Weyl's “Purely Infinitesimal” Constitution of Field Physics

Thomas Ryckman

in The Reign of Relativity

Published in print February 2005 | ISBN: 9780195177176
Published online April 2005 | e-ISBN: 9780199835324 | DOI:

Series: Oxford Studies in the Philosophy of Science

 Weyl's “Purely Infinitesimal” Constitution of Field Physics

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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

Chapter.  16896 words. 

Subjects: Philosophy of Science

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