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I understand that photons, like the other elementary particles, is a point particle and doesn't technically have definite boundaries.

However, protons and other baryonic matter have a mean atomic radius, or "charge radius".

But because baryonic matter is made of elementary particles (namely quarks); which means that there is some volume to which quarks are fundamentally confined.

Do other elementary particles, namely photons, have such volumes, albeit vague?

I ask because of my understanding of quantization. If photons have no "volume", then can't an infinite number of photons exist in the same space? Shouldn't there be some area around a photon that it keeps to itself? (Maybe not even necessarily photons, but any elementary particle).

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    $\begingroup$ Possible duplicate: physics.stackexchange.com/q/264676/50583 $\endgroup$ – ACuriousMind Dec 8 '16 at 16:58
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    $\begingroup$ Protons and other baryons are not elementary particles. They are built out of quarks and therefore have substructure. $\endgroup$ – dmckee --- ex-moderator kitten Dec 8 '16 at 16:59
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    $\begingroup$ As for the tight packing part of your question, you might want to search "Bose-Einstein condensate". Bosons (particles with integer spin; including photons) are not affected by the Pauli exclusion principle and you can put as many into a single quantum state as you like. $\endgroup$ – dmckee --- ex-moderator kitten Dec 8 '16 at 17:05
  • $\begingroup$ @dmckee I know baryons are not elementary particles, but are instead composed of them. I mean that since quarks bind together to form a proton, the proton has an (almost) constant volume. So the upper limits of quarks volumes can be described through the volume of the proton or other baryonic particles. Is this wrong? $\endgroup$ – A. Forty Dec 8 '16 at 18:48
  • $\begingroup$ Much smaller scales are probed in deep inelastic scattering experiments. Quarks, like electrons and other leptons, have no known size and are point-like in theory. I don't think the experimental limit on quark sizes is quite a good as that on electrons, but it is much smaller than a proton. $\endgroup$ – dmckee --- ex-moderator kitten Dec 8 '16 at 19:55
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In the quantum regime the answer to such questions really depends on what you mean by "volume".

A photon has no volume in the sense that it can theoretically be confined in an arbitrarily small region of space. Although such confining would result in the photon having extremely high energy fluctuations (basically due to the uncertainty principle) so that for extremely small sizes something else would probably happen, like pair creation in vacuum or similar complicated quantum field theory effects.

A photon can also have any volume you want, if you think of volume as the region of space in which you will be sure to detect the photon: a photon can come in any shape and size.

As per the last part of your question, yes it is absolutely possible to have an arbitrarily large number of photons in the same state, so in particular to have an arbitrarily large number of identical photons in the same identical region in space. This is a general property of bosonic particles, and the phenomenon is called Bose-Einstein condensation.

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  • $\begingroup$ I'm not sure about your statement that a confined photon will have large energy fluctuations. A cavity in space can be made small, but the field inside will have a single well-defined frequency. The spatial field pattern (solution of the Helmholtz equation) is confined, but a single frequency was already assumed when the Helmholtz equation was written down. $\endgroup$ – garyp Apr 1 '17 at 13:27
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At the present knowledge (i.e. as far as the Standard Model of particle physics is constructed), the particles are described as 'excitations' of some field permeating spacetime. Now, the interacting terms that we write down in equations describing the model, are local function of the fields, namely they depend on the value of the field on one point only.

Sentences like "there is an electron / photon / other elementary particle is at point $x$" really means "there is an excitation of the related field at point $x$". In this sense writing down a local interaction is equivalent to thinking to particles as point-like, and at the present state of the experimental physics there is no evidence of any whatsoever discrepancy with this assumption.

On the other hand, non-elementary particles are bound states of elementary particles, that means that there is no field associated to them (you can build effective models valid at some energy scale, but this is another story). This bound states are not easily describable in terms of their constituents (actually talking about constituents is improper), if looked "far enough" they look like having a volume because of all the interactions between the fundamental fields. A good analogy comes from chemistry: we know that atoms are basically empty, even though matter looks continuous and solid to us!

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