The causal set approach to quantum gravity

Abstract

The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity. In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

Latex, 78 pages, 22 Figures. Invited review article for Living Reviews in Relativity. Version 2 includes an Appendix with definitions and abbreviations. Typos corrected and some discussions made clearer

References in corpus (34)

• Gravitational action with null boundaries
• Dimension and Dimensional Reduction in Quantum Gravity
• Discreteness without symmetry breaking: a theorem
• Quantum Dynamics without the Wave Function
• Feynman Propagator for a Free Scalar Field on a Causal Set
• Particle propagators on discrete spacetime
• Generalized Causal Set d'Alembertians
• On Recovering Continuum Topology from a Causal Set
• An exercise in "anhomomorphic logic"
• On a Recent Construction of "Vacuum-like" Quantum Field States in Curved Spacetime
• Spacelike distance from discrete causal order
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Boundary and Corner Terms in the Action for General Relativity
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• Evidence for an entropy bound from fundamentally discrete gravity
• The Discrete Geometry of a Small Causal Diamond
• Evolution of Universes in Causal Set Cosmology
• Suppression of non-manifold-like sets in the causal set path integral
• A Strong Constraint on Ever-Present Lambda
• On the Causal Set-Continuum Correspondence
• On extending the Quantum Measure
• Hilbert Spaces from Path Integrals
• A 2D model of Causal Set Quantum Gravity: The emergence of the continuum
• Surface Tension and the Cosmological Constant
• Gravity and Matter in Causal Set Theory
• Discreteness and the transmission of light from distant sources
• The Random Discrete Action for 2-Dimensional Spacetime
• Low energy bounds on Poincare violation in causal set theory
• Everpresent Lambda - II: Structural Stability
• A new topology on the space of Lorentzian metrics on a fixed manifold
• The CMB in a Causal Set Universe
• The Sorkin-Johnston State in a Patch of the Trousers Spacetime
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity
• Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond

Cited by in corpus (116)

• Locality & Entanglement in Table-Top Testing of the Quantum Nature of Linearized Gravity
• Relaxing cosmological tensions with a sign switching cosmological constant
• 30 years in: Quo vadis generalized uncertainty principle?
• Constraining power of asymptotic safety for scalar fields
• Dynamical features and shadows of quantum Schwarzschild black hole in effective field theories of gravity
• Black hole image encoding quantum gravity information
• White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era
• Black Holes and Covariance in Effective Quantum Gravity
• Light charged fermions in quantum gravity
• Absorption, Scattering, Geodesics, Shadows and Lensing Phenomena of Black Holes in Effective Quantum Gravity
• Complex Quantum Networks: a Topical Review
• Ollivier-Ricci curvature convergence in random geometric graphs
• Predictive power of grand unification from quantum gravity
• Inevitable manifestation of wiggles in the expansion of the late Universe
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Non-unitarity of Minkowskian non-local quantum field theories
• Path integral suppression of badly behaved causal sets
• On Quantum Gravity If Non-Locality Is Fundamental
• Ultraviolet-complete quantum field theories with fractional operators
• The Complete Barrett-Crane Model and its Causal Structure
• Mean-field phase transitions in TGFT quantum gravity
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Scattering amplitudes in affine gravity
• Tensor network formulation of two dimensional gravity
• Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
• A Lorentzian analog for Hausdorff dimension and measure
• Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons
• Causality and gravity
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Unattainability of the Trans-Planckian regime in Nonlocal Quantum Gravity
• Dimensionally Restricted Causal Set Quantum Gravity: Examples in Two and Three Dimensions
• Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Time functions on Lorentzian length spaces
• Entanglement Entropy of Causal Set de Sitter Horizons
• Entropy and the Link Action in the Causal Set Path-Sum
• Scale-invariance at the core of quantum black holes
• On the continuum limit of Benincasa-Dowker-Glaser causal set action
• Visions in Quantum Gravity
• Horizon Molecules in Causal Set Theory
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Can the latent signatures of quantum superposition be detected through correlation harvesting?
• Configuration space for quantum gravity in a locally regularized path integral
• Spin foam amplitude of the black-to-white hole transition
• Convergence of Combinatorial Gravity
• Time-space duality in 2D quantum gravity
• Analogue gravity simulation of superpositions of spacetimes
• The birth of geometry in exponential random graphs
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• A manifestly covariant framework for causal set dynamics
• The effective Equation of State in Palatini $f(R)$ cosmology
• Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets
• Scalar Cosmological Perturbations from Quantum Gravitational Entanglement
• Admissible Causal Structures and Correlations
• Causal completions as Lorentzian pre-length spaces
• Physics in non-fixed spatial dimensions via random networks
• Lectures in Quantum Gravity
• Curvature effects in the spectral dimension of spin foams
• Phases of a matrix model with non-pairwise index contractions
• The structure of covtree: searching for manifestly covariant causal set dynamics
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Causal structure in spin-foams
• Modified Measures as an Effective Theory for Causal Fermion Systems
• A Monte Carlo algorithm for spin foam intertwiners
• Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity
• Lorentzian Spectral Geometry with Causal Sets
• Path Sums for Propagators in Causal Sets
• Light ray fluctuations in simplicial quantum gravity
• A Stochastic Origin of Spacetime Non-Commutativity
• Spacetime Entanglement Entropy: Covariance and Discreteness
• On the horizon entropy of a causal set
• Everything You Always Wanted to Know About How Causal Set Theory Can Help with Open Questions in Cosmology, but Were Afraid to Ask
• Conformal Cores of Quantum Black Holes in Quadratic Gravity
• Expectation values of minimum-length Ricci scalar
• Measuring spatial distances in causal sets via causal overlaps
• Poincaré crystal on the one-dimensional lattice
• Manifold Properties from Causal Sets using Chains
• Strict renormalizability as a paradigm for fundamental physics
• Causal structure and topology change in (2+1)-dimensional simplicial gravity
• Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
• Timelike boundary and corner terms in the causal set action
• An alternative formalism for modeling spin
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• A Tale of Two Actions: A Variational Principle for Two-Dimensional Causal Sets
• Multidimensional arrow of time
• Universal Entanglement and an Information-Complete Quantum Theory
• Emergence of Lie group symmetric classical spacetimes in canonical tensor model
• World quantum gravity: Quantum test objects and Synge's world function
• Effects of underlying topology on quantum state discrimination
• Majorization requires infinitely many second laws
• Causality, Uncertainty Principle, and Quantum Spacetime Manifold in Planck Scale
• The Repulsive Effect of Covariant Effective Quantum Gravity
• Destructuring Physics: A functional derivation of spacetime
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Local d'Alembertian for causal sets
• Renormalization on the DFR Quantum Spacetime
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes
• On the Cardinality of Future Worldlines in Discrete Spacetime Structures
• Simpler embeddings of causal sets into Minkowski spacetime
• Non-Equilibrium Dynamics of Hard Spheres in the Fluid, Crystalline, and Glassy Regimes
• Benincasa-Dowker-Glaser causal set actions by quantum counting
• Quantum interferometry in external gravitational fields
• Results on Lorentzian metric spaces
• On the physical running of the electric charge in a dimensionless theory of gravity
• The Dynamics of Quantum Gravity: the Missing Piece in the Spacetime Emergentist Account
• A quantum theory of gravity
• Generalized relative locality and causal sets
• Fundamental physics asks philosophers new questions
• Null Geodesics from Ladder Molecules
• Operational verification of the existence of a spacetime manifold