2025/04/12 by Westhoff, Bela Schulte
#Classical Physics (physics.class-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2504.10532
For over a century, the electrodynamics of material media has been characterized by competing formulations, persistent paradoxes, and a fundamental lack of consensus on force and energy. This manuscript demonstrates that these long-standing challenges are not a sign of intrinsic ambiguity in the laws of physics, but are the direct consequence of historical and pedagogical models becoming disconnected from a foundational principle of mechanics. The resolution begins with the axiom that a physical force must act upon a well-defined mass. From this single principle, a rigorous Force-Energy Consistency Criterion is derived. When applied as a diagnostic tool, this criterion reveals a shared foundational inconsistency in the mechanical structure of the seminal formulations of Minkowski, Abraham, and conventional textbook approaches: their postulated forces are shown to be irreconcilable with their own descriptions of energy conversion. The analysis is completed by proving a profound epistemological limit inherent in any macroscopic theory: the indeterminacy of the local force density. This result reframes the historical search for a unique force law as an ill-posed question. By demanding mechanical consistency and respecting this fundamental limit, the ambiguity that has plagued the field is resolved. A single, unique framework emerges not as a choice, but as a necessary logical conclusion: the universal vacuum-form energy-momentum tensor (TμνEM(E,B)) and the total Lorentz force. This work establishes this framework as the sole description consistent with determinable physics and formally separates it from the distinct task of building pragmatic models to estimate the unknowable internal forces. The result is a complete, consistent, and methodologically sound restoration of the electrodynamics of matter.