Part 2 of a series that begins with Part 1: The Smallest Units; companion to the working paper and to the scorecard Aspden’s Numbers at a Glance. Downloads: Word · Markdown · analysis scripts (quarks.py, particles.py, toolkit.py).
What Aspden said about quarks and the other particles, what his units have to do with quarks, and how his particle numbers have fared as measurements improved
By Doug Westmoreland (project lead: direction and review) and Claude, Anthropic (research and analysis) · Version 1.0, 31 October 2026. Draft 0.1 was checked by an independent reader (Opus, extra effort) who had not seen how it was produced; the 28 points raised are all addressed here. Draft 0.3 recomputes the uncertainty of today’s deuteron binding energy from the masses in atomic mass units (0.37 eV, not 0.81 eV: the old figure added the uncertainty of the shared conversion to MeV three times, where it cancels), which moves P26 from 91σ to 199σ; compares the electron anomaly (P06) with the direct measurement of Fan et al. (2023), 0.00115965218059(13), instead of the CODATA 2022 adjusted value, which is partly a fit through QED theory (109σ becomes 149σ); adds a companion table, Aspden’s Numbers at a Glance, giving the digits right for every number; and moves the W, Z, Higgs, top and neutron-lifetime values to PDG 2026 (the W mass is now 80.3625(77) GeV without the CDF 2022 measurement, which moves P27 from 125σ to 216σ and P32 from 3.8σ to 7.5σ; the neutron mean life is 878.3(4) s, which moves P22 from 39σ to 49σ). The counts in summary item 5 are unchanged · Companion to Aspden’s Aether from the Bottom Up, Part 1 (v1.5) and its supplement Part 1A (v1.2)
Summary
This part follows up the references to other particles and predictions in Aspden’s work, with particular attention to quarks: for example, whether quons and quarks are at the same energy levels. Two reading passes went through all 719 texts on the site and catalogued every particle claim, with every quotation checked against the texts (section 1). The numbers were then tested against Particle Data Group (PDG) and CODATA values, with scripts that print every figure quoted here.
- Quons and quarks are different things at different energies (tests Q1–Q5).
- A quon has rest energy 20.8 keV. The lightest quark, the up quark, is 2.16 MeV, about 100 times heavier.
- None of Aspden’s eight characteristic energies lands within 5% of any of ten quark masses, current or constituent; chance would be expected to give about half a hit. (His 1980 "quark theory" does produce 336.9 MeV, within 0.3% of today’s constituent u, d mass, by a different route; section 8.)
- A quon carries the whole electron charge e; quarks carry +2/3 e or −1/3 e. A quon’s charge sphere is 23 fm in radius, 27 times the proton’s radius; quarks show no size down to about 10⁻²⁰ m.
- Aspden accepted three constituents in the proton; on fractional charge he moved (section 2). In 1969–1980 and again from 1994 he held that each constituent carries a whole charge ±e. In 1986–1989 he left fractional charge open in print, and in 1986 wrote that the fractional charges "can be deduced" from his space-conservation rule. In 1998 he said his earlier use of quark language had been a disguise, and from 1994 he explained fractional charge as a time average of whole charges flipping between states.
- The time-average picture is excluded by deep-inelastic scattering (Q7–Q8). Scattering measures the average of the squared charge, which for a charge that is always −1, 0 or +1 can never be smaller than the size of its average charge. Charged-lepton scattering counts squared charges; neutrino scattering counts quarks. Fixed charges of 2/3 and −1/3 predict a ratio of 5/18, confirmed to 2–3%. Flipping whole charges would give at least 1.8 times that. (The rate at which electron–positron collisions make hadrons fits fractional charges in three colours, but Aspden has no colour, and without colour it does not by itself exclude flipping charges.) His 1986–89 option, fractional charges inside the Thomson sphere, falls instead to the size argument (item 4).
- His particles are charge spheres of the wrong size (Q6). Aspden treats each particle as a sphere of charge of Thomson radius 2e²/3mc² ("The electron I have in mind is a sphere filled by electric charge", 1972). The electron is then 1.9 fm in radius, which large-angle electron–positron scattering at LEP would have shown by a suppression of at least 10¹¹. His composite proton contains an electron and a positron, each by his own formula 1.9 fm in radius, larger than the measured proton (0.841 fm), while its core is 822 times smaller.
- Most of his particle numbers matched the measurement of their day and now miss (tests P01–P35). Of 27 numbers he set against a measurement when he published, 24 agreed within two standard deviations at the time; against today’s values, 4 do. For 20 of the 27 his number sits nearer the value he used than today’s. That is the signature of numbers tuned, by choices among alternatives, to the measurement of the day, and the same pattern as his fine-structure constant. Clear cases: the deuteron binding energy (199σ today), the electron g-factor (149σ), the W and Z masses, the tau mass of 1986 (45σ), the neutron lifetime (49σ). In 7 cases his number sits nearer today’s value, among them his final muon mass ratio, his final muon g-factor and the charged-pion lifetime.
- What still holds. His neutron magnetic moment, −44/23 nuclear magnetons, is 0.4 ppm from the measured value (1.6σ). His neutral-pion lifetime is within 1.8σ. The upper end of his 1989 neutral-pion mass range is within 1.6σ (the end he called less representative). His 1998 tau mass agrees, after two revisions following the measurement.
- His advance predictions failed (section 7).
- A charged lepton at 2.587 GeV, predicted from the mid-1960s and called "a firm prediction" in 1989: no such particle exists. A point-like spin-½ particle of that mass and charge would be pair-produced in electron–positron collisions at almost the tau rate, and none has been seen.
- Further W-like states at 35 and 137 GeV, a second Z at 204 GeV, resonances at 226 and 378 GeV: none has been seen.
- His October 2000 list of energy levels (… 92.3, 114.9, 138.4 GeV …) does not contain the Higgs boson found in 2012 at 125.13 GeV.
- Meson lifetimes below Einstein’s value in flight (1983): his final formula disagrees with the kaon and pion data he cited himself by 10–17σ, and with the 1977 CERN muon measurement by 3.4σ. In his favour, the 1970 muon data he featured fitted him (1.5σ) better than relativity (6.4σ); the purpose-built 1977 measurement removed that discrepancy. This settles an item the working paper had left unchecked.
- Neutrinos without mass: oscillations measured since 1998 require at least two neutrino masses, one of at least 0.05 eV.
- His formulas reach many targets (test P40). The operations in his published tables, applied to his base energies, put a value within 0.3% of an arbitrary mass about a quarter of the time (28%). Applied to ten well-known particles he never addressed, they hit 2, where chance predicts 2.8: no sign of predictive power, though the sample is small.
- Connections to quarks worth noting (section 9).
- His cell energy, 210.9 MeV, is 1.2% from the QCD scale Λ in its standard convention (208.4 MeV for five quark flavours), and close to MacGregor’s 210 MeV "subquark". Λ depends on convention (226 MeV at two loops; larger for fewer flavours), so the closeness carries little weight, but it is close.
- His decuplet formula steps by 146 MeV, close to the measured 152, 149 and 139 MeV spacings that the quark model attributes to the strange quark. It reformulates the equal-spacing pattern known since 1962.
1. How this was done
- Reading. Two reading passes, run at Doug Westmoreland’s direction on Opus at extra effort, went through all 719 texts: one for quarks, one for every other particle. Each produced a catalogue with exact quotations, the formula, the number, the year, the source address and whether the number came before or after the measurement. Every quotation was checked against the texts by script; obvious scanning errors (such as "|" for "I") are silently corrected, and Aspden’s own slips are marked [sic]. Where scanning had damaged a formula, the formula was rebuilt and accepted only if it reproduced the number Aspden prints.
- Independent check. Draft 0.1 was read by a separate reviewer who had not seen how it was produced. It found the number transcriptions clean and raised 28 points of physics, fairness and sourcing, all addressed in this draft. The main changes: the lifetime test now uses Aspden’s final formula; the hadron-production argument is limited to what it shows without colour; his 1986–89 position on fractional charge is stated; the then-and-now comparison now records which value his number sits nearer.
- Today’s values. CODATA 2022 for fundamental constants, masses and magnetic moments; PDG 2024, 2025 and 2026 summary tables for particles (PDG 2026 for the W, Z, Higgs and top masses and the neutron mean life); the Muon g-2 Collaboration’s 2025 world average for the muon anomaly. The scripts list every source.
- Scripts.
quarks.py(Q1–Q9),particles.py(P01–P35 and blocks B–E),toolkit.py(P40). Each prints every number used here. - Test identifiers. Q for the quark questions, P for particle numbers. They are listed in this paper and will be added to the test register.
2. Aspden on quarks, 1969–2001
| Period | His position | Key words |
|---|---|---|
| 1969, Physics without Einstein | Quarks noted; fractional charge rejected; but the proton does contain three particles: "the electron, the positron and a heavy elementary nucleon of positive charge e" | "This quark theory is untenable with the theory presented in this work. Here, there is complete reliance upon the indivisibility of the charge quantum e" |
| 1972, Modern Aether Science | The quark search set against Earnshaw’s theorem; aggregation of charges accepted | "we do not have to believe all about quarks to accept this aggregation idea" |
| 1974, "The Chain Structure of the Nucleus" | Feynman’s three-quark charge pattern reproduced with charges ±1 plus a vacuum "state" | "since no experimental evidence exists supporting the fractionally-charged quarks but since experimental evidence does support other features of quark theory, then the alternative is to accept that some features of Dirac’s aether theory need scrutiny" |
| 1980, Physics Unified ch. 7 | His own "quark theory" with charges ±e; a transient "multiple charge quark" of charge 43e used to derive MacGregor’s quark masses and the neutral pion | "we will take a Z value of 43 as the firm basis on which to develop a quark theory" |
| 1981–1984, Lettere al Nuovo Cimento | "quarklike" composites: the muon as a +e core with two electrons, the neutron as two constituents | "A quarklike model of the muon based upon the Thomson formula for the electron" |
| 1986–1989, Hadronic Journal, Physics Essays | An alternative to the quark model and QCD; fractional charge left open, and in 1986 said to be derivable | "there is a way in which the fractional charges of the three quarks can be deduced from the space conservation principles outlined above" (1986d); "nor does it preclude belief in fractionally charged quarks, provided these are contained within the Thomson radius assigned to unit charge" (1986e); "The author has reserved his own position on such quarks" (1989c) |
| 1994–2001, web essays | Fractional charge rejected: a time average of whole charges; gluons are electron–positron chains | "All the evidence points instead to transmuting forms of unitary charge particles which only appear on a statistical average to be fractionally charged" (Energy Science Report 5, 1994); "I referred to quarks in my Physics Letters paper in order [sic] disguise my true opinion" (Lecture 22, 1998) |
In his scheme the proton is a heavy positive core plus an electron and a positron (1969–1980), a group of charges +e, −e, +e (1986), or an antiproton with two positrons (1994–1997). He never uses colour; in 1999 he mocks "colour" and "charm" as terminology. The full catalogue, with every quotation and source, is in the companion file extract_quarks.md.
3. Are quons and quarks at the same energy levels? (Q1–Q5)
Aspden’s energies (Part 1’s chain, from The Physics of Creation ch. 7):
| Unit | Electron masses | Energy |
|---|---|---|
| Quon rest energy m₀c² | 0.0408 | 20.8 keV |
| Electron | 1 | 0.511 MeV |
| 27 quons (the photon unit) | 1.10 | 0.563 MeV |
| Half the cell energy (his "virtual muon") | 206.3 | 105.4 MeV |
| Cell energy E₀ (his "virtual muon pair") | 412.7 | 210.9 MeV |
| E₀/3 | 137.6 | 70.3 MeV |
| N = 1843 electron masses | 1843 | 941.8 MeV |
| "Graviton" | 5063 | 2.587 GeV |
Quark masses, three ways:
| Quark | Current mass (PDG 2024) | Constituent mass (naive quark model) |
|---|---|---|
| u, d | 2.16 and 4.70 MeV (at 2 GeV) | 336.0 MeV, from the proton’s magnetic moment (m_p/μ_p) |
| s | 93.5 MeV (at 2 GeV) | 510.2 MeV, from the Λ’s magnetic moment |
| c | 1.273 GeV | 1.548 GeV (half the J/ψ) |
| b | 4.183 GeV | 4.730 GeV (half the Υ(1S)) |
| t | 172.57 GeV | — |
The comparison (Q3–Q4). The nearest pairs are half the cell energy against the strange quark (+12.8%), E₀/3 against the strange quark (−24.8%), N electron masses against the charm quark (−26%), and the cell energy against the constituent u, d mass (−37%). None is within 5%. With ten quark masses spread over the range from 10 keV to 200 GeV, an arbitrary energy has a 5.8% chance of landing within 5% of one of them, so eight energies would be expected to give about 0.5 hits by chance. They give none. (Aspden’s 1980 quark theory produces 336.9 MeV, within 0.3% of the constituent u, d mass, by a route described in section 8.)
Property by property (Q5):
| Property | Quon (Aspden) | Quark (measured) |
|---|---|---|
| Charge | e (the electron’s) | +2e/3 (u, c, t), −e/3 (d, s, b) |
| Rest energy | 20.8 keV | 2.16 MeV and up (current); about 336 MeV (constituent) |
| Size | charge radius 23 fm | no structure seen: contact-interaction scales above 9–36 TeV (PDG 2024), distances below about 2 × 10⁻²⁰ m |
| Where found | everywhere, 3.9 × 10³⁶ per cubic metre, in a fixed lattice | only inside hadrons; PDG: all free-quark searches since 1977 negative |
Verdict: quons and quarks are not at the same energy levels, and they differ in every measurable property.
4. Fractional charge: the evidence and Aspden’s alternatives (Q7–Q8)
What the measurements count.
- Deep-inelastic scattering. Charged leptons (electrons, muons) scatter off quarks in proportion to their squared charge; neutrinos scatter off quarks through the weak force, regardless of charge. For a target with equal numbers of protons and neutrons the ratio is (q_u² + q_d²)/2 = 5/18 for fixed fractional charges. The measured "charge ratio" (CCFR/NuTeV neutrino data against NMC muon data) is 1 within 2–3% between x = 0.1 and 0.4, and after reanalysis down to x = 0.01.
- Hadron production in electron–positron collisions. The ratio R = σ(e⁺e⁻ → hadrons)/σ(e⁺e⁻ → μ⁺μ⁻) equals the number of colours times the sum of the squared charges of the quark types that can be made, with a small strong-force correction.
- Fractional charges with three colours: R = 2 below the charm threshold and 10/3 above it; with the first-order correction (1 + α_s/π), 2.16 at 3 GeV and 3.55 at 10.5 GeV.
- Measured: 2.277 ± 0.003 ± 0.046 at 3.08 GeV (BESIII 2022; about 2σ above the perturbative prediction, and BESIII notes a 2.7σ excess at 3.4–3.6 GeV) and 3.56 ± 0.01 ± 0.07 at 10.52 GeV (CLEO 1998).
- Fixed whole charges: R = 4 below charm and 6 above with three colours (Han–Nambu); 3 and 4 without colour. Both are excluded.
Aspden’s 1994–2001 picture: whole charges flipping, fractional on average. In his words, a "particle of charge e that stands alone for one third of the time but is part of a three-charge, e, -e, e group, the remaining two thirds of the time" appears, on average, as two charges of 2e/3 and one of −e/3. A scattering probe sees the charge present at the moment of the collision, provided the charge changes slowly compared with the collision. His own clock for such changes is the Compton period, 8.1 × 10⁻²¹ s; a collision at 2 GeV lasts about ħ/Q = 3 × 10⁻²⁵ s, 25,000 times shorter. For a charge that can only be −1, 0 or +1, the average squared charge equals the fraction of time it is non-zero, which can never be smaller than the size of its average charge.
- Averages of 2/3 and −1/3 then give average squared charges of at least 2/3 and 1/3, against 4/9 and 1/9 for fixed charges.
- The deep-inelastic ratio becomes at least 1/2 instead of 5/18: at least 1.8 times the measured value. This assumes neutrinos count his constituents as they count quarks; his theory makes no neutrino prediction of its own, since he regards the neutrino as illusory.
- R does not settle it alone. Aspden has no colour, and without colour flipping charges allow R anywhere from 4/3 to 3 below charm and from 2 to 4 above, ranges that contain the measured 2.28 and 3.56. R does exclude fixed whole charges, and it fits fixed fractional charges in three colours.
Verdict on the time-average picture: excluded by deep-inelastic scattering, on the stated assumption about neutrinos.
His 1986–89 option: fractional charges inside the Thomson sphere. This leaves the charge question open and is not tested by the measurements above. It depends on charges being confined within a Thomson radius, which section 5 tests.
5. Sizes: Thomson charge spheres against measured sizes (Q6)
Aspden’s particles are spheres of charge whose radius follows from the mass by J. J. Thomson’s formula, a = 2e²/3mc². The electron’s radius enters his central number, N = (b/a)³ = 1843 (Part 1, U05). His words: "The electron I have in mind is a sphere filled by electric charge" (Modern Aether Science, 1972); protons "have a core charge radius that is less than one thousandth that of the electron" (Research Note 4/98).
| Particle | Aspden’s charge radius | Measured |
|---|---|---|
| Electron | 1.879 fm | no structure seen; lepton–quark contact scales above 24–36 TeV |
| Muon | 0.0091 fm | no structure seen |
| Proton core | 0.00102 fm | proton charge radius 0.841 fm (CODATA 2022) |
- The electron. Take the case most favourable to him, a thin shell of charge 1.879 fm in radius. Probed at a momentum transfer of 100 GeV (resolution 2 × 10⁻¹⁸ m), its form factor is at most 1/(qa) = 0.00105, so large-angle electron–positron (Bhabha) scattering at LEP would have been suppressed by a factor of at least 8 × 10¹¹. A uniformly filled sphere, as he describes it, falls off faster still. The measured rates agree with point-like electrons.
- The proton. His proton is a composite: a heavy core with an electron and a positron (1969–1980), or an antiproton with two positrons (1994–1997). He never computed its charge radius. The core alone is 822 times smaller than the measured radius; the electron and positron are, by his own formula, each 1.879 fm in radius, larger than the whole measured proton.
Verdict: excluded for the electron, and inconsistent for the proton whichever part of his composite is taken. The only escape is that the Thomson radius is a bookkeeping quantity rather than a physical size; but then it cannot carry the "charge volume" meaning that N = 1843 needs, and fractional charges "contained within the Thomson radius" (his 1986–89 option) lose their container.
6. His particle numbers, then and now (P01–P35)
"He compared with" is the measured value Aspden quoted when he published. "σ then" is how far his number was from it, in that measurement’s standard deviations; "σ now" uses today’s value and uncertainty. "Nearer" says whether his number is closer to the value he used or to today’s. All numbers are printed by particles.py.
| ID | Particle and quantity | Year | Aspden | He compared with | Today | σ then | σ now | Nearer |
|---|---|---|---|---|---|---|---|---|
| P01 | Muon/electron mass ratio | 1983 | 206.7683078 | 206.76835(11) | 206.7682827(46) | 0.4 | 5.5 | now |
| P02 | Muon/electron mass ratio, first model | 1983 | 206.7687 | 206.76859(29) | 206.7682827(46) | 0.4 | 91 | then |
| P03 | Muon/electron mass ratio | 1980 | 206.7688 | 206.76859(29) | 206.7682827(46) | 0.7 | 112 | then |
| P04 | Muon anomaly (g − 2)/2 | 1984 | 0.001165918 | 0.0011659230(85) | 0.001165920715(145) | 0.6 | 19 | now |
| P05 | Muon anomaly, first model | 1983 | 0.00116589 | 0.001165895(27) | 0.001165920715(145) | 0.2 | 212 | then |
| P06 | Electron anomaly, with his gravitational term | 1981 | 0.001159652200 | 0.001159652200(40) | 0.00115965218059(13) | 0.0 | 149 | then |
| P07 | Tau mass, 3^(7/12) × proton | 1986 | 1781 MeV | 1783 ± 3 | 1776.93 ± 0.09 | 0.7 | 45 | then |
| P08 | Tau mass, revised | 1996 | 1776.51 MeV | 1777.1 ± 0.5 | 1776.93 ± 0.09 | 1.2 | 4.7 | now |
| P09 | Tau mass, revised again | 1998 | 1777.02 MeV | 1777.05 ± 0.02 ¹ | 1776.93 ± 0.09 | 1.5 | 1.0 | then |
| P10 | Charged pion mass | 1989 | 139.5678 MeV | 139.5685 ± 0.0010 | 139.57039 ± 0.00018 | 0.7 | 14 | then |
| P11 | Charged pion mass | 1980 | 139.5672 MeV | 139.5686 ± 0.0020 | 139.57039 ± 0.00018 | 0.7 | 18 | then |
| P12 | Neutral pion mass, from the 43e quark | 1980 | 134.959 MeV | 134.9645 ± 0.0074 | 134.9768 ± 0.0005 | 0.7 | 36 | then |
| P13 | Neutral pion mass, lower end of his range (his preferred) | 1989 | 134.960 MeV | 134.9642 ± 0.0038 | 134.9768 ± 0.0005 | 1.1 | 34 | then |
| P13b | Neutral pion mass, upper end of his range | 1989 | 134.976 MeV | 134.9642 ± 0.0038 | 134.9768 ± 0.0005 | 3.1 | 1.6 | now |
| P14 | Neutral pion lifetime | 1989 | 8.2 × 10⁻¹⁷ s | (8.7 ± 0.4) × 10⁻¹⁷ | (8.43 ± 0.13) × 10⁻¹⁷ | 1.3 | 1.8 | now |
| P15 | Charged pion lifetime ² | 1982 | 2.61 × 10⁻⁸ s | (2.551 ± 0.026) × 10⁻⁸ | (2.6033 ± 0.0005) × 10⁻⁸ | 2.3 | 13 | now |
| P16 | Charged kaon mass | 1989 | 493.633 MeV | 493.667 ± 0.014 ³ | 493.677 ± 0.015 | 2.4 | 2.9 | then |
| P17 | Neutral kaon mass | 1989 | 497.557 MeV | — | 497.611 ± 0.013 | — | 4.2 | — |
| P18 | J/ψ | 1978 | 3095 MeV | 3095 | 3096.900 ± 0.006 | — | 317 | then |
| P19 | ψ(2S) | 1978 | 3683 MeV | 3684 | 3686.097 ± 0.011 | — | 282 | then |
| P20 | Λ, 2^(1/4) × proton | 1986 | 1115.80 MeV | — | 1115.683 ± 0.006 | — | 20 | — |
| P21 | Ω⁻ | 1986 | 1674 MeV | — | 1672.45 ± 0.29 | — | 5.3 | — |
| P22 | Neutron mean life ⁴ | 1986 | 898 s | "the median of the recommended value" | 878.3 ± 0.4 s | — | 49 | — |
| P23 | Neutron mean life ⁴ | 1981 | 921.8 s | 918 ± 14 | 878.3 ± 0.4 s | 0.3 | 109 | then |
| P24 | Neutron magnetic moment, −44/23 | 1986 | −1.913043478 | −1.91304308(54) | −1.91304276(45) | 0.7 | 1.6 | then |
| P25 | Proton magnetic moment | 1988 | 2.792847367 | 2.792847386(63) | 2.79284734463(82) | 0.3 | 27 | then |
| P26 | Deuteron binding energy | 1980 | 2.22464 MeV | 2.22464(4) | 2.22456636(37) MeV | 0.0 | 199 | then |
| P27 | W boson | 1983 | 82.03 GeV | 82 ± 2.4 | 80.3625 ± 0.0077 | 0.0 | 216 | then |
| P28 | Z boson | 1984 | 96.86 GeV | "96" | 91.1879 ± 0.0020 | — | 2,840 | then |
| P29 | Z boson | 1986 | 93.79 GeV | 93.8 ± 2.3 | 91.1879 ± 0.0020 | 0.0 | 1,300 | then |
| P30 | Z boson | 1989 | 92.59 GeV | 92.6 ± 1.7 | 91.1879 ± 0.0020 | 0.0 | 700 | then |
| P31 | Z boson, revised | 1997 | 91.02 GeV | "close to 91 GeV" | 91.1879 ± 0.0020 | — | 84 | — |
| P32 | Weinberg angle, sin²θ = 2/9, against 1 − m_W²/m_Z² | 1986 | 0.22222 | 0.215 ± 0.014 | 0.22334 ± 0.00015 | 0.5 | 7.5 | now |
| P33 | "Higgs" level 122 × 1843 × 0.511 MeV | 2000 | 114.9 GeV | 114.9 (LEP hint) | 125.13 ± 0.11 | — | 93 | then |
| P34 | Top quark, proton-based levels ⁵ | 2001 | 174.97 GeV | 174.3 ± 5.1 | 172.60 ± 0.27 | 0.1 | 8.8 | then |
| P35 | Top quark, graviton-based levels ⁵ | 2001 | 174.78 GeV | 174.3 ± 5.1 | 172.60 ± 0.27 | 0.1 | 8.1 | then |
¹ He quotes "1777.05 MeV with an uncertainty of 0.02 MeV"; the 0.02 is probably his misquote of the PDG uncertainty. ² In 1982 he gave two alternatives, 2.61 or 2.56 × 10⁻⁸ s; the second was 0.35σ from the value he quoted. In 1989 he restated "approximately 26.1 ns" against 26.030 ± 0.023 ns. ³ He noted that his value was within the 1981 measurement’s error (493.640 ± 0.054) and 1.2–1.3σ from the 1975 and 1979 values. ⁴ Measurements of the neutron lifetime disagree by method: trapped neutrons give 878.4 ± 0.5 s (the PDG average), neutron beams 887.7 ± 2.2 s. Against the beam value his 898 s is 4.7σ off. ⁵ He called these "speculation" and the proton-based value "a quite curious coincidence"; they are included because he set them against the measurement.
What the table shows.
- Then: 24 of the 27 numbers with a stated comparison were within 2σ of the measurement he used. Several were exact or nearly so because a final step chose among alternatives or added a correction: the gravitational term in the electron g-factor (P06), the resonance choices for the muon (P01) and the proton moment (P25).
- Now: 4 are within 2σ of today’s value: the 1998 tau mass (P09, revised twice to follow the measurement), the upper end of his neutral-pion range (P13b), the neutral-pion lifetime (P14) and the neutron moment (P24).
- Which value his number sits nearer. A large σ today partly reflects the 10- to 1,000-fold gain in precision, which would sink any formula that is slightly off. The sharper signature of tuning is a number that sits nearer the old central value than the new one. That holds for 20 of the 27: the electron g-factor, the deuteron binding energy, the W and Z masses, the 1986 tau mass, the pion and kaon masses and the neutron lifetime among them. For these the measurement moved and his number did not: the charged pion mass rose by about 2 keV after 1989, the tau mass fell by about 6 MeV after 1986, the neutron lifetime fell from about 898 s to 878.4 s, and the deuteron binding energy fell by 74 eV. This is the same pattern as his fine-structure constant, which agreed with the 1973 measurement and is now about 4,000σ away (working paper section 10).
- The other 7 sit nearer today’s value: his final muon mass ratio (P01) and muon g-factor (P04), the 1996 tau mass, the upper end of his π⁰ range, the π⁰ and π± lifetimes and the Weinberg angle. For the muon numbers the measurement moved towards him, though both are now outside today’s much smaller errors (5.5σ and 19σ). The working paper notes the same for his proton/electron mass ratio, which the measurement approached after 1975.
- The exception. The neutron moment −44/23 = −1.913043478 is 0.4 ppm from today’s value (1.6σ), and was 0.7σ in 1986. The 46 comes from his four-state model of the neutron (46 transitions per cycle, populations 34:4:6:2), which he set by a counting rule with several free choices and himself called tortuous; 23 is the largest prime factor of 207. Among fractions with denominators up to 46, 20 lie between 1.90 and 1.93, so a value in that range has about a 1 in 1,000 chance of being this close to one of them; with 36 numbers tested here, about 1 in 30 for at least one such hit somewhere (
particles.py, block E). The same populations give his neutron–proton mass difference, which is 63σ from today’s value (working paper section 8), so the model has already failed one test on a different quantity.
7. Predictions made before the measurement
| Prediction | Year | What happened | Verdict |
|---|---|---|---|
| A charged lepton at 5063 electron masses (2.587 GeV): "In the mid-1960s the theory was built on the recognition that the g-lepton had to exist"; "it remains a firm prediction of this theory that there is a lepton at 2.587 GeV" (1989b) | mid-1960s; restated 1972, 1989 | A point-like spin-½ particle of charge ±e and mass 2.587 GeV is pair-produced in electron–positron collisions above 5.17 GeV at almost the tau rate (0.76 nb against 0.77 nb at 10.58 GeV; 0.13 nb if it had spin 0). The B factories alone made about a billion tau pairs. No such lepton appears in the PDG listings; PLUTO at PETRA excluded new heavy leptons from 4 to 14.5 GeV in 1981. I have not found a published search that names 2.6 GeV explicitly; this is a sourcing item. Aspden pointed to candidate states near 2.6 GeV: a 2583 ± 26 MeV entry in a 1982 review (Prentice), the PDG 1986 "(2585) bump", and a 2.60 GeV state reported in 1977 (Apostolakis). These were hadronic or unconfirmed, and none is a lepton | Not found |
| Further W-like states at 35.13 and 137.2 GeV; a second Z at 204.1 GeV; proton–antiproton resonances at 226.16 and 378.22 GeV | 1984, 1986 | None appears in the PDG listings. The only bosons known in this range are the W, Z and Higgs | Not observed |
| Meson lifetimes in flight below Einstein’s value: "when the particle has a speed for which its total mass is doubled we expect its lifetime to be 6.25% below the relativistic value" | 1983 (1983g) | The paper has two formulas. Eq. (10) gives his printed 6.25% and 0.56%. For speeds where the energy exceeds twice the rest energy he replaces it with eq. (17), which, rebuilt from the scan, gives his printed 0.9853 (26.30 μs). Against the data he cites, eq. (17) gives: muon at γ = 12.2 (1970), −1.48% against measured −1.20 ± 0.19% (1.5σ; relativity 6.4σ); K⁺ at E/E₀ = 3.38 and 4.17, −6.0% and −5.3% against measured −0.9 ± 0.3% (17σ and 15σ; relativity 3σ); π at E/E₀ = 2.44, −6.2% against +2.5 ± 0.9% (9.7σ; he calls the pion "a misfit"); muon at γ = 29.3 (Bailey et al. 1977), −0.33% against −0.02 ± 0.09% (3.4σ; relativity 0.2σ) | Disagrees with the data he cited, except the 1970 muon point, which the purpose-built 1977 measurement superseded |
| An energy-level spectrum: 22.6, 46.1, 68.7, 92.3, 114.9, 138.4, 161.0, … GeV, matched to a 114.9 GeV LEP event | Oct 2000 | The LEP event was not confirmed. The Higgs boson found in 2012 is at 125.13 ± 0.11 GeV, between his levels at 114.9 and 138.4 (spacing 23.5 GeV) | Not on his list |
| Neutrinos have no mass: "Concerning neutrino mass, that too seems to me to be an imaginary notion" | 1998 | Oscillations give mass-squared differences of 7.5 × 10⁻⁵ and 2.45 × 10⁻³ eV² (PDG 2025), so at least two neutrinos have mass, one of at least 0.05 eV | Excluded |
Two further numbers were stated before precise measurements and are covered elsewhere: the proton/electron mass ratio (1975; 0.19 ppm low today, working paper section 6) and the tau mass of 1986 (P07, 45σ today).
The working paper (section 9.1) had listed the 6.25% lifetime claim as "not yet checked". It is now checked.
8. MacGregor’s quarks and the 43e quark (Q9)
In 1980 Aspden took a "multiple charge quark" of charge 43e (43 being the nearest whole number to √1843 and to √1836) and derived four quark masses from M. H. MacGregor’s 1974 constituent-quark model. His arithmetic reproduces:
| MacGregor’s mass | Aspden’s formula | Value |
|---|---|---|
| S⁺ = 330.6 MeV | 43:42 pair, eq. (209), 43^(5/3)(5/4 − 25/1032) m_e | 330.58 MeV |
| S⁺⁺ = 336.9 MeV | 44:42 pair, eq. (211) as read | 337.01 MeV (he prints 336.9; the difference may be in the scanned formula) |
| M± = 74.6 MeV | [(3/2)^½ − 1] × 330.6 | 74.30 MeV, 0.4% below MacGregor’s 74.6; Aspden prints 74.3 and offers it as a possibility ("Possibly it comes from…") |
| M⁰ = 70.0 MeV | ½(273.126 + 1) electron masses, half a charged pion plus half an electron | 70.04 MeV |
- These are fits to a particular 1974 model, not to quantities in today’s standard model. MacGregor’s 70 MeV is close to mₑ/α = 70.03 MeV, and the pion is close to twice that, 140.05 MeV against 139.57. The 336.9 MeV value is within 0.3% of today’s naive constituent u, d mass, m_p/μ_p = 336.0 MeV.
- No particle or state of charge 43e has ever been observed. His link from Z = 43 to the scarcity of technetium (1987a) is a numerical coincidence; technetium’s instability is explained by nuclear binding systematics.
Verdict: the arithmetic reproduces (three values to 0.1% or better, one to 0.4%); the physical claim is untestable as stated.
9. Connections to quarks that are worth noting
- Three constituents. From 1969 Aspden held that the proton is made of three charged constituents. The quark model had proposed three constituents in 1964, and deep-inelastic scattering found point-like constituents from 1968. The agreement is in the count only: his three are one heavy core and two light leptons, while scattering shows three valence quarks sharing the proton’s momentum, and their charges are fractional (section 4).
- The cell energy and the QCD scale. E₀ = 210.9 MeV, the cell energy he called a virtual muon pair, is close to MacGregor’s 210 MeV "subquark" (which Aspden identified with it) and 1.2% from Λ, the scale at which the strong force becomes strong, in its standard convention: from the measured α_s(m_Z) = 0.1180, three- and four-loop running with five flavours gives 208.4 MeV. Λ depends on convention: 226 MeV at two loops, and larger for fewer flavours. The closeness is notable but carries little weight, because the convention could have been chosen to match.
- The decuplet spacing. Aspden’s 1986 formulas for the Σ*(1385), Ξ*(1530) and Ω⁻ have the form (τ + nQ)/3^(1/3), stepping by Q/3^(1/3) = 146 MeV. The measured steps are 152.6, 148.8 and 139.0 MeV. In the quark model the steps come from replacing one light quark by a strange quark each time, and the near-equal spacing was the basis of Gell-Mann’s 1962 prediction of the Ω⁻. The tau and Q are fixed elsewhere in his scheme; the empirical choice is the form of the formula. It reformulates a known pattern rather than predicting a new one.
- The neutron moment. −44/23 is within 1.6σ of the measurement. The quark model’s simplest prediction, μ_n/μ_p = −2/3, gives −1.862, 2.7% off. Aspden’s number is far more precise, but section 6 explains why that carries limited weight: a 1-in-30 chance across the numbers tested here, and the same model fails for the neutron–proton mass difference.
10. Research list: what was done and what could come next
| # | Question | Status |
|---|---|---|
| R1 | Catalogue every particle Aspden derives or predicts | Done: extract_quarks.md (about 40 works) and extract_particles.md (97 claims) |
| R2 | Score each against today’s values | Done for 36 numbers (P01–P35, P13b) |
| R3 | Quons and quarks at the same energy levels? | Done (Q1–Q5): no |
| R4 | His accounts of quarks against the fractional-charge evidence | Done (Q7–Q8): time-average picture excluded; the 1986–89 option falls with the sizes (Q6) |
| R5 | Property-by-property comparison | Done (Q5) |
| R6 | Charge spheres against measured sizes | Done (Q6): excluded |
| R7 | MacGregor’s 70 MeV quantum and the 43e quark | Done (Q9) |
| R8 | Which numbers came before the measurement | Done (section 7) |
| R9 | W, Z, Higgs, top, neutrinos | Done (P27–P35, section 7) |
| R10 | How much chance alone would give | Done (P40, toolkit.py) |
| R11 | Independent review of this draft | Done: 28 points, all addressed in draft 0.2 |
| Next 1 | A published search covering a charged lepton at 2.6 GeV, to source the exclusion in section 7 | Open |
| Next 2 | The neutron’s four-state model applied out of sample (e.g. the neutron charge radius) | Proposed; the n–p mass difference already fails (63σ) |
| Next 3 | Locate the 1966 Theory of Gravitation, which holds the original graviton derivation | Open |
| Next 4 | Check the scanned-page images for the formulas rebuilt from damaged text, especially 1983g eq. (17) | Open |
| Next 5 | Add the P and Q tests to the test register | Next |
References
- Catalogues for this part:
extract_quarks.mdandextract_particles.md(every quotation with its source address on aetherscience.org). - CODATA 2022 recommended values, NIST SP 961. https://
www. physics. nist. gov/ cuu/ pdf/ wall_ 2022. pdf - Particle Data Group, 2024 summary tables: quarks https://
ccwww. ; mesons https://kek. jp/ pdg/ 2024/ tables/ rpp2024- sum- quarks. pdf ccwww. ; gauge and Higgs bosons https://kek. jp/ pdg/ 2024/ tables/ rpp2024- sum- mesons. pdf ccwww. kek. jp/ pdg/ 2024/ tables/ rpp2024- sum- gauge- higgs- bosons. pdf - Particle Data Group, 2025 lepton summary (tau mass, neutrino mass differences). https://
ccwww. kek. jp/ pdg/ 2025/ tables/ rpp2025- sum- leptons. pdf - Particle Data Group, neutron listing (2025: mean life 878.4 ± 0.5 s; beam value 887.7 ± 2.2 s), https://
ccwww. ; PDG 2026 summary table, 878.3 ± 0.4 s, https://kek. jp/ pdg/ 2025/ listings/ rpp2025- list- n. pdf pdg. lbl. gov/ 2026/ tables/ rpp2026- sum- baryons. pdf - Particle Data Group, searches for quark and lepton compositeness (2024 review). https://
ccwww. kek. jp/ pdg/ 2024/ reviews/ rpp2024- rev- searches- quark- lep- compositeness. pdf - Particle Data Group, charged heavy lepton searches. https://
ccwww. kek. jp/ pdg/ 2006/ listings/ s025. pdf - Particle Data Group, Quantum Chromodynamics review (running of α_s, used for Λ). https://
pdg. lbl. gov/ 2024/ reviews/ rpp2024- rev- qcd. pdf - Muon g-2 Collaboration, final Fermilab result and new world average a_μ = 116 592 0715(145) × 10⁻¹² (2025). https://
www. alphaxiv. org/ overview/ 2506. 03069 - BESIII Collaboration, "Measurement of the cross section for e⁺e⁻ → hadrons at energies from 2.2324 to 3.6710 GeV" (2022). https://
arxiv. org/ pdf/ 2112. 11728 - CLEO Collaboration, "A measurement of the total cross section for e⁺e⁻ → hadrons at √s = 10.52 GeV" (1998). https://
arxiv. org/ abs/ hep- ex/ 9707018 - "Constraints on parton charge symmetry and implications for neutrino reactions" (2004), on the 5/18 charge-ratio test. https://
arxiv. org/ pdf/ hep- ph/ 0407247 - J. Bailey et al., "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit", Nature 268, 301 (1977). https://
www. nature. com/ articles/ 268301a0. pdf - H. Aspden, "Meson lifetime dilation as a test for special relativity", Lett. Nuovo Cimento (1983) [1983g]. https://
aetherscience. org/ www- aspden- org/ papers/ bib/ 1983g. pdf - Part 1 and Part 1A of this series, and the working paper: https://
aetherscience. ; https://org/ aspden- aether- units/ aetherscience. ; https://org/ aspden- quon- model/ aetherscience. org/ aspden- analysis/