Spectral dimension in causal set quantum gravity
arXiv:1311.2530 · doi:10.1088/0264-9381/31/12/125007
Abstract
We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can be connected to the non-locality of causal set theory that is deeply rooted in its fundamentally Lorentzian nature. Based on its large-scale behaviour, we conjecture that the spectral dimension can serve as a tool to distinguish causal sets that approximate manifolds from those that do not. As a new tool to probe quantum spacetime in different quantum gravity approaches, we introduce a novel dimensional estimator, the causal spectral dimension, based on the meeting probability of two random walkers, which respect the causal structure of the quantum spacetime. We discuss a causal-set example, where the spectral dimension and the causal spectral dimension differ, due to the existence of a preferred foliation.
16 pages, 11 figures
References in corpus (5)
Cited by in corpus (27)
- The causal set approach to quantum gravity
- Dimension and Dimensional Reduction in Quantum Gravity
- Multifractional theories: an unconventional review
- Dimensional reduction in causal set gravity
- Quantum Gravity signatures in the Unruh effect
- ABC of multi-fractal spacetimes and fractional sea turtles
- Induced Spatial Geometry from Causal Structure
- Spectral Dimension from Nonlocal Dynamics on Causal Sets
- What is the dimension of citation space?
- Emergence of Spacetime in a restricted Spin-foam model
- Imprint of quantum gravity in the dimension and fabric of spacetime
- Spectral dimensions from the spectral action
- Thermal dimension of quantum spacetime
- Spontaneous Dimensional Reduction in Quantum Gravity
- Quantum spectral dimension in quantum field theory
- Echoes of Asymptotic Silence in Causal Set Quantum Gravity
- Standard Model in multiscale theories and observational constraints
- Quantum Gravity on the computer: Impressions of a workshop
- Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
- Towards Spectral Geometry for Causal Sets
- Spectral dimension on spatial hypersurfaces in causal set quantum gravity
- Ultraviolet dimensional reduction of spacetime with zero-point length
- Discrete Spacetime: a Web of Chains
- Curvature effects in the spectral dimension of spin foams
- Ultralocal nature of geometrogenesis
- Path length distribution in two-dimensional causal sets
- Spacetime causal structure and dimension from horismotic relation