Oskar Klein, the sixth dimension and the strength of a magnetic pole

TL;DR

This paper extends Klein's five-dimensional theory to six dimensions, deriving a formula linking the sixth dimension's length to magnetic monopole strength and relating it to fundamental constants like the fine structure constant.

Contribution

It introduces a novel six-dimensional model connecting magnetic monopoles to the geometry of extra dimensions, expanding Klein's original framework.

Findings

Derived a formula for the sixth dimension's length in terms of magnetic monopole strength

Linked the ratio of fifth and sixth dimension lengths to twice the fine structure constant

Discussed potential implications for quantum theory and fundamental constants

Abstract

This work extends to six dimensions the idea first proposed by Klein regarding a closed space in the context of a fifth dimension and its link to quantum theory. The main result is a formula that expresses the value of the characteristic length of the sixth dimension in terms of the strength of a magnetic monopole $g$. It is shown that in the case of Dirac's monopole, the ratio of the characteristic lengths of the fifth and sixth dimension corresponds to twice the fine structure constant $\alpha$. Possible consequences of the idea are discussed.