Empirical underdetermination for physical theories in \(C^*\) algebraic setting: comments to an Arageorgis's argument
type: Item
instance of: scholarly article
title: Empirical underdetermination for physical theories in \(C^*\) algebraic setting: comments to an Arageorgis's argument
zbMATH Open document ID: 1464.81035
author: Chrysovalantis Stergiou
published in: Foundations of Physics
publication date: 2021-01-08T00:00:00Z
review text: \textit{A. Arageorgis} in his PhD dissertation [Fields, particles, and curvature: foundations and philosophical aspects of quantum field theory in curved spacetime. Pittsburgh, PA: University of Pittsburgh (PhD Thesis) (1995)] argues that the actual state of a physical system is distinguishable from its possible states and can be defintely determined in \(C^*\)-algebraic framework with all possible empirical evidence into account. In this paper, the author points out that Arageorgis's argument follows from topological assumptions formulated in the \(C^*\)-algebra setting: the state space is first countable and the algebra of observables is separable. The author illustrates several physical systems failing to satisfy the assumptions and then argues that one cannot expect Arageorgis's argument to hold for those cases. This paper aims, as the author wrote, to support the claim that two theories, defined in terms of (faithful) representations of abstract algebraic quantum field systems, may describe equally well all available empirical evidence, yet they may fail to provide equivalent descriptions with respect all possible empirical evidence.
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 81P16
Mathematics Subject Classification ID: 81P42
zbMATH DE Number: 7291400
zbMATH Keywords: empirical underdetermination
zbMATH Keywords: algebraic formulation of physical theories
zbMATH Keywords: state space
zbMATH Keywords: first countable
zbMATH Keywords: separability
MaRDI profile type: Publication
full work available at URL: s10701-020-00358-0
OpenAlex ID: W3042917943
cites work: Q4112980
cites work: The Heisenberg dynamics of spin systems: A quasi*-algebras approach
cites work: Q4023404
cites work: Mathematical implications of Einstein-Weyl causality
cites work: Inductive Limits of Finite Dimensional C ∗ -Algebras
cites work: Q4208848
cites work: Q4396177
cites work: Notes on the separability of \(C^*\)-algebras
cites work: Q4891080
cites work: An Algebraic Approach to Quantum Field Theory
cites work: Q4692965
cites work: Q5569793
cites work: Q3997462
cites work: Particle weights and their disintegration. II
cites work: Q5667036
cites work: Interpreting Quantum Theories
cites work: Q5709395
cites work: Theory of operator algebras I.
cites work: Q5605131
DOI: 10.1007/S10701-020-00358-0
description: scientific article; zbMATH DE number 7291400