11 相对论：第八章 狭义相对论

2000Italian2000ItalianLirotLirotHOMESS':S'Sxxxutyyzztt′=−⎧⎪′=⎪⎨′=⎪⎪′=⎩xxutyyzztt′′=+⎧⎪′=⎪⎨′=⎪⎪′=⎩00ttxx′′====SSSS′′SSHOMEzxyz'x'y'(,,,)(,,,)xyztxyzt′′′′xxyyzzvvuvvvv′⎧=−⎪′=⎨⎪′=⎩xxyyzzvvuvvvv′⎧=+⎪′=⎨⎪′=⎩xxyyzzduaadtaaaa′=−′=′=xxyyzzduaadtaaaa′=+′′=′=xxyyzzaaaaaa′=′=′=zzyyxxaaaaaa′=′=′=aa′=GGHOMEuS||FG||m||aGF′GS′m′a′GFma=GGFma′′′=GG:,Sxxuttt′′=−=:,Sxxuttt′′′′=+=HOMExxtt′Δ=Δ⎧⎨′Δ=Δ⎩1()001cεμ=23HOMExxvvu′=−EinsteinNewtonNewtonEinsteinxyzOO′y′z′x′uS'()xxut′=−S()xxut′′=+(1)(2)kk′=xctxct′′==000,OOtt′′==PPtttt′′kk′PSS''uuSSxxxxxxSSSS''xxxx''1ccβ=vv(1)(2)2()()xxkxutxut′′′=−+2211kkuc′⇒==−22222,11utxxutcxtucuc−−′′==−−211γβ≡−,ucβ≡()2xxutyyzzuttxcγγ′⎧=−⎪′=⎪⎪′=⎨⎪⎛⎞⎪′=−⎜⎟⎪⎝⎠⎩()2xxutyyzzuttxcγγ′′⎧=+⎪′=⎪⎪′=⎨⎪⎛⎞⎪′′=+⎜⎟⎪⎝⎠⎩·2aauS′Sxx′o′o21S0xxx′′′′Δ=−=2()uttxcγ′′=+S2()uttxcγ′′Δ=Δ+Δ0tτ′Δ=ttγ′⇒Δ=Δ0τγτ=τ0()S′P0xΔ≠u0.99c52m82.510s−×0τγτ=0221ucττ=−71.810s−=×=53mLut=Δ10luSS′021Slxx′′′=−21Slxx=−21tt=()xxutγ′=−=()xxutγ′⇒ΔΔ−Δ0=llγ0llγ=l01x′2x′1x2xl“”uS′Sxx′o′oaaabaabbS,baxxxΔ=−0tΔ=S′battt′′′Δ=−2()utxcγ=Δ−Δ2uxcγ=−Δ0≠“”!battt′′′Δ=−2[()()]babauttxxcγ=−−−(0=Sbabavxt=ΔΔS′2()bababauttxcγ′′′Δ=Δ−Δ2(1)utvcγ=Δ−022()()bbaauutxtxccγγ=−−−L0EWvaMSS'S0=2,=0xLtΔΔxx′S′t′Δ2022uLcγ=−2()utxcγ=Δ−Δ8.3xdxvdt′′=′(),xdxvudtγ′=−2(1)xdtuvdtcγ′=−21xxxvuvuvc−′=−dxdtdtdt′=′dxdtdtdt′′=dydydtdt′=′′,dydtdtdt=′2(1)xdtuvdtcγ′=−22211yyxvuvucvc′=−−22211zzxvuvucvc′=−−dzdzdtdt′=′′,dzdtdtdt=′2(1)xdtuvdtcγ′=−yz,yyzz′′==21xxxvuvuvc−′=−22211yyxvuvucvc′=−−22211zzxvuvucvc′=−−21xxxvuvuvc′+=′+22211yyxvuvucvc′=−′+22211zzxvuvucvc′=−′+0.80c0.90cS′Sxv′uS′Sxx′0.80,uc=0.90xvc′=21xxxvuvuvc′+=′+0.900.8010.800.90cc+=+×0.99c=8.41.()dPddvdmFmvmvdtdtdtdt===+GGGGG()ABmm≠222211BAucmmuc+⇒=−2.xyzOO′y′z′x′uAxvu′=−Bxvu′=0Axv=SS′SS''uuSSxxMMOO''S'S'2221Bxuvuc=+222()1BABmummuuc⇒+=+SABMmm=+BBxMumv=ABmm′′=ttABmm≠2221Buvuc=+22211BBvcuvc⎡⎤=−−⎢⎥⎢⎥⎣⎦mB221ABBmmvc=−mAm0mBm0221mmvc=−0vcmm⇒≈2Ãv104m/s10020115.6101mmmβ−−=−≈×−Ãv=0.98c05.03mm=Ãvcm0221mmvc=−Ã8.5∫⋅=rdFEKGG∫⋅=rddtPdGG∫⋅=)(vmdvGG0´v∫⋅=)1(220cv-vmdvGG∫−⋅−−⋅=vvcvvdvmcvvvm0220022011GGGGvcvcmcvvm02220222011−−−=vdvvdv=⋅GG2022201cmcvcm−−=202cmmc−=220KEmcmc=−1.220KEmcmc=−zvc2122221(1)1vcvc−=−−22112vc≈+⋅2012KEmv⇒≈vcvc20221(1)1KEmcvc=−−z0.8vc=2023mc=LargeHadronCollider220KEmcmc=−22011022kKmcEmcE+=[phone]kKEEmcmc−=−20102()EmmcΔ=−20EmcΔ=Δ200Emc=()2Emc=0KEEE=+vc220KmcEmc=+z91016J4.6107Jzm“235”430:8.510~110mm−−Δ××!!v0mvM1122mvmvMV+=GGG0V=2202mcMc=0022221mMmvc==−02mVG0221mmvc=−222240Epcmc=+222202vmmmc⇒−=pmv=20KEEmc=+⇒222202KKEEmcpc+=z00mEpc=⇒=Ehpccν⇒==2Emc=22Ehmccν⇒==hpλ=⇒1/4Mevmoc2=0.5Mev0KEEE=−220mcmc=−20(1)mcγ=−123γ=22419vc⇒−=0.745vc⇒=E3000MevE0=100Mev210-6s030EEγ==0τγτ=,svτ=0.99944vc⇒=41.79910sm⇒=×