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On Reichenbach's common cause principle and Reichenbach's notion of common cause
"... It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlation ..."
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It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
Common Cause Completability of Classical and Quantum Probability Spaces
"... It is shown that for a given set of correlations either in a classical or in a quantum probability space both the classical and the quantum probability spaces are extendable in such a way that the extension contains common causes of the given correlations, where common cause is taken in the sense of ..."
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It is shown that for a given set of correlations either in a classical or in a quantum probability space both the classical and the quantum probability spaces are extendable in such a way that the extension contains common causes of the given correlations, where common cause is taken in the sense of Reichenbach's denition. These results strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle and indicate that EPR type quantum correlations might very well have a common cause explanation. 1 The problem The aim of this paper is to present two results on the following problem, raised rst within the framework of classical, Kolmogorovian probability theory in ([4], Chapter 1 14.): Let (L; p) be a generalized probability space with the orthomodular lattice L and additive, normalized measure p on L and let f(A i ; B i )ji 2 Ig be a set of events in L that are (positively) correlated with respect p, i.e. p(A i ^B i ) > p(A i )p(B i ), with A i and B i being c...
Contextuality and Nonlocality in ‘No Signaling ’ Theories
, 903
"... We define a family of ‘no signaling ’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the KochenSpecker theorem, so we call these boxes KochenSpeckerKlyachko boxes or, briefly, ..."
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We define a family of ‘no signaling ’ bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the KochenSpecker theorem, so we call these boxes KochenSpeckerKlyachko boxes or, briefly, KSboxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the ClauserHorneShimonyHolt inequality, when the KSbox is a generalized PRbox (hence a vertex of the ‘no signaling ’ polytope). We show that for certain marginal probabilities a KSbox is classical with respect to nonlocality as measured by the ClauserHorneShimonyHolt correlation, i.e., no better than shared randomness as a resource in simulating a PRbox, even though such KSboxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in ‘no signaling ’ theories. PACS numbers: 03.65.Ud, 03.65.Ta, 03.67.a 1
Measurement Dependence is not Conspiracy: A Common Cause Model of EPR Correlations
, 905
"... In this paper I assess the adequacy of noconspiracy conditions present in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these can not be ..."
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In this paper I assess the adequacy of noconspiracy conditions present in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these can not be ruled out. I argue that an appropriate common cause explanation requires that noconspiracy conditions are reinterpreted as mere common causemeasurement independence conditions. Violations of measurement independence thus need not entail any kind of conspiracy (nor backwards in time causation). This new reading of measurement dependence provides the grounds for an explicitly nonfactorizable (in the sense of Bell’s factorizability) common cause model for EPR. 1
WHY ARE (MOST) LAWS OF NATURE MATHEMATICAL?
"... Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas —Einstein In a frequently quoted but scarcely read paper, the Hungarian physicist Eugene Wigner rediscovered a question that had been implicitly posed for the first time by ..."
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Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas —Einstein In a frequently quoted but scarcely read paper, the Hungarian physicist Eugene Wigner rediscovered a question that had been implicitly posed for the first time by the Transcendental Aesthetics of the “Critique of Pure Reason”. More precisely, rather than asking, in the typical style of Kant, “how is mathematics possible”, Wigner was wondering how it could be so “unreasonably effective in the natural sciences ” (Wigner, 1967). The effectiveness in question refers to the numerous cases of mathematical theories, often developed without regard to their possible applications, that later have played an important and unexpected descriptive, explanatory and predictive role in physics and other natural sciences. A frequently given example is that of the conic sections, already known by the Greeks before Christ and used by Kepler many centuries after their discovery to describe the orbits of celestial bodies. Even more striking is the case of nonEuclidean geometries, applied by Einstein to describe how heavy matter bends the structure of spacetime in his general theory of relativity: the theory of curved, nonEuclidean spaces had already been built a century earlier by Gauss, Lobacevski and Riemann. A literary quotation addressing the role of complex numbers, due to the German writer Robert Musil, will conclude my necessarily short list of