julianb said:
Apologies, I don't follow.
So, the paper you linked starts off with this assumption: "Consider the well-known processes of emission and absorption of photons by atoms" ... which in turn, I understand, assumes that photons only exist in quantums.
That's not an assumption, it's the evidence-based starting point: All interactions between electromagnetic fields and matter, if examined at a sufficiently low intensity, involve the transfer of discrete amounts of energy and momentum. (We do make an assumption beyond that, namely that at high intensities it's the same physics but scaled up - we know what a drop of water is, we know what a rainstorm is, and we can model a rainstorm as a very large number of drops. There's no observational evidence to make us distrust this common-sense assumption so we'll run with it). That motivates us to seek a theory consistent with these observations - and, yes, such a theory might conceivably allow for other so far unobserved interactions as you suggest in your initial post.
So we proceed to develop such a theory, and eventually we find that the Hamiltonian can be written in the form at the bottom of page 7, as a superposition of quantum oscillators. At this point we decide that "quantized excitation of the electromagnetic field" is an unwieldy phrase and we decide to use the word "photon" instead to name the terms that appear in this Hamiltonian. So we aren't assuming "that photons only exist in quantums", we've constructed a viable theory that describes electromagnetic fields in terms of quanta, and now that we have a viable theory we've decided to name the quanta "photons".
So, when you then wrote 'Thus there's no such thing as "less than 1 photon worth of energy".' -- I'm unsure how that follows? Does the paper demonstrate this? Or merely presume it?
The Hamiltonian at the bottom of page 7, by construction from its starting point at Maxwell's equations, includes all the energy in any arbitrary configuration of an electromagnetic field and there's nothing but photons in that Hamiltonian - that's a demonstration.
Isn't that just still claiming (basically) "we can only detect photons ergo that must be the smallest amount of light"? I don't understand how that is any different from "the atom is the smallest possible particle."
The crucial difference is that there is no "smallest photon". Thus there is no amount of energy so small that it cannot be described as a superposition of photon states. It's analogous to how there's no volume of water that I cannot measure in "spoonfuls" if I have an infinite collection of measuring spoons, one for each real number.
To be fair, there is a LOT of corner-cutting and oversimplifying in that paper and that may reasonably leave you with the suspicion that we're trying to sneak some circular reasoning past you. However, I don't know of any simpler presentation that doesn't totally misrepresent what photons are. For more complete presentation, Lancaster and Blundell "Quantum Field Theory for the Gifted Amateur" is (barely) accessible to someone with a bachelor's degree background. Or if you want free online, there is Srednicki
https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf which is way more demanding but available free on the internet.