Why an electron at rest cannot emit a photon?

[Docdan6]

Hi!

Could someone explain to me why an electron at rest without any influence from a magnetic or electric field cannot emit a photon ?

Could you explain it mathematically too ?

Thanks in advance...

 

[anorlunda]

Think about it. Momentum must be conserved. Energy must be conserved.

 

[Docdan6]

Think about it. Momentum must be conserved. Energy must be conserved.

I know that ! But how can I prove it mathematically? (I don't have a background in physics I'm a pharmacologist...)

 

[anorlunda]

There is no solution where energy and momentum before emission equal energy and momentum after. Therefore, it can't happen.

You must be interested in physics, that is hardly a pharmacological question.

 

[mfb]

Not even a moving electron, without influence of an electric or magnetic field, can emit a photon.

A photon at rest has energy just from its mass (mass-energy equivalence). If it would emit a photon, you would have energy from the electron mass, plus energy from the photon, plus kinetic energy from the electron (it has to move to keep the center of mass at the same place). That doesn't work.

For a moving electron, you can consider the process in the rest frame of the electron, with the same conclusion.

 

[rcgldr]

Just in case this was a possible option, current belief is that an electron can't decay into a neutrino and a photon, because charge would be lost, which would violate the law of charge conservation (this assumes there isn't some smaller charged particle that no one has discovered yet).