Natural units, numbers and numerical clusters

Abstract

Defined by Lord Kelvin as the science of measurement it is described a fundamental fact of physics. The so called `natural' units represent the unique system of units conveniently used in the realm of High Energy Physics. The system of natural units is defined by the consistent providing of the adimensional unit value to the velocity c of the eletromagnetic radiation in the vacuum, related to the Maxwell classical electromagnetic theory and to the special relativity theory, to the reduced Planck constant $\hbar\equiv\frac{h}{2π}$ having the dimension of action, which is the fundamental constant of the quantum mechanics as well as to the Boltzmann constant $k_B$ which has the dimension of heat capacity, being the fundamental constant associated to the statistical mechanics, $c=\hbar = k_B = 1$. Such prescription is mandatory as we investigate the ultimate constituents of matter and their dynamics, since the atoms, leptons and quarks up to the grand unification, strings, superstrings, and the supergravity theories, as well as the total unification of the interactions in the M-theory. The one-dimensional character of this phenomenology is totally featured by the use of the natural units, reflecting the fact that in order to be possible the investigation of the fundamental constituents of matter it is being necessary the resolution of lengths of the order of $10^{-16} cm$ or to reach energies of the order of at least 1 TeV. The application of this system of natural units results exceptionally adequate in the description of the Universe since the Planck scale, up to the Hubble large scale expanding Universe, resulting in the curious formation of the regular numerical clusters.