ua nt - p h / 02 07 18 2 v 1 3 1 Ju l 2 00 2 Weak Values and Counterfactual Statements in Quantum Theory

A relation is obtained between weak values of quantum observ-ables and the consistency criterion for histories of quantum events. It is shown that " strange " weak values (such as values less than zero for projection operators) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives conceptually inconsistent results. This problem is shown to be remedied by using the standard quantum conditional probability for weak values involving inconsistent histories. It is argued that an assumption of reverse causality (a form of time symmetry) implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, the problem of how to interpret strange weak values and their associated strange probabilities is discussed. It is concluded that these values cannot generally be interpreted as the answers to a set of counterfactual questions for the same individual particle, but instead describe properties of an ensemble.