第7章 狭义相对论动力学

7712…7.17.172727.27.27.37.3*1*7.17.1.Fd()/dt:p=mv,F=d(mv)/dtFpvc,mvmvvmm(v)m(v)2mm((vv))ABSΒvrΑ+ΒVr(A+B)ΑΒvΑ+ΒA:v,mvB:m0(A+B)V,M0S’ABA:m0(A+B)Vr′A+B3vr−0B:-v,mvV’,M**MV=mvMV’=m(-v)Mmv+m0*V’=-VMV=mvvMV=mv(-v)v/V=(mv+m0)/mv=1+m0/mv…1*u=vV=VxV2VVvvVV−=−−=′21…2211cvVv−±=c214+”10mmmγ==m0——0221mcvmvγ−0mv——cvmvmmvp0γvmvmvp02201γ=−==——c2vc,1,p=m0vv——098v=0.98c,m=5m0v=0.99c,m=7.09m05.tvmFd)d(rr=tmvtvmFddddrrr+=tdttddaF/m,m=mm=m0*m=m0dm/dt=0ppvFrrrr⊥→⊥d0ptvF⊥→⊥ddmFrr60dd=tmamFr=qBmvR=m1909BuchererqBr+70vEr-7.27.2.?=kE*vprprFEddddd⋅=⋅=⋅=rrrrrrmvvmvmvvvmvprtrFEKddddddddd22++⋅=⋅=⋅=rrmvvmvmvvvmdddd+=+⋅=m201vmm−=mcmvvmvddd22=+821cmcEkdd2=202cmmcEk−=Ek32022041111cmvcmEK=−=)(cv53=21c−5911()202050921cmvmEk==221mv——200cmE=9——02EEmcEk+==*E0=0.511MeV***∑2*∑=+.const20cmEk∑∑,0,0mmkEcm→∆20235200MeV10310104.91026w101010kg107.1170×=∆mEk=92.8109eV,vEmc20511106evEkm0c0.511106ev202cmmcE∴2201vmcEk−=≈∴2cc2-v2=(m0c2/Ek)2c2(0k))(2))((22vccvcvcvc−≈−+=−m/s5)(1220==∴ccmvc)())((11m/s5)(2==−∴cEvck2mv00=→=VMV0MM=222Mcmc→022mMMcmc→=2mMM=22001vM−=002mMM=2c12.20vmm=42222cmpcE+=21cv−0cmpcE+=Ecpm0c2E0cpEm=→=00νhhhEλννhchphE==→=13cpEEcmEkk≈≈→→20)(ν′′pθ)(νp)(νp′′epθννννcos)()(chchchchpe′−′+=2222θ—eeEhcmh+′=+νν2042222E420222cmpcEeee+=)~(~θλθν∆∆14)~(~θλθν∆∆7.37.3vmpmcErr==,2—′′S→S’——)(222222pcEpcE′−′=−2E)(22222zyxpppcE++−c15)(22222zyxtc++−),,,(zyxtEppp2czyxppp,,)()(tt′′′′→uE),,,(),,,(zyxtzyxt′′′′→yypp=′),(xxcuEpp−=′γ2zzpp=′)(xupEE−=′γ16SS’S’S’′′hEνννSuS’0,,00=′=′′−=′==yxpppphEνννRcr′,zyxppppSxpuEpuEEx′−′=′+′=)()(γγ00ννν+−=∴ucucEucuccEuE′+−=′−′=)(γ17ucc+0ννgeneraltheoryofrelativity11218111()()rfrGmfr1()()Gmrfrgr=f()()rgmrfrr=()()ramrfrr=M()()rgmrfG=()()ramrfI=rrga=19IGmm=2ga=ggmGgmIG:gIGImm=20gmI)(rggmG)(rg“21…g“g2223equivalenceprinciple23424rvg(r)25122612“3272RR“28ππR2RπRπ2Pρπρ2PQρπ≠πρ2BCQR∆ABCπ≠29Aπ∆ABC““s)dωP′SSS′P′SP30S’s)dω()srs′−=))d1d2ωscs=d1d2′P′rr′=rsπ2=∆()21rssω′∆∆rsπ2=∆rs′≠′∆π2()21ssc∆=−∆rrgˆ2ω=r311232333SS′SSS()rvSSS′()()rgrv)(rgS′r()rg)(rg34Sv21CCSS´C′)(rgSSC′C′C′S′CC21CCSC′C′S′S’C′S′Sτ′dσ′d35τdσd2d1dtv=′τ´021,d1dtc−=τ´02d11dxv=′σ21c−r12⎞⎜⎛GMmGM220212=⎠⎞⎜⎝⎛−+rGMmmvrGMv22=36rS’S1⎞⎛r022d21dtrcGM⎟⎠⎞⎜⎝⎛−=τrc⎠⎝0dt212GM−⎞⎛0022d21dxrcGM⎠⎞⎜⎝⎛−=σ370dx10212d21dtGM⎠⎞⎜⎝⎛−=τ02rc⎠⎜⎝20212d21dxGM−⎞⎜⎛−=σ02d1dxrc⎠⎜⎝σ338;d21d21tGM⎞⎜⎛−=τ21d21dxGM−⎞⎜⎛=σ;d1d02trc⎠⎜⎝=τ02d1dxrc⎠⎜⎝−=σM12GM0rsM12=src0d=τkg106330×≈=⊕MM2GMm10242==cGMrssr39318mg/10k=ρ“212GM⎞⎛12GM−⎞⎛022d21dtrcGM⎟⎠⎞⎜⎝⎛−=τ022d21dxrcGM⎟⎠⎞⎜⎝⎛−=σrc⎠⎝rc⎠⎝GMr−r40——“31ν2ν1r2r112−∆ννν21212⎥⎤⎢⎡−GM1121=νν12112−⎥⎥⎥⎢⎢⎢=GMrc11−=TT41122⎥⎥⎦⎢⎢⎣−rcG2T2121⎥⎤⎢⎡−GM12ννννν−=∆12112−⎥⎥⎥⎢⎢⎢−=GMrc11νν2122⎥⎥⎦⎢⎢⎣−rcGM⎥⎤⎢⎡−≈∆11GMν12〈〈GM⎥⎦⎢⎣≈1221rrcν2rc621012.2−⊕×−=−≈∆RGMν“21⊕Rcν42112610981′′±175.′′191952904.061.161.098.1′′±±191952943