Geometric Electrodynamics – the Geometrization of Charge and Mass and Its Implications for General Relativity

This manuscript furthers a recently published theory, Geometric Electrodynamics, in which gravity emerges and mass and charge are defined as geometric quantities rather than as externally introduced entities as in classical electrodynamics. 1 The theory is founded on a single fundamental equation coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor, and then developed through a logical progression based on Riemannian geometry as the underlying structure of spacetime. Geometric Electrodynamics presents a radically different perspective than Classical Electrodynamics: its solutions satisfy all the equations of Classical Electrodynamics, but gravitation also emerges in every solution. In this framework, the source terms—charge and mass—are defined geometrically in terms of the fundamental fields. Requiring that these definitions are self-consistent across the fundamental equations of a theory is taken as a criterion for the theory’s logical consistency. Applying this check to Geometric Electrodynamics demonstrates its consistency, while a similar check of classical physics—defined as the merger of Classical Electrodynamics and General Relativity—reveals an inconsistency in its multiple definitions of mass. This discrepancy has significant implications for current problems in gravitational theory.