How to get from static to dynamic electromagnetism

TL;DR

This paper derives Maxwell's equations from the relativity principle, offering an alternative to traditional methods by connecting static and dynamic electromagnetism through Lorentz transformations.

Contribution

It presents a novel derivation of Maxwell's equations emphasizing the relativity principle, avoiding explicit reference to the speed of light.

Findings

Explicit expressions for Lorentz transformations derived

Faraday's law obtained as a consequence of relativity

Alternative derivation of Lorentz transformation without c

Abstract

We demonstrate how to derive Maxwell's equations, including Faraday's law and Maxwell's correction to Amp\`ere's law, by generalizing the description of static electromagnetism to dynamical situations. Thereby, Faraday's law is introduced as a consequence of the relativity principle rather than an experimental fact, in contrast to the historical course and common textbook presentations. As a by-product, this procedure yields explicit expressions for the infinitesimal Lorentz and, upon integration, the finite Lorentz transformation. The proposed approach helps to elucidate the relation between Galilei and Lorentz transformations and provides an alternative derivation of the Lorentz transformation without explicitly referring to the speed of light.