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Meyl-Konstantin: Mathematician review (STEP 2)

Reviewer: PhD mathematician. Date: 2026-10-08. Scope: derivations, notation, units and hidden assumptions in the seven claims of claims.md. Verdicts use the prompt.txt scale. Tags: [read] from the project documents or the deep reads, [calc] my own computation (SymPy/NumPy in the project venv, 2026-10-08), [web] with URL, [memory] with confidence.

Inputs read: claims.md, facts.json (summaries), every file in deep/ (all 19), the digests that bear on the claims, sites.md "Leads for review", research/ notes (Bruhn, IGF Wayback, patents, k-meyl.de), and research/files/kmeyl-NET_Protonradius.pdf. Not re-read from the PDFs: the equations were verified from the deep readers' page-image transcriptions, then re-derived by me.

Source gap (repeated from claims.md): in the 2003 textbook only ch.5, 7, 11-13, 21-23, 26-30 were deep-read from page images. The free-energy device chapters (ch.14-20, incl. Meyl's own 1989-1999 experiments in ch.19) rest on digests only. No verdict below depends on them. The Treskatis 2010 thesis (the only measured capacitor data) and Meyl's PIERS 2012 paper (the vortex-loss formula) are not in the folder; where a verdict turns on them I say so.

0. The mathematical core in one page (for the reader)

Everything Meyl builds rests on three short steps. I check each below.

  1. Start from E = v x B (1) and H = -v x D (2), where v is the relative velocity of observer and field source. These are the first-order (v much less than c) forms of the Lorentz transformation of the fields [memory, high; Jackson ch.11; Griffiths ch.12].
  2. Take the curl, read the convective derivative (v.grad)B as dB/dt, and get Faraday's and Ampere's laws plus a left-over term b = -v div B. Meyl keeps b, writes it B/tau2 ("potential vortex"), and gets his "fundamental field equation" c^2 Delta E = E_tt + (1/tau1 + 1/tau2) E_t + E/(tau1 tau2).
  3. Treat the divergence part of the vector wave equation as a "scalar wave" of arbitrary speed v; setting tau2 = r/c gives v^2 - vc - c^2 = 0, v = 1.618 c.

Worked example of why step 1 is not a free-standing law, using Meyl's own two equations. Put (2) into (1): E = -mu eps v x (v x E). For E perpendicular to v this is E = (v^2/c^2) E, which holds only if v = c [calc]. Meyl prints exactly this as "result: v = c" (28.5, textbook p.583 [read: deep read]). So his own starting equations force v = c, and the "arbitrary v" of step 3 contradicts them. This is the point Bruhn made in 2003 in words [web: Bruhn pages as quoted in research/2026-10-08-tu-darmstadt-bruhn.md]; the calculation confirms it.

1. Claim 1: "Maxwell's equations are an approximation; the dropped term is the potential vortex"

a. Internally consistent? No, in the strong form. - Correct pieces [calc]: the curl identity (3)/(4); the algebra from (5.1)+(5.4) to the fundamental equation (SymPy: dispersion relation -k^2 c^2 = s^2 + s/tau1 + s/tau2 + 1/(tau1 tau2) matches); all units of the new terms (b in V/m^2; B/tau2 in V/m^2). - Step (6)/(27.10) changes the meaning of d/dt. (v.grad)B is the change seen by an observer moving through a field that is static in the lab; Maxwell's dB/dt in rot E = -dB/dt is the partial derivative at a fixed point. For a pattern B(r - vt) moving with v the fixed-point derivative is -(v.grad)B, the opposite sign [calc; textbook deep read H.1.2]. The "comparison of coefficients" therefore equates two different quantities. Result: (1),(2) are consistent with Maxwell (they are its low-speed frame transformation) but Maxwell does not follow from them [memory, high]. - "Derives Maxwell from textbook transformations, without postulate" fails at three points: (i) j = -v div D is identified with a current by importing Gauss's law (itself a Maxwell equation); (ii) b = -v div B is "kept" only by not imposing div B = 0 (another Maxwell equation, supported by experiment); (iii) in the Objectivity paper (Part 1) the same derivation reads dD/dx x dx/dt = dD/dt and defines j as whatever is left over (dH_o/dx = j), true by construction [read: deep read, Objektivitaetstheorie 1, sect. 3]. - B/tau2 = -v div B forces B parallel to v wherever b is nonzero [calc]. Then B has no transverse part, rot B = 0 for B(x), and the transverse term of the "general wave equation" (26) vanishes. Longitudinal and transverse parts cannot both come from (14). Eq. (25), -|v|^2 grad div B, is only the x-component; SymPy shows the omitted y,z components v^2[0, d_y div B, d_z div B] [calc]. - Within Meyl's own ansatz (E, B perpendicular to v) the x-component of (26) reduces to (v^2 - c^2) d_x(d_y B_y + d_z B_z) = 0 [calc]. Arbitrary v is not supported by the ansatz it is derived from. - Meaning of "div B nonzero": b has exactly the form of a magnetic-current density. Taking the divergence gives d(div B)/dt + div b = 0, so nonzero b needs magnetic charge [calc]. Meyl says monopoles cannot form in vacuum but keeps div B nonzero there; the text does not resolve this [read: Faraday-or-Maxwell p.10; textbook p.572]. - tau2 is internally inconsistent across the book: eq. 5.11 says tau2 ~ musigma (which has units s/m^2, a length squared missing, and goes to 0 in vacuum), while p.70 says vortices are most stable where sigma is smallest. With tau1 = eps/sigma and tau2 = k mu sigma, the product tau1tau2 = k/c^2 is independent of sigma, so term (e) does not vanish in vacuum, contrary to 5.3 [calc; read: deep read ch.5]. No value of tau2 is given anywhere. - Naming errors that matter for the reader: eq. 5.8 (c^2 Delta psi = psi/(tau1 tau2)) is a screened (Yukawa-type) Helmholtz equation with decay length c*sqrt(tau1 tau2), not Poisson's equation; the d'Alembert wave equation is called "Laplace" throughout [memory, high]. Meyl's tau1 = eps/sigma is the textbook charge-relaxation time, not an "eddy-current decay time" [memory, high]. - Meyl's "Laplace versus Maxwell" argument (26.11-26.13): 26.13 comes from applying the vacuum equation (26.12) inside a conductor. Taken at face value its divergence is a diffusion equation with the wrong sign, perturbations grow at rate s = c^2 k^2 tau [calc], so it is ill-posed [read: deep read B.1]. - What Meyl gets right, kept on record: the vector identity Delta E = grad div E - rot rot E is correct; the vector wave equation by itself admits longitudinal solutions; Maxwell excludes them in vacuum through Gauss's law, a separate equation [calc]. In media with mobile charge, longitudinal waves (plasma waves) are ordinary Maxwell-plus-matter physics [memory, high].

b. Consistent with experiment? The extra term b needs magnetic charge in ordinary dielectrics. No free magnetic monopole has been found [memory, high; MoEDAL/CERN searches]. The 2009 HZB result Meyl cites (Morris et al., Science 326, 411) concerns emergent quasi-particle monopoles in spin ice: sources of M and H, while the microscopic B still has zero divergence [memory, high]. Meyl's own citation of it is inconsistent ("[9 Science]" is a Maxwell encyclopedia entry dated 1798) [read: Consequences deep read, 2]. The textbook transformations (1),(2) agree with experiment (generators, Rowland/Rontgen convection currents) but those results support Maxwell-Lorentz theory [memory, high].

c. Tested? The extended Faraday law has no test on record: no value of tau2 means no prediction. The only "test" is the capacitor-loss plot (claim 2).

d. If true: Gauss's law for magnetism would fail inside matter; Maxwell's equations would acquire a dissipative magnetic-current term; the vacuum would need finite tau2 (damping of light in empty space, amplitude exp(-t/2 tau2) for case 1 of 5.12) [calc].

Verdict (split): - "Maxwell is derived as a special case of E = v x B, H = -v x D, so b is a neglected physical term": Internally inconsistent (derivative mismatch; Gauss's laws imported; arbitrary-v contradicts the ansatz). - "Div B is nonzero in dielectrics (magnetic-current term B/tau2)": Tested, not supported in the sense that div B = 0 is supported to the limit of all monopole searches; as a quantitative theory it is Not testable as stated (tau2 has no value).

2. Claim 2: potential vortices explain noise, capacitor losses, near field

a. Mathematics. - "Complex permittivity implies complex c": epsmu = 1/c^2 is the vacuum relation. In a medium epsmu = 1/v^2 with v the phase velocity. A complex eps gives a complex wavenumber k = omegasqrt(mueps): real part gives the phase velocity (real), imaginary part the attenuation. Vacuum c never becomes complex [memory, high; Jackson ch.7, Griffiths 9.4]. Worked example (polypropylene, eps_r 2.2, tan delta 2e-4): n = 1.483, extinction coefficient about 1.5e-4: a slightly damped wave at c/1.483 [read: deep read, About Vortex 4.2]. Refuted by calculation. - Meyl's own relaxation term D/tau1 in Ampere's law is equivalent in the frequency domain to eps(1 + 1/(j omega tau1)), a complex permittivity. So "you cannot use both" is false [read: deep read]. - "Constant tan delta contradicts hysteresis": backwards. Rate-independent hysteresis loses fixed energy per cycle: power P is proportional to f, tan delta constant [calc]. Constant or slowly rising tan delta of polymers is the standard Jonscher / distributed-relaxation behaviour [memory, high]. - Noise formula hf/(1 - exp(-hf/kT)) is the quantum noise form with a full hf of zero-point term where Callen-Welton has hf/2 [read: deep read]. Its crossover kT/h is 6 THz at 293 K (7.8 THz at 373 K) [calc]. The capacitor tan delta rise in Meyl's Fig. 11 is at 0.1-100 kHz, eight to ten decades lower. The "same characteristic course" is a comparison of shapes on unscaled axes [read: deep reads]. - Magnitude check: 100 W into an antenna of 80% efficiency loses 20 W; thermal noise power kTB in 1 MHz at 290 K is 4e-15 W. Ratio about 5e15. "20% loss = 20% noise" is off by 15 orders [calc; read: textbook deep read B.2]. - Fig. 11 (the only measured data): three straight lines, vertical axis tan delta from 1 to 10000 with no multiplier (must be times 1e-4 or 1e-3), no capacitance, voltage, temperature, instrument, formula or fitted parameters; caption says "qualitative". The "orthodox" comparator is a single Lorentz oscillator (tan delta proportional to f, slope 1) which nobody uses for a polyester film at audio frequencies. A flat dielectric term plus electrode series resistance (tan delta_ESR = omega R_s C: e.g. 1 microfarad, 10 milliohm gives 6.3e-6 at 100 Hz and 6.3e-3 at 100 kHz [calc]) reproduces "flat then rising" with no new physics [read: deep reads]. Measured slope 0.24 per decade is typical of ordinary MKT behaviour [memory, medium]. - Fig. 12 circles (450 V, 60 Hz, 100 C, 110x) are Yializis 1980 photographs, titled electrode corrosion; the Meyl paper cites Taylor 1984 for a mechanism and still calls the cause "unsolved". Radial growth from a nucleus between 40 h and 52 h is what a spreading front does [read: deep read]. - Noise from rolling up of a wave (f = c/(2 pi r), uniform spread of radii) gives a 1/f-weighted, not flat, spectrum; no calculation in the papers [calc; read: deep read].

b. Experiment. The mainstream explanation (fluctuation-dissipation: loss and noise are linked, Nyquist 1928) already predicts a loss-noise correspondence for a thermal reason [memory, high]. Antenna noise is sky, ground, man-made and thermal.

c. Tests. One qualitative plot from a 2010 bachelor thesis (Treskatis, Konstanz); not in the folder, not peer reviewed as thesis; the paper was in an Ashdin journal and in PIERS proceedings; OMICS/Ashdin publishers carry the FTC/Beall caveats noted by the deep readers [read: deep reads; memory, medium for Beall]. No replication.

d. If true: dielectric loss theory (Debye, Cole-Cole, Jonscher) would be incomplete and Kramers-Kronig causality of eps(omega) would need a different carrier.

Verdict (split): "complex eps implies complex c is physically wrong": Refuted by calculation. "Capacitor loss is vortex decay": Never properly tested (no formula, no raw data, comparator not the mainstream model; the deciding record is Treskatis 2010 plus PIERS 2012). "Antenna noise is the scalar part": Refuted by calculation for the 20%-equals-noise magnitude; otherwise Not testable as stated.

3. Claim 3: vortices travel as longitudinal scalar waves of variable speed; stability limit 1.618 c

a. Mathematics. I re-derived both versions with SymPy [calc]. - Meyl's trial solution is E = Psi e^(-x/r) with dE/dt = v dE/dx. Written as a travelling profile this is E0 e^(-(x + v t)/r), a pattern moving toward -x (inward). It solves c^2 E_xx = E_tt + (c/r) E_t with v = c(1+sqrt 5)/2. The outward-moving profile e^(-(x - v t)/r), which is what "v points radially outward" means, gives v = c(sqrt 5 - 1)/2 = 0.618 c [calc: both outputs above]. The 1.618 c depends on a sign. - The golden ratio is put in: with a general damping time tau, v = r/(2 tau) + sqrt(r^2/(4 tau^2) + c^2); this equals 1.618 c only when tau = r/c [read: deep read; calc]. Meyl picks tau2 = r/c ("swirl velocity c, radius r") and then the quadratic has coefficients +-1. Nothing predicts it. - Self-contradiction: step 1 sets sigma = 0 and div E = 0 to get Delta E = -rot rot E; step 3 then takes E along x, a function of x only, for which rot E = 0 and div E = dE/dx, nonzero. The left side as derived vanishes identically for the field inserted [calc; read: deep read D2 (iii)]. The "longitudinal" equation (29.12) does not follow from (29.11). The same flaw appears in the 2016 Fluid Mechanics paper: it states div E = 0 and uses a longitudinal E(x) with nonzero divergence; it also drops the 2/x radial term [read: deep read, K-Fluid 6f]. - The exponential profile is not a signal: the damped wave (telegraph) equation has fronts at exactly c; a non-oscillating exponential "speed" is a ratio of rates, like a phase velocity [read: deep reads; memory, high]. - Scalar-wave derivation of ch.21 (Fig. 21.3-21.5) [calc]: inserting E = -grad phi in grad div E = (1/c^2) E_tt gives grad[Delta phi - phi_tt/c^2] = 0, so Delta phi - phi_tt/c^2 = F(t), a function of time only, removable by shifting phi. Meyl instead sets the "integration constant" equal to -rho/eps, which depends on position. His own 21.8 (Delta phi = -rho/eps) and 21.9 together give phi_tt = 0: no oscillation [calc]. The "plasma wave" w^2 = c^2 k^2 + w_p^2 printed as proof of a longitudinal wave is the transverse-wave relation in a plasma; the longitudinal (Bohm-Gross) relation is w^2 = w_p^2 + 3 k^2 v_th^2 [memory, high]. The textbook split equation itself assumed div E = 0 when derived. - "Variable speed" (21.10): E, H proportional to 1/v^2 is an imported proportionality with no constant; it fails for negative E and sound speed in a medium does not oscillate with amplitude [read: deep read 4.3]. - Near-field numbers: lambda/(2 pi) = 0.159 lambda ("one sixth") is the standard crossover of the Hertzian dipole's 1/r^2,1/r^3 terms against 1/r [memory, high]; 100 kHz gives lambda = 3 km not "several metres" (textbook p.474) [calc]; 6 Hz near-field radius 7960 km is correct [calc]. - Claimed benefit "frequency and wavelength can be modulated separately" requires v to be a free controllable variable; 21.4-21.9 fix it at c [read: deep read 3.8].

b. Experiment. Longitudinal waves exist in plasmas, solids and fluids [memory, high]. In vacuum no longitudinal E-wave has been found. Evanescent-mode tunnelling (Nimtz/Enders 1993, Chiao): group delay shorter than vacuum transit but no signal front faster than c; Maxwell solutions [memory, medium; not web-checked]. Meyl's own concession (Neutrino Power pp.108-109): a tunnel or cage output cannot reveal which share was scalar from the start [read: deep read]. SN1987A: neutrinos arrived about 3 hours before light after about 168,000 light-years; at 1.618 c they would have arrived about 64,000 years early [calc: 168000 x (1 - 1/1.618) = 64,168]. OPERA 2011 was a fibre fault [memory, high]. This bears on the later identification with neutrinos (claim 5).

c. Tests. The kit (claim 4). Gao Peng (viXra 1607.0130, 2016; Beijing Wellan Century Co.) reports a torsion-balance signal near a resonant dual Tesla coil with resonances 2.65 and 4.17 MHz (ratio 1.57) [read: Investigator, sites.md; PDF in research/files not re-read by me for its balance data]; it is independent of Meyl, with on/off controls only; I treat it as an unreplicated report and as another frequency ratio of two coil modes, which proves nothing about speed unless the wavelength is shown equal.

d. If true: Gauss's law and the causal structure of Maxwell/Lorentz; signalling faster than c.

Verdict (split): the derivation of v = 1.618 c: Internally inconsistent (sign, div E contradiction, tau2 chosen). Longitudinal E-waves in vacuum from the wave equation: Refuted by calculation (Gauss's law; the 21.8/21.9 contradiction). "Tunnelling through Faraday cages": Never properly tested (no cage measurement in either side's published record; IGF report 1 claims to have tested the cage but prints none).

4. Claim 4: the two-coil kit shows scalar-wave effects (energy transfer, feedback, over-unity 500-1000%, 1.5 c, ineffective Faraday cage)

a. Mathematics of the numbers. - 1.5 c: 7/4.7 = 1.489. v = f x lambda gives a speed ratio only if the wavelength is the same at both resonances. A coil-plus-sphere system is a capacitively loaded, coiled Lecher line whose resonances are not integer multiples [read: IGF]. The IGF measured the line: 5.35 MHz fundamental, 29.5 MHz node map, and a correct c/5.35 MHz = 56.07 m [calc]. The wavelengths differ between modes, so the ratio is a mode ratio. The IGF's own report 1 contains a wavelength slip (44.4 m on p.10 versus 56.07 m on p.6; 44.4 m corresponds to 6.75 MHz [calc]); the qualitative conclusion (shortening by coiling and end capacitance) does not change. Meyl's two independent "1.5 c" values (Tesla's 12 Hz versus Schumann 7.8 Hz = 1.54; his 7/4.7) are different quantities presented as one. Tesla could not have compared with the Schumann resonance (predicted 1952) [memory, high]. - "Over-unity": the manual's own tests compare an LED lit above a 2 V threshold at the receiver with an LED that does not light at the transmitter. That compares voltages at two points of resonant circuits, not power (no input power, no current, no impedance). The DC test compares 400 mV across 100 ohm at the receiver (1.6 mW) with 100 mV (0.1 mW) at the transmitter plate; this is not the generator input [read: deep read, kit manual 3.9-3.10]. The manual says the voltage factor 1.4 means "already a duplication of power", which equates V with P. - The IGF energy check: oscillator 1.2 V x 16 mA = 19.2 mW; two identical LEDs fed 8.5 mW DC matched the RF-fed receiver LEDs by eye; 8.5/19 = 45% [read: IGF]. Eye matching is poor, but the 45% against the claimed 500-1000% is a factor 10 to 20 off in the claim's direction. The follow-up report (Weidner, 10 Aug 2001, Wayback) adds coil copper loss: 13.1 ohm x (3.4 mA)^2 = 0.15 mW of 19 mW (0.8%) [calc 0.151 mW] and states that with a low-harmonic oscillator and LEDs removed the described effects no longer exist [web: http://www.gravitation.org:80/meyl2.html via Wayback; research/files copy]. The IGF's two efficiency figures are different quantities (whole link 45%; one coil 99%); do not compare them directly (Investigator's note, agreed). - Meyl's own lecture paper gives an internally inconsistent split: "factor 1-10" (100-1000%) and "less than 5% of the received power comes from the transmitter" which is a factor 20 (2000%) [read: deep read, Fortschrittliche 4]. - Meyl's patent DE10348862B4 (granted 2009) describes the same link as a capacitive path plus a conducting return forming one L-C circuit at self-resonance, "ist eine Rückleitung erforderlich ... einadriges Kabel oder Masseverbindung", with no over-unity claim [web: https://patents.google.com/patent/DE10348862B4/en, via Investigator]. This is Meyl's own conventional description of what the kit does. - Near-field range: lambda/(2 pi) at 7 MHz is 6.8 m [calc]. Experiment 6 (receiver lit "at more than 6 m") is at the boundary, not at a multiple of it, and the distance is set by a 6 m ground cable that is a conductor between the coils [read: deep read].

b. Consistent with experiment? The IGF reproduced the manual's effects first and then explained them by standing waves on the coiled Lecher line, LED-generated harmonics (LEDs clip at about 1.7 V and square the wave; third harmonic 21.6 MHz is 5.6 to 10 times the fundamental at some probe positions) and a 3.4 mA rms current (28% of oscillator current) in the one-wire link [read: IGF]. Ordinary circuit theory fits.

c. Tested? Yes by the IGF (six authors, private institute, Waldaschaff, September 2001; funded via the Goede foundation per the Investigator's note [web: Wayback page, sites.md]); Waser, NET-Journal 12/2000, also reported no scalar effects [read: IGF p.13]. The IGF is a private institute, which Meyl dismissed as "questionable" [read: CoMed 01/03]; its authors also say the kit is far too small and low-powered to count as a replication of Tesla and that Tesla's apparatus has not been exactly replicated, and urge that it be done [read: IGF p.13]. Gaps in the IGF record, kept on record: no cage measurement, no wire-removed control, wavelength slip, eye-matched LED power. Claimed confirmations on Meyl's side ("some universities", "over 50 universities", TU Clausthal 1000%, 6 July 2000, 50 mW to 500 mW per his FAQ 2009 [web per Investigator]) name no measurer, instrument, report or date. The dean of the CEE faculty at Furtwangen (CoMed 12/2002) stated that independent expert opinions on the case were negative and that positive ones were not sourced [web: Bruhn page quoting the dean; interested party on the critics' side]. Meyl sells the kit (800 and 1400 EUR) and says the manual deliberately omits winding data, which also prevents independent construction [read: deep read].

d. If true: energy conservation (open-system gain from "neutrino radiation", see claim 5); signalling at 1.5 c.

Verdict (split): energy transfer and feedback "as observed": Established as circuit effects (both sides reproduce them); interpretation as scalar waves: Tested, not supported. Over-unity 500-1000%: Tested, not supported (IGF 45%; no input-power measurement behind the claim). 1.5 c: Refuted by calculation as inference (equal-wavelength assumption is contradicted by the measured mode structure). Faraday cage ineffective: Never properly tested (no shield attenuation, no feed-through control, the manual says a gap or a cable gives "perfect coupling"). Full-scale Tesla apparatus: Never properly tested (the IGF and Meyl agree on this; no one has built it).

5. Claim 5: Tesla radiation is neutrino radiation; Neutrinopower; Earth growth

a. Mathematics. - Neutrino as a ring vortex alternating between electron and positron: no equation is given (Teslas Radiations paper has none) [read: deep read]. A zero time-average of charge and mass does not by itself yield a net force; the claim rests on phase matching, uncalculated. - Energy budget (the papers attempt none; the 1996 patent DE19614575A1 does: 66e9 /cm^2/s gives "about 27 W/m^2" if all were converted, i.e. 0.26 MeV each [web via Investigator; calc agrees: 6.6e14 m^-2 s^-1 x 4.2e-14 J = 27 W/m^2]). Taking that figure: total solar neutrino power on Earth's cross-section pi R^2 = 3.4e15 W [calc]. Growth by 8e16 kg/yr (as printed in 2003/2015) needs E = mc^2: 7.2e33 J/yr = 2.28e26 W [calc]. Ratio 6.6e10: even 100% absorption of the whole solar neutrino flux supplies one part in 7e10 of Meyl's requirement. The requirement is 60% of the Sun's luminosity (3.8e26 W) [calc; memory, high]. Meyl's own phrase "entirely different orders of magnitude are collected" has no number [read: JGG deep read]. - Earth growth, the angular-momentum formula: J = (2/5) M R^2 (2 pi/t) constant gives R^n/t = (R+dR)^n/(t+dt), n = 2 (constant mass), n = 5 (constant density) [read: Erdwachstum p.7]. The numbers 45 and 18-19 cm/yr are reproduced only if t = 1 year and dt = 0.71 s, i.e. dt/t = 2.25e-8 [calc; read: deep read]. That is a misreading of the data. The quantity 0.71 s/yr (leap seconds) is the yearly accumulated excess of the mean solar day over 86400 SI seconds (about 2 ms/day), a level; it is not the yearly increase of the day length. In the formula t is the rotation period and dt the change of period. Meyl's chosen dt/t would mean the day lengthens by 5 x 2.87e-2 m / 6.371e6 m x 86400 s = 1.9 ms every year [calc]. Measured: about 1.8 ms per century (0.018 ms/yr), with literature values 1.1-1.8 ms/century [web: https://arxiv.org/pdf/2110.09037 and ILRS presentation (3.79 +-0.07 cm/yr recession, +1.8 ms/century), via search]. Meyl's rate is about 100 times the measured one, and the tidal torque from the Moon (not in his angular-momentum budget) already accounts for the observed slowing. The accreted mass would also bring its own angular momentum, assumed zero. This error is not noted in any Step 1 file (it is a correction below). - The 2003 textbook version (11.x) adds: "less than 0.1 mm/yr" against its own 29 mm/yr mean (diameter) and 65 mm/yr present; day length 18.84 h at 200 Myr from (R - R*)^2/R^2 instead of t proportional to R^2 (correct from his premise: 6.9 h; 6.0 h at 900 Myr) [calc, read: deep read]; Moon recession 5.88 m/yr against measured 3.8 cm/yr (factor 155) with the sign reversed by his "v constant" premise (conserving L/m = sqrt(GMr) gives r proportional to 1/M, an inward drift of 5.9 m/yr at his rate) [read: deep read G]; Earth-Sun recession 1.024 km/yr against ephemeris limits of centimetres per year [memory, medium]; core spin once per 32 min with centripetal acceleration 38 m/s^2 against g about 10.7 m/s^2 at the core boundary, and total angular momentum "zero" assumed (it is conserved, not zero) [read: deep read F]; 214 ns for Hafele-Keating where the sign-correct difference is 273 - (-59) = 332 ns [web: https://hyperphysics.gsu.edu/hbase/Relativ/airtim.html as returned by search; the page numbering of the paper differs among sources]. - 1.618 c and 1.414 c for neutrinos: sqrt 2 is where |1 - beta^2| = 1, no physical content; see SN1987A in claim 3. - Neutrino numbers: ratio 66 to 3 billion /cm^2/s read as "96% materialise" confuses detector sensitivities (Gallium sees pp neutrinos, Kamiokande only high-energy 8B) [memory, high; Meyl's argument per Erdwachstum p.4]. The "day-night half" is an unsourced claim; the Super-Kamiokande day-night asymmetry is a few percent [memory, medium]. - Pauli did not propose a massless particle [memory, high]; oscillations (Super-Kamiokande 1998, SNO 2001) prove nonzero mass [memory, high]. Meyl's "oscillating mass and charge" is not mainstream flavour oscillation; the paper never mentions flavour change [read: deep read].

b. Experiment. Space geodesy (VLBI, SLR, GPS) bounds any radius change at about 0 +-0.2 mm/yr; Meyl's 28.6 mm/yr (radius 2.87 cm/yr for 18 cm circumference) is 100 times that [memory, medium, not web-checked]. Plate spreading is 2-3 cm/yr in the Atlantic, not 10.2 [memory, medium]. Oldest ocean floor about 180-200 Ma is the standard subduction prediction [memory, high]. These are physics/geophysics checks; the mathematics of the arithmetic is the reviewer's piece.

c. Tests. None in the papers. A "measured" day-night neutrino absorption is asserted; Moray 1960 is cited for a 1930s finding; no primary source. Meyl's own 1996 patent (DE19614575A1) ceased as an application; it was cited by a Chinese patent (CN106772547) per Google Patents [web via Investigator, citation list only].

d. If true: neutrino cross-sections would be about 10^10 times larger than measured; mass-energy conservation and the weak interaction would need rewriting; the Sun would also have to gain mass at 4.3e11 t/s as Meyl computes [read: deep read], which the planetary ephemerides rule out at about 1e-13/yr relative [memory, medium].

Verdict (split): neutrinos as collectable free energy at the scale required by Earth growth: Refuted by calculation (factor 7e10 short even at 100% absorption). Earth growth 18-19 cm/yr from the day-length drift: Refuted by calculation (dt misread by a factor of about 100) and by the book's own internal inconsistencies. Tesla radiation = neutrino radiation: Not testable as stated (no cross-section, energy, or detector prediction in the papers; the 1996 patent supplies only the flux conversion). Superluminal neutrinos: Tested, not supported (SN1987A timing).

6. Claim 6: theory of objectivity; masses; Schroedinger

a. Mathematics, step by step. - Part 1 (E, H proportional to 1/l^2): E_z = -(v^2/c^2)E uses scalar products of cross products. With Meyl's own geometry (v along x, H along y, E along z) the vector algebra gives E_z = +(v^2/c^2)E: E_o = E(1 + v^2/c^2), not (1 - v^2/c^2) [calc by deep reader, SymPy; I re-derived: -mu eps v x (v x E) = mu eps [v^2 E - v (v.E)] = +(v^2/c^2) E for v perpendicular to E]. The field ratio is then set equal to the length ratio by "!=" in eq. 10, a postulate. Special relativity gives E'_perp = gamma E (7.09 at 0.99 c); Meyl's formula gives 0.02, a factor 350 apart, directly measurable in beam physics [calc table in deep read]. Eqs. (1),(2) are first-order; substituting each into the other applies the boost twice. "Overlap of the overlap" (28.6-28.15) sums the geometric series to 1/(1 - beta^2) = gamma^2, not gamma. The light-clock geometry (28.16) gives time dilation of a perpendicular signal; the perpendicular length does not contract [memory, high]. - The Moon: with E proportional to 1/l^2, l is proportional to field^(-1/2); a field one sixth as strong gives a length factor sqrt(6) = 2.45, not 36 [calc]. Eq. 11 relates electromagnetic fields to length; the gravitational ratio (6.04) is inserted without a conversion. Apollo 11 should be Apollo 15 (Hadley); the rover odometer and LRO images agree with mapped distances [read: deep read; memory, high]. The geostationary factor 6.64 and Moon 2.457 reproduce arithmetically [calc]; Meyl's Hubble "5%" is 9.4% by his own formula. If every ruler scales together, nothing could be observed (Meyl himself says so at p.2 of Part 2), so the astronauts' "observation" contradicts the theory. Hubble's blur was spherical aberration from a mis-assembled null corrector, fixed with COSTAR, which a refocusing could not have done [memory, high]. - Tamarack plumb-line: arithmetic reproduces (0.061%, 39.7 cm versus 47.4 cm, a 16% miss); the premise (the wire shrinks but the shaft separation does not) is not argued; thermal expansion of a 1.3 km steel wire is 1.5 cm per kelvin, so 47 cm is 31 K [calc]. The only source is a hollow-earth web page [read: deep read L]. - Hafele-Keating "confirmation": his derivation ends in (1/2) m (v_E +- v_f)^2 with m = hf/c^2, which is the ordinary first-order time-dilation factor v^2/(2 c^2); the claim that special relativity "doesn't appear" is false. 207 ns (half-circumnavigation by construction) versus a measured difference of 332 ns; he subtracts magnitudes (273 - 59 = 214) and drops the eastward sign [web: hyperphysics via search; calc]. - Particle masses (ch.7): the outputs follow m = 1836 (z_e/3)^3 (E_outer/E_1)^2 m_e with E_outer from alternating equal-thickness shells; every table entry reproduces [read: deep read]. Inputs: e, m_e, eps_0; m_p = 1836 m_e as anchor; m_mu = 207 m_e appears as a measured input in 7.11. The single derived ratio is m_p/m_mu = 9 (measured 8.88, 1.35% high). The neutron comes out 5.35% above the proton against 0.138% measured, about 39 times too large; tau +8.6%; pi- +24.5%; B0 -15.8%; composites are plain sums with a free choice of structure ("an infinite lot of combinations are conceivable"). The electron mass and any absolute radius are not computed (the text says so, p.156). The quoted "classical electron radius" 2.82 fm follows from W = Q^2/C (textbook is Q^2/(2C), giving 1.41 fm); it is a convention. The proton moment points the wrong way relative to measurement as Meyl states it [read: deep read; memory, high]. Radius ratio r_mu = 3 r_p conflicts with the absence of muon structure [memory, high]. - Proton radius prediction (NET-Journal 11/12 2014, research/files): R_p(mu)/R_p(e) = sqrt((m_p + m_e)/(m_p + m_mu)) = 0.9483 [calc 0.94830]. He divides the muonic 0.84087 fm by one electron-based value 0.886 (Sick) to get 0.949, and notes that CODATA 2010 (0.8775 fm) "falls in the tolerance band". The check is selective (he picked the high electron value). Since 2019, electron-scattering (PRad, 0.831 +-0.007 +-0.012 fm) and hydrogen spectroscopy agree with the muonic value within errors, ratio near 1, not 0.948 [web: https://www.newsarchive.msstate.edu/newsroom/article/2019/11/msu-physics-facultys-breakthrough-research-resolves-years-old-proton-size and the Nature PRad abstract via https://researchportal.ip-paris.fr/en/publications/a-small-proton-charge-radius-from-anelectronproton-scattering-exp/; the PRad abstract itself still calls the puzzle unresolved because of a spectroscopy tension; the CODATA 2018 value 0.8414 fm is [memory, high], not retrieved]. So this prediction has been tested and did not hold. - Schroedinger and Klein-Gordon (ch.5): algebra 5.17 -> 5.20 is correct. But (i) with e^(-omega t) a pure decay, the "mass term" is 1/(tau1 tau2) - omega^2 = -(1/4)(1/tau1 - 1/tau2)^2 <= 0: the sign of an imaginary mass, vanishing at tau1 = tau2; (ii) two different omegas are identified (decay rate (1/tau1 + 1/tau2)/2 and quantum phase frequency mc^2/hbar) without saying so; (iii) replacing omega^2 psi by i omega psi_t is valid for one frequency only; (iv) 5.28 gives v = c for a massive particle then uses (1/2) m v^2; (v) the derived potential is a constant U = (1/2) m c^2 = 255.5 keV (about 19,000 times 13.6 eV) with no position dependence, so no bound states or spectrum; the end state is a free wave at c with wavelength the Compton wavelength [calc, SymPy per deep reader]. With tau1 = tau2 the damping and the vortex term have dropped out, so the result carries no trace of the potential-vortex term beyond omega. "Any experiment confirming Schroedinger confirms the potential vortex" does not follow.

b/c. Experiments: Meyl names no controlled test of the objectivity relations. Michelson-Morley, Kennedy-Thorndike (1932), Alvager 1964, Fizeau 1851 (contradicts "Galilean addition never fails") and the Shapiro delay (Cassini, about 1e-5) are not addressed [memory, high]. Meyl concedes it cannot be tested in a terrestrial laboratory (rods, light and eyes all change together) [read: Part 2].

d. If true: special relativity would be replaced by a field-dependent length scale; all dimensionless constants would have to be derived.

Verdict (split): "fields determine lengths and c; E,H proportional to 1/l^2": Internally inconsistent (sign slip; double boost; a "!" postulate; Moon factor 36 against its own 2.45) and Tested, not supported (transverse field of fast charges grows as gamma). "Derives particle masses": Refuted by calculation in the sense of the claim (inputs include m_p/m_e and m_mu/m_e; table residuals up to 25%; neutron 39 times off); Never properly tested for any new prediction. "Derives Schroedinger/Klein-Gordon": Internally inconsistent (imaginary-mass sign; two omegas; constant potential). Proton-radius ratio 0.948: Tested, not supported [web above].

7. Claim 7: scalar waves as biological carrier; electrosmog harm; vibration medicine

a. Mathematics: none is given. Nerve conduction as a longitudinal standing wave (nodes of Ranvier) is argued by analogy; the mainstream saltatory conduction is not addressed [read: deep read]. Mobile phone: "3 W in, 3 microwatt out" is an assumed one-millionth, order-of-magnitude plausible [read: deep read]. The ground wave "through the earth on a chord" predicts the opposite of the range-versus-frequency pattern (Sommerfeld-Norton attenuation rises with frequency) [read: deep read 4.1]. The antiquity chapters: lambda/2 arithmetic is correct but archaeomagnetic fields were at most 1.5-2 times today's, not 1000 times [memory, high]. The Golden Proportion in temples is numerology (no tolerance, no count of other near ratios). Dowsing grids: Curry 2.5 m x sqrt 2 = 3.54 m reproduces [calc]; a table built "empirically by different persons". Meyl himself writes that a wavelength table "should be looked at with scepticism" [read: deep read]. b. Experiment: no trial or measurement data in the documents. von Klitzing's EEG work is cited; Meyl says his reading differs from von Klitzing's [read: deep read]. Concessions on record: a cage or tunnel cannot show which share was scalar; frequency therapy "should not work" by present physics; a scalar telephone needs more than 40 years [read: claims.md]. c. Tests: none presented. Retractions 2013 (DNA and Cell Biology; J. Cell Commun. Signal., fourfold duplicate publication) are in the Investigator's record [web per sites.md, one organisation's complaint]; I note them without drawing a mathematical conclusion. d. If true: a non-ionising, non-thermal, non-electromagnetic biological interaction channel; most of bioelectromagnetics.

Verdict: Not testable as stated (no measurable prediction; carrier, dose, receiver undefined) for the mechanism; the specific claims (cancer as neutrino-deficiency, Article 2 of the Basic Law) are outside mathematics; Never properly tested.

8. Investigator findings kept on record (whatever the verdict)

  • DE19614575A1 (1996): only neutrino energy balance in Meyl's corpus; 27 W/m^2 if all converted; recorded and used above (claim 5). It also shows the kit geometry predates 2000.
  • DE10348862B4 (granted 2009): Meyl's own patent describes the link as a conventional L-C resonant circuit with a required return line; no over-unity (claim 4).
  • IGF follow-up (Weidner, 10 Aug 2001): Q 353 for L = 105 microhenry (the page says mH, a typo; Q = 2 pi x 7e6 x 105e-6 / 13.1 = 352 [calc]), coil efficiency about 99%, no effects with a low-harmonic oscillator and LEDs removed; an open invitation to Meyl to repeat tests at the IGF. Kept next to Meyl's rebuttal ("questionable private institute... what the physicist does not want to see will stay hidden").
  • Bruhn (TU Darmstadt): 2001 JSE critique printed after Meyl's paper (JSE editorial: Meyl's talk had already been on the web); 2003-08 pages: transformation equations give transverse waves with v = c; Pohl's equations describe a transverse wave at c; chain-rule misuse; Meyl's reply is that Bruhn is a "Betrueger" and the TU Darmstadt distanced itself; Bruhn is a mathematician and an organised critic (GWUP), Meyl an interested party; each is reported as that party's characterisation. My calculations above agree with the mathematical content of Bruhn's objection and I derived it independently.
  • Runckel (Ulm) opinion, Nov 2003: the one academic opinion Meyl named when his dean asked; text not found; known only via Bruhn's rebuttal. Runckel is credited in Meyl's book for the geometric-series step (28.3). I find the series sum correct; the premise is the problem. Record to obtain.
  • Gao Peng (viXra 2016): independent torsion-balance report, resonances 2.65 and 4.17 MHz (ratio 1.57); unreplicated, on/off controls only. Kept.
  • Furtwangen dean Hoenl statement (CoMed 12/2002), chancellor Kusserow (SWR 2008): institutional record; the university is an interested party in its reputation.
  • Absence-of-evidence anomaly (SOURCE HONESTY): the record after 2014 goes quiet (company accounts filed to 2013 only; a reported 2014 stroke from a critic wiki, one source, no second found; retirement 2018; announced 2004 "withdrawal" not found in the Wayback). Competing explanations (health, retirement, commercial wind-down, continued low-profile sales of devices) are in sites.md; none affects the mathematics.
  • Rexresearch / k-meyl.de later papers (PIERS 2012, 2015; BEM 2016; IJEE 2015) not fetched by the Investigator and not read by me; the deciding vortex-loss formula (PIERS 2012) is among them.

9. Corrections to Step 1 (and earlier documents)

  1. claims.md claim 5 says Earth circumference growth of "18-19 cm per year by neutrino absorption (8e16 kg per year)" without noting that the input (0.71 s/yr) is a misread level, not a rate; the deep read Erdwachstum flags the possible issue but no Step 1 summary carries it. Correction: with the formula's t as the rotation period, Meyl's growth would lengthen the day by 1.9 ms per year; measured about 0.018 ms/yr. Anyone repeating "the day-length drift implies 18-19 cm/yr" should add this.
  2. claims.md claim 3: "a vortex with tau2 = r/c gives v^2 - vc - c^2 = 0, hence v = 1.618 c". Correct the statement that v = 1.618 c is the result: it holds for an inward-moving exponential profile; the outward-moving one gives 0.618 c (SymPy). The deep read of ch.29 and the K-Fluid read agree.
  3. claims.md claim 6 lists "the Schroedinger and Klein-Gordon equations follow from the fundamental field equation when tau1 = tau2". Add: only a constant-potential, single-frequency free-wave equation follows; the KG mass term has the wrong sign; they do not follow in the sense of the textbook equations.
  4. claims.md "Independent evidence" says IGF finding of "no cage measurement, no wire-removed control, wavelength inconsistency (56.07 m versus 44.4 m)". Correct the arithmetic detail: 56.07 m is the right value for 5.35 MHz; 44.4 m corresponds to 6.75 MHz [calc]. The IGF follow-up (Wayback, signed H. Weidner alone) supplies a with-LEDs-removed control but still no cage measurement. Already in sites.md Corrections; agreed.
  5. claims.md claim 5 "No energy balance with measured neutrino fluxes is attempted in the papers." Agreed with the Investigator: true of the papers, not of the 1996 patent. I add: using the patent's own 27 W/m^2, the shortfall is a factor 6.6e10.
  6. Three internal numbers in claims.md Corrections are confirmed by my recomputation: "Hafele-Keating 214 ns" (332 ns), "Moon factor 36" (2.45), "Apollo 11 Hadley" (Apollo 15). One slip in the deep read About-Vortex (4.2 worked number): "eight orders of magnitude" for kT/h versus the capacitor rise; the Consequences read says "ten decades". The correct statement is 8 to 10 depending on the end of the 0.1-100 kHz range [calc: 6e12/1e5 = 6e7 and 6e12/1e2 = 6e10].
  7. Deep read Faraday-or-Maxwell 4.2(11): the text cites the antenna book at "S.335", the reference list says "page 351". Not a Step 1 fact; recorded as a source inconsistency in Meyl's paper.
  8. facts.json/claims.md name the IGF authors "six authors at the private IGF" (already corrected). I confirm; the Wayback follow-up shows the institute thanked the Goede-Wissenschaftsstiftung for the kit and instruments, a funder sympathetic to unconventional claims, not a hostile one [web per Investigator, research/2026-10-08-goede-stiftung.md].
  9. Textbook deep read, Hafele-Keating: "the sign-correct difference of the published 273 and -59 ns is 332 ns [memory, high]". Now [web: https://hyperphysics.gsu.edu/hbase/Relativ/airtim.html via search result], retagged from [memory] to [web]. The same applies to "lunar recession about 3.8 cm/yr" [web: ILRS presentation, 3.79 +-0.07 cm/yr].
  10. Still [memory], not web-checked (6 searches used): VLBI radius bound 0.2 mm/yr; Maxwell 1865 text with the v x B term (a 2019 arXiv paper on Maxwell's Article 598 supports it [web: https://arxiv.org/pdf/1911.04605]; the Heaviside/Hertz compact form is [memory, high]); Nimtz tunnelling reading; ephemeris limit on the AU drift; Super-Kamiokande day-night asymmetry size. Verdicts do not rest on these alone.

10. What would settle the open items (mathematical)

  1. Obtain Treskatis 2010 (raw tan delta data, capacitance, instrument, temperature) and PIERS 2012 (the vortex-loss formula); fit Debye/Cole-Cole/Jonscher plus ESR as the comparator; the vortex model wins only if it needs fewer parameters and predicts a second dataset (another film, another temperature).
  2. A value for tau2 from any independent measurement; one measurement of light damping in vacuum (case 1 of eq. 5.12 predicts exp(-t/2 tau2)).
  3. Time-of-flight (not frequency-ratio) measurement of the kit link, with measured wavelength at both resonances, wire removed, and power measured with a calibrated RF wattmeter at the generator and the load.
  4. A Faraday-cage test with measured shield attenuation and a filtered feed-through.
  5. Transverse field of a charged beam at 0.99 c: Meyl predicts 0.02 E, relativity 7.09 E (routine in accelerator diagnostics).

Files used: review/Meyl-Konstantin/{claims.md,facts.json,sites.md,deep/,research/,research/files/kmeyl-NET_Protonradius.pdf}. Output: review/Meyl-Konstantin/mathematician.md.