Geometrical interpretation of the wave-pilot theory and manifestation of the spinor fields

TL;DR

This paper offers a new geometrical interpretation of the wave-pilot theory for spinning particles, suggesting that spinor fields shape the geometry of space, which influences particle motion through torsion and curvature.

Contribution

It introduces a geometrical model where spinor wave functions determine space's geometry, linking spin to space torsion and providing a new perspective on wave-pilot theory.

Findings

Spin vector rotates along geodesics with torsion.

Particle motion follows a geometrized guidance equation.

Space torsion influences spin and particle dynamics.

Abstract

Using the hydrodynamical formalism of quantum mechanics for a Schrodinger spinning particle, developed by T. Takabayashi, J. P. Vigier and followers, that involves vortical flows, we propose the new geometrical interpretation of the wave-pilot 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, that is 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 an tetrad $e^a_{\mu}$, forms from the bilinear combinations of spinor wave function. It was 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.