Reichenbach’s common cause principle and quantum field theory

Abstract

As we have seen in Chapter 10, Bell’s inequalities are violated in relativistic quantum field theory, and this has the consequence that quantum field theory predicts superluminal correlations i. e. correlations between events as represented by projections lying in local von Neumann algebras belonging to spacelike separated spacetime regions. We also have seen in the previous chapter that an explanation of the superluminal correlations by assuming that there is a direct causal influence between the correlated events is unlikely to be correct, since the correlated algebras do satisfy a number of independence conditions. The aim of this chapter is to investigate another possible way of explaining the correlations in question: the explanation by a probabilistic common cause. Now it is far from obvious what is meant by a “probabilistic common cause” of a probabilistic correlation. We shall utilize here the classic analysis given by Reichenbach in 1956 [136]. Our aim is to specify Reichenbach’s notion of a probabilistic common cause in terms of ARQFT in order to raise the problem of whether the superluminal correlations predicted by ARQFT can be causally explained in field theory in the sense of Reichenbach’s probabilistic theory of common cause, suitably adapted to ARQFT. In what follows, first we summarize briefly Reichenbach’s common cause principle, and in particular his notion of “screening off” (Section 12.1). We shall distinguish two types of screening off: the strong one, in which the causing event actually implies both of the correlated events; and the genuinely probabilistic case, in which the probabilistic cause does not entail any of the correlated events.