Observing Ghost Entanglement Beyond Scattering Amplitudes in Quantum Electrodynamics

A fully local quantum account of the interactions experienced between charges requires us to use all four modes of the electromagnetic vector potential in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are “real” in that they contain photons that can actually be detected. The photons present in the other two modes, the scalar and the longitudinal, are considered unobservable and are referred to as “virtual particles” or “ghosts”. Here we argue that this view, which is rooted in standard quantum electrodynamics, is a consequence of assuming that charges are always dressed in such modes and that naked charges do not have an independent existence. In particular, we present a thought experiment where, assuming that naked charges can be independently manipulated, one can then measure the entanglement generated between a charge and the scalar modes. This entanglement is a direct function of the number of photons present in the scalar field. Our conclusion, therefore, is that the scalar quantum variables, under this assumption, would be as “real” as the transverse ones, where reality is defined by their ability to affect the charge. A striking consequence of this is that there is a critical value of charge beyond which we cannot detect its spatial superposition by local means.