Brush-Charles: Mathematician's review (Step 2)

Reviewer role: PhD mathematician (derivations, units, hidden assumptions). Source tags: [read] document itself; [read: OCR] as reported in facts.json by Step 1 (I did not re-OCR the scans); [web] URL; [memory] with confidence. Web search budget was exhausted, so only WebFetch of Wikipedia was available; checks are marked accordingly.

Source gap (repeated from claims.md)

Only brush-rexresearch.pdf (Nature 1911, Lodge letter, APS 1929) has a text layer; I read it in full [read]. Everything else is scan/OCR via Step 1. Not obtained: Brush's 1921, 1923, 1924, 1926, 1927 and 1928 experimental papers (raw tables, plates), any Bureau of Standards report, any replication. Conclusions on the experiments below rest on Brush's own 1929 summary plus Step 1's OCR reports, and on [memory]/[web] for modern limits. Where a conclusion rests on [memory] alone I say so.

Corrections to Step 1

1. claims.md claim 5 and facts.json say the Bureau of Standards was "checking" his calorimetry. The 1929 paper [read] says more: the Bureau "received official announcement that [air-dried Sandusky clay] does continually generate a measurable amount of heat" and is "about to commence" the nickel-cobalt silicate. So Step 1's "any Bureau report not obtained" is right, but note the only evidence of a positive Bureau result is Brush's own second-hand statement; the Bureau's own measurement size, uncertainty and whether it was about the same effect are unknown. No Bureau test of the gravity (drop) effect is mentioned anywhere I read.
2. claims.md claim 4 says "about 1 part in 4450 (falling containers, barium aluminate)". [read] This is the figure for the barium aluminate alone after dividing by its 40.3 % mass fraction. The raw container figure is 0.099 mm in 110 cm = 1 part in 11,000. I recomputed: 11,111 x 0.403 = 4,478, consistent with Brush's "4450" within rounding. Also the "1 part in 32,000" pendulum figure is a period difference (zinc vs bismuth), not a g difference; Step 1 is correct in the facts.json but claim 4 lumps the quantities as if the same kind. A period change of 1/32,000 corresponds to a g (weight per mass) difference of about 1/16,000 [calc: T ~ g^-1/2, so dg/g = 2 dT/T]. Brush's drop figure is directly dg/g.
3. facts.json for the 1928 address says the 0.0125 mm spark threshold converts to about 1/400,000 s. I checked: 0.0125 mm over 1.22 m is 1.02e-5 of the distance; fall time 0.499 s; timing difference = (1/2)(1.02e-5)(0.499) = 2.6e-6 s = 1/390,000 s. Correct.
4. Minor: in the 1911 Nature text [read], Brush writes "two-pound weight" after introducing a "pound-weight" (typo in source or transcription), and the 1911 text is Nature 86, pp.130-132 although Lodge cites p.129; not material.
5. facts.json lists the claim "recognised in metallurgy" for quenched-steel heat (from the 1928 address); this is Brush's assertion, unverified by me. Treat as [read: OCR] of Brush's own statement.

Claim 1: The energy of a falling body comes from the aether, not from "potential energy of position"

a. Internal consistency. The argument [read] has a genuine mathematical mistake. Brush places a pound of iron at the neutral point between Earth and Moon and says its potential energy "has disappeared entirely" because the net force is zero and the body "remains stationary". Force zero is not potential zero. Potential energy depends on the potential phi, not on its gradient. Worked numbers (GM_E = 3.986e14, GM_M = 4.90e12 m^3/s^2, Earth-Moon 3.844e8 m): the neutral point is 3.46e8 m from Earth (3.84e7 m from the Moon); phi there = -1.28e6 J/kg; at Earth's surface phi = -6.26e7 J/kg. Energy to lift = 6.13e7 J/kg, i.e. 2.8e7 J for one pound (0.4536 kg). Brush's other numbers check: that is a speed sqrt(2E/m) of about 11 km/s (about 10x a ~1 km/s cannon-ball) [calc]. The energy has not disappeared: the system potential is still 6.1e7 J/kg higher than at the surface, and the neutral point is a saddle (maximum along the Earth-Moon line, unstable equilibrium), which is why the body "remains stationary". The rhetorical paradox therefore dissolves. Lodge's 1911 letter [read] makes the qualitative version of the same reply (a weight on a hook; the force is simply balanced). Second point: "potential energy of position" is not a defect Brush has uncovered; in textbook physics the energy is a property of the Earth-body system (field energy), and Brush's move "it is in the aether" is a relabeling unless the aether has dynamics that reproduce the same function phi(r) with a different, testable consequence. His own text says only that the aether holds kinetic energy and "may" do so; no equation for the aether energy density, its dependence on position, or conservation bookkeeping is given. So the claim as stated has no mathematics to be consistent or inconsistent with. Third: conservation. If the aether supplies the KE by the net wave push, the work done equals force x distance, F dx, which is exactly the textbook result; so the claim is not contradictory, but it adds nothing quantitative. b. Experiments. Energy conservation of falling bodies (Galileo through modern tests, e.g. mechanical energy conserved in vacuum drops) [memory, high]. Nothing in them distinguishes "stored in field" from "stored in aether" because the aether has no separate observable. The Michelson-Morley null result (1887) and later tests found no preferred aether frame [memory, high]; an aether carrying isotropic kinetic wave energy of enormous amount is not by itself ruled out by that (isotropic in what frame?), but see claim 2. c. Tested? Not as an experiment; a conceptual reinterpretation. Brush's own 1910-11 attempt at resonance heating of the upper atmosphere "unsatisfactory" [read]. No tests. d. If true: conservation of energy would be redistributed into the aether; field energy in general relativity/classical field theory would be replaced by a medium. Mainstream impact is nil unless the medium has measurable properties.

Verdict: Not testable as stated (as a reinterpretation of potential energy), with the specific supporting paradox (energy "disappears" at the neutral point) Refuted by calculation (energy is 2.8e7 J/lb, still stored; potential is not zero there).

Claim 2: Gravity is a push from isotropic penetrating aether waves; each atom casts an inverse-square "energy shadow"

a. Internal consistency. This is a Le Sage / shadow model, so the standard mathematics applies. - Inverse square: for small absorbing cross-sections sigma, in an isotropic flux the fractional shielding by body 1 at body 2 is sigma_1/(4 pi r^2); the net force on 2 is proportional to sigma_1 sigma_2 / r^2. That gives 1/r^2 and (if sigma is proportional to number of atoms) proportionality to the product of masses. Brush states exactly this [read]. So the idealised geometric claim is consistent. - The proportionality to mass requires no saturation (shadows of atoms inside a body must not overlap appreciably). Lodge [read] flags "the absence of noticeable screening", the classic Le Sage problem. For a body to deliver gravity with the observed G, the absorbed fraction must be tiny, but then the absorbed momentum/energy flux must be enormous. Brush says the waves are not absorbed ("pass freely through all bodies") yet also that they push atoms and are absorbed ("some absorption of ethereal energy"). These requirements pull in opposite directions: force requires momentum transfer, and momentum transfer from waves requires absorption or scattering. He does not quantify. - Drag. The decisive calculation: a body moving at speed v through an isotropic flux of waves moving at c feels a head-on/tail asymmetry of order v/c, giving a drag force of order F_grav x (v/c) when the same flux provides F_grav (the factor is of order unity; the exact factor depends on the model, but it cannot be zero for waves absorbed isotropically). For the Earth: orbital speed v = 29.8 km/s, v/c = 1.0e-4; solar pull per unit mass = G M_sun / r^2 = 5.9e-3 m/s^2; drag deceleration about 5.9e-7 m/s^2, a velocity loss of about 19 m/s per year [calc]. The Earth's orbital speed would change by 19 m/s each year; over about 10^6 years the orbit would be drastically changed, while geology and astronomy show a stable orbit over 4.5e9 years. Wikipedia [web: https://en.wikipedia.org/wiki/Le_Sage%27s_theory_of_gravitation] reports Poincaré's analysis demanding particle speeds of order 10^18 c and Laplace's lower bound on the speed of gravity of about 10^8 c; Feynman noted the drag kills the scheme [web, same URL; the quantitative numbers there I did not independently reproduce]. Brush's reply (claim 3) concerns an infinite speed vs c; the drag problem is the same one in other clothing. - Longitudinal waves "gripping" atoms through "alternating flow and ebb" [read]: no equation; units cannot be checked. "Velocity of a falling body tends asymptotically to the wave velocity" [read] is a stated consequence of a force that shuts off as v approaches c; in the model the push force depends on relative wave speed c - v, so F -> 0 as v -> c. This is a testable, differing consequence (a falling body's acceleration would decrease with speed) but it applies at a fraction v/c far beyond any free fall, except for fast particles, where the gravitational (equivalence principle) behaviour is well tested in other ways. No quantitative form given. - The 1929 text [read] says the gravitational waves have frequency "very high up", about 10^27 s^-1 range (6.54e27 for "quanta waves"), above cosmic rays, and that they "pass freely". He gives no coupling constant relating wave energy density u to G. A dimensional sketch: if flux F = u c and absorbed cross-section per unit mass kappa, gravity needs G = kappa^2 u c / (pi) (up to O(1) factor, in a standard Le Sage derivation) [calc; derivation not in source]. Heating of any body by absorbing that flux is unavoidable; Brush in effect proposes the heating is the small observed heating in silicates, but the heat then needed for gravity at the Earth-scale (the same absorption that produces gravity) is far larger than anything measured. Not computed by Brush. b. Experiments. Planetary orbits (stable, Newtonian to ppm, GR corrections observed; see claim 3) [memory, high]. No observed drag. Gravity's inverse-square law verified to about 0.05 mm in the lab [memory, medium; not rechecked]. Absence of mass-dependent absorption: eclipse experiments (e.g., Moon eclipsing the Sun: Allais claims, disputed) [memory, medium]; not needed here. c. Tested? Le Sage models have been analysed and rejected on the drag/heating grounds since Maxwell (1875), Poincaré and others [memory, medium; the Wikipedia page above corroborates Laplace, Poincaré, Feynman]. Brush's particular wave variant was not tested except by his own resonance-heating attempt (unsatisfactory, [read]). No replication of the 'heat/gravity link' (claim 5). d. If true: gravity would have to be a derived, dissipative, frame-dependent (aether-frame) effect; GR's geometric equivalence of inertial and gravitational mass would need a mass-composition-dependent absorption, and an enormous energy density in the aether (the 1929 text says "most of the vast intrinsic energy of the ether lies" there) would have to gravitate.

Verdict: Refuted by calculation (strong form: wave push providing the full measured gravitation with no orbital drag; orbital drag of about 19 m/s per year for Earth); the weak form (a geometric shadow picture reproduces 1/r^2 and mass-proportionality) is internally consistent but only with unspecified parameters. Dismissed rather than directly tested.

Claim 3: Bodies that accelerate absorb aether energy so gravity departs slightly from inverse-square (Mercury, lunar irregularities); gravity may travel at c without wrecking the Moon's orbit

a. Internal consistency. As described [read: OCR facts.json; I have not seen the 1914 equations], force = (1/r^2)(1 + x), x small, growing with velocity of fall, zero for circular orbits, alternately positive and negative for eccentric ones. I tested whether such a term can produce the perihelion advance. Taking x proportional to radial velocity r-dot, i.e. perturbing radial force R = A r-dot / r^2 (odd under time reversal), the orbit-averaged Gauss equations give: d(omega)/dt proportional to the integral of -R cos f dt = integral of sin f cos f df = 0 (sympy, exact), while d(e)/dt proportional to the integral of R sin f dt = integral of sin^2 f df = pi (non-zero). So a velocity-of-fall-dependent correction of that form changes the eccentricity, not the perihelion direction: it gives no net precession (and a secular change of e that would be observable). If x is instead even in r-dot (an energy-absorption term), the sign alternation described cannot hold. As described, Brush's mechanism cannot produce the Mercury advance, which is a rotation of the major axis (about 43 arcsec per century unexplained in 1914, matched by GR's 42.98 [web: https://en.wikipedia.org/wiki/Tests_of_general_relativity]; observed total 574.10 +/- 0.65 arcsec/century). Caveat: I only have Step 1's summary of the equations, not the text; he calls it a hope, not a derivation. Finite-speed gravity: Brush's argument [read: OCR] that a speed of light causes only a few seconds of arc per century of mean-motion retardation, a 52 ft Earth-centre displacement, and a tangential force 1/24,000,000 of gravity "at the moon's distance". I could not reproduce 1/24,000,000. The naive aberration estimate for Moon-Earth is v/c = 1.02 km/s / 3.0e5 km/s = 3.4e-6 = 1/294,000 [calc]; for Earth-Sun it is 1/10,000. I do not know which configuration Brush's figure refers to (it may be a different geometric quantity); flagged unverified, not asserted wrong. Brush's reply to Laplace (a partial cancellation by his own x term) needs the same velocity-dependent force, so any cancellation is fine-tuned: Laplace's secular term is proportional to v/c with the same sign for every orbit, whereas Brush's x is said to alternate sign; they cannot cancel in general. b. Experiments. Planetary ephemerides fit GR to better than 1e-4 of the 43 arcsec effect (e.g. gamma, beta tests) [memory, medium]; binary pulsar orbital decay matches GR's quadrupole radiation [memory, high]; GW170817 constrained the speed of gravitational waves equal to c to about 1e-15 [memory, high; Wikipedia fetch did not return the number, so tag stays memory]. Gravity as an instantaneous aberration-free field is consistent in GR because the field of a uniformly moving source points at the present position, a known result [memory, high], which resolves the Laplace objection without a Le Sage mechanism. c. Tested? Not by Brush. The Mercury question was resolved by Einstein in 1915 [web as above]; Brush's 1914 paper preceded it. d. If true: a velocity-dependent force would contradict Newtonian/GR conservative dynamics and the inertial-frame equivalence (Lorentz-like frame dependence).

Verdict: Historically superseded but instructive (Mercury: a reasonable 1914 hope, replaced by GR). Internally inconsistent in the narrow sense that the described form of x cannot give a perihelion advance and cannot cancel Laplace's secular drag. Finite-speed-without-instability: Never properly tested by Brush; GR gives it in a different way.

Claim 4: Weight is not exactly proportional to mass; materials differ by about 1 part in 32,000 (pendulums: zinc/bismuth) and about 1 part in 4450 (falling containers: barium aluminate)

a. Internal consistency and error analysis. - Arithmetic [read: 1929 text]: 0.099 mm lag over 110 cm = 9.0e-5 = 1/11,100; divided by the mass fraction 0.403 gives 1/4,480; matches the stated 4450. Equivalently dg/g (silicate) = 2.2e-4, and the lag in time Delta-t = (1/2)(dx/h) t = 2.1e-5 s on a 0.474 s fall [calc; for h = 1.10 m]. Unit/definition remark: "impairment of falling velocity" is used for what is actually a difference in distance/acceleration at the same time; dx/h = (1/2) dg t^2 / ((1/2) g t^2) = dg/g, so the ratio is dg/g, fine. - The correction by dividing by the mass fraction assumes the effect scales with the mass of the specimen and that the whole retardation of the container comes from the specimen alone. That is built-in and untested; the container, the cork, the lead sawdust and the air gap are all in the apparatus. Also the lead companion is assumed to fall at exactly g. - Dominant systematic: air drag. For a roughly 2 cm diameter, 30.6 g body falling 1.1 m, drag/weight at the end is about 1.5 percent [calc: 0.5 rho Cd A v^2 with Cd ~ 1, v = 4.6-4.9 m/s]. The measured effect is a 9e-5 difference in g, i.e. only a 0.6 percent difference in drag between the two containers would produce it. Brush himself reports [read] that "small lateral air currents" altered the lag between exposures and that mutual shielding of the containers matters; the container drag also depends on the fill (powder settling, loose cork). The scatter he describes (one of the six photographs 'very slightly fast', the lag 'unevenly slow') is of the same order as the effect. The 0.099 mm figure is a mean over six photographs including one negative; no standard error is quoted [read]. A 0.1 mm lag is also near the guiding-tube friction effect ("first millimeter of their fall") he mentions. The pendulum paper [read: OCR] reports that doubling the drag with large vanes changed the effect by roughly 50 percent and that a soft-iron cylinder near a bob changed things by 11 percent: both controls are larger than a few percent of the effect, so the systematics are at the same scale as the signal. - A material-dependent weight would also show up in the pendulum and the drop with different magnitude per unit of mass; the two experiments give 1/16,000 (zinc-bismuth, pendulum) and 1/4,500 (barium aluminate vs lead), different materials, so they cannot be cross-checked. - Pendulum: gaining one beat in 5-7 hours (T of about 3 s) is a fractional rate of 1/(7.3 h x 3600 / 3 s) = 1/8,800 per beat... using one beat gained: dT/T = T/(t_gain) = 3/26,300 = 1.1e-4? That does not match the stated 1/32,000 without the 22 percent correction and the unknown period [Step 1 gives only the final figure]; the pendulum length of 2.284 m implies T = 2 pi sqrt(L/g) = 3.03 s [calc], giving 1 beat in 7.3 h (26,300 s = 8,670 periods): dT/T = 1/8,670 = 1.15e-4 raw. The stated 1/32,000 would need 7.3 h to be for a different quantity (beat = half period, or elapsed time in a different table). I cannot resolve this from Step 1's summary; this is flagged: the raw rate seems about 3.7x larger than the quoted effect, and there is no way to confirm without the paper. Not asserted as an error. b. Experiments. Eötvös: torsion-balance null results to about 2e-9 (1908/1922), Bessel's pendulum (1832) to about 2e-5, Roll-Krotkov-Dicke to 3e-11, MICROSCOPE (2022) to about 1e-15 [web: https://en.wikipedia.org/wiki/Equivalence_principle]. Brush's claimed composition effects (3e-5 to 2e-4) are 4-5 orders of magnitude larger than the Eötvös limit that includes many substances (e.g. the classic ones involve lead-like heavy metals, not necessarily bismuth, zinc or barium aluminate; I did not check the substance list) and 11 orders above MICROSCOPE. Brush's materials (a hydrated barium aluminate powder; nickel-cobalt silicate) were not tested in those modern experiments, but the composition dependence he claims is large and across atomic number would have been seen (Ti vs Pt in MICROSCOPE) [memory, medium]. The Bessel-level 1832 pendulum limit (2e-5) is already comparable to or smaller than his effects of 1/4,500, so his silicate results exceed the Bessel limit for a similar class of materials [memory/web: same URL; Bessel's materials were brass, iron, silver, lead, gold, etc., not silicates]. c. Tested? Brush's own tests only; Dayton Miller did not do the suggested Eötvös comparison (Step 1: no evidence in folder). No independent replication on record in the folder; the Bureau of Standards checked only heat (claim 5). Reported replications or negative tests: none I can source. d. If true: the weak equivalence principle (and therefore GR) would fail at the 1e-4 level for common compounds; NYT/Webster's reaction [read: OCR] "would disprove Einstein" is correct as a logical conditional. Earth-density calculations would change (Brush's remark). All Eötvös-type experiments would have to be wrong by 5 orders of magnitude.

Verdict: Split. Strong form (weight per mass differs between substances at 3e-5 to 2e-4): Tested, not supported (Eötvös, Roll-Krotkov-Dicke, MICROSCOPE bound composition dependence at 1e-9 to 1e-15 for tested materials; Brush's materials were not tested by them), and the measurement is plausibly an air-drag/guide systematic (calculation above: a 0.6 percent drag asymmetry suffices). Brush's own experiment: Never properly tested by neutral parties in the sources I have (no replication on record). I would rate the specific claim for the silicates as closer to "not supported" than "never tested" given the size of the claimed effect vs the equivalence-principle limits; the arithmetic itself is fine.

Claim 5: Some rocks/silicates continuously generate heat (not radioactivity), and the same materials show slower fall; the correlation is the evidence that both come from the aether waves

a. Internal consistency. - Energetics. The relation between the two effects is never quantified in the text I read [read]: no ratio of watts to dg/g, only the ordinal statements "small, moderate or large". A correlation of ranks across a handful of materials is weak. The proposed mechanism for the heat (fortuitous resonance of molecular collisions with gravitation-wave frequency, [read]) ties to frequencies of order 1e27 s^-1 and above (energy per quantum about 4e3 GeV for 1e27 Hz: E = h f = 6.6e-34 x 1e27 = 6.6e-7 J = 4 TeV [calc]); thermal-molecular collision frequencies are about 1e13 s^-1, fourteen orders of magnitude lower. A resonance between those is not defined in any dimensionally coherent way; the "wave frequency" and the collision frequency cannot match. In the 1911 text the opposite requirement was stated: gravity waves of extremely low frequency so atoms cannot respond; by 1929 they are extremely high frequency "above cosmic rays". The theory flips from very low to very high frequency between 1911 and 1929 [read] while keeping the same shadow mechanism. This is a change in the hypothesis, not an inconsistency of a single equation. - Energy source/sink. If the heat is continuous with no depletion, then the heat production over time must be accounted for as taken from the wave energy; the absorption needed is tiny relative to the aether reservoir; consistent trivially but with no testable prediction (a first-law account of the heat would need a measurement of the wave flux changing downstream of the sample, not given). - The two measurements have different type: calorimetric power (watts per gram) vs fractional acceleration; no calibration linking them. Brush "found no exception", but with no blinding or randomised sample identity [read: statement about procedure]; he knew which container held which load. - Calorimetry error budget not obtained; ice calorimeters have thermal baselines vulnerable to chemical reactions (hydration, oxidation, adsorption/hysteresis), particularly for freshly prepared hydrated wet-way silicates, which Brush prepares and then measures within weeks [read]. Materials that are "wet" and "air dried" can continuously evolve chemical heat for months. That is a mundane explanation; Brush says "not radioactive" but only "minutely" so. b. Experiments. No mainstream observation of non-radioactive, non-chemical continuous heat in rocks; radiogenic heat (U, Th, K-40) accounts for rock heat flow [memory, high]. The conservation of energy within each sample over timescales of weeks to years has not been shown to be violated in other calorimetry [memory, medium]. c. Tested? By Brush only, in two home-built calorimeters. The Bureau of Standards, per Brush [read], reported the Sandusky clay generates "a measurable amount of heat"; that statement is second-hand and unquantified; the follow-on test of nickel-cobalt silicate was "about to commence". Cleveland Press 1927 [read: OCR] says Brush financed the Bureau repetition himself. No independent replication of the drop effect. No published Bureau report was obtained. d. If true: a continuous energy source (non-radioactive) in common minerals, violating or reinterpreting conservation of energy; geophysics heat flow budgets would change.

Verdict: Never properly tested (calorimetry: a single-lab result with only a second-hand Bureau of Standards mention and a plausible mundane chemical/hydration source; no neutral controlled test I can source). The causal link between heat and slow fall: Not testable as stated beyond the ordinal correlation (no quantitative relation is predicted), and the mechanism has a frequency inconsistency (frequencies of 1e27 s^-1 vs 1e13 s^-1 molecular frequencies; 1911 required low frequency, 1929 high frequency).

Claim 6: Recently quenched steel spontaneously gives off heat for days to weeks (precursor result)

a. Internal consistency. [read: OCR] Apparatus: two silvered Dewar flasks, thermocouples calibrated at 55 galvanometer divisions per degree C, peak excess of a bit over 100 divisions, i.e. about 2 K, with the specimen bars twelve half-inch, five-inch bars (about 0.5 in square or 0.5 in diameter; mass unknown to me, a rough 12 bars x (pi/4 x 0.5^2 in^2 x 5 in) = 12 x 0.98 in^3 x 16.4 cm^3/in^3 x 7.8 g/cm^3 = about 1.5 kg [calc, assumes round bars; 0.5 in dia]). A 2 K peak on 1.5 kg steel (c about 0.46 J/g K) in a calorimeter with copper block thermal mass: stored energy needed about 1.5 kg x 460 J/kg/K x 2 K = 1.4 kJ plus losses, i.e. around 1 J/g order, a modest amount. This is within the range of stored-energy release by martensite tempering and carbon redistribution/retained-austenite transformation in tool steels [memory, medium: values of order 1-10 J/g]. So the magnitude is internally plausible; no calculation in the text I read compares it to a physical mechanism except "relaxation of molecular strain". Control: slow-cooled unquenched bars show no heat [read: OCR]; this addresses oil/oxide and thermocouple artefacts well. The twelve vs water comparison matches thermal capacity (a sound design). b. Experiments. Heat release from quenched and aged martensite is known (calorimetry of low-temperature tempering/aging, 'first stage of tempering' near room temperature to 100 C) [memory, medium; not verified on the web]. Brush's data are not contradicted by it. c. Tested? By Brush (1915, 1917), and per Brush with Hadfield's samples; physically replicable and, in modern metallurgy, associated with martensite ageing [memory, medium]. I did not find a source for replication specifically of Brush's measurements; do not count this as a documented replication. d. If true: nothing in mainstream physics changes; it is ordinary solid-state energy release. Brush's later use of it as support for the aether-heat idea is unsupported by the 1917 paper itself (Step 1: not tied to gravity there).

Verdict: Plausible, untested in the sense that no independent replication is documented in what I read, but consistent with known physics (stored energy release in martensite) and not evidence for aether waves. [memory medium for the mechanism; not web-verified because the search budget ran out.]

Claim 7: The Eötvös experiments are flawed or too insensitive; a better test would show lead vs sulphur/selenium differing

a. Internal consistency. [read: OCR letters] Brush says the true effect is "a hundred times too small" in Eötvös's results, or that there is an error in theory/mathematics/interpretation, but he gives no equation or error analysis. An Eötvös balance measures a torque proportional to the difference of the ratios (weight/inertial mass) for two samples at the horizontal gravity gradient; Brush's own claimed effect sizes (3e-5 to 2e-4 in his experiments) would make torques hundreds of thousands of times larger than the 2e-9 sensitivity quoted [web: Equivalence_principle page]. So Brush's claim is mathematically self-contradictory unless the effect in torsion balance is suppressed by some mechanism (a horizontal vs vertical difference, or material-specific); "a hundred times too small" refers to a different, smaller effect. If Brush's effect were 1e-4 and Eötvös's sensitivity 2e-9, the experiment could not have missed it by a factor of 1e5; saying it is "too insensitive" is not consistent with the numbers. The statement "flawed" is not supported by an error computation. b. Experiments. Eötvös (1908/1922), later Roll-Krotkov-Dicke 3e-11 (1964), Eöt-Wash and MICROSCOPE 1e-15 (2022) [web: https://en.wikipedia.org/wiki/Equivalence_principle]. Lead, sulphur and selenium: I do not know that these exact pairs were tested by Eötvös; Eötvös's materials included many substances but the list was not checked [memory, low]. c. Tested? Brush asked Miller to mount a torsion balance on the Mt Wilson interferometer; Miller replied that he knew the experiment only from manufacturers' circulars [read: OCR]; no evidence it was done. The proposal was therefore "never carried out"; it was not dismissed as a failed test. d. If true: all torsion-balance equivalence principle tests would be wrong by many orders; same implications as claim 4.

Verdict: Refuted by calculation (the 'too insensitive' part: 2e-9 sensitivity vs the claimed effect 1e-4 or 1e-5 is five orders of magnitude margin); the 'flawed' part is Not testable as stated (no specific flaw identified); Brush's proposed test was Never properly tested (never carried out).

Summary table

Reproducible calculations (scratch): neutral-point energy, steel-cable diameters (Earth-Moon: about 500 miles for steel strength about 0.4 GPa, about 310 miles at 1 GPa; Earth-Sun: about 6,600 miles at 0.4 GPa; Brush's quoted 500 and 6,000 miles are consistent for a weak steel), drop times and lag, drag/weight, Le Sage drag, and Gauss-equation integrals were done with Python/SymPy in the project venv.