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After talking with a colleague about the possible nature of the limitation of information propagation to c, and how everything can be seen relative to it, we wondered if the nature to this could be that information propagation works like in conways game of life (that is only adjacent cells can influence others), or even that we are an $n$ (10, 11, 26, or any other number that is present in e.g. string theories) dimensional game of life equivalent.

Searching around I had to stumble over wolframs NKS and as is written here:

Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?

many generally believe that such a base for our universe is impossible due to evidently existing nonlocal effects.

Besides this effect (that some might hope to solve one day) and being far from making any predictions that anyone could experimentally test, is there anything else that fundamentally makes it impossible for our universe to be an elaborate game of life?

(Semi) Relevant xkcd: http://www.xkcd.com/505/

Note: I tried a simulation with a torus of size 11 in 11 dimensions, but besides being awfully slow and having problems to visualize anything there, no sentient life did evolve so far that could answer me this question.

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  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/759 , physics.stackexchange.com/q/47511/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Dec 3, 2014 at 13:23
  • $\begingroup$ @Qmechanic: I don't think those are duplicates, as they are asking if we are living in a simulation (or if quantum physics suggests such), whereas I am asking for arguments/hints that we are not living in a specific kind of "simulation" e.g. things that could not be simulated with such a simulation that we nevertheless observe (like some say is the case for nonlocality). $\endgroup$
    – PlasmaHH
    Commented Dec 3, 2014 at 13:33

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Yes, you can simulate non-locality in celular automata, even if the rules are local. In such a case, contiguous cells do not represent adjacent points in our space. In these models space is an approximate, macroscopic emergent property (it is discussed in detail in NKS). This emergent space can have, at microspcopic scales, functional links that resemble the entanglement of particles. The basic idea is that two particles that move in this emergent space, stay linked in a way that for a macroscopic observer they are far appart in space, but to them they are actually next to each other. This happend when you create an entangled pair. He even went further to show that the probabilistic behaviour resembles the shrodinger equation. A more general argument about why you can simulate nonlocal behaviour with local rules, including bell inequalities, is that the local rule cellular automata is universal, that is, it can simulate any physical process to any degree of accuracy. The argument that Bell's inequalities rule out local realism is based on the assumpion of locality on space, but cellular automata are local on the rules of its elements, not necessarily on the rules for the emergent spacetime. A good analogy is a virtual world. Agents in that world could have non local laws of physics, including quantum mechanical ones, but they arise from a classically programmed computer that interacts locally in a different space (our physical space).

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  • $\begingroup$ I am not sure how this answers the question for something else than locality (it being true or not is irrelevant for this point) possibly making it impossible for us to be in a game of life $\endgroup$
    – PlasmaHH
    Commented Dec 3, 2014 at 12:13
  • $\begingroup$ The game of life is turing universal, it can simulate anyting. But it will not look like at all like the game of life to us. Actually it doiesnt matter which automata you chose, it doesnt have to be the game of life, it just has to be universal. So in the end, the universe could in principle be modeled as consisting of 1) one kind of object: a celular atomata cell, that can take two possible states, and that are locally connected and whose evolution laws on the states are simple local rules. The complexity is in the software, that is, on the initial conditions of the cells. $\endgroup$
    – user65081
    Commented Dec 3, 2014 at 12:20
  • $\begingroup$ Is this a convoluted try to say that there isn't anything else? $\endgroup$
    – PlasmaHH
    Commented Dec 3, 2014 at 12:22
  • $\begingroup$ well, at least that there exist the logical possibility that there isn't anything else. But that is methaphysics, not physics. $\endgroup$
    – user65081
    Commented Dec 3, 2014 at 12:24
  • $\begingroup$ I appologize for being very unclear, I am not a native speaker and tried to convey complex ideas as fast ans short as possible. It might have resulted in somethig unintelligible, but I am gonna edit it tomorrow with more time. $\endgroup$
    – user65081
    Commented Dec 3, 2014 at 12:26

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