Is there a maximum amount of photons that can exist in a certain amount of space?

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?

Answer

1. 
   

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

   
   


2. 
   

   Photons have zero mass, but they 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.