Can you pass an infinite number of photons through a small hole?

Is it at least theoretically possible to have a limit to the number of photons that can be passed through a defined space?

I was wondering could we focus a huge number of photons through a lens to where they ‘colide’ at the focal point? Is that even possible?

If they can collide, or crowd each other…what would happen? Does the focal point get bigger? do the photons scatter out? do they 'splode?

I don’t think your question makes sense. Do you mean is there an upper limit on the number of photons that can be within a finite prescribed volume at one instant? It sounds like a quantum mechanics problem. but there are relativity issues as well since volume and instant have different meanings from different reference frames and are probably not defined meaningfully from the reference frame of a photon.

A simpler question which is what you might be asking is, "If elementary particles like neutrinos are assumed to be point particles, can they be packed to arbitrary density? Well they’d form a black hole at some point and that might have a singularity, but then space might be quantized as well.

Photons exhibit superposition.
The intensity at the hole is related to the instantaneous phase of the light as each photon passes through the hole. In air, if enough in-phase photons pass through the same volume at the same time, the dielectric breakdown strength of the air will be exceeded, and you will get a small explosion.

Photons do interact with each other, but only very weakly. Roughly speaking, it requires one photon to fluctuate ever so briefly into a particle-antiparticle pair, and for the other photon to interact with this pair before they recombine to form the other photon. This does place a limit on how many photons you can put into a volume before you have to take into account their interactions; however, exactly how many you can put into a given volume depends on their energy and the size of the volume. If they do interact, they’ll scatter off of each other essentially randomly, rather than just passing by each other without interacting like they normally do.

You need to specify the problem further before it has an answer. A photon is a mathematical idealization, whose spatial distribution depends on the boundary conditions that you are using. If you are talking about photons in infinite space, they have zero energy density and zero flux density through any aperture. You could have an infinite number of these passing through an aperture for any finite flux. If you quantize in a box of finite volume, then you’ll have to deal with the non-linearity discussed above, i.e. the superposition theorem fails for sufficiently high energy densities.

I asked my physics professor if photons can occupy the same space, and he said they can’t occupy the same xyz space.

This makes me wonder if it’s possible to make a light “curtain”.

Do you mean a “plane” of photons?

Yes, if you had, say, a vacuum between 2 sheets of glass and shot lots of photons between the glass, wouldn’t they “knock out” photons traveling across the vacuum?

That’s wrong. Photons are bosons. They will happily occupy the same xyz coordinates. And they do quite commonly. Those radiowaves reaching your antenna? Many, many photons on top of one another moving in unison. The same applies to every other form of light you encounter in your daily life.

So how about deuterium? Can deuterium atoms overlap too?

Deuterium is a composite boson, of which fermions are the fundamental constituents. See wikipedia’s explanation:

Ah thanks. So the answer to the op is yes?

My answer to the OP is that there is no clear limit to how many photons can be fit through an arbitrarily small hole. It is true that photons can “collide”, however this is an incredibly rare occurrence and the effect is so small as to be unnoticeable even with our most sensitive experiments (or focal lenses). But yes, some tiny percentage of the photons would scatter out (note this does not contradict the fact that the photons will happily fit through a tiny hole – the vast majority that do not scatter do not mind being on top of one-another, and even the ones that scatter will also be on top of one-another until they exit the hole).

I’d say at least 1,000.

The following scene occurs in a lab somewhere in Japan:

“Doctor, what does the scouter say about the number of photons coming through that lens?”

“THERE ARE OVER 900!!!” Crushes the scouter with his bare hands

“What, 9000? There’s no way that could be right.”

Yes; if you have enough photons in a region they will collapse into a black hole; this is known as a “kugelblitz”.

It depends how those photons are moving relative to one-another; if they are moving parallel to one-another (as they roughly will be when focused through an aperture) they will not form a black hole because they have zero CM energy.

Look Around You.
Look Around You.
Look Around You

(“This is known as the Helvetica Scenario.”)

a pencil points to an empty jar labled “photons”

Thank you, Der Trihs. While I was familiar with the situation described, I’d never actually encountered the wonderfully fun term “kugelblitz” to name it. That’s definitely my new Word for the Day.

Incidentally, a fun fact about kugelblitzen: If you’re at (or near) the target of one, you can cross the forming black hole’s event horizon while in a region of spacetime of perfectly flat curvature, and in fact have no forewarning at all about that fact until it’s too late. It’s perfectly possible (though fantastically unlikely) that we are, even at this very moment, crossing the event horizon of just such a black hole.