How to (properly) strengthen Bell's theorem using counterfactuals

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):58-66 (2010)
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Abstract

Bell’s theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell’s theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein’s criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein’s criterion rather than the locality assumption.

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Tomasz Bigaj
University of Warsaw

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Ungrounded Dispositions in Quantum Mechanics.Tomasz Bigaj - 2012 - Foundations of Science 17 (3):205-221.

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