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The Reign of RelativityPhilosophy in Physics 1915-1925$
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Thomas Ryckman

Print publication date: 2005

Print ISBN-13: 9780195177176

Published to Oxford Scholarship Online: April 2005

DOI: 10.1093/0195177177.001.0001

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Weyl's “Purely Infinitesimal” Constitution of Field Physics

Weyl's “Purely Infinitesimal” Constitution of Field Physics

(p.145) Weyl's “Purely Infinitesimal” Constitution of Field Physics
The Reign of Relativity

Thomas Ryckman

Oxford University Press

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. In response to the Einstein-Pauli objection, Weyl put forth a second version of his theory, arguing on various non-empirical grounds for the conceptual superiority of his gauge-theoretic approach to general relativity. Speculation is made regarding Weyl’s philosophical reasons for opposing Élie Cartan’s “moving frame” generalization of Weyl’s notion of an affine connection, and it is suggested that the basic approach of Weyl’s transcendental phenomenological foundation of differential geometry can be accommodated within the modern fiber bundle formulation of gauge field theories.

Keywords:   Hermann Weyl, pure infinitesimal geometry, gravitation, electromagnetism, Élie Cartan, moving frame, affine connection, differential geometry, fiber bundle, gauge field theory

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