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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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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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  • $\begingroup$ So is it true that future data storage devices ("harddisks") can have unlimited storage (except, only limited by time) since light is massless and spaceless? $\endgroup$ – Pacerier Aug 16 '17 at 1:44
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    $\begingroup$ @Pacerier No, there are limits that arise for different physical reasons. But that would be a matter for another question. $\endgroup$ – David Z Aug 16 '17 at 3:18
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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 - http://en.wikipedia.org/wiki/Pair-instability_supernova.

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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    $\begingroup$ Little correction at the end. The amounts of photons is exactly what determines their total energy! E=hf for one photon. h is constant and if we consider just one specific frequency of a total EM wave it's easily deductable that only the amount of photons determine the total energy. I even presume that this is exactly why the OP question arose. $\endgroup$ – e-motiv Feb 16 at 21:32
  • $\begingroup$ @e-motiv Yes, but photons of different frequencies will have the amount different - so it's not that photons "occupy space". Indeed, if you think about photons as packets with size increasing with wavelength, you'd expect lower frequency photons to "occupy" more space. In reality, it's the opposite - so lower frequencies allow you to fit more photons in the same volume. $\endgroup$ – Luaan Feb 17 at 14:21
  • $\begingroup$ Contradictory and besides my point. But, never mind...I'm out. $\endgroup$ – e-motiv Feb 20 at 20:14
  • $\begingroup$ @e-motiv Okay, keeping it short. Just because amount and energy have a relationship doesn't mean they're the same thing. Total energy in a given region space is limited, total amount of bosons isn't. What exactly is contradictory about that? $\endgroup$ – Luaan Feb 21 at 8:22
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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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    $\begingroup$ I'm pretty sure your dates aren't right. Pretty much since Maxwell, people have realized that circular polarization states could exert torques on conductors, and the Beth experiment measured this in 1936. Also, there's no classical spin without extension, but the conception of angular momentum as a Noether charge and its consequent conservation doesn't need this classical idea to make it work, weird thought that intuitively seems. $\endgroup$ – WetSavannaAnimal Aug 1 '16 at 0:44
  • $\begingroup$ @WetSavannaAnimalakaRodVance: Mathematically one can prove virtually anything. Sadly, contemporary physics forgets that mathematics is abstract, and and such may describe real events, but as well have nothing to do with physical reality, and therefore not be valid for physics use. It used to be common knowledge, but then came guys such as Gell-Man and Gross who claim that: "In order to obtain such relations that we conjecture to be true ... we construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable ... $\endgroup$ – bright magus Aug 1 '16 at 6:47
  • $\begingroup$ ... algebraic relations that hold in the model, postulate their validity, and then throw away the model. We may compare this process to a method sometimes employed in French cuisine: a piece of pheasant meat is cooked between two ices of veal, which are then discarded." (nobelprize.org/nobel_prizes/physics/laureates/2004/…) Well, I'm quite old fashioned as regards science - in such a sense that I do not buy magic, however entertaining it might be. $\endgroup$ – bright magus Aug 1 '16 at 6:49

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