Kochen-Specker theorem revisited

TL;DR

This paper presents a simplified, geometrical proof of the Kochen-Specker theorem applicable to any dimension, emphasizing the theorem's foundational implications for quantum realism and contextuality.

Contribution

It introduces a new, minimalistic geometrical proof of the Kochen-Specker theorem valid in all dimensions, reducing complexity and highlighting fundamental issues.

Findings

Provides a simplified geometrical proof applicable to any dimension

Reduces technical complexity of existing proofs

Emphasizes the foundational significance of contextuality in quantum mechanics

Abstract

The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to discussions of "contextuality" in quantum physics. Original proofs of the Kochen-Specker theorem proceeded via brute force counter-examples; often quite complicated and subtle (albeit mathematically "elementary") counter-examples. Only more recently have somewhat more "geometrical" proofs been developed. We present herein yet another simplified geometrical proof of the Kochen-Specker theorem, one that is valid for any number of dimensions, that minimizes the technical machinery involved, and makes the seriousness of the issues raised manifest.