Reading around about various CA models I saw that there are even those who are following the track to provide a single mechanicist model of the universe. For example Gerard van 't Hooft claims that there may well be a CA system with classical properties underlying quantum mechanics. In this view and in all the models that try to see the universe as an immense CA I do not understand how it is conceived Time. Are there two kinds of Time? The first is the clock one that updates the automata synchronously. Where is this clock?Outside the universe? And what about the "inner time" that flows in the universe and what that is it's relationship with clock time? I hope I made my doubt clear. Thank you
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1$\begingroup$ it might be that this topic is addressed in Wolfram's "A new kind of science". $\endgroup$– Phoenix87Commented Feb 11, 2015 at 10:45
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2 Answers
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yes, the time step of such cellular automaton would be a different time than the one in our universe. It depends of you definition of universe, but it is outside our physical realm in the same sense that the internal time in a computer virtual would be is. We can run the simulation at any pace, with or without interruptions, or even backwards. The "beings" inside the simulation would still experience a continuous time. A nice article on the subject is "pigs in cyberspace" by Hans Moravec. You 'll find it online.
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The time in our universe would obviously be intimately linked to the CA-time, but I feel there is an important nuance here that I haven't seen properly adressed; The smallest possible amount of time in the "real" universe would correspond to a single generation of the CA, so that any amount of "work" or calculation required to update the CA a single step adds nothing to the "real" time of the process. For instance, there are CA algorithms that can factor integers in polynomial generations. If you run such an algorithm on a computer, the algorithm has to spend time computing every cell, and thus cannot finish in polynomial time. However, the same algorithm implemented directly in the CA fabric of the universe, should be able to factor integers in polynomial time. My hunch is that something like this explains the expected performance of quantum computers.