tashja:
A Feynmam diagram describing the space-time processes of two electrons exchanging a virtual photon, emitted at A and absorbed at B....
Q: So, do photons travel faster that light between particles and sometimes at less speeds, too?
There's a difference between
virtual photons (like the ones in Feynman diagrams) and
real photons (like the ones that you see or that carry radio signals). Real photons never travel faster than light. In fact, they always travel at exactly the speed of light.*
Real photons can carry useful information from place to place. Virtual photons, on the other hand, are more like carriers of electromagnetic forces - for example, they "tell" two positively-charged particles to repel one another by carrying a kind of message from one particle to the other. We can detect real photons with our eyes, a camera or whatever. We can't detect virtual photons, because they spring into existence only for a tiny fraction of a second, do their job then disappear again. If they were detectable they would violate conservation of energy, effectively acting like energy appearing out of nowhere.
''The self energy of the electron (an electron interacts with its own EM field) by emitting a photon and then capturing it again.''
How could a electron catch the same photon it emitted? The electron would have to be moving faster than the photon, no?
In quantum physics, a photon actually doesn't have a well-defined path through space. A photon is, in some ways, a wave of probability that is spread throughout space. An equivalent way of looking at it is in terms of Feynman's "sum over histories", in which you can consider the photon to simultaneously "explore" all possible paths between the point of emission and the point of detection or absorption.
In the Feynman picture, a photon doesn't have to travel in a straight line between its emission and absorption points. Some of the paths it explores will be straight lines, but some will be curved paths and some will be circles or spirals or squares or any shape you care to name. So, an electron can catch its own photon just by the photon travelling in some kind of loop and coming back to the electron.
For
real photons, if the photon is unimpeded between two points then when we add up all possible probabilistic Feynman paths the end result is the same as it would be if a point-like particle had travelled in a straight line between the two points at constant speed. (*This is the more complex explanation referred to by the asterisk above.) The curvy paths kind of cancel each other out when you do the Feynman sum. When you're dealing with
virtual photons to calculate something like the self-energy of an electron, things are quite different.
So, in short, when you're dealing with the quantum field theory picture of photons (e.g. Feynman picture), you're getting into rather complicated and technical territory, and the rules that apply to the real photons you're familiar with don't exactly apply to virtual photons.