Originally posted by Symmetric Chaos
The light would be absorbed very quickly. Even if the mirrors are extremely reflective (say only .01% of light is absorbed) it would be gone in less than a second.
He's talking about what we'd see IF it was 100% reflective. That would also indicate that it needs to be a pure vacuum. Impossible for several reasons, though.
In that instance, the sphere would just grow brighter up to a point of saturation. There's several ways it can become saturated. The clothing of the individual only reflects certain wavelengths of light and absorbs others (in the case of the visible spectrum). Photons are bosons. Bosons can occupy the same physical space as others. There is no limit to the number of photons that can occupy the same space (as far as I know...and this is probably the actual premise of your question, is it not? That photons are bosons? ). Other reasons that it would saturate are: you are evaporating through processes known as sublimation, respiration, and perspiration. So you will quickly fill up the vacuum with your own gas particles causing them to absorb some of the energy and reflect and scatter SOME of that energy. Then you have the components of your eyes that will interfere, reflect, and/or absorb some of the EMR: the aqueous and vitreous humour, lens, possibly the hyaloid canal, and the retina. Then there's the exposed flesh of yourself that also absorbs, reflects, and/or scatters EMR. Then there's the material of the sphere, itself, sublimating, which leads to the same.
Also, if you turn the flashlight on, there is a finite amount of photons emitted from the flashlight. Meaning, it wouldn't have an infinitely long wave-form: it would only be able to reflect around so many times. Of course, that would strongly depend on how long you left the flashlight on.
Summary: No perfect mirror can exist in our universe for the reasons I have outlined. In addition, Hawking radiation ensures that the instant your mirror is created, an antiparticle-particle pair will pop into existence with the anti-particle coming into contact with a particle from your mirror and annihilating (thus destroying your perfection) so you would not be able to produce the "infinite brightness". Next, your own body would interfere. Next, sublimation ensures that the vacuum of the sphere would quickly cease being a vacuum as the gas particles would fill the empty space (just think...you can smell certain metals. How can you smell them unless particles have not evaporated for you to smell? AHA! lol)
However, I am in no position to tell you how bright it would get inside the sphere if you turned on and left on your flashlight. Your body would block much of the light from being reflected so you would reach a saturation point and quite quickly. It would be far brighter than must people would assume, of course.
It feels like I am missing a bunch of other stuff like QED or QCD...but I don't know if that applies. I don't know enough about it. There's other stuff that I am also forgetting. In order to create the system that you desire, you'd need an infinitely small observer directly in the perfect center of the sphere. You'd then need the inside of the sphere to be a perfect vacuum. Then your sphere would need to be made of "immortal matter": matter that is not subject to decay, annihilation, sublimation, and so forth. Then you'd need to introduce the light from an infinitely small source so it does not interfere with the reflection. So you'd have to create a different universe with a different set of physics to accomplish your thought experiment.