518654,
0.010720930993556976,
-0.01663331314921379,
0.01924404688179493,
0.031282953917980194,
-0.005896652117371559,
-0.03231082856655121,
0.013137077912688255,
-0.024130970239639282,
0.02864333987236023,
-0.03716161102056503,
0.019941041246056557,
0.042501404881477356,
-0.0013921210775151849,
0.013227417133748531,
-0.00035439804196357727,
-0.012898053973913193,
-0.01068719383329153,
0.03547455742955208,
-0.006687164772301912,
0.018984632566571236,
0.02026616409420967,
-0.027218665927648544,
0.04315447807312012,
-0.04112546145915985,
-0.0092354416847229,
-0.053357623517513275,
0.005349036306142807,
0.018780866637825966,
0.01565667986869812,
0.02690606564283371,
-0.04844530671834946,
-0.03639882057905197,
-0.0035804149229079485,
-0.02875204011797905,
-0.03841009736061096,
0.00027231007697992027,
-0.040152113884687424,
-0.0032358975149691105,
-0.008355620317161083,
-0.024816829711198807,
-0.004744907841086388,
-0.018635142594575882,
-0.0012145864311605692,
-0.021495116874575615,
-0.010469007305800915,
-0.07875386625528336,
0.007506501395255327,
-0.0029329946264624596,
-0.0005734649021178484,
-0.02587663196027279,
-0.03155050799250603,
0.015007336623966694,
-0.005764183588325977,
-0.04459429532289505,
-0.021081240847706795,
-0.04928165674209595,
-0.045867908746004105,
-0.02017901837825775,
0.01857019029557705,
0.027258018031716347,
-0.048388320952653885,
0.017201898619532585,
0.03587520122528076,
-0.036361269652843475,
0.012877173721790314,
-0.03087017871439457,
-0.036412570625543594,
-0.012802649289369583,
0.0039176917634904385,
0.05878518894314766,
-0.014298691414296627,
0.014143926091492176,
0.04493141546845436,
0.03483141213655472,
-0.023762157186865807,
-0.040801241993904114,
-0.05031229555606842,
-0.0018154466524720192,
-0.054824333637952805,
0.04510549083352089,
0.02691088244318962,
-0.031199878081679344,
0.007568002212792635,
-0.012572540901601315,
-0.032873447984457016,
0.02537224255502224,
0.006841394118964672,
-0.01811911165714264,
-0.004492009524255991,
-0.04160652309656143,
0.018235355615615845,
0.04758629947900772,
0.023242343217134476,
-0.05275937542319298,
0.01699233613908291,
0.0025838499423116446,
0.045169901102781296,
0.02034187503159046,
-0.04114091768860817,
0.05289626866579056,
0.012006941251456738,
0.02580544538795948,
-0.022609548643231392,
0.004855182021856308,
0.02051895298063755,
0.013261137530207634,
-0.008381471037864685,
0.030114302411675453,
0.022389423102140427,
0.041131678968667984,
-0.01876796782016754,
0.03446062281727791,
0.0506172701716423,
0.006035226862877607,
-0.008781567215919495,
0.003974115010350943,
-0.023148631677031517,
-0.00020670803496614099,
-0.03333326056599617,
-0.0036273726727813482,
0.06674031168222427,
0.047013867646455765,
0.04034629836678505,
-0.013410845771431923,
-0.02191021665930748,
-0.04214264824986458,
-0.057073578238487244,
-0.0030770967714488506,
-0.05075807124376297,
0.06550820916891098,
-0.009304716251790524,
0.057125870138406754,
0.03554800525307655,
0.024125581607222557,
0.013024589978158474,
-0.011982819996774197,
-0.10962684452533722,
0.03711583837866783,
0.007887440733611584,
0.014896737411618233,
-0.028659695759415627,
-0.01369341742247343,
-0.01484701968729496,
-0.010809089057147503,
-0.01803366281092167,
0.002597867278382182,
-0.019967565312981606,
-0.013431156054139137,
0.004317638464272022,
-0.02115539275109768,
-0.05861958488821983,
-0.0017681889003142715,
0.051085103303194046,
0.05557825043797493,
0.022150496020913124,
0.01852233149111271,
0.005828109569847584,
-0.015311324037611485,
0.034538377076387405,
-0.029602237045764923,
0.025547407567501068,
0.008486886508762836,
0.04389346390962601,
0.047338925302028656,
0.041674744337797165,
-0.0354163758456707,
-0.007483483292162418,
-0.0005002982798032463,
0.01633010059595108,
0.02617698349058628,
-0.0320284441113472,
0.0024022161960601807,
-0.03774343430995941,
-0.00010229409235762432,
0.03671460971236229,
0.0746656283736229,
-0.052928484976291656,
-0.008250200189650059,
0.012971136718988419,
-0.009094366803765297,
-0.04587365314364433,
0.037227436900138855,
0.02374991402029991,
-0.010284020565450191,
-0.03418515995144844,
-0.008877546526491642,
0.010305858217179775,
-0.028444183990359306,
0.0014821561053395271,
-0.0016916727181524038,
0.021649328991770744,
-0.010494248010218143,
-0.020204156637191772,
-0.004770204424858093,
0.010845651850104332,
-0.04497534781694412,
0.003947919234633446,
-0.027470795437693596,
0.02888534963130951,
-0.05639871209859848,
0.018927380442619324,
0.004867967218160629,
0.038382917642593384,
0.0015959133161231875,
-0.0075039928779006,
-0.028454845771193504,
-0.0909539982676506,
-0.0104395542293787,
0.015674347057938576,
0.001377092208713293,
0.007015900686383247,
-0.0445113331079483,
-0.06427670270204544,
-0.012277234345674515,
0.014048405922949314,
-0.0038917928468436003,
0.051028501242399216,
-0.0081505561247468,
-0.014030005782842636,
-0.021493220701813698,
0.00016931514255702496,
0.008131911978125572,
0.04365050792694092,
0.02389860711991787,
0.015570406801998615,
-0.02958483248949051,
0.00564368162304163,
-0.010002251714468002,
0.05499308183789253,
0.03910541161894798,
0.018206583335995674,
-0.027739785611629486,
-0.01355224009603262,
0.022713489830493927,
0.003046472556889057,
-0.03170294687151909,
-0.05819961056113243,
-0.0025009214878082275,
0.04448385536670685,
-0.026252206414937973,
0.03612833842635155,
-0.034697938710451126,
-0.08059753477573395,
0.01932717300951481,
0.019805237650871277,
0.002354965778067708,
-0.015978654846549034,
-0.0030784662812948227,
-0.001829312415793538,
0.02374027855694294,
0.0038153238128870726,
0.05297894775867462,
0.07483214139938354,
-0.016637440770864487,
0.02332950383424759,
0.002652491442859173,
0.030462846159934998,
-0.013422218151390553,
-0.023301750421524048,
-0.004589920397847891,
-0.006595927756279707,
-0.04291783645749092,
0.041632503271102905,
0.009793341159820557,
0.010460260324180126,
0.034040410071611404,
-0.034461360424757004,
0.011459702625870705,
0.044301602989435196,
-0.01152059156447649,
-0.004141455516219139,
-0.008280538022518158,
0.02868182398378849,
-0.014928873628377914,
0.019523940980434418,
-0.008230122737586498,
-0.008079754188656807,
-0.029447119683027267,
0.0231791865080595,
0.01675398088991642,
0.03917059302330017,
-0.05291571095585823,
0.009830624796450138,
-0.010482292622327805,
-0.04868931323289871,
0.053593959659338,
-0.013509326614439487,
0.05435395985841751,
0.05457348749041557,
-0.0723152756690979,
-0.02360384352505207,
0.0012209193082526326,
-0.04767177626490593,
-0.007858983241021633,
-0.0033651620615273714,
0.04800354689359665,
-0.013463933952152729,
-0.041366636753082275,
-0.06491202116012573,
0.006641210522502661,
0.004243694711476564,
0.026689883321523666,
-0.025385845452547073,
-0.017855145037174225,
-0.017482198774814606,
0.000374361639842391,
-0.02120588906109333,
-0.033452123403549194,
0.013621462509036064,
-0.0017260056920349598,
-0.02035408280789852,
0.022007886320352554,
-0.015514031983911991,
0.09184041619300842,
-0.007921164855360985,
-0.014905312098562717,
0.002031829673796892,
-0.025478120893239975,
0.006190258543938398,
0.012519187293946743,
0.03654655069112778,
-0.019638994708657265,
-0.06821838021278381,
-0.017817165702581406,
0.027495138347148895,
0.03394578397274017,
-0.0180972907692194,
0.0031810086220502853,
0.03233814612030983,
0.021625705063343048,
0.028829721733927727,
-0.025194482877850533,
0.011600800789892673,
0.0029122948180884123,
0.03458831459283829,
-0.035240523517131805,
0.02431580238044262,
-0.028085915371775627,
-0.024752380326390266,
0.0016673541394993663,
0.0009838880505412817,
0.03239591047167778,
0.022734269499778748,
0.04621923714876175,
-0.036399584263563156,
-0.0031101314816623926,
0.019368741661310196,
-0.013716007582843304,
0.028799057006835938,
-0.043320052325725555,
0.03420324623584747,
-0.01080718357115984,
0.010498317889869213,
-0.006624729372560978,
-0.05044712498784065,
-0.022482236847281456,
-0.025318140164017677,
0.016664963215589523,
0.03256535157561302,
0.053865861147642136,
0.03236781433224678,
0.0022477838210761547,
-0.011497040279209614,
-0.05024470016360283,
-0.033161431550979614,
-0.018324024975299835,
0.010502240620553493,
-0.0013889926485717297,
-0.008747834712266922,
0.00772029347717762,
-0.008909839205443859,
0.020352674648165703,
0.008955691009759903,
0.03560212627053261,
0.042821966111660004,
0.02623567543923855,
0.001910761115141213,
-0.04035505652427673,
-0.031096700578927994,
0.026314791291952133,
-0.04095024988055229,
0.008993149735033512,
0.04037626460194588,
0.02771100029349327,
0.03023950569331646,
-0.014575674198567867,
0.03470993414521217,
-0.04805842414498329,
0.009624257683753967,
-0.06700806319713593,
0.03323248028755188,
0.010336639359593391,
0.025413837283849716,
0.022833531722426414,
-0.008517301641404629,
0.004895518999546766,
-0.012781522236764431,
0.03242252394556999,
-0.03982583433389664,
-0.06346101313829422,
-0.03138310834765434,
-0.03960774466395378,
-0.0339900366961956,
0.0690452829003334,
-0.006633074954152107,
-0.05534780025482178,
0.031985752284526825,
-0.042399812489748,
0.038889750838279724,
0.019221089780330658,
0.043940477073192596,
-0.020579345524311066,
0.039888348430395126,
-0.02519332990050316,
0.013967566192150116,
0.015089974738657475,
0.02523656375706196,
0.11820854991674423,
0.023503463715314865,
0.012869812548160553,
-0.07040011137723923,
-0.026894573122262955,
-0.04891957715153694,
0.012899606488645077,
0.010506520047783852,
0.015566029585897923,
-0.027555810287594795,
0.017855830490589142,
-0.015350825153291225,
0.01638353429734707,
0.006652815733104944,
0.005946692079305649,
0.024414174258708954,
-0.022967014461755753,
0.011214595288038254,
0.00815342366695404,
-0.008367670699954033,
-0.014967023395001888,
0.05008658394217491,
-0.07091216742992401,
0.00010086476686410606,
-0.005938151851296425,
-0.00935401115566492,
-0.019635265693068504,
-0.032747186720371246,
0.020295649766921997,
0.04314151406288147,
-0.03831126168370247,
0.006988158915191889,
0.04022183641791344,
0.007826576940715313,
0.012771818786859512,
0.01402620505541563,
0.02139340154826641,
-0.019726155325770378,
0.007047754246741533,
0.013694931752979755,
0.016759103164076805,
-0.03790764883160591,
0.007536290679126978,
0.0022483565844595432,
-0.02194328047335148,
-0.009812931530177593,
-0.06126226484775543,
0.025300581008195877,
-0.024136384949088097,
-0.0382639542222023,
-0.03436025232076645,
-0.017876971513032913,
-0.023888034746050835,
-0.047317422926425934,
-0.0003881908196490258,
-0.013916068710386753,
0.027151472866535187,
-0.03082956001162529,
-0.04685622826218605,
-0.03372064605355263,
0.017436590045690536,
-0.014638718217611313,
0.04006361588835716,
-0.019098946824669838,
0.008421418257057667,
0.02097753807902336,
-0.00031412640237249434,
0.053874678909778595,
0.03170892968773842,
-0.023327607661485672,
-0.04953886941075325,
-0.02785363607108593,
-0.055024951696395874,
-0.034338273108005524,
0.009931064210832119,
0.030216287821531296,
0.014809435233473778,
0.022676682099699974,
0.009172129444777966,
-0.024686923250555992,
-0.05208127200603485,
0.013573303818702698,
0.008701731450855732,
-0.03853233531117439,
0.030971823260188103,
-0.0229300856590271,
0.05171795189380646,
0.033835459500551224,
0.0025573549792170525,
0.025759469717741013,
0.012789806351065636,
-0.010640161111950874,
0.036850109696388245,
-0.0488414391875267,
-0.018465956673026085,
0.030578751116991043,
-0.007288483437150717,
0.020925918594002724,
-0.031002387404441833,
0.05544409528374672,
0.00018341555551160127,
-0.02733924239873886,
0.004192714113742113,
0.026455560699105263,
-0.05876796320080757,
-0.012057495303452015,
-0.0033445076551288366,
-0.016242563724517822,
0.0267335195094347,
-0.013657153584063053,
0.018783453851938248,
-0.008911024779081345,
-0.04449469968676567,
-0.05069233477115631,
-0.021287983283400536,
-0.016225336119532585,
0.010019517503678799,
-0.021203022450208664,
0.025648172944784164,
-0.0052702706307172775,
0.0020869721192866564,
-0.04889794811606407,
-0.005181859713047743,
-0.04747377708554268,
0.023267408832907677,
-0.011564064770936966,
-0.007450723554939032,
-0.003648524871096015,
0.023516209796071053,
-0.03552169352769852,
-0.010350847616791725,
0.028825122863054276,
0.04131871089339256,
-0.0008255084394477308,
-0.001298697548918426,
0.00699825631454587,
-0.02536129392683506,
0.06595094501972198,
-0.019401930272579193,
0.002499582711607218,
0.03817325830459595,
-0.02425866201519966,
-0.011551988311111927,
0.020580358803272247,
-0.03573103994131088,
0.016512762755155563,
0.05553632974624634,
-0.004801304079592228,
0.04619992896914482,
0.03209496662020683,
-0.0005659385933540761,
-0.02993910200893879,
0.03023112379014492,
0.019531726837158203,
0.04459569975733757,
0.013903744518756866,
0.039820246398448944,
-0.00590940797701478,
-0.030851252377033234,
0.050330910831689835,
0.012069009244441986,
0.00579421129077673,
0.009855704382061958,
-0.014137842692434788,
0.015978774055838585,
0.03413869068026543,
0.028512459248304367,
0.007262679282575846,
0.032811496406793594,
0.03399844840168953,
-0.05277518182992935,
0.043669018894433975,
0.016820302233099937,
-0.0014358359621837735,
-0.11079708486795425,
-0.010339480824768543,
-0.013586682267487049,
0.018100017681717873,
0.004888882394880056,
-0.03903019428253174,
0.020368320867419243,
0.010092061944305897,
-0.07936276495456696,
0.009163867682218552,
0.004468299448490143,
-0.031247364357113838,
-0.03817380964756012,
0.031935032457113266,
-0.06271293759346008,
0.01555320993065834,
0.043370090425014496,
0.02460617385804653,
-0.004750832915306091,
0.018810726702213287,
0.031337521970272064,
0.019030632451176643,
-0.015912333503365517,
0.011262785643339157,
-0.03748532384634018,
0.009027711115777493,
0.018013309687376022,
-0.024498017504811287,
-0.01972218230366707,
-0.0005108125042170286,
-0.009167205542325974,
0.0481671541929245,
-0.00504186050966382,
0.006607027258723974,
-0.011139816604554653,
0.025024062022566795,
0.046004097908735275,
-0.0477556474506855,
-0.059469856321811676,
0.015071181580424309,
0.015621600672602654,
0.03897108882665634,
0.036189042031764984,
0.0038400194607675076,
0.018997400999069214,
-0.05102967470884323,
-0.0007950618746690452,
0.031269773840904236,
-0.015091374516487122,
0.007434549275785685,
0.018431559205055237,
0.019551405683159828,
-0.02532290481030941,
0.010136441327631474,
-0.02082415670156479,
-0.07656940817832947,
0.03051111288368702,
0.014345439150929451,
0.025211596861481667,
0.013128518126904964,
-0.027097593992948532,
-0.03990790620446205,
-0.05664180591702461,
0.03286711126565933,
-0.007981421425938606,
-0.046316735446453094,
0.024043329060077667,
0.021052690222859383,
0.05180255323648453,
0.016626674681901932,
0.00012861679715570062,
0.008033785037696362,
-0.04053230956196785,
0.029805464670062065,
-0.0026400175411254168,
0.002826050156727433,
-0.020587442442774773,
-0.06175103783607483,
-0.02883477695286274,
-0.058765582740306854,
0.05014442279934883,
-0.012428506277501583,
0.0015207858523353934,
-0.07677998393774033,
-0.019516577944159508,
0.01239386573433876,
0.04511154443025589,
0.024989034980535507,
-0.009905810467898846,
-0.02791476435959339,
-0.009099151939153671,
-0.0011465268908068538,
0.021524472162127495,
-0.011063599959015846,
0.010283632203936577,
0.02013084664940834,
-0.02742655947804451,
-0.0011965816374868155,
-0.015102452598512173,
-0.0527816042304039,
0.0100758858025074,
0.042688511312007904,
0.013036636635661125,
0.015337444841861725,
0.02324383147060871,
-0.030886121094226837,
0.05625540018081665,
-0.00702339643612504,
-0.03256027027964592,
0.04953806474804878,
0.03152672201395035,
-0.013262279331684113,
0.01583918370306492,
0.0025111197028309107,
0.0030035001691430807,
0.0034046934451907873,
-0.013174639083445072,
0.0014411634765565395,
0.005556762684136629,
-0.02666560932993889,
0.004108664114028215,
-0.025074221193790436,
-0.010275288484990597,
0.03548908978700638,
-0.0008884670678526163,
-0.01768876239657402,
0.03197883069515228,
-0.001189969014376402,
0.013731149025261402,
-0.012797645293176174,
0.004206888377666473,
-0.007853655144572258,
0.021386586129665375,
-0.03167149797081947,
0.023947957903146744,
0.007321775890886784,
0.015876173973083496,
0.03657492250204086,
0.0424036979675293,
0.02040162868797779,
-0.02014564909040928,
0.031269580125808716,
0.035217855125665665,
-0.02578437142074108,
-0.010738227516412735,
0.04246519133448601,
0.01992398127913475,
0.014374994672834873,
0.015233121812343597,
-0.008178845047950745,
0.11456303298473358,
-0.027747895568609238,
-0.009823543019592762,
-0.020481860265135765,
0.01000223308801651,
-0.04419155418872833,
0.008402157574892044,
-0.008164480328559875,
0.018827665597200394,
0.001885857549495995,
-0.048614200204610825,
-0.024878226220607758,
0.030460011214017868,
0.052852652966976166,
-0.05667884275317192,
0.036719270050525665,
-0.01944301277399063,
-0.00029785765218548477,
-0.0025006451178342104,
0.011716398410499096,
0.01557106152176857,
-0.023670092225074768,
-0.011494825594127178,
0.03865142539143562,
0.02002653479576111,
0.028725236654281616,
-0.008273483254015446,
-0.023837018758058548,
0.036974456161260605,
-0.07889287173748016,
-0.019304867833852768,
-0.009775448590517044,
0.031159602105617523,
-0.013732719235122204,
-0.021284248679876328
] |
<p>I am trying to get a clear picture of the valence band, conduction band, and the band gap. Now I've been researching it for a little while now and understand most of what's going on. I'm still a little confused about some specifics though, so if you could please address the following, that would be great!</p>
<p>My favorite description thus far has been</p>
<p><em>"The most important aspect of semiconductor bandstructure may be summarised as follows; at absolute
zero the highest completely filled band (the valence band) is separated from the lowest empty band (the
conduction band) by an energy gap or band gap Eg of forbidden states. Therefore the material does
not conduct electricity at T = 0."</em></p>
<p>So from this description I have a pretty clear idea of what the valence band is (with the supplement of a few diagrams). Also, I know the conduction band is above the valence band in terms of energy, and is where electrons are free to roam the material as conduction electrons. My problem is where this "conduction band" is physically. It seems like there should be some allowed state, where if you just excite one electron you pass into that new state. From the above description, it seems to say some of these states are "forbidden", and that is my main question resides. Where is this conduction band, what determines its range (an example would be fantastic), and how do we determine what is necessarily a "forbidden" state?</p>
<p>Thanks =)</p>
| 7,641 |
[
-0.01045731920748949,
-0.03799119591712952,
0.03303913772106171,
-0.0114778196439147,
0.00476048793643713,
-0.006586665753275156,
-0.015184841118752956,
-0.019871043041348457,
0.016666751354932785,
-0.05151450261473656,
0.03599332273006439,
0.013568121939897537,
-0.0036620432510972023,
0.016119729727506638,
0.0053517771884799,
0.009960189461708069,
-0.03836158663034439,
-0.05604717507958412,
-0.036119382828474045,
-0.02042095549404621,
0.003176815574988723,
0.026131020858883858,
-0.021401477977633476,
0.039286427199840546,
-0.03635590523481369,
0.0071769217029213905,
0.017713408917188644,
0.04132527485489845,
0.038551244884729385,
0.02894441783428192,
-0.0009412592626176775,
-0.03391677886247635,
-0.01665535755455494,
-0.03170597180724144,
0.039206814020872116,
0.010520420037209988,
-0.03787456825375557,
-0.07190109044313431,
-0.029355378821492195,
0.029908401891589165,
-0.0173171553760767,
0.00958047341555357,
0.0003342935524415225,
0.00634103873744607,
0.0002720218035392463,
-0.025572750717401505,
0.02892693318426609,
-0.0002838236396200955,
0.005360303446650505,
-0.07730115950107574,
0.03229702264070511,
-0.008719694800674915,
0.06773023307323456,
0.029805997386574745,
0.05957421660423279,
0.003634210443124175,
0.09161854535341263,
0.06509573012590408,
-0.012785788625478745,
-0.03781783953309059,
-0.014499099925160408,
-0.04938788339495659,
-0.031440019607543945,
-0.03276597335934639,
-0.04492856562137604,
0.020008061081171036,
-0.007331248372793198,
-0.03579425811767578,
0.012381401844322681,
0.015449786558747292,
0.007669585756957531,
0.02924124151468277,
-0.027068087831139565,
-0.0334017351269722,
0.034386273473501205,
-0.041648391634225845,
0.050527624785900116,
0.006524942349642515,
0.016084490343928337,
0.04528027027845383,
-0.023447087034583092,
0.030981019139289856,
0.0000784504009061493,
0.02832510694861412,
-0.01284918375313282,
-0.027730967849493027,
0.08444338291883469,
-0.017955169081687927,
0.03511933609843254,
0.04347529262304306,
-0.01502065360546112,
0.01136332843452692,
0.01915615051984787,
-0.0003130282857455313,
-0.04161694645881653,
0.011394239962100983,
-0.001518138567917049,
0.0733310878276825,
-0.018429378047585487,
-0.047615550458431244,
0.033443618565797806,
0.009764491580426693,
0.07094919681549072,
0.07866452634334564,
-0.010261771269142628,
-0.02794307842850685,
-0.023000890389084816,
0.012056267820298672,
0.013879573903977871,
-0.011637096293270588,
-0.018393103033304214,
0.04250001534819603,
0.007120327092707157,
-0.0057968636974692345,
0.014134630560874939,
-0.019252562895417213,
0.014723410829901695,
-0.042113617062568665,
0.022443581372499466,
0.03013729862868786,
0.01893133483827114,
-0.019911305978894234,
0.058568693697452545,
0.0021029592026025057,
-0.08825703710317612,
0.017145471647381783,
0.02110600471496582,
0.012532584369182587,
0.00040593722951598465,
0.007404413539916277,
-0.02283451147377491,
-0.03157486394047737,
0.01617194525897503,
-0.012892775237560272,
0.060692355036735535,
-0.027285395190119743,
-0.08523932099342346,
-0.04703310504555702,
0.03349725157022476,
-0.0020624047610908747,
-0.020799918100237846,
-0.03715357184410095,
0.010884992778301239,
0.006715442985296249,
0.07975586503744125,
-0.004615785088390112,
0.014531723223626614,
-0.026023397222161293,
0.0045722853392362595,
0.016079310327768326,
-0.004313897341489792,
-0.040768057107925415,
0.014731470495462418,
-0.029792670160531998,
0.023702090606093407,
-0.035879142582416534,
0.058263830840587616,
0.015917211771011353,
0.005850530229508877,
-0.06069622188806534,
0.06242131441831589,
-0.02628425881266594,
-0.020929992198944092,
0.02925793081521988,
-0.01959798112511635,
-0.0011315906886011362,
0.09137730300426483,
0.010237450711429119,
0.0024617204908281565,
0.057391636073589325,
0.0393839105963707,
-0.0013112712185829878,
0.003984312992542982,
0.044799454510211945,
0.018915969878435135,
-0.02812838926911354,
-0.014887739904224873,
-0.07835554331541061,
0.0059014176949858665,
-0.0004848505777772516,
-0.05103268846869469,
-0.004730838350951672,
0.016477959230542183,
0.03360835462808609,
0.0024573667906224728,
0.02474302425980568,
-0.0051772394217550755,
-0.017124071717262268,
0.0033309529535472393,
-0.03455141559243202,
-0.012166847474873066,
-0.04419245943427086,
0.01243410725146532,
0.019943110644817352,
-0.022815639153122902,
0.045425064861774445,
-0.01594371907413006,
0.015933554619550705,
-0.02322310395538807,
-0.019651630893349648,
-0.0013350622029975057,
0.017466837540268898,
-0.008213376626372337,
-0.02216721884906292,
0.040062908083200455,
0.038287453353405,
0.021579600870609283,
0.01684737019240856,
0.04353109747171402,
-0.01397764589637518,
-0.0352056510746479,
-0.008924760855734348,
-0.02482053078711033,
0.061068858951330185,
0.017213160172104836,
0.012880686670541763,
-0.014499538578093052,
-0.015955669805407524,
-0.031106071546673775,
0.012161925435066223,
-0.0072333719581365585,
0.10466247797012329,
0.04711778461933136,
0.03524002432823181,
-0.04521510377526283,
0.030045198276638985,
-0.015074383467435837,
-0.02353445626795292,
-0.0483534000813961,
-0.029510051012039185,
-0.06145816296339035,
-0.001393871963955462,
0.036939240992069244,
0.014831651002168655,
0.010089235380291939,
-0.007097969762980938,
0.0020627568010240793,
0.020167790353298187,
0.05279524624347687,
0.025297218933701515,
-0.04914187267422676,
0.02108020894229412,
0.017408005893230438,
-0.010278516449034214,
0.02437921240925789,
0.019688598811626434,
0.019480939954519272,
0.03604904189705849,
0.014151527546346188,
-0.018419994041323662,
-0.0131187429651618,
0.0784466490149498,
0.03222601115703583,
0.0049849930219352245,
0.009020749479532242,
-0.07419590651988983,
0.0020010683219879866,
-0.043594684451818466,
0.021111905574798584,
0.04128948971629143,
-0.00446551525965333,
0.018691329285502434,
-0.03899332135915756,
-0.01750081777572632,
0.029651647433638573,
-0.004367672838270664,
-0.023518018424510956,
0.0038397873286157846,
-0.00403880700469017,
-0.04562047868967056,
0.022547584027051926,
-0.029672786593437195,
0.010266873054206371,
-0.05039505288004875,
-0.02456040307879448,
0.051298532634973526,
0.026154272258281708,
0.04633617773652077,
-0.04261959344148636,
-0.03168244659900665,
-0.00808956939727068,
-0.04564788192510605,
0.03938664495944977,
0.01890241727232933,
-0.03165625035762787,
-0.003735559992492199,
-0.03747314214706421,
-0.03994176536798477,
0.05260426551103592,
0.00864795595407486,
-0.015929866582155228,
0.014470377936959267,
-0.02224193699657917,
-0.055739205330610275,
0.020748624578118324,
0.0030220395419746637,
-0.013549523428082466,
-0.009168660268187523,
-0.00494585745036602,
0.04009846970438957,
-0.005367871839553118,
-0.04031427949666977,
0.043088894337415695,
-0.02189452387392521,
-0.02703043818473816,
-0.01972907967865467,
-0.01254184264689684,
-0.006138993427157402,
-0.01652764528989792,
0.04678516089916229,
0.0289758313447237,
-0.04171854630112648,
0.0010863502975553274,
-0.03829362615942955,
-0.02587115205824375,
0.011334042996168137,
-0.006658976897597313,
0.0014040995156392455,
-0.031057989224791527,
-0.01963849365711212,
0.06301284581422806,
0.012815003283321857,
0.004754542838782072,
-0.021417276933789253,
-0.030639171600341797,
-0.007017968688160181,
-0.011998295783996582,
0.034464240074157715,
0.06513050943613052,
0.0020825383253395557,
-0.002173667773604393,
0.035405054688453674,
0.06466968357563019,
0.038529228419065475,
-0.012118492275476456,
0.008755166083574295,
0.006767982617020607,
-0.003500457853078842,
-0.003777479287236929,
0.04575305059552193,
0.014813615009188652,
-0.016301283612847328,
0.034227099269628525,
-0.018656928092241287,
0.03135613724589348,
0.0354473777115345,
-0.031045230105519295,
0.003769788658246398,
-0.011029712855815887,
0.02468319796025753,
-0.05114871263504028,
0.027154024690389633,
0.004025047644972801,
-0.0025228268932551146,
0.011020236648619175,
0.04495982080698013,
0.014756225049495697,
-0.02773071639239788,
-0.00027355412021279335,
0.019808944314718246,
0.010423894971609116,
-0.011021789163351059,
-0.016532720997929573,
0.036843765527009964,
0.017738331109285355,
0.0121911047026515,
-0.0033377944491803646,
-0.004693258553743362,
0.0412716381251812,
0.011304362677037716,
0.06917571276426315,
-0.0028227814473211765,
-0.031177615746855736,
-0.027408499270677567,
-0.04564320296049118,
-0.02401970885694027,
0.022248828783631325,
0.07084094732999802,
0.009856619872152805,
0.06095223128795624,
0.03225581720471382,
0.04853217676281929,
-0.0054593258537352085,
0.007376395165920258,
-0.07974833250045776,
0.0171702578663826,
-0.031176207587122917,
-0.001537832897156477,
-0.035792626440525055,
0.026940511539578438,
-0.014497457072138786,
-0.013600178062915802,
-0.051226578652858734,
-0.0049772909842431545,
0.0007445308729074895,
-0.054575834423303604,
0.012174117378890514,
-0.031004110351204872,
0.0016685317968949676,
-0.03712921589612961,
-0.0009588346001692116,
0.011267459951341152,
-0.020369576290249825,
0.006794236600399017,
0.025183234363794327,
0.0076625230722129345,
0.03188742324709892,
-0.017293782904744148,
-0.0011226937640458345,
0.032135870307683945,
0.04458530992269516,
0.027801236137747765,
-0.002966953907161951,
-0.006879051215946674,
-0.018441686406731606,
-0.018066059798002243,
0.05911387503147125,
0.026881640776991844,
0.013895682990550995,
-0.009471639059484005,
-0.04106225445866585,
-0.023810459300875664,
-0.014119859784841537,
0.038072507828474045,
-0.0031256237998604774,
0.019618870690464973,
0.03102295473217964,
0.004109521862119436,
-0.05950147658586502,
0.035201359540224075,
0.017237378284335136,
-0.008169911801815033,
0.0037845366168767214,
-0.03488662838935852,
-0.04232184961438179,
-0.05266539752483368,
0.016762597486376762,
0.05765616521239281,
0.002496009226888418,
0.01362198032438755,
0.01179871428757906,
0.03736010938882828,
-0.002881211694329977,
-0.02293933928012848,
-0.01504120696336031,
-0.001581830671057105,
0.02170281670987606,
-0.008163436315953732,
-0.03411777690052986,
0.004999919328838587,
-0.009207332506775856,
0.031775131821632385,
0.004206526093184948,
0.003059668932110071,
-0.07914432883262634,
-0.015102016739547253,
0.05251822993159294,
0.03046119585633278,
-0.007381065748631954,
-0.020744992420077324,
-0.04928112402558327,
0.0024042828008532524,
0.012886887416243553,
-0.014402506873011589,
0.035160131752491,
-0.023968180641531944,
-0.004173994529992342,
-0.062289897352457047,
-0.01825510524213314,
0.018303515389561653,
0.015517211519181728,
0.02352355420589447,
0.02667227014899254,
-0.01621743105351925,
-0.01737004891037941,
-0.010382541455328465,
-0.004248769488185644,
0.01699024811387062,
0.0873308926820755,
-0.005195346660912037,
0.0018875316018238664,
0.06129167228937149,
0.00879767257720232,
-0.011651529930531979,
-0.10025174915790558,
-0.03992805629968643,
0.027478152886033058,
0.04018949717283249,
0.045521240681409836,
-0.03973500430583954,
-0.05276230350136757,
0.03869246318936348,
0.014218566007912159,
-0.004145869053900242,
-0.0010779967997223139,
-0.010071930475533009,
0.08602127432823181,
0.005222085863351822,
-0.013140208087861538,
0.03451026976108551,
0.002997070085257292,
-0.00038369966205209494,
0.022730570286512375,
-0.025627505034208298,
0.034133125096559525,
-0.033548299223184586,
0.006150257308036089,
-0.05599319189786911,
0.01235338393598795,
-0.029501160606741905,
0.06161937490105629,
-0.022983413189649582,
0.0015502668684348464,
-0.006311968434602022,
-0.04437973350286484,
-0.01615912653505802,
-0.01624884456396103,
-0.028090378269553185,
-0.013753263279795647,
-0.017054133117198944,
0.05046007037162781,
-0.01606445573270321,
-0.024914419278502464,
0.019964566454291344,
-0.0006380191771313548,
0.01419111993163824,
0.02959640510380268,
0.01755300536751747,
0.02753320522606373,
-0.026740221306681633,
-0.018322795629501343,
-0.012809639796614647,
-0.04256807267665863,
0.08483249694108963,
-0.02625105157494545,
0.004043859429657459,
0.006214294582605362,
-0.060090646147727966,
-0.038463376462459564,
0.03472323343157768,
-0.0009968578815460205,
0.03287290781736374,
-0.030143020674586296,
0.03767368569970131,
0.0038856847677379847,
0.003302661469206214,
-0.10718200355768204,
-0.07579322904348373,
0.02227257937192917,
0.019894246011972427,
-0.035435162484645844,
-0.009696719236671925,
0.01676880568265915,
-0.022005382925271988,
-0.0276122335344553,
0.06943155080080032,
0.022546548396348953,
-0.02525992877781391,
0.0015242238296195865,
-0.0006264960975386202,
0.01856333762407303,
0.08371368050575256,
0.010852868668735027,
-0.04064027965068817,
-0.0037464031483978033,
-0.025251975283026695,
0.010441550984978676,
-0.0040857805870473385,
0.020640285685658455,
-0.008413347415626049,
-0.021068572998046875,
-0.04398028552532196,
0.0056702932342886925,
0.058106884360313416,
0.0030574859119951725,
-0.028028203174471855,
0.028482895344495773,
0.013546076603233814,
-0.008686177432537079,
-0.02914184145629406,
0.023694517090916634,
0.005959684960544109,
0.0029540134128183126,
-0.0007364697521552444,
-0.020882952958345413,
-0.052305322140455246,
-0.04425278678536415,
0.031079279258847237,
-0.002805389231070876,
0.0501675046980381,
-0.000412969384342432,
0.063194140791893,
-0.005674139596521854,
0.01964578777551651,
0.02771318331360817,
-0.014751702547073364,
0.023436283692717552,
-0.00756154116243124,
-0.009293791837990284,
0.00514235207810998,
0.009992465376853943,
-0.05404804274439812,
-0.021335560828447342,
-0.04589945822954178,
-0.007921778596937656,
0.04072338342666626,
-0.008904403075575829,
0.037842947989702225,
-0.0001868859544629231,
-0.017803385853767395,
0.005314868874847889,
-0.02077578194439411,
-0.022513195872306824,
0.007591184228658676,
-0.017007604241371155,
0.017163287848234177,
-0.007879115641117096,
0.0031807366758584976,
0.021352333948016167,
0.02895343489944935,
-0.0005724231014028192,
0.02487548440694809,
0.05615963414311409,
0.003783779451623559,
0.04642312601208687,
-0.002687651664018631,
-0.0456840842962265,
0.03179781138896942,
-0.007007379084825516,
0.032365188002586365,
0.050958264619112015,
-0.00795758981257677,
0.0326978825032711,
0.0051482985727488995,
0.006417973432689905,
-0.02148107811808586,
-0.05785626173019409,
-0.041828688234090805,
0.05377286672592163,
-0.007513964083045721,
-0.007028636522591114,
-0.00011897227523149922,
-0.025487009435892105,
-0.0018665638053789735,
-0.005238002631813288,
0.009072178974747658,
0.0017413723981007934,
-0.04356275498867035,
-0.02280278317630291,
-0.022242559120059013,
-0.008919221349060535,
-0.00373587547801435,
0.01789269782602787,
-0.036559175699949265,
0.006388450041413307,
-0.03764619678258896,
0.00536225875839591,
-0.017783155664801598,
0.04379328340291977,
0.005706341005861759,
0.022950386628508568,
-0.007066717371344566,
0.028028579428792,
-0.00012013939704047516,
0.03197269141674042,
0.11337511241436005,
0.05993397533893585,
-0.006259291898459196,
-0.0630868449807167,
-0.005471441894769669,
-0.01750168763101101,
-0.005760693922638893,
-0.028140071779489517,
0.029849689453840256,
-0.021329224109649658,
0.029972760006785393,
-0.01949223130941391,
0.04112013429403305,
-0.003715659724548459,
0.04972134158015251,
0.05641070380806923,
-0.0346030592918396,
-0.008972708135843277,
0.01911793276667595,
0.024922488257288933,
0.010850438848137856,
0.03132660686969757,
-0.05501847714185715,
0.009010083973407745,
-0.04276588559150696,
-0.026528874412178993,
-0.04069266840815544,
-0.01717056892812252,
0.07713156193494797,
0.0011762408539652824,
-0.0062920162454247475,
-0.04345761239528656,
0.02597907930612564,
0.0013346672058105469,
-0.039750516414642334,
-0.006736083421856165,
0.011557522229850292,
-0.002190232975408435,
0.03312680497765541,
0.0113192955031991,
0.017670907080173492,
-0.015236102975904942,
0.03334689140319824,
0.01678360067307949,
-0.012322114780545235,
-0.01768326386809349,
0.002085906220600009,
0.012304997071623802,
-0.019180240109562874,
0.011482201516628265,
0.006717069540172815,
0.014334645122289658,
0.007389332167804241,
-0.02799682505428791,
-0.02129475586116314,
-0.04009705409407616,
0.038236889988183975,
-0.026726651936769485,
-0.011891622096300125,
-0.0028536354657262564,
0.0009776810184121132,
-0.0005007046856917441,
-0.0016649868339300156,
-0.02482631616294384,
0.015295910649001598,
0.01764858327805996,
-0.008650272153317928,
0.024878408759832382,
-0.030803943052887917,
-0.019891733303666115,
0.0036242895293980837,
-0.017360111698508263,
-0.03233526647090912,
-0.037859249860048294,
0.02863354980945587,
0.03359472379088402,
0.02953045628964901,
0.016550324857234955,
-0.001004701596684754,
-0.015050925314426422,
-0.06460030376911163,
0.007243768312036991,
0.005103421397507191,
-0.021074164658784866,
-0.021916979923844337,
-0.0006138004246167839,
0.01139398105442524,
0.0611119419336319,
-0.043922923505306244,
0.021641159430146217,
0.018597638234496117,
0.00403583375737071,
0.022811271250247955,
-0.04651833698153496,
-0.011158606968820095,
0.018551159650087357,
-0.04067624360322952,
0.04882833734154701,
0.0179623831063509,
0.05953240394592285,
0.012623798102140427,
0.004442967474460602,
-0.03783863037824631,
0.03632625937461853,
-0.055931881070137024,
-0.00518473144620657,
0.009451733902096748,
-0.03905617818236351,
0.006744257174432278,
0.012590421363711357,
0.028143029659986496,
-0.011912264861166477,
-0.0318247452378273,
-0.017247574403882027,
-0.009941870346665382,
-0.0001620716939214617,
0.019916974008083344,
-0.00016330792277585715,
0.015990154817700386,
-0.01941976323723793,
-0.025592373684048653,
-0.05821920186281204,
-0.020653512328863144,
-0.027178708463907242,
0.021151209250092506,
0.0300911832600832,
-0.013425142504274845,
-0.011944287456572056,
0.01504956278949976,
-0.020993810147047043,
0.0013949532294645905,
0.04189499095082283,
0.03543626889586449,
0.015155482105910778,
-0.003863679012283683,
-0.01277067419141531,
-0.030602244660258293,
0.06083125248551369,
-0.02347509190440178,
-0.002098238794133067,
0.022343751043081284,
-0.04490397870540619,
-0.028735430911183357,
0.0013457884779199958,
0.01763908378779888,
0.051179103553295135,
-0.005700205452740192,
-0.028226984664797783,
-0.031674083322286606,
0.048273973166942596,
0.004693577531725168,
0.008105707354843616,
-0.00396354915574193,
-0.02574540302157402,
-0.01690792851150036,
0.020521201193332672,
-0.011053348891437054,
-0.014786220155656338,
0.01620844565331936,
0.038175664842128754,
0.009562126360833645,
0.005755032412707806,
-0.026183130219578743,
-0.020436305552721024,
-0.02634173259139061,
0.0053184437565505505,
0.059253811836242676,
0.014785821549594402,
0.007735167630016804,
0.04732388257980347,
-0.00945016834884882,
0.04503457620739937,
0.01827734149992466,
0.02144014462828636,
-0.06926998496055603,
-0.018420860171318054,
0.0027788809966295958,
-0.019011078402400017,
-0.004487206228077412,
-0.038027454167604446,
-0.003126284806057811,
0.012358425185084343,
-0.07276846468448639,
0.012579326517879963,
-0.02396586909890175,
-0.016248121857643127,
-0.041174374520778656,
-0.008053815923631191,
-0.04528261721134186,
0.01467664074152708,
0.01967969723045826,
0.03425981104373932,
0.0011683920165523887,
0.024195274338126183,
-0.0065171909518539906,
-0.010374312289059162,
-0.0342397503554821,
0.03683929517865181,
-0.021584903821349144,
-0.02438853308558464,
0.036295171827077866,
-0.010841455310583115,
-0.00621693953871727,
0.003831228706985712,
-0.033053066581487656,
-0.018766378983855247,
0.005797476042062044,
0.009971162304282188,
-0.023875389248132706,
0.04681247100234032,
0.02305782400071621,
-0.0074888733215630054,
-0.012304740957915783,
-0.0074234772473573685,
0.03758554905653,
0.024634823203086853,
0.012997917830944061,
0.0010895971208810806,
0.031060783192515373,
-0.03466656431555748,
-0.01035786047577858,
0.008295217528939247,
-0.007967040874063969,
-0.0014332393184304237,
0.022947244346141815,
0.02927708625793457,
0.040263667702674866,
-0.04712188243865967,
-0.019304940477013588,
-0.04533445090055466,
-0.059288620948791504,
0.012883519753813744,
0.014061161316931248,
0.03874847665429115,
-0.011058544740080833,
-0.019516242668032646,
-0.026373710483312607,
0.040084756910800934,
0.006760894786566496,
-0.014446980319917202,
-0.045829787850379944,
-0.004163667093962431,
0.014513162896037102,
-0.028443267568945885,
0.002479245886206627,
-0.024517623707652092,
-0.0276198573410511,
0.03539144992828369,
-0.007428751792758703,
0.003541142912581563,
-0.03297479823231697,
-0.07807186245918274,
0.00019371854432392865,
-0.03126751258969307,
0.04713614657521248,
-0.04550496116280556,
-0.005363195203244686,
-0.017818180844187737,
-0.032307785004377365,
0.012210994958877563,
0.03596153482794762,
0.08447262644767761,
-0.007720553781837225,
-0.000052625542593887076,
-0.009312246926128864,
-0.012564178556203842,
0.03301501274108887,
-0.023076435551047325,
-0.0019416691502556205,
0.005371394567191601,
-0.04165228456258774,
-0.014474889263510704,
-0.005003939848393202,
-0.0679628849029541,
0.019135693088173866,
0.0214618481695652,
-0.009491304866969585,
-0.006511586718261242,
-0.020232228562235832,
-0.018919527530670166,
0.03380146250128746,
0.02882840670645237,
-0.016220923513174057,
0.09785003960132599,
-0.03615405410528183,
-0.021565154194831848,
0.010349147021770477,
0.015801504254341125,
-0.052735619246959686,
0.04339016601443291,
-0.029317611828446388,
-0.02079928293824196,
0.013388697989284992,
0.02396034635603428,
0.049343448132276535,
-0.04009602963924408,
0.004035367630422115,
0.04164274036884308,
-0.03409091755747795,
-0.006805285345762968,
0.0705266073346138,
0.00785249937325716,
0.043479204177856445,
-0.020709365606307983,
-0.012489589862525463,
-0.02817525900900364,
0.003999451640993357,
-0.015242223627865314,
0.021074427291750908,
0.04639068990945816,
0.016298815608024597,
0.004870045464485884,
0.029335225000977516,
-0.01785459741950035,
-0.0006971795810386539,
0.012168408371508121,
0.015915019437670708,
-0.0626729354262352,
0.016152381896972656,
0.049184300005435944,
-0.001066895667463541,
-0.0012939712032675743,
0.007462596520781517,
-0.026787573471665382,
0.10114005953073502,
-0.03589672967791557,
0.002723678480833769,
-0.015601273626089096,
-0.014459466561675072,
-0.015042365528643131,
0.010669748298823833,
-0.0033301860094070435,
0.049318909645080566,
-0.03236411139369011,
-0.024883875623345375,
-0.04136141017079353,
0.02284330129623413,
0.06124537065625191,
-0.05059555172920227,
0.047923650592565536,
-0.012502511963248253,
-0.026473237201571465,
-0.006740296259522438,
-0.000891858187969774,
-0.015175963751971722,
0.046759478747844696,
0.04877113178372383,
0.037292685359716415,
-0.0034955614246428013,
0.023409921675920486,
0.00010576840577414259,
0.0012162020429968834,
0.03399154543876648,
-0.05146564543247223,
-0.014431770890951157,
-0.032341476529836655,
0.02119828201830387,
-0.03984953090548515,
-0.0020728919189423323
] |
<p>I'm having a problem following a derivation of <a href="http://en.wikipedia.org/wiki/Bloch_wave" rel="nofollow">Bloch's theorem</a>, looking at a one dimensional lattice with $N$ nodes and spacing a, we impose periodic boundary conditions, meaning that the wave-function of a single electron $\psi(x)$ can be decomposed in the following modes:</p>
<p>$$\psi(x)=\sum_{q}\phi(q)\text{e}^{iqx},$$ </p>
<p>where </p>
<p>$$q = \frac{2\pi m}{N a}\; m\in \mathbb{Z}.$$ </p>
<p>Otherwise it would be multivalued.</p>
<p>Schrodinger's equation gives:$$(\epsilon - \frac{\hbar^2q^2}{2m})\phi(q)=\sum_{k \in B}\tilde{V}(k)\phi(q+k)$$
where $\epsilon$ is the energy eigenvalue of $\psi$, $B$ is the reciprocal Bravais lattice ($k=\frac{2\pi n}{a}$ with $n\in \mathbb{Z}$), $\tilde{V}$ is the Fourier transform of the potential.
So the $\phi$ modes separated by a vector belonging to the reciprocal Bravais lattice are coupled but I don't see how it implies that only $q$ vectors that are in this class of equivalence (whose difference belongs to $B$) should appear in the first sum (the expansion of $\psi$ in modes).</p>
| 7,642 |
[
-0.012917155399918556,
-0.010867763310670853,
0.030982669442892075,
-0.04068789258599281,
0.029078062623739243,
-0.01655643992125988,
-0.03601420298218727,
-0.029215946793556213,
0.009957476519048214,
-0.01952163130044937,
0.05475926771759987,
-0.011451301164925098,
0.06628844141960144,
0.03783465176820755,
0.034932561218738556,
0.03720322251319885,
0.0012571702245622873,
-0.013089409098029137,
-0.012183786369860172,
-0.03590131923556328,
-0.01659981906414032,
0.05250287801027298,
0.02780727855861187,
-0.011155575513839722,
-0.021948283538222313,
0.0207599475979805,
0.020704515278339386,
0.021657545119524002,
0.03609209507703781,
0.032042086124420166,
0.01898903399705887,
-0.047860950231552124,
0.046475671231746674,
0.03907892853021622,
0.019386371597647667,
-0.02154240384697914,
-0.06841065734624863,
0.0035463108215481043,
0.014564716257154942,
0.00758757721632719,
-0.02887611649930477,
-0.026822173967957497,
0.004369052592664957,
0.04600431025028229,
-0.011125731281936169,
-0.01958615332841873,
0.04856383427977562,
-0.01827755942940712,
0.06518834084272385,
-0.059803854674100876,
0.044922977685928345,
0.012960297055542469,
0.02125762589275837,
0.03119649738073349,
0.0025928139220923185,
-0.023449784144759178,
0.04270971193909645,
0.0758642628788948,
0.014577111229300499,
-0.035531941801309586,
-0.003317529335618019,
-0.013118182308971882,
0.0004924043896608055,
0.026739517226815224,
-0.05708508566021919,
0.012185567989945412,
-0.02236473560333252,
-0.04853396490216255,
0.016297977417707443,
-0.02764671854674816,
0.01887420006096363,
0.008444354869425297,
0.016730137169361115,
-0.07926375418901443,
0.02415495365858078,
0.02813907340168953,
0.012669376097619534,
0.011778132058680058,
0.022402098402380943,
-0.01869666948914528,
-0.018576525151729584,
0.006054580211639404,
0.01791125349700451,
0.015053815208375454,
0.00864942092448473,
-0.03769063949584961,
0.031373530626297,
-0.028124792501330376,
-0.004663711879402399,
-0.009875853545963764,
0.003558560973033309,
0.028091121464967728,
0.048419903963804245,
0.0013153376057744026,
-0.033002179116010666,
-0.010971271432936192,
-0.007718047127127647,
0.03483935445547104,
0.0019193259067833424,
-0.0638529509305954,
-0.002024540677666664,
-0.014466864056885242,
0.02476893924176693,
0.05656014755368233,
-0.008997081778943539,
0.020444434136152267,
-0.01732286438345909,
0.010849639773368835,
0.02364950254559517,
-0.014874261803925037,
-0.04351584613323212,
0.020003756508231163,
-0.03676599636673927,
0.03308519348502159,
0.006994243711233139,
0.0003164021181873977,
-0.020273976027965546,
0.0003403434529900551,
0.056536659598350525,
0.05944925546646118,
0.04515046253800392,
0.003582523437216878,
0.015335791744291782,
-0.037994034588336945,
-0.10032273828983307,
0.012277158908545971,
0.00705368397757411,
-0.004443703219294548,
-0.048113010823726654,
0.021771274507045746,
0.05276273563504219,
0.019338399171829224,
0.020140066742897034,
-0.0061621167697012424,
0.016759062185883522,
-0.01825096271932125,
-0.09186477959156036,
-0.052532825618982315,
0.03196355700492859,
-0.008784681558609009,
-0.011241470463573933,
-0.043404992669820786,
-0.02013595588505268,
0.044165343046188354,
0.08544544875621796,
-0.01496594026684761,
0.030555734410881996,
-0.01925789937376976,
0.06688335537910461,
0.05779971927404404,
-0.0027348832227289677,
-0.011810085736215115,
-0.02268102578818798,
-0.058430664241313934,
-0.026073411107063293,
0.01358742918819189,
0.005665181204676628,
-0.010057014413177967,
-0.014194095507264137,
0.012622733600437641,
0.09998299181461334,
0.019973307847976685,
-0.017061417922377586,
0.01656568981707096,
-0.036716364324092865,
-0.025425899773836136,
0.040875811129808426,
-0.005229787901043892,
0.017757263034582138,
0.056864529848098755,
0.005603434052318335,
-0.0107122752815485,
-0.017910657450556755,
0.03210260719060898,
-0.0000024521664272469934,
-0.01762683503329754,
0.00038284657057374716,
-0.034348007291555405,
0.04112871363759041,
0.016795562580227852,
-0.04265226423740387,
-0.05452628433704376,
0.00975332036614418,
0.04535915330052376,
0.015859059989452362,
0.04019656404852867,
0.0034664017148315907,
-0.026147115975618362,
-0.013839682564139366,
-0.03690579906105995,
-0.032704416662454605,
-0.03544991463422775,
0.0051650614477694035,
-0.002917973790317774,
-0.037049200385808945,
0.04295188933610916,
0.009712578728795052,
0.010639113374054432,
-0.01858600415289402,
-0.047766849398612976,
-0.021596578881144524,
-0.00564276659861207,
0.003062227740883827,
-0.03312397375702858,
0.02719918265938759,
0.03906003758311272,
0.03346756473183632,
0.03314584866166115,
0.058616720139980316,
-0.027977613732218742,
-0.01645839773118496,
0.00784396007657051,
-0.03953373059630394,
0.02644437737762928,
0.023848919197916985,
-0.008053948171436787,
0.022222697734832764,
-0.014049823395907879,
-0.0033637117594480515,
0.03986034542322159,
-0.045674584805965424,
0.06850580126047134,
0.05658125504851341,
0.0020238261204212904,
-0.04022500291466713,
0.04809865728020668,
0.036917634308338165,
0.02601698786020279,
-0.0349498949944973,
-0.06654092669487,
-0.017046527937054634,
0.0013765707844868302,
0.025823062285780907,
0.020946787670254707,
-0.029395457357168198,
0.0127926180139184,
0.013177660293877125,
0.030189363285899162,
0.044026296585798264,
0.010179771110415459,
-0.029918761923909187,
0.0050023142248392105,
0.03422258421778679,
0.03439635783433914,
0.0024923670571297407,
-0.004560355097055435,
0.017092566937208176,
-0.005802680738270283,
0.009430778212845325,
-0.02924458310008049,
-0.019800718873739243,
0.014211094938218594,
-0.02637932263314724,
0.0036838653031736612,
-0.016753440722823143,
-0.021075572818517685,
0.010978635400533676,
-0.018655842170119286,
0.021247299388051033,
0.018660414963960648,
-0.037533704191446304,
-0.0065839155577123165,
-0.020330585539340973,
-0.003918948583304882,
0.04942866787314415,
0.009590994566679,
-0.025027301162481308,
-0.006224668584764004,
0.03135150671005249,
-0.0385170504450798,
-0.030109914019703865,
-0.02725887857377529,
-0.0151359299197793,
0.023789186030626297,
0.001595241716131568,
0.03247767686843872,
0.01404749508947134,
0.028561638668179512,
-0.057942602783441544,
-0.04439134523272514,
-0.00893813744187355,
0.0009377942187711596,
0.023966221138834953,
0.01291340310126543,
-0.014295694418251514,
0.03569813817739487,
-0.05133528262376785,
-0.022229986265301704,
0.022841718047857285,
0.003736976534128189,
-0.013573279604315758,
-0.035674598067998886,
-0.015553058125078678,
-0.07429797947406769,
-0.00129778275731951,
-0.008595573715865612,
-0.015032959170639515,
-0.03834029287099838,
0.010096091777086258,
0.06385184824466705,
0.021933838725090027,
-0.04439155384898186,
0.012270222418010235,
-0.02483500726521015,
-0.00997842475771904,
-0.02560409903526306,
-0.030299024656414986,
0.007699041627347469,
-0.013411222025752068,
0.009754767641425133,
0.009492692537605762,
-0.017851198092103004,
-0.006697418633848429,
-0.01660904847085476,
-0.06054674834012985,
-0.00585951330140233,
0.007405277341604233,
0.027861250564455986,
0.020869996398687363,
-0.025562232360243797,
0.08496997505426407,
0.01774759590625763,
-0.04357123747467995,
0.010054134763777256,
0.02990945242345333,
-0.006728879176080227,
-0.03784026950597763,
0.004446839448064566,
0.0699504092335701,
-0.000402003905037418,
0.06381380558013916,
-0.021523945033550262,
0.04462922737002373,
0.0516129732131958,
-0.025962894782423973,
-0.018505947664380074,
0.03922032192349434,
-0.0014676823047921062,
-0.009702990762889385,
0.03357736021280289,
-0.020504271611571312,
0.012258368544280529,
-0.020251190289855003,
0.012239126488566399,
0.008823717013001442,
0.032584454864263535,
-0.06202307343482971,
0.027214549481868744,
-0.005826245993375778,
0.028013741597533226,
-0.011415371671319008,
0.024790650233626366,
0.01859907992184162,
-0.00012093114492017776,
-0.012187446467578411,
0.027178945019841194,
0.06872012466192245,
-0.047297749668359756,
0.010402479209005833,
0.009861093014478683,
0.028671512380242348,
-0.015036191791296005,
-0.0012316368520259857,
-0.008390954695641994,
0.007231882773339748,
0.033384352922439575,
-0.04564325883984566,
-0.046709589660167694,
0.014928696677088737,
0.023231498897075653,
0.05693730339407921,
-0.00017536211817059666,
-0.028482958674430847,
0.0021726449485868216,
-0.020745761692523956,
-0.023187004029750824,
-0.030166145414114,
0.07306069880723953,
-0.013303759507834911,
0.006731051951646805,
0.044966500252485275,
-0.0005525469314306974,
-0.00903607252985239,
0.018931694328784943,
-0.06641510874032974,
-0.029955781996250153,
0.01874355413019657,
0.013880905695259571,
-0.009070212952792645,
-0.036006178706884384,
-0.027806119993329048,
-0.028569277375936508,
-0.03604200482368469,
0.004144344478845596,
-0.036322157829999924,
-0.06798127293586731,
-0.009562878869473934,
-0.04818812385201454,
0.0005346851539798081,
-0.011387493461370468,
0.03769545629620552,
0.05140219256281853,
-0.03298639506101608,
-0.015223035588860512,
0.057336922734975815,
-0.030398929491639137,
-0.01827957294881344,
-0.016717923805117607,
0.02727183699607849,
0.016918756067752838,
0.04874452203512192,
0.017266826704144478,
0.05241842940449715,
0.014163624495267868,
-0.016726821660995483,
0.004283322021365166,
0.08224834501743317,
-0.0018345455173403025,
-0.02498467080295086,
0.018424682319164276,
0.01811259053647518,
-0.003380293259397149,
0.015859834849834442,
0.06949886679649353,
0.007286779582500458,
0.022478675469756126,
0.02564101479947567,
0.0027124967891722918,
-0.03290189802646637,
0.05250906944274902,
0.027009421959519386,
-0.007197728380560875,
-0.007783117238432169,
-0.029470158740878105,
0.015114552341401577,
-0.03323640674352646,
-0.022328002378344536,
-0.0040579624474048615,
-0.01741756685078144,
-0.0344243124127388,
0.023108486086130142,
0.034221261739730835,
0.022626889869570732,
0.01342504657804966,
0.005995653569698334,
-0.007391331251710653,
0.02019163966178894,
0.010494391433894634,
-0.02268405072391033,
0.007344861514866352,
-0.01389735471457243,
0.020343758165836334,
-0.03211388364434242,
-0.011458704248070717,
-0.07394637912511826,
-0.012012943625450134,
0.03141636773943901,
0.004054357297718525,
0.03770163655281067,
0.003305309684947133,
-0.05353635549545288,
-0.010453891009092331,
0.04487261921167374,
-0.006916482467204332,
0.04305972903966904,
0.018612535670399666,
0.010591007769107819,
-0.022788135334849358,
-0.04133113473653793,
-0.017843181267380714,
-0.046116191893815994,
0.011603925377130508,
0.041874296963214874,
0.008932859636843204,
-0.002890758914873004,
-0.021972572430968285,
0.011227920651435852,
0.009261153638362885,
0.03233981505036354,
0.011649045161902905,
-0.038823001086711884,
-0.0005547144683077931,
0.007531195878982544,
-0.0023460574448108673,
-0.08189035207033157,
0.032010339200496674,
-0.006193152163177729,
0.04307694733142853,
0.03151433914899826,
-0.036271147429943085,
-0.06420665979385376,
0.05961265042424202,
0.037082429975271225,
-0.0073114666156470776,
0.03153450787067413,
-0.004226794000715017,
0.0669364482164383,
0.0025061110500246286,
0.01783047243952751,
0.07136303186416626,
0.040182262659072876,
0.02103995531797409,
-0.0066749658435583115,
-0.03863358870148659,
0.023498909547924995,
-0.01469942182302475,
0.025109564885497093,
-0.02923804521560669,
0.03836722671985626,
-0.003464850364252925,
0.04536370187997818,
-0.014252647757530212,
0.02922745607793331,
0.00662730447947979,
-0.0169695895165205,
-0.00815951731055975,
-0.013990736566483974,
-0.03196917846798897,
0.03513973578810692,
-0.02453334629535675,
0.01476756390184164,
0.004558087792247534,
-0.002983385231345892,
0.025862129405140877,
-0.016731159761548042,
-0.003797491081058979,
0.030870504677295685,
-0.021274417638778687,
0.016958624124526978,
-0.0343254879117012,
0.0017076348885893822,
0.004242934286594391,
-0.08293366432189941,
0.05611273646354675,
-0.020289696753025055,
0.023774564266204834,
0.007478440646082163,
-0.03060409426689148,
-0.020136820152401924,
-0.0017263159388676286,
0.010524160228669643,
-0.00571100041270256,
-0.02953232079744339,
-0.007460038643330336,
0.03212114796042442,
-0.034948285669088364,
-0.10023892670869827,
0.000028452124752220698,
0.006656541954725981,
-0.023385776206851006,
-0.0069670663215219975,
-0.01908256486058235,
0.02976304665207863,
-0.005069420672953129,
-0.006705576088279486,
0.040678247809410095,
-0.0034568274859339,
-0.028492046520113945,
-0.03981787711381912,
0.015214724466204643,
0.03682093322277069,
0.018446268513798714,
0.02612921968102455,
-0.004888804163783789,
0.028440464287996292,
-0.037988971918821335,
0.025955379009246826,
0.026941565796732903,
0.02287175878882408,
-0.033579111099243164,
-0.008571590296924114,
-0.042051468044519424,
0.01268485002219677,
0.06101416423916817,
-0.029284924268722534,
-0.017709502950310707,
-0.006621192209422588,
-0.011932836845517159,
0.018990617245435715,
0.0055709220468997955,
-0.02466382086277008,
0.009266565553843975,
0.028466155752539635,
-0.012580400332808495,
0.00015548337250947952,
-0.03667888417840004,
-0.019356098026037216,
0.010579939000308514,
-0.04149782657623291,
0.013998479582369328,
0.01339846383780241,
0.08556950837373734,
0.00037155154859647155,
0.026233725249767303,
0.01770702749490738,
0.009018795564770699,
-0.004238573368638754,
-0.03272983059287071,
0.0033592097461223602,
0.0011418148642405868,
0.01137029379606247,
-0.023907480761408806,
-0.055474087595939636,
-0.03074972704052925,
0.02872295491397381,
0.012244357727468014,
-0.0033205959480255842,
0.03610779345035553,
0.02965497598052025,
-0.014839805662631989,
-0.0060606771148741245,
0.00045719638001173735,
-0.013521581888198853,
0.01724572665989399,
0.0019253481877967715,
0.03827483206987381,
-0.05122336372733116,
-0.03246635943651199,
-0.023295598104596138,
0.051719095557928085,
-0.03139418363571167,
0.0031450979877263308,
0.03673870116472244,
0.039237361401319504,
0.02821231260895729,
0.01447275560349226,
-0.019216036424040794,
0.05830894410610199,
-0.01718747615814209,
0.014218452386558056,
0.006259555462747812,
-0.03227764740586281,
0.050635237246751785,
0.04231850802898407,
0.012486621737480164,
-0.04373360797762871,
-0.055477384477853775,
-0.029078029096126556,
0.0366598516702652,
-0.012722590006887913,
0.011539828032255173,
0.02402239851653576,
0.006420631892979145,
0.021138839423656464,
0.038556911051273346,
-0.003914815839380026,
0.0027768746949732304,
-0.023942917585372925,
0.003080580150708556,
-0.046026356518268585,
-0.03756941109895706,
0.022117773070931435,
-0.026322241872549057,
-0.01686459593474865,
0.014877961948513985,
-0.027763625606894493,
0.029796896502375603,
-0.0008239603484980762,
-0.024542905390262604,
-0.04054331034421921,
0.05889863148331642,
0.013334214687347412,
0.0041786921210587025,
0.04639444127678871,
-0.02091081440448761,
0.1199205070734024,
0.05418458580970764,
0.06465037167072296,
-0.07131761312484741,
0.045022450387477875,
-0.013109324499964714,
0.017429111525416374,
-0.06214836612343788,
-0.017321929335594177,
-0.014958512037992477,
-0.015464283525943756,
-0.03815808147192001,
0.07450461387634277,
0.00023894595506135374,
-0.0065032243728637695,
0.03806468844413757,
-0.04160904884338379,
-0.038131486624479294,
0.020437663421034813,
0.015760449692606926,
0.022817295044660568,
0.013086595572531223,
-0.015120857395231724,
0.014031955972313881,
-0.0367564894258976,
-0.002757070818915963,
-0.06502818316221237,
-0.009548860602080822,
0.026270674541592598,
0.044920358806848526,
-0.017174307256937027,
0.029068898409605026,
0.020602697506546974,
-0.011660180054605007,
0.017632070928812027,
0.045463304966688156,
0.03595587611198425,
-0.023899702355265617,
0.06291002035140991,
-0.0028297104872763157,
-0.00995470117777586,
-0.00694579491391778,
0.03691050410270691,
-0.00028429360827431083,
-0.035632409155368805,
-0.02240021713078022,
-0.01318778470158577,
0.04470035433769226,
0.0038088711444288492,
-0.05352059006690979,
-0.0067847855389118195,
0.008277973160147667,
0.0009121734765358269,
-0.07811278104782104,
-0.016693370416760445,
-0.04170325770974159,
-0.0032250727526843548,
-0.032905325293540955,
-0.01803990639746189,
-0.00041436238097958267,
0.016000298783183098,
-0.01601676642894745,
0.002585523994639516,
0.009335408918559551,
-0.03403155133128166,
0.00885227881371975,
-0.039237380027770996,
0.023880254477262497,
0.00627924082800746,
-0.0010524340905249119,
-0.030780890956521034,
-0.008761752396821976,
-0.0462980717420578,
-0.042724303901195526,
-0.009981128387153149,
0.034869659692049026,
0.058758847415447235,
-0.0176040381193161,
-0.02851908840239048,
-0.01883193664252758,
-0.06841405481100082,
0.0015944233164191246,
-0.013227731920778751,
-0.03095397539436817,
0.015560244210064411,
0.005824506748467684,
-0.010193441063165665,
0.06503824889659882,
-0.09484398365020752,
-0.011749312281608582,
-0.008214134722948074,
0.012411022558808327,
0.01846615970134735,
-0.04553070291876793,
-0.056874457746744156,
-0.03874698281288147,
-0.04885990917682648,
0.01963556557893753,
-0.013788813725113869,
-0.009304491803050041,
0.007889708504080772,
0.002904418623074889,
0.02151668816804886,
0.063645139336586,
-0.032564837485551834,
-0.019576746970415115,
-0.024365795776247978,
-0.049220867455005646,
0.06685832142829895,
0.06808434426784515,
0.041138727217912674,
-0.04053632542490959,
-0.03596186265349388,
0.01662283204495907,
-0.012036796659231186,
0.03168349340558052,
-0.001058658235706389,
-0.029475843533873558,
-0.018407441675662994,
-0.01540333405137062,
0.02140745520591736,
-0.05661437287926674,
-0.00777217885479331,
-0.032713498920202255,
-0.0023356955498456955,
-0.015272244811058044,
0.03868219256401062,
-0.0277035403996706,
0.02440023608505726,
-0.05793474614620209,
-0.052945591509342194,
0.06098691746592522,
0.03640061616897583,
-0.007740031462162733,
0.00689767487347126,
0.004018302075564861,
0.03682447224855423,
0.03541283309459686,
0.0046447282657027245,
-0.02111712284386158,
0.024737274274230003,
-0.0347033329308033,
0.00030744605464860797,
0.021380018442869186,
0.014548094943165779,
-0.0008370460709556937,
0.046911682933568954,
0.029323633760213852,
-0.03589626029133797,
0.03039885312318802,
-0.02961810678243637,
-0.005538829602301121,
0.04259096831083298,
-0.039249237626791,
-0.012452072463929653,
-0.05519299581646919,
-0.012459807097911835,
0.02619466930627823,
0.01222030445933342,
0.017188794910907745,
0.025918105617165565,
-0.03173298388719559,
-0.02529584802687168,
-0.026791172102093697,
-0.005427991040050983,
0.021281922236084938,
0.02718740701675415,
0.02942214533686638,
-0.006075218785554171,
0.045889027416706085,
-0.03527502343058586,
0.0228690505027771,
-0.005541917867958546,
0.017965693026781082,
-0.045450251549482346,
-0.030190905556082726,
0.004562677815556526,
0.013755976222455502,
0.02162201888859272,
-0.022063346579670906,
0.008490570820868015,
0.0014355177991092205,
-0.06153516471385956,
0.016708368435502052,
0.0070548513904213905,
-0.017199285328388214,
-0.04950061812996864,
0.0009770402684807777,
-0.0587192140519619,
-0.009106328710913658,
0.04458484426140785,
0.03869924321770668,
0.01655089482665062,
0.009519907645881176,
-0.007450349163264036,
-0.06296892464160919,
-0.0078261848539114,
0.01541683916002512,
-0.016329605132341385,
-0.01205392461270094,
0.0490776002407074,
0.010031321085989475,
-0.04089437797665596,
-0.002735013607889414,
0.003910185303539038,
-0.02375929057598114,
0.005200287327170372,
0.015442868694663048,
0.007619764655828476,
0.0652356892824173,
-0.006016972474753857,
-0.0023934149648994207,
-0.0009709708974696696,
-0.000999460811726749,
0.036581847816705704,
0.009199040941894054,
-0.00674256170168519,
0.0035417666658759117,
0.0198101457208395,
-0.01698831096291542,
-0.025512533262372017,
0.005874718073755503,
-0.010247251018881798,
0.006419155281037092,
-0.01870470866560936,
0.0007164911366999149,
0.06085501238703728,
-0.030858805403113365,
-0.015667332336306572,
-0.03918975591659546,
-0.019650716334581375,
0.0038834691513329744,
0.038685355335474014,
0.0013710010098293424,
0.0013249552575871348,
-0.03357437252998352,
-0.06261777132749557,
0.011908849701285362,
0.01565001718699932,
-0.018512044101953506,
-0.0488339364528656,
-0.0112615916877985,
0.01849397085607052,
0.008626681752502918,
-0.001744771027006209,
-0.001400477485731244,
-0.02284882217645645,
0.035251159220933914,
-0.022245094180107117,
0.03606140613555908,
-0.06617863476276398,
-0.042713265866041183,
-0.020338864997029305,
-0.038829654455184937,
0.03135136514902115,
0.0226090457290411,
-0.03314715251326561,
0.0060114325024187565,
-0.02376200258731842,
0.028239840641617775,
0.031748659908771515,
0.05910078063607216,
0.009950747713446617,
-0.005768490489572287,
0.012062529101967812,
-0.03684814274311066,
0.03216562420129776,
-0.02214878983795643,
0.018572958186268806,
0.004512406885623932,
-0.00922827236354351,
0.019611185416579247,
-0.00497019337490201,
-0.0401252843439579,
0.022270292043685913,
0.01284026075154543,
-0.013352720066905022,
-0.02682534232735634,
-0.01763097010552883,
-0.042851198464632034,
0.03032989241182804,
-0.00468640960752964,
0.0030530481599271297,
0.037314124405384064,
-0.019773731008172035,
0.020014574751257896,
0.029971061274409294,
-0.013694103807210922,
-0.05460222065448761,
0.03240356221795082,
-0.03807184845209122,
0.011967768892645836,
-0.007517801132053137,
0.023044783622026443,
0.02552781067788601,
-0.002900332910940051,
-0.011239125393331051,
0.0351657010614872,
-0.03515123203396797,
-0.01621706411242485,
0.04803623631596565,
0.009322904981672764,
0.0246424563229084,
-0.0013420621398836374,
-0.013723335228860378,
0.001096511259675026,
0.013124068267643452,
0.04015021398663521,
0.0440765842795372,
0.013288945890963078,
0.021347442641854286,
0.030011260882019997,
0.046533189713954926,
-0.019573884084820747,
-0.0049977353774011135,
-0.01410022471100092,
-0.01445605419576168,
-0.018662840127944946,
-0.014035079628229141,
0.019042199477553368,
-0.04038045182824135,
-0.01181053277105093,
0.02689807303249836,
-0.005879969336092472,
0.07777465134859085,
-0.012411464937031269,
0.07727647572755814,
-0.021409964188933372,
0.026605963706970215,
0.004912934266030788,
0.05586066469550133,
0.03376162424683571,
0.02198193222284317,
-0.024953573942184448,
-0.0213481355458498,
-0.04199134185910225,
-0.024031030014157295,
-0.006022732239216566,
-0.055981721729040146,
-0.03215385228395462,
0.0052514635026454926,
-0.00032275234116241336,
0.015209953300654888,
0.013609977439045906,
-0.006152154412120581,
0.012564160861074924,
0.020228080451488495,
0.06287602335214615,
-0.005476516671478748,
0.003678264794871211,
-0.0016681869747117162,
-0.031333278864622116,
0.06022374704480171,
-0.04706127569079399,
-0.012156818993389606,
-0.014053274877369404,
-0.022372225299477577,
-0.005428041331470013,
0.03464348986744881
] |
<p>Here's the conundrum I have been facing. Yesterday I asked the question: how can batteries constantly motivate electrons to complete a circuit? (<a href="http://physics.stackexchange.com/questions/126971/what-maintains-constant-voltage-in-a-battery">What maintains constant voltage in a battery?</a>)
After some thought I realized that the concept is that of an energy source. The batteries are a source of energy, and regardless of the mechanism, they will constantly 'push' for a goal. My solution finally came when I realized that speaking about someone's 'motivation' was identical to the constant push of the battery. Here's the issue:</p>
<p>My sister wanted to get me coffee yesterday for my birthday. She was attempting to give it to me before my class started. Unfortunately, she had difficulty with traffic, and so was able to deliver only after my class started. I realized when she told me that she tried as hard as she could, and that what really mattered was her motivation. The push she gave was constant regardless of the resistance she encountered. The parallel here to the constant push of a battery was strong; voltage didn't matter in respect to resistance for a given battery. </p>
<p>Now I have a different issue. The voltage drop is described as the per-capita potential energy difference of electric charges at points a and b right? The total energy would then be the amount of 'capitas' multiplied by this per capita potential energy difference. More capitas mean more total energy. </p>
<p>Here's the problem. If the motivation of a battery is described by voltage, then if we look at a circuit with a resistor and compare it to another circuit with an equal-length resistor but with a wider surface area, the potential difference is supposed to stay the same in both cases. However, in taking the charge from one surface to the other, more energy is required for the resistor with larger surface area! The amount of energy supplied is different in either case, yet from the same 'constant' energy source. This seems so wrong to me right now. </p>
<p>Yet I know that Power=Voltage*(Current)^2, so this actually makes sense in terms of the equation. I wonder what is lacking in my fundamental understanding of the potential difference in comparison to the idea of motivation/constant energy source. I'm really fundamentally misunderstanding something complex here that I don't quite have my finger put on yet. Please help clear up my view of a battery as a constant pusher to line up with this changing energy ouput a battery can give. </p>
| 7,643 |
[
-0.029583455994725227,
-0.017436670139431953,
0.018748320639133453,
0.007249829825013876,
0.030634548515081406,
0.005722402594983578,
-0.023196455091238022,
-0.016506072133779526,
-0.0008200728334486485,
-0.01358588133007288,
0.017797019332647324,
0.05000494420528412,
0.024043124169111252,
0.035670556128025055,
-0.0032814498990774155,
-0.004252783954143524,
0.008151901885867119,
-0.007588932756334543,
-0.021818626672029495,
0.01100689172744751,
0.010760544799268246,
0.03418313339352608,
-0.009351085871458054,
-0.00647670729085803,
0.016090327873826027,
0.036123037338256836,
0.03432760760188103,
-0.057349566370248795,
-0.050575658679008484,
0.034978099167346954,
-0.006659979000687599,
-0.06039053946733475,
0.009754727594554424,
0.0009944989578798413,
0.034148477017879486,
0.0060016014613211155,
-0.0004333785327617079,
-0.018080489709973335,
0.002104339422658086,
0.04589793086051941,
0.014686010777950287,
0.007626196835190058,
-0.021074846386909485,
0.033868301659822464,
-0.04704296216368675,
0.045337580144405365,
-0.015493132174015045,
-0.02898411639034748,
0.040945183485746384,
-0.06047987937927246,
0.026132984086871147,
0.008092550560832024,
0.053073350340127945,
0.04075968638062477,
0.003920672927051783,
-0.019516246393322945,
0.033024005591869354,
0.05060884356498718,
-0.0026268665678799152,
-0.04336902126669884,
-0.00522819347679615,
-0.015765290707349777,
-0.03688564896583557,
-0.04482043907046318,
0.0008077213424257934,
0.00848409067839384,
0.015029354952275753,
-0.01853194646537304,
0.02472785674035549,
-0.01121029257774353,
0.05048711597919464,
0.03933781012892723,
0.014743865467607975,
0.0038529047742486,
-0.003123452188447118,
-0.02361668087542057,
0.011835223063826561,
0.003047937760129571,
0.03129221871495247,
0.03972436860203743,
-0.01634502038359642,
-0.0030903636943548918,
0.05488252267241478,
0.08829030394554138,
0.012678478844463825,
-0.028645779937505722,
0.040320299565792084,
-0.03701841086149216,
0.028626954182982445,
0.017688628286123276,
0.024848634377121925,
-0.0012130163377150893,
0.010378806851804256,
-0.0026844521053135395,
0.005530437920242548,
0.03358471766114235,
-0.009669210761785507,
0.029857778921723366,
0.029682565480470657,
-0.004764832090586424,
-0.02495526894927025,
-0.013986590318381786,
0.009256694465875626,
0.06510517001152039,
0.022412842139601707,
-0.02054714225232601,
-0.016794661059975624,
0.03150434419512749,
-0.01039049495011568,
0.007470562122762203,
-0.05174696817994118,
0.022118080407381058,
0.03043028898537159,
0.033404961228370667,
-0.031614962965250015,
-0.01806754805147648,
0.003438700456172228,
-0.001987333409488201,
0.053625382483005524,
-0.004656387958675623,
0.027816306799650192,
-0.017470484599471092,
0.0006208239356055856,
-0.05929800495505333,
-0.05915852263569832,
0.01687241718173027,
0.007040155585855246,
-0.014632896520197392,
0.012392790988087654,
-0.01700366847217083,
-0.010141666978597641,
0.018826182931661606,
-0.03727206587791443,
-0.010169742628932,
0.02707994543015957,
0.020321274176239967,
-0.07783201336860657,
-0.053938526660203934,
0.0397832989692688,
0.024499785155057907,
-0.02025916799902916,
-0.05871356651186943,
-0.03547465801239014,
0.031582340598106384,
0.04415063187479973,
-0.0065413047559559345,
-0.010229072533547878,
0.0007360480376519263,
0.0065533677116036415,
-0.0007257277611643076,
-0.0036399781238287687,
0.005194376222789288,
-0.027639340609312057,
-0.02624049037694931,
-0.021758122369647026,
-0.04756076633930206,
0.013945414684712887,
0.030781123787164688,
0.03654370829463005,
0.020201299339532852,
0.04787164181470871,
-0.014050234109163284,
-0.0631508007645607,
-0.007178411819040775,
-0.007293726783245802,
-0.026092788204550743,
0.08403411507606506,
0.00020789731934200972,
-0.001128719188272953,
0.04413142055273056,
0.0039857965894043446,
0.016534093767404556,
0.0016498961485922337,
0.002376785036176443,
0.027639809995889664,
-0.0388309508562088,
-0.04340602830052376,
-0.05031702667474747,
-0.011725811287760735,
0.008329312317073345,
-0.0450274683535099,
-0.07271818071603775,
-0.043143607676029205,
0.007725692354142666,
0.00656075868755579,
0.03293927386403084,
0.004598790314048529,
-0.01368589885532856,
-0.012414751574397087,
-0.015601652674376965,
-0.03485707566142082,
-0.03975469991564751,
0.056871477514505386,
0.007091621868312359,
-0.008063310757279396,
0.044818583875894547,
-0.056911714375019073,
-0.007890762761235237,
-0.04628613218665123,
0.002590809715911746,
0.0034190979786217213,
0.04742467775940895,
-0.00067283766111359,
0.015520782209932804,
0.012284585274755955,
0.029683010652661324,
-0.0020007642451673746,
0.01624656841158867,
0.037243377417325974,
-0.017056772485375404,
-0.005090310238301754,
-0.014241144061088562,
-0.023725688457489014,
0.029984159395098686,
0.0331907644867897,
0.03859582170844078,
-0.042592499405145645,
-0.0003572992864064872,
-0.0115144532173872,
0.06188754364848137,
-0.03423956036567688,
0.052135780453681946,
0.04747818037867546,
0.019565660506486893,
-0.017460493370890617,
0.045509472489356995,
-0.0012360884575173259,
0.0032251360826194286,
-0.032711971551179886,
-0.013369463384151459,
-0.03385591879487038,
0.015622342005372047,
0.06065572425723076,
-0.003404496004804969,
-0.026042496785521507,
0.01519123837351799,
0.026246733963489532,
0.046388253569602966,
0.029458630830049515,
0.005868748761713505,
0.0021699799690395594,
-0.0032806433737277985,
0.033674173057079315,
0.0053113666363060474,
0.0019340977305546403,
0.05933762341737747,
-0.010962793603539467,
-0.00556538812816143,
-0.0028887197840958834,
-0.0072705005295574665,
0.009321203455328941,
0.017295749858021736,
0.041448261588811874,
0.023537663742899895,
0.02115938812494278,
0.009545445442199707,
0.03268986567854881,
-0.028939319774508476,
0.020740685984492302,
0.021849414333701134,
-0.0017669970402494073,
0.006604937836527824,
-0.05904980003833771,
-0.04691874980926514,
-0.025896357372403145,
-0.010986000299453735,
0.010151457972824574,
0.0057332469150424,
0.03723530471324921,
-0.02976791374385357,
0.03687860071659088,
-0.008423395454883575,
-0.025676971301436424,
0.006057681515812874,
-0.009444931522011757,
-0.00999446026980877,
0.03659844771027565,
0.02147597447037697,
-0.05860022455453873,
0.009769042953848839,
-0.00008987827459350228,
-0.006944610737264156,
0.005786564201116562,
-0.016605978831648827,
-0.010935052298009396,
0.016658097505569458,
-0.004578183405101299,
-0.012623106129467487,
0.06362766772508621,
0.02077268809080124,
0.00681154802441597,
0.03094271384179592,
0.0046005877666175365,
-0.050008442252874374,
0.026590339839458466,
-0.020876623690128326,
0.019445957615971565,
-0.012341702356934547,
-0.0064403400756418705,
0.06978487223386765,
-0.00046916439896449447,
-0.08251441270112991,
0.02316025272011757,
-0.025297852233052254,
-0.0359257310628891,
-0.010940262116491795,
-0.04369306191802025,
0.026824072003364563,
0.005129373632371426,
0.03321738913655281,
0.013835406862199306,
-0.012424570508301258,
-0.03731841593980789,
-0.05551775172352791,
-0.0553017184138298,
0.011934719979763031,
-0.020899329334497452,
0.06117228791117668,
-0.0226166732609272,
-0.03478187322616577,
0.08574412763118744,
0.03850492835044861,
-0.01204741932451725,
-0.016446296125650406,
-0.026408573612570763,
0.0031169659923762083,
-0.031167887151241302,
-0.013188108801841736,
0.07682442665100098,
-0.015254765748977661,
0.017715370282530785,
-0.0009879563003778458,
0.08917573094367981,
0.0491887703537941,
0.0073420023545622826,
-0.00794691126793623,
0.01701645366847515,
0.019791267812252045,
0.003270296147093177,
0.07378855347633362,
0.013004333712160587,
-0.04692913219332695,
0.011813919991254807,
-0.03235173970460892,
0.05988848954439163,
-0.012550861574709415,
-0.05187145620584488,
0.016929425299167633,
-0.03381545841693878,
0.016916684806346893,
-0.03520893305540085,
0.012754114344716072,
0.00958282221108675,
-0.05845467001199722,
0.007734103128314018,
0.002089007059112191,
0.05958797037601471,
-0.05983785167336464,
-0.00016801095625851303,
0.02108651027083397,
0.04812423884868622,
-0.01549272146075964,
-0.054533831775188446,
0.015613559633493423,
0.018125467002391815,
-0.006881175562739372,
0.00024604552891105413,
-0.018063925206661224,
0.038448408246040344,
0.015602955594658852,
0.022739838808774948,
0.013941979967057705,
-0.07381407916545868,
-0.016104521229863167,
-0.07340462505817413,
-0.014282718300819397,
-0.024628199636936188,
0.05468326807022095,
0.007888211868703365,
0.030443742871284485,
-0.016202261671423912,
0.02917751669883728,
-0.022890733554959297,
0.006523488089442253,
-0.10303637385368347,
-0.00008175350376404822,
-0.02348908595740795,
-0.02582021802663803,
0.008350299671292305,
-0.03272198513150215,
0.03549478203058243,
-0.0037105814553797245,
-0.027566956356167793,
-0.04543377459049225,
0.02257758006453514,
-0.028382843360304832,
0.04161297157406807,
-0.05229717120528221,
-0.04425494372844696,
-0.017963126301765442,
0.006057884078472853,
0.050472602248191833,
-0.04113085940480232,
0.030707918107509613,
0.019816890358924866,
-0.00550846615806222,
-0.010532615706324577,
-0.005861424840986729,
-0.030012797564268112,
0.008626664057374,
-0.017154181376099586,
-0.028016867116093636,
0.019938001409173012,
0.04019111022353172,
-0.015563379973173141,
0.004044089000672102,
0.025913212448358536,
-0.005817784462124109,
-0.030812015756964684,
-0.06758285313844681,
-0.03740319609642029,
-0.041058532893657684,
-0.006222371011972427,
0.049040716141462326,
-0.0361652709543705,
0.011083797551691532,
0.0037430550437420607,
0.010289056226611137,
0.010094539262354374,
0.04632154107093811,
0.007640672381967306,
-0.005185636226087809,
-0.05717983469367027,
-0.05768740549683571,
0.010617509484291077,
-0.024924740195274353,
0.0044197323732078075,
0.044529516249895096,
0.00017046193534042686,
-0.03367419168353081,
-0.015935886651277542,
0.03225524723529816,
0.009092822670936584,
-0.017053944990038872,
0.0394756980240345,
-0.0006766206352040172,
0.014205523766577244,
-0.008435308001935482,
0.024377569556236267,
0.02957003191113472,
-0.012292700819671154,
0.02653445303440094,
-0.015002749860286713,
-0.015022380277514458,
-0.07016786932945251,
-0.07590816915035248,
0.022196343168616295,
0.06396672874689102,
-0.03963727131485939,
-0.0008120026905089617,
-0.02850424125790596,
-0.011323118582367897,
0.05450564622879028,
-0.026634257286787033,
0.04352676868438721,
0.011969858780503273,
0.015630047768354416,
-0.04235074669122696,
-0.0435032993555069,
-0.029686957597732544,
0.021543364971876144,
-0.026289766654372215,
0.05458409711718559,
0.009615094400942326,
0.0002366170665482059,
0.016801659017801285,
0.029581712558865547,
0.027456464245915413,
0.06829976290464401,
-0.011110897175967693,
-0.03340786322951317,
0.02163495309650898,
-0.0026718475855886936,
-0.017628850415349007,
-0.12132125347852707,
0.035014767199754715,
-0.00871187448501587,
0.0040059322491288185,
-0.00477581936866045,
-0.04094051942229271,
-0.04996433109045029,
0.011915383860468864,
0.014171048998832703,
-0.00027991094975732267,
-0.01092714723199606,
-0.06180684641003609,
0.06063512712717056,
0.026272213086485863,
-0.014570165425539017,
0.028193850070238113,
0.017049182206392288,
-0.07585638761520386,
-0.018017688766121864,
-0.00230432883836329,
0.0029984149150550365,
-0.0027853422798216343,
-0.004031923599541187,
-0.010280662216246128,
-0.00923916231840849,
-0.02686900645494461,
0.01527593657374382,
0.008110991679131985,
0.011441080830991268,
-0.04216083511710167,
-0.05683029443025589,
-0.013891755603253841,
-0.0024695247411727905,
-0.007434404455125332,
0.026853090152144432,
-0.01904948242008686,
0.030944298952817917,
0.018308108672499657,
-0.02135133370757103,
-0.01683301292359829,
-0.020773420110344887,
0.021641436964273453,
0.02487248368561268,
0.004690219182521105,
-0.004993315786123276,
-0.042208146303892136,
-0.005351870786398649,
0.020912883803248405,
-0.028349410742521286,
0.06013135984539986,
0.009113702923059464,
0.011191275902092457,
0.018436089158058167,
-0.02341894432902336,
-0.06370487809181213,
0.04703599959611893,
0.005162843968719244,
0.01733214221894741,
-0.029019905254244804,
0.006236082874238491,
0.006695805117487907,
0.020873723551630974,
-0.03476144000887871,
-0.03453558310866356,
0.018490146845579147,
0.03272688388824463,
-0.013784549199044704,
0.01909305527806282,
-0.02696915529668331,
-0.0006990277324803174,
-0.03629223629832268,
0.04625095799565315,
0.006612342316657305,
-0.046763982623815536,
0.0019409438828006387,
-0.00011992832878604531,
0.005698884837329388,
0.061202723532915115,
0.01673964597284794,
0.015128076076507568,
-0.007713714614510536,
-0.00536890747025609,
0.012701638974249363,
-0.032328519970178604,
0.031912125647068024,
-0.055841028690338135,
-0.023031001910567284,
-0.018325908109545708,
-0.004142295103520155,
0.059831611812114716,
-0.028788018971681595,
-0.009019682183861732,
0.042237382382154465,
-0.002776817651465535,
-0.03765237703919411,
-0.03789236769080162,
0.04370274394750595,
0.023181555792689323,
0.00692737428471446,
0.01156697142869234,
0.016528578475117683,
-0.009840828366577625,
-0.032443925738334656,
0.016617698594927788,
0.0031649989541620016,
-0.003394367638975382,
-0.029964562505483627,
0.044428154826164246,
-0.03022126480937004,
-0.010420824401080608,
0.061408717185258865,
0.03432855010032654,
0.043104011565446854,
-0.0007948730490170419,
0.007777249440550804,
-0.012603924609720707,
-0.03865872696042061,
-0.03508696332573891,
-0.004984367173165083,
-0.06489455699920654,
0.020664583891630173,
0.02603365294635296,
0.0210079587996006,
0.02489766851067543,
0.024253366515040398,
-0.04437686502933502,
0.01418520137667656,
-0.02242213301360607,
0.006874142214655876,
-0.013671370223164558,
0.002642923966050148,
0.020147208124399185,
-0.049372199922800064,
-0.023879338055849075,
0.06371310353279114,
0.0024836522061377764,
-0.028586888685822487,
0.006807713303714991,
0.030905811116099358,
0.032696302980184555,
0.03175089508295059,
-0.047443170100450516,
-0.044724076986312866,
0.021361855790019035,
-0.011866265907883644,
0.04003114625811577,
0.0038608615286648273,
-0.005175191443413496,
0.07215438783168793,
0.001945474767126143,
-0.02018464170396328,
-0.05309392139315605,
0.0015268222196027637,
-0.055427078157663345,
-0.008927700109779835,
0.0173763707280159,
0.018950607627630234,
-0.01855481043457985,
-0.01718747802078724,
-0.006361984182149172,
-0.023253120481967926,
0.017380986362695694,
-0.054430194199085236,
-0.038975831121206284,
-0.007644779980182648,
-0.014677826315164566,
-0.07189337909221649,
0.042193204164505005,
-0.004281847737729549,
-0.027002427726984024,
0.006401920225471258,
-0.03235286474227905,
0.017397500574588776,
0.05976323410868645,
0.011351360008120537,
0.003399109235033393,
0.06010423228144646,
-0.037520211189985275,
0.018229661509394646,
-0.04227553308010101,
-0.03346749767661095,
0.14594325423240662,
0.04343496263027191,
0.002592455130070448,
-0.027015892788767815,
0.03355911374092102,
-0.006811094470322132,
0.040632184594869614,
0.00939555186778307,
-0.013664436526596546,
-0.018691273406147957,
-0.008280421607196331,
0.0036632362753152847,
0.009953465312719345,
-0.007602401077747345,
0.008886769413948059,
0.03528699651360512,
-0.04495064541697502,
-0.02000068873167038,
0.0417896993458271,
0.031199460849165916,
-0.009627354331314564,
0.03735383599996567,
-0.03066208027303219,
0.00774915749207139,
-0.01160972286015749,
-0.020091542974114418,
-0.03779321163892746,
-0.004490695893764496,
0.042252399027347565,
-0.0018334819469600916,
-0.02627279795706272,
0.048747505992650986,
0.028592320159077644,
0.008478264324367046,
0.0004223113937769085,
0.049005329608917236,
0.042106155306100845,
0.00010038152686320245,
-0.017307855188846588,
0.043789688497781754,
0.006762082222849131,
-0.012526621110737324,
0.014492186717689037,
-0.005522693041712046,
-0.04831240698695183,
-0.007887435145676136,
-0.06624237447977066,
0.03929993137717247,
-0.015618545934557915,
0.038375552743673325,
0.01297434326261282,
0.004275425802916288,
-0.006561547517776489,
-0.03354813531041145,
-0.05798356980085373,
-0.016340166330337524,
0.020679062232375145,
0.015437175519764423,
-0.022971872240304947,
0.01719176396727562,
0.010279501788318157,
0.0004858959873672575,
-0.011168505065143108,
0.028913380578160286,
0.009909935295581818,
-0.018471136689186096,
0.023147273808717728,
0.019503431394696236,
0.0029941867105662823,
-0.016975723206996918,
0.001483379048295319,
0.021715370938181877,
-0.03328317776322365,
-0.028083842247724533,
-0.02379762940108776,
0.018173502758145332,
0.0047245933674275875,
0.0022494469303637743,
-0.00998641923069954,
-0.017610793933272362,
-0.02107168175280094,
0.03288176655769348,
0.019095584750175476,
-0.007543132174760103,
-0.006159236654639244,
0.03880462050437927,
-0.0015955285634845495,
0.03639655560255051,
0.02085852436721325,
0.014277254231274128,
0.042351435869932175,
0.03714269399642944,
0.02180488593876362,
0.004716899711638689,
-0.021286336705088615,
0.015188283286988735,
-0.05343187600374222,
0.024233996868133545,
0.023236501961946487,
0.015812991186976433,
-0.012129553593695164,
-0.014313511550426483,
0.0005122417933307588,
0.01028869953006506,
-0.011815350502729416,
0.014933513477444649,
0.023986343294382095,
-0.000410125037888065,
-0.021443495526909828,
0.022316690534353256,
0.007445810362696648,
-0.004068785347044468,
-0.014008702710270882,
-0.025763191282749176,
0.036186929792165756,
-0.008314842358231544,
0.014619900844991207,
0.008650456555187702,
0.0030399204697459936,
-0.02968890219926834,
0.048072636127471924,
-0.03380165621638298,
-0.025845550000667572,
-0.03178492933511734,
-0.03881443291902542,
0.032959483563899994,
0.04148915410041809,
0.006104290019720793,
0.05070171877741814,
-0.03876836970448494,
0.025079699233174324,
0.02409396693110466,
0.012347761541604996,
-0.013963126577436924,
-0.048225823789834976,
0.01367905642837286,
0.018532568588852882,
0.016585659235715866,
-0.04311063513159752,
-0.06500411033630371,
0.05421830713748932,
0.012009160593152046,
-0.018490338698029518,
-0.02507937327027321,
-0.005318496376276016,
0.018655387684702873,
0.0002601265150588006,
0.0002779093920253217,
0.002986242761835456,
0.047137025743722916,
-0.017014728859066963,
0.02201591618359089,
0.0012715236516669393,
-0.026873791590332985,
-0.013990304432809353,
-0.005907303187996149,
-0.007071586325764656,
0.02012396790087223,
0.017116965726017952,
0.0006027817726135254,
0.01247686892747879,
-0.0424935556948185,
0.0002447234292048961,
-0.00487960409373045,
-0.012159399688243866,
-0.020893851295113564,
0.0010424613719806075,
0.04332098737359047,
0.01913662627339363,
0.011586625128984451,
-0.034994252026081085,
0.021749841049313545,
0.006625824142247438,
0.002919857855886221,
-0.07225413620471954,
0.005132535472512245,
0.013964368030428886,
-0.016099628061056137,
0.015284089371562004,
-0.032070208340883255,
-0.001574234222061932,
-0.04129331558942795,
-0.07782308012247086,
0.0077131339348852634,
-0.022315172478556633,
0.02380780316889286,
-0.007020764518529177,
-0.007314005866646767,
0.009208028204739094,
0.002570848446339369,
0.01831321232020855,
0.0630268007516861,
0.012030414305627346,
0.055744633078575134,
0.010588938370347023,
-0.04025917127728462,
-0.001970085548236966,
0.034340787678956985,
-0.006368307862430811,
0.020303701981902122,
0.05992218479514122,
-0.01977027952671051,
0.03467762470245361,
0.00886696670204401,
-0.04138636589050293,
-0.011444450356066227,
-0.04754137992858887,
0.0058161234483122826,
0.009187658317387104,
0.05899291858077049,
-0.008997512049973011,
-0.0018756772624328732,
-0.029719367623329163,
-0.026736175641417503,
0.007180054672062397,
0.04844534397125244,
0.019032685086131096,
0.005508246831595898,
0.0557623952627182,
-0.01668044924736023,
-0.019963985309004784,
0.01823793165385723,
-0.023675335571169853,
-0.033517949283123016,
0.032425325363874435,
-0.02321367710828781,
0.02559523843228817,
0.0038818013854324818,
-0.0471099391579628,
-0.03241289407014847,
-0.023320700973272324,
0.04482955113053322,
0.012836463749408722,
0.027019403874874115,
-0.0026492446195334196,
-0.005574266891926527,
-0.00543388444930315,
0.030786044895648956,
-0.0015549063682556152,
-0.007418484427034855,
-0.10005596280097961,
0.022835714742541313,
0.0019211068283766508,
-0.023755917325615883,
0.021014228463172913,
-0.022917192429304123,
-0.021959669888019562,
0.011722859926521778,
0.028261488303542137,
0.015040654689073563,
-0.021478628739714622,
-0.03494316339492798,
-0.0034777228720486164,
-0.08488988876342773,
0.05387001857161522,
0.005692341830581427,
-0.003060930175706744,
-0.05496826395392418,
-0.06931068003177643,
0.015849625691771507,
0.051026660948991776,
0.08545976877212524,
-0.01314797904342413,
-0.0439167357981205,
0.015413434244692326,
-0.03898181393742561,
0.02419245056807995,
-0.012919558212161064,
0.01093549095094204,
0.02093368209898472,
0.02091561071574688,
0.030077515169978142,
0.011010024696588516,
-0.02647666446864605,
0.011908131651580334,
0.03665114939212799,
0.024948034435510635,
-0.032130979001522064,
-0.031760018318891525,
0.009937857277691364,
0.023634010925889015,
-0.008883291855454445,
-0.03142882138490677,
0.07614985853433609,
0.003991367761045694,
0.028248179703950882,
-0.029616806656122208,
-0.03612830862402916,
-0.04133849963545799,
0.028439322486519814,
-0.04949851706624031,
0.021870065480470657,
0.030652204528450966,
-0.04696385934948921,
0.053998470306396484,
-0.010122722014784813,
-0.07352490723133087,
0.03550448268651962,
-0.02563473768532276,
-0.019734367728233337,
0.030956456437706947,
0.019352920353412628,
0.0026004821993410587,
-0.010601489804685116,
0.022906672209501266,
-0.04552082344889641,
0.0007390500977635384,
-0.029052332043647766,
0.017478272318840027,
0.04800228029489517,
-0.013719129376113415,
-0.01288605760782957,
0.06908254325389862,
0.008000346831977367,
0.02634417451918125,
0.014836316928267479,
-0.0057957470417022705,
-0.02189807780086994,
-0.0480046384036541,
0.01234461460262537,
0.038568321615457535,
-0.0011260819155722857,
0.019007323309779167,
0.005441206507384777,
0.09027677774429321,
0.03485439345240593,
-0.005351893603801727,
-0.012616794556379318,
0.01199178583920002,
-0.007414491847157478,
0.01135757565498352,
0.0194341279566288,
0.04069831967353821,
-0.006734537426382303,
-0.034495722502470016,
-0.0389397069811821,
0.018764350563287735,
0.027639515697956085,
-0.01945277862250805,
0.022799067199230194,
0.009394270367920399,
-0.012792760506272316,
-0.008100270293653011,
0.02268124744296074,
-0.02871026284992695,
-0.03687969967722893,
0.07038494199514389,
0.029173579066991806,
-0.007356294896453619,
0.015444534830749035,
-0.024478722363710403,
-0.0041563003323972225,
0.06767617166042328,
-0.028917834162712097,
-0.022895148023962975,
0.007918830029666424,
-0.0006624080706387758,
0.04109871760010719,
-0.046294163912534714
] |
<p>I have been given this formula from optics here, with no background:
$$\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$$</p>
<p>Where $n$ is the refractive index and $\hat{u}$ is a unit vector tangent to the path $s$ that light takes inside a medium.</p>
<p>Does anyone know if this formula has a name? I am looking specifically for a derivation of it. I have looked through the optics book by Hecht with no luck - I assume it comes from fermats principle of least time in some form.</p>
<p>Any help greatly appreciated.</p>
| 7,644 |
[
-0.01519264280796051,
-0.03694135323166847,
0.015448101796209812,
-0.033342957496643066,
0.0016385575290769339,
0.002103984821587801,
-0.04389306530356407,
0.019610410556197166,
-0.021542292088270187,
-0.013518476858735085,
0.027284886687994003,
0.07324910908937454,
0.08090319484472275,
0.02798023447394371,
0.014736243523657322,
0.01393390353769064,
-0.015352742746472359,
0.044955022633075714,
-0.021378889679908752,
-0.08771692961454391,
0.0203347560018301,
0.03968018293380737,
-0.009616054594516754,
0.0028052569832652807,
0.0002995567047037184,
0.026561003178358078,
-0.01793833076953888,
-0.01945122703909874,
-0.020907539874315262,
0.005271368194371462,
-0.015022621490061283,
-0.008122741244733334,
0.006026583258062601,
0.022488676011562347,
-0.004331621807068586,
-0.014610277488827705,
-0.023919690400362015,
-0.06593132019042969,
-0.024691380560398102,
0.012568521313369274,
-0.0035784554202109575,
-0.01787177287042141,
-0.0244890209287405,
0.05146895721554756,
-0.005870264954864979,
0.022440986707806587,
0.04685000330209732,
-0.010920844972133636,
0.034814972430467606,
-0.06391357630491257,
0.0857900083065033,
0.00594673864543438,
0.037856753915548325,
-0.0048661064356565475,
-0.03926793858408928,
0.017666170373558998,
0.05409185215830803,
0.07290273904800415,
0.00018210658163297921,
-0.0479598343372345,
-0.01293442863970995,
-0.033848173916339874,
-0.001911019440740347,
-0.05277419462800026,
-0.006907418370246887,
0.005657263100147247,
-0.015418113209307194,
-0.025074532255530357,
0.023768505081534386,
0.003442968474701047,
-0.002420511096715927,
-0.006029172800481319,
0.03902001678943634,
0.009664527140557766,
-0.01025847252458334,
-0.03299884870648384,
0.016333309933543205,
0.02899542637169361,
0.03014315851032734,
-0.004409123677760363,
-0.014599365182220936,
0.020848914980888367,
0.0074815647676587105,
0.04915231093764305,
-0.019084399566054344,
0.0004472198779694736,
0.0757376030087471,
-0.03488767147064209,
0.04244902357459068,
0.014674936421215534,
-0.04500905051827431,
0.01944083534181118,
0.041658665984869,
0.00534965330734849,
-0.02889474295079708,
-0.008705674670636654,
0.011272438801825047,
0.021430211141705513,
0.004990090616047382,
-0.04224503040313721,
-0.018788078799843788,
-0.014673659577965736,
-0.005483342334628105,
0.07701403647661209,
-0.004923572298139334,
-0.05555977299809456,
-0.051123905926942825,
0.012972299009561539,
-0.023290172219276428,
0.025680014863610268,
-0.05809040367603302,
0.03526092693209648,
0.005184664856642485,
0.03940907120704651,
-0.027132989838719368,
-0.043347518891096115,
0.01701355166733265,
0.00019449315732344985,
0.0599198080599308,
0.07452037930488586,
0.029716694727540016,
-0.03215673193335533,
0.02265113592147827,
-0.04446040838956833,
-0.08404834568500519,
0.034188706427812576,
0.028992723673582077,
0.01082318089902401,
0.012949127703905106,
0.01139927189797163,
0.0030798758380115032,
0.00243426114320755,
0.0044555882923305035,
0.028882846236228943,
-0.012116929516196251,
-0.010204303078353405,
-0.06729205697774887,
-0.06151587516069412,
0.04176172614097595,
-0.022278277203440666,
-0.0024967039935290813,
-0.04310040920972824,
0.0480673685669899,
0.044003453105688095,
0.06696206331253052,
0.02577589824795723,
0.03236887976527214,
-0.032034873962402344,
0.05120548605918884,
-0.007248069625347853,
-0.009274877607822418,
-0.041387226432561874,
0.02827877178788185,
-0.006043653003871441,
0.008640779182314873,
-0.04540194943547249,
0.03767237812280655,
0.03884894400835037,
0.0001828850945457816,
-0.0044873557053506374,
0.08015990257263184,
-0.02104264311492443,
0.012008482590317726,
0.015516169369220734,
0.004839526489377022,
-0.060464970767498016,
0.07595435529947281,
0.03435273468494415,
0.03815017640590668,
0.0077688852325081825,
0.008276034146547318,
0.020875295624136925,
0.026098420843482018,
0.06171174347400665,
0.056803349405527115,
-0.026567019522190094,
0.008111966773867607,
0.028001343831419945,
-0.01554261613637209,
0.03353489190340042,
-0.00943751074373722,
-0.033746346831321716,
0.011507310904562473,
0.025685803964734077,
-0.012450813315808773,
0.023927319794893265,
-0.015437779948115349,
-0.011253204196691513,
-0.013230469077825546,
-0.036460161209106445,
0.020461007952690125,
-0.021600252017378807,
0.011887540109455585,
-0.004528606776148081,
-0.0023239857982844114,
0.06488215923309326,
0.0025457129813730717,
-0.004729564301669598,
-0.025730138644576073,
-0.05185849964618683,
-0.00042144066537730396,
-0.003973457962274551,
0.02097638137638569,
-0.05289500206708908,
0.006727256346493959,
0.027553319931030273,
0.020464887842535973,
-0.009070544503629208,
0.046026285737752914,
-0.023597538471221924,
-0.014761733822524548,
-0.018345946446061134,
-0.006816959008574486,
0.0384681299328804,
-0.01606154441833496,
-0.01089965645223856,
0.020355192944407463,
0.001033655134961009,
0.023427722975611687,
0.018758948892354965,
-0.04751737788319588,
0.019514484331011772,
0.08323116600513458,
0.02947518602013588,
0.0035315852146595716,
0.02233186922967434,
-0.001917355926707387,
0.015890076756477356,
0.007918443530797958,
-0.028782470151782036,
-0.011620687320828438,
-0.0024977102875709534,
0.05300509184598923,
0.02369793690741062,
-0.038904253393411636,
-0.017072053626179695,
0.02392416261136532,
0.04290470480918884,
0.09212463349103928,
0.03479820489883423,
-0.03389335796236992,
-0.04569718986749649,
-0.004426246043294668,
0.028826288878917694,
-0.015025757253170013,
0.031136425212025642,
0.0030444562435150146,
0.020537754520773888,
0.030808793380856514,
-0.001748506329022348,
-0.028417550027370453,
0.014130949042737484,
0.020696766674518585,
0.011804516427218914,
0.012477999553084373,
-0.020099926739931107,
0.04828357696533203,
-0.005933643318712711,
0.032470785081386566,
0.05770194157958031,
-0.008639817126095295,
0.020491011440753937,
-0.049745284020900726,
0.00913808960467577,
0.03488139063119888,
0.007007936015725136,
-0.024803882464766502,
-0.025540519505739212,
0.020551607012748718,
-0.03291221708059311,
0.02287316881120205,
-0.018290238454937935,
-0.012302791699767113,
-0.048150599002838135,
-0.03156698867678642,
-0.018559163436293602,
0.041696563363075256,
0.000741171243134886,
0.01500330213457346,
-0.006083676125854254,
0.009611855261027813,
-0.012629276141524315,
-0.007605583872646093,
0.0161212757229805,
-0.048223983496427536,
0.014230574481189251,
-0.0004812766273971647,
-0.047089654952287674,
0.07407216727733612,
-0.02361913025379181,
0.003616087604314089,
0.015275429002940655,
-0.03347685933113098,
-0.04766380041837692,
-0.041268594563007355,
0.02184116281569004,
-0.010708393529057503,
-0.0510188490152359,
0.01574261486530304,
0.02394608035683632,
-0.00616095308214426,
-0.02957873046398163,
0.028080854564905167,
-0.027175042778253555,
-0.0696980208158493,
-0.04276333376765251,
0.0009516061982139945,
0.015551641583442688,
-0.04269114509224892,
0.02903742901980877,
0.029110893607139587,
0.012113122269511223,
0.005794818047434092,
-0.05843045562505722,
-0.05904798582196236,
0.05126050487160683,
-0.0034308547619730234,
0.02428087778389454,
0.020708685740828514,
-0.047067008912563324,
0.07756905257701874,
0.04477688670158386,
-0.026139065623283386,
-0.02032327651977539,
-0.0026586693711578846,
0.004529827274382114,
-0.016100212931632996,
0.03579011559486389,
0.043801695108413696,
-0.0029738866724073887,
0.00657787686213851,
-0.03868716582655907,
0.011020133271813393,
0.051106590777635574,
0.015802424401044846,
0.03710143268108368,
0.006442708894610405,
-0.04482037201523781,
-0.02390722930431366,
0.018147137016057968,
0.03571176156401634,
-0.03826064243912697,
0.0043322681449353695,
0.004570235498249531,
0.054562877863645554,
0.03452325239777565,
-0.03704555705189705,
0.023674478754401207,
0.0129172932356596,
0.006590610835701227,
0.011705778539180756,
0.016848841682076454,
-0.014103683643043041,
-0.002462120493873954,
-0.007185980677604675,
0.06470374763011932,
0.02283114194869995,
-0.02686602622270584,
0.0021869258489459753,
-0.007670350838452578,
0.0014548501931130886,
-0.031463637948036194,
0.00564320245757699,
-0.034508708864450455,
0.005894744303077459,
0.023172875866293907,
-0.039092157036066055,
0.00032609651680104434,
0.04824858903884888,
0.006247928831726313,
0.0030021448619663715,
-0.0006965773645788431,
-0.05458344519138336,
-0.011315107345581055,
-0.030686136335134506,
0.012591560371220112,
0.0014690120005980134,
0.02027057856321335,
-0.014304517768323421,
0.02346046268939972,
0.0224520955234766,
0.057118210941553116,
0.03286370262503624,
-0.01592126674950123,
-0.10180871933698654,
0.019657526165246964,
-0.04800751060247421,
-0.0392257422208786,
-0.052238285541534424,
-0.012817496433854103,
-0.016036521643400192,
-0.02162272110581398,
-0.019879214465618134,
0.011314863339066505,
0.022801300510764122,
-0.04016075283288956,
0.017291449010372162,
-0.003311075968667865,
-0.02368113584816456,
-0.010281890630722046,
0.025969145819544792,
0.02086951583623886,
-0.039827533066272736,
-0.034570034593343735,
0.0418429896235466,
-0.024317588657140732,
-0.03499113395810127,
-0.010913043282926083,
-0.015353232622146606,
0.018032150343060493,
-0.0014265566132962704,
-0.0020902438554912806,
-0.0036003265995532274,
-0.02713480032980442,
0.043755121529102325,
-0.007705341093242168,
0.024289356544613838,
-0.0024135068524628878,
-0.015432306565344334,
-0.05783887580037117,
-0.03341324254870415,
0.010024194605648518,
0.010410727001726627,
0.05737968534231186,
0.013611285015940666,
0.006467819679528475,
0.039563316851854324,
-0.025203218683600426,
-0.03250233083963394,
-0.005358604714274406,
-0.008509516716003418,
0.021423790603876114,
-0.0026476671919226646,
-0.04752863571047783,
0.03571351617574692,
-0.013934492133557796,
0.02965252473950386,
0.029112594202160835,
0.013816464692354202,
-0.026475058868527412,
-0.016001302748918533,
-0.026742273941636086,
-0.007439565844833851,
0.03134123608469963,
0.006441355682909489,
-0.0008319627377204597,
-0.027253171429038048,
0.001960287569090724,
-0.002845942974090576,
0.017314886674284935,
0.06906259059906006,
0.037798505276441574,
0.016638299450278282,
-0.005407819990068674,
-0.05340047553181648,
-0.019073642790317535,
0.017512580379843712,
0.006016841158270836,
-0.02572793699800968,
0.006850249599665403,
-0.037762269377708435,
-0.027284299954771996,
0.030342716723680496,
0.0013289084890857339,
0.00429535610601306,
-0.0037036065477877855,
-0.031705088913440704,
-0.008402437902987003,
-0.02718757465481758,
-0.02961849980056286,
0.005007054191082716,
0.008633029647171497,
0.008066479116678238,
0.011199388653039932,
-0.004906997550278902,
-0.0051893373019993305,
0.037933334708213806,
0.018772689625620842,
0.048693638294935226,
0.016649160534143448,
-0.01671975664794445,
0.03427458554506302,
0.01920577883720398,
-0.04693233221769333,
-0.06488733738660812,
0.01209576241672039,
0.02368561364710331,
-0.015519725158810616,
0.00623723492026329,
-0.012435775250196457,
-0.02670714259147644,
0.060126904398202896,
0.02030353993177414,
-0.005286335479468107,
0.03387349471449852,
-0.018659407272934914,
0.01853909343481064,
0.012462184764444828,
-0.02556857280433178,
0.020255208015441895,
0.01877228356897831,
0.00004027898467029445,
-0.03711260110139847,
-0.019167087972164154,
0.07888013124465942,
-0.02048139087855816,
-0.03256010264158249,
-0.015256689861416817,
0.005206326954066753,
-0.05813039466738701,
0.07283195108175278,
-0.013353382237255573,
0.023881934583187103,
-0.008908765390515327,
-0.03743531182408333,
-0.03299126774072647,
0.023506924510002136,
0.0419045127928257,
-0.019298434257507324,
0.030406929552555084,
0.027708465233445168,
0.06520746648311615,
-0.024936990812420845,
0.010448332875967026,
-0.0343279205262661,
0.030125264078378677,
0.05514435097575188,
0.033409036695957184,
-0.0007261893479153514,
-0.03376983478665352,
-0.010500483214855194,
0.037229910492897034,
-0.03397298976778984,
0.04028814658522606,
-0.011489168740808964,
0.006491672247648239,
0.026895221322774887,
-0.037092458456754684,
-0.03251859173178673,
0.026130083948373795,
-0.013648835010826588,
0.03811478242278099,
-0.09761237353086472,
0.008101901970803738,
-0.0013301657745614648,
0.034838397055864334,
-0.03282366693019867,
-0.02011886052787304,
0.011035176925361156,
-0.013373268768191338,
-0.05020725354552269,
-0.05893944203853607,
0.0055216895416378975,
-0.015846574679017067,
-0.06037423759698868,
0.03931548446416855,
0.04311357066035271,
-0.007812868803739548,
-0.028736496344208717,
-0.017587440088391304,
0.0408058799803257,
0.013029707595705986,
-0.018075892701745033,
-0.012409370392560959,
-0.020235836505889893,
-0.020202413201332092,
0.002746215555816889,
0.04223683848977089,
0.06312082707881927,
-0.014927877113223076,
-0.004651399329304695,
-0.025882428511977196,
-0.009085138328373432,
0.0511813759803772,
-0.020429985597729683,
0.029562631621956825,
0.013741857372224331,
0.005645644385367632,
-0.041853323578834534,
-0.020596161484718323,
0.008467513136565685,
-0.015667669475078583,
0.011470007710158825,
0.028016241267323494,
-0.017003636807203293,
-0.034450192004442215,
-0.005155060440301895,
0.02215796336531639,
-0.001880536088719964,
0.03930693119764328,
-0.017801830545067787,
0.02633448876440525,
-0.01089522521942854,
-0.000024707889679120854,
0.020261336117982864,
-0.018024733290076256,
-0.007890697568655014,
0.042649947106838226,
0.016087180003523827,
0.014298002235591412,
-0.007607484236359596,
-0.024296963587403297,
-0.05577855184674263,
-0.04360460862517357,
0.0490027479827404,
0.08100025355815887,
-0.043718669563531876,
0.05337494611740112,
0.0274822898209095,
-0.013666699640452862,
0.008831390179693699,
-0.019815335050225258,
-0.03932315856218338,
0.008766058832406998,
-0.017488161101937294,
0.07207348942756653,
0.008252815343439579,
-0.0028966679237782955,
0.013535127975046635,
0.050846509635448456,
-0.007653384003788233,
0.01488209143280983,
-0.010368489660322666,
0.022428061813116074,
0.022599533200263977,
-0.011741813272237778,
-0.046775564551353455,
0.057522453367710114,
-0.043596088886260986,
0.02422131597995758,
0.018304219469428062,
0.0003809590998571366,
0.01245033834129572,
-0.002146936021745205,
0.015087742358446121,
-0.023598385974764824,
-0.02060268260538578,
0.003912081476300955,
-0.0015257169725373387,
0.04276549443602562,
-0.02002813294529915,
-0.019612889736890793,
0.014204185456037521,
0.04381096363067627,
0.01414047833532095,
0.047094352543354034,
0.023783544078469276,
-0.016021691262722015,
-0.0014425398549064994,
-0.06731200218200684,
-0.0460287407040596,
0.026677804067730904,
0.000171264837263152,
-0.03003537282347679,
0.00039882076089270413,
-0.03361932188272476,
0.017781345173716545,
0.04149293154478073,
0.02519223652780056,
0.021254397928714752,
0.09103959053754807,
0.02906009554862976,
0.011231381446123123,
-0.008625279180705547,
-0.029748298227787018,
0.11881164461374283,
0.03838703781366348,
0.019691819325089455,
-0.01888711005449295,
-0.0020383417140692472,
-0.0450926311314106,
-0.010463949292898178,
-0.06265977025032043,
0.02735748328268528,
-0.01304357498884201,
0.0008300665067508817,
0.04281162843108177,
0.04665972292423248,
0.012719685211777687,
-0.0005417157080955803,
0.015427160076797009,
-0.035852231085300446,
0.006595917046070099,
0.031226826831698418,
-0.008904177695512772,
-0.012370286509394646,
0.022266481071710587,
-0.03771723434329033,
0.02735965885221958,
-0.00012411379429977387,
-0.008745245635509491,
-0.022978127002716064,
-0.013336335308849812,
0.01147195789963007,
-0.0006373869837261736,
-0.029453657567501068,
0.01061546616256237,
0.004156311973929405,
-0.013922145590186119,
-0.01839151792228222,
0.016838837414979935,
0.01684672199189663,
0.012837733142077923,
0.04097704216837883,
0.020901577547192574,
0.028827106580138206,
0.015306169167160988,
0.034024469554424286,
0.009684826247394085,
-0.020999016240239143,
0.000032557865779381245,
-0.007825273089110851,
0.024437306448817253,
-0.027961652725934982,
0.016961125656962395,
-0.005913859698921442,
0.005961863789707422,
0.030112706124782562,
-0.07871763408184052,
-0.018740450963377953,
-0.032894622534513474,
0.010193174704909325,
-0.027535799890756607,
-0.0000701079479767941,
0.012744600884616375,
-0.006428564433008432,
0.04139486700296402,
0.01900864951312542,
0.0029584395233541727,
0.016315899789333344,
0.008561967872083187,
-0.0003844909369945526,
0.0047828806564211845,
-0.04064789041876793,
-0.03759430721402168,
-0.02584807202219963,
-0.009505687281489372,
-0.02099434845149517,
-0.0012730953749269247,
0.012998140417039394,
-0.01769414357841015,
-0.021089041605591774,
-0.020571287721395493,
-0.030116818845272064,
-0.03195447847247124,
-0.09672927111387253,
0.030989928171038628,
-0.02506565861403942,
-0.015433110296726227,
-0.025798356160521507,
0.01331896148622036,
0.009475396946072578,
0.03778510168194771,
-0.04317157715559006,
0.0038187599275261164,
0.03464687615633011,
0.03575136885046959,
0.004786208737641573,
-0.027032896876335144,
-0.025866474956274033,
0.011200974695384502,
0.012734822928905487,
-0.0016365995397791266,
0.01255018636584282,
0.02817629836499691,
0.05980807542800903,
0.0005668213707394898,
-0.008649078197777271,
0.04003382474184036,
-0.045990388840436935,
0.009852536953985691,
-0.008307588286697865,
-0.04530738666653633,
0.04013655334711075,
0.018187586218118668,
-0.01401960663497448,
-0.05479113385081291,
-0.017794359475374222,
-0.04154151305556297,
0.007483943365514278,
-0.013493797741830349,
0.012492846697568893,
-0.03790593892335892,
0.0028135739266872406,
-0.009397286921739578,
0.015533712692558765,
-0.037649694830179214,
-0.025327039882540703,
-0.03528227284550667,
0.03771009296178818,
-0.0364767424762249,
0.030004683881998062,
-0.028674056753516197,
0.046300582587718964,
-0.01369805820286274,
-0.039052341133356094,
0.03255561366677284,
-0.0007201302796602249,
0.019641771912574768,
0.007644528988748789,
0.0037450147792696953,
-0.020597636699676514,
0.048884421586990356,
-0.00399897713214159,
-0.03811534494161606,
0.03235308825969696,
-0.03227157145738602,
-0.0636458545923233,
0.028485961258411407,
0.013218840584158897,
0.007183988578617573,
-0.0035117268562316895,
0.0038315386045724154,
0.030567102134227753,
0.04972729831933975,
-0.012698473408818245,
-0.027906065806746483,
-0.03203510120511055,
-0.07549414038658142,
0.014467415399849415,
-0.049406565725803375,
0.018367229029536247,
0.0009605535306036472,
-0.01016330812126398,
-0.00647343322634697,
0.016003353521227837,
-0.014821161516010761,
0.007572614122182131,
0.03432375565171242,
-0.012039342895150185,
-0.026710795238614082,
0.01594536192715168,
0.014026926830410957,
0.0033380608074367046,
0.05626053735613823,
-0.032971326261758804,
0.033488258719444275,
0.017803160473704338,
0.023672396317124367,
-0.09820538759231567,
-0.01910484954714775,
-0.020267795771360397,
0.04915008693933487,
0.04678919538855553,
-0.10953211784362793,
0.03456354886293411,
0.00030407457961700857,
-0.050322674214839935,
0.06763071566820145,
-0.027748841792345047,
0.012163442559540272,
-0.047200191766023636,
0.01571454480290413,
0.023580724373459816,
0.05952742323279381,
0.021026508882641792,
-0.0034512600395828485,
0.04445047676563263,
0.02675492875277996,
-0.0275118388235569,
-0.03599579632282257,
-0.004993237555027008,
0.03578108549118042,
0.010807820595800877,
-0.043872810900211334,
0.046611037105321884,
0.026177439838647842,
-0.032209362834692,
0.04617404192686081,
-0.006957144010812044,
-0.037039369344711304,
-0.012504041194915771,
-0.0037643068935722113,
0.021838711574673653,
-0.013322449289262295,
-0.001556812901981175,
-0.012110644951462746,
0.0008266818476840854,
0.0020593979861587286,
0.013991021551191807,
-0.0026434955652803183,
-0.0033927380573004484,
-0.019130531698465347,
0.004129485227167606,
-0.012861443683505058,
-0.055713165551424026,
0.011677776463329792,
-0.007886984385550022,
-0.0024291870649904013,
0.025891512632369995,
-0.04940517246723175,
-0.001489474205300212,
-0.032323990017175674,
0.007207560818642378,
-0.04953698068857193,
-0.006179620511829853,
0.03478202596306801,
-0.003493945812806487,
-0.03695198893547058,
0.012782159261405468,
-0.0021519227884709835,
-0.07287716865539551,
0.004904802888631821,
0.009263602085411549,
-0.0017274538986384869,
-0.04366939887404442,
-0.01657496578991413,
0.0036622928455471992,
-0.01380635891109705,
0.00445814011618495,
-0.016938921064138412,
-0.012149530462920666,
0.020021144300699234,
0.0336637869477272,
0.0076922266744077206,
0.0036158007569611073,
-0.006539465859532356,
0.002614150056615472,
-0.057743269950151443,
0.008675255812704563,
-0.024492044001817703,
0.002605284098535776,
-0.02545321173965931,
0.005894641857594252,
-0.014491130597889423,
0.01046376209706068,
0.06138867139816284,
-0.011862208135426044,
-0.01800963096320629,
0.009162700735032558,
-0.0065603661350905895,
0.010223018005490303,
-0.05574275553226471,
-0.01412728987634182,
-0.005236645694822073,
-0.025606760755181313,
-0.007991200312972069,
0.02642473392188549,
-0.009292883798480034,
-0.028002526611089706,
-0.02086099050939083,
0.007547158282250166,
0.007275112438946962,
-0.0030350596643984318,
-0.007665774319320917,
0.01091579906642437,
0.01048910990357399,
-0.015567110851407051,
0.04500991478562355,
-0.028721634298563004,
-0.01321355253458023,
0.0020355982705950737,
-0.02459261752665043,
-0.07561231404542923,
0.004643602296710014,
-0.04342976212501526,
-0.02226600982248783,
-0.02206077054142952,
-0.017747655510902405,
0.03591284900903702,
-0.016138382256031036,
-0.0372934527695179,
0.0035207306500524282,
-0.05123312026262283,
-0.006658558268100023,
0.021270480006933212,
-0.04434754326939583,
0.06202641874551773,
0.014286587946116924,
-0.0028385224286466837,
0.02093050256371498,
-0.02870013378560543,
-0.016353603452444077,
0.056616246700286865,
0.02180747129023075,
-0.009706560522317886,
0.02712808921933174,
0.028949588537216187,
-0.012598133645951748,
0.04775244742631912,
0.0210124384611845,
0.032978300005197525,
0.01311451569199562,
-0.016132140532135963,
0.040559954941272736,
-0.025229500606656075,
-0.039121370762586594,
0.015613818541169167,
-0.00934706162661314,
0.07739477604627609,
0.011919009499251842,
0.033362001180648804,
-0.03916490077972412,
0.030987227335572243,
-0.024750102311372757,
0.028926800936460495,
0.03262435644865036,
0.035787809640169144,
-0.02264496684074402,
-0.0035105685237795115,
0.011568477377295494,
-0.02127608098089695,
-0.002808480989187956,
-0.015587729401886463,
0.05082332715392113,
0.028927188366651535,
-0.002390004927292466,
0.008476685732603073,
-0.042679525911808014,
0.0034516945015639067,
-0.01670534908771515,
-0.010790636762976646,
0.019702080637216568,
0.014616327360272408,
0.04221870005130768,
0.040001168847084045,
-0.006294274237006903,
0.08387388288974762,
-0.09444369375705719,
-0.04092637822031975,
-0.016480952501296997,
0.0315072201192379,
-0.002686696592718363,
-0.004883901681751013
] |
<p>Yesterday I looked underwater with my eyes open (and no goggles) and I realized I can't see anything clearly. Everything looks very, very blurry. My guess is that the eye needs direct contact with air in order to work properly. With water, the refraction index is different, and the eye lens are not able to compensate for correct focalization on the retina.</p>
<p>Am I right ? If so, what lenses should one wear in order to see clearly while under water ?</p>
| 7,645 |
[
0.0008018032531253994,
-0.04020768404006958,
0.013043852522969246,
-0.005884608719497919,
0.024266337975859642,
0.006608782336115837,
-0.02809314802289009,
-0.006473954766988754,
0.00580962747335434,
-0.02574959397315979,
0.04138325899839401,
0.07028456777334213,
0.038307853043079376,
-0.003258548444136977,
-0.02345849759876728,
-0.024894168600440025,
-0.00986931286752224,
-0.04709871858358383,
-0.006399448961019516,
-0.017634648829698563,
0.0018312308238819242,
0.02114979736506939,
-0.0035374807193875313,
0.028378618881106377,
-0.05847666785120964,
0.027722790837287903,
0.026720739901065826,
-0.014827515929937363,
0.031497541815042496,
-0.015643982216715813,
-0.01782967522740364,
-0.008979386650025845,
-0.000588298193179071,
-0.015855930745601654,
-0.003328468184918165,
0.0050084833055734634,
-0.017688008025288582,
-0.031167255714535713,
-0.03439098596572876,
0.009785632602870464,
0.020578306168317795,
-0.0006408344488590956,
0.0003357364912517369,
0.03583402559161186,
-0.002993313828483224,
0.025850515812635422,
-0.00012269133003428578,
-0.06821773201227188,
0.0030528646893799305,
-0.05650563910603523,
0.03826238960027695,
-0.014009271748363972,
0.06368701905012131,
0.03243168443441391,
0.009725023992359638,
0.03784849867224693,
0.08056911826133728,
0.08801320195198059,
0.00009779149695532396,
-0.06058686599135399,
0.03142508119344711,
0.0032567756716161966,
-0.010252261534333229,
-0.03101024404168129,
-0.010831906460225582,
0.023630591109395027,
-0.03300880640745163,
-0.0375346764922142,
0.04947083443403244,
-0.008710645139217377,
0.006800716742873192,
0.01640751212835312,
0.03444375470280647,
-0.014081263914704323,
0.01980610005557537,
-0.08243081718683243,
0.008893925696611404,
0.03285526856780052,
0.0632159486413002,
0.042392220348119736,
0.009322723373770714,
0.002859391737729311,
-0.022842342033982277,
0.008255823515355587,
0.020015671849250793,
-0.022409023717045784,
0.07263254374265671,
-0.0077265421859920025,
-0.0070222956128418446,
-0.00010992569877998903,
-0.029224276542663574,
0.007290777750313282,
0.02144191414117813,
-0.010267690755426884,
0.007350137922912836,
0.00907513964921236,
-0.017201654613018036,
0.04642738401889801,
0.014285765588283539,
-0.04423325136303902,
0.012781881727278233,
-0.008691826835274696,
0.025430431589484215,
0.08476239442825317,
0.018816696479916573,
-0.03136271983385086,
-0.02351430617272854,
0.029962219297885895,
-0.041672736406326294,
-0.005051011219620705,
0.002616406185552478,
0.011905298568308353,
-0.07010287791490555,
0.019047455862164497,
0.022344211116433144,
-0.022003406658768654,
0.02917660027742386,
-0.003167344955727458,
0.06132406368851662,
0.08594320714473724,
0.07702140510082245,
-0.025596745312213898,
0.009309545159339905,
-0.013952893204987049,
-0.07108432799577713,
0.04043351113796234,
0.02861946076154709,
0.005086991935968399,
-0.01049666665494442,
0.009711719118058681,
-0.030147964134812355,
0.009822038933634758,
0.06067695468664169,
0.003640047274529934,
0.032150402665138245,
-0.017748920246958733,
-0.08209890127182007,
-0.0749347060918808,
0.0630665123462677,
-0.015205596573650837,
-0.04322361573576927,
-0.10831823199987411,
0.02474009059369564,
0.05300457403063774,
0.06888768821954727,
0.00637600664049387,
0.012039540335536003,
-0.01850474439561367,
0.00870119035243988,
-0.038115523755550385,
-0.027261577546596527,
0.00538393622264266,
0.0004984614206478,
-0.013475109823048115,
0.05237962678074837,
-0.048351529985666275,
0.009343510493636131,
0.016795115545392036,
0.03531687334179878,
-0.05024241283535957,
0.04702829569578171,
-0.025165384635329247,
-0.004396705888211727,
-0.007194208446890116,
-0.032861240208148956,
-0.04740834981203079,
0.0453014001250267,
-0.027861909940838814,
0.050472989678382874,
0.022803092375397682,
0.001051599974744022,
0.03628150746226311,
0.005276653449982405,
0.0009946438949555159,
0.022421853616833687,
0.0013161383103579283,
-0.003120817942544818,
-0.06539394706487656,
0.007930933497846127,
0.03494272753596306,
-0.009718511253595352,
0.007052662316709757,
-0.011090429499745369,
0.0021138503216207027,
0.04010705649852753,
0.027875423431396484,
0.017892563715577126,
-0.037926413118839264,
0.013169302605092525,
-0.03439458832144737,
0.004769804887473583,
-0.020770926028490067,
0.010321511887013912,
-0.01732678711414337,
0.05263190716505051,
0.020453551784157753,
-0.006461535580456257,
0.03476492315530777,
0.0041443174704909325,
-0.015030989423394203,
-0.03169820457696915,
0.004816836211830378,
0.014403998851776123,
-0.017312388867139816,
0.0317797027528286,
0.03612557053565979,
0.02559009939432144,
0.004020578693598509,
0.017772629857063293,
0.013549359515309334,
-0.0016690060729160905,
-0.00421112310141325,
-0.007414925843477249,
0.024345017969608307,
-0.0013314144453033805,
-0.0071220118552446365,
-0.009102996438741684,
0.03394722193479538,
-0.02140963450074196,
-0.0010244211880490184,
-0.008772026747465134,
0.07504253834486008,
0.01332514826208353,
-0.010067930445075035,
0.004145588260143995,
0.007095763459801674,
0.016723282635211945,
-0.024200668558478355,
0.010808388702571392,
0.008986878208816051,
-0.057047002017498016,
0.03103245608508587,
0.059703927487134933,
-0.00443253805860877,
-0.017312373965978622,
0.019962118938565254,
-0.0034477345179766417,
0.03799062967300415,
0.03571466729044914,
0.043296534568071365,
-0.02944297343492508,
-0.05303559824824333,
-0.015634359791874886,
0.030116410925984383,
0.048156168311834335,
0.03985561057925224,
0.02850302867591381,
0.003432010766118765,
0.002554427133873105,
-0.08104512095451355,
-0.019187232479453087,
-0.003726356662809849,
-0.00759122334420681,
0.06799430400133133,
-0.02810729667544365,
-0.005952300038188696,
0.03435178101062775,
-0.020274678245186806,
-0.0023535192012786865,
-0.0071016536094248295,
0.034995660185813904,
-0.020858610048890114,
-0.03735698387026787,
-0.022865915670990944,
0.032542869448661804,
0.03924024477601051,
-0.046146199107170105,
0.0011275681899860501,
0.03118588961660862,
-0.06118661165237427,
-0.013377904891967773,
-0.048705827444791794,
-0.0032393785659223795,
-0.025262480601668358,
-0.008481006138026714,
0.009648523293435574,
0.0471973642706871,
0.06547854095697403,
-0.014486816711723804,
-0.019954262301325798,
0.017585601657629013,
-0.013066134415566921,
0.03045840747654438,
0.004558395128697157,
-0.043307870626449585,
0.022666968405246735,
-0.0010311525547876954,
-0.019346699118614197,
0.02894815243780613,
0.01467803493142128,
0.0005301478668116033,
-0.015166160650551319,
-0.006254165433347225,
-0.020204197615385056,
0.0009396843379363418,
-0.022507810965180397,
-0.002708704676479101,
0.016646521165966988,
-0.01058400422334671,
0.00800465140491724,
-0.02388565056025982,
0.004099776037037373,
-0.0013441272312775254,
-0.060678448528051376,
-0.05946726351976395,
-0.00426593329757452,
0.04866134375333786,
0.0032122291158884764,
-0.04338277503848076,
-0.0309713464230299,
0.003046562662348151,
-0.03185521066188812,
0.032330770045518875,
-0.031517405062913895,
-0.0811094343662262,
0.06076226010918617,
0.04535343125462532,
0.001780231948941946,
-0.00864246767014265,
0.0007879390032030642,
0.025843430310487747,
-0.007400573696941137,
-0.019213998690247536,
-0.023244887590408325,
0.01350930705666542,
-0.02768024057149887,
-0.0505814366042614,
0.005067950114607811,
0.054561421275138855,
-0.011937210336327553,
0.04285135120153427,
0.018454615026712418,
0.014336992055177689,
0.0354621522128582,
0.041442543268203735,
0.005332727916538715,
-0.012603132985532284,
0.03856872767210007,
-0.024357179179787636,
0.0029447346460074186,
0.036517247557640076,
-0.009889472275972366,
0.019851109012961388,
-0.015575235709547997,
0.007632032036781311,
0.056106291711330414,
-0.007684096693992615,
0.04967494681477547,
0.007800980005413294,
-0.002891009906306863,
0.015326360240578651,
0.012911827303469181,
-0.004310473334044218,
0.06956148892641068,
0.0017995131202042103,
0.0398988351225853,
0.03527011722326279,
-0.03080129623413086,
0.011408704333007336,
0.08258363604545593,
0.05304642394185066,
-0.0402839221060276,
-0.036947596818208694,
-0.013708923943340778,
0.01600777544081211,
0.02557137794792652,
-0.004722665995359421,
-0.00565917044878006,
0.05682267248630524,
0.0025543987285345793,
0.0122244693338871,
-0.006698586046695709,
-0.017889801412820816,
0.028096787631511688,
-0.07240808010101318,
0.014153126627206802,
-0.004210441838949919,
0.04640518128871918,
0.020793769508600235,
0.012776916846632957,
0.0333031602203846,
0.022122347727417946,
0.009936473332345486,
0.02153337188065052,
-0.04690932855010033,
0.015416827984154224,
-0.007878162898123264,
-0.010331899859011173,
-0.03390543535351753,
-0.017233887687325478,
-0.0060948822647333145,
-0.036378584802150726,
-0.03777129203081131,
-0.02376549132168293,
-0.010364174842834473,
-0.00778058310970664,
0.024110915139317513,
0.037773165851831436,
-0.03792398050427437,
-0.04783731326460838,
-0.006284428760409355,
-0.016566261649131775,
0.036337852478027344,
0.02122086100280285,
0.00874943658709526,
-0.019038235768675804,
0.004433018621057272,
-0.01298146229237318,
0.030431510880589485,
-0.02131321281194687,
0.028611604124307632,
-0.0022406161297112703,
0.02178386226296425,
-0.005346567835658789,
-0.0007124508265405893,
-0.011305962689220905,
0.014290728606283665,
-0.04960571974515915,
0.020188242197036743,
-0.014741785824298859,
-0.05678967013955116,
-0.0225997157394886,
-0.0055537899024784565,
0.03490676358342171,
-0.007414345163851976,
-0.023357318714261055,
0.04107360541820526,
-0.029983513057231903,
-0.04656226560473442,
0.01904408447444439,
-0.023712631314992905,
0.015054812654852867,
-0.01788940653204918,
-0.035376306623220444,
-0.02591431327164173,
-0.06832614541053772,
0.022632228210568428,
0.05711846798658371,
0.06349975615739822,
-0.025506680831313133,
-0.0248795747756958,
0.05069718509912491,
-0.014483997598290443,
-0.002982780570164323,
0.017615502700209618,
-0.018385685980319977,
0.001766965608112514,
-0.016541779041290283,
0.023300817236304283,
0.03322116658091545,
0.04465651139616966,
0.06277024745941162,
0.012913822196424007,
-0.005654073320329189,
-0.06625386327505112,
0.02519262582063675,
0.03111911751329899,
0.010272285901010036,
-0.019116898998618126,
0.011622360907495022,
-0.06184304878115654,
-0.05150393024086952,
0.020329425111413002,
-0.02086075209081173,
-0.0016674938378855586,
-0.018468845635652542,
0.004837315063923597,
0.006299895234405994,
-0.01290188729763031,
-0.014485562220215797,
0.00441621383652091,
0.0001887775433715433,
0.016524408012628555,
-0.02939096838235855,
0.021118037402629852,
-0.02156926691532135,
0.012582085095345974,
0.016405094414949417,
0.07335115969181061,
0.05431371554732323,
-0.02501211315393448,
0.01945572905242443,
-0.02088581770658493,
-0.03895942494273186,
-0.03600085526704788,
-0.002854473190382123,
-0.005283713806420565,
-0.007283539976924658,
0.01819535531103611,
-0.011414860375225544,
-0.035026777535676956,
0.034207552671432495,
0.003405764000490308,
0.006809981539845467,
-0.012865465134382248,
-0.04283671826124191,
-0.06134888529777527,
0.010634524747729301,
0.04022540524601936,
0.03674973547458649,
-0.000340005848556757,
-0.03161745145916939,
-0.022411050274968147,
-0.05737115815281868,
0.04659585654735565,
-0.015128026716411114,
-0.021747086197137833,
0.023452116176486015,
-0.04940011724829674,
-0.01690218411386013,
0.040931861847639084,
-0.014180025085806847,
0.033565931022167206,
0.04705272614955902,
-0.04366575554013252,
-0.026639267802238464,
0.013215942308306694,
0.007625652011483908,
-0.016195768490433693,
0.0449986457824707,
0.005717766471207142,
0.024288203567266464,
0.02383265644311905,
0.01149002555757761,
-0.0244342852383852,
0.004765222780406475,
0.020129691809415817,
-0.023906094953417778,
0.0061478265561163425,
-0.028821101412177086,
0.00022621250536758453,
-0.004467335995286703,
-0.04672640934586525,
0.07185202091932297,
-0.03129633888602257,
-0.007707745768129826,
0.040988191962242126,
-0.03751666471362114,
-0.02549790032207966,
0.020440425723791122,
-0.02915094792842865,
0.027561159804463387,
-0.05762835592031479,
0.04956665262579918,
0.046730510890483856,
-0.00029354894650168717,
-0.041681207716464996,
-0.04966716468334198,
0.01707734912633896,
0.035251434892416,
0.0016481948550790548,
-0.03885655850172043,
0.040163472294807434,
-0.0034260249231010675,
-0.038052335381507874,
-0.004313232377171516,
0.03312253579497337,
0.006032951176166534,
-0.008244846947491169,
0.009007679298520088,
0.006256659049540758,
0.05608208850026131,
-0.018579190596938133,
-0.05629561096429825,
0.03859894722700119,
-0.024226568639278412,
-0.00038850755663588643,
0.013201393187046051,
0.042746130377054214,
-0.017468377947807312,
-0.009701973758637905,
-0.03769667074084282,
-0.009361476637423038,
0.02238420769572258,
-0.010949543677270412,
0.04108762741088867,
0.011088547296822071,
0.00035622032009996474,
0.019908953458070755,
-0.020150622352957726,
0.030841058120131493,
-0.0080675408244133,
0.026804905384778976,
-0.019574720412492752,
-0.015197055414319038,
-0.02120605856180191,
-0.04279168322682381,
0.037011612206697464,
-0.01730666495859623,
0.047553759068250656,
-0.0373106487095356,
0.07276173681020737,
-0.026762371882796288,
-0.011577402241528034,
0.019466247409582138,
-0.010224134661257267,
0.03602392598986626,
0.018115922808647156,
-0.022523412480950356,
-0.005111408419907093,
0.04450222849845886,
-0.020554251968860626,
-0.05443393811583519,
-0.006469221320003271,
0.003212729236111045,
0.06846843659877777,
-0.01622438058257103,
0.042405225336551666,
0.024692147970199585,
-0.025654565542936325,
0.0031412688549607992,
-0.03823082894086838,
-0.007952266372740269,
0.013087684288620949,
-0.031700193881988525,
0.05666779354214668,
-0.03609205037355423,
0.029521189630031586,
-0.020223122090101242,
0.06247170269489288,
0.04605865851044655,
0.05334552004933357,
0.032591454684734344,
0.047094348818063736,
0.009249155409634113,
-0.04753263294696808,
-0.06315676867961884,
0.019740255549550056,
-0.06143566966056824,
0.04475795850157738,
0.010203814134001732,
-0.014631356112658978,
0.050051044672727585,
-0.014634761959314346,
-0.005300647113472223,
0.0061553772538900375,
-0.007590282242745161,
-0.0007873795693740249,
-0.0065641156397759914,
0.0011767044197767973,
-0.002230729442089796,
-0.0353056937456131,
0.029478082433342934,
0.050872866064310074,
-0.017017116770148277,
0.05236278846859932,
-0.02072596363723278,
-0.08721093088388443,
-0.005034144036471844,
-0.032586243003606796,
-0.025754308328032494,
0.027498511597514153,
-0.013243913650512695,
-0.029283247888088226,
-0.020933596417307854,
-0.0284181609749794,
0.0031156386248767376,
0.007904449477791786,
0.00210461369715631,
-0.032702744007110596,
0.0054094670340418816,
-0.0022984633687883615,
-0.0025556792970746756,
0.03722696751356125,
-0.01319719199091196,
0.12743422389030457,
0.01569143682718277,
0.01388065330684185,
-0.036781031638383865,
-0.028589200228452682,
-0.07023068517446518,
0.003966771997511387,
-0.013195095583796501,
0.02721002697944641,
0.001711966935545206,
0.04947889596223831,
-0.012391173280775547,
0.018917953595519066,
0.04940285533666611,
-0.03360896185040474,
0.029019540175795555,
-0.018441572785377502,
-0.015140373259782791,
0.0023027544375509024,
-0.0008038234082050622,
-0.009410412050783634,
0.04382886365056038,
-0.00013711904466617852,
0.05378372222185135,
-0.032789506018161774,
-0.0425972118973732,
-0.009374850429594517,
-0.027940737083554268,
0.02324792370200157,
0.03483550250530243,
-0.026225319132208824,
-0.012645818293094635,
-0.015446285717189312,
-0.008253296837210655,
-0.040756579488515854,
0.0122911985963583,
0.01489999983459711,
-0.013813218101859093,
0.0035878880880773067,
-0.025011375546455383,
0.0053606159053742886,
0.034130390733480453,
-0.0010487785330042243,
-0.001727545284666121,
-0.008908242918550968,
-0.010348539799451828,
-0.038191184401512146,
0.006554911844432354,
0.02824724093079567,
0.013521107845008373,
-0.013448779471218586,
0.020040063187479973,
0.006708498578518629,
-0.09598241001367569,
-0.01909947395324707,
-0.0023231026716530323,
0.010710052214562893,
-0.0002525888558011502,
-0.054832879453897476,
-0.013950299471616745,
0.03940531983971596,
0.037019554525613785,
0.016493335366249084,
0.0028708004392683506,
0.020516492426395416,
-0.02561166137456894,
-0.015940839424729347,
0.021361248567700386,
-0.02113872766494751,
-0.02654901146888733,
-0.0430912971496582,
0.032769665122032166,
-0.01687774993479252,
0.015359437093138695,
0.012930952943861485,
0.009704978205263615,
0.06089840456843376,
0.020945362746715546,
-0.0017166623147204518,
0.004615266341716051,
-0.09427712857723236,
0.03416210040450096,
-0.05705827847123146,
-0.004380764439702034,
-0.00894957035779953,
0.014971122145652771,
0.04209452494978905,
-0.008491376414895058,
-0.022176550701260567,
0.006218636408448219,
0.0018574370769783854,
-0.000646359461825341,
0.04731399193406105,
-0.016893312335014343,
-0.04714418947696686,
-0.014224529266357422,
-0.004744557663798332,
0.02143637090921402,
-0.008472224697470665,
0.015131664462387562,
0.022066475823521614,
0.00009587874228600413,
0.007683020085096359,
0.006209166720509529,
-0.010940573178231716,
-0.005329546984285116,
-0.013573437929153442,
-0.015226691961288452,
0.026283105835318565,
-0.01975720003247261,
0.04172666743397713,
0.0016210014000535011,
-0.025989891961216927,
-0.08715733140707016,
0.014773759059607983,
-0.01260725874453783,
0.023131409659981728,
0.025176187977194786,
0.003186462912708521,
-0.02532361075282097,
-0.00027960966690443456,
-0.004936898127198219,
-0.024417810142040253,
-0.04983167350292206,
-0.0045038615353405476,
0.0033509882632642984,
0.03318560868501663,
-0.036216698586940765,
0.02407609112560749,
-0.032100845128297806,
-0.02345287799835205,
0.007104028481990099,
-0.048772651702165604,
-0.005467167589813471,
0.03291558474302292,
0.02519402839243412,
-0.015892012044787407,
0.041987426578998566,
-0.0005701634217984974,
-0.014310774393379688,
0.017364945262670517,
-0.013471588492393494,
-0.016604863107204437,
0.03191755712032318,
0.0009102938929572701,
0.029524650424718857,
0.02023669146001339,
0.0013645412400364876,
-0.04929507151246071,
0.08353380858898163,
0.010212416760623455,
0.00007662612188141793,
-0.014766649343073368,
0.023830078542232513,
0.03585603088140488,
0.017520908266305923,
0.02321907877922058,
-0.017582282423973083,
-0.0421435572206974,
0.03411409258842468,
-0.0006736420909874141,
0.01846545934677124,
0.015015846118330956,
0.02463456243276596,
-0.022542955353856087,
-0.021231388673186302,
0.009591477923095226,
-0.019526537507772446,
0.025030003860592842,
0.02088204398751259,
-0.000931599410250783,
0.03722972422838211,
0.02867305651307106,
0.009744151495397091,
-0.0958830937743187,
-0.012431453913450241,
-0.02210015431046486,
0.04303715378046036,
0.03469008952379227,
-0.067062146961689,
-0.005705964285880327,
0.030620094388723373,
-0.06330206990242004,
-0.01774635724723339,
-0.03057754784822464,
-0.05115954950451851,
-0.04346270114183426,
0.027211515232920647,
-0.007618767209351063,
0.0020104513969272375,
-0.007982251234352589,
0.002088218927383423,
0.009354480542242527,
-0.02334241010248661,
-0.019772252067923546,
-0.014556294307112694,
0.014997574500739574,
0.05190619081258774,
0.0070219566114246845,
0.023866405710577965,
0.018890604376792908,
-0.0396583117544651,
-0.029659954831004143,
-0.009155773557722569,
-0.010806402191519737,
0.027117693796753883,
0.039457567036151886,
0.023802125826478004,
-0.0013378466246649623,
0.024783039465546608,
0.009577271528542042,
-0.013792279176414013,
-0.02289056032896042,
-0.0006010649958625436,
0.027819806709885597,
0.027447497472167015,
-0.014885473065078259,
0.0241509061306715,
0.0027217729948461056,
-0.038973692804574966,
-0.07154349237680435,
0.01756855845451355,
-0.01709468849003315,
-0.0010768832871690392,
0.04023103788495064,
-0.024389972910284996,
0.027376824989914894,
-0.02570132166147232,
-0.026316775009036064,
-0.04173004999756813,
0.0003763283893931657,
-0.007212270516902208,
-0.03152532875537872,
0.006078981328755617,
0.016572637483477592,
-0.0447828434407711,
-0.03646397590637207,
-0.028820928186178207,
-0.006711426191031933,
-0.01234279852360487,
-0.03863265737891197,
-0.013112759217619896,
0.01593875326216221,
-0.007474831771105528,
0.025081893429160118,
-0.03465781360864639,
0.032741039991378784,
0.033491067588329315,
0.020755019038915634,
-0.014705425128340721,
0.052899643778800964,
-0.02118312567472458,
-0.025836322456598282,
-0.053820863366127014,
0.03787321224808693,
0.00903388299047947,
-0.02701881155371666,
0.008444572798907757,
-0.02074478566646576,
-0.011089617386460304,
0.06310906261205673,
0.06040583923459053,
-0.029418274760246277,
0.027508966624736786,
-0.0022373804822564125,
0.015307790599763393,
-0.023872410878539085,
-0.01832423359155655,
0.000165962366736494,
0.030361222103238106,
-0.06856659799814224,
-0.008166634477674961,
0.012846163474023342,
-0.02476218156516552,
-0.0007455075974576175,
0.005716017447412014,
-0.015565168112516403,
0.040967393666505814,
0.01121291983872652,
-0.021011384204030037,
0.06300045549869537,
0.010283434763550758,
-0.019458968192338943,
0.04080090671777725,
-0.001156315323896706,
-0.03907075896859169,
0.007075735367834568,
-0.03934067115187645,
-0.047700051218271255,
0.053864285349845886,
-0.03353150561451912,
0.002147550927475095,
0.020115066319704056,
-0.010826623998582363,
0.04413975402712822,
-0.04483744502067566,
0.05009667947888374,
-0.021956047043204308,
-0.026647228747606277,
-0.014127138070762157,
0.055288780480623245,
-0.00866257306188345,
-0.005732426419854164,
-0.036071114242076874,
-0.0017758512403815985,
-0.005815988406538963,
-0.02489202655851841,
0.004591230768710375,
0.06025942414999008,
0.05652422830462456,
0.009739984758198261,
0.017795421183109283,
0.030590293928980827,
0.015010134316980839,
0.034058306366205215,
-0.03332080692052841,
0.030384376645088196,
-0.037250448018312454,
-0.009332487359642982,
-0.031856149435043335,
-0.013258250430226326,
-0.03888380154967308,
0.0038513417821377516,
-0.012757853604853153,
0.045160792768001556,
-0.002200232818722725,
-0.009804598055779934,
-0.014948260970413685,
-0.005516489502042532,
-0.037054140120744705,
0.029042141512036324,
0.02681460976600647,
0.019359812140464783,
-0.006982594728469849,
-0.0249335914850235,
-0.013327216729521751,
-0.00497054448351264,
0.040809113532304764,
-0.020925989374518394,
0.04220708832144737,
0.01001915242522955,
0.019680030643939972,
-0.020264483988285065,
-0.011004665866494179,
-0.014104115776717663,
-0.024607865139842033,
0.019583137705922127,
-0.009441214613616467,
-0.013762304559350014,
-0.005776386708021164,
-0.038568850606679916,
-0.021690621972084045,
0.07725876569747925,
-0.08414719998836517,
0.018615953624248505,
0.01537553034722805,
0.01591874659061432,
0.00033170130336657166,
-0.006236029323190451
] |
<p>Consider a theory of one complex scalar field with the following Lagrangian.
$$
\mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2.
$$
The potential is
$$
V(\phi )=-\mu ^2|\phi |^2+\frac{\lambda}{2}|\phi|^4.
$$
The classic stable minimum of this potential is given by $\phi =\frac{\mu}{\sqrt{\lambda}}e^{i\theta}=:v$ for any $\theta \in \mathbb{R}$.</p>
<p>We then define a new field $\psi: =\phi -|v|$, rewrite the Lagrangian in terms of the new field $\psi$, et voilà: out pops the mass term
$$
2|v|^2\lambda \psi ^*\psi .
$$
People usually explain that this shows the existence of a field whose quanta are particles of mass $|v|\sqrt{2\lambda}$. In this sense, the original field has $\phi$ acquired a mass.</p>
<p>I don't buy it. I don't see where this argument has actually used the fact that $v$ is the vacuum expectation value of the field. Yes, it is natural to expand about the classical minima, but why not do something stupid instead and define a new field $\psi :=\phi -7$. Once again, after rewriting the Lagrangian in terms of the new field, you should find that it has indeed acquired has a mass term. Playing this trick over and over, by picking a number different than $7$, you should be able to find a mass term with any mass you like. Obviously, this doesn't make any physical sense.</p>
<p>There is something special about the substitution $\psi :=\phi -|v|$. There must be more to it than a tedious algebraic manipulation, but what is it? Why does nature possess particles of the mass that this substitution yields, as opposed to any other substitution?</p>
<p>On another note, what exactly does this have to do with the global $U(1)$ symmetry present. It seems that the only thing that has played a role so far is that the vacuum expectation value of the field is non-zero, but yet I've always seen this mass generation presented alongside symmetry breaking. What precisely is the relationship between the two?</p>
| 7,646 |
[
-0.004571337252855301,
0.006554775405675173,
0.00033247729879803956,
-0.045374974608421326,
0.0031701161060482264,
-0.007966642268002033,
-0.01688147708773613,
-0.029937952756881714,
-0.02473308891057968,
-0.018577102571725845,
0.000995212816633284,
0.008534244261682034,
0.04704923555254936,
-0.01313263550400734,
0.013730251230299473,
0.0457918718457222,
0.018626827746629715,
-0.01223103515803814,
-0.04706857353448868,
-0.020201602950692177,
-0.00638587586581707,
0.027456752955913544,
0.011780966073274612,
0.010513865388929844,
-0.018572309985756874,
0.008129256777465343,
0.0004160190001130104,
-0.010452822782099247,
-0.051857415586709976,
0.10904886573553085,
-0.020746547728776932,
-0.0196867473423481,
-0.0009571792325004935,
-0.00046906364150345325,
0.027672164142131805,
0.031851738691329956,
-0.0051317461766302586,
-0.03158074989914894,
-0.0066823880188167095,
0.02147178165614605,
-0.03503776341676712,
0.013690841384232044,
0.003126934403553605,
0.03335438668727875,
-0.026708941906690598,
0.010828115046024323,
0.006335482932627201,
-0.020366806536912918,
0.07933347672224045,
-0.05522861331701279,
0.04654616490006447,
0.0486062616109848,
-0.007213133852928877,
0.016981031745672226,
-0.022437231615185738,
-0.056317947804927826,
0.05948595702648163,
0.053838059306144714,
0.02659761905670166,
-0.04480946436524391,
-0.04942489042878151,
-0.02050541527569294,
-0.0044756606221199036,
-0.0036574536934494972,
0.0024914820678532124,
0.02966567501425743,
0.029509330168366432,
0.03565080091357231,
0.05123903974890709,
0.0011779695050790906,
0.010279317386448383,
-0.005161312408745289,
0.01609901152551174,
0.02231133170425892,
0.0249920841306448,
0.005793485790491104,
0.003725472604855895,
0.02951751835644245,
-0.004617344122380018,
-0.013082219287753105,
0.010185481980443,
0.04865000769495964,
0.04707414284348488,
0.03453383967280388,
-0.011746483854949474,
-0.0033364365808665752,
0.06590430438518524,
0.018471553921699524,
-0.001417604391463101,
0.03782643750309944,
0.009653469547629356,
-0.0027794598136097193,
0.03267230466008186,
-0.037495680153369904,
-0.009036796167492867,
0.03539662808179855,
0.01669004000723362,
0.009949452243745327,
0.017079537734389305,
0.007733503822237253,
-0.019527500495314598,
-0.005915593821555376,
0.00006399606354534626,
0.058904241770505905,
-0.00033054850064218044,
-0.0133138969540596,
-0.030553139746189117,
-0.009081612341105938,
-0.04085265100002289,
-0.011470368131995201,
-0.031457412987947464,
0.0012285899138078094,
0.019528834149241447,
0.004842495080083609,
-0.03191854804754257,
-0.033978644758462906,
0.008634908124804497,
-0.04075025022029877,
0.07210787385702133,
0.03653121739625931,
0.04132596403360367,
-0.03209935501217842,
0.013564934954047203,
-0.05856167525053024,
-0.044682785868644714,
-0.003067496931180358,
0.02746332436800003,
-0.0007352308603003621,
-0.05416789650917053,
-0.03441490978002548,
0.028411805629730225,
0.039683517068624496,
0.030389174818992615,
0.03535318002104759,
0.010190154425799847,
-0.046815820038318634,
-0.08355101943016052,
-0.05935166776180267,
0.026393765583634377,
-0.006350375711917877,
-0.020341647788882256,
-0.05509578436613083,
-0.03945770114660263,
0.03267360106110573,
0.06622045487165451,
0.0028105764649808407,
0.006075612269341946,
0.03708091005682945,
0.014942409470677376,
-0.006404190324246883,
0.028844788670539856,
-0.01429778803139925,
-0.006712369620800018,
-0.034204673022031784,
0.015803324058651924,
-0.05003645271062851,
0.008427617140114307,
-0.005636055488139391,
-0.004188799299299717,
0.005037963856011629,
0.07606305927038193,
-0.0537964291870594,
0.01885262131690979,
0.005085793323814869,
-0.025016317144036293,
0.013688407838344574,
0.02545918896794319,
0.020916538313031197,
-0.02291957288980484,
0.02479601837694645,
-0.01619897037744522,
0.04068976640701294,
-0.004244052339345217,
0.046344269067049026,
0.0403892956674099,
-0.034652214497327805,
0.001761624589562416,
-0.048551224172115326,
0.02761102095246315,
-0.005950547754764557,
-0.022462064400315285,
-0.04713231697678566,
-0.030074557289481163,
0.003074406646192074,
-0.00651412270963192,
0.032540496438741684,
-0.0012782687554135919,
0.03240220621228218,
0.0025611829478293657,
-0.06139807403087616,
-0.03262009471654892,
-0.030832193791866302,
0.007613708730787039,
0.051641661673784256,
-0.023306068032979965,
0.033560529351234436,
0.017370836809277534,
0.0014224713668227196,
-0.03362599015235901,
-0.026343438774347305,
0.03445572033524513,
0.05305220186710358,
-0.0003963469644077122,
0.0009063092875294387,
0.04573360085487366,
0.04908629506826401,
0.012464838102459908,
0.016256507486104965,
0.01973509043455124,
-0.0013514823513105512,
-0.02636823058128357,
0.027104679495096207,
0.03223250433802605,
0.0399731770157814,
-0.007744717877358198,
0.008565500378608704,
0.0006796667585149407,
-0.014364447444677353,
0.004027318209409714,
0.05032205209136009,
-0.07008283585309982,
0.026796074584126472,
0.037575557827949524,
-0.018502559512853622,
-0.01709763891994953,
0.06899209320545197,
-0.02319950982928276,
0.041845232248306274,
-0.00020660521113313735,
-0.023275237530469894,
-0.02277415432035923,
-0.010655167512595654,
0.06182503327727318,
0.048978161066770554,
-0.02278752066195011,
0.02802632935345173,
0.03029513545334339,
0.04676764830946922,
0.04582640901207924,
0.009645617567002773,
-0.06632858514785767,
-0.041374627500772476,
0.07747587561607361,
0.012109346687793732,
-0.003170943586155772,
0.020012008026242256,
0.06027653068304062,
-0.0032590581104159355,
0.015833083540201187,
-0.01671062782406807,
-0.0025764743331819773,
0.01992282271385193,
0.00530658895149827,
0.0034741470590233803,
-0.0037489845417439938,
-0.00449672294780612,
0.022729957476258278,
-0.026511019095778465,
0.060585927218198776,
0.03552998602390289,
-0.028046535328030586,
-0.018735280260443687,
-0.05366673320531845,
-0.002513023093342781,
0.018224069848656654,
0.002801361493766308,
-0.004915807396173477,
0.005133552011102438,
0.029821384698152542,
-0.05092374607920647,
-0.022668717429041862,
-0.009727700613439083,
-0.02496781013906002,
-0.03918352723121643,
-0.011532570235431194,
0.021363649517297745,
-0.017329880967736244,
-0.011561735533177853,
0.004420449957251549,
-0.004340810235589743,
0.03922760859131813,
-0.019272703677415848,
0.007826591841876507,
0.03344372659921646,
-0.023499585688114166,
-0.023478249087929726,
-0.061327457427978516,
-0.0351940281689167,
0.05619974434375763,
0.00849630031734705,
0.03142203763127327,
0.019130036234855652,
0.007886611856520176,
-0.04427725449204445,
-0.019235070794820786,
-0.0421997532248497,
-0.03224189579486847,
-0.020823819562792778,
0.008007868193089962,
0.03018263168632984,
0.02262226678431034,
-0.0643685832619667,
-0.012238298542797565,
-0.01767788454890251,
-0.0414426252245903,
-0.04884367808699608,
-0.005119773559272289,
0.012950778938829899,
-0.029857207089662552,
0.05030106008052826,
0.010503066703677177,
0.022756991907954216,
0.020535383373498917,
-0.05253828316926956,
-0.006175094284117222,
-0.0012257996713742614,
-0.03779241070151329,
-0.002373191760852933,
0.019458981230854988,
-0.021891700103878975,
0.11428574472665787,
0.06588665395975113,
-0.03369626775383949,
-0.023074213415384293,
0.053694948554039,
-0.01565929502248764,
-0.01540957111865282,
0.012201097793877125,
0.026982655748724937,
-0.02013557218015194,
0.02804957889020443,
0.010996784083545208,
0.01391225028783083,
-0.023196211084723473,
0.003094695508480072,
-0.02515977993607521,
0.025601478293538094,
-0.02457982860505581,
-0.005621882155537605,
0.03157752379775047,
-0.031077945604920387,
-0.01510787196457386,
0.0068757189437747,
0.031770188361406326,
0.03559420630335808,
-0.01040370762348175,
-0.03250104561448097,
0.07767097651958466,
0.029742727056145668,
0.020984601229429245,
-0.010100818239152431,
0.021675745025277138,
-0.018485065549612045,
-0.04676021635532379,
-0.006501448340713978,
-0.015158555470407009,
0.005764968227595091,
-0.01992058753967285,
-0.024284888058900833,
0.014772648923099041,
0.020156366750597954,
-0.0406559482216835,
0.000183411524631083,
-0.03206788748502731,
-0.018690092489123344,
0.01880825124680996,
-0.021185575053095818,
-0.05007723718881607,
0.029750365763902664,
0.045870717614889145,
-0.009460141882300377,
-0.045192357152700424,
-0.03533449396491051,
-0.032005537301301956,
-0.02057540975511074,
0.013089117594063282,
0.014545661397278309,
0.022068899124860764,
0.015273326076567173,
0.03506148234009743,
0.016012035310268402,
0.004479733761399984,
-0.014382847584784031,
-0.012624206021428108,
-0.07741567492485046,
0.017435429617762566,
-0.020046252757310867,
-0.014385462738573551,
-0.005043904762715101,
-0.015514593571424484,
-0.007856202311813831,
-0.019973577931523323,
-0.03447175398468971,
-0.04244557023048401,
-0.03470081835985184,
-0.05597452446818352,
0.019671976566314697,
-0.014765978790819645,
-0.03449295088648796,
-0.043831028044223785,
0.011635914444923401,
0.10691630840301514,
-0.019797179847955704,
-0.012151832692325115,
-0.0060169813223183155,
-0.04130742698907852,
-0.00010607431613607332,
-0.030634675174951553,
0.0058147902600467205,
0.021337635815143585,
0.012107500806450844,
-0.0007072194712236524,
0.015109075233340263,
-0.022113211452960968,
0.0205166544765234,
-0.014836806803941727,
0.05137297883629799,
0.011915168724954128,
0.023510754108428955,
0.002399313962087035,
-0.04745890945196152,
-0.022475430741906166,
0.03000529296696186,
0.05572662502527237,
0.005921130999922752,
-0.029466774314641953,
0.036436211317777634,
-0.013409432023763657,
-0.00434214947745204,
0.01469527930021286,
0.03531266748905182,
-0.02551521360874176,
-0.029523244127631187,
-0.04173436760902405,
0.006057453341782093,
-0.016881637275218964,
0.0021539765875786543,
-0.005638150032609701,
-0.01904737763106823,
-0.011296557262539864,
-0.037610191851854324,
0.029040563851594925,
-0.017172742635011673,
-0.011950680054724216,
-0.01486749853938818,
0.00648169731721282,
0.0043557267636060715,
0.002976155374199152,
-0.004800578113645315,
0.012971452437341213,
0.036131005734205246,
0.0447547510266304,
0.016820965334773064,
0.031205017119646072,
-0.0664861798286438,
-0.020099502056837082,
0.027717698365449905,
0.05170730501413345,
0.009398925118148327,
-0.024564987048506737,
-0.051712632179260254,
-0.04599984362721443,
0.02971769869327545,
-0.050497885793447495,
0.04177914187312126,
-0.011628611944615841,
0.009853355586528778,
0.009538278914988041,
-0.07440949976444244,
-0.003525262698531151,
0.03213009983301163,
-0.020167240872979164,
-0.001758923172019422,
-0.01574876345694065,
0.014083114452660084,
0.01329164020717144,
0.03645923361182213,
0.016801128163933754,
0.052470892667770386,
0.01639007031917572,
-0.010832165367901325,
-0.0023251078091561794,
-0.022002331912517548,
-0.020268511027097702,
-0.08542107045650482,
-0.011457031592726707,
-0.021765321493148804,
-0.005564387422055006,
-0.0031967132817953825,
-0.0074518099427223206,
-0.038109201937913895,
0.0011057942174375057,
0.025122832506895065,
-0.026156950742006302,
0.044175148010253906,
-0.033455219119787216,
0.028161874040961266,
0.03988918662071228,
0.04125199094414711,
0.06388884782791138,
0.024343086406588554,
-0.029878774657845497,
-0.019222624599933624,
-0.0713486298918724,
0.001566434046253562,
-0.010179735720157623,
-0.00736811151728034,
-0.035152554512023926,
0.003354098415002227,
-0.023699428886175156,
0.05403175577521324,
-0.007719250861555338,
0.0040338910184800625,
-0.012436818331480026,
-0.019747445359826088,
-0.040760233998298645,
0.015413346700370312,
0.011680790223181248,
-0.0033838492818176746,
0.010017781518399715,
0.024649707600474358,
0.031779155135154724,
0.009361131116747856,
0.015934674069285393,
0.03351641073822975,
-0.007932953536510468,
0.04559557884931564,
-0.01577754132449627,
0.045565132051706314,
-0.003524759318679571,
-0.0074978419579565525,
0.02031143568456173,
-0.06879045069217682,
0.07456980645656586,
0.031120365485548973,
-0.016417015343904495,
0.001818654127418995,
-0.03397040814161301,
-0.08378595858812332,
-0.013842754065990448,
-0.03486311435699463,
-0.016680847853422165,
-0.02620704285800457,
-0.03094949759542942,
0.03648918494582176,
0.017621129751205444,
-0.08943150192499161,
-0.01723409816622734,
-0.010850519873201847,
-0.026764871552586555,
-0.01299645658582449,
0.008624020032584667,
-0.012342782691121101,
-0.016068458557128906,
-0.04403817281126976,
-0.012268604710698128,
0.03409397229552269,
-0.02026423253118992,
-0.004570893011987209,
-0.029159987345337868,
0.056432027369737625,
0.012915399856865406,
-0.021396255120635033,
-0.0029726922512054443,
0.024457208812236786,
0.0058774459175765514,
0.032206326723098755,
0.02741594985127449,
0.0452873557806015,
-0.012504609301686287,
-0.01348698791116476,
-0.00034405456972308457,
-0.0036515758838504553,
0.018377702683210373,
0.025144608691334724,
-0.025412380695343018,
0.014221835881471634,
-0.011914407834410667,
-0.0036144345067441463,
-0.0015049106441438198,
-0.020968982949852943,
-0.021342255175113678,
0.045918695628643036,
0.014172432012856007,
0.0066708349622786045,
0.011547180823981762,
-0.052777037024497986,
0.03649016469717026,
-0.010008050128817558,
0.0008864392293617129,
-0.037413228303194046,
0.04094897583127022,
-0.011021419428288937,
-0.024913160130381584,
0.002878030762076378,
0.002009392250329256,
-0.008346701972186565,
0.02438911236822605,
0.027328483760356903,
0.0031810093205422163,
0.003757918020710349,
-0.05065836012363434,
-0.006989020388573408,
-0.027393154799938202,
0.03535771742463112,
0.053260687738657,
0.023495325818657875,
0.020661506801843643,
-0.01199980266392231,
-0.044382814317941666,
-0.014927421696484089,
-0.026324620470404625,
-0.037421535700559616,
0.006690868642181158,
-0.019707512110471725,
0.040720026940107346,
-0.03644873574376106,
0.013674727641046047,
0.029179399833083153,
0.024451633915305138,
-0.01595098339021206,
0.03203660249710083,
0.041825465857982635,
0.03613007068634033,
-0.002465961268171668,
-0.024754710495471954,
-0.04953889176249504,
0.06840720772743225,
-0.03002879023551941,
0.04267120733857155,
0.01447959803044796,
-0.01658639684319496,
-0.0026114422362297773,
-0.019433218985795975,
0.00006940760795259848,
-0.008802147582173347,
-0.015444781631231308,
-0.04707638546824455,
0.010574414394795895,
0.03225528448820114,
-0.037071652710437775,
0.026723360642790794,
-0.01109878160059452,
0.01070911530405283,
-0.00776628078892827,
0.039900846779346466,
0.011563481763005257,
-0.005951265804469585,
-0.019264480099081993,
-0.042418088763952255,
-0.08574216812849045,
0.06442297995090485,
-0.017594151198863983,
-0.014561353251338005,
0.0018975655548274517,
-0.016603320837020874,
-0.0007492739241570234,
0.025118418037891388,
0.026203880086541176,
-0.04401508346199989,
0.057128019630908966,
0.003273438662290573,
0.02079746313393116,
-0.01873631775379181,
0.017334111034870148,
0.16407451033592224,
0.056820452213287354,
0.006613193545490503,
-0.04882685840129852,
0.025422660633921623,
-0.027115000411868095,
0.028599049896001816,
-0.0548967607319355,
0.03345346078276634,
-0.04405314102768898,
-0.004441601224243641,
-0.03650098666548729,
0.042507052421569824,
-0.0015813293866813183,
0.009812211617827415,
0.03345547243952751,
-0.031703706830739975,
-0.033370792865753174,
-0.03351873904466629,
0.030536150559782982,
-0.017654597759246826,
0.024737253785133362,
-0.015882965177297592,
0.01403734926134348,
-0.00513218529522419,
0.036239661276340485,
-0.0068490346893668175,
-0.021361196413636208,
0.006111089140176773,
0.00018875504611060023,
-0.043268442153930664,
-0.019143108278512955,
0.018636643886566162,
-0.033200401812791824,
-0.0029709204100072384,
-0.011977133341133595,
0.0032530436292290688,
-0.01444348506629467,
0.011481864377856255,
0.048537760972976685,
0.005184672307223082,
0.012355305254459381,
0.0035865395329892635,
0.004015198443084955,
-0.0406586155295372,
0.0030837205704301596,
-0.05101323500275612,
0.08379312604665756,
-0.028453366830945015,
0.023196181282401085,
0.022286394611001015,
-0.017863040789961815,
0.01632818393409252,
-0.0074919830076396465,
-0.032865382730960846,
-0.02307305671274662,
0.046726077795028687,
0.0016066636890172958,
0.02069893106818199,
0.004113215021789074,
0.036548957228660583,
0.03494149073958397,
0.0010318753775209188,
0.0030572013929486275,
-0.013802210800349712,
-0.0475650429725647,
-0.011187361553311348,
0.03788754716515541,
-0.007132717873901129,
0.00034271166077814996,
0.003229147056117654,
-0.015436949208378792,
-0.04084676504135132,
-0.03731044381856918,
-0.029424559324979782,
0.010585588403046131,
0.03753293678164482,
-0.02833065204322338,
-0.01605592854321003,
-0.022168638184666634,
-0.06621530652046204,
-0.006450672168284655,
-0.014589617028832436,
-0.012796832248568535,
0.0003509299422148615,
0.012024717405438423,
-0.033411864191293716,
0.02287062630057335,
-0.032986126840114594,
-0.004601902328431606,
0.007631955202668905,
0.05624065548181534,
0.008254388347268105,
-0.062345948070287704,
-0.020837368443608284,
0.009151667356491089,
0.004737889394164085,
0.014734474942088127,
0.01004026923328638,
-0.0022434736602008343,
0.009071966633200645,
0.026931755244731903,
0.013140800409018993,
0.019191330298781395,
0.006622111424803734,
0.024246469140052795,
0.03794311359524727,
-0.009268859401345253,
0.020531343296170235,
0.04425688460469246,
0.062076136469841,
-0.025843195617198944,
-0.053599726408720016,
-0.012528344988822937,
-0.026487253606319427,
0.008804287761449814,
0.02943258360028267,
-0.05545247346162796,
0.011499532498419285,
0.0011642358731478453,
0.009305787272751331,
-0.03896430507302284,
-0.01937737688422203,
-0.049812041223049164,
0.0523817241191864,
-0.0241899024695158,
-0.01743394322693348,
-0.019759774208068848,
0.018170922994613647,
-0.026158995926380157,
-0.014539102092385292,
0.010093605145812035,
0.006529216654598713,
-0.01313860435038805,
-0.006360273342579603,
-0.0031455771531909704,
0.007419157307595015,
0.0019585152622312307,
0.037087105214595795,
-0.023062415421009064,
0.00002087143911921885,
-0.011360772885382175,
-0.05724150314927101,
0.03658086806535721,
0.005395927466452122,
0.023962505161762238,
0.06099773570895195,
-0.01681453175842762,
-0.002860922832041979,
0.014027776196599007,
-0.012775244191288948,
-0.02736091800034046,
-0.03322811797261238,
-0.019695112481713295,
0.008044391870498657,
-0.01072638388723135,
0.0371791273355484,
-0.001755884033627808,
0.0063396780751645565,
0.0001212062343256548,
0.016257353127002716,
-0.02684107981622219,
-0.0034785971511155367,
0.01029813289642334,
-0.029178272932767868,
0.05351007357239723,
0.008298571221530437,
0.015962637960910797,
0.015514521859586239,
0.03335227817296982,
-0.008891711011528969,
-0.004475720692425966,
0.0353255532681942,
-0.008179250173270702,
-0.08679484575986862,
-0.037994079291820526,
-0.010401503182947636,
0.04411524161696434,
0.0657288208603859,
-0.036835722625255585,
0.04225728288292885,
0.008556836284697056,
-0.06829210370779037,
-0.014910764992237091,
0.0001288746134378016,
0.018016045913100243,
-0.0024838410317897797,
-0.0387459322810173,
-0.05371696501970291,
0.02373058721423149,
0.0371432900428772,
0.04171457886695862,
0.01196992862969637,
0.022498684003949165,
-0.0017032561590895057,
-0.03664935380220413,
-0.01587185449898243,
0.032157521694898605,
-0.014208685606718063,
0.01741943694651127,
0.07399892061948776,
0.006413275375962257,
-0.026277858763933182,
0.03261556848883629,
0.05479132756590843,
0.005970343016088009,
-0.020207462832331657,
0.05009135976433754,
0.029882211238145828,
0.036362890154123306,
-0.0017063877312466502,
0.007825924083590508,
-0.014457251876592636,
-0.008619798347353935,
0.050730157643556595,
0.03404804319143295,
0.006618782877922058,
-0.014507529325783253,
0.00009029720968101174,
-0.03353165090084076,
-0.020480826497077942,
0.05086135491728783,
-0.03613344952464104,
-0.0286223404109478,
0.0032658760901540518,
-0.008914037607610226,
-0.02461078390479088,
-0.046091992408037186,
0.01767168752849102,
-0.03204787150025368,
-0.009057315066456795,
0.035297781229019165,
0.018155425786972046,
0.01049513928592205,
0.014667520299553871,
0.008565996773540974,
0.021351302042603493,
0.024898048490285873,
0.04064404219388962,
0.02373662404716015,
-0.06667736172676086,
-0.029986977577209473,
-0.008328176103532314,
0.003644431009888649,
0.01864265836775303,
-0.004914125893265009,
-0.045802220702171326,
0.007337032817304134,
0.027949823066592216,
0.023023735731840134,
-0.0816144272685051,
-0.03434548154473305,
0.019952697679400444,
-0.06366229802370071,
0.020354239270091057,
0.01788233406841755,
0.01361991185694933,
-0.021329713985323906,
-0.04435853287577629,
0.025316616520285606,
0.027725137770175934,
0.06811030209064484,
-0.0007055352325551212,
-0.03964722529053688,
0.04708922654390335,
-0.012620897963643074,
0.015472707338631153,
-0.027403250336647034,
-0.02325192093849182,
0.007699804380536079,
0.016271594911813736,
0.014180995523929596,
0.020267106592655182,
0.022510681301355362,
0.0343300960958004,
0.012064329348504543,
0.003176488447934389,
-0.016432495787739754,
0.03261933475732803,
-0.017901567742228508,
0.042289849370718,
-0.026055414229631424,
-0.03274532034993172,
0.050559937953948975,
0.0285948459059,
0.038543954491615295,
-0.0061467369087040424,
-0.04013211652636528,
0.004746771417558193,
0.015641603618860245,
-0.051223356276750565,
-0.005963391624391079,
-0.027982397004961967,
0.010918783955276012,
0.01901460811495781,
-0.01586967147886753,
0.004724652506411076,
0.0646599680185318,
-0.01253268402069807,
-0.047065369784832,
0.06599369645118713,
0.01756684109568596,
0.08617663383483887,
0.04075148329138756,
0.03050420619547367,
0.009176559746265411,
0.0005011745379306376,
0.027301723137497902,
0.016814222559332848,
0.02457542158663273,
-0.007239323575049639,
-0.02529987134039402,
0.04014664888381958,
-0.039087191224098206,
0.026866652071475983,
-0.009233337827026844,
0.02610447257757187,
-0.008892757818102837,
-0.005035418551415205,
-0.01159875188022852,
-0.011981592513620853,
0.00497086625546217,
-0.01662043295800686,
-0.009614347480237484,
0.09205421805381775,
0.022168204188346863,
0.0030209256801754236,
-0.03623569756746292,
0.05231558531522751,
-0.0005686521762982011,
0.013325061649084091,
-0.0015218027401715517,
0.030300606042146683,
0.011333205737173557,
-0.007624088320881128,
-0.06094842031598091,
0.0071274880319833755,
-0.015777094289660454,
-0.07962270081043243,
-0.008669614791870117,
0.03926434740424156,
0.011904426850378513,
-0.005346820689737797,
-0.017739111557602882,
-0.015439659357070923,
-0.035525791347026825,
0.013371304608881474,
0.043628156185150146,
0.02861587516963482,
0.009600852616131306,
-0.05667947232723236,
-0.02257859893143177,
0.043859705328941345,
-0.02312898449599743,
-0.01670905016362667,
-0.014491763897240162,
-0.039505671709775925,
-0.002604420529678464,
-0.02516627125442028
] |
<p>My question is the following. Are there solutions to the Einstein field equations, which have the property that there is a hypersurface of constant time and to the past of that surface space is empty (Minkowski space-time) and to the future it is not (non-vanishing stress-energy tensor)? At first thought it seems strange to have nothing and suddenly something. On the other hand define $g_{\mu\nu}(x)$ to be the Minkowski metric for the past of the surface and any functions (sufficiently smooth) that match it on the surface and are different than the Minkowski for the future. There are many ways (infinitely many) to do this. Then one can define the stress-energy tensor using Einstein's equations. This would seem to work, but there are certain conditions on the tensor, for example positivity, or other restrictions for physical reasons that I am unaware of, so it may be there are no such functions. </p>
<p>So the questions is: does anyone know of an explicit example or a more convincing argument than "there are so many functions, there has got to be some that work"? Of course a reason why it doesn't work, if that is the case, would be good too.</p>
<p>Thanks. </p>
| 7,647 |
[
-0.026874493807554245,
-0.0030962051823735237,
0.00023449663422070444,
-0.036120641976594925,
0.034885305911302567,
0.008280607871711254,
-0.037529729306697845,
-0.036572571843862534,
-0.015090730972588062,
-0.0297311432659626,
-0.008781666867434978,
0.02832503244280815,
0.06949169933795929,
-0.000756169087253511,
0.021483786404132843,
-0.013789943419396877,
-0.015935612842440605,
-0.0350467823445797,
-0.050252605229616165,
-0.02812594547867775,
0.016600966453552246,
0.045571547001600266,
-0.006629577372223139,
-0.016538389027118683,
0.019496526569128036,
-0.014089778065681458,
-0.011194436810910702,
-0.027945008128881454,
0.021287547424435616,
0.09894673526287079,
-0.04190327972173691,
-0.04477371275424957,
-0.031317610293626785,
0.055051613599061966,
-0.027441125363111496,
-0.013712918385863304,
-0.021011866629123688,
-0.028151709586381912,
-0.010415020398795605,
0.007022871170192957,
-0.02649819478392601,
0.0056484658271074295,
-0.004974494222551584,
0.07648330926895142,
-0.02677074447274208,
0.03182385861873627,
0.018016116693615913,
-0.02024378813803196,
0.03667363524436951,
-0.03887893259525299,
0.07106584310531616,
-0.014997866936028004,
0.05763997137546539,
0.006838067434728146,
-0.030626025050878525,
-0.007204317022114992,
0.07844781130552292,
0.06014742702245712,
-0.012261325493454933,
-0.03496133163571358,
-0.0394190214574337,
0.03986547142267227,
-0.009044678881764412,
-0.02818421460688114,
-0.01796344295144081,
0.04472789540886879,
-0.017072323709726334,
0.0010200076503679156,
0.01870070770382881,
-0.03194357082247734,
-0.0126250134781003,
0.015198931097984314,
0.025145908817648888,
0.020040879026055336,
-0.012976249679923058,
-0.009667204692959785,
0.033662643283605576,
-0.017400890588760376,
0.025143276900053024,
0.0210932157933712,
-0.022703668102622032,
0.0027121182065457106,
0.04500340297818184,
0.04738287255167961,
0.017850613221526146,
0.020296882838010788,
0.04123907536268234,
-0.005284758284687996,
0.029024681076407433,
0.04689240828156471,
0.01458275318145752,
-0.03666895627975464,
0.04007900506258011,
-0.01740577071905136,
-0.05455300956964493,
0.008619007654488087,
0.005752679891884327,
0.016806697472929955,
0.0030047863256186247,
-0.00728915398940444,
0.0014930397737771273,
-0.020588790997862816,
-0.028865689411759377,
0.03596162796020508,
0.024839263409376144,
0.006355048157274723,
-0.032561760395765305,
0.014966623857617378,
-0.011361082084476948,
0.024632668122649193,
-0.051066700369119644,
0.011519378051161766,
-0.024985872209072113,
-0.02125386707484722,
0.011750870384275913,
-0.03487052023410797,
0.009094695560634136,
-0.04217900335788727,
0.004277056083083153,
0.09720670431852341,
0.047418516129255295,
-0.031076859682798386,
0.0001767609064700082,
-0.033128079026937485,
-0.0891415998339653,
0.002895922400057316,
0.02664598450064659,
0.018164077773690224,
-0.022875001654028893,
-0.010613581165671349,
-0.007430634927004576,
-0.016077177599072456,
0.03309075906872749,
0.023127304390072823,
0.042851194739341736,
-0.04631500691175461,
-0.0601402223110199,
-0.06495625525712967,
0.00989982858300209,
-0.0050497218035161495,
-0.017590533941984177,
-0.044806648045778275,
0.007780746556818485,
0.029662378132343292,
0.0769755020737648,
0.03974694013595581,
-0.010541904717683792,
0.011130151338875294,
0.07649319618940353,
0.005783716682344675,
-0.025694848969578743,
-0.0011530494084581733,
0.017513422295451164,
-0.026004545390605927,
-0.019887303933501244,
-0.0735941156744957,
0.012489011511206627,
0.024263348430395126,
0.008141270838677883,
-0.03603675961494446,
0.0930003896355629,
0.000729256309568882,
-0.0011506278533488512,
-0.02061622031033039,
-0.00013840825704392046,
-0.03293232619762421,
0.0647222027182579,
0.010100302286446095,
0.003197205951437354,
0.024463701993227005,
0.014955474063754082,
0.025785919278860092,
0.020489143207669258,
0.04503677412867546,
0.003181229345500469,
-0.03694356232881546,
0.002183359581977129,
0.03766964003443718,
-0.016307173296809196,
0.024691693484783173,
0.012730545364320278,
-0.008514504879713058,
-0.016413934528827667,
-0.026459425687789917,
-0.017819270491600037,
0.0622410848736763,
0.0017336462624371052,
-0.0033074887469410896,
0.011005482636392117,
-0.06016182526946068,
0.026567798107862473,
-0.04654117301106453,
0.020424220710992813,
0.041952867060899734,
0.002076346194371581,
0.00925230048596859,
-0.009252578020095825,
0.012524391524493694,
-0.04773806035518646,
-0.04293914511799812,
0.02235804870724678,
0.042997632175683975,
0.011365702375769615,
-0.0067346058785915375,
-0.008209613151848316,
0.01471676118671894,
0.05346767604351044,
0.007551977876573801,
0.02977862022817135,
0.017419354990124702,
-0.012466160580515862,
0.0288709569722414,
-0.03098120167851448,
0.03180515021085739,
-0.021325692534446716,
0.014779727905988693,
-0.0038027926348149776,
0.007371911779046059,
0.035656727850437164,
0.032441649585962296,
-0.06179143115878105,
0.03859540820121765,
0.03907075524330139,
-0.0030487580224871635,
-0.007019676733762026,
0.03490493819117546,
0.012549541890621185,
0.03571139648556709,
-0.006195296533405781,
-0.040443941950798035,
-0.03521544113755226,
-0.003979637287557125,
0.03223002701997757,
0.03545695170760155,
-0.042338158935308456,
0.041249830275774,
0.03455706685781479,
0.02310621738433838,
0.011039353907108307,
0.03379770368337631,
-0.009248415008187294,
-0.025127792730927467,
0.03703268989920616,
-0.012050092220306396,
0.04357245936989784,
0.0416654534637928,
0.014177468605339527,
0.033069804310798645,
-0.017771489918231964,
-0.013843901455402374,
0.019565723836421967,
0.019600821658968925,
-0.006482056342065334,
0.0037429400254040956,
-0.006519484333693981,
-0.010992003604769707,
0.015029014088213444,
-0.010181598365306854,
0.03746305778622627,
0.047014277428388596,
0.006801777519285679,
-0.03338310495018959,
-0.03813052177429199,
-0.021137626841664314,
0.027781818062067032,
0.011001757346093655,
0.013289982452988625,
-0.023222845047712326,
0.019769439473748207,
-0.0299002006649971,
-0.0011577829718589783,
-0.012000289745628834,
-0.008254014886915684,
-0.01868130825459957,
0.008856058120727539,
0.022946570068597794,
0.017535561695694923,
0.026014983654022217,
-0.009624292142689228,
-0.03026633709669113,
0.033741433173418045,
-0.028488267213106155,
0.014577528461813927,
0.01169657614082098,
-0.04121720790863037,
0.043618131428956985,
-0.02435789443552494,
-0.02575013041496277,
0.06624739617109299,
-0.02430718019604683,
0.02973591350018978,
0.02401057444512844,
-0.03976094350218773,
-0.022335082292556763,
-0.014584340155124664,
-0.08812679350376129,
0.0060620238073170185,
-0.0022493235301226377,
0.011263865046203136,
0.059481214731931686,
-0.007755074184387922,
-0.06279236078262329,
0.0286245197057724,
-0.0040656267665326595,
-0.05930972471833229,
-0.06318998336791992,
-0.018209323287010193,
0.020858587697148323,
-0.03786792233586311,
0.0218284260481596,
0.02379443682730198,
-0.038913071155548096,
0.018728185445070267,
-0.04479243606328964,
-0.057968661189079285,
0.04145461693406105,
-0.031260937452316284,
0.04229743033647537,
-0.0007908459519967437,
-0.03026350401341915,
0.04607975482940674,
0.006981139071285725,
-0.027067560702562332,
-0.026507234200835228,
0.015939859673380852,
0.04722636565566063,
-0.016832515597343445,
-0.012989601120352745,
-0.0010803256882354617,
-0.013474857434630394,
0.027283266186714172,
0.015352366492152214,
0.03305070474743843,
0.030796503648161888,
0.015324846841394901,
-0.022816717624664307,
-0.013997916132211685,
0.014879407361149788,
0.03850925341248512,
0.03328306972980499,
0.024537615478038788,
-0.010911384597420692,
0.000959752534981817,
0.0005798800848424435,
0.004590265452861786,
0.005799149628728628,
-0.040157970041036606,
0.05836720019578934,
0.0011126684257760644,
0.018289150670170784,
-0.032035332173109055,
0.0020535921212285757,
-0.03980351239442825,
-0.030912263318896294,
0.002915014512836933,
0.011252723634243011,
0.044598329812288284,
-0.02792970836162567,
0.0267576202750206,
0.009994330815970898,
0.011627228930592537,
-0.05660783126950264,
-0.015998419374227524,
-0.008631860837340355,
-0.013535303063690662,
0.02065827138721943,
-0.005445150192826986,
0.0002828632132150233,
0.05555901303887367,
0.05424264073371887,
0.028961431235074997,
0.024061888456344604,
-0.030066868290305138,
0.0022638067603111267,
-0.06710958480834961,
-0.009814135730266571,
0.024211933836340904,
0.0648086741566658,
0.019617227837443352,
-0.0074778962880373,
0.0422186553478241,
0.03308911994099617,
0.026377037167549133,
-0.0034183550160378218,
-0.09312411397695541,
0.028475705534219742,
-0.042744964361190796,
0.003136997576802969,
-0.02100175805389881,
-0.025915291160345078,
0.002602960215881467,
-0.0025884502101689577,
-0.020961256697773933,
0.005886841099709272,
0.0047221919521689415,
-0.09760021418333054,
0.00785873830318451,
-0.04303840175271034,
-0.07159949839115143,
-0.02246720716357231,
0.044214971363544464,
0.05934282764792442,
-0.003241183701902628,
-0.0120439687743783,
0.018237603828310966,
-0.026380671188235283,
-0.010711073875427246,
0.02359817363321781,
0.019693946465849876,
-0.006572688464075327,
0.010493088513612747,
0.01418494526296854,
0.039842743426561356,
0.0029341978952288628,
0.013924864120781422,
0.040138211101293564,
0.04033360630273819,
0.004885103553533554,
0.0027135948184877634,
-0.043203044682741165,
-0.03356336057186127,
-0.03140956908464432,
0.011125695891678333,
0.07693196088075638,
0.028948696330189705,
-0.017341451719403267,
0.008479757234454155,
0.037395816296339035,
0.015531244687736034,
0.04105202481150627,
0.07373207807540894,
-0.008333529345691204,
-0.024396462365984917,
-0.020932907238602638,
-0.03554922342300415,
-0.046780914068222046,
0.014348968863487244,
-0.008497340604662895,
-0.025834286585450172,
-0.042200639843940735,
-0.006317669525742531,
-0.006893415469676256,
0.0008386060944758356,
-0.00807994231581688,
-0.02700420282781124,
0.01670088618993759,
0.025291725993156433,
0.011586125008761883,
0.023274924606084824,
0.010500553995370865,
0.06224564090371132,
0.039290789514780045,
0.026772066950798035,
-0.000849770032800734,
-0.06941977143287659,
-0.016585329547524452,
0.040845535695552826,
-0.00071180664235726,
0.007416963577270508,
-0.04612339660525322,
-0.07332104444503784,
0.006970841437578201,
0.010407261550426483,
-0.014636813662946224,
0.024089500308036804,
0.012658022344112396,
-0.0019222467672079802,
0.01614972949028015,
-0.006534785497933626,
-0.0020694006234407425,
0.014037545770406723,
-0.02362336404621601,
0.004954578820616007,
-0.01577039808034897,
0.007972191087901592,
-0.011584912426769733,
0.02374288998544216,
-0.009792515076696873,
0.04221397265791893,
0.024430377408862114,
-0.015769777819514275,
0.024357812479138374,
0.020999744534492493,
-0.0319652184844017,
-0.08813390135765076,
-0.005030323285609484,
0.010750181041657925,
-0.04879745468497276,
0.037684496492147446,
-0.022412624210119247,
-0.025886982679367065,
0.02294127456843853,
0.005134486593306065,
-0.01462303102016449,
0.06711629033088684,
-0.03860589116811752,
-0.013285047374665737,
0.009507505223155022,
0.02806072309613228,
0.02618754468858242,
0.03979846090078354,
0.00329469982534647,
0.0062125506810843945,
-0.0416194349527359,
0.01477214228361845,
-0.05348210036754608,
0.023615296930074692,
-0.008082909509539604,
-0.01431212667375803,
-0.04141492024064064,
0.007496825885027647,
-0.03510227054357529,
-0.0125783896073699,
0.0013342935126274824,
-0.018804986029863358,
-0.01188999880105257,
0.04308095574378967,
0.02222183160483837,
-0.01623844914138317,
0.0185849666595459,
-0.024683546274900436,
0.010924072004854679,
0.0032156745437532663,
0.01997123844921589,
0.02052176371216774,
-0.010795217007398605,
0.04968622326850891,
0.021879469975829124,
0.017441144213080406,
0.018737714737653732,
-0.025747189298272133,
0.02036157064139843,
-0.023050885647535324,
0.04427442327141762,
0.004724134225398302,
0.008349454030394554,
0.036138154566287994,
-0.012146815657615662,
0.003612722037360072,
0.005070582963526249,
0.01985427550971508,
-0.00540278572589159,
-0.054528262466192245,
0.005250723101198673,
0.04748982563614845,
-0.0022256053052842617,
-0.1041608452796936,
-0.027049191296100616,
0.05306236073374748,
0.018182404339313507,
-0.021643023937940598,
-0.02911490947008133,
-0.028550444170832634,
-0.05926230177283287,
-0.019804678857326508,
0.012442173436284065,
0.04237811639904976,
-0.009313683025538921,
-0.009120078757405281,
-0.002431278582662344,
0.033035147935152054,
0.02134254015982151,
-0.02555219829082489,
0.025823744013905525,
0.04569237679243088,
0.006642699241638184,
-0.019624222069978714,
0.0026694948319345713,
0.01519803423434496,
-0.034294500946998596,
0.0008211209205910563,
-0.00012030025391140953,
0.0029816769529134035,
0.025402165949344635,
0.006100687198340893,
-0.012059939093887806,
0.05336388945579529,
-0.010272828862071037,
-0.032382044941186905,
-0.030043289065361023,
0.01532734464854002,
-0.05781941115856171,
0.0013400126481428742,
-0.03555840998888016,
0.00021130780805833638,
-0.00021925961482338607,
-0.06115926057100296,
0.043763015419244766,
-0.031112484633922577,
0.003969770390540361,
-0.013336742296814919,
0.0469803661108017,
0.0037815438117831945,
-0.05741320177912712,
0.0027555045671761036,
-0.01599286124110222,
0.04557570815086365,
0.04105624184012413,
0.01274033822119236,
-0.0031405091285705566,
0.003928490448743105,
-0.0632014125585556,
-0.05917172133922577,
0.00411786837503314,
0.0177578367292881,
0.08451416343450546,
-0.03652558475732803,
0.03677789121866226,
0.01967841014266014,
-0.017396895214915276,
-0.03276245668530464,
-0.02570919506251812,
-0.027666576206684113,
0.022681821137666702,
-0.010598729364573956,
0.026513323187828064,
-0.007446866016834974,
0.007068002130836248,
0.04673623666167259,
0.021038547158241272,
0.0020809262059628963,
0.032414186745882034,
-0.018353311344981194,
0.03577880188822746,
0.02770933508872986,
-0.03393860161304474,
-0.04801894724369049,
0.02633795514702797,
-0.020277392119169235,
0.03220362961292267,
0.012157982215285301,
-0.0075939735397696495,
-0.018373925238847733,
0.00444160308688879,
0.0427585244178772,
-0.030060075223445892,
-0.027950430288910866,
-0.04124388098716736,
-0.011519976891577244,
0.04452318698167801,
0.011129573918879032,
0.004518622066825628,
0.0007435894221998751,
0.036314040422439575,
0.02146020345389843,
0.010534454137086868,
-0.014883275143802166,
-0.06095956265926361,
-0.006184602156281471,
-0.07409204542636871,
-0.05574610456824303,
0.038516636937856674,
0.023892009630799294,
-0.03839656338095665,
-0.007346208207309246,
-0.03350327908992767,
0.0024669505655765533,
0.014130857773125172,
0.036231089383363724,
-0.029229270294308662,
0.09968819469213486,
-0.019859090447425842,
0.03217466548085213,
-0.02668190933763981,
0.014049526304006577,
0.11001642793416977,
0.06934956461191177,
0.011786730960011482,
-0.056656062602996826,
0.013857627287507057,
-0.0350874587893486,
-0.03301241621375084,
-0.04636849835515022,
0.0640854462981224,
-0.011011209338903427,
-0.014487650245428085,
-0.012830475345253944,
0.04250802472233772,
-0.025989560410380363,
-0.04458403214812279,
0.04071329906582832,
-0.03349313139915466,
-0.019077276811003685,
0.0008108372567221522,
0.007668958976864815,
0.019212594255805016,
0.004782673437148333,
-0.021159397438168526,
0.044381219893693924,
-0.007027840707451105,
0.02176828496158123,
-0.011934819631278515,
-0.012066643685102463,
0.005140063818544149,
0.03186721354722977,
-0.05283300578594208,
0.022483037784695625,
0.007650585845112801,
-0.007360014133155346,
-0.010378142818808556,
-0.014266768470406532,
0.020385976880788803,
0.006369958631694317,
0.016374340280890465,
0.04955753684043884,
-0.003973923157900572,
0.017926204949617386,
0.022020582109689713,
-0.013410673476755619,
-0.05538826435804367,
-0.011876697652041912,
-0.06891796737909317,
0.06369186192750931,
-0.01244038064032793,
-0.009560524486005306,
0.035754501819610596,
-0.035261329263448715,
0.00424555316567421,
-0.02241336926817894,
-0.03343809396028519,
-0.012514322996139526,
0.01928229071199894,
0.015747807919979095,
0.009247089736163616,
0.010400515981018543,
0.05388306453824043,
0.020778337493538857,
0.03273496776819229,
-0.005331247579306364,
-0.014195979572832584,
0.03805554285645485,
-0.04169983044266701,
0.03834589943289757,
-0.0006055752164684236,
-0.0350518673658371,
-0.006066452711820602,
-0.04044109582901001,
-0.008769333362579346,
-0.018176542595028877,
0.02129778265953064,
0.0027364350389689207,
0.03636295720934868,
0.009577185846865177,
-0.021204126998782158,
0.007146856747567654,
-0.025270115584135056,
0.029942961409687996,
-0.02772493287920952,
-0.03875721991062164,
-0.009765218943357468,
0.014693697914481163,
-0.006686108652502298,
0.030490759760141373,
-0.013512243516743183,
-0.020236128941178322,
-0.03938999027013779,
-0.009613246656954288,
-0.025829268619418144,
-0.023177646100521088,
-0.05806081369519234,
-0.009332810528576374,
-0.007680045906454325,
0.001926289638504386,
0.006097130477428436,
0.014264306984841824,
0.01521334145218134,
0.018774960190057755,
0.009680351242423058,
0.04239968955516815,
-0.0048630330711603165,
0.005289916880428791,
0.02452058717608452,
-0.024011651054024696,
0.009420474991202354,
-0.010136918164789677,
0.0314912311732769,
-0.045651406049728394,
-0.043757516890764236,
-0.017244838178157806,
0.017822304740548134,
0.017112379893660545,
0.016725141555070877,
-0.013954243622720242,
0.021775024011731148,
0.01803339459002018,
0.0027199385222047567,
-0.044027332216501236,
0.003051064908504486,
-0.03666968643665314,
0.003192004282027483,
0.012185067869722843,
-0.025069445371627808,
0.03590879216790199,
0.019449546933174133,
-0.04784538596868515,
-0.04890989512205124,
-0.00725538982078433,
0.02746448665857315,
-0.05447103828191757,
0.029632922261953354,
0.0459296740591526,
0.029360488057136536,
0.07265821844339371,
-0.002057354897260666,
-0.015805628150701523,
0.00030583736952394247,
-0.0706331729888916,
-0.059341754764318466,
0.025742463767528534,
0.008992661722004414,
0.008386386558413506,
0.0046570803970098495,
-0.0188835971057415,
-0.01583791896700859,
0.0635610893368721,
-0.005369651596993208,
0.020922603085637093,
0.0145376892760396,
-0.014730038121342659,
-0.005902539938688278,
-0.04710964113473892,
0.011058111675083637,
0.016280489042401314,
-0.0031516323797404766,
0.017428213730454445,
-0.0029921114910393953,
-0.006240712013095617,
-0.02349201776087284,
-0.0012022082228213549,
-0.018333086743950844,
-0.02664737030863762,
0.009725882671773434,
-0.0031588624697178602,
0.04347332939505577,
0.05905405804514885,
-0.05230316147208214,
0.042664121836423874,
0.03551128879189491,
0.0101156672462821,
-0.06728014349937439,
0.011828364804387093,
0.003915600012987852,
0.027776584029197693,
0.058743853121995926,
-0.040028709918260574,
0.02984580583870411,
0.028897695243358612,
-0.019764306023716927,
0.015021178871393204,
0.005757251754403114,
-0.015379555523395538,
-0.02489994280040264,
-0.018837755545973778,
-0.025642262771725655,
0.0410686619579792,
0.07123460620641708,
0.08398597687482834,
0.0073934984393417835,
0.008886940777301788,
0.010772692039608955,
-0.03728346526622772,
-0.01250271312892437,
0.009023734368383884,
-0.033409468829631805,
-0.009901360608637333,
0.06522782146930695,
0.0036193146370351315,
-0.041870053857564926,
0.04112808033823967,
-0.004983325954526663,
0.0009494427358731627,
-0.003880735719576478,
-0.006995409727096558,
0.026198187842965126,
0.004470253363251686,
0.024278244003653526,
-0.018536509945988655,
0.005666473880410194,
0.04003463312983513,
-0.023325642570853233,
0.007999842055141926,
-0.0015259335050359368,
0.019983433187007904,
-0.0026497726794332266,
-0.05773172900080681,
-0.022735361009836197,
0.030535561963915825,
-0.011126558296382427,
-0.059921689331531525,
-0.018981970846652985,
-0.03548002615571022,
0.04510755091905594,
-0.007156874984502792,
-0.0387021042406559,
-0.03920627757906914,
0.0018221873324364424,
0.020817099139094353,
-0.013916589319705963,
-0.006281806621700525,
0.05166138708591461,
-0.028477948158979416,
-0.03768134489655495,
0.007855841889977455,
-0.01968351937830448,
0.022270213812589645,
-0.02963845245540142,
-0.00718383165076375,
-0.011591723188757896,
-0.012378517538309097,
0.00048472019261680543,
-0.008694459684193134,
0.005799038335680962,
0.014214618131518364,
0.00922227930277586,
0.0066709574311971664,
0.0035365731455385685,
-0.016881873831152916,
-0.03719150647521019,
-0.060027968138456345,
0.021616213023662567,
-0.01893237978219986,
0.024158552289009094,
-0.03475433588027954,
-0.013702379539608955,
-0.028703855350613594,
0.0009538084268569946,
0.03881610557436943,
-0.07995577156543732,
-0.009225966408848763,
0.02697164937853813,
0.014718933030962944,
0.019903864711523056,
-0.03066565841436386,
0.021664559841156006,
0.026588618755340576,
-0.006177176255732775,
-0.010011211968958378,
0.02194228209555149,
-0.011735493317246437,
0.008482888340950012,
0.029058506712317467,
-0.02346554957330227,
0.027802661061286926,
0.022783035412430763,
-0.024906670674681664,
0.01545790396630764,
0.04162430763244629,
-0.02716120518743992,
0.04115203022956848,
-0.012364054098725319,
0.021549919620156288,
0.005080472212284803,
-0.01725655235350132,
-0.04827096313238144,
0.013902917504310608,
-0.033074770122766495,
-0.045196205377578735,
-0.020920932292938232,
-0.020923905074596405,
0.026023637503385544,
-0.05187186598777771,
-0.038919586688280106,
0.07073243707418442,
-0.02322508580982685,
-0.022878026589751244,
0.0470864437520504,
-0.005737247411161661,
0.015216713771224022,
-0.0097352871671319,
-0.020889461040496826,
-0.0037389113567769527,
0.02752945013344288,
0.019451681524515152,
0.013049970380961895,
0.04924733564257622,
0.009275087155401707,
-0.010257240384817123,
0.031692277640104294,
-0.04674708843231201,
-0.0010988296708092093,
-0.0026877059135586023,
0.05330704152584076,
-0.02840692549943924,
-0.016965096816420555,
0.016917191445827484,
0.023864561691880226,
0.00250823050737381,
-0.02110738307237625,
-0.011619663797318935,
0.05729623883962631,
-0.012657214887440205,
0.024722378700971603,
-0.0558919720351696,
0.004398811142891645,
-0.019415471702814102,
0.030438000336289406,
0.012048084288835526,
0.0444079264998436,
-0.0072217113338410854,
-0.020234204828739166,
0.006380241829901934,
0.014169573783874512,
0.029326526448130608,
-0.02097216621041298,
-0.012882152572274208,
0.0071415528655052185,
-0.027093369513750076,
0.0034015425480902195,
-0.044894393533468246,
-0.002912994474172592,
-0.02451193332672119,
0.01876327395439148,
0.017242005094885826,
0.050889164209365845,
-0.03909500688314438,
0.01571277529001236,
-0.0634348914027214,
0.08156484365463257,
-0.07664447277784348,
0.01935085654258728,
-0.011865435168147087,
0.005181762855499983,
0.005878944881260395,
-0.00003274274058640003
] |
<p>In <a href="http://en.wikipedia.org/wiki/The_Adventures_of_Tintin_%28film%29" rel="nofollow"><em>The Adventures of Tintin</em></a>, an opera singer (the Milanese Nightingale) broke a bulletproof glass case using her voice. Is that scientifically possible?</p>
<p>From the <em><a href="http://en.wikipedia.org/wiki/Bulletproof_glass" rel="nofollow">Wikipedia</a></em> page, a typical bulletproof glass</p>
<blockquote>
<p>is usually made from a combination of two or more types of glass, one hard and one soft. The softer layer makes the glass more elastic, so it can flex instead of shatter.</p>
</blockquote>
<p>When they <a href="http://www.youtube.com/watch?v=IZD8ffPwXRo#t=2m05s" rel="nofollow">did it on Mythbusters</a>, the singer had to stand really close to the glass that is so thin for it to break.
Any thoughts on whether the movie scene is even humanly possible?</p>
| 7,648 |
[
-0.04071790352463722,
-0.07544699311256409,
0.018935557454824448,
-0.039723239839076996,
0.01885101944208145,
0.009941798634827137,
-0.003400738351047039,
-0.021205658093094826,
-0.003450544085353613,
0.006506533827632666,
0.05278535187244415,
0.016533266752958298,
0.0265826229006052,
0.04022163152694702,
-0.02018900029361248,
-0.006102458573877811,
0.018666023388504982,
-0.04365694522857666,
0.0128016397356987,
-0.025224901735782623,
-0.012603350915014744,
0.03354862704873085,
-0.05407465621829033,
0.021627817302942276,
-0.02658833935856819,
0.0017700109165161848,
0.027158144861459732,
-0.027455922216176987,
0.002837213920429349,
0.01706530898809433,
-0.007309177424758673,
0.007463205140084028,
0.03573567047715187,
0.011900539509952068,
0.041807521134614944,
0.0031612152233719826,
-0.02310798317193985,
0.0355365052819252,
-0.000395378126995638,
-0.008005945943295956,
-0.028068210929632187,
0.018744399771094322,
0.037686631083488464,
0.06349111348390579,
-0.029556097462773323,
0.0008390012662857771,
-0.0060453941114246845,
-0.03532915934920311,
0.01249600574374199,
-0.05342962220311165,
0.04732828587293625,
0.009263711050152779,
0.052265714854002,
0.04897850379347801,
0.018817994743585587,
-0.03933989629149437,
0.04829616844654083,
0.07478898018598557,
-0.016497407108545303,
-0.051250822842121124,
0.0027469501364976168,
-0.018264448270201683,
-0.025656012818217278,
0.02641472779214382,
0.002214292995631695,
0.026332901790738106,
-0.027958575636148453,
-0.04498821869492531,
0.03136904537677765,
0.007232361473143101,
0.010722827166318893,
0.020078642293810844,
0.03839629143476486,
-0.02004339173436165,
0.035760436207056046,
-0.029459089040756226,
0.022708164528012276,
0.01493854634463787,
0.03776824474334717,
0.03432619571685791,
0.025996854528784752,
-0.009343801997601986,
0.03491993620991707,
0.05577727034687996,
0.016113022342324257,
-0.04456043243408203,
0.11330892890691757,
-0.025566913187503815,
-0.0011035281931981444,
0.027469666674733162,
0.01874571479856968,
-0.029711149632930756,
0.019250240176916122,
0.04075111076235771,
-0.04102737456560135,
0.030845388770103455,
0.0149020254611969,
0.07563208788633347,
-0.012171094305813313,
-0.011558356694877148,
0.005206964444369078,
0.026186320930719376,
0.03222107142210007,
0.08583945035934448,
-0.00323486584238708,
-0.03282776474952698,
-0.000360793259460479,
0.018429148942232132,
0.033355921506881714,
0.008630767464637756,
-0.056994032114744186,
0.009619085118174553,
-0.009815435856580734,
-0.03592536970973015,
-0.0003948786179535091,
0.013390351086854935,
-0.014942639507353306,
-0.020116494968533516,
0.0763934925198555,
0.059820763766765594,
0.0302240252494812,
-0.04702521488070488,
0.026561079546809196,
-0.026315728202462196,
-0.05227671563625336,
0.019941359758377075,
0.006726664490997791,
-0.009532934986054897,
-0.021967288106679916,
0.05916917324066162,
0.029475156217813492,
-0.015864908695220947,
0.006468987092375755,
-0.006970273330807686,
0.05962817743420601,
-0.025730138644576073,
-0.09405633807182312,
-0.031153203919529915,
0.060995712876319885,
0.0034721402917057276,
-0.02201894298195839,
-0.08659160137176514,
0.024052642285823822,
-0.03069947473704815,
0.06157458573579788,
-0.0067908125929534435,
0.02729778178036213,
-0.013183411210775375,
0.03619637340307236,
0.013217068277299404,
-0.014116180129349232,
0.032000791281461716,
0.003130644792690873,
-0.019601114094257355,
-0.0033360780216753483,
-0.07314258068799973,
0.02332962118089199,
0.020861808210611343,
0.029587021097540855,
-0.030114881694316864,
0.03818885236978531,
-0.028019702062010765,
0.0026153819635510445,
0.016200363636016846,
0.0017704436322674155,
-0.017207957804203033,
0.058911923319101334,
0.005658688489347696,
-0.005337767768651247,
0.024716349318623543,
0.0055941129103302956,
0.026904430240392685,
0.029512878507375717,
-0.012674435041844845,
0.030539661645889282,
-0.02843356877565384,
0.001731903525069356,
-0.051265183836221695,
0.03020087629556656,
0.017185835167765617,
-0.032382771372795105,
0.01434693019837141,
-0.03753352910280228,
0.007265507243573666,
0.04785618185997009,
0.023116152733564377,
-0.02691817097365856,
0.015121808275580406,
0.0029109332244843245,
-0.05556955188512802,
-0.02123425528407097,
-0.023140517994761467,
0.0496445931494236,
-0.02291611023247242,
-0.01651468314230442,
0.0046225739642977715,
-0.058127839118242264,
0.07452144473791122,
-0.04800507053732872,
0.007454649079591036,
-0.035894013941287994,
-0.013026679866015911,
0.025462588295340538,
0.006664666347205639,
0.001219655736349523,
0.06519988924264908,
-0.012113150209188461,
-0.017684023827314377,
0.04878249019384384,
-0.02941041626036167,
0.011481264606118202,
0.04085085541009903,
-0.03659050539135933,
0.03302023559808731,
-0.001751322764903307,
-0.03671250119805336,
0.04516381770372391,
-0.00409554922953248,
0.009488251991569996,
0.03405565023422241,
0.005752198863774538,
0.03597448393702507,
0.01380911748856306,
-0.02000628598034382,
0.008234457112848759,
0.010657898150384426,
0.01249074749648571,
0.01748635806143284,
0.01631954312324524,
-0.0420653410255909,
-0.08390238881111145,
-0.03243447467684746,
0.037574976682662964,
0.015042215585708618,
0.0008832337916828692,
0.022307218983769417,
0.006673612166196108,
0.03902500495314598,
0.039374202489852905,
-0.025512058287858963,
0.0023675239644944668,
-0.01594000868499279,
-0.020166272297501564,
0.01633874885737896,
0.011425795033574104,
0.008455094881355762,
-0.02447168156504631,
0.007995137013494968,
0.03337319940328598,
-0.015956925228238106,
0.008142917416989803,
0.00019001941836904734,
-0.001061793533153832,
0.027021562680602074,
0.007827701978385448,
-0.019335897639393806,
0.052811238914728165,
-0.03595820441842079,
0.014419368468225002,
0.037763725966215134,
0.01798018254339695,
0.005448644049465656,
-0.062091901898384094,
0.007243475876748562,
-0.015370977111160755,
0.025390127673745155,
-0.01765141636133194,
0.02097480557858944,
0.023940151557326317,
-0.03863658010959625,
-0.02921488881111145,
0.010684790089726448,
0.02274392917752266,
0.019635362550616264,
-0.007346687372773886,
0.00022071140119805932,
-0.00043164720409549773,
0.05235935375094414,
-0.055824700742959976,
-0.0003243224637117237,
0.00041968192090280354,
-0.04244144260883331,
-0.014239401556551456,
-0.017894970253109932,
-0.021073006093502045,
0.022275246679782867,
0.006753489375114441,
0.022380420938134193,
0.011661860160529613,
-0.00264909490942955,
-0.0009437846019864082,
0.03314730152487755,
0.003827938111498952,
-0.02192923054099083,
0.02006874419748783,
-0.03388948366045952,
0.0540325902402401,
-0.00863549392670393,
0.0026490045711398125,
-0.0015744984848424792,
0.03018386848270893,
-0.03929750621318817,
0.040769629180431366,
-0.0212467759847641,
-0.06971641629934311,
-0.04435250535607338,
-0.004042427055537701,
-0.0031112267170101404,
-0.005494184326380491,
0.009600719437003136,
0.03111143596470356,
0.009556506760418415,
-0.00006773334462195635,
-0.03620132431387901,
-0.02414979226887226,
0.026328403502702713,
-0.0008486575097776949,
0.053437601774930954,
-0.01617101952433586,
-0.02521907165646553,
0.07328172773122787,
0.022976811975240707,
-0.06691649556159973,
-0.03634854406118393,
-0.051306262612342834,
-0.01828516460955143,
-0.04929950460791588,
-0.0016202621627599,
0.05519869178533554,
-0.024774346500635147,
0.0597664900124073,
0.023442979902029037,
-0.0028558014892041683,
0.005992131773382425,
0.013593105599284172,
-0.010046148672699928,
-0.032489750534296036,
-0.0015268223360180855,
-0.06832336634397507,
0.05256002023816109,
0.04824711009860039,
-0.01836925745010376,
0.03257536515593529,
-0.058299675583839417,
0.041568003594875336,
0.0358695425093174,
-0.03197382763028145,
0.0281679630279541,
0.014575433917343616,
-0.03228766471147537,
-0.028601329773664474,
0.02144492417573929,
0.010040590539574623,
-0.02966197207570076,
0.014385851100087166,
0.031408436596393585,
0.04572472721338272,
-0.0022533852607011795,
-0.030262529850006104,
0.0041032577864825726,
0.060665201395750046,
-0.016048628836870193,
-0.015325833112001419,
-0.022923218086361885,
0.050522416830062866,
0.020531870424747467,
-0.0018596142763271928,
-0.0037455460987985134,
0.05670029670000076,
0.042109616100788116,
0.06825456023216248,
0.0027407698798924685,
-0.021297341212630272,
0.008811584673821926,
-0.058467235416173935,
0.0042938971891999245,
-0.016649793833494186,
-0.019712433218955994,
0.005311630200594664,
0.02426568791270256,
0.04492751508951187,
0.06123180687427521,
0.026513749733567238,
-0.004839029163122177,
-0.07331378012895584,
-0.00015821485430933535,
0.0024015663657337427,
-0.022017724812030792,
-0.026603784412145615,
-0.04798348248004913,
-0.05192409083247185,
0.0017505526775494218,
-0.008646897971630096,
-0.026527300477027893,
0.03032905049622059,
-0.04592087119817734,
-0.02905278280377388,
-0.03877123072743416,
-0.029395276680588722,
0.02948877029120922,
0.03746536746621132,
0.05119512230157852,
0.0001000936099444516,
0.013430660590529442,
-0.01643260568380356,
0.02717444859445095,
0.012812953442335129,
-0.012062578462064266,
-0.01579643040895462,
-0.00945672020316124,
0.05258260667324066,
-0.008803166449069977,
0.012772529385983944,
0.010869079269468784,
-0.0028745464514940977,
0.004447629675269127,
0.016589676961302757,
-0.0038991698529571295,
0.018137894570827484,
-0.06523802131414413,
0.0037116289604455233,
-0.006160990335047245,
-0.008757345378398895,
0.028758209198713303,
-0.031423419713974,
0.009373935870826244,
0.00602441281080246,
0.010954058729112148,
-0.05114210024476051,
0.012680266052484512,
0.03887404873967171,
-0.0005748338298872113,
0.005638810805976391,
-0.052941374480724335,
-0.023916056379675865,
-0.03471080958843231,
-0.03005349636077881,
0.00970105454325676,
0.05429886654019356,
0.008334123529493809,
0.022626549005508423,
0.04275260120630264,
-0.005203646142035723,
-0.05033566430211067,
0.05229055881500244,
-0.00696919159963727,
-0.010298090055584908,
-0.0009658216149546206,
-0.021812284365296364,
-0.0015476392582058907,
0.019111908972263336,
0.03698159381747246,
0.002409393200650811,
-0.04190591722726822,
-0.06490525603294373,
-0.01170386467128992,
0.03562808781862259,
0.042057596147060394,
-0.04182640463113785,
0.0307537280023098,
-0.03125434368848801,
-0.030453147366642952,
0.017031537368893623,
0.00042021539411507547,
-0.015358319506049156,
-0.02146797813475132,
0.002723743673413992,
-0.05345259606838226,
-0.0300296600908041,
0.014132712036371231,
-0.005217708647251129,
-0.014440536499023438,
-0.026206064969301224,
0.0036917845718562603,
-0.0168332327157259,
-0.027259407564997673,
0.022058282047510147,
-0.0011964199366047978,
0.041978511959314346,
-0.00009623894584365189,
0.011038324795663357,
-0.025170952081680298,
0.006913371849805117,
-0.03243652358651161,
-0.04159305617213249,
0.009137721732258797,
-0.021413816139101982,
-0.04361787438392639,
-0.000055441170843550935,
-0.032713986933231354,
-0.027229582890868187,
0.03802160918712616,
0.013003063388168812,
-0.008104820735752583,
-0.0004932248848490417,
-0.0119519317522645,
-0.01382807083427906,
0.02384531870484352,
-0.0025322064757347107,
0.02553555555641651,
0.06200019642710686,
0.008862881921231747,
0.005293790251016617,
-0.039007727056741714,
0.01983797736465931,
-0.003960017114877701,
-0.009736420586705208,
-0.00996837206184864,
0.0028250236064195633,
-0.0010563078103587031,
0.006949266884475946,
0.03152267634868622,
0.048099335283041,
-0.012931636534631252,
-0.014395705424249172,
0.004298167768865824,
0.014631972648203373,
0.008560646325349808,
0.00907694362103939,
-0.013745916076004505,
0.03315635025501251,
-0.015876872465014458,
0.0014816035982221365,
-0.014160014688968658,
0.010530560277402401,
-0.004232662729918957,
0.04956870898604393,
-0.025911469012498856,
-0.002921580569818616,
-0.0653933584690094,
-0.018266914412379265,
0.019931087270379066,
-0.06896155327558517,
0.04651926830410957,
-0.018040243536233902,
0.030934546142816544,
0.043384991586208344,
-0.013176241889595985,
0.018794851377606392,
-0.007341240998357534,
-0.015847932547330856,
0.0748131275177002,
-0.06420855969190598,
0.04727952554821968,
0.00363318738527596,
-0.0030127582140266895,
-0.020757747814059258,
-0.001686113653704524,
0.04083883389830589,
0.0088981157168746,
-0.01638604886829853,
-0.027449995279312134,
-0.0063138990662992,
-0.012011511251330376,
-0.015087869949638844,
0.00785842165350914,
0.02542298659682274,
-0.044274065643548965,
-0.008747528307139874,
0.007433478720486164,
-0.03673770651221275,
0.05047622695565224,
0.013475904241204262,
0.0014697500737383962,
-0.021745242178440094,
-0.012823138386011124,
-0.009525475092232227,
-0.03474544361233711,
0.026457203552126884,
-0.020872896537184715,
-0.030776413157582283,
0.005147273186594248,
0.01378583163022995,
0.0158905778080225,
-0.02159043774008751,
0.04303259402513504,
0.04385252669453621,
0.0061317672953009605,
0.0007070567226037383,
-0.011989173479378223,
0.021518854424357414,
0.009986698627471924,
0.02770070917904377,
-0.0458577461540699,
0.029093893244862556,
-0.04842161014676094,
-0.028938112780451775,
0.0205378420650959,
0.027330635115504265,
0.03256787732243538,
0.0026182509027421474,
0.05346178263425827,
-0.035909269005060196,
0.01806986890733242,
0.057506538927555084,
-0.04958310350775719,
0.05850525200366974,
-0.025043195113539696,
-0.009031236171722412,
-0.02938307262957096,
-0.020363112911581993,
-0.015421008691191673,
-0.027081850916147232,
-0.0034170581493526697,
0.01479585561901331,
-0.008581598289310932,
-0.06460216641426086,
0.026289811357855797,
-0.00036827303119935095,
-0.025193098932504654,
0.0007109653088264167,
-0.016574690118432045,
-0.013776280917227268,
0.03173254057765007,
-0.03062966652214527,
0.04565178230404854,
-0.020445797592401505,
0.04579012468457222,
0.01730377785861492,
0.0380217507481575,
0.01705985516309738,
-0.03308290243148804,
0.0587962381541729,
0.008355961181223392,
0.020095868036150932,
-0.02427711710333824,
0.007055927067995071,
0.06996897608041763,
-0.062352102249860764,
0.014507845975458622,
0.00872207060456276,
0.04095789045095444,
0.045270536094903946,
0.01664540357887745,
-0.021600179374217987,
-0.04623372107744217,
-0.023368224501609802,
-0.032497674226760864,
0.0248283501714468,
0.0018200278282165527,
0.010828562080860138,
0.03758589178323746,
-0.03239517658948898,
-0.0019517987966537476,
0.009421007707715034,
0.021746892482042313,
-0.016029970720410347,
-0.06565169245004654,
0.011121110990643501,
0.004124649800360203,
-0.01458343118429184,
0.043002478778362274,
0.010337669402360916,
-0.02257070317864418,
0.055246591567993164,
-0.025853727012872696,
0.06215493753552437,
0.024935424327850342,
0.04632294550538063,
-0.004879401996731758,
0.05745364725589752,
0.0008000099915079772,
0.02505355142056942,
-0.006656258832663298,
0.034211430698633194,
0.13480712473392487,
0.03344070911407471,
0.028312627226114273,
-0.005755673162639141,
-0.032411567866802216,
0.004696602467447519,
-0.01259833574295044,
-0.004707137122750282,
-0.013804485090076923,
0.004184460733085871,
-0.015649227425456047,
0.00028445792850106955,
0.11629237234592438,
0.0248353760689497,
0.029889607802033424,
-0.0027016049716621637,
-0.03514310345053673,
0.013996968977153301,
0.024774219840765,
-0.002890672069042921,
-0.030664123594760895,
0.00020534185750875622,
-0.010614453814923763,
0.023238960653543472,
-0.03229490667581558,
-0.025958839803934097,
-0.0171124916523695,
-0.045326314866542816,
0.05073787644505501,
0.032136399298906326,
-0.05517587810754776,
-0.01783917285501957,
0.02334832027554512,
-0.008816318586468697,
-0.004053195007145405,
0.0042133270762860775,
0.01584642194211483,
-0.00690589239820838,
-0.00782718975096941,
0.014398245140910149,
0.014219888485968113,
-0.011113733053207397,
0.021880395710468292,
0.019036436453461647,
-0.046856001019477844,
-0.04678552225232124,
-0.003975562751293182,
-0.012022250331938267,
-0.0007098761852830648,
-0.011373206973075867,
0.009383956901729107,
-0.010979730635881424,
0.01088044699281454,
-0.03265039622783661,
-0.03174689784646034,
0.019287772476673126,
0.014305579476058483,
0.010263048112392426,
-0.07773879170417786,
-0.006352055352181196,
-0.007357445079833269,
-0.008969614282250404,
-0.03493599221110344,
-0.030390765517950058,
0.026227764785289764,
-0.03910408169031143,
-0.03688334301114082,
0.01817585714161396,
-0.023622453212738037,
-0.04288627952337265,
-0.04716412350535393,
-0.0061740633100271225,
-0.07938912510871887,
0.0006692680763080716,
0.006665131542831659,
0.05263502895832062,
0.039302367717027664,
0.0094566335901618,
-0.005394600797444582,
-0.023301785811781883,
-0.013592740520834923,
0.05691390112042427,
-0.0036512550432235003,
-0.001468577771447599,
-0.048525404185056686,
-0.031521935015916824,
0.04146037623286247,
0.011105377227067947,
0.005699301604181528,
-0.0005680897156707942,
-0.001194029115140438,
0.03952481225132942,
0.036343444138765335,
-0.04524443671107292,
-0.030173063278198242,
-0.00009509835945209488,
0.0005245553911663592,
-0.004910798743367195,
-0.014600730501115322,
0.042507171630859375,
-0.005864948965609074,
-0.01735539734363556,
0.014013166539371014,
0.01153892558068037,
-0.03448762372136116,
-0.015331009402871132,
0.028501074761152267,
-0.025845590978860855,
-0.0036721352953463793,
0.004246101249009371,
0.0313880555331707,
-0.010854963213205338,
-0.049377840012311935,
0.0017221937887370586,
-0.019141361117362976,
-0.013932461850345135,
0.017105771228671074,
0.014451497234404087,
0.009974347427487373,
-0.021984810009598732,
-0.002261603018268943,
-0.03784439340233803,
-0.011314256116747856,
-0.014603490009903908,
-0.021531425416469574,
-0.01821199804544449,
0.014488725923001766,
-0.021891379728913307,
0.018235664814710617,
-0.02326575666666031,
-0.03559352830052376,
0.021275676786899567,
0.005286460742354393,
-0.021602725610136986,
-0.03853805735707283,
0.005582075100392103,
-0.013471217826008797,
-0.012399738654494286,
-0.00895673967897892,
-0.013682592660188675,
0.051113683730363846,
-0.04093369096517563,
-0.061907809227705,
0.00009271643648389727,
-0.042440347373485565,
0.009849590249359608,
-0.008255455642938614,
-0.000982820289209485,
0.02082735113799572,
0.11502178758382797,
-0.0018699156353250146,
-0.005942249670624733,
0.03525495529174805,
-0.04884185642004013,
-0.014500067569315434,
-0.008083071559667587,
0.01740770787000656,
-0.005007483530789614,
-0.016158612444996834,
0.052388716489076614,
0.04019194096326828,
0.0030965604819357395,
0.014411752112209797,
0.042861636728048325,
-0.058008912950754166,
0.008850901387631893,
0.009246350266039371,
0.0500396303832531,
0.0025816436391323805,
0.05026751384139061,
0.0029659965075552464,
0.04216178506612778,
0.005147385410964489,
-0.030711067840456963,
-0.11788107454776764,
-0.01854080520570278,
-0.015620552003383636,
-0.022722512483596802,
0.037751197814941406,
-0.07683073729276657,
0.05453414097428322,
0.004573202691972256,
-0.054420601576566696,
-0.007363811135292053,
-0.03234200179576874,
-0.03133460879325867,
-0.035831425338983536,
0.029692785814404488,
-0.04317395016551018,
0.0009286814602091908,
0.01563548855483532,
0.04277734085917473,
0.04723694175481796,
0.04246588796377182,
-0.017115937545895576,
0.0025594031903892756,
0.003299939911812544,
0.01576555334031582,
0.009879120625555515,
0.0027309563010931015,
0.08497566729784012,
-0.03202377259731293,
-0.04168582707643509,
-0.000976874609477818,
0.005163758993148804,
0.04311562702059746,
0.01389266550540924,
-0.024458814412355423,
0.007934949360787868,
-0.025043155997991562,
-0.02033976837992668,
0.030407357960939407,
-0.00481816241517663,
0.06023816019296646,
0.018479233607649803,
0.009193398989737034,
-0.022610649466514587,
-0.007104513701051474,
0.013609766960144043,
-0.0035561707336455584,
-0.034130144864320755,
0.005177101120352745,
0.012326390482485294,
0.0005590619402937591,
-0.0003415158425923437,
0.01901542954146862,
0.008715376257896423,
-0.0064812651835381985,
0.006667356472462416,
-0.028956493362784386,
0.012466682121157646,
-0.012282820418477058,
0.06056183949112892,
-0.008248137310147285,
0.03968515619635582,
-0.04352628067135811,
-0.009336023591458797,
-0.017208542674779892,
-0.020405596122145653,
-0.06441062688827515,
0.010884050279855728,
-0.019129399210214615,
0.00783560425043106,
0.016722407191991806,
-0.00341280666179955,
0.010990582406520844,
-0.029261162504553795,
0.027323758229613304,
0.033628303557634354,
0.03341992199420929,
0.011625861749053001,
-0.025307582691311836,
-0.042505599558353424,
-0.0847211703658104,
0.01707969419658184,
-0.0026210297364741564,
-0.00654431851580739,
-0.04729963466525078,
-0.02874089777469635,
0.012869047932326794,
0.046353768557310104,
0.07342158257961273,
-0.043793242424726486,
0.023933690041303635,
-0.0032763248309493065,
-0.024190865457057953,
-0.01654212549328804,
-0.026402799412608147,
-0.02703329361975193,
0.00029474790790118277,
-0.012810676358640194,
-0.03617120906710625,
0.028628626838326454,
-0.024850672110915184,
0.007059446536004543,
0.049725376069545746,
-0.00261089694686234,
0.021680008620023727,
0.018780283629894257,
-0.018508726730942726,
0.003980994690209627,
0.009589492343366146,
0.008722478523850441,
0.09478561580181122,
-0.03138495981693268,
-0.015223588794469833,
-0.03598424792289734,
0.014835127629339695,
-0.03446074575185776,
0.03769723325967789,
-0.021133743226528168,
0.00557671207934618,
-0.05347774922847748,
-0.024657661095261574,
0.01757785864174366,
-0.03454845771193504,
0.02458738535642624,
0.0157261174172163,
-0.01902848482131958,
-0.0066865370608866215,
0.009700484573841095,
0.012679604813456535,
0.025293918326497078,
-0.038374751806259155,
-0.005322734825313091,
0.021853333339095116,
0.010396011173725128,
-0.008787516504526138,
0.01771414279937744,
0.034509945660829544,
-0.023511774837970734,
-0.015913760289549828,
0.0334550142288208,
0.005302808713167906,
-0.030568057671189308,
0.014489513821899891,
0.014350799843668938,
-0.029314380139112473,
-0.025584159418940544,
0.008432755246758461,
-0.005704427603632212,
-0.01898902654647827,
0.02223341539502144,
-0.008938130922615528,
0.07340115308761597,
0.008370926603674889,
0.025782737880945206,
0.007663366384804249,
0.032841891050338745,
-0.01783205196261406,
0.018534593284130096,
0.020483488216996193,
-0.009989609010517597,
0.02016153745353222,
-0.03391920030117035,
-0.022501565515995026,
0.019977761432528496,
-0.009543395601212978,
-0.03970250487327576,
-0.009574458003044128,
-0.045348793268203735,
-0.004796444438397884,
-0.05408177897334099,
0.0006009445060044527,
-0.01576143503189087,
0.0100619001314044,
0.028591858223080635,
0.01028408482670784,
-0.03196552395820618,
-0.013742415234446526,
-0.02683434635400772,
-0.0171623807400465,
0.05464950203895569,
-0.05588420853018761,
0.022465920075774193,
-0.04467029124498367,
0.020701946690678596,
-0.03225807473063469,
-0.006264861207455397
] |
<p>The Super-Symmetry operators reduce or increase helicity by a half unit. And this result in an algebra that where the fermions and bosons vacuum energy sums to zero. And it seems to generate gravity, when the upgraded to a local symmetry. But as yet, physicist seem to have found no good way to break super-symmetry, i.e. Supergravity. What other transformations can one do at the same time as applying a super-symmetry operator? And still keep the good properties of super-symmetry.</p>
<p>At first view, I think one could swap left and right handed particles/fields, and swap sets of particles from one group containing both fermion and boson to another. I.e. switch to the other one of a direct product group. Does mirror-symmetry commute and/or co-operate with super-symmetry?</p>
| 7,649 |
[
-0.030271831899881363,
0.00681327423080802,
0.015387071296572685,
-0.016820864751935005,
0.040407486259937286,
0.028151344507932663,
-0.0260662492364645,
-0.0552581325173378,
-0.008562632836401463,
-0.05062440037727356,
0.0005485425936058164,
-0.013649345375597477,
0.022199446335434914,
0.02195822261273861,
0.011196608655154705,
0.0016296998364850879,
0.01057411264628172,
-0.041939590126276016,
-0.026638738811016083,
-0.003687361255288124,
-0.009145475924015045,
0.03296680375933647,
-0.017594339326024055,
0.006715100258588791,
0.008268357254564762,
-0.0013162726536393166,
-0.0014978090766817331,
0.0096494872123003,
-0.003714262507855892,
0.03778958320617676,
-0.00034753314685076475,
-0.019749492406845093,
0.015611742623150349,
0.044139936566352844,
-0.047056376934051514,
-0.002082427963614464,
0.005083183292299509,
-0.07192795723676682,
-0.008964347653090954,
0.005538633558899164,
-0.05103503540158272,
0.015586566179990768,
-0.03582095727324486,
0.055892184376716614,
0.017083726823329926,
0.021836988627910614,
-0.05060875788331032,
-0.003572294721379876,
0.07950162887573242,
-0.0705684944987297,
0.09987501055002213,
0.023911023512482643,
-0.003049802267923951,
-0.0063570463098585606,
-0.011311441659927368,
0.0014519346877932549,
0.04849286377429962,
0.05174921452999115,
0.02461640164256096,
-0.03542248159646988,
-0.02129427343606949,
-0.029832901433110237,
0.005700842477381229,
-0.033470991998910904,
-0.021537652239203453,
0.012063923291862011,
0.026230087503790855,
0.01698286272585392,
-0.006483403500169516,
0.01102339755743742,
0.010185346007347107,
-0.022203683853149414,
0.04558231681585312,
0.00483528058975935,
-0.001229426939971745,
-0.01887919194996357,
0.0020840608049184084,
-0.005002734251320362,
0.05532339587807655,
0.03910820931196213,
-0.00623101694509387,
0.013379381038248539,
0.02880004420876503,
0.0443812720477581,
0.020406551659107208,
-0.010654964484274387,
0.05568468198180199,
-0.006298246793448925,
0.008412298746407032,
0.05480277165770531,
-0.008740715682506561,
-0.03395457565784454,
0.04826940968632698,
0.004832237958908081,
-0.052941396832466125,
0.045263975858688354,
0.029596421867609024,
0.051219623535871506,
0.0008565399912185967,
-0.006184208672493696,
-0.01753702387213707,
0.009238175116479397,
-0.000748503371141851,
0.072667695581913,
0.00877430196851492,
-0.012977181002497673,
-0.03125917539000511,
-0.010215727612376213,
-0.03168141469359398,
0.015808621421456337,
-0.03591412305831909,
-0.040362898260354996,
-0.012673522345721722,
-0.006344675552099943,
0.015484207309782505,
-0.003771086223423481,
-0.003371769329532981,
-0.029917169362306595,
0.05591808632016182,
0.09587250649929047,
0.04914706200361252,
0.014085916802287102,
0.016360556706786156,
-0.03374740853905678,
-0.10155579447746277,
-0.023493820801377296,
0.03229564428329468,
0.0038049009162932634,
-0.030897539108991623,
0.0004957761848345399,
0.03984084725379944,
-0.04488799721002579,
-0.011534334160387516,
-0.054288774728775024,
0.014313735999166965,
-0.029770541936159134,
-0.08848776668310165,
-0.04055967926979065,
0.027997203171253204,
-0.005979808513075113,
-0.004018384963274002,
-0.0403713621199131,
0.01108335517346859,
0.028391148895025253,
0.10838581621646881,
-0.011018234305083752,
0.01596146821975708,
0.0047766114585101604,
0.03443722426891327,
0.029812630265951157,
0.03584163635969162,
-0.01474150363355875,
0.027689533308148384,
-0.033981889486312866,
-0.028470296412706375,
-0.04753891006112099,
0.01875169202685356,
0.02575606480240822,
-0.010870036669075489,
0.0010045451344922185,
0.0869881883263588,
-0.03473992645740509,
0.03854009509086609,
0.0071768308989703655,
-0.0017606581095606089,
-0.013509789481759071,
0.059990353882312775,
0.004132680594921112,
0.004979392047971487,
0.029335059225559235,
-0.024917947128415108,
0.02973523922264576,
0.024747628718614578,
0.042509812861680984,
0.019277768209576607,
-0.02344457618892193,
-0.005738270469009876,
-0.003877033945173025,
0.003666800679638982,
-0.029563715681433678,
0.00035677285632118583,
-0.011725131422281265,
0.003753610188141465,
0.00551881967112422,
-0.028788266703486443,
0.014806900173425674,
-0.012792588211596012,
-0.023491065949201584,
0.02540879137814045,
-0.07393567264080048,
-0.02530902810394764,
-0.06536301225423813,
-0.012301279231905937,
0.0019231332698836923,
-0.007849368266761303,
0.03908592835068703,
0.03534388169646263,
0.004492788575589657,
-0.05842512100934982,
-0.06244252994656563,
0.008109393529593945,
0.04871455207467079,
0.025153758004307747,
0.04091193899512291,
-0.011715061031281948,
0.02591315098106861,
0.0512780025601387,
-0.002412759233266115,
0.023616133257746696,
0.014291283674538136,
-0.008129194378852844,
0.01699262484908104,
0.0005958453984931111,
-0.002771012717857957,
-0.01406905148178339,
0.009366256184875965,
0.013794803991913795,
0.046164508908987045,
-0.04320118576288223,
0.025478608906269073,
-0.03288077190518379,
0.02688535489141941,
0.030782002955675125,
0.020692940801382065,
0.03009873814880848,
0.05595336854457855,
0.005297647323459387,
0.02153901383280754,
-0.006589737720787525,
-0.03265352174639702,
-0.046907372772693634,
0.0053635225631296635,
-0.000662213540636003,
0.013582631014287472,
-0.02551545947790146,
0.03792572394013405,
0.01702672429382801,
0.030325083062052727,
0.017927294597029686,
-0.017040928825736046,
-0.037226952612400055,
-0.007971595972776413,
0.028731966391205788,
-0.018269380554556847,
0.040555816143751144,
0.012262953445315361,
0.036626338958740234,
-0.00628342479467392,
0.002411553869023919,
0.0070184022188186646,
-0.052626240998506546,
0.02464119717478752,
0.010438745841383934,
0.000696812872774899,
0.03719069063663483,
-0.05626829341053963,
0.00916292704641819,
-0.0027749515138566494,
0.03183800354599953,
0.034431714564561844,
0.00677746906876564,
-0.0062579005025327206,
-0.04314868897199631,
-0.003588648745790124,
-0.023481136187911034,
0.01980673521757126,
0.009229437448084354,
-0.0355198010802269,
0.006311061326414347,
-0.01985926739871502,
-0.004539774265140295,
-0.011228779330849648,
0.0037171209696680307,
-0.03750115633010864,
0.005416072439402342,
-0.013874860480427742,
-0.010363168083131313,
0.055971723049879074,
-0.02278485707938671,
-0.025392582640051842,
0.02572210505604744,
-0.0076735252514481544,
0.037338562309741974,
0.04432590305805206,
-0.05870336666703224,
0.03375035151839256,
-0.06350365281105042,
-0.0257711224257946,
0.03330107778310776,
0.02597200684249401,
0.0652175024151802,
-0.010949206538498402,
-0.005825478583574295,
-0.03105800412595272,
-0.007046593353152275,
-0.013212648220360279,
0.022514894604682922,
-0.0239761620759964,
0.017469611018896103,
0.029781784862279892,
0.017419645562767982,
-0.048378560692071915,
-0.026729309931397438,
-0.020193887874484062,
-0.040493085980415344,
-0.008477061055600643,
0.005449205636978149,
-0.0066474308259785175,
-0.04769406095147133,
0.05157489329576492,
0.027313996106386185,
-0.03343275934457779,
0.04276489093899727,
-0.038575753569602966,
-0.03825559839606285,
0.0004077196354046464,
0.005287491716444492,
0.007792485412210226,
0.014505014754831791,
-0.042041633278131485,
0.06429505348205566,
0.044384218752384186,
-0.048012442886829376,
0.009227774105966091,
0.024289634078741074,
-0.011376569047570229,
-0.028072750195860863,
0.007017843425273895,
0.023074820637702942,
0.025070535019040108,
0.034677229821681976,
0.018408387899398804,
0.027632221579551697,
0.007055487483739853,
0.017492467537522316,
-0.09232473373413086,
-0.04775068536400795,
0.021570973098278046,
0.017378708347678185,
0.019378354772925377,
-0.03323621302843094,
-0.010922142304480076,
-0.015811210498213768,
0.020708641037344933,
-0.020868293941020966,
0.00848096702247858,
-0.06429504603147507,
0.044426970183849335,
0.029134631156921387,
0.031155182048678398,
-0.02328314259648323,
0.03250189498066902,
0.00027238510665483773,
-0.01818160153925419,
-0.0014148883055895567,
0.034510537981987,
0.058929238468408585,
-0.016157666221261024,
0.008485334925353527,
-0.003349027829244733,
0.035159964114427567,
-0.022189844399690628,
-0.038654252886772156,
-0.005200110841542482,
0.002338316524401307,
0.003231775714084506,
-0.014734337106347084,
-0.00619224039837718,
0.022692430764436722,
0.05249452590942383,
0.00868941843509674,
0.03779802471399307,
-0.04350931942462921,
0.023980548605322838,
-0.019512124359607697,
0.030391985550522804,
-0.018444236367940903,
0.045260827988386154,
-0.00614619767293334,
0.034978803247213364,
0.05185207724571228,
0.026322368532419205,
-0.0014581974828615785,
-0.02650049328804016,
-0.09914181381464005,
0.0430777370929718,
-0.031160729005932808,
0.023050090298056602,
0.0050952136516571045,
-0.029083039611577988,
0.014278280548751354,
-0.024893028661608696,
-0.05164163559675217,
-0.060061801224946976,
-0.010657456703484058,
-0.024861494079232216,
0.010797016322612762,
-0.04001663625240326,
-0.06678777933120728,
0.02154015749692917,
0.01873171702027321,
0.04503028839826584,
-0.02571757882833481,
-0.0007188229938037694,
-0.003920522518455982,
-0.03341848775744438,
0.005939363501966,
-0.005166817456483841,
0.0633268803358078,
0.015801580622792244,
0.042316850274801254,
0.016337091103196144,
0.03720000013709068,
-0.01867714896798134,
-0.00604208605363965,
0.03781084716320038,
0.04350840300321579,
-0.021603625267744064,
-0.009170287288725376,
0.00337716331705451,
-0.07986956089735031,
-0.052556272596120834,
-0.0045283786021173,
0.06349419802427292,
0.01544805709272623,
-0.01104761566966772,
0.0530039444565773,
0.030307916924357414,
-0.05580564960837364,
0.04525328055024147,
0.07055354118347168,
0.008738254196941853,
-0.05159836634993553,
-0.037256114184856415,
-0.02176981419324875,
-0.0017538595711812377,
-0.03417221084237099,
0.018920861184597015,
-0.01200042013078928,
-0.0375945046544075,
0.022031869739294052,
0.032225437462329865,
0.03428410738706589,
-0.04688374325633049,
0.0011210241355001926,
0.01789923943579197,
0.0215575210750103,
0.020998282358050346,
0.03398197889328003,
-0.008833970874547958,
0.048100546002388,
0.03752192482352257,
-0.010877272114157677,
0.008895928040146828,
-0.04060590639710426,
0.027753818780183792,
0.03628554195165634,
0.020520584657788277,
-0.019618039950728416,
-0.010069566778838634,
-0.030147401615977287,
-0.00540023623034358,
0.017253421247005463,
-0.057666096836328506,
0.033027492463588715,
-0.03870810195803642,
-0.005074490327388048,
-0.021351493895053864,
-0.017234455794095993,
0.005520331207662821,
0.05912730470299721,
-0.028666095808148384,
-0.02234581671655178,
-0.016597019508481026,
-0.004068885929882526,
0.0016983927926048636,
0.029224654659628868,
0.00689988536760211,
-0.007994317449629307,
0.03869704157114029,
0.04109425097703934,
0.012983156368136406,
0.05557733401656151,
-0.045039404183626175,
-0.11133714020252228,
-0.012086089700460434,
0.03405016288161278,
-0.04583752155303955,
0.018855590373277664,
-0.020205358043313026,
-0.030949527397751808,
0.014099206775426865,
-0.015642313286662102,
0.004329576622694731,
-0.00550464540719986,
-0.04213966429233551,
0.015144257806241512,
0.04915764927864075,
0.016527511179447174,
0.04751376435160637,
0.028568444773554802,
-0.033927321434020996,
-0.00204636063426733,
0.005365346092730761,
0.005435378290712833,
-0.02180756814777851,
0.02851535752415657,
-0.005971352569758892,
-0.003532091388478875,
-0.023371852934360504,
0.04026643559336662,
-0.024394875392317772,
0.004136290401220322,
0.005913410801440477,
-0.021661993116140366,
-0.02243993431329727,
0.005475896410644054,
0.010157674551010132,
-0.05098053440451622,
0.009791170246899128,
0.0473332554101944,
0.022623946890234947,
-0.03551569581031799,
0.009610448963940144,
0.020014548674225807,
-0.024096759036183357,
-0.00047128123696893454,
-0.003965278621762991,
0.009134363383054733,
-0.024473804980516434,
-0.009695924818515778,
0.021814841777086258,
-0.06066415086388588,
0.02395543083548546,
-0.0029371476266533136,
-0.011201772838830948,
0.0238800086081028,
-0.03796567767858505,
-0.026781167834997177,
0.011223627254366875,
-0.014317595399916172,
-0.05344707891345024,
-0.03197028115391731,
0.03601763769984245,
0.03083004243671894,
0.015818491578102112,
-0.06814981251955032,
-0.08525815606117249,
0.0197601281106472,
-0.02529766783118248,
-0.0075510297901928425,
0.008755876682698727,
0.00258902320638299,
-0.042759545147418976,
-0.03887835144996643,
0.01381963025778532,
0.02902466617524624,
-0.054861679673194885,
0.027602605521678925,
0.002306754933670163,
0.029205692932009697,
0.03844472020864487,
-0.021815922111272812,
-0.01799379289150238,
-0.02210134081542492,
-0.015260308980941772,
0.06391284614801407,
0.03332292288541794,
0.038435500115156174,
0.004147568717598915,
-0.0243388619273901,
-0.005928946193307638,
-0.01867649145424366,
0.0328245535492897,
-0.001843503676354885,
0.02940133586525917,
0.03541446104645729,
0.043850772082805634,
0.00585747417062521,
-0.0363633967936039,
0.03154332563281059,
0.008554002270102501,
0.026795867830514908,
-0.02138439193367958,
0.035124484449625015,
0.0013099214993417263,
-0.024703292176127434,
0.05676320567727089,
0.005860794335603714,
-0.0034630210138857365,
-0.007631034590303898,
0.04287097603082657,
-0.00012970076932106167,
-0.03287964314222336,
0.013494828715920448,
-0.037040531635284424,
-0.01807871274650097,
-0.001592407701537013,
0.023968977853655815,
-0.005960389971733093,
0.014193926006555557,
0.005926427897065878,
-0.06660183519124985,
0.0035408588591963053,
-0.0042853462509810925,
0.06000208482146263,
-0.03153471276164055,
0.04148959740996361,
0.05635404586791992,
-0.011329706758260727,
-0.046766553074121475,
-0.04027166590094566,
-0.014933754689991474,
0.022331425920128822,
-0.007036636117845774,
0.0476468987762928,
-0.014993615448474884,
0.017093315720558167,
0.023297423496842384,
0.05321788415312767,
-0.025128427892923355,
0.04375148564577103,
0.02465813234448433,
0.022291583940386772,
0.030686436221003532,
-0.032687634229660034,
-0.024637185037136078,
0.014929474331438541,
-0.05017746984958649,
0.0408657006919384,
-0.010126038454473019,
0.01555902510881424,
-0.012108919210731983,
0.0064496565610170364,
0.031956471502780914,
-0.022112539038062096,
-0.051626864820718765,
-0.06638484448194504,
-0.004194777924567461,
0.04144461452960968,
0.015947794541716576,
0.009454065933823586,
0.0088809197768569,
0.04052703455090523,
0.014670349657535553,
-0.0020561267156153917,
-0.01695927605032921,
-0.05271342396736145,
-0.02220086194574833,
-0.04063514620065689,
-0.043091945350170135,
0.05859501287341118,
-0.01646709069609642,
0.006791085470467806,
-0.01822321116924286,
-0.008140858262777328,
0.008762997575104237,
-0.005447529722005129,
0.02478610910475254,
0.012493764981627464,
0.01977831870317459,
-0.04416520148515701,
0.05498729646205902,
0.027330687269568443,
0.005208320450037718,
0.11459524184465408,
0.03505288437008858,
-0.0020892429165542126,
-0.06599928438663483,
0.05879458412528038,
-0.0332527682185173,
-0.005205434747040272,
-0.028192788362503052,
0.023429064080119133,
0.013266545720398426,
0.018342046067118645,
-0.010869775898754597,
0.07123870402574539,
-0.01197016891092062,
-0.03858933597803116,
0.05153315141797066,
-0.03824644535779953,
-0.03156878799200058,
-0.004267503507435322,
0.006922162137925625,
0.002980237128213048,
0.01573614589869976,
-0.035789020359516144,
0.008111055940389633,
-0.029634008184075356,
0.003843926591798663,
-0.015629570931196213,
-0.05602977052330971,
0.02526410110294819,
0.0455215647816658,
-0.012237584218382835,
0.018624279648065567,
-0.027655446901917458,
-0.025625409558415413,
-0.057065267115831375,
-0.006748970597982407,
0.010868510231375694,
-0.01595870964229107,
0.03660734370350838,
0.040401898324489594,
0.020537201315164566,
0.008592860773205757,
0.01213135290890932,
0.0030315862968564034,
-0.04128395766019821,
-0.009849105030298233,
-0.006472487933933735,
0.03572284057736397,
-0.02215755172073841,
0.007298621349036694,
0.016840729862451553,
0.004312868230044842,
0.004553653299808502,
-0.023038586601614952,
-0.0325884111225605,
-0.015941360965371132,
0.02441226691007614,
0.0025373271200805902,
-0.021764108911156654,
0.009813753888010979,
0.03174179047346115,
-0.017962880432605743,
0.031080642715096474,
-0.06612462550401688,
-0.003328574588522315,
-0.01917194575071335,
-0.02269027568399906,
0.02305857464671135,
-0.015437566675245762,
-0.018542544916272163,
-0.01208956353366375,
0.0018643452785909176,
-0.012352092191576958,
0.030647194012999535,
0.022006623446941376,
0.028216876089572906,
0.01282032672315836,
-0.0028171848971396685,
-0.009989438578486443,
-0.018503917381167412,
-0.021739695221185684,
0.0016043366631492972,
-0.04751543328166008,
-0.009941227734088898,
0.011418581008911133,
-0.011886649765074253,
0.05272366479039192,
0.04065156728029251,
-0.044241636991500854,
0.006073227152228355,
0.004840082488954067,
0.0020059586968272924,
-0.0013696860987693071,
-0.03208891302347183,
-0.04336847737431526,
-0.003840301651507616,
-0.02940232679247856,
-0.012333864346146584,
-0.034064192324876785,
0.0020186773035675287,
0.030432511121034622,
-0.036540687084198,
-0.009255345910787582,
0.040483057498931885,
-0.002604859881103039,
-0.01568588986992836,
0.043866995722055435,
-0.0297713465988636,
0.023564955219626427,
0.009075685404241085,
0.017507122829556465,
-0.013279758393764496,
-0.03280080854892731,
0.016825154423713684,
-0.00333873531781137,
-0.011881929822266102,
0.016925424337387085,
-0.035111285746097565,
0.011862637475132942,
-0.03286899998784065,
0.030637171119451523,
-0.020743457600474358,
0.008844031020998955,
-0.07007431238889694,
0.0410727858543396,
-0.014644132927060127,
-0.017923614010214806,
0.002963820705190301,
0.022794658318161964,
0.028522565960884094,
-0.03516244515776634,
0.02254584990441799,
0.049095772206783295,
-0.032493025064468384,
0.012968168593943119,
0.04368853569030762,
-0.003169433446601033,
0.018594110384583473,
-0.012990832328796387,
-0.012977764941751957,
0.029111361131072044,
-0.032831061631441116,
-0.04334622994065285,
0.05496849864721298,
-0.01999533176422119,
-0.005719535052776337,
0.02304084785282612,
-0.035964109003543854,
-0.022613951936364174,
0.006373873446136713,
-0.02858525700867176,
0.010796573013067245,
-0.0023863986134529114,
-0.03753909468650818,
-0.033108144998550415,
-0.005428734235465527,
0.01936684176325798,
-0.023803574964404106,
-0.05197017267346382,
0.01136214192956686,
0.02920827828347683,
0.000162448690389283,
-0.0020631179213523865,
-0.019267715513706207,
-0.0037638426292687654,
0.017962981015443802,
0.0024145671632140875,
-0.009500137530267239,
-0.006773056462407112,
0.03097367286682129,
-0.04454774409532547,
0.017779869958758354,
0.016711266711354256,
-0.02068929374217987,
-0.07098592817783356,
0.007231783587485552,
0.021607518196105957,
-0.026289284229278564,
0.044944778084754944,
-0.06507416069507599,
0.04138064384460449,
0.00764126842841506,
-0.04341324046254158,
0.05399588868021965,
-0.055672787129879,
-0.017533104866743088,
-0.006813187152147293,
0.007522377651184797,
-0.012545052915811539,
0.0682632178068161,
0.014333012513816357,
0.024696851149201393,
-0.004837836138904095,
0.005368426442146301,
0.006141376681625843,
-0.01565445587038994,
-0.03121011145412922,
-0.010174074210226536,
0.03622205927968025,
0.008363524451851845,
0.09388400614261627,
-0.0443725511431694,
-0.047160763293504715,
0.036112476140260696,
0.01803157851099968,
-0.024245569482445717,
-0.01569058746099472,
0.007429186720401049,
0.011663665063679218,
0.05016529932618141,
-0.011303362436592579,
0.013558854348957539,
-0.0338946171104908,
0.04092888906598091,
0.023407377302646637,
0.035194989293813705,
0.009905938990414143,
-0.005955800414085388,
-0.047952890396118164,
-0.03271140903234482,
0.04182669147849083,
0.021669205278158188,
-0.04094478860497475,
-0.04413998872041702,
-0.003985685296356678,
0.005030904430896044,
0.00961284153163433,
0.007245215587317944,
-0.009490493685007095,
-0.05211281403899193,
-0.020209405571222305,
0.013480357825756073,
-0.023758262395858765,
0.02001582831144333,
0.059922195971012115,
-0.015125475823879242,
-0.009795060381293297,
0.051094647496938705,
0.005891697946935892,
-0.023071641102433205,
-0.0014525523874908686,
0.007644212804734707,
0.02578013204038143,
-0.00010876051965169609,
0.009054497815668583,
-0.044628217816352844,
-0.0076384712010622025,
0.058514829725027084,
0.0006184845697134733,
0.05734143406152725,
-0.06307829916477203,
-0.012731505557894707,
0.011071762070059776,
-0.027317456901073456,
0.040524814277887344,
0.01486615464091301,
0.033335041254758835,
0.00012020594294881448,
-0.018314125016331673,
0.0076230308040976524,
-0.004821883514523506,
0.026229871436953545,
-0.03148190677165985,
-0.0331970676779747,
0.021177023649215698,
0.006983106955885887,
0.03229651227593422,
0.0006313116755336523,
-0.0004061106883455068,
-0.020573493093252182,
-0.03730209916830063,
-0.035032179206609726,
-0.004674634430557489,
-0.021574728190898895,
0.03334609046578407,
0.004628905560821295,
-0.03484553098678589,
0.029852135106921196,
0.03230132535099983,
-0.02552577666938305,
0.030707815662026405,
0.005507363472133875,
-0.023021303117275238,
0.038799334317445755,
-0.024777496233582497,
-0.001556235714815557,
0.014959735795855522,
-0.007788731716573238,
-0.010979210957884789,
-0.00932138692587614,
-0.03178055211901665,
-0.026376742869615555,
-0.02204623818397522,
-0.013589372858405113,
0.01610228791832924,
0.003010850865393877,
0.042320944368839264,
0.04056873172521591,
-0.010419935919344425,
-0.01708352379500866,
0.0698750913143158,
-0.009257080033421516,
-0.004682406783103943,
0.01579609140753746,
0.000009114694876188878,
0.01869317516684532,
0.032580889761447906,
0.0513160340487957,
0.03734944760799408,
-0.016433048993349075,
0.03127878159284592,
0.0039020252879709005,
0.010815835557878017,
0.00860530138015747,
0.05777445435523987,
0.010656165890395641,
0.01569519378244877,
-0.037537332624197006,
0.03636481985449791,
0.032071538269519806,
-0.01951860822737217,
0.00816916860640049,
-0.01776592805981636,
-0.028313947841525078,
0.08545836806297302,
-0.02111385203897953,
-0.004257921129465103,
-0.010485910810530186,
-0.01037533674389124,
0.01592370867729187,
-0.039452340453863144,
-0.03023352287709713,
0.06624110043048859,
-0.01185238640755415,
-0.015683554112911224,
-0.03693600744009018,
0.029025744646787643,
0.011839454062283039,
-0.051189571619033813,
0.027692051604390144,
0.00972017366439104,
-0.021916847676038742,
0.016990911215543747,
-0.02883671410381794,
-0.04342665150761604,
-0.04786129295825958,
0.010527427308261395,
0.03329743072390556,
0.03834350034594536,
0.020457930862903595,
-0.05076897144317627,
0.0019597152713686228,
0.011147070676088333,
-0.03596426546573639,
-0.04488448053598404,
-0.009458898566663265,
-0.014315826818346977,
-0.035036712884902954,
0.010227258317172527
] |
<p>I want to ask if anyone has gone through the derivation of the second equality in the following formula </p>
<p><img src="http://i.stack.imgur.com/okF7P.jpg" alt="enter image description here"></p>
<p>which comes from <a href="http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102" rel="nofollow">http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102</a>.</p>
| 7,650 |
[
-0.03917309641838074,
-0.029684634879231453,
-0.016177618876099586,
0.022760434076189995,
0.02378038689494133,
0.00006226098776096478,
-0.029744936153292656,
-0.020494244992733,
0.009803730063140392,
-0.04050610959529877,
0.036378439515829086,
0.0380510538816452,
0.06665412336587906,
0.025654500350356102,
0.025415293872356415,
0.006293134298175573,
-0.0033251603599637747,
0.030238749459385872,
0.011364422738552094,
-0.04337646812200546,
0.010212068445980549,
0.021460218355059624,
-0.015349114313721657,
-0.00041174382204189897,
-0.003901898395270109,
0.05658496543765068,
0.028041033074259758,
0.008875538595020771,
0.01249481551349163,
0.07769482582807541,
-0.012358695268630981,
-0.025255979970097542,
0.014118824154138565,
0.06477367877960205,
0.013305778615176678,
0.03153045475482941,
-0.014556731097400188,
-0.03605854883790016,
-0.024273518472909927,
0.04736246168613434,
-0.013469419442117214,
0.0006944391061551869,
0.012586570344865322,
0.05681079998612404,
-0.006059702485799789,
0.011269809678196907,
-0.006151198409497738,
-0.016751285642385483,
0.053103312849998474,
-0.08771156519651413,
0.10097387433052063,
0.025042233988642693,
0.06070110201835632,
0.010242733173072338,
-0.029492387548089027,
0.02721690572798252,
0.07667548954486847,
0.06878648698329926,
-0.0037277599330991507,
-0.06236531212925911,
-0.011193368583917618,
-0.043996661901474,
-0.028131062164902687,
-0.014119011349976063,
-0.03189993277192116,
-0.001953469356521964,
-0.011455375701189041,
-0.038665518164634705,
0.015428171493113041,
-0.007709503639489412,
0.00913610402494669,
0.01408025249838829,
0.06993371248245239,
-0.03564057499170303,
0.017013458535075188,
-0.023769009858369827,
0.007332388777285814,
-0.0004451211716514081,
0.020027730613946915,
0.018307968974113464,
-0.021333646029233932,
0.011404205113649368,
0.03245196118950844,
0.04289138689637184,
0.01058409083634615,
0.00016417985898442566,
0.08428331464529037,
-0.012880876660346985,
0.04936233162879944,
0.023931000381708145,
0.002370225265622139,
0.032164812088012695,
0.029430994763970375,
-0.003581386059522629,
-0.015703806653618813,
0.028745731338858604,
-0.00400459673255682,
0.05110748112201691,
-0.007092118728905916,
-0.02293679490685463,
0.011051654815673828,
-0.018579740077257156,
-0.007773517165333033,
0.06463167071342468,
0.0038903176318854094,
0.001637527602724731,
-0.02106546238064766,
0.020399538800120354,
0.011751949787139893,
-0.022259149700403214,
-0.03005567565560341,
0.010627887211740017,
-0.003327405545860529,
-0.007061050273478031,
-0.016721993684768677,
-0.049971889704465866,
-0.015020221471786499,
0.005252117291092873,
0.048172302544116974,
0.06485214084386826,
0.04278205335140228,
-0.006972950883209705,
0.030401891097426414,
-0.01632283255457878,
-0.0597301684319973,
-0.00013761672016698867,
0.021249040961265564,
0.005717525724321604,
-0.030687760561704636,
0.023984825238585472,
-0.014251126907765865,
-0.022808074951171875,
0.035799138247966766,
0.016522882506251335,
-0.002843553200364113,
-0.002928286325186491,
-0.09113483875989914,
-0.04493161290884018,
0.03406989946961403,
-0.02653326652944088,
-0.012655536644160748,
-0.08927717059850693,
0.026950322091579437,
0.03648807853460312,
0.08790598064661026,
-0.008438964374363422,
-0.019573314115405083,
-0.03152010589838028,
0.02625421993434429,
0.015291010029613972,
-0.014555031433701515,
-0.03927271440625191,
0.017310716211795807,
-0.06161244213581085,
-0.012595581822097301,
-0.07360795885324478,
0.010268796235322952,
0.0314437672495842,
-0.009389127604663372,
-0.013645442202687263,
0.08924001455307007,
-0.010105070658028126,
-0.015564951114356518,
0.00528725516051054,
0.02091570384800434,
-0.035691700875759125,
0.08467485755681992,
0.00873237568885088,
-0.014416184276342392,
0.03220151737332344,
0.0053051975555717945,
0.03288863226771355,
0.008248746395111084,
0.01423188392072916,
0.03405985236167908,
-0.01447042915970087,
-0.018352065235376358,
-0.05273125693202019,
-0.00592170050367713,
0.028687981888651848,
-0.059416014701128006,
-0.044405508786439896,
-0.013182069174945354,
0.009548105299472809,
-0.004439974203705788,
0.03429294377565384,
0.003737464314326644,
-0.019532887265086174,
0.015455847606062889,
-0.04412388429045677,
-0.0033861801493912935,
-0.07177296280860901,
-0.009529642760753632,
0.002294059144333005,
-0.03352442756295204,
0.016814498230814934,
0.012109999544918537,
0.028214620426297188,
0.003185840090736747,
-0.035692304372787476,
-0.0035343121271580458,
0.012231351807713509,
0.004446240607649088,
-0.0036406866274774075,
0.01547103002667427,
0.05353544279932976,
0.0645052120089531,
0.013787300325930119,
0.040725961327552795,
-0.04103682562708855,
-0.007313515990972519,
-0.0008892826153896749,
-0.016885902732610703,
0.038483452051877975,
-0.019072238355875015,
0.01111540850251913,
0.015685774385929108,
0.009598448872566223,
0.0462980754673481,
0.026011139154434204,
-0.0619017630815506,
0.06898748874664307,
0.05076044052839279,
0.07975808531045914,
-0.0003520738100633025,
0.020416680723428726,
0.013125624507665634,
0.011322293430566788,
-0.014260242693126202,
-0.049136627465486526,
-0.007700472604483366,
-0.005844898521900177,
0.04111006110906601,
0.018386391922831535,
-0.02381523884832859,
0.0032308183144778013,
0.025636600330471992,
0.03049994632601738,
0.026570530608296394,
0.023965731263160706,
-0.007268338929861784,
-0.012452798895537853,
-0.007333338726311922,
0.02457788959145546,
-0.0007666685851290822,
0.04290037229657173,
0.0036733043380081654,
-0.003369313897565007,
0.02037866786122322,
0.004195535089820623,
-0.0358317494392395,
0.0379532165825367,
-0.015824144706130028,
0.002250230871140957,
-0.011372009292244911,
-0.022498521953821182,
0.051269225776195526,
-0.03377728536725044,
0.023766303434967995,
0.026901409029960632,
-0.01443508267402649,
0.009559101425111294,
-0.03559757024049759,
-0.01634703204035759,
0.031958628445863724,
-0.006748811341822147,
-0.04021277651190758,
-0.0001019822375383228,
0.00336850224994123,
-0.017876992002129555,
0.013553233817219734,
-0.01215830072760582,
-0.013043367303907871,
-0.007022720295935869,
-0.023453887552022934,
0.006788880098611116,
0.018208954483270645,
0.02769399620592594,
-0.03078678622841835,
-0.045207198709249496,
-0.008012124337255955,
-0.038705240935087204,
0.0019727249164134264,
0.00020115423831157386,
-0.0532381646335125,
0.012337683700025082,
-0.02848477102816105,
-0.04359123483300209,
0.026018353179097176,
0.01420484110713005,
0.007148686330765486,
0.008478973992168903,
-0.019215693697333336,
-0.06330708414316177,
-0.03663919121026993,
0.007547932211309671,
0.00650007976219058,
-0.04155375063419342,
0.013957501389086246,
0.02730187401175499,
-0.012012501247227192,
-0.03078722022473812,
0.021494898945093155,
-0.02925502508878708,
-0.040382564067840576,
-0.03362605720758438,
0.01779237575829029,
-0.00007127943536033854,
-0.05035467445850372,
0.011866171844303608,
0.014079795219004154,
-0.0007520862855017185,
-0.0011602670419961214,
-0.07208140939474106,
-0.04005808010697365,
0.03195575624704361,
0.028759147971868515,
0.04372091591358185,
-0.004203102085739374,
-0.054971907287836075,
0.09864142537117004,
0.03335585072636604,
-0.0248858779668808,
-0.02976364828646183,
0.0012617732863873243,
-0.0013373014517128468,
-0.0024041456636041403,
-0.003469953080639243,
0.020372159779071808,
-0.013992751948535442,
0.03517629951238632,
0.007787421345710754,
0.008524532429873943,
0.058964017778635025,
0.001590654021129012,
0.02342362143099308,
0.032558880746364594,
0.025997621938586235,
-0.004484280943870544,
0.06290837377309799,
-0.012503976002335548,
-0.01440429501235485,
0.020647292956709862,
0.03580262139439583,
0.031054457649588585,
-0.011311110109090805,
-0.059622835367918015,
0.028137071058154106,
0.015456411987543106,
0.010231388732790947,
-0.03291856124997139,
0.04673143848776817,
0.010518400929868221,
0.019235432147979736,
-0.005014935974031687,
0.036967094987630844,
0.07358716428279877,
-0.03364300727844238,
0.006527245044708252,
0.05076713114976883,
0.00582772446796298,
-0.005792947020381689,
-0.05197758600115776,
-0.016415635123848915,
-0.021497076377272606,
0.0341472327709198,
-0.04273352771997452,
-0.038413986563682556,
0.04586627706885338,
0.008765640668570995,
0.03151765093207359,
-0.004588794894516468,
-0.03149788826704025,
0.020993586629629135,
-0.08462291210889816,
-0.010118251666426659,
-0.014702633023262024,
0.04633723571896553,
0.009668820537626743,
0.0885559543967247,
0.0012980466708540916,
0.012366845272481441,
0.029785998165607452,
0.011237107217311859,
-0.09801074862480164,
0.01904582604765892,
-0.010594571940600872,
-0.019088011234998703,
-0.009951804764568806,
-0.025937922298908234,
0.029712969437241554,
-0.0350201353430748,
-0.026509486138820648,
-0.02367200143635273,
-0.006860234308987856,
-0.0416821651160717,
0.013905327767133713,
-0.012842133641242981,
0.009385371580719948,
-0.042555175721645355,
0.041841842234134674,
0.02030261978507042,
-0.014582043513655663,
-0.02025463990867138,
0.046437133103609085,
-0.03292123228311539,
0.0034711987245827913,
-0.04265761375427246,
0.019493717700242996,
0.016489814966917038,
-0.012819685973227024,
0.004426388069987297,
0.01725991815328598,
0.0024406141601502895,
-0.008974055759608746,
-0.05976692959666252,
0.04623420909047127,
0.03847205266356468,
-0.020715298131108284,
-0.03290087729692459,
-0.01753295212984085,
-0.03304882347583771,
0.002327364170923829,
0.07308816909790039,
-0.009917081333696842,
0.026722444221377373,
0.031112222000956535,
0.003184960689395666,
-0.037516020238399506,
0.048258088529109955,
0.07146269083023071,
0.017152270302176476,
-0.015118221752345562,
-0.055853404104709625,
0.00756658473983407,
-0.04241431877017021,
0.00263928878121078,
0.023027729243040085,
-0.001840068376623094,
-0.03871779888868332,
-0.017053432762622833,
0.013894268311560154,
0.010090543888509274,
0.009720887988805771,
0.0012423985172063112,
-0.013841512612998486,
0.007423311471939087,
-0.008646156638860703,
-0.00783928669989109,
0.0017904408741742373,
0.0611734576523304,
0.03058571182191372,
-0.02213488705456257,
0.003226149594411254,
-0.06074630841612816,
-0.015662210062146187,
0.015283656306564808,
0.032881688326597214,
-0.01552628818899393,
-0.002382482634857297,
-0.07324904948472977,
-0.006744730286300182,
0.037052251398563385,
-0.009715479798614979,
0.06985428929328918,
0.010815301910042763,
-0.018648959696292877,
0.01440782006829977,
-0.03621566295623779,
-0.0223088338971138,
0.02096102014183998,
-0.002095879055559635,
0.0008652882534079254,
-0.013662438839673996,
-0.002240137429907918,
-0.012619653716683388,
0.025286704301834106,
0.02768627181649208,
0.06459904462099075,
-0.0028173751197755337,
-0.0006727785803377628,
-0.001548125292174518,
0.009729454293847084,
-0.045907557010650635,
-0.07445983588695526,
0.013406169600784779,
-0.0030461507849395275,
0.02241339720785618,
0.02523859590291977,
-0.04704151302576065,
-0.03895491361618042,
0.019252823665738106,
0.02276141569018364,
-0.003174514276906848,
0.009824533015489578,
-0.007713570725172758,
0.03790907561779022,
0.06028430163860321,
-0.03133459761738777,
0.059829600155353546,
0.02166701853275299,
-0.02334541641175747,
-0.01300114020705223,
-0.011685201898217201,
0.05395788326859474,
-0.00009444826719118282,
-0.007494807243347168,
-0.044889770448207855,
0.03846515342593193,
-0.05861140787601471,
0.022167878225445747,
-0.025364652276039124,
0.018172599375247955,
-0.005665069445967674,
-0.02657533995807171,
0.007806504610925913,
0.018182596191763878,
0.005934759974479675,
0.01738230511546135,
0.014130295254290104,
0.03603621572256088,
0.020737631246447563,
-0.032580506056547165,
0.027150718495249748,
-0.02957521565258503,
-0.018192844465374947,
0.031283073127269745,
-0.014227405190467834,
0.044531505554914474,
-0.022697122767567635,
0.0016505853272974491,
0.012898326851427555,
-0.04010230675339699,
0.0283440463244915,
-0.02126975916326046,
0.006063008680939674,
0.004027043003588915,
-0.05061289295554161,
-0.03574271872639656,
0.010462550446391106,
-0.031111247837543488,
0.01285715401172638,
-0.03243377059698105,
0.028818655759096146,
0.017597908154129982,
-0.008333818055689335,
-0.07724227756261826,
-0.06532666832208633,
0.0500553697347641,
0.022998446598649025,
-0.03420441970229149,
-0.024127567186951637,
-0.014194718562066555,
-0.010826938785612583,
-0.04803544655442238,
0.011730795726180077,
0.03838731721043587,
-0.02018197625875473,
-0.054583124816417694,
0.005897916853427887,
0.0004328145878389478,
0.05090940371155739,
0.009238820523023605,
-0.0071269613690674305,
-0.00784561038017273,
-0.030154524371027946,
-0.02835783176124096,
0.026996459811925888,
0.07302480936050415,
-0.02561018615961075,
-0.02057267725467682,
-0.046788085252046585,
0.0024785606656223536,
0.047269269824028015,
-0.040374740958213806,
-0.03365897014737129,
-0.008753826841711998,
0.02851821295917034,
0.0072209034115076065,
-0.024872181937098503,
0.011789543554186821,
0.007606263738125563,
0.00969760026782751,
0.011982685886323452,
-0.004921244457364082,
-0.027095235884189606,
-0.019258759915828705,
0.005761883687227964,
0.012240570038557053,
-0.0006516913999803364,
-0.018485968932509422,
0.12201264500617981,
-0.010007127188146114,
0.001451935269869864,
0.01661359705030918,
-0.0063994694501161575,
-0.0015424625016748905,
0.02831309475004673,
0.012744290754199028,
0.055777180939912796,
-0.008860448375344276,
-0.04440552368760109,
-0.021836554631590843,
-0.04670354351401329,
0.02907031774520874,
0.08470200002193451,
-0.049403849989175797,
0.05767102539539337,
0.0065612695179879665,
0.005733154248446226,
0.020643897354602814,
0.003745913039892912,
-0.03003976121544838,
-0.010520217940211296,
-0.020584892481565475,
0.03430863469839096,
-0.014531426131725311,
0.016217423602938652,
0.03657670319080353,
0.03325492516160011,
-0.018871989101171494,
0.013048590160906315,
0.020636029541492462,
-0.0006443801685236394,
0.0170216653496027,
0.0015203832881525159,
-0.021345216780900955,
0.040390387177467346,
-0.009868555702269077,
0.04176553711295128,
-0.013207721523940563,
-0.023818446323275566,
0.0549916997551918,
0.000577665981836617,
-0.0001339953887509182,
-0.030474066734313965,
-0.05251052975654602,
-0.025345347821712494,
0.01757814548909664,
0.00632498599588871,
0.00992185901850462,
0.033270277082920074,
0.019266854971647263,
0.012339971959590912,
0.039571668952703476,
0.044811397790908813,
-0.02732597477734089,
-0.036151766777038574,
0.00034014115226455033,
-0.024567333981394768,
-0.05164937302470207,
0.012446231208741665,
0.015603624284267426,
-0.02552984096109867,
0.00979362241923809,
-0.0014209809014573693,
0.0009920092998072505,
0.02605915069580078,
0.035631757229566574,
0.016371993348002434,
0.0781686082482338,
0.006185767240822315,
0.02239353209733963,
-0.0036734570749104023,
-0.018541369587183,
0.10246984660625458,
0.06788045912981033,
0.015650734305381775,
-0.07448651641607285,
0.05003979429602623,
-0.01897287927567959,
0.005987045355141163,
-0.03985941410064697,
0.03656388819217682,
-0.018346518278121948,
-0.00204474781639874,
0.009287308901548386,
0.05350840836763382,
-0.011427734047174454,
-0.005376248620450497,
0.02244243584573269,
-0.02045997977256775,
-0.03602221980690956,
0.032643746584653854,
0.003622553078457713,
-0.018115680664777756,
-0.021623406559228897,
-0.00571031216531992,
0.02061484567821026,
-0.03894780948758125,
0.008063080720603466,
-0.048246365040540695,
-0.031642571091651917,
0.003833166556432843,
0.01946074701845646,
-0.015460988506674767,
0.02082834579050541,
0.009045910090208054,
0.0013796715065836906,
-0.02372908778488636,
0.018618617206811905,
0.012356222607195377,
-0.005845584906637669,
0.01979978382587433,
0.04290163889527321,
0.02907164953649044,
-0.0021138559095561504,
0.021926162764430046,
0.0056635295040905476,
-0.05014314502477646,
-0.012062914669513702,
-0.038446441292762756,
0.05050137639045715,
-0.02064414881169796,
-0.00039682473288848996,
-0.010019955225288868,
-0.020607132464647293,
0.0014985878951847553,
-0.06049452722072601,
-0.010729259811341763,
0.002026793546974659,
0.01605219952762127,
-0.044820647686719894,
0.004759704228490591,
-0.04873820021748543,
0.017309781163930893,
0.03052063100039959,
0.015109919011592865,
-0.011378427036106586,
-0.009420763701200485,
0.018206648528575897,
0.009617947041988373,
0.060231439769268036,
-0.03300770744681358,
-0.02931349352002144,
-0.028382359072566032,
-0.03354237601161003,
-0.05023374408483505,
-0.020695259794592857,
0.030361825600266457,
0.025065677240490913,
0.037628695368766785,
-0.01004281360656023,
-0.01230440940707922,
-0.00891733169555664,
-0.08036979287862778,
0.02009674906730652,
-0.0003505999338813126,
-0.01088318694382906,
-0.00963215809315443,
-0.013007136061787605,
0.025420499965548515,
0.03505456820130348,
-0.05321317911148071,
0.04454716667532921,
-0.014041784219443798,
0.051315583288669586,
-0.0069052912294864655,
-0.04482771083712578,
-0.043783873319625854,
0.0012167204404249787,
-0.0060018934309482574,
-0.004157584626227617,
0.01039956510066986,
-0.0118193868547678,
0.016728347167372704,
0.03444285690784454,
0.021738776937127113,
0.02448362112045288,
-0.03938765078783035,
0.006196875590831041,
-0.011564180254936218,
-0.03062034212052822,
0.02130027674138546,
-0.0021108100190758705,
-0.012577143497765064,
0.013007082045078278,
0.007934309542179108,
-0.028963765129446983,
-0.0206773541867733,
0.01884215697646141,
0.010751844383776188,
-0.03801030293107033,
-0.018566031008958817,
-0.013655339367687702,
-0.009684726595878601,
-0.02998456358909607,
-0.01320074126124382,
-0.03713962063193321,
0.0124456025660038,
0.02006925456225872,
0.0016267368337139487,
-0.02098514698445797,
0.044728174805641174,
-0.020384926348924637,
-0.01406833529472351,
0.05070400610566139,
0.017068877816200256,
-0.012392689473927021,
-0.008872832171618938,
0.010249403305351734,
0.0036772056482732296,
0.06747740507125854,
-0.020676391199231148,
-0.036943741142749786,
0.008719217032194138,
-0.04729847237467766,
-0.004576957784593105,
0.02504861168563366,
0.015408709645271301,
0.016992993652820587,
0.017345642670989037,
-0.013337161391973495,
-0.006482716649770737,
0.08282764256000519,
0.0031810584478080273,
-0.015657130628824234,
0.012286346405744553,
-0.03753294795751572,
0.02315416745841503,
-0.02130007930099964,
-0.025682583451271057,
-0.0004892139113508165,
0.007688581012189388,
0.023099571466445923,
0.013673958368599415,
-0.023540638387203217,
-0.012592797167599201,
-0.001619673683308065,
-0.012413416057825089,
0.01036240253597498,
0.02483787201344967,
0.002287059323862195,
0.014409277588129044,
0.047339729964733124,
-0.00702622439712286,
0.018773306161165237,
-0.014761117286980152,
0.00484769232571125,
-0.06850311160087585,
-0.0061694602482020855,
0.003134497907012701,
0.01085880771279335,
0.008518608286976814,
-0.0921097919344902,
0.023436307907104492,
0.025037257000803947,
-0.04211489111185074,
-0.018142646178603172,
-0.03438630327582359,
0.0028014814015477896,
-0.03481602668762207,
0.004719826392829418,
-0.004610477015376091,
0.020099474117159843,
0.029196782037615776,
0.04359390214085579,
0.053758032619953156,
0.013956413604319096,
-0.02591465227305889,
-0.022015439346432686,
0.00505274161696434,
-0.003122679889202118,
0.04020621255040169,
-0.05518786981701851,
0.049509838223457336,
0.004704304039478302,
-0.0210597924888134,
0.038422711193561554,
-0.0418526791036129,
0.014218713156878948,
-0.026808707043528557,
0.04936932027339935,
0.0009737198706716299,
-0.008827826008200645,
-0.008995385840535164,
0.004893956705927849,
0.0011446205899119377,
0.0023624501191079617,
0.016028618440032005,
0.01142511609941721,
-0.01862967759370804,
-0.0027956378180533648,
0.021992523223161697,
-0.027217384427785873,
-0.04954157769680023,
0.051997583359479904,
-0.019050711765885353,
0.009855193085968494,
-0.014569340273737907,
-0.011129616759717464,
0.01919373869895935,
-0.03992799296975136,
0.022500943392515182,
-0.07297064363956451,
-0.01601533219218254,
0.02694110944867134,
-0.02447921223938465,
-0.007441600784659386,
0.03061785362660885,
-0.029108965769410133,
-0.028440585359930992,
0.011592973954975605,
0.017521854490041733,
-0.019030803814530373,
-0.036850444972515106,
0.006952052935957909,
0.0019122230587527156,
-0.02112017758190632,
0.017367957159876823,
-0.04409546032547951,
-0.042741090059280396,
0.02710249274969101,
0.009649131447076797,
0.02451350912451744,
0.020909853279590607,
-0.05766424909234047,
-0.02898448333144188,
-0.046169403940439224,
0.03438062593340874,
-0.006321329157799482,
-0.03375137969851494,
-0.021053258329629898,
-0.03540177270770073,
0.013225769624114037,
0.019099393859505653,
0.052658554166555405,
-0.03913101926445961,
-0.06071222946047783,
0.0055633126758039,
0.0037153069861233234,
0.0067246900871396065,
-0.034655001014471054,
0.0001254953967873007,
-0.00029769580578431487,
-0.023833375424146652,
-0.0041838278993964195,
0.0039590452797710896,
-0.006745174527168274,
0.026932131499052048,
0.002111771609634161,
-0.005180278792977333,
0.005983002483844757,
0.0007202543783932924,
-0.021917473524808884,
0.027024758979678154,
-0.028748521581292152,
-0.010487379506230354,
0.08360561728477478,
-0.0070866611786186695,
0.003292546607553959,
0.028274791315197945,
0.005445581860840321,
-0.05494178831577301,
0.02649822272360325,
-0.04315810650587082,
-0.0008919239044189453,
-0.015258886851370335,
0.00017604048480279744,
0.029947418719530106,
-0.051858555525541306,
-0.0016466552624478936,
0.004896679427474737,
-0.026032498106360435,
-0.04927507042884827,
0.053026437759399414,
-0.007037919480353594,
0.03209038823843002,
-0.007358880247920752,
0.03145631030201912,
0.0006190556450746953,
0.0014274707064032555,
-0.001997987972572446,
0.02926071733236313,
-0.0034641274251043797,
0.0006654635071754456,
0.017549864947795868,
0.010397704318165779,
0.006272940430790186,
0.010219716466963291,
0.005515886936336756,
0.0034257639199495316,
0.0033379998058080673,
-0.019840888679027557,
0.016724718734622,
-0.05653878673911095,
0.020446663722395897,
0.020341388881206512,
-0.02087586373090744,
0.08681299537420273,
-0.03420966863632202,
0.026669781655073166,
-0.0021796582732349634,
0.032164085656404495,
-0.03170967102050781,
0.005220521707087755,
0.036923620849847794,
0.006793685723096132,
-0.025754334405064583,
-0.025261592119932175,
0.0018716816557571292,
-0.020020997151732445,
-0.015536388382315636,
-0.032957177609205246,
0.018520962446928024,
-0.002982792677357793,
-0.005960937589406967,
-0.018984004855155945,
-0.018652064725756645,
-0.004362923093140125,
-0.024606037884950638,
0.011545195244252682,
0.026083804666996002,
-0.007881072349846363,
0.006915683392435312,
0.03559010475873947,
-0.026788268238306046,
0.0996406078338623,
-0.08097352087497711,
-0.03477680683135986,
-0.001123484573327005,
0.0001611660118214786,
-0.01047247089445591,
-0.034512102603912354
] |
<p>The uncertainty principle is listed in most textbooks and articles as
$$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$
This can be derived in many ways in many different settings, most of them involving commutation relations with appropriate operators.</p>
<p>This is often interpreted such that $\Delta E$ is the amount of energy that can be "borrowed" and $\Delta t$ is the time for which it can be borrowed. The uncertainty principle is then used to argue that if $\Delta t$ is large (that is, if the energy is borrowed for long times), then
$$ \Delta E \sim \hbar/2\Delta t$$
is small, making this effect negligible on large time scales.</p>
<p>However, the uncertainty relation is an inequality. If $\Delta E$ is actually the amount of energy we can borrow, and if $\Delta t$ is the time for which it can be borrowed, then if $\Delta t$ is large, $\hbar/2\Delta t$ is small, and
$$\Delta E \geq \hbar/2\Delta t.$$</p>
<p>This puts no upper limit on $\Delta E$ at all, and in fact gives it a lower limit. $\Delta E$ must be <i> at least </i> $\hbar/2\Delta t$, but it could also be orders of magnitude larger and still satisfy the uncertainty principle. In fact, $\Delta E$ and $\Delta t$ can both be infinite and satisfy the uncertainty principle.</p>
<p>My question is, then, since this argument is so frequently cited in textbooks, what justifications are used for interpreting $\Delta E$ and $\Delta t$ as relating to energy nonconservation? Am I missing something? Is there a reason for the switch from $\geq$ to $\sim$ in the relation? Why don't we observe the infinite violations of conservation of energy (in time and energy) that are predicted by this interpretation of the uncertainty principle? Why are only the minimum-uncertainty cases used in the literature?</p>
<p>I'm assuming there is a reason, and trying to figure it out. Thanks in advance for clarification!</p>
| 7,651 |
[
-0.004156194627285004,
-0.04644673690199852,
0.03869315981864929,
-0.032709140330553055,
0.03702578693628311,
-0.0009604855440557003,
-0.05017992854118347,
-0.039403654634952545,
-0.013434631749987602,
-0.03086433932185173,
-0.010824313387274742,
0.004742864519357681,
0.025299742817878723,
0.0004299997235648334,
0.002984254388138652,
0.03133747726678848,
-0.0063493335619568825,
-0.04448416084051132,
-0.02374899387359619,
-0.022038055583834648,
-0.00672141881659627,
0.025195620954036713,
0.03689808025956154,
-0.015908729285001755,
-0.02142016962170601,
0.012661314569413662,
0.02598382905125618,
0.033448997884988785,
0.002700736979022622,
0.07804793864488602,
0.003035056870430708,
-0.028297273442149162,
0.001482998370192945,
0.04970816522836685,
-0.03265334293246269,
0.02115422673523426,
0.016569675877690315,
-0.022848807275295258,
0.009597704745829105,
0.009236971847712994,
-0.06644608825445175,
0.014534938149154186,
0.008913549594581127,
0.04184875264763832,
0.001497437828220427,
0.0109722800552845,
0.011323899030685425,
-0.016570812091231346,
0.03777967765927315,
-0.022615309804677963,
0.04760383814573288,
-0.000870362448040396,
0.05675897002220154,
0.010890298523008823,
-0.01391168124973774,
0.009907139465212822,
0.06077194958925247,
0.0796888992190361,
-0.010166729800403118,
-0.048229750245809555,
-0.02870982699096203,
-0.042056165635585785,
0.004171954467892647,
0.0015102354809641838,
-0.0018618865869939327,
0.028642525896430016,
0.0424562506377697,
-0.005200787913054228,
0.0033759938087314367,
0.009636332280933857,
0.024385152384638786,
-0.016993097960948944,
0.026351697742938995,
-0.012193498201668262,
0.03263775259256363,
0.0030034531373530626,
0.007016285788267851,
0.03580941632390022,
0.051585603505373,
0.08132613450288773,
-0.011372619308531284,
0.006353714969009161,
0.04444054514169693,
0.021496526896953583,
0.015351750887930393,
-0.006005878560245037,
0.03869004175066948,
0.005888945888727903,
0.03645559400320053,
0.044077903032302856,
0.008379066362977028,
0.01143004558980465,
0.003362630493938923,
-0.04467230662703514,
0.001332485000602901,
0.05455765128135681,
0.019017154350876808,
0.018611090257763863,
-0.019617853686213493,
-0.050093814730644226,
-0.003116337349638343,
-0.03130464628338814,
0.0587703138589859,
0.08225756883621216,
0.013892658986151218,
-0.024894438683986664,
-0.04398862272500992,
0.032675132155418396,
-0.0048612370155751705,
0.002511804923415184,
-0.011314294300973415,
-0.002428576583042741,
-0.007768511772155762,
0.03181134909391403,
-0.010795061476528645,
-0.015763163566589355,
0.014811531640589237,
-0.0038351542316377163,
0.048887304961681366,
0.05364569276571274,
0.025574272498488426,
-0.03269839286804199,
-0.013752460479736328,
0.0006914062541909516,
-0.06207156181335449,
0.03712614253163338,
0.03216152265667915,
0.010839862748980522,
-0.046021122485399246,
-0.0037158350460231304,
0.011794223450124264,
0.0026149137411266565,
0.02592904306948185,
0.014103389345109463,
0.05028617009520531,
-0.023695463314652443,
-0.09208516776561737,
-0.04901444539427757,
0.06851303577423096,
-0.011735464446246624,
-0.04058338701725006,
-0.10715135186910629,
0.005071419291198254,
0.03302927687764168,
0.0561639629304409,
0.0028264359571039677,
0.015476463362574577,
-0.0035684555768966675,
-0.0023089502938091755,
0.005646680947393179,
-0.01619311422109604,
-0.04663993418216705,
0.0482170507311821,
-0.030654601752758026,
0.0170420054346323,
-0.02003748156130314,
0.02698684111237526,
0.042013417929410934,
-0.0013020598562434316,
0.003396571846678853,
0.04603980854153633,
-0.006181006785482168,
-0.02495136670768261,
-0.032948143780231476,
0.031207066029310226,
-0.046498775482177734,
0.09259707480669022,
0.02407838962972164,
0.018748460337519646,
0.01630531996488571,
0.015407238155603409,
0.008509395644068718,
-0.0031977337785065174,
0.005171661265194416,
0.025918560102581978,
-0.059728529304265976,
-0.009685873053967953,
-0.04032517969608307,
-0.02683391235768795,
0.017928199842572212,
-0.03994716331362724,
-0.004556482657790184,
-0.021475832909345627,
0.008000046014785767,
0.03146018460392952,
0.016421131789684296,
-0.018810419365763664,
-0.004516834858804941,
0.01156150083988905,
-0.048687662929296494,
-0.002132975962013006,
-0.07053078711032867,
-0.019183559343218803,
0.02968890778720379,
-0.013533017598092556,
0.017416883260011673,
-0.009730272926390171,
-0.020703239366412163,
-0.06647702306509018,
-0.048724621534347534,
0.01980450004339218,
0.03539028391242027,
0.005224571563303471,
-0.030574960634112358,
0.05652391538023949,
0.0532652772963047,
0.05479131639003754,
0.05269639939069748,
-0.00848325900733471,
0.008423155173659325,
-0.08026178926229477,
0.025846920907497406,
-0.018545640632510185,
0.014089666306972504,
0.030191151425242424,
-0.01929350569844246,
0.010308297351002693,
-0.020192675292491913,
-0.011649057269096375,
0.009935230016708374,
0.0014302587369456887,
0.031232895329594612,
0.01453460194170475,
-0.005442366935312748,
-0.047131262719631195,
0.0765419527888298,
0.0037266723811626434,
0.03383580967783928,
-0.05200960487127304,
-0.046910807490348816,
-0.04759823530912399,
0.006690497510135174,
0.008497809059917927,
0.08629979938268661,
-0.028715819120407104,
-0.006076062098145485,
-0.016317568719387054,
0.02367190085351467,
0.05816669389605522,
0.005890178494155407,
0.004502835217863321,
-0.05598099157214165,
0.00045115602551959455,
-0.020769411697983742,
0.013653402216732502,
0.017797060310840607,
0.02243776246905327,
0.016610605642199516,
0.026378903537988663,
-0.013881239108741283,
-0.002642686478793621,
0.004180200397968292,
-0.019036561250686646,
0.020422138273715973,
0.008915946818888187,
-0.037455663084983826,
0.026798753067851067,
-0.011710629798471928,
0.007737642154097557,
0.030384672805666924,
-0.04132428020238876,
0.03976694494485855,
-0.039735861122608185,
-0.02448676899075508,
0.009323791600763798,
-0.008100173436105251,
-0.016367625445127487,
-0.007793638855218887,
0.0014948240714147687,
0.0021250597201287746,
-0.004816094879060984,
-0.0031752153299748898,
-0.035574883222579956,
-0.016099529340863228,
-0.034418851137161255,
0.04750315099954605,
-0.010946756228804588,
0.03549973666667938,
-0.03956278786063194,
-0.006998878903687,
-0.012106035836040974,
-0.022446421906352043,
-0.012531223706901073,
-0.015066158026456833,
0.0001603318814886734,
0.01299276016652584,
-0.024223197251558304,
-0.02568444237112999,
0.07443025708198547,
-0.008147458545863628,
0.04113225266337395,
-0.0032253791578114033,
-0.02946585789322853,
-0.0802527442574501,
-0.01098605990409851,
-0.023728741332888603,
-0.026485079899430275,
0.000004801514933205908,
-0.031776901334524155,
0.06834366172552109,
-0.04279790446162224,
-0.05804053694009781,
0.04588564112782478,
-0.02702142670750618,
-0.08484804630279541,
-0.004677667282521725,
0.012446713633835316,
-0.005674093496054411,
-0.037166401743888855,
0.059310588985681534,
0.010372116230428219,
-0.03946435824036598,
-0.05124957114458084,
-0.026723695918917656,
-0.05670098587870598,
0.016494544222950935,
0.009274727664887905,
0.03841114044189453,
-0.004354408942162991,
-0.026261895895004272,
0.07604183256626129,
0.017877399921417236,
0.008917314000427723,
0.03513135015964508,
-0.021873455494642258,
0.050855331122875214,
-0.008369853720068932,
-0.01285621989518404,
0.024990128353238106,
0.022475188598036766,
0.02348230592906475,
0.0037884186021983624,
0.03502793237566948,
-0.004027960356324911,
-0.0037109158001840115,
-0.014054165221750736,
-0.00164986087474972,
0.009385787881910801,
0.0242623258382082,
0.036590103060007095,
0.0012184312799945474,
-0.036178119480609894,
-0.013737683184444904,
-0.0017121585551649332,
0.04514371231198311,
-0.005000513978302479,
-0.043608833104372025,
0.08330249041318893,
0.010150915943086147,
0.0019460450857877731,
-0.05592826008796692,
0.04648004099726677,
-0.004237718880176544,
-0.00939921848475933,
0.014841843396425247,
-0.011862307786941528,
0.01986715942621231,
0.003348943777382374,
0.02867686003446579,
0.008409971371293068,
0.023126913234591484,
-0.00043119789916090667,
-0.014095158316195011,
-0.005458255764096975,
-0.00451854569837451,
0.024577954784035683,
-0.010375742800533772,
-0.027640540152788162,
0.04047191143035889,
0.04249466955661774,
0.0013077843468636274,
-0.018282121047377586,
-0.03183986246585846,
-0.03355919569730759,
-0.039281707257032394,
-0.022549962624907494,
-0.019616393372416496,
0.05332715064287186,
-0.0020847576670348644,
0.07069424539804459,
0.0332111231982708,
0.020109599456191063,
0.01152917928993702,
-0.01278820913285017,
-0.055712420493364334,
0.027750862762331963,
-0.03996160253882408,
-0.020428428426384926,
-0.021429026499390602,
0.013424723409116268,
0.010697868652641773,
-0.007615096867084503,
-0.019333310425281525,
-0.043467793613672256,
0.03406568616628647,
-0.06181483343243599,
0.03230833634734154,
-0.029793884605169296,
-0.049963220953941345,
-0.041690483689308167,
0.043516866862773895,
0.042782776057720184,
-0.01792287826538086,
-0.014886736869812012,
0.034457288682460785,
-0.04942060634493828,
0.005536830518394709,
0.002603930654004216,
-0.011841938830912113,
0.004450191278010607,
0.014814521186053753,
0.018641026690602303,
-0.001600323710590601,
-0.0061920564621686935,
0.005648489110171795,
0.028256017714738846,
0.05941852182149887,
-0.009928176179528236,
-0.019596487283706665,
-0.0018682522932067513,
-0.02725375071167946,
0.017700787633657455,
0.021081464365124702,
0.0541093647480011,
0.00825839675962925,
0.03389062359929085,
0.024684544652700424,
0.006907307542860508,
-0.009631392545998096,
0.034610215574502945,
0.02784358151257038,
-0.006966444663703442,
-0.013104310259222984,
-0.056892119348049164,
0.009292550384998322,
-0.04764702916145325,
-0.0026332593988627195,
0.00978051871061325,
0.0013964009704068303,
-0.02648831345140934,
-0.016129562631249428,
-0.005664106924086809,
0.038008932024240494,
-0.03744374215602875,
0.002627996727824211,
0.030927034094929695,
-0.0027455887757241726,
0.025970596820116043,
-0.012869849801063538,
0.017833437770605087,
-0.01567697711288929,
0.04604527726769447,
0.023255690932273865,
0.03122527152299881,
-0.06405875086784363,
-0.023273298516869545,
0.014990896917879581,
0.0458892285823822,
-0.01456404384225607,
0.008835271000862122,
-0.05120134726166725,
-0.04141036421060562,
0.03375764563679695,
-0.031083425506949425,
0.02597569115459919,
-0.0339936725795269,
-0.031368985772132874,
-0.04248269274830818,
-0.05955544859170914,
0.016034385189414024,
0.009744776412844658,
0.022091904655098915,
0.00044769170926883817,
-0.01860845647752285,
0.004375438205897808,
-0.007027314510196447,
-0.015650508925318718,
0.016551105305552483,
0.03981396183371544,
-0.003671836107969284,
-0.00825225468724966,
0.012450097128748894,
0.033440738916397095,
-0.03861469030380249,
-0.05140266939997673,
-0.006986189633607864,
0.0035469650756567717,
0.012606754899024963,
0.024058828130364418,
-0.04964407533407211,
-0.06276987493038177,
0.04034778103232384,
0.004144337959587574,
-0.034307897090911865,
0.005797718185931444,
-0.031830258667469025,
0.03760898858308792,
0.022985944524407387,
-0.01750813238322735,
0.06895698606967926,
0.0472162701189518,
0.005308858118951321,
0.019519219174981117,
-0.03180078789591789,
0.038389965891838074,
-0.0693134292960167,
0.02242068015038967,
-0.06535104662179947,
-0.011396989226341248,
-0.04474275931715965,
0.02831726334989071,
-0.02337641455233097,
0.05131470784544945,
0.011517968028783798,
-0.05467425286769867,
-0.022028548642992973,
0.03645571321249008,
0.0017932587070390582,
0.01036607101559639,
-0.014982715249061584,
0.017569689080119133,
-0.0018225329695269465,
0.003932599443942308,
-0.0016021233750507236,
0.02529796026647091,
-0.021650392562150955,
0.03834909200668335,
-0.03133561462163925,
0.016125205904245377,
-0.035418376326560974,
-0.014562642201781273,
0.023680323734879494,
0.00037399865686893463,
0.010080553591251373,
-0.025682106614112854,
-0.0011678209993988276,
-0.0062522864900529385,
-0.025200512260198593,
-0.05294592306017876,
0.017051687464118004,
0.0022729882039129734,
0.028597213327884674,
-0.03865558281540871,
0.005467880051583052,
0.0392230860888958,
0.018666785210371017,
-0.06833839416503906,
-0.02881482243537903,
0.022786565124988556,
0.00035487645072862506,
-0.029729055240750313,
-0.010428015142679214,
0.015652280300855637,
-0.01602029986679554,
-0.0033116142731159925,
-0.0016908480320125818,
0.03421633690595627,
0.02050389163196087,
0.011658555828034878,
-0.0018805027939379215,
-0.004681908059865236,
0.04385484755039215,
-0.032221484929323196,
0.007306351326406002,
0.02234535478055477,
-0.028176747262477875,
-0.015582856722176075,
0.0008782818331383169,
0.03462938591837883,
-0.03627342730760574,
0.004201091825962067,
0.03292990103363991,
-0.013533705845475197,
0.02800845168530941,
-0.010220939293503761,
-0.019507506862282753,
0.04708919674158096,
-0.030698731541633606,
0.004052352160215378,
0.0010394747368991375,
0.027588658034801483,
-0.011080252006649971,
0.059071194380521774,
0.011165434494614601,
-0.018235111609101295,
-0.01891244202852249,
-0.04256897792220116,
0.0031783878803253174,
0.008866303600370884,
-0.008366457186639309,
-0.003288858337327838,
0.03188451752066612,
0.0015691746957600117,
-0.0006044396432116628,
0.011734724044799805,
-0.013705780729651451,
-0.00216129538603127,
0.006763886194676161,
0.014282732270658016,
0.018256209790706635,
-0.009341303259134293,
-0.03514409810304642,
-0.04081271216273308,
-0.05672205612063408,
0.012587555684149265,
0.04890325665473938,
-0.005634177476167679,
0.02994188666343689,
0.01683865673840046,
-0.010303310118615627,
-0.004956267308443785,
-0.03347095474600792,
-0.011791439726948738,
0.010222933255136013,
-0.013959529809653759,
-0.005492196884006262,
-0.0386115163564682,
-0.03531448170542717,
0.043110210448503494,
-0.015630358830094337,
-0.017067452892661095,
0.011807477101683617,
-0.007461346220225096,
0.02400185912847519,
-0.0021439180709421635,
-0.05018230900168419,
-0.043932486325502396,
0.039954815059900284,
-0.020784422755241394,
0.024955831468105316,
0.02089819870889187,
-0.032945431768894196,
0.01128363236784935,
0.005796887446194887,
-0.015438368543982506,
-0.006336123216897249,
-0.004075582604855299,
-0.062480367720127106,
0.009405295364558697,
-0.0039057733956724405,
0.0028715557418763638,
0.0024470884818583727,
-0.0007667397730983794,
0.008058884181082249,
0.0164689552038908,
-0.002678603632375598,
-0.005428879056125879,
-0.04886755719780922,
0.005428081378340721,
-0.017196258530020714,
-0.04265308007597923,
0.026169300079345703,
-0.008107135072350502,
-0.042190007865428925,
-0.006825894583016634,
-0.03942325338721275,
0.029077254235744476,
0.018713846802711487,
0.012536360882222652,
-0.01834108680486679,
0.05411996692419052,
0.008366101421415806,
0.02968277409672737,
-0.02549820765852928,
0.04322316497564316,
0.12664523720741272,
0.029592368751764297,
-0.0004446469829417765,
-0.03498867526650429,
0.03674028068780899,
0.025629403069615364,
0.012457133270800114,
-0.021552644670009613,
0.03588724136352539,
0.03482513502240181,
0.005932064261287451,
-0.002537218853831291,
0.008805329911410809,
0.0007449917029589415,
-0.06002286449074745,
0.03275379538536072,
-0.05438696965575218,
-0.002899784129112959,
0.004763976205140352,
0.02812194637954235,
-0.005429248791188002,
0.0005969699122942984,
-0.008680709637701511,
-0.0229983888566494,
-0.05086657777428627,
0.02013450674712658,
0.002902938751503825,
-0.03808073699474335,
0.018266664817929268,
-0.024161070585250854,
-0.03950564190745354,
-0.005133517552167177,
-0.02451016753911972,
-0.012798740528523922,
-0.028506509959697723,
0.0038480383809655905,
0.005110868252813816,
0.012177408672869205,
0.006243196316063404,
0.02549615688621998,
-0.0018536500865593553,
-0.001630261423997581,
0.008887465111911297,
0.01664488948881626,
-0.025730732828378677,
-0.03912324085831642,
-0.027381854131817818,
0.06180979311466217,
-0.018315093591809273,
0.02127140946686268,
0.014476833865046501,
-0.032239124178886414,
0.014510705135762691,
-0.04044637456536293,
-0.012436294928193092,
-0.0036753355525434017,
0.031662244349718094,
0.008086750283837318,
-0.0063173905946314335,
-0.04339238256216049,
0.018611332401633263,
-0.024367332458496094,
0.05260464921593666,
-0.009277324192225933,
-0.01099847350269556,
-0.013437692075967789,
-0.006570898927748203,
-0.004481898620724678,
-0.009177113883197308,
0.010553926229476929,
0.00919340830296278,
-0.0142769580706954,
-0.05278589949011803,
-0.03165678307414055,
0.025047598406672478,
0.03129233047366142,
0.05253356695175171,
0.028112957254052162,
-0.01887069083750248,
-0.04866226762533188,
-0.07634135335683823,
0.039139751344919205,
-0.008748105727136135,
-0.02503509633243084,
-0.005057770758867264,
0.016106244176626205,
0.032504599541425705,
0.03675910457968712,
-0.04148556664586067,
0.03264635056257248,
-0.014947722665965557,
-0.0007761007291264832,
0.037920501083135605,
0.011725052259862423,
-0.021969597786664963,
0.02236739546060562,
-0.025231165811419487,
0.01958395540714264,
-0.013273372314870358,
-0.004881393164396286,
0.03747887164354324,
0.01359177939593792,
0.017191411927342415,
0.024343302473425865,
-0.02679448388516903,
-0.013522379100322723,
0.01847156509757042,
-0.0031678802333772182,
-0.017330283299088478,
0.055965177714824677,
0.03714572638273239,
0.014285420067608356,
-0.03324543312191963,
-0.012344777584075928,
0.007617385126650333,
-0.049868401139974594,
0.012490734457969666,
0.008808695711195469,
-0.016991019248962402,
-0.030018016695976257,
0.047714002430438995,
-0.014047551900148392,
-0.028163401409983635,
-0.06295847147703171,
0.004568344447761774,
-0.003019023686647415,
-0.00585177494212985,
-0.019677316769957542,
0.0372406430542469,
-0.0035286354832351208,
-0.04398876056075096,
0.022879816591739655,
0.05017004534602165,
-0.018385864794254303,
0.003104043658822775,
0.016487067565321922,
-0.01450976263731718,
0.022343488410115242,
0.0020866505801677704,
-0.018030749633908272,
0.05570770800113678,
-0.03299832344055176,
-0.046637166291475296,
0.027989108115434647,
0.003609523642808199,
0.016811508685350418,
0.02976774051785469,
-0.0290468018501997,
-0.035582590848207474,
0.04991678148508072,
-0.04510517790913582,
0.020339995622634888,
0.020820269361138344,
-0.037167154252529144,
-0.03176462650299072,
-0.008373969234526157,
0.03250136971473694,
-0.022938596084713936,
0.01044370885938406,
0.026904091238975525,
0.017491012811660767,
-0.012701385654509068,
-0.005031080916523933,
0.02198217250406742,
-0.009455932304263115,
0.01702900417149067,
0.04205390810966492,
-0.004173902329057455,
0.03320575878024101,
0.05037776380777359,
-0.04367488622665405,
0.041354041546583176,
0.026398567482829094,
0.019866537302732468,
-0.09137370437383652,
0.012075533159077168,
-0.013291784562170506,
0.029222529381513596,
0.07069384306669235,
-0.028160082176327705,
0.012188773602247238,
0.0329817458987236,
-0.06226038932800293,
0.017610900104045868,
-0.05352550745010376,
-0.00910702720284462,
-0.02557159960269928,
-0.006440027616918087,
-0.045472752302885056,
0.02611648663878441,
0.04136913642287254,
0.04410844296216965,
0.004185437224805355,
0.04077767953276634,
-0.012784186750650406,
-0.024764442816376686,
-0.034970298409461975,
0.04263478145003319,
-0.02168303355574608,
0.031162746250629425,
0.01208579819649458,
0.0016397088766098022,
0.0032398393377661705,
0.0498514361679554,
0.007421861868351698,
0.004398960620164871,
-0.008603530935943127,
0.035203203558921814,
0.022055499255657196,
0.03696221858263016,
0.03369874507188797,
-0.03162836283445358,
-0.006960367318242788,
0.016227753832936287,
0.015066406689584255,
0.011712696403265,
0.005581864155828953,
-0.0332370363175869,
-0.013563345186412334,
-0.07065363973379135,
-0.0373174212872982,
0.03596273064613342,
0.0024374902714043856,
-0.038684163242578506,
0.04573303088545799,
0.0032131229527294636,
0.005858514923602343,
-0.004021958913654089,
-0.00041582706035114825,
-0.0314674898982048,
-0.028403345495462418,
0.03955892100930214,
-0.0008607407216913998,
0.018319740891456604,
0.02016596496105194,
-0.018567895516753197,
-0.03215877339243889,
0.06749628484249115,
0.03201304376125336,
-0.03866029530763626,
-0.06266304850578308,
-0.0002289504191139713,
0.014988185837864876,
0.009434029459953308,
0.005614259280264378,
-0.034882545471191406,
-0.06310513615608215,
0.015059959143400192,
0.0006970197428017855,
0.035915110260248184,
-0.05260411649942398,
-0.02561533823609352,
-0.03215348720550537,
-0.08326989412307739,
0.024327103048563004,
-0.017151741310954094,
0.016303379088640213,
-0.09379278123378754,
-0.03042030520737171,
0.017179159447550774,
0.005798782221972942,
0.061725325882434845,
0.0031978373881429434,
-0.02735714800655842,
0.042341284453868866,
0.014198727905750275,
0.024215055629611015,
-0.02609068714082241,
0.013432583771646023,
-0.01050091814249754,
-0.018681762740015984,
-0.004334758967161179,
-0.0031597053166478872,
-0.021982457488775253,
0.022576790302991867,
0.020175231620669365,
-0.010493632405996323,
0.003901807125657797,
0.011525150388479233,
-0.015353617258369923,
0.09587450325489044,
0.009728658013045788,
-0.0017465578857809305,
0.03219250962138176,
-0.013456801883876324,
0.026160646229982376,
0.01728617586195469,
-0.019274814054369926,
-0.03324992582201958,
0.005517689045518637,
0.009914446622133255,
-0.012259094044566154,
-0.024384545162320137,
0.03146957978606224,
0.03869184851646423,
-0.00904845166951418,
-0.008147710002958775,
0.0767553374171257,
-0.04005535691976547,
-0.0230657160282135,
0.09988178312778473,
0.013614749535918236,
0.043199341744184494,
0.008202753029763699,
0.0478123240172863,
0.009302720427513123,
0.026450347155332565,
0.03520872816443443,
-0.006339292507618666,
0.0034177082125097513,
-0.04066544398665428,
-0.003933778963983059,
-0.004159236326813698,
-0.027497267350554466,
-0.021326139569282532,
0.021017586812376976,
0.01841634139418602,
-0.03843369707465172,
-0.03610100597143173,
0.015223669819533825,
-0.02183050476014614,
-0.055747296661138535,
0.06911580264568329,
-0.031080154702067375,
0.09156743437051773,
0.03395865485072136,
0.02742632105946541,
-0.0004074212920386344,
0.029506979510188103,
0.011020608246326447,
0.010937036015093327,
-0.0207472313195467,
0.049896109849214554,
-0.02878406271338463,
0.027069125324487686,
-0.03359241411089897,
0.014381738379597664,
-0.003930801525712013,
-0.048075441271066666,
0.019425412639975548,
0.040840111672878265,
-0.02012217976152897,
-0.06208539381623268,
-0.024993939325213432,
-0.03501734510064125,
-0.06220903992652893,
0.019601179286837578,
0.0567140206694603,
0.025233712047338486,
0.019519463181495667,
-0.025067046284675598,
-0.0006973372073844075,
0.055196285247802734,
-0.009498466737568378,
0.011874987743794918,
-0.0120593486353755,
0.02505980059504509,
-0.006672040093690157,
-0.008567320182919502
] |
<p>Does anyone have an intuitive explanation of why this is the case? </p>
| 7,652 |
[
-0.05418393760919571,
-0.024132363498210907,
-0.01563994027674198,
-0.012220270931720734,
0.01940748654305935,
0.007110497448593378,
0.01731305569410324,
0.001909965998493135,
-0.005133143160492182,
-0.019575893878936768,
-0.0007771142409183085,
0.03925773873925209,
0.047500357031822205,
-0.0004425868100952357,
0.007180642802268267,
0.015062117017805576,
0.005923007614910603,
-0.005973213817924261,
0.001737457001581788,
-0.02114686369895935,
-0.00715604005381465,
0.06464351713657379,
0.011558400467038155,
0.007537299767136574,
-0.031249236315488815,
0.050442058593034744,
0.039006903767585754,
0.009623563848435879,
0.03695797175168991,
0.0677093043923378,
-0.005482203792780638,
0.0021447676699608564,
0.008977141231298447,
0.07935305684804916,
0.035298075526952744,
-0.009194409474730492,
-0.011503295041620731,
-0.011198041029274464,
-0.011369519867002964,
0.03882472217082977,
-0.004875781014561653,
-0.0033029443584382534,
-0.018883269280195236,
0.04934544116258621,
-0.0416526198387146,
0.04223362356424332,
-0.01479862816631794,
-0.03541850298643112,
0.05291900411248207,
-0.034641653299331665,
0.07022738456726074,
-0.0031960103660821915,
0.012588943354785442,
0.008506493642926216,
-0.009534384123980999,
-0.007005451247096062,
0.09260488301515579,
0.06768732517957687,
-0.026422185823321342,
-0.03642323613166809,
0.005594955291599035,
-0.035675983875989914,
-0.03839966654777527,
-0.012613934464752674,
-0.01240504626184702,
0.02195473201572895,
0.006693374831229448,
-0.04067883640527725,
0.044027794152498245,
-0.001911126310005784,
-0.0031949542462825775,
0.0349922813475132,
0.05294204130768776,
-0.01817523129284382,
0.028169414028525352,
-0.012011979706585407,
0.03547023981809616,
0.018689386546611786,
0.04262576997280121,
0.017155304551124573,
-0.0062124719843268394,
-0.008829724043607712,
0.03452009707689285,
0.05205775052309036,
0.0279387254267931,
0.017015725374221802,
0.055919863283634186,
-0.038406576961278915,
0.018839063122868538,
0.05154667794704437,
-0.031822025775909424,
-0.019461218267679214,
0.04608471691608429,
-0.01531638577580452,
-0.022993898019194603,
0.015773959457874298,
-0.020637933164834976,
0.02888329327106476,
0.029424160718917847,
-0.014864766038954258,
-0.007371377199888229,
-0.028787629678845406,
0.002744535682722926,
0.04382086172699928,
0.0009028926724568009,
-0.02710413932800293,
-0.060596663504838943,
0.02553649991750717,
0.015200887806713581,
0.005243471823632717,
-0.029840605333447456,
0.009596404619514942,
0.002288219751790166,
-0.004613376688212156,
0.010466807521879673,
-0.04404154419898987,
0.0033545957412570715,
-0.027528228238224983,
0.04460925608873367,
0.08385045826435089,
0.024029698222875595,
-0.0353890024125576,
0.03601215407252312,
-0.03200692683458328,
-0.050336483865976334,
0.0280461385846138,
0.028832022100687027,
-0.02864113636314869,
-0.015731848776340485,
0.0076079764403402805,
-0.010228101164102554,
-0.03832248970866203,
0.0454762727022171,
0.016888801008462906,
0.025757720693945885,
-0.012646418064832687,
-0.08741733431816101,
-0.0690874233841896,
0.05902984365820885,
-0.014893405139446259,
-0.0027967127971351147,
-0.0884643942117691,
-0.004614388104528189,
0.013615814968943596,
0.07855380326509476,
-0.02279648371040821,
0.014950633980333805,
0.01787414401769638,
-0.0047857859171926975,
0.025068582966923714,
-0.028665270656347275,
-0.010113797150552273,
-0.017763696610927582,
-0.047532301396131516,
-0.0007994690095074475,
-0.07331091910600662,
0.011603248305618763,
0.01706131175160408,
-0.014903291128575802,
-0.04129206761717796,
0.01605609804391861,
-0.018060097470879555,
-0.013266408815979958,
-0.01913461834192276,
0.007764292880892754,
-0.030734967440366745,
0.08010745048522949,
0.020892813801765442,
-0.001852483139373362,
0.05571851506829262,
0.01064887922257185,
0.06064128130674362,
0.027402305975556374,
0.07184095680713654,
-0.001788365188986063,
-0.03860818222165108,
-0.0026437132619321346,
-0.04330221191048622,
0.005658297333866358,
-0.010423379018902779,
-0.05692886561155319,
-0.04830677807331085,
-0.010446412488818169,
0.014669259078800678,
0.0056783277541399,
0.057212863117456436,
-0.016664259135723114,
-0.03262573108077049,
-0.010124164633452892,
-0.07364466786384583,
-0.03809455782175064,
-0.09775741398334503,
0.035810597240924835,
0.026669900864362717,
-0.009768415242433548,
0.038552891463041306,
0.030241739004850388,
0.025774413719773293,
-0.03437706455588341,
-0.01815071515738964,
-0.035640325397253036,
-0.031200503930449486,
0.037454646080732346,
-0.04482464864850044,
0.03383658453822136,
0.07373158633708954,
0.04115353897213936,
0.015000986866652966,
0.033548615872859955,
-0.02676241844892502,
-0.02941405586898327,
0.029250625520944595,
-0.01796906441450119,
0.01825505681335926,
-0.012788061052560806,
-0.018320661038160324,
0.017447223886847496,
0.017698857933282852,
-0.024459386244416237,
0.06447551399469376,
-0.04250537231564522,
0.08178027719259262,
0.014480240643024445,
0.003348974045366049,
-0.01967703551054001,
0.016601886600255966,
0.013950550928711891,
0.01074432022869587,
-0.02714538760483265,
-0.02657737024128437,
-0.04220562055706978,
-0.012711118906736374,
0.036593202501535416,
0.01805315725505352,
-0.024293527007102966,
0.0061415936797857285,
0.028454111889004707,
0.0475027821958065,
-0.008979297243058681,
0.029370898380875587,
0.028823528438806534,
0.004390269983559847,
0.010969760827720165,
0.033701103180646896,
0.0031682117842137814,
0.009717301465570927,
0.04718463495373726,
0.0025969974230974913,
0.008148140273988247,
0.005697491113096476,
-0.03788207471370697,
0.030719520524144173,
0.0012686001136898994,
0.03395594283938408,
-0.0004882616049144417,
0.004262277856469154,
0.028833724558353424,
-0.04174215346574783,
0.01153506152331829,
-0.003977602813392878,
0.01806304045021534,
-0.01982734724879265,
-0.022095179185271263,
-0.044215913861989975,
0.043619249016046524,
0.012154924683272839,
-0.03015531785786152,
0.01484175305813551,
0.049397941678762436,
-0.01094850990921259,
0.00958984810858965,
-0.03913253918290138,
-0.02903207391500473,
-0.00984223559498787,
-0.003675485262647271,
0.028857655823230743,
0.006835346110165119,
0.025524286553263664,
-0.01943986676633358,
-0.01584639959037304,
-0.04169445484876633,
-0.033040851354599,
0.018102889880537987,
0.0051390063017606735,
-0.05231175199151039,
-0.008333439007401466,
0.005834882613271475,
-0.041668131947517395,
0.043833162635564804,
0.008093725889921188,
0.0031730197370052338,
0.012408806942403316,
-0.024768495932221413,
-0.0191901046782732,
-0.028258075937628746,
-0.03798986226320267,
0.015119696035981178,
-0.018697300925850868,
0.006638612598180771,
0.05106940120458603,
-0.024619625881314278,
-0.03166227787733078,
0.028336049988865852,
-0.043058522045612335,
-0.040773872286081314,
-0.01366385817527771,
-0.0348755307495594,
-0.03219865262508392,
-0.05955405905842781,
0.005241336766630411,
0.012727892957627773,
-0.04830138012766838,
-0.012970676645636559,
-0.06241907179355621,
-0.04567548260092735,
0.011250268667936325,
-0.004594172351062298,
0.0383666530251503,
-0.011473297141492367,
-0.032848112285137177,
0.06245185434818268,
0.006532082799822092,
-0.020397281274199486,
-0.022809233516454697,
-0.023576728999614716,
-0.0292124692350626,
-0.025983339175581932,
0.02173639088869095,
0.061280880123376846,
-0.013243384659290314,
0.052709925919771194,
0.029914822429418564,
0.036955252289772034,
0.013546548783779144,
-0.011142976582050323,
-0.0070548877120018005,
0.027681082487106323,
0.001083564362488687,
-0.021539859473705292,
0.0013412305852398276,
0.006430321838706732,
-0.03996262326836586,
0.018978331238031387,
0.008035427890717983,
0.024420425295829773,
-0.0253615565598011,
-0.04360147938132286,
0.05364760011434555,
-0.0018053564708679914,
0.03752601146697998,
-0.035121042281389236,
0.05256371945142746,
-0.01644725538790226,
0.010363542474806309,
-0.03627733513712883,
0.015399380587041378,
0.07765984535217285,
-0.05087277293205261,
-0.0044608344323933125,
0.039881471544504166,
0.012078064493834972,
-0.015804758295416832,
-0.02396702952682972,
-0.016274966299533844,
-0.023926012217998505,
0.02640685997903347,
-0.0032232163939625025,
-0.012300470843911171,
0.06117914244532585,
0.033872026950120926,
0.01834399439394474,
-0.0006063841283321381,
-0.05076286196708679,
0.02354133129119873,
-0.08713585138320923,
0.007880555465817451,
0.01203134749084711,
0.029740899801254272,
-0.011247411370277405,
0.06381305307149887,
0.034568268805742264,
0.03614088147878647,
-0.019162239506840706,
0.00830045621842146,
-0.07339206337928772,
-0.022731652483344078,
-0.02774905040860176,
0.010239820927381516,
-0.02341575361788273,
-0.03996856138110161,
-0.0003293156041763723,
-0.025682825595140457,
-0.029493333771824837,
-0.004733438603579998,
-0.003813811345025897,
-0.04104340821504593,
0.006420148070901632,
0.011281905695796013,
-0.011149127967655659,
-0.02039335109293461,
-0.00405653053894639,
-0.00033493596129119396,
-0.010532788932323456,
0.009441294707357883,
0.04654696583747864,
-0.003829502733424306,
-0.028903886675834656,
-0.04471120610833168,
0.035362787544727325,
0.02764858305454254,
-0.0005830342415720224,
0.03363755717873573,
0.004388552159070969,
-0.02581762708723545,
-0.008708871901035309,
-0.0312374085187912,
0.021057384088635445,
0.022289644926786423,
-0.008189987391233444,
-0.027587875723838806,
-0.030411941930651665,
-0.02407727763056755,
0.008081372827291489,
0.03999229520559311,
0.002093879273161292,
0.032971180975437164,
0.0237490925937891,
0.034308332949876785,
-0.004914566408842802,
0.016520701348781586,
0.01894298754632473,
0.008844058029353619,
-0.028793497011065483,
-0.0464293509721756,
0.008684289641678333,
-0.044235438108444214,
-0.0022995988838374615,
0.01232998725026846,
-0.013533505611121655,
-0.027732038870453835,
-0.014963222667574883,
0.02520471066236496,
-0.023251168429851532,
-0.009570636786520481,
-0.003339361399412155,
-0.035545073449611664,
0.019095664843916893,
-0.004161050543189049,
0.011692827567458153,
0.02096686325967312,
0.03491917997598648,
0.043981779366731644,
0.0443938784301281,
-0.031004013493657112,
-0.07288626581430435,
-0.012756316922605038,
0.02162959612905979,
0.011114696972072124,
-0.01829442009329796,
-0.019730830565094948,
-0.06441863626241684,
-0.030953101813793182,
0.02942759171128273,
-0.004431192297488451,
0.03132568299770355,
-0.00495422026142478,
-0.014138810336589813,
-0.026129737496376038,
-0.03835856541991234,
-0.02531977742910385,
-0.01703813299536705,
0.003823727136477828,
0.04069013521075249,
0.003936289343982935,
-0.01053275540471077,
-0.0364191010594368,
0.009989212267100811,
0.019855016842484474,
0.031268611550331116,
-0.006688814610242844,
0.008011848665773869,
-0.02585885301232338,
0.05416984483599663,
-0.04987391084432602,
-0.08119533956050873,
0.015441755764186382,
0.005718897096812725,
0.011921608820557594,
0.03827575966715813,
-0.031164543703198433,
-0.04835110157728195,
0.0013779079308733344,
-0.039365898817777634,
-0.013240419328212738,
0.0005032318294979632,
-0.009250464849174023,
0.011921240948140621,
0.04804922640323639,
0.00841484684497118,
0.03356996551156044,
0.0049514141865074635,
-0.02522277645766735,
-0.017542937770485878,
0.00048763881204649806,
0.029268797487020493,
-0.03850537911057472,
-0.016623713076114655,
-0.027052199468016624,
0.013207318261265755,
-0.018197065219283104,
0.02312658168375492,
0.015230200253427029,
0.014992652460932732,
-0.00502033531665802,
-0.040223378688097,
-0.017220433801412582,
-0.013673527166247368,
0.03298398107290268,
-0.00944322906434536,
-0.01400162372738123,
0.008197402581572533,
0.0063329944387078285,
-0.02989550679922104,
0.05741505324840546,
-0.05331558361649513,
-0.009927848353981972,
0.04159526526927948,
-0.0071285078302025795,
0.03100908361375332,
-0.02001316472887993,
0.000551183708012104,
0.02816843055188656,
-0.022265441715717316,
0.01653881184756756,
-0.03666809946298599,
0.003024797420948744,
-0.005519624799489975,
-0.0616702102124691,
-0.0179574117064476,
0.011427532881498337,
-0.043014734983444214,
0.03857261687517166,
0.003434675047174096,
0.038015156984329224,
0.010984444059431553,
-0.010032733902335167,
-0.09552933275699615,
-0.07653053849935532,
0.03136637806892395,
0.03546430170536041,
-0.021323611959815025,
-0.0031236247159540653,
0.0015897494740784168,
-0.01351186353713274,
-0.03948329761624336,
-0.011603344231843948,
0.07039326429367065,
-0.023956745862960815,
-0.02813604287803173,
0.00007829580863472074,
0.017009539529681206,
0.04352511093020439,
0.0004115398332942277,
-0.035977426916360855,
0.004287113435566425,
-0.02483266219496727,
-0.010017951019108295,
-0.010396305471658707,
0.06852323561906815,
-0.029450582340359688,
-0.0035790109541267157,
0.013894871808588505,
-0.00995585136115551,
0.052035506814718246,
-0.03581854701042175,
0.011462047696113586,
0.02957380749285221,
0.00042171607492491603,
0.007050251122564077,
-0.009585237130522728,
0.009860589168965816,
0.02205498144030571,
0.012431008741259575,
0.020342055708169937,
-0.0046328091993927956,
-0.0008686108631081879,
-0.009355473332107067,
0.04361557587981224,
0.03102155588567257,
-0.004950708243995905,
-0.0016754884272813797,
0.09200417250394821,
-0.029226643964648247,
-0.012631602585315704,
0.01798492670059204,
-0.008314302191138268,
0.023163244128227234,
0.02458798699080944,
-0.007615996059030294,
-0.004678353201597929,
0.029773587360978127,
-0.023790856823325157,
0.008211310021579266,
-0.01951848715543747,
0.0521145835518837,
0.048596203327178955,
-0.01583659090101719,
0.053686752915382385,
0.021247992292046547,
0.005641827825456858,
0.0049467533826828,
-0.013083182275295258,
-0.008001488633453846,
-0.007981077767908573,
-0.026806818321347237,
0.01426684856414795,
-0.028687601909041405,
0.008286495693027973,
0.05083281174302101,
0.0335087813436985,
-0.0017066914588212967,
-0.000035438926715869457,
0.06472951918840408,
0.007390983402729034,
0.03874300420284271,
-0.004773623775690794,
-0.03659186139702797,
0.041380349546670914,
-0.047817058861255646,
0.028401337563991547,
-0.02785693109035492,
-0.016068195924162865,
0.04115360975265503,
-0.00035439711064100266,
-0.004513892345130444,
-0.041907135397195816,
-0.04281895235180855,
-0.009542410261929035,
-0.02149542048573494,
0.0003045766206923872,
0.025304164737462997,
-0.00033568241633474827,
0.0035497243516147137,
0.03816160187125206,
0.014835687354207039,
0.0060645658522844315,
-0.0011102636344730854,
-0.04653359204530716,
-0.05115886405110359,
-0.014801530167460442,
-0.022442542016506195,
0.014633643440902233,
-0.025422468781471252,
-0.019132638350129128,
0.019444577395915985,
-0.035635292530059814,
-0.0015323738334700465,
-0.014453659765422344,
0.040828656405210495,
0.006230934988707304,
0.07338180392980576,
0.04096221178770065,
0.027646109461784363,
-0.0224609412252903,
-0.018120398744940758,
0.11940301209688187,
0.0700015053153038,
0.013771038502454758,
-0.09176339954137802,
0.033625632524490356,
-0.020025288686156273,
0.02762971818447113,
-0.01051016803830862,
0.05228332057595253,
0.01616678573191166,
0.00047666195314377546,
0.02395412139594555,
0.07293528318405151,
0.028042523190379143,
-0.00008602673187851906,
0.0497240275144577,
-0.06442028284072876,
-0.03665294870734215,
0.005119489971548319,
0.020099645480513573,
0.01374457124620676,
-0.019281607121229172,
-0.02093537710607052,
0.016718776896595955,
-0.031425315886735916,
-0.012147048488259315,
0.006867159623652697,
-0.021878542378544807,
-0.009983202442526817,
0.018219586461782455,
-0.02237880975008011,
0.0101476376876235,
0.025115562602877617,
0.016134055331349373,
-0.03594661504030228,
0.03799564391374588,
0.04348653554916382,
-0.011806732043623924,
0.01149861142039299,
0.003993806429207325,
0.016482733190059662,
0.014720484614372253,
-0.01048244722187519,
-0.01664825715124607,
-0.04065162315964699,
-0.008530762046575546,
-0.05841972306370735,
0.041090227663517,
-0.03186632692813873,
0.006361386738717556,
0.00014818871568422765,
0.009575574658811092,
-0.0012541682226583362,
-0.06602773070335388,
-0.038815103471279144,
0.007115816231817007,
-0.018298665061593056,
-0.003800687612965703,
-0.03184051066637039,
-0.015459444373846054,
-0.01080215722322464,
0.013291269540786743,
0.011489084921777248,
-0.005706272087991238,
-0.01896047033369541,
-0.007948930375277996,
-0.00641156081110239,
0.029751921072602272,
-0.01889992691576481,
-0.021196424961090088,
0.006007233634591103,
-0.025193603709340096,
-0.04221932590007782,
-0.027402928099036217,
0.005981048569083214,
0.034424249082803726,
0.046372734010219574,
-0.01128381211310625,
-0.012819920666515827,
-0.005414524581283331,
-0.028557972982525826,
0.03146250173449516,
-0.011755154468119144,
-0.004564390517771244,
-0.04270108416676521,
-0.008231616578996181,
-0.007062858901917934,
0.0017050731694325805,
-0.013367642648518085,
0.043785154819488525,
-0.020923659205436707,
0.069574736058712,
-0.03229665756225586,
-0.02846391312777996,
-0.06055741384625435,
0.012650792486965656,
-0.04305483028292656,
0.008141412399709225,
0.04285922646522522,
0.023206502199172974,
-0.0056220609694719315,
0.034094955772161484,
0.027710024267435074,
0.021564440801739693,
-0.020845556631684303,
0.006949234288185835,
0.02792615443468094,
-0.03824509680271149,
-0.03973444178700447,
0.048743393272161484,
-0.036219287663698196,
-0.016845421865582466,
-0.018378710374236107,
-0.03638307750225067,
0.014051235280930996,
0.01694258116185665,
0.021511882543563843,
-0.005320995580404997,
0.005710472818464041,
-0.017947273328900337,
0.0495460070669651,
-0.04487833008170128,
-0.03105759806931019,
-0.08581627905368805,
-0.02245786227285862,
0.010827388614416122,
-0.0181499645113945,
0.0015902535524219275,
0.020182698965072632,
0.0013791368110105395,
-0.012578506954014301,
0.04664536193013191,
0.010461339727044106,
-0.022090435028076172,
-0.006079466547816992,
0.024349387735128403,
-0.0087746512144804,
0.04214559495449066,
-0.029922829940915108,
-0.06891890615224838,
0.032745130360126495,
-0.060207705944776535,
-0.02099776268005371,
0.0005614205729216337,
0.0006712347385473549,
0.03170232102274895,
0.0037481363397091627,
-0.0054974933154881,
-0.013160157948732376,
0.07156825810670853,
-0.04249108210206032,
-0.015958525240421295,
0.013194197788834572,
0.01878720335662365,
0.026687411591410637,
-0.014455110765993595,
-0.01619412936270237,
-0.007511742878705263,
0.00151769386138767,
0.011991437524557114,
0.021753989160060883,
-0.01977880857884884,
-0.013677497394382954,
0.011415213346481323,
-0.006550428923219442,
0.02317238785326481,
0.03561749681830406,
0.0242789164185524,
0.012928735464811325,
0.02597929537296295,
-0.04986405372619629,
0.013900404796004295,
0.006694403942674398,
0.012086937204003334,
-0.07470457255840302,
-0.01542644202709198,
-0.009762795642018318,
-0.03148239105939865,
0.029777953401207924,
-0.054590754210948944,
0.011903095990419388,
0.020069153979420662,
-0.07039647549390793,
0.008832618594169617,
-0.0011110184714198112,
-0.014431439340114594,
-0.04775244742631912,
-0.014970459043979645,
0.012895248830318451,
0.03005605936050415,
0.030322404578328133,
0.030529005452990532,
0.03540746495127678,
0.008964111097157001,
-0.02497664839029312,
-0.025682302191853523,
-0.004759864881634712,
0.03093310445547104,
-0.021564172580838203,
-0.024912312626838684,
0.03160042315721512,
-0.029830222949385643,
-0.012392058968544006,
0.058776162564754486,
0.005630841013044119,
0.0053766341879963875,
0.013955307193100452,
0.050596922636032104,
0.025953833013772964,
0.018928466364741325,
-0.006386051885783672,
-0.013412917964160442,
0.006427666172385216,
0.03178129345178604,
0.019915228709578514,
0.042756300419569016,
0.0072066690772771835,
0.011813819408416748,
0.007671563886106014,
-0.04190456494688988,
-0.029138557612895966,
0.0026883098762482405,
-0.00641509797424078,
0.005798595026135445,
0.00693453149870038,
0.025865463539958,
0.0299402866512537,
-0.024387231096625328,
0.0370681956410408,
-0.07831620424985886,
-0.03507906571030617,
0.021518681198358536,
0.005726052448153496,
-0.0019565776456147432,
-0.0021009782794862986,
-0.020635761320590973,
-0.007822776213288307,
-0.03108298033475876,
0.038920216262340546,
0.014940527267754078,
-0.017011217772960663,
-0.0015419978881254792,
-0.019759036600589752,
0.0056688375771045685,
-0.012408426962792873,
-0.05637690797448158,
-0.04770279675722122,
0.03372838720679283,
0.026901178061962128,
0.03735861927270889,
0.01761677861213684,
-0.047912172973155975,
-0.028484176844358444,
-0.06248440966010094,
0.06669391691684723,
-0.046859532594680786,
-0.003794000018388033,
-0.037665385752916336,
-0.029486000537872314,
-0.009404255077242851,
-0.001795483403839171,
0.06656381487846375,
-0.0262630395591259,
-0.02899164706468582,
0.009061083197593689,
0.015759030357003212,
-0.004693971481174231,
-0.02995316870510578,
0.04648774489760399,
-0.03716336190700531,
-0.013482889160513878,
0.007399559020996094,
-0.015304279513657093,
0.009230702184140682,
0.018484080210328102,
0.015313336625695229,
-0.019996769726276398,
0.014443599618971348,
-0.03794366121292114,
0.02475401572883129,
0.0384133905172348,
0.010637895204126835,
-0.01301033329218626,
0.0701666995882988,
0.02816351316869259,
0.011526202782988548,
0.022135857492685318,
-0.021968206390738487,
-0.06996911019086838,
0.06705215573310852,
-0.004859597887843847,
-0.0003935116110369563,
-0.012606441974639893,
0.013597585260868073,
0.025778597220778465,
-0.019972097128629684,
0.008843506686389446,
0.03911850228905678,
-0.025465814396739006,
-0.024123162031173706,
0.015887489542365074,
0.03602724149823189,
0.027938667684793472,
-0.018214836716651917,
0.02389148436486721,
0.009271633811295033,
-0.004051804076880217,
0.01767328381538391,
0.02812178246676922,
0.02710440754890442,
0.024273144081234932,
0.030984045937657356,
0.016563566401600838,
-0.020481925457715988,
0.03420994430780411,
-0.024182669818401337,
0.041797470301389694,
-0.05022697523236275,
-0.03352070227265358,
0.019769661128520966,
-0.03827570751309395,
0.02521996945142746,
-0.010087928734719753,
0.016787050291895866,
0.12437170743942261,
0.0016329319914802909,
0.03943686559796333,
0.0105630187317729,
0.04420209676027298,
0.0031473515555262566,
-0.021937280893325806,
0.057925641536712646,
-0.0066892001777887344,
-0.0067940386943519115,
-0.023429716005921364,
-0.004757081624120474,
-0.007484033238142729,
0.02809223160147667,
0.011859305202960968,
0.023236138746142387,
0.007515845820307732,
-0.019757568836212158,
-0.030775630846619606,
0.00876504648476839,
-0.007357623428106308,
-0.013731837272644043,
0.018118401989340782,
0.043522562831640244,
0.02517230436205864,
0.013717607595026493,
-0.03772301971912384,
-0.016588974744081497,
0.06358730047941208,
-0.04398932307958603,
-0.0186788197606802,
-0.027134275063872337,
0.02998538874089718,
0.007372772786766291,
-0.004115667659789324
] |
<p>I have arm wrestled people with less strength than me who win simply because they have thicker wrists, or larger hands. It has nary to do with having better technique either, because their wrist size alone seems to be a big advantage.</p>
<p>I want to know why, as explained by physics, why the torque they produce is so much larger, even with less muscular force by the axis than with me having greater strength, but smaller wrists & hands?</p>
<p>For example, I have 7-inch wrists, and 7.2-inch hands.</p>
<p>My opponent has 8-inch wrists, and 8.2-inch hands.</p>
<p>They have been tested to have less physical power in every muscle group used in arm wrestling compared to me, yet, they win, and they have no technical advantage over me in the sport either.</p>
<p>I have noticed that this advantage goes beyond arm wrestling, but to ANY angular/torque-like position of some grasping another's hand/wrist outwards in front of their bodies:
<img src="http://i.stack.imgur.com/s0Fls.jpg" alt="enter image description here">
<img src="http://i.stack.imgur.com/aqkBc.jpg" alt="enter image description here"></p>
<p>Please tell me why this is.</p>
<p>EXTRA: This question, or a question of this nature, has never been asked on this site, so please cut me some slack here! I know the question is poor at best, but some insight would be nice!</p>
| 7,653 |
[
-0.026186568662524223,
-0.035281095653772354,
-0.025971706956624985,
-0.03391619399189949,
0.0012668042909353971,
0.023737000301480293,
-0.026600193232297897,
-0.037307579070329666,
-0.015302661806344986,
0.010798675939440727,
0.018724652007222176,
0.0013308555353432894,
0.04935144633054733,
0.015050232410430908,
0.0000484575612063054,
-0.019043931737542152,
-0.012054228223860264,
-0.004744089674204588,
-0.00826868787407875,
0.007969447411596775,
-0.022494357079267502,
0.011145148426294327,
-0.009694647043943405,
0.00541724031791091,
-0.0230243019759655,
0.021413106471300125,
0.047294892370700836,
-0.011812938377261162,
0.028023887425661087,
0.04279503971338272,
0.035570044070482254,
0.02436140365898609,
-0.012484212405979633,
-0.015012454241514206,
-0.0015480052679777145,
0.004836037755012512,
-0.04235602542757988,
-0.009233576245605946,
0.03787943720817566,
0.04372907429933548,
-0.041974201798439026,
0.01604286953806877,
0.012016449123620987,
0.027085183188319206,
0.004458928480744362,
0.05222101882100105,
-0.034564629197120667,
-0.006976657547056675,
0.03724868968129158,
-0.039285965263843536,
0.05843893438577652,
0.009175596758723259,
0.06043172627687454,
0.03822566568851471,
0.009075535461306572,
0.00017876976926345378,
0.06362013518810272,
0.06279462575912476,
-0.019436761736869812,
-0.052413515746593475,
-0.005593438632786274,
-0.02382092922925949,
-0.035211920738220215,
-0.005865098442882299,
0.0041426680982112885,
0.056313406676054,
-0.03043941594660282,
-0.03076871857047081,
0.010450568050146103,
0.008986248634755611,
0.02581154927611351,
0.037072401493787766,
0.050631921738386154,
-0.005305969621986151,
0.015079904347658157,
-0.028432419523596764,
-0.008297944441437721,
0.025512801483273506,
0.050765033811330795,
0.03535354882478714,
-0.04216911271214485,
0.003724315669387579,
0.05484277009963989,
0.05504533275961876,
0.03857111185789108,
-0.0024748779833316803,
0.05489040166139603,
-0.01072081271559,
0.013002585619688034,
0.04785548523068428,
-0.015363545157015324,
-0.001899575931020081,
0.026539355516433716,
-0.013637591153383255,
-0.008009116165339947,
-0.026083197444677353,
-0.02402922324836254,
0.06007806956768036,
0.03580503165721893,
0.009254658594727516,
-0.013349703513085842,
-0.06423995643854141,
0.025482192635536194,
0.07407151162624359,
0.057411838322877884,
-0.016598768532276154,
-0.019009312614798546,
0.01046095322817564,
0.00427292799577117,
0.019502272829413414,
-0.02347641810774803,
-0.001832438400015235,
-0.0161273330450058,
0.00454134214669466,
0.0033193237613886595,
-0.06162633001804352,
0.010015110485255718,
0.03720051422715187,
0.0805288627743721,
0.06071144714951515,
0.021600395441055298,
-0.0497366338968277,
-0.004857043270021677,
-0.04120619222521782,
-0.01990598253905773,
-0.002330016577616334,
0.01749628596007824,
-0.017567945644259453,
-0.013014320284128189,
0.023465847596526146,
0.004442492965608835,
-0.002672275761142373,
0.019127875566482544,
-0.04401862993836403,
0.024073386564850807,
0.034450970590114594,
-0.08436621725559235,
-0.08255176991224289,
0.1060883104801178,
0.026994217187166214,
-0.011225559748709202,
-0.10040467232465744,
-0.023094965144991875,
0.024830421432852745,
0.04456852376461029,
0.037081338465213776,
0.012881219387054443,
-0.006156479474157095,
0.048679668456315994,
0.010567673482000828,
0.015726758167147636,
-0.011385899968445301,
-0.012753257527947426,
-0.018580827862024307,
0.028416728600859642,
-0.0734892264008522,
-0.003591363551095128,
0.0025782743468880653,
-0.01803441159427166,
0.000043697677028831095,
0.06920219212770462,
-0.0022818383295089006,
0.01745018921792507,
-0.019410492852330208,
-0.026764363050460815,
-0.026677226647734642,
0.08850491791963577,
0.008941110223531723,
0.014575482346117496,
0.035388290882110596,
-0.008078415878117085,
0.042475130409002304,
0.024622943252325058,
-0.01656503602862358,
0.012657870538532734,
-0.00018265597464051098,
-0.0022221647668629885,
0.018545547500252724,
-0.028935018926858902,
-0.013276014477014542,
-0.013152209110558033,
-0.05892743542790413,
-0.009380043484270573,
-0.029179979115724564,
0.04958829656243324,
0.06505018472671509,
0.014908229932188988,
-0.00744460616260767,
0.017277292907238007,
-0.01755082979798317,
-0.04545796662569046,
-0.0659613162279129,
0.021289037540555,
-0.02306545525789261,
-0.0283214021474123,
0.017585214227437973,
-0.02015860192477703,
0.01697741448879242,
0.0022250839974731207,
-0.018829116597771645,
0.009963151067495346,
0.02866015024483204,
0.04958654195070267,
0.022681154310703278,
0.00871999654918909,
0.04778457060456276,
0.054147686809301376,
-0.027277089655399323,
0.011400783434510231,
-0.012559313327074051,
-0.05591481924057007,
0.05200261250138283,
-0.025323251262307167,
0.026305699720978737,
0.026555752381682396,
-0.0012465269537642598,
0.0162214282900095,
0.033377788960933685,
-0.03482716530561447,
0.016504213213920593,
0.02708861231803894,
0.09646005928516388,
0.0011471292236819863,
0.012565757147967815,
0.007959004491567612,
0.035616349428892136,
0.009811620227992535,
-0.004163139499723911,
-0.013302581384778023,
-0.003718717023730278,
-0.045621518045663834,
0.0030563725158572197,
0.02409031242132187,
-0.0011079463874921203,
-0.06061045080423355,
0.03043016791343689,
0.02353666163980961,
0.05919172242283821,
0.006273168604820967,
-0.0026988470926880836,
-0.01757965423166752,
-0.032724011689424515,
-0.002215165877714753,
0.0367421992123127,
0.0008243141928687692,
0.009344544261693954,
0.0032602031715214252,
0.03489130735397339,
-0.00910880696028471,
0.03129643574357033,
-0.025199860334396362,
0.008008452132344246,
0.03000655584037304,
0.025058643892407417,
-0.004031401593238115,
-0.003888065228238702,
0.028058966621756554,
-0.03339356556534767,
0.019583819434046745,
0.04999784752726555,
0.00794018991291523,
-0.006785547826439142,
-0.03879372775554657,
-0.012310467660427094,
0.02966807223856449,
0.025089165195822716,
-0.001074054162018001,
0.029898278415203094,
0.01100721675902605,
-0.0501750148832798,
-0.015237648971378803,
-0.010703688487410545,
-0.010388541966676712,
-0.012774545699357986,
-0.00756423082202673,
0.0007343015749938786,
0.017899764701724052,
0.03349774703383446,
-0.025282680988311768,
0.02432151883840561,
-0.0084801921620965,
-0.03057783655822277,
0.04568522423505783,
-0.0025208324659615755,
-0.04597475007176399,
-0.013471567071974277,
-0.0397241935133934,
-0.014235340058803558,
0.048259198665618896,
0.018940100446343422,
0.029969142749905586,
0.012493237853050232,
0.004174160771071911,
-0.023835983127355576,
-0.04256071150302887,
-0.007848139852285385,
0.01356279756873846,
0.023545632138848305,
-0.010855026543140411,
0.046654682606458664,
0.015123991295695305,
-0.011046295054256916,
0.04622206836938858,
-0.04659940302371979,
-0.031098388135433197,
0.00042114025563932955,
0.03510460630059242,
0.012486032210290432,
-0.010010183788836002,
-0.018586155027151108,
-0.015410315245389938,
-0.028230035677552223,
-0.023858051747083664,
-0.029810860753059387,
-0.04863951727747917,
0.020550241693854332,
0.023719673976302147,
0.021602094173431396,
0.008289911784231663,
-0.019698500633239746,
0.06710734963417053,
0.0066855051554739475,
-0.03105078637599945,
-0.05966334789991379,
-0.010340171866118908,
-0.03308922052383423,
-0.042479511350393295,
0.025611257180571556,
0.0275262538343668,
-0.0030320947989821434,
0.0539243258535862,
0.01947234570980072,
0.023997386917471886,
0.0699167400598526,
-0.017643896862864494,
-0.055809274315834045,
0.003420853288844228,
0.0010662113782018423,
-0.028110088780522346,
0.02573329210281372,
-0.005185857880860567,
-0.03933367133140564,
-0.009008885361254215,
0.02840106375515461,
0.02060077339410782,
-0.04345725476741791,
-0.08082469552755356,
0.013029086403548717,
0.012691842392086983,
0.0045629641972482204,
0.012395739555358887,
0.0242142453789711,
-0.008450116030871868,
0.01370289921760559,
0.01709219254553318,
0.0013841321924701333,
0.03147013485431671,
-0.01551730465143919,
0.025263046845793724,
0.04227932170033455,
0.014658461324870586,
-0.007588669657707214,
-0.0021270893048495054,
-0.0006440107827074826,
-0.026243388652801514,
-0.005034744739532471,
-0.03186378255486488,
-0.038942404091358185,
0.03235655277967453,
-0.0005313336150720716,
0.02124982886016369,
0.027511827647686005,
-0.03130998834967613,
0.008676223456859589,
-0.05046214163303375,
-0.00375345884822309,
-0.009728196077048779,
0.06550522148609161,
-0.028777463361620903,
0.03706814721226692,
0.03496428206562996,
0.025736765936017036,
-0.025015169754624367,
0.025572875514626503,
-0.04993068426847458,
0.05223174765706062,
-0.03226310387253761,
-0.007331222295761108,
0.0449480339884758,
-0.014448199421167374,
0.007308549247682095,
-0.01429518312215805,
-0.0206903126090765,
-0.022067049518227577,
0.002726092701777816,
-0.04813854396343231,
-0.009362420998513699,
-0.011964553967118263,
-0.012482930906116962,
0.0033516581170260906,
0.02468668669462204,
0.008595653809607029,
-0.012444511987268925,
0.043515875935554504,
0.03531070426106453,
-0.03242862597107887,
-0.02992384508252144,
-0.04815010726451874,
0.0535852313041687,
-0.016716020181775093,
0.015439213253557682,
0.02413603477180004,
-0.003500433173030615,
0.001264582620933652,
-0.0197612177580595,
-0.017832234501838684,
0.03697976842522621,
0.025572001934051514,
0.010931114666163921,
-0.011679780669510365,
-0.08415716141462326,
-0.0428648442029953,
-0.008866293355822563,
0.038304295390844345,
-0.02915826439857483,
-0.00558847188949585,
0.04159931093454361,
-0.0002561976434662938,
-0.011375981383025646,
0.06220477074384689,
-0.0018647313117980957,
0.030390098690986633,
-0.04296037182211876,
-0.07560572028160095,
-0.02092745155096054,
0.020663278177380562,
0.0019205092685297132,
0.03216283768415451,
-0.009802565909922123,
0.029116330668330193,
-0.030113613232970238,
0.0686662346124649,
-0.03713390976190567,
-0.02878895401954651,
0.03803512826561928,
-0.0315239243209362,
0.01445896178483963,
0.0203746035695076,
0.014919299632310867,
0.00928633101284504,
0.016684623435139656,
0.01915125548839569,
-0.0170094333589077,
0.015329410322010517,
-0.04770413041114807,
-0.04493597894906998,
0.021564096212387085,
0.04168658331036568,
-0.025301696732640266,
0.008473047986626625,
0.010338876396417618,
-0.006637662183493376,
0.027972539886832237,
-0.05718019977211952,
0.08852413296699524,
-0.0654294490814209,
0.006874199490994215,
-0.06466613709926605,
-0.03390839323401451,
-0.030545208603143692,
-0.011721605435013771,
0.007602794095873833,
0.012079888954758644,
-0.02305515669286251,
0.007159298285841942,
-0.0024176551960408688,
0.004788391292095184,
0.042896490544080734,
-0.00003915136767318472,
-0.006233367137610912,
-0.032038260251283646,
-0.04469737783074379,
0.0024584101047366858,
-0.02287466824054718,
-0.035311680287122726,
-0.012515125796198845,
-0.01372323464602232,
-0.03023284673690796,
0.011966877616941929,
-0.044087283313274384,
-0.03906847909092903,
0.030729686841368675,
-0.02674833871424198,
-0.008326560258865356,
0.008785448968410492,
-0.009170643985271454,
0.043769560754299164,
0.03701752796769142,
-0.03128993883728981,
0.0210193432867527,
0.07301413267850876,
-0.030943147838115692,
0.006542990915477276,
-0.02031797543168068,
0.0021347233559936285,
0.02832360751926899,
-0.045383743941783905,
-0.03427879884839058,
0.00024702088558115065,
0.014079883694648743,
0.045832715928554535,
-0.014898326247930527,
0.07593721151351929,
-0.03745754063129425,
-0.053778134286403656,
0.005108821205794811,
0.010059713385999203,
0.03711696341633797,
-0.014305699616670609,
0.026872210204601288,
-0.03926148638129234,
-0.009795143269002438,
0.005259786266833544,
0.024299630895256996,
0.011246253736317158,
0.026629170402884483,
0.020690249279141426,
-0.029168320819735527,
0.020151633769273758,
-0.025916675105690956,
0.002379943849518895,
-0.018489087000489235,
-0.03902686759829521,
0.05026266351342201,
-0.006947403773665428,
0.011778470128774643,
0.01396956481039524,
-0.045418255031108856,
-0.023354751989245415,
-0.026319997385144234,
-0.033556509763002396,
0.059656161814928055,
0.003659720765426755,
0.0043870508670806885,
0.010548784397542477,
-0.02089419774711132,
-0.036994606256484985,
-0.04841014742851257,
0.01609097234904766,
0.05385112017393112,
0.01496482826769352,
0.018375331535935402,
-0.0007057758630253375,
0.007445470429956913,
-0.008211750537157059,
-0.007593603804707527,
0.03553127497434616,
-0.0070597706362605095,
0.008373291231691837,
0.02810557372868061,
-0.032747916877269745,
0.0701279416680336,
0.015636933967471123,
-0.038714706897735596,
0.027100522071123123,
-0.002439788542687893,
0.009888152591884136,
-0.008409014903008938,
0.033564481884241104,
-0.0413028858602047,
-0.025938570499420166,
0.018925728276371956,
0.002776227192953229,
0.016655348241329193,
0.007667833007872105,
-0.0012254118919372559,
-0.013377439230680466,
0.001507664448581636,
0.046103280037641525,
-0.026986513286828995,
0.047300320118665695,
0.004117727279663086,
0.01449662260711193,
-0.004683437291532755,
0.00021252395526971668,
-0.03693888336420059,
-0.04430181533098221,
-0.030264679342508316,
0.008969351649284363,
-0.03291140869259834,
-0.018230566754937172,
0.06259649991989136,
-0.041224826127290726,
0.005936517845839262,
0.007349260151386261,
-0.03126285597681999,
0.05417945608496666,
0.02308562770485878,
0.015441874973475933,
0.028824901208281517,
0.06087680906057358,
-0.04703432321548462,
-0.03262447565793991,
-0.032079923897981644,
0.028973083943128586,
0.057214416563510895,
-0.01950882002711296,
0.05759401619434357,
0.07305791229009628,
0.002053073374554515,
0.023845748975872993,
-0.022911785170435905,
0.0077338432893157005,
-0.021217279136180878,
-0.03287634998559952,
0.036475770175457,
0.02242921106517315,
0.017805911600589752,
0.05733182653784752,
0.01017837505787611,
-0.001549941604025662,
0.0013042828068137169,
0.04542204737663269,
0.03886870667338371,
-0.0009170746780000627,
-0.003620838513597846,
-0.018745558336377144,
0.02276959829032421,
-0.037047240883111954,
0.0074721951968967915,
0.025330588221549988,
-0.02313065715134144,
0.04038560390472412,
0.005953477695584297,
0.0012198506155982614,
-0.016383830457925797,
-0.00959907379001379,
-0.0037429598160088062,
-0.0031256251968443394,
0.007612875197082758,
0.00034100841730833054,
0.03249673545360565,
-0.004945472348481417,
0.029725156724452972,
-0.006021266337484121,
0.019550278782844543,
-0.03555608540773392,
-0.044879183173179626,
-0.017348680645227432,
-0.030645057559013367,
-0.09835173934698105,
0.009561565704643726,
0.000481138878967613,
0.0018044988391920924,
0.03245428949594498,
-0.030239198356866837,
0.027148308232426643,
-0.016132386401295662,
0.0016653109341859818,
-0.024367226287722588,
0.08829361200332642,
-0.02740207128226757,
-0.0006330900359898806,
0.021186217665672302,
-0.013030938804149628,
0.10505186021327972,
0.02187100425362587,
0.01616019383072853,
-0.010827433317899704,
0.04327889904379845,
0.012990184128284454,
-0.018506014719605446,
-0.029424544423818588,
0.0016877715243026614,
0.007474634330719709,
-0.03519080951809883,
0.004128799773752689,
0.03347849100828171,
0.026899145916104317,
-0.002661031438037753,
0.04478830099105835,
-0.04129930958151817,
-0.012842070311307907,
0.029494434595108032,
0.012041994370520115,
0.01513750571757555,
-0.027210336178541183,
-0.018206479027867317,
0.02625800110399723,
0.03833932802081108,
-0.037624508142471313,
-0.017024703323841095,
0.006014247424900532,
0.01670338772237301,
0.01776742748916149,
-0.03824958950281143,
-0.0154654486104846,
-0.019157813861966133,
-0.017532439902424812,
-0.08066008985042572,
0.001386290299706161,
0.01018585730344057,
-0.017513457685709,
-0.01670810952782631,
-0.007401141803711653,
0.003078358480706811,
-0.01683550886809826,
0.026128938421607018,
-0.008700753562152386,
-0.02248942293226719,
0.01395884808152914,
-0.010839921422302723,
0.02147991582751274,
0.013189110904932022,
0.03112218901515007,
0.01730600744485855,
-0.041869886219501495,
-0.021634940057992935,
-0.048953913152217865,
-0.028519282117486,
0.0028941344935446978,
0.020530905574560165,
-0.019440941512584686,
-0.042815402150154114,
-0.013725555501878262,
0.02744806371629238,
-0.011214383877813816,
0.03804750367999077,
-0.014204716309905052,
-0.02634304389357567,
-0.022633841261267662,
-0.020860737189650536,
-0.012457453645765781,
0.040253426879644394,
-0.004360244609415531,
-0.058636415749788284,
0.013033427298069,
-0.04169299080967903,
-0.008415210992097855,
0.015640629455447197,
0.02465519867837429,
0.04427265748381615,
0.014243172481656075,
-0.037508461624383926,
-0.0051396992057561874,
-0.03701809048652649,
0.038693707436323166,
-0.05280226096510887,
-0.007190188858658075,
-0.034465182572603226,
0.0033366777934134007,
0.013871828094124794,
0.026182612404227257,
-0.0022633301559835672,
-0.014981817454099655,
-0.034140799194574356,
0.03959911689162254,
0.005842108745127916,
-0.020604493096470833,
-0.07639351487159729,
0.0038960082456469536,
-0.023346293717622757,
-0.030741378664970398,
-0.023103229701519012,
0.027064267545938492,
0.04133272171020508,
-0.004124614875763655,
0.017734017223119736,
-0.024424051865935326,
-0.018544889986515045,
-0.002134796231985092,
0.012225130572915077,
-0.032910097390413284,
-0.003792324336245656,
-0.007934371009469032,
-0.03389769792556763,
-0.03647935763001442,
-0.04958464950323105,
-0.038510579615831375,
-0.05976642668247223,
0.0047070602886378765,
0.03399791941046715,
0.0052907830104231834,
-0.02053496614098549,
-0.04890526831150055,
0.0033399397507309914,
-0.034730229526758194,
-0.005464585497975349,
-0.042764369398355484,
-0.031706877052783966,
-0.020607847720384598,
0.008459832519292831,
-0.017671804875135422,
0.017694368958473206,
0.00897546298801899,
-0.015368156135082245,
0.012561829760670662,
0.020539868623018265,
0.015405411832034588,
-0.021891361102461815,
-0.019663652405142784,
-0.023638049140572548,
0.016665462404489517,
0.0011818382190540433,
-0.021088311448693275,
0.07256408035755157,
-0.030904997140169144,
0.021426988765597343,
0.018386004492640495,
-0.05152158439159393,
0.02177942916750908,
0.03503071889281273,
-0.04596449434757233,
-0.0294350553303957,
0.07849124073982239,
-0.00995729397982359,
-0.021859060972929,
-0.015196208842098713,
0.031667787581682205,
0.023216525092720985,
0.03230765834450722,
-0.03255991265177727,
-0.03214191272854805,
0.00996696762740612,
0.028751932084560394,
0.00569266127422452,
0.029650159180164337,
-0.03927446901798248,
0.017944710329174995,
0.042734403163194656,
-0.03295225277543068,
0.006738121621310711,
-0.0007553938776254654,
0.02272501029074192,
0.01333837490528822,
-0.006359248887747526,
0.049961332231760025,
-0.02688964270055294,
0.019409166648983955,
-0.056648075580596924,
-0.005957610905170441,
-0.015521243214607239,
0.022736603394150734,
0.04427079111337662,
-0.06022205203771591,
-0.007451831828802824,
-0.0011881082318723202,
-0.10035520046949387,
-0.04821654409170151,
-0.015013682655990124,
-0.02477339096367359,
-0.047394320368766785,
-0.005230800248682499,
0.015417358838021755,
0.038209885358810425,
-0.008257630281150341,
0.049554966390132904,
0.009730769321322441,
0.011790502816438675,
-0.02484954334795475,
-0.007179948966950178,
-0.03457481786608696,
0.04464757442474365,
-0.011948306113481522,
-0.024228747934103012,
0.029206683859229088,
0.015510276891291142,
-0.04573134705424309,
0.029963018372654915,
0.004094515461474657,
0.016503406688570976,
0.017176691442728043,
0.01709243841469288,
-0.0315261036157608,
0.02222941257059574,
-0.010606082156300545,
-0.024213237687945366,
-0.01912359893321991,
0.012688086368143559,
-0.021042674779891968,
0.018629349768161774,
-0.016013680025935173,
0.032848890870809555,
0.046537093818187714,
-0.03857473284006119,
0.010514378547668457,
0.03143594413995743,
-0.03644324094057083,
0.012863915413618088,
0.01827208325266838,
0.012976054102182388,
0.06841480731964111,
-0.006806784775108099,
0.017103716731071472,
-0.012095987796783447,
-0.02632303535938263,
0.020323608070611954,
-0.003498827340081334,
-0.001546166487969458,
0.03971158713102341,
0.022934362292289734,
-0.018367744982242584,
-0.033122651278972626,
0.020536087453365326,
-0.00039313005981966853,
-0.004756234586238861,
0.010715118609368801,
-0.0009195017046295106,
0.00989210233092308,
-0.026386253535747528,
-0.030371572822332382,
-0.06394723057746887,
0.015286346897482872,
-0.019992927089333534,
0.05979335680603981,
0.027666758745908737,
-0.016649475321173668,
-0.0030267417896538973,
-0.09710397571325302,
0.024327056482434273,
-0.01855388842523098,
-0.050703201442956924,
-0.05595840886235237,
-0.020109647884964943,
0.014004133641719818,
0.003554691793397069,
0.025625139474868774,
0.0015996599104255438,
-0.013509492389857769,
-0.001605321536771953,
-0.03132183104753494,
-0.029189366847276688,
-0.04228053241968155,
0.025107597932219505,
0.001772242016158998,
-0.023725440725684166,
0.04218291491270065,
0.009684634394943714,
0.018902797251939774,
0.03713145852088928,
0.06337661296129227,
-0.022988852113485336,
-0.00909177865833044,
-0.016866421326994896,
-0.052172835916280746,
0.041688330471515656,
-0.012304415926337242,
0.014031213708221912,
0.05636805295944214,
-0.019270602613687515,
-0.0011455073254182935,
0.014839047566056252,
-0.009951167739927769,
-0.02851751074194908,
0.06657583266496658,
-0.03547560051083565,
0.016112063080072403,
-0.01208699494600296,
0.00845948327332735,
0.02380598522722721,
-0.03492732718586922,
0.02101539820432663,
0.04520827531814575,
0.004432674031704664,
-0.017884409055113792,
0.052390534430742264,
0.07221940159797668,
-0.023080788552761078,
-0.03696131706237793,
0.036568351089954376,
-0.0036544818431138992,
-0.03626954182982445,
-0.023011639714241028,
0.027175594121217728,
0.05325813591480255,
0.024926025420427322,
0.006778707727789879,
0.03115098364651203,
-0.027954960241913795,
0.053931403905153275,
-0.02990598790347576,
0.035439953207969666,
-0.04080488160252571,
-0.04665081575512886,
-0.04450139403343201,
-0.009562172926962376,
0.02180437557399273,
0.03660108894109726,
-0.02304849773645401,
0.04977705702185631,
0.00010518300405237824,
-0.044029198586940765,
0.014234291389584541,
-0.0026362838689237833,
0.0018884239252656698,
-0.0372367762029171,
0.020602663978934288,
0.005143831484019756,
-0.054936714470386505,
0.016035638749599457,
-0.017006101086735725,
-0.014498712494969368,
0.07185810059309006,
-0.007190079428255558,
0.00008094074291875586,
0.010628242045640945,
-0.005477595143020153,
0.003756845137104392,
-0.019996952265501022,
-0.028829816728830338,
-0.008756401017308235,
0.03384608402848244,
0.013775601051747799,
0.014182879589498043,
-0.03713927045464516,
-0.02226717583835125,
-0.022943390533328056,
0.05765428766608238,
-0.04244263470172882,
-0.029820727184414864,
-0.008222467266023159,
0.04584016650915146,
0.037296611815690994,
-0.0035738577134907246
] |
<p>It's easy to find the "magic" numbers of neutrons on the diagrams of alpha-decay energy: 82, 126, 152, 162. Such "magic" nuclei should be more stable than their neighbors.</p>
<p><IMG src="http://elementy.ru/blogs/u/i/2598.gif">
<IMG src="http://elementy.ru/blogs/u/i/2599.gif"></p>
<p>But why some nuclei with "magic" numbers of neutrons have a half-life less than their neighbor isotopes with odd numbers of neutrons?</p>
<p>Examples for "magic" number 126:</p>
<p>A half-life of "magic" Po-210 is <strong>138 days</strong>, whereas a half-life of neighbor isotope Po-209 is <strong>102 years</strong>.</p>
<p>A half-life of "magic" Ra-214 is <strong>2.46 sec</strong>, whereas a half-life of neighbor isotope Ra-213 is <strong>2.74 min</strong>. </p>
<p>Examples for "magic" number 152:</p>
<p>A half-life of "magic" Cm-248 is <strong>348 thousand years</strong>, whereas a half-life of neighbor isotope Cm-247 is <strong>16 million years</strong>!</p>
<p>A half-life of "magic" Cf-250 is <strong>13 years</strong>, whereas a half-life of neighbor isotope Cf-249 is <strong>351 years</strong>.</p>
<p>P.S. <a href="http://www.nndc.bnl.gov/masses/mass.mas03" rel="nofollow">Source</a> of the diagrams data</p>
| 7,654 |
[
-0.020502101629972458,
-0.038557156920433044,
0.013718788512051105,
-0.0390726737678051,
0.006673245225101709,
0.01202429085969925,
-0.02319655753672123,
-0.07330437004566193,
-0.006173326168209314,
-0.030343160033226013,
0.08042962104082108,
0.01986539736390114,
0.04714525118470192,
0.01845066249370575,
-0.014031260274350643,
0.016196178272366524,
-0.00008925741713028401,
-0.02301187813282013,
-0.029276486486196518,
-0.04048476368188858,
0.0494864396750927,
-0.010507896542549133,
-0.0252377912402153,
0.008765041828155518,
-0.030748827382922173,
0.03669511899352074,
0.006525065749883652,
0.024483541026711464,
0.018484152853488922,
0.03833742067217827,
-0.013100030831992626,
-0.03872433304786682,
0.08084772527217865,
0.01576153188943863,
0.01842976175248623,
-0.0031775282695889473,
-0.014354628510773182,
0.0015059731667861342,
-0.0037839598953723907,
0.06126323714852333,
-0.05843745917081833,
-0.05187181010842323,
-0.02865026146173477,
0.018198542296886444,
-0.0155985988676548,
0.020350482314825058,
0.0035222219303250313,
-0.02934255078434944,
0.06535445153713226,
-0.016683703288435936,
0.03625275194644928,
-0.008956480771303177,
0.043502435088157654,
0.030810663476586342,
-0.02033909782767296,
-0.035534609109163284,
0.04916997626423836,
0.06323029845952988,
-0.012978320941329002,
-0.03310412913560867,
-0.04126604273915291,
-0.02342916838824749,
0.005650447215884924,
0.0334717258810997,
0.025698114186525345,
0.06984901428222656,
-0.0007503561791963875,
0.011113607324659824,
0.018105871975421906,
0.030124735087156296,
0.035848911851644516,
0.006229539401829243,
0.04068106412887573,
-0.021862618625164032,
0.02117750234901905,
0.01061303075402975,
0.010024339891970158,
0.00604295264929533,
0.05482922121882439,
0.0773957222700119,
-0.031872618943452835,
-0.001241048565134406,
0.047810669988393784,
0.014338151551783085,
-0.014147921465337276,
0.0015893479576334357,
0.054171573370695114,
0.0027091805823147297,
-0.01883161999285221,
0.025120550766587257,
0.012814625166356564,
-0.022990776225924492,
0.043137770146131516,
-0.0004039863124489784,
-0.025239821523427963,
0.02559777908027172,
0.004306907765567303,
0.007900203578174114,
0.00003600376658141613,
0.0351322740316391,
0.010875111445784569,
-0.047082897275686264,
0.03267166391015053,
0.051157742738723755,
0.011596255004405975,
-0.01837984286248684,
-0.04325767606496811,
-0.012258411385118961,
-0.0325896218419075,
0.009328777901828289,
0.001556424074806273,
-0.023510171100497246,
-0.0029184306040406227,
0.003568850690498948,
0.01776977628469467,
-0.038104165345430374,
0.01792607270181179,
-0.000045517335820477456,
0.08880703151226044,
0.041596438735723495,
0.02199365384876728,
-0.006278704386204481,
0.0011011261958628893,
-0.07151410728693008,
-0.0671473816037178,
0.006216310430318117,
0.0359472818672657,
0.013709849677979946,
-0.048315681517124176,
0.026851382106542587,
0.016852209344506264,
-0.000693212728947401,
0.04475712031126022,
-0.05989096686244011,
0.05201595649123192,
0.010498571209609509,
-0.09341475367546082,
-0.02997583895921707,
0.05591356009244919,
0.026215508580207825,
-0.03138317912817001,
-0.07703133672475815,
0.018662750720977783,
0.015674222260713577,
0.06011470407247543,
0.02742833085358143,
0.0072997696697711945,
0.013134357519447803,
0.02029380016028881,
0.03453736752271652,
-0.004140876233577728,
0.011333552189171314,
0.04635414108633995,
-0.013853315263986588,
-0.021624870598316193,
-0.08657096326351166,
0.018642770126461983,
-0.008619796484708786,
-0.008855165913701057,
0.018118485808372498,
0.07613803446292877,
-0.04143958538770676,
0.037480100989341736,
-0.019126906991004944,
0.011527169495821,
-0.03710181266069412,
0.09006794542074203,
0.0706549808382988,
-0.011254065670073032,
0.05882002040743828,
-0.04370860755443573,
0.04163733497262001,
-0.016961753368377686,
0.02089405246078968,
0.03673434630036354,
-0.03514232113957405,
-0.027933456003665924,
-0.02570432610809803,
-0.0019011336844414473,
0.020029421895742416,
-0.06485876441001892,
-0.007493890356272459,
-0.04716987907886505,
0.026990903541445732,
0.0097702257335186,
0.02491038292646408,
-0.010910597629845142,
-0.007827633060514927,
0.04304564371705055,
-0.07230465114116669,
-0.04753901809453964,
-0.06739569455385208,
-0.0026988121680915356,
0.01177931483834982,
-0.05241897329688072,
0.016979988664388657,
-0.03917156159877777,
-0.037301015108823776,
-0.028178196400403976,
-0.004573035053908825,
-0.02099546417593956,
0.01130179688334465,
0.025073016062378883,
-0.007738567888736725,
0.03652404621243477,
0.052629705518484116,
0.00285143731161952,
-0.012677202001214027,
0.03854862228035927,
-0.03024360164999962,
-0.04661323130130768,
0.018498355522751808,
-0.025604136288166046,
-0.015254608355462551,
0.0291342344135046,
-0.022420255467295647,
0.015144512057304382,
-0.004941235762089491,
-0.027522100135684013,
0.011880743317306042,
-0.02992173656821251,
0.072983518242836,
0.04596564918756485,
0.02382836677134037,
0.007505209185183048,
0.017306361347436905,
0.039816975593566895,
0.02509830705821514,
-0.01765376701951027,
-0.03383215144276619,
-0.06485673040151596,
-0.06088731065392494,
0.0006928924703970551,
-0.0017321264604106545,
-0.061489325016736984,
0.06164415925741196,
0.010379377752542496,
0.04284340888261795,
0.025350552052259445,
0.001785848755389452,
-0.03255936875939369,
-0.031621064990758896,
0.012298129498958588,
-0.00034977507311850786,
-0.009919064119458199,
0.04031847417354584,
0.02579985000193119,
0.02620333433151245,
-0.019627559930086136,
0.0002346815454075113,
0.012222849763929844,
0.04218412563204765,
-0.06531823426485062,
-0.05615030229091644,
0.0011555406963452697,
-0.05410834774374962,
0.027723928913474083,
-0.033309634774923325,
0.01871749386191368,
-0.01794123277068138,
-0.012867572717368603,
-0.01062456052750349,
-0.02873864397406578,
-0.040920160710811615,
0.023657826706767082,
0.010586685501039028,
0.01708693988621235,
-0.023921150714159012,
0.00789274275302887,
-0.004378722980618477,
0.026931196451187134,
-0.012272195890545845,
-0.02450135163962841,
-0.008566426113247871,
0.00026717339642345905,
0.03090902976691723,
0.021843476220965385,
0.0012669569114223123,
-0.02111619897186756,
-0.009545867331326008,
-0.02170812152326107,
-0.028417665511369705,
-0.004927871283143759,
0.04188912734389305,
-0.021914323791861534,
0.010187999345362186,
0.02321268431842327,
0.0025566050317138433,
0.057211533188819885,
0.008528944104909897,
-0.015729811042547226,
0.005837663076817989,
0.01862078160047531,
-0.05982319265604019,
-0.029213326051831245,
-0.02029743418097496,
-0.03249959647655487,
-0.008702840656042099,
-0.014165403321385384,
0.060430917888879776,
-0.013727162033319473,
-0.04023747518658638,
-0.003823700128123164,
-0.03177834302186966,
-0.0012561542680487037,
-0.009852433577179909,
0.019771570339798927,
-0.013596252538263798,
-0.00525620998814702,
0.004520487505942583,
0.05755024775862694,
-0.04313737526535988,
-0.02149001695215702,
-0.06211143359541893,
-0.02093515358865261,
0.01925837993621826,
-0.021739531308412552,
0.031073851510882378,
0.02818813920021057,
-0.004554331302642822,
0.07635722309350967,
0.03604770451784134,
-0.03992893174290657,
-0.019741859287023544,
-0.007361322641372681,
-0.033934056758880615,
-0.011845056898891926,
-0.032939810305833817,
0.03588956594467163,
0.0159591156989336,
0.007313617505133152,
0.0230257585644722,
0.036831919103860855,
-0.0014608916826546192,
-0.04094826057553291,
-0.013429559767246246,
0.00402054050937295,
0.005078480578958988,
-0.02192816697061062,
0.0613737627863884,
-0.011954713612794876,
-0.024233903735876083,
-0.016023382544517517,
-0.00017201079754158854,
0.05924384295940399,
0.0018671425059437752,
-0.10952644050121307,
0.024997850880026817,
-0.02342243120074272,
0.026247788220643997,
-0.024123873561620712,
0.05005884915590286,
-0.03212666139006615,
-0.031184837222099304,
-0.029235539957880974,
0.005766522139310837,
0.06791232526302338,
-0.03452112153172493,
0.0217305738478899,
0.027258578687906265,
0.06422354280948639,
0.013707815669476986,
-0.012150374241173267,
-0.044930197298526764,
-0.011009891517460346,
0.005802566651254892,
-0.04576393589377403,
-0.036853060126304626,
0.020338773727416992,
0.008388034068048,
0.00293530011549592,
0.005381262861192226,
-0.0011829674476757646,
-0.003749792231246829,
-0.08165182918310165,
-0.002532666316255927,
-0.021971073001623154,
0.04432317614555359,
0.013462529517710209,
0.019409045577049255,
0.026909803971648216,
-0.03109731711447239,
-0.03642212599515915,
-0.05817778408527374,
-0.05840602517127991,
0.019866563379764557,
-0.03083638660609722,
-0.02068898268043995,
0.002978178206831217,
-0.03594988211989403,
-0.024671820923686028,
-0.027943015098571777,
-0.03047274984419346,
0.0038770113606005907,
0.0035555195063352585,
-0.034205250442028046,
0.000013652597772306763,
-0.06472713500261307,
-0.046388376504182816,
-0.02688995562493801,
0.04932539165019989,
0.04936425760388374,
-0.020733650773763657,
0.031467292457818985,
-0.0023171708453446627,
-0.06680688261985779,
-0.0019438191084191203,
-0.0081327510997653,
0.020029740408062935,
0.004762332420796156,
-0.000608676637057215,
0.02429702877998352,
0.019185204058885574,
-0.009427135810256004,
-0.03547748923301697,
0.05002586543560028,
0.04986364021897316,
0.028872912749648094,
-0.020875269547104836,
-0.004054572898894548,
-0.025101561099290848,
0.008510359562933445,
0.023487068712711334,
0.025246208533644676,
0.024154525250196457,
0.030526459217071533,
0.001377477659843862,
-0.03248324990272522,
-0.03485700115561485,
0.07696785777807236,
0.013032048009335995,
0.002644725376740098,
-0.035745516419410706,
-0.05448788031935692,
-0.0070561859756708145,
-0.005492924712598324,
-0.049754682928323746,
0.02514103427529335,
0.0012279223883524537,
-0.013546455651521683,
-0.0014530076878145337,
-0.011247238144278526,
0.018485603854060173,
-0.019672449678182602,
0.00975806824862957,
0.0215926393866539,
-0.016076572239398956,
-0.017934758216142654,
-0.01002798043191433,
0.03263707831501961,
0.020042553544044495,
0.021169696003198624,
0.009934880770742893,
0.03548764809966087,
-0.03629324585199356,
-0.014118736609816551,
0.052495311945676804,
0.0633401945233345,
-0.012834309600293636,
-0.01404132042080164,
-0.07743174582719803,
-0.01962967775762081,
0.03592294827103615,
-0.032126426696777344,
0.05442798137664795,
0.00731781218200922,
0.03634989634156227,
-0.04936988279223442,
-0.021957430988550186,
-0.008657929487526417,
0.04363884776830673,
0.038517095148563385,
0.030418027192354202,
-0.04572743922472,
0.008490567095577717,
0.01934998668730259,
0.025923697277903557,
0.027772534638643265,
0.01971336267888546,
-0.0166484247893095,
0.011961963027715683,
0.009146771393716335,
0.0018353963969275355,
0.012985005043447018,
-0.06892795115709305,
0.03593873605132103,
-0.0372246652841568,
-0.01033648382872343,
0.022724604234099388,
-0.061897143721580505,
-0.06879717856645584,
0.022020991891622543,
0.015681691467761993,
0.011211153119802475,
-0.023812107741832733,
-0.03159121796488762,
0.008623798377811909,
0.03620292246341705,
-0.028966406360268593,
0.02377093769609928,
0.07699514925479889,
-0.01787470653653145,
0.009293747134506702,
-0.023703914135694504,
0.005847805645316839,
-0.024366987869143486,
0.004106232896447182,
-0.020085522904992104,
-0.009277697652578354,
-0.0321744903922081,
0.03816599398851395,
-0.010766253806650639,
0.001912962645292282,
0.026952188462018967,
0.0024577488657087088,
-0.007315086666494608,
0.001879245275631547,
-0.003900953335687518,
0.0132511081174016,
-0.012294469401240349,
-0.0005474159843288362,
0.006570430938154459,
0.0029070221353322268,
0.03231080248951912,
-0.03748153895139694,
0.005194890778511763,
0.012958727777004242,
-0.01951732113957405,
-0.0005649908562190831,
-0.015469103120267391,
-0.029474880546331406,
0.026967454701662064,
0.01630469411611557,
0.029649119824171066,
-0.005189764779061079,
0.018558522686362267,
0.013263574801385403,
-0.024911027401685715,
-0.013042296282947063,
0.006838876288384199,
-0.03663226589560509,
0.015039419755339622,
-0.02069513499736786,
0.022740941494703293,
0.054131925106048584,
-0.010809430852532387,
-0.0645936131477356,
0.006543475203216076,
0.004964315332472324,
0.04709501937031746,
-0.042333610355854034,
-0.01631477288901806,
0.011087811551988125,
-0.01325171161442995,
-0.0004973220638930798,
-0.004505195189267397,
0.021647192537784576,
-0.021350327879190445,
-0.02166145108640194,
0.0014746416127309203,
0.006845720577985048,
0.06578661501407623,
-0.024838261306285858,
-0.010556093417108059,
-0.019217392429709435,
0.0221073180437088,
0.004885717760771513,
-0.0029128119349479675,
0.021590257063508034,
-0.02163424901664257,
-0.045309051871299744,
0.021934106945991516,
0.002635834040120244,
0.03734426945447922,
-0.028849521651864052,
-0.006734286434948444,
0.0019374422263354063,
-0.010705788619816303,
0.047336336225271225,
0.016682233661413193,
0.024379940703511238,
0.027976160869002342,
0.03934492915868759,
-0.016280509531497955,
0.025515001267194748,
0.015647318214178085,
-0.01312956865876913,
0.004919676575809717,
-0.0015033177332952619,
0.002320174826309085,
0.004671341273933649,
0.04103752598166466,
-0.014225292019546032,
0.004445222672075033,
0.015422426164150238,
-0.01874144747853279,
0.02655435912311077,
-0.002585568930953741,
0.025021536275744438,
-0.0014749423135071993,
-0.000902084051631391,
-0.013262049295008183,
-0.010711681097745895,
-0.045866645872592926,
0.010196798481047153,
0.010442675091326237,
-0.0010727751068770885,
-0.008104872889816761,
0.010773232206702232,
-0.0007931725704111159,
0.007910238578915596,
-0.024710237979888916,
-0.04294513911008835,
-0.043259888887405396,
-0.011529186740517616,
0.02009374275803566,
-0.03726498782634735,
0.008454591035842896,
0.003881434677168727,
0.0450776107609272,
-0.008838176727294922,
-0.007233052048832178,
0.03236456215381622,
0.05707494914531708,
-0.009545850567519665,
-0.04087856039404869,
-0.02264329418540001,
0.08794194459915161,
-0.014010549522936344,
0.0034901259932667017,
0.030542265623807907,
0.044437672942876816,
-0.002024977235123515,
-0.010612830519676208,
0.0457148514688015,
-0.05951784923672676,
-0.01657448522746563,
-0.050413988530635834,
-0.011784961447119713,
0.025342119857668877,
0.0020242666359990835,
-0.031045980751514435,
-0.011084032244980335,
0.023346930742263794,
0.026585519313812256,
0.007287139073014259,
0.0071858870796859264,
-0.03006276860833168,
0.00461742514744401,
-0.02370542474091053,
-0.045789167284965515,
0.06082257255911827,
-0.03017304837703705,
-0.05345607176423073,
0.018503312021493912,
-0.0033266707323491573,
0.00402069790288806,
-0.013155262917280197,
-0.0088034737855196,
-0.010209348052740097,
0.028729179874062538,
0.009921100921928883,
0.03596925735473633,
0.013611613772809505,
-0.027620438486337662,
0.14641621708869934,
0.03668712079524994,
-0.008024870418012142,
-0.025941412895917892,
0.030987059697508812,
-0.009541647508740425,
0.06368939578533173,
-0.019363660365343094,
-0.03312431648373604,
-0.004400563891977072,
0.03334929421544075,
0.033166076987981796,
0.02262703701853752,
0.007331459317356348,
0.04596713185310364,
0.026105020195245743,
-0.031331028789281845,
-0.012628224678337574,
0.003297333838418126,
0.03243212401866913,
-0.012220539152622223,
-0.008577423170208931,
-0.025819994509220123,
0.03475784510374069,
0.012327556498348713,
-0.0044641876593232155,
-0.0036254418082535267,
0.007294306065887213,
0.0351254940032959,
0.024844948202371597,
0.0020321994088590145,
0.002940583974123001,
0.011698834598064423,
0.018446490168571472,
0.024053025990724564,
0.02404160611331463,
0.027117080986499786,
0.005653620697557926,
0.019337978214025497,
0.0372108519077301,
0.025378819555044174,
-0.015904061496257782,
-0.00975482352077961,
0.02434977889060974,
-0.05687239021062851,
-0.02355082891881466,
-0.07176719605922699,
0.025047792121767998,
-0.021661601960659027,
-0.01334173884242773,
0.009967341087758541,
0.00565737672150135,
-0.023925956338644028,
-0.030836328864097595,
-0.012451781891286373,
-0.0015676843468099833,
-0.016439061611890793,
-0.06183987110853195,
-0.014505640603601933,
-0.004536676686257124,
0.03742235153913498,
-0.026127679273486137,
0.010345281101763248,
-0.031691186130046844,
-0.05853067710995674,
-0.006107287015765905,
-0.008585219271481037,
0.02437250316143036,
-0.0155631173402071,
-0.012816403992474079,
-0.022909050807356834,
0.010137605480849743,
-0.027847953140735626,
0.01765647530555725,
-0.006511210929602385,
0.007819750346243382,
0.04518085718154907,
0.02908230572938919,
0.013373246416449547,
-0.001955110812559724,
-0.00803978368639946,
0.08380980789661407,
0.011371906846761703,
-0.016559837386012077,
-0.011998414993286133,
-0.04746910557150841,
-0.013663506135344505,
0.027650123462080956,
-0.0022927257232367992,
0.053181350231170654,
-0.011627411469817162,
0.025219809263944626,
0.0020995165687054396,
-0.042315542697906494,
0.0008092828211374581,
0.006499569863080978,
-0.06879254430532455,
0.013182805851101875,
-0.01842484250664711,
0.020877614617347717,
0.011739999055862427,
-0.01866963319480419,
0.02745300531387329,
0.03040146268904209,
0.0023546237498521805,
-0.009788489900529385,
0.014533670619130135,
-0.022372283041477203,
0.0054013351909816265,
-0.019997769966721535,
-0.014709405601024628,
-0.05009029805660248,
-0.0198349766433239,
-0.014975466765463352,
0.008467143401503563,
0.036148618906736374,
0.014730146154761314,
-0.02269125171005726,
0.013137033209204674,
-0.03521930053830147,
0.01418420672416687,
0.017771052196621895,
-0.0057030534371733665,
-0.04890826344490051,
-0.02455136552453041,
-0.025598349049687386,
-0.004330608062446117,
-0.039258409291505814,
0.016808850690722466,
0.027695033699274063,
0.013185350224375725,
0.02930464968085289,
0.020088855177164078,
-0.048529550433158875,
-0.013591798022389412,
0.036809567362070084,
0.024300675839185715,
0.020007459446787834,
-0.014634129591286182,
-0.013850419782102108,
-0.006451980676501989,
0.0009375525405630469,
-0.07552135735750198,
0.036514513194561005,
0.0007039961055852473,
0.013604356907308102,
0.01724202185869217,
-0.012559870257973671,
-0.000087942615209613,
0.07161814719438553,
-0.048598047345876694,
-0.014773804694414139,
0.015085836872458458,
0.04200485721230507,
0.027184367179870605,
-0.002067038556560874,
-0.012131290510296822,
-0.005754005629569292,
-0.011019889265298843,
-0.006583011243492365,
0.020858842879533768,
-0.0018740753876045346,
0.005261319223791361,
-0.05720109865069389,
-0.024399304762482643,
0.020435653626918793,
-0.017561843618750572,
0.06625441461801529,
0.04457290098071098,
0.03723106160759926,
-0.017925579100847244,
0.030692528933286667,
0.0062651317566633224,
-0.03369196131825447,
-0.0685722678899765,
0.003906085854396224,
-0.013980699703097343,
0.004431035369634628,
0.022607387974858284,
-0.044753290712833405,
0.042242661118507385,
0.030779369175434113,
-0.08693702518939972,
-0.010164774022996426,
-0.0369100421667099,
-0.0074183945544064045,
-0.04240408539772034,
-0.014208315871655941,
-0.0034590852446854115,
0.06432317942380905,
-0.00007490807911381125,
0.018003690987825394,
0.021025288850069046,
0.03297307714819908,
0.0006448855274356902,
-0.0332513302564621,
-0.038917940109968185,
-0.00447305990383029,
0.00830080732703209,
-0.011326815001666546,
0.05212060362100601,
-0.0018543618498370051,
0.0064787124283611774,
0.01586761325597763,
-0.02840460278093815,
0.04634808376431465,
-0.023477477952837944,
0.03250932693481445,
-0.021749140694737434,
0.02947692759335041,
-0.015012209303677082,
-0.002554203849285841,
-0.04216816648840904,
-0.010925638489425182,
0.0031629654113203287,
0.021766990423202515,
0.013989610597491264,
0.00028686606674455106,
0.013600543141365051,
-0.003066558390855789,
-0.016308646649122238,
0.007754771504551172,
0.023164208978414536,
-0.03953603282570839,
0.02250850386917591,
0.006569189950823784,
0.04428127035498619,
-0.02373693324625492,
0.0007271452341228724,
-0.016836151480674744,
0.00845676101744175,
0.027003828436136246,
0.013724005781114101,
0.010766007006168365,
0.029166949912905693,
-0.02323773503303528,
-0.019505705684423447,
0.0022118957713246346,
0.05956711247563362,
0.008086593821644783,
-0.008681576699018478,
0.008664099499583244,
0.03110702522099018,
0.0277155339717865,
-0.011715193279087543,
-0.02411518059670925,
-0.0646246001124382,
0.04540453106164932,
0.09201725572347641,
0.03564302623271942,
-0.02774566225707531,
-0.035523783415555954,
-0.005621185526251793,
-0.05738767236471176,
0.03365464136004448,
0.014236032962799072,
0.029971685260534286,
-0.04328995943069458,
-0.014526814222335815,
-0.01363539882004261,
-0.01105995662510395,
0.04242357984185219,
0.03554012253880501,
-0.01925600878894329,
0.013246015645563602,
-0.028402019292116165,
-0.013405430130660534,
-0.02378339320421219,
0.016522178426384926,
0.013159333728253841,
-0.02590085193514824,
0.031153464689850807,
0.003450924763455987,
-0.010151196271181107,
0.035985980182886124,
0.018749233335256577,
-0.006435256917029619,
-0.014453418552875519,
0.045323971658945084,
0.024829106405377388,
0.05248403921723366,
-0.016740204766392708,
-0.041105981916189194,
0.05445248633623123,
0.001656435546465218,
0.000882653403095901,
0.03273303061723709,
-0.03337986767292023,
-0.0456947423517704,
0.033695146441459656,
-0.011046761646866798,
-0.0024824931751936674,
-0.02811114676296711,
-0.06457753479480743,
0.010059279389679432,
-0.03578760474920273,
-0.016092484816908836,
0.032305989414453506,
-0.021689319983124733,
-0.004840175621211529,
0.02783103659749031,
0.012906036339700222,
0.024314960464835167,
0.02842027135193348,
0.03520774468779564,
0.0042176926508545876,
-0.00237249955534935,
0.020199378952383995,
0.006287936586886644,
0.011821871623396873,
0.014738162979483604,
0.04369904100894928,
0.006831408478319645,
0.0034721673000603914,
0.0013833785196766257,
0.041857048869132996,
0.0395122691988945,
0.01223572064191103,
-0.021641988307237625,
0.03366271033883095,
-0.019784802570939064,
-0.0025152999442070723,
0.039800263941287994,
-0.012625970877707005,
0.07295843958854675,
-0.021576208993792534,
0.025223271921277046,
-0.03498581051826477,
-0.018788352608680725,
-0.00333395809866488,
0.00954962708055973,
-0.003642865689471364,
0.02711586095392704,
0.008260466158390045,
0.012886885553598404,
-0.005405037198215723,
0.010468803346157074,
0.0050524938851594925,
-0.06531225889921188,
-0.017938189208507538,
0.00005282464189804159,
0.02464171126484871,
-0.0025935033336281776,
0.024211768060922623,
-0.0210742074996233,
-0.022481851279735565,
0.029301341623067856,
0.037062887102365494,
0.06064446642994881,
-0.025923386216163635,
-0.0539383701980114,
-0.03291930630803108,
0.04003371670842171,
-0.07340214401483536,
-0.03933873027563095,
-0.04271196946501732,
0.006983161438256502,
-0.05434291064739227,
-0.014338845387101173
] |
<p>For example, let's assume a chair here: It can be "slid" across the force if we use minimal upwards force, but not enough to actually "lift" the chair. Why should it move?</p>
<p>Here's a better example: I have seen some strong people lift and slide the back of cars, however, the back tires of the car never elevate completely off the ground. With regards to friction, though, how is it possible to actually "move" something without lifting it completely? How does this work is a better question. This image should illustrate the car example:</p>
<p><img src="http://i.stack.imgur.com/foRJg.jpg" alt="enter image description here"></p>
<p>Is there enough space within it to allow the angular force to make it "slid" a pinch, or what else would explain its ability to move without being completely suspended in the air that would, say, differ from this with a human?</p>
| 7,655 |
[
-0.022105466574430466,
-0.011957976035773754,
-0.012644513510167599,
-0.0157735925167799,
0.021597497165203094,
-0.011156575754284859,
-0.013671486638486385,
-0.026707494631409645,
-0.03908102214336395,
-0.018543666228652,
0.0014063019771128893,
0.03716288506984711,
0.03232474625110626,
-0.02427983656525612,
0.012375891208648682,
-0.006737774237990379,
-0.00979661289602518,
-0.038891565054655075,
0.008492526598274708,
0.004893691744655371,
-0.029824022203683853,
-0.0016533953603357077,
0.007834273390471935,
0.0006055313860997558,
0.004656670615077019,
-0.006368726491928101,
0.029843952506780624,
-0.02517368085682392,
0.025541482493281364,
0.04487954080104828,
0.010136733762919903,
0.008160116150975227,
-0.019421204924583435,
-0.017337508499622345,
0.03825552016496658,
0.01632917858660221,
-0.0394492968916893,
0.025566045194864273,
0.014116613194346428,
0.02258780039846897,
-0.018833288922905922,
0.010779758915305138,
-0.025756165385246277,
0.08032173663377762,
-0.04539332538843155,
0.0145955141633749,
0.014590059407055378,
0.019222017377614975,
0.05804911628365517,
-0.059960126876831055,
0.02586052007973194,
-0.007806739304214716,
0.04931425675749779,
0.04815339297056198,
0.04039374738931656,
-0.01547942403703928,
0.056223493069410324,
0.05257732793688774,
-0.021717142313718796,
-0.03481033444404602,
-0.027904842048883438,
-0.050762519240379333,
-0.036891549825668335,
-0.016044236719608307,
-0.024230515584349632,
0.007687132339924574,
-0.021781420335173607,
-0.026156989857554436,
0.013158794492483139,
0.03985828161239624,
0.03660571947693825,
0.010077749378979206,
0.022752894088625908,
0.004875346086919308,
0.008698727935552597,
-0.029266007244586945,
0.013120703399181366,
0.02477746084332466,
0.018819589167833328,
0.03418345749378204,
0.00040264203562401235,
-0.0038727966602891684,
0.03643270954489708,
0.058575402945280075,
0.01123514212667942,
-0.021878419443964958,
0.05706357583403587,
-0.008531449362635612,
0.038929834961891174,
0.031148230656981468,
0.028225254267454147,
-0.02194954641163349,
-0.012408941984176636,
-0.0010952624725177884,
-0.009543130174279213,
0.001921421498991549,
0.014754078350961208,
0.006275543011724949,
0.028996674343943596,
0.004684256389737129,
0.004038517829030752,
-0.0038954000920057297,
0.01936359517276287,
0.044287919998168945,
-0.0018041386501863599,
0.0043284157291054726,
-0.00590319512411952,
0.006127036642283201,
-0.020429980009794235,
-0.0017903173575177789,
-0.019811606034636497,
0.023131517693400383,
-0.016133448109030724,
-0.015247236005961895,
-0.008263801224529743,
0.004453510046005249,
-0.025151066482067108,
-0.01915091462433338,
0.06873441487550735,
0.03654259070754051,
0.042311158031225204,
-0.057232920080423355,
-0.010001863352954388,
-0.057902462780475616,
-0.027708565816283226,
0.008872494101524353,
0.036060042679309845,
-0.007625226862728596,
-0.009134525433182716,
0.022673876956105232,
0.02828766405582428,
-0.014491257257759571,
-0.005201040301471949,
0.019073639065027237,
0.03802312910556793,
-0.011836879886686802,
-0.08640410006046295,
-0.05297985300421715,
0.05710643529891968,
0.004174120724201202,
-0.026548948138952255,
-0.06540850549936295,
-0.010647248476743698,
0.019104963168501854,
0.07112383842468262,
0.019822681322693825,
0.01684410870075226,
0.002708843443542719,
0.02343018725514412,
-0.018641002476215363,
0.021183418110013008,
-0.020759863778948784,
-0.018984869122505188,
-0.03534479811787605,
-0.029427040368318558,
-0.09003052860498428,
0.05969821661710739,
0.046629127115011215,
0.007261420600116253,
-0.0368749275803566,
0.03529396280646324,
-0.020025841891765594,
0.015581457875669003,
-0.0023110515903681517,
-0.0020716662984341383,
-0.009465692564845085,
0.062244802713394165,
0.001111180754378438,
0.03722571209073067,
0.04524369165301323,
0.03424450382590294,
0.012632742524147034,
-0.007408901583403349,
0.04521181434392929,
0.02574450522661209,
-0.014335082843899727,
-0.015465968288481236,
-0.029458152130246162,
-0.017763840034604073,
-0.01225589495152235,
-0.06537223607301712,
-0.04360438138246536,
-0.00955403782427311,
0.007771600969135761,
-0.008893318474292755,
0.031170513480901718,
0.00524887116625905,
-0.002406398532912135,
0.0037747612223029137,
-0.05270959809422493,
-0.037910714745521545,
-0.08086042106151581,
0.029458217322826385,
-0.00013968898565508425,
-0.019433971494436264,
0.01716652698814869,
0.011175923980772495,
0.05716220661997795,
-0.055767837911844254,
0.002844462636858225,
-0.01706407032907009,
0.021824175491929054,
0.010600748471915722,
-0.009883160702884197,
0.014049459248781204,
0.056148774921894073,
0.05927036702632904,
0.005624364595860243,
0.005302549805492163,
-0.03569386899471283,
-0.028023460879921913,
0.02481522038578987,
-0.03497401252388954,
0.0021153853740543127,
0.0368061400949955,
0.04712435603141785,
0.018719758838415146,
0.009664738550782204,
-0.05379856750369072,
0.01842644065618515,
-0.003557766554877162,
0.08625660836696625,
0.04377974197268486,
0.016591930761933327,
-0.02026447281241417,
0.05079726129770279,
-0.010692019015550613,
-0.022157400846481323,
-0.012648606672883034,
0.003938852343708277,
-0.07730932533740997,
-0.003924169111996889,
0.006709170062094927,
0.04499053955078125,
-0.053459662944078445,
-0.007093077525496483,
0.03364580497145653,
0.03984589874744415,
0.03304530307650566,
0.00413783872500062,
-0.02307884581387043,
-0.03561045601963997,
0.02420181781053543,
0.003485289169475436,
0.04694543033838272,
0.030304456129670143,
0.02323543280363083,
0.038862042129039764,
0.026324978098273277,
-0.0027002738788723946,
-0.00932562630623579,
0.048578642308712006,
0.025105467066168785,
0.0056692129001021385,
-0.0041874730959534645,
-0.01596521958708763,
0.05297458544373512,
-0.03348058462142944,
-0.00927454512566328,
0.0042078071273863316,
0.013672926463186741,
0.002828972414135933,
-0.03792354837059975,
-0.013391117565333843,
0.048303551971912384,
-0.006182636599987745,
-0.03348804637789726,
-0.011821446940302849,
0.03443149849772453,
-0.021286778151988983,
-0.011808483861386776,
-0.02925455942749977,
0.0032447429839521646,
-0.027223769575357437,
-0.0006344494759105146,
0.039090875536203384,
0.0030142678879201412,
0.046836454421281815,
-0.006663116626441479,
-0.003904620185494423,
-0.02314681001007557,
-0.04359607771039009,
0.014230849221348763,
-0.002114721108227968,
-0.06591407209634781,
0.02496257796883583,
-0.045757729560136795,
-0.029414400458335876,
0.06982066482305527,
0.008032215759158134,
-0.00342314294539392,
-0.010080360807478428,
0.0012063485337421298,
-0.0419623889029026,
-0.034190915524959564,
-0.011937047354876995,
0.0019371178932487965,
-0.05340808257460594,
-0.03339029476046562,
0.0665225014090538,
0.001661262009292841,
-0.031746964901685715,
0.04894976690411568,
-0.047306932508945465,
-0.01254171784967184,
0.01664184033870697,
0.0120293153449893,
0.017917146906256676,
-0.01734473556280136,
-0.01931428164243698,
-0.014018270187079906,
-0.03317171707749367,
0.024020565673708916,
-0.04129178822040558,
-0.013952014036476612,
-0.02096610888838768,
-0.011996233835816383,
0.05437934771180153,
0.013698866590857506,
0.007641294971108437,
0.09738486260175705,
0.01619402877986431,
-0.0505705326795578,
-0.015866313129663467,
-0.01882014609873295,
-0.05053184926509857,
-0.061103492975234985,
0.03116377256810665,
0.05206773057579994,
-0.037171412259340286,
0.016278307884931564,
0.02040630578994751,
-0.028924448415637016,
0.009513769298791885,
-0.006013219710439444,
-0.015080963261425495,
-0.02290814369916916,
0.008580588735640049,
-0.0385860912501812,
0.05444915220141411,
0.03374793007969856,
-0.04547104611992836,
-0.0031203872058540583,
-0.00726926838979125,
0.043378543108701706,
0.003241604659706354,
-0.07072138041257858,
0.055416204035282135,
0.013003654778003693,
-0.02524237334728241,
0.005264184903353453,
0.056185975670814514,
-0.006085591856390238,
-0.012703596614301205,
0.0025340847205370665,
0.015435099601745605,
0.03076847456395626,
-0.009169481694698334,
0.01508372277021408,
0.049699652940034866,
0.03969728574156761,
-0.022293696179986,
-0.03467182815074921,
-0.025138648226857185,
0.01229505892843008,
0.024003315716981888,
-0.02613273821771145,
-0.012495164759457111,
0.01913076639175415,
0.03146960586309433,
0.0478389710187912,
0.0120617114007473,
-0.037908948957920074,
-0.0028697694651782513,
-0.07110273838043213,
0.011624723672866821,
0.009383703581988811,
0.05412650853395462,
0.009456628002226353,
0.03932160511612892,
0.022412041202187538,
0.06310111284255981,
0.01001124456524849,
-0.007996173575520515,
-0.09860225766897202,
0.045765962451696396,
-0.020320817828178406,
-0.05086766183376312,
-0.004014329053461552,
-0.002705866238102317,
0.014784593135118484,
-0.026183895766735077,
-0.01668083295226097,
-0.015228521078824997,
0.02380608767271042,
-0.04401884600520134,
-0.003694979241117835,
-0.014482028782367706,
-0.02680550515651703,
0.009531191550195217,
-0.0008148416527546942,
0.05458436533808708,
-0.017116064205765724,
0.02294026128947735,
0.02690320834517479,
-0.018815983086824417,
0.011531736701726913,
-0.0018031945219263434,
0.0017359545454382896,
0.015113537199795246,
0.02430964820086956,
-0.01588558405637741,
0.010797475464642048,
-0.004346727859228849,
-0.0014701508916914463,
-0.030658863484859467,
0.027969125658273697,
0.021969009190797806,
0.012800785712897778,
-0.028108661994338036,
-0.0569646991789341,
-0.044033028185367584,
-0.023859728127717972,
0.06176890432834625,
-0.019304120913147926,
0.00550829665735364,
0.013692247681319714,
0.01749453879892826,
-0.024556688964366913,
0.03316954895853996,
0.03315921127796173,
0.049625493586063385,
-0.03037962131202221,
-0.10011136531829834,
-0.033131375908851624,
-0.025048840790987015,
0.0032807444222271442,
0.026396341621875763,
-0.022941751405596733,
-0.017435507848858833,
-0.003531242487952113,
0.018599864095449448,
0.01627231203019619,
-0.014579659327864647,
0.02233058027923107,
-0.04134950786828995,
0.004408012144267559,
-0.025353580713272095,
0.0022360370494425297,
0.01236017607152462,
0.04319772869348526,
0.052830588072538376,
-0.00012621677888091654,
-0.02035077102482319,
-0.06646507233381271,
-0.020823577418923378,
0.039458658546209335,
0.02281942404806614,
-0.035660795867443085,
-0.0047375778667628765,
-0.0009991895640268922,
-0.01970745623111725,
0.054243143647909164,
-0.034556545317173004,
0.03800555691123009,
-0.030841266736388206,
0.0030289292335510254,
-0.03431156277656555,
-0.03477153927087784,
-0.030079025775194168,
-0.014799587428569794,
-0.025977712124586105,
0.009654675610363483,
-0.041832804679870605,
-0.010192678309977055,
-0.01771393045783043,
0.02152273803949356,
0.029202500358223915,
0.03517450764775276,
0.011056543327867985,
0.021124208346009254,
-0.018144259229302406,
0.0009786223527044058,
-0.029256314039230347,
-0.07586172968149185,
-0.027140218764543533,
0.0005260300822556019,
-0.01967884786427021,
-0.01721155270934105,
-0.03085516206920147,
-0.046138402074575424,
-0.01159632857888937,
-0.014006407931447029,
-0.01808779127895832,
0.004569830372929573,
-0.02283346652984619,
0.04920085892081261,
0.05411383882164955,
0.003587668528780341,
0.055497631430625916,
0.06086866930127144,
-0.004559998866170645,
0.009936733171343803,
-0.0006769762840121984,
-0.004833783954381943,
0.02033146098256111,
-0.04476489871740341,
-0.06915085017681122,
0.029052771627902985,
-0.014952030032873154,
0.014322242699563503,
-0.009277370758354664,
0.046350590884685516,
-0.02563157118856907,
-0.06517613679170609,
-0.04105899855494499,
0.046485137194395065,
0.03998575359582901,
-0.016118157655000687,
-0.02390475757420063,
0.005652152933180332,
0.0031187667045742273,
-0.020920883864164352,
-0.010351601988077164,
0.01603698916733265,
-0.006383626256138086,
0.02638782560825348,
-0.016925398260354996,
0.0019352049566805363,
-0.03891615569591522,
-0.029718447476625443,
0.007879792712628841,
-0.07582291215658188,
0.03697655349969864,
-0.018748857080936432,
0.030131904408335686,
0.03572486713528633,
-0.051162466406822205,
-0.014650899916887283,
0.011420194059610367,
0.013159091584384441,
0.01819661632180214,
-0.022116463631391525,
0.019021296873688698,
-0.006908189970999956,
-0.029548000544309616,
-0.005134455393999815,
-0.06945095211267471,
0.02485552430152893,
0.023805653676390648,
-0.005005012731999159,
0.011974737048149109,
0.0037603219971060753,
-0.04777413234114647,
-0.03273884952068329,
-0.004101105500012636,
0.06588613986968994,
-0.034509364515542984,
0.03905142843723297,
0.08099781721830368,
-0.028348218649625778,
0.035746991634368896,
-0.0098193334415555,
-0.042506296187639236,
0.0006359027465805411,
-0.0269673690199852,
-0.0020650471560657024,
-0.009611282497644424,
0.04358705133199692,
-0.04546097666025162,
-0.04879835993051529,
0.013464216142892838,
0.010464319959282875,
0.030609482899308205,
-0.000500931404531002,
0.01582697592675686,
0.024558844044804573,
-0.006518315989524126,
0.0013715242967009544,
-0.02578982710838318,
0.04786049574613571,
0.021734055131673813,
0.019317317754030228,
0.031523361802101135,
0.022095240652561188,
-0.019189003854990005,
-0.07459427416324615,
0.015034860000014305,
0.032426364719867706,
0.03615264222025871,
0.02534554712474346,
0.0471683144569397,
-0.031341876834630966,
0.009791119955480099,
0.031767260283231735,
-0.0027622731868177652,
0.07544337213039398,
0.025343280285596848,
-0.01991979591548443,
0.002919475780799985,
-0.005631354637444019,
-0.04097848758101463,
-0.02666986547410488,
0.008974595926702023,
-0.016879640519618988,
0.02805868536233902,
-0.030883418396115303,
0.08055038005113602,
0.0492057241499424,
-0.031106142327189445,
-0.04588447883725166,
0.0019615860655903816,
-0.025995122268795967,
-0.0010137779172509909,
0.028051339089870453,
0.0007755098049528897,
-0.026082558557391167,
0.05147245153784752,
0.03477415069937706,
0.033631764352321625,
-0.01796663925051689,
0.00435648811981082,
0.02898756042122841,
0.029324376955628395,
0.011745196767151356,
-0.0026602009311318398,
-0.03229314088821411,
0.012050850316882133,
-0.004233132116496563,
0.07150939851999283,
-0.01048958394676447,
-0.019309082999825478,
0.03552932292222977,
0.024382032454013824,
0.021163806319236755,
-0.052150048315525055,
-0.012529933825135231,
-0.04576999694108963,
0.012939064763486385,
0.007223048713058233,
0.006770383100956678,
0.018574658781290054,
-0.022650107741355896,
0.04255406931042671,
-0.02665123902261257,
0.014942466281354427,
-0.019497912377119064,
-0.04348327964544296,
-0.03557474911212921,
-0.009542555548250675,
-0.042963966727256775,
0.035329341888427734,
0.010963408276438713,
-0.014811098575592041,
0.03415816277265549,
-0.04323453828692436,
0.011658085510134697,
0.05231918394565582,
0.05433497577905655,
0.005247357301414013,
0.054557930678129196,
-0.018863948062062263,
0.013298684731125832,
-0.04014953598380089,
0.02350446954369545,
0.11762683093547821,
0.01086385827511549,
0.019481973722577095,
-0.00897842925041914,
-0.010180285200476646,
-0.005636760499328375,
-0.018843017518520355,
0.0005120895802974701,
0.0009234906174242496,
-0.011528975330293179,
0.02595730870962143,
0.0018938598223030567,
0.04939364269375801,
-0.001473474083468318,
-0.001490053371526301,
0.01801847107708454,
-0.019880030304193497,
-0.002203994430601597,
-0.024120014160871506,
0.01993585377931595,
-0.05202107131481171,
-0.012295063585042953,
-0.03991607204079628,
0.027619386091828346,
0.01695821061730385,
-0.007853880524635315,
0.0013344704639166594,
-0.040704403072595596,
-0.023426281288266182,
-0.0033232613932341337,
-0.06380671262741089,
-0.0049729133024811745,
0.020237639546394348,
-0.028775440528988838,
-0.049875058233737946,
0.05455058068037033,
-0.017150187864899635,
-0.026592928916215897,
-0.0007777792634442449,
0.0276381503790617,
0.019509706646203995,
0.015003741718828678,
0.04615676775574684,
-0.009976530447602272,
-0.02199762500822544,
-0.017979534342885017,
-0.027398312464356422,
0.016734467819333076,
-0.05395829677581787,
0.01179394032806158,
0.036233775317668915,
-0.006965835113078356,
-0.012628556229174137,
-0.04507709667086601,
-0.026047680526971817,
-0.025155063718557358,
0.020234739407896996,
-0.00361672998405993,
-0.04139876365661621,
0.010254045017063618,
0.018331283703446388,
0.01417267881333828,
-0.015066834166646004,
-0.004406859632581472,
0.01514872070401907,
-0.007830866612493992,
0.009579911828041077,
0.025774501264095306,
-0.043264348059892654,
0.0174744613468647,
-0.007315147668123245,
0.0038246375042945147,
-0.03033054992556572,
0.015515507198870182,
0.03699492663145065,
0.04208410531282425,
-0.0009449321078136563,
-0.015469321981072426,
-0.027003617957234383,
-0.04281005635857582,
0.01680949702858925,
0.04764004796743393,
-0.026400811970233917,
-0.00587087869644165,
-0.017549417912960052,
-0.030271178111433983,
0.0355428121984005,
0.021955834701657295,
-0.0009004584862850606,
-0.012302001006901264,
-0.013860920444130898,
0.031952548772096634,
-0.00013204931747168303,
-0.008841006085276604,
-0.049129072576761246,
0.03412957116961479,
-0.002575760008767247,
0.006398783065378666,
0.018075568601489067,
0.039368607103824615,
0.058625414967536926,
-0.007310682442039251,
-0.04118315875530243,
0.011616642586886883,
-0.01180428545922041,
0.02462153695523739,
0.050066202878952026,
-0.04292190074920654,
-0.03337641805410385,
0.012279468588531017,
-0.022460855543613434,
-0.014706873334944248,
-0.03297515958547592,
-0.009858550503849983,
-0.03934255242347717,
-0.009968879632651806,
0.05568331107497215,
0.006210874766111374,
-0.002433736575767398,
-0.030080284923315048,
0.05251692980527878,
-0.0259146336466074,
0.01254170574247837,
-0.05978279188275337,
0.0013052087742835283,
0.05196205526590347,
0.01581263355910778,
-0.03416585177183151,
-0.00679743429645896,
-0.027395376935601234,
0.01858549565076828,
-0.04280915856361389,
-0.007573505863547325,
-0.012823015451431274,
-0.016025705263018608,
0.0021571828983724117,
-0.03354068845510483,
0.03634706512093544,
0.009448778815567493,
-0.008652509190142155,
0.04748876392841339,
-0.03633784130215645,
-0.03396512195467949,
-0.005483329761773348,
-0.02918921411037445,
0.05094592645764351,
-0.00442899577319622,
-0.04252633452415466,
-0.002587240422144532,
0.07518891245126724,
-0.03339960798621178,
-0.023062635213136673,
-0.018890254199504852,
-0.01884320192039013,
-0.03355605900287628,
-0.03112223371863365,
0.0338633693754673,
-0.06077456846833229,
0.024123752489686012,
0.04977928102016449,
0.022453607991337776,
-0.029495438560843468,
-0.061202991753816605,
0.012001769617199898,
-0.000013972737178846728,
-0.02289203368127346,
-0.003281573299318552,
0.04267425835132599,
0.004957938566803932,
0.02178558148443699,
-0.03332609683275223,
0.028121506795287132,
-0.009507632814347744,
0.0473494678735733,
-0.10189603269100189,
-0.03164459392428398,
0.018183110281825066,
-0.01975153014063835,
0.043670590966939926,
-0.08530973643064499,
-0.03643898293375969,
0.026214757934212685,
-0.06169348210096359,
-0.007656323257833719,
-0.027613693848252296,
-0.01324976235628128,
-0.030136482790112495,
0.00957243237644434,
0.04236779361963272,
0.04602374881505966,
0.00825564842671156,
0.061256974935531616,
-0.012524300254881382,
-0.007947811856865883,
-0.012858803384006023,
-0.0027393277268856764,
0.0010030536213889718,
0.07210346311330795,
-0.011376402340829372,
0.023867422714829445,
0.07493682950735092,
0.022571485489606857,
-0.030808711424469948,
0.03300995007157326,
0.00044381749466992915,
0.025517309084534645,
0.01019215490669012,
-0.03183714672923088,
-0.01195924635976553,
0.018035296350717545,
-0.002535970415920019,
-0.021863840520381927,
-0.004745609126985073,
0.05596494302153587,
0.0006302293040789664,
0.05114329233765602,
-0.005826498847454786,
0.002705206163227558,
0.02066882885992527,
-0.03787228465080261,
-0.020488394424319267,
0.020297177135944366,
-0.02896888740360737,
-0.0007821554900147021,
0.02592960186302662,
0.026856347918510437,
0.024846568703651428,
-0.021777337417006493,
-0.01608254760503769,
-0.024891575798392296,
0.0064081898890435696,
0.0004741512530017644,
-0.032606225460767746,
-0.02317098155617714,
0.059920258820056915,
0.009213539771735668,
0.005923180375248194,
0.00935276411473751,
0.019961044192314148,
-0.029399234801530838,
-0.02591734379529953,
-0.0033370524179190397,
0.005467809736728668,
-0.03097863309085369,
-0.0011867760913446546,
-0.01282438263297081,
-0.029909638687968254,
0.004661947954446077,
0.03823612630367279,
0.01895853690803051,
0.017594819888472557,
-0.03010186180472374,
-0.015055864118039608,
-0.07328271120786667,
0.03106955997645855,
0.015770697966217995,
-0.053352128714323044,
-0.04019182175397873,
-0.0024759958032518625,
0.012219740077853203,
0.0006543799536302686,
0.0500863753259182,
-0.032587986439466476,
0.0030154380947351456,
-0.0028720886912196875,
-0.009472178295254707,
0.0033609075471758842,
-0.006855951622128487,
0.008665181696414948,
-0.0000767483506933786,
-0.039672017097473145,
-0.004898636136204004,
0.0330357700586319,
0.000059341953601688147,
0.0017809614073485136,
0.042207662016153336,
-0.0029612809885293245,
0.04797738790512085,
-0.02176641672849655,
-0.029726838693022728,
0.022130416706204414,
0.0381627082824707,
-0.027766652405261993,
0.06450837105512619,
-0.002742332872003317,
-0.004784447140991688,
-0.005017526913434267,
-0.00603003054857254,
0.007553469855338335,
0.047387171536684036,
-0.04125998541712761,
0.01090945303440094,
-0.012383856810629368,
-0.012966465204954147,
0.03148570656776428,
-0.04205562174320221,
0.025963429361581802,
0.04369794577360153,
-0.02849305048584938,
0.0028715424705296755,
0.012073900550603867,
0.04107296094298363,
0.033981505781412125,
-0.02917696349322796,
0.008883988484740257,
0.006307882722467184,
-0.01644689217209816,
-0.001735194120556116,
0.013815199956297874,
0.040706705302000046,
-0.012408607639372349,
-0.02668009325861931,
0.0544886514544487,
0.015147215686738491,
0.027180006727576256,
-0.005772384814918041,
0.032424651086330414,
0.007329421117901802,
0.020330490544438362,
-0.00524872587993741,
-0.01068772654980421,
-0.004286722280085087,
0.02060774713754654,
0.00004349546361481771,
0.08539412915706635,
-0.040941353887319565,
0.006803599651902914,
0.003709872253239155,
0.04154370725154877,
-0.008223995566368103,
-0.0025883777998387814,
0.014501302503049374,
0.02723846398293972,
-0.04237718880176544,
-0.046344026923179626,
-0.0016885275254026055,
0.014369017444550991,
0.025795571506023407,
0.025520605966448784,
0.04729175940155983,
-0.018891938030719757,
0.00502146128565073,
-0.000428445462603122,
-0.02082875557243824,
-0.010038337670266628,
0.007797212339937687,
0.05596011504530907,
0.021621309220790863,
0.012702865526080132,
-0.014442356303334236,
-0.02038159966468811,
0.013160993345081806,
0.05145082622766495,
-0.06947387009859085,
-0.015686850994825363,
-0.012075420469045639,
0.06350161880254745,
0.023828206583857536,
0.00006810828199377283
] |
<p>Is my understanding of this <a href="http://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat" rel="nofollow">experiment</a> correct?
There is the quantity $MC\delta \theta$ associated to the heat which I think is not an absolute value to be compared with $mgh$ since the $\delta \theta$ could be defined arbitrarily. So this experiment does not prove : thermal energy = $mgh$ it could however show a linear relation between $\delta \theta$ and $h$. </p>
| 7,656 |
[
-0.0545465312898159,
-0.043037351220846176,
-0.033923011273145676,
-0.010724140331149101,
0.04832102358341217,
0.01248799916356802,
-0.06380775570869446,
-0.023965254426002502,
-0.005949263460934162,
-0.012222718447446823,
0.019572395831346512,
0.0015260091749951243,
0.033924028277397156,
0.01843806728720665,
0.05218931660056114,
0.041561685502529144,
-0.021147483959794044,
0.02010059356689453,
0.0001580093812663108,
-0.004050785675644875,
0.009245729073882103,
0.03793240711092949,
0.016880979761481285,
-0.03121710941195488,
-0.011366358958184719,
0.03527755290269852,
0.033277109265327454,
-0.011634103022515774,
-0.004557984881103039,
0.05734187737107277,
-0.028818512335419655,
-0.00002298581057402771,
-0.005450989119708538,
0.014008291065692902,
-0.010084087029099464,
0.023370681330561638,
-0.026330187916755676,
-0.0012609686236828566,
0.002286694012582302,
0.06444486975669861,
-0.03095194138586521,
-0.01738261803984642,
-0.008357238955795765,
0.06893353909254074,
-0.029265491291880608,
-0.029880786314606667,
-0.022829467430710793,
-0.013200807385146618,
-0.010846871882677078,
-0.034447453916072845,
0.06436020880937576,
-0.00489695044234395,
0.012723693624138832,
0.04559878632426262,
0.0019466630183160305,
0.011097798123955727,
0.05453763157129288,
0.0453343503177166,
-0.038540612906217575,
-0.03614317253232002,
0.0030335751362144947,
-0.056573059409856796,
-0.0220798309892416,
-0.01178301963955164,
-0.0018626934615895152,
0.020539643242955208,
0.017658233642578125,
-0.016656063497066498,
0.04970526695251465,
0.024228224530816078,
0.03288818523287773,
0.024708744138479233,
0.04778875410556793,
0.016605408862233162,
0.012155233882367611,
-0.038468748331069946,
0.0018581701442599297,
0.026628892868757248,
0.016884036362171173,
0.065648153424263,
-0.007065017241984606,
0.033276453614234924,
0.0388178676366806,
0.09708549827337265,
0.005539965350180864,
-0.002003413625061512,
0.04817604273557663,
-0.0051997569389641285,
0.03745931014418602,
0.031614623963832855,
0.024455158039927483,
0.02373260073363781,
-0.03550075739622116,
-0.007326413877308369,
-0.02136482112109661,
0.022403042763471603,
-0.018783189356327057,
0.0225670225918293,
-0.00894966535270214,
-0.020459100604057312,
0.008231563493609428,
0.005864220205694437,
0.04962332174181938,
0.021871594712138176,
0.022944411262869835,
-0.05722754821181297,
-0.013123318552970886,
0.00518554262816906,
0.017550794407725334,
-0.0140894940122962,
-0.0491652637720108,
0.0044555324129760265,
-0.005540880840271711,
-0.010460653342306614,
-0.01047586090862751,
-0.01886383444070816,
0.010066085495054722,
-0.011512079276144505,
0.058261677622795105,
0.034292273223400116,
0.032533884048461914,
-0.031813304871320724,
0.021945642307400703,
-0.02220803312957287,
-0.0582951083779335,
0.03413901850581169,
0.010442214086651802,
-0.03233157470822334,
-0.006262649782001972,
0.026008710265159607,
-0.0008497394155710936,
0.0181120578199625,
0.0039611691609025,
-0.004653017036616802,
0.02825099229812622,
-0.0329723097383976,
-0.09845642000436783,
-0.07779404520988464,
0.0524156279861927,
0.0031835250556468964,
-0.02716035023331642,
-0.06104004755616188,
0.03598135709762573,
0.037965938448905945,
0.029962461441755295,
0.004259456880390644,
0.033356573432683945,
-0.0375949963927269,
0.029513560235500336,
0.014118645340204239,
0.023016123101115227,
-0.028973493725061417,
0.03822869807481766,
-0.06380199640989304,
-0.03134944289922714,
-0.05940600484609604,
0.02109653316438198,
0.02004053443670273,
-0.0101850600913167,
-0.024330778047442436,
0.05890114605426788,
-0.007725100964307785,
-0.0026098161470144987,
0.024096472188830376,
0.0013185662683099508,
-0.020004989579319954,
0.1018642708659172,
-0.024982858449220657,
-0.017406733706593513,
-0.007608253508806229,
0.006168671417981386,
-0.010265987366437912,
0.017596766352653503,
0.03629573434591293,
0.027305493131279945,
-0.019227951765060425,
0.010035300627350807,
-0.04449879750609398,
0.02394556626677513,
0.02118292637169361,
-0.05636818706989288,
-0.03234230354428291,
-0.01100409496575594,
0.0007923882221803069,
0.031319379806518555,
0.06482604146003723,
0.017799053341150284,
-0.0010559415677562356,
0.04142766818404198,
-0.054435279220342636,
-0.05272560939192772,
-0.06480039656162262,
0.029715873301029205,
0.015848804265260696,
-0.0000849196658236906,
0.006792827509343624,
0.0035604790318757296,
0.03613607585430145,
-0.047535959631204605,
-0.011827945709228516,
0.052815452218055725,
0.026383260264992714,
-0.021548626944422722,
0.013224886730313301,
0.03914409503340721,
0.05637140944600105,
0.0541556179523468,
0.025525663048028946,
-0.037513770163059235,
-0.013764763250946999,
-0.04368496313691139,
0.0098960492759943,
-0.03911740332841873,
0.006388033740222454,
0.016892865300178528,
0.003963660914450884,
0.009934932924807072,
-0.011696589179337025,
-0.025591567158699036,
0.04786970838904381,
-0.022462422028183937,
0.06318426877260208,
0.011035715229809284,
-0.01234882976859808,
-0.00330949854105711,
0.037700243294239044,
0.033141497522592545,
0.03674193471670151,
-0.037572603672742844,
-0.001491243252530694,
-0.043918222188949585,
0.012377079576253891,
0.03924641013145447,
0.015519735403358936,
-0.06962122768163681,
0.00656228419393301,
0.03605257347226143,
0.0423344187438488,
0.02420327626168728,
0.012080421671271324,
0.00034564381348900497,
-0.03948073461651802,
0.02395552769303322,
0.039686620235443115,
-0.008514047600328922,
0.02714783139526844,
-0.00549976946786046,
0.02133115939795971,
0.002232759026810527,
0.008849355392158031,
0.029305336996912956,
0.06700465083122253,
-0.010388767346739769,
0.010765397921204567,
-0.003082514740526676,
0.0013390962267294526,
0.026023130863904953,
-0.01902817189693451,
0.04249773174524307,
0.016171785071492195,
-0.005547189153730869,
0.025440827012062073,
-0.04024188220500946,
-0.02076857164502144,
0.0040348428301513195,
-0.0005817761993966997,
-0.0003354005457367748,
-0.030085865408182144,
0.02396331913769245,
-0.0332007110118866,
-0.006263056304305792,
-0.039377838373184204,
-0.014253810048103333,
-0.010101383551955223,
-0.01796562410891056,
0.020267214626073837,
0.015011287294328213,
0.04987703263759613,
-0.04890217259526253,
-0.01529946830123663,
-0.018780840560793877,
-0.029707372188568115,
-0.0011350333224982023,
0.01011750753968954,
-0.022490235045552254,
-0.0008742114878259599,
-0.026144005358219147,
-0.020967211574316025,
0.02032570354640484,
0.0013067867839708924,
0.01922222226858139,
0.03218957409262657,
0.0068802195601165295,
-0.05352973937988281,
-0.0061347587034106255,
-0.0035992288030683994,
-0.01508211251348257,
-0.04037913680076599,
-0.004073569551110268,
0.02642483450472355,
-0.015268819406628609,
-0.02284177392721176,
0.024415183812379837,
-0.038873329758644104,
-0.03823944926261902,
-0.002387725282460451,
-0.004455625079572201,
0.0007861825870350003,
-0.006665050983428955,
0.05017270892858505,
0.05316933989524841,
-0.03377504646778107,
-0.03565845638513565,
-0.05293101817369461,
-0.03800150379538536,
0.021581260487437248,
-0.002862185938283801,
0.02952832542359829,
0.004909079521894455,
-0.05223482474684715,
0.09184751659631729,
0.014635979197919369,
-0.04742295667529106,
-0.025677045807242393,
-0.00697410199791193,
0.011254179291427135,
-0.012408614158630371,
0.009747656062245369,
0.039574578404426575,
-0.027844905853271484,
0.023275412619113922,
0.016748329624533653,
0.049436043947935104,
0.0322595089673996,
0.027115849778056145,
0.016120530664920807,
-0.02247094176709652,
-0.0003240140504203737,
0.02469894103705883,
0.07177209109067917,
0.020461974665522575,
-0.02215665578842163,
0.014709115028381348,
0.02109120786190033,
0.06091482192277908,
0.007965318858623505,
-0.09054827690124512,
0.09391862154006958,
-0.008195074275135994,
0.028733601793646812,
-0.0720578134059906,
0.05651254206895828,
0.01021007914096117,
-0.02205481566488743,
0.017340153455734253,
0.032657135277986526,
0.01433487981557846,
-0.002638649195432663,
0.0016215317882597446,
0.036255259066820145,
-0.01565493270754814,
-0.008161882869899273,
-0.009325597435235977,
0.016937756910920143,
-0.017337152734398842,
0.001808604458346963,
-0.0012288312427699566,
-0.021109746769070625,
0.02076578512787819,
0.05260668694972992,
0.03123394399881363,
0.0051079317927360535,
-0.03894243761897087,
0.010990851558744907,
-0.0376359261572361,
-0.009150364436209202,
-0.017055269330739975,
0.025317346677184105,
-0.009954078122973442,
0.08241239935159683,
0.03940194472670555,
0.03189507871866226,
0.0428818017244339,
-0.022936861962080002,
-0.08507678657770157,
0.02349347434937954,
-0.044001609086990356,
-0.021306250244379044,
0.01134498417377472,
-0.020191172137856483,
0.009927642531692982,
-0.03565400838851929,
0.004528192337602377,
0.003013037610799074,
-0.011112612672150135,
-0.0495942123234272,
-0.001451020478270948,
-0.01891525648534298,
-0.0328582264482975,
-0.017073869705200195,
0.007289020344614983,
0.038093965500593185,
-0.03165585547685623,
0.01330751832574606,
0.05381385609507561,
-0.04389343783259392,
0.013040997087955475,
-0.027381515130400658,
-0.0018041006987914443,
0.01982950046658516,
0.022429855540394783,
0.02771657146513462,
0.007088501937687397,
0.007470965851098299,
0.004663851112127304,
0.026668451726436615,
0.030969899147748947,
0.004915913566946983,
-0.045554447919130325,
-0.0659935250878334,
-0.015391171909868717,
-0.041825372725725174,
0.008038355968892574,
0.05362492427229881,
-0.01000565942376852,
0.027165569365024567,
0.01119095180183649,
0.008306623436510563,
-0.01367123518139124,
0.06442434340715408,
0.030283818021416664,
-0.04364145174622536,
-0.006799441762268543,
-0.05932781845331192,
-0.04850766807794571,
-0.02637874335050583,
-0.02643466927111149,
0.04582725465297699,
-0.023051628842949867,
-0.05076724663376808,
-0.026699930429458618,
0.0063151405192911625,
0.025723446160554886,
0.008828647434711456,
0.011615388095378876,
0.003226695116609335,
0.04741743952035904,
0.03709708899259567,
-0.0031463480554521084,
0.002752206986770034,
0.04845678433775902,
0.026655834168195724,
-0.038686446845531464,
-0.010006016120314598,
-0.05951634794473648,
-0.018009427934885025,
0.0014312489656731486,
0.05416827276349068,
-0.032512836158275604,
0.002973106224089861,
0.0009579518809914589,
-0.00514837633818388,
0.04974732920527458,
-0.02518610656261444,
0.048430733382701874,
-0.01158059574663639,
0.02443048357963562,
-0.037845537066459656,
-0.002120597753673792,
-0.049054402858018875,
0.018671458587050438,
0.005546898115426302,
-0.008035379461944103,
-0.024220168590545654,
-0.017253583297133446,
0.0021968185901641846,
-0.014299738220870495,
0.024575207382440567,
0.0028469013050198555,
-0.0049450574442744255,
-0.005702558439224958,
-0.007171369157731533,
0.031999822705984116,
-0.01975381188094616,
-0.05439815670251846,
-0.012592185288667679,
-0.0029766052030026913,
-0.01336121466010809,
-0.0008404194377362728,
-0.05796343460679054,
-0.06950943171977997,
0.042215537279844284,
0.01700657233595848,
-0.017467506229877472,
0.006575004197657108,
-0.038180265575647354,
0.030364345759153366,
0.052945639938116074,
-0.021180761978030205,
0.04553857818245888,
0.02788590081036091,
-0.03770158067345619,
-0.0037735258229076862,
-0.0176626518368721,
0.0013122900854796171,
-0.04321074113249779,
-0.010039187967777252,
-0.04975389689207077,
0.023253105580806732,
-0.03606598451733589,
0.025373470038175583,
0.002160044386982918,
0.03336158022284508,
-0.02576696313917637,
-0.04438302665948868,
0.0076137324795126915,
0.010959925130009651,
0.0194036103785038,
0.0074994792230427265,
-0.01592838205397129,
0.015388596802949905,
0.016320504248142242,
-0.014844757504761219,
-0.007980027236044407,
0.010060977190732956,
-0.016101546585559845,
0.020743796601891518,
-0.04282987117767334,
0.03304865583777428,
-0.01464067678898573,
-0.010185819119215012,
0.011101685464382172,
-0.021924421191215515,
0.006454072427004576,
-0.028724294155836105,
0.0007801183382980525,
0.00717164995148778,
-0.052054084837436676,
-0.022353854030370712,
0.008777928538620472,
0.01240532472729683,
0.017808767035603523,
-0.008251353166997433,
0.02312416397035122,
0.019175995141267776,
0.018703222274780273,
-0.052315887063741684,
-0.031880784779787064,
0.009011347778141499,
-0.01513370219618082,
-0.000784897361882031,
-0.007756457198411226,
-0.02197343483567238,
-0.02191578783094883,
-0.026489417999982834,
0.013236705213785172,
0.04568875581026077,
-0.012570572085678577,
0.014757021330296993,
-0.006553695537149906,
0.012730088084936142,
0.035837024450302124,
-0.018341345712542534,
-0.04305720329284668,
0.0004756953567266464,
-0.004000318702310324,
-0.035586774349212646,
0.0011361015494912863,
0.06222109496593475,
-0.017110386863350868,
-0.0124366981908679,
0.01252939272671938,
-0.0072189681231975555,
0.036197248846292496,
0.025147829204797745,
-0.03549123927950859,
0.016929103061556816,
0.035427507013082504,
-0.024958228692412376,
-0.03947921097278595,
0.06018946319818497,
0.027622845023870468,
0.029479170218110085,
-0.02054443396627903,
-0.01519097201526165,
-0.018672462552785873,
-0.034966662526130676,
0.005610139109194279,
0.002391799120232463,
-0.019659126177430153,
0.016367467120289803,
0.10087402164936066,
-0.04726395383477211,
0.014899322763085365,
0.02810659632086754,
-0.025124290958046913,
-0.009960928931832314,
-0.0023456341587007046,
0.03944404050707817,
-0.018164776265621185,
-0.005258732941001654,
-0.029860662296414375,
-0.004527505021542311,
-0.05991746857762337,
-0.004729319829493761,
0.06346038728952408,
0.017676634714007378,
0.0842779353260994,
0.016595661640167236,
-0.025131994858384132,
0.024255912750959396,
-0.02135438285768032,
-0.010907867923378944,
0.008331028744578362,
0.0022280134726315737,
0.008099811151623726,
-0.023676060140132904,
-0.020234011113643646,
0.035323917865753174,
0.02798745408654213,
-0.043272823095321655,
0.0051150014623999596,
0.03452938422560692,
0.03533018380403519,
0.0019958189222961664,
-0.005283589940518141,
-0.01797427237033844,
0.02134956233203411,
-0.015159700065851212,
0.03200457617640495,
-0.029535843059420586,
-0.0029352689161896706,
0.03500908985733986,
0.03858988732099533,
0.01574561558663845,
-0.06767452508211136,
-0.0003089006058871746,
-0.03413424640893936,
0.02753736451268196,
0.032861772924661636,
0.0077124061062932014,
0.036759745329618454,
-0.0018869256600737572,
0.008994185365736485,
0.025788135826587677,
0.04902208223938942,
0.0217960886657238,
-0.02856197953224182,
0.003032940672710538,
-0.011962870135903358,
-0.043220117688179016,
0.05848370119929314,
-0.00992556568235159,
-0.024442259222269058,
0.02547322027385235,
-0.05491960048675537,
-0.0023915928322821856,
0.01651289314031601,
-0.005036266520619392,
0.000987703911960125,
0.05296589061617851,
-0.020096663385629654,
0.023596948012709618,
-0.0037441852036863565,
-0.003679428482428193,
0.10123182088136673,
0.023295395076274872,
0.010805238038301468,
-0.06607984751462936,
0.035360611975193024,
-0.005975749809294939,
-0.03529937192797661,
-0.035300128161907196,
0.01772439107298851,
-0.021827643737196922,
0.011903475038707256,
0.002067415276542306,
0.06485958397388458,
-0.0406973622739315,
0.005723286420106888,
0.03225863724946976,
-0.00988408736884594,
-0.02674379013478756,
0.02059362642467022,
0.027744757011532784,
-0.01451234519481659,
-0.0031287430319935083,
0.013064390048384666,
0.01826605200767517,
-0.03188344091176987,
-0.005244226194918156,
-0.006035253871232271,
-0.05610223859548569,
0.018523674458265305,
-0.01115848682820797,
-0.06506651639938354,
0.02503526583313942,
0.0012689045397564769,
-0.01655585505068302,
-0.05285557731986046,
0.011461562477052212,
0.00635869475081563,
0.0383046492934227,
0.01684102788567543,
0.03527937829494476,
0.02138916589319706,
-0.013011666014790535,
0.04112837836146355,
-0.003020921256393194,
-0.052195340394973755,
0.010952095501124859,
-0.03783261403441429,
0.06455190479755402,
-0.013590768910944462,
0.006690971553325653,
0.011510301381349564,
-0.014251737855374813,
-0.034914933145046234,
-0.037720710039138794,
0.0021836403757333755,
-0.0223572738468647,
0.043167661875486374,
-0.005186709109693766,
-0.03769571706652641,
-0.030599074438214302,
-0.0028569898568093777,
-0.006668213754892349,
0.03785580024123192,
0.005004026461392641,
-0.02808253839612007,
0.024865852668881416,
0.005077154375612736,
0.030274581164121628,
0.0043852790258824825,
-0.04818890616297722,
-0.03139982372522354,
-0.015422577038407326,
-0.051947709172964096,
-0.0077397171407938,
-0.01760687306523323,
0.01734333485364914,
0.05227310582995415,
0.01132162380963564,
3.4566136264402303e-7,
0.00184544175863266,
-0.07966245710849762,
-0.0046226633712649345,
0.0002980398421641439,
-0.003697505919262767,
-0.025416450574994087,
0.0013586916029453278,
0.012571873143315315,
0.04878367856144905,
-0.026374902576208115,
0.00606429623439908,
0.011576948687434196,
0.013416046276688576,
-0.0013773365644738078,
-0.0420558825135231,
-0.02365957386791706,
0.015948699787259102,
-0.0628257766366005,
-0.006511167157441378,
0.01846596784889698,
0.015317951329052448,
0.027250386774539948,
0.02558629773557186,
0.010971554554998875,
0.017033757641911507,
0.0018765322165563703,
0.013344762846827507,
0.013643396086990833,
-0.009519003331661224,
0.015480815432965755,
0.0392298549413681,
-0.017149420455098152,
-0.025901610031723976,
-0.04813336953520775,
-0.009105059318244457,
0.011100669391453266,
-0.036010853946208954,
0.007310336921364069,
-0.0214709285646677,
0.016187461093068123,
0.0035559299867600203,
0.03584150969982147,
-0.050455447286367416,
-0.03964962810277939,
-0.031730715185403824,
-0.01179681159555912,
0.027802785858511925,
-0.010036822408437729,
-0.02381657250225544,
0.0361635722219944,
-0.009662155993282795,
0.007280770689249039,
0.03641101345419884,
0.0451316237449646,
-0.01054147258400917,
-0.07497663050889969,
0.030094105750322342,
-0.016417188569903374,
0.041373297572135925,
-0.05302482098340988,
-0.05420147255063057,
0.04823753610253334,
-0.03673158213496208,
0.0058008041232824326,
0.03739788755774498,
0.006266860291361809,
0.017085812985897064,
0.015001045539975166,
-0.012066889554262161,
0.007261138875037432,
0.055191028863191605,
-0.048397522419691086,
0.010235962457954884,
-0.0059524052776396275,
-0.05023084953427315,
-0.014186800457537174,
-0.008289817720651627,
0.019285202026367188,
-0.0048529235646128654,
0.014372262172400951,
0.05752507224678993,
0.029322851449251175,
-0.008291245438158512,
-0.0035315616987645626,
-0.023147493600845337,
-0.009734033606946468,
0.0012483511818572879,
0.0272853784263134,
0.02221602201461792,
0.017233846709132195,
0.03361033275723457,
-0.0641193687915802,
0.03679285943508148,
0.0078652398660779,
-0.004883862100541592,
-0.10608313232660294,
-0.01625789888203144,
0.0055787586607038975,
0.004777046386152506,
0.01273591909557581,
-0.07147281616926193,
0.020602300763130188,
0.012194635346531868,
-0.05776512995362282,
-0.03345934674143791,
-0.012009297497570515,
-0.012198803015053272,
-0.027010131627321243,
-0.023584606125950813,
0.0064957938157022,
0.023561587557196617,
0.033744893968105316,
0.06467688083648682,
0.025291921570897102,
-0.010810717940330505,
-0.038126587867736816,
-0.029237432405352592,
-0.005864281672984362,
0.04014843702316284,
0.006493160035461187,
-0.018099529668688774,
0.07067715376615524,
0.010140159167349339,
-0.05522650107741356,
0.01966593787074089,
-0.00954433623701334,
0.027297688648104668,
0.003323453012853861,
0.03713538125157356,
-0.022791342809796333,
0.011754035949707031,
0.041394565254449844,
-0.024780167266726494,
-0.009240522980690002,
0.004888418596237898,
0.02643636427819729,
0.04475945606827736,
-0.005981820169836283,
-0.02585766837000847,
0.037561338394880295,
-0.0336182601749897,
-0.03907177597284317,
0.059547167271375656,
-0.03344676271080971,
-0.019310973584651947,
0.008477986790239811,
0.0013032606802880764,
0.014072492718696594,
-0.04742329195141792,
0.0017879644874483347,
-0.053737565875053406,
-0.008757184259593487,
0.06953021883964539,
-0.012654081918299198,
0.02194012887775898,
-0.02011983096599579,
0.010059085674583912,
0.007732992991805077,
0.009661615826189518,
0.006275479681789875,
-0.02821592427790165,
-0.058834679424762726,
-0.004071047063916922,
-0.005201222840696573,
0.01126431580632925,
-0.006179306656122208,
-0.033860184252262115,
-0.05099824443459511,
0.04587108641862869,
0.017082003876566887,
0.030907616019248962,
-0.046781398355960846,
-0.04938653111457825,
-0.0588521771132946,
-0.06099013239145279,
0.011797062121331692,
-0.02930815890431404,
-0.04705396667122841,
-0.03302793577313423,
-0.008908523246645927,
0.004312473349273205,
-0.03871558979153633,
0.04880450293421745,
-0.005009002517908812,
-0.045682620257139206,
0.025666244328022003,
-0.030556300655007362,
0.0314769372344017,
-0.047729942947626114,
0.006701360456645489,
-0.047114573419094086,
0.0026416669134050608,
0.02303592674434185,
0.00862923264503479,
-0.039635464549064636,
0.012774846516549587,
0.03704574331641197,
-0.0377705879509449,
0.03230806812644005,
-0.0015849763294681907,
-0.010246057994663715,
0.047942474484443665,
0.011121939867734909,
-0.03684532642364502,
0.06436510384082794,
0.015928490087389946,
0.034693822264671326,
0.016314860433340073,
-0.0023899038787931204,
-0.068941131234169,
0.04598347842693329,
0.001264747348614037,
0.02779480069875717,
-0.026379570364952087,
0.0035760749597102404,
0.033616941422224045,
-0.030104031786322594,
-0.013395044952630997,
0.03268437087535858,
-0.04034166783094406,
-0.01872703619301319,
-0.007948477752506733,
0.04468071460723877,
0.02083665505051613,
0.008334505371749401,
0.058862172067165375,
-0.00028659094823524356,
0.019373571500182152,
0.023922977969050407,
0.043519362807273865,
0.051066894084215164,
0.003973496612161398,
-0.016629114747047424,
0.046643394976854324,
-0.023904209956526756,
-0.02167467400431633,
0.021201418712735176,
0.014867201447486877,
-0.01593755930662155,
-0.04633347690105438,
0.013047155924141407,
-0.021344786509871483,
-0.006751739885658026,
0.026430318132042885,
-0.0016645455034449697,
0.07044098526239395,
-0.0031277562957257032,
0.005589631851762533,
-0.040395259857177734,
0.009250249713659286,
-0.01600346900522709,
-0.01715228520333767,
0.02929854393005371,
0.038635678589344025,
-0.02385852485895157,
-0.005820758640766144,
0.01487174816429615,
0.013580523431301117,
0.03377050533890724,
-0.01506943441927433,
-0.0166630856692791,
-0.009122656658291817,
-0.014644531533122063,
-0.0028304492589086294,
-0.021910719573497772,
-0.040874581784009933,
-0.013404776342213154,
0.03507211431860924,
0.036742884665727615,
-0.0010898036416620016,
0.023657020181417465,
-0.03368261829018593,
-0.0022935906890779734,
0.029733676463365555,
-0.06712644547224045,
-0.011538502760231495,
0.01753358729183674,
0.032949768006801605,
0.009362292475998402,
-0.026042994111776352
] |
<p>I know they have accurate means of measuring the distance of the planets in the Solar System from the Sun. I'm skeptical how can they use the same tools or techniques for other systems so far away as 22 light years.</p>
<p>According to this <a href="http://www.dailygalaxy.com/my_weblog/2012/02/newsflash-habitable-zone-earth-like-planet-discovered-22-light-years-away.html">link</a> the planet GJ667Cc resides in the "habitable zone". How are they able to measure the distance of something from something while observing it from a distance of 22 light years?</p>
| 7,657 |
[
0.04193606227636337,
-0.02754455991089344,
-0.015118769370019436,
-0.01143260020762682,
0.059409819543361664,
0.00439242972061038,
-0.037796538323163986,
-0.026787355542182922,
-0.002768648322671652,
-0.02108692191541195,
0.00022356185945682228,
0.05794602259993553,
0.014878172427415848,
0.05832616612315178,
0.011834131553769112,
0.010105549357831478,
-0.03619629144668579,
0.02346860244870186,
-0.018063059076666832,
-0.024401742964982986,
0.01628302037715912,
0.012758182361721992,
0.015168800950050354,
-0.012344351038336754,
-0.005660897120833397,
-0.003511750604957342,
-0.007926683872938156,
-0.02410486713051796,
0.022509992122650146,
0.017592405900359154,
0.03163902834057808,
-0.002440956886857748,
0.02290145866572857,
0.02143850550055504,
0.022564712911844254,
-0.006499891169369221,
-0.038376081734895706,
-0.02676665224134922,
0.006106853019446135,
0.04418044537305832,
-0.07144583016633987,
-0.017478538677096367,
-0.008360936306416988,
0.04373164102435112,
-0.02380083128809929,
0.014591705985367298,
-0.013924997299909592,
-0.048926059156656265,
0.07222829759120941,
-0.040387824177742004,
0.02904985286295414,
-0.017163431271910667,
0.018792135640978813,
-0.01769726723432541,
0.017804685980081558,
0.03929024934768677,
0.10782922804355621,
0.06943988054990768,
0.000275245780358091,
-0.039206426590681076,
-0.018676288425922394,
0.03678854927420616,
-0.013585776090621948,
-0.029005257412791252,
0.012504403479397297,
0.018936002627015114,
-0.030946116894483566,
-0.06524091958999634,
0.01045716181397438,
0.058714769780635834,
0.029966026544570923,
0.06270451098680496,
-0.009538550861179829,
-0.009866771288216114,
0.010732321999967098,
-0.05102568492293358,
-0.009192414581775665,
0.018988320603966713,
0.07508102059364319,
0.02037953771650791,
-0.007119296118617058,
-0.024032818153500557,
0.00829981453716755,
0.03953026607632637,
0.01126871444284916,
0.006343825254589319,
0.0289524644613266,
-0.00354325701482594,
-0.00556016294285655,
-0.0039009382016956806,
-0.019884437322616577,
0.06230669096112251,
0.013561873696744442,
0.0191454216837883,
-0.01254917960613966,
0.02522309124469757,
-0.006064821965992451,
0.03152013570070267,
0.00675988057628274,
-0.014819172210991383,
-0.002941462676972151,
0.016643915325403214,
0.010500193573534489,
0.036362309008836746,
0.012737560085952282,
-0.027187608182430267,
-0.03243981674313545,
0.011172992177307606,
0.03761329874396324,
0.015890005975961685,
-0.04155554622411728,
-0.016122981905937195,
0.048698391765356064,
0.0053777252323925495,
0.05617067590355873,
-0.013683543540537357,
-0.014034854248166084,
-0.001241230871528387,
0.058959200978279114,
0.07232162356376648,
0.0012596226297318935,
-0.012367535382509232,
-0.0006012147641740739,
-0.03849058225750923,
-0.024814870208501816,
0.028112653642892838,
0.015047987923026085,
-0.027847375720739365,
-0.01682163029909134,
0.005590397864580154,
0.008371734991669655,
-0.005123245995491743,
-0.009172615595161915,
-0.029239056631922722,
0.019414657726883888,
-0.0009665894904173911,
-0.07781677693128586,
-0.07208481431007385,
0.08360444754362106,
0.017802374437451363,
0.026577945798635483,
-0.06295350939035416,
0.012370684184134007,
0.04586595296859741,
0.08668960630893707,
0.012577515095472336,
-0.0056608896702528,
-0.01702015846967697,
0.013090018182992935,
-0.027478646486997604,
-0.017421210184693336,
-0.0026470059528946877,
-0.026570048183202744,
-0.047062620520591736,
0.0008617413113825023,
-0.08519033342599869,
0.010712162591516972,
0.014140976592898369,
0.027256319299340248,
-0.03649270161986351,
0.07151863723993301,
-0.03077881783246994,
-0.001015631016343832,
-0.0033302956726402044,
0.00400979770347476,
-0.03312644362449646,
0.10563807189464569,
0.02597872167825699,
-0.01611485704779625,
0.07120300829410553,
-0.029776640236377716,
0.023439064621925354,
0.054533664137125015,
0.009250074625015259,
0.05131886899471283,
-0.021455980837345123,
-0.02453899197280407,
0.00847429409623146,
0.032703351229429245,
-0.010486951097846031,
-0.01882455311715603,
0.002686541061848402,
0.039401400834321976,
0.02120250277221203,
0.028951015323400497,
0.057850178331136703,
-0.01548058446496725,
0.018962908536195755,
0.041715651750564575,
-0.056206028908491135,
0.0032210403587669134,
0.002558701205998659,
-0.03069363906979561,
0.014461244456470013,
-0.008824202232062817,
0.020639479160308838,
0.041990507394075394,
0.020409587770700455,
-0.0043341610580682755,
-0.01902962103486061,
0.007412184961140156,
0.023918461054563522,
0.02392507903277874,
0.00011198125866940245,
0.016919245943427086,
0.05817857384681702,
0.05864493548870087,
0.01289887260645628,
0.03542033210396767,
-0.0105903260409832,
-0.04988868534564972,
-0.009728041477501392,
-0.019697509706020355,
0.00887240469455719,
0.014494220726191998,
0.0024380809627473354,
-0.012321813963353634,
0.03806811571121216,
0.005862773396074772,
0.029924923554062843,
0.0013314761454239488,
0.07713677734136581,
0.04212668910622597,
0.04765402153134346,
-0.02291719801723957,
0.011396233923733234,
0.001909958547912538,
0.0196773000061512,
0.019038936123251915,
-0.02876952476799488,
-0.09078646451234818,
-0.0240370724350214,
0.014998101629316807,
0.015557870268821716,
-0.014165393076837063,
-0.0015488100470975041,
0.03527151048183441,
0.03713148087263107,
-0.004863970912992954,
-0.00821237824857235,
-0.0034267669543623924,
-0.003295221831649542,
0.01259686704725027,
0.024707982316613197,
0.007113415747880936,
0.016771430149674416,
0.021242955699563026,
0.05784570798277855,
0.021544309332966805,
-0.03992227464914322,
0.006930030882358551,
0.04239244386553764,
-0.02445538155734539,
0.026316747069358826,
0.007898389361798763,
-0.004193930421024561,
0.02985675074160099,
-0.045446477830410004,
0.010822592303156853,
0.017091825604438782,
0.019703729078173637,
-0.0018636675085872412,
-0.0336870513856411,
0.003783901920542121,
-0.012043979950249195,
0.032751020044088364,
-0.048253074288368225,
-0.02171900123357773,
0.03863610699772835,
-0.06835979223251343,
0.016943616792559624,
-0.05344349145889282,
0.015927642583847046,
-0.015815189108252525,
0.012423018924891949,
0.05244199186563492,
0.01303169596940279,
0.0065930685959756374,
0.0016791571397334337,
-0.037422746419906616,
-0.010228809900581837,
-0.028758369386196136,
0.005326962564140558,
-0.0043172952719032764,
-0.013099403120577335,
0.026164846494793892,
0.006821010261774063,
0.00531330332159996,
-0.008358118124306202,
-0.030276603996753693,
0.0014031640021130443,
-0.010046291165053844,
-0.01304343156516552,
-0.041461680084466934,
0.019373375922441483,
-0.01031712256371975,
-0.022341007366776466,
-0.022056376561522484,
0.011861319653689861,
0.018749728798866272,
0.012633111327886581,
0.0021166782826185226,
0.0080003272742033,
-0.04765532538294792,
-0.005600887816399336,
0.00917339138686657,
0.010274081490933895,
-0.025100331753492355,
-0.023801583796739578,
0.04195743426680565,
0.018816225230693817,
-0.05816423520445824,
-0.007962916046380997,
-0.026740575209259987,
-0.03882872313261032,
0.039498116821050644,
0.0002639687736518681,
0.040353190153837204,
-0.008710934780538082,
-0.022181585431098938,
0.055060166865587234,
0.013259959407150745,
-0.02647808939218521,
-0.057720787823200226,
0.0005082683055661619,
-0.05041923373937607,
0.020280903205275536,
-0.00981236808001995,
0.017565077170729637,
0.012309427373111248,
0.02812904678285122,
0.024076145142316818,
-0.015173454768955708,
0.027437452226877213,
-0.004476908128708601,
-0.001898671151138842,
-0.03512909635901451,
-0.015895139425992966,
-0.014846100471913815,
0.06558793783187866,
-0.003638499416410923,
-0.035815972834825516,
0.026844684034585953,
-0.009187277406454086,
0.030042901635169983,
0.009811862371861935,
-0.07236062735319138,
0.011766521260142326,
0.024775363504886627,
-0.028223266825079918,
0.003653592197224498,
-0.010467169806361198,
0.019733693450689316,
0.026010600849986076,
0.006957737263292074,
0.003185226581990719,
0.0741393193602562,
0.0003674132458399981,
-0.02935555949807167,
0.032218314707279205,
0.0397331528365612,
-0.022135429084300995,
-0.0224149189889431,
0.008036989718675613,
-0.018358903005719185,
-0.00733092101290822,
-0.024527432397007942,
-0.0473439022898674,
0.046780720353126526,
0.001374104875139892,
0.019690923392772675,
0.0032306713983416557,
-0.007390201091766357,
-0.013080484233796597,
-0.0629468485713005,
-0.01034917775541544,
-0.01702379435300827,
0.03171032667160034,
0.004117847885936499,
0.01210852712392807,
0.020773399621248245,
-0.003993930760771036,
0.005381282884627581,
-0.06133047491312027,
-0.059237297624349594,
0.019419267773628235,
-0.025250235572457314,
-0.032963577657938004,
-0.011265558190643787,
-0.033642929047346115,
-0.02419009990990162,
-0.0055259340442717075,
0.016261020675301552,
-0.05270780995488167,
-0.011916432529687881,
-0.046710655093193054,
-0.038651224225759506,
-0.009216482751071453,
-0.03111770935356617,
-0.04394548386335373,
0.02521822415292263,
0.012276862747967243,
-0.03522616997361183,
0.024379048496484756,
0.018248017877340317,
-0.016725270077586174,
-0.03899132460355759,
-0.008222215808928013,
0.013372816145420074,
0.009286252781748772,
0.043421827256679535,
0.019534727558493614,
0.03803440183401108,
-0.04356612637639046,
-0.03063088282942772,
0.0036340258084237576,
0.008381975814700127,
0.020400678738951683,
-0.014182263985276222,
-0.017692875117063522,
0.012517748400568962,
-0.023820478469133377,
-0.0009290818125009537,
0.05317811667919159,
-0.02535131573677063,
0.05824700742959976,
0.0419883094727993,
-0.010712256655097008,
-0.019861366599798203,
0.007746852934360504,
0.026508525013923645,
0.00024579427554272115,
0.015080252662301064,
-0.03248721733689308,
-0.06606069207191467,
-0.03522923216223717,
-0.005502407904714346,
0.004706889390945435,
0.021905316039919853,
-0.023028317838907242,
-0.038772162050008774,
0.014680370688438416,
-0.009196839295327663,
-0.04550095647573471,
-0.015234661288559437,
-0.025146808475255966,
0.011834848672151566,
-0.007960566319525242,
0.03258027881383896,
-0.007255039643496275,
0.06277673691511154,
0.03495673090219498,
-0.039080310612916946,
-0.0009798126993700862,
-0.07786844670772552,
-0.013785750605165958,
-0.021244755014777184,
0.033877260982990265,
0.00927016232162714,
-0.015821751207113266,
-0.07551984488964081,
0.005812063347548246,
0.06475193798542023,
-0.04253426194190979,
0.05414610356092453,
-0.031100230291485786,
0.01323625911027193,
-0.015895841643214226,
0.016401492059230804,
0.009364506229758263,
0.027776869013905525,
0.004922925028949976,
0.005232077091932297,
-0.02421678602695465,
0.0202237106859684,
-0.020566727966070175,
-0.00527137191966176,
0.008522417396306992,
0.06500960141420364,
0.03905796259641647,
-0.00919112004339695,
0.013157861307263374,
0.007814242504537106,
-0.019664891064167023,
-0.04738273844122887,
-0.008715110830962658,
-0.008880085311830044,
-0.04277310520410538,
0.043097082525491714,
-0.059949081391096115,
-0.0378732867538929,
0.025894412770867348,
0.0034168094862252474,
-0.02240540273487568,
-0.035600967705249786,
-0.02898607775568962,
-0.03149380907416344,
0.03007609210908413,
-0.017539067193865776,
0.05543634295463562,
0.008690867573022842,
-0.021362842991948128,
0.027679607272148132,
-0.021464290097355843,
0.02738041803240776,
-0.04756322130560875,
-0.040140550583601,
0.024516770616173744,
-0.03602441027760506,
-0.017435820773243904,
0.021476656198501587,
0.011282738298177719,
0.028240066021680832,
0.04314447194337845,
0.0034951649140566587,
-0.0012964800698682666,
0.038057517260313034,
-0.007233248557895422,
0.06184767186641693,
-0.0010067070834338665,
0.0538029782474041,
-0.0023258328437805176,
-0.023994607850909233,
0.023554427549242973,
-0.013821757398545742,
0.01846848987042904,
0.004843255039304495,
0.010771500878036022,
0.0073612043634057045,
-0.01118299551308155,
0.017526302486658096,
0.030063046142458916,
-0.05374201014637947,
0.02594444714486599,
-0.02392352931201458,
-0.004409322049468756,
0.004213778302073479,
-0.05091627314686775,
-0.010540983639657497,
-0.023273589089512825,
-0.0636778324842453,
0.02175704948604107,
-0.05824775993824005,
0.00004184375939075835,
0.018272144719958305,
0.005875173024833202,
-0.07068629562854767,
0.004207242745906115,
0.022962242364883423,
0.03754090517759323,
-0.020038990303874016,
-0.040684837847948074,
0.0007822709158062935,
-0.003981877584010363,
-0.04407041147351265,
-0.052160777151584625,
0.029778145253658295,
0.017438579350709915,
-0.051822032779455185,
-0.013032680377364159,
-0.007547701243311167,
0.04739440977573395,
-0.029504122212529182,
-0.00670251902192831,
0.02909833751618862,
0.02465067245066166,
-0.0106922322884202,
-0.014821193180978298,
0.003960505127906799,
-0.05555446445941925,
-0.035359907895326614,
-0.02436526119709015,
0.013997618108987808,
-0.039807263761758804,
-0.017161959782242775,
0.0023917064536362886,
0.021910201758146286,
0.02214830182492733,
-0.0024262256920337677,
-0.007425894495099783,
0.05885925889015198,
0.0012621940113604069,
-0.013227480463683605,
-0.04242587462067604,
-0.006765836849808693,
-0.017850972712039948,
-0.021221213042736053,
0.03856751322746277,
-0.03176230564713478,
0.011710511520504951,
-0.009818240068852901,
0.05111333355307579,
-0.007338192779570818,
-0.008693566545844078,
0.07757222652435303,
0.003937598317861557,
0.006309701129794121,
-0.015676550567150116,
0.020695896819233894,
0.01647399365901947,
-0.000853352656122297,
-0.0332849845290184,
0.0015030114445835352,
-0.03459659591317177,
-0.00818152166903019,
0.07928137481212616,
-0.014612688682973385,
0.02781732752919197,
-0.013254978694021702,
-0.01639781892299652,
-0.005227186717092991,
-0.04479409381747246,
-0.031266648322343826,
0.03135373815894127,
-0.001389249344356358,
0.035243939608335495,
-0.016550706699490547,
-0.040020957589149475,
0.017119426280260086,
0.043001607060432434,
-0.027110349386930466,
-0.00020467088324949145,
0.03895202651619911,
0.03333376720547676,
0.02813173644244671,
-0.01868712529540062,
-0.02754618227481842,
0.040874697268009186,
-0.04601665213704109,
0.04079345241189003,
0.030392780900001526,
0.011175418272614479,
0.03124442882835865,
-0.03632574528455734,
0.021338339895009995,
-0.0498916320502758,
-0.050207726657390594,
-0.005131101235747337,
0.05567904934287071,
0.08298172801733017,
0.018780728802084923,
0.025077074766159058,
-0.018348682671785355,
0.001847665524110198,
0.007126680575311184,
0.025091588497161865,
-0.009339780546724796,
-0.06193319335579872,
-0.045716769993305206,
-0.03566373512148857,
-0.05988885089755058,
0.07310882210731506,
-0.017145618796348572,
-0.039920855313539505,
0.015658987686038017,
-0.00619596429169178,
0.0035242156591266394,
-0.010406497865915298,
0.004148554056882858,
-0.034019771963357925,
0.058363176882267,
0.005278554279357195,
0.01565069705247879,
-0.020066414028406143,
0.013604260049760342,
0.11182758957147598,
0.05656519532203674,
0.004204580560326576,
-0.042629972100257874,
-0.009770347736775875,
-0.021822752431035042,
0.00006116636359365657,
-0.05736452713608742,
0.029409321025013924,
-0.013036574237048626,
0.01675812155008316,
-0.012718815356492996,
0.030704492703080177,
-0.0028238301165401936,
-0.005441268440335989,
0.043813638389110565,
0.006916519720107317,
-0.017010442912578583,
0.045091208070516586,
0.015493830665946007,
-0.003358497517183423,
0.00220409850589931,
-0.017699897289276123,
0.0019396796124055982,
0.011836790479719639,
-0.027488064020872116,
-0.012551412917673588,
-0.012287263758480549,
-0.021170005202293396,
0.048637840896844864,
-0.07489264011383057,
0.01930478774011135,
-0.004195211920887232,
-0.018890181556344032,
-0.04063039645552635,
0.02444307506084442,
0.020773369818925858,
0.004791936371475458,
-0.04852830618619919,
0.03462506830692291,
-0.021301977336406708,
-0.012571491301059723,
0.009704609401524067,
0.006298683118075132,
-0.010073207318782806,
-0.0015067997155711055,
-0.030926993116736412,
0.01750279776751995,
-0.015987107530236244,
-0.006679827813059092,
0.022565487772226334,
0.030606715008616447,
0.002057211007922888,
-0.048674583435058594,
0.036495182663202286,
0.0497179739177227,
-0.007442080415785313,
-0.017341990023851395,
-0.03443509712815285,
0.03720512613654137,
0.04498913511633873,
-0.014216023497283459,
0.010185349732637405,
-0.017746886238455772,
0.006243086885660887,
-0.025690985843539238,
-0.006229708902537823,
0.010376117192208767,
-0.02383158728480339,
-0.008930628187954426,
-0.04499562829732895,
0.03996216133236885,
-0.061200376600027084,
0.01947520300745964,
-0.007192087359726429,
0.026487644761800766,
-0.021349532529711723,
0.010329462587833405,
-0.007277436554431915,
-0.019340891391038895,
-0.03012845106422901,
0.017876874655485153,
-0.04424463212490082,
-0.05166797339916229,
-0.02404951862990856,
-0.026372971013188362,
0.04538774862885475,
0.005090960767120123,
0.017635833472013474,
0.032022397965192795,
-0.013268950395286083,
0.007253164425492287,
0.018641678616404533,
-0.022184964269399643,
0.005187296308577061,
0.000650279747787863,
-0.04394632950425148,
0.006515889428555965,
-0.010756542906165123,
0.02498404122889042,
0.06898659467697144,
-0.005732892081141472,
-0.0008099028491415083,
-0.022960325703024864,
-0.05201415717601776,
0.010675751604139805,
0.017111986875534058,
-0.011431028135120869,
-0.007849725894629955,
-0.012049362994730473,
0.025204326957464218,
-0.03593531996011734,
-0.05264221504330635,
-0.04727661609649658,
-0.034163638949394226,
-0.0015603103674948215,
0.015649814158678055,
-0.06226480379700661,
0.02144221030175686,
0.01508997194468975,
0.005135420709848404,
-0.04320724308490753,
0.0018322031246498227,
-0.012592107988893986,
-0.0015511008678004146,
-0.041131697595119476,
-0.001978413201868534,
0.01615002006292343,
0.018726592883467674,
-0.029981650412082672,
-0.009026635438203812,
0.04992934688925743,
-0.0028668225277215242,
0.026928380131721497,
0.006077601108700037,
0.042111046612262726,
-0.02424054965376854,
0.02380913309752941,
-0.016752246767282486,
-0.010839937254786491,
0.009381754323840141,
-0.025742970407009125,
-0.06806939095258713,
0.04000699520111084,
-0.04302005097270012,
0.04649309441447258,
-0.008012819103896618,
-0.029903486371040344,
-0.021257219836115837,
0.055880725383758545,
-0.009940399788320065,
-0.008990730158984661,
-0.02065403386950493,
0.022113647311925888,
0.024710439145565033,
0.05925101786851883,
0.0060230400413274765,
-0.03845524415373802,
-0.011006179265677929,
0.02658173441886902,
0.016466811299324036,
0.04344508424401283,
0.031227078288793564,
-0.012312648817896843,
-0.04115759953856468,
-0.00035281103919260204,
0.0028229267336428165,
0.013127285987138748,
0.017775975167751312,
0.018274348229169846,
0.004780622199177742,
0.06538203358650208,
0.06516602635383606,
-0.012197829782962799,
-0.07805345207452774,
0.030246950685977936,
-0.00028782893787138164,
0.009724315255880356,
0.013779781758785248,
-0.032489653676748276,
0.03278671205043793,
0.008813155815005302,
-0.08913730829954147,
0.021644890308380127,
-0.03953925892710686,
-0.040677886456251144,
-0.022674523293972015,
0.025683753192424774,
0.010919854044914246,
0.04263744875788689,
0.03123883530497551,
0.025639371946454048,
-0.006270517595112324,
0.037352897226810455,
-0.025525588542222977,
-0.04337112978100777,
-0.016955291852355003,
0.02993098832666874,
0.0009123262716457248,
0.014245012775063515,
0.04338163137435913,
-0.0006299702799879014,
-0.006583841051906347,
0.027140460908412933,
-0.003660447197034955,
0.06325840950012207,
0.014360783621668816,
-0.010944202542304993,
0.008200118318200111,
0.010706917382776737,
0.021969735622406006,
-0.03779922425746918,
-0.03998199850320816,
-0.02898143045604229,
0.018854575231671333,
0.03335319459438324,
0.006136061158031225,
-0.013735596090555191,
0.03727040812373161,
-0.014151165261864662,
0.0058348895981907845,
0.01790463738143444,
0.006883346009999514,
0.01537715457379818,
-0.0007937265327200294,
0.05290134623646736,
-0.02456608973443508,
-0.07758557796478271,
0.004061350133270025,
-0.07568151503801346,
-0.0016460872720927,
0.010609332472085953,
0.024416783824563026,
-0.033752214163541794,
0.004753805231302977,
-0.022717095911502838,
-0.00780539121478796,
0.001879858667962253,
0.011038579046726227,
0.009093540720641613,
-0.030504608526825905,
-0.024264611303806305,
-0.0014026868157088757,
-0.005814260337501764,
0.009994304738938808,
-0.025734087452292442,
-0.0543905571103096,
0.04794761538505554,
-0.009644606150686741,
0.009505837224423885,
0.014225916936993599,
0.008424964733421803,
-0.010293977335095406,
-0.05331841856241226,
0.0786592960357666,
-0.019087087363004684,
-0.007786280009895563,
-0.0229099839925766,
-0.04697020351886749,
-0.018625736236572266,
-0.014685594476759434,
0.06554118543863297,
0.014801780693233013,
0.011297451332211494,
-0.01711602322757244,
0.00278350873850286,
-0.013553800992667675,
-0.0586719736456871,
0.0538187250494957,
0.014239275828003883,
-0.036297302693128586,
0.015578916296362877,
-0.042385853826999664,
-0.025985555723309517,
0.0038431892171502113,
0.022391419857740402,
-0.005128543823957443,
0.0850558653473854,
0.028506238013505936,
-0.05718972161412239,
0.021170129999518394,
0.006946314591914415,
0.015093937516212463,
0.05184042453765869,
0.005855541210621595,
0.018500175327062607,
0.03480789065361023,
-0.009939858689904213,
-0.06322513520717621,
0.045763175934553146,
-0.04052291065454483,
-0.005655534099787474,
-0.03022867813706398,
-0.0034372417721897364,
0.018809756264090538,
-0.0652969628572464,
0.007822949439287186,
0.04915934428572655,
-0.018150394782423973,
0.019752994179725647,
0.057765182107686996,
-0.01681666448712349,
0.004395348485559225,
-0.014199808239936829,
0.03549506142735481,
0.0061313435435295105,
0.01477239839732647,
-0.01884319819509983,
0.04807436466217041,
0.03839879482984543,
0.008848726749420166,
0.056662026792764664,
0.024676809087395668,
-0.00023501091345679015,
0.0387759730219841,
0.01635846123099327,
0.033198293298482895,
-0.004275559447705746,
0.010744226165115833,
0.003302147379145026,
0.0208862517029047,
0.013741078786551952,
0.01603708788752556,
-0.013286218047142029,
0.08676353096961975,
-0.039923377335071564,
-0.023537958040833473,
-0.024983519688248634,
-0.04586492478847504,
-0.023817509412765503,
-0.014755666255950928,
-0.004814193584024906,
-0.009186890907585621,
0.03995097056031227,
0.0374930202960968,
-0.01699417270720005,
0.011320342309772968,
0.016738612204790115,
-0.044380541890859604,
0.0010150765301659703,
-0.013148872181773186,
0.030911218374967575,
0.02513052336871624,
-0.02018299326300621,
-0.014057023450732231,
-0.01990465261042118,
0.021329347044229507,
0.029908737167716026,
0.0014299460453912616,
0.01594950444996357,
-0.0060507385060191154,
0.005789215210825205,
0.024066295474767685,
-0.07458779215812683,
-0.004661360289901495,
-0.016491081565618515,
0.019421664997935295,
-0.0025315620005130768,
-0.03854519501328468
] |
<p><img src="http://i.stack.imgur.com/0dOhU.jpg" alt="enter image description here"></p>
<p>In this picture if the only parts of an object in contact with a surface are the lines AB and CD am I right in saying that the centre of mass has to be in the area enclosed by ABCD (as shown). I think this is correct as if the mass lies outside this region taking moments about e.g.an axis AC would lead to a resultant moment. If this is true please can you also give me a more generalised rule. thanks</p>
| 7,658 |
[
-0.002415773458778858,
-0.018410634249448776,
-0.018738310784101486,
-0.019640887156128883,
0.043127112090587616,
-0.010058575309813023,
-0.05277549847960472,
-0.021461213007569313,
-0.0053219180554151535,
-0.03056645765900612,
0.00075244449544698,
0.0036198091693222523,
0.09396567940711975,
0.04462587460875511,
0.01141880452632904,
0.006596551742404699,
0.002725368831306696,
-0.02953685075044632,
-0.011251538060605526,
-0.05524633079767227,
-0.0034802621230483055,
-0.004379848018288612,
0.005996770691126585,
-0.02045600861310959,
-0.014667133800685406,
0.018013840541243553,
-0.008581620641052723,
-0.008325811475515366,
0.049444831907749176,
0.06426911801099777,
-0.019055919721722603,
-0.026891600340604782,
-0.005003433674573898,
-0.01286614965647459,
0.054477136582136154,
0.0034285092260688543,
-0.0072598145343363285,
-0.02047520875930786,
0.013454350642859936,
0.02735736221075058,
-0.008803922683000565,
0.0003045199846383184,
-0.002602283377200365,
0.06126822158694267,
-0.018212076276540756,
0.028356123715639114,
-0.004605525638908148,
-0.027466416358947754,
0.052523404359817505,
-0.08747313916683197,
0.08873885124921799,
-0.0002568771305959672,
0.06722203642129898,
0.04233018681406975,
-0.011678669601678848,
-0.012689445167779922,
0.04226560890674591,
0.00969821959733963,
-0.023520508781075478,
-0.027859870344400406,
-0.007203907705843449,
-0.006437288131564856,
-0.0009844335727393627,
-0.028706908226013184,
-0.01694665290415287,
0.04645359888672829,
-0.023032115772366524,
-0.011572124436497688,
0.024230001494288445,
0.03919026628136635,
-0.0024455240927636623,
0.004544985946267843,
0.039144255220890045,
-0.018906252458691597,
-0.013494986109435558,
-0.03607568517327309,
0.06524987518787384,
-0.001264185644686222,
0.011738212779164314,
0.00813364889472723,
-0.0009824594017118216,
0.02177310176193714,
0.032129496335983276,
0.027969462797045708,
0.05067024007439613,
-0.020018836483359337,
0.06215327978134155,
0.0062615349888801575,
0.01607024110853672,
0.01286762673407793,
-0.004774372559040785,
0.029322916641831398,
0.021152984350919724,
-0.02996503934264183,
-0.0034562561195343733,
0.00963099580258131,
0.022310199216008186,
0.057087525725364685,
-0.028596876189112663,
-0.01759953424334526,
-0.02773154526948929,
0.005040640011429787,
0.04874449223279953,
0.050359562039375305,
0.017107469961047173,
-0.02606734074652195,
-0.06241915002465248,
0.028218666091561317,
0.01706714741885662,
-0.010032206773757935,
-0.034465186297893524,
0.04247507452964783,
-0.0015053314855322242,
-0.010566610842943192,
0.040360528975725174,
-0.0048269000835716724,
0.0035238810814917088,
-0.010560717433691025,
0.036389339715242386,
0.013526844792068005,
0.029127895832061768,
-0.0768994465470314,
-0.0073090000078082085,
-0.022584842517971992,
-0.0688338428735733,
0.004597409628331661,
0.023401714861392975,
0.017658814787864685,
0.0008507419261150062,
0.03923129290342331,
0.008148876950144768,
-0.005930221639573574,
-0.0035274287220090628,
0.00924740545451641,
-0.0001379395107505843,
-0.03849411383271217,
-0.05507116764783859,
-0.057021744549274445,
0.00529616279527545,
-0.004778204020112753,
-0.029044706374406815,
-0.05639206990599632,
-0.03508082777261734,
0.05239744856953621,
0.04910691827535629,
-0.015201292000710964,
0.0037868614308536053,
0.013247803784906864,
0.04259861633181572,
-0.011697388254106045,
-0.0002635943819768727,
-0.031344298273324966,
-0.0022761754225939512,
-0.05739691108465195,
-0.016118023544549942,
-0.07479265332221985,
0.005632991436868906,
0.02940625697374344,
0.010491159744560719,
-0.041698310524225235,
0.028863735496997833,
-0.02899913676083088,
-0.013156634755432606,
0.011807874776422977,
-0.004626347683370113,
-0.033210188150405884,
0.052975770086050034,
0.016577890142798424,
-0.006733758840709925,
0.040303390473127365,
0.053015243262052536,
0.02354305051267147,
-0.023811863735318184,
0.022901752963662148,
0.05601944401860237,
-0.020126786082983017,
-0.010440905578434467,
-0.02280740812420845,
0.025327062234282494,
0.004757930524647236,
-0.07206425815820694,
-0.04328848794102669,
-0.03005285933613777,
0.04145723953843117,
-0.017006730660796165,
0.08003382384777069,
0.005545236635953188,
-0.012508867308497429,
0.023336729034781456,
-0.01638885773718357,
0.0001930258731590584,
-0.03206344693899155,
0.052909478545188904,
0.005535557866096497,
-0.017220817506313324,
-0.02731640264391899,
0.020421143621206284,
0.014384619891643524,
-0.031007859855890274,
-0.00707430113106966,
0.008628548122942448,
0.016233162954449654,
-0.00038330041570588946,
-0.04039691388607025,
0.01347492728382349,
0.05555873364210129,
0.02500452846288681,
-0.001618729904294014,
0.011899358592927456,
-0.024380305781960487,
-0.01675967127084732,
0.03150176629424095,
-0.020454103127121925,
0.017861640080809593,
0.015407119877636433,
0.01215419452637434,
0.03206596150994301,
0.01525775995105505,
-0.02342737279832363,
0.053022272884845734,
0.025867832824587822,
0.10139323025941849,
0.035659827291965485,
-0.016197117045521736,
0.002076133619993925,
0.01416152436286211,
0.04378465190529823,
0.010865525342524052,
0.013242470100522041,
-0.028887126594781876,
-0.04605746269226074,
-0.007193392608314753,
-0.011230473406612873,
0.005283648613840342,
-0.033419590443372726,
-0.0144544942304492,
0.06202801689505577,
-0.0020485620480030775,
0.04799065738916397,
0.007832170464098454,
0.0046387468464672565,
-0.006840930320322514,
0.006824077107012272,
0.04415781423449516,
-0.02387119270861149,
-0.005490381270647049,
-0.005150940734893084,
0.02859552390873432,
0.060342490673065186,
-0.014508659951388836,
0.02382221817970276,
0.019353851675987244,
-0.01972975581884384,
0.03987055644392967,
0.0075523569248616695,
-0.012928251177072525,
0.06267184764146805,
-0.028395069763064384,
0.021367281675338745,
0.040174953639507294,
0.0033391008619219065,
-0.008066271431744099,
-0.02934480644762516,
-0.016814779490232468,
0.021597007289528847,
0.008659248240292072,
-0.04722709208726883,
-0.03621114417910576,
0.02910822443664074,
-0.04556332528591156,
-0.01155527587980032,
-0.018414504826068878,
-0.02397873066365719,
-0.032259732484817505,
0.0135860750451684,
0.07004214823246002,
0.035583097487688065,
0.036842674016952515,
-0.02391176111996174,
-0.010411183349788189,
-0.05103081092238426,
-0.02764435112476349,
0.01080930233001709,
0.00018683985399547964,
-0.06553871929645538,
-0.026738768443465233,
-0.06844194233417511,
-0.04088032990694046,
0.02858217991888523,
-0.014275757595896721,
0.005133260972797871,
-0.0028224510606378317,
-0.016551755368709564,
-0.0192051213234663,
-0.002916897414252162,
-0.008815934881567955,
-0.009431716986000538,
-0.027010178193449974,
-0.01936856471002102,
0.061294808983802795,
0.028185974806547165,
-0.003155662678182125,
0.04339233785867691,
0.010975932702422142,
-0.06298860907554626,
-0.05168488621711731,
-0.008203164674341679,
0.021872280165553093,
-0.022670255973935127,
0.021327612921595573,
0.03793395310640335,
-0.004942021798342466,
-0.00037067700759507716,
-0.038551732897758484,
-0.036967046558856964,
0.013670526444911957,
-0.03330226242542267,
0.05140199512243271,
0.00035142485285177827,
-0.02381589449942112,
0.0810466855764389,
0.02527446486055851,
-0.052408572286367416,
-0.015241282992064953,
-0.0028536587487906218,
-0.023577246814966202,
-0.016437986865639687,
-0.03653842583298683,
0.021394064649939537,
-0.026509003713726997,
0.018045326694846153,
0.017026614397764206,
0.014300011098384857,
0.020381968468427658,
0.0012911484809592366,
-0.000915925542358309,
-0.003248397260904312,
0.01773032732307911,
-0.029966024681925774,
0.06503642350435257,
0.010944530367851257,
0.027411600574851036,
0.02932005375623703,
-0.020415356382727623,
0.04588436707854271,
0.0054319011978805065,
-0.03871986269950867,
0.011031053960323334,
-0.0408480241894722,
0.027144495397806168,
0.011064887046813965,
0.02543596364557743,
0.014874284155666828,
-0.010498475283384323,
0.03854130581021309,
-0.009105423465371132,
0.048031195998191833,
-0.0012043261667713523,
-0.019509751349687576,
0.05045581981539726,
-0.010212650522589684,
0.01994086056947708,
-0.007711633108556271,
0.021195054054260254,
-0.011053897440433502,
0.00015607313252985477,
-0.014870503917336464,
-0.04332186281681061,
0.02150539681315422,
0.03892029449343681,
0.03149993345141411,
0.000390182773116976,
-0.04530122131109238,
-0.00349692115560174,
-0.0822923555970192,
0.006583326030522585,
0.036809373646974564,
0.031329527497291565,
-0.016984373331069946,
0.019280588254332542,
0.06346551328897476,
-0.019902804866433144,
-0.015770740807056427,
0.016372421756386757,
-0.10919345915317535,
0.026285599917173386,
0.00024560416932217777,
0.003996929619461298,
-0.00621058139950037,
-0.03922724723815918,
-0.015208043158054352,
-0.009388763457536697,
-0.026742642745375633,
-0.009173971600830555,
-0.007585891988128424,
-0.051103778183460236,
0.006614606361836195,
-0.06574130058288574,
0.0008770761778578162,
-0.01080793235450983,
0.01386497262865305,
0.05173629894852638,
0.00021038750128354877,
0.021891595795750618,
0.059006836265325546,
0.0012702068779617548,
-0.012370024807751179,
0.0122617082670331,
0.01624717377126217,
0.00026828827685676515,
0.054937660694122314,
0.02094394899904728,
0.004850808065384626,
-0.02685161679983139,
0.029274389147758484,
-0.0053350962698459625,
0.07061759382486343,
-0.01808461919426918,
-0.04844867065548897,
-0.04917808994650841,
-0.02916783280670643,
-0.039154451340436935,
-0.002583619672805071,
0.026944376528263092,
-0.030396049842238426,
-0.019174955785274506,
0.04438270255923271,
-0.031222570687532425,
-0.007447582203894854,
0.06028757989406586,
0.06883464753627777,
0.06938771158456802,
-0.03309331834316254,
-0.0752030462026596,
-0.018567226827144623,
-0.023252159357070923,
-0.02412618324160576,
0.028199853375554085,
0.014477173797786236,
-0.0011692841071635485,
0.006765746045857668,
0.0400729663670063,
0.018772520124912262,
-0.01281892042607069,
0.04043954610824585,
-0.0013031680136919022,
0.0009641180513426661,
-0.010903415270149708,
-0.014460345730185509,
0.057202912867069244,
-0.028864353895187378,
0.04417426139116287,
0.017792958766222,
-0.022945651784539223,
-0.06707809865474701,
-0.05180051922798157,
0.03183571249246597,
0.026710717007517815,
-0.004502219147980213,
0.0006110764807090163,
-0.03334726393222809,
-0.003775940742343664,
0.06741580367088318,
-0.0555475689470768,
0.028527384623885155,
-0.06304606795310974,
0.01710480824112892,
-0.01112095732241869,
-0.013256294652819633,
-0.027733074501156807,
-0.007819416001439095,
0.006001881789416075,
0.012402745895087719,
-0.01890338957309723,
-0.032337237149477005,
0.027227018028497696,
0.0044433739967644215,
0.014421245083212852,
0.021038739010691643,
0.029070794582366943,
-0.03951635584235191,
0.002945404499769211,
0.014417982660233974,
-0.02593311294913292,
-0.06844126433134079,
0.011685575358569622,
-0.011738455854356289,
0.010545634664595127,
0.025332167744636536,
-0.01247783750295639,
-0.020276544615626335,
0.016973543912172318,
0.03189152106642723,
-0.0027814004570245743,
-0.008356393314898014,
0.010368401184678078,
0.04552874714136124,
0.028452124446630478,
-0.035879459232091904,
0.019772302359342575,
0.026697486639022827,
0.014885537326335907,
-0.05171689763665199,
-0.0301828570663929,
0.024212464690208435,
0.019328724592924118,
-0.04148881137371063,
-0.05391179770231247,
0.01791127398610115,
-0.02200729213654995,
0.008450118824839592,
-0.01684129796922207,
0.024044286459684372,
-0.04344392567873001,
-0.03610629588365555,
-0.0018694084137678146,
0.018246468156576157,
0.014347470365464687,
0.011624583974480629,
-0.02010207809507847,
0.033408887684345245,
-0.009784970432519913,
0.006470764521509409,
0.0036620954051613808,
-0.005368609447032213,
0.008667020127177238,
0.01702783815562725,
0.008299303241074085,
0.011393790133297443,
-0.04803870618343353,
-0.02336963824927807,
-0.055914927273988724,
-0.07991209626197815,
0.02036258950829506,
-0.0030510053038597107,
0.01669098250567913,
0.0016399354208260775,
-0.033242177218198776,
-0.023667965084314346,
-0.006456172559410334,
0.018004970625042915,
0.031941454857587814,
-0.06664849072694778,
0.03594718128442764,
0.017967073246836662,
0.02817395329475403,
-0.048402089625597,
-0.07185832411050797,
0.010289518162608147,
0.0488196536898613,
-0.006130652967840433,
-0.01839628256857395,
-0.015722719952464104,
-0.002176036359742284,
-0.03587090224027634,
-0.00773199088871479,
0.02697562426328659,
-0.056584909558296204,
0.013986059464514256,
0.08166982233524323,
-0.015706660225987434,
0.06682130694389343,
0.01905130036175251,
0.005156239029020071,
0.043302200734615326,
0.02578214555978775,
-0.023711394518613815,
0.003212972776964307,
0.05929999053478241,
-0.03826890513300896,
-0.02600964345037937,
-0.011413057334721088,
0.017971783876419067,
0.04595804959535599,
0.05015042424201965,
-0.0021345627028495073,
0.0005365709075704217,
0.04265027865767479,
-0.023564651608467102,
-0.02600335329771042,
0.0061493837274611,
0.003706572111696005,
-0.010173792019486427,
0.026241393759846687,
0.01530103012919426,
-0.009218120016157627,
-0.036454204469919205,
-0.00788149330765009,
-0.011479995213449001,
0.037709612399339676,
0.018448513001203537,
0.05581728368997574,
0.0002802038216032088,
0.019684184342622757,
-0.03577188029885292,
-0.048508431762456894,
0.06906622648239136,
0.001197757781483233,
-0.03433604538440704,
0.0260862335562706,
0.013736935332417488,
0.016738008707761765,
-0.002194742439314723,
-0.03930826857686043,
0.035044703632593155,
0.05455321818590164,
0.014285935088992119,
0.07367584109306335,
0.039111945778131485,
0.02947183884680271,
0.013196006417274475,
-0.020411932840943336,
-0.016505738720297813,
-0.020027047023177147,
0.010769397020339966,
0.008602629415690899,
-0.06515036523342133,
-0.0164276622235775,
0.03678203374147415,
0.012660080567002296,
-0.014187897555530071,
0.008352041244506836,
0.024678509682416916,
0.0024140984751284122,
0.004372617695480585,
0.04928123578429222,
-0.011982550844550133,
0.015196957625448704,
0.00637419568374753,
0.05685378611087799,
-0.0070291622541844845,
-0.030523020774126053,
-0.010531395673751831,
-0.01846996694803238,
0.0016861107433214784,
0.002665773266926408,
-0.033465251326560974,
-0.022395920008420944,
0.04633466899394989,
-0.017389733344316483,
0.003428476396948099,
-0.026282770559191704,
-0.02675507962703705,
0.040975071489810944,
-0.007333231158554554,
0.005055652000010014,
-0.01769825629889965,
-0.031463008373975754,
-0.027585312724113464,
-0.05787408724427223,
-0.05495304986834526,
0.03233916312456131,
-0.004364960826933384,
-0.01584763638675213,
0.051234353333711624,
-0.05519741028547287,
-0.001666522235609591,
0.006455195602029562,
0.03908772021532059,
0.010300018824636936,
0.07951885461807251,
0.01855638436973095,
0.001589844236150384,
-0.003276138100773096,
0.01261634100228548,
0.1181267648935318,
0.03344495967030525,
-0.02962544560432434,
-0.03952592611312866,
0.02984967827796936,
-0.027442235499620438,
-0.009562096558511257,
-0.0369810089468956,
0.0327872559428215,
-0.03524082154035568,
0.009783124551177025,
0.032992418855428696,
0.009778177365660667,
0.006132947281002998,
0.011208646930754185,
0.029212603345513344,
-0.007321344222873449,
-0.04381049796938896,
-0.011601414531469345,
0.025959743186831474,
-0.03451288864016533,
0.01306920312345028,
-0.04325513914227486,
0.010359358042478561,
-0.027416953817009926,
-0.010738883167505264,
-0.0008195855771191418,
-0.034702107310295105,
-0.009749090299010277,
0.014301992021501064,
-0.05066611245274544,
0.009454314596951008,
0.008736156858503819,
-0.06318844854831696,
-0.04764318838715553,
0.014164951629936695,
0.0052008433267474174,
-0.012793206609785557,
-0.0022897219751030207,
0.009267319925129414,
-0.025856059044599533,
-0.0044789789244532585,
0.013008831068873405,
0.018844114616513252,
-0.06529280543327332,
-0.011910287663340569,
-0.04435526952147484,
0.03790195286273956,
-0.009275820106267929,
0.017653411254286766,
0.03363864868879318,
-0.006850092671811581,
0.024118509143590927,
-0.06860684603452682,
-0.01643870770931244,
-0.012433159165084362,
0.004383469466120005,
-0.028437737375497818,
-0.0004212278581690043,
-0.04480266198515892,
0.002547478536143899,
-0.010340065695345402,
0.00010808451770571992,
-0.001185493660159409,
0.0009198516490869224,
0.0040154955349862576,
-0.020829560235142708,
0.06147502735257149,
0.002996646799147129,
-0.005875147879123688,
0.01843694970011711,
-0.022747281938791275,
-0.03835390508174896,
-0.01089760847389698,
-0.00040957590681500733,
0.0385035015642643,
0.018079401925206184,
0.004261626861989498,
0.01477491669356823,
-0.024087419733405113,
-0.03814706951379776,
0.031244583427906036,
-0.030705414712429047,
-0.024355361238121986,
-0.038524460047483444,
0.01180155947804451,
0.040744733065366745,
0.062227893620729446,
-0.022043753415346146,
-0.008608637377619743,
-0.015885643661022186,
0.03681947663426399,
-0.008008257485926151,
-0.016334887593984604,
-0.02263662777841091,
0.023704899474978447,
-0.024124875664711,
0.008738190867006779,
0.02105828933417797,
0.011441337876021862,
0.019154902547597885,
0.012434265576303005,
0.013291699811816216,
0.02798549272119999,
-0.02286560647189617,
0.04114711284637451,
-0.022894565016031265,
-0.01101917214691639,
0.0003114371211268008,
0.02740204893052578,
-0.012084505520761013,
-0.0656590387225151,
-0.022243641316890717,
-0.026711810380220413,
-0.02247580885887146,
-0.010515876114368439,
0.06807533651590347,
-0.011165603064000607,
0.03973912447690964,
-0.023162269964814186,
0.006196310743689537,
-0.029314905405044556,
0.005977158434689045,
-0.08806781470775604,
-0.005477378144860268,
0.041219938546419144,
-0.005986052565276623,
-0.05341335013508797,
0.015970682725310326,
0.00866579357534647,
-0.00233120727352798,
-0.003820404876023531,
0.02541913278400898,
0.018816977739334106,
-0.019951071590185165,
0.02062823995947838,
0.003292861394584179,
0.049752745777368546,
-0.029633980244398117,
-0.008393391966819763,
0.024036362767219543,
-0.02986335940659046,
-0.036446575075387955,
0.025428952649235725,
-0.007778696250170469,
0.008389242924749851,
0.02337035723030567,
-0.00997330341488123,
0.023864788934588432,
0.05993722379207611,
-0.006513751577585936,
-0.013005626387894154,
-0.0022918765898793936,
-0.022611340507864952,
-0.005810105707496405,
0.03604087606072426,
-0.011761220172047615,
-0.008061399683356285,
-0.017379561439156532,
0.02398129180073738,
0.021826984360814095,
-0.008709241636097431,
-0.02154460921883583,
0.017185306176543236,
-0.007160256151109934,
0.002725105732679367,
0.0417817160487175,
0.02284085378050804,
0.017426257953047752,
0.036764465272426605,
-0.03402508795261383,
0.026687119156122208,
0.014581361785531044,
0.017851829528808594,
-0.0872095450758934,
-0.05134395509958267,
0.00816860981285572,
0.010437892749905586,
0.05410133674740791,
-0.007416794542223215,
-0.004844876006245613,
0.03378578647971153,
-0.06629036366939545,
0.004256619140505791,
-0.03176066279411316,
-0.021549103781580925,
-0.03577062115073204,
-0.010927747935056686,
0.0018203102517873049,
0.05076499655842781,
-0.014435764402151108,
0.04445648938417435,
0.030218496918678284,
0.013177798129618168,
-0.039980579167604446,
-0.017123593017458916,
0.020479194819927216,
0.03841538354754448,
-0.02752538211643696,
-0.027308810502290726,
0.054172333329916,
0.0022923899814486504,
-0.058053258806467056,
0.035223908722400665,
-0.03415551781654358,
-0.0219716839492321,
0.02325286529958248,
-0.005337605718523264,
0.008960778824985027,
0.02280259132385254,
0.011134910397231579,
-0.03024127334356308,
0.010792306624352932,
0.02410435676574707,
0.021103249862790108,
-0.00024490946088917553,
-0.020461907610297203,
0.0025949340779334307,
0.02633322775363922,
-0.05358399078249931,
-0.02146041952073574,
0.011823002249002457,
-0.03233634680509567,
-0.02285858802497387,
-0.02229553833603859,
0.02713005430996418,
-0.0037988482508808374,
-0.04867813363671303,
0.017486469820141792,
-0.0603158064186573,
0.02635183185338974,
0.04959774389863014,
-0.011647483333945274,
-0.022174933925271034,
0.007577995769679546,
0.02128920704126358,
-0.01765299029648304,
-0.0008407729910686612,
0.025717219337821007,
-0.05470934882760048,
-0.031073519960045815,
0.0027670967392623425,
0.001197877456434071,
-0.031631406396627426,
-0.00019842122856061906,
-0.06751571595668793,
-0.02173345908522606,
0.019869066774845123,
-0.0025123744271695614,
-0.008957971818745136,
0.01915794424712658,
-0.03563743457198143,
-0.04586991295218468,
-0.09352398663759232,
0.039236199110746384,
-0.02578401006758213,
-0.06808735430240631,
-0.040845610201358795,
0.000521478068549186,
0.003964263945817947,
-0.015238448046147823,
0.02421404793858528,
-0.006811144761741161,
0.015297415666282177,
-0.008196672424674034,
-0.020701058208942413,
-0.007608170621097088,
0.0046632117591798306,
0.020222071558237076,
0.02318090759217739,
-0.017240134999155998,
0.025736654177308083,
-0.010206135921180248,
-0.012978211045265198,
0.00011714347783708945,
0.012080566957592964,
-0.0135273989289999,
0.05495676398277283,
0.012336921878159046,
-0.023438071832060814,
0.030217347666621208,
0.04243211820721626,
0.008650821633636951,
0.07973994314670563,
0.001668872544541955,
0.0020073254127055407,
0.024328039959073067,
-0.033464543521404266,
-0.01763949915766716,
0.041212499141693115,
-0.028626395389437675,
0.010019666515290737,
-0.013839730992913246,
0.030848706141114235,
0.025790559127926826,
-0.05711353197693825,
0.028525590896606445,
0.004514581523835659,
0.0020622259471565485,
-0.033113256096839905,
0.058029647916555405,
0.024303453043103218,
0.05104226619005203,
-0.010586760938167572,
0.05345867946743965,
0.03158402815461159,
-0.024113493040204048,
0.0051027690060436726,
0.006883814465254545,
0.028670968487858772,
0.015024284832179546,
-0.03926287218928337,
0.05021349713206291,
-0.010466624051332474,
0.034841641783714294,
-0.046730004251003265,
-0.0060853371396660805,
0.00951180700212717,
-0.008675163611769676,
0.0022222583647817373,
-0.013715123757719994,
0.02834218367934227,
0.017455974593758583,
-0.015439697541296482,
0.05918901786208153,
-0.004501486662775278,
0.017873095348477364,
-0.024014221504330635,
0.017866550013422966,
0.0008601256995461881,
0.009640144184231758,
0.03828631713986397,
0.010763640515506268,
-0.02990385703742504,
-0.04560093581676483,
-0.003012779401615262,
-0.0023860810324549675,
0.02308560349047184,
0.031695447862148285,
0.059315357357263565,
-0.02746446430683136,
0.038833703845739365,
-0.0024216745514422655,
-0.006969038397073746,
-0.02508028782904148,
0.007630477659404278,
0.009194395504891872,
0.048247914761304855,
0.015000996179878712,
0.018028726801276207,
0.004685814026743174,
-0.02971894107758999,
0.04628690704703331,
-0.06484848260879517,
-0.04915589094161987,
-0.006661984138190746,
0.020719066262245178,
0.03605856001377106,
-0.014181128703057766
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2175/is-it-possible-for-information-to-be-transmitted-faster-than-light">Is it possible for information to be transmitted faster than light?</a> </p>
</blockquote>
<p>I mean by using a perfect solid stick long enough and moving it forward and backward can I send information fastest than light ? Can you imagine a solid stick long enough to reach the moon and using it to comunicate with the lunar base. Will be information faster than light? What are the theoretical reason other than technical reason for rules this as impossible?
We should rule that a perfect unelastic solid exist ?</p>
| 4 |
[
-0.01113947294652462,
-0.05353502184152603,
-0.007489360868930817,
-0.08619727939367294,
0.0180024653673172,
-0.014687171205878258,
0.0003971173136960715,
-0.021681759506464005,
-0.001640454982407391,
-0.007023158948868513,
0.03778095915913582,
0.04114561155438423,
0.02631698176264763,
0.03785097971558571,
0.029914310202002525,
0.0014832017477601767,
-0.0028901482000947,
0.01699163019657135,
-0.013805646449327469,
-0.0025076388847082853,
0.014271516352891922,
-0.0025065476074814796,
-0.007737183477729559,
0.007209782488644123,
-0.0051474375650286674,
0.005026158876717091,
0.027202149853110313,
0.01081773079931736,
0.027350211516022682,
0.058745451271533966,
0.034870635718107224,
0.003875205758959055,
0.03809257969260216,
0.03270349279046059,
0.03203164041042328,
0.025150654837489128,
-0.023246003314852715,
0.007562687620520592,
0.025448007509112358,
-0.0056669097393751144,
-0.03153710067272186,
-0.023169714957475662,
0.016775449737906456,
0.0490214079618454,
-0.018324818462133408,
0.041702501475811005,
0.017659949138760567,
-0.034132543951272964,
0.02021319605410099,
-0.04302183538675308,
0.04821282997727394,
-0.016384081915020943,
0.0474214106798172,
0.005260386969894171,
-0.0013459831243380904,
-0.021061556413769722,
0.09791123867034912,
0.07799482345581055,
-0.014590689912438393,
-0.040849268436431885,
0.0013706518802791834,
0.02218654379248619,
-0.005047043319791555,
-0.0320587158203125,
-0.017802337184548378,
0.05168209224939346,
-0.04329518601298332,
0.04163888469338417,
0.029053090140223503,
-0.013246218673884869,
-0.02075948938727379,
0.005794860888272524,
0.03857075795531273,
0.030960969626903534,
-0.00868039671331644,
-0.02500276081264019,
-0.0053281644359230995,
0.017132630571722984,
0.011875552125275135,
0.08591693639755249,
-0.004160703159868717,
0.018694886937737465,
0.03320220857858658,
0.03445351496338844,
0.05104294791817665,
-0.018522750586271286,
0.03055965155363083,
-0.005152690690010786,
0.030472641810774803,
0.008256664499640465,
-0.025478897616267204,
-0.004053655080497265,
0.015185336582362652,
0.004267528187483549,
0.01329121645539999,
-0.005229309666901827,
-0.00541685102507472,
0.0332360565662384,
0.003594702109694481,
-0.04649573937058449,
0.01979200914502144,
-0.026235757395625114,
0.018050018697977066,
0.07829989492893219,
0.01132937427610159,
-0.038439296185970306,
-0.030979467555880547,
0.010604176670312881,
-0.03093535825610161,
-0.003937403671443462,
0.009130383841693401,
0.006665756460279226,
0.010968349874019623,
0.005128874909132719,
0.009060266427695751,
-0.057256899774074554,
0.01083153486251831,
-0.03672735020518303,
0.07719185203313828,
0.05468130111694336,
0.026010379195213318,
-0.030085518956184387,
0.04383470490574837,
-0.033286213874816895,
-0.01682874746620655,
0.025116223841905594,
0.008076991885900497,
0.0025758002884685993,
0.00624885642901063,
0.01516831386834383,
0.019304312765598297,
0.0021343028638511896,
-0.00975166168063879,
-0.007343614939600229,
0.06473954766988754,
-0.01953396573662758,
-0.10328343510627747,
-0.051262807101011276,
0.050740476697683334,
0.016470732167363167,
-0.03648525848984718,
-0.10077207535505295,
0.04233485087752342,
0.013165093027055264,
0.04433314874768257,
0.019610101357102394,
0.010359336622059345,
-0.013406869024038315,
0.037880390882492065,
0.024139370769262314,
-0.04690156131982803,
0.012146440334618092,
0.026024458929896355,
-0.03262099251151085,
0.02606433816254139,
-0.08218134939670563,
-0.02839428000152111,
0.03949829190969467,
-0.015524751506745815,
-0.023581981658935547,
0.039864491671323776,
-0.03436454012989998,
0.03542537987232208,
0.016653329133987427,
-0.046261344105005264,
-0.03917255252599716,
0.09602038562297821,
0.02571849524974823,
-0.005254438612610102,
0.05441712588071823,
0.010911966674029827,
0.045641493052244186,
-0.013827616348862648,
-0.011596659198403358,
0.028483852744102478,
-0.05366192385554314,
-0.01493729930371046,
-0.008542025461792946,
-0.015432305634021759,
-0.019130704924464226,
-0.0529450848698616,
-0.03575212135910988,
0.009170391596853733,
0.010748103260993958,
0.022904854267835617,
0.050783731043338776,
-0.003694933606311679,
0.02689356543123722,
0.03150324150919914,
-0.041079577058553696,
-0.015355093404650688,
-0.0025823141913861036,
0.037005867809057236,
0.031160686165094376,
-0.010434575378894806,
0.02775203436613083,
0.0007065243553370237,
0.0027172532863914967,
-0.015061631798744202,
-0.013424280099570751,
-0.006059031933546066,
0.04859468713402748,
0.036958176642656326,
0.024979885667562485,
0.036082927137613297,
0.09548820555210114,
0.018336985260248184,
-0.023431532084941864,
-0.012751146219670773,
0.02294132485985756,
-0.04283933341503143,
0.007156871259212494,
-0.0020731708500534296,
0.03878176957368851,
-0.0018407328752800822,
0.02523137256503105,
0.06430289149284363,
0.024850405752658844,
-0.025574928149580956,
0.025474848225712776,
-0.009228884242475033,
0.05489140748977661,
0.008750035427510738,
-0.02320350892841816,
-0.00837776344269514,
0.02089945785701275,
0.04355911910533905,
0.009085040539503098,
-0.0071145701222121716,
-0.04790019616484642,
-0.07364533096551895,
-0.02140483818948269,
0.00977460015565157,
0.017416080459952354,
-0.050083860754966736,
0.021625647321343422,
0.02543490193784237,
0.05604655295610428,
0.050204940140247345,
0.0356939360499382,
-0.031683217734098434,
-0.03947116434574127,
0.0038754113484174013,
-0.007728257216513157,
0.0005533468793146312,
0.026208290830254555,
0.03407023102045059,
0.04340777173638344,
-0.00582853052765131,
-0.018172504380345345,
0.005635674111545086,
-0.009172312915325165,
-0.008115113712847233,
-0.01946250908076763,
0.04423452168703079,
-0.02228080853819847,
0.025378894060850143,
-0.020589696243405342,
0.01813105307519436,
0.022071948274970055,
0.014971522614359856,
-0.004127675201743841,
-0.04812926799058914,
0.0189333725720644,
-0.020547496154904366,
0.025928527116775513,
-0.01947728544473648,
-0.014175712130963802,
0.03112560138106346,
-0.02678935043513775,
0.015507955104112625,
-0.023425361141562462,
-0.014793016016483307,
0.013474564999341965,
-0.0059539624489843845,
0.04354165494441986,
0.01509531307965517,
0.024440696462988853,
-0.037109002470970154,
-0.017864184454083443,
-0.009884271770715714,
-0.03833778202533722,
-0.009592847898602486,
0.004507594741880894,
-0.02213863842189312,
0.028420638293027878,
-0.019035013392567635,
-0.03612387925386429,
0.04555909335613251,
-0.04106387495994568,
0.017628876492381096,
-0.0014172449009492993,
-0.06377295404672623,
-0.031118951737880707,
-0.007860766723752022,
-0.0262650977820158,
0.02744589000940323,
-0.04055898264050484,
0.012388477101922035,
0.031713973730802536,
-0.023881522938609123,
-0.05056062340736389,
-0.020272156223654747,
-0.06403443217277527,
-0.053244538605213165,
0.04064752534031868,
-0.009875338524580002,
0.025744080543518066,
-0.05033876374363899,
0.02413908950984478,
-0.026490122079849243,
-0.04149461165070534,
0.02984567917883396,
-0.05030856281518936,
-0.06207825243473053,
0.0539969839155674,
-0.010464743711054325,
0.03743128851056099,
-0.022663425654172897,
-0.02141188643872738,
0.05938153341412544,
0.02949606068432331,
-0.036337655037641525,
-0.017597388476133347,
-0.012813751585781574,
-0.0056302533484995365,
-0.07518860697746277,
0.03554496914148331,
0.009754366241395473,
0.0034895676653832197,
-0.006794334854930639,
0.029642214998602867,
0.0017679057782515883,
0.009125101380050182,
0.009357117116451263,
0.008376230485737324,
-0.03845108300447464,
0.03635258227586746,
-0.007998506538569927,
0.019432308152318,
0.04426559805870056,
-0.052804287523031235,
0.002160509116947651,
0.00204899488016963,
0.014370192773640156,
0.024722205474972725,
-0.04362030327320099,
0.056316737085580826,
0.040650300681591034,
0.03930523246526718,
-0.008983532898128033,
0.03962624818086624,
-0.011419897899031639,
-0.0119234723970294,
-0.017698001116514206,
0.0203876756131649,
0.024261286482214928,
0.04137647897005081,
-0.007543357089161873,
0.05827027186751366,
0.04067444056272507,
0.013946792110800743,
-0.013070536777377129,
-0.0583372600376606,
-0.016239548102021217,
-0.010288242250680923,
-0.011844356544315815,
-0.00648529315367341,
0.0086183100938797,
0.049293722957372665,
-0.0018428023904561996,
0.013201862573623657,
-0.0007031871937215328,
-0.019332069903612137,
-0.055747851729393005,
-0.018274135887622833,
-0.05414528399705887,
0.04494360834360123,
0.01879567839205265,
0.04298661649227142,
0.04223005846142769,
0.04076649993658066,
0.02626163512468338,
-0.012563374824821949,
-0.10365850478410721,
0.021747207269072533,
-0.03723815456032753,
-0.01279801968485117,
-0.010499447584152222,
-0.024591557681560516,
-0.027081996202468872,
-0.009801006875932217,
-0.04307107999920845,
-0.01157382782548666,
0.015623075887560844,
-0.04975998029112816,
0.015205277130007744,
0.0036076707765460014,
0.003818398341536522,
0.0020791981369256973,
0.06542211771011353,
0.027106575667858124,
-0.01705862209200859,
0.021701419726014137,
0.00637054443359375,
-0.052340347319841385,
0.01596708595752716,
0.003981076646596193,
-0.015967652201652527,
-0.00043305224971845746,
0.018201511353254318,
0.012752112001180649,
-0.001176626537926495,
-0.012294234707951546,
0.007392860949039459,
0.03698553517460823,
0.0359494723379612,
-0.02748713456094265,
-0.02983386255800724,
-0.06672094017267227,
-0.03447650372982025,
0.04040815681219101,
-0.03674159571528435,
0.06005670502781868,
-0.03409205377101898,
0.013935399241745472,
0.01278701238334179,
-0.013667220249772072,
0.01620754413306713,
0.030952271074056625,
0.02865408919751644,
-0.02642509527504444,
-0.03920743986964226,
-0.048920389264822006,
-0.05734734237194061,
-0.0009606123203411698,
0.013455300591886044,
0.03903432935476303,
-0.01123429462313652,
-0.008696209639310837,
0.006651994306594133,
-0.012353705242276192,
0.02663407474756241,
-0.01558037381619215,
-0.010467839427292347,
-0.021107519045472145,
0.0022722131107002497,
0.008736570365726948,
-0.016610905528068542,
-0.031800612807273865,
0.027133507654070854,
0.042729709297418594,
0.02073446474969387,
-0.037066392600536346,
-0.061456870287656784,
-0.023744290694594383,
0.01213909313082695,
0.07197590172290802,
-0.01665918342769146,
0.008173144422471523,
-0.05305229872465134,
-0.008746102452278137,
0.015987664461135864,
-0.012121643871068954,
0.04502735286951065,
-0.06361117213964462,
0.009202837012708187,
-0.00996754877269268,
-0.02307233028113842,
0.015127104707062244,
-0.0008686091750860214,
0.0007042140350677073,
-0.01045233104377985,
-0.02603813447058201,
0.018139399588108063,
0.024239936843514442,
0.01427161879837513,
0.03470269963145256,
0.06603315472602844,
0.011744692921638489,
0.027679169550538063,
0.011460760608315468,
0.01087629422545433,
-0.05817604809999466,
-0.058743152767419815,
0.032462481409311295,
0.041489940136671066,
-0.06476924568414688,
0.020964697003364563,
-0.034473590552806854,
-0.028371205553412437,
0.07369689643383026,
0.024697253480553627,
-0.0057873837649822235,
0.006316508632153273,
-0.026621630415320396,
0.024891426786780357,
-0.0010236725211143494,
0.021524818614125252,
-0.0002487212186679244,
0.03816588968038559,
-0.008244622498750687,
0.00475080031901598,
-0.005561959929764271,
0.02060564234852791,
-0.04275963455438614,
0.030946210026741028,
0.0025585326366126537,
0.04797927662730217,
-0.039377011358737946,
0.03277376666665077,
-0.017230501398444176,
-0.008155938237905502,
-0.008687484078109264,
-0.011423635296523571,
-0.026341231539845467,
0.03634048253297806,
0.0282429289072752,
0.014276023022830486,
-0.05804949626326561,
0.019106464460492134,
-0.0009821080602705479,
-0.014207093045115471,
0.024498790502548218,
-0.004024559631943703,
-0.006668956484645605,
0.031669970601797104,
0.025790110230445862,
0.0012825761223211884,
-0.02681548334658146,
-0.027189671993255615,
-0.016596095636487007,
-0.028200659900903702,
0.04151305928826332,
0.013844197615981102,
-0.01790696382522583,
0.030258456245064735,
-0.0511973612010479,
-0.0071327174082398415,
0.01878923736512661,
-0.03101053275167942,
0.018231714144349098,
-0.044140927493572235,
0.02254405990242958,
0.005546228028833866,
-0.02806204743683338,
-0.04051366075873375,
-0.05271462723612785,
0.04317252337932587,
0.024822687730193138,
-0.017593063414096832,
-0.02332799881696701,
0.017500661313533783,
-0.029040448367595673,
-0.021199068054556847,
-0.022628236562013626,
0.011371678672730923,
-0.023620394989848137,
-0.007738159038126469,
0.036729712039232254,
-0.022500261664390564,
0.025572286918759346,
-0.019432077184319496,
-0.0334462933242321,
-0.0033655057195574045,
-0.0006372914067469537,
-0.015559379011392593,
-0.025970257818698883,
0.02883625403046608,
-0.024639157578349113,
-0.06305158883333206,
0.0032943962141871452,
-0.01688942313194275,
0.0023339951876550913,
0.007789005525410175,
0.0021818422246724367,
0.028650688007473946,
0.02598167024552822,
-0.03212525695562363,
-0.02897087298333645,
0.031312692910432816,
0.01943034492433071,
0.013264949433505535,
-0.02765411138534546,
0.019722631201148033,
-0.058525968343019485,
-0.042784031480550766,
0.03207172453403473,
0.0016576750203967094,
0.01717318780720234,
-0.022336380556225777,
0.055859554558992386,
-0.021291470155119896,
-0.03101818449795246,
-0.0069747501984238625,
-0.005007909145206213,
0.025253744795918465,
-0.023694822564721107,
-0.000941744539886713,
-0.008217591792345047,
-0.01036441046744585,
-0.030159950256347656,
-0.0410982146859169,
0.006510766223073006,
-0.02552277222275734,
0.07141731679439545,
-0.02279980666935444,
0.032738275825977325,
-0.004206836223602295,
-0.009820397943258286,
-0.02653789333999157,
-0.013901442289352417,
-0.015124618075788021,
0.02192658558487892,
0.030842987820506096,
0.025485286489129066,
-0.036205440759658813,
-0.027216436341404915,
0.02513791434466839,
0.05900018289685249,
0.01923196017742157,
0.02205616608262062,
0.03702748939394951,
0.004874760750681162,
0.015689270570874214,
-0.03402000293135643,
-0.01286356057971716,
0.024891210719943047,
-0.06946251541376114,
0.02750166319310665,
-0.01260627992451191,
-0.028522564098238945,
0.03482545167207718,
0.004509250167757273,
0.021176913753151894,
-0.012441711500287056,
-0.021538764238357544,
-0.06528173387050629,
-0.019816257059574127,
0.028521409258246422,
0.051248084753751755,
0.022693229839205742,
-0.03450401872396469,
0.00892904493957758,
0.01243925653398037,
0.019178789108991623,
-0.02777634561061859,
-0.11996156722307205,
-0.03564544394612312,
0.004393212031573057,
-0.05183728411793709,
0.05612771213054657,
0.024593135342001915,
-0.04188022390007973,
0.023988693952560425,
-0.043871477246284485,
0.02346905879676342,
0.007939191535115242,
0.05626191943883896,
-0.05779983475804329,
0.09414378553628922,
-0.0207237396389246,
0.04479456692934036,
-0.0014620611909776926,
0.0080764414742589,
0.1010965034365654,
0.005282166413962841,
-0.022357875481247902,
-0.058750804513692856,
0.02799554541707039,
0.004029195290058851,
0.018368752673268318,
-0.052514124661684036,
0.005986672826111317,
-0.010610594414174557,
0.00867551751434803,
0.04909205064177513,
0.05276833847165108,
-0.040482208132743835,
0.0035220233257859945,
0.029838474467396736,
-0.03237706050276756,
-0.005053920671343803,
-0.01773199811577797,
0.022900480777025223,
0.0027866505552083254,
0.02780952863395214,
-0.015885451808571815,
0.030648840591311455,
-0.019240371882915497,
-0.013960869051516056,
-0.0261175949126482,
-0.009837091900408268,
0.018318206071853638,
-0.0010513926390558481,
-0.04737680405378342,
-0.022041872143745422,
0.0016425774665549397,
-0.018346579745411873,
-0.03842161223292351,
0.02133866772055626,
0.011350824497640133,
0.007708137389272451,
-0.0005763553199358284,
0.0346246175467968,
0.0108930803835392,
0.00560531672090292,
0.012523866258561611,
0.013258818536996841,
-0.07496853917837143,
0.0011991164647042751,
-0.026072097942233086,
-0.012057779356837273,
-0.025785747915506363,
-0.020632470026612282,
0.025938138365745544,
0.009934809058904648,
0.01417529582977295,
-0.014498841017484665,
-0.004195100627839565,
0.035046108067035675,
0.03304992988705635,
0.025638289749622345,
0.004622857552021742,
-0.0067011509090662,
0.005343100056052208,
-0.019462281838059425,
0.0012148485984653234,
-0.020347053185105324,
-0.00567712914198637,
-0.005448502488434315,
0.008919293992221355,
0.02012902870774269,
0.005473280791193247,
-0.015851514413952827,
-0.0336047038435936,
-0.0048249647952616215,
-0.009676664136350155,
0.015801725909113884,
0.029502084478735924,
0.008526292629539967,
0.01549555268138647,
0.02800990641117096,
-0.0021259416826069355,
-0.04073701053857803,
-0.024215126410126686,
0.02764621376991272,
-0.02592698112130165,
0.020534805953502655,
-0.04563327506184578,
-0.007723948452621698,
0.0374431386590004,
0.02476382441818714,
0.004101227968931198,
0.005188177805393934,
-0.016507448628544807,
0.010262052528560162,
0.014433187432587147,
-0.014071197248995304,
-0.013552017509937286,
-0.018679525703191757,
-0.0307486392557621,
0.01567564159631729,
-0.024257732555270195,
0.030841879546642303,
0.058663759380578995,
0.02050946280360222,
-0.004586729686707258,
0.0020822598598897457,
-0.018490731716156006,
-0.012342422269284725,
0.03468342125415802,
-0.0021765194833278656,
-0.021323733031749725,
0.02130960114300251,
0.01907692849636078,
-0.009958237409591675,
-0.04320400208234787,
-0.009505181573331356,
-0.01446930319070816,
-0.006944608874619007,
0.004378432873636484,
-0.0035932527389377356,
0.02720286138355732,
0.02114803157746792,
-0.03050904907286167,
-0.04836553335189819,
0.03000212088227272,
0.0033002241980284452,
0.006144297309219837,
-0.028671063482761383,
-0.02133597992360592,
-0.02614564076066017,
0.05059061199426651,
-0.004139421042054892,
0.0006483744364231825,
-0.0019778271671384573,
0.011304682120680809,
0.0008962485007941723,
0.0031673687044531107,
0.019502010196447372,
-0.012906502932310104,
0.04435758292675018,
-0.0026184457819908857,
-0.033728621900081635,
0.03440195322036743,
-0.015219511464238167,
-0.04708036780357361,
0.02988377958536148,
-0.02482352964580059,
0.0073038325645029545,
-0.0009387002210132778,
-0.012647044844925404,
0.014277317561209202,
0.09603717178106308,
-0.015389547683298588,
0.026378227397799492,
0.018253717571496964,
-0.05090763419866562,
-0.04111941531300545,
-0.003357571316882968,
0.01276374887675047,
-0.022749321535229683,
0.013594177551567554,
0.04352094605565071,
-0.005336074158549309,
0.002851644065231085,
0.04122922196984291,
0.006727403961122036,
-0.007864589802920818,
-0.015772636979818344,
0.019398076459765434,
-0.0014522620476782322,
0.02207866683602333,
0.04410812258720398,
-0.012299466878175735,
0.06882565468549728,
0.03117804229259491,
0.01578911393880844,
-0.12344596534967422,
0.03404831141233444,
0.010082973167300224,
-0.009175009094178677,
-0.0012280672090128064,
-0.04830664023756981,
0.024990014731884003,
0.009116925299167633,
-0.07795696705579758,
0.023126935586333275,
-0.053874000906944275,
0.005016840994358063,
-0.046602945774793625,
0.037084322422742844,
-0.04237052798271179,
0.033458296209573746,
0.05515294894576073,
0.036042213439941406,
-0.007842487655580044,
0.03897637128829956,
-0.029265621677041054,
-0.028910266235470772,
-0.009699600748717785,
0.018632011488080025,
-0.009764695540070534,
0.01741454191505909,
0.08406363427639008,
-0.022798748686909676,
-0.0023664922919124365,
-0.010903422720730305,
-0.005235091783106327,
0.04168105125427246,
0.0025976747274398804,
0.013551387935876846,
0.037059422582387924,
0.022700626403093338,
0.007894758135080338,
-0.03787989541888237,
-0.027980562299489975,
0.021032866090536118,
-0.013304159976541996,
0.02587713487446308,
-0.01051592268049717,
-0.03425082936882973,
-0.04547256976366043,
-0.02288498915731907,
-0.025717508047819138,
0.00042177329305559397,
-0.038631025701761246,
-0.01667490042746067,
0.006626580376178026,
0.04037623107433319,
0.027094822376966476,
-0.037754908204078674,
0.01628788374364376,
-0.008288655430078506,
-0.006153441499918699,
-0.001924975891597569,
0.026615429669618607,
-0.03549797832965851,
-0.02458975650370121,
-0.030226310715079308,
-0.009919194504618645,
-0.009831231087446213,
-0.026349758729338646,
0.030747918412089348,
-0.0710671916604042,
-0.024115921929478645,
-0.0037115528248250484,
0.014587708748877048,
0.03095906227827072,
-0.030963433906435966,
-0.03447369113564491,
0.0380026139318943,
0.029221324250102043,
0.03294221684336662,
0.029988355934619904,
-0.041998397558927536,
-0.011016164906322956,
-0.03951051086187363,
-0.006075997371226549,
-0.042866386473178864,
0.03951752185821533,
-0.06213976815342903,
-0.026795588433742523,
-0.022252317517995834,
0.04233650863170624,
0.059698641300201416,
0.014427841641008854,
0.0034488653764128685,
0.03983037546277046,
-0.020365290343761444,
0.005289815366268158,
-0.027971303090453148,
-0.025342479348182678,
-0.01900056004524231,
-0.031060881912708282,
0.01771738938987255,
-0.03512534871697426,
0.0042079780250787735,
0.019614873453974724,
0.022547060623764992,
-0.029774589464068413,
-0.004791715648025274,
0.02779722772538662,
-0.02570614591240883,
0.027873167768120766,
0.021750839427113533,
-0.006064474117010832,
0.053666505962610245,
0.0064810821786522865,
-0.010032248683273792,
-0.0037048172671347857,
-0.019987815991044044,
-0.026556337252259254,
0.035257842391729355,
-0.033634480088949203,
0.011760527268052101,
-0.023687835782766342,
0.013466156087815762,
-0.004885350354015827,
-0.06266754120588303,
-0.008993083611130714,
0.04956383258104324,
-0.04859926551580429,
-0.0032183362636715174,
0.027589648962020874,
-0.00435292162001133,
0.05653050169348717,
-0.028192514553666115,
0.022918730974197388,
-0.016878824681043625,
-0.018840989097952843,
-0.017924537882208824,
0.014990161173045635,
0.0032036600168794394,
-0.012102729640901089,
0.0004252866783645004,
0.026653286069631577,
0.024596955627202988,
0.04715113341808319,
0.007815019227564335,
0.04869745671749115,
0.00424939813092351,
-0.019374743103981018,
0.0027075326070189476,
0.003986324183642864,
0.004671704024076462,
0.06613520532846451,
-0.007021328434348106,
0.0581064410507679,
0.0033013150095939636,
0.01433023065328598,
0.0029325177893042564,
0.0090794013813138,
0.009435858577489853,
0.005769504699856043,
-0.002014572499319911,
0.012925448827445507,
-0.02986285649240017,
-0.021819869056344032,
-0.011829142458736897,
-0.026650087907910347,
0.04374219477176666,
-0.03440430760383606,
-0.018880696967244148,
-0.032789263874292374,
-0.010434582829475403,
0.017853502184152603,
-0.0650055930018425,
-0.021919356659054756,
0.01146811805665493,
0.0028447669465094805,
-0.007633852772414684,
-0.015720712020993233,
-0.007893425412476063,
-0.026720276102423668,
0.03674780949950218,
0.083036869764328,
-0.015130293555557728,
0.03065592236816883,
-0.05316150560975075,
0.012510262429714203,
-0.03868752717971802,
0.002840564353391528
] |
<p>In a recent answer (here: <a href="http://physics.stackexchange.com/questions/20944/the-equipartition-theorem-in-momentum-space/20981#20981">The equipartition theorem in momentum space</a> ), I suggested that if you have an appropriate first order equation (in the answer I used a second order equation, but it is more likely to be true for a first order equation) of the form:</p>
<p>$$ i\partial_t \phi = (\nabla^2)^N \phi + \lambda \phi^3 + f + D $$</p>
<p>(EDIT: I first had $|\phi|^2\phi$, which is the nonlinear Schrodinger equation, but this has the same frequency shifting property as the relativistic version--- the frequencies are not completely perturbatively decoupled even with a resonance condition. The only reason I went to first order was to fix this annoying problem, and there is no condition of being physical. Although this will not conserve the total $|\phi|^2$, it has a conserved energy.)</p>
<p>Where f is a driving force with only long-wavlength components, and D is a damping force which only affects short wavelength components. The field $\phi$ is a complex scalar. Then if N is large and $\lambda$ is sufficiently small (by scaling, $\phi$'s magnitude can substitute for $\lambda$, so the limit of small $\lambda$ is really the limit of small $|\phi|$), the cascade due to the nonlinear term is a thermal gradient draining energy from the hot low frequency modes to the cold high-frequency modes.</p>
<p>I don't know if this model is in the literature, of if the thermal analysis is accurate (I am pretty sure it is correct, because the resonance matching does lead to local flow of energy in |k|, but I am not sure if there isn't a block to thermalization due to some problem with mixing in each |k| modes separately).</p>
<p>In the original answer, I used a second order equation, which has frequencies of both signs. This allows some extra mixing between distant modes, which shifts the frequency of low modes based on the occupation of high modes. While I don't think this changes the cascade significantly, I wanted a clean example, so I used a first order equation here. (EDIT: The clean example does not use the absolute value, so that the frequencies have to strictly additively combine.)</p>
<p>Is this model analyzed in the literature? Does it thermalize into a thermal gradient cascade?</p>
| 7,659 |
[
-0.021413978189229965,
-0.02969173528254032,
0.0019622170366346836,
-0.0031073451973497868,
0.039316326379776,
-0.0004156947834417224,
-0.04699171334505081,
-0.015589338727295399,
-0.0051311650313436985,
-0.050079330801963806,
0.027907181531190872,
0.006962895859032869,
0.03518947586417198,
0.016528738662600517,
-0.009624279104173183,
0.03254418447613716,
-0.015183608047664165,
-0.014979432336986065,
-0.004713090136647224,
-0.05905143916606903,
0.02577109821140766,
0.03562005236744881,
-0.03667738661170006,
-0.004957342054694891,
-0.03798331320285797,
0.01642468012869358,
0.02302025444805622,
0.013887278735637665,
-0.004541018046438694,
0.01234491728246212,
-0.010441774502396584,
-0.0018592642154544592,
-0.015426811762154102,
0.04953060299158096,
0.014761066995561123,
0.02675693854689598,
-0.004760161507874727,
-0.02408137172460556,
0.010687368921935558,
-0.001581928227096796,
-0.029516376554965973,
-0.01140732504427433,
-0.025164639577269554,
0.03150543197989464,
-0.010416989214718342,
0.004751826170831919,
0.012859201058745384,
0.005609910003840923,
0.06926845014095306,
-0.0386350192129612,
0.06567168235778809,
0.018428929150104523,
0.027815626934170723,
0.015185450203716755,
-0.04096958413720131,
-0.04242865741252899,
0.07092326879501343,
0.10262728482484818,
0.015215973369777203,
-0.05172641575336456,
-0.0350782573223114,
0.008568020537495613,
-0.03362192213535309,
0.01484097633510828,
0.011283570900559425,
0.03912084922194481,
-0.001120139379054308,
-0.01949138194322586,
-0.00823760312050581,
0.0106776999309659,
0.0034902505576610565,
-0.04407350718975067,
0.03135400637984276,
-0.02500389888882637,
0.02502913400530815,
0.005915270186960697,
-0.0037881233729422092,
0.021086983382701874,
0.032682668417692184,
0.01022442989051342,
-0.044394876807928085,
0.0057399035431444645,
0.002827814081683755,
0.009634960442781448,
-0.003611459629610181,
-0.03339070454239845,
0.09723568707704544,
-0.003079766873270273,
0.0035479837097227573,
0.04373474419116974,
-0.01818166859447956,
0.037749264389276505,
0.01008862629532814,
0.0075615765526890755,
0.011445045471191406,
0.001811169902794063,
0.017591796815395355,
0.027773289009928703,
-0.01022021472454071,
-0.03380180150270462,
-0.007658601738512516,
-0.0015837966930121183,
0.014434849843382835,
0.0763600543141365,
0.0033986761700361967,
-0.00843488983809948,
-0.030328016728162766,
-0.009600017219781876,
-0.03899909183382988,
-0.024218758568167686,
-0.061035770922899246,
-0.016561418771743774,
-0.05081396922469139,
-0.012731842696666718,
-0.02574293315410614,
-0.020027395337820053,
-0.0022774769458919764,
-0.03415549173951149,
0.042884014546871185,
0.08711636066436768,
0.03935609385371208,
-0.020499996840953827,
0.01152169331908226,
-0.004426706116646528,
-0.05832737684249878,
0.02168688178062439,
0.018855521455407143,
0.004934175405651331,
-0.02442770265042782,
-0.019833829253911972,
0.0052179452031850815,
-0.025012891739606857,
-0.010514573194086552,
-0.03972683474421501,
0.03271738439798355,
-0.01794576272368431,
-0.09814846515655518,
-0.04110241308808327,
0.061104461550712585,
-0.031159918755292892,
-0.010653947480022907,
-0.08228008449077606,
-0.010151335038244724,
0.039917826652526855,
0.0694139301776886,
-0.007702659349888563,
0.0006199413328431547,
-0.01097897719591856,
0.061021074652671814,
0.02630399726331234,
-0.024539221078157425,
-0.025896310806274414,
-0.028903460130095482,
-0.03988422453403473,
-0.025063171982765198,
-0.009516872465610504,
0.038460906594991684,
0.03203370422124863,
0.006811406463384628,
0.0426131896674633,
0.04987432807683945,
-0.018599022179841995,
-0.004535770509392023,
0.006491038948297501,
0.002953985007479787,
-0.028291963040828705,
0.04047359153628349,
0.021097153425216675,
0.039890483021736145,
0.019083935767412186,
-0.030397597700357437,
0.023649724200367928,
-0.019509971141815186,
0.018785420805215836,
0.008290217258036137,
-0.0459027923643589,
0.043871261179447174,
-0.04717129096388817,
-0.03767673671245575,
0.0027060683351010084,
-0.018691057339310646,
-0.046243056654930115,
-0.02022223174571991,
0.02794571965932846,
-0.02602911740541458,
0.04566069692373276,
0.009019791148602962,
0.015171273611485958,
0.021579783409833908,
-0.05716446414589882,
0.0006036992999725044,
-0.0105699198320508,
0.019490256905555725,
-0.0014686279464513063,
-0.016555722802877426,
0.01839149370789528,
-0.013127480633556843,
0.03142917901277542,
0.009705848060548306,
-0.03319323807954788,
0.03508748486638069,
0.03948066383600235,
0.014760376885533333,
-0.023881511762738228,
0.05278148129582405,
0.060659464448690414,
0.02422063983976841,
0.03294138237833977,
0.0652846097946167,
0.015906929969787598,
-0.048266809433698654,
-0.01603938452899456,
-0.0008790860301814973,
0.03342006355524063,
-0.020397813990712166,
0.004243979696184397,
0.006815835367888212,
-0.03435869142413139,
0.021700944751501083,
0.0008617368876002729,
-0.04667656123638153,
0.03869950398802757,
0.014796828851103783,
0.006391018163412809,
-0.023381633684039116,
0.08869536966085434,
-0.02529514767229557,
0.03444443643093109,
-0.024832891300320625,
-0.013209553435444832,
-0.020208783447742462,
0.03358388692140579,
0.05172088369727135,
0.04767072945833206,
-0.06768187135457993,
0.031079832464456558,
0.009740970097482204,
0.003998155705630779,
0.06579533219337463,
-0.02385668456554413,
-0.0053370799869298935,
-0.049255985766649246,
0.02994462475180626,
-0.0022137810010463,
-0.008050010539591312,
0.0025261379778385162,
0.03718645125627518,
-0.04469287022948265,
0.021054083481431007,
0.0057240938767790794,
-0.009552912786602974,
0.014060684479773045,
-0.0007867752574384212,
-0.0015430746134370565,
-0.009646422229707241,
-0.047324568033218384,
0.05720103159546852,
0.036068208515644073,
0.028911827132105827,
0.03287835046648979,
-0.04568472132086754,
0.013619550503790379,
0.0028053387068212032,
-0.016356080770492554,
0.013440105132758617,
-0.042035263031721115,
0.010939952917397022,
-0.0017815473256632686,
0.028116481378674507,
-0.035778384655714035,
0.0020284883212298155,
-0.018797755241394043,
0.013448053039610386,
-0.006768979597836733,
-0.026872899383306503,
0.013273085467517376,
-0.00397863145917654,
-0.0012280379887670279,
-0.04838336631655693,
-0.01271477434784174,
0.018566759303212166,
0.0012996225850656629,
-0.0036860425025224686,
0.021287018433213234,
-0.05282757431268692,
0.006846883334219456,
-0.035646773874759674,
-0.046218983829021454,
0.03600345179438591,
-0.013834839686751366,
0.003506298875436187,
0.02460169792175293,
-0.01870700530707836,
-0.07694907486438751,
-0.014027650468051434,
-0.037419501692056656,
-0.010570158250629902,
-0.047789208590984344,
0.04054907709360123,
0.07436756789684296,
0.00820179283618927,
-0.06911104172468185,
0.02313987724483013,
0.004944534506648779,
-0.03938151150941849,
-0.03067394532263279,
-0.009852781891822815,
-0.004973586183041334,
-0.017716100439429283,
0.06227557361125946,
0.009659253992140293,
-0.017718279734253883,
0.025264784693717957,
-0.04895605891942978,
-0.03385239467024803,
0.030187077820301056,
0.00320613500662148,
0.08506282418966293,
0.013302834704518318,
0.000698708463460207,
0.06373955309391022,
0.029749426990747452,
-0.011588260531425476,
-0.009377664886415005,
0.004363597836345434,
0.014186791144311428,
-0.051126204431056976,
-0.007162312977015972,
0.02686384506523609,
0.0021437732502818108,
0.01401828695088625,
0.00782173965126276,
-0.012965276837348938,
0.01746208220720291,
0.008560975082218647,
-0.04171879589557648,
0.0471002422273159,
-0.024342266842722893,
0.010876763612031937,
0.02765124849975109,
-0.002047704067081213,
-0.024933647364377975,
-0.013538520783185959,
-0.016643838956952095,
0.006580079905688763,
0.017037153244018555,
-0.07065438479185104,
0.03976338729262352,
0.016011398285627365,
-0.011594978161156178,
-0.019033825024962425,
0.03372204676270485,
-0.0012655570171773434,
-0.03013196773827076,
-0.00976887159049511,
0.02191704884171486,
0.029614483937621117,
0.006018142215907574,
0.025871677324175835,
0.0356673039495945,
0.021952960640192032,
0.03230767697095871,
0.009026763029396534,
-0.013746382668614388,
-0.023082416504621506,
0.005447390954941511,
-0.013132416643202305,
-0.019890587776899338,
0.011503657326102257,
-0.01712985709309578,
0.028913680464029312,
0.009673446416854858,
-0.00009927678183885291,
-0.025776848196983337,
-0.006238664034754038,
-0.011010716669261456,
-0.028234364464879036,
0.0279280636459589,
0.008180077187716961,
0.05481196567416191,
0.021293880417943,
0.0176925640553236,
0.014697156846523285,
-0.009029080159962177,
-0.07755327224731445,
0.03074905276298523,
-0.008923434652388096,
-0.0221901535987854,
-0.010413405485451221,
0.01309547945857048,
-0.036367956548929214,
-0.02141721174120903,
-0.010197472758591175,
-0.024063564836978912,
-0.0018935108091682196,
-0.0381040945649147,
0.012467416934669018,
-0.021216364577412605,
-0.042295895516872406,
0.014393297024071217,
0.024096008390188217,
0.09790739417076111,
-0.031170589849352837,
-0.004843974951654673,
0.024472033604979515,
-0.03380081057548523,
-0.017787614837288857,
-0.02659803070127964,
0.04085042327642441,
0.0025683254934847355,
0.03236589953303337,
0.014718345366418362,
0.02778816968202591,
-0.023730458691716194,
-0.008826473727822304,
0.04381411522626877,
0.007130797952413559,
0.0058211456052958965,
-0.0357927568256855,
0.018741102889180183,
-0.02429029531776905,
-0.009900963865220547,
0.036454323679208755,
0.12301994115114212,
0.0013848345261067152,
0.007428363431245089,
0.008552826941013336,
0.003991567064076662,
0.019772112369537354,
0.011827436275780201,
-0.014958237297832966,
0.013325459323823452,
-0.022226938977837563,
-0.04983873292803764,
0.03279003128409386,
-0.009874619543552399,
0.03746602684259415,
0.011648435145616531,
-0.017457541078329086,
-0.013205976225435734,
0.012241940014064312,
-0.0021018243860453367,
0.02560434676706791,
0.003122389316558838,
-0.005509508308023214,
-0.005705889780074358,
-0.00020081667753402144,
-0.022375380620360374,
0.011587454006075859,
-0.017838066443800926,
0.05164313316345215,
0.06633136421442032,
0.015639813616871834,
0.0315544493496418,
-0.08778251707553864,
-0.04076416417956352,
0.01244827825576067,
-0.0002196246787207201,
-0.00011387492850190029,
-0.004339149221777916,
-0.05396590381860733,
-0.03434763476252556,
0.02951541170477867,
-0.005292356945574284,
0.04831576719880104,
0.011690613813698292,
0.007475301157683134,
-0.00347646395675838,
-0.06426548957824707,
-0.030214110389351845,
0.01747160032391548,
-0.0008006640709936619,
-0.024005942046642303,
-0.026065832003951073,
-0.031996291130781174,
-0.010663638822734356,
0.016464469954371452,
0.026458729058504105,
0.02875506691634655,
-0.017806965857744217,
-0.014861645177006721,
0.006359392311424017,
-0.018703848123550415,
-0.0169052891433239,
-0.09930571168661118,
0.001671511447057128,
-0.007899891585111618,
0.006274734158068895,
0.021417299285531044,
-0.03053242526948452,
-0.037857044488191605,
0.03303135931491852,
0.04822058230638504,
-0.030683033168315887,
-0.0028391468804329634,
-0.013294404372572899,
0.09467721730470657,
-0.010638698004186153,
0.005760689731687307,
0.07188543677330017,
0.06281202286481857,
-0.016195053234696388,
-0.019007187336683273,
0.0006266178097575903,
0.023983972147107124,
-0.043887123465538025,
0.030863091349601746,
-0.0317174457013607,
-0.002962751779705286,
-0.014971708878874779,
0.07095935195684433,
-0.014106996357440948,
0.005360801238566637,
0.0061519695445895195,
-0.018256118521094322,
-0.011537671089172363,
0.009278220124542713,
-0.03611772507429123,
-0.0020463590044528246,
0.01862385869026184,
0.03995118290185928,
0.03555210679769516,
-0.01913643442094326,
0.028531908988952637,
0.0046593742445111275,
-0.008174118585884571,
0.04210498183965683,
-0.05177176743745804,
0.02762557379901409,
-0.03775336965918541,
0.0030656384769827127,
-0.024264447391033173,
-0.04325997829437256,
0.02900235913693905,
-0.01234642043709755,
0.0339948832988739,
0.017747929319739342,
-0.031888991594314575,
-0.023070333525538445,
0.017399083822965622,
0.0057074641808867455,
0.009307973086833954,
0.02920844405889511,
-0.01889714039862156,
0.007905522361397743,
0.016875389963388443,
-0.06200391799211502,
-0.03651443496346474,
0.01026949379593134,
-0.008856475353240967,
-0.026966743171215057,
-0.031130198389291763,
-0.01591707020998001,
-0.04031897336244583,
-0.05395703762769699,
0.013754017651081085,
0.03952093422412872,
-0.02075543999671936,
0.025046776980161667,
0.004574252292513847,
0.019316859543323517,
0.00038766543730162084,
0.0025055701844394207,
-0.019132278859615326,
-0.012176957912743092,
-0.032963138073682785,
-0.0023007765412330627,
0.0031076676677912474,
0.05011952668428421,
-0.037299223244190216,
-0.008750501088798046,
-0.014470282942056656,
0.011911705136299133,
-0.00005936286470387131,
0.011710533872246742,
-0.05136904492974281,
0.04403174668550491,
-0.011015708558261395,
0.006620051339268684,
-0.012179292738437653,
-0.00433408422395587,
-0.00439608097076416,
0.028728971257805824,
0.004092654678970575,
-0.025615409016609192,
0.00888359360396862,
-0.052822619676589966,
0.01421163696795702,
-0.0010911538265645504,
0.00008833676110953093,
-0.004369601607322693,
0.06662767380475998,
0.01096813939511776,
0.02178589068353176,
-0.03923888877034187,
0.013201368041336536,
0.017496053129434586,
-0.02178766205906868,
0.035253144800662994,
-0.03677406907081604,
0.006737114395946264,
-0.005987103562802076,
-0.04521395266056061,
-0.05786731466650963,
0.01213728729635477,
0.05604800581932068,
-0.0007370584644377232,
0.029523033648729324,
-0.00019774926477111876,
0.016999291256070137,
0.015775253996253014,
-0.001860899617895484,
0.005378733854740858,
0.012440706603229046,
-0.015565196052193642,
0.04116908088326454,
-0.053662512451410294,
-0.008445018902420998,
0.0350133553147316,
0.02640479803085327,
-0.015805553644895554,
0.0381346233189106,
0.021942105144262314,
0.047686684876680374,
0.016004420816898346,
-0.010481065139174461,
-0.057409558445215225,
0.021123263984918594,
-0.07079091668128967,
0.0553402416408062,
0.027014179155230522,
-0.019605467095971107,
0.00275812903419137,
0.022602207958698273,
-0.0047096689231693745,
-0.044063784182071686,
-0.001001876313239336,
-0.043623898178339005,
0.005226821638643742,
0.02080921269953251,
0.014957724139094353,
0.025268658995628357,
0.025039460510015488,
0.02157977595925331,
0.01422306802123785,
0.023939015343785286,
0.0032301838509738445,
-0.0022201123647391796,
0.0009293768089264631,
-0.010806916281580925,
-0.06349720060825348,
0.06018049269914627,
-0.004502009134739637,
-0.044891782104969025,
0.024710923433303833,
-0.030725855380296707,
0.03797212615609169,
0.045992664992809296,
0.011065080761909485,
-0.003130122786387801,
0.022047996520996094,
-0.0037282779812812805,
-0.01501084491610527,
-0.03615228831768036,
0.004179293289780617,
0.15117938816547394,
0.06347135454416275,
0.034004613757133484,
-0.02642310969531536,
0.025281209498643875,
0.005087124649435282,
0.012373710982501507,
-0.04100978001952171,
-0.005032689310610294,
-0.03128412365913391,
-0.006379241589456797,
0.028475044295191765,
0.06973215192556381,
-0.014450318180024624,
0.002248792676255107,
0.03470806032419205,
-0.05688115954399109,
-0.008433115668594837,
0.02770979516208172,
-0.017069753259420395,
0.004972429480403662,
0.0010620199609547853,
0.02376450039446354,
0.020190251991152763,
-0.008937014266848564,
0.006313962396234274,
-0.033611662685871124,
-0.0404253825545311,
0.03282470628619194,
-0.04185806214809418,
-0.07040222734212875,
0.002871619537472725,
0.009726819582283497,
-0.02932712435722351,
-0.01314485352486372,
0.009615795686841011,
0.02003747969865799,
-0.02425149641931057,
0.03325676918029785,
0.009143523871898651,
-0.024792617186903954,
0.0348159596323967,
0.016083937138319016,
0.027921069413423538,
-0.008381489664316177,
-0.011716261506080627,
-0.03372557833790779,
0.03958655521273613,
0.01576620526611805,
-0.03648540750145912,
0.00011737441673176363,
0.02287895418703556,
0.02794569358229637,
-0.025320639833807945,
-0.0033826688304543495,
-0.009894789196550846,
0.032011959701776505,
-0.034449443221092224,
-0.014427512884140015,
0.00044313620310276747,
0.0008241599425673485,
0.028298940509557724,
-0.0006188176339492202,
-0.0029472047463059425,
0.010863645933568478,
-0.024068819358944893,
0.0032350511755794287,
0.02455412596464157,
0.008716165088117123,
-0.022074351087212563,
-0.012713944539427757,
0.007156818639487028,
-0.026131823658943176,
-0.02744545228779316,
0.022184859961271286,
0.026087384670972824,
0.036070749163627625,
-0.0032033612951636314,
-0.04285459220409393,
-0.06990198791027069,
-0.07817608118057251,
0.02074827253818512,
0.017544737085700035,
-0.014027822762727737,
0.012604876421391964,
-0.019812200218439102,
-0.008966340683400631,
0.046988971531391144,
-0.0114951366558671,
0.0027533976826816797,
0.030332371592521667,
0.07075530290603638,
0.04571956396102905,
-0.004714200273156166,
-0.04424547031521797,
0.00004928751150146127,
-0.028364937752485275,
-0.016931448131799698,
-0.013144669122993946,
0.012064079754054546,
0.013689671643078327,
0.010212134569883347,
0.021759187802672386,
0.03663508966565132,
-0.04969087615609169,
0.0001264819293282926,
0.02998940274119377,
-0.04809722304344177,
0.012151007540524006,
0.03044070117175579,
0.005468280054628849,
-0.04444215074181557,
-0.04953653737902641,
0.004223166964948177,
0.005447274073958397,
0.005554308649152517,
0.015884041786193848,
-0.015742748975753784,
0.02371610701084137,
-0.013150054961442947,
0.022778311744332314,
-0.04776232689619064,
-0.03674263879656792,
-0.04345373436808586,
0.016690539196133614,
-0.03436007350683212,
0.03072245605289936,
-0.02148297429084778,
0.030315540730953217,
-0.038794856518507004,
-0.010476217605173588,
0.01135779358446598,
0.01011846773326397,
-0.03138810396194458,
0.016166798770427704,
0.009035670198500156,
0.029257195070385933,
0.007522297091782093,
0.029949840158224106,
-0.040233224630355835,
0.045575857162475586,
-0.06669103354215622,
-0.02937540039420128,
0.03701325133442879,
-0.003986242227256298,
-0.0037909504026174545,
0.05182529613375664,
-0.02760452963411808,
-0.0148286959156394,
0.06066660210490227,
0.027372928336262703,
-0.01269692461937666,
0.02264394797384739,
-0.04288531839847565,
0.006004697643220425,
-0.03045535273849964,
-0.020591599866747856,
-0.013153132982552052,
0.0020557318348437548,
0.03169839084148407,
0.03036172315478325,
-0.033028606325387955,
-0.018190819770097733,
-0.03297307342290878,
-0.043565161526203156,
0.014721128158271313,
0.016768403351306915,
0.04209277406334877,
-0.005289556924253702,
0.02958264760673046,
-0.022591490298509598,
-0.022781481966376305,
0.020817629992961884,
0.028520746156573296,
-0.13814425468444824,
-0.021060697734355927,
-0.007296097464859486,
0.00072463508695364,
0.02718924917280674,
-0.0732521265745163,
0.02363983541727066,
-0.0169687457382679,
-0.040743522346019745,
0.007601719815284014,
0.033054910600185394,
0.03893475979566574,
-0.0492900051176548,
0.022871650755405426,
-0.036796316504478455,
0.004834056831896305,
0.042511358857154846,
0.05529185011982918,
-0.03524084761738777,
0.018975360319018364,
-0.01571843773126602,
-0.027939535677433014,
0.0030891657806932926,
0.031629446893930435,
0.018560189753770828,
-0.005090916063636541,
0.05584694445133209,
0.009113317355513573,
-0.014338541775941849,
0.014398683793842793,
-0.011284266598522663,
-0.0008715449366718531,
-0.005814125761389732,
0.04711064323782921,
0.0319160521030426,
0.026565715670585632,
0.009783599525690079,
-0.01219960581511259,
0.04084279015660286,
0.005662908777594566,
0.02221103385090828,
0.03300732746720314,
-0.025438915938138962,
-0.031109021976590157,
0.059017859399318695,
-0.0818110927939415,
-0.020972352474927902,
0.05293266847729683,
-0.02081231027841568,
-0.002779801143333316,
0.03468381613492966,
-0.0192001610994339,
-0.010170341469347477,
0.008773108944296837,
-0.01193490531295538,
-0.054730188101530075,
-0.03002927079796791,
-0.0056759063154459,
0.01957015134394169,
-0.012332710437476635,
0.013616081327199936,
0.0010440070182085037,
-0.02570553496479988,
0.000810237426776439,
0.006998592987656593,
-0.006614805199205875,
-0.05122050270438194,
-0.026363635435700417,
-0.0025232641492038965,
0.02425919659435749,
-0.017422938719391823,
-0.030008560046553612,
-0.03840840235352516,
0.03655046597123146,
-0.014364202506840229,
0.04552392661571503,
-0.04691629111766815,
-0.02300177328288555,
0.007176221814006567,
-0.05987352505326271,
-0.023394865915179253,
0.032755296677351,
0.017737800255417824,
-0.02533295564353466,
-0.024183345958590508,
0.013291413895785809,
0.030654963105916977,
0.05531882867217064,
0.005973901133984327,
-0.06040767580270767,
0.039732206612825394,
-0.018900830298662186,
0.04651353508234024,
-0.042493853718042374,
-0.002439243020489812,
-0.022869843989610672,
0.026071665808558464,
-0.00554606132209301,
0.010794014669954777,
-0.012596060521900654,
0.015164853073656559,
0.03138214722275734,
0.03771442174911499,
0.00225549703463912,
0.027633069083094597,
-0.03106020949780941,
0.05721630901098251,
-0.017152991145849228,
-0.0024045025929808617,
0.028492417186498642,
-0.021340038627386093,
0.005372953601181507,
0.0344277061522007,
-0.04997061938047409,
-0.03935684263706207,
-0.004861996974796057,
-0.028647184371948242,
0.008963972330093384,
0.013031285256147385,
-0.006125975865870714,
0.02956610918045044,
-0.013284759595990181,
0.022423889487981796,
0.06761627644300461,
-0.034625906497240067,
-0.03552500903606415,
0.04825019836425781,
-0.015603643842041492,
0.017596526071429253,
0.020343024283647537,
0.009298362769186497,
0.008987432345747948,
0.029060635715723038,
-0.0038478411734104156,
0.022354790940880775,
0.006781416013836861,
0.006991357076913118,
0.035033948719501495,
-0.0009143967181444168,
-0.029779572039842606,
0.010275955311954021,
-0.0024603435304015875,
-0.007660736795514822,
-0.03206992149353027,
-0.021494682878255844,
0.0684889480471611,
-0.008812833577394485,
-0.02652037888765335,
0.04387081414461136,
0.0004289080388844013,
0.09099295735359192,
-0.009040812030434608,
0.02362767793238163,
-0.015045935288071632,
-0.011150207370519638,
0.028254108503460884,
0.05756232887506485,
0.017783161252737045,
0.0386740043759346,
-0.024342834949493408,
0.017706848680973053,
-0.017625153064727783,
-0.03042013570666313,
-0.03254207968711853,
-0.06016352027654648,
-0.03252848982810974,
0.025320958346128464,
0.010517977178096771,
-0.022089332342147827,
0.005164214875549078,
-0.004246431402862072,
-0.029590414837002754,
0.031092945486307144,
-0.019620317965745926,
-0.011371279135346413,
0.014150470495223999,
0.029272882267832756,
-0.0063688792288303375,
0.042423103004693985,
-0.026616744697093964,
-0.003403723705559969,
0.012817387469112873,
-0.03754108026623726,
-0.010268627665936947,
0.004611423704773188
] |
<p>Higher velocity implies low pressure. So in whirlpool the velocity of water have to decrease with radius in order to have force towards its center.</p>
<p>My question is how is explained whirlpool formation in simple words.</p>
| 7,660 |
[
-0.05317848175764084,
-0.0263981856405735,
-0.002284455578774214,
0.005323787685483694,
0.030118295922875404,
-0.029510559514164925,
-0.04761183634400368,
-0.012754429131746292,
0.021712053567171097,
-0.023320214822888374,
-0.009855043143033981,
0.05514763295650482,
-0.001677528372965753,
-0.003691989229992032,
0.040009766817092896,
0.010679100640118122,
0.012414838187396526,
0.009622661396861076,
0.0301394984126091,
-0.012810499407351017,
-0.04543392360210419,
-0.016548866406083107,
0.0069237384013831615,
0.026135504245758057,
-0.017372148111462593,
0.02405727282166481,
0.03324621170759201,
0.002959257923066616,
0.0072098602540791035,
0.031187985092401505,
0.012312199920415878,
0.010353186167776585,
-0.011286580003798008,
0.014252114109694958,
0.020870132371783257,
-0.0007155759376473725,
-0.051394347101449966,
-0.007639172021299601,
-0.05090511590242386,
0.016774749383330345,
-0.021971996873617172,
0.008145910687744617,
-0.022353151813149452,
0.05508241429924965,
-0.04608866572380066,
0.01637224853038788,
0.02355404570698738,
-0.021779710426926613,
0.04518475756049156,
-0.0646253302693367,
0.035108115524053574,
0.012652802281081676,
0.05991189181804657,
0.003144757356494665,
0.03471405431628227,
0.033609431236982346,
0.06693380326032639,
0.06115276739001274,
-0.06940393894910812,
-0.029922695830464363,
0.0047902376390993595,
-0.0007252414943650365,
-0.006447619292885065,
-0.03546348586678505,
-0.008804618380963802,
0.02303428016602993,
-0.0004282150766812265,
-0.00032439816277474165,
0.02208155393600464,
-0.026294464245438576,
0.023002563044428825,
-0.007116103079169989,
0.027390317991375923,
-0.009599769487977028,
0.019639180973172188,
-0.0360114723443985,
0.007416994776576757,
0.010103235021233559,
-0.01724684052169323,
0.060987453907728195,
-0.015382894314825535,
0.029637539759278297,
0.03783382102847099,
-0.006936832796782255,
0.004109562374651432,
-0.017353832721710205,
0.05851086974143982,
0.009078079834580421,
0.019850904121994972,
0.03527616709470749,
-0.016319124028086662,
-0.020076535642147064,
0.02885359898209572,
-0.025112533941864967,
-0.008491444401443005,
-0.0035821390338242054,
-0.0049479445442557335,
0.04002436622977257,
0.04865766689181328,
-0.02744770422577858,
0.008795144036412239,
-0.02934330515563488,
-0.0023847806733101606,
0.11084593087434769,
0.011404487304389477,
-0.014631747268140316,
-0.0690043494105339,
0.017664076760411263,
-0.04977643862366676,
-0.0273663941770792,
-0.02798522263765335,
0.0035610434133559465,
0.005682123824954033,
-0.024010377004742622,
-0.02525768242776394,
-0.0025045040529221296,
0.013422305695712566,
0.010769139975309372,
0.08419055491685867,
0.03728904202580452,
0.053875818848609924,
-0.037975020706653595,
0.019726404920220375,
-0.0030793307814747095,
-0.05770789459347725,
0.04044146463274956,
0.01776842214167118,
-0.01922103390097618,
-0.0027577050495892763,
0.028790757060050964,
0.00425292644649744,
0.016216004267334938,
0.015057145617902279,
0.027328576892614365,
0.0335715226829052,
-0.0002170518273487687,
-0.11203562468290329,
-0.07808290421962738,
0.08014631271362305,
-0.02641899697482586,
-0.012915657833218575,
-0.0765506848692894,
0.008391250856220722,
0.030706249177455902,
0.12312039732933044,
-0.030191048979759216,
-0.010129234753549099,
0.03692622482776642,
0.03413514047861099,
0.012560584582388401,
-0.005268688313663006,
0.00221298192627728,
0.031124085187911987,
-0.018192721530795097,
-0.015589814633131027,
-0.07265148311853409,
-0.004494603723287582,
0.02415926568210125,
0.0014334953157231212,
-0.04126351699233055,
0.015327086672186852,
-0.05575836822390556,
0.01218599546700716,
0.01996679976582527,
0.02889448031783104,
-0.02621789649128914,
0.08092065900564194,
0.02511163242161274,
-0.01718921586871147,
0.046567827463150024,
0.0010589093435555696,
0.023157786577939987,
-0.02656797133386135,
0.017462532967329025,
0.027286093682050705,
-0.02972710132598877,
0.004970876034349203,
-0.01364513486623764,
0.02832510508596897,
0.0006882832385599613,
-0.017087919637560844,
-0.03394418954849243,
-0.010370413772761822,
0.03480933979153633,
0.008463285863399506,
0.060835305601358414,
-0.004787181969732046,
0.004715248942375183,
-0.012378644198179245,
-0.03434279188513756,
-0.01836949773132801,
-0.07268081605434418,
0.020402830094099045,
-0.040593910962343216,
-0.00980326347053051,
0.003069916507229209,
0.02005353569984436,
0.022400425747036934,
-0.020585957914590836,
0.015437282621860504,
-0.0010791963431984186,
0.04364053159952164,
-0.024420687928795815,
-0.004276669584214687,
0.025246087461709976,
0.030605383217334747,
0.005622769705951214,
-0.0007498793420381844,
0.0013725393218919635,
0.003064977703616023,
-0.026684194803237915,
0.007690169848501682,
-0.027032295241951942,
-0.002354855416342616,
-0.02522510476410389,
-0.03410607576370239,
0.028092024847865105,
0.010629961267113686,
0.026029527187347412,
0.013635418377816677,
-0.03781771659851074,
0.10539625585079193,
0.040151868015527725,
0.038788676261901855,
0.015359516255557537,
0.025612881407141685,
-0.0011960961855947971,
-0.01208744291216135,
0.013967891223728657,
-0.008369931019842625,
-0.049964454025030136,
0.00289365672506392,
0.02396376244723797,
0.036392632871866226,
-0.049103591591119766,
0.0106824254617095,
0.027095958590507507,
0.04045942425727844,
0.03329111263155937,
0.03660198673605919,
-0.03024432249367237,
-0.04727008566260338,
0.026304559782147408,
0.060197196900844574,
0.020951835438609123,
0.032038044184446335,
0.05853000283241272,
0.0478702150285244,
0.013947288505733013,
-0.025329001247882843,
-0.04708568751811981,
0.03359466418623924,
-0.007302845362573862,
-0.004084654152393341,
0.00042138880235143006,
-0.015195014886558056,
0.022326955571770668,
-0.04432125762104988,
-0.01660769432783127,
0.01342757884413004,
0.02415996976196766,
0.03220829367637634,
-0.04092870280146599,
0.0034710264299064875,
0.035551298409700394,
0.0009566721855662763,
0.0062123313546180725,
-0.03876565396785736,
0.019472230225801468,
-0.07247579842805862,
0.01685648038983345,
-0.006956412456929684,
-0.01898658648133278,
-0.025042450055480003,
0.004592256620526314,
0.020226975902915,
0.0042318319901824,
0.034378521144390106,
-0.0050482661463320255,
-0.02249712310731411,
-0.0069410125724971294,
-0.008087720721960068,
-0.028102243319153786,
-0.019855283200740814,
-0.036787647753953934,
0.04574950039386749,
-0.007524106185883284,
0.014862732030451298,
0.05438697710633278,
-0.01780828833580017,
0.004458044655621052,
-0.01985734887421131,
0.010004689916968346,
-0.015279860235750675,
-0.004781146068125963,
-0.038706809282302856,
0.04578360170125961,
0.007119534537196159,
0.008612745441496372,
0.04019598662853241,
-0.026515301316976547,
-0.021976957097649574,
0.029232552275061607,
-0.0369051918387413,
-0.029353830963373184,
-0.03694576025009155,
0.015702461823821068,
0.0452643521130085,
-0.042860761284828186,
0.01375433336943388,
0.011789262294769287,
-0.060128699988126755,
0.0012446338078007102,
-0.0029574956279248,
-0.04353160411119461,
0.01324302889406681,
-0.024768022820353508,
0.05084982141852379,
-0.0008079093531705439,
-0.05389131233096123,
0.04782517999410629,
-0.02964271418750286,
-0.040273189544677734,
-0.03368943929672241,
-0.002244326751679182,
-0.04339056834578514,
-0.030711477622389793,
0.02440609782934189,
0.07518570870161057,
-0.03226573020219803,
-0.01905977353453636,
0.013704816810786724,
0.015828685835003853,
0.04339338093996048,
-0.010726007632911205,
-0.013581898994743824,
0.0032131909392774105,
0.03637732192873955,
0.002464974531903863,
0.028277546167373657,
-0.012690331786870956,
0.0024344006087630987,
0.009146623313426971,
0.0033729292917996645,
0.03453477472066879,
0.047263722866773605,
-0.05888798087835312,
0.027731681242585182,
-0.00020968602620996535,
-0.017850439995527267,
-0.0026522683911025524,
0.014667469076812267,
-0.03639381751418114,
0.0016868086531758308,
0.012447056360542774,
0.010985564440488815,
0.07399134337902069,
0.012109505943953991,
-0.0030582041945308447,
0.021174579858779907,
0.012610831297934055,
-0.014087767340242863,
-0.03107047826051712,
-0.023083945736289024,
-0.039551664143800735,
0.048043228685855865,
-0.013594440184533596,
-0.0002886932925321162,
0.042727865278720856,
0.006265298463404179,
-0.013874652795493603,
-0.012977728620171547,
-0.02675371803343296,
0.018070874735713005,
-0.06880335509777069,
0.012178420089185238,
-0.0008905620197765529,
0.024465398862957954,
-0.010237359441816807,
0.07435700297355652,
0.00119874463416636,
0.02892594411969185,
0.016907276585698128,
-0.023187071084976196,
-0.06648722290992737,
0.002649389673024416,
-0.03636975958943367,
0.009731488302350044,
-0.010102045722305775,
-0.01732983998954296,
-0.02466629259288311,
-0.028317652642726898,
-0.016142040491104126,
0.011975014582276344,
-0.02662930265069008,
-0.05081858113408089,
0.01876426488161087,
-0.011496647261083126,
-0.016696786507964134,
-0.008879990316927433,
0.021324876695871353,
0.02506726235151291,
-0.012903333641588688,
0.0760580375790596,
0.025009939447045326,
-0.0052446178160607815,
-0.010445118881762028,
-0.02693195454776287,
-0.013371570035815239,
0.011746230535209179,
-0.002322535729035735,
0.023060256615281105,
0.008541743271052837,
-0.0033537636045366526,
-0.015580354258418083,
-0.009545029141008854,
0.008190319873392582,
0.021417899057269096,
0.028855793178081512,
-0.021015247330069542,
-0.0401996485888958,
0.02585495263338089,
0.01243048906326294,
0.024922901764512062,
-0.0020144886802881956,
-0.020607667043805122,
0.020489294081926346,
-0.04321765527129173,
-0.02304878830909729,
0.04987958446145058,
0.03380969539284706,
0.013112201355397701,
-0.027582982555031776,
-0.05728750303387642,
-0.015643207356333733,
-0.009364531375467777,
-0.01683458872139454,
0.01910826377570629,
-0.006117898505181074,
-0.04314333200454712,
0.015410389751195908,
0.03737282752990723,
-0.012958092615008354,
-0.008683688938617706,
0.0075930580496788025,
-0.004072658251971006,
0.020020494237542152,
-0.04599444568157196,
0.026041829958558083,
0.032479897141456604,
0.021476401016116142,
0.029427550733089447,
-0.026528682559728622,
-0.019185030832886696,
-0.043460212647914886,
-0.04777292162179947,
0.023481061682105064,
0.05626417696475983,
-0.03293084353208542,
0.0035879723727703094,
-0.05783503130078316,
-0.03515106812119484,
0.062474414706230164,
-0.04919816181063652,
0.027752162888646126,
-0.024758487939834595,
0.0075032529421150684,
-0.0004015895538032055,
-0.012607323937118053,
-0.006154573056846857,
-0.0036457732785493135,
-0.059662945568561554,
0.025003908202052116,
-0.03804206848144531,
0.0053966715931892395,
-0.04347316548228264,
0.0004824063216801733,
0.033369626849889755,
0.03356358781456947,
0.03438083082437515,
0.01643931306898594,
-0.03592103719711304,
0.02967468649148941,
-0.03756779804825783,
-0.07343039661645889,
0.017072180286049843,
-0.012459411285817623,
0.026002271100878716,
0.01626436598598957,
-0.03014538250863552,
-0.029827814549207687,
-0.003224941436201334,
0.03651559352874756,
-0.027093175798654556,
0.0018403874710202217,
-0.020653825253248215,
0.019133899360895157,
0.02557210996747017,
0.0186021588742733,
0.052457544952631,
0.04716948792338371,
-0.04411065950989723,
-0.06199558079242706,
-0.023407286033034325,
0.03714566305279732,
-0.035239994525909424,
-0.03020457550883293,
-0.0357946939766407,
0.030671339482069016,
-0.028097357600927353,
0.04773746430873871,
-0.021309278905391693,
-0.015675321221351624,
-0.023304952308535576,
-0.029321378096938133,
0.012601785361766815,
0.023296767845749855,
0.047258347272872925,
-0.031842879951000214,
0.0016332026571035385,
0.007486429065465927,
0.02251879870891571,
-0.01691065914928913,
0.017298104241490364,
-0.019410017877817154,
0.030239274725317955,
0.03053831309080124,
0.010019736364483833,
-0.013332213275134563,
-0.022328805178403854,
-0.029030712321400642,
0.013229083269834518,
-0.052867159247398376,
0.0664001926779747,
-0.002904804889112711,
-0.0021929063368588686,
0.04344393312931061,
-0.05941999703645706,
-0.015482802875339985,
0.007561300881206989,
-0.02251124568283558,
0.018664678558707237,
-0.05546027794480324,
0.01845541037619114,
0.039554569870233536,
0.024904953315854073,
-0.058070193976163864,
-0.05882145091891289,
0.042569663375616074,
0.006588096264749765,
0.010028201155364513,
-0.04075700044631958,
0.01207074336707592,
-0.06027749925851822,
-0.027167856693267822,
-0.03441745042800903,
0.03753478452563286,
-0.031248461455106735,
0.00831276923418045,
0.00913890078663826,
-0.010487702675163746,
0.05346408858895302,
0.019183635711669922,
-0.037252314388751984,
0.0002086075401166454,
-0.022612933069467545,
-0.01261441595852375,
-0.01475739385932684,
0.07339252531528473,
-0.03381887823343277,
-0.019732274115085602,
0.0007642458658665419,
-0.03109368123114109,
0.04059351980686188,
-0.002039465354755521,
0.035601601004600525,
-0.016351349651813507,
0.03825383633375168,
-0.0063315401785075665,
-0.009374523535370827,
0.01782035268843174,
-0.008204875513911247,
0.03185885027050972,
0.02584666572511196,
-0.028993917629122734,
-0.028788870200514793,
-0.03541288524866104,
0.011136494576931,
-0.001268449705094099,
-0.035819292068481445,
-0.03400687873363495,
0.07183809578418732,
-0.019816018640995026,
-0.0019520596833899617,
-0.013555990532040596,
-0.03415187448263168,
0.014517327770590782,
0.024200163781642914,
-0.04045529663562775,
-0.00009247774869436398,
0.04732542484998703,
-0.01310198288410902,
-0.022341113537549973,
-0.027083052322268486,
0.026809528470039368,
0.07782894372940063,
-0.03961939737200737,
0.05904238298535347,
0.008153945207595825,
0.0016030574915930629,
0.020909465849399567,
-0.017945876345038414,
0.00797752384096384,
0.008019966073334217,
-0.0035317526198923588,
0.05266760662198067,
-0.02130521647632122,
0.010382979176938534,
0.031621672213077545,
0.033627890050411224,
-0.014020855538547039,
0.023533033207058907,
0.045456137508153915,
-0.00031633576145395637,
-0.015920601785182953,
-0.006872698199003935,
-0.06444980949163437,
0.02939828671514988,
-0.004894921090453863,
0.06994893401861191,
0.004671401809900999,
0.014040546491742134,
0.08507094532251358,
-0.0009630272397771478,
0.0015426515601575375,
-0.03930332511663437,
0.01149581465870142,
-0.009869564324617386,
0.0022960156202316284,
-0.006021934561431408,
-0.007220791187137365,
-0.057583753019571304,
0.03162238746881485,
0.021810438483953476,
0.013433843851089478,
0.009764062240719795,
-0.025321995839476585,
-0.03727610036730766,
-0.007215789519250393,
-0.026115378364920616,
-0.03783002495765686,
0.01866975799202919,
0.024554075673222542,
-0.029101742431521416,
0.020366868004202843,
-0.008098985068500042,
-0.013126577250659466,
0.006396827287971973,
0.006573105230927467,
-0.015213441103696823,
0.06075521931052208,
0.027076872065663338,
0.0037918214220553637,
-0.008688073605298996,
0.012310179881751537,
0.12102168053388596,
0.06002911552786827,
0.015561013482511044,
-0.0650225281715393,
0.005128692369908094,
-0.019870737567543983,
-0.021949224174022675,
-0.026660338044166565,
0.013493222184479237,
-0.0014546308666467667,
0.008113653399050236,
0.010405450128018856,
0.0398193895816803,
0.012282363139092922,
0.026138974353671074,
0.05960258096456528,
-0.0507761612534523,
-0.03646479919552803,
-0.02873138338327408,
-0.00811282079666853,
-0.03791224956512451,
0.059433337301015854,
-0.06103745102882385,
0.033729229122400284,
-0.011452654376626015,
-0.01607450656592846,
-0.03311796486377716,
-0.02043059654533863,
0.03911348432302475,
-0.02075963467359543,
-0.07251469045877457,
-0.003025126876309514,
0.012256443500518799,
-0.03164667636156082,
-0.06095866858959198,
0.0338725745677948,
0.006530972197651863,
-0.04178360104560852,
0.017747433856129646,
-0.0023008249700069427,
0.010419944301247597,
0.035475995391607285,
-0.023570304736495018,
0.04757342487573624,
-0.03071342594921589,
0.017411746084690094,
0.006410809233784676,
0.020866738632321358,
0.0057217879220843315,
0.015624606981873512,
-0.011222156696021557,
0.00763464393094182,
-0.006021663546562195,
-0.04274052754044533,
-0.01114747952669859,
0.0130379693582654,
0.032622694969177246,
-0.008238093927502632,
-0.04436890035867691,
-0.03134778514504433,
-0.006104240193963051,
-0.02992950938642025,
0.01670454442501068,
-0.034009385854005814,
0.002066755900159478,
-0.002904892200604081,
-0.0144919753074646,
0.042968668043613434,
-0.05228502303361893,
-0.009781853295862675,
-0.02597823552787304,
0.02394559048116207,
-0.05918138846755028,
-0.005591598805040121,
0.021957870572805405,
0.01127132773399353,
0.010620408691465855,
0.026768486946821213,
-0.03598108887672424,
0.027359003201127052,
-0.051301248371601105,
0.044822219759225845,
-0.0031272799242287874,
-0.03834453225135803,
-0.0379025973379612,
0.003172896569594741,
0.012823312543332577,
0.04732002317905426,
-0.02717469073832035,
0.0012409602059051394,
-0.02809961885213852,
0.017443887889385223,
0.019918318837881088,
-0.023009343072772026,
-0.05139351636171341,
0.02818169631063938,
-0.00888002198189497,
-0.012330332770943642,
-0.00402451166883111,
0.036997921764850616,
0.05265945941209793,
-0.01842242106795311,
0.014556766487658024,
0.016835181042551994,
-0.012497826479375362,
-0.0164891816675663,
0.02370564639568329,
-0.012368411757051945,
-0.013176695443689823,
0.01793038100004196,
0.010696420446038246,
-0.03853673115372658,
-0.01530885323882103,
-0.004636119585484266,
-0.011044761165976524,
0.003390984144061804,
0.04607231169939041,
-0.04030008986592293,
0.018692271783947945,
-0.052010323852300644,
0.02747402898967266,
-0.04250042885541916,
-0.022004032507538795,
-0.08020170032978058,
0.001242929371073842,
0.004619461949914694,
-0.00007405076758004725,
-0.04482408985495567,
0.03111044503748417,
-0.023495899513363838,
0.020864665508270264,
-0.014635900966823101,
-0.012235851027071476,
-0.02880706451833248,
0.03167593106627464,
0.031304821372032166,
-0.022634515538811684,
0.048285387456417084,
-0.0228861253708601,
-0.04873001202940941,
0.06047382950782776,
-0.027885744348168373,
-0.026707356795668602,
0.01590905338525772,
-0.008551250211894512,
0.02106131985783577,
0.02033059485256672,
-0.007432997692376375,
0.012004463002085686,
0.07695647329092026,
0.005091319791972637,
0.012222174555063248,
-0.011510512791574001,
-0.005272547248750925,
0.012751581147313118,
0.004927496425807476,
0.022748587653040886,
-0.02954900451004505,
-0.009092247113585472,
0.04490809142589569,
0.0456627681851387,
0.02520141564309597,
-0.01855861395597458,
0.027403779327869415,
0.03232518583536148,
0.045883338898420334,
0.0024990360252559185,
-0.0057472968474030495,
0.02013552561402321,
0.03397923335433006,
-0.0406213104724884,
0.012599063105881214,
-0.0005633336259052157,
-0.019947828724980354,
-0.10540186613798141,
-0.0007997244247235358,
-0.00937113631516695,
-0.00004532212915364653,
0.035653870552778244,
-0.0323539599776268,
-0.005372285842895508,
0.045070067048072815,
-0.06325797736644745,
-0.02203514613211155,
-0.012951990589499474,
-0.004277465865015984,
-0.03915518894791603,
-0.02478756569325924,
-0.0040235030464828014,
0.0891357958316803,
0.012589002959430218,
0.041352566331624985,
0.030090199783444405,
-0.008096732199192047,
-0.016664648428559303,
0.003755867015570402,
-0.0048717595636844635,
0.030700629577040672,
-0.010202146135270596,
0.0075011709704995155,
0.058776818215847015,
-0.02502785436809063,
-0.030785853043198586,
0.05289732664823532,
-0.02686339244246483,
0.022088488563895226,
0.007174903992563486,
-0.007308252155780792,
-0.007662071846425533,
0.020064981654286385,
-0.0007184604182839394,
0.0034449019003659487,
-0.0388285331428051,
0.04308350384235382,
0.01121110562235117,
0.028953637927770615,
0.004666880238801241,
-0.020620211958885193,
0.04690052568912506,
-0.03108701854944229,
0.0039072115905582905,
0.02616064064204693,
-0.027243072167038918,
0.019416993483901024,
0.002195998327806592,
-0.015417644754052162,
0.03227086365222931,
0.006640989799052477,
0.010552826337516308,
-0.006087245419621468,
0.017145974561572075,
0.0216164980083704,
0.011071194894611835,
-0.041105907410383224,
0.054613713175058365,
0.025857500731945038,
-0.030213208869099617,
-0.021035993471741676,
-0.021147871389985085,
-0.004385324195027351,
-0.03594088926911354,
-0.0027224430814385414,
-0.006858646869659424,
-0.03909764066338539,
-0.0021339973900467157,
-0.02531072311103344,
-0.02166309766471386,
0.05640735477209091,
0.022409360855817795,
0.005650854669511318,
0.04176309332251549,
-0.00834148470312357,
-0.014333202503621578,
-0.05672440677881241,
0.040857937186956406,
0.0013546068221330643,
-0.03099057450890541,
-0.024282220751047134,
-0.035281457006931305,
0.007719310466200113,
0.029250742867588997,
0.050682906061410904,
0.004486334044486284,
-0.008343352004885674,
0.019382474943995476,
0.017548782750964165,
0.025158466771245003,
-0.030320866033434868,
-0.013970660977065563,
0.0027306247502565384,
-0.043796055018901825,
0.021598462015390396,
-0.033046215772628784,
0.0029629492200911045,
0.004786980338394642,
0.03608936816453934,
0.00807596743106842,
0.030561121180653572,
-0.012424582615494728,
-0.01081936713308096,
0.03711409121751785,
-0.004185429308563471,
-0.017321646213531494,
0.08060553669929504,
-0.02466868981719017,
0.00010795941489050165,
0.01716606691479683,
-0.01698082499206066,
-0.04887915775179863,
0.010717839002609253,
-0.03180980309844017,
0.008595896884799004,
0.01646847277879715,
-0.032090820372104645,
0.03572326898574829,
-0.05048556998372078,
0.003070768201723695,
0.010550097562372684,
-0.04462658613920212,
-0.009777024388313293,
0.04307130351662636,
0.037874139845371246,
0.027092037722468376,
-0.040803633630275726,
-0.013642266392707825,
0.005212364252656698,
-0.022208794951438904,
-0.033430423587560654,
0.0517270490527153,
0.03635659068822861,
0.014861083589494228,
0.0038579360116273165,
0.030645690858364105,
0.009065328165888786,
0.035730600357055664,
0.002092136535793543,
0.010150182992219925,
-0.007839576341211796,
-0.04851611703634262,
-0.011904018931090832,
-0.04802229627966881,
0.02998281456530094,
0.014922679401934147,
0.0020708623342216015,
0.06874163448810577,
0.005102695431560278,
0.011162872426211834,
0.003175501711666584,
-0.024717794731259346,
-0.03956584259867668,
-0.020746201276779175,
0.013303115032613277,
0.03323820233345032,
-0.001986510818824172,
-0.020124761387705803,
-0.0015536271966993809,
-0.01477206964045763,
0.03293167054653168,
0.032946065068244934,
0.010547418147325516,
0.00040905975038185716,
0.003444927977398038,
-0.006642400752753019,
0.013201447203755379,
-0.015176333487033844,
-0.00556291826069355,
0.029685482382774353,
0.041629381477832794,
0.013083589263260365,
0.01866745948791504,
0.01013190671801567,
-0.04021267965435982,
0.043125949800014496,
-0.09078338742256165,
-0.00515947537496686,
-0.0159177016466856,
0.020816782489418983,
0.004011877346783876,
-0.01537023764103651
] |
<blockquote>
<p>A man pulling sled of his daughter by a massless rope, climbing a snowy hill whose slope is equal to 15 °. Considering that the mass of the sled is $4Kg$, the girl's $26Kg$ and $\mu _c = 0,25$, calculate the work done by the tension of the string after walking with constant speed a distance of $130m \Delta x$</p>
</blockquote>
<p>So, I know:</p>
<p>$\varphi=15°; \alpha =30°; m_d=26Kg; m_s=4Kg; \mu _c =0,25; d=130m$</p>
<p>So, the equations will be:</p>
<p>Weight in Y:</p>
<p>$P_y=P.\cos\varphi $</p>
<p>Weight in X:</p>
<p>$P_x=P.\sin\varphi$</p>
<p>Tension in Y:</p>
<p>$T_y=T.\sin\alpha$</p>
<p>Tension in X:</p>
<p>$T_x=T.\cos\alpha$</p>
<p>Normal force:</p>
<p>$P_y-N-T_y=0 \implies N = T_y-P_y$</p>
<p>Newton's 2nd law:</p>
<p>$\sum F = m_t.a \implies T_x-F_r-P_x=m_t.a$</p>
<p>Frictional force:</p>
<p>$F_r=\mu _c.N$</p>
<p>work definition:</p>
<p>$W=m_t.a.d$</p>
<p>Total mass:</p>
<p>$m_t=m_d+m_s \implies m_t =30Kg$</p>
<p>I want to get the acceleration of the object and then replacing $a$ I can get the string tension, so (...)</p>
<p>$a={{T_x-F_r-P_x}\over m_t}$</p>
<p>Now, ${T_x-F_r-P_x} = \sum F \implies {T_x-F_r-P_x} = W =m_t.a.d$</p>
<p>But again, If such replacement, the unknown $a$ appears again.</p>
<p>¿How can I solve this?</p>
| 7,661 |
[
-0.015308945439755917,
0.016300566494464874,
0.0076150670647621155,
-0.031629711389541626,
0.014525835402309895,
-0.006291496101766825,
-0.028928261250257492,
-0.023042866960167885,
0.0028847805224359035,
0.005537174642086029,
0.029892493039369583,
0.023517711088061333,
0.007670311722904444,
0.03174440562725067,
0.01174271758645773,
0.015969671308994293,
0.007283738348633051,
-0.02719694748520851,
0.005399433430284262,
0.0019607716239988804,
-0.022582462057471275,
0.000152800785144791,
-0.02122441679239273,
-0.0008529205224476755,
0.01837446168065071,
-0.004838733002543449,
0.03122011572122574,
-0.038109034299850464,
-0.017506742849946022,
0.03537860885262489,
-0.014448597095906734,
-0.01503266766667366,
-0.0052764215506613255,
0.0060914927162230015,
0.005096651613712311,
0.04091355577111244,
-0.024233300238847733,
0.019241007044911385,
0.003474039724096656,
0.03459779918193817,
-0.06066766008734703,
0.01502304058521986,
0.016865437850356102,
0.01816016435623169,
-0.02964777499437332,
0.06228717043995857,
0.01229537557810545,
-0.00022977497428655624,
0.046150483191013336,
-0.03874640911817551,
0.09700130671262741,
-0.009668550454080105,
0.022781632840633392,
-0.024613002315163612,
-0.013123536482453346,
-0.03703952580690384,
0.06619704514741898,
0.02495885081589222,
0.006538863759487867,
-0.08162669837474823,
-0.04332438483834267,
-0.023848000913858414,
-0.015809522941708565,
-0.06314438581466675,
-0.012912203557789326,
0.004283925984054804,
-0.004297063685953617,
0.005700909998267889,
0.036468636244535446,
-0.020722059532999992,
0.0037819070275872946,
0.019237032160162926,
0.017640739679336548,
-0.024185936897993088,
0.004109146073460579,
-0.04266241192817688,
-0.008985157124698162,
0.0003431361401453614,
0.013702643103897572,
0.06455592066049576,
-0.002521336078643799,
0.04801937937736511,
0.031518448144197464,
0.03121737390756607,
0.01702186092734337,
-0.042282748967409134,
0.04720371589064598,
0.02336650714278221,
0.010180642828345299,
0.02672538347542286,
0.052605099976062775,
0.00002356499135203194,
0.02339397743344307,
-0.011717066168785095,
0.014295247383415699,
-0.0010703321313485503,
0.006518146023154259,
0.004685851279646158,
0.008725590072572231,
-0.016142552718520164,
0.014798380434513092,
-0.05009786784648895,
-0.008931049145758152,
0.09582192450761795,
0.029960058629512787,
0.0027662452775985003,
0.007477015256881714,
-0.03660719469189644,
-0.016327066347002983,
-0.037689875811338425,
-0.039673373103141785,
-0.011016584001481533,
-0.016670888289809227,
-0.020570969209074974,
-0.029412781819701195,
-0.012005137279629707,
-0.03355623036623001,
-0.01911158487200737,
0.07445617020130157,
0.035524141043424606,
0.04014400392770767,
-0.017422746866941452,
0.04745357111096382,
-0.042988572269678116,
-0.06627698987722397,
-0.019945671781897545,
0.024803370237350464,
-0.027046924456954002,
-0.009984063915908337,
0.027329938486218452,
0.020795194432139397,
0.01987704262137413,
-0.010831221006810665,
-0.004504202865064144,
0.027377525344491005,
0.009657474234700203,
-0.05900881066918373,
-0.07135679572820663,
0.0059179700911045074,
0.016891051083803177,
-0.00035797804594039917,
-0.034740056842565536,
0.018296979367733,
0.0120003130286932,
0.07356997579336166,
0.01809246838092804,
0.018808575347065926,
0.014901366084814072,
-0.014199620112776756,
-0.014928966760635376,
0.015138882212340832,
-0.026514239609241486,
0.015518182888627052,
-0.03475847840309143,
-0.01288538333028555,
-0.09071169048547745,
0.026421844959259033,
0.027719952166080475,
0.0002991092042066157,
0.011629408225417137,
0.019948557019233704,
0.014363214373588562,
-0.004496906418353319,
0.03437839820981026,
-0.014298207126557827,
-0.05453977361321449,
0.061426855623722076,
0.015220221132040024,
-0.00792134553194046,
0.019796893000602722,
-0.0007929062121547759,
-0.011424016207456589,
-0.00488751195371151,
0.004939822480082512,
0.020722627639770508,
-0.04574275389313698,
-0.02325521595776081,
-0.021462712436914444,
-0.021097548305988312,
0.043874189257621765,
-0.049596142023801804,
-0.05229493975639343,
-0.03014533780515194,
0.037462539970874786,
-0.005967286881059408,
0.051340289413928986,
0.007641530130058527,
0.028231484815478325,
0.003760614199563861,
-0.039622679352760315,
-0.01804460398852825,
-0.07747749239206314,
0.04207173362374306,
0.02190067619085312,
-0.0044678510166704655,
0.006943544838577509,
-0.012056538835167885,
0.022774627432227135,
-0.02723236195743084,
0.004557910840958357,
0.04988585785031319,
0.04199734330177307,
0.01017503160983324,
-0.023154910653829575,
-0.007712004240602255,
0.031257882714271545,
0.063172847032547,
0.0395757220685482,
0.03258318826556206,
-0.03150997310876846,
0.054470762610435486,
-0.013228503987193108,
-0.04109448567032814,
0.012188788503408432,
0.037537623196840286,
0.04860469698905945,
0.039741598069667816,
-0.02407299168407917,
0.006901218090206385,
0.02784566767513752,
-0.006904634181410074,
0.048658326268196106,
0.0605204813182354,
0.029814250767230988,
0.010262438096106052,
0.00825119111686945,
-0.02570027858018875,
0.06326597929000854,
0.00993084255605936,
-0.07340560853481293,
-0.0291699580848217,
-0.010809147730469704,
-0.04340382292866707,
0.0044294991530478,
-0.06575274467468262,
0.02208792418241501,
0.07721768319606781,
0.02383599244058132,
0.04799238592386246,
0.020101310685276985,
0.013912802562117577,
-0.05840012803673744,
0.0305235143750906,
0.00449433084577322,
-0.014129390940070152,
0.0412118025124073,
-0.001909798476845026,
0.0462547242641449,
-0.0009156762389466166,
-0.02672046795487404,
-0.0018114442937076092,
0.009646802209317684,
0.0008319602347910404,
-0.00023842674272600561,
-0.013654517009854317,
-0.033121343702077866,
0.06208937242627144,
-0.029653770849108696,
0.02725609950721264,
0.07192999124526978,
-0.004878821782767773,
-0.003094625659286976,
-0.03043534606695175,
-0.013860265724360943,
0.006138679105788469,
-0.01655830815434456,
0.018683694303035736,
0.0020370108541101217,
0.042181309312582016,
-0.019664978608489037,
0.0153574850410223,
0.009222087450325489,
-0.022938722744584084,
-0.005635806359350681,
0.012682868167757988,
0.04798310250043869,
0.047893352806568146,
0.04910314455628395,
-0.02835722640156746,
0.013248099014163017,
0.0032291433308273554,
-0.025318307802081108,
0.0211491622030735,
0.004315205384045839,
-0.07060781121253967,
-0.007343492936342955,
-0.03211237117648125,
-0.046942055225372314,
0.02814643271267414,
0.007525397464632988,
-0.011317431926727295,
0.005172889679670334,
-0.007371681276708841,
0.018781151622533798,
0.003512672381475568,
-0.00035389381810091436,
0.021722670644521713,
-0.06815268099308014,
0.03909071907401085,
0.022851448506116867,
0.016238465905189514,
-0.04832396283745766,
-0.0024631989654153585,
-0.06534461677074432,
-0.04062293842434883,
-0.002191550098359585,
0.012633011676371098,
-0.02745450846850872,
-0.011279923841357231,
0.00926430057734251,
0.019266026094555855,
-0.0002236729342257604,
0.008921725675463676,
-0.08834851533174515,
-0.015157841145992279,
-0.0032545216381549835,
-0.01679159887135029,
0.03377706557512283,
-0.012936481274664402,
-0.04748385399580002,
0.08444325625896454,
0.019192660227417946,
-0.03357866033911705,
-0.039471585303545,
0.018498079851269722,
-0.004008735064417124,
-0.0495993047952652,
-0.016039708629250526,
0.04458199813961983,
-0.019567428156733513,
0.0008248466183431447,
-0.008145837113261223,
0.016548437997698784,
0.04368036240339279,
-0.0032937503419816494,
0.010915685445070267,
0.006732039153575897,
0.00038651982322335243,
-0.02422066032886505,
0.07009375840425491,
0.007926259189844131,
0.0065747471526265144,
-0.007941990159451962,
-0.011616392061114311,
0.041848741471767426,
0.0012143709463998675,
-0.021266929805278778,
0.03404706344008446,
0.003329475875943899,
0.0013625883730128407,
-0.011626388877630234,
0.02676391415297985,
0.022939054295420647,
-0.05825749412178993,
-0.028894536197185516,
-0.02779889479279518,
0.011082888580858707,
0.002911005634814501,
0.025527553632855415,
0.06000155583024025,
0.06745384633541107,
-0.0036317133344709873,
-0.05306674912571907,
-0.015259101055562496,
0.02356494404375553,
0.024045391008257866,
-0.06111934408545494,
-0.027428388595581055,
-0.03760460019111633,
0.029984168708324432,
0.0042595816776156425,
-0.018026750534772873,
-0.032668087631464005,
0.020143132656812668,
-0.07581695169210434,
-0.042261116206645966,
-0.040119897574186325,
0.03668256103992462,
0.00047951750457286835,
0.03475339710712433,
0.035894978791475296,
0.004881349392235279,
0.04261954873800278,
-0.0038102250546216965,
-0.09840061515569687,
0.031025348231196404,
-0.0374024473130703,
-0.0610322505235672,
0.05169738456606865,
-0.004280483350157738,
0.011629927903413773,
-0.015958460047841072,
0.004589996300637722,
0.007588524837046862,
-0.010954546742141247,
-0.058131638914346695,
0.0025494794826954603,
0.004888720344752073,
-0.0620875246822834,
-0.011726569384336472,
0.018301723524928093,
0.0491175651550293,
-0.027313394472002983,
-0.008016128093004227,
0.008683139458298683,
0.002587944269180298,
0.00021581917826551944,
-0.029848311096429825,
0.00043372990330681205,
0.019273649901151657,
-0.018357913941144943,
0.019410252571105957,
0.01324855349957943,
0.009549944661557674,
0.009718392044305801,
-0.016572466120123863,
0.02904718928039074,
0.015279347077012062,
-0.02452305145561695,
-0.019103797152638435,
-0.01951841078698635,
-0.0118322242051363,
-0.013665263541042805,
0.04240402951836586,
-0.02742784097790718,
0.005330583080649376,
0.002567282412201166,
-0.0051815444603562355,
-0.012362344190478325,
0.05316082760691643,
0.023886598646640778,
-0.007288658991456032,
-0.027752969413995743,
-0.012656033970415592,
-0.027886109426617622,
-0.05623754486441612,
-0.03900379687547684,
0.003482448635622859,
-0.004330621100962162,
-0.011661271564662457,
-0.0021145138889551163,
0.07152115553617477,
0.0666205957531929,
-0.04536087065935135,
0.04905223473906517,
-0.019607672467827797,
0.01681414246559143,
0.006785185541957617,
-0.009887783788144588,
0.018082302063703537,
-0.009319323115050793,
0.012852978892624378,
-0.02953910082578659,
0.005416716914623976,
-0.02711167186498642,
-0.045251473784446716,
0.002508319914340973,
0.07611139118671417,
-0.006257120054215193,
0.013012337498366833,
-0.010438665747642517,
-0.011044791899621487,
0.04664411023259163,
0.008212985470890999,
0.06482035666704178,
0.00891538430005312,
0.02156696282327175,
0.004488207399845123,
-0.02313106507062912,
-0.07070255279541016,
-0.006778554990887642,
-0.013576592318713665,
-0.008084900677204132,
-0.020331816747784615,
-0.0438208170235157,
-0.006375160068273544,
-0.006059371400624514,
0.005754211451858282,
0.03161292523145676,
-0.005878808908164501,
-0.03625538945198059,
0.004426680505275726,
-0.01146459300071001,
-0.005292678251862526,
-0.06490729749202728,
0.026960372924804688,
-0.004173280205577612,
-0.03099490888416767,
-0.02608211152255535,
0.01434234157204628,
-0.0650375559926033,
0.0411621630191803,
-0.03649822622537613,
0.0018603313947096467,
0.035379718989133835,
-0.041550472378730774,
0.00698870187625289,
0.04139859974384308,
0.009472113102674484,
0.024935364723205566,
0.05345941707491875,
-0.07022012770175934,
0.0063318051397800446,
-0.016265589743852615,
0.0006628829287365079,
-0.02742723375558853,
-0.004266072995960712,
-0.02104225941002369,
0.006808226928114891,
-0.009216868318617344,
0.031858235597610474,
-0.021975398063659668,
0.0384974405169487,
-0.03422936797142029,
-0.014550704509019852,
-0.010248076170682907,
0.005431541241705418,
0.005315505899488926,
-0.014128324575722218,
-0.008169238455593586,
0.011110395193099976,
0.0007784551125951111,
-0.010217731818556786,
-0.023498225957155228,
0.020968446508049965,
0.006813150364905596,
0.020369675010442734,
0.007047278806567192,
-0.017917247489094734,
-0.016648026183247566,
-0.015293357893824577,
0.020513663068413734,
-0.0459599643945694,
-0.020894117653369904,
-0.0022354840766638517,
0.017823530361056328,
0.018121585249900818,
-0.017538907006382942,
-0.0558059997856617,
0.02637641131877899,
0.020484192296862602,
-0.00393678667023778,
-0.004837118089199066,
0.010707370936870575,
0.028871586546301842,
0.025081375613808632,
-0.02410818822681904,
-0.020997842773795128,
0.017990561202168465,
-0.006926394999027252,
-0.0048022461123764515,
0.02000429481267929,
0.01392234954982996,
0.006436952855437994,
-0.033917635679244995,
0.027021896094083786,
0.05906039476394653,
-0.04181511327624321,
0.016563130542635918,
-0.01036257017403841,
0.012721816077828407,
0.057332687079906464,
0.011047093197703362,
-0.003596952650696039,
-0.008952412754297256,
0.0037904682103544474,
-0.012572884559631348,
0.00595123739913106,
0.05354351922869682,
-0.03057822398841381,
-0.008973918855190277,
0.010401014238595963,
-0.04118741303682327,
0.018208513036370277,
0.029453204944729805,
-0.007981395348906517,
0.001831559929996729,
0.04556884989142418,
-0.036140941083431244,
-0.010008246637880802,
0.019330622628331184,
0.009200625121593475,
0.07181473076343536,
-0.04883413761854172,
0.012912014499306679,
-0.00830241572111845,
0.013222732581198215,
-0.011744770221412182,
-0.002064069500193,
0.00842576939612627,
0.008299054577946663,
0.09681345522403717,
-0.03228064626455307,
-0.03149328753352165,
-0.004536930471658707,
0.02657761611044407,
0.04883961006999016,
0.021517379209399223,
-0.004336400423198938,
0.015027130953967571,
-0.025508038699626923,
-0.0256813857704401,
-0.009137667715549469,
-0.03806950896978378,
0.0015388780739158392,
0.05970378592610359,
-0.010377587750554085,
0.08108360320329666,
0.00497621251270175,
-0.01298778411000967,
0.04190647229552269,
0.03429776057600975,
-0.02765744924545288,
0.0036412631161510944,
-0.0007455373997800052,
0.0011669887462630868,
-0.0074947914108633995,
-0.03651749715209007,
0.0716157853603363,
-0.008062644861638546,
-0.03836909309029579,
0.00010373790428275242,
-0.000004439230906427838,
-0.004225387237966061,
-0.003671064740046859,
-0.04839114099740982,
-0.022465234622359276,
0.004631017800420523,
-0.011777961626648903,
0.05733640491962433,
0.01494777575135231,
-0.011059536598622799,
0.047044187784194946,
0.05912511423230171,
0.01679648458957672,
-0.029213806614279747,
-0.006266132462769747,
-0.062187742441892624,
-0.03939581289887428,
0.03326772525906563,
-0.010564910247921944,
-0.006472207605838776,
-0.010113555938005447,
0.025599274784326553,
-0.0038280959706753492,
0.04015086591243744,
-0.04559267684817314,
-0.04765846207737923,
-0.0021659277845174074,
-0.007265869993716478,
-0.017484774813055992,
0.08316763490438461,
0.004378666635602713,
-0.031186839565634727,
0.023829426616430283,
0.008256609551608562,
0.034382566809654236,
0.06782398372888565,
-0.010231779888272285,
-0.024815643206238747,
0.05460674688220024,
-0.05391624569892883,
-0.0010813333792611957,
-0.03324150666594505,
-0.013856509700417519,
0.15700480341911316,
0.04166247695684433,
0.040277574211359024,
-0.017532527446746826,
0.01648537442088127,
-0.032196883112192154,
-0.02211347594857216,
-0.02798403613269329,
0.022040748968720436,
0.035110242664813995,
-0.048461876809597015,
0.0025581098161637783,
0.04679736867547035,
-0.0193807240575552,
-0.018762165680527687,
0.024400515481829643,
-0.052527379244565964,
-0.06190371513366699,
-0.02829776518046856,
0.025595247745513916,
-0.004302464425563812,
0.013025464490056038,
0.0013216602383181453,
0.014166394248604774,
-0.02754156105220318,
-0.0074359942227602005,
-0.03833853453397751,
-0.030430927872657776,
0.0273328498005867,
-0.013056696392595768,
-0.0714176669716835,
0.011316865682601929,
0.006462635938078165,
-0.012074372731149197,
-0.0008227661601267755,
0.04251427203416824,
0.02992033213376999,
-0.021550416946411133,
0.03138360381126404,
0.040246523916721344,
0.030993560329079628,
0.025636328384280205,
0.018874645233154297,
0.009923853911459446,
-0.049929097294807434,
0.008339179679751396,
-0.05334248021245003,
0.04778159037232399,
-0.025691907852888107,
0.01150424126535654,
0.033451564610004425,
-0.0022659352980554104,
-0.007350650150328875,
-0.03912566229701042,
0.030945520848035812,
0.01458138320595026,
0.01883303001523018,
-0.021451225504279137,
0.015267382375895977,
0.014597050845623016,
-0.0026752534322440624,
0.026786701753735542,
-0.016244567930698395,
0.014318852685391903,
-0.004629813600331545,
-0.030603010207414627,
0.022917604073882103,
0.06534838676452637,
-0.014216226525604725,
-0.02970104292035103,
-0.02632390335202217,
-0.028617219999432564,
0.004007273819297552,
-0.004067386034876108,
-0.02335062436759472,
0.0025059026665985584,
0.009251483716070652,
-0.0020083277486264706,
-0.037063486874103546,
-0.07584675401449203,
-0.03596685826778412,
0.012567803263664246,
0.007322805467993021,
-0.006772271823137999,
-0.045923154801130295,
-0.03058547154068947,
0.008871381171047688,
0.048069462180137634,
0.03421793133020401,
0.005478916689753532,
-0.001292655011638999,
0.09183253347873688,
0.028472594916820526,
-0.04195069149136543,
-0.030688539147377014,
-0.015217237174510956,
-0.027465801686048508,
-0.0041907718405127525,
0.016913114115595818,
-0.005797282326966524,
0.0486910343170166,
-0.0006803772412240505,
-0.044861577451229095,
0.06034674122929573,
-0.024957804009318352,
0.015805043280124664,
0.008447869680821896,
-0.034372925758361816,
0.013286459259688854,
0.07017297297716141,
-0.0020223374012857676,
-0.03445170074701309,
0.015044402331113815,
-0.002128340769559145,
0.0070479088462889194,
0.028289366513490677,
-0.00649948138743639,
-0.020485905930399895,
0.02521246112883091,
-0.026006802916526794,
0.032027654349803925,
-0.03969564288854599,
0.04801494628190994,
-0.015122336335480213,
-0.014869077131152153,
0.010331034660339355,
0.007139178924262524,
-0.019635740667581558,
-0.006327601615339518,
-0.026896564289927483,
0.013777177780866623,
0.017096737399697304,
0.02968498133122921,
0.005372533109039068,
-0.05668698251247406,
0.017562592402100563,
0.03792678192257881,
0.015782291069626808,
-0.014973470009863377,
-0.01983923278748989,
0.028641780838370323,
-0.02444596029818058,
-0.004109432455152273,
0.03278573602437973,
0.0007955368491820991,
0.027046946808695793,
-0.01285074558109045,
-0.00897850189357996,
0.004459024872630835,
0.07416441291570663,
-0.028577584773302078,
-0.004492319654673338,
-0.011327509768307209,
-0.05538894236087799,
-0.007792350836098194,
-0.016483912244439125,
-0.013631792739033699,
0.010566177777945995,
0.000290257012238726,
0.024875378236174583,
0.008443833328783512,
-0.01102528627961874,
-0.010497007519006729,
0.03538186103105545,
-0.006973083131015301,
-0.023825448006391525,
0.024394147098064423,
-0.011334671638906002,
0.025366535410284996,
0.012394298799335957,
-0.0004242122231516987,
-0.014262848533689976,
0.01716652698814869,
0.007084726821631193,
-0.08055222779512405,
-0.01777602545917034,
0.03817204013466835,
-0.013020575977861881,
0.07039405405521393,
-0.05261573940515518,
0.031098058447241783,
0.014351308345794678,
-0.07792200148105621,
0.016270166262984276,
-0.03465297445654869,
0.013495564460754395,
0.013619961217045784,
0.02085268311202526,
0.02530449442565441,
0.03128265589475632,
-0.005806263070553541,
0.07186693698167801,
-0.0146654536947608,
0.06484591960906982,
0.0013259057886898518,
-0.03665247932076454,
0.024601126089692116,
0.032113928347826004,
0.002921187551692128,
-0.008247971534729004,
0.03774702548980713,
-0.019119413569569588,
0.01954171434044838,
-0.005369987804442644,
-0.01117803156375885,
0.02319694682955742,
-0.03825218230485916,
0.039152905344963074,
0.0007573760813102126,
0.034680403769016266,
-0.004561689216643572,
0.025381427258253098,
-0.028085092082619667,
0.020132174715399742,
0.005366844590753317,
0.004752432927489281,
-0.022970136255025864,
-0.019215352833271027,
0.05291770026087761,
-0.028344571590423584,
-0.015198028646409512,
-0.005113427992910147,
0.0019080700585618615,
0.01070516649633646,
0.02845744788646698,
-0.020117582753300667,
-0.014543591998517513,
-0.022204997017979622,
-0.0330638624727726,
0.001995119731873274,
0.02080666273832321,
0.01151073258370161,
-0.0038689165376126766,
-0.01335079688578844,
0.023328682407736778,
-0.036905936896800995,
-0.016598137095570564,
0.006149293389171362,
-0.0048156362026929855,
-0.04283064603805542,
-0.016854777932167053,
0.021637342870235443,
0.002391063841059804,
-0.03039679303765297,
-0.005825836211442947,
-0.03367938473820686,
-0.049237847328186035,
-0.01482414174824953,
-0.010297536849975586,
0.0015800426481291652,
-0.006422639824450016,
0.008360400795936584,
-0.0038641602732241154,
-0.06935159862041473,
0.03297397494316101,
0.0044561587274074554,
-0.030488241463899612,
-0.030628560110926628,
-0.00851005595177412,
-0.004831684287637472,
0.035807639360427856,
0.04759276658296585,
-0.032033007591962814,
-0.016241082921624184,
0.023138830438256264,
-0.014288811013102531,
0.0039023039862513542,
-0.033086810261011124,
0.04038567468523979,
0.004949857946485281,
-0.0061140237376093864,
0.019069813191890717,
0.0260609220713377,
-0.008984878659248352,
-0.002470117062330246,
0.055434029549360275,
-0.015265217050909996,
-0.0036844955757260323,
-0.015301738865673542,
-0.014734586700797081,
-0.0024653738364577293,
0.014875330962240696,
-0.018298005685210228,
0.031245781108736992,
-0.030696788802742958,
-0.0066051785834133625,
0.018253857269883156,
-0.020087523385882378,
-0.056494906544685364,
0.0628470778465271,
-0.053407393395900726,
0.034296806901693344,
0.002982448786497116,
-0.02249588444828987,
0.052342746406793594,
-0.07374291867017746,
0.0063713365234434605,
0.0017048448789864779,
-0.005229951348155737,
-0.050524622201919556,
0.01358597818762064,
0.0505276620388031,
-0.00255263177677989,
-0.011694117449223995,
0.06329811364412308,
-0.008493281900882721,
-0.04154524952173233,
0.027075158432126045,
-0.03650655597448349,
0.04153786972165108,
-0.027317682281136513,
0.0003070858074352145,
0.05062146112322807,
-0.0028473392594605684,
0.054194074124097824,
0.00777070689946413,
0.012553581967949867,
0.00833217054605484,
-0.03295467793941498,
0.011550662107765675,
-0.002012585988268256,
0.007317458279430866,
0.021253570914268494,
-0.014097265899181366,
0.05855109170079231,
-0.036608245223760605,
0.025452611967921257,
0.017336813732981682,
0.006039935164153576,
-0.03024684637784958,
-0.06405061483383179,
-0.019948948174715042,
0.02555498294532299,
0.009058057330548763,
-0.03334527835249901,
-0.015817906707525253,
-0.020302720367908478,
-0.01329452358186245,
-0.011092735454440117,
-0.029490558430552483,
0.04693397507071495,
0.0008129070629365742,
0.022230172529816628,
-0.005905402824282646,
-0.07061373442411423,
-0.03302404284477234,
0.05771135911345482,
0.04217009246349335,
0.006121047306805849,
-0.029704028740525246,
0.005069296807050705,
-0.010948656126856804,
0.06282616406679153,
-0.016771439462900162,
-0.007473343051970005,
0.002676919335499406,
-0.006851662416011095,
0.05946062505245209,
-0.022991744801402092
] |
<p>how to define electric charge ? How to explain this term ? As learned by me
electric charge is an intrinsic property of atoms like mass of different atoms. </p>
| 253 |
[
-0.022595996037125587,
-0.002611457370221615,
0.008255448192358017,
-0.023060336709022522,
0.006252485793083906,
0.011845696717500687,
-0.02809790149331093,
-0.000418373936554417,
0.013659645803272724,
-0.02486542798578739,
0.05032743886113167,
0.03530331328511238,
0.04297889396548271,
0.001871967688202858,
-0.004833444952964783,
0.006350493058562279,
0.019699322059750557,
-0.01971595175564289,
0.0024338983930647373,
-0.01254794467240572,
-0.009135198779404163,
0.0021142030600458384,
0.01750102825462818,
0.04023279622197151,
0.0078396862372756,
0.03811410069465637,
0.040805354714393616,
0.0016585532575845718,
0.05489803105592728,
0.04252558946609497,
0.010708414018154144,
-0.037168215960264206,
0.016401853412389755,
-0.008841766975820065,
0.012151106260716915,
-0.016673220321536064,
0.0025298832915723324,
-0.029171468690037727,
-0.018843278288841248,
0.005643707700073719,
-0.0032071468885987997,
-0.045743174850940704,
0.01676349900662899,
0.004409387242048979,
-0.048603933304548264,
0.004016793332993984,
-0.003056721528992057,
-0.02122088149189949,
0.026993731036782265,
-0.06148027256131172,
0.05435510352253914,
0.008268008939921856,
0.09711486101150513,
0.021936729550361633,
0.018410492688417435,
0.0019150448497384787,
0.06958185881376266,
0.04743384197354317,
-0.02903192862868309,
-0.03529158979654312,
-0.03665265068411827,
-0.04407363757491112,
0.02160743996500969,
-0.057713620364665985,
-0.0019133787136524916,
0.060473259538412094,
-0.00506691774353385,
-0.031063979491591454,
0.020002055913209915,
0.0393119640648365,
0.002695416798815131,
0.0031948289833962917,
-0.015145411714911461,
-0.006335629150271416,
0.01437742542475462,
-0.05650530755519867,
0.01222339179366827,
-0.010339813306927681,
0.04121975228190422,
0.036788295954465866,
-0.017386505380272865,
0.01981944404542446,
0.0026301415637135506,
0.027370130643248558,
-0.009382987394928932,
-0.03743951395153999,
0.06563422083854675,
-0.020183753222227097,
0.01995151676237583,
0.013158602640032768,
-0.026422902941703796,
0.009557230398058891,
0.007699317764490843,
-0.0007315605180338025,
-0.01870725303888321,
0.02788025327026844,
-0.016173001378774643,
0.047471631318330765,
0.0077346391044557095,
-0.020935703068971634,
0.049631573259830475,
-0.010721462778747082,
0.05351688712835312,
0.05897509679198265,
-0.006087192799896002,
-0.03580678254365921,
-0.04017546772956848,
-0.001232227892614901,
0.0026030773296952248,
-0.0004408714303281158,
-0.04184288904070854,
0.01625792123377323,
0.014889810234308243,
0.0032394903246313334,
0.04850958660244942,
-0.011572365649044514,
0.0261229295283556,
-0.019497549161314964,
0.05106276646256447,
0.040327444672584534,
0.014771085232496262,
-0.047464389353990555,
0.0348043330013752,
-0.009167559444904327,
-0.07996292412281036,
-0.0018090084195137024,
0.03947204351425171,
0.011830907315015793,
-0.00968896970152855,
0.03166333958506584,
-0.016345977783203125,
-0.031633052974939346,
-0.0027634475845843554,
0.0063884262926876545,
0.043469611555337906,
-0.009955578483641148,
-0.12736840546131134,
-0.032865721732378006,
0.018721161410212517,
-0.0014269191306084394,
-0.041585128754377365,
-0.0883738100528717,
0.00403099087998271,
0.016888143494725227,
0.041738349944353104,
0.048393383622169495,
-0.03118695504963398,
0.0089592095464468,
0.014318631030619144,
0.03508458286523819,
-0.024309072643518448,
-0.03339790180325508,
-0.00009170340490527451,
-0.01356579177081585,
0.01163421105593443,
-0.04756518080830574,
0.02263493277132511,
0.009027230553328991,
-0.024020196869969368,
-0.024285146966576576,
0.0511334054172039,
-0.04381662607192993,
-0.025088734924793243,
0.03549690172076225,
0.01220039464533329,
-0.034706778824329376,
0.04564398527145386,
0.027662906795740128,
-0.010039488784968853,
0.07616027444601059,
0.017138339579105377,
0.030753351747989655,
0.03106703609228134,
0.05202759429812431,
0.01433818880468607,
-0.02785278856754303,
-0.013733740895986557,
-0.041862472891807556,
0.009785385802388191,
0.01771237887442112,
-0.06179323047399521,
-0.048573851585388184,
0.045646484941244125,
0.030186912044882774,
0.001245438470505178,
0.026015829294919968,
-0.015632331371307373,
-0.008881120011210442,
0.005035738460719585,
-0.037701547145843506,
-0.03625687584280968,
-0.07301627844572067,
0.07407013326883316,
0.012304458767175674,
-0.03799930959939957,
0.010332874022424221,
-0.0069501022808253765,
-0.006544729229062796,
-0.06957031041383743,
-0.01402195729315281,
-0.002994837239384651,
0.04849768429994583,
-0.005007944535464048,
-0.023338301107287407,
0.018175693228840828,
0.04306710511445999,
0.03343476355075836,
0.008926326408982277,
0.007397673558443785,
0.030604243278503418,
-0.024176716804504395,
-0.0015484760515391827,
-0.009896044619381428,
0.01785138063132763,
0.012728573754429817,
0.004695442039519548,
-0.00258258986286819,
-0.0004663438885472715,
-0.01756838895380497,
0.08041078597307205,
0.017123185098171234,
0.0615970715880394,
0.049680158495903015,
0.005624622106552124,
-0.009605656377971172,
0.0350462943315506,
0.0008874502964317799,
0.007998104207217693,
-0.0199257992208004,
-0.03795855492353439,
-0.04212019592523575,
0.0154932402074337,
0.03833010047674179,
0.035238124430179596,
-0.0318070612847805,
0.007992533035576344,
0.011204758659005165,
0.04197974130511284,
0.04317472502589226,
0.022755177691578865,
-0.03403544798493385,
-0.036359019577503204,
0.02965143881738186,
-0.011976621113717556,
0.011415124870836735,
0.02313169650733471,
0.019928034394979477,
0.017082206904888153,
0.03716708719730377,
-0.006478062830865383,
0.004209922160953283,
0.04802415892481804,
-0.02060716785490513,
0.011450611986219883,
0.014913455583155155,
-0.0452997125685215,
-0.0012677867198362947,
-0.030660657212138176,
0.046280138194561005,
0.008924596942961216,
-0.040838055312633514,
0.005980363581329584,
-0.01920495182275772,
-0.012844591401517391,
0.004559233784675598,
-0.0005954481894150376,
-0.0074675544165074825,
-0.014798682183027267,
0.02803920954465866,
-0.020282402634620667,
0.04015398025512695,
0.022278008982539177,
-0.014758868142962456,
-0.02070731855928898,
-0.00021914218086749315,
0.04072369635105133,
0.0019815389532595873,
0.030086131766438484,
-0.012590707279741764,
-0.050688236951828,
0.0016349541256204247,
-0.04151036590337753,
-0.005211493466049433,
-0.009523964487016201,
-0.021989546716213226,
0.01819019205868244,
-0.03873211517930031,
-0.02061372995376587,
0.046897076070308685,
0.023150049149990082,
0.013490059413015842,
0.004671848379075527,
0.004210967104882002,
-0.016739023849368095,
0.0431741438806057,
-0.040030259639024734,
0.01263051200658083,
-0.002855791477486491,
-0.01281477976590395,
0.031084565445780754,
-0.029863139614462852,
-0.0015930143417790532,
-0.0006476338603533804,
-0.04745113477110863,
-0.03339690342545509,
0.011801284737884998,
-0.0412105955183506,
0.015040487982332706,
-0.03482646867632866,
0.013488729484379292,
0.0321260467171669,
-0.07824084907770157,
-0.02260471135377884,
-0.033024828881025314,
-0.03591534495353699,
0.04053359106183052,
-0.008295943029224873,
0.022075463086366653,
-0.013420507311820984,
-0.07508999109268188,
0.05942615866661072,
0.009318905882537365,
-0.032722108066082,
0.012130101211369038,
-0.039682209491729736,
-0.04212425649166107,
-0.001592491869814694,
-0.022160809487104416,
0.04598253592848778,
0.014145336113870144,
-0.005177184008061886,
0.032722800970077515,
0.024653097614645958,
0.0012400439009070396,
0.019374459981918335,
-0.02262970246374607,
0.026727616786956787,
-0.014079377055168152,
0.013315604999661446,
0.02640458568930626,
0.031446877866983414,
-0.06249215453863144,
0.024286743253469467,
0.01978950947523117,
0.01797543466091156,
-0.0061595384031534195,
-0.014648089185357094,
0.04183042421936989,
0.005291195586323738,
0.022289559245109558,
-0.03582310304045677,
0.03180183470249176,
-0.016534727066755295,
-0.034101467579603195,
0.032733120024204254,
0.025995107367634773,
0.008287647739052773,
-0.004359479062259197,
-0.009563857689499855,
0.03124399110674858,
0.04821508377790451,
-0.05629616603255272,
-0.0430898554623127,
-0.008536151610314846,
-0.001126222312450409,
0.015409822575747967,
-0.0012232300359755754,
0.0018166035879403353,
0.03230025991797447,
0.026648111641407013,
0.04427480697631836,
0.014920552261173725,
-0.03602822124958038,
-0.008890713565051556,
-0.051998335868120193,
0.0015796117950230837,
0.009228638373315334,
0.038138024508953094,
-0.009572627954185009,
0.08920589834451675,
0.017525969073176384,
0.028614183887839317,
-0.00981366727501154,
0.0010999210644513369,
-0.06708811223506927,
-0.005052662454545498,
-0.035869333893060684,
-0.00006620468775508925,
-0.060069553554058075,
-0.011841186322271824,
-0.02012641169130802,
-0.02309441566467285,
-0.024732764810323715,
-0.03538152202963829,
-0.034621257334947586,
-0.018952632322907448,
0.006928775459527969,
-0.020964760333299637,
0.0063241468742489815,
-0.01630924828350544,
-0.0008598154527135193,
0.024381954222917557,
-0.03159930557012558,
-0.015411417931318283,
0.04697594791650772,
-0.013811754994094372,
-0.009600521996617317,
-0.0014648156939074397,
-0.014665544964373112,
0.03193644434213638,
-0.007561670150607824,
0.03773299977183342,
0.0013608649605885148,
-0.009130840189754963,
0.021669814363121986,
-0.006116086151450872,
0.07681548595428467,
0.02030855044722557,
-0.02668836899101734,
-0.02977941557765007,
-0.05112264305353165,
-0.012566094286739826,
-0.023841599002480507,
0.04546738043427467,
-0.0075564696453511715,
0.017128845676779747,
0.030993076041340828,
0.0028446733485907316,
-0.028643926605582237,
0.06576434522867203,
0.04288063943386078,
0.0585552453994751,
-0.06546225398778915,
-0.045444048941135406,
0.025150757282972336,
-0.017376571893692017,
0.007726273033767939,
0.04524245858192444,
-0.012739768251776695,
-0.0002244998759124428,
0.0010864706709980965,
-0.005244468338787556,
-0.028226613998413086,
-0.02318616956472397,
-0.021530985832214355,
0.008943584747612476,
0.008571350015699863,
-0.013962662778794765,
0.011994008906185627,
0.018826056271791458,
0.008450579829514027,
0.02806159295141697,
0.01992354542016983,
-0.045873455703258514,
-0.08877293020486832,
0.03262218087911606,
0.04084800183773041,
0.03303316980600357,
-0.0508425235748291,
-0.0172719806432724,
-0.027554597705602646,
0.0013787166681140661,
0.032552991062402725,
-0.029739001765847206,
0.005830975715070963,
-0.05186360329389572,
0.0018588332459330559,
-0.016180144622921944,
0.004309641197323799,
-0.0056612733751535416,
0.05271362513303757,
-0.013816851191222668,
-0.00793086364865303,
-0.01854718290269375,
0.009868855588138103,
-0.009596656076610088,
0.032415781170129776,
0.01453281007707119,
0.057510606944561005,
-0.009817332029342651,
-0.002779024885967374,
-0.017798367887735367,
0.024733973667025566,
-0.008683496154844761,
-0.08691053837537766,
-0.01086044404655695,
-0.005517203826457262,
-0.007523074746131897,
0.0030616032890975475,
-0.019896093755960464,
-0.05149976536631584,
0.0017871959134936333,
-0.004669577814638615,
0.006304516922682524,
-0.027677573263645172,
-0.037785276770591736,
0.011114844121038914,
0.02990986965596676,
-0.0038218661211431026,
0.05901314318180084,
0.0016046225791797042,
-0.053690455853939056,
0.0008116847020573914,
-0.02803213708102703,
0.05792029947042465,
-0.005293643102049828,
-0.029309358447790146,
-0.016882000491023064,
0.03770134970545769,
-0.044016074389219284,
0.07608211785554886,
-0.006496525835245848,
0.006642412394285202,
-0.01669962704181671,
-0.03967328369617462,
-0.0342559851706028,
0.010861590504646301,
0.016002655029296875,
-0.006859154440462589,
-0.03369290009140968,
0.021193852648139,
0.017717083916068077,
-0.004343333654105663,
-0.01469137892127037,
0.032828107476234436,
0.01658693328499794,
-0.0055613028816878796,
-0.004316908773034811,
0.018637463450431824,
-0.023742789402604103,
-0.028236184269189835,
0.028489695861935616,
-0.04003279656171799,
0.027440056204795837,
-0.02444501407444477,
-0.04068585857748985,
-0.01770411990582943,
-0.10178469121456146,
-0.05266699194908142,
0.03945096582174301,
0.022759156301617622,
0.03649399057030678,
-0.02735685557126999,
0.024996383115649223,
0.02519349567592144,
0.010621113702654839,
-0.07225371897220612,
-0.06800197809934616,
0.01499059610068798,
0.025855381041765213,
-0.01708078943192959,
-0.005719899665564299,
0.00831026490777731,
-0.002675979631021619,
-0.044057734310626984,
0.006000112742185593,
0.06731989979743958,
-0.016986483708024025,
-0.009661459363996983,
0.01063085999339819,
0.01798759214580059,
0.041844263672828674,
-0.0004742499440908432,
-0.02539093792438507,
0.00838859099894762,
-0.002147594466805458,
0.015369351021945477,
0.012161594815552235,
0.051106300204992294,
-0.0061648073606193066,
-0.0530521385371685,
-0.00689682736992836,
-0.025508932769298553,
0.016528667882084846,
-0.03324319049715996,
-0.011662526056170464,
0.008266055956482887,
0.006346025038510561,
-0.040690403431653976,
-0.029788237065076828,
0.0264109019190073,
-0.009613667614758015,
0.06847255676984787,
-0.014157640747725964,
-0.0023933646734803915,
-0.05965796858072281,
-0.03683246299624443,
0.03038688935339451,
0.038218967616558075,
0.022579295560717583,
0.008283042348921299,
0.042286116629838943,
-0.014741964638233185,
0.023944159969687462,
0.029090700671076775,
0.00357204582542181,
0.02049420401453972,
0.003243242623284459,
-0.007607444189488888,
0.02375715784728527,
0.004534536972641945,
0.015307743102312088,
0.004572127480059862,
-0.02437032014131546,
-0.0015940674347802997,
0.0667642205953598,
0.00014359138731379062,
0.07442089170217514,
0.03447038680315018,
-0.006312522105872631,
0.013088495470583439,
-0.0033159293234348297,
-0.019059710204601288,
0.012495892122387886,
0.007854606956243515,
0.024465318769216537,
-0.020097117871046066,
-0.017283529043197632,
0.03591307997703552,
0.05753612145781517,
-0.057096708565950394,
0.014359129592776299,
0.03704417496919632,
0.034473542124032974,
-0.004895320627838373,
-0.029764816164970398,
-0.042539045214653015,
0.034739598631858826,
-0.02858530357480049,
0.013021943159401417,
0.006241324823349714,
-0.031948626041412354,
0.03621829301118851,
-0.010359708219766617,
-0.014153692871332169,
-0.011528627015650272,
-0.03426332399249077,
-0.04028676822781563,
0.013173033483326435,
0.015349224209785461,
0.006181093864142895,
-0.02707064151763916,
0.030493784695863724,
-0.0022468757815659046,
-0.03817669674754143,
0.023028235882520676,
0.031362514942884445,
-0.07163435220718384,
-0.047146350145339966,
-0.034694988280534744,
-0.023036155849695206,
0.04313526302576065,
-0.008427037857472897,
-0.026667406782507896,
-0.01141401194036007,
0.0026405388489365578,
0.01803920976817608,
0.029909469187259674,
0.012735307216644287,
-0.02695758268237114,
0.049024272710084915,
-0.018432216718792915,
0.015023366548120975,
-0.009093054570257664,
0.019827773794531822,
0.11914433538913727,
0.058192502707242966,
-0.0005785614484921098,
-0.07277572900056839,
-0.0010596233187243342,
-0.017548320814967155,
-0.021554242819547653,
-0.01791091449558735,
0.031581051647663116,
-0.031224282458424568,
0.0583232119679451,
0.004027236253023148,
0.020842591300606728,
0.02335735782980919,
0.024665934965014458,
0.05051339417695999,
-0.03292781487107277,
-0.05800584331154823,
0.011083618737757206,
0.018822327256202698,
-0.015157879330217838,
0.0425257571041584,
-0.06488765776157379,
0.030373334884643555,
-0.0141825620085001,
-0.010916206985712051,
-0.04976794868707657,
-0.002487993100658059,
0.02819083072245121,
0.030358387157320976,
-0.0298164039850235,
-0.0236701350659132,
-0.006745274644345045,
-0.022503076121211052,
-0.015917465090751648,
0.02256770431995392,
0.042243048548698425,
0.017837604507803917,
-0.024001816287636757,
-0.0010517791379243135,
0.03757084533572197,
-0.0047236476093530655,
0.01859297789633274,
0.027146412059664726,
-0.058230213820934296,
0.015519512817263603,
0.0018757134675979614,
0.020127639174461365,
-0.04457039758563042,
0.02532835118472576,
-0.009126308374106884,
0.030474476516246796,
-0.05852261558175087,
-0.04406339302659035,
-0.03102755919098854,
0.0008319824119098485,
0.030543139204382896,
-0.0073257493786513805,
-0.00885192584246397,
-0.032511867582798004,
0.01800471544265747,
-0.027633246034383774,
0.034197065979242325,
-0.0013400412863120437,
0.010551097802817822,
0.08082900941371918,
0.01520091388374567,
-0.02259359322488308,
0.004570146556943655,
-0.0118882916867733,
-0.009611107409000397,
-0.0316491425037384,
-0.027425942942500114,
-0.04431750252842903,
-0.006358710117638111,
0.04304021596908569,
0.04166059195995331,
0.016978997737169266,
0.012173808179795742,
0.003012903267517686,
-0.07589910179376602,
0.04769457131624222,
0.01091041136533022,
-0.03657978028059006,
-0.03214218094944954,
0.001829740242101252,
0.03081142157316208,
0.04443849250674248,
-0.010379811748862267,
0.03261319547891617,
-0.00757855037227273,
0.007158597931265831,
-0.002068326808512211,
-0.0369114987552166,
0.02470436319708824,
0.02907978929579258,
-0.033667393028736115,
0.021902868524193764,
0.00432891258969903,
-0.003012870904058218,
0.021602608263492584,
0.007069002371281385,
-0.012780539691448212,
0.037364307790994644,
-0.031000323593616486,
0.005691033788025379,
0.03782140463590622,
0.013605865649878979,
0.003694494254887104,
0.03190777823328972,
-0.018203822895884514,
-0.05150304362177849,
-0.026263738051056862,
-0.027459779754281044,
-0.018150413408875465,
0.010645439848303795,
0.045751236379146576,
-0.01478089764714241,
-0.015731483697891235,
-0.02492581680417061,
0.01827121153473854,
-0.05375969782471657,
-0.027806922793388367,
-0.05135224014520645,
-0.0002890094474423677,
-0.013211327604949474,
-0.0060006119310855865,
-0.006979749538004398,
-0.011479507200419903,
-0.021933538839221,
0.017218777909874916,
0.02033056877553463,
0.012467685155570507,
0.004124618601053953,
0.013763505965471268,
-0.0018697824561968446,
-0.040058206766843796,
0.08226331323385239,
-0.03621019050478935,
-0.024951593950390816,
0.03275855630636215,
-0.030929628759622574,
-0.04688551276922226,
-0.00032395729795098305,
-0.015833813697099686,
0.031173698604106903,
0.05219963565468788,
-0.0006001543952152133,
0.009083369746804237,
0.033683422952890396,
-0.025303855538368225,
-0.024048248305916786,
-0.003350676503032446,
-0.007339658681303263,
-0.05420968309044838,
-0.011047037318348885,
0.0036790533922612667,
-0.026527611538767815,
-0.007186539005488157,
0.06359685957431793,
0.03140220791101456,
-0.0035969954915344715,
-0.016815276816487312,
0.04790254682302475,
0.027401557192206383,
0.00880818348377943,
0.05814744532108307,
0.04381809011101723,
0.015991847962141037,
0.03863587975502014,
-0.021325917914509773,
0.032831817865371704,
0.005733699072152376,
-0.010545878671109676,
-0.06096230447292328,
-0.015814222395420074,
-0.015408866107463837,
-0.01644251123070717,
0.012079168111085892,
-0.025876587256789207,
-0.004303112626075745,
0.01760517619550228,
-0.05726597458124161,
0.0004918994382023811,
-0.04025489091873169,
-0.014134722761809826,
0.011049287393689156,
-0.03509986400604248,
-0.009951835498213768,
0.06614038348197937,
0.03636931627988815,
0.04127894714474678,
0.0001247696200152859,
0.012986396439373493,
0.022590437904000282,
-0.026130100712180138,
-0.03136346489191055,
0.053711600601673126,
-0.008828798308968544,
-0.02304503321647644,
0.06664740294218063,
0.006051705218851566,
0.016560032963752747,
0.030232155695557594,
0.005096614360809326,
-0.004233633633702993,
0.03526690602302551,
0.01808185689151287,
-0.004314537160098553,
0.047846823930740356,
-0.010728881694376469,
-0.011296767741441727,
-0.06182568892836571,
0.01444078516215086,
0.03949161618947983,
0.04232332855463028,
0.01550260093063116,
-0.026070408523082733,
0.0065903440117836,
-0.015469545498490334,
-0.057244982570409775,
0.048179686069488525,
-0.01744551584124565,
-0.018705621361732483,
0.0139855882152915,
0.016069278120994568,
-0.003992548678070307,
-0.04732577130198479,
-0.0011071213521063328,
-0.04495253413915634,
-0.012462876737117767,
0.037004463374614716,
0.0000690099477651529,
0.017613600939512253,
0.025318332016468048,
-0.009274055249989033,
-0.01878625713288784,
0.043530095368623734,
0.052354179322719574,
0.0062071834690868855,
-0.06759314239025116,
0.02180739864706993,
0.03319627046585083,
-0.026909926906228065,
-0.0008809658465906978,
-0.04501930996775627,
-0.040732789784669876,
0.04588426649570465,
0.03224426880478859,
-0.01817472279071808,
0.012272863648831844,
-0.0744503065943718,
0.0018414107616990805,
-0.06372170895338058,
0.050511159002780914,
-0.013105416670441628,
-0.006170851644128561,
-0.020947841927409172,
-0.04407786205410957,
-0.004378818906843662,
0.032074976712465286,
0.07566935569047928,
0.0030245338566601276,
-0.05784640833735466,
0.013953747227787971,
0.010492424480617046,
0.018320191651582718,
-0.057105839252471924,
-0.023547686636447906,
-0.020011920481920242,
-0.0149207329377532,
-0.003937958274036646,
-0.014791633002460003,
-0.038128551095724106,
0.034415025264024734,
0.005833592265844345,
-0.0029408240225166082,
0.004109964706003666,
-0.03113352134823799,
-0.019433585926890373,
0.06109434738755226,
0.035613201558589935,
-0.02270006202161312,
0.07000647485256195,
-0.012202986516058445,
-0.0002490859478712082,
0.02994709089398384,
-0.006687500048428774,
-0.02224918268620968,
0.00943982694298029,
-0.02046293206512928,
0.015266950242221355,
-0.02011849917471409,
-0.010940584354102612,
0.029903465881943703,
-0.03179560974240303,
-0.01753178797662258,
0.03574410453438759,
-0.032201752066612244,
-0.010871841572225094,
0.01283650565892458,
0.02201443538069725,
0.055625222623348236,
0.029940247535705566,
-0.017694706097245216,
-0.015867039561271667,
-0.0012610285775735974,
-0.014186629094183445,
0.03461381047964096,
0.06695222854614258,
-0.01216898113489151,
0.024516990408301353,
0.007125950884073973,
0.02068215049803257,
0.009350070729851723,
0.014181426726281643,
0.0037222756072878838,
-0.014151225797832012,
-0.01981574296951294,
0.012849288992583752,
0.014790822751820087,
0.046023279428482056,
-0.016937145963311195,
-0.02750435099005699,
0.06844998896121979,
-0.04298551008105278,
0.02031080052256584,
-0.0034721200354397297,
0.037223633378744125,
-0.018909960985183716,
0.004205170553177595,
0.010579448193311691,
0.024113424122333527,
-0.01801392436027527,
-0.022376438602805138,
-0.03674442693591118,
0.009410219267010689,
0.022033566609025,
-0.03441396355628967,
0.02917560562491417,
0.0014866115525364876,
-0.002029705559834838,
-0.020744342356920242,
0.008601098321378231,
-0.017284078523516655,
-0.0032642327714711428,
0.024026520550251007,
0.026478445157408714,
0.045281507074832916,
0.005326797720044851,
-0.0106700100004673,
-0.027141019701957703,
0.039874251931905746,
-0.08959724754095078,
-0.023825254291296005,
-0.024260202422738075,
0.00004799250382347964,
-0.028754394501447678,
0.011627462692558765
] |
<p>Let's have the spherical spinors:
$$
\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} \\ \sqrt{l \mp m +\frac{1}{2}}Y_{l, m + \frac{1}{2}} \end{pmatrix}.
$$
How to prove the relation
$$
(\hat {\sigma} \cdot \mathbf r )\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = -r\mathbf {Y}_{j, m, l = j \mp \frac{1}{2}}?
$$
I tried to rewrite the $(\hat {\sigma} \cdot \mathbf r )$ as
$$
(\hat {\sigma} \cdot \mathbf r ) = r\begin{pmatrix} \cos(\theta ) & \sin(\theta )\,e^{-i\varphi } \\ \sin(\theta )\, e^{i \varphi } & -\cos(\theta ) \end{pmatrix},
$$
but it's hard to use recurrence relations for associated Legendre functions after that. Is there some hint which simplifies the proof?</p>
<p>Maybe, I can first show that $(\hat {\sigma} \cdot \mathbf r )\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = -ra\mathbf {Y}_{j, m, l = j \mp \frac{1}{2}}$,
because the parity of the left side is opposite to the parity of $\mathbf {Y}_{j, m, l = j \pm \frac{1}{2}}$, and $(\hat {\sigma} \cdot \mathbf r )$ commutes with rotation operator, because refers to the scalar pdoduct?</p>
| 7,662 |
[
-0.012958521023392677,
-0.0009812223725020885,
-0.01825561374425888,
-0.03808605670928955,
0.05700021982192993,
-0.022507360205054283,
-0.012541617266833782,
-0.02791173756122589,
0.0014856549678370357,
-0.031071921810507774,
0.05564434081315994,
0.005145355127751827,
0.030066311359405518,
0.04814644902944565,
0.0006500323070213199,
0.012039648368954659,
-0.025705259293317795,
0.01485399343073368,
-0.01641252264380455,
0.0019205671269446611,
0.004267169162631035,
0.03262975439429283,
-0.015024682506918907,
0.0058069778606295586,
-0.016319090500473976,
0.04888460412621498,
0.018876057118177414,
-0.02538299560546875,
-0.011762818321585655,
0.07909981906414032,
-0.017553061246871948,
0.0008989024790935218,
0.06654540449380875,
0.01650218479335308,
0.01407544780522585,
0.008109109476208687,
-0.005181434098631144,
0.008532635867595673,
0.015292446129024029,
0.052312131971120834,
-0.054812241345644,
-0.029025718569755554,
-0.024190282449126244,
0.04623933881521225,
0.011924412101507187,
0.007298713084310293,
-0.01549375057220459,
0.020648961886763573,
0.06297837197780609,
-0.0487825833261013,
0.11747819930315018,
0.014177310280501842,
0.010843977332115173,
-0.02154804766178131,
-0.04521647095680237,
0.012680059298872948,
0.045872531831264496,
0.07208915054798126,
0.011919076554477215,
-0.03894529119133949,
-0.034563418477773666,
-0.06925582140684128,
-0.0038364161737263203,
-0.009223206900060177,
0.0018925340846180916,
-0.017086360603570938,
0.038805846124887466,
0.002361635211855173,
0.025253310799598694,
-0.012754686176776886,
-0.00591813400387764,
-0.006535076070576906,
0.03842289745807648,
-0.03348046913743019,
0.006516467779874802,
0.0018869397463276982,
-0.017067715525627136,
0.01142590120434761,
-0.011804734356701374,
-0.021901726722717285,
-0.0024725913535803556,
0.04725190997123718,
0.0053579676896333694,
0.029983118176460266,
-0.012915636412799358,
0.02052011899650097,
0.0524829626083374,
0.03683021664619446,
0.029621919617056847,
0.03057992272078991,
0.014138363301753998,
0.00841985922306776,
0.03940926492214203,
-0.011590448208153248,
-0.049530964344739914,
0.057243455201387405,
-0.005817157682031393,
0.004343338776379824,
0.008036618120968342,
-0.0353037565946579,
-0.035653918981552124,
-0.04628140851855278,
-0.015363545157015324,
0.052570641040802,
-0.019355356693267822,
-0.019672349095344543,
-0.0031680031679570675,
-0.04336988925933838,
-0.04236865043640137,
-0.0642729252576828,
-0.013750195503234863,
0.040492236614227295,
-0.03108840435743332,
-0.013943392783403397,
-0.0360235758125782,
-0.004526567179709673,
-0.023738116025924683,
-0.004269114229828119,
0.010356477461755276,
0.06701992452144623,
0.03307390585541725,
-0.021535109728574753,
-0.0002993085654452443,
-0.04434565082192421,
-0.05769475921988487,
0.014568294398486614,
0.039676301181316376,
-0.015696343034505844,
-0.04362456128001213,
-0.003034664550796151,
0.06293164938688278,
-0.022875942289829254,
0.03338818624615669,
-0.0044001322239637375,
0.015071514062583447,
-0.017946060746908188,
-0.10054001957178116,
-0.030754929408431053,
0.024861562997102737,
-0.04735422506928444,
0.0010111226001754403,
-0.06552919745445251,
0.011755484156310558,
0.009491993114352226,
0.10146912932395935,
0.018534282222390175,
0.04013943299651146,
0.007595714181661606,
0.023702597245573997,
0.004377612378448248,
-0.0014096701052039862,
-0.010295705869793892,
0.0029298635199666023,
-0.05949070304632187,
-0.012576837092638016,
-0.05141305923461914,
0.018756194040179253,
0.023949868977069855,
0.023410627618432045,
0.00006477510032709688,
0.056026652455329895,
-0.01722082309424877,
0.03191475197672844,
0.02041555568575859,
-0.016805533319711685,
-0.021335197612643242,
0.05303386598825455,
0.004790256265550852,
-0.015036064200103283,
0.028121445327997208,
-0.045251887291669846,
-0.0034048447851091623,
-0.004480223171412945,
0.035926710814237595,
0.05446286126971245,
-0.08644431829452515,
-0.022199880331754684,
-0.051849365234375,
-0.003725716145709157,
-0.005590646993368864,
-0.05590874329209328,
0.00015819814871065319,
-0.03561310097575188,
0.03263772651553154,
0.008540935814380646,
0.058532774448394775,
0.010155761614441872,
-0.024580471217632294,
0.00022328404884319752,
-0.05025266855955124,
0.02789841964840889,
-0.037796199321746826,
0.012271421030163765,
0.017180582508444786,
-0.07757750153541565,
0.06662161648273468,
-0.0005813136231154203,
0.04098805785179138,
0.004502336494624615,
-0.027940677478909492,
-0.029109692201018333,
0.03942834585905075,
0.01825069449841976,
-0.016555054113268852,
0.023426176980137825,
0.014033710584044456,
0.04390694200992584,
0.03848739340901375,
0.013924927450716496,
-0.03192275017499924,
0.005951006896793842,
-0.0057793473824858665,
0.0385669469833374,
0.01234470121562481,
0.03696451336145401,
0.005016280338168144,
-0.030868571251630783,
-0.016354937106370926,
-0.024825630709528923,
0.02671283483505249,
-0.031576644629240036,
0.011789833195507526,
0.02947559580206871,
-0.03625798597931862,
0.019435178488492966,
0.016192736104130745,
0.027657773345708847,
0.04018145427107811,
-0.0014975442318245769,
-0.007101126946508884,
-0.011415432207286358,
0.015933487564325333,
0.03530789539217949,
0.07094878703355789,
-0.06022626534104347,
0.019004719331860542,
0.05298076197504997,
0.037499334663152695,
0.005493651609867811,
0.029415426775813103,
-0.015584363602101803,
-0.0557907335460186,
0.024803491309285164,
0.006068610120564699,
0.0037114934530109167,
0.034502409398555756,
0.009203857742249966,
0.00332011585123837,
0.0050205048173666,
0.009353594854474068,
-0.05542800948023796,
0.019289331510663033,
-0.02409699745476246,
-0.03206062689423561,
0.03750312700867653,
0.01410750299692154,
0.047205451875925064,
0.035085685551166534,
0.009291388094425201,
0.017994454130530357,
-0.02579420432448387,
0.008946855552494526,
-0.03264154493808746,
-0.003850084962323308,
-0.018285434693098068,
-0.024271421134471893,
-0.022097740322351456,
0.006160293705761433,
0.017622414976358414,
-0.023267263546586037,
-0.0017251850804314017,
0.02377854846417904,
-0.04716220870614052,
0.004751600790768862,
0.0038733347319066525,
0.0204607043415308,
0.038624465465545654,
0.004027393646538258,
0.013642880134284496,
0.0005936106899753213,
0.047920651733875275,
0.0284649059176445,
0.03408613055944443,
0.02009694278240204,
-0.053328316658735275,
-0.005828469526022673,
-0.06244705244898796,
0.00188732473179698,
0.03615175187587738,
0.01865031011402607,
-0.023108715191483498,
-0.012891043908894062,
-0.000006518350801343331,
-0.054173603653907776,
-0.029744617640972137,
-0.01422360260039568,
0.02144109271466732,
-0.0304191242903471,
-0.002336695324629545,
0.022821908816695213,
0.005526901222765446,
-0.03686566278338432,
-0.03596574440598488,
-0.027059709653258324,
-0.021776285022497177,
-0.023079967126250267,
-0.0062119062058627605,
0.010222403332591057,
-0.03414483368396759,
0.039204567670822144,
-0.0021261873189359903,
-0.008684284053742886,
0.002919935155659914,
-0.09132886677980423,
0.01936643198132515,
-0.00196232576854527,
0.013141278177499771,
0.0138247674331069,
0.01997203566133976,
-0.02747022919356823,
0.08746588230133057,
-0.0026927809230983257,
0.002657238394021988,
-0.020119136199355125,
0.03773725405335426,
0.00685912324115634,
-0.03817120939493179,
0.025163711979985237,
0.026844443753361702,
-0.027856172993779182,
0.056864265352487564,
0.011252334341406822,
-0.011073103174567223,
0.04003208503127098,
-0.023454386740922928,
-0.0031586557161062956,
-0.003233167575672269,
-0.02745583839714527,
-0.01680205948650837,
0.06549293547868729,
0.005938767921179533,
0.018353968858718872,
0.024869004264473915,
0.03774077072739601,
-0.004304759670048952,
0.021925698965787888,
-0.03483172878623009,
0.030739611014723778,
-0.025788117200136185,
0.020511966198682785,
0.022072190418839455,
0.046715084463357925,
0.038082316517829895,
-0.020307250320911407,
-0.012871063314378262,
0.018123624846339226,
0.040690891444683075,
-0.042618487030267715,
-0.018724946305155754,
0.042335931211709976,
-0.007664711680263281,
0.012927437201142311,
0.00019304041052237153,
0.020749997347593307,
-0.009891294874250889,
0.027981458231806755,
-0.009679654613137245,
-0.02272702194750309,
-0.014989878982305527,
0.022207848727703094,
-0.01522637065500021,
-0.05269956961274147,
-0.004747136030346155,
-0.0005126102478243411,
-0.0426485538482666,
0.02819361910223961,
-0.04708594083786011,
-0.0012147489469498396,
-0.008651280775666237,
0.07229556888341904,
-0.014301670715212822,
-0.022412898018956184,
-0.0037387635093182325,
0.016486449167132378,
-0.04352743923664093,
-0.002190991770476103,
-0.015765603631734848,
0.03103877231478691,
-0.002146146958693862,
0.012179246172308922,
0.04036429524421692,
-0.027858316898345947,
-0.00402090884745121,
-0.02580714412033558,
-0.02133381925523281,
-0.031057897955179214,
0.030894072726368904,
-0.04999784380197525,
-0.03155502676963806,
-0.04104867950081825,
0.06964670121669769,
0.04985529184341431,
-0.03658723458647728,
0.03324183076620102,
0.059887081384658813,
-0.06733432412147522,
0.03793254867196083,
-0.018580367788672447,
0.029225867241621017,
0.010037529282271862,
0.011182351969182491,
0.029932362958788872,
-0.019633706659078598,
-0.00757526746019721,
-0.03143908083438873,
-0.0008829703438095748,
0.01983305625617504,
0.02834510989487171,
-0.03228024020791054,
-0.002073342213407159,
-0.02455092966556549,
0.02087370865046978,
0.004011489450931549,
0.08443041890859604,
-0.020430859178304672,
0.016611654311418533,
0.0515657402575016,
-0.035900041460990906,
0.02571932226419449,
-0.011454669758677483,
0.03064950928092003,
-0.01318756677210331,
0.0068620238453149796,
-0.020620323717594147,
-0.01753660850226879,
0.002472169231623411,
0.00727933831512928,
0.01461163442581892,
-0.01567276380956173,
-0.0292934849858284,
-0.02444423921406269,
0.048794880509376526,
-0.003006950719282031,
0.007272688206285238,
0.016493959352374077,
0.018691537901759148,
0.06202629953622818,
0.014028426259756088,
0.011866016313433647,
-0.0037748890463262796,
0.03323123976588249,
0.002032943069934845,
0.020220529288053513,
0.007060933858156204,
-0.02564537711441517,
-0.0009632142609916627,
0.027769038453698158,
0.025488529354333878,
-0.016590064391493797,
0.010775670409202576,
-0.041805148124694824,
-0.016241593286395073,
0.05934980511665344,
-0.025287454947829247,
0.04561002552509308,
0.01946363039314747,
-0.01619579643011093,
-0.006310317665338516,
-0.06356136500835419,
-0.06121310964226723,
0.044073037803173065,
-0.02537713758647442,
0.03192546218633652,
-0.050280287861824036,
-0.018935665488243103,
-0.039996758103370667,
-0.028296448290348053,
0.01663358137011528,
0.03326895087957382,
0.021527796983718872,
-0.0019301644060760736,
-0.005302005913108587,
0.03391469642519951,
0.006239320617169142,
-0.06423380970954895,
0.015276561491191387,
-0.0004597152001224458,
-0.03504122048616409,
0.018767204135656357,
-0.06119327247142792,
-0.037871770560741425,
0.0228018369525671,
0.03791000321507454,
0.021002622321248055,
0.046600352972745895,
-0.04396185278892517,
0.019399428740143776,
0.032890524715185165,
-0.01647328957915306,
0.019013836979866028,
-0.005469218827784061,
0.0005313188303261995,
-0.013917735777795315,
-0.025961652398109436,
-0.008261080831289291,
-0.011760418303310871,
-0.00831532757729292,
0.007998212240636349,
-0.005178747233003378,
-0.03418036922812462,
0.052014417946338654,
-0.01849971152842045,
-0.008271162398159504,
-0.017384247854351997,
-0.012636087834835052,
-0.0028832668904215097,
0.05227864533662796,
-0.029443062841892242,
0.00801048707216978,
-0.022919422015547752,
0.025749029591679573,
0.03199734166264534,
0.00431919377297163,
0.006687827408313751,
-0.0445110984146595,
-0.010862528346478939,
0.04620947688817978,
-0.016386715695261955,
-0.006128637120127678,
-0.033503834158182144,
0.009765437804162502,
-0.045503947883844376,
-0.06533899903297424,
0.05956028774380684,
-0.007435968145728111,
-0.005988458637148142,
0.030992358922958374,
-0.025892533361911774,
-0.040106549859046936,
0.013653410598635674,
-0.02399132400751114,
0.004618959967046976,
-0.012091625481843948,
-0.05451975390315056,
0.03788966313004494,
-0.013979888521134853,
-0.057751476764678955,
-0.011226117610931396,
-0.0008822046802379191,
-0.0021614108700305223,
-0.014794874005019665,
0.024455813691020012,
-0.0031952448189258575,
0.01104220375418663,
-0.053663063794374466,
0.002833031117916107,
0.0398273691534996,
-0.052750248461961746,
0.000043164567614439875,
0.018481483682990074,
0.018531572073698044,
0.044663891196250916,
-0.05920463800430298,
-0.01002451404929161,
0.03168351948261261,
-0.023224009200930595,
0.003145738737657666,
-0.007304755039513111,
0.03104333207011223,
-0.00950214546173811,
-0.05344775691628456,
-0.014319464564323425,
-0.0036343797110021114,
0.019351335242390633,
-0.043948352336883545,
-0.03447250649333,
-0.0062166061252355576,
-0.002387674991041422,
-0.012729579582810402,
-0.0168306902050972,
-0.02938990108668804,
-0.0003902134485542774,
0.0004805237695109099,
-0.023823672905564308,
-0.0222689900547266,
-0.03223440423607826,
-0.02254348061978817,
0.034151557832956314,
-0.00888963881880045,
0.018301639705896378,
-0.016872413456439972,
0.06896798312664032,
-0.0068063512444496155,
-0.013024883344769478,
0.03310978412628174,
0.0208895280957222,
-0.02338588424026966,
-0.003135334001854062,
0.030378732830286026,
-0.01793595403432846,
0.006090435665100813,
-0.031431280076503754,
-0.025839289650321007,
0.0013654784997925162,
0.030244488269090652,
0.07551950961351395,
0.05089643970131874,
0.01885329931974411,
0.004803897812962532,
0.020777471363544464,
-0.02276269719004631,
-0.019714273512363434,
-0.03884156420826912,
0.017154701054096222,
-0.02180243842303753,
0.05589897558093071,
-0.038048893213272095,
0.03283904865384102,
0.051194168627262115,
0.07171224802732468,
-0.021686891093850136,
-0.008172090165317059,
0.010302487760782242,
-0.0007162480033002794,
0.012436416000127792,
-0.003412324469536543,
-0.008596156723797321,
0.0510016605257988,
-0.03526460751891136,
0.05843453109264374,
-0.01306183636188507,
0.022357458248734474,
0.018144458532333374,
0.06825663894414902,
0.027242474257946014,
-0.020205505192279816,
0.0019774974789470434,
0.0010377735598012805,
0.01672283001244068,
0.05913466587662697,
-0.016911713406443596,
0.000006433047019527294,
0.020767327398061752,
0.05293377488851547,
-0.006472080945968628,
0.0340607576072216,
-0.03695323318243027,
-0.03084968775510788,
0.01923643797636032,
-0.02539224550127983,
-0.04770345240831375,
0.03704618290066719,
-0.006927343085408211,
-0.0011043515987694263,
-0.0073317475616931915,
0.006852384656667709,
0.019294926896691322,
0.04256901144981384,
-0.0039062160067260265,
-0.03035910800099373,
0.07271646708250046,
-0.009400755167007446,
0.022601688280701637,
0.015074077993631363,
-0.0009814921068027616,
0.1270240843296051,
-0.009725045412778854,
0.03969912230968475,
-0.06014522537589073,
0.023638322949409485,
0.015119700692594051,
0.007108651101589203,
-0.04385989531874657,
0.0276514682918787,
-0.01545837800949812,
-0.018304117023944855,
-0.011411424726247787,
0.04653774946928024,
-0.03717237710952759,
0.0025123371742665768,
0.008493458852171898,
-0.01973831281065941,
-0.013417753390967846,
-0.04196539521217346,
0.009444722905755043,
0.01420830562710762,
0.04605782404541969,
-0.039224397391080856,
0.015167771838605404,
-0.06318826228380203,
0.01987878791987896,
-0.024508249014616013,
-0.028468653559684753,
0.006964914966374636,
0.002742792246863246,
-0.029814397916197777,
0.025662777945399284,
-0.0023086904548108578,
0.016914451494812965,
0.017949342727661133,
0.03608887270092964,
0.022985732182860374,
0.008539610542356968,
0.05853855609893799,
0.039852216839790344,
-0.013625993393361568,
0.04854011535644531,
0.03518051281571388,
0.005475870333611965,
-0.057517509907484055,
-0.013898457400500774,
-0.06199701875448227,
0.08256155997514725,
-0.024541884660720825,
-0.022914055734872818,
0.015909021720290184,
-0.0422096848487854,
0.00784462969750166,
-0.058374661952257156,
0.01274913176894188,
0.022400466725230217,
0.007232903968542814,
-0.05135701596736908,
-0.0009597103344276547,
0.0008174125687219203,
0.025866355746984482,
0.05752260982990265,
0.0253253486007452,
-0.01380977313965559,
-0.027077261358499527,
-0.03733138367533684,
0.00409723212942481,
0.03151118755340576,
-0.002438947558403015,
-0.026940105482935905,
-0.010768122039735317,
-0.018604392185807228,
-0.038186151534318924,
-0.021866440773010254,
0.009529104456305504,
0.0032775034196674824,
0.025057312101125717,
0.011850916780531406,
-0.03310086950659752,
-0.03147377073764801,
-0.07270406186580658,
-0.024914346635341644,
0.0009518996230326593,
-0.051413167268037796,
0.02208734303712845,
-0.02262268029153347,
0.03503274545073509,
0.03096177615225315,
-0.02475597895681858,
-0.03444407507777214,
0.009248326532542706,
0.06862432509660721,
0.024036921560764313,
-0.04009418562054634,
-0.035443633794784546,
0.014505334198474884,
-0.016052475199103355,
0.007883962243795395,
-0.011085527017712593,
0.005248675122857094,
0.032018546015024185,
0.02948582172393799,
-0.0036944723688066006,
0.030463838949799538,
-0.016231756657361984,
-0.006902346853166819,
0.0044853417202830315,
-0.027830861508846283,
-0.009905408136546612,
0.015997223556041718,
0.007827681489288807,
-0.021602509543299675,
0.002239524619653821,
0.015624216757714748,
0.002716651652008295,
0.01125611737370491,
-0.02971191518008709,
-0.02937505766749382,
-0.03499352186918259,
-0.006451261229813099,
-0.0037309357430785894,
-0.008974039927124977,
-0.0011351010762155056,
-0.021574852988123894,
0.02129342034459114,
-0.0054466440342366695,
-0.005927630700170994,
-0.0012502472382038832,
0.03185112401843071,
-0.02356230467557907,
-0.02088625356554985,
0.052804503589868546,
0.05061629042029381,
-0.023304203525185585,
-0.028999818488955498,
0.030875829979777336,
-0.012833354994654655,
0.013879910111427307,
-0.00804111361503601,
-0.05259111151099205,
-0.010933514684438705,
0.009670094586908817,
-0.032907530665397644,
0.016176322475075722,
0.010631143115460873,
0.05193150416016579,
0.011187653057277203,
-0.01978040672838688,
-0.04168421030044556,
0.031429972499608994,
-0.014961308799684048,
-0.0138382064178586,
-0.039353277534246445,
-0.003015211783349514,
0.018027059733867645,
-0.04592568427324295,
0.038947153836488724,
-0.036523766815662384,
0.0019063923973590136,
0.039769504219293594,
0.0073882401920855045,
-0.06862732023000717,
0.001893256907351315,
0.003324661636725068,
0.0353471077978611,
0.03265025466680527,
0.011512666940689087,
0.013029567897319794,
0.03001180849969387,
0.001457018661312759,
-0.03430572897195816,
0.04790147766470909,
0.020051775500178337,
-0.013854388147592545,
-0.07934331893920898,
-0.005305424798280001,
-0.004219635855406523,
0.03553426265716553,
0.07364023476839066,
-0.07907861471176147,
0.012900437228381634,
0.04478180781006813,
-0.042112573981285095,
-0.01397384237498045,
-0.020413033664226532,
-0.004608228337019682,
-0.00944338645786047,
-0.0033854814246296883,
-0.024849556386470795,
0.005925914738327265,
0.017153996974229813,
0.04260465130209923,
0.016679754480719566,
0.02726242132484913,
-0.029370445758104324,
-0.05093510448932648,
-0.03789682313799858,
0.005702935624867678,
0.002475365763530135,
-0.01564069278538227,
0.0749417170882225,
-0.021277207881212234,
0.01668022945523262,
0.018407810479402542,
-0.02392970584332943,
0.0009358985698781908,
-0.02326291985809803,
0.026219118386507034,
-0.024544209241867065,
0.04076706990599632,
-0.03096894919872284,
-0.01704588532447815,
-0.007279584184288979,
-0.032835423946380615,
0.05213017016649246,
0.025808217003941536,
-0.03500332310795784,
-0.010067257098853588,
0.0009954078122973442,
-0.022357439622282982,
-0.03992090001702309,
0.03539286181330681,
-0.002966874511912465,
-0.01552722230553627,
0.03425213694572449,
0.004427273292094469,
-0.007199662737548351,
-0.05670442432165146,
0.06837724894285202,
-0.017881620675325394,
0.03816630318760872,
0.002458761213347316,
0.02535058930516243,
0.0035247961059212685,
0.021161450073122978,
-0.008829724043607712,
-0.05073273181915283,
0.060819827020168304,
0.005137160886079073,
-0.03310151770710945,
-0.030190492048859596,
0.025208372622728348,
0.022378193214535713,
0.0026809521950781345,
-0.01163073256611824,
-0.0056106336414813995,
-0.04333336278796196,
0.020023100078105927,
0.007566547486931086,
0.02609526552259922,
-0.028626492246985435,
0.012949483469128609,
-0.022569771856069565,
-0.06532011926174164,
0.0047845616936683655,
0.019065171480178833,
-0.04240969195961952,
0.01276944950222969,
-0.025003626942634583,
0.013608594425022602,
0.008483202196657658,
0.08655652403831482,
-0.010938132181763649,
-0.00872127152979374,
0.008906603790819645,
0.007160834968090057,
-0.009902254678308964,
-0.07052911072969437,
0.017131591215729713,
-0.011109394952654839,
-0.0005184754845686257,
0.023401005193591118,
0.0005026810686104,
-0.01623457297682762,
0.03639712184667587,
0.019033219665288925,
0.026904573664069176,
-0.0235283263027668,
0.03975481912493706,
-0.055671416223049164,
0.033335041254758835,
-0.021942362189292908,
-0.014534489251673222,
0.05753631144762039,
0.046515967696905136,
-0.011272290721535683,
-0.0005684506613761187,
-0.05336368829011917,
-0.05286289379000664,
0.013322784565389156,
-0.038275282829999924,
-0.016035879030823708,
-0.03988557308912277,
-0.004085664637386799,
0.04526602476835251,
-0.015579837374389172,
0.0004280232824385166,
0.0301208533346653,
-0.02890542335808277,
-0.021616986021399498,
0.025532156229019165,
-0.006346849724650383,
0.013527372851967812,
0.008770018815994263,
0.025897357612848282,
-0.011674284934997559,
-0.0031039982568472624,
0.06413193792104721,
0.010383760556578636,
0.007309910375624895,
0.015131388790905476,
-0.02856202982366085,
0.017535345628857613,
-0.019130181521177292,
0.02817596308887005,
-0.025454198941588402,
0.01456291414797306,
0.008821568451821804,
0.005604847799986601,
0.056339532136917114,
-0.06699482351541519,
-0.02886311523616314,
0.026200486347079277,
-0.004819427616894245,
0.05019645020365715,
-0.015290001407265663,
-0.00024084761389531195,
-0.020307259634137154,
-0.023782925680279732,
0.00446812529116869,
0.0007664400618523359,
0.03698145970702171,
-0.005220276769250631,
0.0108686788007617,
-0.01047159917652607,
-0.014910954050719738,
-0.03166176378726959,
0.015192140825092793,
-0.014187687076628208,
0.024742180481553078,
0.04231511428952217,
-0.0021620227489620447,
-0.008883300237357616,
-0.050069041550159454,
0.016082951799035072,
-0.03818529099225998,
0.009961755014955997,
0.03514799475669861,
0.01402090210467577,
-0.01671672984957695,
-0.008117730729281902,
-0.03797680512070656,
0.04250713065266609,
-0.04407762363553047,
-0.0589979849755764,
0.004346266854554415,
0.017762938514351845,
0.003422333160415292,
0.007140865083783865
] |
<p>I have searched around the web and looked at Wiki entries and I am overcome by the number of catalogs available. What I want is a catalog that includes all objects you might conceivably see with equipment under $500k (I hope that captures all backyard astronomers).</p>
<p>Apart from that the main requirements are that it is up to date, machine readable (CSV is relatively easy. SQL might be too much to hope for?) and free to use. </p>
<p>Can anyone say which catalog would be best for that purpose and where I can get it?</p>
<p>(Is there one numbering system used for stars? I'm seeing HDE, SAO and Gliese numbers, Bayer and Flamsteed designations and proper names e.g. Rigol. If there isn't a universally identified system there must be some kind of cross reference? Thinking like a programmer - what's my primary key?)</p>
<p>While Physics isn't my first choice for this question the SE Astronomy site didn't make it through beta, and its page now directs users here.</p>
| 7,663 |
[
-0.032180603593587875,
-0.04539044201374054,
-0.028730789199471474,
-0.010282215662300587,
0.037154421210289,
0.010549555532634258,
-0.020322119817137718,
-0.015742288902401924,
0.008106245659291744,
-0.04926983639597893,
0.018013043329119682,
0.06343164294958115,
0.01973065175116062,
0.03031456284224987,
0.027365321293473244,
0.0006333364290185273,
-0.011347182095050812,
-0.03728358447551727,
-0.025162044912576675,
-0.008536060340702534,
0.018133249133825302,
-0.01148280780762434,
0.022503573447465897,
0.016376590356230736,
-0.04367534816265106,
0.045544352382421494,
0.004813306964933872,
0.030250566080212593,
0.011903907172381878,
0.06529205292463303,
-0.034176286309957504,
-0.01363772340118885,
0.013601054437458515,
0.04766811057925224,
0.008942433632910252,
-0.00026868359418585896,
-0.019739167764782906,
-0.016718801110982895,
-0.03298681974411011,
-0.003165802452713251,
-0.04213179647922516,
-0.01626129448413849,
0.004410381428897381,
0.01167004182934761,
-0.014859656803309917,
-0.015277977101504803,
-0.014326932840049267,
-0.01060002576559782,
0.01095790695399046,
-0.046512421220541,
0.042924415320158005,
0.003164566121995449,
0.06636683642864227,
0.025128155946731567,
-0.025485137477517128,
0.004826006945222616,
0.05143433436751366,
0.07664766162633896,
-0.00968940183520317,
-0.03390087932348251,
-0.02882065623998642,
-0.0087577560916543,
0.014819514937698841,
-0.02313723973929882,
-0.01828431896865368,
0.05479710176587105,
-0.05441437289118767,
-0.008834979496896267,
0.018775878474116325,
0.0258957352489233,
0.01978609897196293,
0.017282307147979736,
0.03772648051381111,
-0.006938466336578131,
-0.0023884368129074574,
-0.041886694729328156,
0.016157934442162514,
-0.019185293465852737,
0.027072956785559654,
0.04830346256494522,
-0.019217969849705696,
0.005418956279754639,
0.008094570599496365,
0.03544482961297035,
0.049142614006996155,
-0.02292614057660103,
0.056403424590826035,
-0.006615662481635809,
-0.008418964222073555,
-0.013168559409677982,
0.009158067405223846,
0.029661044478416443,
0.047190286219120026,
-0.015378241427242756,
-0.032563719898462296,
0.036090508103370667,
-0.023469969630241394,
0.04694404453039169,
-0.020940672606229782,
-0.026173805817961693,
0.03084365837275982,
0.01404485572129488,
-0.012427878566086292,
0.0612211711704731,
-0.0044728838838636875,
-0.0023313695564866066,
-0.04928691312670708,
-0.03584606200456619,
-0.03537910804152489,
-0.007362262345850468,
-0.01371446717530489,
0.01630675233900547,
0.017461733892560005,
-0.005073077045381069,
0.021512962877750397,
-0.04127664864063263,
-0.005273543763905764,
0.01930670253932476,
0.06265614181756973,
0.05422944948077202,
0.07670743018388748,
-0.030000552535057068,
0.022376837208867073,
-0.028861641883850098,
-0.053443994373083115,
0.009978827089071274,
0.026460805907845497,
-0.020238110795617104,
-0.01048438623547554,
0.024102067574858665,
-0.025436948984861374,
-0.01499083824455738,
0.053419820964336395,
-0.025824442505836487,
0.02329125441610813,
-0.03163160756230354,
-0.07815291732549667,
-0.06757158041000366,
0.007398457266390324,
0.012490704655647278,
-0.018713129684329033,
-0.06045808270573616,
0.046969205141067505,
0.002006211318075657,
0.04488242417573929,
0.0030650196131318808,
-0.0005545313470065594,
0.02359982579946518,
0.052067019045352936,
-0.009186830371618271,
-0.05712268128991127,
-0.017074499279260635,
-0.0030463167931884527,
-0.00820810254663229,
0.0023815524764358997,
-0.06402088701725006,
0.023112930357456207,
-0.006465577986091375,
0.026939207687973976,
-0.04064227268099785,
0.08080504834651947,
-0.03134894371032715,
-0.016287382692098618,
-0.012143203988671303,
0.03728548809885979,
-0.027619101107120514,
0.08009159564971924,
0.011915181763470173,
0.015675822272896767,
0.039425354450941086,
-0.009197366423904896,
0.02571919560432434,
0.026623399928212166,
-0.00828240904957056,
0.06926513463258743,
-0.034955210983753204,
-0.01159064844250679,
-0.012556701898574829,
0.02363889291882515,
-0.008046400733292103,
-0.009519532322883606,
-0.040465205907821655,
-0.01146500650793314,
-0.010411527007818222,
0.037476055324077606,
0.02165113016963005,
0.044500019401311874,
-0.0025782575830817223,
0.047035571187734604,
-0.04917478561401367,
-0.036883722990751266,
-0.03498305007815361,
-0.02011193335056305,
-0.027537357062101364,
-0.019072234630584717,
0.026086151599884033,
0.0356128066778183,
0.007260143291205168,
0.01735650934278965,
-0.020421378314495087,
0.0018564211204648018,
0.02512074075639248,
0.024952935054898262,
-0.031322069466114044,
0.021674109622836113,
0.03900415077805519,
0.05860677361488342,
-0.02783026546239853,
0.027572978287935257,
-0.00700945220887661,
-0.06948292255401611,
-0.004818575456738472,
0.01024301815778017,
0.0164056234061718,
0.011929427273571491,
0.02488722838461399,
0.00949839223176241,
0.014496183954179287,
0.004766971804201603,
0.020805208012461662,
-0.020801715552806854,
0.07597555965185165,
0.020463941618800163,
0.012075753882527351,
0.027498912066221237,
0.01823742315173149,
0.012990595772862434,
-0.006116937845945358,
-0.031256891787052155,
0.03022799640893936,
-0.04852929711341858,
-0.0015899715945124626,
0.06332144141197205,
-0.002317392732948065,
-0.038906361907720566,
0.03762183338403702,
0.05779017135500908,
0.01822442002594471,
0.06726280599832535,
0.001190811744891107,
-0.04274463281035423,
-0.03565974533557892,
-0.01881205104291439,
0.009337438270449638,
-0.00021853459475096315,
0.05389624461531639,
0.008105020970106125,
-0.0003671041049528867,
0.025226181373000145,
-0.023218069225549698,
-0.0108122443780303,
0.02359187975525856,
-0.007918001152575016,
0.011213094927370548,
-0.005049893166869879,
-0.05170943960547447,
0.07432006299495697,
-0.013671976514160633,
0.0222448892891407,
-0.006547984667122364,
0.012036233209073544,
0.0033038565889000893,
-0.04275478422641754,
0.001680067041888833,
0.014485056512057781,
0.017283717170357704,
-0.03988288715481758,
-0.012146738357841969,
0.01727699488401413,
-0.05876431241631508,
0.06733575463294983,
-0.02844364382326603,
-0.015345386229455471,
-0.07230556756258011,
-0.0009485583868809044,
0.0004174275672994554,
0.01854507066309452,
0.018512818962335587,
-0.01734023168683052,
-0.03776688128709793,
0.009305176325142384,
-0.02561834640800953,
-0.0076332432217895985,
0.046320945024490356,
-0.039317481219768524,
-0.007267273496836424,
-0.006176494527608156,
-0.04772516340017319,
0.06170794740319252,
-0.0036336376797407866,
-0.02568000741302967,
0.010633616708219051,
-0.004928313195705414,
-0.04073389247059822,
0.0014471265021711588,
-0.011236987076699734,
-0.0024265600368380547,
-0.051380276679992676,
-0.004622127395123243,
0.03661360591650009,
-0.02096019871532917,
-0.041108276695013046,
-0.03201569989323616,
-0.06594835966825485,
-0.05182083323597908,
-0.03497335687279701,
0.021235058084130287,
-0.017123110592365265,
-0.05904390290379524,
-0.02967001684010029,
0.03484361618757248,
-0.014346986077725887,
0.015953345224261284,
-0.0103253573179245,
-0.05330710485577583,
0.010123088955879211,
0.006109712645411491,
0.007525986526161432,
0.02207004465162754,
0.015167757868766785,
0.01828649267554283,
0.0642872005701065,
-0.017022233456373215,
-0.03249799832701683,
0.008003261871635914,
0.021614601835608482,
-0.031283654272556305,
0.011705413460731506,
-0.026008054614067078,
-0.01833491399884224,
-0.009596919640898705,
0.014792775735259056,
-0.029067406430840492,
0.012718221172690392,
0.015495361760258675,
0.015271359123289585,
0.0006004906026646495,
-0.016404490917921066,
0.007493496872484684,
0.06295333802700043,
0.050885625183582306,
-0.05492822825908661,
0.00621240446344018,
-0.021896885707974434,
0.021292071789503098,
0.03921952471137047,
-0.029901377856731415,
0.013431730680167675,
-0.019958628341555595,
-0.0013503608061000705,
-0.010473649017512798,
-0.04626549780368805,
0.027795447036623955,
-0.010722472332417965,
0.015219899825751781,
-0.0017707495717331767,
0.019158901646733284,
0.01313322689384222,
-0.02069978602230549,
0.005608581006526947,
0.029942817986011505,
-0.008589125238358974,
-0.01988327130675316,
-0.01319840643554926,
-0.02619577944278717,
-0.02370641939342022,
-0.01601250283420086,
0.006773667875677347,
0.028862494975328445,
0.039192084223032,
0.04357444494962692,
-0.024346595630049706,
-0.038436826318502426,
0.018452303484082222,
-0.06157121807336807,
-0.016933677718043327,
-0.06187518313527107,
0.04601578414440155,
-0.007203906308859587,
0.03567657247185707,
0.0003054398111999035,
-0.016427304595708847,
0.004253183025866747,
0.02771482989192009,
-0.06768769770860672,
0.039599377661943436,
-0.028095075860619545,
0.0036175581626594067,
-0.01068731676787138,
0.02295747399330139,
-0.04548369720578194,
0.021261947229504585,
-0.006325224414467812,
-0.03257173299789429,
-0.015898743644356728,
-0.039455778896808624,
-0.014728762209415436,
-0.027460016310214996,
-0.030410267412662506,
0.003010660409927368,
0.026287592947483063,
0.010261712595820427,
0.000025318731786683202,
0.030206846073269844,
0.007844353094696999,
0.013700497336685658,
-0.04447578266263008,
-0.012577138841152191,
0.04127127304673195,
-0.018237581476569176,
0.0167170949280262,
0.010122571140527725,
0.03960251808166504,
-0.03698759526014328,
-0.027199722826480865,
-0.0029735288117080927,
0.03102184645831585,
-0.006689782720059156,
0.013668574392795563,
0.020844485610723495,
-0.05592288449406624,
-0.012149062007665634,
0.007648209575563669,
0.04350753501057625,
0.0032969601452350616,
-0.01311037689447403,
0.04540985822677612,
0.0036873200442641973,
-0.04484999552369118,
0.01109616830945015,
0.05281899869441986,
-0.03209933266043663,
-0.018823161721229553,
-0.0037048286758363247,
-0.028313327580690384,
-0.031059689819812775,
0.007845407351851463,
0.012155774980783463,
0.07988306879997253,
-0.01583186350762844,
-0.012863921001553535,
-0.014156143181025982,
-0.01332104578614235,
-0.025643551722168922,
0.014944841153919697,
0.00123147526755929,
0.036505937576293945,
-0.03726918622851372,
0.006368041969835758,
0.03934936970472336,
0.04128822684288025,
0.05761232227087021,
-0.0034425368066877127,
0.006953184027224779,
-0.0827995166182518,
-0.016117528080940247,
0.037002529948949814,
0.04415135458111763,
-0.022037670016288757,
-0.06221954524517059,
-0.055650949478149414,
-0.046425748616456985,
0.025352058932185173,
-0.031933482736349106,
0.003120274981483817,
-0.03641640394926071,
-0.01871567778289318,
0.018785543739795685,
-0.006032487377524376,
-0.009823874570429325,
0.018626360222697258,
0.02795993909239769,
0.037349093705415726,
0.0014764623483642936,
0.04742561653256416,
-0.044772226363420486,
0.0389632023870945,
0.026743551716208458,
0.04256363585591316,
0.003176184371113777,
-0.034902557730674744,
0.03964722529053688,
-0.003513893811032176,
-0.03691038861870766,
-0.047303758561611176,
-0.022652210667729378,
-0.02097698301076889,
0.004615506157279015,
0.04939192160964012,
-0.0267022717744112,
-0.02691337652504444,
0.017666738480329514,
0.02865702472627163,
-0.03566141054034233,
-0.003539178753271699,
-0.004998846910893917,
0.01630505360662937,
0.03522927686572075,
0.039539456367492676,
0.06798248738050461,
0.024934997782111168,
-0.026238352060317993,
0.03498303145170212,
-0.040538620203733444,
0.01774565316736698,
-0.047607362270355225,
-0.021059351041913033,
-0.032165952026844025,
-0.015012762509286404,
-0.07012224197387695,
0.030128154903650284,
-0.04002300277352333,
0.015856405720114708,
-0.0035135182552039623,
-0.023766670376062393,
-0.025100819766521454,
0.04388085752725601,
-0.010260959155857563,
0.01664005033671856,
0.012778055854141712,
0.05040842667222023,
0.014538886025547981,
-0.00811189878731966,
0.04499822109937668,
0.013750291429460049,
-0.010679125785827637,
-0.0171196348965168,
-0.01914839819073677,
0.014496859163045883,
-0.04318930581212044,
-0.013361426070332527,
-0.004588133655488491,
-0.013093782588839531,
0.07146172970533371,
0.01745867170393467,
0.060774676501750946,
0.05635645240545273,
-0.09638121724128723,
-0.0466790534555912,
-0.02651429921388626,
-0.03167974203824997,
0.011491378769278526,
-0.03048637881875038,
0.02016293816268444,
-0.025906896218657494,
0.024862857535481453,
-0.06277842074632645,
-0.01334882527589798,
0.0112119996920228,
0.01489096786826849,
-0.02189820073544979,
-0.015576604753732681,
0.0431240014731884,
-0.02038179151713848,
0.014558658003807068,
-0.00340055744163692,
0.06651055067777634,
-0.031034650281071663,
0.008201047778129578,
0.01398967020213604,
0.044040389358997345,
0.043832894414663315,
-0.02270265482366085,
-0.0010910253040492535,
0.02291206456720829,
0.03784756362438202,
0.003397766500711441,
-0.010251788422465324,
0.06255082786083221,
-0.03471394255757332,
-0.04613808915019035,
-0.019450001418590546,
0.0026255070697516203,
0.02459121122956276,
-0.028197579085826874,
0.04154563322663307,
0.0009932151297107339,
-0.021482834592461586,
-0.014519931748509407,
-0.01730697602033615,
0.034416668117046356,
-0.023764517158269882,
0.007464468479156494,
-0.05601075291633606,
-0.02397366799414158,
0.015254872851073742,
-0.020733172073960304,
0.018862761557102203,
0.002461738884449005,
0.03669053316116333,
0.018581926822662354,
0.009913803078234196,
0.010768587701022625,
-0.0003725197457242757,
0.01860843598842621,
-0.01242042426019907,
-0.0054639363661408424,
0.022254183888435364,
0.027664341032505035,
0.0030392867047339678,
-0.018091486766934395,
-0.014958396553993225,
-0.0155978137627244,
-0.01869112066924572,
-0.02665955014526844,
0.06034306064248085,
0.02600208856165409,
0.044266365468502045,
0.0077727618627250195,
0.00019550652359612286,
0.006619144696742296,
-0.02486211434006691,
-0.02421448566019535,
0.014522187411785126,
0.03228076547384262,
0.01223234087228775,
-0.0224462877959013,
0.004211087711155415,
0.0054413634352386,
0.010007159784436226,
0.046331506222486496,
0.03914155811071396,
0.03872346505522728,
0.03603057935833931,
-0.008243191987276077,
-0.05068514496088028,
-0.010267501696944237,
0.05571037530899048,
-0.022297712042927742,
0.020783601328730583,
0.029393335804343224,
-0.028438035398721695,
0.01108370441943407,
0.004758494906127453,
-0.002935322467237711,
-0.026909522712230682,
-0.010493157431483269,
-0.03801831975579262,
0.01958337053656578,
0.049504876136779785,
0.014118236489593983,
-0.007441805675625801,
-0.011372593231499195,
0.0028933717403560877,
0.0001840633194660768,
0.024560632184147835,
-0.004565373063087463,
-0.05956536903977394,
-0.04315662384033203,
-0.026962848380208015,
-0.07263544946908951,
0.05447953939437866,
0.034068331122398376,
-0.012235392816364765,
-0.0452827587723732,
-0.01510757114738226,
-0.010390172712504864,
-0.0011579992715269327,
0.028241928666830063,
-0.022114256396889687,
0.03187186270952225,
-0.029132382944226265,
0.018847450613975525,
-0.008222639560699463,
-0.0037279364187270403,
0.13624289631843567,
0.028393007814884186,
0.027936214581131935,
-0.022046027705073357,
-0.004538267385214567,
0.00909952912479639,
0.008978880010545254,
-0.04117931053042412,
0.03718412667512894,
-0.006034875754266977,
-0.00036488103796727955,
0.017989879474043846,
0.049816444516181946,
0.009183059446513653,
-0.0008754577138461173,
0.0778670608997345,
-0.0026761970948427916,
-0.011031241156160831,
0.005356974899768829,
0.03250494226813316,
0.030199900269508362,
0.023367390036582947,
-0.04603854566812515,
0.03890940919518471,
0.007389067206531763,
-0.006837766617536545,
-0.02350117638707161,
-0.04440534859895706,
0.026221992447972298,
0.0293326023966074,
-0.015984445810317993,
0.0013290147762745619,
0.025044746696949005,
-0.018897362053394318,
0.010971790179610252,
0.014762995764613152,
0.0424695685505867,
0.00651215948164463,
0.006809401325881481,
0.03615492954850197,
-0.014575825072824955,
0.01449653785675764,
-0.012470316141843796,
-0.002501033479347825,
-0.022879470139741898,
-0.016136247664690018,
-0.05318402126431465,
0.022036533802747726,
-0.037872668355703354,
-0.0012343351263552904,
-0.045879192650318146,
0.0028228177689015865,
0.00019140866061206907,
-0.05102385953068733,
0.007963063195347786,
0.014934051781892776,
-0.004376293625682592,
-0.036080166697502136,
-0.04332125559449196,
-0.019110308960080147,
0.05408841744065285,
-0.007477061823010445,
0.026466626673936844,
-0.02657669223845005,
-0.01875699684023857,
-0.004050528164952993,
-0.037411198019981384,
-0.005428148899227381,
0.013186792843043804,
-0.011519571766257286,
-0.008987617678940296,
0.001351617742329836,
-0.05171304568648338,
-0.0322839617729187,
0.008643162436783314,
0.03801235184073448,
0.020481042563915253,
0.02064397931098938,
0.0019609713926911354,
-0.022231265902519226,
-0.030382944270968437,
0.020936258137226105,
-0.015898220241069794,
-0.04641185328364372,
-0.0194801464676857,
-0.023046236485242844,
0.0127589525654912,
-0.0018641592469066381,
0.013416510075330734,
0.04993017762899399,
0.007782739121466875,
0.04407886043190956,
0.025290019810199738,
0.00830801110714674,
-0.02839265577495098,
0.01570194959640503,
-0.04820873960852623,
0.021616753190755844,
-0.02011656016111374,
0.0353858508169651,
0.015095123089849949,
0.01063393335789442,
0.04328082874417305,
0.023389730602502823,
-0.030625762417912483,
0.025427130982279778,
-0.021616466343402863,
-0.04480273649096489,
-0.007256342563778162,
-0.026138072833418846,
0.03875783830881119,
-0.009364224039018154,
-0.05516711249947548,
-0.03967565298080444,
0.01996033824980259,
-0.025800606235861778,
0.005245869047939777,
-0.04376501962542534,
0.05774376913905144,
-0.05248007923364639,
-0.0073082465678453445,
-0.039622075855731964,
0.01923760585486889,
-0.03314061835408211,
0.01417536847293377,
-0.011359906755387783,
0.009077331982553005,
-0.0032582730054855347,
0.009737704880535603,
-0.01851917989552021,
-0.04308155179023743,
-0.016150709241628647,
-0.018411360681056976,
-0.012692345306277275,
0.013311428017914295,
-0.01515459269285202,
-0.04193345829844475,
0.052290525287389755,
-0.014444826170802116,
0.011298757046461105,
0.006815081462264061,
-0.01991281844675541,
-0.06387902796268463,
0.022884519770741463,
-0.03276513144373894,
0.018884265795350075,
0.03207648918032646,
-0.03465297073125839,
-0.038198262453079224,
0.07239016145467758,
-0.029134735465049744,
-0.046550583094358444,
-0.00027928792405873537,
0.028049232438206673,
0.058710161596536636,
0.031150171533226967,
0.038757797330617905,
-0.025461073964834213,
-0.026351967826485634,
0.018776798620820045,
0.011007154360413551,
0.028940390795469284,
-0.0032225162722170353,
0.007387065794318914,
-0.026700826361775398,
0.010480117052793503,
0.012304170057177544,
0.005313614383339882,
0.029088275507092476,
0.0012699248036369681,
-0.062476709485054016,
0.07931114733219147,
0.06539204716682434,
0.011455644853413105,
-0.04015034809708595,
-0.0010061830980703235,
-0.02136911265552044,
0.0166639257222414,
0.041917625814676285,
-0.07073009014129639,
0.02973298355937004,
0.03635229915380478,
-0.07265141606330872,
0.019075101241469383,
-0.03597448021173477,
-0.04135224223136902,
-0.02560315653681755,
0.018551118671894073,
0.023219605907797813,
0.020477043464779854,
0.018691156059503555,
-0.01289350539445877,
0.013954346999526024,
-0.003697543404996395,
0.0001554918708279729,
-0.000524562259670347,
0.00037210332811810076,
0.007489162031561136,
0.004998266696929932,
-0.025245830416679382,
0.05030931904911995,
-0.03065132349729538,
-0.03660358116030693,
0.03708770126104355,
0.025298235937952995,
0.01444555539637804,
0.00923869851976633,
0.0017737080343067646,
-0.014105570502579212,
0.03314146026968956,
0.04028264433145523,
-0.012403670698404312,
-0.005128846969455481,
0.024814480915665627,
0.037052299827337265,
0.057149745523929596,
0.027476370334625244,
-0.008130613714456558,
0.033142752945423126,
-0.02124321088194847,
-0.0321456678211689,
0.028790690004825592,
-0.006851749494671822,
0.03596506267786026,
-0.01920153945684433,
-0.020531494170427322,
0.027439458295702934,
0.00851905532181263,
0.0029072368051856756,
-0.05669378116726875,
0.01685543730854988,
0.036185797303915024,
-0.03145477920770645,
0.056761253625154495,
0.005721034482121468,
0.007813308387994766,
-0.044894926249980927,
0.004688543733209372,
0.015195815823972225,
0.013209291733801365,
-0.04667140170931816,
-0.021959897130727768,
0.04495774582028389,
-0.03254201263189316,
0.01771264709532261,
0.0013852623524144292,
-0.041288942098617554,
0.05945358797907829,
-0.0005547098116949201,
-0.017771532759070396,
0.044598955661058426,
-0.0202585831284523,
-0.009955679066479206,
-0.0440669059753418,
0.00939021073281765,
0.019221918657422066,
0.016112837940454483,
-0.024423005059361458,
-0.03184597194194794,
-0.002801697002723813,
-0.03408980369567871,
0.03932207077741623,
-0.0328049473464489,
-0.008007442578673363,
-0.023704499006271362,
-0.019327888265252113,
0.03338991105556488,
-0.07489220798015594,
0.03630160167813301,
-0.0008905448485165834,
-0.05592498555779457,
-0.02010943554341793,
-0.013438191264867783,
-0.0028169050347059965,
0.0028626276180148125,
0.05524175614118576,
-0.021475305780768394,
0.03750215470790863,
0.00869329646229744,
-0.024507727473974228,
0.03024863637983799,
0.023072071373462677,
-0.02621355839073658,
0.043477192521095276,
0.002755572088062763,
0.0019586693961173296,
0.04251692071557045,
0.0011471161851659417,
-0.0068219322711229324,
0.046620629727840424,
-0.04976658523082733,
-0.044467195868492126,
0.012681243009865284,
0.025139959529042244,
-0.021166423335671425,
-0.05084234103560448,
0.0423528254032135,
0.02094600349664688,
0.00998596753925085,
-0.020812736824154854,
0.04803488776087761,
-0.016182953491806984,
0.05204015597701073,
0.0017906276043504477,
0.044483061879873276,
0.04379485547542572,
-0.03641437739133835,
-0.019157757982611656,
0.021959366276860237,
0.024547941982746124,
0.020955704152584076,
0.04050508141517639,
0.012775504030287266,
0.015743225812911987,
0.010048645548522472,
-0.006411585956811905,
0.07525905221700668,
-0.029253238812088966,
0.005521566141396761,
0.03542190417647362,
0.020524343475699425,
0.028010498732328415,
0.029967887327075005,
-0.013771547935903072,
0.07019556313753128,
-0.028691504150629044,
-0.013997499831020832,
-0.05840848758816719,
0.01597409136593342,
-0.02268197573721409,
-0.016518142074346542,
-0.051834285259246826,
0.029016008600592613,
-0.043986834585666656,
0.0011014981428161263,
-0.04842984303832054,
0.02050349861383438,
0.04154690355062485,
-0.06705208122730255,
0.03155166655778885,
0.006921140942722559,
0.03662382438778877,
-0.005064953584223986,
0.03224391117691994,
-0.007509724237024784,
-0.015176034532487392,
-0.008964598178863525,
0.06574854254722595,
-0.011812913231551647,
-0.02219112031161785,
-0.009221507236361504,
-0.0405566431581974,
0.015322395600378513,
-0.05482824891805649,
0.011768457479774952,
-0.0244283489882946,
0.009582459926605225,
-0.00811730045825243,
-0.013268919661641121
] |
<p>(Rest) mass of proton = (rest) mass of neutron (approximately) = $1.67 \times 10^{-27}$ kg.</p>
<p>let $m$ be the mass of nitrogen atom then $m = 2.32 \times 10^{-26}$ kg.</p>
<p>$c = 3 \times 10^8$ m/s (approx).</p>
<p>Energy $E = mc^2$.</p>
<p>$E = 2.32 \times 10^{-26} \times 3 \times 10^8 \times 3 \times 10^8$ Joules.</p>
<p>$E = 20.88 \times 10^{-26+16}$ Joules.</p>
<p>$E = 20.88 \times 10^{-10}$ Joules.</p>
<p>Energy required to propel a nitrogen atom at the speed of light is very less. Is my calculation wrong?</p>
<p>Because even if we take a cluster of 10000 atoms of nitrogen we can make them cross the speed of light easily.</p>
| 7,664 |
[
-0.010012966580688953,
-0.029929092153906822,
-0.04792691022157669,
-0.050228871405124664,
0.05857250466942787,
-0.0139980623498559,
-0.0483260303735733,
-0.04046569764614105,
-0.012874678708612919,
-0.037688978016376495,
0.05468429625034332,
0.0704188123345375,
0.07131074368953705,
0.010214670561254025,
0.0014096455415710807,
0.05779441446065903,
-0.030070435255765915,
-0.00281483493745327,
-0.003124242415651679,
-0.026658281683921814,
0.02674240432679653,
0.010680938139557838,
-0.005009232554584742,
-0.00435955636203289,
-0.0330745130777359,
0.02663005143404007,
0.015713011845946312,
-0.009991480968892574,
-0.00006251026934478432,
0.042984314262866974,
0.0032466782722622156,
-0.014974071644246578,
0.06305655092000961,
0.02489459700882435,
-0.00739070400595665,
0.028403213247656822,
-0.044035088270902634,
-0.026872357353568077,
0.005678271874785423,
0.027654515579342842,
-0.024684082716703415,
-0.03574249520897865,
-0.02873961254954338,
0.031011806800961494,
0.009628957137465477,
0.026581941172480583,
0.042523037642240524,
-0.012339368462562561,
0.07518856972455978,
-0.04815666005015373,
0.0676511600613594,
0.01073239091783762,
0.021371951326727867,
-0.012634479440748692,
-0.025315431877970695,
-0.047567129135131836,
0.09351224452257156,
0.060456532984972,
-0.01010036189109087,
-0.03385227918624878,
-0.010535605251789093,
-0.016795603558421135,
-0.008039167150855064,
-0.007590917870402336,
-0.00006537371518788859,
0.01995999366044998,
-0.054557476192712784,
-0.002777733374387026,
0.015477633103728294,
0.01613517478108406,
0.03681270033121109,
0.002012004377320409,
0.03282430022954941,
0.006241504102945328,
-0.009917029179632664,
-0.028636837378144264,
0.010910404846072197,
0.007883870042860508,
0.03506869077682495,
0.06407659500837326,
-0.03976154699921608,
0.035850126296281815,
0.06308425962924957,
0.04310135170817375,
0.00874677486717701,
-0.024199895560741425,
0.060129281133413315,
-0.01953566074371338,
0.01631147600710392,
0.03569354861974716,
-0.012257303111255169,
0.00480082118883729,
0.033706117421388626,
0.045814771205186844,
0.002587422728538513,
0.054458729922771454,
-0.012162183411419392,
0.048826783895492554,
0.00655260868370533,
-0.03104119561612606,
-0.006260736845433712,
-0.003422981360927224,
0.025791531428694725,
0.09039922803640366,
0.005401861388236284,
-0.02934158407151699,
-0.05757392942905426,
-0.0031581425573676825,
-0.03666357696056366,
0.0007641062256880105,
-0.039656490087509155,
0.01970009133219719,
0.0023622617591172457,
-0.014965686947107315,
0.01659572497010231,
-0.04700300469994545,
-0.006650323048233986,
-0.031825847923755646,
0.05660347267985344,
0.0438418872654438,
0.027630211785435677,
-0.020642569288611412,
0.03724154457449913,
-0.02068067155778408,
-0.037662800401449203,
-0.008963069878518581,
0.03949690982699394,
0.008325918577611446,
-0.002980983816087246,
-0.015407592058181763,
-0.027167977765202522,
0.002686496125534177,
-0.002737463917583227,
-0.009130935184657574,
0.018330570310354233,
-0.007375039160251617,
-0.08364495635032654,
-0.04626711830496788,
0.0320545993745327,
-0.015689045190811157,
0.009135306812822819,
-0.10514070838689804,
0.026270080357789993,
0.005922268610447645,
0.0789087638258934,
0.011032856069505215,
-0.01812022179365158,
-0.001377622364088893,
0.038344718515872955,
-0.009316125884652138,
-0.01382608525454998,
0.0023301695473492146,
-0.014100750908255577,
-0.043974172323942184,
0.011381039395928383,
-0.07790227234363556,
0.01412393618375063,
0.021467672660946846,
0.0033413153141736984,
0.006373165175318718,
0.029698925092816353,
-0.044849593192338943,
0.01718193292617798,
-0.020541908219456673,
0.010937037877738476,
-0.04812036454677582,
0.05925380438566208,
0.04954364150762558,
0.009177048690617085,
0.030707113444805145,
-0.004640636965632439,
0.01917874813079834,
-0.0023019465152174234,
-0.007766996044665575,
0.06384143978357315,
-0.0596407912671566,
0.004733367823064327,
-0.03237038478255272,
-0.004432877991348505,
0.003555110888555646,
-0.0503898486495018,
-0.038267459720373154,
-0.009457150474190712,
0.0007647234597243369,
0.023838713765144348,
0.042035240679979324,
-0.018876828253269196,
0.009658385068178177,
-0.0026850481517612934,
-0.01886928267776966,
-0.006898174993693829,
-0.06609111279249191,
0.03137202560901642,
0.05007828027009964,
-0.005078466609120369,
0.004653170704841614,
-0.0018865243764594197,
0.011668497696518898,
-0.0064716278575360775,
-0.048559240996837616,
-0.017297472804784775,
0.05018877610564232,
-0.01808786951005459,
-0.004740503150969744,
0.01893877424299717,
0.04579900950193405,
0.019768286496400833,
-0.00946789886802435,
0.001146514667198062,
0.004130044486373663,
-0.0370749868452549,
0.023896599188447,
-0.027523430064320564,
0.010259508155286312,
0.043007805943489075,
-0.010446632280945778,
0.05890157073736191,
0.011588269844651222,
-0.009722529910504818,
0.055997658520936966,
0.005367066711187363,
0.09681933373212814,
0.002032970078289509,
0.013077206909656525,
0.02930314652621746,
0.03355026617646217,
0.006309471093118191,
0.030910763889551163,
0.00893860962241888,
-0.03344614431262016,
-0.05112152919173241,
-0.029583703726530075,
0.0186555664986372,
0.013334173709154129,
-0.08175016194581985,
0.018034717068076134,
0.044516291469335556,
0.04003600403666496,
0.04566328972578049,
-0.014702126383781433,
-0.012807155027985573,
-0.04545595124363899,
0.025036945939064026,
0.04683715105056763,
-0.0401233546435833,
-0.010779147036373615,
0.010171926580369473,
0.012987561523914337,
-0.011879479512572289,
-0.008421249687671661,
0.001973153091967106,
0.036886341869831085,
0.005267765372991562,
-0.009491735137999058,
0.01176567655056715,
-0.03927632048726082,
0.03296767175197601,
-0.0019531173165887594,
0.03538588806986809,
0.027023548260331154,
0.005093787331134081,
0.021937020123004913,
-0.009994739666581154,
-0.031782105565071106,
0.007211014628410339,
0.012900186702609062,
-0.008493389934301376,
-0.017729386687278748,
0.018525879830121994,
-0.024069249629974365,
0.05838869512081146,
-0.03158308565616608,
0.006280792877078056,
-0.009079043753445148,
0.001596543937921524,
0.012360002845525742,
0.022305740043520927,
0.02816961146891117,
-0.048972517251968384,
-0.018695132806897163,
0.007776438258588314,
-0.05952313169836998,
-0.023303896188735962,
0.007320737466216087,
-0.03422125428915024,
0.0011477118823677301,
-0.020010236650705338,
-0.038277700543403625,
0.034504350274801254,
-0.006043284200131893,
-0.023735158145427704,
0.027933506295084953,
-0.026247238740324974,
-0.060669731348752975,
0.014850028790533543,
-0.04315765202045441,
-0.004034080542623997,
-0.031783170998096466,
-0.013224408961832523,
0.028490418568253517,
-0.004697100259363651,
-0.03464316576719284,
0.045862242579460144,
-0.00784335844218731,
-0.020201116800308228,
-0.004120924975723028,
0.003849951783195138,
0.015655893832445145,
-0.033979449421167374,
0.026728931814432144,
0.011043105274438858,
-0.03129399195313454,
0.013898955658078194,
-0.06266472488641739,
-0.03201139718294144,
0.01990777626633644,
-0.0031854738481342793,
0.028491690754890442,
-0.004401480313390493,
-0.023249255493283272,
0.05582035705447197,
0.022832613438367844,
-0.04396144673228264,
0.0037032528780400753,
-0.011547727510333061,
-0.004050788469612598,
-0.010941422544419765,
-0.02476487308740616,
0.048145171254873276,
0.0008137503755278885,
-0.006115434691309929,
-0.00395958824083209,
0.037135813385248184,
0.025719014927744865,
-0.018845682963728905,
0.019674060866236687,
-0.02131427265703678,
0.0018868576735258102,
-0.002332794014364481,
0.056601863354444504,
-0.007877955213189125,
-0.028462260961532593,
0.04675496742129326,
-0.0033036801032721996,
0.07042177766561508,
0.011830846779048443,
-0.04622083157300949,
0.03865737468004227,
0.03723961114883423,
0.012920594774186611,
-0.013614151626825333,
0.02306872233748436,
-0.0008043724810704589,
-0.036306075751781464,
0.04428035765886307,
0.019604405388236046,
0.049429669976234436,
0.004102883394807577,
-0.024268435314297676,
0.028955038636922836,
0.05571005120873451,
0.013449258171021938,
-0.04569442942738533,
-0.006540924310684204,
-0.017362426966428757,
-0.02421502210199833,
-0.006442383863031864,
-0.01074567437171936,
0.03181200474500656,
0.05047197639942169,
0.030737562105059624,
0.009723765775561333,
-0.011456512846052647,
0.026976220309734344,
-0.06591405719518661,
-0.01529772486537695,
-0.02852921187877655,
0.028576795011758804,
-0.012079010717570782,
0.050028979778289795,
0.023337645456194878,
0.01852083019912243,
0.015662815421819687,
-0.024488378316164017,
-0.0687379240989685,
0.041221778839826584,
-0.02267787978053093,
-0.02062349207699299,
-0.02472831681370735,
-0.030903756618499756,
-0.03782500699162483,
-0.028129521757364273,
0.023384684696793556,
-0.002085997024551034,
0.01105454470962286,
-0.02823527716100216,
0.03798242285847664,
-0.03693385794758797,
-0.02279621548950672,
0.013283430598676205,
0.041660476475954056,
0.02572641149163246,
-0.002319226274266839,
-0.02621678076684475,
0.03583059832453728,
-0.039909251034259796,
-0.025721745565533638,
-0.006236481945961714,
0.005060186609625816,
-0.015243728645145893,
0.024014126509428024,
0.04119037464261055,
0.034292858093976974,
-0.006000005640089512,
-0.018960556015372276,
0.006016416009515524,
-0.0016548361163586378,
-0.005655249115079641,
0.009724419564008713,
-0.05247735604643822,
-0.014252583496272564,
-0.01769666187465191,
0.023525318130850792,
0.04163786396384239,
-0.01861703023314476,
0.05667790398001671,
0.012539415620267391,
-0.0184098519384861,
0.015474600717425346,
0.054195553064346313,
0.05001245439052582,
-0.0019214280182495713,
-0.043405596166849136,
-0.056618545204401016,
0.0011986215831711888,
-0.024502666667103767,
-0.02698899619281292,
0.0584142841398716,
-0.02424982562661171,
-0.011803700588643551,
0.0015156652079895139,
0.004898513201624155,
0.010229128412902355,
-0.046931855380535126,
0.03829631581902504,
-0.026430604979395866,
0.01708504557609558,
0.0065341065637767315,
-0.009449624456465244,
-0.009609653614461422,
-0.003390219062566757,
0.03332267329096794,
-0.0031383326277136803,
-0.019507501274347305,
-0.06567441672086716,
-0.021303407847881317,
0.016799932345747948,
0.060227811336517334,
-0.03420986980199814,
0.0031691521871834993,
-0.08608569204807281,
0.02601235918700695,
0.003324297023937106,
-0.05914481356739998,
0.02138274908065796,
0.009973390027880669,
-0.00900640245527029,
-0.0090572414919734,
-0.014234214089810848,
-0.002419230528175831,
0.03316007927060127,
-0.011129135265946388,
-0.00674742367118597,
-0.02264736033976078,
0.010200826451182365,
0.020207609981298447,
0.012217285111546516,
0.04742502421140671,
0.03970250487327576,
-0.012146730907261372,
-0.014716639183461666,
0.017505045980215073,
0.000986218685284257,
0.0036740051582455635,
-0.06989727169275284,
0.013458658941090107,
-0.008977023884654045,
-0.03131119906902313,
0.04901250824332237,
-0.05359677970409393,
-0.05231801047921181,
0.043220750987529755,
0.008297765627503395,
-0.023445503786206245,
-0.06404617428779602,
-0.07738412171602249,
0.042394474148750305,
0.03016514517366886,
-0.018615223467350006,
0.019877322018146515,
0.0457763746380806,
-0.029213491827249527,
0.05207657814025879,
-0.024786219000816345,
0.010924888774752617,
-0.04096655920147896,
0.03408452123403549,
-0.014146755449473858,
-0.006493713706731796,
-0.00579803204163909,
0.04796049743890762,
-0.019163362681865692,
-0.002143120625987649,
0.005889548920094967,
-0.015161868184804916,
0.010119708254933357,
0.00982667226344347,
0.021134471520781517,
0.03297337517142296,
-0.027557745575904846,
0.007135172374546528,
-0.004419631324708462,
-0.03396083042025566,
0.021240435540676117,
0.01647076942026615,
-0.010617358610033989,
0.002585516544058919,
-0.002493416192010045,
-0.008701854385435581,
-0.006838738918304443,
-0.005379149224609137,
0.017096776515245438,
-0.06586208194494247,
0.04472167417407036,
-0.007770536467432976,
-0.008862032555043697,
0.002996348077431321,
-0.052264753729104996,
-0.07470457255840302,
0.0028180466033518314,
-0.016027089208364487,
-0.002110427711158991,
-0.034599605947732925,
-0.00805713515728712,
0.00838369783014059,
0.022716207429766655,
-0.043310970067977905,
-0.019985927268862724,
0.010835790075361729,
0.0035001046489924192,
0.0045740436762571335,
-0.05379119887948036,
-0.011206205002963543,
-0.027817267924547195,
-0.023986857384443283,
-0.028429122641682625,
0.045057326555252075,
-0.028037341311573982,
-0.04174860566854477,
-0.008042290806770325,
0.011622261255979538,
0.05936233326792717,
-0.014655854552984238,
-0.04481634125113487,
-0.002326910849660635,
0.00654465239495039,
-0.004122888203710318,
0.0015786387957632542,
0.05892017111182213,
-0.012633442878723145,
-0.055915430188179016,
0.007761161308735609,
-0.024106189608573914,
0.031321607530117035,
-0.017263583838939667,
-0.006156789138913155,
0.05328622832894325,
0.030879318714141846,
-0.01407500822097063,
0.009423479437828064,
0.01834176480770111,
0.01115511730313301,
0.046472471207380295,
-0.009677032008767128,
0.013531683012843132,
-0.051166925579309464,
-0.025060907006263733,
0.046354543417692184,
-0.009746870025992393,
0.006186891812831163,
-0.010703999549150467,
0.06083555892109871,
0.0028314681258052588,
-0.016386203467845917,
0.01653829962015152,
-0.025730201974511147,
0.018730105832219124,
0.009694553911685944,
-0.009569571353495121,
0.0011704545468091965,
-0.0018747596768662333,
0.010421291925013065,
-0.009373679757118225,
-0.05083732679486275,
0.01305543165653944,
0.04467111825942993,
-0.005850097164511681,
0.021915653720498085,
-0.02580670639872551,
0.02791908197104931,
0.011266302317380905,
-0.011529374867677689,
-0.017364364117383957,
0.0008988367044366896,
0.0351034477353096,
0.02330336719751358,
0.017657820135354996,
-0.025241419672966003,
0.06823109835386276,
0.0483529306948185,
-0.004891658667474985,
0.0021398868411779404,
0.030792204663157463,
0.004041123203933239,
-0.02878531813621521,
-0.021573474630713463,
-0.0277293361723423,
-0.0008319827611558139,
-0.01992993801832199,
0.04992382600903511,
-0.017301838845014572,
0.028661472722887993,
0.023538127541542053,
0.01748746633529663,
0.028476886451244354,
-0.024012882262468338,
0.0066371639259159565,
-0.017813045531511307,
-0.018729068338871002,
0.01524841133505106,
-0.005059557035565376,
-0.028459887951612473,
0.010411228984594345,
0.015004081651568413,
0.032587893307209015,
0.06513132154941559,
0.010924402624368668,
-0.04669175297021866,
-0.05692816525697708,
-0.01568698324263096,
-0.029792504385113716,
0.023035133257508278,
0.003797384677454829,
-0.02935030497610569,
0.04219440370798111,
0.007766113616526127,
0.023089846596121788,
0.006604020483791828,
0.026580343022942543,
-0.008458496071398258,
0.08877968043088913,
0.017511090263724327,
0.02018667198717594,
-0.003821571124717593,
0.02536877430975437,
0.12899041175842285,
0.021784255281090736,
-0.0032589335460215807,
-0.036024514585733414,
0.02324088104069233,
-0.0500769317150116,
0.024797389283776283,
-0.035827189683914185,
-0.0005881162360310555,
-0.0180036760866642,
0.0031268673483282328,
0.016606023535132408,
0.056711744517087936,
-0.007151484023779631,
0.01585179939866066,
0.01829770766198635,
-0.018487902358174324,
-0.03478767350316048,
-0.00761620607227087,
0.021772194653749466,
0.0015549198724329472,
-0.022010905668139458,
0.0013605405110865831,
0.03536126762628555,
-0.03887997940182686,
0.00004094607720617205,
-0.049494754523038864,
-0.0017960149561986327,
0.019576717168092728,
-0.003025403246283531,
-0.03102763555943966,
-0.019984472543001175,
-0.005709369666874409,
-0.07136181741952896,
-0.04235997051000595,
0.007415387313812971,
0.03145984932780266,
-0.009788581170141697,
0.01370098628103733,
0.02963980659842491,
-0.009765960276126862,
0.04160436615347862,
0.010544064454734325,
0.012834691442549229,
-0.07136551290750504,
0.0213478934019804,
-0.0425189845263958,
0.029163680970668793,
-0.010900083929300308,
0.0016769401263445616,
0.016550298780202866,
0.03018471598625183,
-0.012923846021294594,
-0.06204947829246521,
-0.009887797757983208,
0.001176347490400076,
-0.0005394548643380404,
0.00606536353006959,
-0.012578249908983707,
-0.03126635029911995,
-0.001440682215616107,
0.008126959204673767,
0.01085712481290102,
-0.024910997599363327,
0.033100198954343796,
-0.002514395397156477,
0.01798592321574688,
0.022373177111148834,
-0.015599417500197887,
0.0070824092254042625,
-0.026413317769765854,
-0.03289473429322243,
-0.05457206815481186,
-0.005883501376956701,
0.031281568109989166,
0.03410346433520317,
0.02511414885520935,
0.007097091060131788,
0.029333017766475677,
-0.02549445442855358,
-0.10411350429058075,
0.034375108778476715,
0.006427580490708351,
-0.02250991202890873,
-0.023062964901328087,
-0.0223705917596817,
0.006410060450434685,
0.04111478105187416,
-0.023935139179229736,
0.04079107567667961,
-0.011638627387583256,
0.0349239818751812,
0.008290844969451427,
-0.03622771054506302,
0.0036967406049370766,
-0.003329878905788064,
-0.017619427293539047,
0.03555230051279068,
-0.005553938448429108,
0.03746962547302246,
0.018578682094812393,
0.0006269995938055217,
-0.0012930795783177018,
0.013632192276418209,
-0.03564515709877014,
-0.009107879363000393,
-0.0019417803268879652,
-0.032819874584674835,
0.007130042649805546,
-0.006232015788555145,
0.010637574829161167,
-0.03502832353115082,
-0.018324539065361023,
-0.019536901265382767,
-0.012361954897642136,
0.030803509056568146,
-0.021492313593626022,
-0.013570315204560757,
0.012443941086530685,
-0.021034983918070793,
-0.009840228594839573,
-0.03919170796871185,
0.0324091762304306,
-0.015492123551666737,
0.03733695670962334,
-0.022723963484168053,
-0.020880211144685745,
-0.0516199953854084,
0.038676775991916656,
-0.030382506549358368,
0.005263211205601692,
0.0667288601398468,
0.02318778820335865,
-0.0011787823168560863,
-0.04210978001356125,
0.019381044432520866,
0.030325662344694138,
0.04414168745279312,
-0.015260223299264908,
-0.01488207932561636,
0.022472599521279335,
-0.023375356569886208,
-0.05806245282292366,
0.01287792157381773,
-0.02052616886794567,
0.02984178252518177,
0.0027741417288780212,
-0.019794886931777,
0.00041232703370042145,
0.08420539647340775,
-0.03726858273148537,
0.006018650718033314,
0.017626376822590828,
-0.022167768329381943,
-0.000264022994088009,
-0.010975964367389679,
-0.015239719301462173,
-0.010996517725288868,
0.004106476437300444,
0.06877760589122772,
0.023548414930701256,
-0.01710611581802368,
0.026519980281591415,
-0.021909236907958984,
-0.02543381229043007,
-0.011313577182590961,
0.02586636319756508,
0.012522175908088684,
-0.019732065498828888,
0.04464421793818474,
-0.017886335030198097,
0.03219976648688316,
-0.00366988661698997,
0.015840871259570122,
-0.1069173589348793,
-0.011604947037994862,
0.0007517696358263493,
-0.015215056948363781,
0.045353736728429794,
-0.03770221397280693,
0.059865329414606094,
-0.0016985457623377442,
-0.05737238749861717,
0.011590065434575081,
-0.047256119549274445,
-0.0009656536276452243,
-0.03822430595755577,
-0.017882755026221275,
-0.021290801465511322,
0.03577754646539688,
0.030642056837677956,
0.056567952036857605,
0.03420616313815117,
0.01910305954515934,
-0.02044798620045185,
-0.025447629392147064,
0.015981217846274376,
0.010915575549006462,
0.017911970615386963,
-0.014886398799717426,
0.07538434118032455,
-0.015693513676524162,
-0.035045646131038666,
0.020465686917304993,
0.02579529769718647,
0.007771842647343874,
-0.013167284429073334,
0.01358824409544468,
-0.0040390403009951115,
0.02460094727575779,
0.01646590232849121,
-0.006397884804755449,
0.00751776248216629,
0.034331317991018295,
-0.004618251230567694,
0.0022024260833859444,
-0.0032762326300144196,
-0.009789209812879562,
-0.005259115714579821,
-0.025543175637722015,
-0.05253984034061432,
0.02649933658540249,
-0.01384859997779131,
-0.0009723276598379016,
0.0228387713432312,
0.01601765863597393,
0.026416471228003502,
-0.041557759046554565,
-0.006032210309058428,
-0.07038712501525879,
-0.0002351575967622921,
0.06570713222026825,
0.0037261792458593845,
0.003537461394444108,
0.018556084483861923,
-0.019053079187870026,
-0.023516030982136726,
-0.021075867116451263,
0.0014074619393795729,
-0.021715659648180008,
-0.025626135990023613,
0.037043213844299316,
0.042012885212898254,
0.024977855384349823,
-0.013399249874055386,
-0.03407026082277298,
-0.039073582738637924,
0.045249130576848984,
0.023437801748514175,
0.02241404913365841,
0.014865152537822723,
-0.0076163276098668575,
0.0015514785191044211,
-0.053313739597797394,
-0.013272371143102646,
-0.017005356028676033,
0.04461866617202759,
-0.06101340427994728,
-0.040217235684394836,
-0.0065977307967841625,
0.00652081286534667,
0.08810383826494217,
-0.01036773156374693,
-0.029109952971339226,
0.012909550219774246,
-0.017120644450187683,
-0.022128134965896606,
-0.06065475940704346,
-0.007167380303144455,
-0.00680284621194005,
-0.05283720791339874,
-0.0027556344866752625,
-0.014084877446293831,
-0.018274318426847458,
0.008172040805220604,
0.01509121898561716,
-0.002416125265881419,
-0.03050961345434189,
0.004586258437484503,
0.003057005349546671,
0.03028416447341442,
-0.03274867311120033,
-0.0010183023987337947,
0.0679788589477539,
0.016948936507105827,
0.04110242426395416,
0.03985682874917984,
-0.005308574065566063,
-0.03843839466571808,
0.04207852855324745,
-0.03770621120929718,
0.006264830008149147,
-0.019878633320331573,
-0.024577569216489792,
0.019955269992351532,
-0.0704597532749176,
0.02157510444521904,
0.047472693026065826,
-0.04813831299543381,
-0.011735196225345135,
0.03272482007741928,
0.012643025256693363,
0.05397719889879227,
0.02436961606144905,
0.03211160749197006,
0.00916487816721201,
0.008116672746837139,
0.020951779559254646,
0.04366576671600342,
0.020409952849149704,
-0.023094570264220238,
0.04908084124326706,
0.019499193876981735,
-0.012302694842219353,
-0.011603130027651787,
0.04760688543319702,
0.045792657881975174,
-0.04453741014003754,
-0.018731053918600082,
0.03261368349194527,
-0.020128875970840454,
0.0015208545373752713,
0.0538766123354435,
-0.006829765159636736,
0.07801136374473572,
0.009563217870891094,
0.042713455855846405,
0.005068158730864525,
-0.001266679260879755,
-0.020144635811448097,
0.013141869567334652,
-0.0540478453040123,
0.0028878648299723864,
-0.010584793984889984,
0.023280799388885498,
0.0013761756708845496,
-0.00819444190710783,
0.03464754670858383,
-0.05769168213009834,
-0.017016327008605003,
-0.025849048048257828,
-0.010959812439978123,
-0.04768333211541176,
-0.02599361352622509,
-0.0019901294726878405,
-0.030583783984184265,
0.0037774411030113697,
0.03010559268295765,
0.0007142669637687504,
0.009004415012896061,
0.0015858125407248735,
0.011859724298119545,
0.07965758442878723,
-0.03373941406607628,
-0.004675246309489012,
-0.04713296890258789,
-0.01578129641711712,
-0.05972471460700035,
-0.024281010031700134
] |
<p>I have a question regarding the <a href="http://en.wikipedia.org/wiki/Holstein%E2%80%93Primakoff_transformation" rel="nofollow">Holstein-Primakoff representation</a>.</p>
<p>In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators.</p>
<p>$$
S_j^+ = \sqrt{2S - n_j} a_j \\
S_j^- = a^\dagger_j\sqrt{2S - n_j} \\
S^z_j = S - n_j
$$</p>
<p>Where $a_j$ and $n_j$ are operators. When we derive the magnon dispersion relation, we make the assumption that</p>
<p>$$
\frac{\langle n_j \rangle}{\langle S^z \rangle}\ll 1
$$</p>
<p>which is fine. As far as I understand this only means that we assume that most of the spins are pointing along the z-direction. However, when we go further in the derivation, we do a series expansion in $n_j/S$, so that i.e.</p>
<p>$$
S_j^+ = \sqrt{2S}\sqrt{1- \frac{n_j}{2S}+...} \approx \sqrt{2S}\sqrt{1- \frac{n_j}{2S}}
$$</p>
<p>This is where I don't understand. Say that we are in a spin $1/2$-system. In that case we can for one site have at most 1 magnon excitation and $S=\pm 1/2$, so for each individual site $n_j/2S$ is not much smaller than one. </p>
<p>My question is then, how can we justify that the series expansion makes sense in the operators at each individual site? Will the contributions from each site when summed up not contribute because</p>
<p>$$
\frac{\langle n_j \rangle}{\langle S^z \rangle}\ll 1
$$</p>
<p>or have I misunderstood something?</p>
<p>Any thoughts would be much appreciated.</p>
| 7,665 |
[
0.027712810784578323,
-0.03550572693347931,
0.0018199019832536578,
-0.041227057576179504,
0.03590448200702667,
-0.0048751989379525185,
-0.03361691161990166,
-0.028790589421987534,
-0.002387452870607376,
-0.05588475614786148,
0.026984507218003273,
-0.014668421819806099,
0.05927235633134842,
0.009730706922709942,
-0.0006805903976783156,
0.016531577333807945,
-0.012301167473196983,
-0.02611064724624157,
-0.012564267963171005,
-0.012829282321035862,
0.00746533740311861,
0.032641999423503876,
0.0022333876695483923,
-0.01429936196655035,
-0.011049672029912472,
0.025359641760587692,
-0.004611581098288298,
0.04459373280405998,
0.04614713788032532,
0.06171564757823944,
0.01897335797548294,
-0.05557161942124367,
0.04576580226421356,
0.01842757873237133,
0.02110403962433338,
0.012662498280405998,
-0.03428463637828827,
-0.039351169019937515,
0.026516910642385483,
0.034730587154626846,
-0.04488566517829895,
0.03209218382835388,
-0.03263413533568382,
0.013604406267404556,
-0.01639568619430065,
-0.009227043949067593,
-0.016107570379972458,
-0.022045519202947617,
0.06394242495298386,
-0.04588393494486809,
0.035627417266368866,
0.020169634371995926,
-0.00018017709953710437,
-0.000898231752216816,
-0.023248115554451942,
-0.011182252317667007,
0.06256669014692307,
0.04482731595635414,
0.018142081797122955,
-0.06383541971445084,
-0.003431605640798807,
-0.010137639008462429,
-0.016715485602617264,
-0.01600005105137825,
0.01828288659453392,
-0.0031614969484508038,
0.02686110883951187,
-0.014381090179085732,
0.017367448657751083,
0.010749061591923237,
0.03265253081917763,
-0.01956672966480255,
0.04968462884426117,
-0.03556188941001892,
0.0012333403574302793,
-0.007759551517665386,
0.012312037870287895,
0.02321399189531803,
0.029773443937301636,
0.021653413772583008,
-0.020954804494976997,
0.015217689797282219,
0.0292087122797966,
0.024939753115177155,
-0.005785663146525621,
-0.0012427459005266428,
0.03737731650471687,
-0.00959993340075016,
0.011144028045237064,
0.02712137997150421,
0.0026534704957157373,
0.018164033070206642,
0.0649348795413971,
-0.00014866524725221097,
-0.009521634317934513,
-0.006556518375873566,
0.007307317573577166,
0.05430372431874275,
0.004708582069724798,
-0.0013433895073831081,
-0.040274444967508316,
-0.05544717609882355,
-0.02424304559826851,
0.04640655964612961,
0.018788769841194153,
0.0035438023041933775,
-0.019939986988902092,
0.01697109453380108,
-0.05079621821641922,
-0.04865952581167221,
-0.04605288803577423,
0.04582101106643677,
-0.03634512424468994,
0.024749858304858208,
-0.009664954617619514,
-0.020913586020469666,
-0.02933887392282486,
0.023708419874310493,
0.038458120077848434,
0.05398206785321236,
0.03442469611763954,
-0.020697444677352905,
0.002797110006213188,
-0.031100966036319733,
-0.06449590623378754,
0.05273096635937691,
0.02371431328356266,
-0.000008958843864093069,
-0.04473233222961426,
-0.010621815919876099,
0.058139216154813766,
0.0017977486131712794,
0.01793285459280014,
-0.016584303230047226,
0.016867127269506454,
-0.014400525018572807,
-0.0932789221405983,
-0.040682096034288406,
0.011917781084775925,
-0.05418413504958153,
0.020107781514525414,
-0.07414142787456512,
-0.017041413113474846,
0.02403336390852928,
0.10058993846178055,
-0.02631133422255516,
0.006812662351876497,
0.009506710804998875,
0.04674910381436348,
-0.002512141829356551,
0.016793500632047653,
-0.03101702593266964,
-0.02278377301990986,
-0.05144350975751877,
0.017083728685975075,
-0.02710566110908985,
0.05669539421796799,
0.02623571828007698,
0.024903450161218643,
-0.003279814962297678,
0.07936933636665344,
-0.0162851233035326,
0.03570031002163887,
0.033537037670612335,
0.02011271007359028,
-0.00847599096596241,
0.0709616020321846,
-0.0029018083587288857,
0.018506182357668877,
0.045372460037469864,
-0.04847124218940735,
-0.023669486865401268,
-0.008136607706546783,
0.05182212218642235,
0.0480579137802124,
-0.027789445593953133,
-0.013200211338698864,
-0.013736479915678501,
0.003057654947042465,
0.0022561964578926563,
-0.03419341519474983,
-0.02523721754550934,
-0.025401093065738678,
0.031190311536192894,
0.015908269211649895,
0.032163843512535095,
0.03236890956759453,
-0.0058411466889083385,
-0.0137289734557271,
-0.06017066910862923,
-0.00572994677349925,
-0.04387965053319931,
-0.006267382297664881,
0.02523348666727543,
-0.009877088479697704,
0.04653524234890938,
0.025041108950972557,
-0.01258839201182127,
0.0027404918801039457,
-0.05692875757813454,
0.008220440708100796,
0.02161693200469017,
0.02786659263074398,
-0.000060661430325126275,
0.04447878152132034,
0.028175700455904007,
0.04901181161403656,
0.028573013842105865,
0.03798166289925575,
-0.01865212991833687,
-0.033437877893447876,
0.013971643522381783,
-0.007574473507702351,
0.04157300665974617,
0.04034044221043587,
0.010890674777328968,
-0.008185477927327156,
-0.0022440096363425255,
-0.03396550193428993,
0.0023754325229674578,
-0.058598656207323074,
0.05621739476919174,
0.05764181166887283,
-0.04706522822380066,
0.011998699977993965,
0.03512543439865112,
0.01697080209851265,
0.05389437824487686,
-0.03748114034533501,
-0.023395895957946777,
-0.056966107338666916,
0.010717852972447872,
0.04605276882648468,
0.04217250272631645,
-0.07373497635126114,
-0.039014752954244614,
0.03061816655099392,
0.013848620466887951,
0.011253918521106243,
0.00296441069804132,
-0.03881700709462166,
-0.01432715728878975,
0.010120154358446598,
0.01165136881172657,
-0.021435819566249847,
0.01477907132357359,
-0.004839163739234209,
0.0029031436424702406,
0.01762903295457363,
0.016377929598093033,
-0.03809574246406555,
0.013753119856119156,
-0.015609248541295528,
0.0013818569714203477,
-0.00440592784434557,
0.013400808908045292,
0.018633130937814713,
0.00015768384037073702,
0.029828982427716255,
0.02792440541088581,
-0.019084392115473747,
0.007447708863765001,
-0.02676176093518734,
-0.05233253538608551,
-0.010034839622676373,
-0.02948315069079399,
-0.01815558224916458,
-0.004288254771381617,
0.014458684250712395,
-0.029097387567162514,
-0.01610436663031578,
-0.04188620299100876,
-0.01843496412038803,
0.028839580714702606,
-0.025216011330485344,
0.03895648196339607,
0.05109240487217903,
0.012315153144299984,
-0.05088989809155464,
-0.017796339467167854,
0.009513739496469498,
0.01257535070180893,
0.0671439915895462,
0.011741184629499912,
-0.04134393483400345,
-0.010992013849318027,
-0.08433736860752106,
0.009470542892813683,
0.032007887959480286,
-0.000022532627554028295,
0.0076158903539180756,
-0.013508941978216171,
-0.0053124455735087395,
-0.05366988480091095,
-0.05470879748463631,
0.009600087068974972,
-0.009310172870755196,
-0.05566243827342987,
-0.0058583603240549564,
0.04254310578107834,
-0.003155878046527505,
-0.02100067026913166,
-0.00941200740635395,
-0.006540450733155012,
-0.03575289994478226,
-0.000171870575286448,
-0.021616263315081596,
0.016548683866858482,
-0.035146623849868774,
0.016031213104724884,
0.035042423754930496,
-0.0068054539151489735,
-0.010679134167730808,
-0.03637448325753212,
-0.030469678342342377,
0.015349902212619781,
0.007562311366200447,
0.01894637942314148,
-0.006905585993081331,
-0.05667809396982193,
0.09004954993724823,
0.027375543490052223,
-0.015924623236060143,
0.0058112251572310925,
0.009206073358654976,
0.024688048288226128,
-0.049821361899375916,
0.03655366227030754,
0.031614407896995544,
0.004781022202223539,
0.023399749770760536,
-0.002220091875642538,
0.06512904167175293,
0.07069936394691467,
0.0030012214556336403,
0.015124840661883354,
0.009851910173892975,
0.004732455592602491,
-0.016791969537734985,
0.04762383922934532,
-0.00040076926234178245,
-0.02275846153497696,
0.02403436414897442,
-0.015553575940430164,
0.004995754454284906,
-0.010231893509626389,
-0.07769403606653214,
0.06688226014375687,
0.01003732718527317,
-0.003309862222522497,
-0.031023120507597923,
0.0383259616792202,
0.004497229121625423,
-0.041065480560064316,
-0.0007050688145682216,
0.008150888606905937,
0.03179658576846123,
-0.0339987613260746,
0.029832888394594193,
0.014827498234808445,
-0.004751206841319799,
-0.011315093375742435,
-0.010955220088362694,
0.011475603096187115,
-0.00743471086025238,
0.01587611250579357,
-0.046702902764081955,
-0.014534263871610165,
-0.0011271733092144132,
0.03666885569691658,
-0.007020452059805393,
-0.036052390933036804,
-0.03215258568525314,
0.014815900474786758,
-0.06724987179040909,
-0.019122131168842316,
-0.01168573834002018,
0.02678423747420311,
-0.016992470249533653,
0.0454680472612381,
-0.008802918717265129,
0.02963734045624733,
-0.0013740144204348326,
0.0013151586754247546,
-0.09721929579973221,
-0.02423747442662716,
0.007870093919336796,
0.0010923336958512664,
-0.011048792861402035,
-0.058577872812747955,
-0.0018762759864330292,
-0.037529878318309784,
0.011417515575885773,
-0.04178081080317497,
-0.002596850972622633,
-0.04316341131925583,
0.04883916676044464,
-0.020738467574119568,
-0.027215709909796715,
-0.018678465858101845,
0.04847405478358269,
0.023928645998239517,
-0.02816443331539631,
-0.02420150861144066,
0.01873931661248207,
-0.034808993339538574,
0.009150681085884571,
-0.028854433447122574,
0.03973819687962532,
0.05691784247756004,
0.008394270204007626,
0.08017247170209885,
-0.020456407219171524,
-0.04545729607343674,
-0.02790151536464691,
0.014242692850530148,
0.057759229093790054,
0.020602906122803688,
-0.017947398126125336,
0.018247293308377266,
-0.010975321754813194,
-0.017582261934876442,
0.004048055503517389,
0.07358568906784058,
0.0010850777616724372,
0.0367378331720829,
0.057711709290742874,
-0.007514602039009333,
-0.0032923303078860044,
0.011583884246647358,
0.0694606825709343,
-0.01205945760011673,
-0.0006884806789457798,
-0.05579707771539688,
-0.001562384539283812,
-0.01880457252264023,
-0.009875867515802383,
-0.0016088868724182248,
-0.011183308437466621,
-0.005625897087156773,
0.006454548332840204,
0.011993838474154472,
0.015111428685486317,
-0.007505779154598713,
0.022211333736777306,
0.017832370474934578,
0.01828622631728649,
0.044631365686655045,
0.023949481546878815,
0.009548919275403023,
-0.001541801611892879,
0.0354764349758625,
-0.003678549313917756,
-0.004585469141602516,
-0.044890087097883224,
-0.015867553651332855,
0.011760074645280838,
0.04673941433429718,
-0.0066266050562262535,
-0.0034305218141525984,
-0.01185766700655222,
-0.026011429727077484,
0.02805420383810997,
-0.04160846024751663,
0.039440106600522995,
0.014367942698299885,
-0.032703299075365067,
-0.020963415503501892,
-0.0521467924118042,
-0.023803291842341423,
0.021753426641225815,
-0.044851697981357574,
-0.0012763695558533072,
-0.03580223768949509,
-0.004711039364337921,
-0.02504538744688034,
-0.023086873814463615,
-0.006694626063108444,
0.02049451693892479,
-0.027913972735404968,
0.01801108941435814,
-0.00673232227563858,
0.08799447119235992,
-0.02141621522605419,
-0.087624192237854,
0.026630206033587456,
-0.02793137915432453,
-0.015801390632987022,
0.0336100198328495,
-0.0017009546281769872,
-0.042306989431381226,
0.023097043856978416,
0.03847746178507805,
0.01976507157087326,
0.005042735021561384,
-0.0041908626444637775,
0.05703253298997879,
0.05149850249290466,
-0.027117813006043434,
0.06475358456373215,
0.0434190034866333,
-0.0396355502307415,
0.018851926550269127,
-0.047203391790390015,
0.015208842232823372,
-0.00982273742556572,
0.016485311090946198,
-0.04221612587571144,
0.03832727670669556,
-0.011842803098261356,
0.037483278661966324,
-0.053596239537000656,
-0.022321565076708794,
-0.017557723447680473,
-0.002876873593777418,
0.012499495409429073,
0.007534995675086975,
-0.003186980728060007,
0.004003462847322226,
-0.030875306576490402,
0.045108612626791,
0.021404104307293892,
0.009709140285849571,
0.03769969195127487,
-0.028911525383591652,
-0.014023520983755589,
-0.008799881674349308,
0.004361345432698727,
0.024114297702908516,
-0.023119760677218437,
-0.0025485288351774216,
0.04336107522249222,
-0.045039523392915726,
0.0607377253472805,
0.022948306053876877,
0.00035226059844717383,
-0.031112786382436752,
-0.004526626318693161,
-0.052958156913518906,
0.010574918240308762,
-0.01652509532868862,
-0.0033154538832604885,
-0.009827753528952599,
-0.02009395882487297,
0.04326852411031723,
-0.01175669115036726,
-0.0646238923072815,
-0.0462554469704628,
0.00018967455253005028,
0.00997654628008604,
-0.002336735837161541,
-0.016826389357447624,
-0.0069761499762535095,
-0.004240262787789106,
-0.02445029281079769,
0.028907060623168945,
0.06000710651278496,
-0.04122035950422287,
-0.017713066190481186,
0.018122145906090736,
0.05443483591079712,
0.06842730194330215,
0.0030222651548683643,
-0.06243926286697388,
0.02574860490858555,
-0.009924869984388351,
0.02559899166226387,
0.00015804065333213657,
0.014581839554011822,
-0.011361329816281796,
-0.03919512405991554,
-0.040438711643218994,
0.004148302599787712,
0.02755396068096161,
-0.007271783892065287,
-0.022179797291755676,
-0.010306175798177719,
0.03184623643755913,
0.0320608876645565,
-0.03533656895160675,
-0.015975335612893105,
0.0016614316264167428,
0.051026180386543274,
-0.015237086452543736,
-0.03817044571042061,
-0.019974257797002792,
0.006006547715514898,
0.006689411122351885,
0.03554416075348854,
-0.026443159207701683,
0.0020976848900318146,
0.05248023197054863,
-0.016905315220355988,
-0.002697404008358717,
0.041054289788007736,
-0.032824061810970306,
0.0003996753948740661,
0.012231697328388691,
0.02413858473300934,
0.03561089560389519,
-0.0028030676767230034,
-0.011704922653734684,
-0.012137247249484062,
-0.08836907893419266,
0.046321623027324677,
0.07197991758584976,
0.0011220391606912017,
0.006348309572786093,
-0.011393696069717407,
0.005994614213705063,
-0.0039325919933617115,
-0.04524955153465271,
-0.03602873533964157,
0.0452955886721611,
-0.04644143953919411,
0.06458140164613724,
-0.05362258106470108,
-0.014735574834048748,
0.036255933344364166,
0.033643968403339386,
-0.056466322392225266,
0.0075703877955675125,
0.04213178530335426,
0.0016272256616503,
-0.007220255210995674,
-0.0032587593887001276,
-0.03573232889175415,
0.021754322573542595,
-0.0172952301800251,
0.019835280254483223,
-0.0102305319160223,
-0.003846858162432909,
0.028684241697192192,
0.012834915891289711,
0.03379010781645775,
-0.027658767998218536,
-0.009135929867625237,
-0.04540904983878136,
0.010359060950577259,
-0.0008955897064879537,
-0.009073213674128056,
0.020669493824243546,
0.01495177112519741,
0.04666207358241081,
-0.023931315168738365,
0.03049318492412567,
0.007022394798696041,
-0.01941441185772419,
0.02421489916741848,
-0.03513684868812561,
-0.062828429043293,
0.01556332129985094,
-0.030588144436478615,
-0.02419624850153923,
-0.002583704423159361,
-0.03154192492365837,
0.047559935599565506,
0.009490474127233028,
0.017456945031881332,
-0.002181050833314657,
0.057365600019693375,
-0.0049389321357011795,
0.019801154732704163,
0.004251963458955288,
-0.004239462316036224,
0.1453871726989746,
0.027598435059189796,
0.0016693462384864688,
-0.06940501183271408,
-0.014265019446611404,
0.009690131060779095,
0.0365200936794281,
-0.015289568342268467,
0.014717772603034973,
0.015033591538667679,
-0.02397763542830944,
0.003499632701277733,
0.041357945650815964,
-0.00391780398786068,
-0.014407305978238583,
0.025785958394408226,
-0.032891396433115005,
-0.04000306501984596,
0.022702744230628014,
0.02173161506652832,
0.00871756300330162,
0.0019839643500745296,
-0.025951573625206947,
-0.010220642201602459,
0.011672621592879295,
0.030270272865891457,
-0.026080120354890823,
-0.02717483974993229,
-0.017828838899731636,
0.03889770805835724,
-0.020532475784420967,
0.030377980321645737,
-0.013164227828383446,
0.00593649921938777,
-0.030957547947764397,
0.004088319838047028,
0.020882245153188705,
-0.031687114387750626,
0.02735697105526924,
0.05244094133377075,
-0.014321990311145782,
0.0017931496258825064,
0.061453670263290405,
0.03547919914126396,
-0.03786418214440346,
0.009890668094158173,
-0.030782250687479973,
0.07615407556295395,
-0.0005801764782518148,
-0.0011210670927539468,
0.03124920465052128,
-0.030726782977581024,
0.03550861030817032,
-0.02719251438975334,
-0.0033500378485769033,
0.013528073206543922,
0.03697313368320465,
-0.015881119295954704,
-0.006734851747751236,
0.020039841532707214,
-0.017509885132312775,
0.04532213136553764,
-0.009408144280314445,
0.0017139181727543473,
0.00984201394021511,
-0.0009649638668633997,
0.027582060545682907,
0.015719618648290634,
0.024610793218016624,
-0.0008104415028356016,
0.01637456938624382,
0.03326680511236191,
-0.050776250660419464,
-0.0033185591455549,
0.01381311658769846,
-0.00652086827903986,
0.051022883504629135,
0.009274744428694248,
-0.025040464475750923,
-0.011954602785408497,
-0.03733973577618599,
0.0058788638561964035,
0.0003937522415071726,
-0.03716180846095085,
0.010891860350966454,
0.01671055518090725,
0.017671573907136917,
0.061360377818346024,
-0.04685824364423752,
0.04437396675348282,
0.0058587524108588696,
0.03932436928153038,
0.0075054834596812725,
-0.02620861865580082,
-0.034902650862932205,
-0.0018547266954556108,
-0.03385385498404503,
-0.011175784282386303,
0.02156173251569271,
0.01449242327362299,
0.02290153317153454,
0.015028219670057297,
0.013919795863330364,
0.014491693116724491,
-0.005141947418451309,
-0.02993106096982956,
0.024382157251238823,
-0.03517577797174454,
0.030673328787088394,
0.03687858209013939,
0.005516615696251392,
-0.030602630227804184,
-0.000977379735559225,
0.012650752440094948,
-0.0034877974539995193,
0.022995365783572197,
0.04061206802725792,
-0.05115421116352081,
-0.03671729192137718,
-0.031815506517887115,
0.00398140586912632,
-0.014250366948544979,
-0.0036161618772894144,
-0.019508933648467064,
0.03212336078286171,
-0.010746248997747898,
0.01257102657109499,
0.04221675172448158,
-0.0074012200348079205,
0.006717568263411522,
-0.008003783412277699,
0.036659449338912964,
0.04086465761065483,
-0.002562617650255561,
-0.046768829226493835,
0.013254540972411633,
0.01063502300530672,
-0.0012739852536469698,
-0.009528067894279957,
-0.03832405060529709,
-0.017351243644952774,
-0.005996345076709986,
-0.03653881326317787,
0.018395548686385155,
0.02495112083852291,
0.03191012144088745,
0.03704828768968582,
0.008313668891787529,
-0.0582764632999897,
0.02338171936571598,
-0.03931213170289993,
-0.016198787838220596,
-0.01770380325615406,
0.004283782560378313,
-0.000052005336328875273,
-0.04689957946538925,
0.00875852257013321,
0.043009497225284576,
0.010828555561602116,
0.01940690539777279,
0.040660884231328964,
-0.018004607409238815,
-0.002589902374893427,
-0.01741081476211548,
-0.011298241093754768,
0.01653658226132393,
0.020878365263342857,
0.00799469742923975,
-0.01913280226290226,
0.043915070593357086,
-0.02674795314669609,
0.025367137044668198,
0.0008511418127454817,
0.03700699657201767,
-0.034388765692710876,
-0.025510026142001152,
-0.028697209432721138,
0.009893194772303104,
0.015451897867023945,
-0.02419058047235012,
0.021110815927386284,
0.022730864584445953,
-0.08226662874221802,
0.03865274041891098,
0.0074625322595238686,
-0.028286166489124298,
-0.013611421920359135,
-0.03816814348101616,
-0.04648115485906601,
0.0676361471414566,
0.014734525233507156,
0.05170232802629471,
-0.007931318134069443,
0.003710187040269375,
-0.045167047530412674,
-0.0037958333268761635,
-0.03769947215914726,
-0.01933731883764267,
-0.0013511624420061707,
-0.01772194355726242,
0.061157889664173126,
-0.028241882100701332,
-0.03477492183446884,
0.007349587045609951,
-0.04141206294298172,
-0.013315514661371708,
0.011116146109998226,
0.01983622834086418,
0.0020428569987416267,
0.05382817983627319,
-0.012536074966192245,
-0.03253083676099777,
-0.0011613084934651852,
-0.014934773556888103,
0.04361195117235184,
0.049692824482917786,
-0.009832534939050674,
0.023316873237490654,
0.020600732415914536,
-0.04123128205537796,
-0.025759782642126083,
0.02752825804054737,
-0.004509667865931988,
-0.002047488233074546,
0.005760325584560633,
-0.000718476832844317,
0.019315313547849655,
-0.02928372658789158,
0.04742434248328209,
-0.07722004503011703,
0.02524193376302719,
0.024510782212018967,
0.014377138577401638,
-0.003685883479192853,
0.00999159924685955,
-0.008169499225914478,
-0.04185926541686058,
0.01325603574514389,
-0.00002295282502018381,
-0.05692463740706444,
-0.03410995379090309,
-0.05006903409957886,
0.007704359013587236,
0.05339923873543739,
-0.011053777299821377,
-0.01607888750731945,
-0.0412786640226841,
0.009357349947094917,
-0.02829793468117714,
0.028004955500364304,
-0.04617173597216606,
-0.047880012542009354,
-0.002061496488749981,
-0.05572478845715523,
0.01471080631017685,
0.003520440310239792,
-0.01341805700212717,
-0.031949225813150406,
-0.020242977887392044,
0.013629954308271408,
0.027058465406298637,
0.07268253713846207,
0.015162580646574497,
-0.017138095572590828,
-0.005914806388318539,
-0.029293084517121315,
0.05391460657119751,
-0.012494010850787163,
0.03938983753323555,
-0.010166135616600513,
-0.0035424758680164814,
0.002681163139641285,
0.01938289776444435,
-0.05701887607574463,
0.0738016739487648,
0.014518569223582745,
0.020220089703798294,
0.00027344009140506387,
0.017364390194416046,
-0.023322585970163345,
0.03905796259641647,
-0.04907400906085968,
-0.004362683743238449,
0.03755026310682297,
0.02048264630138874,
-0.01958456076681614,
0.05539325624704361,
-0.028086500242352486,
-0.061019375920295715,
-0.01927042379975319,
0.0024879041593521833,
-0.006793954409658909,
0.020966211333870888,
-0.01977188140153885,
0.05526289343833923,
-0.03598584234714508,
0.014593468979001045,
0.004412053152918816,
-0.025566106662154198,
-0.024994390085339546,
0.03563813492655754,
-0.008379459381103516,
-0.023212118074297905,
0.006794922985136509,
0.030840767547488213,
0.010926097631454468,
-0.010547908022999763,
0.042581964284181595,
0.04148862138390541,
0.016354314982891083,
0.0397106297314167,
-0.0005712806014344096,
-0.005135989282280207,
-0.025785395875573158,
0.007545554079115391,
0.0008540389826521277,
-0.023735981434583664,
-0.016211850568652153,
0.007436545565724373,
0.04061964899301529,
-0.019204851239919662,
-0.020001333206892014,
0.039808306843042374,
-0.021002909168601036,
0.09958571940660477,
-0.027122778818011284,
0.007556958589702845,
-0.05991188436746597,
-0.01339052151888609,
0.0017120864940807223,
-0.0031518228352069855,
-0.011962234042584896,
0.02533264085650444,
-0.048863641917705536,
-0.022418085485696793,
-0.015832196921110153,
-0.033392284065485,
0.03389674425125122,
-0.07404427230358124,
-0.005612815264612436,
0.02517986297607422,
-0.009755190461874008,
-0.01455579325556755,
-0.03014305606484413,
-0.0632886067032814,
-0.014165742322802544,
0.03667937591671944,
0.03972627967596054,
-0.028147418051958084,
0.004494169261306524,
-0.02626338042318821,
-0.026173777878284454,
0.009420209564268589,
-0.020402133464813232,
-0.005742519628256559,
-0.01688319444656372,
-0.0026981153059750795,
-0.020505469292402267,
-0.0020425929687917233
] |
<p>One of the quantities appearing in the integral form of Maxwell's Equations is the line integral of the magnetic field around a closed loop. (The relevant equation states that this is equal to the current through any surface bounded by that loop, plus the displacement current in the case of changing electric fields, with some constant coefficients possibly thrown in, depending on how you manage your units. This is usually called Ampère's Law, with Maxwell's correction for the displacement current.)</p>
<p>Is there a name for this quantity? More generally, is there a name for the line integral of the magnetic field along an arbitrary non-closed curve? (Then this is not equal to any other named quantity or sum of quantities.) Ideally, I'd want a name for the integral of the H-field (rather than the B-field, when one distinguishes them) in amperes (or the equivalent in non-SI units), but I am not really picky about those details.</p>
<p>It seems that every other quantity in the integral form of Maxwell's Equations has a name (magnetic flux, electric flux, charge, etc), so I'd hope that this one does too. Of course, the term for the line integral of the electric field (electromotive force) is somewhat of a historical oddity, so maybe this quantity is too obscure to have a name. Still, you'd think that somebody would have given it one sometime!</p>
<p>ETA: A theoretical way to measure this quantity is to place a conductive tube (as conductive as possible, with as small diameter as possible) around the curve in question. The magnetic flux through the tube will induce a current running around (not along) the inside of the tube, which will in turn serve to cancel (or shield) the source of the magnetizing field, in accordance with Lenz's Law (in the broad sense). The current so induced, serving to completely cancel the magnetic field near the curve in question, should equal this quantity, if I'm thinking about this correctly. (Well, I'm having a little trouble getting the sign straight, but one way or the other it should work!)</p>
| 7,666 |
[
-0.04702926054596901,
0.027794744819402695,
0.0031445184722542763,
-0.029623810201883316,
0.05783352255821228,
0.032597534358501434,
-0.05677996575832367,
-0.03430658578872681,
-0.01520418282598257,
0.009697685949504375,
0.043541111052036285,
0.036054741591215134,
0.09987904876470566,
0.02081947773694992,
0.012504336424171925,
0.010708537884056568,
-0.002506065182387829,
-0.005984927527606487,
0.00041147766751237214,
-0.10094587504863739,
-0.0027948638889938593,
-0.010393952019512653,
-0.0028540475759655237,
0.032375894486904144,
-0.00853930227458477,
0.06626047939062119,
0.017880907282233238,
-0.01763688027858734,
0.0028665023855865,
0.03326339274644852,
-0.029083190485835075,
-0.028489628806710243,
0.025306424126029015,
0.014460398815572262,
0.017442580312490463,
-0.01525021716952324,
0.012225593440234661,
-0.055302880704402924,
-0.016074329614639282,
0.040552400052547455,
-0.030452106148004532,
-0.005351573694497347,
0.009053006768226624,
0.017966749146580696,
-0.01274171657860279,
0.005857133772224188,
-0.005084183532744646,
-0.006430645473301411,
0.035508379340171814,
-0.060085102915763855,
0.059374772012233734,
-0.0049405344761908054,
0.04392509162425995,
-0.0135614899918437,
-0.004087972454726696,
0.001552702160552144,
0.060838036239147186,
0.04585559666156769,
-0.0033826541621237993,
-0.05689280852675438,
-0.024479174986481667,
-0.019476456567645073,
0.007604309823364019,
-0.043946512043476105,
-0.019076867029070854,
0.060047976672649384,
-0.02448677085340023,
-0.027165349572896957,
0.030546138063073158,
0.027889760211110115,
-0.00029982937849126756,
0.04317498207092285,
0.026206940412521362,
-0.05100312456488609,
0.023836400359869003,
-0.024467336013913155,
0.02634255774319172,
-0.013472050428390503,
0.03629050776362419,
0.03711310029029846,
-0.021428551524877548,
-0.012454581446945667,
0.04680410772562027,
0.02976267971098423,
0.006982136517763138,
0.0032385860104113817,
0.047744520008563995,
0.0003703509864863008,
0.022192543372511864,
0.03175276890397072,
-0.00408903555944562,
0.03967316821217537,
0.015041083097457886,
-0.0294667799025774,
-0.022520150989294052,
0.026091748848557472,
-0.004441687371581793,
0.043525006622076035,
0.021452905610203743,
-0.013675177469849586,
0.005853254348039627,
-0.004053730983287096,
0.01947763003408909,
0.0839078426361084,
0.021439576521515846,
-0.043859899044036865,
-0.01299351453781128,
-0.004707963205873966,
-0.01891004852950573,
0.012576024048030376,
-0.02208651602268219,
0.01574094034731388,
0.012199323624372482,
-0.007612134329974651,
0.019255662336945534,
-0.03946183621883392,
0.01593445986509323,
0.022400490939617157,
0.05416130647063255,
0.05649470165371895,
0.038524236530065536,
-0.056014254689216614,
0.029045917093753815,
-0.01875993423163891,
-0.10879427939653397,
0.019689347594976425,
0.02283809892833233,
0.027684111148118973,
-0.03144421800971031,
0.031342215836048126,
0.002868346404284239,
-0.044494763016700745,
0.006525617092847824,
0.0027634466532617807,
0.0432148277759552,
-0.01501443050801754,
-0.04200869798660278,
-0.07724759727716446,
0.021026156842708588,
-0.02984369546175003,
0.0017251081299036741,
-0.03561686724424362,
0.005552626680582762,
0.030457183718681335,
0.10474417358636856,
0.013269570656120777,
-0.02642429806292057,
-0.02397874929010868,
0.027627479285001755,
-0.0022470070980489254,
0.004350382834672928,
-0.03577417880296707,
0.0218674186617136,
-0.022403571754693985,
-0.015889910981059074,
-0.023492256179451942,
0.04463774338364601,
0.05363252013921738,
-0.02237093262374401,
0.01038470957428217,
0.06965108215808868,
-0.030093178153038025,
0.00020319651230238378,
0.020582351833581924,
-0.012120756320655346,
-0.03857601433992386,
0.07839922606945038,
0.002938336692750454,
0.016195593401789665,
0.03348982334136963,
0.02499043010175228,
-0.006310971453785896,
0.013896793127059937,
0.034910496324300766,
0.09159212559461594,
-0.060578927397727966,
-0.01565016433596611,
-0.009285186417400837,
0.015209440141916275,
0.019418079406023026,
-0.024161847308278084,
-0.03866634890437126,
0.0050305649638175964,
0.030330657958984375,
0.006544622592628002,
0.05594373121857643,
-0.026661466807127,
-0.04172349348664284,
0.032806430011987686,
-0.04121536388993263,
0.00416986271739006,
-0.026268843561410904,
0.045645128935575485,
-0.02153213880956173,
-0.03270845487713814,
0.020033428445458412,
0.0016099974745884538,
-0.005802937317639589,
-0.06893140822649002,
-0.07152323424816132,
0.016116125509142876,
0.05043797940015793,
-0.0001415643928339705,
-0.026195166632533073,
-0.014525306411087513,
-0.013977051712572575,
0.020352892577648163,
0.00801432877779007,
0.05153216794133186,
-0.015787562355399132,
-0.05795782431960106,
-0.016369016841053963,
-0.052768368273973465,
0.04657646641135216,
-0.017921188846230507,
-0.003467999631538987,
0.010669865645468235,
-0.006711842957884073,
0.014712028205394745,
0.027152851223945618,
-0.019165711477398872,
0.04606914147734642,
0.03464248776435852,
0.03524251654744148,
0.010692915879189968,
0.0366140753030777,
-0.005607428029179573,
0.018961291760206223,
-0.04681938514113426,
-0.016503289341926575,
-0.056429848074913025,
-0.003886544844135642,
0.06112157925963402,
0.023745428770780563,
-0.02856309898197651,
-0.02385690249502659,
0.014845739118754864,
0.03670387342572212,
0.03190990909934044,
0.00903338473290205,
-0.04915939271450043,
-0.05901094153523445,
-0.02576206997036934,
0.01381676085293293,
-0.022449001669883728,
0.00784315075725317,
0.018901297822594643,
0.005590157117694616,
0.041196469217538834,
0.02608378417789936,
-0.014874622225761414,
0.009470048360526562,
-0.020733213052153587,
0.012268499471247196,
0.0029427260160446167,
-0.023133479058742523,
0.04030155763030052,
-0.02512754686176777,
0.051852039992809296,
0.004384160041809082,
-0.02226840890944004,
0.015023976564407349,
-0.01770782470703125,
0.009887965396046638,
-0.012608054094016552,
-0.044853575527668,
-0.002892611548304558,
-0.02165142260491848,
0.0030247620306909084,
-0.013580606319010258,
-0.006293585989624262,
-0.0247050691395998,
0.024986421689391136,
-0.042540449649095535,
0.016568820923566818,
-0.014219418168067932,
0.023082178086042404,
0.0642511248588562,
-0.013622733764350414,
-0.029819853603839874,
-0.00932292453944683,
-0.022901976481080055,
0.03754531964659691,
0.02343127690255642,
-0.014930197969079018,
-0.008690349757671356,
-0.01627676747739315,
-0.04373627528548241,
0.06867285072803497,
0.00016969055286608636,
-0.018598027527332306,
0.022521736100316048,
0.0002952198265120387,
-0.07335302978754044,
0.001618094276636839,
-0.042718783020973206,
0.016350628808140755,
0.0043863654136657715,
0.005205634981393814,
0.03901878744363785,
-0.015690209344029427,
-0.03494289517402649,
0.051089949905872345,
-0.04084799438714981,
-0.02142082154750824,
-0.03665560483932495,
-0.022883586585521698,
0.03249624744057655,
-0.017242468893527985,
0.006864174269139767,
0.03848271444439888,
-0.019718755036592484,
-0.016336388885974884,
-0.03947410732507706,
-0.024794090539216995,
-0.010764431208372116,
-0.039559680968523026,
0.03185530751943588,
-0.009320908226072788,
-0.024927986785769463,
0.07638338953256607,
0.02884318120777607,
-0.03679221495985985,
-0.016237277537584305,
-0.03251158818602562,
-0.000007571177320642164,
-0.04230049252510071,
-0.010764215141534805,
0.026631463319063187,
0.001878751558251679,
-0.0020912352483719587,
0.010684153065085411,
0.02375483699142933,
-0.002613067626953125,
0.04203438758850098,
0.019169585779309273,
0.032491810619831085,
-0.03405459225177765,
0.003602704033255577,
0.07435201108455658,
0.0356375090777874,
-0.01034050527960062,
-0.0014860411174595356,
0.013914483599364758,
0.027605587616562843,
0.03119012713432312,
-0.05454925820231438,
0.030550306662917137,
0.009546599350869656,
0.014493810944259167,
-0.009875582531094551,
0.014105497859418392,
0.005845160223543644,
-0.018482567742466927,
-0.027218451723456383,
0.05689771845936775,
0.01563674956560135,
-0.02604854665696621,
0.01987617462873459,
0.03109855204820633,
0.023911040276288986,
-0.022204900160431862,
-0.01784197986125946,
-0.009052380919456482,
-0.00348878582008183,
0.0015096482820808887,
-0.017099283635616302,
-0.038400813937187195,
0.03763943910598755,
0.041116565465927124,
0.004725269041955471,
0.03356916457414627,
-0.04535383731126785,
0.024348977953195572,
-0.08130218088626862,
-0.040921662002801895,
0.00436663581058383,
0.03640979155898094,
0.02030797488987446,
0.014130734838545322,
0.012351666577160358,
0.00755572784692049,
0.027489401400089264,
0.013561266474425793,
-0.09338410943746567,
0.023967193439602852,
-0.03143974393606186,
-0.039702579379081726,
-0.02760753035545349,
0.013178309425711632,
-0.0045868693850934505,
0.0057097612880170345,
0.0030853513162583113,
-0.016705378890037537,
-0.02266421914100647,
-0.05954122543334961,
0.019392920657992363,
0.004780708346515894,
-0.03764455392956734,
-0.028150467202067375,
0.0528111606836319,
0.024237627163529396,
-0.030289312824606895,
0.016639722511172295,
0.00036037107929587364,
0.003171134041622281,
-0.025208033621311188,
-0.019053500145673752,
-0.018434807658195496,
0.024764128029346466,
0.02150370553135872,
0.030858568847179413,
-0.009687104262411594,
-0.045805301517248154,
0.012867605313658714,
0.013939162716269493,
0.03869539871811867,
0.030760284513235092,
-0.005152948200702667,
-0.009318194352090359,
-0.04044616222381592,
-0.023405520245432854,
-0.017602182924747467,
0.07020021229982376,
-0.012283287942409515,
0.02593866176903248,
0.00010324783943360671,
0.022490985691547394,
-0.015989750623703003,
0.025983542203903198,
0.018557080999016762,
0.04360995441675186,
-0.03288549557328224,
-0.04358028993010521,
0.011030605062842369,
-0.02251763828098774,
0.024436676874756813,
-0.024367304518818855,
0.012855617329478264,
-0.012738153338432312,
-0.042561039328575134,
0.010423339903354645,
0.018128249794244766,
0.020953191444277763,
-0.010690596885979176,
0.01033527497202158,
0.0013845416251569986,
0.015553813427686691,
0.01079618465155363,
0.018925493583083153,
0.02613816410303116,
0.03232957795262337,
0.026665151119232178,
-0.015916630625724792,
-0.10587596893310547,
-0.017540747299790382,
0.044955842196941376,
0.04574637487530708,
0.016931964084506035,
-0.05287054926156998,
-0.04082271084189415,
-0.007053160574287176,
0.05215950310230255,
-0.026477502658963203,
-0.0034090131521224976,
-0.032928138971328735,
0.007326169405132532,
-0.03979870676994324,
-0.01827591098845005,
-0.044427353888750076,
0.025215547531843185,
0.022780492901802063,
0.015359198674559593,
-0.020908117294311523,
0.01731269247829914,
0.015596947632730007,
0.04051494970917702,
0.025045663118362427,
0.008039179258048534,
0.030116388574242592,
-0.006755460985004902,
0.007236965931952,
0.05102026090025902,
-0.03148876130580902,
-0.09001322090625763,
-0.0014687811490148306,
0.012477665208280087,
-0.01727108843624592,
0.026332104578614235,
-0.030353764072060585,
-0.03376330807805061,
0.00149335409514606,
-0.011745846830308437,
0.014072056859731674,
0.01348237693309784,
-0.024571966379880905,
0.04892699047923088,
0.06170414015650749,
0.03867688775062561,
0.040472421795129776,
0.01499142311513424,
0.000027230940759181976,
-0.001975726569071412,
-0.00190155697055161,
0.04279881715774536,
-0.010730121284723282,
-0.03814893588423729,
-0.03469075635075569,
0.018971694633364677,
-0.05339061841368675,
0.07000718265771866,
-0.0038544978015124798,
-0.017728062346577644,
-0.039261505007743835,
-0.015561789274215698,
-0.01807165890932083,
-0.003882284974679351,
-0.035534366965293884,
-0.031176982447504997,
0.004513524938374758,
0.011117503978312016,
0.00946229137480259,
-0.01572691835463047,
0.03117261826992035,
0.02494441345334053,
-0.0027372532058507204,
0.04461009427905083,
0.003972404170781374,
-0.0013617275981232524,
-0.005150266457349062,
0.006768842693418264,
0.014835555106401443,
0.0003516312863212079,
0.020578421652317047,
-0.031154263764619827,
0.002245997777208686,
-0.028535006567835808,
-0.03722335770726204,
-0.0464317686855793,
-0.006195607129484415,
0.0036670782137662172,
0.027467284351587296,
-0.07220064103603363,
0.022127920761704445,
0.012058534659445286,
0.021532131358981133,
-0.038853131234645844,
-0.04176691919565201,
0.03305847942829132,
0.002139715012162924,
-0.006045144982635975,
-0.00018034171080216765,
-0.021951457485556602,
0.021154122427105904,
-0.05395948514342308,
0.044060997664928436,
0.0336698479950428,
-0.04645039513707161,
0.0033248832914978266,
-0.0006411898648366332,
0.00828393455594778,
0.04084508493542671,
0.022640693932771683,
-0.026024648919701576,
0.014646614901721478,
-0.010308807715773582,
-0.013080661185085773,
0.03104391135275364,
0.060358546674251556,
-0.023455701768398285,
-0.008567542769014835,
-0.007183421868830919,
-0.0322427973151207,
0.030681278556585312,
-0.01773589476943016,
-0.02077677845954895,
0.02813253365457058,
-0.0001893805747386068,
-0.04303671047091484,
-0.022323470562696457,
0.007906160317361355,
0.003358867485076189,
-0.010242355056107044,
-0.004906950984150171,
-0.007472846191376448,
-0.03574439883232117,
0.0013238417450338602,
-0.0030597583390772343,
0.013986493460834026,
-0.021497396752238274,
-0.06231171265244484,
0.023539362475275993,
-0.020175985991954803,
-0.014414829201996326,
0.025436129420995712,
0.0013064807280898094,
0.03726419433951378,
-0.010899322107434273,
0.008294087834656239,
0.013925396837294102,
0.01576295495033264,
-0.037283048033714294,
-0.030178768560290337,
-0.010194350965321064,
-0.014340057969093323,
0.05172530561685562,
-0.056737203150987625,
0.07099509239196777,
0.014058543369174004,
-0.020571714267134666,
0.022240104153752327,
-0.015394031070172787,
-0.020772095769643784,
0.010303152725100517,
-0.002213082043454051,
0.031048575416207314,
0.00791214406490326,
0.011207201518118382,
0.012231891043484211,
0.021084722131490707,
-0.04815002158284187,
-0.014572122134268284,
-0.015897618606686592,
0.04259149357676506,
0.028237365186214447,
0.007979363203048706,
-0.057992707937955856,
0.051190245896577835,
-0.01773405633866787,
0.0211793202906847,
0.02723947912454605,
-0.003894411027431488,
0.04146072268486023,
0.024154111742973328,
0.03236318752169609,
-0.0014151624636724591,
-0.028458314016461372,
-0.019904164597392082,
-0.004219092894345522,
0.02490149810910225,
-0.034044697880744934,
-0.002702461089938879,
-0.016464265063405037,
0.021012531593441963,
-0.019290601834654808,
0.00809523370116949,
0.004144891165196896,
-0.038057658821344376,
0.0031108087860047817,
-0.05878462642431259,
-0.03227999433875084,
0.08547718822956085,
-0.017750626429915428,
-0.024105189368128777,
-0.0006723280530422926,
-0.021923348307609558,
0.019314996898174286,
0.019217243418097496,
-0.0069633047096431255,
0.019821343943476677,
0.06182112172245979,
-0.060110945254564285,
0.01193176582455635,
-0.06321453303098679,
-0.03655169904232025,
0.11730463057756424,
0.02641608938574791,
0.02798433229327202,
-0.061294447630643845,
0.024048984050750732,
-0.03763515502214432,
-0.0012121289037168026,
-0.03590971231460571,
0.02458137646317482,
-0.05513177067041397,
-0.010818650014698505,
0.040297817438840866,
0.039394862949848175,
-0.02150433138012886,
0.004451101180166006,
0.07029946893453598,
-0.011416131630539894,
0.007997364737093449,
0.03353399038314819,
0.031447090208530426,
0.013467874377965927,
0.01259606797248125,
-0.07375291734933853,
0.01881515607237816,
-0.022785862907767296,
0.009298517368733883,
-0.03536320477724075,
-0.021664101630449295,
0.045284468680620193,
0.030377298593521118,
-0.07804739475250244,
0.038642410188913345,
-0.004141009878367186,
0.0025623447727411985,
-0.008229508996009827,
-0.004427457228302956,
0.06303296238183975,
0.033080775290727615,
0.010692812502384186,
0.0311881210654974,
0.034670062363147736,
-0.009857120923697948,
0.026228636503219604,
0.03338097035884857,
-0.04124317690730095,
-0.010674598626792431,
-0.010989445261657238,
0.03812089562416077,
-0.027021734043955803,
0.029851147904992104,
-0.011020602658390999,
0.03035162016749382,
0.0226962398737669,
-0.02142154984176159,
-0.04114270955324173,
-0.04004199430346489,
0.019819218665361404,
0.008202594704926014,
-0.0012037272099405527,
0.0013403783086687326,
0.04651673510670662,
0.003682401031255722,
-0.010363956913352013,
-0.035144709050655365,
-0.018001917749643326,
0.027933180332183838,
0.029679633677005768,
0.05524880066514015,
0.0036565642803907394,
-0.024994054809212685,
-0.012420537881553173,
-0.04402186721563339,
-0.026305193081498146,
0.05068594589829445,
-0.02989957667887211,
0.009802930988371372,
0.02992631308734417,
-0.013763749040663242,
-0.02896389737725258,
-0.0039145974442362785,
-0.058351919054985046,
0.04092943295836449,
0.013013415969908237,
0.0019575210753828287,
-0.008679132908582687,
-0.03320639207959175,
0.02166512794792652,
0.01703111082315445,
-0.018581856042146683,
-0.004584084264934063,
0.008979151956737041,
0.03365010395646095,
0.0017549155745655298,
-0.014890525490045547,
-0.03447045758366585,
0.000379979086574167,
-0.01642134040594101,
0.003909114748239517,
0.013024712912738323,
0.011570798233151436,
0.02526274137198925,
0.009560475125908852,
-0.002197879832237959,
0.039731916040182114,
-0.004551926162093878,
-0.018220260739326477,
-0.01210937649011612,
-0.01539685856550932,
0.013354253023862839,
-0.020459337159991264,
-0.003771787043660879,
-0.04111499339342117,
-0.0017840956570580602,
-0.032716408371925354,
0.012630361132323742,
0.007416734006255865,
0.0425126738846302,
-0.02721336856484413,
0.016968129202723503,
-0.02636997029185295,
-0.031048648059368134,
-0.02089848555624485,
0.004801259841769934,
-0.06896348297595978,
-0.024830324575304985,
0.027945781126618385,
0.0036950730718672276,
-0.002504475647583604,
0.03713460639119148,
-0.017934896051883698,
-0.020556697621941566,
0.001881762407720089,
0.013376975432038307,
-0.02709507942199707,
-0.0221928209066391,
-0.014648830518126488,
0.0273323655128479,
0.03524072840809822,
-0.017954498529434204,
-0.004078663419932127,
0.051728956401348114,
-0.014436090365052223,
-0.049291156232357025,
0.04815956577658653,
-0.004087573383003473,
-0.00022038313909433782,
0.03462541475892067,
0.009204204194247723,
-0.018715068697929382,
0.006497364025563002,
-0.012170113623142242,
-0.02690509520471096,
-0.02301650308072567,
-0.04073502495884895,
-0.004693920724093914,
-0.04083152115345001,
0.0223056860268116,
-0.0005929798353463411,
-0.012029285542666912,
-0.016527986153960228,
0.019155709072947502,
0.008885336108505726,
0.004540134221315384,
0.014860320836305618,
0.011777849867939949,
-0.006273444276303053,
0.026348350569605827,
-0.009382852353155613,
0.03038104996085167,
0.024215828627347946,
-0.04665432497859001,
0.001717310631647706,
0.02842453122138977,
0.017346465960144997,
-0.10339492559432983,
0.015326626598834991,
-0.004534787964075804,
0.04992986097931862,
0.02967490628361702,
-0.065692238509655,
-0.004182531964033842,
0.02803531475365162,
-0.07837992906570435,
-0.013478344306349754,
-0.032602109014987946,
-0.012820778414607048,
-0.01201833225786686,
-0.03889522701501846,
-0.00040262608672492206,
0.025085341185331345,
0.024918440729379654,
0.03291679173707962,
0.02015766315162182,
-0.007168332114815712,
-0.026244254782795906,
-0.04170742258429527,
-0.016883669421076775,
0.016609983518719673,
-0.015190291218459606,
-0.06303184479475021,
0.052346788346767426,
-0.012663731351494789,
-0.004264782648533583,
0.042227961122989655,
-0.00944479275494814,
0.020464418455958366,
-0.03413216397166252,
0.006938552483916283,
0.01158650778234005,
0.03200284391641617,
-0.0031761685386300087,
-0.023142678663134575,
-0.01834767498075962,
0.024430500343441963,
0.013724524527788162,
0.04171176254749298,
-0.004048295319080353,
-0.02219737321138382,
0.026255767792463303,
-0.02681368589401245,
-0.02931622788310051,
0.07356119155883789,
-0.03152390941977501,
-0.014453336596488953,
-0.02913033775985241,
0.01200504694133997,
0.028264543041586876,
-0.022425943985581398,
-0.019424106925725937,
-0.028994830325245857,
-0.009538703598082066,
0.029562106356024742,
-0.043751440942287445,
-0.00854507926851511,
-0.001465296489186585,
0.0063519771210849285,
-0.036153096705675125,
0.059921808540821075,
0.02460363693535328,
0.004818087909370661,
-0.03868960961699486,
0.005650467239320278,
-0.001198638346977532,
-0.022662265226244926,
0.02742665633559227,
-0.010679402388632298,
-0.03826329484581947,
0.018079375848174095,
0.017397303134202957,
-0.00004678234472521581,
0.010943559929728508,
-0.06348147243261337,
0.00897816102951765,
-0.03769901767373085,
0.03975219279527664,
-0.00074983254307881,
-0.012778384611010551,
-0.008980710990726948,
-0.04565756767988205,
0.03278780356049538,
0.0007302144658751786,
0.07273179292678833,
-0.0022394859697669744,
-0.032056573778390884,
-0.0007879259064793587,
0.002645849948748946,
0.04740079492330551,
-0.055396370589733124,
0.0005416721687652171,
0.02416297420859337,
0.0024173406418412924,
0.010927450843155384,
-0.008377895690500736,
-0.0023322177585214376,
0.012923330068588257,
0.022707408294081688,
0.052101634442806244,
-0.006012240890413523,
-0.06051291897892952,
-0.0374775230884552,
0.014966467395424843,
-0.0034942280035465956,
-0.04714464396238327,
0.030992409214377403,
0.010597487911581993,
-0.010752875357866287,
-0.0002599431318230927,
-0.008494071662425995,
-0.04979274049401283,
-0.004383182618767023,
-0.022000599652528763,
0.010852150619029999,
-0.05696875974535942,
0.015240214765071869,
0.037152718752622604,
-0.006578194908797741,
0.01386936940252781,
0.05998174101114273,
-0.007058188784867525,
-0.03576409071683884,
0.04517423361539841,
-0.005963866598904133,
0.048139892518520355,
-0.0013069460401311517,
0.0422058142721653,
0.02444579266011715,
-0.030102279037237167,
-0.014108535833656788,
0.043175842612981796,
0.0444551557302475,
-0.007717345375567675,
-0.013986969366669655,
0.03643394261598587,
-0.020892981439828873,
0.001988103147596121,
0.009336915798485279,
0.011902551166713238,
-0.03709800913929939,
-0.019846249371767044,
0.024323027580976486,
-0.02099727839231491,
0.04630691558122635,
0.004633170086890459,
-0.006479139905422926,
0.07868145406246185,
-0.009537557139992714,
0.016752159222960472,
-0.0387742780148983,
0.018106069415807724,
0.0011833816533908248,
0.002495557302609086,
0.0335100032389164,
0.0305008627474308,
-0.019613586366176605,
-0.012971806339919567,
-0.013948135077953339,
0.0034042121842503548,
0.02885132096707821,
-0.05437011271715164,
0.06694206595420837,
-0.004235133063048124,
0.015036375261843204,
-0.03637631982564926,
-0.024821588769555092,
-0.012763961218297482,
-0.025579307228326797,
0.0431358702480793,
0.023983843624591827,
0.05460049957036972,
0.02182745561003685,
0.018778476864099503,
-0.02490813285112381,
0.04704853147268295,
-0.08880020678043365,
0.021450793370604515,
-0.0073978896252810955,
0.05501805245876312,
0.046669166535139084,
-0.005980785004794598
] |
<p>I guess that everything that happens to me (or I do), happens before my shadow "records" the information. Is that right? Is it the same for any observer?</p>
| 7,667 |
[
-0.013701372779905796,
-0.0701415091753006,
-0.009616867639124393,
-0.028535310178995132,
0.02739955671131611,
0.02373550646007061,
-0.02960231713950634,
0.018659843131899834,
-0.01364031620323658,
-0.0009364357683807611,
-0.02120012789964676,
0.011701621115207672,
0.01734750345349312,
0.036628853529691696,
0.010014346800744534,
-0.050605811178684235,
-0.01798480749130249,
0.022565031424164772,
0.00852859579026699,
-0.03342585638165474,
0.0007427265518344939,
0.020097723230719566,
0.027286425232887268,
-0.006444759201258421,
-0.01635640859603882,
0.016740720719099045,
-0.013062837533652782,
-0.01815352402627468,
0.02090415731072426,
0.056238193064928055,
-0.024873776361346245,
-0.017177477478981018,
0.005481506232172251,
0.03450204059481621,
0.03983085975050926,
-0.01097026839852333,
-0.0683632493019104,
0.0021874476224184036,
-0.003097366075962782,
-0.008983919396996498,
-0.004423795733600855,
0.01155188400298357,
-0.04096416383981705,
0.04136797413229942,
-0.02227555774152279,
-0.02660338021814823,
0.0025975818280130625,
-0.013423630967736244,
0.009720224887132645,
-0.05477815866470337,
0.0478205569088459,
-0.0036827391013503075,
0.022753754630684853,
0.03408701717853546,
-0.04087663069367409,
0.020755374804139137,
0.08173871785402298,
0.05606180429458618,
0.0030908153858035803,
0.001106784911826253,
-0.002867314498871565,
-0.006070410832762718,
-0.014008685015141964,
-0.01966564729809761,
-0.02206878736615181,
-0.003256152616813779,
-0.003468828508630395,
-0.01948314905166626,
0.05158326029777527,
-0.012840142473578453,
-0.00883911270648241,
0.002595429075881839,
0.03529941663146019,
0.044986527413129807,
0.019247863441705704,
-0.030365558341145515,
0.04647544026374817,
0.015734519809484482,
0.05563315749168396,
0.018193628638982773,
0.013897528871893883,
0.008245889097452164,
0.04341224953532219,
0.02092771604657173,
-0.012840783223509789,
-0.008489501662552357,
0.062517449259758,
-0.016127847135066986,
0.020059775561094284,
0.01866169646382332,
-0.02466394565999508,
0.0018379620742052794,
-0.007715411018580198,
-0.024069158360362053,
0.00018175336299464107,
-0.011346668004989624,
-0.008770173415541649,
0.03964897245168686,
0.024242473766207695,
-0.05893247202038765,
-0.008514301851391792,
-0.008803757838904858,
0.030242951586842537,
0.04997923970222473,
-0.0025135737378150225,
-0.03146916627883911,
-0.01473277434706688,
0.05733782425522804,
-0.013341380283236504,
-0.017105266451835632,
-0.03365136310458183,
-0.01596113108098507,
-0.0063478099182248116,
0.047661881893873215,
0.0014916445361450315,
-0.0224967822432518,
0.021231114864349365,
-0.00836115051060915,
0.05583295226097107,
0.06025158613920212,
0.048666585236787796,
-0.04296986758708954,
-0.012339649721980095,
-0.05436618626117706,
-0.032646339386701584,
0.040272634476423264,
0.04825158044695854,
-0.05069950222969055,
-0.036598507314920425,
0.008423238061368465,
0.020455775782465935,
-0.06068115308880806,
0.026436088606715202,
-0.03462357446551323,
0.01974933035671711,
0.032523106783628464,
-0.1227320209145546,
-0.047167375683784485,
0.028285318985581398,
-0.005128735210746527,
-0.02829062193632126,
-0.0994015783071518,
-0.024859780445694923,
0.030624208971858025,
0.05220688134431839,
0.013415670022368431,
-0.015310820192098618,
0.022499829530715942,
0.033810731023550034,
-0.007803424261510372,
-0.051000941544771194,
-0.013260508887469769,
0.01297290064394474,
-0.04193252697587013,
-0.004036257974803448,
-0.0366886705160141,
0.021090645343065262,
0.05386996269226074,
-0.03395169600844383,
-0.009241321124136448,
0.06502795219421387,
-0.022803859785199165,
0.030140895396471024,
0.03651968017220497,
-0.0121931042522192,
-0.04517609626054764,
0.05751704052090645,
0.015466717071831226,
-0.003243275685235858,
0.017147667706012726,
0.07003669440746307,
0.03265892714262009,
-0.006032469682395458,
0.05476394668221474,
0.06006687507033348,
-0.008564004674553871,
-0.04138679802417755,
0.007901329547166824,
-0.012863734737038612,
-0.02203783579170704,
-0.03818932920694351,
-0.026897985488176346,
0.0254646185785532,
0.007013598922640085,
0.004480382893234491,
0.04140558838844299,
-0.010085254907608032,
-0.016065064817667007,
-0.019163498654961586,
-0.04257107153534889,
-0.04375689849257469,
-0.0051485151052474976,
0.02215261198580265,
-0.03259902074933052,
-0.01994972862303257,
-0.008386787958443165,
-0.0006573584978468716,
0.05264876037836075,
-0.013189042918384075,
-0.03505771607160568,
-0.0279488954693079,
0.0020519455429166555,
0.040294598788022995,
-0.05142921954393387,
-0.011108345352113247,
0.06279141455888748,
0.013341596350073814,
0.00013885398220736533,
-0.004257251042872667,
-0.015027012676000595,
-0.04306028038263321,
0.009221764281392097,
0.030546292662620544,
0.044520314782857895,
-0.014586875215172768,
-0.01166306622326374,
0.012215103022754192,
-0.0002622177707962692,
0.007682453375309706,
0.028830232098698616,
-0.009903631173074245,
0.030029907822608948,
0.026337631046772003,
-0.012714969925582409,
-0.03510851785540581,
0.03721661493182182,
0.035857535898685455,
-0.022483056411147118,
-0.011288356967270374,
-0.019610952585935593,
-0.015684254467487335,
-0.04068581387400627,
0.0003647653211373836,
-0.014204316772520542,
-0.03135961666703224,
0.0300787054002285,
0.02199288085103035,
0.03870944678783417,
-0.00020337122259661555,
0.00047303669271059334,
0.00654689222574234,
-0.03479662165045738,
-0.04020199924707413,
0.027808481827378273,
0.03327358141541481,
0.0026382056530565023,
0.05325545370578766,
0.015654586255550385,
-0.0053747594356536865,
-0.01998238079249859,
-0.037979088723659515,
0.03471124917268753,
-0.04033569619059563,
0.0357007272541523,
0.012589403428137302,
-0.04325368255376816,
0.04061345010995865,
-0.014935900457203388,
-0.005659256596118212,
0.01173136942088604,
0.018577400594949722,
-0.023319948464632034,
-0.015678592026233673,
0.009328687563538551,
0.01260641124099493,
0.015660151839256287,
-0.04394258186221123,
-0.011946802027523518,
0.04429488629102707,
-0.009229330345988274,
0.039901118725538254,
-0.005756749771535397,
0.0024422858841717243,
-0.04620257019996643,
-0.013850449584424496,
0.0025795246474444866,
0.01576060615479946,
0.029046496376395226,
-0.018315184861421585,
-0.07568316161632538,
-0.0438656285405159,
-0.008543507196009159,
0.031067539006471634,
0.05282590910792351,
-0.07265578955411911,
0.009001144208014011,
0.017901113256812096,
-0.013227969408035278,
0.04995421692728996,
-0.02406298741698265,
0.019357936456799507,
0.004011834040284157,
-0.022266175597906113,
-0.012032467871904373,
-0.024393437430262566,
-0.01541456114500761,
-0.05714963749051094,
-0.006409440189599991,
0.0029656165279448032,
0.05601757764816284,
0.0026555098593235016,
-0.07806992530822754,
0.01866132579743862,
-0.044023655354976654,
-0.022927189245820045,
-0.005014524795114994,
-0.017245566472411156,
-0.02323194593191147,
-0.06038453057408333,
0.019824335351586342,
-0.020968738943338394,
-0.042715705931186676,
-0.0009188924450427294,
-0.036958981305360794,
-0.06813295185565948,
0.026410194113850594,
-0.002074458170682192,
0.03661564365029335,
-0.013243491761386395,
-0.0052079688757658005,
0.04002860561013222,
0.019788013771176338,
-0.049813952296972275,
-0.03685363754630089,
-0.02486295998096466,
-0.007538731675595045,
-0.0314093679189682,
0.011570769362151623,
0.0039007053710520267,
-0.018497731536626816,
0.00582616264000535,
0.023169001564383507,
0.016893872991204262,
0.0055639841593801975,
0.01401427946984768,
-0.025605855509638786,
-0.007542774546891451,
0.02144981548190117,
-0.013127103447914124,
-0.005054627079516649,
0.03313245624303818,
-0.010745728388428688,
0.014476497657597065,
-0.006205279380083084,
0.04966685175895691,
0.025925397872924805,
-0.039742812514305115,
0.06011663377285004,
-0.008845428936183453,
0.031543243676424026,
-0.011667211540043354,
0.031482528895139694,
-0.048273324966430664,
0.021474752575159073,
-0.0627090111374855,
0.02998453751206398,
0.027196068316698074,
-0.016505979001522064,
0.0032905724365264177,
0.00936769600957632,
0.01061561144888401,
0.01079484447836876,
-0.0030226169619709253,
-0.03396362066268921,
-0.0334961861371994,
0.02902890555560589,
0.009587204083800316,
-0.012082817032933235,
0.04632589593529701,
0.045827798545360565,
0.008102220483124256,
0.003716029692441225,
-0.06886979937553406,
-0.03192194551229477,
-0.07934343814849854,
0.002754312241449952,
0.04620419815182686,
0.0033322558738291264,
-0.012268060818314552,
0.05959091708064079,
0.00020682867034338415,
0.03637592867016792,
0.024655986577272415,
0.019124720245599747,
-0.06737776100635529,
-0.02595779486000538,
-0.03562140837311745,
0.01568482257425785,
-0.007841755636036396,
0.00479477271437645,
0.030910726636648178,
-0.02590477652847767,
0.01716780476272106,
-0.004241100512444973,
-0.029523376375436783,
-0.05957081913948059,
-0.004652734380215406,
-0.03382808715105057,
-0.01099486742168665,
-0.030638378113508224,
0.029752839356660843,
0.01995399221777916,
-0.00012061576853739098,
0.03593239560723305,
0.05081118643283844,
-0.009195135906338692,
0.017079226672649384,
-0.01179371029138565,
-0.0049648345448076725,
-0.022724846377968788,
0.031238770112395287,
0.0749436765909195,
-0.03487442061305046,
-0.06500954926013947,
0.03300730884075165,
-0.0153476158156991,
0.03531358018517494,
0.03292306512594223,
-0.048631615936756134,
-0.018338046967983246,
-0.0068268016912043095,
-0.026650799438357353,
-0.009542378596961498,
0.04210662841796875,
0.010924795642495155,
0.03463432565331459,
0.014627519063651562,
-0.014876211062073708,
-0.01395193487405777,
0.05180611461400986,
0.055186014622449875,
0.003701057517901063,
-0.0246487595140934,
-0.04542740806937218,
0.014038993045687675,
0.018124671652913094,
-0.013194108381867409,
-0.010469353757798672,
-0.005427879747003317,
0.0049592554569244385,
-0.02448764443397522,
-0.06147385388612747,
-0.025813983753323555,
0.0028281453996896744,
0.00881790742278099,
0.0063467565923929214,
0.04350002110004425,
0.005780785344541073,
0.024601811543107033,
0.048628367483615875,
0.007105645723640919,
0.04752274602651596,
0.025294549763202667,
-0.028477562591433525,
-0.07323591411113739,
0.004557515028864145,
0.01880054920911789,
0.02887342870235443,
-0.005243128631263971,
0.02250673994421959,
-0.043293844908475876,
-0.06123674660921097,
0.028237486258149147,
0.004441829398274422,
0.040038514882326126,
-0.005027281120419502,
-0.018477726727724075,
-0.03209847956895828,
-0.026890672743320465,
0.02122669108211994,
0.04132581129670143,
0.001803548657335341,
0.037951670587062836,
0.019300954416394234,
0.005147659685462713,
-0.04124396666884422,
0.008448784239590168,
-0.007545103318989277,
0.07277429103851318,
0.01564725674688816,
0.00979332160204649,
-0.0069427937269210815,
0.022510912269353867,
-0.029392605647444725,
-0.03018159046769142,
0.01878681778907776,
0.018729733303189278,
-0.01613583043217659,
0.027104387059807777,
0.031605448573827744,
-0.04305146262049675,
0.010463953018188477,
0.020966142416000366,
-0.03597847744822502,
-0.017365824431180954,
-0.06458670645952225,
0.036833859980106354,
-0.004313652869313955,
-0.011578410863876343,
0.036587607115507126,
0.041250985115766525,
0.0058677042834460735,
-0.006981358397752047,
0.007391361054033041,
0.04084877297282219,
-0.005435712169855833,
0.010048167780041695,
0.0032142612617462873,
0.00638294592499733,
-0.02457006834447384,
0.043455205857753754,
0.007137616630643606,
0.01616857759654522,
-0.012669115327298641,
-0.02948535792529583,
-0.032017070800065994,
0.0038049547001719475,
0.020408358424901962,
-0.005697670858353376,
-0.047178614884614944,
-0.004141760058701038,
-0.024965187534689903,
0.0004074042371939868,
0.0035269828513264656,
-0.006537857931107283,
0.023376015946269035,
0.05656689405441284,
-0.010026747360825539,
0.007395720109343529,
-0.04313770681619644,
-0.022415824234485626,
0.04716735705733299,
-0.030709533020853996,
0.01981727033853531,
-0.018919287249445915,
-0.002698887139558792,
0.05231700465083122,
-0.0640619620680809,
-0.007080680690705776,
-0.0026953150518238544,
-0.04937796667218208,
0.018341941758990288,
-0.06630967557430267,
0.02837980166077614,
0.007522162515670061,
-0.006984406150877476,
-0.08004410564899445,
-0.04474158212542534,
0.02225259691476822,
-0.0063297804445028305,
-0.008279122412204742,
-0.003563354955986142,
0.032242465764284134,
-0.033911265432834625,
-0.032244373112916946,
-0.008706451393663883,
-0.0028289700858294964,
-0.018927332013845444,
-0.0014594875974580646,
0.045219920575618744,
0.0057800584472715855,
0.0452747568488121,
0.0033056337852030993,
-0.006738911382853985,
0.018792150542140007,
-0.02612706832587719,
-0.03823137655854225,
0.008975116536021233,
0.027958035469055176,
-0.013434628024697304,
-0.006870517507195473,
-0.014726635068655014,
-0.012359051033854485,
0.020685866475105286,
-0.02971700020134449,
0.015805810689926147,
0.03460412099957466,
-0.007773467339575291,
0.014415965415537357,
-0.06902240216732025,
0.015772152692079544,
0.009096738882362843,
-0.038827184587717056,
0.005263535771518946,
0.0191316120326519,
-0.01594863459467888,
-0.027144059538841248,
0.014674467034637928,
0.03451055660843849,
0.02300107665359974,
-0.01846741884946823,
0.048431478440761566,
0.01850413717329502,
-0.014541041105985641,
0.03403700888156891,
0.00181121239438653,
-0.007427379488945007,
-0.01850677840411663,
0.03707399591803551,
0.03487248346209526,
-0.004700510296970606,
-0.035894110798835754,
-0.0030471552163362503,
-0.028970278799533844,
-0.007534702308475971,
0.05254874378442764,
-0.0356781929731369,
0.04304672032594681,
-0.005366628523916006,
0.010634778998792171,
-0.01567157357931137,
-0.053965095430612564,
-0.005971649195998907,
0.027010217308998108,
0.008048806339502335,
0.04815269261598587,
-0.03711993619799614,
0.04203160107135773,
-0.006445060949772596,
0.06053820624947548,
-0.014804973267018795,
0.00811913050711155,
0.039332058280706406,
0.0127031235024333,
0.0589316263794899,
0.010398081503808498,
-0.026964247226715088,
0.01092493999749422,
-0.044573020190000534,
-0.000004223551059112651,
-0.02249595709145069,
0.010972017422318459,
0.0570082888007164,
0.01993064023554325,
0.0457259826362133,
-0.03240049630403519,
-0.04472316429018974,
-0.024803800508379936,
-0.006361313629895449,
0.0038521140813827515,
0.042039498686790466,
0.04028859734535217,
-0.028078323230147362,
0.04783181846141815,
0.011070560663938522,
0.03159160166978836,
0.0005497206002473831,
-0.08676115423440933,
-0.04844753071665764,
0.00041029471321962774,
-0.06846915185451508,
0.07340583950281143,
-0.028010275214910507,
0.0066346968524158,
0.010870590806007385,
-0.024222660809755325,
0.016457008197903633,
0.024093523621559143,
0.02593873254954815,
0.032699838280677795,
0.067689910531044,
0.028070298954844475,
0.03645158186554909,
-0.022457938641309738,
0.03822155296802521,
0.11648183315992355,
0.03140272572636604,
-0.005517686251550913,
-0.06985844671726227,
-0.009245495311915874,
-0.011624852195382118,
0.024159995838999748,
0.012575497850775719,
0.03592565283179283,
0.013262689113616943,
-0.01811879314482212,
0.040016308426856995,
0.04796789586544037,
0.037214245647192,
-0.020968256518244743,
0.0625806525349617,
-0.03464733436703682,
-0.026092585176229477,
-0.0004399517201818526,
0.009476653300225735,
-0.023639678955078125,
0.003889806102961302,
-0.021034378558397293,
-0.0217738039791584,
0.024090152233839035,
0.005134067963808775,
0.007078119087964296,
-0.02793055772781372,
-0.0002998222189489752,
0.021335963159799576,
-0.00570892496034503,
0.040818408131599426,
0.02825877070426941,
-0.005122044123709202,
-0.047304339706897736,
0.007425026036798954,
0.012895887717604637,
-0.0012698863865807652,
0.018176671117544174,
0.04984213784337044,
-0.004625077359378338,
0.004250991158187389,
-0.012164400890469551,
-0.021665003150701523,
-0.0668337345123291,
-0.032606713473796844,
-0.012761586345732212,
0.023552734404802322,
-0.01817730814218521,
-0.007220792584121227,
0.0013584395637735724,
-0.01640726439654827,
0.03777248039841652,
-0.04616192355751991,
-0.04253656789660454,
0.032326698303222656,
0.012127941474318504,
-0.03272080421447754,
-0.04473348334431648,
-0.00343043333850801,
0.0072974576614797115,
-0.013546264730393887,
0.017102552577853203,
-0.001784036518074572,
0.017376907169818878,
-0.03322688862681389,
-0.028343530371785164,
-0.02376580238342285,
-0.010273811407387257,
0.018339160829782486,
0.01550078485161066,
-0.0037132594734430313,
-0.04998698830604553,
-0.02185097336769104,
0.03648027032613754,
0.006967540830373764,
0.01183406449854374,
-0.004897288512438536,
-0.007193297613412142,
-0.017877299338579178,
-0.02180183306336403,
0.029711993411183357,
-0.024710763245821,
-0.014157603494822979,
-0.03774320334196091,
0.03018527664244175,
0.05893391743302345,
0.029107755050063133,
0.0022600661031901836,
0.04108898341655731,
0.0008482217090204358,
0.045085858553647995,
0.016399681568145752,
0.01812184415757656,
0.005579063668847084,
0.04205009341239929,
-0.022026829421520233,
0.02534211054444313,
-0.04314377158880234,
0.025544296950101852,
0.009021447040140629,
0.019131014123558998,
0.03083786740899086,
0.04028540477156639,
0.016619956120848656,
0.014329816214740276,
-0.012506010010838509,
-0.0363188162446022,
0.009257804602384567,
-0.012938875705003738,
0.023417023941874504,
0.0308076199144125,
-0.024136751890182495,
-0.038761500269174576,
0.024793628603219986,
-0.027661053463816643,
-0.012914332561194897,
-0.03864094614982605,
0.029598331078886986,
0.032134417444467545,
0.05988255515694618,
-0.014592432416975498,
-0.027518220245838165,
-0.049932606518268585,
0.012899588793516159,
0.013509833253920078,
0.002499714959412813,
-0.0239347405731678,
0.03376550227403641,
-0.0076658641919493675,
-0.06162025034427643,
-0.02251727133989334,
-0.039689529687166214,
-0.053443972021341324,
-0.029181135818362236,
0.01753719337284565,
-0.027219928801059723,
0.02558708004653454,
0.0315212719142437,
-0.044473275542259216,
0.010500889271497726,
-0.016606951132416725,
-0.0656304806470871,
0.06111990287899971,
0.003232473274692893,
0.028453003615140915,
0.02278931625187397,
0.018634866923093796,
0.03269191086292267,
0.08309657126665115,
-0.004136077594012022,
0.0016496486496180296,
0.06502912193536758,
-0.0016005277866497636,
-0.018781624734401703,
0.02145707607269287,
0.05041955038905144,
-0.01334953773766756,
-0.04639805108308792,
0.020970270037651062,
-0.017724551260471344,
0.03103962168097496,
0.017212379723787308,
0.011481153778731823,
0.011750428006052971,
0.01854526437819004,
-0.0002530098718125373,
0.00189759093336761,
0.011100169271230698,
0.02903788350522518,
-0.03633761405944824,
0.06174642965197563,
0.030855057761073112,
0.016508953645825386,
-0.0855446308851242,
-0.0097444336861372,
-0.0057988897897303104,
0.04405008256435394,
0.018018659204244614,
-0.018943000584840775,
0.017719905823469162,
0.021098166704177856,
-0.05463239178061485,
-0.004606505855917931,
0.0277875903993845,
-0.009852869436144829,
0.0009626589016988873,
0.021932397037744522,
-0.04027073085308075,
0.03027041256427765,
0.06144395470619202,
0.01825052686035633,
0.018354032188653946,
0.017448432743549347,
-0.0041196937672793865,
-0.03174856677651405,
-0.07070112973451614,
0.032617948949337006,
0.008313636295497417,
0.00415799068287015,
0.05342934653162956,
-0.04270681366324425,
-0.012737906537950039,
0.012708432972431183,
0.019476553425192833,
0.006373720243573189,
-0.006492202170193195,
0.035203419625759125,
0.039179399609565735,
0.02458322048187256,
-0.019833561033010483,
-0.008007586002349854,
0.018956409767270088,
0.025651199743151665,
0.018605079501867294,
0.03310472518205643,
-0.040522731840610504,
-0.013575443997979164,
-0.007673796731978655,
0.00011206240742467344,
-0.04230358824133873,
0.017853520810604095,
-0.005053080152720213,
0.0036614518612623215,
-0.01022720243781805,
0.04428655281662941,
-0.009336643852293491,
-0.014899206347763538,
-0.029650069773197174,
-0.028514590114355087,
0.0061033801175653934,
0.002700385171920061,
0.03155379742383957,
-0.0321151427924633,
0.01337750069797039,
0.010231837630271912,
-0.029067255556583405,
-0.0009468104690313339,
0.0115412138402462,
-0.0035804249346256256,
-0.048463694751262665,
-0.023295994848012924,
-0.03584878146648407,
0.015368915162980556,
0.015112040564417839,
-0.03336438909173012,
-0.045376408845186234,
0.02757091075181961,
0.013467837125062943,
-0.013638374395668507,
0.013239704072475433,
-0.06438609212636948,
-0.02477341704070568,
-0.062212985008955,
0.02597947232425213,
-0.0028295412193983793,
0.020161528140306473,
-0.0583808571100235,
0.016748594120144844,
0.020483242347836494,
-0.005107410717755556,
0.02921677567064762,
-0.02324153669178486,
-0.02792777493596077,
0.03151431679725647,
-0.015678485855460167,
0.0023231087252497673,
-0.01907019503414631,
0.01724318414926529,
-0.0052593424916267395,
-0.0010895751183852553,
-0.016122430562973022,
-0.06533487141132355,
-0.030623549595475197,
0.02400779351592064,
0.01738307811319828,
0.0017869981238618493,
0.0011953555513173342,
-0.03057057410478592,
0.008722081780433655,
0.03991410881280899,
0.00806962139904499,
0.009582450613379478,
0.03908207640051842,
0.028597809374332428,
0.020784499123692513,
0.07761922478675842,
-0.04581410437822342,
-0.0746784582734108,
0.03176211565732956,
-0.01099895965307951,
0.0038330312818288803,
-0.02114562690258026,
-0.0002528742188587785,
0.03063230775296688,
-0.019021224230527878,
-0.03902619704604149,
0.006088979076594114,
-0.018507888540625572,
0.036634497344493866,
0.03674541413784027,
-0.02017553523182869,
0.02449321374297142,
0.0009572922717779875,
0.03223308175802231,
0.0331115759909153,
0.005599596071988344,
0.0057269674725830555,
0.060874760150909424,
0.06973813474178314,
-0.012483393773436546,
-0.008076222613453865,
0.032189905643463135,
0.005324545316398144,
0.03504294157028198,
-0.0229239109903574,
0.052065134048461914,
-0.03993930667638779,
0.002543181646615267,
0.031936440616846085,
0.0038288619834929705,
-0.01293796207755804,
0.02784603461623192,
-0.012013722211122513,
0.07951025664806366,
-0.0263426061719656,
0.004840266425162554,
-0.031309574842453,
0.03742826357483864,
-0.06582067161798477,
-0.003034739987924695,
0.0067990925163030624,
0.021557467058300972,
-0.01856938563287258,
-0.027177652344107628,
-0.06244909018278122,
0.016408614814281464,
0.01440193597227335,
-0.07093114405870438,
-0.0014642936876043677,
-0.01652172952890396,
0.036901138722896576,
0.0068347761407494545,
-0.010418583638966084,
0.008059901185333729,
-0.033407095819711685,
0.024055372923612595,
0.007680465932935476,
-0.007787353824824095,
-0.012908583506941795,
-0.019987119361758232,
-0.024049121886491776,
0.04946647956967354,
-0.06385087221860886,
-0.007642707787454128,
-0.047976650297641754,
0.06158209219574928,
0.014083453454077244,
-0.027320757508277893
] |
<p>Does someone know simple model of energy loss in solid materials for a solid bullet?</p>
<p>For example: I want to estimate momentum transferred to a thin plastic plate given by a small bullet. No matter how difficult model is. But it should depend only on plate/projectile parameters?</p>
<p><strong>EDIT:</strong></p>
<p>No precise solution is needed. It is interesting to know order of energy transfer.
One simple model that i suggested was model of exponential suppression:
$$ {\delta E}(r) \approx E_{0} e^{ - \frac{r}{d} } $$
where $d$ is a "terminal length" - after crossing this length bullet loses $e$ units of energy. So, knowing max distance in material one can find parameter $d$</p>
<p>It is not obvious that this formula is close to reality, but it is first step. Also it is not clear if one can use this formula for thin plates.</p>
<p>I have no experience solving such problems, so i asked if someone can point me (links, books, ideas). </p>
| 7,668 |
[
-0.036993175745010376,
-0.043539587408304214,
0.004800606518983841,
-0.03924495726823807,
-0.017651215195655823,
0.010778463445603848,
-0.04306013137102127,
-0.00994040071964264,
0.023392468690872192,
-0.03562626615166664,
0.007813883945345879,
0.0016278261318802834,
0.036014266312122345,
0.013220584951341152,
0.03195951133966446,
-0.0025098228361457586,
-0.016791483387351036,
-0.012288509868085384,
-0.0019067295361310244,
-0.08529740571975708,
0.012731388211250305,
-0.03539971634745598,
0.029733378440141678,
-0.02595958672463894,
-0.034945953637361526,
0.030010148882865906,
0.019988451153039932,
0.007362912409007549,
0.021738575771450996,
0.02427317574620247,
0.004782765172421932,
-0.017898058518767357,
-0.005064197350293398,
0.005342582706362009,
-0.025392908602952957,
0.014801698736846447,
-0.05546306446194649,
-0.052607737481594086,
-0.011908454820513725,
0.011612902395427227,
-0.04826289042830467,
-0.008658132515847683,
0.02642226032912731,
0.043847229331731796,
-0.007596946787089109,
-0.0061189704574644566,
-0.005816577933728695,
-0.03235763683915138,
0.030038684606552124,
-0.046288225799798965,
0.062487032264471054,
0.001858266768977046,
0.08927615731954575,
0.004741291515529156,
-0.0014981598360463977,
-0.0069518135860562325,
0.05409587547183037,
0.08428210765123367,
-0.01524018868803978,
-0.05765640363097191,
-0.03368058428168297,
-0.024855028837919235,
-0.014611957594752312,
-0.016995754092931747,
0.007677949033677578,
0.04277607053518295,
-0.007806381676346064,
-0.03951479494571686,
0.005123895592987537,
-0.003920344635844231,
-0.005540783517062664,
0.011459583416581154,
0.05119160935282707,
0.03232897073030472,
0.022603949531912804,
0.00017262242909055203,
0.028650693595409393,
0.045632533729076385,
0.035761091858148575,
0.062017105519771576,
-0.03566111624240875,
-0.006965016480535269,
0.04677681624889374,
0.06355427205562592,
-0.014083728194236755,
-0.022507840767502785,
0.07875274866819382,
0.012775491923093796,
0.020974833518266678,
0.026529250666499138,
-0.023722106590867043,
0.009531671181321144,
0.010602643713355064,
-0.008806528523564339,
-0.0216843094676733,
0.04029959812760353,
0.016337499022483826,
0.08400827646255493,
-0.011001690290868282,
-0.016218457370996475,
-0.020441051572561264,
-0.013794578611850739,
0.03272799775004387,
0.08661723881959915,
0.02313522808253765,
-0.01977413333952427,
-0.03512100502848625,
-0.009617641568183899,
-0.012420940212905407,
-0.00431544566527009,
-0.026355162262916565,
0.030004508793354034,
0.00443312618881464,
-0.007640480995178223,
-0.0071001905016601086,
-0.025656182318925858,
0.012942830100655556,
-0.04575086012482643,
0.005512550473213196,
0.04709212854504585,
0.03373564034700394,
-0.016428273171186447,
0.006875687278807163,
-0.025284333154559135,
-0.070994071662426,
-0.01075732707977295,
0.06199454516172409,
-0.038670554757118225,
-0.026437226682901382,
0.01907273754477501,
0.026585722342133522,
-0.031100109219551086,
0.01850014552474022,
-0.030080875381827354,
0.05859891325235367,
-0.0030792856123298407,
-0.07971007376909256,
-0.040125805884599686,
0.032734569162130356,
-0.019410572946071625,
-0.017883947119116783,
-0.05654340982437134,
-0.02858649007976055,
0.03417033702135086,
0.02849004603922367,
-0.0005422221729531884,
0.0014079809188842773,
-0.00124360469635576,
0.005893104709684849,
-0.032744474709033966,
-0.016458578407764435,
0.004542675334960222,
-0.007144412025809288,
0.011159472167491913,
0.00958066713064909,
-0.03623387962579727,
0.0359080545604229,
0.0009567050728946924,
-0.006617415696382523,
-0.007028763182461262,
0.05746998265385628,
-0.012070865370333195,
-0.027472637593746185,
-0.007906998507678509,
-0.0001786469656508416,
-0.02953959070146084,
0.08238034695386887,
0.006197636481374502,
0.00855579786002636,
-0.01223493181169033,
0.018989017233252525,
-0.004889592528343201,
0.030770080164074898,
-0.014828941784799099,
0.030395979061722755,
-0.04411529377102852,
-0.028573865070939064,
-0.02731626108288765,
-0.04865547642111778,
0.0209601279348135,
-0.05446111783385277,
-0.029381118714809418,
0.04301901534199715,
0.01850663498044014,
0.013116279616951942,
0.020437436178326607,
0.01355252880603075,
-0.021870259195566177,
-0.0215890072286129,
0.0038112772163003683,
-0.038604699075222015,
-0.07414153218269348,
0.059726931154727936,
-0.0013979299692437053,
0.0323413647711277,
0.0294148288667202,
-0.02592937834560871,
-0.011074328795075417,
0.018085351213812828,
-0.01064479723572731,
-0.011103581637144089,
0.009587706997990608,
-0.018326817080378532,
-0.03255670890212059,
-0.0016479509649798274,
0.035520076751708984,
0.020625106990337372,
0.0025443253107368946,
0.018938744440674782,
-0.018765602260828018,
-0.008120715618133545,
-0.015983708202838898,
-0.03469165787100792,
0.02354400046169758,
-0.01852252520620823,
-0.029035693034529686,
0.01850740984082222,
-0.03525927662849426,
0.030019210651516914,
0.014300140552222729,
-0.024043582379817963,
0.0793876126408577,
0.07738929986953735,
0.017584461718797684,
-0.022285858169198036,
0.04138343036174774,
-0.00457239244133234,
0.02610447071492672,
-0.029465943574905396,
-0.024970712140202522,
-0.04512377455830574,
-0.010765096172690392,
0.011375625617802143,
0.02848506160080433,
-0.04386798292398453,
0.01109873317182064,
0.021911734715104103,
-0.0153806759044528,
0.04042144492268562,
0.014064209535717964,
0.0016047561075538397,
-0.045940984040498734,
0.0017728360835462809,
0.00748994667083025,
-0.03816191852092743,
0.029486358165740967,
-0.020717564970254898,
0.002897842787206173,
-0.009438017383217812,
-0.013255076482892036,
0.006560053676366806,
0.02687324397265911,
0.039759404957294464,
-0.004499547183513641,
0.014743121340870857,
-0.05703112483024597,
0.04216165095567703,
-0.012543953023850918,
0.019155943766236305,
0.05919426307082176,
-0.019320722669363022,
0.024564450606703758,
-0.03896785527467728,
-0.002745335455983877,
0.03162652999162674,
0.011727026663720608,
0.014588870108127594,
0.00016186614811886102,
0.012652029283344746,
-0.047892361879348755,
0.007202639244496822,
0.003493656637147069,
-0.0035312040708959103,
-0.025345783680677414,
-0.01651758886873722,
0.03397497162222862,
0.030749524012207985,
0.0077270944602787495,
-0.026305845007300377,
-0.024889836087822914,
0.014256139285862446,
-0.028499938547611237,
-0.008189775049686432,
-0.004881829954683781,
-0.03192616626620293,
0.0031500596087425947,
-0.04472150281071663,
-0.03866012021899223,
0.041857291013002396,
-0.0008781972574070096,
-0.002291411394253373,
0.040690429508686066,
0.0053323376923799515,
-0.06826428323984146,
0.01910792663693428,
0.02128715254366398,
-0.012134167365729809,
-0.04739546775817871,
0.031959328800439835,
0.05443299189209938,
0.03209991008043289,
-0.019600091502070427,
0.028604447841644287,
-0.01836903765797615,
-0.03522012382745743,
-0.017222076654434204,
0.015387165360152721,
0.008374922908842564,
0.017361905425786972,
0.02750752493739128,
0.045680321753025055,
-0.010919109918177128,
-0.00007720086432527751,
-0.0711931511759758,
-0.023812660947442055,
0.03094596602022648,
-0.0003401107096578926,
0.029907314106822014,
0.000579573679715395,
-0.025840573012828827,
0.0967457965016365,
0.017587080597877502,
-0.03586774691939354,
-0.004509536549448967,
-0.030638929456472397,
0.027553236111998558,
-0.013068600557744503,
0.0026861894875764847,
0.015549538657069206,
0.004503102041780949,
0.00452542444691062,
-0.005118714179843664,
0.003753700526431203,
-0.0027670676354318857,
0.011561727151274681,
0.019922392442822456,
-0.015594800934195518,
0.01041624415665865,
-0.03627558425068855,
0.01656973734498024,
0.019976938143372536,
-0.030712425708770752,
0.046603910624980927,
-0.024186642840504646,
0.03509948030114174,
0.028812624514102936,
-0.06161213666200638,
0.03101983293890953,
-0.0059098247438669205,
-0.06326010823249817,
-0.017901599407196045,
0.01991705782711506,
0.002894933335483074,
-0.0226827971637249,
0.01619899831712246,
0.054379478096961975,
0.05264365300536156,
0.020526284351944923,
0.024484731256961823,
0.014227986335754395,
0.0312667116522789,
-0.014114873483777046,
-0.02556181140244007,
-0.027786685153841972,
0.016558421775698662,
0.022511065006256104,
0.019669171422719955,
0.0006939944578334689,
0.025639008730649948,
0.035801734775304794,
0.030001414939761162,
0.024278197437524796,
-0.013146107085049152,
0.01302808616310358,
-0.042501050978899,
-0.01926550827920437,
-0.042160846292972565,
0.06981076300144196,
-0.004081670194864273,
0.0652717873454094,
0.05278956517577171,
0.032984741032123566,
0.05704451724886894,
0.013251480646431446,
-0.07492602616548538,
0.044451918452978134,
-0.012551859021186829,
-0.009570226073265076,
-0.025671418756246567,
0.04226750135421753,
-0.009136254899203777,
-0.009251678362488747,
-0.0038803720381110907,
-0.006437760777771473,
-0.008759534917771816,
-0.04839223623275757,
0.010987987741827965,
-0.027049992233514786,
-0.033965546637773514,
0.0021767111029475927,
0.053403645753860474,
0.02299177646636963,
-0.022302988916635513,
-0.024100089445710182,
0.03737128898501396,
-0.029865918681025505,
-0.020369991660118103,
-0.04764912277460098,
0.007642967160791159,
-0.014893478713929653,
0.07420006394386292,
0.017303474247455597,
0.011449356563389301,
-0.007990099489688873,
0.0041679865680634975,
-0.0004963288083672523,
0.055749986320734024,
-0.013164258562028408,
-0.012671317905187607,
-0.018388111144304276,
-0.07895708829164505,
0.03255282714962959,
0.006823222152888775,
0.03598492592573166,
-0.02471998892724514,
0.01525562908500433,
0.037641119211912155,
0.0073081073351204395,
-0.05103525519371033,
0.01752958633005619,
0.029252104461193085,
0.007480239495635033,
0.013249348849058151,
-0.06568733602762222,
-0.009784269146621227,
-0.021277982741594315,
0.0022630514577031136,
-0.00899883545935154,
0.00641353614628315,
0.027290672063827515,
0.011288977228105068,
0.04978135973215103,
-0.004901100881397724,
0.003750643925741315,
-0.01853432133793831,
-0.022588731721043587,
-0.0020242072641849518,
-0.0150230024009943,
-0.007134844549000263,
0.04934751242399216,
0.0436844639480114,
0.048630692064762115,
0.03237674757838249,
0.017213480547070503,
-0.04858803376555443,
0.010893131606280804,
0.02151673659682274,
0.03024456650018692,
-0.0024473611265420914,
-0.00882615428417921,
-0.04999644681811333,
-0.040393128991127014,
0.03699833154678345,
0.004962073639035225,
0.011173087172210217,
-0.016282226890325546,
0.0036057198885828257,
-0.00013125127588864416,
-0.02296820841729641,
-0.05115453153848648,
0.02075982093811035,
-0.0015683055389672518,
-0.004449645988643169,
-0.06299395859241486,
-0.000799851433839649,
-0.018336372449994087,
0.027756327763199806,
0.03288029506802559,
0.06201354041695595,
-0.01568431966006756,
0.0024785473942756653,
0.007600410841405392,
-0.001923850504681468,
-0.033382680267095566,
-0.05867193639278412,
0.006070861127227545,
-0.006062965840101242,
-0.017031218856573105,
0.002193805994465947,
-0.03209894895553589,
-0.023250604048371315,
0.06186448037624359,
0.016413522884249687,
-0.04324138164520264,
0.013960699550807476,
-0.03906005993485451,
0.029568567872047424,
0.01838788390159607,
-0.03582590073347092,
0.05098646134138107,
0.05937160551548004,
-0.0072304182685911655,
-0.009180232882499695,
0.0015297207282856107,
0.036623816937208176,
-0.020599283277988434,
-0.018938682973384857,
-0.06429830938577652,
0.038507506251335144,
-0.03307885304093361,
0.032396238297224045,
0.02084992825984955,
0.05110662430524826,
0.0056313397362828255,
-0.021271763369441032,
0.0026389267295598984,
0.009217406623065472,
-0.00032617541728541255,
0.036441363394260406,
0.005806302651762962,
0.04346252232789993,
0.02346148155629635,
-0.010330243036150932,
-0.03693974018096924,
0.04307686537504196,
-0.004551333840936422,
0.02950240485370159,
-0.026889385655522346,
-0.011776651255786419,
-0.06572140008211136,
-0.03125379979610443,
0.026923762634396553,
-0.04726901650428772,
0.0641145184636116,
-0.002472973195835948,
-0.008699330501258373,
0.0424933098256588,
-0.045501772314310074,
-0.021519744768738747,
0.017531290650367737,
0.004464740864932537,
0.022768491879105568,
-0.030064303427934647,
0.002875866834074259,
0.009109717793762684,
0.032142724841833115,
-0.05204742029309273,
-0.03617960959672928,
0.03707427531480789,
0.003443511901423335,
-0.036638904362916946,
-0.07202611118555069,
-0.0028586327098309994,
-0.011949020437896252,
-0.03251541405916214,
0.016897425055503845,
0.03756531700491905,
0.00819707103073597,
0.01165340282022953,
0.0014918027445673943,
-0.02520676702260971,
0.03720622882246971,
0.013623302802443504,
-0.0389990359544754,
0.007377893663942814,
-0.0022479917388409376,
-0.027055801823735237,
-0.026898257434368134,
0.049424465745687485,
-0.006592488847672939,
0.015836820006370544,
0.010438795201480389,
-0.009639601223170757,
0.03312850371003151,
-0.015477572567760944,
0.02040664479136467,
0.013044665567576885,
0.018300972878932953,
-0.03616298362612724,
-0.0035641805734485388,
0.02028506249189377,
-0.003165486268699169,
0.026089848950505257,
-0.030732549726963043,
0.005465238820761442,
-0.039886489510536194,
-0.04695533961057663,
0.024626953527331352,
0.008360094390809536,
0.028065090999007225,
-0.006587668787688017,
0.048863478004932404,
-0.000895640638191253,
0.011007266119122505,
0.03244119510054588,
-0.01075987983494997,
0.046305663883686066,
-0.043630149215459824,
0.02369779907166958,
-0.003738995408639312,
-0.004532999359071255,
-0.02178649604320526,
-0.06664343923330307,
-0.048170872032642365,
0.026361307129263878,
0.03371405974030495,
-0.04207388684153557,
0.05041137710213661,
-0.004726056940853596,
0.02318394184112549,
-0.0031130595598369837,
-0.0034019427839666605,
-0.005164756439626217,
-0.007105673663318157,
-0.0055962977930903435,
0.06619878113269806,
-0.004954113624989986,
-0.004341344814747572,
0.009792882949113846,
0.02352416329085827,
-0.02670486643910408,
0.041824519634246826,
-0.01842469349503517,
0.00484861247241497,
0.029229136183857918,
-0.07377202063798904,
0.003218143479898572,
0.025162138044834137,
-0.048015136271715164,
0.034881655126810074,
-0.018228789791464806,
-0.02332192286849022,
0.040691036731004715,
0.014090108685195446,
0.004834209103137255,
-0.044115953147411346,
-0.02020508050918579,
-0.030088083818554878,
0.03038509003818035,
0.03712347149848938,
-0.014070132747292519,
-0.0020163499284535646,
0.025607986375689507,
0.02513679675757885,
-0.0056325532495975494,
0.042003706097602844,
-0.018091978505253792,
-0.022058699280023575,
-0.012844174169003963,
-0.032146818935871124,
-0.05529957637190819,
0.0226705614477396,
0.026864830404520035,
0.0016681266715750098,
0.017791423946619034,
-0.0028106418903917074,
0.022548003122210503,
-0.0006956314318813384,
0.010042564943432808,
-0.0038531178142875433,
0.07275280356407166,
0.009600632824003696,
-0.013460466638207436,
-0.012042948044836521,
0.033340029418468475,
0.11990859359502792,
0.0665164589881897,
0.015074784867465496,
-0.025176862254738808,
-0.013024703599512577,
-0.007564481347799301,
0.006959713529795408,
-0.031988367438316345,
0.027416981756687164,
-0.007381002884358168,
-0.014370391145348549,
0.023503722622990608,
0.07417388260364532,
0.0015298492508009076,
-0.023524057120084763,
0.049467213451862335,
-0.030210651457309723,
-0.02371164783835411,
0.019957521930336952,
-0.011337384581565857,
-0.016003485769033432,
0.005352351814508438,
-0.008622551336884499,
0.035726241767406464,
0.034888170659542084,
-0.03458419442176819,
-0.04502343758940697,
-0.049163442105054855,
0.006755859591066837,
-0.010917401872575283,
-0.0033691388089209795,
-0.022723017260432243,
0.0008559212437830865,
-0.02206725999712944,
0.012994209304451942,
0.0032671468798071146,
0.038187168538570404,
-0.0011042881524190307,
0.0017060540849342942,
0.0019984638784080744,
0.02207162231206894,
0.03373868018388748,
0.027371559292078018,
0.018876293674111366,
-0.020994149148464203,
-0.046566132456064224,
-0.03464386984705925,
0.032861340790987015,
-0.034154754132032394,
0.02963227406144142,
-0.01623104326426983,
-0.00559596810489893,
0.0004654770018532872,
-0.046958066523075104,
-0.046770211309194565,
0.014785191975533962,
0.040032874792814255,
-0.027370721101760864,
-0.012657228857278824,
-0.005525724496692419,
0.03551995009183884,
0.020021462813019753,
-0.01417576428502798,
0.0024632923305034637,
-0.008340648375451565,
-0.013390808366239071,
-0.0087805837392807,
0.06462355703115463,
-0.04347529262304306,
-0.04389016330242157,
-0.011128700338304043,
-0.01316500548273325,
-0.033752452582120895,
-0.0034310214687138796,
0.009453344158828259,
0.021392449736595154,
0.01587514951825142,
-0.010593351908028126,
0.0097502451390028,
-0.04825180396437645,
-0.0865471214056015,
0.02696668915450573,
0.00010372286487836391,
-0.0013430359540507197,
-0.05386950075626373,
-0.010762340389192104,
0.014239353127777576,
0.04923805594444275,
-0.02003028243780136,
0.004864651709794998,
-0.0303436741232872,
0.04678777605295181,
0.04716860502958298,
-0.03999057784676552,
-0.007471999153494835,
0.0006389424670487642,
-0.023141587153077126,
0.06031988561153412,
-0.04105763882398605,
0.03205776959657669,
0.021728426218032837,
0.019757358357310295,
0.01843634806573391,
0.025968510657548904,
-0.04605526104569435,
0.008263008669018745,
-0.013722066767513752,
-0.05424205958843231,
0.0032451306469738483,
-0.00262179272249341,
0.00269624893553555,
-0.008119472302496433,
0.008597472682595253,
-0.02480650693178177,
-0.036658573895692825,
-0.02641284093260765,
0.008896378800272942,
-0.020205870270729065,
0.014288554899394512,
-0.0691046342253685,
-0.01683795638382435,
-0.0526210181415081,
0.01945641078054905,
0.01575288735330105,
0.007231041323393583,
-0.0014888796722516418,
-0.026151642203330994,
-0.023468872532248497,
0.019700374454259872,
-0.03549395501613617,
-0.013477732427418232,
-0.0026577175594866276,
-0.00552848307415843,
0.002878752537071705,
0.021757254377007484,
0.025958549231290817,
-0.0052747768349945545,
0.0353829450905323,
0.04438074305653572,
-0.011122584342956543,
0.02480177767574787,
-0.06382596492767334,
-0.07204259186983109,
0.0336902029812336,
0.021703585982322693,
0.06772631406784058,
0.014419560320675373,
-0.02798115462064743,
-0.0061948783695697784,
0.07894184440374374,
0.01590055599808693,
-0.027178112417459488,
-0.005277521908283234,
-0.02755809761583805,
0.013726815581321716,
-0.019630134105682373,
0.014401624910533428,
-0.03629802167415619,
-0.0005494924844242632,
0.03791971132159233,
-0.03461144119501114,
-0.0198048185557127,
0.026108529418706894,
0.050635941326618195,
-0.022470509633421898,
-0.010291995480656624,
0.023080848157405853,
0.0532982274889946,
0.026607738807797432,
0.0772598460316658,
0.02531622163951397,
0.044672977179288864,
0.027882136404514313,
-0.005444925278425217,
-0.09793349355459213,
0.01805371791124344,
-0.03223452717065811,
0.03353391960263252,
0.027066778391599655,
-0.0725662112236023,
0.04009314626455307,
0.01231700461357832,
-0.07690521329641342,
0.004331163130700588,
-0.05951758474111557,
0.0015887556364759803,
-0.024441715329885483,
-0.019834568724036217,
-0.02168048545718193,
0.006734730210155249,
0.004722840618342161,
0.062331050634384155,
0.05059489980340004,
0.04901958629488945,
0.01199305895715952,
0.013760935515165329,
-0.00650915177538991,
0.03930521383881569,
0.03002183884382248,
0.002515204017981887,
0.0713445171713829,
-0.006392951589077711,
0.005629681050777435,
-0.008591223508119583,
0.0015005538007244468,
0.01091329287737608,
0.01781090535223484,
0.04415407404303551,
0.0034033956471830606,
0.017595602199435234,
0.02165146730840206,
-0.014299722388386726,
-0.011501076631247997,
-0.00872894749045372,
-0.027930134907364845,
-0.005517803598195314,
-0.0601416677236557,
0.02377721481025219,
0.030485527589917183,
-0.01626250520348549,
-0.014467524364590645,
0.008786186575889587,
-0.017681784927845,
-0.024564363062381744,
0.022847648710012436,
-0.018182028084993362,
0.032926756888628006,
-0.0246927160769701,
-0.010616978630423546,
-0.041639503091573715,
-0.019919786602258682,
0.03159531578421593,
0.006591135170310736,
0.0026760755572468042,
0.0427575521171093,
-0.01814260147511959,
-0.01809435710310936,
0.007845739834010601,
0.020702235400676727,
-0.023979170247912407,
-0.04728980362415314,
0.0015270387521013618,
0.010878310538828373,
0.023473430424928665,
-0.03867647796869278,
-0.047764040529727936,
-0.04157645255327225,
0.01579110510647297,
0.017702123150229454,
0.028671057894825935,
0.0005174217512831092,
-0.015091571025550365,
0.006781484466046095,
-0.09104537963867188,
0.020914997905492783,
-0.030330967158079147,
-0.028840331360697746,
-0.00632480438798666,
-0.04366889223456383,
0.042822372168302536,
0.02365138940513134,
0.07275467365980148,
-0.0511813759803772,
-0.039534613490104675,
0.032340966165065765,
-0.02740759775042534,
-0.01651896722614765,
-0.04367601498961449,
-0.016323454678058624,
-0.01397621538490057,
-0.001937779481522739,
-0.050486523658037186,
0.015997735783457756,
-0.01045734342187643,
0.008666332811117172,
0.014979592524468899,
0.003976082429289818,
-0.03365686163306236,
-0.023174531757831573,
-0.04778105765581131,
0.0298114325851202,
0.008231639862060547,
0.0030944040045142174,
0.08487513661384583,
-0.018888643011450768,
-0.012355173006653786,
-0.019339974969625473,
-0.02440618723630905,
-0.03156326338648796,
0.0038286077324301004,
-0.04326224327087402,
-0.026292406022548676,
-0.012501389719545841,
0.029245754703879356,
0.030589651316404343,
-0.05696841701865196,
0.012720351107418537,
0.037991177290678024,
-0.04949311912059784,
-0.033687297254800797,
0.02926352247595787,
0.02514835074543953,
0.04406966641545296,
-0.004431968554854393,
0.01644682139158249,
0.023979242891073227,
0.005239225458353758,
-0.022586245089769363,
0.007792141288518906,
0.01871366612613201,
-0.0065497406758368015,
0.018984336405992508,
-0.0045402925461530685,
-0.03562638908624649,
0.00006660731014562771,
0.004586729221045971,
0.002587389899417758,
-0.007950082421302795,
-0.03054850921034813,
0.03386810049414635,
0.01358103472739458,
-0.039908744394779205,
0.002229983452707529,
-0.03836202621459961,
0.07644639164209366,
0.01695176400244236,
0.004899221938103437,
-0.032135069370269775,
0.006370721850544214,
-0.013930960558354855,
0.06218697503209114,
0.002907475456595421,
-0.0019632764160633087,
0.031157273799180984,
0.04414628446102142,
-0.005222596228122711,
0.029369689524173737,
0.024508098140358925,
-0.028283515945076942,
0.02864273451268673,
-0.016885215416550636,
-0.005002568941563368,
0.005789817310869694,
-0.02020479179918766,
-0.0049715652130544186,
-0.007388886995613575,
0.04588008671998978,
0.02429131604731083,
0.024218866601586342,
0.009366512298583984,
0.01918170042335987,
0.027449991554021835,
0.055680446326732635,
-0.07454101741313934,
-0.00313590164296329,
-0.034019481390714645,
0.020157763734459877,
-0.030396893620491028,
0.019185392186045647
] |
<p>It is well known that you can trap water in a drinking straw by placing the tip of your finger over the top while the straw is in the water, and then lifting it out. The inner diameter of the straw is 0.5 cm; the height of the trapped water column inside the straw is 5.0 cm. Find the pressure in the air pocket between your finger and the water.</p>
| 7,669 |
[
-0.006611980032175779,
-0.030569400638341904,
-0.00553940748795867,
-0.0013128943974152207,
0.02754763886332512,
-0.04442140460014343,
-0.0327288918197155,
-0.03845340758562088,
0.003327856073155999,
0.0013398739974945784,
0.06054830923676491,
0.05476345494389534,
0.042273376137018204,
0.019213536754250526,
-0.0026096105575561523,
0.031720105558633804,
0.016203252598643303,
-0.02120465785264969,
0.010844758711755276,
-0.015017703175544739,
-0.0357343852519989,
0.031346648931503296,
-0.025317812338471413,
-0.023412806913256645,
-0.03349544107913971,
0.03137977421283722,
0.04181889072060585,
-0.024108685553073883,
0.032440099865198135,
0.034933868795633316,
-0.038032714277505875,
-0.012268602848052979,
0.01690847799181938,
0.0457141287624836,
0.04360831901431084,
-0.01872720941901207,
-0.03996701166033745,
-0.05848463252186775,
-0.03836532682180405,
0.010285717435181141,
0.005575994960963726,
-0.014529109001159668,
0.0010093041928485036,
0.038988180458545685,
-0.04461503028869629,
0.05359623208642006,
0.015141421929001808,
-0.025124400854110718,
0.012397605925798416,
-0.06676657497882843,
0.035387877374887466,
0.028120238333940506,
0.036974839866161346,
0.034893233329057693,
0.00500183692201972,
0.0030300565995275974,
0.05571066960692406,
0.030096272006630898,
-0.04307490587234497,
-0.052133213728666306,
0.009467309340834618,
0.004685179330408573,
-0.029259542003273964,
-0.004424269311130047,
-0.026676299050450325,
0.0028730810154229403,
-0.030231885612010956,
0.0041936165653169155,
0.02244294434785843,
-0.0044178287498652935,
0.0225491002202034,
0.0002687959058675915,
0.040434837341308594,
-0.01395532675087452,
0.024342717602849007,
-0.01503785140812397,
-0.022114524617791176,
0.0255665872246027,
0.030704550445079803,
0.06127336993813515,
0.026569608598947525,
0.050472404807806015,
0.00793020986020565,
0.02943928726017475,
0.014745897613465786,
-0.05465707927942276,
0.0745602697134018,
-0.016355153173208237,
-0.003582325531169772,
0.03365155681967735,
-0.033976539969444275,
-0.00558845279738307,
0.007669989950954914,
0.016302475705742836,
-0.003856991184875369,
0.0018397418316453695,
-0.01069092657417059,
0.07265246659517288,
0.012571125291287899,
-0.03397862985730171,
0.018816646188497543,
0.015664314851164818,
0.004548466298729181,
0.08927537500858307,
-0.015722235664725304,
-0.044931285083293915,
0.00022288471518550068,
0.025553641840815544,
-0.0005763887311331928,
0.0033644356299191713,
-0.019988566637039185,
-0.025231221690773964,
-0.024416137486696243,
-0.02919013425707817,
0.03617672249674797,
-0.0013395267305895686,
0.0053191715851426125,
-0.014549839310348034,
0.04713284224271774,
0.018940329551696777,
0.04732108116149902,
-0.040855079889297485,
0.01632855087518692,
-0.02821112424135208,
-0.07896661758422852,
0.011950870975852013,
0.0011170234065502882,
-0.004562880843877792,
-0.044188208878040314,
0.024306481704115868,
-0.00666244188323617,
0.0003139882755931467,
0.023034263402223587,
-0.004450609907507896,
0.04533875733613968,
0.018062902614474297,
-0.10295531153678894,
-0.08007057756185532,
0.07578425854444504,
0.023950699716806412,
-0.0669088065624237,
-0.04168834164738655,
0.018024111166596413,
0.03621498495340347,
0.045698560774326324,
0.010655398480594158,
0.004241930320858955,
-0.022768935188651085,
0.01596435345709324,
0.008206267841160297,
-0.03382880240678787,
-0.010964046232402325,
-0.015660179778933525,
-0.03332950174808502,
-0.01575135439634323,
-0.0830838680267334,
0.010700688697397709,
0.021273696795105934,
-0.01665823720395565,
-0.041343558579683304,
0.04150138050317764,
-0.012381390668451786,
-0.007801729720085859,
-0.03407203406095505,
-0.030322879552841187,
-0.03174559026956558,
0.05205410718917847,
-0.007985365577042103,
-0.01378205232322216,
0.03499835357069969,
-0.001493750256486237,
0.067665234208107,
-0.06526921689510345,
-0.0000922875915421173,
0.05362702161073685,
-0.01264459453523159,
0.025478145107626915,
-0.04499833285808563,
0.020134268328547478,
0.0251279566437006,
-0.015613667666912079,
-0.02124902792274952,
-0.021647460758686066,
0.02999170683324337,
0.0038242137525230646,
0.0229530967772007,
-0.00270329462364316,
-0.06949684768915176,
-0.052587494254112244,
-0.06172784045338631,
-0.031212536618113518,
-0.0687653198838234,
0.02497796155512333,
-0.01471757609397173,
0.025178389623761177,
0.00005934090950177051,
-0.013841831125319004,
0.05367410182952881,
-0.057434070855379105,
-0.025713611394166946,
-0.027128834277391434,
0.007876960560679436,
0.024849064648151398,
0.0040285708382725716,
-0.0038357116281986237,
0.045381005853414536,
0.058077145367860794,
-0.020658688619732857,
-0.005450436379760504,
-0.02926359511911869,
0.0005266148946247995,
-0.021386709064245224,
-0.01500459760427475,
0.007090818136930466,
0.008070145733654499,
0.007331361528486013,
0.027580853551626205,
0.004384187050163746,
0.03287235647439957,
0.020476408302783966,
0.010479568503797054,
0.09881503134965897,
0.05294591933488846,
0.021230943500995636,
0.008082428015768528,
-0.016347510740160942,
0.01170705072581768,
0.0086424071341753,
0.018255678936839104,
-0.007719806395471096,
-0.014858429320156574,
-0.042797286063432693,
-0.01383176725357771,
0.022811178117990494,
-0.029649099335074425,
-0.005530921276658773,
0.011654701083898544,
0.011635059490799904,
0.037818022072315216,
0.006255113985389471,
0.024325145408511162,
0.004831049591302872,
-0.007491802331060171,
0.05728091672062874,
-0.007050657644867897,
0.016775842756032944,
0.03485330939292908,
0.03150571510195732,
0.029822785407304764,
-0.04158003628253937,
0.015753144398331642,
0.002031983807682991,
-0.002188639482483268,
0.03748031705617905,
-0.013203732669353485,
-0.025715049356222153,
0.0156607236713171,
-0.039656419306993484,
-0.027349479496479034,
0.006152187008410692,
-0.008191936649382114,
0.01376716885715723,
-0.05275252088904381,
-0.001501773134805262,
0.009521053172647953,
-0.02064604125916958,
-0.013050896115601063,
0.0003288094885647297,
0.050408512353897095,
-0.027442187070846558,
0.03734924644231796,
-0.02567346952855587,
0.016858862712979317,
-0.007113268133252859,
0.006971882656216621,
0.0467352494597435,
0.013922834768891335,
0.037698473781347275,
-0.01967695914208889,
-0.03468964248895645,
-0.030235303565859795,
0.003603982273489237,
-0.018232448026537895,
0.011623643338680267,
-0.07387921214103699,
-0.002309483475983143,
-0.022826168686151505,
0.004203220829367638,
0.04955918714404106,
0.008624493144452572,
-0.027873924002051353,
-0.00571040716022253,
0.010675391182303429,
-0.044635891914367676,
-0.005737898405641317,
-0.037181735038757324,
0.022290045395493507,
-0.002772471634671092,
0.016741188243031502,
0.041299570351839066,
-0.01114271767437458,
-0.026275847107172012,
0.0661160871386528,
-0.02368955872952938,
-0.055453743785619736,
-0.04637883976101875,
0.003322337754070759,
-0.01485036127269268,
-0.026058288291096687,
-0.006202175747603178,
0.0010407472727820277,
-0.044419366866350174,
0.009185465052723885,
-0.06571052223443985,
-0.027392372488975525,
0.008056746795773506,
0.01786336861550808,
0.06384918093681335,
0.01386668998748064,
-0.015768228098750114,
0.08608172088861465,
-0.028736064210534096,
-0.0694211944937706,
-0.005221541039645672,
-0.025889301672577858,
-0.05169478803873062,
0.005191463977098465,
-0.012102904729545116,
0.06992815434932709,
-0.03463961184024811,
0.007570269983261824,
0.0309718269854784,
0.025851251557469368,
0.05106499046087265,
0.03197064250707626,
-0.006267441902309656,
-0.024820925667881966,
0.008999151177704334,
0.01341964676976204,
0.04837658628821373,
-0.012724681757390499,
-0.0040448070503771305,
0.0033423923887312412,
-0.029689522460103035,
0.021283404901623726,
0.0072215041145682335,
-0.008561158552765846,
0.03326098993420601,
-0.001417049439623952,
0.0055304053239524364,
-0.029616964980959892,
0.056021422147750854,
-0.022483766078948975,
-0.023601850494742393,
0.00023323138884734362,
0.03471546992659569,
0.02273130603134632,
0.012466521933674812,
-0.030882252380251884,
0.04759957641363144,
0.06699050962924957,
-0.005919173825532198,
-0.047207385301589966,
0.005418719258159399,
-0.03072400763630867,
0.037054289132356644,
-0.030490364879369736,
-0.031764499843120575,
0.057551827281713486,
0.0011870719026774168,
0.007692176848649979,
-0.006663760636001825,
-0.03136957436800003,
0.007779359817504883,
-0.05876360833644867,
-0.025651386007666588,
0.021102970466017723,
0.027330609038472176,
-0.0034407146740704775,
0.04798386991024017,
0.022549128159880638,
0.015052149072289467,
0.025342166423797607,
0.010520410723984241,
-0.039782796055078506,
0.030089475214481354,
-0.01275896467268467,
0.01386851817369461,
-0.01776774227619171,
0.0068410225212574005,
0.05327451601624489,
-0.004751155152916908,
0.011327932588756084,
0.007634514477103949,
0.018661942332983017,
-0.025374412536621094,
0.01667156256735325,
0.012658433988690376,
-0.010646221227943897,
-0.005645128898322582,
-0.0017667686333879828,
0.05124756693840027,
0.014276772737503052,
0.04213740676641464,
0.02961597964167595,
-0.027363481000065804,
-0.0349883995950222,
0.014066479168832302,
0.003203059546649456,
0.007380664814263582,
0.024262074381113052,
0.029063750058412552,
0.018567349761724472,
0.006505861412733793,
-0.03838222473859787,
-0.03729308024048805,
0.022028697654604912,
0.008271596394479275,
0.03052622452378273,
-0.006608862429857254,
-0.04253154993057251,
0.006273051258176565,
-0.007313143461942673,
0.03468509018421173,
-0.047273702919483185,
0.04355212301015854,
0.016909105703234673,
-0.044975243508815765,
0.0006366927409544587,
0.055573225021362305,
0.05342050641775131,
0.01963209919631481,
-0.006020271219313145,
-0.052944641560316086,
-0.005445376038551331,
-0.045888129621744156,
0.0014352770522236824,
0.019118407741189003,
0.010438823141157627,
-0.03402857482433319,
0.011484445072710514,
0.03781140595674515,
0.01685836911201477,
-0.0055118221789598465,
0.039071422070264816,
0.002062675077468157,
0.0058942269533872604,
-0.013081998564302921,
-0.012363854795694351,
0.047871217131614685,
0.011176693253219128,
0.032953426241874695,
-0.003525863168761134,
-0.03216780722141266,
-0.08372494578361511,
-0.025271721184253693,
0.03331718221306801,
0.05448316037654877,
0.0028714605141431093,
0.04617854952812195,
-0.09228796511888504,
-0.027609629556536674,
0.08495142310857773,
-0.03750663250684738,
0.01796930655837059,
-0.019266195595264435,
-0.0031887218356132507,
-0.007430866826325655,
0.015016407705843449,
-0.04095284268260002,
-0.013749892823398113,
-0.05154598131775856,
0.01769598014652729,
-0.024708792567253113,
-0.04641745984554291,
-0.024019896984100342,
0.029432358220219612,
0.00757192587479949,
0.04231920465826988,
0.023854736238718033,
0.01037731021642685,
-0.03248310089111328,
0.012103368528187275,
-0.05894603580236435,
-0.04512106254696846,
-0.004308312200009823,
0.00544501468539238,
-0.001486648921854794,
0.024616727605462074,
-0.021008308976888657,
-0.04620068892836571,
0.006621906533837318,
-0.012594322673976421,
-0.007805478293448687,
-0.007663367781788111,
-0.030263660475611687,
-0.0077681937254965305,
0.02938707172870636,
0.018845677375793457,
0.037075307220220566,
0.041228435933589935,
0.02039891481399536,
-0.026581501588225365,
-0.012958199717104435,
-0.004342722240835428,
-0.005794457625597715,
-0.006742309313267469,
-0.019354112446308136,
0.007721417583525181,
-0.03722510486841202,
0.057092562317848206,
0.013795709237456322,
0.0164321418851614,
0.021637465804815292,
-0.034615445882081985,
-0.014289388433098793,
0.009311160072684288,
0.0001793805422494188,
-0.0018258522031828761,
0.03758808225393295,
-0.0011703447671607137,
0.05881408974528313,
-0.037728793919086456,
0.004348251037299633,
0.018363596871495247,
0.04028378799557686,
0.026589002460241318,
-0.01506957970559597,
0.017817441374063492,
0.0031551665160804987,
-0.00699291005730629,
0.022544601932168007,
-0.02641795389354229,
0.04931161552667618,
-0.05517430976033211,
0.016476744785904884,
0.028398966416716576,
-0.027765465900301933,
-0.04222581908106804,
0.03396216779947281,
-0.018902862444519997,
0.057115502655506134,
-0.04476819932460785,
0.04322541505098343,
0.037522848695516586,
-0.0030978387221693993,
-0.055560093373060226,
-0.027192912995815277,
0.02183825708925724,
0.041950248181819916,
-0.00586278410628438,
-0.03665302321314812,
-0.01384052075445652,
-0.012731722556054592,
-0.03547801449894905,
-0.0028005121275782585,
0.027536021545529366,
-0.022672537714242935,
-0.0019772297237068415,
0.0014184957835823298,
-0.020491991192102432,
0.07186539471149445,
0.018109796568751335,
-0.003113815328106284,
-0.0038574005011469126,
-0.008102620020508766,
-0.029968414455652237,
-0.010041180066764355,
-0.00663222698494792,
-0.04280463978648186,
-0.023539172485470772,
0.008842331357300282,
-0.0018611699342727661,
0.03448696434497833,
-0.02689000591635704,
0.01828320510685444,
0.02144058607518673,
0.0027043907903134823,
-0.027055349200963974,
-0.0006641395739279687,
0.035238683223724365,
0.012173943221569061,
0.025769546627998352,
0.016088826581835747,
0.005164233036339283,
-0.037188246846199036,
-0.012844797223806381,
-0.00041574586066417396,
-0.024566730484366417,
-0.03782587870955467,
-0.02625756710767746,
0.0808914452791214,
-0.009840822778642178,
0.01969686895608902,
0.029614821076393127,
-0.015020453371107578,
-0.0018440071726217866,
-0.012333756312727928,
-0.048437025398015976,
-0.0055188206024467945,
0.030037330463528633,
-0.04887496680021286,
-0.05174881964921951,
-0.0040231142193078995,
0.01706349290907383,
0.025379473343491554,
0.008764924481511116,
0.029859192669391632,
0.03196048364043236,
-0.01830911822617054,
0.008970431052148342,
0.015056663192808628,
0.02027696743607521,
0.031549062579870224,
-0.02974759228527546,
0.04720379412174225,
-0.005112326238304377,
0.025023138150572777,
0.04083910956978798,
0.025232408195734024,
-0.02359926514327526,
-0.00015742550021968782,
0.06422915309667587,
0.02387138456106186,
0.006978172343224287,
-0.03699865564703941,
-0.062244515866041183,
0.04711046814918518,
-0.032796237617731094,
0.01368025317788124,
-0.006397905759513378,
-0.02343449369072914,
0.046004462987184525,
-0.011354748159646988,
-0.018858330324292183,
-0.04239146411418915,
-0.013261830434203148,
-0.0027177580632269382,
-0.012953788973391056,
-0.008822634816169739,
0.02614823915064335,
-0.029401438310742378,
0.008451994508504868,
0.012712041847407818,
0.004237583838403225,
0.018358848989009857,
-0.019647736102342606,
-0.04600876569747925,
-0.024830255657434464,
-0.05163612961769104,
-0.036467671394348145,
0.014981342479586601,
0.0012534656561911106,
-0.058491602540016174,
0.03789933770895004,
-0.01761072874069214,
-0.0016355251427739859,
0.006983480416238308,
0.00806653592735529,
0.003994650207459927,
0.050034280866384506,
-0.0053093768656253815,
-0.0031260927207767963,
-0.0459388829767704,
0.007586031220853329,
0.1151275783777237,
0.059176646173000336,
0.029426144436001778,
-0.06722258776426315,
0.0068796672858297825,
-0.007879162207245827,
0.002480312017723918,
-0.03906092792749405,
0.01315949484705925,
-0.043089233338832855,
0.03380727022886276,
0.002697327407076955,
0.035035185515880585,
-0.016999443992972374,
0.04292969033122063,
0.034285303205251694,
-0.048581309616565704,
0.0017670928500592709,
0.012759413570165634,
-0.009028644300997257,
-0.008267813362181187,
0.01266416721045971,
-0.02165800891816616,
0.049261074513196945,
-0.036941032856702805,
-0.037941474467515945,
-0.04362928867340088,
-0.022272275760769844,
0.042307138442993164,
-0.029810799285769463,
-0.04517625272274017,
0.01354668103158474,
-0.027050195261836052,
-0.013909660279750824,
-0.03029707632958889,
0.03868132084608078,
0.02758900076150894,
0.0038066499400883913,
0.007551823742687702,
0.029486628249287605,
0.002546328119933605,
-0.0005724397487938404,
-0.01585034281015396,
0.031073519960045815,
-0.059476930648088455,
0.007680531125515699,
0.035596881061792374,
0.011771053075790405,
-0.0128621282055974,
-0.03387058898806572,
0.018209250643849373,
-0.015288792550563812,
-0.03414294123649597,
-0.028898581862449646,
-0.07877356559038162,
0.014622746035456657,
0.031617600470781326,
-0.026644844561815262,
-0.030916530638933182,
-0.02456028014421463,
0.005491720978170633,
-0.0034277071245014668,
0.03891071304678917,
-0.0399443581700325,
0.021854545921087265,
-0.009156964719295502,
0.031652387231588364,
0.0038710080552846193,
-0.031420063227415085,
0.005649580620229244,
-0.03847940266132355,
-0.003952109254896641,
-0.04274866357445717,
0.0336078405380249,
-0.00693146139383316,
0.022185662761330605,
0.04297721013426781,
0.002452919725328684,
0.012844886630773544,
-0.007128250319510698,
-0.06004543602466583,
0.04259498417377472,
-0.04645374417304993,
-0.015524373389780521,
-0.05328605696558952,
0.010819743387401104,
0.005108404438942671,
0.07863172143697739,
-0.013247912749648094,
-0.021705156192183495,
-0.014271133579313755,
0.02537202462553978,
0.029541125521063805,
-0.02163144201040268,
-0.013776460662484169,
-0.030689511448144913,
-0.027777282521128654,
0.023480964824557304,
0.0044087632559239864,
0.03681754693388939,
0.047266636043787,
0.046323079615831375,
0.009726577438414097,
-0.00176978949457407,
-0.03216015174984932,
0.005447420757263899,
-0.01389126107096672,
-0.04425618052482605,
-0.036657873541116714,
0.0023921008687466383,
0.026659412309527397,
-0.05964640900492668,
-0.010740069672465324,
0.0020014101173728704,
-0.037948619574308395,
-0.006933893077075481,
0.02824471704661846,
-0.023987069725990295,
0.009176983498036861,
0.003028883831575513,
0.02322068251669407,
-0.044480592012405396,
0.016948921605944633,
-0.04840133711695671,
-0.035264838486909866,
0.005586154293268919,
-0.013113702647387981,
-0.00959969125688076,
0.00754918297752738,
-0.06763314455747604,
0.006160734687000513,
0.02162775583565235,
0.01667867787182331,
0.0037289997562766075,
-0.01013624481856823,
0.04902225360274315,
0.025819480419158936,
0.037744227796792984,
-0.022054320201277733,
-0.01854482851922512,
0.035441406071186066,
-0.02308684028685093,
-0.015211457386612892,
0.014773479662835598,
-0.00951023306697607,
0.03542393818497658,
0.047796182334423065,
-0.029739461839199066,
0.01505208108574152,
0.06606052815914154,
-0.021195771172642708,
0.008959352970123291,
-0.025089548900723457,
0.001484953099861741,
0.014491708017885685,
-0.014118603430688381,
-0.001957727363333106,
-0.01210423931479454,
-0.02157876454293728,
0.012864114716649055,
0.018218429759144783,
0.052799176424741745,
-0.02790038101375103,
0.04596838355064392,
0.0256049744784832,
-0.012414444237947464,
0.015009080991148949,
-0.0015727793797850609,
0.024419743567705154,
0.06544598191976547,
-0.028007004410028458,
0.0399833619594574,
0.01549829076975584,
0.012362955138087273,
-0.12398188561201096,
-0.01949238032102585,
0.008253703825175762,
-0.00460497522726655,
0.061233654618263245,
-0.04755626991391182,
-0.014541610144078732,
0.05491756275296211,
-0.02940705232322216,
-0.037996236234903336,
-0.042075783014297485,
-0.020967265591025352,
-0.02464655414223671,
0.02114798128604889,
-0.005610799416899681,
0.05118422582745552,
0.027632761746644974,
0.025094864889979362,
-0.0038586389273405075,
0.02019144594669342,
-0.009502178989350796,
-0.025899583473801613,
-0.011456362903118134,
0.01955966092646122,
-0.010304560884833336,
-0.003502623876556754,
0.06277675181627274,
0.009146089665591717,
0.002521549118682742,
-0.004738965071737766,
-0.03693490847945213,
0.017522016540169716,
0.019163653254508972,
0.004281851463019848,
-0.0039844810962677,
0.05487437546253204,
0.00456329807639122,
0.009845713153481483,
-0.03220965340733528,
0.044161733239889145,
0.002569738542661071,
0.002260993467643857,
0.007612499408423901,
-0.014026476070284843,
-0.007585003972053528,
-0.019477637484669685,
-0.020702874287962914,
0.025297993794083595,
-0.00921409111469984,
0.03933529555797577,
0.030977066606283188,
-0.030387237668037415,
0.009861928410828114,
-0.0247093066573143,
-0.021723276004195213,
-0.032181452959775925,
0.009034952148795128,
0.028327791020274162,
0.00006793312059016898,
-0.046387381851673126,
0.01309011597186327,
0.010442059487104416,
-0.024609940126538277,
0.0029959368985146284,
0.011322654783725739,
-0.027195846661925316,
-0.027652762830257416,
0.006760203279554844,
0.026672493666410446,
-0.019889995455741882,
0.021966714411973953,
-0.0401606447994709,
-0.029888207092881203,
0.023887308314442635,
0.06483373045921326,
0.012094156816601753,
0.0530228316783905,
0.005628649145364761,
-0.00694554578512907,
-0.07862963527441025,
0.06071113049983978,
-0.007756358478218317,
-0.010463225655257702,
-0.017489539459347725,
-0.019893793389201164,
0.008597541600465775,
0.025607824325561523,
0.05316474661231041,
-0.028142763301730156,
-0.01746125891804695,
0.015168697573244572,
-0.01295132003724575,
-0.010452713817358017,
-0.036141589283943176,
-0.013471330516040325,
0.0505293570458889,
-0.039963722229003906,
0.025682445615530014,
0.006598719861358404,
0.01600198820233345,
-0.009426646865904331,
0.01077237632125616,
0.014394429512321949,
0.001536196214146912,
-0.0017283064080402255,
0.014611232094466686,
0.0016278713010251522,
0.0256508719176054,
0.010257021524012089,
0.08838570863008499,
0.020561955869197845,
0.01096066553145647,
-0.01780223473906517,
-0.026060068979859352,
-0.03558735176920891,
0.03723675757646561,
-0.04975959658622742,
-0.014537274837493896,
0.0016287908656522632,
-0.014435936696827412,
-0.00879321713000536,
-0.05543898791074753,
0.006211027968674898,
0.014646083116531372,
-0.014870519749820232,
-0.01894189417362213,
0.027196761220693588,
0.020231040194630623,
0.06356145441532135,
-0.03628092631697655,
0.007213784847408533,
0.05289946123957634,
0.0015139784663915634,
-0.01058667991310358,
0.05063226819038391,
0.07271923869848251,
-0.0203191339969635,
-0.004217422101646662,
0.01865559071302414,
0.03302126005291939,
0.027549928054213524,
0.00870350282639265,
0.006341293454170227,
-0.027954375371336937,
-0.06393912434577942,
0.010419970378279686,
-0.04696207121014595,
-0.0026113863568753004,
0.005060333758592606,
-0.009372049942612648,
0.06336448341608047,
-0.02212216518819332,
0.0054023307748138905,
-0.03111504390835762,
0.02882618084549904,
-0.010571859776973724,
0.031269513070583344,
0.013365513645112514,
0.014162806794047356,
-0.002438954310491681,
0.003127308329567313,
-0.009876192547380924,
0.017269371077418327,
-0.003777759615331888,
0.0020812531001865864,
0.014817183837294579,
-0.008452278561890125,
0.008491524495184422,
-0.042502034455537796,
-0.02386627532541752,
-0.01298707164824009,
-0.02049851045012474,
0.04225970059633255,
0.020777573809027672,
0.01695893704891205,
0.0038130241446197033,
0.004159044474363327,
0.006791707128286362,
0.1148422360420227,
-0.04635188728570938,
-0.0437018908560276,
-0.003694051643833518,
0.016453340649604797,
-0.0002491729974281043,
-0.03681560978293419
] |
<p>I read couple of similar question on this forum and few blogs on web, though I am still confused,I am determined to calculate object displacement using accelerometer data.</p>
<p>So, I tried using www.freescale.com/files/sensors/doc/app_note/AN3397.pdf , which gives nearly 20-50% error.</p>
<p>I also tried this equation on data and got some better results.</p>
<pre><code>V1 = V0 + ((a1) * t)
X2 = abs((V1 * t) + (((a1)/2)*t*t))
X2 = X0 + X2
V0 = V1
X0 = X2
</code></pre>
<p>Here
t is the time differance between two samples.
X0 is the final displacement.
V1,a1 current values.
V0 previous value.</p>
<p><a href="https://www.dropbox.com/s/qnux0f61mjbmaap/Idle_to_standing_sensor_readings.xls?dl=0" rel="nofollow">Here</a> is my graphs for the movement from Android sensors readings.</p>
<p>1)From Linear Acceleration Z axis graph, how do I calculate the distance?
2)Which values should I take and which should not? how many data samples I should use for calculation. For positive acceleration only or for an entire positive negative cycle of acceleration data?
3) What the Linear acceleration graph means. Please explain its values based on movement of object.</p>
| 7,670 |
[
0.00030302643426693976,
-0.02103138528764248,
-0.009767829440534115,
0.03332251310348511,
0.047237083315849304,
-0.004708522465080023,
-0.06011515110731125,
-0.005894300527870655,
-0.010804694145917892,
0.029737284407019615,
0.010696443729102612,
0.01353131327778101,
0.018914353102445602,
0.004140402656048536,
0.03735971078276634,
-0.026762617751955986,
-0.0003263665421400219,
-0.02956477738916874,
0.006522409152239561,
-0.05084548890590668,
0.022460883483290672,
-0.02320980839431286,
0.024238258600234985,
0.009188610129058361,
-0.037880849093198776,
0.018179800361394882,
0.037353646010160446,
-0.01999896951019764,
-0.0064393593929708,
0.03031880035996437,
-0.05787558853626251,
-0.01965368539094925,
-0.018860695883631706,
0.015034460462629795,
0.03345451131463051,
0.014979081228375435,
-0.04269937798380852,
-0.046122387051582336,
-0.015236208215355873,
0.07254141569137573,
-0.0201198011636734,
-0.0026036137714982033,
-0.023973792791366577,
0.06193166226148605,
-0.029629524797201157,
-0.00979915913194418,
0.015213938429951668,
-0.008342241868376732,
0.05712561309337616,
-0.032429229468107224,
0.04451495409011841,
-0.007875482551753521,
0.05807727202773094,
-0.003171056043356657,
-0.00869216863065958,
0.010986611247062683,
0.06460975855588913,
0.024242287501692772,
-0.024951493367552757,
-0.0337170846760273,
-0.0123685821890831,
-0.02718794159591198,
-0.02832224778831005,
-0.028304478153586388,
0.019023016095161438,
0.023669354617595673,
-0.02293541468679905,
-0.0074249571189284325,
0.022638047114014626,
0.019382182508707047,
0.027819735929369926,
0.01486569456756115,
0.038314174860715866,
-0.026303619146347046,
0.0230766162276268,
-0.028578683733940125,
-0.01970403827726841,
0.013380230404436588,
0.04320397228002548,
0.049154240638017654,
-0.01930760033428669,
0.0019337531412020326,
0.06628869473934174,
0.018974995240569115,
0.009932432323694229,
-0.06218377873301506,
0.06860736012458801,
0.03408324345946312,
-0.010135308839380741,
-0.014653518795967102,
0.028543619439005852,
-0.005728792864829302,
0.003762907814234495,
0.020780351012945175,
0.009226803667843342,
0.031431835144758224,
0.00533490302041173,
0.05667740851640701,
-0.006168661173433065,
-0.01729937456548214,
-0.0024440553970634937,
0.01850060187280178,
0.038301724940538406,
0.014364097267389297,
-0.0298842191696167,
0.018653877079486847,
0.011327289044857025,
-0.005466330796480179,
-0.033560533076524734,
-0.028309602290391922,
-0.03502422198653221,
-0.009887988679111004,
0.014757576398551464,
-0.0068805646151304245,
0.01515186857432127,
-0.047152310609817505,
-0.02204952761530876,
-0.0026444830000400543,
0.028410019353032112,
0.038370974361896515,
0.02502766065299511,
-0.01769355498254299,
0.002779192989692092,
-0.001380767673254013,
-0.07004120200872421,
0.015771232545375824,
0.012049216777086258,
-0.025321828201413155,
-0.029525604099035263,
0.06935006380081177,
0.012574942782521248,
0.021264689043164253,
0.04794039949774742,
-0.018881188705563545,
0.02622295171022415,
0.02491159923374653,
-0.09061756730079651,
-0.0651135966181755,
0.03548520430922508,
0.004760718904435635,
-0.005396888591349125,
-0.06802627444267273,
0.006508855149149895,
0.02296234667301178,
0.07174468785524368,
0.028262993320822716,
-0.005677506327629089,
0.0023960440885275602,
-0.006440894212573767,
-0.028744274750351906,
-0.013303511776030064,
-0.015148353762924671,
-0.025731634348630905,
-0.02368873357772827,
0.0019397238502278924,
-0.0406033992767334,
0.014066793955862522,
0.012057512067258358,
-0.02346087247133255,
-0.020647959783673286,
0.05968160927295685,
0.03395591303706169,
-0.0230557918548584,
0.04886025935411453,
0.013640820980072021,
-0.05404031649231911,
0.07602193206548691,
-0.007559271063655615,
-0.016003334894776344,
-0.0006556051084771752,
0.014694889076054096,
0.01675529219210148,
0.005358053836971521,
-0.0005673356354236603,
0.06626823544502258,
0.03002028912305832,
-0.023856783285737038,
-0.028396274894475937,
0.0024774877820163965,
0.01644679717719555,
-0.07010434567928314,
-0.043082769960165024,
-0.04647044464945793,
0.006590880453586578,
0.004914842080324888,
0.008065136149525642,
-0.015033728443086147,
0.025045407935976982,
0.05748147517442703,
-0.028383564203977585,
-0.02109944075345993,
-0.0638849064707756,
0.030489103868603706,
0.02281389757990837,
0.0066335261799395084,
0.014611713588237762,
0.009577477350831032,
0.025896739214658737,
-0.003426499431952834,
-0.015165356919169426,
0.01813800260424614,
0.016026174649596214,
0.023644082248210907,
-0.027682896703481674,
0.0006911336095072329,
0.0703192949295044,
0.00858212448656559,
0.007371876854449511,
0.019236929714679718,
-0.008737770840525627,
0.0013892872957512736,
0.014645170420408249,
-0.02780742757022381,
-0.0037755488883703947,
0.02090027928352356,
-0.0006339558167383075,
0.020835136994719505,
0.011974516324698925,
-0.011779556050896645,
0.012947211973369122,
-0.0063229831866919994,
0.09450246393680573,
0.12371240556240082,
0.0062906164675951,
-0.0016182268736883998,
0.014508182182908058,
0.005670286249369383,
-0.002245997078716755,
-0.03924712538719177,
-0.00021620452753268182,
-0.057665321975946426,
-0.04568469896912575,
0.02520962432026863,
0.010668821632862091,
-0.007539896760135889,
-0.02140289917588234,
0.04046865925192833,
0.007455381099134684,
0.008794727735221386,
-0.013917227275669575,
-0.022561559453606606,
-0.031221024692058563,
0.021972842514514923,
0.009333949536085129,
0.008005400188267231,
-0.013523385860025883,
-0.010557614266872406,
0.00025352666852995753,
0.04139042645692825,
0.009062660858035088,
-0.0002879461389966309,
0.03439256548881531,
0.018666569143533707,
0.023880992084741592,
0.000644882267806679,
-0.02310357242822647,
0.024421336129307747,
-0.013412010855972767,
0.027269519865512848,
0.061461273580789566,
-0.014520833268761635,
0.002352024894207716,
0.013493910431861877,
0.009700210765004158,
0.01929412968456745,
0.008904964663088322,
-0.02149568311870098,
-0.029045352712273598,
0.0085986889898777,
-0.07023458182811737,
0.015626266598701477,
-0.053493089973926544,
-0.0163298137485981,
-0.020674820989370346,
0.0026386245153844357,
0.04281177371740341,
0.03617475554347038,
0.022731484845280647,
-0.023989729583263397,
-0.015973323956131935,
0.015383024699985981,
0.0014096708036959171,
-0.0089986901730299,
0.054819900542497635,
-0.04981934651732445,
0.022756775841116905,
-0.042209308594465256,
-0.05025630444288254,
0.04721657186746597,
0.018073631450533867,
0.00900205783545971,
0.03924677148461342,
0.028969109058380127,
-0.061585694551467896,
-0.05771864205598831,
-0.027023300528526306,
0.009722908958792686,
-0.014757911674678326,
-0.009768984280526638,
0.033854033797979355,
0.0027572265826165676,
-0.04291493073105812,
0.03918742761015892,
-0.02956615947186947,
-0.0010188837768509984,
-0.029999352991580963,
0.012138092890381813,
-0.00995657779276371,
-0.007745835464447737,
-0.009472564794123173,
-0.0038802665658295155,
-0.005566402338445187,
0.015354699455201626,
-0.05317382887005806,
-0.05062837153673172,
0.029176734387874603,
0.00307251513004303,
0.06090294569730759,
0.03657332435250282,
0.004687706474214792,
0.0786382332444191,
0.011692184023559093,
-0.01536183524876833,
-0.04009319469332695,
-0.010203426703810692,
-0.014484548009932041,
-0.013528775423765182,
-0.03370579704642296,
0.028785040602087975,
0.003790442133322358,
0.01870570331811905,
-0.029435373842716217,
0.026161041110754013,
0.050293922424316406,
-0.01898689568042755,
0.025433100759983063,
-0.007744449656456709,
0.021452445536851883,
-0.03020554967224598,
0.08252593129873276,
0.002074398333206773,
0.003351854393258691,
0.02068783901631832,
-0.0057742176577448845,
0.020402584224939346,
0.0058556837029755116,
-0.10244134068489075,
0.005532171111553907,
-0.006851011421531439,
-0.01341584138572216,
-0.0461195632815361,
0.02113908715546131,
0.012057051062583923,
-0.031107278540730476,
0.002929834183305502,
0.045252393931150436,
0.06471183896064758,
-0.007864349521696568,
-0.01976422220468521,
0.0485219843685627,
0.003074019681662321,
-0.005609735380858183,
-0.04926249757409096,
-0.030304094776511192,
-0.0011308040702715516,
0.020100081339478493,
-0.014478353783488274,
0.002634479897096753,
0.010616889223456383,
0.04115278646349907,
0.007708412129431963,
0.011574139818549156,
-0.04397327080368996,
0.021706342697143555,
-0.06294591724872589,
-0.014805978164076805,
-0.019839927554130554,
0.04976905882358551,
-0.02432427369058132,
0.028154706582427025,
0.013600055128335953,
-0.011104338802397251,
0.015781372785568237,
-0.011386238038539886,
-0.07415638118982315,
0.048096995800733566,
-0.051765501499176025,
-0.04949022829532623,
0.011722222901880741,
-0.011677004396915436,
-0.005789600778371096,
-0.03879211097955704,
0.015725640580058098,
-0.016400828957557678,
0.027068819850683212,
-0.05996241047978401,
-0.0007194837089627981,
-0.0068723903968930244,
0.013539879582822323,
-0.024705123156309128,
0.0015112521359696984,
0.00971257034689188,
-0.014736603014171124,
0.03231487795710564,
0.029394498094916344,
0.02417966164648533,
-0.018485816195607185,
0.007302233949303627,
0.00510314991697669,
0.015823082998394966,
0.019567733630537987,
0.03228289633989334,
-0.0266224704682827,
-0.019965942949056625,
-0.011711406521499157,
-0.02194981835782528,
0.013729538768529892,
0.023647746071219444,
-0.012737457640469074,
-0.02284001000225544,
-0.043120771646499634,
-0.02252928726375103,
-0.005466938484460115,
0.02826312556862831,
0.014475210569798946,
0.006084865424782038,
0.023024238646030426,
-0.0027331949677318335,
-0.03203016147017479,
0.019322469830513,
0.08140970766544342,
-0.019827911630272865,
0.0011219615116715431,
-0.07032544165849686,
-0.05573072284460068,
0.0018309757579118013,
-0.012538679875433445,
0.06223692744970322,
0.011820304207503796,
0.005949296988546848,
0.011924984864890575,
0.033428676426410675,
0.016137097030878067,
-0.007162853144109249,
0.03813325986266136,
0.015873704105615616,
0.05804299935698509,
-0.02093709446489811,
-0.012336191721260548,
0.020486576482653618,
0.040344368666410446,
0.0796482115983963,
-0.013078263029456139,
-0.02413124591112137,
-0.08199703693389893,
-0.018441829830408096,
0.019039638340473175,
0.052661482244729996,
0.008756128139793873,
0.004559648223221302,
-0.03267872333526611,
-0.039368439465761185,
0.04315244033932686,
-0.019658884033560753,
0.03857970982789993,
0.0024704704992473125,
0.039623238146305084,
-0.026655331254005432,
-0.042216770350933075,
-0.03849420323967934,
0.002861716551706195,
-0.011332957074046135,
0.011277432553470135,
-0.04192866012454033,
-0.008569486439228058,
0.015143383294343948,
0.06021104380488396,
0.027290789410471916,
0.08381292223930359,
-0.01763090118765831,
0.003963984549045563,
-0.03320099785923958,
-0.01885317824780941,
-0.03522980958223343,
-0.05020148679614067,
0.004637792706489563,
-0.0162180345505476,
0.014697511680424213,
0.03549915552139282,
0.01131981797516346,
-0.0015690805157646537,
0.026699362322688103,
0.030016973614692688,
-0.020037934184074402,
-0.06902727484703064,
-0.024891946464776993,
0.0060703568160533905,
0.07358821481466293,
-0.023022029548883438,
0.07431831955909729,
0.02885507605969906,
-0.021514039486646652,
0.02451004460453987,
0.002274221507832408,
0.02725842408835888,
-0.01440057996660471,
0.002141365548595786,
-0.04786976799368858,
0.0028105219826102257,
-0.0673547312617302,
0.035047098994255066,
-0.010233220644295216,
0.06795365363359451,
-0.023816978558897972,
-0.05521462485194206,
0.017192469909787178,
0.04960080608725548,
-0.012007014825940132,
0.002244700212031603,
-0.00862992461770773,
0.011016437783837318,
-0.007119601126760244,
-0.036592066287994385,
-0.00851120613515377,
0.0077614872716367245,
0.0000905228007468395,
0.023068996146321297,
-0.004599670879542828,
0.008994068019092083,
-0.029654063284397125,
0.00015202000213321298,
0.02363774925470352,
-0.06800113618373871,
-0.0013680169358849525,
0.003591307206079364,
0.0004406426742207259,
-0.002406787360087037,
-0.026464099064469337,
-0.03348545730113983,
0.015932386741042137,
0.012406694702804089,
0.05170030519366264,
-0.06098461523652077,
0.02322331815958023,
-0.006038850639015436,
0.015830103307962418,
-0.04394117742776871,
-0.05588269978761673,
0.012368042953312397,
-0.001545967417769134,
-0.018698669970035553,
-0.046444252133369446,
0.010964025743305683,
-0.014048057608306408,
-0.04216497391462326,
0.03133564069867134,
0.03852074593305588,
-0.01912759430706501,
-0.010700853541493416,
0.00921216793358326,
-0.024414170533418655,
0.07900610566139221,
-0.007842954248189926,
0.00882604718208313,
0.004268992226570845,
0.024561600759625435,
-0.032065652310848236,
-0.019662873819470406,
0.07876424491405487,
-0.027680978178977966,
-0.006832392420619726,
-0.025042271241545677,
-0.010500039905309677,
0.06003890559077263,
-0.01430465467274189,
-0.045785944908857346,
-0.017150716856122017,
0.03483403101563454,
-0.0061567481607198715,
-0.045717187225818634,
0.019985327497124672,
-0.008831818588078022,
-0.02365673892199993,
-0.02197931334376335,
-0.00994803849607706,
-0.03647962957620621,
-0.02337801270186901,
-0.011852037161588669,
0.04220760613679886,
-0.024175608530640602,
-0.0007336367852985859,
0.012802732177078724,
-0.019600745290517807,
0.006819379981607199,
0.02914731204509735,
-0.015566936694085598,
0.03830700367689133,
-0.02163192629814148,
0.0029988291207700968,
0.011537633836269379,
0.016758479177951813,
-0.01671728305518627,
0.010107511654496193,
-0.0336611345410347,
-0.022437002509832382,
0.07656622678041458,
-0.0023586491588503122,
0.05906984210014343,
0.016809875145554543,
0.0016637101070955396,
-0.025366535410284996,
0.007788143586367369,
0.011131386272609234,
-0.016498561948537827,
-0.03574773669242859,
0.04141346365213394,
-0.04121863469481468,
-0.021898167207837105,
-0.0008316985331475735,
-0.02089659869670868,
-0.004038827493786812,
-0.01860417053103447,
-0.0008362935041077435,
-0.0008621893357485533,
-0.026389174163341522,
-0.0011836697813123465,
-0.03227777034044266,
0.0026099917013198137,
0.007276497315615416,
0.06558021157979965,
0.013520687818527222,
-0.0318099707365036,
0.04118252173066139,
0.0012299349764361978,
0.010509572923183441,
-0.0553121455013752,
-0.0007139162626117468,
-0.06919163465499878,
-0.01700441539287567,
0.012890749610960484,
-0.005157151725143194,
-0.0024616094306111336,
-0.004253223538398743,
0.053196825087070465,
0.006994344759732485,
0.0351116843521595,
-0.011724557727575302,
-0.05699947476387024,
-0.029651300981640816,
-0.03326624631881714,
-0.042107053101062775,
0.032006457448005676,
-0.006084098014980555,
-0.040863167494535446,
0.02701714262366295,
-0.004163979087024927,
0.05023503303527832,
0.017229001969099045,
0.05415567010641098,
-0.016789337620139122,
0.09929964691400528,
-0.026434950530529022,
-0.0029178308323025703,
-0.009046100080013275,
-0.011023151688277721,
0.12524762749671936,
0.059871017932891846,
0.0019521033391356468,
-0.010262197814881802,
0.023593666031956673,
0.00494798831641674,
0.0013904377119615674,
-0.01854933239519596,
0.04353072866797447,
0.013497062027454376,
0.010565849021077156,
0.026164479553699493,
0.019604505971074104,
-0.01098616048693657,
-0.03478353098034859,
0.057120002806186676,
0.018215809017419815,
-0.004516232758760452,
-0.006539273075759411,
0.005789666902273893,
-0.0012851719511672854,
-0.023445239290595055,
-0.021685142070055008,
0.04564254358410835,
-0.03440851345658302,
-0.047829579561948776,
-0.022421125322580338,
-0.03715303912758827,
0.01782194897532463,
-0.007702527567744255,
-0.04303395003080368,
0.015605919994413853,
0.02648278884589672,
0.005119026638567448,
-0.006177596282213926,
0.0071248700842261314,
-0.034661684185266495,
-0.006290449760854244,
0.034280866384506226,
0.03378544747829437,
0.015636786818504333,
-0.018153132870793343,
0.013673344627022743,
-0.020163707435131073,
-0.041914213448762894,
-0.018161052837967873,
-0.056827764958143234,
0.02808753214776516,
0.0280761681497097,
-0.014575472101569176,
0.018587546423077583,
0.036490123718976974,
-0.03304395079612732,
-0.050593338906764984,
-0.04486001282930374,
0.022142434492707253,
0.048156965523958206,
-0.024952024221420288,
-0.005746133159846067,
-0.0071204956620931625,
0.0032790915574878454,
0.030406825244426727,
-0.008976162411272526,
0.02561533823609352,
0.024792855605483055,
0.023323778063058853,
0.008969397284090519,
0.06948772817850113,
-0.0338144488632679,
-0.004123258404433727,
0.03031187318265438,
0.0009700146620161831,
-0.026750709861516953,
0.01650836691260338,
0.0055085280910134315,
0.03142404556274414,
0.002465292112901807,
0.002557786414399743,
-0.01156760472804308,
-0.029646867886185646,
-0.03580823168158531,
0.001477259211242199,
-0.021713608875870705,
-0.01925136148929596,
-0.0403473861515522,
0.00723713543266058,
0.03201909363269806,
0.021399028599262238,
-0.0069341338239610195,
-0.002692859387025237,
-0.028887543827295303,
0.03894396871328354,
-0.014961407519876957,
-0.005100533831864595,
-0.014505796134471893,
-0.0027034154627472162,
-0.0365542471408844,
0.03748571500182152,
-0.031406283378601074,
0.08015589416027069,
0.04226192086935043,
0.020390307530760765,
0.006891633849591017,
-0.007315362337976694,
-0.021876979619264603,
0.025429224595427513,
-0.006496472749859095,
-0.023911017924547195,
-0.019381199032068253,
0.016249731183052063,
-0.027183983474969864,
-0.028096670284867287,
-0.014710147865116596,
-0.029118966311216354,
-0.05919449031352997,
-0.009179550223052502,
0.0272915530949831,
-0.008751468732953072,
-0.0009099511080421507,
-0.05908830091357231,
-0.0132564976811409,
0.004684461280703545,
0.03607828542590141,
-0.03804786130785942,
0.00568340765312314,
-0.03856934979557991,
-0.027134055271744728,
-0.0162022914737463,
0.006086146924644709,
-0.008968391455709934,
0.014482248574495316,
0.007765122689306736,
-0.023023774847388268,
0.03826327621936798,
-0.014855108223855495,
0.04174521937966347,
-0.03372206538915634,
0.01367997843772173,
-0.004279314074665308,
-0.006257292348891497,
0.0254887156188488,
-0.027864007279276848,
-0.01994464360177517,
0.04163423925638199,
-0.009278376586735249,
0.012096974067389965,
-0.033165253698825836,
-0.021033689379692078,
0.03468289598822594,
0.05061720311641693,
-0.020022479817271233,
-0.03122067078948021,
-0.03518472984433174,
-0.03682248666882515,
-0.03265834227204323,
0.016293840482831,
0.014838055707514286,
-0.019904725253582,
-0.00760792288929224,
0.024629568681120872,
0.01398745458573103,
-0.009332939982414246,
0.036772679537534714,
-0.008993159979581833,
-0.0004906501853838563,
-0.01602241024374962,
0.03720441833138466,
0.012083365581929684,
0.048807140439748764,
0.04043102636933327,
-0.011378654278814793,
0.0023440660443156958,
-0.020433327183127403,
0.02460562251508236,
-0.043082207441329956,
0.0015794762875884771,
-0.009187878109514713,
-0.004783084616065025,
0.04745505377650261,
-0.08415298908948898,
0.004219190217554569,
0.06497206538915634,
-0.029041968286037445,
0.024181922897696495,
-0.024589769542217255,
-0.0030404392164200544,
-0.004174379166215658,
0.0008325838716700673,
0.04133480414748192,
0.02294895239174366,
0.05021126568317413,
0.03648883104324341,
0.005542099475860596,
0.024008113890886307,
-0.019604457542300224,
-0.01214298140257597,
0.01638791337609291,
0.02632213942706585,
0.024614430963993073,
-0.05657404661178589,
0.046340204775333405,
-0.029434410855174065,
-0.02615317516028881,
0.03529765456914902,
-0.039820488542318344,
0.01750774495303631,
0.02672426402568817,
0.027661433443427086,
-0.018421979621052742,
0.046745024621486664,
0.008430535905063152,
-0.03111608698964119,
-0.03766591101884842,
0.012634942308068275,
-0.0019207036821171641,
0.03545356169342995,
-0.006813975516706705,
0.038323137909173965,
-0.012022007256746292,
-0.018407221883535385,
-0.016440387815237045,
0.01729695498943329,
0.001488704001531005,
-0.028163805603981018,
0.0001341724710073322,
0.007986616343259811,
0.022959355264902115,
-0.06684689223766327,
-0.01407314371317625,
-0.020108211785554886,
-0.02724473550915718,
0.04767034947872162,
-0.01938876137137413,
-0.04834924638271332,
-0.028286702930927277,
-0.021217308938503265,
-0.005713718943297863,
0.013228765688836575,
-0.033636078238487244,
0.025306766852736473,
-0.08702973276376724,
0.004807977471500635,
-0.01817004196345806,
-0.04687262699007988,
-0.012934789061546326,
0.001754366559907794,
-0.00744621129706502,
0.057004500180482864,
-0.0033502380829304457,
-0.004447884391993284,
0.05806005746126175,
-0.004978436976671219,
-0.03394670784473419,
-0.07716535031795502,
0.04541165754199028,
0.01546742394566536,
-0.041963860392570496,
-0.03866904601454735,
-0.020670276135206223,
0.010348734445869923,
0.011075561866164207,
0.021666454151272774,
0.020585540682077408,
-0.00439903698861599,
-0.031663790345191956,
-0.006634349934756756,
-0.0030498094856739044,
0.008624937385320663,
0.025323333218693733,
-0.0005483540589921176,
-0.03338369354605675,
0.017837990075349808,
-0.023439204320311546,
-0.03257672116160393,
-0.006723333615809679,
0.022090686485171318,
-0.0411507673561573,
0.06410881876945496,
0.017752552404999733,
0.01651252806186676,
-0.009454901330173016,
0.021157152950763702,
0.0007624567952007055,
0.09506604820489883,
0.008253268897533417,
-0.0008918516105040908,
0.04701949283480644,
0.006440636236220598,
-0.04914814606308937,
0.03916511312127113,
-0.011942211538553238,
-0.0140343327075243,
-0.025150472298264503,
-0.000015095385606400669,
0.03003377467393875,
-0.09538814425468445,
-0.03626224771142006,
0.02619381994009018,
-0.009874185547232628,
0.006811574101448059,
0.008090294897556305,
0.0011864847037941217,
0.011488224379718304,
-0.013049615547060966,
0.06368852406740189,
0.02144869789481163,
0.006730471272021532,
0.031384360045194626,
0.01758580654859543,
0.0023521289695054293,
-0.005968254990875721,
-0.015527955256402493,
0.04094487428665161,
-0.011086145415902138,
0.06452938914299011,
0.022089749574661255,
0.03929533436894417,
0.01383945345878601,
0.026844946667551994,
-0.023104913532733917,
-0.004259898792952299,
0.013893580064177513,
0.04387667775154114,
-0.0058157555758953094,
0.061965469270944595,
-0.062651626765728,
0.006834743078798056,
0.0009175828308798373,
-0.04141261801123619,
-0.032804958522319794,
0.04180451110005379,
-0.0039900545962154865,
0.041105352342128754,
-0.007826144807040691,
0.025843176990747452,
0.005588018801063299,
-0.0011437200009822845,
0.04539312422275543,
-0.02712544985115528,
0.030026603490114212,
0.0008791122818365693,
-0.0247786995023489,
0.028620827943086624,
-0.03814813867211342,
-0.014902964234352112,
-0.012052396312355995,
0.04542359337210655,
0.03912525996565819,
0.029646873474121094,
-0.010592282749712467,
-0.041359249502420425,
-0.030399849638342857,
0.005051501095294952,
-0.053708575665950775,
-0.010606948286294937,
-0.04045924171805382,
0.008001643233001232,
0.0009694733889773488,
0.004826271906495094
] |
<p>I need to know the consumption of a water tap in Liters. </p>
<p>I'm able to know the cross-sectional area of the pipe and how long the tap is open. With these data, how can I know the consumption/volume of water that pass through the water tap?</p>
<p>It can be rough estimation. I can assume a maximum volume of water...</p>
<p>Thanks in advance!</p>
| 7,671 |
[
-0.030554208904504776,
-0.012540297582745552,
-0.009865256026387215,
0.03233149275183678,
0.025456001982092857,
0.01291109062731266,
-0.0031884347554296255,
-0.03005673736333847,
0.044121358543634415,
0.008766396902501583,
0.030461672693490982,
0.053231507539749146,
0.01643701270222664,
0.028130339458584785,
0.028805499896407127,
0.014633226208388805,
-0.015509119257330894,
-0.016425253823399544,
0.011447275057435036,
-0.04396304860711098,
-0.0010925560491159558,
0.036609310656785965,
0.009604022838175297,
-0.016606943681836128,
-0.01730746403336525,
0.03974047303199768,
0.03621595725417137,
-0.035580698400735855,
-0.005955488421022892,
0.027752099558711052,
0.007604966405779123,
-0.06180235743522644,
0.013719122856855392,
0.05367685481905937,
-0.00043014949187636375,
-0.023320309817790985,
-0.06094399094581604,
-0.043817874044179916,
-0.0060266065411269665,
0.027823220938444138,
-0.059840742498636246,
-0.013636298477649689,
0.024539247155189514,
0.04746037349104881,
-0.016622398048639297,
0.03733702749013901,
0.0003743925772141665,
-0.04473027214407921,
-0.019658837467432022,
-0.07969620078802109,
0.06462503224611282,
0.02320043183863163,
0.07088994234800339,
0.026743080466985703,
-0.028696071356534958,
0.016586769372224808,
0.0747603178024292,
0.09154009073972702,
-0.026778962463140488,
-0.05407173931598663,
-0.0008414114126935601,
0.01823495700955391,
-0.03153578191995621,
-0.021736664697527885,
-0.04205046594142914,
-0.019029634073376656,
-0.03669090196490288,
-0.00862122792750597,
0.018972020596265793,
-0.02475721947848797,
0.032528236508369446,
0.0029886863194406033,
0.05592234432697296,
0.019881313666701317,
0.017951473593711853,
-0.006636015605181456,
0.030487816780805588,
0.045987024903297424,
0.05448601767420769,
0.05208299309015274,
-0.005818681791424751,
0.014007153920829296,
0.03811420127749443,
0.02693135291337967,
0.03402784466743469,
-0.04645523801445961,
0.07376952469348907,
0.008346013724803925,
0.03155368193984032,
0.011826906353235245,
0.011951948516070843,
0.0004033499862998724,
-0.005218447186052799,
0.04096122086048126,
-0.011935620568692684,
0.03593633323907852,
-0.028793713077902794,
0.04963097348809242,
0.030559824779629707,
-0.041530244052410126,
0.029919449239969254,
-0.019871721044182777,
0.01586565561592579,
0.0623970665037632,
0.004961748141795397,
0.011284098029136658,
-0.003940246999263763,
0.000906122091691941,
0.02267828956246376,
0.009659691713750362,
-0.021778695285320282,
-0.019649939611554146,
0.043651048094034195,
0.010060776025056839,
0.0026814991142600775,
-0.01944737508893013,
-0.011125022545456886,
-0.01429448276758194,
0.033551741391420364,
0.03893328458070755,
0.035475146025419235,
-0.02551007643342018,
0.01931634545326233,
-0.009734854102134705,
-0.056003592908382416,
0.04618614912033081,
-0.017167912796139717,
0.0033246639650315046,
-0.06575126200914383,
0.06337852030992508,
-0.01869254931807518,
-0.015405402518808842,
0.04112337902188301,
-0.041683923453092575,
0.05275565758347511,
-0.006205656100064516,
-0.07582443952560425,
-0.05015900731086731,
0.027786992490291595,
0.019063003361225128,
-0.03907485678792,
-0.041009191423654556,
0.028580009937286377,
0.04365703836083412,
0.033926092088222504,
-0.017916129902005196,
0.03723598271608353,
0.02632998488843441,
-0.024720339104533195,
-0.024644693359732628,
-0.03399674594402313,
-0.013236521743237972,
0.03620622679591179,
0.013745452277362347,
0.038525257259607315,
-0.015820534899830818,
0.007276838179677725,
0.04049426689743996,
0.009762098081409931,
-0.030630994588136673,
0.04687359556555748,
-0.0008735835435800254,
-0.04554286226630211,
0.03327515348792076,
-0.0010230711195617914,
-0.05622745677828789,
0.04975052922964096,
-0.016654716804623604,
0.007455805316567421,
0.00989218894392252,
0.01866917684674263,
-0.012392790988087654,
0.011210093274712563,
0.01944105513393879,
0.0564863495528698,
0.0035489697474986315,
-0.019840775057673454,
-0.016992514953017235,
0.0324883796274662,
0.03460143133997917,
-0.010229421779513359,
-0.020752359181642532,
-0.008561346679925919,
0.017546555027365685,
0.054739367216825485,
-0.015453415922820568,
0.023656519129872322,
-0.05559196695685387,
-0.00640033558011055,
-0.05051245540380478,
-0.005862903781235218,
-0.05287999287247658,
0.010223153047263622,
-0.03055729530751705,
0.03180714696645737,
0.00962862093001604,
-0.0010044716764241457,
-0.006096599157899618,
-0.04059513658285141,
-0.014438287355005741,
-0.007084659766405821,
-0.009443542920053005,
0.013592171482741833,
-0.013360309414565563,
0.006041625514626503,
0.04637490585446358,
0.06851927191019058,
-0.014876686967909336,
0.00019645169959403574,
-0.03213982284069061,
0.008367177098989487,
-0.029736757278442383,
-0.026842840015888214,
0.02019386924803257,
-0.03456481918692589,
-0.01886945590376854,
-0.005742112640291452,
0.020591625943779945,
0.004096363205462694,
0.01904418133199215,
-0.03775715082883835,
0.07462906837463379,
0.05235647037625313,
0.006713287904858589,
0.0037096424493938684,
-0.02536211535334587,
0.0030474907252937555,
-0.00486158300191164,
0.007092977873980999,
-0.024083111435174942,
-0.04971124604344368,
0.009951501153409481,
0.011430771090090275,
-0.033885642886161804,
-0.018514826893806458,
-0.029043050482869148,
0.032103363424539566,
-0.006177097093313932,
0.01801968552172184,
-0.018294425681233406,
-0.009712856262922287,
0.01634967513382435,
-0.029423054307699203,
0.02364637702703476,
-0.004274141043424606,
0.004317217506468296,
0.01680017076432705,
0.0311367679387331,
0.054290566593408585,
-0.02277662232518196,
-0.010972663760185242,
0.016856523230671883,
-0.011855480261147022,
0.04306551069021225,
0.005545701831579208,
-0.027629483491182327,
0.05757823586463928,
-0.04433038458228111,
-0.017241638153791428,
0.004886444192379713,
0.008056281134486198,
0.019586671143770218,
-0.02878749370574951,
-0.014443240128457546,
0.033673014491796494,
0.020533408969640732,
-0.007778420113027096,
0.026516033336520195,
0.025778913870453835,
-0.03233032673597336,
0.051155027002096176,
-0.04486125335097313,
0.0008700174512341619,
-0.03944356366991997,
-0.004791285376995802,
0.02914249151945114,
-0.010570097714662552,
0.007260357029736042,
-0.04220046103000641,
-0.03015252947807312,
-0.014285344630479813,
0.00972483865916729,
-0.023844372481107712,
0.0035999093670397997,
-0.023626133799552917,
-0.014409550465643406,
0.012207568623125553,
-0.01524037029594183,
0.021078426390886307,
0.012328204698860645,
-0.024997245520353317,
0.016559215262532234,
0.012940729968249798,
-0.04121137410402298,
0.0017013936303555965,
-0.0121877770870924,
0.041485510766506195,
-0.02853579632937908,
0.035221390426158905,
0.03331422060728073,
0.00020359437621664256,
-0.06478223204612732,
0.017794856801629066,
-0.05957523733377457,
-0.03608835116028786,
-0.03759585693478584,
0.009912929497659206,
0.00969404075294733,
-0.01955016888678074,
0.015176687389612198,
0.03176204487681389,
-0.04186567664146423,
-0.011141732335090637,
-0.0620635524392128,
-0.062004148960113525,
0.03440915420651436,
0.03375450149178505,
0.03680354356765747,
0.021520929411053658,
-0.028401052579283714,
0.01685388945043087,
-0.026344114914536476,
-0.09072238951921463,
-0.042568936944007874,
-0.015941785648465157,
0.015600730665028095,
-0.03836393728852272,
0.002524391748011112,
0.039131417870521545,
-0.04318786785006523,
0.022853493690490723,
0.014862735755741596,
0.047388941049575806,
0.03701822832226753,
0.04861658066511154,
0.01585787534713745,
-0.006100396625697613,
0.005050077103078365,
0.0032431192230433226,
0.04322437569499016,
0.020020687952637672,
-0.03813670575618744,
0.004530744627118111,
-0.03950502350926399,
0.02517842687666416,
0.03397343307733536,
-0.014758030883967876,
0.027766719460487366,
-0.02022530883550644,
-0.011495589278638363,
-0.05541018769145012,
0.007399601861834526,
0.0007479068008251488,
0.007609308697283268,
0.00839322991669178,
0.01450283918529749,
0.01623094640672207,
0.006912172771990299,
-0.020414823666214943,
0.03242800012230873,
0.04497230798006058,
-0.05107344686985016,
-0.055368538945913315,
0.0005101305432617664,
-0.01367226429283619,
0.010779470205307007,
0.011308659799396992,
-0.011187871918082237,
0.040099840611219406,
0.05041373893618584,
-0.006287511438131332,
-0.00020431420125532895,
-0.02582833729684353,
-0.006474515423178673,
-0.08230437338352203,
-0.024854103103280067,
-0.006654488388448954,
0.03995935618877411,
0.004558289423584938,
0.04220736026763916,
0.034041229635477066,
-0.012998881749808788,
0.03556182235479355,
-0.002596649806946516,
-0.05007980763912201,
0.02069241739809513,
-0.007581165060400963,
0.007180702872574329,
0.01348400954157114,
-0.05310242623090744,
0.011183422990143299,
-0.050924524664878845,
-0.027411919087171555,
0.015917543321847916,
0.015005622990429401,
-0.04214077442884445,
0.014289196580648422,
0.0037148098926991224,
0.008489793166518211,
-0.023416271433234215,
0.013258558697998524,
0.04927115887403488,
-0.03830300271511078,
0.02074940875172615,
0.03692122548818588,
-0.0021678872872143984,
-0.030014192685484886,
-0.01532894279807806,
0.023334085941314697,
-0.0026555408257991076,
0.04160865768790245,
0.01751604676246643,
0.011398130096495152,
-0.031585630029439926,
0.0017968850443139672,
-0.03609596565365791,
0.058400269597768784,
-0.008977011777460575,
-0.021250734105706215,
-0.03786417841911316,
-0.03503885120153427,
0.02349463477730751,
0.021320641040802002,
0.017016081139445305,
-0.011904386803507805,
0.012352998368442059,
0.03500888869166374,
-0.00974102970212698,
-0.058233264833688736,
0.04860154539346695,
0.07424227893352509,
0.01392403244972229,
-0.0014403646346181631,
-0.021625731140375137,
0.00045791195589117706,
-0.017271582037210464,
-0.015155553817749023,
0.020705150440335274,
0.04794146493077278,
-0.012672359123826027,
0.014173977077007294,
0.02669481188058853,
0.0011325724190101027,
-0.03445044904947281,
-0.0030982643365859985,
0.04294738173484802,
0.021065888926386833,
-0.02879146672785282,
-0.020244525745511055,
0.0557231679558754,
0.018621165305376053,
0.03688184171915054,
0.02524441108107567,
-0.010099970735609531,
-0.10873152315616608,
-0.037830840796232224,
0.04373546689748764,
0.053212232887744904,
0.0008800171781331301,
0.002685010666027665,
-0.03849716857075691,
-0.023596763610839844,
0.05843508988618851,
-0.03691883012652397,
-0.0003914327244274318,
-0.030888082459568977,
0.01928897760808468,
-0.027929875999689102,
-0.015534221194684505,
-0.010503118857741356,
-0.004361252766102552,
-0.044166311621665955,
0.004194709472358227,
-0.01355890091508627,
0.012594779022037983,
-0.033124107867479324,
0.01102884765714407,
0.012807653285562992,
0.054358724504709244,
0.014031583443284035,
-0.01418386958539486,
0.01510974857956171,
0.052615564316511154,
-0.04363463073968887,
-0.06463617831468582,
0.03186903893947601,
-0.0190432146191597,
0.025854190811514854,
0.03202489763498306,
0.020329779013991356,
-0.031533267349004745,
0.059068020433187485,
-0.011219189502298832,
-0.02322867140173912,
-0.0020892734173685312,
-0.049896061420440674,
0.03496693819761276,
0.003912101034075022,
0.03406127914786339,
0.054734718054533005,
0.025454500690102577,
0.0344429649412632,
-0.003361060516908765,
-0.005773613229393959,
0.023548055440187454,
-0.01786261983215809,
-0.03298209235072136,
-0.03283288702368736,
-0.012250489555299282,
-0.02227957360446453,
0.019773297011852264,
-0.018692439422011375,
0.04617593064904213,
-0.016974473372101784,
-0.05165678262710571,
-0.005649684928357601,
0.008888011798262596,
0.0005780336214229465,
-0.01647968217730522,
0.012821780517697334,
0.016987143084406853,
0.021536534652113914,
-0.03867620602250099,
0.0070950426161289215,
-0.024770434945821762,
0.024358727037906647,
-0.009930284693837166,
-0.01572941616177559,
0.00960289966315031,
-0.025717293843626976,
-0.013585520908236504,
0.05712969973683357,
-0.016471104696393013,
0.05902440473437309,
-0.048739057034254074,
0.04768341779708862,
0.019491052255034447,
-0.05052981525659561,
-0.0026049278676509857,
0.05314918980002403,
0.015050161629915237,
0.017488008365035057,
-0.030290840193629265,
0.01873025670647621,
-0.008420825935900211,
0.02117612585425377,
-0.046710316091775894,
-0.04305016249418259,
0.04944366216659546,
0.04173213988542557,
-0.014182299375534058,
-0.021960701793432236,
-0.008973794989287853,
-0.005011124070733786,
-0.023264247924089432,
-0.011582968756556511,
-0.0009699250804260373,
-0.02060849405825138,
0.04407829791307449,
0.015118909999728203,
0.012859131209552288,
0.07343607395887375,
-0.011359810829162598,
0.02453354373574257,
0.00042723846854642034,
-0.018765363842248917,
-0.04757101088762283,
0.003617132781073451,
-0.02032334730029106,
-0.013653968460857868,
-0.03227872774004936,
-0.014715333469212055,
0.008859471417963505,
0.06660030782222748,
-0.059547603130340576,
0.01859918236732483,
-0.014781189151108265,
0.01341940090060234,
-0.04749955236911774,
0.005662725307047367,
0.023499656468629837,
0.015194298699498177,
0.028598282486200333,
-0.05302968621253967,
-0.027223147451877594,
-0.06480275094509125,
-0.007074500899761915,
-0.0016390454256907105,
-0.03134309500455856,
-0.024647919461131096,
-0.0008657624130137265,
0.05046829953789711,
-0.028038855642080307,
-0.01164250262081623,
0.034326281398534775,
-0.015171781182289124,
0.017188094556331635,
0.009324813261628151,
-0.017085151746869087,
0.005751624237746,
-0.017442762851715088,
-0.0537138432264328,
-0.03780597448348999,
-0.015164271928369999,
-0.054317645728588104,
-0.003211698727682233,
0.0072794463485479355,
0.039877403527498245,
0.02558164671063423,
-0.009638610295951366,
0.022403685376048088,
-0.021712206304073334,
-0.023638352751731873,
0.025861846283078194,
0.017691154032945633,
0.06048939749598503,
0.027037257328629494,
-0.02629188448190689,
0.0017234974075108767,
0.004687840584665537,
-0.029955336824059486,
0.016946163028478622,
0.017879022285342216,
0.014934803359210491,
0.020694773644208908,
-0.027269503101706505,
-0.03864068537950516,
0.008514232002198696,
-0.039292603731155396,
-0.03190508112311363,
-0.03109094128012657,
-0.0031945831142365932,
0.06646605581045151,
-0.037282951176166534,
-0.027437560260295868,
-0.03705006465315819,
0.0035426586400717497,
-0.03222046419978142,
0.0029115655925124884,
0.04538979008793831,
0.03717164695262909,
-0.007325248327106237,
0.04490809142589569,
0.0416233092546463,
-0.032105665653944016,
0.03433329984545708,
-0.015776311978697777,
-0.03854839876294136,
0.008231296204030514,
-0.03508373722434044,
-0.06081947684288025,
0.03706502914428711,
-0.0025402780156582594,
-0.010445242747664452,
0.016869205981492996,
-0.030803969129920006,
-0.01313814241439104,
-0.019057881087064743,
0.0402386449277401,
-0.01353437639772892,
0.04857799783349037,
-0.0008272104896605015,
0.008029868826270103,
-0.005909299943596125,
0.002922388957813382,
0.11193211376667023,
0.05508863180875778,
0.019562596455216408,
-0.05663657188415527,
-0.004840581212192774,
0.023212246596813202,
0.0013971481239423156,
-0.03428087383508682,
0.005197049118578434,
0.001712987432256341,
0.014496643096208572,
0.017529761418700218,
0.023839332163333893,
-0.020967815071344376,
0.03870198503136635,
0.05609213933348656,
-0.035341229289770126,
-0.005865943618118763,
0.07380830496549606,
0.03259728476405144,
-0.04306551441550255,
0.029955793172121048,
-0.05230886489152908,
0.0695192813873291,
0.0015818160027265549,
-0.031768545508384705,
-0.039101194590330124,
-0.03756415471434593,
0.03917956352233887,
-0.02127421833574772,
-0.04123929888010025,
0.042863573879003525,
0.026422368362545967,
-0.006235186010599136,
-0.029667431488633156,
0.0014662315370514989,
0.03820747137069702,
0.02226865291595459,
-0.015112190507352352,
0.029738297685980797,
0.022585082799196243,
-0.027610428631305695,
-0.01551538985222578,
0.04459196329116821,
-0.053286198526620865,
-0.014150099828839302,
-0.035968929529190063,
0.001113545149564743,
0.009771854616701603,
-0.01131887175142765,
-0.017236562445759773,
0.025266701355576515,
0.004669637884944677,
-0.06605149805545807,
-0.025105366483330727,
0.03249717876315117,
0.01882186345756054,
-0.008468563668429852,
-0.031005125492811203,
-0.02096087858080864,
-0.0065973191522061825,
-0.023847291246056557,
0.007658743299543858,
-0.024279074743390083,
-0.02003578469157219,
0.010939921252429485,
-0.03503192216157913,
0.002021835884079337,
0.01031859964132309,
-0.014816953800618649,
-0.0046074362471699715,
-0.009626602753996849,
-0.04631999507546425,
0.012809070758521557,
0.01012494694441557,
0.011253273114562035,
0.013450649566948414,
0.017896389588713646,
0.035310205072164536,
-0.0025952463038265705,
-0.07376022636890411,
0.027396908029913902,
-0.02475579082965851,
-0.042461901903152466,
-0.031792446970939636,
0.01608358509838581,
-0.008985219523310661,
0.0578877329826355,
-0.011745540425181389,
-0.019288895651698112,
0.012346490286290646,
0.03578372299671173,
0.0463220551609993,
-0.033875543624162674,
-0.025643017143011093,
-0.006878934800624847,
-0.02490886300802231,
0.02759660594165325,
-0.007993252016603947,
0.0505528450012207,
0.0509757325053215,
0.023112516850233078,
-0.03255440294742584,
-0.007246282417327166,
-0.028208358213305473,
0.012840447947382927,
-0.021292874589562416,
-0.05847259983420372,
-0.03462629020214081,
-0.018888648599386215,
0.016853684559464455,
-0.02246841974556446,
-0.015128414146602154,
-0.011813731864094734,
-0.007135828025639057,
0.011519591324031353,
-0.014651459641754627,
-0.03884727135300636,
0.026182077825069427,
-0.046493422240018845,
0.01212280336767435,
0.0036353461910039186,
0.02219512313604355,
-0.056125372648239136,
-0.06338237971067429,
-0.022939354181289673,
-0.021231381222605705,
-0.02211853861808777,
0.03853032737970352,
-0.018217401579022408,
-0.010565056465566158,
0.02850295603275299,
-0.0027261641807854176,
-0.004041493870317936,
-0.0003019282885361463,
0.008233293890953064,
0.0025775025133043528,
0.04157910868525505,
-0.027168033644557,
-0.025283614173531532,
0.06047132983803749,
0.003032763721421361,
0.034825459122657776,
0.02436908707022667,
-0.025396602228283882,
0.06542108207941055,
0.03931526839733124,
-0.02814120426774025,
-0.008520739153027534,
0.05248194560408592,
-0.020201964303851128,
0.01383630558848381,
-0.02681906335055828,
-0.0000993047360680066,
0.02130885049700737,
0.012748540379106998,
0.012370130978524685,
-0.005105958320200443,
0.0033703544177114964,
0.016363922506570816,
0.0018419011030346155,
0.03332337364554405,
-0.0021205097436904907,
0.003734245663508773,
-0.008335055783390999,
0.025364521890878677,
0.046760670840740204,
-0.016686132177710533,
0.005736649967730045,
0.027005966752767563,
-0.03668555989861488,
0.005860019940882921,
0.002561199478805065,
-0.024014487862586975,
-0.07972975075244904,
0.02675797790288925,
-0.02683993987739086,
0.010927315801382065,
0.03396759182214737,
-0.059991639107465744,
0.004731892608106136,
0.050914060324430466,
-0.05164803937077522,
0.011983513832092285,
-0.02722916752099991,
-0.0004114765615668148,
-0.03769689053297043,
0.0002814199833665043,
0.004109685774892569,
0.05476291850209236,
0.035920582711696625,
0.045025285333395004,
0.016941387206315994,
0.024279356002807617,
-0.0029057711362838745,
-0.05368956923484802,
-0.0010136131895706058,
0.019441774114966393,
0.003365816082805395,
-0.016691133379936218,
0.014339066110551357,
-0.043817415833473206,
-0.004418831784278154,
0.024873483926057816,
-0.04651438817381859,
0.06163052096962929,
0.015921611338853836,
-0.00930110178887844,
-0.0029868599958717823,
0.055514514446258545,
0.04111310467123985,
0.027521362528204918,
-0.005489273462444544,
0.0024275067262351513,
0.01975432224571705,
0.008565224707126617,
-0.013178347609937191,
0.007685203105211258,
0.007457710802555084,
-0.01109762117266655,
-0.020815357565879822,
0.020767714828252792,
-0.03415277227759361,
0.007940971292555332,
0.035965561866760254,
-0.03536424785852432,
0.03096342645585537,
-0.03993070498108864,
0.002284187590703368,
-0.027063295245170593,
0.01035201083868742,
0.050773728638887405,
-0.0067065111361444,
-0.001970278099179268,
-0.029948489740490913,
0.01249044481664896,
-0.02372674085199833,
0.004103087820112705,
0.017384016886353493,
-0.026521172374486923,
-0.057728663086891174,
0.006063035223633051,
-0.022665241733193398,
-0.00789997261017561,
0.009458237327635288,
-0.007033183239400387,
-0.038548197597265244,
0.03149260953068733,
0.005533671472221613,
-0.012566122226417065,
0.0482918843626976,
0.006463074591010809,
-0.01343579962849617,
-0.08375443518161774,
0.05045732855796814,
0.01592141017317772,
-0.022116228938102722,
-0.013625324703752995,
-0.006840217858552933,
0.020004918798804283,
0.0008419619407504797,
0.09113286435604095,
0.002821721136569977,
-0.008232970722019672,
-0.001008401857689023,
0.017003115266561508,
0.024272818118333817,
-0.05506422370672226,
-0.0022705625742673874,
-0.046394091099500656,
-0.06874086707830429,
0.00866905227303505,
-0.03612871840596199,
0.021166294813156128,
0.01329620461910963,
0.005319543182849884,
0.01765429601073265,
0.00791096594184637,
-0.015558822080492973,
-0.0038774653803557158,
-0.005167241208255291,
0.006510468665510416,
-0.001709728385321796,
0.07333256304264069,
-0.018638523295521736,
0.016828006133437157,
0.03613894805312157,
0.0005573497619479895,
-0.05946291238069534,
-0.004156922921538353,
-0.03167441859841347,
-0.02364370971918106,
-0.029667694121599197,
-0.007676668930798769,
0.0038917080964893103,
-0.03339919447898865,
-0.010448010638356209,
0.04469968006014824,
-0.047475047409534454,
-0.015688423067331314,
0.07401668280363083,
0.036061618477106094,
0.05518605187535286,
-0.023638617247343063,
0.040212735533714294,
0.01346955168992281,
-0.011608820408582687,
0.005426538642495871,
0.034756727516651154,
0.06461205333471298,
-0.01443957444280386,
-0.015194889158010483,
0.05530191585421562,
0.040810905396938324,
0.0019646233413368464,
-0.0018187984824180603,
0.04934227466583252,
-0.031671542674303055,
-0.050652340054512024,
-0.014117914251983166,
-0.014260146766901016,
0.030456727370619774,
0.012262203730642796,
-0.017326345667243004,
0.04448900371789932,
0.003301253542304039,
0.0017588435439392924,
-0.0592566542327404,
-0.02364255115389824,
-0.0176370982080698,
0.009893800131976604,
0.0038254407700151205,
-0.004430905915796757,
0.015808995813131332,
0.018258841708302498,
-0.016429061070084572,
-0.004177802242338657,
0.010855983942747116,
-0.00925665907561779,
0.04091176390647888,
0.0009046945488080382,
-0.0077166808769106865,
-0.051254384219646454,
0.003968368284404278,
-0.010927638970315456,
0.0017505655996501446,
0.045337531715631485,
0.06960735470056534,
-0.014665289781987667,
0.02339969016611576,
-0.01874668151140213,
-0.0011063436977565289,
0.04939160495996475,
-0.0884343683719635,
-0.006057485938072205,
-0.035819243639707565,
-0.005400306545197964,
0.016865350306034088,
-0.026340484619140625
] |
<p>Are the stars in our galaxy spiraling inwards towards the center, or are they in a permanent orbit?</p>
<p>And if we are heading towards the center then what is the rate of this process?</p>
<p>I started wondering this while watching this documentary: <a href="http://www.youtube.com/watch?v=zKE4Bt8ylhM" rel="nofollow">http://www.youtube.com/watch?v=zKE4Bt8ylhM</a></p>
| 1,017 |
[
-0.04076147824525833,
-0.03744163364171982,
-0.005782414693385363,
-0.02928394079208374,
0.07158950716257095,
0.008320911787450314,
-0.04681777209043503,
-0.027100220322608948,
0.004183140117675066,
-0.0620107501745224,
-0.002930144313722849,
0.07867402583360672,
-0.00004501215516938828,
0.018714066594839096,
-0.013566012494266033,
0.01551016140729189,
-0.005344034172594547,
0.02727893739938736,
-0.024684198200702667,
0.01017270889133215,
-0.019863270223140717,
0.008365154266357422,
-0.003015070455148816,
0.025261646136641502,
-0.05550546571612358,
0.04672269895672798,
0.04658379778265953,
-0.005555311683565378,
-0.006408967077732086,
0.0665736272931099,
0.0032974800560623407,
0.003867876483127475,
0.033047519624233246,
0.025019720196723938,
0.04131685197353363,
0.0027810230385512114,
-0.029099831357598305,
-0.014736098237335682,
-0.026887476444244385,
0.03292537480592728,
-0.03608251363039017,
-0.039200883358716965,
-0.027851317077875137,
0.02190314792096615,
-0.019113846123218536,
-0.02754412218928337,
-0.015436782501637936,
0.026770763099193573,
0.04650990292429924,
-0.037495460361242294,
0.051336225122213364,
-0.014258209615945816,
0.004280922003090382,
0.004136553034186363,
0.014187880791723728,
-0.01560881081968546,
0.08407909423112869,
0.02752009779214859,
-0.004287935793399811,
-0.029605917632579803,
-0.0034123591613024473,
0.023616375401616096,
-0.009946365840733051,
-0.020878633484244347,
-0.008190235123038292,
0.027321510016918182,
-0.010397374629974365,
-0.009059588424861431,
0.04289617761969566,
0.028106171637773514,
-0.012612949125468731,
0.006774540059268475,
0.009621369652450085,
-0.04092658683657646,
-0.0032352153211832047,
-0.06007866561412811,
0.046909648925065994,
0.0006702147657051682,
0.037329722195863724,
0.021929582580924034,
-0.0031638045329600573,
-0.005596639588475227,
0.03985849767923355,
-0.012080278247594833,
0.016481608152389526,
0.041261203587055206,
0.08290417492389679,
-0.011776980012655258,
0.019871219992637634,
0.036377716809511185,
0.023436320945620537,
0.021021179854869843,
0.014007252641022205,
-0.02653910219669342,
-0.0052426597103476524,
0.05605193227529526,
0.006821679882705212,
0.046235013753175735,
-0.00630944175645709,
-0.020739177241921425,
-0.01688791625201702,
0.014714401215314865,
-0.004789102356880903,
0.0816228911280632,
0.005833263974636793,
-0.030876344069838524,
-0.06409823149442673,
-0.021019648760557175,
-0.04186473786830902,
-0.017314648255705833,
-0.07013049721717834,
-0.011936107650399208,
-0.016513394191861153,
0.0033808413427323103,
0.027652624994516373,
0.006877940613776445,
-0.005683403927832842,
0.008224531076848507,
0.06878490746021271,
0.04806267470121384,
0.03179871290922165,
-0.007712514139711857,
0.022871362045407295,
-0.0382353812456131,
-0.02184140868484974,
0.0391998253762722,
0.055486369878053665,
-0.0003498273727018386,
-0.043051183223724365,
0.03347785398364067,
0.03305851295590401,
-0.0083569111302495,
-0.004575182683765888,
-0.006502148695290089,
0.05611267313361168,
0.013779835775494576,
-0.08384472131729126,
-0.0682087317109108,
0.04638596251606941,
-0.0011248108930885792,
-0.01637144200503826,
-0.04758041352033615,
-0.00474209152162075,
0.013458344154059887,
0.09361686557531357,
-0.01867440715432167,
-0.015209106728434563,
0.014928613789379597,
0.03954123333096504,
-0.010774718597531319,
0.0007830943795852363,
0.006493306253105402,
-0.03264017030596733,
-0.04863659664988518,
-0.011353228241205215,
-0.09343571215867996,
0.02690252475440502,
0.035752635449171066,
0.0076547348871827126,
-0.05678689107298851,
0.046402379870414734,
-0.028968587517738342,
0.010614383965730667,
0.00726676918566227,
-0.020817503333091736,
-0.032092172652482986,
0.060509081929922104,
0.03457796573638916,
0.010480952449142933,
0.03780050948262215,
-0.0029391429852694273,
0.02846907079219818,
0.008067077957093716,
0.00989361573010683,
0.045421160757541656,
-0.03859884291887283,
-0.008442791178822517,
-0.03586706146597862,
-0.018608028069138527,
-0.02455105632543564,
-0.01811208203434944,
-0.028285594657063484,
-0.014267622493207455,
-0.007556882221251726,
0.049188386648893356,
0.08657179027795792,
0.0001020157869788818,
-0.0005845024716109037,
-0.007059843745082617,
-0.027043743059039116,
0.015170421451330185,
-0.05312783271074295,
0.010395905934274197,
-0.02491568587720394,
-0.015974756330251694,
-0.018543653190135956,
0.011822368018329144,
0.017544252797961235,
0.012097416445612907,
-0.03466910868883133,
0.023672696202993393,
0.05590038746595383,
0.03783928230404854,
-0.013895146548748016,
0.02588748000562191,
0.04548429697751999,
0.005053318105638027,
-0.022095641121268272,
0.006276184692978859,
-0.013399027287960052,
-0.02170921117067337,
-0.01680331863462925,
-0.005503085907548666,
0.018766889348626137,
-0.0027413114439696074,
0.0037631976883858442,
0.044545531272888184,
0.025109950453042984,
0.01569286733865738,
0.013026981614530087,
-0.03895670548081398,
0.07498788088560104,
0.017731621861457825,
0.01910196989774704,
0.042598266154527664,
0.02025366947054863,
-0.008160736411809921,
0.03011898323893547,
-0.009141167625784874,
-0.009495601058006287,
-0.051501620560884476,
0.005156568717211485,
0.03289661929011345,
-0.0027027353644371033,
-0.018009008839726448,
-0.0008074006182141602,
0.04696645215153694,
0.05089779570698738,
0.006755745504051447,
-0.003579627489671111,
0.007223003078252077,
-0.03887905552983284,
-0.03699054196476936,
0.021313359960913658,
0.007968606427311897,
0.05289911851286888,
0.03940966725349426,
-0.01583310030400753,
0.02350429818034172,
0.014304939657449722,
-0.0325651615858078,
0.04153833165764809,
0.026048926636576653,
0.002981686033308506,
0.01853846199810505,
-0.048685017973184586,
0.046670231968164444,
-0.004935633856803179,
-0.0040307724848389626,
0.014513316564261913,
-0.006242762319743633,
0.031128866598010063,
-0.021998321637511253,
0.03676857054233551,
-0.028599131852388382,
0.04437493905425072,
-0.02136572264134884,
-0.00562979094684124,
0.030504804104566574,
-0.02258210815489292,
0.07021402567625046,
-0.029700515791773796,
-0.0006695008487440646,
-0.016489019617438316,
-0.007856584154069424,
0.028400838375091553,
0.01815793849527836,
-0.025613054633140564,
-0.014937594532966614,
-0.0488269217312336,
0.03200998529791832,
-0.03317943215370178,
0.004774746485054493,
0.03529522567987442,
-0.06471695005893707,
0.03403022140264511,
0.00006034810212440789,
-0.026382258161902428,
0.03257028013467789,
0.02785615622997284,
0.013616963289678097,
0.02271346189081669,
-0.0002861910033971071,
-0.07041391730308533,
0.004098198842257261,
0.004071448463946581,
-0.006093009375035763,
-0.03936275467276573,
0.021004004403948784,
0.058480072766542435,
-0.025644902139902115,
-0.014668498188257217,
0.031066976487636566,
-0.04445388913154602,
-0.06717316806316376,
-0.029231373220682144,
0.020544279366731644,
0.006135809235274792,
-0.01691696047782898,
0.0009581698686815798,
0.025145849213004112,
-0.009241263382136822,
0.006308090873062611,
-0.07505080848932266,
-0.00652245432138443,
0.016736598685383797,
-0.027258669957518578,
0.01207774505019188,
-0.018833579495549202,
-0.013341494835913181,
0.0776069238781929,
0.053299933671951294,
0.003984062001109123,
-0.04642682522535324,
-0.014642252586781979,
-0.04725203290581703,
-0.01525905355811119,
0.013682164251804352,
0.015211706981062889,
-0.02615469880402088,
-0.029258091002702713,
-0.015611371956765652,
-0.008086579851806164,
0.031011231243610382,
0.003930601291358471,
-0.01580093428492546,
0.04804142192006111,
-0.01793607324361801,
0.006670201662927866,
0.06669452041387558,
0.027138644829392433,
-0.008949321694672108,
0.028446489945054054,
-0.01441245712339878,
0.02885698713362217,
0.009115641936659813,
-0.03486143797636032,
0.03371700271964073,
-0.007378373295068741,
0.006057392805814743,
-0.0021686118561774492,
0.004629744216799736,
0.027763046324253082,
-0.0021641431376338005,
-0.024739569053053856,
0.019709503278136253,
0.04452018439769745,
0.036748893558979034,
-0.0024697009939700365,
-0.01705816574394703,
0.011940968222916126,
-0.0018761957762762904,
-0.005707463715225458,
-0.013505120761692524,
-0.030078411102294922,
0.00828937441110611,
-0.05052707716822624,
-0.03038237802684307,
0.02879493683576584,
0.035504844039678574,
-0.025985829532146454,
-0.013384099118411541,
-0.05457724630832672,
0.004412129055708647,
-0.08421538025140762,
-0.013851771131157875,
-0.0018415714148432016,
0.004756392911076546,
0.0009857626864686608,
0.05890039727091789,
-0.0031090218108147383,
0.023731544613838196,
-0.0009542125626467168,
-0.001015610178001225,
-0.0961955264210701,
-0.004792212042957544,
-0.024423839524388313,
-0.010989518836140633,
-0.029858069494366646,
0.0019683733116835356,
-0.01899634301662445,
-0.0386277437210083,
0.004947985056787729,
-0.035446640104055405,
-0.025105802342295647,
0.021011294797062874,
0.0003483385662548244,
-0.03832567483186722,
-0.028711887076497078,
0.00929991714656353,
0.024766970425844193,
0.0375029593706131,
-0.01069660298526287,
0.06321661919355392,
0.008285841904580593,
-0.012730267830193043,
-0.012747586704790592,
-0.011797616258263588,
-0.04134315624833107,
0.02365681901574135,
0.005269493907690048,
0.03924090415239334,
0.01593504287302494,
-0.04718666896224022,
0.012495379894971848,
0.03269059583544731,
-0.0035411028657108545,
0.014932502061128616,
-0.05473718419671059,
-0.0031560484785586596,
-0.03572119399905205,
-0.03867015987634659,
0.01439397968351841,
0.02177775464951992,
-0.004013827536255121,
0.012322911992669106,
0.04565280303359032,
-0.012396248988807201,
-0.014824530109763145,
0.01687535271048546,
0.04301534220576286,
-0.007957696914672852,
-0.01913006603717804,
-0.06445058435201645,
-0.03378547728061676,
0.0003992791462223977,
0.017440535128116608,
0.031471554189920425,
-0.029307447373867035,
-0.02760094404220581,
0.004251742735505104,
0.019488655030727386,
0.00019663899729494005,
0.002629124093800783,
0.03247145935893059,
-0.03969331830739975,
0.039754804223775864,
-0.0346168652176857,
0.021866098046302795,
0.022948840633034706,
0.06888411194086075,
0.04401267319917679,
0.018101472407579422,
-0.023608949035406113,
-0.04940513148903847,
-0.007766563445329666,
0.04029132425785065,
0.02898230217397213,
-0.03299468755722046,
0.011176555417478085,
-0.06469698995351791,
-0.028236521407961845,
0.03773549944162369,
-0.0012784262653440237,
0.053833410143852234,
-0.011134305968880653,
-0.015803635120391846,
0.04014407470822334,
-0.04694366082549095,
-0.020115230232477188,
0.007819545455276966,
-0.015672380104660988,
-0.014337527565658092,
-0.025675268843770027,
0.03252376988530159,
-0.020531337708234787,
0.010244916193187237,
0.013470642268657684,
0.01667027175426483,
-0.028902195394039154,
-0.015712613239884377,
0.029561243951320648,
0.0020037111826241016,
-0.003755341051146388,
-0.07343003153800964,
0.011536399833858013,
0.002268071286380291,
0.003453502431511879,
0.04175371676683426,
-0.01575167290866375,
-0.06493909657001495,
0.021283956244587898,
0.03303562477231026,
-0.0014534731162711978,
0.021393606439232826,
-0.03622330352663994,
0.011005613952875137,
0.025419164448976517,
0.008967884816229343,
0.031058592721819878,
0.04577821120619774,
-0.0261874757707119,
-0.02852039225399494,
-0.012511823326349258,
0.03221132978796959,
-0.02513160929083824,
-0.002443632809445262,
-0.0065741147845983505,
-0.02407008223235607,
-0.015814676880836487,
0.01845436356961727,
0.03186127915978432,
0.014899267815053463,
0.024338241666555405,
0.001576052512973547,
0.015574349090456963,
0.028771908953785896,
0.010214574635028839,
0.002602323656901717,
0.015298169106245041,
0.02101476490497589,
-0.002792918123304844,
-0.026620883494615555,
0.019365854561328888,
-0.012362646870315075,
0.005062950309365988,
0.019540095701813698,
-0.0004427187377586961,
-0.025290880352258682,
-0.053158536553382874,
-0.04523518681526184,
-0.02041124366223812,
-0.017774168401956558,
0.04585050046443939,
-0.03579911217093468,
0.01874103769659996,
0.048847902566194534,
-0.032934654504060745,
-0.01712455227971077,
-0.01418190449476242,
-0.07465969026088715,
0.0021027433685958385,
-0.010947291739284992,
0.03178726136684418,
0.0036621412727981806,
0.025344884023070335,
-0.06685641407966614,
-0.011927565559744835,
0.03135449439287186,
-0.022938979789614677,
-0.054909106343984604,
-0.018069706857204437,
0.0425102524459362,
-0.025361206382513046,
-0.0293854009360075,
-0.023794034495949745,
0.05060618743300438,
-0.03922593221068382,
-0.008250832557678223,
0.012120150029659271,
0.0026803629007190466,
0.07076098024845123,
0.0020611167419701815,
-0.015013585798442364,
-0.013291391544044018,
-0.006668847985565662,
-0.004474432207643986,
-0.010520334355533123,
0.05763184279203415,
-0.013926034793257713,
-0.05129934474825859,
-0.004677116870880127,
-0.012378351762890816,
-0.0006312954938039184,
-0.00567262526601553,
0.023846516385674477,
0.05303075537085533,
-0.014565691351890564,
0.018114127218723297,
0.015705596655607224,
0.03530962020158768,
-0.03051103465259075,
0.016043689101934433,
0.006239861249923706,
0.02547418512403965,
0.03548772633075714,
-0.03379080072045326,
0.06526055932044983,
0.020096099004149437,
-0.00847033690661192,
0.007047594524919987,
0.061610493808984756,
-0.0005654865526594222,
-0.012237277813255787,
-0.004881654400378466,
-0.0038528176955878735,
0.01827695220708847,
-0.0017718421295285225,
0.007810384035110474,
-0.0026265685446560383,
0.0018100289162248373,
-0.016590217128396034,
-0.012537212111055851,
-0.019777469336986542,
0.023653481155633926,
0.04481217637658119,
0.024174712598323822,
0.03960401192307472,
-0.026824574917554855,
0.008190208114683628,
-0.017345353960990906,
-0.05656622350215912,
-0.0008669063681736588,
0.0010155192576348782,
0.018829243257641792,
0.002525380114093423,
-0.03407220542430878,
-0.002791668986901641,
0.04186239838600159,
0.016033804044127464,
-0.0216356348246336,
0.013193805702030659,
0.0297759547829628,
-0.04188447818160057,
0.032223179936409,
-0.0010316132102161646,
-0.029546208679676056,
0.022570649161934853,
-0.018608909100294113,
0.0519561730325222,
-0.016236014664173126,
-0.022379744797945023,
0.03762972727417946,
0.03791205212473869,
0.028923584148287773,
-0.03950602188706398,
0.014170601032674313,
-0.04604560509324074,
-0.02054000273346901,
-0.004927527159452438,
-0.012460462749004364,
-0.03526550903916359,
0.025491565465927124,
0.005429791286587715,
0.00203796848654747,
0.0001331847015535459,
-0.00632465397939086,
-0.05833312124013901,
-0.03460630774497986,
-0.01452072523534298,
-0.06416728347539902,
0.026272747665643692,
0.007664537988603115,
-0.033803168684244156,
-0.0009609299595467746,
-0.0029649247881025076,
-0.020920732989907265,
0.04403357580304146,
0.042366575449705124,
-0.02803129330277443,
0.07247298955917358,
0.010073285549879074,
0.009167030453681946,
-0.031417492777109146,
0.019125068560242653,
0.12742961943149567,
0.03780465945601463,
-0.010669590905308723,
-0.05345255509018898,
0.025777634233236313,
-0.010805790312588215,
0.02848796918988228,
-0.03309907391667366,
0.01897716335952282,
0.012555782683193684,
0.016246337443590164,
0.008985119871795177,
0.027743661776185036,
-0.005361281801015139,
-0.042198654264211655,
0.033117108047008514,
-0.008266284130513668,
-0.005277169402688742,
0.008788649924099445,
0.0003724143607541919,
-0.01787801831960678,
0.025819627568125725,
-0.03987281024456024,
0.05365515872836113,
-0.04554397985339165,
-0.01597321778535843,
-0.008046755567193031,
-0.023344511166214943,
-0.007787039969116449,
-0.010484617203474045,
-0.07114303112030029,
-0.04233747720718384,
0.037718385457992554,
-0.06915131211280823,
-0.03306903317570686,
0.028469862416386604,
0.0008926148875616491,
-0.05192152410745621,
0.050642989575862885,
0.04518571496009827,
0.006024986505508423,
0.03654138743877411,
-0.008192733861505985,
0.010246245190501213,
-0.04472435265779495,
-0.0043920716270804405,
-0.027350837364792824,
0.027359798550605774,
-0.010012536309659481,
0.0239782202988863,
-0.01466570794582367,
0.010273721069097519,
0.03770337626338005,
-0.0327671580016613,
0.03807755187153816,
0.004587534815073013,
0.004697712138295174,
0.00584624195471406,
-0.02206149883568287,
-0.02508610114455223,
-0.016025174409151077,
0.0052960035391151905,
0.020723819732666016,
-0.019085239619016647,
0.003969568759202957,
0.023957200348377228,
0.0037232921458780766,
0.054592590779066086,
-0.03640387952327728,
0.025762241333723068,
-0.020189763978123665,
0.0161912702023983,
-0.04133102670311928,
0.019894763827323914,
-0.00015304451517295092,
-0.0016696070088073611,
0.010945453308522701,
0.028988339006900787,
-0.022137343883514404,
-0.025148678570985794,
-0.0332513190805912,
0.023406730964779854,
0.0008505136938765645,
-0.02397102303802967,
-0.010324870236217976,
0.00865950807929039,
0.05112489312887192,
0.018451236188411713,
-0.044187210500240326,
0.01682191714644432,
0.014720259234309196,
0.030848734080791473,
0.01879858411848545,
-0.029514949768781662,
-0.028034957125782967,
0.008358664810657501,
-0.01684509962797165,
-0.005893019028007984,
-0.05919204279780388,
0.02196674607694149,
0.015696240589022636,
0.025130556896328926,
-0.0004164172860328108,
0.003348888363689184,
-0.017187004908919334,
0.022252188995480537,
0.004767604172229767,
-0.021940594539046288,
0.013024278916418552,
-0.021315595135092735,
0.022153379395604134,
-0.05000128597021103,
-0.02795766107738018,
-0.04588249325752258,
0.027616867795586586,
-0.026825908571481705,
0.0039307065308094025,
-0.043657734990119934,
0.05966082215309143,
-0.025250140577554703,
0.0231577567756176,
-0.061282992362976074,
0.02023734152317047,
-0.05556422844529152,
-0.006000036373734474,
-0.0034745268058031797,
0.0008784298552200198,
0.0041346256621181965,
0.03344075009226799,
-0.009504901245236397,
-0.028074277564883232,
0.0203296709805727,
-0.03332086279988289,
-0.017123131081461906,
0.015331832692027092,
0.0369437076151371,
-0.020443355664610863,
-0.015320125967264175,
-0.0072664907202124596,
-0.03832586109638214,
0.0518379881978035,
-0.010574715211987495,
-0.07387379556894302,
0.01666891761124134,
-0.04451321065425873,
0.004822791088372469,
0.011291963048279285,
-0.017449811100959778,
0.016490938141942024,
0.0032331186812371016,
-0.00441993260756135,
-0.04708554223179817,
0.009766330942511559,
0.018620600923895836,
-0.007799145765602589,
0.04831280559301376,
0.036460041999816895,
-0.023647863417863846,
-0.013460003770887852,
0.030594725161790848,
0.024878835305571556,
-0.027779242023825645,
0.020179372280836105,
-0.033505313098430634,
-0.049364566802978516,
0.015888823196291924,
-0.0229507926851511,
0.02355065569281578,
0.019993454217910767,
0.02290245145559311,
-0.025409210473299026,
0.06131008267402649,
0.030728647485375404,
-0.039581090211868286,
-0.10625051707029343,
-0.016452094539999962,
-0.004445008002221584,
-0.007359019946306944,
0.02462688647210598,
-0.0416727177798748,
-0.003529016859829426,
0.037502143532037735,
-0.08199663460254669,
0.05098791792988777,
-0.009546427987515926,
-0.013643679209053516,
-0.02350134775042534,
0.008054250851273537,
-0.022952599450945854,
0.06519551575183868,
0.0380692221224308,
0.008442125283181667,
0.00839685183018446,
0.0015609043184667826,
-0.019041279330849648,
0.0023791235871613026,
0.032140038907527924,
0.008589922450482845,
-0.01685534603893757,
-0.0038721889723092318,
0.07489465922117233,
-0.040514055639505386,
-0.025961104780435562,
0.0258643738925457,
-0.005761716049164534,
0.04420841112732887,
-0.006216087378561497,
-0.013235032558441162,
0.00018555563292466104,
0.022306131199002266,
-0.006501693744212389,
0.0032864443492144346,
-0.018594034016132355,
0.0158612672239542,
0.02286236546933651,
0.035619813948869705,
-0.030218960717320442,
0.0011479804525151849,
0.021461710333824158,
-0.04196823015809059,
-0.0033012968488037586,
0.021658040583133698,
-0.01448681391775608,
0.041237182915210724,
-0.020186083391308784,
-0.005255719646811485,
-0.009059826843440533,
-0.03460102900862694,
0.0214140173047781,
-0.05422380566596985,
0.034679800271987915,
-0.0030211766716092825,
-0.021129490807652473,
0.007176357787102461,
-0.0023177526891231537,
0.04611784964799881,
-0.0038779322057962418,
0.04679696634411812,
-0.016419600695371628,
0.003835008479654789,
-0.038322534412145615,
0.0012926335912197828,
0.007951195351779461,
-0.025733403861522675,
0.0008959394763223827,
-0.01558254286646843,
-0.02961183711886406,
0.0781179666519165,
0.020826412364840508,
0.024119198322296143,
0.011879073455929756,
-0.08078958094120026,
-0.017087476328015327,
-0.058638326823711395,
0.010858030058443546,
-0.016198940575122833,
0.023950325325131416,
-0.036215294152498245,
-0.08927954733371735,
-0.013807930983603,
-0.044445864856243134,
0.05114080011844635,
0.03851019963622093,
0.011996125802397728,
0.04421592876315117,
-0.019117126241326332,
0.0192426647990942,
-0.08706860989332199,
0.008684661239385605,
0.014498735778033733,
-0.021885540336370468,
0.0049684736877679825,
-0.014210202731192112,
-0.015626881271600723,
0.03009680286049843,
0.03192141652107239,
-0.008739861659705639,
0.05569000542163849,
0.03947259485721588,
-0.0033357772044837475,
0.0377856083214283,
-0.007917877286672592,
0.01721692457795143,
0.1043689101934433,
-0.002998191164806485,
0.004199892282485962,
0.04753081128001213,
-0.01354627963155508,
-0.002711074659600854,
0.017732730135321617,
-0.01835213415324688,
-0.0027832407504320145,
-0.02369585633277893,
-0.046406783163547516,
0.042978037148714066,
-0.03628307580947876,
-0.022766901180148125,
0.027763886377215385,
-0.04822074621915817,
-0.025854097679257393,
0.03392878174781799,
0.007962891831994057,
0.04231451451778412,
-0.034695446491241455,
-0.0003879479190800339,
0.024952013045549393,
0.014381441287696362,
-0.03040366806089878,
0.05060429498553276,
0.026393331587314606,
0.018297120928764343,
0.025107184424996376,
0.009465235285460949,
0.028296837583184242,
0.02263561077415943,
-0.0470014363527298,
0.0516141876578331,
-0.03189387544989586,
0.00419608224183321,
0.007437949068844318,
-0.026919005438685417,
-0.013553695753216743,
0.010298439301550388,
-0.015959694981575012,
0.08434194326400757,
-0.023545214906334877,
0.005306089762598276,
0.031890563666820526,
-0.02782922424376011,
-0.025027960538864136,
0.027905015274882317,
-0.007154329679906368,
0.012703543528914452,
0.005266355350613594,
-0.03681892156600952,
-0.00022744415036868304,
0.05108458921313286,
0.03801015391945839,
-0.027255535125732422,
0.024031508713960648,
-0.009709891863167286,
0.014925189316272736,
-0.012236935086548328,
0.007138070650398731,
-0.03241618350148201,
-0.0587899386882782,
0.022420523688197136,
0.04315372556447983,
0.01062350906431675,
0.01455902773886919,
0.02031630277633667,
-0.03586684539914131,
0.05186967924237251,
-0.042351555079221725,
-0.021577728912234306,
-0.03684993460774422,
0.03017449378967285,
-0.00880505796521902,
-0.029161911457777023
] |
<p>While hiking through the Grand Canyon, I started wondering. Say we have a pipe for the purpose of transporting water across a canyon, with the bottom submerged in a pool of water. Like the blue line in this terribly drawn image:</p>
<p><img src="http://i.stack.imgur.com/7iVLE.png" alt="enter image description here"></p>
<p>Now let's seal the two ends of the pipe, which is full of water. What would happen if the pipe broke at the bottom of the U?</p>
<p>Note: It shouldn't matter whether the pipe is a U or a vertical line, I simply thought about this with a U-shaped pipe.</p>
<hr>
<p>If the ends of the pipe weren't sealed, the water inside the pipe would leak out until the height of the water outside the pipe was the same as the height of the water inside the pipe. But the ends are sealed.</p>
<p>A vacuum can support 10m of water, so perhaps the water will drain out of the pipe until it is 10m above the height of the water outside of the pipe, leaving a big near-vacuum behind. This would explain why the Grand Canyon's pipe has such a large number of valves.</p>
<p>On the other hand, we learn from <a href="http://what-if.xkcd.com/6/" rel="nofollow">http://what-if.xkcd.com/6/</a> that water boils into a vacuum. Does this leave a significant amount of water vapour behind?</p>
| 7,672 |
[
0.02385134994983673,
-0.018526997417211533,
0.030792778357863426,
-0.0029094149358570576,
0.0245498213917017,
-0.009677428752183914,
0.004222481045871973,
-0.00028579699574038386,
0.026626383885741234,
-0.032265037298202515,
-0.010874583385884762,
0.04161084443330765,
0.028502196073532104,
-0.01753194071352482,
-0.001782627310603857,
0.026699889451265335,
0.03332899510860443,
-0.02991865761578083,
0.020884498953819275,
-0.04387784004211426,
-0.04141375422477722,
0.01300183217972517,
-0.004104846157133579,
-0.00542268855497241,
-0.02526056580245495,
0.022795656695961952,
0.02251306362450123,
-0.03181597962975502,
0.018429283052682877,
0.012926996685564518,
0.017798373475670815,
-0.02409583330154419,
0.0000918058431125246,
0.008169302716851234,
0.02088654227554798,
0.000038116642826935276,
-0.03463213890790939,
-0.058118052780628204,
-0.03553818166255951,
0.022213846445083618,
0.0021129853557795286,
0.004856498911976814,
0.010665126144886017,
0.04113255813717842,
-0.05765421688556671,
0.016125623136758804,
0.016130872070789337,
-0.01836327090859413,
0.024993695318698883,
-0.06755926460027695,
0.0013910739216953516,
0.04980713129043579,
0.03377532958984375,
0.032835233956575394,
0.0013245228910818696,
0.005480004940181971,
0.07554950565099716,
0.05558423697948456,
-0.04208122193813324,
-0.03987681120634079,
-0.019524792209267616,
-0.00005170936856302433,
-0.037285368889570236,
0.03008112870156765,
-0.018125934526324272,
0.015034055337309837,
-0.020804721862077713,
-0.008585778065025806,
-0.012734932824969292,
0.005566448904573917,
0.04114985838532448,
-0.016360746696591377,
0.028850320726633072,
0.016717426478862762,
0.0395209901034832,
0.008822577074170113,
0.04445536434650421,
0.031784869730472565,
0.02114740014076233,
0.03937480226159096,
-0.010711884126067162,
-0.017875690013170242,
0.047316573560237885,
0.02942756377160549,
0.022984402254223824,
0.0055993772111833096,
0.06705876439809799,
-0.02325427159667015,
0.049116600304841995,
0.03402741625905037,
0.009019328281283379,
-0.0007572231697849929,
0.0024131808895617723,
0.013308817520737648,
-0.03676540404558182,
-0.024876035749912262,
0.00637939665466547,
0.029427003115415573,
0.027821678668260574,
0.0013372446410357952,
0.014018667861819267,
0.007315764669328928,
0.01330573484301567,
0.07135092467069626,
0.038050275295972824,
-0.018361223861575127,
-0.025558216497302055,
0.021268226206302643,
-0.004971751011908054,
-0.007124872412532568,
-0.07439568638801575,
-0.05606595426797867,
0.0020392783917486668,
-0.008594496175646782,
-0.0013039818732067943,
-0.032529160380363464,
0.04412081092596054,
-0.04632498696446419,
0.05605828016996384,
0.02047380991280079,
0.062076639384031296,
-0.019930636510252953,
0.04583459720015526,
-0.027745695784687996,
-0.049687180668115616,
0.047888848930597305,
0.003991491626948118,
0.000887754955329001,
-0.025920629501342773,
0.03984104469418526,
-0.0011786780087277293,
-0.0034712927881628275,
0.010073506273329258,
-0.015976017341017723,
0.06046333536505699,
0.01631656475365162,
-0.10862599313259125,
-0.08506251126527786,
0.03130096197128296,
0.0330716036260128,
-0.007851860485970974,
-0.0500345453619957,
0.0031662466935813427,
0.0069816638715565205,
0.0786433294415474,
-0.04318815842270851,
0.016205623745918274,
-0.0038713214453309774,
0.018335888162255287,
-0.006862583104521036,
-0.033004481345415115,
0.025851720944046974,
0.019892888143658638,
-0.04994823783636093,
-0.012272653169929981,
-0.06666649132966995,
0.012279369868338108,
0.05457368120551109,
0.040752727538347244,
-0.02310687117278576,
0.028592148795723915,
-0.014118890278041363,
0.022936753928661346,
-0.012058557942509651,
-0.03885696455836296,
-0.038490474224090576,
0.056400593370199203,
0.006809148471802473,
0.010574142448604107,
0.04469083249568939,
0.025263739749789238,
-0.005028699990361929,
0.007006407715380192,
-0.0041388557292521,
0.03795173764228821,
-0.06191565468907356,
0.053618721663951874,
-0.025540076196193695,
0.017085380852222443,
0.028608661144971848,
-0.026409052312374115,
-0.025852538645267487,
0.014960515312850475,
-0.01359566580504179,
0.027115827426314354,
0.03509178012609482,
0.005326240789145231,
-0.023828210309147835,
0.004654953721910715,
-0.05290936678647995,
-0.0226945448666811,
-0.0295496117323637,
0.012959565967321396,
0.004808718338608742,
0.018576711416244507,
-0.014001467265188694,
-0.0018958034925162792,
0.023254530504345894,
-0.037892092019319534,
0.015325701795518398,
0.0024816051591187716,
0.04132717475295067,
0.03014289401471615,
-0.00397157808765769,
-0.03856952115893364,
0.020885169506072998,
0.05989211052656174,
0.009028381668031216,
0.017915382981300354,
-0.017475854605436325,
-0.014009681530296803,
0.011195759288966656,
-0.0027157228905707598,
0.030983926728367805,
-0.04145289212465286,
-0.012469151057302952,
0.05491669103503227,
-0.012081651017069817,
0.037799008190631866,
0.014944618567824364,
-0.03534283488988876,
0.06796708703041077,
0.018684888258576393,
0.02289848029613495,
0.011907336302101612,
-0.017601020634174347,
0.01776011288166046,
0.013045493513345718,
0.005614058580249548,
-0.02652466855943203,
-0.049694258719682693,
-0.000013057469914201647,
-0.00509342085570097,
-0.009581427089869976,
0.01497092004865408,
0.014701640233397484,
0.021665427833795547,
0.026799065992236137,
-0.011278116144239902,
-0.025139935314655304,
-0.01687469333410263,
0.00971172284334898,
-0.009360343217849731,
0.06094846501946449,
0.043332744389772415,
0.00844932347536087,
0.019043616950511932,
0.03307819366455078,
0.019678527489304543,
-0.05969966575503349,
-0.02285935916006565,
0.025318488478660583,
0.013185880146920681,
0.03328144922852516,
-0.0035605821758508682,
-0.019465956836938858,
0.054728955030441284,
-0.05638132616877556,
-0.003948677331209183,
0.018963327631354332,
0.04339442402124405,
-0.02141299843788147,
-0.06697236001491547,
0.0006360635161399841,
0.01721673458814621,
0.018998676910996437,
-0.00903284177184105,
-0.013652215711772442,
0.04538451507687569,
-0.06432779878377914,
0.02987593598663807,
-0.06197838485240936,
0.006863235030323267,
-0.022485679015517235,
0.026250343769788742,
0.042679063975811005,
-0.016016215085983276,
0.026683343574404716,
-0.0698106586933136,
-0.06451544165611267,
-0.029694441705942154,
-0.022111447528004646,
-0.006103674881160259,
0.011436676606535912,
-0.011141680181026459,
0.04516301676630974,
-0.011676551774144173,
-0.040031954646110535,
0.05552905797958374,
0.00030818284722045064,
-0.0012836805544793606,
0.002012097742408514,
0.004223954398185015,
-0.010872446931898594,
-0.010423255153000355,
-0.05323237553238869,
0.00006978983583394438,
-0.0176593866199255,
-0.028340524062514305,
0.048804547637701035,
-0.020117109641432762,
-0.019872620701789856,
0.04412151873111725,
-0.06639891117811203,
-0.058407194912433624,
-0.006260075140744448,
0.020199589431285858,
0.013826930895447731,
-0.019201219081878662,
0.030223270878195763,
0.018844157457351685,
-0.058114077895879745,
-0.038370776921510696,
-0.03496502712368965,
-0.07830027490854263,
0.029393071308732033,
0.013107462786138058,
0.04827231541275978,
0.010696456767618656,
-0.024721594527363777,
0.03806038200855255,
-0.018418943509459496,
-0.08594592660665512,
-0.02326211892068386,
-0.028533637523651123,
-0.0061531635001301765,
0.0026393739972263575,
-0.011362109333276749,
0.057851098477840424,
0.007608707528561354,
0.011066044680774212,
0.020646296441555023,
0.046564407646656036,
0.007402196526527405,
0.03078189678490162,
-0.019046712666749954,
0.010942037217319012,
0.029773343354463577,
0.025220222771167755,
0.034443989396095276,
0.01059419009834528,
-0.001100502093322575,
-0.00039076004759408534,
-0.04033209756016731,
0.019707903265953064,
0.018235282972455025,
-0.04466629773378372,
0.05235878750681877,
0.020099446177482605,
0.0027191496919840574,
-0.029430264607071877,
0.0012644017115235329,
-0.03013029135763645,
0.00682475371286273,
-0.024908779188990593,
0.004486889578402042,
0.0735505074262619,
-0.04136861115694046,
0.01012700330466032,
-0.0006797754904255271,
0.09139478206634521,
-0.02376706898212433,
-0.029352393001317978,
-0.04239678755402565,
-0.01013050228357315,
0.014284733682870865,
0.030578190460801125,
-0.020945055410265923,
0.05991005152463913,
0.026132212951779366,
0.020455749705433846,
0.032150499522686005,
-0.02090509794652462,
0.0005891926120966673,
-0.03980822488665581,
-0.027495527639985085,
-0.009924356825649738,
0.02878531627357006,
0.028740759938955307,
0.022526726126670837,
0.01999780163168907,
0.014173431321978569,
-0.028317077085375786,
0.008505098521709442,
-0.09036832302808762,
-0.029673876240849495,
-0.01625700108706951,
-0.015832290053367615,
0.006598885636776686,
-0.004261470399796963,
-0.0012461248552426696,
-0.033395152539014816,
0.0004666368186008185,
0.031562965363264084,
0.010280230082571507,
-0.06322034448385239,
0.02379635162651539,
-0.012506907805800438,
-0.037408437579870224,
-0.010499057359993458,
0.009625392965972424,
0.07045888155698776,
-0.016143687069416046,
0.017387840896844864,
0.0027239974588155746,
-0.035952381789684296,
-0.017399922013282776,
-0.011101298965513706,
0.03826815262436867,
0.041454628109931946,
0.01304084062576294,
-0.0005582444136962295,
0.019390979781746864,
-0.01279362291097641,
-0.02558964304625988,
-0.024777768179774284,
0.034146733582019806,
-0.057696953415870667,
0.04013745114207268,
0.0036256033927202225,
0.00633593974635005,
-0.023106545209884644,
0.055607665330171585,
0.014185421168804169,
-0.03115185908973217,
0.051640529185533524,
0.00793539360165596,
-0.05674818158149719,
-0.027968736365437508,
0.04373752325773239,
0.04794462025165558,
-0.015852810814976692,
-0.02850407361984253,
-0.040976304560899734,
-0.006800261326134205,
-0.0011440141825005412,
-0.04218217730522156,
-0.0095364386215806,
0.03165057674050331,
-0.06719592958688736,
-0.00023089781461749226,
0.04260094463825226,
-0.0019274792866781354,
-0.0206769909709692,
0.019096793606877327,
0.0046658930368721485,
0.04375815764069557,
-0.026613136753439903,
0.008694859221577644,
0.0300996545702219,
-0.005685563199222088,
0.009525435976684093,
0.03552200272679329,
-0.012216446921229362,
-0.06931855529546738,
-0.03175653517246246,
0.051335010677576065,
0.03864266723394394,
0.028030285611748695,
-0.024024972692131996,
-0.057140052318573,
-0.07386351376771927,
0.06702417880296707,
-0.021701226010918617,
-0.001159249572083354,
-0.009818701073527336,
0.004297943785786629,
-0.03269539773464203,
-0.04838167130947113,
0.006876225583255291,
-0.013404272496700287,
-0.03881983458995819,
0.02099836990237236,
0.01155874039977789,
-0.013528330251574516,
-0.0042555364780128,
0.007700381800532341,
0.034423720091581345,
0.019867515191435814,
0.00158925901632756,
-0.002805885160341859,
-0.01722242496907711,
0.03636549413204193,
-0.03475859388709068,
-0.04937206953763962,
0.012123984284698963,
0.009534496814012527,
0.0067581054754555225,
0.05151117593050003,
-0.01781291700899601,
-0.009037763811647892,
0.044869616627693176,
0.02307973802089691,
0.00733827892690897,
0.020768502727150917,
-0.0002282081841258332,
0.023596446961164474,
0.03442762792110443,
0.017828505486249924,
0.03916512057185173,
0.03583168610930443,
-0.0036067054606974125,
-0.008259122259914875,
-0.0026568779721856117,
0.05831620842218399,
-0.027293039485812187,
-0.01685984618961811,
-0.019003449007868767,
-0.017655596137046814,
-0.023602642118930817,
0.06328927725553513,
0.010765559040009975,
0.009547099471092224,
0.001113547245040536,
-0.020962614566087723,
0.020938429981470108,
-0.03180812671780586,
0.03170938789844513,
0.003495280398055911,
-0.010818356648087502,
0.03586607426404953,
0.008182466961443424,
-0.0218777097761631,
-0.0009024970349855721,
-0.0006945366621948779,
0.02274121716618538,
-0.0010933064622804523,
-0.01565546728670597,
0.01583929918706417,
-0.008059784770011902,
0.006433938164263964,
0.03145093843340874,
-0.055405981838703156,
0.08503548055887222,
0.0073766279965639114,
0.005260775797069073,
0.047343987971544266,
0.011804530397057533,
0.023821597918868065,
0.053440723568201065,
-0.0076158251613378525,
0.00909842737019062,
-0.03824714198708534,
0.04838532581925392,
0.022586209699511528,
0.05417116358876228,
-0.034741874784231186,
-0.03318898379802704,
0.05038728937506676,
0.02907736413180828,
-0.008964193984866142,
-0.012832319363951683,
-0.02640674263238907,
-0.040504034608602524,
-0.06241219490766525,
-0.03871982544660568,
0.020178087055683136,
-0.03874481841921806,
0.017673198133707047,
0.011342380195856094,
0.013585492968559265,
0.06966972351074219,
0.0047166780568659306,
-0.00280749867670238,
-0.002694577444344759,
-0.003926744684576988,
0.005798297002911568,
0.02191336825489998,
0.01940307766199112,
-0.034567940980196,
-0.02564929611980915,
0.028112776577472687,
0.007473303936421871,
0.03562724590301514,
-0.04149901866912842,
-0.0012879702262580395,
0.0059496620669960976,
0.008489293046295643,
-0.01871856115758419,
0.02053072676062584,
0.01778363063931465,
0.01634572632610798,
0.03525438532233238,
0.0031467038206756115,
-0.0031068772077560425,
-0.0035044848918914795,
-0.018404265865683556,
-0.01175274420529604,
-0.004586422815918922,
-0.032136064022779465,
0.014160986989736557,
0.016384059563279152,
-0.002847078489139676,
-0.03267186880111694,
0.004494649823755026,
-0.027305113151669502,
0.03933068737387657,
-0.0048234653659164906,
-0.022969039157032967,
0.03070095181465149,
0.017830779775977135,
-0.02916010096669197,
-0.05573359131813049,
-0.010128889232873917,
0.009457603096961975,
0.01901225373148918,
-0.015157154761254787,
0.025298919528722763,
-0.0005790869472548366,
-0.04453625902533531,
0.030961740761995316,
-0.056306421756744385,
-0.002170003717765212,
0.055455975234508514,
0.007215998601168394,
-0.0007705410243943334,
-0.018305515870451927,
-0.019564079120755196,
0.019097179174423218,
0.014619612134993076,
0.01067809946835041,
0.00041216035606339574,
0.0009146383381448686,
0.02158595249056816,
0.015139058232307434,
-0.04835566133260727,
-0.03429214283823967,
0.04674763232469559,
-0.06714165955781937,
0.011186831630766392,
0.01152166910469532,
0.052472423762083054,
0.019131561741232872,
-0.03204197436571121,
-0.016613813117146492,
-0.07780804485082626,
-0.042311977595090866,
-0.04123528674244881,
0.010071192868053913,
0.024492431432008743,
0.033562663942575455,
-0.022453585639595985,
0.009848061949014664,
0.04040214419364929,
-0.0059375823475420475,
0.026874704286456108,
-0.044347282499074936,
-0.06266545504331589,
-0.013562474399805069,
-0.03279721364378929,
0.023650070652365685,
0.03953788802027702,
0.01049759890884161,
-0.013497755862772465,
0.0037421889137476683,
-0.051148343831300735,
0.007747106719762087,
-0.020899930968880653,
0.028654247522354126,
-0.02967008389532566,
0.06436410546302795,
-0.012040117755532265,
0.034964319318532944,
-0.06301175057888031,
0.030550897121429443,
0.12733779847621918,
0.03549734130501747,
0.037357430905103683,
-0.009674572385847569,
-0.011563395150005817,
-0.025198372080922127,
0.009074042551219463,
-0.02694561332464218,
0.008482888340950012,
-0.0022059676703065634,
0.018609242513775826,
0.021249204874038696,
0.04553494229912758,
-0.01958012394607067,
0.03953879326581955,
0.08275553584098816,
-0.07804082334041595,
0.01724444516003132,
-0.011238985694944859,
-0.005360383074730635,
-0.03902389481663704,
0.03933289274573326,
-0.014436300843954086,
0.03680674359202385,
-0.022030476480722427,
-0.01784415915608406,
-0.05627816170454025,
-0.021077396348118782,
0.05740389972925186,
0.006256457418203354,
-0.0036843137349933386,
0.004035009536892176,
0.0005592253874056041,
-0.04249674826860428,
-0.011470380239188671,
-0.002918174723163247,
0.0465904138982296,
-0.029363341629505157,
0.02490423433482647,
0.029674097895622253,
0.01549321785569191,
-0.013866792432963848,
-0.0015128982486203313,
0.04385218024253845,
-0.04137216880917549,
-0.014651340432465076,
-0.02590992860496044,
0.03792670741677284,
0.008339272812008858,
-0.011428595520555973,
-0.0241133663803339,
-0.014043218456208706,
0.011373735964298248,
-0.03876204788684845,
-0.06271369010210037,
-0.03287658840417862,
0.03312937170267105,
0.01912020891904831,
-0.03253408521413803,
0.010453327558934689,
0.021008888259530067,
0.03607461228966713,
0.03469756618142128,
-0.0530531220138073,
0.0009792387718334794,
-0.051935188472270966,
-0.01973135769367218,
0.02885037288069725,
-0.03552664816379547,
0.005711055360734463,
-0.03830931335687637,
0.02595663070678711,
-0.03774481266736984,
-0.025561273097991943,
-0.008922528475522995,
0.007352728862315416,
0.03298167139291763,
0.011708191595971584,
0.003513780189678073,
0.015135332010686398,
-0.020977796986699104,
0.06581968814134598,
-0.023655517026782036,
-0.01668660342693329,
-0.014019409194588661,
-0.020228290930390358,
-0.032514993101358414,
0.024529458954930305,
-0.03038066439330578,
-0.021737121045589447,
0.021139835938811302,
0.054758019745349884,
0.011466161347925663,
-0.015954667702317238,
-0.040997475385665894,
-0.023178549483418465,
-0.029374869540333748,
0.00005913507629884407,
-0.01075730286538601,
0.042028866708278656,
0.015975788235664368,
0.028912371024489403,
-0.015633482486009598,
0.02548430860042572,
-0.024306323379278183,
-0.0035910916049033403,
0.03911670669913292,
-0.016471361741423607,
-0.033992700278759,
0.0023920536041259766,
-0.019896535202860832,
-0.023095009848475456,
-0.046296484768390656,
-0.006807495374232531,
-0.0036864751018583775,
0.02389949932694435,
-0.02333809621632099,
-0.02416933886706829,
0.04923202097415924,
-0.04376120865345001,
0.046514786779880524,
-0.04373611882328987,
0.009944232180714607,
-0.050905756652355194,
-0.017870241776108742,
0.0043115862645208836,
-0.017252516001462936,
-0.026209907606244087,
-0.012063185684382915,
-0.044268250465393066,
-0.03158310428261757,
0.0008056487422436476,
0.011067469604313374,
-0.0186611320823431,
-0.02353878878057003,
0.0040731849148869514,
0.04264841601252556,
0.03459181636571884,
-0.03151163458824158,
-0.04305051267147064,
0.013651822693645954,
-0.018350936472415924,
-0.029817378148436546,
0.05076393857598305,
0.006602013949304819,
0.0392250195145607,
0.025754759088158607,
-0.004226626828312874,
-0.02511090226471424,
0.05180729925632477,
-0.016522014513611794,
0.01769481785595417,
-0.018963022157549858,
-0.046688858419656754,
-0.016594387590885162,
-0.025167590007185936,
0.003078276291489601,
-0.019837040454149246,
-0.00061175343580544,
0.012436232529580593,
0.049740020185709,
0.0193993728607893,
-0.005901977885514498,
0.013123623095452785,
-0.008597091771662235,
0.02760252170264721,
-0.0025645256973803043,
0.0005500133265741169,
0.014084036462008953,
0.05684858560562134,
-0.0573531873524189,
0.026921024546027184,
0.031183473765850067,
-0.002192332409322262,
-0.0975058525800705,
0.0007684362353757024,
0.011234613135457039,
0.007970877923071384,
0.002812022576108575,
-0.03402270749211311,
-0.005496269091963768,
0.02503824047744274,
-0.04738273471593857,
-0.02205905318260193,
-0.04085587337613106,
-0.00034524346119724214,
-0.07100802659988403,
-0.005485392175614834,
-0.041891008615493774,
0.05555703863501549,
0.02539697289466858,
0.028750190511345863,
0.03863529488444328,
0.0297830943018198,
-0.022184140980243683,
-0.03602058067917824,
-0.010521802119910717,
0.009549548849463463,
-0.025718050077557564,
0.014251879416406155,
0.06499835103750229,
-0.017994508147239685,
-0.0061646937392652035,
0.008237525820732117,
-0.02130945399403572,
0.020505353808403015,
-0.0065436153672635555,
-0.008117948658764362,
0.006650255061686039,
0.028071068227291107,
0.029990265145897865,
0.014236321672797203,
0.0029994335491210222,
0.01746237464249134,
-0.002648369874805212,
-0.003474552882835269,
0.04898018762469292,
-0.0010790888918563724,
0.0014608680503442883,
-0.020338186994194984,
0.018230868503451347,
0.05129922926425934,
-0.016684208065271378,
0.009976583532989025,
-0.0004231823259033263,
-0.020191499963402748,
0.013557004742324352,
-0.03165838122367859,
0.0022012030240148306,
-0.009736642241477966,
0.017873303964734077,
0.042294036597013474,
-0.0007224914734251797,
0.0026474555488675833,
-0.0024620695039629936,
0.025183338671922684,
-0.01763235591351986,
0.0009579458856023848,
0.006294983439147472,
-0.0029738936573266983,
-0.016057390719652176,
-0.008420288562774658,
-0.03416328877210617,
0.01211541797965765,
0.011692469008266926,
-0.049002423882484436,
-0.01696068048477173,
0.03145306929945946,
0.0436578094959259,
0.043214570730924606,
-0.01661825180053711,
-0.012004953809082508,
-0.0005473775672726333,
-0.032312072813510895,
0.011956351809203625,
-0.01052409503608942,
0.019595589488744736,
-0.03985031694173813,
-0.03544766083359718,
0.03969057649374008,
0.0036447946913540363,
0.054461508989334106,
-0.013249858282506466,
0.007237276062369347,
0.02637183852493763,
-0.00013115401088725775,
0.023176927119493484,
-0.03648894652724266,
-0.03459668904542923,
0.00594778498634696,
-0.027161143720149994,
-0.003415176412090659,
-0.027079392224550247,
0.02105732262134552,
0.0011534529039636254,
0.07496717572212219,
-0.004631911404430866,
-0.0023557234089821577,
-0.016747772693634033,
0.015334319323301315,
-0.01874217391014099,
-0.0060872770845890045,
0.00107848783954978,
0.08663135021924973,
0.01676362194120884,
0.03126191347837448,
-0.04103900492191315,
-0.032215189188718796,
-0.03412893787026405,
0.05751008540391922,
-0.006578815169632435,
-0.010033470578491688,
-0.004830427933484316,
-0.045080967247486115,
0.0283820740878582,
-0.01711297407746315,
0.004805110394954681,
0.012437468394637108,
-0.039378821849823,
-0.011086869053542614,
0.040052380412817,
0.02513895183801651,
0.033592335879802704,
-0.06347435712814331,
0.016582420095801353,
0.03711520507931709,
-0.007770081516355276,
-0.027772508561611176,
0.043866947293281555,
0.044318582862615585,
0.019034164026379585,
-0.026405617594718933,
0.029918136075139046,
-0.013383517041802406,
0.036657266318798065,
-0.007319393567740917,
0.01863943785429001,
-0.04250137880444527,
-0.06168215721845627,
0.0041647376492619514,
-0.008881807327270508,
-0.03595823422074318,
0.00752625847235322,
-0.01663549803197384,
0.08727767318487167,
-0.011431661434471607,
-0.0032221388537436724,
-0.02793986164033413,
-0.013122783042490482,
-0.014569293707609177,
0.02526293694972992,
-0.012565325945615768,
-0.011607781983911991,
-0.0195084810256958,
-0.029368219897150993,
-0.03351965174078941,
0.025016557425260544,
0.004044440109282732,
0.01851506158709526,
0.02101016789674759,
-0.030323339626193047,
-0.02659684605896473,
-0.017078178003430367,
-0.023631952702999115,
-0.02898162417113781,
-0.028110381215810776,
0.05275719612836838,
0.05784380063414574,
0.012000915594398975,
-0.0074507263489067554,
-0.025937730446457863,
0.009032858535647392,
0.08175206929445267,
-0.055447112768888474,
-0.009593443013727665,
-0.013913160189986229,
0.025046981871128082,
-0.007339311297982931,
-0.022970592603087425
] |
<p>Theorem 5.1 on page 80 of <a href="http://arxiv.org/abs/hep-th/0307199" rel="nofollow">this</a> paper says that </p>
<p><em>Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding energy-momentum tensor is traceless.</em></p>
<p>If I have understood this right, Weyl invariance reduces to scale invariance in flat spacetime, which is basically what I am up to at the moment.</p>
<p>My question now is:</p>
<p>If one has Weyl or scale invariance in accordance with this theorem, does this mean that global Weyl or scale invariance (such that the scaling parameter does not depend on position) is guaranteed too? If not why not?</p>
| 7,673 |
[
-0.04634877294301987,
-0.028794720768928528,
-0.011635999195277691,
-0.012368831783533096,
0.042793504893779755,
0.004791003651916981,
-0.07070214301347733,
-0.002218987327069044,
0.004112471826374531,
-0.06390274316072464,
-0.017580637708306313,
-0.005525856278836727,
0.055728234350681305,
0.020739013329148293,
0.020843837410211563,
0.015940453857183456,
-0.03623808175325394,
0.009572730399668217,
-0.048314083367586136,
-0.04550651088356972,
0.020789163187146187,
0.03187550976872444,
0.0014333395520225167,
-0.033040694892406464,
-0.020995313301682472,
-0.011183894239366055,
-0.01503721997141838,
0.032567549496889114,
-0.005502825602889061,
0.07982946187257767,
-0.008252638392150402,
-0.024313315749168396,
-0.008807700127363205,
0.04273064434528351,
-0.00006920634768903255,
0.004872996360063553,
-0.017070991918444633,
-0.04579164460301399,
0.004004740156233311,
-0.015095528215169907,
-0.04978718236088753,
-0.0352640263736248,
-0.004124745726585388,
0.04187457635998726,
0.004292610101401806,
0.03280934318900108,
0.003149973228573799,
0.019176309928297997,
0.07284513860940933,
-0.03196004778146744,
0.08971259742975235,
-0.002003281842917204,
0.01375751756131649,
0.015666047111153603,
-0.02667361870408058,
-0.022069208323955536,
0.07051100581884384,
0.03713749721646309,
-0.014275100082159042,
-0.05890455096960068,
-0.041290033608675,
-0.00666452944278717,
0.02085212804377079,
-0.03034105896949768,
-0.008013448677957058,
0.026809770613908768,
-0.019062958657741547,
0.013585636392235756,
-0.006493425462394953,
-0.02135259099304676,
0.00278924941085279,
-0.010063250549137592,
0.04493004456162453,
-0.029795512557029724,
0.011464745737612247,
-0.0020166770555078983,
0.03326572850346565,
0.016538308933377266,
0.025355789810419083,
0.04397861286997795,
-0.024635495617985725,
0.034075815230607986,
0.021324872970581055,
0.009415533393621445,
0.0022564688697457314,
0.0031621900852769613,
0.03498220071196556,
0.006806617137044668,
0.013677532784640789,
0.059882164001464844,
-0.004922572057694197,
-0.00945353601127863,
0.030483119189739227,
-0.02761756256222725,
-0.048441946506500244,
0.03224598243832588,
0.017533889040350914,
0.03417111188173294,
-0.04819391667842865,
-0.007825106382369995,
-0.02303098328411579,
-0.0428912453353405,
-0.033751871436834335,
0.04854189231991768,
0.013272625394165516,
-0.015175513923168182,
-0.06682199239730835,
0.0043634409084916115,
-0.027492690831422806,
-0.008309761993587017,
-0.013593313284218311,
-0.015491035766899586,
-0.004768573213368654,
-0.01820845901966095,
-0.003947635646909475,
-0.009248687885701656,
0.023796705529093742,
-0.018058504909276962,
0.034028369933366776,
0.06501105427742004,
0.029655033722519875,
-0.007892390713095665,
-0.00832969881594181,
-0.0028710411861538887,
-0.04463963955640793,
-0.010096357204020023,
0.035680726170539856,
0.000996739137917757,
-0.0347079262137413,
0.013472779653966427,
0.0243789404630661,
0.011351991444826126,
0.006744265556335449,
0.026582922786474228,
0.03393574804067612,
-0.0066116428934037685,
-0.07945402711629868,
-0.046647731214761734,
0.039428725838661194,
0.013789106160402298,
-0.008780373260378838,
-0.040122825652360916,
0.0007761617307551205,
0.0378505140542984,
0.08368849754333496,
-0.03731979429721832,
0.017501959577202797,
0.008688951842486858,
0.05301762372255325,
0.0019355776021257043,
-0.045318618416786194,
-0.03293512389063835,
-0.051980212330818176,
-0.04057396575808525,
-0.029060538858175278,
-0.06610294431447983,
0.03101806342601776,
0.03437618166208267,
-0.021838096901774406,
-0.01038456056267023,
0.08364830166101456,
-0.00357957580126822,
0.026938164606690407,
-0.013458740897476673,
-0.011339012533426285,
0.024387402459979057,
0.03397499397397041,
-0.01672719232738018,
0.020633386448025703,
0.01822149008512497,
0.047257713973522186,
0.01062771026045084,
-0.01861841045320034,
0.049394842237234116,
0.03922209516167641,
-0.049173858016729355,
-0.021972311660647392,
-0.03663096949458122,
0.0020476814825087786,
0.02409445308148861,
-0.044770583510398865,
-0.03415944054722786,
-0.018835831433534622,
0.020527172833681107,
-0.028803179040551186,
0.03353428468108177,
0.0011483067646622658,
0.011313560418784618,
-0.0028413981199264526,
-0.031329698860645294,
-0.003351031569764018,
-0.07380924373865128,
0.019610540941357613,
0.012167030945420265,
-0.024142304435372353,
0.057995136827230453,
0.022091764956712723,
0.022243300452828407,
-0.02209337055683136,
-0.05167888104915619,
-0.009641200304031372,
0.04381810128688812,
0.006549788173288107,
-0.013955753296613693,
0.012528934516012669,
0.018741924315690994,
0.03979301452636719,
0.023350054398179054,
0.04144243896007538,
-0.017034433782100677,
-0.037634942680597305,
0.046288445591926575,
-0.00598411587998271,
0.033858414739370346,
0.002663948806002736,
-0.008658031933009624,
-0.005157170817255974,
-0.0024089054204523563,
-0.008440033532679081,
0.04162857308983803,
-0.02208860218524933,
0.06142783910036087,
0.025606943294405937,
-0.02780061773955822,
0.044192586094141006,
0.04723244905471802,
0.0011454683262854815,
0.01300997193902731,
-0.004705159459263086,
-0.04509086534380913,
-0.06225822493433952,
-0.027678851038217545,
0.03985104709863663,
0.03457794710993767,
-0.012688122689723969,
0.02170403301715851,
0.04015814885497093,
0.006579987704753876,
0.02965046651661396,
0.021814869716763496,
0.008062501437962055,
-0.06616269052028656,
0.007141771260648966,
0.016713911667466164,
0.037624239921569824,
0.007633643690496683,
0.02660062536597252,
-0.018196646124124527,
0.04582356661558151,
-0.005153566598892212,
0.012017671950161457,
0.009760536253452301,
-0.020734427496790886,
0.01758011430501938,
0.009512452408671379,
0.00048079443513415754,
0.03267983719706535,
-0.007553933188319206,
0.03364105150103569,
0.02259625308215618,
0.01670198142528534,
-0.0036095776595175266,
-0.02485702931880951,
-0.0017223901813849807,
0.040827676653862,
0.0021862052381038666,
-0.037702277302742004,
-0.031251441687345505,
-0.011084496043622494,
-0.04789799079298973,
0.002403185237199068,
-0.0023454739712178707,
-0.021609369665384293,
-0.016975725069642067,
0.008226864971220493,
0.056723471730947495,
0.0008071346674114466,
0.00801200233399868,
-0.04594150930643082,
-0.04191994667053223,
0.012887046672403812,
-0.011095847003161907,
0.012685836292803288,
0.052026621997356415,
-0.044826507568359375,
0.00010867240780498832,
-0.054763831198215485,
-0.008249958045780659,
0.05558779463171959,
0.0004337275167927146,
0.028563620522618294,
0.028338884934782982,
0.00661817193031311,
-0.05582457408308983,
0.013424841687083244,
-0.020225422456860542,
0.01867728866636753,
-0.02875099517405033,
0.013113440945744514,
0.07127458602190018,
0.006458458956331015,
-0.029479870572686195,
0.01899614930152893,
0.009709890931844711,
-0.05650685727596283,
-0.01540363673120737,
0.03745536133646965,
-0.014510558918118477,
-0.040797024965286255,
0.06215180829167366,
0.028187831863760948,
-0.06576765328645706,
-0.035102710127830505,
-0.015896504744887352,
-0.02363709732890129,
0.040780775249004364,
0.003025730838999152,
0.05131378397345543,
-0.025754405185580254,
-0.023157449439167976,
0.09579506516456604,
0.03370668366551399,
-0.026876060292124748,
-0.024896612390875816,
-0.029321765527129173,
0.00030991295352578163,
-0.021469710394740105,
0.004053357522934675,
0.010650533251464367,
0.011169683188199997,
0.03731847181916237,
0.02005888521671295,
0.0286299679428339,
0.023134099319577217,
0.005516963545233011,
-0.018493717536330223,
0.0009567498927935958,
0.03501252830028534,
0.01080839429050684,
0.039466194808483124,
0.02865821309387684,
0.006444853264838457,
-0.032590217888355255,
0.010244039818644524,
0.0004310825315769762,
0.01317602302879095,
-0.023268911987543106,
0.07252053171396255,
0.00003968196688219905,
0.002438022056594491,
-0.046946290880441666,
0.024587251245975494,
-0.003841673955321312,
-0.023367347195744514,
-0.012438328005373478,
0.000013826686881657224,
0.04652822017669678,
0.0193718820810318,
0.02197149023413658,
0.031489744782447815,
0.02940228395164013,
-0.02813633345067501,
-0.025905653834342957,
-0.004196833819150925,
-0.013851230032742023,
0.017239337787032127,
-0.012981879524886608,
-0.020317506045103073,
0.053211525082588196,
0.026767760515213013,
0.018777793273329735,
-0.008057881146669388,
-0.03916563838720322,
-0.01040041446685791,
-0.057951413094997406,
0.015277930535376072,
-0.006404762156307697,
0.009327329695224762,
0.0100972019135952,
0.028966786339879036,
0.06524142622947693,
0.02705172821879387,
-0.013269650749862194,
-0.006008170545101166,
-0.070746049284935,
0.005024254322052002,
-0.030065147206187248,
-0.0016618416411802173,
0.007745929528027773,
-0.00923503004014492,
0.013173372484743595,
0.007542002480477095,
-0.025304635986685753,
-0.024901576340198517,
0.006965478416532278,
-0.03660791367292404,
0.023115284740924835,
-0.048831041902303696,
-0.0761406421661377,
-0.013058842159807682,
0.016530437394976616,
0.05115659162402153,
-0.04097990691661835,
0.0036501099821180105,
0.012849201448261738,
-0.02762681618332863,
-0.020134249702095985,
-0.005170427728444338,
0.01752498373389244,
-0.00039528802153654397,
0.0035378856118768454,
0.047370608896017075,
0.00920492596924305,
-0.02321154624223709,
-0.01069589238613844,
0.03532667085528374,
0.04556930810213089,
0.004358911421149969,
-0.033380262553691864,
0.00571872852742672,
-0.05149092897772789,
0.0005876923678442836,
0.02602989412844181,
0.057154618203639984,
0.015880027785897255,
-0.04757069796323776,
0.027440177276730537,
0.008070827461779118,
-0.027251169085502625,
0.030152715742588043,
0.0895048975944519,
0.006100097205489874,
0.0073551395907998085,
-0.08043865859508514,
-0.0015369040193036199,
0.006453467532992363,
-0.027102690190076828,
0.030642719939351082,
-0.016376566141843796,
-0.03931913524866104,
-0.012960304506123066,
0.01044557522982359,
0.03198647499084473,
-0.06967151165008545,
-0.0222089271992445,
0.008388107642531395,
0.011674442328512669,
-0.00975815299898386,
0.012761242687702179,
0.0259855929762125,
0.019111990928649902,
0.036692216992378235,
0.02971208468079567,
0.0035137441009283066,
-0.05325613543391228,
0.004317390266805887,
-0.00016838301962707192,
0.015282856300473213,
-0.001494944212026894,
-0.008953772485256195,
-0.05400068312883377,
-0.0044379583559930325,
0.04372411593794823,
-0.008634126745164394,
0.024339912459254265,
0.02155551314353943,
-0.011252380907535553,
0.0004704930179286748,
-0.017948176711797714,
-0.05430947616696358,
0.01673150807619095,
-0.004190822597593069,
-0.014517294242978096,
-0.050980329513549805,
-0.008015013299882412,
-0.04686998203396797,
0.02790321223437786,
-0.006650637369602919,
0.05142572149634361,
0.047195952385663986,
0.024039512500166893,
-0.015166612342000008,
0.019256385043263435,
-0.032451897859573364,
-0.07606251537799835,
0.010708996094763279,
0.013918205164372921,
0.013741081580519676,
0.03279682621359825,
-0.033909521996974945,
-0.05707789957523346,
0.026823733001947403,
0.00209648790769279,
-0.031305763870477676,
0.0203749667853117,
-0.027870845049619675,
0.06548016518354416,
0.03704289719462395,
-0.016606178134679794,
0.02818368561565876,
0.015367899090051651,
0.021237770095467567,
-0.02608535625040531,
0.012265891768038273,
0.011816279962658882,
-0.04381488636136055,
0.04357157275080681,
-0.06041477620601654,
-0.016819855198264122,
-0.039643242955207825,
0.01892174780368805,
-0.008608280681073666,
-0.006679934915155172,
0.003331335261464119,
-0.033422887325286865,
-0.01330207847058773,
0.029368272051215172,
0.03254670277237892,
-0.03968405723571777,
0.014291924424469471,
0.0250177513808012,
0.0007256718818098307,
-0.0234068650752306,
0.030386436730623245,
0.036033183336257935,
-0.020376766100525856,
0.011685830540955067,
0.04911118745803833,
0.009030591696500778,
0.0038019632920622826,
-0.025315145030617714,
0.005805852822959423,
-0.0447516143321991,
0.030674902722239494,
-0.001164396875537932,
-0.02297789789736271,
0.006781280040740967,
-0.022271711379289627,
-0.010105602443218231,
0.00918214488774538,
-0.03891715034842491,
-0.0005598879652097821,
-0.031241344287991524,
-0.01167136337608099,
0.03082360327243805,
0.03368109092116356,
-0.10196223855018616,
-0.04970959946513176,
0.0070075527764856815,
0.009379440918564796,
0.002604380017146468,
-0.02168073132634163,
-0.02354658953845501,
-0.05686030164361,
-0.02535063773393631,
-0.013849863782525063,
0.08364393562078476,
-0.02895510382950306,
-0.0034412438981235027,
0.0022944642696529627,
0.05100972205400467,
0.0750751793384552,
-0.024872343987226486,
-0.0016980440123006701,
0.012938485480844975,
0.004193973261862993,
0.020313864573836327,
0.0051851458847522736,
0.10046098381280899,
-0.00764266075566411,
-0.014688368886709213,
-0.020944993942975998,
-0.006593151018023491,
-0.021669602021574974,
0.006032476667314768,
-0.00006823800504207611,
0.03804308548569679,
0.02374212071299553,
0.0026509903836995363,
-0.006301961373537779,
0.0002804508258122951,
-0.005376937799155712,
0.016250314190983772,
-0.00278530758805573,
0.002642309293150902,
-0.012719720602035522,
-0.03180966153740883,
0.0429355651140213,
-0.003555451286956668,
0.018151963129639626,
0.020846068859100342,
0.05917222797870636,
0.011464577168226242,
0.007733611389994621,
0.0219630915671587,
-0.03241058066487312,
0.0031109165865927935,
-0.028770960867404938,
0.039974797517061234,
-0.008450191468000412,
-0.013537605293095112,
-0.014539290219545364,
-0.01145624928176403,
-0.045324523001909256,
0.008737518452107906,
0.054765526205301285,
0.026332831010222435,
0.04640893265604973,
0.010251618921756744,
-0.009500328451395035,
0.0023887406568974257,
-0.032427266240119934,
-0.021191393956542015,
-0.008890995755791664,
0.023126894608139992,
0.03965415805578232,
-0.021823151037096977,
0.001964299939572811,
0.045772090554237366,
0.06503737717866898,
-0.013394354842603207,
0.024222951382398605,
0.04685467481613159,
-0.0034027385991066694,
0.027360949665308,
0.006450335960835218,
-0.060950420796871185,
0.03875516355037689,
-0.025660844519734383,
0.023602528497576714,
0.006645562127232552,
-0.0008366891415789723,
0.04342443495988846,
0.0229889377951622,
-0.018323471769690514,
0.005910159088671207,
-0.020804107189178467,
-0.03969113901257515,
0.03346697613596916,
0.0011038666125386953,
0.01475647371262312,
-0.004884906578809023,
-0.003293517278507352,
0.03681260347366333,
-0.0010025741066783667,
0.014137129299342632,
-0.013456144370138645,
-0.03634905442595482,
-0.02339397370815277,
-0.039210110902786255,
0.004464195109903812,
0.036832503974437714,
-0.005951703526079655,
-0.035793840885162354,
-0.03069038689136505,
-0.04342097416520119,
-0.0033676044549793005,
0.017983993515372276,
0.05121498554944992,
-0.013392552733421326,
0.06538006663322449,
0.002615223405882716,
0.016640009358525276,
0.007341915741562843,
0.02475854754447937,
0.1184936910867691,
0.06677313148975372,
-0.015909887850284576,
-0.08904878795146942,
0.0027510072104632854,
-0.027759501710534096,
-0.010110096074640751,
-0.013886227272450924,
0.01312071830034256,
-0.034965045750141144,
-0.01814671978354454,
0.025371765717864037,
0.030073510482907295,
0.023955337703227997,
-0.03280074521899223,
0.059327710419893265,
-0.052285075187683105,
-0.04428193345665932,
-0.0008283611969090998,
0.023075783625245094,
0.0004943665117025375,
0.036025118082761765,
-0.004936183337122202,
0.02021334134042263,
-0.015767550095915794,
0.022450892254710197,
0.002500189235433936,
-0.03591516986489296,
-0.01799381710588932,
0.02075202576816082,
-0.04452225938439369,
0.0030983760952949524,
-0.004887012764811516,
-0.018506258726119995,
-0.061307940632104874,
-0.047273654490709305,
0.011865166015923023,
0.015268964692950249,
0.03301671892404556,
0.013722952455282211,
-0.025145141407847404,
0.017636790871620178,
0.008321559987962246,
0.025939906015992165,
-0.02142370119690895,
-0.017265165224671364,
-0.02912975661456585,
0.06081388145685196,
-0.008450297638773918,
-0.017996182665228844,
0.03392494469881058,
-0.03705550730228424,
0.010415477678179741,
-0.08138881623744965,
0.035606879740953445,
-0.004243809729814529,
-0.009957117028534412,
-0.005880535580217838,
0.006637100595980883,
-0.035606011748313904,
0.06472565233707428,
0.008451588451862335,
-0.002582878340035677,
0.007540430873632431,
-0.008165579289197922,
0.009021231904625893,
-0.005643158219754696,
0.052636854350566864,
0.012749691493809223,
-0.0028741813730448484,
0.01200740784406662,
-0.013533677905797958,
-0.045828063040971756,
0.011610792949795723,
0.03307639807462692,
0.007693000603467226,
0.021543370559811592,
0.007543596904724836,
0.027697298675775528,
-0.024434372782707214,
-0.0631420761346817,
0.020741358399391174,
-0.05988512560725212,
-0.03561217710375786,
-0.0003400299174245447,
0.04309016838669777,
0.023630015552043915,
0.06869532912969589,
-0.04221644625067711,
-0.01560597587376833,
-0.009187690913677216,
0.030840281397104263,
0.024159306660294533,
-0.012754767201840878,
0.022962842136621475,
0.02364577353000641,
-0.040807146579027176,
-0.024903127923607826,
-0.0019496865570545197,
-0.0028869861271232367,
0.0523996576666832,
0.003701894311234355,
0.007788937538862228,
0.040207430720329285,
-0.0028973498847335577,
-0.006486271973699331,
0.015382165089249611,
-0.01810595393180847,
-0.01751895248889923,
0.02774348109960556,
-0.016456814482808113,
-0.03352255001664162,
-0.040068015456199646,
-0.04867114499211311,
0.006076436955481768,
-0.012723683379590511,
0.004570402204990387,
-0.03325752168893814,
-0.0006216265028342605,
-0.0038513382896780968,
0.02433948777616024,
-0.07536216825246811,
-0.00946443434804678,
-0.04665211960673332,
0.019836509600281715,
0.009415177628397942,
0.009039565920829773,
-0.009990296326577663,
0.03361894190311432,
-0.0321553610265255,
-0.033336151391267776,
0.008685460314154625,
0.022507542744278908,
-0.044203020632267,
0.00541333295404911,
0.025476856157183647,
0.00037891007377766073,
0.05986809730529785,
0.011038410477340221,
-0.03902670741081238,
0.013794601894915104,
-0.016723351553082466,
-0.06552319973707199,
0.057847198098897934,
-0.029131755232810974,
0.01678793504834175,
0.0289857666939497,
-0.03261341154575348,
-0.006633434444665909,
0.051397357136011124,
0.01439377199858427,
-0.0013217116938903928,
-0.008763660676777363,
-0.04819159209728241,
-0.01958956941962242,
-0.024318013340234756,
0.03948580101132393,
-0.0029185127932578325,
-0.00018150587857235223,
0.026095857843756676,
0.011513938196003437,
-0.0019815184641629457,
-0.010769114829599857,
0.009010725654661655,
-0.03116215020418167,
0.0270555317401886,
0.002412498462945223,
-0.01670105941593647,
-0.0007517493213526905,
0.061577532440423965,
-0.04308092221617699,
0.009454387240111828,
0.0003562289057299495,
0.021484708413481712,
-0.08721364289522171,
-0.03710921108722687,
0.008178326301276684,
0.03353148326277733,
0.03615335747599602,
-0.05875151976943016,
0.011774269863963127,
0.03039112314581871,
-0.05287020280957222,
0.03500962257385254,
-0.030400926247239113,
-0.021833952516317368,
-0.04357445240020752,
-0.006822444498538971,
-0.0055068666115403175,
0.04739707335829735,
0.041367270052433014,
0.03474767506122589,
0.0172435250133276,
0.028240114450454712,
-0.039505645632743835,
-0.037427328526973724,
-0.027166351675987244,
0.03603328391909599,
0.0027380436658859253,
-0.03670256584882736,
0.05717286467552185,
0.020424414426088333,
-0.040285661816596985,
0.0017600456485524774,
-0.023971624672412872,
-0.03551359474658966,
-0.015369405969977379,
0.03700792044401169,
0.027439620345830917,
0.0072616529650986195,
0.011534970253705978,
-0.022228535264730453,
0.010691710747778416,
0.013750482350587845,
0.00495360791683197,
0.018201246857643127,
-0.008231157436966896,
0.005950904451310635,
-0.014714771881699562,
-0.07685726881027222,
-0.0014158600242808461,
0.018811075016856194,
-0.02990708127617836,
-0.05836474150419235,
-0.0122038209810853,
0.005582612473517656,
0.003352217609062791,
-0.00586262671276927,
0.014698904938995838,
-0.04677308723330498,
-0.03246472775936127,
0.053116269409656525,
0.00793980248272419,
-0.011366810649633408,
0.024246126413345337,
0.01824134774506092,
-0.01103612408041954,
0.028555091470479965,
0.019781792536377907,
-0.021169044077396393,
-0.01763748936355114,
-0.02162065915763378,
-0.005468422081321478,
0.00624501658603549,
-0.01035277359187603,
-0.05492652580142021,
-0.01043353509157896,
-0.01690615713596344,
0.005535991862416267,
0.02040695585310459,
-0.0027821531984955072,
0.00764475530013442,
-0.019880155101418495,
-0.06819382309913635,
0.055991120636463165,
-0.006378862541168928,
-0.0029740731697529554,
-0.021601425483822823,
-0.008511756546795368,
-0.02505425550043583,
-0.011006955988705158,
0.010242313146591187,
-0.03601214662194252,
-0.038339678198099136,
0.044179413467645645,
0.019459117203950882,
0.005203149747103453,
-0.025915129110217094,
-0.015659576281905174,
-0.028237268328666687,
-0.011622995138168335,
-0.0031165345571935177,
-0.01136221457272768,
-0.01278601586818695,
0.043745268136262894,
0.015292915515601635,
-0.007252957671880722,
0.037689607590436935,
0.007957225665450096,
-0.07711522281169891,
0.04375329613685608,
0.03394610807299614,
0.007418413180857897,
0.05578933283686638,
-0.0006256528431549668,
0.019836025312542915,
0.023563163354992867,
-0.01277341041713953,
-0.010902836918830872,
0.026217272505164146,
-0.06811348348855972,
-0.045203134417533875,
-0.014330899342894554,
0.018597494810819626,
0.006150055676698685,
-0.05286792293190956,
0.030485866591334343,
0.05394170433282852,
-0.033191461116075516,
-0.044779904186725616,
0.039926785975694656,
0.023226674646139145,
0.034195754677057266,
0.026029415428638458,
-0.024701230227947235,
0.03168791905045509,
0.03915054723620415,
0.015139906667172909,
0.04757697507739067,
0.018899396061897278,
0.008222763426601887,
0.029391484335064888,
0.013562334701418877,
-0.02742951735854149,
0.008705198764801025,
0.00010323609603801742,
0.06905798614025116,
-0.058112528175115585,
-0.02505304478108883,
0.024636412039399147,
-0.000044382242776919156,
0.027253396809101105,
0.03003285825252533,
-0.04785516485571861,
0.08559189736843109,
-0.007200330961495638,
-0.0010074414312839508,
-0.039825938642024994,
0.013744529336690903,
-0.02870243601500988,
0.017044618725776672,
-0.025230932980775833,
0.043661363422870636,
0.020529000088572502,
0.0031615227926522493,
-0.015848485752940178,
-0.012081553228199482,
0.021726040169596672,
-0.03340623527765274,
0.01384563185274601,
0.013342553749680519,
-0.004731573164463043,
0.015015117824077606,
-0.01888399012386799,
-0.062537282705307,
0.011922595091164112,
-0.00914715975522995,
0.002081475453451276,
0.03055736795067787,
-0.01642856001853943,
0.012553172186017036,
-0.03391816094517708,
0.04702823981642723,
-0.05820940062403679,
0.0028680493123829365,
0.010625366121530533,
0.007509293500334024,
0.0390489436686039,
-0.004827176686376333
] |
<p>I was reading about <a href="http://it.wikipedia.org/wiki/Mulinello_di_Joule" rel="nofollow">the experiment of Joule</a> (Italian wiki page). I'm not sure how it's called in English, since there is only an Italian and French version. In any case, in the page it is stated that (my translation):</p>
<blockquote>
<p>Through this experiment, Joule determined the <a href="http://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat" rel="nofollow">mechanical equivalent of heat</a> to be equal to 4,186 J/cal, value of extraordinary precision for the time.</p>
</blockquote>
<p>Is the importance of this experiment "only" ascribable to the fact that the evaluation was really precise and exact for the time? Or are there other reasons? </p>
<p>I don't need a whole list of reasons, just the most exemplary/important<sup>1</sup> fact(s) will suffice. </p>
<hr>
<p><sup>1: Objectively considered as such by most researchers, experts, etc.</sup></p>
| 7,674 |
[
-0.046177782118320465,
-0.048022542148828506,
-0.016369948163628578,
-0.038560234010219574,
0.05522215738892555,
0.03275993838906288,
-0.03993038088083267,
-0.005582116544246674,
-0.026345090940594673,
0.0032137141097337008,
0.04479502514004707,
-0.003362818621098995,
0.04072145000100136,
0.011490389704704285,
-0.0035007386468350887,
-0.0037543184589594603,
0.008584290742874146,
0.004574818070977926,
-0.01602672040462494,
0.0031582138035446405,
-0.0017789039993658662,
0.013363873586058617,
-0.05043358355760574,
-0.003954931162297726,
-0.01654091849923134,
0.0226678978651762,
0.007998611778020859,
-0.005546065978705883,
-0.004421165678650141,
0.04716867208480835,
-0.013727727346122265,
-0.01819104142487049,
0.016165602952241898,
-0.009544280357658863,
0.011820996180176735,
0.02677619643509388,
-0.013383608311414719,
0.04063361510634422,
0.025319498032331467,
0.030179709196090698,
-0.022444624453783035,
-0.044748034328222275,
0.0005001238896511495,
0.010283675976097584,
-0.021390320733189583,
0.0038263234309852123,
-0.022760162129998207,
-0.006758223753422499,
0.05691596865653992,
-0.02483752742409706,
0.03319573029875755,
0.019740339368581772,
0.01585734263062477,
-0.015900839120149612,
0.02424613945186138,
0.005537780001759529,
0.03383180871605873,
0.035251591354608536,
-0.01984471268951893,
-0.059316523373126984,
0.018802961334586143,
0.0011192387901246548,
0.015523415990173817,
0.012933715246617794,
0.011756735853850842,
0.0306906346231699,
-0.0024590350221842527,
-0.05276038870215416,
0.05132124945521355,
0.0031700823456048965,
0.009987534955143929,
0.03268818557262421,
0.03324752300977707,
0.023442396894097328,
0.041192490607500076,
-0.03381763771176338,
-0.001895704073831439,
0.0031280722469091415,
0.02954961732029915,
0.03834507614374161,
-0.0016832625260576606,
-0.030604353174567223,
0.045409899204969406,
0.07117028534412384,
0.025699833407998085,
0.0038016822654753923,
0.06983617693185806,
0.002528359880670905,
0.0516827218234539,
0.011893835850059986,
0.004990340210497379,
0.00010924107482424006,
0.01067295391112566,
0.008255870081484318,
-0.012710059992969036,
0.013565033674240112,
0.009250649251043797,
0.05497283115983009,
0.003267429070547223,
-0.02115698531270027,
0.0020137790124863386,
0.011496803723275661,
0.02002737857401371,
0.06058669835329056,
0.0019741852302104235,
-0.023291489109396935,
-0.007071811705827713,
-0.003095409134402871,
-0.012301547452807426,
0.0002746090176515281,
-0.018277939409017563,
-0.010776066221296787,
-0.014559454284608364,
0.017453191801905632,
0.04076921567320824,
-0.008248766884207726,
0.014498522505164146,
0.017505284398794174,
0.0772177204489708,
0.05290233716368675,
0.021515492349863052,
-0.027496708557009697,
0.008162476122379303,
-0.03748330846428871,
-0.05321543291211128,
0.05003552883863449,
0.03912259265780449,
-0.017593875527381897,
-0.022400639951229095,
0.027392687276005745,
0.026202121749520302,
0.03231159225106239,
-0.024072811007499695,
-0.007778644561767578,
0.005326536018401384,
-0.032619886100292206,
-0.10486078262329102,
-0.08383125811815262,
0.05011313781142235,
0.011810142546892166,
-0.01683669164776802,
-0.10482750087976456,
0.027955997735261917,
0.0172958355396986,
0.04515371844172478,
0.021723764017224312,
0.010089046321809292,
-0.01289761159569025,
0.03691527992486954,
-0.025946810841560364,
-0.014880361035466194,
-0.0308440700173378,
0.03417890518903732,
-0.07090205699205399,
-0.011398245580494404,
-0.05845927074551582,
0.019458234310150146,
0.024829361587762833,
0.012117182835936546,
-0.027990374714136124,
0.06541719287633896,
0.00454454543069005,
-0.03181077912449837,
0.03004082664847374,
0.0006901496089994907,
-0.020180583000183105,
0.12519395351409912,
0.004029892850667238,
0.00514261657372117,
0.008367531932890415,
0.02338854968547821,
0.009974556975066662,
0.023458871990442276,
0.022026341408491135,
0.028068337589502335,
-0.05556841567158699,
0.0010935338214039803,
-0.0069614374078810215,
0.012190507724881172,
-0.014600307680666447,
-0.06406234949827194,
-0.008988111279904842,
0.019345594570040703,
0.005519959144294262,
0.022573592141270638,
0.06963500380516052,
-0.02166958525776863,
-0.005865372251719236,
0.03601889684796333,
-0.04071797803044319,
-0.035449281334877014,
-0.02549273520708084,
0.01808343641459942,
-0.014422877691686153,
-0.03809031844139099,
0.0002271846024086699,
-0.04219843074679375,
0.008389869704842567,
-0.017401495948433876,
0.014368905685842037,
0.023895198479294777,
0.038603439927101135,
0.04907846823334694,
-0.012781008146703243,
0.02561221644282341,
0.03466548025608063,
0.03202986344695091,
-0.04284616559743881,
0.009007645770907402,
0.004154356196522713,
-0.04596998170018196,
0.0006478863651864231,
-0.02795506827533245,
-0.006692004390060902,
0.02897709794342518,
0.010460826568305492,
0.005656180437654257,
-0.038263991475105286,
-0.01060091145336628,
0.06267023831605911,
-0.018605107441544533,
0.09906737506389618,
-0.006089582107961178,
-0.028864560648798943,
0.008071971125900745,
0.04656515270471573,
0.02309102565050125,
0.04525621607899666,
0.004967878572642803,
-0.02110663801431656,
-0.05532097816467285,
-0.018360545858740807,
0.03387896716594696,
0.04166387394070625,
-0.04619109630584717,
-0.0071886456571519375,
0.011985596269369125,
0.016761373728513718,
0.009017844684422016,
0.02769418992102146,
-0.0237905103713274,
-0.024468040093779564,
0.021212318912148476,
0.025825463235378265,
-0.006904832553118467,
0.056978024542331696,
0.002382287522777915,
0.04119490087032318,
0.003328859806060791,
-0.046199820935726166,
0.06296280771493912,
0.043921686708927155,
0.01361679658293724,
0.009403498843312263,
0.02019352652132511,
0.02414778433740139,
0.025647863745689392,
-0.05044685676693916,
0.035907499492168427,
-0.0012807567836716771,
-0.02794366516172886,
0.024270804598927498,
-0.014698532409965992,
-0.024411294609308243,
0.0017240693559870124,
0.0009185324888676405,
-0.025310127064585686,
-0.0355587936937809,
0.027027394622564316,
-0.03380534052848816,
-0.002125884173437953,
-0.04245894402265549,
-0.02611515298485756,
0.011430966667830944,
-0.008383462205529213,
0.023571154102683067,
-0.012285973876714706,
0.015108269639313221,
-0.03719235584139824,
-0.019879784435033798,
-0.052921101450920105,
-0.05492052063345909,
0.005895610898733139,
0.00804952997714281,
0.007460034918040037,
0.0002649861853569746,
0.012208269909024239,
0.00196488993242383,
0.07173079252243042,
-0.027468565851449966,
0.007133831735700369,
0.031926412135362625,
0.014203912578523159,
-0.054878976196050644,
-0.02273273840546608,
-0.039256751537323,
-0.010055591352283955,
-0.008364111185073853,
0.003867899999022484,
0.05459965765476227,
-0.042177606374025345,
-0.05454961583018303,
0.039948470890522,
-0.039731018245220184,
-0.038512736558914185,
-0.020336061716079712,
-0.01569793000817299,
0.007217920385301113,
0.015049183741211891,
0.024007385596632957,
0.013814923353493214,
-0.04584880545735359,
-0.04696393385529518,
-0.03239232301712036,
-0.08867742866277695,
0.035000331699848175,
-0.034065667539834976,
0.051600076258182526,
-0.00508227339014411,
-0.0518064945936203,
0.07148852199316025,
0.018992654979228973,
-0.06019464507699013,
-0.0537094809114933,
-0.007843422703444958,
0.022837743163108826,
0.007057070732116699,
-0.00880894623696804,
0.024249527603387833,
-0.004082372412085533,
0.019668815657496452,
-0.003196133067831397,
0.04977035894989967,
-0.0116445766761899,
0.03762050345540047,
0.020007366314530373,
-0.01473263930529356,
-0.006586217787116766,
-0.021597156301140785,
0.006021927110850811,
0.06158175691962242,
-0.05905795097351074,
0.03329914063215256,
-0.007459333166480064,
0.0130947669968009,
0.04510173574090004,
-0.062496840953826904,
0.06241549551486969,
0.009844247251749039,
-0.0004806236538570374,
-0.05185084044933319,
0.02363787777721882,
0.019379448145627975,
-0.03546915575861931,
0.013728262856602669,
-0.0016530643915757537,
0.011258382350206375,
0.002679819706827402,
-0.010285687632858753,
0.021723097190260887,
0.031480226665735245,
-0.027767032384872437,
-0.005953559186309576,
-0.00020011866581626236,
0.007577404845505953,
0.03253990411758423,
-0.02326667495071888,
-0.018673647195100784,
0.0328979566693306,
0.056551866233348846,
0.02508082240819931,
-0.002364514861255884,
-0.04336831346154213,
-0.03784714266657829,
-0.0735211968421936,
-0.01829010248184204,
-0.032504308968782425,
0.07043767720460892,
0.0045741256326437,
0.017581984400749207,
0.02769523672759533,
0.02265045791864395,
-0.024074651300907135,
0.006137077230960131,
-0.10505039989948273,
0.01072460226714611,
-0.0020506875589489937,
-0.004425714258104563,
-0.010449370369315147,
-0.020989077165722847,
-0.021865615621209145,
-0.048369504511356354,
-0.021733662113547325,
0.0075286072678864,
0.026468852534890175,
-0.039600446820259094,
0.009664565324783325,
-0.034640442579984665,
-0.03635239601135254,
-0.05398053675889969,
0.03586795553565025,
0.030361978337168694,
-0.014173277653753757,
0.01778368465602398,
0.028455916792154312,
-0.05773507431149483,
-0.035536989569664,
-0.03130056709051132,
0.025146108120679855,
0.01419367641210556,
0.061972636729478836,
0.023977139964699745,
0.03267710283398628,
-0.043335359543561935,
0.024137767031788826,
0.029954520985484123,
0.04347756505012512,
0.02193448133766651,
-0.028434818610548973,
-0.07281959056854248,
-0.01060352474451065,
-0.006748310290277004,
0.012166066095232964,
0.03909626230597496,
-0.002839387394487858,
0.016979234293103218,
0.01172278169542551,
-0.009193618781864643,
0.007048170082271099,
0.03467051312327385,
0.011569846421480179,
-0.013998507522046566,
0.023985441774129868,
-0.04202020913362503,
-0.02167111076414585,
-0.016938278451561928,
-0.006992826238274574,
0.003619150025770068,
0.018097972497344017,
-0.011195356026291847,
-0.0854138657450676,
-0.018060727044939995,
0.022642917931079865,
0.0031820025760680437,
0.02835971862077713,
0.036768995225429535,
0.03869803249835968,
-0.022177722305059433,
-0.00045756425242871046,
-0.018146086484193802,
0.02985421009361744,
0.037530671805143356,
-0.0039948211051523685,
-0.04158322140574455,
-0.040662359446287155,
0.016987890005111694,
0.019158639013767242,
0.0796126127243042,
-0.04484880715608597,
0.0031394187826663256,
-0.004456997849047184,
0.03490632027387619,
0.03758082166314125,
-0.033679671585559845,
0.016464313492178917,
-0.04117823764681816,
0.0050246138125658035,
-0.03739026188850403,
-0.004923471715301275,
0.001030266284942627,
0.006890051066875458,
0.0017286387737840414,
0.020176086574792862,
-0.017386144027113914,
-0.016194483265280724,
-0.013411415740847588,
-0.009938440285623074,
0.010249304585158825,
0.0546107217669487,
0.006600296124815941,
-0.009646041318774223,
-0.008039678446948528,
0.01034130621701479,
-0.051324039697647095,
-0.07402856647968292,
-0.019337115809321404,
-0.028592417016625404,
-0.013204069808125496,
0.0004475403402466327,
-0.03370201960206032,
-0.09049256891012192,
0.025903843343257904,
0.014484859071671963,
-0.01982283405959606,
-0.007697451394051313,
-0.010218240320682526,
0.02298569865524769,
0.0056059821508824825,
-0.024338673800230026,
0.01945497840642929,
0.035133469849824905,
-0.04309951886534691,
0.005812676623463631,
-0.008557788096368313,
-0.005968398414552212,
-0.034671999514102936,
0.007027054205536842,
-0.018458444625139236,
0.05761927366256714,
-0.04175889492034912,
0.021724386140704155,
0.0046303714625537395,
0.03706490620970726,
-0.03534310683608055,
-0.0334366150200367,
-0.022346090525388718,
0.010635465383529663,
-0.007877177558839321,
-0.038632191717624664,
-0.053811460733413696,
0.027327844873070717,
-0.0022761463187634945,
-0.0537215992808342,
-0.006362955551594496,
0.030626608058810234,
0.03829439356923103,
0.04016343504190445,
0.005147574469447136,
0.025507839396595955,
-0.021070342510938644,
-0.005317261442542076,
0.027135349810123444,
-0.029523583129048347,
0.03658927232027054,
-0.00010819352610269561,
-0.0016851061955094337,
0.0188568364828825,
-0.04438447579741478,
-0.0012104790657758713,
0.010661356151103973,
0.023081548511981964,
0.04638976976275444,
-0.04374948516488075,
0.02278320863842964,
-0.02321508154273033,
0.0030204951763153076,
-0.044932808727025986,
-0.013094316236674786,
0.04071767255663872,
-0.004796584136784077,
-0.038324881345033646,
-0.002128861378878355,
-0.04964226484298706,
-0.03969050198793411,
-0.007015341892838478,
0.019879132509231567,
0.049604106694459915,
0.006892200093716383,
-0.02671695686876774,
0.0233461894094944,
0.047534968703985214,
0.04139774292707443,
-0.02483910135924816,
-0.01447343174368143,
-0.0033431437332183123,
-0.0073133064433932304,
-0.0140799256041646,
0.009272304363548756,
0.04586600884795189,
-0.023375069722533226,
-0.013095134869217873,
-0.017584217712283134,
0.006672773510217667,
0.01023474708199501,
0.024059703573584557,
0.01667698286473751,
0.04932012781500816,
0.009862707927823067,
-0.02844269946217537,
0.016241662204265594,
0.036212801933288574,
0.011947443708777428,
0.03520829975605011,
0.032186225056648254,
0.01297939196228981,
-0.013955471105873585,
-0.03577001020312309,
0.008026978000998497,
-0.014285560697317123,
-0.028832372277975082,
0.01654919795691967,
0.06332824379205704,
-0.01763167977333069,
0.02260892651975155,
0.04168989509344101,
-0.013374723494052887,
0.018873846158385277,
0.0019713265355676413,
0.0019757261034101248,
-0.03943951055407524,
0.009061270393431187,
-0.012239407747983932,
0.005385551601648331,
-0.034584756940603256,
0.009776655584573746,
0.03348008543252945,
-0.004156278446316719,
0.0765952467918396,
0.019319940358400345,
-0.030954815447330475,
0.014660424552857876,
-0.0037693597842007875,
0.001165231573395431,
-0.004875239450484514,
0.013859283179044724,
0.019402939826250076,
-0.014543096534907818,
-0.024062249809503555,
0.030506649985909462,
0.046665165573358536,
-0.005661576054990292,
-0.015209413133561611,
0.04997951537370682,
0.05036604404449463,
-0.010582057759165764,
-0.025230279192328453,
-0.02161427028477192,
0.025277333334088326,
-0.014934438280761242,
0.02383718453347683,
0.0026600495912134647,
-0.022979864850640297,
0.008149712346494198,
-0.0043318928219377995,
0.00411806907504797,
-0.03847905620932579,
-0.011075061745941639,
-0.07401937246322632,
0.03767888993024826,
0.03718946874141693,
-0.01984669640660286,
-0.013471555896103382,
-0.02046041749417782,
0.019277647137641907,
0.02393500879406929,
0.03688621148467064,
-0.021315202116966248,
-0.043685685843229294,
-0.01870233565568924,
-0.007935580797493458,
-0.03537130355834961,
0.048432786017656326,
0.00857075396925211,
-0.07257328182458878,
0.010713810101151466,
-0.030372729524970055,
0.02613392099738121,
0.03836605325341225,
0.008801632560789585,
-0.011966085992753506,
0.06261991709470749,
0.003390316851437092,
-0.016148671507835388,
-0.009764882735908031,
0.011862728744745255,
0.12120628356933594,
0.06642735004425049,
0.02053198218345642,
-0.02157251164317131,
0.024609869346022606,
0.011512687429785728,
0.02242174744606018,
0.012633804231882095,
-0.029659509658813477,
-0.03597240522503853,
-0.029751503840088844,
0.03702502325177193,
0.03000270575284958,
-0.022000573575496674,
0.039075516164302826,
0.017660003155469894,
-0.05150076374411583,
-0.025913666933774948,
0.0017394321039319038,
0.026527808979153633,
0.005838304758071899,
-0.03205963224172592,
-0.01987692527472973,
-0.028820427134633064,
-0.020987002179026604,
-0.007892318069934845,
0.000292732089292258,
-0.053293950855731964,
0.014061195775866508,
0.014184731058776379,
-0.030103061348199844,
0.03444547951221466,
0.04778844863176346,
0.02145388536155224,
-0.08620119094848633,
0.0024713852908462286,
0.02351396530866623,
0.0058799805119633675,
0.011373010464012623,
0.04046417772769928,
0.04295359551906586,
-0.03090059943497181,
0.0444023460149765,
0.0387396402657032,
-0.07410726696252823,
-0.042940594255924225,
-0.014823327772319317,
0.01770862750709057,
0.0031733873765915632,
-0.01621207222342491,
-0.006732387468218803,
-0.029432149603962898,
-0.016668563708662987,
-0.02906317450106144,
-0.059107013046741486,
-0.012005094438791275,
0.03525787964463234,
-0.0381748229265213,
-0.06913307309150696,
-0.0032993145287036896,
0.005105387885123491,
-0.02109050564467907,
0.01644766889512539,
0.029622649773955345,
-0.034343212842941284,
-0.02014404535293579,
0.0020133289508521557,
0.018356798216700554,
-0.041218191385269165,
-0.016149502247571945,
0.0032152445055544376,
-0.04216890037059784,
-0.06793982535600662,
-0.01241665706038475,
-0.018763629719614983,
0.027387261390686035,
0.02311776950955391,
0.015490376390516758,
-0.009736394509673119,
-0.031735651195049286,
-0.018299711868166924,
0.0037884421180933714,
0.00907943770289421,
0.0007753146928735077,
-0.02963533066213131,
-0.009972178377211094,
0.0001336082787020132,
-0.005499386228621006,
-0.017506485804915428,
0.004143170081079006,
0.019859014078974724,
0.0008246119832620025,
0.013133332133293152,
-0.0029114324133843184,
-0.026759037747979164,
0.014635574072599411,
-0.034290436655282974,
0.004292117431759834,
0.0032871258445084095,
-0.0040175579488277435,
-0.007722422014921904,
-0.0038251783698797226,
0.0491551049053669,
0.038999758660793304,
-0.00552563788369298,
0.0019489096011966467,
0.04400140419602394,
-0.0036678502801805735,
-0.023516755551099777,
0.008284912444651127,
0.023888828232884407,
-0.010946420952677727,
-0.010110558941960335,
-0.07761549949645996,
0.022036734968423843,
-0.024159837514162064,
0.013545937836170197,
-0.007425267249345779,
0.006592907942831516,
-0.03471987694501877,
0.05339813232421875,
-0.04915526509284973,
-0.03006872348487377,
-0.033255435526371,
-0.011611207388341427,
0.0037871648091822863,
0.027634551748633385,
0.03533509001135826,
0.04602251946926117,
-0.006241065450012684,
-0.033470313996076584,
0.0091919656842947,
0.015247327275574207,
-0.039531007409095764,
-0.03151140362024307,
-0.015529295429587364,
0.0010393050033599138,
0.020479664206504822,
-0.04655569791793823,
-0.008873287588357925,
0.02272910438477993,
-0.04128620773553848,
-0.037057001143693924,
0.053335223346948624,
-0.0054032448679208755,
-0.035895876586437225,
0.03865892067551613,
-0.0025641247630119324,
-0.004208051599562168,
0.07288447767496109,
-0.010906697250902653,
0.02227417752146721,
0.021771304309368134,
-0.005231321323662996,
0.00446464866399765,
0.03210032358765602,
-0.008811895735561848,
-0.004423216450959444,
0.014151319861412048,
0.03594454750418663,
0.03190983459353447,
0.018605051562190056,
-0.002975411945953965,
0.010820083320140839,
0.021686391904950142,
-0.0318368636071682,
0.020006051287055016,
-0.01940973661839962,
0.0029079115483909845,
0.05701182410120964,
-0.04373963922262192,
0.05322788655757904,
-0.00009156019950751215,
-0.010991490446031094,
-0.06403990834951401,
-0.026696275919675827,
-0.019291605800390244,
-0.0082807382568717,
0.0002433047047816217,
-0.02376484125852585,
0.05242784321308136,
0.022136911749839783,
-0.031872186809778214,
-0.0035796009469777346,
-0.03546896576881409,
-0.01374012790620327,
-0.0014316088054329157,
-0.0533122755587101,
-0.004339195322245359,
0.04355117678642273,
0.031894031912088394,
0.03131696209311485,
0.031274549663066864,
0.0003673350438475609,
-0.024678939953446388,
-0.013102592900395393,
-0.02093038707971573,
0.036511193960905075,
-0.03274859860539436,
-0.01397397369146347,
0.048399727791547775,
0.014801477082073689,
-0.030263163149356842,
0.02731458470225334,
-0.012860327027738094,
0.010257036425173283,
-0.025053486227989197,
0.03424770385026932,
-0.010996690019965172,
0.06509913504123688,
0.03259439021348953,
-0.022002534940838814,
-0.036888666450977325,
0.021768299862742424,
-0.00028827160713262856,
0.03869672119617462,
-0.00416838563978672,
0.006527538876980543,
0.008775540627539158,
0.004971073940396309,
-0.0375947505235672,
0.008971716277301311,
-0.003641313873231411,
-0.011889861896634102,
-0.006962745450437069,
0.005247871857136488,
0.006306889932602644,
-0.020920971408486366,
0.016884226351976395,
-0.04384578391909599,
-0.0008268431411124766,
0.023107556626200676,
0.026229673996567726,
0.011702040210366249,
0.011128741316497326,
0.001230367342941463,
-0.0036937794648110867,
0.03138798102736473,
0.005600586999207735,
-0.03523368760943413,
-0.06003390997648239,
-0.010709686204791069,
0.0038022538647055626,
0.015238398686051369,
-0.02180192619562149,
-0.049906712025403976,
-0.06361478567123413,
0.02986467257142067,
0.04004117101430893,
0.00988518912345171,
0.0015283533139154315,
-0.022327275946736336,
-0.015226073563098907,
-0.08249936252832413,
0.04471735283732414,
0.021152304485440254,
-0.021361855790019035,
-0.02441251464188099,
-0.003617921844124794,
0.021927615627646446,
0.058095261454582214,
0.05174827203154564,
-0.008010423742234707,
-0.047007299959659576,
0.01161640603095293,
-0.029486773535609245,
0.0033663411159068346,
-0.03074651025235653,
0.028468681499361992,
-0.017638791352510452,
-0.007811171934008598,
0.0037839538417756557,
0.00875718705356121,
-0.029729973524808884,
-0.0071526458486914635,
0.015143214724957943,
-0.007449874188750982,
0.03264616057276726,
-0.03496667370200157,
0.0020382849033921957,
0.05100120231509209,
0.04431423917412758,
-0.017846832051873207,
0.05502001941204071,
0.016958093270659447,
0.02874390408396721,
0.0002500921254977584,
-0.03601979464292526,
-0.053586509078741074,
0.03187680244445801,
-0.0023789184633642435,
0.007494146935641766,
0.00014931728946976364,
0.007737177889794111,
0.04287876561284065,
-0.05204138532280922,
0.014813747256994247,
0.050398088991642,
-0.010663751512765884,
-0.030861902981996536,
-0.007567750755697489,
0.03881172090768814,
0.01666853204369545,
0.003794365329667926,
0.018212363123893738,
-0.021907087415456772,
-0.04019693285226822,
-0.037886593490839005,
0.05220566689968109,
0.043468259274959564,
0.019953951239585876,
0.011850060895085335,
0.024665793403983116,
-0.0034430085215717554,
0.012999048456549644,
0.033734031021595,
0.029940851032733917,
-0.027532896026968956,
-0.04538806527853012,
0.04325638711452484,
-0.0009515545680187643,
-0.02423829212784767,
0.04034380242228508,
-0.005243298131972551,
0.0692022368311882,
0.0010529259452596307,
0.013721604831516743,
-0.027497975155711174,
0.026738200336694717,
-0.035234712064266205,
-0.041309379041194916,
0.032755330204963684,
0.05982453003525734,
-0.016542328521609306,
-0.00016706604219507426,
-0.019498437643051147,
-0.012309796176850796,
0.028420129790902138,
-0.01090729609131813,
-0.018824502825737,
-0.0005997727275826037,
0.0031064047943800688,
-0.011089928448200226,
-0.006518236827105284,
-0.03892791271209717,
0.005982544738799334,
0.0492091178894043,
0.02346014603972435,
-0.006541442591696978,
-0.02410310134291649,
-0.047295745462179184,
0.03263576328754425,
0.08249708265066147,
-0.06809849292039871,
0.0031455960124731064,
-0.014338658191263676,
0.03547985479235649,
-0.008314626291394234,
0.008121541701257229
] |
<p>In 2008, NASA astronaut Clayton Anderson <a href="http://www.space.com/6056-space-station-trash-burns-south-pacific.html" rel="nofollow">tossed a 635-kg tank of ammonia coolant</a> overboard from the International Space Station (ISS). Subsequently the tank burned up in earth atmosphere as planned.</p>
<p>Obviously in the 1-g environment on Earth's surface, no human could have lifted the tank let alone tossed it. The astronaut was only able to do so because the tank weighed much less in the microgravity environment of the orbiting (free-falling) ISS. </p>
<p>Because I was asleep in much of physics class in high school, I am unable to work out a formula for how much <s>weight</s> mass a human can chuck overboard from the ISS unassisted. In particular, I have only the vaguest notions of inertia and action/reaction. (What I mean is, I can look up Newton's laws of motion but I am unable to use them to solve my question.) </p>
<p>In the picture within the article that I linked to in my first paragraph above, we see that the astronaut appears to have his feet strapped into a footrest at the end of a robotic arm. </p>
<p>Am I right that this is vitally important because otherwise he would not have a backstop to push off from?</p>
<p>Anyway, can you give me a way to calculate, using simple arithmetic, what is the heaviest object that an average-strength human can toss overboard from the ISS? </p>
<p>Also, why is not all trash discarded from the ISS by being thrown overboard manually or using a device instead of being packed into a space-craft that will depart from ISS and burn up in the atmosphere?</p>
<p><sup><em>(A day later:)</em> Thank you to all three who took the time to reply so far, I upvoted each of your Answers. I could not for the life of me single out one for "acceptance" so no green checkmark from me this time :)</sup></p>
| 7,675 |
[
-0.034597430378198624,
-0.05195700377225876,
-0.02685287594795227,
-0.02410622127354145,
0.024395283311605453,
-0.0031777576077729464,
-0.028865525498986244,
-0.00853409431874752,
0.007484813686460257,
-0.054228655993938446,
0.02048790454864502,
0.05037771537899971,
0.07491518557071686,
0.0071082706563174725,
-0.0017516951775178313,
-0.004523875657469034,
0.042512670159339905,
-0.010098515078425407,
0.038734838366508484,
-0.0016204543644562364,
0.021892618387937546,
-0.011900249868631363,
0.013325209729373455,
-0.013519844971597195,
-0.036919839680194855,
-0.019646290689706802,
0.04942804574966431,
-0.018035273998975754,
0.013957877643406391,
0.05469147488474846,
-0.0214689914137125,
-0.00675848126411438,
0.033223651349544525,
-0.02903657779097557,
0.030968334525823593,
0.018409287557005882,
-0.031750988215208054,
0.01583501137793064,
-0.0059978351928293705,
0.030803797766566277,
0.0023560109548270702,
-0.014439997263252735,
-0.03330133855342865,
0.0470731146633625,
-0.039028141647577286,
0.02732267417013645,
-0.03020116686820984,
0.02357872575521469,
0.05016699060797691,
-0.0950552225112915,
0.05274736508727074,
0.0038522444665431976,
0.052941132336854935,
0.03944192826747894,
-0.0037422559689730406,
-0.012651616707444191,
0.04945218563079834,
0.07406140863895416,
0.00038699526339769363,
-0.03652498126029968,
-0.032558463513851166,
0.0013327548513188958,
-0.061175696551799774,
0.016004392877221107,
0.05460407957434654,
0.013489260338246822,
-0.022101853042840958,
-0.01251690648496151,
0.00826492253690958,
0.027703972533345222,
0.021931806579232216,
0.02076314575970173,
0.005621050950139761,
0.004900490865111351,
0.04629005491733551,
-0.02206009067595005,
0.032968562096357346,
0.020191553980112076,
0.034477896988391876,
0.048165615648031235,
-0.015541085042059422,
-0.010510092601180077,
0.06921201944351196,
0.023626793175935745,
0.0008246536017395556,
0.004904310684651136,
0.08378884941339493,
0.011571223847568035,
-0.008853607811033726,
0.023440614342689514,
-0.0026999872643500566,
0.003414343809708953,
-0.02549171820282936,
0.020535707473754883,
-0.008373253978788853,
0.030363041907548904,
0.0011138393310829997,
0.09896409511566162,
0.00614264328032732,
-0.0197269506752491,
-0.014537611044943333,
-0.006143180187791586,
0.02966500073671341,
0.08266325294971466,
-0.00032654486130923033,
-0.028480416163802147,
-0.015028148889541626,
0.009672034531831741,
0.00458925124257803,
-0.036458998918533325,
-0.030737482011318207,
0.016068316996097565,
0.011086233891546726,
-0.04608738794922829,
0.0042280592024326324,
0.006125906016677618,
-0.026377452537417412,
-0.04958060383796692,
0.06067933142185211,
0.030134038999676704,
0.02715190127491951,
0.0379004031419754,
0.008885570801794529,
-0.0666334480047226,
-0.012098735198378563,
0.03727448731660843,
0.03716396540403366,
-0.034582775086164474,
-0.013426323421299458,
0.024011028930544853,
-0.0029453234747052193,
0.001383504830300808,
0.0077077168971300125,
-0.02509164623916149,
0.005207448732107878,
0.02344178408384323,
-0.06813295930624008,
-0.04716646298766136,
0.04346269369125366,
0.022193603217601776,
-0.025427067652344704,
-0.053504206240177155,
-0.01007136795669794,
0.010227134451270103,
0.011618146672844887,
0.018846342340111732,
0.03779960423707962,
-0.03607495501637459,
0.010321896523237228,
0.0086944829672575,
-0.0244874507188797,
0.008912022225558758,
-0.007433783728629351,
-0.054367199540138245,
-0.016996655613183975,
-0.06187944486737251,
0.010463728569447994,
0.02930925413966179,
0.038110315799713135,
-0.020561762154102325,
0.03964751586318016,
-0.0341220460832119,
0.02388274483382702,
-0.030681928619742393,
0.009534450247883797,
-0.03374231234192848,
0.0954599678516388,
0.030211353674530983,
-0.02888392098248005,
0.027989685535430908,
0.01282356958836317,
0.026117175817489624,
0.0022075993474572897,
-0.03239646181464195,
0.0720081552863121,
-0.025988999754190445,
-0.028389962390065193,
-0.04180291295051575,
-0.03127237781882286,
-0.0026203803718090057,
-0.05267702788114548,
-0.02670406363904476,
-0.0009025356848724186,
-0.0085281478241086,
0.019288258627057076,
0.02440084144473076,
0.030932975932955742,
-0.02115424908697605,
0.007517301477491856,
0.003340024733915925,
-0.017270533367991447,
-0.03803163766860962,
0.04194144904613495,
-0.04295065999031067,
0.018853167071938515,
-0.012350528500974178,
-0.03346623107790947,
0.03660937026143074,
-0.03887787461280823,
-0.012087889015674591,
0.046732526272535324,
0.02262602560222149,
0.014959744177758694,
0.01777677610516548,
-0.03287547081708908,
0.05657121166586876,
0.010039983317255974,
-0.017291149124503136,
-0.02254651114344597,
-0.018450267612934113,
-0.027232185006141663,
-0.023512771353125572,
-0.02954920008778572,
-0.014375113882124424,
0.02050672098994255,
-0.012189364060759544,
0.04767705127596855,
-0.015312476083636284,
-0.008885985240340233,
0.0203690342605114,
0.0073960162699222565,
0.0948062539100647,
0.045864351093769073,
0.021914593875408173,
0.019409365952014923,
0.046718765050172806,
0.006526791024953127,
-0.03747519478201866,
0.0503554493188858,
0.00007746673509245738,
-0.04501847177743912,
-0.03806476667523384,
0.004698819015175104,
0.019677171483635902,
-0.001135449856519699,
0.011334214359521866,
0.025216391310095787,
0.02048376388847828,
0.04363259673118591,
-0.0005328089464455843,
0.0015795560320839286,
0.005777890328317881,
0.02787237986922264,
-0.0018124262569472194,
-0.000583382323384285,
-0.003999184351414442,
-0.009858175180852413,
0.025270862504839897,
-0.014570964500308037,
0.0183796938508749,
-0.01725367084145546,
-0.006490870378911495,
0.018180955201387405,
0.024828210473060608,
-0.015109919011592865,
-0.02038850635290146,
0.04572196677327156,
-0.05356840044260025,
0.0030486471951007843,
0.056367091834545135,
0.00849804375320673,
-0.010950720869004726,
-0.03939470648765564,
0.005270363762974739,
0.006631886586546898,
-0.012404099106788635,
-0.003628983860835433,
0.016081592068076134,
0.04578666761517525,
-0.01645580492913723,
-0.019181234762072563,
-0.013156150467693806,
0.00401225034147501,
-0.027126625180244446,
0.04149070754647255,
-0.004764800425618887,
-0.015611177310347557,
0.018869757652282715,
-0.02482060343027115,
0.0012327610747888684,
-0.044086895883083344,
-0.018956197425723076,
0.008154914714396,
0.023495757952332497,
-0.04114614427089691,
-0.014512547291815281,
-0.02337072044610977,
-0.01685434766113758,
0.03347499296069145,
0.009740781970322132,
-0.025600817054510117,
0.05257834121584892,
0.007340764161199331,
-0.02004658244550228,
0.0005907604936510324,
-0.008241326548159122,
0.01112772524356842,
-0.015601231716573238,
-0.02112712152302265,
0.045917656272649765,
-0.0030966594349592924,
-0.05584236606955528,
0.07440263777971268,
-0.04205800220370293,
-0.052506424486637115,
-0.016577046364545822,
0.013098456896841526,
0.006589710712432861,
-0.04242948815226555,
-0.018573492765426636,
-0.004597496706992388,
0.01117566879838705,
0.011579299345612526,
-0.06985493749380112,
-0.05404782295227051,
-0.016998866572976112,
-0.004341727588325739,
0.04619690403342247,
-0.02199513465166092,
-0.01459292322397232,
0.0825350359082222,
0.007271287497133017,
-0.025800229981541634,
-0.020612528547644615,
0.011399472132325172,
0.0019194417400285602,
-0.006075629033148289,
0.02042621374130249,
0.023096486926078796,
-0.005562859121710062,
0.01745537295937538,
0.006302900146692991,
0.007615427486598492,
0.00338601297698915,
0.014325419440865517,
-0.004914129618555307,
-0.021207867190241814,
-0.010809875093400478,
-0.014190508052706718,
0.05687424913048744,
0.023888079449534416,
-0.013104137033224106,
0.0654018446803093,
-0.04695605859160423,
0.04535720497369766,
-0.01959642954170704,
-0.08183842152357101,
0.02730480581521988,
0.0029542825650423765,
0.0024592382833361626,
0.0054585556499660015,
0.03528089448809624,
0.028261562809348106,
-0.04428654909133911,
0.017541293054819107,
-0.019681479781866074,
0.05670802667737007,
-0.010486124083399773,
-0.018700480461120605,
0.02678694948554039,
0.09753156453371048,
0.014914791099727154,
-0.04464998468756676,
-0.00041225471068173647,
0.03563985601067543,
0.0029324006754904985,
-0.00978122092783451,
-0.015591190196573734,
0.04765260964632034,
0.012800002470612526,
0.02595645934343338,
0.01680869050323963,
-0.02093113213777542,
0.023926211521029472,
-0.06546162068843842,
-0.03534960374236107,
-0.0018106115749105811,
0.057381629943847656,
0.0069606429897248745,
0.030802713707089424,
0.007510812487453222,
0.005506801884621382,
0.002878893632441759,
0.014325306750833988,
-0.05946772173047066,
0.02026679739356041,
0.014651088044047356,
-0.047127172350883484,
0.023209907114505768,
0.014611933380365372,
0.001178547739982605,
-0.01801692135632038,
-0.003491444978863001,
-0.005669291131198406,
0.0467696338891983,
-0.04072406515479088,
0.04003884270787239,
-0.025630170479416847,
-0.023598793894052505,
0.03430905565619469,
0.01509721390902996,
0.03449169546365738,
-0.04262421280145645,
0.010777679271996021,
0.01885964162647724,
0.00877842865884304,
-0.02930031344294548,
-0.04700259491801262,
0.003993317950516939,
0.00223953602835536,
0.024121902883052826,
-0.006651279982179403,
0.0349026657640934,
-0.01212475635111332,
-0.005157541949301958,
-0.031623370945453644,
0.0024469983763992786,
-0.018851106986403465,
0.0010867677628993988,
-0.026263020932674408,
-0.027312006801366806,
0.02603570744395256,
0.0517650805413723,
-0.013002028688788414,
-0.037976764142513275,
0.03418949618935585,
0.03867510333657265,
-0.017200063914060593,
-0.022209445014595985,
0.037646327167749405,
0.033969320356845856,
-0.009207889437675476,
0.005184520967304707,
-0.04083649441599846,
-0.013209613040089607,
-0.015014249831438065,
-0.03384072333574295,
0.03507424145936966,
0.06455651670694351,
0.03237832337617874,
-0.012157286517322063,
0.04604686424136162,
0.04174380376935005,
-0.047730911523103714,
0.023423830047249794,
-0.007263510022312403,
0.04521774873137474,
-0.045465338975191116,
0.008944646455347538,
-0.00901853572577238,
0.03979796543717384,
0.09864279627799988,
-0.03050304390490055,
0.016371475532650948,
-0.04511718079447746,
-0.018842177465558052,
-0.0001606691803317517,
0.04680812358856201,
0.01869170553982258,
0.022660573944449425,
-0.009337293915450573,
-0.017036382108926773,
0.038964420557022095,
-0.023945217952132225,
0.0023383579682558775,
-0.016552306711673737,
0.031642697751522064,
0.017251577228307724,
-0.043467991054058075,
-0.01565648429095745,
-0.014077489264309406,
-0.014899879693984985,
0.01043437048792839,
-0.004255561623722315,
-0.025210265070199966,
-0.009368060156702995,
0.0405077189207077,
0.03930327296257019,
0.0235956571996212,
0.022403454408049583,
0.015438156202435493,
-0.04475199058651924,
-0.005524353124201298,
-0.07084809243679047,
-0.04660682752728462,
-0.053861528635025024,
-0.00744669372215867,
-0.009150381200015545,
0.04466301202774048,
-0.03971380740404129,
-0.06277774274349213,
0.02186908759176731,
0.008121716789901257,
0.005742920096963644,
-0.03767206519842148,
-0.0575600229203701,
0.024219578132033348,
0.04038255661725998,
0.010282841511070728,
0.02719106711447239,
0.047861937433481216,
0.005029851570725441,
0.019698534160852432,
-0.033308275043964386,
0.003383726580068469,
-0.010605860501527786,
-0.040370672941207886,
-0.0280425027012825,
0.022201716899871826,
-0.018570665270090103,
0.02725161425769329,
0.04047184810042381,
0.01157210860401392,
-0.021065983921289444,
-0.06381912529468536,
0.011268768459558487,
0.007784515153616667,
0.012195497751235962,
-0.0063093602657318115,
0.005744114518165588,
0.04799949750304222,
0.011497252620756626,
-0.024675384163856506,
0.003140064887702465,
0.025150882080197334,
-0.0003601988428272307,
0.0074905394576489925,
-0.04473329335451126,
0.024365514516830444,
-0.045416370034217834,
-0.020220359787344933,
0.0004857383028138429,
-0.027606334537267685,
0.05467166379094124,
-0.01229676604270935,
-0.005763974506407976,
0.020325740799307823,
-0.03960054740309715,
-0.026913056150078773,
-0.016009023413062096,
0.01955314911901951,
0.002126581035554409,
-0.029052266851067543,
0.018506355583667755,
0.010968811810016632,
0.03813551738858223,
-0.014697196893393993,
-0.006804514676332474,
0.01543298177421093,
0.01274194661527872,
0.010559814050793648,
-0.030852504074573517,
0.0030897038523107767,
-0.02150394581258297,
-0.02035490982234478,
-0.0378713421523571,
0.05535995960235596,
-0.05803901329636574,
0.002346774097532034,
0.023469295352697372,
0.03430191054940224,
0.05853128433227539,
-0.0019329051719978452,
-0.040469806641340256,
0.011908700689673424,
-0.036593008786439896,
-0.00608515040948987,
0.00047835599980317056,
0.04765862971544266,
-0.028887415304780006,
-0.0664823055267334,
-0.0038160362746566534,
-0.036076631397008896,
0.006433750037103891,
-0.021079257130622864,
0.01315442007035017,
0.05475336313247681,
-0.019378310069441795,
0.009008257649838924,
0.014315652661025524,
0.044722698628902435,
-0.004027326125651598,
0.030767161399126053,
0.006301861722022295,
0.03090037778019905,
-0.007151625119149685,
-0.01567082665860653,
-0.016027655452489853,
-0.012815034948289394,
0.00031674440833739936,
0.0042384909465909,
0.03750372305512428,
0.00961508322507143,
-0.0018206960521638393,
0.06900651752948761,
-0.026981865987181664,
0.06482280790805817,
-0.010299467481672764,
-0.006649118382483721,
0.0364452563226223,
-0.013542454689741135,
-0.02809820882976055,
-0.037609562277793884,
-0.012985379435122013,
-0.018336284905672073,
0.014859218150377274,
-0.027621855959296227,
0.006340296007692814,
-0.02166016399860382,
0.008847513236105442,
0.014767722226679325,
-0.0086817666888237,
0.03494133800268173,
-0.003976913634687662,
0.019944796338677406,
0.03987182676792145,
-0.014501580037176609,
0.008045610971748829,
0.07041541486978531,
-0.00040025421185418963,
-0.016603071242570877,
-0.025816811248660088,
0.010972002521157265,
-0.003879572730511427,
0.012002135626971722,
-0.060935091227293015,
-0.017438054084777832,
0.03537379950284958,
-0.006031806115061045,
0.01715041510760784,
0.009896719828248024,
-0.04098944738507271,
0.03806520625948906,
-0.004683930426836014,
-0.022136714309453964,
-0.062015142291784286,
-0.02782677486538887,
-0.047238126397132874,
-0.025501292198896408,
0.02668219618499279,
-0.026403281837701797,
-0.011682837270200253,
-0.026930753141641617,
0.054584454745054245,
0.017327643930912018,
-0.005546731874346733,
-0.02476324886083603,
-0.029972383752465248,
-0.026964940130710602,
-0.01654956117272377,
-0.06221190467476845,
0.031351421028375626,
0.0025460291653871536,
-0.009957951493561268,
0.01574801094830036,
-0.007650672923773527,
0.011941145174205303,
-0.017175476998090744,
0.03297792747616768,
-0.0312964953482151,
0.07370592653751373,
-0.054780710488557816,
0.03234462812542915,
-0.018414035439491272,
0.023662427440285683,
0.14211496710777283,
0.03425521403551102,
0.04373010993003845,
-0.018068771809339523,
-0.048659779131412506,
0.013437782414257526,
-0.0099258441478014,
-0.0003111941332463175,
-0.0320182740688324,
-0.00040934907156042755,
-0.021854320541024208,
0.007531439885497093,
0.03917846828699112,
-0.02429155260324478,
-0.03902873396873474,
0.0244058258831501,
-0.027899162843823433,
-0.016682013869285583,
-0.006623269524425268,
-0.006353398784995079,
-0.019966628402471542,
-0.018742760643363,
-0.004157085902988911,
0.03567492216825485,
0.03066221997141838,
-0.02280959114432335,
-0.03260191157460213,
-0.017083648592233658,
0.028308577835559845,
0.004890213720500469,
-0.032262250781059265,
-0.010982075706124306,
-0.0224533062428236,
0.01552849356085062,
-0.015602199360728264,
0.05555243790149689,
0.012485054321587086,
-0.012735441327095032,
0.021687719970941544,
0.03339957445859909,
0.027455171570181847,
0.026128452271223068,
0.03240330517292023,
-0.010785792954266071,
-0.03500811383128166,
-0.013805556111037731,
-0.021152421832084656,
0.011601131409406662,
-0.0067654806189239025,
-0.021356001496315002,
-0.028068076819181442,
-0.012769165448844433,
-0.022428132593631744,
-0.05739239603281021,
-0.03853771835565567,
0.0152447409927845,
0.03203458711504936,
0.004386790096759796,
-0.019589103758335114,
0.02546602673828602,
-0.01967501826584339,
-0.004682305734604597,
0.003945502918213606,
0.021215615794062614,
-0.01458400022238493,
-0.01351588498800993,
-0.012546489015221596,
0.014134524390101433,
0.025892451405525208,
-0.0186670683324337,
-0.07958997786045074,
-0.03617323935031891,
-0.022569218650460243,
0.011081102304160595,
-0.0041104331612586975,
0.03669740632176399,
0.047977034002542496,
-0.008615795522928238,
0.013067083433270454,
-0.05254274234175682,
-0.04719489812850952,
0.05985679104924202,
-0.031157448887825012,
-0.017883827909827232,
-0.033142685890197754,
-0.059468626976013184,
0.00512140104547143,
0.020046044141054153,
0.0030090310610830784,
-0.006426411215215921,
0.02815292589366436,
0.07803025841712952,
-0.01805059425532818,
-0.038998305797576904,
-0.005090723745524883,
0.024716179817914963,
-0.027980763465166092,
0.022982370108366013,
-0.02533595822751522,
0.01697860285639763,
0.0227170679718256,
-0.0012168552493676543,
-0.0013356187846511602,
-0.01741345413029194,
-0.018919603899121284,
0.011084537953138351,
0.03956598788499832,
-0.009670328348875046,
-0.037967782467603683,
0.008001316338777542,
0.013864994049072266,
-0.05850895121693611,
-0.03855232521891594,
-0.030363256111741066,
-0.03233525529503822,
-0.008267228491604328,
0.035586096346378326,
-0.017459670081734657,
0.036533985286951065,
-0.02339356206357479,
0.013537459075450897,
-0.044877082109451294,
0.02546827308833599,
-0.057630591094493866,
-0.014477173797786236,
-0.009813555516302586,
0.0006074440898373723,
-0.06721417605876923,
0.038729071617126465,
-0.02055736444890499,
-0.007137511856853962,
-0.009338180534541607,
-0.0027213459834456444,
-0.03287443891167641,
-0.03896891325712204,
-0.006157662719488144,
-0.028643107041716576,
0.022735750302672386,
-0.01224630605429411,
-0.026835691183805466,
0.020517507568001747,
-0.026788856834173203,
-0.0364261195063591,
0.05169961601495743,
-0.041166532784700394,
0.026783466339111328,
0.038499053567647934,
-0.04831415042281151,
-0.023419354110956192,
0.11371050029993057,
-0.053237367421388626,
-0.02744753286242485,
-0.01685674674808979,
-0.013535422272980213,
-0.0269340667873621,
0.00568234920501709,
0.008060836233198643,
-0.015621407888829708,
-0.02268492430448532,
0.0436171256005764,
0.02443605847656727,
0.00936186034232378,
0.008631400763988495,
-0.021182583644986153,
-0.004552632104605436,
-0.008688532747328281,
0.00907121691852808,
-0.009774630889296532,
-0.014694251120090485,
0.04373231157660484,
-0.04339655116200447,
0.018925199285149574,
-0.0003360183327458799,
0.008483669720590115,
-0.09137388318777084,
-0.012315090745687485,
-0.026301803067326546,
0.018651707097887993,
0.06412316113710403,
-0.05755280703306198,
0.02014242857694626,
0.025777971372008324,
-0.07060305029153824,
-0.0036863689310848713,
-0.043955978006124496,
-0.030244601890444756,
-0.03966924920678139,
0.01395509298890829,
0.019892480224370956,
0.010019547306001186,
-0.0015010022325441241,
0.013457017950713634,
0.008865049108862877,
0.031155414879322052,
-0.03417882323265076,
-0.027610566467046738,
0.02656504325568676,
0.04058803245425224,
-0.008657053112983704,
-0.007414953783154488,
0.08868663012981415,
-0.030404914170503616,
-0.012409123592078686,
0.040031321346759796,
0.03866772726178169,
0.02142040617763996,
-0.004401647485792637,
0.027094190940260887,
-0.03938939422369003,
0.03608785942196846,
0.0017346207750961185,
-0.023464951664209366,
-0.026248104870319366,
0.038405321538448334,
0.026020754128694534,
0.008373630233108997,
-0.011071575805544853,
0.010408230125904083,
0.027193333953619003,
-0.0221569687128067,
-0.005926790181547403,
-0.007664460223168135,
-0.014679092913866043,
-0.003881217213347554,
0.035656463354825974,
-0.00276236142963171,
0.019115429371595383,
-0.023339319974184036,
0.01501897070556879,
-0.04822525382041931,
0.0024080085568130016,
0.045500386506319046,
-0.019119156524538994,
0.005265405867248774,
0.011709146201610565,
-0.009099846705794334,
0.010830776765942574,
0.0020904606208205223,
-0.009901599958539009,
-0.03687009960412979,
-0.03609659895300865,
-0.009049921296536922,
-0.034716714173555374,
0.0149479815736413,
-0.007655768189579248,
-0.061941780149936676,
-0.04636266455054283,
0.04505605250597,
0.009793032892048359,
0.005467304494231939,
0.029783401638269424,
-0.03622293099761009,
0.017753729596734047,
-0.08322136849164963,
0.006273571867495775,
0.03134966269135475,
0.020240865647792816,
-0.04545648396015167,
-0.039307013154029846,
0.045539069920778275,
0.014781195670366287,
0.024866890162229538,
-0.013172594830393791,
0.003806352848187089,
0.04267944395542145,
-0.03919927403330803,
-0.029048806056380272,
-0.04367649927735329,
0.06837975233793259,
-0.017190340906381607,
-0.021060699597001076,
-0.009624676778912544,
0.0001149654490291141,
0.032775215804576874,
-0.03390822187066078,
0.046999357640743256,
-0.0014933127677068114,
0.0007537819328717887,
0.01922634430229664,
-0.008992516435682774,
0.024450484663248062,
0.029433703050017357,
0.02140108123421669,
0.08324131369590759,
0.01470591314136982,
0.041854094713926315,
0.04907572269439697,
-0.013313804753124714,
-0.011075043119490147,
0.04645543545484543,
-0.0057944972068071365,
-0.020743992179632187,
-0.006792659405618906,
0.0019708515610545874,
0.017111634835600853,
-0.04539044573903084,
0.013962662778794765,
0.024232953786849976,
0.0045965430326759815,
-0.010122972540557384,
0.014090036042034626,
0.039844810962677,
0.0381198413670063,
0.025272423401474953,
-0.0006050461670383811,
0.03548811003565788,
-0.024961121380329132,
-0.0024307456333190203,
-0.002928344998508692,
0.0361359529197216,
0.0020467934664338827,
0.0023358871694654226,
0.03923841938376427,
0.035721633583307266,
0.028531944379210472,
0.03918209299445152,
0.020287098363041878,
-0.024630853906273842,
-0.001465284964069724,
0.004289684351533651,
-0.009288967587053776,
-0.0313209593296051,
0.046956319361925125,
-0.019141582772135735,
0.06657487154006958,
0.009554347954690456,
-0.0020703133195638657,
0.00009975658031180501,
0.030104773119091988,
0.017554856836795807,
0.014669248834252357,
-0.013816865161061287,
0.019525326788425446,
-0.02461014874279499,
-0.010613922029733658,
0.0008178707794286311,
0.03875302895903587,
0.021693609654903412,
-0.013147324323654175,
0.017863430082798004,
0.025114944204688072,
0.019818486645817757,
-0.02238711342215538,
-0.05321087688207626,
-0.03359439596533775,
-0.01621146686375141,
0.04523357003927231,
0.015596590004861355,
-0.007024343125522137,
-0.01744118705391884,
-0.018517768010497093,
-0.0614396333694458,
0.05744529888033867,
-0.045017559081315994,
-0.03400769084692001,
-0.009180577471852303,
0.05406690761446953,
-0.037243060767650604,
-0.008373860269784927
] |
<p>Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that I am serious.</p>
<p>How do Vectors transform from one inertial reference frame to another inertial reference frame in [special relativity].</p>
<p>A bound vector in an inertial reference frame ($x$,$ct$) has its line of action as one of the space axis in that frame and is described by $x$*<em>i</em>*,then what would it be in form of new base vectors (<strong>a</strong>) and (<strong>b</strong>) in a different inertial system ($x`$,$ct`$) moving with respect to the former inertial system with $v$*<em>i</em>* velocity.Let (<strong>i</strong>) and (<strong>j</strong>) be the two bounded unit vectors with the line of action as co-ordinate axis($x$) and($ct$) respectively and senses in the positive side of co-ordinates and similarly (<strong>a</strong>) and (<strong>b</strong>) are defined for co-ordinates ($x`$) and ($ct`$) respectively.</p>
| 7,676 |
[
0.013314851559698582,
-0.029336798936128616,
0.011259033344686031,
-0.0014313788851723075,
0.03725067153573036,
0.02998100034892559,
-0.02145688235759735,
-0.03977552428841591,
0.01907223090529442,
-0.031494852155447006,
0.051551446318626404,
0.031317006796598434,
0.11347493529319763,
0.050731830298900604,
0.028280146420001984,
0.005815344396978617,
-0.015199756249785423,
-0.004870738368481398,
-0.03805568441748619,
-0.029072236269712448,
0.03053472191095352,
-0.013121256604790688,
0.03216329962015152,
0.02777993679046631,
-0.014260279946029186,
0.03471522405743599,
0.02055208757519722,
-0.03485271707177162,
0.027684366330504417,
0.06618820130825043,
-0.017607472836971283,
-0.017586112022399902,
-0.015999842435121536,
0.003255431307479739,
-0.0021798303350806236,
0.005540693178772926,
-0.023740530014038086,
-0.03174580633640289,
0.008945956826210022,
-0.0030483996961265802,
-0.08192115277051926,
-0.018345575779676437,
-0.020221127197146416,
0.09707965701818466,
-0.005122662056237459,
0.02774304710328579,
0.015194463543593884,
0.014881010167300701,
0.02157454751431942,
-0.04589027538895607,
0.10393571108579636,
0.002427789382636547,
0.029533246532082558,
0.021596752107143402,
-0.009681609459221363,
0.0015076969284564257,
0.06415656954050064,
0.044036660343408585,
-0.006318101193755865,
-0.04020778834819794,
0.022702207788825035,
-0.027788590639829636,
-0.019802968949079514,
-0.0080460449680686,
-0.008542380295693874,
0.01293084304779768,
-0.01997382566332817,
-0.011493789963424206,
-0.001062192372046411,
-0.054086167365312576,
0.035462286323308945,
0.009557302109897137,
-0.013536837883293629,
-0.08124316483736038,
0.012578634545207024,
-0.04375915974378586,
0.027988066896796227,
0.0043304692953825,
0.02783621847629547,
0.051711197942495346,
-0.003361993934959173,
0.011731695383787155,
0.04595690593123436,
0.00046249994193203747,
0.0016973543679341674,
-0.027425240725278854,
0.04347444698214531,
-0.009767378680408001,
0.015102187171578407,
0.014366996474564075,
0.027023598551750183,
-0.0085816141217947,
0.02045394293963909,
-0.019038720056414604,
-0.03474274277687073,
0.04080069810152054,
0.0017039850354194641,
0.03608235716819763,
0.007384459022432566,
-0.018992459401488304,
0.014658670872449875,
-0.01893826760351658,
0.014175012707710266,
0.05706819146871567,
0.029978949576616287,
0.03198728337883949,
-0.016523946076631546,
-0.000021722400560975075,
-0.03518145903944969,
-0.030850188806653023,
-0.0312713086605072,
0.021407168358564377,
-0.02769092097878456,
0.034361742436885834,
-0.0020455007907003164,
-0.04403849318623543,
0.01634700782597065,
-0.01712219975888729,
0.03822022303938866,
0.05651357024908066,
0.07118289172649384,
0.001497517223469913,
0.009794876910746098,
0.01343293022364378,
-0.07320760190486908,
-0.00641757482662797,
-0.009955564513802528,
0.025984007865190506,
-0.046265486627817154,
0.016852915287017822,
0.002560991095378995,
-0.009684470482170582,
-0.015462170355021954,
0.04634961485862732,
0.013219009153544903,
-0.021965859457850456,
-0.10742048919200897,
-0.05920156091451645,
0.04508569836616516,
0.006167616695165634,
-0.0037056575529277325,
-0.0880780965089798,
0.028548650443553925,
0.011565183289349079,
0.07228207588195801,
0.0245741568505764,
0.03641320765018463,
0.00953881535679102,
0.028874749317765236,
0.02658371441066265,
-0.001342912670224905,
0.014684121124446392,
-0.05049764737486839,
-0.05701810494065285,
0.0029877913184463978,
-0.08145666867494583,
0.018798479810357094,
0.004948242101818323,
-0.008301260881125927,
-0.0235816091299057,
0.07633460313081741,
-0.018244879320263863,
-0.00036032911157235503,
0.0077300164848566055,
0.015327402390539646,
-0.016404936090111732,
0.03703238442540169,
0.015607624314725399,
-0.021120170131325722,
0.051042553037405014,
0.017889095470309258,
0.05303917080163956,
-0.02793293073773384,
0.035437148064374924,
0.030237913131713867,
-0.0188610777258873,
-0.012285375036299229,
0.01633310690522194,
-0.014177843928337097,
-0.007463221903890371,
-0.03140148147940636,
-0.05225396901369095,
-0.02370651252567768,
-0.022681407630443573,
-0.002451303182169795,
0.05968168005347252,
0.008492675609886646,
-0.007414277642965317,
-0.01605924963951111,
-0.04604484513401985,
0.01940073072910309,
-0.07210380584001541,
0.0065963189117610455,
-0.009814071469008923,
-0.031183620914816856,
0.04567072167992592,
-0.003128286451101303,
0.041645679622888565,
-0.028523458167910576,
-0.0029278898146003485,
-0.03144891560077667,
0.008296067826449871,
0.006338673178106546,
-0.012558226473629475,
0.019981300458312035,
0.058876968920230865,
0.030641263350844383,
0.012736067175865173,
0.004036205820739269,
0.010509097948670387,
0.012726525776088238,
0.025238683447241783,
-0.017395472154021263,
0.017798254266381264,
0.028445249423384666,
-0.0038960797246545553,
-0.010154598392546177,
0.035179466009140015,
0.012526743113994598,
0.03356420248746872,
-0.030082393437623978,
0.05299665778875351,
0.05446550250053406,
0.00894027017056942,
0.009662582539021969,
0.0655287355184555,
0.0016269572079181671,
0.04010936990380287,
0.019735833629965782,
-0.05806998163461685,
-0.030160492286086082,
0.009096462279558182,
0.020122861489653587,
0.01757819764316082,
-0.03845443204045296,
0.024794956669211388,
0.030778126791119576,
0.009128784760832787,
0.02140948735177517,
0.0347815603017807,
-0.0028461136389523745,
-0.057167746126651764,
0.005878695752471685,
-0.015685677528381348,
0.012218713760375977,
0.011790960095822811,
-0.02663901261985302,
0.018787045031785965,
0.02190515026450157,
0.013812188059091568,
-0.029609259217977524,
0.03878349810838699,
-0.012378282845020294,
-0.011143602430820465,
0.0009274689364247024,
-0.008975782431662083,
0.050793830305337906,
-0.008126603439450264,
0.04491187259554863,
0.03416803851723671,
0.00833924300968647,
-0.01635521836578846,
0.004873995669186115,
0.025978663936257362,
-0.0031903355848044157,
0.023540325462818146,
0.025904957205057144,
-0.008822932839393616,
0.00536801852285862,
-0.06903589516878128,
0.006047625560313463,
-0.01104023214429617,
-0.02349119260907173,
-0.013895262032747269,
0.0076580229215323925,
0.018456798046827316,
0.026635631918907166,
0.0016982225934043527,
-0.031614501029253006,
-0.006243371870368719,
-0.006528280675411224,
-0.02612515725195408,
0.034137219190597534,
0.0047422172501683235,
-0.014216688461601734,
0.02534394897520542,
-0.07260619848966599,
-0.05066811293363571,
0.04722873494029045,
-0.029952943325042725,
0.01430013868957758,
0.039230603724718094,
-0.029852386564016342,
-0.08410374075174332,
-0.0377717949450016,
-0.03552484139800072,
-0.0071952566504478455,
-0.0057915085926651955,
-0.005060713272541761,
0.09546966105699539,
-0.0037133495789021254,
-0.05075804516673088,
-0.011695362627506256,
-0.037412602454423904,
-0.053022321313619614,
-0.03202711045742035,
0.0077479127794504166,
0.009340954013168812,
-0.015626210719347,
0.030756931751966476,
0.03761686757206917,
0.012028573080897331,
-0.0185141209512949,
-0.05078870430588722,
-0.009008599445223808,
0.011736378073692322,
0.010867763310670853,
0.03732002153992653,
0.03434588015079498,
-0.004351229406893253,
0.08548353612422943,
0.011658559553325176,
-0.05109492689371109,
-0.055654335767030716,
0.011627105996012688,
-0.015636591240763664,
0.003173300065100193,
-0.0036463309079408646,
0.0191325806081295,
-0.0007457052124664187,
0.032534122467041016,
0.05707162618637085,
0.01239354070276022,
0.038496509194374084,
-0.00203275540843606,
-0.03118630312383175,
0.005809873808175325,
0.008335656486451626,
-0.008933871984481812,
0.02547905221581459,
0.01903463900089264,
-0.006127377040684223,
-0.018710408359766006,
-0.010533406399190426,
0.026448292657732964,
0.027815960347652435,
-0.05307997390627861,
0.001144368783570826,
0.0034944156650453806,
-0.015227364376187325,
-0.004486207850277424,
0.03285469859838486,
-0.005403537303209305,
0.0012477237032726407,
-0.004049157723784447,
0.01904555968940258,
0.017621442675590515,
-0.04211694002151489,
-0.001233816845342517,
0.01391957700252533,
0.029819462448358536,
-0.03928081691265106,
-0.021501751616597176,
-0.0038089826703071594,
0.007994798943400383,
0.01613803580403328,
-0.04689019173383713,
-0.01760905794799328,
0.03827280551195145,
0.04922383651137352,
0.007419387809932232,
0.044626329094171524,
-0.019482756033539772,
0.026642482727766037,
-0.03959006816148758,
-0.015958338975906372,
0.040586456656455994,
0.034697964787483215,
-0.005975589621812105,
0.033658403903245926,
0.030414270237088203,
0.0008745919330976903,
0.0012286501005291939,
-0.010347475297749043,
-0.06889431923627853,
0.03729072958230972,
-0.0010027071693912148,
-0.026249675080180168,
0.009780916385352612,
-0.003115534083917737,
-0.015225635841488838,
-0.04086758568882942,
-0.02882579155266285,
-0.006579796317964792,
-0.013715418986976147,
-0.07003051042556763,
0.01826542615890503,
-0.03250962495803833,
-0.049909550696611404,
-0.0316888652741909,
0.04355413839221001,
0.06427476555109024,
-0.05039919540286064,
0.0325249582529068,
0.04697854071855545,
-0.0459638312458992,
0.0007588927983306348,
-0.006908260751515627,
-0.013275709934532642,
0.038623128086328506,
0.0017139959381893277,
0.0035899251233786345,
0.009529601782560349,
0.013169492594897747,
0.03257765620946884,
-0.0003114936116617173,
0.04159139469265938,
0.02078658901154995,
-0.03006991744041443,
-0.016962137073278427,
-0.0658264309167862,
-0.010886517353355885,
0.004325406160205603,
0.05980094149708748,
0.03061494417488575,
-0.013120414689183235,
0.03927439823746681,
0.02775370143353939,
-0.003023993456736207,
0.060503099113702774,
0.07742396742105484,
0.028145652264356613,
-0.014032699167728424,
-0.04097095876932144,
-0.015810757875442505,
0.004865522496402264,
-0.024509787559509277,
0.037693120539188385,
-0.031819600611925125,
-0.018040206283330917,
-0.026586508378386497,
0.04043363034725189,
0.04085806384682655,
-0.031967438757419586,
0.026080409064888954,
-0.023484818637371063,
0.003971832804381847,
0.017236998304724693,
0.01521273422986269,
-0.043893810361623764,
0.008839242160320282,
0.07136932015419006,
-0.03705694153904915,
0.020751822739839554,
-0.06670408695936203,
-0.012294944375753403,
0.028604019433259964,
0.036796506494283676,
0.025173263624310493,
-0.01735091581940651,
-0.029214957728981972,
-0.016530867666006088,
0.060617830604314804,
-0.043287985026836395,
0.027770426124334335,
-0.007757064886391163,
-0.006472375243902206,
-0.03153199329972267,
-0.033362727612257004,
-0.03584615886211395,
0.004178453236818314,
-0.012095622718334198,
0.04635179415345192,
0.006896087899804115,
0.029228463768959045,
0.00035779233439825475,
-0.014025620184838772,
0.022917484864592552,
0.01423647440969944,
0.022066425532102585,
-0.020629817619919777,
0.0004424669314175844,
0.024795962497591972,
-0.02444128505885601,
-0.048762306571006775,
-0.008311164565384388,
0.046142466366291046,
-0.017331628128886223,
0.057229481637477875,
-0.026247618719935417,
-0.0345180407166481,
0.024927843362092972,
0.001528624095954001,
0.010831627063453197,
0.012147431261837482,
-0.04490681365132332,
0.037422001361846924,
-0.017825933173298836,
-0.012419871054589748,
0.026857681572437286,
-0.0019302874570712447,
-0.017528431490063667,
0.0026469193398952484,
-0.007623530924320221,
0.017567776143550873,
-0.016464922577142715,
-0.020911356434226036,
-0.04309909790754318,
0.01077685784548521,
-0.020989537239074707,
0.1001218780875206,
-0.005514251533895731,
-0.018734171986579895,
-0.040002159774303436,
0.0013685268349945545,
0.001402350957505405,
0.05575134605169296,
-0.013037487864494324,
0.013552239164710045,
-0.024680186063051224,
0.0425383560359478,
-0.017942165955901146,
-0.04234248772263527,
0.011272745206952095,
-0.023314835503697395,
0.0002512198989279568,
0.024565190076828003,
-0.023418234661221504,
0.024872763082385063,
0.002246721414849162,
0.004677504766732454,
0.013328771106898785,
-0.07040874660015106,
0.032236941158771515,
0.008385474793612957,
-0.0057056620717048645,
0.04359181597828865,
-0.04052570089697838,
-0.04934195429086685,
0.018926952034235,
-0.02399497479200363,
-0.016742637380957603,
-0.048030953854322433,
0.014888145960867405,
0.03299229219555855,
0.013682962395250797,
-0.06627502292394638,
-0.05738886818289757,
0.0313248373568058,
-0.02413112111389637,
-0.024381903931498528,
-0.0454082190990448,
0.010477203875780106,
-0.025941280648112297,
-0.012652517296373844,
-0.0799349769949913,
0.051395878195762634,
-0.04094122350215912,
-0.01949312724173069,
0.026058560237288475,
0.010389845818281174,
0.03162722662091255,
-0.022910842671990395,
0.003926411736756563,
0.009792409837245941,
0.022878076881170273,
0.012378278188407421,
0.005606797523796558,
0.025250466540455818,
-0.0066726431250572205,
-0.05126721039414406,
-0.021345632150769234,
0.00905841775238514,
-0.005833867006003857,
-0.017807932570576668,
-0.00023508134472649544,
0.01810384914278984,
-0.008456901647150517,
-0.020770015195012093,
-0.023350004106760025,
-0.021259309723973274,
0.011368900537490845,
0.006936301942914724,
-0.010555870831012726,
0.014222146943211555,
-0.004655290395021439,
-0.020508749410510063,
0.014522356912493706,
0.01061429176479578,
0.00832196045666933,
-0.0003765499568544328,
0.027612604200839996,
-0.031968388706445694,
0.04763796553015709,
0.028765935450792313,
0.00905461423099041,
0.04465923085808754,
-0.0011004921980202198,
-0.0031634545885026455,
0.03352362662553787,
-0.03196551650762558,
-0.031145941466093063,
-0.01585041917860508,
-0.054185427725315094,
0.027005501091480255,
0.057478103786706924,
-0.019526470452547073,
0.019913583993911743,
0.031894750893116,
0.0016779279103502631,
0.010582194663584232,
0.012894642539322376,
-0.019444826990365982,
-0.026445884257555008,
-0.014120538718998432,
0.0004732088418677449,
-0.027450883761048317,
-0.029447410255670547,
0.02372520975768566,
0.03383556008338928,
-0.03579387441277504,
-0.004915547091513872,
-0.004614683799445629,
0.018546462059020996,
-0.016414133831858635,
0.03442453220486641,
-0.029450029134750366,
0.01871628500521183,
-0.0044231293722987175,
0.014545661397278309,
0.006274485029280186,
-0.014349939301609993,
0.024344325065612793,
0.0199754536151886,
0.02220511995255947,
-0.05341370403766632,
-0.030055591836571693,
-0.07161901891231537,
0.013995866291224957,
0.021299779415130615,
-0.0009408054174855351,
-0.02792757749557495,
0.019396940246224403,
0.0656357929110527,
-0.01888473518192768,
-0.010143894702196121,
-0.035195242613554,
-0.04891258478164673,
-0.025930659845471382,
-0.05859346315264702,
-0.044667523354291916,
0.06234627589583397,
-0.01744958944618702,
0.002215777523815632,
0.006144887302070856,
-0.012989643961191177,
0.02088136412203312,
-0.0022564923856407404,
0.040344953536987305,
0.0032548534218221903,
0.1007426381111145,
0.000627101631835103,
-0.004862926434725523,
0.014263532124459743,
-0.0058006164617836475,
0.11513793468475342,
0.0456223301589489,
-0.0029722857289016247,
-0.0824355036020279,
0.02128004841506481,
-0.00695867370814085,
0.002000560751184821,
-0.0367259755730629,
0.037952035665512085,
0.016316473484039307,
0.028894813731312752,
0.004032490309327841,
0.03661055862903595,
-0.0025559093337506056,
-0.017182834446430206,
0.0325465127825737,
-0.052197568118572235,
-0.05682782456278801,
-0.009300912730395794,
0.02558831125497818,
-0.024192681536078453,
-0.0040337503887712955,
-0.01645103096961975,
0.0031738136895000935,
0.0024813255295157433,
0.021693162620067596,
-0.03435094282031059,
-0.025017287582159042,
0.035616811364889145,
-0.003277577692642808,
-0.053429022431373596,
0.024953782558441162,
0.03856722638010979,
-0.005159109365195036,
-0.021117916330695152,
-0.0008504136349074543,
0.005850557703524828,
-0.017076630145311356,
0.04093485325574875,
0.011236985214054585,
0.012943797744810581,
0.004854124970734119,
0.055317044258117676,
0.012391844764351845,
-0.0292928796261549,
-0.00357980839908123,
-0.04500691592693329,
0.0522141270339489,
-0.033980462700128555,
0.00573574285954237,
-0.0027613842394202948,
0.03364603593945503,
0.012518809176981449,
-0.07403586804866791,
-0.006215854547917843,
-0.01985963061451912,
0.026829343289136887,
-0.007278453093022108,
0.00998615100979805,
-0.02996833249926567,
0.011077041737735271,
-0.009494516998529434,
0.02119503915309906,
-0.012736703269183636,
-0.011666139587759972,
0.01905391551554203,
-0.014426746405661106,
0.05294305831193924,
-0.014129995368421078,
0.02556728571653366,
-0.03832933306694031,
0.026330411434173584,
-0.010735291056334972,
-0.011855220422148705,
0.023970449343323708,
0.014295288361608982,
-0.002888444112613797,
-0.0030794579070061445,
0.010291045531630516,
0.01506835874170065,
-0.06480661034584045,
0.0149083798751235,
-0.013605918735265732,
-0.012638348154723644,
0.0013770131627097726,
0.015065951272845268,
0.025669241324067116,
0.054196931421756744,
-0.000488841556943953,
0.0269627645611763,
0.0010775172850117087,
0.016001084819436073,
0.02355055883526802,
-0.029805509373545647,
-0.024521417915821075,
0.021314125508069992,
-0.02986156940460205,
-0.03900871425867081,
-0.030628137290477753,
0.04731690138578415,
0.03770531713962555,
0.032406505197286606,
0.0008886402938514948,
0.025716399773955345,
-0.003962247166782618,
-0.029666317626833916,
0.026799779385328293,
-0.03320348262786865,
0.0442582406103611,
0.0397009514272213,
0.016545649617910385,
-0.044819850474596024,
0.012868423946201801,
-0.015698358416557312,
-0.013162768445909023,
0.02097717672586441,
0.009961975738406181,
-0.014090290293097496,
0.009814959950745106,
-0.04565463215112686,
-0.0019376121927052736,
-0.009777883067727089,
0.021454568952322006,
-0.025426428765058517,
0.0444193072617054,
-0.001957677071914077,
-0.01602712832391262,
-0.04765869304537773,
0.028015434741973877,
-0.025463150814175606,
-0.022243279963731766,
0.011917827650904655,
0.035533610731363297,
-0.03358234837651253,
-0.014300907030701637,
-0.018514001742005348,
0.008052663877606392,
0.033725541085004807,
-0.011828368529677391,
-0.05071474611759186,
0.0006137596792541444,
-0.005835637450218201,
0.002905230037868023,
0.05056069418787956,
0.0052088904194533825,
0.01428905874490738,
0.026315536350011826,
-0.019168540835380554,
-0.02162698283791542,
0.06628511101007462,
-0.003942470066249371,
-0.008176833391189575,
0.0005795686738565564,
-0.044326238334178925,
-0.0032745199277997017,
-0.0005770772695541382,
0.03475506603717804,
-0.0011953491484746337,
-0.01567748747766018,
0.02122434601187706,
0.06008122116327286,
-0.01301649957895279,
0.011036556214094162,
-0.0017196416156366467,
0.0060728550888597965,
0.01985093019902706,
0.0014985543675720692,
-0.008488878607749939,
0.03621114417910576,
0.04567515477538109,
-0.03630826622247696,
0.010301534086465836,
0.0063509042374789715,
0.03699473664164543,
-0.10002748668193817,
0.0028922369237989187,
0.020643509924411774,
0.0048470827750861645,
0.03499796614050865,
-0.06145881116390228,
0.0016386797651648521,
0.04250924661755562,
-0.053577542304992676,
-0.023055190220475197,
-0.023219052702188492,
-0.01967647857964039,
-0.0023515215143561363,
-0.005486074835062027,
-0.001972612924873829,
0.05602582171559334,
0.034773822873830795,
0.019270112738013268,
0.015188092365860939,
0.03373076021671295,
-0.01648864708840847,
-0.05870579555630684,
-0.023887814953923225,
0.002538532018661499,
-0.01894037239253521,
-0.027937026694417,
0.0562509149312973,
0.01444885041564703,
-0.04558533430099487,
0.037784356623888016,
-0.008583921939134598,
0.008600827306509018,
0.023962879553437233,
0.00720604183152318,
0.01365753822028637,
0.023893630132079124,
0.02687912806868553,
-0.015378878451883793,
0.003316944930702448,
-0.009028336964547634,
0.01010805182158947,
-0.004979579709470272,
0.0035324988421052694,
-0.01800764538347721,
0.021478086709976196,
-0.07031247764825821,
-0.002527519827708602,
0.03237641975283623,
-0.02937757968902588,
-0.010483726859092712,
-0.017131604254245758,
0.021715756505727768,
0.03876124322414398,
-0.03869466856122017,
-0.007018250413239002,
-0.04406758025288582,
-0.008709264919161797,
0.038031723350286484,
-0.04126370698213577,
-0.0025475765578448772,
-0.002952882554382086,
-0.031167712062597275,
-0.029609370976686478,
0.01631476916372776,
-0.009282508864998817,
0.0041449107229709625,
-0.053605251014232635,
-0.01319370698183775,
0.006808554287999868,
-0.006196265108883381,
-0.049888353794813156,
-0.018933085724711418,
-0.05803925171494484,
0.043884579092264175,
0.018771324306726456,
0.025437047705054283,
-0.015892161056399345,
0.013066284358501434,
-0.01344407256692648,
-0.024448212236166,
0.0025065636727958918,
0.031090062111616135,
-0.060666635632514954,
-0.046895742416381836,
-0.029941903427243233,
-0.014873976819217205,
0.05127999931573868,
0.04377570375800133,
0.022793982177972794,
-0.019333841279149055,
0.015729643404483795,
0.0053072841838002205,
0.02865748293697834,
-0.06508161127567291,
-0.0038215378299355507,
-0.005802054423838854,
-0.05056220665574074,
0.03670512139797211,
-0.013373822905123234,
-0.04590333253145218,
-0.007862895727157593,
0.0017955806106328964,
-0.027485782280564308,
0.07180067896842957,
0.009509319439530373,
-0.043811045587062836,
-0.021484926342964172,
0.012031950987875462,
-0.014102139510214329,
0.0699886679649353,
0.03820112720131874,
0.006696086376905441,
0.047657594084739685,
-0.02481754869222641,
-0.022508345544338226,
0.016888335347175598,
-0.04195284843444824,
-0.013127959333360195,
-0.0010988578433170915,
-0.020366523414850235,
-0.00022536888718605042,
-0.0695488452911377,
0.005187125410884619,
0.0679473727941513,
-0.0226226095110178,
-0.007447532843798399,
0.07010306417942047,
0.04312370717525482,
0.0021182962227612734,
0.00020035631314385682,
0.012668758630752563,
0.0026520704850554466,
-0.0065424456261098385,
0.03796004503965378,
0.01191898062825203,
0.024792373180389404,
-0.012043016031384468,
-0.01325247809290886,
0.010652239434421062,
-0.028664235025644302,
0.032332293689250946,
-0.02097228541970253,
0.03270786628127098,
-0.004127795808017254,
0.025641819462180138,
-0.006956249941140413,
-0.051624611020088196,
0.016341015696525574,
0.01397229265421629,
-0.04101045802235603,
0.05923619121313095,
-0.07563575357198715,
0.011259019374847412,
-0.01980835199356079,
0.017670508474111557,
-0.021085817366838455,
0.014086470007896423,
0.010082262568175793,
0.018382640555500984,
0.01237410493195057,
-0.007829198613762856,
-0.008840788155794144,
-0.04994944483041763,
0.015702536329627037,
-0.04033339023590088,
-0.007425469812005758,
0.015709446743130684,
0.00016184734704438597,
0.00899282656610012,
-0.00543554313480854,
-0.013410038314759731,
-0.002659628866240382,
0.010821884498000145,
0.028622901067137718,
0.045196425169706345,
-0.03132466971874237,
-0.011457061395049095,
-0.03915324807167053,
0.027044931426644325,
-0.06485744565725327,
-0.023869939148426056,
-0.011374454945325851,
-0.007846737280488014,
-0.01154001709073782,
-0.008958878926932812
] |
<p>What common household liquids / foodstuffs show Herschel-Bulkley fluid behavior?
I assume tomato soup to be one, since when sloshing it around lightly on a spoon the visible surface moves as one (as can be seen by following the dots of black pepper that don't change relative position) - is this observation basically correct?</p>
<p>What are (other) easy and sure ways to identify yield-stress behavior (vs. other non-Newton flows)?</p>
<p>How can common states of flow (through a pipe/ open channel, discharge from a small source into a large standing volume of the fluid, mixing) be observed - not necessarily quantitatively?</p>
<p>Are there easy to produce transparent yield stress fluids?</p>
| 7,677 |
[
-0.016819193959236145,
-0.011092768050730228,
0.015387214720249176,
-0.023774806410074234,
0.017456084489822388,
-0.017014646902680397,
0.012186289764940739,
0.009371262975037098,
-0.00608500512316823,
-0.01628575287759304,
0.0336834080517292,
0.022043991833925247,
0.04096439108252525,
-0.005916104651987553,
-0.002889438532292843,
-0.012247598730027676,
0.01192997582256794,
-0.00612238934263587,
0.007312095258384943,
-0.01251919288188219,
-0.004031052812933922,
-0.03112095780670643,
0.012280951254069805,
0.015184729360044003,
0.0007670237682759762,
0.02136032097041607,
0.025698089972138405,
-0.03487847000360489,
0.035038501024246216,
0.021409744396805763,
-0.03041929192841053,
-0.03494371846318245,
-0.03365208953619003,
0.012747145257890224,
0.030532589182257652,
0.014507045969367027,
-0.059342943131923676,
-0.044767219573259354,
0.0020805546082556248,
0.015223783440887928,
-0.07250159233808517,
0.0013725158059969544,
0.02112991362810135,
0.03637314960360527,
-0.024280289188027382,
-0.006855800282210112,
0.009352460503578186,
-0.026931030675768852,
0.06300844252109528,
-0.06956233829259872,
0.022920655086636543,
0.019144851714372635,
0.04236777126789093,
0.05791646987199783,
0.027506401762366295,
-0.00019883696222677827,
0.04473715275526047,
0.05186774209141731,
-0.010876329615712166,
-0.06813991069793701,
0.026039019227027893,
0.02648179419338703,
-0.03966468200087547,
-0.021228181198239326,
-0.047867678105831146,
0.012838330119848251,
-0.033276237547397614,
-0.044320859014987946,
0.019287144765257835,
-0.023496096953749657,
0.0008596302359364927,
-0.01411549560725689,
0.054831065237522125,
-0.003951653838157654,
-0.009279764257371426,
-0.02089490182697773,
0.004114419221878052,
0.007892562076449394,
-0.0066794753074646,
0.044243223965168,
-0.01269735861569643,
-0.0009030315559357405,
-0.011675490066409111,
0.05306500196456909,
0.004838367458432913,
-0.022449346259236336,
0.08945091813802719,
-0.02037723921239376,
0.024547386914491653,
0.03953440859913826,
0.012374982237815857,
-0.0025661024264991283,
0.024000776931643486,
0.003572032554075122,
-0.0027875821106135845,
-0.03565444052219391,
-0.01202327199280262,
0.02254435420036316,
-0.0029144994914531708,
-0.0056620691902935505,
-0.015519651584327221,
-0.01608983241021633,
0.014474418014287949,
0.11431746184825897,
-0.026071032509207726,
-0.030186153948307037,
-0.014745024032890797,
-0.026826364919543266,
-0.010944667272269726,
0.006522757932543755,
-0.027369806542992592,
-0.049321498721838,
0.023145170882344246,
0.01225909311324358,
-0.020027238875627518,
-0.02850516326725483,
-0.008551862090826035,
0.013636232353746891,
0.04324857518076897,
0.08759855479001999,
0.04828643798828125,
-0.02168193832039833,
0.024889590218663216,
-0.05277480557560921,
-0.08379000425338745,
0.04082322120666504,
0.0032112787012010813,
-0.04405971243977547,
-0.05159349739551544,
0.016390632838010788,
0.0005501027917489409,
-0.0036934560630470514,
-0.033950332552194595,
-0.02387084811925888,
0.05354989320039749,
0.014538135379552841,
-0.08362516760826111,
-0.0758509486913681,
0.08881691843271255,
-0.0030329462606459856,
-0.021209590137004852,
-0.05764162167906761,
0.03319960832595825,
0.03744617849588394,
0.05107732117176056,
-0.028864959254860878,
-0.025663981214165688,
0.0135767487809062,
0.06600877642631531,
-0.0018592767883092165,
-0.040560413151979446,
0.04238613322377205,
0.01801016554236412,
-0.029891280457377434,
-0.002461860189214349,
-0.05373823642730713,
0.032346297055482864,
0.02813553623855114,
0.015081892721354961,
-0.07093217968940735,
0.0835750475525856,
-0.015178710222244263,
0.012364479713141918,
0.014645252376794815,
0.009234558790922165,
-0.036350853741168976,
0.09778903424739838,
0.0027482379227876663,
0.01478204969316721,
0.0030695851892232895,
0.005440867505967617,
-0.002642453648149967,
0.014886816032230854,
0.003729411866515875,
0.028988927602767944,
-0.02635038271546364,
-0.0026930749882012606,
0.02519889920949936,
-0.017299214377999306,
0.008340447209775448,
-0.018454628065228462,
-0.005992935970425606,
-0.03132014721632004,
-0.0106075219810009,
0.02371913753449917,
-0.0009071322274394333,
-0.013960094191133976,
-0.026632212102413177,
0.028849394991993904,
-0.08753277361392975,
-0.0018202356295660138,
-0.022432781755924225,
0.016268184408545494,
-0.02598951943218708,
0.007008547428995371,
0.03353608399629593,
-0.046606265008449554,
0.0035909065045416355,
-0.009528513997793198,
-0.011863674968481064,
0.011676246300339699,
0.008521868847310543,
-0.003118668682873249,
-0.018838653340935707,
-0.013755271211266518,
-0.004180406220257282,
0.0026527123991400003,
-0.017805492505431175,
-0.021993428468704224,
-0.019939186051487923,
-0.05226415395736694,
0.014518857933580875,
-0.03619629517197609,
0.04436309263110161,
-0.05347384884953499,
-0.012966843321919441,
-0.008862141519784927,
0.010825985111296177,
0.01683732122182846,
0.038445018231868744,
-0.040566541254520416,
0.06647618114948273,
0.055295441299676895,
0.01509661041200161,
0.024967670440673828,
-0.03673272207379341,
-0.019492406398057938,
-0.0056915911845862865,
0.027515718713402748,
-0.015744101256132126,
-0.038157518953084946,
-0.02432366833090782,
0.03675534576177597,
0.047415997833013535,
-0.035309839993715286,
0.016362028196454048,
0.0400061160326004,
0.02699766866862774,
-0.013832212425768375,
0.008357628248631954,
-0.037135615944862366,
-0.025915710255503654,
-0.007485206704586744,
0.03309735655784607,
0.02428644709289074,
0.022825323045253754,
-0.02910512126982212,
0.022668251767754555,
0.038702886551618576,
0.009470220655202866,
0.026105716824531555,
-0.017323557287454605,
-0.017086073756217957,
-0.013725420460104942,
-0.014065192081034184,
-0.003663432551547885,
0.029839802533388138,
-0.017420457676053047,
-0.04486503824591637,
0.05107974633574486,
-0.00041269470239058137,
0.02021203748881817,
-0.034403249621391296,
-0.018850259482860565,
0.04711484909057617,
-0.0020561714190989733,
0.006533540785312653,
-0.024319076910614967,
0.022764243185520172,
-0.030503705143928528,
0.01059384923428297,
-0.03608051687479019,
-0.0030345835257321596,
-0.01799793355166912,
0.02753407694399357,
0.024324119091033936,
-0.004666601773351431,
0.014198523946106434,
-0.0388033352792263,
0.019653819501399994,
0.0295722596347332,
-0.018021102994680405,
-0.009700416587293148,
-0.01780056022107601,
-0.045894891023635864,
0.05194713547825813,
-0.038720160722732544,
-0.01092382613569498,
0.05604094639420509,
0.01965874433517456,
-0.020227061584591866,
0.03812399134039879,
0.02833896316587925,
-0.03706943988800049,
0.012787937186658382,
-0.014313395135104656,
0.029809599742293358,
-0.024070370942354202,
0.013251073658466339,
0.03959979489445686,
-0.01999972015619278,
-0.025372140109539032,
0.024218808859586716,
-0.008530148304998875,
-0.009811519645154476,
-0.03886322304606438,
0.011769786477088928,
-0.012629850767552853,
-0.010435807518661022,
0.02069726400077343,
0.028421513736248016,
-0.038914501667022705,
-0.01110061351209879,
-0.04125301539897919,
-0.05043688416481018,
-0.02573668584227562,
-0.015546176582574844,
0.058700788766145706,
0.028392767533659935,
-0.03651449829339981,
0.03088865987956524,
-0.0273029375821352,
-0.07787923514842987,
-0.002405563136562705,
-0.023375129327178,
-0.0024735850747674704,
-0.04865917190909386,
0.034608613699674606,
0.03549298271536827,
-0.019326908513903618,
0.004348218906670809,
0.015187397599220276,
0.06355580687522888,
0.013957574032247066,
0.02465001307427883,
-0.007670345716178417,
0.022225268185138702,
0.008289443328976631,
-0.03064342960715294,
0.012661486864089966,
0.027789698913693428,
-0.047212596982717514,
-0.010567904449999332,
0.008459222503006458,
0.027826683595776558,
0.05870557203888893,
-0.06197373569011688,
0.02397589385509491,
-0.001318102004006505,
-0.04368007928133011,
-0.024119021371006966,
-0.017978446558117867,
-0.0029013557359576225,
-0.0019758923444896936,
0.01881507784128189,
0.017663614824414253,
0.04095318913459778,
0.02339581772685051,
0.015216181986033916,
0.04001389816403389,
0.03563248738646507,
-0.0218583382666111,
-0.01190622802823782,
-0.016574308276176453,
-0.020120738074183464,
0.05121941864490509,
-0.04241735488176346,
0.007179953157901764,
0.055049002170562744,
0.001487915636971593,
0.010972680523991585,
-0.020691992715001106,
-0.018464557826519012,
-0.013606063090264797,
-0.0490150973200798,
-0.010740865021944046,
-0.028797360137104988,
0.03924943506717682,
0.007290191482752562,
0.06701084971427917,
0.018388956785202026,
0.03935971111059189,
0.026339564472436905,
0.011661404743790627,
-0.07114525884389877,
-0.0015185249503701925,
-0.03119591996073723,
0.026195582002401352,
-0.036862365901470184,
-0.010964961722493172,
0.015408345498144627,
-0.028089750558137894,
-0.018101656809449196,
-0.007663019932806492,
0.039288222789764404,
-0.03207847476005554,
0.006250634323805571,
-0.026518478989601135,
-0.02347288653254509,
0.018514737486839294,
0.004590061027556658,
-0.026008624583482742,
-0.034738410264253616,
0.07453085482120514,
0.013856875710189342,
0.004755871836096048,
0.012169692665338516,
-0.03608041629195213,
0.023845789954066277,
0.020911412313580513,
0.059964023530483246,
0.009771826677024364,
0.02134924940764904,
0.0049111139960587025,
0.009269002825021744,
0.03169913962483406,
0.05704386159777641,
-0.008734256029129028,
0.003253225004300475,
-0.02989150956273079,
-0.05104135721921921,
-0.01849873550236225,
0.04878460615873337,
0.04910494014620781,
0.02290835604071617,
0.059249699115753174,
-0.016433142125606537,
0.010146655142307281,
-0.016432225704193115,
0.047724876552820206,
0.014460168778896332,
-0.024069366976618767,
-0.012486521154642105,
-0.03990998864173889,
-0.03032098338007927,
-0.007341771386563778,
0.037944450974464417,
0.025075681507587433,
0.067825086414814,
0.01289182249456644,
-0.01746346615254879,
0.014770732261240482,
0.04699358344078064,
-0.02121577598154545,
-0.003071012906730175,
-0.005551667883992195,
0.030508531257510185,
-0.02781839109957218,
0.03269338235259056,
-0.004191105253994465,
0.06731845438480377,
0.01888868771493435,
0.010332908481359482,
-0.04236818850040436,
-0.06866531074047089,
-0.0013512163423001766,
0.03926723450422287,
0.024143140763044357,
-0.034789010882377625,
0.019123217090964317,
-0.05168681964278221,
-0.010255847126245499,
0.03185991570353508,
-0.01521169114857912,
-0.0036870278418064117,
-0.03678862005472183,
0.024927888065576553,
-0.02425968274474144,
-0.019104860723018646,
-0.025729041546583176,
0.004154826048761606,
0.006814311724156141,
0.005898032803088427,
-0.01138922106474638,
0.01898578181862831,
-0.03586294502019882,
0.031403977423906326,
-0.01619444601237774,
0.019933925941586494,
0.026822494342923164,
0.006944636814296246,
-0.014415591023862362,
-0.009224490262567997,
-0.06023586168885231,
-0.061428386718034744,
0.01764494553208351,
-0.007262556813657284,
-0.0012623396469280124,
0.026236873120069504,
-0.02389531023800373,
-0.08026202768087387,
0.02270648442208767,
0.019907312467694283,
-0.020435910671949387,
0.03940605744719505,
0.002567904070019722,
0.016495922580361366,
0.022759249433875084,
0.0007964565884321928,
0.055504415184259415,
0.06340455263853073,
-0.0012119158636778593,
-0.03156869113445282,
0.03516555204987526,
0.023893233388662338,
-0.03004726953804493,
-0.010072887875139713,
-0.0386551134288311,
0.03324608877301216,
-0.05903846397995949,
0.05328003317117691,
0.021733170375227928,
0.03489292412996292,
0.028109373524785042,
-0.03089025430381298,
0.038181744515895844,
0.0452447384595871,
0.037946686148643494,
-0.02709566429257393,
-0.016642773523926735,
0.042589325457811356,
-0.000056269818742293864,
-0.007614846806973219,
0.022518008947372437,
0.030223751440644264,
0.005465772934257984,
0.030748853459954262,
-0.015992576256394386,
0.03109755553305149,
-0.019802836701273918,
-0.0015198471955955029,
0.020129917189478874,
-0.026887377724051476,
0.04374696686863899,
0.005347805563360453,
0.04320939630270004,
0.011979950591921806,
-0.02103305235505104,
0.057883523404598236,
0.04172011464834213,
-0.003069358877837658,
0.04216035082936287,
-0.033329159021377563,
0.028079066425561905,
0.021284105256199837,
0.004060435574501753,
-0.049832820892333984,
-0.06625793129205704,
0.05020894855260849,
0.06182170286774635,
-0.024823863059282303,
-0.016115153208374977,
0.002058295300230384,
-0.025758937001228333,
-0.02472565323114395,
0.01206061989068985,
0.07464388757944107,
-0.039538126438856125,
-0.008279613219201565,
0.005633242428302765,
0.0178045853972435,
0.06066889688372612,
-0.003333946457132697,
-0.01784520410001278,
0.034602124243974686,
-0.0049816942773759365,
-0.016782056540250778,
-0.0005389084108173847,
0.0074201906099915504,
-0.03432809188961983,
-0.0026855275500565767,
-0.011080928146839142,
-0.013463462702929974,
0.040334902703762054,
-0.011747127398848534,
0.046695221215486526,
0.03816551715135574,
-0.0033880078699439764,
-0.01374838873744011,
-0.018218940123915672,
0.026333598420023918,
0.008101028390228748,
0.03937261924147606,
-0.007366667967289686,
-0.04809102416038513,
-0.009980855509638786,
-0.05267548933625221,
0.011680961586534977,
-0.015337272547185421,
-0.0336424820125103,
-0.013538409024477005,
0.03348095715045929,
-0.00022968136181589216,
0.004770271014422178,
0.055665235966444016,
0.0030124415643513203,
0.053469426929950714,
0.0044275810942053795,
0.02103310078382492,
-0.020899660885334015,
0.00344052049331367,
-0.03744734078645706,
-0.05527825653553009,
-0.03948517143726349,
0.018630942329764366,
0.08053284138441086,
-0.03966882824897766,
0.02180362679064274,
0.015683991834521294,
-0.00993521511554718,
-0.005031262058764696,
0.010805376805365086,
-0.01382663007825613,
-0.018400277942419052,
-0.04999157041311264,
0.007345172576606274,
-0.004007975570857525,
-0.0155764389783144,
-0.020388003438711166,
0.044925566762685776,
-0.03535289689898491,
-0.0014375861501321197,
0.04342063143849373,
-0.010711351409554482,
0.0525406152009964,
-0.05339595675468445,
-0.04381631314754486,
0.024877749383449554,
-0.033404961228370667,
0.03481069952249527,
0.005401794798672199,
-0.029146157205104828,
0.0426698699593544,
0.04850959777832031,
0.016968687996268272,
-0.03820802643895149,
-0.00014846243720967323,
-0.04305307939648628,
0.033735115081071854,
-0.007944158278405666,
-0.058667417615652084,
-0.0063761076889932156,
-0.007378838025033474,
-0.034977275878190994,
-0.0014528281753882766,
-0.008811409585177898,
-0.026102956384420395,
-0.07563964277505875,
0.014702036045491695,
0.008430891670286655,
0.0007278976263478398,
0.03656567633152008,
0.030992496758699417,
-0.036590952426195145,
0.006473087705671787,
-0.005203824024647474,
0.022539960220456123,
-0.0008075061487033963,
0.005663475953042507,
0.028532011434435844,
0.020268471911549568,
-0.06661953032016754,
0.03789808973670006,
-0.045332375913858414,
0.01337104570120573,
0.11696894466876984,
0.025404563173651695,
0.027179593220353127,
-0.04150627553462982,
-0.014083359390497208,
-0.013738312758505344,
0.023288842290639877,
-0.006542135030031204,
0.015165962278842926,
0.028197934851050377,
0.04601934552192688,
0.0011936565861105919,
0.06732228398323059,
-0.003864375874400139,
0.02673528529703617,
0.03919586166739464,
-0.04146194085478783,
-0.02168993651866913,
-0.026712767779827118,
0.0262167789041996,
-0.03416143357753754,
0.039946313947439194,
-0.06094472482800484,
0.04994349554181099,
0.010657897219061852,
-0.016413552686572075,
-0.00577207189053297,
-0.033109474927186966,
0.007888485677540302,
-0.01756012998521328,
-0.018021030351519585,
-0.014641459099948406,
0.00020691441022790968,
-0.005411652382463217,
-0.023957250639796257,
0.02915332093834877,
0.00009258210775442421,
-0.04053572192788124,
0.025056131184101105,
0.01791839860379696,
0.01079478394240141,
-0.005439604166895151,
0.009854002855718136,
-0.0013937304029241204,
-0.03503353148698807,
-0.013580706901848316,
-0.04644032567739487,
0.026923350989818573,
-0.021630873903632164,
-0.03197513148188591,
-0.0220688097178936,
-0.01788378693163395,
0.009132440201938152,
-0.051896918565034866,
-0.0668751522898674,
-0.020669231191277504,
0.028197849169373512,
-0.0013745588948950171,
-0.017399869859218597,
-0.020911019295454025,
0.01143542118370533,
-0.003217588644474745,
-0.0031514884904026985,
0.028141522780060768,
-0.007581457030028105,
-0.04113520681858063,
0.008188214153051376,
0.04771820455789566,
-0.0006193473236635327,
-0.0415365993976593,
-0.031892627477645874,
0.028120486065745354,
-0.04242870211601257,
0.03218561038374901,
0.00111365073826164,
0.05028698220849037,
0.029648222029209137,
0.015682943165302277,
-0.005100482143461704,
-0.004583627916872501,
-0.061488907784223557,
0.057608477771282196,
-0.02592380903661251,
0.0029089846648275852,
-0.03702564910054207,
-0.013867116533219814,
0.03597117215394974,
0.059111014008522034,
0.0010191315086558461,
0.006555051542818546,
-0.02698167972266674,
0.05174608528614044,
0.019924331456422806,
-0.021971382200717926,
-0.058063264936208725,
0.0021894152741879225,
-0.010868238285183907,
-0.04289413243532181,
0.007840449921786785,
0.06853266060352325,
0.0277973935008049,
0.019410181790590286,
-0.0078020174987614155,
-0.023171868175268173,
0.0007989025325514376,
0.05123145505785942,
0.06410223990678787,
-0.034722406417131424,
-0.04186480864882469,
0.007604261394590139,
0.005329124629497528,
-0.009895809926092625,
-0.05098329111933708,
-0.029968999326229095,
-0.01694282330572605,
-0.05939514935016632,
0.007921515963971615,
-0.017376558855175972,
-0.0033401423133909702,
-0.011152048595249653,
0.01928858831524849,
-0.00962432473897934,
0.02829534374177456,
-0.05445728078484535,
-0.0505652092397213,
-0.004816140979528427,
0.024024901911616325,
-0.002566590439528227,
0.0244850255548954,
-0.022362470626831055,
0.022165264934301376,
0.005617915187031031,
0.04778359830379486,
0.03677346929907799,
-0.024310078471899033,
0.03984067216515541,
-0.007993137463927269,
-0.0026387516409158707,
-0.008804326876997948,
-0.023010196164250374,
0.04246452823281288,
-0.02079368196427822,
-0.03899388015270233,
0.013220969587564468,
-0.02163236401975155,
0.0029964277055114508,
0.0036621280014514923,
-0.014391192235052586,
0.015642700716853142,
0.0734625980257988,
0.0075373053550720215,
0.002719410927966237,
-0.004173551220446825,
-0.0020845450926572084,
0.0059396387077867985,
0.008515432476997375,
0.0286721121519804,
-0.029297640547156334,
0.021638253703713417,
0.03834046795964241,
0.017177119851112366,
0.008051292039453983,
-0.015682632103562355,
0.015429339371621609,
-0.020841974765062332,
-0.0011386857368052006,
0.012115823104977608,
0.005361128132790327,
0.03128911927342415,
0.05286172777414322,
-0.024722013622522354,
0.0169731006026268,
0.0024259653873741627,
0.013753587380051613,
-0.06389351189136505,
0.022968914359807968,
-0.02439180575311184,
0.022535759955644608,
-0.03278202936053276,
-0.03225629776716232,
-0.011131014674901962,
0.028953202068805695,
-0.03748133406043053,
0.007441137917339802,
-0.025876155123114586,
-0.016992388293147087,
-0.023030772805213928,
0.0288371779024601,
-0.030870184302330017,
0.05172400176525116,
0.016820918768644333,
0.014879979193210602,
0.03202325105667114,
0.04183227941393852,
-0.0038967651780694723,
0.0338645875453949,
-0.013681109994649887,
0.008611093275249004,
-0.0177533570677042,
-0.027580760419368744,
0.04742283374071121,
-0.016475161537528038,
-0.03325289115309715,
-0.00454165181145072,
-0.004644504748284817,
0.009229232557117939,
-0.026952628046274185,
-0.03579402714967728,
-0.035428959876298904,
0.0315217524766922,
0.0035638369154185057,
0.03328599035739899,
-0.0032165476586669683,
0.02852322719991207,
-0.034438930451869965,
0.04086959362030029,
-0.048889268189668655,
-0.0006731792236678302,
0.02257053181529045,
-0.01635761559009552,
-0.004091565031558275,
0.017147045582532883,
-0.030840355902910233,
-0.028312938287854195,
0.01875847391784191,
-0.004373001400381327,
0.07839934527873993,
0.008865582756698132,
0.041656915098428726,
-0.06114962324500084,
0.009802774526178837,
0.0012329363962635398,
0.05469086021184921,
-0.03574535623192787,
-0.0013360920129343867,
0.027119945734739304,
-0.018542081117630005,
-0.021823029965162277,
-0.016201525926589966,
-0.021351898089051247,
-0.025562750175595284,
-0.008200008422136307,
-0.014716445468366146,
0.0079586710780859,
-0.003947939723730087,
-0.02597690559923649,
-0.024227352812886238,
0.071693055331707,
0.023246759548783302,
0.04415428265929222,
0.026787256821990013,
-0.01553833857178688,
-0.017009180039167404,
-0.05242275074124336,
0.006640588864684105,
-0.009362754411995411,
-0.01015063188970089,
0.023611318320035934,
-0.01712368242442608,
0.01341297384351492,
0.024901865050196648,
0.03522634506225586,
-0.0009101714240387082,
-0.018274934962391853,
0.011220283806324005,
0.015558178536593914,
-0.007945195771753788,
-0.04544892907142639,
0.0064986287616193295,
-0.032549090683460236,
-0.016508987173438072,
0.003919262904673815,
0.01311532687395811,
-0.02116292528808117,
-0.028462115675210953,
0.041873998939991,
-0.010144599713385105,
0.002499060472473502,
-0.04739973321557045,
-0.04543062299489975,
0.027241265401244164,
0.027876736596226692,
-0.04773910716176033,
0.08853919804096222,
-0.04444252699613571,
0.0110745495185256,
0.004978255834430456,
-0.01998990960419178,
-0.03860442712903023,
0.05677616223692894,
-0.03173907473683357,
-0.037564028054475784,
-0.03432348370552063,
-0.023937653750181198,
0.012310612946748734,
-0.04785577952861786,
-0.021744433790445328,
0.003356482135131955,
-0.0396059975028038,
0.006375189404934645,
0.023208605125546455,
0.04666696488857269,
0.006322478409856558,
0.003711866680532694,
0.008968510664999485,
-0.006425101310014725,
0.017909547314047813,
-0.0399506576359272,
0.03334281966090202,
0.07510680705308914,
0.0053315190598368645,
0.00009915030386764556,
0.019673960283398628,
-0.038904521614313126,
-0.0022740724962204695,
-0.006398227531462908,
-0.008814645931124687,
-0.006069120019674301,
-0.004305259324610233,
0.012354628182947636,
-0.00008786744729150087,
0.024500278756022453,
0.023261157795786858,
0.02058589644730091,
0.06691587716341019,
-0.022566741332411766,
0.00020668325305450708,
-0.07617691904306412,
0.01804383285343647,
-0.00881237629801035,
0.012963103130459785,
0.011018861085176468,
0.026405980810523033,
0.016114678233861923,
0.0075922077521681786,
-0.014832769520580769,
-0.013523847796022892,
0.06331449747085571,
-0.012583570554852486,
-0.0040519507601857185,
-0.010256845504045486,
0.01151628140360117,
0.013475942425429821,
-0.04162607714533806,
-0.00037191639421507716,
-0.020116465166211128,
0.029743226245045662,
0.028666207566857338,
0.02029518596827984,
-0.013395481742918491,
-0.013991408981382847,
-0.012768779881298542,
0.050111088901758194,
-0.053559862077236176,
-0.010405790992081165,
-0.012613763101398945,
0.031662628054618835,
-0.025415822863578796,
-0.013176137581467628
] |
<p>When we derive Ohm's Law using the Drude Model, we assume at one point of time that $E=V/L$, when is fact, $E=dV/dL$, unless $E$ is constant, in which case the assumption $E=V/L$ is true. But I don't understand why the electric field in a conductor must be constant as current flows. Is there a convincing explanation that is perhaps related to the way atoms behave and orient themselves?</p>
<p>Also, if the assumption $V=E\cdot L$ makes sense, I can understand why Ohm's Law should work for a homogeneous electric circuit. However, I don't understand why it should work for a heterogeneous circuit - perhaps one with two different resistors connected in series. And please don't use the traffic jam analogy. Surely there must a more theoretical way to explain this (using Classical Physics).</p>
| 7,678 |
[
-0.04396189749240875,
0.007911386899650097,
0.014162678271532059,
-0.056607991456985474,
0.02932792156934738,
-0.042598042637109756,
0.007026934530586004,
-0.006303670350462198,
0.0021128379739820957,
0.013400598429143429,
0.03347424790263176,
0.03215021267533302,
0.07586310803890228,
0.00038700297591276467,
0.04858102649450302,
-0.028836924582719803,
0.011279826983809471,
-0.022501623257994652,
-0.011609016917645931,
-0.023882685229182243,
-0.031403932720422745,
0.019597196951508522,
0.012602795846760273,
-0.019779471680521965,
-0.00021262923837639391,
0.026135973632335663,
-0.026031984016299248,
0.026904867962002754,
0.03647509589791298,
0.023785388097167015,
0.004613232798874378,
-0.019371002912521362,
-0.017243588343262672,
0.03483544662594795,
0.01338936761021614,
0.020053323358297348,
-0.031055783852934837,
-0.036994367837905884,
-0.029359765350818634,
0.01917092129588127,
0.0002975208917632699,
-0.004179241135716438,
0.012469802051782608,
0.05628383904695511,
-0.02057846449315548,
0.041795287281274796,
0.03763079643249512,
-0.00996899139136076,
0.04454868286848068,
-0.06202584132552147,
0.0510413721203804,
-0.01966021955013275,
0.06788639724254608,
0.05203688517212868,
-0.001116145751439035,
-0.006586090195924044,
0.06320247799158096,
0.04589349776506424,
-0.023363778367638588,
-0.016068048775196075,
-0.03924033045768738,
-0.008319917134940624,
0.010156826116144657,
-0.05216820165514946,
-0.028801072388887405,
0.02246066927909851,
0.005933820270001888,
-0.02874119020998478,
0.020864732563495636,
-0.0034911162219941616,
-0.015902288258075714,
0.02896910347044468,
0.006485300604254007,
-0.01161500159651041,
0.005879311356693506,
-0.010676597245037556,
-0.0012366021983325481,
0.00022203168191481382,
0.013415792025625706,
0.0211234912276268,
-0.04795381426811218,
-0.013775967061519623,
0.05041076987981796,
0.015493142418563366,
-0.0017563068540766835,
-0.03421283885836601,
0.041822414845228195,
0.002166507765650749,
0.0058554173447191715,
-0.007097132038325071,
0.0033458208199590445,
0.05026358366012573,
0.020646071061491966,
-0.00945371761918068,
-0.0016905363881960511,
0.03171178326010704,
-0.008681369945406914,
0.013528362847864628,
0.0012534458655864,
-0.009596271440386772,
0.023296378552913666,
0.0021699476055800915,
0.010449813678860664,
0.046714019030332565,
0.0008879894157871604,
-0.07034922391176224,
-0.014581435360014439,
0.013672292232513428,
-0.029489504173398018,
-0.015622719191014767,
-0.0617435984313488,
0.0431240051984787,
0.025373190641403198,
0.04543200880289078,
-0.0071701304987072945,
-0.016100304201245308,
0.016944224014878273,
-0.042117029428482056,
0.028092361986637115,
0.05951373279094696,
0.017613427713513374,
-0.04605348780751228,
0.005502132698893547,
-0.015085980296134949,
-0.0588582307100296,
0.013826812617480755,
-0.005187568720430136,
0.023223066702485085,
-0.018724830821156502,
0.01566191203892231,
-0.022714808583259583,
0.0013000868493691087,
-0.0025196594651788473,
0.022813215851783752,
0.028726505115628242,
-0.02755032479763031,
-0.08930665254592896,
-0.0429672971367836,
0.0014627841301262379,
-0.025535063818097115,
-0.029968982562422752,
-0.09620580077171326,
-0.023286661133170128,
-0.014009866863489151,
0.07576683908700943,
-0.010377475060522556,
-0.0038662997540086508,
-0.004645674955099821,
0.029917817562818527,
0.02192210964858532,
-0.02930556610226631,
-0.06375257670879364,
0.014518006704747677,
-0.014403666369616985,
0.03728212043642998,
-0.04217290133237839,
0.01122018788009882,
0.0406227707862854,
-0.0045298314653337,
-0.010981900617480278,
0.04249218478798866,
-0.011514971032738686,
-0.018183330073952675,
0.011461885645985603,
-0.0103437015786767,
-0.0268226470798254,
0.08726595342159271,
-0.00751694617792964,
0.04911287501454353,
0.04878649860620499,
0.041961923241615295,
0.02152438461780548,
0.006053390447050333,
0.025844940915703773,
0.006095332093536854,
-0.0323653370141983,
0.0044935024343431,
-0.0131912250071764,
0.011356692761182785,
0.013918984681367874,
-0.06477060168981552,
-0.05214300751686096,
0.05150759965181351,
-0.009630035609006882,
-0.022858932614326477,
0.04869808256626129,
-0.006916909012943506,
0.010477262549102306,
-0.0034289988689124584,
-0.021609945222735405,
-0.018908975645899773,
-0.07685110718011856,
0.06036269664764404,
0.0017749808030202985,
0.0043719555251300335,
0.03525146096944809,
0.005499390419572592,
0.014647685922682285,
-0.01992766372859478,
-0.006329534575343132,
-0.008113848976790905,
0.025059359148144722,
0.006985352840274572,
-0.045239854604005814,
0.03356004133820534,
0.02683042548596859,
0.017663195729255676,
0.02542913146317005,
0.029671402648091316,
-0.015249731950461864,
-0.039077870547771454,
0.03505168482661247,
-0.05361488088965416,
0.04235556721687317,
0.006304128561168909,
0.0035756321158260107,
-0.04206652566790581,
-0.033571261912584305,
0.01782083883881569,
0.08023901283740997,
-0.02466888353228569,
0.07243570685386658,
0.049294691532850266,
0.007532086689025164,
0.0031639542430639267,
0.06282688677310944,
-0.03416716307401657,
-0.006218666210770607,
-0.029447076842188835,
-0.05073394998908043,
-0.03859911486506462,
0.03381601721048355,
0.06259408593177795,
0.01949424296617508,
-0.015413651242852211,
0.012646776624023914,
0.015804026275873184,
0.05714133381843567,
0.02660483494400978,
0.01854022964835167,
-0.04180631786584854,
-0.048200178891420364,
0.022763164713978767,
0.00545564666390419,
0.002762545133009553,
0.005450365133583546,
0.02002876251935959,
0.015132942236959934,
-0.0024014203809201717,
-0.03167033940553665,
-0.005361780524253845,
0.03898122161626816,
0.012723132967948914,
0.03636641427874565,
0.013989817351102829,
-0.031032850965857506,
0.0011250623501837254,
-0.013309497386217117,
0.045104868710041046,
0.02011866495013237,
-0.01507617812603712,
0.01701298914849758,
-0.04774428531527519,
0.0004284671158529818,
0.008299635723233223,
-0.003064307849854231,
-0.021504303440451622,
-0.02238685078918934,
0.022958990186452866,
-0.03633226826786995,
0.0378275066614151,
-0.018874183297157288,
-0.005026210565119982,
-0.0376327745616436,
-0.016329603269696236,
0.025016414001584053,
0.007481908891350031,
0.05389983206987381,
-0.07423097640275955,
-0.016515836119651794,
-0.00855603814125061,
-0.01758687198162079,
-0.01277968566864729,
0.019456896930933,
-0.008686362765729427,
0.010016355663537979,
0.019897742196917534,
-0.04675811901688576,
0.07390252500772476,
0.05099954828619957,
0.019969739019870758,
0.013355028815567493,
-0.007991298101842403,
-0.05481751635670662,
-0.006473632529377937,
-0.0368812195956707,
0.011065815575420856,
-0.0000258824038610328,
-0.029180478304624557,
0.052014391869306564,
-0.03778444975614548,
-0.02658945322036743,
0.016727568581700325,
-0.030479922890663147,
-0.03896869719028473,
-0.01119217462837696,
-0.01870790123939514,
0.0018228311091661453,
-0.03279394283890724,
0.03994591534137726,
0.017345331609249115,
-0.0761578381061554,
-0.043158888816833496,
-0.032606832683086395,
-0.0456106960773468,
0.03102322667837143,
-0.015396708622574806,
0.038979850709438324,
0.02658119611442089,
-0.046518415212631226,
0.021915003657341003,
0.028086071833968163,
-0.07109715789556503,
-0.012777595780789852,
-0.034948788583278656,
-0.024543028324842453,
-0.02775380201637745,
0.02554941549897194,
0.07945487648248672,
-0.022110482677817345,
0.0295172780752182,
0.034181464463472366,
0.05569968745112419,
-0.000017717226000968367,
0.004641270264983177,
0.0011906975414603949,
0.007059697061777115,
0.011155526153743267,
0.0025684922002255917,
0.0448806956410408,
0.03800061717629433,
-0.01177436113357544,
0.006274392828345299,
-0.0014374065212905407,
0.03580532595515251,
0.0434829518198967,
-0.029076190665364265,
0.03723974525928497,
-0.02786913700401783,
0.00040262530092149973,
-0.09069850295782089,
0.02121436409652233,
-0.0004060631908942014,
0.0024023186415433884,
-0.02687728963792324,
0.015386196784675121,
0.017994405701756477,
-0.030143821612000465,
-0.003099072026088834,
0.04515322297811508,
0.014247270300984383,
-0.03739680349826813,
-0.04537133872509003,
0.016716772690415382,
0.009827468544244766,
0.041093286126852036,
-0.02149968221783638,
-0.0027803087141364813,
0.029028411954641342,
0.04503297060728073,
-0.024828370660543442,
-0.009672492742538452,
-0.05413560941815376,
-0.022503886371850967,
-0.05984168127179146,
-0.02099497802555561,
0.01956949010491371,
0.03129883483052254,
-0.000728841230738908,
0.06307191401720047,
0.010748238302767277,
0.007142945192754269,
0.006547030992805958,
-0.004533295053988695,
-0.07203873991966248,
0.005232314579188824,
-0.017340384423732758,
0.010190927423536777,
-0.04420014098286629,
-0.01083778403699398,
0.012558337301015854,
-0.03869861736893654,
-0.034093115478754044,
-0.03296678885817528,
0.012823090888559818,
-0.05277450755238533,
0.03689359501004219,
-0.013990657404065132,
-0.04681115970015526,
-0.028466707095503807,
0.05385267361998558,
0.014236778020858765,
-0.051776718348264694,
0.007853816263377666,
0.03133036941289902,
-0.04110579565167427,
-0.05261906236410141,
-0.02084140107035637,
0.000875265512149781,
0.029097989201545715,
0.006319653242826462,
0.04124390706419945,
-0.021365631371736526,
-0.013272594660520554,
0.02078237198293209,
0.02549506537616253,
0.07404123991727829,
-0.003333464963361621,
0.016035672277212143,
-0.029026392847299576,
-0.05721760541200638,
-0.030179321765899658,
-0.0013078313786536455,
0.05312814190983772,
0.006400849670171738,
0.015777012333273888,
0.037627268582582474,
0.030916763469576836,
-0.02485554851591587,
0.03349620848894119,
0.0038380955811589956,
0.0024445797316730022,
-0.014912477694451809,
-0.0548035204410553,
0.02223874442279339,
-0.05367805063724518,
0.0075052520260214806,
0.047707606106996536,
-0.035355597734451294,
-0.010130097158253193,
0.000195007654838264,
0.028821904212236404,
0.02806677669286728,
-0.01256639789789915,
-0.005817034747451544,
-0.003491160459816456,
0.018476519733667374,
0.016966374590992928,
-0.00683961994946003,
0.02201545238494873,
-0.005550866015255451,
0.02436734177172184,
0.02069944329559803,
-0.029613714665174484,
-0.10245465487241745,
-0.008405743166804314,
0.016094382852315903,
0.010536386631429195,
-0.026449302211403847,
0.01972426474094391,
-0.05113735795021057,
0.0029844888485968113,
0.03361264243721962,
-0.01004809234291315,
0.015604600310325623,
0.004077737219631672,
-0.0288489181548357,
-0.022935640066862106,
-0.05160488560795784,
0.0013491013087332249,
0.013431787490844727,
-0.010252969339489937,
0.013003154657781124,
-0.024065213277935982,
-0.007924878969788551,
-0.01641674153506756,
0.007267360109835863,
0.03053290955722332,
0.04842235520482063,
-0.02148103155195713,
-0.02116996794939041,
0.015036766417324543,
0.026302028447389603,
-0.014234890230000019,
-0.0665842816233635,
0.01197561714798212,
0.004435997921973467,
0.028831616044044495,
0.039169833064079285,
-0.021435894072055817,
-0.04354637488722801,
0.012574667111039162,
0.008552172221243382,
0.01362538244575262,
0.004123844671994448,
0.0047194152139127254,
0.08836285769939423,
0.021545782685279846,
0.013715771958231926,
0.044532570987939835,
-0.00744163803756237,
-0.0070528751239180565,
-0.012976512312889099,
0.003445620648562908,
0.04023556411266327,
-0.037436921149492264,
0.029434440657496452,
-0.00834204163402319,
0.03257998451590538,
-0.027154279872775078,
0.07841373980045319,
-0.010992135852575302,
0.0276348814368248,
0.00833476334810257,
-0.03736976534128189,
0.00786606315523386,
0.006213048007339239,
0.004067123867571354,
-0.014702234417200089,
-0.020153863355517387,
0.029708877205848694,
-0.004881626460701227,
-0.04425238072872162,
0.0126136289909482,
-0.0063506257720291615,
0.018489018082618713,
0.01360485702753067,
0.019154449924826622,
0.018649470061063766,
-0.039997391402721405,
-0.009824598208069801,
0.013619310222566128,
-0.043794844299554825,
0.01796325109899044,
0.001323531148955226,
0.01744280569255352,
0.004060820210725069,
-0.029748234897851944,
-0.04358075186610222,
0.0006595238228328526,
-0.018725071102380753,
0.033855851739645004,
-0.026761898770928383,
-0.011654607020318508,
0.020134488120675087,
0.004617906175553799,
-0.0648326501250267,
-0.06567257642745972,
0.03489721193909645,
-0.005271595437079668,
0.032206811010837555,
-0.036559008061885834,
-0.004686011932790279,
0.019785447046160698,
-0.06313713639974594,
0.03285551071166992,
0.0760403722524643,
-0.010538339614868164,
-0.008723894134163857,
-0.011975228786468506,
0.036907412111759186,
0.08711589127779007,
0.021329546347260475,
-0.007388940546661615,
-0.003072607098147273,
-0.060719188302755356,
0.018286723643541336,
-0.0009180285851471126,
0.04377350956201553,
-0.029552001506090164,
-0.021602939814329147,
0.016221825033426285,
-0.01298863161355257,
0.08954817056655884,
-0.01504769641906023,
-0.029265543445944786,
0.0264048520475626,
-0.0030918868724256754,
-0.028145238757133484,
-0.003521725069731474,
0.023838404566049576,
-0.003661232301965356,
0.046529751271009445,
0.0026185214519500732,
0.0022416075225919485,
-0.05400565639138222,
-0.04256657510995865,
0.009736664593219757,
0.03117750957608223,
0.0276100542396307,
-0.014759320765733719,
0.05506650730967522,
-0.021967781707644463,
-0.026570627465844154,
0.028452135622501373,
-0.018473917618393898,
0.031326401978731155,
-0.021765323355793953,
-0.014885558746755123,
0.0037828281056135893,
0.02389015629887581,
-0.03607301414012909,
-0.056201234459877014,
-0.019816027954220772,
0.028540320694446564,
0.050903283059597015,
-0.04593059420585632,
0.05493230000138283,
0.020105181261897087,
-0.01107465848326683,
0.01139081921428442,
-0.017565999180078506,
-0.03421435505151749,
-0.0020899721421301365,
-0.008225373923778534,
0.008029949851334095,
-0.030366236343979836,
0.0026415803004056215,
0.04785854369401932,
0.03891646862030029,
-0.010093950666487217,
-0.01677766814827919,
0.05766262114048004,
0.03012051247060299,
0.03038082830607891,
0.025693753734230995,
-0.017543338239192963,
0.0015661736251786351,
-0.033224139362573624,
0.021707771345973015,
-0.010683467611670494,
-0.021378835663199425,
0.058022841811180115,
0.0030481149442493916,
-0.010808336548507214,
-0.01526018138974905,
-0.003478448837995529,
-0.025555459782481194,
0.024056389927864075,
0.006407113745808601,
0.01381606049835682,
0.011489449068903923,
0.034829575568437576,
0.007963994517922401,
0.0002887801092583686,
0.0024747932329773903,
0.007379218470305204,
-0.06282465904951096,
-0.018483841791749,
0.014933866448700428,
-0.004095868673175573,
0.031836509704589844,
0.025035204365849495,
-0.05202075093984604,
-0.018747126683592796,
-0.024094488471746445,
0.033566854894161224,
0.038252707570791245,
0.031876493245363235,
-0.0009644886595197022,
0.04685477167367935,
-0.006336010526865721,
0.005721181631088257,
-0.02659771218895912,
0.004675287287682295,
0.1148516982793808,
0.032457005232572556,
0.02367071434855461,
-0.03910107910633087,
-0.011254431679844856,
-0.03702898696064949,
0.004716844297945499,
-0.01683962158858776,
0.017142193391919136,
-0.022929348051548004,
0.045598797500133514,
0.009713642299175262,
0.02754153311252594,
0.023900391533970833,
-0.004897849168628454,
0.04451341554522514,
-0.023947717621922493,
-0.02196415141224861,
-0.007658157031983137,
0.04358774796128273,
-0.022790759801864624,
0.02005528099834919,
-0.053917743265628815,
0.0003487931680865586,
-0.03335903584957123,
0.01581062562763691,
-0.020348865538835526,
-0.01100056804716587,
0.028251178562641144,
0.022825341671705246,
-0.05737243965268135,
0.014106682501733303,
0.024173570796847343,
-0.034453634172677994,
-0.03583653271198273,
0.014914914965629578,
0.03287805989384651,
0.012434764765202999,
0.020522933453321457,
0.04436973109841347,
-0.004525712691247463,
-0.0032403345685452223,
0.026158567517995834,
0.008920086547732353,
-0.012175748124718666,
-0.02307593636214733,
-0.05323374271392822,
0.0466877780854702,
-0.022682426497340202,
0.036156222224235535,
0.04212489724159241,
-0.0016583297401666641,
-0.03175891935825348,
-0.05101443827152252,
-0.04000276327133179,
-0.03499046713113785,
0.021951084956526756,
-0.00022161551169119775,
0.0000017702334389468888,
-0.014601136557757854,
0.027344610542058945,
-0.020043637603521347,
0.006098112091422081,
0.02243644744157791,
-0.012380044907331467,
-0.01857544481754303,
-0.01386470627039671,
0.03314780816435814,
-0.02561032958328724,
-0.03828972578048706,
0.0020900072995573282,
-0.020398631691932678,
-0.05324983596801758,
-0.030377700924873352,
0.024395912885665894,
0.02433663420379162,
0.04759852588176727,
-0.011674641631543636,
-0.02676604501903057,
0.009625091217458248,
-0.08617794513702393,
0.022889770567417145,
0.03152348846197128,
-0.018582187592983246,
-0.024582404643297195,
0.020471148192882538,
0.004733971785753965,
0.02422451227903366,
-0.018964527174830437,
0.019204841926693916,
0.011879977770149708,
0.01973869279026985,
-0.00859742984175682,
-0.004448140040040016,
-0.04693876579403877,
-0.023001454770565033,
-0.04838889092206955,
0.039637114852666855,
0.0524863600730896,
0.019203994423151016,
-0.004366058390587568,
0.03741615638136864,
-0.03676852211356163,
0.06419306248426437,
-0.005236504599452019,
0.025291357189416885,
0.0032392675057053566,
-0.01956990733742714,
0.015287349000573158,
0.03167148306965828,
0.014829249121248722,
-0.026749901473522186,
-0.041717931628227234,
-0.027639275416731834,
0.00659447256475687,
-0.004380848724395037,
0.001325144781731069,
-0.016360528767108917,
0.0010726493783295155,
-0.017742279917001724,
0.027879871428012848,
-0.015281831845641136,
-0.028227536007761955,
-0.03839230537414551,
-0.01834952086210251,
0.028139827772974968,
0.003634497057646513,
-0.0017523459391668439,
0.0595574714243412,
-0.01635223627090454,
-0.024447988718748093,
0.028415076434612274,
0.026527516543865204,
-0.003839168231934309,
-0.02120717242360115,
-0.009768450632691383,
-0.007200462277978659,
0.04195087030529976,
-0.031655795872211456,
-0.06593222171068192,
0.08065508306026459,
-0.0027980313170701265,
-0.03466498851776123,
-0.005185346119105816,
0.008530166931450367,
0.028917232528328896,
0.025991175323724747,
0.012680938467383385,
0.00048538800911046565,
0.02159813977777958,
-0.01044077891856432,
0.018891392275691032,
-0.003559139557182789,
-0.02167024277150631,
0.0005099959671497345,
-0.029978929087519646,
-0.011641714721918106,
0.0006427080952562392,
0.009898357093334198,
0.03425412252545357,
0.04153165593743324,
0.0017389486311003566,
0.006922424305230379,
-0.0038286722265183926,
0.004709928296506405,
-0.006545206066220999,
0.06147141009569168,
0.037554074078798294,
0.011889544315636158,
0.07392851263284683,
-0.04365887865424156,
0.03274444863200188,
-0.008261769078671932,
-0.0277576744556427,
-0.0478556789457798,
0.0034400243312120438,
0.006099898833781481,
0.014899522066116333,
0.0017692613182589412,
-0.02000039629638195,
-0.01512856688350439,
0.03344550356268883,
-0.06564636528491974,
-0.028396839275956154,
-0.017601650208234787,
-0.017229126766324043,
-0.02946159802377224,
-0.06024888530373573,
-0.04187103733420372,
0.03200678899884224,
0.03908083587884903,
0.05393544211983681,
0.030712539330124855,
-0.0073828850872814655,
0.04489097744226456,
-0.003055453533306718,
-0.03539268299937248,
0.06050820276141167,
-0.02857244573533535,
0.01162303052842617,
0.011666479520499706,
0.0007824470521882176,
0.012509113177657127,
0.016508115455508232,
-0.014000399969518185,
-0.010654940269887447,
0.0061127794906497,
-0.018452070653438568,
0.01860908977687359,
0.023902807384729385,
-0.01382469292730093,
-0.0011127246543765068,
-0.031418099999427795,
-0.003654362168163061,
0.009916175156831741,
0.01541847363114357,
0.0007912727887742221,
-0.011400260962545872,
0.0322348028421402,
-0.03710091486573219,
-0.04199892655014992,
0.04670468717813492,
-0.019666222855448723,
-0.036700841039419174,
0.011391420848667622,
0.02089686691761017,
0.028009461238980293,
-0.0354490764439106,
0.017945365980267525,
-0.02547801099717617,
-0.03154328092932701,
0.057326167821884155,
0.052846625447273254,
0.011420379392802715,
-0.018267765641212463,
-0.0024782312102615833,
-0.038057707250118256,
0.019595440477132797,
0.047343526035547256,
0.0017707479419186711,
-0.06646846979856491,
-0.017701130360364914,
-0.003894821973517537,
-0.015522029250860214,
0.013293634168803692,
-0.049781639128923416,
-0.019968636333942413,
0.03309124708175659,
-0.0032500261440873146,
0.030355125665664673,
-0.021067297086119652,
-0.0716150775551796,
-0.031514182686805725,
-0.02726517803966999,
0.07836911827325821,
-0.0038085910491645336,
-0.02207614667713642,
-0.027071513235569,
-0.05015592277050018,
-0.02903583273291588,
0.04689143970608711,
0.07792741805315018,
0.008971554227173328,
-0.03907616436481476,
0.039466336369514465,
-0.0002214487176388502,
0.03434022516012192,
-0.027773145586252213,
-0.010868278332054615,
-0.004304791335016489,
-0.0057694255374372005,
0.009123026393353939,
0.012242387048900127,
-0.002862973138689995,
-0.00009462115122005343,
0.00903063453733921,
-0.0025279365945607424,
0.01725911907851696,
-0.019909141585230827,
-0.03374699875712395,
-0.011912830173969269,
0.017416147515177727,
-0.022936029359698296,
0.0497642382979393,
-0.010887778364121914,
0.01984681375324726,
-0.007484850473701954,
-0.011312502436339855,
-0.061926137655973434,
0.01368954498320818,
-0.04636235162615776,
0.00789999682456255,
-0.03557662293314934,
0.020854555070400238,
0.04277673736214638,
-0.024778511375188828,
0.0011341144563630223,
0.05263391137123108,
-0.06159785017371178,
-0.014837912283837795,
0.05097654089331627,
-0.01383957453072071,
0.016538484022021294,
0.00047164526768028736,
-0.0032419234048575163,
-0.01881949044764042,
-0.002636473858729005,
-0.00417855940759182,
0.020097291097044945,
0.051066428422927856,
-0.024558281525969505,
0.014182670041918755,
0.06572848558425903,
-0.015649911016225815,
0.029396289959549904,
-0.030001718550920486,
0.0020485972054302692,
-0.008384771645069122,
-0.02653748355805874,
0.016222549602389336,
-0.029951555654406548,
-0.009880013763904572,
0.025260189548134804,
-0.0006468860665336251,
0.09376411885023117,
-0.02382306382060051,
0.01507722306996584,
0.012160678394138813,
0.01114599872380495,
-0.001434565638191998,
0.009281338192522526,
0.0050630709156394005,
0.028688684105873108,
-0.021411621943116188,
0.0015338120283558965,
-0.010765818879008293,
-0.020217010751366615,
0.03299185261130333,
-0.036680519580841064,
0.01564377173781395,
0.01597180776298046,
-0.03802434727549553,
-0.012025443837046623,
-0.012763604521751404,
-0.033518947660923004,
-0.030269546434283257,
0.05345083400607109,
0.039665982127189636,
0.014113889075815678,
0.005745384376496077,
-0.010051067918539047,
-0.029046667739748955,
0.05050143599510193,
-0.07495466619729996,
-0.00974135659635067,
-0.03786623477935791,
-0.004957066848874092,
0.035356760025024414,
0.005273106973618269
] |
<p>To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think.</p>
<p>Here is the historical context I'm imagining (in particular taking into account the development of differential geometry in the 19th century):</p>
<p>Classical mechanics is about Lagrangians of matter fields on $\mathbb{R}^3$ (with the flat metric)</p>
<p>Sometime in the 1820s Gauss speculated about replacing the flat metric on $\mathbb{R}^3$ by one with non-vanishing curvature</p>
<p>Special relativity is about Lagrangians of matter fields on $\mathbb{R}^{3,1}$ (with the flat metric). I'm taking this jump for granted since as I understand it, it was arrived at from experimental results on electromagnetism at the end of the 19th century.</p>
<p>Now in line with Gauss, it seems like it would be extremely natural to speculate about replacing the flat metric on $\mathbb{R}^{3,1}$ by one with non-vanishing curvature (and in the same spirit also considering more exotic topologies for the underlying manifold).</p>
<p>Given that then we would have to ask exactly which metric we are looking for, it seems natural to say that there should be a Lagrangian term corresponding to the metric. The Einstein-Hilbert functional is probably the simplest one to try. And so we get the Einstein equations.</p>
<p>Alternatively (as I heard from someone is the actual history) you could observe that the energy-momentum tensor is of course a 2-tensor, and so for an Euler-Lagrange equation the most natural metric-dependent expression would be $\operatorname{Ric}=T$. Since $T$ is always divergence free it would be natural to replace $\operatorname{Ric}$ by $\operatorname{Ric}-\frac{1}{2}Rg$ just from taking the contracted second Bianchi identity into account. And so again we get the Einstein equations.</p>
<p>I've often heard it said that if Einstein had not come up with special relativity, someone else probably would have in the next five or ten years. However if he had not come up with general relativity, it would have taken much longer to discover. <b>Why is this?</b> I feel that I must be missing something here.</p>
| 7,679 |
[
-0.018074022606015205,
0.013764060102403164,
0.04709434509277344,
-0.03648582845926285,
0.025793038308620453,
-0.0022589238360524178,
-0.05286097899079323,
-0.009165237657725811,
-0.013858901336789131,
-0.05477438494563103,
-0.008487513288855553,
-0.0017335867742076516,
0.07142762094736099,
-0.0012702427338808775,
0.01556449942290783,
0.011949733830988407,
0.02079726941883564,
-0.005730274133384228,
-0.04835691675543785,
-0.03751895949244499,
0.05530489981174469,
-0.012951639480888844,
-0.0012731296010315418,
0.008115507662296295,
-0.03702924773097038,
0.0050940862856805325,
-0.0088984789326787,
-0.03346865996718407,
-0.017544526606798172,
0.05867498740553856,
-0.04292033612728119,
0.004022921901196241,
0.002857562620192766,
0.00599181093275547,
0.010676607489585876,
0.020229827612638474,
-0.031222080811858177,
-0.03600091114640236,
-0.009910248219966888,
0.004378149285912514,
-0.05988495796918869,
-0.017569445073604584,
-0.024385342374444008,
0.03269882872700691,
-0.03593490272760391,
0.05376040190458298,
0.029954278841614723,
-0.0028320495039224625,
0.01767701283097267,
-0.05419328436255455,
0.07157015055418015,
0.0011594472452998161,
0.03949262201786041,
-0.011490349657833576,
-0.05924138054251671,
-0.01949913240969181,
0.06903654336929321,
0.0627327710390091,
0.036594316363334656,
-0.07069100439548492,
-0.01582254096865654,
0.027971869334578514,
-0.005894760135561228,
-0.04019910842180252,
-0.0035578312817960978,
0.0330343022942543,
0.02118690498173237,
-0.019970698282122612,
0.05834388732910156,
-0.025552693754434586,
-0.018537599593400955,
-0.0280391164124012,
0.011721985414624214,
0.015335334464907646,
0.039134953171014786,
0.007943952456116676,
-0.023369252681732178,
-0.026881452649831772,
0.03112381137907505,
0.02854655310511589,
-0.0016051530838012695,
-0.011430690065026283,
0.05992347374558449,
0.03306257352232933,
0.0012008381308987737,
0.013538600876927376,
0.07368744164705276,
-0.009323312900960445,
0.004917625337839127,
0.03591444715857506,
-0.00010582728282315657,
0.0009220988140441477,
0.06438342481851578,
-0.004469361621886492,
0.00045695758308283985,
0.026206333190202713,
0.014343776740133762,
0.03480370342731476,
0.010805653408169746,
-0.004785147495567799,
-0.0071145836263895035,
-0.04535771906375885,
-0.04258467257022858,
0.0879831314086914,
0.012703735381364822,
-0.02840026281774044,
-0.03458280488848686,
-0.00006555633444804698,
-0.08701159805059433,
-0.018796736374497414,
-0.019107962027192116,
0.0349939800798893,
-0.014916818588972092,
-0.009791361168026924,
0.016670111566781998,
-0.0316162072122097,
0.019037991762161255,
-0.041060272604227066,
0.06459934264421463,
0.09693072736263275,
0.03855618089437485,
0.013064843602478504,
0.0012294604675844312,
-0.013922709040343761,
-0.04455813392996788,
0.016033079475164413,
0.05894618108868599,
0.02599317394196987,
0.011213806457817554,
-0.031162511557340622,
0.010901998728513718,
-0.030287673696875572,
-0.00043273321352899075,
0.04730686917901039,
0.0021145783830434084,
-0.0635690838098526,
-0.08437136560678482,
-0.03441120311617851,
0.027695437893271446,
0.029995128512382507,
-0.021294541656970978,
-0.057976432144641876,
0.005770337302237749,
0.008774188347160816,
0.06877434253692627,
-0.00027105319895781577,
0.020201856270432472,
0.03299792483448982,
0.028503110632300377,
-0.039819687604904175,
-0.010038028471171856,
-0.010898259468376637,
-0.014324666932225227,
-0.02406342513859272,
-0.008965833112597466,
-0.044237732887268066,
-0.004478128161281347,
0.0239417627453804,
-0.003216438926756382,
0.020174067467451096,
0.06433126330375671,
-0.0011726075317710638,
0.0053771487437188625,
0.025762833654880524,
-0.013659375719726086,
-0.0022925427183508873,
0.03217533230781555,
0.028991684317588806,
0.0020375410094857216,
0.026882309466600418,
0.018566200509667397,
0.026847198605537415,
0.02600996568799019,
0.025242088362574577,
0.030849143862724304,
-0.06742691248655319,
0.014252867549657822,
0.01474737748503685,
-0.003244328312575817,
0.04655038192868233,
-0.01854521781206131,
-0.021580100059509277,
-0.006613781210035086,
-0.03687872365117073,
-0.017564205452799797,
0.050045669078826904,
-0.0010603135451674461,
0.035264041274785995,
0.04199308902025223,
-0.030540045350790024,
0.02222542278468609,
-0.05084667354822159,
-0.011235522106289864,
0.014135876670479774,
-0.003763067303225398,
0.04066908359527588,
0.010864012874662876,
-0.0014201559824869037,
-0.03315111994743347,
-0.014843990094959736,
-0.006494552828371525,
0.05607287585735321,
0.01545369066298008,
0.0021509802900254726,
0.0327703133225441,
0.024944813922047615,
0.02860909327864647,
0.0063894507475197315,
0.0011879055527970195,
0.018101559951901436,
-0.004702126141637564,
0.025054456666111946,
0.0008405171683989465,
0.04447852447628975,
-0.00909456703811884,
0.008626837283372879,
-0.011786101385951042,
-0.017191965132951736,
-0.03450993075966835,
0.012440729886293411,
-0.06881619989871979,
0.044215619564056396,
0.02091299183666706,
-0.024437708780169487,
0.0020996483508497477,
0.04952903464436531,
-0.007038587238639593,
0.02812120132148266,
0.02649938501417637,
-0.02604321762919426,
-0.027898333966732025,
-0.0007121097878552973,
0.05531249940395355,
0.07032984495162964,
-0.060010120272636414,
-0.004093020688742399,
0.030602481216192245,
0.009588521905243397,
-0.021232640370726585,
0.008818830363452435,
-0.031106438487768173,
-0.04560014232993126,
0.052355896681547165,
-0.02120978571474552,
-0.018661364912986755,
-0.0039172787219285965,
0.024803292006254196,
0.011446954682469368,
0.008593341335654259,
-0.019277842715382576,
-0.0028008909430354834,
0.020676812157034874,
0.0073473332449793816,
-0.010780064389109612,
0.007138270419090986,
0.0033092901576310396,
0.03674422204494476,
-0.0047233859077095985,
0.016513416543602943,
0.012942425906658173,
0.015330501832067966,
-0.03833124414086342,
-0.046284131705760956,
-0.023093031719326973,
0.0029921806417405605,
-0.005446300376206636,
0.01101007778197527,
-0.02597741037607193,
0.018281426280736923,
-0.031624313443899155,
-0.03242097795009613,
0.015139098279178143,
-0.012589069083333015,
-0.027365218847990036,
-0.007673307787626982,
-0.012058928608894348,
0.02429925464093685,
-0.022370530292391777,
0.017113856971263885,
-0.0025863347109407187,
0.05041367560625076,
0.008556481450796127,
0.00786431785672903,
0.054810795933008194,
-0.02823103591799736,
0.03390767052769661,
-0.06463085860013962,
-0.008790337480604649,
0.045822519809007645,
0.003456497099250555,
0.031272921711206436,
0.03119012713432312,
-0.021995173767209053,
-0.04929644986987114,
-0.0007021005148999393,
-0.06092901527881622,
0.03567015752196312,
-0.009755538776516914,
0.006117241457104683,
0.05895412713289261,
-0.013869290240108967,
-0.06380034238100052,
-0.027531838044524193,
-0.05625062808394432,
-0.03373619168996811,
-0.040212005376815796,
0.0009565057698637247,
0.009664859622716904,
-0.03010512888431549,
0.023278221487998962,
0.06457759439945221,
0.016087345778942108,
0.009389306418597698,
-0.0809994712471962,
-0.05385853722691536,
0.040561649948358536,
-0.0007761241868138313,
0.016773372888565063,
-0.018915792927145958,
-0.054807525128126144,
0.06047094240784645,
0.015698956325650215,
-0.035043179988861084,
-0.03044288419187069,
0.02576974406838417,
0.030204491689801216,
-0.04047620669007301,
0.006184309720993042,
0.0010374134872108698,
0.0034052692353725433,
0.02123725414276123,
0.01514745969325304,
0.0349637046456337,
-0.03109370358288288,
0.029676640406250954,
0.0014129092451184988,
0.016942517831921577,
0.003099593799561262,
0.0008951007039286196,
0.04791929945349693,
0.05389709770679474,
-0.010091726668179035,
0.005589439067989588,
0.003767284331843257,
0.015034791082143784,
0.004449522588402033,
-0.056648820638656616,
0.053156282752752304,
0.023237787187099457,
0.002791718812659383,
0.02463182620704174,
0.016602948307991028,
-0.021546868607401848,
-0.035631295293569565,
0.028714483603835106,
0.017067458480596542,
-0.005432267673313618,
-0.01463427022099495,
0.009360834956169128,
0.0020498924423009157,
0.037807613611221313,
-0.027251897379755974,
-0.012139886617660522,
-0.021977053955197334,
-0.017785372212529182,
0.042494986206293106,
-0.0255562923848629,
-0.007082641124725342,
0.021792028099298477,
0.018493646755814552,
0.019102197140455246,
0.035475194454193115,
-0.03551588952541351,
-0.0017903854604810476,
-0.07905731350183487,
-0.027476495131850243,
0.01912880502641201,
0.05313555896282196,
-0.008165768347680569,
0.00418044300749898,
-0.006711126305162907,
0.017518341541290283,
0.020364554598927498,
-0.008983977138996124,
-0.06060429662466049,
0.020212139934301376,
-0.03678877651691437,
-0.0015206916723400354,
0.020908018574118614,
-0.003647784935310483,
0.03320644795894623,
-0.04955586418509483,
-0.020037898793816566,
-0.03636625036597252,
0.0022304565645754337,
-0.08272914588451385,
0.019499270245432854,
-0.009093827567994595,
-0.09946940839290619,
-0.00953243300318718,
0.022901853546500206,
0.038501739501953125,
0.011663881130516529,
-0.009709199890494347,
0.018550271168351173,
0.0029078805819153786,
-0.020603159442543983,
-0.006145861465483904,
0.011365656740963459,
0.03940652310848236,
0.008098797872662544,
-0.006443609483540058,
0.005962603725492954,
0.05155002698302269,
0.030059829354286194,
0.034112777560949326,
0.04613522067666054,
-0.015230103395879269,
0.0044829766266047955,
-0.029017021879553795,
-0.04859468340873718,
-0.01388990692794323,
0.007317160721868277,
0.07903096824884415,
0.0014237291179597378,
-0.03225104883313179,
-0.0018029948696494102,
0.026380235329270363,
0.04043538495898247,
-0.00928248930722475,
0.014153247699141502,
0.008535229600965977,
-0.033423058688640594,
-0.047238294035196304,
-0.007262280210852623,
-0.012383761815726757,
0.000053586485591949895,
0.009553664363920689,
0.027536794543266296,
-0.019416630268096924,
0.03615771606564522,
0.009690063074231148,
0.02199389785528183,
-0.026219798251986504,
-0.029133670032024384,
0.03785230591893196,
0.02702603116631508,
0.025534948334097862,
-0.002085242886096239,
-0.004824043717235327,
0.0305883027613163,
0.06063006445765495,
-0.024909723550081253,
0.04704244062304497,
-0.057981304824352264,
-0.029409173876047134,
0.017685789614915848,
0.008346511982381344,
-0.013205903582274914,
-0.03811010718345642,
-0.04607996717095375,
0.007209496106952429,
0.020215487107634544,
-0.009952436201274395,
-0.024516554549336433,
0.0097981421276927,
0.004525277763605118,
0.01647922210395336,
-0.03683792054653168,
-0.03361761197447777,
0.027844883501529694,
-0.010813800618052483,
-0.024161387234926224,
-0.030724532902240753,
0.03263907507061958,
0.009846514090895653,
0.01666661724448204,
0.011571520008146763,
0.038301076740026474,
0.02447522059082985,
0.0034416746348142624,
0.004538563080132008,
0.06160581484436989,
-0.012521831318736076,
-0.08002767711877823,
0.018688099458813667,
0.03871326521039009,
-0.009230087511241436,
-0.016718309372663498,
-0.005025782622396946,
-0.03655359148979187,
0.0033496497198939323,
-0.020446451380848885,
0.0030961509328335524,
0.06269685924053192,
-0.04291225224733353,
0.009251397103071213,
0.05621235817670822,
0.00462003517895937,
-0.0009702392853796482,
0.035258110612630844,
0.003779089078307152,
-0.0029114740900695324,
-0.014636632055044174,
0.008765471167862415,
-0.02602224051952362,
-0.017971159890294075,
-0.05654950812458992,
0.008588738739490509,
-0.05307752266526222,
0.022318394854664803,
-0.0292687825858593,
0.009867298416793346,
-0.036260366439819336,
-0.047685783356428146,
-0.002283315872773528,
0.023468490689992905,
0.004097386728972197,
-0.016779137775301933,
-0.013046396896243095,
0.00763858063146472,
0.034000497311353683,
-0.03603589907288551,
0.010113832540810108,
-0.01059179287403822,
-0.009164632298052311,
0.052323825657367706,
0.006199881434440613,
0.022784510627388954,
-0.013762937858700752,
-0.01790919154882431,
0.02691274881362915,
-0.016389070078730583,
0.04363961145281792,
0.0034172572195529938,
-0.0011301893973723054,
0.004809819161891937,
0.0019955849274992943,
-0.04489444941282272,
-0.021483302116394043,
-0.030999140813946724,
0.019598349928855896,
-0.008080679923295975,
-0.05558604374527931,
0.015669377520680428,
-0.020779142156243324,
-0.0673433318734169,
-0.015874609351158142,
0.009500953368842602,
-0.020009957253932953,
-0.007884517312049866,
-0.006083304528146982,
0.01681949943304062,
-0.056140415370464325,
-0.015581824816763401,
0.016322821378707886,
0.06713611632585526,
-0.030055029317736626,
0.02264651656150818,
-0.02680760808289051,
0.016400497406721115,
-0.029339881613850594,
-0.04400921240448952,
0.002441176911816001,
0.0031858799047768116,
0.0036515414249151945,
0.010495876893401146,
-0.0059755356051027775,
0.08207916468381882,
0.003270536195486784,
0.013293283060193062,
-0.031993020325899124,
-0.029176950454711914,
0.0273941308259964,
-0.019105827435851097,
-0.0029715413693338633,
0.057841550558805466,
-0.016129419207572937,
-0.030233273282647133,
-0.045987531542778015,
-0.0031617649365216494,
0.024258757010102272,
0.017674267292022705,
-0.03726079314947128,
-0.006918726023286581,
-0.008884025737643242,
-0.03201249614357948,
0.039651669561862946,
-0.00047592338523827493,
-0.030855828896164894,
-0.03922352194786072,
0.043164994567632675,
0.03924515098333359,
-0.02702253684401512,
0.0022778708953410387,
0.010062207467854023,
0.036058854311704636,
-0.020902812480926514,
0.016195235773921013,
0.017131512984633446,
0.019466690719127655,
-0.017066922038793564,
-0.02076956257224083,
-0.0392715148627758,
0.010895988903939724,
0.08159375935792923,
-0.007124654948711395,
0.037701938301324844,
0.0066859181970357895,
-0.02764659747481346,
0.02824697084724903,
-0.03347382694482803,
-0.002402297453954816,
0.01447314117103815,
0.004475843161344528,
0.029219403862953186,
-0.053171902894973755,
0.022023161873221397,
0.03231131657958031,
0.039295874536037445,
-0.05313740670681,
0.026486841961741447,
-0.03248834237456322,
0.04336842894554138,
-0.0012498846044763923,
-0.04140353202819824,
-0.06927144527435303,
0.058635249733924866,
-0.016132107004523277,
0.04571155086159706,
0.02639325149357319,
-0.012862424366176128,
0.026286806911230087,
0.03810558840632439,
-0.012659967876970768,
-0.018412593752145767,
-0.01821260154247284,
-0.06960614770650864,
0.01310265064239502,
0.03696047142148018,
0.011195626109838486,
-0.019225673750042915,
0.003344110678881407,
0.033261533826589584,
-0.024606501683592796,
0.016509540379047394,
0.017013004049658775,
-0.026976844295859337,
0.026501687243580818,
-0.06329898536205292,
-0.04325096681714058,
0.053420133888721466,
0.021646399050951004,
-0.01588180474936962,
-0.03856910765171051,
-0.013235772959887981,
0.013496638275682926,
0.019061271101236343,
0.030941329896450043,
-0.01742369495332241,
0.0798376202583313,
-0.022429855540394783,
0.00225841230712831,
-0.03229745477437973,
-0.0005734935402870178,
0.1341528296470642,
0.029209520667791367,
0.0222213976085186,
-0.05008575692772865,
-0.001616801368072629,
-0.014388089999556541,
-0.012993844226002693,
-0.02617121860384941,
0.051891956478357315,
-0.008640080690383911,
-0.0012734479969367385,
0.020384836941957474,
0.05666474252939224,
-0.009862978011369705,
-0.026428066194057465,
0.06550366431474686,
-0.04188970476388931,
-0.011156152933835983,
0.014562336727976799,
0.012552632950246334,
-0.013474622741341591,
0.006731526926159859,
-0.017605923116207123,
0.0512114092707634,
-0.027320820838212967,
0.03460007905960083,
-0.030947618186473846,
-0.053288303315639496,
0.00005222712206887081,
0.019779479131102562,
-0.050068389624357224,
-0.010234972462058067,
-0.01632990874350071,
0.012527109123766422,
-0.0660955011844635,
-0.028663577511906624,
0.01308058574795723,
-0.027922526001930237,
0.039918236434459686,
0.007042448967695236,
0.017757875844836235,
0.03497624397277832,
0.007911207154393196,
-0.013311265036463737,
-0.050761736929416656,
0.00824825745075941,
-0.077517569065094,
0.08061110973358154,
-0.021912366151809692,
0.014583062380552292,
-0.005784898065030575,
-0.005072835832834244,
0.019191879779100418,
-0.03199094906449318,
-0.015840696170926094,
-0.033021144568920135,
0.00863914005458355,
-0.004019453190267086,
0.01485278271138668,
-0.0037496990989893675,
0.018841372802853584,
0.0125441187992692,
0.030841438099741936,
-0.018941553309559822,
-0.013509641401469707,
-0.006637681275606155,
-0.009740173816680908,
0.06584952771663666,
-0.015703247860074043,
-0.02661646343767643,
-0.0034140662755817175,
-0.04396709427237511,
-0.02259477972984314,
-0.02338508702814579,
0.014299877919256687,
0.01987835206091404,
0.030696803703904152,
0.001202753046527505,
0.003863547695800662,
-0.01077823806554079,
-0.05090916156768799,
0.025573696941137314,
-0.03810425102710724,
0.016375912353396416,
-0.016757771372795105,
0.0002620866580400616,
-0.015149428509175777,
0.03889044374227524,
-0.009212132543325424,
-0.03300857916474342,
0.028973432257771492,
0.030784429982304573,
0.006804265081882477,
-0.0053426362574100494,
0.011842248030006886,
0.0246034674346447,
-0.05342093110084534,
-0.010193106718361378,
-0.02818313241004944,
-0.0010050819255411625,
0.020424051210284233,
0.02235383540391922,
-0.019450055435299873,
0.03098081797361374,
0.003611820749938488,
-0.01923682726919651,
-0.003470606403425336,
-0.006666058674454689,
0.016022007912397385,
0.018399948254227638,
0.03690939396619797,
-0.05293991416692734,
-0.025030488148331642,
-0.018793286755681038,
0.00026543025160208344,
-0.023943360894918442,
0.01009086612612009,
-0.01811765693128109,
0.0008795600151643157,
-0.01927025057375431,
0.008085650391876698,
-0.028469795361161232,
0.017154503613710403,
-0.03164534270763397,
0.06404992192983627,
-0.00658210227265954,
-0.030726438388228416,
-0.0008387612760998309,
0.0335724875330925,
0.0047377352602779865,
-0.019649408757686615,
0.0035808247048407793,
-0.01612192764878273,
-0.036857593804597855,
0.007175096310675144,
0.024166960269212723,
-0.02004758082330227,
0.03213899955153465,
0.024903355166316032,
0.002645708154886961,
-0.00047775660641491413,
-0.03248357027769089,
-0.06382039934396744,
0.02811388112604618,
-0.001256134593859315,
0.01547901052981615,
0.026706155389547348,
-0.04043404012918472,
0.00025007323711179197,
0.02997516468167305,
-0.0002904408611357212,
0.021641014143824577,
0.006829928606748581,
-0.046359866857528687,
-0.005805503576993942,
-0.05624088644981384,
0.02676224708557129,
0.01948496699333191,
-0.022712772712111473,
0.008414383977651596,
0.01946866139769554,
-0.041560642421245575,
-0.010749251581728458,
0.04324363172054291,
-0.061112768948078156,
-0.03147420659661293,
-0.00663960725069046,
-0.012357381172478199,
0.042862437665462494,
0.03999365121126175,
-0.04600907117128372,
-0.037862710654735565,
0.057429708540439606,
0.019465504214167595,
-0.10806512832641602,
-0.006897347513586283,
0.0019471931736916304,
0.02944220043718815,
0.06827165186405182,
-0.05938325449824333,
0.027981597930192947,
-0.004145598970353603,
-0.05666445195674896,
0.04627079516649246,
-0.010975883342325687,
0.0013022933853790164,
-0.0069313389249145985,
-0.00584370968863368,
-0.02352670207619667,
0.04022357985377312,
0.029213860630989075,
0.02428603172302246,
0.03012707270681858,
0.035615645349025726,
-0.007168170530349016,
-0.01892581395804882,
-0.011115305125713348,
0.00945053156465292,
-0.007918348535895348,
0.009974717162549496,
0.07039106637239456,
-0.019057026132941246,
-0.02124507911503315,
0.01687556877732277,
0.026636878028512,
-0.0009772763587534428,
-0.010609983466565609,
-0.028463328257203102,
0.020093003287911415,
-0.013304478488862514,
0.02891950123012066,
-0.029865292832255363,
0.002604288747534156,
0.010971911251544952,
-0.009013526141643524,
0.017615988850593567,
-0.030659452080726624,
-0.007769570220261812,
0.02304128371179104,
-0.05703074485063553,
-0.00424379575997591,
0.019407089799642563,
-0.011089525185525417,
-0.03272996097803116,
0.014967100694775581,
0.004919125232845545,
-0.022422363981604576,
-0.004718750715255737,
-0.009609945118427277,
-0.04541460797190666,
-0.01562616415321827,
0.007078766357153654,
-0.016233419999480247,
0.009316300973296165,
0.055931683629751205,
-0.02512102946639061,
-0.014032460749149323,
0.003294745460152626,
-0.032709527760744095,
-0.0039883446879684925,
-0.06701625138521194,
-0.024211909621953964,
-0.008726632222533226,
-0.008554955944418907,
-0.03155559301376343,
-0.019360162317752838,
0.0028896797448396683,
0.06317050009965897,
0.04545295611023903,
0.012207343243062496,
-0.010876215994358063,
-0.00012028556375298649,
-0.0021405776496976614,
-0.060398709028959274,
-0.0063624014146625996,
0.03853348270058632,
0.01898341253399849,
-0.016335535794496536,
-0.048056766390800476,
-0.008136151358485222,
0.012933336198329926,
0.07596372812986374,
-0.04163925349712372,
0.012152569368481636,
0.04514714702963829,
-0.0003488787042442709,
0.02691570483148098,
-0.027292417362332344,
0.007900930009782314,
-0.017980355769395828,
0.022761913016438484,
-0.012495837174355984,
0.023638594895601273,
0.020882945507764816,
0.016969960182905197,
0.01240377128124237,
-0.0055398475378751755,
0.0210105087608099,
0.029008250683546066,
-0.02997284010052681,
0.043244536966085434,
0.015293646603822708,
-0.0314951092004776,
0.03890566527843475,
-0.012289443053305149,
-0.021510500460863113,
0.0138129573315382,
-0.05277417600154877,
0.008792917244136333,
-0.011355276219546795,
-0.012200609780848026,
-0.04403533414006233,
0.012414497323334217,
-0.001401777844876051,
0.02874576300382614,
-0.029819272458553314,
0.016382990404963493,
0.06564073264598846,
-0.04130110889673233,
-0.0029757628217339516,
0.021533485502004623,
-0.03306557983160019,
0.0601436085999012,
0.01034995261579752,
0.015631645917892456,
0.040288589894771576,
0.00048375315964221954,
0.03003367967903614,
0.047053102403879166,
0.041083257645368576,
-0.015702836215496063,
-0.0169655941426754,
0.00023808212426956743,
-0.02868647873401642,
0.026604987680912018,
0.03431129455566406,
0.05368786305189133,
-0.04532754048705101,
0.008588873781263828,
0.017606357112526894,
-0.0069080195389688015,
-0.006025682669132948,
-0.008176060393452644,
-0.0004293982347007841,
0.0889580026268959,
0.013243574649095535,
-0.02506246790289879,
-0.021897979080677032,
0.05403817817568779,
-0.017820462584495544,
0.017527805641293526,
0.005731393117457628,
0.05434592068195343,
-0.003934768494218588,
0.014146781526505947,
-0.018291596323251724,
0.004838318098336458,
0.014654139056801796,
-0.025253312662243843,
0.017167862504720688,
0.016674932092428207,
-0.0023566221352666616,
0.00035320711322128773,
-0.009456143714487553,
-0.004571124445647001,
-0.013571352697908878,
0.003992833197116852,
0.004341833759099245,
0.0771053284406662,
-0.007295226212590933,
0.01757158152759075,
-0.04395170882344246,
0.07160095125436783,
-0.06830740720033646,
-0.033774618059396744,
-0.006417089607566595,
0.014395004138350487,
-0.007221569307148457,
0.012926803901791573
] |
<p>Many of the most brilliant ideas of modern physics are very much unpopperian. In view of this, it has become more and more difficult to hold an orthodox Popperian attitude in physics. It simply looks like more of a philosophical dogma nowadays. My question is, should physicists abandon this criterion at least partially for good? If so, what criterion should replace it?</p>
| 7,680 |
[
-0.000041566516301827505,
-0.01970794051885605,
0.0033012886997312307,
-0.0558166578412056,
0.03435717150568962,
-0.004959635902196169,
-0.030992969870567322,
-0.020401226356625557,
-0.008426085114479065,
-0.008840210735797882,
0.015521546825766563,
0.018233705312013626,
0.040104083716869354,
0.022770842537283897,
-0.0011757402680814266,
-0.0165539663285017,
0.013045812956988811,
-0.024306654930114746,
-0.029312316328287125,
-0.0452534481883049,
0.0004242977302055806,
0.028792094439268112,
0.006487324833869934,
0.04016561806201935,
-0.014462767168879509,
0.014439599588513374,
0.0320388600230217,
0.030593035742640495,
0.03349621966481209,
0.07088886946439743,
0.004369253758341074,
-0.01417786255478859,
0.0041499570943415165,
-0.0036284655798226595,
0.03328031301498413,
-0.017982009798288345,
-0.006732019130140543,
-0.021306341513991356,
-0.027389606460928917,
0.018814103677868843,
-0.028340529650449753,
-0.0003773413773160428,
-0.038494378328323364,
0.000014642248061136343,
-0.003254427807405591,
0.04537993669509888,
-0.014528478495776653,
-0.011167685501277447,
0.06524833291769028,
-0.07251156121492386,
0.03810592740774155,
0.04383242875337601,
-0.0011975516099482775,
0.01157933659851551,
-0.008717909455299377,
-0.04102742299437523,
0.07769331336021423,
0.07296212762594223,
-0.025252507999539375,
-0.056280139833688736,
-0.04465332627296448,
0.000748277991078794,
-0.003883069148287177,
-0.028718847781419754,
-0.025064624845981598,
0.06955613195896149,
0.019179798662662506,
-0.00004722157245851122,
0.02731654979288578,
0.0035360276233404875,
-0.021556230261921883,
-0.030416835099458694,
0.058807119727134705,
0.01756221428513527,
0.005371244624257088,
-0.006810626480728388,
0.0075444504618644714,
-0.009608845226466656,
0.012795507907867432,
0.034817468374967575,
0.025435492396354675,
0.008247514255344868,
0.04475731775164604,
0.06408268958330154,
-0.007818920537829399,
-0.030598033219575882,
0.05886195972561836,
-0.04282277077436447,
-0.007152399513870478,
0.024482017382979393,
-0.003947964403778315,
-0.023226531222462654,
0.04865501821041107,
-0.021816996857523918,
-0.054209861904382706,
0.03419698774814606,
0.0009011487127281725,
0.06428162008523941,
0.005992806050926447,
-0.030580412596464157,
0.0164360199123621,
-0.02173518016934395,
0.03602578118443489,
0.05888798087835312,
-0.002603548811748624,
-0.03741643205285072,
-0.04127607122063637,
0.004766035825014114,
0.007326355203986168,
-0.025521930307149887,
-0.0387464202940464,
0.031535327434539795,
0.01145323459059,
0.025959955528378487,
0.02623284049332142,
-0.01234432589262724,
-0.008179561235010624,
-0.0465620681643486,
0.0665491372346878,
0.04668305814266205,
0.03932996466755867,
0.0027651353739202023,
0.05363820120692253,
-0.017898818477988243,
-0.09125659614801407,
-0.009636844508349895,
0.04058792442083359,
0.022608919069170952,
-0.007125732023268938,
0.03246036171913147,
0.03955565020442009,
-0.0040803272277116776,
0.001576883951202035,
0.053873807191848755,
0.03378435969352722,
-0.01692722737789154,
-0.10724221915006638,
-0.03372284770011902,
0.03764892742037773,
0.02038288675248623,
-0.0030362652614712715,
-0.09125024080276489,
0.004093424882739782,
0.02702902816236019,
0.0627744197845459,
-0.014313780702650547,
-0.03221499174833298,
0.012054268270730972,
0.08159834146499634,
-0.018490269780158997,
-0.04931073635816574,
-0.03536749631166458,
-0.0020350883714854717,
-0.03018144704401493,
-0.02206517942249775,
-0.0858134776353836,
-0.016680020838975906,
0.015929048880934715,
-0.006941353436559439,
-0.020085984840989113,
0.06373618543148041,
-0.053820304572582245,
-0.007317870389670134,
-0.007773208897560835,
-0.014869322068989277,
-0.0008374506724067032,
0.06505342572927475,
0.017649708315730095,
0.01893576793372631,
0.03295845538377762,
0.01667558029294014,
0.03366857394576073,
-0.002197550144046545,
0.02052706852555275,
0.012600325047969818,
-0.05087561532855034,
-0.011087224818766117,
-0.0026710517704486847,
0.011833138763904572,
-0.014878589659929276,
-0.02618742175400257,
-0.010350997559726238,
-0.030146723613142967,
0.02803557552397251,
-0.02262355200946331,
0.03861658275127411,
0.004416327457875013,
-0.0053708720952272415,
0.020230723544955254,
-0.03339417278766632,
-0.021002020686864853,
-0.09066639095544815,
0.008542139083147049,
0.017308738082647324,
-0.009369103237986565,
0.04714315012097359,
0.008777325972914696,
-0.006487071514129639,
-0.05842766538262367,
-0.03267993405461311,
-0.007086952682584524,
0.060819435864686966,
-0.010057132691144943,
-0.015826284885406494,
0.02135070599615574,
0.027308454737067223,
0.012297564186155796,
0.009164038114249706,
0.018283285200595856,
0.028815805912017822,
-0.06895463168621063,
0.011836291290819645,
-0.00924126897007227,
0.01904224045574665,
-0.004844117444008589,
-0.00510091707110405,
0.031495459377765656,
-0.04925587773323059,
-0.0159161239862442,
0.039531007409095764,
-0.05453573539853096,
0.0663059800863266,
0.012925674207508564,
0.017500439658761024,
-0.0015293719479814172,
0.061416685581207275,
-0.0053184363059699535,
0.022579198703169823,
-0.005031873472034931,
-0.01102431770414114,
-0.02039450779557228,
0.03285634517669678,
0.023471198976039886,
0.0599852055311203,
-0.0425025075674057,
0.025700068101286888,
-0.021450303494930267,
0.05525721609592438,
0.019384058192372322,
0.027813667431473732,
-0.032448865473270416,
-0.056844938546419144,
0.007527136243879795,
0.005245230160653591,
-0.012632407248020172,
0.04480649158358574,
0.028189642354846,
0.01534972433000803,
-0.009494861587882042,
-0.014578849077224731,
0.0011400089133530855,
0.02030506171286106,
-0.004287271294742823,
0.005217791069298983,
0.01682933233678341,
-0.04382096976041794,
0.011513683013617992,
-0.014437200501561165,
0.0538911409676075,
0.04312826320528984,
0.01197402086108923,
0.007048271130770445,
-0.04649428650736809,
-0.011362292803823948,
-0.020009789615869522,
-0.0012334727216511965,
-0.03731444478034973,
-0.023990627378225327,
0.03425905480980873,
-0.008043861947953701,
-0.017380215227603912,
0.00039582818862982094,
-0.0075102560222148895,
-0.013301952742040157,
0.01231375988572836,
0.013083400204777718,
-0.005660966504365206,
0.0096628088504076,
0.0014551420463249087,
-0.013207492418587208,
0.002201525727286935,
-0.029252884909510612,
-0.027292799204587936,
0.05197187885642052,
-0.011505655013024807,
-0.0012167836539447308,
-0.01032761950045824,
-0.03143942356109619,
0.05615722015500069,
-0.026282500475645065,
0.031235234811902046,
-0.01978427916765213,
0.019537635147571564,
0.002697416115552187,
0.0049957456067204475,
-0.014090410433709621,
-0.029675407335162163,
0.011017518118023872,
-0.016446299850940704,
0.029807860031723976,
-0.005421184003353119,
-0.04707292094826698,
0.017317846417427063,
-0.03800388053059578,
-0.09565255045890808,
-0.010681056417524815,
-0.025897210463881493,
0.014227055944502354,
0.003243363229557872,
0.01689847931265831,
0.06826088577508926,
-0.0480063296854496,
-0.016810698434710503,
-0.04546802490949631,
-0.09554797410964966,
0.007277618627995253,
-0.033157628029584885,
0.034246958792209625,
0.02549164369702339,
-0.019808277487754822,
0.057584285736083984,
0.050248388200998306,
-0.04164741560816765,
-0.014286363497376442,
0.007773364428430796,
-0.007787922862917185,
0.03137501701712608,
-0.01763237453997135,
0.013703261502087116,
0.011936797760426998,
0.03252159059047699,
-0.002046408364549279,
-0.003344232216477394,
0.01876363530755043,
0.01594969816505909,
-0.019945042207837105,
-0.007394962944090366,
0.012971834279596806,
-0.03284933418035507,
-0.01948968879878521,
0.02180596813559532,
-0.020274654030799866,
-0.000966553867328912,
0.0028756854590028524,
0.003012043656781316,
0.018548525869846344,
-0.024878984317183495,
0.06641814112663269,
-0.0027578151784837246,
0.02999146282672882,
0.020758939906954765,
0.01662660762667656,
0.0013552582822740078,
-0.007277815602719784,
0.011804678477346897,
0.0491088330745697,
-0.008137303404510021,
-0.0105282599106431,
0.011554507538676262,
0.05433792620897293,
0.02549641765654087,
-0.03089904598891735,
-0.008931654505431652,
0.027843451127409935,
0.00462178373709321,
0.02008971758186817,
0.043416235595941544,
-0.014985186979174614,
0.03841405361890793,
0.008612105622887611,
0.04576994478702545,
0.004673257004469633,
-0.04574441909790039,
0.012538268230855465,
-0.04454849287867546,
0.0009743921109475195,
0.002245476469397545,
0.05483239144086838,
0.010060237720608711,
0.018060734495520592,
0.03919622674584389,
0.019260361790657043,
-0.008571343496441841,
0.018778476864099503,
-0.07664743065834045,
0.02354539930820465,
-0.05791078135371208,
0.004667152184993029,
0.010954061523079872,
0.029054490849375725,
-0.0067137544974684715,
-0.01752893067896366,
-0.027560291811823845,
-0.06055707484483719,
0.028805218636989594,
-0.05666663870215416,
-0.004456107039004564,
-0.040084972977638245,
-0.06525233387947083,
-0.026206497102975845,
0.02639920264482498,
0.051807355135679245,
-0.0040810913778841496,
0.014638175256550312,
0.049855202436447144,
-0.036425910890102386,
-0.01867419108748436,
0.006526282988488674,
-0.00024549278896301985,
-0.006236196029931307,
0.006076938938349485,
0.004236770328134298,
0.01629881002008915,
-0.044429123401641846,
0.04730833321809769,
0.0029038109350949526,
0.053187090903520584,
-0.007585382089018822,
-0.036879442632198334,
-0.003035165136680007,
-0.027979344129562378,
-0.027389749884605408,
-0.027799565345048904,
0.05588936060667038,
0.017496174201369286,
-0.0265788733959198,
0.044411551207304,
-0.020457683131098747,
-0.019261952489614487,
0.04820268973708153,
0.059781763702631,
0.004538788925856352,
-0.026700392365455627,
-0.009031460620462894,
-0.04502410441637039,
-0.02900979481637478,
-0.007017063908278942,
0.015253143385052681,
0.03247372806072235,
-0.027793530374765396,
0.005883497651666403,
0.002718370407819748,
0.003929003607481718,
-0.05335396155714989,
0.0019100412027910352,
-0.006048641633242369,
0.0058632222935557365,
-0.013239218853414059,
-0.009396628476679325,
-0.0008616643026471138,
0.04881874844431877,
0.046802494674921036,
0.011703290045261383,
-0.005549030378460884,
-0.04759484529495239,
0.019027842208743095,
0.031836964190006256,
0.02496384270489216,
-0.02366674318909645,
-0.0314200259745121,
-0.03679757937788963,
-0.024305667728185654,
0.04474193602800369,
-0.019423561170697212,
0.005197352264076471,
-0.03315379098057747,
-0.005190068390220404,
-0.029084980487823486,
-0.02360083907842636,
-0.037934307008981705,
0.02925766259431839,
0.005358278751373291,
0.01525037083774805,
-0.02306690253317356,
-0.023792458698153496,
-0.017951559275388718,
0.00789709948003292,
-0.023516518995165825,
0.06712225079536438,
0.028074171394109726,
-0.03299371898174286,
-0.01590743660926819,
0.008203454315662384,
-0.028865771368145943,
-0.07970927655696869,
-0.0015471362276002765,
-0.006309800781309605,
-0.021740954369306564,
0.013858000747859478,
-0.00794926006346941,
-0.07076779007911682,
-0.020428119227290154,
-0.022893311455845833,
-0.031633611768484116,
0.04423331096768379,
-0.0036775392945855856,
0.04662861302495003,
0.0031708115711808205,
0.031793512403964996,
-0.0011707439552992582,
0.040143825113773346,
-0.03558358550071716,
-0.003260861849412322,
-0.01578279212117195,
-0.007057609036564827,
-0.04939901456236839,
0.010917848907411098,
-0.049982018768787384,
-0.01657169684767723,
-0.04221910983324051,
0.04417094215750694,
0.006949681788682938,
-0.00727170892059803,
0.0027075684629380703,
-0.04987027868628502,
-0.008760770782828331,
-0.0024021125864237547,
-0.01388525776565075,
0.0005346765974536538,
0.0010536148911342025,
0.029489122331142426,
-0.011950341984629631,
-0.009884512983262539,
0.004601786378771067,
-0.0011296735610812902,
0.017152294516563416,
0.013913009315729141,
-0.019518539309501648,
0.02427213452756405,
-0.027189256623387337,
-0.0402756929397583,
-0.015253477729856968,
-0.030238449573516846,
0.05043666437268257,
-0.0132517134770751,
0.01972154900431633,
-0.0040847244672477245,
-0.06740272790193558,
-0.047117434442043304,
0.027464663609862328,
0.021139925345778465,
0.04838342219591141,
-0.05110355094075203,
-0.010456716641783714,
-0.016635283827781677,
0.01913643628358841,
-0.0775504931807518,
-0.02354252152144909,
-0.0008131448412314057,
0.0012863419251516461,
-0.03539200499653816,
-0.016617586836218834,
0.021785607561469078,
-0.02627522125840187,
-0.00890881847590208,
-0.03057144396007061,
0.044265639036893845,
-0.008555075153708458,
-0.019247977063059807,
0.008168438449501991,
0.01609009876847267,
0.06355351209640503,
-0.040511056780815125,
0.01996263675391674,
0.01665542833507061,
0.008425506763160229,
0.011464578099548817,
0.00766322948038578,
0.03750964254140854,
-0.023018764331936836,
-0.029082536697387695,
-0.0027453696820884943,
-0.024657538160681725,
0.001018428592942655,
-0.010903449729084969,
-0.007378585170954466,
0.021757081151008606,
-0.043634045869112015,
-0.041309062391519547,
0.000688569329213351,
0.008945676498115063,
0.005593367852270603,
0.0071983435191214085,
0.01551173347979784,
0.004714917857199907,
0.013651558198034763,
-0.08650508522987366,
0.03610432147979736,
-0.008549578487873077,
-0.01746341399848461,
0.005712475161999464,
0.006986675783991814,
0.009899980388581753,
-0.020404936745762825,
0.02472701109945774,
-0.009392195381224155,
-0.0011092619970440865,
0.008898777887225151,
0.03030765801668167,
0.005771392025053501,
-0.009870150126516819,
0.0012325237039476633,
-0.06512410193681717,
-0.029401538893580437,
-0.003335735760629177,
0.04562823474407196,
-0.0041231075301766396,
0.03404675051569939,
0.044606905430555344,
0.000006084640972403577,
-0.02423299103975296,
-0.02903960831463337,
0.022908253595232964,
0.003210586728528142,
0.01680469512939453,
0.012835467234253883,
-0.05382845178246498,
0.011754878796637058,
0.0333046019077301,
0.04738672077655792,
-0.01848589815199375,
0.013573280535638332,
0.021664844825863838,
0.06559960544109344,
0.02181832864880562,
-0.022732002660632133,
-0.012879679910838604,
0.04373300075531006,
-0.05243043228983879,
0.02154521644115448,
0.008202377706766129,
-0.04643917828798294,
-0.032679855823516846,
0.017048316076397896,
-0.02105991169810295,
0.012073768302798271,
0.015381507575511932,
-0.011675157584249973,
0.010738812386989594,
0.01348857395350933,
0.024965954944491386,
0.006226506549865007,
-0.020541587844491005,
-0.018527455627918243,
0.03369508683681488,
0.04544128477573395,
0.005275092553347349,
-0.05954131484031677,
-0.04662483185529709,
-0.043201979249715805,
-0.05664760619401932,
0.025845926254987717,
0.007325152400881052,
-0.019465038552880287,
0.008753764443099499,
0.008256450295448303,
-0.024549223482608795,
0.011174679733812809,
0.03430173918604851,
-0.020342016592621803,
0.03287815302610397,
-0.003456167411059141,
0.002602791180834174,
-0.003528638742864132,
0.01594923436641693,
0.11741214990615845,
0.046446263790130615,
0.03317951783537865,
-0.04895298555493355,
0.06727492809295654,
-0.03548232838511467,
0.02564886026084423,
-0.04250968620181084,
0.03272460401058197,
-0.0026092957705259323,
-0.005946280900388956,
-0.019480163231492043,
0.024331217631697655,
0.0541025847196579,
0.0005926448502577841,
0.07806767523288727,
-0.07746196538209915,
-0.020509302616119385,
0.0277089886367321,
0.00422839168459177,
-0.006326624192297459,
-0.003095557214692235,
-0.010813510976731777,
-0.001220908248797059,
0.0059110489673912525,
0.02488948218524456,
0.02533421292901039,
-0.00542745366692543,
-0.007851635105907917,
-0.003001264063641429,
-0.002359625417739153,
0.0020501194521784782,
0.00890926644206047,
-0.018851619213819504,
-0.03167874738574028,
-0.008418839424848557,
0.004054795950651169,
-0.007473146542906761,
0.007626413833349943,
0.015184663236141205,
0.02796313725411892,
-0.034640755504369736,
0.0012397585669532418,
0.012115143239498138,
-0.017305880784988403,
0.02001292258501053,
0.009513331577181816,
0.04375274479389191,
-0.015843508765101433,
0.05448896437883377,
0.01605752483010292,
-0.024813391268253326,
-0.025695232674479485,
-0.039254650473594666,
-0.016697436571121216,
0.0009387750178575516,
0.031186196953058243,
-0.006157856900244951,
-0.025746487081050873,
0.0038315753918141127,
-0.0017433195607736707,
-0.0021503991447389126,
0.033738959580659866,
-0.04632271081209183,
-0.007222973275929689,
-0.029415421187877655,
0.03788720816373825,
0.01738358475267887,
0.024787846952676773,
-0.012208854779601097,
-0.034220967441797256,
-0.011683251708745956,
-0.09032445400953293,
0.003989603370428085,
0.019120005890727043,
-0.005435914266854525,
0.023689933121204376,
-0.0010770864319056273,
0.016429932788014412,
-0.023118918761610985,
-0.02506387047469616,
0.019512169063091278,
-0.015314644202589989,
-0.00010862751514650881,
-0.04220978915691376,
0.010090118274092674,
0.048875924199819565,
0.038889337331056595,
-0.01890828274190426,
-0.039201389998197556,
0.0008353124721907079,
0.028005436062812805,
0.005212200805544853,
-0.03675317019224167,
-0.002722274512052536,
-0.01257304660975933,
-0.010150345042347908,
0.01714087463915348,
0.0013833956327289343,
0.007336494047194719,
0.024918345734477043,
0.010253002867102623,
-0.017080023884773254,
0.026198744773864746,
0.026830732822418213,
-0.007868772372603416,
0.03021651692688465,
-0.001970603596419096,
-0.029806341975927353,
0.026837360113859177,
0.027593759819865227,
-0.04190617427229881,
-0.009981793351471424,
-0.04672548919916153,
0.010954608209431171,
0.0044141183607280254,
0.02491302229464054,
-0.012450676411390305,
-0.001979104708880186,
0.019482634961605072,
0.05027648061513901,
-0.024014156311750412,
0.0044870516285300255,
-0.030428042635321617,
-0.018011493608355522,
0.004557420965284109,
-0.00889573059976101,
-0.03180450201034546,
0.06883027404546738,
0.010054443962872028,
-0.04671629145741463,
0.05073528736829758,
0.02521534077823162,
-0.026953591033816338,
-0.020596886053681374,
0.03455987572669983,
-0.027228275313973427,
0.05871867015957832,
-0.037943482398986816,
-0.03246614336967468,
-0.004312142729759216,
-0.03362641856074333,
-0.07502563297748566,
-0.004726924933493137,
-0.021298183128237724,
-0.0035975391510874033,
0.018633490428328514,
-0.023580186069011688,
-0.03462236374616623,
0.009724711999297142,
-0.023854786530137062,
-0.0031115638557821512,
0.027978628873825073,
0.0020708751399070024,
-0.04414709284901619,
0.00036002887645736337,
0.038656219840049744,
-0.00913602951914072,
-0.018042951822280884,
0.01841064728796482,
0.05899238958954811,
0.002724309219047427,
0.00625357823446393,
-0.0008162742014974356,
-0.04213796555995941,
0.005966007709503174,
0.01633232831954956,
0.02686099335551262,
0.021744458004832268,
0.05493944138288498,
-0.043577998876571655,
0.013812143355607986,
0.013448907993733883,
0.005278666503727436,
-0.09263844043016434,
-0.017237070947885513,
-0.010461860336363316,
0.01302762795239687,
0.038910944014787674,
-0.026435423642396927,
0.05067576840519905,
0.00673400703817606,
-0.05153420567512512,
-0.004302070941776037,
0.005262946709990501,
-0.02302013896405697,
-0.005474562291055918,
-0.02696320414543152,
-0.047513727098703384,
0.07149133086204529,
0.01345780584961176,
0.03329683467745781,
0.00795381236821413,
0.037257518619298935,
-0.0031783832237124443,
-0.005261994432657957,
-0.026942569762468338,
0.039654579013586044,
-0.04681908339262009,
-0.014915633015334606,
0.04852064326405525,
-0.014155648648738861,
-0.054616741836071014,
0.08313190937042236,
0.021934224292635918,
-0.007871313951909542,
-0.0051516941748559475,
0.031631454825401306,
0.026832371950149536,
0.046791307628154755,
0.012634861283004284,
-0.01711983233690262,
-0.01618942618370056,
0.022640306502580643,
0.011202349327504635,
0.02613416500389576,
-0.012000915594398975,
-0.005042131524533033,
0.01172685343772173,
-0.03495411202311516,
-0.0465693473815918,
0.015599091537296772,
-0.01401175931096077,
0.00576297240331769,
-0.03448156267404556,
0.023593660444021225,
-0.007198353298008442,
-0.03885343298316002,
0.027651816606521606,
-0.061942536383867264,
-0.009088912047445774,
0.0151367811486125,
-0.031100038439035416,
-0.021329881623387337,
-0.006874653045088053,
-0.01215572003275156,
-0.028647683560848236,
0.03252718225121498,
0.013472529128193855,
-0.0095545444637537,
-0.048715703189373016,
0.00342361512593925,
0.008194960653781891,
0.0032254045363515615,
0.030182937160134315,
-0.07036691159009933,
-0.02032075822353363,
0.06091189384460449,
-0.012083645910024643,
0.03833671286702156,
-0.013305550441145897,
-0.02302425540983677,
0.005399538669735193,
-0.07699927687644958,
0.05455128848552704,
-0.00661482335999608,
0.05577997490763664,
-0.024441758170723915,
-0.030980607494711876,
-0.0015514139086008072,
-0.0010282552102580667,
0.06435622274875641,
-0.018564535304903984,
-0.031618665903806686,
0.017224794253706932,
-0.0055891377851367,
0.005341260693967342,
0.005645230878144503,
0.011290067806839943,
-0.011659566313028336,
0.010609949007630348,
-0.03368697687983513,
-0.028090910986065865,
-0.011467307806015015,
0.005447360686957836,
0.050629716366529465,
0.01746533066034317,
0.005441316869109869,
0.0438397079706192,
-0.03883366286754608,
0.0686432272195816,
-0.007386315148323774,
-0.010836882516741753,
0.04662519693374634,
-0.016589922830462456,
0.0723881721496582,
0.019342221319675446,
-0.030917515978217125,
-0.023648882284760475,
0.04735627397894859,
-0.03214308246970177,
-0.07204481214284897,
-0.03753397613763809,
0.03158164769411087,
-0.013345411978662014,
-0.027366485446691513,
0.013045864179730415,
0.05242061987519264,
-0.05370640754699707,
-0.0214562825858593,
0.025678712874650955,
0.005827036686241627,
0.02785485051572323,
-0.014047735370695591,
0.00845552608370781,
0.015302695333957672,
-0.009844569489359856,
-0.014297014102339745,
0.061433613300323486,
0.06271763890981674,
0.014260883443057537,
0.05799707770347595,
0.03291011229157448,
-0.00995437428355217,
0.049763746559619904,
0.042633604258298874,
0.032972607761621475,
-0.016049016267061234,
0.005183843430131674,
0.05328357219696045,
0.008550415746867657,
0.03598802909255028,
0.01761908084154129,
0.01457055564969778,
0.04809027537703514,
-0.00426509277895093,
0.007362323813140392,
-0.027668526396155357,
-0.0005457516526803374,
-0.025348341092467308,
-0.015330333262681961,
0.02299881912767887,
0.06521141529083252,
-0.00044726868509314954,
-0.009956765919923782,
-0.022240642458200455,
0.04510640725493431,
0.02596214972436428,
-0.03515869006514549,
0.04118137061595917,
0.006277976557612419,
0.00029938825173303485,
0.006161317694932222,
0.012276191264390945,
-0.014798653312027454,
0.008912972174584866,
0.025888634845614433,
0.028518328443169594,
0.06230132281780243,
0.007370889186859131,
0.007141155656427145,
-0.0345359668135643,
0.009166274219751358,
-0.04137851670384407,
0.026980167254805565,
-0.04875487834215164,
0.005570437293499708,
0.013166680932044983,
-0.005120341200381517
] |
<p>So, one thing has been annoying me ever since I learned about <a href="http://en.wikipedia.org/wiki/Orbital_hybridisation">orbital hybridization</a>: you explain the shape of molecules by postulating that the orbitals of multi-electron atoms are linear combinations of the orbitals of the hydrogen atom. Fine.</p>
<p>Here's what gets me, and I've asked several chemistry professors about this, and I haven't gotten an answer. If I measure the orbital angular momentum of an electron in a hydrogen atom, I get the value $L = \hbar \sqrt{\ell(\ell +1)}$, so an s orbital has angular momentum $0$ and a p orbital has angular momentum $\hbar$.</p>
<p>So, what happens when I measure the orbital angular momentum of a sp${}^{3}$ electron? Do I get $\frac{3\hbar}{4}$ with probability 1? Or do I get $\hbar$ with probability 0.75, and $0$ with probability 0.25? Are the original orbitals really the fundamental thing, and the hybridized orbitals fundamentally just quantum superpositions of these things? Or does the multi-electron potential create a state that just looks like a linear combination of one s and 3 p orbitals?</p>
<p>Or is the actual answer more complicated and this a heuristic picture that I'm taking too seriously?</p>
| 7,681 |
[
-0.06639380753040314,
0.009843691252171993,
0.009025185368955135,
-0.018649807199835777,
0.016211779788136482,
-0.011069447733461857,
-0.006343596149235964,
-0.023124439641833305,
0.040379613637924194,
-0.014509651809930801,
0.04324734956026077,
0.03861909732222557,
0.049875494092702866,
-0.005209519062191248,
-0.011036645621061325,
0.039354316890239716,
0.025008494034409523,
-0.0005142005393281579,
-0.028083691373467445,
0.02111740969121456,
0.0035227539483457804,
0.01636960543692112,
0.024650074541568756,
-0.01261449046432972,
-0.01962352730333805,
0.045180562883615494,
0.010161377489566803,
-0.02826850488781929,
0.05343898385763168,
0.05100353807210922,
-0.017179442569613457,
-0.029151571914553642,
0.06756577640771866,
0.010371798649430275,
-0.014021818526089191,
-0.011727431789040565,
0.0019959465134888887,
-0.026853594928979874,
-0.036470748484134674,
0.05163959041237831,
-0.0355522558093071,
-0.008215988986194134,
-0.04974103346467018,
0.04631486162543297,
-0.002678442047908902,
0.020127877593040466,
-0.02852545864880085,
-0.01474746037274599,
0.06170926243066788,
-0.07194971293210983,
0.06438931822776794,
0.019233934581279755,
0.007090438157320023,
0.031831663101911545,
0.002379057463258505,
-0.004726675804704428,
0.07961001992225647,
0.0715520977973938,
-0.010415160097181797,
-0.03897770866751671,
-0.033111754804849625,
-0.005137480329722166,
0.022880246862769127,
0.0035245155449956656,
-0.05659877881407738,
0.015842702239751816,
0.02744489535689354,
-0.0324212983250618,
0.03165913000702858,
-0.016295230016112328,
0.031510598957538605,
0.025429220870137215,
0.013728800229728222,
-0.019490886479616165,
0.0053849294781684875,
-0.014170448295772076,
0.018053650856018066,
0.013657565228641033,
0.07435685396194458,
0.0169987790286541,
-0.00020546736777760088,
0.005262978840619326,
0.011440224945545197,
0.021336065605282784,
0.012775675393640995,
-0.02177109755575657,
0.07583292573690414,
0.00020075085922144353,
0.0029612963553518057,
0.03668031468987465,
-0.017691435292363167,
0.02285643294453621,
0.024262959137558937,
-0.028504222631454468,
-0.018968332558870316,
0.06818971782922745,
-0.019246404990553856,
0.057991817593574524,
0.013093814253807068,
-0.010469181463122368,
-0.01565592922270298,
-0.03760549798607826,
-0.006274888291954994,
0.07143945246934891,
-0.0314369834959507,
-0.02192048728466034,
-0.0022746126633137465,
0.03596208989620209,
0.0039445022121071815,
-0.01006448082625866,
0.004300175700336695,
0.06358420848846436,
0.0001812378759495914,
-0.01460800226777792,
-0.023252222687005997,
-0.017098532989621162,
0.008963439613580704,
-0.02034996636211872,
0.015900887548923492,
0.06480904668569565,
-0.009932905435562134,
-0.04678761214017868,
-0.001526310108602047,
-0.0469050258398056,
-0.0548633448779583,
0.0065761748701334,
-0.0034735905937850475,
0.03161294758319855,
-0.03249029442667961,
0.029054870828986168,
0.006229263264685869,
-0.00033009026083163917,
0.03890202194452286,
-0.01584808900952339,
-0.0059346649795770645,
-0.03952646628022194,
-0.11705166846513748,
-0.03946913778781891,
0.03187233582139015,
-0.025415025651454926,
-0.018340785056352615,
-0.06841673702001572,
-0.012587666511535645,
0.021098120138049126,
0.05946029722690582,
-0.018272073939442635,
-0.00693141296505928,
-0.0006634799647144973,
0.04090818017721176,
0.03968894109129906,
-0.002341765444725752,
-0.0032055526971817017,
-0.020635314285755157,
-0.06585495173931122,
0.014378029853105545,
-0.05347539111971855,
0.03567752614617348,
0.011972054839134216,
0.046321094036102295,
-0.02115866355597973,
0.0569981150329113,
-0.0152196129783988,
-0.006060340907424688,
0.004170284606516361,
0.010743800550699234,
-0.04197628051042557,
0.08077728003263474,
0.020552976056933403,
0.0058217355981469154,
0.04365396499633789,
-0.016194451600313187,
0.0228035356849432,
0.006759547628462315,
0.05060029774904251,
0.03117460571229458,
-0.05908135697245598,
-0.013804878108203411,
-0.04376591369509697,
0.02078583464026451,
-0.021468762308359146,
-0.0538303442299366,
-0.0060735344886779785,
0.0032363005448132753,
0.013198303058743477,
0.02773759700357914,
0.03349172696471214,
0.017549365758895874,
-0.00954341609030962,
-0.029179029166698456,
-0.04092056304216385,
-0.012819292023777962,
-0.08480962365865707,
-0.007287157233804464,
0.008869192562997341,
-0.017580177634954453,
0.0718265026807785,
-0.0054658991284668446,
0.004172607325017452,
-0.0033311445731669664,
-0.04800526052713394,
-0.006518540438264608,
0.054291293025016785,
0.02847767435014248,
-0.015574534423649311,
0.033555228263139725,
0.08768583834171295,
0.037237025797367096,
-0.004478621296584606,
-0.011655139736831188,
-0.032197460532188416,
-0.016989829018712044,
-0.01405510026961565,
-0.010326660238206387,
0.03237360343337059,
0.014137606136500835,
0.01639215089380741,
-0.017359228804707527,
-0.009724314324557781,
0.022562343627214432,
0.036410193890333176,
-0.040423352271318436,
0.054537851363420486,
0.049222562462091446,
0.02412865124642849,
0.01043704990297556,
0.04831411689519882,
-0.011725164949893951,
0.019780399277806282,
0.032297227531671524,
-0.012734448537230492,
-0.0382503867149353,
0.030307786539196968,
0.02610231190919876,
0.03196259215474129,
-0.002915199613198638,
0.015427101403474808,
0.0024366960860788822,
0.05450412631034851,
0.01988416537642479,
0.022303853183984756,
-0.028178902342915535,
-0.012936455197632313,
-0.009688685648143291,
-0.02101132459938526,
0.017052803188562393,
0.012568742036819458,
0.009055837988853455,
0.01701398193836212,
0.00964271929115057,
0.008152145892381668,
-0.030360860750079155,
0.04317561164498329,
-0.035123009234666824,
0.01863839291036129,
-0.003919774200767279,
-0.015334602445363998,
0.010139315389096737,
-0.00818826723843813,
-0.0043068937957286835,
0.049012310802936554,
-0.03467763587832451,
0.004125073552131653,
-0.03914295509457588,
0.011256863363087177,
-0.0064591895788908005,
0.02036331407725811,
-0.006710262503474951,
0.0214785598218441,
0.022139422595500946,
-0.028294244781136513,
0.02060566283762455,
-0.026992449536919594,
0.018778562545776367,
-0.004528816789388657,
0.01799936220049858,
-0.004622708540409803,
-0.01026648748666048,
0.020286304876208305,
-0.04235485568642616,
-0.04480228200554848,
0.006788983941078186,
-0.012635826133191586,
0.0390937477350235,
-0.016814658418297768,
-0.06908586621284485,
0.0013318228302523494,
-0.056199051439762115,
-0.009132339619100094,
0.02612464316189289,
0.010565156117081642,
0.02360396645963192,
-0.041321855038404465,
0.0028578105848282576,
-0.050261687487363815,
-0.03238643333315849,
-0.035675838589668274,
0.013201955705881119,
-0.028273990377783775,
-0.030650213360786438,
0.03818640112876892,
-0.035388290882110596,
-0.012035035528242588,
0.041858747601509094,
-0.01550050638616085,
-0.0346556082367897,
0.01053739432245493,
0.002874647034332156,
0.0019833247642964125,
-0.004051049705594778,
0.012993749231100082,
0.03587017580866814,
-0.030090834945440292,
-0.023262832313776016,
-0.04254292696714401,
-0.047817256301641464,
-0.0015970217064023018,
0.005716352257877588,
0.005619288422167301,
0.0081739267334342,
-0.04211071878671646,
0.082473985850811,
-0.0033771160524338484,
-0.023445388302206993,
-0.023365981876850128,
0.008625448681414127,
-0.020748620852828026,
-0.008339542895555496,
0.026439931243658066,
0.03877492621541023,
0.025443393737077713,
0.02055267244577408,
-0.0007814857526682317,
0.030281689018011093,
-0.0003812647482845932,
0.022465083748102188,
-0.019501661881804466,
0.045140545815229416,
-0.02560497261583805,
-0.012562432326376438,
0.06403622776269913,
0.012000749818980694,
-0.0103732505813241,
-0.019934797659516335,
-0.006563539616763592,
-0.018911199644207954,
0.03823389858007431,
-0.038517288863658905,
0.051261261105537415,
0.01898634247481823,
0.02796172723174095,
-0.008710039779543877,
0.06294805556535721,
0.013899260200560093,
-0.01266887504607439,
0.011404044926166534,
0.008457689546048641,
0.05375082045793533,
0.00005035413050791249,
-0.008880767971277237,
0.06371244788169861,
0.005274283234030008,
-0.032084014266729355,
-0.03167041391134262,
0.022517014294862747,
0.007798964623361826,
-0.007601229473948479,
-0.010648980736732483,
-0.06555341929197311,
0.028789034113287926,
0.028320323675870895,
0.024660278111696243,
-0.022994140163064003,
-0.032484862953424454,
-0.019639942795038223,
-0.05513458326458931,
-0.012721105478703976,
-0.003390625352039933,
0.03780815377831459,
0.008113271556794643,
0.07779532670974731,
-0.004249901976436377,
0.0061803171411156654,
-0.014376436360180378,
-0.010176046751439571,
-0.038688015192747116,
0.013192144222557545,
-0.011943626217544079,
-0.023384226486086845,
-0.040486015379428864,
-0.00017461369861848652,
-0.01009739562869072,
-0.035845354199409485,
-0.013570013456046581,
-0.032588616013526917,
-0.056435227394104004,
-0.00990505050867796,
-0.003045491175726056,
-0.04723688215017319,
0.008558417670428753,
-0.03368264436721802,
0.06521019339561462,
0.0070771705359220505,
-0.009763074107468128,
0.014801684767007828,
0.03735285624861717,
-0.03403199091553688,
-0.00875571183860302,
-0.041320085525512695,
0.04052455350756645,
-0.0019669586326926947,
0.037371471524238586,
0.03523939847946167,
0.0024241763167083263,
0.006577681750059128,
-0.003834222909063101,
0.008659295737743378,
0.06622191518545151,
0.01693475805222988,
0.008421989157795906,
0.005339763127267361,
-0.017089223489165306,
-0.002886733040213585,
0.003778064390644431,
0.006285498850047588,
0.0053412397392094135,
0.05515849217772484,
0.014063368551433086,
0.012706871144473553,
-0.018854985013604164,
0.03846267983317375,
0.0033978931605815887,
-0.001715382793918252,
-0.027145206928253174,
-0.07206942141056061,
0.007946567609906197,
-0.041031304746866226,
-0.00731781218200922,
0.020860349759459496,
-0.011983196251094341,
0.0010763409081846476,
-0.010443828999996185,
0.014443188905715942,
0.0013531058793887496,
0.006916095037013292,
0.006811345927417278,
-0.05560951679944992,
-0.007114192936569452,
-0.016457730904221535,
0.012007392011582851,
0.020997406914830208,
0.039501313120126724,
0.016760563477873802,
0.03158918023109436,
-0.02402978017926216,
-0.07246614247560501,
0.0183254461735487,
-0.001866342150606215,
0.044120050966739655,
-0.02400953881442547,
0.00005539194535231218,
-0.01853266730904579,
-0.03579489141702652,
0.02274099737405777,
-0.02489149384200573,
0.02054225280880928,
-0.043812382966279984,
-0.006255907006561756,
-0.023813799023628235,
-0.0444495752453804,
-0.042515240609645844,
0.011808674782514572,
0.012669311836361885,
0.0020833888556808233,
-0.0387321338057518,
0.023085100576281548,
-0.045932698994874954,
0.02286967635154724,
0.027640793472528458,
0.06174294278025627,
-0.009860798716545105,
-0.010663790628314018,
0.003120374632999301,
0.027545232325792313,
-0.027254892513155937,
-0.0841323584318161,
0.0000645874097244814,
-0.009906484745442867,
-0.001102691050618887,
0.04806815832853317,
-0.07255083322525024,
-0.08261927217245102,
0.02054593712091446,
0.0029049913864582777,
-0.001833257731050253,
0.018771391361951828,
-0.01998954452574253,
0.04657828062772751,
0.045751478523015976,
0.037757910788059235,
0.02661454863846302,
0.04225069284439087,
-0.015418929979205132,
-0.0065611582249403,
-0.04710158705711365,
0.007876136340200901,
-0.029921676963567734,
0.0012093529803678393,
-0.050527818500995636,
0.028533753007650375,
-0.013665696606040001,
0.0627041682600975,
0.012327417731285095,
0.011165941134095192,
-0.019873948767781258,
-0.03572412580251694,
-0.005928024649620056,
0.00571746751666069,
0.015973642468452454,
0.005854124203324318,
-0.008793802931904793,
-0.0013611094327643514,
0.03391534462571144,
-0.015005950815975666,
-0.0037333436775952578,
-0.02500695176422596,
0.04605482146143913,
0.01966535672545433,
-0.023942509666085243,
0.05681575462222099,
-0.015930697321891785,
0.009232254698872566,
-0.010281283408403397,
-0.07050615549087524,
0.020624374970793724,
-0.0276423841714859,
-0.00782851129770279,
0.025010835379362106,
-0.05216136947274208,
0.006654032040387392,
0.017187485471367836,
-0.0333288349211216,
0.003765567671507597,
-0.037905555218458176,
0.0005309177795425057,
-0.014272416941821575,
0.008790899999439716,
-0.05480676516890526,
-0.019276389852166176,
0.02300773747265339,
0.03689219057559967,
-0.027294369414448738,
-0.009057195857167244,
0.009462451562285423,
-0.011824815534055233,
-0.03688676282763481,
-0.004510640632361174,
0.014913245104253292,
-0.05707550048828125,
-0.031138310208916664,
0.014362686313688755,
-0.0025479572359472513,
0.06886903196573257,
-0.0410141795873642,
-0.03218647465109825,
-0.0014041770482435822,
-0.010386565700173378,
-0.0018527278443798423,
-0.000047986439312808216,
0.0166757944971323,
-0.040370382368564606,
-0.026589123532176018,
-0.01937178149819374,
-0.043064702302217484,
0.024141427129507065,
-0.027862247079610825,
-0.02191329002380371,
0.0002223188930656761,
-0.0007560744998045266,
0.00755740562453866,
0.0020983750000596046,
-0.0025333852972835302,
0.004779463168233633,
0.027435149997472763,
0.034829143434762955,
0.02596871927380562,
-0.01756226271390915,
-0.01713808998465538,
0.02148287184536457,
0.008789530955255032,
0.009273999370634556,
0.00504297437146306,
0.03684961423277855,
0.016613531857728958,
0.010479499585926533,
0.011560115963220596,
-0.012747840955853462,
0.02055518329143524,
0.011151930317282677,
-0.015397992916405201,
0.01923336647450924,
0.02799983322620392,
-0.026235491037368774,
-0.04463226720690727,
-0.042380645871162415,
0.051165103912353516,
0.02624485269188881,
-0.048549480736255646,
0.02384999953210354,
0.011417296715080738,
-0.002994501031935215,
-0.045028943568468094,
-0.04174381494522095,
-0.020717008039355278,
-0.0016748921480029821,
-0.016513723880052567,
0.03869367390871048,
-0.022226138040423393,
0.024033090099692345,
0.027952831238508224,
0.044891975820064545,
-0.01217528898268938,
0.016614658758044243,
0.08248430490493774,
0.003186378860846162,
0.054764289408922195,
-0.02548249065876007,
-0.05126148834824562,
0.06584221124649048,
-0.010195993818342686,
0.03592545911669731,
0.011016007512807846,
-0.00675986148416996,
0.04674603417515755,
0.02553727477788925,
-0.0015737134963274002,
-0.05694527551531792,
-0.007550600916147232,
0.003005087608471513,
0.018702631816267967,
0.034625470638275146,
-0.01753709651529789,
0.0175153985619545,
0.00901862047612667,
0.03958267346024513,
0.010269416496157646,
0.00503388699144125,
-0.007594984024763107,
-0.052350446581840515,
-0.02562321349978447,
-0.008119291625916958,
-0.04482626914978027,
0.03972649574279785,
-0.022222675383090973,
-0.015226577408611774,
0.024971989914774895,
-0.021012550219893456,
0.03352336958050728,
0.010278532281517982,
0.015553290955722332,
-0.028318723663687706,
0.03610668331384659,
-0.0005236600991338491,
-0.0017367344116792083,
-0.038125067949295044,
-0.012876121327280998,
0.11765533685684204,
0.05806630849838257,
0.023802557960152626,
-0.08140648901462555,
0.00048787123523652554,
0.007253825198858976,
-0.005916123278439045,
0.005584006663411856,
0.0237022265791893,
0.004691055044531822,
0.009328843094408512,
-0.049343012273311615,
0.07663100212812424,
-0.026730479672551155,
0.02374199591577053,
0.014928668737411499,
-0.02679687924683094,
-0.007744731847196817,
-0.030973002314567566,
-0.015364381484687328,
-0.009744999930262566,
-0.004447197075933218,
-0.0768483579158783,
-0.007193011697381735,
-0.04767632484436035,
0.019164474681019783,
-0.033386945724487305,
-0.0186337660998106,
0.0346401073038578,
0.002663041464984417,
-0.019320283085107803,
0.012450168840587139,
-0.01945984922349453,
-0.038832809776067734,
-0.023305222392082214,
0.05621394142508507,
0.05422968789935112,
0.007048693485558033,
0.019456710666418076,
0.06277573853731155,
-0.01156775001436472,
0.009103100746870041,
-0.004569119308143854,
0.024285804480314255,
-0.06643474102020264,
-0.028685985133051872,
-0.010959937237203121,
0.05599562078714371,
-0.03109491989016533,
-0.039096198976039886,
-0.04648926481604576,
-0.02050710655748844,
0.00028418522560968995,
-0.03931834176182747,
-0.0074974666349589825,
-0.013754376210272312,
0.05131293833255768,
0.0028176235500723124,
-0.03302337974309921,
-0.007310172542929649,
-0.01295517198741436,
0.007615989074110985,
0.007815917953848839,
-0.004043864086270332,
0.011413220316171646,
0.00225686258636415,
0.022008346393704414,
0.026715794578194618,
0.026177963241934776,
0.0004980689263902605,
-0.04931759834289551,
-0.009063544683158398,
-0.04125683382153511,
-0.009110172279179096,
0.0468156524002552,
0.023762086406350136,
0.07318727672100067,
-0.0021597135346382856,
0.01727825589478016,
-0.015002608299255371,
-0.09255998581647873,
0.011662975884974003,
-0.003381025977432728,
-0.014924353919923306,
0.008937579579651356,
0.017383648082613945,
0.03322499990463257,
0.024078309535980225,
-0.00040160291246138513,
0.0403696671128273,
0.018876709043979645,
0.010133442468941212,
0.009842216968536377,
-0.055462319403886795,
-0.001152576645836234,
0.028014132753014565,
-0.014132790267467499,
0.009946825914084911,
-0.03219083324074745,
0.004351071547716856,
-0.0020523518323898315,
0.030952274799346924,
0.013834168203175068,
0.031634584069252014,
0.024828320369124413,
0.0223701111972332,
0.025786537677049637,
-0.0352308489382267,
0.014238635078072548,
0.010037708096206188,
0.028511522337794304,
-0.027010798454284668,
-0.024778980761766434,
-0.038329117000103,
0.006644415203481913,
0.015378674492239952,
0.002384176477789879,
-0.022904418408870697,
0.00819438323378563,
-0.009861266240477562,
0.02580735646188259,
-0.01567302644252777,
-0.002248889533802867,
-0.029386412352323532,
0.04812450334429741,
0.03636951744556427,
-0.0035147664602845907,
0.009294712916016579,
0.012205761857330799,
0.011492189951241016,
-0.022395338863134384,
0.046954844146966934,
0.03996455669403076,
-0.005816632881760597,
-0.02337980829179287,
0.016465691849589348,
-0.04970686510205269,
0.029717331752181053,
-0.02700231783092022,
-0.010329454205930233,
0.03139203041791916,
-0.06307769566774368,
-0.039839766919612885,
0.010320744477212429,
-0.023224180564284325,
0.028160376474261284,
0.0517798513174057,
-0.014934448525309563,
-0.013375746086239815,
0.04790531471371651,
-0.028346294537186623,
-0.004310826770961285,
-0.011901812627911568,
0.0028315898962318897,
0.00012681720545515418,
0.016424698755145073,
0.007806579582393169,
-0.004370656330138445,
0.010296786203980446,
0.05677325278520584,
-0.017637455835938454,
-0.02497979998588562,
0.03191453963518143,
-0.024663599207997322,
-0.003607635386288166,
0.04180074483156204,
0.014261245727539062,
-0.010389971546828747,
0.03204723447561264,
0.014716343954205513,
-0.027900731191039085,
0.07356609404087067,
0.055283695459365845,
0.0326891653239727,
-0.07236291468143463,
-0.02792791649699211,
0.0029767616651952267,
-0.022370457649230957,
0.019698426127433777,
-0.04251165688037872,
-0.03907453268766403,
0.04290645942091942,
-0.10456550121307373,
-0.00016328961646649987,
0.0005239408346824348,
0.00357537972740829,
-0.029241058975458145,
-0.014022254385054111,
-0.045591454952955246,
0.05204791575670242,
-0.022060249000787735,
0.062070731073617935,
-0.0013124620309099555,
0.02914034016430378,
-0.012400725856423378,
-0.013570391573011875,
-0.013522681780159473,
0.03371216356754303,
-0.020528485998511314,
-0.025764521211385727,
0.056215159595012665,
-0.036768823862075806,
-0.046660106629133224,
0.042025890201330185,
0.007248923648148775,
-0.001574997790157795,
-0.04202517122030258,
-0.010637594386935234,
-0.016398750245571136,
0.022704865783452988,
0.006296795792877674,
-0.011462708935141563,
-0.013888755813241005,
0.022713612765073776,
0.03842036426067352,
0.03325646370649338,
-0.02396363578736782,
-0.027440354228019714,
0.04477166011929512,
-0.024310553446412086,
-0.057749971747398376,
0.010547099635004997,
0.00918661244213581,
0.008593667298555374,
-0.0038465100806206465,
-0.0039327749982476234,
-0.01639671064913273,
-0.026235975325107574,
0.0004079520294908434,
-0.02106965146958828,
0.017867280170321465,
0.015179199166595936,
0.02516995742917061,
0.04112780839204788,
0.014368696138262749,
-0.05120845139026642,
-0.05265429988503456,
0.025412708520889282,
-0.018969960510730743,
-0.03130332753062248,
-0.0771552175283432,
0.013441074639558792,
0.018392087891697884,
0.006514448206871748,
0.018506759777665138,
-0.021493973210453987,
-0.02547409012913704,
0.047471459954977036,
-0.024554017931222916,
0.0018555449787527323,
-0.020503507927060127,
-0.062248386442661285,
-0.020944470539689064,
-0.07235191762447357,
0.0649636760354042,
0.018844930455088615,
0.0034166278783231974,
-0.0488835945725441,
-0.00975604634732008,
-0.009298537857830524,
0.022345446050167084,
0.05025932565331459,
0.013112770393490791,
-0.011717184446752071,
-0.02649698406457901,
0.018530845642089844,
0.03429505228996277,
-0.031849730759859085,
-0.01512422226369381,
0.027083497494459152,
0.0205845907330513,
0.018696650862693787,
-0.017135802656412125,
-0.02956109121441841,
0.00979166105389595,
0.01726730354130268,
-0.014905204065144062,
0.0013609114103019238,
-0.022319000214338303,
-0.027163181453943253,
0.0511554554104805,
0.003711697878316045,
-0.0263482965528965,
0.06960570812225342,
0.037918999791145325,
0.006215945351868868,
0.023582810536026955,
-0.02774781733751297,
-0.018423665314912796,
0.005707624834030867,
-0.02597043290734291,
-0.0186439361423254,
-0.010378857143223286,
-0.03124387562274933,
0.05897904187440872,
-0.024659335613250732,
0.023590970784425735,
0.04145597293972969,
-0.03346848860383034,
-0.04595804214477539,
0.053877826780080795,
-0.028476588428020477,
0.026972100138664246,
0.010010980069637299,
0.02476404421031475,
-0.004923765081912279,
-0.022990060970187187,
0.010945563204586506,
0.033075034618377686,
0.06274109333753586,
0.008776161819696426,
0.02297019213438034,
0.04703693464398384,
0.01575404219329357,
0.001775437267497182,
0.037635352462530136,
0.04289638251066208,
-0.026264455169439316,
0.006440676748752594,
0.03827103227376938,
-0.009632905013859272,
-0.018512465059757233,
-0.0230570025742054,
-0.009005961939692497,
0.08473264425992966,
-0.0012054304825142026,
-0.014712739735841751,
-0.01691816747188568,
0.03808870539069176,
-0.021662920713424683,
-0.01127819437533617,
-0.010586597956717014,
0.038935381919145584,
-0.007725634146481752,
-0.02227257378399372,
-0.06975717842578888,
0.032197944819927216,
0.07074817270040512,
-0.0222186166793108,
0.013016865588724613,
-0.010702400468289852,
-0.01408894918859005,
-0.029969647526741028,
-0.021706044673919678,
-0.03458539396524429,
-0.010324629954993725,
0.0012438161065801978,
0.02276747301220894,
0.023459015414118767,
-0.018483726307749748,
0.012826265767216682,
-0.011233001947402954,
0.026750847697257996,
-0.02826305478811264,
-0.03628796339035034,
-0.017556065693497658,
0.03893937170505524,
-0.0038478693459182978,
-0.02697451040148735
] |
<p>If our universe comes from a flux compactification of string theory over 6 dimensions with a nonzero flux, then it can't be continually deformed to another compactification with zero flux as the total flux is a topological invariant. The cosmological constant of our universe is positive, which in string theory means it is a metastable state. The stable vacuum for a flux compactification in string theory is a BPS compactification with negative cosmological constant.</p>
<p>What if our metastable observable universe is actually embedded in a larger stable anti de Sitter background? An inflating metastable or slowly rolling or chaotically inflating patch of this asymptotically AdS universe inflates to our observable universe. By the AdS/CFT correspondence, our universe can be described by a superconformal field theory in 2+1D with no gravity.</p>
<p>Is there any flaw in my reasoning?</p>
| 7,682 |
[
0.000019773342501139268,
0.006578111555427313,
0.0009405614109709859,
-0.04955996200442314,
0.036922067403793335,
-0.01624126359820366,
-0.05548536032438278,
-0.023369118571281433,
-0.012929494492709637,
-0.0838150829076767,
-0.01634719967842102,
0.013715116307139397,
0.0042759268544614315,
0.04266683757305145,
0.004941447172313929,
-0.02036427892744541,
-0.019202692434191704,
0.0017524078721180558,
0.0023152902722358704,
-0.01742587797343731,
0.03140340372920036,
0.03235481306910515,
0.002260304754599929,
0.000201665869099088,
-0.020591290667653084,
0.0022485938388854265,
-0.005776239559054375,
0.016896670684218407,
0.005299112293869257,
0.06418749690055847,
0.0068185217678546906,
-0.0276020597666502,
-0.0016471694689244032,
0.02572799101471901,
0.028052767738699913,
-0.014138145372271538,
-0.03594927489757538,
-0.035451680421829224,
-0.05321570113301277,
0.01251490693539381,
-0.024763677269220352,
-0.012379148043692112,
-0.037967827171087265,
0.06158481538295746,
-0.01456497609615326,
-0.005849776789546013,
-0.015821997076272964,
0.002767350524663925,
0.08461885154247284,
-0.07321610301733017,
0.027599694207310677,
-0.01183746661990881,
0.031865112483501434,
0.04566323757171631,
-0.008879581466317177,
-0.05767199024558067,
0.09418126940727234,
0.08978273719549179,
-0.003662389237433672,
-0.0262345802038908,
-0.03688859939575195,
0.004796454682946205,
0.0016425602370873094,
-0.0170326866209507,
-0.033215805888175964,
0.03847803547978401,
-0.0002701760968193412,
0.01916099153459072,
0.0102311996743083,
0.009921911172568798,
0.014685693196952343,
0.02545267343521118,
-0.02755400352180004,
0.009422861970961094,
0.01892080530524254,
-0.03287087380886078,
0.04062209278345108,
0.03691539913415909,
0.022096240893006325,
0.05979958549141884,
0.01542731374502182,
-0.015008216723799706,
0.011161711998283863,
0.0467633455991745,
0.03854018822312355,
0.027809644117951393,
0.06638070195913315,
-0.00003256015770602971,
-0.0008508499013260007,
0.08442274481058121,
0.01709013804793358,
-0.03561676666140556,
0.03168085962533951,
-0.01512947678565979,
-0.01382810715585947,
0.02850249595940113,
-0.005210190080106258,
0.03463879972696304,
-0.05843985453248024,
0.004701161291450262,
-0.04160439968109131,
-0.010919706895947456,
0.03164936229586601,
0.0827270969748497,
0.021988097578287125,
-0.016936978325247765,
-0.033345844596624374,
0.0032955820206552744,
-0.03602736443281174,
-0.02758503332734108,
-0.04443208500742912,
-0.012738736346364021,
-0.0003073914849665016,
-0.02709176577627659,
0.003499343991279602,
-0.03622771427035332,
0.01121149118989706,
-0.06963063776493073,
-0.012736923061311245,
0.06868842989206314,
0.06067279726266861,
-0.0052584814839065075,
-0.001660967362113297,
-0.01859521120786667,
-0.07711167633533478,
0.027424249798059464,
0.04024228826165199,
0.0024140921887010336,
-0.030989494174718857,
0.0024542335886508226,
-0.002037332160398364,
-0.023044774308800697,
0.02917891927063465,
0.011112242005765438,
0.09398248046636581,
0.0060490998439490795,
-0.08572361618280411,
-0.0409134104847908,
0.011748508550226688,
0.0009529648232273757,
-0.024558642879128456,
-0.05351177230477333,
-0.011122950352728367,
0.05202288553118706,
0.0788579061627388,
-0.015729479491710663,
-0.020410746335983276,
0.034969620406627655,
0.051052555441856384,
0.009690669365227222,
-0.05495641380548477,
-0.01689096726477146,
-0.023585189133882523,
-0.07629676908254623,
-0.04332682862877846,
-0.042561374604701996,
0.011902249418199062,
0.029377412050962448,
-0.010321680456399918,
-0.03763000667095184,
0.06365443766117096,
-0.029963867738842964,
-0.011451201513409615,
-0.018502674996852875,
0.0036272085271775723,
-0.034052349627017975,
0.07099193334579468,
0.01740756630897522,
0.018336500972509384,
-0.017321277409791946,
-0.01781523786485195,
-0.029858173802495003,
0.01999383233487606,
0.03466695547103882,
0.017634596675634384,
-0.06203435733914375,
-0.00019845995120704174,
0.010735881514847279,
-0.0024562401231378317,
0.0050849467515945435,
-0.018795151263475418,
-0.026546478271484375,
-0.05816543474793434,
-0.005742952693253756,
0.03546195849776268,
0.01830189675092697,
-0.01936127431690693,
-0.004987086169421673,
0.015761306509375572,
-0.08511015772819519,
-0.0027609739918261766,
-0.039548829197883606,
-0.02174188382923603,
0.014638074673712254,
0.01928800903260708,
0.018350260332226753,
-0.00859353318810463,
0.0014128496404737234,
-0.013882512226700783,
-0.011403406970202923,
0.02180805802345276,
0.029676679521799088,
0.019292499870061874,
-0.0032689792569726706,
0.004215307999402285,
0.018921025097370148,
0.017762452363967896,
-0.04545580968260765,
0.012993616051971912,
-0.024870924651622772,
-0.032312195748090744,
0.02503473125398159,
0.011654227040708065,
0.03472140058875084,
-0.023391565307974815,
-0.001654700725339353,
0.052942365407943726,
-0.014216167852282524,
-0.014297020621597767,
0.07205930352210999,
-0.0346757248044014,
0.04589410126209259,
0.03620362654328346,
-0.011041593737900257,
-0.0052181752398610115,
0.04430299252271652,
-0.03243262693285942,
-0.002575864316895604,
-0.029917480424046516,
-0.009454970248043537,
-0.08170302212238312,
-0.003039643634110689,
0.039261624217033386,
0.027244485914707184,
0.016720613464713097,
0.04646332189440727,
0.011534340679645538,
-0.00349736912176013,
0.02602916583418846,
0.021689658984541893,
0.008127553388476372,
-0.02531220205128193,
-0.007494855206459761,
-0.020234307274222374,
0.05920839309692383,
0.0359979048371315,
0.02431856282055378,
0.014244774356484413,
-0.00047755983541719615,
0.012503085657954216,
0.0025619997177273035,
0.018615389242768288,
0.006983121857047081,
0.020760096609592438,
-0.007966376841068268,
0.0020532377529889345,
-0.012275956571102142,
-0.01494463812559843,
0.01663731411099434,
0.03268852084875107,
0.008977682329714298,
0.012702162377536297,
-0.02291741594672203,
0.021910948678851128,
0.016550276428461075,
0.004291823599487543,
-0.003400121582672,
-0.0496063269674778,
0.012190442532300949,
-0.048444963991642,
0.011313765309751034,
-0.010509511455893517,
-0.019152486696839333,
0.0033054230734705925,
0.01767779141664505,
0.02732633799314499,
0.01866677962243557,
0.013549553230404854,
-0.03128889203071594,
-0.013890103437006474,
0.04038923978805542,
-0.009351857006549835,
-0.0014007491990923882,
0.03354034200310707,
-0.04842090606689453,
0.03745182231068611,
0.002464133780449629,
-0.03230952471494675,
0.044586148113012314,
-0.012188398279249668,
0.024499468505382538,
-0.020029986277222633,
-0.01856303960084915,
-0.05619805306196213,
0.004655315075069666,
-0.018037887290120125,
0.0004854551225434989,
-0.03417017683386803,
-0.022193407639861107,
0.07547593861818314,
0.03274271637201309,
-0.046810127794742584,
0.00321662868373096,
-0.017888642847537994,
-0.02621772512793541,
0.010951651260256767,
-0.024181481450796127,
0.0003072040854021907,
-0.029333127662539482,
0.059663593769073486,
-0.004183798562735319,
-0.048023104667663574,
-0.014248531311750412,
-0.05008958280086517,
-0.049768321216106415,
0.005435429513454437,
-0.02055591344833374,
0.05147069692611694,
0.002881118096411228,
-0.06829651445150375,
0.08866257965564728,
0.027391763404011726,
-0.0201646126806736,
-0.0009983211057260633,
-0.011316811665892601,
-0.028516370803117752,
-0.03202114626765251,
0.02780710533261299,
0.02464780956506729,
-0.0019660156685858965,
0.00959737878292799,
0.02262835018336773,
0.03538611903786659,
0.026798902079463005,
-0.0034500749316066504,
-0.0527973547577858,
-0.005244144704192877,
-0.0003429168136790395,
0.05175790190696716,
0.043224211782217026,
-0.03500494360923767,
-0.018386613577604294,
0.0069312769919633865,
-0.0253309216350317,
-0.009315027855336666,
0.0009968886151909828,
-0.05351443961262703,
0.028879234567284584,
-0.0017142512369900942,
0.03637576848268509,
-0.03260711580514908,
0.016873598098754883,
0.0012165398802608252,
-0.04334641620516777,
-0.014416497200727463,
0.0005776754696853459,
0.018774785101413727,
0.01891079545021057,
0.008050034753978252,
-0.002055961871519685,
-0.005128693301230669,
0.009618008509278297,
-0.014994453638792038,
-0.01730099692940712,
0.005048007238656282,
0.0006085666827857494,
-0.017838304862380028,
-0.03112439252436161,
0.06070725619792938,
0.016900261864066124,
0.024679142981767654,
-0.01928609423339367,
-0.021252982318401337,
0.01400306448340416,
-0.04428235441446304,
-0.01453262846916914,
0.00519345048815012,
0.023501424118876457,
0.021720146760344505,
-0.014141896739602089,
0.025547415018081665,
-0.007272651884704828,
-0.04444558918476105,
-0.007101576309651136,
-0.08442076295614243,
-0.04341692477464676,
-0.04025819152593613,
-0.00015410910418722779,
-0.014943075366318226,
-0.011079434305429459,
0.008740144781768322,
-0.0001641799753997475,
-0.025144992396235466,
-0.03708641603589058,
-0.024677442386746407,
-0.0638345256447792,
-0.010150984860956669,
-0.05840486288070679,
-0.003213373711332679,
0.008925706148147583,
0.03428943082690239,
0.05662020668387413,
-0.01593131572008133,
0.027620835229754448,
0.010137755423784256,
0.012048503383994102,
0.002125243190675974,
-0.03312504664063454,
0.026001356542110443,
0.035293035209178925,
0.01973544992506504,
0.04608695209026337,
0.013010979630053043,
-0.026623915880918503,
0.03768966346979141,
0.02875281125307083,
-0.011417457833886147,
-0.030400147661566734,
-0.0009066598722711205,
-0.016029905527830124,
-0.04080494865775108,
-0.04830612987279892,
0.005993951577693224,
0.05264914035797119,
0.01905938610434532,
-0.005193780642002821,
0.04769539088010788,
-0.0010175982024520636,
-0.006488120649009943,
0.03364558145403862,
0.06516801565885544,
-0.03264876827597618,
-0.015526456758379936,
-0.05151035636663437,
-0.019018158316612244,
-0.023519355803728104,
0.020888209342956543,
0.0016013080021366477,
-0.031156687065958977,
-0.056327544152736664,
0.010533762164413929,
0.015825005248188972,
0.007503820117563009,
-0.043568167835474014,
0.016327889636158943,
0.012700890190899372,
0.020051276311278343,
0.003076453460380435,
0.031198639422655106,
0.020008284598588943,
0.05296136438846588,
0.04925375431776047,
0.007536002434790134,
-0.015358729287981987,
-0.08498034626245499,
-0.020078321918845177,
0.0021298278588801622,
0.03851408511400223,
0.04716677591204643,
-0.012792779132723808,
-0.04963739216327667,
-0.06920325756072998,
0.051181405782699585,
-0.02801220864057541,
0.024219773709774017,
-0.001663819421082735,
0.0022168855648487806,
0.007197258993983269,
-0.01710554026067257,
0.012411833740770817,
0.005596728529781103,
-0.017350416630506516,
0.010643569752573967,
0.008823061361908913,
0.03545508533716202,
-0.014972787350416183,
0.027465390041470528,
-0.0003039420989807695,
0.039960939437150955,
0.014742894098162651,
0.008078392595052719,
0.011530312709510326,
0.006715456955134869,
-0.030475571751594543,
-0.0686182975769043,
0.03622985631227493,
0.0121906204149127,
-0.029248837381601334,
0.05068162828683853,
-0.004792064428329468,
-0.015666227787733078,
-0.017155535519123077,
0.0026322121266275644,
-0.00984396506100893,
0.010320761241018772,
-0.02563180960714817,
0.04301677644252777,
0.015963908284902573,
-0.000983838108368218,
-0.003701802808791399,
0.052437011152505875,
0.02239188179373741,
0.020406927913427353,
-0.007043059449642897,
0.00746177788823843,
-0.05950178951025009,
0.030849963426589966,
-0.021349646151065826,
-0.01265791617333889,
-0.029718151316046715,
0.03514855355024338,
-0.020603710785508156,
-0.017689617350697517,
0.016087278723716736,
-0.05131182447075844,
-0.011064743623137474,
0.011430555954575539,
0.015299775637686253,
0.013186504133045673,
0.0013299917336553335,
0.015332570299506187,
-0.01122059766203165,
-0.014007190242409706,
0.06134243682026863,
0.005226882640272379,
0.0052103945054113865,
0.047223255038261414,
-0.004511251114308834,
0.04664231836795807,
-0.033083733171224594,
-0.0070749307051301,
0.005771583877503872,
-0.04814371466636658,
0.02971775084733963,
-0.0018011368811130524,
0.016710622236132622,
-0.004961070604622364,
-0.04705315828323364,
-0.021972913295030594,
0.00849810428917408,
-0.021802062168717384,
-0.0018230329733341932,
-0.014200471341609955,
0.04572503641247749,
0.0376809723675251,
0.00038889257120899856,
-0.08949659764766693,
-0.0625801682472229,
-0.00618059653788805,
0.04606551304459572,
-0.019012831151485443,
-0.00439418014138937,
0.027307681739330292,
-0.02884448878467083,
0.006202493328601122,
-0.034698329865932465,
0.03267695754766464,
-0.06329745799303055,
0.011520260013639927,
0.037650272250175476,
0.031569868326187134,
0.027173655107617378,
-0.013096692971885204,
0.006038658786565065,
0.015363232232630253,
-0.0020169587805867195,
0.02257159911096096,
-0.015012944117188454,
0.04207940399646759,
-0.01931927353143692,
-0.02893827296793461,
0.012484651058912277,
-0.027847222983837128,
0.03136587515473366,
-0.023276437073946,
0.0031598249915987253,
0.010241116397082806,
0.009793358854949474,
0.03913266211748123,
-0.009723384864628315,
-0.0024389473255723715,
-0.03182359039783478,
0.01684841513633728,
-0.00955374725162983,
0.01140174362808466,
0.0020428369753062725,
-0.0401000902056694,
0.04010443016886711,
0.020319318398833275,
-0.02075325697660446,
0.01336322445422411,
0.04441876336932182,
0.003473586170002818,
-0.05257338657975197,
0.014989713206887245,
-0.04767434298992157,
0.03337964788079262,
0.0477120541036129,
0.03520273417234421,
0.010417666286230087,
-0.0031930727418512106,
-0.05085454136133194,
-0.06815721094608307,
-0.028878742828965187,
-0.023749396204948425,
0.03485095500946045,
-0.01700826734304428,
0.02112048864364624,
-0.025812605395913124,
-0.04763453081250191,
0.04011937230825424,
-0.024427661672234535,
-0.01730044186115265,
0.021731050685048103,
-0.034095648676157,
0.004816065076738596,
-0.06054491177201271,
0.0037330531049519777,
0.010591063648462296,
0.04249564930796623,
-0.0034995831083506346,
0.05433666706085205,
0.044587329030036926,
0.015283018350601196,
0.03912491351366043,
0.0022079325281083584,
-0.07380437850952148,
0.07847058027982712,
-0.030930178239941597,
0.017204590141773224,
0.0021036420948803425,
-0.017605401575565338,
0.027498073875904083,
-0.004631522111594677,
0.04387972503900528,
-0.008187361992895603,
-0.02923222817480564,
-0.04003297910094261,
0.013866358436644077,
-0.02445315383374691,
0.051002196967601776,
0.02186073176562786,
-0.0021650453563779593,
0.03122613951563835,
0.012844296172261238,
0.0068321842700243,
-0.007702372968196869,
-0.06859761476516724,
-0.018167374655604362,
-0.027462314814329147,
-0.01629769429564476,
0.053612906485795975,
0.004162844270467758,
-0.030985668301582336,
-0.012358942069113255,
-0.026149094104766846,
-0.014412103220820427,
0.026230430230498314,
0.045702867209911346,
-0.020512741059064865,
0.025009697303175926,
-0.050997044891119,
0.05732646584510803,
-0.039808489382267,
0.026530949398875237,
0.16636799275875092,
0.04355461522936821,
0.016150707378983498,
-0.06101968139410019,
0.015135330148041248,
-0.026566583663225174,
0.012711195275187492,
-0.040628377348184586,
0.04748215526342392,
0.0038987654261291027,
-0.01689552702009678,
-0.005588493775576353,
0.07086288183927536,
-0.0015602272469550371,
-0.0410827212035656,
0.034527167677879333,
-0.03947050869464874,
0.0011332930298522115,
-0.012214911170303822,
0.0019756057299673557,
-0.009484088979661465,
0.011558596976101398,
-0.0322943739593029,
0.02323819510638714,
-0.005301726516336203,
0.014354214072227478,
-0.02168305218219757,
-0.0067864167504012585,
-0.02336937189102173,
0.018261590972542763,
-0.0407894067466259,
0.010402383282780647,
-0.0018143145134672523,
-0.0460493378341198,
-0.028850896283984184,
-0.004244949668645859,
-0.010483927093446255,
-0.01152008306235075,
0.02038448303937912,
0.06337367743253708,
0.02350357547402382,
0.016424870118498802,
-0.007226675283163786,
0.01437712274491787,
-0.040428176522254944,
0.012871523387730122,
-0.03933173418045044,
0.03741127997636795,
-0.042267244309186935,
0.017077019438147545,
0.0044211954809725285,
-0.01785430870950222,
0.02746180072426796,
-0.009257429279386997,
-0.004250972531735897,
0.003623903263360262,
0.002440937329083681,
-0.010538416914641857,
-0.019650774076581,
0.005951848346740007,
0.04631054773926735,
0.02345716953277588,
0.016644813120365143,
-0.0021533058024942875,
0.014068792574107647,
0.016385838389396667,
0.017372338101267815,
0.05564155802130699,
0.008812129497528076,
0.03828077390789986,
0.0023268130607903004,
0.03405476361513138,
-0.047015078365802765,
0.015435501001775265,
0.013368519954383373,
0.003024646081030369,
0.018293876200914383,
0.04303275793790817,
0.008766311220824718,
-0.025468243286013603,
-0.0018197508761659265,
0.028509996831417084,
-0.023124434053897858,
-0.013391281478106976,
-0.009739360772073269,
-0.002538912231102586,
0.021238811314105988,
0.029617534950375557,
-0.04481537267565727,
-0.008974970318377018,
0.0075426651164889336,
0.03981052339076996,
0.0023272254038602114,
-0.011287796311080456,
0.009702524170279503,
-0.016296688467264175,
-0.0378585159778595,
-0.021426888182759285,
0.01359629351645708,
0.01234380342066288,
0.012650280259549618,
0.014301211573183537,
0.012200922705233097,
0.05889929458498955,
-0.01456223614513874,
0.013708029873669147,
0.024033011868596077,
-0.029965829104185104,
0.009600459598004818,
0.0174284465610981,
0.04543460160493851,
-0.009662875905632973,
-0.05798199400305748,
-0.016369201242923737,
-0.0071146669797599316,
-0.020722122862935066,
0.007777784019708633,
-0.027158109471201897,
-0.0008410641457885504,
0.007820322178304195,
-0.02342372015118599,
-0.07403688877820969,
0.0032137935049831867,
-0.029020041227340698,
-0.015402490273118019,
0.00506415544077754,
0.024792499840259552,
0.008646095171570778,
0.030946651473641396,
-0.03965812921524048,
-0.04862634465098381,
0.041537024080753326,
-0.002390945330262184,
-0.04020898416638374,
0.0432441271841526,
0.046597424894571304,
0.009069324471056461,
0.03320464491844177,
-0.012433435767889023,
-0.06208552420139313,
0.02265295758843422,
-0.040162645280361176,
-0.07010653614997864,
0.05670158937573433,
0.003519962774589658,
0.029288606718182564,
0.008561067283153534,
-0.024797435849905014,
-0.024986140429973602,
0.018730826675891876,
-0.014609213918447495,
-0.014399232342839241,
0.04044908285140991,
-0.015652868896722794,
0.005624809302389622,
-0.0029784641228616238,
0.03811586648225784,
0.030089396983385086,
0.010852820239961147,
0.010621858760714531,
0.03112017922103405,
0.004554864950478077,
-0.016590168699622154,
-0.03562229499220848,
-0.025204898789525032,
0.005865090060979128,
-0.03881978616118431,
-0.005335373338311911,
-0.004732298199087381,
0.0263185016810894,
-0.04414826259016991,
0.008522243238985538,
0.03888527303934097,
-0.014601257629692554,
-0.0956633985042572,
-0.01900031603872776,
0.024320421740412712,
-0.005341043695807457,
0.0298544242978096,
-0.022624313831329346,
0.03563087806105614,
0.028697237372398376,
-0.03522265702486038,
0.03284739702939987,
-0.04289155825972557,
-0.037658583372831345,
-0.018152819946408272,
-0.040621690452098846,
-0.05478527396917343,
0.048045314848423004,
0.03655000776052475,
0.03308930993080139,
-0.013197548687458038,
0.0056210774928331375,
-0.014103948138654232,
-0.016849465668201447,
-0.02964336797595024,
-0.003052164800465107,
-0.0035987922456115484,
-0.004267451819032431,
0.05996682867407799,
-0.007271712180227041,
-0.01861105114221573,
0.04009026661515236,
0.020107140764594078,
-0.026160962879657745,
-0.007901675999164581,
-0.009398773312568665,
0.01478202547878027,
0.025128601118922234,
0.01981177367269993,
-0.0028892792761325836,
-0.007916301488876343,
0.03502033278346062,
0.027148419991135597,
0.007272477261722088,
0.0006536290165968239,
0.03429165482521057,
0.009814666584134102,
-0.04123334586620331,
0.01499202847480774,
0.005773109849542379,
-0.04018639773130417,
0.016618801280856133,
-0.011843602173030376,
0.005300163757055998,
0.003769227070733905,
-0.010255350731313229,
-0.03372713178396225,
-0.041361596435308456,
0.006249523721635342,
0.03707754611968994,
0.029512625187635422,
-0.02571982704102993,
0.05262969434261322,
0.04046408832073212,
-0.0022447770461440086,
0.03142944350838661,
0.04616902768611908,
0.0016557637136429548,
0.0027425887528806925,
-0.02621402032673359,
-0.011314066126942635,
-0.010431818664073944,
0.037417199462652206,
-0.03707794100046158,
0.019856726750731468,
0.048031214624643326,
0.017807569354772568,
0.04963232949376106,
-0.01349298469722271,
-0.07596641778945923,
0.0007373339612968266,
-0.04091856628656387,
0.005489196162670851,
-0.03660201281309128,
0.017875276505947113,
-0.01526062935590744,
-0.018913855776190758,
0.014301687479019165,
-0.01869640313088894,
0.038315657526254654,
-0.004337436053901911,
-0.014510422945022583,
0.06096635386347771,
-0.006202679127454758,
0.013383421115577221,
0.007701952941715717,
0.020889759063720703,
0.008270679041743279,
-0.054344795644283295,
0.038424521684646606,
-0.015500989742577076,
-0.013830273412168026,
0.014774548821151257,
0.038209594786167145,
0.005394930951297283,
0.007851882837712765,
0.0024943044409155846,
-0.03420872986316681,
0.029672596603631973,
-0.028348248451948166,
-0.020189665257930756,
0.0763164609670639,
-0.0035158961545675993,
0.02458098717033863,
0.00020706265058834106,
-0.009962925687432289,
0.0009168859105557203,
0.03286875784397125,
-0.007255258969962597,
0.016353294253349304,
-0.022556409239768982,
-0.025379031896591187,
-0.004924444016069174,
-0.01455287542194128,
-0.012176570482552052,
0.03986365720629692,
-0.008809812366962433,
-0.004725280217826366,
0.05332861840724945,
-0.012236164882779121,
0.0662200078368187,
-0.02800818346440792,
0.007227353285998106,
0.03371209651231766,
0.05763323977589607,
0.014161608181893826,
0.00339072966016829,
-0.0034231271129101515,
-0.008519841358065605,
-0.007146296091377735,
0.03131689503788948,
-0.01952633075416088,
0.031257208436727524,
-0.004885703790932894,
0.051996998488903046,
-0.03544958308339119,
-0.00028618649230338633,
-0.0044462718069553375,
-0.02451338991522789,
0.01710108481347561,
0.02027585357427597,
-0.02474595606327057,
0.10103730112314224,
0.026385238394141197,
-0.0020666259806603193,
0.003125337650999427,
0.008639534004032612,
-0.03602341189980507,
0.03136200085282326,
-0.0011511399643495679,
0.04531992971897125,
-0.010532602667808533,
-0.025766989216208458,
-0.0040209731087088585,
0.026059342548251152,
-0.005046624690294266,
-0.03332125395536423,
0.00380779174156487,
-0.020085470750927925,
-0.015112127177417278,
0.004922722466289997,
0.00030442868592217565,
-0.0440407395362854,
-0.01975971646606922,
0.03341907262802124,
0.03161107003688812,
0.027194302529096603,
-0.01930246129631996,
-0.013288487680256367,
-0.0476340688765049,
0.04089805483818054,
-0.032773278653621674,
-0.01210082322359085,
-0.0346771702170372,
-0.011989625170826912,
0.008404701948165894,
-0.04709726572036743
] |
<p>The WIKI Higgs boson site has an interesting diagram illustrating likely Higgs mass intervals that experiments (LEP & Tevatron) or indirect measurements have determined with a 95% confidence level. It posits that the feasible mass ranges are in the intervals of about 115-158 GeV or 175-185 GeV. The Tevatron confirmed the existance of the top quark (172 GeV) in 1995, so it had the energy and time to detect the Higgs in the 115-158 GeV ranges, but could not.
Given LHC's greater energy and luminosity, why haven't there been anouncements of the Higgs discovery? Do we understand enough about potential particle creation to definitively know they are Higgs decays? </p>
| 7,683 |
[
-0.005378433037549257,
-0.01618226058781147,
0.019679157063364983,
-0.029258212074637413,
0.04726041480898857,
0.005664824042469263,
-0.012129198759794235,
-0.05124959722161293,
-0.0035819178447127342,
-0.019428465515375137,
0.010068709962069988,
-0.012449010275304317,
0.03679124638438225,
-0.004848336335271597,
0.02282608486711979,
0.021677223965525627,
-0.0011679715244099498,
-0.0167530607432127,
-0.020684022456407547,
-0.026346122846007347,
-0.014705851674079895,
0.027736274525523186,
0.005381750874221325,
0.015714824199676514,
-0.007791820447891951,
-0.028074519708752632,
0.015494846738874912,
0.03157424554228783,
-0.0033774343319237232,
0.0808754563331604,
-0.030515743419528008,
-0.015905627980828285,
0.03470486402511597,
0.015458575449883938,
0.007781777065247297,
0.002850593999028206,
0.006457083858549595,
-0.051202014088630676,
-0.03839866816997528,
0.02392107993364334,
-0.05356111750006676,
-0.022228719666600227,
-0.022648662328720093,
0.06803978234529495,
-0.04718753695487976,
0.0112563231959939,
-0.04304586350917816,
-0.015091161243617535,
0.07139261066913605,
-0.07860061526298523,
0.022736340761184692,
0.040749091655015945,
0.049329973757267,
0.04478335753083229,
-0.01720043644309044,
-0.02099127694964409,
0.037340592592954636,
0.07497277110815048,
-0.015455995686352253,
-0.0635245069861412,
-0.037450727075338364,
-0.05168475955724716,
0.0263648871332407,
-0.03250923380255699,
-0.007054975721985102,
0.04885304719209671,
-0.029376288875937462,
-0.007041634060442448,
0.0028331908397376537,
0.008234921842813492,
0.029451273381710052,
0.02136104367673397,
0.01560707576572895,
0.0444888211786747,
0.017878333106637,
-0.024017449468374252,
0.02636844664812088,
-0.0063461000099778175,
0.03057028353214264,
0.03018697164952755,
-0.028446877375245094,
0.0019580149091780186,
0.020613189786672592,
0.0311447624117136,
0.0003600511699914932,
0.0022559426724910736,
0.06226815655827522,
-0.04836022108793259,
-0.01836845651268959,
0.028245536610484123,
-0.03272557631134987,
-0.021261295303702354,
0.08337662369012833,
-0.018526915460824966,
0.0017952924827113748,
0.020247599110007286,
-0.0014656838029623032,
0.0381816141307354,
-0.01599270850419998,
-0.0034105891827493906,
0.051154978573322296,
0.007540940772742033,
0.02151651494204998,
0.06714123487472534,
-0.0007792154210619628,
-0.03641568496823311,
-0.021750206127762794,
-0.022275282070040703,
-0.032331682741642,
-0.015531780198216438,
-0.03425481542944908,
0.0021464405581355095,
-0.003319684648886323,
-0.0018668350530788302,
-0.02233598195016384,
-0.018420394510030746,
-0.0026145679876208305,
-0.039737749844789505,
0.07390224933624268,
0.011294107884168625,
0.036115530878305435,
-0.02228124625980854,
0.049705687910318375,
-0.0573415607213974,
-0.07476425915956497,
-0.003064484102651477,
0.0500815212726593,
0.005980554968118668,
-0.04392249137163162,
0.0439283549785614,
-0.03328210487961769,
-0.0036437141243368387,
0.02493193745613098,
-0.03877926245331764,
0.037780024111270905,
-0.042337749153375626,
-0.07360962778329849,
-0.056930504739284515,
0.049701206386089325,
-0.004130769986659288,
-0.04220389947295189,
-0.07240122556686401,
-0.01709524542093277,
0.04740847274661064,
0.048565104603767395,
-0.02447551116347313,
0.0012195640010759234,
-0.03672589734196663,
0.02382388897240162,
-0.03061831369996071,
-0.01569499634206295,
-0.026434997096657753,
0.005686260759830475,
-0.01788189820945263,
-0.00563560938462615,
-0.0597088560461998,
-0.026159491389989853,
-0.006710789632052183,
-0.002257374580949545,
-0.02728370577096939,
0.05751577019691467,
0.0063599878922104836,
0.022327447310090065,
0.006561432499438524,
0.017289938405156136,
-0.030121808871626854,
0.058004230260849,
0.0003431827062740922,
0.012097693048417568,
0.04903806373476982,
-0.01799887977540493,
0.01715158484876156,
0.03390362113714218,
0.013440332375466824,
0.050717711448669434,
-0.038332585245370865,
-0.04589217156171799,
-0.00980963371694088,
0.05864889919757843,
-0.02968541532754898,
-0.006681314203888178,
-0.012159401550889015,
-0.023257624357938766,
0.025283513590693474,
0.009300656616687775,
0.03254261240363121,
-0.05821145698428154,
-0.02743517979979515,
0.06656847149133682,
-0.05722084268927574,
-0.03506053239107132,
-0.049477752298116684,
-0.04120590165257454,
0.02502664364874363,
0.010241311974823475,
0.03337443992495537,
-0.009486746042966843,
-0.008811356499791145,
-0.04602111876010895,
-0.018579084426164627,
0.042266327887773514,
0.038739919662475586,
0.04042211174964905,
0.015979740768671036,
0.011816122569143772,
0.035031501203775406,
0.026775717735290527,
0.008572317659854889,
0.03502204269170761,
-0.026622019708156586,
-0.070541150867939,
-0.015552397817373276,
-0.03670867159962654,
-0.010770426131784916,
-0.0003367290482856333,
0.01891964115202427,
-0.03636418282985687,
-0.04406783729791641,
-0.04039764031767845,
0.049445971846580505,
-0.006512962747365236,
0.051684729754924774,
0.021324768662452698,
0.02625555545091629,
-0.028908295556902885,
0.02323610894382,
0.005340247880667448,
0.008532868698239326,
-0.04865080118179321,
-0.021493099629878998,
-0.06677188724279404,
-0.026876745745539665,
0.03684495389461517,
0.015201683156192303,
-0.03675239160656929,
0.04131276533007622,
0.031261932104825974,
0.03176458925008774,
-0.0006545905489474535,
0.03929642215371132,
-0.032781630754470825,
-0.07280535250902176,
0.021443281322717667,
0.04719651862978935,
0.006050412543118,
0.01964488811790943,
0.04885312542319298,
0.009813222102820873,
0.013727772980928421,
0.026410093531012535,
-0.022676458582282066,
-0.0010822333861142397,
-0.00090798269957304,
-0.037507183849811554,
-0.0027806961443275213,
-0.010873519815504551,
0.04270852729678154,
-0.01070223655551672,
0.040057841688394547,
-0.023214779794216156,
-0.03239460662007332,
-0.010922474786639214,
-0.012921268120408058,
-0.018980665132403374,
0.03597196936607361,
0.01660597324371338,
-0.020116126164793968,
-0.031093349680304527,
0.034026846289634705,
-0.028047963976860046,
0.04717019945383072,
-0.036463186144828796,
-0.011995702981948853,
-0.008630195632576942,
0.023397915065288544,
0.015304298140108585,
-0.011461862362921238,
0.045489661395549774,
-0.05313042923808098,
-0.029575221240520477,
0.021145574748516083,
-0.004890352953225374,
0.019095323979854584,
0.026607535779476166,
-0.04784383624792099,
-0.01576557196676731,
-0.039578743278980255,
-0.026651382446289062,
0.0032033047173172235,
-0.008512256667017937,
0.01585029624402523,
0.009932075627148151,
0.00274923094548285,
-0.015072273090481758,
-0.02474939078092575,
-0.0020949505269527435,
0.0022993346210569143,
-0.004968735855072737,
0.017809567973017693,
0.015850644558668137,
-0.003237520344555378,
-0.015553198754787445,
0.03851135075092316,
0.013249419629573822,
-0.013945343904197216,
-0.04794823005795479,
0.03839697316288948,
-0.008900082670152187,
-0.024771373718976974,
0.07731086760759354,
0.03694829344749451,
-0.03207097202539444,
0.016049275174736977,
-0.02866002358496189,
-0.00806715153157711,
0.011407711543142796,
-0.02562001161277294,
0.043880973011255264,
0.009861819446086884,
-0.05771135911345482,
0.09161698818206787,
0.03328898176550865,
-0.027539577335119247,
-0.029767101630568504,
-0.011996272020041943,
-0.0061195543967187405,
-0.024574756622314453,
-0.016016481444239616,
0.015890847891569138,
0.0006151056732051075,
0.020690355449914932,
0.02187514305114746,
0.02183404751121998,
0.0284405630081892,
0.03483494743704796,
-0.009525780566036701,
0.004323896486312151,
0.0013832683907821774,
0.006328894291073084,
0.021165067330002785,
0.006051321513950825,
-0.03965355083346367,
-0.0033240369521081448,
-0.008574808947741985,
0.039265915751457214,
-0.017429644241929054,
-0.029446803033351898,
0.08490092307329178,
0.0041164373978972435,
0.022159341722726822,
-0.017971327528357506,
-0.008301462978124619,
0.010189477354288101,
-0.00044314702972769737,
-0.004758463706821203,
0.02607068046927452,
0.04099079594016075,
-0.02275344915688038,
-0.0010845678625628352,
0.016569677740335464,
0.009135731495916843,
-0.018913138657808304,
-0.016174277290701866,
0.00013933579612057656,
-0.016536511480808258,
0.016231227666139603,
0.0273596104234457,
-0.03950272127985954,
0.02548184059560299,
0.043284203857183456,
0.01066831685602665,
-0.02202378213405609,
0.005644018761813641,
-0.03040161170065403,
-0.009459509514272213,
0.007370120380073786,
0.0037107456009835005,
0.00499079329892993,
-0.020133405923843384,
0.021319709718227386,
0.010881044901907444,
-0.0012400704436004162,
-0.02503341995179653,
-0.005589081905782223,
-0.06369175016880035,
-0.027324801310896873,
-0.0968656912446022,
-0.017237136140465736,
-0.016278041526675224,
-0.032393380999565125,
-0.014713957905769348,
-0.009388502687215805,
-0.01069469191133976,
-0.031432557851076126,
0.02287166565656662,
-0.058459218591451645,
-0.003465228248387575,
-0.029492804780602455,
-0.02168450690805912,
-0.02802075259387493,
-0.009371601045131683,
0.015320394188165665,
0.0026476720813661814,
0.025996120646595955,
0.026037922129034996,
-0.03340218588709831,
-0.005522741470485926,
-0.007254962809383869,
0.054322849959135056,
-0.030867213383316994,
0.017260730266571045,
0.042487483471632004,
0.034881215542554855,
-0.05165107175707817,
-0.000040154212911147624,
0.02479618787765503,
0.07550111413002014,
0.021828286349773407,
0.007600532844662666,
0.003925955854356289,
-0.038865961134433746,
-0.03620642051100731,
0.04930060729384422,
0.0484924353659153,
-0.00304627837613225,
0.038002680987119675,
0.03082505613565445,
0.0038581148255616426,
-0.0014017617795616388,
0.045628465712070465,
0.062137093394994736,
-0.022336509078741074,
-0.036999356001615524,
-0.05707329884171486,
0.00006835329259047285,
-0.012173746712505817,
-0.01690906099975109,
0.010659008286893368,
-0.012829731218516827,
-0.009001223370432854,
-0.002033766359090805,
0.0009703841060400009,
0.01811252161860466,
-0.02911885268986225,
0.014337477274239063,
0.0022171789314597845,
0.04820389673113823,
-0.003935112617909908,
-0.010235621593892574,
0.008203834295272827,
0.024403980001807213,
0.03848128393292427,
-0.027774427086114883,
0.009353497996926308,
-0.06987424939870834,
-0.004121859557926655,
0.04875241219997406,
0.043000079691410065,
-0.015382234007120132,
-0.020083388313651085,
-0.025911899283528328,
0.001905917888507247,
0.04793483391404152,
-0.03099672868847847,
0.01931740716099739,
-0.031172122806310654,
0.01670846901834011,
-0.015316066332161427,
-0.01931172050535679,
0.045525722205638885,
0.0372786819934845,
0.0019649751484394073,
0.0037299469113349915,
-0.028689930215477943,
-0.018181506544351578,
0.004755646921694279,
0.0016196700744330883,
0.02560943178832531,
0.04261086508631706,
0.03580740466713905,
0.012380740605294704,
-0.02308359555900097,
0.013697812333703041,
-0.01577298529446125,
-0.09177756309509277,
-0.026925232261419296,
-0.0003265513514634222,
-0.0371282659471035,
0.04560811445116997,
-0.005632076878100634,
-0.05496557801961899,
0.029360124841332436,
0.017903761938214302,
-0.0048163337633013725,
-0.0203156229108572,
-0.053354520350694656,
0.0010974375763908029,
0.04305628687143326,
0.01105584017932415,
0.026340076699852943,
0.02769344672560692,
-0.023567819967865944,
-0.0010659076506271958,
-0.023454492911696434,
0.05275987833738327,
-0.024281861260533333,
0.007963315583765507,
-0.0077328914776444435,
-0.01729951798915863,
-0.018854396417737007,
0.051230546087026596,
0.01164242997765541,
0.0212855264544487,
-0.01663060486316681,
-0.011050079949200153,
-0.028500225394964218,
0.020542368292808533,
0.02096365951001644,
-0.011424869298934937,
-0.03832854703068733,
0.04371768236160278,
0.004772342275828123,
-0.022550545632839203,
0.004481651354581118,
-0.0016818966250866652,
0.014826682396233082,
-0.002874263096600771,
0.0006182697834447026,
0.024899432435631752,
-0.028693372383713722,
-0.01760670356452465,
0.07505382597446442,
-0.013066374696791172,
0.029485493898391724,
-0.0133286751806736,
-0.016838401556015015,
0.006288127973675728,
-0.050990864634513855,
-0.03800218552350998,
0.0023732539266347885,
0.03030686266720295,
0.021042220294475555,
-0.02793615497648716,
0.04407045245170593,
0.0004598816449288279,
0.02086181752383709,
-0.04437609016895294,
0.0029830809216946363,
-0.00494376989081502,
0.033156365156173706,
-0.002464690711349249,
0.009255338460206985,
-0.01867980696260929,
-0.06104357913136482,
0.004474228713661432,
-0.030896486714482307,
0.049243148416280746,
0.010025245137512684,
-0.002126180799677968,
-0.009848075918853283,
0.03497358784079552,
0.03717707097530365,
-0.004328975919634104,
0.008057378232479095,
0.033713746815919876,
0.0322965569794178,
-0.03138682618737221,
0.01822100207209587,
0.03659815341234207,
-0.009737403132021427,
-0.03126237913966179,
0.012669546529650688,
0.007641303353011608,
0.063824363052845,
-0.04216758534312248,
0.014229652471840382,
0.054045483469963074,
-0.01697157323360443,
0.01958581991493702,
-0.029856590554118156,
0.044728394597768784,
-0.02346828766167164,
0.017828281968832016,
-0.012614492326974869,
-0.013505366630852222,
0.019916458055377007,
-0.016147250309586525,
0.05943974852561951,
-0.01924162358045578,
0.046308353543281555,
-0.015313607640564442,
-0.007530402857810259,
0.012490672059357166,
-0.013114157132804394,
-0.0017460191156715155,
-0.008749094791710377,
0.005127085838466883,
-0.012123573571443558,
0.04038374871015549,
0.02706814929842949,
-0.028323503211140633,
-0.034140653908252716,
-0.04171188175678253,
-0.030225306749343872,
-0.00931988749653101,
0.06727269291877747,
-0.006238033063709736,
0.03679976239800453,
-0.030506525188684464,
-0.044975750148296356,
0.012465049512684345,
-0.02817670814692974,
-0.01511994656175375,
0.007630232255905867,
0.029014794155955315,
-0.001293026260100305,
-0.012420359998941422,
-0.009975854307413101,
0.03403399512171745,
-0.0033099246211349964,
-0.020885929465293884,
0.014099975116550922,
0.03544211760163307,
0.058254424482584,
0.02626490592956543,
-0.009974885731935501,
-0.0019293669611215591,
0.024356555193662643,
0.005994716659188271,
0.006184667814522982,
-0.003523528575897217,
-0.027505477890372276,
0.03102218545973301,
-0.0013110267464071512,
-0.01311320997774601,
0.018483763560652733,
-0.024534443393349648,
-0.0821988582611084,
0.04580824822187424,
0.03500274568796158,
0.012982693500816822,
-0.01747959479689598,
0.036401957273483276,
-0.028895361348986626,
0.038891348987817764,
0.02297275699675083,
0.041783854365348816,
-0.09193950891494751,
-0.05789966881275177,
-0.016065672039985657,
-0.054641399532556534,
0.024669261649250984,
0.002493534004315734,
-0.03744223713874817,
-0.006039800122380257,
-0.025644509121775627,
-0.020106231793761253,
-0.030409734696149826,
0.023304250091314316,
-0.01726878061890602,
0.03606346249580383,
-0.024450885131955147,
0.024843361228704453,
-0.029005305841565132,
0.0281722042709589,
0.13456037640571594,
0.08834857493638992,
-0.013490448705852032,
-0.04639049619436264,
0.055893123149871826,
-0.008266117423772812,
-0.014773103408515453,
-0.028524113819003105,
0.045744653791189194,
0.0061458381824195385,
0.0038747997023165226,
-0.03605794906616211,
0.05213037133216858,
-0.0007968013524077833,
0.005205960478633642,
0.05843207612633705,
-0.029042923822999,
-0.037304215133190155,
0.006476139184087515,
0.06057238206267357,
0.004559652879834175,
-0.012673445045948029,
-0.004155277740210295,
0.032608017325401306,
-0.01007743738591671,
0.009520419873297215,
0.023183608427643776,
-0.049559108912944794,
0.0023562503047287464,
-0.00806040782481432,
-0.030567819252610207,
0.010234836488962173,
0.027154404670000076,
-0.004430450964719057,
-0.04528917744755745,
0.01722525618970394,
-0.01568232849240303,
0.010821212083101273,
0.010519811883568764,
0.042445454746484756,
0.047125086188316345,
-0.03404722362756729,
-0.023852191865444183,
0.03451916575431824,
-0.04494181275367737,
-0.024064209312200546,
0.0068594589829444885,
0.054835278540849686,
-0.023245742544531822,
-0.026078952476382256,
0.0016975454054772854,
-0.012912510894238949,
-0.02570035494863987,
0.018780486658215523,
-0.026890244334936142,
-0.02879379130899906,
0.01081542856991291,
-0.004126506857573986,
0.014213193207979202,
-0.002209134167060256,
0.03170619159936905,
0.0009143406059592962,
0.03375032916665077,
0.0039476971141994,
0.008229507133364677,
0.0063165174797177315,
-0.012563204392790794,
0.01277721207588911,
-0.03451430797576904,
-0.00511449109762907,
0.0014959728578105569,
0.02771208994090557,
-0.054415587335824966,
-0.04361342266201973,
0.01740431599318981,
0.001717580365948379,
0.024948636069893837,
0.038623470813035965,
-0.029504552483558655,
-0.02003544196486473,
-0.013112988322973251,
0.03393004834651947,
-0.00622073607519269,
-0.026427725329995155,
-0.02625337615609169,
0.0007193883648142219,
-0.007588744163513184,
0.034478262066841125,
-0.031603001058101654,
0.02478582039475441,
-0.025874745100736618,
0.019948188215494156,
-0.02582361549139023,
-0.03613027185201645,
0.01181031297892332,
0.03313104808330536,
-0.026185620576143265,
0.0009560517501085997,
-0.010421240702271461,
0.03608943521976471,
0.00412230147048831,
0.023358896374702454,
0.0509570874273777,
0.010358037427067757,
0.013044864870607853,
0.002300168154761195,
0.04215068742632866,
-0.053943730890750885,
-0.008559789508581161,
-0.007838962599635124,
0.031960178166627884,
-0.024647807702422142,
-0.05929940566420555,
-0.01975366659462452,
-0.001723086112178862,
0.03660671040415764,
0.03092402033507824,
-0.03864683210849762,
0.025725847110152245,
-0.014975698664784431,
0.02800983004271984,
-0.037691839039325714,
-0.019815437495708466,
-0.018989579752087593,
0.03395788371562958,
-0.010527198202908039,
-0.001149150193668902,
0.017052149400115013,
0.01672193966805935,
-0.01357363723218441,
-0.022480497136712074,
-0.0009643713710829616,
0.025784002617001534,
-0.03724806010723114,
-0.01285315677523613,
0.020285923033952713,
-0.012401655316352844,
0.015209960751235485,
-0.019804662093520164,
-0.03849704563617706,
0.03277042508125305,
-0.022373223677277565,
-0.08272670209407806,
0.03348437324166298,
0.041214846074581146,
-0.0018762588733807206,
0.016679270192980766,
-0.024813883006572723,
-0.009034611284732819,
0.07069596648216248,
-0.05676352605223656,
0.009145671501755714,
0.033019114285707474,
0.01186013501137495,
-0.05641844868659973,
0.019965048879384995,
0.01728132553398609,
0.009256500750780106,
0.01879812777042389,
0.0427415557205677,
0.008776599541306496,
0.001168140210211277,
-0.017217230051755905,
-0.02501349151134491,
-0.04227752238512039,
0.07191663980484009,
0.007224339991807938,
0.019453231245279312,
0.0007761675515212119,
0.041249144822359085,
-0.0724765881896019,
0.021273063495755196,
0.027803601697087288,
0.018813109025359154,
-0.07201924920082092,
-0.022272301837801933,
-0.017527690157294273,
-0.026870829984545708,
0.047156475484371185,
-0.050680216401815414,
0.02223513275384903,
0.03223210945725441,
-0.05615539476275444,
0.01241256669163704,
-0.044771287590265274,
-0.018466327339410782,
-0.02819865755736828,
-0.036540038883686066,
0.02781793847680092,
0.0548158697783947,
0.03249948099255562,
0.03832145780324936,
0.007274208590388298,
0.002094532363116741,
0.03776286542415619,
-0.017033632844686508,
-0.028587883338332176,
0.02859479933977127,
0.03380131348967552,
-0.07378481328487396,
0.07500970363616943,
-0.0016634586500003934,
0.015478096902370453,
0.006188888102769852,
0.007847272790968418,
0.015185091644525528,
0.017093349248170853,
0.006194524001330137,
-0.0073607731610536575,
0.06112785264849663,
0.06111236289143562,
-0.020254036411643028,
-0.02414420060813427,
0.030729293823242188,
-0.03043407015502453,
0.031143832951784134,
0.015717292204499245,
0.014042864553630352,
-0.01967458799481392,
-0.010897397063672543,
-0.016842598095536232,
0.024336080998182297,
-0.02165078930556774,
-0.024763667955994606,
0.009840579703450203,
-0.001032262109220028,
-0.007371428422629833,
-0.007036618888378143,
0.005889296066015959,
-0.06482750922441483,
0.0133286751806736,
0.03023671545088291,
0.004813418257981539,
0.007485166657716036,
0.009858015924692154,
-0.041892897337675095,
-0.007978148758411407,
0.014453898184001446,
0.028633104637265205,
-0.0010376005666330457,
-0.047942791134119034,
0.023240888491272926,
-0.03107151947915554,
0.0147474966943264,
0.019566889852285385,
-0.03329033777117729,
-0.07898864150047302,
0.049245771020650864,
-0.013067170977592468,
0.05269623175263405,
-0.005566256586462259,
-0.01818046160042286,
-0.02841370552778244,
-0.0339355506002903,
0.07006511092185974,
-0.006844356190413237,
0.024912286549806595,
-0.034073587507009506,
0.014053644612431526,
0.012559959664940834,
-0.039502158761024475,
0.015260202810168266,
0.0024507639463990927,
-0.03655648231506348,
0.01251213625073433,
0.005605703219771385,
-0.0027257034089416265,
-0.018909575417637825,
0.0026568970642983913,
-0.008819706737995148,
-0.004498458467423916,
0.007096695713698864,
-0.03518577665090561,
0.006552670616656542,
0.05098541080951691,
0.04708898440003395,
-0.015950053930282593,
0.03064349852502346,
0.0013950663851574063,
0.02395586483180523,
0.07619912922382355,
-0.013140915893018246,
-0.003148744348436594,
0.06358520686626434,
-0.012836161069571972,
0.019501736387610435,
0.025350794196128845,
-0.006808034144341946,
-0.025411222130060196,
0.02996020019054413,
-0.03405868634581566,
-0.020800644531846046,
0.01072975154966116,
-0.0014729468384757638,
-0.008442272432148457,
-0.03715801611542702,
0.0070437113754451275,
0.020694434642791748,
-0.0016368221258744597,
-0.016708094626665115,
0.023470554500818253,
0.02065283991396427,
0.007842578925192356,
0.013268843293190002,
-0.010238801129162312,
0.016368640586733818,
0.003704581642523408,
0.026831110939383507,
0.028871623799204826,
0.0226198211312294,
0.003752104938030243,
-0.00027186988154426217,
-0.008288090117275715,
-0.002779166679829359,
0.02329033426940441,
0.02921534702181816,
0.05646723881363869,
-0.010696337558329105,
-0.058836255222558975,
0.016551490873098373,
0.00577332079410553,
-0.0026012230664491653,
0.002009607618674636,
-0.01264470349997282,
0.07163555175065994,
-0.015916677191853523,
-0.008692985400557518,
-0.025436734780669212,
-0.05308498442173004,
0.0007807284709997475,
0.018993590027093887,
0.011084377765655518,
0.049063727259635925,
-0.022921526804566383,
0.012651966884732246,
0.010530173778533936,
0.04881718009710312,
0.01877381093800068,
-0.053363192826509476,
-0.031362373381853104,
0.008601862005889416,
-0.013309461064636707,
-0.027739426121115685,
-0.030460525304079056,
-0.016072554513812065,
-0.017147963866591454,
-0.005007646512240171,
0.029864665120840073,
0.06899286806583405,
-0.020194314420223236,
-0.055485691875219345,
-0.07032877951860428,
0.014474923722445965,
-0.0015832316130399704,
0.02421780861914158,
-0.04249498248100281,
0.013375393114984035,
-0.04531159996986389,
0.02548976242542267
] |
<p>It can be shown the sum over all Feynman diagrams in quantum field theory leads to a unitary S-matrix. Where can I find a proof that the sum over string worldsheets with varying genuses also leads to a unitary S-matrix?</p>
| 7,684 |
[
-0.005485286936163902,
-0.021703090518712997,
0.00296424119733274,
-0.0280802883207798,
-0.022046446800231934,
0.010326853021979332,
-0.04391120374202728,
0.011386163532733917,
0.041871119290590286,
-0.06672956794500351,
0.006584348157048225,
0.009790807962417603,
0.06205831095576286,
0.02775321528315544,
0.01960173062980175,
-0.000814438855741173,
-0.023438306525349617,
-0.008366561494767666,
-0.01478293165564537,
-0.023601312190294266,
-0.0047658225521445274,
0.02081172727048397,
0.023553095757961273,
0.017707793042063713,
0.0068724793381989,
0.010534289292991161,
0.01573210209608078,
0.03369712457060814,
0.03214186429977417,
0.07786562293767929,
-0.017852574586868286,
-0.014680393971502781,
0.02699614129960537,
0.0473204106092453,
0.021571379154920578,
-0.010441217571496964,
-0.017647098749876022,
-0.001711554592475295,
-0.012407188303768635,
-0.01988949067890644,
0.008363250643014908,
-0.00772400526329875,
-0.043416161090135574,
0.08317175507545471,
-0.021989919245243073,
0.04086219519376755,
-0.033894866704940796,
-0.018973758444190025,
0.05234145000576973,
-0.10445817559957504,
0.10237213224172592,
-0.000392371992347762,
0.046893972903490067,
0.029423516243696213,
-0.02371695265173912,
-0.006880853790789843,
0.057062335312366486,
0.06779327243566513,
0.027030203491449356,
-0.028102628886699677,
-0.034075673669576645,
-0.05782812833786011,
0.01172231137752533,
-0.05395419895648956,
-0.04237382486462593,
0.013667447492480278,
0.019665775820612907,
-0.014017743989825249,
-0.00832973513752222,
-0.02866223454475403,
-0.02852870337665081,
0.019860759377479553,
0.040969740599393845,
-0.021861542016267776,
-0.004297239705920219,
-0.002861677436158061,
0.032754916697740555,
0.03872628137469292,
0.03774566575884819,
0.020986875519156456,
-0.02493845485150814,
0.026507511734962463,
0.015246724709868431,
-0.012208421714603901,
0.007182853762060404,
-0.010428758338093758,
0.04838874563574791,
0.009208985604345798,
-0.024286530911922455,
0.05903194844722748,
-0.007824364118278027,
-0.02044113166630268,
0.05576234310865402,
-0.00011992151121376082,
-0.038764189928770065,
0.01142064854502678,
0.019044212996959686,
0.04234030470252037,
0.0035674108657985926,
-0.044320762157440186,
-0.024769216775894165,
-0.045621536672115326,
0.01018973346799612,
0.08720844984054565,
0.02432139590382576,
0.040981002151966095,
-0.06233348324894905,
0.021601712331175804,
-0.016532637178897858,
-0.0184917151927948,
-0.05017806589603424,
0.01859191432595253,
-0.028444340452551842,
-0.034134358167648315,
-0.02588079310953617,
-0.0035093347541987896,
-0.02183987759053707,
0.015531045384705067,
0.04176046699285507,
0.06506682932376862,
0.03259947523474693,
-0.012887431308627129,
0.006920346524566412,
-0.043977804481983185,
-0.07149302959442139,
0.03519893065094948,
0.04271754249930382,
-0.026736274361610413,
-0.018446804955601692,
0.03598490357398987,
0.018002837896347046,
-0.036203909665346146,
-0.0005498918471857905,
-0.01715124398469925,
0.04313686490058899,
-0.0003198552585672587,
-0.09267023950815201,
-0.041406307369470596,
0.02539014257490635,
-0.010574222542345524,
0.009960334748029709,
-0.04924175888299942,
0.0072771236300468445,
0.037387993186712265,
0.07622180879116058,
-0.02268744632601738,
0.0253526009619236,
0.01149248331785202,
0.038734324276447296,
0.036121562123298645,
0.0030807815492153168,
-0.037557415664196014,
-0.019913507625460625,
-0.04786011204123497,
0.0017849225550889969,
-0.02919134683907032,
0.030146021395921707,
0.004403003491461277,
-0.016285521909594536,
0.009846874512732029,
0.06793714314699173,
0.0005663160700351,
0.030539609491825104,
0.01699291542172432,
-0.014596679247915745,
-0.01578971929848194,
0.074408158659935,
0.03598738834261894,
0.010216598398983479,
0.013697180896997452,
-0.03492772951722145,
-0.020748842507600784,
0.02077385224401951,
0.036587875336408615,
0.017579248175024986,
-0.04644811153411865,
-0.03962188959121704,
0.037528663873672485,
0.028241056948900223,
-0.006927703972905874,
-0.033073458820581436,
-0.03366135433316231,
0.0061488826759159565,
0.04711582511663437,
-0.002447953913360834,
0.010443512350320816,
-0.023591572418808937,
-0.03515893965959549,
-0.01833999902009964,
-0.05471963807940483,
-0.05113617330789566,
-0.04664841666817665,
-0.002176426351070404,
0.010219583287835121,
-0.0175392534583807,
0.026620181277394295,
0.017934143543243408,
0.012999364174902439,
-0.024058111011981964,
-0.03988524153828621,
-0.014949275180697441,
0.04494525492191315,
0.012757474556565285,
-0.011919594369828701,
-0.017916899174451828,
0.005306231789290905,
0.09457052499055862,
-0.022014133632183075,
0.08746907114982605,
-0.048241257667541504,
-0.01828927733004093,
0.010900919325649738,
-0.0260300375521183,
0.02708418108522892,
-0.006062477361410856,
0.009300769306719303,
0.003882546443492174,
-0.002247449941933155,
-0.006486133206635714,
0.02896769903600216,
-0.020573655143380165,
0.027570117264986038,
0.06687438488006592,
0.0480387881398201,
-0.018896492198109627,
-0.0037918523885309696,
-0.011596870608627796,
0.042095672339200974,
0.007355610374361277,
-0.04477953910827637,
-0.03924050182104111,
-0.003032602369785309,
-0.004899096209555864,
0.05245806649327278,
-0.007356701884418726,
-0.0043474771082401276,
0.041485268622636795,
0.048113539814949036,
0.006121427286416292,
0.03183341398835182,
-0.004700412508100271,
-0.00009880452853394672,
0.0071389866061508656,
-0.005632676649838686,
0.00354956416413188,
0.0033737358171492815,
0.013300903141498566,
0.022762907668948174,
-0.01695234514772892,
0.01886030100286007,
-0.09328580647706985,
0.027410047128796577,
-0.06032629683613777,
0.002871202304959297,
0.01603163219988346,
-0.05174562707543373,
0.024638213217258453,
-0.030583931133151054,
0.03343860059976578,
0.036235276609659195,
-0.01292822603136301,
-0.010555547662079334,
-0.02985154464840889,
-0.03591512516140938,
0.02937917783856392,
-0.022664571180939674,
-0.0006370494375005364,
-0.00030683595105074346,
0.031159335747361183,
-0.04478687047958374,
0.025761011987924576,
-0.0007647580932825804,
-0.015562235377728939,
0.0026468439027667046,
0.05180159956216812,
0.021852636709809303,
-0.02005198411643505,
-0.0029287547804415226,
-0.01952829211950302,
-0.0224294550716877,
0.011970756575465202,
-0.005943241063505411,
0.009005383588373661,
0.002892228541895747,
-0.07077986747026443,
-0.011460098437964916,
-0.038701653480529785,
-0.02662353590130806,
0.03146394342184067,
0.01714903861284256,
0.0026550341863185167,
0.01732342690229416,
-0.012707982212305069,
-0.011859772726893425,
-0.03486606478691101,
0.02061326429247856,
0.03725007548928261,
-0.03198213130235672,
0.022250285372138023,
0.02380734495818615,
0.04330015555024147,
-0.019803762435913086,
0.016722558066248894,
-0.015646379441022873,
-0.04473245143890381,
0.014988575130701065,
-0.03188131004571915,
0.032102975994348526,
-0.032384976744651794,
0.018688727170228958,
-0.014967046678066254,
-0.05268018692731857,
-0.007129146251827478,
-0.029645448550581932,
-0.03303278610110283,
0.028923070058226585,
0.005367903038859367,
0.03781023621559143,
0.011859391815960407,
-0.0944637581706047,
0.08464135974645615,
0.0210128054022789,
-0.03151412308216095,
-0.02330106683075428,
0.011439012363553047,
0.004863514564931393,
-0.015617300756275654,
0.045478664338588715,
0.008022679015994072,
-0.052580732852220535,
0.047019168734550476,
0.02533392235636711,
-0.008783410303294659,
0.04168935865163803,
-0.019127799198031425,
-0.03424297273159027,
0.011063470505177975,
-0.03620518371462822,
0.02961326576769352,
0.03165155276656151,
-0.03098083660006523,
-0.021714331582188606,
-0.012874579057097435,
0.027703825384378433,
-0.022042324766516685,
-0.004655203316360712,
-0.019912516698241234,
0.04447150602936745,
0.03336106985807419,
0.020289301872253418,
-0.05491190031170845,
0.04647976905107498,
0.012511464767158031,
-0.048815976828336716,
-0.01954757422208786,
0.022977791726589203,
0.027339337393641472,
-0.01274022925645113,
0.012893456034362316,
-0.007716266438364983,
0.030028432607650757,
-0.006672567687928677,
-0.02055533230304718,
0.0008559109410271049,
-0.02253267727792263,
0.03745438531041145,
-0.052264537662267685,
-0.04532233998179436,
0.012064831331372261,
0.0395597480237484,
0.016660211607813835,
-0.0057106614112854,
-0.05420038476586342,
-0.010452743619680405,
-0.04137929156422615,
-0.00038794087595306337,
-0.03258441388607025,
0.06509508192539215,
-0.00947242509573698,
0.0035274468827992678,
-0.0071736411191523075,
-0.0005627941573038697,
-0.009710236452519894,
-0.03497731313109398,
-0.052786294370889664,
-0.013811538927257061,
-0.02362639643251896,
-0.024536188691854477,
0.04987911134958267,
-0.025996152311563492,
0.002105988096445799,
-0.0033771998714655638,
-0.04520148038864136,
-0.018443146720528603,
-0.025013862177729607,
-0.059860959649086,
0.01783088780939579,
-0.02648329548537731,
-0.009448541328310966,
-0.0009859493002295494,
0.07097501307725906,
0.0025212992914021015,
-0.018323423340916634,
0.005830354522913694,
0.024128494784235954,
-0.03312629088759422,
0.011500763706862926,
0.006431637331843376,
0.046368394047021866,
0.015983179211616516,
0.018669424578547478,
0.062065012753009796,
0.03696543723344803,
-0.05300586670637131,
0.005686737596988678,
-0.021547839045524597,
0.04647368937730789,
-0.00684959813952446,
-0.03456328064203262,
0.006100382190197706,
-0.036525994539260864,
-0.03504494950175285,
0.004368583671748638,
0.054256372153759,
0.014935808256268501,
-0.012183783575892448,
0.06332551687955856,
0.015035494230687618,
-0.03873297572135925,
0.04766898229718208,
0.05241326242685318,
-0.01371555682271719,
-0.025239383801817894,
-0.0036381324753165245,
-0.0035900536458939314,
-0.0028355459216982126,
0.0022205905988812447,
0.0007878980250097811,
-0.00017247619689442217,
-0.04514528438448906,
-0.0002351527800783515,
0.029502933844923973,
-0.019902067258954048,
-0.025136388838291168,
-0.021457381546497345,
0.0160408616065979,
0.019822726026177406,
-0.01798887923359871,
0.01449157390743494,
0.016252567991614342,
0.039269547909498215,
0.01480758935213089,
0.007099737413227558,
-0.03967906907200813,
-0.023644568398594856,
-0.026655031368136406,
-0.003768177470192313,
0.026030749082565308,
0.02113475650548935,
0.003490016795694828,
-0.011254314333200455,
-0.006423546466976404,
0.0587395615875721,
-0.0022437768056988716,
0.025525132194161415,
0.02571464702486992,
0.00582490861415863,
0.013284573331475258,
-0.01699734292924404,
0.041637539863586426,
0.057097818702459335,
0.005429806653410196,
0.03665334731340408,
-0.027906509116292,
0.004249250516295433,
-0.03578915446996689,
0.028284674510359764,
0.008847706019878387,
0.04965290427207947,
0.01966569758951664,
0.0608464814722538,
0.005675062537193298,
0.04833175614476204,
-0.03900403901934624,
-0.070277638733387,
0.02904924750328064,
-0.00864963885396719,
-0.015727298334240913,
0.03464892506599426,
-0.022634008899331093,
-0.013538265600800514,
-0.0034547452814877033,
0.005982448812574148,
-0.0003985537332482636,
-0.002821906004101038,
-0.02419455163180828,
0.026205088943243027,
0.01483984012156725,
0.009712278842926025,
0.02297370694577694,
0.024000823497772217,
-0.01757165603339672,
0.01115703396499157,
-0.0431932732462883,
0.05169626325368881,
-0.00783506128937006,
0.0025520874187350273,
-0.069581538438797,
0.015041929669678211,
-0.02015063352882862,
-0.01052969228476286,
-0.032940708100795746,
0.007846073247492313,
0.011620556935667992,
-0.04359109327197075,
-0.07613196223974228,
-0.00512089254334569,
0.011930223554372787,
0.008847109042108059,
0.0483761690557003,
0.03683976083993912,
0.0298817977309227,
-0.01383986696600914,
0.04519036412239075,
-0.03205020725727081,
-0.010504258796572685,
-0.02713051065802574,
0.047697652131319046,
0.020471271127462387,
-0.022298725321888924,
-0.015962477773427963,
0.014392497949302197,
-0.040602393448352814,
0.049696166068315506,
-0.012200289405882359,
0.024428073316812515,
-0.007201962172985077,
-0.044286098331213,
-0.005719135515391827,
-0.0223789494484663,
-0.011741723865270615,
0.009123897179961205,
-0.034550897777080536,
0.02408130280673504,
0.0002266362280352041,
0.0076938653364777565,
-0.04553283751010895,
-0.055205583572387695,
0.03255691006779671,
0.024393541738390923,
-0.02667887508869171,
-0.03842209279537201,
0.022421298548579216,
-0.03055659681558609,
-0.003654816886410117,
-0.022696001455187798,
0.041438888758420944,
-0.0480874627828598,
-0.015116607770323753,
0.047555048018693924,
0.05104079097509384,
0.057360731065273285,
0.020102832466363907,
0.0020584992598742247,
0.01730690710246563,
-0.04614708945155144,
0.002033151453360915,
-0.03239008039236069,
-0.001018008915707469,
-0.015827780589461327,
-0.01449351292103529,
0.006907903589308262,
-0.021434247493743896,
0.022359782829880714,
-0.027151796966791153,
0.010772528126835823,
0.018968241289258003,
0.031427014619112015,
0.027761414647102356,
-0.021031683310866356,
0.019528120756149292,
-0.044538989663124084,
0.05095117539167404,
-0.02737133763730526,
0.02955547347664833,
0.0038843899965286255,
-0.017579570412635803,
0.017203763127326965,
0.014462098479270935,
-0.019016817212104797,
0.003961748443543911,
0.055218640714883804,
0.035687725991010666,
-0.03438635915517807,
0.03930894285440445,
-0.03747041895985603,
-0.0004948725108988583,
0.03606858104467392,
0.028043391183018684,
0.015349582768976688,
0.008740839548408985,
0.002643563086166978,
-0.04896077513694763,
-0.030931465327739716,
0.03224227949976921,
0.053134605288505554,
-0.008207585662603378,
0.02913878858089447,
0.05345458909869194,
-0.006695765070617199,
0.02546108141541481,
-0.01063461136072874,
-0.016930997371673584,
0.00597927812486887,
-0.01488572172820568,
0.02432464435696602,
-0.04596564173698425,
-0.013146226294338703,
0.038967400789260864,
0.07784821093082428,
-0.04154568910598755,
0.05444895103573799,
0.033049896359443665,
-0.017637863755226135,
0.04152727499604225,
0.008815785869956017,
-0.035362087190151215,
0.0638391524553299,
-0.03762589022517204,
0.045463018119335175,
0.024299023672938347,
-0.003593654604628682,
0.02904828079044819,
0.02136716991662979,
-0.010868712328374386,
0.024311665445566177,
-0.035476334393024445,
-0.05209549143910408,
0.02965611033141613,
0.021526815369725227,
0.009115230292081833,
-0.008438799530267715,
0.007496275473386049,
0.04678668826818466,
-0.0012795239454135299,
0.003408983815461397,
-0.008254336193203926,
-0.05172374099493027,
-0.01106986589729786,
-0.02859320677816868,
-0.04175962135195732,
0.051038019359111786,
0.039370097219944,
0.006118789315223694,
0.02554597146809101,
0.016787072643637657,
-0.0040974910371005535,
0.014500015415251255,
0.0725080743432045,
-0.033319905400276184,
0.020947033539414406,
-0.0159122534096241,
0.03147323429584503,
-0.020064976066350937,
0.011266585439443588,
0.1225212886929512,
0.031027358025312424,
0.04053729027509689,
-0.061612822115421295,
0.002033016411587596,
-0.015031425282359123,
0.009763430804014206,
-0.05047078803181648,
0.029381953179836273,
0.005504620261490345,
-0.014945720322430134,
-0.0206727534532547,
0.0697958916425705,
-0.005832626949995756,
-0.013194328173995018,
0.05286064371466637,
-0.05781181901693344,
-0.02694888226687908,
0.008142989128828049,
0.030155673623085022,
-0.003950588405132294,
0.017600983381271362,
-0.08527267724275589,
-0.008844300173223019,
0.01610235497355461,
-0.02398795261979103,
-0.04364274442195892,
-0.011657275259494781,
0.018454566597938538,
0.025819767266511917,
0.0029285820201039314,
-0.006055171601474285,
0.016030095517635345,
0.0005979146808385849,
-0.020753147080540657,
0.0013826421927660704,
0.005894928239285946,
0.004718732554465532,
0.02404484897851944,
0.032267265021800995,
0.017983220517635345,
0.03623773530125618,
0.005918648559600115,
0.040389545261859894,
-0.053521331399679184,
0.0029119406826794147,
-0.012163070030510426,
0.005236541386693716,
-0.02253415621817112,
0.003178505226969719,
-0.012873024679720402,
0.009787315502762794,
0.009310719557106495,
-0.04236763343214989,
0.0035749529488384724,
-0.004616145510226488,
0.06492090225219727,
-0.05122458562254906,
-0.00341400527395308,
-0.0024265479296445847,
0.034584809094667435,
0.026694435626268387,
0.0030261611100286245,
0.026442935690283775,
-0.02681855857372284,
0.011033854447305202,
0.012385038658976555,
-0.022977758198976517,
0.0012148934183642268,
-0.04713689163327217,
-0.020701074972748756,
-0.016195064410567284,
-0.013686679303646088,
-0.027266813442111015,
0.0071841515600681305,
0.03762125223875046,
0.03380561247467995,
0.018452944234013557,
-0.0009208109695464373,
-0.004983878694474697,
-0.054368503391742706,
-0.014531108550727367,
-0.04712364822626114,
-0.02725878544151783,
-0.02894732542335987,
-0.004021871834993362,
0.06828577071428299,
0.02849656343460083,
-0.018883712589740753,
0.0019956317264586687,
-0.0012166775995865464,
0.020663267001509666,
0.007529478520154953,
-0.029466453939676285,
-0.027007143944501877,
-0.01677217334508896,
-0.03975352644920349,
-0.0010930018033832312,
-0.007190122734755278,
0.00588263850659132,
0.06807585805654526,
-0.0074659776873886585,
-0.006437886506319046,
0.05675673484802246,
-0.03189793974161148,
-0.007439576089382172,
0.0024746160488575697,
-0.03135812282562256,
0.02197389118373394,
0.06031788885593414,
-0.0061480398289859295,
0.0009041557786986232,
-0.03528527915477753,
-0.00646555470302701,
-0.008649440482258797,
0.021898413076996803,
0.02831696905195713,
-0.06196261942386627,
-0.006920947693288326,
-0.021904515102505684,
0.01617462746798992,
-0.05208554491400719,
0.006677976809442043,
-0.027348842471837997,
0.021297099068760872,
-0.0018952945247292519,
0.010319077409803867,
-0.032935865223407745,
-0.02381206303834915,
-0.042275529354810715,
-0.03635779395699501,
0.027021726593375206,
0.0013604210689663887,
-0.016593635082244873,
-0.01597648672759533,
0.007612305693328381,
0.021648388355970383,
0.037269722670316696,
-0.0008762889774516225,
-0.03450746089220047,
0.01712122932076454,
-0.038677383214235306,
-0.030973879620432854,
0.03879711031913757,
-0.027938786894083023,
0.020003462210297585,
0.040287647396326065,
-0.026540765538811684,
-0.01545463502407074,
0.023499852046370506,
-0.04465271160006523,
-0.021490979939699173,
0.010582420974969864,
0.007886994630098343,
0.024201475083827972,
-0.006970181129872799,
0.013971175998449326,
0.006747695617377758,
0.0063818832859396935,
-0.0006146964151412249,
0.023180976510047913,
-0.01957666128873825,
0.004746139049530029,
-0.0031624857801944017,
-0.02704722434282303,
0.02485796809196472,
0.03126206621527672,
0.0016752909868955612,
-0.0038526684511452913,
0.036930203437805176,
-0.016269993036985397,
-0.0052536483854055405,
-0.01866455003619194,
-0.012498002499341965,
-0.05896987393498421,
-0.023609818890690804,
0.014887700788676739,
0.023713193833827972,
0.013064848259091377,
-0.06491407752037048,
0.009936156682670116,
-0.0004491790314204991,
-0.06991267204284668,
0.0555119626224041,
-0.0061260852962732315,
-0.023622723296284676,
-0.04149666801095009,
-0.025685712695121765,
-0.026333916932344437,
0.03853953629732132,
0.018641697242856026,
0.031604036688804626,
-0.024901697412133217,
0.004308056086301804,
-0.007408089470118284,
-0.0297344159334898,
-0.038338977843523026,
-0.0030570810195058584,
-0.01440032571554184,
-0.03192134574055672,
0.057500291615724564,
-0.002114933216944337,
-0.04460310563445091,
0.02129078283905983,
0.01471521146595478,
-0.032814156264066696,
0.0010582472896203399,
0.023088930174708366,
0.04099327698349953,
0.026641473174095154,
0.015432842075824738,
-0.014798250049352646,
-0.01018666010349989,
-0.022436905652284622,
0.01946386694908142,
0.002740466734394431,
-0.059353459626436234,
0.02338266558945179,
-0.00950880441814661,
-0.0211804136633873,
-0.050788890570402145,
0.031193111091852188,
-0.011262779124081135,
-0.0008089879411272705,
-0.020282117649912834,
-0.026573432609438896,
0.023773839697241783,
0.016745366156101227,
-0.028928760439157486,
-0.06388441473245621,
0.020748795941472054,
0.019412143155932426,
0.0012887519551441073,
0.007529256399720907,
0.039369847625494,
0.02025337517261505,
-0.0485495924949646,
0.05256136506795883,
0.026826592162251472,
0.003980637528002262,
-0.04025888442993164,
-0.020139705389738083,
0.021799348294734955,
0.027512408792972565,
0.026945888996124268,
-0.059402670711278915,
0.018550867214798927,
0.022943619638681412,
0.0362592488527298,
-0.006157154217362404,
-0.03598317876458168,
-0.05136532336473465,
0.025018591433763504,
-0.041080135852098465,
0.008776631206274033,
0.02792651206254959,
0.008660395629703999,
-0.01513050775974989,
0.03085947595536709,
0.04208232834935188,
0.05676767975091934,
0.011398729868233204,
-0.017984937876462936,
0.0024632757995277643,
0.012063786387443542,
-0.024794576689600945,
0.02020381949841976,
-0.0016031546983867884,
0.03060624934732914,
-0.03784187138080597,
-0.04007597267627716,
-0.02384701743721962,
0.0012150986585766077,
0.018176216632127762,
0.01921297423541546,
0.025156304240226746,
-0.030288228765130043,
-0.023485591635107994,
-0.048696890473365784,
-0.05197853967547417,
0.0550488606095314,
0.004191165789961815,
-0.006588038057088852,
0.056414030492305756,
-0.028986604884266853,
0.01866069994866848,
0.012831510975956917,
-0.008596020750701427,
0.009315302595496178,
0.011326896026730537,
-0.02689852938055992,
-0.011851361021399498,
-0.005614880006760359,
0.0182951707392931,
0.029443826526403427,
-0.03482384234666824,
0.02323540858924389,
0.03930343687534332,
-0.007276071235537529,
-0.04233526438474655,
0.054351337254047394,
0.004319349303841591,
0.017786800861358643,
0.020097477361559868,
0.008231913670897484,
0.025476351380348206,
-0.04575395584106445,
0.03222683444619179,
0.04351204261183739,
0.033163703978061676,
0.01421105396002531,
-0.003498760284855962,
0.01375306025147438,
-0.027203107252717018,
0.047553010284900665,
0.009285831823945045,
-0.003946854267269373,
-0.024287942796945572,
-0.005033864174038172,
0.019997771829366684,
-0.03848789632320404,
0.02783120796084404,
0.019443735480308533,
-0.049373406916856766,
0.06603727489709854,
-0.017364278435707092,
0.004453727975487709,
-0.026308387517929077,
-0.01769138313829899,
-0.05813877657055855,
-0.00012291620078030974,
0.02776523120701313,
0.08371040970087051,
-0.038036953657865524,
-0.02148214913904667,
-0.003568759886547923,
-0.028302151709794998,
0.011037170886993408,
-0.03815905749797821,
0.018950989469885826,
-0.001707274466753006,
-0.008452791720628738,
-0.01792324334383011,
-0.01430447306483984,
0.010487513616681099,
0.00874030776321888,
0.007744940929114819,
0.03584698960185051,
-0.006161928176879883,
-0.04557013884186745,
-0.006406769156455994,
-0.03647153079509735,
0.013348208740353584,
-0.04332336410880089,
-0.006696508731693029,
-0.03224692493677139,
0.018830886110663414,
-0.03276054188609123,
0.0041324966587126255
] |
<p>The current zeitgeist here is on interpretations of quantum mechanics, so let me add my own two cents here. As you may know, consistent histories is an alternative interpretation proposed in a series of papers 1990-1994 by Gell-Mann and Hartle. In a shocking article, <a href="http://arxiv.org/abs/gr-qc/9412067" rel="nofollow">Dowker and Kent</a> proved there are many distinct consistent histories for most quantum systems. Even if we constrain ourselves to quasiclassical histories, i.e. those histories which are close to classical, being quasiclassical now does not guarantee being quasiclassical in the future, or in the past. This is disturbing. Do histories which are quasiclassical for all times exist? If they do, are they unique? Is the nightmare scenario of two everywhere quasiclassical consistent histories which are mutually incompatible possible? </p>
| 7,685 |
[
-0.028673702850937843,
-0.026493825018405914,
0.016489768400788307,
-0.02307160757482052,
0.051316291093826294,
0.007966035045683384,
-0.022429591044783592,
-0.008755002170801163,
0.00609142379835248,
-0.010643187910318375,
0.029302896931767464,
0.05014688894152641,
0.016268732026219368,
0.0022459281608462334,
0.014607650227844715,
0.013782134279608727,
0.03011513501405716,
-0.03682827204465866,
-0.011603277176618576,
0.0030308517161756754,
-0.009985901415348053,
0.04135807231068611,
-0.012363502755761147,
0.0053969696164131165,
-0.051976658403873444,
0.005265723913908005,
0.009611261077225208,
0.008085069246590137,
0.01400904729962349,
0.04425068199634552,
-0.024319931864738464,
-0.0226882454007864,
-0.004154971335083246,
-0.013836057856678963,
0.018344763666391373,
-0.021201372146606445,
-0.012086989358067513,
-0.04328892007470131,
-0.003193553537130356,
0.058813948184251785,
-0.056971874088048935,
-0.02566445805132389,
-0.009403800591826439,
0.05643600597977638,
-0.037521589547395706,
0.017068317160010338,
-0.020755380392074585,
-0.016781141981482506,
0.06450271606445312,
-0.048897452652454376,
0.06198763847351074,
-0.000633775838650763,
0.0019236599327996373,
0.006883055437356234,
-0.059191569685935974,
0.009610820561647415,
0.07867757230997086,
0.05580658093094826,
-0.02287275157868862,
-0.05428614467382431,
-0.014296133071184158,
-0.00912120658904314,
0.023271411657333374,
0.0027211785782128572,
-0.01942567341029644,
0.04015960916876793,
0.017077770084142685,
-0.04361104592680931,
0.008799481205642223,
-0.051383860409259796,
-0.010719060897827148,
0.01949308253824711,
0.06081484630703926,
0.0034326347522437572,
0.017361490055918694,
-0.022766921669244766,
0.035941168665885925,
-0.013134508393704891,
0.026139196008443832,
0.030128374695777893,
0.014967062510550022,
0.0014265126083046198,
0.031215131282806396,
0.0010046352399513125,
0.025084424763917923,
-0.025962211191654205,
0.07268038392066956,
-0.013361632823944092,
-0.009145193733274937,
0.02775568515062332,
0.021149076521396637,
0.016738902777433395,
0.021587584167718887,
-0.005121431779116392,
-0.03667783364653587,
0.02309252694249153,
0.00904284231364727,
0.020734203979372978,
-0.02191668190062046,
-0.007740652654320002,
0.020370492711663246,
-0.03764839470386505,
0.010667618364095688,
0.02898458018898964,
0.0012171952985227108,
-0.0031217054929584265,
-0.023863114416599274,
0.024512168020009995,
-0.008415638469159603,
-0.007385373115539551,
-0.05680206045508385,
0.011068101041018963,
0.018665269017219543,
0.005340185482054949,
0.0007862380589358509,
0.006378422025591135,
-0.011065882630646229,
0.012197502888739109,
0.0392046719789505,
0.07592877745628357,
0.007802682463079691,
-0.056222014129161835,
0.03137342631816864,
-0.0226785559207201,
-0.06355658173561096,
-0.0060133617371320724,
0.061075594276189804,
-0.004362382926046848,
-0.013885176740586758,
0.006988454610109329,
-0.013069507665932178,
0.005639299750328064,
0.0015135606518015265,
0.002258660737425089,
0.0380261167883873,
-0.05531008914113045,
-0.12458648532629013,
-0.07195067405700684,
0.02274695597589016,
-0.03871912509202957,
-0.0412883386015892,
-0.09040173143148422,
0.0009585996740497649,
0.005861685611307621,
0.09147879481315613,
0.00307252025231719,
-0.0011087072780355811,
0.0013521561631932855,
0.027536319568753242,
-0.010844211094081402,
-0.015391298569738865,
-0.002051197225227952,
0.038521215319633484,
-0.04666176438331604,
-0.015281185507774353,
-0.05475834757089615,
0.030748799443244934,
0.02356676757335663,
0.016834937036037445,
-0.021496878936886787,
0.06466776132583618,
-0.011503031477332115,
-0.013242016546428204,
0.028548892587423325,
-0.00006629430572502315,
0.01474014762789011,
0.10479168593883514,
0.018358301371335983,
0.0016659583197906613,
0.06510010361671448,
0.024031948298215866,
0.037242501974105835,
0.021078435704112053,
0.02898336574435234,
-0.021898990496993065,
-0.0688323974609375,
0.0008878129301592708,
-0.02653510682284832,
-0.005404174327850342,
-0.03707956150174141,
-0.01991966739296913,
0.002818624721840024,
0.004432325717061758,
-0.01201386284083128,
-0.0035907498095184565,
0.026480237022042274,
0.00870649702847004,
0.014760018326342106,
-0.02639339305460453,
-0.04406411573290825,
-0.029672371223568916,
-0.07750552147626877,
0.018465593457221985,
0.0021665729582309723,
-0.015642601996660233,
0.07574772089719772,
0.012728624045848846,
0.020511362701654434,
-0.01795060560107231,
-0.06335628777742386,
-0.014891854487359524,
0.0249264445155859,
-0.02193896472454071,
-0.021415747702121735,
0.026598483324050903,
0.026140039786696434,
0.03872103616595268,
-0.01685279607772827,
0.030026443302631378,
-0.014967598952353,
-0.0727013573050499,
0.01754864677786827,
-0.047031063586473465,
0.06889552623033524,
0.028044376522302628,
0.02676738239824772,
0.01242775097489357,
-0.013018776662647724,
-0.020054077729582787,
0.0022344496101140976,
-0.04739147797226906,
0.03395581990480423,
-0.004433945287019014,
0.003867150517180562,
-0.03454842045903206,
0.07130609452724457,
0.013926315121352673,
-0.005975104868412018,
0.007386494427919388,
-0.034715522080659866,
-0.006625211797654629,
0.02296767383813858,
0.03331054747104645,
0.047507502138614655,
-0.014043590053915977,
0.029292933642864227,
0.02821042761206627,
0.06267240643501282,
0.005724424961954355,
0.02826555259525776,
-0.02272242121398449,
-0.00561147416010499,
0.009820260107517242,
-0.013002952560782433,
0.0010098504135385156,
0.013849395327270031,
0.014126386493444443,
-0.005183747038245201,
-0.030185062438249588,
-0.006479992996901274,
-0.030529998242855072,
0.03281707689166069,
-0.012814857997000217,
0.027353718876838684,
0.021968811750411987,
-0.0675174742937088,
-0.0072651151567697525,
-0.005609987303614616,
0.05311572924256325,
0.0248678307980299,
0.015233559533953667,
-0.0009193235891871154,
-0.008499400690197945,
-0.008483435027301311,
-0.022871771827340126,
-0.014744837768375874,
-0.03135776147246361,
-0.020114708691835403,
0.024929875507950783,
-0.026413820683956146,
-0.00018200589693151414,
-0.043064288794994354,
-0.0020384672097861767,
0.0038676043041050434,
-0.00667907577008009,
0.008151394315063953,
0.028778407722711563,
0.02487492561340332,
-0.04311584681272507,
-0.03559502586722374,
0.02661372721195221,
-0.013753586448729038,
-0.0026106988079845905,
0.009711253456771374,
-0.025693446397781372,
0.0290638729929924,
-0.048129767179489136,
0.001186252455227077,
0.03684261813759804,
0.002071529161185026,
0.020387860015034676,
0.013703719712793827,
0.000963229569606483,
-0.024461252614855766,
-0.036214571446180344,
-0.027300231158733368,
-0.004518813453614712,
-0.01677115075290203,
-0.02211790718138218,
0.025577247142791748,
-0.03519684448838234,
-0.029815230518579483,
-0.02203684113919735,
-0.033228956162929535,
-0.038776472210884094,
-0.016791440546512604,
-0.007509582210332155,
-0.004113421309739351,
-0.03181343153119087,
0.0007172117475420237,
0.04202497750520706,
-0.05160164460539818,
-0.02055218257009983,
-0.03354161977767944,
-0.05258098617196083,
0.04379473999142647,
0.000767934718169272,
0.05074645206332207,
-0.006922694854438305,
-0.004296674858778715,
0.0359540730714798,
0.016440337523818016,
-0.022109096869826317,
0.010185112245380878,
-0.0073343077674508095,
-0.0013109761057421565,
0.0037914325948804617,
-0.017267102375626564,
0.022929757833480835,
-0.024447673931717873,
0.048511896282434464,
-0.011802221648395061,
0.008054983802139759,
0.013171220198273659,
0.0277584008872509,
-0.0056654117070138454,
0.017101313918828964,
0.031238865107297897,
0.047392357140779495,
0.020122148096561432,
0.012194473296403885,
-0.030375715345144272,
-0.02258692868053913,
-0.04184911772608757,
0.015308666042983532,
0.017872018739581108,
-0.04455141723155975,
0.08354176580905914,
0.014405449852347374,
0.03418958559632301,
-0.03395994007587433,
0.018092460930347443,
-0.025337468832731247,
0.000027540569135453552,
-0.011910800822079182,
0.040141232311725616,
0.00740344962105155,
-0.00882591214030981,
0.016370654106140137,
0.05340862274169922,
0.026727808639407158,
-0.01845070905983448,
0.012465439736843109,
0.02925165556371212,
-0.008892843499779701,
0.06851968914270401,
-0.03571807220578194,
-0.010816521942615509,
0.02886311709880829,
-0.014076544903218746,
0.030314721167087555,
-0.00800297874957323,
-0.043075185269117355,
-0.018101705238223076,
-0.09112842381000519,
0.002687313361093402,
0.002436399692669511,
0.041161611676216125,
0.0021886660251766443,
0.019845377653837204,
0.03294625133275986,
0.020547837018966675,
-0.002634716685861349,
0.00047928871936164796,
-0.041928160935640335,
0.04050256311893463,
-0.03709208220243454,
0.019961483776569366,
-0.019095854833722115,
0.005809491965919733,
0.004950902424752712,
-0.003306078026071191,
-0.05862918496131897,
-0.011355238035321236,
-0.008378982543945312,
-0.07351133227348328,
-0.0036905822344124317,
-0.059652332216501236,
-0.0557093545794487,
-0.013918690383434296,
0.03109894134104252,
0.035835184156894684,
0.01720326580107212,
0.039614930748939514,
0.025008071213960648,
-0.058721281588077545,
0.027081627398729324,
-0.0006320755346678197,
0.03343278169631958,
0.02638186514377594,
0.0260587427765131,
0.024375367909669876,
0.026708941906690598,
0.021559182554483414,
0.009758852422237396,
0.041396088898181915,
0.03995998203754425,
0.01921904645860195,
-0.02174638770520687,
0.002733157016336918,
-0.040127772837877274,
-0.014633364975452423,
0.007341283373534679,
0.04211565479636192,
0.033558439463377,
0.01752907782793045,
0.0294939037412405,
0.02946600131690502,
-0.013856416568160057,
0.029965708032250404,
0.04011361673474312,
-0.00073554104892537,
-0.007984931580722332,
-0.019955139607191086,
-0.034969497472047806,
-0.002568124094977975,
0.013868944719433784,
-0.021151211112737656,
-0.018770329654216766,
0.023517070338129997,
0.02602713741362095,
-0.0030678664334118366,
0.013146190904080868,
-0.0013255552621558309,
-0.02677350677549839,
-0.027323758229613304,
0.02889244630932808,
0.02148596942424774,
0.03968660905957222,
0.00539868138730526,
0.008523454889655113,
0.02303195372223854,
0.02016926370561123,
-0.0076251886785030365,
-0.043405164033174515,
0.005716280080378056,
0.03314967453479767,
0.0027710788417607546,
0.0076047396287322044,
0.007031104993075132,
-0.03995732590556145,
-0.034256741404533386,
0.04982239753007889,
0.0035640473943203688,
0.040560282766819,
-0.007705232594162226,
0.0090891532599926,
-0.04512391611933708,
-0.02300097607076168,
0.019848696887493134,
0.0307312048971653,
0.021095603704452515,
0.007669693790376186,
0.015282436273992062,
-0.010770220309495926,
-0.021826185286045074,
-0.012831306084990501,
-0.004306393209844828,
0.06199084594845772,
0.017109205946326256,
-0.017344117164611816,
0.0007221807027235627,
0.023803867399692535,
-0.011185544542968273,
-0.08374905586242676,
-0.002032093470916152,
-0.0014441681560128927,
-0.026474783197045326,
0.045995082706213,
-0.045410919934511185,
-0.035392895340919495,
0.0035186512395739555,
-0.04474475607275963,
-0.01629793643951416,
0.04677490517497063,
-0.02255251072347164,
0.04098029434680939,
-0.00603901781141758,
-0.019886696711182594,
0.015471404418349266,
0.004858833737671375,
-0.03434671461582184,
0.03127168491482735,
-0.010799438692629337,
0.04126119241118431,
-0.03553898632526398,
0.05637422204017639,
-0.026196680963039398,
0.013732376508414745,
-0.024953145533800125,
0.058569762855768204,
-0.0400666669011116,
-0.010527517646551132,
-0.004011779557913542,
-0.02851884998381138,
0.017662644386291504,
0.02156524360179901,
-0.009969961829483509,
-0.005919599439948797,
-0.007828247733414173,
0.002401048084720969,
-0.027228867635130882,
-0.013976151123642921,
-0.010334503836929798,
0.01023170817643404,
0.014364642091095448,
0.06510575860738754,
-0.005430563818663359,
0.04810621961951256,
-0.025120925158262253,
-0.011795274913311005,
0.00816075038164854,
-0.04853498190641403,
0.04085562750697136,
-0.008153121918439865,
0.02043069340288639,
0.03389618173241615,
-0.05312572419643402,
-0.02795809507369995,
0.015740400180220604,
-0.03231288865208626,
-0.004536367021501064,
-0.03433433920145035,
0.013229620642960072,
0.05120783671736717,
0.025700801983475685,
-0.08201903104782104,
-0.026949532330036163,
0.027802523225545883,
0.00620688172057271,
-0.043398234993219376,
-0.01048967707902193,
0.032640572637319565,
-0.05066492781043053,
-0.02662837505340576,
-0.024869218468666077,
0.0674075037240982,
0.0030599129386246204,
-0.031702920794487,
0.014381841756403446,
0.07491285353899002,
0.06016666814684868,
0.0023606012109667063,
0.019586410373449326,
0.021407971158623695,
-0.01092046033591032,
0.0021757453214377165,
-0.012471206486225128,
0.016616880893707275,
-0.004997551441192627,
-0.00277541927061975,
0.00044675215031020343,
0.0004885956877842546,
0.024732695892453194,
-0.022274881601333618,
-0.0023078734520822763,
0.031928639858961105,
-0.013906791806221008,
0.014397159218788147,
-0.01575726829469204,
0.028623556718230247,
-0.019475508481264114,
0.020760580897331238,
-0.013853655196726322,
-0.012347867712378502,
0.00031464739004150033,
-0.06653635203838348,
0.01812773197889328,
-0.018127597868442535,
-0.042652249336242676,
0.02370482310652733,
0.022151492536067963,
-0.007632602471858263,
-0.027257777750492096,
0.028670087456703186,
-0.03904302790760994,
-0.014754264615476131,
-0.016802726313471794,
0.028868919238448143,
0.00502570066601038,
-0.02533715032041073,
-0.018229784443974495,
-0.05029759183526039,
-0.018415935337543488,
0.03366678208112717,
0.03858004882931709,
-0.017852842807769775,
0.05001058429479599,
0.01988617517054081,
-0.013610096648335457,
-0.0336858294904232,
-0.03849385306239128,
-0.00937043596059084,
0.019909832626581192,
-0.015484509989619255,
0.02500537969172001,
-0.049957890063524246,
0.01718389429152012,
0.02784830704331398,
0.03565039113163948,
0.017047179862856865,
-0.0006306219729594886,
0.002828264608979225,
0.015771575272083282,
0.035257771611213684,
-0.008484799414873123,
-0.03312499821186066,
0.05533077195286751,
-0.0669584646821022,
0.0000924673440749757,
0.014719556085765362,
-0.021097760647535324,
-0.009442610666155815,
0.00797833688557148,
-0.005281917285174131,
-0.007855398580431938,
-0.04254201427102089,
-0.031986553221940994,
0.028030192479491234,
-0.021934963762760162,
0.04567863047122955,
0.026916582137346268,
-0.007048791740089655,
0.00595915736630559,
0.02859850414097309,
0.04293002933263779,
0.01938759908080101,
-0.08406303822994232,
-0.036072585731744766,
-0.020597686991095543,
-0.009623849764466286,
0.01631937175989151,
-0.026466678828001022,
0.007308349944651127,
0.0010208392050117254,
-0.024374527856707573,
0.007552238181233406,
0.03832071274518967,
0.02892223373055458,
-0.031510546803474426,
0.06268002092838287,
-0.008793744258582592,
0.028595956042408943,
-0.004854921251535416,
0.00013243244029581547,
0.13760964572429657,
0.06570836901664734,
0.03534289821982384,
-0.06538084149360657,
-0.01707330159842968,
0.0039043596480041742,
0.01728002540767193,
0.004630178678780794,
0.04561213403940201,
0.008708112873136997,
0.019284624606370926,
-0.002547029871493578,
0.03170091286301613,
0.02204292267560959,
-0.0019340832950547338,
0.04725656658411026,
-0.023471100255846977,
-0.04214354231953621,
-0.01851056143641472,
0.01376301608979702,
0.009549646638333797,
-0.003537884447723627,
-0.018516993150115013,
-0.00892143789678812,
-0.0036191942635923624,
0.02008514106273651,
0.012814550660550594,
-0.022560399025678635,
0.01022469811141491,
0.014186554588377476,
-0.017470423132181168,
0.0021058344282209873,
0.047061361372470856,
-0.02198805660009384,
-0.031287506222724915,
0.016525520011782646,
0.001388095086440444,
0.029217788949608803,
0.03986146301031113,
0.04295859485864639,
0.009342219680547714,
-0.03914710506796837,
0.026743963360786438,
0.025557423010468483,
-0.01662164181470871,
0.0036216494627296925,
-0.032519467175006866,
0.03808574378490448,
-0.03881087899208069,
-0.0008670742972753942,
-0.026613669469952583,
-0.057594746351242065,
0.016286220401525497,
-0.04546135291457176,
-0.0018104140181094408,
-0.005112662445753813,
0.034828342497348785,
-0.0016710656927898526,
0.0026680962182581425,
-0.007996747270226479,
-0.00641742255538702,
0.019869672134518623,
0.04005326330661774,
-0.02462494745850563,
-0.022271255031228065,
0.0022641720715910196,
-0.0074487593956291676,
0.032964855432510376,
-0.00444098562002182,
0.003384444396942854,
-0.03529426082968712,
-0.018775079399347305,
-0.10122504085302353,
-0.03436092287302017,
0.029430808499455452,
0.005186809692531824,
0.10131121426820755,
0.007346633356064558,
-0.004230841062963009,
-0.02354438044130802,
-0.06915400177240372,
0.016250580549240112,
-0.016751300543546677,
0.0027572752442210913,
0.022710192948579788,
0.017873598262667656,
0.05445002019405365,
0.033587366342544556,
-0.020308133214712143,
0.03876195102930069,
0.023328624665737152,
0.006958361249417067,
0.03422260284423828,
-0.012574007734656334,
-0.013701489195227623,
-0.010704807005822659,
-0.04618814215064049,
0.00602251710370183,
-0.046282581984996796,
0.04070766270160675,
-0.013537186197936535,
-0.011343270540237427,
0.03417852520942688,
0.028898175805807114,
0.025165939703583717,
-0.00771417235955596,
0.028259923681616783,
-0.02495633251965046,
-0.021459465846419334,
0.014782518148422241,
0.045591652393341064,
-0.04023370146751404,
-0.04865846410393715,
-0.05623580142855644,
0.007532030809670687,
-0.004275599494576454,
-0.007822629064321518,
-0.04918994382023811,
0.01928926818072796,
-0.003334613749757409,
0.01767324097454548,
-0.03336431458592415,
-0.044837288558483124,
-0.052186381071805954,
0.02601490542292595,
-0.01489830482751131,
-0.005905319470912218,
0.02226356416940689,
0.040083494037389755,
-0.010960723273456097,
-0.02799084596335888,
0.0314149484038353,
0.07327379286289215,
-0.048355355858802795,
-0.031106699258089066,
-0.0031688055023550987,
0.022610509768128395,
0.02532944269478321,
-0.03093809075653553,
-0.05051874369382858,
-0.012543934397399426,
-0.0023704201448708773,
-0.0736488476395607,
0.03641063719987869,
0.012227565981447697,
0.01997780054807663,
0.021367572247982025,
0.005232094321399927,
-0.013899218291044235,
0.048887286335229874,
-0.050163548439741135,
0.016408609226346016,
0.022557055577635765,
-0.005939899943768978,
-0.000742004718631506,
-0.028155721724033356,
-0.010593492537736893,
0.021420860663056374,
-0.037529896944761276,
0.024882355704903603,
0.0279415063560009,
0.013942582532763481,
0.011041154153645039,
-0.0028520512860268354,
-0.021517639979720116,
0.06187805160880089,
0.0365750789642334,
0.014045595191419125,
0.04392358660697937,
0.045950133353471756,
-0.059936653822660446,
0.034245628863573074,
0.049095481634140015,
-0.007346135564148426,
-0.10314079374074936,
-0.008549747988581657,
-0.00917549803853035,
-0.026510555297136307,
0.056060541421175,
-0.003041459945961833,
-0.00869215838611126,
0.022773992270231247,
-0.0711616799235344,
0.014716235920786858,
-0.01650143601000309,
-0.017352499067783356,
0.025511499494314194,
0.008376757614314556,
-0.03780091553926468,
0.05923539027571678,
0.02857145294547081,
0.050291210412979126,
0.01150978822261095,
0.0010995263000950217,
-0.0012023852905258536,
-0.006898408755660057,
-0.0013942444929853082,
-0.0142165282741189,
-0.020032357424497604,
0.0006216943729668856,
0.06288980692625046,
-0.04351005703210831,
-0.0612025111913681,
0.044316329061985016,
-0.02283470518887043,
0.0016686103772372007,
-0.00032382391509599984,
-0.022756362333893776,
0.022015636786818504,
-0.017264552414417267,
0.05468279495835304,
-0.05364217981696129,
-0.02544328384101391,
0.003464908106252551,
-0.012196243740618229,
0.04295498877763748,
-0.0018505752086639404,
-0.010464651510119438,
-0.01775462180376053,
-0.07281094044446945,
-0.03399466723203659,
0.025038762018084526,
0.0029998209793120623,
0.031131766736507416,
0.020773697644472122,
0.013538972474634647,
0.00028531975112855434,
0.012152603827416897,
0.018365709111094475,
-0.04420928284525871,
0.008369158953428268,
0.014595738612115383,
0.04120539501309395,
0.04365192726254463,
0.009910456836223602,
-0.03746144101023674,
-0.015827728435397148,
0.022106235846877098,
0.007797535043209791,
0.0011576095130294561,
-0.0560465082526207,
0.005042181815952063,
-0.025762667879462242,
-0.008412542752921581,
0.023984834551811218,
-0.05402278155088425,
-0.022717513144016266,
0.03790726885199547,
0.0012151735136285424,
0.020097138360142708,
-0.01846068911254406,
-0.04486541077494621,
-0.022126182913780212,
-0.03525635227560997,
0.014821179211139679,
-0.0015102566685527563,
0.027140561491250992,
-0.027265600860118866,
-0.03167039901018143,
0.03111940808594227,
0.01930728368461132,
0.055112775415182114,
-0.02480730600655079,
-0.01950201578438282,
0.031830646097660065,
-0.008874808438122272,
0.023094333708286285,
-0.03489547595381737,
0.030686331912875175,
-0.025433054193854332,
0.021920476108789444,
-0.004985397681593895,
0.006446856074035168,
-0.04099883884191513,
0.01047761645168066,
0.03657311201095581,
-0.032309390604496,
0.0001908294652821496,
0.049294363707304,
-0.05288636311888695,
0.06351393461227417,
-0.005242077633738518,
0.0016027354868128896,
0.04717026650905609,
-0.005593154113739729,
0.0387364886701107,
0.011066270992159843,
-0.024588583037257195,
-0.05876541882753372,
0.04823002964258194,
-0.019575636833906174,
-0.061135049909353256,
-0.028478190302848816,
0.005105051212012768,
0.026126127690076828,
-0.023837678134441376,
-0.023303179070353508,
0.02690313570201397,
-0.02720160037279129,
0.02014078199863434,
0.03660781681537628,
-0.011238905601203442,
0.01956186816096306,
0.00045293712173588574,
0.013252878561615944,
-0.010022665373980999,
0.03198052942752838,
-0.015811577439308167,
-0.0009101946488954127,
0.039390794932842255,
0.01636469177901745,
0.02097448520362377,
0.045593131333589554,
-0.029990648850798607,
0.010424302890896797,
0.006935732904821634,
0.05287564545869827,
-0.05873294919729233,
0.030713366344571114,
0.01525365561246872,
0.005121084861457348,
-0.017398441210389137,
0.03674965724349022,
-0.007792935706675053,
0.020057691261172295,
-0.030029157176613808,
-0.015251670964062214,
-0.0205319132655859,
-0.043733857572078705,
-0.030914930626749992,
-0.028270628303289413,
0.007445984520018101,
0.02349846437573433,
-0.016892293468117714,
-0.010906040668487549,
-0.013025468215346336,
0.029666345566511154,
0.018686018884181976,
-0.04558902978897095,
-0.022285766899585724,
-0.027414869517087936,
-0.01158145908266306,
-0.015364877879619598,
-0.033717211335897446,
-0.03289959579706192,
-0.03021257184445858,
0.003661074908450246,
0.04580317437648773,
0.03606870397925377,
-0.033798277378082275,
-0.005447438918054104,
-0.04580676555633545,
0.04732804745435715,
-0.0369354784488678,
0.024516470730304718,
-0.03684171661734581,
0.040091171860694885,
0.004395302385091782,
0.025135399773716927
] |
<p>There're some easy concepts which I don't get exactly in my mind. I've been studying these things for two years of my engineering but they still bother me. Battery is one of them. Can someone explain?</p>
<ul>
<li>Whether a battery store energy or simply it makes energy?</li>
</ul>
<p>I have searched it on Google and Yahoo but didn't find any helpful thing there (for me). So I will be glad if I got my problem solved here.</p>
<p>P.S. I hope that the question would not again be an off-topic, as it always does and moreover people don't suggest then where to go. It's a real sad thing.</p>
| 7,686 |
[
-0.048196714371442795,
-0.019772548228502274,
-0.000110364388092421,
0.02118878997862339,
0.00806673988699913,
-0.005602833814918995,
-0.006702587474137545,
-0.02221999503672123,
0.010023493319749832,
-0.03180072084069252,
0.010217184200882912,
0.05195283517241478,
0.02510225772857666,
0.037392642349004745,
0.003701139008626342,
-0.00031115810270421207,
0.0021228790283203125,
-0.06194723770022392,
-0.03067311830818653,
0.0184004046022892,
0.0045108008198440075,
-0.025522921234369278,
0.003653280669823289,
0.015609200112521648,
-0.004706925246864557,
0.014692464843392372,
0.04327448457479477,
0.010210937820374966,
-0.009152454324066639,
0.04433468356728554,
0.00273609790019691,
-0.06627469509840012,
0.013912798836827278,
0.01620337925851345,
0.019156476482748985,
-0.01770085096359253,
-0.03732910007238388,
0.00546901673078537,
-0.011931036598980427,
0.012445182539522648,
0.0019431986147537827,
-0.017194509506225586,
0.0003017315175384283,
0.0400153212249279,
-0.023371942341327667,
0.043460261076688766,
0.010315920226275921,
-0.02384093403816223,
0.038943879306316376,
-0.07641138136386871,
0.030021632090210915,
-0.0038737435825169086,
0.014403920620679855,
0.0377546101808548,
0.02283128909766674,
0.00787218939512968,
0.03789287060499191,
0.05601145699620247,
-0.011554988101124763,
-0.02244289219379425,
-0.021843982860445976,
0.012937585823237896,
-0.020155273377895355,
-0.023271912708878517,
-0.02877860702574253,
0.031473223119974136,
0.010379360988736153,
-0.028253767639398575,
0.060571957379579544,
0.0019751593936234713,
-0.0035450016148388386,
0.03737518936395645,
0.018542977049946785,
0.003472436685115099,
0.04347887635231018,
-0.034149762243032455,
0.058577172458171844,
0.014674056321382523,
0.030601685866713524,
0.06845032423734665,
-0.03311442211270332,
0.00683876546099782,
0.029411135241389275,
0.05121147632598877,
-0.011350329965353012,
-0.05081825330853462,
0.0696711465716362,
-0.017810039222240448,
0.03290964290499687,
-0.009746097959578037,
0.05539727210998535,
0.01747066341340542,
0.011198478750884533,
-0.012424927204847336,
-0.0041716378182172775,
0.04551011323928833,
-0.020399540662765503,
0.05193568393588066,
0.012432117015123367,
-0.03333944082260132,
0.018191182985901833,
0.00700558302924037,
0.06264829635620117,
0.04981590062379837,
-0.01625310629606247,
-0.05064006522297859,
-0.020787160843610764,
0.01719781942665577,
0.03219161182641983,
0.021556930616497993,
-0.01851683482527733,
0.018869636580348015,
0.03400416672229767,
-0.006676981225609779,
0.006848171353340149,
-0.031671904027462006,
-0.00508881127461791,
0.0031992997974157333,
0.057023242115974426,
0.06641016155481339,
0.031856879591941833,
-0.04362034797668457,
0.03557426482439041,
-0.0297896359115839,
-0.07743753492832184,
-0.00467825960367918,
0.0009387835743837059,
-0.0072548240423202515,
-0.008411378599703312,
0.02501571923494339,
0.008476964198052883,
0.024106618016958237,
0.008999605663120747,
-0.003570311702787876,
0.06850619614124298,
-0.0049066850915551186,
-0.0829269215464592,
-0.029200777411460876,
0.03668618202209473,
0.02619599550962448,
0.007409913465380669,
-0.0736439898610115,
0.019648944959044456,
-0.007625842932611704,
0.0414872020483017,
-0.009498060680925846,
-0.03667452186346054,
0.024784144014120102,
-0.0007644249708391726,
-0.015274807810783386,
-0.02395659312605858,
-0.04300827533006668,
0.005263792350888252,
-0.01732189767062664,
0.05872124806046486,
-0.02740572579205036,
0.02698642574250698,
0.03636767715215683,
0.030246024951338768,
-0.03769860789179802,
0.061907343566417694,
-0.01895405910909176,
-0.032177653163671494,
-0.0028564194217324257,
0.025655526667833328,
-0.02500653825700283,
0.06700531393289566,
0.005812077317386866,
-0.005642257630825043,
0.042902275919914246,
0.019093254581093788,
0.010274204425513744,
-0.037072524428367615,
0.018095633015036583,
0.046432483941316605,
-0.04252513125538826,
-0.05706803500652313,
-0.06078295037150383,
0.03977319225668907,
0.013634689152240753,
-0.08222115784883499,
-0.04642584174871445,
0.00243684952147305,
0.014442029409110546,
-0.005430925637483597,
0.03858489170670509,
0.0010579697554931045,
-0.0006798511021770537,
-0.010573074221611023,
-0.03413451090455055,
-0.0014936175430193543,
-0.032213933765888214,
0.04888658598065376,
-0.02345573529601097,
-0.010909868404269218,
0.02771947719156742,
-0.02812821790575981,
-0.003799228696152568,
-0.058998338878154755,
-0.007819311693310738,
0.011992081068456173,
0.048452310264110565,
-0.0376451313495636,
-0.014011066406965256,
0.016584517434239388,
0.05607757717370987,
0.0008025167044252157,
-0.002538461470976472,
0.01390070654451847,
0.006611478514969349,
-0.02444160357117653,
-0.021396102383732796,
-0.039721276611089706,
0.008792169392108917,
0.009876716881990433,
-0.0429035946726799,
-0.01715010777115822,
0.0042587085627019405,
-0.0074986061081290245,
0.042838551104068756,
-0.00987422838807106,
0.07480211555957794,
0.05185357481241226,
-0.020528459921479225,
0.006572297308593988,
0.040659792721271515,
-0.0011252937838435173,
0.010222143493592739,
-0.03190327435731888,
-0.0036966765765100718,
-0.0391792431473732,
0.021956073120236397,
0.04212227836251259,
0.007299037184566259,
-0.049267418682575226,
0.03836623951792717,
0.0044580562971532345,
-0.002814187668263912,
0.030653517693281174,
0.000024018732801778242,
-0.04158829152584076,
-0.01687740720808506,
0.04099766165018082,
0.027650415897369385,
-0.019744643941521645,
0.03244514390826225,
-0.021474618464708328,
0.008900368586182594,
0.003228425048291683,
-0.011872849427163601,
-0.0015821921406313777,
0.07717864215373993,
-0.010351036675274372,
0.0494227409362793,
0.013413017615675926,
0.004049201961606741,
0.038234271109104156,
-0.034750644117593765,
0.03111356683075428,
-0.02750035561621189,
0.001785061089321971,
0.02953326888382435,
-0.012865129858255386,
-0.0049909246154129505,
-0.03521208465099335,
0.044221606105566025,
-0.02723604626953602,
0.002547726733610034,
0.036196790635585785,
-0.021715087816119194,
0.030306832864880562,
-0.0027034147642552853,
0.001648454461246729,
-0.017181186005473137,
0.012507281266152859,
0.039511408656835556,
-0.0279844980686903,
0.022214742377400398,
-0.03401060774922371,
0.0061684660613536835,
-0.03984273225069046,
-0.07544734328985214,
-0.013764627277851105,
-0.0352417416870594,
-0.007934881374239922,
-0.004343063570559025,
-0.028472285717725754,
-0.01704554818570614,
0.05361104756593704,
0.020047776401042938,
0.010508989915251732,
-0.0006864621536806226,
0.0066761597990989685,
-0.05930009111762047,
0.028678786009550095,
-0.03207950294017792,
0.033699750900268555,
-0.005844241473823786,
-0.012834083288908005,
0.050941046327352524,
-0.020161986351013184,
-0.026332233101129532,
0.016537636518478394,
-0.07224297523498535,
-0.02478993870317936,
0.004068294074386358,
-0.023992380127310753,
0.04331992566585541,
-0.012550472281873226,
0.019456656649708748,
0.03117528185248375,
-0.06653505563735962,
-0.008619931526482105,
-0.039427656680345535,
-0.03109763003885746,
0.008651267737150192,
0.004012002144008875,
0.024381445720791817,
-0.0018851495115086436,
0.003901414107531309,
0.0391681045293808,
0.018201623111963272,
-0.051290422677993774,
-0.0023420744109898806,
-0.06776981800794601,
0.015384688042104244,
-0.048126135021448135,
-0.01072610542178154,
0.05130760744214058,
-0.009109181351959705,
0.002984857652336359,
0.011965093202888966,
0.050172168761491776,
0.017292015254497528,
0.025776425376534462,
-0.028687693178653717,
-0.02989303134381771,
0.02917013317346573,
0.00864169280976057,
0.061898648738861084,
0.006567392032593489,
-0.049637775868177414,
-0.01051834411919117,
-0.045349061489105225,
0.0634486973285675,
0.021568896248936653,
-0.0332992821931839,
0.035490501672029495,
-0.003630663501098752,
-0.00655647087842226,
-0.06178591027855873,
0.032229647040367126,
-0.01757822372019291,
-0.017645956948399544,
0.023191114887595177,
0.008580411784350872,
0.06327220797538757,
-0.007396108005195856,
0.0035567940212786198,
-0.02180575765669346,
0.04551287367939949,
-0.06431388854980469,
-0.05678577721118927,
0.027076276019215584,
-0.0010255719535052776,
-0.03599027916789055,
0.02047397382557392,
-0.034249428659677505,
0.04808936268091202,
0.04303433746099472,
0.029757533222436905,
-0.006314567755907774,
-0.02149827964603901,
0.013412185944616795,
-0.081976979970932,
-0.04236395284533501,
0.02120191603899002,
0.06791031360626221,
-0.004660273902118206,
0.03457866609096527,
0.03248342126607895,
-0.021340932697057724,
0.030329963192343712,
-0.002261324319988489,
-0.08329429477453232,
0.03944205865263939,
-0.01906125433743,
0.011028174310922623,
-0.013478425331413746,
0.0220063216984272,
-0.012266460806131363,
-0.03783240169286728,
-0.02131957933306694,
-0.008984405547380447,
0.01691977120935917,
-0.0393802747130394,
0.011335756629705429,
-0.02488892339169979,
-0.03036547265946865,
-0.032665424048900604,
0.006433406379073858,
0.04081139713525772,
-0.024009207263588905,
0.04045826196670532,
0.02017933316528797,
-0.06943589448928833,
-0.021179871633648872,
0.007055933587253094,
-0.006718786433339119,
0.009996715001761913,
0.011216757819056511,
0.012174027971923351,
0.0181050356477499,
0.02942625992000103,
0.0063778916373848915,
0.025461187586188316,
0.011135957203805447,
-0.0020544256549328566,
-0.020979516208171844,
-0.02391958422958851,
-0.020566366612911224,
-0.0013027681270614266,
-0.016864286735653877,
0.028872942551970482,
-0.01913383975625038,
0.021969003602862358,
-0.009581253863871098,
0.007396860979497433,
-0.010522096417844296,
0.018530745059251785,
0.06679093837738037,
-0.021322017535567284,
-0.03643980249762535,
-0.05740359425544739,
-0.0016497429460287094,
-0.02407550811767578,
-0.0018234214512631297,
0.030863214284181595,
0.0015337199438363314,
-0.006989502348005772,
-0.02691628783941269,
0.006869928445667028,
-0.004340034443885088,
0.0034680329263210297,
0.030893145129084587,
0.003315844340249896,
0.012064757756888866,
-0.008354623802006245,
-0.020938392728567123,
0.04537701606750488,
0.00035238644341006875,
0.04505090042948723,
0.026699332520365715,
0.02282397635281086,
-0.08348887413740158,
0.010737262666225433,
0.039696309715509415,
0.033073171973228455,
-0.015840129926800728,
-0.018675895407795906,
-0.0431009866297245,
-0.00491138594225049,
0.05506317690014839,
-0.035168781876564026,
0.045081738382577896,
-0.05128191038966179,
-0.01566808857023716,
-0.016767384484410286,
0.00020943793060723692,
0.0006746635190211236,
-0.0008814622415229678,
-0.03379161283373833,
0.05419665947556496,
0.012082543224096298,
-0.016900790855288506,
-0.01276149321347475,
0.03735832870006561,
0.025896506384015083,
0.061244864016771317,
-0.013336840085685253,
0.007255160715430975,
0.002714930335059762,
0.03416701778769493,
-0.027755793184041977,
-0.08164564520120621,
0.0008139790152199566,
0.004806503653526306,
-0.020015379413962364,
0.022450566291809082,
-0.046854663640260696,
-0.08935593068599701,
0.012343620881438255,
0.02381002902984619,
0.005857700482010841,
-0.02836661972105503,
-0.06618191301822662,
0.00633659865707159,
0.018688926473259926,
0.0011067423038184643,
0.034887153655290604,
0.05455193668603897,
-0.04429622367024422,
-0.0018047969788312912,
0.00910305604338646,
0.0004656128294300288,
-0.033172763884067535,
-0.0012199704069644213,
-0.005619171541184187,
0.012836042791604996,
-0.03709564730525017,
0.030855121091008186,
0.00027437254902906716,
0.024914616718888283,
-0.04820922017097473,
-0.04209151491522789,
-0.028237778693437576,
0.016603874042630196,
-0.03239661082625389,
-0.025187581777572632,
-0.006491340231150389,
0.04062340408563614,
-0.009514626115560532,
-0.02029123157262802,
-0.011077226139605045,
-0.008108092471957207,
0.02820747345685959,
0.033520620316267014,
-0.015433549880981445,
0.011992570012807846,
-0.04205040633678436,
-0.032617174088954926,
0.022623397409915924,
-0.010749101638793945,
0.04871014133095741,
-0.01332577783614397,
0.006542861927300692,
0.036417827010154724,
-0.07221842557191849,
-0.07710066437721252,
0.007166494149714708,
0.013854662887752056,
0.009018697775900364,
-0.035438310354948044,
0.04837873950600624,
0.023384347558021545,
0.0017558182589709759,
-0.062154680490493774,
-0.07497909665107727,
0.04338809847831726,
0.016182297840714455,
0.0009794480865821242,
-0.04144488275051117,
0.01695147156715393,
-0.002293771132826805,
-0.04286433011293411,
0.006561472546309233,
-0.02039763331413269,
-0.02844436839222908,
0.01763797365128994,
0.01900109089910984,
0.01455471757799387,
0.08051803708076477,
0.02003725990653038,
0.015986386686563492,
0.016418687999248505,
0.002460668794810772,
-0.013295336626470089,
-0.060520417988300323,
0.047952521592378616,
-0.035400617867708206,
0.010487576946616173,
-0.020318489521741867,
0.0011082745622843504,
0.042770568281412125,
-0.024454688653349876,
0.01611381396651268,
0.030451836064457893,
-0.008074197918176651,
-0.04013020917773247,
-0.03912649676203728,
0.02420666441321373,
0.011954572051763535,
0.019996903836727142,
-0.00533101474866271,
-0.01457526721060276,
-0.0060791140422225,
-0.02328285202383995,
-0.031928885728120804,
-0.030280526727437973,
-0.0021361582912504673,
-0.014121750369668007,
0.019294213503599167,
-0.030843261629343033,
-0.004782264120876789,
0.030090417712926865,
-0.0018960912711918354,
0.011672312393784523,
-0.02372625097632408,
0.00030687713297083974,
-0.01588371954858303,
-0.007298384793102741,
-0.017794564366340637,
-0.023785782977938652,
-0.02116943709552288,
0.0027456365060061216,
0.038675155490636826,
0.0026531131006777287,
0.035964254289865494,
0.023522168397903442,
0.007907889783382416,
-0.02529551088809967,
-0.00793556310236454,
-0.013785332441329956,
0.006375848315656185,
-0.0031773042865097523,
0.037052981555461884,
-0.004983826540410519,
-0.014677505008876324,
0.028070926666259766,
0.031108355149626732,
-0.003212382085621357,
-0.004410626832395792,
0.05298808962106705,
0.024113815277814865,
0.04307996854186058,
-0.009835499338805676,
-0.03576945140957832,
-0.003758766455575824,
-0.010695856995880604,
0.021365245804190636,
0.010366154834628105,
-0.014174675568938255,
0.08775390684604645,
-0.002856259699910879,
0.00940870214253664,
-0.029784930869936943,
-0.012262185104191303,
-0.06596317142248154,
-0.00964407343417406,
0.00895609986037016,
0.018645865842700005,
-0.04275547340512276,
0.011949809268116951,
-0.021485991775989532,
0.017558882012963295,
-0.028753360733389854,
0.004183962941169739,
-0.04871949926018715,
-0.011705062352120876,
-0.011492661200463772,
-0.041531287133693695,
0.030920198187232018,
0.006563239265233278,
-0.03072052262723446,
0.0033070524223148823,
-0.012679372914135456,
0.017183437943458557,
0.03547417372465134,
0.06914053112268448,
-0.025698406621813774,
0.04305347800254822,
-0.0154013242572546,
0.01984447054564953,
-0.028131162747740746,
0.014531713910400867,
0.12718690931797028,
0.0026843533851206303,
-0.007020709104835987,
-0.07455470412969589,
-0.00403094757348299,
0.004672467242926359,
0.01335935853421688,
0.0033404906280338764,
0.03460131213068962,
0.005772702861577272,
0.011607476510107517,
0.023962194100022316,
0.00491359643638134,
0.009297369979321957,
0.023502297699451447,
0.03953339904546738,
-0.038491036742925644,
-0.029613565653562546,
0.015533179976046085,
0.008504853583872318,
-0.05795995891094208,
0.025224974378943443,
-0.032279182225465775,
0.03004602901637554,
-0.03315533697605133,
-0.01605553925037384,
-0.020816955715417862,
-0.05851252004504204,
0.01864943653345108,
-0.010352310724556446,
-0.0334429033100605,
0.014000569470226765,
-0.011763137765228748,
-0.007262359838932753,
-0.017139460891485214,
0.022309405729174614,
0.03854387626051903,
0.03174153342843056,
-0.011623206548392773,
0.037201881408691406,
0.013446370139718056,
-0.002012307057157159,
0.022013410925865173,
0.03634624928236008,
-0.030262494459748268,
-0.0050773024559021,
-0.020412502810359,
0.027107270434498787,
-0.006933174561709166,
0.004663554485887289,
-0.019327625632286072,
0.04909095540642738,
0.0332198366522789,
-0.06377775967121124,
-0.03246338292956352,
0.004305175505578518,
0.04046545922756195,
-0.024429144337773323,
-0.02922671101987362,
-0.009894860908389091,
0.01440531574189663,
-0.033562302589416504,
0.01903029903769493,
0.016521619632840157,
0.02820201963186264,
0.027645554393529892,
0.01098038349300623,
-0.001260471297428012,
0.005835182499140501,
0.043680693954229355,
-0.02193710394203663,
-0.01691766269505024,
-0.022398168221116066,
-0.03155592828989029,
0.03161513805389404,
0.0336640328168869,
0.033725298941135406,
-0.0036511458456516266,
0.002653363859280944,
0.008586999960243702,
-0.04684402421116829,
0.05563916638493538,
0.024037053808569908,
-0.03737702593207359,
-0.03997288644313812,
0.02385527826845646,
-0.002983510959893465,
0.038720011711120605,
0.025842906907200813,
0.02786119095981121,
-0.0024574953131377697,
-0.010053264908492565,
-0.013634192757308483,
-0.023191889747977257,
-0.032093096524477005,
0.02140768989920616,
-0.051257871091365814,
0.01919463649392128,
0.013149205595254898,
0.016038479283452034,
-0.0005930623738095164,
-0.004489382728934288,
-0.004461933393031359,
0.023193474858999252,
-0.0211411714553833,
0.0059343730099499226,
0.0014175267424434423,
-0.0032342367339879274,
-0.007776896469295025,
0.01870260387659073,
0.005880843847990036,
-0.0016048136167228222,
-0.02717341110110283,
-0.008515934459865093,
0.002484138123691082,
-0.010327079333364964,
0.03892126306891441,
0.01686272583901882,
0.003148720832541585,
-0.0443948470056057,
0.04946328327059746,
-0.03660831227898598,
0.0008154547540470958,
-0.04944896325469017,
-0.011153125204145908,
0.059447601437568665,
0.01750684529542923,
-0.030791446566581726,
0.03037896938621998,
-0.006419364362955093,
-0.0019344175234436989,
-0.005771259777247906,
0.016182810068130493,
-0.03649807721376419,
-0.023624388501048088,
0.00022267618624027818,
0.0008175735711120069,
0.05785045400261879,
-0.04621518775820732,
-0.03200123831629753,
0.05706256255507469,
-0.013335979543626308,
-0.013333814218640327,
-0.013810377568006516,
-0.023637747392058372,
0.011924898251891136,
0.03734369948506355,
0.008979803882539272,
0.0020412460435181856,
0.045765943825244904,
0.004925019107758999,
0.023647421970963478,
0.02397032454609871,
-0.014530042186379433,
-0.009830927476286888,
0.030741196125745773,
-0.009774933569133282,
-0.059772785753011703,
-0.011863208375871181,
0.018079174682497978,
0.03373056277632713,
0.02793683297932148,
-0.003974358085542917,
-0.004714012145996094,
0.044459614902734756,
-0.014359349384903908,
0.0075787813402712345,
0.010420748963952065,
-0.016956115141510963,
0.022474205121397972,
-0.013936501927673817,
0.04289396107196808,
0.012201923877000809,
0.0009400957496836782,
-0.05775950103998184,
-0.003704214468598366,
-0.008733725175261497,
-0.037441324442625046,
0.01632564887404442,
-0.038256239145994186,
-0.022058485075831413,
0.030013689771294594,
-0.09450411796569824,
0.010214390233159065,
0.00037055654684081674,
-0.045576922595500946,
-0.007901899516582489,
-0.007503920700401068,
-0.034836072474718094,
0.024546487256884575,
0.0264565572142601,
0.07399454712867737,
0.0148154953494668,
0.01154874823987484,
0.014895731583237648,
-0.01935778744518757,
-0.015605319291353226,
0.053189072757959366,
-0.01787022314965725,
0.023267898708581924,
0.07907139509916306,
-0.0680839791893959,
0.014254224486649036,
0.04023829102516174,
-0.02096826210618019,
-0.0036187756340950727,
0.0059936437755823135,
0.007678397931158543,
-0.015295694582164288,
0.06138591840863228,
0.034598689526319504,
-0.030839838087558746,
-0.021220987662672997,
0.006758193019777536,
0.0501205176115036,
0.04071517661213875,
0.04188619926571846,
0.0327833816409111,
0.02294657565653324,
-0.028832441195845604,
-0.0293622687458992,
0.01717216521501541,
-0.02070009708404541,
0.025046996772289276,
-0.009554505348205566,
-0.020545518025755882,
0.02298976108431816,
-0.02471488155424595,
-0.048154041171073914,
-0.033944178372621536,
-0.025011181831359863,
0.02648983895778656,
-0.040208809077739716,
0.0380365215241909,
0.010360266081988811,
-0.027494458481669426,
-0.03876057639718056,
0.03189888596534729,
-0.02853352762758732,
0.0007579029188491404,
-0.042885273694992065,
0.01035366952419281,
0.026018019765615463,
-0.012076577171683311,
-0.0019037374295294285,
-0.029599424451589584,
-0.0469522587954998,
0.06891302764415741,
0.01837753690779209,
0.007136710919439793,
-0.0020753308199346066,
-0.05111290141940117,
-0.004209408536553383,
-0.07146260887384415,
0.04791063815355301,
-0.005690256133675575,
-0.009466718882322311,
-0.044984884560108185,
-0.06488677859306335,
0.020556503906846046,
0.052254319190979004,
0.057400669902563095,
-0.029828310012817383,
-0.029643524438142776,
0.00012800142576452345,
-0.03905358538031578,
0.04779656231403351,
-0.03250035643577576,
0.03515895456075668,
-0.00022519032063428313,
-0.007500628940761089,
0.015362572856247425,
-0.02814410999417305,
-0.042542099952697754,
0.0022190704476088285,
0.06163181737065315,
-0.0011919115204364061,
-0.019243896007537842,
-0.04078202322125435,
0.0014806031249463558,
0.03447997570037842,
0.011851841583848,
0.02547648549079895,
0.07523339241743088,
-0.0152619369328022,
0.03702402859926224,
0.03061809577047825,
-0.006828252226114273,
-0.016671670600771904,
0.018542619422078133,
-0.04372692480683327,
0.030007610097527504,
-0.009016184136271477,
-0.042551152408123016,
0.0647445023059845,
-0.025192758068442345,
-0.025793256238102913,
0.04033350944519043,
-0.04610114544630051,
-0.03299563378095627,
0.04970775172114372,
0.026856238022446632,
0.04186567664146423,
-0.0015446194447577,
0.029652882367372513,
-0.015355852432549,
0.014623580500483513,
-0.015106217935681343,
0.012002631090581417,
0.026334337890148163,
-0.029059262946248055,
0.003959828056395054,
0.031263213604688644,
0.017274420708417892,
0.023205747827887535,
-0.015661029145121574,
0.03926442563533783,
-0.033492423593997955,
-0.04312916472554207,
0.027312714606523514,
0.0035360930487513542,
0.003418082371354103,
0.009380708448588848,
-0.026645492762327194,
0.06849255412817001,
-0.027105551213026047,
-0.0057700336910784245,
-0.0030521235894411802,
0.041541412472724915,
-0.017476333305239677,
-0.004822162911295891,
-0.019082991406321526,
0.02345234900712967,
0.011138960719108582,
0.0027272505685687065,
-0.03333168104290962,
0.029807504266500473,
0.028499886393547058,
-0.00006330793985398486,
0.015686020255088806,
-0.00137469416949898,
-0.006963539868593216,
-0.030049173161387444,
0.0049063414335250854,
-0.030302582308650017,
-0.06673772633075714,
0.0627688616514206,
0.04870269075036049,
0.016552789136767387,
-0.010916728526353836,
-0.0028824249748140574,
-0.030763773247599602,
0.044975198805332184,
-0.05727935954928398,
-0.015485081821680069,
-0.01855795830488205,
-0.01039537787437439,
-0.00006408522312995046,
-0.01881728507578373
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.