Quantum Features of Non-Symmetric Geometries

TL;DR

This paper reveals that non-symmetric geometries inherently exhibit quantum-like features in their paths, which are solely due to the torsion component of the affine connection, independent of the specific geometry.

Contribution

It demonstrates that paths in non-symmetric geometries are naturally quantized through torsion, providing a geometric origin for quantum features without explicit quantization schemes.

Findings

Quantum features arise only from the torsion term.

Vanishing torsion eliminates quantum features.

All examined non-symmetric geometries share the same quantum properties.

Abstract

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization schemes, paths in such geometries are naturally quantized. Two different non-symmetric geometries are examined for these features. It is proved that, whatever the non-symmetric geometry is, we always get the same quantum features. It is shown that these features appear only in the pure torsion term (the anti-symmetric part of the affine connection) of the path equations. The vanishing of the torsion leads to the disappearance of these features, regardless of the symmetric part of the connection. It is suggested that, in order to be consistent with the results of experiments and observations, torsion term in path equations should be parametrized using an appropriate parameter.