Using a set of rules for hypergraph evolution they construct a directed graph. Then they decide to embed it into a lattice that they equip with the Minkowski metric. This embedding is completely ad hoc. It establishes as much connection between their formalism and relativity, as writing the two formalisms next to each other on the same page would.
Some discussion by Gorard here, which makes it sound like the Minkowski embedding was meant as an illustration, and not meant to do any heavy lifting. Given that, it’s not surprising that it might seem a bit ad hoc.
The problem is, there is no heavy lifting. “We made a causal network, therefore, special relativity”. Sorry, but no, you need to actually explain why the vacuum seems Lorentz invariant on the macroscopic level, something that’s highly non-obvious given that you start from something discrete. A discrete object cannot be Lorentz invariant, the best you can hope for is something like a probability measure over discrete objects that is Lorentz invariant, but there is nothing like that in the paper. Moreover, if the embedding is just an illustration, then where do they even get the Riemannian metric that is supposed to satisfy the Einstein equation?
Some discussion by Gorard here, which makes it sound like the Minkowski embedding was meant as an illustration, and not meant to do any heavy lifting. Given that, it’s not surprising that it might seem a bit ad hoc.
The problem is, there is no heavy lifting. “We made a causal network, therefore, special relativity”. Sorry, but no, you need to actually explain why the vacuum seems Lorentz invariant on the macroscopic level, something that’s highly non-obvious given that you start from something discrete. A discrete object cannot be Lorentz invariant, the best you can hope for is something like a probability measure over discrete objects that is Lorentz invariant, but there is nothing like that in the paper. Moreover, if the embedding is just an illustration, then where do they even get the Riemannian metric that is supposed to satisfy the Einstein equation?