ON THE CONSISTENT HISTORIES APPROACH TO QUANTUM-MECHANICS

We review the consistent histories formulations of quantum mechanics d eveloped by Griffiths, Omnes, and Gell-Mann and Hartle, and describe t he classification of consistent sets. We illustrate some general featu res of consistent sets by a few simple lemmas and examples. We conside r various interpretations of the formalism, and examine the new proble ms which arise in reconstructing the past and predicting the future. I t is shown that Omnes' characterization of true statements-statements which can be deduced unconditionally in his interpretation-is incorrec t. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, predi ction, and retrodiction, and conclude that their explanation of the ap parent persistence of quasiclassicality relies on assumptions about an as-yet-unknown theory of experience. Our overall conclusion is that t he consistent histories approach illustrates the need to supplement qu antum mechanics by some selection principle in order to produce a fund amental theory capable of unconditional predictions.