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

Abstract

In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant and metric-independent way. The electromagnetic field is then given in terms of the excitation H = (H, D) and the field strength F = (E, B). Additionally, a local and linear "spacetime relation" is assumed between H and F , namely H ∼ κF , with the constitutive tensor κ. The propagation is studied of electromagnetic wave fronts (surfaces of discontinuity) with a method of Hadamard. We find a generalized Fresnel equation that is quartic in the wave covector of the wave front. We discuss under which conditions the waves propagate along the light cone. Thereby we derive the metric of spacetime, up to a conformal factor, by purely electromagnetic methods.

Area metric gravity and accelerating cosmology

“…Given that electrodynamics is the historical birth place of the concept of a spacetime metric, this is certainly noteworthy. It is known that electrodynamics may be formulated on any ddimensional smooth manifold without even introducing the concept of a metric [32,33,34].The idea of this so-called pre-metric approach goes back to a paper by Peres [35], and is based on the observation that charges, and in certain situations, magnetic flux lines can be counted, which is nicely explained in [33]. Hence one may define the notions of a field strength two-form F and an electromagnetic induction (d − 2)-form H. The equations of vacuum electrodynamics are then given by dF = 0 and dH = 0.…”

“…In this limit one considers waves as propagating discontinuities in the derivatives of the fields F and of the electromagnetic induction (d − 2)-form H along a wavefront surface described by the level lines of some scalar function Ψ on M. The rays of the wavefront are then given by the gradient p = dΨ. Extending an insightful argument of Hehl, Obukhov and Rubilar [33,34], where a detailed derivation may be found, to arbitrary dimension d, we find that the wavefront gradients must obey the Fresnel equatioñwhereG is the totally symmetric tensor density of weight −2 given bỹwith C being the cyclic part of the inverse area metric G −1 as in (3). As explained in appendix A we use the convention that the summation over numbered anti -symmetric indices is ordered, i.e., i 1 < i 2 < · · · < i d−1 and similarly for the j k .…”

Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

“…One can gain further insight into the wave propagation by decomposing the constitutive tensor into the three irreducible parts [18,19] …”

Dimensions and units in electrodynamics

“…(1) and (2). Clearly, the spacetime relations (18) are perturbed by the vacuum polarization of QED, provided a semiclassical approximation is sufficient.…”