Long range, long lived and gauge invariant massive photons via Stückelberg scalar coupling.

Abstract

It is largely believed (or strongly assumed) that photons are massless particles and the most compelling evidence there—it is said—is found in the manifestations of photons being long ranged and long lived particles. As we have done before, albeit, with a much better and clear insight in the present than before; we argue herein that massive photons can still enjoy the special and rare privilege of travelling at the speed of light c while being long ranged, long lived and most of all, obeying the much desired gauge symmetry. This we achieve by breaking the traditional Lorenz gauge and in its place, we introduce a new Special Gauge Condition (SGC) that does the work of assuring the photon its longevity, long range-ness and that it [photon] propagates at the speed c. However, the most melancholic outcome of our investigation is that if the present scheme is what subtle Nature has chosen to endow the photon a non-zero mass so that it [photon] still obeys gauge invariance, is long ranged, long lived and travels at the sacred speed c; then, this non-zero photon mass may be very difficult, if not impossible to measure. We use the equations developed to investigate Lorentz violation in γ-ray bursts.