Non-Riemannian model of the space-time responsible for quantum effects

TL;DR

This paper proposes a non-Riemannian, homogeneous isotropic space-time model where quantum effects are incorporated through a constant in the world function, unifying classical and quantum particle descriptions.

Contribution

It introduces a novel space-time model with a modified world function that accounts for quantum effects via a constant proportional to Planck's constant.

Findings

World tubes of particles are geometrical structures of space-time.

Quantum effects are modeled through a constant in the world function.

The model generalizes pseudo-Euclidean space to include quantum phenomena.

Abstract

A class of homogeneous isotropic space-time models including pseudo-Euclidean space as a special case is considered. Such a model is chosen, where the particle motion is described in the most adequate way. It means that the world tubes of all free particles (both classical and quantal) are characteristic geometrical structures of the space-time. The world function $\sigma $ of this model has the form $\sigma =\sigma_E+\sigma_{0}$, $\sigma_E>\sigma_{0}$, where \sigma_E is the world function of the pseudo-Euclidean space, \sigma_0 is a constant responsible for quantum effects. It is proportional to Planck's constant \hbar .