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Total noob here.

I realize that photons do not have a mass. However, they must somehow occupy space, as I've read that light waves can collide with one another.

Do photons occupy space? and if so, does that mean there is a theoretically maximum brightness in which no additional amount of photons could be present in the same volume?

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+1 good question. Can the uncertainty principle be applied to show that a photon's wave function is going to have a non-zero spatial dimension? Maybe it is infinite, meaning the photon occupies the entire space along the ray of light at the same time. – ja72 Apr 30 '14 at 20:29
up vote 29 down vote accepted

However, they must somehow occupy space, as I've read that light waves can collide with one another.

That's not true. Yes, light waves can "collide" and interact with each other (rarely), but that itself doesn't imply that they need to occupy space.

It's not even entirely clear what it means for a subatomic particle to occupy space. A particle like a photon is a disturbance in a quantum field, and is "spread out" across space in a sense; it doesn't have a definite size in the same sense that a macroscopic material object does. But you'll probably agree that, if it's possible to make any sensible definition of "occupying space" for a subatomic particle, it should involve preventing other things from also occupying that same space. Photons don't do that. They're bosons, and as a consequence of that they are not subject to the Pauli exclusion principle, so if you have a photon occupying some space (whatever that may mean), you can in theory pack an unlimited number of additional photons into the same space.

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There is a limit to photon density, though: if the energy density is high enough you'll start to see nonlinear effects like particle-antiparticle creation. – rob Apr 30 '14 at 21:31
I am under the impression that photons will collide with electrons. See the passage in this question. – Immortal Player May 1 '14 at 2:10
That's true. Photons do interact with electrons. – David Z May 1 '14 at 5:23
@Godparticle Part of the trouble here is that laymen look at, say, Compton scattering and say "Ah ha! They collided", but the math that describes that interaction doesn't have a "thing-hitting-thing" character, it has a "the-field-of-a-thing-affecting-the-other-thing" character. That's what DavidZ keeps saying "interact" not "collide". Interaction does not imply extent. – dmckee May 1 '14 at 16:36
@rob GTR would also impose limits, but at much higher densities. But David's answer goes to the nub of the problem IMO: the idea of "taking up space" being defined by exclusion. – WetSavannaAnimal aka Rod Vance May 2 '14 at 1:49

David Z answers a part of your question great, so let me fill in the other part:

does that mean there is a theoretically maximum brightness in which no additional amount of photons could be present in the same volume

(Disclaimer: I'm just an amateur - this is the way I understand the subject matter)

The answer is mostly a yes. While as David says, photons are bosons and therefore do not really have a meaning of "personal space", the accumulation of the photon's energy causes another very interesting thing to happen - the spontaneous creation of new particles. In fact, there's a kind of supernova that's theorized to occur because of this -

In theory, this can happen as soon as there's enough energy to produce any pair of particle-antiparticle. However, at the same time, there's considerable support for the idea that for a short time after the big bang, everything was photons - that was probably the biggest amount of photons in the smallest space ever. At that point, the universe was too "hot" to enable pair production.

So under "normal" conditions, the amount of photons in a given volume is constrained. However, it's not about the amount of photons - it's about their total energy.

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Well, if prof. Miles J Padgett is right, when he says here that:

Orbital momentum of light

It has been known since the middle ages that light exerts a radiation pressure. Not so well known is that light also exerts a twist.

The intricate nature of this twist was not recognised until the 1990s and we have been working on it ever since. Beyond the fascination of setting microscopic objects into rotation, this orbital angular momentum may hold the key to better communication sensing and imaging systems.

Than certainly photons must occupy space. There is no spin without extension.

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I did a lit search of Miles Pagett's work and there is a review paper by him here that discusses the work you refer to. The orbital angular momentum is a classical phenomenon and unrelated to the properties of individual photons. It requires the light beam have a non-zero area, but of course this is true as it's a classical object. So your conclusion Then certainly photons must occupy space does not follow. – John Rennie Jun 21 '14 at 15:01
In any case we know photons have an angular momentum of $\hbar$. The question is whether this shows they must occupy space. Classically a point particle cannot have any angular momentum, but elementary particles are not classical objects. It is an assumption in QM that the spin is an intrinsic property and can be carried by a point particle. You claim otherwise, but present no proof for your claim. – John Rennie Jun 21 '14 at 15:01
"You claim otherwise, but present no proof for your claim". So doesn't QM. The difference being that angular momentum is not physically possible if the particle has no dimensions. Because what would be spinning there? Point means there is no volume, no sphere, no size, nothing. The logic is on my side, and not on QM's. It is QM that goes against reason and definitions. As long as we are talking about mathematical spin, which is still weird, one does not need to present proofs, but when spin becomes real, something must spin. – bright magus Jun 21 '14 at 15:22
... many particles you include in your calculation, you don't converge on a solid answer. In the end we have to make educated guesses, or models. And these are always adjustable." "I think of this rather gruesomely as a skeleton of hard predictions inside and squidgy body of best guesses. The body can change shape. You can push in its stomach quite painlessly, but you really know about it if you break a bone.... Anyway, marrying the squidgy models to the rigid perturbation theory is mostly done using Monte Carlo event generators" – bright magus Jun 22 '14 at 13:32
Looks like an addendum to 10 commandments. – bright magus Jun 15 at 5:56

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