# Photon in a massless mirrored box

## Main Question or Discussion Point

Suppose we have a photon bouncing around in a massless mirrored box - does this system have inertial and/or gravitational mass? To be more realistic, if we have a massive black body cavity at some temperature above absolute zero, will the inertial and/or gravitational mass be equal to the mass of the heated cavity enclosure plus a mass associated with the enclosed photon gas, which I guess would be the sum of $$h\nu/c^2$$ over every photon enclosed?

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Yes.

Do you know of any references that deal with the inertial/gravitational mass of a photon?

Do you know of any references that deal with the inertial/gravitational mass of a photon?
Anyway it's not difficult to prove it: the photon gas system has zero total momentum p, in the frame of reference in which the box or the cavity is still, so, from the equation:

E2 = (mc2)2 + (cp)2

you deduce that E = mc2. That is: the photon gas has a non zero mass m equal to its total energy divided by c2.
Of course it's invariant mass (not "relativistic" mass or other).

This is what I thought. In other words, although a photon has no rest mass, a system consisting of a photon trapped in a massless mirrored box will have a rest mass > 0. I am looking for a reference for this idea.