Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy

• URL: http://arxiv.org/abs/2412.15502v1
• Date: Fri, 20 Dec 2024 02:29:55 GMT
• Title: Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• Authors: Julian De Vuyst, Stefan Eccles, Philipp A. Hoehn, Josh Kirklin,
• Abstract summary: We provide an in-depth analysis of gravitational entropy using quantum reference frames (QRFs) We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. We show how the clock may simply be partially traced' out when evaluating the entropy.
• Score: 0.0
• License:
• Abstract: A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subregion to a Type II crossed product, whose entropy reduces to the generalized entropy formula in a semiclassical limit. The observers thus used are also known as quantum reference frames (QRFs); as noted in our companion work [arXiv:2405.00114], using different QRFs result in different algebras, and hence different entropies -- so gravitational entropy is observer-dependent. Here, we provide an in-depth analysis of this phenomenon, with full derivations of many new results. Using the perspective-neutral QRF formalism, we extend previous constructions to allow for arbitrarily many observers, each carrying a clock with possibly degenerate energy spectra. We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. Unlike previous works, we allow the clocks and fields to be arbitrarily entangled. At leading order the von Neumann entropy still reduces to the generalized entropy, but linear corrections are typically non-vanishing and quantify the degree of entanglement between the clocks and fields. We also describe an `antisemiclassical' regime as the opposite of the semiclassical one, with suppressed fluctuations of the clock energy; in this regime, we show how the clock may simply be `partially traced' out when evaluating the entropy. Four explicit examples of observer-dependent entropy are then given, involving a gravitational interferometer, degenerate clock superselection, a semiclassical approximation applying to some clocks but not others, and differences between monotonic and periodic clocks.

Related papers

• Relational Dynamics with Periodic Clocks [0.0]
  We show that a relational dynamics can be established relative to periodic clocks both in the classical and quantum theories. We show how a system evolving periodically with respect to a periodic clock can evolve monotonically with respect to an aperiodic clock, without inconsistency.
  arXiv  Detail & Related papers  (2024-09-10T13:07:46Z)
• Gravitational entropy is observer-dependent [0.0]
  A proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion. 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.
  arXiv  Detail & Related papers  (2024-04-30T18:03:22Z)
• Finite Pulse-Time Effects in Long-Baseline Quantum Clock Interferometry [45.73541813564926]
  We study the interplay of the quantum center-of-mass $-$ that can become delocalized $-$ together with the internal clock transitions. We show at the example of a Gaussian laser beam that the proposed quantum-clock interferometers are stable against perturbations from varying optical fields.
  arXiv  Detail & Related papers  (2023-09-25T18:00:03Z)
• Entanglement entropy in conformal quantum mechanics [68.8204255655161]
  We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory.
  arXiv  Detail & Related papers  (2023-06-21T14:21:23Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Clocking the Quantum Sojourn Time: Spurious Scatterings and Correction to the Larmor Clock [0.0]
  We revisit the notions of the quantum-mechanical sojourn time in the context of the quantum clocks. We trace its origins to the non-trivial inadvertent scattering arising from the disparity, however weak, engendered by the very clock potential.
  arXiv  Detail & Related papers  (2021-06-29T03:57:42Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Measuring the thermodynamic cost of timekeeping [0.0]
  In some form or another, all clocks use the evolution of nature towards higher entropy states to quantify the passage of time. We show theoretically that the maximum possible accuracy for this classical clock is proportional to the entropy created per tick. We find that there is a linear relation between accuracy and entropy and that the clock operates within an order of magnitude of the theoretical bound.
  arXiv  Detail & Related papers  (2020-06-15T18:17:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.