Tolman-R: Arbiter (Step 3)

Project: Richard C. Tolman, The Theory of the Relativity of Motion (University of California Press, 1917). Tags: [read] document or project file, [web] URL, [memory] with confidence, [calc] my own recomputation (Python venv, .venv).

Source gap note (carried over)

The only document is one OCR scan of the 1917 book (text layer garbles nearly every equation). Chapters III-IV and X-XI were deep-read from page images in Step 1b. Chapters I-II, V-IX, XII-XIII rest on digests, but the reviewers read the clean Project Gutenberg re-typesetting (research/files/Tolman-1917-Gutenberg-32857.pdf) for sections 21-23, 64, 77, 103, 109-111, 117-120, 146-150, 151-167 and 172. Still NOT read by anyone in full: Chapter V (Fresnel drag, aberration), Chapter VII/IX Lagrangian details beyond sections 109-111 and 120/143, Chapter XIII, sections 168-171. Conclusions about those parts rest on digests plus [memory, high] standard physics. The Gutenberg text is a volunteer re-typesetting and contains at least one error (below); equations used in a verdict must be checked against the scan.

The project is a mainstream textbook, not an outsider's theory. "Verdict" therefore has two layers: (A) is the physics right today, and (B) was the 1917 evidential case as strong as the book says. Where they differ I give both.

Where the three reviewers agree

All three give the same core verdicts on claims 1, 2, 3 (outcome), 4 (entropy, pressure, E, G) and 5 (physics): Established. All three independently found that claims.md overstates the book on emission theories (Claim 6) and on "derived from least action" (Claim 5). All three keep the Investigator's leads in the record (Gutenberg edition, Tolman 1910 and 1912 papers, Martinez 2004 / Fox, the two temperature papers, Shapiro 2012, Caltech papers). All three found no gap in the record of Tolman himself.

Disagreements and my rulings (with recomputation)

1. Is "1 gram = 10^21 erg" a rounding or does the book give the exact figure? Contrarian: the exact 9 x 10^20 appears in section 77 and 10^21 "only in the Chapter III passage". Physicist and mathematician: 10^21 is an 11% rounding, repeated. Ruling: both are partly right. [read: Gutenberg text] section 77 gives "1 gram = 9 x 10^20 ergs" (87). But "10^21 ergs" appears four times: Chapter III (c^2 = (2.9986 x 10^10)^2 = "approx. 10^21"), section 105 (twice, "c^2 will be 10^21"), and section 167. [calc] (2.9986e10)^2 = 8.99e20; 10^21 is 11.2% high. So the contrarian's "only in Chapter III" is wrong; the physicist/mathematician "repeated rounding" is right, and the contrarian is right that the book also states the exact value. Not a derivation error.

2. Gutenberg equation (229). Only the mathematician caught that Gutenberg prints u_z; the scan (printed p.169, PDF p.186) has u_x. [calc/read: page image p.186, which I re-rendered: the subscript reads x] and rho' = gamma(rho - V j_x/c^2) requires x. Ruling: mathematician correct; the Investigator's "clean copy of every equation" is too strong. Physicist and contrarian did not use (229) for a verdict, so no verdict changes.

3. Did the Step 1 / deep read leave the stress transformation (167) unverified? Physicist (isotropic fluid, Green strain) and mathematician (boost of the stress-energy tensor, shear case) both checked and agree with Tolman; contrarian flagged it as unverified without redoing it. Ruling: checked by two reviewers by independent routes (pressure invariance and shear t_xy = gamma sigma, with p = t + g u symmetric and equal to the modern T^{ij}). Treat as confirmed for isotropic and shear stress. Not checked for general anisotropic strain.

4. What does the moving-body temperature law depend on? (the one numerical disagreement). I recomputed for a photon gas (p0 v0 = E0/3) at beta = 0.6, gamma = 1.25, fixed rest volume, adding rest-frame heat dE0 [calc]: - E = gamma(E0 + p0 v0) - p v; dE/dE0 = 1.40 (physicist's number, confirmed; equals (3 + beta^2)/(3 sqrt(1-beta^2)) = 1.40). - dE - u dG = 0.80 dE0 = dE0/gamma: the Planck-Einstein / Tolman form. Exact in general: E - uG = E0/gamma [calc, holds for any p0, v0]. - The mathematician writes that the energy increase at fixed u is "T0 dS / sqrt(1-beta^2)", i.e. 1.25 dE0, giving Ott-Arzelies. That is true only if the pressure change is ignored: in general E = gamma E0 + gamma beta^2 p0 v0, so dE = gamma dE0 + gamma beta^2 v0 dp0, which is 1.40 for a photon gas, not 1.25. The physicist's statement ("a bare dE gives yet another factor ... gamma dE0 would give Ott-Arzelies") is the more accurate one. Ruling: both agree on the main point (the answer depends on what is called "heat" and whether the momentum carried in by heat counts as work); the mathematician's Ott shortcut should read "gamma dE0 if heat is defined as the energy increase excluding the pressure term". - Mathematician's table recomputed [calc], T0 = 300 K: beta 0.1: 298.5 / 301.5 / 300 / 301.0 K; beta 0.6: 240 / 375 / 300 / 345.0 K; beta 0.8: 180 / 500 / 300 / 406.5 K (Planck-Einstein / Ott-Arzelies / Landsberg / effective from photon-gas energy density). All match.

5. Numbers where reviewers overlapped, all reproduced [calc]. Binary-star shift 2ul/c^2 with u = 100 km/s: l = 100 pc gives 79.5 days (physicist); l = 10 light-years gives 2.44 days (mathematician): both right, different distances. Transverse momentum density 1e9 Pa x 1000 m/s / c^2 = 1.11e-5 kg m^-2 s^-1. Lever torque at 30 km/s, F1 l1 = 100 N m: 1.0e-6 N m. c/2 + c/2 -> 0.8c.

6. Lever claim label. Contrarian discards "Refuted by calculation" and writes "Established by calculation", which is not on the scale. Ruling: use Established for the no-rotation outcome and energy-flow momentum; the explanation (Laue energy current vs Tolman-Epstein relativistic force/acceleration non-parallelism vs angular momentum and simultaneity vs "hidden momentum") is a live pedagogical dispute, not a dispute about the outcome. [web] https://en.wikipedia.org/wiki/Trouton%E2%80%93Noble_experiment confirms the 1901-1903 experiment, repeats by Tomaschek (1925-26), Chase (1926-27), Hayden (1994), Laue 1911 as standard solution, and Tolman-Epstein 1911 as an alternative solution (Wikipedia's attribution; the original papers were not opened). That retags the physicist's "did not verify" item as [web] at encyclopedia level.

7. Trouton-Noble and the lever. Trouton-Noble tests the electromagnetic cousin of the lever (absence of torque on a moving capacitor). No reviewer found a test of the stress-specific transverse momentum in a solid. Agreed: Never properly tested at that level, because the effect is far below any known measurement (1e-5 kg m^-2 s^-1 at an extreme 1e9 Pa shear and 1 km/s). It was not dismissed; it simply has no feasible test yet.

8. Strength of the 1917 electron evidence. Physicist: Established, "thinner than the book says". Contrarian: 1917 ground Historically superseded but instructive. Mathematician: same as physicist. Ruling: the same fact, scored two ways. [web] https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments (fetched by me): Hupka (1910) at about 0.5c agreed with Lorentz-Einstein "even though Hupka remarked that this experiment didn't represent a definitive result"; Zahn and Spees (1938) argued the Bucherer-Neumann experiments could show only a qualitative mass increase; Rogers et al. (1940) agreed with Lorentz-Einstein within 1% and were "sufficiently precise to distinguish between the theories". This confirms the contrarian's 1938 point (previously [memory, medium], now [web]) and adds that Hupka himself called his result not definitive. The book's word "triumph" (p.56) and "closely verified" overstate 1917 precision. Kaufmann's own 1905-06 reading favoured Abraham's rigid electron [web, same URL]. Physicist's "Established" is right for the physics; contrarian's label is right for the 1917 evidential case. I give both.

9. Emission theories (Claim 6) and Fox's extinction critique. All three agree on the corrected text of the book: the Stark-effect and sun-limb evidence bear on emission variants (1) and (2); against Ritz's variant (3) Tolman cites only the Comstock/de Sitter astronomical argument and says optical Einstein-vs-Ritz experiments "have never been performed" [read: Gutenberg, section 22; I confirmed the sentence at line 1291 of the extracted text]. Fox's extinction critique (Ewald-Oseen) comes from one secondary source (Martinez 2004, historian; the Fox papers Am. J. Phys. 1962, 1965 were not opened by any reviewer) and is physically coherent; it is evidence and stays. Later extinction-aware tests: [web] https://en.wikipedia.org/wiki/Tests_of_special_relativity: Alvager et al. 1964 (photons from fast-decaying mesons did not take the source speed), and "the de Sitter double star experiment (1913) was repeated by Brecher (1977) under consideration of the extinction theorem, ruling out a source dependence as well". The numerical bounds (Alvager k about 1e-4 / (-3 +- 13) x 10^-5; Brecher k <= 2e-9) are reported at Wikipedia level by physicist and contrarian from other Wikipedia pages and are consistent; I did not open the primary papers. Ruling: 1917 status for Ritz specifically = Never properly tested (neither dismissed without testing nor neutrally tested); today = Tested, not supported.

10. "Derived from least action" and "temperature follows from H". Physicist, mathematician and contrarian agree on content. Ruling: Maxwell-Lorentz theory is assumed (eq. 209, "known to lead to" the familiar equations), shown consistent with the H/sqrt(1-u^2/c^2) rule, not derived from relativity. The temperature law is a theorem about a definition (heat treated as work, T dt invariant), not an independent derivation; section 103's kinetic-theory temperature is defined in the rest frame and does not fix the moving-frame law (contrarian and physicist agree).

Corrected claim list (final)

1. Light speed is independent of source motion and absolute motion is undetectable; from these postulates follow time dilation, length contraction (by sqrt(1 - V^2/c^2)), clock offset l'V/c^2, Lorentz transformation and velocity addition (Chapters II-V). Corrections: the derivation in Chapters III-IV is heuristic by the author's own statement (p.45), obtains the transformation "by trial", never states linearity, and the Newtonian limit needs c -> infinity (t' = t - Vx/c^2 has a first-order term). The book itself says optical tests between Einstein and Ritz were never performed. QE revision: section 46 (PDF p.68) proposes the canal-ray test of time dilation (view the rays at right angles; frequency of fast atoms 'ought to be less'), but cites no experiment; the second-order Doppler shift is eq. (40), nu = nu0 sqrt(1 - V^2/c^2).
2. Mass is m0/sqrt(1 - u^2/c^2); kinetic-energy change equals c^2 times mass change (exact for kinetic energy by integration; "all energy has mass" is argued by generalisation, "every reason to believe", "pragmatic"); particle mechanics follows from a Lagrangian whose H/sqrt(1-u^2/c^2) is invariant (H not uniquely determined, p.172). QE revision: the general energy formula E = (m0 c^2 + E0)/sqrt(1 - u^2/c^2) (235) fixes its integration constant by the convention 'zero energy goes with zero mass' and takes phi(u) from the earlier mechanics, so the 'all energy has mass' step is inductive. In section 77 Tolman states experimental proof of mass-energy equivalence "will be hard to find" beyond electron data and light momentum.
3. Momentum density = energy-flow density / c^2 including stress; a strained body moving along X has transverse momentum; Tolman's stress tensor t is unsymmetrical (t_yx = (1 - beta^2) t_xy, with symmetric p = t + g u equal to the modern tensor); a moving right-angled lever needs torque F1 l1 V^2/c^2, absorbed as angular-momentum growth, not rotation.
4. Entropy and pressure are invariant; energy E = gamma(E0 + p0 v0) - p v and momentum G = (E + pv)u/c^2 (Planck-Einstein-Laue); temperature T = T0 sqrt(1 - u^2/c^2) follows from the chosen H and treating heat as work (in Chapter VIII, by contrast, the gas temperature is defined in the gas's own frame: pV = NkT exactly and kT = 1/h, with the equipartition quantity = 3kT, not the kinetic energy); the hohlraum 4/3 factor holds for a cavity held by external pressure (a closed system with its wall stresses gives G = E u/c^2, Tolman's own (193)).
5. Maxwell-Lorentz theory, with the Lagrangian assumed (not derived), is Lorentz covariant; (227)-(229) transform e, h, rho (with u_x in (229); Gutenberg misprints u_z); charge is invariant; field energy E0 carries inertia E0/c^2; the ether is "unnecessary" (economy, not measurement). Section 172: Tolman's moving-dielectric equations agree with Wilson's experiment, but only the first-order form was tested (permeability near 1, where Tolman's (251) and the Lorentz form coincide; they differ by (V/c)(mu - 1) H_y), and he asks for a repeat with a high-permeability dielectric. His 'complete accord ... with all other experiments' is asserted on the page with no list.
6. Electron-deflection experiments (Kaufmann, Bucherer, Hupka) are described by the book as a "triumph"; emission theories: first two variants are excluded by Stark-effect and sun-limb evidence; Ritz's variant only by Comstock/de Sitter astronomy, with no optical test (the book says so).

Final verdict per claim

Claim 1. Reviewer agreement: unanimous on the physics. (a) Maths consistent; gaps are expository. (b) Consistent with Michelson-Morley, Kennedy-Thorndike, Ives-Stilwell (1938; modern deviation <= 1e-8 [web] https://en.wikipedia.org/wiki/Tests_of_special_relativity), muons, GPS [memory, high]. (c) Tested many times, replicated. (d) Nothing in mainstream physics changes. The nuance all three note: the Lorentz-ether interpretation is empirically equivalent; "ether unnecessary" is an economy argument. Verdict: Established (Lorentz transformation, dilation, contraction). Split: the book's 1917 evidential case for the second postulate was Never properly tested in the laboratory (not dismissed without testing); decisive tests came 1964 and 1977. Derivation: valid but heuristic.

Claim 2. (a) Consistent (u d(mu) = c^2 dm confirmed). (b) Accelerators, Bertozzi 1964 and nuclear mass defects [memory, high / medium for Bertozzi, not web-checked: the Wikipedia tests page does not mention it]. (c) Tested, replicated; 1917 data coarse (item 8). (d) Nothing. Verdict: Established (physics). Split: the 1917 electron evidence Historically superseded but instructive; "relativistic mass" as terminology Historically superseded but instructive; Tolman's own general E = mc^2 argument is inductive (Plausible, untested as an argument in the book; the physics is established by later tests).

Claim 3. Reviewers differ only in labels (item 6). Verdict (split): energy-flow momentum and no rotation of the lever: Established; explanation: debated, not outcome. Tolman's unsymmetrical tensor as formalism: Historically superseded but instructive (a bookkeeping choice; also fairly Not testable as stated). Measurable transverse momentum in an ordinary stressed solid: Never properly tested (not dismissed; effect about 1e-5 SI units at extreme conditions; Tolman says no experiment of sufficient accuracy existed, p.172).

Claim 4. Verdict (split): entropy invariance, pressure invariance, E, G, hohlraum with the container-stress proviso: Established. T = T0 sqrt(1 - u^2/c^2) as "the" temperature of a moving body: Not testable as stated (definition-dependent: one operational choice yields 240 K, another 375 K, another 300 K at beta = 0.6 [calc]) and Historically superseded but instructive (the majority view to the 1960s, still "supported by many authors" per Heras and Osorno 2022, one of three live conventions; not refuted by any experiment). Not Internally inconsistent. Modern hydrodynamics uses rest-frame T and the four-vector beta^mu [memory, medium-high]. CMB dipole shows direction-dependent radiation temperature T(theta) = T0 sqrt(1 - beta^2)/(1 - beta cos theta) [memory, high], which equals none of the three single-number laws. Cubero et al. 2007 (PRL 99, 170601) simulation favours an observer-independent statistical temperature [web, abstract level, per contrarian].

Claim 5. Verdict: Maxwell-Lorentz covariance, field transformations, charge invariance, E0/c^2 inertia: Established. "Follows from least action": Not testable as stated / presentation (the Lagrangian is assumed). "Ether unnecessary": Not testable as stated (empirical equivalence with a Lorentz ether). Wilson-experiment high-permeability term (section 172): Never properly tested in the book's text; whether a later repeat exists was not found (web search cap reached; unknown, not claimed either way). Sections 168-171 unread by reviewers.

Claim 6. Verdict (split): relativistic mass law: Established (Rogers 1940 within 1%, accelerators); 1917 electron evidence Historically superseded but instructive (Kaufmann first favoured Abraham; Hupka himself said his result was not definitive; Zahn-Spees 1938 said the early experiments showed only a qualitative increase). Emission theories: variants (1) and (2): Tested, not supported by canal-ray Doppler data as read by Tolman in 1912 (the extinction objection also applies to light that passes through matter, per Fox/Martinez). Ritz variant in 1917: Never properly tested (not dismissed without testing: Tolman ran a sun-limb test 1910, called in 1912 for a sunlight Michelson-Morley test); today Tested, not supported (Alvager 1964, Brecher 1977).

What would settle it

• Temperature (claim 4): fix the operational definition (what a comoving or lab thermometer exchanges; whether heat's momentum counts as work), then the calculation above gives each law exactly. Physical test: none known; the lab-feasible analogue is direction-resolved radiation temperature, already measured as the CMB dipole. A relativistic gas thermometer experiment is not feasible.
• Fox extinction critique (claim 6): obtain Fox 1962 and 1965 and compute the extinction length for the sight lines of de Sitter's binaries; then compare with Brecher's X-ray design, which was chosen to avoid it.
• Stress-specific transverse momentum (claim 3): a torsion-balance or optical measurement on a rapidly moving stressed body; the 1e-5 SI level shows why none exists. Calculation that would settle the formalism question: boost the full stress-energy tensor (done by mathematician for shear and by physicist for isotropic stress); the remaining check is general anisotropic strain.
• Lever explanation dispute (claim 3): compare Laue 1911, Tolman-Epstein 1911 and Shapiro 2012 on one worked case; all give no rotation.
• Wilson high-permeability test (claim 5): a rotating-cylinder measurement with a high-permeability dielectric; a literature search for any repeat.
• Electron data (claim 6): reanalysis of Bucherer/Hupka raw data; superseded in practice by Rogers 1940 and later.
• Gutenberg transcription: compare every equation used with the scan; (229) is known wrong.

Open questions

1. Is there any measurement that distinguishes the Planck-Einstein, Ott-Arzelies and Landsberg temperature laws, or is the question only definitional? (Heras-Osorno 2022 say neither classic law satisfies group closure; Pouryazdan-Vakili 2026 find an effective temperature rising with speed; both theoretical.)
2. Was the Wilson experiment with a high-permeability dielectric ever repeated?
3. What do Fox's original 1962/1965 papers argue, and does extinction in interstellar gas actually matter for de Sitter's data? (Only a secondary account has been read.)
4. Do the Caltech Tolman papers (12 boxes) contain drafts or lectures behind the 1917 book? The NAS memoir (1952) was not read.
5. Chapters V, XIII and sections 168-171 were not checked equation by equation.
6. The book's 1917 confidence versus Tolman's 1910-1912 caution: why did the 1917 text drop the open tone on Ritz and the "may not really indicate" caveat on electron data? The record read gives no answer (Tolman 1910 and 1912 papers are the evidence; Carmichael 1913 wrote that there was then no undoubted evidence either way, per Martinez).

Absence-of-evidence analysis

The record does not go dark for Tolman or the book: career continuous from Berkeley through war work, Fixed Nitrogen Research Laboratory, Caltech and the Manhattan Project [read: research/2026-10-04-caltech-oac.md]. No anomaly there. Two other places the record is thin deserve analysis:

1. Ritz's emission theory after 1909. Ritz died in 1909; Martinez records that neither Tolman nor Ehrenfest developed it. Explanations: (a) the theory was reasonably dropped because it was incomplete and Einstein's gave all results (commercial/scientific failure analogue); (b) no one with the means to test the optical variant bothered because a successful theory was already available (social prestige and economy); (c) technical difficulty plus the extinction loophole meant early null results were not informative, so there was little to publish; (d) suppression: no evidence found (Tolman published his own emission papers in Phys. Rev.; Martinez reports no blocked publication). Evidence for (b)/(c): Martinez and Carmichael 1913; Tolman's 1912 call for a test that does not appear to have been run until Tomaschek/Miller 1924, contested by Fox. Evidence against (d): the 1910 and 1912 papers. What would decide: Fox's papers, Martinez's references, journal correspondence of 1912-1925. Extinction-free tests (1964, 1977) now decide the physics, so the anomaly is historical only.
2. The Wilson high-permeability repeat and direct tests of stress-induced momentum. Tolman asked for a repeat in 1917. No reviewer found a record of one; the web search cap prevented a check. Competing explanations: (a) done but unfound by us; (b) not done because nobody needed it once the general theory matched other tests; (c) technically hard. Evidence: none in hand. What would decide: a literature search on moving magnetic dielectrics (Wilson 1905 follow-ups). Marked unknown.

Web checks done by the arbiter (budget 8; search tool at its cap, so fetches only)

1. https://en.wikipedia.org/wiki/Trouton%E2%80%93Noble_experiment: dates, repeats, Laue and Tolman-Epstein 1911 attribution (retags physicist's unverified item).
2. https://en.wikipedia.org/wiki/Tests_of_special_relativity: Alvager 1964, Brecher 1977 incl. extinction, Ives-Stilwell <= 1e-8. Bertozzi not mentioned there.
3. https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments: Zahn-Spees 1938, Hupka caveat, Rogers 1940.
4. https://en.wikipedia.org/wiki/Relativistic_heat_conduction: no relevant temperature-transformation content (negative).
5. Failed: web searches for Fox 1962/65, Bertozzi 1964 and the Wilson-experiment follow-ups (session search cap reached); a Wilson-experiment Wikipedia URL returned 404. These items remain [memory, medium]: Fox papers' content, Bertozzi 1964, von Ignatowski 1910, Wilson 1905 date, atomic neutrality ~1e-20 to 1e-21 of electron charge. No verdict turns on a unique one of them: Fox's critique is carried as Martinez's account [read], and Bertozzi is one of several modern confirmations (accelerators, nuclear data). All Wikipedia pages are secondary sources; primary papers were not opened.

Summary table

QE revision

Inputs: qe.md (verdict MINOR) and the new deep reads appended to deep/The-theory-of-the-relativity-of-motion-634dc2.md (Ch. XII sections 154-161 and 165-172; Ch. VIII sections 91-107; Ch. V sections 43-57; Ch. XIII). Page references are PDF pages; book page = PDF page minus 17. I re-read those deep reads. I did not re-open the page images myself; where I rely on them, the deep reader's image reading is cited. Web checks (budget 8): the search tool is at its session cap, so 3 fetches were tried (below). No verdict changes label, except the temperature-law label in claim 4. The Wilson verdict is sharpened, not changed.

Changes in verdicts and labels

1. Claim 4, temperature law. QE 6(b) is right. "Not testable as stated" and "Historically superseded but instructive" contradict the same paragraph's "one of three live conventions", "not refuted" and "supported by many authors (2022)". Ruling: the moving-body law T = T0 sqrt(1 - u^2/c^2) is Not testable as stated (definition-dependent). The word "superseded" is dropped. In words only: it was the majority view to the 1960s, and modern relativistic hydrodynamics now uses the rest-frame temperature and a four-vector beta^mu [memory, medium-high]; no experiment refuted it.
2. Claim 2, "Plausible, untested" applied to an argument. QE 6(c) is right: the scale grades claims, not arguments. The claim "energy has inertia E/c^2" is Established. The book's route is stated in words as inductive. The Chapter XII deep read shows this precisely [read: deep read, section 166, PDF p.197]: E = (m0 c^2 + E0)/sqrt(1 - u^2/c^2) (235) holds with the constant of integration fixed by the convention "zero energy goes with zero mass", and phi(u) is borrowed from the mechanical result (82); that phi does not depend on E0 is asserted. This confirms "inductive". It is not an error.
3. Claim 3, label disagreement (QE 6a). The physicist gave "Plausible, untested" and the contrarian and I gave "Never properly tested" for a measurable stress-specific transverse momentum in an ordinary solid. Reason for my label: the claim is testable in principle and consistent with known physics, but no neutral test is on record, and the scale puts "no test on record" under "Never properly tested". The physicist's label states consistency; mine states the test record. The two do not conflict on facts. Not dismissed: the effect is about 1e-5 SI units at extreme conditions.
4. Claim 5, Wilson experiment (section 172), now checked against page images [read: deep read, PDF pp.203-204]. - Wilson's experiment: a rotating hollow dielectric cylinder, axial magnetic field, metallised surfaces, wire brushes to electrometer quadrants, field reversed while rotating; the surface charge fitted D_z per cm^2. Tolman gives no date, place, number, material or citation. - Equation (251): D_z = eps E_z + (V/c)(eps mu - 1) H_y. The deep reader redid the algebra from (248)-(249) and found no error. Setting mu = 1 gives (eps - 1), and that is what was tested. - Lorentz's equation, as Tolman prints it: D_z = eps E_z + (V/c)(eps - 1) mu H_y. The two differ by (V/c)(mu - 1) H_y [calc: (eps mu - 1) - (eps - 1) mu = mu - 1]. For non-magnetic Wilson dielectrics (mu about 1) the experiment cannot tell Tolman and Lorentz apart. - Verdict: the mu-dependent term is Never properly tested within the book's text, as before. Tolman asked for the repeat himself. His statement "in complete accord with ... all other experiments that have been performed on moving media" is broader than anything he shows on the page. - Unresolved lead, not a verdict: the deep reader recalls that Wilson and Wilson (1913) used a magnetic dielectric and agreed with the (eps mu - 1) form [memory, medium; not from the document]. My web checks failed: the search tool is capped; https://en.wikipedia.org/wiki/Harold_Albert_Wilson and https://en.wikipedia.org/wiki/History_of_special_relativity mention neither the 1904 nor the 1913 experiment. So this stays [memory, medium]. If true, the question had a test around the time the book was written, and the answer to open question 2 would be "yes, and Tolman's form was supported". If it is false or misremembered, the "never tested" verdict stands. I do not assert either. Settling it needs the 1913 paper.
5. Claim 1, the book predicted a later-tested effect. Added to the evidence (QE 3.1). - [read: PDF p.68, section 46] "A possible opportunity for testing this interesting conclusion ... is presented by the phenomena of canal rays. We may regard the atoms which are moving in these rays as little clocks ... the frequency of the emitted light ought to be less than that of light from stationary atoms of the same kind ... It would of course be necessary to view the canal rays at right angles to their direction of motion". - Size: from eq. (40), the shift is -V^2/(2c^2), about 2.1e-5 of the frequency at V/c = 0.0065 [calc, deep read]. Tolman cites no experiment, speed, spectrometer or experimenter. In section 54 he repeats that "the possibilities of direct experimental verification should not be overlooked" [read: pp.75-76]. - Later test: Ives and Stilwell (1938) used hydrogen canal rays and a different geometry (forward and backward longitudinal Doppler shifts, whose mean shifts to the red by the second-order term). The first-order terms cancel in the mean. A direct transverse measurement was reported by Hasselkamp et al. (1979). [web] https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment (fetched by me; secondary source) gives the 1938/1941 method and Hasselkamp 1979. I did not open the primary papers. The page does not mention Tolman, so that Ives-Stilwell followed Tolman's proposal is not established: say "tested the same quantity", not "carried out his proposal". - Pertinent counterweight kept in the record: [web, same URL] Ives preferred to interpret his result in terms of the Lorentz-Larmor ether theory, not Einstein's. This sits with claim 5's "ether unnecessary", an economy argument, and with claim 1's empirical equivalence. - The deep reader also notes a practical weakness of the transverse design: at beta = 0.0065 a viewing-angle spread of 0.01 rad leaves a first-order term of 6.5e-5, three times the second-order effect [calc, deep read; my arithmetic agrees: 0.0065 x 0.01 = 6.5e-5 against 0.0065^2/2 = 2.1e-5]. This is the stated reason the 1938 geometry was useful. It is the deep reader's analysis, not Tolman's. - Verdict for claim 1 unchanged: Established. The 1917 case remains Never properly tested in the laboratory; the book proposed a test (not performed in the text).

Material the QE found that I add to the record (no verdict needed)

• Section 159 (homopolar dynamos). Quoted in full by the deep reader [read: PDF p.189]: "We also see that the 'electromotive' force which acts on a charge moving through a magnetic field finds its interpretation as an 'electric' force provided we make use of a system of coordinates which are themselves stationary with respect to the charge. Such considerations throw light on such questions, for example, as to the seat of the 'electromotive' forces in 'homopolar' electric dynamos where there is relative motion of a conductor and a magnetic field." Three sentences: no equations, no Faraday disc named, no conclusion. Reading from the book's own equations (227): the "magnetic" force on a charge is the electric force e' in the charge's rest frame, so the EMF sits locally in each conductor element. The deep reader flags that the equations hold between non-accelerated frames; a rotating disc needs the momentarily-co-moving-frame extension, which Tolman does not state, and the case of a rotating magnet with symmetric field is not addressed. Treat it as a pointer. That the passage explains why the book is in this collection is a candidate, not established.
• Section 77 footnote (PDF p.102). "Our theory points to the presence of enormous stores of interatomic energy which are still left in substances cooled to the absolute zero" (quoted by the contrarian and by the QE; the Chapter VI deep read, QE item 3, has not been done, so I leave it as read by those two). The same section says experimental proof of mass-energy equivalence "will be hard to find" (claim 2). The radioactive atomic-weight discussion is still uncarried.
• Section 105, the massless gas [read: deep read, PDF p.118 page image]. Tolman derives E = 3nRT for particles of negligible mass, twice the Newtonian (3/2)nRT, and prints a mole at 300 K as 3 x 8.31e7 x 300 / 10^21 = 7.47e-11 g, "a field of fascinating if profitless speculation". [calc] 3 x 8.31e7 x 300 = 7.479e10 erg; /1e21 = 7.48e-11 g (printed value is truncated). With c^2 = 8.99e20 it is 8.32e-11 g, 11% higher. The digest's 7.47e-8 is wrong. This confirms the 10^21 rounding (item 1 above).
• Chapter VIII results, now checked by a deep reader [read: deep read, page images pp.124-137]. The distribution law (121), pV = NkT exactly (127)-(129), and the series (132)-(134) are correct. The equipartitioned quantity is = 3kT (126), which Tolman says "is not the relativity expression for kinetic energy"; so "equipartition of energy is merely an approximation" in his own words [read: p.128-129]. His "substantially exact" for electrons at ordinary temperatures holds with room to spare (second term about 3.4e-6 percent of the first at 300 K, printed 3.5; the exact Maxwellian correction is about 1.9 times Tolman's lower estimate, because he uses = ^2). The treatment is for a classical, non-interacting gas, relying on the ergodic assumption he flags in a footnote; conduction electrons in metals are not covered. The Chapter VIII temperature is defined in the gas's own rest frame, so it does not fix the moving-frame temperature law (claim 4).
• Section 52 (causality). Tolman's argument [read: PDF p.72]: a causal signal faster than c would reach B before A in some frame; his wording is cautious ("might not be a logical impossibility ... might incline us to believe"). He expressly allows non-causal superluminal sequences (a row of independently timed blocks). Not a proof; a plausibility argument.
• Chapter V checks [read: deep read, page images pp.66-77]. Equations (21)-(23), (25)-(29), (32)-(35) and (38)-(46) are correct. Aberration is shown: sin delta = V/c exactly, tan delta only to second order (20.6 arcsec at 30 km/s). The Fresnel coefficient is (mu^2 - 1)/mu^2 = 0.437 for water [calc]; Tolman gives no experimental numbers and cites Fizeau and Michelson-Morley by name only. His prescription of using the index at the medium-frame frequency is correct; dispersion data (Zeeman) are not discussed. "Agrees with experimental determinations" for first-order Doppler is stated without names.
• Chapter XIII (low priority). (317)-(332) agree with Chapters X and XII; the deep reader rebuilt the tensors in SymPy and found no printed error. Tolman defines a tensor by its divergence condition (294), which is loose by modern standards, and does not prove T_m and T_e transform as tensors; the deep reader flags it as an unstated assumption. He names Wilson and Lewis as the source of the real-time method; Preface (PDF p.21) leaves out accelerated frames and Einstein's gravity work. Neither changes a verdict.
• Section 165-167 confirmations. The field of a uniformly moving charge (232)-(233) is correct. (235) is as the QE says. "10^21 ergs ... 1 gram" is in section 167 [read: PDF p.198, page image] and is 11% high against 8.99e20 erg. Charge invariance (231) rests on the electron-counting argument; Tolman's footnote cites his own Phys. Rev. 3, 244 (1914) (not opened).

Corrections to earlier arbiter text

• Equation (229). I wrote above that "Gutenberg prints u_z". The Chapter XII deep reader attributes the u_z/u_x confusion to the text layer and OCR of the scan, and says the same confusion appears in the OCR of the force components of section 160 (PDF p.190); the scan has u_x in both. I did not re-open the Gutenberg text for this revision. Safe statement: the scan reads u_x [read: page image p.186, by me earlier and by the deep reader]; some transcription (text layer, and per the mathematician Gutenberg) has u_z. Use the scan.
• Digest errors now corrected from page images (add to facts.json): c = 2.9986e10 cm/s not e8 (p.27-28); 7.47e-11 g not e-8 (p.134); K = 12.4e7 T + (7.77e-6/M) T^2 erg (p.135-136); the series (132) has all plus signs; E = (m0 c^2 + E0)/sqrt(1 - u^2/c^2) in section 166 (p.195-197); 10^21 not 10^11 (p.197-198); Wilson field is along Y, so the term is H_y (p.198-203).
• Open questions. Question 2 (Wilson repeat) gains the lead above, still unconfirmed. Question 5 narrows: Chapters V, XIII and sections 168-171 now have deep reads with no equation errors found. Chapter VI (sections 75-80) and sections 44-58 outside the read ranges still rest on digests and reviewers' Gutenberg readings; the Chapter VI deep read in the QE list has not been done.

Retention items (QE section 5) to carry into the primer

• Tolman's 1910 remark that the source-speed difference "is destroyed near the earth is not entirely excluded" [read: reported in mathematician.md claim 6a from the Wikisource note, research/2026-10-04-wikisource.md; I did not find the phrase verbatim in that note, so the exact wording needs rechecking before it is printed in quotation marks]. It shows Tolman himself saw the extinction-type loophole that Fox later pressed, which strengthens absence-of-evidence item 1 (explanation (c): technical difficulty plus the loophole). It is evidence against suppression (d).
• Tolman's 1912 wording is "does not seem to have received the critical attention which it deserves" [read: research/2026-10-04-wikisource.md, line 31]; the primer's "deserves more attention" is a paraphrase and must not be in quotation marks.
• Carmichael 1913 (no undoubted evidence either way) and Tolman-La Rosa 1912 -> sunlight Michelson-Morley test done 1924 by Tomaschek (starlight) and Miller (sunlight) (Martinez), contested by Fox.

Web checks added (budget 8, 3 used, search tool capped)

1. https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment: 1938/1941, canal rays, Ives's Lorentz-Larmor interpretation, Hasselkamp 1979. Positive. Secondary source.
2. https://en.wikipedia.org/wiki/Harold_Albert_Wilson: negative for the rotating-dielectric experiments.
3. https://en.wikipedia.org/wiki/History_of_special_relativity: negative for Wilson/Roentgen/Eichenwald dielectric experiments. Failed: web search for Wilson and Wilson 1913 (search cap). The 1904 date and Phil. Trans. A 204 reference remain [memory, medium].