Velocity of the centre of mass of two photons


by Fek
Tags: centre, mass, photons, velocity
Fek
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#1
Jan8-13, 11:57 AM
P: 1
1. The problem statement, all variables and given/known data

Find the velocity of the centre of mass of two photons with different energies (they happen to be approaching).

2. Relevant equations
E = hf p(photon) = E/C E=gamma(mc^2)


3. The attempt at a solution

I have calculated the energy of the two photons in the centre of mass frame (using conservation of 4- momentum) and also the momentum of the centre of mass. However I have no idea how to get a velocity out of this.

Thank you.
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mfb
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#2
Jan8-13, 12:19 PM
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How does the momentum of the center of mass look like in our lab frame?
If you know energy and momentum of that frame, you can calculate the corresponding velocity - it is like a particle at rest in this frame.
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#3
Jan8-13, 02:37 PM
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Welcome to PF, Fek!

From the definitions of 4-momentum and 4-velocity:

P=(E/c,p)
P=mU
U=γ(c,v)

Furthermore, for a photon we have:
E=pc

Can you deduce v from this?


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