München 2019 – scientific programme
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GR: Fachverband Gravitation und Relativitätstheorie
GR 2: General Aspects: Units, History and Quantum
GR 2.1: Invited Talk
Monday, March 18, 2019, 17:30–18:15, HS 4
Physical dimensions/units and universal constants: their invariance in special and general relativity — •Friedrich W. Hehl1 and Claus Lämmerzahl2 — 1Inst.Theor.Physik, Univ., 50923 Köln, Germany — 2ZARM, Univ., 28359 Bremen, Germany
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, we are naturally led, besides the dimensions of length and time, to the fundamental units of action h, electric charge q, and magnetic flux φ. We have q×φ= action and q/φ=1/resistance. 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, we are 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, that is, if gravity is thought to be switched off versus the case in the gravitational field. Relations to the new International System of Units (SI) of 2019 are pointed out.