Foundations of Physics

, Volume 44, Issue 7, pp 781–791 | Cite as

Constraints on Determinism: Bell Versus Conway–Kochen

Article

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 

Notes

Acknowledgments

The authors are indebted to Jeff Bub, Jeremy Butterfield, Dennis Dieks, Richard Gill, Hans Maassen, and Matt Leifer for various comments on this work (including predecessors).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of Science, Institute for Mathematics, Astrophysics, and Particle PhysicsRadboud University NijmegenNijmegenThe Netherlands

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