On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

TL;DR

This paper explores the limitations of noncontextual hidden variable theories in quantum mechanics, demonstrating that such models require accepting finite null covers, which challenge classical probability assumptions.

Contribution

It generalizes Feintzeig's theorem to show that noncontextual, non-Kolmogorovian hidden variable theories imply the existence of finite null covers in quantum experiments.

Findings

Noncontextual hidden variable models imply finite null covers.

Generalization of Feintzeig's theorem to broader hidden variable theories.

Challenges classical probability structures in quantum models.

Abstract

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.