Feynman's different approach to electromagnetism

Abstract

We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feynman in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the existing approaches deriving electromagnetism from special relativity, the present one extends a long way towards the derivation of Maxwell's equations with minimal physical assumptions. In particular, without postulating Coulomb's law, homogeneous Maxwell's equations are written down by following a route different from the standard one, i.e. first introducing electromagnetic potentials in order to write down a relativistic invariant action, which is just the inverse approach to the usual one. Also, Feynman's derivation of the Lorentz force exclusively follows from its linearity in the charge velocity and from relativistic invariance. Going further, i.e. adding the inhomogeneous Maxwell's equations, requires some more physical input, and can be done by just following conventional lines, hence this task was not pursued here. Despite its incompleteness, this way of proceeding is of great historical and epistemological significance. We also comment about its possible relevance to didactics, as an interesting supplement to usual treatments.