Relativistic theory of reflection and refraction of electromagnetic waves at a moving interface

Abstract In this work, we shall show that, referring to general relativity and Fermat’s principle, in material media, the usual definition of interval should be modified to correctly describe behaviors of an electromagnetic wave obliquely traveling through an interface. Correspondingly, the modified Lorentz transformations (MLTs, in which speed of light in vacuum is replaced by phase speed of electromagnetic wave in the material medium involved) are proposed. Furthermore, it is demonstrated that, based on MLTs of both 4-dimensional wave vectors (4-DWVs) and electromagnetic field tensors (EMFTs), at a moving interface, boundary condition equations, and then laws of reflection and refraction may be derived. The later can also be self-consistently obtained by applying Snell’s law, Fresnel’s law and MLTs of both 4-DWVs and EMFTs. This work provides a possible candidate for solution of reflection and refraction of electromagnetic waves at a moving interface, which may be helpful to deepen the understanding of foundations of electrodynamics of moving media.