lecture_4

lecture_4 - 1 ′ x = x- vt 1- v 2 c 2 ′ t = t- vx c 2 1-...

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Unformatted text preview: 1 ′ x = x- vt 1- v 2 c 2 ′ t = t- vx c 2 1- v 2 c 2 ′ y = y ′ z = z x = ′ x + v ′ t 1- v 2 c 2 t = ′ t + v ′ x c 2 1- v 2 c 2 ′ y = y ′ z = z 2 All observers measure c • Burst of light in frame S at t = 0 • S’ moves with respect to S at velocity v • The origins of S and S’ coincide only at the instant t = t’= 0 • In S at a later time the light will have reached all points on a sphere such as r = ct , i.e., a sphere centered on the origin of S. • In S’ is the same thing: burst of light is again a sphere now centered on the origin of S’ 3 All observers measure c r = ct x 2 + y 2 + z 2 = c 2 t 2 x = γ ( ′ x + v ′ t ) t = γ ( ′ t + v ′ x c 2 ) ′ y = y ′ z = z γ 2 ( ′ x + v ′ t ) 2 + ( ′ y ) 2 + ( ′ z ) 2 = γ 2 c 2 ( ′ t + v ′ x c 2 ) 2 γ 2 ( ′ x ) 2 (1- v 2 c 2 ) + ( ′ y ) 2 + ( ′ z ) 2 = γ 2 ( ′ t ) 2 ( c 2- v 2 ) ′ x 2 + ′ y 2 + ′ z 2 = c 2 ′ t 2 ′ r = c ′ t Points which, as measured in S, are reached at the same time t, are reached at different times as measured in S’, in such a fashion that the light is properly described as lying on a spherical shell expanding at speed c in both frames. 4 x = γ ( ′ x + v ′ t ) t = γ ( ′ t +...
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This note was uploaded on 04/15/2008 for the course PHY 361 taught by Professor Alarcon during the Spring '08 term at ASU.

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lecture_4 - 1 ′ x = x- vt 1- v 2 c 2 ′ t = t- vx c 2 1-...

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