If TOE is a CA then how we can find its definition/rules?
Theoretically the problem of TOE could be expressed as:
Find any/simplest CA that can recreate Quantum Mechanics(, Newtonian Mechanics), Relativity (each in their own different (macro) scales)
as its emergent properties.
I think using our knowledge of CA and the general laws of physics (like conservation of energy etc.)
we could find some of the general properties of the target CA(s).
Then maybe we could setup a massive super computer search to find any one target CA.
The computer could create new CA candidates one by one/N by N, using random selection
and would test them as a potential solution by numerically simulating them
and checking for 2(3) different macro scale behaviors, if matching to Quantum Mechanics(, Newtonian Mechanics), Relativity.
The search maybe done faster by using any general intelligent search algorithms, like Genetic Algorithms as an example.
Also it maybe possible to train a deep learning AI network to gain expertise about CAs and use that to try to find a solution,
find candidates and/or try to develop an algorithm for faster search.
Experimentally what we could do is to build more and more powerful particle accelerators.
Because what we see already happening is, as the scale increases from size of particles to size of humans
and to size of stars, the laws of physics change slowly,
from Quantum Mechanics to Newtonian Mechanics, and from that to Relativity (Einstein Mechanics?).
So as we build more and more powerful particle accelerators,
and check the laws of Quantum Mechanics at smaller and smaller scales
then we may expect to see the rules of Quantum Mechanics followed less and less precisely,
giving us the first glimpses of the TOE CA operating at Planck Scale.
And of course we may find new surprises (gifts for physics) when keep going smaller scales.
(Should we worry about creating micro Black Holes?
I read that it is practically impossible to reach the necessary energy using any kind of accelerator.
(Could we send particle detectors to space to observe the cosmic ray behaviors for highest energies?
Could we expect to see any micro Black Holes then?)
But if we could someday then should we really try?
I think that depends on how much faith we have on Hawking Radiation. :-)
Especially if it is observed in space someday it should not be a problem.
Creating micro Black Holes could also allow us to observe and experiment with them and answer some big questions.)
If we find any CA as the solution of TOE problem then why we should accept it as the TOE?
I think first question to answer would be how unique it is as a CA.
Can it be simplified any further?
Can we create equivalent CAs from it in same level of complexity or higher?
Can we find any other solutions by keep searching?
Are there any other theories of physics that has the same powers of explanation/validity?
I think it is highly possible that the solution will be unique but only as the simplest CA (that can do it).
What we could do with it?
I think if TOE is a Planck Scale CA then it would not be useful to create perfect virtual reality (like the Matrix)
because amount of computation required to simulate any volume close to human scale, using Planck Scale cells,
would be way beyond any computer we could create.
But it should be possible to use it to answer some of the biggest questions in physics,
like what really happens in the center of a Black Hole or its event horizon,
and/or what are the true values of all constants in physics,
and/or what is the full structure, shape/geometry of the Universe,
what is the true nature of spacetime, Dark Energy/Matter, inflation,
what are the all possible forms of matter and energy,
what fully (?) happened in Big Bang,
what is the expected future of the Universe,
is it really possible to create wormholes, warp drives, teleporters, time machines, (true) artificial gravity, super energy sources.
What would be next for physics if we found TOE?
Keep creating better computer simulations for all kinds of physical systems/processes/experiments.
Try to design and simulate our own artificial Universes?
Try to answer if Multiverse really physically possible?