搜索
DOESTHEINERTIAOFABODYDEPENDUPONITSENERGY-CONTENT?ByA.EINSTEINSeptember27,1905Theresultsofthepreviousinvestigationleadtoaveryinterestingconclusion,whichisheretobededuced.IbasedthatinvestigationontheMaxwell-Hertzequationsforemptyspace,togetherwiththeMaxwellianexpressionfortheelectromagneticenergyofspace,andinadditiontheprinciplethat:—Thelawsbywhichthestatesofphysicalsystemsalterareindependentofthealternative,towhichoftwosystemsofcoordinates,inuniformmotionofparalleltranslationrelativelytoeachother,thesealterationsofstatearereferred(principleofrelativity).Withtheseprinciples∗asmybasisIdeducedinteraliathefollowingresult(§8):—Letasystemofplanewavesoflight,referredtothesystemofco-ordinates(x,y,z),possesstheenergyl;letthedirectionoftheray(thewave-normal)makeanangleφwiththeaxisofxofthesystem.Ifweintroduceanewsystemofco-ordinates(ξ,η,ζ)movinginuniformparalleltranslationwithrespecttothesystem(x,y,z),andhavingitsoriginofco-ordinatesinmotionalongtheaxisofxwiththevelocityv,thenthisquantityoflight—measuredinthesystem(ξ,η,ζ)—possessestheenergyl∗=l1−vccosφp1−v2/c2wherecdenotesthevelocityoflight.Weshallmakeuseofthisresultinwhatfollows.Lettherebeastationarybodyinthesystem(x,y,z),andletitsenergy—referredtothesystem(x,y,z)beE0.Lettheenergyofthebodyrelativetothesystem(ξ,η,ζ)movingasabovewiththevelocityv,beH0.Letthisbodysendout,inadirectionmakinganangleφwiththeaxisofx,planewavesoflight,ofenergy12Lmeasuredrelativelyto(x,y,z),andsimultaneouslyanequalquantityoflightintheoppositedirection.Meanwhilethebodyremainsatrestwithrespecttothesystem(x,y,z).Theprincipleof∗TheprincipleoftheconstancyofthevelocityoflightisofcoursecontainedinMaxwell’sequations.1energymustapplytothisprocess,andinfact(bytheprincipleofrelativity)withrespecttobothsystemsofco-ordinates.IfwecalltheenergyofthebodyaftertheemissionoflightE1orH1respectively,measuredrelativelytothesystem(x,y,z)or(ξ,η,ζ)respectively,thenbyemployingtherelationgivenaboveweobtainE0=E1+12L+12L,H0=H1+12L1−vccosφp1−v2/c2+12L1+vccosφp1−v2/c2=H1+Lp1−v2/c2.BysubtractionweobtainfromtheseequationsH0−E0−(H1−E1)=L(1p1−v2/c2−1).ThetwodifferencesoftheformH−Eoccurringinthisexpressionhavesimplephysicalsignifications.HandEareenergyvaluesofthesamebodyreferredtotwosystemsofco-ordinateswhichareinmotionrelativelytoeachother,thebodybeingatrestinoneofthetwosystems(system(x,y,z)).ThusitisclearthatthedifferenceH−EcandifferfromthekineticenergyKofthebody,withrespecttotheothersystem(ξ,η,ζ),onlybyanadditiveconstantC,whichdependsonthechoiceofthearbitraryadditiveconstantsoftheenergiesHandE.ThuswemayplaceH0−E0=K0+C,H1−E1=K1+C,sinceCdoesnotchangeduringtheemissionoflight.SowehaveK0−K1=L(1p1−v2/c2−1).Thekineticenergyofthebodywithrespectto(ξ,η,ζ)diminishesasaresultoftheemissionoflight,andtheamountofdiminutionisindependentofthepropertiesofthebody.Moreover,thedifferenceK0−K1,likethekineticenergyoftheelectron(§10),dependsonthevelocity.NeglectingmagnitudesoffourthandhigherorderswemayplaceK0−K1=12Lc2v2.Fromthisequationitdirectlyfollowsthat:—2IfabodygivesofftheenergyLintheformofradiation,itsmassdiminishesbyL/c2.Thefactthattheenergywithdrawnfromthebodybecomesenergyofradiationevidentlymakesnodifference,sothatweareledtothemoregeneralconclusionthatThemassofabodyisameasureofitsenergy-content;iftheenergychangesbyL,themasschangesinthesamesensebyL/9×1020,theenergybeingmeasuredinergs,andthemassingrammes.Itisnotimpossiblethatwithbodieswhoseenergy-contentisvariabletoahighdegree(e.g.withradiumsalts)thetheorymaybesuccessfullyputtothetest.Ifthetheorycorrespondstothefacts,radiationconveysinertiabetweentheemittingandabsorbingbodies.AboutthisDocumentThiseditionofEinstein’sDoestheInertiaofaBodyDependuponitsEnergy-ContentisbasedontheEnglishtranslationofhisoriginal1905German-languagepaper(publishedasIstdieTr¨agheiteinesK¨orpersvonseinemEn-ergiegehaltabh¨angig?,inAnnalenderPhysik.18:639,1905)whichappearedinthebookThePrincipleofRelativity,publishedin1923byMethuenandCompany,Ltd.ofLondon.MostofthepapersinthatcollectionareEnglishtranslationsbyW.PerrettandG.B.JefferyfromtheGermanDasRelativat-sprinzip,4thed.,publishedbyin1922byTuebner.Allofthesesourcesarenowinthepublicdomain;thisdocument,derivedfromthem,remainsinthepublicdomainandmaybereproducedinanymannerormediumwithoutpermission,restriction,attribution,orcompensation.Thefootnoteisasitappearedinthe1923edition.The1923EnglishtranslationmodifiedthenotationusedinEinstein’s1905papertoconformtothatinusebythe1920’s;forexample,cdenotesthespeedoflight,asopposedtheVusedbyEinsteinin1905.InthispaperEinsteinusesLtodenoteenergy;theitalicisedsentenceintheconclusionmaybewrittenastheequation“m=L/c2”which,usingthemoremodernEinsteadofLtodenoteenergy,maybetriviallyrewrittenas“E=mc2”.ThiseditionwaspreparedbyJohnWalker.Thecurrentversionofthisdocumentisavailableinavarietyofformatsfromtheeditor’sWebsite: