Kochen-Specker non-contextuality through the lens of quantization

• URL: http://arxiv.org/abs/2409.13071v1
• Date: Thu, 19 Sep 2024 20:10:37 GMT
• Title: Kochen-Specker non-contextuality through the lens of quantization
• Authors: Simon Friederich, Mritunjay Tyagi,
• Abstract summary: The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics. We show that for quantum theories obtained by quantizing some classical theory, this condition is implausible from the start. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 illustrate this point and its relevance 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.

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