Empirical underdetermination for physical theories in \(C^*\) algebraic setting: comments to an Arageorgis's argument
\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.
algebraic formulation of physical theories
scientific article; zbMATH DE number 7291400