Fine Structure Constants in n-dimensional Physical Spaces through Dimensional Analysis

Abstract

We use Vaschy-Buckhingham Theorem as a systematic tool to build univocal n-dimensional extensions of the electric and gravitational fine structure constants and show that their ratio is dimensionally invariant. The results allow us to obtain the relative standard uncertainty on the three-dimensionality of space as 1.08 $10^{-13}$.

5 pages, 1 figure, latex