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Emergence of Minkowski-spacetime by simple deterministic graph rewriting

This new arXiv paper of mine could be highly useful to the Wolfram physics project:

https://arxiv.org/pdf/2110.03388.pdf

Title: Emergence of Minkowski-Spacetime by Simple Deterministic Graph Rewriting

Main Figures:

Figure 3

Figure 4

3 Replies
Posted 2 years ago

Your depiction in Figure 3 looks just like the diagrams from pg. 489 of NKS! I can't say I understand exactly how you got there but well done sir.

POSTED BY: Dante Michael

Thanks, Fig 3 is literally just a blue grid on top of a red grid, which could still be generated by Zuse's cellular automata from the 60s (https://philpapers.org/archive/ZUSRR.pdf) whom I should also have mentioned. More valuable are the Poincare disks, which show a perspective on the graphs that cannot be simulated on a simple cellular automaton anymore, in accordance with Zuse's suspicion that cellular automata would become insufficient ultimately. The modern Wolfram hypergraph models could be highly useful to reproduce these types of isotropic-relativistic graphs and so forth.

It solves the problem of how rotational invariance emerges (along with the rest of the Poincare group). Therefore, the next logical step for the Wolfram physics project is to find the Wolfram model rules that can maintain such a flat Minkowski spacetime, as described in this paper. Afterwards, to test what happens if you run such rules starting at the beginning of time. On the more mathematical side, the insights of this paper can be utilized in order to complete Gorard's derivation of the complete version of general relativity from Wolfram models.

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