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14
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.
Local primitive causality and the common cause principle in quantum field theory
 FOUND. PHYS
, 2002
"... If {A(V)} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system (A(V 1), A(V 2), f) is said to satisfy the Weak Reichenbach’s Common Cause Principle iff for every pai ..."
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If {A(V)} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system (A(V 1), A(V 2), f) is said to satisfy the Weak Reichenbach’s Common Cause Principle iff for every pair of projections A ¥ A(V 1), B ¥ A(V 2) correlated in the normal state f there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2, a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system (A(V 1), A(V 2), f) with a locally normal and locally faithful state f and suitable bounded V 1 and V 2 satisfies the
Nocommoncause EPRlike funny business in branching spacetimes
 PHILOSOPHICAL STUDIES
, 2003
"... There is "no EPRlike funny business" if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPRlike quantummechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theor ..."
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There is "no EPRlike funny business" if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPRlike quantummechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theory of branching spacetimes can be used to sharpen the theoretical dichotomy between "EPRlike funny business" and "no EPRlike funny business." Belnap 2002 offered
Stochastic Einstein Locality Revisited
, 2007
"... I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, i.e. the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach’s Principle of the Common Cause (PCC), and Bell’s Local Causality. My main a ..."
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I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, i.e. the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach’s Principle of the Common Cause (PCC), and Bell’s Local Causality. My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand. Finally, I briefly discuss how to formulate relativistic causality if there is no
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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Cited by 6 (2 self)
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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...
Remarks on causality in relativistic quantum field theory
 International Journal of Theoretical Physics
, 2005
"... It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras A(V1), A(V2) associated with spacelike separated spacetime regions V1, V2 have a (Reichenbachian) common cause located in the union of the backw ..."
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It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras A(V1), A(V2) associated with spacelike separated spacetime regions V1, V2 have a (Reichenbachian) common cause located in the union of the backward light cones of V1 and V2. Further comments on causality and independence in quantum field theory are made. 1
Reconsidering Relativistic Causality
, 2007
"... Forthcoming (after an Appendectomy) in ..."
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Reichenbach’s notion of common cause
, 2008
"... On Reichenbach’s common cause principle and ..."
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NUEL BELNAP NOCOMMONCAUSE EPRLIKE FUNNY BUSINESS IN BRANCHING SPACETIMES
"... ABSTRACT. There is “no EPRlike funny business ” if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPRlike quantum mechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theory ..."
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ABSTRACT. There is “no EPRlike funny business ” if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPRlike quantum mechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theory of branching spacetimes can be used to sharpen the theoretical dichotomy between “EPRlike funny business ” and “no EPRlike funny business”. Belnap (2002) offered two analyses of the dichotomy, and proved them equivalent. This essay adds two more, both connected with Reichenbach’s “principle of the common cause”, the principle that sends us hunting for a commoncausal explanation of distant correlations. The two previous ideas of funny business and the two ideas introduced in this essay are proved to be all equivalent, which increases one’s confidence in the stability of (and helpfulness of) the BST analysis of the dichotomy between EPRlike funny business and its absence. 1. BACKGROUND: TWO IDEAS OF EPRLIKE FUNNY BUSINESS The vast philosophical literature on quantum mechanics is filled with (a) accounts of EPRlike or Belllike correlations between spacelike related (I write SLR) events, and also with (b) discussions of the same phenomena under the heading of superluminal causation. Belnap (2002) used the austere language of branching spacetimes (BST) in order to define the following two sharp concepts corresponding respectively to these rough concepts: Primary SLR modalcorrelation funny business (see Definition
Forthcoming in International Journal of Theoretical Physics
"... A partition {Ci}i∈I of a Boolean algebra S in a probability measure space (S, p) is called a Reichenbachian common cause system for the correlated pair A, B of events in S if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index ..."
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A partition {Ci}i∈I of a Boolean algebra S in a probability measure space (S, p) is called a Reichenbachian common cause system for the correlated pair A, B of events in S if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set I is called the size of the common cause system. It is shown that given any correlation in (S, p), and given any finite size n> 2, the probability space (S, p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of S contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated. 1 Reichenbach’s notion of common cause Let (S, p) be a classical probability space with Boolean algebra S of random events and probability measure p on S. If the joint probability p(A ∩ B) of A and B is greater than the product of the single probabilities, i.e. if p(A ∩ B)> p(A)p(B) (1)