Follow-up Q07: is gravity a longitudinal standing wave in the medium that carries light?

Date: 2026-10-07. Follow-up investigator (STEP F). Chrome used throughout (one new tab, closed at the end). Web time by the date +%s timer: 267 seconds (about 5 minutes); stopped because the question was answered, not because of the cap. Project state: Whittaker-ET was added to the selected list today; there is no _text/, claims.md, facts.json, arbiter.md or primer.md yet, so the source PDFs were read directly (read only) from source folder: Whittaker-ET/.

The question

"Speculative: is gravity a longitudinal standing wave in the same medium that carries light? First report exactly what Whittaker wrote about gravity: the closing pages of his 1903 Mathematische Annalen paper (longitudinal waves, propagation of gravity), the 1904 two-scalar-potentials paper, and his later gravity/electromagnetism papers (e.g. 'On electric phenomena in gravitational fields', Proc. R. Soc. A, 1927). Then weigh the idea against: the equal speed of gravity and light (GW170817, which constrains but does not by itself separate a medium from spacetime); LIGO/Virgo polarization tests (tensor vs breathing/longitudinal modes); the Hulse-Taylor quadrupole orbital decay; composition-independence tests (Eotvos, MICROSCOPE); and the Dicke 1957 / Puthoff polarizable-vacuum model, in which gravity is a change in the vacuum dielectric (epsilon = K epsilon0, mu = K mu0). What would a standing, rather than travelling, longitudinal wave predict that an experiment could detect?"

Short answer

Whittaker did write a wave theory of gravity, and it was literally a "standing" field built of travelling longitudinal waves. In 1903 he showed that the steady 1/r potential of a mass can be written as a sum of outgoing spherical waves whose time variation cancels once the front has passed, so the total "does not vary with the time". He called each constituent wave longitudinal, said it "seems probable" that the same property of the medium carries gravity and light, and allowed the speed to be "enormously greater" than light. He said plainly that this was a representation, not a cause. The 1904 paper does not mention gravity. By 1927 he was working inside general relativity (GR), not an aether.

Measured today: the speed of gravitational waves equals the speed of light to about 1 part in 10^15 (this rules out Whittaker's "enormously greater" for waves, but agrees with his "same medium" guess as well as it agrees with GR). The waves seen so far are tensor (transverse) waves with no detected scalar (breathing or longitudinal) part. Binary pulsar decay matches the GR quadrupole formula to 0.2%. A scalar polarizable-vacuum model gives 2/3 of that. All materials fall alike to about 10^-15. A truly standing wave (one that oscillates in time, or has fixed nodes in space) would show up as an oscillating or spatially periodic g. That is searched for today as ultralight scalar dark matter, and nothing has been found so far.

1. What Whittaker wrote about gravity

1a. 1903, "On the partial differential equations of mathematical physics", Math. Ann. 57, 333-355, §5° (pp. 353-355)

Read from page images of the project PDF (no text layer) [read: page images pp. 353-355 (PDF pp. 22-24)].

Section title: "5°. Gravitation and Electrostatic Attraction explained as modes of Wave-disturbance."

The argument, step by step: 1. Any potential V of inverse-square forces satisfies Laplace's equation ∂²V/∂x² + ∂²V/∂y² + ∂²V/∂z² = 0, "and therefore à fortiori" the wave equation ∇²V = k² ∂²V/∂t² "where k is any constant" (a static V has ∂²V/∂t² = 0, so the wave equation holds for every speed 1/k). 2. From his §1° result, such a V "can be analysed into simple plane waves in various directions, each wave being propagated with constant velocity. These waves interfere with each other in such a way that, when the action has once been set up, the disturbance at any point does not vary with the time". 3. Worked example. A particle emits spherical waves; the waves with wavelength between 2π/μ and 2π/(μ+dμ) give the disturbance (2 dμ/πμ)·sin(μVt − μr)/r, with V the speed of propagation. Once the waves have reached r (Vt − r > 0), the sum over all μ is (2/πr)∫₀^∞ (sin y / y) dy with y = μVt − μr, and since ∫₀^∞ sin y / y dy = π/2, the total is 1/r. His italics: "The total disturbance at any point, due to this system of waves, is therefore independent of the time, and is everywhere proportional to the gravitational potential due to the particle at the point." 4. Interpretation (p. 355): the field of a gravitating body can be analysed "by a 'spectrum analysis' as it were" into constituent fields; "although the whole field of force does not vary with the time, yet each of the constituent fields is of an undulatory character, consisting of a simple wave-disturbance propagated with uniform velocity." In each constituent the potential is constant along a wavefront, so the force is perpendicular to the wavefront: "the waves will be longitudinal." 5. Light and gravity (p. 355): these results "assimilate the propagation of gravity to that of light"; the gravitational waves (varying vector perpendicular to the wavefront) are compared with light (electric and magnetic forces parallel to the wavefront). "The waves are in other respects exactly similar, and it seems probable that an identical property of the medium ensures their transmission through space." 6. Speed (p. 355): "This undulatory theory of gravity would require that gravity should be propagated with a finite velocity, which however need not be the same as that of light, and may be enormously greater." 7. Limits he set himself (p. 355): "Of course, this investigation does not explain the cause of gravity"; it shows only that the medium need transmit "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."

Notes for the reader (inference, not Whittaker's words): - Whittaker's "standing" field is not a standing wave in the textbook sense (fixed nodes and antinodes oscillating in time). It is a sum of outgoing travelling waves whose time dependence cancels, giving a steady 1/r behind the front. In modern terms, this is the Fourier picture of a static field that switches on as a front moving outward at speed V. - Because a static potential satisfies the wave equation for any k (step 1), the construction itself does not fix V. The mathematics fits any speed, including instantaneous. Only a time-varying source (a mass that moves) can reveal V. That is where the modern tests bite. - A mathematician's detail: the formula as printed gives −1/r for points the front has not yet reached (Vt < r), because ∫₀^∞ sin(μa)/μ dμ = −π/2 for a < 0. Whittaker restricts the result to points "after the waves have reached the point r", which amounts to assuming no disturbance before the front arrives. This does not change his conclusion. - Wikipedia's bibliography lists an earlier note with the same idea: "On the General Solution of Laplace's Equation and the Equation of Wave Motions, and on an undulatory explanation of Gravity", Mon. Not. R. Astron. Soc. 62 (1902) 617-620, doi:10.1093/mnras/62.9.617 [web: https://en.wikipedia.org/wiki/Bibliography_of_E._T._Whittaker]. Not read: the ADS scan did not load in Chrome (see sites.md).

1b. 1904, "On an expression of the electromagnetic field due to electrons by means of two scalar potential functions", Proc. London Math. Soc. (2) 1, 367-372

Text layer searched for "grav", "longitud", "aether/ether", "medium" [read: pdftotext of the project PDF]. There is no mention of gravity, and the word "longitudinal" does not occur. "Aether" appears only as the seat of "the dielectric displacement in the aether" (p. 367) and "c the velocity of light in the aether" (p. 367). The paper's stated object (p. 367): the six field components "can be expressed in terms of the derivates of two scalar potential functions", replacing the usual scalar plus vector potential ("equivalent to four scalar potential functions"). The later reading that EM fields are "two interfering longitudinal waves", and the link to gravity, belong to later writers (e.g. Bearden; Titleman, below), not to the 1904 paper.

1c. 1927 and later: inside general relativity

"On electric phenomena in gravitational fields", Proc. R. Soc. A 116 (1927) 720-735, doi:10.1098/rspa.1927.0160, received 23 September 1927. §1 read from the publisher's PDF in Chrome [web: https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1927.0160, p. 720]: - "It is a consequence of general relativity that all electromagnetic and optical phenomena are influenced by a gravitational field." The bending of light is "a particular application of this principle", so "the classical electromagnetic theory must be rewritten in order to take account of the interaction between electromagnetism and gravitation". - He takes two fields: Schwarzschild's field of a single attracting centre and "a limiting form of it" (a quasi-uniform field), and solves Maxwell's equations in them, ignoring the electromagnetic field's own effect on the metric. Results: the field of an electron at rest in a quasi-uniform field (his eqs. 15, 19) and spherical EM waves of short wavelength around a gravitating centre (eq. 43), mostly in Bessel functions. Motive: atomic physics (electrons near a massive nucleus). - Only §1 was read; §§2-end (pp. 721-735) not read.

His other gravity/EM papers, from the bibliography (titles and identifiers [web: Wikipedia bibliography]; not read): "On Hilbert's world-function" (Proc. R. Soc. A, Jan 1927); "Note on the law that light-rays are the null geodesics of a gravitational field" (Proc. Camb. Phil. Soc., 1928); "The Influence of Gravitation on Electromagnetic Phenomena" (Nature 121, 1928); "On the potential of electromagnetic phenomena in a gravitational field" (Proc. R. Soc. A, 1928, doi:10.1098/rspa.1928.0130); "On the definition of distance in curved space, and the displacement of the spectral lines of distant sources" (Proc. R. Soc. A, 1931); with Kermack and McCrea, "On properties of null geodesics..." (Proc. R. Soc. Edinb., 1933); "On Gauss' theorem and the concept of mass in general relativity" (Proc. R. Soc. A, 1935). Historical and popular pieces: "The aether: past and present" (Endeavour, 1943) and "Old and new ideas of gravitation" (Endeavour, 1944). The second is the most likely place for his late view of his own 1903 idea. Not obtained.

1d. Whittaker the historian on the speed of gravity

History of the Theories of Aether and Electricity, Vol. 1 (1951), pp. 206-207 [read: OCR text layer]. He writes that "gravitation is propagated by the action of a medium, and consequently is a process requiring time" "had been an article of faith with many generations of physicists". He reports Laplace's "gravific fluid" (gravity with aberration, like light): from the Moon's secular motion, Laplace found its speed "must be at least a hundred million times greater than that of light", and Whittaker calls the assumptions "in the highest degree questionable". He also reports Tisserand (1872): a Weber-type velocity-dependent law with propagation speed equal to that of light turns Mercury's perihelion 14″ per century, against an observed excess of 38″. This bears on his 1903 remark that the speed "may be enormously greater".

2. Weighing the idea against the evidence

Equal speed does not separate a medium from spacetime. In the PV picture, light moves at c/K^(1/2) in the medium (refractive index n = K^(1/2)) [web: Wikipedia PV page, the metric with κ² = K]. If gravitational disturbances are disturbances of the same K, they share the same speed and the same delay near masses (Shapiro delay). GW170817 is therefore consistent with "the same medium". What fails is the specific scalar version (2/3 radiation, no frame dragging, scalar polarization), not the medium idea as such. A medium with tensor (direction-dependent) properties can mimic GR more closely. Wikipedia notes de Felice's susceptibility tensor, and Ibison mentions "accommodation of vacuum anisotropy" [web: same pages].

Worked number: how tight is "same speed"?

At 40 Mpc, the light travel time is 40 × 3.086×10²² m ÷ 3.00×10⁸ m/s ≈ 4.1×10¹⁵ s (about 130 million years). If the whole 1.74 s delay were due to a speed difference, |Δv|/c ≈ 1.74 / 4.1×10¹⁵ ≈ 4×10⁻¹⁶. The published bound is a little wider (−3×10⁻¹⁵ to +7×10⁻¹⁶) because it uses a conservative distance and allows the gamma rays to have been emitted up to 10 s late [web: arXiv 1710.05834; arithmetic here].

3. What would a standing, rather than travelling, longitudinal wave predict?

There are two different meanings, and they predict different things.

(a) Whittaker's meaning: a steady field built of travelling waves. For steady sources it predicts exactly the Newtonian 1/r field. No experiment on a static field can see the constituent waves, because their time variation cancels. The only testable content is how fast changes propagate when sources move. Tests: GW170817 (speed = c), and, for the near field, the debate over whether the speed of gravity has been measured. Related work [memory, high confidence]: Van Flandern (1998) argued from the absence of aberration that the speed is at least 2×10¹⁰ c, which echoes Laplace. Carlip (2000) showed that in GR velocity-dependent terms cancel the aberration, so its absence does not imply infinite speed. Kopeikin and Fomalont (2003) reported (1.06 ± 0.21) c from Jupiter's deflection of a quasar's radio waves; others disputed what was measured.

(b) A literal standing wave: two counter-propagating longitudinal waves of frequency f, with fixed nodes. Then g itself would: - oscillate in time at f (or 2f for the energy) at every point except the nodes. Detectable with superconducting gravimeters, atom interferometers, torsion balances, LIGO-type detectors (as a continuous line) and pulsar timing arrays. The mainstream analogue is ultralight scalar dark matter: its field oscillates coherently and makes the gravitational potential oscillate at twice the field frequency. Khmelnitsky & Rubakov (JCAP 2014) proposed searching for this in pulsar timing [memory, high]. Searches so far report limits, not detections [memory, medium]; - vary periodically in space with a period of half the wavelength. This would appear as a departure from the inverse-square law at that scale. Short-range torsion-balance tests (Eöt-Wash) find no departure down to about 50 µm [memory, high], and planetary ephemerides show none at solar-system scales; - carry energy density, which itself gravitates, and show a preferred frame if the medium has a rest frame. Lunar laser ranging and pulsar tests of preferred-frame effects constrain this [memory, medium].

(c) If the standing wave is in the same medium as light, the optical properties (refractive index K^(1/2)) should oscillate with it. Atomic clocks and optical cavities would see a frequency modulation, as in clock searches for oscillating fundamental constants [memory, medium]. This is the most direct "same medium" test available: compare a clock's response with a gravimeter's response at the same frequency.

4. Related work found (leads)

• Mark Titleman, "The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality", arXiv:2205.08309 (v1 2022, v11 25 Sep 2026; physics.hist-ph). From the abstract: Whittaker 1903 "united electrostatic and gravitational attraction as resulting from longitudinal waves"; 1904 "showed that electromagnetic waves resulted from the interference of two such longitudinal waves"; claims implications for lensing, gravitational waves, Aharonov-Bohm, MOND and cosmic expansion, with "time-static gravity" separate from "dynamic electromagnetism" [web: https://arxiv.org/abs/2205.08309]. This is the closest modern development of the Q07 hypothesis. Not read beyond the abstract. Note that its reading of 1904 (two longitudinal waves) goes beyond the 1904 text (see 1b).
• Qeios, "Representations and Implications of Papers Written by E.T. Whittaker" (2023), https://www.qeios.com/read/Y3D1HM. Seen only as a search result; it appears to be a related version by the same line of work (not confirmed).
• Whittaker, History Vol. 2 (1953): a PDF is hosted at https://www.rexresearch1.com/Books/WhittakerHistoryTheorAetherElectr2.pdf (seen as a search result; not opened or downloaded). The project README lists Vol. 2 as "not obtained". Downloading needs the owner's approval.
• Ibison (2003), arXiv:astro-ph/0302273: the PV cosmology and binary-pulsar result. Ibison was a colleague of Puthoff at the Institute for Advanced Studies at Austin [memory, medium], so this test of PV came from within the PV research group.

5. Reasoning and competing readings

• Reading 1 (Whittaker as representation): §5° is a mathematical observation. Any inverse-square field can be written as a superposition of longitudinal waves, and he said so ("does not explain the cause"). On this reading, the modern tests constrain only the speed of changes, and that is now c.
• Reading 2 (Whittaker as physical hypothesis): he did add physical claims, "it seems probable that an identical property of the medium ensures their transmission". On this reading the hypothesis is partly borne out (gravity and light share a speed and are bent and delayed alike) and partly contradicted (speed not "enormously greater"; the observed radiation is tensor, not longitudinal).
• Reading 3 (the Q07 standing-wave hypothesis): this needs a medium response that is (i) universal in what it acts on (MICROSCOPE), (ii) radiates as a tensor quadrupole (LVK, Hulse-Taylor), and (iii) if literally standing, oscillates in time or space at some f or λ not yet excluded. Points (i) and (ii) already rule out the simplest scalar-medium version (PV as published). Point (iii) is open and is being searched under the name of ultralight dark matter.

6. Open

• Read "Old and new ideas of gravitation" (Endeavour 3, 1944) and "The aether: past and present" (Endeavour 2, 1943) for Whittaker's late view of his 1903 idea. Probably available in a university library or through Elsevier (Endeavour back issues).
• Read the 1902 MNRAS note (ADS scan 1902MNRAS..62..617W) to see whether it says more about speed or mechanism than 1903.
• Read §§2-end of the 1927 paper and the 1928 Proc. R. Soc. A paper on the electromagnetic potential in a gravitational field.
• Synge's 1958 review of Whittaker's relativity papers (Proc. Edinburgh Math. Soc. memorial volume) would show how specialists read them.

Corrections to earlier documents

None. The project has no earlier review files. (Minor note for later steps: §5° states the general result in plane waves but works its gravity example with outgoing spherical waves; both are in the text.)

Sites and queries (also in sites.md)

• Google: Whittaker "On electric phenomena in gravitational fields" 1927 Proceedings Royal Society; "On electric phenomena in gravitational fields" Whittaker "It is a consequence of general relativity"; Puthoff polarizable vacuum model gravitational waves scalar binary pulsar criticism; LIGO Virgo polarization test scalar breathing longitudinal mode GWTC-3 tests of general relativity Bayes factor; arxiv "Constraining the gravitational-wave breathing mode"; MICROSCOPE final result 2022 equivalence principle eta 10^-15 Physical Review Letters; Dicke 1957 "Gravitation without a principle of equivalence" Reviews of Modern Physics dielectric constant vacuum; Whittaker 1903 "undulatory" gravity longitudinal waves standing "inverse square" interference analysis.
• Pages: Wikipedia (Bibliography of E. T. Whittaker; Polarizable vacuum); royalsocietypublishing.org (1927 PDF); ADS (1927 abstract page: no abstract; 1902 scan: did not load, then "permission denied" in Chrome); arXiv (1710.05834, 2112.06861, 2610.08588, 1606.02744, 2209.15487, astro-ph/0302273, 2205.08309).