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

📝 Original Info

• Title: Pascual Jordan’s ‘Erweiterte Gravitationstheorie’ - A Historical Analysis of its Mathematical Framework
• ArXiv ID: 2507.23758
• Date: 2025-07-31
• Authors: ** 작성자: ChatGPT (OpenAI) 협업 검토: 김현수 (서울대학교 물리학과), 박지은 (고려대학교 수학과) **

📝 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.

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