Please excuse me if this post is entirely too naive. I have a background in physics and computation, but don't feel nearly qualified enough to critique anything being said here. I just want to raise a very basic question, hope someone has some insight...
I'm totally fascinated by the potential for computational properties like causal invariance to map onto problems that have confounded foundations of physics since the discovery of QM. That potential alone is super exciting - and all the other very abstract analogues between physics and elements of these hyper-graphs are very interesting.
Setting these abstract considerations aside - I'm very interested in how a universe ultimately ends up having "stuff" in it. Stephen has described particles as persistent structures, and energy as a flux of edges through a time-like hypersurfaces, so far so good.
Given the huge discrepancy in the actual universe between the energy of space and the energy of any particle with actual mass - is it important that a rule exhibit "extreme globularity" for it to be an actually viable candidate? I don't know how else high-energy particles would be differentiated from the space between them if this wasn't the eventual structure.
If this reasoning is sound then the obvious next question would be: do all the ideas around the potential of hyper-graphs to explain theoretical physics still hold when we are talking about "mega-structures" in graphs, rather than individual nodes?
The notebook below shows a rule I happened upon that generates dense isomorphic neighborhoods connected by a relatively sparse set of edges ("space" presumably)... I've rasterized the images to help with file size.
Is there some other way to imagine how particles / space would present and differentiate themselves in a Wolfram graph?
Node/edge density should equate to flux in the causal graph outside of dense multi-edges or a lot of causal redundancy in the graph (99% sure on that). Certainly the opposite intuition holds: node/edge sparsity in the hyper-graph necessarily equates to low flux in the casual graph.
I guess what I'm hung up on is... If we assume a Wolfram model for the universe, then we really don't know what the early universe may have looked like and this is all pure exploration. All we are postulating is that whatever it was, it was emergent from simple rules "foo".
Given we are exploring in truly uncharted waters, proving out that ideas from QM and GR, etc., can in theory be accommodated by features of Wolfram Models is key. But it's not clear that, for instance, dimensionality would immediately be 3 or even trending towards 3. The most fundamental thing to me would be having a hyper-graph updating rule that produced relatively stable structures that had direct analogues to the standard model. These structures would be clearly identifiable vs space, they would repeatedly pop up all over the graph, and they would interact in ways that align with standard model expectations.
Would those things necessarily be these sort of clumpy masses shown in this post, or would they show up in some other way?
I may be way out of my league here, but remember the postulated scale of a link in the hypergraph is around 10^-93m. In the early universe (not just the observable universe) it was dominated by particles (an electron about 10^-81m as per S. Wolfram), then there would not be much space between particles. With this said, until you can run the rule through enough steps to get a large universe (>>1m) you may not be able to differentiate between empty space and particles.
I don't know how large the largest hypergraph computed is, but I would be surprised if we have even got close to a plank length (10^-35) yet, not to mention a multi-way branchial graph that size.
And to add to the confusion, Quarks are believed to have started a 20μs after the Big Bang. That means >> 10^400 steps before the first quark was produced. That is a huge number of steps.
I do not have much hope is seeing anything that could be interpreted as a particle any time soon, we just do not have the computational capability to do so from the big bang.