# (3) Relations to Other Approaches

(10)May 2, 2019

## Is the project related to sacred geometry?

Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. 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 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

March 14, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to homotopy theory, derived geometry and higher category theory?

The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. Read more

March 15, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to twistor theory?

Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory.
The twistor correspondence, at least in Penrose’s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. Read more

March 16, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to spin networks, spin foams and loop quantum gravity?

One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, Read more

March 16, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to tensor networks?

Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, Read more

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, Read more

March 18, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to string theory?

The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as “snake states”â€”sets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, Read more