# (4) Spacetime / Relativity

(9)March 6, 2020

*Answered by: Jonathan Gorard*

## How can your models be Lorentz invariant?

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

March 7, 2020

*Answered by: Jonathan Gorard*

## How do black holes work within the context of your models?

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

March 9, 2020

*Answered by: Jonathan Gorard*

## Do your models permit the possibility of time travel (i.e. the existence of closed timelike curves)?

The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, Read more

March 10, 2020

*Answered by: Jonathan Gorard*

## Why do you get a Euclidean/Riemannian metric, as opposed to a taxicab metric, induced on your hypergraphs?

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

March 11, 2020

*Answered by: Jonathan Gorard*

## What do your models imply regarding dark energy and the cosmological constant?

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

March 11, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with the ER=EPR conjecture?

Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. Read more

March 12, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with inflationary cosmology?

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

March 13, 2020

*Answered by: Jonathan Gorard*

## What do your models imply regarding the black hole information paradox?

The maximum rate of quantum entanglement (i.e. the natural propagation velocity of geodesics in the multiway evolution graph) is, in general, much higher than the speed of light (i.e. the natural propagation velocity of geodesics in the purely relativistic causal graph); however this ceases to be the case in the presence of a sufficiently high mass density in spacetime (i.e. Read more

March 13, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with the holographic principle/AdS-CFT correspondence?

They certainly seem to be! Indeed, as discussed in the answer about implication for the black hole information paradox, the structure of the multiway causal graph seems to imply a form of the holographic principle in a very natural way.

Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, Read more

Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, Read more