The Classical Electron Problem

TL;DR

This paper introduces a modified Maxwell theory using source proper-time, leading to a new symmetry, a dissipative wave equation, and a resolution to classical self-energy issues, with implications for global simultaneity and action-at-a-distance.

Contribution

It presents a reformulation of Maxwell theory based on source proper-time, resulting in a new symmetry group and a dissipative wave equation that addresses classical self-energy problems.

Findings

New symmetry group related to source proper-time

Dissipative wave equation with inertial resistance to acceleration

No self-energy divergence in the modified theory

Abstract

In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a "charge" on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (invariant) global proper-time (for each observer) from which to observe the system. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this clock is the historical clock of Horwitz, Piron, and Fanchi. At this level, the theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy.