We investigate whether standard counterfactual analyses of causation imply that the outcomes of space-like separated measurements on entangled particles are causally related. Although it has sometimes been claimed that standard CACs imply such a causal relation, we argue that a careful examination of David Lewis’s influential counterfactual semantics casts doubt on this. We discuss ways in which Lewis’s semantics and standard CACs might be extended to the case of space-like correlations.

Bell’s theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell’s theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on (...) the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein’s criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein’s criterion rather than the locality assumption. (shrink)

In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it (...) appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford. (shrink)