Discreteness and Determinism in Superstrings
Abstract
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 spacetime 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 spacetime 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1207.3612
 Bibcode:
 2012arXiv1207.3612T
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 30 pages (incl. title page). No figures. In version 2, extensive discussions were added on the subject of the CA interpretation of quantum mechanics, hidden variables and Bell's inequalities, in response to criticism aired by several readers of version 1