Measuring spatial distances in causal sets via causal overlaps

Abstract

Causal set theory is perhaps the most minimalistic approach to quantum gravity, in the sense that it makes next to zero assumptions about the structure of spacetime below the Planck scale. Yet even with this minimalism, the continuum limit is still a major challenge in causal sets. One aspect of this challenge is the measurement of distances in causal sets. While the definition and estimation of time-like distances is relatively straightforward, dealing with space-like distances is much more problematic. Here we introduce an approach to measure distances between space-like separated events based on their causal overlap. We show that the distance estimation errors in this approach vanish in the continuum limit even for smallest distances of the order of the Planck length. These results are expected to inform the causal set geometrogenesis in general, and in particular the development of evolving causal set models in which space emerges from causal dynamics.

References in corpus (20)

• A Classical Sequential Growth Dynamics for Causal Sets
• Forks in the Road, on the Way to Quantum Gravity
• The causal set approach to quantum gravity
• Crystalline Order on a Sphere and the Generalized Thomson Problem
• The Scalar Curvature of a Causal Set
• Towards a Definition of Locality in a Manifoldlike Causal Set
• On Recovering Continuum Topology from a Causal Set
• Spacelike distance from discrete causal order
• Evidence for a Phase Transition in 2D Causal Set Quantum Gravity
• Manifold dimension of a causal set: Tests in conformally flat spacetimes
• Indications of de Sitter Spacetime from Classical Sequential Growth Dynamics of Causal Sets
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• A general solution for classical sequential growth dynamics of Causal Sets
• Induced Spatial Geometry from Causal Structure
• On the Causal Set-Continuum Correspondence
• Observables in Extended Percolation Models of Causal Set Cosmology
• A 2D model of Causal Set Quantum Gravity: The emergence of the continuum
• The continuum limit of a 4-dimensional causal set scalar d'Alembertian
• On the continuum limit of Benincasa-Dowker-Glaser causal set action
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity

Cited by in corpus (3)

• Local d'Alembertian for causal sets
• Reconstructing Minkowski geometry from causal separations
• Simpler embeddings of causal sets into Minkowski spacetime