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Quantum-like model from generalized cellular automata rules

Posted 1 year ago
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Dear Reader, it seems to be reasonable to consider the following generalization of cellular automata rules. Let us consider a square matrix lines (rows and columns) in place of an automaton cells. Furthermore, let rules for changing a value of given cell (here, a line) are elementary matrix operations like switching lines. In a pre-print https://arxiv.org/abs/1705.04376, I introduced a model of matrices based on these assumptions for a simple relation of order (which could be understood as some kind of relation which puts some abstract objects in order). As a consequence, eigenvectors for these matrices generate a set of three-dimensional orthogonal vectors which could represent three-dimensional physical objects with some property. An evolution of the relations matrix postulated here gives quantized values of a 'state' vector which I tried to incorporate. My model starts from reasonable claim of an existence of a simple relation between simple objects. As a consequence, it reveals some simple characteristics, like three dimensional sub-spaces or a quantized spectrum of values. Its compatibility to quantum mechanics description is still hypothetical but coincidences with a quantum description are promising. I would be thankful for all your comments.

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