The Mechanics of Macroscopic Electrodynamics

Abstract

Classical Electrodynamics in ponderable media remains defined by a century-long debate over force and energy localization. While the prevailing view treats competing formulations (Minkowski, Abraham, etc.) as equivalent conventions, this monograph argues that global conservation is insufficient for physical validity. A formulation must be mechanically coherent: power transfer must strictly equal the work rate of the force acting on the mass target. We formalize this requirement as the Force--Energy Consistency Criterion (FECC) -- a ``Kinematic Lock'' ($ P = \mathbf{f} \cdot \mathbf{v} $) -- and use it to audit standard macroscopic tensors. The analysis demonstrates that only the Macroscopic Vacuum (Lorentz) Formulation offers a mechanically consistent description of total energy-momentum transfer. The internal distribution of this energy is shown to be macroscopically indeterminate. By reinterpreting spatial averaging as spectral filtering, we reconstruct the theory from the microscopic baseline. This perspective identifies a universal host interface that routes electromagnetic energy into mechanical work, heat, and reversible storage, revealing a structural isomorphism where thermodynamics, mechanics, and electrodynamics emerge as coupled spectral projections.