Physical Dimensions/Units and Universal Constants

Their Invariance in Special and General Relativity

authored by
Friedrich W. Hehl, Claus Lämmerzahl

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 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.

External Organisation(s)
University of Cologne
University of Bremen
Annalen der Physik
Publication date
Publication status
Peer reviewed
ASJC Scopus subject areas
Physics and Astronomy(all)
Electronic version(s) (Access: Unknown)