Geometrization of Classical Wave Fields

TL;DR

This paper proposes a geometrical model where classical wave fields are represented as topological defects in a higher-dimensional space, offering explanations for quantum phenomena like wave-particle duality and nonlocal correlations.

Contribution

It introduces a novel geometrical framework modeling wave fields as topological defects in five-dimensional space, unifying quantum properties with space topology.

Findings

Fields as topological defects explain quantum properties

Model accounts for nonlocal correlations in EPR experiments

Probabilistic outcomes arise from defect shape uncertainty

Abstract

Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations for these fields can be considered as relations describing the space topological defects. These defects, being closed topological manifolds, are embedded in the outer five-dimensional space, and observable objects appear to be intersections of above defects with the physical space. 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. Wave-corpuscular properties arise as a result of the defect periodical movement in the outer space relative to its intersection with the physical space, and just this periodical movement attributes phase to the propagating object. Appearance of probabilities within the formalism is a consequence of uncertainty of the closed topological manifold shape, and ensemble of all possible shapes for the same object can be considered as an ensemble of hidden variables that leads to probabilistic description. Embedded in the outer space topological defects provide channels for nonlocal correlations between their intersections-- noninteracting particles in EPR-experiments, and this means that the proposed approach can be considered as a nonlocal model with hidden variables.