Possible experience: From Boole to BellK. 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
received 1 July 2009; accepted in final form 11 September 2009; published September 2009
published online 9 October 2009
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.
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