  In a continuum setting, the energy-momentum tensor embodies the relations
between conservation of energy, conservation of linear momentum, and
conservation of angular momentum. The well-defined total energy and the
well-defined total momentum in a thermodynamically closed system with complete
equations of motion are used to construct the total energy-momentum tensor for
a stationary simple linear material with both magnetic and dielectric
properties illuminated by a quasimonochromatic pulse of light through a
gradient-index antireflection coating. The perplexing issues surrounding the
Abraham and Minkowski momentums are bypassed by working entirely with
conservation principles, the total energy, and the total momentum. We derive
electromagnetic continuity equations and equations of motion for the
macroscopic fields based on the material four-divergence of the traceless,
symmetric total energy-momentum tensor. We identify contradictions between the
macroscopic Maxwell equations and the continuum form of the conservation
principles. We resolve the contradictions, which are the actual fundamental
issues underlying the Abraham-Minkowski controversy, by constructing a unified
version of continuum electrodynamics that is based on establishing consistency
between the three-dimensional Maxwell equations for macroscopic fields, the
electromagnetic continuity equations, the four-divergence of the total
energy-momentum tensor, and a four-dimensional tensor formulation of
electrodynamics for macroscopic fields in a simple linear medium.
