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Discreteness and Determinism in Superstrings?

  1. Jul 17, 2012 #1
    Gerard 't Hooft has just uploaded a new paper on arxiv: http://arxiv.org/abs/1207.3612

    Ideas presented in two earlier papers are applied to string theory. It had been found that a deterministic cellular automaton in one space- and one time dimension can be mapped onto a bosonic quantum field theory on a 1+1 dimensional lattice. We now also show that a cellular automaton in 1+1 dimensions that processes only ones and zeros, can be mapped onto a fermionic quantum field theory in a similar way. The natural system to apply all of this to is superstring theory, and we find that all classical states of a classical, deterministic string propagating in a rectangular, D dimensional space-time lattice, with some boolean variables on it, can be mapped onto the elements of a specially chosen basis for a (quantized) D dimensional superstring. This string is moderated ("regularized") by a 1+1 dimensional lattice on its world sheet, which may subsequently be sent to the continuum limit. The space-time lattice in target space is not sent to the continuum, while this does not seem to reduce its physically desirable features, including Lorentz invariance.
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  3. Jul 18, 2012 #2


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    1+1 is so special than it even seems a good idea.
  4. Jul 20, 2012 #3
    I'm not sure whether or not I should consider this to be surprising -- (some) 1+1 dim CAs are capable of universal computation, so it's not really a wonder that one could formulate string theory -- or any computable theory -- within CAs: it just corresponds to writing a program that simulates the theory. That it works in some reasonably simple fashion is probably a bit surprising, but one can perhaps always find some special-purpose (i.e. non-universal) CA in which things are simple enough.

    Of course, it would be very surprising if this simulation can be done in an efficient manner, seeing as how this would run counter to the idea of the quantum speedup (one could then simulate a quantum computer efficiently with a classical one, so if t'Hooft's CA can do that, you could use it to break every encryption based on the difficulty of factorizing large numbers, which now suddenly isn't so difficult anymore...).
  5. Jul 21, 2012 #4
    ... 't Hooft might be onto something here ... and I don't necessarily mean in our fundamental understanding of string theory (although I don't rule this out), but I'm rather referring to the striking door this statement seems to open: the prospect of putting the quantum superstring onto a computer and solving it ... Wow!

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