Mathematician review: zzz-Unknown ("The Subquantum Plenum")

Role: PhD mathematician (Step 2). Checks derivations, units, notation and hidden assumptions. Tags: [read] = from the project document or a file in research/files; [web] = URL given; [memory] = recalled, with confidence; [calc] = my own arithmetic (Python, numpy), reproducible from the numbers shown.

Inputs read: facts.json, claims.md, deep/Subquantum-Plenum-623ba4.md, the essay text (_text/Subquantum-Plenum-623ba4.txt, passages quoted below), sites.md "Leads for review", research/ notes (Piggott, Mendeleev, Irvine Ranch, Boyd Wayback) and research/files (Dehmelt 1989 lecture, Mendeleev 1904 OCR, Boyd's 2001 uncertainty page, Boyd's RTF copy of the essay).

No source gap: the essay text is available. The one equation was not seen as a page image (the .doc was not rendered), but see Corrections: the garbling is in the source itself.

Plain-language orientation

The essay is an unsigned prose argument (now known from the Investigator to be R. N. Boyd's, [web] worlds-within-worlds.org/rnboyd.php) that has almost no mathematics. Only four things in it can be checked as mathematics: (i) the Mendeleev numbers, (ii) one wave equation, (iii) the Dehmelt "momentum equals rest mass" step, (iv) the "3000 m/s" light-speed figure. Other claims (La Sage gravity, light bending, Piggott) are verbal models with no equations; for those I supply the missing quantitative test, because a model with no numbers cannot be checked, and I show what the numbers would have to be.

Symbols used: c = speed of light (2.998e8 m/s); h-bar = reduced Planck constant (1.055e-34 J s); G = gravitational constant; M, R = mass and radius of the Sun; n = refractive index; k_B = Boltzmann constant; "statvolt" = CGS (centimetre-gram-second) unit of voltage, 1 statvolt = 299.79 V.

Corrections to Step 1

1. The equation garble is not an extraction artifact. Step 1 (deep/ and facts.json) says the first line "d'Alembertian r" is "probably the d'Alembertian acting on theta, symbol lost" in extraction. Boyd's own RTF copy of the essay (research/files/boyd-wayback-subquantum-plenum-peer-reviewed.rtf) contains the identical typed text "i@theta/@r = d'Alembertian r" and "theta = exp[-iKr]lamda (x^u)" [read]. So the author typed it that way; there was no symbol to recover from a page image. Read literally, "d'Alembertian r" is the wave operator applied to the parameter r, which is zero (r is not a field), so the equation as printed is meaningless; the intended reading must be box-theta. The intended reading is my inference [calc], not stated by the author.
2. Mendeleev numbers. facts.json gives "1e-8 of hydrogen, 2.5e6 m/s" as one pair as if Mendeleev's. The Investigator's primary-source read shows Mendeleev's preferred pair is about 1e-6 of hydrogen at about 2.25e6 m/s, with bounds 9.6e-7 to 5.3e-11 [read: research/files/mendeleeff-1904 OCR, lines ~1121 and ~1927]. The essay's pair is not Mendeleev's pair, and (see Claim 1) is not self-consistent under the kinetic theory he used. Also, "Zero Group before the noble gases in the 1869 table" is contradicted by Mendeleev: "I dared not put forward such a proposal" in 1869 [read, same file].
3. Claim 5 context. claims.md presents the Boyd photon "proof" as supporting the Dehmelt argument. Boyd's own 2001 page (the essay's ref 33) says: "These arguments fail completely, however, when discussing the subatomic particles, e.g., the electron. For these, the Uncertainty Relation holds." [read: research/files/boyd-wayback-heisenburg-refute.htm]. The essay (2002 or later) cites that same page as support for the opposite conclusion about the electron. This is a self-contradiction across the author's two texts, not noted in Step 1.
4. Step 1's "Dehmelt: months-long trapped electron" is right in substance: Dehmelt's lecture says the method made it possible to keep an electron for 10 months [read: dehmelt-1989-nobel-lecture.pdf, line ~100]. Step 1 correctly left the "three months" figure as the essay's. No correction needed except that the lecture, not the essay, gives the trap parameters used below.
5. Step 1's Klein-Gordon summary ("K = m0^2") omits that the sign of K depends on the sign convention of the wave operator (see Claim 7).

Claim 1. A real aether exists as a gas of extremely light, very fast "Zero Group" particles (Mendeleev, Tesla)

a. Internal consistency. The essay gives two numbers: atomic weight 1e-8 of hydrogen and speed 2.5e6 m/s. For a gas in thermal equilibrium the root-mean-square speed is v = sqrt(3 k_B T / m) (introductory kinetic theory), so the pair fixes a temperature, T = m v^2 / (3 k_B). - Essay pair (m = 1e-8 m_H, v = 2.5e6 m/s): T = 2.5 K [calc]. At 0 deg C (273 K) the same particle would move at 2.6e7 m/s, ten times faster. - Mendeleev's own pair (1e-6 m_H, 2.25e6 m/s): T = 204 K [calc], i.e. an ordinary terrestrial temperature, which is what a chemist of 1904 would use. So Mendeleev's numbers hang together; the essay's recombined pair describes a gas at 2.5 K. That is not impossible, but the essay never says so, and it contradicts the essay's own picture of the gas as hot, stellar in origin and "permeating all matter". - Mendeleev's velocity came from an escape-velocity argument (must exceed about 2.24e6 m/s to leave a star of 50 solar masses, and stay below c), giving his bounds [read]. The essay drops the argument and keeps the number. - Other quantities the essay needs and never gives: number density, collision cross-section, mean free path, pressure. Without them "rarefied, yet appear to be very dense" cannot be checked.

b. Experimental consistency. No direct detection of any gas lighter than hydrogen. The Investigator confirms Mendeleev's proposal is genuine but dated 1902/1904, not 1869 [read]. Mendeleev's proposal predates the electron-based atomic picture. A particle of 1e-8 hydrogen masses is about 1.7e-35 kg, about 1.8e-5 electron masses; no such particle is known. Known particle physics excludes new light charged particles at that mass; a neutral one would need a coupling to be a gas "permeating matter" and none is specified. [memory, medium] for the particle-physics statement; I did not check it on the web.

c. Tested? Mendeleev's gas was never tested as such; coronium (his "y") turned out to be highly ionised iron lines, not an element [memory, medium]. The essay's version has no defined measurable prediction.

d. If true: the aether would be a medium with a rest frame, requiring a violation of Lorentz invariance at some level (see Claim 4).

Verdict (split). Mendeleev's 1904 proposal: Historically superseded but instructive (it was a reasoned proposal with escape-velocity bounds; his numbers are self-consistent). The essay's version: Not testable as stated (no density, interaction or equations), with the added defect that its two numbers do not belong together.

Claim 2. Gravity and inertia are pressure of the gas (La Sage, Laplace); light bending is refraction

a. Consistency. The essay asserts the Laplace model "produces all the results of Relativity theory" [read]. Three separate checks:

(i) Light bending as refraction is mathematically sound in the weak field, and the Investigator's lead matters here. If the "Zero Group" density gives a refractive index n(r) = 1 + 2GM/(r c^2) around the Sun, ray theory gives total deflection = integral of (gradient of n perpendicular to the ray) along the ray = 4GM/(b c^2) for a ray passing at distance b. At b = R (solar limb): GM/(R c^2) = 2.12e-6, n - 1 = 4.2e-6, deflection = 1.75 arcseconds [calc], which equals the observed/GR value. So the essay's "refraction" idea is not absurd; it is a known effective description (equivalent to GR in the weak field, in isotropic coordinates) [memory, medium: Eddington 1920, Dicke 1957, Puthoff's "polarizable vacuum"]. But the essay supplies no density profile, no link between gas density and n (n - 1 = N alpha, number density times polarisability), and no reason for the profile 1/r. The number 1.75" comes from choosing n, not from the gas. Also an ordinary gas is dispersive (n depends on frequency), while observed bending is the same at optical and radio frequencies [memory, medium]; the essay does not address this.

(ii) "All the results of Relativity" is false by omission. Pressure gravity as described yields a force law; GR also gives Mercury perihelion advance (43 arcseconds per century), gravitational redshift, time dilation in orbit (GPS), frame dragging and gravitational waves. The essay computes none of them [read: none given].

(iii) The La Sage mechanism fails an energy budget (Poincare/Maxwell style objection), and the essay's own mechanism triggers it. The essay says incoming particles are "refracted and slowed down by interactions with the pre-existing matter" and that this causes planetary heating [read]. If each absorbed particle of momentum p and speed u delivers energy of order p u, then a force F needs a heating power of about F u [my estimate; assumption: the momentum lost is transferred with energy p u, as for light, F = P/c]. Laplace's own lower bound on u, from the absence of orbital drag, is about 7e6 c (the essay says "millions of times the speed of light"); u = 7e6 c = 2.1e15 m/s [calc]. A 1 kg mass (weight 9.8 N) then needs about 2e16 W; the whole Earth (weight force g M, M = 5.97e24 kg) about 1e41 W [calc]. Earth's actual internal heat flow is about 4.7e13 W and the Sun's light on Earth about 1.7e17 W [memory, medium]. The mismatch is about 28 orders of magnitude. The assumption (all momentum arrives with energy p u) is the load-bearing step; a model in which the particles scatter elastically escapes the heat but then transfers no net momentum. The essay does not say which.

b. Experiment. Light bending: 1.75" at the limb is confirmed (eclipse and radio interferometry) [memory, high]. Pressure gravity: the heating argument above; no direct evidence. The essay's "1935 experiments" on a star at eclipse: date as given, unverified.

c. Tested? The Investigator's lead: Laplace's 1853 date is also questionable (Laplace died 1827) [memory, high]: the essay says "About 1853, the Marquis de LaPlace"; Laplace's gravity-by-pressure work was published around 1805-1825 [memory, medium]. Not verified on the web. The essay also proposes a test of its own ("Were a similar experiment performed today, where variations in the speed of light and variations in the force of gravitation were constantly measured ... correlations") [read]. No such experiment was found by the Investigator.

d. If true: GR's geometric account of gravity would be replaced by a medium theory; Lorentz invariance would only hold approximately; the equivalence principle would need an explanation for why the gas pushes all materials equally.

Verdict (split). Light bending as a refractive-index effect: Plausible, untested as an effective weak-field description (the arithmetic works; the physical medium and profile are unspecified; not a distinguishing test since it equals GR). Pressure/La Sage gravity as the essay describes it: Refuted by calculation (the energy budget above, under the stated assumption). Claim that it reproduces all of relativity: Not testable as stated (nothing computed).

Claim 3. Fast positive discharges above 500,000 statvolts neutralise gravity (Piggott 1920); Tesla transformers conduct aether

a. Units and internal consistency. The essay writes "500,000 statvolts" [read]. 500,000 statvolts = 1.5e8 V; Piggott's own article says the machine voltage was "in the neighborhood of 500,000", in volts, i.e. about 1,670 statvolts [read, via Investigator: research/2026-10-04-rexresearch-piggott.md; web transcription; not checked against the scan]. The essay is therefore off by a factor of about 300 in the device voltage if "statvolts" is meant. The essay also contradicts itself on the threshold ("exceeding 500,000" versus Piggot's generator "at 500,000"), and Boyd's 2006 page gives 400,000 [read: Investigator]. The essay says the grounded plate makes a purely electrical explanation impossible; Piggott says the ground "can be entirely eliminated" once the object is suspended, Vassilatos says the opposite [read, Investigator's table].

b. Is an ordinary electrostatic force big enough? Using Piggott's figures (silver ball 11 mm diameter, 1.3 g) [read, as transcribed]: weight = 0.0128 N. A conducting sphere of radius a = 5.5 mm can carry at most Q = 4 pi eps0 a^2 E_max before the air breaks down at the surface; with E_max = 3e6 V/m (air at 1 atm, introductory E&M) Q = 1.0e-8 C [calc]. Force needed to hold the ball: E = W/Q = 1.26e6 V/m. The average field of 500 kV across 25 cm (Piggott's stated distance of the ball from the field centre) is 2e6 V/m, which would give a force of 0.020 N, above the weight [calc]. So the magnitude of an ordinary electric force on a charged ball is enough to carry the ball with no gravity-cancelling at all. This does not prove that is what happened; it removes the need for a new mechanism by the numbers given. The essay's statement that "gravity was locally neutralised" has no weight measurement behind it (Piggott measured none, as far as the transcription shows) [read].

c. Stability. Earnshaw's theorem (a consequence of Laplace's equation, div grad V = 0 in empty space) forbids stable levitation of a charged or a conducting body in a static electric field alone. A hovering ball therefore needs either moving charge (corona/ion wind, which Piggott describes as a bluish aura of "darting particles", and oscillation toward and away from the centre) or something time-dependent [read]. The "remained suspended for 1.25 s after power off" is the discharge time of the stored charge and air ions, not a gravity effect, in my reading; that is an interpretation [calc/inference].

d. Tesla "conducts aether" (10,000 V per inch, up to 1e8 V, no measurable current) [read]. At 10,000 V per inch, 1e8 V requires 10,000 inches = 254 m of winding on the essay's own figure [calc]; the essay says a 10-inch coil gives "more than 100,000 volts" (consistent with 10 x 10,000 V) and that improved designs reached 1e8 V without saying their length. The statement "no measurable current" is not a measurement of absence of electrons: a coil with a voltage across it and a capacitance C to its surroundings carries a displacement current I = C dV/dt, which can be small in a DC-like meter and large in a spark. No instrument, bandwidth or number is given.

Tested? Piggott's 1920 article is the primary account; the Investigator found no independent replication and no weight measurement. Replications of "Biefeld-Brown"-type lifters exist in the wider literature but are not this claim [memory, medium; not part of the folder].

d. If true: a screening of gravity by a field would contradict the equivalence principle and the weight measurements that show no change of weight in strong electric fields at the level of Eotvos-type experiments [memory, medium].

Verdict (split). Piggott's suspension as a gravity effect: Never properly tested (the only account is his own, no weight measurement, no neutral replication found; not tested and not dismissed in controlled form on the record I have; the essay's statvolt figure is a unit error). The ordinary-electrostatics explanation fits the numbers. Tesla coils "conduct aether not electrons": Not testable as stated.

Claim 4. Ether-drift records (Michelson-Morley, Miller, Kehr, Silvertooth) show light-speed variations up to 3000 m/s and an Earth-entrained aether

a. The 3000 m/s figure fails against the experiment's own sensitivity. A Michelson interferometer does not measure the speed of light; it measures fringe shift. For arm length L and wavelength lambda, an aether wind v gives a shift of N = 2 L v^2 / (lambda c^2) fringes (standard, second-order). With the 1887 values L = 11 m, lambda = 550 nm [memory, high]: - v = 30,000 m/s (Earth's orbital speed): N = 0.40 fringe [calc]. - v = 3,000 m/s: N = 0.004 fringe [calc], 100 times smaller than the effect Michelson and Morley were looking for, and below the roughly 0.01 fringe they could reliably read [memory, medium]. - Observed shift below about 0.01 fringe corresponds to v below about 4.7 km/s [calc]. - If the speed of light itself differed by 3000 m/s in one arm (fractional difference 1.0e-5), the shift would be 2 L (3000/c) / lambda = 400 fringes [calc], which no one saw. So "3000 m/s variation, well outside the margin for error" is not what the instrument can say: either it means an inferred "wind speed" of 3 km/s (then it is 0.004 fringe, inside the noise), or an actual change in c (then it is 400 fringes, never seen). The essay cites no table. It is unsourced; I could not find the figure. The Investigator found no source giving 3000 m/s [read: research/2026-10-04-otherhand-irvine.md].

b. What is documented. Miller's 1933 report claimed a positive drift of about 10 km/s [memory, medium]; later analyses attributed it to temperature effects (Shankland et al. 1955) [memory, medium]. Silvertooth's 378 km/s toward Leo is his own characterization; the Investigator notes Marett found no data graphs in the papers and, in his 2012 replication, reproduced the 12-hour pattern and then traced it to laser beam-angle thermal drift [read: sites.md]. That is one documented independent test, against the drift reading, from a source I have not rechecked. The Michelson, Pease and Pearson (1935) Irvine Ranch record shows "strange, unexplained cyclic drifts" and an unresolved 22 km/s gap between two campaigns [read: otherhand.org via the Investigator] (299,774 versus 299,796 km/s, a fractional 7e-5 [calc]); this is a genuine record of unexplained scatter in an early measurement of c itself, but it is not a 3000 m/s drift and nothing in it points to an aether.

c. Modern tests. Rotating-cavity and resonator experiments of Michelson-Morley type have since reached sensitivities of a part in 1e15 to 1e17 on any direction dependence of c [memory, medium: Mueller et al. 2003, Herrmann et al. 2009]; I did not verify these on the web. They are not mentioned in the essay.

d. If true: a preferred rest frame for light would have to exist; special relativity would be an approximation. Mainstream physics would have to reinterpret every null result above.

Verdict. Aether drift with Earth entrainment: Tested, not supported (original and repeated interferometer tests; the one independent replication of Silvertooth found; Miller reanalysed). The specific "3000 m/s variation well outside error": Refuted by calculation as a statement about the Michelson-Morley records (it is either 0.004 fringe or 400 fringes, neither a result). The Irvine Ranch scatter is kept as a documented anomaly in early c measurement, not evidence for an aether.

Claim 5. Dehmelt's trapped electron refutes Heisenberg uncertainty; Boyd's "proof" for monochromatic photons

a. Internal consistency: the key step is dimensionally wrong. The essay: "the momentum of the fixed object must be equal to its rest mass. In this case, we know that the momentum of the electron is equal to its rest mass" [read: essay, p.1]. Momentum has units kg m/s; rest mass has units kg. They cannot be equal. The charitable rewriting is "rest energy" mc^2 (J), but a fixed object has momentum p = 0, not mc^2, and rest energy is not momentum. Even then, "p = 0 exactly" is not what the trap gives: a trapped electron is not stationary, it oscillates.

b. What Dehmelt's electron actually does. From the lecture [read: dehmelt-1989-nobel-lecture.pdf]: Penning trap at 4 K, B = 5 T, axial oscillation about 60 MHz, cyclotron frequency 141 GHz, trapped for 10 months. Using those numbers: - Axial ground-state width sqrt(h-bar / (2 m w)) = 0.39 micrometre, velocity spread about 148 m/s, momentum spread 1.3e-28 kg m/s [calc]; product Dx Dp = h-bar/2 by construction. - At the actual 4 K the axial motion is thermal: position spread about 21 micrometre, speed about 7.8 km/s [calc]; Dx Dp is about 1,400 h-bar, comfortably above the bound. - The cyclotron orbit has magnetic length sqrt(h-bar/(eB)) = 11 nm [calc]. So the electron is "held" to micrometre accuracy, not "frozen with exact position and momentum". Lasting for months is about stability of the trap, not precision of position and momentum. Dehmelt's lecture claims nothing against uncertainty; he measures the g-factor from frequencies [read].

c. Monochromatic photons. A photon of exactly known frequency has exactly known momentum (p = h f / c) only if its wave train is infinitely long, so its position is completely undetermined (Dx infinite): consistent with Dx Dp >= h-bar/2, not a refutation. Boyd's page reaches "known position" by timing emission to 10 femtoseconds [read: boyd-wayback-heisenburg-refute.htm]. But a pulse 10 fs long (Dt = 1e-14 s) has frequency spread of at least 1/(4 pi Dt) = 8e12 Hz [calc], not zero; at c this also means a position uncertainty of about 3 micrometre [calc]. So the page's own timing assumption contradicts "no uncertainty in frequency/momentum". And, as in Correction 3, Boyd's page itself says the electron obeys uncertainty.

d. Experimental. Uncertainty has been tested continuously in ion traps, squeezing and single-photon experiments [memory, medium]; the Dehmelt trap, if anything, is one of the best confirmations of quantised motion. Not verified on the web.

d. If true: the Fourier-transform relation between position and momentum representations would have to fail for matter waves, which would break the whole of standard wave mechanics.

Verdict. Electron claim: Refuted by calculation (dimensional error plus the actual Dehmelt numbers above). Photon claim: Internally inconsistent (own timing assumption implies frequency spread; author's earlier page says the argument fails for the electron). The photon "proof" is also a short verbal argument and was never shown with an experiment in the document; the essay says it "is easily demonstrated experimentally" [read] and no demonstration is in the folder or found by the Investigator.

Claim 6. Superluminal subquantum particles carry quantum information; attention and intention change antenna patterns and the quantum potential

a. Internal consistency. Two stated properties clash: - The essay says "All of Planck's constants have perfectly vanished where subquantum events and masses are involved" [read] and that the particles carry Bohm's "active information". - In Bohm's theory the quantum potential is Q = -(h-bar^2 / 2m) (laplacian R)/R (R = amplitude of the wave function). It is proportional to h-bar^2; with h-bar = 0 it vanishes, and with m -> 0 it grows without bound [calc, from the standard formula; memory, high]. A medium in which h-bar is zero cannot carry the quantum potential in Bohm's sense. The essay does not reconcile the two. - Speed argument: relativistic energy E = gamma m c^2, with gamma = 1/sqrt(1 - v^2/c^2). For a particle with m -> 0 and finite energy, v -> c, not beyond: that is what a photon does. For v > c, gamma is imaginary and requires imaginary mass (tachyon, E^2 = p^2 c^2 - mu^2 c^4) [memory, high]. The essay says the speed limit "does not apply because there is no mass" [read]; the algebra says the opposite: zero mass means exactly c.

b. Experiment. Bell-type tests (Aspect and later) agree with quantum mechanics and are compatible with relativity because no signal can be sent (no-signalling theorem) [memory, high]. Bohm's theory is non-local by design but predicts the same results as quantum mechanics, so it does not need a particle flow, and a particle flow with a speed does not by itself reproduce the instantaneous correlations. The essay says the author has "not yet devised an experiment" for the multidimensional part [read]. The Gariaev, PEAR and French antenna claims are cited to unlisted or non-primary sources. Haisch-Rueda-Dobyns 2001 (essay ref 26) is a zero-point-field theory of inertia, not a consciousness paper [read: Investigator lead].

c. Tested? Antenna pattern depending on operator state: no data, paper, numbers or authors given. The 1999 "Los Alamos archive" paper is missing from the record (essay: "posted ... in 1999, then removed about 2000"); the Investigator's three Google queries found nothing, and set out four candidate explanations (author withdrawal, moderation rejection, other host, misremembering) with the records that would decide (arXiv withdrawn listings 1999-2000, Quantum-Mind list archives, Sarfatti-group correspondence, the French experimenters) [read: sites.md]. I keep this as an unresolved anomaly in the record; the absence neither confirms nor refutes the claim. Gelinas/Honeywell curl-free vector-potential signalling patent (1980 family; US 4,432,098 is the essay's ref 24) is a corporate assignee's characterization of a working method, which assumes finite propagation speed (Investigator) and so does not itself support superluminal signalling.

d. If true: relativity's causal structure (no signalling above c) and quantum mechanics' no-signalling theorem would both fail; human intention would couple to radiation fields at a measurable level.

Verdict (split). Superluminal subquantum carrier of quantum information: Not testable as stated (no mass, speed, coupling or detection method; also internally inconsistent with h-bar = 0 and with the m -> 0 limit). Operator intention changing antenna patterns: Never properly tested on the record I have (no data, no paper found; the one cited paper is missing, which is an anomaly kept open).

Claim 7. A Klein-Gordon-type equation with free parameter K allows arbitrary masses; Planck's constant varies

a. The equation, checked step by step. Intended reading (see Correction 1): i dtheta/dr = box theta, where box is the wave operator (d'Alembertian) and r an extra "order of development" parameter. Try theta = exp(-i K r) lambda(x), lambda depending on position/time only. Then i dtheta/dr = i (-iK) theta = K theta, so K theta = box theta [calc]. The algebra is correct. Remaining points: - Sign and units. With signature (+,-,-,-) the Klein-Gordon (KG) equation is (box + m^2 c^2/h-bar^2) phi = 0, so K = -m^2; with (-,+,+,+) it is K = +m^2 [memory, high]. "K = m0^2" is right only in one convention and in natural units (h-bar = c = 1). In SI, K has units of 1/length^2 and r of length^2. The essay defines none of this. - Nothing new. KG already contains the mass as a free parameter: any m gives a KG equation. So "arbitrary K gives room for an infinite range of masses" is true of the ordinary KG equation. The extra parameter r only adds a trivial phase; the general solution is a superposition over K (a Fourier decomposition in r), so K is a separation constant, not a physical freedom. In effect this is the proper-time formulation of Fock and Nambu, where r plays the role of the proper time [memory, medium; Nambu's paper exists: Prog. Theor. Phys. 5 (1950) 82-94, [web] https://academic.oup.com/ptp/article/5/1/82/1857573; I did not read its content]. - Claim "both theories require masses down to infinitesimals" is unsupported: neither quantum theory nor relativity requires a continuum of masses [read: essay; memory, high]. - Because the equation has no interaction terms, it says nothing about subquantum particles.

b. Planck's constant. The essay: "It has been determined by experiment that Planck's constant ... is not a constant under all circumstances. [30]" with ref 30 = Webb, PRL 87, 091301 [read]. That paper (published 2001) concerns the fine-structure constant alpha = e^2/(4 pi eps0 h-bar c) measured from quasar absorption lines; its combined result was Delta-alpha/alpha = (-0.57 +/- 0.10) x 10^-5 [web] https://doi.org/10.1103/physrevlett.87.091301 (via search result). It is not a measurement of Planck's constant. A change in alpha could come from e, h-bar or c, and only dimensionless ratios are measurable [memory, high]. Later quasar results disagree with it in places (the ongoing debate is listed in the same search results, e.g. the high-precision single-system limits [web] https://academic.oup.com/mnras/article/464/3/3679/2514573), so even the alpha change is not settled. The Investigator's lead (Physics Today called for confirmation or refutation) is consistent with this.

c. Tested? The KG equation: extremely well tested for spin-0 particles [memory, medium]. The Planck-constant variation claim: not tested as stated (no measurement of h-bar alone exists).

d. If true: varying h-bar would change atomic spectra and chemistry; tests such as the Oklo natural reactor limit alpha variation at about 1e-7 [memory, low-medium; not checked].

Verdict (split). The equation: Established as mathematics (internally consistent and it is just KG with a separation constant), but it adds nothing and does not support subquantum masses. "Subquantum particles with arbitrary masses": Not testable as stated. "Planck's constant varies, per Webb": Not testable as stated by the cited source (it concerns alpha, not h-bar, and remains contested).

Investigator's findings that bear on my claims (kept whatever my verdict)

• Authorship: the essay is R. N. Boyd's; submitted by invitation to the 9th Space, Time and Gravitation conference, St Petersburg, Aug 2006, "Publication is pending"; later file labelled "peer-reviewed" (STG-IX status unchecked). [web: worlds-within-worlds.org/rnboyd.php, Wayback 2007-02-25]. Hosting at noosphere.princeton.edu/papers/misc/ is hosting, not endorsement.
• Boyd's self-described record (plasma-confinement design tested at Los Alamos, NASA laser ranging, Sarfatti group, Project Greenglow, Gariaev's staff): an interested party's description of himself, one source, not corroborated by the one query run; check OSTI/DOE/patent records.
• Mendeleev's primary text exists and supports the historical proposal of an ether gas in a zero group; it differs from the essay in date and numbers (Claim 1).
• Piggott's primary article, the place/units/ground/duration differences between Piggott, Vassilatos and Boyd (Claim 3).
• Silvertooth, Marett replication, Sherwin 1989 critique, Irvine Ranch anomalies (Claim 4).
• Correa aetherometry, Haisch-Rueda-Dobyns, Webb 2001, T. J. J. See push gravity, Shoulders, Gradient Dynamics patent US9306527: related work, listed as leads (Claims 3, 6, 7).
• The missing 1999 Los Alamos paper (Claim 6) and the later Boyd papers (Boyd & Klein, Christianto-Smarandache-Boyd 2018-2024), not read by me; I cannot say whether they supply the missing derivations.

Summary table

Files: review/zzz-Unknown/mathematician.md