An Examination of Two Competing Interpretations of Quantum Mechanics with a Critique of the Kochen-Specker Theorem

Eliza Miller

Published Jan 28, 2024• 0 citations

Abstract

There is ongoing discourse in philosophical and physics literature about whether the probabilistic essence of quantum mechanics indicates that deterministic interpretations of nature must be false. In 1967 two mathematicians, Simon Kochen and Ernst Specker, developed a mathematical theorem to the effect that particles do not have well-defined property values at a given time. A logical consequence of this is that there can be no well-defined hidden variables responsible for the outcomes of mysterious quantum behaviors. The theorem is thus fatal to the many deterministic interpretations of quantum mechanics that assume hidden variables, including pilot wave mechanics, a quantum theory developed by Louis de Broglie and David Bohm a few decades prior to the formulation of the Kochen-Specker Theorem. The purpose of this essay is to evaluate the legitimacy of the logical basis of Kochen’s and Specker’s argument considering its severe implications. It is concluded that Kochen and Specker do not provide sufficient evidence that deterministic theories must fail, due to their misinterpretation of the axioms on which hidden variable theories rely. This paper also finds that pilot wave mechanics is mathematically successful while remaining consistent with the deterministic understanding of broader physics and deserving of more serious consideration as a quantum theory. Above all it is emphasized that the nonsensicality of absolute randomness and indeterminism should be acknowledged, and theorems purporting to prove their existence should be critically examined, for such a discovery would undermine the legitimacy of logic itself.

DOI: 10.55894/dv2.23

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