PHYS-3301 Lecture 5. Chapter 2. Announcement. Sep. 12, Special Relativity. What about y and z coordinates? (x - direction of motion)

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1 Announemen Course webpage hp:// Tebook PHYS-33 Leure 5 HW (due 9/4) Chaper, 6, 36, 4, 45, 5, 5, 55, 58 Sep., 7 Chaper Speial Relaiiy. Basi Ideas. Consequenes of Einsein s Posulaes 3. The Lorenz Transformaion Equaions 4. The Twin Parado 5. The Doppler Effes 6. Veloiy Transformaion 7. Momenum Energy 8. General Relaiiy a s Look a Cosmology 9. The Ligh Barrier. The 4 h Dimension Wha abou y and z oordinaes? ( - direion of moion)

2 Doppler Effe Parallel o he Direion of Relaie moion Orhogonal o he Direion of Relaie moion Relaiisi Dynamis Epressions for (oal) Energy and Momenum of a parile of mass m, moing a eloiy u Ouline: Relaiisi Momenum Relaiisi Kinei Energy Toal Energy Momenum and Energy in Relaiisi Mehanis General Theory of Relaiiy Ne Week Quanum Physis

3 E INTERNAL ENERGY E INTERNAL m Kinei Energy KE E TOTAL ENERGY E p (m ) u u

4 u Is here Absolue Causaliy? Migh ause preede effe in one referene frame bu effe preede ause in differen referene frame(s)? e.g. an someone see you firs die, and hen see you ge born? Is here Absolue Causaliy? Le s assume ha he order of eens is hanged in some referene frame S Migh ause preede effe in one referene frame bu effe preede ause in differen referene frame(s)? e.g. an someone see you firs die, and hen see you ge born? Is ha Possible? and are he ime inerals beween he same wo eens obsered in S and S, respeiely

5 Le s assume ha he order of eens is hanged in some referene frame S Is ha Possible? and are he ime inerals beween he same wo eens obsered in S and S, respeiely Using Lorenz ransformaions. if hen Using Lorenz ransformaions. if hen Using Lorenz ransformaions. if hen Impossible??

6 Is here Absolue Causaliy? YES Migh ause preede effe in one referene frame bu effe preede ause in differen referene frame(s)? NO Relaiisi Dynamis Some Eamples e.g. an someone see you firs die, and hen see you ge born? NO s. Wha is he momenum of an eleron wih K m? s. Wha is he momenum of an eleron wih K m? 4 E p m E m K p m m 4m m 3m. How fas is a proon raeling if is kinei energy is /3 of is oal energy?. How fas is a proon raeling if is kinei energy is /3 of is oal energy? K E ( m K) E 3m 3 3 m E V / ( ) V 8 3 V / 9 3 ( V )

7 An eleron iniially moing wih momenum pm is passed hrough a rearding poenial differene of V ols whih slows i down; i ends up wih is final momenum being m/. (a) Calulae V in ols. (b) Wha would V hae o be in order o bring he eleron o res? An eleron iniially moing wih momenum pm is passed hrough a rearding poenial differene of V ols whih slows i down; i ends up wih is final momenum being m/. (a) Calulae V in ols. (b) Wha would V hae o be in order o bring he eleron o res? (a) E p m m m m pm: ( ) ( ) ( ) Thus, he rearding poenial differene 5 pm/: E m ( m ) m Δ E E E m.3m.3(.5 ev).5 ev (b) ( ) 5 V.5 V E m E m Δ E m. 5 ev V. 5 V The kinemai energy of a proon is half is inernal energy. (a) Wha is he proon s speed? (b) Wha is is oal energy? () Deermine he poenial differene V hrough whih he proon would hae o be aeleraed o aain his speed. An unsable parile of mass m moing wih eloiy relaie o an inerial lab RF disinegraes ino wo gamma-ray phoons. The firs phoon has energy 8 MeV in he lab RF and raels in he same direion as he iniial parile; he seond phoon has energy 4 MeV and raels in he direion opposie o ha of he firs. Wrie he relaiisi equaions for onseraion of momenum and energy and use he daa gien o find he eloiy and res energy, in MeV, of he unsable parile. phoon phoon before afer

8 An unsable parile of mass m moing wih eloiy relaie o an inerial lab RF disinegraes ino wo gamma-ray phoons. The firs phoon has energy 8 MeV in he lab RF and raels in he same direion as he iniial parile; he seond phoon has energy 4 MeV and raels in he direion opposie o ha of he firs. Wrie he relaiisi equaions for onseraion of momenum and energy and use he daa gien o find he eloiy and res energy, in MeV, of he unsable parile. (a) (b) before m ( ) / m ( ) / phoon afer phoon ph ph m ( ) / m ( ) / E E ph ph E E ph ph E E 8MeV 4MeV 4MeV E E 8MeV 4MeV MeV ph ph ( ph ph ) ( ) ( ) momenum onseraion energy onseraion ( a) 4 () b 3 m E E MeV MeV / /9.3 A moing eleron ollides wih a saionary eleron and an eleron-posiron pair omes ino being as a resul. When all four pariles hae he same eloiy afer he ollision, he kinei energy required for his proess is a minimum. Use a relaiisi alulaion o show ha K min 6m, where m is he eleron mass. p 4 p E m 4E energy onseraion before ( ) ( ) ( ) ( ) E m p E m p E m 4E p 4p In he ener-of-mass RF: p before afer p 4p momenum onseraion 6 ( ) ( ) E Em m 6( E ) 6 ( m ) ( p) afer ( m ) ( ) p ( ) ( E) ( p ) Em ( m ) 6( m ) E 4 m / m 7m E 4m E γ m ( m ) ( ) 3 4 V / 3/ K E m m 6 γ ( 48/49) relaie speed V m K m m 6 General Relaiiy General Relaiiy General relaiiy is he geomeri heory of graiaion published by Alber Einsein in 96. Many prediions of general relaiiy differ signifianly from hose of lassial physis. I is he urren desripion of graiaion in modern physis. I unifies speial relaiiy and Newon s law of uniersal graiaion, and desribes graiy as a geomeri propery of spae and ime. In pariular, he uraure of spae-ime is direly relaed o he fourmomenum (mass-energy and momenum). The relaion is speified by he Einsein s field equaions, a sysem of parial differenial equaions (graduae leel ourse). Eamples of suh differenes inlude graiaional ime dilaion, he graiaional red-shif of ligh, and he graiaional ime delay. General relaiiys prediions hae been onfirmed in all obseraions and eperimens o dae. Howeer, unanswered quesions remain, soluion is he quanum graiy sounds quie ompliae..