Information content and minimum-length metric: A drop of light

Abstract

In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is put on that well-known thermodynamic results related to null hypersurfaces (i.e. to lightsheets and to generalized covariant entropy bound) can be interpreted as implying an irreducible intrinsic nonlocality of gravity. This nonlocality even if possibly concealed at ordinary scales(depending on which matter is source of the gravitational field, and which matter we use to probe the latter) unavoidably shows up at the smallest scales, read the Planck length $l_p$, whichever are the circumstances we are considering. Some consequences are then explored of this nonlocality when embodied in the fabric itself of spacetime by endowing the latter with a minimum length $L$, in particular the well-known and intriguing fact that this brings to get the field equations, and all of gravity with it, as a statistical-mechanical result. This is done here probing the neighborhood of a would-be (in ordinary spacetime) generic event through lightsheets (instead of spacelike or timelike geodesic congruences as in other accounts) from it. The tools for these derivations are nonlocal quantities, and among them the minimum-length Ricci scalar stands out both for providing micro degrees of freedom for gravity in the statistical account and for the fact that intriguingly the ordinary, or `classical', Ricci scalar can not be recovered from it in the $L\to 0$ limit. Emphasis is put on that classical gravity is generically obtained this way for $\hslash \ne 0$, but not in the $\hslash \to 0$ limit (the statistically derived field equations become singular in this limit), adding to previous results in this sense. (truncated Abstract; see the paper for full Abstract)

arXiv comment40 pages, 1 figure, contribution to the special issue of GERG dedicated to the memory of Prof. Thanu Padmanabhan

References in corpus (78)

• The World as a Hologram
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Thermodynamics of Spacetime: The Einstein Equation of State
• Black Hole Entropy is Noether Charge
• Quantum gravity and minimum length
• Thermodynamical Aspects of Gravity: New insights
• A Spin Entanglement Witness for Quantum Gravity
• A Covariant Entropy Conjecture
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• The motion of point particles in curved spacetime
• Minimal Length Scale Scenarios for Quantum Gravity
• On Black Hole Entropy
• Holography and hydrodynamics: diffusion on stretched horizons
• Viscosity, Black Holes, and Quantum Field Theory
• Spectral Dimension of the Universe
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• Reconstructing the Universe
• Equipartition of energy in the horizon degrees of freedom and the emergence of gravity
• Relative entropy and the Bekenstein bound
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Proof of Classical Versions of the Bousso Entropy Bound and of the Generalized Second Law
• On the possibility of laboratory evidence for quantum superposition of geometries
• Locality & Entanglement in Table-Top Testing of the Quantum Nature of Linearized Gravity
• White Holes as Remnants: A Surprising Scenario for the End of a Black Hole
• Entropy of Null Surfaces and Dynamics of Spacetime
• General Relativity from a Thermodynamic Perspective
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• The Shear Viscosity to Entropy Ratio: A Status Report
• Dimension and Dimensional Reduction in Quantum Gravity
• Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling
• Proof of a Quantum Bousso Bound
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• Thermodynamical interpretation of the geometrical variables associated with null surfaces
• Simple sufficient conditions for the generalized covariant entropy bound
• Minimal Length and Small Scale Structure of Spacetime
• Small black/white hole stability and dark matter
• The Atoms Of Space, Gravity and the Cosmological Constant
• van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
• A Quantum Bousso Bound
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• Action principle for the Fluid-Gravity correspondence and emergent gravity
• Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity
• Spacetime with zero point length is two-dimensional at the Planck scale
• Signature change events: A challenge for quantum gravity?
• From Unruh temperature to generalized Bousso bound
• Distribution function of the Atoms of Spacetime and the Nature of Gravity
• Small scale structure of spacetime: van Vleck determinant and equi-geodesic surfaces
• The bound on viscosity and the generalized second law of thermodynamics
• Augmented Variational Principles and Relative Conservation Laws in Classical Field Theory
• Entropy density of spacetime from the zero point length
• Gravity and Quantum Theory: Domains of Conflict and Contact
• Bekenstein-Hod Universal Bound on Information Emission Rate Is Obeyed by LIGO-Virgo Binary Black Hole Remnants
• The atoms of spacetime and the cosmological constant
• Raychaudhuri equation with zero point length
• Intrinsic and Extrinsic curvatures in Finsler-esque spaces
• Comments on a Covariant Entropy Conjecture
• Null boundary terms for Lanczos-Lovelock gravity
• Virtual Black Holes, Remnants and the Information Paradox
• Quantum metric for null separated events and spacetime atoms
• Covariant singularities in Quantum Field Theory and Quantum Gravity
• A note on the connection between the universal relaxation bound and the covariant entropy bound
• Gravity from the entropy of light
• Action and Observer dependence in Euclidean quantum gravity
• On the statistical-mechanical meaning of the Bousso bound
• Probing the Planck scale: The modification of the time evolution operator due to the quantum structure of spacetime
• Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant
• Euclidean Action and the Einstein tensor
• Entropy Bounds, Holographic Principle and Uncertainty Relation
• Minimum-length Ricci scalar for null separated events
• A proof of the Bekenstein bound for any strength of gravity through holography
• Effective null Raychaudhuri equation
• Gravitation, Thermodynamics, and the Bound on Viscosity
• From Thermodynamics to the Bound on Viscosity
• Spacetime atoms and extrinsic curvature of equi-geodesic surfaces
• Zero-point gravitational field equations
• Quantum states for a minimum-length spacetime
• The Kinetic Theory of the Mesoscopic Spacetime