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Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

Formalizing the separability condition in Bell's theorem

Brandon Fogel

Published Jun 27, 2007• 11 citations
Publisher
DOI
10.1016/j.shpsb.2007.04.001

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This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals (subjunctive conditionals) enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis’s famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactual semantics to strengthen Bell’s theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell’s theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.
The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlation between two spatially separated photons. By interpreting the correlation non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view based on his separability principle and his ensemble interpretation of ψ-functions in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. This paper shows that Bell's theorem is incorrect and presents an explanation of the correlation based on Einstein's argument. The correlation is deterministic. A formal analysis supporting Einstein's explanation is also presented.