On modifications of Reichenbach's principle of common cause in light of Bell's theorem

Journal of Physics A: Mathematical and Theoretical 47 (42):424018 (2014)
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Abstract

Bellʼs 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbachʼs principle of common cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as much less bitter medicine than the perceived alternative—dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbachʼs principle could be maintained even with relativistic causality. Here we break down Reichenbachʼs principle into two independent assumptions—the principle of common cause proper and factorization of probabilities. We show how Bellʼs theorem can be derived from these two assumptions plus relativistic causality and the law of total probability for actual events, and we review proposals to drop each of these assumptions in light of the theorem. In particular, we show that the non-commutative common causes of Hofer-Szabó and Vecsernyés fail to have an analogue of the notion that the common causes can explain the observed correlations. Moreover, we show that their definition can be satisfied trivially by any quantum product state for any quantum correlations. We also discuss how the conditional states approach of Leifer and Spekkens fares in this regard.

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Eric Cavalcanti
Griffith University

References found in this work

Causality: Models, Reasoning and Inference.Judea Pearl - 2000 - New York: Cambridge University Press.
The direction of time.Hans Reichenbach - 1956 - Mineola, N.Y.: Dover Publications. Edited by Maria Reichenbach.
The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.
Abstract.[author unknown] - 2011 - Dialogue and Universalism 21 (4):447-449.
Review of T he Direction of Time.Henryk Mehlberg - 1962 - Philosophical Review 71 (1):99.

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