Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
Abstract
We explore in stochastic gravity theory whether non-Gaussian noises from the higher order correlation functions of the stress tensor for quantum matter fields when back-reacting on the spacetime may reveal hints of multi-scale structures. Anomalous diffusion may depict how a test particle experiences in a fractal spacetime. The hierarchy of correlations in quantum matter field induces the hierarchy of correlations in geometric objects via the set of Einstein-Langevin equations for each correlation order. This correlation hierarchy kinetic theory conceptual framework, aided by the characteristics of stochastic processes, may serve as a conduit for connecting the low energy `Bottom-Up' approach with the `Top-Down' theories of quantum gravity which predict the appearance of fractal spacetimes at the Planck scale.
Cite
@article{arxiv.1702.08145,
title = {Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy},
author = {B. L. Hu},
journal= {arXiv preprint arXiv:1702.08145},
year = {2017}
}
Comments
16 pages. Invited talk at DICE2016 conference: "Spacetime - Matter - Quantum Mechanics", September 2016