Is thermal conduction really radiation? I have no doubt thermal conduction is a useful model for heat transfer, wherein kinetic energy is transferred between particles when they collide. However, according to explanations that I believe are canonical, two molecules collide due to electromagnetic repulsion (and possibly Pauli Exclusion) of their electron "clouds". In the standard model of particle physics, electromagnetic repulsions between electrons occur via the exchange of force-carrying particles, which happen to be photons. (Virtual photons, if I'm not mistaken, and perhaps that is an important point here.)
So, if thermal conduction is microscopic kinetic energy transfer due to molecular collisions, and molecular collisions occur by the exchange of photons, then it appears to me that at a fundamental level thermal conduction is a special case of energy transfer by photons, which in my understanding, is the radiation mechanism of heat transfer.
Is this conclusion incorrect (and if so, why)?
 A: The important distinction between thermal conduction and thermal radiation is that the heat exchange is driven by the difference in temperature for thermal conduction and the heat exchange is driven by the fourth power of the difference in temperature for thermal radiation. Perhaps it would be possible to derive, on a microscopic level, the relationship between this fourth-power microscopic radiation and the macroscopic first-power conduction equation. However, I am not aware of such a derivation and it is not immediately obvious. Certainly, even if such a microscopic derivation is possible, the macroscopic form is sufficiently different to warrant its own category
A: You are correct that virtual photons are not photons; what we refer to as radiative heat transfer is mediated by the latter. Conductive heat transfer occurs through physical contact and is not radiation.
A: Perhaps this analogy will help. You and your image in a mirror are real and virtual, respectively. When you collide in the real world with something physically, you "know". Your energy and momentum state are affected. In the image world, your image and the object's image "exchange" virtual packets.
Would you say that collisions in the real world are not real because the mirror world collision is not "real" (it is virtual)? Or would you say that you can assign mass to objects in the image world?
Hopefully, you would say no to both above. Therefore, you would say that real collisions of atoms or molecules (as one form of conduction) are not the same as the virtual exchanges of photons that we use to model them.
Alternatively, real objects with mass and even without mass (photons) collide. Virtual objects (virtual photons) are exchanged.
Finally, to throw a caveat in the mix, how will you consider one of the other three modes of conduction, lattice vibrations, since it is not a direct collision (and therefore has no need to consider virtual photons to model electrostatic repulsions)?
