A generalisation of classical electrodynamics for the prediction of scalar field effects
Koen J. van Vlaenderen
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In one page
Koen van Vlaenderen asks a question that standard electrodynamics answers by assumption rather than by measurement. Maxwell’s equations are written in terms of two potentials, and there is one combination of their rates of change — he calls it S — that the textbooks are free to set to zero, because nothing in the equations depends on it. That choice is the Lorenz gauge. Van Vlaenderen’s proposal is to stop choosing, and instead let S be a real, measurable field. Add its derivatives back into the Gauss and Ampère laws and you get the same potential wave equations without needing any gauge condition at all, and the ordinary Maxwell equations return exactly when S is zero. What is new is what comes with it: a longitudinal electro-scalar wave in vacuum, a force that pushes along a current rather than across it, and power drawn from static charge in the presence of a changing S. He argues Tesla was optimising exactly this quantity.
Why it matters hereChapter 10 is built on the claim that the potentials are physical and that what they control is phase and structure, not merely bookkeeping. This paper takes that one step further and asks whether the piece of the potentials that gauge freedom throws away is itself a field with observable effects — longitudinal waves, longitudinal forces, and a power term that involves static charge. It is the clearest statement of the scalar-wave programme’s testable content. Read it beside the author’s fuller treatment at /library/stm-3c776cfafe, and the Weber-force line of the same argument at /library/stm-bc8f1e5c8c and /library/stm-717b3fa832.
What it claims
01Classical electrodynamics contains a scalar expression S, defined as minus the vacuum permittivity times the vacuum permeability times the rate of change of the scalar potential, minus the divergence of the vector potential. The Lorenz gauge condition is simply the choice to set this quantity to zero. Van Vlaenderen argues that treating S as unphysical is a presumption built in before the gauge transformation is even introduced, and that the argument for it is therefore circular rather than experimental.Section I, Introduction, Equations 7 and 15
What to watch02Adding derivatives of S back into the Gauss and Ampère laws — in the same spirit in which Maxwell added the displacement current — yields the inhomogeneous potential wave equations automatically, with no gauge condition required. The generalised equations reduce exactly to the Maxwell-Heaviside equations in the special case where S is zero, so the Lorenz condition survives as a physical condition rather than as a free choice.Section I, Introduction, Equations 18 to 21
What to watch03Because charge is conserved, S obeys a homogeneous wave equation, so the theory expects sources of dynamic scalar fields and not of static ones — which is why, on this account, S was never found by the simple static experiments that revealed the electric and magnetic fields. The named exception is collective quantum tunnelling, for instance at Josephson junctions, because tunnelling read classically is a local violation of charge continuity and could therefore induce a static scalar field.Section II, The induction of scalar fields, Equation 24
What to watch04The generalised power and force theorems produce four new terms with physical readings. The Poynting vector becomes the electric field crossed with the magnetic field minus the electric field times S. The square of S is the energy density of the scalar field. The term charge density times S divided by the permittivity is applied power drawn from static charge in the presence of a dynamic scalar field. And the term current density times S is a longitudinal force, always parallel to the current, which the standard field stress tensor cannot produce.Section III, Generalised power/force laws, Equations 33 and 34
What to watch05Setting the magnetic field to zero in the generalised equations leaves a pair of wave equations whose solution is a longitudinal electro-scalar wave in vacuum — a wave with no magnetic component, carrying energy in the direction it travels. This is the theory’s sharpest testable prediction, and the scalar field behaves, in the author’s phrase, like a scalar form of magnetism: it acts on current elements and it interacts with the electric field in vacuum.Section III, Equations 35 and 36
What to watch06Four bodies of existing measurement are offered as qualitative support, with quantitative tests named as the next step: Ignatiev’s spherical-antenna transmission, which found a longitudinal electric wave with the magnetic component excluded and unusually high transmitted energy; Monstein and Wesley’s Europhysics Letters observation of 2002, whose measured energy-flux and energy-density laws match the generalised power theorem once S is admitted; the longitudinal forces seen in the exploding-wire work of Nasilowski and Graneau; and the finite propagation speed of the Coulomb interaction reported by Tzontchev, Chubykalo and Rivera-Juárez. Van Vlaenderen also reads Tesla’s resonant transformer — low-capacity spherical capacitor, low self-induction pancake coil, a million volts — as a machine deliberately optimised for the rate-of-change-of-potential half of S.Section IV, Experimental Evidence, parts A to C; Section V, Conclusions
What to watch
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Abstract
Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be unphysical. However, these scalar expressions might have the meaning of a new physical field, S. If this is the case, then a generalised CED is required such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED. The IPWE are viewed as a generalised Gauss law and a generalised Ampère law, that also contain derivatives of S, after reformulating the IPWE in terms of fields.
Since charge is conserved, scalar field S satisfies the homogeneous wave equation, thus one should expect primarily sources of dynamic scalar fields, and not sources of static scalar fields. The collective tunneling of charges might be an exception to this, since quantum tunneling is the quantum equivalent of a classical local violation of charge continuity. Generalised power/force theorems are derived that are useful in order to review historical experiments since the beginning of electrical engineering, for instance Nikola Tesla’s high voltage high frequency experiments. Longitudinal electro-scalar vacuum waves, longitudinal forces that act on current elements, and applied power by means of static charge and the S field, are predicted by this theory. The energy density and field stress terms of scalar field S are defined.
Some recent experiment show positive results that are in qualitative agreement with the presented predictions of scalar field effects, but further quantitative tests are required in order to verify or falsify the presented theory. The importance of Nikola Tesla’s pioneering research, with respect to the predicted effects, cannot be overstated.
The way in
https://arxiv.org/abs/physics/0305098Posted to arXiv in 2003 under the pre-2004 assumed licence, which is not a Creative Commons licence, so only the abstract is reproduced here — taken from the paper itself, which carries three paragraphs the arXiv listing abridges. Author affiliation on the paper: Institute for Basic Research.
How to cite it
Koen J. van Vlaenderen (2003) A generalisation of classical electrodynamics for the prediction of scalar field effects. arXiv:physics/0305098
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