狭义相对论与时空观

4.1Galilean-NewtonianRelativity4.2*TheMichelson-MorleyExperiment4.3PostulatesoftheSpecialTheoryRelativity4.4Simultaneity4.5TimeDilationandtheTwinParadox4.6LengthContraction4.7Four-DimensionalSpace-Time4.8GalileanandLorentzTransformations4.9RelativisticMomentumandMass4.10TheUltimateSpeed4.11EnergyandMass;E=mc24.12*DopplerShiftforLight,狭义相对论与时空观,SpecialTheoryofRelativity,Forinertialreferenceframes.,GeneralTheoryofRelativity,Fornon-inertialreferenceframes.,(1916),AlbertEinstein(18791955),1921:Nobelprize,(1905),QuantumofLight,(1905),爱因斯坦的哲学观念：自然界应当是和谐而简单的.理论特色：出于简单而归于深奥.,4.1Galilean-NewtonianRelativity,IntwoinertialframesAandB,whichrelativevelocityis,InertialframeisoneinwhichNewtonslawhold,Theparticlesvelocityis,Theaccelerationis,AccordingtoNewtonssecondlaw,经典力学的相对性原理,Observersindifferentinertialframedagreeonthenetforceactingonanobject.,Newtonssecondlaw,Galilean-NewtonianRelativitytoMechanics,Galilean-NewtonianRelativitytoMechanics:thatthebasiclawsofphysicsarethesameinallinertialreferenceframes.,经典力学的相对性原理:对于任何惯性参照系,牛顿力学的规律都具有相同的形式.,Allinertialreferenceframesareequivalentforthedescriptionofmechanicalphenomena.,伽利略变换,经典力学认为1）空间的量度是绝对的,与参考系无关；2）时间的量度也是绝对的,与参考系无关.,TheSpacetimeCoordinatesofAnEvent(事件):(x,y,z,t),Four-DimensionalSpace-Time,在两相互作匀速直线运动的惯性系中，牛顿运动定律具有相同的形式.,伽利略变换,相对于不同的参考系,长度和时间的测量结果是一样的吗?,绝对时空概念：时间和空间的量度和参考系无关,长度和时间的测量是绝对的.,二经典力学的绝对时空观,牛顿力学的相对性原理，在宏观、低速的范围内，是与实验结果相一致的.,实践已证明,绝对时空观是不正确的.,对于不同的惯性系,电磁现象基本规律的形式是一样吗？,真空中的光速,对于两个不同的惯性参考系,光速满足伽利略变换吗？,结果:观察者先看到投出后的球，后看到投出前的球.,试计算球被投出前后的瞬间，球所发出的光波达到观察者所需要的时间.(根据伽利略变换),900多年前（公元1054年5月）一次著名的超新星爆发，这次爆发的残骸形成了著名的金牛星座的蟹状星云。北宋天文学家记载从公元1054年1056年均能用肉眼观察,特别是开始的23天,白天也能看见.,物质飞散速度,当一颗恒星在发生超新星爆发时,它的外围物质向四面八方飞散,即有些抛射物向着地球运动,现研究超新星爆发过程中光线传播引起的疑问.,实际持续时间约为22个月,这怎么解释?,理论计算观察到超新性爆发的强光的时间持续约,A点光线到达地球所需时间,B点光线到达地球所需时间,4.2TheMichelson-MorleyExperiment,MichelsonsInterferometer,迈克尔孙莫雷实验,为了测量地球相对于“以太”的运动,1881年迈克尔孙用他自制的干涉仪进行测量,没有结果.1887年他与莫雷以更高的精度重新做了此类实验,仍得到零结果,即未观测到地球相对“以太”的运动.,MichelsonsInterferometer,IfM2ismovedby,thenandthefringepatternisshiftedbyonefringe,设“以太”参考系为S系，实验室为系,（从系看）,人们为维护“以太”观念作了种种努力，提出了各种理论，但这些理论或与天文观察，或与其它的实验相矛盾，最后均以失败告终.,仪器可测量精度,实验结果未观察到地球相对于“以太”的运动.,MichelsonsInterferometer,MichelsonsInterferometer46”,MichelsonsInterferometer46”,1.TheRelativityPostulate:,4.3PostulatesoftheSpecialTheoryRelativity,Thelawsofphysicsarethesameforminallinertialreferenceframes.Noframeisperfected.,2.ConstancyoftheSpeedofLightPostulate:,Lightpropagatesthroughemptyspacewithadefinitespeedcindependentofthespeedofthesourceorobserver.,TheUltimateSpeed:,一狭义相对论的基本原理,1）爱因斯坦相对性原理：物理定律在所有的惯性系中都具有相同的表达形式.,2）光速不变原理：真空中的光速是常量，它与光源或观察者的运动无关，即不依赖于惯性系的选择.,关键概念：相对性和不变性.,相对性原理是自然界的普遍规律.,所有的惯性参考系都是等价的.,伽利略变换与狭义相对论的基本原理不符.,TheRelativityofSimultaneity,4.4Simultaneity,事件1:车厢后壁接收器接收到光信号.事件2:车厢前壁接收器接收到光信号.,和光速不变紧密联系在一起的是：在某一惯性系中同时发生的两个事件，在相对于此惯性系运动的另一惯性系中观察，并不一定是同时发生的.,TheRelativityofSimultaneity,(Simultaneity),InS:,InS:,ACloserLookatSimultaneity(2),TheRelativityofTheTimeInterval,4.5TimeDilationandtheTwinParadox,运动的钟走得慢,TheRelativityoftheTimeInterval,(时间的延缓),ProperTimeInterval(固有时间),Thepropertimeisthetimeintervalbetweentwoeventsoccuratthesamelocationinaninertialreferenceframe.,(propertime),TimeDilation(时间延缓),Clocksmovingrelativetoanobserveraremeasuredbythatobservertorunmoreslowly(ascomparedtoclocksatrest),(Lorentzfactor),(speedparameter),TimeDilation(时间延缓),TheLorentzFactor,Thespeedparameter,TheTestsofTimeDilation,1.MicroscopicClocks,Thelifetimeofmuons()intherestframeis:,Whenthemuonsaremovingatspeedv=0.9994c:,2.MacroscopicClocks,TheTimeDilation(2),Inatravelingboxcar,awell-equippedhobofiresalaserpulsefromthefrontoftheboxcartoitsrear.Isourmeasurementofthespeedofthepulsegreaterthan,lessthan,orthesameasthatmeasurementbythehobo?(b)Ishismeasurementoftheflighttimeofthepulseapropertime?(c)Arehismeasurementandourmeasurementoftheflighttimerelatedby?,Solution:,CP.1(H.p.928),(a)Same(Bythespeedofpostulate).,(b)no.,Thepropertimeisthetimeintervalbetweentwoeventsoccuratthesamelocationinaninertialreferenceframe.,(c)no.,A,B,YourstarshippassesEarthwitharelativespeedof0.9990c.Aftertraveling10.0y(yourtime),youstopatlookoutpostLP13,turn,andthentravelbacktoEarthwiththesamerelativespeed.Thetripbacktakesanother10.0y(yourtime).HowlongdoestheroundtriptakeaccordingtomeasurementsmadeonEarth?(Neglectanyeffectsduetotheaccelerationsinvolvedwithstopping,turning,andgettingbackuptospeed.),Solution:,Ex.2(H.p.928),Event1:thestartofthetripatEarthEvent2:theendofthetripatLP13.,t1=0,t1=0,Inyourframe:,InEarthframe:,InEarthframe:,E,P,AstudentmustcompleteatestintheteachersframeofreferenceS.Thestudentputsonhisrocketskatesandsoonismovingataconstantspeedof0.75crelativitytotheteacher.When1h(onehour)haspassedontheteachersclock,howmuchtimehaspassedonaclockthatmoveswiththestudent,asmeasuredbytheteacher?,Solution:,Ex.3,ForastudentrestsintheteachersframeS:,ForamovingclockwiththestudentinframeS:,t1=0,t1=0,TheTwinsParadox(343”),Sally,Sally,TheProperLength(RestLength),4.6LengthContraction,TheproperlengthL0oftheplatformmeasuredbySam:ThetrainmovesthroughthelengthL0inatime:,ForSally,LengthLoftheplatform:,Sally,LengthContraction(长度收缩),(ContractedLength),Therelativemotioncausesalengthcontraction!,Inthefigure,Sally(atpointA)andSamsspaceship(ofproperLengthL0=230m)passeachotherwithconstantrelativespeedv.Sallymeasuresatimeintervalof3.57sfortheshiptopassher.Intermsofc,whatistherelativespeedvbetweenSallyandtheship?,Solution:,Ex.4(H.p.931),InSallysframe:,InSamsframe:L0,Therelativespeed:,TheTestsofTimeDilation,1.MicroscopicClocks,Thelifetimeofmuons()intherestframeis:,Whenthemuonsaremovingatspeedv=0.9994c:,2.MacroscopicClocks,AstudentmustcompleteatestintheteachersframeofreferenceS.Thestudentputsonhisrocketskatesandsoonismovingataconstantspeedof0.75crelativitytotheteacher.When1h(onehour)haspassedontheteachersclock,howmuchtimehaspassedonaclockthatmoveswiththestudent,asmeasuredbytheteacher?,Solution:,Ex.,ForastudentrestsintheteachersframeS:,ForamovingclockwiththestudentinframeS:,t1=0,t1=0,(a)C1tt,Afriendofyourtravelsbyyouinherfastsportscarataspeedof0.660c.Itismeasuredinyourframetobe4.80mlongand1.25mhigh.(a)Whatwillbeitslengthandheightatrest?(b)Howmanysecondswouldyousayelapsedonyourfriendswatchwhen20.0spassedonyou?(c)Howfastdidyouappeartobetravelingaccordingtoyourfriend?(d)Howmanysecondswouldshesayelapsedonyourwatchwhenshesaw20.0spassonher?,Solution:,10(p.758),Afriendofyourtravelsbyyouinherfastsportscarataspeedof0.660c.Itismeasuredinyourframetobe4.80mlongand1.25mhigh.(a)Whatwillbeitslengthandheightatrest?(b)Howmanysecondswouldyousayelapsedonyourfriendswatchwhen20.0spassedonyou?(c)Howfastdidyouappeartobetravelingaccordingtoyourfriend?(d)Howmanysecondswouldshesayelapsedonyourwatchwhenshesaw20.0spassonher?,Solution:,10(p.758),狭义相对论的时空观1）两个事件在不同的惯性系看来，它们的空间关系是相对的，时间关系也是相对的，只有将空间和时间联系在一起才有意义.2）时空不互相独立，而是不可分割的整体.3）光速C是建立不同惯性系间时空变换的纽带.,3）时，.,1）时间延缓是一种相对效应.,2）时间的流逝不是绝对的，运动将改变时间的进程.（例如新陈代谢、放射性的衰变、寿命等.）,TheSpacetimeCoordinatesofAnEvent:(x,y,z,t),4.7Four-DimensionalSpace-Time,x=3.7m,y=1.2m,z=0m,t=34.5s,TheGalileanTransformationEquations,4.8GalileanandLorentzTransformation,y=y,z=z(Approximatelyvalidatlowspeed),TheLorentzTransformationEquations,(validatallphysicallypossiblespeed),TheGalileanTransformationforPairofEvents,LetlabelEvent1forx1,t1andEvent2forx2,t2,then,TheLorentzTransformationforPairofEvents,TheLorentzTransformation(130”),Foreachsituation,ifwechoosetheblueframetobestationary,thenisvintheequationsofTable38-2apositiveornegativequantity?,Solution:,CP3.(p.933),(a)positive,(b)negative,(c)positive,Table38-2,Simultaneity,ConsequencesoftheLorentzTransformationEquations,IftwoeventsoccuratdifferenceplacesinS:,andtheeventsaresimultaneousinS:,(simultaneousinS),InS：,(notsimultaneousinS),Simultaneity,ConsequencesoftheLorentzTransformationEquations,IftwoeventsoccuratdifferenceplacesinS:,andtheeventsaresimultaneousinS:,InS：,TimeDilation,InS:,TheGalileanTransformationforPairofEvents,LetlabelEvent1forx1,t1andEvent2forx2,t2,then,TheLorentzTransformationforPairofEvents,LengthConstantinGalileanTransformation,Ifweput,Therodsendpointsaremeasuredsimultaneously.,LengthContraction,Ifweput,Therodsendpointsaremeasuredsimultaneously.,Astheshipfollowsastraight-linecoursefirstpasttheplanetandthenpastthemoon,itdetectsahigh-energymicrowaveburstattheReptulianmoonbaseandthen,1.10slater,anexplosionattheEarthoutpost,whichis4.00108mfromtheReptilianbaseasmeasuredfromtheshipsreferenceframe.TheReptulianshaveobviouslyattackedtheEarthoutpost,sothestarshipbeginstoprepareforaconfrontationwiththem.,Solution:,SP4.(p.935),InSframe:,Earthoutpost,(a)Thespeedoftheshiprelativetotheplanetanditsmoonis0.980c.Whatarethedistanceandtimeintervalbetweentheburstandtheexplosionasmeasuredintheplanet-mooninertialframe?,Solution:,SP4.(p.935),InSframe:,InSframe:,Solution:,SP4.(p.935),(b)Whatisthemeaningoftheminussighinthevaluefor?,InSframe:,InSframe:,(c)Doestheburstcausetheexplosion,orviceversa?,InSframe:,Impossible!,Theburstdosentcausetheexplosion,theyareunrelatedevents!,讨论：1)在某一惯性系中的同步钟，在另一相对其运动的惯性系中是否是同步的?2)两事件发生的时序与因果律,即在系中观测，事件1有可能比事件2先发生、同时发生、或后发生，时序有可能倒置。,与因果律是否矛盾？,有因果关联的事件时序不变，无因果关联的事件才可能发生时序变化。,Solution:,IntheoldWest,amarshalridingonatraintraveling50m/sseesaduelbetweentwomenstandingontheEarth50mapartparalleltothetrain.Themarshalsinstrumentsindicatethatinhisreferenceframethetwomenfiredsimultaneously,(a)Whichofthetwomen,thefirstonethetrainpasses(A)orthesecondone(B)shouldbearrestedforfiringthefirstshot?Thatis,inthegunfightersframeofreference,whofiredfirst?(b)Howmuchearlierdidhefire?(c)Whowasstruckfirst?,22(p.759),Solution:,IntheoldWest,amarshalridingonatraintraveling50m/sseesaduelbetweentwomenstandingontheEarth50mapartparalleltothetrain.Themarshalsinstrumentsindicatethatinhisreferenceframethetwomenfiredsimultaneously,(a)Whichofthetwomen,thefirstonethetrainpasses(A)orthesecondone(B)shouldbearrestedforfiringthefirstshot?Thatis,inthegunfightersframeofreference,whofiredfirst?(b)Howmuchearlierdidhefire?(c)Whowasstruckfirst?,22(p.759),TheGalileanVelocityTransformation,TheLorentzVelocityTransformation,TheLorentzVelocityTransformation,TheLorentzVelocityTransformation(40),4.9RelativisticMomentumandMass,ClassicalMomentum,(lowspeed),牛顿定律与光速极限的矛盾,物体在恒力作用下的运动,经典力学中物体的质量与运动无关,ClassicalMomentum,(lowspeed),RelativityMomentum,RelationofMassandVelocity,4.10TheUltimateSpeed,TheUltimateSpeed,Noentitythatcarriesenergyorinformationcanexceedthelimitc.,Testingthespeedoflightpostulate,Neutralpion:v=0.99975c,Newtons2ndLawinRelativity,4.11EnergyandMass;E=mc2,TheRelativisticKineticEnergy,Foraparticle,Usingthework-energytheorem,TheRelativisticKineticEnergy,TheRelativisticKineticEnergy,(classicalkineticenergy),(Relativistickineticenergy),TheRelativisticKineticEnergy,MassEnergy(RestEnergy),TotalEnergy,MomentumandKineticEnergy,质能关系预言：物质的质量就是能量的一种储藏.,电子的静质量,电子的静能,质子的静能,相对论质能关系,1千克的物体所包含的静能,1千克汽油的燃烧值为焦耳.,静能：物体静止时所具有的能量.,质子的静质量,质能关系预言：物质的质量就是能量的一种储藏。,相对论能量和质量守恒是一个统一的物理规律。,1千克的物体所包含的静能,1千克汽油的燃烧值为焦耳.,例：,现有100座楼，每楼200套房，每套房用电功率10000W，总功率，每天用电10小时，年耗电量，可用约33年。,反应质量亏损,释放能量,1kg核燃料释放能量,锂原子的核反应,两粒子所具有的总动能,两粒子质量比静质量增加,惯性质量的增加和能量的增加相联系，质量的大小应标志着能量的大小，这是相对论的又一极其重要的推论.,相对论的质能关系为开创原子能时代提供了理论基础,这是一个具有划时代的意义的理论公式.,四质能公式在原子核裂变和聚变中的应用,质量亏损,原子质量单位,放出的能量,1g铀235的原子裂变所释放的能量,1核裂变,我国于1958年建成的首座重水反应堆,2轻核聚变,释放能量,质量亏损,轻核聚变条件温度要达到时，使具有的动能，足以克服两之间的库仑排斥力.,例1设一质子以速度运动.求其总能量、动能和动量.,解质子的静能,也可如此计算,例2已知一个氚核和一个氘核可聚变成一氦核,并产生一个中子,试问这个核聚变中有多少能量被释放出来.,解核聚变反应式,氘核和氚核聚变为氦核的过程中，静能量减少了,Energy,TheDopplerEffectforLight,4.12DopplerShiftforLight,(sourceanddetectorseparation),Low-SpeedDopplerEffect,(sourceanddetectorseparation),(vistherelativevelocitybetweensourceanddetector),AstronomicalDopplerEffect,-correspondingtomotionawayfromus+correspondingtomotiontowardus,radialspeedoflightsource,vc,DopplerShift,RedShift:,BlueShift:,f0properfrequency,correspondingtomotionawayfromuscorrespondingtomotiontowardus,TransverseDopplerEffect,T0properperiod,ThefigureshowscurvesofintensityversuswavelengthforlightreachingusfrominterstellargasontwooppositesidesofgalaxyM87.Onecurvepeaksat499.8nm;Theotherat501.6nm.Thegasorbitsthecoreofthegalaxyataradiusr=100light-year,apparentlymovingtowardusononesideofthecoreandmovingawayfromusontheoppositeside.(a)Whichcurvecorrespondstothegasmovingtowardus?WWhatisthevofthegastous?,Solution:,SP5.(p.939),501.6nm:correspondingtomotionawayfromus499.8nm:correspondingtomotiontowardus,Properwavelength:,Thespeedofthegas:,TheDopplershift:,Aspaceshipofrestlength130mracespastatimingstationataspeedof0.740c.(a)Whatisthelengthofthespaceshipasmeasuredbythetimingstation?(b)Whattimeintervalwillthestationclockrecordbetweenthepassageofthefrontandbackendsoftheship?,Solution:,11P.(p.949),(a)Therestlengthofthespaceship:L0=130manditslengthLasmeasuredbythetimingstationLTherefore,L=87.4m.(b)Thetimeintervalforthepassageofthespaceshipis,(a)Isthespatialseparationxbetweenthefiringoftheprotonanditsimpactapositiveornegativequantity?(b)Isthetemporalseparationtbetweenthoseeventsapositiveornegativequantity?,Solution:,Q.5(p.948),(a)negative,(b)positive,Fig.ashowstwoclocksinstationaryframeS(theyaresynchronizedinthatframe)andoneclockinmovingframeS.ClocksC1andC1readzerowhentheypasseachother.WhenclocksC1andC2passeachother,(a)Whichclockhasthesmallerreading?and(b)whichclockmeasuresapropertime?,Solution:,Q.2(p.947),(b)C1,t1=0,t1=0,(a)C1t1t2,Solution:,(a)C1:t1t2,(b)C1,Fig.bshowstwoclocksinstationaryframeS(theyaresynchronizedinthatframe)andoneclockinmovingframeS.ClocksC1andC1readzerowhentheypasseachother.WhenclocksC1andC2passeachother,(a)Whichclockhasthesmallerreading?and(b)whichclockmeasuresapropertime?,Q.3(p.947),Quasarsarethoughttobethenucleiofactiongalaxiesintheearlystagesoftheirformation.Atypicalquasarradiatesenergyattherateof1041W.Atwhatrateisthemassofthisquasarbeingreducedtosupplythisenergy?,Solution:,37P.(p.950),SincetherestenergyE0andthemassmofthequasararerelatedbyE0=mc2,theratePofenergyradiationandtherateofmasslossarerelatedbyP=dE0/dt=(dm/dt)c2.Thus,Sinceasolarmassis2.01030kgandayearis3.156107s,Showthatwhenthekineticenergyofaparticleequalsitsrestenergy,thespeedoftheparticleisabout0.866c,Solution:,35(p.759),Whatisthemomentumofa750-MeVproton(thatis,itskineticenergyis750MeV)?,Solution:,39(p.759),Twoidenticalparticlesofrestmassmapproacheachotheratequalandoppositespeeds,v.Thecollisioniscompletelyinelasticandresultsinasingleparticleatrest.Whatistherestmassofthenewparticle?Howmuchenergywaslostinthecollision?Howmuchkineticenergyislostinthiscollision?,Solution:,43(p.760),(a)Whatisthespeedofanelectronwhosekineticenergyis10,000timesitsrestenergy?SuchspeedsarereachedintheStanfordLinearAccelerator,SLAC.(b)Iftheelectronstravelinthelabthroughatube3.0kmlong(asatSIAC),howlongisthistubeintheelectronsreferenceframe?,Solution:,65(p.761),Afriendofyourtravelsbyyouinherfastsportscarataspeedof0.660c.Itismeasu