Gábor Hofer-Szabó

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 correlations in the sense of Reichenbachs 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 Reichenbachs definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbachs Common Cause Principle.

Common‐Causes are Not Common Common‐Causes

A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common‐cause and it is shown that there exists pairs of correlated events, probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common‐cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach’s definition of common‐cause. The significance of the difference between common‐causes and common common‐causes is emphasized from the perspective of 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 quantumprobability space both the classical and the quantum probability spaces areextendable in such a way that the extension contains common causes of thegiven correlations, where common cause is taken in the sense of Reichenbachsdefinition. These results strongly restrict the possible ways of disprovingReichenbachs common cause principle and indicate that EPR-type quantumcorrelations might very well have a common cause explanation.

Reichenbach’s Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom

In the paper it will be shown that Reichenbach’s Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones

Noncommuting local common causes for correlations violating the Clauser–Horne inequality

{\mathcal{O}}_{a}

Noncommutative Common Cause Principles in algebraic quantum field theory

and

Reichenbach's Common Cause Definition on Hilbert Lattices

{\mathcal{O}}_{b}

Formal existence and uniqueness of the Reichenbachian common cause on Hilbert lattices

, respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of

On the concept of Bell’s local causality in local classical and quantum theory

{\mathcal{O}}_{a}

Conditioning using conditional expectations: the Borel–Kolmogorov Paradox

and