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.