ABSTRACT: A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values 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 inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' (...) Rule. It is argued that an assumption of reverse causality 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, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

A brief review of the attempts to define “elements of reality” in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.