A Conceptual Shift to Rectify a Defect in the Lorentz-Dirac Equation

TL;DR

This paper proposes a conceptual shift in the Lorentz-Dirac equation, treating the particle as a composite system, which resolves instabilities and aligns with causality, supported by exact solutions and physical reasoning.

Contribution

It introduces a new interpretation of the self-field energy as kinetic energy, rectifying a defect in the Lorentz-Dirac equation and ensuring causality and physical consistency.

Findings

Exact solutions demonstrate outward spiral motion due to self-force.

The new model aligns with established physical principles.

Reversible self-field energy is interpreted as kinetic energy.

Abstract

In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938) draws attention to the characteristic instability of solutions to the third order equation of motion. He remarks that changing the sign of the self-force eliminates the runaway solutions and gives `reasonable behaviour'. Dirac rejects such a change and proceeds with an ad hoc modification to the solutions of the initial value problem that is not consistent with the principle of causality. We argue that his reasons for rejecting the change of sign are invalid on both physical and mathematical grounds. The conceptual shift is to treat the physical particle as a composite of the source particle and the energy-momentum that is reversibly generated in its self-field by its motion. The reversibly generated energy in the self-field is interpreted as kinetic energy, and the changes that follow result in Dirac's change of sign. Several exact solutions to the new equation of motion and its linearisation are given. For a particle in orbital motion the self-force enables the applied force to generate radiation and kinetic energy in the self-field that results in an outward spiral motion. The theory is consistent with all well-established principles of physics, including the principle of causality.