Gravity, Fine-Structure Constant and Natural Units -- some Thoughts based on Dimensional Analysis --

Abstract

Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the constants $G$, $c$, $\hbar$ and $e$}. We find that the \corr{form} of the fine-structure constant is a direct consequence of this connection. Additionally, our approach emphasises that gravity is a quite distinct area of physics which is not yet successfully quantised, i.e. not yet combined with quantum mechanics. We also discuss different unit systems based on dimensional analysis and natural constants.