Minimalist's Electromagnetism - Different Axioms and Different Insight

TL;DR

This paper demonstrates that electromagnetism and electrodynamics can be derived solely from the constancy of the speed of light and the existence of charged particles, eliminating observational assumptions.

Contribution

It introduces a new axiomatic approach to derive EM and ED from minimal assumptions, providing a theoretically grounded foundation free of observational dependencies.

Findings

Poisson's equation emerges as a corollary

Coulomb's law is exact within this framework

Magnetic monopoles are shown to not exist in classical theory

Abstract

That the speed of light is a universal constant is a logical consequence of Maxwell's equations. Here we show the converse is also true. Electromagnetism (EM) and electrodynamics (ED), in all details, can be derived from two simple assumptions: i) the speed of light is a universal constant and, ii) the common observations that there are the so-called charged particles that interact with each other. Conventional EM and ED are observation based. The proposed alternative spares all those observational foundations, only to reintroduce them as theoretically derived and empiricism-free laws of Nature. There are merits to simplicity. For instance, when one learns that Poisson's equation emerges as a corollary of the formalism, one immediately concludes that Coulomb's $1/r^2$ law of force is exact. Or, if it turns out that $\nabla.\mathbf{B}=0$ follows from the theory, then non-existence of (at least classical) magnetic monopoles will be an exact law of Nature. The list is longer than the these two examples.