Constraints on Determinism: Bell Versus Conway–Kochen

Foundations of Physics 44 (7):781-791 (2014)

Authors
Klaas Landsman
Radboud University Nijmegen
Abstract
Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories
Keywords Free will theorem  Bell’s theorem  Hidden variable theories  Determinism
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DOI 10.1007/s10701-014-9815-z
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References found in this work BETA

Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.
The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.

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Citations of this work BETA

Conway–Kochen and the Finite Precision Loophole.Ronnie Hermens - 2014 - Foundations of Physics 44 (10):1038-1048.
An Operationalist Perspective on Setting Dependence.Ronnie Hermens - 2019 - Foundations of Physics 49 (3):260-282.
On the Notion of Free Will in the Free Will Theorem.Klaas Landsman - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 57:98-103.

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