I'm unconvinced by the paragraph beginning, "However, the above result leads to a striking contradiction with the covariance principle, which is a fundamental p

I'm unconvinced by the paragraph beginning, "However, the above result leads to a striking contradiction with the covariance principle, which is a fundamental prerequisite of the special theory of relativity." It is pretty well accepted that light can have mass, in the sense that the authors are using the term. For example, light trapped as a standing wave between two mirrors in an etalon must have zero momentum. (By symmetry: if it has momentum, which way does the vector point?) But that light has energy, so it has mass in the sense that m must be non-zero to satisfy E² = p²c² + m²c⁴. More precisely, the momentum-energy vector of the light is timelike instead of lightlike. This makes me suspect the whole paper, because it seems really plausible that a light wave in a medium is partly like a standing wave. In particular, there is a limit of a dense medium whose momentum is negligible. (Maybe the refractive index approaches 1 in a very dense medium, but I can't imagine why that would be so.) I'd have to spend a morning reading and thinking about it to be sure. Also, the paper is suspiciously detailed; these questions should be resolvable at a much higher level of abstraction, and certainly without computer simulations.