Comment on "Spacetime Information"

TL;DR

This paper critiques Hartle's proposed definition of spacetime information, identifying errors in its analysis, but confirms its consistency with standard quantum mechanics and offers a generalized, more rigorous definition.

Contribution

It corrects and clarifies Hartle's definition of spacetime information, providing a more general and consistent framework applicable beyond specific cases.

Findings

Hartle's analysis contains errors invalidating some conclusions.

The proposed definition aligns with standard quantum mechanics.

A generalized definition of consistent sets of histories is provided.

Abstract

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.