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12
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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Cited by 12 (5 self)
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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.
Reichenbach's Common Cause Principle and Quantum Field Theory
, 1997
"... Reichenbach's principle of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebras ..."
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Cited by 12 (6 self)
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Reichenbach's principle of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebras A(V1) and A(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events in A(V1) and A(V2) have a genuinely probabilistic common cause, then the local algebras A(V1) and A(V2) must be statistically independent in the sense of C*independence.
EPRlike "funny business" in the theory Of Branching SpaceTimes
 IN PLACEK AND BUTTERFIELD 2002
, 2002
"... EPRlike phenomena are (presumably) indeterministic, but they furthermore suggest that our world involves seemingstrange "funny business." Without invoking any heavy mathematics, the theory of branching spacetimes offers two apparently quite different ways in which EPRlike funny business goes ..."
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Cited by 9 (6 self)
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EPRlike phenomena are (presumably) indeterministic, but they furthermore suggest that our world involves seemingstrange "funny business." Without invoking any heavy mathematics, the theory of branching spacetimes offers two apparently quite different ways in which EPRlike funny business goes beyond simple indeterminism. (1) The first is a modal version of a Belllike correlation: There exist two spacelike separated indeterministic initial events whose families of outcomes are nevertheless modally correlated. That is, although the occurrence of each outcome of each of the two spacelike separated initial events is separately possible, some joint occurrence of their outcomes (one from each) is impossible. (2) The second sounds like superluminal causation: A certain initial event can bear a causelike relation to a certain outcome event without being in the causal past of that outcome. The two accounts of EPRlike funny business are proved equivalent, a result that supports the claim of each as useful to mark the line between mere indeterminism and EPRlike funny business.
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 theory of bran ..."
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Cited by 7 (4 self)
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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
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...
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
Concrete Transitions
, 2002
"... Following von Wright, "transitions" are needed for understanding agency. I indicate how ..."
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Cited by 2 (1 self)
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Following von Wright, "transitions" are needed for understanding agency. I indicate how
On Infinite EPRlike Correlations
, 705
"... The paper investigates, in the framework of branching spacetimes, whether an infinite EPRlike correlation which does not involve finite EPRlike correlations is possible. 1 ..."
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The paper investigates, in the framework of branching spacetimes, whether an infinite EPRlike correlation which does not involve finite EPRlike correlations is possible. 1
On Minkowskian Branching Structures
, 706
"... Contrary to its initial idea, Belnap’s (1992) theory of Branching SpaceTimes (BST) has models in which histories do not resemble relativistic spacetimes or any other physical spacetimes. The aim of this paper is to define a certain class of BST models, called ”Minkowskian Branching Structures ” ( ..."
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Contrary to its initial idea, Belnap’s (1992) theory of Branching SpaceTimes (BST) has models in which histories do not resemble relativistic spacetimes or any other physical spacetimes. The aim of this paper is to define a certain class of BST models, called ”Minkowskian Branching Structures ” (MBS), in which histories are isomorphic to Minkowski spacetime. By focusing on these models rather than on general BST models, we hope that one may be able to improve on earlier BST analyzes of physical phenomena. Also, introducing MBS’ sets the stage for recent discussions about whether or not ‘branching is a bad idea’, physically speaking. 1