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

We show that the incompatible Laue and Rosen treatments of special relativity in a dielectric are both correct but have different regimes of applicability. The Laue theory has a fundamental physical basis in Einstein's special relativity and the relativistic velocity sum rule. The Rosen version of dielectric special relativity was derived heuristically. Consequently, the Rosen theory and its consequences are almost completely ignored in the scientific literature and there is little to no discussion about the incompatibility of the two theories of relativity in a dielectric. We derive both versions of relativity using inertial reference frames moving at constant velocity along the interface between a simple linear dielectric medium and the vacuum. We show that the Rosen theory applies to relativistic physics in the interior of a simple linear dielectric medium and the Laue theory is used to relate these physics to a Laboratory Frame of Reference in the vacuum where measurements can be performed.