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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 9: The role of the metric investigated

AGPhil 9.2: Invited Talk

Friday, March 20, 2015, 10:15–11:00, A 060

The status of Kottler’s premetric program in Newtonian gravity and in electrodynamics: an essay — •Friedrich W. Hehl¹, Yakov Itin², and Yuri N. Obukhov³ — ¹U. Cologne, U. Missouri, Columbia — ²Hebrew U. Jerusalem — ³RAS Moscow

In the year 1922, Kottler published two articles on ‘Newton’s law and metric’ and on ‘Maxwell’s equations and metric.’ Because of the omnipresence of the gravitational field, the metric g_ij (and its reciprocal), according to general relativity, is intervening in most physical laws. The innocently looking raising of an index, Aⁱ:= g^ik A_k, contaminates the electromagnetic 4-potential with the presence of the gravitational potential g^ik. The program of Kottler was to investigate where in physics the occurrence of the metric is essential and where it is misleading. Taking the Maxwell equations as our main guinea pig, we show that they are of a “pre-metric” nature. that is, they are independent of the metric altogether. Furthermore we demonstrate how one can derive a metric, up to a factor, from data of local and linear electrodynamics.

H., Obukhov, Foundations of Classical Electrodynamics: charge, flux, and metric, Birkhäuser, Boston (2003); Itin, H., Is the Lorentz signature of the metric of space-time electromagnetic in origin?, Annals of Physics (NY) 312, 60 (2004); H., Itin, Obukhov, Recent developments in pre metric classical electrodynamics, Złatibor Proceedings, see arXiv:physics/0610221 (2006).