The Electrodynamics of Continuous Electromagnetic Fields

Electrodynamics is formulated as a field theory rather than as a particle and field theory. Electromagnetic fields are taken to be continuous everywhere. Maxwell’s equations are assumed to be valid, and second order calculus of variations is used to obtain fundamental equations from a covariant action in which the usual term involving particle mass m has been replaced by a term involving an integral over the covariant mass density µ associated with the fields. These equations yield (1) a fully covariant equation of motion for a charged body’s center of inertia (COI), (2) Solutions of the Dirac and Schrodinger equations, which give mass densities (not probability densities) arising from the interaction of a body with its environment, and (3) Partition of a body’s electromagnetic mass into an interaction mass, an intrinsic mass co-located with charge, and an extrinsic (dark) mass outside the charged region. If the interior momentum of a body balances, then the body is stable, and the fundamental equations can, in principle, predict its structure, charge density, mass density, shape, and observable properties, all calculated from the fields. The concepts invoked are fewer and more easily understood than those in the usual theoretical treatments.