Chrysovalantis Stergiou (The American College of Greece): “On Empirical Underdetermination of Physical Theories in C*Algebraic Setting”

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Abstract: Empirical underdetermination of physical theories by observational data lies at the heart of the debate over scientific realism. Antirealists of different strands contend that if observation cannot determine the state of a physical system then to talk about a uniquely defined state of the system is just a matter of convention. In the context of Algebraic Quantum Field Theory (AQFT) this stance is related to the claim that the physical topology of the state space is the weak*-topology and to what has become known as Algebraic Imperialism, the operationalist attitude which characterized the first steps of the theory. Aristidis Arageorgis (1995) devised a mathematical argument against empirical underdetermination of the state of a system in C*-algebraic setting which rests on two topological properties of the state space: being T1 and being first countable in the weak*-topology. The first property is possessed trivially by the state space while the latter is highly non-trivial and it can be derived from the assumption that the algebra of observables is separable.

In this talk we will reconstruct Arageorgis’ argument and examine its soundness with regard to the separability of the algebra of observables. We will show that separability is related to two factors: (a) the dimension of the algebra, considered as a vector space; (b) whether it is a C*- or von Neumann algebra. Finite-dimensional C*-algebras and von Neumann algebras are separable, infinite-dimensional von Neumann algebras are non-separable and infinite-dimensional C*-algebras can be separable. These considerations will be discussed with reference to classical systems of N particles, the Heisenberg model for ferromagnetism, the Haag-Araki formulation of AQFT and a separable reformulation of AQFT in Minkowski spacetime suggested by Porrmann (1999, 2004).

This talk is dedicated to the memory of my beloved teacher, colleague and friend Aris Arageorgis who untimely passed away in 2018.