Ohmura’s extended electrodynamics: longitudinal aspects in general relativity

Abstract

Jiménez and Maroto ((2011) Phys. Rev. D 83, 023514) predicted that free-space, longitudinal electrodynamic waves can propagate in curved space-time, if the Lorenz condition is relaxed. The present work studies this possibility by combining and extending the original theory by Ohmura ((1956) Prog. Theor. Phys. 16, 684) and Woodside's uniqueness theorem ((2009) Am. J. Phys. 77, 438) to general relativity. Our formulation results in a theory that applies to both the field-(E, B) and potential-(Φ, A) domains. We establish a self-consistent, longitudinal wave-propagation theory for the microscopic longitudinal part of the electric field (E L ). We first show that the product of the parameters used previously for the extension of classical electrodynamics can be expressed as a superposition of microscopic displacement modes, which are confined to the energy shell, |ω|=cq. We then show that nonlinear electrodynamic mixing allows creation of longitudinal waves in the near-field region of a source. A propagator approach gives substantial physical insight into the emission process.

Implications of Gauge-Free Extended Electrodynamics

“…Equation 13explicitly decomposes J into solenoidal (∇× B) and irrotational (∇C) parts, in accord with the Helmholtz theorem. The new terms in Equations (13) and (14) change only the irrotational (longitudinal) electrodynamics, as elucidated by Keller and Hively [82,83]. These irrotational components sre gauged away in CED by Equation 3.…”

“…Other work examined extended electrodynamics or the effects of relaxing the Lorenz gauge: Fock and Podolsky [53] [82,83] in 2019; and Haralick [84] in 2018. Other recent works are relevant [85][86][87][88][89].…”

“…Keller and Hively [82,83] published a GR-extension of EED, showing that only the longitudinal dynamics are changed by EED, allowing elucidation of the SLW and its source. The work [82] is important, because: (i) the Cand E L -fields do not cancel, as in QED but rather form the SLW; (ii) a dispersion relation arises for E L -waves in terms of the Hubble constant (H o ) and the E L wave-vector amplitude (q o ); and (iii) this approach is a first-principles path to an EED-quantum theory that includes acceleration and gravity.…”

“…The work [82] is important, because: (i) the Cand E L -fields do not cancel, as in QED but rather form the SLW; (ii) a dispersion relation arises for E L -waves in terms of the Hubble constant (H o ) and the E L wave-vector amplitude (q o ); and (iii) this approach is a first-principles path to an EED-quantum theory that includes acceleration and gravity. The work [83] is important, because: (iv) C and γ (scale factor in Equation (7)) allow consistency between E L and A µ ; (v) γC arises from superposition of longitudinal fields on the energy shell, |ω| = cq; and (vi) free-space SLWs can be emitted by nonlinear, electrodynamic mixing. A quantum-gravity simulation of a spherically-symmetric, lattice with a stationary metric produces polarized regions of positive and negative curvature [71].…”

The Proton and Occam’s Razor

“…Prior to [22,11], gaugeless electrodynamics has been already introduced and explored by other authors [1,18,19,21,29,30,31,33,34,39,41]. Most of these preceding works introduce the electromagnetic scalar eld as an additional entity besides charges and currents, rather than the entity that actually produces the apparent charges and currents.…”