Possible experience: From Boole to Bell

¹  Beckman Institute, Department of Electrical and Computer Engineering and Department of Physics, University of Illinois - Urbana, IL 61801, USA
²  Institute for Advanced Simulation, Jülich Supercomputing Centre, Research Centre Jülich D-52425 Jülich, Germany, EU
³  Department of Applied Physics, Zernike Institute for Advanced Materials, University of Groningen Nijenborgh 4, NL-9747 AG Groningen, The Netherlands, EU

Corresponding authors: k-hess@illinois.edu k.michielsen@fz-juelich.de h.a.de.raedt@rug.nl

Received: 1 July 2009
Accepted: 11 September 2009

Abstract

Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob'ev as related to these inequalities. These findings together with a space-time generalization of Boole's elements of logic lead us to a completely transparent Einstein local counterexample from everyday life that violates certain variations of the Bell inequalities. We show that the counterexample suggests an interpretation of the Born rule as a pre-measure of probability that can be transformed into a Kolmogorov probability measure by certain Einstein local space-time characterizations of the involved random variables.