Abstract
Standard derivations of the Bell inequalities assume a common-common-cause-system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper (Graßhoff et al., The British Journal for the Philosophy of Science, 56, 663–680 (2005)) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case of perfect correlations can be reduced to the assumptions of a common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabó’s (International Journal of Theoretical Physics, 39, 911 (2004)) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a δ-neighborhood of perfect EPR correlations.
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References
Belnap N., & Szabó L.E. (1996). Branching space-time analysis of the GHZ theorem. Foundations of Physics 26, 982–1002
Graßhoff G., Portmann S., Wüthrich A. (2005). Minimal assumption derivation of a Bell-type inequality. The British Journal for the Philosophy of Science 56, 663–680
Hofer-Szabó G., Rédei M., Szabó L.E. (1999). On Reichenbach’s common cause principle and on Reichenbach’s notion of common cause. The British Journal for the Philosophy of Science 50, 377–399
Hofer-Szabó G., Rédei M., Szabó L.E. (2002). Common causes are not common common causes. Philosophy of Science 69, 623–633
Hofer-Szabó G., Rédei M. (2004). Reichenbachian common cause systems. International Journal of Theoretical Physics 43, 1819–1826
Hofer-Szabó G., Rédei M. (2006). Reichenbachian common cause systems of arbitrary finite size exist. Foundations of Physics 35, 745–756
Placek T. (2000). Is nature deterministic?. Kraków, Jagiellonian University Press
Portmann, S., & Wüthrich, A. (2007). Minimal assumption derivation of a weak Clauser–Horne inequality. Studies in History and Philosophy of Modern Physics, electronic preprint <www.arxiv.org/quant-ph/0604216>.
Reichenbach H. (1956). The direction of time. Berkeley, University of California Press
Szabó L.E. (2000). On an attempt to resolve the EPR–Bell paradox via reichenbachian concept of common cause. International Journal of Theoretical Physics 39, 911
Wüthrich, A. (2004). Quantum correlations and common causes. Master’s Thesis. Bern Studies in the History and Philosophy of Science, Bern.
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Hofer-Szabó, G. Separate- versus common-common-cause-type derivations of the Bell inequalities. Synthese 163, 199–215 (2008). https://doi.org/10.1007/s11229-007-9198-1
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DOI: https://doi.org/10.1007/s11229-007-9198-1