Historical research guide · 0621 · 2016
General Classical Electrodynamics
Koen J. van Vlaenderen
In one minute
Koen van Vlaenderen argues that the standard Maxwell-Lorentz theory has three loose threads, and that pulling them yields a larger theory rather than a smaller one. The threads: the usual force law breaks Newton’s third law for circuits whose current diverges at a source or sink; Jefimenko’s general solution contains two long-range electric terms that fall off like a wave but have no partner field to wave with; and the classic calculation of a charged sphere’s energy and momentum comes out wrong by a factor of four-thirds. His remedy is to restore a scalar magnetic field alongside the familiar vector one, recovering the reciprocal force law Whittaker wrote down. The enlarged theory keeps ordinary light exactly as it is and adds two longitudinal waves: one carried by the current potential at light speed, and one carried by the charge potential at a speed he argues must be far greater. Setting that speed equal to light speed collapses the theory back to Maxwell’s — and reintroduces the inconsistencies.
Connection
Chapter 10 is built on the claim that Maxwell’s equations, honestly decomposed, already permit longitudinal solutions and give the potentials physical standing; this paper is the fullest published attempt to write that theory down with its force law, its energy accounting and its named experimental tests. Chapter 6 takes the last section seriously: if a natural longitudinal wave field exists, receiving it is an energy technology, and chapter 2 gains a medium that supports sound-like modes rather than only transverse ones.
From the source
The Maxwell-Lorentz theory is charged with three specific inconsistencies. First, its force law violates Newton’s third law for stationary current distributions whose divergence is non-zero — real circuits fed by a battery or a capacitor bank — which would mean momentum is not conserved, for which there is no experimental evidence. Second, Jefimenko’s general electric field solution contains two longitudinal far-field terms that fall off with distance like waves but have no partner fields to induce them, so they cannot be waves. Third, the ratio of the electrodynamic energy to the momentum of a uniformly moving charged sphere carries the well-known and incorrect factor of four-thirds.Abstract; Sec. 1, Introduction
The proposed repair is to restore the scalar magnetic field — minus the divergence of the vector potential — as a physical field alongside the vector magnetic field, and to add its force to the Lorentz force. This reproduces Whittaker’s reciprocal force law, which does satisfy Newton’s third law for open-circuit stationary currents, and it makes the potentials determinate: the gauge freedom of the standard theory is treated as a symptom of the missing field rather than as a principle.Sec. 2; Sec. 3.1; Sec. 3.5
The enlarged theory predicts two longitudinal wave types alongside the ordinary transverse electromagnetic wave. The longitudinal electromagnetic wave is carried by the curl-free part of the current potential and travels at the speed of light; the potential wave is carried by the charge potential alone, is not induced by currents at all, and travels at a velocity the theory requires to be much greater than the speed of light. Setting that velocity equal to the speed of light — the Lorentz premise — collapses the theory back to Maxwell’s and restores its inconsistencies; requiring it to be far greater — the Whittaker premise — is what makes the force law reciprocal.Sec. 3.4, Eqs. (3.22)–(3.27); Sec. 3.5
The theory claims experimental support already on the record. Measurements of a uniformly moving electron beam report that the Coulomb near field is rigidly carried by the beam itself rather than arriving with the retardation the standard solution requires. Ampère’s hairpin experiment and the stationary-current motors of Marinov and Nikolaev are presented as demonstrations of the longitudinal Ampère force, and Nikolaev’s reading of the Aharonov-Bohm phase shift is that it is a longitudinal force that delays or advances electrons passing either side of a shielded solenoid without deflecting them.Sec. 4.1; Sec. 4.2
Longitudinal transmission has been tested directly. Wesley and Monstein, and later Ignatiev and Leus, drove centrally fed ball antennas and confirmed the longitudinal polarity of the received electric field, the latter at a wavelength of 2.5 km over half a kilometre; van Vlaenderen reads both as detections of the light-speed longitudinal electromagnetic wave rather than of the faster potential wave. Podkletnov’s impulse generator, in which a two-million-volt discharge from a superconducting electrode emits a pulse along the discharge axis at a speed of at least sixty-four times the speed of light over 1211 metres, is read as the potential wave.Sec. 4.4; Sec. 4.5
The application the paper puts first is energy: converting naturally occurring longitudinal electric far fields into electricity. A high-frequency potential wave would penetrate the earth and its atmosphere far deeper than an electromagnetic wave, and the paper proposes that receiving one requires the fastest available electron motion — quantum tunnelling through a barrier — which is why negative-resistance and negative-conductance oscillators built on cold-cathode tunnelling and avalanche effects are named as the candidate receivers. Named next measurement: Nikolaev’s induction law, that a divergent primary current induces a divergent secondary electric field ninety degrees or more out of phase, has never been tested.Sec. 4.3; Sec. 4.5; Sec. 4.6
The way in
https://doi.org/10.13189/ujpa.2016.100404How to cite it
Koen J. van Vlaenderen (2016) General Classical Electrodynamics doi:10.13189/ujpa.2016.100404