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Metafizika

STATISTICAL ORIGIN OF QUANTUM DESCRIPTION AND MIE-EINSTEIN FIELD PARADIGME

Yu. P. Rybakov

Published Dec 15, 2020• 0 citations
Publisher

Abstract

We discuss the statistical origin of quantum theoretical description and show that within the scope of the Mie-Einstein field approach, with particles being considered as lumps of some material field satisfying nonlinear equations, such a description appears to be natural and inevitable since it is impossible to specify initial conditions for the extended particle-soliton. Beside this, it is shown that on solitons’ basis, the special stochastic representation of quantum mechanics can be constructed, the latter one being equivalent to the theory of nonlocal hidden variables.

DOI
10.22363/2224-7580-2020-3-57-63

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We discuss the statistical origin of quantum theoretical description and show that within the scope of the Mie-Einstein field approach, with particles being considered as lumps of some material field satisfying nonlinear equations, such a description appears to be natural and inevitable since it is impossible to specify initial conditions for the extended particle-soliton. Beside this, it is shown that on solitons’ basis, the special stochastic representation of quantum mechanics can be constructed, the latter one being equivalent to the theory of nonlocal hidden variables.
Background Using the Einstein's idea on particles-solitons, the stochastic representation of the wave function as a large sum of solitons with random phases is suggested.Purpose To illustrate the main idea of the stochastic representation, let us recall the lectures by N. Wiener on nonlinear problems in random theory.Method In these lectures Wiener used the so-called 𝛼-representation of the wave function for a nonrelativistic particle in three-dimensional space, the wave function being considered as an element of the random Hilbert space with the Gaussian dispersion.Results This representation appears to be equivalent, in accordance with the central limiting theorem, to the sum of many complex solitons with random phases.Conclusions On the basis of this representation it is possible to substantiate the Born's rule for measuring physical observables and also to explain the "spin-statistics" correlation in quantum mechanics.
We study the behavior of the atomic matter immersed in a zero-point radiation field, which is taken as the source of the endless stochastic motion of electrons. The starting point is a statistical phase-space equation for a particle in interaction with the field. Under certain natural approximations, the system reaches a stationary condition; the corresponding reduced description obtained in configuration space is just the Schrodinger quantum mechanics. Quantum nonlocality is revisited from this point of view and is shown to appear as an artifact of the reduced description. The theory presented also serves to explain why usual quantum mechanics is not amenable to a phase-space formulation.
Quantum nonlocality is revisited from a novel point of view by studying the problem of an originally classical particle immersed in the stochastic zero-point radiation field (zpf). The entire system is left to evolve until it reaches a state in which the radiative terms cancel each other in the mean in a first approximation. The ensuing approximate statistical description reduced to the particle's configuration space contains a nonclassical term due to the dispersion of the momentum, which depends on the density of particles ρ(x) and thus is nonlocal. This description is shown to be equivalent to Schrödinger's equation and its complex conjugate. The nonlocal term is recognized as the so-called quantum potential, thus solving the long standing problem of the origin and meaning of this term. Further, the relationship between the Wigner function and a true Kolmogorovian probability density in phase space is discussed from the perspective provided by this theory.
With general arguments it is motivated that we are still in search of a hidden-variables theory or sub-quantum mechanics. Aspects of a solvable model for quantum measurements are discussed, and a solution of the quantum measurement problem within ordinary quantum theory. The related statistical interpretation of quantum mechanics is advocated. Soliton approaches for elementary particles are proposed and some classical looking aspects of the relativistic hydrogen atom are mentioned. The integration of these solitons with stochastic electrodynamics is sketched.