Toward the (non-cellular) automata interpretation of quantum mechanics: Volovich postulates as a roadmap

Abstract

The paper announces results which may lead to a novel (basically, information-theoretic) interpretation of quantum mechanics under assumptions of causality and existence of the smallest temporal interval. The main mathematical tool of the interpretation is p-adic 1-Lipschitz maps. The latter maps are exactly the maps produced by letter-to-letter transducers (or, sequential Mealy machines) rather than by cellular automata. Physically the maps can be judged as causal functions over discrete time which are models of physical systems. A wide class of the maps can naturally be expanded to continuous real functions; therefore the maps may serve as mathematical models of physical systems both over discrete and over continuous time.