TY - JOUR

T1 - Physical Dimensions/Units and Universal Constants

T2 - Their Invariance in Special and General Relativity

AU - Hehl, Friedrich W.

AU - Lämmerzahl, Claus

N1 - Funding information: The authors would like to thank the organizers of the Wilhelm and Else Heraeus workshop for the invitation: to Klaus Blaum (Heidelberg), to Dmitry Budker (Mainz), and to Andrey Surzhykov (Braunschweig). F.W.H. is most grateful to Yuri Obukhov (Moscow) and Yakov Itin (Jerusalem) for past collaborations on the issue of physical dimensions. The authors also acknowledge very helpful remarks by Jens Boos (Edmonton), Alberto Favaro (London), Michael Krystek (Berlin), James Nester (Chung-li), and Volker Perlick (Bremen). And last, but not least, the authors thank Joachim Ullrich (Braunschweig) for useful hints and interesting discussions and two anonymous referees for their careful evaluations. C.L. acknowledges support of the DFG-funded Research Training Group 1620 “Models of Gravity” and of the Collaborative Research Center (SFB) 1128 “geo-Q” and 1227 “DQ-mat.” This article is part of the Special Issue on The Revised SI: Fundamental Constants, Basic Physics and Units, highlighting the revision and redefinition of the International System of Units (SI) to come into effect in May 2019. The authors would like to thank the organizers of the Wilhelm and Else Heraeus workshop for the invitation: to Klaus Blaum (Heidelberg), to Dmitry Budker (Mainz), and to Andrey Surzhykov (Braunschweig). F.W.H. is most grateful to Yuri Obukhov (Moscow) and Yakov Itin (Jerusalem) for past collaborations on the issue of physical dimensions. The authors also acknowledge very helpful remarks by Jens Boos (Edmonton), Alberto Favaro (London), Michael Krystek (Berlin), James Nester (Chung-li), and Volker Perlick (Bremen). And last, but not least, the authors thank Joachim Ullrich (Braunschweig) for useful hints and interesting discussions and two anonymous referees for their careful evaluations. C.L. acknowledges support of the DFG-funded Research Training Group 1620 ?Models of Gravity? and of the Collaborative Research Center (SFB) 1128 ?geo-Q? and 1227 ?DQ-mat.? This article is part of the Special Issue on The Revised SI: Fundamental Constants, Basic Physics and Units, highlighting the revision and redefinition of the International System of Units (SI) to come into effect in May 2019.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - physical dimensions

KW - relativistic invariance

KW - SI

KW - speed of light

KW - units

KW - universal constants

UR - http://www.scopus.com/inward/record.url?scp=85060650264&partnerID=8YFLogxK

U2 - 10.1002/andp.201800407

DO - 10.1002/andp.201800407

M3 - Article

AN - SCOPUS:85060650264

VL - 531

JO - Annalen der Physik

JF - Annalen der Physik

SN - 0003-3804

IS - 5

M1 - 1800407

ER -