Poincar\'e, the Dynamics of the Electron, and Relativity

TL;DR

Poincaré's 1905 note on electron dynamics introduced a model with a positive cosmological constant inside the electron and contributed to the mathematical foundations of Special Relativity, highlighting early insights into relativistic physics.

Contribution

The paper discusses Poincaré's early electron model and his novel mathematical contributions to Special Relativity, which are often underappreciated in historical accounts.

Findings

Electron model with positive cosmological constant inside the worldtube

Early mathematical contributions to Special Relativity by Poincaré

Recognition of Poincaré's subtle advancements in relativistic physics

Abstract

On June 5, 1905 Poincar\'e presented a Note to the Acad\'emie des Sciences entitled "Sur la dynamique de l'\'electron" ("On the Dynamics of the Electron"). After briefly recalling the context that led Poincar\'e to write this Note, we comment its content. We emphasize that Poincar\'e's electron model consists in assuming that the interior of the worldtube of the (hollow) electron is filled with a positive cosmological constant. We then discuss the several novel contributions to the physico-mathematical aspects of Special Relativity which are sketched in the Note, though they are downplayed by Poincar\'e who describes them as having only completed the May 1904 results of Lorentz "dans quelques points de d\'etail" ("in a few points of detail").