Gravitational entropy is observer-dependent
arXiv:2405.00114 · doi:10.1007/JHEP07(2025)146
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.
27 pages + references, 2 figures. References added, and minor corrections. Comments welcome
References in corpus (43)
- Towards a derivation of holographic entanglement entropy
- Generalized gravitational entropy
- Reference frames, superselection rules, and quantum information
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Black hole entropy in Loop Quantum Gravity
- Notes on Some Entanglement Properties of Quantum Field Theory
- Local subsystems in gauge theory and gravity
- Partial and Complete Observables for Hamiltonian Constrained Systems
- An Algebra of Observables for de Sitter Space
- Quantum mechanics and the covariance of physical laws in quantum reference frames
- Entanglement Temperature and Entanglement Entropy of Excited States
- A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
- Gravity and the Crossed Product
- Quantum Time
- Large N algebras and generalized entropy
- A change of perspective: switching quantum reference frames via a perspective-neutral framework
- Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
- The Role of Type III Factors in Quantum Field Theory
- Generalized entropy for general subregions in quantum gravity
- Quantizing time: Interacting clocks and systems
- Quantum clocks observe classical and quantum time dilation
- Physics within a quantum reference frame
- Notes on the type classification of von Neumann algebras
- Quantum reference frames for general symmetry groups
- Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
- Spacetime Quantum Reference Frames and superpositions of proper times
- The Observer's Ghost: a field-space connection-form and its application to gauge theories and general relativity
- Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
- Quantum Relativity of Subsystems
- Edge modes as reference frames and boundary actions from post-selection
- Quantum reference frame transformations as symmetries and the paradox of the third particle
- Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
- Construction of quantum Dirac observables and the emergence of WKB time
- Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
- Edge modes as dynamical frames: charges from post-selection in generally covariant theories
- Relative Quantum Time
- Quantum Reference Frames at the Boundary of Spacetime
- Operational Quantum Reference Frame Transformations
- Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
- A Type Approximation of the Crossed Product
- Nonrelativistic spatiotemporal quantum reference frames
- Extremality as a Consistency Condition on Subregion Duality