The electrodynamic origin of the wave-particle duality

TL;DR

This paper derives pilot waves from electrodynamic self-interactions, suggesting a classical electromagnetic basis for wave-particle duality and linking it to quantum phenomena like zitterbewegung.

Contribution

It introduces a novel derivation of pilot waves from extended charged particles and electromagnetic self-interactions, challenging point-particle models and connecting classical electrodynamics with quantum behavior.

Findings

Oscillations related to zitterbewegung frequency are generated.

Self-energy includes a quantum potential-like contribution.

Electromagnetic origin of inertia is proposed.

Abstract

A derivation of pilot waves from electrodynamic self-interactions is presented. For this purpose, we abandon the current paradigm that describes electrodynamic bodies as point masses. Beginning with the Li\'enard-Wiechert potentials, and assuming that inertia has an electromagnetic origin, the equation of motion of a nonlinear time-delayed oscillator is obtained. We analyze the response of the uniform motion of the electromagnetic charged extended particle to small perturbations, showing that very violent oscillations are unleashed as a result. The frequency of these oscillations is intimately related to the zitterbewegung frequency appearing in Dirac's relativistic wave equation. Finally, we compute the self-energy of the particle. Apart from the rest and the kinetic energy, we uncover a new contribution presenting the same fundamental physical constants that appear in the quantum potential.