How Weyl stumbled across electricity while pursuing mathematical justice

TL;DR

This paper explores how Weyl's pursuit of mathematical justice, emphasizing equal rights for direction and length, led to his theory unifying gravitation and electromagnetism, deriving source-free electromagnetism from symmetry principles.

Contribution

It reveals that Weyl's concept of mathematical justice and symmetry principles naturally led to deriving electromagnetism, highlighting the foundational role of these ideas in physics.

Findings

Weyl's theory derives all source-free electromagnetism from symmetry principles.

Mathematical justice influenced Weyl's approach to unifying gravity and electromagnetism.

Coordinates and gauge are expressions of equal treatment of direction and length.

Abstract

It is argued that Weyl's theory of gravitation and electricity came out of `mathematical justice': out of the equal rights direction and length. Such mathematical justice was manifestly at work in the context of discovery, and is enough (together with a couple of simple and natural operations) to derive all of source-free electromagnetism. Weyl's repeated references to coordinates and gauge are taken to express equal treatment of direction and length.