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Relativity Question

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data
    In reference frame S two events occur at the same point; event A occurs 1.90 seconds before
    event B. In another frame, S′, event A occurs 2.45 seconds before event B. How far apart
    are events A and B in frame S′?


    2. Relevant equations
    x'=gamma (x-vt)
    t' = [t - vx/c^2] gamma


    3. The attempt at a solution
    I used the aforementioned mentioned Lorentz transformations. I know both T and t'. I'm trying to find x'. So I solved for x in both equations and tried to calculate x' but could not do so. Am I approaching the question correctly?
     
  2. jcsd
  3. Nov 12, 2008 #2

    CompuChip

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    Science Advisor
    Homework Helper

    You can do that, but you don't want to solve for x. In the frame S, to which the coordinate x belongs, the events are at the same point, so you can take x to be zero. You know then x, t, t' and you want to find x'. You have two equations: one that will give you v, and the other can be used to then find x'.

    I don't know if you have learned this already, but it may also be useful that in (special relativistically) equivalent frames such as S and S', the quantity
    [tex]\Delta s^2 = - c^2 \Delta t^2 + d^2 [/tex]
    where [itex]d^2 = \Delta x^2 + \Delta y^2 + \Delta z^2[/itex] is the "ordinary" spatial distance given by Pythagoras' law, is a constant. So you could, for example, calculate [itex]\Delta s^2[/itex] in S first and then find [itex]\Delta x[/itex] in S' from that.

    If you have no idea what I just said in the second paragraph, please forget it and stick to the first one, that works as well :smile:
     
  4. Nov 12, 2008 #3
    Thank you so much!! I can't believe I didn't realize that x = 0!
     
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