Extended Structural Dynamics and the Lorentz Abraham Dirac Equation: A Deformable Charge Interpretation

TL;DR

This paper models charged particles as finite, deformable spheres with internal dynamics to derive a causal, stable radiation reaction force that avoids classical issues like runaway solutions and pre acceleration.

Contribution

It introduces a deformable charge model within Extended Structural Dynamics, providing a causal, physically interpretable derivation of radiation reaction free from traditional singularities.

Findings

Derives a delay kernel dependent on past motion and internal state.

Shows the Schott term as reversible energy in internal deformation.

Recovers LAD dynamics in the point particle limit.

Abstract

Radiation reaction in classical electrodynamics is traditionally described by the Lorentz Abraham Dirac equation (LAD), whose point particle formulation leads to well known difficulties including runaway solutions, pre acceleration, and the ambiguous status of the Schott term. We analyze radiation reaction within the framework of Extended Structural Dynamics (ESD), in which charged particles are modeled as finite systems possessing internal dynamical structure. In the present formulation the particle is represented as a finite, deformable sphere with a single radial breathing mode describing internal charge redistribution. This internal degree of freedom introduces a finite response time and ensures that changes in the charge distribution propagate at finite speed. Starting from the full particle field Hamiltonian, we derive the retarded self force for such a deformable charge and obtain a delay kernel that depends on both the past motion and the past internal configuration. In the adiabatic regime the kernel reduces to an effective causal form that is free of pre acceleration and exhibits a band pass frequency response, suppressing high frequency instabilities associated with runaway behavior. The Schott term is shown to correspond to reversible energy stored in the internal deformation mode, providing a direct mechanical interpretation of this contribution. The LAD dynamics are recovered only in the double limit of vanishing spatial extent and frozen internal dynamics, where the causal delay structure collapses to the familiar point particle approximation. Within this framework radiation reaction arises as the leading order effective dynamics of a finite deformable charge, while higher order corrections encode finite size and internal structural effects without modifying Maxwell's equations or introducing ad hoc regularization.