Center of momentum frame with photons?

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SUMMARY

The discussion confirms that a center of momentum (CM) frame can exist in a system comprising a photon and a massive particle. In this unique frame, the massive particle can possess momentum defined as -E/c, where E represents the energy of the photon. The analysis emphasizes the importance of relativistic effects, such as the Doppler shift, which alters the energy and momentum of the photon as reference frames change. This establishes a clear relationship between the photon and the massive particle's momentum in the CM frame.

PREREQUISITES
  • Understanding of relativistic physics concepts, particularly momentum and energy.
  • Familiarity with the properties of photons, including their constant speed c.
  • Knowledge of Doppler shift and its effects on light and energy.
  • Basic grasp of reference frames in physics.
NEXT STEPS
  • Study the implications of relativistic momentum in systems with massless particles.
  • Explore the mathematical formulation of the Doppler effect in different reference frames.
  • Investigate the concept of center of momentum frames in multi-particle systems.
  • Learn about energy-momentum relations in special relativity.
USEFUL FOR

Physicists, students of relativity, and anyone interested in the interactions between light and matter in relativistic contexts.

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Is it possible to have a center of momentum frame in a system with a photon and a massive particle?

If you were to do so in a system with two massive particles, this would involve redefining the velocity of the particles in the CM frame. E.g. if A moves towards B with speed 2v, in the CM frame, A and B would move towards each other at v.

Since the photon will have speed c in all frames, is it possible to have a unique frame in which the massive particle has momentum -E/c (where E is the energy of the photon)?
 
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Yes, it is possible. Remember that as you change reference frames the photon will red-shift or blue-shift. The Doppler shift will change the energy and therefore the momentum of the photon. There will be a unique frame where it is opposite that of the massive particle.
 

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