X-ray crystallography is explained as scattering of photons on the electrons of a crystal. But what is the force that leads to this scattering? The usual explanation in terms of absorption and re-emission seems a bit phenomenological to me.
All hypotheses are tested against reality and rely on phenomena to invalidate them.
If the Compton model is not to your liking, is the Feynman model any better?
First two pages of (http://bit.ly/LWHFx1)
Feynman's model ntroduces the possibility of apparent reversal of causation depending on the frame of the observer, and is a far more 'beautiful' explanation but considerably less 'commonsense-ical' than Compton's model.
At the end of the day, only the model's predictions matter, we're not trying to uncover the truth of the situation (whatever that means) but to develop models that simply but accurately reflect the data we have access to. It is a deep mystery that the human mind finds the more generally accurate models (Feynman) to be somehow more aesthetically pleasing, even at the expense of common sense.
Photons are the "force" particle between charged particles (electrons, protons, and the like). This definition is according to the Standard Model. So, the wording of your question is not a proper problem statement, IMHO.
The question I think you are asking is"How does a photon's 'energy' get emitted or absorbed by an atom's electron?" In the last month I have started researching this answer, and what is available is hard to find, and the answers are deep. I would read any citations posted.
The EM photon field energy travels towards a surface of atoms, and one of those atoms outer electron's quantum mechanics wave form "feels" this approaching EM field, and beats out all the surrounding atoms' electrons for absorbing this photon's EM field, and that electron's wave form collapses to a state of higher kinetic energy in the form of a velocity vector away from the nucleus. How does this happen?
Sanjay is right that it's a QED question, but the way I have worded it, may make it outside of normal QED's scope or ability to answer.
I think my question goes in that direction, yes. I always felt this idea of absorption and instantaneous re-emission with the same energy lacks a mechanism. In that sense QED doesn't really add very much to Compton. I was looking for some mediator of this interaction just like gravitons mediate the interaction between two masses. Now I think that probably the question doesn't really make sense. It's a bit like asking what mediates the interaction between a graviton and a particle with mass. In any case I suppose a question like that is outside any existing theory, as you say. It would be interesting to hear more about your findings. Is there some published and easily accessible information about it?
Just to explain why I asked the question in the first place: When a charged particle is scattered by another charged particle the charged particle can be observed whereas photons are responsible for the force that leads to the scattering. When a mass is scattered by another mass the masses can be observed whereas gravitons produce the force. When a photon is scattered by an electron the photon and the electron can be observed... In analogy I was looking for some other particle that's responsible for the force. It seemed to me that something was missing for a "symmetric" description of nature.