My students have sometimes teased me about a candid way I have of answering difficult questions. I say, "I really don't know the answer, but I'll answer it anyway". This is to say that I do not understand the subject well enough to be able to construct a simple definitive answer which can satisfy a discerning person (indeed, there may be no such answer) but what I am going to say contains -- I believe --some elements of the truth and may be useful to you." I sometimes add, "Don't ask me to explain this further as I have already told you more than I know."

So, in that spirit I'll try to comment usefully on your subtle question. As you probably know, your question --only slightly rephrased -- is also relevant to neutrinos which also couple to massive virtual states. Less obviously, the question you raise is also relevant to heavy particles such as the electron as I will explain.

A simple statement that is wholly correct -- but is not to me completely satisfying -- is that the mass of a particle in a vacuum includes the effects of all virtual transitions and is constant. Moreover that mass must be a Lorentz invariant and then independent of the velocity of the observer -- or of the particle. The mass of the photon has been measured to be zero -- with a very small uncertainty. To say that an electron is part of the time a virtual electron-positron pair is a reasonable verbal picture of our mathematical (or precise logical) description of the photon -- albeit with elements of metaphor. However, the total mass of that electron-positron pair is zero; that is why we call it virtual. Why am I unhappy with that answer? Consider an electron. The energy density stored in an electric field is just E per unit volume in appropriate units where E is the electric field strength. Then there is mass stored in that field equal to E~/c~ per unit volume. The electron is point-like down to very small distances and the total mass 0f the field down to that distance is far greater than the measured electron mass. In the same sense as the electron generates a field by emission of virtual photons, the photon (and neutrino) generate fields through their coupling to virtual states. However, although the simple addition of the field energies (or masses) adds up to a finite -- and even large amount, the mass of the photon and neutrino are very small and consistent with zero.

0f course, what I am complaining about is that I have no simple way 0f "explaining' this. The full logical (or mathematical) treatment does not stumble over the problem.