  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.
