  We treat continuum electrodynamics as an axiomatic formal theory based on the
macroscopic Maxwell--Minkowski equations applied to a thermodynamically closed
system consisting of an antireflection-coated block of a simple linear
dielectric material situated in free-space that is illuminated by a
quasimonochromatic field. We prove that valid theorems of the formal theory of
Maxwellian continuum electrodynamics are inconsistent with conservation laws
for the inviscid incoherent flow of non-interacting particles (photons) in the
continuum limit (light field) in the absence of external forces, pressures, or
constraints. We also show that valid theorems of Maxwellian continuum
electrodynamics are contradicted by the refractive index-independent Lorentz
factor of von Laue's application of Einstein's special relativity to a
dielectric medium. Obviously, the fundamental physical principles in the vacuum
are not affected. However, the extant theoretical treatments of
electrodynamics, special relativity, and energy--momentum conservation must be
regarded as being mutually inconsistent in a simple linear dielectric in which
the effective speed of light is $c/n$. Having proven that the established
applications of fundamental physical principles to dielectric materials lead to
mutually inconsistent theories, we derive, from first principles, a mutually
consistent, alternative theoretical treatment of electrodynamics, special
relativity, and energy--momentum conservation in an isotropic, homogeneous,
linear dielectric-filled, flat, non-Minkowski, continuous material spacetime.
