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ONTHEELECTRODYNAMICSOFMOVINGBODIESByA.EinsteinJune30,1905ItisknownthatMaxwell'selectrodynamics--asusuallyunderstoodatthepresenttime--whenappliedtomovingbodies,leadstoasymmetrieswhichdonotappeartobeinherentinthephenomena.Take,forexample,thereciprocalelectrodynamicactionofamagnetandaconductor.Theobservablephenomenonheredependsonlyontherelativemotionoftheconductorandthemagnet,whereasthecustomaryviewdrawsasharpdistinctionbetweenthetwocasesinwhicheithertheoneortheotherofthesebodiesisinmotion.Forifthemagnetisinmotionandtheconductoratrest,therearisesintheneighbourhoodofthemagnetanelectricfieldwithacertaindefiniteenergy,producingacurrentattheplaceswherepartsoftheconductoraresituated.Butifthemagnetisstationaryandtheconductorinmotion,noelectricfieldarisesintheneighbourhoodofthemagnet.Intheconductor,however,wefindanelectromotiveforce,towhichinitselfthereisnocorrespondingenergy,butwhichgivesrise--assumingequalityofrelativemotioninthetwocasesdiscussed--toelectriccurrentsofthesamepathandintensityasthoseproducedbytheelectricforcesintheformercase.Examplesofthissort,togetherwiththeunsuccessfulattemptstodiscoveranymotionoftheearthrelativelytothe``lightmedium,''suggestthatthephenomenaofelectrodynamicsaswellasofmechanicspossessnopropertiescorrespondingtotheideaofabsoluterest.Theysuggestratherthat,ashasalreadybeenshowntothefirstorderofsmallquantities,thesamelawsofelectrodynamicsandopticswillbevalidforallframesofreferenceforwhichtheequationsofmechanicsholdgood.1Wewillraisethisconjecture(thepurportofwhichwillhereafterbecalledthe``PrincipleofRelativity'')tothestatusofapostulate,andalsointroduceanotherpostulate,whichisonlyapparentlyirreconcilablewiththeformer,namely,thatlightisalwayspropagatedinemptyspacewithadefinitevelocitycwhichisindependentofthestateofmotionoftheemittingbody.ThesetwopostulatessufficefortheattainmentofasimpleandconsistenttheoryoftheelectrodynamicsofmovingbodiesbasedonMaxwell'stheoryforstationarybodies.Theintroductionofa``luminiferousether''willprovetobesuperfluousinasmuchastheviewheretobedevelopedwillnotrequirean``absolutelystationaryspace''providedwithspecialproperties,norassignavelocity-vectortoapointoftheemptyspaceinwhichelectromagneticprocessestakeplace.Thetheorytobedevelopedisbased--likeallelectrodynamics--onthekinematicsoftherigidbody,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.''3Itmightappearpossibletoovercomeallthedifficultiesattendingthedefinitionof``time''bysubstituting``thepositionofthesmallhandofmywatch''for``time.''Andinfactsuchadefinitionissatisfactorywhenweareconcernedwithdefiningatimeexclusivelyfortheplacewherethewatchislocated;butitisnolongersatisfactorywhenwehavetoconnectintimeseriesofeventsoccurringatdifferentplaces,or--whatcomestothesamething--toevaluatethetimesofeventsoccurringatplacesremotefromthewatch.Wemight,ofcourse,contentourselveswithtimevaluesdeterminedbyanobserverstationedtogetherwiththewatchattheoriginoftheco-ordinates,andco-ordinatingthecorrespondingpositionsofthehandswithlightsignals,givenoutbyeveryeventtobetimed,andreachinghimthroughemptyspace.Butthisco-ordinationhasthedisadvantagethatitisnotindependentofthestandpointoftheobserverwiththewatchorclock,asweknowfromexperience.Wearriveatamuchmorepracticaldeterminationalongthefollowinglineofthought.IfatthepointAofspacethereisaclock,anobserveratAcandeterminethetimevaluesofeventsintheimmediateproximityofAbyfindingthepositionsofthehandswhicharesimultaneouswiththeseevents.IfthereisatthepointBofspaceanotherclockinallrespectsresemblingtheoneatA,itispossibleforanobserveratBtodeterminethetimevaluesofeventsintheimmediateneighbourhoodofB.Butitisnotpossiblewithoutfurtherassumptiontocompare,inrespectoftime,aneventatAwithaneventatB.Wehavesofardefinedonlyan``Atime''anda``Btime.''Wehavenotdefinedacommon``time''forAandB,forthelattercannotbedefined