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Ken Wheeler and the "missing secrets" of magnetism: a primer

What this primer covers. The project folder holds one document: Ken L. Wheeler, Uncovering the Missing Secrets of Magnetism, 3rd edition, 25 September 2014, 236 pages (file magnetism1small.pdf). It has a readable text layer, so there is no source gap for the text. But many of its formulas and diagrams are pictures inside the PDF. After the quality check (QE, Step 4b), every page of the book has now been deep-read, with page images for the formula, photograph and demonstration pages (arbiter.md, "QE revision", lists which). A few peripheral remarks (the p.18 oil-cube demonstration quoted from Dollard, the p.75 Alaska pipeline remark) still rest on page-by-page digests; they bear on no verdict. The 4th edition, announced on p.235, is not in the folder and has not been found. No page of the book reports a quantitative measurement: no number read from an instrument, no instrument model, units, repeat count or control. The book does make one qualitative instrument statement (p.145, a gauss meter; see section 4), and it agrees with the textbook. So every number-based judgement below comes from arithmetic, units and calculation, not from Wheeler's data. Page images of p.149 were re-checked for this primer [read: page image p.149].

Interested parties. Wheeler wrote the book, sold it ($10, p.2) and is the only source for his theory. The publisher emediapress says he offered the book's proceeds to Eric Dollard's non-profit EPD Laboratories, and the book was then released free [web: https://emediapress.com/shop/uncovering-missing-secrets-magnetism/, via Investigator]. Timm Vanderelli (Ferrocell USA) sells the Ferrocell whose images Wheeler uses, and he co-authors the published ferrocell optics papers cited below. His own technical report, "Electromagnetic lensing using a Ferrofluid thinfilm" (Helmholtz coil and laser; copy in research/files), is the maker's account of the device and is listed in section 9 as such. Their descriptions are reported as theirs.

Tags. [read] from the book or the project's review files; [web] with URL (as found by the Investigator or the reviewers); [memory] from training, with confidence; [calc] computed in example.py or by the reviewers, where marked. Verdicts are the arbiter's (arbiter.md); this primer adds none.

1. The idea in one paragraph

Ken Wheeler is an independent writer who publishes through his own Darkstar Publications of Lexington, Kentucky, which earlier issued Buddhist translations and a 2005 work on the golden ratio in Plato (cited in a University of South Carolina thesis, known so far from a search snippet) [web, via Investigator]. In a 2025 interview he states no physics training [web: https://gallowglassbooks.com/blogs/news/interview-with-ken-wheeler, via Investigator]. His vocabulary comes from a lineage he names or hosted on his website: Eric Dollard's "conjugate" dielectric and magnetic fields; the word "counterspace", most likely from George Adams's Physical and Ethereal Spaces, a book on projective geometry (a geometry in which points and planes swap roles) that Wheeler's site hosted in 2015; and a vortex-atom Ether text, "The Ether and Its Vortices" (attributed to Carl F. Krafft [memory: medium]), hosted in 2014 [read: sites.md]. He argues that textbooks have magnetism backwards. In his account there is no such thing as magnetic attraction. A magnet is really an "electrified dielectric object" (a dielectric is an insulator that stores electric energy). What looks like iron being pulled to a magnet is "dielectric voidance": the space between them being taken away by a deeper, unmeasurable medium he calls the Ether or "counterspace". The field around a magnet, he says, is a double vortex (one part spiralling out, one spiralling in) shaped like a hyperbolic surface, with a still "inertial plane" around its middle. He holds that its proportions are fixed by the golden ratio φ (phi, 1.618...), the same number found in sunflower seed spirals. From φ he derives a "true" value for how fast a proton's spin turns in a magnetic field. He also gives a "field formula" that puts the field's boundaries at fixed fractions of the magnet's radius. He backs this with photographs of ferrofluid and of a Ferrocell (a thin film of magnetic fluid between glass plates that glows in striking patterns over a magnet), with a "programmed" bismuth casting, and with a coloured-LED effect. Along the way he rejects electrons, photons, relativity and quantum mechanics. Much of his starting material is real physics: the paired roles of electric and magnetic fields, energy flowing through the space around wires, golden-ratio geometry, and genuinely beautiful ferrocell patterns. This primer shows where those starting points are sound, and then checks, with numbers you can reproduce, the two places where the book makes a precise, testable statement.

2. What you need to know first

Magnetic fields from currents and from magnetised matter. A steady current makes a magnetic field B (unit: tesla, T). Two laws fix it: ∇·B = 0 (no magnetic charges, so field lines never start or end) and ∇×B = μ₀J (Ampère's law; J is the current density, μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space). A permanent magnet has a magnetisation M: magnetic moment per unit volume, in A/m. Its field is exactly that of a bound current: a volume current J_b = ∇×M and a surface current K_b = M × n̂ (n̂ is the outward unit normal to the surface). For a uniformly magnetised cylinder, J_b = 0 and the only bound current is a sheet running round the side wall, like a solenoid. Outside the magnet there is no current, so ∇×B = 0 there. Read: Griffiths, Introduction to Electrodynamics, Chapter 5 (magnetostatics) and Chapter 6 (magnetic fields in matter).

Magnetic dipoles and their forces. Far from a small magnet, its field is that of a magnetic dipole of moment m (A·m²). The field falls as 1/r³ with distance r. The energy of a second dipole m₂ in a field B is U = −m₂·B, and the force is F = ∇(m₂·B). For two dipoles on a common axis the force is F = 3μ₀m₁m₂/(2πr⁴): it falls as 1/r⁴, not 1/r² [memory: high]. A permanent magnet's remanence B_r (the field the material keeps after magnetising, about 1.3 T for an N42 neodymium magnet [memory: medium]) is μ₀M. Read: Griffiths, Chapters 5-6.

Electric fields in insulators (dielectrics). An insulator placed in an electric field E polarises: its molecules' charges shift slightly. This adds a field of its own and stores energy. The permittivity ε (epsilon) measures how much: ε = ε_r ε₀, with ε₀ = 8.854 × 10⁻¹² F/m and ε_r the relative permittivity (about 1 for air, about 2 for oil, about 80 for water [memory: high]). The electric and magnetic constants are tied to the speed of light by μ₀ε₀ = 1/c². Read: Griffiths, Chapter 4 (electric fields in matter).

Energy flow in fields: the Poynting vector. In any electromagnetic system the energy flows through the fields, with flux S = E × B / μ₀ (watts per square metre). Around a wire carrying power, S points along the wire through the space outside the metal. This is the true physics behind a quotation Wheeler takes from Eric Dollard: energy moves in the space around conductors [read: p.15]. Read: Griffiths, Chapter 8 (conservation laws).

Spin precession (Larmor precession) and NMR. A proton has a magnetic moment tied to its spin. In a field B₀ the moment precesses (its axis sweeps a cone, like a tilted spinning top) at angular frequency ω = γB₀. γ (gamma) is the gyromagnetic ratio. For the proton, γ/2π = 42.577 478 461(18) MHz/T, known to about 4 parts in 10¹⁰ [web: https://physics.nist.gov/cgi-bin/cuu/Value?gammapbar]. The frequency does not depend on the tilt angle of the cone. Nuclear magnetic resonance (NMR) and medical MRI (magnetic resonance imaging) work by tuning a radio transmitter to exactly this frequency. Read: Griffiths, Introduction to Quantum Mechanics, the spin chapter (Larmor precession example); any MRI physics text.

Magnetic domains and Bloch walls. Inside a ferromagnet (iron, neodymium magnet) the atomic moments line up in regions called domains. A Bloch wall is the thin transition layer between two domains, typically tens of nanometres thick, across which the magnetisation direction rotates [memory: high]. It is a structure inside the material, seen directly with magneto-optical (Kerr) microscopes. Read: Kittel, Introduction to Solid State Physics, the ferromagnetism chapter.

The golden ratio. φ = (1 + √5)/2 = 1.618 034. Its defining property is φ² = φ + 1, which gives φ³ = 2φ + 1 = 4.236, 1/φ = φ − 1 = 0.618, 1/φ² = 2 − φ = 0.382 and 1/φ³ = √5 − 2 = 0.236. The golden angle is 360°/φ² = 137.508°. Many plants place each new leaf or seed about 137.5° round from the last (phyllotaxis); this packs them efficiently [memory: high]. Read: Mario Livio, The Golden Ratio (2002), a careful popular book that also sorts real from claimed appearances of φ.

Hyperbolic geometry and the Poincaré disk. On a flat plane, the angles of a triangle add up to 180°. In hyperbolic geometry they add up to less. The Poincaré disk is a map of the whole infinite hyperbolic plane drawn inside a unit circle. "Straight lines" (geodesics) appear as circular arcs that meet the rim at right angles, and the rim is infinitely far away. It can be made by projecting one sheet of the two-sheet hyperboloid t² − x² − y² = 1 onto a disk. A horocycle is a circle inside the disk that touches the rim at one point. No tensors are needed to use it. Read: Needham, Visual Complex Analysis, the chapter on non-Euclidean geometry.

Ferrofluids and the Ferrocell. A ferrofluid is a liquid carrying magnetic nanoparticles (about 10 nm). In a strong field normal to its surface it forms spikes (the Rosensweig or normal-field instability) [memory: high]. In a thin film between glass, the particles line up into chains along the in-plane field. Lit from the side, the chains scatter and diffract light, so the film glows in curved lines that depend on where the lights are. That is the Ferrocell. Read: R. E. Rosensweig, Ferrohydrodynamics (1985); A. Tufaile and co-authors' ferrocell papers (Further reading).

3. The textbook view

Magnetic forces. The force between magnets, and between a magnet and iron, comes from magnetic moments in a magnetic field. For a moment m in field B:

U = −m·B, F = ∇(m·B).

Here U is the energy, F the force, ∇ the gradient. "Attraction" and "repulsion" are just the two signs of one quantity, the energy gradient. Soft iron is pulled because the magnet's field induces a moment in it. For iron of susceptibility χ (chi; dimensionless, how strongly a material magnetises) and volume V, the energy is U = −(χV/2μ₀)B², so the pull points toward stronger field. Bismuth has χ ≈ −1.66 × 10⁻⁴ (negative: diamagnetic), so it is pushed toward weaker field. This weak push is why bismuth can stabilise a levitating magnet [memory: high]. Nothing in these formulas involves the permittivity ε of the gap. A magnet attracts iron in vacuum, uncharged. Neutral silver atoms are deflected by a field gradient (Stern and Gerlach, 1922). A magnet loses its pull above its Curie temperature [memory: high].

The field of a cylinder magnet. Model it as the side-wall current sheet K = M (section 2). Then B follows from the Biot-Savart law (the law that gives the field of each bit of current). Two facts matter for this project:

  1. On the axis, a cylinder of radius R and length L, with its top face at z = 0, has

B_z(0, h) = (B_r/2) [ (h + L)/√((h + L)² + R²) − h/√(h² + R²) ]

at height h above the face. B_z is the axial (along-the-axis) component. At the face (h = 0) of a cylinder as long as it is wide (L = 2R), B_z = B_r/√5 = 0.447 B_r.

  1. The return flux. Field lines leave the top face, curve round, and go back into the bottom face. So a little way outside the rim, B_z on a plane above the face points down, the opposite way to over the face. There is a ring where B_z = 0. Where that ring sits depends on how high above the face you look.

Scale. The field of a uniformly magnetised body depends only on its shape and B_r. Double every dimension and the field pattern is the same, scaled up. So a feature at a fixed fraction of the radius is not absurd in itself: geometrically similar magnets do share the same pattern at the same relative height [calc, mathematician].

Outside a magnet, no vortex. In free space outside the magnet ∇×B = 0 and ∇·B = 0. Field lines have no circulation around any loop that does not enclose a current. For a cylinder magnet, symmetry also forbids an azimuthal (round-the-axis) component: the field lines lie in flat planes through the axis. The only "swirl" is the bound current in the magnet's skin [memory: high; Griffiths ch. 6].

Light. In vacuum a plane electromagnetic wave is transverse: E and B are at right angles to each other and to the direction of travel. Energy flows along S = E × B/μ₀. A beam of finite width w has a small field component along its direction of travel, about λ/(2πw) of the main one (λ is the wavelength) [memory: high]. Light comes in photons of energy E = hf (h is Planck's constant, f the frequency). In the photoelectric effect, the maximum kinetic energy of an ejected electron is K_max = hf − W, where W is the work function of the metal. Below a threshold frequency no electrons come out at any intensity [memory: high].

Nuclear energy. Bismuth-209 alpha-decays to thallium-205 with a half-life of (1.9 ± 0.2) × 10¹⁹ years, emitting 3.14 MeV alpha particles (Orsay, 2003) [web: https://physicsworld.com/a/bismuth-breaks-half-life-record-for-alpha-decay/]. That 3.14 MeV is the Q-value: the mass of Bi-209 minus the masses of Tl-205 and He-4, times c². A positive Q-value is the reason the decay can happen. It does not break energy conservation.

4. Where Wheeler departs

Each row puts the textbook statement beside Wheeler's, with the exact point of departure. Page numbers are from the book.

Topic Textbook Wheeler Point of departure
What pulls iron to a magnet Magnetic moment in a field gradient, F = ∇(m·B); no permittivity enters "Magnetic attraction does not exist"; it is "dielectric voidance", the "voiding" of space between objects; a magnet is "an electrified dielectric object" (pp.3, 8, 26, 54-56) [read] Renames the force and assigns it to the electric (dielectric) side of the field pair. The one formula, "D.V. = M1 x M2 / Distance^2" (p.30), is Newton's gravity law without G and with no units, and it falls as 1/d² where magnet forces fall as 1/d⁴ [read: page image p.30; calc, mathematician]. A second formula, a pressure equal to "one half the product of dielectric and magnetic density" (p.76), has the wrong units for a pressure if read literally (½ D·B is in J·s/m⁴, a pressure in J/m³), and around an uncharged magnet D = 0, so it would predict no force at all [calc, deep reader; arbiter 6i]. In 2025 he says instead that attraction "is identical to the phenomenon called gravity" [web: https://kenwheeler.substack.com/p/the-codex-of-gravity]
Electric and magnetic fields Two aspects of one field, linked by μ₀ε₀ = 1/c²; energy flows through space (Poynting) Dielectricity and magnetism are "conjugate" partners; magnetism is the "radiative discharge" of stored dielectric inertia (pp.8, 96) [read] The conjugate pairing is real (Heaviside, Steinmetz, Dollard's vocabulary). The departure is making dielectricity the hidden cause, and declaring its root quantity one that "cannot be measured" (pp.116, 117, 123) [read]
Shape of the field Curl-free, divergence-free outside; field lines in planes through the axis; no swirl A "magneto-dielectric hyperboloid", a double "centrifugal/centripetal" vortex, following the Poincaré disk; the "dielectric inertial plane" at the equator is "the Bloch wall" (pp.58-74, 112-127) [read] The Poincaré-disk geometry he reproduces is correct (one factor of 4 missing in the p.125 metric). But he pictures a one-sheet hyperboloid, which is not the Poincaré construction, and he never links the geometry to the field equations. The Bloch wall is a nanometre layer inside the metal, not the external equator [deep read; mathematician]. In 2025 he restates the plane differently: "The plane of inertia is the dielectric 45 degrees from magnetic flux and 90 degrees from gyromagnetic precession" [web: Substack, 2025-01-03, via Investigator], angles that are not in the book's φ set. Like the 2025 "attraction = gravity" shift above, it shows claims 2 and 3 are not stable across his own writings
Proton precession γ/2π = 42.577 478 MHz/T, measured; precession rate independent of cone angle "This angle is 42.492 (42.5~) degrees, which is also the frequency in Mhz/T of the proton, however this is incorrectly published as 42.5781" (p.46) [read]; 42.4923 = 180/φ³ Treats an angle in degrees and a frequency per tesla as the same number. The match depends on the 360° circle, the megahertz and the tesla. In rad·s⁻¹·T⁻¹ the proton value is 2.675 × 10⁸ [memory: high]. His "published" 42.5781 matches no standard value
Golden ratio φ appears in phyllotaxis and in some quantum magnets (an excitation ratio in the CoNb₂O₆ Ising chain) [web: https://arxiv.org/abs/1103.3694] φ "fixes" the magnet: 68.7539° maximum precession (180/φ²), "dielectric:magnetic" ratio 3.23606:1 (2φ), field lines at the golden angle 137.5077° with an 85° sector (pp.43-51) [read] Every number is built from φ; none is measured. They already appear in the 2nd edition (1 July 2014, 110 pp.), before any ferrocell, bismuth or field-formula material [web: https://web.archive.org/web/20140731145835/http://www.kathodos.com/magnetism.pdf, via Investigator]. The numbers came first and the demonstrations were added later
Field boundaries The B_z = 0 ring moves outward with height; no feature at 0.24 R or 0.38 R "Magnetic & Dielectric Field Formula", 7-28-2014: radii 0.23606, 0.381966, 1, and 1.23606 times the magnet's radius, for length:diameter 1 to φ, cubes and spheres (p.149) [read: page image p.149] A fixed fraction with no height named. This is the one place the book gives an exact geometric prediction. Section 5 tests it
Light and the photoelectric effect Transverse waves; photons, E = hf; threshold and K_max = hf − W No photons or electrons; light has a "Z-axis radial dielectric component"; the photoelectric effect is "corrected", but "h Planck and f frequency remain the same" (p.217); energy then "increases on two levels exponentially" as wavelength falls (p.219) [read] Keeps E = hf and then contradicts it. "C squared" as a speed limit (pp.115-118) has units of m²/s², energy per mass, not speed
Bismuth Bi-209 decays with Q = 3.14 MeV; diamagnetic χ ≈ −1.66 × 10⁻⁴ Bismuth "exhibits overunity" and "breaks the rule of conservation" (p.103); its measured half-life is "spurious" (pp.98-109); a disk cast "with applied charge and field" levitates a magnet higher (p.99) [read] Reads the positive Q-value as a violation, while quoting the 3.14 MeV line on the same page. The levitation caption shows a 1-inch N50 "lifter" magnet doing the lifting; the bismuth stabilises. The page images of the p.99 photo pair show the cube within roughly 1 mm of the disk in both photos, with different backgrounds, cameras and resolutions, so the pair does not show the "much lower" levitation the caption claims (rough pixel estimate by one deep reader). The "137.5077 and 85 degree" marks on the castings (p.105) are a drawn overlay of the golden-angle partition, not measured angles [read: page images pp.99, 105, via deep read; arbiter 6c]
What a gauss meter shows (p.145) Close to the face of a short magnet, the field's magnitude B is largest near the rim; the axial component B_z alone is largest at the centre (section 5, Step 5) "As any gauss meter will register to you, the highest pressure points on a magnet are its divergent centrifugal edge, and secondly its convergent centripetal point at the center of every polarized side" [read: p.145]. He adds that every magnet "is in reality a quadrapole" (p.146) No departure for the observation. example.py Part E gives a field magnitude of 0.649 B_r at the rim against 0.438 B_r on the axis at h = 0.02 R (h is height above the face), and 0.405 against 0.402 at h = 0.1 R; by h = 0.25 R the axis is higher [calc]. So near the face Wheeler's qualitative observation is correct, a point in his favour as an observer. No meter, distance or value is given. The "quadrapole" reading is his own and adds nothing measurable (illustrated with borrowed weather diagrams, not magnet data)
Field strength and reach (pp.66-68) At fixed shape B is proportional to B_r: a stronger grade gives more field at every distance with the same profile "Gauss ratings ... are a complete misnomer"; a higher-gauss magnet has a shallower field [read] For a 25 mm × 25 mm cylinder, N42 gives 0.581, 0.359, 0.206 T at 0, 5, 10 mm and N52 gives 0.648, 0.400, 0.230 T; the field halves at 6.9 mm for both [calc: example.py Part F]. Reach is set by size and shape. His shallow high-gauss tips on cones and stacked "apex" magnets are ordinary flux concentration
The CRT demonstration (pp.157-162) An axial field rotates an electron-beam image, by an angle proportional to ∫B dz along the beam, and the sense reverses with the field; a transverse field deflects the beam sideways (F = qv × B); coloured patches near a magnet on a colour tube are the known "purity" error that degaussing coils remove [memory: high] He holds neodymium magnets against a large CRT (cathode-ray tube) showing a camcorder feed of a spiral test pattern. The image twists one way at one face and the other way at the other, which he reads as "proving that the centrifugal magnetism on this side of the magnet is CCW"; a vertical magnet gives "four loops" (pp.157-161) [read: page images] The observation agrees with the textbook. The pole-dependent twist is what electron optics predicts (one deep reader's illustration: 25 kV beam, ∫B dz = 5 × 10⁻⁴ T·m gives about 27°, assumed values). No CRT voltage, distance, pole marking, measured angle, or monochrome-tube or LCD control is given. The p.159 "inverse pole" pair shows two different magnets, not one turned over. Plain fact: the device works by the electron beam Wheeler denies, and he calls it a "cathode ray dielectric projector" (p.157)
Gyroscopes and gravity (pp.60, 181, 190) A spinning rotor weighs the same as a still one (equivalence principle) Quotes Eric Laithwaite on "how a 50 pound spinning wheel loses weight" (p.181) and says "gravitational polarization" is "the principle behind gyroscopic weight loss ... nothing to do with torque or angular momentum" (p.190); the p.60 "dead gyroscope spins up" passage is a thought experiment [read] No test of his own is described. The experimental history is real and is given in section 6 under 6h

Wheeler's best points, stated fairly. (1) Calling attraction and repulsion one phenomenon is right: they are two signs of one energy gradient. (2) The electric-magnetic pairing (1/c² = μ₀ε₀) and energy flow through space around wires are real physics that he uses correctly in places (p.15, p.212). (3) Iron filings are a 2D slice and do mislead about 3D field shape. (4) Hyperbolic geometry does describe ferrocell images: Tufaile, Snyder and Tufaile, "Horocycles of Light in a Ferrocell", Condensed Matter 6(3):30 (2021), model the patterns with horocycles [web: https://www.mdpi.com/2410-3896/6/3/30]. They do not cite Wheeler, and their model is of light scattered by particle chains, "magneto-optical effects and not just magnetic effects" in the Tufaile guide's words [read via Investigator], not of the field itself. Vanderelli, who co-authors papers in this group's ferrocell series, has a stake. (5) His field formula is an exact, falsifiable statement, which is more than most of the book offers. Section 5 takes it at its word. (6) Where he reports what he saw, he is usually right about the direction of the effect: the gauss-meter edge peak (p.145), the pole-dependent twist on a CRT (pp.157-161), and the tabletop demonstrations of pp.54-96 (a copper square dragging when waved across a magnet's face, a thin magnet standing on edge where a steel disk lies flat, fragments of a broken ring magnet rejoining flipped) all agree with standard magnetostatics and electron optics (arbiter 6g, 6i). What none of them does is separate his "dielectric" account from the standard one.

5. Worked example: does a magnet's field have a fixed boundary at 1.236 times its radius?

example.py in this folder reproduces every number below. Run it with .venv/bin/python review/Wheeler-Ken/example.py.

Step 0. What Wheeler says, exactly

The formula slide on p.149 reads [read: page image p.149]:

C3radius x .23606 = C4radius (centripetal boundary)
C3radius x .381966 = C1radius (dielectric boundary)
C1radius x 3.23606 = C2radius (centrifugal boundary)
C2radius = spatial divergent boundary

It adds: "L to H, or H to L must approximate close to 1 to Phi, or Phi to 1; cube and sphere magnets are exempt from this limitation". The caption calls it "my formula and discovery for calculating the MEAN FIELD divergences, and convergence of the idealized magnet". On p.152 he adds that "the field extends both further and shorter than this" [read]. C3 is the magnet's own radius R. "L to H" is not defined; the deep reader reads it as the length-to-diameter ratio of the magnet.

The drawings show the rings face-on, looking down the magnet's axis. So the plain reading is: on a plane parallel to the pole face, there are boundaries at 0.236 R, 0.382 R, R and 1.236 R. The book gives no height for that plane and no field component. It describes no gaussmeter measurement.

Step 1. The numbers are golden-ratio identities

Using φ² = φ + 1 (section 2):

  • C4 = 0.23606 = 1/φ³ = √5 − 2.
  • C1 = 0.381966 = 1/φ².
  • C2 = C1 × 3.23606 = (1/φ²)(2φ) = 2/φ = 1.23607 = 1 + 1/φ³.

The script prints 0.23607, 0.381966 and 1.23607 [calc]. These are exact. So the formula is golden-ratio algebra with the magnet's radius as the unit. That is fine as algebra. The physics question is whether a real magnet's field has features at these radii.

The same φ algebra gives Wheeler's proton number: 180/φ³ = 42.4922. The measured value is 42.577 478 MHz/T. The gap is 0.085 178 MHz/T, which is 0.200 % and about 4.7 million times the published standard uncertainty [calc]. In an MRI scanner at 1.5 T the proton frequency is 63.866 MHz. Wheeler's value gives 63.739 MHz, 128 kHz away, and at 3 T 256 kHz away [calc]. NMR lines are far narrower than that, so a scanner tuned to Wheeler's value would see no signal. This is why the arbiter's verdict on the proton value is Tested, not supported: the value Wheeler rejects is a measured constant, checked by every NMR instrument. (The arbiter first called it "Refuted by calculation" and relabelled it after QE pointed out that the ruling-out is experimental; the arithmetic above only sizes the gap.)

Step 2. Pick a physical quantity a Hall probe can measure

A Hall probe (a cheap semiconductor sensor) measures one component of B at a point. The natural candidate for a "boundary" outside the rim is the ring where the axial component B_z changes sign: inside it the field points out of the face, outside it the return flux points back. It is the only sharp ring-shaped feature of B_z on a plane above the face. It also matches Wheeler's words: C2 is the "centrifugal boundary", where outgoing ("divergent") meets returning field. This reading is the reviewers' choice; Wheeler does not name a component.

Step 3. Build the field from the bound current

Take a cylinder with radius R, length L, top face at z = 0 and uniform magnetisation M along +z. From section 2, its field is that of a stack of circular current loops of radius R running from z₀ = −L to z₀ = 0, each slice of thickness dz₀ carrying current M dz₀.

The field of one circular loop (radius a, at height z₀, current I) at a point a distance ρ (rho) from the axis and height z is a standard result [memory: high; Jackson, Classical Electrodynamics, section 5.5]:

B_z = (μ₀I/2π) · [K(m) + (a² − ρ² − Δz²)/((a − ρ)² + Δz²) · E(m)] / √((a + ρ)² + Δz²)

with Δz = z − z₀ and m = 4aρ/((a + ρ)² + Δz²). K(m) and E(m) are the complete elliptic integrals of the first and second kind. They are standard special functions, like sine or log: just numbers that a short routine computes (the script uses the arithmetic-geometric mean). The radial component B_ρ has a similar formula.

Adding the loops means integrating over z₀ from −L to 0. Write lengths in units of R and fields in units of B_r = μ₀M. The script does the integral numerically. Before using it, it runs three checks [calc]:

  1. On the axis it matches the closed form of section 3 to six decimals. At the face of an L = 2R magnet it gives 0.447 214 B_r = B_r/√5.
  2. Its elliptic integrals match tables: K(0.5) = 1.854 074 677 3, E(0.5) = 1.350 643 881 0.
  3. Off the axis, at ρ = 1.2 R, h = 0.1 R, it matches a brute-force Biot-Savart sum (each loop cut into 720 straight pieces, 4000 loops) to five decimals: B_ρ = +0.228 40 B_r, B_z = +0.013 09 B_r.

(A first draft of the script had a factor of ½ wrong in the series for E(m). Check 1 cannot catch that, because on the axis m = 0. Checks 2 and 3 caught it. This is why a model is checked off the axis as well as on it.)

Step 4. Find the zero ring at several heights

For each height h, the script finds the radius where B_z = 0 by bisection (halving an interval until the sign change is pinned down). Results, in units of R [calc]:

Magnet length:diameter h = 0.05 R 0.10 R 0.25 R 0.50 R 1.00 R
1 1.149 1.267 1.560 1.978 2.739
φ = 1.618 1.263 1.443 1.846 2.368 3.246
Wheeler's C2 1.236 1.236 1.236 1.236 1.236

These agree with the mathematician's independent table (1.148, 1.266, 1.56, 1.98; 1.263, 1.442, 1.85, 2.37) and with the physicist's, the deep reader's and the arbiter's to within the arbiter's stated 0.05 R.

Three things stand out:

  1. The ring moves. Above a 1:1 magnet it goes from 1.15 R just above the face to 2.7 R one radius up. Nothing about it is fixed.
  2. It does pass 1.236 R, once. Solving for the height where the ring is exactly at 1.23607 R gives h = 0.086 R for a 1:1 magnet and h = 0.043 R for a 1:φ magnet [calc, Part D]. This is guaranteed. The ring's radius is a continuous function of h, starting near R at the face and growing past 2R. So by the intermediate value theorem it must cross every value in between, 1.236 R included, at some height. A match at one unnamed height is therefore no evidence for the formula [mathematician].
  3. It depends on the magnet's shape. At the same relative height, the 1:1 and 1:φ magnets give different rings (1.267 R and 1.443 R at h = 0.1 R). The formula claims one value for the whole range of shapes.

Step 5. Anything at 0.236 R or 0.382 R?

Across the face of a 1:1 magnet at h = 0.1 R the script prints [calc]:

r 0 0.236 R 0.382 R 0.6 R 0.8 R 0.9 R 1.0 R 1.236 R
B_z / B_r 0.402 0.400 0.397 0.386 0.352 0.301 0.177 0.005
tilt of B from the axis 0° 7.8° 13.0° 22.6° 35.7° 46.8° 64.1° 88.6°

B_z falls smoothly and the field tilts smoothly. There is no peak, zero, kink or sign change at Wheeler's C4 (0.236 R) or C1 (0.382 R). The real features are at the rim (r = R, where the radial field is largest close to the face) and the return-flux zero outside it. C3 = R is a real feature, as it should be: it is the edge of the magnet.

Step 6. Real numbers you could measure

Take a 20 mm diameter, 20 mm long N42 cylinder (R = 10 mm, length:diameter 1, B_r ≈ 1.30 T [memory: medium]). The field at the centre of the face is 0.447 × 1.30 T = 581 mT [calc]. Wheeler's C2 ring is at 12.36 mm from the axis. Standard magnetostatics says the B_z = 0 ring is at [calc]:

Hall probe height above the face B_z = 0 at radius radial field there
0.5 mm 11.49 mm 365 mT
1.0 mm 12.67 mm 250 mT
2.5 mm 15.60 mm 127 mT
5.0 mm 19.78 mm 62 mT
10.0 mm 27.39 mm 24 mT

The difference between "stays at 12.4 mm" and "moves from 11.5 mm to 27.4 mm" is several millimetres. A hobby Hall probe on a ruler can see it. Note that the probe must be read for its B_z (axial) component only, with its sensitive face parallel to the pole face. (Any real magnet is not perfectly uniform, so expect a few per cent of difference from these numbers, but not a fixed ring.)

Step 7. What the example shows

  • The radii in the formula are exact φ identities. As arithmetic they are Established.
  • Read as fixed features of every such magnet at any height, the formula is Refuted by calculation: the one sharp ring-shaped feature outside the rim moves with height and with shape, and there is no feature at 0.236 R or 0.382 R.
  • Read as "a ring crosses 1.236 R at some height", it is Plausible, untested, but trivially so: continuity guarantees it.
  • Read as the radii of the rings in Wheeler's ferrocell photographs, it is Never properly tested: the photographs give no scale, gap or lighting.

Why this is fair to Wheeler: he did not say "B_z at height 0.1 R". He said "mean field", and he hedged that the field "extends both further and shorter". The reviewers picked the most natural measurable quantity. If Wheeler or a supporter named a different quantity (|B|, field direction, a ring in a ferrocell at a stated gap and lighting), the same method would test it. That is the open invitation in this result.

6. Evidence table

Verdicts are the arbiter's final verdicts (arbiter.md, including its "QE revision" section). "Tested?" means a test of the claim or of a clear consequence of it.

Claim Tested? Result Replicated? Verdict
1. Attraction is "dielectric voidance", renaming form No measurable difference stated — — Not testable as stated
1. Force on iron is dielectric, not magnetic (strong form) Indirectly: routine force measurements in vacuum, Stern-Gerlach, Curie point [memory: high]. Wheeler's own version never tested Forces follow magnetic moments; no permittivity dependence known Yes (mainstream measurements) Tested, not supported
1. D.V. = M1 M2 / d² as a law for magnets Units and falloff checked No units; magnet forces fall as 1/d⁴ — Internally inconsistent
2. Poincaré-disk geometry as mathematics Checked Correct, with slips (missing factor 4; one-sheet vs two-sheet hyperboloid) — Established
2. Field = hyperboloid; "0 = 1 = infinite inertia"; space a "posterior attribute" No — — Not testable as stated; Internally inconsistent where read literally
2. External vortex/spiral; equator = Bloch wall Magnetostatic theory and field mapping No swirl component; Bloch walls are internal, nm-scale Yes (mainstream) Tested, not supported
2. Ferrocell horocycles as a bridge (Tufaile et al. 2021) Optical model published; bridge to Wheeler not drawn by its authors — — Plausible, untested
3. Identities among 42.4923, 68.7539, 137.5077, 85, 3.23606 Checked [calc] Correct φ algebra (a few slips) — Established
3. 42.4923 MHz/T is the true proton γ/2π Every NMR/MRI instrument Measured 42.5775; Wheeler's 0.2 % low, ~4.7 million σ Yes Tested, not supported (relabelled from Refuted by calculation in the arbiter's QE revision)
3. Degrees = MHz/T Units Different dimensions — Internally inconsistent
3. "Precession angle" of a magnet; dielectric:magnetic 3.23606 No definition or units — — Not testable as stated
3. Field lines spiral at 137.5° Axisymmetric static field: no azimuthal component. Ferrocell: unmeasured — — Refuted by calculation (static field); Never properly tested (ferrocell)
4. Radii are φ identities Checked Exact — Established
4. Fixed boundaries at any height Biot-Savart (section 5), four independent calculations Zero ring moves 1.15 R → 2.7 R Yes (four calculations) Refuted by calculation
4. Ring at 1.236 R at some height Calculation At 0.086 R (1:1), 0.043 R (1:φ) — Plausible, untested (expected by continuity)
4. Ferrocell ring radii No scale, gap or lighting given — — Never properly tested
5. "C squared" as a speed limit Units m²/s² is not a speed — Internally inconsistent
5. Photoelectric "correction" Logic Keeps E = hf, then contradicts it — Internally inconsistent
5. Longitudinal "Z-axis" field of a vacuum plane wave Maxwell's equations Must vanish (finite beams have a small standard part) — Refuted by calculation
5. Nuclear energy from "empty space" Mass-defect budget Fission's ~200 MeV = 0.091 % of rest energy, matches mass defect Yes Refuted by calculation
5. No electrons, photons, relativity, QM A century of experiments Contradicted Yes Tested, not supported
5. Newton's first law wrong; Ether restored Definitional — — Not testable as stated
5. Equivalence principle rejected (p.190) Torsion-balance tests near 10⁻¹³ [memory: high] No violation Yes Tested, not supported
5. "Beta is not particle emission"; no electrons (pp.195-196) Magnetic deflection of beta rays, continuous spectrum, neutrino detected 1956 [memory: high] Contradicted Yes Tested, not supported
5. "0 capacitance = infinite speed"; frequency proportional to capacitance (pp.212, 215) No rate or prediction stated — — Not testable as stated
6a. Ferrocell patterns, mainstream optical account Published optics Diffraction/absorption by particle chains Yes (Tufaile group) Established
6a. Ferrocell patterns confirm Wheeler No quantitative comparison, no controls — No Never properly tested
6b. RGB LED colour separation (18 June 2014) One photograph by Kris Lang (p.136); exposure varied by colour (p.135); no exposure time, camera, polariser or LED current stated anywhere Mundane candidates (blue absorption by ferrofluid, per-colour exposure) not excluded; Lang's photo is almost all red-brown, with "confirmation" in Wheeler's caption No second source found Never properly tested
6c. "Programmed" bismuth: observed height difference One photograph pair, not controlled for lifter or disk position Page images: cube about 1 mm from the disk in both photos; the pair does not show the claimed difference No Never properly tested
6c. Casting angles 137.5077° and 85° (p.105) Page image, one reader's estimate A drawn golden-angle overlay; drawn arms about 103°, 130°, 130° No Never properly tested
6c. Bismuth lifts the cube 5 inches Dipole calculation Lifter magnet alone sets ~4.5 in; bismuth force ~10⁻⁸ mN there — Refuted by calculation
6c. Bismuth "overunity", breaks conservation Q-value 3.14 MeV is the alpha-decay Q-value Yes (Orsay 2003, Gran Sasso) Refuted by calculation
6c. "Dielectric inertia" mechanism — — — Not testable as stated
6d. Objects rest at the "precession angle" No angle measured Ordinary static equilibria — Never properly tested
6e. Stronger grade gives visibly greater "throw" Gardi 2020, homemade Hall gauge (secondary wiki summary) No difference seen; expected effect only ~3 % in distance One test Tested, not supported (at that resolution)
6e. Vortex videos (Tinmanpower, Ufopolitics) No neutral replication with data; videos not viewed — — Never properly tested
6f. Vortex technology (100+ TB drive, communication, regeneration) No device, data or patent found — — Not testable as stated
6g. CRT image twists opposite ways at the two poles Wheeler's photographs, pp.157-162 Real; the pole-dependent twist is standard electron optics Ordinary physics, yes Established (as electron optics)
6g. CRT twist as proof of opposite vortex spin No control (monochrome tube, LCD, measured angle) Ordinary account available No Never properly tested
6g. "Four loops" reading — — — Not testable as stated
6h. Gyroscope weight loss: Hayasaka and Takeuchi (PRL 1989, up to ~12 mg) Controlled repeat by Faller and colleagues (NIST/Colorado) No effect found [web summaries; paper not read] One repeat confirmed; others recalled but unchecked Tested, not supported
6h. Laithwaite's large weight loss Royal Institution rejected the lecture text for publication; no controlled test found — — Never properly tested (low confidence)
6h. "Gravitational polarization" as the cause (p.190) No test described — — Not testable as stated
6i. Tabletop demonstrations (copper square, edge-resting magnet, refrigerator, putty, flipped ring, magnet ring), pp.54-96 Described, no instrument Reported outcomes agree with standard magnetostatics — Established (phenomena); Never properly tested (as confirmation)
6i. Broken hard-drive magnets shoot "electrical charges ... 3 to 5 inches" (p.78) First-hand, "on several occasions", no photo or measurement Candidates: pyrophoric NdFeB sparks; a 3-5 inch arc would need tens of kV No Never properly tested
6i. Pyrolytic graphite and a magnet on bismuth spin off CW at one pole, CCW at the other (pp.68-90) No trials counted, no record, no control Plain diamagnetic forces cannot tell N from S; one deep reader suggests a Hall-angle eddy effect (inference) No Never properly tested
6i. Withheld tests: "20 bits" written (p.61), 7/15/2014 test medium "undisclosed" (p.79) Methods withheld — — Not testable as stated
6i. "Higher gauss = shallower field" (grade at fixed shape) Calculation (example.py Part F) Same profile, field ∝ B_r — Refuted by calculation (grade); Established (cones, stacks: flux concentration)
6i. "400 % beyond N55" magnets Material ceiling ~150 MGOe — — Not testable as stated
6i. Pressure = ½ product of dielectric and magnetic density (p.76) Units Not a pressure; zero for an uncharged magnet — Internally inconsistent
6i. Ψ × Φ = Q, "electrification" (pp.18, 54, 64) Units (example.py Part G) C × Wb = J·s, action, not charge — Not testable as stated
Gauss-meter statement: highest field at the edge, then the centre (p.145) Calculation (example.py Part E) Agrees near the face — Established (qualitatively); "quadrapole" reading Not testable as stated

Kept in the record whatever the verdict. Lori Anne Gardi's 2020 Hall-sensor work (a sympathetic experimenter using Wheeler's vocabulary) found the same 1.44 V maximum for N42 magnets from 5 mm to 2 inches and a zero at the equator [web: https://wiki.naturalphilosophy.org/index.php?title=On_The_Fractal_Nature_of_Magnets_(and_the_universe)., secondary summary]. The equatorial zero is expected by symmetry; the identical maximum across sizes may be sensor saturation (contrarian). Ufopolitics' 2015 Energetic Forum induction test (pages 2-27 unread) and Wheeler's 2026 account of the Tinmanpower videos ("proved it's 100% accurate") are on record as claims, unviewed. VIDEO 73, "M-D-Programmed Bismuth" (2014-08-17) [web: https://www.youtube.com/watch?v=LeQ057E8v5w], is the primary record of the bismuth claim and has not been watched by any reviewer. Bismuth's diamagnetism is direction-dependent in a crystal (about −1.24 × 10⁻⁴ and −1.76 × 10⁻⁴ along different axes [web: https://www.mrs-j.org/pub/tmrsj/vol25_no1/vol25_no1_069.pdf, via search summary]), so casting in a field could plausibly change a disk's grain texture and susceptibility; no measurement of that for bismuth was found. The Bi-209 numbers Wheeler quotes are the real Orsay result.

Gyroscopes: the anomaly and its tests (6h). Wheeler's gyroscope pages point to a real piece of experimental history. Eric Laithwaite, Professor of Electrical Engineering at Imperial College, gave a Royal Institution Friday Evening Discourse on gyroscopes on 8 November 1974. By the Royal Institution's own account it met "utter hostility" and the text failed review for the Institution's Proceedings, so it was published elsewhere [web: https://www.rigb.org/explore-science/explore/blog/gyroscope-engineer-and-christmas-lectures]. Wheeler says Laithwaite retired in 1981 (p.181); the Royal Institution gives his chair as 1964-1986, and a mailing-list quotation gives 1981; both are reported. The "50 pound wheel" remark was not checked. Separately, Hayasaka and Takeuchi reported in Physical Review Letters 63, 2701 (1989) that rotors lost up to about 12 mg when spun one way. J. E. Faller and colleagues (NIST and University of Colorado) repeated it over six days and found no weight change depending on speed or direction, and S. H. Salter in Nature noted that rotor imperfections can produce spurious effects [web: https://www.skeptic.org.uk/?p=49388; https://journals.aps.org/prl/issues/63/25; summaries, papers not read]. Other repeats sometimes named (Nitschke and Wilmarth; Quinn and Picard) were not confirmed by the arbiter's search [memory: medium]. The Faller result addresses Hayasaka and Takeuchi, not Laithwaite's larger claim, for which this review found no controlled test. Wheeler describes no gyroscope test of his own.

Wheeler's other first-hand reports (6i). Breaking powerful hard-drive magnets, he writes that they "split and self-fold along their dielectric planes" and that "on several occasions" electrical charges shot out "like lightning" 3 to 5 inches at the instant of breaking (p.78) [read]. It is one published first-hand account with no photograph or measurement. Ordinary candidates are sparks from freshly exposed, pyrophoric NdFeB fragments (manufacturers warn of this) and fracto-emission, which is normally far smaller [memory: medium]; a true electrical arc of 3 to 5 inches in air would need tens of kilovolts (air breaks down at about 3 kV/mm) [memory: high]. A filmed test in air and in argon, with a field meter, would decide it. He also reports, without counts or records, that pyrolytic graphite and a small magnet floating over bismuth always spin off clockwise from one pole and counter-clockwise from the other (pp.68, 72, 90). Plain diamagnetic forces depend on B² and cannot tell north from south, so this is the one report in the core chapter that textbook forces do not obviously cover; the arbiter flags it for a controlled test without crediting Wheeler's explanation. Finally, two tests are stated but withheld: "I have already written 20 bits of data to a magnetized subject and reproduced the results, by means I will not explain here" (p.61), and a 15 July 2014 discovery "using a testing medium as yet undisclosed" (p.79) [read]. They are on record as his statements; with the methods withheld they cannot be weighed.

The record that went quiet. The 4th edition was announced "very soon" in 2014 (p.235), still "scheduled" in 2018, and "to expand over time" on Substack in 2024-2026; it has not been found. There is no patent and no journal paper. The arbiter lists competing explanations: the work moved to videos and Substack (136 posts exist); a 480/580-page edition listed by booksellers may be it (unchecked); the project was postponed; or the author prefers not to submit to review (the book is hostile to degrees and review, pp.9, 11). No refusal by a journal or funder is documented, but for an outside author that record would be thin by nature. Deciding records: the Amazon page count and edition, the 67 MB kathodos "magnetism" file (2015-10-14, Wayback), the 2018 conference talk, VIDEO 73 and the "Magnetic Egg" video (2015-05-10, probably the explanation promised for the p.234 ice photograph) [web: https://www.youtube.com/watch?v=GwG1p5C5miQ], none viewed by any reviewer.

A date puzzle. The RGB LED "discovery" is dated 18 June 2014 (p.133). The 2nd-edition PDF ("2nd Edition July 1 2014", 110 pages) was created on 28 June 2014, ten days later, yet contains no RGB, ferrocell or Vanderelli text; it has one passing sentence on bismuth but no bismuth chapter or levitation claim [read: research/files/kathodos-magnetism-20140731.pdf, checked by QE]. The archive.org item was created on 25 June 2014, but its current file dates from 19 September 2014 (the Kindle date) and is identical to the project PDF, so the June item first held an earlier file; archive.org's item history may preserve it. None of this settles the puzzle.

7. What a learner should take away

What is solid. - The golden-ratio arithmetic is correct, and the golden angle really does organise sunflower seeds. - Electric and magnetic fields really are a conjugate pair tied by 1/c² = μ₀ε₀, and energy really does flow through the space around wires (Poynting). Wheeler's lineage (Heaviside, Steinmetz, Dollard) uses this honestly. - Ferrocell patterns are real, reproducible and beautiful. A peer-reviewed optical account exists, and it even uses hyperbolic geometry (horocycles), though for the light, not the field. - The Poincaré-disk geometry he reproduces is standard mathematics.

What is wrong, and why the mistake is instructive. - Numbers built before data. Every constant in the book comes from φ, and the φ numbers were in the July 2014 edition before any demonstration. A number that fits a theory by construction cannot also confirm it. The proton value shows the cost: 0.2 % looks small, but NMR is accurate to parts per billion, so it is millions of standard uncertainties off. - Units carry physics. "42.49 degrees = 42.49 MHz/T" works only in one choice of units. "C squared" is not a speed. D.V. = M1 M2 / d² is not a force. A units check is the fastest test of any formula, and the reader can always do it. - Name the quantity, the place and the instrument. The field formula fails not because fixed ratios are absurd (scale invariance makes them possible in form) but because the field feature that a probe can find moves with height. A prediction that does not say where to put the probe can be "confirmed" by continuity at some height, which is no confirmation at all. - Same word, different object. The Bloch wall is real, but it is inside the metal. The Poincaré construction is real, but it uses a different hyperboloid from the one pictured. The horocycle paper is real, but it models light, not field. - An observation is not its explanation. The edge peak on a gauss meter, the twisting CRT image and the copper square that drags when waved across a magnet are all real, and Wheeler reports their direction correctly. But each is predicted by standard physics too, so seeing it cannot favour his account. A test must be one where the two accounts predict different numbers (for example, a high-permittivity insulating square in place of the copper one). - Read the number you quote. The book quotes the 3.14 MeV alpha line of Bi-209 and in the same chapter says bismuth breaks conservation. The 3.14 MeV is the energy bookkeeping.

What is genuinely open. - Does casting bismuth in a field ("applied charge and field in casting") change its grain texture or susceptibility? Cheap to test, never done on record. - What, quantitatively, sets the ring radii and colours in ferrocell photographs under different LED rings and gaps? The independent ferrocell-angle studies (Gardi and Snyder 2024; Dave and Mehta, Optik 2024) have not been read. - The RGB LED effect: a controlled repeat (fixed exposure and white balance, magnet removed, LEDs swapped, absorbance spectrum measured) has not been done. - Does a diamagnet released near a magnet really spin off in a pole-dependent sense (pp.68-90)? Twenty releases per pole with a fixed push, then a low-mobility diamagnet as control, would answer it. - Do freshly broken NdFeB magnets throw inch-long discharges, and are they electrical or burning fragments (p.78)? - What the 4th edition and the unviewed videos contain.

8. Check yourself

  1. Wheeler's "corrected Newton" law for magnets is D.V. = M1 × M2 / d². If two small magnets on a common axis follow the dipole law instead, by what factor does their force drop when you double the distance? By what factor does Wheeler's law say it drops?
  2. Convert the proton's γ/2π = 42.5775 MHz/T to rad·s⁻¹·T⁻¹, and convert the angle 42.4923° to radians. Do the two numbers still look alike? What does this tell you about the claim that they are "the same"?
  3. In section 5, why does B_z have to change sign somewhere outside the rim of a cylinder magnet? (Hint: ∇·B = 0 and closed field lines.)
  4. Suppose a supporter scans a 1:1 magnet with a Hall probe at 0.9 mm above its face (R = 10 mm) and finds B_z = 0 at 12.4 mm. Is that evidence for Wheeler's formula? What single extra measurement would decide?
  5. Bi-209 decays to Tl-205 plus an alpha particle with Q = 3.14 MeV. Explain in one or two sentences why a positive Q-value is required by energy conservation rather than a violation of it.
  6. Wheeler's "electrification" is Q = Ψ × Φ, dielectric flux Ψ (psi, in coulombs) times magnetic flux Φ (phi, in webers) (p.64). Work out the SI unit of the product, using 1 Wb = 1 V·s and 1 C = 1 A·s. Is it the unit of charge? Which famous constant has this unit?

9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics: Chapter 4 (electric fields in matter), Chapter 5 (magnetostatics), Chapter 6 (magnetic fields in matter: bound currents, the field of a magnetised cylinder), Chapter 8 (Poynting vector). - J. D. Jackson, Classical Electrodynamics, section 5.5 (field of a circular current loop with elliptic integrals). Advanced; only for the formula used in section 5. - D. J. Griffiths, Introduction to Quantum Mechanics, the spin chapter (Larmor precession). - C. Kittel, Introduction to Solid State Physics, the ferromagnetism and domains chapter (Bloch walls). - R. E. Rosensweig, Ferrohydrodynamics (1985), for ferrofluid spikes. - T. Needham, Visual Complex Analysis, the non-Euclidean geometry chapter (Poincaré disk). - M. Livio, The Golden Ratio (2002). - NIST value of the proton gyromagnetic ratio, from CODATA (the Committee on Data for Science and Technology, which publishes the internationally recommended values of physical constants): https://physics.nist.gov/cgi-bin/cuu/Value?gammapbar - A. Tufaile, M. Snyder, A. P. B. Tufaile, "Horocycles of Light in a Ferrocell", Condensed Matter 6(3):30 (2021): https://www.mdpi.com/2410-3896/6/3/30 (Vanderelli co-authors other papers in this series; see Interested parties). - Physics World on the Bi-209 half-life measurement (2003): https://physicsworld.com/a/bismuth-breaks-half-life-record-for-alpha-decay/ - H. Hayasaka and S. Takeuchi, "Anomalous weight reduction on a gyroscope's right rotations around the vertical axis on the Earth", Phys. Rev. Lett. 63, 2701 (1989), and the null repeat by J. E. Faller and colleagues, "The Gyroscope-Weighing Experiment Revisited - With a Null Result" (1990): https://journals.aps.org/prl/issues/63/25 (known here from summaries). - Royal Institution on Eric Laithwaite's 1974 gyroscope discourse and its reception: https://www.rigb.org/explore-science/explore/blog/gyroscope-engineer-and-christmas-lectures

The inventor's own work and its lineage. - K. L. Wheeler, Uncovering the Missing Secrets of Magnetism, 3rd ed., 2014 (this project's document). Key pages: 30 (D.V. formula), 43-51 (φ constants), 54-96 (core chapter and tabletop demonstrations), 97-111 (bismuth), 112-127 (hyperboloid), 133-142 (RGB LED), 145-146 (gauss meter, "quadrapole"), 149-156 (field formula), 157-176 (CRT and ferrocell gallery), 181-190 (gyroscopes, gravity), 207-219 (light). - 2nd edition, 1 July 2014 (110 pp.): https://web.archive.org/web/20140731145835/http://www.kathodos.com/magnetism.pdf - Wheeler's Substack (2024-2026), e.g. "The Codex of Gravity" (2025, attraction = gravity): https://kenwheeler.substack.com/p/the-codex-of-gravity, and "Unification of Light, Matter..." (2025-01-03, the "45 degrees" inertial plane): https://kenwheeler.substack.com - Interview with Ken Wheeler, Gallowglass Books (2025), for his background: https://gallowglassbooks.com/blogs/news/interview-with-ken-wheeler - George Adams, Physical and Ethereal Spaces (Rudolf Steiner Press), the projective-geometry source of "counterspace"; a copy was hosted on Wheeler's site in 2015 (research/files). - "The Ether and Its Vortices" (attributed to Carl F. Krafft [memory: medium]), a vortex-atom Ether text hosted on Wheeler's site in 2014. - Darkstar Publications, 2005 work on the golden ratio in Plato (cited in a University of South Carolina thesis; not yet obtained), an earlier source of the φ numbers. - T. Vanderelli, "Electromagnetic lensing using a Ferrofluid thinfilm" (research/files), the Ferrocell maker's own technical account (interested party). - VIDEO 73, "M-D-Programmed Bismuth" (2014): https://www.youtube.com/watch?v=LeQ057E8v5w - Eric P. Dollard's writings on dielectricity and "conjugate space" (copies in research/files/), the main source of Wheeler's vocabulary. - L. A. Gardi (2020), Hall-sensor tests of magnet claims (secondary summary): https://wiki.naturalphilosophy.org/index.php?title=On_The_Fractal_Nature_of_Magnets_(and_the_universe). The Gardi-Lori project in this review covers her own work.

Corrections to earlier documents

  • primer.md (this file), earlier version, opening and section 6: "No page of the book reports a measurement" overstated the record. p.145 makes a qualitative gauss-meter statement (no numbers), and it agrees with standard magnetostatics near the face (QE correction 2; arbiter QE revision, verdict change 3). Now reads "no quantitative measurement". The same earlier version gave the proton-value verdict as "Refuted by calculation"; it now carries the arbiter's relabelled verdict, Tested, not supported.
  • arbiter.md, "Recomputed numbers", field-ring test: the arbiter's coarse-grid values for L/D = 1.618 (1.21 R at h = 0.05 R, 1.40 R at 0.1 R, 1.82 R at 0.25 R) are 0.03-0.05 R lower than a finer calculation, which gives 1.263, 1.443 and 1.846 R [calc: example.py, checked against the on-axis closed form, elliptic-integral tables and brute-force Biot-Savart]. The mathematician's table (1.263, 1.442, 1.85) is the accurate one. This is within the 0.05 R the arbiter itself stated and changes no verdict.

Answers

  1. Dipole law, F ∝ 1/d⁴: doubling d cuts the force by 2⁴ = 16. Wheeler's law, 1/d²: by 4. A spring balance and a ruler can tell 16 from 4.
  2. 42.5775 MHz/T × 2π = 2.675 × 10⁸ rad·s⁻¹·T⁻¹. 42.4923° × π/180 = 0.7416 rad. The digits no longer resemble each other. The original match depends on choosing degrees, megahertz and tesla, none of which nature prefers, so it cannot express a physical law.
  3. Field lines leave the top face and must return into the bottom face (∇·B = 0: they cannot end). On their way back they pass outside the rim heading downward. Over the face B_z points up; outside, the returning lines point down; a continuous B_z must pass through zero in between.
  4. No. At about 0.86 mm above a 1:1 magnet, standard magnetostatics itself puts the zero ring at 1.236 R = 12.4 mm (section 5, Part D), so the reading fits both. The deciding measurement is a second scan at a different height, say 5 mm: magnetostatics predicts the zero near 19.8 mm; the fixed-boundary reading of Wheeler's formula predicts it still at 12.4 mm.
  5. Q is the rest energy of Bi-209 minus the rest energies of Tl-205 and He-4. Energy is conserved, so that surplus must appear somewhere, and it does: as the kinetic energy of the alpha particle and recoiling nucleus (3.14 MeV, the line Wheeler himself quotes on p.103). If Q were negative, the decay could not happen at all.
  6. C × Wb = (A·s)(V·s) = (V·A)·s² = W·s² = J·s. That is the unit of action, the unit of Planck's constant h, not of charge (C) or energy (J). Standard physics does have such a product: the electron charge e times the superconducting flux quantum h/(2e) is h/2 = 3.313 × 10⁻³⁴ J·s (example.py Part G). So Ψ × Φ is consistent in units, but it is not a charge, and using the symbol Q for it hides that.