Institute Output
Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems
Jonathan Gorard
This study extends the Raychaudhuri equation to discrete spacetimes, exploring conditions under which they might exhibit geodesic incompleteness, and applies numerical simulations to predict black hole formations.
Some Relativistic and Gravitational Properties of the Wolfram Model
Jonathan Gorard
The article shows that causal invariance in the Wolfram Model leads to discrete general and Lorentz covariance, introducing curvature concepts for hypergraphs related to the Ricci tensor and Einstein field equations
Hypergraph Discretization of the Cauchy Problem in General Relativity via Wolfram Model Evolution
Jonathan Gorard
This article introduces a numerical general relativity code using the Z4 formulation with hypergraph-based Cauchy data and adaptive mesh refinement, validating results against standard spacetimes and comparing with Wolfram model evolution.
Some Quantum Mechanical Properties of theWolfram Model
Jonathan Gorard
By exploring hypergraph rules that deliberately break causal invariance, we show that the Wolfram Model’s multiway evolution functions like a quantum superposition whose geometry converges to projective Hilbert space. By proving that observers can “collapse” these histories via Knuth–Bendix completion—and deriving multiway analogues of Einstein’s equations, the path integral and the Schrödinger equation—we unify discrete spacetime, quantum mechanics and relativity within one framework.