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ONTHEELECTRODYNAMICSOFMOVINGBODIESByA.EINSTEINJune30,1905ItisknownthatMaxwell’selectrodynamics—asusuallyunderstoodatthepresenttime—whenappliedtomovingbodies,leadstoasymmetrieswhichdonotappeartobeinherentinthephenomena.Take,forexample,therecipro-calelectrodynamicactionofamagnetandaconductor.Theobservablephe-nomenonheredependsonlyontherelativemotionoftheconductorandthemagnet,whereasthecustomaryviewdrawsasharpdistinctionbetweenthetwocasesinwhicheithertheoneortheotherofthesebodiesisinmotion.Forifthemagnetisinmotionandtheconductoratrest,therearisesintheneighbour-hoodofthemagnetanelectricfieldwithacertaindefiniteenergy,producingacurrentattheplaceswherepartsoftheconductoraresituated.Butifthemagnetisstationaryandtheconductorinmotion,noelectricfieldarisesintheneighbourhoodofthemagnet.Intheconductor,however,wefindanelectro-motiveforce,towhichinitselfthereisnocorrespondingenergy,butwhichgivesrise—assumingequalityofrelativemotioninthetwocasesdiscussed—toelec-triccurrentsofthesamepathandintensityasthoseproducedbytheelectricforcesintheformercase.Examplesofthissort,togetherwiththeunsuccessfulattemptstodiscoveranymotionoftheearthrelativelytothe“lightmedium,”suggestthatthephenomenaofelectrodynamicsaswellasofmechanicspossessnopropertiescorrespondingtotheideaofabsoluterest.Theysuggestratherthat,ashasalreadybeenshowntothefirstorderofsmallquantities,thesamelawsofelectrodynamicsandopticswillbevalidforallframesofreferenceforwhichtheequationsofmechanicsholdgood.1Wewillraisethisconjecture(thepurportofwhichwillhereafterbecalledthe“PrincipleofRelativity”)tothestatusofapostulate,andalsointroduceanotherpostulate,whichisonlyapparentlyirreconcilablewiththeformer,namely,thatlightisalwayspropagatedinemptyspacewithadefinitevelocitycwhichisindependentofthestateofmotionoftheemittingbody.ThesetwopostulatessufficefortheattainmentofasimpleandconsistenttheoryoftheelectrodynamicsofmovingbodiesbasedonMaxwell’stheoryforstationarybodies.Theintroductionofa“luminiferousether”willprovetobesuperfluousinasmuchastheviewheretobedevelopedwillnotrequirean“absolutelystationaryspace”providedwithspecialproperties,nor1TheprecedingmemoirbyLorentzwasnotatthistimeknowntotheauthor.1assignavelocity-vectortoapointoftheemptyspaceinwhichelectromagneticprocessestakeplace.Thetheorytobedevelopedisbased—likeallelectrodynamics—onthekine-maticsoftherigidbody,sincetheassertionsofanysuchtheoryhavetodowiththerelationshipsbetweenrigidbodies(systemsofco-ordinates),clocks,andelectromagneticprocesses.Insufficientconsiderationofthiscircumstanceliesattherootofthedifficultieswhichtheelectrodynamicsofmovingbodiesatpresentencounters.I.KINEMATICALPART§1.DefinitionofSimultaneityLetustakeasystemofco-ordinatesinwhichtheequationsofNewtonianmechanicsholdgood.2Inordertorenderourpresentationmorepreciseandtodistinguishthissystemofco-ordinatesverballyfromotherswhichwillbeintroducedhereafter,wecallitthe“stationarysystem.”Ifamaterialpointisatrestrelativelytothissystemofco-ordinates,itspositioncanbedefinedrelativelytheretobytheemploymentofrigidstandardsofmeasurementandthemethodsofEuclideangeometry,andcanbeexpressedinCartesianco-ordinates.Ifwewishtodescribethemotionofamaterialpoint,wegivethevaluesofitsco-ordinatesasfunctionsofthetime.Nowwemustbearcarefullyinmindthatamathematicaldescriptionofthiskindhasnophysicalmeaningunlesswearequiteclearastowhatweunderstandby“time.”Wehavetotakeintoaccountthatallourjudgmentsinwhichtimeplaysapartarealwaysjudgmentsofsimultaneousevents.If,forinstance,Isay,“Thattrainarriveshereat7o’clock,”Imeansomethinglikethis:“Thepointingofthesmallhandofmywatchto7andthearrivalofthetrainaresimultaneousevents.”3Itmightappearpossibletoovercomeallthedifficultiesattendingthedefini-tionof“time”bysubstituting“thepositionofthesmallhandofmywatch”for“time.”Andinfactsuchadefinitionissatisfactorywhenweareconcernedwithdefiningatimeexclusivelyfortheplacewherethewatchislocated;butitisnolongersatisfactorywhenwehavetoconnectintimeseriesofeventsoccurringatdifferentplaces,or—whatcomestothesamething—toevaluatethetimesofeventsoccurringatplacesremotefromthewatch.Wemight,ofcourse,contentourselveswithtimevaluesdeterminedbyanobserverstationedtogetherwiththewatchattheoriginoftheco-ordinates,andco-ordinatingthecorrespondingpositionsofthehandswithlightsignals,givenoutbyeveryeventtobetimed,andreachinghimthroughemptyspace.Butthisco-ordinationhasthedisadvantagethatitisnotindependentofthestandpointoftheobserverwiththewatchorclock,asweknowfromexperience.2i.e.tothefirstapproximation.3Weshallnotherediscusstheinexactitudewhichlurksintheconceptofsimultaneityoftwoeventsatapproximatelythesameplace,whichcanonlyberemovedbyanabstraction.2Wearriveatamuchmorepracticaldeterminationalongthefollowinglineofthought.IfatthepointAofspacethereisaclock,anobserveratAcandeterminethetimevaluesofeventsintheimmediateproximityofAbyfindingthepositionsofthehandswhicharesimultaneouswiththeseevents.IfthereisatthepointBofspaceanotherclockinallrespectsresemblingtheoneatA,itispossibleforanobserveratBtodeterminethetimevaluesofeventsintheimmediateneigh-bourhoodofB.Butitisnotp