If the spatial extent of the proton is not infinite, this would imply that the charged quarks making up the proton are accelerating. Why aren't these quarks then emitting electromagnetic radiation, thus slowing down? I thought electrons were essentially standing waves around the nucleus, and thus not accelerating. Maybe there is a good youtube video explainer? Seems like there would also be an associated temperature and blackbody radiation of these quarks.
Quarks don't have quantum energy states to transition between, hence they aren't subject to radiating photons due to acceleration.
Similar to why the electron in a hydrogen atom doesn't keep emitting radiation and crash into the nucleus once it reaches its ground state... there's no lower state for it to jump to.
That's a good point, I don't know what's up with that. Google just says, "A single oscillating electron does not continuously emit radio waves; it has a microscopic probability of emitting a single RF photon during a given cycle." It would be necessary to delve into the whole QED thing to get a better explanation, based on what I'm reading.
Either way, quarks don't have an electron-like magnetic moment, so they aren't capable of coupling to the EM field.