I feel like I've been frequently presented with an interpretation of EM waves that goes something like this:
Light is an oscillating electromagnetic field. Because changes in the electric field produce changes in the magnetic field and vice versa, it is self propagating. The electric field of light can be represented as a sine wave with a phase, frequency, and amplitude. The amplitude however, only takes on discrete values. For monochromatic light, it is an integer multiple of the "photon energy".
This seems fairly intuitive for collimated beams of light (such as from a distant source) and so the light arrives as a plane wave. That is to say, the "sine wave" moves more-or-less like a "ray of light". And if you put a sensor within that ray of light, you'll detect the light.
But I start to get confused when I think of reflections. Feynman's QED and other sources talk about reflection in terms of interference. That the light incident on a surface causes the charges in that material to oscillate, which produces new EM waves. These EM waves interfere with one another giving us the classical macroscopic perspective of the light being specularly reflected. Feynman in this context though, is talking about this in terms of the probability of detecting a photon, and so where the probabilities constructively interfere (along the line where angle of exittance equals angle of incidence), we are likely to find a photon and along all other directions we are unlikely to find a photon.
Similarly, say we have a single electron in space that is oscillating in the $+z$ direction. Then it would emit EM radiation out into the entire $xy$ plane. The intensity of this would necessarily have to decrease over distance, but we know that light is quantized. If the EM waves it was emitting were probabilities, then we should expect that for a given observer, the odds of detecting a photon decrease with distance but once we actually make a detection, the photon would have a definitive energy. This is, as far as I know, true.
It seems like both of these scenarios are pushing me towards viewing the EM wave as a representation of the probability of finding a photon, rather than the actual strength of the electric field itself. But this doesn't seem right either, as afterall charges react to light's oscillating electric field. Plus the wave doesn't just take values between 0 or 1 as a probability should, but rather has an amplitude based on the energy, and oscillates between $-A$ and $A$. Feynman refers to the square of the amplitude as the probability, but this doesn't fully solve my confusion as now the values range from $0$ to $A^2$.
What am I missing here? Talking about the wave as purely the oscillation of the electric field feels incomplete, but viewing it as a probability also seems incomplete. Afterall, the literal oscillating electric field is what produces the oscillating magnetic field, and it is what drives the oscillation of charged particles it comes across. Yet at any given point in space, you only have a probability of actually detecting a photon there, and it's energy is definitively known. So I must be misunderstanding something. I can't understand what else the wave actually is. Or are there two waves, one for the probability and one for the electric field?
Edit: I should say I have only read the first 2 chapters of Feynman's QED. Perhaps as I continue reading, my questions will be answered. I'm just finding myself very confused at the moment.
