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On the notion of indiscernibility in the light of Galois-Grothendieck Theory

Catren, Gabriel and Page, Julien (2013) On the notion of indiscernibility in the light of Galois-Grothendieck Theory. [Preprint]

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Abstract

We analyze the notion of indiscernibility in the light of the Galois theory of field extensions and the generalization to K-algebras proposed by Grothendieck. Grothendieck's reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a
duality between G-spaces and the minimal observable algebras that separate theirs points. In order to address the Galoisian notion of indiscernibility, we propose what we call an epistemic reading of the Galois-Grothendieck theory.
According to this viewpoint, the Galoisian notion of indiscernibility results from the limitations of the `resolving power' of the observable algebras used to discern the corresponding `coarse-grained' states. The resulting Galois-Grothendieck duality is rephrased in the form of what we call a Galois indiscernibility principle. According to this principle, there exists an inverse correlation between the coarsegrainedness of the states and the size of the minimal observable algebra that discern these states.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Catren, Gabrielgabrielcatren@gmail.com
Page, Julienju.page@hotmail.fr
Keywords: Galois-Grothendieck, Indiscernibility, Symmetries-Invariants, State-Observable Duality
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Gabriel Catren
Date Deposited: 03 Dec 2013 17:00
Last Modified: 03 Dec 2013 17:00
Item ID: 10117
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Symmetries/Invariances
Date: 31 November 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/10117

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