Stochastic processes for indirectly interacting particles and stochastic quantum mechanics

Abstract

This work has two objectives. The first is to begin a mathematical formalism appropriate to treating particles which only interact with each other indirectly due to hypothesized memory effects in a stochastic medium. More specifically we treat a situation in which a sequence of particles consecutively passes through a region (e.g., a measuring apparatus) in such a way that one particle leaves the region before the next one enters. We want to study a situation in which a particle may interact with other particles that previously passed through the system via disturbances made in the region by these previous particles. Second, we apply the type of stochastic process appearing in this context to the stochastic interpretation of quantum mechanics to obtain a modified version of this interpretation. This version is free of many of the criticisms made against the stochastic interpretation of quantum mechanics.