Tolman-R: Physicist review (Step 2)

Project: Richard C. Tolman, The Theory of the Relativity of Motion (University of California Press, 1917). Reviewer: PhD physicist. Tags: [read] document or research file, [web] URL given, [memory] with confidence, [calc] my own calculation (Python/SymPy in .venv).

Source note repeated from claims.md. The project folder holds one OCR scan whose equations are garbled. Chapters III-IV and X-XI were deep-read from page images by Step 1. Chapters I-II, V-IX and XII-XIII rest on digests alone. To reduce that gap I read the clean Project Gutenberg typesetting that the Investigator found (research/files/Tolman-1917-Gutenberg-32857.pdf, text extracted by me) for: sections 21-23 (emission theories), section 64 (mass of the electron), section 103 (temperature scale), sections 117-120 and 146-150 (elasticity and thermodynamics) and sections 151-167 (electromagnetism). I did NOT re-check every equation of Chapters V-IX and XIII; verdicts on material only from those chapters rest on the digest plus standard physics [memory, high]. The Gutenberg text is a volunteer re-typesetting, not the original.

This is a mainstream textbook, not an outsider's theory. "Mainstream view" below therefore mostly means "the textbook view today", and the interest lies in where Tolman's 1917 choices differ from today's.

How to read the maths here (reader note)

Tolman writes sqrt(1 - u^2/c^2) throughout; modern texts write 1/gamma with gamma = 1/sqrt(1 - u^2/c^2). Below I use gamma and beta = u/c for brevity. c = speed of light. A superscript ° (Tolman's notation) means "measured by an observer moving with the material".

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Claim 1. Light-speed constancy and relativity of motion give time dilation, length contraction, clock offset l'V/c^2, the Lorentz transformation and velocity addition

a. Mathematics. Consistent. The deep read checked every equation of Chapters III-IV with SymPy and found no printed error [read: deep/, section 4.9]. I confirm the logic of the key steps independently: the transverse light clock gives gamma; the c/2 + c/2 example is (c/2 + c/2)/(1 + 1/4) = 0.8c [calc]. The gaps the deep reader lists are real and are gaps of exposition, not errors: Tolman finds the Lorentz transformation "by trial" and never states linearity (which follows from homogeneity of space and time); he promotes preservation of the light-sphere equation to invariance of the full interval without argument; and his Newtonian limit needs c -> infinity, not only V -> 0, because t' = t - Vx/c^2 has a first-order term [read: deep/, section 4.7]. Tolman warns that Chapter III lays "no stress on mathematical elegance or logical exactness" [read: p.45]. A fully rigorous derivation of the same transformation from homogeneity, isotropy and the relativity principle alone (without the light postulate, leaving c as a free constant) was given by von Ignatowski in 1910 [memory, medium]; Tolman does not use it.

b. Experiments. Consistent with a long list. Michelson-Morley (1887) and its successors, which Tolman cites as null results [read: p.38]; Kennedy-Thorndike (1932) for the clock-and-length combination; Ives-Stilwell (1938) for the transverse Doppler shift (time dilation); the lifetime of cosmic-ray muons (Rossi-Hall 1941); Hafele-Keating airborne clocks (1971); and modern GPS timing, which needs both special- and general-relativistic corrections [memory, high]. None of these was available to Tolman in 1917, so he leaned on null ether-drift results and electron mass data [read: pp.37-38, 56].

c. Tested? By many, repeatedly, and by independent groups over a century [memory, high]. No replication failure is known to me. I did not run a web check on each experiment (budget), so these are [memory, high].

d. If false: all of the above would need a different explanation, and so would particle accelerators and Maxwell's theory in moving frames. Nothing in mainstream physics has to change, because this is mainstream physics. One legitimate nuance: the experiments fix the Lorentz transformation but cannot choose between "Einstein's interpretation" and Lorentz's ether theory with real contraction and a hidden preferred frame; the two are empirically equivalent [memory, high]. Tolman's remark that the ether is "unnecessary" (section 163) is a choice of economy, not a measurement [read: Gutenberg text, section 163].

Verdict: Established (the transformation laws). The 1917 derivation is heuristic in places (see a).

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Claim 2. Mass rises as m0/sqrt(1 - u^2/c^2); mass and energy are one entity (Delta E = c^2 Delta m); relativistic particle mechanics follows from a modified Lagrangian

a. Mathematics. Consistent. The colliding-spheres argument (Lewis-Tolman) reproduces the momentum p = gamma m0 u; the step "momentum changes equal and opposite" uses conservation of momentum with speed-dependent mass; the derivation of Delta E = c^2 Delta m from f = d(mu)/dt is correct and checked [read: deep/, sections 4.5-4.6]. Its limit: it derives the relation only for kinetic energy; the extension to "all energy has mass, all mass is energy" is an argument by generalization, Tolman's own words being "every reason to believe" and "pragmatic" [read: deep/, section 4.6]. Tolman's Chapter XII gives a second route for electromagnetic energy: a closed system has E = gamma (m0 c^2 + E0), so E0/c^2 adds inertia [read: Gutenberg, sections 166-167]. The kinetic potential H = -m0 c^2 sqrt(1 - u^2/c^2) for a free particle is the standard relativistic Lagrangian [memory, high]; the requirement that H/sqrt(1 - u^2/c^2) be invariant is the statement that the action is a Lorentz scalar (H dt = H dtau/gamma... the proper-time form) [memory, high]. Rounding: "1 gram = approx. 10^21 erg" is 11% high; his own c gives 8.99e20 erg = 8.99e13 J [calc; read: deep/].

b. Experiments. Consistent. Electron deflection (see Claim 6). Modern confirmations: accelerator momentum and energy relations (Bertozzi, MIT 1964, electrons at up to 0.99c, kinetic energy versus speed) [memory, high]; nuclear reaction energy balances, first by Cockcroft and Walton (1932, lithium plus proton) [memory, high]; the whole of high-energy physics. Rogers et al. (1940) agreed with Lorentz-Einstein within 1% for electrons [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments].

c. Tested by many groups; replicated. Nothing here is in dispute.

d. Nothing changes. One terminology point (the Corrections section expands it): "relativistic mass" m = gamma m0 is now mostly avoided; modern texts keep m0 as "the mass" and write p = gamma m0 u, E = gamma m0 c^2. This is bookkeeping, not different physics [memory, high].

Verdict: Established. Split on wording only: the "mass rises with speed" language is Historically superseded but instructive as a convention, while the physics (momentum and energy laws) is Established.

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Claim 3. Momentum density = energy-flow density / c^2 (including energy carried by stress); a stressed body moving along X has transverse momentum; its stress tensor is unsymmetrical; a moving right-angled lever needs an external torque F l V^2/c^2 to stay in equilibrium

a. Mathematics. I verify the lever algebra [calc]: with l1 = l1°, l2 = l2°/gamma, F1 = F1°, F2 = F2°/gamma, the net torque is F1° l1° - F2° l2°/gamma^2 = F1 l1 beta^2 when F1° l1° = F2° l2°. The torque is balanced by the rate of growth of angular momentum, dM/dt = integral of (u x g) dV, with g_y = t_xy u/c^2 [read: deep/, sections 4-6]. Tolman's statement that a body moving in a straight line with constant velocity and stress has increasing angular momentum about a fixed point is correct [read: p.168]. For F1 l1 = 100 N m and V = 30 km/s (Earth's orbital speed) the torque is 1e-6 N m [calc]; no rotation results. Independent check of the stress transformations (167). I could not confirm this from the deep read, which flagged the comparison with the modern tensor as unchecked [read: deep/, section 9, last item]. I did the following. Tolman's strain is the Green strain, sqrt(1 + 2 eps) = L/L0 [read: Gutenberg, eq. 149-151], so a small change satisfies d eps_xx = L dL/L0^2. That is why his factor in (160) is 1/(1 - beta^2) rather than gamma. For an isotropic fluid with pressure p0, the work equation in the rest frame gives t°_xx = p0/gamma and t°_yy = gamma p0 (using L° = gamma in the reference state), and (167) then returns t_xx = t_yy = t_zz = p0, i.e. pressure invariant, in agreement with Tolman's separate thermodynamic result (200) and the modern perfect-fluid tensor [calc, derivation by hand]. So the stress transformation is internally consistent with the rest of the book. The stress t is defined per unit volume of unstrained material, which is why it differs from the modern Cauchy stress in a boosted frame [memory, medium].

b. Experiments. The lever and its electrical twin are consistent with the Trouton-Noble null result (1901-1903): a charged capacitor in motion shows no torque, as relativity with Laue's energy-flow term predicts [web: https://en.wikipedia.org/wiki/Trouton%E2%80%93Noble_experiment]. Repeated with better sensitivity by Tomaschek (1925-26), Chase (1926-27) and Hayden (1994) per the same page [web, same URL]. Tolman himself says "At present we have no experiments of sufficient accuracy" to separate his elasticity theory from older ones [read: p.172]. Energy-flow carries momentum (T^{0i} = T^{i0} in the modern stress-energy tensor) is established on other grounds, e.g. radiation pressure and the inertia of stressed bodies [memory, high].

c. Tested? The overall principle (no rotation; momentum = energy flux/c^2) is supported indirectly by Trouton-Noble-type nulls and by the whole of relativistic mechanics. The specific transverse-momentum effect in a strained solid at everyday speeds (about 1e-5 kg m/s per cubic metre for a 1e9 Pa shear at 1 km/s [calc]) has, to my knowledge, no direct measurement [memory, medium]. Not replicated because not isolated.

d. Nothing to change. The literature records continuing disagreement about the best explanation, not about the result. Investigator lead: Shapiro (arXiv:1206.4487, 2012) writes that the problem has seen "extensive discussion and indeed controversy", credits Lewis and Tolman (1909) with the paradox and von Laue (1911) with the resolution, and argues the resolution is via angular momentum and simultaneity [read: research/2026-10-04-lever-paradox.md]. The Wikipedia Trouton-Noble page lists Laue's hidden-momentum/energy-current resolution and a separate Tolman-Epstein 1911 resolution (relativistic force and acceleration are not always parallel) [web: URL above]; I did not verify that second attribution in the original papers. Tolman's 1917 text uses the energy-flow account (section 136) [read: p.170].

Verdict (split): - Energy-flow momentum, no net rotation of the lever, and the Laue-style resolution: Established (accepted theory; null results of Trouton-Noble type). Alternative explanations exist and are debated; the prediction is not. - Tolman's particular unsymmetrical stress tensor t as the right formalism: Historically superseded but instructive (replaced by the symmetric stress-energy tensor; the symmetric p he constructs from t is the modern object). - Measurable transverse momentum in an ordinary strained solid: Plausible, untested as a direct measurement.

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Claim 4. Entropy and pressure are invariant; temperature transforms as T = T0 sqrt(1 - u^2/c^2); momentum of a moving system G = (E + pv)u/c^2; hohlraum G = (4/3) a v0 T0^4 u/(sqrt(1 - u^2/c^2) c^2)

This claim has several parts with different standing.

a. Mathematics. - Entropy invariance (197): argued from S = k log W (the number of microstates does not depend on who counts it). Standard [memory, high]. - Pressure invariance (200): derived from the Lagrangian; I checked it consistent with the stress transformation and with force/area transformation (above). Standard: the pressure in a perfect-fluid stress-energy tensor is a scalar [memory, high]. - Temperature (201): internally consistent, but it is a consequence of Tolman's choice of H = -E° sqrt(1 - u^2/c^2) combined with defining T as the generalized force conjugate to S, T = -dH/dS. The deep read notes the factor comes "entirely from the chosen form of H" and that Tolman gives no thermometer argument [read: deep/, section 8]. Tolman himself says the choice of kinetic potential "was not absolutely uniquely determined" [read: p.172]. So the temperature law is a theorem about a definition, not a derivation from independent physics. - My own check of the dependence on definition [calc]. For a photon gas (p0 v0 = E0/3) with Tolman's energy (204), E = gamma (E0 + p0 v0) - p0 v, and momentum (205), hold u and the rest volume fixed and add rest-frame heat dE0 = T0 dS. At beta = 0.6 (gamma = 1.25): the lab energy rises by 1.40 dE0; the energy minus the work term u dG rises by 0.80 dE0, which equals dE0/gamma, giving T0/gamma (the Planck-Einstein, Tolman form); a bare dE gives yet another factor, (3 + beta^2)/(3 sqrt(1 - beta^2)) dE0; and gamma dE0 would give the Ott-Arzelies form. So which law you get depends on what you call "heat" in the moving frame. That is the whole disagreement, and I reproduce it with the book's own formulas. - Momentum of a moving system (205)-(206) and hohlraum (208): reproduces the Planck-Einstein results of 1907-08 [memory, high]. The factor 4/3 (G = (4/3) E u/c^2 for radiation in a cavity, if walls and their stresses are ignored) is the same "4/3 problem" as for electromagnetic mass. For a complete closed system the stresses in the walls cancel it and G = E u/c^2, which is Tolman's own (193) [read: p.171; deep/, section 9; memory, high von Laue 1911]. Tolman (208) applies to a system acted on by external pressure; the two statements are consistent but a reader should not take (208) as the momentum of a complete container. - The kinetic-theory temperature scale of section 103 is defined in the rest frame (T proportional to the average of m0 u^2/sqrt(1 - u^2/c^2) in the frame where the gas is at rest) [read: Gutenberg, section 103], so it does not on its own fix the moving-frame rule.

b. Experiments. Entropy and pressure invariance: nothing contradicts them. Temperature: no laboratory measurement discriminates among the proposed laws. Heras and Osorno (arXiv:2204.12572, 2022) list three live positions: Planck-Einstein T/gamma ("supported by many authors"), Ott-Arzelies gamma T, Landsberg invariant T, and argue that none of the two classic laws satisfies group closure [read: research/2026-10-04-arxiv-temperature.md]. Pouryazdan and Vakili (arXiv:2606.00521; Phys. Lett. A 590, 2026) define an effective temperature from the transformed energy density of an isotropic system and find it "consistently increases with velocity", which they say supports the Ott view, and conclude temperature is observer-dependent [read: same note]; both papers are theoretical, and neither cites a measurement [read: same note]. Cubero et al., Phys. Rev. Lett. 99, 170601 (2007), relativistic molecular-dynamics simulations, found the rest-frame temperature unchanged under boosts for the Maxwell-Juttner distribution in a specific operational sense [web: search result confirming title and citation; content of conclusion from [memory, medium]]. A moving thermometer is also direction-dependent: for blackbody radiation seen by a moving observer, T(theta) = T0 sqrt(1 - beta^2)/(1 - beta cos theta) [memory, high], which equals none of the three single-number laws. The cosmic microwave dipole is the everyday case.

c. Tested? Never directly, and the question as posed may not be testable (see verdict). Not replicated.

d. If Ott's, Landsberg's or a covariant (four-vector inverse temperature, beta^mu = u^mu/(k T0)) view is right, then Tolman's temperature law is a convention that does not survive as a physical statement; the equations of motion, momentum and energy are unaffected. Modern relativistic hydrodynamics uses the rest-frame T and the four-vector [memory, medium-high].

Verdict (split): - Entropy invariant, pressure invariant: Established. - Energy and momentum of a moving thermodynamic system (E, G, hohlraum 4/3): Established as Planck-Einstein-Laue theory, with the proviso above about walls. - T = T0 sqrt(1 - u^2/c^2) as "the" temperature of a moving body: Not testable as stated (definition-dependent; no measurement separates the proposals) and Historically superseded but instructive (it was the standard view until the 1960s and is now one of several contested conventions).

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Claim 5. Maxwell-Lorentz electrodynamics follows from the same least-action principle; fields and charge density transform between frames with charge invariant; electromagnetic energy carries mass E0/c^2; the ether is unnecessary

Source status: Step 1 had digest only. I read sections 151-167 in the Gutenberg text.

a. Mathematics. The statement "follows from the same least-action principle" needs a qualification that Step 1 did not catch. Tolman does not derive the electromagnetic Lagrangian from relativity. He says that in electrodynamics, "on account of the closely interwoven historical development", it is not necessary to modify the kinetic potential and "may take for H the following expression, which is known to lead to the familiar equations of the Lorentz electron theory" (209) [read: Gutenberg, section 151]. So he assumes the Lagrangian that yields Maxwell's equations and then shows the equations follow. This is a consistency demonstration, not a derivation of Maxwell from relativity. He also notes his own dimensional slip: the expression "is not quite correct" dimensionally and is repaired by factors eps0 and mu0 equal to 1 in his units [read: footnote, same page]. The field transformations (227)-(228) are the standard Lorentz boost of E and B (with Gaussian-type units) [memory, high], and match the form E'_y = gamma (E_y - (V/c) B_z) etc. Charge invariance is argued from the density transformation: rho'/rho equals the ratio of Lorentz-shortened volumes, so total charge is unchanged [read: section 157]. That is correct given (229), and Tolman adds a supporting argument from counting electrons [read: same]. The energy result E = gamma (m0 c^2 + E0) for a closed system acted on by no net external force at the start and end is correct [read: section 166]; the condition is real, since the derivation fails for open systems (the same wall/stress point as in Claim 4) [memory, high].

b. Experiments. Relativistic invariance of Maxwell's equations: confirmed by every test of the null ether drift and of the Lorentz force on moving charges [memory, high]. Charge invariance: the electrical neutrality of atoms and of molecules whose electrons move at different speeds is tested to roughly 1e-20 of the electron charge or better [memory, medium; not web-checked]. If charge depended on speed, atoms of different Z would not be neutral. Inertia of electromagnetic energy: confirmed through nuclear binding energies and pair production [memory, high].

c. Tested widely, replicated.

d. Nothing changes. The statement that the ether is superfluous is a matter of interpretation and scientific economy (see Claim 1d). Tolman makes it clearly [read: section 163]. An alternative-science reader will note that the Lorentz-style ether is empirically equivalent and that Tolman's argument is simplicity, not a refutation.

Verdict: Established for the physics (Lorentz covariance of Maxwell theory, charge invariance, E/c^2 inertia of field energy). The phrase "derived from least action" is Not testable as stated / a presentation choice, since the Lagrangian is assumed. "Ether unnecessary": an interpretation, Not testable as stated (no measurable difference from a Lorentz ether).

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Claim 6. Electron-deflection experiments (Kaufmann, Bucherer, Hupka) support the relativistic mass law; emission (Ritz-type) theories are ruled out by astronomical and Stark-effect evidence (Comstock, de Sitter)

Source status: Step 1 read this from the digest. I read sections 21-23 and section 64 in the Gutenberg text.

First a correction of how the book presents the evidence (details in "Corrections to Step 1"): Tolman does NOT say the Stark-effect evidence rules out Ritz's theory. He says it rules out the first two emission variants (mirror as new source; Stewart's), says optical experiments to decide between Einstein and Ritz "have never been performed, although such experiments are entirely possible", and offers only Comstock and de Sitter against Ritz [read: Gutenberg, section 22].

a. Mathematics. - Binary-star argument [read: section 21]. If light speed is c + u at one side of the orbit and c - u at the other, the apparent half-periods become Delta t + 2ul/c^2 and Delta t - 2ul/c^2, with l the distance. The algebra is right to first order. Numbers [calc]: u = 100 km/s, l = 100 parsecs gives 2ul/c^2 = 79 days, larger than the half-period of a close spectroscopic binary (days), so orbits would look badly non-Keplerian. They do not. Constraint from de Sitter's data: the source-velocity parameter k < 2e-3 [web: https://en.wikipedia.org/wiki/Emission_theory_(relativity)]. - Tolman's argument that the electron-mass data exclude a charge decrease with speed: his mass derivation uses no charge, so "the increase in mass is alone sufficient" [read: section 64, p.77-78]. True in his scheme, since the mass law is derived from collisions and the electron experiments only measure e/m.

b. Experiments. - Electron mass. Kaufmann's 1901-1906 results; in 1905 he concluded he had "disproven the formula of Lorentz-Einstein" in favour of Abraham's rigid-electron theory; Planck's 1906-07 reanalysis found the data not decisive. Bucherer (1908), with crossed electric and magnetic fields, agreed with Lorentz-Einstein; Bestelmeyer criticized the method; Hupka (1910) and Wolz (1909) supported Lorentz-Einstein; Neumann (1914) confirmed it for 0.4c-0.7c; Guye and Lavanchy (1915); Rogers et al. (1940) agreement within 1% [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments]. The book (1917) calls this "one of the most striking triumphs" and does not mention the earlier contrary reading [read: p.56; deep/]. In 1910 Tolman had himself written that the Kaufmann-Bucherer experiment "may not really indicate an increase in the mass of an electron", if forces at high speed differed from Maxwell's law [read: research/2026-10-04-wikisource.md, 1910 paper]. His 1917 argument that mass alone explains the data is the answer he then gave. - Emission theories. Tolman's 1910 sun-limb experiment (a Lloyd's mirror, expected about 2 fringes on the emission hypothesis, observed none) and the 1912 Stark-effect analysis [read: research notes] test variants (1) and (2) of section 22, not Ritz. Investigator lead (Martinez 2004): J. G. Fox (1962-65) argued, from the Ewald-Oseen extinction theorem, that light passing through matter is re-emitted at c relative to the matter, so interferometer tests "like those of Tomaschek or Miller or those using Tolman's apparatus" and de Sitter's binary-star evidence are not decisive; Martinez adds that early evidence "was misconstrued as telling against it more conclusively than actually was the case" [read: research/2026-10-04-martinez-ritz.md]. Fox's point is a real physical criticism of the binary-star argument, and it also applies to Tolman's own sun-limb experiment [web: Wikipedia summary, extinction distance in air about 0.2 cm, https://en.wikipedia.org/wiki/Emission_theory_(relativity)]. Tests designed to avoid it: Alvager et al. (1964), photons from pi-zero decay at 0.9998c, k = (-3 +- 13) x 10^-5 (source speed adds essentially nothing); Brecher (1977), X-ray binaries, k < 2 x 10^-9 [web: same URL; the page is Wikipedia's summary, I did not read the original papers].

c. Tested? Mass law: yes, by several groups, with a documented dispute in 1905-1915 that was settled by better experiments (Neumann 1914, Rogers 1940, later accelerator work). Emission theories: the 1917 evidence was weaker than the book says; the controlled, extinction-free tests came in 1964 and 1977 and found no source-speed addition.

d. If emission theories were right: the second postulate would be false, and so would Maxwell's wave-equation speed being a constant independent of source. The Ritz alternative also faces other objections (Pauli's, discussed in Martinez), which Fox disputed; this is history, not the present consensus [read: research/2026-10-04-martinez-ritz.md].

Verdict (split): - Electron-deflection data support the relativistic mass law: Established (the 1917 case was thinner than the book states; later tests settled it). - Ritz-type emission theories excluded: Tested, not supported (Alvager 1964, Brecher 1977 [web], plus the broad success of relativity). The specific 1917 evidence (Comstock, de Sitter, Stark-effect) was Historically superseded but instructive: reasonable then, challenged by Fox on extinction grounds, and not decisive by itself. The record shows the test was proposed but not performed in Tolman's lifetime of the 1910s (Tolman 1912 called a sunlight Michelson-Morley test "a matter of the highest importance") [read: research notes], so for Ritz specifically the claim was "Never properly tested" in 1917 and "Tested, not supported" today.

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Investigator findings: what I keep and how I weigh them

All kept in the record whatever my verdict: 1. Clean typeset edition (Gutenberg #32857) [web: https://www.gutenberg.org/files/32857/32857-pdf.pdf]. Used above to read Chapters II, VI, VIII, XII equations directly. 2. Tolman 1910 "The Second Postulate of Relativity", Phys. Rev. 31, 26: he first treated the emission hypothesis as simple and consistent with the first postulate, ran his sun-limb test, and derived the light postulate from the mass law while warning the electron data "may not really indicate" a mass increase [read: research/ notes; web: https://en.wikisource.org/wiki/The_Second_Postulate_of_Relativity]. Bears on Claims 1, 2, 6. It shows a physicist changing the logical order of the argument, and the book of 1917 does not repeat the caveat. 3. Tolman 1912 "Some Emission Theories of Light": rules out the first two emission variants by canal-ray Doppler data (Stark, Paschen) and says Ritz's theory "deserves" attention and a sunlight Michelson-Morley test [read: research notes; web: https://en.wikisource.org/wiki/Some_Emission_Theories_of_Light]. Bears on Claim 6. Weighs toward my correction of Step 1. 4. Martinez 2004 and Fox extinction critique (see Claim 6). Reported as the historian's account of Fox; I have not read Fox's papers (Am. J. Phys. 1962, 1965) [memory, medium]. 5. Temperature literature (Heras-Osorno 2022; Pouryazdan-Vakili 2026) and the lever literature (Shapiro 2012) as in Claims 3 and 4. Both temperature papers are by interested theorists proposing their own laws, so their conclusions are theirs; neither reports a measurement. 6. Tolman papers at Caltech (12 boxes: lecture notes, technical notes, manuscripts) and the NAS memoir (not read). The Investigator found no gap in the historical record of Tolman: he went from Berkeley relativity teaching to war work, the Fixed Nitrogen Research Laboratory, Caltech and the Manhattan Project [read: research/2026-10-04-caltech-oac.md]. No "absence of evidence" anomaly arises. Unread: folder lists, which might show drafts behind the 1917 book. Not reached by the Investigator and not touched by me: H. A. Wilson moving-dielectric experiment (book section 172, where Tolman says a repetition "would be a matter of great interest"; the Wilson experiment was done in 1905 [memory, medium]). 7. Wikisource list of further Tolman papers not yet read (Lewis-Tolman 1909; "Non-Newtonian Mechanics" 1911-12): worth reading before a final lever or mass history.

Corrections to Step 1

1. claims.md, claim 6, and facts.json "mainstream_conflict" item 5: Step 1 says emission theories are "ruled out by astronomical and Stark-effect evidence (Comstock and de Sitter)". Per the book (section 22), the Stark-effect and sun-limb evidence bear on variants (1) and (2); against Ritz's variant only the Comstock/de Sitter astronomical argument is cited, and Tolman writes that Einstein-versus-Ritz optical experiments "have never been performed" [read: Gutenberg, section 22, text above]. The wording "direct experimental evidence" is Tolman's: "the observations described above, comprise the whole of the direct experimental evidence". Also, Step 1 said Tolman "gives no data, numbers or apparatus" for either; true within the book (it gives only the 2ul/c^2 argument and references), but Tolman did publish apparatus and numbers in 1910 and 1912 (see Investigator).
2. claims.md, claim 5: "Maxwell-Lorentz electrodynamics follows from the same least-action principle" overstates. Tolman assumes the Lagrangian (209) because it is "known to lead to" Maxwell-Lorentz theory (section 151); he does not derive it from relativity.
3. claims.md, claim 4: "follows from Tolman's chosen kinetic potential" is correct, but the claim also bundles three things that deserve separate verdicts (entropy and pressure invariance, the momentum/energy laws, and the contested temperature law). The hohlraum momentum with 4/3 holds for a system acted on by external pressure, not for a complete closed system (Tolman's own (193) gives E u/c^2 for that case).
4. facts.json states the alternatives to Tolman's temperature as "Ott and Arzelies: T0/sqrt(1-u^2/c^2)". Check: Pouryazdan-Vakili name Ott, Eddington and Moller for the gamma T0 form [read: research note]. The form is right; the attribution list is longer.
5. deep/ section 9 says Tolman's (204)-(206) "are the Planck-Einstein results" and that the 4/3 term is resolved by walls: I agree [memory, high]. The deep read left the stress transformation (167) as "unverified against the modern tensor"; I checked it for the isotropic case (Claim 3a) and found it consistent (pressure invariant), once one notes that Tolman uses Green strain and stress per unit unstrained volume. Not checked for shear components.
6. deep/ and facts.json attribute the Kaufmann experiments to [memory, medium] only. I web-checked: Kaufmann 1905 favoured Abraham; Planck 1906-07 found it not decisive; Bucherer 1908; Hupka 1910; Neumann 1914; Rogers 1940 [web: Wikipedia URL above]. Retag [web].
7. facts.json says the book's coverage of equipartition (Chapter VIII, digest only) says "zero-mass particles give E = 3nRT". I did not check this; I read only section 103 of Chapter VIII, where Tolman defines temperature in the rest frame by the Carnot-type cycle and the average of m0 u^2/sqrt(1 - u^2/c^2) [read]. Left as digest-level.
8. Minor: the Step 1 digest-level claim that the "Newtonian limit" of the Lorentz transformation is trivially V -> 0 is repeated in claims.md claim 1 without the caveat in deep/ (needs c -> infinity); already listed in deep/ but not carried into claims.md.

Summary of verdicts

Web checks done: Kaufmann-Bucherer-Neumann (Wikipedia), emission-theory tests (Wikipedia), Trouton-Noble (Wikipedia), Cubero et al. citation (search). Wikipedia pages were summarised through a fetch tool and are secondary sources; primary papers (Alvager 1964, Brecher 1977, Fox 1962-65, Bucherer 1908, Neumann 1914) were not opened. The temperature search of Wikipedia found no relevant discussion.