Jeans-JH: Physicist review (Step 2)

Reviewer: PhD physicist. Project: three books by J. H. Jeans (Dynamical Theory of Gases 1904; Mathematical Theory of Electricity and Magnetism, 2nd ed. 1911; Atomicity and Quanta, lecture 11 May 1925, printed 1926). Tags: [read] from the project documents (deep reads and my own page-image check of Atomicity PDF p.28), [web] with URL, [memory] with confidence, [calc] my own arithmetic (Python, CODATA constants).

Source note: all three books have text; equations were read from page images by the deep readers. None of the verdicts below rests on a digest alone. Jeans is the author of every experiment he reports, so those are his descriptions, not the original papers.

How to read the verdicts: Jeans was a first-rate mathematical physicist who was wrong about some physics in instructive ways. Several claims therefore get split verdicts: the mathematics (or the mechanism as dynamics) is often right, while the physical application was overtaken.

Corrections to Step 1

1. claims.md "Thread", the Gases deep read section 9 and facts.json (Gases, mainstream_conflict) say Jeans accepted quantum theory "by 1913-14 [memory medium]". The Investigator's correction stands, and I checked its basis: the lecture itself says "Poincare (1912) and myself (1910) shewed that Planck's analysis could be reversed" [read: Atomicity p.9, deep read section 2a], and Hudson 1989 dates his move to the quantum side to 1910 [web: Investigator, research/2026-10-08-montambaux.md; abstract only]. Use "accepted the quantum hypothesis during 1910; the 1914 Report spread it". This matters for claims 1-2: by the 2nd edition (1916) he had replaced the 1904 explanation with the quantum one [web: Investigator, archive.org dynamicaltheoryo00jeanuoft].
2. Deep read Atomicity section 10b says Adams was "a Princeton physicist [memory medium]" and the spheres "brass". The 1901 paper is signed from the Jefferson Physical Laboratory, Harvard, used copper spheres on brass rods, and measured magnetic convection effects, not radiation [web: Investigator, archive.org londonedinburgh621901lond]. Accept. The radiation claim is Jeans's own calculation.
3. facts.json (Atomicity, mainstream_conflict) and the deep read ask for the Bothe-Geiger and Compton-Simon dates: Bothe-Geiger reported April 1925 (before 11 May), Compton-Simon published 1 September 1925 (after) [web: Investigator, Wikipedia Bothe-Geiger page]. Tolman 1926 called the timing "almost simultaneous" [web: Investigator]. So the lecture did not ignore Compton-Simon, but it post-dated Bothe-Geiger by about a month; whether Jeans knew of it is unknown.
4. facts.json (electricity, mainstream_conflict item 2) says the purely electromagnetic electron was "abandoned because Poincare stresses and quantum effects". That is loosely worded. The precise points: (a) the energy and the momentum of a surface-charged sphere's field give the same electromagnetic mass, (2/3) e^2/(a C^2); the 4/3 is the ratio of that mass to U/C^2 (the "4/3 problem") [corrected 2026-10-09 after QE: was "give electromagnetic masses that differ by a factor 4/3"; see arbiter correction 19], which Jeans's section 625 does not mention (he uses the energy route, giving 2/3 e^2/(aC^2)) [memory high]; (b) Poincare stresses (1905-06) were introduced to hold the electron together [memory high]; (c) under special relativity all mass carries the same velocity factor, so Bucherer-type agreement does not show that mass is electromagnetic [read: deep read 3m]. Also [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments]: Zahn-Spees (1938) and Farago-Janossy (1954/57) argued the early deflection experiments (Kaufmann, Bucherer, Neumann) rested on assumptions too imprecise to do more than show a qualitative mass increase; Rogers et al. (1940) matched the Lorentz-Einstein curve to about 1%. So "Bucherer confirmed Lorentz's electron" (claim 4) was a reasonable reading of 1908 data that later work judged over-strong.
5. claims.md claim 4 says electron theory "proves the Ampere element law". Jeans's text (section 624) says so, but what he derives is the low-speed Biot-Savart field of a moving point charge, e u sin(theta)/(C r^2), summed over the carriers in an element. Ampere's force law between current elements is a different formula. Judged in claim 4e.
6. Gases deep read section 1: notation. In Ch. VII Jeans's n already includes the three translational terms (gamma = 1 + 2/n); in Ch. X (eq. 522) he writes n+3 with n counting internal terms. claims.md claim 1 uses the Ch. X form, which is fine, but a reader comparing chapters will be confused.
7. Wien's decay time (Atomicity): 1/(5.4 x 10^7) s = 18.5 ns is of the order of the modern lifetime of hydrogen n=3 states, about 16 ns [memory high], so Jeans's figure is physically sensible. The Investigator's search for Wien's paper was negative, so the source is still unlocated.

No error was found in the deep reads' arithmetic: I re-ran the key numbers (below) and they reproduce.

Calculations I ran

• Classical collapse of hydrogen: t = a0^3/(4 r_e^2 c) = 1.56e-11 s [calc]. Jeans's "about 10^-10 s" and "small fraction of a millionth of a second" are the right order.
• Sun's mass loss: L/c^2 = 4.26e9 kg/s = 256 million tonnes per minute [calc]; Jeans's "250 million tons" is correct. That the Sun loses mass at a continuous rate says nothing about whether energy comes in discrete units.
• K in hC/2pi = K(4 pi e)^2: K = 1/(16 pi^2 alpha) = 0.868 [calc].
• Jeans escape: Jeans's x = 3ga/C^2 with C^2 = 3kT/m equals GMm/(a k T), today called the Jeans parameter at radius a [calc]. Surface values at T = 250 K: x = 30 for H on Earth, 120 for He, 6 for H on Mars, 1.4 for H on the Moon, 38 for N2 on the Moon, 60 for CO2 on the Moon; at T = 1000 K, x for H on Earth falls to 7.5 [calc].
• His flux formula 1e-2 (1+x) e^-x per second gives an e-folding time of 0.65 yr at x = 15 and 1.1 million years at x = 30 [calc]; at x = 40 it gives 1.8e10 years. So his criterion "retained through millions of years" is a retention time of about a million years, not 4.5 billion.
• Boltzmann factor for a visible-light mode (H-alpha, 1.89 eV) at 300 K: e^(-1.89/0.0259) = e^-73 [calc]; at 3000 K e^-7.3. That is quantum freeze-out in one line (claim 1).
• Time-symmetric field, far zone (analytic): E ~ cos A + cos B, the transverse B-field ~ cos A - cos B (outgoing minus incoming, the incoming wave carrying the opposite Poynting direction), A = w(t - r/c), B = w(t + r/c). Radial flux ~ cos^2 A - cos^2 B, time average zero [calc]. So Jeans's "time-averaged radiation is zero" is correct for strictly periodic motion; the deep read reached the same result.

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

What Jeans argues [read: deep read Gases, Ch. VII end and Ch. VIII]: a molecule that emits thousands of spectral lines has thousands of vibrational modes; equipartition would give gamma near 1.0010 (example: 2000 extra quadratic terms) against the observed 5/3 for monatomic gases. His fix (section 204): the molecules radiate into the ether, so the system is not conservative and equipartition does not apply to those modes. Liouville's theorem is replaced by D rho/Dt = rho Delta F and the gas settles onto a "normal state" with internal "subsidiary temperatures" far below the translational temperature.

Mainstream view, stated fairly. The puzzle Jeans identified is real (one of Kelvin's "clouds"). The solution is quantum: a mode of frequency nu holds energy only in units h nu, so its equilibrium energy is suppressed by exp(-h nu/kT) when h nu >> kT (Einstein 1907 for solids; Nernst and Eucken 1910-12 for gases) [memory high]. For a 1.9 eV electronic transition the factor is e^-73 at room temperature (above); no radiation by the gas is involved. Jeans's mechanism and the quantum one both give "internal modes empty", but they differ elsewhere.

a. Is the mathematics internally consistent? The flow argument (eqs. 428-455) is legitimate dynamics: in a dissipative flow phase-space density rises along trajectories and points gather on an attracting set. Jeans himself says (section 234) that the general theory proves only existence of a normal state and that internal modes being empty is shown only for toy models (the two-vessel analogue; damped loaded spheres, which the deep reader's numerical check confirms converge on the semi-cubic parabola eps H = (1/3) beta nu K^(3/2)). His remark in section 233 that the conservative case is not the epsilon -> 0 limit is correct (non-commuting limits). Consistent, with a hidden physical assumption (next).

b. Is it consistent with established experiments? - The ether is treated as a zero-temperature sink: "the further face being kept at a zero temperature" (section 206) [read]. A gas in an enclosure at its own temperature absorbs thermal radiation as fast as it emits (Kirchhoff's law) [memory high], so the net loss is zero in equilibrium and the 1904 steady state does not exist there. Jeans saw this: his 1905 reply to Rayleigh says the true final state is equipartition including the ether (ratio A:B = 5:infinity) and that "millions of years would hardly suffice for any perceptible change" [web: Investigator, Nature 71, 607, 27 Apr 1905, files/montambaux/04]. That 5:infinity ratio is the ultraviolet catastrophe, which Planck-law radiation data contradict at high frequency. - Hydrogen and nitrogen are homonuclear, with no electric-dipole radiation from rotation or vibration [memory high]. Yet H2 rotation is "frozen" at low temperature: its molar C_v falls from 5/2 R toward 3/2 R below about 100 K (Eucken 1912) [memory high; the heat-capacity web page I tried did not mention it], the effect is reversible and fast, and its explanation is the rotational quantum ladder. A radiative-drain mechanism cannot act on H2 rotation, yet H2 is the first gas in Jeans's n+3 = 5 list (section 270). - Polyatomics and halogens do not fit his integers (Jeans admits: sections 271-272; CCl4 n+3 = 15.4), and gamma falling with T as vibrations unfreeze is what quantum theory gives without free parameters.

c. Has it been tested? Only by Jeans's own comparison with gamma tables: agreement for n+3 = 3 and 5 gases is real but equally what any account that freezes vibrations gives, and Jeans notes that C_v was derived from C_p and gamma, so that table is not independent [read: section 264]. Leduc's gamma falling with T (CO2 1.3190 at 0 C, 1.2827 at 100 C) is quoted as support [read]; quantum theory predicts the same. Jeans dropped the explanation: the 1916 2nd edition calls the quantum account "at best only partial" but "probably... satisfactory" and the classical difficulties "left unsolved" [web: Investigator].

d. If true, what would change? Quantum freeze-out would be unnecessary for heat capacities, but black-body radiation and the photoelectric effect would be unexplained, and h would be an accident of time scales. Equilibrium thermodynamics would be replaced by "non-equilibrium for millions of years".

Verdict (split): - Strong form (radiative drain makes the equilibrium internal temperatures low): Refuted by calculation (Kirchhoff's law, the gas in its own enclosure) and Tested, not supported (H2, polyatomics). - Weak form (energy transfer into internal modes is so slow that freeze-out might be a rate effect): Plausible, untested for real gases; for classical model systems later mathematics supports it (see Investigator findings), but it does not describe equilibrium heat capacities. - As a historical position: Historically superseded but instructive.

Claim 2. Slow feeding of internal modes: the exp(-2 p beta) collision effect and the "temperature of incandescence"

Jeans's derivation [read: deep read Ch. IX-X]: a collision applies force U(t) to an oscillator of angular frequency p; the mean energy gain is (1/2) b (X^2 + Y^2), with X + iY = (1/ap) times the Fourier transform of U at p. Closing the contour in the upper half plane picks the pole nearest the real axis, at distance beta, giving energy ~ exp(-2 p beta) (eq. 492); a Lorentzian pulse gives (I^2/2a) e^(-2pc) exactly (eq. 495).

Mainstream view. This is a correct standard result: a smooth pulse transfers exponentially little energy to an oscillator whose period is much shorter than the pulse (adiabatic invariance). It is the core of Landau-Teller vibrational relaxation theory (1936) [memory high]; the Milan-Padua school calls the approximation "Jeans-Landau-Teller" and has proved exponentially slow exchange for classical diatomic models [web: Investigator, air.unimi.it Benettin-Carati-Gallavotti 1995].

a. Mathematically consistent? Yes. Checks: e^-16 = 1.1e-7 and e^-800 = 10^-347 [calc]. Two flags. (i) The italic conclusion of section 241 says dissipation is slow if collision-time x frequency is "small"; the mathematics requires "large". This is a misprint in the book, not in its corrigenda [read]. (ii) beta is not computed from any intermolecular potential: with 1/100-radius penetration, p x time = 16, and Jeans says dissipation would then be "much too great"; with half-radius penetration it is 800 and "amply small enough", with "not the slightest evidence" for either [read: sections 242-243]. The mechanism hinges on an input it cannot fix. Resonant energy transfer (q = p) is excluded by assumption. b. Consistent with experiment? The exponential law is consistent with measured vibrational relaxation (Landau-Teller) [memory high], but real relaxation times at room temperature for common modes are microseconds to much shorter, not millions of years [memory medium], so gases equilibrate on laboratory times and internal modes are empty because the equilibrium populations are quantum, not because they are starved. The "temperature of incandescence" prediction (between 0 C and 28,000 C, "to within less than a power of 10" in C) is too wide to be a prediction; 28,000 C is just 100 x 273 K (27,300 K [calc]). c. Tested? The rate law: yes in vibrational relaxation and mathematically for model systems [web: Investigator]. Its use to explain observed specific heats: not borne out. d. If true: equilibrium heat capacities would be kinetic artefacts; the accounts of c_v(T), black-body radiation and oscillator statistics would have to change.

Verdict (split): - The exp(-2 p beta) law as dynamics: Established (survives as Landau-Teller). - Its use to explain observed specific heats: Historically superseded but instructive. The incandescence-temperature prediction as stated: Not testable as stated.

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

Escape. Jeans's criterion (credit to Johnstone Stoney; mathematical treatment by G. H. Bryan, which Jeans borrows [read: p.342]): x = 3ga/C^2 below 15, atmosphere "certainly lost"; above 30, "retained through millions of years".

Mainstream view. This is textbook "Jeans escape", and Jeans's x is today's Jeans parameter GMm/(akT) (calculation above) [web: https://en.wikipedia.org/wiki/Atmospheric_escape]. Where the modern view differs: - Retention: x = 30 means about 10^6 years by his own flux formula (calc), not the age of the planet. His wording is right; it should not be read as "retained for 4.5 Gyr". - Earth: Jeans says the outer atmosphere is "certainly less than 230 C", so "no perceptible escape" and any hydrogen is an addition from chemistry [read: p.340]. Today Earth is estimated to lose about 3 kg/s of hydrogen (Jeans escape about 10-40%, charge exchange 60-90%, polar wind 10-15%) and about 50 g/s of helium, mainly by polar wind [web: https://en.wikipedia.org/wiki/Atmospheric_escape]. The exosphere is hotter than Jeans assumed (order 1000 K [memory high]; x about 7.5 for hydrogen in my table, in the escaping range). His Earth hydrogen/helium conclusion is superseded, though the method is right and the non-thermal channels were unknown in 1904. - Moon, Mercury, Venus: the conditional Moon statement (if the Moon ever had an atmosphere "at a temperature much above zero", all but CO2 and denser gases would "rapidly escape") matches my table (H 1.4, N2 38, CO2 60 at 250 K). The Moon and Mercury have only trace exospheres and Venus keeps a massive CO2 atmosphere [memory medium-high; not web-checked]. Consistent with Jeans. - Stoney's dissent: Jeans reports that Stoney "now maintains that the Kinetic Theory is not competent to decide on the question... and that the conclusions of the Kinetic Theory are inconsistent with the facts" (Phil. Mag. June 1904) and does not answer [read: p.342]. Stoney originated the escape idea, so this is the view of an informed party; later escape physics favours the kinetic treatment with added non-thermal channels. I have not read Stoney's letter (not in the folder).

Molecular sizes. Radii of 1-2 x 10^-8 cm from viscosity, conduction, diffusion, van der Waals b, density limits and the Mossotti refractive-index estimate. Mainstream: kinetic radii of N2, O2, Ar, CO2 are about 1.5-1.9 x 10^-8 cm [memory high], so the order is right. Quantitative slips recorded by the deep reader are real: N = 4e19 cm^-3 vs modern 2.69e19 (49% high), H2 mass 2.25e-24 g vs 3.35e-24 g, the Mossotti equation printed without the factor 2 his number uses, "two million years". They shift density-based radii by about 14% and none changes the order of magnitude [calc, deep read]. Jeans himself says the vapour and mercury values are "almost worthless except as regards order of magnitude" [read: section 419].

a. Mathematically consistent? Yes; the deep reader reproduced every table and threshold within printed rounding. b. Consistent with experiment? Yes for escape physics and sizes (orders of magnitude); the Earth hydrogen conclusion is superseded. c. Tested? Escape: planetary data and in-situ measurements (modern record) [web above]. Sizes: later X-ray, scattering and kinetic data [memory high]. d. If true: nothing would change; this is mainstream.

Verdict (split): - Jeans escape and the planetary pattern (Moon, Mercury, Mars lose light gases; Venus keeps its atmosphere): Established. - Earth "no perceptible escape" of hydrogen and helium: Historically superseded but instructive. - Molecular radii of order 1-2 x 10^-8 cm: Established (order of magnitude), with the numerical slips above.

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

Divided into five parts, because the verdicts differ.

4a. Electromagnetic mass and size. m = m0 + (2/3) e^2/(aC^2) from the magnetic energy outside radius a (eq. 624); the integral is right (deep reader, SymPy). The field-momentum mass equals the kinetic-energy mass, (2/3) e^2/(a C^2); 4/3 is its ratio to U/C^2, the rest energy of the field over C^2 (the 4/3 problem; not discussed by Jeans) [memory high] [corrected 2026-10-09 after QE: was "The field momentum gives 4/3 instead of 2/3"; see arbiter correction 19]. The radius 2e-13 cm follows from m0 = 0 and m = 8e-28 g (deep reader reproduces 2.0e-13 cm). Mainstream: no electron size has been measured; scattering and g-2 bound it far below 10^-16 cm [memory medium; bound not web-checked], so a classical radius of order 10^-13 cm is not a physical size. Verdict: Historically superseded but instructive.

4b. The Lorentz-FitzGerald contraction as a real physical effect, with Michelson-Morley "almost positive proof". The contraction (1 - u^2/C^2)^(1/2) is right as a result of special relativity (where it is kinematic). Jeans derives it from the corresponding-states theorem under the condition "if we suppose all forces in the ether to be electrical" (section 660; section 659 credits Lorentz and Einstein). The inference that M-M "almost proves" it is not sound as stated: the Kennedy-Thorndike experiment (1932) showed that contraction alone cannot explain the null results and time dilation is also needed [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment]. That experiment did not exist in 1911, so this is a gap in the evidence stated in strong words, not a calculational error. The 1911 text keeps a real ether and never says "relativity"; the 4th edition (1919) adds a relativity chapter [web: Investigator, archive.org 5thedmathematica00jeanuoft]. Verdict: Historically superseded but instructive.

4c. Bucherer versus Abraham, and "mass is purely electromagnetic". The Lorentz transverse-mass formula fits Bucherer's data with m0 = 0, and it is also the special-relativity formula, so the data support the velocity dependence but cannot show that the mass is electromagnetic (deep read 3m). Abraham's rigid electron was ruled out by 1908-1917 results; Rogers (1940) reached about 1%; Zahn-Spees and Farago-Janossy considered the early data qualitative [web: Kaufmann-Bucherer-Neumann page above]. Jeans hedged ("seem to shew") [read]; the 5th edition (1927) still reads Bucherer as showing the electron mass wholly electromagnetic [web: Investigator]. Verdict: velocity dependence of transverse mass: Established; "mass is purely electromagnetic": Historically superseded but instructive.

4d. Radiation from acceleration, (2/3) e^2 a^2/C^3, "its velocity contributes nothing". This is the Larmor formula, and the dipole condition (sum of e x acceleration = 0, no radiation) is standard [memory high]. The deep reader notes the derivation drops local-time variations over the electron and gives no relativistic (Lienard) form; the low-speed statement is correct. Retarded potentials, the Lorentz force from least action, Poynting flux/c^2 as momentum density, the Hall effect, Zeeman splitting delta p = eH/(2mC) and X-ray pulses from sudden deceleration are standard. Verdict: Established. Notes: the Zeeman treatment is for the normal effect (complex patterns explained only qualitatively, as Jeans says); "universally believed" Stokes pulses were overtaken by crystal diffraction (1912) [memory high], though the continuous bremsstrahlung spectrum from sudden deceleration is right.

4e. "Electron theory proves the Ampere element law for every element of a circuit." Section 624 derives the field of a moving point charge at low speed (Biot-Savart form), which is real and measured. An isolated current element is not physical (it fails charge conservation), only closed circuits are testable, and the "Ampere" force law between elements is a different formula, so the claim as worded overstates what the derivation gives. Verdict: Established for the field of a moving charge; Not testable as stated for element-by-element Ampere forces on non-closed pieces of circuit. Relevant to other projects in this collection that rest on Ampere-type element forces.

a. Internal consistency: good. Misprints recorded by the deep reader (Y0 = .33 for .033; "even" for "odd" in the Zeeman line count; "contracted/uncontracted" swapped; "In 1908, Kauffmann" against a 1906 footnote) are slips, not errors in the results. b. Consistent with experiment: all but the ether, the real contraction and the purely electromagnetic mass. c. Tested: Bucherer and successors for mass; Michelson-Morley (1887) and Kennedy-Thorndike (1932) for the contraction. d. If true: an ether frame would exist and special relativity would be unnecessary; Michelson-Morley, Kennedy-Thorndike and later tests exclude that.

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

Split, because the parts get different verdicts.

5a. Space and time are continuous because relativity mixes them; a granular continuum would need a universal constant of dimension length x time. The argument rests on the absence of such a constant in 1925. A Planck length and time (from G, hbar, c) exist but cannot be probed [memory high; the deep reader says the same]. Verdict: Not testable as stated.

5b. An "atom of energy mC^2" revealed by astronomy. His numbers are right (250 Mt/min; I get 256), but the inference from a continuous mass-loss rate to atomicity of energy is a non sequitur; he states it as an inference. The Sun's energy comes from hydrogen fusion (about 0.7% of the mass converted) [memory high], not annihilation of matter. Verdict: Historically superseded but instructive.

5c. Emission and absorption occur in single quanta h nu; with h = 0 hydrogen would collapse in about 10^-10 s (my figure 1.6e-11 s). Verdict: Established. The collapse time is a correct classical order-of-magnitude result.

5d. Free radiation must remain undulatory, because indivisible bullet quanta contradict interference over about 10^6 wavelengths, Wien's decay (a quantum several metres long), starlight diffraction (Lorentz 1906) and Taylor's feeble-light pattern. Mainstream view: the argument is sound against a localised bullet photon, and modern quantum optics agrees a photon is not a tiny bullet (a single-photon state has the extent of its wave packet, and interference builds up detection by detection; Taylor's 1909 low-intensity experiment is on record, with the 2000-hour figure from Jeans's own 1924 Report [web: Investigator; https://en.wikipedia.org/wiki/Double-slit_experiment lists the experiment but not the exposure]). What does not survive is the conclusion that free radiation is classical Maxwell waves only: coincidence experiments (Bothe-Geiger April 1925; Compton-Simon September 1925) show event-by-event energy and momentum conservation [web: Investigator, Wikipedia], and later single-photon anticorrelation experiments (Grangier-Roger-Aspect 1986: no coincidences at a beam splitter, impossible for a classical wave) [memory high; not web-checked]. Jeans's picture also does not explain how a spherical wave delivers all its energy to one atom among many, which he admits (the "weak link", p.20). Verdict: Tested, not supported (purely classical-wave free radiation with quantisation only at matter exchange).

5e. A free electron can neither absorb nor emit a quantum of non-zero frequency. The argument (energy balance in the frame where the final electron is at rest) is correct and standard; the deep reader verified momentum is not needed once that frame is chosen and the relativistic version gives the same. Verdict: Established. His inference that radiation "produces no acceleration" in a free electron goes beyond the argument and conflicts with Thomson scattering, the classical low-frequency limit of Compton scattering [memory high; deep read agrees]. Verdict for that inference: Refuted by calculation and experiment.

5f. Bound-electron momentum: electron momentum 2h nu/v against photon momentum h nu/C; ratio v/(2C) (1e-3 at 1 eV, 3e-2 at 1 keV, deep read). The conclusion that absorption is by the atom as a corporate whole is standard. Established.

a. Internal mathematics: sound; the printed sentence "rate of exchange is taken to be C" should read C^2 [read: deep read 1d]. b. Consistent with: spectra, the Planck law, the photoelectric law, X-ray production. In conflict with: photon coincidences, Thomson scattering, fusion. c. Tested: Taylor, Lorentz, Wien are Jeans's evidence for waves; Bothe-Geiger, Compton-Simon and later work argue against a wave-only account [web, memory high]. Photon coincidence has been replicated widely [memory high]. d. If true: the photon would be an artefact and the Compton shift would need a new mechanism (no equations given); QED would be replaced by a classical wave theory with source and sink rules.

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)

My own check: book pp.[52]-[53] (PDF p.28) reads phi = (1/r){F(t - r/a) + Phi(t + r/a)}; equal prominence gives Psi = integral ([rho] + {rho})/2r dV and F = integral ([rho U] + {rho U})/2r dV; "The latter, averaged over a sufficient time, is found to be zero" [read: page image p.28]. Jeans shows no calculation.

Mainstream view. Time-symmetric electrodynamics is a legitimate classical theory developed by Schwarzschild (1903), Tetrode (1922), Fokker (1929) and Wheeler-Feynman (1945) [web: Investigator, Wikipedia absorber-theory page]. Wheeler-Feynman showed a perfectly absorbing universe gives ordinary retarded radiation and radiation reaction from half-retarded plus half-advanced fields; Cramer's transactional interpretation (1986) revived the emitter-absorber handshake [memory high]. Jeans's lecture is an early instance of this idea; the standard histories do not mention him (Wikipedia page; Kennefick 1997 has no mention) [web: Investigator]. That is a silence in the histories; whether Jeans knew Tetrode or Ritz is unknown.

a. Is the mathematics consistent? Both terms solve the wave equation; the mean Poynting flux of a periodic source with equal retarded and advanced parts is zero (far-zone check above); the two-atom solution (atom 1 purely retarded, atom 2 purely advanced) has zero net flux through a large sphere if the motions are identical. Jeans lists the gaps himself: infinite field energy, no selection of Bohr orbits, no phenomenon explaining "source" and "sink" at frequencies the atom does not "beat time" to, no equations for the Compton alternative. I add two points. (i) The half-sum differs from the retarded solution by a source-free field (the radiation-reaction field in Dirac's 1938 decomposition [memory high]), so the "non-radiating atom" is an atom with an incoming wave exactly cancelling its outgoing one, a standing field of infinite extent. (ii) "Equal weight" is justified by a reversibility principle, not derived, and the claim that observed radiation direction needs an absorbing universe is Wheeler-Feynman's, not Jeans's. b. Consistent with experiment? It gives stability without quantisation (his own objection). A wave-only emitter-absorber flow does not give event-by-event conservation or the directional correlations of Bothe-Geiger and Compton-Simon; Tolman (1926): these "greatly increased the difficulties of the wave theory" [web: Investigator]. As a reformulation of ordinary retarded radiation (Wheeler-Feynman) it is consistent with classical experiments. c. Tested? As a framework it was developed as an equivalent reformulation of classical electrodynamics and an interpretive alternative, not as a rival with distinct predictions [memory high]. As a replacement for the photon in photoelectric and Compton effects, Jeans wrote no calculation, so there is nothing to test; the experiments above argue against its wave-only form. Reception: E. P. Adams 1926 (favourable, brief, no comment on the advanced-potential step; his 1901 experiment is used in the lecture, so he is not a neutral reviewer), Tolman (fair, flags the new experiments), Loring 1927 (finds "convergence" promising and notes Jeans did not offer it as a solution; a minor writer) [web: Investigator]. d. If true: quantum emission would be a classical wave flow with sources and sinks, or classical electrodynamics would need absorbers built into its boundary conditions; the photon would be an artefact. Mainstream physics would have to derive E1 - E2 = h nu from a classical field, which Jeans says he cannot do.

Related work (Investigator): Shuang-ren Zhao's "mutual energy flow" papers (arXiv:1606.08710 and later) describe a photon as a retarded wave from the source plus an advanced wave from the sink, the same structure as Jeans's two-atom solution; outside the mainstream journals, reported as related work, not as support [web: Investigator].

Verdict (split): - The mathematics of the time-symmetric field and its zero mean flux for periodic sources: Established (as mathematics). - The time-symmetric atom as a classical non-radiating model: Plausible, untested (stability without quantisation; gaps stated by Jeans). - The source-and-sink flow as the mechanism that gathers a quantum onto one absorber, and the Compton alternative: Never properly tested (no equations written, so no test could be run on Jeans's version; not dismissed without testing, just never calculable); in its wave-only form against the coincidence results: Tested, not supported. - Historical priority (Jeans 1925 before Wheeler-Feynman 1945) is a matter of record, not a verdict on the physics.

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

Jeans: hC/2pi = K (4 pi e)^2 with K "not greatly different from unity". K = 1/(16 pi^2 alpha) = 0.868 [calc]. In Gaussian units hbar c = e^2/alpha, so the relation restates the fine-structure constant (Sommerfeld 1916) [memory high]. It is dimensionally forced (hbar c and e^2 share dimensions); "K near 1" depends on the 4 pi in a charge's flux (with e^2 alone the ratio is 137). The same remark appears in cautious form in the 1924 Report section 85, with Jeans adding that atomicity of e would not by itself give the quantum theory, "for if it did the quantum-theory would have been fully developed long ago" [web: Investigator, archive.org bwb_W9-CSF-029]. No derivation of alpha is known in mainstream physics [memory high]. a. Mathematically consistent: yes; an identity plus a numerical near-coincidence. b. Consistent with experiment: it is the measured alpha; the interpretation is not testable. c. Tested: nothing to test. d. If true: h would follow from e and c; nothing in current theory implies it. Verdict: Not testable as stated.

Investigator findings: how each bears on the verdicts (kept whatever the verdict)

Priority 1 (Jeans's own work) - Nature 71, 607 (27 Apr 1905): the 1904 theory restated as a time-scale claim ("millions of years would hardly suffice for any perceptible change"), the true final state being equipartition. This is Jeans's own retreat to the weak form within a year and is the reason claims 1-2 are split [web: Investigator]. - Dynamical Theory of Gases 2nd ed. (1916): the quantum theory has "revolutionised" the kinetic theory; the quantum account is "at best only partial" but "probably... satisfactory"; classical difficulties "left unsolved" [web: Investigator]. His own revision of claims 1-2. - Report on Radiation and the Quantum-Theory (1914; 2nd ed. 1924): slow transfer restated ("millions of years", citing Ch. IX); the 1924 Report already holds the tube-of-force relation (claim 7), the Lorentz and Taylor evidence with references and "matter, and not ether or radiant energy" as what is quantised (claim 5), and the "no force X on a free electron in a radiation field" passage, but no advanced potentials. So the advanced-wave step is new in 1925 [web: Investigator]. - Electricity textbook, 4th (1919) and 5th (1927) editions: relativity chapter added; electromagnetic-mass reading of Bucherer still printed in 1927 [web: Investigator]. Bears on claim 4. - Lodge, Nature 118, 81 (1926): credits Jeans with the 8 pi R factor of the Rayleigh-Jeans law [web: Investigator]. Jeans's classical law is the one that fails at high frequency. - Not read by me or the Investigator: Montambaux files (1900-1905 papers, Solvay 1911, Hudson 1989 in full), Royal Society JHJ papers (1901-07 sanatorium letters), HRC Richardson letters.

Priority 2 (supporting information by others) - Boltzmann-Jeans conjecture (Benettin, Galgani, Giorgilli 1989, 1993; Benettin-Carati-Gallavotti 1995): later rigorous support for exponentially slow classical energy exchange in model systems. It supports the weak form of claim 2 and does not change the verdict on equilibrium heat capacities [web: Investigator]. No stake evident (academic authors). - Tolman, Adams, Loring reviews (1926-27): see claim 6.

Priority 3 (related work) - Time-symmetric lineage (Schwarzschild, Ritz-Einstein 1909 where Ritz blamed advanced potentials for the Rayleigh-Jeans catastrophe [web: Investigator, shadetreephysics snippet; the Ritz-Einstein note itself was not obtained], Tetrode 1922, G. N. Lewis 1926, Fokker 1929, Wheeler-Feynman 1945). Zhao: see claim 6. Kragh-Carazza 1994 cites Atomicity p.8 on discrete time (claim 5a); not read.

Priority 4 (historical record) - Bothe-Geiger April 1925 and Compton-Simon 1 Sep 1925 against the lecture of 11 May 1925: see Corrections 3. - Adams 1901: 2 x 16 copper spheres on brass rods, 10,000-cell battery, 75-85 rev/s, magnetic convection effect [web: Investigator]. The radiation figure is Jeans's calculation. - Not reached: Milne 1947 obituary, Nature 117, 46 review, Wien's decay paper, HathiTrust search. These would add most for claims 1-2 and 5-6.

Absence of evidence

The 1904 theory did not die by a decisive experiment; Jeans himself retreated within a year (1905 reply) and replaced it by 1916, and his later editions record the change, so there is no sign of suppression. The 1925 advanced-wave idea was never tested because it was never put in calculable form, and it then drops out of the standard histories of time-symmetric electrodynamics. Competing readings: (a) matrix and wave mechanics (1925-26) overtook it; (b) it was incomplete, as Jeans said; (c) historians of absorber theory simply did not cite it. Records that would decide: citations of Jeans 1925 in Lewis 1926, Fokker, Wheeler and Feynman correspondence, and Jeans's letters to Richardson.

Summary table

Web checks done (budget about 6)

1. Kennedy-Thorndike [web: https://en.wikipedia.org/wiki/Kennedy%E2%80%93Thorndike_experiment]: contraction alone insufficient; time dilation also needed.
2. Kaufmann-Bucherer-Neumann experiments [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments].
3. Atmospheric escape [web: https://en.wikipedia.org/wiki/Atmospheric_escape]: Earth loses about 3 kg/s H and 50 g/s He.
4. Double-slit page [web: https://en.wikipedia.org/wiki/Double-slit_experiment]: Taylor 1909 listed; exposure time not on the page (2000 hours rests on Jeans's 1924 Report via the Investigator).
5. Heat capacity page: no mention of Eucken 1912; that fact stays [memory high].
6. Not done or failed: Grangier-Roger-Aspect 1986, the electron-size bound, Moon and Mercury exospheres (all tagged [memory]); Taylor and Wien originals not obtained; a Taylor-Dempster-Batho page returned 404.