Propagation of electromagnetic waves in a random medium and nonzero rest mass of the photon (Q1915372)

Maxwell's equations have been studied by Vigier in vacuum with nonzero conductivity coefficient \(\sigma\). This \(\sigma\) produces a dissipative term in the field equations, so that, if one considers the propagation of a photon through this type of vacuum, the photon acquires a mass at cosmological scale. This dissipation can be related to the fluctuation of the refractive index of the underlying vacuum. The authors study the wave equation with random refractive index and show that there exists a bounded and unique solution of this wave equation for small \(\sigma\) at \(r \to \infty\). In this model the velocity of propagation of disturbance is shown to be finite and so superluminal transmission is allowed. One remarks that the geometric structure of the background spacetime is based on the Synge's metric \(G^{\mu \nu} = g^{\mu \nu} + (1 - {1\over \eta^2}) u^\mu u^\nu\), which is non-Riemannian as in relativistic optics.