Gravitational entropy is observer-dependent (2405.00114v3)

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.

• The paper argues that gravitational entropy is observer-dependent, changing based on the quantum reference frame of the observer.
• It proposes a framework using quantum reference frames to demonstrate how different observers perceive varying entropies by altering the algebraic structure of observables.
• The work introduces "subsystem relativity," suggesting gravitational entropy calculations are relative to the observer's reference frame, with implications for concepts like black hole entropy.

Overview of "Gravitational Entropy is Observer-Dependent"

The paper "Gravitational entropy is observer-dependent" by Julian De Vuyst et al. explores the foundational role of observers within quantum gravity frameworks, focusing on how gravitational entropy is inherently dependent on the observer's reference frame. The work leverages the concept of quantum reference frames (QRFs) to expand on recent developments regarding the algebraic structure of observables in quantum gravity and its implications for gravitational entropy.

Central Thesis and Motivation

The authors argue that traditional definitions of entropy in quantum gravity—rooted in von Neumann algebras—are observer-dependent. This dependence arises from the nature of the QRFs, which are crucial for making sense of the entropy assigned to a spacetime subregion's gravitational observables. The principal claim is that the entropy of a gravitational system changes according to the observer's frame, described mathematically through the transition from Type III to Type II von Neumann algebras when incorporating an observer's viewpoint.

Key Contributions and Results

1. Quantum Reference Frames (QRFs): The paper identifies what CLPW (Chandrasekaran, Longo, Penington, and Witten) define as 'observers' as QRFs, previously explored in broader theoretical contexts. This recognition makes it possible to apply the QRF formalism to understand gravitational systems' entropy properties better.
2. Observed Algebraic Structures: The authors construct a generalized framework where the algebra of observables is re-evaluated in terms of QRFs. This framework demonstrates that different observers can perceive varying entropies due to differences in QRFs applied to a given semiclassical regime and also in scenarios extending beyond it.
3. Subsystem Relativity: A critical theoretical advancement proposed in this work is "subsystem relativity," indicating that gravitational entropy is relative to the observer's reference frame. Different combinations of QRFs—determining which observer measurements are made—yield differing entropy calculations.
4. Entropy in Semiclassical and Antisemiclassical Regimes: The paper provides calculations illustrating how entropy manifests under certain assumptions. Examples provided include semiclassical regimes, where time is sharply peaked, leading to simplified entropy computations.
5. Illustrative Example with Clifford Algebras: The authors present an example using clocks subject to interferometry, showing how two clocks with different properties (differing energy spectra) lead to observer-dependent entropy. Such examples elucidate entropy relativity's quantitative mechanisms.

Implications and Future Directions

The paper's theoretical framework has broad implications for understanding quantum gravity and its ties to quantum information. It challenges traditional views on horizon entropy, suggesting that known metrics, such as black hole entropy, might not be invariant across QRFs. Moreover, the work hints at a deeper connection between subsystem relativity and thermodynamic laws' extensions to gravitational settings.

Future research directions include exploring the dynamics of interacting QRFs, investigating entanglement properties in quantum gravity across different observational perspectives, and extending these concepts to in-depth studies on how gravitational observables are impacted by various geometries and topologies in spacetime.

Overall, this work serves as a foundational step in bridging quantum gravity’s theoretical constructs with the operational realities dictated by the nature of quantum reference frames. It provides a methodological pathway for future research to consider the observer's role and offers rich theoretical ground for developing new insights in understanding how gravitational systems manifest in quantum frameworks.