# Test Register: Harold Aspden's Aether Physics **Every test in the Aspden analysis, set out step by step so that each can be checked or challenged** By Doug Westmoreland (project lead: direction and review) and Claude, Anthropic (research and analysis) · Version 1.4, 31 October 2026 · Covers *Testing Harold Aspden's Aether Physics Against Modern Measurements* (working paper v2.1) and *Aspden's Aether from the Bottom Up, Part 1: The Smallest Units* (v1.5), whose model is derived step by step in the supplement Part 1A (https://aetherscience.org/aspden-quon-model/) --- ## How to use this register Each test has an identifier: **M** numbers for the working paper (https://aetherscience.org/aspden-analysis/) and **U** numbers for Part 1 (https://aetherscience.org/aspden-aether-units/). Every entry uses the same headings: - **Paper section**: where the test is discussed in full. - **Aspden's claim**: what he says, with the work, year and equation or page. - **What was tested**: one sentence. - **Steps**: each calculation step, with the formula and the number it produced. - **Inputs**: the measured or reference values used, their uncertainties and sources. - **Script and output**: the script that does the calculation and the exact lines it prints. Every script is in https://aetherscience.org/aspden-analysis-files/analysis-scripts.zip and runs on its own with Python 3, so any number here can be regenerated and any input changed. - **Result** and **Verdict**: - *Excluded*: ruled out by measurement, usually by a wide margin. - *Disagrees*: off by more than the measurement allows, but stated by Aspden as approximate or open to adjustment. - *Consistent*: agrees within the uncertainty that applies. - *Credited*: Aspden's step is sound or can be justified from his own rules. - *Open*: cannot yet be decided. - **Assumptions you could challenge**: the choices made in this analysis, not by Aspden, that the verdict depends on, such as which measurement was used, which reading of his text, a model choice or a cut-off. Where the effect of changing one is known it is stated; otherwise it is marked untested. To challenge a test, cite its identifier and the step number. The register ends with the discrepancies found while compiling it and what was done about each. ## Summary of all tests | ID | Test | Section | Verdict | Script | |---|---|---|---|---| | M01 | Note 18 drag derivation (internal check) | §3.1 | Disagrees | none | | M02 | Earth-centred aether vs rotating cavities | §3.1 | Excluded | none | | M03 | Mirror-reflection objection | §3.2 | Excluded | none | | M04 | Nested-vortex aether vs ring lasers and cavities | §3.3 | Excluded | none | | M05 | Static-aether redshift vs supernova time dilation and CMB | §3.4 | Excluded | none | | M06 | Crest conservation (internal check of Note 18) | §3.4 | Disagrees | none | | M07 | Tolman surface-brightness test (credit) | §3.4 | Credited | none | | M08 | Note 10 space domains and quantized redshift | §3.4 | Excluded | environment_constants.py | | M09 | Rotating-magnet "Aspden effect" | §4 | Open | none | | M10 | Photon-unit algebra and force balance | §5.1–5.2 | Credited | planck.py | | M11 | Lattice energy and orbit ratio r/d | §5.2 | Credited | planck.py | | M12 | Odd, round-down rule selects N = 1843 | §5.1–5.2 | Credited | planck.py | | M13 | Final 1/α vs measurement | §5.2 | Excluded | planck.py, environment_constants.py | | M14 | Finite-size term as the quon's void potential | §5.3 | Credited | alpha_finite_size.py | | M15 | Window for the finite-size coefficient; other conventions | §5.3 | Credited | alpha_finite_size.py, planck.py | | M16 | Orbit radius equals zitterbewegung amplitude | §5.4 | Credited | none | | M17 | Proton/electron mass ratio | §6.1 | Excluded | aspden_G.py, environment_constants.py, chain.py | | M18 | Charge-inequality explanation of the proton residual | §6.2 | Excluded | environment_constants.py (fixed text) | | M19 | Rydberg energy from his α | §6.3 | Excluded | environment_constants.py | | M20 | Search for a non-relativistic fine-structure account | §6.3 | Disagrees | mercury_aether.py (ratio only) | | M21 | Constants stepping with temperature: white dwarfs and Sun | §6.4 | Excluded | environment_constants.py | | M22 | Constants stepping: distant galaxies | §6.4 | Excluded | environment_constants.py | | M23 | α³/2 lead for the proton residual | §6.5 | Open | environment_constants.py | | M24 | G chain reproduction and Note 20 table | §7.1–7.2 | Credited | aspden_G.py, chain.py, compare.py | | M25 | The 1.875 cluster | §7.2 | Credited | chain.py, aspden_G_variants.py | | M26 | Taons per graviton | §7.2 | Open | none printed (coincidence.py internal) | | M27 | Taon vs tau lepton | §7.2 | Open | aspden_G.py, chain.py | | M28 | History of his published G | §7.2 | Disagrees | compare.py, chain.py | | M29 | Aspden's G vs modern measurements | §7.2–7.3 | Excluded | aspden_G_variants.py, compare.py, chain.py | | M30 | Charge-model k and lattice N varied | §7.4 | Excluded | aspden_G_variants.py | | M31 | All 22 lattice clusters | §7.4 | Open | aspden_G_variants.py | | M32 | Averaging, motion and composite-rule variants | §7.4 | Open | aspden_G_variants.py | | M33 | Justification for a 2 mₑ ejected charge | §7.5 | Open | deuteron.py (one line) | | M34 | Doubled-electron G vs measurements and family | §7.3, §7.5 | Consistent | aspden_G_variants.py, compare.py | | M35 | Deuteron core mass deficits | §8 | Credited | deuteron.py | | M36 | Deuteron magnetic moment | §8 | Excluded | deuteron.py | | M37 | Neutron–proton mass difference | §8 | Excluded | np_mass.py | | M38 | Muon lifetime (Note 15) | §9.1 | Disagrees | none | | M39 | Mercury: Lecture 2 objection to Einstein | §9.1, §6.3 | Disagrees | environment_constants.py, mercury_aether.py | | M40 | 1969 aether-sphere density arithmetic | §9.2 | Credited | mercury_aether.py | | M41 | Sign of the 1969 mechanism | §9.2 | Disagrees | mercury_aether.py | | M42 | 1969 mechanism applied to other planets | §9.2 | Excluded | mercury_aether.py | | M43 | Double pulsar and the structure of the advance | §9.2 | Excluded | mercury_aether.py | | M44 | Electron anomaly from the cavity model | §9.3 | Excluded | cavity_1983.py | | M45 | Muon anomaly and muon–electron difference | §9.3 | Excluded | cavity_1983.py | | M46 | Hydrogen Lamb shift | §9.3 | Excluded | cavity_1983.py | | M47 | Step (13): which quantum number | §9.3 | Disagrees | cavity_1983.py | | M48 | Ionised-helium Lamb shift | §9.3 | Excluded | cavity_1983.py | | M49 | Derived or chosen? 21 cavity variants | §9.3 | Credited | cavity_variants.py | | M50 | Absolute gravitational potential: routes and what sets φ | §9.4 | Disagrees | cavity_1983.py | | M51 | QED bound on a φ term | §9.4 | Excluded | cavity_1983.py | | M52 | Annual variation of φ | §9.4 | Disagrees | cavity_1983.py | | M53 | Limited range of gravity vs Gaia | §9.4 | Excluded | cavity_1983.py | | M54 | The 3 K route today | §9.4 | Disagrees | cavity_1983.py | | M55 | Search for a first-principles g = 9.8 m/s² | §9.5 | Disagrees | none | | M56 | Moving-atom Rydberg factors vs fast-ion time dilation | §9.6 | Excluded | moving_atom.py | | M57 | Timeline against improving measurements | §10 | Excluded | environment_constants.py, np_mass.py | | M58 | Chance of the α agreement | §11 | Open | coincidence.py | | M59 | Chance of the proton agreement | §11 | Open | coincidence.py | | M60 | Chance of the deuteron agreement | §11 | Open | coincidence.py | | M61 | Chance of the G agreement with 2 mₑ | §11 | Open | coincidence.py | | M62 | Joint chance and career correction | §11.3 | Open | coincidence.py | | M63 | Other first-principles α formulas | §12 | Excluded | none | | M64 | Out-of-sample test of the doubled electron | §7.6 | Disagrees | out_of_sample.py | | U01 | Orbit radius = zitterbewegung amplitude and QED vacuum-polarization range | Part 1 §5 | Credited (correspondence; input, not derived) | aether_units.py | | U02 | Orbital frequency = Compton frequency | Part 1 §5 | Consistent | aether_units.py | | U03 | Lattice spacing d = 6.374 × 10⁻¹³ m = 108πa | Part 1 §5 | Consistent | aether_units.py | | U04 | Quon mass from the force balance (7.5) = (7.25) | Part 1 §5 | Credited | aether_units.py | | U05 | Quon radius, Thomson mass, N | Part 1 §5 | Credited (the halved-mass analogy carries the result: f = 1 gives 1/α 0.56% low) | aether_units.py | | U06 | Photon-unit inertia gives 144π(r/d) | Part 1 §5 | Credited (algebra) | aether_units.py | | U07 | Lattice density 143.5 g/cm³ (1969: 144) | Part 1 §5 | Consistent | aether_units.py | | U08 | Cell energy vs two muon masses | Part 1 §5 | Disagrees (−0.21%) | aether_units.py | | U09 | Aether energy density vs dark energy | Part 1 §5 | Open (2.5 × 10³⁵; same kind of problem as mainstream) | aether_units.py | | U10 | Natural frequency = Compton frequency | Part 1 §5 | Consistent (Aspden 1982 agrees) | aether_units.py | | U11 | Static lattice polarization = ε₀E | Part 1 §5 | Withdrawn as a credit (it is complete screening; U36) | aether_units.py | | U12 | Aspden's resonance picture: dispersion below 511 keV, no light above | Part 1 §5 | Prediction (of his 1982 picture) | aether_units.py | | U13 | Gamma rays above 511 keV propagate at c | Part 1 §5 | Excluded (3,105σ for reading A; reading B forbids propagation) | aether_units.py | | U14 | GRB 090510 arrival times; the 1982 tuned-vacuum remedy | Part 1 §5 | Excluded (10¹⁷); remedy open but unsupported | aether_units.py | | U15 | Resonance scale needed to pass GRB 090510 | Part 1 §5 | Excluded as a repair (electron 4 × 10¹³ too heavy) | aether_units.py | | U16 | Lattice cutoff vs 1.4 PeV photons | Part 1 §5 | Excluded (factor 1.4 × 10⁹) | aether_units.py | | U17 | Light holes as evidence for the quon mass | Part 1 §5 | Not supported | aether_units.py | | U18 | 1969 version (y = 0.000456; 1/α = 137.038) | Part 1 §5 | Consistent at printed precision; reproduced | aether_units.py | | U19 | 2003 k term (k = 8.34) | Part 1 §5 | Credited (reproduced, 8.347) | aether_units.py | | U20 | The 0.6 ppm is one number (all unit relations exact with his α) | Part 1 §6 | Credited | aether_units.py | | U21 | His printed figures | Part 1 §6 | Credited (all reproduce) | aether_units.py | | U22 | What a correction must do (0.41 ppm photon unit, 3.69 ppm size ratio, to 1 part in 4,000) | Part 1 §6 | Target defined | aether_units.py | | U23 | Restoring coefficient 4πσq | Part 1 §6 | Credited (Maxwell, unbounded medium) | aether_units.py | | U24 | Photon-unit inertia at spin speeds 0.41–0.58c | Part 1 §6 | Disagrees internally (omitted effects 10³–10⁵ × the gap) | aether_units.py | | U25 | k calculated from his description (11.67) | Part 1 §6 | Credited (improvement; α unchanged) | aether_units.py | | U26 | Small numbers of the right size (α³, 1/N², (α/2π)²) | Part 1 §6 | None closes the gap | aether_units.py | | U27 | The orbit in an endless lattice | Part 1 §7 | Credited (exact; no magnetic field) | lattice_dynamics.py | | U28 | Stability of the endless simple cubic lattice | Part 1 §7 | Disagrees (18% of modes unstable electrostatically; bcc stable) | lattice_dynamics.py | | U29 | Magnetic coupling between the photon unit's moving quons | Part 1 §7 | Disagrees (adds 9–29% to its inertia; 1/α 149–177) | lattice_dynamics.py | | U30 | Speeds in a wave picture of the same 27 quons | Part 1 §7 | Disagrees (0.48c whatever the pattern) | lattice_dynamics.py | | U31 | Spreading the wave over more quons | Part 1 §7 | Open (7.5 million quons needed; the 36 then has to be put in) | lattice_dynamics.py | | U32 | A quon feels only the average field (no local spring) | Part 1 §8 | Credited (Aspden's statement is exact) | quon_model.py | | U33 | The orbit is the plasma oscillation of the two frames | Part 1 §8 | Credited | quon_model.py | | U34 | Light below 511 keV cannot travel | Part 1 §8 | Excluded | quon_model.py | | U35 | The same as a photon of electron mass | Part 1 §8 | Excluded (5 × 10²³ above the limit) | quon_model.py | | U36 | Static charges screened beyond about 10⁻¹⁰ m | Part 1 §8 | Excluded | quon_model.py | | U37 | No restoring force is needed for a plasma (ionosphere example) | Part 1 §8 | Consistent with U34 | quon_model.py | | U38 | The lattice flexing as an elastic solid (shear waves 0.2–0.3c, unstable on cube axes) | Part 1 §8 | Excluded as the carrier of light | quon_model.py | | U39 | Background (CMB) driven motion of the quons | Part 1 §8 | Does not change U34 | quon_model.py | | U40 | Light's reference frame: the background's frame and Aspden's Earth-carried frame | Part 1 §8 | Excluded (about 1,500 in Aspden's frame; 7.6 × 10¹⁰ in the background's) | quon_model.py | | U41 | The postulate that the frames move at c relative to each other | Part 1 §8 | Open (assumed, not derived; cancels out of α, N and d) | quon_model.py | --- ## Part A. Tests in the working paper (M01–M64) ### M01. Note 18 drag derivation (internal check) - **Paper section:** §3.1 - **Aspden's claim:** The Earth drags the aether with it, a counterflowing component keeps the aether's total momentum at zero, and with a refractive-index argument light then moves at c relative to the moving Earth in every direction, so the Michelson–Morley null result needs no relativity. Source: Tutorial Note 18, "Michelson–Morley revisited" (ref. 1, https://aetherscience.org/category/tutorial-notes/); no equation number given. - **What was tested:** Whether the Note 18 derivation actually yields a null result at the order where the Michelson–Morley effect appears. - **Steps:** 1. Order check: the Michelson–Morley effect is second order in v/c, and the Note 18 derivation drops second-order terms. No number. 2. 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 made by calling the result a vector, not derived. No number. 3. Conclusion: the argument assumes the aether moves with the apparatus (Stokes's complete drag). No number. 4. Worked through in Part 1A, section 13.5 (`quon_model.py`, W13). Momentum balance (61) gives a backflow fraction k ≈ 2v/c when the backflow moves at c/2, and (62) gives light a gain of v × c/2|u|, exactly v at |u| = c/2. Because the gain comes from a density change, it is the same in every direction. Relative to the Earth light then goes at c ahead, c + 2v behind and c + v across: at 29.78 km/s, −1.5, +59,559 and +29,777 m/s from c. The Michelson–Morley signal stays ½(v/c)² (4.93 × 10⁻⁹ against 4.93 × 10⁻⁹). - **Inputs:** Earth's orbital speed 29.78 km/s (step 4 only). - **Script and output:** steps 1–3 no script (reasoning in the text); step 4 `quon_model.py`, W13: `Michelson-Morley signal t_along/t_across - 1 with this scalar c1, and (1/2)(v/c)^2 = 4.93278e-9 4.93376e-9` - **Result:** The derivation does not establish a second-order null result. It amounts to assuming complete drag. The c/2 backflow speed is what makes the drag complete in the forward direction; the null result in every direction rests on the asserted "vector" step. - **Verdict:** Disagrees. The terms that carry the effect are dropped and the key step is asserted. - **Assumptions you could challenge:** - The reading of Note 18 (that the "vector" step is asserted, not derived). Part 1A, section 13.5, quotes the note and works through its algebra (added in register v1.4), so this can now be checked against his text. - The paper credits Aspden with one point: Lorentz's aether with contraction also gives a null result, so Michelson–Morley alone does not exclude every aether. ### M02. Earth-centred aether vs rotating-cavity experiments - **Paper section:** §3.1 - **Aspden's claim:** As M01. The Earth's electromagnetic reference frame "is a non-rotating frame of reference which moves linearly with the space lattice" (*Physics Unified* 1980, ch. 9); "Michelson found he could detect the Earth's rotation relative to that non-rotating ether" (Lecture 8). He named this test himself: 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" (1983b). He also read the Brillet & Hall (1979) lab-fixed signal of about 2×10⁻¹³ as Earth-rotation anisotropy (§3.1 table; his 1981 paper, ref. 3). - **What was tested:** Whether an aether that moves with the Earth's centre but does not turn with its rotation is compatible with modern rotating-resonator results. - **Steps:** 1. Model: the aether moves with the Earth's centre but does not co-rotate (co-rotation is excluded separately by ring lasers, M04). A mid-latitude lab then moves through it at "roughly 300 m/s". 2. Expected lab-fixed signal without length contraction, at twice the turntable rate: ½(v/c)² ≈ 4×10⁻¹³ (text). 3. Herrmann et al. 2009: lab-fixed signals at twice the rotation rate below 3×10⁻¹⁶; overall anisotropy about 1×10⁻¹⁷. 4. Nagel et al. 2015: orientation-dependent change (9.2 ± 10.7)×10⁻¹⁹. 5. Ratio 4×10⁻¹³ / 3×10⁻¹⁶: "more than three orders of magnitude" (text). - **Inputs:** - Lab speed about 300 m/s: from Earth's rotation; latitude not stated in §3.1 (Berlin in §3.2–3.3). - Herrmann et al. 2009, < 3×10⁻¹⁶ (ref. 5). - Nagel et al. 2015, (9.2 ± 10.7)×10⁻¹⁹ (ref. 6). - Brillet & Hall 1979, about 2×10⁻¹³: source not stated in the paper (no reference entry). - **Script and output:** no script (hand calculation in the text). - **Result:** Predicted about 4×10⁻¹³ against a limit of 3×10⁻¹⁶, more than 1,000 times too large. No σ given. Register check: ½(v/c)² is 5.0×10⁻¹³ at 300 m/s and 4.5×10⁻¹³ at 283 m/s (Berlin), so the text's 4×10⁻¹³ matches the lower speed; the ratio exceeds 1,000 either way. - **Corrected in v1.9:** the paper now gives ½(v/c)² ≈ 5×10⁻¹³ at 300 m/s (4.5×10⁻¹³ at Berlin's 283 m/s). - **Script check (register v1.4):** `quon_model.py`, W12 lines 5–9: Berlin 282.69 m/s, ½(v/c)² = 4.4458×10⁻¹³, ratio to 3×10⁻¹⁶ = 1481.93; 355.889 m/s at 40°N. - **Corrected in v1.4:** earlier versions of this entry called the non-rotating, Earth-carried aether "the analysis's construction". It is Aspden's own (sources above), so this test addresses his stated model. - **Verdict:** Excluded. The predicted signal is over 1,000 times the Herrmann limit, and the Brillet–Hall anomaly did not recur. - **Assumptions you could challenge:** - The non-rotating, Earth-carried frame is Aspden's own (PU ch. 9; Lecture 8; 1983b). If the aether co-rotated instead, this test would predict nothing and the ring-laser test (M04) applies. - The coefficient ½(v/c)² assumes no length contraction. With full Lorentz contraction the signal is zero (§3.3, last bullet). - Using the lab-fixed limit (3×10⁻¹⁶) rather than the overall 1×10⁻¹⁷; the latter would strengthen the exclusion. ### M03. Mirror-reflection objection (1981–1982) - **Paper section:** §3.2 - **Aspden's claim:** Light reflecting from a mirror that moves through the aether is deflected; laser anisotropy experiments are unreliable unless this is included; this explains the Brillet–Hall signal. Sources: Aspden 1981, *Phys. Lett. A* 85, 411 (ref. 3, https://research.ibm.com/publications/laser-interferometry-experiments-on-light-speed-anisotropy) and 1982, *Spec. Sci. Tech.* 5, 421. §2: abstracts and secondary accounts only. - **What was tested:** Whether the mirror effect, at Aspden's own coefficient, could explain or hide a lab-fixed signal in modern resonators. - **Steps:** 1. History: Michelson and Morley treated reflection from the moving mirror in 1887 (ref. 7); Hicks, and Morley and Miller, debated the second-order treatment around 1902. 2. Klauber (2004, ref. 4): Brillet and Hall measured only frequency, and a change in reflected-ray angle does not change a frequency measured in the apparatus frame. 3. Predicted signal at Berlin's latitude with his coefficient: 0.262 × ½v²/c² ≈ 1×10⁻¹³. 4. Against the 3×10⁻¹⁶ lab-fixed limit: about 400 times too large. 5. Sapphire resonators with no separate mirrors (Nagel 2015) see nothing at the 10⁻¹⁸ level. - **Inputs:** - Coefficient 0.262: Aspden, page or equation not stated; the investigation saw only abstracts and secondary accounts of the 1981–82 papers. - Lab speed at Berlin: as M02. - Herrmann 2009, 3×10⁻¹⁶ (ref. 5); Nagel 2015, (9.2 ± 10.7)×10⁻¹⁹ (ref. 6). - Hicks; Morley and Miller (c. 1902): source not stated in the paper. - **Script and output:** no script (hand calculation in the text). - **Result:** About 1×10⁻¹³ predicted, roughly 400 times the limit. Register check: 0.262 × 4.5×10⁻¹³ = 1.2×10⁻¹³, about 390 times 3×10⁻¹⁶. - **Verdict:** Excluded. At his own coefficient the effect is about 400 times the limit, and resonators without mirrors also see nothing. - **Assumptions you could challenge:** - The 0.262 coefficient comes from a paper read only in abstract or secondary form. Untested. - Same lab-speed model as M02. - Klauber's frequency argument is accepted as stated; the paper does not reproduce it. - The paper notes the objection concerns mirrors, not lenses, correcting a recollection. ### M04. Nested-vortex aether vs frame dragging, ring lasers and cavities - **Paper section:** §3.3 - **Aspden's claim:** None. The hypothesis was proposed during the investigation: rotating matter drags the aether into nested spinning disks (Earth's inside the Sun's inside the galaxy's), with boundary conditions that might hide simple signals. - **What was tested:** Whether any co-rotating or vortex flow of aether at the Earth's surface fits ring-laser and rotating-cavity measurements. - **Steps:** 1. Frame dragging in general relativity: Gravity Probe B −37.2 ± 7.2 mas/yr against −39.2 predicted; LARES-2 (2026) measured Earth's frame dragging to 0.2%. The effect is fixed by mass and spin, with no adjustable boundary conditions. 2. Ring lasers (Wettzell) sense Earth's full rotation to 48 parts per billion, so the surface aether does not co-rotate. 3. Rotating cavities limit aether flow past the Berlin lab to about 7 m/s. 4. Stokes's theorem over the polar cap north of Berlin: the rotation ring lasers see needs aether motion relative to the ground averaging about 280 m/s. 5. 280 / 7 ≈ 40 times the cavity limit. - **Inputs:** - GP-B −37.2 ± 7.2 mas/yr, prediction −39.2 (ref. 8). - LARES-2 0.2% (ref. 9, cited through a news report). - Wettzell 48 ppb (ref. 10). - Cavity limit about 7 m/s: derived from Herrmann 2009 (ref. 5); the derivation is not shown. - **Script and output:** no script (hand calculation in the text). - **Result:** Required flow about 280 m/s against a limit of about 7 m/s, a factor of about 40. Register check: 7 m/s follows from ½(v/c)² = 3×10⁻¹⁶; 280 m/s equals the ground's rotation speed at Berlin's latitude, as Stokes's theorem with the vertical component of rotation requires. - **Verdict:** Excluded. Ring lasers rule out co-rotation, and the cavities rule out the flow that the ring lasers then require. Only an aether with Lorentz contraction and time dilation escapes, and that one is undetectable. - **Assumptions you could challenge:** - The ring-laser signal is read as rotation relative to the local aether. In special relativity it is rotation relative to local inertial frames; the argument needs the aether reading. - The 7 m/s limit uses the ½(v/c)² coefficient with no contraction (as M02). - LARES-2 is cited only through a news site; it is not used in the decisive step. ### M05. Static-aether redshift vs supernova time dilation and CMB temperature - **Paper section:** §3.4 - **Aspden's claim:** Light loses frequency in proportion to distance in a static aether, mimicking cosmic expansion. Source: Tutorial Note 18 (ref. 1). - **What was tested:** Whether two signatures of expansion that a static aether should lack are observed. - **Steps:** 1. Dark Energy Survey (2024), 1,504 type Ia supernovae: light-curve stretch exponent b = 1.003 ± 0.005 (stat) ± 0.010 (sys). Static aether predicts b = 0. 2. Planck SZ clusters: CMB temperature deviation parameter β = 0.013 ± 0.011, consistent with expansion (β = 0). - **Inputs:** DES b (ref. 11); Luzzi et al. 2015 β (ref. 12). - **Script and output:** no script (comparison in the text). - **Result:** b ≈ 1, not 0. The paper gives no σ for either test. - **Verdict:** Excluded. Supernova light curves show time dilation at the expansion value. - **Assumptions you could challenge:** - That his static aether predicts b = 0 (no stretching of light curves). The paper asserts this without quoting Note 18 on it. If his mechanism also slowed arrival rates, the test would change. Untested. - The CMB test needs a static-aether prediction for β, which the paper does not state. As written it shows agreement with expansion, not a measured exclusion of Aspden. ### M06. Crest conservation (internal check of Note 18) - **Paper section:** §3.4 - **Aspden's claim:** As M05 (Note 18). - **What was tested:** Whether a frequency that falls with distance at constant speed is possible in Note 18's static two-field aether. - **Steps:** 1. In a static medium, a frequency that falls with distance at constant speed requires wave crests to disappear in transit. No number. 2. The note's two-field equations were checked for a mechanism that removes crests: none. No number. - **Inputs:** none numerical. - **Script and output:** no script (reasoning in the text). - **Result:** No mechanism for the frequency loss. - **Verdict:** Disagrees. The claim conflicts with crest conservation in a static medium, and his equations do not supply a way out. - **Assumptions you could challenge:** - That the aether is strictly time-independent along the path. A slowly evolving aether would allow a frequency change. Untested. - The note's equations are not reproduced in the paper. ### M07. Tolman surface-brightness test (credit) - **Paper section:** §3.4 - **Aspden's claim:** As M05 (Note 18), together with his relation between wave energy and frequency. - **What was tested:** Whether the Tolman surface-brightness test, which rules out ordinary "tired light", also rules out his version. - **Steps:** 1. His energy–frequency relation implies surface-brightness dimming as (1+z)⁴, the same as expansion (text; derivation not shown). 2. The Tolman test (Lubin & Sandage 2001) therefore does not distinguish his model from expansion. - **Inputs:** Lubin & Sandage 2001 (ref. 13). - **Script and output:** no script. - **Result:** The Tolman test does not directly refute his version. - **Verdict:** Credited. His version avoids the standard objection to tired light. - **Assumptions you could challenge:** - The (1+z)⁴ scaling is asserted, not derived in the paper. Untested. - The credit does not survive M05: the same model fails the supernova time-dilation test. ### M08. Note 10 "space domains" and quantized redshift - **Paper section:** §3.4 (uses the scalings of §6.4; Appendix C.7) - **Aspden's claim:** Galaxies sit in "space domains" with different lattice integers N, producing Tifft's quantized redshift steps of about 72 km/s (Tutorial Note 10). Note 20 states that distant regions sit at N = 1841, 1839 (ref. 1). - **What was tested:** Whether the change of α that a different N implies is allowed by a quasar-absorber measurement, and whether the claim is self-consistent. - **Steps:** 1. From 1/α = 108π(8/N)^(1/6), one unit step 1843 → 1842 changes α by −90.45 ppm. 2. N 1843 → 1841 (Note 20) changes α by −180.9 ppm. 3. ESPRESSO, absorber at z = 1.15: Δα/α = 1.3 ± 1.3 (stat) ± 0.4 (sys) ppm. One step is "about 70 times" larger (text); the script gives 67.5σ with the errors combined. 4. Internal check: Note 10 says all spectral lines shift in the same proportion, which cannot hold if α changes. 5. Tifft's periodicity has not been independently confirmed; a 2dF survey test of galaxy–quasar pairs found none. - **Inputs:** - ESPRESSO Δα/α = 1.3 ± 1.3 (stat) ± 0.4 (sys) ppm (ref. 14). - Tifft periodicity and the 2dF test: only a Wikipedia overview is cited (ref. 15). - **Script and output:** environment_constants.py: - `N 1843 -> 1842: d(alpha)/alpha = -90.45 ppm, d(mu)/mu = 723.9 ppm, d(R)/R = -180.9 ppm, line shift 72.31 km/s (N^4/9) or 18.08 km/s (N^1/9)` - `N 1843 -> 1841: d(alpha)/alpha = -180.9 ppm, d(mu)/mu = 1449.0 ppm, d(R)/R = -361.9 ppm, line shift 144.6 km/s (N^4/9) or 36.17 km/s (N^1/9)` - `Quasar absorber z = 1.15 (ESPRESSO), alpha predicted -90.45 ppm measured 1.3 +/- 1.4 ppm -> 67.5 sigma` - **Result:** One step is −90.45 ppm against a measurement of 1.3 ± 1.4 ppm, a difference of 67.5σ. Note 20's N = 1841 would be −180.9 ppm. - **Verdict:** Excluded. One step of N is about 70 times the measured limit, and the claim contradicts itself on uniform line shifts. - **Assumptions you could challenge:** - That α follows his 1/α formula when N changes from region to region (his formula, applied by the analysis). - That the z = 1.15 absorber sits in a different "space domain". If all absorbers shared our N, this test would not apply. Untested. - The 72 km/s periodicity itself is not tested; the paper relies on its non-confirmation. ### M09. Rotating-magnet "Aspden effect" (1995) - **Paper section:** §4 - **Aspden's claim:** In "Discovery of Virtual Inertia" (*New Energy News*, February 1995), an 800 g rotor at 3,250 rpm held about 15 J but drew about 300 J extra when started from rest, the surge dying over about two minutes. After five minutes or more of running, a restart within a minute or so needed only about 30 J, in either direction. Something ethereal with about 20 times the rotor's effective mass density spins with the rotor and decays over minutes. Link: not given in the paper. - **What was tested:** Whether the report supports a spinning-aether interpretation over conventional explanations. - **Steps:** 1. Extra energy: 300 J over about two minutes ≈ 2.5 W, typical of warm-up losses in small motors. 2. Direction: the low restart energy holds for either direction. An aether left spinning one way should help a same-direction restart and resist a reversal. 3. Conventional candidates (grease redistribution and heating in rolling bearings) are not ruled out by the report; housings judged cool by touch cannot exclude a few degrees of internal warming. 4. The report has no description of how energy was measured, no error bars and no independent replication. 5. The closest modern tests (Tajmar 2006–2011; Graham et al. 2008) found signals later attributed to acoustic noise, or nulls. - **Inputs:** all figures are Aspden's (the 1995 note, as listed in §2); Tajmar and Graham (ref. 16). - **Script and output:** no script (hand calculation in the text). - **Result:** About 2.5 W of extra loss; direction-independent; unreplicated. - **Verdict:** Open. The report cannot be tested quantitatively, and a conventional explanation is not excluded. - **Assumptions you could challenge:** - That direction independence counts against a spinning medium. A medium that decays to a non-rotating excited state could behave differently. Untested. - The Tajmar and Graham experiments are related, not repetitions of this one. ### M10. Photon-unit algebra and force balance - **Paper section:** §5.1–5.2 (Appendix C.4) - **Aspden's claim:** A 3×3×3 block of quons is a spinning photon unit with moment of inertia 36m₀d²; its energy is the orbital rate c/2r times its angular momentum; it radiates at four times its spin rate; centripetal force balances the lattice restoring force 4πe²/d³ acting over 2r. This gives h = 288π²e²r/(dc), so hc/(2πe²) = 144π(r/d). Source: Tutorial Notes 7 and 8 (ref. 1). The printed force balance has a typo. - **What was tested:** Whether the stated steps give his h formula. - **Steps:** 1. Moment of inertia: 12 quons at distance d and 12 at √2·d from the spin axis: I = 36m₀d². 2. E = (c/2r)·I·ω with ω = 2πf/4 (four-fold symmetry); h = E/f. 3. Corrected force balance: m₀(c/2r)²·r = (4πe²/d³)(2r), solved for m₀. 4. Symbolic result: h = 288π²e²r/(cd), and hc/(2πe²) = 144π r/d. - **Inputs:** none numerical (symbolic). - **Script and output:** planck.py: - `h = 288*pi**2*e**2*r/(c*d) => h c/(2 pi e^2) = 144*pi*r/d` - **Result:** Reproduces his h exactly once the force balance is corrected. - **Verdict:** Credited (after the typo correction). - **Assumptions you could challenge:** - The "evident correction" of the printed force balance is the analysis's reading; the printed form is not quoted. Untested. - The four-fold radiation rule and the energy = (c/2r) × angular momentum rule are his and are taken as given. ### M11. Lattice energy and orbit ratio r/d - **Paper section:** §5.2 (Appendix C.4) - **Aspden's claim:** The quon's electric potential must be at its smallest non-negative value. Summing lattice and background potentials, adding the displacement energy 8π(r/d)² and the finite-size term fixes r/d; his 1972 computer value is r/d = 0.302875. Source: Tutorial Notes 7 and 8 (ref. 1), including his QBASIC finite-cube sums. - **What was tested:** Whether an exact infinite-lattice calculation reproduces his r/d. - **Steps:** 1. Ewald potential at a site of a simple cubic lattice in a neutralising background (mean-zero convention): −2.8372974795; two values of the Ewald parameter agree. 2. Add the whole-cell boundary term π/6: M = −2.3136987039 e²/d. 3. Solve 8πx² + x⁻⁴/(4608π) = −M: x = r/d = 0.3028737692. 4. Pure-lattice 1/α = 144πx = 137.016865, about 140 ppm below 137.035999177. 5. Finite-cube rebuild of his method for N = 5, 10, 30, 60, 120 shells converges to the same r/d. - **Inputs:** - Measured 1/α = 137.035999177(21), CODATA 2022 (Appendix B). - His 1972 value 0.302875: source not stated beyond "his 1972 computer value"; §14 lists the 1972 paper (1972a) as not yet read. - His finite-cube r/d values for N = 5, 10, 30 are typed into planck.py: source not stated in the paper. - **Script and output:** planck.py: - `Ewald site potential (mean-zero convention): -2.8372974795 (two eta values agree: -2.8372974795)` - `Infinite cubic aether, his convention: M = -2.3136987039` - `r/d = 0.3028737692 144 pi r/d = 137.016865 quon/electron volume ratio N = 1844.538` - `5 0.3028976690 0.3028877950 137.023210` - `10 0.3028807822 0.3028776183 137.018607` - `30 0.3028746524 0.3028742254 137.017072` - `120 nan 0.3028737985 137.016878` - **Result:** r/d = 0.3028737692 against his 0.302875. Pure-lattice 1/α = 137.016865, about −140 ppm. The rebuilt finite-cube values do not match the values attributed to him (for N = 5: 0.3028877950 rebuilt, 0.3028976690 his), although both series approach the same limit. The paper does not mention this. - **Verdict:** Credited. The exact infinite-lattice value matches his. - **Assumptions you could challenge:** - The whole-cell (π/6) convention. With the mean-zero convention the pure-lattice 1/α becomes 151.85 (M15). - Finite-size coefficient F = 1 (M14). - The finite-cube mismatch suggests his QBASIC subtracted the continuum differently from planck.py's version; this is not resolved. ### M12. The odd, round-down integer rule selects N = 1843 - **Paper section:** §5.1–5.2 (Appendix C.4) - **Aspden's claim:** 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 at or below the zero-potential value (non-negative energy), which gives N = 1843 (Tutorial Notes 7 and 8, ref. 1). - **What was tested:** Whether 1843 follows from his rule or was picked to fit. - **Steps:** 1. N = (9/(8x²))³ with x = 0.3028737692: 1844.538. 2. Largest odd integer at or below 1844.538: 1843. 3. Nearest odd integer: 1845. - **Inputs:** r/d from M11. - **Script and output:** planck.py: - `r/d = 0.3028737692 144 pi r/d = 137.016865 quon/electron volume ratio N = 1844.538` - `his model lattice alpha^-1 = 137.0169 N = 1844.54 -> 1843 alpha^-1 = 137.0359` - **Result:** His rule gives 1843; the nearest odd integer would have been 1845. - **Verdict:** Credited. 1843 follows from his stated rule, not from a choice made to fit. - **Assumptions you could challenge:** - The reading "at or below" (round down). Rounding to the nearest odd integer gives 1845 and 1/α 181.4 ppm low (M13). - Register check: smaller N means larger r/d, which raises the displacement energy, so "below" does correspond to non-negative energy. ### M13. Final 1/α vs measurement - **Paper section:** §5.2 (Appendix C.4, C.7) - **Aspden's claim:** 1/α = hc/(2πe²) = 108π(8/N)^(1/6) with N = 1843 (Tutorial Notes 7 and 8; *Phys. Lett.* 41A, 423, 1972, as cited in the C.7 docstring). - **What was tested:** His 1/α against the CODATA 2022 value. - **Steps:** 1. N = 1843: 1/α = 137.0359148. 2. Against 137.035999177(21): −0.6154 ppm, −4.02×10³σ. 3. Neighbouring odd N: 1841 gives +180.4 ppm, 1845 gives −181.4 ppm; spacing 181 ppm. 4. Because h and e are exact in the SI since 2019, a prediction of ħc/e² is a prediction of 1/α: his ħ is 0.6 ppm low. - **Inputs:** 1/α = 137.035999177(21), CODATA 2022 (Appendix B). - **Script and output:** planck.py and environment_constants.py: - `N=1841: alpha^-1 = 137.0607155 (180.4 ppm)` - `N=1843: alpha^-1 = 137.0359148 (-0.6154 ppm)` - `N=1845: alpha^-1 = 137.0111456 (-181.4 ppm)` - `spacing between neighbouring odd N in alpha^-1: 0.02477 (181 ppm)` - `1/alpha 137.0359148472 measured 137.035999177 -0.6154 ppm (-4.02e+3 sigma)` - **Result:** −0.615 ppm, −4,020σ. Neighbours are 181 ppm away. - **Verdict:** Excluded as an exact prediction (−4,000σ). How unusual the 0.6 ppm closeness is gets assessed in M58. - **Assumptions you could challenge:** - CODATA 2022 as the target. The Rb and Cs atom-recoil values (Appendix B) differ from it by about 1 ppb, which is negligible here. - All of M11–M12 and M14–M15. ### M14. Finite-size term as the potential of the quon's own void - **Paper section:** §5.3 (Appendix C.5) - **Aspden's claim:** Aspden adds ΔE = ∫₀ᵇ 4πσe x dx = 2πσeb² = (d/r)⁴/(4608π) in units of e²/d, using d/b = 96π(r/d)² (Tutorial Notes 7 and 8, ref. 1). - **What was tested:** Whether this term is exact within his model, and whether the version 1.1 claim (averaging over the quon's charge reduces it to one-sixth) holds. - **Steps:** 1. Each background shell at radius x (charge 4πx²σ dx) adds 4πσx dx to the potential at the centre, so the term is e times the potential at the centre of a spherical void of radius b. 2. Point quon in its own void: coefficient 1.0. 3. Spread (Thomson) quon with no void (version 1.1): 0.16666667. 4. Spread quon in its own void: 1.0. Inside a cavity the outside charge gives a constant potential. 5. Voids in neighbouring cells: volume fraction v = 0.0001978 (d/b = 27.6659); if this entered the finite-size term alone, F would change by about 0.000396. - **Inputs:** none measured; d/b = 96π(r/d)² is his relation (from his quon energy-radius constant 1/3). - **Script and output:** alpha_finite_size.py: - `point quon in its void (Aspden) 1.0` - `spread quon, no void (our earlier 1/6) 0.16666667` - `spread quon in its void (consistent) 1.0` - `void volume fraction per cell v = 0.0001978 (d/b = 27.6659); if it entered the finite-size term alone, F would change by about 0.000396` - **Result:** F = 1 exactly in a model where charges exclude the background. Version 1.1's F = 1/6 is withdrawn. Neighbouring voids give about 0.04%. - **Verdict:** Credited. His term is exact for a quon that excludes the background, the same principle his G theory uses. - **Assumptions you could challenge:** - That charges exclude the background continuum. This is the analysis's reading of his integral, supported by his G theory. If the quon overlaps background charge, F = 1/6 and the α result fails (M15). - The bound on neighbouring voids ("at most about 0.04%") rests on an argument in the script's comments (the zero-energy condition keeps its form), which is not computed. The printed number is only the estimate "if it entered the finite-size term alone". - Register check: 2πσeb² with σ = e/d³ and d/b = 96π(r/d)² gives (d/r)⁴/(4608π); the algebra is right. ### M15. How tightly the finite-size coefficient is pinned, and alternative conventions - **Paper section:** §5.3 (Appendix C.4, C.5) - **Aspden's claim:** As M14; F = 1 and the whole-cell potential convention. - **What was tested:** The range of F that still selects N = 1843, and what the result becomes under other treatments of the quon's size and the potential reference. - **Steps:** 1. F scanned from 1/6 to 2. F = 0.9 gives N = 1841; F = 0.95 and 1.0 give 1843; F = 1.05 gives 1845. 2. Window where his rule selects 1843: F from 0.92241 to 1.0233 (−7.76% / +2.33%). 3. No finite-size term (F = 0): pure-lattice 1/α 137.2606, N 1824.97 → 1823, final 1/α 137.2853 (+1,819 ppm). 4. Spread quon with no void (F = 1/6): 137.2202, 1827, 137.2352 (+1,454 ppm). 5. Mean-zero potential instead of whole cells: 151.8546, 995, 151.8628. 6. The term is 0.36% of the energy budget (text). For the lattice alone to give α exactly, F would need to be 0.922 (text). - **Inputs:** 1/α measured, CODATA 2022 (Appendix B). - **Script and output:** alpha_finite_size.py and planck.py: - `F=0.1667 lattice 1/alpha= 137.220233 N= 1828.196 -> 1827 1/alpha=137.235205 (1454.0 ppm)` - `F= 0.9 lattice 1/alpha= 137.041414 N= 1842.556 -> 1841 1/alpha=137.060715 (180.4 ppm)` - `F= 1.0 lattice 1/alpha= 137.016865 N= 1844.538 -> 1843 1/alpha=137.035915 (-0.6154 ppm)` - `F= 1.05 lattice 1/alpha= 137.004576 N= 1845.531 -> 1845 1/alpha=137.011146 (-181.4 ppm)` - `His rule selects 1843 (N in [1843, 1845)) for F from 0.92241 to 1.0233, i.e. the term must be right to within -7.76% / +2.33%` - `no finite-size correction lattice alpha^-1 = 137.2606 N = 1824.97 -> 1823 alpha^-1 = 137.2853` - `Ewald mean-zero potential (no pi/6 term) lattice alpha^-1 = 151.8546 N = 995.32 -> 995 alpha^-1 = 151.8628` - **Result:** F must lie within −7.8% / +2.3% of 1; F = 1 is inside. Dropping the term, spreading the quon without a void, or changing the potential reference each breaks the agreement. - **Verdict:** Credited. His F = 1 lies inside the window and is the consistent value in his model. The α result rests on four stated assumptions. - **Assumptions you could challenge:** - The four assumptions listed in §5.3: the void; the whole-cell π/6 reference (which moves 1/α to 151.86 if dropped); the quon energy-radius constant 1/3; the odd round-down rule. - "F = 0.922 for exact α": the script computes the F at which N = 1843 exactly (0.92241), not the F at which the pure lattice gives α exactly. Register check: the latter is 0.92207. Both round to 0.922. ### M16. Orbit radius equals the zitterbewegung amplitude - **Paper section:** §5.4 - **Aspden's claim:** The quon orbit radius is r = ħ/(2mc) and the orbital speed is c/2 (Tutorial Notes 7 and 8, ref. 1). - **What was tested:** Comparison with the zitterbewegung that Dirac's equation predicts for the electron. - **Steps:** 1. Dirac zitterbewegung amplitude ħ/(2mc): equal to his r. 2. His orbital angular frequency (c/2)/r = mc²/ħ is half the zitterbewegung frequency 2mc²/ħ. - **Inputs:** none numerical. - **Script and output:** no script (comparison in the text). - **Result:** The radius matches exactly; the frequency is half. - **Corrected in v1.9:** §13 now calls the zitterbewegung match a correspondence rather than evidence, since r is taken from the electron's mass. - **Verdict:** Credited. His radius coincides with a standard quantity. - **Assumptions you could challenge:** - r = ħ/(2mc) is an input to his model (the docstring of aspden_G_variants.py says the lattice cell d is fixed by his α relation and this radius), so the match is a correspondence, not a prediction. ### M17. Proton/electron mass ratio (1975) - **Paper section:** §6.1 (Appendix C.1, C.7; chain.py) - **Aspden's claim:** The lattice charge-volume count gives a dimuon energy Q = 944784π²/1843^(4/3) = 412.6658 mₑ. 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). Aspden and Eagles, *Il Nuovo Cimento* 30A, 235 (1975), abstract: 1836.15232 against the then-measured 1836.15152(70) (ref. 30, https://aetherscience.org/www-aspden-org/papers/bib/1975a.htm). - **What was tested:** His P against the CODATA 2022 ratio. - **Steps:** 1. Q = 944784π²/1843^(4/3) = 412.6658162. 2. Q/P = √(3/2) − 1 (contact minimum for Thomson spheres, k = 2/3). 3. P = 1836.15231648. 4. Against 1836.152673426(32): −0.1944 ppm, −1.12×10⁴σ. - **Inputs:** mp/mₑ = 1836.152673426(32), CODATA 2022 (Appendix B). - **Script and output:** aspden_G.py, environment_constants.py, chain.py: - `dimuon Q = 412.6658162` - `proton P = 1836.15231648 (measured 1836.152673426)` - `mp/me 1836.152316484 measured 1836.152673426 -0.1944 ppm (-1.12e+4 sigma)` - `P (proton, theory) = 1836.15231648 measured 1836.152673426 diff ppm = -0.1944` - **Result:** −0.19 ppm, about −11,000σ. No new adjustable number: N = 1843 is fixed by α. - **Verdict:** Excluded as an exact prediction (−11,000σ). It is the closest match in the corpus; its chance is assessed in M59. - **Assumptions you could challenge:** - Register check: the √(3/2) − 1 ratio comes from minimising the pair energy over the dimuon's size with the proton held fixed. Minimising over the proton instead gives a different ratio. The paper does not say which is held fixed. - The Thomson energy constant k = 2/3. Other k fail badly (M30). - N = 1843 is carried over from α (M12). ### M18. Charge-inequality explanation of the proton residual (1983) - **Paper section:** §6.2 (Appendix C.7) - **Aspden's claim:** The small residual comes from the proton and electron charges differing in magnitude by 1.07 parts in 10⁷, because the electron displaces aether continuum charge. "The Assessment of a Theory for the Proton-Electron Mass Ratio", *Lett. Nuovo Cimento* 38, 423 (1983) (ref. 31, https://aetherscience.org/www-aspden-org/papers/bib/1983i.htm). - **What was tested:** The proposed charge difference against the measured neutrality of matter. - **Steps:** 1. Bressi et al. 2011, acoustic test on SF₆ gas: |q_p + q_e|/e = (−0.1 ± 1.1)×10⁻²¹. 2. 1.07×10⁻⁷ against about 10⁻²¹: excluded by a factor of about 10¹⁴. - **Inputs:** Bressi et al. 2011 (ref. 37). - **Script and output:** environment_constants.py (a fixed sentence; nothing is computed): - `Measured neutrality of matter: |q_p + q_e|/e = (-0.1 +/- 1.1) x 10^-21 -> excluded by a factor of about 10^14` - **Result:** About 10¹⁴ times larger than the measured limit. - **Verdict:** Excluded. - **Assumptions you could challenge:** - That his charge difference would show up as a net charge on neutral molecules. If his effect applied only to free or moving charges, this test might not apply. Untested. - The paper does not check whether 1.07×10⁻⁷ is the size needed to explain the residual. ### M19. Rydberg energy from his α - **Paper section:** §6.3 (Appendix C.7) - **Aspden's claim:** None directly; in his framework the Rydberg constant follows from α by the standard hcR∞ = (α²/2)mₑc². - **What was tested:** The Rydberg energy implied by his α against CODATA. - **Steps:** 1. hcR∞ = mₑc²/(2(1/α)²) with his 1/α: 13.60570986838 eV. 2. Against 13.60569312299 eV: +1.231 ppm, 1.12×10⁶σ. - **Inputs:** mₑc² = 510998.95069 eV and hcR∞ = 13.605693122990(15) eV (CODATA 2022, as typed in the script; the Rydberg energy is not in Appendix B). - **Script and output:** environment_constants.py: - `Rydberg energy hcR (eV) 13.60570986838 measured 13.60569312299 1.231 ppm (1.12e+6 sigma)` - **Result:** +1.23 ppm, about a million times the measurement uncertainty. - **Verdict:** Excluded. Not independent of M13: R ∝ α², so −0.615 ppm in 1/α becomes +1.23 ppm. - **Assumptions you could challenge:** - That the standard relation holds in his framework (the analysis's assumption). ### M20. Search for a non-relativistic account of the fine structure - **Paper section:** §6.3 (Appendix C.9 for the Sommerfeld share) - **Aspden's claim:** None found. The search was prompted by a remembered passage linking the Rydberg constant and Einstein's theory, which turned out to be "Atomic Spectra and the Moving Atom" (1996) and *Physics Unified* (1980) ch. 3 (M56). - **What was tested:** Whether any text on the site derives the hydrogen fine structure without relativity. - **Steps:** 1. Text search of all 678 posts and pages: no non-relativistic derivation found. 2. *Modern Aether Science* (1972, ch. 7) mentions the fine structure only as one of the results that "flow out of the Dirac formalism in an almost miraculous fashion". 3. 1983c uses the Rydberg levels as given. 4. Sommerfeld (1916): relativistic mass in a Kepler orbit makes it precess, and that gives the fine structure. For Mercury it gives πGM☉/(c²p) per orbit, one-sixth of the relativistic advance: 7.16 of 42.98″/cy. - **Inputs:** site copy of 30 October 2026 (547 entries, §2); Mercury's 42.98″/cy relativistic advance (Will 2018, ref. 39). - **Script and output:** mercury_aether.py (the step divides 42.98 by 6; it is not an orbit calculation): - `Mercury: GR 6 pi GM/(c^2 p) per orbit; relativistic mass alone gives pi GM/(c^2 p) -> 7.16"/cy of the 42.98"/cy` - **Result:** No such derivation exists in the site's texts. - **Verdict:** Disagrees. The corpus contains no non-relativistic fine-structure derivation. - **Assumptions you could challenge:** - Completeness of the site copy and of the search. The search terms are not listed; 98 scanned PDFs were OCR'd and OCR errors could hide a passage. Untested. - Register check: the special-relativity share πGM/(c²p) is one-sixth of 6πGM/(c²p); correct. ### M21. Constants stepping with temperature: white dwarfs and the Sun - **Paper section:** §6.4 (Appendix C.7) - **Aspden's claim:** The lattice integer N falls in integer steps as energy or thermal activity rises in a region of space. "The Fifth Question: What is a Neutrino?" (Energy Science Q&A, ref. 32, https://aetherscience.org/www-energyscience-org-uk-question-es0105/). Line frequencies scale as N^(4/9) (Note 10) or N^(1/9) (his revised radio analysis in the Q&A). - **What was tested:** One step of N against measurements of μ = mp/mₑ, α and line positions in hot stellar atmospheres. - **Steps:** 1. Scalings from his formulas: α ∝ N^(1/6), μ ∝ N^(−4/3), Rydberg energy in mₑc² ∝ N^(1/3), lines ∝ N^(4/9) or N^(1/9). 2. One step 1843 → 1842: Δα/α = −90.45 ppm, Δμ/μ = +723.9 ppm, ΔR/R = −180.9 ppm, line shift 72.31 km/s (N^(4/9)) or 18.08 km/s (N^(1/9)). Two steps double these. 3. GD133 (H₂ at 11,800 K): Δμ/μ = (−27 ± 47) ppm → 16.0σ. 4. G29-38 (H₂ at 14,500 K): (−58 ± 38) ppm → 20.6σ. 5. G191-B2B Fe V: Δα/α = (42 ± 16) ppm → 8.28σ. Ni V: (−61 ± 58) ppm → 0.508σ. 6. Sun: measured line shift 638 ± 6 m/s minus the GR redshift 633.1 m/s leaves 4.9 ± 6 m/s. Predicted 72,307 m/s → 12,050σ; 18,078 m/s → 3,012σ. - **Inputs:** - GD133 and G29-38: Bagdonaite et al. 2014 (ref. 34). - G191-B2B: Berengut et al. 2013 (ref. 35). - Sun: 638 ± 6 m/s, González Hernández et al. 2020 (ref. 38); the 638 appears only in the script; GR 633.1 m/s (script). - **Script and output:** environment_constants.py: - `N 1843 -> 1842: d(alpha)/alpha = -90.45 ppm, d(mu)/mu = 723.9 ppm, d(R)/R = -180.9 ppm, line shift 72.31 km/s (N^4/9) or 18.08 km/s (N^1/9)` - `White dwarf GD133, H2 at 11,800 K, mu predicted 723.9 ppm measured -27.0 +/- 47.0 ppm -> 16.0 sigma` - `White dwarf G29-38, H2 at 14,500 K, mu predicted 723.9 ppm measured -58.0 +/- 38.0 ppm -> 20.6 sigma` - `White dwarf G191-B2B, Fe V, alpha predicted -90.45 ppm measured 42.0 +/- 16.0 ppm -> 8.28 sigma` - `White dwarf G191-B2B, Ni V, alpha predicted -90.45 ppm measured -61.0 +/- 58.0 ppm -> 0.508 sigma` - `Sun, 5,800 K photosphere, line shift (N^4/9): predicted 72307.0 m/s, residual measured 4.9 +/- 6.0 m/s -> 1.205e+4 sigma` - `Sun, 5,800 K photosphere, line shift (N^1/9): predicted 18078.0 m/s, residual measured 4.9 +/- 6.0 m/s -> 3012.0 sigma` - **Result:** Excluded at 16σ, 21σ, 8σ and 3,000–12,000σ; only the less precise Ni V value (0.5σ) allows a step. - **Verdict:** Excluded, if "energy or thermal activity" includes stellar atmospheres. - **Assumptions you could challenge:** - The test uses one step (1843 → 1842), which his odd rule forbids. The smallest allowed step is two, which doubles every prediction and strengthens the exclusion. - That stellar photospheres count as "energy or thermal activity in a region of space". If they do not, only M22 applies. - His two line-frequency scalings are used for the Sun. The Rydberg row (−180.9 ppm) would give a third prediction that is not tested; all three are far outside the residual. - The two G191-B2B results (Fe V, Ni V) disagree with each other, and Fe V is itself non-zero by more than 2σ. The paper takes both at face value. ### M22. Constants stepping: distant galaxies - **Paper section:** §6.4 (Appendix C.7) - **Aspden's claim:** As M21, and Note 10/Note 20 (distant regions sit at different N). - **What was tested:** One step of N against μ and α measured in absorbers at z = 0.89 and z = 1.15. - **Steps:** 1. Predictions as M21: Δμ/μ = +723.9 ppm; Δα/α = −90.45 ppm. 2. z = 0.89 methanol (7.5 billion years ago): Δμ/μ = (−0.10 ± 0.13) ppm → 5.65×10³σ. 3. z = 1.15 ESPRESSO: Δα/α = (1.3 ± 1.4) ppm → 67.5σ. - **Inputs:** - z = 0.89: (−1.0 ± 0.8 stat ± 1.0 sys)×10⁻⁷ combined in quadrature (script), Bagdonaite et al. 2013 (ref. 36). - z = 1.15: 1.3 ± 1.3 (stat) ± 0.4 (sys) ppm combined in quadrature (script), Murphy et al. 2022 (ref. 14). - **Script and output:** environment_constants.py: - `Quasar absorber z = 0.89 (methanol), mu predicted 723.9 ppm measured -0.1 +/- 0.13 ppm -> 5.65e+3 sigma` - `Quasar absorber z = 1.15 (ESPRESSO), alpha predicted -90.45 ppm measured 1.3 +/- 1.4 ppm -> 67.5 sigma` - **Result:** 5,600σ and 68σ. - **Corrected in v1.9:** the table rows are now labelled as quasar absorbers. - **Verdict:** Excluded, if the claim means the aether energy of distant regions. - **Assumptions you could challenge:** - That these absorbers lie in regions with a different N. Untested. - Statistical and systematic errors combined in quadrature (script choice). - The §6.4 table calls both absorbers "Galaxy"; the script and §3.4 call the z = 1.15 system a quasar absorber. Labels only. ### M23. α³/2 numerical lead for the proton residual - **Paper section:** §6.5 (Appendix C.7) - **Aspden's claim:** None. The lead was found during the investigation. - **What was tested:** How closely a simple α-power correction matches the −0.19 ppm residual, and how often such a match occurs by chance. - **Steps:** 1. Needed correction: measured/Aspden − 1 = 1.94397×10⁻⁷. 2. Best of 60 candidates (15 coefficients × α¹ to α⁴): α³/2 = 1.94297×10⁻⁷, 0.0514% off. 3. Corrected ratio 1836.152673243 against 1836.152673426: −0.0999 ppb, −5.73σ. 4. Chance that the best of 60 lands this close (global estimate over the candidates' log range): 0.0032, about 1 in 300. - **Inputs:** mp/mₑ and α, CODATA 2022 (Appendix B). - **Script and output:** environment_constants.py: - `needed correction 1.94397e-7; best of 60 candidates: 1/2 x alpha^3 = 1.94297e-7 (0.0514% off)` - `mp/me x (1 + 1/2 x alpha^3) = 1836.152673243 vs 1836.152673426: -0.0999 ppb (-5.73 sigma)` - `chance that the best of 60 such candidates lands this close: 0.0032` - **Result:** Matches to 1 part in 10¹⁰ but is still 5.7σ off; 1-in-300 chance. - **Verdict:** Open. A numerical coincidence found by searching, not motivated by his theory; as an exact correction it misses by 5.7σ. - **Assumptions you could challenge:** - The 60-candidate family. A larger family would raise the chance. Untested. - The chance estimate spreads targets uniformly in log over the candidates' range. ### M24. G chain reproduction (Notes 6, 8, 9) and the Note 20 table - **Paper section:** §7.1–7.2 (Appendix C.1; chain.py, compare.py) - **Aspden's claim:** Gravity is the electrodynamic attraction between voids that gravitons make in the background charge. √G = 4π(e/mₑ)g⁻⁴/(108π)³, with g the graviton/electron mass ratio from the chain lattice → dimuon (412.666) → proton (1836.1523) → taon (two proton–dimuon pairs minus an ejected 1.875 cluster, 3484.94) → graviton = taon/x, 3x⁴ + x³ = 1 (x = 0.688408), giving g = 5062.318 and G = 6.67216×10⁻¹¹. Tutorial Notes 6, 8, 9 (ref. 1). Note 20 (1998) prints rows with g = 5600–5603. - **What was tested:** Whether the chain reproduces his numbers, and whether the Note 20 rows are a misprint. - **Steps:** 1. Q = 412.6658162; P = 1836.15231648. 2. Taon T = 2Q(3 + √(3/2)) − 15/8 = 3484.940581; the closed form equals the step-by-step value. 3. x = 0.6884080245 from 3x⁴ + x³ = 1. 4. g = T/x = 5062.31836; G = 6.672161×10⁻¹¹. 5. chain.py recomputes G for g values of Aspden's tables: g = 5062.32 gives 6.67214; g = 5060.95 gives 6.68661, matching Note 20's 6.686. 6. Note 20 rows printed as 5600–5603 should read 5060–5063 (G ∝ g⁻⁸ rules out 5600). - **Inputs:** e = 4.80320471257×10⁻¹⁰ esu and mₑ = 9.1093837139×10⁻²⁸ g (CODATA 2022, in the scripts). - **Script and output:** aspden_G.py, compare.py, chain.py: - `taon T = 3484.940581 (measured tau = 3477.37)` - `graviton g = 5062.31836 (CODATA G needs 5062.1156)` - `G = 6.672161 x 10^-11 m^3 kg^-1 s^-2 (CODATA 6.67430(15))` - `closed-form taon: 3484.94058138 stepwise: 3484.94058138` - `table check g= 5062.32 G= 6.67214` - `table check g= 5060.95 G= 6.68661` - `G with measured proton mass, 1.875: 6.672151 shift ppm: -1.56` - **Result:** The chain gives his g and G; the Note 20 rows are a misprint. - **Verdict:** Credited. His arithmetic is reproduced. - **Assumptions you could challenge:** - The paper says the rebuild "reproduces every value in Aspden's Note 9 table", but neither the paper nor any script lists the Note 9 table. chain.py prints G for five g values with no column of Aspden's values to compare. - Modern e/mₑ is used. Using the measured proton mass instead of his shifts G by only −1.56 ppm (compare.py). - Register check: the √G formula follows from dV/dE of a Thomson-sphere void (as chain.py's comments derive it) and is dimensionally consistent in Gaussian units. ### M25. The 1.875 cluster - **Paper section:** §7.2 (Appendix C.2; chain.py) - **Aspden's claim:** The taon is two proton–dimuon pairs at minimum energy minus an ejected cluster of 1.875 mₑ (Tutorial Note 9, ref. 1). - **What was tested:** Whether 1.875 has a basis in his rules. - **Steps:** 1. Three touching electron-sized Thomson charges in a +−+ line: rest energy 3, two touching pairs −½ each, ends +¼, in units where e²/a = (3/2)mₑc²: 3 − 9/8 = 15/8 = 1.875. 2. Net charge ±1, so a charged taon remains, as his charge bookkeeping requires. - **Inputs:** none measured. - **Script and output:** chain.py and aspden_G_variants.py: - `in-line triplet energy = 1.875` - `3 1.875 6.67216 YES CODATA:-14.3σ HUST-TOS-18:-25.9σ HUST-AAF-18:-29.8σ UWash-00:-22.8σ UZur-06:-17.4σ UCI-14:-16.8σ` - **Result:** 1.875 is exactly the straight +−+ triplet. - **Verdict:** Credited. It is the most defensible choice by his own rules. - **Assumptions you could challenge:** - That an ejected cluster must carry net unit charge (the paper's reading of his bookkeeping). - Straight rather than L-shaped (M31). ### M26. Taons per graviton - **Paper section:** §7.2 (Appendix C.6, used internally) - **Aspden's claim:** The graviton is formed with two taons; the composite rule 3x⁴ + x³ = 1 (Tutorial Note 9, ref. 1). - **What was tested:** What G results if the graviton is built from one, three or four taons instead. - **Steps:** 1. Generalised rule (1 + n/x³) = 3(1 + nx); n = 2 reduces to 3x⁴ + x³ = 1. 2. With the 1.875 taon: n = 1, 3, 4 give G = 3.50, 8.52, 9.70 (text). - **Inputs:** none measured. - **Script and output:** no printed output. coincidence.py computes these values inside its G family but does not print them. Register check with the same rule: x = 0.63502, 0.70982, 0.72136 and G = 3.498, 8.525, 9.699. - **Result:** Only n = 2 lands near the measured G. - **Verdict:** Open. Two taons is his stated rule, and the alternatives fail by large factors, but the paper does not examine why the rule uses two. - **Assumptions you could challenge:** - The generalisation of his composite rule to n taons is the analysis's construction (coincidence.py). ### M27. Taon vs the tau lepton - **Paper section:** §7.2 (Appendix C.1; chain.py) - **Aspden's claim:** The taon (3484.94 mₑ) is a separate virtual particle (as the paper reports his position). - **What was tested:** Whether the taon can be identified with the measured tau, which would give the chain an independent check. - **Steps:** 1. Taon 3484.940581 mₑ. 2. Tau 1776.93 MeV / 0.51099895069 MeV = 3477.3653 mₑ. 3. They differ by about 7.6 mₑ. - **Inputs:** tau mass 1776.93 ± 0.09 MeV (Particle Data Group, Appendix B). - **Script and output:** aspden_G.py and chain.py: - `taon T = 3484.940581 (measured tau = 3477.37)` - `measured tau = 1776.93 MeV = 3477.3653 me` - **Result:** The taon is not the tau. - **Verdict:** Open. Because he treats it as a separate virtual particle, the taon has no independent check. - **Assumptions you could challenge:** - None beyond the identification question. ### M28. History of Aspden's published G - **Paper section:** §7.2 (compare.py, chain.py) - **Aspden's claim:** His published G values: 1966: 6.6676; Note 8: 6.668; Note 9: 6.672; Note 20 (1998): 6.686 (as listed in the paper; sources: Tutorial Notes, ref. 1; the 1966 source is not given). - **What was tested:** Whether his derived G stayed fixed across his writings. - **Steps:** 1. Note 8 route (taon = 3^(7/12)·P): G = 6.667976 (compare.py, chain.py). 2. Note 9 route (1.875 cluster): G = 6.672161. 3. Note 20's 6.686 corresponds to g = 5060.95 (chain.py). 4. The paper's reading: the values tracked "the measurement of the day". - **Inputs:** none measured are given for 1966 or 1998. - **Script and output:** compare.py and chain.py: - `G (taon=3^(7/12)P, Note 8): 6.667976` - `G (1.875 triplet, Note 9): 6.672161` - `table check g= 5060.95 G= 6.68661` - **Result:** His G moved from 6.6676 to 6.686. The uncited scripts show that the Note 8 → Note 9 change came from a different taon formula, not only from new inputs. - **Corrected in v1.9:** the range now reads 6.6676 to 6.686, and the unsupported phrase "tracking the measurement of the day" is removed. - **Verdict:** Disagrees. His derived G was not stable across his writings. - **Assumptions you could challenge:** - "Tracking the measurement of the day" is asserted; the paper gives no measured values for 1966 or 1998. - Dates of Notes 8 and 9 are not given. - The row says G "moved between 6.668 and 6.686" but lists 6.6676 for 1966. ### M29. Aspden's G against modern measurements - **Paper section:** §7.2–7.3 (Appendix C.2; chain.py, compare.py) - **Aspden's claim:** G = 6.67216×10⁻¹¹ m³ kg⁻¹ s⁻² (Tutorial Note 9, ref. 1). - **What was tested:** His G against CODATA and individual experiments, and how sensitive G is to the chain. - **Steps:** 1. CODATA 6.67430(15): −320.5 ppm, −14.3σ. 2. HUST-TOS-18 −25.9σ; HUST-AAF-18 −29.8σ; UWash-00 −22.8σ; UZur-06 −17.4σ; UCI-14 −16.8σ. 3. BIPM-14 −21.1σ; JILA-10 (corrected) −1.76σ; LENS-14 +0.254σ (compare.py). 4. NIST-26 6.67387: −257 ppm (text). 5. Sensitivity: G ∝ g⁻⁸, so 1 mₑ in the taon moves G by 2,296 ppm. 6. Cluster each measurement needs: 1.8586 (LENS-14) to 2.0897 mₑ (chain.py) or 1.859 to 2.099 mₑ (compare.py), a spread of about a quarter of an electron mass. - **Inputs:** CODATA 2018/2022 6.67430(15) (Appendix B). The experiments' values are in the §7.3 table; Appendix B does not list them and the paper gives no reference per value (refs. 17–19 cover G tables, HUST and NIST). NIST-26 has no uncertainty in the paper. - **Script and output:** aspden_G_variants.py, compare.py, chain.py: - `3 1.875 6.67216 YES CODATA:-14.3σ HUST-TOS-18:-25.9σ HUST-AAF-18:-29.8σ UWash-00:-22.8σ UZur-06:-17.4σ UCI-14:-16.8σ` - `BIPM-14 6.67554 0.00016 | -506.1 -21.1 | -219.3 -9.15 | 2.096` - `JILA-10 6.6726 0.00025 | -65.76 -1.76 | 221.2 5.9 | 1.904` - `LENS-14 6.67191 0.00099 | 37.65 0.254 | 324.7 2.19 | 1.859` - `ppm change in G per 1 me change in taon: -2295.6` - `CODATA 2018/22 G=6.67430 g_needed=5062.11555 cluster_needed=2.0146 me` - `BIPM-13 G=6.67545 g_needed=5062.00654 cluster_needed=2.0897 me` - `LENS-14 atom int. G=6.67191 g_needed=5062.34218 cluster_needed=1.8586 me` - **Result:** −320 ppm (−14σ) from CODATA; −17σ to −30σ from the five most precise experiments; consistent only with JILA-10 and LENS-14. NIST-26: register check gives −256.0 ppm, not −257. - **Corrected in v1.9:** NIST-26 now reads −256 ppm. - **Verdict:** Excluded. - **Assumptions you could challenge:** - Which measurements are used. The BIPM-14, JILA-10 and LENS-14 σ values in the paper come only from compare.py, which the paper does not cite; the cited script prints six comparisons. - JILA-10 "corrected" (6.67260(25)); chain.py uses the uncorrected 6.67234(14). - chain.py also uses 6.674215 for UWash-00 where the paper and other scripts use 6.674255, and BIPM-13 6.67545(18) instead of BIPM-14. The "quarter of an electron mass" spread holds for both sets (0.23 and 0.24 mₑ). ### M30. Charge-model constant k and lattice integer N varied - **Paper section:** §7.4 (Appendix C.2) - **Aspden's claim:** Thomson charges with energy (2/3)e²/a, and N = 1843 (Notes 8, 9). - **What was tested:** Whether a different charge model or the N that makes α exact improves the proton or G. - **Steps:** 1. Surface-charge electron (k = 1/2): proton 2361.51327, G = 0.471772. 2. Uniform-ball electron (k = 3/5): proton 1945.29855, G = 2.99413. 3. k tuned to give the measured proton: k = 0.666666195842 (−0.7 ppm from 2/3); G = 6.672133 (−4 ppm change). 4. N that makes α exact: 1842.993195; proton 1836.161356 (+4.7 ppm); G = 6.671898. - **Inputs:** mp/mₑ and α, CODATA 2022 (Appendix B). - **Script and output:** aspden_G_variants.py: - `surface shell 1/2 proton= 2361.51327 (meas 1836.152673) taon= 3911.183 G=0.471772` - `uniform ball 3/5 proton= 1945.29855 (meas 1836.152673) taon= 3559.4 G=2.99413` - `k that reproduces measured proton exactly: 0.666666195842 (2/3 = 0.666666666667 ) G there: 6.672133` - `N= 1842.993195 proton=1836.161356 G=6.671898` - **Result:** Other charge models fail by large factors; tuning k for the proton barely moves G; exact-α N worsens the proton. - **Verdict:** Excluded. None of these variants improves his results. - **Assumptions you could challenge:** - The lattice cell d = 72πe²/(mₑc²) is held fixed when k changes (script docstring); the triplet energy is recomputed as 3 − 3/(4k). ### M31. All 22 charge-conserving clusters on his cubic lattice - **Paper section:** §7.4 (Appendix C.2) - **Aspden's claim:** As M25 (1.875 straight triplet). - **What was tested:** Every connected cluster of touching Thomson charges with net charge ±1 (1, 3 or 5 charges) on a simple cubic lattice, as the ejected cluster. - **Steps:** 1. Enumerate polycubes of 1–5 sites; signs alternate with lattice parity; keep net charge ±1: 22 distinct energies. 2. Count those with G inside the span of precise modern measurements (LENS-14 6.67191 to BIPM-14 6.67554): 2. 3. Straight 1.875 → 6.67216 (CODATA −14.3σ); L-shape 2.03033 → 6.67454 (CODATA +1.6σ). - **Inputs:** G span from LENS-14 and BIPM-14 (§7.3 values). - **Script and output:** aspden_G_variants.py: - `3 1.875 6.67216 YES CODATA:-14.3σ HUST-TOS-18:-25.9σ HUST-AAF-18:-29.8σ UWash-00:-22.8σ UZur-06:-17.4σ UCI-14:-16.8σ` - `3 2.03033 6.67454 YES CODATA:+1.6σ HUST-TOS-18:+4.6σ HUST-AAF-18:+0.7σ UWash-00:+3.1σ UZur-06:+2.4σ UCI-14:+1.5σ` - `distinct cluster energies: 22, landing in modern G range: 2` - **Result:** Two of 22 land in range; the L-shape fits CODATA better than his straight triplet. - **Corrected in v1.9:** the claim that the rules were "fixed before computing G" is removed. The paper now states that the measured G was known throughout, and that an earlier script already printed the cluster each measurement requires (2.0146 mₑ for CODATA). - **Verdict:** Open. Two candidates survive and his rules do not choose between them. - **Assumptions you could challenge:** - The "in range" window spans LENS-14 to BIPM-14. It includes the low-precision LENS-14 value, which is what admits 1.875. A window based on CODATA ± a few σ would exclude 1.875. Not run. - Clusters up to 5 charges only. - "His rules, fixed before computing G": a process claim that cannot be checked. chain.py, which already printed the cluster each measurement needs (2.0146 mₑ for CODATA), has an earlier file time than explore.py, the uncited first version of this search. ### M32. Averaging, motion and composite-rule variants - **Paper section:** §7.4 (Appendix C.2) - **Aspden's claim:** As M25. - **What was tested:** Other ways to get a cluster energy near 2 mₑ, or to fit with the 1.875 triplet. - **Steps:** 1. Orientation average of the 15 three-charge arrangements around a site (3 straight, 12 L): 1.999264 → G = 6.67406 (CODATA −1.6σ). 2. Equal weight per shape: 1.952665 → 6.67335 (−6.3σ). 3. Straight triplet with interactions reduced by (1 − v²/c²), v = c/2: 2.15625 → 6.67647 (+14.5σ). 4. Averaging G instead of energy over orientations: 6.67406. 5. Composite-rule factor needed with the straight triplet: 2.9996204 instead of 3. - **Inputs:** CODATA G (Appendix B) and the §7.3 values. - **Script and output:** aspden_G_variants.py: - `orientation-weighted triplet (15 ways) cluster= 1.999264 G=6.67406 CODATA:-1.6σ HUST-TOS-18:-1.5σ HUST-AAF-18:-5.4σ UWash-00:-2.1σ UZur-06:-1.5σ UCI-14:-2.2σ` - `equal weight per shape cluster= 1.952665 G=6.67335 CODATA:-6.3σ HUST-TOS-18:-10.7σ HUST-AAF-18:-14.5σ UWash-00:-9.8σ UZur-06:-7.5σ UCI-14:-7.7σ` - `straight triplet in jitter motion (v=c/2) cluster= 2.15625 G=6.67647 CODATA:+14.5σ HUST-TOS-18:+29.3σ HUST-AAF-18:+25.5σ UWash-00:+24.1σ UZur-06:+18.5σ UCI-14:+16.3σ` - `orientation-weighted, averaging G instead of energy: G = 6.67406` - `with straight triplet, composite factor needed for CODATA: 2.9996204 (Aspden: 3)` - **Result:** The orientation average fits; equal weighting and motion fail; the composite tweak would fit but has no mechanism. - **Corrected in v1.9:** "two independent routes" now reads "two routes", both found with the measured G known. - **Verdict:** Open. One variant fits, but all were tried after the target was known. - **Assumptions you could challenge:** - The weighting scheme (per orientation vs per shape) decides pass or fail. - The (1 − v²/c²) reduction at v = c/2 is one choice among several possible motion corrections. ### M33. Justification for an ejected charge of exactly 2 mₑ - **Paper section:** §7.5 (Appendix C.3 for reason 3) - **Aspden's claim:** None. This is the analysis's proposal, supported by four features of his work: the dimuon and duon rule (Tutorial Notes 9 and 16; *Creation: The Physical Truth*, 2006, ref. 2); Note 17's pair-creation condition; his deuteron averaging (1986; 2006); and Note 14's compacted fast particle. - **What was tested:** Whether a 2 mₑ ejected charge follows from his own rules. - **Steps:** 1. A charge that contracts to half its radius doubles its energy (E ∝ 1/radius); applied to the electron this gives 2 mₑ. 2. Note 17: 2/3a = 2/3b − 1/(b+c) + 2/3c with a = b gives c = 2b (register check: correct), so factor-of-two steps (1, 2, 4 … mₑ) form a natural family. 3. His deuteron triplets 7/4 and 9/4 average to exactly 2. 4. A γ = 2 compacted electron is the same object as step 1 (supporting). 5. The 2 mₑ charge carries one unit of charge, so a charged taon remains. - **Inputs:** none measured. - **Script and output:** deuteron.py (step 3 only): - `heavy-centred triplets used for his 7/4 and 9/4: p e- e+ -> -1.75 e+ p- e+ -> -2.25` - **Result:** A coherent reading of his rules points to 2 mₑ. It was identified after the measured G was known. - **Corrected in v1.9:** the triplets are now described as p e⁻ e⁺ (7/4) and e⁺ p̄ e⁺ (9/4), not both heavy-centred. The dimuon is described as about the energy of two muons (412.67 against 413.54 mₑ). - **Verdict:** Open. Plausible, but post hoc. The paper's own decisive test (the same replacement in the 1986 *Hadronic Journal* masses) has not been done. - **Assumptions you could challenge:** - Reason 1 describes the dimuon as "the energy of two muons (412.67 mₑ)". Two measured muon masses are 413.54 mₑ (2 × 206.7682830, the ratio used in cavity_variants.py), so the dimuon is 0.21% lighter than two muons. The name, not the value, is two muons. - Reason 3 calls 7/4 and 9/4 "heavy-centred triplets". In deuteron.py the 7/4 comes from p e⁻ e⁺, with the proton at one end. With point protons any alternating heavy-centred triplet gives 9/4. - "The same averaging" for the 15 lattice orientations uses equal weights per orientation, not his deuteron weights (2, 1, 4). - explore.py, an uncited earlier version of aspden_G_variants.py, labels this variant "electron ejected with gamma=2", i.e. the rationale the paper now lists as only supporting (reason 4). ### M34. Doubled-electron G against measurements and the doubling family - **Paper section:** §7.3, §7.5 (Appendix C.2; compare.py) - **Aspden's claim:** None (analysis's variant; see M33). - **What was tested:** G with ejected charges of 1, 1.875, 2, 4 and 1.9993 mₑ against CODATA and individual experiments. - **Steps:** 1. 1 mₑ: taon 3485.8156, g 5063.5894, G 6.65877, −2,326 ppm. 2. 1.875 mₑ: 3484.9406, 5062.3184, 6.67216, −320 ppm. 3. 2 mₑ: 3484.8156, 5062.1368, 6.67408, −34 ppm (−1.5σ). 4. 4 mₑ: 3482.8156, 5059.2315, 6.70480, +4,570 ppm. 5. 1.9993 mₑ: 3484.8163, 5062.1379, 6.67406, −36 ppm (−1.6σ). 6. 2 mₑ against experiments: HUST-TOS-18 −1.4σ, HUST-AAF-18 −5.2σ, UWash-00 −1.9σ, UZur-06 −1.4σ, UCI-14 −2.1σ, BIPM-14 −9.15σ, JILA-10 +5.9σ, LENS-14 +2.19σ, NIST-26 +31 ppm. - **Inputs:** as M29. - **Script and output:** aspden_G_variants.py, compare.py: - `1 1.0 6.65877` - `doubled electron (exactly 2 me) cluster= 2.0 G=6.67408 CODATA:-1.5σ HUST-TOS-18:-1.4σ HUST-AAF-18:-5.2σ UWash-00:-1.9σ UZur-06:-1.4σ UCI-14:-2.1σ` - `graviton masses: straight 5062.31836 L 5062.09272 weighted 5062.13785` - `G (2.0, two electrons): 6.674076` - `CODATA-18/22 6.6743 0.00015 | -320.5 -14.3 | -33.55 -1.49 | 2.015` - `MSL-03 6.67387 0.00027 | -256.0 -6.33 | 30.88 0.763 | 1.987` - the 4 mₑ row is not printed by any script (coincidence.py includes 4.0 in its family without printing it). - **Result:** −34 ppm (−1.5σ) from CODATA; within about 2σ of four of the five most precise experiments, but −5.2σ from HUST-AAF-18, −9.2σ from BIPM-14 and +5.9σ from JILA-10. Register checks: the 4 mₑ row gives 6.704798 and +4,569.5 ppm (agrees); the 1.9993 row gives −35.2 ppm (the paper's −36 comes from rounding G to 6.67406 first). The NIST-26 +31 ppm uses the same G value as compare.py's MSL-03 row (6.67387). - **Corrected in v1.9:** the 1.9993 mₑ row now reads G = 6.674065, −35 ppm. - **Verdict:** Consistent with CODATA (−1.5σ), not with HUST-AAF-18, BIPM-14 or JILA-10. Post hoc. - **Assumptions you could challenge:** - CODATA as the main target; the experiments disagree with each other by more than their errors, so the verdict depends on which is taken. - Only the 2 mₑ member of the family lands near G. Whether 2 belongs to a family {1, 2, 4} or is one of many candidates is the question in M33 and M61. ### M35. Deuteron model: core mass deficits - **Paper section:** §8 (Appendix C.3) - **Aspden's claim:** The deuteron spends time in three states, each a straight chain of touching Thomson charges: A (e⁺ p⁻ e⁺ p⁻ e⁺, weight 2), B (p e⁻ e⁺ p⁻ with a satellite positron, weight 1, neutral core), C (p e⁻ p with a satellite e⁻e⁺ pair, weight 4). Core mass deficits 11/8, 9/8, 10/8 mₑ; heavy-centred triplet interactions 7/4 and 9/4. Sources: 2007 commentary on *Creation: The Physical Truth* (ref. 2, https://aspden.org/); *Hadronic Journal* 9, 129 (1986). - **What was tested:** Whether touching point protons and Thomson leptons reproduce his deficits. - **Steps:** 1. Chain positions from touching radii; pair interactions ±1.5/D (in mₑ, D in lepton radii). 2. Deficits: A 1.375, B 1.125, C 1.25 mₑ. 3. Weighted (2, 1, 4): 71/56 = 1.2678571. 4. Triplet interactions: −1.75 and −2.25. - **Inputs:** none measured. - **Script and output:** deuteron.py: - `Aspden: point protons, R=1836 deficits A=1.375 B=1.125 C=1.25 avg=1.2678571` - `heavy-centred triplets used for his 7/4 and 9/4: p e- e+ -> -1.75 e+ p- e+ -> -2.25` - **Result:** All his deficits and triplet energies are reproduced exactly. - **Corrected in v1.9:** "heavy-centred" removed, as for M33. - **Verdict:** Credited. - **Assumptions you could challenge:** - Point protons (his choice); M36 refines this. - The 7/4 triplet in the script is p e⁻ e⁺, which is not heavy-centred (see M33). ### M36. Deuteron magnetic moment - **Paper section:** §8 (Appendix C.3) - **Aspden's claim:** μd/μN = (6/7)·2/[2 − (71/56)/1836] (sources as M35). - **What was tested:** His moment against CODATA, with his R = 1836, with the measured ratio, and with protons given their own Thomson radius. - **Steps:** 1. Aspden's formula, R = 1836: 0.8574389111, +793.0 ppb (141.7σ). 2. Measured R: 0.8574388865, +764.3 ppb (136.5σ). 3. Protons of Thomson radius a/R: deficits 1.372619, 1.123446, 1.248775, average 1.266255; μ = 0.8574385122, +327.9 ppb (58.57σ). 4. The refinement closes 57% of the gap (text). 5. 6/7 alone is 344 ppm low; the weighted deficit is accurate to 0.22% (0.10% refined) (text). - **Inputs:** μd/μN = 0.8574382311(48), CODATA 2014 (Appendix B); R = 1836.15267389 (script). - **Script and output:** deuteron.py: - `mu_d = 0.8574389111 vs measured 0.8574382311: 793.0 ppb (141.7 sigma)` - `mu_d = 0.8574388865 vs measured 0.8574382311: 764.3 ppb (136.5 sigma)` - `finite Thomson proton radius a/R, measured R deficits A=1.372619 B=1.123446 C=1.248775 avg=1.266255` - `mu_d = 0.8574385122 vs measured 0.8574382311: 327.9 ppb (58.57 sigma)` - **Result:** +0.79 ppm (his), +0.33 ppm refined. Register checks (not printed by any script): 57.1% of the gap is closed relative to the measured-R version; the deficit the data need is 1.26505, so 71/56 is 0.22% high and the refined 1.266255 is 0.095% high; 6/7 is 344.5 ppm low. - **Verdict:** Excluded as an exact prediction (59σ even refined). Most of the moment comes from the simple fraction 6/7, so the ppm-level figure overstates the precision of the physics. - **Assumptions you could challenge:** - Giving protons the Thomson radius a/R is the analysis's refinement. - Weights 2, 1, 4 are his; other weights are covered in M60. - The deuteron moment is the CODATA 2014 value while other constants are CODATA 2022; the paper does not say why. ### M37. Neutron–proton mass difference (1986d) - **Paper section:** §8, §10 (Appendix C.12) - **Aspden's claim:** The Thomson-charge model gives (mₙ − mₚ)/mₑ = 2.5309419, which he converted with the 1984 electron mass to 1.2933214 MeV. *Hadronic Journal* 9, 129 (1986) = 1986d (no link in the paper; listed in the restored bibliography, §14). - **What was tested:** His ratio against the measured ratio in 1984 and today. - **Steps:** 1. 1984: 1.293323(16) MeV / 0.5110034 MeV = 2.530947935 ± 3.1×10⁻⁵ → −2.38 ppm, −0.193σ. 2. 2022: 1838.68366200 − 1836.152673426 = 2.530988574 ± 7.4×10⁻⁷ → −18.4 ppm, −63.1σ. 3. In MeV with today's mₑ: 1.29330866 vs 1.29333251. 4. His printed MeV value against today's MeV value (mixed units): −8.59 ppm (script). The paper says version 1.6 reported −8.2 ppm. - **Inputs:** CODATA 2022 ratio 2.53098857(74) (Appendix B). PDG 1984 values 1.293323(16) MeV and 0.5110034 MeV: stated only in the script. - **Script and output:** np_mass.py: - `1984 measurement (m_n-m_p)/m_e = 2.530947935 +/- 3.1e-5; Aspden 2.5309419: -2.38 ppm, -0.193 sigma` - `CODATA 2022 (m_n-m_p)/m_e = 2.530988574 +/- 7.4e-7; Aspden 2.5309419: -18.4 ppm, -63.1 sigma` - `In MeV with today's electron mass: Aspden 1.29330866 MeV vs measured 1.29333251 MeV` - `His printed 1.2933214 MeV used the 1984 m_e; against today's 1.29333251 MeV that mixes units and gives -8.59 ppm` - **Result:** −18.4 ppm (−63σ) today; −2.4 ppm (−0.2σ) in 1984. - **Corrected in v1.9:** the version-1.6 mixed-unit figure now reads −8.6 ppm. - **Verdict:** Excluded today. Consistent with the 1984 value. His step-by-step derivation, including an α-dependent subtraction of (3/47)/137, has not been checked. - **Assumptions you could challenge:** - Comparing the ratio rather than MeV (the paper argues the theory predicts the ratio). - The input 2.5309419 is his number; nothing in the scripts derives it. - Register check: 2.5309419 × 0.511004 = 1.2933214, so he used 0.511004 MeV, while the script's 1984 ratio uses 0.5110034 MeV. The effect is below 1 ppm. ### M38. Muon lifetime (Note 15) - **Paper section:** §9.1 - **Aspden's claim:** A simple "virtual muon hit" model of the muon lifetime (Tutorial Note 15, ref. 1). - **What was tested:** His lifetime at the real muon mass against the measured lifetime. - **Steps:** 1. His formula at the real muon mass: 2.251 μs (text; the formula is not given). 2. Measured: 2.197 μs. Difference +2.5%. - **Inputs:** 2.197 μs: source and uncertainty not stated in the paper. - **Script and output:** no script (hand calculation in the text). - **Result:** +2.5%. - **Verdict:** Disagrees. 2.5% off; no σ can be given because the paper states no uncertainty. - **Assumptions you could challenge:** - Using the real muon mass rather than any mass his model implies. - The more elaborate version in *Physics Unified* was not available. ### M39. Mercury: the Lecture 2 objection to Einstein - **Paper section:** §9.1 and §6.3 (Appendix C.7, C.9) - **Aspden's claim:** Einstein holds the angular-momentum term constant despite the relativistic mass increase, and solar oblateness could destroy his result. Lecture 2, "Why Einstein Was Wrong" (1997), and appendix (ref. 33, https://aetherscience.org/category/lectures/le02.htm and https://aetherscience.org/www-energyscience-org-uk-le-le02app/). - **What was tested:** Both parts of the objection. - **Steps:** 1. In general relativity the conserved angular momentum is per unit proper time, which already includes the mass increase. 2. Special relativity alone (Sommerfeld) gives one-sixth of the advance: 7.16 of 42.98″/cy; space curvature supplies the rest. 3. Oblateness: J₂ = (2.4 ± 0.2)×10⁻⁷ gives 3πJ₂(R☉/p)² per orbit = 0.0305″/cy, 0.07% of 42.98. 4. MESSENGER ranging pins the relativistic parameters to within 2.5×10⁻⁵ of Einstein's values (text). 5. His own 1960 aether formula gave 44.3″/cy; his later retardation argument reproduces Gerber's 1898 formula, the same as Einstein's for the perihelion. - **Inputs:** - J₂ = (2.4 ± 0.2)×10⁻⁷ "MESSENGER ranging": no reference entry. - 2.5×10⁻⁵ bound: no reference entry. - R☉ = 6.957×10⁸ m, a = 5.7909×10¹⁰ m, e = 0.205630, period 87.9691 d (script). - 42.98″/cy relativistic term (Will 2018, ref. 39). - 1960 value 44.3″/cy: *The Theory of Gravitation* (1960), §2; page not given. - **Script and output:** environment_constants.py and mercury_aether.py: - `J2 contribution = 0.0305 arcsec/century, against the 42.98 arcsec/century relativistic term` - `Mercury: GR 6 pi GM/(c^2 p) per orbit; relativistic mass alone gives pi GM/(c^2 p) -> 7.16"/cy of the 42.98"/cy` - **Result:** Oblateness contributes 0.07% of the relativistic term; the mass increase is already in GR's conserved quantity. - **Verdict:** Disagrees. Neither part of the objection holds. - **Assumptions you could challenge:** - The J₂ formula is the leading-order result for an orbit in the Sun's equatorial plane; inclination is ignored (a small correction). - The 2.5×10⁻⁵ and 44.3″/cy figures are not computed or sourced in detail. ### M40. 1969 aether-sphere account: density arithmetic - **Paper section:** §9.2 (Appendix C.9) - **Aspden's claim:** Each planet carries a sphere of aether lattice slightly larger than itself; its centre of mass must stay at rest, so it sheds substance that streams backward; lattice and stream carry net angular momentum −(2/5)MR²ω; the advance per revolution is (8π/5)(M/P)(R/X)². With the lattice extending 10% beyond Mercury's surface and a 38″/cy anomaly (after Dicke's 1967 oblateness), the lattice density is "about 150 g/cc"; chapter 6 derives 144 g/cc independently from the lattice spacing and a lattice particle of mₑ/24.52. *Physics without Einstein* (1969), ch. 5 pp. 84–86, eq. (5.9), and ch. 6 (ref. 40, https://aetherscience.org/category/books/Pwech5.pdf). - **What was tested:** His arithmetic, and the density with today's inputs. - **Steps:** 1. His inputs (38″/cy, P 3.27×10²⁶ g, X 5.7×10¹² cm, R 2.495×10⁸ cm, 88 d): 143.8 g/cc. 2. Today's inputs (42.98″/cy, 3.3011×10²⁶ g, 5.7909×10¹² cm, 2.4397×10⁸ cm, 87.969 d): 189.6 g/cc. 3. Density ∝ (boundary radius)⁻⁵: a 10% change in the boundary moves it 60%. 4. To keep 144 g/cc with today's anomaly, the boundary must sit at 1.1622 × the radius. 5. Dicke's oblateness has since been shown to be about 100 times too large (J₂ ≈ 2.2–2.4×10⁻⁷, 0.03″/cy). - **Inputs:** his values as listed; today's Mercury values (script; source not stated); 42.98″/cy (ref. 39). Dicke's J₂ value is not given in the paper and has no reference. - **Script and output:** mercury_aether.py: - `Aspden's inputs (38"/cy, P 3.27e26 g, X 5.7e12 cm, R 2.495e8 cm, 88 d): 143.8 g/cc (he wrote 'about 150'; ch. 6 lattice gives 144)` - `today's inputs (42.98"/cy, P 3.3011e26 g, a 5.7909e12 cm, R 2.4397e8 cm, 87.969 d): 189.6 g/cc` - `to keep 144 g/cc the lattice boundary must sit at 1.1622 x Mercury's radius` - `the 38"/cy rested on Dicke's 1967 solar oblateness; helioseismology gives J2 = 2.2e-7, worth only 0.03"/cy` - **Result:** His two routes agree even better than he said (143.8 vs 144), but the agreement rests on a guessed boundary and an oblateness value that did not survive. - **Verdict:** Credited for the arithmetic. The inputs no longer hold. - **Assumptions you could challenge:** - Using 42.98″/cy as "today's anomaly" (the GR value, which observation matches). - The 10% boundary is his guess; the steep R⁻⁵ dependence makes the density test weak either way. ### M41. Sign of the 1969 mechanism - **Paper section:** §9.2 (Appendix C.9) - **Aspden's claim:** As M40: conserving total angular momentum of planet plus aether, (r² − k)dθ/dt = constant with k = (2/5)(M/P)R², gives a perihelion advance of (8π/5)(M/P)(R/X)² per revolution (his 5.7 and the text after 5.8; eq. 5.9). - **What was tested:** Whether the conservation law moves the perihelion forward or backward. - **Steps:** 1. Integrate (r² − k)θ̇ = L with the Newtonian radial equation, e = 0.2, three orbits. 2. k/a² = 10⁻⁴: perihelion moves −1.370×10⁻³ rad per orbit; formula magnitude 4πk/a² = 1.257×10⁻³. 3. k/a² = 10⁻³: −1.370×10⁻²; formula 1.257×10⁻². 4. Aether angular momentum opposite to the orbit acts like an extra outward force falling as 1/r⁵, which makes orbits regress. Reversing the sign of k gives an advance. - **Inputs:** none measured. - **Script and output:** mercury_aether.py: - `k/a^2 = 0.0001: perihelion moves -1.370e-03 rad per orbit; (5.9) magnitude 4 pi k/a^2 = 1.257e-03 -> REGRESSION (backward)` - `k/a^2 = 0.001: perihelion moves -1.370e-02 rad per orbit; (5.9) magnitude 4 pi k/a^2 = 1.257e-02 -> REGRESSION (backward)` - **Result:** Regression of about the size of his formula, not advance. The integrated size is 9% larger than 4πk/a²; register check: first-order perturbation gives −4πk/p²·(1 + e²/8) = −1.370×10⁻³ at e = 0.2, matching the integration. The 9% is the eccentricity factor (his X read as a rather than p). - **Corrected in v1.9:** the text now says the regression is about 9% larger than his formula (an eccentricity factor). - **Verdict:** Disagrees. His own conservation law moves the perihelion backward. - **Assumptions you could challenge:** - The script models his law as a modified θ̇ with an unmodified Newtonian radial equation. If the streaming aether also exerted a radial force, the sign could differ. Untested. - Test orbit e = 0.2 in scaled units (Mercury's e is 0.2056). ### M42. The same mechanism applied to the other planets - **Paper section:** §9.2 (Appendix C.9) - **Aspden's claim:** As M40 (one lattice density, 144 g/cc, and the 10% boundary rule). - **What was tested:** Predictions for six planets, with the sign fixed, against GR and ephemeris limits. - **Steps:** 1. GR advance 6πGM☉/(c²a(1−e²)) per orbit, per century: Mercury 42.980, Venus 8.625, Earth 3.839, Mars 1.351, Jupiter 0.062, Saturn 0.014″/cy. 2. Aspden mechanism (144 g/cc, 1.1 × radius): 32.65, 23.32, 7.91, 0.7186, 12.32, 1.96″/cy. 3. Ratios 0.76, 2.7, 2.06, 0.532, 198, 144. 4. Boundary needed to match GR: 1.1622, 0.9016, 0.9519, 1.2480, 0.3821, 0.4073 × radius. 5. EPM2017 formal limits on extra motion: Mercury 0.008, Venus 0.315, Earth 0.033, Mars 0.003, Jupiter 33.9, Saturn 0.067 mas/cy; realistic limits 10–50 times larger. - **Inputs:** planetary masses, radii, orbits (script; source not stated); EPM2017 limits (Iorio 2019, ref. 49). - **Script and output:** mercury_aether.py: - `Mercury 42.980 32.65 0.76 1.1622 x radius` - `Venus 8.625 23.32 2.7 0.9016 x radius` - `Earth 3.839 7.91 2.06 0.9519 x radius` - `Mars 1.351 0.7186 0.532 1.2480 x radius` - `Jupiter 0.062 12.32 198 0.3821 x radius` - `Saturn 0.014 1.96 144 0.4073 x radius` - `ephemeris (EPM2017) formal limits on any extra perihelion motion: Mercury 0.008 mas/cy, Venus 0.315 mas/cy, Earth 0.033 mas/cy, Mars 0.003 mas/cy, Jupiter 33.9 mas/cy, Saturn 0.067 mas/cy (realistic: x10-50)` - **Result:** Misses Venus by about 15″/cy and Jupiter by about 12″/cy; matching each planet needs boundaries from 0.38 to 1.25 times its radius, sometimes below the surface. Saturn holds any such contribution below about 1% of the prediction (text). - **Verdict:** Excluded. Observed motions agree with GR for all six planets. - **Assumptions you could challenge:** - One density and one boundary rule for all planets (his single-density claim). A rule tied to density, core or magnetosphere is suggested in §14 as untried. - Using GR as the observed value for each planet, with ephemeris limits on extra motion. ### M43. Double pulsar and the structure of the advance - **Paper section:** §9.2 (Appendix C.9) - **Aspden's claim:** As M40. - **What was tested:** Whether an advance that depends on the orbiting body's own size and density, not the central mass, can match a system where GR's dependence on the central mass is tested strongly. - **Steps:** 1. GR: advance per orbit depends only on the central mass and orbit size. 2. PSR J0737−3039: neutron stars of radius about 12 km, 2.5-hour orbit, advance 16.899°/yr. 3. 144 g/cc lattice around a 1.338 M☉, 12 km star: M_lattice/P = 5.21×10⁻¹³; predicted 1.21×10⁻¹⁶ °/yr. - **Inputs:** 16.90°/yr (Kramer et al. 2006, 2021; refs. 50–51; Appendix B); pulsar mass 1.338 M☉, radius 12 km, orbit 8.79×10¹⁰ cm, period 0.10225 d (script; sources not stated). - **Script and output:** mercury_aether.py: - `M_lattice/P = 5.21e-13; predicted periastron advance 1.21e-16 deg/yr; measured 16.899 deg/yr` - **Result:** Predicted about 10⁻¹⁶ °/yr against 16.9°/yr. - **Verdict:** Excluded. - **Assumptions you could challenge:** - That the same 144 g/cc and 10% rule apply to a neutron star. Any other rule would need to scale with the central mass to work here. Untested. ### M44. Electron anomalous moment from the cavity model - **Paper section:** §9.3 (Appendix C.8) - **Aspden's claim:** The electron is a charge at the centre of a spherical cavity, with radial waves at the Compton frequency between radii r and R ≈ h/2mc, πr² equal to half the Thomson cross-section (r = (2/√3)e²/mc²), and a spin mass that excludes field energy outside R. Result: a = 1/(2π/α − 1 + 4/√3). "The Lamb Shift for a Cavity-Resonant Electron", *Lett. Nuovo Cimento* 36, 364 (1983c), eq. (8) (ref. 42, https://aetherscience.org/www-aspden-org/papers/bib/1983c.pdf). - **What was tested:** His aₑ against the 2023 measurement and against QED, and his formula's power series against QED's. - **Steps:** 1. With CODATA α: aₑ = 0.0011596461988, −5.16 ppm. 2. With α from Rb atom recoil: Aspden − measured = −5,982×10⁻¹² (−6.0×10⁻⁹). 3. QED with α(Rb): −0.339×10⁻¹². 4. Series in α/π: Aspden 0.5, −0.32735, +0.214316, −0.140313; QED 0.5, −0.328479, +1.181241, −1.912246. 5. The second-order coefficient agrees with QED's to 0.35% (text); the third-order is 5.5 times too small and "accounts for most of his 6×10⁻⁹ shortfall" (text). - **Inputs:** - aₑ = 0.00115965218059(13), Fan et al. 2023 (Appendix B). - α(Rb) 137.035999206(11), Morel et al. 2020; α(Cs) 137.035999046(27), Parker et al. 2018 (Appendix B). - QED inputs in the script: fifth-order coefficient 6.7 and non-universal terms 4.47×10⁻¹²; source not stated. - **Script and output:** cavity_1983.py: - `CODATA 2022 a_e = 0.0011596461988 ( -5.16 ppm vs 2023) a_mu = 0.001165890916 (-25.5 ppm, -203.0 sigma vs Fermilab 2025)` - `series coefficients of (alpha/pi)^n, n = 1..4: Aspden ['0.5', '-0.32735', '0.214316', '-0.140313'] QED ['0.5', '-0.328479', '1.181241', '-1.912246']` - `QED with alpha(Rb): a_e = 0.001159652180251, minus measured = -0.339 x 10^-12` - `Aspden with alpha(Rb): minus measured = -5982.0 x 10^-12` - **Result:** −5.2 ppm (−6.0×10⁻⁹) against a measurement uncertainty of 1.3×10⁻¹³; QED agrees to 3×10⁻¹³. Register check of the series: term by term, Aspden minus QED is +6.09×10⁻⁹ (second order), −12.12×10⁻⁹ (third), +0.05×10⁻⁹ (fourth), sum −5.98×10⁻⁹. The third-order deficit is twice the net shortfall, and half of it is cancelled by the second-order term; the 0.34% second-order miss contributes an error as large as the whole net shortfall. - **Corrected in v1.9:** the paper now gives the term-by-term account (+6.09, −12.12, +0.05 × 10⁻⁹) and 0.34%. - **Verdict:** Excluded. - **Assumptions you could challenge:** - α from atom recoil rather than CODATA (CODATA α is itself fitted to aₑ via QED). All choices give −4.5 to −5.2 ppm. - The "0.35%" second-order agreement is 0.344% relative to QED's coefficient. ### M45. Muon anomaly and the muon–electron difference - **Paper section:** §9.3 (Appendix C.8) - **Aspden's claim:** For the muon the cavity resonates on the inside wall, flipping the sign of 4/√3: aμ = 1/(2π/α − 1 − 4/√3). In 1983 he called the muon agreement "exact accord" (1983c, ref. 42). - **What was tested:** His aμ against the CERN 1979 and Fermilab 2025 values, and the muon–electron difference. - **Steps:** 1. With his 1979 α: aμ = 0.001165891225. 2. Against CERN 1979 0.001165924(8.5×10⁻⁹): −3.86σ. 3. Against Fermilab 2025 0.001165920705(147): −25.3 ppm, −201σ (with CODATA α: −25.5 ppm, −203σ). 4. Difference aμ − aₑ: 6.2447×10⁻⁶ against 6.2685×10⁻⁶ measured (−0.4%). - **Inputs:** CERN 1979 aμ (no reference entry in the paper); Fermilab 2025 (ref. 45; Appendix B); Williams–Olsen 1979 α 137.035963 (script; no reference entry). - **Script and output:** cavity_1983.py: - `Williams-Olsen 1979 (Aspden's input) a_e = 0.00115964650448 ( -4.89 ppm vs 2023) a_mu = 0.001165891225 (-25.3 ppm, -201.0 sigma vs Fermilab 2025)` - `muon in 1983: Aspden 0.00116589123 vs CERN 1979 0.001165924(8.5e-9): -3.86 sigma` - `muon minus electron: Aspden 6.2447 x 10^-6, measured 6.2685 x 10^-6` - **Result:** −3.9σ in 1983, about −200σ today. The difference matches to 0.4%, but M49 shows this follows from the electron fit. - **Verdict:** Excluded. - **Assumptions you could challenge:** - The CERN 1979 uncertainty is taken as 8.5×10⁻⁹ in the script and quoted as (9) in the text; no effect on the verdict. ### M46. Hydrogen Lamb shift (1983c) - **Paper section:** §9.3 (Appendix C.8) - **Aspden's claim:** Field energy flowing through an orbiting electron's cavity adds angular momentum (2/3)(α/2π)mR²ω, shifting the 2P azimuthal number by δn₀ and its energy by 2hcR∞δn₀ (eq. 13). Leading result (4π/15)α³R∞c (eq. 17), then factors (1 + 2α/(√3π)) for the exact cavity radius, 1/(1 + 2α) for "reasons a little beyond the scope of this paper", and the nuclear-mass factor (eq. 18): 1,057.848 MHz against the 1981 measurement 1,057.845(9) MHz (1983c, ref. 42). - **What was tested:** Eq. (18) against the 1981 and 2019 measurements, and the size of the correction factors. - **Steps:** 1. Eq. (17), his inputs: 1,070.999 MHz. 2. Eq. (18), his inputs: 1,057.8479 MHz; CODATA 2022 inputs: 1,057.8491 MHz. 3. Against Lundeen & Pipkin 1981 (1,057.845 ± 0.009): +4.138 kHz, 0.46σ. 4. Against Bezginov et al. 2019 (1,057.8298 ± 0.0032): +19.34 kHz, 6.04σ. 5. The factors move eq. (17) by −1.23%. - **Inputs:** Bezginov 2019 (ref. 46; Appendix B); Lundeen & Pipkin 1981 (named in the script; no reference entry); R∞ = 109737.31568157 cm⁻¹ (script). - **Script and output:** cavity_1983.py: - `Aspden's inputs (1983) eq.(17) 1070.999 MHz; eq.(18) 1057.8479 MHz` - `CODATA 2022 inputs eq.(17) 1071.0 MHz; eq.(18) 1057.8491 MHz` - `vs Lundeen & Pipkin 1981 1057.845 +/- 0.009 MHz: difference 4.138 kHz = 0.46 sigma` - `vs Bezginov et al. 2019 1057.8298 +/- 0.0032 MHz: difference 19.34 kHz = 6.04 sigma` - `the two correction factors move eq.(17) by -1.23 %` - **Result:** +0.5σ against 1981, +6.0σ against 2019. - **Corrected in v1.9:** now "two correction factors totalling −1.17% (−1.23% with the nuclear-mass factor)". - **Verdict:** Excluded by the 2019 measurement. The 1981 agreement came only after late correction factors, one explicitly deferred. - **Assumptions you could challenge:** - The paper and the script call the −1.23% "two correction factors", but the script's ratio includes the nuclear-mass factor as well. Register check: the two correction factors alone give −1.17%. - The 2019 value agrees with QED and with the muonic-hydrogen proton radius; the 1981 value is now superseded. ### M47. Step (13): which quantum number carries the shift - **Paper section:** §9.3 (Appendix C.8) - **Aspden's claim:** The energy shift is 2hcR∞δn₀/n₀³ with n₀ = 1, the energy "includes a term hcR′/n₀²" (1983c, eq. 13; stated without derivation). - **What was tested:** Whether the Bohr–Sommerfeld theory he says he is tracing gives this factor. - **Steps:** 1. In Bohr–Sommerfeld theory the energy depends on the azimuthal number only through the principal number n. 2. Shift of 2P: 2hcR∞δn/n³ with n = 2, which is 8 times smaller. 3. Result: 132.23 MHz instead of 1,057.85 MHz. - **Inputs:** as M46. - **Script and output:** cavity_1983.py: - `step (13) uses dE = 2 hcR dn0 / n0^3 with n0 = 1; Bohr-Sommerfeld gives 2 hcR dn / n^3 with n = 2 -> 8x smaller: 132.23 MHz` - **Result:** A factor of 8 rests on an unexplained choice of n₀ = 1. - **Verdict:** Disagrees. The key step does not follow from the theory he cites. - **Assumptions you could challenge:** - The reading that his n₀ is the principal quantum number of the 1S-like reference. If his R′ is a differently defined Rydberg term, the factor could differ. Untested. ### M48. Ionised-helium Lamb shift - **Paper section:** §9.3 (Appendix C.8) - **Aspden's claim:** "Much now depends upon the development of this method to explain other transitions" (1983c). - **What was tested:** The same formula applied to He⁺ (Z = 2). - **Steps:** 1. ω scales as Z² and the Rydberg term as Z², so the shift scales as Z⁴; nuclear-mass factor for the α particle (7294.29954 mₑ). 2. With 1/(1 + 2α): 16,932.5 MHz; with 1/(1 + 2Zα): 16,692.4 MHz. 3. Measured 14,041.9 ± 1.5 MHz: +19% to +21%. - **Inputs:** van Wijngaarden et al. 1987 (ref. 47; Appendix B). - **Script and output:** cavity_1983.py: - `He+ (Z = 2), same formula scaled Z^4: 16932.5 MHz (with 1+2a) or 16692.4 MHz (with 1+2Za); measured 14041.9 +/- 1.5 MHz` - **Result:** 19–21% too high. QED gets He⁺ right because its main term carries ln(1/(Zα)²), which shrinks with Z. - **Verdict:** Excluded. - **Assumptions you could challenge:** - The Z⁴ scaling is the analysis's extension of his formula; he did not apply it to helium. Other ways of carrying his correction factors to Z = 2 are untested (only the two shown). ### M49. Derived or chosen? The cavity formula and 21 variants - **Paper section:** §9.3 (Appendix C.10) - **Aspden's claim:** His equations (1)–(7) lead to (8); the muon flips the sign of 4/√3; a footnote alternative for a muon "created by charge pair annihilation" (1983d, footnote eq. 4; ref. 43). - **What was tested:** Whether 4/√3 is derived from stated choices, how special his choice is among natural alternatives, and whether the muon is an independent success. - **Steps:** 1. Chain (1)–(7) gives a = 0.00115964619855784, identical to the closed form (8). 2. Data need j + k = 1.30495 (electron) and j − k = −3.33132 (muon); with j = −1, k_e = 2.30495 and k_μ = 2.33132 against his 2.3094, a 1.14% asymmetry that a symmetric ± construction cannot give. 3. Sum k_e + k_μ = 4.63627 against 8/√3 = 4.6188 (−0.377%): this sum sets the muon–electron difference, so the 0.4% agreement of M45 follows from the electron fit. 4. 21 variants (7 inner radii × 3 mass forms): his is the only one within 30 ppm (−5.158 ppm); next best −32.91 ppm; every other variant 354 ppm or more for the electron and 76 ppm or more for the muon. 5. Chance that one of 21 constants lands this close to a random target in their span (5.27): 0.035, about 1 in 29. 6. Footnote muon formula: −39.93 ppm (reading the printed 4√3 as 4/√3); 5,259 ppm as printed. 7. The second-order coefficient is −(j + k), the same constant judged in step 4, so it is not a separate success; QED's target −1.3139 in units of (α/2π)² "sits among many simple numbers" (text). - **Inputs:** aₑ, aμ and α(Rb) as M44–M45. - **Script and output:** cavity_variants.py: - `1. chain (1)-(7) gives a = 0.00115964619855784; closed form (8) = 0.00115964619855784` - `2. data need j+k = 1.30495 (electron) and j-k = -3.33132 (muon)` - `with j = -1: k_e = 2.30495, k_mu = 2.33132 (Aspden 4/sqrt3 = 2.3094); asymmetry 1.14 %` - `sum k_e + k_mu = 4.63627 vs Aspden 8/sqrt3 = 4.6188 (-0.377 %): this sum is what sets the muon-electron difference` - `half Thomson cross-section (Aspden) spin mass excludes E_out (j=-1, Aspden) a_e -5.158 ppm a_mu -25.55 ppm` - `Thomson-sphere radius 2/3 a = E_out/mc^2 (j=0) a_e -32.91 ppm a_mu -2324.0 ppm` - `classical radius spin mass excludes E_out (j=-1, Aspden) a_e 353.8 ppm a_mu -386.1 ppm` - `chance that one of 21 such constants lands this close to a random target in that span: 0.035` - `5. muon, footnote form with 4/sqrt3 : a_mu = 0.001165874147 (-39.93 ppm)` - `5. muon, footnote form with 4 sqrt3 (as printed) : a_mu = 0.001172052325 (5259.0 ppm)` - **Result:** 4/√3 is derived from three choices; his combination is a 1-in-29 coincidence for the electron; the muon, with no free parameter left, fails (M45). - **Verdict:** Credited. The formula follows from his stated model, and among 21 natural variants only his lands within 30 ppm. - **Assumptions you could challenge:** - The variant set (seven radii, three mass forms) is the analysis's choice. Three of the 21 give the same constant (j + k = 1), and several others coincide; register count: 17 distinct values. Counting distinct values would lower the 1-in-29 chance somewhat. - The 30 ppm threshold. The runner-up at 33 ppm uses his own Thomson-sphere radius (2/3 of the classical radius), arguably as natural in his framework as half the cross-section. - "Half-wave is forced" (a full or quarter wave would move the leading term from α/2π) is argued in the script docstring and not computed. - The "76 ppm or more" muon figure is not in the printed output (only the top eight variants are printed); register check confirms 76.2 ppm (full Thomson cross-section, j = 0). - The "many simple numbers" near −1.3139 are not shown; the script's list of simple numbers (2/√3, 7/6, π/e) is for the muon–electron difference (1.16181), a different quantity. - Reading the footnote's printed 4√3 as 4/√3. ### M50. "Absolute gravitational potential": the two routes and what sets φ - **Paper section:** §9.4 (Appendix C.8) - **Aspden's claim:** A gravitational term enters the g-factor: g/2 = (1 + φ/2c²)(1 + 1/(2π/α − 1 + 4/√3)), φ being the magnitude of the absolute gravitational potential where the electron sits. Route 1: the 1979 g and α give φ = 10.25×10¹² cm²/s². Route 2: φm* = kT with the 2.7 K background and m* = 0.04 mₑ gives 10.24×10¹². The solar system contributes 9.49×10¹², so the rest of the universe adds only 8% and gravity has a range of "a few hundred light years". "The Determination of Absolute Gravitational Potential", *Lett. Nuovo Cimento* 37, 169 (1983d), eqs. (3) and (5) (ref. 43, https://aetherscience.org/www-aspden-org/papers/bib/1983d.pdf). - **What was tested:** Whether his inputs reproduce φ, what φ becomes with today's inputs, and what actually sets it. - **Steps:** 1. φ = 2c²[(1 + a_meas)/(1 + a_Aspden) − 1]. 2. 1979 g-factor with his 1979 α: 10.23×10¹². 3. 2023 g-factor with α from Rb or Cs atom recoil: 10.74×10¹². 4. 2023 g-factor with his own lattice α: 9.46×10¹². 5. Solar-system potential at the Earth's surface (GM☉/AU + GM⊕/R⊕): 9.497×10¹². 6. Excess over the solar system: 13% (today's α), 0% (his α), 8% (his 1983 values). 7. φ/2c² ≈ 6×10⁻⁹ equals his formula's shortfall (M44), so φ measures the formula's error. - **Inputs:** aₑ 1979 = 0.001159652200 (script; source not stated); α 1979 = 137.035963 (Williams–Olsen; script only); aₑ 2023 and α(Rb), α(Cs) as M44; GM☉ = 1.32712440018×10²⁶ cm³/s², GM⊕ = 3.986004418×10²⁰ cm³/s², R⊕ = 6.371×10⁸ cm (script; GM⊕ in Appendix B). - **Script and output:** cavity_1983.py: - `1979 g-factor, alpha Williams-Olsen 1979 (Aspden's input) phi = 10.23 x 10^12 cm^2/s^2` - `2023 g-factor, alpha Rb atom recoil 2020 phi = 10.74 x 10^12 cm^2/s^2` - `2023 g-factor, alpha Cs atom recoil 2018 phi = 10.74 x 10^12 cm^2/s^2` - `2023 g-factor, alpha Aspden's own lattice value phi = 9.46 x 10^12 cm^2/s^2` - `solar-system potential at the Earth's surface: 9.497 x 10^12 (Aspden: 9.49)` - **Result:** The rebuild with his inputs gives 10.23, not his 10.25. With today's inputs the inferred "rest of the universe" is 13% or 0% depending only on which α is used. - **Corrected in v1.9:** his printed 10.25 and 10.24 are now shown alongside the recomputed 10.23. - **Verdict:** Disagrees. φ is his g-factor formula's own shortfall rescaled, not a measurement of gravity. - **Assumptions you could challenge:** - The 0.2% gap between the rebuilt 10.23 and his 10.25 is not discussed in the paper; it could come from his rounding of inputs. Untested. - Reading his eq. (3) as a multiplicative factor on g/2, as in the script. ### M51. QED leaves no room for a φ term - **Paper section:** §9.4 (Appendix C.8) - **Aspden's claim:** As M50. - **What was tested:** How large any φ term in g/2 can be, given that QED already reproduces aₑ. - **Steps:** 1. QED with α(Rb) reproduces aₑ to −0.339×10⁻¹² (text: 3×10⁻¹³). 2. Taking |a_QED − a_meas| ≈ 10⁻¹² as the room left: φ/2c² < 10⁻¹², so φ < 0.0018×10¹² ≈ 2×10⁹ cm²/s². 3. That is "5,000 times" smaller than his 10.25×10¹² (text) and smaller than the Earth's own surface potential, 6.3×10¹¹. - **Inputs:** as M44. - **Script and output:** cavity_1983.py: - `QED with alpha(Rb): a_e = 0.001159652180251, minus measured = -0.339 x 10^-12` - `QED leaves no room: |a_QED - a_meas| ~ 1e-12 -> phi/(2c^2) < ~1e-12 -> phi < 0.0018 x 10^12` - **Result:** φ < about 2×10⁹ cm²/s². Register check: 10.25×10¹² / 1.8×10⁹ ≈ 5,700, so "5,000 times" is rounded down. - **Corrected in v1.9:** now "about 5,700 times". - **Verdict:** Excluded. - **Assumptions you could challenge:** - The 10⁻¹² room is a rounded choice, not a formal σ bound; it is about the size of the Rb–Cs α disagreement. A tighter choice strengthens the result. - The QED sum uses a fifth-order coefficient and non-universal terms typed into the script without a source. ### M52. Annual variation of φ - **Paper section:** §9.4 (Appendix C.8) - **Aspden's claim:** As M50 (φ includes the Sun's potential). - **What was tested:** The size of the yearly change in g/2 that his φ implies. - **Steps:** 1. The Sun's potential at Earth varies by ±1.67% over the year (orbital eccentricity): ±0.148×10¹² cm²/s². 2. g/2 changes by ±8.24×10⁻¹¹. 3. Against the 2023 uncertainty 1.3×10⁻¹³: 634 times. - **Inputs:** Earth's orbital eccentricity 0.0167 (script); aₑ 2023 uncertainty (Appendix B). - **Script and output:** cavity_1983.py: - `annual change of phi from Earth's eccentricity: +/- 0.148 x 10^12 -> g/2 changes +/- 8.24e-11, versus the 2023 uncertainty 1.3e-13 (634.0 x)` - **Result:** A drift about 600 times the 2023 uncertainty, which "would be hard to miss" given agreement with the 2008 Harvard value. - **Verdict:** Disagrees. The predicted drift is far above the precision, but the paper does not examine time-resolved data. - **Assumptions you could challenge:** - That the 2008 and 2023 measurements sample different times of year, or contain internal time series that would show the drift. Not shown. - The 2008 Harvard value has no reference entry. ### M53. Limited range of gravity vs the Galaxy and Gaia - **Paper section:** §9.4 (Appendix C.8) - **Aspden's claim:** As M50: gravity has a limited range of "a few hundred light years". - **What was tested:** Whether gravity acts over galactic distances. - **Steps:** 1. The Sun orbits the Galaxy at about 230 km/s, so the Galaxy's potential at the Sun is at least v² = 529×10¹² cm²/s², 55.7 times the solar-system value. 2. Expected acceleration toward the galactic centre, v²/R₀ with R₀ = 8.2 kpc: 2.09×10⁻¹⁰ m/s². 3. Gaia EDR3 measured (2.32 ± 0.16)×10⁻¹⁰ m/s² toward the galactic centre. - **Inputs:** v = 230 km/s and R₀ = 8.2 kpc (script; sources not stated); Gaia EDR3 (ref. 48; Appendix B). - **Script and output:** cavity_1983.py: - `Milky Way: Sun orbits at ~230 km/s, so |phi_galaxy| > v_c^2 = 529.0 x 10^12 = 55.7 x the solar-system value` - `expected pull toward the galactic centre v^2/R0 = 2.09 x 10^-10 m/s^2; Gaia EDR3 measured 2.32 +/- 0.16 x 10^-10 m/s^2 toward the galactic centre` - **Result:** Gravity acts with full strength over at least 26,000 light-years. - **Verdict:** Excluded. - **Assumptions you could challenge:** - |φ| ≥ v² holds for realistic mass distributions; the paper does not show it. It does not affect the Gaia comparison, which is direct. ### M54. The 3 K route today - **Paper section:** §9.4 (Appendix C.8) - **Aspden's claim:** As M50, route 2: φm* = kT, T = 2.7 K, m* = 0.04 mₑ (from the light-hole mass in germanium, identified with his lattice particle), giving 10.24×10¹². - **What was tested:** Whether the two routes still agree with today's inputs. - **Steps:** 1. His values: T = 2.7 K, m* = 0.04 mₑ: 10.23×10¹² (rebuild). 2. T = 2.72548 K, m* = 0.04 mₑ: 10.33×10¹². 3. T = 2.72548 K, m* = mₑ/24.52 (his lattice particle): 10.13×10¹². 4. Against route 1 today (10.74 with atom α, 9.46 with his α): differences of 4–9%. - **Inputs:** T = 2.72548 K (COBE/FIRAS, Fixsen 2009; Appendix B, no reference entry); m* values are his. - **Script and output:** cavity_1983.py: - `3 K route, Aspden 1983: T = 2.7 K, m* = 0.04 m_e phi = 10.23 x 10^12` - `3 K route, T = 2.72548 K (COBE/FIRAS), m* = 0.04 m_e phi = 10.33 x 10^12` - `3 K route, T = 2.72548 K, m* = m_e/24.52 (his lattice particle) phi = 10.13 x 10^12` - **Result:** Agreement to 0.1% in 1983; 4–9% apart today. The rebuild gives 10.23 for his own inputs, not his 10.24. - **Verdict:** Disagrees. The agreement does not survive today's inputs. - **Assumptions you could challenge:** - Which m* to use; the two choices bracket the result. ### M55. Search for a first-principles g = 9.8 m/s² - **Paper section:** §9.5 - **Aspden's claim:** None found. The question came from a recollection that Aspden derived the Earth's surface gravity. - **What was tested:** Whether any text on the site derives g = 9.8 m/s². - **Steps:** 1. Search all posts and pages for 981 cm/s², 9.8 m/s² and 32 ft/s²: one passing mention in Lecture 16, in a critique of someone else's theory. 2. Likely source of the recollection: 1983d, whose summary speaks of "the absolute value of φ at the Earth's surface"; OCR renders φ as "g". The paper computes a potential, not an acceleration, using measured G, Earth mass and radius. 3. g = GM⊕/R⊕² less a centrifugal term; GM⊕ is measured to about 2 parts in 10⁹, so a theory of G alone changes only the inferred Earth mass, not g. - **Inputs:** GM⊕ = 3.986004418×10¹⁴ m³/s² (IERS/WGS 84; Appendix B). - **Script and output:** no script (text search). - **Result:** No derivation of g exists in the corpus; none could exist without a theory of the Earth's mass and radius. - **Verdict:** Disagrees. The recollected derivation is not in the corpus. - **Assumptions you could challenge:** - Completeness of the site copy and of the three search strings (other forms, such as "981 cm sec⁻²" or "9.81", are not listed). Untested. - Lecture 16 has no link in the paper. ### M56. Rydberg factors for a moving atom vs fast-ion time dilation - **Paper section:** §9.6 (Appendix C.11) - **Aspden's claim:** Moving atomic clocks are not slowed by time dilation; the Bohr levels of a moving atom change instead. 1980: R(v)/R(0) = 2 − γ (*Physics Unified*, ch. 3, eq. 56; ref. 53, https://aetherscience.org/book-physics-unified/). 1996: R(v)/R(0) = (2 − β²)β³, from the electrodynamic force offsetting the Coulomb force by β², mass rising as 1/β, and vr being quantised ("Atomic Spectra and the Moving Atom", *Aether Science Papers* 1996, pp. 41–47; ref. 52, https://aetherscience.org/www-aspden-org/books/Asp/4147.htm). He argued that the experiments of his day could not tell these apart from Einstein's β. - **What was tested:** Agreement with time dilation by order of v/c, and the predictions for fast-ion Ives–Stilwell experiments. - **Steps:** 1. Series at v²/c² = 0.01: SR 0.99498743710662; 1980 0.994962184740788; 1996 0.994887938362909. All agree with 1 − x/2 at first order. 2. Exact: 1996 F/β = 1 − (v/c)⁴; 1980 F/β = 1 − (v/c)⁴/4 + … 3. At v/c = 0.03, (v/c)⁴ = 8.1×10⁻⁷, so his claim about older experiments was right. 4. Test quantity, lab at rest in the aether: ε = ν_aν_p/ν₀² − 1 = (Fγ)² − 1; zero for F = β. 5. Heidelberg TSR, v = 0.064c, ε = 0 ± 3.4×10⁻¹⁰: 1980 predicts −8.44×10⁻⁶ (2.45×10⁴σ); 1996 predicts −3.355×10⁻⁵ (9.75×10⁴σ). 6. GSI ESR, v = 0.338c, ε = (1.5 ± 2.3)×10⁻⁹: 1980 −0.007806 (3.39×10⁶σ); 1996 −0.02593 (1.13×10⁷σ). - **Inputs:** Botermann et al. 2014 (ref. 54) and Reinhardt et al. 2007 (ref. 55), Appendix B. The Heidelberg ±3.4×10⁻¹⁰ is derived in the script as α̂ × β² with α̂ = 8.4×10⁻⁸. - **Script and output:** moving_atom.py: - `special relativity F = 0.99498743710662 (1 - x/2 = 0.995)` - `Aspden 1980 (2 - gamma) F = 0.994962184740788 (1 - x/2 = 0.995)` - `Aspden 1996 ((2 - beta^2) beta^3) F = 0.994887938362909 (1 - x/2 = 0.995)` - `exact: Aspden 1996 F/beta = 1 - (v/c)^4; Aspden 1980 F/beta = 1 - (v/c)^4/4 + ...` - `Heidelberg TSR, Li+ (Saathoff 2003; Reinhardt 2007) (v = 0.064 c), measured 0.0 +/- 3.4e-10` - `Aspden 1980 (2 - gamma) predicts eps = -8.44e-6 -> 2.45e+4 sigma` - `Aspden 1996 ((2 - beta^2) beta^3) predicts eps = -3.355e-5 -> 9.75e+4 sigma` - `GSI ESR, Li+ (Botermann et al. 2014) (v = 0.338 c), measured 1.5e-9 +/- 2.3e-9` - `Aspden 1980 (2 - gamma) predicts eps = -0.007806 -> 3.39e+6 sigma` - `Aspden 1996 ((2 - beta^2) beta^3) predicts eps = -0.02593 -> 1.13e+7 sigma` - **Result:** Both versions miss by 10⁴ to 10⁷σ. - **Verdict:** Excluded. Lorentz's own aether electrodynamics gives time dilation exactly; what fails is Aspden's force law applied to the Bohr atom. - **Assumptions you could challenge:** - The lab is taken to be at rest in the aether (script docstring). A lab moving through the aether would add terms; untested. - F is read as the clock factor seen in the lab frame. - Conversion of the Heidelberg α̂ limit to ε. In the usual Mansouri–Sexl form, a clock-rate deviation α̂β² gives a product deviation ε ≈ 2α̂β², which would double the ±3.4×10⁻¹⁰ and halve the Heidelberg σ values. To check against refs. 54–55; the verdict does not change. Checked after compiling: Botermann et al. (2014, ref. 54) define ε = ν_aν_p/(ν₁ν₂) − 1 = α̂β² for this observable, so the script's conversion (±3.4×10⁻¹⁰) is consistent and no change was made. ### M57. Timeline: predictions against improving measurements - **Paper section:** §10 (Appendix C.7, C.12) - **Aspden's claim:** 1/α = 137.035915 (1972); mp/mₑ = 1836.15232 (1975); G = 6.6722 (date not stated); (mₙ − mₚ)/mₑ = 2.5309419 (1986). - **What was tested:** Each value against the measurements of 1973, 1986 and today. - **Steps:** 1. 1/α: 1973 137.03604(11) → −1.1σ; 1986 137.0359895(61) → −12σ; today → "about −3,800σ" (text). 2. mp/mₑ: 1973 1836.15152(70) → +1.1σ; 1986 1836.152701(37) → −10σ; today → about −11,000σ. 3. G: 1973 6.6720(41) → +0.04σ; 1986 6.67259(85) → −0.5σ; today → −14σ. 4. (mₙ − mₚ)/mₑ: 1984 → −0.2σ; today → −63σ. - **Inputs:** CODATA 1973 (ref. 22); CODATA 1986 (ref. 23); today's values from Appendix B; 1984 n–p as M37. - **Script and output:** today's values from environment_constants.py and np_mass.py; the 1973 and 1986 comparisons are hand calculations in the text: - `1/alpha 137.0359148472 measured 137.035999177 -0.6154 ppm (-4.02e+3 sigma)` - `mp/me 1836.152316484 measured 1836.152673426 -0.1944 ppm (-1.12e+4 sigma)` - `1984 measurement (m_n-m_p)/m_e = 2.530947935 +/- 3.1e-5; Aspden 2.5309419: -2.38 ppm, -0.193 sigma` - `CODATA 2022 (m_n-m_p)/m_e = 2.530988574 +/- 7.4e-7; Aspden 2.5309419: -18.4 ppm, -63.1 sigma` - **Result:** Each value agreed when published and failed as precision improved. The proton measurement moved toward his value after 1975. Register check: the "today" figure for 1/α is −4,020σ (script) or −4,008σ (using 137.035915), not −3,800σ. The other 1973 and 1986 σ values check out (−1.14, −12.2, +1.14, −10.3, +0.04 with 6.67216, −0.51). - **Corrected in v1.9:** now "about −4,000σ". - **Verdict:** Excluded today. The pattern is the usual signature of a formula fitted at the precision of its time. - **Assumptions you could challenge:** - Which of his G values is "6.6722", and when it was published, is not stated. His 1966 value (6.6676, M28) would sit at about −1σ against 1973. - The 1972 dating of 137.035915 comes from secondary sources; §14 lists the 1972 paper as not yet read. ### M58. Chance of the α agreement - **Paper section:** §11.1–11.2 (Appendix C.6) - **Aspden's claim:** None (analysis's probability estimate). - **What was tested:** How often a toolkit like his would put 1/α within 0.615 ppm by chance. - **Steps:** 1. Grid hit: odd-N values are spaced 181 ppm, so landing within ±0.615 ppm of a random point on the grid: 2 × 0.615 / 181 = 0.0068. 2. Multiply by 4 rounding rules and by n × 181 ppm / ln 10 for n structural variants (n = 65 or 650). 3. p = 1.39×10⁻⁴ (65 variants) to 1.39×10⁻³ (650 variants): 1 in 7,200 to 1 in 720. - **Inputs:** his miss 0.615 ppm (M13). - **Script and output:** coincidence.py: - `[3] alpha: grid hit 0.0068; p(alpha) = 1.39e-04 (65 variants) to 1.39e-03 (650 variants)` - **Result:** 1 in 7,200 to 1 in 720. - **Corrected in v1.9:** §11.1 now states the one-decade assumption and the independence assumption as open to challenge. - **Verdict:** Open. The figure depends on counts that cannot be recovered from his work. - **Assumptions you could challenge:** - The numbers 65 and 650 and the 4 rounding rules: the paper does not justify them. - The script divides by ln 10, i.e. it assumes the target could lie anywhere within one decade of values. The paper does not state this. A wider assumed range would lower p in proportion. Untested. - Register note: in this construction the 181 ppm spacing cancels; p equals (variants × rules × 1.23 ppm) / ln 10, the same "count over range" logic as the other global estimates. ### M59. Chance of the proton/electron agreement - **Paper section:** §11.2 (Appendix C.6) - **Aspden's claim:** None. - **What was tested:** How many lattice-style formulas land within 0.194 ppm of mp/mₑ by chance. - **Steps:** 1. Family: prefactors 2ⁱ3ʲ (up to 2×10⁶), π^(−3…3), 1843^(b/6) for b = −12…12, 17 Thomson-cluster factors: 464,100 formulas. 2. Expected hits: global (distinct values spread over their full log range) 0.0026; local (density within ±1% of the target) 0.0055. 3. p = 1 − e^(−expected): 1 in 380 (global) to 1 in 180 (local). - **Inputs:** mp/mₑ CODATA 2022 (Appendix B). - **Script and output:** coincidence.py: - `[1] proton/electron ratio: 464,100 formulas, Aspden error 0.194 ppm` - `expected chance hits: global 0.0026, local 0.0055` - **Result:** 1 in 380 to 1 in 180. - **Verdict:** Open. - **Assumptions you could challenge:** - The family's make-up (which prefactors, powers and cluster factors). Untested. - The ±1% local window; other constants use ±0.01% (deuteron) and ±0.5% (G). - The null model: the measured value is unrelated to the toolkit. ### M60. Chance of the deuteron agreement - **Paper section:** §11.2 (Appendix C.6) - **Aspden's claim:** None. - **What was tested:** How many combinations of his chain states and weights land within 0.328 ppm of μd. - **Steps:** 1. Family: straight chains of two protons (Thomson radius 1/R) and 0–4 leptons, no two protons adjacent; choose two charged chains (for A and C) and one neutral chain (for B), with weights 1–4 each: 7,680 combinations. 2. Best error in the family: 0.328 ppm (his refined model). 3. Expected hits: global 0.0035; local (±0.01% window) 0.6885. 4. 1 in 290 (global) to 1 in 2 (local). - **Inputs:** μd CODATA 2014 (Appendix B). - **Script and output:** coincidence.py: - `[2] deuteron moment (refined): 7,680 combinations, best error 0.328 ppm` - `expected chance hits: global 0.0035, local 0.6885` - **Result:** 1 in 290 to 1 in 2. - **Verdict:** Open. The answer depends on whether the closeness of 6/7 to the target counts as part of the hit. - **Assumptions you could challenge:** - Global vs local: the paper says the local estimate takes the 6/7 pile-up as given. - The family is built with the refined proton radius, which was itself chosen after seeing that it helped (§8). ### M61. Chance of the G agreement with 2 mₑ - **Paper section:** §11.1–11.2 (Appendix C.6) - **Aspden's claim:** None. - **What was tested:** How many chain variants land within 34 ppm (or 150 ppm) of CODATA G. - **Steps:** 1. Family: 29 taon forms (3^(7/12)·P, 2P(√6 − 3/2) with no cluster, 22 lattice clusters, 5 further cluster ideas: 1.999264, 1.952665, 2.15625, 2.0, 4.0) × graviton built from 1–4 taons: 116 variants. 2. Error of the 2 mₑ variant: 33.5 ppm. 3. Expected hits: global at 34 ppm 0.0076; global at 150 ppm (spread between labs) 0.0338; local (±0.5%) 0.195. 4. 1 in 130; 1 in 30; 1 in 6. - **Inputs:** CODATA G (Appendix B). - **Script and output:** coincidence.py: - `[4] G with 2 m_e: 116 chain variants (all ideas tried), error 33.5 ppm` - `expected chance hits: global 0.0076 (34 ppm); global 0.0338 (150 ppm lab spread); local 0.195` - **Result:** 1 in 130 (global, 34 ppm), 1 in 30 (global, 150 ppm), 1 in 6 (local). - **Corrected in v1.9:** the test family is now described as 116 cluster and chain variants, excluding the non-cluster ideas of §7.4. - **Verdict:** Open. - **Assumptions you could challenge:** - "Including every idea tried" (§11.2 table): the family leaves out the §7.4 variants that are not clusters (k = 1/2, 3/5 and tuned k; N = 1842.993; the composite-rule factor 2.99962). §11.1's narrower "every cluster idea" is accurate. - The global range is set by the 1-, 3- and 4-taon variants (G of about 3.5 to 9.7, M26), which spread the log range and lower the global estimate. The local estimate avoids this. The effect of dropping them is untested. - Ideas not written down are not counted (the paper says so in §11.4). ### M62. Joint chance of all four, and the career correction - **Paper section:** §11.3–11.4 (Appendix C.6) - **Aspden's claim:** None. - **What was tested:** The chance that one wrong toolkit matches α, the proton ratio, the deuteron moment and G this closely, with corrections for combining tests and for unpublished failures. - **Steps:** 1. Strict (fewest variants, global): 1.39×10⁻⁴, 2.65×10⁻³, 3.47×10⁻³, 7.54×10⁻³. 2. Central (geometric-mean α, local proton, geometric-mean deuteron, G at 150 ppm): 4.39×10⁻⁴, 5.49×10⁻³, 4.16×10⁻², 3.33×10⁻². 3. Generous (most variants, 10 target particles for the proton, local deuteron and G): 1.39×10⁻³, 5.49×10⁻², 0.498, 0.177. 4. Product; Fisher's combination of four p-values; and the order-statistics probability that among M = 10 or 30 attempted constants at least four beat these thresholds. 5. Central, M = 30: 5.34×10⁻⁴, about 1 in 1,900 ("about 1 in 2,000"). Range over scenarios at M = 30: 1 in 31 to 1 in 430,000. - **Inputs:** M58–M61. - **Script and output:** coincidence.py: - `strict 1.39e-04 2.65e-03 3.47e-03 7.54e-03 | 9.61e-12 2.95e-08 1.94e-08 2.30e-06` - `central 4.39e-04 5.49e-03 4.16e-02 3.33e-02 | 3.33e-09 4.83e-06 7.04e-06 5.34e-04` - `generous 1.39e-03 5.49e-02 4.98e-01 1.77e-01 | 6.71e-06 2.45e-03 3.95e-03 3.24e-02` - **Result:** Every figure in the §11.3 table matches the output after rounding. Best single figure about 1 in 2,000; full range about 1 in 30 to 1 in 430,000. - **Corrected in v1.9:** §11.1 now states that the four chances are combined as if independent, although they share 1843 and the lattice. §11.4 adds a caution from the companion paper: the α mechanism neglects effects of 10–30%. - **Verdict:** Open. Suggestive, not decisive; the paper says this and gives an out-of-sample test (§11.4) that has not been run. - **Assumptions you could challenge:** - Independence: the product and Fisher's method treat the four p-values as independent. All four use the same toolkit and N = 1843, and G's chain is built on the proton. The paper does not discuss this. Untested. - Two of the four were improved during the investigation (G and the deuteron), with the target known (§11.4). - M = 10 and M = 30 attempted constants are assumptions; the paper says the true number cannot be recovered. - The choice of mixing global and local estimates in the central scenario. ### M63. Other first-principles formulas for α - **Paper section:** §12 - **Aspden's claim:** Aspden (1972): 1/α = 108π(8/1843)^(1/6) = 137.0359148, for comparison. - **What was tested:** How other simple formulas for α compare with the measured value. - **Steps:** 1. Eddington (1929): 136, later 137. Integer values excluded. 2. Wyler (1969–71): α = (9/8π⁴)(π⁵/2⁴5!)^(1/4) → 137.0360824, +0.61 ppm. 3. Rosen (1976): α = 4π/(42·41) → 137.0324, −26 ppm. 4. Aspden: −0.62 ppm. - **Inputs:** 1/α CODATA 2022 (Appendix B); historical review arXiv:1411.4673 (ref. 28). - **Script and output:** no script (hand calculation in the text). Register check: evaluating Wyler's and Rosen's expressions gives 137.0361 and 137.0324, consistent with the table. - **Result:** Wyler and Aspden miss by the same amount in opposite directions. - **Verdict:** Excluded, as exact formulas. The comparison illustrates how easily simple formulas reach the ppm level. - **Assumptions you could challenge:** - These formulas were chosen as examples; no count of such attempts is made. ### M64. Out-of-sample test of the doubled electron - **Paper section:** §7.6 (Appendix C.15) - **Aspden's claim:** the in-line three-charge factor 1.875 (3 − ¾ − ¾ + ⅜) in three derivations: - the G chain (Tutorial Note 9); - the 1976 "upsilon" as (g∗:g∗:g∗) = 1.875 × 3259 MeV (1986j, *Hadronic J.* 9, 153, p. 154); - the muon lifetime (*The Physics of Creation*, 2003, ch. 3). - **What was tested:** the rule written in §7.5 before the test: replace 1.875 by 2 everywhere outside the G chain, change nothing else, and see whether the results improve. - **Steps:** 1. **Census.** All 719 site texts were searched for 1.875 and 15/8 before computing anything. Three in-line triplet uses were found (G, 1986j, 2003 muon); two other matches are unrelated series coefficients. 2. **G (in-sample).** 1.875 gives 6.672161 (−320 ppm); 2 gives 6.674076 (−34 ppm). Excluded from the score because 2 was chosen here. 3. **1986j.** 1.875 × 3259 = 6110.6 MeV; 2 × 3259 = 6518.0 MeV. His target, the 6 GeV peak of Hom et al. (1976), was withdrawn after the same experiment's 1977 data; the real upsilon is 9460.4 MeV. Not testable. 4. **Muon lifetime with 1.875.** Triplet energy 2.70422; threshold n = 17; shed 0.29578; separated form 3.24506; two quanta per separated form, so 17:8; lifetime 2.19908 μs (+0.095%). This reproduces his printed 2.199. 5. **Muon lifetime with 2.** Triplet energy 2.8845; threshold n = 17; shed 0.1155; four quanta per separated form, so 17:4; lifetime 3.69445 μs (+68%). 6. **Effect on the joint chance (§11).** Central scenario, 30 constants: about 1 in 1,869 with G, about 1 in 802 without it. - **Inputs:** PDG muon mean life 2.1969811(22) μs; CODATA 2022 G; Hom et al. 1976 and its withdrawal; PDG Υ(1S) 9460.40 MeV. - **Script and output:** out_of_sample.py: - ` 6 1.875 (his): lifetime ((n+m)/m) x base (microseconds); vs PDG 2.1969811 2.19908 0.09534 %` - ` 6 2 (replacement): lifetime ((n+m)/m) x base (microseconds); vs PDG 2.1969811 3.69445 68.16 %` - ` 2 central scenario, G left out (treated as unsupported): career M = 30 1 in 802` - **Result:** of two out-of-sample uses, none improved, one got much worse and one could not be tested. - **Verdict:** Disagrees. The doubled electron is a one-off fit to G, not a correction supported elsewhere in his framework. - **Assumptions you could challenge:** - **The literal rule.** Every 1.875 becomes 2, and the separated muon form ((3 − ¾)∛3) is left unchanged because it is not a 1.875 cluster. - **The reading of his muon argument.** It is informal ("somewhat complicated", in his words). The rebuild reproduces his 17:8 and 2.199 μs exactly, which supports the reading. Any reading in which separation is paid for out of the shed energy gives fewer separated forms when the shed energy falls, and so a longer lifetime. - **The 1986e paper.** Its in-line three-charge systems have unequal energies and were left out. Extending the rule to them would add a new free choice. --- ## Part B. Tests in Part 1, the smallest units (U01–U41) ### U01. The orbit radius equals the zitterbewegung amplitude - **Paper section:** Part 1, §5, test U01 - **Aspden's claim:** "the continuum and q charge systems, the G and E frames … are displaced 2r one from the other owing to their relative motion at speed c in circular orbits of radius r given by r = h/4πmc" (POC 7.1). - **What was tested:** whether r is derived or put in, and how it compares with known quantum scales. - **Steps:** 1. r = ħ/(2mₑc) = 1.9307963 × 10⁻¹³ m. 2. The amplitude of the electron's zitterbewegung (trembling motion) in Dirac's theory is ħ/(2mₑc), the same expression. 3. The vacuum-polarization (Uehling) potential of quantum electrodynamics falls off as exp(−2mₑc x/ħ). Its range is ħ/(2mₑc), again the same. - **Inputs:** ħ, mₑ, c (CODATA 2022). - **Script and output:** `aether_units.py`, block of the same ID: `1 r = hbar/(2 m_e c) 1.9307963e-13 m` - **Result:** r is put in, not derived. It combines the electron's Compton frequency (I1a) with the postulate that the two frames move at c relative to each other (I1b, U41). It coincides exactly with two scales of established physics. - **Verdict:** Credited (correspondence). The correspondence is not evidence for the lattice: both known scales follow from the electron's mass alone, so any theory built on ħ/mₑc lands on them. - **Assumptions you could challenge:** whether Aspden derives r elsewhere. *Physics without Einstein* ch. 4 introduces it through a photon unit compensating an electron's motion (the Schrödinger-equation argument), which still takes mₑ as given. ### U02. The orbital frequency is the Compton frequency - **Paper section:** Part 1, §5, test U02 - **Aspden's claim:** the frames move at c/2 in circles of radius r (POC 7.1); the quon's "natural rhythmic motion at the Compton electron frequency" (Fifth Question, 2001). - **Steps:** 1. Ω = (c/2)/r = 7.7634407 × 10²⁰ rad/s. 2. ħΩ/mₑc² = 1.0 exactly. 3. Dirac's zitterbewegung frequency 2mₑc²/ħ is 2Ω. - **Script and output:** `aether_units.py`, block of the same ID: `2 hbar Omega / (m_e c^2) (= 1: the electron Compton angular frequency) 1.0` - **Verdict:** Consistent. Aspden's frequency is half Dirac's, because his speed is c/2 where Dirac's trembling speed is c. - **Assumptions you could challenge:** none in the arithmetic. The step that matters is U10, which shows this is also the vacuum's natural frequency. ### U03. Lattice spacing - **Paper section:** Part 1, §5, test U03 - **Aspden's claim:** d = 6.374 × 10⁻¹¹ cm (Fifth Question, 2001). d/a = 108π, where a is the electron's Thomson radius (POC ch. 2, 7.24–7.26). - **Steps:** 1. r/d = (3/4)(8/1843)^(1/6) = 0.3029158782. 2. d = r/(r/d) = 6.3740348 × 10⁻¹³ m. 3. d/a = 339.29222, against 108π = 339.29201. 4. d/r_e = 226.195 = 72π. - **Script and output:** `aether_units.py`, block of the same ID: `2 d = r/(r/d) 6.3740348e-13 m` - **Verdict:** Consistent. The 0.6 ppm difference in step 3 is the gap between his α and the measured one (U06). - **Assumptions you could challenge:** d depends on the integer rule through r/d. With the pure lattice value r/d = 0.3028738, d would be 0.014% larger. ### U04. The quon mass from the force balance - **Paper section:** Part 1, §5, test U04 - **Aspden's claim:** m₀(c/2r)²r = 4πσq(2r) (7.5), giving m₀c² = 32πσqr² (7.6) and m₀/mₑ = (4/9)(r/d)² (7.25). - **What was tested:** whether the three expressions agree when computed independently. - **Steps:** 1. Restoring force per unit displacement, SI form: k = σe/ε₀ with σ = e/d³. 2. m₀ from (7.5) is 0.04078132126 mₑ. 3. m₀ from (7.25) is 0.04078134634 mₑ. 4. Ratio 0.999999385. 5. m₀c² = 20.839 keV. - **Script and output:** `aether_units.py`, block of the same ID: `3 ratio (identity: should be 1) 0.999999385229` - **Verdict:** Credited. The 0.6 ppm gap is the α gap again. The main paper (§5.2) found and corrected a typo in the printed form of (7.5) in Tutorial Note 8. The POC form is correct. - **Assumptions you could challenge:** the force 4πσq per unit displacement is the field inside a uniformly charged medium (plasma-like). It treats the displacement as collective, so that all quons move together. That is the natural reading of a lattice moving as a frame. ### U05. The quon radius, the Thomson mass and N - **Paper section:** Part 1, §5, test U05 - **Aspden's claim:** E = 2q²/3b (7.2); the effective mass is half of E/c² (7.4); b/d = (d/r)²/96π (7.15); N = (9/8)³(d/r)⁶ (7.26), "approximately 1844.53" with r/d = 0.302874. - **Steps:** 1. b = d(d/r)²/96π = 2.3032933 × 10⁻¹⁴ m (b/d = 0.036136; POC rounds to 0.035). 2. m₀ from q²/3bc², divided by m₀ from (7.25): 0.999999385. 3. Quon Thomson energy: 41.678 keV, which is mₑc²/N^(1/3). 4. (b/a)³ with his r/d is 1843.0034, equal to 1843 by construction. 5. With the pure-lattice r/d: 1844.5379. 6. The mass factor f, where m₀c² = f × 2q²/3b, was varied, re-solving the zero-energy lattice and applying his integer rule each time: | Mass factor f | N before rule | Odd N | 1/α | vs measured | |---|---|---|---|---| | ½ (Aspden: buoyancy) | 1844.54 | 1843 | 137.0359148 | −0.6 ppm | | 1 (full Thomson mass) | 15,254 | 15,253 | 136.26294 | −5,641 ppm | | 5/4 (own mass plus a fluid added mass of half the displaced ½) | 30,583 | 30,583 | 135.66837 | −9,980 ppm | - **Script and output:** `aether_units.py`, block of the same ID: `6 (9/8)^3 (d/r)^6 with the pure-lattice r/d (POC: 1844.53) 1844.5379`; `7 f = 1 (full Thomson mass): … 15254.2 15253 136.262937 -5641.3 ppm` - **Verdict:** Credited (consistent). The halving of the mass (input I3) is an analogy, not a derivation, and it carries the result. - **Assumptions you could challenge:** - **The hydrodynamic factor ½.** In ideal-fluid hydrodynamics, buoyancy offsets weight, not inertia. A sphere accelerating through a fluid behaves as if heavier, its own mass plus half the mass of the fluid it displaces. Aspden's text notes this "apparent increase in mass", but it uses buoyancy to halve the mass. The direct hydrodynamic reading is the f = 5/4 row, which moves 1/α by 1%. Only f = ½ gives N near 1843. So I3 is the most consequential single assumption in the chain, and the same 1843 enters his proton and G derivations. - **The fluid's density.** The 5/4 row assumes the displaced "fluid" has half the quon's energy density, as his pressure-balance argument states (POC pp. 112–113). ### U06. The photon unit and Planck's constant - **Paper section:** Part 1, §5, test U06 - **Aspden's claim:** the 3×3×3 photon unit has moment of inertia 36m₀d² = 4hr/cπ (7.21, PWE 6.59), giving ħc/e² = 144π(r/d) (7.24). - **Steps:** 1. 36m₀d²/(4hr/cπ) = 1.0. 2. 144π × 0.30291588 = 137.035914847. 3. Measured 137.035999177(21). 4. Difference −0.615 ppm. - **Script and output:** `aether_units.py`, block of the same ID: `4 difference, ppm -0.6154 ppm` - **Verdict:** Credited for the algebra. The comparison with α is the main paper's test (§5; register M-entries), not repeated here. - **Assumptions you could challenge:** the four-fold radiation rule and "energy = Ω × angular momentum" (I5) are assumptions. The main paper checks the algebra, not the physics of these rules. ### U07. Number and mass density of the lattice - **Paper section:** Part 1, §5, test U07 - **Aspden's claim:** "3.87 × 10³⁰ lattice particles per cc … equivalent to … 144 gm/cc" (PWE p. 117). - **Steps:** 1. 1/d³ = 3.862 × 10³⁶ m⁻³ = 3.862 × 10³⁰ cm⁻³. 2. m₀/d³ = 143.5 g/cm³. - **Script and output:** `aether_units.py`, block of the same ID: `3 mass density m0/d^3 143.5 g/cm^3` - **Verdict:** Consistent. Aspden used this density in 1969 to explain Mercury's perihelion. That mechanism is excluded (main paper §9.2). - **Assumptions you could challenge:** none in the arithmetic. ### U08. The cell energy and the "virtual muon pair" - **Paper section:** Part 1, §5, test U08 - **Aspden's claim:** E₀ = 412.6658 mₑc², "the energy quantum that is regarded as the virtual muon pair, the occupants of each cubic cell of aether" (POC 7.29). In 1980: "very close to the energy of two muons … it is tempting to suggest" (PU 160). - **Steps:** 1. E₀ from (7.29) = 412.6658162 mₑc² (210.87 MeV). 2. E₀ from (7.3), using b and d from U03 and U05, divided by step 1: 0.99999939. 3. Two muon masses: 413.5365654 mₑ. 4. E₀/2m_μ − 1 = −2106 ppm. - **Inputs:** m_μ/mₑ = 206.7682827(46) (CODATA 2022). - **Script and output:** `aether_units.py`, block of the same ID: `4 E0 / (2 m_mu) - 1, ppm -2105.6 ppm` - **Verdict:** Disagrees, if read as two real muons: 0.21% low, against a muon mass known to 22 parts per billion. Aspden presents it as an approximate identification. In 2003 he flags the "approximation" himself and answers "or rather hoping" that the muons' interaction energy makes up the difference (POC p. 112). - **Assumptions you could challenge:** the proton-mass derivation (main paper §6) uses E₀ itself, not the muon mass. So the 0.19 ppm proton result does not depend on this identification. ### U09. The energy density of the aether - **Paper section:** Part 1, §5, test U09 - **Aspden's claim:** E₀ per cell is "the energy density of the aether, on average" (POC 7.3). It is balanced by "a negative interaction energy that exactly matches the positive energy of the quon and its equal measure of associated graviton energy" (POC p. 112). - **Steps:** 1. E₀/d³ = 1.305 × 10²⁶ J/m³. 2. Observed dark-energy density Ω_Λ·3H₀²c²/8πG = 5.25 × 10⁻¹⁰ J/m³. 3. Ratio 2.5 × 10³⁵. - **Inputs:** H₀ = 67.4 km/s/Mpc, Ω_Λ = 0.6847 (Planck 2018); G (CODATA 2022). - **Script and output:** `aether_units.py`, block of the same ID: `3 ratio 2.48e+35` - **Verdict:** Open. Mainstream physics has the same kind of problem. A vacuum energy at the strong-interaction scale is about 3 × 10³⁴ J/m³, comparable to Aspden's, and the full quantum estimate is vastly larger; no accepted mechanism cancels it. Aspden's cancellation is stated as a hope, not derived. - **Assumptions you could challenge:** whether this energy gravitates in his theory at all. His gravity comes from gravitons displacing the continuum (main paper §7), so he could argue the cell energy is not a source of gravity. That argument is not made in the texts examined. ### U10. The natural frequency of the quon system is the Compton frequency - **Paper section:** Part 1, §5, test U10 - **Aspden's claim:** "the ether sets a critical frequency threshold (the Compton electron frequency) and so may have an electrical structure conforming with this resonant frequency … in proposing a kind of crystal structure for the vacuum medium and establishing … that it has a natural frequency … one is led directly into the question of frequency dispersion" (*Wireless World*, 1982; Lecture 24). - **What was tested:** whether his own units give that natural frequency without further assumptions. - **Steps:** 1. Both frames orbit with radius r about their common centre, so their inertias per cell are equal (M_G = m₀). 2. The relative displacement X obeys X'' = −k(1/m₀ + 1/M_G)X, with k = σe/ε₀ (U04). 3. A circular orbit under a linear restoring force is itself the free oscillation, so its frequency is the natural frequency: √(2k/m₀)/Ω = 0.9999997. 4. ħ × natural frequency = 510.999 keV. 5. If the continuum did not move (infinite M_G), it would be 361.3 keV. - **Script and output:** `aether_units.py`, block of the same ID: `2 hbar x natural frequency 510.99879 keV` - **Verdict:** Consistent. Aspden says so himself, and his units give exactly mₑc². This is the plasma frequency of the two frames (U33). - **Assumptions you could challenge:** the equal-inertia step. It follows from his description of two frames circling a common centre with equal radii. If the G frame were much heavier, the resonance would move to 361 keV, which does not change any conclusion below. ### U11. The static polarization of the lattice equals the vacuum's - **Paper section:** Part 1, §5, test U11 - **Aspden's claim:** displacement currents in the vacuum are displacements of the quon lattice (POC ch. 6). Electromagnetic waves are "oscillations of the quon lattice system". - **Steps:** 1. A static field E displaces the frames by X = eE/k. 2. The polarization is P = neX = ne²E/k, and with k = ne²/ε₀ this is P = ε₀E exactly. 3. The same holds for any ratio of the two inertias (script: M_G = 10m₀ gives 1.0). - **Script and output:** `aether_units.py`, block of the same ID: `1 static P / (eps0 E) (=1: quon displacement alone gives exactly the vacuum D = eps0 E) 1.0` - **Verdict:** Withdrawn as a credit (version 1.3). The restoring force k used here is the field of the displaced lattice itself (Part 1A, section 4). So "P = ε₀E" means the lattice's own field cancels the applied field inside it. That is complete screening, as in a metal, not a vacuum (U36). - **Assumptions you could challenge:** this is a general property of any charge lattice in a neutralizing continuum, whatever its spacing. It shows consistency, not evidence for these particular values. ### U12. Aspden's resonance picture: dispersion below 511 keV and no light above it - **Paper section:** Part 1, §5, test U12 - **Aspden's claim:** none. This is the consequence of U10 and U11 that his 1982 article set out to avoid. In his words, "the major problem confronting aether theory, namely the issue of its non-dispersion property" (1982a commentary). - **What was tested:** how light would travel if the quons alone carried the displacement current, in two readings. - **Reading B:** the quons are the whole displacement field, so ε_r(ω) = Ω²/(Ω² − ω²). - **Reading A:** a bare vacuum plus the quons, ε_r = 1 + Ω²/(Ω² − ω²), with the bare speed set so that radio waves still travel at c. - **Steps:** 1. Reading B, group velocity v_g = c(1 − ω²/Ω²)^(3/2): | Photon energy | 1 − v_g/c | |---|---| | 2 eV (visible light) | 2.3 × 10⁻¹¹ | | 1 keV | 5.7 × 10⁻⁶ | | 10 keV | 5.7 × 10⁻⁴ | | 100 keV | 0.057 | | 300 keV | 0.47 | 2. Reading B: above 511.0 keV, ε_r < 0, so no wave propagates. A 661.7 keV gamma ray would decay within 2.5 × 10⁻¹³ m. 3. Reading A: no wave propagates between 511.0 and 722.7 keV (6.1 × 10⁻¹³ m decay length at 661.7 keV). Above that band light travels faster than c, reaching √2 c = 1.414c at GeV energies. - **Script and output:** `aether_units.py`, block of the same ID: `B reading B: eps_r < 0 (no propagating wave) for every photon energy above 510.999 keV`; `A reading A, photon 6.0e+6 keV: v_group/c 1.414214` - **Verdict:** this is the prediction of Aspden's 1982 resonance picture, in which each quon has its own spring of frequency Ω. U13–U14 compare it with data. Version 1.3 note: the lattice he describes has no such spring (Part 1A, section 4). Its self-consistent response is a plasma (U34), which fails at all energies below 511 keV instead. - **Assumptions you could challenge:** - **The wave's magnetic force.** The quons move at c/2, so the wave's magnetic force on them is comparable to the electric force. It does not enter here: the quon and its continuum charge have opposite charges and opposite velocities, so the magnetic forces on them are equal. They move the pair together, not apart, and so do not polarize the lattice. - **Resonance damping.** Damping is ignored. It would broaden the resonance without removing it. ### U13. Gamma rays above 511 keV travel, and at the speed c - **Paper section:** Part 1, §5, test U13 - **Aspden's claim:** above "the frequency at which electron-positron pair creation occurs … there is no counter-displacement" (Lecture 24, 1982 article). So above that frequency his remedy is absent by his own account, and the single-displacement response of U12 applies. - **Steps:** 1. **Propagation.** - Caesium-137 (661.7 keV) and cobalt-60 (1173 and 1332 keV) gamma rays cross metres of air and vacuum in every gamma-spectroscopy laboratory. - INTEGRAL detected the 847 and 1238 keV cobalt-56 lines from supernova SN 2014J in M82, just over 10 million light-years away. - Reading B forbids all of these; reading A forbids the 662 keV line, which lies inside its 511–723 keV stop band. 2. **Speed.** Alväger et al. (1964) timed gamma rays above 6 GeV from decaying neutral pions at c′ = (2.9977 ± 0.0004) × 10⁸ m/s, that is 0.999925c. Reading A predicts 1.414c, excluded by 3,105σ. - **Inputs:** Churazov et al., *Nature* 512, 406 (2014); MPA press release (distance); Alväger, Farley, Kjellman and Wallin, *Phys. Lett.* 12, 260 (1964). - **Script and output:** `aether_units.py`, block of the same ID: `3 reading A excluded by (sigma) 3105.0 sigma` - **Verdict:** Excluded, for both readings of the resonance picture. (The self-consistent plasma model of U34 lets these gamma rays through, slowly, but blocks everything below 511 keV.) - **Assumptions you could challenge:** - **Pair-creation threshold.** Aspden's "pair creation frequency" may mean mₑc² or 2mₑc² (1.022 MeV). Either way, the cobalt and GeV results lie above it. - **The 511 keV line is not used.** The Galactic annihilation line (Siegert et al., *A&A* 586, A84, 2016) sits at the resonance, but light just below it is slowed rather than stopped. A steady source would still be seen, so the line does not discriminate. ### U14. GRB 090510: the same arrival time from keV to 31 GeV after 7.5 billion years - **Paper section:** Part 1, §5, test U14 - **Aspden's claim:** below the limit frequency the vacuum "adapts to any frequency and exhibits the properties of a tuned LC system … the local vacuum resonates at the optimum frequency set by these displacements. In this way the signal frequency is preserved over vast distances" (Lecture 24). - **What was tested:** first, how far the simple lattice (U12) misses this burst; second, whether his tuned-vacuum remedy can be tested at all. - **Steps:** 1. The light-travel time to z = 0.903 (Planck 2018 flat ΛCDM) is 7.535 billion years. 2. Fermi detected a 31 GeV photon 0.829 s after the burst began. Abdo et al. limit the delay between it and the low-energy (keV–MeV) emission to |Δt| < 0.859 s. 3. So |Δv|/c ≲ 0.859 s ÷ 7.535 Gyr = 3.6 × 10⁻¹⁸. This is approximate; dedicated analyses weight the distance by (1 + z). 4. Reading B: v(10 keV) − v(300 keV) = 0.47c. The arrivals would spread over 3.5 billion years, about 10¹⁷ times the limit, and the 31 GeV photon could not travel at all. 5. Reading A: v(10 keV) − v(31 GeV) = 0.41c, about 2 × 10¹⁷ times the limit. 6. Aspden's tuned vacuum gives no equation from which a delay can be computed. His description makes the vacuum at each point tune to the frequency of the signal passing through it. The burst sent photons from about 10 keV to 31 GeV through the same space at the same time, as ordinary starlight sends all its colours, so a single local tuning cannot serve them all. A response that depends on the signal is also a nonlinear one, under which crossing beams would interact. - **Inputs:** Abdo et al., *Nature* 462, 331 (2009); Planck 2018 cosmology (H₀ = 67.4, Ω_m = 0.315). - **Script and output:** `aether_units.py`, block of the same ID: `5 excess over the limit 1.3e+17`; `7 excess over the limit 2.05e+17` - **Verdict:** Excluded for the simple lattice. Open but unsupported for the 1982 remedy: no equations are given, and its central idea conflicts with light of many frequencies sharing the same space. - **Assumptions you could challenge:** - The distance measure; using the (1 + z)-weighted distance changes the limit by less than a factor of 2. - Whether a full mathematical version of the dual-displacement idea could avoid superposition problems. None exists in the texts examined. This is the place where a defender of the theory would need to supply one. ### U15. What the scale would have to be - **Paper section:** Part 1, §5, test U15 - **What was tested:** how high the vacuum resonance would have to sit for an oscillator-type vacuum to pass GRB 090510, and what that would do to his units. - **Steps:** 1. Well below resonance, 1 − v_g/c ≈ (3/2)(E/E_res)². Requiring this to be under 3.6 × 10⁻¹⁸ at 31 GeV gives E_res > 2.0 × 10¹⁰ GeV. 2. That is 3.9 × 10¹³ times mₑc². 3. Since Ω = c/2r, the orbit radius would have to be below 4.9 × 10⁻²⁷ m. 4. But r = ħ/2mₑc is what ties the lattice to the electron (I1). It also fixes m₀, b, N and E₀ in electron units. - **Script and output:** `aether_units.py`, block of the same ID: `3 in electron rest energies (Aspden: exactly 1) 3.91e+13` - **Verdict:** Excluded as a repair. Because α and h depend only on r/d, a smaller lattice could keep them. But the electron would then have to be about 4 × 10¹³ times heavier than it is. For the self-consistent plasma model, the requirement is far stronger: ħΩ below the photon-mass limit of 10⁻¹⁸ eV (U35). - **Assumptions you could challenge:** the quadratic form assumes an oscillator-like response. A non-oscillator response (U14 step 6) is not covered by this bound. ### U16. Lattice discreteness - **Paper section:** Part 1, §5, test U16 - **Aspden's claim:** the photon "will emerge as the largest symmetrical unit of that lattice structure", and electromagnetic waves are lattice oscillations (POC 7; ch. 6). - **Steps:** 1. A lattice of spacing d carries no wave shorter than 2d = 1.275 × 10⁻¹² m. That is a photon of 0.97 MeV. 2. The highest nearest-neighbour lattice frequency is ħ·2c/d = 0.62 MeV. 3. LHAASO detects photons up to 1.4 PeV (wavelength 8.9 × 10⁻²² m), 1.4 × 10⁹ times shorter than 2d. 4. Below the cutoff, a cubic lattice slows short waves by about (kd)²/24: | Light | Speed deficit (kd)²/24 | Direction difference, [100] vs [111], (kd)²/36 | |---|---|---| | 500 nm (visible) | 2.7 × 10⁻¹² | 1.8 × 10⁻¹² | | 10 keV X-ray | 4.4 × 10⁻⁵ | 2.9 × 10⁻⁵ | | 100 keV gamma | 4.4 × 10⁻³ | 2.9 × 10⁻³ | - **Inputs:** Cao et al. (LHAASO), *Nature* 594, 33 (2021). - **Script and output:** `aether_units.py`, block of the same ID: `5 2d / that wavelength 1.44e+9` - **Verdict:** Excluded, unless high-energy photons are something other than lattice waves. The one passage found on this point asks whether "those high energy gamma rays are really nothing other than references to energy transactions involving the aether" (Fifth Question, 2001), which does not say how they travel. - **Assumptions you could challenge:** - The (kd)²/24 form assumes nearest-neighbour coupling; long-range Coulomb coupling changes the coefficient but not the cutoff. - The visible-light direction effect (about 10⁻¹² at 500 nm, with four-fold symmetry under rotation) has not been compared here with the rotating-cavity experiments. Those are usually analysed for two-fold signals, and checking this is listed as an open lead. ### U17. Semiconductor light holes as evidence for the quon mass - **Paper section:** Part 1, §5, test U17 - **Aspden's claim:** the quon "has an effective mass 0.04078 times that of the electron. It is debatable whether the effective mass of positive holes in semi-conductors may in some way reflect the transitional states of electrons and sub-electrons … Experiments on p-type germanium crystals have given effective masses m* of positive holes as m*/m = 0.04 and m*/m = 0.3" (Lecture 1 appendix, citing Ehrenberg). - **Steps:** light-hole masses compared with his 0.04078: | Crystal | Light hole (mₑ) | Ratio to 0.04078 | Source | |---|---|---|---| | InSb | 0.015 | 0.37 | Ioffe | | Ge | 0.043 | 1.05 | Ioffe | | Ge | 0.044 | 1.08 | Van Zeghbroeck | | GaAs | 0.082 | 2.01 | Van Zeghbroeck | | Si | 0.16 | 3.92 | Van Zeghbroeck | The spread is a factor of 10.7. - **Inputs:** Ioffe Institute semiconductor database (Ge, InSb); B. Van Zeghbroeck, *Principles of Semiconductor Devices* (Ge, Si, GaAs). - **Script and output:** `aether_units.py`, block of the same ID: `2 spread of light-hole masses across these crystals (max/min) 10.7` - **Verdict:** Not supported. Light-hole masses follow each crystal's band structure (k·p theory ties them to the band gap at the zone centre), so a universal aether particle cannot set them. Germanium's match is one point inside a tenfold spread. Aspden himself called the link "debatable". - **Assumptions you could challenge:** the comparison uses room-temperature band-edge masses. Light-hole masses also vary with temperature, strain and direction (band warping), which only widens the spread. ### U18. The 1969 version of the lattice - **Paper section:** Part 1, §5, test U18 - **Aspden's claim:** r/d = 0.30292 after a correction y = 0.000456 e²/d, "introduce[d] … at this stage without proof" (PWE 6.57–6.58). It is derived later in the chapter from one electron paired with each graviton, 5,063 lattice particles per electron, and energy ½m₀(c/2)² doubled for the G frame (6.74–6.75). 1/α = 137.038, "exactly the value measured" (6.61). - **Steps:** 1. y = 2(m₀c²/8)/5063 in units of e²/d = 0.0004555 (printed 0.000456). 2. 144π × 0.30292 = 137.03778. 3. Rounding r/d to five digits allows ±16.5 ppm. 4. The July 1969 adjustment gave 1/α = 137.03602(21). Aspden's value is 12.8 ppm above it, inside his rounding. - **Inputs:** CODATA 1969 value as tabulated in the Wikipedia article "Fine-structure constant" (historical values table). - **Script and output:** `aether_units.py`, block of the same ID: `1 y = 2 (m0 c^2/8)/5063 in units of e^2/d (PWE prints 0.000456) 0.0004555` - **Verdict:** Consistent at the precision he printed. The correction is reproducible from his description. It ties α to the graviton mass (5,063 mₑ, the same number that sets his G). The 1980 integer rule replaced it, so his α derivation was changed after 1969 by swapping one small correction for another. - **Assumptions you could challenge:** - The sixth digit of 137.038 is not reproducible from the five printed digits of r/d. - The measured value he compared with in 1969 has not been identified. The pre-1969 accepted value is not checked here. ### U19. The 2003 k term - **Paper section:** Part 1, §5, test U19 - **Aspden's claim:** the finite-size term carries a factor (1 − 2/3k), where kb is the mean distance to which the continuum charge displaced by a quon moves (7.17–7.18). "This is when r/d has the value 0.302916 and k is 8.34" (POC p. 109). - **Steps:** 1. Let F = 1 − 2/3k be the factor on the finite-size term. The F at which the zero-energy r/d equals the N = 1843 value is 0.920134 with his printed lattice sum 2.31368, giving k = 8.347 (his 8.34). With the exact sum 2.3136987 it is 0.922413, giving k = 8.593. 2. If the displaced charge stays within its cell (kb ≤ d/2), then k ≤ d/2b = 13.84 (F ≤ 0.952). 3. So any k from about 8.4–8.6 up to 13.8 keeps N = 1843 and leaves 1/α at 137.035915. - **Script and output:** `aether_units.py`, block of the same ID: `2 k at that point (Aspden's 2.31368; POC: 8.34) 8.347` - **Verdict:** Credited (reproduced and consistent). The term was absent in 1980. It adds a parameter, but over a range wide enough not to affect the result. It ties in with the main paper's finding that the finite-size coefficient must lie in a narrow window (§5.3): k values near 8.5 sit at that window's lower edge. - **Assumptions you could challenge:** the k term is a physical correction added in 2003. It is needed only if the continuum yields to compression, as Aspden notes, offering a third alternative (POC p. 113). ### U20. The 0.6 ppm is one number - **Paper section:** Part 1, §6, test U20 - **Aspden's claim:** 1/α = 108π(8/N)^(1/6) = 137.035915 with N = 1843 (PU 157; POC 7.24–7.26). - **What was tested:** whether the small mismatches seen in U03–U08 are separate errors or one. - **Steps:** 1. His 1/α divided by the measured 1/α is 0.999999384616, that is −0.615 ppm. 2. The quon mass from the force balance, using the measured e², divided by the quon mass from (7.25), is 0.999999385229: the same −0.615 ppm (U04). 3. Repeating step 2 with the e² that his own α implies (q² = αħc with his α) gives exactly 1. 4. The same holds for b from (7.4) against (7.15) and for E₀ from (7.3) against (7.29): exactly 1 with his α. - **Script and output:** `aether_units.py`, block of the same ID: `3 m0 (force balance, his alpha) / m0 (7.25) 1.0` - **Result:** every relation among his units is exact. The 0.6 ppm appears wherever the measured electron charge meets his lattice ratio r/d. It is a single number: the difference between his α and the measured α. - **Verdict:** Credited (internally exact). The question becomes why his α is 0.615 ppm low. - **Assumptions you could challenge:** none in the arithmetic. The measured value used is CODATA 2022, 1/α = 137.035999177(21). The atom-recoil values (Rb 2020, Cs 2018) move the gap by less than 0.002 ppm. ### U21. His printed figures - **Paper section:** Part 1, §6, test U21 - **What was tested:** whether any arithmetic or transcription error in his published numbers explains the gap. - **Steps:** | Quantity | Aspden printed | Recomputed | |---|---|---| | N with r/d = 0.302874 | "approximately 1844.53" (POC p. 108) | 1844.53 | | 1/α = 108π(8/1843)^(1/6) | 137.035915 (PU 157) | 137.0359148 | | E₀ = (3/4π)(108π)³ 1843^(−4/3) mₑc² | 412.665816 (PU 160) | 412.6658162 | | Lattice term in (7.18) | 2.31368 (hand sum) | 2.3136987 (exact Ewald sum; main paper §5.2) | | b/d | 0.035 (POC p. 109) | 0.036136 | | kb for k = 8.34 | "more than 0.29d" | 0.301d | - **Script and output:** `aether_units.py`, block of the same ID: `5 1/alpha with his hand sum and with the exact sum, after the integer rule 137.0359148` - **Result:** every figure reproduces. His hand lattice sum is 1.9 × 10⁻⁵ below the exact value, and his b/d is rounded, but neither changes the final α, because the integer rule absorbs them. - **Verdict:** Credited. No slip in his figures causes the gap. ### U22. What a correction would have to do - **Paper section:** Part 1, §6, test U22 - **What was tested:** which parts of the derivation can move the final α, and by how much they would have to move. - **Steps:** 1. Under the integer rule the final value is 1/α = 108π(8/N)^(1/6). It depends only on N = 1843 and on two relations: - the photon-unit relation, ħc/e² = 144π(r/d); - the size relation, N = (9/8)³(d/r)⁶. 2. The lattice sum, the finite-size term and the k factor only decide which odd integer is chosen. Any finite-size factor F from 0.93 to 1.02 gives exactly the same 137.035914847. 3. A fractional change ε in the photon-unit relation moves 1/α by 1.5ε. Closing the gap needs ε = +0.410 ppm. 4. A fractional change δ in the size relation moves 1/α by δ/6. Closing the gap needs δ = +3.69 ppm, which is the same as replacing N = 1843 by 1842.9932. 5. A change η in the orbit radius r = ħ/2mₑc enters N as its cube. Closing the gap needs η = +1.23 ppm. 6. Today's measurement fixes 1/α to 0.00015 ppm. So a real correction must predict the 0.615 ppm gap to within about 1 part in 4,000. - **Script and output:** `aether_units.py`, block of the same ID: `1 required change to the photon-unit relation, eps (1/alpha moves by 1.5 eps) 0.41026 ppm` - **Verdict:** this defines the target for U23–U26. - **Assumptions you could challenge:** step 2 assumes the integer rule. Without the rule, the lattice details set α directly (U25). ### U23. The restoring-force coefficient is justified - **Paper section:** Part 1, §6, test U23 - **Aspden's claim:** the force on a quon displaced by D from the continuum is 4πσqD (POC 7.5, quoting his chapter 6 eq. 6.1). His basis is "the Maxwell displacement field theory governing that motion" (Fifth Question, 2001). - **What was tested:** whether the coefficient 4π is forced, since electrostatics alone gives different values for different shapes. - **Steps:** 1. **Shape dependence in electrostatics.** For a finite body displaced uniformly against its background, the electrostatic restoring field depends on shape: 4πσD for a flat slab, 2πσD for a cylinder, (4π/3)σD for a sphere. 2. **No boundaries.** In an unbounded medium there is no surface charge. A uniform displacement still makes a uniform current, and Maxwell's equations with uniform fields give dE/dt = −4πJ, so E = −4πP = −4πσD in every direction. This is the long-wavelength plasma mode, and it gives Aspden's coefficient. 3. **Alternatives.** With the sphere's coefficient the chain gives N = 67 and 1/α = 79.4. With the cylinder's it gives N = 229 and 1/α = 97.0. - **Script and output:** `aether_units.py`, block of the same ID: `2 electrostatic sphere coefficient 4 pi/3 instead: odd N, 1/alpha 67 79.363639` - **Verdict:** Credited. His coefficient is the one Maxwell's equations require for an unbounded lattice. It is better justified than his text shows, and no other value comes close. - **Assumptions you could challenge:** step 2 treats the aether as unbounded on the scale of the motion. Near matter, or at the edge of an aether region, the coefficient would change, and with it α. That is not considered by Aspden. ### U24. The photon unit's inertia leaves out effects far larger than the gap - **Paper section:** Part 1, §6, test U24 - **Aspden's claim:** the 3×3×3 photon unit has moment of inertia 36m₀d², from twelve quons at distance d from the axis and twelve at √2 d (POC 7.21). It spins at a quarter of the orbital rate, since it "radiates at four times its spin rate" (main paper §5.1). - **What was tested:** whether the effects this sum leaves out are small enough for a 0.6 ppm result to be meaningful. - **Steps:** 1. Spin rate Ω/4 = c/8r. The quons at distance d move at 0.413c, and those at √2 d at 0.584c. 2. **Speed-dependent mass.** Aspden accepted that mass rises with speed; *Physics Unified* ch. 4 relies on "the relativistic formula for increase of mass with speed", which he held could be justified without Einstein. Applying it to the spin speeds alone raises the angular momentum by 18.7%. Carried through the chain, N becomes 3083 and 1/α becomes 162.6. 3. **Quons turning with the unit.** If each quon also turns with the unit, its own inertia adds 1.26% when its Thomson field mass is spread out to d/2 (1/α = 138.76), or 0.039% as a uniform sphere of radius b (N jumps to 1845, 1/α = 137.092). 4. **Continuum turning with the unit.** If the continuum's equal inertia (U10) were carried round with the unit, the inertia would rise 112% (1/α = 291). 5. The change actually needed is 0.000041% (U22). The omitted effects are 1,000 to 450,000 times larger. - **Script and output:** `aether_units.py`, block of the same ID: `3 angular momentum increase if mass rises with speed (Aspden accepts this, PU ch. 4) 18.69 %` - **Result:** the formula 36m₀d² treats the photon unit as 27 rigid point masses moving slowly. Their actual speeds are 41–58% of the speed of light. - **Verdict:** Disagrees, internally. Taken as a mechanical calculation, the photon-unit step cannot be accurate to better than about 10%. The 0.6 ppm agreement therefore cannot come from the calculation's precision. Either some reason, not given, makes these effects cancel exactly, or the closeness of 137.036 is a coincidence. The chance of that is estimated in the main paper, §11. - **Assumptions you could challenge:** - **The speed estimate.** Step 2 counts only the spin speeds. Adding the orbital c/2 motion of every quon would change the size of the correction but not its order. - **What "spin" means.** A defender could argue that the spin is a travelling pattern of phase in the lattice rather than a rotation of mass. But then I = 36m₀d² has no basis, because a moment of inertia describes moving mass. - **The continuum.** Whether the continuum turns with the unit is not stated by Aspden. Step 4 is included to show the size of that question, not as his claim. ### U25. The 2003 constant k can be calculated from his own description - **Paper section:** Part 1, §6, test U25 - **Aspden's claim:** the continuum charge pushed aside by a quon's volume moves "to a mean distance kb, where kb can have a value approaching d/2 if the displaced charge is spread over much of the aether cell" (POC 7.17). He requires only k ≥ 8.34. - **What was tested:** whether his description fixes k, turning a free constant into a calculated one. - **Steps:** 1. In (7.17), kb is the distance at which the displaced charge's interaction energy equals that of the spread charge, so 1/(kb) is the mean of 1/R over where the charge goes. 2. The mean of d/R over a cube of side d about its centre is 2.380077. This is his own constant I₀ in (7.12), 2.380077382. It has the closed form 2[3 ln((1 + √3)/√2) − π/4]. 3. Excluding the quon's own void of radius b changes it to 2.3723. 4. So k = d/(b × 2.3723) = 11.665, inside his allowed range of 8.35–13.8 (U19), and F = 1 − 2/3k = 0.94285. 5. With his integer rule, N stays 1843 and 1/α stays 137.0359148. 6. Without the integer rule, the pure lattice gives 1/α = 137.0308995. That is −37.2 ppm, against −139.6 ppm with his F = 1. - **Script and output:** `aether_units.py`, block of the same ID: `2 k = d/(b x mean of d/R outside the void) 11.665` - **Verdict:** Credited, as an improvement. His free constant can be calculated from his own words, and the value fits his constraints. It does not touch the 0.6 ppm gap, which the integer rule fixes, but it removes one adjustable number from the 2003 version. - **Assumptions you could challenge:** - **Uniform spreading.** Spreading the displaced charge uniformly through the cell is one reading of "spread over much of the aether cell". Spreading it to a thinner shell near the cell wall would raise k, up to 13.8. - **Neighbouring voids.** The voids in neighbouring cells are ignored. They occupy 0.02% of each cell. ### U26. Small numbers of the right size are not fixes - **Paper section:** Part 1, §6, test U26 - **What was tested:** whether simple small quantities of about the needed size close the gap, as a check against reading a match as a mechanism. - **Steps:** each candidate value of ε was put into the chain: | Candidate ε | Size (ppm) | Resulting 1/α | Remaining gap | In today's σ | |---|---|---|---|---| | α³ | 0.389 | 137.035994724 | −0.033 ppm | −212σ | | 1/N² | 0.294 | 137.035975364 | −0.174 ppm | −1,134σ | | (α/2π)² | 1.349 | 137.036192113 | +1.41 ppm | +9,187σ | - **Script and output:** `aether_units.py`, block of the same ID: `1 eps = alpha^3 = 0.3886 ppm: 1/alpha, residual ppm, residual in today's sigma 137.035994724 -0.0325 ppm -212.0 sigma` - **Verdict:** none closes the gap. α³ comes nearest and still leaves a 212σ miss. With enough candidates one will always fall near the target, so a correction counts only if a mechanism produces it, derived before comparing with the measurement, and it lands within 1 part in 4,000 (U22). No such mechanism was found. - **Assumptions you could challenge:** the main paper (§6.5) notes that the proton/electron residual is close to α³/2. One rule fixing both residuals would be worth a look. Applying α³ here leaves 212σ, so a single α³ rule does not do it. ### U27. The orbit in endless space is exact - **Paper section:** Part 1, §7, test U27 - **Aspden's claim:** both frames orbit with radius r at speed c/2, and the restoring force is 4πσq per unit displacement (POC 7.1, 7.5). - **What was tested:** whether the coupling between all quons in an endless lattice changes the orbit. - **Steps:** 1. **No net force from the other quons.** In the orbit every quon moves by the same vector at the same time. Their relative positions never change, so the force on any quon from all the others, summed over the endless lattice, is zero at every instant. 2. **The Ewald check.** The lattice's dynamical matrix at long wavelength gives exactly the plasma frequency for motion along the wave and zero across it: `1.000000 -1.31e-10`. The only restoring force on the uniform motion is the continuum's (U23). 3. **Magnetic coupling.** The two frames carry opposite charges moving in opposite directions, so their currents add: σc = 1.86 × 10²⁶ A/m². In an endless medium a uniform current is exactly cancelled by the displacement current of the same motion (Maxwell: dE/dt = −4πJ). So no magnetic field arises, and there is no magnetic coupling in the orbit. - **Script and output:** `lattice_dynamics.py`, block of the same ID: `1 D(k -> 0 along x) / w_p^2: longitudinal xx (expect 1), transverse yy (expect 0) 1.000000 -1.31e-10` - **Verdict:** Credited. The orbit radius, speed and frequency survive the endless-lattice treatment unchanged, given his inputs. - **Assumptions you could challenge:** the speed c/2 is relativistic. Aspden absorbs this into his "effective mass in orbit" m₀ (POC 7.4); that choice is his, not tested here. ### U28. The endless simple cubic lattice is unstable - **Paper section:** Part 1, §7, test U28 - **Aspden's claim:** the quons form a simple cubic lattice. He also says that if the lattice were allowed its minimum energy "the aether lattice particles would all be at rest … in a structure that was body-centred cubic, as in iron" (POC ch. 7), and that the zero-energy condition and the motion prevent this. - **What was tested:** whether the simple cubic arrangement is mechanically stable. In crystal terms this means checking that every lattice wave (every wavevector k in the Brillouin zone, every polarization) has a real frequency. - **Steps:** 1. **The method.** The dynamical matrix D(k) of point charges q, mass m₀, spacing d in a rigid uniform continuum was built by Ewald summation. Checks: - the trace of D equals the plasma frequency squared at every k, as it must for Coulomb forces; - the results do not depend on the Ewald splitting parameter. 2. **Along the symmetry lines Γ–X–M–Γ–R–X**, the two transverse branches have ω² < 0 along Γ–X, X–M and M–Γ. The worst point is M = (π/d, π/d, 0), with ω² = −0.093 ω_p². 3. **Over a 16³ grid of the Brillouin zone**, 18.4% of all modes are unstable. 4. **The same code for a body-centred cubic lattice** finds every mode stable, with lowest ω² = +0.003 ω_p². This also checks the method. 5. At the zone face X, the transverse frequencies are imaginary (82.5i keV) and the longitudinal one is 379.7 keV, using ħω_p = 361.3 keV for the quons against a still continuum. - **Script and output:** `lattice_dynamics.py`, block of the same ID: `5 fraction of grid modes with w^2 < 0 (unstable) 0.184` - **Verdict:** Disagrees, on electrostatics alone. A simple cubic lattice of like charges in a uniform background shears spontaneously toward another structure. Aspden's text accepts that the static minimum would be body-centred cubic and relies on the orbital motion to hold the simple cubic form, but he gives no calculation showing that the motion stabilizes these shear modes. - **Assumptions you could challenge:** - **The orbital motion.** The quons move at c/2, so velocity-dependent (magnetic) forces between disturbed quons are about (v/c)² = 25% of the electric ones. That is the same order as the instability (9% of ω_p²), so the motion could in principle stabilize the lattice. Whether it does is untested here and would need a relativistic lattice-dynamics calculation. - **A rigid continuum.** The continuum is held rigid for these internal waves, as a frame that moves only as a whole. A continuum that can compress would change the longitudinal branch, not the transverse instability. - **If the lattice were body-centred cubic.** His lattice sums (the Ewald value 2.8373 and the π/6 cell term) and with them r/d, N and α would all change. ### U29. Coupling between moving quons changes the photon unit's inertia by 9–29% - **Paper section:** Part 1, §7, test U29 - **What was tested:** how much the magnetic coupling between the 27 moving quons of a spinning photon unit changes its moment of inertia, and so Planck's constant in his formula. - **Steps:** 1. **The coupling.** To first order in (v/c)², the coupling between moving charges is the Darwin interaction, L = (q²/2c²r)[vᵢ·vⱼ + (vᵢ·n)(vⱼ·n)]. Summed over the 351 pairs of a 3×3×3 block spinning about a lattice axis, the sum is 97.44 (in units of ω²d). 2. **The added inertia.** This acts as extra inertia, I_D/I = (3b/d) × 97.44/36 = 29.3%, using q²/c² = 3bm₀. 3. **Screening by the surrounding lattice.** The rest of the endless lattice screens the magnetic field over the skin depth c/ω_p = 0.857d. Including that cuts the addition to 9.1%. 4. **Through his chain.** Carried through his chain, the added inertia gives 1/α = 177.2 (unscreened) or 149.4 (screened), against 137.04. 5. The change actually needed is 0.000041% (U22). - **Script and output:** `lattice_dynamics.py`, block of the same ID: `4 added inertia with the surrounding lattice screening the field (Yukawa, length c/w_p) 9.059 %` - **Verdict:** Disagrees. Coupling between the moving charges does change the simple formula, as the challenge said, but by about 10–30%. That moves the result further from α, not closer, and is far beyond the 0.41 ppm a fix needs. - **Assumptions you could challenge:** - **Leading order only.** The Darwin form is the leading order in (v/c)². At 0.4–0.6c, higher orders are not small. - **The screening model.** Screening is modelled as a simple exponential over the skin depth. A full calculation would use the lattice's actual magnetic response. - **The continuum.** The continuum inside the spinning block is taken not to turn with it (U24). ### U30. The speeds do not depend on the picture - **Paper section:** Part 1, §7, test U30 - **What was tested:** whether describing the photon unit as a wave rather than a rigid body lowers the quons' speeds. - **Steps:** 1. **Energy of any circular motion.** For any motion in which particles circle at angular frequency ω (a rigid spin, or any circularly polarized wave), the kinetic energy is exactly half the angular momentum times ω. With angular momentum ħ and ω = Ω/4 this is ħΩ/8 = 63.9 keV. 2. **Compared with rest energy.** The 27 quons' rest energy is 27 × 20.84 = 562.7 keV, so the kinetic energy is 11.4% of it. 3. **The speed.** The rms speed is therefore √(2 × 0.1135) c = 0.476c, whatever the pattern of motion, as long as these 27 quons carry the angular momentum. - **Script and output:** `lattice_dynamics.py`, block of the same ID: `4 rms speed sqrt(2 KE / 27 m0), any pattern of circular motion at that frequency 0.4765 c` - **Verdict:** Disagrees. A wave description of the same 27 quons gives the same speeds. The speeds follow from the energy, not from the rigid-body picture. ### U31. Spreading the wave over more quons - **Paper section:** Part 1, §7, test U31 - **What was tested:** whether a wave spread over many quons could carry the same angular momentum slowly while keeping Aspden's inertia, and what that costs. - **Steps:** 1. **Spreading keeps the inertia.** The inertia I = Σm₀aᵢ² stays 36m₀d² if the same sum of squared radii is shared among more quons. Their speeds then fall as 1/√(number of quons). 2. **Speeds and mass corrections:** | Quons sharing the angular momentum | rms speed | mass correction v²/2c² | |---|---|---| | 27 | 0.476c | 114,000 ppm | | 1,000 | 0.078c | 3,070 ppm | | 100,000 | 0.0078c | 31 ppm | | 10,000,000 | 0.00078c | 0.31 ppm | 3. **How many are needed.** The correction falls below the 0.41 ppm a fix needs at about 7.5 million quons. That is a cube about 195 lattice spacings, or 1.25 × 10⁻¹⁰ m, on a side, roughly twice the Bohr radius. - **Script and output:** `lattice_dynamics.py`, block of the same ID: `2 quons needed for the mass correction (v^2/2c^2) to fall below 0.41 ppm 7.47e+06` - **Verdict:** Open, and it carries a cost. A wave spread over roughly atomic dimensions could carry ħ slowly. But Aspden's value of h comes from the number 36, the moment of inertia of a rigid 3×3×3 cube in units of m₀d². In a spread-out wave, the sum of squared amplitudes is fixed by requiring the angular momentum to be ħ, so 36m₀d² would have to be imposed rather than derived. The derivation of h, and with it the formula for α, would become an input. - **Assumptions you could challenge:** the spread-out wave would also need magnetic coupling (U29) and the lattice's own wave modes (U28) included before its inertia could be stated. No such calculation exists in Aspden's work or here. ### U32. A quon feels only the average field - **Paper section:** Part 1, §8, test U32 - **Aspden's claim:** under an applied field the quons move together, and "there will be no change in the Coulomb force on any particle due to the action of its neighbours". The restoring force 4πσqD comes from the uncovered "planar slice" of continuum charge (POC ch. 6, eq. 6.1). - **What was tested:** whether a quon has any restoring force of its own when the whole lattice shifts, or only the average field of the displaced system. - **Steps:** 1. **Its own cell's continuum** (a sphere) pulls the quon back with −(4π/3)σqu. 2. **All other cells** form a polarized medium with P = σu. At the quon, they give the average field plus the Lorentz cavity field +(4π/3)P. 3. **The two local terms cancel exactly.** The quon feels only qE, the average field. 4. **Exact Ewald lattice sums confirm it:** - for long-wavelength motion along the wave, the restoring force is exactly the plasma value; - across the wave, it is zero; - for one quon moved alone, it is one-third of the plasma value. - **Script and output:** `quon_model.py` (block W3, derived in Part 1A): `6 Ewald check, k -> 0: transverse / w_p^2 (no local restoring force) = -1.31e-10` - **Verdict:** Credited. Aspden's statement is exact. His restoring force 4πσqD is therefore the field of the displaced lattice, not a separate spring. - **Assumptions you could challenge:** - **The cancellation** holds for cubic lattices of point charges. A quon of finite size changes it by about (b/d)³ ≈ 5 × 10⁻⁵. ### U33. The orbit is the plasma oscillation of the two frames - **Paper section:** Part 1, §8, test U33 - **Steps:** 1. **Equations of motion.** m₀ü_E = qE and Mü_G = −qE, with E = −4πP and P = nq(u_E − u_G). 2. **Combined,** P̈ = −4πnq²(1/m₀ + 1/M)P. With M = m₀ this gives Ω_pl² = 8πnq²/m₀, Aspden's 7.5. 3. **Numbers.** ħΩ_pl = 510.999 keV; Ω_pl/Ω = 1.0. - **Script and output:** `quon_model.py` (block W4, derived in Part 1A): `3 Omega_pl / Omega (Aspden's orbital frequency) = 1.0` - **Verdict:** Credited. His orbit is the plasma oscillation of the quon frame against the continuum, consistent with Coulomb's and Newton's laws, at exactly the Compton frequency. ### U34. Light below 511 keV cannot travel - **Paper section:** Part 1, §8, test U34 - **Steps:** 1. **Driven by a light wave,** P(ω) = −(Ω²/4πω²)E, the response of a plasma. 2. **With Maxwell's equations,** c²k² = ω² − Ω². No wave exists below Ω. A blocked wave dies away within c/Ω = 2r = 3.9 × 10⁻¹³ m. 3. **Predicted:** - radio, visible light, 10 keV X-rays and 100 keV gamma rays are all blocked; - 661.7 keV gamma rays travel at 0.635c; - between 35 MeV and 31 GeV the speed difference is 1.1 × 10⁻⁴ of c, 3 × 10¹³ times the GRB 090510 limit. - **Script and output:** `quon_model.py` (block W5, derived in Part 1A): `visible, 500 nm -4.2466e+10 no` - **Verdict:** Excluded, by the fact that light reaches us at all. - **Assumptions you could challenge:** this assumes Maxwell's equations with their usual vacuum term. If the quons carry all the displacement current with no separate vacuum term, as Aspden says, then c²k² = −Ω² and nothing propagates at any frequency (Part 1A, 6.6). ### U35. The same thing as a photon mass - **Paper section:** Part 1, §8, test U35 - **Steps:** 1. **The equivalence.** c²k² = ω² − Ω² is the wave equation of a photon with rest energy ħΩ = 511 keV. 2. **The limits:** - Particle Data Group, from the solar wind's magnetic field (Ryutov 2007): below 10⁻¹⁸ eV; - laboratory (Lakes 1998): below 10⁻¹⁷ eV; - test of Coulomb's law (Williams, Faller and Hill 1971): below 10⁻¹⁴ eV. - **Script and output:** `quon_model.py` (block W6, derived in Part 1A): `PDG limit (Ryutov 2007, solar wind): limit (eV) and ratio = 1.0e-18 x 5.1e+23` - **Verdict:** Excluded by a factor of 5 × 10²³. A lattice tied to the electron (ħΩ = mₑc²) cannot pass. Passing would need ħΩ < 10⁻¹⁸ eV, which would mean r = ħc/2E > 10¹¹ m. ### U36. Static charges would be screened - **Paper section:** Part 1, §8, test U36 - **Steps:** 1. **Exact lattice sums.** An applied field that varies over λ is reduced to the fraction 1 − ω_p²/ω_L(k)² of itself. 2. **Fraction left:** - λ = 200 lattice spacings (1.3 × 10⁻¹⁰ m): 0.003%; - λ = 20 spacings: 0.26%; - λ = 2 spacings: 9%. 3. **His own equation says the same.** Aspden's 6.1 says the quon stops where the restoring force equals Vq. In Coulomb's law that is where the total field at the quon is zero, for every other charge there as well. - **Script and output:** `quon_model.py` (block W7, derived in Part 1A): `k = 0.01 pi/d w_L^2/w_p^2 = 1.00003 field left = +0.00003 of the applied field` - **Verdict:** Excluded. A charge's field would vanish beyond about 10⁻¹⁰ m, so there would be no electrostatics at laboratory scale. - **Assumptions you could challenge:** avoiding this needs a force law in which the lattice's own field acts on quons but not on ordinary matter. Aspden does not state one, and it would contradict Coulomb's law (Part 1A, 6.7). ### U37. No restoring force is needed for a plasma - **Paper section:** Part 1, §8, test U37 - **Objection tested:** the quons need not have any restoring force. - **Steps:** 1. **Agreement.** Section 4 of Part 1A already finds no local restoring force (U32). 2. **What sets the plasma frequency.** ω_p² = nq²/ε₀m contains only density, charge and mass, with no spring constant. 3. **A real example.** The Earth's ionosphere has about 10¹² free electrons per m³ with nothing holding them. Its cutoff is f_p = 8.98 MHz, and it reflects radio below that. 4. **Aspden's quons.** The same formula gives 361 keV, or 511 keV with the continuum moving. - **Script and output:** `quon_model.py` (block W9, derived in Part 1A): `ionosphere F layer, electrons n = 1e12 m^-3: f_p = 8.97866e+6 Hz` - **Verdict:** Consistent with U34. The plasma result does not depend on a restoring force; removing one makes the lattice more plasma-like, not less. ### U38. The lattice flexing as an elastic solid - **Paper section:** Part 1, §8, test U38 - **Objection tested:** the medium flexes to carry the waves. - **Steps:** 1. **The shear waves.** A crystal's elastic flexing (neighbours shifting relative to one another) carries shear waves. The exact lattice sums give their speeds at long wavelength: - along [111], 0.215c; - along [110], 0.279c, plus one unstable mode; - along [100], both modes unstable (0.134c × i). 2. **What light would need.** To carry light at c the lattice would have to be 13–22 times stiffer, stable along the cube axes, and the same in every direction to 10⁻¹⁷. - **Script and output:** `quon_model.py` (block W10, derived in Part 1A): `shear-wave speeds along [111] body diagonal = 0.215c, 0.215c` - **Verdict:** Excluded as the carrier of light. Flexing as a polarizable medium is U34; flexing as a solid is this test. Both fail with Aspden's charges, masses and spacing. ### U39. Background (CMB) driven motion of the quons - **Paper section:** Part 1, §8, test U39 - **Objection tested:** the quons may be in periodic motion driven by the cosmic background. - **Steps:** 1. **Energy available.** kT at 2.725 K is 2.3 × 10⁻⁴ eV. 2. **How far and how fast the quons move.** A free quon would move at 55 km/s. In the lattice the thermal amplitude is 5.8 × 10⁻¹⁷ m, 0.0001 of the spacing. 3. **Still a solid.** The crystal's coupling parameter is 1.6 × 10⁷ (melting near 175). 4. **Already larger.** Aspden already gives every quon an orbital motion at 149,896 km/s. 5. **No effect on the response.** The response to a wave is linear and adds to any existing motion without being changed by it. - **Script and output:** `quon_model.py` (block W11, derived in Part 1A): `thermal amplitude in the lattice, sqrt(kT/(m0 w_p^2)), and as a fraction of d = 5.79761e-17 m 9.09566e-5` - **Verdict:** Does not change U34. Background motion is far too small to matter, and would not alter the response even if larger, while it stays linear. ### U40. Light's reference frame: the background's frame and Aspden's Earth-carried frame - **Paper section:** Part 1, §8, test U40 - **Objection tested:** the medium is the reference frame against which light travels, and it moves with the planet. - **Aspden's claim:** the Earth's electromagnetic reference frame "is a non-rotating frame of reference which moves linearly with the space lattice" (*Physics Unified*, ch. 9). 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" (1983b). His statements are collected in Part 1A, section 1.3. - **Steps:** 1. **The background's frame (version 1.4 of this test; not Aspden's).** The Earth moves through it at 369.8 km/s (Planck 2018). Without length contraction, light's speed in the laboratory would depend on direction by ½(v/c)² = 7.6 × 10⁻⁷, against cavity limits of about 10⁻¹⁷ to 10⁻¹⁸: a factor of 7.6 × 10¹⁰. 2. **Aspden's frame.** The 370 km/s disappears, because the frame travels with the Earth. A laboratory turning with the Earth crosses the frame at Ω_E R cos(latitude): 283 m/s at Berlin (52.5°N), 356 m/s at 40°N. 3. **The prediction.** A laboratory-fixed signal at twice the turntable rate, ½(v/c)² = 4.4 × 10⁻¹³ at Berlin. 4. **The measurement.** Herrmann et al. (2009), Berlin: laboratory-fixed signals below 3 × 10⁻¹⁶. The ratio is about 1,500. The largest steady flow of the frame past the laboratory that this allows is 7.3 m/s. 5. **A frame turning with the Earth** would hide the signal, but a ring laser would then sense no rotation. The Wettzell ring laser senses the full rotation to 48 parts per billion. By Stokes's theorem, if ring lasers sense the full rotation, the frame's mean flow past the ground round Berlin's latitude circle is 283 m/s, 38 times the cavity limit. - **Inputs:** the Earth's rotation rate 7.2921150 × 10⁻⁵ rad/s and mean radius 6,371 km; Planck 2018 dipole 369.82 km/s; Herrmann et al. 2009 and Nagel et al. 2015 (refs 22–23); Wettzell ring laser (main paper §3.3). - **Script and output:** `quon_model.py` (block W12, derived in Part 1A): `ratio = 1481.93` (Aspden's frame, W12 line 9); `ratio = 7.6e+10` (background's frame, W12 line 4) - **Verdict:** Excluded: by a factor of about 1,500 in Aspden's own frame, and 7.6 × 10¹⁰ in the background's frame, unless moving rulers and clocks change exactly as relativity says. That is Lorentz's aether, which cannot be detected (main paper, section 3.3). - **Assumptions you could challenge:** - The coefficient ½(v/c)² assumes no length contraction. With full contraction the signal is zero. - The limit used is the laboratory-fixed one (3 × 10⁻¹⁶). The overall limit, about 10⁻¹⁷, would strengthen the result. - Version 1.4 of this test used the background's frame, which was this analysis's choice, not Aspden's. Corrected in version 1.5. ### U41. The postulate that the two frames move at c relative to each other - **Paper section:** Part 1, §8, test U41 - **Aspden's claim:** "the relative velocity between the system of aether particles and the medium constituting the background continuum is assumed to be the speed of light" (*The Theory of Gravitation*, 1998 note); "a likely candidate is the relative velocity between the E-frame and the G-frame, meaning the quantity Ω(2r)" (POC 6.6). Each frame then moves at c/2 (POC 6.13–6.15). His other statements, from 1960 to 2003, are collected in Part 1A, section 1.2. - **What was tested:** whether the dynamics fixes the relative speed, and which of his results depend on it. - **Steps:** 1. **The force balance contains no radius.** m₀Ω² = 8πq²/d³ (7.5 with σ = q/d³). The orbit's frequency is fixed, and its size is free. In the self-consistent model the orbit is a plasma oscillation, whose frequency does not depend on its amplitude (U33). 2. **His chain with a general relative speed.** Write Ω·2r = s·c. Aspden converts (7.19), I = 2h/πΩ, into (7.20) "because Ω is c/2r". Keeping s, (7.19) and the force balance give ħc/q² = 144π(r/d)/s in place of (7.24), m₀/mₑ = (4/9)(r/d)²/s² in place of (7.25), and N = (9/8)³s⁶(d/r)⁶ in place of (7.26). 3. **For a given N, s cancels.** 1/α = 108π(8/N)^(1/6). The lattice spacing d = cN^(1/6)/(2Ω(9/8)^½), the quon mass, the quon radius and the cell energy are unchanged. Only r = s·ħ/2mₑc and r/d scale with s. 4. **Where s still enters.** In the zero-energy condition (7.18), through r/d and the finite-size term, which goes as s⁴. With the exact lattice sum, N = 1843 is chosen for any s from 0.999862 to 1.0000414 (−138 to +41 ppm). Outside that range N becomes 1841 or 1845, and 1/α jumps by 181 ppm. - **Inputs:** Aspden's equations 7.18–7.26; the lattice sum 2.3136987 (U21). - **Script and output:** `quon_model.py` (block W14, derived in Part 1A): `range of s that keeps N = 1843 (the zero-energy N between 1843 and 1845) = 0.99986198 to 1.0000414` (W14 line 6) - **Result:** The postulate is not derived, and Aspden calls it an assumption. In his own chain it fixes only the orbit radius. It reaches α only through the choice of N, which tolerates a change of −138 to +41 ppm, so it cannot be the source of the 0.6 ppm gap. - **Verdict:** Open: an assumption, not derived. α, N and the lattice spacing do not depend on it. - **Assumptions you could challenge:** - The finite-size term is taken to scale as s⁴, from b/d = s²/96π(r/d)² (7.15 with s). If that term were fixed independently of the force balance, the range would shift slightly. - Whether the frames' relative speed could set light's speed at all. In the self-consistent model, light's speed comes from the field equations (Part 1A, section 6). The relative velocity turns with the orbit, so there is no steady stream for a wave to ride on (Part 1A, section 1.2). --- ## Discrepancies found while compiling, and what was done ### Items in the working paper with no test of their own These are mentioned in sections 3–13 but not tested, so they have no entry. - §3.3, last bullet: an aether with Lorentz contraction and time dilation reproduces relativity and is undetectable. This is an argument, not a test. - §9.1: Note 13 electrodynamic force law (no numerical prediction); Note 14 meson lifetimes 6.25% below relativistic values near γ = 2 ("not yet checked"); graviton at 2.587 GeV (Notes 16, 20; "no direct test"). Register check: g = 5062.318 × 0.51099895 MeV = 2,587 MeV, consistent with the stated mass. - §12, mainstream status table (BMW hadron masses and n–p difference, Shaposhnikov–Wetterich Higgs mass, Koide tau mass): literature values quoted for context. Register check: Gm_p²/ħc ≈ 5.9×10⁻³⁹ is correct. - §13: summary only. Its claims match the entries above. ### What was done about each discrepancy (working paper v1.9) | Item | Action | |---|---| | A1 1/α today −3,800σ | Corrected to about −4,000σ (paper §10 and the site note) | | A2 NIST-26 −257 ppm | Corrected to −256 ppm | | A3 1.9993 mₑ row −36 ppm | Corrected to G = 6.674065, −35 ppm | | A4 version-1.6 figure −8.2 ppm | Corrected to −8.6 ppm (§8 and the revision history) | | A5 "two correction factors −1.23%" | Corrected: −1.17% for the two factors, −1.23% with the nuclear-mass factor. The script's printed label is unchanged, so quoted output stays verbatim | | A6 series attribution | Rewritten with the term-by-term figures | | A7 0.35% | Changed to 0.34% | | A8 his φ values | His printed values now shown with the recomputed 10.23 | | A9 n–p "looser match" | Rewritten: closer than G, far outside its own uncertainty | | A10 "every idea tried" | Rewritten: 116 cluster and chain variants; non-cluster ideas not included | | A11 "heavy-centred" 7/4 | Corrected in §7.5 and §8; the label in deuteron.py's printed output is left as is | | A12 G history range | Corrected to 6.6676–6.686 | | A13 4×10⁻¹³ | Corrected to 5×10⁻¹³ at 300 m/s (4.5×10⁻¹³ at 283 m/s) | | A14 "by the amount of his formula" | Rewritten: about 9% larger (eccentricity factor) | | A15 5,000 times | Corrected to about 5,700 | | A16 "Galaxy" labels | Relabelled as quasar absorbers | | B1–B7, B9–B13 | Register checks agree, or the figure is historical. No change to the paper, beyond noting here that these numbers are not printed by any script | | B8 finite-cube r/d values typed in as Aspden's | Not resolved. The rebuild converges on the infinite-lattice value, so the result is unaffected. The source of the typed values must be found (they may come from his QBASIC program's boundary treatment) | | C4 "tracking the measurement of the day" | Removed | | C5 "fixed before computing G" and "independent routes" | Removed; the paper now says the measured G was known throughout | | C11, C12 chance-calculation assumptions | Now stated in §11.1 as open to challenge | | C15 zitterbewegung as a merit | §13 now calls it a correspondence, not evidence | | C1–C3, C6–C10, C13, C14 | Left as stated assertions. Each is a point a reader may challenge, and each is listed here so it is not hidden | | D1–D3, D5, D6 | Corrected (as A5, A6, A11, A14 and the dimuon wording in §7.5) | | D4 Heidelberg factor of two | Checked: Botermann et al. (2014) define ε = α̂β² for this observable, so the script is consistent. No change | | E1–E23 missing sources | Not yet fixed. Each is an open item for the next revision; none changes a verdict | ### The full list as compiled "Register check" numbers are this register's own recomputation from values printed in the paper or the scripts. #### A. Paper text disagrees with script output, or with its own inputs 1. **§10 timeline, 1/α today.** Paper: "about −3,800σ". environment_constants.py: `-4.02e+3 sigma`. Register check with the table's own 137.035915: −4,008σ. The figure should be about −4,000σ. 2. **§7.3, NIST-26 row.** Paper: Aspden's G is −257 ppm from 6.67387. Register check: −256.0 ppm. compare.py prints `-256.0` for the identical G value (its MSL-03 row, also 6.67387). The +31 ppm for 2 mₑ is right. 3. **§7.5 table, 1.9993 mₑ row.** Paper: −36 ppm. From G = 6.674065 the miss is −35.2 ppm; −36 appears only if G is first rounded to 6.67406. The −1.6σ is right. 4. **§8 and revision history v1.8: version 1.6's mixed-unit figure.** Paper: −8.2 ppm. np_mass.py, doing that same mixed-unit comparison: `-8.59 ppm`. Register check: −8.2 ppm is obtained only against a rounded 1.293332 MeV (−8.47 ppm against 1.29333236 MeV). The paper's figure is a historical v1.6 number that the current script does not reproduce. 5. **§9.3, "two correction factors totalling −1.23%".** The script's −1.23% is eq. (18) / eq. (17) − 1, which also contains the nuclear-mass factor (1 − m/M), but the output labels it `the two correction factors`. Register check: the two correction factors alone give −1.17%. 6. **§9.3 series: "the third-order coefficient ... accounts for most of his 6 × 10⁻⁹ shortfall".** Register check, term by term from the printed coefficients with α(Rb): second order +6.09×10⁻⁹, third order −12.12×10⁻⁹, fourth order +0.05×10⁻⁹, sum −5.98×10⁻⁹. The third-order deficit is twice the net shortfall, and the second-order term cancels half of it. The second-order coefficient, which the paper calls "a notable coincidence" for agreeing to 0.35%, contributes an error as large as the whole net shortfall. 7. **§9.3, second-order agreement "0.35%"** (stated twice). Computed: 0.344% relative to QED's coefficient (0.345% relative to Aspden's). Rounding only. 8. **§9.4, his φ values not reproduced exactly.** Route 1: text 10.25×10¹²; rebuild with his inputs 10.23 (paper's table and output). Route 2: text 10.24; rebuild with T = 2.7 K, m* = 0.04 mₑ gives `10.23` (output line not in the paper's table). The paper does not comment. 9. **§11.2, n–p mass difference "a looser match than the four above".** At 18.4 ppm it is tighter than G's 34 ppm. It is looser only than α, the proton and the deuteron. 10. **§11.2 G row, "116 chain variants, including every idea tried"** (output: `(all ideas tried)`). The 116 are 29 taon forms × 1–4 taons. They leave out the §7.4 non-cluster ideas: k = 1/2, k = 3/5, tuned k, N = 1842.993 and the composite factor 2.99962. §11.1's narrower "every cluster idea" is accurate. 11. **§7.5 reason 3 and §8, "heavy-centred triplets" 7/4 and 9/4.** deuteron.py computes 7/4 from p e⁻ e⁺, where the proton is at one end. With point protons every alternating heavy-centred triplet gives 9/4. The label, or the reading of Aspden, needs fixing; the arithmetic (7/4 + 9/4)/2 = 2 is unaffected. 12. **§7.2 History row.** "His published G moved between 6.668 and 6.686" while listing 1966: 6.6676, which is below that range. 13. **§3.1.** "Roughly 300 m/s" with "½(v/c)² ≈ 4×10⁻¹³": at 300 m/s the value is 5.0×10⁻¹³. 4.5×10⁻¹³ corresponds to Berlin's 283 m/s. The conclusion is unchanged. 14. **§9.2, sign check "by the amount of his formula".** The integration gives 1.370×10⁻³ rad per orbit against 4πk/a² = 1.257×10⁻³, which is 9% larger. Register check: first-order perturbation gives −4πk/p²·(1 + e²/8), matching the integration, so the 9% is the eccentricity factor. Minor. 15. **§9.4, "5,000 times smaller than his value".** 10.25×10¹² / 1.8×10⁹ ≈ 5,700. Rounding. 16. **§6.4 table labels.** The z = 0.89 and z = 1.15 systems are called "Galaxy"; the script and §3.4 call them quasar absorbers. Labels only. #### B. Numbers that no script output shows (register checks where possible) 1. **§7.2, one, three or four taons give G = 3.50, 8.52, 9.70.** No output prints them; coincidence.py computes them internally. Register check: 3.498, 8.525, 9.699 (agrees). 2. **§7.5 table, 1 mₑ and 4 mₑ rows.** Not printed. Register check: 4 mₑ gives taon 3482.81558, g 5059.23153, G 6.704798, +4,569.5 ppm; 1 mₑ gives taon 3485.81558, g 5063.58941 (agree). 3. **§7.3, BIPM-14, JILA-10 and LENS-14 σ values.** The cited aspden_G_variants.py prints only six comparisons. These three are reproduced only by compare.py, which the paper does not cite. 4. **§8, "closes 57% of the gap", "6/7 ... 344 ppm low", "deficit accurate to 0.22% (0.10% refined)".** Not printed. Register check: 57.1%, 344.5 ppm, 0.22%, 0.095% (agree). 5. **§9.3, "every other variant (18) ... 76 ppm or more" (muon).** Only the top eight variants are printed. Register check: the minimum is 76.2 ppm (agrees). 6. **§5.3, "for the lattice alone to give α exactly ... F would need to be 0.922".** The script computes the F at which N = 1843 exactly (0.92241), a different quantity. Register check: the F that makes the lattice give α exactly is 0.92207. Both round to 0.922. 7. **§7.2, "the rebuild reproduces every value in Aspden's Note 9 table".** Neither the paper nor any script lists the Note 9 table. chain.py prints G for five g values with no column of Aspden's values. Not verifiable from the files. 8. **§5.2 / Appendix C.4, finite lattice sums.** planck.py's rebuild of his finite-cube method does not reproduce the values typed in as his: N = 5: 0.3028976690 vs 0.3028877950; N = 10: 0.3028807822 vs 0.3028776183; N = 30: 0.3028746524 vs 0.3028742254. Both series approach the infinite-lattice value, so the conclusion stands, but the paper does not mention the mismatch. 9. **§6.2, "excluded by a factor of about 10¹⁴".** environment_constants.py prints a fixed sentence; nothing is computed. The arithmetic is right. 10. **§9.1, muon lifetime 2.251 μs.** No script, and the formula is not given. 11. **§9.1, MESSENGER bound of 2.5×10⁻⁵ on the relativistic parameters, and Aspden's 1960 value of 44.3″/cy.** Not computed or derived. 12. **§3.1–3.3 hand figures (4×10⁻¹³; 1×10⁻¹³ and 400×; 7 m/s; 280 m/s), §10's 1973 and 1986 σ values, §12's Wyler and Rosen values.** No script. Register checks agree within rounding, apart from A1 and A13. 13. **Historical figures from earlier versions (§11.3 "Version 1.2 ... 1 in 16 to 1 in 1,500"; §11.2 "roughly even odds").** The current scripts do not reproduce the older methods. #### C. Steps asserted without being shown 1. **§3.4 Tolman credit.** "Aspden's relation between wave energy and frequency implies surface-brightness dimming as (1+z)⁴" is not derived. 2. **§3.4 supernova and CMB tests.** That his static aether predicts b = 0 is not derived from Note 18. For the CMB, no static-aether prediction for β is given, so that row shows agreement with expansion, not a measured exclusion of Aspden. 3. **§5.3, neighbouring voids change F "by at most about 0.04%".** The bound rests on an argument in the script's comments. The printed number is only the estimate "if it entered the finite-size term alone". 4. **§7.2, published G values "tracking the measurement of the day".** No measured values for 1966 or 1998 are given. compare.py and chain.py (uncited) show that the Note 8 → Note 9 change (6.668 → 6.672) comes from a different taon formula (3^(7/12)·P vs 2P(√6 − 3/2) − 1.875). The paper does not mention this. 5. **§7.4, "his rules, fixed before computing G", and "two independent routes converge on a cluster of about 2 electron masses".** chain.py, which already prints the cluster each measurement needs (2.0146 mₑ for CODATA), has an earlier file time (18:56) than explore.py (19:14), the uncited first version of the cluster search and averaging variants. explore.py labels the 2 mₑ variant "electron ejected with gamma=2". The routes were explored with the needed value known. §7.5 concedes this for the 2 mₑ choice only. 6. **§9.3, "a half-wavelength standing wave ... is forced".** Argued only in the cavity_variants.py docstring; not computed. 7. **§9.3, the QED target −1.3139 "sits among many simple numbers".** No list is given. The script's simple-number list (2/√3, 7/6, π/e) is for the muon–electron difference (1.16181), a different quantity. 8. **§9.4, the annual drift "would be hard to miss".** No time-resolved data or measurement dates were examined. 9. **§9.4, galactic potential "at least v²".** Stated, not shown. The Gaia comparison does not depend on it. 10. **§3.3, cavity limit of about 7 m/s.** Derivation not shown. Register check: it follows from ½(v/c)² = 3×10⁻¹⁶. 11. **§11.1–11.2, α chance.** coincidence.py assumes the target could lie anywhere in one decade (it divides by ln 10); the paper does not state this. The 65 and 650 structural variants and the 4 rounding rules are not justified. 12. **§11.3, independence.** The product, Fisher's method and the career calculation all treat the four p-values as independent. All four share the toolkit and N = 1843, and G's chain is built on the proton. Not discussed. 13. **§6.1, which energy is minimised.** The √(3/2) − 1 ratio requires minimising the pair energy over the dimuon's size with the proton fixed; the paper does not say so. 14. **§3.1 and §5.2, readings of Aspden's text.** That Note 18's "vector" step is asserted, and the "evident correction" of the printed force balance: neither printed text is quoted, so the reading cannot be checked from the paper. 15. **§5.4 and §13, zitterbewegung.** §13 lists the zitterbewegung-sized orbit as a merit, but aspden_G_variants.py's docstring treats r = ħ/(2mₑc) as an input that fixes the lattice cell. If so, the match was built in, not predicted. #### D. Physics errors or likely errors 1. The §9.3 series attribution (A6). 2. The "heavy-centred" label for the 7/4 triplet (A11). 3. The "two correction factors" total that includes the reduced-mass factor (A5). 4. **§9.6 / moving_atom.py, possible factor of two in the Heidelberg bound.** The script turns the Reinhardt et al. limit α̂ ≤ 8.4×10⁻⁸ into ε = α̂β² = 3.4×10⁻¹⁰. With a clock factor F = β(1 + α̂β²), the script's own definition ε = (Fγ)² − 1 gives ε ≈ 2α̂β² = 6.9×10⁻¹⁰. Check which form refs. 54–55 use, and whether Botermann's (1.5 ± 2.3)×10⁻⁹ is for ν_aν_p/ν₀² − 1 (as Appendix B states) or for √(ν_aν_p)/ν₀ − 1. A factor of two would halve the Heidelberg σ values (2.45×10⁴ and 9.75×10⁴). The verdict is unaffected. 5. **§7.5 reason 1, the dimuon described as "the energy of two muons (412.67 mₑ)".** Two muon masses are 413.54 mₑ (2 × 206.7682830, the ratio used in cavity_variants.py); the dimuon is 0.21% lighter. Only the wording is affected, not the calculation. 6. **§9.2 eccentricity factor (A14).** Minor. #### E. Missing or weak sources 1. Brillet & Hall (1979): cited in §3.1–3.2, no reference entry. 2. Hicks; Morley and Miller (c. 1902): no reference. 3. Tifft's periodicity and the 2dF galaxy–quasar test: only a Wikipedia overview (ref. 15). 4. "Discovery of Virtual Inertia", *New Energy News* (February 1995): listed in §2, no reference entry or link. 5. Aspden's 0.262 mirror coefficient: no page or equation; the source papers were seen only in abstract or secondary form. 6. Aspden's 1972 r/d = 0.302875 and 1/α = 137.035915: §14 lists the 1972 paper as not yet read. The finite-cube values typed into planck.py as "his" have no stated source. 7. Dicke (1967) oblateness: no reference, and the J₂ value is not given. 8. MESSENGER J₂ = (2.4 ± 0.2)×10⁻⁷ and the 2.5×10⁻⁵ bound on relativistic parameters: no reference (ref. 39, Will 2018, covers a different point). 9. Lundeen & Pipkin (1981) Lamb shift and the CERN (1979) muon g−2 value: named in the script and text, no reference entries. 10. Williams–Olsen (1979) α = 137.035963 and the 1979 aₑ = 0.001159652200: in the script only. 11. Harvard 2008 aₑ: no reference. 12. COBE/FIRAS (Fixsen 2009): in Appendix B, not in the reference list. 13. PDG 1984 n–p values (1.293323(16) MeV; mₑ 0.5110034 MeV): in the script only. 14. NIST-26 G: no uncertainty given (ref. 19 links a NIST news page rather than the Metrologia paper). 15. Aspden's 1966 G (6.6676) and the dates of Notes 8 and 9: no source. 16. Measured muon lifetime 2.197 μs: no source or uncertainty. Note 15's formula: not given. 17. QED inputs in cavity_1983.py (fifth-order coefficient 6.7; non-universal terms 4.47×10⁻¹²): no source. 18. Rydberg energy 13.605693122990(15) eV: used in §6.3 but missing from Appendix B. 19. Deuteron moment from CODATA 2014 while other constants are CODATA 2022 (Appendix B): not explained. 20. LARES-2 (2026): cited only through a news site (ref. 9). 21. Lecture 16 (§9.5) and *Modern Aether Science* (1972, §6.3): no links. 22. Today's planetary data in mercury_aether.py, and the Sun's 230 km/s and R₀ = 8.2 kpc in cavity_1983.py: no source stated. 23. The values for individual G experiments (HUST, UWash, UZur, UCI, BIPM, JILA, LENS): no reference per value (refs. 17–19 are general). chain.py uses older values for three of them: UW-00 6.674215 (paper 6.674255), BIPM-13 6.67545(18) (paper BIPM-14 6.67554(16)), and JILA-10 6.67234(14) (paper's "corrected" 6.67260(25)). ### Corrections in register v1.4 (with working paper v2.1, Part 1 v1.5, Part 1A v1.2) | Item | Action | |---|---| | F1 M02 called the non-rotating, Earth-carried aether "the analysis's construction" | Corrected: it is Aspden's own frame (*Physics Unified* ch. 9; Lecture 8; 1983b, where he named the test). The verdict is unchanged; the test now cites his texts | | F2 U40 (v1.4) tested a lattice at rest in the cosmic background's frame | That was this analysis's choice. U40 now tests Aspden's Earth-carried frame as well: excluded by a factor of about 1,500 (W12) | | F3 Part 1's input I1 combined two assumptions | Split into I1a (Compton frequency) and I1b (the frames' relative speed is c). New test U41 shows I1b cancels out of α, N and d | | F4 M01 said Note 18 was not quoted, so the reading could not be checked | Part 1A, section 13.5 now quotes it and works through the algebra (W13); M01 step 4 added | | F5 Earlier reply to Doug: "every absolute size, and so 1/α, depends on" the c/2 postulate | Overstated. Working through POC 7.19–7.26 shows the postulate cancels out of α, N, d, m₀, b and E₀ for a given N (U41) |