相对论Word文档格式.docx
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相对论Word文档格式.docx
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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.DefinitionofSimultaneity
Letustakeasystemofco-ordinatesinwhichtheequationsofNewtonianmechanicsholdgood.2Inordertorenderourpresentationmorepreciseandtodistinguishthissystemofco-ordinatesverballyfromotherswhichwillbeintroducedhereafter,wecallitthe``stationarysystem.'
Ifamaterialpointisatrestrelativelytothissystemofco-ordinates,itspositioncanbedefinedrelativelytheretobytheemploymentofrigidstandardsofmeasurementandthemethodsofEuclideangeometry,andcanbeexpressedinCartesianco-ordinates.
Ifwewishtodescribethemotionofamaterialpoint,wegivethevaluesofitsco-ordinatesasfunctionsofthetime.Nowwemustbearcarefullyinmindthatamathematicaldescriptionofthiskindhasnophysicalmeaningunlesswearequiteclearastowhatweunderstandby``time.'
Wehavetotakeintoaccountthatallourjudgmentsinwhichtimeplaysapartarealwaysjudgmentsofsimultaneousevents.If,forinstance,Isay,``Thattrainarriveshereat7o'
clock,'
Imeansomethinglikethis:
``Thepointingofthesmallhandofmywatchto7andthearrivalofthetrainaresimultaneousevents.'
3
Itmightappearpossibletoovercomeallthedifficultiesattendingthedefinitionof``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,forthelattercannotbedefinedatallunlessweestablishbydefinitionthatthe``time'
requiredbylighttotravelfromAtoBequalsthe``time'
itrequirestotravelfromBtoA.Letarayoflightstartatthe``Atime'
fromAtowardsB,letitatthe``Btime'
bereflectedatBinthedirectionofA,andarriveagainatAatthe``Atime'
.
Inaccordancewithdefinitionthetwoclockssynchronizeif
Weassumethatthisdefinitionofsynchronismisfreefromcontradictions,andpossibleforanynumberofpoints;
andthatthefollowingrelationsareuniversallyvalid:
--
1.IftheclockatBsynchronizeswiththeclockatA,theclockatAsynchronizeswiththeclockatB.
2.IftheclockatAsynchronizeswiththeclockatBandalsowiththeclockatC,theclocksatBandCalsosynchronizewitheachother.
Thuswiththehelpofcertainimaginaryphysicalexperimentswehavesettledwhatistobeunderstoodbysynchronousstationaryclockslocatedatdifferentplaces,andhaveevidentlyobtainedadefinitionof``simultaneous,'
or``synchronous,'
andof``time.'
The``time'
ofaneventisthatwhichisgivensimultaneouslywiththeeventbyastationaryclocklocatedattheplaceoftheevent,thisclockbeingsynchronous,andindeedsynchronousforalltimedeterminations,withaspecifiedstationaryclock.
Inagreementwithexperiencewefurtherassumethequantity
tobeauniversalconstant--thevelocityoflightinemptyspace.
Itisessentialtohavetimedefinedbymeansofstationaryclocksinthestationarysystem,andthetimenowdefinedbeingappropriatetothestationarysystemwecallit``thetimeofthestationarysystem.'
2.OntheRelativityofLengthsandTimes
Thefollowingreflexionsarebasedontheprincipleofrelativityandontheprincipleoftheconstancyofthevelocityoflight.Thesetwoprincipleswedefineasfollows:
1.Thelawsbywhichthestatesofphysicalsystemsundergochangearenotaffected,whetherthesechangesofstatebereferredtotheoneortheotheroftwosystemsofco-ordinatesinuniformtranslatorymotion.
2.Anyrayoflightmovesinthe``stationary'
systemofco-ordinateswiththedeterminedvelocityc,whethertheraybeemittedbyastationaryorbyamovingbody.Hence
wheretimeintervalistobetakeninthesenseofthedefinitionin§
1.
Lettherebegivenastationaryrigidrod;
andletitslengthbelasmeasuredbyameasuring-rodwhichisalsostationary.Wenowimaginetheaxisoftherodlyingalongtheaxisofxofthestationarysystemofco-ordinates,andthatauniformmotionofparalleltranslationwithvelocityvalongtheaxisofxinthedirectionofincreasingxisthenimpartedtotherod.Wenowinquireastothelengthofthemovingrod,andimagineitslengthtobeascertainedbythefollowingtwooperations:
(a)
Theobservermovestogetherwiththegivenmeasuring-rodandtherodtobemeasured,andmeasuresthelengthoftheroddirectlybysuperposingthemeasuring-rod,injustthesamewayasifallthreewereatrest.
(b)
Bymeansofstationaryclockssetupinthestationarysystemandsynchronizinginaccordancewith§
1,theobserverascertainsatwhatpointsofthestationarysystemthetwoendsoftherodtobemeasuredarelocatedatadefinitetime.Thedistancebetweenthesetwopoints,measuredbythemeasuring-rodalreadyemployed,whichinthiscaseisatrest,isalsoalengthwhichmaybedesignated``thelengthoftherod.'
Inaccordancewiththeprincipleofrelativitythelengthtobediscoveredbytheoperation(a)--wewillcallit``thelengthoftherodinthemovingsystem'
--mustbeequaltothelengthlofthestationaryrod.
Thelengthtobediscoveredbytheoperation(b)wewillcall``thelengthofthe(moving)rodinthestationarysystem.'
Thisweshalldetermineonthebasisofourtwoprinciples,andweshallfindthatitdiffersfroml
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