Pascual Jordan's "Erweiterte Gravitationstheorie" - A Historical Analysis of its Mathematical Framework

TL;DR

This paper explores Pascual Jordan's 1952 axiomatic approach to the covariant derivative within his extended gravity theory, highlighting its historical context and mathematical significance in the development of differential geometry and relativity.

Contribution

It provides a detailed historical and mathematical analysis of Jordan's covariant derivative definition and its role in his extended gravity theory, connecting it to broader developments in relativity.

Findings

Jordan's covariant derivative aligns with modern definitions.

Historical context links Jordan's work to Veblen and Eisenhart's group.

The formalism contributed to the development of differential geometry in relativity.

Abstract

This paper aims to highlight Pascual Jordan's axiomatic definition of the covariant derivative, as set out in his 1952 textbook "Schwerkraft und Weltall". Developed in light of his \emph{Erweiterte Gravitationstheorie} - a projective reformulation of relativity theory that incorporates a variable gravitational constant - Jordan's definition resembles those in contemporary usage. The paper contextualises Jordan's work within the broader historical frameworks of differential geometry and projective relativity, with a particular focus on the Princeton relativity group led by Oswald Veblen and Luther Pfahl Eisenhart. It also provides a summary of Jordan's formalism, focusing particularly on his definition of the covariant derivative, as well as a brief history of the origin and development of the covariant derivative.