Jeans-JH: Science Contrarian review (Step 2)

Reviewer role: Science Contrarian (judges by experimental evidence, builds the strongest honest case, examines how claims were rejected, applies the same rigour to the inventor). Project: three books by J. H. Jeans (1904 gases, 1911 electricity and magnetism, 1925-26 "Atomicity and Quanta"). Source folder (read only): source folder: Jeans-JH.

Tags: [read] from the documents (I re-read the pages named below myself); [web] with URL; [memory] with confidence. Units: Gaussian where Jeans uses them.

0. What I checked myself, and a framing point

Read directly from page images (not only the deep reads): Gases PDF p.221 (section 241, eqs. 493-495); Atomicity PDF p.21 (book pp.[38]-[39], the free-electron argument); Electricity PDF p.588 (book p.578, section 661, Michelson-Morley). I also read Jeans's own 1905 Phil. Mag. paper (opening) and the Investigator's notes and saved files. I did not re-read all deep reads' page images; where I rely on a deep read I say so.

Framing, important for every claim: Jeans is a mainstream mathematical physicist, not an outsider inventor. These are three textbook-level books by a Fellow of the Royal Society (FRS), and his positions were mostly abandoned by Jeans himself within years (quantum theory 1910, relativity by the 1919 edition). So "how was the claim rejected" is mostly "how did the inventor and his contemporaries replace it", and the anomaly-hunting question is which of his ideas were superseded for good reason and which were dropped without a decisive test. I found no suppression story. I did find two ideas where the record is thin (claims 6 and 2's modern revival), which I treat below.

1. Corrections to Step 1 (facts.json, claims.md, deep reads)

Each is a correction or sharpening; the earlier documents are not otherwise changed. Where Step 1 or the Investigator already flagged an item I say so.

1. "Accepted quantum theory by 1913-14 [memory medium]" (claims.md Thread; facts.json Gases mainstream_conflict; Gases deep read section 9). Wrong date. Jeans's own lecture says "Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed" [read: Atomicity PDF p.9], and Hudson 1989 says "During 1910, Jeans repositioned himself on the side of quantum theory" [web: Investigator, research/2026-10-08-montambaux.md, from files/montambaux/jeans-comment-Hudson.pdf]. Suggested wording: accepted the quantum hypothesis during 1910; his 1914 Report spread it. (The Investigator made this correction already; I confirm it.)
2. claims.md Thread: "giving up each in turn as experiment advanced." Too strong. The documents and Investigator material show: 1904 classical-dissipative theory kept in 1905 as a time-scale claim ("millions of years would hardly suffice", Nature 71, 607, [web: files/montambaux/04]) then given up for the quantum theory in 1910 for reasons Hudson attributes to "empirical and theoretical reasons" (abstract only read); the 1911 ether stance revised by Jeans with a relativity chapter in the 1919 edition [web: Investigator, archive-org note, 5th ed. preface]; and the 1925 lecture is itself a classical-wave position kept against the bullet photon. The thread is "seeks classical wave or field explanations as long as he can", not "gave up each as experiment advanced".
3. claims.md claim 1 and facts.json: the 1904 argument is presented as a claim that real gases "do not follow equipartition because molecules radiate". The documents show Jeans did not hold this as a statement about the final equilibrium. His own 1901 sentence, quoted at the head of the 1905 paper, says applying Boltzmann's theorem to matter plus ether gives "no steady state is possible until all the energy of the gas has been dissipated by radiation into the ether" [read: files/jeans-1905-...PhilMag.pdf p.91], and the 1905 Nature reply says equipartition "may be the true final ratio" but the approach takes "millions of years" [web: Investigator note]. Claim 1 should be restated: "equipartition between a gas and the ether is not reached on any observable time scale, so observed heat capacities reflect a quasi-steady state". The "non-conservative, so equipartition does not apply" wording (section 204) is the 1904 text; the 1905 reply is a retreat from it.
4. claims.md claim 2: omission. The claim states the exponential suppression exp(-2 p beta) and the incandescence prediction but not Jeans's own two admissions on the same pages: (a) with the "spheres of molecular action" (hard spheres, 1/100 penetration) p x duration = 16, e^-16 about 1e-7, "obvious that the dissipation of energy per second would be much too great to agree with observation" [read: deep read section 5, section 242]; only with an assumed half-radius penetration (e^-800) does slowness follow, and "there is not the slightest evidence" for the molecular-sphere picture (section 243). (b) The general theorem proves only that a normal state exists; emptiness of the internal modes is shown for toy models only (section 234). Add both.
5. claims.md claim 2 and Gases deep read section 4: section 241 misprint. I read the page myself: the printed italic conclusion says the dissipation is slow "provided that the product of the time occupied by a collision and the frequency of vibration is small" [read: Gases PDF p.221, book p.204]. The equations on the same page (e^{-2pc}, eq. 495) require "large". Confirmed as a misprint in the source (not in the corrigenda per the deep read).
6. claims.md claim 3 and facts.json: "the Moon and Mercury lose hydrogen, helium and most other gases". Not what the text says. For Mercury Jeans says the critical speeds are "exactly similar to that of Mars", and for Mars "hydrogen and helium would escape ... while water vapour, air, and heavier gases would be retained" at moderate temperature; Mercury is hotter, so losses larger, and he says astronomy "leaves little doubt that Mercury is entirely devoid of atmosphere" [read: Gases deep read section 1.5-1.6]. For the Moon the sentence is conditional ("if the moon ever possessed an atmosphere at a temperature much above zero, all constituents, except possibly carbon-dioxide and denser gases, would rapidly escape"). Restate accordingly.
7. Gases deep read section 2.8: "I have not examined how N enters" the viscosity radii. It enters. A mean free path L = 1/(sqrt2 pi N sigma^2) is obtained from the measured viscosity, density and mean speed, so sigma goes as N^(-1/2). With the modern N = 2.69e19 per cm^3 [memory high] against Jeans's 4e19, every viscosity-derived radius rises by (4/2.69)^(1/2) = 1.22 [calc, mine]. Rescaled: H2 1.02 to 1.25, He 0.905 to 1.10, Ar 1.39 to 1.70, N2 1.45 to 1.77, O2 1.41 to 1.71, CO2 1.74 to 2.12 (x 10^-8 cm). Modern viscosity-based kinetic radii (about 1.1 He, 1.7 Ar, 1.9 N2) [memory medium; not web-checked] agree within about 10 percent. So his method was sound and the dated constant N explains most of the difference from modern values. The claim in claims.md ("order 1 to 2 x 10^-8 cm") stands.
8. Gases deep read (flagged there) "two million years" half-life: I agree with the deep reader: 3e-14 per second gives 0.7 million years half-life, 1.1 million years mean life. Small slip in the book; keep.
9. Atomicity deep read section 10b (Adams was Princeton). The Investigator's correction is right: the experiment was signed from the Jefferson Physical Laboratory, Harvard, with copper (not brass) spheres on brass rods [web: archive.org londonedinburgh621901lond, via research/2026-10-08-archive-org.md]. I add that Jeans's remark is not a physics error (the experiment measured magnetic effects of convection, not radiation; the radiation figure is Jeans's calculation) but it does mean "Adams's spheres radiated" is a calculation, not an observation.
10. facts.json, Atomicity: "the material energy of the universe would turn into radiation in about 10^-9 s". Only in words ("thousand-millionth parts of a second"); the printed exponent is 10^-10 s for the hydrogen atom (deep read section 2e already says this; facts.json should match). My check: classical Bohr collapse time a0^3/(4 r_e^2 c) = 1.55e-11 s [calc, mine], so Jeans's 1e-10 is high by a factor of about 6 and is an order-of-magnitude statement.
11. Electricity deep read section 3i-3j: I agree with its misprint list (Y0 .33 for .033, "even" for "odd", contracted/uncontracted swapped, "In 1908 Kauffmann"). I add a seventh point of substance on Bucherer below (claim 4), where Jeans's "agrees exactly" is itself contested in the historical literature.
12. Atomicity deep read, section 8c analyst's note: confirmed and strengthened. Jeans writes "an electric force X, if it results from a field of radiation, produces no acceleration in an electron" [read: deep read p.22]. That sentence is refuted by observed Thomson scattering (see claim 5). His own 1924 Report makes the same claim [web: Investigator, archive-org note, section 87], so it is a settled position of his, not a slip of the lecture.

2. Evidence base for the contrarian case

Honest summary of what a reader should know about the experimental record behind these books.

3. Claim by claim

Claim 1. Real gases do not follow equipartition because molecules radiate (1904)

a. Internal consistency. The generalised-space flow argument (D rho / Dt = rho Delta F, eqs. 433-455) is internally consistent at the level Jeans claims: dissipation contracts phase-space volume, so gas points gather on one "normal state" depending on the present energy. Jeans himself admits that the neglected cubic term is of the same order as the retained terms at the cluster edge (section 219) and that the theorem gives only existence, not the form (section 234) [read: deep read]. The loaded-sphere example (eqs. 459-470) is clean and I accept the deep reader's finding that the epsilon to 0 and K to 0 limits do not commute (section 233): this is a real mathematical insight, not an error. Internal inconsistency exists only between the 1904 text and Jeans's 1901/1905 statements: the final state is equipartition with the ether (point 3 in section 1). The physical premise that fails is not mathematical: that every spectral line is an independent harmonic oscillator, each carrying RT (equations 417-419). The Ritz combination principle (1908) shows lines are differences of term values, not independent oscillators [memory high; not web-checked]; the Bohr picture of 1913 replaced the oscillator-per-line model. The step "thousands of lines, so n is in the thousands" thus rests on a model of the atom that Jeans himself later gave up. b. Experiment. (i) Monatomic gases with gamma = 5/3 and diatomics with 7/5 at room temperature agree with Jeans's table and are also exactly what quantum freeze-out predicts: his tables do not discriminate. (ii) The decisive discriminators are temperature dependence and low-temperature behaviour: Eucken 1912, hydrogen's heat capacity falls by about R near 40 K [web above]. For homonuclear H2 the rotational modes hardly radiate, so in Jeans's model the dissipation rate epsilon is tiny and the rotation should be strongly coupled by collisions (his own result in section 233 for epsilon to 0 is equipartition); yet rotation freezes. His slow-transfer story needs collision time times frequency to be large, but rotational frequencies of H2 (about 1e13 per second) times a collision time of 1e-13 s is of order 1, so e^{-2pbeta} gives no strong suppression. Heat capacities of solids falling toward zero at low temperature (Nernst and Lindemann 1911 [memory high]) are equilibrium measurements over hours. So the experimental record is against the equilibrium reading, and the time-scale reading (millions of years) is not what these experiments measure. (iii) The prediction "gamma falls with T" is supported by the Leduc figures Jeans quotes (CO2 1.3190 at 0 C, 1.2827 at 100 C) [read: deep read section 10], and is also what quantum partial excitation predicts. No discriminating prediction survived. c. Tested? Not by a controlled test designed to separate the two accounts in 1904. Rayleigh (Nature 71, 559, 13 Apr 1905) objected that appealing to the ether brings in "an infinitude of new modes"; Jeans answered 27 Apr 1905 with the time-scale form [web: research/2026-10-08-montambaux.md]. The explanation was then overtaken by the 1910-1912 measurements. Jeans abandoned it himself: 1916 second edition Preface says quantum theory "revolutionised" kinetic theory and the classical difficulties "have been left unsolved" [web: Investigator, archive-org note, dynamicaltheoryo00jeanuoft]. Replication of the 1904 claim as an equilibrium claim: none. Rejection was by data and by its author, not by suppression. d. If true. Heat capacities of gases and solids at low temperature would be non-equilibrium (time-scale) artefacts; Planck's law a quasi-steady state of matter plus ether. Kirchhoff's law (a gas in a cavity at its own temperature absorbs what it emits) would have to give net radiation loss zero, so the "zero-temperature sink" assumption is the weak joint [read: deep read section 2; memory high]. Verdict, split. Equilibrium form (non-conservative systems do not equipartition, hence observed gamma): Tested, not supported (Eucken 1912, solid-state low-T data) and Historically superseded but instructive. Time-scale form: see claim 2.

Claim 2. Slow feeding of the internal modes comes from a collision-time effect (1904)

a. Internal consistency. The Duhamel/Cauchy derivation (eqs. 471-492) is correct and standard: for an analytic force pulse the energy transferred to an oscillator of angular frequency p falls as exp(-2 p beta). This is the adiabatic-invariant result of classical mechanics [memory high]. Jeans's number checks reproduce (e^-16 = 1.1e-7; e^-800 = 10^-347) [read: deep read]. Flaws: the misprint "small" for "large" (verified, section 1 point 5); the resonance exception (q = p) is set aside with "there can be little doubt" the result holds generally (section 239, [read: deep read]); his incandescence range "0 C to 28,000 C" is wide (but he claims to fix the molecular speed to within less than a factor 10, and the arithmetic holds: 13 e^-12 = 8e-5). b. Experiment. The mechanism (exponentially slow vibration-translation energy exchange) is what later experiment and theory confirmed: Landau-Teller 1936 form, and the rigorous classical results above [web]. Vibrational relaxation requiring many thousands to billions of collisions is known for light diatomic gases (N2 especially) [memory medium; not web-checked]. This is the best part of the 1904 book for the contrarian case. It does not rescue his use of it: equilibrium Cv is quantum freeze-out. c. Tested? Yes, in a real sense, by the later literature: Jeans's rate law (his eq. 1.2 in Benettin et al.) is the origin of the Jeans-Landau-Teller approximation. The modern "Boltzmann-Jeans conjecture" research (Benettin, Galgani, Giorgilli; Carati; Contopoulos and Voglis) is replication of the mathematics, not of the explanation of heat capacity [web: research/2026-10-08-unimi-boltzmann-jeans.md]. Whether classical metastability can reproduce quantum heat capacity and Planck's law: claimed by Carati and Galgani for model systems [web: https://sites.unimi.it/carati/papers.html]; not established, not refuted in what I found. I could not verify a completed derivation; the search tool reported none. Mainstream silence on it is the sort of record that should be marked "open". d. If true. Equilibrium specific heats and Planck's law would be metastability effects of classical dynamics; the need for Planck's constant would be weakened. Verdict, split. (i) Rate law exp(-2 p beta) for collision-induced vibrational excitation, as a classical mechanism: Established (adiabatic invariance; Landau-Teller; rigorous results for models). (ii) As the explanation of observed gamma and heat-capacity values: Tested, not supported / Historically superseded but instructive; with the live minority programme noted as Never properly tested for the strong classical-metastability form. (iii) "Temperature of incandescence between 0 and 28,000 C": Not testable as stated.

Claim 3. Kinetic theory fixes planetary atmospheres and molecular sizes (1904)

a. Math. Consistent. I checked: with C^2 = 3kT/m the quantity x = 3ga/C^2 equals G M m / (a k T), the modern Jeans parameter lambda [calc, mine]. His planetary table (g a proportional to M/a) reproduces. Slips: "two million years" (should be 0.7 to 1.1 million), the Mossotti equation factor of 2 (deep read), N = 4e19 (49 percent high). None changes an order of magnitude conclusion. b. Experiment. Escape: the Jeans-escape formalism is textbook. Jeans placed the collisionless region at r = 2a (an assumed outer atmosphere); modern exobase estimates put it much nearer the surface, so his thresholds (15 and 30) are not the modern ones. My values [calc]: Earth exobase hydrogen at 1000 K, lambda about 7.0; Moon N2 at 390 K, lambda 24; Ar at 390 K, 35; H2 and He on the Moon, 1.7 and 3.5; Mercury He at 440 K, 9.9. Jeans's rule (loss for x below 15, retention above 30) gives the right qualitative result that hydrogen and helium are lost from the Moon and Mercury; it puts N2 at 390 K on the Moon at the edge of loss, and his own condition "at a temperature much above zero" is exactly what makes his statement true. The Moon is not atmosphere-free (a tenuous exosphere exists) [memory medium; not web-checked], which is consistent with a conditional statement, not a contradiction. Sizes: his radii, rescaled for the correct N, agree with modern kinetic radii to about 10 percent (section 1 point 7). c. Tested. Stoney objected that the kinetic theory "is not competent" and conclusions "inconsistent with the facts" (Phil. Mag. June 1904) [read: deep read section 1.7]. Jeans reports this and does not answer it in the pages read. Stoney is a party credited by Jeans, so his letter is a dissent from a source whose work Jeans built on. I did not read Stoney's letter; it is a lead. Later planetary science vindicates the escape formalism with refinements. d. If true. Nothing in mainstream physics has to change; this is mainstream. Verdict. Escape criterion: Established (with modern revision of thresholds). Molecular size by several methods: Established (order of magnitude; numbers dated by N). "Mercury loses most other gases": not in the text (see section 1 point 6).

Claim 4. The electron is a purely electromagnetic object in a real ether; bodies physically contract (1911)

a. Math. Internally consistent apart from the misprints listed in the deep read. I verified section 661 on the page: (680) t1 = (2l/C)(1 - u^2/C^2)^-1, (681) t2 = (2L/C)(1 - u^2/C^2)^-1/2, and equality after contraction; [read: Electricity PDF p.588]. The electromagnetic mass 2e^2/(3aC^2) from the energy of the field of a surface-charged sphere reproduces a = 2e-13 cm from m = 8e-28 g (deep read). Known mathematical problem not discussed on these pages: the energy and momentum of the Coulomb field give different masses (factor 4/3) and a charged spherical shell is not stable without non-electromagnetic stresses (Poincare 1905-06) [memory high; not web-checked]. So "m0 = 0, all mass electromagnetic" cannot be completed within Maxwell-Lorentz theory without something non-electromagnetic: this is Jeans's gap, not just later criticism, because he says "all forces in the ether" must be electrical for the contraction to be "inevitable" (section 660). b. Experiment. - Radiation by acceleration, Larmor (2/3) e^2 a^2 / C^3, the Zeeman effect, Hall effect, field of a moving charge, radiation pressure (Lebedew, Nichols and Hull): Established (mainstream physics). - Michelson-Morley: Jeans calls it "almost positive proof" of a real contraction. It shows the two arms' round-trip times agree to first order in the sense of (680)-(682); a null result fits the contraction, but also relativity; the discriminating tests were later (Kennedy-Thorndike 1932; Ives-Stilwell 1938) [memory high; not web-checked]. "Almost positive proof" is an overstatement even for 1911; Jeans qualifies by "almost", but reads one null as selecting one theory among several (Lorentz-FitzGerald, Ritz emission theory, Stokes drag). - Kaufmann and Bucherer: Jeans writes that Bucherer's experiments "agree exactly with experiment provided m0 is taken to be zero" and "Abraham's theory must be discarded" [read: deep read section 3m]. The historical record: Kaufmann (1906) had favoured Abraham over Lorentz-Einstein; Bucherer's 1908 results favouring Lorentz-Einstein were "seriously questioned"; Bestelmeyer's work "generally regarded as inconclusive"; generally accepted data came "almost a decade" later [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments; summary also in Potters 2023 per https://philsci-archive.pitt.edu/22988]. So "exactly" and "must be discarded" outran the data in 1911. Jeans hedged: "seem to shew". The data did turn out to favour the Lorentz-Einstein transverse mass. Besides, in the relativistic reading the same factor multiplies all mass, so the fit does not show the mass is electromagnetic (deep read, [memory high]). - Electron size: Jeans: radius 2e-13 cm = 2e-15 m. The best collider bound found is r < 2.8e-19 m [web: https://arxiv.org/pdf/2506.02450], about 10^4 times smaller. The model "m0 = 0 with a 2e-15 m surface charge" is therefore excluded by high-energy scattering; modern theory treats the electron as pointlike with renormalised self-energy [memory high]. "Tested, not supported", with a test not available to Jeans. - Section 624, "electron theory proves Ampere's element law for every element of a circuit": what he proves (eq. 623) is the Biot-Savart field of a moving charge or current element, which is mainstream and Established at low speed. (Anglophone 1911 usage of "Ampere's formula" for this field is a point of terminology that a reader should know [memory medium].) It does not settle the separate dispute about the force between non-closed current elements (Ampere's original law versus Grassmann's form), which agree for closed circuits; that dispute is experimentally contested in the fringe literature [memory medium; not web-checked] and the reader should not read section 624 as a verdict on it. c. Tested. Yes, repeatedly, and the answer was "ether not needed, mass not purely electromagnetic". Rejection process: sound-in-principle experiments with disputed accuracy (Kaufmann's own photographic plates; Bucherer's selection of speeds), settled by repetition (Neumann, Guye-Lavanchy, around 1914-1916 [memory medium]). I found no data suppression; the earlier contrary data (Kaufmann) were published and discussed. d. If true. Special relativity would be Lorentz's ether theory with a real contraction. That version is empirically equivalent to special relativity for the experiments in question [memory high]; the difference is philosophical (no test of the ether apart from SR's predictions). Mainstream would have to restore a preferred frame that is undetectable. Verdict, split. Radiation and field formulae: Established. Purely electromagnetic mass, radius 2e-13 cm: Tested, not supported (collider bounds; the 4/3 and stability problems), and Historically superseded but instructive. Real ether with dynamical contraction: Not testable as stated (observationally equivalent to special relativity), Historically superseded but instructive. "MM is almost positive proof": overstated. Jeans himself revised the stance in 1919 (relativity chapter) and in 1927 still printed the "wholly electromagnetic" reading of Bucherer [web: Investigator, archive-org note, item 4].

Claim 5. Energy is atomic; quantisation is in matter-radiation exchange; free radiation is wave-like (1925)

This claim has several separable parts. I give a verdict per part.

a. Math. The free-electron argument, which I read on the page [read: Atomicity PDF p.21], is correct for pure absorption or emission by an electron with no third body: choose the frame in which the final electron is at rest and the energy equation cannot be satisfied for positive hnu. The deep reader's check (relativistic energies, gamma >= 1) holds. It forbids absorption, not scattering; Jeans transfers the job to the bound atom. The Boltzmann-factor paragraph uses RT for kT (deep read section 2c) which is a unit slip, not a conceptual one. The astronomical argument is not mathematics; it is an inference (see below). Planck's law and its h-zero limit [read: deep read section 2d] are as printed. b. Experiment, part by part. - Matter-radiation exchange occurs by single quanta, E1 - E2 = hnu: Established. - Free electron cannot absorb a quantum: Established. No acceleration of a free electron in a radiation field: Refuted by experiment. Thomson scattering (the low-frequency limit of Compton scattering) is observed, and an electron in a laser field oscillates [memory high; not web-checked]. His own argument does not imply it; the Investigator found it also in Jeans's 1924 Report, so it is a persistent belief of his. - "Atom of energy mC^2", revealed by astronomy, solar mass loss: the arithmetic of 250 million tons per minute is right (3.85e26 W / c^2 = 4.3e9 kg/s [calc, mine]). The inference that this shows atomicity is not supported: a continuous mass loss rate does not show discreteness. The astronomical premise that radiation explains the mass difference between young and old stars is Refuted by calculation: radiating at luminosity L for a time t removes L t / c^2. For the Sun over 4.6 Gyr that is 3.1e-4 of its mass; over 10 Gyr, 6.8e-4 [calc, mine]; a 40-solar-mass star radiating 1e5 L_sun for 3 Myr loses 5e-4 of its mass [calc, mine, luminosity and mass illustrative]. Mass differences between star types are tens of percent to factors of ten, so radiation cannot account for them. The premise reflects the giant-to-dwarf stellar evolution picture of that era (Russell) [memory medium] and annihilation as the energy source, replaced by hydrogen fusion (Eddington's 1920 suggestion [memory high]). Historically superseded but instructive. - Space-time continuity because a granular continuum would need a universal constant with dimensions length x time: a reasoned argument from the absence of such a constant in 1925. Planck units now provide such a scale [memory high], and whether space-time is granular is open. Not testable as stated at present energies (testing at Planck scale is not possible directly). - Hydrogen atom would collapse in 1e-10 s if h were zero: a classical Larmor calculation; Established (my value 1.55e-11 s, same order, section 1 point 10). - Free radiation is wave-like, quanta cannot be indivisible bullets: Jeans's evidence (interference over about 1e6 wavelengths, Wien's decay time 1/(5.4e7) s, which gives 18.5 ns and a length of 5.6 m [calc, mine], Taylor's feeble-light diffraction, Lorentz 1906) is real. His two conclusions are separate. (1) Free radiation propagates by Maxwell's equations: correct, and in modern terms it is the field operator's evolution [memory high]. (2) Therefore quanta must be spread waves, not indivisible: not supported, because the modern single-photon experiment finds both: anticorrelation at a beam splitter (indivisible) and interference visibility above 98 percent with the same source [web: Grangier-Roger-Aspect 1986, links in section 2]. A single photon from H-alpha with a 18.5 ns lifetime is a wave packet several metres long; the beam splitter does not "cut it in half" in the sense of two partial detections. His "bullet" alternative is rejected by modern evidence, and his pure-wave alternative is rejected by the anticorrelation. So, in its strong form (quanta have no individuality in free space), Tested, not supported; in its weak form (the free field is described by Maxwell's wave equation and the quantum character shows up only in exchange), Plausible in the sense that semiclassical theories give the photoelectric threshold and onset without photons [web: Lamb and Scully]. Those authors themselves say photons are needed for Compton scattering and blackbody radiation. So the weak form accounts for part of what Jeans wanted it to. - Compton alternative: Jeans admits the equations are not worked out and "experiments are [not] as yet precise enough to decide". The coincidence work that bears on it: Bothe-Geiger, reported April 1925, five weeks before the 11 May lecture; Compton-Simon, published 1 September 1925 [web: https://en.wikipedia.org/wiki/Bothe%E2%80%93Geiger_coincidence_experiment, via the Investigator]. Tolman 1926 called the timing "almost simultaneous" and said they "greatly increased the difficulties of the wave theory, even for radiation in free space" [web: Investigator, research/2026-10-08-reviews-1926.md]. Jeans kept per-event energy conservation, so BKS-type statistical conservation is not what his scheme requires, and the coincidence results do not refute it directly; whether a spread emitted wave can give the observed direction correlation is unworked. Never properly tested (not worked out far enough to test). c. Tested? Contemporary reception (Investigator): E. P. Adams (Bull. AMS 1926, favourable, brief), Tolman (Phys. Rev. 1926, fair, sceptical in the light of the coincidence work), Loring (Chemical News 1927, took up the convergent-wave photoelectric idea as "promising" but noted "Jeans does not put forward the convergence idea as a solution") [web: Investigator]. Nature 117, 46 review: paywalled, not read. Replication: none; the 1925-27 development of quantum mechanics and quantum field theory made the question moot in the form Jeans posed it. d. If true. Photon would be an exchange event, not a travelling object; the quantised radiation field would be unnecessary for most of optics. Mainstream would have to treat photon antibunching and correlation as artefacts of exchange. Verdict, split. Exchange by single quanta; free-electron no-absorption; hydrogen collapse: Established. Refusal of indivisible quanta in free space, strong form: Tested, not supported. Weak semiclassical form: Plausible, untested for the whole picture (supported in part for the photoelectric effect). "No acceleration of a free electron": Refuted (by observation). "Atom of energy from the Sun's mass loss": Refuted by calculation (astronomical premise) and Historically superseded but instructive. Space-time continuity argument: Not testable as stated.

Claim 6. A time-symmetric (advanced plus retarded) field can make a non-radiating atom and carry a whole quantum from emitter to absorber (1925)

a. Math. Consistent, with the caveats Jeans lists himself. The general spherical solution phi = (1/r){F(t - r/a) + Phi(t + r/a)} satisfies the wave equation for any F, Phi (verified symbolically by the deep reader); the potentials Psi = integral ([rho] + {rho})/2r are half-retarded plus half-advanced; for periodic motion the far field is a standing wave and the mean Poynting flux is zero [read: deep read sections 10c-10e]. Jeans states the zero but does not show the calculation (the deep reader's check holds for strictly periodic motion). The two-atom form (retarded from atom 1, advanced from atom 2, no factor 1/2) is a solution because each integral solves the wave equation with its own source [read: deep read section 11b]. Physical problems he lists: infinite field energy, no selection of Bohr orbits, no equations for the Compton alternative, no source-sink phenomenon at frequencies the atom does not "beat time" to. One more that I add: a half-retarded plus half-advanced self-field has no radiation-reaction (the Dirac radiation-reaction field is (retarded minus advanced)/2) [memory high], so a symmetric atom is non-radiating by construction, and an isolated excited atom would not decay spontaneously. Observed spontaneous emission (for instance hydrogen 2p to 1s, about 1.6 ns [memory high]) needs the absorber side to be supplied: this is the Wheeler-Feynman completeness requirement (the universe as perfect absorber). b. Experiment. No experiment tests Jeans's pair solution as such. Absorber theory (Tetrode 1922; Fokker 1929; Wheeler-Feynman 1945) is built to be empirically equivalent to ordinary electrodynamics for the observed phenomena; it was neither refuted nor distinctively confirmed [memory high; Wikipedia history via Investigator]. The Ritz-Einstein 1909 dispute is the earliest recorded debate on advanced potentials, with Ritz blaming advanced potentials for the Rayleigh-Jeans catastrophe (a snippet only) [web: Investigator]. Photoelectric threshold and one electron per quantum: a source-sink picture would have to give them; Jeans says only it "suggests the possibility". c. Tested; how it was received. There is no record of a test, and the standard histories of time-symmetric electrodynamics do not mention Jeans 1925 (Wikipedia's history; Kennefick 1997 has zero mentions of Jeans) [web: Investigator]. This is an anomaly to analyse, not a neutral gap. Competing explanations: (i) the lecture was a short (64-page) public lecture whose real new content is six pages; (ii) quantum mechanics (Heisenberg 1925, Schrodinger 1926) arrived within months and made the physical-picture programme moot; (iii) Jeans moved into cosmology (the 1928 Astronomy and Cosmogony manuscripts are in JHJ/5 [web: Royal Society note]); (iv) Wheeler and Feynman cited Tetrode and Ritz, because Einstein told them of those [web: Wikipedia history, Investigator]; Jeans may simply have been unknown to that lineage; (v) a later Jeans text may have used or dropped the idea: not checked. Evidence for (i)-(iii) is circumstantial; for (v) none. Records that would decide: Jeans's own later writings (1927 5th edition, Physics and Philosophy), the 23 Jeans letters to O. W. Richardson at the Harry Ransom Center, JHJ/2 and JHJ/4 at the Royal Society, G. N. Lewis 1926 PNAS (does it cite Jeans?) [web: Investigator]. Nobody blocked or suppressed the idea on this record; it was not engaged. Related work: Shuang-ren Zhao's "mutual energy flow" (arXiv:1606.08710 onward) uses the retarded-from-source plus advanced-from-sink structure and is outside mainstream journals; characterised as outside the mainstream by venue, and included here as related work, not endorsed (not opened by the Investigator or by me) [web: Investigator]. Cramer's transactional interpretation (1986) is the best-known successor [memory high]. d. If true. Atoms in equilibrium with radiation would be non-radiating electromagnetic systems; photon indivisibility would be a property of source-sink geometry. Mainstream would have to accept a time-symmetric, absorber-dependent electrodynamics and explain atomic structure through it. Verdict, split. Existence of the non-radiating time-symmetric solution (mathematics): Plausible, untested as physics; the mathematics is Established. The two-atom source-sink account of a whole quantum, and of the photoelectric effect: Never properly tested (not dismissed by test; not engaged by the literature; incomplete as Jeans states). The "atom as a source and sink for frequencies it does not beat time to": Not testable as stated (Jeans: "I know of no phenomenon in the whole of physics which helps").

Claim 7. The quantum may be another face of charge atomicity (1925, conjecture)

a. Math. hC/(2 pi) = hbar c = e^2/alpha in Gaussian units, so K = hbar c / (16 pi^2 e^2) = 1 / (16 pi^2 alpha) = 0.8678 [calc, mine, with alpha = 1/137.036]. K is a pure number, so the relation is the fine-structure constant rewritten with a factor (4 pi)^2 chosen to make it near 1. By dimensional analysis some K must exist; its smallness of deviation from 1 is the content, and it is not a coincidence in the sense of being derived. His 1924 Report states the same relation more cautiously and adds that the atomicity of e "will not lead to the quantum-theory, for if it did the quantum-theory would have been fully developed long ago" [web: Investigator, archive-org note section 3]. So in 1925 the claim is "suggests", not "shows". b. Experiment. Nothing contradicts it; nothing supports it. Why alpha is about 1/137 is still unexplained [memory high]. Any proposal tying h to e must explain the number 137, which Jeans's tube-of-force picture does not. c. Tested? Not testable as phrased. Related idea: Dirac's 1931 monopole links charge quantisation to hbar through e g = n hbar c / 2 [memory high; not web-checked], a different route to a connection between charge atomicity and h. Jeans did not use it. The tube-of-force reading has an experimental problem he states himself: beta-particle scattering shows the full nuclear force acts on an entering electron, so discrete tubes are not real [read: deep read section 9b]. d. If true. A theory of alpha; a derivation of h from e and c; mainstream would have to find structure beneath alpha. Not predicted by any current theory. Verdict: Not testable as stated. (Instructive as a dimensional observation: it is the earliest printed form I know in these documents of "hbar c over e^2 is near 1/137 times 4 pi squared".)

4. Pertinent material from the Investigator, retained

I keep these in the record whatever my verdict, with their claim number. All are the Investigator's finds [web] unless I say I read them.

• Claims 1, 2: Jeans's 1905 Nature reply (the time-scale framing, "millions of years", and the closed-vessel argument with perfectly reflecting walls); his 1901 sentence on matter plus ether quoted at the head of the 1905 Phil. Mag. paper [read, by me: files/jeans-1905-...PhilMag.pdf p.91]; 1916 second edition Preface (kinetic theory "to some extent revolutionised" by quantum theory, classical difficulties "left unsolved"); 1914 Report restating "millions of years"; Rayleigh's 13 Apr 1905 criticism; Lodge 1926 crediting Jeans with the 8 pi R factor in the Rayleigh-Jeans law; Hudson 1989 on the 1910 shift; Benettin-Galgani-Giorgilli and Benettin-Carati-Gallavotti 1995 as rigorous classical support for the mechanism; Royal Society JHJ/2 sanatorium letters 1901-1907 (unread).
• Claim 4: Jeans's 1919 relativity chapter and 1927 5th edition (still printing Bucherer as showing "wholly electromagnetic" mass, a = 1.874e-13 cm, with Millikan's e) [web: archive.org 5thedmathematica00jeanuoft].
• Claims 5-7: Jeans's own 1924 Report (sections 85-87: the h versus (4 pi e)^2 relation, Lorentz and G. I. Taylor 1909 (Proc. Camb. Phil. Soc. 15, 114), G. P. Thomson 1923, "it is matter, and not ether or radiant energy, which proves to be different"), showing that all of the 1925 lecture except the advanced-potential step was already in print in 1924; Adams 1901 paper details (two sets of sixteen copper spheres, 10,000 cells, 75-85 revolutions per second, magnetic not radiative measurement); reviews by Adams (Bull. AMS 32, 720), Tolman (Phys. Rev. 1926 p.1048), Loring (Chemical News 134, 129), and the Nature 117, 46 notice (not read); Kragh-Carazza 1994 citing the continuity argument (not read); time-symmetric lineage (Schwarzschild 1903, Ritz-Einstein 1909, Tetrode 1922, Lewis 1926, Fokker 1929, Wheeler-Feynman 1945) and the silence of its histories on Jeans; Zhao's mutual-energy work; Bothe-Geiger and Compton-Simon dates; Milne 1947 obituary and the Chandrasekhar-papers obituary typescript (unread).
• Not yet found (Investigator's list, repeated for the arbiter): Milne 1947 text; Nature 117, 46 text; G. N. Lewis 1926 text; Ritz-Einstein 1909 note; HRC finding aid for Jeans-Richardson letters; the Wien H-alpha decay paper; Jeans 1903 collision-excitation paper (probably among files/montambaux/Jeans-1903-*, unread).

5. How were these rejected? (Mallove-style audit, applied evenly)

6. Where Jeans is wrong or loose (same rigour as for the critics)

• The 1904 "non-conservative" argument overreaches: the final state is equipartition with the ether (his own 1901 and 1905 words), and Jeans needs the ether as a zero-temperature sink (deep read section 2).
• His hard-sphere collision-time estimate fails by his own arithmetic (p x duration = 16); the success case relies on an unevidenced half-radius penetration.
• The misprint "small" for "large" in the italic conclusion of section 241 (verified).
• Dated constants (N = 4e19, hydrogen molecule mass 2.25e-24 g, corpuscle 1/700 of hydrogen).
• "Almost positive proof" of the contraction from Michelson-Morley; "exactly" and "must be discarded" for Bucherer, against a record of ten years' dispute.
• Radius of electron 2e-13 cm and "m0 = 0" resting on the Lorentz model without the 4/3 and stability problems.
• "Atom of energy" argument: a continuous mass-loss rate cannot show discreteness; the stellar-mass premise fails by about three orders of magnitude.
• "No acceleration" of a free electron in a radiation field.
• Numbers without sources in the 1925 lecture: Taylor's 2000 hours, "million wavelengths" interference experiments, Wien's decay time (his own 1924 Report gives the Taylor and Lorentz references).
• Adams's spheres are copper, and measured magnetic effects, not radiation.

7. Summary table of verdicts

Web checks used (about 6 plus one for Grangier): Carati-Galgani (search); Lamb-Scully (search); Kaufmann-Bucherer-Neumann (Wikipedia); electron radius bound (arXiv 2506.02450, hep-ph/0002172); Eucken 1912 (Wikipedia and APS abstracts); Grangier-Roger-Aspect 1986 (illinois.edu PDF and arXiv 2209.06136). Not web-checked and tagged [memory]: Ritz combination principle; Kennedy-Thorndike and Ives-Stilwell; Neumann and Guye-Lavanchy dates; N2 vibrational relaxation; Poincare stresses and the 4/3 problem; Dirac radiation reaction; Moon exosphere; modern viscosity radii.