$\Psi$ - model of micro- and macrosystems

TL;DR

The paper introduces the $ ext{ extsterling}$-model, a mathematical framework combining continuum and quantum mechanics to describe micro- and macrosystems with spiral velocity fields, explaining phenomena like spin and cosmic structures.

Contribution

It presents a novel $ ext{ extsterling}$-model that unifies micro- and macrosystem descriptions, naturally deriving spin and interpreting astrophysical objects without modifications.

Findings

Derives intrinsic magnetic moments (spin) from the model.

Provides a formal interpretation of black holes, wormholes, and galaxy structures.

Describes velocity fields with spiral structures on spherical surfaces.

Abstract

A mathematical model (referred as $\Psi$ - model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. $\Psi$ - model is based on continuum and quantum mechanics. $\Psi$ - model describes micro- and macrosystems, in which vector field of velocities of probability flows, charge, mass has specific spiral structure. The field of velocities has spiral structure on concentric spherical surfaces. The velocity field is not defined and has a characteristic property on the poles of sphere and on the axis and tends to zero at infinity. The behavior of $\Psi$ - model can be described in the general case with unsteady periodic singular solution of the Schr\"odinger equation. The application of $\Psi$ - model to the description of elementary particles gives naturally the intrinsic magnetic moment (spin) without need in modification of g-factor. The spin is interpreted as rotation in the framework of the relativity theory. The application of $\Psi$ -model to astrophysics gives formally an interpretation of black and white hole, wormhole, structure of the galaxy, anti-galaxy and {\guillemotleft}enclosed worlds{\guillemotright}.