Okay I understand that, I guess my question is more about what happens when you infinitely increase the amount photons within a given space, would their interactions become important at some point? And if so what would the interactions result in.
Correct me if I'm wrong, but doesn't light have momentum, but no mass? and for the sake of the "perfect mirror" we are assuming that the momentum of the photons are not lost on the inside of the box, though if they were than under a normal outside light situation, the amount of light coming in...
Lets say that since this is a "perfect" mirror, the photons do not lose any of their momentum when being reflected, therefore their would be no increase in internal energy or pressure, plus the fact that it is a vacuum means that their are no interactions within the interior of the box.
Here's the scenerio: you have box (shape is not necessarily important, but for simplicity we'll say its a cube), within the cube is a vacuum and the inside of the box consists of "perfect" mirrors, meaning that no light is absorbed (obviously this is not possible in the real world), however...