Eur. Phys. J. D 62, 139−154 (2011)
https://doi.org/10.1140/epjd/e2010-10359-8

Bell’s theorem with no locality assumption: putting free will at work

IBM, P.O. Box 218, Yorktown Heights, 10598 NY, USA

^a e-mail: charlestresser@yahoo.com

Received: 18 June 2010
Received in final form: 10 December 2010
Published online: 25 March 2011

Abstract

We prove a version of Bell’s Theorem which does not assume Locality but instead only the conjunction of a Free Will Principle (so weak that one’s will needs not be free from one’s past) and what we call the Effect After Cause Principle (EACP) according to which for any Lorentz observer the value of an observable measured at (x₀, t₀) cannot further change to another value at (x₀, t₀) because of any cause which happens after said observable has been measured at (x₀, t₀) for that observer, with a similar condition on variables which depend on Realism. Since the EACP, which does not forbid all forms of dependance upon future effects, is compatible both with Locality and with Non-Locality, Locality cannot be considered as the common cause of all the contradictions obtained in all versions of Bell’s Theory. By the very nature of what is a Bell’s Inequality, all versions of Bell’s Theorem assume Weak Realism according to which the value of an observable needed in the discussion of Bell’s Theorem is well defined whenever the measurement could have been made and some measurement is made. This work supports the view that it is Weak Realism, not Locality, which needs to be negated to avoid the contradictions in microscopic Physics associated to Bell’s Theory, at least if one refuses as false the de Broglie-Bohm Hidden Variable theory, e.g., because of its essential violation not only of Locality but also of Lorentz invariance.