Using the hydrodynamical formalism of quantum mechanics for a Schrödinger 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_μ⁠, 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.

After Schrödinger formulated the famous wave equation in 1926, which solution is a de Broglie's plane wave, the issue arose of interpreting the wave function and its physical reality. It is accepted that a wave field, that transfers energy or momentum, can be physically real, as a result, difficulties arose in understanding the physical reality of the wave function. After the Solvay Congress, the so-called Copenhagen or probabilistic interpretation of quantum mechanics was adopted, according to which the wave function was matched by an abstract probability wave. However, not all leading scientists have accepted this interpretation. A. Einstein argued that the description of quantum phenomena in the framework of the probabilistic concept is not complete, and the deterministic laws are the basis of physical reality.

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Progress of Theoretical and Experimental Physics, ptaa106,

https://doi.org/10.1093/ptep/ptaa106