Bell's inequality: Physics meets Probability

Abstract

We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables -- impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality -- a few pairs of random variables (two dimensional vector variables) involved in the EPR-Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) `` death of reality''; d) non-Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.

Legget's inequality and experiment of S. Gröblacher, T. Paterik, R. Kaltenbaek, C. Brukner, M. Zukowski, A. Aspelmeyer, and A. Zeilinger, see section 14

Cited by in corpus (15)

• Where Bell went wrong
• Is the Moon there if nobody looks: Bell Inequalities and Physical Reality
• The contextuality loophole is fatal for Bell inequalities: Reply to a comment by I. Schmelzer
• EPR Paradox, Quantum Nonlocality and Physical Reality
• Embedding Quantum Mechanics Into a Broader Noncontextual Theory: A Conciliatory Result
• Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
• Quantum Mechanics and modelling of physical reality
• "Quantization is a mystery"
• Context-invariant and local quasi hidden variable (qHV) modelling versus contextual and nonlocal HV modelling
• Reinterpreting Quantum Probabilities in a Realistic and Local Framework: The Modified BCHSH Inequalities
• On Universality of Classical Probability with Contextually Labeled Random Variables
• What do we learn from computer simulations of Bell experiments?
• Comments on New Ontology of Quantum Mechanics called CSM
• From a 1D completed scattering and double slit diffraction to the quantum-classical problem: A new approach
• On Universality of Classical Probability with Contextually Labeled Random Variables: Response to A. Khrennikov