Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-10-31
Phys.Rev. D56 (1997) 2469-2472
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, LaTeX with ReVTeX. References updated
Scientific paper
10.1103/PhysRevD.56.2469
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 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 general definition of the relevant class of sets that agrees with Hartle's definition in the cases explicitly considered and that generalizes to other cases.
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