Stochastic quantum mechanics

Stochastic quantum mechanics (or the stochastic interpretation) is an interpretation of quantum mechanics. This interpretation is based on a reformulation of quantum mechancis in which the dynamics of all particles is governed by a stochastic differential equation. Thus, according to the stochastic interpretation, quantum particles follow well-defined random trajectories in space(time), similar to a Brownian motion. The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations (John Archibald Wheeler's "quantum foam"), and that the averaged result of these fluctuations recreates a more conventional-looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics is due to persistent vacuum fluctuation. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it as it is usually considered. The first relatively coherent stochastic theory of quantum mechanics was put forward by Hungarian physicist Imre Fényes who was able to show the Schrödinger equation could be understood as a kind of diffusion equation for a Markov process. Louis de Broglie felt compelled to incorporate a stochastic process underlying quantum mechanics to make particles switch from one pilot wave to another. Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero, Pavon and others. The postulates of Stochastic Mechanics can be summarized in a stochastic quantization condition that was formulated by Nelson and reformulated by Kuipers.