Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

Abstract

We formulate a premetric version of classical electrodynamics in terms of the excitation H = (H, D) and the field strength F = (E, B). A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday's law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.

Two miracles of general relativity

“…This tension is not necessarily problematic, however, for what is sufficient for the (B)-view to go through in the general relativistic context (for the reasons detailed above) is that, in an appropriate neighbourhood of any p ∈ M , terms featuring the Riemann tensor or its contractions may be ignored-so that EP1' holds in this neighbourhood. 28 What is a plausible (A)-type counterpart to the (B)-view in the context of GR? We take this to be the following: the metric field has a primitive connection to spacetime geometry, and in the regime in which terms featuring the Riemann tensor or its contractions may be ignored, the dynamical laws governing non-gravitational fields in a suitable neighbourhood of any point p ∈ M are constrained to be invariant with respect to the local symmetries of this field in the same manner as for the (A)-story in the context of SR.…”

“…For example, the minimal coupling of electromagnetism to gravity leads to curvature terms in second (and higher) order dynamical equations governing non-gravitational fields, written at any point; 1 however, there also exist different possible coupling schemes, according to which one recovers different dynamical equations at any point. In literature such as [25,28], authors have attempted to elaborate the physical and mathematical details of these different possible coupling schemes.…”

To Consider the Electromagnetic Field as Fundamental, and the Metric Only as a Subsidiary Field

“…They are all diffeomorphism invariant, that is, completely independent of the coordinates used. With the exceptions of (6) and (11), the equations are also invariant under arbitrary linear frame transformations. In contrast, Eqs.…”

“…In contrast, Eqs. (6) and (11), like the frame e α , transform linearly, that is, they are covariant under linear frame transformations.…”

The Kirchhoff gauge

“…Euclidean fields are seen to satisfy an Euclidean version of Maxwell's equations which was discussed some years ago by Zampino [4] and Brill [5] and more recently by the author [6], kobe [7] and Itin and Hehl [8]. In vector notation the Euclidean equations can be written as…”