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A transparent linear magneto-dielectric material in free space that isilluminated by a finite quasimonochromatic field is a thermodynamically closedsystem, definitively, regardless of what field and material subsystems that onedefines. The energy--momentum tensor that is formally derived from theMaxwell--Minkowski field equations is inconsistent with both angular and linearmomentum conservation in this closed system; this very solid fact is thefoundational and continuing issue of the Abraham--Minkowski controversy. Theextant resolution of the Abraham--Minkowski dilemma is to treat Maxwelliancontinuum electrodynamics as being a subsystem and to write the totalenergy--momentum tensor as the sum of a Maxwellian electromagnetic subsystemenergy--momentum tensor and a phenomenological material subsystemenergy--momentum tensor. We prove that fundamental principles of physics areviolated by Maxwellian continuum electrodynamics and that fundamentalprinciples of physics are violated by Maxwellian continuum electrodynamicssupplemented by the material subsystem conjecture. We use field theory toderive legitimate equations for macroscopic electromagnetic fields in atransparent linear magneto-dielectric medium. The new field equations are apart of a self-consistent formulation of macroscopic electrodynamics,conservation laws, special relativity, and invariance in a continuous linearmedium. In the new formulation, the temporal and spatial coordinates arerenormalized by the continuous linear medium instead of the permittivity andpermeability being carried as independent material parameters. Then anisotropic, homogeneous, flat, four-dimensional, continuous, linear,non-Minkowski spacetime is the proper setting for the continuum electrodynamicsof a simple linear medium in which the effective speed of light is $c/n$ andeach medium will be associated with a different spacetime.

Alternative formulation of the macroscopic field equations in a linear magneto-dielectric medium: Lagrangian field theory and spacetime setting