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

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 $α$. Possible consequences of the idea are discussed.