Gravitational entropy is observer-dependent

Gravitational entropy is observer-dependent

18 May 2024 | Julian De Vuyst, Stefan Eccles, Philipp A. H"ohn, Josh Kirklin
Gravitational entropy is observer-dependent. This paper explores how the entropy of a subregion in a quantum gravitational system depends on the observer's reference frame. The key idea is that the von Neumann algebra of observables in a given spacetime subregion can be promoted from Type III to Type II when accounting for an observer, allowing for a mathematically precise definition of entropy. However, this procedure depends on which observer is used, leading to different entropies for different observers. The paper shows that the 'observers' considered here are quantum reference frames (QRFs), and that the description of physical states and observables by Chandrasekaran et al. is equivalent to the Page-Wootters formalism, leading to the slogan "PW = CLPW." The paper generalizes previous approaches to consider multiple QRFs and computes entropies in both semiclassical and antisemiclassical regimes. It demonstrates that the entropy seen by different observers can drastically differ, highlighting the observer-dependence of gravitational entropy. The paper also discusses the implications of this observer-dependence for quantum gravity and quantum reference frames, and concludes that the entropy of all degrees of freedom in a subregion is not observer-dependent, but the choice of QRFs used to measure the fields can lead to different entropies. The paper emphasizes the importance of quantum reference frames in understanding the role of observers in quantum gravity.Gravitational entropy is observer-dependent. This paper explores how the entropy of a subregion in a quantum gravitational system depends on the observer's reference frame. The key idea is that the von Neumann algebra of observables in a given spacetime subregion can be promoted from Type III to Type II when accounting for an observer, allowing for a mathematically precise definition of entropy. However, this procedure depends on which observer is used, leading to different entropies for different observers. The paper shows that the 'observers' considered here are quantum reference frames (QRFs), and that the description of physical states and observables by Chandrasekaran et al. is equivalent to the Page-Wootters formalism, leading to the slogan "PW = CLPW." The paper generalizes previous approaches to consider multiple QRFs and computes entropies in both semiclassical and antisemiclassical regimes. It demonstrates that the entropy seen by different observers can drastically differ, highlighting the observer-dependence of gravitational entropy. The paper also discusses the implications of this observer-dependence for quantum gravity and quantum reference frames, and concludes that the entropy of all degrees of freedom in a subregion is not observer-dependent, but the choice of QRFs used to measure the fields can lead to different entropies. The paper emphasizes the importance of quantum reference frames in understanding the role of observers in quantum gravity.
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