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MP: Theoretische und Mathematische Grundlagen der Physik

MP 1: Klassische Feldtheorie, Nichtkommutative Geometrie

MP 1.1: Fachvortrag

Montag, 24. März 2003, 15:00–15:30, F309

Is the Lorentz signature of spacetime induced by the Lenz rule of electrodynamics? — •Friedrich W. Hehl¹ und Yakov Itin² — ¹Univ. zu Köln and Univ. of Missouri-Columbia, MO, USA — ²Hebrew Univ. of Jerusalem. Email: hehl@thp.uni-koeln.de

We consider a generally covariant pre-metric formulation of electrodynamics. We show that the plus sign of Ḃ in Faraday’s induction law (the Lenz rule), as compared to the minus sign of Ḋ in the Oersted-Ampère law, leads to a minus sign in the electric/magnetic reciprocity relation H → ζ F, F → − H/ζ. Here H=( H, D) and F=(E,B) are electromagnetic excitation and field strength, respectivly, and ζ is a pseudoscalar function. The last minus sign in turn is shown to be necessary for the positiveness of the energy-momentum of the electromagnetic field.

If the propagation of electromagnetic waves is studied in the geometrical optics limit, then this minus sign finally yields the Lorentz signature of the metric of spacetime. Thus it is shown (for the first time?) that there is relation between four signs in electrodynamics: the + sign in Faraday’s law, the - sign in Oersted-Ampère’s law, the + sign of the electromagnetic energy, and the (+—) signature of the Lorentz metric. [1] Y.Itin & FWH, in preparation (2002/3) [2] FWH & Yu.N.Obukhov, The Foundations of Classical Electrodynamics. Birkhäuser, Boston (2003).