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24.8 Lorentz Transformation: Examples
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Module 24: Lorentz Transformation: Examples - Problem 3

Imagine a team of observers (Team Red) are riding a red broomstick, and zip by Earth at speed vv. Assume the origins of Team Earth and Team Red cross at t=t′=0t = t^\prime=0 (that is, (t=0,x=0)=(t′=0,x′=0)(t=0, x=0) = (t^\prime= 0, x^\prime= 0)). Imagine that a member of Team Red located at their origin has stolen a top secret file. So, you jump on your new super-broomstick, and chase after Team Red at speed VV which is larger than vv. You leave Earth at time t=t1t = t_1. (To distinguish the various γ\gamma factors, write γ[w]=11−w2\gamma[w]= \frac{1}{\sqrt{1-w^2}} for any ww expressed in units with c=1c = 1).

  1. 1. Question

    At what time t2t_2 according to Earth clocks do you catch up with the outlaw in Team Red?

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  2. 2. Question

    What is the time according to Team Red when you start chasing after them?

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  3. 3. Question

    According to Team Red, how far away are you from the outlaw when you start chasing them?

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  4. 4. Question

    According to Team Red, at what time do you catch up with the outlaw?

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  5. 5. Question

    According to your watch (which read t1t_1 when you left Earth), what time is it when you catch up with the outlaw? (Don't concern yourself with the effects of acceleration. Instead, if you are bothered, imagine that the question is more precise: Another observer moving past Earth with speed VV, passes the origin of the Earth's frame at time t1t_1 on their own clock (and on Team Earth's clock). What time will that observer say it is when they catch up with the outlaw who is at the origin of Team Red?)

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