The Philosophy of Reconstructions of Quantum Theory: Axiomatization, Reformulation, and Explanation

Abstract

The quantum reconstruction programme is a novel research program in theoretical physics aimed at deriving the key features of quantum mechanics from fundamental physical postulates. Unlike standard interpretations of quantum theory, which take the Hilbert space formalism at face value, quantum reconstructions seek to derive this formalism from axiomatic principles. Reconstructions represent a new shift in foundations of physics away from interpreting quantum theory and towards understanding its foundational origins. The reconstruction programme has been a major focus of research in physics, beginning with Hardy (2001)’s “Quantum Theory from Five Reasonable Axioms.” However, the quantum reconstruction programme has been met with very little interest in philosophy. The goal of this project is to situate the quantum reconstruction programme in a broader philosophical context, investigating themes such as scientific methodology, explanation, the applicability of mathematics to physical theories, and theory exploration and development in the philosophy of science.

I argue that reconstructions demonstrate a contemporary application of axiomatization with significant points of continuity to historical axiomatizations. I also argue that we should best understand reconstructions as provisional, practical representations of quantum theory that are conducive to theory exploration and development. Further, I contend that reconstructions function as alternative formulations of quantum theory, which is methodologically advantageous. I discuss Bokulich (2019)’s “Losing the Forest for the Ψ: Beyond the Wavefunction Hegemony” which argues that the existence of alternative formulations of quantum theory undermines our ability to literally interpret a single formulation. I argue that Bokulich (2019)’s conclusions further support the reconstructionist’s rejection of the standard interpretative project. I also argue that reconstructionists have gone beyond Bokulich (2019)’s insistence on the consideration of alternative formulations to develop a methodology that systematically constructs alternative formulations of quantum theory. Additionally, I argue that reconstructions of quantum theory are genuinely explanatory as they answer Wheeler (1971)’s “Why the quantum?” question. I contend that reconstructions are explanatory in the same spirit as Bokulich (2016)’s account of explanation in “Fiction As a Vehicle for Truth: Moving Beyond the Ontic Conception” which focuses on patterns of counterfactual dependence that correctly capture underlying dynamics. However, in order to accommodate the reconstruction case, I expand Bokulich’s account to consider theories and models as well as representations that are neither fictional nor literal interpretations. Thus, I offer an account of explanation in the reconstruction programme that is noncausal and non–interventionist, utilizing w–questions a la Woodward (2003). I conclude that reconstructions of quantum theory give us genuine insight into the structure of quantum theory via the generalized physical principles which carry physical content.