Non-Uniqueness of the Lienard-Wiechert Potential

TL;DR

This paper demonstrates that the Lienard-Wiechert potential is not unique by deriving a general formula for other potentials that satisfy the same wave equation, gauge condition, and propagation properties in classical electrodynamics.

Contribution

The paper introduces a general formula showing the existence of multiple potentials satisfying key properties of the Lienard-Wiechert potential, challenging its uniqueness.

Findings

Existence of non-unique retarded potentials

Derivation of a general formula for such potentials

Implications for classical electrodynamics theory

Abstract

The Lienard-Wiechert potential is one of the central equations of classical electrodynamics. Among its properties are these: it satisfies the (linear) homogeneous wave equation and Lorenz Gauge condition in free space, it varies inversely with distance from the classical point-source that is movong arbitrarily, and its effects propagate along straight lines at constant speed (the speed of light). Do any other retarded potentials satisfy these properties? It is shown here that other such potentials do exist, and a general formula is derived.