van Vlaenederen Koen · Source catalogue

A 6-page theoretical paper (plus references) that builds on Hofer's Material Wave Theory (MWT). It takes the quantum wave function psi to be a real, physical charge density, attaches a velocity u to it, and defines electric and magnetic fields and potentials from psi and u (eqs 2.4-2.12). It shows that the Lorenz gauge condition is the mass (or charge) continuity equation when A is proportional to rho*u and Phi to rho*u^2 with constant speed |u|, and that Maxwell's equations then follow, but with propagation speed u = 1/sqrt(eps*mu) rather than c unless u = c is set later. The deep reader notes that the sources are defined as the wave operator acting on the potentials, so the 'derivation' is the textbook Lorenz-gauge route run backwards. The 'self-potential' step replaces a constant by -rho/2 so that rho_s = rho = psi, giving self-potential equations (3.11-3.14); a point of space is a 'source' only where psi satisfies them. The reader found these reduce to one equation of Klein-Gordon form with a tachyonic-sign mass term, not mentioned in the paper. A mechanical copy of the same structure (3.17-3.27) is said to give 'the law of gravity in differential form' (3.23) but no link to Newton's G. The energy identity (1/2)rho_mass*u^2 + field energy = rho*Phi (3.16) is asserted and then shown (3.28) to follow from the two self-potential equations; the reader verified the algebra symbolically and found that it means field energy equals kinetic energy, and that the two self-potential equations may hold only at isolated points or curves. Setting |u| = c gives total energy density rho_mass*c^2 = rho*Phi (5.1), offered as the link between two mass models: electrostatic mass (Petkov, Collins; mc^2 = q*Phi) and Zero Point Field (ZPF) mass (Haisch-Rueda-Puthoff, stochastic electrodynamics). No ZPF quantity enters any equation. A units section sets C = 1 with charge density squared = mass density, giving charge = sqrt(kg m^3), and the author reads the 3/2 exponent as a fractal dimension of 3/2 for a charge's trajectory. The paper has no experiments, data, figures or numerical values.

Key claims

• The quantum wave function psi is a real, physical charge density, and a speed u can be associated with it.
• With A = (rho_mass/rho)u and mass continuity, the Lorenz gauge condition is the mass or charge continuity equation, and Maxwell's equations follow for a matter wave with eps*mu = 1/u^2 and constant |u|.
• A point in space is a source of Coulomb or gravity interaction only if psi satisfies the 'self-potential' equations (3.11-3.12); not all points of space are sources.
• A mechanical analogue of Maxwell's equations built from psi^2 contains 'the law of gravity in differential form' (eq. 3.23).
• For a particle at rest modelled as a massless 'parton' moving at speed c on a fractal path in a closed volume, total energy density equals rho_mass*c^2 = rho*Phi, which relates the electrostatic-mass model and the ZPF-mass model.
• A monochromatic plane matter wave carries no intrinsic electromagnetic energy (g x u = 0), so it cannot describe a particle with intrinsic electromagnetic energy.
• Charge has spatial dimension 3/2 (read from the units sqrt(kg m^3)); a charge may be a point-like particle following a fractal trajectory of dimension 3/2.

Relevance: Earliest of the three papers. Sets out the author's picture of the electron as a self-generated electromagnetic structure and the idea of scalar/longitudinal potentials as physical. It is not on the scalar field S or the longitudinal Ampere force, which carry the later papers. It ties the author to Hofer's MWT, stochastic electrodynamics and Petkov's electrostatic mass.

Mainstream conflict: Mainstream quantum mechanics treats psi as a complex probability amplitude, not a real charge density, and does not tie mass to electrostatic or ZPF energy in this way. The paper's own text says its 'derivation' of Maxwell's equations depends on the choice of definitions and on a constant-speed condition. Its gravity claim is by analogy of form only. The mainstream conflict is largely interpretive since no testable numerical prediction is made.

Defines the scalar S = -eps0*mu0*dPhi/dt - div A (minus the Lorenz gauge expression) and, in the way Maxwell added the displacement term, adds derivatives of S to Gauss's and Ampere's laws: div E - dS/dt = rho/eps0 and curl B + grad S - eps0*mu0*dE/dt = mu0*J (eqs 18-21). The result is the inhomogeneous potential wave equations (16)-(17) with no gauge condition; S is declared physical and observable, and the Lorenz condition S = 0 a special case. The deep reader checked every equation as stated and the paper's own statement of circularity: the usual gauge freedom rests on assuming S has no physical role. The only new field equation is (24): the wave operator on S equals -mu0(div J + drho/dt), so with conserved charge S is a source-free wave. Generalised Poynting and force theorems (33)-(34) contain a scalar energy density S^2/(2 mu0), an energy flux -ES/mu0, a static-charge power term (rho/eps0)S and a longitudinal force term J*S along current elements. Setting B = 0 gives 'longitudinal electro-scalar (LES) waves' (35)-(36) with E parallel to propagation, travelling at c. A source transformation (27)-(28) maps ordinary Maxwell onto the generalised equations. The paper reports no experiment of its own. Section IV cites: Tesla's patents and high-voltage work; Ignatiev (a spherical antenna, speed about 1.2c, magnetic component excluded, error margin said to be under review); Monstein and Wesley (Europhysics Letters 2002, longitudinal polarisation); Tzontchev, Chubykalo and Rivera-Juarez (Coulomb interaction speed approximately c); exploding-wire experiments (Nasilowski, Graneau); Assis and Bueno (Ampere vs Grassmann force laws); Ampere's hairpin. It also says rumours exist of static-charge power conversion but no published experiment is known. The author disputes priority: he says Monstein and Wesley's energy flux and density (37)-(38) require his scalar field and theorem (33) (published in 2001 with A. Waser in Hadronic Journal) and implies they used it without citation. The deep reader notes the pair (37)-(38) is also a conservation law that follows from eq. (16) alone, so the two sides disagree about the physical identification, and that Wesley and Monstein's own paper was not read. Author's summary: results are qualitative; further quantitative tests needed. QE follow-up (deep read, reviewer's derivation, not in the paper): divided by mu0, (33)-(34) are the time and space parts of the 4-force density f^nu = F^{nu lambda} J_lambda + S J^nu, with S = -d_mu A^mu a Lorentz scalar, so the S part is S(c rho, J) and the pair is covariant [checked]. Field-side balance is an identity [checked]. For a point charge this gives dm/dtau = qS: total energy-momentum is conserved only if charged matter's rest (internal) energy changes at c^2 rho S (Reading 1: exchange with internal energy); if rest mass is fixed (Reading 2) the static-charge term has no matter-side counterpart and energy is unbalanced. The paper itself never says where the energy goes: it mentions no mass, internal energy or matter equation of motion, calls (rho/eps0)S 'applied power' (and says 'applied power' should read 'converted power'), and gives no magnitude for S anywhere. Its named sources of S are d(Phi)/dt, div A and non-conservation of charge (eq. 24); the reviewer notes a charging capacitor conserves charge, so by eq. 24 it is not a source term, a tension the paper does not address. Hypothetical illustration: q = 1 microC, S = 1e-6 T gives c^2 q S about 9e4 W and dm/dt = 1e-12 kg/s. The generalised stress-energy tensor is non-symmetric (S energy flux/c^2 is -eps0 E S, S momentum density is +eps0 E S), so angular-momentum conservation is not addressed. Also from the paper (p.8): Ignatiev reports that 'transmitted energy was unusually high' (single-source, no numbers given), a second reported anomaly besides the phase velocity.

Key claims

• The scalar S = -eps0*mu0*dPhi/dt - div A is a physical, observable field, not a gauge artefact; the Lorenz condition S = 0 is a special case, not a gauge freedom.
• Adding S-derivative terms to Gauss's and Ampere's laws (eqs 18-19) gives the potential wave equations without any gauge condition.
• Longitudinal electro-scalar (LES) waves exist in vacuum with E parallel to the direction of travel, no B, and speed c, carrying energy flux -ES/mu0 and energy density S^2/(2 mu0).
• A longitudinal force J*S acts on current elements along the current direction, which the standard stress tensor cannot describe.
• A scalar field S can turn a static charge density rho into an electrical power source through the term (rho/eps0)S in the power theorem.
• Collective quantum tunnelling, as at Josephson junctions, is a local violation of charge conservation and might induce a static scalar field.
• Experiments by Tesla, Ignatiev, Monstein and Wesley, Tzontchev et al. and the exploding-wire work are in qualitative agreement with these scalar-field effects.
• Monstein and Wesley's flux and energy density (37)-(38) cannot be derived from the potential wave equation alone but need S and theorem (33), which the author published first (2001).
• Ignatiev's spherical-antenna experiment is reported (p.8) to have shown unusually high transmitted energy as well as a phase velocity of about 1.2c (no numbers given for the energy).
• Total energy-momentum of the generalised theory closes only if charged matter's rest (internal) energy changes at c^2 rho S (reviewer's derivation from theorems 33-34; the paper itself does not state where the energy goes).

Relevance: Core statement of the author's scalar-field theory (Phi, A, S) and the longitudinal-wave programme, and the first paper in the set to cite experimental support (Tesla, Ignatiev, Monstein-Wesley, Graneau). It is the root of later papers' Phi/LEM wave work. Priority basis: the 2001 Hadronic Journal paper with A. Waser (origin of theorem 33) and a 2002 conference draft are in research/files but have not been read in full (page-image reading needed).

Mainstream conflict: Mainstream electrodynamics regards S (the Lorenz-gauge quantity) as gauge-dependent and not observable, with the Lorenz condition a free choice, and says free-space waves are transverse. The theory differs observably from standard Maxwell only when charge is not conserved, since for conserved charge S is a source-free wave and eq. (24) shows ordinary charge conservation holds exactly when S satisfies the homogeneous wave equation. The proposed power conversion from static charge and the J*S force have no accepted experimental support. The paper itself reports no quantitative test.

The most developed paper. Starting from the claim that the Ampere (Grassmann) force between open-circuit stationary currents violates Newton's third law (N3LM), it adds a curl-free 'scalar magnetic field' B_l = -div A_l and a longitudinal Ampere force J*B_l, with the force kernel (2.6) antisymmetric as required (checked). B_l is zero for closed stationary circuits (deep reader's check), so the change matters only for open circuits. Using the Helmholtz theorem (split into curl-free 'l' and divergence-free 't' parts) the author argues Maxwell's E includes an unneeded induced field E_l; dropping it gives a 'simple Maxwell' theory equivalent, per the deep reader, to Maxwell in the Coulomb gauge, which the author says satisfies N3LM only for closed circuits. He generalises with new displacement terms (4.1-4.3), postulated by analogy with Maxwell's displacement current, and three vacuum wave types: Phi waves (speed a), longitudinal electromagnetic (LEM) waves (speed b) and transverse electromagnetic (TEM) waves (speed c). Requiring the force law to read rho*E + J x B_t + J*B_l fixes b = c (a requirement, not derived from a separate principle), and rejecting the Lorenz condition and the 'v-gauge' of his own 2004 chapter gives a >> c (Phi waves superluminal, i.e. Coulomb-like). The deep reader found eq. 4.22, offered as the selector, is the continuity equation and holds for any a. Power and force theorems (4.33-4.34) check as identities; in the paper's own equations open-circuit magnetostatics still has time-varying field momentum, which bears on its claim that it is free of electromagnetic momentum. The paper adopts D.E. Rutherford's solution of the 4/3 problem: with the extra LEM momentum eps0*B_l*E the electron momentum mass equals the energy mass (4.35-4.36). The reader's shell calculation reproduces the sum of 2/3 + 1/3 of mu0 q^2 v/(4 pi R) but shows agreement requires a self-energy twice the standard eps0 E^2/2, which conflicts with the paper's own eq. 4.33. Retarded solutions (4.37-4.44) give three near-field and six far-field terms. Section 5 (now deep-read from the text layer, pp.16-21; these are the author's characterisations of others' work, none of the cited originals was read): says Ampere, Gauss and Weber used open circuits; explains the Aharonov-Bohm effect as a longitudinal Ampere force; says no experiment has verified or falsified induction law 3.2; reinterprets Ignatiev and Leus (2.5 km wavelength, 0.5 km distance, phase velocity 1.12c; author attributes the 0.12c excess to data interpretation and expects LEM at c) and Monstein and Wesley (longitudinal polarisation; author assumes divergent currents so LEM waves, not Phi); cites Strebkov single-wire transmission, Podkletnov's 'impulse gravity' signal (reported speed >= 64c, read as a Phi wave), a 'Phi photoelectric effect' to explain T. Henry Moray's radiant-energy device (Harvey Fletcher's signed document as cited by the author), P.N. Correa's abnormal glow discharge and Chernetsky's hydrogen discharge tube. The author calls for revising relativity and quantum mechanics and describes Moray as 'the greatest electrical engineer ever'. QE additions (deep read, pp.16-21): (a) Ampere, Gauss and Weber experiments are asserted to be open-circuit (batteries or capacitor banks 'typically show time varying charge densities'), no sources, dates or numbers; the only 'truly closed circuit stationary current' is a superconductor current induced by an approaching magnet [p.16]. (b) The AB explanation: a longitudinal Ampere force slightly delays or advances electrons depending on the side they pass the solenoid; B_l 'isn't shieldable, apparently'; Caprez, Barwick and Batelaan's null is called 'premature'; the author gives no time-delay figure of his own [p.17]. (c) Induction law 3.2, the author's named test: sinusoidal divergent (curl-free) primary currents induce a curl-free secondary field and currents 90 degrees or more out of phase; 'The first experimenter who verifies this law also verifies the existence of the scalar magnetic field Bl'; no amplitude, frequency or geometry given [p.17]. (d) Wesley-Monstein ball antenna: the author accepts the measurement and rewrites the interpretation from Phi to LEM; he notes Phi-only emission would violate charge conservation, and proposes many-electron macroscopic tunnelling as the only way to emit Phi waves [p.18]. (e) Tesla: 'teleforce' effects from non-dispersive emissions of high-voltage discharges, 'similar to Podkletnov's gravity impulse signal', supported only by refs [28][29]; no dates or voltages [pp.18-19]. (f) Ignatiev-Leus: 2.5 km wavelength, 0.5 km baseline (one fifth of a wavelength), phase velocity 1.12c from comparison with an optical-fibre signal; the author attributes the 0.12c excess to the fibre being slower than c (about 200,000 km/s) and says the signal is 'definitely a far field'; whether the fibre delay was corrected for is not stated [pp.18-19]. (g) Strebkov [6]: 'A very efficient single wire resonant energy transport systems has been developed and tested', no figures. Discriminator: with a ground return the signals are TEM waves; without one 'the electric wave component is longitudinal and the signal is most likely a LEM wave with a unidirectional energy flow of S = (1/mu0) B_l E_l'. The question is posed, not tested: the author assumes no ground return because applications 'do not require grounding' [p.19]. (h) Podkletnov: at least 64c, discharge up to 2 million volts from a superconducting flat electrode, pulse parallel to the discharge, no transverse TEM radiation, read as Phi waves generated by macroscopic tunnelling; the author states the electrodynamic nature 'has not yet been fully investigated by Podkletnov and Modanese'; no timing method or error figure, no replication cited [pp.19-20]. (i) 'Phi photoelectric effect': reception of natural Phi waves by tunnelling; 'has not been researched and it has not been verified nor falsified' [p.20]. (j) Moray: 'kilo Watts of useful electricity, day and night' [16]; Fletcher 'filed a signed document [9]'; germanium cold-cathode detector tube; first stage at least 200,000 V; the author calls him 'the greatest electrical engineer ever'; no dates, figures or witnesses beyond Fletcher; the Fletcher document itself is not quoted [p.20]. (k) Correa [5] and Chernetsky [4]: excess energy attributed to the Phi photoelectric effect; no input/output figures [p.21]. (l) Conclusions [p.21]: Maxwell-Lorentz force is wrong w.r.t. N3LM and Lorenz-gauge Maxwell is 'far field inconsistent'; calls for revising relativity and quantum mechanics; 'We suspect the ratio a/c has fundamental physical meaning'; cites Caroline H. Thompson's Phi wave aether [24]; advises teaching the Helmholtz theorem. Far-field inconsistency argument (follow-up deep read, pp.8-10, 21): the paper's premise is its own definition that 'far fields are defined as two mutually inducing fields', and it says two 'longitudinal' 1/r terms in the Jefimenko-form field (3.18, the d rho/dt and dJ_l/dt terms) are therefore unexplained, while its 'simple Maxwell' field (3.16) is far field consistent. Explicit calculation for an oscillating point dipole (reviewer's check, [check] SymPy-style closed forms): each longitudinal term is real as an integrand piece (each radial, 1/r) but they cancel exactly, so 3.16 and 3.18 give identical E and B everywhere and the total far field is purely transverse, with B = n x E/c. The two readings of 'longitudinal' differ (radial vs curl-free in the Helmholtz sense). The argument is therefore a statement about splitting one integral into terms plus the author's definition, not about a difference between the two forms of the field; it does hold within the author's own Section 4 theory, in which longitudinal currents propagate at their own speed.

Key claims

• The Maxwell-Lorentz (Grassmann) force law between current elements violates Newton's third law for open-circuit stationary currents, and adding the longitudinal force J*B_l restores it.
• The scalar B_l = -div A (the 'scalar magnetic field') is a physical field that mediates a longitudinal Ampere force and is not a gauge artefact.
• A time-varying B_l induces a curl-free electric field E_l (law 3.2) that Maxwell's electrodynamics does not describe; this induction has not yet been verified or falsified by experiment.
• Maxwell's theory in the Lorenz gauge is far-field inconsistent, and the Lorenz condition is invalid.
• Three vacuum waves exist: Phi (speed a >> c), LEM (speed b = c) and TEM (speed c); the force law agrees with N3LM only if a >> b and b = c.
• Rutherford's solution of the 4/3 problem of electromagnetic mass is supported, because the LEM field momentum eps0*B_l*E supplies the missing factor.
• The Aharonov-Bohm effect is a longitudinal Ampere force on electrons, so the vector potential is a classical physical quantity.
• The signals of Ignatiev-Leus and Monstein-Wesley are LEM waves at speed c (not 1.12c); Podkletnov's gravity-impulse signal (>= 64c) is a Phi wave.
• Moray's radiant-energy device and the Correa and Chernetsky discharge tubes may operate through a 'Phi photoelectric effect', converting natural Phi or LEM radiation into useful electricity.
• Ampere, Gauss and Weber's historic magnetostatic force experiments all used open circuits (batteries, capacitor banks); the only truly closed stationary circuit current is a superconductor current induced by a magnet.
• Strebkov's single-wire resonant energy transport is a LEM-wave system if it has no ground return, with energy flow S = (1/mu0) B_l E_l; the author assumes no return.
• Tesla observed 'teleforce' effects from non-dispersive high-voltage discharge emissions, similar to Podkletnov's impulse signal.
• Ignatiev-Leus: the 1.12c phase velocity is a misinterpretation caused by slower light in the optical fibre; the signal is a far field at luminal speed.
• Induction law 3.2 is the discriminating test: sinusoidal curl-free primary currents induce a curl-free secondary field 90 degrees or more out of phase; verification would verify B_l and the physicality of A.

Relevance: The author's mature, most comprehensive statement; it ties together the scalar potentials of paper 2 with the Ampere-force and N3LM argument, the Helmholtz decomposition and a wide claimed experimental base including Tesla, Moray and Podkletnov. It is the paper where wave-speed hierarchy a >> b = c appears.

Mainstream conflict: Mainstream electrodynamics treats B_l (the divergence of A) as gauge-dependent and not physical, holds that Maxwell plus the Lorentz force conserves total (mechanical plus field) momentum, with the open-circuit 'violation' balanced by field momentum eps0 E x B, and treats Lorenz and Coulomb gauge fields as the same physical field. It has no superluminal Phi waves and regards the Lorenz condition as a free choice. The deep reader notes the 'simple Maxwell' theory is the Coulomb gauge. Moray, Podkletnov, Correa and Chernetsky effects are not accepted mainstream results. Follow-up calculation (oscillating dipole, deep read section 7): Coulomb-gauge and Jefimenko (Lorenz-gauge) expressions give the identical field, so the 'far-field inconsistency' is not a difference between two physical fields.