Causality and time: Toward automaton interpretation of quantum mechanics

During the talk it will be introduced a vast class of functions which are defined by deterministic sequential machines. Functions from that class can be uniquely expanded to continuous functions with respect to both p-adic and real metrics. By using functions of that class a model of wave function can be constructed. Within the model, it can be interpreted the collapse, uncertainty relations, Born’s rule, holographic property and some other properties of quantum systems. The model is based on two physical assumptions: (1) discreteness of time at Planck’s scale and (2) causality. Ideologically the model is related to works by I.Volovich and to recent monograph by G. `t Hooft «The Cellular Automaton Interpretation of Quantum Mechanics». In comparison with general cellular automata models from the mentioned monograph, our model is based on significantly smaller class of automata which are «computationally the least powerful».