Velocity of the centre of mass of two photons

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SUMMARY

The discussion focuses on calculating the velocity of the center of mass of two photons with different energies. Key equations utilized include the energy-momentum relationship E = hf and the conservation of 4-momentum. The participants emphasize the importance of understanding the momentum of the center of mass in the lab frame to derive the corresponding velocity. The relationship between energy and momentum for photons is highlighted, specifically E = pc, which is crucial for deducing the velocity.

PREREQUISITES
  • Understanding of 4-momentum and 4-velocity in relativistic physics
  • Familiarity with the energy-momentum relationship for photons
  • Knowledge of conservation laws in physics
  • Basic concepts of special relativity
NEXT STEPS
  • Study the derivation of 4-momentum and its applications in relativistic scenarios
  • Learn about the implications of conservation of momentum in different reference frames
  • Explore the concept of center of mass in relativistic systems
  • Investigate the relationship between energy and momentum for various particles
USEFUL FOR

Students and professionals in physics, particularly those focusing on relativistic mechanics and photon interactions, will benefit from this discussion.

Fek
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Homework Statement



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

Homework Equations


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

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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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.
 
Welcome to PF, Fek! :smile:

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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