Discreteness and Determinism in Superstrings

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. We claim that our observations add a new twist to discussions concerning the interpretation of quantum mechanics, which we call the cellular automaton (CA) interpretation. Detailed discussions of this interpretation, and in particular its relation to the Bell inequalities, are now included.