Kochen-Specker non-contextuality through the lens of quantization

TL;DR

This paper argues that the Kochen-Specker non-contextuality assumption is implausible in quantized theories because quantization alters algebraic relations, limiting the theorem's relevance to assigning sharp values to dynamical variables.

Contribution

It demonstrates that Kochen-Specker non-contextuality is incompatible with typical quantization procedures using deformation quantization and star products.

Findings

Quantization changes algebraic relations among variables.

Kochen-Specker theorem's relevance is limited in quantized theories.

Examples include Weyl and coherent state quantizations.

Abstract

The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators commute are the same as those among the operators themselves. We point out that, for quantum theories obtained by quantizing some classical theory, this condition -- Kochen-Specker non-contextuality -- is implausible from the start because quantization usually changes algebraic relations. We explain why this is so, using the formalism of deformation quantization and its conception of star products, and we illustrate the relevance of this point using various examples of dynamical variables quantized via Weyl quantization and coherent state quantization. Our observations suggest that the relevance of the Kochen-Specker theorem to the question of whether one can assign sharp values to all dynamical variables is rather limited