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# p09fl36 - Lecture 36 Lorentz(25 Nov 09 homework for Dec 7...

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Unformatted text preview: Lecture 36: Lorentz (25 Nov 09) homework for Dec 7 is SUPPL09.pdf, *.ps. Review 23 Nov homework. A. Lorentz transformation –review 1. Barger-Olsson Mechanics Sec.10.3. Special geometry: relative motion along z . 2. Let the origins of S and S coincide at t = t = 0 and set off a light pulse, evolves as a sphere in both frames. x 2 + y 2 + z 2 = c 2 t 2 ; x 2 + y 2 + z 2 = c 2 t 2 3. The division of space-time into space and time becomes different for dif- ferent observers, but can guess at some features of the transformation, trying a linear relation: (a) transverse degrees of freedom unaffected, x = x , y = y but allow for mixing of z,t : z = γ ( z + at ); t = ˜ γ ( t + bz ) (b) As v → 0, γ, ˜ γ → 1, a → v to recover Galileo. 4. Now try to maintain the light cone for all x ,t γ 2 ( z 2 +2 z vt + v 2 t 2 )- c 2 ˜ γ 2 ( t 2 +2 bt z + b 2 z 2 ) = x 2 + y 2 + z 2- c 2 t 2 Match coefficients for t 2 , z 2 , z t ( a ) : c 2 ˜ γ 2- v 2 γ 2 = c 2 ; ( b ) : γ 2- c 2 b 2 ˜ γ...
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p09fl36 - Lecture 36 Lorentz(25 Nov 09 homework for Dec 7...

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