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.

Based partly on proving that algebraic relativistic quantum eld theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT, (Summers and Werner 1987a-c), is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic local hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise denition of hidden-variables theory within the operator algebraic framework of quantum mechanics it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that can not be reduced in a given way. In some particular...

Butterfield's (1992 a-c) claim of the equivalence of absence of Lewisian probabilistic counterfactual causality (LC) to Hellman's Stochastic Einstein Locality (SEL) is questioned. Butterfield's assumption on which the proof of his claim is based would suce to prove that SEL implies absence of LC also for appropriately given versions of these notions in algebraic quantum field theory - but the assumption is not an admissible one. The conclusion must be that the relation of SEL and absence of LC is open, and that they may be independent.