When light is refracted it changes momentum in direction not magnitude.
(Now I do know it's kind of breaking the rules to take a wave described phenomena and apply particle-like theory to it. Or to apply any theory outside its domain of applicability. But what other tools do we have to look for some more general insight?)
Anyway isn't it right that individual photons, whether behaving as particles or waves, have to obey conservation of energy; and also that individual photons can be refracted (well they definitely get diffracted in the double slit experiment).
For an individual photon to change momentum (direction) there must be force applied and an equal and opposite reaction on the refracting media (there are two at a refracting boundary).
Applying a force tangential to the photons path to change it's direction does no (zero) work, but...
Q1: The medium receiving the reacting force is in random thermal motion, to have a situation in which there is no work done to conserve energy and momentum there must never be a component of the movement of the medium in the direction of the reaction force. How can that be the case when it is in random motion?
Also even though no work is done the photon "knows" of the presence of the refracting boundary and changes direction. Picking on quantum field (perturbation) theory now, there must have been an "exchange".
Q2: What is the force carrier? Refraction is an electormagnetic effect. Is the force carrier for the interaction a zero energy virtual photon? - is a photon with no energy something that can exist, even briefly? Is it right that a photon could interact with a photon (even a virtual one) - my understanding is that photons do not interact with each other and I think it causes all kinds of problems, for example in cosmology?
Speculative I know, but perhaps something else is being exchanged to apply the force and turn the photon, maybe virtual photons only get exchanged when work is done?