I'm in my fourth year of a Masters Physics course, and am quite concerned that I don't fully understand this.
Suppose a photon is emitted at point A and absorbed at point B one light-minute away. We 'look at' the system 20s after the photon is emitted. Define point C as the point one-third of the way between A and B.
- How should the light be described? I want to say "the photon is at point C" but I know Fock states are unphysical and coherent states are how best to describe light. But, is this superposition of photon numbers still at point C, or is there a spatial distribution too? If there is a spatial distribution, does that not give a chance that it will be absorbed at B at eg 59s or 61s?
- Where are the magnetic and electric fields modified? Is it just at point C ; everywhere along the path from A to B (which would seem to have information travel faster than light) ; everywhere between A and C ; some Gaussian-like volume around C ; something else?
- How are the E and B fields modified? I "know" that it's by sin(kx-wt), but depending on the answer to Q2 that may mean different things. (Eg, if E and B change only between A and C, do they just "switch off" once it's absorbed at B (again raising locality questions), or does the magnitude dampen with time after it's initially altered? In general, how do they change with time, and at various events (emission, absorption, 'the phtoton passing point C'?)
- What does it mean to say that E and B are perpendicular? Do they literally vary spatially, ie if I move upwards from C with my detector I read a B but no E field, while if I move sideways then I get an E but no B field? If not, to what does the perpendicularity refer?
The bold is my questions (obviously); after that is my guesses at answers and/or hints at where I'm confused, but feel free to ignore these and talk about anything that's relevant to answering.
To be clear, I'm not asking about if I actually made a measurement at point C, I'm asking what we can deduce from the equations etc we know describing light and the EM field. (Think calculating where a ball I throw in the air will be after 0.2s, as opposed to catching and measuring it after 0.2s and hence changing the rest of the motion.)
Also, I'm looking for a model of what happens, and (as far as possible) the simplest full explanation why. (I tried asking one lecturer but he started talking about Fourier transforms and stuff I didn't really understand/see the relevance of, and didn't give a direct "they're modified like this" answer, hence this note.)
Finally, if you refer to modes of EM waves/fields in your answer (or are feeling particularly generous), please define exactly what you mean by this as well - many times I've Googled and still I don't entirely understand these.
Much much thanks!