Simultaneous inference of Jefimenko's and Maxwell's equations from retardation

TL;DR

This paper demonstrates how Jefimenko's and Maxwell's equations can be derived from the principle of retardation starting with retarded Coulomb and Biot-Savart fields, using an iterative refinement process.

Contribution

It introduces a novel inference method that derives fundamental electromagnetic equations from retarded field expressions without prior knowledge of their differential laws.

Findings

Successfully infers Jefimenko's fields from retarded potentials.

Derives Maxwell's equations through iterative refinement of initial ansatz.

Shows the derivation parallels static field law inference from experimental data.

Abstract

Assuming the idea of retardation as an underlying axiom, we investigate how Jefimenko's and Maxwell's equations can be inferred. In the inference, we begin with the retarded versions of Coulomb's and Biot-Savart's field expression as an incomplete, starting ansatz. By calculating and comparing their divergences, curls, and time derivatives, we improve the ansatz. Thus improved ansatz is further improved through the same procedure and the final ansatz fields are identified with Jefimenko's fields. Our inference of Maxwell's equations is in much the same spirit as the derivation of static differential equations (divergences and curls) from the Coulomb's and Biot-Savart's fields known experimentally without knowing their governing laws of the divergence and curl equations.