what i said is not backwards unless you use the inverse understanding of "exist". and how can photons exist without interaction? they don't. they're localizations by detectors. until then, they only "exist" as the probability wave. that's due to nothing localizing them. that's how i mean "exist". so it's not really meaningful to use that word.
btw "any other particle" doesn't fall out of EM fields.
I very obviously meant that XYZ-particle states fall out of mode expansions of the XYZ-field, not that all particles are EM quanta.
> what i said is not backwards unless you use the inverse understanding of "exist". and how can photons exist without interaction?
Exactly the same way any other field configuration can? The state space of the free EM field simply is the photon Fock space.
The state space of an interacting 4D EM field is unknown and may well not exist, hence the need for perturbative approaches and renormalization - in which particle states again emerge as terms in the perturbation series.
> The state space of the free EM field simply is the photon Fock space.
but I'm not sure what your point in mentioning this is. When people hear things like "particles exist between their emission and measurement", they might get the idea that there could be said to be any reality to the existence of particles in transit. They simply aren't particles the way people think of them - they are probability waves. A great example we could discuss is the HBT experiment in which photon bunching was seen. If the bunched photons were really "particles" by any sense of the word, they wouldn't bunch in time of detection merely by the fact they are entangled with each other. That would be like saying entanglement affects the flight of a particle which is simply not able to be said.
They're not anything the way laymen think of them. They're not classical particles, they're not classical waves, they're not classical anything. They're not really probability waves either, for that matter, or even field configurations - the real object is the algebra of observables. But laymen don't get to dictate the vocabulary of physics, and neither do mathematicians. Fields are the things that would be dual to the observable algebra, were it always equipped with a dual; particles are the things whose creation and annihilation operators would generate it, were there only always such things.