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Lorentz transformation problem

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data

    two photons travel along the x-axis of S , WITH A CONSTANT DISTANCE L betweenthem. Prove that in S's the distance between these photons is L(c+v)^1/2/(c-v)^1/2.

    2. Relevant equations


    x'=gamma*(x-vt), x=gamma*(x'+vt), t=gamma*(t'+vx'/c^2), t=gamma*(t'-vx'/c^2)
    3. The attempt at a solution

    L(c+v)^1/2/(c-v)^1/2=L((c+v)/(c-v))^.5=L((+v/c)/(1-v/c))^.5. So will the two photons reach a midpoint along the x-axis. I think I should either find the difference between x_2 and x_`1 or the difference between x'_1 and x'_2. I thinkl in one reference frame , the time would be dilated with the moving frame for both photons . Is my line of thinking correct?
     
  2. jcsd
  3. Jan 23, 2010 #2

    diazona

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    Homework Helper

    That is the quantity you should be looking for, keeping in mind that the definition of simultaneity is not the same in S' as in S - so you need to calculate the difference between [itex]x_1'[/itex] and [itex]x_2'[/itex] as measured at the same time in S', not at the same time in S.

    Consider drawing a spacetime diagram. I find that doing that helps with these kinds of problems.
     
  4. Jan 23, 2010 #3
    In order to calculate x_2' and x_1' should I calculate t_1 and t_2 first?
     
  5. Dec 28, 2010 #4
    I'm trying to teach myself special relativity (using the book 'Introduction to Special Relativity' by Wolfgang Rindler). I'm currently working on the problem stated above.

    My first approach was : x1=ct ; x2=L+ct.
    Then using x'=gamma(x-vt) and t'=gamma(t-vx/c²) I calculate x1' and x2'. However I'm always arriving at L'=gamma(L) which is the formula for Length contraction.

    Where is my mistake ? There obviously is a difference between the length contraction (of a rod in S seen from S') and the 'length contraction' in this problem (the distance between 2 moving photons).
     
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