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Mathematician review: Wallace-Byran (The Farce of Physics, 1993)

Reviewer: PhD mathematician (Step 2). Source tags: [read] from a document, [web] with URL, [memory] with confidence. Scratch calculations were run with sympy/numpy in the project venv.

Source gap (repeated from claims.md)

The book prints no equation of "mass dynamics", no atomic/nuclear model, no radar data table and no program listing. The equations are in papers not in the folder (Found. Phys. 3, 381 (1973); Spectroscopy Letters 1969-71; J. Clas. Phys. 1982; Speculations Sci. Technol. 1986). What I could check: (i) the 1969 radar paper itself (Spectroscopy Letters 2, 361-367), a 4-page scan found by the Investigator at http://sciliterature.50webs.com/SpecLetters1969-p361-367.pdf, which I read as page images [read: page image p.361-367]; (ii) the book's Chapter 5 text and Chapter 7. For the theory of Chapter 7, every conclusion below about its mathematics rests on the book's prose alone, and says so.

Corrections to Step 1

  1. facts.json says the radar chapters (4-6) were digest-only. I read the key Ch.5 passages (text lines ~2495-2530, 2790-2900, 3395-3480) and the 1969 paper. The "3 ms against 10 microseconds, 30,000%" figures [read: farce lines 2506-2510] come from the 1993 book and the 1971 abstract; the 1969 paper itself gives no such numbers. It shows a graph in units of 10^-6 astronomical units (AU; mean Earth-Sun distance, 1.496e8 km) and says "variations far larger than their maximum estimate of all possible errors" [read: page image p.363]. The arithmetic is consistent: 3 ms / 10 us = 300 = 30,000%.
  2. claims.md (claim 2) says Shapiro's side "is not given". It is partly given: Wallace relays Shapiro's 17 Jan 1969 letter that the radar data "are not consistent with the 'ballistic theory' of light, but are consistent with general relativity", citing Shapiro, Ash and Tausner, PRL 17, 933 (1966) [web: Investigator note 2026-10-04-ekkehard-friebe.md; ADS]. So the statement "c+v was never tested" is Wallace's reading of a conference exchange; Shapiro's letter says a ballistic test (via the Doppler formula) had been made. The full 1966 paper was not read by me.
  3. The Investigator's leads cite "claim 11" (Hafele-Keating). That is key_claims item 11 in facts.json, not a claims.md number; in claims.md it sits inside claim 5/context of the absolute frame. I treat it under claim 5 below.
  4. Deep read flag M9 (Andrews, "less dense than best vacuum") was computed as inverted; I recomputed: v = sqrt(G_s/rho) = c with G_s = 8e10 Pa gives rho = 8.9e-7 kg/m^3, about 1e8 times denser than a 1e-10 Pa vacuum (~1e-15 kg/m^3). So the book's wording "less than our best vacuum" is the opposite of what the numbers give, unless Andrews says something else. Andrews p.53 not checked; minor, not load-bearing.
  5. The deep reader's other flags (M3 spin, M4-M7, M10-M12) I re-derived and agree with, with the additions in claims 3-4 below.

Mathematics of the central radar argument (claims 1-2), checked by me

What Wallace does

[read: page image p.364] Equation (1), the Einstein "c" theory: D_E = tc/2 - tv/2. Equation (2), the "c+v" theory: D_G = t(c+v)/2 - tv/2 = tc/2. Here t is the measured round-trip time, v the radial approach speed of Venus (from the Doppler shift d: v = dc/2f), D the Earth-Venus distance. The text says the second term "corrects the distance to the time the beam returned"; the first term of (2) rests on "c + (c+2v) = 2(c+v)", i.e. an out-leg speed c and a return-leg speed c+2v averaged arithmetically. Fig. 1 plots E and G (converted to heliocentric radius) against Newcomb's tabulated ephemeris N; G lies near N, E does not. The conclusion: "Note the close fit between Newton's Laws and his c+v corpuscular theory" [read: page image p.365-366].

Defects found

(a) D_G = tc/2 - the "difference" between E and G is built in by algebra. Subtracting the two equations gives D_G - D_E = tv/2 exactly, for any data. For the scale: a round trip near inferior conjunction is t ~ 290 s; v of 3, 5, 10 km/s gives tv/2 = 435, 725, 1450 km = 2.9, 4.8, 9.7 x10^-6 AU. That is the vertical scale of his Fig. 1 (curves differ by a few to ~8 x10^-6 AU) [calc: sympy/numpy]. So the plot shows tv/2 and nothing about light. Whether it matches Newcomb's ephemeris N depends only on which epoch (instant of emission, reflection or reception) N refers to, which the paper does not state. (b) The c theory itself gives tc/2 at the reflection epoch. Take Earth station at rest in the frame where light has speed c (the "ether" model), Venus approaching at v. Outgoing leg: closing speed c+v, time t1 = D0/(c+v). Venus is then at D1 = D0 c/(c+v). Return leg at c: t2 = D1/c = D0/(c+v). Total t = 2D0/(c+v) and D1 = tc/2 exactly (sympy confirmed; residual 0). So the constant-c model's distance at the moment of reflection is the same tc/2 that Wallace assigns to c+v; his Eq. (1) is the c model's distance at the later instant of reception (D1 minus v t2 = tc/2 - tv/2). Comparing the c-model at reception epoch with the c+v model at reflection epoch is an epoch mismatch, not a test. Caveat: his station is not at rest and the real analysis uses barycentric ephemerides; but the same shift of tv/2 is a time-labelling shift, not a difference of theory. (c) The "average speed" step is unjustified. A round trip with legs at different speeds is not t = 2D/(arithmetic mean speed); distance divided by speed per leg is needed (harmonic mean). Under the most direct ballistic assumption (leg 1 at c+v closing, reflected light at c relative to Venus, i.e. c+v toward Earth) I get t = D0(2c+v)/(c+v)^2 and distance at reflection D1 = tc/2 + tv/4 + O(v^2/c), not tc/2 [calc: sympy]. So Eq. (2) does not follow from a stated reflection law; "c+2v" on the return leg assumes a mirror-image rule for moving reflectors that is not stated or justified. (d) The two models do differ at first order, but only as a time shift, and the test needs a joint fit. Doing a full 1-D comparison (station velocity uE, Venus uV, light at c+uE out and c-uV... relative to the reflector back) against the wave model, the difference in round-trip time is, to first order, -(D0/c^2)(uE-uV) ~ 4.8 ms for D0 = 43e6 km and relative speed 10 km/s; it depends only on the relative velocity, as Galilean invariance requires; second-order differences are ~1 us [calc]. A first-order delay shift proportional to D times range-rate is not a free parameter in a proper orbit fit but it can be partly absorbed by changing orbital elements and the AU; deciding which model fits better requires both models to be fitted with all parameters free to the same data. Wallace compared an unfitted formula against a fixed tabulated ephemeris (N), computed from eight 1961 points he calls "the sparse set of data that was published" [read: farce line ~3470; page image p.364]. That cannot discriminate. He concedes this in the paper's conclusion: "I don't think it can be considered reasonably conclusive until a full c+v investigation is made" [read: page image p.367]. (e) Frequency dependence points to plasma, not c+v. Wallace notes the 30-day term at 440 MHz is "about five times larger" than at 1295 MHz [read: page image p.363]. Dispersion of a plasma delay scales as 1/f^2: (1295/440)^2 = 8.7. A speed-of-light effect (c vs c+v) is frequency independent. His own datum thus favours an ionospheric/solar-plasma delay, which he partly acknowledges ("part of the 30-day variation is due to intervening plasma") and then treats the remainder as c+v without a model for the plasma term. The ratio 5 vs 8.7 is rough (different epochs and stations), so this is a pointer not a proof. (f) Residual terms tied to Earth rotation, the 30-day month and relative orbital speed are exactly the signatures of any imperfectly modelled target/station motion during the light time (Earth rotation 0.46 km/s x 290 s / 2 = 67 km = 0.22 ms), so their presence does not itself identify c+v. This is the kind of residual a mis-reduced or low-precision early data set produces; whether Lincoln Lab's own residuals showed them depends on the original papers (not read). (g) The Moyer (JPL) equation Wallace calls "nearly equivalent to Galilean c+v" [read: farce ~line 2830] is a light-time iteration with positions evaluated at the reception/retarded times. Evaluating positions at retarded times is how constant-c propagation is computed (a signal at speed c leaves a moving emitter and meets a moving target at a later position); it does not imply c+v. Moyer's formulation also adds relativistic terms (Shapiro delay, time dilation) that Wallace's own quoted text lists. I have not read Moyer (1981). [memory: medium] that the standard light-time algorithm is a speed-c iteration.

Others' tests of the c+v (ballistic, Ritz) hypothesis (for question c)

Not mathematics of the book, but needed: the ballistic hypothesis predicts photons from a source moving at v travel at c+v. Alvager et al. (CERN 1964) measured photons from neutral pions moving at 0.99975c and found speed c within error; this is described in [web] https://arxiv.org/pdf/0912.3818 and the search summary at the Alvager query (confidence: web summary, not the primary paper). The search result also lists J. G. Fox, whose 1965 review Wallace cites as saying no direct evidence refutes the remaining theories. Fox's later view (extinction-theorem argument) is not read by me. Double-star arguments (de Sitter) were what Sekerin's 1987 paper, relayed by Wallace [read: farce ~line 2881], tries to rescue.

Chapter 7 theory (claims 3-4): the mathematics that is there

Reconstruction in plain terms. A particle of mass m at rest is mass flowing round a loop at speed c (centre of mass at rest). At annihilation the loop "unrolls" into a straight line at c. Three properties: conservation of mass, of momentum, and "equality of action" (two ether quantities meeting attract, deflecting by an amount proportional to their masses). [read: p.1, L5056-5098, deep read]

Findings. 1. No energy law. Photon momentum p = E/c = mc matches a lump of mass m moving at c. But in this Galilean mass picture the kinetic energy of a lump m at speed c is (1/2)mc^2, not mc^2. For e+ e- annihilation the two rest energies total 2mc^2 while the circulating kinetic energy is 2 x (1/2) m c^2 = mc^2; the photons' linear kinetic energy is again (1/2)m c^2 each (total mc^2 for two). Whether total energy balances depends on potential energy of the binding, which is never given. Energy conservation is not among the three properties, and E = mc^2 is used as an input from relativity, the theory he rejects. [calc by hand; derived from the reconstruction] 2. Spin. The deep reader's M3 stands: one rotation in 1.2e-22 s at speed c means radius <= 5.7e-15 m and angular momentum m c r ~ 1.6e-36 J s, about 34 times too small for spin hbar/2 = 5.3e-35 J s (ratio ~ 1/(4 alpha), alpha = fine-structure constant). Matching spin with speed c needs r = hbar/(2mc) = 1.9e-13 m (half the reduced Compton wavelength), 34 times larger than the model's cell scale. The two numbers cannot both be inputs. (Also, a circulation of rest mass m at exactly c has infinite energy in special relativity; Wallace's reply is Galilean mechanics, which brings back item 1.) 3. Frame. The speed c of the internal motion is stated in no frame (deep read M12). Yet he asserts c+v for light. If the particle's internal flow is c in the particle's frame, a moving electron has flow of magnitude |c+v| > c on one side and the 12-cell model (all cells moving at c) is not Galilean-covariant; if c is relative to an absolute frame, a boosted electron needs its own explanation, which the book defers to a "c+v model [that] will have to be developed". The model as stated is not well-posed kinematically. 4. Gravity. Gravity of two electrons relative to Coulomb: G m_e^2 / (e^2/4 pi eps0) = 2.4e-43 [calc]. Matching Newtonian gravity "to 3 significant figures" with a surface-tension term requires that 1e-43 coupling to be put in; whether derived or fitted cannot be told without UNIFIED. A 13-digit BASICV program cannot resolve a 1e-43 relative effect against a Coulomb-sized term unless the gravity term is computed separately (deep read M5). Until the source is seen: not checkable. 5. Cell sizes. 12 cells of radius 2.8e-15 m is the classical electron radius r_e = 2.818e-15 m: charge is evidently put in by hand, not derived (deep read M4). 6. Lorentz-force check. For parallel charges moving together the lab force is Coulomb x (1 - v^2/c^2)^(1/2) = Coulomb/gamma (gamma, the Lorentz factor, is the very relativity Wallace rejects; comparing to the "Lorentz force" thus takes relativity as the benchmark). The predicted deviation below 1.1e-14 m (extended electron) is testable in principle; [memory: high] high-energy e+e- scattering finds no structure down to ~1e-18 m or smaller, so this prediction is contradicted by others' experiment (physicist to cite). 7. Pion. pi0 mass 134.98 MeV = 264.1 m_e. "104" e+/e-: 53 MeV, binding would need to add 82 MeV; "10^4": 5110 MeV, binding removing 97% of the mass. Neither mass-defect account is given; also π0→2γ and π±→μν are not derived [calc]. 8. Numerics. Time step 1e-25 s moves cdt = 3e-17 m, ~1% of a cell; 1200 steps per rotation; "1/2 step integration" is unspecified; conservation of mass/momentum numerically over a rotation is not reported. 9. Experiments reported.* Crossed-beam e-e scattering at 90 degrees, 300 eV, 1.2 and 1.3 uA agreeing with Moller's cross section is a confirmation of standard QED/QM scattering; the kinematic claim (max scattered energy 2E) is correct (c.m. speed v/sqrt2, scattered along c.m. gives sqrt2 v). It does not test mass dynamics. [read: deep read; checked by hand]

Cosmology numbers (claim 5)

  • Jupiter "radiates 2 1/2 times more energy than it receives" [read: CP437 decode, deep read L5207]. Voyager gives 1.67 +/- 0.09 and a Cassini-era update gives 2.13 +/- 0.05 [web: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6137063/ and Voyager value summary via search]. So 2.5 is high for either, but the existence of an internal heat source is correct. Standard explanation: Kelvin-Helmholtz contraction and residual heat; pressure-induced annihilation is not needed.
  • Hafele-Keating: published means -59 ns (east) and +273 ns (west) are correct [memory: high; Hafele and Keating, Science 177, 166 (1972)]. Their predictions were computed in a non-rotating geocentric frame, which is not "a frame at rest with distant galaxies"; with the rotation of the Earth the asymmetry arises. Interpretation, not arithmetic, is at issue. A. G. Kelly's FOIA reanalysis (listed on sciliterature.50webs.com) disputes the data's significance [web: Investigator]; not read by me.
  • No equations for redshift-by-photon-photon interaction, galaxy evolution, or "columns of dynamic ether" are given; claim 5 has no mathematics to check.

Answers per claim

Claim 1: Venus radar residuals show light speed is c+v

a. Maths consistent? Arithmetic consistent (3 ms / 10 us = 30,000%). Derivation not: D_G - D_E = tv/2 by construction; epoch mismatch between the two models (defect b); unjustified arithmetic-mean speed (c); no joint fit (d); plasma frequency scaling (e). b. Consistent with experiment? The ballistic hypothesis conflicts with Alvager et al. 1964 [web above]; Shapiro's 1966 Doppler paper is cited by Shapiro as ruling out a ballistic Doppler law [web: Investigator; not read by me]. c. Tested? By Wallace on eight 1961 points (not a fit); Shapiro's group did full c/GR fits (Ash, Shapiro, Smith AJ 72, 338 (1967)) [web: ADS]; Wallace requested their data, got an AFCRL card deck he judged unusable (stations too close, constant observing times) [read: farce, via Investigator], and Shapiro in Dec 1969 declined to lead an investigation. No neutral, controlled, joint c vs c+v refit of the full radar data on record that I found. Not replicated by anyone I could find in the print record; Tolchelnikova-Murri's related work argues round-trip radar is insensitive to solar-system velocity (the models differ only through relative velocity), so radar "neither confirms nor refutes SR" [web: https://ritz-btr.narod.ru/tolchel.html; her rendering]. d. If true: the second postulate fails; Lorentz covariance of Maxwell's equations; GPS-type light-time models and pion-decay photon speed would need re-deriving. Verdict (split): Wallace's radar argument as published: Internally inconsistent at the derivation step (epoch mismatch and averaging), so it is not a valid test; the underlying question of a full joint c vs c+v refit with all parameters free is Never properly tested (dismissed without a testing offer accepted; Shapiro replied, but no joint refit was done on record). The c+v hypothesis in its strong form: Tested, not supported (Alvager 1964; others).

Claim 2: Second postulate is the linchpin; analysts admitted c+v untested

a. The claim is about events, not equations; the mathematical content is the same as claim 1. b. Shapiro's relayed letter says ballistic light was tested through the Doppler formula (PRL 17, 933, 1966) [web/read second-hand]. The Investigator notes the Texas Symposium date conflict (Dallas 1968 vs Soviet Astronomy listing Dec 1967); unresolved. c. No transcript found; one account (Wallace's), single source, quoted fairly above; no second source found yet. Shapiro is an interested party (he led the analysis); both accounts are given. d. Nothing in physics would change from the "admission" alone. Verdict: Never properly tested as to Wallace's specific c+v refit; the historical statement is Not testable as stated by me (one account of a conversation). The wider c+v hypothesis: Tested, not supported.

Claim 3: Inertial mass = photon virtual mass; internal circulation at c; ether with three properties

a. Not consistent as a calculation: no energy law; Galilean kinetic energy (1/2)mc^2 conflicts with E = mc^2; spin 34x too small at the model radius; frame of c unspecified (see Chapter 7 findings 1-3). Property III is not a formula. b. Photon momentum E/c and annihilation momentum balance are reproduced (but that is already standard). Spin 1/2 and magnetic moment not derived. c. No test on record; the postulates are not stated in a form that predicts a number apart from the force-law deviation (claim 4). No replication. d. If true: photons carry inertial mass in the Newtonian sense; special relativity's rest-mass concept, quantum spin and the vacuum would be reinterpreted. Verdict (split): The verbal postulate "E/c = mc" is Established as a bookkeeping identity (standard physics has it). The dynamic-ether model built on it: Not testable as stated (no equations in the book) and Internally inconsistent on energy as reconstructed (fixable only by supplying the missing equations).

Claim 4: Mass-in-cell model reproduces photon, electron, gravity, nuclear forces; deviation below 1.1e-14 m; pion of ~104 or 10^4 e+/e-

a. Cannot be checked (no code, no equations); checkable parts: spin mismatch, 1e-43 gravity coupling, pion mass defect (above). b. The predicted deviation scale is contradicted by high-energy lepton scattering [memory: high; physicist to confirm]. Moller scattering experiment agrees with standard theory, not specific to the model. c. Run by Wallace and students on a PRIME 750; published in J. Clas. Phys. 1982 and Speculations Sci. Technol. 1986 (not in folder; ADS indexes 1971/1973 items, not those). Not independently replicated: no citation found by the Investigator (ADS lists 12 citing papers, none a replication of the computer model). d. If true: quarks and QCD replaced by composite e+e- states; gravity derived from electron structure. Verdict: Never properly tested; Not testable as stated from the book alone. The 1.1e-14 m deviation: Tested, not supported by others' point-likeness limits (physicist to cite).

Claim 5: Infinite eternal universe; non-Doppler redshift; pressure annihilation powering bodies

a. No equations to check. Jupiter figure misquoted high (2.5 vs 1.67 or 2.13). b. Physicist/contrarian to weigh (Arp, M82, etc.). c. Arp and others tested redshift anomalies; not replicated as non-Doppler explanations in the sources here (not read). d. Big Bang cosmology, nucleosynthesis, CMB. Verdict: Not testable as stated (mathematically empty here); the Hafele-Keating absolute-frame reading is Plausible, untested in the sense of an alternative frame interpretation of the same numbers, but the non-rotating geocentric standard treatment already reproduces them.

Claim 6: Journals, referees, funders obstructed the work; QCD, quarks, relativity meet Langmuir's pathological-science criteria

a. Outside mathematics. The Langmuir argument (Ch.2) is analogy, not calculation. b-c. Documented in Wallace's own letters and quotes: 1969 PRL referee reversal; NSF rejection Feb 1978; Robinson's letters of 1979 and 1990 [read: farce]. All single-source, Wallace's account; the NSF rejection language ("no reason to abandon conventional and remarkably successful theories") is quoted from the rejecting official. Independent partial evidence: the journal did print a rebuttal (Horedt and Ruck, Spectroscopy Letters 5, 455 (1972)) and a sympathetic paper (Rapier 1971), and ADS lists 12 citations [web: Investigator]. Silence of other sources is not contradiction. The abrupt end of Wallace's journal publication after 1986 ("my ninth, and last research paper") is an anomaly: competing explanations are loss of access to referees (his account), lack of a data path after the AFCRL deck, and his own turn to letters and conferences (NPA, Leningrad 1989, 1991). Records that would decide: PRL/Physics Today editorial files, Robinson correspondence, NSF reviews. d. N/A. Verdict: Not testable as stated by a mathematician; flagged for the contrarian and arbiter. I keep the Investigator's rebuttal and citations in the record.

Investigator's findings I weighed (kept whatever my verdict)

  • Wallace's papers online (GSJ author page; sciliterature scan): read the 1969 one; the 1971 paper (Spectroscopy Letters 4, 79) was not read.
  • Tolchelnikova-Murri (Pulkovo): independent astrometrist who reads the same radar papers differently; argues Doppler/range reductions used classical kinematics (Clemence remark, IAU Symposium 21). Not c+v. Her claim that radar reductions were not relativistic bears directly on claim 1; I have not read her derivation (Russian).
  • Horedt and Ruck 1972, Rapier 1971, Wegener and Øhrstrøm 1975, Malykin 2010/2012 reviews: related literature; none read in full.
  • Wallace's own Eq. (D = t(c+v)/2 - tv/2) was the Investigator's request to the mathematician: my verdict above.
  • Biography: born 1933, died 1997 [web: NPA wiki; secondary]. A source that labels him "radio astronomer" differs; no evidence found.