Does a smaller reflective box filled with trapped photons make the box heavier? In Leonard Susskind's video lecture on the Higgs Boson, he uses a model of a box made from very light, very reflective material containing photons, explaining how in this way, for example, the proton can get its mass. Would it be intuitive to think that a smaller container would make the box more massive due to more reflections?
Lecture, @ $40:14$
https://www.youtube.com/watch?v=JqNg819PiZY&t=3267s
 A: Simply putting the photons in a smaller box does not change the gravitational mass of the box + photons, because the box will contain the same amount of energy.  This is not quite true, because when the photons are closer together they have lower gravitational potential energy, so the overall energy is very slightly reduced.
On the other hand, putting the photons in a large box and then squeezing the box to make it smaller will raise the frequency of the photons and increase their energy, thereby increasing the gravitational mass of the box + photons.  Squeezing the box requires energy, which becomes added photon energy.
A: It's not the reflections that make the box massive, it is the energy. If you put the same energy in a smaller box, the box isn't more massive.
Furthermore, it is not necessarily easy to describe what "a reflection" is in a small box, because radiation is a wave and does not undergo isolated reflection events, the way lots of fast bouncing balls in a box would. In a sense the radiation is being reflected all the time.
