The concept of the metric tensor should be treated as a model, not as an actual and physical fact, it seems to me.

*List comment: Because the vacuum can be polarized, it is reasonable to assume that charge is everywhere, thus it may be a non-sequitor to consider that E x B/H only works in the presence of charge. Maxwell’s original equations made a dozen assumptions, one of which was that there was an aether.*

To determine which of Maxwell’s equations do not depend on a metric, please refer to “Transformation behavior of Maxwell’s PDE’s.” and “Charge as a Pseudo-Scalar”

Also see “Spinors, Minimal Surfaces, Torsion, Helicity, Chirality, Spin, Twistors, Orientation, Continuity, Fractals, Point Particles, Polarization, the Light Cone and the Hopf Map.”

A connection is established between all the concepts in the title!

Maxwell’s equations still hold as valid. In my view, Maxwell’s aether has never been empirically refuted. I hold that there is a sub-quantum aether in addition to the quantum aether which is described by Wheeler in his geometrodynamics, which according to Wheeler’s calculations, is a sea of energetic fluctuations (called “quantum foam”) with an energy density of 10 e94 g /cc per individual fluctuation. (Correcting the erroneous figure I gave last week, from cross-connected memory, of 10 e72 g/cc.) These fluctuations are also known as the Zero Point Energy fluctuations. Wheeler derived this value by inserting the empirical observations used to generate the ZPE’s spectral energy-density expression of quantum mechanics, into the stress-energy tensor of general relativity.

According to Wheeler’s “Geometrodynamics” [Academic Press, NY], The high frequency modes of the ZPE result in a huge local energy densities, resulting in space-time warps, similar to the black hole solutions of relativity, which Wheeler called “wormholes”. Wheeler’s “wormholes” channel electric flux between two separate locations in a 3D space or between our 3-space and other 3D universes, which universes are in what Wheeler called a “super space”. In our local 3-space, these wormholes look like primitive charged particles or “mini holes”, as Wheeler called them, whose polarity is determined by the direction of the electric flux. This electric flux normally passes orthogonally through our universe from a 4th physical dimension. According to Wheeler, small residual components of this flux can become aligned in our particular 3-space to manifest the zitterbewegung and the ZPE. This electric flux, as described by Wheeler, is shown to enter through what he calls “mini white holes” and exits our universe by way of what he calls “mini black holes”. According to Wheeler, this is the basis mechanism of pair production. [Pairs of electrons and positrons] These pairs are constantly being created and annihilated in a fluctuating state of chaotic turbulence, resembling that of a turbulent plasma.

This is an ideal foundation upon which to model QED’s “virtual charge” activities. Thus, Wheeler’s model of the vacuum is an already unified field theory which combines QM and relativity theory, resulting in a specific model for the vacuum, which, when viewed from 3-space, looks like a turbulent plasma at the scale of the Planck length and below. The actual curvatures of 3-space created by the hyperflux of charge are calculated to be on the order of 10 e-66 cm^-2. Wheeler’s charge pairs can easily be seen to be consistent with Kiehn’s Falaco Soliton Pair descriptions. It seems to me, as I have expressed before on this forum, that these charge pairs may well remain superluminally connected, in a manner similar to Falaco solitons, by a hyperdimensional thread, regardless of the degree of separation of the particles in 3-space. Since the goal of Wheeler’s geometrodynamics was to model the behaviors of elementary particles, and since the ZPE flux is orthogonal to 3-space, some kind of vortex flow is required by Wheeler’s expressions so that the elementary particles can persist in 3-space. Now, here we are, back to Maxwell’s original hyperdimensional aether vortex description of elementary particles.

Do you see the connection?

Heaviside could not understand quaternions. So he dispensed with them. Unfortunately, Heaviside had a large influence on subsequent studies of E/M, which excluded the original quaternionic expressions of Maxwell, and thus excluded a wealth of information regarding the true nature of E/M. The most unfortunate exclusion which resulted was the understanding that charge has a hyperdimensional component of flux. This is expressed in the quaternionic version of the Maxwell equations, but has vanished from Heaviside’s truncations of the original equations, as found in common use today.