Can one distinguish real and virtual photons?

There is a widespread view that external legs of Feynman diagrams are in reality just internal legs of larger diagrams. This would blur the distinction between real and virtual particles, as in reality, every leg is internal.

The basic argument behind this view is the fact that the photons that hit an eye (and this give evidence of something real) were produced by excitation form some distant object. This view is consistent with regarding the creation or destruction of photons as what happens at a vertex containing a photon line. In this view, it follows that the universe is a gigantic Feynman diagram with many loops of which we and our experiments are just a tiny part.

But single Feynman diagrams don't have a technical meaning. Only the sum of all Feynman diagrams has predictive value, and the small ones contribute most - otherwise we couldn't do any perturbative calculations.

Moreover, this view contradicts the way QFT computations are actually used. Scattering matrix elements are always considered between on-shell particles. Without exception, comparisons of QFT results with scattering experiments are based on these on-shell results. It must necessarily be so, as off-shell matrix elements don't make formal sense: Matrix elements are taken between states, and all physical states are on-shell by the basic structure of QFT. Thus the structure of QFT itself enforces a fundamental distinction between real particles representable by states and virtual particles representable by propagators only.

Creation and destruction of particles in space and time cannot be identified with vertices in Feynman diagrams. For Feynman diagrams lack any dynamical properties, and their interpretation in space and time is sterile.

A photon that travelled from Andromeda to the eye of an observer must have had a probability of entering the solar system, and a probability of causing an electronic transition in the eye, causing a neuron to fire. Firing is an activity in time, which happens with a certain probability rate computable from the incident wave function of the photon beam. According to QFT, this wave function only involves an integration over on-shell momenta. No approximation of off-shell momenta is involved. Thus all photons from Andromeda detected here are on-shell, real.

In contrast, propagator contributions of virtual photons involve integration over all 4D momenta. The context in which the two integration processes are used is completely different.

Thus virtual photons have nothing at all to do with real photons. We are not living in a gigantic Feynman diagram. The view that in reality there are no external lines is based on a superficial, tempting but invalid identification of theoretical concepts with very different properties.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ