Weatherall, James Owen and March, Eleanor (2025) Natural Theories. [Preprint]

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Abstract

We consider the class of physical theories whose dynamics are given by natural equations, which are partial differential equations determined by a functor from the category of n-manifolds, for some n, to the category of fiber bundles, satisfying certain further conditions. We show how the theory of natural equations clarifies several important foundational issues, including the status and meaning of minimal coupling, symmetries of theories, and background structure. We also state and prove a fundamental result about the initial value problem for natural equations.

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Item Type:	Preprint
Creators:	Creators Email ORCID Weatherall, James Owen weatherj@uci.edu 0000-0003-1461-7821 March, Eleanor eleanor.march@balliol.ox.ac.uk 0009-0004-7077-0980
Keywords:	natural theories, general covariance, minimal coupling, symmetries of a theory, hole argument
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	James Owen Weatherall
Date Deposited:	08 Apr 2025 14:22
Last Modified:	08 Apr 2025 14:22
Item ID:	25019
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25019

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