Hopper-WJ (William J. Hooper): Physicist review (Step 2)

Spelling note: the folder says "Hopper"; the documents say William J. Hooper (1895-1971), PhD Berkeley, Professor of Physics at Principia College 1931-64. Tags: [read] from documents, [web] with URL, [memory] with confidence.

Source gap: the project folder holds only the patent US 3,610,971 and a 10-page typescript essay; neither contains a measurement. The Investigator found the numbers in other Hooper texts (the "Similarities" paper, the Gibson 1983 monograph, US 3,656,013) and one independent NASA test. Those are used below and tagged. I have read the Similarities PDF and the NASA/Investigator notes myself; I did not read the 137-page New Horizons manuscript in full (the WWII shielding experiments are described there; see "Open items"). Where a verdict rests on Hooper's own transcribed reports, I say so.

1. The mainstream view, stated fairly

1. A steady current in a neutral wire produces a static magnetic field B and, outside the wire, no electric field apart from small surface-charge fields that carry the resistive voltage drop. The field pattern is a static map; "flux lines" are a way of drawing it, not objects with a velocity [memory, high: Griffiths ch. 5, 7; Feynman Lectures II, 17-2 on the flux rule].
2. A force qv x B acts on a charge q that is itself moving with velocity v. A charge at rest near the wire feels nothing from B. The "motional emf" of a conductor moving through B is this same Lorentz force acting on the conductor's own charges [memory, high].
3. Faraday's law, curl E = -dB/dt, gives curl E = 0 for DC. A steady E field is therefore conservative, i.e. of the form -grad(phi). A conservative field is exactly what conductors screen (charges rearrange until E = 0 inside the metal). There is no separate kind of steady E field that is both "non-electrostatic" and unshieldable [memory, high].
4. Drift velocity is v = J/(n e): current density J over (conduction-electron density n times charge e). It depends on J, not on temperature or resistance, and n comes independently from the Hall effect. Copper: n e = 8.5e28 m^-3 x 1.6e-19 C = 1.36e10 C/m^3 [memory, high].
5. Gravity is a force on mass-energy, independent of charge and composition (weak equivalence principle). It is tested to about 2e-15 in the Eötvös ratio by the MICROSCOPE satellite: eta(Ti,Pt) = [-1.5 +/- 2.3 (stat) +/- 1.5 (syst)] x 10^-15 [web] https://arxiv.org/abs/2209.15487. Antihydrogen falls downward, and neutral atoms and neutrons fall with the same acceleration as charged matter [web] https://www.nature.com/articles/s41586-023-06527-1 (ALPHA-g, 2023; "within about 25% of normal gravity" at 1 sigma [web] https://phys.org/news/2023-09-antimatter-embraces-earth-falling-downward.html).

2. Verifying Step 1: Corrections to Step 1

• Step 1's reading of the patent is accurate. The deep read's 3.6e-2 cm/s check (v = J/ne = 3.5e-2 cm/s at 480 A/cm^2) reproduces. I re-did it: ne = 14,355 C/cm^3, 480/14,355 = 3.3e-2 cm/s; the small difference is the density used (8.5e22 vs 8.96e22 cm^-3). Fine.
• Missed by Step 1 and the Investigator: Hooper's own worked example (Similarities, eq. 3) is printed with the ln factor in the wrong place. Eq. (2) gives P.D. = (mu0 n I V / 2 pi) ln(r2/r1); solving for V must divide by the log, but eq. (3) as transcribed multiplies by it. With his inputs (r1 = 0.1 m, r2 = 0.1035 m, n = 4020, I = 10 A, P.D. = 5e-6 V) the printed formula gives 2.1e-5 m/s; the correct inversion gives V = 2 pi (5e-6) / (4 pi e-7 x 4020 x 10 x ln 1.035) = 1.8e-2 m/s, which matches his stated 1.78e-2 m/s. So the number is right and the typeset equation is wrong (possibly a transcription error in the 2009 retyping; unknown) [read: hooper-similarities.pdf p.4; my calculation].
• The Investigator noted a "factor of about 100"; I confirm and sharpen it. At the classical drift velocity 1.76e-4 m/s the same formula predicts P.D. = 4.9e-8 V (49 nV). Hooper measured 5e-6 V, 100 times larger. His text says both "in good agreement with accepted values" and that a 100-fold decrease in n "would bring the experimental value of the same order". These conflict, and a 100-fold change in n contradicts Hall-effect measurements of n in copper [memory, high].
• Hooper's geometry is self-consistent with his current density: j = 239.69 A/cm^2 at 10 A means one wire of 0.0417 cm^2 (2.3 mm diameter); 4020 such wires occupy 168 cm^2, a cylinder about 14.6 cm across, inside r1 = 10 cm. So the setup is physically plausible and his numbers are not obviously invented.
• The Investigator's description of the Millis-Williamson test is fair. One correction of emphasis: the NASA test is an agency propulsion screen that tested the weight claim, not the capacitor claim; the capacitor readings were "too erratic" [read: research/2026-10-04-nasa-ntrs.md]. I treat it as a null on weight only.
• Step 1's claim 6 reading is right and worth keeping prominent: Hooper himself reports that a sound absorber removed the rotor signal and a buzzer reproduced it [read: essay p.3].

3. Calculations used (my own; inputs tagged)

(i) Conductor heating in Hooper's generator. 4020 wires x 0.229 m (9 in) = 920 m of copper of 4.17 mm^2 each. R = 1.7e-8 x 920 / 4.17e-6 = 3.7 ohm. At 30 A: I^2 R = 3.4 kW (Hooper says about 3300 W: agrees). At 10 A: 375 W. Voltage across the winding: 37 V at 10 A, 112 V at 30 A [memory high for rho; read for the rest]. (ii) Heat capacity. Copper mass about 4020 x 0.0417 cm^2 x 22.9 cm x 8.96 g/cm^3 = 34 kg; C = 13 kJ/K. At 375 W, warming is 0.03 K/s: about 0.3 K in 10 s. Copper-to-stainless thermocouple voltages are of order microvolts per kelvin [memory, medium], so a fraction of a kelvin of junction temperature difference gives microvolts, the size of the signal. Heating power goes as I^2, which also gives Hooper's "parabola". (iii) What the B x V theory predicts. B outside from n I at r = 0.1 m: mu0 (4020)(10)/(2 pi 0.1) = 0.08 T (Hooper's own treatment). With the correct drift speed 1.76e-4 m/s, E = 1.4e-5 V/m, and across 3.5 cm gives 5e-8 V. Measured: 5e-6 V. (iv) Gravity-as-polarization scale. Polarizability of a copper atom, alpha = 4 pi eps0 x 6 A^3 = 6.8e-40 C m^2/V [memory, medium]. Force on an induced dipole in a gradient: F = alpha E dE/dx ~ alpha E^2/L. With L = 0.1 m and Hooper's E = 1.4e-4 V/m: F = 1.3e-47 N. Weight of one copper atom: 63.5 x 1.66e-27 kg x 9.8 = 1.0e-24 N. Ratio 1e-23. To equal the weight one needs E ~ 1.2e7 V/m, about a hundred billion times larger than anything Hooper measured (and above air breakdown, 3e6 V/m [memory, high]). (v) Superconductor enhancement. In a superconductor the carriers are n_s with v = J/(n_s e). A good critical current density is 1e5-1e6 A/cm^2 [memory, medium], so v up to 1e6/14,355 = 70 cm/s, versus 3.5e-2 cm/s: a factor of about 2000, and only because J is larger, not because of temperature. The patent's "10^8 cm/s", the Fermi speed, would need J = 1.4e12 A/cm^2. The "10^10 times" figure is not reachable.

4. Claim by claim

Claim 1. Flux around a current moves with the electrons' drift velocity, producing E = B x V

a. Mathematics: the single relation E = B x V is a coordinate-dependent Lorentz-force expression, internally unobjectionable as an algebra statement, but it is applied to B and V from different objects (B of the wire, V of the electrons that make that very B). Evaluated at a point outside the wire, a "field" B x V with V the drift velocity would act as a force on a stationary charge. Nothing in Maxwell's equations produces that. Units are consistent. The formula P.D. = B V l in the patent is dimensionally fine. b. Established experiments: static neutral current-carrying wires show no E outside beyond surface-charge fields; and E and B transform under a boost with v/c of 1e-12 for drift velocities, leaving no room for a radial E of this kind [memory, high]. The unipolar-induction literature does have an unresolved-sounding debate about whether flux "rotates with the magnet", but experiment and theory agree on the observable (the emf), since the result depends only on relative motion of conductor and magnet, and the "flux motion" question is a matter of description [memory, high; matches Cravens' "no critical experiment" remark, which is about the interpretation]. Hooper's FIG. 11 yoke experiment [read via Investigator, US 3,656,013] is a standard unipolar-induction configuration; his reading that the flux follows the yoke is an interpretation of an emf measured with a galvanometer, with no numbers. c. Tested: by Hooper alone (capacitor/electrometer data, below). Not independently replicated. Cullwick (1957) is cited by Hooper as a predecessor; I did not verify Cullwick's text, so how far Cullwick agrees is unchecked [Hooper's report only]. d. If true: Maxwell's equations would acquire a source term not in them, and the Lorentz force on stationary test charges near every current-carrying wire would be nonzero. Charge neutrality of current-carrying wires is a standard null result [memory, medium]. Verdict: Refuted by calculation, in the strong form (a real E = B x V field at rest charges outside wires); Not testable as stated, in the weak form ("flux moves" as a description). The mainstream view is that the weak form has no measurable content distinct from ordinary induction.

Claim 2. Non-inductive 4020-wire coil gives an isolated, shield-immune field that charges an external capacitor

a. Mathematics: the sign argument (B and V both reverse between the up and down halves, so B x V adds) is correct as algebra within Hooper's model. But the model's field for each half is zero in the lab (item 1 above), and zero plus zero is zero. Internal inconsistencies in Hooper's own record: (1) he explains the DC curve as a parabola because B is proportional to I and V is proportional to I, yet for AC, with the same B and V proportional to I, he reports a straight line. The theory predicts the same I^2 law for AC (and a rectified, doubled-frequency signal), so the AC result contradicts his own model. (2) Gibson reports P.D. rising when circuit resistance was added; at fixed current B and V do not change [read via Investigator: Gibson 1983]. (3) The dry-ice run follows I^4, not I^2, with no model for it. (4) "In good agreement" versus the factor 100 (Corrections above). (5) Immunity to "every kind of shielding", yet the same text says a grounded steel pail and a grounded inner capacitor cylinder shield the electrostatic part; it is not explained how the same enclosure stops one and passes the other. b. Established experiments: DC E fields from steady currents are curl-free and shielded by conductors. The WWII drift-meter failure has a textbook explanation: in a rigidly translating aircraft in a uniform B, the voltmeter circuit moves too, and the total emf around the loop is zero; the charges on the airframe cancel the v x B force inside the metal, as Hooper himself found (his "careful analysis" gave exactly equal and opposite fields) [read: essay pp.1-2; memory, high]. Hooper's reply, that two equal fields that "cancel" are not identical, is an analogy ("a monkey and a man") not a measurement. c. Tested: by Hooper (reported controls: quick current stepping against thermal emf, a second outer capacitor against contact potential, gaussmeter and a five-wire pickup loop against stray flux, a balanced supply against lead-wire charging; an unnamed "disinterested expert" confirmed readings on an oscilloscope) [read: Similarities]. These are real efforts and I state them in full. The weaknesses: (i) the "quick stepping" test lasts "a few seconds" per reading, but at 375 W-3.4 kW the winding warms by 0.03-0.3 K/s (calc ii), enough for microvolt thermal emfs, and Hooper himself reports that readings grow as the device warms; (ii) the winding carries 37-112 V end to end, so capacitive or leakage coupling at the 1e-7 level gives microvolts; Gibson's own data show -11/+17 versus +28 microvolts with current reversed before the supply was balanced, i.e. pickup of the same size as the signal, and "earlier readings were not redone"; (iii) the readout was a vibrating-capacitor electrometer with µV-level readings, sensitive to contact potentials and microphonics (Hooper's rotor experiments were ruined by sound) [memory, medium on the instrument sensitivities]; (iv) no blank test (dummy winding with current but no bifilar cancellation, or a unifilar reversal of every second wire to remove the claimed effect) is described; (v) no numbers beyond a few points, no error bars, no independent replication. NASA 1995 tried the capacitor readout and found readings "too erratic to reach definite conclusions", and suggested thermal effects [read: nasa-ntrs.md]. d. If true: shielding theorems would fail, and a steady field with zero curl would pass through grounded conductors. Verdict: Never properly tested for the capacitor effect (Hooper's own controls are incomplete, the only independent attempt was inconclusive), with the proposed mechanism Refuted by calculation (a static field cannot be unshieldable) and the prosaic explanations (heating, thermoelectric, supply leakage) not excluded. Hooper's reported data are evidence of a small, real instrument reading that I cannot attribute either way.

Claim 3. P.D. = B V l measures drift velocity and electron density; drift velocity rises at low temperature, up to 1e10 in superconductors

a. Mathematics: the arithmetic is fine after the Certificate of Correction (3.6e-2 cm/s). The temperature inference is not: v = J/(n e) contains no temperature [memory, high; also stated by Millis and Williamson]. The 1e10 ratio is 1e8/3.6e-2 = 2.8e9, a round-up; the numerator is the Fermi speed, which is not the drift speed of any current at realistic J (calc v). The printed 3.6e12 cm/s (above c) was a typo, corrected after Hooper's death. b. Established: Hall-effect and conductivity measurements fix n in copper at about 8.5e22 cm^-3 [memory, high]; a 100-fold lower n (Hooper's suggestion) contradicts it. Supercurrent velocities are given by J/(n_s e) and are slow. c. Tested only by Hooper and Gibson (dry-ice run 28 Feb 1969: 1.5, 6, 17, 45, 95 µV at 10-30 A, fit to I^4; temperature unrecorded) [read via Investigator]. Not replicated. d. If true: Hall-effect and Fermi-gas determinations of n would be wrong by 100. Verdict: Refuted by calculation (temperature/superconductor enhancement, the 100-fold n shift); the capacitor-as-drift-meter idea is Never properly tested.

Claim 4. The field polarizes neutral atoms and attracts matter like gravity, so gravity is an electric polarization effect

a. Mathematics: the dielectric force F = alpha E grad E is standard (Jeans, Griffiths ch. 4 [memory, high]). The identification with gravity has no equation: no force law, no dependence on mass. b. Equivalence principle: a polarization force scales with polarizability and field, not with mass; gravity acts equally on neutrons, antimatter and atoms of different composition to about 1e-15 (MICROSCOPE [web] https://arxiv.org/abs/2209.15487; ALPHA-g [web] https://www.nature.com/articles/s41586-023-06527-1). Hooper's belief that "neutrons also consist of electrons and protons" does not rescue this. Calc (iv): at his measured field the attraction is 1e-23 of an atom's weight. c. Not tested (the essay says the attraction experiment was only "planned", [read: essay p.7]); Brauner (plants) and Burridge (magazine) are the only support cited, and neither is a gravity-field measurement [read: essay fn 9]. d. If true: the equivalence principle and general relativity as the account of weight would fail; also the dipole-type forces would be composition-dependent. Verdict: Refuted by calculation (the magnitude, 23 orders short, and the composition-independence of gravity); the weaker statement "an inhomogeneous E field attracts neutral matter" is Established and irrelevant to gravity.

Claim 5. A strong B x V field can cancel/reverse gravity-induced polarization: weight loss, weightlessness, antigravity

a. Mathematics: no equation links polarization to weight; the patent states no field strength needed. FIG. 3 (collapsing flux) and FIG. 4 (steady non-inductive disk) are described qualitatively. FIG. 3 is an ordinary inductive coil with a conducting shell, where Faraday induction and eddy currents give ordinary forces that Hooper does not discuss. b. Gravity is not an induced polarization (Claim 4); weight is not reduced by electromagnetic fields at laboratory strength. c. Tested: Tested, not supported. NASA Lewis (Millis and Williamson, TM-106963, 1995) built FIG. 4-type self-cancelling coils, 555 g acrylic disk on a balance beam, resolution 0.001 g, threshold 0.02 g; accelerometer threshold about 40 µg; coils also in ice. No weight change at any current [read: nasa-ntrs.md; [web] https://ntrs.nasa.gov/citations/19950022472]. Caveats stated fairly: this is an agency propulsion screen interested in large effects; "a genuine, but minuscule effect" below threshold was not excluded; superconducting coils were not tried; Hooper's own claim in the patent is only a prediction, with no weight measurement reported by him. Hooper's own 1957-59 rotor tests (Claim 6) also gave no real gravity signal. d. If true: gravity would be shieldable/modifiable by EM fields, contradicting every precision weight and equivalence test. Verdict: Tested, not supported (weak-field, room-temperature coils); Refuted by calculation in principle (Claim 4). Superconducting version: Never properly tested.

Claim 6. 1957-59 Fisher/Hooper rotor evidence linking the field to gravity

a. Not a mathematical claim. b. Gravity meters are mechanical spring systems and respond to vibration and sound; Hooper's own absorber and buzzer test shows exactly this [read: essay p.3]. c. Tested by the researchers themselves, who found the effect was acoustic: "A high pitched sound alone was found to produce a deflection... Thus our joint project collapsed." Hooper reported this against his own earlier claim and kept the belief, on the strength of the "immunity to shielding" (the absorber result is itself evidence against an unshieldable field). Fisher's 1957 Gravity Research Foundation paper and the APS 1958 abstract were not found. Historian Kragh confirms the APS work and that it "resulted in two US patents to Hooper" [web, via Investigator: dokumen.pub Kragh 2016]. d. Nothing changes. Verdict: Tested, not supported (by the experimenters' own control). Credit to Hooper for reporting it.

Claim 7. Field penetrates barriers; communication, power and detonation signals through concrete and armor; energy "available everywhere" can be tapped

a. No quantitative statement; the receiver is a capacitor plus electrometer. b. Mainstream: low-frequency magnetic signals do pass through earth and water (ELF through-earth communication), but electric fields are screened [memory, high]; there is no free energy in Earth's gravity field to tap, since a static field does no work on a closed cycle. c. Not tested; no signalling data. The patent says only "I have demonstrated that AC current can be used" [read: p.5]. The Moray link (Hooper thought Moray tapped gravity [read via Investigator: Gibson 1983, New Horizons]) is a statement of belief. d. If true: energy conservation and shielding theory. Verdict: Not testable as stated (no specification); the energy-extraction part is Refuted by calculation (conservative field).

5. The Investigator's findings, weighed

Kept in the record whatever the verdict: - US 3,656,013 (parent, 1968) and FR 2039172 A1: Hooper's FIG. 11 unipolar experiment and the counter-rotating rotor-in-box experiment. Physics: standard unipolar induction; the reading ("flux follows the yoke") is interpretive. The box experiment is the rotating analogue of Claim 2 and shares its pickup problems. The French family member was withdrawn; the reason is unknown. - Similarities paper: the only quantitative account. I verified geometry, current density and heating (calcs i-iii) and found the eq. (3) typo and the AC/DC law mismatch. - Gibson 1983: a participant witness (secretary from March 1968; later company president and publisher, so an interested party). Her data show pickup of the signal's size from supply imbalance and the I^4 dry-ice fit. Her statement that equipment was kept and nobody continued the work is a single-source account. - NASA TM-106963: the one independent test, a null on weight, inconclusive on capacitor charge. It disagrees with Hooper's low-temperature drift claim for the same reason I do. - Cravens 1990 (USAF), Hartman 1996 (witness claim "Hooper and others" saw gravitational forces; no witnesses named, one secondary review), and later patents citing Hooper (Banduric, PST Associates, WWK Trust, Lockheed Martin homopolar motor) show continued interest; citing a patent is not corroboration of its physics. - Historical record: Electrodynamic Gravity, Inc. (Florida, 1969, dissolved 1991); Hooper died 14 Feb 1971 before either patent was granted, and the Certificate of Correction (including the drift-velocity misprint) came after his death. "Record goes dark" analysis: after 1971 no experiment is reported. Competing explanations: death of the sole investigator and end of private funding (Warren Gibson, 1968-71); the vacuum-tube follow-up burned out and was dropped (Gibson); absence of positive results; no evidence for secrecy or suppression has been found. Records that would decide: Ohio corporate filings, USPTO file wrappers, and the 1972 USAF AFRPL-TR-72-31 survey (not yet read). - Joel E. Fisher (1891-1966) and the pre-1960 rotor work are documented by Kragh; the acoustic result is documented by Hooper himself.

6. Verdict table

7. Open items

• New Horizons Chapter 3 (WWII shielding experiments) and the 1969-70 Experimental Notes (not online) are the primary records for the shielding claim. I did not read them; the verdict on Claim 2's "immunity" rests on Hooper's secondhand statements and mainstream theory.
• A decisive test for Claim 2: build the bifilar winding, then repeat with every second layer's current reversed (so the net current-carrying structure is the same but the claimed B x V no longer adds), with a temperature-controlled enclosure and a DC supply isolated from ground; the claimed effect should vanish or persist accordingly.