TWO NON-KOLMOGOROVIAN GENERALIZATIONS OF REICHENBACH'S COMMON CAUSE DEFINITION

Abstract

Given a probabilistic correlation between two events, this correlation might be explained in terms of a common cause. In [1] Reichenbach defines the notion of common cause and shows that the definition is consistent with the explicable correlation, i.e. if two events have a common cause then they do correlate. In this paper we generalize the notion of common cause to Hilbert lattices in two different ways according to the two different definitions of conditional probability in the quantum case, and show that Reichenbach's theorem does not hold in either case. There will be given counter-examples when a common cause 'causes' correlation, anticorrelation and independence, respectively.