Towards a Definition of Locality in a Manifoldlike Causal Set

Abstract

It is a common misconception that spacetime discreteness necessarily implies a violation of local Lorentz invariance. In fact, in the causal set approach to quantum gravity, Lorentz invariance follows from the specific implementation of the discreteness hypothesis. However, this comes at the cost of locality. In particular, it is difficult to define a "local" region in a manifoldlike causal set, i.e., one that corresponds to an approximately flat spacetime region. Following up on suggestions from previous work, we bridge this lacuna by proposing a definition of locality based on the abundance of m-element order-intervals as a function of m in a causal set. We obtain analytic expressions for the expectation value of this function for an ensemble of causal set that faithfully embeds into an Alexandrov interval in d-dimensional Minkowski spacetime and use it to define local regions in a manifoldlike causal set. We use this to argue that evidence of local regions is a necessary condition for manifoldlikeness in a causal set. This in addition provides a new continuum dimension estimator. We perform extensive simulations which support our claims.

35 pages, 17 figures

References in corpus (8)

• Discreteness without symmetry breaking: a theorem
• Feynman Propagator for a Free Scalar Field on a Causal Set
• Causal set d'Alembertians for various dimensions
• Particle propagators on discrete spacetime
• On Recovering Continuum Topology from a Causal Set
• Spacelike distance from discrete causal order
• Directions in Causal Set Quantum Gravity
• The Discrete Geometry of a Small Causal Diamond

Cited by in corpus (28)

• The causal set approach to quantum gravity
• A closed form expression for the causal set d'Alembertian
• Infinite order quantum-gravitational correlations
• Path integral suppression of badly behaved causal sets
• Boundary Terms for Causal Sets
• Echoes of Asymptotic Silence in Causal Set Quantum Gravity
• Finite Size Scaling in 2d Causal Set Quantum Gravity
• Quantum Gravity on the computer: Impressions of a workshop
• Dimensionally Restricted Causal Set Quantum Gravity: Examples in Two and Three Dimensions
• Dimensional reduction in manifold-like causal sets
• On the continuum limit of Benincasa-Dowker-Glaser causal set action
• Steps towards Lorentzian quantum gravity with causal sets
• Causal Set Generator and Action Computer
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity
• The Ising model coupled to 2d orders
• Discrete Spacetime: a Web of Chains
• Phase transitions in 2d orders coupled to the Ising model
• Path length distribution in two-dimensional causal sets
• Recovering General Relativity from a Planck scale discrete theory of quantum gravity
• Measuring spatial distances in causal sets via causal overlaps
• Manifold Properties from Causal Sets using Chains
• Timelike boundary and corner terms in the causal set action
• High Performance Algorithms for Quantum Gravity and Cosmology
• Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime
• Out of Nowhere: The emergence of spacetime from causal sets
• Benincasa-Dowker-Glaser causal set actions by quantum counting
• Null Geodesics from Ladder Molecules
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers