Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, Read more

Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is “causally disconnected” Read more

If one measures distances by considering lengths of single geodesics between pairs of points in a hypergraph, using (for instance) some variant of Dijkstra’s algorithm, then evidently the induced metric will be discrete, and akin to a generalized taxicab metric. However, our derivation of the Einstein field equations involves first defining the Ollivier-Ricci curvature, Read more

Our derivation of general relativity in the continuum limit of Wolfram model systems that satisfy causal invariance and asymptotic dimensionality preservation defines the Einstein field equations only up to an integration constant, thus implying that the model is compatible with both zero and non-zero values of the cosmological constant. Since the energy-momentum tensor for a Wolfram model evolution corresponds to a measure of the flux of causal edges through certain discrete hypersurfaces in the causal graph, Read more

Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. Read more