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I just read this answer to "What exactly is a Photon?" which has me a bit confused. It seems to be arguing that "photon" is just a catch-all term for any sort of interaction with the EM field and the implication is that it's not even a particularly useful concept, in contrast to the fundamental particles of other fields. But how is that any different from other elementary particles, when all particles are just excitations in quantized fields?

I also found several threads talking about whether photons have wavefunctions or not, such as this one: Wave function of a photon? and I'm seeing conflicting information. If photons don't have wavefunctions, are they even particles at all, in the sense of being localized disturbances in a field?

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  • $\begingroup$ in the question you quote, I have an answer from the experimental point of view physics.stackexchange.com/questions/273032/… $\endgroup$
    – anna v
    Commented May 2, 2023 at 3:42
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    $\begingroup$ I'd like a compromise. Whatever is the quanta of EM wave that is violently, discretely exchanged in order for describe the properties of light's interaction with matter, is the photon. I do not claim that it is localised (I hope it is not localised, in fact), or that it behaves like the other quantum particles. I would also avoid the baggaged term of particles. Whatever that thing is, is what we mean by photons. $\endgroup$ Commented May 2, 2023 at 4:54
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    $\begingroup$ See How does quantization arise in quantum mechanics? and Particle- and wave-like properties In short - it depends on what one calls a particle. Photon is not a particle in classical sense, but it has particle properties. $\endgroup$
    – Roger V.
    Commented May 2, 2023 at 10:06
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    $\begingroup$ A photon is an irreversible energy exchange between the quantized electromagnetic field and an external system that we call "emitter" or "absorber". There isn't much of a mystery here... it's just not being taught very well beyond the high school level which, curiously, is about as "exact" as you will get about it. Once you go past the photoelectric effect, there is a lot of confusion in the way we teach undergrad physics that comes from a misunderstanding of von Neumann's solution theory for the Schroedinger equation as an expression of physical reality. That's simply not the case. $\endgroup$ Commented May 3, 2023 at 17:41

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Photons are different from other particles because photons are massless and hence have no meaningful non-relativistic limit as they always move at $c$. I will not rehash the various approaches to actually pinning down what a photon "is" - that's what the linked question is for - but merely give several arguments for why you shouldn't actually expect the photon to be "a particle" like all the other particles.

The only known rigorous construction of "free particle states" in quantum field theory (Haag-Ruelle scattering theory) requires a mass gap - the lowest lying excitation of the interacting Hamiltonian needs to have a distinct mass. The presence of massless photons destroys this notion, and it becomes essentially impossible to distinguish between "single massive particle" and "single massive particle surrounded by a cloud of low-energy massless particles".

The lesson here is that the notion of "a particle" as something that has a definite position or can be localized to arbitrary degrees is inherently non-relativistic. It is well-known that there are no good relativistic position operators, the closest being the Newton-Wigner operators, so the picture of some little object that has a "position" that can be measured to arbitrary precision simply only makes sense in a non-relativistic viewpoint.

"Photons" are inherently relativistic - you cannot construct a proper position wavefunction for them because there is no position operator - and so their nature is very different from the other massive particles. They are not "localized disturbances in a field" because, as vague as that notion may be already for massive particles, the notion of "localized" simply is impossible for a relativistic particle. There exists a general notion that relativistic quantum states can never be localized in the sense we desire called Malament's theorem.

More specifically for the photon, note that a classical electromagnetic wave - a state with definite electric and magnetic fields - is a coherent state where the number of photons is indeterminate. Hence it is not particularly useful to conceive of any electromagnetic radiation as being "composed of photons" - thinking in terms of definite photons uses a different eigenbasis, and you would have to consider the EM wave as a superposition of the states of definite photon numbers, which certainly destroys any intuition you might have (just think of the non-intuitive behaviours other QM superpositions show).

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    $\begingroup$ 'Hence it is not particularly useful to conceive of any electromagnetic radiation as being "composed of photons"' Except, whenever you make a detector of electromagnetic radiation sufficiently sensitive, you see photons. We count them, and do things like photometry and spectroscopy from the counts. So, it's tremendously useful to conceive of electromagnetic radiation as composed of photons. $\endgroup$
    – John Doty
    Commented May 1, 2023 at 23:57
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    $\begingroup$ @JohnDoty It may be a useful model, but it's probably not as clear-cut as you think. See physics.stackexchange.com/q/68147/50583 for discussions of why even "obvious" demonstrations of photons like the photoelectric effect may not necessarily require the notion of photons. $\endgroup$
    – ACuriousMind
    Commented May 2, 2023 at 0:04
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    $\begingroup$ @JohnDoty, OP was not asking whether it was "useful to conceive of radiation as composed of photons." OP was asking what kind of sense it makes sense to call those photons "particles." Of course, each time your detector counts one, that's an event that happened in a particular time and place—just like how a collision between two tiny balls would happen at a particular time and place. So, that's kind of "particle" like. But is that enough to justify calling them particles? I won't attempt to answer that myself because I am not a physicist. But, I'll check back here to see what y'all decide. $\endgroup$ Commented May 2, 2023 at 0:12
  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – ACuriousMind
    Commented May 3, 2023 at 20:34
  • $\begingroup$ Actually, you can have (strictly) localized disturbances in a field - it's just that such "disturbances" cannot be regarded as single particles, i.e. the corresponding states do not eigenize the number operator for the field. $\endgroup$ Commented Oct 13, 2023 at 1:31

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