Constraints on determinism: Bell versus Conway-Kochen

Abstract

Bell's Theorem from 1964 and the (Strong) Free Will Theorem of Conway and Kochen from 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 & Bob experiment, and satisfy a locality condition called 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.

10 pages, v2: references [19] and [37] added, footnote 2 expanded. Accepted by Foundations of Physics

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• The Free Will Theorem
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• No extension of quantum theory can have improved predictive power
• The Two Bell's Theorems of John Bell
• Local Causality and Completeness: Bell vs. Jarrett
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Cited by in corpus (5)

• Randomness? What randomness?
• On the foundations of quantum theory
• Conway-Kochen and the Finite Precision Loophole
• The Undecidable Charge Gap and the Oil Drop Experiment
• on some (so-called) paradoxes of quantum physics