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European Journal for Philosophy of Science

Reconstructions of quantum theory: methodology and the role of axiomatization

Jessica Oddan

Published Apr 30, 2024• 1 citation
Publisher
DOI
10.1007/s13194-024-00581-w

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The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles (ARQITs) can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of Quantum Theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative case studies, I take Clifton's, Bub's and Halvorson's characterization theorem and Popescu's and Rohrlich's toy models, and their explanatory contribution with respect to quantum nonlocality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of (some aspects of) quantum nonlocality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory.
The quantum reconstruction program seeks to uncover the deeper physical meaning of the quantum formalism by distilling its content into a set of physically graspable postulates. Once reconstructed, one can further elucidate the theory by reflecting philosophically upon the postulates rather than the inscrutable formalism in which the theory is couched. Quantum reconstruction thereby opens up a two-step strategy for developing a quantum conceptual framework that reflects the full physical content of quantum theory and can be used to establish precisely what aspects of the classical conceptual framework are retained, modified, or abandoned. The chapter is organized as follows. Section 11.2 describes the tripartite structure of classical physics, whose coherency I argue underlies its intelligibility. Section 11.3 discusses the lack of intelligibility of quantum physics, analyses the limitations of the main traditional elucidative approaches, and describes how reconstruction can remove the fundamental interpretative bottleneck. Section 11.4 discusses the methodology of reconstruction per se , showing that it is part of the natural life-cycle of physical theories, and summarizes its use in the elucidation of the theories of classical physics. Finally, circling back to quantum theory, Section 11.5 summarizes the reconstruction of quantum theory, and Section 11.6 describes some of the interpretative insights obtained thus far through interpretation of reconstructions of the abstract quantum formalism and the quantum symmetrization postulate.
In this paper I shall outline a possibility for incorporating category theory in an essential way into the foundations of quantum theory. The role for category theory which I shall sketch here is strictly foundational in the sense that it offers no new perspectives for a physicist working within the quantum formalism, but rather provides a way of interpreting the algebraic structure by giving an alternative axiomatization of the underlying logic of the theory. The axiomatization is given without recourse to any classical set theory by invoking methods closely connected with the work of F. W. Lawvere. More precisely, then, a possible approach to the foundations of physics which axiomatizes its algebraic structure in a way which is independent of set theory and hence points, as it were, to a structuralist foundation of physical theories, will be proposed.