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

1. Sep 26, 2007

### hartin

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.