What is exactly meant by a statement like "there are about 400 photons per cubic cm in certain region"? Should I mentally picture this as 400 discrete photons enclosed in that volume, each moving at speed of light in that medium (independently of one another)? Also by one photon I should not mean something like a particle (localized at a point) but a changing electric and magnetic field in phase spread over exactly one full wavelength. If I were able to take a snapshot of the changing fields, these would be like sinusoidal variations in space and if I knew the velocity I would know that after one second the entire field variation will be shifted exactly "c" distance away from the previous location of wave (along the wave vector) and effects of field variation at previous location is obliterated. To these one may add characteristics of polarizations etc but is the above picture basically correct?

Also, is there any restriction on the number of photons in such a picture (if it is correct at all)? Or is there any condition so that we must consider multiple photons (so that we get continous wave) rather than a single photon?

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    $\begingroup$ You should be careful with the way you talk about the photons moving after one second. It sounds like you're picturing the photons as localized. If you have an actual photon number state (with defined frequency) then your photons are necessarily delocalized throughout your box or all of space. If you want something like a Gaussian wave-packet whose pattern unambiguously moves from point A to point B, you necessarily need higher frequency photons contributing to the packet. $\endgroup$ – aquirdturtle Aug 1 '16 at 3:13

You don't give a reference for the quote, but I would guess it means the energy per cubic cm is $400h\nu$, where $\nu$ is the wavelength of the light. Since the energy of a photon is $h\nu$ this could be interpreted as 400 photons in your cubic centimetre.

Light is neither a photon nor a wave, however when you're describing how light interacts it can be convenient to choose one of these two descriptions as an approximation. For example if your cubic cm had walls made from a metal the light would eject 400 photoelectrons and a photon description is a good way to describe this. On the other hand if the cubic cm had walls made from a diffraction grating you'd describe the light inside as a wave. In your example I would probably regard the light as a wave.

In principle you can raise the energy, and therefore the multiples of $h\nu$ in your cubic cm to any value you want. At very high energies you might get non-linear interactions, and at ridiculously high densities you would form a black hole, however these are unlikely to be practical restrictions.


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