Natural Systems of Units

systems of units in which the fundamental units are the fundamental physical constants, such as the gravitational constant G, the velocity of light in a vacuum c, Planck’s constant h, Boltzmann’s constant k, Avogadro’s number N_A, the charge of an electron e, and the rest mass of an electron m_e.

The magnitude of the fundamental units in a natural system of units is determined by natural phenomena. This is what basically differentiates the natural systems from other systems of units, in which the selection of units is governed by the practical measurement requirements. According to M. Planck, who first proposed a natural system of units (1906) with the fundamental units h, c, G, and k, it would be independent of terrestrial conditions and suitable for all times and locations in the universe. A number of other natural systems of units was proposed (G. Lewis, D. Hartree, A. Ruark, P. Dirac, A. Grescy, and others). The natural systems of units are characterized by extremely small units of length, mass, and time (for example, these quantities in Planck’s system are, respectively, 4.03 x 10^-35 m, 5.42 x 10^-8 kg, and 1.34 x 10^-43 sec) and, conversely, by extremely large temperature units (3.63 x 10³²°C). The natural systems of units are, therefore, inconvenient for practical measurements. In addition, the accuracy of reproducing the units is lower by several orders of magnitude than in the International System of Units, since the former is limited by the accuracy of the determination of the physical constants. In theoretical physics, however, the natural systems of units make it possible to sometimes simplify equations and offer some other advantages (for example, the system of Hartree makes it possible to simplify the notation of quantum-mechanical equations).