C Quantum Theory 3%e General Relativity Gru Adde OEot Quaffing Quantum

Transcription

od,1-"Physicalcosmology.mm"""physics CspecialErelativitygeneralrelativityquantumtheory, Y -79OE-!3%eome--,AddeoEotGru--849k -creatimfannihilationparade -'%IIGMgut! -rangephysics alfermionsLeptonstheoryxnuclearWeak 3h42nuclearStrongEH ?describeto 0 fingHttofEb )interactionaccumulates !,EarlyHWE(It.-.i,8)Jianyin?Gravity!!universe.

②UnitsC\Natural:3 105reKIs②-I.natural10-27 1.4 10 'tdyn.cm erglkNote4 10-23?:!unitC K-.KB-)versionOomg.am/sz ergergs(unitdyn{II.JfkKBants3 10 Astronomical&)particle physics"km/s10-34ICunit-:I-let:-' '1,6 06 1512.If Jerg.'Notergs-xw.am/g erg-er8Is{3 Xto"1027 cmtik ,,am"-152KcI 3 15 erg an.-"eV"GeV erg"6.3 10-'"toerg-ywsye.geto:Conversion ererg1.6 1024'-eV"" Usefulergt's1.6 10 18.9 10-6I"eV6.3 10 "GeVan-.fmMeV200eV6.3 10I-femtometer2.7KPeak2.4 10-4 ofPlanckeVfuI12"343Tn.(xanK@ -0.08am0.23mm)I( o.8mmD 2.4 10-4eV 3193T@5me'r180GHz3-8 101140GHz380GHzw f"1.4mmrun") mmC- 15km )

②-Planck2.unitGnomfg6.7 10-8 15 6/7 10-813 10-(x"txio13 b- X'Is \Im,b- Ig"XloGeV6.3 1023 ,Get1.6 1024 g. ,,Innaturalsidenoteunit" GeV ,Mpl,ReducedGeVGeVi's4 104 uunitPlanck,,to"-Ipewipe q33-In,7 10-20 15445tpenfx ,-z--2 17 10,1.6 1024 GeVYgey""Relativist:10-39 GeV2 1043 ,,µµ,10-8 39-23 "48- )/('GeVXtom2 10-5nofmy,,GeV8IGn Isets,instead"massMpe ofGn.Mg Zxiocevm

②-3Astronomical.Mo{Lo4 1033 .Me-1033g2x .Unit"8 10 .So an Rot,6 108 So an p, 6 IAllI parsectoosecondlightI too "parallax3 10xtf " "Itu-r216000 AU1/80/3600All216000 (tooxlightsecondo8000000alyr 3.26Lynmmto{totheM 31thecentertheofto0.78 edgeofGalaxyMpcthe 2.Universe 8-tkpc 2. b-1022cmx1024am3X 14Gpc-4 1028an3 10''103glansanIt216000X"tfxlo antoxglansIn6 1027g# .Iserg6 1027 ,Ro,an'

tly024C]Ito /[ ICEDfaiththeotcxie)-4tfdeJCE )potential.Gns4Th theLlactionthe,nice)&-4,I m-:]ie,]nicest,foie)se,-2,4 CI:tiScotch-,grauextrcmizef dtflckthtfxth &)dt2fortakesmotiontICEMDI equation,Tuesima.equationSS CIheld( Poisson 'sfromTat yNewtonian*Generalof-ItsLC,niceties) ftp.fi/toC8x4 -.fE.ise. , C s )I Elat:# .3 sci E -.L T-U tzmxz-my--. E )toes.o) mic--mat,0/0

eddefines e.g.theX.,Z,ofproductinnerydescribedisspacetime( t do . L)IndbytheanygivenK K2, LtwoVectors% Z .dxndxugyu'gyu: ConventionEinsteinof( dxn , dxu goKMofCurvature t'pgravityenergy yµ4pmpuC at If;!::[:spacetimemomentum-( ,pm Po ) )vector- theE--local- -scalarmP'i2 11512inertialCmuse E,--f !;)p)(' m""restmass)observer )generalbeC'oh'observerthesame)forallobservers.

"tellsspacetimeoiC"tomove)geodesic equationtheminimizesgeodesicAction howmassS intervalspacetimemfdt-!thealong(de pathdsa-gyudxmdxo )- limitSR' S--mfdemf- -defC-Imfdtfdtfmtkm.li)Kia )- mf.dk/-8mdIITYI-- Leg .) (f )3 L' )lxncxl withGuiche-he2L mf-gmdffdf.IT-} md -rinse-,-1FiILIt#12L 3 --.Shivmagnifymagma t d megaEsmaKI l . f -m(-(game) (n-- 2g.quasigaingrain ) gaitto) senior]Had' ],: -EI .2 .Is."e I zaed .de# g.dIIetsmdII--- t 'Yasmin.: I ]

(s."e Id %e 1g.it#.-ismd:I3--smald Izg.io#. gm.aIEoiI-s.e.dfIdEI-q.pdoEIEHere""only,a28*917( .④(tzgdmrealtheis%index-a.gear-dummyare.) III 1 )SI others 97 g. inverseDIETTIPtmetricYasir (- gaapgangawherealland,t-g spaspa-.HII.IET;i i III IIIi--ogeodesicequation- Christoffelsymbol.".ChristoffelSymbolTae: inatevelocityvector i'accelerationVWEE :a' doYdoffsofdat ee UP Taguao eEeg"- ( IItTofuezHasEE--u'Effie :

:ogeodesic equationExamplesa ( Parallelommtransportation)FfsurfaceonC X )ONewtonianvsRelativistic.MotionduetoGravity "Central force"-,two-body problem"Spacetime geodesic

."Otellsmassspacetimee. gyuWhatamdetermines"tensorGyu)EinsteinGmgyu n"howof"energy Rico,ScalarR--gyuRN gmRµ RMµtensor RdranrunIRiemannRamu ( TratensorIIe-III.-tQq )toUd -.RdppuTETEUP

Ii )EnergyTmoToo{ Ty(µ Jpgcomponent-IIIflowStress:8D,Toi(tensorfluidC( Tru Continuity 8 2T's antiTTFuk guw)yLevi ), oIcsuiui,, TnSE(Hatodit)EETI- spacetime )TITI-11 0Ort-oto -un)symmetricTn Tmo:(PgmtUnhIRTIGust pkm )- (hethrough TmNotefcpflowmomentumofdensityenergy-perfect energynTottensormomentum-TfaTf -a-"Again,connection"!o

Action*SCtheforgyu]EinsteinSEH tequationSm qJd4x FgRfd4x LmFgTsImatterLagrangiandensityscalarRicciFgu a #fttqf Egg:*:'kissing-tfRapRyuFgtgoSgRg )me I g[ Rm to -EFF-Ya RgmusesJacobiformula:surface]term.o quo.Rm CH-Ieat Yim-e*AIAISIGIffgRforetrh TG Trunxnany's -Ag )Yzfggmsgru matrixAlgltrlg 8 IfsgaggertKit"--4

ExampleofSmmatterC ] SsnfolkFfLfolkFg(forex ( scalaractionFg(0'-field24,kg forexFg8g"xthx ) ))On 4a -( %gr fSgm- ;0:"[-YaV coli)04Lay-Veon)tuco,'-k9404]Yasu(8in'kTaypaymm -Ya Tm)-Ya74Or of]

③ Review of General theory of relativity key quantity of dynamics: Tat) from ICE) & J CE) * Newtonian theory of gravity eat. of motion: I-ima MDI dt2 {gravitational held equation for the grau. potential otcxie) ( Poisson's equation) 024C I,-4 4Th Gns CI,-4 & I -m 0/0 Equivalently, motion takes to extrcmize the action: tf S [ICED / de Ll the nice, ie] ti S C Tues t faith]-Scotch] f .