Probing the quantum nature of spacetime by diffusion

Abstract

Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semi-definite probability densities, applicable to Asymptotically Safe gravity, Horava-Lifshitz gravity and Loop Quantum Gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime.

14 pages, 5 figures; v2: minor typos corrected

References in corpus (13)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Nonperturbative Quantum Gravity
• Asymptotic safety in higher-derivative gravity
• Fractional diffusion equations and processes with randomly varying time
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Brownian subordinators and fractional Cauchy problems
• The R^2 phase-diagram of QEG and its spectral dimension
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• Thermodynamics of photons on fractals
• Brownian-Time Processes: The PDE Connection and the Half-Derivative Generator
• Diffusion in multiscale spacetimes
• Iterated Brownian motion in an open set

Cited by in corpus (74)

• The nonperturbative functional renormalization group and its applications
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Dimension and Dimensional Reduction in Quantum Gravity
• Black holes within Asymptotic Safety
• Observable traces of non-metricity: new constraints on metric-affine gravity
• Upper bound on the Abelian gauge coupling from asymptotic safety
• Dynamical renormalization of black-hole spacetimes
• Asymptotic safety in an interacting system of gravity and scalar matter
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Multifractional theories: an unconventional review
• Multi-scale gravity and cosmology
• Diffusion on $\kappa$-Minkowski space
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Dimensional flow in discrete quantum geometries
• On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric
• Complex Quantum Networks: a Topical Review
• Multiscale spacetimes from first principles
• The topological Dirac equation of networks and simplicial complexes
• Spectral dimension in causal set quantum gravity
• Spectral dimension of quantum geometries
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Planck-scale dimensional reduction without a preferred frame
• Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
• Complex Quantum Network Manifolds in Dimension $d>2$ are Scale-Free
• Black-hole entropy and minimal diffusion
• Quantum Gravity signatures in the Unruh effect
• Laplacians on discrete and quantum geometries
• ABC of multi-fractal spacetimes and fractional sea turtles
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Towards the map of quantum gravity
• Spectral dimension and diffusion in multi-scale spacetimes
• Imprint of quantum gravity in the dimension and fabric of spacetime
• Multifractional spacetimes, asymptotic safety and Hořava-Lifshitz gravity
• Noncommutative fields and the short-scale structure of spacetime
• Spectral dimensions from the spectral action
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Thermal dimension of quantum spacetime
• Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime
• Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations
• Quantum spectral dimension in quantum field theory
• Observational constraints on dual intermediate inflation
• On the UV dimensions of Loop Quantum Gravity
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Geometric operators in the asymptotic safety scenario for quantum gravity
• Echoes of Asymptotic Silence in Causal Set Quantum Gravity
• The mass of simple and higher-order networks
• Standard Model in multiscale theories and observational constraints
• Canonical tensor model through data analysis -- Dimensions, topologies, and geometries --
• Quantum Gravity on the computer: Impressions of a workshop
• Spectral dimension with deformed spacetime signature
• Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations
• Particle-physics constraints on multifractal spacetimes
• An asymptotically safe guide to quantum gravity and matter
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Quantum Phase Transitions in the BKL Universe
• L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity
• Relativistic particle in multiscale spacetimes
• Dimensional flow in the kappa-deformed space-time
• Reappraisal of a model for deformed special relativity
• Black Hole Remnants from Dynamical Dimensional Reduction?
• UV dimensional reduction to two from group valued momenta
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Localization and diffusion in polymer quantum field theory
• From Causal Dynamical Triangulations To Astronomical Observations
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• Local topological moves determine global diffusion properties of hyperbolic higher-order networks
• Spectral Dimension of kappa-deformed space-time
• Spectral dimension in graph models of causal quantum gravity
• Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers
• Making the case for causal dynamical triangulations
• Three-dimensional gravity and deformations of relativistic symmetries