The Physical Foundation of Quantum Theory

David Geoffrey Holdsworth

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.

Travis Norsen

R. McWeeny

Vikram Athalye, Emmanuel Haven

One of the main purposes of this chapter is to explain, albeit in an abstract manner, how quantum physics–like models of the economics-finance contexts would differ from quantum math-like (or simply, quantum-like) models. For this, the chapter begins by considering, what may be called, the “physical” foundations of quantum theory. These include the foundations pertaining to the theoretical, experimental, and interpretational aspects of quantum theory. With reference to the physical foundations, the chapter elaborates on certain expectations from agent-centric economics-finance models to qualify as “quantum physics–analogous”. Then, by briefly reviewing some of the prominent theories of analogical arguments and reasoning from the philosophy of science (for instance, Aristotle’s theory, Hesse’s theory, Gentner’s structure-mapping theory and Bartha’s articulation model), the chapter ends by proposing a strategy for the systematic construction of quantum physics–analogous models of economics and finance.