A Simple Proof of the Kochen-Specker Theorem on the Problem of Hidden Variables

TL;DR

This paper provides a straightforward proof of the Kochen-Specker theorem, demonstrating the fundamental incompatibility of quantum mechanics with non-contextual hidden variable theories, highlighting the challenges in completing quantum theory.

Contribution

It offers a simplified derivation of the Kochen-Specker theorem, emphasizing its significance in understanding quantum contextuality and the limitations of hidden variable models.

Findings

Quantum mechanics cannot be embedded into a classical stochastic theory.

The proof underscores the inherent contextuality in quantum measurements.

It clarifies the difficulties in developing a 'complete' quantum theory.

Abstract

In this talk I present a simple derivation of an old result of Kochen and Specker, which is apparently unrelated to the famous work of Bell on hidden variables, but is presumably equally important. Kochen and Specker showed in 1967 that quantum mechanics cannot be embedded into a classical stochastic theory, provided the quantum theoretical probability distributions are reproduced and one additional highly desirable property is satisfied. This showed in a striking manner what were the difficulties in implementing the Einstein programme of a `complete' version of quantum mechanics.