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Possibly in the search for a grand unified theory, it seems trendy at the moment for some writers and commentators to claim that space-time is grid-like and discrete rather than continuous.

I wonder what research is being done to see if the Standard Model etc. could be replaced or superseded by a model based on cellular automata? Is this idea even plausible?

EDIT added: this question is not a duplicate of "is space-time discrete or continuous" because I'm mostly asking whether or not a model based on cellular automata could plausibly replace existing models, under the assumption that space-time is discrete and grid-like.


marked as duplicate by Gert, John Rennie, user36790, ACuriousMind, user259412 Aug 27 '16 at 15:37

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    $\begingroup$ For some reason this opinion is extremely popular among programmers, but it's nowhere near mainstream in physics. $\endgroup$ – knzhou Aug 27 '16 at 1:32
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    $\begingroup$ Angular momentum. Angular momentum and Noether's theorem is the first place to look for why this is unpopular among physicists. Not that there aren't people noodling the idea, but it has certain obstacles that are still to be overcome. $\endgroup$ – dmckee Aug 27 '16 at 1:47
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    $\begingroup$ For some related questions, see this and this. $\endgroup$ – knzhou Aug 27 '16 at 1:56
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    $\begingroup$ @Gert Our IT intuitions tend to favor discrete, pixel-like, cellular automata models since some decades ago. Anybody having experience in programming, will easily think that the non-deterministic, analogous world of the QM should have a deeper, deterministic, discrete level below it. But the world doesn't work as we would like it better. Thus, asking from it, is in my opinion, not non-mainstream, and explaining, why it seems very unlikely, could be a very HQ answer. $\endgroup$ – user259412 Aug 27 '16 at 15:36
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    $\begingroup$ There are other questions about cellular automata on this site. Please be more specific about what you want to know. Currently, this question seems rather vague. $\endgroup$ – ACuriousMind Aug 28 '16 at 23:08

The following probably isn't what you have in mind, but it does raise a point that is very relevant to the physical content, as opposed to the mathematical content, of your question.

The fact is that many lattice theories are used everyday by physicists in calculating numerical approximations to the continuum theories we believe they approximate. All computer modelling outputs the results of discrete, difference equations and in many fields of modern physics there simply are no analytical solutions to replace them. Lattice QCD, numerical general relativity and numerical fluid dynamics are excellent examples as there is almost no other practical way of calculating what these theories actually foretell. And the experimental observation (as well as the theoretical reality for many physical theories) is that the predictions made by discretized theories are excellent models both of reality and of corresponding continuous models where these latter exist - often to well within experimental error. So here is the crucial point that applies to your question:

Whether the underlying theory should be a continuous model, or a discrete system, is a proposition that so far cannot be tested by experiment. Continuum and discretized models yield the same results as the discretized theory deals with finer and finer meshes

So I think in a very real sense, so far your question really doesn't belong to physics as it cannot be answered experimentally. And there doesn't seem to be any prospect on the horizon of its being so.

So the physics answer is quite different from the mathematical one, which amounts to whether the universe is a countable, or even finite, collection of fundamental "atoms" as opposed to an uncountable continuum. The uncountable / countable distinction is utterly real (and extremely important) in mathematics, but so far we haven't found a way that such a distinction might express itself as an experimental, measurable result.


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