Apparently, this result from Leonhardt–Piwnicki theory is essentially different from the result from wang's theory, where the light ray velocity or photon's velocity is argued, according to Fermat's principle and relativity principle, to be parallel to the wave vector, observed in all inertial frames. This difference between the two theories comes from the different understandings of Fermat's principle. In Leonhardt–Piwnicki understanding, the light rays are the "zero-geodesic lines "two points" with respect to Gordon's metric", and only "in the special case of a medium at rest, this result is equivalent to Fermat's principle", namely Fermat's principle is valid only in the medium-rest frame, while in Wang's understanding, Fermat's principle is valid in all inertial frames, and the light rays are the paths with the minimum optical length between "two equiphase planes" (instead of two points). Apparently, Leonhardt–Piwnicki theory (where as a physical law, Fermat's principle is valid only in the medium-rest frame) would not support the principle of relativity. On the other hand, a moving isotropic medium becomes "anisotropic". For a plane light wave in a uniform anisotropic medium, the light power (energy) must flow along the wave vector, otherwise energy conservation will be broken; namely Fermat's principle is consistent with energy conservation law. Thus according to Wang's analysis, the Gordon-metric geodesic lines defined as light rays in moving media in Leonhardt–Piwnicki theory would contradict against energy conservation law.