Does the photon have a rest mass equal to $E/c^2$, where $E =$ photon energy?

Question

When a photon is emitted, does the rest mass of the emitting body decrease by $E/c^2$ wherein E =photon energy? If yes, does the photon have a rest mass equal to $E/c^2$?

Answer 1

Energy is conserved; rest mass is not.

The photon has relativistic mass $E/c^2$ but rest mass $0$.

If the emitting body's initial four-momentum is $p^\mu$, without loss of generality its revised four-momentum $p'^\mu$ satisfies $$p'^0=p^0-E/c,\,p'^1=p^1-E/c,\,p'^2=p^2=0,\,p'^3=p^3=0.$$The emitter's squared rest mass changes from $c^{-2}p^\mu p_\mu=c^{-2}(p_0^2-p_1^2)$ to $$c^{-2}p'^\mu p'_\mu=c^{-2}(p^\mu p_\mu-(2E/c)(p_0-p_1)).$$The squared rest mass reduction is $2Ec^{-3}(p_0-p_1)$; the rest mass reduction is unlikely to be $E/c^2$.

Answer 2

To answer your question, first we need to clarify:

1. photons do not have rest mass
2. photons have mass
3. photons' mass comes from their energy
4. this energy comes from the photons' frequency E=h*f (h is planck constant)
5. easiest is to see when an electron emits a photon
6. in this case, the electron's energy decreases exactly with the photon's energy
7. so the electron's mass (which is equal to it's energy) decreases
8. the electron has a rest mass, but that will not decrease

So to answer your question, yes the electron's mass (equal to energy) will decrease, but the rest mass will not