2.3 The Lorentz Transformation Eq.
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1 Announemen Course webage h://highenergy.hys.u.edu/~slee/4/ Tebook PHYS-4 Leure 4 HW (due 9/3 Chaer, 6, 36, 4, 45, 5, 5, 55, 58 Se. 8, 6.3 The Lorenz Transformaion q. We an use γ o wrie our ransformaions. Chaer Seial Relaiiy. Basi Ideas. Consequenes of insein s Posulaes 3. The Lorenz Transformaion quaions 4. The Twin Parado 5. The Doler ffes 6. Veloiy Transformaion 7. Momenum nergy 8. General Relaiiy a s Look a Cosmology 9. The Ligh Barrier. The 4 h Dimension Frame S Frame S 4
2 Proer Time (Δ The ime measured in he frame where all eens our in he same loaion in ha frame: The ime differene from our Lorenz Transformaion would hen be Proer Lengh The lengh measured in a frame where he obje being measured is a res, so ha i doesn maer WHN we measure he end oins. Bu in any MOVING frame, S, he ends mus be esablished SIMULTANOUSLY o obain a meaningful lengh: The lengh differene from our Lorenz Transformaion would hen be In more general form, In more general form, L is measured in he frame where he obje a res Consequene 3: Time Dilaion : he ime differene in he frame in whih he eens our a he same loaion 5 Consequene 3: Lengh Conraion 6 Relaiisi Dynamis Parallel o he Direion of Relaie moion Orhogonal o he Direion of Relaie moion Ouline: Relaiisi Momenum Relaiisi Kinei nergy Toal nergy Momenum and nergy in Relaiisi Mehanis General Theory of Relaiiy Ne Week Quanum Physis
3 m Newon s nd Law: Relaiisi Momenum he momenum of a arile, m is inarian (does no deend on he eloiy F d d m d d m a eressed in erms of 3-eors, inarian under G.Tr. (bu no L.Tr. Relaiisi Kinei nergy Relaiisi form of he nd Law (inrodued by insein: F d γ m d d m d ( where m γm definiion of he momenum in relaiisi mehanis β V / amle: Calulae he momenum of an eleron moing wih a seed of.98. (.98 me 4.9m e.98 By ignoring relaiisi effes, one would ge.98m e Relaiisi Kinei nergy In relaiisi mehanis, he one of energy is more useful han he fore : d K F dl d dl d dl d m d ( d (inegraion by ars dy y y d, y * m f d m d / / / m, m /. / - m f f / f / f / ( ( m m K m m / ( γ m ( / ( d m f f / m m f / m m / ( / f / m f kinei energy of a arile of he mass m moing wih seed Relaiisi Kinei nergy Show ha m 4 follows from γ u mu and γ u m for momenum and energy in erms of m and u
4 4 m INVARIANT z y z y z y ( ( ( m m m TOTAL NRGY Reoluionary Cone Wha abou m? (m m? (m TOTAL NRGY INTRNAL NRGY (when INTRNAL m (m TOTAL NRGY INTRNAL NRGY
5 ressions for (oal nergy and Momenum of a arile of mass m, moing a eloiy u Classial Limi mu mu m Classial Limi Kinei nergy K mu NW mu m FAMILIAR kinei energ
6 nergy Maer nergy Maer Aomi Bomb (Chaer : nergy is CRATD From he Mass of Nulei (Inernal energy is ransformed ino kinei energy u u
7 u Is here Absolue Causaliy? Migh ause reede effe in one referene frame bu effe reede 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 reede effe in one referene frame bu effe reede 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, reseiely
8 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, reseiely Using Lorenz ransformaions. if hen Using Lorenz ransformaions. if hen Using Lorenz ransformaions. if hen Imossible??
9 Is here Absolue Causaliy? YS Migh ause reede effe in one referene frame bu effe reede ause in differen referene frame(s? e.g. an someone see you firs die, and hen see you ge born? NO NO
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