Even that would prove nothing. Wolfram himself makes a pretty big deal about how cellular automata, being Turing-complete, can model anything. I can give you any number of cellular automata that model our current understanding of quantum physics right now, no problem. It only becomes interesting if it can make different, better predictions than our existing theories.
> I can give you any number of cellular automata that model our current understanding of quantum physics right now, no problem
Ok, I'm interested in seeing something like that. If you have a link, I'll take a look--thanks. (If you're thinking of 't Hooft's, then I know about it, but its predictions are in serious conflict with mainstream physics, from what I understand).
It's not really that interesting. Can you write it in a computer program? Then you can write it in a cellular automata, because many of them are Turing complete:
And yes, this is a cheap trick. That's the point. "Porting" our current theories to some new, whacky substrate, peeking at the textbooks all the while, is Not Interesting and will not lead to new results.
No I don't see how to implement QM as a computer program while preserving basic complexity invariants of Turing machines. That is the point of quantum computing: that the complexity classes for quantum computers are different than those for Turing machines. If you take the view that that the whole Universe is one gigantic entangled quantum state, the cellular automaton simulation would get pretty bogged down.
Quantum Computers are no more powerful than Turing Machines, complexity has little to do with this. Quantum Mechanics, being a linear theory (if we exclude measurement) is actually relatively easy to describe computationally. The computations are incredibly slow, but otherwise they are perfectly in line with any other formulation of the theory.
> Quantum Computers are no more powerful than Turing Machines
They are more powerful in the sense that P-time for quantum computers (aka BQP) is hypothesized to be larger than P-time for Turing machines. That is different from every classical model of computation (RAM machines, etc.) that we usually talk about. It's hard to call something a cellular automaton if it has to expand exponentially in size as it evolves. Thus, 't Hooft concretely predicts that if his CA model is right, then quantum computers can't work. Idk whether Wolfram addresses this issue.
As using CA like a substrate is clearly "theory free" in the sense it doesn't impose any restrictions on how calculations should be done, do you concede that CA doesn't actually provide any theory as the OP lamented?
Wolfram's new physics is based on "hypergraphs", not quite cellular automata, but the point stand that they are an entirely general framework, and therefore useless for the stated purpose.
With the correct initial state, any Turing complete cellular automata (like CGoL) can model any computable system. We can computationally model prevailing quantum models (albeit incredibly slowly), so an unbounded CGoL field would fit the criteria.
