Glimmers of a post-geometric perspective

• URL: http://arxiv.org/abs/2108.12362v2
• Date: Thu, 23 Sep 2021 18:01:27 GMT
• Title: Glimmers of a post-geometric perspective
• Authors: Federico Piazza
• Abstract summary: Quantum gravitational effects can become important at low energy if the wavefunction of the metric field fails to be peaked around a classical configuration. We try to understand such deviations from classicality within canonical quantum gravity by introducing a "fluid of observers" We find that, even in the presence of relevant fluctuations in the metric field, a locally flat limit is recovered in the neighbourhood of each observer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum gravitational effects can become important at low energy if the wavefunction of the metric field fails to be peaked around a classical configuration. We try to understand such deviations from classicality within canonical quantum gravity by introducing a "fluid of observers" in the low energy theory and defining a distance operator "at equal time" among them. We find that, even in the presence of relevant fluctuations in the metric field, a locally flat limit is recovered in the neighbourhood of each observer. Deviations from classicality have no particular consequence, locally. However, at larger separations the expectation value of the distance operator behaves differently than a standard Riemannian distance. In particular, it is non-additive and thus cannot be obtained by the integral of a differential line element. This emerging "beyond Riemannian" geometry is a metric space similar to embedded Riemannian manifolds equipped with chord distances that cut through the ambient space. We study deviations from flat space by looking at triangles in the limit where their sizes go to zero. Beyond-Riemannian deviations with respect to flat space are of the same order as standard Riemannian ones, but qualitatively different. Possible connections with holography and with the black hole information paradox are briefly discussed.

Related papers

• Laser-Dressed States on Riemannian Manifolds: A Generalization of the Kramers-Henneberger Transformation [0.0]
  We analytically study the laser-driven nonlinear dynamics of a quantum particle. The geometry of space results in a potential-like term that supports bound states on the manifold. We deduce a Schr"odinger-like equation in the Kramers-Henneberger frame.
  arXiv  Detail & Related papers  (2024-02-16T10:57:34Z)
• The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State [44.99833362998488]
  We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. An area law is proven in the limiting cases where the volume tends to infinity and/or the regularization length tends to zero.
  arXiv  Detail & Related papers  (2023-10-05T12:08:03Z)
• The minimal length: a cut-off in disguise? [0.0]
  The minimal-length paradigm is a possible implication of quantum gravity at low energies. We show that this modification is equivalent to a cut-off in the space conjugate to the position representation. We find a direct relation between the ensuing bound in wave-number space and the minimal-length scale.
  arXiv  Detail & Related papers  (2023-02-09T11:03:31Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Metriplectic geometry for gravitational subsystems [0.0]
  In general relativity, it is difficult to localise observables such as energy, angular momentum, or centre of mass in a bounded region. A self-gravitating system, confined by its own gravity to a bounded region, radiates some of the charges away into the environment. Dissipation implies that some diffeomorphisms are not Hamiltonian.
  arXiv  Detail & Related papers  (2022-05-31T18:01:59Z)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• Gravitational orbits, double-twist mirage, and many-body scars [77.34726150561087]
  We explore the implications of stable gravitational orbits around an AdS black hole for the boundary conformal field theory. The orbits are long-lived states that eventually decay due to gravitational radiation and tunneling.
  arXiv  Detail & Related papers  (2022-04-20T19:18:05Z)
• Relativistic Extended Uncertainty Principle from Spacetime Curvature [0.0]
  Investigation directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. Applying the 3+1-splitting in accordance with the ADM-formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface.
  arXiv  Detail & Related papers  (2021-11-30T17:21:49Z)
• Generalized uncertainty principle or curved momentum space? [0.0]
  Curved momentum space is at the heart of similar applications such as doubly special relativity. We introduce a duality between theories yielding generalized uncertainty principles and quantum mechanics on nontrivial momentum space. We explicitly derive the vielbein corresponding to a generic generalized uncertainty principle in $d$ dimensions.
  arXiv  Detail & Related papers  (2021-10-21T11:26:36Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.