March 17, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to causal set theory and causal dynamical triangulation?

Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, antisymmetry, transitivity (by virtue of the analog with the causal structure of a Lorentzian manifold), and local finiteness (by virtue of the discrete nature of the events), just as in a standard causal set. The formal structure of the Wolfram model may, in fact, be thought of as being an abstract generalization of a causal dynamical triangulation, in which spacetime is triangulated topologically into a simplicial complex of “pentachora” (4-simplices), which evolve in accordance with some deterministic dynamical law; the only difference in our case is that the choice of simplex is less constrained, because our formulation in terms of hypergraphs is more topologically generic.