Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

Abstract

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action h, electric charge q, and magnetic flux φ. Also, q × φ = action and q/φ = 1/resistance are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and φ (and also of h): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, φ appears quantized in the form of fluxons (Abrikosov vortices). And h leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.

Universal constants and natural systems of units in a spacetime of arbitrary dimension

“…Replacing G with the universal length R, we obtain a homogeneous set and thus have such invariance. The methodological reason for the assumption of universality of R lies in the properties of a possible kinematic group of spacetime, which 1 In the context of this paper, the terms "fundamental length" and "universal length" are, strictly speaking, not synonymous. Indeed, the Planck length is, by no doubt, fundamental, as it is constructed of fundamental constants.…”

“…The recent reform of the SI system made the definitions of its primary units (except the second) dependent on world constants, such as c, , k B . It thus sharpens a question about the conceptual nature of physical constants in theoretical physics (see, e.g., recent review [1]). This question can be traced back to Maxwell and Gauss, and many prominent scientists made their contribution to the discussion of it.…”

“…In classical mechanics, three quantities with nontrivial dimension can be adopted as base units. They are usually chosen to have units of length, mass, and time, although other choices are possible (and even were recently advocated [1]). Let us consider the Galilean group, which is a symmetry group of classical mechanics (a pedagogical explanation of the properties of the Galilean group and its generators can be found, e.g., in [29].…”

Gauging the spacetime metric -- looking back and forth a century later

“…35 For the recent revision of the international standard system SI see (Hehl/Lämmerzahl, 2019). It has implemented measurement definitions with time as only fundamental unit, u T = 1 s such that "the ground state hyperfine splitting frequency of the caesium 133 atom ∆ν( 133 Cs) hfs is exactly 9 192 631 770 hertz" (Bureau International, 2011, 24f.).…”

Classical Planck Spectrum for Relative Thermal Radiation, Classical Zero-Point Radiation, and Scale Parameter

“…The foregoing would indicate that radiation emitted by hot bodies can also arise in a classical context, with the incorporation of the Special Theory of Relativity in the formulation of classical electrodynamics and the classical relativistic field theory. In reference to Planck's constant part of the scientific community discards its use as a universal constant, it can appear in diverse contexts [18][19][20][21], and in this classical approximation, a parameter of the order of Planck's constant emerges, In this article, we incorporate to the Planck radiation law derived from classical relativistic electrodynamics and with zero-point radiation a scale parameter associated with the geometrical and electromagnetic characteristics of the thermal radiation contained in a finite enclosure of volume V. This scale parameter is associated with experimental measures of Casimir forces, in such a way that the structure of Planck's law differs from that generally presented in literature in terms of Planck's constant .…”