Gleason, Kochen-Specker, and a competition that never was

TL;DR

This paper reviews the Gleason and Kochen-Specker theorems, exploring the extent of Hilbert space usable without triggering these theorems and examining the roles of specific geometric structures like cubes, graphs, and pentagrams.

Contribution

It proposes investigating the portions of Hilbert space that avoid the theorems' implications and analyzes geometric configurations relevant to quantum foundations.

Findings

Identifies regions of Hilbert space not constrained by the theorems

Analyzes geometric structures like cubes, graphs, and pentagrams in quantum contexts

Suggests directions for future research on Hilbert space utilization

Abstract

I review the two theorems referred to in the title, and then suggest that it would be interesting to know how much of Hilbert space one can use without forcing the proof of these theorems. It would also be interesting to know what parts of Hilbert space that are essential for the proofs. I go on to discuss cubes, graphs, and pentagrams.