Abstract
Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.
Highlights
Using the hydrodynamical formalism of quantum mechanics for a Schrodinger spinning particle, developed by T
The simplest generalization of the four-dimensional Minkowskian geometry to the case of the manifold of oriented points is the geometry of absolute parallelism [15], constructed on the manifold, that is represented as a vector bundle with a base formed by the manifold of the translational coordinates and time
We are trying to build a geometric theory in which the evolution of a material particle controlled by a wave is a manifestation of the geometry of space
Summary
The electromagnetic, weak and strong interactions are described in the language of gauge theories built on the principle of local internal symmetry, and are not directly related to the space-time geometry. The hypothesis underlying this paper is that rotation of a physical object generates a field that has new physical nature, and construction of a new theory requires the use of new ideas about the structure of space and time. From the geometrical point of view, this means that the rotational motion is reflected in a certain way on the geometry of the event space, making it different from the pseudo-Riemannian one [15], [16]. We use the idea of geometrizing the motion of a particle with spin, and represent the field of a spinor wave using concepts borrowed from geometry. We stop using the concept of a force field, and assign a geometric image to the particle evolution
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