Gravitational entropy is observer-dependent

In quantum gravity, it has been argued that a proper accounting of the roleplayed by an observer promotes the von Neumann algebra of observables in agiven spacetime subregion from Type III to Type II. While this allows for amathematically precise definition of its entropy, we show that this proceduredepends on which observer is employed. We make this precise by considering asetup in which many possible observers are present; by generalising previousapproaches, we derive density operators for the subregion relative to differentobservers (and relative to arbitrary collections of observers and for arbitraryglobal physical states), and we compute the associated entropies in asemiclassical regime, as well as in some specific examples that go beyond thisregime. We find that the entropies seen by distinct observers can drasticallydiffer. Our work makes extensive use of the formalism of quantum referenceframes (QRF); indeed, as we point out, the `observers’ considered here and inthe previous works are nothing but QRFs. In the process, we demonstrate thatthe description of physical states and observables invoked by Chandrasekaran etal. [arXiv:2206.10780] is equivalent to the Page-Wootters formalism, leading tothe informal slogan “PW=CLPW”. It is our hope that this paper will helpmotivate a long overdue union between the QRF and quantum gravity communities.Further details will appear in a companion paper.

Further reading#

• Access Paper in arXiv.org