Whittaker-ET: Science Contrarian review (Step 2)
Reviewer stance: I judge by experiment and by how claims were handled, not by consensus. I build the strongest honest case for each claim, and I apply the same rigour to Whittaker as to his critics. Source tags: [read] from the documents (I re-read the 1903 gravity pages 23-24 of the PDF as images myself), [web] from Investigator notes or the Q07 follow-up (I did not re-fetch these URLs; they are as retrieved by those agents), [calc] my own computation, [memory] with confidence.
Source gap, repeated from claims.md: the 1903 paper is a scan without text layer (equations read from images; journal pp. 347-353, the Helmholtz and generalized-Bessel parts, rest on a digest). The 1910 book is digest only. Not read by anyone yet: History Vol. 2 (1953), the 1927 paper beyond section 1, "Old and new ideas of gravitation" (Endeavour 1944), "From Euclid to Eddington". Where a conclusion below rests on those, or on [memory], I say so.
0. What kind of project this is (and why it matters for a contrarian)
Whittaker is not an outsider inventor with an anomalous device. He was a Cambridge/Edinburgh mathematical physicist, FRS, Royal Astronomer of Ireland, Secretary of the Royal Astronomical Society 1901-06 [web: research/2026-10-07-mactutor.md]. There is no experiment in the folder. So "tested or not?" has two layers: (1) the mathematics, tested by checking it, which it passes; (2) one physical suggestion (gravity as longitudinal waves in the medium of light), which is a hypothesis that later experiments can speak to. The hypothesis put to the review (Q07), "gravity as a longitudinal standing wave", is a third thing: a descendant of (2) that Whittaker did not write. I keep the three apart.
1. Claim-by-claim
Claim 1. General solutions of Laplace's and the wave equation as superpositions of functions of one variable (1903)
a. Internally consistent? Yes, with small defects. The deep reader reconstructed the proof (count of 2n+1 independent coefficients of degree n for Laplace; (n+1)^2 for the wave equation) and checked it with SymPy/NumPy [read: deep/On-the-Patial... section 5 table; calc by deep reader]. Proved per polynomial degree; extended to the whole solution V by assertion, with no convergence argument, so the result is local near a regular point. Misprints: the 1/r identity on journal p.334 holds only for z > c (for z < c the integral gives -1/r); a sign error and P2-for-P3 slip in the Legendre series on p.342; a missing x on p.346; the spheroid equation printed "= 0" for "= 1". None changes the theorem. b. Consistent with experiment? It is mathematics, so experiments neither support nor contradict it. It is consistent with every use made of it since (it is cited as "Whittaker's integral", the root of the Penrose transform and twistor theory [web: research/2026-10-07-zbmath.md; memory high]). c. Tested? Checked by others as a theorem: Stoney in 1903 called it "a singularly elegant proof" of a "recently discovered theorem" and "striking and most useful" [web: research/2026-10-07-oup-mnras.md, MNRAS 63, 424]. Bateman and later workers extended it [memory, medium]. d. If true, what changes? Nothing; it is already mainstream.
Verdict: Established (as mathematics; local, with the convergence step asserted rather than proved).
Claim 2. Every finite solution of the wave equation is a sum of plane waves in all directions
a. Consistent, conditional on F being "finite and continuous" over a range; this is Fourier-integral-theorem rigour of 1903, not a full statement of conditions [read: deep/On-the... section 4]. The deep reader also found that the wave moves toward negative x along the named axis, which is harmless since all directions are included. b-d. Same as Claim 1. Plane-wave analysis is standard Fourier analysis. Whittaker credits Stoney's 1897 physical reasoning for the same conclusion [read: deep/On-the... p.16 footnote; Stoney's paper itself not read].
Verdict: Established.
Claim 3. The 1904 two-scalar-potential expression of the field of moving electrons
a. Consistent. The deep reader checked numerically (30-digit mpmath) that the formulas reproduce the Lienard-Wiechert field (the exact field of a moving, accelerating point charge) including radiation terms to 12 digits, and that a single scalar plane-wave term of F or G gives an ordinary transverse EM wave [read: deep/the-electromagnetic-field...; calc by deep reader]. Whittaker states himself that no axis-free (symmetric) choice exists. b. Consistent with all classical electrodynamics; it is a reformulation (Hertz-vector / Debye-potential type [memory, high]). c. Tested in the sense that it is used: "scalar Whittaker potentials" appear in plasmon optics (Berthel et al., Phys. Rev. E 92, 033202, 2015) [web: research/2026-10-07-qeios.md]. All such uses give ordinary transverse fields. d. Nothing changes.
The contested part is a later reading, not the paper: that the 1904 potentials show EM fields to be "two interfering longitudinal waves", or tie electromagnetism to gravity (Bearden, Barrett 1993, Titleman arXiv:2205.08309) [web: research/2026-10-07-qeios.md, google.md; Q07 note section 4]. The paper's own text has no mention of gravity or "longitudinal" [read: Q07 text-layer search; deep read agrees]. Two honest statements follow. First, the reading is not in the paper, and the paper's own mathematics gives transverse d and h. Second, the reading is not refuted by anyone's experiment either: it is an interpretation of potentials, which are not directly measured except through fields (apart from the Aharonov-Bohm effect [memory, high]), so it makes no distinct prediction until a specific model is written down.
Verdict, split: (i) the reformulation of Maxwell-Lorentz theory: Established. (ii) "scalar longitudinal waves hidden in the potentials": Not testable as stated (an interpretation with no measurable difference from the transverse result). Not "tested, not supported", because no one has stated a measurable difference to test.
Claim 4. Gravity (any inverse-square field) as a sum of longitudinal waves in the medium of light
This is the claim the project exists for. I take it in the pieces Whittaker wrote.
What he wrote [read: PDF pp.23-24 = journal pp.354-355, page images, re-read by me]: - A static 1/r potential satisfies Laplace's equation, so "a fortiori" the wave equation for "any constant k", and so can be analysed into plane waves that "interfere ... in such a way that, when the action has once been set up, the disturbance at any point does not vary with the time". - Worked example: outgoing spherical waves (2 dmu / pi mu) sin(mu V t - mu r)/r sum, once Vt - r > 0, to (2/pi r) times the integral of sin y / y dy = 1/r. His italics: "independent of the time, and is everywhere proportional to the gravitational potential due to the particle". - Constituents "consisting of a simple wave-disturbance propagated with uniform velocity"; "the gravitational force in each constituent field will be perpendicular to the wave-front, i.e. the waves will be longitudinal"; "it seems probable that an identical property of the medium ensures their transmission through space"; the velocity "need not be the same as that of light, and may be enormously greater"; "this investigation does not explain the cause of gravity". - The Investigator found that every one of these sentences, including the "identical property" and "enormously greater" lines, appears word for word first in his 1902 MNRAS note, 62, 617-620 [web: research/2026-10-07-oup-mnras.md, page images pp.619-620]. He had the idea a year earlier and used the same words, so it was a settled view and not an aside.
a. Is the mathematics consistent? The identity is correct, with two caveats I checked [calc]: 1. For points the front has not yet reached (Vt < r) the printed sum gives -1/r, not 0. Whittaker restricts to Vt > r ("after the waves have reached the point"), which silently assumes no disturbance before the front. With a sharp cutoff in wavelength (no waves shorter than 2 pi / mu_max) the sum is (2/pi r) Si(mu_max (Vt - r)), where Si is the sine integral. Numerically for mu_max = 10, r = 1: at Vt - r = 1 the value is 1.056 (5.6% too high), at 5 it is 0.988, at 20 it is 0.9985, at 100 it is 0.9996 (times 1/r). So with any real cutoff, the "steady" field is steady only approximately, with a ringing remainder that falls off like 1/(mu_max (Vt - r)). That is exactly the physical worry in Stoney's critique below, put in numbers. 2. Each constituent force has a 1/r and a 1/r^2 part, flickering at frequency mu; they cancel in the sum only for the special amplitude weighting 1/mu [web: Stoney, research/2026-10-07-oup-mnras.md; I checked the derivative by hand: d/dr [sin(mu(kt - r))/r] = -sin/r^2 - mu cos/r]. Also the construction fixes no speed: any static potential satisfies the wave equation for every k. The equation is satisfied by "speed" 0.5c, 5c, or 10^10 c with identical static field. The mathematics cannot test the physical hypothesis. Only moving sources can. Verdict on (a): consistent; its physical content is smaller than its wording suggests.
b. Consistent with established experiments? Piece by piece, using Q07's web-sourced results [web: URLs as in research/2026-10-07-followup-Q07.md section 2, not re-fetched by me]: - Static field, Newtonian limit: consistent by construction (it is the same field). - Speed "enormously greater" than c: contradicted for gravitational waves. GW170817 / GRB 170817A: -3e-15 <= (v_gw - c)/c <= +7e-16 [web: arxiv 1710.05834]. A calculation by Q07 reproduces the scale: 1.74 s over about 4.1e15 s of travel gives about 4e-16. Whittaker's escape clause in 1903 (speed free) is therefore closed for radiation. Note the distinction: Laplace's old bound (at least 10^8 c from the Moon's motion) and Van Flandern's 1998 claim of at least 2e10 c from missing aberration were answered by Carlip (2000), who showed that velocity-dependent terms in general relativity cancel aberration at the first order [memory, high for the existence of the dispute; medium for the numbers]. The Kopeikin-Fomalont 2003 Jupiter measurement ((1.06 +/- 0.21) c) is disputed as to what it measured [memory, medium]. So "gravity is instantaneous" was a live issue for a century and the best direct test now says c. - "Same medium as light": this is where I give the idea its strongest honest case. Equal speed to 1 part in 10^15 is exactly what a shared medium predicts. It is also what general relativity's shared light cone predicts, so GW170817 does not separate them [web: Q07]. Light is bent and delayed by gravity (Shapiro delay, deflection), which is what a medium of variable index would do; the Dicke 1957 / Puthoff polarizable-vacuum model reproduces redshift, bending and perihelion at first order [web: Q07, citing Wikipedia "Polarizable vacuum" and Ibison]. Dicke was not an outsider; the idea is a respectable minority formulation. - "Longitudinal": gravitational waves observed by LIGO-Virgo-KAGRA are tensor (transverse); GWTC-3 reports "no evidence for ... non-GR modes of polarization" [web: arxiv 2112.06861]. A preprint (Jin and Zheng, arxiv 2610.08588, dated 6 Oct 2026, not peer reviewed) disfavours a breathing-mode amplitude comparable to the tensor amplitude in three events but notes interferometers respond weakly to breathing, so smaller scalar parts remain allowed [web: Q07]. A strictly longitudinal polarization is not tested well by two- and three-detector networks [memory, medium: a pure longitudinal mode has very low response in an interferometer]. So: tensor modes are seen; the absence of longitudinal ones is constrained, but not as hard as the tensor result. - Binary pulsar PSR B1913+16: observed orbital decay is 0.9983 +/- 0.0016 of the quadrupole prediction [web: arxiv 1606.02744]. Any extra scalar radiation channel must be small. The polarizable-vacuum model as published predicts 2/3 of the GR radiation power [web: Ibison, arxiv astro-ph/0302273]. Note the stake: Ibison was a colleague of Puthoff at the Institute for Advanced Studies at Austin [memory, medium], so this adverse result comes from inside the model's own research group, which makes it more credible, not less. - A scalar (single-potential) theory has a further known problem: Nordstrom's scalar gravity gives no light deflection and the wrong perihelion advance [memory, high]. Whittaker's 1903 scheme, read literally, is a scalar potential whose gradient is the force, so it needs the later general-relativistic content added to pass the classic tests. Whittaker himself did not pursue it: by 1927 he was solving Maxwell's equations inside general relativity (Schwarzschild field) with no aether [web: Q07, Proc. R. Soc. A 116, 720; only section 1 read]. That is a quiet but real fact: the author moved on from his own 1903 picture, though I have not read his 1944 "Old and new ideas of gravitation", which is the most likely place for his own late view. I do not treat his 1927 paper as a retraction. - Composition independence: MICROSCOPE finds eta = [-1.5 +/- 2.3 (stat) +/- 1.5 (syst)] x 10^-15 for Ti vs Pt [web: arxiv 2209.15487]. This constrains any medium response that depends on material. Related claims go the other way and I keep them in the record: C. F. Brush (1911-1929) reported that silicates fall slower by about 1e-5, with a Bureau of Standards check whose result has not been located [web: research/2026-10-07-rexresearch.md]; Munera 2019 and Darmos 2022 argue composition dependence from Cavendish-type data (a published response to Darmos exists) [web: research/2026-10-07-google.md]. Against them: Eotvos-type tests were reaching about 1e-13 or better by the 1990s-2000s [memory, medium; not checked] and MICROSCOPE is far tighter than 1e-5. These claims are not evidence for the Whittaker idea in any case: they concern composition, not wave character. The Brush record is an honest "never properly tested" for the specific 1e-5 claim as made (the check is missing), though later, far more sensitive tests cover the same effect.
c. Tested? By whom? - By argument, immediately: G. Johnstone Stoney (who named the electron), MNRAS 63 (1903) 424-428. He praised the mathematics and rejected the physics: each constituent force "flickers" at frequency mu, they sum to a steady force only for one special set of amplitudes, "the improbability of this assumption is so overwhelming that no physicist can feel himself justified in seriously arguing from the supposition that it represents the state of things which exists in nature, however much he may be impressed by the mathematical ingenuity of the investigation" [web: research/2026-10-07-oup-mnras.md]. This is a reasoned objection, not an experiment, and it is the earliest and best-aimed piece of criticism. Its force: nature has no reason to arrange waves with amplitude proportional to 1/mu. Its limit: Whittaker never said nature did; the field is the sum, and Fourier analysis of any static field always leads to such weights. The objection is stronger against physical reality of the constituents than against the representation. - A postscript to Stoney records a suggestion at the RAS meeting that Laplace's equation needs changing for moving bodies (Mercury) [web: same]. Whittaker's reply, if any, has not been found. Dismissed without an experiment? Not exactly: it was argued against in the journal where it was presented, in the same year. No funding or publication was blocked: it was published in Math. Annalen and MNRAS, and covered by the daily press (McCrea 1957 [web: research/2026-10-07-mactutor.md]); the press articles themselves were not found. The Jahrbuch review (JFM 34.0827.01) summarised it neutrally as "longitudinal waves ... with very great speed in a medium" [web: zbmath note]. - Sympathetic contemporary reading: McCrea 1957 says the result shows "how a static gravitational field can be regarded as resulting from effects that are being propagated through the field. In this way he anticipated some features of general relativity" [web: mactutor note]. I weigh this as a modest credit. The idea of finite propagation of gravity was old (Gauss, Riemann, Laplace, Weber [read: History Vol. 1 pp.206-207 per Q07; Chapter VIII deep read]). What Whittaker added was a demonstration that a steady 1/r field is compatible with any wave speed, which is true but, as noted above, follows from the fact that a static field satisfies the wave equation for every k. - By modern experiment: the speed (GW170817), the polarization (LVK), the radiation rate (Hulse-Taylor), and universality (MICROSCOPE), as above. Nobody has tested "Whittaker's 1903 idea" by name. They have tested the properties it would have to have. So "tested, not supported" applies to the specific properties (speed far above c; longitudinal radiation; a scalar radiation channel of the polarizable-vacuum type), and "never properly tested" applies to the residual (a shared medium with tensor response; an oscillating or spatially periodic component).
d. If true, what would change? Gravitation would have to be radiated as a longitudinal (scalar-like) mode, which would require a scalar partner to the tensor graviton with comparable coupling, or a different theory; the pulsar decay budget and LVK polarization bounds would need to be reinterpreted; light and gravity would share a medium with a rest frame, so Lorentz-invariance tests (lunar laser ranging, pulsar tests of preferred-frame effects [memory, medium]) become tests of it.
Verdict, split by piece: - The mathematical representation (static 1/r as a sum of longitudinal-looking waves with cancelling time dependence): Established (as an identity; caveats a.1-a.2). - Speed of gravitational waves "enormously greater" than c: Tested, not supported (GW170817). For the static field itself the speed is not testable. - Gravitational radiation is longitudinal: Tested, not supported (tensor modes seen; strictly longitudinal modes weakly constrained by interferometers, and I say so). - Gravity and light share an "identical property of the medium": Not testable as stated in the generic form (equal speed fits both a medium and spacetime geometry). The specific scalar polarizable-vacuum version: Tested, not supported (pulsar 2/3 result, as published; Ibison's calculation is one paper, not a replicated test; the question of a tensor-response medium stays open). - Physical reality of the constituent waves with the 1/mu spectrum (Stoney's objection): Never properly tested; not dismissed without argument, but argued against, not measured.
Claim 4b. A hypothesis put to the review (Q07): gravity as a longitudinal standing wave
This is not Whittaker's claim. "Standing" does not appear in the 1902 note or the 1903 paper [web: research/2026-10-07-oup-mnras.md; read: 1903 pp.23-24 by me]. The word comes from later writers: Barrett 1993 (as quoted by Titleman), Bearden from the late 1980s, Titleman 2023 and arXiv:2205.08309, with current "longitudinal standing wave" papers by others (Meyl; Gouveia 2025; CCSE in/out matter waves) [web: research/2026-10-07-qeios.md, google.md]. The labels these sources carry ("fringe" and similar) belong to the sources that gave them. Whittaker's field is a steady interference pattern of outgoing travelling waves, not one with fixed nodes. The distinction matters, because the two readings predict different things (Q07 section 3): - If "standing" means Whittaker's steady field: no static experiment can see it, since the constituents cancel by construction. Only the propagation speed of changes can test it, and that is c. - If "standing" means literally two counter-propagating waves at frequency f with fixed nodes: g would oscillate in time at each non-node point (testable with superconducting gravimeters, atom interferometers, torsion balances, pulsar timing); would vary periodically in space (short-range tests of the inverse-square law, with torsion-balance null results to about 50 micrometres [memory, high]); would carry energy that itself gravitates; and, if in the same medium as light, would modulate the optical refractive index (clock and optical-cavity comparisons, as in searches for oscillating constants [memory, medium]). Nothing like this has been seen. But also: no specific standing-wave model with a stated f and amplitude has been tested, so these are open "never specified, therefore never properly tested", not "tested and failed". Ultralight scalar dark matter is the mainstream analogue and is being searched for in pulsar timing, with so far limits and no detections [memory, medium; not re-checked].
Verdict: Not testable as stated (no frequency, wavelength or amplitude given); each concrete version is Never properly tested, and the simplest scalar-medium form runs into Tested, not supported (pulsar radiation, polarization).
Claim 5. Whittaker's 1951 view: the aether name may fitly be kept for the quantum vacuum; and his history of gravity in the medium
a. Not a derivation, so internal consistency is not the issue. The history is accurate to what the deep reader checked in Chapter VIII (Riemann 1853; Maxwell 1861-2 vortices, 1864 attempt at gravity abandoned for the enormous energy the medium would need; Kelvin 1896 on condensational waves, contested by FitzGerald in a private letter to Heaviside, one party's account) [read: deep/1951-A-History...]. He gives no derivation of longitudinal EM waves. Items the deep reader could not verify (Maxwell's 1869 dispersion algebra, signs in the 1864 equations, the Poynting-Barlow coefficient "3P") do not bear on the verdict. b. The preface's argument has experimental footing: the vacuum is not "nothing": zero-point effects, vacuum polarization, the Lamb shift and the Casimir force are measured [memory, high]. Against it: the gravitational weight of that vacuum energy is off from observation by of order 10^120 on naive estimates (the cosmological constant problem [memory, high]), so "rich in physical properties" is also where the largest known mismatch in physics sits. Keeping the word "aether" is a terminology choice; mainstream physics does not use it. c. Whittaker had an interested stake in this view: Navarro (History of Science 59, 2020) attributes the shape of Vol. 2's treatment of Einstein to general relativity's low standing in the early 1950s and Whittaker's commitment to the aether and to a gravity-EM link; the antisemitism question is left open by Navarro; Vol. 2's relativity chapter credits Poincare and Lorentz, a priority dispute [web: research/2026-10-07-sagepub.md; README]. This is reported as that historian's account, with Vol. 2 still unread by us. It bears on reading Whittaker's later aether views as partly personal and partly period-typical, not as a physical argument. d. Nothing in mainstream physics would have to change for a terminology revival.
Verdict: Historically superseded but instructive (the aether as the physical seat of fields); the vacuum-as-aether proposal: Not testable as stated (terminology/interpretation).
2. How the claims were rejected: the record
- Whittaker's gravity suggestion was published in a major journal (Math. Annalen) and in the RAS Monthly Notices, got press attention and one prompt, reasoned rejection (Stoney). I found no sign of suppression, blocked funding or suppressed data; the record is thin rather than hostile. After 1903 the trail goes quiet on the idea itself: no reply to Stoney has been found, and no further papers on the aether wave theory of gravity are known to us until the 1943-44 Endeavour articles (unread). Per SOURCE HONESTY this is an anomaly to analyse, not a gap to ignore. Competing explanations: (1) he abandoned it after Stoney and the arrival of relativity (supported by his 1927 work inside GR; not documented in his own words); (2) he treated it as a representation, not a theory (supported by "does not explain the cause of gravity"); (3) he kept the view privately (Fisher Library letters and an autobiography in Box 11, MS COLL 00219, exist but only the owner can obtain them [web: research/2026-10-07-utoronto-fisher.md]). The 1944 Endeavour article and Vol. 2 would decide among them.
- The mainstream destiny of the mathematics is the opposite of rejection: it became a major tool, including for gravitational radiation itself (Thompson, Swearngin and Bouwmeester 2014 build linearised gravitational waves from the "Whittaker solution" [web: research/2026-10-07-zbmath.md, google.md]), but there as tensor, transverse waves with no medium. That is the clearest honest summary: the maths won; the physical picture lost.
- The negative experiments (GW170817, LVK, Hulse-Taylor, MICROSCOPE) are sound as far as I can tell; they are public data analysed by large collaborations and were not tailored to defeat this idea. I found no reanalysis disputes against them in the notes. Not checked beyond the notes: [memory] only for the dispute around speed-of-gravity interpretations noted above.
3. Strongest honest case for Whittaker, and the strongest case against
For: (1) the maths is sound and productive. (2) He saw in 1902-03 that a static inverse-square field can be understood as the zero-frequency sum of propagating disturbances, and that a finite propagation speed does not disturb it; the modern retarded-field picture is the cleaner form of this. (3) He explicitly held back from a cause ("does not explain the cause of gravity") and gave a testable-in-principle speed hypothesis. (4) "Same medium, same speed" has been vindicated in its weak form (speed equality to 1e-15). (5) Dicke's later polarizable-vacuum model is a serious relative; Ibison's pulsar objection applies to the scalar version as published, not to tensor-response media.
Against: (1) the longitudinal character is a feature of how the scalar potential is split into plane waves, not a physical property proved by anything; the radiation actually observed is tensor. (2) The constituents require a fine-tuned 1/mu spectrum and leave ringing under any cutoff [calc above]. (3) The speed escape clause is ruled out by direct observation. (4) The mathematics fixes no speed, so it cannot be tested with static fields. (5) He moved to GR within 25 years. (6) Later "standing wave" readings add a property not in his text.
Rigour toward the critics: Stoney's objection is strong against physical reality of the constituents but does not touch the representation; the pulsar objection by Ibison comes from inside the model's own group and is a single paper; Van Flandern's aberration argument was answered by Carlip in GR (my [memory] only, not re-fetched); "longitudinal modes absent" is a weaker statement than "tensor modes present". I would not call any of these a hearing in which the whole idea was tested.
4. Corrections to Step 1
- claims.md Source gap lists the 1902 MNRAS note as "not obtained". The Investigator has since read it (MNRAS 62, 617-620 [web: page images]); it contains the same gravity statement word for word and first states the longitudinal character. This is an addition, not an error in what claims.md says; claim 4 should cite 1902 as the first statement and note that the "identical property of the medium" and "enormously greater" sentences are in both. A07's open item "1902 MNRAS note ... unread" is now read (its own Corrections section in sites.md already says this).
- claims.md claim 4 and facts.json: the printed sum gives -1/r for Vt < r, and the "steady" result needs Vt > r; with a wavelength cutoff it only approximates 1/r and rings [calc]. The facts.json summary already notes the -1/r issue for the z > c identity on p.3, but not this one on journal p.354; add it. Note that I read journal p.354 directly: the printed formula says "after the waves have reached the point r, so that (Vt - r) is positive", consistent with Whittaker having been aware of the restriction.
- facts.json says Whittaker's "field is a steady interference pattern, not a textbook standing wave". I agree and reconfirmed from PDF pp.23-24; but facts.json and claims.md do not tell the reader where the "standing wave" wording comes from. Add: it is from Barrett (1993), Bearden and Titleman, not from Whittaker [web: qeios and google notes].
- claims.md claim 3 correctly says the 1904 paper does not mention gravity; the reader should also be told that the later "two longitudinal waves" reading (Titleman, Bearden) is not in that paper and differs from its own result that each scalar plane-wave term gives a transverse EM wave. Added above under Claim 3.
- _text/README (project note) states that Internet Archive copies of History Vol. 2 are lending-restricted; the Investigator found an item on archive.org that lists an original PDF and OCR text, access flag unchecked [web: research/2026-10-07-archive-org.md, sites.md Corrections]. Treat as unconfirmed rather than wrong; also a rexresearch1.com copy of Vol. 2 was seen in a search result (Q07). Both need the owner's approval to download.
- followups.json A07 attributes the page range "pp. 353-355" to section 5 part 5; I verified it: the 1/r sum is on journal p.354, and the longitudinal/medium/speed sentences are on p.355. The deep reader labels these as PDF p.23/24, which is correct for PDF pages. No error, but a reader checking the journal should use p.354-355 and PDF pp.23-24.
- Weak point in Step 1 weighting: facts.json says the 1903 deep read covered journal pp.333-347 only and that the gravity section (pp.353-355) rests on the digest and A07. I read PDF pp.23-24 myself and found both consistent with A07 and the deep reader's quotes. That upgrades confidence on claim 4's wording; parts 2-4 of section 5 (pp.347-353) remain unread.
5. Investigator findings kept in this review (whatever the verdict)
- Whittaker 1902 MNRAS note (own work; first statement; same words) and the History Vol. 2 (1953) and Fisher Library (letters, autobiography) leads, plus his later gravity-EM papers (1928 lecture comparing EM in a gravitational field to a medium of variable epsilon and mu, "not quite perfect"; 1935 Observatory; 1943-44 Endeavour) [web: sites.md lead 1].
- Stoney 1903 critique and its Mercury postscript (against), the JFM reviews, McCrea 1957 (sympathetic) [web: lead 2].
- Twistor lineage (Hitchin, Mason, Ward 1989, Dunajski 2005), Thompson-Swearngin-Bouwmeester 2014 gravitational waves from Whittaker's solution; Barrett/Bearden/Titleman "standing wave" line; Brush 1911-1929 aether-wave gravity with a missing Bureau of Standards check; Lodge's 1911 objections to Brush; Munera 2019; Darmos 2022 with a published response; T. J. J. See 1917; Meyl; Gouveia 2025; scalar Whittaker potentials in plasmon optics (Berthel 2015) [web: lead 3]. The source labels ("fringe" and the like) are the sources' own and are not my verdict.
- Whittaker was RAS Secretary when the 1902 note appeared; the exchange was indexed across the 1903-04 abstracting services; Navarro 2020 and 2025 on Vol. 2, the priority dispute and his Catholicism and physics [web: lead 4].
- Records still wanted: Whittaker's reply to Stoney (if any); the 1903 press articles; 1944 Endeavour "Old and new ideas of gravitation"; History Vol. 2; Fisher Library MS COLL 00219; the Bureau of Standards result on Brush's experiment.
6. What would settle it
- For the representation: nothing is needed; it is correct.
- For the physical claim: a measured departure of the gravitational response of a moving source from the GR retarded form that is better fitted by a scalar longitudinal channel, or a detected scalar (breathing or longitudinal) polarization in gravitational waves with a detector network able to see it. Also, for the standing-wave variants: a gravimeter, atom interferometer or pulsar-timing signal at a fixed frequency that correlates with an optical-clock modulation at the same frequency (the most direct "same medium" test, Q07).
- For why Whittaker moved on: the 1944 Endeavour article and Vol. 2.
7. Verdict summary
| Claim | Verdict |
|---|---|
| 1. General solutions of Laplace's and wave equations | Established (local, convergence asserted) |
| 2. Plane-wave decomposition of all finite wave solutions | Established |
| 3. Two-scalar-potential field of moving electrons (1904) | Established (reformulation); "hidden longitudinal scalar waves" reading: Not testable as stated |
| 4. Gravity as longitudinal waves in the medium of light (1902-03) | Split: representation Established; speed far above c Tested, not supported; longitudinal radiation Tested, not supported; shared medium (generic) Not testable as stated, scalar polarizable-vacuum form Tested, not supported; physical reality of constituents Never properly tested |
| 4b. Q07 hypothesis, "longitudinal standing wave" | Not testable as stated; concrete versions Never properly tested |
| 5. 1951 view: vacuum as aether | Historically superseded but instructive; vacuum-as-aether Not testable as stated |