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Velocity of the centre of mass of two photons

by Fek
Tags: centre, mass, photons, velocity
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Fek
#1
Jan8-13, 11:57 AM
P: 3
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
#2
Jan8-13, 12:19 PM
Mentor
P: 11,631
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.
I like Serena
#3
Jan8-13, 02:37 PM
HW Helper
I like Serena's Avatar
P: 6,187
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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