Who's afraid of coordinate systems? An essay on representation of spacetime structure

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 67:125-136 (2019)
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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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David Wallace
University of Pittsburgh

Citations of this work

Fundamental and Emergent Geometry in Newtonian Physics.David Wallace - 2020 - British Journal for the Philosophy of Science 71 (1):1-32.
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Functional Gravitational Energy.James Read - 2018 - British Journal for the Philosophy of Science 71 (1):205-232.

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References found in this work

Effective spacetime geometry.Eleanor Knox - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):346-356.
On Einstein Algebras and Relativistic Spacetimes.Sarita Rosenstock, Thomas William Barrett & James Owen Weatherall - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):309-316.

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