Uniform formalism for description of dynamic quantum and stochastic systems

TL;DR

This paper introduces a unified dynamic formalism that describes quantum, stochastic, and classical systems without relying on probability, enabling a consistent treatment of diverse physical phenomena including pair processes.

Contribution

It presents a novel, purely dynamic formalism that unifies the description of deterministic, stochastic, and quantum particles using a single framework without probabilistic assumptions.

Findings

Describes quantum particles as stochastic particles without quantum principles.

Can describe classical inviscid fluids within the same formalism.

Applicable to relativistic phenomena like pair production and annihilation.

Abstract

The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is primordially deterministic, seems to be unsuitable. The statistical ensemble of stochastic (or deterministic) systems is considered to be the main object of dynamics. At such a logical reloading the statistical description becomes a component of dynamics, and capacities of dynamics increase. At such an approach one can describe deterministic, stochastic and quantum particles by means of the uniform technique. The quantum particle is described as a stochastic particle, i.e. without a reference to the quantum principles. Besides, by means of this technique one can describe classical inviscid fluid. There are four different versions of the formalism: (1) description in Euler dynamic variables, (2) description in Lagrange dynamic variables, (3) description in terms of the generalized stream function, (4) description in terms of the wave function. The uniform formalism is purely dynamic. Even describing stochastic systems, it does not refer to probability and probabilistic structures. In relativistic case the uniform formalism can describe pair production and pair annihilation.