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.

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

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...

There is "no EPR-like funny business" if (contrary to apparent fact) our world is as indeterministic as you wish, but is free from the EPR-like quantum-mechanical phenomena such as is sometimes described in terms of superluminal causation or correlation between distant events. The theory of branching space-times can be used to sharpen the theoretical dichotomy between "EPR-like funny business" and "no EPR-like funny business." Belnap 2002 offered

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 re-assess 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

It is shown that the correlations predicted by relativistic quantum eld theory in locally normal states between projections in local von Neumann algebras A(V 1 ); A(V 2 ) associated with spacelike separated spacetime regions V 1 ; V 2 have a (Reichenbachian) common cause located in the union of the backward light cones of V 1 and V 2 . Further comments on causality and independence in quantum eld theory are made.

Forthcoming (after an Appendectomy) in

On Reichenbach’s common cause principle and