On the selection of preferred consistent sets

The theme of this paper is the multiplicity of the consistent sets emerging in the consistent histories approac to quantum mechanics. We propose one criterion for choosing preferred families among them: that the physically realizable quasiclassical domain ought to be one corresponding to classical histories. We examine the way classical mechanics arises as a particular window, and in the important role played by the canonical group. We finally discuss a possible implication of our selection criterion: that only a class of Hilbert space operators correspond to physical quantities and hence the full non-distributivity of the lattice of quantum propositions is redundant. The consistent histories approach [1, 2, 3, 4, 5, 6, 7, 8] (or rather approaches taking into account its diverse existing formulations ) has been a subject of increasing interest in recent years. It provides a view of time as an intrinsic object in the quantum theory (particularly appealing when considering quantum cosmology), a natural language for discussion of the emergence of classical behaviour and is believed to constitute a converging point for diverse ideas from different interpretations of quantum theory. Still it seems that an old problem (or at least a point of unease) of the Copenhagen interpretation has been transferred into the histories approach: