Comment on “ Spacetime Information ”

A recent paper by Hartle [1] 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 the analysis of Ref. [1] 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 timeneutral generalized quantum theories and for generalized quantum theories with non-unitary 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 ∗E-mail: [email protected]