Issue
EPL
Volume 87, Number 6, September 2009
Article Number 60007
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/87/60007
Published online 09 October 2009
EPL, 87 (2009) 60007
DOI: 10.1209/0295-5075/87/60007

Possible experience: From Boole to Bell

K. Hess1, K. Michielsen2 and H. De Raedt3

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

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

received 1 July 2009; accepted in final form 11 September 2009; published September 2009
published online 9 October 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.

PACS
03.65.Ud - Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).
03.65.Ta - Foundations of quantum mechanics; measurement theory.
03.65.-w - Quantum mechanics.

© EPLA 2009