Primer: William J. Hooper and the "motional electric field" (project Hopper-WJ)

The folder is spelled "Hopper", but the inventor is William J. Hooper (1895-1971). He took his PhD at Berkeley in 1925 and taught physics at Principia College, Elsah, Illinois, from 1931 to 1964. He then founded Electrodynamic Gravity, Inc. [read: essay p.10; web: http://wiki.naturalphilosophy.org/index.php?title=William_J_Hooper].

Source tags used: [read] means taken from a document (the two folder documents, or the documents the Investigator downloaded into research/files/). [web] means from an Internet source and gives the URL. [memory] means recalled textbook physics, with a confidence level. [calc] means computed in example.py. Verdicts are the arbiter's (arbiter.md). This primer adds no new verdicts.

Source gap (repeated from claims.md and arbiter.md). The project folder holds only US patent 3,610,971 and a 10-page typescript essay. Neither contains a measurement. All the numbers below come from documents the Investigator found: - Hooper's paper "Similarities of the Motional Electric & Gravitational Forces"; - Frances Gibson's 1983 monograph; - the New Horizons manuscript; - NASA TM-106963.

No reviewer could read four sources: Hooper's dated lab notes (Experimental Notes, 1969-70, not online), the 1958 APS abstract, Fisher's 1957 paper, and the 1985 Montana State student course paper (T. Lamb). The verdicts on "immunity to shielding" therefore rest on Hooper's published summaries plus textbook theory, not on his notebooks.

QE revision. After the quality check, six Investigator documents were read in full: the whole New Horizons manuscript (main text and appendix), Gibson 1983, US 3,656,013, NASA TM-106963 and Klicker 1986. This primer now includes what they added, following the arbiter's QE revision (arbiter.md section 8). The only raw generator data anywhere are Gibson's tables. Gibson was an interested party (section 6), and her tables were read by hand across several days.

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1. The idea in one paragraph

A current in a wire is a slow drift of electrons, and it is surrounded by a loop-shaped magnetic field. Hooper proposed that this magnetic field is carried along the wire by the drifting electrons. A magnetic field that moves should make an electric field, just as a magnet swept past a wire does. To isolate this "motional electric field", he built a cylinder of 4020 short copper wires joined in series, so that half carry current up and half carry it down. The two magnetic fields cancel outside. In his reasoning, though, the two motional electric fields add, because both the field direction and the electron direction flip between the halves. He reported that this device charged a capacitor wrapped around it, through a grounded steel jacket. He concluded three things from this: - the field cannot be shielded, like gravity; - the field is what gravity is; - a strong enough version could make objects weightless.

The arithmetic that connects the reading to the theory is clean and easy to check, and Hooper's own papers record controls and doubts. Together they make this a good case study in how a microvolt reading can carry a large idea.

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2. What you need to know first

2.1 The Lorentz force and motional EMF. A charge q moving with velocity v through a magnetic field B feels the force F = q v x B. A conductor moving through B therefore has a force per unit charge v x B pushing its electrons along it. Summed around a circuit, this gives a voltage called the motional EMF (electromotive force), for example B l v for a rod of length l sliding at speed v. That is how generators work. Read: Griffiths, Introduction to Electrodynamics, ch. 5 (Lorentz force) and ch. 7 (motional EMF, Faraday's law) [memory, high].

2.2 The magnetic field of a straight wire. Ampère's law gives B = mu0 I / (2 pi r) at distance r from a long straight wire carrying current I. Here mu0 = 4 pi x 10^-7 T m/A is the permeability of free space. The field lines are circles around the wire. If many wires with total current N I are bundled on an axis, the field outside the bundle is the same as for one wire carrying N I. Read: Griffiths ch. 5 [memory, high].

2.3 Drift velocity. In copper, each atom gives up about one free (conduction) electron. That makes n = 8.5 x 10^28 electrons per cubic metre. The electrons move randomly at about 1.6 x 10^6 m/s (the Fermi speed), but a current only adds a tiny average drift, v = I / (n e A). Here e = 1.602 x 10^-19 C is the electron charge and A is the wire's cross-sectional area. For 10 A in a 4 mm^2 wire, v is about 0.2 mm/s. The value of n is measured independently with the Hall effect. Read: Ashcroft and Mermin, Solid State Physics, ch. 1 (Drude model) and ch. 2 (Sommerfeld model), or any introductory modern-physics text [memory, high].

2.4 Faraday's law and the vector potential. Faraday's law in differential form says curl E = -dB/dt: a changing B makes a curling E. A steady current gives dB/dt = 0, so it induces no E. Physicists often write B = curl A, where A is the "vector potential", and the induced field is then E = -dA/dt. Outside a toroid (a doughnut-shaped coil), B is zero but A is not. So an alternating current in a toroid does produce an E field outside it, where B = 0. Hooper uses this correctly as an analogy (section 4). For a steady (DC) current, A does not change, and the induced E is zero. Read: Griffiths ch. 7 and ch. 10 (potentials) [memory, high].

2.5 Conductors and shielding. In a static situation the electric field inside a conductor is zero, because the free charges rearrange until it is. So a closed, grounded metal box excludes any static outside field, and fields from charges inside it do not reach outside. This works for any steady field that can be written E = -grad(phi) (a "conservative" field), and Faraday's law with dB/dt = 0 says every steady E is of this kind. It does not stop a changing magnetic field, nor the EMF around a closed loop that cuts magnetic flux. Read: Griffiths ch. 2 (conductors) and ch. 3 (uniqueness theorems) [memory, high].

2.6 How E and B look to a moving observer (special relativity). Magnetism and electricity mix when you change reference frame. An observer moving at velocity v sees an electric field E' = gamma (E + v x B), where gamma = 1/sqrt(1 - v^2/c^2) and c is the speed of light. For a drift speed of 0.2 mm/s, gamma = 1 to about 25 decimal places. Consider a neutral current-carrying wire, which has E = 0 in the lab. An observer riding along with the electrons sees an electric field of size v B around it, because in that frame the wire carries a small net charge. This is the textbook way to show that magnetism is a relativistic side-effect of electricity. Hooper's patent cites exactly this section of Feynman. Read: Feynman, Leighton and Sands, The Feynman Lectures on Physics, vol. II, ch. 13, section 13-6 "The relativity of magnetic and electric fields" [read: patent p.1 cites Feynman pp. 13-6 to 13-11]. Also Purcell and Morin, Electricity and Magnetism, the chapter on fields of moving charges [memory, high].

2.7 Thermoelectric (Seebeck) voltage. A junction of two different metals at different temperatures produces a voltage of order microvolts per kelvin. Copper's own coefficient is about +1.5 to +2 microvolts per kelvin [web: https://en.wikipedia.org/wiki/Seebeck_coefficient, via arbiter]. A reading of a few microvolts in an apparatus that heats up must therefore always be checked against temperature differences of about a kelvin. Read: Kittel, Introduction to Solid State Physics, or a thermocouple handbook [memory, high].

2.8 Induced dipoles and the dielectrophoretic force. A neutral atom in a field E becomes a small dipole p = alpha E, where alpha is its polarizability. In a field whose strength varies with position, the atom is pulled toward stronger field by the force F = (alpha/2) grad(E^2), which is of order alpha E^2 / L when the field changes over a length L. This is real and is used to sort cells and particles (dielectrophoresis). Read: Griffiths ch. 4 [memory, high].

2.9 The equivalence principle. All bodies fall with the same acceleration, whatever they are made of. The MICROSCOPE satellite found no difference between titanium and platinum at the level of about 10^-15 [web: https://arxiv.org/abs/2209.15487]. Any theory in which gravity depends on an electrical property of matter (charge, polarizability) must explain why that property is in exactly the same proportion to mass in every material. Read: any general-physics text on gravitation; Will, Theory and Experiment in Gravitational Physics for depth [memory, high].

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3. The textbook view

Field of a wire. A long straight wire carrying current I has a magnetic field B(r) = mu0 I / (2 pi r) circling it, where r is the distance from the wire. Outside an electrically neutral wire, the steady electric field is zero, apart from small surface-charge fields that drive the current through the wire's resistance [memory, high: Griffiths ch. 7; Jackson].

Force on a charge. A test charge q at rest (velocity zero) near the wire feels q E = 0 from the electric field and q (0) x B = 0 from the magnetic field. A charge at rest does not respond to a magnetic field. Only a moving charge, or a conductor moving through B, gets the v x B push [memory, high].

Steady fields cannot be unshieldable. A steady current gives dB/dt = 0, so curl E = 0 and E = -grad(phi). Every such field ends on charges, obeys Gauss's law (div E = rho/eps0, where rho is charge density and eps0 = 8.85 x 10^-12 F/m is the permittivity of free space), and is excluded by a closed grounded conductor. So mainstream electromagnetism has no room for a steady, curl-free, non-electrostatic field [memory, high].

What a moving observer sees. Using 2.6, an observer moving with the electrons sees around a straight wire a radial field E' = v B = mu0 I v / (2 pi r). That is exactly the field of a line charge lambda' = I v / c^2 per metre [memory, high; calc step 4]. In the lab, where the capacitor and electrometer sit, this field is not present.

Drift speed. v = I / (n e A) = J / (n e), where J = I/A is the current density. Temperature does not appear in this formula. At a fixed current in a fixed wire, cooling the wire lowers its resistance but does not change v [memory, high; also stated by Millis and Williamson, read per reviewers].

Gravity. Gravity acts on mass-energy, falls off as 1/r^2 from a point mass, and is the same for every material to 10^-15. No electromagnetic field at laboratory strength has ever been shown to change weight [web: MICROSCOPE above; memory, high].

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4. Where Hooper departs

Hooper's starting points are real physics, and he used them correctly in several places:

• The motional EMF B l v exists, and his 1954 "Ironing Board" student experiment measured it to within a few percent of theory: 10.64 microvolts observed against about 10.8 microvolts predicted [read per mathematician: New Horizons ch. 3, Table 3.1].
• A closed-circuit motional EMF is not removed by an electrostatic shield. That is standard: an electrostatic field contributes nothing to a voltage summed around a closed loop. His iron-tube demonstration in "Similarities" (p.8) is also correct: a wire moved together with a magnetic shield still has an EMF induced in it [read: Similarities p.8].
• The toroid analogy is correct for AC. Outside a toroid, B is zero, yet an alternating current induces an E field there [read: Similarities p.8; memory, high].
• The sign algebra of the 4020-wire generator is correct as algebra: (-B) x (-V) = B x V [read: Similarities p.3; verified by all reviewers].
• Jeans and Winch did write that the v x B term in the relativistic transformation "is not due to a distribution of charges" [read: Similarities p.9, quoting Winch]. Hooper took this as licence for a second kind of electric field.

The exact point of departure:

So the central departure is one assumption: a steady magnetic field has a velocity, and that velocity produces a lab-frame electric field. A mainstream physicist would add that the bifilar generator can never show this assumption directly, because its readings can also have ordinary causes (sections 5 and 6). The unipolar-induction question ("does the field of a spinning magnet rotate with it?") is closely related. For a symmetric magnet it has no measurable consequence. A 1990 US Air Force study put it this way: "there has been no critical experiment which can disprove whether a magnetic flux rotates with its source" [web: https://www.rexresearch.com/hooper/hooper1.htm, Cravens excerpt].

Hooper's own spinning-magnet experiment is in US 3,656,013 (FIG. 11). Two magnets sit on a brass rod inside a U-shaped iron yoke. A conductor sweeps the gap, and a galvanometer (a sensitive current meter) is wired to it. He reports four results without numbers [read per deep read: 3,656,013]: - moving the conductor deflects the galvanometer; - turning the magnets and yoke together gives an equal and opposite deflection; - turning the yoke with the magnets fixed to the conductor gives a deflection; - turning only the magnets gives no deflection.

He concluded that "the yoke structure plays an important part in controlling movement of the magnetic flux". The arbiter reads all four results as what the textbook predicts. The U-shaped yoke sets the shape of the field in the gap, so turning the yoke moves the field pattern relative to the conductor. Turning symmetric magnets inside a fixed yoke leaves the pattern where it was. Result 4 is the one that would have come out positive if flux rotated with a spinning magnet. Hooper got zero and attributed it to the yoke. So this experiment cannot tell the two views apart, and if anything it sides with the textbook (arbiter 8.3).

Klicker's 1986 thesis supports Hooper only in a qualified way. A moving-flux model reproduces the small (v/c)^2 correction from special relativity only if the flux moves at half the electrons' speed, not at their full speed as Hooper assumed. Klicker obtained the factor one half by matching the accepted theory, not by measuring it: "only experimental evidence can determine if this is true" [read per deep read: Klicker pp.44-49].

History box: how mainstream physics answered Hooper at the time. Hooper's question began in the Second World War. He planned an aircraft drift and ground-speed meter that would sense the v x B voltage produced as the plane moves through the vertical part of the earth's magnetic field. In his account, the US National Bureau of Standards (NBS) reviewed the plan and "its workability [was] confirmed under a certain restriction. It was stated that the device would be inoperable within a conducting cavity such as a metal clad aircraft" [read per deep read: New Horizons preface p.9]. He gives no date, report number or reviewer name, so the review is documented only in Hooper's own account. New Horizons (p.45) quotes two mainstream statements [read per deep read]: - An unnamed NBS colleague's letter. Two assumptions are both "not in conflict with anything observed experimentally": either two equal and opposite electric fields exist inside a shielded enclosure that moves, or there is no field or charge at any point inside it. "Any prediction not in accord with both ... should be considered as lacking an experimental basis." - W. R. Smythe, Static and Dynamic Electricity (1939), p.500: in a shielded aircraft "the induced electromotive forces in the shields will set up electric fields tending to counteract the fields induced inside".

Hooper's reply was that this position was taken "without a single iota of direct experimental evidence" (p.34). He reports that Fermi, asked at Principia College in 1944, could recall no such evidence (Hooper's paraphrase, one source). The arbiter's weighing: the two textbook descriptions predict the same result for every measurement, so in a symmetric geometry "does the flux move?" cannot be tested. Hooper was right that the answer had been assumed rather than measured, and neither side ever measured it (arbiter 8.3). His original question was whether an open-circuit voltmeter, at rest inside a closed grounded shield that moves as a whole, reads a voltage. None of the experiments he describes does that (section 6, claim 2b).

Where the detector sat. Every shielding experiment Hooper describes puts the detector on the same side of the shield as the source, or uses a closed loop that cuts flux. In New Horizons ch.7 he writes of the generator: "The generator, capacitor and electrometer are completely surrounded by a grounded electrostatic [shield] ... a stainless steel box with a door" [read per deep read and QE: New Horizons pp.70-72]. He says the field "readily passes through the stainless steel walls", but he describes no reading taken outside the box (arbiter 8.4).

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5. Worked example: Hooper's own capacitor reading, step by step

Everything here is reproduced by example.py. Run it with .venv/bin/python review/Hopper-WJ/example.py. Inputs are from "Similarities" pp.2-5 [read] unless marked.

Apparatus [read]. N = 4020 copper conductors, each 9 in (0.2286 m) long, joined in series, with 2010 carrying current up and 2010 carrying it down. Current I = 10 A. Current density J = 239.69 A/cm^2, so each wire has a cross-section A = 10/239.69 = 0.04172 cm^2 = 4.172 mm^2. A stainless cylindrical capacitor has its inner plate at r1 = 0.100 m and its outer plate at r2 = 0.1035 m. The measured voltage is P.D. = 5 x 10^-6 V.

Step 1: drift speed. Copper has density 8960 kg/m^3 and molar mass 0.063546 kg/mol, with one conduction electron per atom [memory, high]: - n = 8960 x 6.022e23 / 0.063546 = 8.49 x 10^28 m^-3 - v = I / (n e A) = 10 / (8.49e28 x 1.602e-19 x 4.172e-6) = 1.762 x 10^-4 m/s (0.18 mm/s).

This matches Hooper's own "1.762 x 10^-2 cm/s" [calc; read]. (His text misprints copper's density as 9.96 g/cm^3 and the denominator as 8.96e22, but the result he prints is right.)

Step 2: what his model predicts. One set of 2010 wires acts, outside the bundle, like a single wire on the axis carrying 2010 I: - B1(r) = mu0 (2010 I) / (2 pi r). At r1 this is 0.0402 T (402 gauss) [calc]. - Hooper's field is E(r) = 2 B1 V = mu0 N I V / (2 pi r), with N = 4020. - Integrating from r1 to r2 gives his eq. (2): P.D. = (mu0 N I V / 2 pi) ln(r2/r1). - Numbers: mu0 N I / 2 pi = 2e-7 x 4020 x 10 = 8.04e-3 T m. ln(1.035) = 0.0344. With the classical V from step 1:

P.D. = 8.04e-3 x 1.762e-4 x 0.0344 = 4.87 x 10^-8 V (about 49 nV) [calc].

• Measured: 5 x 10^-6 V. The reading is 103 times larger than his own model predicts.
• The 5 microvolts is the figure from "Similarities". Gibson's tables give 7, 10 and 15 microvolts at 10 A on three days (4 Feb, 11 Feb and 19 Jul 1969) [read per deep read: Gibson Fig. 3]. Those readings are 144, 205 and 308 times the model [calc, example.py step 2]. So the gap is a range of about 100 to 300 times, not one number. The same day-to-day spread appears at 30 A: 60, 90 and 125 microvolts, or 140 on a warm pass (arbiter 8.2).

Step 3: running it backwards. Solving eq. (2) for V gives V = 2 pi P.D. / (mu0 N I ln(r2/r1)) = 5e-6 / (8.04e-3 x 0.0344) = 1.81 x 10^-2 m/s. Hooper quotes 1.78 x 10^-2 m/s, which agrees within 1.5%. Two points follow [calc; read]: - His eq. (3) is typeset with ln(r2/r1) multiplying instead of dividing. Used as printed, it gives 2.14 x 10^-5 m/s. The number he quotes comes from the correct form, so this is a typesetting slip (it is not known whether it is in the original or the 2009 retyping). - His V is 103 times the classical drift speed. He wrote both that his values are "in good agreement with accepted values" (p.6) and that "a decrease of 100-fold in n, as indicated by Fermi-Dirac statistics" would close the gap (p.5) [read]. Fermi-Dirac statistics do not lower n; they take n as an input. Hall-effect measurements fix n at about one electron per atom in copper [memory, high]. The arbiter rules that one reading cannot fix both V and n, so the "drift-velocity meter" proposal is circular as presented.

Step 4: what Gauss's law says the field would need. The field Hooper infers at the inner plate is E = 2 B1 V = 2 x 0.0402 x 0.0181 = 1.45 x 10^-3 V/m. (The arbiter gives 1.43e-3 using Hooper's rounded 1.78e-2. The physicist's "1.4e-4" was a slip, corrected by the arbiter.) Hooper's own book is consistent with this. New Horizons ch.7 puts the field near the generator at "approximately of the order of ~10^-2 volts/meter, with a current of 30 amperes", and scaling 1.45e-3 V/m by (30/10)^2 gives 1.3e-2 V/m [read per deep read; calc]. A radial field E(r) proportional to 1/r that is steady and curl-free is mathematically identical to the field of a line charge on the axis, lambda = 2 pi eps0 r E = 8.1 x 10^-15 C/m (about 50,000 extra electrons per metre). That is exactly N I V / c^2, the line charge an observer riding with the electrons would see (section 3) [calc]. In the lab, the winding is neutral and enclosed by a grounded plate. For the field to be real, Maxwell's equations would need a new source term. For scale, the relativistic correction that mainstream physics does assign to moving charges is of relative size (v/c)^2 = 3.5 x 10^-25 [calc]. Klicker's 1986 thesis shows that a moving-flux model, done carefully, reproduces this second-order term, but only if the flux moves at half the electrons' speed (section 4) [read per mathematician: Klicker pp.10, 52, 54].

Step 5: the ordinary-cause scale. - Resistance: 4020 x 0.2286 m = 919 m of 4.172 mm^2 copper gives R = 1.68e-8 x 919 / 4.172e-6 = 3.70 ohm. Gibson measured 3.7 ohm [read]. - At 10 A: 370 W of heat and 37 V end to end. At 30 A: 3.3 kW and 111 V. Hooper gives "approximately 3300 watts" [read]. The 34 kg of copper warms on average at 0.028 K/s at 10 A [calc]. - At a net junction thermopower of 2 to 5 microvolts per kelvin, a 5 microvolt reading needs a temperature difference of only 1 to 2.5 K between the plate junctions [calc]. Hooper tested for this, which is to his credit. He stepped the current 30-25-20-15-10-15-...-30 A over a few seconds per reading and found "substantially identical" values. He also reported that when the device "really warms up, each of the observed potential differences becomes enhanced" [read: Similarities p.6]. - A 37-111 V winding inside a grounded can couples electrostatically to the plates. Coupling of 1 part in 10^7 gives microvolts. Hooper himself showed that raising the housing's potential moved the electrometer, and built a balanced power supply to remove this [read: Similarities p.7]. - Gibson's added-resistance runs [read per deep read: Gibson Fig. 5; calc, example.py step 8]. She held the current fixed and added resistance in series outside the winding, using a carbon-pile rheostat or 1500 W photoflood lamps. The supply voltage therefore had to rise. - At 13 A: 15 microvolts with nothing added (3.7 ohm, 48 V supply), against 100 microvolts with 12.3 ohm in total (160 V). That is a factor of 6.7. The rheostat and the lamps gave "exactly the same PD reading". - At 30 A: 60 microvolts at 110 V, 200 at 160 V and 360 at 225 V. That fits P.D. proportional to (supply voltage)^2.5. - Under B x V, the reading depends only on B (set by the winding current) and V (set by the current density and n). A resistor outside the winding changes neither, so the model predicts no change. - Heating does not explain this effect either. The winding carries the same current in both 13 A runs, so its own heating is the same, and two different kinds of resistor gave the same reading. What does change is the voltage on the leads. The supply-imbalance episode had already shown that lead voltage gets into the reading (about 11 microvolts at 100 V). - The arbiter's fit of 13 DC rows finds that P.D. follows the supply voltage (about V^1.9) much better than the current (about I^0.3, once voltage is allowed for). It calls this "a strong indication, not a proof", because the rows were read by hand from an interested party's tables over several days (arbiter 8.4). - Gibson and Hooper read the same data differently: the number of conduction electrons n falls when resistance is added. The arbiter rules this Refuted by calculation, because a resistor outside the winding cannot change the n of the copper inside it.

Step 6: the exponent test. In Hooper's model B is proportional to I and V is proportional to I, so P.D. should go as I^2 for DC. AC should also give I^2, because B and V reverse together and B x V keeps its sign. Hooper reports a parabola-like curve for DC but a straight line for AC [read: Similarities p.5, Fig. 3]. Gibson's dry-ice run of 28 Feb 1969 gave 1.5, 6, 17, 45 and 95 microvolts at 10, 15, 20, 25 and 30 A [read: Gibson 1983]. A log-log fit gives an exponent of 3.78, not 2 [calc]:

Gibson's table labels its I^4 column "Parabola" [read per mathematician]. Joule heating goes as I^2 too, so even a clean I^2 law would not have singled out B x V.

Step 7: could this field be gravity? - Copper atom polarizability: alpha is about 6.5 cubic angstroms (4 pi eps0 x 6.5e-30 m^3 = 7.2 x 10^-40 C m^2/V) [memory, medium]. The physicist used 6; free-atom tables give about 41-47 atomic units, and one atomic unit is 0.148 cubic angstroms. - One atom's weight: 63.5 x 1.66e-27 kg x 9.81 m/s^2 = 1.04 x 10^-24 N. - Take L = 0.1 m and F = alpha E^2 / L [calc]: - with the classical field (1.4e-5 V/m): F/weight = 1.4 x 10^-24; - with Hooper's inferred field (1.45e-3 V/m): F/weight = 1.5 x 10^-20. - For the pull to equal the weight, E would have to be about 1.2 x 10^7 V/m. That is four times the field at which air breaks down (3 x 10^6 V/m) and about 8 x 10^9 times what Hooper inferred [calc].

(Note: the arbiter's first pass converted about 41 atomic units into about 15 cubic angstroms and so got 7.9e6 V/m. Its QE revision corrects this to 6.1 cubic angstroms, about 1.2e7 V/m, and 1.3e-20 of the weight at Hooper's field (arbiter 8.2). The small difference from the 1.5e-20 here comes from using 6.5 rather than 6.1 cubic angstroms. This changes nothing in the verdict: either way the force is 20 or more orders of magnitude short.)

This dielectrophoretic force also has the wrong distance law: it falls as 1/r^3 around a line source and 1/r^5 around a point source, not 1/r^2. And it scales with polarizability, not mass, which the equivalence-principle tests rule out at 10^-15 [read per mathematician; web: MICROSCOPE].

What the example shows. Hooper's formula is internally neat and dimensionally right. His own readings disagree with it by a factor of about 100 to 300. The size of the reading is the size that ordinary heating and pickup produce, and in Gibson's tables the reading follows the supply voltage, which B x V says it should not. The force that would follow, even taking the reading at face value, is 20 orders of magnitude too weak to be gravity.

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6. Evidence table

Kept in the record whatever the verdict (from the Investigator, the reviewers and the QE deep reads; see arbiter.md sections 4 and 8.9):

• Hooper's second patent. US 3,656,013 (filed 1968, granted 1972 after his death) contains the FIG. 11 yoke experiment (section 4) and a counter-rotating rotor in a grounded box. It also proposes desalination, arc-plasma confinement and "transmuting hydrogen into helium" (rows 8-10). Its French family member, FR 2039172 A1, was withdrawn; the reason is unknown.
• The rotor experiment. It gave 15 V AC in a pickup coil at 10,000 rpm, and a DC capacitor voltage that reversed with both rotation direction and current direction [read: Similarities p.8]. Gibson's account that rotor measurements were swamped by vibration and noise sits beside it.
• Gibson's monograph. Gibson was a participant, the financier's wife, and later company president and publisher, so she is an interested party. Her monograph is unusually candid, including the data that count against the claim. She is the only source for all the raw tables.
• Inventor-side rebuttals in Gibson 1983 (her statements, kept beside the artefact evidence from the same source) [read per deep read]: 1. The supply imbalance "was always a negative factor, causing our readings to be less, never more", so the tables were not redone. Hooper "did not feel that it changed the conclusions". The arbiter notes her example (17 and 28 microvolts in the two directions, with no balanced value given) cannot show whether the error was one-sided. 2. The rise with a hot generator "was not totally due to thermoelectric effects, because there was a substantial jump back at 25 amps" (hot 30 A gave 220 microvolts). The arbiter accepts that heat is not the whole story in that run. 3. Up-and-down current scans repeated: at 15 A 30, 27 and 26 microvolts; at 10 A 10 and 10. "If our readings had been due to heat, they would not go up and down the scale with the current". The arbiter notes that this answers slow thermal drift but not pickup that rises and falls with the current. 4. Readings held steady while the current was held, "never just a swing of the needle and then back". 5. An unnamed "disinterested expert" confirmed the readings with an oscilloscope (Hooper's report; no name or readings).
• The NBS review, the NBS letter and Smythe (section 4 history box). This is the contemporaneous mainstream position, documented through Hooper's own account.
• Klicker's 1986 sympathetic thesis. He "has not been able to disprove Hooper's claims". His Montana State "duplication" is a 1985 student course paper on closed-circuit shielding, not on the generator. He writes that Hooper "(with possibly one exception) has been the only one to actually measure this effect". His only generator number (14 microvolts at 30 A) is a calculation that uses Hooper's own extracted drift speed, so it is circular as support. He also states that "the only way to shield a material from a motional electric field is to use a magnetic shield (high u material) around the source", which conflicts with Hooper's "immune to shielding, magnetic or electrostatic" (his reasoning, with no experiment).
• Graneau remark. Klicker relays a private conversation (IEEE Tesla Symposium, 1986) in which P. Graneau "mentioned ... that an experiment had been done where a charged object reacted to steady state current flow in a metallic conductor". This is one source with no data. An ordinary candidate is the small surface-charge field outside any wire with resistance [memory, high], and the record does not say which effect was meant.
• Hooper's 1963 APS paper, "Rotation of Flux about a Magnetic Axis" (published as "Unipolar Electromagnetic Induction"; St. Louis, March 1963), bears directly on claim 1. It has not been read. Its uptake: the DePalma N-machine papers and the homopolar-machine patent US5587618A cite Hooper, and Lockheed Martin's US5844345A cites US 3,656,013 [web, per Investigator]. (A homopolar or "N-machine" is a spinning-disc generator in which the unipolar-induction question arises.)
• Later patents that cite Hooper: Banduric, PST Associates, WWK Trust, and the Lockheed Martin homopolar motor. A citation is continued interest, not corroboration.
• Historian H. Kragh (Varying Gravity, Springer 2016, pp. 68-69) confirms Joel E. Fisher (1891-1966) and the APS talks. Kragh documents Fisher as a promoter of an expanding-Earth hypothesis that influenced Pascual Jordan's proposal that the gravitational constant G varies with time.
• Moray and Eyring. New Horizons (p.68) discusses T. Henry Moray's device, said to capture "cosmic radiant energy continuously, to the extent of 50 kw", and quotes Dr. Carl Eyring (head of physics at Brigham Young University in 1925) as concluding that the energy came "(at least in part) from field energy generated '...in the earth itself'". The quotation comes through Moray's own self-published books, and no independent document is cited. Gibson adds that Hooper was "convinced that Moray had tapped the earth's gravitational field". This is a cross-link to the Morray-TH and TernionAG reviews and is not weighed here.
• Gilstrap 2017, "A New Way to View Electrodynamics" (ResearchGate), is said to build on Hooper's approach. Not opened.
• Hooper's supporting literature (New Horizons pp.14-36): his six "operationally unique" fields, a switching-circuit argument against the usual statement of Faraday's law (after G. I. Cohn), and citations of Slepian, Moon and Spencer, Page and Adams, and Bridgman. These are kept as leads and are not weighed.

The record goes dark after 1971. - What happened: Hooper died in February 1971, before either patent was granted, and the drift-speed misprint was corrected after his death [web: naturalphilosophy wiki]. Electrodynamic Gravity, Inc. (Florida) was dissolved on 9 December 1991 [read per Investigator: Sunbiz]. - After that, nothing was published until Klicker (1986) and NASA (1995). In 1983 Gibson wrote that "all the original equipment is still available" [read: Gibson]. - Competing explanations: - The death of the sole investigator and the end of private funding. This fits the record and needs no extra assumption. - The effect faded on closer testing. Artefacts as large as the signal were recorded, and Gibson burned out a vacuum-tube follow-up and stopped. - Commercial failure. - Secrecy. No evidence has been found; the patents were published. - Suppression. No evidence has been found; the one agency that looked engaged by testing. - Records that would decide: the USPTO file wrappers, the Ohio and Florida corporate filings, the 1972 USAF survey AFRPL-TR-72-31, and the Experimental Notes. - The arbiter's reading: a cheap apparatus that was never rebuilt at a neutral lab means the generator effect is untested, not refuted.

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7. What a learner should take away

Solid. - Motional EMF, the B field of a wire, superposition, and the toroid case of induction where B = 0 are all real, and Hooper used them competently. - His 1954 closed-loop shielding measurements agree with textbook theory to within about 1.5%. - The drift-speed arithmetic in the corrected patent (3.6 x 10^-2 cm/s at 480 A/cm^2) is right. - Hooper also reported his own negative result on the rotor and ran real controls on the generator. - He was right on one historical point. The mainstream answer to his wartime question (no net field inside a moving closed shield) was reasoned from theory, and the NBS letter itself says experiments agreed with both descriptions. Nobody had measured it, and in symmetric geometry nobody can (section 4 history box).

Wrong, and why it is instructive. 1. A field pattern is not an object. "The flux moves" sounds physical, but for a steady current nothing at any point changes, so there is no velocity to measure. The field Hooper wrote down, v B, is real in the frame moving with the electrons. His mistake is to carry it into the lab frame. This is a useful lesson in keeping track of which observer a field belongs to. 2. Check your own formula against your own number. His model predicts 49 nV and he read 5 microvolts (7 to 15 microvolts in Gibson's tables). Calling this "good agreement" and then adjusting n by 100 to fit is the step a careful reader should catch. 3. A shape test is more powerful than a size test. The model demands I^2 for both AC and DC. The data gave a linear AC response and I^3.8 for DC on dry ice. The data that does not fit the curve says more than the data that does. 4. Size the ordinary explanation first. 5 microvolts is about one kelvin of thermocouple difference, or about 10^-7 of a 37 V winding coupled capacitively. Gibson's added-resistance runs are the most telling internal clue. At the same 13 A the reading went from 15 to 100 microvolts when the supply voltage rose from 48 to 160 V, and at 30 A from 60 to 200 to 360 microvolts as the supply rose from 110 to 160 to 225 V. Under B x V, an external resistor cannot change B or V. It does change lead and housing potentials. 5. Gravity has two signatures that any rival must reproduce: a 1/r^2 distance law and the same response from every material. A polarization force has neither.

Genuinely open (small, cheap and never done). - Does the generator reading survive these tests? - a dummy winding of the same geometry wound inductively; - a swap from copper to a second metal whose n is measured by the Hall effect, or to aluminium (n about twice copper's). B x V predicts P.D. proportional to 1/n at fixed current and cross-section, while heating and pickup change differently. An earlier version of this primer and of the reviews said nichrome has the same n as copper. No source supports that, and the arbiter withdrew it; - repeating Gibson's 13 A test with 0, 5 and 12 ohm in series and a floating, a grounded and a balanced supply, with leads of fixed geometry (B x V predicts no change); - putting the capacitor and electrometer outside the grounded box, compared with a dummy winding of the same geometry carrying the same current; - an open-circuit voltmeter at rest inside a closed, grounded shield that moves as a whole (Hooper's original NBS question, never done); - a step-response measurement from microseconds to minutes (a thermal signal lags by seconds or more; a direct field would follow at once). - What does the 16 Dec 1969 shielding entry in the Experimental Notes show? (The 1985 Montana State work is now identified as a student course paper on closed-circuit shielding, not on the generator; the paper itself is still unread.) - In Gibson's 100 V, 26 A supply-imbalance example, what was the reading once the supply was balanced? That value decides whether the imbalance error was one-sided, as she says. - Does Hooper's 1963 APS paper on unipolar induction contain an experiment that can tell rotating flux from stationary flux? - Who were Hartman's "others" who witnessed gravitational forces? - Why was the French application withdrawn?

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8. Check yourself

1. A copper wire of cross-section 1 mm^2 carries 5 A. What is the electron drift speed? Does it change if you cool the wire to 77 K at the same 5 A?
2. Using Hooper's eq. (2), what P.D. would his generator give at 30 A if V were the classical drift speed? How does it compare with the 95 microvolts Gibson recorded at 30 A on dry ice?
3. A friend says: "Each half of the bifilar coil has B x V pointing inward, so they add." Give the relativity-based reason a physicist says the lab-frame field of each half is zero to begin with.
4. Why is a sound absorber removing the gravity-meter signal (1957-59) evidence against an unshieldable field, quite apart from showing the signal was acoustic?
5. NASA saw no weight change within 0.02 g on a 555 g disk. What fraction of the weight is that? Name two reasons it does not test the superconducting form of the claim.

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9. Further reading

Mainstream - D. J. Griffiths, Introduction to Electrodynamics (4th ed.): ch. 4 (polarization), 5 (magnetostatics), 7 (electrodynamics), 12 (electrodynamics and relativity) [memory, high]. - R. P. Feynman et al., The Feynman Lectures on Physics, vol. II, ch. 13 section 13-6 (relativity of electric and magnetic fields; cited in Hooper's patent) and ch. 17 (the flux rule and its exceptions). Free online at https://www.feynmanlectures.caltech.edu [memory, high]. - E. M. Purcell and D. J. Morin, Electricity and Magnetism (3rd ed.), the chapters on fields of moving charges and the magnetic field: the best derivation of magnetism from relativity at this level [memory, high]. - N. W. Ashcroft and N. D. Mermin, Solid State Physics, ch. 1-2 (Drude and Sommerfeld models; Hall effect) [memory, high]. - E. G. Cullwick, Electromagnetism and Relativity (Longmans, 1957), p.245: the moving-flux discussion Hooper cites [read: essay fn 6; not checked by reviewers]. - MICROSCOPE final result, https://arxiv.org/abs/2209.15487 (equivalence principle to about 10^-15). - H. Kragh, Varying Gravity (Springer, 2016), pp. 68-69, on Fisher and Hooper, and Fisher's influence on Pascual Jordan's varying-G hypothesis. - W. R. Smythe, Static and Dynamic Electricity (McGraw-Hill, 1939), p.500 (shielded aircraft) and p.488 (the transformation terms), as quoted in New Horizons [read per deep read; not checked against the original].

Hooper's own works and the primary record - W. J. Hooper, US Patent 3,610,971, "All-Electric Motional Electric Field Generator" (1971; Certificate of Correction 1972), in the project folder. - W. J. Hooper, untitled typescript essay on the B x V theory of gravity (about 1969-70), in the project folder (hooper.pdf). - W. J. Hooper, US Patent 3,656,013, "Apparatus for Generating Motional Electric Field" (1972): https://patents.google.com/patent/US3656013A/en - W. J. Hooper, "Similarities of the Motional Electric & Gravitational Forces": https://www.rexresearch.com/hooper/similarities.pdf (research/files/hooper-similarities.pdf). - W. J. Hooper, New Horizons in Electric, Magnetic and Gravitational Field Theory (manuscript; original at Principia College Library): https://www.rexresearch.com/hooper/NewHorizons.pdf. The preface has the NBS story; ch. 3 has the 1954 shielding experiments and the NBS and Smythe quotations; ch. 5-6 have the gravity and energy mechanisms; ch. 7 has the generator setup. - W. J. Hooper, "The Motional Electric Field Generator", Bull. APS ser. II, 15(2):209 (Feb 1970), and the Boulder Conference proceedings p.483 (1970) [read: essay fn 7; not obtained]. - W. J. Hooper, "Rotation of Flux about a Magnetic Axis" ("Unipolar Electromagnetic Induction"), APS meeting, St. Louis, March 1963 [web, per Investigator; not obtained]. - F. G. Gibson, The All-Electric Motional Field Generator & Its Potential (1983): https://www.rexresearch.com/hooper/gibson.htm - F. G. Gibson (comp.), Experimental Notes of Dr. William J. Hooper (1991), not online: http://www.tfcbooks.com/mall/more/565hen.htm - M. G. Millis and G. S. Williamson, "Experimental Results of Hooper's Gravity-Electromagnetic Coupling Concept", NASA TM-106963 (1995): https://ntrs.nasa.gov/citations/19950022472 - K. Klicker, Motional Electric Field Associated with Moving Charges (thesis, 1986): https://archive.org/details/MotionalElectricFieldAssociatedWithMovingCharges

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Answers

1. A = 1e-6 m^2, so v = 5 / (8.49e28 x 1.602e-19 x 1e-6) = 3.7 x 10^-4 m/s (0.37 mm/s). Cooling to 77 K lowers the resistance, but v = I/(n e A) has no temperature term and n is fixed by the number of atoms. So at the same 5 A, v is unchanged.
2. P.D. scales as I^2 (because V is proportional to I). 49 nV x (30/10)^2 = 0.44 microvolts. Gibson recorded 95 microvolts, about 220 times more. The gap is larger than at 10 A because the data rise faster than I^2.
3. In the lab the wire is neutral, so E = 0 outside, and a charge at rest feels no magnetic force. The v B field is what an observer moving with the electrons sees: in that frame the wire has a small net charge. The two halves of the coil drift in opposite directions, so no single observer moves with both, and the capacitor is at rest in the lab. Adding the two electron-frame fields in the lab frame mixes frames.
4. An absorber is a non-electrical barrier. If the signal came from a field that passes through everything, putting matter in its path would not remove it. The signal vanished, so whatever moved the meter was stopped by a barrier. That contradicts unshieldability for that signal (Hooper did not draw this inference).
5. 0.02/555 = 3.6 x 10^-5 of the weight. It does not test the superconducting form because (i) no superconducting coil was used, so currents and claimed drift speeds were far below what the patent says is needed, and (ii) a "minuscule" effect below threshold was not excluded. Other caveats: the coils were toggled on and off without the warm-up Hooper used, and the flat coil differed from the 4020-wire cylinder on which Hooper's capacitor data were taken.