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首页 相对论原版.pdf

相对论原版.pdf

相对论原版.pdf

上传者: tonnyzheng2004 2010-11-08 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《相对论原版pdf》,可适用于高等教育领域,主题内容包含Relativity:TheSpecialandGeneralTheoryAlbertEinsteinAlbertEinsteinRelativit符等。

Relativity:TheSpecialandGeneralTheoryAlbertEinsteinAlbertEinsteinRelativityTheSpecialandGeneralTheoryWritten:(thisrevisededition:)Source:Relativity:TheSpecialandGeneralTheoryPublisher:MethuenCoLtdFirstPublished:December,Translated:RobertWLawson(Authorisedtranslation)TranscriptionMarkup:BrianBasgenConvertiontoPDF:SjoerdLangkemperOfflineVersion:EinsteinReferenceArchive(marxistsorg)PrefacePartI:TheSpecialTheoryofRelativityPhysicalMeaningofGeometricalPropositionsTheSystemofCoordinatesSpaceandTimeinClassicalMechanicsTheGalileianSystemofCoordinatesThePrincipleofRelativity(intheRestrictedSense)TheTheoremoftheAdditionofVelocitiesemployedinClassicalMechanicsTheApparentIncompatabilityoftheLawofPropagationofLightwiththePrincipleofRelativityOntheIdeaofTimeinPhysicsTheRelativityofSimultaneityOntheRelativityoftheConceptionofDistanceTheLorentzTransformationTheBehaviourofMeasuringRodsandClocksinMotionTheoremoftheAdditionofVelocitiesTheExperimentofFizeauTheHueristicValueoftheTheoryofRelativityGeneralResultsoftheTheoryExpereinceandtheSpecialTheoryofRelativityMinkowski'sFourdimensialSpacePartII:TheGeneralTheoryofRelativitySpecialandGeneralPrincipleofRelativityTheGravitationalFieldTheEqualityofInertialandGravitationalMassasanArgumentfortheGeneralPostulateofRelativityInWhatRespectsaretheFoundationsofClassicalMechanicsandoftheSpecialTheoryofRelativityUnsatisfactoryRelativity:TheSpecialandGeneralTheoryAFewInferencesfromtheGeneralPrincipleofRelativityBehaviourofClocksandMeasuringRodsonaRotatingBodyofReferenceEuclideanandnonEuclideanContinuumGaussianCoordinatesTheSpaceTimeContinuumoftheSpeicalTheoryofRelativityConsideredasaEuclideanContinuumTheSpaceTimeContinuumoftheGeneralTheoryofRealtiivtyisNotaEculideanContinuumExactFormulationoftheGeneralPrincipleofRelativityTheSolutionoftheProblemofGravitationontheBasisoftheGeneralPrincipleofRelativityPartIII:ConsiderationsontheUniverseasaWholeCosmologicalDifficultiesofNetwon'sTheoryThePossibilityofa"Finite"andyet"Unbounded"UniverseTheStructureofSpaceAccordingtotheGeneralTheoryofRelativityAppendices:SimpleDerivationoftheLorentzTransformation(supch)Minkowski'sFourDimensionalSpace("World")(supch)TheExperimentalConfirmationoftheGeneralTheoryofRelativityTheStructureofSpaceAccordingtotheGeneralTheoryofRelativity(supch)RelativityandtheProblemofSpaceNote:ThefifthappendixwasaddedbyEinsteinatthetimeofthefifteenthreprintingofthisbookandasaresultisstillundercopyrightrestrictionssocannotbeaddedwithoutthepermissionofthepublisherEinsteinReferenceArchiveRelativity:TheSpecialandGeneralTheoryAlbertEinsteinRelativity:TheSpecialandGeneralTheoryPreface(December,)Thepresentbookisintended,asfaraspossible,togiveanexactinsightintothetheoryofRelativitytothosereaderswho,fromageneralscientificandphilosophicalpointofview,areinterestedinthetheory,butwhoarenotconversantwiththemathematicalapparatusoftheoreticalphysicsTheworkpresumesastandardofeducationcorrespondingtothatofauniversitymatriculationexamination,and,despitetheshortnessofthebook,afairamountofpatienceandforceofwillonthepartofthereaderTheauthorhassparedhimselfnopainsinhisendeavourtopresentthemainideasinthesimplestandmostintelligibleform,andonthewhole,inthesequenceandconnectioninwhichtheyactuallyoriginatedIntheinterestofclearness,itappearedtomeinevitablethatIshouldrepeatmyselffrequently,withoutpayingtheslightestattentiontotheeleganceofthepresentationIadheredscrupulouslytothepreceptofthatbrillianttheoreticalphysicistLBoltzmann,accordingtowhommattersofeleganceoughttobelefttothetailorandtothecobblerImakenopretenceofhavingwithheldfromthereaderdifficultieswhichareinherenttothesubjectOntheotherhand,Ihavepurposelytreatedtheempiricalphysicalfoundationsofthetheoryina"stepmotherly"fashion,sothatreadersunfamiliarwithphysicsmaynotfeellikethewandererwhowasunabletoseetheforestforthetreesMaythebookbringsomeoneafewhappyhoursofsuggestivethought!December,AEINSTEINNext:ThePhysicalMeaningofGeometricalPropositionsRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityPartITheSpecialTheoryofRelativityPhysicalMeaningofGeometricalPropositionsInyourschooldaysmostofyouwhoreadthisbookmadeacquaintancewiththenoblebuildingofEuclid'sgeometry,andyourememberperhapswithmorerespectthanlovethemagnificentstructure,ontheloftystaircaseofwhichyouwerechasedaboutforuncountedhoursbyconscientiousteachersByreasonofourpastexperience,youwouldcertainlyregardeveryonewithdisdainwhoshouldpronounceeventhemostoutofthewaypropositionofthissciencetobeuntrueButperhapsthisfeelingofproudcertaintywouldleaveyouimmediatelyifsomeoneweretoaskyou:"What,then,doyoumeanbytheassertionthatthesepropositionsaretrue"LetusproceedtogivethisquestionalittleconsiderationGeometrysetsoutformcertainconceptionssuchas"plane,""point,"and"straightline,"withwhichweareabletoassociatemoreorlessdefiniteideas,andfromcertainsimplepropositions(axioms)which,invirtueoftheseideas,weareinclinedtoacceptas"true"Then,onthebasisofalogicalprocess,thejustificationofwhichwefeelourselvescompelledtoadmit,allremainingpropositionsareshowntofollowfromthoseaxioms,ietheyareprovenApropositionisthencorrect("true")whenithasbeenderivedintherecognisedmannerfromtheaxiomsThequestionof"truth"oftheindividualgeometricalpropositionsisthusreducedtooneofthe"truth"oftheaxiomsNowithaslongbeenknownthatthelastquestionisnotonlyunanswerablebythemethodsofgeometry,butthatitisinitselfentirelywithoutmeaningWecannotaskwhetheritistruethatonlyonestraightlinegoesthroughtwopointsWecanonlysaythatEuclideangeometrydealswiththingscalled"straightlines,"toeachofwhichisascribedthepropertyofbeinguniquelydeterminedbytwopointssituatedonitTheconcept"true"doesnottallywiththeassertionsofpuregeometry,becausebytheword"true"weareeventuallyinthehabitofdesignatingalwaysthecorrespondencewitha"real"objectgeometry,however,isnotconcernedwiththerelationoftheideasinvolvedinittoobjectsofexperience,butonlywiththelogicalconnectionoftheseideasamongthemselvesItisnotdifficulttounderstandwhy,inspiteofthis,wefeelconstrainedtocallthepropositionsofgeometry"true"Geometricalideascorrespondtomoreorlessexactobjectsinnature,andtheselastareundoubtedlytheexclusivecauseofthegenesisofthoseideasGeometryoughttorefrainfromsuchacourse,inordertogivetoitsstructurethelargestpossiblelogicalunityThepractice,forexample,ofseeingina"distance"twomarkedpositionsonapracticallyrigidbodyissomethingwhichislodgeddeeplyinourhabitofthoughtWeareaccustomedfurthertoregardthreepointsasbeingsituatedonastraightline,iftheirapparentpositionscanbemadetocoincideforobservationwithoneeye,undersuitablechoiceofourplaceofobservationIf,inpursuanceofourhabitofthought,wenowsupplementthepropositionsofEuclideangeometrybythesinglepropositionthattwopointsonapracticallyrigidbodyalwayscorrespondtothesamedistance(lineinterval),independentlyofanychangesinpositiontowhichwemaysubjectthebody,thepropositionsofEuclideangeometrythenresolvethemselvesintopropositionsontheRelativity:TheSpecialandGeneralTheorypossiblerelativepositionofpracticallyrigidbodies)GeometrywhichhasbeensupplementedinthiswayisthentobetreatedasabranchofphysicsWecannowlegitimatelyaskastothe"truth"ofgeometricalpropositionsinterpretedinthisway,sincewearejustifiedinaskingwhetherthesepropositionsaresatisfiedforthoserealthingswehaveassociatedwiththegeometricalideasInlessexacttermswecanexpressthisbysayingthatbythe"truth"ofageometricalpropositioninthissenseweunderstanditsvalidityforaconstructionwithruleandcompassesOfcoursetheconvictionofthe"truth"ofgeometricalpropositionsinthissenseisfoundedexclusivelyonratherincompleteexperienceForthepresentweshallassumethe"truth"ofthegeometricalpropositions,thenatalaterstage(inthegeneraltheoryofrelativity)weshallseethatthis"truth"islimited,andweshallconsidertheextentofitslimitationNext:TheSystemofCoordinatesNotes)ItfollowsthatanaturalobjectisassociatedalsowithastraightlineThreepointsA,BandConarigidbodythuslieinastraightlinewhenthepointsAandCbeinggiven,BischosensuchthatthesumofthedistancesABandBCisasshortaspossibleThisincompletesuggestionwillsufficeforthepresentpurposeRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityTheSystemofCoordinatesOnthebasisofthephysicalinterpretationofdistancewhichhasbeenindicated,wearealsoinapositiontoestablishthedistancebetweentwopointsonarigidbodybymeansofmeasurementsForthispurposewerequirea"distance"(rodS)whichistobeusedonceandforall,andwhichweemployasastandardmeasureIf,now,AandBaretwopointsonarigidbody,wecanconstructthelinejoiningthemaccordingtotherulesofgeometrythen,startingfromA,wecanmarkoffthedistanceStimeaftertimeuntilwereachBThenumberoftheseoperationsrequiredisthenumericalmeasureofthedistanceABThisisthebasisofallmeasurementoflength)Everydescriptionofthesceneofaneventorofthepositionofanobjectinspaceisbasedonthespecificationofthepointonarigidbody(bodyofreference)withwhichthateventorobjectcoincidesThisappliesnotonlytoscientificdescription,butalsotoeverydaylifeIfIanalysetheplacespecification"TimesSquare,NewYork,"AIarriveatthefollowingresultTheearthistherigidbodytowhichthespecificationofplacerefers"TimesSquare,NewYork,"isawelldefinedpoint,towhichanamehasbeenassigned,andwithwhichtheeventcoincidesinspace)Thisprimitivemethodofplacespecificationdealsonlywithplacesonthesurfaceofrigidbodies,andisdependentontheexistenceofpointsonthissurfacewhicharedistinguishablefromeachotherButwecanfreeourselvesfrombothoftheselimitationswithoutalteringthenatureofourspecificationofpositionIf,forinstance,acloudishoveringoverTimesSquare,thenwecandetermineitspositionrelativetothesurfaceoftheearthbyerectingapoleperpendicularlyontheSquare,sothatitreachesthecloudThelengthofthepolemeasuredwiththestandardmeasuringrod,combinedwiththespecificationofthepositionofthefootofthepole,suppliesuswithacompleteplacespecificationOnthebasisofthisillustration,weareabletoseethemannerinwhicharefinementoftheconceptionofpositionhasbeendeveloped(a)Weimaginetherigidbody,towhichtheplacespecificationisreferred,supplementedinsuchamannerthattheobjectwhosepositionwerequireisreachedbythecompletedrigidbody(b)Inlocatingthepositionoftheobject,wemakeuseofanumber(herethelengthofthepolemeasuredwiththemeasuringrod)insteadofdesignatedpointsofreference(c)WespeakoftheheightofthecloudevenwhenthepolewhichreachesthecloudhasnotbeenerectedBymeansofopticalobservationsofthecloudfromdifferentpositionsontheground,andtakingintoaccountthepropertiesofthepropagationoflight,wedeterminethelengthofthepoleweshouldhaverequiredinordertoreachthecloudFromthisconsiderationweseethatitwillbeadvantageousif,inthedescriptionofposition,itshouldbepossiblebymeansofnumericalmeasurestomakeourselvesindependentoftheexistenceofmarkedpositions(possessingnames)ontherigidbodyofreferenceInthephysicsofmeasurementthisisattainedbytheapplicationoftheCartesiansystemofcoordinatesThisconsistsofthreeplanesurfacesperpendiculartoeachotherandrigidlyattachedtoarigidbodyReferredtoasystemofcoordinates,thesceneofanyeventwillbedetermined(forthemainpart)bythespecificationofthelengthsofthethreeperpendicularsorcoordinates(x,y,z)whichcanbedroppedfromthesceneoftheeventtothosethreeplanesurfacesThelengthsoftheseRelativity:TheSpecialandGeneralTheorythreeperpendicularscanbedeterminedbyaseriesofmanipulationswithrigidmeasuringrodsperformedaccordingtotherulesandmethodslaiddownbyEuclideangeometryInpractice,therigidsurfaceswhichconstitutethesystemofcoordinatesaregenerallynotavailablefurthermore,themagnitudesofthecoordinatesarenotactuallydeterminedbyconstructionswithrigidrods,butbyindirectmeansIftheresultsofphysicsandastronomyaretomaintaintheirclearness,thephysicalmeaningofspecificationsofpositionmustalwaysbesoughtinaccordancewiththeaboveconsiderations)Wethusobtainthefollowingresult:EverydescriptionofeventsinspaceinvolvestheuseofarigidbodytowhichsucheventshavetobereferredTheresultingrelationshiptakesforgrantedthatthelawsofEuclideangeometryholdfor"distances"the"distance"beingrepresentedphysicallybymeansoftheconventionoftwomarksonarigidbodyNext:SpaceandTimeinClassicalMechanicsNotes)HerewehaveassumedthatthereisnothingleftoveriethatthemeasurementgivesawholenumberThisdifficultyisgotoverbytheuseofdividedmeasuringrods,theintroductionofwhichdoesnotdemandanyfundamentallynewmethodAEinsteinused"PotsdamerPlatz,Berlin"intheoriginaltextIntheauthorisedtranslationthiswassupplementedwith"TranfalgarSquare,London"Wehavechangedthisto"TimesSquare,NewYork",asthisisthemostwellknownidentifiablelocationtoEnglishspeakersinthepresentdayNotebythejanitor)Itisnotnecessaryheretoinvestigatefurtherthesignificanceoftheexpression"coincidenceinspace"Thisconceptionissufficientlyobvioustoensurethatdifferencesofopinionarescarcelylikelytoariseastoitsapplicabilityinpractice)Arefinementandmodificationoftheseviewsdoesnotbecomenecessaryuntilwecometodealwiththegeneraltheoryofrelativity,treatedinthesecondpartofthisbookRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativitySpaceandTimeinClassicalMechanicsThepurposeofmechanicsistodescribehowbodieschangetheirpositioninspacewith"time"IshouldloadmyconsciencewithgravesinsagainstthesacredspiritofluciditywereItoformulatetheaimsofmechanicsinthisway,withoutseriousreflectionanddetailedexplanationsLetusproceedtodisclosethesesinsItisnotclearwhatistobeunderstoodhereby"position"and"space"Istandatthewindowofarailwaycarriagewhichistravellinguniformly,anddropastoneontheembankment,withoutthrowingitThen,disregardingtheinfluenceoftheairresistance,IseethestonedescendinastraightlineApedestrianwhoobservesthemisdeedfromthefootpathnoticesthatthestonefallstoearthinaparaboliccurveInowask:Dothe"positions"traversedbythestonelie"inreality"onastraightlineoronaparabolaMoreover,whatismeantherebymotion"inspace"FromtheconsiderationsoftheprevioussectiontheanswerisselfevidentInthefirstplaceweentirelyshunthevagueword"space,"ofwhich,wemusthonestlyacknowledge,wecannotformtheslightestconception,andwereplaceitby"motionrelativetoapracticallyrigidbodyofreference"Thepositionsrelativetothebodyofreference(railwaycarriageorembankment)havealreadybeendefinedindetailintheprecedingsectionIfinsteadof"bodyofreference"weinsert"systemofcoordinates,"whichisausefulideaformathematicaldescription,weareinapositiontosay:Thestonetraversesastraightlinerelativetoasystemofcoordinatesrigidlyattachedtothecarriage,butrelativetoasystemofcoordinatesrigidlyattachedtotheground(embankment)itdescribesaparabolaWiththeaidofthisexampleitisclearlyseenthatthereisnosuchthingasanindependentlyexistingtrajectory(lit"pathcurve")),butonlyatrajectoryrelativetoaparticularbodyofreferenceInordertohaveacompletedescriptionofthemotion,wemustspecifyhowthebodyaltersitspositionwithtimeieforeverypointonthetrajectoryitmustbestatedatwhattimethebodyissituatedthereThesedatamustbesupplementedbysuchadefinitionoftimethat,invirtueofthisdefinition,thesetimevaluescanberegardedessentiallyasmagnitudes(resultsofmeasurements)capableofobservationIfwetakeourstandonthegroundofclassicalmechanics,wecansatisfythisrequirementforourillustrationinthefollowingmannerWeimaginetwoclocksofidenticalconstructionthemanattherailwaycarriagewindowisholdingoneofthem,andthemanonthefootpaththeotherEachoftheobserversdeterminesthepositiononhisownreferencebodyoccupiedbythestoneateachtickoftheclockheisholdinginhishandInthisconnectionwehavenottakenaccountoftheinaccuracyinvolvedbythefinitenessofthevelocityofpropagationoflightWiththisandwithaseconddifficultyprevailinghereweshallhavetodealindetaillaterNext:TheGalileanSystemofCoordinatesRelativity:TheSpecialandGeneralTheoryNotes)Thatis,acurvealongwhichthebodymovesRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityTheGalileianSystemofCoordinatesAsiswellknown,thefundamentallawofthemechanicsofGalileiNewton,whichisknownasthelawofinertia,canbestatedthus:AbodyremovedsufficientlyfarfromotherbodiescontinuesinastateofrestorofuniformmotioninastraightlineThislawnotonlysayssomethingaboutthemotionofthebodies,butitalsoindicatesthereferencebodiesorsystemsofcoordinates,permissibleinmechanics,whichcanbeusedinmechanicaldescriptionThevisiblefixedstarsarebodiesforwhichthelawofinertiacertainlyholdstoahighdegreeofapproximationNowifweuseasystemofcoordinateswhichisrigidlyattachedtotheear

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