  Minkowski applied Einstein's principle of relativity to moving media and
developed electrodynamics of moving media. Like Einstein introduced the EM
field-strength tensor $F^{\mu\nu}$ for electric field $\mathbf{E}$ and magnetic
induction $\mathbf{B}$, Minkowski introduced another EM field-strength tensor
$G^{\mu\nu}$ for the electric displacement $\mathbf{D}$ and magnetic field
$\mathbf{H}$; thus leading to Minkowski 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, based on a careful analysis of previous literature on
this topic, (i) I reasonably argue that Minkowski tensor is a covariant
combination of two EM field-strength tensors, and thus all the physical results
obtained from Minkowski tensor are already embodied in the two EM
field-strength tensors; (ii) I propose three rules for covariantly and
self-consistently constructing the physical tensors in Einstein's special
relativity, with Minkowski tensor following all the rules while both Abraham
tensor and the MP SEM tensor not. 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.
