Gravitational entropy is observer-dependent

TL;DR

This paper demonstrates that gravitational entropy in quantum gravity depends on the observer, showing that different observers perceive different entropies, and connects quantum reference frames with the Page-Wootters formalism.

Contribution

It generalizes previous approaches to account for multiple observers in quantum gravity, revealing observer-dependent entropy and linking QRF formalism with the Page-Wootters approach.

Findings

Observers perceive drastically different entropies.

The formalism of quantum reference frames is used to analyze observer dependence.

The description of states aligns with the Page-Wootters formalism.

Abstract

In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers and for arbitrary global physical states), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the `observers' considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [arXiv:2206.10780] is equivalent to the Page-Wootters formalism, leading to the informal slogan "PW=CLPW". It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.