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Conway–Kochen and the Finite Precision Loophole

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Abstract

Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and 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.

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Notes

  1. This way of introducing hidden variable states is perhaps somewhat cumbersome, but it will be helpful for seeing the analogy with the Conway–Kochen Theorem in the next section.

  2. In three dimensions Conway and Kochen hold the record for the smallest number of vectors (31) [35, p. 114]. The constructions of Peres [35, p. 198] and Bub [11] both use 33 vectors of which the latter requires the least number of frames of all these results. Recently, the number of contexts has been minimized to 7 for the Hilbert space \(\mathbb {C}^6\) [32]. For more discussion on comparing sizes of Kochen–Specker sets see [9, 34] and references therein.

  3. A very incomplete list of examples is [4, 19, 20, 28, 30, 36, 40].

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Acknowledgments

I would like to thank N. P. Landsman for encouraging comments on an early sketch of this paper. This work was supported by the NWO (Vidi Project nr. 016.114.354).

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  1. Department of Theoretical Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL, Groningen, Netherlands

    Ronnie Hermens

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Hermens, R. Conway–Kochen and the Finite Precision Loophole. Found Phys 44, 1038–1048 (2014). https://doi.org/10.1007/s10701-014-9827-8

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