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Homework Help: Reference frames for photon collisions (pair production)

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Hi,
    My question probably has a simple answer, but I've been scratching my
    head over it a little too long so I thought I would ask it here. I
    have three initial photons involved in a collision with 4-momenta k1,
    k2 and k3. I have two reference frames:
    frame 1: the centre of mass frame of photons k1 and k2 (so that 3-momenta k1+k2=0)
    frame 2: the centre of mass frame of all photons k1, k2 and k3 (so that 3-momenta k1+k2+k3=0)

    I want to find out what the relativistic beta v/c and gamma 1/Sqrt(1-(v/c)^2 are.

    2. Relevant equations

    beta=v/c
    gamma=1/Sqrt[1-(v/c)^2]
    (observed frequency/source frequency)^2=(1+beta)/(1-beta)

    3. The attempt at a solution

    So there seems no way to directly find the relative velocity of the two frames is as only photons are involved (relative velocity=c ?!?). I thought to use the expression for the relativistic doppler shift, but that doesn't seem appropriate.
     
  2. jcsd
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