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Unformatted text preview: Lecture 37: Four-vectors (30 Nov 09) Homework for December 7 is available as Supp09.pdf and ps. A. Review: Lorentz transformation 1. Frames S and S * moving with relative velocity v along ˆ x ct * = γ ( ct- βx ) x * = γ ( x- βct ) y * = y ; z * = z ; β = v/c ; γ = 1 / q 1- β 2 2. notation for 4-vector: x = ct , x 1 = x,x 2 = y,x 3 = z 3. Clocks and rods (a) Events E i = ( t i , r i ) and then in moving frame with primes. (b) Compare time interval for clock at rest (same position in S and when observed in lab frame (2 places): time dilation. t 2- t 1 = γ ([ t 2- t 1 ] + ( v/c 2 )[ x 2- x 1 ]) → Δ t = γ Δ t Gedanken experiment: measure time by the distance traveled di- vided by speed of light. Bounce light from a mirror with path at right angles to the relative velocity. Then calculate distance traveled as viewed in rest frame and as viewed in “lab” (c) Compare length of rod L in rest frame S and L S when measured (same times) in lab frame. x 2- x 1 = γ ([ x 2- x 1 ]- v [ t 2- t 1 ]) → L = γL S (d) Relativity of simultaneity: [Symon secs. 13.2 and 13.3] events simultaneous (equal times) in one frame appear at different times...
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at University of Wisconsin.
- Fall '09