  The form of the energy-momentum tensor when a quasimonochromatic field
propagates into and through an antireflection-coated, sourceless, transparent,
continuous, linear magneto-dielectric medium, initially at rest in the local
frame, remains controversial. The Minkowski energy-momentum tensor is the main
component of the electromagnetic conservation law. It has been known for over a
century that the electromagnetic conservation law is unsound as evidenced by
alternative energy-momentum tensors that have been proposed to ameliorate known
physical deficiencies (violation of conservation of angular and linear
momentum) and by the various material energy-momentum tensors and coupling
forces that have been introduced to repair or complete the law. The extant
resolution is to treat the continuum electromagnetic system as a subsystem and
add a phenomenological material subsystem energy-momentum tensor. We show that
the four-divergence of the total, electromagnetic plus material,
energy-momentum tensor produces an energy continuity theorem in which the two
non-zero terms depend on different powers of the refractive index $n$. Then the
extant resolution of the Abraham-Minkowski controversy is self-inconsistent.
