What does mean by restmass for the photon?

Question

So Photon has a zero restmass. And Photon can never be at rest. What does this suppose to mean? Additionally, We know that photon carries energy so Why doesn't have mass? Mass and energy are the same things to some extent.

score 2 · Answer 1 · answered Nov 17 '20 at 20:06

It means that all of light’s energy is tied up in it’s kinetic energy. Here’s the relativistic energy equation you’re looking for:

$$E^2=p^2 c^2 + m^2 c^4$$

where $p$ is the momentum. The first term on the right is the kinetic energy, and the second term is the mass energy. This equation is true for light iff $m=0$.

score 1 · Answer 2 · answered Nov 17 '20 at 20:09

1

Photons are defined as elementary particles in the Standard Model, with no rest mass, you are correct.

You are saying that you see phrases like "a photon can never be at rest", but in reality what we mean is that there is no rest frame for a photon. What we really mean is that there is no inertial frame of reference that could be comoving with the photon. One consequence of this is, that for us, who have rest mass, it is not possible to experience what is would be like to comove with and observe a photon in its own frame (because no such inertial frame exists).

Photons do have energy, even though they do not have rest mass, and this is no contradiction. Photons do have momentum, and $$E^2=p^2 c^2$$ is the correct way to express that for a massless photon energy is related to its momentum.

answered Nov 17 '20 at 20:09

Árpád Szendrei

28,452

2

Suppose me in some closed chamber with a mirror on each wall, Now suppose You weight the chamber (I'm inside) you got some mass on your measurement. Now suppose a light ray just get into the chamber and going around back and forth. Now if you weight the chamber, Do you get the same mass as before or not? If you get the different that means photons have mass? Isn't it? – Young Kindaichi Nov 17 '20 at 20:13
@YoungKindaichi You are correct, that is the famous photon box thought experiment. But that is the weight of the whole system, including the (in the experiment it is weightless) box. The photons do give rest mass to the box, by bouncing off the walls and giving inertia to the (initially weightless) box. So the photons are massless, but they can give rest mass to a system they are confined into. Just like gluons are confined into a proton. – Árpád Szendrei Nov 17 '20 at 22:49

score 0 · Answer 3 · answered Nov 18 '20 at 12:36

The simplest description of the rest mass comes when using the algebra of four-vectors.

The rest mass of a particle is the "length" of the four vector, and this length is invariant to Lorentz transformations.

The length of the energy-momentum 4-vector is given by

The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.

Due to vector algebra, adding the four vectors of two photons if there is a non-zero angle between them in momentum space, will give an invariant mass, a real example is the $π^0$ particle of mass 135MeV which decays into two photons.

What does mean by restmass for the photon?

3 Answers3