The recoil of an electron receding from a photon

[Akihiro]

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?

 

[chroot]

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

 

[Meir Achuz]

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.

 

[Akihiro]

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. And just to add, would this suggest a violation of conservation of energy??

 

[Meir Achuz]

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.