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PHYS126 Supplementary Notes 7

# PHYS126 Supplementary Notes 7 - PHYS126 Supplementary Notes...

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PHYS126 Supplementary Notes 7 You will have a mid-term exam this week and Prof. Du has made the mid-term review in the lecture. So I just show some problems to you to review how to solve the problems. Please notice that the note will not cover the short answer questions. Q1. Observers in a frame S arrange for two simultaneous explosions at time 0 t = . The first explosion is at the origin ( 29 1 1 1 0 x y z = = = while the second is on the positive x axis 4 light years away ( 29 2 2 2 4 , 0 x c years y z = × = = . How about two events as observed in a frame S’ traveling in the standard configuration at speed 0.6c relative to S. Is it a timelike interval or spacelike interval or lightlike interval? Solution: Using Lorentz Transformation: ( 29 2 x x vt y y z z vx t t c γ γ ′ = - ′ = ′ = ′ = - Then we can get ( 29 ( 29 ( 29 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 5 4 1 0.6 1 0 0 0 5 4 0 5 4 0 5 0.6 4 0 3 4 v c x x vt y z vx t t c x x vt c year c year y z vx c c year t t year c c γ γ γ γ γ = = = - - ′ = - = = = ′ = - = ′ = - = × × - = × = = × × ′ = - = × - = - Now let’s calculate the ( 29 2 s In S frame, ( 29 ( 29 ( 29 ( 29 2 2 2 2 0 s c t x x = - ∆ = - ∆ < So it’s a spacelike interval.

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Q2. A galaxy in the constellation Uras Major is receding from the earth at
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PHYS126 Supplementary Notes 7 - PHYS126 Supplementary Notes...

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