[jkp56]

I can't open this link for some reason (uBO?), but the title reminds me one very clever Wolfram's article where he brags about (as usual) about how he derived GTR equations from his graph model. That article had a bunch of comments with and one of them stating that in such a graph model there is always a reference frame. Wolfram didn't respond to that comment.

[mikhailfranco]

I think SW became too obsessed with the mathematical and computational approach to CA, while (as usual) 't Hooft pursued his physics intuitions to create a candidate CA theory:

https://arxiv.org/abs/1405.1548

I say as usual, because G'tH had already formulated the holographic principles that would allow space-time (hence GTR) to be encoded non-locally over a graph.

https://arxiv.org/abs/gr-qc/9310026

There need not be a preferred reference frame if the space-time events do not occur at individual nodes in the graph, but emerge at scales much larger than the graph, with some holographic or permutation symmetry that can reproduce the diffeomorphism invariance of GTR. It is also plausible that the position-momentum duality of space-time could emerge from such a theory.

Space-time would be created by the events that occur, not the other way around, hence the aphorism spooky distance at an action, because the events are primary, and distance is the strange phenomenon that emerges from them.

There has been much recent progress in making space emerge from entanglement, which also implies that locality emerges from non-locality:

https://arxiv.org/abs/1005.3035

https://phys.org/news/2015-05-spacetime-built-quantum-entang...

https://www.scientificamerican.com/article/tangled-up-in-spa...

Note that LQG has produced a nice discretization of space, based on graphs that have observable quanta of area and volume, but not length. Directions and lengths are defined as normals to areas, which is reminiscent of Clifford Algebra. Having derived (emergent) lengths also makes diffeomorphism easier.

https://arxiv.org/abs/gr-qc/9411005

[mikhailfranco]

I haven't followed this closely, but did SW provide a paper showing how he derived GTR from the graph?

[sokrates85]

He made the claims but not sure if that paper ever appeared.