Fractal extra dimension in Kaluza-Klein theory

TL;DR

This paper explores a Kaluza-Klein model where the extra dimension has a fractal geometry, leading to a non-uniform mass spectrum and significantly smaller elementary charge masses compared to traditional models.

Contribution

It introduces a novel fractal geometry for the extra dimension in Kaluza-Klein theory, affecting charge mass scales and mass spectrum periodicity.

Findings

Elementary charge mass is much smaller than the Planck mass

Mass spectrum becomes aperiodic due to fractal geometry

Higher charge states form a non-uniform mass tower

Abstract

Kaluza-Klein theory in which the geometry of an additional dimension is fractal has been considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the "tower" of masses which correspond to higher integer charges becomes aperiodic.