Certain “Curiosities” in Physics Established by Dimensional Analysis

In this article are presented some more special relationships established between the fundamental
constants by applying dimensional analysis. Dimensional analysis is a working method well known to
engineers and researchers. Dimensional analysis has been used in many fields of research from
aerodynamics, hydraulics, electromagnetics, chemical engineering processes, nuclear blast up, to
biology or even economics. In this article, dimensional analysis was used to highlight unknown
relationships that exist between fundamental constants and implicitly between the natural
phenomena. The speed of light, the Planck constant, the gravitational constant, the fine structure
constant, the Avogadro number, the proton/electron mass ratio and other constants were taken into
account. The values of the fundamental constants taken into consideration for the analysis are those
recommended by the CODATA in 2018 to be used for technical and scientific purposes. The
relationships obtained are particularly interesting not only by their originality but also by the
possibilities offered by them for practical applications. The results and conclusions presented in the
article are completely original and were obtained by applying a special method of analysis imagined
by the author. Some researchers have tried to find an explanation of these results using certain
conventional approaches known in current physics. Whereas they have not found a classic physical
background to explain these results, they considered them mere “curiosities”. Even if these results are
mere “curiosities” highlighted by the author as a result of his pure intellectual interest, they may still
have their importance since the pure curiosity without an immediate material benefit can have a
revolutionary effect on human activity.