Testing Harold Aspden’s Aether Physics Against Modern Measurements

A living working paper, revised as the analysis continues. Latest revisions (31 October 2026): the abstract now judges Aspden’s theory as one at an early stage of development and credits what it gets right; section 12.1 compares his numbers with QED and the Standard Model; and two companions are now published, Part 2: Quarks, Particles and Predictions and the scorecard Aspden’s Numbers at a Glance. Downloads: Word · Markdown · analysis scripts. Companion paper: Aspden’s Aether from the Bottom Up, Part 1. Every test, step by step: test register. All of Dr. Aspden’s papers and books are listed in the paper index.

A working record of claims, checks, corrections and extrapolations

By Doug Westmoreland (project lead: direction and review) and Claude, Anthropic (research and analysis) · Working paper, version 2.4, 31 October 2026

Abstract

Harold Aspden (1927–2011) developed an aether theory over five decades that claims to derive the fine-structure constant, Planck’s constant, the proton/electron mass ratio, the constant of gravitation G and several nuclear properties from a lattice of charges filling space. This paper records a systematic examination of that work. Each claim was first evaluated on its own terms, then tested against measurements made since the 1990s, then (where useful) refined or extended on the assumption that the foundation has some merit. Finally, the chance that a framework of this kind would produce its reported agreements by coincidence was estimated by counting how many formulas built from the same ingredients land as close to the measured values.

The main findings, revised in version 2.3 to judge the theory as one at an early stage of development, are:

Many significant digits in critical areas. From one lattice and a few integers, Aspden’s formulas reach seven significant digits for the fine-structure constant and the proton/electron mass ratio. The Standard Model takes both numbers from measurement and does not attempt to derive them. His formulas reach six to eight digits for the muon/electron mass ratio, the deuteron moment and the proton and neutron magnetic moments. His proton/electron ratio (1975) and muon ratio (1983) were closer to today’s values than the measurements of their day. His neutron moment, −44/23 (1986), is still within 1.6σ of today’s value.
Strongest where mainstream calculation is hardest. Section 12.1 scores his numbers side by side with QED and the Standard Model. For the seven quantities set mainly by the strong force, his numbers are nearer the measured values than today’s lattice-QCD calculations in all seven, with more digits right in six. Where the electromagnetic and weak forces do the work, QED and the Standard Model are decisively better.
A theory at an early stage of development. Aspden worked for five decades, but largely alone, and his theory never had the refinement a research community gives a mainstream theory. QED’s prediction of the electron’s magnetic moment began in 1948 as Schwinger’s one-term formula, right to about three digits. It reached ten digits through seventy years of calculation by many physicists. Aspden’s formulas should be read the same way, as leading-order results whose corrections have not been worked out.
Not yet exact, and partly tuned. As published, 44 of the 48 numbers scored miss today’s measurements by more than twice their uncertainty. That alone does not rule a theory out. Bohr’s formula for the hydrogen atom misses its ionization energy by millions of standard deviations, yet it was a real step. Scored by the same standard, the Standard Model’s own predictions are within 2σ for 2 of 17. But about 40% of Aspden’s digits came from selections and revisions made with the measurement of the day in view, and a few from numbers that already encode the answer. Of the 27 numbers he compared with data, 20 sit nearer the value he used than today’s. Allowing for the formulas he could have tried, the odds of matching α, mp/mₑ, the deuteron moment and G all this closely by chance are about 1 in 2,000 under central assumptions (range 1 in 30 to 1 in 430,000). That is suggestive, not decisive. The results with the most digits beyond chance are 1/α and mp/mₑ, which involve no late tuning, and the neutron’s 44/23, which rests on a model that fails elsewhere.
Sound workmanship. His arithmetic and lattice calculations are generally sound. Several unexplained steps follow from his own rules, including the 1.875 cluster and the finite-size term in his α derivation, which is exact for a quon that excludes the background.
Parts excluded on physical grounds, not on precision. These need rethinking rather than refining:

His aether-drag and anti-expansion claims, his claim that the constants shift in steps with energy or temperature, and his 1969 aether account of Mercury’s perihelion are excluded by modern experiments and observations, mostly by factors of hundreds to thousands.
His own frame for light, carried with the Earth but not turning with it, is excluded by rotating-cavity experiments by a factor of about 1,500.
His lattice cannot carry light. Treated with Coulomb’s and Maxwell’s laws it is a plasma whose frequency is exactly the electron’s Compton frequency, and his orbit is its natural oscillation. The same plasma would block all light below 511 keV, equivalent to giving the photon the electron’s mass, 5 × 10²³ times the measured limit (section 15).
His Rydberg-constant argument against time dilation (1980, 1996) matches Einstein to order (v/c)² but is excluded at order (v/c)⁴ by fast-ion experiments.
His 1983 cavity-electron Lamb-shift formula is 6σ from the 2019 measurement and 20% off for ionised helium. The limited range of gravity he drew from the same papers is excluded by Gaia’s measurement of the solar system’s acceleration toward the galactic centre.

Our corrections, tested out of sample. Replacing his 1.875 cluster with an ejected charge of exactly two electron masses improves his G from 320 ppm to 34 ppm below the recommended value. The same change makes his muon lifetime much worse (+0.1% becomes +68%), so it is not adopted.
The question remains open. No accepted theory derives α, mp/mₑ or G from first principles. A search of every text on the site found no first-principles calculation of the Earth’s surface gravity and no non-relativistic account of hydrogen’s fine structure. The work worth doing next is a correction programme derived from his own lattice and written down before comparing with data, together with predictions registered in advance for measurements now under way: G, the muon/electron mass ratio and the neutron moment.

Companion papers rebuild the aether’s smallest units step by step (Part 1 and its supplement), test his particle numbers and his remarks on quarks (Part 2), and score every number against QED and the Standard Model (the scorecard, Aspden’s Numbers at a Glance); see section 15. The tests in this paper and Part 1 are listed step by step in a separate test register.

Revision history

Version	Date	Changes
1.0	30 Oct 2026	Initial record
1.1	30 Oct 2026	Full program listings and outputs added (Appendix C)
1.2	30 Oct 2026	Improved G cluster of exactly 2 mₑ adopted, with the rationale from Aspden’s own work (section 7.5). The finite-size term in the α derivation is shown to be exact in Aspden’s model, withdrawing the version 1.1 claim that refining it breaks the α agreement (section 5.3). New script `alpha_finite_size.py`
1.3	30 Oct 2026	Probability analysis redone with one consistent null model and the corrections in place, including the joint chance of all four constants at once (section 11). Restored aspden.org bibliography added to sources and next steps
1.4	30 Oct 2026	Proton/electron ratio and Rydberg constant examined, including his claim that constants shift with energy or temperature, tested against white-dwarf, solar and quasar spectra (section 6); his 1983 charge-inequality explanation tested against neutrality limits; α³/2 numerical lead recorded; Mercury’s perihelion objection added (section 9). New script `environment_constants.py`
1.5	30 Oct 2026	Physics without Einstein chapters 4–7, Energy Science Report No. 6 and the 1983 papers 1983c and 1983d read in full from supplied scans. Section 9 expanded: the 1969 aether-sphere account of Mercury’s perihelion (wrong sign; fails for the other planets and the double pulsar), the cavity-resonant electron’s anomalous moments and Lamb shift, the "absolute gravitational potential" at the Earth’s surface, and the search for a first-principles g = 9.8 m/s². Rydberg passage still not found (section 6.3). New scripts `cavity_1983.py` and `mercury_aether.py`
1.6	30 Oct 2026	Cavity-electron formula traced to its three modelling choices and tested against 20 alternatives (section 9.3). Site-wide index of Aspden’s papers and books compiled (532 entries) and prepared for publication on aetherscience.org; new leads for the Rydberg passage listed (section 14). New script `cavity_variants.py`
1.7	30 Oct 2026	Complete copy of the site obtained from the server; paper index rebuilt from it (547 entries, nothing missing). The Rydberg/Einstein passage found ("Atomic Spectra and the Moving Atom", 1996, and Physics Unified, 1980) and tested against fast-ion time-dilation experiments (section 9.6). Searches of all site texts close the g = 9.8 m/s² and fine-structure questions. New script `moving_atom.py`
2.0	30–31 Oct 2026	Section 15 updated for Part 1 v1.4 (objections U37–U40) and its supplement Part 1A: the self-consistent model shows the quon lattice is a plasma that blocks light below 511 keV. Out-of-sample test of the doubled electron (section 7.6). Every use of the 1.875 cluster in the site’s texts was found. Besides G there are two: the 1986j "upsilon" at 6.1 GeV, a particle later shown not to exist, and the 2003 muon lifetime, which gets worse (+0.1% becomes +68%). The 1986 meson papers do not otherwise use the cluster, as section 7.5 had assumed. The improved G is now treated as unsupported in the summary figures (sections 11.3, 11.4, 13 and 14). New script `out_of_sample.py`
2.1	31 Oct 2026	Aspden’s own frame for light is now credited to him in sections 3.1 and 3.3: in Physics Unified (1980, ch. 9) it travels with the Earth but does not turn with it, and in 1983 he named the test himself, saying that a laboratory’s West–East speed of "some 350 m/s at 40oN" showing up in light-speed measurements would refute Einstein. Rotating cavities exclude it by a factor of about 1,500. Section 3.1 points to Part 1A, section 13.5, which works through the c/2 backflow in Tutorial Note 18. Section 15 updated for Part 1 v1.5 (input I1 split; U41, the postulate that the frames move at c relative to each other, cancels out of α) and Part 1A v1.2 (Aspden’s texts on c/2 and on the Earth’s own aether, three figures)
2.4	31 Oct 2026	Byline changed to name Doug Westmoreland as project lead (direction and review), with Claude (Anthropic) for research and analysis, in this paper and its companions. Part 2 and the scorecard published (section 15.3 and 15.4)
2.3	31 Oct 2026	Abstract revised to judge the theory as one at an early stage of development and to credit what it gets right. Version 2.2’s first finding, that every derived constant misses today’s measurements by far more than its uncertainty so the theory as a literal account is ruled out, is withdrawn as worded. Four of the 48 numbers scored are within 2σ. A miss by more than the measurement error shows a formula is not exact, which is also true of leading-order theories such as Bohr’s atom, and the Standard Model fails the same test for 15 of its 17 predictions. The exclusions on physical grounds are kept and grouped as finding 6. The figures in the abstract and section 12.1 that come from the scorecard’s digit audit were checked by an independent reviewer (Opus, extra effort) before publication, and its corrections are applied. For example, the integer 273 is no longer described as encoding the pion mass, and 44/23 is no longer called a single simple choice
2.2	31 Oct 2026	Preliminary statement comparing Aspden with QED and the Standard Model added as section 12.1, with finding (9) in the abstract and a bullet in section 13. It draws on the companion scorecard (Aspden’s Numbers at a Glance, draft 0.4, not yet published), which scores Aspden’s numbers and the mainstream predictions the same way and traces where each prediction’s digits come from. The neutron–proton mass difference in section 12’s table is now set beside Aspden’s value
1.9	30 Oct 2026	Companion paper Aspden’s Aether from the Bottom Up, Part 1: The Smallest Units written (31 tests, U01–U31) and summarised in section 15. Section 5.3 adds the photon unit’s relativistic speeds and magnetic coupling as a fifth assumption that α depends on, and §11.4 adds the resulting caution. A test register listing all 94 tests in both papers is added. Compiling it found errors in this paper, all now corrected: −4,000σ not −3,800σ for α today (§10); NIST-26 −256 ppm (§7.3); −35 ppm for the 1.9993 mₑ row (§7.5); version 1.6’s mixed-unit figure −8.6 ppm (§8); the Lamb-shift correction factors −1.17% (§9.3); the series attribution (§9.3); the 7/4 triplet is not heavy-centred (§7.5, §8); the G history range and the removed claim that it tracked the measurements (§7.2); 5×10⁻¹³ at 300 m/s (§3.1); 9% eccentricity factor (§9.2); 5,700 times (§9.4). Also removed: the claims that the cluster rules were fixed before G was computed and that two independent routes led to 2 mₑ (§7.4). The chance-calculation assumptions are now stated (§11.1). New scripts `aether_units.py` and `lattice_dynamics.py`
1.8	30 Oct 2026	Neutron–proton mass difference recompared in Aspden’s own units: −18.4 ppm (−63σ) today, −0.2σ in 1984; version 1.6’s mixed-unit figure, there given as −8.2 ppm, is −8.6 ppm (section 8). Prepared for publication on aetherscience.org with dated analysis notes on the pages examined. New script `np_mass.py`

1. Purpose and method

The investigation was asked to suspend judgment about Aspden’s conclusions and to look at the evidence as presented, then seek independent evidence from the 1990s to the present. The working rules were:

Read each argument and check its internal logic and arithmetic before comparing it with data.
Compare predictions with modern measurements, stating the size of any disagreement in parts per million (ppm) and in standard deviations (σ).
Where an approximation looked crude, try to improve it and record whether the result got better or worse.
Where a step looked unexplained, look for a justification inside Aspden’s own framework before calling it arbitrary.
Treat speculative extensions as leads, not evidence, and record every variant tried, including failures, so that the number of attempts is visible.
Estimate the probability of chance agreement explicitly rather than by impression.

All numerical work was done in Python scripts summarised in Appendix A and listed in full, with their output, in Appendix C, so every number here can be regenerated.

2. Sources examined

Source	Status
aetherscience.org Tutorial Notes 14–20	Read in full
Tutorial Notes 5–10 and 13	Read from category listing pages (5 and 13 partially)
Tutorial Notes 1–4, 11, 12	Not reachable (site serves a generic page for individual note links)
Physics without Einstein (1969), chapters 4–7 (aetherscience.org scans)	Read in full by OCR from copies supplied 30 October 2026; equations checked against the page images. Other chapters not yet seen
Energy Science Report No. 6, "Power from Space: Inertia and Gravitation"	Read in full (text PDF)
Whole site, from a read-only copy of the server files made on 30 October 2026 (all 678 published posts and pages, the file list of 7,274 files, the books and bibliography folders, and the WordPress export)	Indexed completely: 547 entries, with every post, page and PDF accounted for. The April 2026 WordPress conversion turned the scanned books into readable text pages, so all book chapters were searchable. 98 scanned PDFs (845 pages) were also OCR’d
1983c "The Lamb Shift for a Cavity-Resonant Electron" and 1983d "The Determination of Absolute Gravitational Potential" (Lett. Nuovo Cimento 36, 364 and 37, 169)	Read in full by OCR; equations checked against the page images
aspden.org front page (2007 commentary on Creation: The Physical Truth)	Read; most internal links return 404
1995 "Discovery of Virtual Inertia" note (aetherscience.org papers listing)	Read
Aspden 1981 (Phys. Lett. A 85, 411) and 1982 (Spec. Sci. Tech. 5, 421) mirror-reflection papers	Abstracts and secondary accounts only
Restored aspden.org mirror (aetherscience.org/www-aspden-org/), including the paper bibliography (177 entries, 1951–2002)	Restored 30 October 2026; bibliography read. The 1986e and 1986j pages give abstracts; their full text is in the PDF appendix to Aether Science Papers
Paper pages 1975a, 1983i and 1988b; Aspden Research Paper No. 4 (2005)	Abstracts and commentary read; the 1975 proton formula confirmed
Q&A "The Fifth Question: What is a Neutrino?"	Read: the claim that N falls with energy or thermal activity
Lecture 2 "Why Einstein Was Wrong" and appendix; The Theory of Gravitation (1960); Physics without Einstein centenary review (2005) and chapter 5–6 commentaries	Read for Mercury’s perihelion; no discussion of the Rydberg constant found
Lecture 30 "The Aspden Effect"	Located on the restored site (aetherscience.org/category/lectures/Le30/le30.html); not yet read
Tutorial Notes 1–4, 11, 12	Not yet located on the restored site

3. Light-speed and aether-drag claims

3.1 Tutorial Note 18: Michelson–Morley revisited

Claim. The Earth drags the aether with it, while a counterflowing component keeps the aether’s total momentum at zero. Combining this momentum balance with a refractive-index argument, Aspden obtains a light speed of c relative to the moving Earth, explaining the null result without relativity.

Assessment on its own terms. Michelson–Morley alone does not rule out every aether: Lorentz’s aether, with length contraction built in, predicts the same null result. However, the derivation in Note 18 drops second-order terms, while the Michelson–Morley effect is itself second order, and the refractive index used is a scalar density effect. The step to light moving at "c relative to that moving system" in every direction is asserted by calling the result a vector rather than derived. In effect, the argument assumes the aether moves with the apparatus (Stokes’s complete-drag aether). Part 1A, section 13.5, works through the note step by step: the backflow speed u = c/2, taken from the quons’ orbital speed, is exactly what makes the drag complete in the forward direction, but a density change speeds light equally in every direction, so relative to the Earth light would go at c ahead and c + 2v behind, and the Michelson–Morley signal would be the full ½(v/c)².

Modern test. An aether that moves with the Earth’s centre but does not rotate with it is Aspden’s own picture: in Physics Unified (1980, ch. 9) the Earth’s electromagnetic reference frame "is a non-rotating frame of reference which moves linearly with the space lattice", and ring-laser results require the same (section 3.3). It passes a mid-latitude laboratory at roughly 300 m/s. Aspden named this test himself in 1983: if a laboratory’s West–East speed, "some 350 m/s at 40oN", showed up in light-speed measurements confined to the laboratory, "this would clearly refute Einstein’s theory" (paper 1983b on the site). Without length contraction, a rotating Michelson–Morley apparatus should then show a signal fixed in the laboratory of about ½(v/c)² ≈ 5×10⁻¹³ (4.5×10⁻¹³ at Berlin’s 283 m/s), at twice the rotation rate.

Experiment	Result
Brillet & Hall (1979)	A "spurious" lab-fixed signal of about 2×10⁻¹³ that Aspden interpreted as Earth-rotation anisotropy
Herrmann et al. (2009), rotating optical cavities, Berlin	Lab-fixed signals at twice the rotation rate below 3×10⁻¹⁶; overall anisotropy limit about 1×10⁻¹⁷
Nagel et al. (2015), rotating sapphire microwave resonators	Orientation-dependent frequency change (9.2 ± 10.7)×10⁻¹⁹

The Brillet–Hall anomaly did not reappear when the experiment was repeated with better equipment. The drag model is excluded by more than three orders of magnitude.

3.2 The mirror-reflection objection (1981–1982)

Claim. Light reflecting from a mirror that moves through the aether is deflected, and laser anisotropy experiments are unreliable unless this is included. Aspden argued this explains the Brillet–Hall signal.

Findings.

Michelson and Morley treated reflection from the moving mirror in their 1887 paper, and the second-order treatment was debated again by Hicks and by Morley and Miller around 1902.
Klauber (2004) pointed out that Brillet and Hall measured only frequency, and a change in reflected-ray angle does not change a frequency measured in the apparatus frame.
Using Aspden’s own coefficient (0.262 × ½v²/c²), the predicted signal at Berlin’s latitude is about 1×10⁻¹³, roughly 400 times above the observed limit of 3×10⁻¹⁶.
Sapphire resonators that use no separate mirrors also see nothing at the 10⁻¹⁸ level.

The objection concerns mirrors, not lenses, as had been remembered.

3.3 Extension: a nested-vortex aether

Hypothesis (proposed during this investigation). Rotating matter drags the surrounding aether into a spinning disk: Earth’s inside the Sun’s, the Sun’s inside the galaxy’s, with boundary conditions that might hide simple signals. Aspden’s own version is close to this: "a sphere of aether lattice such as is coextensive with body Earth and rotates with body Earth", inside a larger space domain with its own spin axis (reply to Allyn Shell, Feedback Note 4), while the frame that light travels in moves with the Earth but does not turn (section 3.1; Part 1A, section 1.3).

Findings.

General relativity already predicts that a spinning mass drags local frames. Gravity Probe B measured −37.2 ± 7.2 milliarcseconds per year against a prediction of −39.2, and LARES-2 (2026) measured Earth’s frame dragging to 0.2%. The effect is tiny and fixed by mass and spin, leaving no adjustable boundary conditions.
Two surface measurements rule out the vortex version without needing to know the flow elsewhere. Ring lasers such as Wettzell’s sense Earth’s full rotation to 48 parts per billion, so the surface aether is not co-rotating. Rotating cavities limit aether flow past the Berlin laboratory to about 7 m/s.
By Stokes’s theorem, the rotation ring lasers see across the polar cap north of Berlin requires the aether’s motion relative to the ground around that latitude to average about 280 m/s, roughly 40 times the cavity limit.
The only exit is to give light Lorentz contraction and time dilation relative to the aether. That aether then reproduces every prediction of relativity and becomes undetectable.

3.4 Redshift without expansion (Notes 18 and 10)

Claim (Note 18). Light loses frequency in proportion to distance in a static aether, mimicking cosmic expansion.

Test	Result
Supernova light-curve stretching, Dark Energy Survey (2024), 1,504 type Ia supernovae	Stretch exponent b = 1.003 ± 0.005 (stat) ± 0.010 (sys); a static aether predicts b = 0
CMB temperature at cluster redshifts, Planck SZ data	Deviation parameter β = 0.013 ± 0.011, consistent with expansion
Internal consistency	A frequency that falls with distance at constant speed requires wave crests to disappear in transit; the note’s two-field equations supply no mechanism

Credit: Aspden’s relation between wave energy and frequency implies surface-brightness dimming as (1+z)⁴, the same as expansion, so the classic Tolman test that rules out ordinary "tired light" does not directly refute his version.

Claim (Note 10). Galaxies sit in "space domains" with different lattice integers N, producing Tifft’s quantized redshift steps of about 72 km/s.

Each unit step in N changes α by 90 ppm. ESPRESSO measured Δα/α = 1.3 ± 1.3 (stat) ± 0.4 (sys) ppm toward a quasar absorber at z = 1.15, about 70 times smaller than one step. Note 20 states that distant regions sit at N = 1841, 1839, which would imply shifts of 180 ppm or more. The claim is also internally inconsistent: it says all spectral lines shift in the same proportion, which cannot hold if α changes. Tifft’s periodicity has not been independently confirmed; a 2dF survey test of galaxy–quasar pairs found none.

4. The rotating-magnet "Aspden effect" (1995)

Report. In "Discovery of Virtual Inertia" (New Energy News, February 1995), an 800 g rotor driven at 3,250 rpm held about 15 J of kinetic energy but drew about 300 J of extra energy when started from rest, the surge dying away over about two minutes. After running five minutes or more, a restart within a minute or so needed only about 30 J, in either the same or the opposite direction. Aspden proposed that something ethereal, with about 20 times the rotor’s effective mass density, spins with the rotor and decays over minutes.

Findings.

The effect does not depend on direction, which counts against a spinning-medium interpretation: an aether left spinning one way should help a same-direction restart and resist a reversal.
The extra energy, about 2.5 W over two minutes, is typical of warm-up losses in small motors. Grease redistribution and heating in rolling bearings is a strong conventional candidate that the report does not rule out; bearing housings judged cool by touch cannot exclude a few degrees of internal warming.
The report is in a newsletter, with no description of how energy was measured, no error bars, and no independent replication found.
The closest modern tests, gyroscopes and ring lasers beside rotating rings and superconductors (Tajmar 2006–2011; Graham et al. 2008), found signals later attributed to acoustic noise, or nulls.

5. Planck’s constant and the fine-structure constant

5.1 Aspden’s derivation (Tutorial Notes 7 and 8)

Space is a simple cubic lattice of cells of side d, each holding a "quon" of charge e in a uniform background of opposite charge. Each quon circles in an orbit of radius r at speed c/2.
The quon’s electric potential must be at its smallest non-negative value. Summing the lattice and background potentials, adding the displacement energy 8π(r/d)² (in units of e²/d) and a small correction for the quon’s finite size, fixes r/d.
A 3×3×3 block of quons is a spinning "photon unit" with moment of inertia 36 m₀d². Its energy equals the orbital rate c/2r times its angular momentum; it radiates at four times its spin rate (four-fold symmetry); centripetal force balances the lattice restoring force 4πe²/d³ acting over displacement 2r. Together:

h = 288 π² e² r / (d c)        so        h c / (2π e²) = 144 π (r/d)

The quon-to-electron size ratio cubed, N = [(9/8)(d/r)²]³, counts how many electron-sized charges a quon could transmute into. It must be odd (net unit charge) and must sit at or below the zero-potential value (non-negative energy). This gives:

1/α = h c / (2π e²) = 108 π (8/N)^(1/6),   with N = 1843

5.2 Checks

Step	Finding
Printed force balance	Contains a typo and is not dimensionally consistent. With the evident correction, m₀(c/2r)²·r = (4πe²/d³)(2r), symbolic algebra reproduces h = 288π²e²r/(dc) exactly
Lattice energy	Recomputed exactly for an infinite lattice: Ewald site potential −2.8372974795 plus the whole-cell boundary term π/6 gives −2.3136987 e²/d
Resulting r/d	0.3028737692, matching Aspden’s 1972 computer value (0.302875)
Pure-lattice 1/α	137.016865, 140 ppm below the measured value
Size ratio N	1844.538. His rule (odd, at or below the zero-potential value) selects 1843. The nearest odd integer would have been 1845, so 1843 follows from his rule rather than being picked to fit
Final 1/α	137.0359148 versus the measured 137.035999177(21): −0.615 ppm. Neighbouring odd N values sit 181 ppm away

Because h and e have exact defined values in the SI since 2019, a prediction of ħc/e² is a prediction of 1/α. Aspden’s ħ is therefore 0.6 ppm low.

5.3 The finite-size correction, in detail

The step most sensitive to modelling is a small term for the quon’s finite size. Aspden adds

ΔE = ∫₀ᵇ 4π σ e x dx = 2π σ e b²  =  (d/r)⁴ / 4608π   (in units of e²/d, using d/b = 96π(r/d)²)

Each background shell at radius x (charge 4πx²σ dx) contributes 4πσx dx to the potential at the centre, so the term is exactly e times the potential at the centre of a spherical hole of radius b in the background: a point quon sitting in a void the size of itself. It is only 0.36% of the energy budget, but the integer step magnifies it. Because N ∝ (r/d)⁻⁶, his rule selects 1843 only if the term’s coefficient F (Aspden: F = 1) lies between 0.922 and 1.023, so the term must be right to within −7.8% / +2.3%.

Correction to version 1.1. Version 1.1 reported that averaging the correction over the quon’s own charge distribution reduces it to one-sixth and destroys the α agreement. That calculation spread the quon’s charge through background charge filling the quon’s own volume. Aspden’s model does not allow this: his charges exclude the continuum (the same principle that makes gravitons into voids in his G theory), and his integral already assumes the void. Inside a spherical void the surrounding charge produces a constant potential, so any spherically symmetric quon charge distribution has exactly the energy of a point quon at the centre. The consistent refinement therefore reproduces his term exactly (F = 1), and the α result stands.

Treatment of the quon’s size	F	Pure-lattice 1/α	Odd integer	Final 1/α
Point quon in its own void (Aspden)	1	137.0169	1843	137.0359 (−0.6 ppm)
Spread quon in its own void (consistent refinement)	1 exactly	137.0169	1843	137.0359 (−0.6 ppm)
Spread quon with no void (version 1.1; inconsistent with his model)	1/6	137.2202	1827	137.2352 (+1,454 ppm)
No finite-size term	0	137.2606	1823	137.2853 (+1,819 ppm)
Standard mean-zero potential reference instead of whole cells	1	151.85	995	151.86

The voids in neighbouring cells are a second-order effect. They occupy 0.02% of each cell and could change F by at most about 0.04%, far inside the allowed window.

What α still depends on. Four assumptions carry the result:

Charges exclude the background continuum (the void). His G theory uses the same principle, which counts in its favour as internal consistency.
The potential is measured relative to empty space outside a block of whole cells (the π/6 term). This is physically defensible but essential.
The quon’s energy-radius constant is 1/3, half the electron’s 2/3. This fixes d/b = 96π(r/d)² and is what puts N near 1843 at all.
The odd, round-down integer rule.
The photon unit’s moment of inertia 36m₀d², which treats its 27 quons as slow rigid point masses. At the spin rate Ω/4 the outer quons move at 0.41c and 0.58c. With the speed-dependence of mass that Aspden accepted, the angular momentum rises by about 19% and 1/α becomes about 163. The omitted effects are 10³–10⁵ times larger than the 0.6 ppm gap. His restoring-force coefficient 4πσq, by contrast, is exactly what Maxwell’s equations give for an unbounded lattice (companion paper, tests U20–U31). Treating the lattice as an endless crystal does not remove the problem. Magnetic coupling between the moving quons adds a further 9–29% to the photon unit’s inertia (U29), and the simple cubic lattice itself is electrostatically unstable (U28).

For the lattice alone to give α exactly, with no integer step, F would need to be 0.922; no reason for that value was found.

5.4 Connection to established physics

Aspden’s orbit radius r = ħ/(2mc) is exactly the amplitude of the "zitterbewegung" (trembling motion) that Dirac’s equation predicts for the electron. His orbital speed is c/2, giving half Dirac’s zitterbewegung frequency. The same length is the range of vacuum polarization in quantum electrodynamics. The companion paper (section 15, tests U01–U02) follows this further, and shows why the same scale is fatal to the lattice as a carrier of light (tests U10–U16).

6. The proton/electron mass ratio and the Rydberg constant

6.1 Aspden’s derivation (1975)

Derivation. The lattice charge-volume count gives a "dimuon" energy Q = 944784 π² / 1843^(4/3) = 412.6658 electron masses. A proton P and dimuon Q in contact, as Thomson spheres, have minimum combined energy when Q/P = √(3/2) − 1, so P = Q / (√(3/2) − 1). The formula is confirmed by the abstract of Aspden and Eagles (Il Nuovo Cimento 30A, 235, 1975), which gives M/mₑ = 1836.15232 against the then-measured 1836.15152(70).

Result. P = 1836.152316 versus the measured 1836.152673426: −0.19 ppm. No new adjustable number enters: N = 1843 is already fixed by α. This is the strongest single result in the corpus.

6.2 His explanation of the residual (1983)

In "The Assessment of a Theory for the Proton-Electron Mass Ratio" (Lett. Nuovo Cimento 38, 423, 1983), Aspden attributed the small remaining discrepancy to the proton and electron charges differing in magnitude by 1.07 parts in 10⁷, an effect of the electron displacing aether continuum charge. Matter is far more neutral than that: an acoustic measurement on SF₆ gas (Bressi et al. 2011) finds |q_p + q_e|/e = (−0.1 ± 1.1) × 10⁻²¹. His explanation is excluded by a factor of about 10¹⁴, so the residual remains unexplained in his framework.

6.3 The Rydberg constant

In his framework the Rydberg constant follows from α by the standard relation hcR∞ = (α²/2) mₑc². His α gives a Rydberg energy of 13.6057099 eV against the measured 13.605693122990(15) eV: 1.23 ppm high, about a million times the measurement uncertainty.

The passage where Aspden discusses the Rydberg constant in connection with Einstein’s theory has been found, using the copy of the site supplied on 30 October 2026. It is "Atomic Spectra and the Moving Atom" (Aether Science Papers, 1996, pp. 41–47), with an earlier version in Physics Unified (1980), chapter 3. Its appendix links the same electrodynamic law to the perihelion of the planets. It is examined, and tested against modern experiments, in section 9.6.

Neither version explains the hydrogen fine structure. A search of the text of all 678 posts and pages on the site found no non-relativistic derivation of the fine structure; Modern Aether Science (1972, ch. 7) mentions it only as one of the results that "flow out of the Dirac formalism in an almost miraculous fashion". 1983c uses the Rydberg levels as given to derive the Lamb shift (section 9.3).

The physics that links the two topics is Sommerfeld’s 1916 calculation. Treating the electron’s relativistic mass increase in a Kepler orbit makes the orbit precess, and that precession produces the hydrogen fine structure. The same calculation for Mercury gives πGM☉/(c²p) per orbit, where p is the orbit’s semi-latus rectum, which is one-sixth of the observed relativistic advance: 7.16 of the 42.98 arcseconds per century. General relativity supplies the rest through space curvature. Any argument that the fine structure and Mercury’s perihelion are inconsistent under Einstein’s theory turns on this factor of six. The other "R" beside his Mercury discussion is the R of his equation (5.9), the radius of a planet’s aether region (section 9.2).

6.4 Are these constants temperature sensitive?

In "The Fifth Question: What is a Neutrino?" (Q&A), Aspden states that the lattice integer N falls in integer steps as energy or thermal activity rises in a region of space. Through his formulas every constant then changes in discrete steps:

Quantity	Scaling with N	Change for one step (N 1843 → 1842)
α	N^(1/6)	−90 ppm
mp/mₑ	N^(−4/3)	+724 ppm
Rydberg energy in units of mₑc²	N^(1/3)	−181 ppm
Spectral-line frequencies (his Note 10 scaling)	N^(4/9)	72 km/s apparent velocity
Spectral-line frequencies (his revised radio scaling)	N^(1/9)	18 km/s apparent velocity

Under the odd-integer rule of section 5, the smallest step is two units, doubling every entry. Measurements in hot and distant environments test this directly:

Environment	Quantity	One step predicts	Measured	Disagreement
White dwarf GD133 (H₂ at 11,800 K)	Δμ/μ	+724 ppm	(−27 ± 47) ppm	16σ
White dwarf G29-38 (H₂ at 14,500 K)	Δμ/μ	+724 ppm	(−58 ± 38) ppm	21σ
White dwarf G191-B2B (Fe V lines)	Δα/α	−90 ppm	(42 ± 16) ppm	8σ
White dwarf G191-B2B (Ni V lines)	Δα/α	−90 ppm	(−61 ± 58) ppm	0.5σ
The Sun (5,800 K photosphere), lines after the 633 m/s gravitational redshift	line shift	18,078 m/s (or 72,307 m/s)	residual (5 ± 6) m/s	3,000σ (or 12,000σ)
Absorbing galaxy in front of a quasar, z = 0.89 (methanol, 7.5 billion years ago)	Δμ/μ	+724 ppm	(−0.10 ± 0.13) ppm	5,600σ
Quasar absorber at z = 1.15 (ESPRESSO)	Δα/α	−90 ppm	(1.3 ± 1.4) ppm	68σ

Only the less precise Ni V measurement is compatible with a step. If "energy or thermal activity" includes stellar temperatures, the claim is excluded by the white dwarfs and the Sun; if it means only the aether energy of distant regions, the galaxy absorbers exclude it. Either way the proton/electron ratio and the Rydberg constant do not shift in the steps his theory requires.

6.5 A numerical lead for the proton residual

The remaining −0.19 ppm residual equals α³/2 to within 0.05%. Multiplying his proton mass by (1 + α³/2) gives 1836.152673243 against the measured 1836.152673426(32): 1 part in 10¹⁰, or −5.7σ. Among 60 simple candidate corrections (α to α⁴ times small fractions and powers of π), a match this close has about a 1-in-300 chance. Nothing in his theory motivates an α³/2 term, and it was found by searching for a correction, so it is recorded as an unexplained numerical coincidence to examine, not adopted.

7. The constant of gravitation G

7.1 Aspden’s derivation (Tutorial Notes 6, 8, 9)

Gravity is the electrodynamic attraction between the "holes" that gravitons, moving at c relative to matter, make in the aether’s background charge. A body’s gravitational charge √G·M equals the background charge its gravitons displace. With Thomson-sphere gravitons this gives:

√G = 4π (e/mₑ) g⁻⁴ / (108π)³,      g = graviton mass / electron mass

The graviton mass comes from a chain: lattice → dimuon (412.666) → proton (1836.1523) → taon = two proton–dimuon pairs at minimum energy minus an ejected 1.875 cluster (3484.94) → graviton = taon / x, where 3x⁴ + x³ = 1 (x = 0.688408), giving g = 5062.318 and G = 6.67216 × 10⁻¹¹ m³ kg⁻¹ s⁻².

The whole chain reduces to one closed formula:

g = [ 2(3 + √(3/2)) · 944784 π² / 1843^(4/3) − 15/8 ] / x

7.2 Checks and corrections

Item	Finding
Reproduction	The rebuild reproduces every value in Aspden’s Note 9 table
Note 20 table	Rows printed as g = 5600–5603 should read 5060–5063
The 1.875 cluster	Exactly the energy of three touching electron-sized charges in a +−+ line (3 − 9/8). His charge bookkeeping requires an ejected cluster with net unit charge, so this is the most defensible choice by his own rules
Taons per graviton	Only two works. One, three or four taons give G = 3.50, 8.52 or 9.70
Sensitivity	G goes as g⁻⁸, so one electron mass in the taon shifts G by 2,296 ppm. All modern G measurements lie within about a quarter of an electron mass of each other on this scale
Taon vs tau	His taon (3484.94 mₑ) is not the measured tau lepton (3477.37 mₑ); he treats it as a separate virtual particle, so it has no independent check
History	His published G moved between 6.6676 and 6.686 across his writings (1966: 6.6676; Note 8: 6.668; Note 9: 6.672; Note 20, 1998: 6.686). The measured values of the time are not compared here, so whether these changes followed the measurements is not shown

7.3 Comparison with measurements

Measurement	G (×10⁻¹¹)	Aspden 6.67216	"Doubled electron" variant 6.67408
CODATA 2018/2022	6.67430(15)	−320 ppm (−14σ)	−34 ppm (−1.5σ)
HUST-TOS-18	6.674184(78)	−26σ	−1.4σ
HUST-AAF-18	6.674484(78)	−30σ	−5.2σ
UWash-00	6.674255(92)	−23σ	−1.9σ
UZur-06	6.67425(12)	−17σ	−1.4σ
UCI-14	6.67435(13)	−17σ	−2.1σ
BIPM-14	6.67554(16)	−21σ	−9.2σ
JILA-10 (corrected)	6.67260(25)	−1.8σ	+5.9σ
LENS-14 (atom interferometry)	6.67191(99)	+0.3σ	+2.2σ
NIST-26 (rebuilt BIPM apparatus)	6.67387	−256 ppm	+31 ppm

7.4 Extrapolations tried, assuming the foundation has merit

Variant	Basis	Result
Surface-charge electron (k = 1/2)	Improve the Thomson model	Proton 2361.5, G = 0.47 (fails)
Uniform-ball electron (k = 3/5)	Improve the Thomson model	Proton 1945.3, G = 2.99 (fails)
k tuned to give the proton exactly	k = 0.6666662, within 0.7 ppm of 2/3	G changes by only −4 ppm
Lattice integer set to give α exactly	N = 1842.993	Proton worsens to +4.7 ppm; G = 6.67190
All 22 charge-conserving clusters on his cubic lattice	His rules: touching sites, alternating signs, net charge ±1 (the measured G was known to this analysis throughout)	Only two land among measured values: straight line 1.875 (6.67216) and L-shape 2.0303 (6.67454)
Orientation average of the 15 three-charge arrangements	3 straight + 12 L; his deuteron model also averages states	Cluster 1.9993, G = 6.67406
Equal weight per shape	Alternative averaging	G = 6.67335 (−6σ; fails)
Straight triplet with charges in orbital motion	Reduce attraction by (1 − v²/c²), v = c/2	G = 6.67647 (+14σ; fails)
"Doubled electron"	His dimuon and duon rule: a charge shrunk to half its radius has twice the energy; one unit of charge, exactly 2 mₑ	G = 6.67408
Composite-rule tweak	Factor 3 changed to 2.99962	Would fit, but no mechanism found

Two routes, the orientation average and the doubled electron, give a cluster of about 2 electron masses. Both were found with the measured G known; an earlier working script already printed the cluster each measurement requires (2.0146 mₑ for CODATA). Section 7.5 sets out why Aspden’s own work favours exactly 2 mₑ and adopts it as the improved form of his formula.

7.5 Improved choice: an ejected charge of exactly two electron masses

The published chain subtracts 1.875 mₑ, the rest energy of three touching charges in a +−+ line. Four features of Aspden’s own published work point instead to an ejected charge of exactly 2 mₑ:

The dimuon and duon rule. In Tutorial Notes 9 and 16 the dimuon, the quantity from which both his proton and his graviton are built, is a single charge carrying about the energy of two muons (412.67 mₑ, against 413.54 mₑ for two muons). In Creation: The Physical Truth (2006) the duon is a single charge carrying twice the proton’s mass. Both come from one rule: a charge that contracts to half its radius doubles its energy. Applied to the electron, the same rule gives a single charge with exactly 2 mₑ, the electron member of a family he already uses at the muon and proton scales.
Factor-of-two families from his transmutation rule. Note 17’s energy-conserving pair-creation condition, 2/3a = 2/3b − 1/(b+c) + 2/3c, gives c = 2b when a = b: a particle form can produce a charged form of exactly half its energy at no energy cost. This makes factor-of-two steps (1, 2, 4 … mₑ) the natural family of charge forms in his theory. The 1.875 triplet, by contrast, is a bound composite with no special status.
The deuteron precedent. In his deuteron model (1986; 2006) he averages over configurations with fixed weights, and the interaction energies of his two triplets, 7/4 mₑ (p e⁻ e⁺) and 9/4 mₑ (e⁺ p̄ e⁺), average to exactly 2 mₑ, which he says balances the mass of an added electron–positron pair. Applying the same averaging to the 15 ways three touching charges can sit on his cubic lattice (3 straight, 12 L-shaped) gives 1.9993 mₑ.
Moving particles (supporting). Note 14 describes a fast particle spending part of each cycle compacted, holding all its energy in a contracted form. An electron carrying 2 mₑ is that compacted state at γ = 2, the same object as reason 1.

The 2 mₑ charge also satisfies the charge bookkeeping that justified 1.875: it carries one unit of charge, so a charged taon remains.

Effect on the chain.

Ejected charge	Taon (mₑ)	Graviton g	G (×10⁻¹¹)	Versus CODATA 6.67430(15)
1 mₑ (bare electron)	3485.8156	5063.5894	6.65877	−2,326 ppm
1.875 mₑ (Aspden’s triplet)	3484.9406	5062.3184	6.67216	−320 ppm (−14σ)
2 mₑ (doubled electron, improved)	3484.8156	5062.1368	6.67408	−34 ppm (−1.5σ)
4 mₑ (next family member)	3482.8156	5059.2315	6.70480	+4,570 ppm
1.9993 mₑ (orientation-averaged lattice triplet)	3484.8163	5062.1379	6.674065	−35 ppm (−1.6σ)

With the doubled electron, G lies within about 2σ of the CODATA value and of four of the five most precise experiments (HUST-TOS-18, UWash-00, UZur-06, UCI-14), and 31 ppm above NIST’s 2026 result. Only the 2 mₑ member of the doubling family lands near the measured value. Nothing else in the chain changes: the proton, the composite rule and the taon-versus-tau mismatch are unaffected.

Improved formula.

g = [ 2(3 + √(3/2)) · 944784 π² / 1843^(4/3) − 2 ] / x,     3x⁴ + x³ = 1
√G = 4π (e/mₑ) g⁻⁴ / (108π)³     →     G = 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²

Status and test. This is adopted as the improved form of Aspden’s G formula. It was identified after the measured value was known; section 11 allows for this by including every variant tried in its test family. The decisive test is consistency: wherever Aspden’s other derivations eject or subtract a 1.875 cluster (the 1986 Hadronic Journal particle masses), the same replacement must be made, and those results must improve, or at least not worsen. That test has now been run (section 7.6): the replacement finds no support.

7.6 Out-of-sample test of the doubled electron

The rule. This was written in section 7.5 before the test was run: wherever Aspden uses the 1.875 cluster elsewhere, put 2 in its place, change nothing else, and compare with the measurement he compared with. If the doubled electron reflects something real in his framework, those results should improve, or at least not worsen. Nothing in them was tuned during this investigation.

Where the 1.875 appears. Before any replacement was computed, all 719 texts on aetherscience.org were searched for 1.875 and 15/8: posts, pages, the static archive and the 98 OCR’d scans. Five texts matched. Two use 15/8 as an unrelated series coefficient. The other three use the in-line three-charge factor 3 − ¾ − ¾ + ⅜:

Where	What the 1.875 does	With 1.875 (his)	With 2	Compared with	Result
Tutorial Note 9 (G chain)	Ejected +−+ electron cluster	G = 6.672161 (−320 ppm)	G = 6.674076 (−34 ppm)	CODATA 6.67430(15)	In-sample: 2 was chosen here, so this cannot count
1986j, Hadronic J. 9, 153, p. 154	Three g∗ (3259 MeV) in a line: (g∗:g∗:g∗)	6110.6 MeV	6518.0 MeV	The "upsilon of 6.1 GeV" announced in 1976	No test possible. E288’s 6 GeV peak (Hom et al. 1976) was not confirmed by its own 1977 data and was withdrawn (the "Oops-Leon"); the real upsilon is at 9460.4 MeV
The Physics of Creation (2003), ch. 3	Three muon-derived charges in a line, energy 1.875 × ∛3 = 2.704 muon units; sets his 17:8 ratio	Lifetime 2.19908 μs (+0.095%)	Lifetime 3.69445 μs (+68%)	PDG 2.1969811(22) μs	Worse

The muon lifetime, step by step. The step-by-step rebuild reproduces his own numbers exactly: 17:8, then 2.199 μs.

The triplet’s energy. Three charges sharing a muon’s charge volume each carry ∛3 times the energy. In a line the triplet’s energy is 1.875 × ∛3 = 2.7042 muon units.
The threshold multiple. The first multiple within 1 part in 1,000 of an integer is 17 × 2.7042 = 45.97.
Shed energy. Each triplet formed sheds 3 − 2.7042 = 0.2958.
Raising a triplet to the separated form. Raising one triplet to the separated form, (3 − ¾)∛3 = 3.2451, needs 0.2958 + 0.2451. Two shed quanta cover that ("2(0.2958) exceeds (0.2958 + 0.2451)"). So 17 triplets yield 8 separated forms.
The lifetime. Only separated forms decay, so the chance of decay is 8/25. The lifetime is (25/8)(3/4π)²(108π)⁶ h/mₑc² = 2.199 μs.

With 2 in place of 1.875:

The triplet’s energy is 2.8845.
The threshold multiple is again 17 (17 × 2.8845 = 49.04).
Each triplet sheds only 0.1155.
Raising one triplet now needs four shed quanta, so 17 triplets yield only 4 separated forms.
The lifetime becomes (21/4)/(25/8) times longer: 3.694 μs, 68% above the measured value.

Score. Of the two out-of-sample uses, none improves, one is much worse, and one cannot be tested. Section 7.5 also assumed that the 1986 Hadronic Journal papers eject 1.875 clusters. They do not, apart from the upsilon line above. The 1986e meson paper uses in-line three-charge systems with unequal energies, which the rule does not cover. Extending the rule to them would add a new free choice, so it was not done.

Conclusion. Strictly, the test shows that the doubled electron and Aspden’s other uses of 1.875 cannot both be sound. Either 2 is not a correction to his framework, or the derivations it was tested on are not good physics in the first place; his own description of the muon argument as "somewhat complicated" leaves the second possibility open. Either way, the doubled electron gains no support outside G. It stands as a fit to G alone, to be kept on record and revisited if a sounder derivation that uses the cluster turns up. The summary figures in sections 11.3, 11.4, 13 and 14 now say so. His own 1.875 is not vindicated either: its one testable out-of-sample use, the muon lifetime, works, but at +0.095% it is about 950 times the measurement’s uncertainty from today’s value. Its other use matched a particle that does not exist, which also shows how readily this kind of correlation can be found.

The script is out_of_sample.py (Appendix C.15).

8. The deuteron model (2007 commentary; 1986 Hadronic Journal paper)

Model. The deuteron spends time in three states, each a straight chain of touching Thomson charges:

A: positron, antiproton, positron, antiproton, positron (weight 2)
B: proton, electron, positron, antiproton, with a satellite positron (weight 1; core neutral)
C: proton, electron, proton, with a satellite electron–positron pair (weight 4)

Rebuild. Treating protons as points reproduces his core mass deficits of 11/8, 9/8 and 10/8 electron masses exactly, and his triplet interaction energies of 7/4 (p e⁻ e⁺) and 9/4 (e⁺ p̄ e⁺). The weighted deficit is 71/56.

Version	Magnetic moment (μN)	Versus measured 0.8574382311(48)
Aspden: (6/7)·2 / [2 − (71/56)/1836]	0.8574389	+0.79 ppm
Measured mass ratio in place of 1836	0.8574389	+0.76 ppm
Protons given their own Thomson radius (refinement)	0.8574385	+0.33 ppm

The refinement closes 57% of the gap. Most of the moment comes from the simple fraction 6/7 (itself 344 ppm low); the only non-trivial number in the formula, the weighted deficit, is accurate to 0.22% (0.10% refined), so the ppm-level figure overstates the precision of the physics.

Neutron–proton mass difference (1986d, now read in full from the site copy). The Thomson-charge model gives (mₙ − mₚ)/mₑ = 2.5309419. Aspden converted this with the 1984 electron mass to 1.2933214 MeV. The theory predicts the ratio, so the fair test is against the measured ratio (np_mass.py): it agreed with the 1984 value 2.530948(31) to −2.4 ppm (−0.2σ) and is −18.4 ppm (−63σ) from today’s 2.53098857(74). Version 1.6 compared his MeV figure with today’s MeV value, which mixes units and understated the gap (−8.6 ppm). The step-by-step derivation, which includes an α-dependent subtraction of (3/47)/137, has not yet been checked.

9. Other claims

9.1 Tutorial and lecture claims

Claim	Finding
Muon lifetime (Note 15), simple "virtual muon hit" model	2.251 μs at the real muon mass versus 2.197 μs measured: +2.5%. A more elaborate version in Physics Unified was not available
Electrodynamic force law (Note 13)	Allows a net linear force between charges; no numerical prediction to test
Meson lifetimes 6.25% below relativistic values near γ = 2 (Note 14)	Not yet checked
Graviton at 2.587 GeV (Notes 16, 20)	Treated as a hidden virtual particle; no direct test
Mercury’s perihelion (Lecture 2): Einstein holds the angular-momentum term constant despite relativistic mass increase, and solar oblateness could destroy his result	In general relativity that term is defined per unit proper time, which already includes the mass increase; special relativity alone supplies one-sixth of the advance (about 7 arcseconds per century) and space curvature the rest. MESSENGER ranging measures the Sun’s oblateness as J₂ = (2.4 ± 0.2) × 10⁻⁷, which contributes 0.03 arcseconds per century, 0.07% of the 42.98 arcsecond relativistic term, and pins the relativistic parameters to within 2.5 × 10⁻⁵ of Einstein’s values. Aspden’s own 1960 aether formula gave 44.3 arcseconds per century, and his later retardation argument reproduces Gerber’s 1898 formula, which is identical to Einstein’s. His 1969 account is examined in section 9.2

9.2 Mercury’s perihelion in Physics without Einstein (1969)

Chapter 5 of the book gives a third Aspden account of Mercury, different from his 1960 formula and his later retardation argument.

The mechanism.

Each planet carries a sphere of aether ("space-time lattice") a little larger than the planet.
The lattice moves with the planet, but its centre of mass must stay at rest. It therefore sheds substance that streams backward through it and re-forms behind.
Lattice and stream together carry a net angular momentum of −(2/5)MR²ω about the Sun. M and R are the lattice’s mass and radius, and ω is the planet’s orbital angular velocity.
Conserving the total for planet plus aether gives a perihelion advance per revolution of (8π/5)(M/P)(R/X)², where P is the planet’s mass and X its distance from the Sun.

His fit. He guessed that Mercury’s lattice extends 10% beyond its surface, comparable to the height of the Earth’s ionosphere. He took the anomaly as 38 arcseconds per century after Dicke’s 1967 correction for solar oblateness, and inferred a lattice density of "about 150 g/cc". Chapter 6 derives 144 g/cc independently, from the lattice spacing and his lattice-particle mass of mₑ/24.52, and he presents the match as confirmation.

Checks (mercury_aether.py, Appendix C):

Arithmetic. His inputs give 143.8 g/cc, so the two routes agree even more closely than he said. The agreement rests on two inputs that do not survive. The 10% boundary was a guess, and the density varies as the inverse fifth power of the boundary radius, so a 10% change in the guess moves it by 60%. The 38"/cy relied on Dicke’s oblateness, which helioseismology and MESSENGER have since shown to be about 100 times smaller (J₂ ≈ 2.2–2.4 × 10⁻⁷, worth 0.03"/cy). With today’s 42.98"/cy, the required density is 190 g/cc. Alternatively, to keep 144 g/cc the boundary must sit 16% above the surface.
Sign. Integrating an orbit under his conservation law, (r² − k)dθ/dt = constant with k = (2/5)(M/P)R², moves the perihelion backward, not forward, by about 9% more than his formula gives (an eccentricity factor his formula omits). Net aether angular momentum opposite to the orbit acts like an extra outward force falling as 1/r⁵, and such a force makes orbits regress. To produce an advance, the aether’s net angular momentum must run with the orbit. That sign is the first fix needed if the idea is pursued.

The other planets. With the sign fixed, the same density and the same 10% rule predict:

Planet	General relativity ("/cy)	Aspden mechanism ("/cy)	Ratio	Boundary needed to match
Mercury	42.98	32.65	0.76	1.16 × radius
Venus	8.62	23.32	2.7	0.90 × radius
Earth	3.84	7.91	2.1	0.95 × radius
Mars	1.35	0.72	0.53	1.25 × radius
Jupiter	0.062	12.3	198	0.38 × radius
Saturn	0.014	1.96	144	0.41 × radius

Observed perihelion motions agree with general relativity for all six planets. The EPM2017 ephemerides limit any additional motion to formal uncertainties of 0.003–0.3 milliarcseconds per century for the rocky planets, 0.07 for Saturn and 34 for Jupiter; realistic limits are 10–50 times larger. The aether-sphere mechanism misses Venus by 15 arcseconds per century and Jupiter by 12. Matching each planet separately needs boundaries from 0.38 to 1.25 times the planet’s radius, sometimes below its surface, so no single rule fits.

Structure. General relativity’s advance per orbit depends only on the Sun’s mass and the size of the orbit, 6πGM☉/(c²a(1−e²)), and that is the dependence the planets show. Aspden’s advance depends on the planet’s own size and density and not on the Sun at all. The double pulsar PSR J0737−3039 makes the difference stark. Two neutron stars about 24 km across orbit every 2.5 hours, and the orbit advances by 16.9° a year, as general relativity predicts from their masses. A 144 g/cc aether sphere around a body 10¹² times denser than that contributes about 10⁻¹⁶ degrees a year.

For the nested-vortex idea of section 3.3, the lesson is that whatever aether a body carries cannot add measurably to its orbital angular momentum. Even with generous ephemeris limits, Saturn’s orbit holds any such contribution below about 1% of what Aspden’s mechanism predicts, and the double pulsar shows that relativistic precession scales with the central mass.

9.3 The cavity-resonant electron: anomalous moments and the Lamb shift (1983)

The model. In 1983c, building on his 1977–82 papers, Aspden models the electron as a charge at the centre of a spherical cavity. Radial waves at the Compton frequency run between an inner radius r and an outer radius R ≈ h/2mc. He sets πr² to half the Thomson cross-section, because only magnetic radiation escapes, which gives r = (2/√3)e²/mc². The magnetic anomaly arises because the electron’s spin mass excludes the field energy outside R. The result is a = 1/(2π/α − 1 + 4/√3) for the electron; for the muon the cavity resonates on the inside wall, which flips the sign of the 4/√3 term.

The Lamb shift. For the hydrogen Lamb shift, he argues that field energy flowing through the cavity of an orbiting electron adds angular momentum (2/3)(α/2π)mR²ω. That shifts the azimuthal quantum number of the 2P state by δn₀, which shifts its energy by 2hcR∞δn₀ (his eq. 13). The leading result is (4π/15)α³R∞c, which is 1,071.0 MHz. He then applies:

a factor (1 + 2α/(√3π)) for the exact cavity radius;
a factor 1/(1 + 2α), attributed to "reasons a little beyond the scope of this paper";
the nuclear-mass factor.

With these he obtains 1,057.848 MHz, against the 1981 measurement of 1,057.845(9) MHz.

Checks (cavity_1983.py, Appendix C):

Quantity	Aspden	Measured	Difference
Electron anomaly aₑ, with today’s α	0.0011596462	0.00115965218059(13) (2023)	−5.2 ppm, i.e. −6.0 × 10⁻⁹. QED with α from rubidium atoms: −0.3 × 10⁻¹²
Muon anomaly aμ	0.0011658912	0.001165924(9) (CERN 1979); 0.001165920705(147) (Fermilab 2025)	−3.9σ in 1983, when he called it "exact accord"; −25 ppm, about −200σ, today
Muon minus electron	6.245 × 10⁻⁶	6.269 × 10⁻⁶	−0.4%
Hydrogen 2S₁/₂–2P₁/₂ Lamb shift, today’s constants	1,057.849 MHz	1,057.845(9) (1981); 1,057.8298(32) (2019)	+0.5σ; +6.0σ
He⁺ 2S–2P Lamb shift, same formula scaled as Z⁴	16,700–16,900 MHz	14,041.9(1.5) MHz	+19% to +21%

The series. Expanded in powers of α/π, his electron formula gives 0.5, −0.32735, +0.2143, … against QED’s 0.5, −0.32848, +1.1812, … The second-order coefficient agrees with QED’s to 0.34%, a notable coincidence for a formula from a cavity picture. The third-order coefficient is 5.5 times too small. Term by term against QED, his anomaly differs by +6.09 × 10⁻⁹ at second order, −12.12 × 10⁻⁹ at third and +0.05 × 10⁻⁹ at fourth. So the third-order deficit is twice the net 6 × 10⁻⁹ shortfall, and the small second-order difference adds an error as large as the whole shortfall in the other direction.
The muon. His sign switch reproduces the measured muon–electron difference to 0.4%, although his formula contains no muon mass. In QED that difference comes from muon/electron mass logarithms and hadronic loops. The absolute muon value is far outside today’s errors. The next part shows that the 0.4% follows from the electron fit and is not an independent success.
The Lamb shift. The 1981 agreement came after two correction factors totalling −1.17% (−1.23% with the nuclear-mass factor), one of them explicitly deferred. The 2019 measurement, which agrees with QED and with the proton radius from muonic hydrogen, lies 19 kHz below his value.
Step (13). He takes the energy shift as 2hcR∞δn₀/n₀³ with n₀ = 1, stating without derivation that the energy "includes a term hcR′/n₀²". In the Bohr–Sommerfeld theory he says he is tracing, the energy depends on the azimuthal number only through the principal number n, which gives 2hcR∞δn₀/n³ with n = 2. That is 8 times smaller, 132 MHz.
Helium. He wrote that "much now depends upon the development of this method to explain other transitions". Ionised helium is the most direct such test, and the formula misses it by 20%. QED gets He⁺ right because its main term carries a logarithm, ln(1/(Zα)²), that shrinks as the nuclear charge rises.

Derived or chosen? (cavity_variants.py, Appendix C). His equations (1)–(7) reproduce (8) exactly, so the 4/√3 is derived from three modelling choices:

A half-wavelength standing wave between the two radii. This is forced: a full or quarter wave would move the leading term away from Schwinger’s α/2π.
An inner radius from half the Thomson cross-section, justified by his claim that only the magnetic half of the Larmor radiation is scattered.
The spin-mass form a = mc²/(mc² − E_out) − 1, which supplies the −1.

The table below varies the last two: seven natural inner radii (zero, half the classical radius, the Thomson-sphere radius, a quarter or half or all of the Thomson cross-section, and the classical radius) times three mass forms, 21 variants in all.

Variant	aₑ	aμ (no new freedom)
Half Thomson cross-section, spin-mass form (Aspden)	−5.2 ppm	−25.6 ppm
Thomson-sphere radius, a = E_out/mc²	−33 ppm	−2,324 ppm
Classical radius, spin-mass form	+354 ppm	−386 ppm
Every other variant (18)	354 ppm or more	76 ppm or more

The electron. His choice is the only variant within 30 ppm. The chance that one of 21 such constants lands this close to an arbitrary target is about 1 in 29: a modest coincidence, not a strong one.
The muon is a genuine prediction, and it fails. Once the electron fixes the construction, the muon has no free parameter. The data need a constant of 2.305 for the electron and 2.331 for the muon, a 1.1% asymmetry that a symmetric ± construction cannot give. QED gets that asymmetry from ln(mμ/mₑ).
The difference is not independent. The muon–electron difference depends only on the sum of the two constants, which the electron fit already pins to 0.4%. His alternative muon formula, for a muon "created by charge pair annihilation" (1983d, footnote eq. 4), does worse at −40 ppm.
The second-order coefficient. It agrees with QED’s to 0.34%, but the target, −1.3139 in units of (α/2π)², sits among many simple numbers. Among the 21 variants its counterpart is the same constant judged above, so it is not a separate success either.

9.4 The absolute gravitational potential at the Earth’s surface (1983)

His claim. In 1983d Aspden adds a gravitational term to his g-factor formula:

g/2 = (1 + φ/2c²) · (1 + 1/(2π/α − 1 + 4/√3))

Here φ is the magnitude of the absolute gravitational potential, energy per unit mass, where the electron sits. His reasoning is that the negative gravitational energy sets a threshold for thermal energy. Under equal partition this gives the electron a kinetic energy ½mφ that lies outside its cavity and so changes the g-factor.

Route 1. The 1979 measured g and α give φ = 10.25 × 10¹² cm²/s² (his figure; 10.23 recomputed from his inputs).
Route 2. Setting φm* = kT, with the 2.7 K cosmic background and m* = 0.04 mₑ, gives 10.24 × 10¹² (his figure; 10.23 recomputed). He took m* from the measured light-hole mass in germanium and identified it with his aether lattice particle.
Conclusion. The solar system contributes 9.49 × 10¹² at the Earth’s surface, almost all of it from the Sun. He concluded that the rest of the universe adds only 8% more, and therefore that gravity has a limited range of "a few hundred light years".

Route	φ (10¹² cm²/s²)
1979 g-factor, 1979 α (his inputs)	10.23
2023 g-factor, α from Rb or Cs atom recoil	10.74
2023 g-factor, his own lattice α	9.46
3 K route, T = 2.72548 K, m* = 0.04 mₑ	10.33
3 K route, T = 2.72548 K, his lattice particle mₑ/24.52	10.13
Solar system at the Earth’s surface	9.50

The number is set by α, not gravity. φ/2c² ≈ 6 × 10⁻⁹ is exactly the size of his g-factor formula’s shortfall (section 9.3). The inferred excess over the solar system is 13% with today’s α and 0% with his own lattice α, so φ moves with the α input at the level of one part in 10⁹. In effect, φ measures the error in his formula.
QED leaves no room. QED with α from atom-recoil experiments reproduces aₑ to 3 × 10⁻¹³ with no gravitational term. Any φ term must then be below about 2 × 10⁹ cm²/s². That is about 5,700 times smaller than his value and smaller than the Earth’s own potential at its surface, 6.3 × 10¹¹.
It would vary through the year. His φ includes the Sun’s potential, which varies by ±1.7% over the year as the Earth–Sun distance changes. That would move g/2 by ±8 × 10⁻¹¹, about 600 times the uncertainty of the 2023 measurement. A drift that size would be hard to miss in a result quoted to 0.13 parts per trillion and consistent with the 2008 Harvard value.
The range of gravity. The Sun orbits the galaxy at about 230 km/s, so the galaxy’s potential at the Sun is at least v² = 5.3 × 10¹⁴ cm²/s², 56 times the solar-system value. A range of a few hundred light-years would make the galactic centre’s pull, from 26,000 light-years away, negligible. Gaia measured the solar system’s acceleration directly from quasar proper motions: (2.32 ± 0.16) × 10⁻¹⁰ m/s², pointing toward the galactic centre, matching the 2.1 × 10⁻¹⁰ expected from the Sun’s orbit. Gravity therefore acts with full strength over at least 26,000 light-years.
The 3 K agreement has loosened. The two routes agreed to 0.1% in 1983. With today’s background temperature and either value of m*, they differ by 4–9%.

9.5 Is there a first-principles g = 9.8 m/s²?

None was found. A search of the text of every post and page on the site for 981 cm/s², 9.8 m/s² and 32 ft/s² finds only a passing mention of the value of g in Lecture 16, in a critique of someone else’s theory. The likely source of the recollection is 1983d. Its summary speaks of "the absolute value of φ at the Earth’s surface", and in text versions of the scan the Greek φ is rendered as "g": the OCR in this investigation did exactly that. The paper also concerns the electron g-factor. What it computes, however, is a gravitational potential, not the acceleration, and it uses the measured G, Earth mass and radius for the solar-system part.

The Earth’s surface gravity is g = GM⊕/R⊕², less a latitude-dependent centrifugal term. Satellite tracking measures GM⊕ = 3.986004418 × 10¹⁴ m³/s² to about 2 parts in 10⁹. A theory of G alone therefore changes only the inferred mass of the Earth, not g. Deriving 9.8 m/s² from first principles would need the Earth’s mass and radius from theory, which nothing in the corpus attempts.

9.6 The Rydberg constant and the moving atom (1980, 1996)

This is the passage on the Rydberg constant and Einstein’s theory. It appears twice:

"Atomic Spectra and the Moving Atom", pages 41–47 of the Aether Science Papers commentary (1996). Physics Letters A rejected it in September 1995; Aspden prints the referee’s report with it.
An earlier form in Physics Unified (1980), chapter 3, equation (56).

The 1996 appendix ties the same electrodynamic force law to "the correct form of the law of gravity, even with the planetary perihelion refinements", citing Physics Unified chapter 2. There, retardation of the gravitational energy reproduces Einstein’s orbit equation (section 9.1).

His argument. Atomic clocks in motion are not slowed by time dilation; instead, the Bohr energy levels of a moving atom change. The Rydberg energy is the electrostatic interaction energy less the electron’s kinetic energy, so whatever motion does to those two terms shifts the spectrum.

1980 version: only the kinetic term gains relativistic mass, so R(v)/R(0) = 2 − γ, where γ = 1/√(1 − v²/c²).
1996 version: three effects combine. The electrodynamic force between nucleus and electron offsets the Coulomb force by β² = 1 − v²/c². The electron’s mass rises as 1/β. And the quantised quantity is the "charge velocity moment" vr rather than angular momentum. The energy of the electrodynamic interaction cannot be gathered into the photon in time, so it drops out. Together these give R(v)/R(0) = (2 − β²)β³.

Both factors agree with Einstein’s β to order (v/c)². They first differ at order (v/c)⁴: the 1996 factor is exactly β(1 − v⁴/c⁴). He argued that the experiments of his day could not tell the two apart, and he was right. At the ion speeds then used (v/c ≲ 0.03), the difference is below one part in a million.

Test (moving_atom.py, Appendix C). Fast-ion Ives–Stilwell experiments compare the line seen along the beam with the line seen against it. The product of the two frequencies is unchanged in special relativity. For a clock slowed by a factor F, it changes by (Fγ)² − 1.

Experiment	Ion speed	Measured	Aspden 1980	Aspden 1996
Heidelberg storage ring, Li⁺ (2003, 2007)	0.064 c	0, within ±3.4 × 10⁻¹⁰	−8.4 × 10⁻⁶ (2.5 × 10⁴σ)	−3.4 × 10⁻⁵ (9.8 × 10⁴σ)
GSI storage ring, Li⁺ (Botermann et al. 2014)	0.338 c	(1.5 ± 2.3) × 10⁻⁹	−7.8 × 10⁻³ (3.4 × 10⁶σ)	−2.6 × 10⁻² (1.1 × 10⁷σ)

Both versions are excluded. Two further points:

An aether theory need not fail this test. Lorentz’s own aether electrodynamics gives time dilation exactly. What fails is Aspden’s particular force law applied to the Bohr atom.
No account of fine structure. Neither version addresses the hydrogen fine structure, which special relativity (through Sommerfeld and Dirac) accounts for (section 6.3).

10. Timeline: predictions versus improving measurements

Quantity	Aspden	1973 measured	1986 measured	Today
1/α	137.035915 (1972)	137.03604(11): −1.1σ	137.0359895(61): −12σ	137.035999177(21): about −4,000σ
mp/mₑ	1836.15232 (1975)	1836.15152(70): +1.1σ	1836.152701(37): −10σ	1836.152673426(32): about −11,000σ
G	6.6722	6.6720(41): +0.04σ	6.67259(85): −0.5σ	6.67430(15): −14σ
(mₙ − mₚ)/mₑ	2.5309419 (1986)	n/a	2.530948(31) (1984): −0.2σ	2.53098857(74): −63σ

Each value agreed with the data when published and failed as precision improved, the usual signature of a formula fitted at the precision of its time. In Aspden’s favour, the proton measurement moved toward his value after 1975 rather than away from it.

11. How likely are these agreements by chance?

11.1 Method

The question is whether a toolkit as flexible as Aspden’s would produce agreements this close even if his physics were wrong. For each constant, every formula of the same kind he used was generated, and the expected number landing within his accuracy of the measured value was counted. One null model is applied to every constant: the measured value is unrelated to the toolkit. Two estimates bracket the answer:

Global: the target is placed at random within the range the toolkit’s formulas span. This counts it as part of the hit that the target fell where his formulas are.
Local: uses the density of formulas right at the target. This is more conservative: it takes for granted that the target sits where formulas pile up (for the deuteron, beside the simple fraction 6/7) and asks only about the final digits.

For α, which comes from one formula with an integer, the range comes instead from the number of structural variants he could have chosen (65 to 650). The corrections from sections 5, 7 and 8 are in place: α with his finite-size term (exact in his model), G with the 2 mₑ ejected charge, and the deuteron with protons given their Thomson radius. For G, the test family includes every cluster idea tried during this investigation, so the after-the-fact choice is paid for in the count. The script is coincidence.py (Appendix C).

Two assumptions behind these numbers are worth stating. The α estimate assumes the target could have fallen anywhere within one decade (it divides by ln 10). The four chances are also combined as if independent, although α, the proton ratio and G share the integer 1843 and the same lattice. Both choices are open to challenge, and neither has been varied here.

11.2 Each constant on its own

Constant (corrections in place)	His miss	Test family	Chance of a hit this close
1/α	−0.615 ppm	Odd-integer grid spaced 181 ppm; 65–650 structural variants; 4 rounding rules	1 in 7,200 to 1 in 720
mp/mₑ	−0.19 ppm	464,100 lattice formulas (prefactors 2ⁱ3ʲ, powers of π, powers of 1843 in sixths, 17 Thomson-cluster factors)	1 in 380 (global) to 1 in 180 (local)
Deuteron moment, refined	+0.33 ppm	7,680 combinations of his chain states and weights 1–4	1 in 290 (global) to 1 in 2 (local)
G with 2 mₑ	−34 ppm	116 cluster and chain variants (the non-cluster ideas of section 7.4, such as the k variants, N = 1842.993 and the composite-rule factor, are not included)	1 in 130 (global, at 34 ppm); 1 in 30 (global, allowing for the 150 ppm spread between labs); 1 in 6 (local)

Version 1.2 gave the deuteron "roughly even odds". That used only the local estimate; the consistent treatment shows it can count for much more if the 6/7 fraction is regarded as part of the hit rather than given. The neutron–proton mass difference is left out until its derivation has been checked step by step; it is 18.4 ppm from today’s value, closer than G’s 34 ppm but far looser than its measurement uncertainty (63σ).

11.3 All four at the same time

Three scenarios span the assumptions:

Strict: fewest alternatives and the global estimate throughout.
Central: mid-range variants for α, the local estimate for the proton, the geometric mean of global and local for the deuteron, and G judged against the spread between labs.
Generous: most alternatives, ten target particles tried for the proton, and the local estimate for the deuteron and G.

Scenario	α	Proton	Deuteron	G	All four at once	Combined significance	If he tried 10 constants	If he tried 30
Strict	1.4×10⁻⁴	2.6×10⁻³	3.5×10⁻³	7.5×10⁻³	1 in 100 billion	1 in 34 million	1 in 52 million	1 in 430,000
Central	4.4×10⁻⁴	5.5×10⁻³	4.2×10⁻²	3.3×10⁻²	1 in 300 million	1 in 210,000	1 in 140,000	1 in 1,900
Generous	1.4×10⁻³	5.5×10⁻²	0.50	0.18	1 in 150,000	1 in 410	1 in 250	1 in 31

What the columns mean:

All four at once multiplies the four chances: the chance that one wrong toolkit hits all four this closely, before any allowance for how these four were chosen.
Combined significance (Fisher’s method) is the chance that four unrelated tests give a product that small. It corrects for looking at four results rather than one.
If he tried 10 or 30 constants is the chance that, among that many attempts over his career, at least four come out this well. It corrects for publishing the successes and not the failures, and is computed exactly from the order statistics.

The best single figure is about 1 in 2,000 (central scenario, 30 attempted constants), within a full range of about 1 in 30 to 1 in 430,000. The improved G found no support out of sample (section 7.6). Leaving G out and keeping the other three gives about 1 in 800 on the same central assumptions (1 in 18,000 for 10 attempted constants; out_of_sample.py). Counting only the four results we can see, the central figure is about 1 in 200,000. Version 1.2, using two constants and none of the corrections, gave 1 in 16 to 1 in 1,500 for 30 attempts; the improved G and refined deuteron now add real weight.

11.4 Interpretation

Taken together, the four agreements are harder to dismiss as coincidence than any one of them. Even allowing for a career’s worth of attempts, a toolkit this flexible would match all four this closely about once in two thousand tries under central assumptions. That is suggestive, but the generous end, about 1 in 30, shows it is not decisive: the answer depends on how many alternatives Aspden actually explored, which cannot be recovered from his published work. Three cautions remain:

Two of the four agreements were improved during this investigation. The G change was found after the target was known; the 116-variant test family accounts for the ideas that were written down, but not for any that were not. Its out-of-sample test (section 7.6) found no support, so G is better left out of the joint figure (about 1 in 800 without it).
The timeline in section 10 still looks like fitting at 1970s precision.
The physics behind the α formula is not accurate to anything like its 0.6 ppm agreement. The photon-unit step neglects relativistic speeds and magnetic coupling worth 10–30% (companion paper, U24 and U29). The closeness of α therefore cannot be credited to the precision of the mechanism, which weighs toward coincidence or fitting.
The probabilities concern coincidence only. They cannot distinguish partial truth from skilled fitting, and they do not rescue the theory as published, which every modern measurement excludes.

The clean way forward is an out-of-sample test: apply the 2 mₑ cluster and the proton-radius refinement, unchanged, to the particle masses in his 1986 Hadronic Journal papers, and count how many improve. Those papers are now listed in the restored bibliography (section 14).

12. What mainstream physics derives from first principles

No accepted theory today derives α, mp/mₑ or G from first principles. The Standard Model requires about 25 dimensionless constants that are measured rather than derived, and gravity adds G (equivalently the Planck mass). What current theory does provide is summarised below.

Quantity	Status in mainstream physics
1/α	Input. Its running with energy is computed precisely, and QED relates it to the electron’s magnetic moment at about 0.1 ppb, which is how α is measured. Its low-energy value is not predicted
mp/mₑ	Not predicted. The proton mass comes from QCD: lattice QCD computes hadron masses from three inputs (light and strange quark masses and the coupling); BMW 2008 obtained the nucleon at 0.936(25)(22) GeV versus 0.939 measured. The electron mass is a free Higgs coupling
Proton mass versus Planck mass	Partly explained. The strong coupling’s logarithmic running sets an exponentially small scale (dimensional transmutation), which is why Gmp²/ħc ≈ 5.9×10⁻³⁹. The underlying coupling value is still an input
Neutron–proton mass difference	Computed ab initio from QCD plus QED by BMW (2015) to about 0.3 MeV accuracy, establishing that the neutron is heavier at 5σ, given quark masses and α as inputs. Aspden’s value (section 8) is closer, at 18 ppm, but 63σ off as an exact formula
G	Input. Why gravity is so weak relative to the other forces (the hierarchy problem) is unexplained
Higgs mass	Predicted under assumptions: Shaposhnikov and Wetterich (December 2009) obtained about 126 GeV, within a few GeV, from asymptotic safety of gravity; the 2012 discovery found about 125 GeV
Tau lepton mass	Koide’s empirical 1981 relation, (mₑ + mμ + mτ) = (2/3)(√mₑ + √mμ + √mτ)², predicts 1776.97 MeV versus 1776.93 ± 0.09 measured. No accepted derivation

Attempts to derive α directly have the same character as Aspden’s:

Attempt	1/α	Versus measured
Eddington (1929)	136, later 137	Integer values excluded
Wyler (1969–71): α = (9/8π⁴)(π⁵/2⁴5!)^(1/4), from volumes of symmetric domains	137.0360824	+0.61 ppm
Rosen (1976): α = 4π/(42·41)	137.0324	−26 ppm
Aspden (1972): 108π(8/1843)^(1/6)	137.0359148	−0.62 ppm

Wyler’s group-theory formula and Aspden’s aether lattice miss by the same amount in opposite directions, which illustrates how readily simple formulas reach the ppm level. A historical review (arXiv:1411.4673) concludes that none of these is accepted and that the question remains open. Proposals in string theory point to a large "landscape" of possible vacua in which the constants are not unique, and some physicists argue for anthropic selection; neither yields the measured values.

Aspden was asking a legitimate question that current physics has not answered. Where mainstream physics succeeds, it computes relations among constants, or a constant from a few others, with very high precision; it does not reduce the inputs to zero.

12.1 Aspden and QED compared: a preliminary statement

Preliminary, 31 October 2026. This statement draws on the companion scorecard, Aspden’s Numbers at a Glance (https://aetherscience.org/aspden-scorecard/). The scorecard scores 48 of Aspden’s numbers, and the mainstream predictions for the same quantities, in the same way:

digits right;
standard deviations off, against the measurement’s uncertainty alone, the test an exact formula must pass;
standard deviations off again with the theory’s own uncertainty added.

It also traces each prediction through the stages that built it, to separate digits that come from the physics from digits that come from numbers put in or choices made with the answer in view. An independent check of that last part (Opus, extra effort) has been applied.

Where QED and the Standard Model are clearly better. Where the electromagnetic and weak forces do the work, mainstream theory gets more digits right and lands nearer the measurement every time:

Quantity	Standard Model digits	Aspden digits
Hydrogen Lamb shift	6	5
Electron magnetic anomaly	10	8
Muon magnetic anomaly	7	6
W and Z masses	4	1 to 2

With its own error bars the Standard Model is within 2.3σ on each, while Aspden’s values are 5.7σ to 217σ off. Most of these mainstream digits are calculation, not fitting: for the electron, 8.3 of its 9.5 digits come from QED itself, with α as its measured parameter.

Where Aspden is strongest: the strong force. There are seven quantities set mainly by the strong force:

the proton/electron mass ratio;
the neutron–proton mass difference;
the neutral-pion mass;
the Λ and Ω⁻ masses;
the proton and neutron magnetic moments.

Aspden’s numbers are nearer the measured values than the mainstream values in all seven. They have more digits right in six (4 to 8 digits, against 1 to 3 from lattice QCD), and tie on the Ω⁻. There are two reasons.

The strong force is the part of the Standard Model hardest to calculate. Quarks are bound so tightly that the step-by-step expansion that serves QED so well breaks down. Proton, neutron and meson properties must instead be computed numerically on a space-time grid (lattice QCD), with supercomputers. For most of these quantities its precision is limited by computing power to about 1 to 4 percent, so it claims fewer than 2 digits, and its values are within about 1σ of its own error bars. That leaves room for a compact model to compete, which it cannot do in QED, where the calculation has been carried to five loops and checked to ten digits.
Aspden’s model is a model of compact charge structures. It builds particles from charge spheres in contact, sets their energies by minimising electrostatic energy, and takes its integer counts from the lattice. That is the kind of picture that captures regularities in hadron masses and moments. Two results stand out:
- The proton/electron mass ratio. It follows from lattice constants with no adjustable number, and was nearer today’s value in 1975 than the measurement of that year (section 6).
- The neutron moment, −44/23. It is still within 1.6σ of today’s value after forty years.

What limits that strength.

As exact formulas they still fail. Only the neutron moment is within 2σ today. The upper end of his neutral-pion range is too, but he preferred the lower end.
Many of the strong-force digits are not physics. The scorecard’s stage-by-stage audit finds that many come from factors matched to particles already known, such as 2^(1/4) for the Λ. Others come from late revisions, such as three successive versions of the proton moment, or, for the neutral pion, from an integer search that already encodes the answer.
Only a few results survive the chance test without late tuning.
- The proton/electron ratio keeps 2.3 to 2.6 digits beyond chance.
- The neutron’s 44/23 keeps about 3 digits as a single formula (about 1.5 allowing for the 36 particle numbers tested). But the 46 behind it comes from a four-state model with several free choices, and the same model gives a neutron–proton mass difference 63σ off.
- The other is his fine-structure constant, 2.9 to 3.9 digits beyond chance. α is electromagnetic, but it is a constant the Standard Model takes as an input and does not attempt to derive. His mechanism neglects effects of 10 to 30%, and its assumptions date from 1972, when α was known to about 1 ppm, so the agreement cannot reflect the calculation’s precision.
The comparison may move. Lattice QCD improves every few years, so the gap on the strong-force side may close.

Preliminary verdict. On the electromagnetic and weak side, QED and the Standard Model are decisively better. Aspden’s comparative strength lies on the strong-force side and in constants the Standard Model takes as given (α, mp/mₑ). Those are where further work on his theory should concentrate:

a correction programme derived from his own lattice and written down before comparing with data;
predictions registered in advance for measurements now under way.

13. Assessment: what in the corpus has merit

Sound technique. His lattice electrostatics, Thomson-cluster arithmetic and algebra are generally correct apart from transcription typos.
Comparative strength on the strong force (preliminary). For the seven quantities set mainly by the strong force, his numbers are nearer the measured values than lattice QCD’s in all seven and have more digits right in six. QED and the Standard Model are clearly better wherever the electromagnetic and weak forces do the work (section 12.1).
Proton/electron mass ratio. −0.19 ppm from lattice geometry and the integer 1843, with no new adjustable number; the strongest coincidence result. The remaining residual matches α³/2 to 0.05%, an unexplained numerical lead (section 6.5).
Fine-structure constant. −0.6 ppm, with 1843 selected by his own stated rule. His finite-size term, which the result depends on, is exact for a quon that excludes the background, the same principle his G theory uses.
Improved G. Replacing the 1.875 triplet with a doubled electron (exactly 2 mₑ), a choice supported by four features of his own work, brings G from −320 ppm to −34 ppm (section 7.5). It is a fit, not a confirmed correction: applied out of sample, it makes his muon lifetime worse (section 7.6).
Joint agreement. With the corrections in place, matching α, the proton ratio, the deuteron moment and G all this closely by chance has odds of about 1 in 2,000 under central assumptions, even allowing for a career of attempts (section 11).
Zitterbewegung-sized orbit. His jitter radius equals the amplitude predicted by Dirac’s equation. This is a correspondence rather than evidence: the radius is taken from the electron’s mass (companion paper, U01).
Cavity electron (1983). His one-line anomaly formula follows exactly from a stated cavity model, and among 21 natural variants of that model only his lands within 30 ppm of the electron anomaly (about a 1-in-29 coincidence). The muon, which then has no free parameter, misses by 25 ppm (3.9σ in 1983, about 200σ today). His Lamb-shift formula matched the 1981 measurement only after two late correction factors, and fails the 2019 measurement and ionised helium (section 9.3).
Internal consistency of clusters. The 1.875 cluster and the deuteron deficits come from the same calculation and obey his charge bookkeeping.
Michelson–Morley point. He is right that the null result alone does not disprove every aether, though the version he proposed is excluded.

14. Open items and next steps

Read the papers now reachable through the restored bibliography (https://aetherscience.org/www-aspden-org/papers/bib/refs.htm): 1972a (Phys. Lett. 41A, 423; α), 1975a (Il Nuovo Cimento 30A, 235; the proton mass), 1989b (Physics Essays 2, 173; "The Theory of the Gravitation Constant"), 1986e and 1986j (Hadronic Journal 9, 137 and 153; meson masses, full text in the Aether Science Papers PDF appendix) and 1982e (the mirror paper). Lecture 30 and Tutorial Notes 1–4, 11 and 12 still need locating.
Apply the proton-radius refinement, unchanged, across all of Aspden’s particle-mass derivations; if it improves them, the lead gains weight. The doubled-electron half of this item is done (section 7.6): it found no support.
Check Note 14’s predicted 6.25% meson-lifetime shortfall near γ = 2 against accelerator data.
Check the 1986d neutron–proton derivation step by step (the paper is now readable; the result is compared in section 8).
Extend the chance-coincidence test to the full set of particle masses in the 1986 papers.
Closed in v1.7: the Rydberg/Einstein passage is "Atomic Spectra and the Moving Atom" (1996), with a 1980 version in Physics Unified; both are excluded by fast-ion time-dilation tests (section 9.6). No non-relativistic fine-structure derivation exists in the site’s texts.
Look for any mechanism in his framework that would produce an α³/2 correction to the proton mass (section 6.5), and test whether the same correction improves his other particle masses.
Closed in v1.7: no first-principles g = 9.8 m/s² exists in any of the site’s texts; 1983d computes a potential, not g (section 9.5).
If the 1969 Mercury mechanism is to be pursued, reverse its sign and look for a lattice-boundary rule, tied to density, core or magnetosphere rather than radius, that fits all six planets (section 9.2). The double pulsar would still require a separate mechanism that scales with the central mass.
Closed in v1.6: whether the 4/√3 term and the muon’s sign switch are derived or chosen (section 9.3). They are derived from three stated choices, giving a modest coincidence for the electron and a failed prediction for the muon. The 1977–82 cavity papers remain to be read for any further justification of the half-cross-section radius.
Part 2 of the bottom-up review: test the particle chain built on the units (dimuon, proton, taon, graviton) out of sample, as in item 2.
Compare the visible-light direction dependence that a cubic lattice of Aspden’s spacing implies (about 10⁻¹², four-fold under rotation; companion paper U16) with published rotating-cavity analyses.

15. Companion documents

15.1 Aspden’s Aether from the Bottom Up, Part 1: The Smallest Units (abstract)

Published at https://aetherscience.org/aspden-aether-units/ (Word and Markdown versions in /aspden-analysis-files/).

Aspden’s physics rests on a uniform continuum of charge and a simple cubic lattice of "quons", each carrying the electron’s charge, the two circling each other at the electron’s Compton frequency. Part 1 rebuilds these units from The Physics of Creation (2003, chapter 7), traces them through Physics Unified (1980) and Physics without Einstein (1969), and tests them in 41 numbered steps (U01–U41), including four objections: that no restoring force is needed, that the medium need only flex, that background motion keeps the quons moving, and that the medium is light’s reference frame, carried with the Earth as Aspden proposed (U37–U40). A supplement, Part 1A (https://aetherscience.org/aspden-quon-model/), derives the model behind them step by step, with every assumption labelled as Aspden’s, derived, or a modelling choice.

Internally consistent. The dimensionless chain holds together to 0.6 ppm, the same gap as his α. Its most consequential assumption is that a quon’s inertia is half its Thomson mass, by a buoyancy analogy. With the full mass, 1/α comes out 0.56% low.
Real scales. His orbit radius ħ/2mₑc is the Dirac zitterbewegung amplitude and the range of QED vacuum polarization.
The c/2 postulate. The radius rests on a postulate that the two frames move at c relative to each other, each at c/2, which Aspden calls an assumption from 1960 to 2003. Worked through his own equations, it cancels out of α, N and the lattice spacing, and decides only which odd N is chosen (U41).
Fatal for light. The same scale is fatal to the lattice as a medium for light:
- Aspden’s restoring force on a quon is the field of the displaced lattice itself, as his own derivation says. With Coulomb’s and Maxwell’s laws, the lattice is then a plasma, and his orbit is its plasma oscillation at exactly 511 keV, a credit to his consistency;
- the same plasma blocks all light below 511 keV (radio, visible, X-rays), cancels static fields beyond about 10⁻¹⁰ m, and is equivalent to a photon of electron mass, 5 × 10²³ times the measured upper limit;
- his 1982 picture of a vacuum resonating at the Compton frequency, taken literally with each quon on its own spring, fails too: gamma rays of 662 keV, 847 and 1238 keV and 6 GeV travel normally, and photons from 10 keV to 31 GeV from GRB 090510 arrived together after 7.5 billion years;
- a lattice of spacing 6.37 × 10⁻¹³ m cannot carry waves shorter than about 1 MeV, while photons are seen at 1.4 PeV;
- shrinking the lattice would break the tie to the electron that sets every scale in the theory;
- Aspden’s own frame for light, carried with the Earth but not turning with it, is excluded by rotating cavities through the Earth’s rotation, by a factor of about 1,500; a frame turning with the Earth is excluded by ring lasers (U40).
Smaller results.
- The cell energy he calls a virtual muon pair is 0.21% below two muon masses.
- The aether’s energy density is 2.5 × 10³⁵ times the observed dark energy, a cancellation problem shared with mainstream physics.
- The germanium light-hole mass he cited sits inside a tenfold spread across semiconductors.
Earlier versions reproduce. His 1969 correction (y = 0.000456) and his 2003 constant (k = 8.34) both reproduce from his descriptions.
The 0.6 ppm gap. Every relation among his units is exact, and the only gap is his α, 0.615 ppm low. None of his printed figures is wrong. Closing the gap would need a +0.41 ppm change to the photon-unit relation, right to 1 part in 4,000. The photon-unit step itself leaves out effects 10³–10⁵ times larger, because its outer quons spin at 0.41c and 0.58c. So the agreement cannot reflect the calculation’s precision. One improvement was found: his free 2003 constant k can be calculated from his own description (k = 11.7), leaving α unchanged.
The endless lattice. Treated as an endless crystal, the lattice confirms his orbit exactly, but the simple cubic arrangement is electrostatically unstable (18% of its vibration modes). Magnetic coupling between the photon unit’s moving quons adds 9–29% to its inertia. A wave description of the same 27 quons has the same 0.48c speeds. Only a wave spread over about 7.5 million quons would be slow enough, and then the 36 in his formula for h has to be put in by hand.

15.2 Test register

Every test in this paper (M01, M02, …) and in Part 1 (U01–U41) is listed at https://aetherscience.org/aspden-test-register/ in one format: Aspden’s claim and source, each calculation step with its number, the inputs and their sources, the script output, the verdict, and the assumptions made in this analysis that a reader could challenge. The register ends with a list of discrepancies found while compiling it.

15.3 Aspden’s Aether from the Bottom Up, Part 2: Quarks, Particles and Predictions (summary)

Published at https://aetherscience.org/aspden-particles/ (Word and Markdown versions in /aspden-analysis-files/).

Two reading passes catalogued every particle claim in the 719 texts on the site, and the numbers were tested against PDG and CODATA values (tests P01–P35, Q1–Q9).

Quons and quarks are different things. None of Aspden’s characteristic energies matches a quark mass, and his time-average picture of fractional charge is excluded by deep-inelastic scattering.
Then and now. Of 27 numbers he set against a measurement, 24 agreed within 2σ at the time and 4 do today; 20 of the 27 sit nearer the value he used than today’s.
What holds. The neutron moment −44/23 (1.6σ today), the neutral-pion lifetime, and his 1998 tau mass after two revisions.
Advance predictions failed. A charged lepton at 2.587 GeV, further W- and Z-like states, the 2000 Higgs level list, his in-flight meson lifetimes and massless neutrinos.

15.4 Aspden’s Numbers at a Glance (scorecard)

Published at https://aetherscience.org/aspden-scorecard/ (Word, Markdown and sortable CSV files in /aspden-analysis-files/).

Every number of Aspden’s tested in these papers (48 rows) with its digits right, the digits the measurement pins down then and now, and its standard deviations off. QED and the Standard Model are scored the same way, with their earlier predictions too. A stage-by-stage audit, checked by an independent reviewer, shows where each prediction’s digits come from. Section 12.1 above summarises the result.

Appendix A. Scripts

Full source code and output for each script are in Appendix C.

Script	Contents
`aspden_G.py`	The G derivation as one closed formula; change the cluster energy or lattice integer to recompute
`aspden_G_variants.py`	Charge-model constant k, lattice integer, all lattice clusters, averaging and doubled-electron variants
`deuteron.py`	The three deuteron states from touching Thomson charges, with and without a finite proton radius
`planck.py`	Photon-unit algebra (symbolic), Aspden’s finite lattice sums, exact Ewald value, integer step and sensitivity table
`alpha_finite_size.py`	The finite-size term in the α derivation: Aspden’s term, the no-void and void treatments, the window of allowed coefficients and the second-order void effect
`environment_constants.py`	Proton/electron ratio and Rydberg constant from his formulas, the step changes implied by his energy/temperature claim, tests against white-dwarf, solar and quasar data, the charge-neutrality test, Mercury’s J₂ term and the α³/2 lead
`coincidence.py`	Chance-coincidence tests for α, the proton, the refined deuteron and G with 2 mₑ, and the joint probability of all four (product, Fisher-combined, and career-wide for 10 and 30 attempts)
`cavity_1983.py`	The 1983 cavity-electron papers: electron and muon anomalies against 1979–83 and 2023–25 data, series comparison with QED, the "absolute gravitational potential" by both routes, the galactic and annual-modulation tests, and the Lamb shift for hydrogen and He⁺
`cavity_variants.py`	The cavity-electron formula rebuilt from its stated model; the constants the data require; 21 natural variants ranked; the muon prediction and the footnote alternative
`np_mass.py`	The 1986d neutron–proton mass difference compared in Aspden’s own units with the 1984 and 2022 measurements
`moving_atom.py`	Aspden’s 1980 and 1996 Rydberg factors for a moving atom, their series against time dilation, and their predictions for the fast-ion Ives–Stilwell experiments
`aether_units.py`	Companion paper Part 1: Aspden’s smallest units rebuilt (U01–U26; `lattice_dynamics.py` covers U27–U31): identities among the units, the natural frequency and polarization of the quon lattice, the single-displacement response and its tests (Cs-137, SN 2014J, Alväger 1964, GRB 090510), the lattice cutoff, light holes, the 1969 and 2003 versions, and the 0.6 ppm gap (what a fix needs, the restoring coefficient, the photon unit at relativistic speeds, k from his description)
`lattice_dynamics.py`	Companion paper Part 1, U27–U31: the quon lattice as an endless crystal (Ewald dynamical matrix and stability, magnetic coupling in the spinning photon unit, speeds in a wave picture)
`out_of_sample.py`	Out-of-sample test of the doubled electron: every other use of the 1.875 cluster (the 1986j upsilon, the 2003 muon lifetime) recomputed with 2; effect on the chance calculation
`mercury_aether.py`	The 1969 aether-sphere account of Mercury’s perihelion: lattice density from his inputs and today’s, orbit integration showing the sign, predictions for six planets, the double pulsar, and the special-relativity-only (Sommerfeld) share

Appendix B. Reference values used

Quantity	Value	Source
1/α	137.035999177(21)	CODATA 2022 (PDG 2026)
mp/mₑ	1836.152673426(32)	CODATA 2022 (PDG 2026)
G	6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²	CODATA 2018/2022
Deuteron moment μd/μN	0.8574382311(48)	CODATA 2014
Neutron–proton mass difference	(mₙ − mₚ)/mₑ = 2.53098857(74), i.e. 1.29333251 MeV	CODATA 2022 (mₙ/mₑ − mₚ/mₑ)
Tau lepton mass	1776.93 ± 0.09 MeV	Particle Data Group
Electron anomaly aₑ	0.00115965218059(13)	Fan et al. 2023
Muon anomaly aμ	0.001165920705(147)	Fermilab Muon g−2, final (2025)
1/α from atom recoil	137.035999206(11) (Rb, 2020); 137.035999046(27) (Cs, 2018)	Morel et al.; Parker et al.
Hydrogen 2S₁/₂–2P₁/₂ Lamb shift	1057.8298(32) MHz	Bezginov et al. 2019
He⁺ n = 2 Lamb shift	14041.9(1.5) MHz	van Wijngaarden et al. 1987
Cosmic background temperature	2.72548 K	COBE/FIRAS (Fixsen 2009)
Solar-system acceleration	(2.32 ± 0.16) × 10⁻¹⁰ m/s² toward the galactic centre	Gaia EDR3 (2021)
GM⊕	3.986004418 × 10¹⁴ m³/s²	IERS/WGS 84
Double-pulsar periastron advance	16.90 °/yr	Kramer et al. 2006, 2021
Fast-ion time dilation, ε = ν_aν_p/ν₀² − 1	(1.5 ± 2.3) × 10⁻⁹ at v = 0.338c; α̂ within ±8.4 × 10⁻⁸ at 0.03c and 0.064c	Botermann et al. 2014; Reinhardt et al. 2007

Appendix C. Program listings

The Python scripts behind every number in this paper, with their output, are in the Word version of this paper and as runnable files in analysis-scripts.zip.

References

H. Aspden, Tutorial Notes 1–20, Aether Science. https://aetherscience.org/category/tutorial-notes/
H. Aspden, commentary on Creation: The Physical Truth (2007). https://aspden.org/
H. Aspden, "Laser interferometry experiments on light speed anisotropy," Phys. Lett. A 85, 411 (1981). https://research.ibm.com/publications/laser-interferometry-experiments-on-light-speed-anisotropy
R. D. Klauber, "Analysis of the anomalous Brillet and Hall experimental result," Found. Phys. Lett. (2004). https://ar5iv.labs.arxiv.org/html/gr-qc/0210106
S. Herrmann et al., "Rotating optical cavity experiment testing Lorentz invariance at the 10⁻¹⁷ level," Phys. Rev. D 80, 105011 (2009). https://arxiv.org/pdf/1002.1284
M. Nagel et al., "Direct terrestrial test of Lorentz symmetry in electrodynamics to 10⁻¹⁸," Nat. Commun. 6, 8174 (2015). https://pmc.ncbi.nlm.nih.gov/articles/PMC4569797
A. A. Michelson and E. W. Morley, "On the relative motion of the Earth and the luminiferous ether" (1887). https://gutenberg.org/cache/epub/70888/pg70888-images.html
C. W. F. Everitt et al., "Gravity Probe B: final results," Phys. Rev. Lett. 106, 221101 (2011). https://web3.arxiv.org/pdf/1105.3456
LARES-2 frame-dragging measurement, Nature (2026), as reported. https://thedebrief.org/?p=49788
Wettzell ring laser, Physics World. https://physicsworld.com/a/optical-gyroscope-detects-earths-rotation-with-the-highest-precision-yet/
R. M. T. White et al., "Slow supernovae show cosmological time dilation out to z ∼ 1," MNRAS 533, 3365 (2024). https://lss.fnal.gov/archive/2024/pub/fermilab-pub-24-0293-ppd.pdf
G. Luzzi et al., CMB temperature evolution from Planck SZ data, JCAP 09, 011 (2015). https://iac.es/en/science-and-technology/publications/constraining-evolution-cmb-temperature-sz-measurements-planck-data
L. M. Lubin and A. Sandage, "The Tolman surface brightness test for the reality of the expansion IV" (2001). https://arxiv.org/abs/astro-ph/0106566
M. T. Murphy et al., ESPRESSO limit on α variation, A&A (2022). https://www.aanda.org/articles/aa/full_html/2022/02/aa42257-21/aa42257-21.html
Redshift quantization overview. https://en.wikipedia.org/wiki/Redshift_quantization
Review of rotating-superconductor gravitomagnetic experiments (Tajmar; Graham et al.). https://arxiv.org/pdf/2206.07574
Table of G measurements, arXiv:1905.09551. https://arxiv.org/pdf/1905.09551
Q. Li et al., "Measurements of the gravitational constant using two independent methods," Nature 560, 582 (2018). https://ideas.repec.org/a/nat/nature/v560y2018i7720d10.1038_s41586-018-0431-5.html
NIST redetermination of G, Metrologia 63, 025012 (2026). https://www.nist.gov/news-events/news/2026/04/nist-weighs-mystery-gravitational-constant
Particle Data Group, Physical Constants (2026). https://pdgweb.lbl.gov/2026/reviews/rpp2026-rev-phys-constants.pdf
CODATA 2014 recommended values. https://arxiv.org/pdf/1507.07956
CODATA 1973 recommended values. https://wiki.potsdam.edu/wikichem/index.php/CODATA_Recommended_Values_of_the_Fundamental_Physical_Constants/1973
1986 CODATA values. https://s20.xray.aps.anl.gov/Physical_constants_1986.html
S. Dürr et al. (BMW), "Ab initio determination of light hadron masses." https://ar5iv.labs.arxiv.org/html/0906.3599
S. Borsanyi et al. (BMW), "Ab initio calculation of the neutron-proton mass difference," Science 347, 1452 (2015). https://pure.psu.edu/en/publications/ab-initio-calculation-of-the-neutron-proton-mass-difference/
M. Shaposhnikov and C. Wetterich, "Asymptotic safety of gravity and the Higgs boson mass" (2009). https://arxiv.org/abs/0912.0208
Koide relation and the tau mass. https://arxiv.org/pdf/0812.1875
Attempts at a determination of the fine-structure constant from first principles: a brief historical overview, arXiv:1411.4673. https://arxiv.org/pdf/1411.4673
Dimensionless physical constants. https://en.wikipedia.org/wiki/Dimensionless_physical_constant
H. Aspden and D. M. Eagles, "Calculation of the proton mass in a lattice model for the aether," Il Nuovo Cimento 30A, 235 (1975). https://aetherscience.org/www-aspden-org/papers/bib/1975a.htm
H. Aspden, "The assessment of a theory for the proton-electron mass ratio," Lett. Nuovo Cimento 38, 423 (1983). https://aetherscience.org/www-aspden-org/papers/bib/1983i.htm
H. Aspden, "The Fifth Question: What is a Neutrino?" (Energy Science Q&A). https://aetherscience.org/www-energyscience-org-uk-question-es0105/
H. Aspden, Lecture No. 2, "Why Einstein Was Wrong: Part I" (1997), and appendix. https://aetherscience.org/category/lectures/le02.htm and https://aetherscience.org/www-energyscience-org-uk-le-le02app/
J. Bagdonaite et al., "Limits on a gravitational field dependence of the proton–electron mass ratio from H₂ in white dwarf stars," Phys. Rev. Lett. (2014). https://arxiv.org/pdf/1409.1000
J. C. Berengut et al., "Limits on the dependence of the fine-structure constant on gravitational potential from white-dwarf spectra," Phys. Rev. Lett. 111, 010801 (2013). https://arxiv.org/abs/1305.1337
J. Bagdonaite et al., "Robust constraint on a drifting proton-to-electron mass ratio at z = 0.89 from methanol observation at three radio telescopes," Phys. Rev. Lett. 111, 231101 (2013). https://research.chalmers.se/en/publication/188714
G. Bressi et al., "Testing the neutrality of matter by acoustic means in a spherical resonator" (2011). https://arxiv.org/pdf/1102.2766
J. I. González Hernández et al., "The solar gravitational redshift from HARPS-LFC Moon spectra," A&A (2020). https://iac.es/en/science-and-technology/publications/solar-gravitational-redshift-harps-lfc-moon-spectra-test-general-theory-relativity
C. M. Will, "New general relativistic contribution to Mercury’s perihelion advance," Phys. Rev. Lett. 120, 191101 (2018). https://link.aps.org/accepted/10.1103/PhysRevLett.120.191101
H. Aspden, Physics without Einstein (Sabberton, 1969), chapters 4–7. https://aetherscience.org/category/books/Pwech5.pdf (and Pwech4, Pwech6, Pwech7)
H. Aspden, "Power from Space: Inertia and Gravitation," Energy Science Report No. 6. https://aetherscience.org/www-aspden-org/reports/Es6/esr6.pdf
H. Aspden, "The Lamb shift for a cavity-resonant electron," Lett. Nuovo Cimento 36, 364 (1983). https://aetherscience.org/www-aspden-org/papers/bib/1983c.pdf
H. Aspden, "The determination of absolute gravitational potential," Lett. Nuovo Cimento 37, 169 (1983). https://aetherscience.org/www-aspden-org/papers/bib/1983d.pdf
X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse, "Measurement of the electron magnetic moment," Phys. Rev. Lett. 130, 071801 (2023). https://cfp.physics.northwestern.edu/documents/2023MeasurementElectronMangeticMoment.pdf
Muon g−2 Collaboration, final Fermilab result (2025), as reported in CERN Courier. https://cerncourier.com/fermilabs-final-word-on-muon-g-2/
N. Bezginov et al., "A measurement of the atomic hydrogen Lamb shift and the proton charge radius," Science 365, 1007 (2019). https://inspirehep.net/literature/1752910
A. van Wijngaarden et al., "Improved anisotropy measurement of the Lamb shift in He⁺" (1987). https://scholar.uwindsor.ca/physicspub/138/
Gaia Collaboration (S. A. Klioner et al.), "Gaia Early Data Release 3: Acceleration of the solar system from Gaia astrometry," A&A 649, A9 (2021). https://openaccess.inaf.it/handle/20.500.12386/29942
L. Iorio, "Calculation of the uncertainties in the planetary precessions with the recent EPM2017 ephemerides and their use in fundamental physics and beyond" (2019). https://arxiv.org/abs/1810.13415
M. Kramer et al., "Tests of general relativity from timing the double pulsar," Science 314, 97 (2006). https://arxiv.org/abs/astro-ph/0609417
M. Kramer et al., "Strong-field gravity tests with the double pulsar," Phys. Rev. X 11, 041050 (2021). https://arxiv.org/abs/2112.06795
H. Aspden, "Atomic Spectra and the Moving Atom," Aether Science Papers (Sabberton, 1996), pp. 41–47. https://aetherscience.org/www-aspden-org/books/Asp/4147.htm
H. Aspden, Physics Unified (Sabberton, 1980), chapters 2 and 3. https://aetherscience.org/book-physics-unified/
B. Botermann et al., "Test of time dilation using stored Li⁺ ions as clocks at relativistic speed," Phys. Rev. Lett. 113, 120405 (2014). https://arxiv.org/abs/1409.7951
S. Reinhardt et al., "Test of relativistic time dilation with fast optical atomic clocks at different velocities," Nature Physics 3, 861 (2007), as cited in ref. 54.
H. Aspden, "An empirical approach to meson energy correlation," Hadronic J. 9, 153 (1986) (1986j). https://aetherscience.org/book-aether-science-papers/aether-science-paper-1986j/
D. C. Hom et al., "Observation of high-mass dilepton pairs in hadron collisions at 400 GeV," Phys. Rev. Lett. 36, 1236 (1976); its withdrawal: "Oops-Leon", https://en.wikipedia.org/wiki/Oops-Leon
H. Aspden, The Physics of Creation, 2nd ed. (2003), ch. 3, "The Ubiquitous Muon". https://aetherscience.org/2edpocch3/
Particle Data Group, muon mean life τ = 2.1969811(22) × 10⁻⁶ s. https://pdglive.lbl.gov/view/S004T ; Υ(1S) mass 9460.40 MeV (PDG).