The recoil of an electron receding from a photon

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Discussion Overview

The discussion revolves around the behavior of an electron when it interacts with a photon, particularly focusing on the effects of the Doppler shift on the frequency of the photon and the resulting recoil of the electron. The scope includes conceptual understanding and implications for conservation of energy in the context of special relativity.

Discussion Character

  • Conceptual clarification, Debate/contested, Technical explanation

Main Points Raised

  • One participant questions whether an electron moving in the same direction as an incoming photon would recoil as if struck by a photon of lower frequency due to the Doppler effect.
  • Another participant asserts that the electron would indeed recoil as if struck by a photon of lower frequency, noting that frequency corresponds to energy for photons and is frame-dependent.
  • A further contribution provides a formula for the effective frequency of the photon in relation to the electron's mass, momentum, and total energy.
  • One participant expresses concern about whether this scenario suggests a violation of conservation of energy.
  • Another participant responds that the situation is consistent with conservation of energy, explaining that energy is a four-vector in special relativity and varies across different reference frames.

Areas of Agreement / Disagreement

Participants generally agree that the frequency of the photon is frame-dependent and that the electron would recoil as if struck by a photon of lower frequency. However, there is a discussion regarding the implications for conservation of energy, indicating some uncertainty and differing interpretations.

Contextual Notes

The discussion includes assumptions about the frame of reference and the nature of energy in special relativity, which may not be fully resolved. The mathematical relationship provided is not elaborated upon, leaving some steps and definitions open to interpretation.

Who May Find This Useful

This discussion may be of interest to high school students studying physics, particularly those exploring concepts of photon interactions, Doppler effects, and conservation laws in special relativity.

Akihiro
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Hi, everyone, I'm a high school student and i want to ask if an electron moves in the same direction as the photon which is about to strike it, would it recoil away as if struck by one with a lower frequency (due to Dopler's effect/ red-shifting effect) or would it recoil as if struck by the photon of original frequency without any alteration?
 
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It would "recoil" as if struck by one with a lower frequency. "Frequency" is the same as energy for photons, and energy is frame-dependent. Depending upon who's looking at it, the photon can have different energies.

- Warren
 
Yes, the effective frequency of the photon will be less.
It is given by f'=fm/(E+p) for an electron of mass m, momentum p,
and total energy E.
 
chroot said:
It would "recoil" as if struck by one with a lower frequency. "Frequency" is the same as energy for photons, and energy is frame-dependent. Depending upon who's looking at it, the photon can have different energies.

- Warren

Thx for the reply. :approve: And just to add, would this suggest a violation of conservation of energy??
 
It is consistent with conservation of energy. Energy is a four-vector in SR, and is usually different in different systems (as Chroot said). The f' in my answer above is the frequency of the photon in the rest system of the electron.
 

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