On possibility of topological interpretation of quantum mechanics

TL;DR

This paper proposes a topological geometric model for quantum objects, interpreting fundamental equations as relations describing space topological defects, offering explanations for quantum phenomena and gauge invariance.

Contribution

It introduces a novel topological interpretation of quantum mechanics, linking equations to space defects and explaining quantum properties and gauge invariance naturally.

Findings

Equations for Dirac and Maxwell fields describe space topological defects.

Topological interpretation explains wave-particle duality and nonlocality.

Electromagnetic potentials arise from defect connectivities.

Abstract

Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. It is shown also that Dirac equation for hydrogen atom can be also considered as relation describing the space topological defect. Electromagnetic potentials appears within this approach as connectivities of the defect universal covering space and gauge invariance of electromagnetic field happens to be a natural consequence of topological interpretation. Proposed approach can be also considered as a nonlocal model with hidden variables. Preliminary results were published by parts early, and here they are presented completely.