Minkowski tensor in electrodynamics of moving media and three rules for construction of the physical tensors in Einstein 's special relativity

Minkowski applied Einstein's principle of relativity to moving media and developed electrodynamics of moving media, with Minkowski tensor as the stress-energy-momentum tensor. Recently, Partanen and Tulkki criticize that Minkowski tensor contradicts special relativity, and proposed a mass-polariton stress-energy-momentum (MP SEM) tensor to replace Minkowski tensor. In this paper, I reasonably argue: (i) all the physical results obtained from Minkowski tensor are already embodied in two EM field-strength tensors; (ii) all physical tensors in Einstein's special relativity must satisfy three rules, with Minkowski tensor following all the rules while both Abraham tensor and the MP SEM tensor not. Thus the two arguments provide a strong theoretical basis to solve the problem of the momentum of light in a medium. Finally, by enumerating a specific example I show that the Lorentz covariance of a tensor provides no guarantee of the consistency of the tensor with the principle of relativity.