Theory of Refraction, Ray–Wave Tilt, Hidden Momentum, and Apparent Topological Phases in Isotropy-Broken Materials Based on Electromagnetism of Moving Media

The mysterious nature of electromagnetic momentum in materials is considered one of the most significant challenges in physics, surpassing even Hilbert’s mathematical problems. In this paper, we demonstrate that the difference between the Minkowski and Abraham momenta, which consists of Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We show that individual electromagnetic waves with non-unit indices of refraction (n) appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames, these high-k waves are Fresnel–Fizeau dragged from rest to their phase velocities, acquiring longitudinal hidden momentum and related refractive properties. On a material level, all electromagnetic waves belong to Fresnel wave surfaces, which are topologically classified according to hyperbolic phases by Durach and determined by the electromagnetic material parameters. For moving observers, material parameters appear modified, leading to alterations in Fresnel wave surfaces and even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of electromagnetic momentum tilt, defined as the non-zero angle between Abraham and Minkowski momenta or, equivalently, between the rays and the wavefront propagation direction. This momentum tilt is only possible in isotropy-broken media, where the E and H fields can be longitudinally polarized in the presence of electric and magnetic bound charge waves. The momentum tilt can be understood as a differential aberration of rays and waves when observed in the material rest frame.