Comment on “Spacetime information”

A recent paper by Hartle [Phys. Rev. D 51, 1800 (1995)] proposes a definition of “spacetime information” — the information available about a quantum system’s boundary conditions in the various sets of decohering histories it may display — and investigates its properties. We note here that Hartle’s analysis contains errors which invalidate several of the conclusions. In particular, the proof that the proposed definition agrees with the standard definition for ordinary quantum mechanics is invalid, the evaluations of the spacetime information for time-neutral generalized quantum theories and for generalized quantum theories with nonunitary evolution are incorrect, and the argument that spacetime information is conserved on spacelike surfaces in these last theories is erroneous. We show, however, that the proposed definition does, in fact, agree with the standard definition for ordinary quantum mechanics. Hartle’s definition relies on choosing, case by case, a class of fine-grained consistent sets of histories. We supply a possible general definition of a class of sets that includes all the sets considered in Hartle’s paper and that generalizes to other cases.