The Electrodynamics of Continuous Electromagnetic Fields

Electrodynamics is here 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 always, 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is used to obtain fundamental equations from a covariant action in which the usual term involving particle mass m has been replaced by a term involving an integral over the covariant mass density µ associated with the fields.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 a covariant equation of motion for a charged body’s center of inertia (COI) including a radiation reaction term without the anomalies present in the usual particle and field formulation. The solutions to these fundamental equations are also solutions for the Dirac and Schrodinger equations but here give arrangements of mass density in a body interacting with its environment, not probabilities of finding an electron or other body. This field formulation thus describes the motion of a body’s COI and the distribution of mass about the COI without invoking many of the assumptions usual to quantum mechanics.

Future research involves the implications for particle theory and the effect of electrodynamics on gravity.