How to (properly) strengthen Bell's theorem using counterfactuals |
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Authors: | Tomasz Bigaj |
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Institution: | 1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, P.R. China;2. School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand;3. School of Energy Science and Engineering, Vidyasirimedhi Institute of Science and Technology, Wang Chan, Rayong 21210, Thailand |
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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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