Obtaining Maxwell's equations heuristically

TL;DR

This paper heuristically derives Maxwell's equations starting from experimental facts and fundamental principles like simplicity, linearity, and invariance, emphasizing the transformation properties of fields.

Contribution

It presents a novel heuristic approach to deducing Maxwell's equations based on symmetry principles and fundamental invariances, without relying on prior electromagnetic theory.

Findings

Maxwell's equations can be derived from basic principles and symmetry considerations.

The approach naturally introduces electrodynamic units.

The derivation emphasizes the role of invariance and transformation properties.

Abstract

Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light together with Galileo invariance of the Lorentz force allows us to introduce arbitrary electrodynamic units naturally.