Constraints on Determinism: Bell Versus ConwayKochen
Abstract
Bell's Theorem from Physics 36:128 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226232 (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.
 Publication:

Foundations of Physics
 Pub Date:
 July 2014
 DOI:
 10.1007/s107010149815z
 arXiv:
 arXiv:1402.1972
 Bibcode:
 2014FoPh...44..781C
 Keywords:

 Free will theorem;
 Bell's theorem;
 Hidden variable theories;
 Determinism;
 Quantum Physics;
 81Q99
 EPrint:
 10 pages, v2: references [19] and [37] added, footnote 2 expanded. Accepted by Foundations of Physics