Contextual semantics in quantum mechanics from a categorical point of view
type: Item
instance of: scholarly article
title: Contextual semantics in quantum mechanics from a categorical point of view
zbMATH Open document ID: 1396.81014
author: Vassilios Karakostas
author: Elias Zafiris
published in: Synthese
publication date: 2018-03-27T00:00:00Z
full work available at URL: Contextual Semantics in Quantum Mechanics from a Categorical Point of View.pdf
review text: The technical core of this paper is a categorical adjunction between the sheaves of variable local Boolean frames and the category of quantum event algebras. The aspect which is analysed is the subobject classifier in the former category, which is a Grothendieck topos, that provides via a suitable adjunction a subobject classifier in the latter category, thus equipping it with a notion of non-classical truth allowing to interpret propositions in quantum mechanics, which is the ultimate purpose of the article. The article appeared in Synthese, a leading journal in philosophy, and thus the focus of the work is to discuss the philosophical implications of the previous construction. Mathematically, the construction follows a standard path, and although it is by far non-elementary, the result is not surprising in a purely mathematical sense. In the physical sense, the result is, as far as the reviewer can understand, significant and of interest beyond the purely mathematical content, since it provides the conceptual framework to assemble observations in a coherent way, considering that the act of observing influences the outcome of an experiment. Of course, this is an over-simplification, adopted in this review to illustrate the content of the paper; however the same idea is discussed in depth in the first part of the work, in its full complexity, and with a particular emphasis on the physical and philosophical implications, e.g., its relation with the well-known Kochen-Specker's theorem. The paper starts providing the general framework which explains how the physical phenomena are linked to propositions, thus showing what a notion of truth means in the interpretation of a physical system in terms of its events. While in classical mechanics such an interpretation boils down to classical logic, as the semantics of propositions reduces to the lattice of subspaces of the phase space, which is Boolean (Section 1), the same interpretation in quantum Physics does not reduce to…
reviewed by: Marco Benini
Mathematics Subject Classification ID: 81P13
Mathematics Subject Classification ID: 81P05
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 6852938
zbMATH Keywords: Kochen-Specker theorem
zbMATH Keywords: category theory
zbMATH Keywords: categorical adjunction
zbMATH Keywords: subobject classifier
zbMATH Keywords: correspondence truth
zbMATH Keywords: contextual semantics
MaRDI profile type: Publication
OpenAlex ID: W2283680402
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DOI: 10.1007/S11229-015-0970-3
description: scientific article; zbMATH DE number 6852938