  Minkowski spacetime is a convenient setting for the study of the relativistic
dynamics of particles and fields in the vacuum. In order to study events that
occur in a dielectric or other linear medium, we adopt the familiar continuum
assumption of a linear, isotropic, homogeneous, transparent medium of
refractive index n filling all space and seek the principle of relativity that
applies in the filled spacetime. Applying the Einstein postulates with c/n as
the speed of light, we show how the effective signal velocity results in a
scaling of the proper time by the refractive index and examine the consequences
for D'Alembert's principle, the Lagrange equations, and the canonical momentum
field. The principles of dynamics in the filled spacetime are then applied to
the electromagnetic Lagrangian and we derive equations of motion that are
invariant with respect to a material Lorentz transformation. The new
representation of the dynamics of macroscopic fields is shown to be consistent
with the equal-time commutation relation for quantized macroscopic fields,
quantum--classical correspondence, the principle of superposition, and
electromagnetic boundary conditions.
