Photons are the sole free massless particles in the Standard-Model (SM) and light-waves are still studied with the linear Maxwellian theory. But, if we refer to massive formalisms, started by de Broglie-Proca, or non-linear by Euler-Heisenberg (for second order quantum electrodynamics) and Born-Infeld (to normalise the infinitesimal charge), and followers, surprising options emerge for our reading of the universe.
An international collaboration including CERN, London, Napoli, Rio de Janeiro and Tenerife has performed theoretical investigations finding an effective mass to the photon proportional to the Lorentz(-Poincaré) Symmetry Violation (LSV), a group velocity differing from c and birefringence within the SM Extension (SME). Further, it determined three experimental or observational upper limits to the photon mass, published by the Particle Data Group, using solar wind satellite data and Fast Radio Bursts.
In magnetars, the strong magnetic field determines red and blue shifts.
In the SME, we have determined a frequency shift for a photon propagating in vacuum, possibly in presence of a magnetic field. A non-zero vacuum expectation value due by the LSV might explain the discrepancy between the red-shift and luminosity distances for Supernovae without recurring to the proposition of an accelerated expansion. We are now progressing and determining frequency shifts in vacuum when adopting a generalised non-linear electromagnetism described by a Lagrangian in the powers of the electromagnetic field and its dual.
