Reconciliation of the Rosen and Laue theories of special relativity in a linear dielectric medium

The theory of dielectric special relativity was derived by Laue from a fundamental physical basis in Einstein's special relativity and the relativistic velocity sum rule. The Laue theory is experimentally verified by the Fizeau water tube experiment. In contrast, the Rosen version of dielectric special relativity was derived heuristically and has no experimental validation. Consequently, the Rosen theory and its consequences are mostly ignored in the scientific literature and there is little to no discussion about the incompatibility of the two theories of relativity in a dielectric. In this article, the Laue theory is developed from boundary conditions using inertial reference frames moving at constant velocity along the interface between a simple linear dielectric medium and the vacuum. Then, the Rosen theory is derived in the context of inertial frames of reference moving at constant velocity in the interior of an arbitrarily large linear isotropic homogeneous dielectric medium. These derivations show that the Laue and Rosen theories of dielectric special relativity are both correct but have different regimes of applicability. The Rosen theory applies to physics in the interior of a simple linear dielectric and the Laue theory is used to relate these physics to a Laboratory Frame of Reference in the vacuum where measurements can be performed.