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Homework Help: Reference frames

  1. Sep 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Two events happen at the same point x'(0) in frame S' at t(1)' and t(2)'

    a) Use equations x=gamma*(x'+vt') and t=gamma*(t'+vx'/c^2) to show in frame S the time interval between the events is greater than t(2)'-t(1)' by a factor of gamma

    2. Relevant equations



    3. The attempt at a solution

    x=gamma*(x'+vt')
    t=gamma*(t'+vx'/c^2)

    t(2)=gamma*(t(2)'-vx'(2)/c^2) and t(1)=gamma*(t(1)'-vx'(1)/c^2)
    x'(2)=x'(1)=x'(0)
    t(2)-t(1)= gamma*(t'(2)-t'(1))-gamma*v/c^2(-v*x'(0)+v*x'(0))
    t(2)-t(1)=gamma*(t(2)'-t'(1))

    from the reference frame of S' the two events that were at the same reference point in the S prame with not be at the same reference point in the S' frame. hence, x'(1) will not equal x'(2)

    t'(2)= gamma*(t(2)-v*x(2)/c^2)
    t'(1)=gamma*(t(1)-v*x(2)/c^2)
    t'(2)-t'(1)=gamma*(t(2)-t(1))-gamma*v/(c^2)*(x(2)-x(1))

    hence , t(2)-t(1) is large than t'(2)-t'(1)
     
  2. jcsd
  3. Sep 6, 2007 #2

    learningphysics

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    Homework Helper

    Shouldn't you be using +vx'(2)/c^2 etc...

    You've proven your result above. I don't understand the purpose of the part below.

     
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