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Whittaker-ET: central claims

Source gap (partial, updated after the QE-remediation deep reads, 2026-10-07): the key works are now read. The 1903 Mathematische Annalen paper is a scan with no text layer (OCR only, equations lost), so every equation was read from page images; all of journal pp. 333-355 have now been read as images, including section 5 parts 2-4 (Helmholtz equation, generalized Bessel functions, journal pp. 347-353), which are pure mathematics with no physical claim. The 1951 History Vol. 1 was deep-read on Chapters V, VIII, IX and XIII and on the gravity passages (PDF pp. 16-23, 32-33, 56, 71-81, 110-111, 127-154, 200-212); its other chapters rest on digests. The 1910 History is digest plus a deep-read comparison of four passages with 1951. Read on the web by the Investigator, not in the project folder: the 1902 MNRAS note (62, 617-620) and Stoney's 1903 critique (63, 424-428). Not obtained, so conclusions about them rest on [memory] or on the follow-up A07 web notes: the 1927 paper "On electric phenomena in gravitational fields", the 1944 Endeavour article "Old and new ideas of gravitation", and From Euclid to Eddington (1949). History Vol. 2 (1953) is now in the folder (added 2026-10-07 13:03) and has been read this way: all 15 chunks digested; Chapter V 'Gravitation' (PDF pp. 155-207, book pp. 144-196) deep-read from the text layer with page images for the key equations and sentences (PDF = book + 11 in that chapter); the Cunningham, Planck/Nernst zero-point, Einstein 'with some amplifications' and Hargreaves passages checked by text search and context reading only; the rest of the volume (radioactivity, Chapter II beyond one passage, quantum theory, matrix and wave mechanics) rests on digests, and the QE-requested deep reads of the index, Chapter II, the preface and Faraday in Vol. 1 were not run. Unread sources behind the 1951 pulsation-gravity passages: Hicks (1879-80), Leahy (1884-85), Korn (1898), Larmor (1895), Witte and V. Bjerknes (1909-10), Riemann/Hattendorff (1875); only Whittaker's reports of them are known.

Any solution of Laplace's equation is a superposition of functions of one complex variable, V = integral of f(z + ix cos u + iy sin u, u) du, and any solution of the wave equation is V = double integral of f(x sin u cos v + y sin u sin v + z cos u + t/k, u, v) du dv (1903; proved for each polynomial degree, extended to the whole solution by assertion, so valid locally near a regular point and for real-analytic solutions; the sweeping "periodic without loss of generality" step is vacuous for the integral and the real restriction is analyticity and local validity). [read]
Every finite solution of the wave equation (finite and continuous on a range, locally) can therefore be analysed into plane waves travelling in all directions. [read]
The electromagnetic field of any moving electrons, and any source-free field, can be derived from two scalar potential functions F and G (built from retarded charge positions, tied to a chosen axis, each obeying the wave equation) instead of four; this reproduces the Lienard-Wiechert field exactly (1904, checked numerically by the deep reader). The paper itself does not mention gravity, longitudinal waves or any structure of the aether, and each scalar plane-wave term gives an ordinary transverse electromagnetic wave; Whittaker's own 1951 History (book p.409) calls F and G "two plane-polarised components". The reading of these potentials as hidden longitudinal or density ("scalar") waves is later writers' (Bearden, Barrett, Titleman, the AIAS group), criticised by Trovon de Carvalho and Rodrigues (2001) [web]; its 19th-century root is Riemann's 1861 reading of the potential as an aether density (claim 6). [read]
Gravity (and any inverse-square potential) can be viewed as a sum of longitudinal plane or spherical waves in the medium that carries light, whose interference leaves a field that does not vary with time. First stated in the 1902 MNRAS note (62, 617-620) [web], then in 1903 (section 5 part 5): the speed need not equal that of light and "may be enormously greater", "it seems probable that an identical property of the medium ensures their transmission" (both sentences match in 1902 and 1903), and the work "does not explain the cause of gravity". The two closing sentences differ: 1902 says the propagation of inverse-square forces needs no property "other than one which has long been known and accepted"; 1903 says "we have only to suppose that the medium is capable of transmitting, with a definite though large velocity, simple periodic undulatory disturbances, similar to those whose propagation by the medium constitutes, according to the electromagnetic theory, the transmission of light". The worked sum is sgn(Vt - r)/r: +1/r where Vt > r, -1/r outside the front (a source that changes sign from -1 to +1 at t = 0, with a delta-function shell in the force at r = Vt); the field is steady only inside r < Vt. This is a superposition of outgoing travelling waves, not a textbook standing wave with fixed nodes; "standing wave" is the wording of Barrett (1993), Bearden and Titleman, not Whittaker's. It is the root of a speculative hypothesis put to the review (follow-up Q07/A07). In 1953 Whittaker's own History (Vol. 2) says, in his own voice, that Laplace's reasons for a gravity speed far above that of light "do not to twentieth-century minds seem very plausible" (bk 149), that relativity requires gravity to be "propagated with the speed of light" and that observation does not contradict this (Poincare, bk 151), and that gravitational waves travel "with the speed of light" (bk 183); it records Einstein's abandonment of "a single scalar potential-function" (bk 156-157) and Lorentz's 1900 wave-pressure gravity, which needed electromagnetic energy to disappear (bk 149-150). It never mentions his 1902-03 suggestion, his 1903 paper or Stoney, and neither retracts nor repeats the "enormously greater" speed. [read: Vol. 2, PDF pp.157-168, 194; 1902 and Stoney's 1903 critique: web]
In 1951 Whittaker held that the vacuum of quantum electrodynamics (zero-point oscillations, fluctuations, polarisation) is "so rich in physical properties" that the historical word "aether" may fitly be retained. His history records that the aether's resistance to compression gave gravity in Riemann's 1853 model, that Maxwell abandoned a medium explanation of gravity in 1864 for want of a sensible energy distribution, and that Maxwell's own waves are transverse (the only longitudinal electromagnetic wave discussed in Chapter VIII is Kelvin's 1896 speculation, contested by FitzGerald). Vol. 1 mentions his own work only for the 1904 F and G potentials and is silent on his 1902-03 undulatory gravity. Vol. 2 (1953) adds, in his own voice: Cunningham's scheme (the aether given velocity c at every point) is relativistically invariant, "so that an objective aether is not necessarily foreign to the point of view of the principle of relativity" (bk 248); FitzGerald's 1894 "change of structure of the aether" is, for Einstein, "space" or "space-time" and the "structure" is "curvature", and in a static gravitational field feeble electromagnetic phenomena follow Maxwell's theory in a medium whose permittivity and permeability vary from point to point (Copson 1928: epsilon = mu = (r+1)^3/[r^2(r-1)] near a point mass; Wiechert 1920) (bk 157-158); Planck's zero-point energy of 1911-12 and Nernst's 1916 suggestion that the aether everywhere might be occupied by zero-point energy (bk 103-104). The aether he keeps is thus space-time with medium-like properties, not a mechanical substrate with its own longitudinal waves. Setting Whittaker's own framing of the relativity story (Einstein set forth "the relativity theory of Poincare and Lorentz with some amplifications", bk 40) beside the historian Navarro's characterization that his commitments shaped it is left to the reader. [read: Vol. 2 PDF pp.51, 114-115, 168-169, 259; Navarro: web, abstract only]
Whittaker's History (identical in substance in 1910 and 1951) records the 19th-century models in which gravity or the potentials are carried by longitudinal (compressional) motion of a medium, as other people's hypotheses with no test described: Bjerknes (bodies pulsating in phase in an incompressible fluid attract with an inverse-square force; "otherwise attractions would change to repulsions ... at distances greater than a quarter wave-length"), Leahy (in an elastic medium like phases repel), Korn 1898 and Larmor 1895 (gravitation from pulsating bodies or vacuous electrons), Riemann 1853 (gravity from the aether's resistance to compression) and Riemann 1861 (the scalar potential as aether density, with the difficulty that the field energy does not match the model's), plus the older record of gravity through a medium (Newton, Le Sage, Euler, Laplace's gravific fluid of at least 10^8 c, Tisserand's 14 arcsec of Mercury's 38 arcsec excess). He also records how the elastic-solid light medium kept its longitudinal mode quiet by an indefinitely great (Fresnel, Stokes, Green), zero (Cauchy, Kelvin) or absent (MacCullagh) speed. These are the closest historical relatives of the "gravity as a longitudinal standing wave" hypothesis put to the review (Q07) and carry checkable constraints (all sources in phase; d below a quarter wavelength in a compressible medium). [read]

Corrections to earlier documents - Every earlier statement that History Vol. 2 (1953) is "not obtained" or "unread" (this file's Source gap, facts.json's 1951 summary, physicist.md, mathematician.md and contrarian.md line 5, arbiter.md line 5 and Open questions, primer.md Source note, section 7 and section 9, the first qe.md M6) is out of date: Vol. 2 is in the folder and was read as stated in the Source gap. The orchestrator applies this to the arbiter ("QE revision 2"), the primer and followups.json (A07). - QE-2 (qe.md) said Chapter V ends at PDF p.200 and that Whittaker described Nordstroem's theory as scalar and that Lorentz rejected the Mossotti model; the deep read corrects this: Chapter V runs to PDF p.207 (bk 196); Whittaker names Nordstroem with references only (the "scalar" label is QE's and the primer's [web]); he says only that no strong physical reason for the Mossotti hypothesis could be given in 1900. QE's self-citation list omits bk 186 (1931). Vol. 2 does not contain the phrase "not quite perfect" (that is from the 1928 lecture report [web]); it credits the point-charge medium result to Copson (1928) and the dielectric reading of FitzGerald to Wiechert (1920). - Vol. 2's own cross-reference "Vol. I, pp. 207-8" for Laplace uses book pages, supporting the book-page convention below. - digest/On-the-Patial-Diffential-Equations-...-73687e (p.23): reports the total disturbance as "4/r". The page image gives the sum (2/pi r) times the integral of sin y / y dy, which equals 1/r where Vt > r (deep read, journal p.354). Digest p.2 and p.11 also write the wave equation as "d2V/dt2 + d2V/dx2 + ... = 0"; the paper has del^2 V = k^2 d^2V/dt^2. - digest/the-electromagnetic-field-...-58c678 (p.5): the vector formulas lack the time derivatives; the page image shows d = curl curl f + curl (1/c) g-dot and h = curl (1/c) f-dot - curl curl g. The coordinates in F and G are retarded positions (deep read of the 1904 paper). - Earlier claims.md claim 4 (and facts.json, A07) said the sum is 1/r "once Vt > r" and called the field steady; it is sgn(Vt - r)/r, steady only inside r < Vt (arbiter correction 1). The earlier Source gap listed the 1902 note as not obtained; it has been read on the web. "Standing wave" was not Whittaker's wording (arbiter correction 3). Claims 1 and 2 are now qualified (arbiter correction 4). - Page convention: citations of "History Vol. 1 pp. 206-207" in A07, physicist.md and contrarian.md are BOOK pages; Laplace is bk 206-207 (PDF p.110), Tisserand bk 207-208 (PDF p.111). Laplace's bound is "at least a hundred million times" the speed of light (10^8 c), not "millions of times" (primer s3.5) and not 7 x 10^6 c. - QE M1 omitted Leahy's stated condition: his reversal holds when the wavelength is large compared with the separation (an effect of the elastic medium at short range), not the beyond-quarter-wavelength sign change of the compressible case. The two are distinct. - 1903 closing sentences: the contrarian's "every one of these sentences ... appears word for word first in his 1902 MNRAS note" overstates; only the "identical property" and "enormously greater" sentences match (see claim 4). - No discrepancy with followups.json answer A07 beyond the sgn(Vt - r)/r qualification and the A07 line "the scalar version of that medium fails on radiation", which rests on Ibison's analysis of the Dicke-Puthoff model (arbiter correction 6); the orchestrator applies these to followups.json.