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If you have a set amount of space, lets say 10 cubic centimeters, and you would be able to trap photons in there.
If you would then add more and more photons to that space, could you then go on infinitely or would you eventually run into a maximum amount of photons that can be in that space?

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1) Photons are bosons and can exist with the same quantum numbers with an indefinite number of photons.

2)Photons have zero mass but have energy $E=h\times \nu$ ,increasing their number and frequency increases the energy per cubic centimeter.

3)Photons move with the velocity of light, and trapping them presupposes reflectors of one kind or another.

From 1) the answer is "no limit"

From 2) and 3) the limit would come from the melting of the reflectors due to the high energy density. The number would be large and would depend on the frequencies present.

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Thanks for the fast responce, I realize that there is no reflector that reflects 100% of the light so would not be able to reflect 100% of the photons. Only other option to change the direction of light, to my knowledge, is gravity. Trapping or looping light with gravity is beyond our capability. But I was just curious if we would be able to and thank you for your answer. –  user17615 Feb 1 '13 at 16:34
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Also you should take in account if the space you are talking about is vacuum or filled with some matter, plus bounding photons in finite part of space (a box) will lead to their energy quantization, finally very high energy density will lead to electron/positron pair creation out of vacuum that will make your vacuum not really a vacuum any more, the thing that may put restrictions on the "no limit" answer, thus i think the question is not a trivial one. –  TMS Feb 1 '13 at 17:50
    
Extra twist on the question (maybe I should ask it formally): are there limits on the properties of a null fluid beyond which it will collapse to a black hole? i.e. you try to cram enough electromagnetic energy into a region, and you'll eventually create a BH. (OK it will have a classical answer, but the principle is interesting even if the radiation isn't in a photon number eigenstate). –  twistor59 Feb 1 '13 at 18:08
    
@TMS i think i made it clear that a limit exists in the box reality of the question. if the photons have less than 1 mev energy no real pairs will be created. –  anna v Feb 1 '13 at 18:15
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