Wallace, David (2016) Who's afraid of coordinate systems? An essay on representation of spacetime structure. [Preprint]

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Abstract

Coordinate-based approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinate-free differential-geometric approaches. I defend the conceptual and mathematical legitimacy of the coordinate-based approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory of invariance under symmetry groups; I argue that this conception continues to play a very substantial role in contemporary mathematical physics and indeed that supposedly ``coordinate-free'' differential geometry relies centrally on this conception of geometry. I discuss some foundational and pedagogical advantages of the coordinate-based formulation and briefly connect it to some remarks of Norton on the historical development of geometry in physics during the establishment of the general theory of relativity.

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Item Type:	Preprint
Creators:	Creators Email ORCID Wallace, David david.wallace@balliol.ox.ac.uk
Keywords:	coordinates; geometry; spacetime
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Professor David Wallace
Date Deposited:	22 Mar 2016 22:34
Last Modified:	22 Mar 2016 22:34
Item ID:	11988
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	March 2016
URI:	https://philsci-archive.pitt.edu/id/eprint/11988

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