Jonathan Gorard - Discrete Spacetime, Emergent Geometry and Computable Quantum Gravity

The speaker thanks Luca and the audience for the invitation and introduces the topic of modeling SpaceTime as a discrete mathematical structure to develop a computable foundation for classical physics.

The speaker spends approximately half of the talk discussing background material and introduces discrete models of SpaceTime.

Towards the end, the speaker highlights new results related to discreetness and deviations in discrete models of SpaceTime, including simulation results and pictures available in a GitHub repository.

The speaker explains the transition of quantum gravity from a physics branch to a computable theory by representing structures as finite, computable data structures.

Details on representing classical gravity using data structures with a focus on classical and quantum mechanical aspects.

Comparison of the speaker's approach to existing theories like Causal Dynamical Triangulation (CDT) and discussion on discretization with continuous mathematical structures.

Explanation of hypergraph structures as generalizations of graphs and their role in defining Dynamics in discrete models.

Introduction to rewriting frameworks for hypergraphs and their importance in defining Dynamics and evolution in the discrete model.

Discussion on causal invariance, global confluence, and transitive reductions in causal graphs to determine causal relationships and structures in SpaceTime.

Interpretations of geometric structures, including hypergraph metrics, distance calculations, and geometrical discrepancies in the discrete model.

Exploration of dimension anomalies, dimensional limitations, and dynamic behaviors in discrete SpaceTime models.

Derivation of field equations, including the Einstein field equations and the discretization of gravitational interactions within the model.

Discussion on localized topological excitations, field decompositions, and their implications in the discrete model.

The discussion starts with the assumption of working with hypergraphs at the beginning of the evolutionary process, highlighting the challenges in solving the update formalisms.

Exploration of multi-way Evolution graphs that parameterize the evolution of a Harle Hawking wave function is discussed, emphasizing the derivation of a Continuum Riemannian metric and the quantum mechanical aspect of the formalism.

The concept of a Continuum limit and its implications, particularly related to black hole accretion profiles and the stability of accretion near discreet SpaceTime, is explained.

The algebraic structure of hypergraphs and their relation to tensor product operations and dual operations are explored, leading to the definition of a Fubini-Study metric.

Discussion on quantum gravity, discretization of SpaceTime, and the construction of geometric actions and structures from hypergraphs is presented.

Questions on the topology of causal graphs, constructing areas and volumes, and the relationship between hypergraphs and Loop Quantum Gravity are addressed.

The derivation of the Einstein field equations from the hypergraph approach, including the constraints and restrictions involved in the process, is elaborated upon.