I shouldn't have written »absorbed by atoms and reemitted later«, that is really a different thing, interacting with the atoms is better. The superposition of all possible paths and interactions results in a wave function that effectively travels slower than the speed of light.

> If it were true we would see sharp changes in the observed speed of light at wavelengths depending on the absorption spectrum of the material in question.

Uh, we do. The imaginary portion of the index of refraction near a resonance generally looks roughly like a gaussian, and the real portion does have jumps that look a bit like tanh.

Just to be clear, I am not a physicist, only a interested layman. As I understand it currently, photons don't travel any path. They are emitted somewhere at some point in time and detected somewhere else at another point in time, what they did in-between is not a meaningful question, at least in the classical sense of asking for a path the photon took. When we want to calculate the probability of observing the photon at a specific place at a specific point int time, then we consider all possible paths - including the photon traveling to the edge of the universe and returning from there, including the photon going into the future and coming back - and sum them up. There is a relatively simple formula for every possible path and those possibilities interfere when we sum them up, some path amplify each other, some cancel out, in the end you have a probability distribution in space and time telling you where it is likely and where and when it is unlikely to find the photon in case you tried to observe it there. What the photon did in-between, we don't know, is a meaningless question, ... at least I can't tell.

They often do. Momentum must be conserved (despite this article...)

Yes, due to the interaction of the photon with the atoms of the material the photon takes longer to move through certain distance of a material than through the same distance in vacuum.

¯\_(ツ)_/¯