Conway–Kochen and the Finite Precision Loophole

Abstract

Recently Cator & Landsman made a comparison between Bell's Theorem and Conway & Kochen's Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway-Kochen Theorem has been performed thus far, and, secondly, because the Conway-Kochen Theorem is strongly connected to the Kochen-Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In this paper I show that the finite precision loophole does not apply to the Conway-Kochen Theorem.

Constraints on Determinism: Bell Versus Conway–Kochen

“…Second, because of its dependence on the Kochen-Specker Theorem, the Strong Free Will Theorem might lack finite precision robustness, cf. [1,2,18], though this threat recently seems to have been obviated [19]. 3 The only significant exception we could find is the small and otherwise interesting book by Hemmick and Shakur [17], whose scathing treatment of the Free Will Theorem is somewhat undermined by their claim (p. 90) that the assumption of determinism follows from the other assumptions in the Strong Free Will Theorem (notably pi and perfect correlation).…”

On the notion of free will in the Free Will Theorem

“…Part of this interest has been rather critical (cf. Bassi & Ghirardi, 2007;'t Hooft, 2007;Goldstein et al, 2010;Wüthrich, 2011;Hemmick & Shakur, 2012;Cator &Landsman, 2014;Hermens, 2014Hermens, , 2016, mainly on the following grounds:…”