2026-10-04 MDPI (Symmetry)

URL: https://www.mdpi.com/2073-8994/12/12/2110 (read in Chrome; the direct PDF download was refused to a script, returning HTML, so no file was saved).

D. Reed and L.M. Hively, "Implications of Gauge-Free Extended Electrodynamics", Symmetry 12(12):2110 (2020). Funding: none declared. Conflicts: none declared. Hively is the inventor on US 9,306,527, which the paper discusses (see google-patents note), so he is an interested party on the patent's technology.

What it says [web]: - Extended electrodynamics (EED), from the Stueckelberg Lagrangian, has a scalar field C "that equals the quantity usually set to zero as the Lorenz gauge", the same quantity as van Vlaenderen's S. The new terms are -∇C in Ampère's law and ∂C/∂t in Gauss's law, the same structure as the author's 2003 eqs 18-19. - It predicts a "scalar-longitudinal wave (SLW)" with E along the direction of travel plus C, carrying energy and momentum, and a "scalar wave (SW)" carrying energy only. It also predicts a force J·C parallel to the current and a power term ρC/(εμ). These match the author's longitudinal force J·S and power term (ρ/ε0)S (claim 2). - Lists earlier work on relaxing the Lorenz gauge, including "van Vlaederen [62,63] in 2001-2003" (sic), with Fock and Podolsky 1932, Stueckelberg 1938, Ohmura 1956, Aharonov and Bohm 1963, Woodside 1999-2009, Arbab, Hively and Giakos, Modanese, and others. - Experimental claims (all by the authors' account; "preliminary"): the SLW is "unconstrained by the skin effect", with "propagation through thousands of skin-depths of solid copper" reported in Hively and Loebl 2019 [3]. Other evidence it cites: Monstein and Wesley; Graneau and Hering longitudinal-force tests; a Russian solar-eclipse measurement with copper spheres in a Faraday cage; X-ray angular distribution in tape peeling; the TESLAR watch; solar-correlated variation of radioactive decay rates. The paper itself says several of these "need replication". - On the vector potential: it cites the Maxwell-Lodge effect (Rousseaux et al.), Daibo's vector-potential transformer, and Varma's electron-beam work as evidence of a physical curl-free A. - It notes that with long-time charge conservation C obeys a source-free wave equation, and it puts the source of C in short-time charge non-conservation (particle-antiparticle fluctuations).

Bearing

Priority 2 (supporting theory plus claimed preliminary tests) and priority 3 (closely related work). It is the clearest published case of independent researchers (one at Oak Ridge National Laboratory, retired) working with the same S field and the same predicted J·S force and power terms as claim 2, and reporting a bench test (the no-skin-effect copper test). The test report itself (Physics Essays 2019) is paywalled and was not read.