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2010-11-08 0人阅读 0 0 0 暂无简介 举报

简介:本文档为《相对论原版pdf》,可适用于高等教育领域

Relativity:TheSpecialandGeneralTheoryAlbertEinsteinAlbertEinsteinRelativityTheSpecialandGeneralTheoryWritten:(thisrevisededition:)Source:Relativity:TheSpecialandGeneralTheory©Publisher:MethuenCoLtdFirstPublished:December,Translated:RobertWLawson(Authorisedtranslation)TranscriptionMarkup:BrianBasgenConvertiontoPDF:SjoerdLangkemperOfflineVersion:EinsteinReferenceArchive(marxistsorg)PrefacePartI:TheSpecialTheoryofRelativityPhysicalMeaningofGeometricalPropositionsTheSystemofCo−ordinatesSpaceandTimeinClassicalMechanicsTheGalileianSystemofCo−ordinatesThePrincipleofRelativity(intheRestrictedSense)TheTheoremoftheAdditionofVelocitiesemployedinClassicalMechanicsTheApparentIncompatabilityoftheLawofPropagationofLightwiththePrincipleofRelativityOntheIdeaofTimeinPhysicsTheRelativityofSimultaneityOntheRelativityoftheConceptionofDistanceTheLorentzTransformationTheBehaviourofMeasuring−RodsandClocksinMotionTheoremoftheAdditionofVelocitiesTheExperimentofFizeauTheHueristicValueoftheTheoryofRelativityGeneralResultsoftheTheoryExpereinceandtheSpecialTheoryofRelativityMinkowski'sFour−dimensialSpacePartII:TheGeneralTheoryofRelativitySpecialandGeneralPrincipleofRelativityTheGravitationalFieldTheEqualityofInertialandGravitationalMassasanArgumentfortheGeneralPostulateofRelativityInWhatRespectsaretheFoundationsofClassicalMechanicsandoftheSpecialTheoryofRelativityUnsatisfactoryRelativity:TheSpecialandGeneralTheoryAFewInferencesfromtheGeneralPrincipleofRelativityBehaviourofClocksandMeasuring−RodsonaRotatingBodyofReferenceEuclideanandnon−EuclideanContinuumGaussianCo−ordinatesTheSpace−TimeContinuumoftheSpeicalTheoryofRelativityConsideredasaEuclideanContinuumTheSpace−TimeContinuumoftheGeneralTheoryofRealtiivtyisNotaEculideanContinuumExactFormulationoftheGeneralPrincipleofRelativityTheSolutionoftheProblemofGravitationontheBasisoftheGeneralPrincipleofRelativityPartIII:ConsiderationsontheUniverseasaWholeCosmologicalDifficultiesofNetwon'sTheoryThePossibilityofa"Finite"andyet"Unbounded"UniverseTheStructureofSpaceAccordingtotheGeneralTheoryofRelativityAppendices:SimpleDerivationoftheLorentzTransformation(supch)Minkowski'sFour−DimensionalSpace("World")(supch)TheExperimentalConfirmationoftheGeneralTheoryofRelativityTheStructureofSpaceAccordingtotheGeneralTheoryofRelativity(supch)RelativityandtheProblemofSpaceNote:ThefifthappendixwasaddedbyEinsteinatthetimeofthefifteenthre−printingofthisbookandasaresultisstillundercopyrightrestrictionssocannotbeaddedwithoutthepermissionofthepublisherEinsteinReferenceArchiveRelativity:TheSpecialandGeneralTheoryAlbertEinsteinRelativity:TheSpecialandGeneralTheoryPreface(December,)Thepresentbookisintended,asfaraspossible,togiveanexactinsightintothetheoryofRelativitytothosereaderswho,fromageneralscientificandphilosophicalpointofview,areinterestedinthetheory,butwhoarenotconversantwiththemathematicalapparatusoftheoreticalphysicsTheworkpresumesastandardofeducationcorrespondingtothatofauniversitymatriculationexamination,and,despitetheshortnessofthebook,afairamountofpatienceandforceofwillonthepartofthereaderTheauthorhassparedhimselfnopainsinhisendeavourtopresentthemainideasinthesimplestandmostintelligibleform,andonthewhole,inthesequenceandconnectioninwhichtheyactuallyoriginatedIntheinterestofclearness,itappearedtomeinevitablethatIshouldrepeatmyselffrequently,withoutpayingtheslightestattentiontotheeleganceofthepresentationIadheredscrupulouslytothepreceptofthatbrillianttheoreticalphysicistLBoltzmann,accordingtowhommattersofeleganceoughttobelefttothetailorandtothecobblerImakenopretenceofhavingwithheldfromthereaderdifficultieswhichareinherenttothesubjectOntheotherhand,Ihavepurposelytreatedtheempiricalphysicalfoundationsofthetheoryina"step−motherly"fashion,sothatreadersunfamiliarwithphysicsmaynotfeellikethewandererwhowasunabletoseetheforestforthetreesMaythebookbringsomeoneafewhappyhoursofsuggestivethought!December,AEINSTEINNext:ThePhysicalMeaningofGeometricalPropositionsRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityPartITheSpecialTheoryofRelativityPhysicalMeaningofGeometricalPropositionsInyourschooldaysmostofyouwhoreadthisbookmadeacquaintancewiththenoblebuildingofEuclid'sgeometry,andyourememberperhapswithmorerespectthanlovethemagnificentstructure,ontheloftystaircaseofwhichyouwerechasedaboutforuncountedhoursbyconscientiousteachersByreasonofourpastexperience,youwouldcertainlyregardeveryonewithdisdainwhoshouldpronounceeventhemostout−of−the−waypropositionofthissciencetobeuntrueButperhapsthisfeelingofproudcertaintywouldleaveyouimmediatelyifsomeoneweretoaskyou:"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(line−interval),independentlyofanychangesinpositiontowhichwemaysubjectthebody,thepropositionsofEuclideangeometrythenresolvethemselvesintopropositionsontheRelativity:TheSpecialandGeneralTheorypossiblerelativepositionofpracticallyrigidbodies)GeometrywhichhasbeensupplementedinthiswayisthentobetreatedasabranchofphysicsWecannowlegitimatelyaskastothe"truth"ofgeometricalpropositionsinterpretedinthisway,sincewearejustifiedinaskingwhetherthesepropositionsaresatisfiedforthoserealthingswehaveassociatedwiththegeometricalideasInlessexacttermswecanexpressthisbysayingthatbythe"truth"ofageometricalpropositioninthissenseweunderstanditsvalidityforaconstructionwithruleandcompassesOfcoursetheconvictionofthe"truth"ofgeometricalpropositionsinthissenseisfoundedexclusivelyonratherincompleteexperienceForthepresentweshallassumethe"truth"ofthegeometricalpropositions,thenatalaterstage(inthegeneraltheoryofrelativity)weshallseethatthis"truth"islimited,andweshallconsidertheextentofitslimitationNext:TheSystemofCo−ordinatesNotes)ItfollowsthatanaturalobjectisassociatedalsowithastraightlineThreepointsA,BandConarigidbodythuslieinastraightlinewhenthepointsAandCbeinggiven,BischosensuchthatthesumofthedistancesABandBCisasshortaspossibleThisincompletesuggestionwillsufficeforthepresentpurposeRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityTheSystemofCo−ordinatesOnthebasisofthephysicalinterpretationofdistancewhichhasbeenindicated,wearealsoinapositiontoestablishthedistancebetweentwopointsonarigidbodybymeansofmeasurementsForthispurposewerequirea"distance"(rodS)whichistobeusedonceandforall,andwhichweemployasastandardmeasureIf,now,AandBaretwopointsonarigidbody,wecanconstructthelinejoiningthemaccordingtotherulesofgeometrythen,startingfromA,wecanmarkoffthedistanceStimeaftertimeuntilwereachBThenumberoftheseoperationsrequiredisthenumericalmeasureofthedistanceABThisisthebasisofallmeasurementoflength)Everydescriptionofthesceneofaneventorofthepositionofanobjectinspaceisbasedonthespecificationofthepointonarigidbody(bodyofreference)withwhichthateventorobjectcoincidesThisappliesnotonlytoscientificdescription,butalsotoeverydaylifeIfIanalysetheplacespecification"TimesSquare,NewYork,"AIarriveatthefollowingresultTheearthistherigidbodytowhichthespecificationofplacerefers"TimesSquare,NewYork,"isawell−definedpoint,towhichanamehasbeenassigned,andwithwhichtheeventcoincidesinspace)Thisprimitivemethodofplacespecificationdealsonlywithplacesonthesurfaceofrigidbodies,andisdependentontheexistenceofpointsonthissurfacewhicharedistinguishablefromeachotherButwecanfreeourselvesfrombothoftheselimitationswithoutalteringthenatureofourspecificationofpositionIf,forinstance,acloudishoveringoverTimesSquare,thenwecandetermineitspositionrelativetothesurfaceoftheearthbyerectingapoleperpendicularlyontheSquare,sothatitreachesthecloudThelengthofthepolemeasuredwiththestandardmeasuring−rod,combinedwiththespecificationofthepositionofthefootofthepole,suppliesuswithacompleteplacespecificationOnthebasisofthisillustration,weareabletoseethemannerinwhicharefinementoftheconceptionofpositionhasbeendeveloped(a)Weimaginetherigidbody,towhichtheplacespecificationisreferred,supplementedinsuchamannerthattheobjectwhosepositionwerequireisreachedbythecompletedrigidbody(b)Inlocatingthepositionoftheobject,wemakeuseofanumber(herethelengthofthepolemeasuredwiththemeasuring−rod)insteadofdesignatedpointsofreference(c)WespeakoftheheightofthecloudevenwhenthepolewhichreachesthecloudhasnotbeenerectedBymeansofopticalobservationsofthecloudfromdifferentpositionsontheground,andtakingintoaccountthepropertiesofthepropagationoflight,wedeterminethelengthofthepoleweshouldhaverequiredinordertoreachthecloudFromthisconsiderationweseethatitwillbeadvantageousif,inthedescriptionofposition,itshouldbepossiblebymeansofnumericalmeasurestomakeourselvesindependentoftheexistenceofmarkedpositions(possessingnames)ontherigidbodyofreferenceInthephysicsofmeasurementthisisattainedbytheapplicationoftheCartesiansystemofco−ordinatesThisconsistsofthreeplanesurfacesperpendiculartoeachotherandrigidlyattachedtoarigidbodyReferredtoasystemofco−ordinates,thesceneofanyeventwillbedetermined(forthemainpart)bythespecificationofthelengthsofthethreeperpendicularsorco−ordinates(x,y,z)whichcanbedroppedfromthesceneoftheeventtothosethreeplanesurfacesThelengthsoftheseRelativity:TheSpecialandGeneralTheorythreeperpendicularscanbedeterminedbyaseriesofmanipulationswithrigidmeasuring−rodsperformedaccordingtotherulesandmethodslaiddownbyEuclideangeometryInpractice,therigidsurfaceswhichconstitutethesystemofco−ordinatesaregenerallynotavailablefurthermore,themagnitudesoftheco−ordinatesarenotactuallydeterminedbyconstructionswithrigidrods,butbyindirectmeansIftheresultsofphysicsandastronomyaretomaintaintheirclearness,thephysicalmeaningofspecificationsofpositionmustalwaysbesoughtinaccordancewiththeaboveconsiderations)Wethusobtainthefollowingresult:EverydescriptionofeventsinspaceinvolvestheuseofarigidbodytowhichsucheventshavetobereferredTheresultingrelationshiptakesforgrantedthatthelawsofEuclideangeometryholdfor"distances"the"distance"beingrepresentedphysicallybymeansoftheconventionoftwomarksonarigidbodyNext:SpaceandTimeinClassicalMechanicsNotes)HerewehaveassumedthatthereisnothingleftoveriethatthemeasurementgivesawholenumberThisdifficultyisgotoverbytheuseofdividedmeasuring−rods,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"Fromtheconsiderationsoftheprevioussectiontheanswerisself−evidentInthefirstplaceweentirelyshunthevagueword"space,"ofwhich,wemusthonestlyacknowledge,wecannotformtheslightestconception,andwereplaceitby"motionrelativetoapracticallyrigidbodyofreference"Thepositionsrelativetothebodyofreference(railwaycarriageorembankment)havealreadybeendefinedindetailintheprecedingsectionIfinsteadof"bodyofreference"weinsert"systemofco−ordinates,"whichisausefulideaformathematicaldescription,weareinapositiontosay:Thestonetraversesastraightlinerelativetoasystemofco−ordinatesrigidlyattachedtothecarriage,butrelativetoasystemofco−ordinatesrigidlyattachedtotheground(embankment)itdescribesaparabolaWiththeaidofthisexampleitisclearlyseenthatthereisnosuchthingasanindependentlyexistingtrajectory(lit"path−curve")),butonlyatrajectoryrelativetoaparticularbodyofreferenceInordertohaveacompletedescriptionofthemotion,wemustspecifyhowthebodyaltersitspositionwithtimeieforeverypointonthetrajectoryitmustbestatedatwhattimethebodyissituatedthereThesedatamustbesupplementedbysuchadefinitionoftimethat,invirtueofthisdefinition,thesetime−valuescanberegardedessentiallyasmagnitudes(resultsofmeasurements)capableofobservationIfwetakeourstandonthegroundofclassicalmechanics,wecansatisfythisrequirementforourillustrationinthefollowingmannerWeimaginetwoclocksofidenticalconstructionthemanattherailway−carriagewindowisholdingoneofthem,andthemanonthefootpaththeotherEachoftheobserversdeterminesthepositiononhisownreference−bodyoccupiedbythestoneateachtickoftheclockheisholdinginhishandInthisconnectionwehavenottakenaccountoftheinaccuracyinvolvedbythefinitenessofthevelocityofpropagationoflightWiththisandwithaseconddifficultyprevailinghereweshallhavetodealindetaillaterNext:TheGalileanSystemofCo−ordinatesRelativity:TheSpecialandGeneralTheoryNotes)Thatis,acurvealongwhichthebodymovesRelativity:TheSpecialandGeneralTheoryRelativity:TheSpecialandGeneralTheoryAlbertEinstein:RelativityPartI:TheSpecialTheoryofRelativityTheGalileianSystemofCo−ordinatesAsiswellknown,thefundamentallawofthemechanicsofGalilei−Newton,whichisknownasthelawofinertia,canbestatedthus:AbodyremovedsufficientlyfarfromotherbodiescontinuesinastateofrestorofuniformmotioninastraightlineThislawnotonlysayssomethingaboutthemotionofthebodies,butitalsoindicatesthereference−bodiesorsystemsofcoordinates,permissibleinmechanics,whichcanbeusedinmechanicaldescriptionThevisiblefixedstarsarebodiesforwhichthelawofinertiacertainlyholdstoahighdegreeofapproximationNowifweuseasystemofco−ordinateswhichisrigidlyattachedtotheear

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