On a Geometrical Description of Quantum Mechanics

TL;DR

This paper presents a geometric interpretation of quantum mechanics as a modification of Euclidean space into a Weyl affine space, where quantum effects arise from local changes in measurement standards.

Contribution

It introduces a novel geometric framework called Q-wis, linking quantum phenomena to the deformation of measurement rulers within a Weyl affine space.

Findings

Quantum mechanics can be modeled as a Weyl affine space geometry.

Quantum effects correspond to local deformations of measurement standards.

The approach provides a geometric basis for quantum phenomena.

Abstract

We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum Mechanics. In the Q-wis geometry, the length of extended objects changes from point to point. In our proposed geometrical formulation, deformation of the standard rulers used to measure physical distances are in the core of quantum effects.