Primer: Amy Eskridge, gravity modification and the spinning-bismuth experiment

Companion files: arbiter.md (final verdicts), physicist.md, mathematician.md, contrarian.md, claims.md, sites.md and research/ (the Investigator's leads), example.py (reproduces every number in Section 5).

Primer author: Step 4 (Opus), 2026-10-07. No new verdicts: every verdict below is the arbiter's. Where I did a calculation of my own it is tagged [calc] and reproduced in example.py.

Source gap (repeated from claims.md and arbiter.md). Amy Eskridge (c.1988-2022) published no paper, preprint, patent, equation or data [read: README, an owner note; arbiter]. Her own material is one slide deck (HAL5 lecture, Huntsville, 6 Dec 2018), the machine-made captions of that lecture, the machine-made captions of a 3 h 15 min interview (about May 2020, no speaker labels, so who says what is sometimes uncertain) and two archived copies of her Institute for Exotic Science website. None of it contains an equation, data table or protocol of her own. The only documents in the folder with real mathematics and measurements are by others: her father Richard Eskridge's NASA Technical Memorandum TM-20205010911 (with M. Nelson and M. Schoenfeld, Nov 2021; she is not named in it) and the Dresden group's 2024 test of Alzofon's weight-reduction claim (arXiv 2402.15529; she is not named in it either). Not obtained: any NASA Marshall Space Flight Center (MSFC) report of the 2015 pulsed-superconductor test she describes, Alzofon's 1981 AIAA paper 81-1608, the interview audio, the Sept 2020 cease-and-desist letter, and the "V5" rotor data held by the company that funded her father's work. So the physics in this primer is mostly the physics of the claims she pointed to, not of a theory she wrote down. Where a conclusion rests on [memory] alone, it says so.

Interested parties (their descriptions are reported as theirs, with their stake): Amy Eskridge and her Institute (sought investors for gravity-modification research); Richard Eskridge (her father, first author of the NASA memorandum); Quantum Machines LLC (funded the memorandum's work, thought the theory could "provide the basis for an advanced propulsion system" [read: TM p.13], holds the V5 data); Mark Sokol and Falcon Space (her 2020 interviewer, pursuing the Alzofon experiment; runs the APEC conference site that reports it); Podkletnov and Poher (authors of their own claims); The Sentinel Network (argues a suppression thesis).

Source tags: [read] = from the documents in the folder (page, or lecture/interview time stamp); [web] = Internet source with URL; [memory] = recalled from training, with confidence; [calc] = arithmetic done for this review.

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1. The idea in one paragraph

Amy Eskridge was a young Huntsville, Alabama researcher and the president of a small private Institute for Exotic Science, and the daughter of a NASA Marshall propulsion engineer. In a 2018 lecture she surveyed a century of "anti-gravity" claims: high-voltage capacitors (Townsend Brown), spinning gyroscopes (Laithwaite), and above all superconductors, the Russian engineer Podkletnov's report that a spinning superconducting disc made objects above it about 2% lighter, and the French researcher Poher's pulsed superconductor "impulse" device, which she said her father had tested at NASA in 2015 with dramatic but unpublished results. Her argument was that such results keep appearing and then vanish, into classified programmes, into academic stigma, or for lack of money, and that the remedy is a privately funded, independent institute with a testable theory. By 2020 the "next thing to test" in her circle was the idea that lining up the spins of atomic nuclei could change an object's weight. Her father's NASA memorandum had proposed exactly such a "spin-coupled force" and reported a 0.3 g weight change in a spinning bismuth disc in 2016. The reviews found that the anomalies she cites are real claims that were mostly never tested in their original form, that the tests that were run on simpler versions found nothing, and that the bismuth result, while never properly checked, is about 2000 times larger than the memorandum's own formula predicts for the magnet it used. She died in 2022 (ruled a suicide; her father told the press he did not find it suspicious, while in 2020 she had described surveillance and threats); the Institute published nothing.

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2. What you need to know first

Newton's gravity and what a scale reads. Two masses m₁ and m₂ (kg) a distance r (m) apart attract with force F = G m₁ m₂ / r², where G = 6.674 × 10⁻¹¹ N m²/kg² is Newton's gravitational constant. The pull of the whole Earth on a mass m at its surface is the weight mg, where g ≈ 9.81 m/s² is the gravitational acceleration. A scale does not measure gravity directly: it measures the total vertical force the object pushes down with, which also includes air buoyancy, air currents, magnetic forces on or near the scale, and the pull of supporting wires. Every "weight change" claim must first rule those out. Read: Halliday, Resnick and Walker, Fundamentals of Physics, the chapters on gravitation and on forces.

Rotation of rigid bodies. A body spinning at angular rate ω (rad/s; ω = 2πf where f is revolutions per second) about an axis has moment of inertia I (kg m²; I = ½MR² for a uniform disc of mass M and radius R, I = (2/5)MR² for a solid sphere), spin angular momentum s = Iω (kg m²/s = J s) and spin kinetic energy k_s = ½Iω² (J). Angular momentum is a vector along the spin axis, pointing by the right-hand rule. Two results matter here. First, the centre-of-mass theorem: for any body, however it spins inside, the total external force equals the total mass times the acceleration of its centre of mass (F_ext = M a_cm). Spinning changes torques, not that force. Second, kinetic energy is a scalar: it has no direction, so a spin "with" or "against" something has the same kinetic energy. Read: Taylor, Classical Mechanics (the chapters on rotational motion of rigid bodies), or Kleppner and Kleppner-Kolenkow, An Introduction to Mechanics.

Nuclear spin and the Zeeman effect. Many atomic nuclei carry an intrinsic angular momentum ("spin"), measured in units of ħ = 1.0546 × 10⁻³⁴ J s (the reduced Planck constant). A nucleus of spin quantum number I has an angular-momentum magnitude ħ√(I(I+1)), and its component along a chosen axis can take only the 2I+1 values mħ, with m = −I, −I+1, ..., +I. Bismuth-209 has I = 9/2, so ten allowed values. Spin comes with a magnetic moment μ (J/T), and in a magnetic field B (tesla, T; 1 T = 10,000 gauss) each orientation has energy E_m = −m γħB, where γ = μ/(Iħ) is the gyromagnetic ratio (rad/s per T). Nuclear moments are tiny, measured in nuclear magnetons μ_N = 5.05 × 10⁻²⁷ J/T, about 2000 times smaller than the electron's. Read: Griffiths, Introduction to Quantum Mechanics (angular momentum and spin); Slichter, Principles of Magnetic Resonance (for the nuclear case).

Boltzmann statistics and the Curie law. At temperature T (kelvin), a state of energy E is occupied with relative probability e^(−E/k_B T), where k_B = 1.381 × 10⁻²³ J/K is Boltzmann's constant. Applied to the 2I+1 Zeeman levels, this gives the average alignment (the "polarization") P = ⟨m⟩/I, the fraction of full alignment. When the level spacing γħB is much smaller than k_B T (always true for nuclei at room temperature), the sum simplifies to the Curie law:

P ≈ (I+1)/3 × γħB / (k_B T).

That is the entire reason nuclear alignment is hard: nuclear magnetic energies are a million times smaller than thermal energy at room temperature. Read: Schroeder, An Introduction to Thermal Physics (the Boltzmann factor and the paramagnet); Kittel, Introduction to Solid State Physics (paramagnetism).

Superconductors in one paragraph. Below a critical temperature some materials (for example the ceramic YBCO, yttrium barium copper oxide, superconducting below about 92 K, so it works in liquid nitrogen at 77 K) carry current with zero resistance and expel or pin magnetic fields (the Meissner effect and flux pinning). That is why a magnet can float above a cooled YBCO disc. Nothing in the standard theory of superconductivity couples it to gravity at a measurable level; whether any such coupling exists is a research question with no confirmed effect [web: Gallerati 2022 review, https://arxiv.org/pdf/2206.07574]. Read: Griffiths, Introduction to Electrodynamics (magnetic materials), then any solid-state text.

The equivalence principle. All bodies fall with the same acceleration whatever they are made of. Torsion-balance and satellite (MICROSCOPE) tests confirm it to about 1 part in 10¹³ to 10¹⁵ [memory: high]. A material whose weight depends on its internal state (spinning, superconducting, spin-aligned) would violate it, so such a claim needs a new force, not a re-reading of Newton.

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3. The textbook view

Gravity cannot be shielded, and a "2% lighter" claim is enormous

In Newtonian gravity and in general relativity (Einstein's theory, in which gravity is the curvature of space-time produced by mass and energy), every bit of mass-energy attracts and there is no negative gravitational "charge", so there is nothing to make a shield from. Amy's own slides say this fairly: antigravity is "'impossible' according to General Relativity without negative mass" [read: HAL5 slide p.7].

How big is a 2% change in weight? An ordinary mass M at distance r changes g by GM/r². To change g by a fraction f at r = 1 m you need M = f g r²/G [calc; example.py part F]:

A lab disc a few centimetres across would have to act like a small mountain. That does not make the claim impossible (it would be a new coupling, not ordinary gravity), but it means such an effect would be huge on any sensitive gravimeter, and that mundane forces of the same size (convection above boiling liquid nitrogen, buoyancy, magnetic forces on the test object) must be ruled out first. Amy raised the liquid-nitrogen explanation herself in the lecture: "some people would say that all the explanation is just the liquid nitrogen vaporizing" [read: lecture 00:43:29].

Spinning things do not change weight

By the centre-of-mass theorem, a gyroscope on a scale pushes down with Mg whether it spins or not; spinning only changes torques. The Japanese claim of Hayasaka and Takeuchi (1989) that a gyroscope spinning one way weighs less was tested in 1990 and found null: Quinn and Picard (Nature) saw at most about 5% of the claimed effect before corrections, and less after correcting for friction and temperature; Faller and others, and Nitschke and Wilmarth, also found nulls [web: https://link.springer.com/article/10.1038/343732a0 ; https://link.aps.org/doi/10.1103/PhysRevLett.64.2115 ; arbiter]. Those tests were of the Hayasaka-Takeuchi claim, not of Eric Laithwaite's gyroscope demonstrations (his 1974 Royal Institution lecture [memory: high]), for which the review found no test as a weight claim; Amy's own slide says of Laithwaite that "Newton's 2nd Law explains this effect" [read: HAL5 slide p.19]. (Hayasaka is not in her slides or lecture; the reviewers bring him in as the tested case.)

Aligning nuclei changes magnetism, not weight (in standard physics)

Lining up nuclear spins is routine (it is how NMR, nuclear magnetic resonance, and MRI work). It changes a sample's magnetization, and a magnetized sample in a non-uniform field feels a magnetic force F = ∇(m·B), where m here is the sample's magnetic moment. That force can push up or down on a scale and is a known magnetic effect. Standard physics has no coupling of nuclear spin to gravity at any level a scale could see. Laboratory searches for spin-gravity couplings (torsion balances with spin-polarised masses, atomic comagnetometers) have, as far as this review recalls, found none [memory: medium; not web-checked by any reviewer or the arbiter, and no verdict here depends on it].

Two other spin-mechanics effects are real and appear in the NASA memorandum's reasoning [read: TM p.29]: the Einstein-de Haas effect (magnetizing an iron rod makes it twist, because the aligned electron spins carry angular momentum) and the Barnett effect (spinning an iron rod magnetizes it slightly). Spinning at rate ω acts on a spin like a magnetic field of size ω/γ. For bismuth nuclei that is about 7 × 10⁻⁵ T even at 30,000 rpm [calc: ω = 3,140 rad/s, γ = 4.37 × 10⁷ rad/s/T], tiny compared with a 0.2 T magnet.

What the 1990s and 2000s tests of superconductor gravity found

• Podkletnov's rotating YBCO disc (1992, 1997): reported by its author; never copied in full by anyone [web: Gallerati 2022]. Tests of reduced versions were null: an MSFC static test (Li, Noever, Robertson, Koczor and Brantley, Physica C 281, 1997) bounded any change below 2 parts in 10⁸ [web: https://ntrs.nasa.gov/citations/19990039542]; Hathaway et al. 2003 spun at 400-800 rpm against Podkletnov's 5,000 rpm and saw nothing to 0.001% [web: https://arxiv.org/pdf/gr-qc/0404005]. None used his radio-frequency drive or his composite disc.
• Poher-type pulsed devices: Lörincz and Tajmar's scaled replication found an electromagnetic artifact once a double Faraday cage was used, and a 2016 follow-up attributed the remaining accelerometer signal to acoustic noise [web: Gallerati 2022, as reported there; primary papers not opened]. Dembovskis (2024) reports not confirming Poher [web: snippet only, DOI 10.13140/RG.2.2.28989.17129].
• The research area is not taboo: Gallerati's 2022 review in Frontiers in Physics treats superconductor-gravity coupling as an open topic [web: https://arxiv.org/pdf/2206.07574].

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4. Where the inventor departs

Amy Eskridge did not write down a theory, so there are two departures to describe: hers (a position about evidence and institutions) and the one in her father's memorandum (a definite formula). Keep them separate: she is not an author of the memorandum.

4a. Her own position, side by side

Her strongest point is the second row. The arbiter agrees that the nulls are real but are not copies of the original experiments, so the original Podkletnov claim remains "Never properly tested". Her weakest point is that the institutional explanation has no documents behind it; she herself was careful to say she did not know why Ning Li's work stopped ("I don't know what happened" [read: lecture 00:18:16]; her slide p.25 on Li's disappearance is a screenshot of one anonymous Reddit post).

Ning Li, the central "disappearance" case in her lecture, and what the record shows. Li, a University of Alabama in Huntsville (UAH) physicist who worked with NASA Marshall on superconductor gravity in the 1990s [memory: high; Li et al. 1997 is an MSFC paper, web: Section 3], and who received a $500,000 Department of Defense contract in 2001 per Amy's slide p.24 [read], published nothing after 2002; her company AC Gravity LLC renewed its business licence through 2018; she was struck by a vehicle on the UAH campus in 2014 and left with permanent injuries; she died on 27 July 2021 [web: Huntsville Business Journal, https://huntsvillebusinessjournal.com/news/2023/07/30/solving-the-mystery-of-huntsvilles-brilliant-scientist-disappearing/ ; The Sentinel Network, which argues a suppression thesis]. Her son is quoted there saying "The results of that grant were never published" [web: same]. The arbiter sets out competing explanations for the silence (a technical stall, since an audience voice says the discs cracked [read: lecture 00:46:02]; loss of funding; illness and injury; classification or absorption into defence work, for which there is no evidence; an effect that did not hold) and judges that the record supports illness and injury best while leaving the others open. The deciding records are AC Gravity's filings, the 2001 contract record and UAH-NASA collaboration files.

One factual error on her slides. Slide p.12 calls "Patent 1,655,144" Tesla's "'space drive' or anti-electromagnetic propulsion system", citing William Lyne's popular book Occult Ether Physics. US 1,655,144 is a grain-treating machine by Hallgarth and Chandler (1928) [web: https://patents.google.com/patent/US1655144A/en; arbiter QE revision A5]. The number is wrong or the attribution is; no verdict depends on it.

Two of her own statements cut against the suppression reading and must stay in the record: Tajmar offered to test her samples ("send them to me") and she did not send them, giving distrust as the reason [read: interview 01:27:47]; and a first-hand voice in her lecture Q&A said the 2015 MSFC test "did not reproduce [Poher's] signals" under a double Faraday cage [read: lecture 00:51:12].

The same first-hand voice (unidentified; the best-supported reading is her father, from its placement after "my dad did that", but that is an inference and the audio is needed) also gave the account's own case for an anomaly, which stays beside the null [read: lecture 00:49:38-00:52:44, quoted in order]: "we got an excess of 500 Gs, but we never reproduced the waves"; a magnet floated over a second superconductor and "when we fired the Boyer device the little magnet went far away"; "we told management about this"; "getting a signal is never a problem ... it's a question of getting the right signal"; "with a double Faraday cage, we did not reproduce Boyer's signals. However, we did see a whole lot of really strange effects. Like the tossing of the magnet and forces coming off the disc"; and, against a mundane cause, "if it was a thermal explosion between the layers of the disc, it would have destroyed the disc, but you pull it out and it was pristine". He also describes a million-frames-per-second film of "a wave coming off" and says "I was impressed with it". ("Boyer" in the captions is read as Poher, consistent with slide p.29.) The pristine disc is the account's own argument against a thermal explosion inside the disc and is not rebutted in the text. It does not exclude the ordinary candidates the reviewers list (boiling of the liquid nitrogen around the disc, a pulsed magnetic field acting on the magnet, steam shock, electrical pickup), because no control discharge with a warm or non-superconducting disc and no magnet mass, distance or timing is reported. "We told management" points to a record that may exist at MSFC.

4b. The NASA memorandum's spin-coupled force, side by side

The memorandum starts from the Pope-Osborne Angular Momentum Synthesis (POAMS), a theory by two English authors (Galilean Electrodynamics 14, 2003 [read: TM p.55]). NASA reformulated it as a "spin-coupled force" (SCF) [read: deep read of TM pp.13-24]. Symbols: M_e Earth's mass; m the body's mass; v_s, r_s the speed and radius of the circle the body rides on as Earth turns; v_o, r_o the POAMS "natural orbit" speed and radius; k_o = ½ m v_o² orbital kinetic energy; k_s = ½ I_p ω_p² the body's spin kinetic energy (I_p its moment of inertia, ω_p its spin rate); s_p = I_p ω_p its spin angular momentum; F_N the ordinary (Newtonian) force; Δf the extra spin-coupled force. "Co-spin" means spinning the same way as the orbit; "anti-spin" the opposite way.

The mathematician checked every algebraic step of eqs 11-28a and found them correct: the long derivation is an exact rewriting of the POAMS postulate, adding no new physics [mathematician; arbiter]. The physics content is in the postulates in the right-hand column. The gyroscope form also contradicts the centre-of-mass theorem: an arm holding a gyroscope on a circle must supply exactly Mω²r whatever the wheel's spin, while the memorandum predicts 15-19% changes at 60 Hz spin [read: TM Table 1, p.25; mathematician]. Table 1 is a correct output of the printed eq. 28a once the memorandum's sign convention is applied (Appendix B: measured force = gyroscope centripetal force minus the spin-coupled force); an earlier claim in the review that it was not reproducible was a sign error and has been withdrawn [arbiter QE revision A1]. The table was never measured: the gyroscope spun down too fast.

Why the memorandum turned to nuclei. For everyday objects the formula predicts almost nothing: k_s/k_o is tiny because k_o/m ≈ 9 × 10⁹ J/kg (the natural-orbit speed is huge). NASA's own conclusion: "spinning objects will change weight by less than 1 part in 10⁸ for ordinary objects spinning at realistic rates" [read: TM p.16]. But a nucleus, modelled as a classical spinning ball, has an enormous spin energy for its mass. Appendix C computes that a fully aligned bismuth nucleus at Huntsville's latitude would weigh 2.69 times normal in co-spin, and be pushed upward with 2.29 times its weight in anti-spin [read: TM p.29, App. C]. Since ordinary bismuth has its nuclei pointing every which way, the memorandum argues the effects cancel, and an experiment needs to align some fraction of them [read: TM p.30]. Hence the bismuth rotor.

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5. Worked example: could the bismuth rotor's 0.3 g come from the memorandum's own force law?

The experiment, as the memorandum reports it [read: TM pp.31-35]. A 211 g cast bismuth disc spun by a small electric motor inside a magnet assembly of "only 2,000 gauss" (0.2 T), the whole device sitting on a 10 kg OHAUS scale with 0.01 g resolution, powered through supported wires. First test 7 October 2016, at the NASA Propulsion Research Laboratory, with Richard Eskridge, Mike Nelson and Chris Milam (CEO of the funder) present. In anti-spin mode the device "immediately lost about 0.3 g". This "did not inspire much excitement because this weight loss could be due to thermal buoyancy or aerodynamic forces". The rotor and magnets were then flipped over (a disassembly and reassembly) for co-spin, and "the device gained 0.3 g of weight. This was a remarkable result." The memorandum says "These results matched the theory. This would correspond to only a very small alignment fraction of nuclei." The effect then "lessened each time the device was tested", vanished after several tests, and "returned with equal force" with new magnets; it "was later suspected that this was due to some phenomenon in the rare Earth magnets". A later V5 device was built and tested by the funder, who keeps its data.

Two statements in the memorandum argue against ordinary causes and must be weighed with the fading [read: TM p.33, quoted in the TM deep read]: - No current reversal. "A multiphase motor was used ... the direction is controlled by relative phasing of the three pulsed DC signals in the wires. This kind of motor does not have a reversal of DC current which might explain a reversal of forces." This answers one artifact the physicist lists (forces from the power leads). Its limit: in V3 the co-spin run came after the "rotor and magnet assemblies" were flipped over, so the magnets' orientation relative to the scale and to Earth's field, and the motor's position, also changed between the two runs. - Unchanged field. "The external magnetic field of the magnets was measured from test to test and did not change." This is partly in the effect's favour, since a magnet that was weakening would be the first suspect for the fade. Its limit: the instrument and the point of measurement are not named. No control run is reported (no spin-zero rotor, no magnets-only run, no stalled rotor, no temperature or air-flow log); the only comparison is anti-spin against co-spin, and the run count is "many times" with no number [read: TM p.33].

Note in fairness: the sign of each change (lighter in anti-spin, heavier in co-spin) is the sign the theory predicts. The question here is the size.

The calculation below is done in four steps. example.py reproduces every number.

Step A. The memorandum's own per-nucleus factor

Appendix C models the bismuth nucleus as a classical solid sphere [read: TM p.29, App. C]:

• mass m = 208.98 u = 3.470 × 10⁻²⁵ kg (u = 1.6605 × 10⁻²⁷ kg, the atomic mass unit);
• radius R = 1.2 fm × 209^(1/3) = 7.12 × 10⁻¹⁵ m (1 fm = 10⁻¹⁵ m);
• moment of inertia I = (2/5) m R² = 7.04 × 10⁻⁵⁴ kg m²;
• spin angular momentum s = ħ√(I_n(I_n+1)) with I_n = 9/2: s = ħ√24.75 = 5.246 × 10⁻³⁴ J s;
• implied spin rate ω = s/I = 7.46 × 10¹⁹ rad/s.

At latitude 34.5° (Huntsville) the lab rides a circle of radius r_s = cos 34.5° × 6.373 × 10⁶ m = 5.25 × 10⁶ m at speed v_s = cos 34.5° × 464.74 m/s = 383.0 m/s. The cross term under the root of eq. 28 is

X = (m v_s²/r_s) × (s ω / r_s) = 7.21 × 10⁻⁴⁷ N²,

and the sheet divides it by the square of the nucleus's weight, (mg)² with g = 9.81 m/s², to get X/(mg)² = 6.23. Then [calc; matches the TM to three figures]:

• co-spin: total force / weight = √(1 + 6.23) = 2.69, a change of +1.69 times the weight;
• anti-spin (eq. 28b): total force / weight = −√(6.23 − 1) = −2.29 (upward), a change of −3.29 times the weight.

What drives it: the spin energy ½Iω² = 1.96 × 10⁻¹⁴ J (about 122 keV) is 770,000 times the nucleus's orbital kinetic energy ½mv_s² [calc]. The memorandum asks the reader to "suspend our disbelief regarding the actuality of atomic spin" because the nucleus's "surface velocity can easily exceed the speed of light" [read: TM p.29]. With its own numbers the equatorial surface speed is ωR = 5.3 × 10⁵ m/s, only 0.18% of the speed of light c [calc]. The real worry is different: a nuclear spin is a quantum property, not a ball rotating, so ½Iω² is a model number, not a measured energy.

Step B. How many nuclei would have to be aligned?

The measured change is 0.3 g / 211 g = 0.142% of the rotor's weight. If a fraction P of the nuclei were fully aligned and the rest random (cancelling, as the TM assumes), the change would be P × 1.69 in co-spin. So [calc]:

• co-spin: P_needed = 0.00142 / 1.69 = 8.4 × 10⁻⁴ (about 1 nucleus in 1,200);
• anti-spin: P_needed = 0.00142 / 3.29 = 4.3 × 10⁻⁴.

Step C. How many nuclei does a 0.2 T magnet align at room temperature?

Bi-209 has magnetic moment μ = 4.11 μ_N = 2.08 × 10⁻²⁶ J/T [memory: high], so its gyromagnetic ratio is γ = μ/(I_n ħ) = 4.37 × 10⁷ rad/s/T (6.96 MHz/T). At B = 0.2 T and T = 300 K:

• level spacing / thermal energy: γħB/(k_B T) = 2.23 × 10⁻⁷; equivalently μB/(k_B T) = 1.00 × 10⁻⁶;
• Boltzmann average over the ten levels m = −9/2 ... +9/2, P = ⟨m⟩/I_n: P = 4.08 × 10⁻⁷;
• Curie-law shortcut: P ≈ (I_n+1)/3 × γħB/(k_B T) = (5.5/3) × 2.23 × 10⁻⁷ = 4.08 × 10⁻⁷ (identical, as expected when the spacing is so small).

Can anything else raise the alignment? The memorandum names four mechanisms besides the magnet [read: TM pp.31-33, quoted in the TM deep read]: the Barnett effect ("Like the rotating cylinder of Barnett, electrons will align due to self-magnetization"), Overhauser transfer ("Aligned electrons will tend to transfer their alignment to the nuclei"), a field gradient that "induces a small fraction of the nuclei to flip parallel to the spin axis", and the Wallace effect (from a 1971 patent, US 3,626,605). It gives no number for any of them, no rotor speed and no gradient value; it calls the method "very weak" [read: TM p.33] and says that "even for very high magnetic fields and cold temperatures the alignment fraction is limited to a very small fraction of the total" [read: TM p.30]. The arbiter's evaluation [arbiter QE revision A2; calc and memory: high unless marked]: - Barnett (rotation). Spinning at ω acts like an extra field ω/γ. The rotor's speed is not stated; at an assumed 10,000 rpm ω/γ = 2.4 × 10⁻⁵ T, and even 100,000 rpm gives 2.4 × 10⁻⁴ T, about 800 times below the magnet [calc]. Negligible. - Overhauser transfer. Overhauser transfer means: if the spins of a metal's conduction electrons are driven out of equilibrium, their contact with the nuclei pushes the nuclei toward the electrons' much larger polarization. It works only when the electron spin resonance is saturated by a microwave field (about 5.6 GHz at 0.2 T). The ceiling is the thermal nuclear polarization above multiplied by γ_e/γ_n ≈ 4,000 (γ_e = 1.76 × 10¹¹ rad/s/T is the electron's gyromagnetic ratio), giving P up to about 1.6 × 10⁻³ [calc, example.py part C; the arbiter rounds it to 1.7 × 10⁻³], which would be enough (Step B needs 8.4 × 10⁻⁴). But the memorandum describes no microwave source, and without one the electron-nucleus contact only relaxes the nuclei toward the thermal value of this step. Bismuth's very low density of conduction electrons (about 10⁻⁵ per atom [memory: medium; not web-checked]) also works against the scheme. - Gradient flipping. A field gradient pushes on a magnetic moment (force ∇(μ·B)); the torque μ × B makes it precess about the field, not align. The equilibrium alignment is still set by the local B/T, at most 0.2 T here. - Wallace effect. A patent claim; no magnitude given and no independent measurement known to the reviewers [memory: medium]. So the memorandum supplies no number that lifts the alignment above the thermal value. Heating, which the memorandum says "acts to destroy the nucleonic alignment" [read: TM p.33], would only lower it.

Step D. Compare

The predicted change is about one-seventieth of a single step of the 0.01 g scale. By its own formula, the memorandum's theory predicts no visible weight change at all for this device. That is why the arbiter rules the statement "these results matched the theory" Refuted by calculation (about 2000 times too small, 1000 times at the most generous reading) for the means the memorandum describes: a static 0.2 T field, room temperature, rotation, no microwaves. The condition cuts both ways: a microwave-saturated Overhauser process could in principle reach the needed size, and the memorandum does not say one was present [arbiter QE revision A2]. The 0.3 g observation itself stays Never properly tested: nobody ran the controls that would say what caused it.

Step E. Does the conclusion depend on choices?

1. The other ways to apply the formula. The mathematician found that the memorandum's rule gives three different per-nucleus answers depending on which speed and which normalising force one uses [mathematician; arbiter]. Each one still leaves a shortfall of over a thousand [calc, example.py E2]:

2. Field and temperature. Polarization scales roughly as B/T [calc, example.py E1]:

So on the memorandum's own law, a bismuth sample in a cold, high-field NMR magnet should change weight by more than the rotor did, and at 50 millikelvin by around 19% of its weight. NMR magnets at 9 T and 5 K are ordinary laboratory equipment. The memorandum's answer is that "NMR researchers ... never bother to weigh their samples" [read: TM p.30]. The Dresden group did weigh polarized samples in a 9 T, 5 K NMR setup (aluminium, copper and fluorine nuclei, not bismuth): at low pulse counts they saw no change, and at high power they saw signals that also appeared with no sample at all and tracked the temperature [read: arXiv 2402.15529 pp.8-15, deep read]. That test was designed for Alzofon's claim, not POAMS, and used different nuclei, so it is not a test of the memorandum; it is the closest experiment on record.

3. A further check on the memorandum's cancellation argument (primer author's calculation; it adds no verdict, it illustrates the arbiter's "Internally inconsistent"). The memorandum says ordinary, unaligned material shows no effect because "co-spin and anti-spin forces cancel out" [read: TM p.30]. But the formula is not symmetric: a fully co-spin nucleus changes by +1.69 times its weight, a fully anti-spin one by −3.29. Giving each nucleus a spin direction at angle θ to Earth's axis, using the vector form's cos θ dependence (eq. 31), eq. 28a where the root is real and eq. 28b where it is not, and averaging over random directions gives a mean change of about −0.6 times the weight [calc, example.py E3; −0.60 for classical random directions, −0.59 for the ten equally filled quantum levels]. Taken literally, the rule would make every lump of ordinary bismuth weigh about 40% of its real weight, which every chemistry stockroom scale refutes. The rule as written cannot be applied orientation by orientation, and the memorandum does not say how else to apply it. This depends on my assumption about how eqs 28b and 31 combine (the TM gives no rule for mixed orientations), so treat it as a question for the theory's defenders, not a settled point. The arbiter did not re-derive it and asked that it be kept only as an illustration of the "Internally inconsistent" verdict with this assumption stated, which is how it appears here [arbiter QE revision A6].

Physics lesson of the example. The idea (aligned spins carry angular momentum, angular momentum couples to mechanics) rests on real physics, the Einstein-de Haas and Barnett effects. What fails is the bookkeeping: the force law needs a large aligned fraction, and the experiment had essentially none. Whenever a claimed effect depends on alignment, polarization or a fraction of something, compute the fraction first.

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6. Evidence table

Verdicts are the arbiter's, using the review's scale.

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7. What a learner should take away

What is solid. - Nuclear spins are real angular momentum, and angular momentum couples to mechanics: the Einstein-de Haas and Barnett effects are textbook physics, and the memorandum cites both correctly [read: TM p.29]. - Amy's methodological point is correct and documented: the published nulls on Podkletnov's disc were run on static or slower, unpowered versions, so the original claim has never been tested as stated. The arbiter keeps it "Never properly tested", not "refuted". - The NASA memorandum's algebra (eqs 11-28a) is correct, its MathCad arithmetic checks, and its authors were candid about the weaknesses of their data ("rudimentary and preliminary" [read: TM p.36]; the first 0.3 g loss could be "thermal buoyancy or aerodynamic forces" [read: TM p.33]). - It is a fact that NASA MSFC engineers worked on "anomalous gravitational effects of electrically pulsed superconductors" [read: TM pp.37-38], as she said.

What is wrong, and why the mistake is instructive. - Fraction blindness. The memorandum computes a huge per-nucleus effect and then says the observed effect corresponds to "a very small alignment fraction" without computing that fraction. Computing it (Section 5) shows a gap of about 2000; of the mechanisms the memorandum names, only a microwave-driven Overhauser process could close it, and none is described. Any effect that depends on alignment, purity or efficiency needs that number before it can be said to "match". - Restating a postulate is not deriving it. Twenty equations of algebra turned "G changes with spin" into "a new force appears with spin". Rewriting changes the words, not the content. Look for where the physics enters (here: adding a direction-dependent sign to a scalar energy). - Energy is a scalar. A rule in which kinetic energy is added for one spin direction and subtracted for the other has to come from somewhere other than kinetic energy; the memorandum does not say where. - The centre-of-mass theorem already answers every "spinning things weigh less" claim within Newtonian mechanics; a claim against it is a claim for a new force, which needs an experiment, not a reformulation. - A very large claimed effect makes ordinary causes the first suspects. A 2% weight change is a 3-million-tonne mountain at 1 m; 0.3 g on a scale next to rare-earth magnets is easily a magnetic, thermal or air-flow force.

What is genuinely open. - Whether Podkletnov's full original setup does anything: never built by anyone else (the arbiter's deciding experiment: a faithful replication with a calibrated gravimeter, magnetic and convection controls, raw data public). - What caused the bismuth rotor's 0.3 g and its fading. The memorandum's own points (no current reversal in the motor; magnet field measured unchanged) weigh against two ordinary causes but not against the reassembly between modes or air and heat effects. Decided by a matched spin-zero rotor, a closed housing, no disassembly between modes, magnet-only runs, and the V5 data. - Whether Alzofon's DNP experiment does anything at his actual conditions (0.33 T, 9.5 GHz microwaves, room temperature): never tested by a neutral party. - What the 2015 MSFC test recorded (notes, traces, the million-frames-per-second film, whatever was sent to "management"). The first-hand account holds both a null (Poher's signals not reproduced under a double Faraday cage) and its own positive case ("really strange effects ... forces coming off the disc", and a disc that came out "pristine", which argues against a thermal explosion inside it). A control discharge with a warm or non-superconducting disc would separate a superconductor effect from boiling, magnetic and shock forces. Richard Eskridge is alive and could say who spoke in the lecture Q&A. - Why Ning Li's work stopped after 2002: her 2014 injury and 2021 death are documented, and the other explanations (technical stall, funding, classification) remain open until AC Gravity's filings and the 2001 contract record are seen. - Why her Institute went silent after 2020 (the arbiter lists five non-exclusive explanations: a legal or IP restriction including the reported Sept 2020 cease-and-desist, funding failure, health, nothing to publish, and pressure as she described), and what the records she said existed (packet captures, logs, an Uber record) would show. Facts on record: the family's Alabama companies HoloChron Holdings LLC and HoloChron LLC were formed on 16 July 2018 and dissolved in Dec 2020 and Dec 2022 [web: https://al.ltddir.com/companies/holochron-llc/, a mirror of the state register]; a federal (SAM) entity for the Institute dated 17 Dec 2018 is reported by the Sentinel Network (not checked at SAM.gov); NASA assigned the plasmoid-thruster patent US7808353B1 to Richard H. Eskridge on 3 Oct 2018 [web: https://patents.google.com/patent/US7808353B1/en]; in the interview she reads from her calendar that she was "negotiating with maxar about selling them a plasma thruster patent on the 17th of december" (2019) [read: interview 00:57:56] (that this is the same patent is the arbiter's inference); and she says an Austin, Texas real-estate investor "poached" her father out of NASA and brought "Hal" (the arbiter reads this as Hal Puthoff) to the family house [read: interview 00:47:14; investor unnamed, no year]. Whether that investor is Quantum Machines, the memorandum's funder, is unknown. These are historical questions, not physics; the records that would decide them (the patent assignment file, Maxar correspondence, the cease-and-desist text, the Delaware and SAM filings) are listed in arbiter.md.

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8. Check yourself

1. A 150 g gyroscope rests on a scale. When it spins at 20,000 rpm, what does the scale read, and which theorem tells you without any calculation?
2. Using the Curie law, estimate the polarization of protons (I = 1/2, γ = 2.675 × 10⁸ rad/s/T) in a 1.5 T hospital MRI at body temperature, 310 K. Is it bigger or smaller than bismuth's in the NASA rotor, and why?
3. In Step B, why is the needed alignment different for co-spin and anti-spin, and which value gives the theory its most generous reading?
4. The memorandum says unaligned bismuth shows no effect because co-spin and anti-spin cancel. Without computing, explain why a formula of the form √(1 + kx) − 1 (take k small enough that the root stays real), averaged over x from −1 to +1, cannot give zero.
5. Podkletnov's 2% weight reduction would need 2.9 × 10⁹ kg at 1 m. What does that tell you about where to look first for an explanation, and which ordinary effects did Amy herself mention?

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9. Further reading

Mainstream sources - Taylor, Classical Mechanics (rigid-body rotation; centre-of-mass motion). - Schroeder, An Introduction to Thermal Physics (Boltzmann factor; paramagnetism). - Slichter, Principles of Magnetic Resonance (nuclear spin, polarization); Abragam, The Principles of Nuclear Magnetism (dynamic nuclear polarization, for Alzofon). - Gallerati, "Interaction between macroscopic quantum systems and gravity", Frontiers in Physics (2022), a review of Podkletnov, Poher, Tajmar and related work [web: https://arxiv.org/pdf/2206.07574]. - Li, Noever, Robertson, Koczor and Brantley, Physica C 281 (1997) 260-267, MSFC static test [web: https://ntrs.nasa.gov/citations/19990039542]. - Hathaway, Cleveland and Bao, rotating-superconductor test (2003) [web: https://arxiv.org/pdf/gr-qc/0404005]. - Quinn and Picard, Nature 343 (1990) 732, and Faller et al., Phys. Rev. Lett. 64 (1990) 2115, gyroscope nulls [web: URLs in Section 3]. - Stark, Grafe and Tajmar, "Investigation of the Alzofon weight reduction experiment using NMR" (2024) [read: arXiv 2402.15529, in the folder].

The inventor's own works and the documents closest to her - Amy Eskridge, "A Historical Perspective on Anti-Gravity Technology", HAL5 lecture slides and video, Huntsville, 6 Dec 2018 [read: in the folder]. - Interview with Jeremy Rys and Mark Sokol, about May 2020 (YouTube l0O4cEIkUZc) [read: in the folder, machine captions]. - Institute for Exotic Science website, Wayback copies of Nov 2018 and Jul 2019 [read: in the folder]. - R.H. Eskridge, M.A. Nelson and M.P. Schoenfeld, NASA/TM-20205010911, "A Study of the Pope-Osborne Angular Momentum Synthesis Theory (POAMS) Including a Mathematical Reformulation and Validation Experiment", Nov 2021 [read: in the folder]. By her father; she is not named. - Osborne and Pope, "An Angular Momentum Synthesis of 'Gravitational' and 'Electrostatic' Forces", Galilean Electrodynamics 14 (2003) 9-19 [read: cited at TM p.55; not in the folder]. - Her later TV appearances (2021-24, nine credits as Institute president) are listed by the Investigator; their content is unseen [web: https://www.imdb.com/name/nm13210059/].

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Corrections to earlier documents

• Barnett estimates (physicist, contrarian, arbiter item 2). The memorandum does not state the bismuth rotor's spin rate; I searched the extracted text and found rpm figures only for the Hayasaka example and the gyroscope. The 3,000 and 5,000 rpm used by the reviewers are their assumptions. The conclusion does not change: even 100,000 rpm gives an equivalent field of about 2.4 × 10⁻⁴ T, far below the 0.2 T magnet [calc]. (Resolved: arbiter QE revision A2 now says "assumed 10,000 rpm".)
• Step E3 (resolved). The arbiter's QE revision A6 asked that this calculation be kept only as an illustration with its assumption stated, or dropped; it is kept, with the assumption stated.
• QE revision of this primer (2026-10-07). Corrected in this file: the 1990 gyroscope nulls tested Hayasaka-Takeuchi, not Laithwaite (Laithwaite is now "Never properly tested", and Hayasaka is no longer listed among the devices she surveyed); "I don't know what happened" is [read: lecture 00:18:16], not slide p.25; the monolayer/bilayer argument is hers, and the German Air Force remark is her assertion at 01:05:49; the "six forces" remark is attributed to her (medium-high). Added: the memorandum's motor-phasing and unchanged-field statements; the evaluation of the other alignment mechanisms; the first-hand voice's "strange effects" and "pristine disc" statements; Ning Li's documented fate; the suicide ruling, the reported 2026 text and the Shellenberger testimony; Prutchi in the Alzofon row; the company and patent leads; the Tesla patent error on her slide. The spin-gravity-bounds sentence in Section 3 is now marked as unchecked.

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Answers

1. It reads the same as when the gyroscope is still: 150 g (1.47 N). The centre-of-mass theorem (total external force = total mass × centre-of-mass acceleration) says that, with the centre of mass at rest, the scale force equals the weight whatever happens inside. This is why the 1990 Hayasaka replications found nothing.
2. P ≈ (I+1)/3 × γħB/(k_B T) = (1.5/3) × (2.675 × 10⁸ × 1.0546 × 10⁻³⁴ × 1.5)/(1.381 × 10⁻²³ × 310) = 0.5 × 9.9 × 10⁻⁶ ≈ 4.9 × 10⁻⁶. About 12 times bigger than bismuth's 4.1 × 10⁻⁷: the proton's gyromagnetic ratio is about 6 times larger and the field 7.5 times larger, partly offset by the smaller spin factor (I+1)/3 = 0.5 against 1.83. Even so, only about 5 protons in a million are net-aligned; MRI works because there are so many protons.
3. The formula is not symmetric: a fully co-spin nucleus changes by +1.69 times its weight, a fully anti-spin one by −3.29 (eq. 28b). A bigger per-nucleus change needs fewer aligned nuclei, so the anti-spin figure (4.3 × 10⁻⁴, a shortfall of about 1,100) is the most generous reading.
4. √(1 + kx) is a concave function of x (it curves downward), so its average over a symmetric range lies below its value at the middle, √1 = 1. The positive and negative halves therefore do not cancel; the average change is negative. Eq. 28b makes it worse, because it makes the negative side fall steeply. Only a straight-line (linear) law would cancel.
5. An effect equivalent to millions of tonnes of mass would be easy to detect with a gravimeter and would not need fine statistics, so first look for ordinary forces of the same size near the apparatus: convection and vapour from boiling liquid nitrogen, air buoyancy, magnetic forces on the test mass. Amy mentioned the liquid-nitrogen explanation herself ("all the explanation is just the liquid nitrogen vaporizing" [read: lecture 00:43:29]), and an audience member suggested convection currents.