Some mathematical issues regarding a new approach towards quantum foundations

TL;DR

This paper establishes a minimal mathematical foundation for quantum theory's Hilbert space formalism, supporting an epistemic interpretation and discussing applications to Bell experiments and decision theory.

Contribution

It provides the weakest possible theorem for quantum foundations, detailing necessary postulates and mathematical structure, and advocates for an epistemic view of quantum mechanics.

Findings

A minimal foundational theorem for Hilbert space formalism

Supports an epistemic interpretation of quantum mechanics

Discusses applications to Bell experiments and decision theory

Abstract

In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from this approach, a general epistemic interpretation of quantum mechanics is natural. Some applications to the Bell experiment and to decision theory are briefly discussed. The article represents the conclusion of a series of articles and books on quantum foundations.