A hidden variables model for interference phenomena based on $p$-adic random dynamical systems

Abstract

We propose a model based on random dynamical systems (RDS) in information spaces (realized as rings of $p$-adic integers) which supports Buonomano's non-ergodic interpretation of quantum mechanics. In this model the memory system of an equipment works as a dynamical system perturbed by noise. Interference patterns correspond to attractors of RDS. There exists a large class of $p$-adic RDS for which interference patterns cannot be disturbed by noise. Therefore, if the equipment is described by such a RDS then the result of statistical experiment does not depend on noise in the equipment. On the one hand, we support the corpuscular model, because a quantum particle can be described as a corpuscular object. On the other hand, our model does not differ strongly from the wave model, because a quantum particle interacts with the whole equipment. Hence the interaction has nonlocal character. For example, in the two slit experiment a quantum particle interacts with both slits (but it passes only one of them).