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Time dilation - Lorentz transformation using light clock

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    I am trying to derive the time dilation formula using Pythagorean theorem:
    L = ct (in clocks rest frame)
    D = ct'(in observer's frame, the clock moving with velocity u)

    3. The attempt at a solution

    So [tex]D^2 = L^2 +v^2t^2[/tex]
    [tex]c^2{t'}^2=c^2t^2+u^2t^2[/tex]
    So[tex]t'=t*\sqrt{1+v^2/c^2}[/tex]
    but it should be
    [tex]t'=t/\sqrt{1-v^2/c^2}[/tex]

    2. Relevant equations
    This would work if D=ct, not ct' and L=ct', but I guess it isn't right with my choice of frames of reference?

    Sources: http://www.drphysics.com/syllabus/time/time.html
     

    Attached Files:

  2. jcsd
  3. Apr 10, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You're mixing up your frames a bit. The clock moves a distance vt' (not vt) in the observer's frame. (The observer uses his own time measurements, of course.)
     
  4. Apr 10, 2012 #3
    Ok, now it works, thanks for your reply!
     
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